LMFDB - Embedded newform 43.6.g.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(9,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.89650425196$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	43.10
Dual form			43.6.g.a.13.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36214 - 10.3492i) q^{2} +(-5.75023 - 5.33543i) q^{3} +(-72.6953 + 35.0082i) q^{4} +(-7.82578 + 1.17955i) q^{5} +(-41.6347 + 72.1133i) q^{6} +(62.4925 + 108.240i) q^{7} +(322.229 + 404.063i) q^{8} +(-13.5611 - 180.961i) q^{9} +O(q^{10})$	\(q+(-2.36214 - 10.3492i) q^{2} +(-5.75023 - 5.33543i) q^{3} +(-72.6953 + 35.0082i) q^{4} +(-7.82578 + 1.17955i) q^{5} +(-41.6347 + 72.1133i) q^{6} +(62.4925 + 108.240i) q^{7} +(322.229 + 404.063i) q^{8} +(-13.5611 - 180.961i) q^{9} +(30.6929 + 78.2043i) q^{10} +(-541.536 - 260.790i) q^{11} +(604.799 + 186.556i) q^{12} +(-238.584 + 607.902i) q^{13} +(972.583 - 902.425i) q^{14} +(51.2934 + 34.9713i) q^{15} +(1810.76 - 2270.63i) q^{16} +(1356.50 + 204.460i) q^{17} +(-1840.76 + 567.801i) q^{18} +(-107.850 + 1439.16i) q^{19} +(527.604 - 359.714i) q^{20} +(218.162 - 955.830i) q^{21} +(-1419.78 + 6220.48i) q^{22} +(420.174 - 286.470i) q^{23} +(302.958 - 4042.69i) q^{24} +(-2926.31 + 902.648i) q^{25} +(6854.87 + 1033.21i) q^{26} +(-2075.99 + 2603.21i) q^{27} +(-8332.20 - 5680.80i) q^{28} +(-3272.35 + 3036.30i) q^{29} +(240.763 - 613.453i) q^{30} +(-2359.18 - 727.712i) q^{31} +(-12876.1 - 6200.82i) q^{32} +(1722.53 + 4388.93i) q^{33} +(-1088.25 - 14521.7i) q^{34} +(-616.727 - 773.351i) q^{35} +(7320.94 + 12680.2i) q^{36} +(-4376.92 + 7581.05i) q^{37} +(15148.9 - 2283.33i) q^{38} +(4615.33 - 2222.63i) q^{39} +(-2998.31 - 2782.02i) q^{40} +(-311.934 - 1366.67i) q^{41} -10407.4 q^{42} +(-7680.21 - 9382.05i) q^{43} +48496.9 q^{44} +(319.578 + 1400.16i) q^{45} +(-3957.25 - 3671.79i) q^{46} +(-4610.57 + 2220.34i) q^{47} +(-22527.1 + 3395.41i) q^{48} +(592.883 - 1026.90i) q^{49} +(16254.0 + 28152.8i) q^{50} +(-6709.31 - 8413.21i) q^{51} +(-3937.63 - 52544.0i) q^{52} +(-12396.1 - 31584.8i) q^{53} +(31844.9 + 15335.7i) q^{54} +(4545.55 + 1402.12i) q^{55} +(-23598.9 + 60129.1i) q^{56} +(8298.70 - 7700.07i) q^{57} +(39153.0 + 26694.1i) q^{58} +(-19415.9 + 24346.7i) q^{59} +(-4953.07 - 746.556i) q^{60} +(-6595.23 + 2034.36i) q^{61} +(-1958.52 + 26134.6i) q^{62} +(18739.7 - 12776.5i) q^{63} +(-13078.2 + 57299.3i) q^{64} +(1150.06 - 5038.73i) q^{65} +(41353.1 - 28194.0i) q^{66} +(-4500.74 + 60058.2i) q^{67} +(-105769. + 32625.4i) q^{68} +(-3944.54 - 594.544i) q^{69} +(-6546.77 + 8209.39i) q^{70} +(-40715.9 - 27759.7i) q^{71} +(68749.7 - 63790.4i) q^{72} +(31246.6 - 79615.0i) q^{73} +(88796.7 + 27390.2i) q^{74} +(21643.0 + 10422.7i) q^{75} +(-42542.2 - 108396. i) q^{76} +(-5613.98 - 74913.3i) q^{77} +(-33904.5 - 42514.9i) q^{78} +(-32407.5 - 56131.4i) q^{79} +(-11492.3 + 19905.3i) q^{80} +(-17777.6 + 2679.54i) q^{81} +(-13407.1 + 6456.53i) q^{82} +(59256.0 + 54981.5i) q^{83} +(17602.6 + 77121.8i) q^{84} -10856.8 q^{85} +(-78955.0 + 101646. i) q^{86} +35016.7 q^{87} +(-69123.2 - 302849. i) q^{88} +(69547.7 + 64530.9i) q^{89} +(13735.7 - 6614.75i) q^{90} +(-80709.1 + 12164.9i) q^{91} +(-20515.9 + 35534.6i) q^{92} +(9683.20 + 16771.8i) q^{93} +(33869.5 + 42471.0i) q^{94} +(-853.544 - 11389.8i) q^{95} +(40956.7 + 104356. i) q^{96} +(132008. + 63571.5i) q^{97} +(-12028.1 - 3710.18i) q^{98} +(-39848.8 + 101533. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9}+O(q^{10}) $ 204 * q - 468 * q^4 - 85 * q^5 - 22 * q^6 + 454 * q^7 + 698 * q^8 - 333 * q^9	\( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9} + 303 q^{10} - 1340 q^{11} + 858 q^{12} + 814 q^{13} + 1202 q^{14} - 2083 q^{15} - 6248 q^{16} - 214 q^{17} - 174 q^{18} - 246 q^{19} - 17139 q^{20} + 3007 q^{21} + 2118 q^{22} + 3192 q^{23} + 15880 q^{24} + 3652 q^{25} - 1237 q^{26} + 108 q^{27} - 6780 q^{28} - 18827 q^{29} + 98080 q^{30} - 43196 q^{31} - 3930 q^{32} + 28181 q^{33} + 45155 q^{34} + 33275 q^{35} - 49399 q^{36} + 34607 q^{37} - 43374 q^{38} + 15155 q^{39} - 108727 q^{40} + 7156 q^{41} - 48066 q^{42} - 176452 q^{43} + 26068 q^{44} - 96386 q^{45} - 27185 q^{46} + 20402 q^{47} + 198899 q^{48} - 158742 q^{49} + 186243 q^{50} + 98589 q^{51} + 278918 q^{52} + 14102 q^{53} + 270894 q^{54} - 334770 q^{55} + 61999 q^{56} - 202490 q^{57} + 213658 q^{58} - 43753 q^{59} - 389005 q^{60} + 80516 q^{61} + 162349 q^{62} - 75177 q^{63} - 489850 q^{64} + 93726 q^{65} + 246095 q^{66} - 322922 q^{67} + 475089 q^{68} - 397079 q^{69} - 614985 q^{70} - 233345 q^{71} + 379655 q^{72} + 159391 q^{73} + 695938 q^{74} + 344081 q^{75} - 50808 q^{76} + 608177 q^{77} + 605548 q^{78} - 272109 q^{79} + 601054 q^{80} + 193536 q^{81} - 996896 q^{82} + 177813 q^{83} - 919009 q^{84} - 844524 q^{85} - 876752 q^{86} - 188214 q^{87} - 59998 q^{88} - 469041 q^{89} - 453431 q^{90} - 223189 q^{91} - 94922 q^{92} + 569174 q^{93} + 1175168 q^{94} + 435689 q^{95} + 1557688 q^{96} + 643751 q^{97} + 886196 q^{98} + 1422581 q^{99}+O(q^{100}) \) 204 * q - 468 * q^4 - 85 * q^5 - 22 * q^6 + 454 * q^7 + 698 * q^8 - 333 * q^9 + 303 * q^10 - 1340 * q^11 + 858 * q^12 + 814 * q^13 + 1202 * q^14 - 2083 * q^15 - 6248 * q^16 - 214 * q^17 - 174 * q^18 - 246 * q^19 - 17139 * q^20 + 3007 * q^21 + 2118 * q^22 + 3192 * q^23 + 15880 * q^24 + 3652 * q^25 - 1237 * q^26 + 108 * q^27 - 6780 * q^28 - 18827 * q^29 + 98080 * q^30 - 43196 * q^31 - 3930 * q^32 + 28181 * q^33 + 45155 * q^34 + 33275 * q^35 - 49399 * q^36 + 34607 * q^37 - 43374 * q^38 + 15155 * q^39 - 108727 * q^40 + 7156 * q^41 - 48066 * q^42 - 176452 * q^43 + 26068 * q^44 - 96386 * q^45 - 27185 * q^46 + 20402 * q^47 + 198899 * q^48 - 158742 * q^49 + 186243 * q^50 + 98589 * q^51 + 278918 * q^52 + 14102 * q^53 + 270894 * q^54 - 334770 * q^55 + 61999 * q^56 - 202490 * q^57 + 213658 * q^58 - 43753 * q^59 - 389005 * q^60 + 80516 * q^61 + 162349 * q^62 - 75177 * q^63 - 489850 * q^64 + 93726 * q^65 + 246095 * q^66 - 322922 * q^67 + 475089 * q^68 - 397079 * q^69 - 614985 * q^70 - 233345 * q^71 + 379655 * q^72 + 159391 * q^73 + 695938 * q^74 + 344081 * q^75 - 50808 * q^76 + 608177 * q^77 + 605548 * q^78 - 272109 * q^79 + 601054 * q^80 + 193536 * q^81 - 996896 * q^82 + 177813 * q^83 - 919009 * q^84 - 844524 * q^85 - 876752 * q^86 - 188214 * q^87 - 59998 * q^88 - 469041 * q^89 - 453431 * q^90 - 223189 * q^91 - 94922 * q^92 + 569174 * q^93 + 1175168 * q^94 + 435689 * q^95 + 1557688 * q^96 + 643751 * q^97 + 886196 * q^98 + 1422581 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.36214	−	10.3492i	−0.417571	−	1.82950i	−0.546008	−	0.837780i	$-0.683853\pi$
$2$	−2.36214	−	10.3492i	−0.417571	−	1.82950i	0.128437	−	0.991718i	$-0.459004\pi$
$3$	−5.75023	−	5.33543i	−0.368877	−	0.342268i	0.473853	−	0.880604i	$-0.342863\pi$
$3$	−5.75023	−	5.33543i	−0.368877	−	0.342268i	−0.842730	+	0.538336i	$0.819053\pi$
$4$	−72.6953	+	35.0082i	−2.27173	+	1.09401i
$5$	−7.82578	+	1.17955i	−0.139992	+	0.0211004i	−0.218664	−	0.975800i	$-0.570170\pi$
$5$	−7.82578	+	1.17955i	−0.139992	+	0.0211004i	0.0786725	+	0.996901i	$0.474932\pi$
$6$	−41.6347	+	72.1133i	−0.472147	+	0.817782i
$7$	62.4925	+	108.240i	0.482039	+	0.834917i	0.999787	−	0.0206163i	$-0.00656285\pi$
$7$	62.4925	+	108.240i	0.482039	+	0.834917i	−0.517748	+	0.855533i	$0.673230\pi$
$8$	322.229	+	404.063i	1.78008	+	2.23215i
$9$	−13.5611	−	180.961i	−0.0558071	−	0.744694i
$10$	30.6929	+	78.2043i	0.0970596	+	0.247304i
$11$	−541.536	−	260.790i	−1.34941	−	0.649844i	−0.387164	−	0.922011i	$-0.626545\pi$
$11$	−541.536	−	260.790i	−1.34941	−	0.649844i	−0.962250	+	0.272167i	$0.912260\pi$
$12$	604.799	+	186.556i	1.21243	+	0.373986i
$13$	−238.584	+	607.902i	−0.391546	+	0.997643i	0.590168	+	0.807281i	$0.299062\pi$
$13$	−238.584	+	607.902i	−0.391546	+	0.997643i	−0.981714	+	0.190363i	$0.939034\pi$
$14$	972.583	−	902.425i	1.32619	−	1.23053i
$15$	51.2934	+	34.9713i	0.0588618	+	0.0401313i
$16$	1810.76	−	2270.63i	1.76832	−	2.21741i
$17$	1356.50	+	204.460i	1.13841	+	0.171587i	0.691077	−	0.722782i	$-0.257137\pi$
$17$	1356.50	+	204.460i	1.13841	+	0.171587i	0.447330	+	0.894369i	$0.352375\pi$
$18$	−1840.76	+	567.801i	−1.33911	+	0.413061i
$19$	−107.850	+	1439.16i	−0.0685388	+	0.914586i	0.851901	+	0.523702i	$0.175450\pi$
$19$	−107.850	+	1439.16i	−0.0685388	+	0.914586i	−0.920440	+	0.390884i	$0.872169\pi$
$20$	527.604	−	359.714i	0.294939	−	0.201086i
$21$	218.162	−	955.830i	0.107952	−	0.472969i
$22$	−1419.78	+	6220.48i	−0.625412	+	2.74011i
$23$	420.174	−	286.470i	0.165619	−	0.112917i	−0.477674	−	0.878537i	$-0.658520\pi$
$23$	420.174	−	286.470i	0.165619	−	0.112917i	0.643293	+	0.765620i	$0.277568\pi$
$24$	302.958	−	4042.69i	0.107363	−	1.43266i
$25$	−2926.31	+	902.648i	−0.936420	+	0.288847i
$26$	6854.87	+	1033.21i	1.98868	+	0.299746i
$27$	−2075.99	+	2603.21i	−0.548044	+	0.687225i
$28$	−8332.20	−	5680.80i	−2.00847	−	1.36935i
$29$	−3272.35	+	3036.30i	−0.722545	+	0.670423i	−0.953107	−	0.302634i	$-0.902134\pi$
$29$	−3272.35	+	3036.30i	−0.722545	+	0.670423i	0.230562	+	0.973058i	$0.425943\pi$
$30$	240.763	−	613.453i	0.0488412	−	0.124445i
$31$	−2359.18	−	727.712i	−0.440918	−	0.136005i	0.0663446	−	0.997797i	$-0.478866\pi$
$31$	−2359.18	−	727.712i	−0.440918	−	0.136005i	−0.507262	+	0.861792i	$0.669343\pi$
$32$	−12876.1	−	6200.82i	−2.22285	−	1.07047i
$33$	1722.53	+	4388.93i	0.275348	+	0.701574i
$34$	−1088.25	−	14521.7i	−0.161447	−	2.15436i
$35$	−616.727	−	773.351i	−0.0850986	−	0.106710i
$36$	7320.94	+	12680.2i	0.941479	+	1.63069i
$37$	−4376.92	+	7581.05i	−0.525611	+	0.910385i	0.473944	+	0.880555i	$0.342830\pi$
$37$	−4376.92	+	7581.05i	−0.525611	+	0.910385i	−0.999555	+	0.0298299i	$0.990503\pi$
$38$	15148.9	−	2283.33i	1.70185	−	0.256513i
$39$	4615.33	−	2222.63i	0.485894	−	0.233994i
$40$	−2998.31	−	2782.02i	−0.296296	−	0.274923i
$41$	−311.934	−	1366.67i	−0.0289803	−	0.126971i	0.958369	−	0.285534i	$-0.0921710\pi$
$41$	−311.934	−	1366.67i	−0.0289803	−	0.126971i	−0.987349	+	0.158563i	$0.949314\pi$
$42$	−10407.4			−0.910373
$43$	−7680.21	−	9382.05i	−0.633435	−	0.773796i
$43$	−7680.21	−	9382.05i	−0.633435	−	0.773796i
$44$	48496.9			3.77644
$45$	319.578	+	1400.16i	0.0235258	+	0.103073i
$46$	−3957.25	−	3671.79i	−0.275739	−	0.255849i
$47$	−4610.57	+	2220.34i	−0.304446	+	0.146614i	−0.579869	−	0.814710i	$-0.696896\pi$
