LMFDB - Embedded newform 37.8.c.a.10.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(10,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("37.10");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.c (of order $3$, degree $2$, 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:	$11.5582459429$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			10.13
Character	$\chi$	$=$	37.10
Dual form			37.8.c.a.26.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.32071 - 4.01959i) q^{2} +(-46.0982 - 79.8444i) q^{3} +(53.2286 + 92.1946i) q^{4} +(217.309 + 376.390i) q^{5} -427.923 q^{6} +(19.1096 + 33.0988i) q^{7} +1088.22 q^{8} +(-3156.59 + 5467.37i) q^{9} +O(q^{10})$	\(q+(2.32071 - 4.01959i) q^{2} +(-46.0982 - 79.8444i) q^{3} +(53.2286 + 92.1946i) q^{4} +(217.309 + 376.390i) q^{5} -427.923 q^{6} +(19.1096 + 33.0988i) q^{7} +1088.22 q^{8} +(-3156.59 + 5467.37i) q^{9} +2017.24 q^{10} +3754.11 q^{11} +(4907.48 - 8500.01i) q^{12} +(-378.244 - 655.137i) q^{13} +177.392 q^{14} +(20035.1 - 34701.8i) q^{15} +(-4287.82 + 7426.73i) q^{16} +(12968.1 - 22461.4i) q^{17} +(14651.1 + 25376.4i) q^{18} +(22820.0 + 39525.4i) q^{19} +(-23134.1 + 40069.4i) q^{20} +(1761.84 - 3051.59i) q^{21} +(8712.20 - 15090.0i) q^{22} -32866.3 q^{23} +(-50164.8 - 86887.9i) q^{24} +(-55383.7 + 95927.4i) q^{25} -3511.18 q^{26} +380418. q^{27} +(-2034.35 + 3523.61i) q^{28} -36050.0 q^{29} +(-92991.3 - 161066. i) q^{30} +105484. q^{31} +(89547.4 + 155101. i) q^{32} +(-173057. - 299744. i) q^{33} +(-60190.5 - 104253. i) q^{34} +(-8305.37 + 14385.3i) q^{35} -672082. q^{36} +(78562.1 + 297926. i) q^{37} +211835. q^{38} +(-34872.7 + 60401.3i) q^{39} +(236479. + 409593. i) q^{40} +(-40301.6 - 69804.5i) q^{41} +(-8177.43 - 14163.7i) q^{42} +73110.0 q^{43} +(199826. + 346108. i) q^{44} -2.74381e6 q^{45} +(-76273.2 + 132109. i) q^{46} +597754. q^{47} +790644. q^{48} +(411041. - 711944. i) q^{49} +(257059. + 445240. i) q^{50} -2.39123e6 q^{51} +(40266.8 - 69744.1i) q^{52} +(-45453.6 + 78728.0i) q^{53} +(882841. - 1.52912e6i) q^{54} +(815800. + 1.41301e6i) q^{55} +(20795.4 + 36018.6i) q^{56} +(2.10392e6 - 3.64410e6i) q^{57} +(-83661.6 + 144906. i) q^{58} +(-1.34523e6 + 2.33001e6i) q^{59} +4.26576e6 q^{60} +(-688007. - 1.19166e6i) q^{61} +(244797. - 424002. i) q^{62} -241284. q^{63} -266428. q^{64} +(164391. - 284734. i) q^{65} -1.60647e6 q^{66} +(-753583. - 1.30524e6i) q^{67} +2.76110e6 q^{68} +(1.51508e6 + 2.62419e6i) q^{69} +(38548.8 + 66768.4i) q^{70} +(2.30564e6 + 3.99348e6i) q^{71} +(-3.43504e6 + 5.94967e6i) q^{72} -3.68666e6 q^{73} +(1.37986e6 + 375613. i) q^{74} +1.02124e7 q^{75} +(-2.42935e6 + 4.20776e6i) q^{76} +(71739.5 + 124256. i) q^{77} +(161859. + 280348. i) q^{78} +(-2.38032e6 - 4.12283e6i) q^{79} -3.72713e6 q^{80} +(-1.06331e7 - 1.84171e7i) q^{81} -374114. q^{82} +(3.58337e6 - 6.20658e6i) q^{83} +375120. q^{84} +1.12723e7 q^{85} +(169667. - 293872. i) q^{86} +(1.66184e6 + 2.87839e6i) q^{87} +4.08528e6 q^{88} +(-255548. + 442622. i) q^{89} +(-6.36761e6 + 1.10290e7i) q^{90} +(14456.2 - 25038.8i) q^{91} +(-1.74943e6 - 3.03009e6i) q^{92} +(-4.86261e6 - 8.42229e6i) q^{93} +(1.38721e6 - 2.40273e6i) q^{94} +(-9.91797e6 + 1.71784e7i) q^{95} +(8.25594e6 - 1.42997e7i) q^{96} -8.13277e6 q^{97} +(-1.90782e6 - 3.30444e6i) q^{98} +(-1.18502e7 + 2.05251e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9}+O(q^{10}) $ 42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9	\( 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9} + 10028 q^{10} + 14876 q^{11} - 4836 q^{12} - 5922 q^{13} + 20176 q^{14} - 8460 q^{15} - 36726 q^{16} - 19095 q^{17} - 7338 q^{18} - 34334 q^{19} - 75668 q^{20} - 32764 q^{21} + 18526 q^{22} - 99896 q^{23} - 203760 q^{24} - 322660 q^{25} + 101516 q^{26} + 846616 q^{27} - 73490 q^{28} + 168186 q^{29} - 88790 q^{30} - 38052 q^{31} - 172292 q^{32} - 54536 q^{33} + 90724 q^{34} - 247046 q^{35} + 352004 q^{36} + 740185 q^{37} + 1994976 q^{38} - 591380 q^{39} - 38962 q^{40} - 292827 q^{41} - 1499386 q^{42} + 630980 q^{43} - 1727390 q^{44} - 994286 q^{45} + 576988 q^{46} + 3394668 q^{47} - 79840 q^{48} + 728851 q^{49} - 69656 q^{50} - 3970200 q^{51} - 2043140 q^{52} + 584438 q^{53} - 2160774 q^{54} + 2019874 q^{55} - 658986 q^{56} + 4295748 q^{57} - 5684872 q^{58} - 1773152 q^{59} + 20208544 q^{60} - 3596569 q^{61} - 1538738 q^{62} + 11795092 q^{63} - 9622852 q^{64} - 5027290 q^{65} - 17464952 q^{66} - 3249754 q^{67} + 5608668 q^{68} + 9599384 q^{69} - 5102080 q^{70} - 1162530 q^{71} - 4730172 q^{72} - 5266532 q^{73} + 4052290 q^{74} + 35543072 q^{75} - 13781226 q^{76} + 121180 q^{77} - 7012890 q^{78} - 13545718 q^{79} - 17840888 q^{80} - 16689077 q^{81} - 43173544 q^{82} + 7359048 q^{83} + 41186680 q^{84} + 21047382 q^{85} + 6732838 q^{86} + 7672800 q^{87} + 42023140 q^{88} + 2955725 q^{89} - 14596808 q^{90} - 19887752 q^{91} + 13352900 q^{92} + 9156784 q^{93} + 690474 q^{94} - 5667270 q^{95} + 29986904 q^{96} + 52065982 q^{97} - 53664462 q^{98} - 35534038 q^{99}+O(q^{