$47$	−4610.57	+	2220.34i	−0.304446	+	0.146614i	0.275423	+	0.961323i	$0.411182\pi$
$48$	−22527.1	+	3395.41i	−1.41124	+	0.212711i
$49$	592.883	−	1026.90i	0.0352759	−	0.0610997i
$50$	16254.0	+	28152.8i	0.919468	+	1.59256i
$51$	−6709.31	−	8413.21i	−0.361204	−	0.452935i
$52$	−3937.63	−	52544.0i	−0.201942	−	2.69473i
$53$	−12396.1	−	31584.8i	−0.606173	−	1.54450i	−0.822850	−	0.568259i	$-0.807617\pi$
$53$	−12396.1	−	31584.8i	−0.606173	−	1.54450i	0.216677	−	0.976243i	$-0.430478\pi$
$54$	31844.9	+	15335.7i	1.48612	+	0.715680i
$55$	4545.55	+	1402.12i	0.202619	+	0.0624997i
$56$	−23598.9	+	60129.1i	−1.00559	+	2.56221i
$57$	8298.70	−	7700.07i	0.338316	−	0.313912i
$58$	39153.0	+	26694.1i	1.52825	+	1.04194i
$59$	−19415.9	+	24346.7i	−0.726151	+	0.910565i	−0.998669	−	0.0515859i	$-0.983572\pi$
$59$	−19415.9	+	24346.7i	−0.726151	+	0.910565i	0.272517	+	0.962151i	$0.412144\pi$
$60$	−4953.07	−	746.556i	−0.177622	−	0.0267722i
$61$	−6595.23	+	2034.36i	−0.226937	+	0.0700008i	−0.406138	−	0.913812i	$-0.633125\pi$
$61$	−6595.23	+	2034.36i	−0.226937	+	0.0700008i	0.179201	+	0.983812i	$0.442649\pi$
$62$	−1958.52	+	26134.6i	−0.0647066	+	0.863450i
$63$	18739.7	−	12776.5i	0.594856	−	0.405566i
$64$	−13078.2	+	57299.3i	−0.399115	+	1.74864i
$65$	1150.06	−	5038.73i	0.0337626	−	0.147924i
$66$	41353.1	−	28194.0i	1.16855	−	0.796705i
$67$	−4500.74	+	60058.2i	−0.122489	+	1.63450i	0.510172	+	0.860073i	$0.329582\pi$
$67$	−4500.74	+	60058.2i	−0.122489	+	1.63450i	−0.632661	+	0.774429i	$0.718037\pi$
$68$	−105769.	+	32625.4i	−2.77387	+	0.855625i
$69$	−3944.54	−	594.544i	−0.0997410	−	0.0150335i
$70$	−6546.77	+	8209.39i	−0.159692	+	0.200247i
$71$	−40715.9	−	27759.7i	−0.958558	−	0.653534i	−0.0204187	−	0.999792i	$-0.506500\pi$
$71$	−40715.9	−	27759.7i	−0.958558	−	0.653534i	−0.938139	+	0.346258i	$0.887452\pi$
$72$	68749.7	−	63790.4i	1.56293	−	1.45019i
$73$	31246.6	−	79615.0i	0.686270	−	1.74859i	0.0235483	−	0.999723i	$-0.492504\pi$
$73$	31246.6	−	79615.0i	0.686270	−	1.74859i	0.662722	−	0.748865i	$-0.269401\pi$
$74$	88796.7	+	27390.2i	1.88503	+	0.581454i
$75$	21643.0	+	10422.7i	0.444288	+	0.213958i
$76$	−42542.2	−	108396.i	−0.844862	−	2.15267i
$77$	−5613.98	−	74913.3i	−0.107906	−	1.43990i
$78$	−33904.5	−	42514.9i	−0.630987	−	0.791233i
$79$	−32407.5	−	56131.4i	−0.584222	−	1.01190i	−0.994972	−	0.100154i	$-0.968066\pi$
$79$	−32407.5	−	56131.4i	−0.584222	−	1.01190i	0.410750	−	0.911748i	$-0.365267\pi$
$80$	−11492.3	+	19905.3i	−0.200763	+	0.347731i
$81$	−17777.6	+	2679.54i	−0.301064	+	0.0453782i
$82$	−13407.1	+	6456.53i	−0.220192	+	0.106039i
$83$	59256.0	+	54981.5i	0.944141	+	0.876035i	0.992432	−	0.122798i	$-0.0391868\pi$
$83$	59256.0	+	54981.5i	0.944141	+	0.876035i	−0.0482904	+	0.998833i	$0.515377\pi$
$84$	17602.6	+	77121.8i	0.272193	+	1.19256i
$85$	−10856.8			−0.162988
$86$	−78955.0	+	101646.i	−1.15115	+	1.48198i
$87$	35016.7			0.495995
$88$	−69123.2	−	302849.i	−0.951519	−	4.16888i
$89$	69547.7	+	64530.9i	0.930696	+	0.863560i	0.990896	−	0.134627i	$-0.0429835\pi$
$89$	69547.7	+	64530.9i	0.930696	+	0.863560i	−0.0602003	+	0.998186i	$0.519174\pi$
$90$	13735.7	−	6614.75i	0.178749	−	0.0860810i
$91$	−80709.1	+	12164.9i	−1.02169	+	0.153995i
$92$	−20515.9	+	35534.6i	−0.252709	+	0.437705i
$93$	9683.20	+	16771.8i	0.116094	+	0.201081i
$94$	33869.5	+	42471.0i	0.395357	+	0.495762i
$95$	−853.544	−	11389.8i	−0.00970324	−	0.129481i
$96$	40956.7	+	104356.i	0.453572	+	1.15568i
$97$	132008.	+	63571.5i	1.42452	+	0.686014i	0.977971	−	0.208743i	$-0.0669371\pi$
$97$	132008.	+	63571.5i	1.42452	+	0.686014i	0.446553	+	0.894757i	$0.352651\pi$
$98$	−12028.1	−	3710.18i	−0.126512	−	0.0390238i
$99$	−39848.8	+	101533.i	−0.408628	+	1.04117i
$100$	181129.	−	168063.i	1.81129	−	1.68063i
$101$	−11388.3	−	7764.39i	−0.111085	−	0.0757362i	0.506503	−	0.862238i	$-0.330938\pi$
$101$	−11388.3	−	7764.39i	−0.111085	−	0.0757362i	−0.617588	+	0.786502i	$0.711890\pi$
$102$	−71221.7	+	89309.1i	−0.677816	+	0.849954i
$103$	−198247.	−	29881.0i	−1.84126	−	0.277525i	−0.866234	−	0.499638i	$-0.833466\pi$
$103$	−198247.	−	29881.0i	−1.84126	−	0.277525i	−0.975021	+	0.222114i	$0.928704\pi$
$104$	−322510.	+	99481.0i	−2.92388	+	0.901897i
$105$	−579.842	+	7737.45i	−0.00513258	+	0.0684896i
$106$	−297596.	+	202898.i	−2.57254	+	1.75393i
$107$	6098.51	−	26719.3i	0.0514949	−	0.225614i	−0.942632	−	0.333833i	$-0.891658\pi$
$107$	6098.51	−	26719.3i	0.0514949	−	0.225614i	0.994127	+	0.108219i	$0.0345149\pi$
$108$	59781.0	−	261918.i	0.493178	−	2.16075i
$109$	−26851.8	+	18307.3i	−0.216475	+	0.147590i	−0.666703	−	0.745324i	$-0.732295\pi$
$109$	−26851.8	+	18307.3i	−0.216475	+	0.147590i	0.450228	+	0.892914i	$0.351343\pi$
$110$	3773.57	−	50354.8i	0.0297352	−	0.396789i
$111$	65616.5	−	20240.0i	0.505482	−	0.155920i
$112$	358932.	+	54100.3i	2.70375	+	0.407525i
$113$	−61241.2	+	76794.1i	−0.451178	+	0.565759i	−0.954451	−	0.298368i	$-0.903558\pi$
$113$	−61241.2	+	76794.1i	−0.451178	+	0.565759i	0.503273	+	0.864128i	$0.332129\pi$
$114$	−99292.2	−	67696.3i	−0.715572	−	0.487868i
$115$	−2950.29	+	2737.47i	−0.0208027	+	0.0193021i
$116$	131589.	−	335284.i	0.907977	−	2.31349i
$117$	113242.	+	34930.5i	0.764790	+	0.235906i
$118$	297832.	+	143429.i	1.96910	+	0.948267i
$119$	62640.3	+	159605.i	0.405496	+	1.03319i
$120$	2397.66	+	31994.6i	0.0151997	+	0.202826i
$121$	124836.	+	156539.i	0.775133	+	0.971986i
$122$	36632.9	+	63450.0i	0.222829	+	0.385951i
$123$	−5498.09	+	9522.97i	−0.0327679	+	0.0567557i
$124$	196978.	−	29689.6i	1.15044	−	0.173400i
$125$	44118.6	−	21246.4i	0.252549	−	0.121621i
$126$	−176493.	−	163761.i	−0.990377	−	0.918935i
$127$	−47094.1	−	206333.i	−0.259094	−	1.13517i	−0.922222	−	0.386660i	$-0.873629\pi$
$127$	−47094.1	−	206333.i	−0.259094	−	1.13517i	0.663128	−	0.748506i	$-0.269228\pi$
$128$	166569.			0.898605
$129$	−5894.33	+	94926.2i	−0.0311861	+	0.502241i
$130$	−54863.4			−0.284724
$131$	25389.7	+	111240.i	0.129264	+	0.566345i	0.997530	+	0.0702446i	$0.0223780\pi$
$131$	25389.7	+	111240.i	0.129264	+	0.566345i	−0.868265	+	0.496100i	$0.834765\pi$
$132$	−278868.	−	258752.i	−1.39304	−	1.29255i
$133$	−162515.	+	78262.9i	−0.796642	+	0.383642i
$134$	632186.	−	95286.7i	3.04147	−	0.458427i
$135$	13175.6	−	22820.8i	0.0622210	−	0.107770i
$136$	354490.	+	613994.i	1.64345	+	2.84654i
$137$	−229625.	−	287941.i	−1.04525	−	1.31070i	−0.948978	−	0.315342i	$-0.897881\pi$
$137$	−229625.	−	287941.i	−1.04525	−	1.31070i	−0.0962683	−	0.995355i	$-0.530691\pi$
$138$	3164.49	+	42227.2i	0.0141451	+	0.188754i
$139$	17751.8	+	45230.8i	0.0779301	+	0.198563i	0.964529	−	0.263976i	$-0.0850339\pi$
$139$	17751.8	+	45230.8i	0.0779301	+	0.198563i	−0.886599	+	0.462539i	$0.846939\pi$
$140$	71906.8	+	34628.5i	0.310063	+	0.149318i
$141$	38358.3	+	11832.0i	0.162484	+	0.0501198i
$142$	−191114.	+	486950.i	−0.795373	+	2.02658i
$143$	287736.	−	266980.i	1.17667	−	1.09179i
$144$	−435450.	−	296885.i	−1.74998	−	1.19311i
$145$	22027.2	−	27621.3i	0.0870041	−	0.109100i
$146$	−897760.	−	135316.i	−3.48561	−	0.525370i
$147$	−8888.18	+	2741.64i	−0.0339250	+	0.0104645i
$148$	52782.6	−	704335.i	0.198078	−	2.64317i
$149$	376590.	−	256755.i	1.38964	−	0.947443i	0.389998	−	0.920816i	$-0.372476\pi$
$149$	376590.	−	256755.i	1.38964	−	0.947443i	0.999645	−	0.0266268i	$-0.00847658\pi$
$150$	56743.1	−	248608.i	0.205913	−	0.902166i
$151$	−23348.4	+	102296.i	−0.0833326	+	0.365104i	−0.999351	−	0.0360332i	$-0.988528\pi$
$151$	−23348.4	+	102296.i	−0.0833326	+	0.365104i	0.916018	+	0.401137i	$0.131385\pi$
$152$	−616263.	+	420161.i	−2.16350	+	1.47505i
$153$	18603.4	−	248246.i	0.0642488	−	0.857340i
$154$	−762032.	+	235056.i	−2.58923	+	0.798673i
$155$	19320.8	+	2912.15i	0.0645947	+	0.00973608i
$156$	−257703.	+	323149.i	−0.847828	+	1.06314i
$157$	301454.	+	205528.i	0.976049	+	0.665459i	0.942580	−	0.333981i	$-0.108392\pi$
$157$	301454.	+	205528.i	0.976049	+	0.665459i	0.0334690	+	0.999440i	$0.489344\pi$
$158$	−504365.	+	467982.i	−1.60732	+	1.49137i
$159$	−97238.1	+	247759.i	−0.305031	+	0.777206i
$160$	108080.	+	33338.2i	0.333768	+	0.102954i
$161$	57265.3	+	27577.5i	0.174111	+	0.0838475i
$162$	69724.1	+	177654.i	0.208735	+	0.531848i
$163$	−3774.71	−	50370.1i	−0.0111279	−	0.148492i	0.988872	−	0.148769i	$-0.0475310\pi$
$163$	−3774.71	−	50370.1i	−0.0111279	−	0.148492i	−1.00000		0.000276602i	$0.999912\pi$
$164$	70520.8	+	88430.3i	0.204742	+	0.256739i
$165$	−18657.1	−	32315.0i	−0.0533499	−	0.0924047i
$166$	429044.	−	743126.i	1.20846	−	2.09311i
$167$	−397492.	+	59912.3i	−1.10290	+	0.166236i	−0.675165	−	0.737667i	$-0.735928\pi$
$167$	−397492.	+	59912.3i	−1.10290	+	0.166236i	−0.427738	+	0.903903i	$0.640689\pi$
$168$	456514.	−	219845.i	1.24790	−	0.600958i
$169$	−40445.7	−	37528.1i	−0.108932	−	0.101074i
$170$	25645.4	+	112360.i	0.0680591	+	0.298187i
$171$	261894.			0.684912
$172$	886764.	+	413161.i	2.28553	+	1.06487i
$173$	589106.			1.49651			0.748253	−	0.663414i	$-0.230893\pi$
$173$	589106.			1.49651			0.748253	+	0.663414i	$0.230893\pi$
$174$	−82714.3	−	362395.i	−0.207113	−	0.907422i
$175$	−280575.	−	260336.i	−0.692555	−	0.642597i
$176$	−1.57275e6	+	757396.i	−3.82717	+	1.84307i
$177$	241546.	−	36407.2i	0.579518	−	0.0873483i
$178$	503562.	−	872194.i	1.19125	−	2.06330i
$179$	97367.4	+	168645.i	0.227133	+	0.393407i	0.956957	−	0.290228i	$-0.0937313\pi$
$179$	97367.4	+	168645.i	0.227133	+	0.393407i	−0.729824	+	0.683635i	$0.760398\pi$
$180$	−72249.0	−	90597.3i	−0.166207	−	0.208418i
$181$	−24823.9	−	331252.i	−0.0563215	−	0.751558i	−0.951852	−	0.306558i	$-0.900823\pi$
$181$	−24823.9	−	331252.i	−0.0563215	−	0.751558i	0.895531	−	0.445000i	$-0.146796\pi$
$182$	316544.	+	806540.i	0.708362	+	1.80488i
$183$	48778.3	+	23490.4i	0.107671	+	0.0518516i
$184$	251144.	+	77467.8i	0.546864	+	0.168685i
$185$	25310.6	−	64490.4i	0.0543718	−	0.138537i
$186$	150702.	−	139831.i	0.319400	−	0.296360i
$187$	−681272.	−	464484.i	−1.42468	−	0.971329i
$188$	257437.	−	322816.i	0.531223	−	0.666132i
$189$	−411505.	−	62024.4i	−0.837955	−	0.126301i
$190$	−115859.	+	35737.7i	−0.232833	+	0.0718195i
$191$	−7812.78	+	104254.i	−0.0154961	+	0.206781i	0.984081	+	0.177718i	$0.0568714\pi$
$191$	−7812.78	+	104254.i	−0.0154961	+	0.206781i	−0.999578	+	0.0290631i	$0.990748\pi$
$192$	380919.	−	259706.i	0.745727	−	0.508428i
$193$	−29642.0	+	129870.i	−0.0572815	+	0.250967i	−0.995459	−	0.0951866i	$-0.969655\pi$
$193$	−29642.0	+	129870.i	−0.0572815	+	0.250967i	0.938178	+	0.346153i	$0.112512\pi$
$194$	346094.	−	1.51634e6i	0.660222	−	2.89262i
$195$	−33496.9	+	22837.8i	−0.0630838	+	0.0430098i
$196$	−7149.75	+	95406.8i	−0.0132938	+	0.177394i
$197$	−32445.5	+	10008.1i	−0.0595648	+	0.0183733i	−0.324394	−	0.945922i	$-0.605160\pi$
$197$	−32445.5	+	10008.1i	−0.0595648	+	0.0183733i	0.264830	+	0.964295i	$0.414684\pi$
$198$	1.14492e6	+	172568.i	2.07544	+	0.312823i
$199$	−287983.	+	361120.i	−0.515507	+	0.646425i	−0.969648	−	0.244504i	$-0.921375\pi$
$199$	−287983.	+	361120.i	−0.515507	+	0.646425i	0.454141	+	0.890930i	$0.349946\pi$
$200$	−1.30767e6	−	891555.i	−2.31166	−	1.57606i
$201$	346317.	−	321335.i	0.604621	−	0.561007i
$202$	−53454.6	+	136200.i	−0.0921736	+	0.234854i
$203$	−533146.	−	164454.i	−0.908043	−	0.280094i
$204$	782267.	+	376720.i	1.31607	+	0.633786i
$205$	4053.18	+	10327.3i	0.00673614	+	0.0171634i
$206$	159043.	+	2.12228e6i	0.261124	+	3.48446i
$207$	−57537.8	−	72150.1i	−0.0933313	−	0.117034i
$208$	948300.	+	1.64250e6i	1.51980	+	2.63238i
$209$	433723.	−	751229.i	0.686825	−	1.18962i
$210$	81446.1	−	12276.0i	0.127445	−	0.0192092i
$211$	−91049.1	+	43846.9i	−0.140789	+	0.0678005i	−0.502952	−	0.864314i	$-0.667753\pi$
$211$	−91049.1	+	43846.9i	−0.140789	+	0.0678005i	0.362163	+	0.932115i	$0.382038\pi$
$212$	2.00687e6	+	1.86210e6i	3.06676	+	2.84553i
$213$	86016.2	+	376862.i	0.129907	+	0.569158i
$214$	−290929.			−0.434263
$215$	71170.2	+	64362.7i	0.105003	+	0.0949594i
$216$	−1.72080e6			−2.50956
$217$	−68663.6	−	300835.i	−0.0989868	−	0.433690i
$218$	252893.	+	234651.i	0.360409	+	0.334411i
$219$	−604455.	+	291090.i	−0.851636	+	0.410126i
$220$	−379526.	+	57204.3i	−0.528670	+	0.0796842i
$221$	−447931.	+	775839.i	−0.616922	+	1.06854i
$222$	−364463.	−	631269.i	−0.496331	−	0.859670i
$223$	−58011.6	−	72744.2i	−0.0781182	−	0.0979572i	0.741237	−	0.671244i	$-0.234240\pi$
$223$	−58011.6	−	72744.2i	−0.0781182	−	0.0979572i	−0.819355	+	0.573287i	$0.805668\pi$
$224$	−133484.	−	1.78122e6i	−0.177750	−	2.37190i
$225$	203028.	+	517306.i	0.267362	+	0.681227i
$226$	939418.	+	452400.i	1.22345	+	0.589184i
$227$	−39805.2	−	12278.3i	−0.0512714	−	0.0158151i	0.269013	−	0.963136i	$-0.413302\pi$
$227$	−39805.2	−	12278.3i	−0.0512714	−	0.0158151i	−0.320285	+	0.947321i	$0.603779\pi$
$228$	−333711.	+	850281.i	−0.425141	+	1.08324i
$229$	−355513.	+	329867.i	−0.447988	+	0.415672i	−0.871635	−	0.490155i	$-0.836940\pi$
$229$	−355513.	+	329867.i	−0.447988	+	0.415672i	0.423647	+	0.905827i	$0.360750\pi$
$230$	35299.6	+	24066.8i	0.0439997	+	0.0299985i
$231$	−367413.	+	460722.i	−0.453028	+	0.568079i
$232$	−2.28130e6	−	343851.i	−2.78268	−	0.419421i
$233$	−747248.	+	230495.i	−0.901726	+	0.278146i	−0.710746	−	0.703448i	$-0.751643\pi$
$233$	−747248.	+	230495.i	−0.901726	+	0.278146i	−0.190980	+	0.981594i	$0.561166\pi$
$234$	94009.7	−	1.25447e6i	0.112236	−	1.49769i
$235$	33462.4	−	22814.2i	0.0395264	−	0.0269486i
$236$	559108.	−	2.44961e6i	0.653454	−	2.86297i
$237$	−113135.	+	495677.i	−0.130836	+	0.573228i
$238$	1.50382e6	−	1.02529e6i	1.72089	−	1.17328i
$239$	−4758.81	+	63502.0i	−0.00538895	+	0.0719105i	−0.999250	−	0.0387262i	$-0.987670\pi$
$239$	−4758.81	+	63502.0i	−0.00538895	+	0.0719105i	0.993861	+	0.110637i	$0.0352890\pi$
$240$	172287.	−	53143.5i	0.193074	−	0.0595555i
$241$	2033.68	+	306.527i	0.00225548	+	0.000339959i	0.150170	−	0.988660i	$-0.452018\pi$
$241$	2033.68	+	306.527i	0.00225548	+	0.000339959i	−0.147914	+	0.989000i	$0.547256\pi$
$242$	1.32518e6	−	1.66172e6i	1.45457	−	1.82398i
$243$	785031.	+	535225.i	0.852847	+	0.581461i
$244$	408223.	−	378776.i	0.438958	−	0.407294i
$245$	−3428.49	+	8735.65i	−0.00364912	+	0.00929779i
$246$	111542.	+	34406.3i	0.117517	+	0.0362493i
$247$	−849136.	−	408922.i	−0.885595	−	0.426480i
$248$	−466157.	−	1.18775e6i	−0.481286	−	1.22630i
$249$	−47385.3	−	632313.i	−0.0484334	−	0.646299i
$250$	−324097.	−	406405.i	−0.327963	−	0.411253i
$251$	167656.	+	290389.i	0.167971	+	0.290935i	0.937707	−	0.347428i	$-0.112945\pi$
$251$	167656.	+	290389.i	0.167971	+	0.290935i	−0.769735	+	0.638363i	$0.779612\pi$
$252$	−915007.	+	1.58484e6i	−0.907660	+	1.57211i
$253$	−302248.	+	45556.5i	−0.296867	+	0.0447455i
$254$	−2.02414e6	+	974774.i	−1.96859	+	0.948024i
$255$	62429.3	+	57926.0i	0.0601227	+	0.0557857i
$256$	25043.5	+	109723.i	0.0238833	+	0.104640i
$257$	754631.			0.712692			0.356346	−	0.934354i	$-0.384023\pi$
$257$	754631.			0.712692			0.356346	+	0.934354i	$0.384023\pi$
$258$	996334.	−	163227.i	0.931870	−	0.152666i
$259$	−1.09410e6			−1.01346
$260$	92793.2	+	406553.i	0.0851300	+	0.372979i
$261$	593827.	+	550991.i	0.539583	+	0.500660i
$262$	1.09127e6	−	525526.i	0.982149	−	0.472978i
$263$	−229830.	+	34641.2i	−0.204888	+	0.0308819i	−0.250684	−	0.968069i	$-0.580656\pi$
$263$	−229830.	+	34641.2i	−0.204888	+	0.0308819i	0.0457962	+	0.998951i	$0.485418\pi$
$264$	−1.21835e6	+	2.11025e6i	−1.07588	+	1.86348i
$265$	134265.	+	232554.i	0.117449	+	0.203427i
$266$	1.19384e6	+	1.49703e6i	1.03453	+	1.29726i
$267$	−55615.3	−	742135.i	−0.0477437	−	0.637095i
$268$	−1.77535e6	−	4.52351e6i	−1.50989	−	3.84715i
$269$	506259.	+	243802.i	0.426572	+	0.205426i	0.634837	−	0.772646i	$-0.281067\pi$
$269$	506259.	+	243802.i	0.426572	+	0.205426i	−0.208265	+	0.978072i	$0.566782\pi$
$270$	−267300.	−	82451.2i	−0.223146	−	0.0688316i
$271$	−315888.	+	804868.i	−0.261282	+	0.665735i	−0.999965	−	0.00831702i	$-0.997353\pi$
$271$	−315888.	+	804868.i	−0.261282	+	0.665735i	0.738684	+	0.674052i	$0.235448\pi$
$272$	2.92055e6	−	2.70988e6i	2.39355	−	2.22089i
$273$	529001.	+	360667.i	0.429586	+	0.292887i
$274$	−2.43756e6	+	3.05660e6i	−1.96145	+	2.45959i
$275$	1.82010e6	+	274337.i	1.45132	+	0.218752i
$276$	307564.	−	94870.8i	0.243031	−	0.0749652i
$277$	146313.	−	1.95241e6i	0.114573	−	1.52887i	−0.583066	−	0.812425i	$-0.698147\pi$
$277$	146313.	−	1.95241e6i	0.114573	−	1.52887i	0.697639	−	0.716449i	$-0.254234\pi$
$278$	426171.	−	290558.i	0.330729	−	0.225487i
$279$	−99694.0	+	436788.i	−0.0766758	+	0.335939i
$280$	113755.	−	498393.i	0.0867112	−	0.379906i
$281$	626690.	−	427270.i	0.473464	−	0.322802i	−0.302971	−	0.953000i	$-0.597978\pi$
$281$	626690.	−	427270.i	0.473464	−	0.322802i	0.776435	+	0.630198i	$0.217026\pi$
$282$	31843.9	−	424927.i	0.0238453	−	0.318194i
$283$	−1.96801e6	+	607049.i	−1.46070	+	0.450565i	−0.920423	−	0.390924i	$-0.872156\pi$
$283$	−1.96801e6	+	607049.i	−1.46070	+	0.450565i	−0.540274	+	0.841489i	$0.681679\pi$
$284$	3.93167e6	+	592604.i	2.89255	+	0.435982i
$285$	−55861.2	+	70047.7i	−0.0407378	+	0.0510836i
$286$	−3.44271e6	−	2.34720e6i	−2.48877	−	1.69682i
$287$	128435.	−	119170.i	0.0920405	−	0.0854011i
$288$	−947489.	+	2.41416e6i	−0.673121	+	1.71508i
$289$	441512.	+	136188.i	0.310955	+	0.0959170i
$290$	−337890.	−	162719.i	−0.235928	−	0.113617i
$291$	−419893.	−	1.06987e6i	−0.290674	−	0.740624i
$292$	515699.	+	6.88152e6i	0.353948	+	4.72310i
$293$	−1.11943e6	−	1.40372e6i	−0.761776	−	0.955236i	0.238096	−	0.971242i	$-0.423477\pi$
$293$	−1.11943e6	−	1.40372e6i	−0.761776	−	0.955236i	−0.999872	+	0.0160053i	$0.994905\pi$
$294$	49368.9	+	85509.5i	0.0333108	+	0.0576960i
$295$	123226.	−	213434.i	0.0824420	−	0.142794i
$296$	−4.47359e6	+	674286.i	−2.96775	+	0.447316i
$297$	1.80311e6	−	868333.i	1.18613	−	0.571209i
$298$	−3.54677e6	−	3.29092e6i	−2.31362	−	2.14672i
$299$	73898.9	+	323772.i	0.0478035	+	0.209441i
$300$	−1.93823e6			−1.24337
$301$	535559.	−	1.41761e6i	0.340715	−	0.901866i
$302$	1.11383e6			0.702754
$303$	24058.8	+	105408.i	0.0150545	+	0.0659581i
$304$	3.07250e6	+	2.85086e6i	1.90681	+	1.76926i
$305$	49213.2	−	23699.8i	0.0302923	−	0.0145880i
$306$	−2.61309e6	+	393860.i	−1.59533	+	0.240457i
$307$	−1.29807e6	+	2.24832e6i	−0.786053	+	1.36148i	0.142315	+	0.989821i	$0.454545\pi$
$307$	−1.29807e6	+	2.24832e6i	−0.786053	+	1.36148i	−0.928368	+	0.371662i	$0.878788\pi$
$308$	3.03069e6	+	5.24931e6i	1.82039	+	3.15301i
$309$	980539.	+	1.22956e6i	0.584210	+	0.732576i
$310$	−15500.1	−	206834.i	−0.00916072	−	0.122241i
$311$	−1.12823e6	−	2.87467e6i	−0.661447	−	1.68534i	−0.726240	−	0.687441i	$-0.758734\pi$
$311$	−1.12823e6	−	2.87467e6i	−0.661447	−	1.68534i	0.0647933	−	0.997899i	$-0.479361\pi$
$312$	2.38528e6	+	1.14869e6i	1.38724	+	0.668061i
$313$	−1.02488e6	−	316134.i	−0.591306	−	0.182394i	−0.0153607	−	0.999882i	$-0.504890\pi$
$313$	−1.02488e6	−	316134.i	−0.591306	−	0.182394i	−0.575945	+	0.817488i	$0.695366\pi$
$314$	1.41497e6	−	3.60529e6i	0.809886	−	2.06356i
$315$	−131582.	+	122091.i	−0.0747174	+	0.0693276i
$316$	4.32094e6	+	2.94596e6i	2.43422	+	1.65962i
$317$	783823.	−	982882.i	0.438096	−	0.549355i	−0.512944	−	0.858422i	$-0.671445\pi$
$317$	783823.	−	982882.i	0.438096	−	0.549355i	0.951040	+	0.309067i	$0.100017\pi$
$318$	2.79379e6	+	421097.i	1.54927	+	0.233515i
$319$	2.56393e6	−	790867.i	1.41068	−	0.435138i
$320$	34759.9	−	463838.i	0.0189759	−	0.253216i
$321$	−177627.	+	121104.i	−0.0962157	+	0.0655988i
$322$	150137.	−	657792.i	0.0806951	−	0.353548i
$323$	−440548.	+	1.93017e6i	−0.234956	+	1.02941i
$324$	1.19854e6	−	817150.i	0.634293	−	0.432453i
$325$	149450.	−	1.99427e6i	0.0784851	−	1.04731i
$326$	−512374.	+	158046.i	−0.267019	+	0.0823646i
$327$	252081.	+	37995.1i	0.130368	+	0.0196498i
$328$	451707.	−	566422.i	0.231831	−	0.290707i
$329$	−528456.	−	360295.i	−0.269165	−	0.183514i
$330$	−290364.	+	269418.i	−0.146777	+	0.136189i
$331$	−9414.48	+	23987.7i	−0.00472309	+	0.0120342i	−0.933216	−	0.359316i	$-0.883010\pi$
$331$	−9414.48	+	23987.7i	−0.00472309	+	0.0120342i	0.928493	+	0.371351i	$0.121105\pi$
$332$	−6.23244e6	−	1.92245e6i	−3.10322	−	0.957217i
$333$	1.43123e6	+	689243.i	0.707291	+	0.340613i
$334$	1.55898e6	+	3.97220e6i	0.764668	+	1.94834i
$335$	−35619.6	−	475311.i	−0.0173411	−	0.231401i
$336$	−1.77529e6	−	2.22615e6i	−0.857871	−	1.07574i
$337$	1.26896e6	+	2.19791e6i	0.608659	+	1.05423i	0.991462	+	0.130398i	$0.0416256\pi$
$337$	1.26896e6	+	2.19791e6i	0.608659	+	1.05423i	−0.382803	+	0.923830i	$0.625041\pi$
$338$	−292848.	+	507227.i	−0.139428	+	0.241496i
$339$	761881.	−	114835.i	0.360071	−	0.0542719i
$340$	789242.	−	380079.i	0.370265	−	0.178310i
$341$	1.08780e6	+	1.00933e6i	0.506599	+	0.470055i
$342$	−618629.	−	2.71039e6i	−0.285999	−	1.25304i
$343$	2.24882e6			1.03210
$344$	1.31615e6	−	6.12646e6i	0.599665	−	2.79135i
$345$	31570.4			0.0142801
$346$	−1.39155e6	−	6.09678e6i	−0.624897	−	2.73785i
$347$	−1.00092e6	−	928719.i	−0.446248	−	0.414057i	0.424776	−	0.905299i	$-0.360353\pi$
$347$	−1.00092e6	−	928719.i	−0.446248	−	0.414057i	−0.871024	+	0.491241i	$0.836543\pi$
$348$	−2.54555e6	+	1.22587e6i	−1.12677	+	0.542622i
$349$	−1.49430e6	+	225230.i	−0.656713	+	0.0989835i	−0.468942	−	0.883229i	$-0.655364\pi$
$349$	−1.49430e6	+	225230.i	−0.656713	+	0.0989835i	−0.187771	+	0.982213i	$0.560126\pi$
$350$	−2.03151e6	+	3.51868e6i	−0.886439	+	1.53536i
$351$	−1.08720e6	−	1.88308e6i	−0.471021	−	0.815833i
$352$	5.35577e6	+	6.71593e6i	2.30391	+	2.88901i
$353$	19044.5	+	254132.i	0.00813455	+	0.108548i	0.999793	−	0.0203453i	$-0.00647656\pi$
$353$	19044.5	+	254132.i	0.00813455	+	0.108548i	−0.991658	+	0.128893i	$0.958858\pi$
$354$	−947352.	−	2.41381e6i	−0.401794	−	1.02375i
$355$	351378.	+	169215.i	0.147980	+	0.0712635i
$356$	−7.31490e6	−	2.25635e6i	−3.05903	−	0.943586i
$357$	491365.	−	1.25198e6i	0.204049	−	0.519908i
$358$	1.51535e6	−	1.40604e6i	0.624892	−	0.579815i
$359$	3.01104e6	+	2.05289e6i	1.23305	+	0.840679i	0.991550	−	0.129722i	$-0.0414086\pi$
$359$	3.01104e6	+	2.05289e6i	1.23305	+	0.840679i	0.241499	+	0.970401i	$0.422361\pi$
$360$	−462776.	+	580303.i	−0.188198	+	0.235993i
$361$	388897.	+	58616.8i	0.157061	+	0.0236731i
$362$	−3.36956e6	+	1.03937e6i	−1.35146	+	0.416869i
$363$	117370.	−	1.56619e6i	0.0467509	−	0.623847i
$364$	5.44130e6	−	3.70982e6i	2.15253	−	1.46757i
$365$	−150619.	+	659906.i	−0.0591764	+	0.259269i
$366$	127886.	−	560304.i	0.0499022	−	0.218636i
$367$	−2.08731e6	+	1.42311e6i	−0.808951	+	0.551534i	−0.895680	−	0.444698i	$-0.853311\pi$
$367$	−2.08731e6	+	1.42311e6i	−0.808951	+	0.551534i	0.0867292	+	0.996232i	$0.472359\pi$
$368$	110370.	−	1.47279e6i	0.0424847	−	0.566919i
$369$	−243083.	+	74981.3i	−0.0929371	+	0.0286673i
$370$	−727212.	−	109610.i	−0.276157	−	0.0416240i
$371$	2.64408e6	−	3.31557e6i	0.997332	−	1.25061i
$372$	−1.29107e6	−	880239.i	−0.483719	−	0.329794i
$373$	−2.56054e6	+	2.37584e6i	−0.952928	+	0.884188i	−0.993366	−	0.114994i	$-0.963315\pi$
$373$	−2.56054e6	+	2.37584e6i	−0.952928	+	0.884188i	0.0404381	+	0.999182i	$0.487125\pi$
$374$	−3.19778e6	+	8.14780e6i	−1.18214	+	3.01204i
$375$	−367050.	−	113220.i	−0.134787	−	0.0415762i
$376$	−2.38282e6	−	1.14750e6i	−0.869203	−	0.418586i
$377$	−1.06504e6	−	2.71368e6i	−0.385934	−	0.983344i
$378$	330129.	+	4.40526e6i	0.118838	+	1.58578i
$379$	2.82791e6	+	3.54608e6i	1.01127	+	1.26809i	0.963069	+	0.269254i	$0.0867771\pi$
$379$	2.82791e6	+	3.54608e6i	1.01127	+	1.26809i	0.0482002	+	0.998838i	$0.484651\pi$
$380$	460784.	+	798101.i	0.163696	+	0.283530i
$381$	−830073.	+	1.43773e6i	−0.292957	+	0.507417i
$382$	1.09740e6	−	165407.i	0.384776	−	0.0579957i
$383$	−2.90152e6	+	1.39730e6i	−1.01071	+	0.486734i	−0.864561	−	0.502528i	$-0.832404\pi$
$383$	−2.90152e6	+	1.39730e6i	−1.01071	+	0.486734i	−0.146153	+	0.989262i	$0.546689\pi$
$384$	−957809.	−	888717.i	−0.331475	−	0.307564i
$385$	132297.	+	579633.i	0.0454883	+	0.199297i
$386$	1.41407e6			0.483062
$387$	−1.59363e6	+	1.51705e6i	−0.540891	+	0.514898i
$388$	−1.18219e7			−3.98664
$389$	556380.	+	2.43766e6i	0.186422	+	0.816768i	0.978483	+	0.206327i	$0.0661509\pi$
$389$	556380.	+	2.43766e6i	0.186422	+	0.816768i	−0.792061	+	0.610442i	$0.790992\pi$
$390$	315477.	+	292720.i	0.105028	+	0.0974521i
$391$	628538.	−	302688.i	0.207917	−	0.100127i
$392$	605978.	−	91336.4i	0.199178	−	0.0300213i
$393$	447514.	−	775118.i	0.146159	−	0.253155i
$394$	180217.	+	312145.i	0.0584864	+	0.101301i
$395$	319824.	+	401046.i	0.103138	+	0.129331i
$396$	−657672.	−	8.77603e6i	−0.210752	−	2.81229i
$397$	105515.	+	268847.i	0.0335998	+	0.0856109i	0.946689	−	0.322149i	$-0.104405\pi$
$397$	105515.	+	268847.i	0.0335998	+	0.0856109i	−0.913089	+	0.407760i	$0.866310\pi$
$398$	4.41756e6	+	2.12738e6i	1.39789	+	0.673191i
$399$	1.35206e6	+	417056.i	0.425172	+	0.131148i
$400$	−3.24929e6	+	8.27905e6i	−1.01540	+	2.58720i
$401$	−1.91142e6	+	1.77354e6i	−0.593601	+	0.550781i	−0.918729	−	0.394889i	$-0.870783\pi$
$401$	−1.91142e6	+	1.77354e6i	−0.593601	+	0.550781i	0.325128	+	0.945670i	$0.394593\pi$
$402$	−4.14361e6	−	2.82507e6i	−1.27883	−	0.871894i
$403$	1.00524e6	−	1.26053e6i	0.308324	−	0.386626i
$404$	1.09969e6	+	165752.i	0.335210	+	0.0505248i
$405$	135963.	−	41938.9i	0.0411891	−	0.0127051i
$406$	−442601.	+	5.90610e6i	−0.133259	+	1.77822i
$407$	4.34732e6	−	2.96395e6i	1.30087	−	0.886921i
$408$	1.23753e6	−	5.42197e6i	0.368048	−	1.61252i
$409$	1.12953e6	−	4.94878e6i	0.333878	−	1.46282i	−0.477675	−	0.878537i	$-0.658520\pi$
$409$	1.12953e6	−	4.94878e6i	0.333878	−	1.46282i	0.811553	−	0.584279i	$-0.198623\pi$
$410$	97305.4	−	66341.7i	0.0285876	−	0.0194907i
$411$	−215892.	+	2.88088e6i	−0.0630423	+	0.841241i
$412$	1.54577e7	−	4.76807e6i	4.48645	−	1.38389i
$413$	−3.84864e6	−	580089.i	−1.11028	−	0.167348i
$414$	−610784.	+	765899.i	−0.175141	+	0.219619i
$415$	−528578.	−	360378.i	−0.150657	−	0.102716i
$416$	6.84153e6	−	6.34801e6i	1.93830	−	1.79848i
$417$	139249.	−	354801.i	0.0392150	−	0.0999183i
$418$	−8.79914e6	−	2.71418e6i	−2.46320	−	0.759796i
$419$	−892562.	−	429835.i	−0.248372	−	0.119610i	0.305556	−	0.952174i	$-0.401158\pi$
$419$	−892562.	−	429835.i	−0.248372	−	0.119610i	−0.553929	+	0.832564i	$0.686872\pi$
$420$	−228723.	−	582775.i	−0.0632682	−	0.161205i
$421$	139426.	+	1.86051e6i	0.0383389	+	0.511596i	0.983007	+	0.183569i	$0.0587649\pi$
$421$	139426.	+	1.86051e6i	0.0383389	+	0.511596i	−0.944668	+	0.328028i	$0.893616\pi$
$422$	668851.	+	838713.i	0.182830	+	0.229262i
$423$	464318.	+	804222.i	0.126172	+	0.218537i
$424$	8.76786e6	−	1.51864e7i	2.36853	−	4.10241i
$425$	−4.15410e6	+	626130.i	−1.11559	+	0.168148i
$426$	3.69703e6	−	1.78040e6i	0.987028	−	0.475328i
$427$	−632352.	−	586737.i	−0.167838	−	0.155730i
$428$	492062.	+	2.15587e6i	0.129841	+	0.568869i
$429$	−3.07901e6			−0.807732
$430$	497989.	−	888588.i	0.129882	−	0.231755i
$431$	−2.57203e6			−0.666933			−0.333466	−	0.942762i	$-0.608218\pi$
$431$	−2.57203e6			−0.666933			−0.333466	+	0.942762i	$0.608218\pi$
$432$	2.15179e6	+	9.42759e6i	0.554740	+	2.43048i
$433$	4.83142e6	+	4.48290e6i	1.23838	+	1.14905i	0.983273	+	0.182139i	$0.0583020\pi$
$433$	4.83142e6	+	4.48290e6i	1.23838	+	1.14905i	0.255110	+	0.966912i	$0.417888\pi$
$434$	−2.95121e6	+	1.42123e6i	−0.752100	+	0.362192i
$435$	−274033.	+	41303.9i	−0.0694352	+	0.0104657i
$436$	1.31110e6	−	2.27089e6i	0.330307	−	0.572109i
$437$	366960.	+	635593.i	0.0919211	+	0.159212i
$438$	4.44036e6	+	5.56804e6i	1.10594	+	1.38681i
$439$	343215.	+	4.57988e6i	0.0849972	+	1.13421i	0.862747	+	0.505635i	$0.168742\pi$
$439$	343215.	+	4.57988e6i	0.0849972	+	1.13421i	−0.777750	+	0.628574i	$0.783639\pi$
$440$	898167.	+	2.28849e6i	0.221170	+	0.563531i
$441$	−193869.	−	93362.4i	−0.0474692	−	0.0228600i
$442$	9.08739e6	+	2.80309e6i	2.21250	+	0.682466i
$443$	982538.	−	2.50346e6i	0.237870	−	0.606083i	−0.761231	−	0.648481i	$-0.775405\pi$
$443$	982538.	−	2.50346e6i	0.237870	−	0.606083i	0.999101	+	0.0423980i	$0.0134998\pi$
$444$	−4.06144e6	+	3.76847e6i	−0.977739	+	0.907210i
$445$	−620382.	−	422970.i	−0.148511	−	0.101253i
$446$	−615813.	+	772205.i	−0.146593	+	0.183821i
$447$	−3.53538e6	−	532873.i	−0.836888	−	0.126140i
$448$	−7.01937e6	+	2.16519e6i	−1.65235	+	0.509684i
$449$	167438.	−	2.23431e6i	0.0391957	−	0.523031i	−0.942704	−	0.333630i	$-0.891726\pi$
$449$	167438.	−	2.23431e6i	0.0391957	−	0.523031i	0.981900	−	0.189401i	$-0.0606545\pi$
$450$	4.87413e6	−	3.32313e6i	1.13466	−	0.773598i
$451$	−187491.	+	821450.i	−0.0434048	+	0.190169i
$452$	1.76353e6	−	7.72652e6i	0.406009	−	1.77884i
$453$	680052.	−	463652.i	0.155703	−	0.106156i
$454$	−33045.0	+	440955.i	−0.00752431	+	0.100405i
$455$	617263.	−	190400.i	0.139779	−	0.0431161i
$456$	5.78540e6	+	872008.i	1.30293	+	0.196385i
$457$	−99521.2	+	124796.i	−0.0222908	+	0.0279517i	−0.792852	−	0.609414i	$-0.791405\pi$
$457$	−99521.2	+	124796.i	−0.0222908	+	0.0279517i	0.770561	+	0.637366i	$0.219976\pi$
$458$	4.25364e6	+	2.90008e6i	0.947538	+	0.646020i
$459$	−3.34833e6	+	3.10679e6i	−0.741816	+	0.688305i
$460$	118638.	−	302285.i	0.0261415	−	0.0666074i
$461$	3.45579e6	+	1.06597e6i	0.757348	+	0.233611i	0.649297	−	0.760535i	$-0.275063\pi$
$461$	3.45579e6	+	1.06597e6i	0.757348	+	0.233611i	0.108050	+	0.994145i	$0.465539\pi$
$462$	5.63598e6	+	2.71415e6i	1.22847	+	0.591600i
$463$	−211020.	−	537671.i	−0.0457480	−	0.116564i	0.906173	−	0.422906i	$-0.138990\pi$
$463$	−211020.	−	537671.i	−0.0457480	−	0.116564i	−0.951921	+	0.306342i	$0.900895\pi$
$464$	968842.	+	1.29283e7i	0.208909	+	2.78770i
$465$	−95561.7	−	119831.i	−0.0204952	−	0.0257001i
$466$	4.15055e6	+	7.18896e6i	0.885402	+	1.53356i
$467$	3.36929e6	−	5.83579e6i	0.714902	−	1.23825i	−0.248095	−	0.968736i	$-0.579805\pi$
$467$	3.36929e6	−	5.83579e6i	0.714902	−	1.23825i	0.962997	−	0.269511i	$-0.0868620\pi$
$468$	−9.45500e6	+	1.42511e6i	−1.99548	+	0.300770i
$469$	−6.78197e6	+	3.26602e6i	−1.42372	+	0.685626i
$470$	−315152.	−	292418.i	−0.0658075	−	0.0610604i
$471$	−636849.	−	2.79022e6i	−0.132277	−	0.579543i
$472$	−1.60940e7			−3.32513
$473$	1.71236e6	+	7.08363e6i	0.351919	+	1.45581i
$474$	5.39710e6			1.10335
$475$	−983451.	−	4.30878e6i	−0.199995	−	0.876234i
$476$	−1.01411e7	−	9.40960e6i	−2.05149	−	1.90350i
$477$	−5.54750e6	+	2.67154e6i	−1.11635	+	0.537607i
$478$	668436.	−	100750.i	0.133810	−	0.0201687i
$479$	1.13074e6	−	1.95849e6i	0.225176	−	0.390017i	−0.731196	−	0.682167i	$-0.761038\pi$
$479$	1.13074e6	−	1.95849e6i	0.225176	−	0.390017i	0.956372	+	0.292151i	$0.0943709\pi$
$480$	−443611.	−	768356.i	−0.0878818	−	0.152216i
$481$	−3.56427e6	−	4.46946e6i	−0.702438	−	0.880830i
$482$	−1631.51	−	21771.0i	−0.000319869	−	0.00426836i
$483$	−182151.	−	464112.i	−0.0355273	−	0.0905222i
$484$	−1.45551e7	−	7.00939e6i	−2.82425	−	1.36009i
$485$	−1.10805e6	−	341788.i	−0.213897	−	0.0659784i
$486$	3.68480e6	−	9.38872e6i	0.707658	−	1.80308i
$487$	2.38975e6	−	2.21737e6i	0.456594	−	0.423657i	−0.418049	−	0.908424i	$-0.637286\pi$
$487$	2.38975e6	−	2.21737e6i	0.456594	−	0.423657i	0.874643	+	0.484767i	$0.161096\pi$
$488$	−2.94719e6	−	2.00936e6i	−0.560220	−	0.381951i
$489$	−247041.	+	309779.i	−0.0467193	+	0.0585841i
$490$	98505.6	+	14847.3i	0.0185341	+	0.00279356i
$491$	5.60052e6	−	1.72753e6i	1.04839	−	0.323387i	0.277751	−	0.960653i	$-0.410411\pi$
$491$	5.60052e6	−	1.72753e6i	1.04839	−	0.323387i	0.770644	+	0.637266i	$0.219935\pi$
$492$	66303.1	−	884754.i	0.0123487	−	0.164782i
$493$	−5.05974e6	+	3.44967e6i	−0.937586	+	0.639235i
$494$	−2.22624e6	+	9.75382e6i	−0.410446	+	1.79828i
$495$	192085.	−	841580.i	0.0352355	−	0.154377i
$496$	−5.92429e6	+	4.03911e6i	−1.08127	+	0.737194i
$497$	460269.	−	6.14187e6i	0.0835836	−	1.11535i
$498$	−6.43200e6	+	1.98401e6i	−1.16218	+	0.358485i
$499$	1.29919e6	+	195822.i	0.233573	+	0.0352055i	0.264786	−	0.964307i	$-0.414699\pi$
$499$	1.29919e6	+	195822.i	0.233573	+	0.0352055i	−0.0312126	+	0.999513i	$0.509937\pi$
$500$	−2.46341e6	+	3.08902e6i	−0.440669	+	0.552581i
$501$	2.60533e6	+	1.77628e6i	0.463733	+	0.316168i
$502$	2.60927e6	−	2.42105e6i	0.462125	−	0.428790i
$503$	−179162.	+	456497.i	−0.0315737	+	0.0804485i	−0.945791	−	0.324776i	$-0.894711\pi$
$503$	−179162.	+	456497.i	−0.0315737	+	0.0804485i	0.914217	+	0.405224i	$0.132806\pi$
$504$	1.12010e7	+	3.45506e6i	1.96418	+	0.605869i
$505$	98280.5	+	47329.4i	0.0171490	+	0.00825853i
$506$	1.18543e6	+	3.02041e6i	0.205825	+	0.524433i
$507$	32343.2	+	431590.i	0.00558809	+	0.0745679i
$508$	1.06469e7	+	1.33508e7i	1.83047	+	2.29534i
$509$	−5.58579e6	−	9.67488e6i	−0.955631	−	1.65520i	−0.732917	−	0.680319i	$-0.761841\pi$
$509$	−5.58579e6	−	9.67488e6i	−0.955631	−	1.65520i	−0.222715	−	0.974884i	$-0.571492\pi$
$510$	452021.	−	782923.i	0.0769543	−	0.133289i
$511$	1.05702e7	−	1.59320e6i	1.79074	−	0.269910i
$512$	5.87873e6	−	2.83105e6i	0.991080	−	0.477279i
$513$	−3.52253e6	−	3.26843e6i	−0.590965	−	0.548335i
$514$	−1.78254e6	−	7.80983e6i	−0.297599	−	1.30387i
$515$	1.58668e6			0.263617
$516$	−2.89471e6	−	7.10704e6i	−0.478608	−	1.17507i
$517$	3.07583e6			0.506100
$518$	2.58441e6	+	1.13230e7i	0.423192	+	1.85412i
$519$	−3.38750e6	−	3.14314e6i	−0.552027	−	0.512206i
$520$	2.40655e6	−	1.15893e6i	0.390289	−	0.187953i
$521$	1.39936e6	−	210919.i	0.225857	−	0.0340425i	−0.0351385	−	0.999382i	$-0.511187\pi$
$521$	1.39936e6	−	210919.i	0.225857	−	0.0340425i	0.260996	+	0.965340i	$0.415949\pi$
$522$	4.29961e6	−	7.44715e6i	0.690642	−	1.19623i
$523$	−1.99816e6	−	3.46092e6i	−0.319431	−	0.553270i	0.660939	−	0.750440i	$-0.270158\pi$
$523$	−1.99816e6	−	3.46092e6i	−0.319431	−	0.553270i	−0.980369	+	0.197170i	$0.936825\pi$
$524$	−5.74001e6	−	7.19774e6i	−0.913239	−	1.14517i
$525$	224368.	+	2.99398e6i	0.0355273	+	0.474079i
$526$	901399.	+	2.29673e6i	0.142054	+	0.361947i
$527$	−3.05145e6	−	1.46950e6i	−0.478607	−	0.230485i
$528$	1.30847e7	+	4.03610e6i	2.04258	+	0.630053i
$529$	−2.25698e6	+	5.75069e6i	−0.350662	+	0.893471i
$530$	2.08960e6	−	1.93886e6i	0.323127	−	0.299818i
$531$	4.66910e6	+	3.18334e6i	0.718616	+	0.489944i
$532$	9.07420e6	−	1.13787e7i	1.39005	−	1.74306i
$533$	905224.	+	136441.i	0.138019	+	0.0208030i
$534$	−7.54913e6	+	2.32860e6i	−1.14563	+	0.353380i
$535$	−16208.9	+	216293.i	−0.00244833	+	0.0326706i
$536$	−2.57176e7	+	1.75339e7i	−3.86650	+	2.63613i
$537$	339911.	−	1.48925e6i	0.0508662	−	0.222859i
$538$	1.32730e6	−	5.81527e6i	0.197703	−	0.866192i
$539$	−588873.	+	401487.i	−0.0873071	+	0.0595250i
$540$	−158889.	+	2.12022e6i	−0.0234482	+	0.312894i
$541$	−8.79503e6	+	2.71291e6i	−1.29195	+	0.398512i	−0.863177	−	0.504902i	$-0.831529\pi$
$541$	−8.79503e6	+	2.71291e6i	−1.29195	+	0.398512i	−0.428769	+	0.903414i	$0.641053\pi$
$542$	9.07592e6	+	1.36797e6i	1.32707	+	0.200023i
$543$	−1.62463e6	+	2.03722e6i	−0.236459	+	0.296510i
$544$	−1.61987e7	−	1.10441e7i	−2.34683	−	1.60004i
$545$	188542.	−	174941.i	0.0271905	−	0.0252291i
$546$	2.48304e6	−	6.32669e6i	0.356453	−	0.908228i
$547$	6.01324e6	+	1.85484e6i	0.859290	+	0.265056i	0.692926	−	0.721008i	$-0.256321\pi$
$547$	6.01324e6	+	1.85484e6i	0.859290	+	0.265056i	0.166364	+	0.986064i	$0.446797\pi$
$548$	2.67730e7	+	1.28932e7i	3.80843	+	1.83404i
$549$	457578.	+	1.16589e6i	0.0647939	+	0.165092i
$550$	−1.46017e6	−	1.94847e7i	−0.205825	−	2.74654i
$551$	−4.01679e6	−	5.03689e6i	−0.563638	−	0.706779i
$552$	−1.03081e6	−	1.78542e6i	−0.143990	−	0.249398i
$553$	4.05045e6	−	7.01558e6i	0.563236	−	0.975553i
$554$	−2.05515e7	+	3.09764e6i	−2.84491	+	0.428802i
$555$	−489626.	+	235792.i	−0.0674733	+	0.0324934i
$556$	−2.87392e6	−	2.66661e6i	−0.394265	−	0.365824i
$557$	−249676.	−	1.09390e6i	−0.0340987	−	0.149396i	0.955013	−	0.296565i	$-0.0958411\pi$
$557$	−249676.	−	1.09390e6i	−0.0340987	−	0.149396i	−0.989111	+	0.147169i	$0.952984\pi$
$558$	4.75590e6			0.646617
$559$	7.53574e6	−	2.43041e6i	1.01999	−	0.328965i
$560$	−2.87274e6			−0.387102
$561$	1.43925e6	+	6.30577e6i	0.193076	+	0.845923i
$562$	−5.90223e6	−	5.47647e6i	−0.788271	−	0.731408i
$563$	−2.75601e6	+	1.32722e6i	−0.366446	+	0.176471i	−0.608040	−	0.793906i	$-0.708044\pi$
$563$	−2.75601e6	+	1.32722e6i	−0.366446	+	0.176471i	0.241594	+	0.970377i	$0.422330\pi$
$564$	−3.20269e6	+	482727.i	−0.423952	+	0.0639005i
$565$	388678.	−	673210.i	0.0512235	−	0.0887217i
$566$	1.09312e7	+	1.89334e7i	1.43425	+	2.48420i
$567$	−1.40100e6	−	1.75679e6i	−0.183012	−	0.229490i
$568$	−1.90323e6	−	2.53968e7i	−0.247525	−	3.30299i
$569$	−266105.	−	678024.i	−0.0344566	−	0.0877939i	0.912610	−	0.408832i	$-0.134064\pi$
$569$	−266105.	−	678024.i	−0.0344566	−	0.0877939i	−0.947066	+	0.321038i	$0.895968\pi$
$570$	856890.	+	412656.i	0.110468	+	0.0531988i
$571$	3.57153e6	+	1.10167e6i	0.458420	+	0.141404i	0.515360	−	0.856974i	$-0.327658\pi$
$571$	3.57153e6	+	1.10167e6i	0.458420	+	0.141404i	−0.0569399	+	0.998378i	$0.518134\pi$
$572$	−1.15706e7	+	2.94814e7i	−1.47865	+	3.76754i
$573$	601167.	−	557802.i	0.0764907	−	0.0709730i
$574$	−1.53670e6	−	1.04770e6i	−0.194675	−	0.132727i
$575$	−970980.	+	1.21757e6i	−0.122473	+	0.153576i
$576$	1.05463e7	+	1.58959e6i	1.32447	+	0.199632i
$577$	−1.83838e6	+	567064.i	−0.229877	+	0.0709076i	−0.407554	−	0.913181i	$-0.633618\pi$
$577$	−1.83838e6	+	567064.i	−0.229877	+	0.0709076i	0.177677	+	0.984089i	$0.443142\pi$
$578$	366529.	−	4.89100e6i	0.0456341	−	0.608945i
$579$	863362.	−	588631.i	0.107028	−	0.0729703i
$580$	−634305.	+	2.77907e6i	−0.0782939	+	0.343028i
$581$	−2.24815e6	+	9.84981e6i	−0.276303	+	1.21056i
$582$	−1.00804e7	+	6.87273e6i	−1.23359	+	0.841050i
$583$	−1.52405e6	+	2.03371e7i	−0.185707	+	2.47809i
$584$	4.22380e7	−	1.30287e7i	5.12474	−	1.58077i
$585$	−927407.	−	139784.i	−0.112042	−	0.0168876i
$586$	−1.18831e7	+	1.49010e7i	−1.42951	+	1.79255i
$587$	−3.45834e6	−	2.35786e6i	−0.414259	−	0.282437i	0.338202	−	0.941073i	$-0.390181\pi$
$587$	−3.45834e6	−	2.35786e6i	−0.414259	−	0.282437i	−0.752462	+	0.658636i	$0.771134\pi$
$588$	550149.	−	510464.i	0.0656201	−	0.0608866i
$589$	1.30173e6	−	3.31676e6i	0.154608	−	0.393936i
$590$	−2.49995e6	−	771133.i	−0.295666	−	0.0912009i
$591$	239967.	+	115562.i	0.0282607	+	0.0136096i
$592$	9.28816e6	+	2.36658e7i	1.08924	+	2.77535i
$593$	−540347.	−	7.21043e6i	−0.0631010	−	0.842024i	−0.935522	−	0.353269i	$-0.885070\pi$
$593$	−540347.	−	7.21043e6i	−0.0631010	−	0.842024i	0.872421	−	0.488755i	$-0.162549\pi$
$594$	−1.32457e7	−	1.66096e7i	−1.54032	−	1.93150i
$595$	−678471.	−	1.17515e6i	−0.0785667	−	0.136082i
$596$	−1.83878e7	+	3.18486e7i	−2.12038	+	3.67261i
$597$	3.58270e6	−	540005.i	0.411410	−	0.0620100i
$598$	3.17622e6	−	1.52959e6i	0.363210	−	0.174913i
$599$	−2.58488e6	−	2.39842e6i	−0.294356	−	0.273123i	0.519145	−	0.854686i	$-0.326251\pi$
$599$	−2.58488e6	−	2.39842e6i	−0.294356	−	0.273123i	−0.813501	+	0.581564i	$0.802441\pi$
$600$	2.76258e6	+	1.21036e7i	0.313283	+	1.37258i
$601$	−3.11542e6			−0.351828			−0.175914	−	0.984406i	$-0.556288\pi$
$601$	−3.11542e6			−0.351828			−0.175914	+	0.984406i	$0.556288\pi$
$602$	−1.59362e7	−	2.19401e6i	−1.79223	−	0.246744i
$603$	1.09292e7			1.22404
$604$	−1.88388e6	−	8.25383e6i	−0.210117	−	0.920583i
$605$	−1.16158e6	−	1.07779e6i	−0.129021	−	0.119714i
$606$	1.03406e6	−	497978.i	0.114384	−	0.0550844i
$607$	3.35999e6	−	506438.i	0.370141	−	0.0557897i	0.0386618	−	0.999252i	$-0.487691\pi$
$607$	3.35999e6	−	506438.i	0.370141	−	0.0557897i	0.331479	+	0.943463i	$0.392452\pi$
$608$	1.03127e7	−	1.78620e7i	1.13139	−	1.95962i
$609$	2.18828e6	+	3.79021e6i	0.239089	+	0.414115i
$610$	−361523.	−	453335.i	−0.0393379	−	0.0493282i
$611$	−249737.	−	3.33251e6i	−0.0270633	−	0.361135i
$612$	7.33826e6	+	1.86976e7i	0.791980	+	2.01793i
$613$	7.79725e6	+	3.75496e6i	0.838090	+	0.403603i	0.803143	−	0.595786i	$-0.203160\pi$
$613$	7.79725e6	+	3.75496e6i	0.838090	+	0.403603i	0.0349467	+	0.999389i	$0.488874\pi$
$614$	2.63346e7	+	8.12313e6i	2.81906	+	0.869566i
$615$	31794.1	−	81009.9i	0.00338968	−	0.00863675i
$616$	2.84607e7	−	2.64077e7i	3.02200	−	2.80400i
$617$	−2.84373e6	−	1.93882e6i	−0.300729	−	0.205034i	0.403549	−	0.914958i	$-0.367777\pi$
$617$	−2.84373e6	−	1.93882e6i	−0.300729	−	0.205034i	−0.704278	+	0.709925i	$0.748729\pi$
$618$	1.04088e7	−	1.30522e7i	1.09630	−	1.37471i
$619$	6.38787e6	+	962816.i	0.670084	+	0.100999i	0.475268	−	0.879841i	$-0.342351\pi$
$619$	6.38787e6	+	962816.i	0.670084	+	0.100999i	0.194816	+	0.980840i	$0.437589\pi$
$620$	−1.50648e6	+	464688.i	−0.157393	+	0.0485493i
$621$	−126536.	+	1.68851e6i	−0.0131670	+	0.175701i
$622$	−2.70855e7	+	1.84666e7i	−2.80712	+	1.91386i
$623$	−2.63862e6	+	1.15605e7i	−0.272368	+	1.19332i
$624$	3.31053e6	−	1.45044e7i	0.340358	−	1.49120i
$625$	7.58682e6	−	5.17260e6i	0.776890	−	0.529675i
$626$	−850823.	+	1.13534e7i	−0.0867767	+	1.15796i
$627$	−6.50214e6	+	2.00564e6i	−0.660522	+	0.203744i
$628$	−2.91094e7	−	4.38754e6i	−2.94533	−	0.443938i
$629$	−7.48731e6	+	9.38879e6i	−0.754570	+	0.946200i
$630$	1.57436e6	+	1.07338e6i	0.158035	+	0.107746i
$631$	1.08642e7	−	1.00805e7i	1.08623	−	1.00788i	0.0863001	−	0.996269i	$-0.472496\pi$
$631$	1.08642e7	−	1.00805e7i	1.08623	−	1.00788i	0.999933	−	0.0116075i	$-0.00369486\pi$
$632$	1.22380e7	−	3.11819e7i	1.21876	−	3.10534i
$633$	757496.	+	233656.i	0.0751400	+	0.0231776i
$634$	−1.20235e7	−	5.79024e6i	−1.18798	−	0.572101i
$635$	611928.	+	1.55917e6i	0.0602235	+	0.153447i
$636$	−1.60483e6	−	2.14150e7i	−0.157321	−	2.09931i
$637$	482804.	+	605417.i	0.0471436	+	0.0591162i
$638$	−1.42412e7	−	2.46665e7i	−1.38514	−	2.39914i
$639$	−4.47125e6	+	7.74443e6i	−0.433188	+	0.750304i
$640$	−1.30353e6	+	196476.i	−0.125797	+	0.0189609i
$641$	854259.	−	411389.i	0.0821191	−	0.0395465i	−0.392373	−	0.919806i	$-0.628346\pi$
$641$	854259.	−	411389.i	0.0821191	−	0.0395465i	0.474493	+	0.880260i	$0.342632\pi$
$642$	1.67291e6	+	1.55223e6i	0.160190	+	0.148634i
$643$	2.21208e6	+	9.69175e6i	0.210996	+	0.924432i	0.963892	+	0.266293i	$0.0857989\pi$
$643$	2.21208e6	+	9.69175e6i	0.210996	+	0.924432i	−0.752897	+	0.658139i	$0.771344\pi$
$644$	−5.12836e6			−0.487263
$645$	−65842.1	−	749824.i	−0.00623167	−	0.0709676i
$646$	2.10163e7			1.98142
$647$	−2.90389e6	−	1.27228e7i	−0.272721	−	1.19487i	−0.906786	−	0.421590i	$-0.861472\pi$
$647$	−2.90389e6	−	1.27228e7i	−0.272721	−	1.19487i	0.634065	−	0.773280i	$-0.281385\pi$
$648$	−6.81115e6	−	6.31983e6i	−0.637211	−	0.591245i
$649$	1.68638e7	−	8.12117e6i	1.57160	−	0.756845i
$650$	−2.09921e7	+	3.16405e6i	−1.94883	+	0.293738i
$651$	−1.21025e6	+	2.09622e6i	−0.111924	+	0.193858i
$652$	2.03777e6	+	3.52952e6i	0.187731	+	0.325160i
$653$	−1.04701e7	−	1.31290e7i	−0.960873	−	1.20490i	−0.978750	−	0.205056i	$-0.934262\pi$
$653$	−1.04701e7	−	1.31290e7i	−0.960873	−	1.20490i	0.0178774	−	0.999840i	$-0.494309\pi$
$654$	−202231.	−	2.69859e6i	−0.0184886	−	0.246713i
$655$	−329906.	−	840588.i	−0.0300461	−	0.0765561i
$656$	−3.66804e6	−	1.76643e6i	−0.332793	−	0.160265i
$657$	−1.48309e7	−	4.57473e6i	−1.34046	−	0.413478i
$658$	−2.48048e6	+	6.32016e6i	−0.223342	+	0.569067i
$659$	−1.11342e7	+	1.03310e7i	−0.998723	+	0.926679i	−0.997308	−	0.0733197i	$-0.976641\pi$
$659$	−1.11342e7	+	1.03310e7i	−0.998723	+	0.926679i	−0.00141425	+	0.999999i	$0.500450\pi$
$660$	2.48757e6	+	1.69600e6i	0.222288	+	0.151553i
$661$	−1.24849e7	+	1.56556e7i	−1.11143	+	1.39369i	−0.201222	+	0.979546i	$0.564491\pi$
$661$	−1.24849e7	+	1.56556e7i	−1.11143	+	1.39369i	−0.910210	+	0.414147i	$0.864080\pi$
$662$	270492.	+	40770.1i	0.0239888	+	0.00361574i
$663$	6.71514e6	−	2.07135e6i	0.593296	−	0.183007i
$664$	−3.12197e6	+	4.16598e7i	−0.274795	+	3.66688i
$665$	1.17949e6	−	804161.i	0.103428	−	0.0705162i
$666$	3.75236e6	−	1.64401e7i	0.327807	−	1.43622i
$667$	−505149.	+	2.21320e6i	−0.0439648	+	0.192622i
$668$	2.67984e7	−	1.82708e7i	2.32363	−	1.58423i
$669$	−54542.0	+	727813.i	−0.00471157	+	0.0628716i
$670$	−4.83495e6	+	1.49139e6i	−0.416107	+	0.128352i
$671$	4.10209e6	+	618291.i	0.351722	+	0.0530135i
$672$	−8.73601e6	+	1.09546e7i	−0.746260	+	0.935780i
$673$	1.29539e7	+	8.83179e6i	1.10246	+	0.751642i	0.970857	−	0.239661i	$-0.0770363\pi$
$673$	1.29539e7	+	8.83179e6i	1.10246	+	0.751642i	0.131600	+	0.991303i	$0.457989\pi$
$674$	1.97491e7	−	1.83245e7i	1.67455	−	1.55376i
$675$	3.72521e6	−	9.49169e6i	0.314696	−	0.801833i
$676$	4.25400e6	+	1.31219e6i	0.358039	+	0.110441i
$677$	1.03729e7	+	4.99530e6i	0.869814	+	0.418881i	0.814894	−	0.579610i	$-0.196795\pi$
$677$	1.03729e7	+	4.99530e6i	0.869814	+	0.418881i	0.0549206	+	0.998491i	$0.482509\pi$
$678$	−2.98812e6	−	7.61360e6i	−0.249645	−	0.636086i
$679$	1.36849e6	+	1.82613e7i	0.113912	+	1.52004i
$680$	−3.49839e6	−	4.38685e6i	−0.290133	−	0.363815i
$681$	163379.	+	282981.i	0.0134999	+	0.0233824i
$682$	7.87626e6	−	1.36421e7i	0.648424	−	1.12310i
$683$	−221285.	+	33353.4i	−0.0181510	+	0.00273582i	−0.158111	−	0.987421i	$-0.550541\pi$
$683$	−221285.	+	33353.4i	−0.0181510	+	0.00273582i	0.139960	+	0.990157i	$0.455302\pi$
$684$	−1.90384e7	+	9.16843e6i	−1.55593	+	0.749298i
$685$	2.13664e6	+	1.98251e6i	0.173982	+	0.161432i
$686$	−5.31203e6	−	2.32735e7i	−0.430974	−	1.88822i
$687$	3.80427e6			0.307524
$688$	−3.52102e7	+	450207.i	−2.83594	+	0.0362611i
$689$	2.21580e7			1.77821
$690$	−74573.7	−	326729.i	−0.00596297	−	0.0261255i
$691$	−8.12699e6	−	7.54075e6i	−0.647493	−	0.600785i	0.286499	−	0.958081i	$-0.407509\pi$
$691$	−8.12699e6	−	7.54075e6i	−0.647493	−	0.600785i	−0.933992	+	0.357295i	$0.883699\pi$
$692$	−4.28253e7	+	2.06236e7i	−3.39965	+	1.63719i
$693$	−1.34802e7	+	2.03182e6i	−1.06626	+	0.160713i
$694$	−7.24719e6	+	1.25525e7i	−0.571177	+	0.989308i
$695$	−192274.	−	333028.i	−0.0150993	−	0.0261528i
$696$	1.12834e7	+	1.41490e7i	0.882912	+	1.10714i
$697$	−143709.	−	1.91767e6i	−0.0112048	−	0.149517i
$698$	5.86071e6	+	1.49328e7i	0.455314	+	1.16012i
$699$	5.52664e6	+	2.66149e6i	0.427827	+	0.206031i
$700$	2.95104e7	+	9.10275e6i	2.27630	+	0.702146i
$701$	−736689.	+	1.87705e6i	−0.0566225	+	0.144272i	−0.956386	−	0.292106i	$-0.905644\pi$
$701$	−736689.	+	1.87705e6i	−0.0566225	+	0.144272i	0.899763	+	0.436378i	$0.143739\pi$
$702$	−1.69203e7	+	1.56997e7i	−1.29588	+	1.20240i
$703$	−1.04383e7	−	7.11670e6i	−0.796601	−	0.543113i
$704$	2.20254e7	−	2.76190e7i	1.67491	−	2.10027i
$705$	−314140.	−	47349.0i	−0.0238040	−	0.00358788i
$706$	2.58507e6	−	797390.i	0.195192	−	0.0602087i
$707$	128738.	−	1.71788e6i	0.00968627	−	0.129254i
$708$	−1.62847e7	+	1.11027e7i	−1.22095	+	0.832429i
$709$	−2.44001e6	+	1.06904e7i	−0.182295	+	0.798688i	0.798239	+	0.602341i	$0.205765\pi$
$709$	−2.44001e6	+	1.06904e7i	−0.182295	+	0.798688i	−0.980534	+	0.196347i	$0.937092\pi$
$710$	921234.	−	4.03619e6i	0.0685842	−	0.300487i
$711$	−9.71810e6	+	6.62569e6i	−0.720953	+	0.491538i
$712$	−3.66420e6	+	4.88954e7i	−0.270882	+	3.61467i
$713$	−1.19974e6	+	370070.i	−0.0883816	+	0.0272621i
$714$	−1.41177e7	−	2.12789e6i	−1.03638	−	0.156208i
$715$	−1.93685e6	+	2.42873e6i	−0.141687	+	0.177670i
$716$	−1.29821e7	−	8.85106e6i	−0.946375	−	0.645228i
$717$	366175.	−	339761.i	0.0266005	−	0.0246817i
$718$	1.41333e7	−	3.60111e7i	1.02313	−	2.60690i
$719$	1.22047e7	+	3.76465e6i	0.880449	+	0.271583i	0.701838	−	0.712337i	$-0.252363\pi$
$719$	1.22047e7	+	3.76465e6i	0.880449	+	0.271583i	0.178612	+	0.983920i	$0.442839\pi$
$720$	3.75793e6	+	1.80972e6i	0.270157	+	0.130101i
$721$	−9.15464e6	−	2.33256e7i	−0.655848	−	1.67107i
$722$	−311992.	−	4.16324e6i	−0.0222741	−	0.297227i
$723$	−10058.7	−	12613.1i	−0.000715639	−	0.000897383i
$724$	1.34011e7	+	2.32114e7i	0.950156	+	1.64572i
$725$	6.83521e6	−	1.18389e7i	0.482955	−	0.836503i
$726$	−1.64861e7	+	2.48487e6i	−1.16085	+	0.174970i
$727$	1.42299e7	−	6.85276e6i	0.998541	−	0.480872i	0.138098	−	0.990419i	$-0.455901\pi$
$727$	1.42299e7	−	6.85276e6i	0.998541	−	0.480872i	0.860443	+	0.509547i	$0.170187\pi$
$728$	−3.09223e7	−	2.86917e7i	−2.16243	−	2.00644i
$729$	−686314.	−	3.00694e6i	−0.0478304	−	0.209559i
$730$	7.18528e6			0.499042
$731$	−8.49995e6	−	1.42970e7i	−0.588333	−	0.989584i
$732$	−4.36831e6			−0.301325
$733$	40176.5	+	176025.i	0.00276193	+	0.0121008i	0.976290	−	0.216466i	$-0.0694531\pi$
$733$	40176.5	+	176025.i	0.00276193	+	0.0121008i	−0.973528	+	0.228567i	$0.926596\pi$
$734$	1.96585e7	+	1.82404e7i	1.34682	+	1.24967i
$735$	66323.1	−	31939.5i	0.00452842	−	0.00218077i
$736$	−7.18657e6	+	1.08320e6i	−0.489021	+	0.0737080i
$737$	1.80999e7	−	3.13499e7i	1.22746	−	2.12602i
$738$	1.35019e6	+	2.33860e6i	0.0912546	+	0.158058i
$739$	−8.83775e6	−	1.10822e7i	−0.595293	−	0.746473i	0.389343	−	0.921093i	$-0.372702\pi$
$739$	−8.83775e6	−	1.10822e7i	−0.595293	−	0.746473i	−0.984636	+	0.174619i	$0.944131\pi$
$740$	417731.	+	5.57423e6i	0.0280425	+	0.374202i
$741$	2.70095e6	+	6.88191e6i	0.180705	+	0.460430i
$742$	−4.05592e7	−	1.95323e7i	−2.70445	−	1.30240i
$743$	1.70940e7	+	5.27280e6i	1.13598	+	0.350404i	0.805025	−	0.593241i	$-0.202152\pi$
$743$	1.70940e7	+	5.27280e6i	1.13598	+	0.350404i	0.330958	+	0.943646i	$0.392628\pi$
$744$	−3.65665e6	+	9.31698e6i	−0.242187	+	0.617082i
$745$	−2.64426e6	+	2.45351e6i	−0.174547	+	0.161956i
$746$	3.06364e7	+	2.08875e7i	2.01554	+	1.37417i
$747$	9.14591e6	−	1.14686e7i	0.599688	−	0.751985i
$748$	6.57860e7	+	9.91565e6i	4.29912	+	0.647988i
$749$	3.27321e6	−	1.00965e6i	0.213191	−	0.0657608i
$750$	−304714.	+	4.06612e6i	−0.0197806	+	0.263953i
$751$	−4.36944e6	+	2.97903e6i	−0.282700	+	0.192742i	−0.696366	−	0.717687i	$-0.745201\pi$
$751$	−4.36944e6	+	2.97903e6i	−0.282700	+	0.192742i	0.413665	+	0.910429i	$0.364248\pi$
$752$	−3.30711e6	+	1.44894e7i	−0.213257	+	0.934342i
$753$	585290.	−	2.56432e6i	0.0376170	−	0.164811i
$754$	−2.55687e7	+	1.74324e7i	−1.63787	+	1.11668i
$755$	62056.5	−	828087.i	0.00396205	−	0.0528699i
$756$	3.20859e7	−	9.89717e6i	2.04178	−	0.629806i
$757$	−2.61660e7	−	3.94388e6i	−1.65957	−	0.250141i	−0.748726	−	0.662880i	$-0.769334\pi$
$757$	−2.61660e7	−	3.94388e6i	−1.65957	−	0.250141i	−0.910849	+	0.412739i	$0.864572\pi$
$758$	3.00192e7	−	3.76429e7i	1.89769	−	2.37963i
$759$	1.98106e6	+	1.35066e6i	0.124822	+	0.0851025i
$760$	4.32714e6	−	4.01500e6i	0.271748	−	0.252146i
$761$	−1.00011e7	+	2.54824e7i	−0.626016	+	1.59506i	0.167064	+	0.985946i	$0.446571\pi$
$761$	−1.00011e7	+	2.54824e7i	−0.626016	+	1.59506i	−0.793080	+	0.609117i	$0.791524\pi$
$762$	1.68401e7	+	5.19448e6i	1.05065	+	0.324082i
$763$	−3.65962e6	−	1.76238e6i	−0.227575	−	0.109594i
$764$	−3.08180e6	−	7.85231e6i	−0.191017	−	0.486703i
$765$	147231.	+	1.96466e6i	0.00909590	+	0.121376i
$766$	2.13147e7	+	2.67278e7i	1.31252	+	1.64585i
$767$	−1.01681e7	−	1.76117e7i	−0.624097	−	1.08097i
$768$	441412.	−	764548.i	0.0270048	−	0.0467737i
$769$	1.70365e6	−	256784.i	0.103888	−	0.0156586i	−0.0968925	−	0.995295i	$-0.530890\pi$
$769$	1.70365e6	−	256784.i	0.103888	−	0.0156586i	0.200780	+	0.979636i	$0.435652\pi$
$770$	5.68624e6	−	2.73835e6i	0.345619	−	0.166441i
$771$	−4.33930e6	−	4.02628e6i	−0.262896	−	0.243932i
$772$	−2.39169e6	−	1.04787e7i	−0.144431	−	0.632795i
$773$	−2.24188e7			−1.34947			−0.674736	−	0.738059i	$-0.735743\pi$
$773$	−2.24188e7			−1.34947			−0.674736	+	0.738059i	$0.735743\pi$
$774$	1.94646e7	+	1.29093e7i	1.16787	+	0.774552i
$775$	7.56058e6			0.452169
$776$	1.68498e7	+	7.38240e7i	1.00448	+	4.40092i
$777$	6.29132e6	+	5.83749e6i	0.373843	+	0.346875i
$778$	2.39136e7	−	1.15162e7i	1.41643	−	0.682117i
$779$	2.00050e6	−	301527.i	0.118112	−	0.0178025i
$780$	1.63556e6	−	2.83287e6i	0.0962563	−	0.166721i
$781$	1.48097e7	+	2.56511e7i	0.868797	+	1.50480i
$782$	−4.61727e6	−	5.78988e6i	−0.270003	−	0.338573i
$783$	−1.11075e6	−	1.48219e7i	−0.0647458	−	0.863973i
$784$	−1.25814e6	−	3.20569e6i	−0.0731037	−	0.186265i
$785$	−2.60154e6	−	1.25284e6i	−0.150680	−	0.0725638i
$786$	−9.07894e6	−	2.80048e6i	−0.524178	−	0.161688i
$787$	8.40682e6	−	2.14202e7i	0.483832	−	1.23278i	−0.455642	−	0.890163i	$-0.650590\pi$
$787$	8.40682e6	−	2.14202e7i	0.483832	−	1.23278i	0.939474	−	0.342621i	$-0.111315\pi$
$788$	2.00827e6	−	1.86340e6i	0.115214	−	0.106903i
$789$	1.50640e6	+	1.02705e6i	0.0861485	+	0.0587350i
$790$	3.39504e6	−	4.25725e6i	0.193543	−	0.242695i
$791$	−1.21393e7	−	1.82971e6i	−0.689847	−	0.103978i
$792$	−5.38663e7	+	1.66155e7i	−3.05143	+	0.941243i
$793$	336825.	−	4.49462e6i	0.0190205	−	0.253811i
$794$	2.53311e6	−	1.72705e6i	0.142595	−	0.0972194i
$795$	468721.	−	2.05360e6i	0.0263025	−	0.115239i
$796$	8.29288e6	−	3.63335e7i	0.463898	−	2.03247i
$797$	5.89461e6	−	4.01888e6i	0.328707	−	0.224109i	−0.387709	−	0.921782i	$-0.626733\pi$
$797$	5.89461e6	−	4.01888e6i	0.328707	−	0.224109i	0.716416	+	0.697673i	$0.245781\pi$
$798$	1.12244e6	−	1.49779e7i	0.0623958	−	0.832615i
$799$	−6.70821e6	+	2.06921e6i	−0.371741	+	0.114667i
$800$	4.32768e7	+	6.52292e6i	2.39073	+	0.360344i
$801$	1.07344e7	−	1.34605e7i	0.591148	−	0.741276i
$802$	2.28697e7	+	1.55923e7i	1.25552	+	0.856002i
$803$	−3.76839e7	+	3.49656e7i	−2.06237	+	1.91360i
$804$	−1.39262e7	+	3.54835e7i	−0.759791	+	1.93591i
$805$	−480674.	−	148268.i	−0.0261434	−	0.00806416i
$806$	−1.54200e7	−	7.42590e6i	−0.836080	−	0.402635i
$807$	−1.61032e6	−	4.10303e6i	−0.0870419	−	0.221779i
$808$	−532333.	−	7.10349e6i	−0.0286850	−	0.382775i
$809$	7.56470e6	+	9.48584e6i	0.406369	+	0.509571i	0.942336	−	0.334668i	$-0.108624\pi$
$809$	7.56470e6	+	9.48584e6i	0.406369	+	0.509571i	−0.535967	+	0.844239i	$0.680053\pi$
$810$	−755197.	−	1.30804e6i	−0.0404434	−	0.0700500i
$811$	2.79569e6	−	4.84228e6i	0.149258	−	0.258522i	−0.781696	−	0.623660i	$-0.785645\pi$
$811$	2.79569e6	−	4.84228e6i	0.149258	−	0.258522i	0.930953	+	0.365138i	$0.118978\pi$
$812$	4.45145e7	−	6.70948e6i	2.36925	−	0.357107i
$813$	6.11075e6	−	2.94278e6i	0.324241	−	0.156146i
$814$	−4.09435e7	−	3.79900e7i	−2.16583	−	2.00960i
$815$	88953.9	+	389733.i	0.00469106	+	0.0205529i
$816$	−3.12522e7			−1.64307
$817$	1.43306e7	−	1.00412e7i	0.751118	−	0.526296i
$818$	−5.38840e7			−2.81564
$819$	3.29588e6	+	1.44402e7i	0.171697	+	0.752252i
$820$	−656188.	−	608854.i	−0.0340795	−	0.0316212i
$821$	4.69689e6	−	2.26190e6i	0.243194	−	0.117116i	−0.308317	−	0.951284i	$-0.599766\pi$
$821$	4.69689e6	−	2.26190e6i	0.243194	−	0.117116i	0.551511	+	0.834168i	$0.314051\pi$
$822$	3.03248e7	−	4.57073e6i	1.56537	−	0.235942i
$823$	−9.63070e6	+	1.66809e7i	−0.495631	+	0.858458i	−0.999987	−	0.00503781i	$-0.998396\pi$
$823$	−9.63070e6	+	1.66809e7i	−0.495631	+	0.858458i	0.504357	+	0.863496i	$0.331730\pi$
$824$	−5.18073e7	−	8.97329e7i	−2.65811	−	4.60398i
$825$	−9.00232e6	−	1.12885e7i	−0.460489	−	0.577435i
$826$	3.08756e6	+	4.12006e7i	0.157458	+	2.10113i
$827$	−7.24662e6	−	1.84641e7i	−0.368444	−	0.938781i	−0.988087	−	0.153897i	$-0.950818\pi$
$827$	−7.24662e6	−	1.84641e7i	−0.368444	−	0.938781i	0.619642	−	0.784884i	$-0.287278\pi$
$828$	6.70858e6	+	3.23068e6i	0.340059	+	0.163764i
$829$	−2.41080e7	−	7.43633e6i	−1.21836	−	0.375813i	−0.382084	−	0.924128i	$-0.624794\pi$
$829$	−2.41080e7	−	7.43633e6i	−1.21836	−	0.375813i	−0.836272	+	0.548314i	$0.815270\pi$
$830$	−2.48105e6	+	6.32162e6i	−0.125009	+	0.318517i
$831$	−1.12583e7	+	1.04462e7i	−0.565548	+	0.524752i
$832$	−3.17121e7	−	2.16210e7i	−1.58824	−	1.08285i
$833$	1.01421e6	−	1.27177e6i	0.0506423	−	0.0635034i
$834$	−4.00084e6	−	603029.i	−0.199175	−	0.0300209i
$835$	3.04002e6	−	937721.i	0.150890	−	0.0465433i
$836$	−5.23039e6	+	6.97947e7i	−0.258832	+	3.45388i
$837$	6.79202e6	−	4.63072e6i	0.335109	−	0.228473i
$838$	−2.34010e6	+	1.02526e7i	−0.115113	+	0.504343i
$839$	−6.14298e6	+	2.69141e7i	−0.301283	+	1.32000i	0.566911	+	0.823779i	$0.308138\pi$
$839$	−6.14298e6	+	2.69141e7i	−0.301283	+	1.32000i	−0.868193	+	0.496226i	$0.834719\pi$
$840$	−3.31326e6	+	2.25894e6i	−0.162016	+	0.110460i
$841$	−43626.1	+	582150.i	−0.00212695	+	0.0283821i
$842$	1.89255e7	−	5.83774e6i	0.919955	−	0.283769i
$843$	−5.88328e6	−	886762.i	−0.285135	−	0.0429772i
$844$	5.08384e6	−	6.37493e6i	0.245661	−	0.308049i
$845$	360785.	+	245979.i	0.0173823	+	0.0118510i
$846$	7.22627e6	−	6.70500e6i	0.347127	−	0.322087i
$847$	−9.14253e6	+	2.32948e7i	−0.437883	+	1.11571i
$848$	−9.41638e7	−	2.90457e7i	−4.49670	−	1.38705i
$849$	1.45554e7	+	7.00949e6i	0.693032	+	0.333747i
$850$	1.62925e7	+	4.15126e7i	0.773465	+	1.97076i
$851$	332673.	+	4.43922e6i	0.0157469	+	0.210127i
$852$	−1.94462e7	−	2.43848e7i	−0.917775	−	1.15085i
$853$	1.34499e7	+	2.32959e7i	0.632917	+	1.09624i	0.986952	+	0.161012i	$0.0514759\pi$
$853$	1.34499e7	+	2.32959e7i	0.632917	+	1.09624i	−0.354035	+	0.935232i	$0.615191\pi$
$854$	−4.57856e6	+	7.93029e6i	−0.214824	+	0.372087i
$855$	−2.04952e6	+	308916.i	−0.0958820	+	0.0144519i
$856$	1.27614e7	−	6.14556e6i	0.595270	−	0.286667i
$857$	7.78910e6	+	7.22723e6i	0.362272	+	0.336139i	0.840217	−	0.542250i	$-0.182428\pi$
$857$	7.78910e6	+	7.22723e6i	0.362272	+	0.336139i	−0.477945	+	0.878390i	$0.658618\pi$
$858$	7.27304e6	+	3.18653e7i	0.337286	+	1.47774i
$859$	1.15172e7			0.532554			0.266277	−	0.963897i	$-0.414206\pi$
$859$	1.15172e7			0.532554			0.266277	+	0.963897i	$0.414206\pi$
$860$	−7.42696e6	−	2.18732e6i	−0.342425	−	0.100848i
$861$	−1.37436e6			−0.0631818
$862$	6.07548e6	+	2.66184e7i	0.278492	+	1.22015i
$863$	−1.25844e7	−	1.16766e7i	−0.575180	−	0.533689i	0.338053	−	0.941127i	$-0.390232\pi$
$863$	−1.25844e7	−	1.16766e7i	−0.575180	−	0.533689i	−0.913233	+	0.407438i	$0.866422\pi$
$864$	4.28727e7	−	2.06464e7i	1.95387	−	0.940936i
$865$	−4.61022e6	+	694878.i	−0.209499	+	0.0315768i
$866$	3.49820e7	−	6.05905e7i	1.58507	−	2.74543i
$867$	−1.81217e6	−	3.13877e6i	−0.0818751	−	0.141812i
$868$	1.55232e7	+	1.94655e7i	0.699331	+	0.876933i
$869$	2.91131e6	+	3.88487e7i	0.130779	+	1.74513i
$870$	1.07477e6	+	2.73846e6i	0.0481411	+	0.122661i
$871$	−3.54357e7	−	1.70649e7i	−1.58269	−	0.762183i
$872$	−1.60497e7	−	4.95068e6i	−0.714787	−	0.220482i
$873$	9.71377e6	−	2.47503e7i	0.431372	−	1.09912i
$874$	5.71107e6	−	5.29910e6i	0.252894	−	0.234652i
$875$	5.05679e6	+	3.44766e6i	0.223282	+	0.152231i
$876$	3.37505e7	−	4.23218e7i	1.48600	−	1.86339i
$877$	775912.	+	116950.i	0.0340654	+	0.00513453i	0.166053	−	0.986117i	$-0.446898\pi$
$877$	775912.	+	116950.i	0.0340654	+	0.00513453i	−0.131987	+	0.991251i	$0.542136\pi$
$878$	4.65874e7	−	1.43703e7i	2.03954	−	0.629115i
$879$	−1.05248e6	+	1.40443e7i	−0.0459452	+	0.613097i
$880$	1.14146e7	−	7.78235e6i	0.496883	−	0.338769i
$881$	−5.30518e6	+	2.32435e7i	−0.230282	+	1.00893i	0.719124	+	0.694882i	$0.244543\pi$
$881$	−5.30518e6	+	2.32435e7i	−0.230282	+	1.00893i	−0.949406	+	0.314051i	$0.898314\pi$
$882$	−508281.	+	2.22693e6i	−0.0220005	+	0.0963905i
$883$	−2.36175e7	+	1.61021e7i	−1.01937	+	0.694995i	−0.953053	−	0.302804i	$-0.902077\pi$
$883$	−2.36175e7	+	1.61021e7i	−1.01937	+	0.694995i	−0.0663175	+	0.997799i	$0.521125\pi$
$884$	5.40173e6	−	7.20811e7i	0.232489	−	3.10235i
$885$	−1.84734e6	+	569830.i	−0.0792847	+	0.0244561i
$886$	−2.82298e7	−	4.25495e6i	−1.20816	−	0.182100i
$887$	−4.84713e6	+	6.07811e6i	−0.206860	+	0.259394i	−0.874429	−	0.485154i	$-0.838763\pi$
$887$	−4.84713e6	+	6.07811e6i	−0.206860	+	0.259394i	0.667569	+	0.744548i	$0.267335\pi$
$888$	2.93218e7	+	1.99913e7i	1.24784	+	0.850762i
$889$	1.93905e7	−	1.79917e7i	0.822875	−	0.763517i
$890$	−2.91197e6	+	7.41958e6i	−0.123229	+	0.313982i
$891$	1.03260e7	+	3.18514e6i	0.435749	+	0.134411i
$892$	6.76381e6	+	3.25728e6i	0.284629	+	0.137070i
$893$	−2.69816e6	−	6.87481e6i	−0.113224	−	0.288491i
$894$	2.83625e6	+	3.78471e7i	0.118686	+	1.58376i
$895$	−960901.	−	1.20493e6i	−0.0400979	−	0.0502811i
$896$	1.04093e7	+	1.80294e7i	0.433163	+	0.750261i
$897$	1.30253e6	−	2.25605e6i	0.0540513	−	0.0936196i
$898$	−2.35188e7	+	3.54489e6i	−0.973250	+	0.146694i
$899$	9.92963e6	−	4.78186e6i	0.409764	−	0.197332i
$900$	−3.28691e7	−	3.04981e7i	−1.35264	−	1.25507i
$901$	−1.03575e7	−	4.53793e7i	−0.425054	−	1.86228i
$902$	8.94423e6			0.366038
$903$	−1.06432e7	+	5.29417e6i	−0.434362	+	0.216062i
$904$	−5.07634e7			−2.06600
$905$	584994.	+	2.56303e6i	0.0237427	+	0.104024i
$906$	−6.40481e6	−	5.94279e6i	−0.259230	−	0.240530i
$907$	−2.95902e7	+	1.42499e7i	−1.19435	+	0.575166i	−0.922059	−	0.387050i	$-0.873494\pi$
$907$	−2.95902e7	+	1.42499e7i	−1.19435	+	0.575166i	−0.272286	+	0.962216i	$0.587780\pi$
$908$	3.32349e6	−	500936.i	0.133777	−	0.0201636i
$909$	−1.25061e6	+	2.16612e6i	−0.0502010	+	0.0869507i
$910$	−3.42855e6	−	5.93843e6i	−0.137248	−	0.237721i
$911$	2.38183e7	+	2.98673e7i	0.950858	+	1.19234i	0.981238	+	0.192799i	$0.0617567\pi$
$911$	2.38183e7	+	2.98673e7i	0.950858	+	1.19234i	−0.0303804	+	0.999538i	$0.509672\pi$
$912$	−2.45699e6	−	3.27863e7i	−0.0978174	−	1.30528i
$913$	−1.77506e7	−	4.52278e7i	−0.704752	−	1.79568i
$914$	1.52662e6	+	735180.i	0.0604456	+	0.0291091i
$915$	−409436.	−	126294.i	−0.0161672	−	0.00498691i
$916$	1.42960e7	−	3.64257e7i	0.562959	−	1.43440i
$917$	−1.04539e7	+	9.69982e6i	−0.410540	+	0.380926i
$918$	4.00621e7	+	2.73139e7i	1.56901	+	1.06974i
$919$	4.53706e6	−	5.68929e6i	0.177209	−	0.222213i	−0.685292	−	0.728268i	$-0.740325\pi$
$919$	4.53706e6	−	5.68929e6i	0.177209	−	0.222213i	0.862501	+	0.506055i	$0.168897\pi$
$920$	−2.05678e6	−	310009.i	−0.0801158	−	0.0120755i
$921$	1.94600e7	−	6.00260e6i	0.755950	−	0.233180i
$922$	2.86889e6	−	3.82827e7i	0.111144	−	1.48312i
$923$	2.65893e7	−	1.81283e7i	1.02731	−	0.700410i
$924$	1.05802e7	−	4.63548e7i	0.407674	−	1.78614i
$925$	5.96522e6	−	2.61353e7i	0.229230	−	1.00432i
$926$	−5.06601e6	+	3.45394e6i	−0.194150	+	0.132369i
$927$	−2.71882e6	+	3.62801e7i	−0.103916	+	1.38666i
$928$	6.09627e7	−	1.88045e7i	2.32378	−	0.716790i
$929$	−4.98024e6	−	750651.i	−0.189326	−	0.0285364i	0.0536945	−	0.998557i	$-0.482900\pi$
$929$	−4.98024e6	−	750651.i	−0.189326	−	0.0285364i	−0.243021	+	0.970021i	$0.578138\pi$
$930$	−1.01442e6	+	1.27204e6i	−0.0384601	+	0.0482275i
$931$	1.41393e6	+	964004.i	0.0534632	+	0.0364506i
$932$	4.62522e7	−	4.29157e7i	1.74418	−	1.61837i
$933$	−8.85007e6	+	2.25496e7i	−0.332845	+	0.848076i
$934$	−6.83545e7	−	2.10846e7i	−2.56389	−	0.790856i
$935$	5.87937e6	+	2.83135e6i	0.219939	+	0.105917i
$936$	2.23757e7	+	5.70124e7i	0.834810	+	2.12706i
$937$	2.58315e6	+	3.44698e7i	0.0961171	+	1.28259i	0.811704	+	0.584070i	$0.198541\pi$
$937$	2.58315e6	+	3.44698e7i	0.0961171	+	1.28259i	−0.715586	+	0.698524i	$0.753840\pi$
$938$	4.98207e7	+	6.24732e7i	1.84885	+	2.31839i
$939$	4.20659e6	+	7.28602e6i	0.155692	+	0.269666i
$940$	−1.63387e6	+	2.82995e6i	−0.0603112	+	0.104462i
$941$	−2.38802e7	+	3.59936e6i	−0.879151	+	0.132511i	−0.573082	−	0.819498i	$-0.694252\pi$
$941$	−2.38802e7	+	3.59936e6i	−0.879151	+	0.132511i	−0.306070	+	0.952009i	$0.599014\pi$
$942$	−2.73722e7	+	1.31818e7i	−1.00504	+	0.484001i
$943$	−522577.	−	484880.i	−0.0191369	−	0.0177564i
$944$	2.01248e7	+	8.81725e7i	0.735024	+	3.22035i
$945$	3.29351e6			0.119972
$946$	6.92651e7	−	3.44541e7i	2.51644	−	1.25174i
$947$	1.40545e7			0.509260			0.254630	−	0.967038i	$-0.418046\pi$
$947$	1.40545e7			0.509260			0.254630	+	0.967038i	$0.418046\pi$
$948$	−9.12838e6	−	3.99940e7i	−0.329893	−	1.44535i
$949$	4.09432e7	+	3.79897e7i	1.47576	+	1.36931i
$950$	−4.22694e7	+	2.03559e7i	−1.51956	+	0.731780i
$951$	−9.75126e6	+	1.46977e6i	−0.349631	+	0.0526984i
$952$	−4.43059e7	+	7.67400e7i	−1.58442	+	2.74429i
$953$	−659618.	−	1.14249e6i	−0.0235267	−	0.0407494i	0.854022	−	0.520236i	$-0.174156\pi$
$953$	−659618.	−	1.14249e6i	−0.0235267	−	0.0407494i	−0.877549	+	0.479487i	$0.840823\pi$
$954$	4.07522e7	+	5.11017e7i	1.44971	+	1.81788i
$955$	−61831.7	−	825087.i	−0.00219383	−	0.0292746i
$956$	−1.87715e6	−	4.78289e6i	−0.0664284	−	0.169257i
$957$	−1.89628e7	−	9.13200e6i	−0.669303	−	0.322319i
$958$	−2.29398e7	−	7.07599e6i	−0.807561	−	0.249100i
$959$	1.68169e7	−	4.28489e7i	0.590473	−	1.50450i
$960$	−2.67465e6	+	2.48172e6i	−0.0936676	+	0.0869109i
$961$	−1.86183e7	−	1.26938e7i	−0.650328	−	0.443386i
$962$	−3.78360e7	+	4.74449e7i	−1.31816	+	1.65292i
$963$	−4.91784e6	−	741245.i	−0.170887	−	0.0257571i
$964$	−158570.	+	48912.3i	−0.00549576	+	0.00169522i
$965$	78784.0	−	1.05130e6i	0.00272345	−	0.0363420i
$966$	−4.37293e6	+	2.98141e6i	−0.150775	+	0.102797i
$967$	−5.56339e6	+	2.43748e7i	−0.191326	+	0.838252i	0.784575	+	0.620034i	$0.212881\pi$
$967$	−5.56339e6	+	2.43748e7i	−0.191326	+	0.838252i	−0.975900	+	0.218218i	$0.929976\pi$
$968$	−2.30259e7	+	1.00883e8i	−0.789821	+	3.46043i
$969$	1.28315e7	−	8.74839e6i	0.439005	−	0.299308i
$970$	−919867.	+	1.22748e7i	−0.0313903	+	0.418874i
$971$	−7.07016e6	+	2.18085e6i	−0.240647	+	0.0742299i	−0.412733	−	0.910852i	$-0.635426\pi$
$971$	−7.07016e6	+	2.18085e6i	−0.240647	+	0.0742299i	0.172085	+	0.985082i	$0.444949\pi$
$972$	−7.58053e7	−	1.14258e7i	−2.57356	−	0.387901i
$973$	−3.78644e6	+	4.74804e6i	−0.128218	+	0.160780i
$974$	−2.85929e7	−	1.94943e7i	−0.965741	−	0.658431i
$975$	−1.14997e7	+	1.06701e7i	−0.387413	+	0.359466i
$976$	−7.32314e6	+	1.86591e7i	−0.246078	+	0.626997i
$977$	3.92700e7	+	1.21132e7i	1.31621	+	0.405996i	0.871815	−	0.489836i	$-0.162943\pi$
$977$	3.92700e7	+	1.21132e7i	1.31621	+	0.405996i	0.444392	+	0.895832i	$0.353420\pi$
$978$	3.78951e6	+	1.82493e6i	0.126688	+	0.0610098i
$979$	−2.08336e7	−	5.30831e7i	−0.694716	−	1.77011i
$980$	−56584.4	−	755066.i	−0.00188205	−	0.0251142i
$981$	3.67703e6	+	4.61085e6i	0.121990	+	0.152971i
$982$	−3.11078e7	−	5.38803e7i	−1.02941	−	1.78300i
$983$	1.83360e7	−	3.17590e7i	0.605232	−	1.04829i	−0.386783	−	0.922171i	$-0.626414\pi$
$983$	1.83360e7	−	3.17590e7i	0.605232	−	1.04829i	0.992015	−	0.126121i	$-0.0402529\pi$
$984$	−5.61953e6	+	847008.i	−0.185017	+	0.0278869i
$985$	242107.	−	116592.i	0.00795090	−	0.00382895i
$986$	4.76532e7	+	4.42157e7i	1.56099	+	1.44839i
$987$	1.11641e6	+	4.89132e6i	0.0364780	+	0.159821i
$988$	7.60439e7			2.47840
$989$	−5.91470e6	−	1.74195e6i	−0.192284	−	0.0566297i
$990$	−9.16342e6			−0.297146
$991$	−8.68013e6	−	3.80301e7i	−0.280764	−	1.23011i	−0.896816	−	0.442404i	$-0.854126\pi$
$991$	−8.68013e6	−	3.80301e7i	−0.280764	−	1.23011i	0.616052	−	0.787706i	$-0.288731\pi$
$992$	2.58648e7	+	2.39990e7i	0.834506	+	0.774308i
$993$	182120.	−	87704.5i	0.00586118	−	0.00282260i
$994$	−6.46506e7	+	9.74452e6i	−2.07542	+	0.312820i
$995$	1.82774e6	−	3.16573e6i	0.0585269	−	0.101372i
$996$	2.55808e7	+	4.43073e7i	0.817083	+	1.41523i
$997$	−1.48305e7	−	1.85969e7i	−0.472518	−	0.592518i	0.487268	−	0.873252i	$-0.337993\pi$
$997$	−1.48305e7	−	1.85969e7i	−0.472518	−	0.592518i	−0.959786	+	0.280734i	$0.909422\pi$
$998$	−1.04227e6	−	1.39082e7i	−0.0331250	−	0.442022i
$999$	−1.06486e7	−	2.71322e7i	−0.337582	−	0.860144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.g.a.10.1	✓	204
43.13	even	21	inner	43.6.g.a.13.1	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.g.a.10.1	✓	204	1.1	even	1	trivial
43.6.g.a.13.1	yes	204	43.13	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.36214 - 10.3492i) q^{2} +(-5.75023 - 5.33543i) q^{3} +(-72.6953 + 35.0082i) q^{4} +(-7.82578 + 1.17955i) q^{5} +(-41.6347 + 72.1133i) q^{6} +(62.4925 + 108.240i) q^{7} +(322.229 + 404.063i) q^{8} +(-13.5611 - 180.961i) q^{9} +O(q^{10})\)	\(q+(-2.36214 - 10.3492i) q^{2} +(-5.75023 - 5.33543i) q^{3} +(-72.6953 + 35.0082i) q^{4} +(-7.82578 + 1.17955i) q^{5} +(-41.6347 + 72.1133i) q^{6} +(62.4925 + 108.240i) q^{7} +(322.229 + 404.063i) q^{8} +(-13.5611 - 180.961i) q^{9} +(30.6929 + 78.2043i) q^{10} +(-541.536 - 260.790i) q^{11} +(604.799 + 186.556i) q^{12} +(-238.584 + 607.902i) q^{13} +(972.583 - 902.425i) q^{14} +(51.2934 + 34.9713i) q^{15} +(1810.76 - 2270.63i) q^{16} +(1356.50 + 204.460i) q^{17} +(-1840.76 + 567.801i) q^{18} +(-107.850 + 1439.16i) q^{19} +(527.604 - 359.714i) q^{20} +(218.162 - 955.830i) q^{21} +(-1419.78 + 6220.48i) q^{22} +(420.174 - 286.470i) q^{23} +(302.958 - 4042.69i) q^{24} +(-2926.31 + 902.648i) q^{25} +(6854.87 + 1033.21i) q^{26} +(-2075.99 + 2603.21i) q^{27} +(-8332.20 - 5680.80i) q^{28} +(-3272.35 + 3036.30i) q^{29} +(240.763 - 613.453i) q^{30} +(-2359.18 - 727.712i) q^{31} +(-12876.1 - 6200.82i) q^{32} +(1722.53 + 4388.93i) q^{33} +(-1088.25 - 14521.7i) q^{34} +(-616.727 - 773.351i) q^{35} +(7320.94 + 12680.2i) q^{36} +(-4376.92 + 7581.05i) q^{37} +(15148.9 - 2283.33i) q^{38} +(4615.33 - 2222.63i) q^{39} +(-2998.31 - 2782.02i) q^{40} +(-311.934 - 1366.67i) q^{41} -10407.4 q^{42} +(-7680.21 - 9382.05i) q^{43} +48496.9 q^{44} +(319.578 + 1400.16i) q^{45} +(-3957.25 - 3671.79i) q^{46} +(-4610.57 + 2220.34i) q^{47} +(-22527.1 + 3395.41i) q^{48} +(592.883 - 1026.90i) q^{49} +(16254.0 + 28152.8i) q^{50} +(-6709.31 - 8413.21i) q^{51} +(-3937.63 - 52544.0i) q^{52} +(-12396.1 - 31584.8i) q^{53} +(31844.9 + 15335.7i) q^{54} +(4545.55 + 1402.12i) q^{55} +(-23598.9 + 60129.1i) q^{56} +(8298.70 - 7700.07i) q^{57} +(39153.0 + 26694.1i) q^{58} +(-19415.9 + 24346.7i) q^{59} +(-4953.07 - 746.556i) q^{60} +(-6595.23 + 2034.36i) q^{61} +(-1958.52 + 26134.6i) q^{62} +(18739.7 - 12776.5i) q^{63} +(-13078.2 + 57299.3i) q^{64} +(1150.06 - 5038.73i) q^{65} +(41353.1 - 28194.0i) q^{66} +(-4500.74 + 60058.2i) q^{67} +(-105769. + 32625.4i) q^{68} +(-3944.54 - 594.544i) q^{69} +(-6546.77 + 8209.39i) q^{70} +(-40715.9 - 27759.7i) q^{71} +(68749.7 - 63790.4i) q^{72} +(31246.6 - 79615.0i) q^{73} +(88796.7 + 27390.2i) q^{74} +(21643.0 + 10422.7i) q^{75} +(-42542.2 - 108396. i) q^{76} +(-5613.98 - 74913.3i) q^{77} +(-33904.5 - 42514.9i) q^{78} +(-32407.5 - 56131.4i) q^{79} +(-11492.3 + 19905.3i) q^{80} +(-17777.6 + 2679.54i) q^{81} +(-13407.1 + 6456.53i) q^{82} +(59256.0 + 54981.5i) q^{83} +(17602.6 + 77121.8i) q^{84} -10856.8 q^{85} +(-78955.0 + 101646. i) q^{86} +35016.7 q^{87} +(-69123.2 - 302849. i) q^{88} +(69547.7 + 64530.9i) q^{89} +(13735.7 - 6614.75i) q^{90} +(-80709.1 + 12164.9i) q^{91} +(-20515.9 + 35534.6i) q^{92} +(9683.20 + 16771.8i) q^{93} +(33869.5 + 42471.0i) q^{94} +(-853.544 - 11389.8i) q^{95} +(40956.7 + 104356. i) q^{96} +(132008. + 63571.5i) q^{97} +(-12028.1 - 3710.18i) q^{98} +(-39848.8 + 101533. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9}+O(q^{10}) \) 204 * q - 468 * q^4 - 85 * q^5 - 22 * q^6 + 454 * q^7 + 698 * q^8 - 333 * q^9	\( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9} + 303 q^{10} - 1340 q^{11} + 858 q^{12} + 814 q^{13} + 1202 q^{14} - 2083 q^{15} - 6248 q^{16} - 214 q^{17} - 174 q^{18} - 246 q^{19} - 17139 q^{20} + 3007 q^{21} + 2118 q^{22} + 3192 q^{23} + 15880 q^{24} + 3652 q^{25} - 1237 q^{26} + 108 q^{27} - 6780 q^{28} - 18827 q^{29} + 98080 q^{30} - 43196 q^{31} - 3930 q^{32} + 28181 q^{33} + 45155 q^{34} + 33275 q^{35} - 49399 q^{36} + 34607 q^{37} - 43374 q^{38} + 15155 q^{39} - 108727 q^{40} + 7156 q^{41} - 48066 q^{42} - 176452 q^{43} + 26068 q^{44} - 96386 q^{45} - 27185 q^{46} + 20402 q^{47} + 198899 q^{48} - 158742 q^{49} + 186243 q^{50} + 98589 q^{51} + 278918 q^{52} + 14102 q^{53} + 270894 q^{54} - 334770 q^{55} + 61999 q^{56} - 202490 q^{57} + 213658 q^{58} - 43753 q^{59} - 389005 q^{60} + 80516 q^{61} + 162349 q^{62} - 75177 q^{63} - 489850 q^{64} + 93726 q^{65} + 246095 q^{66} - 322922 q^{67} + 475089 q^{68} - 397079 q^{69} - 614985 q^{70} - 233345 q^{71} + 379655 q^{72} + 159391 q^{73} + 695938 q^{74} + 344081 q^{75} - 50808 q^{76} + 608177 q^{77} + 605548 q^{78} - 272109 q^{79} + 601054 q^{80} + 193536 q^{81} - 996896 q^{82} + 177813 q^{83} - 919009 q^{84} - 844524 q^{85} - 876752 q^{86} - 188214 q^{87} - 59998 q^{88} - 469041 q^{89} - 453431 q^{90} - 223189 q^{91} - 94922 q^{92} + 569174 q^{93} + 1175168 q^{94} + 435689 q^{95} + 1557688 q^{96} + 643751 q^{97} + 886196 q^{98} + 1422581 q^{99}+O(q^{100}) \) 204 * q - 468 * q^4 - 85 * q^5 - 22 * q^6 + 454 * q^7 + 698 * q^8 - 333 * q^9 + 303 * q^10 - 1340 * q^11 + 858 * q^12 + 814 * q^13 + 1202 * q^14 - 2083 * q^15 - 6248 * q^16 - 214 * q^17 - 174 * q^18 - 246 * q^19 - 17139 * q^20 + 3007 * q^21 + 2118 * q^22 + 3192 * q^23 + 15880 * q^24 + 3652 * q^25 - 1237 * q^26 + 108 * q^27 - 6780 * q^28 - 18827 * q^29 + 98080 * q^30 - 43196 * q^31 - 3930 * q^32 + 28181 * q^33 + 45155 * q^34 + 33275 * q^35 - 49399 * q^36 + 34607 * q^37 - 43374 * q^38 + 15155 * q^39 - 108727 * q^40 + 7156 * q^41 - 48066 * q^42 - 176452 * q^43 + 26068 * q^44 - 96386 * q^45 - 27185 * q^46 + 20402 * q^47 + 198899 * q^48 - 158742 * q^49 + 186243 * q^50 + 98589 * q^51 + 278918 * q^52 + 14102 * q^53 + 270894 * q^54 - 334770 * q^55 + 61999 * q^56 - 202490 * q^57 + 213658 * q^58 - 43753 * q^59 - 389005 * q^60 + 80516 * q^61 + 162349 * q^62 - 75177 * q^63 - 489850 * q^64 + 93726 * q^65 + 246095 * q^66 - 322922 * q^67 + 475089 * q^68 - 397079 * q^69 - 614985 * q^70 - 233345 * q^71 + 379655 * q^72 + 159391 * q^73 + 695938 * q^74 + 344081 * q^75 - 50808 * q^76 + 608177 * q^77 + 605548 * q^78 - 272109 * q^79 + 601054 * q^80 + 193536 * q^81 - 996896 * q^82 + 177813 * q^83 - 919009 * q^84 - 844524 * q^85 - 876752 * q^86 - 188214 * q^87 - 59998 * q^88 - 469041 * q^89 - 453431 * q^90 - 223189 * q^91 - 94922 * q^92 + 569174 * q^93 + 1175168 * q^94 + 435689 * q^95 + 1557688 * q^96 + 643751 * q^97 + 886196 * q^98 + 1422581 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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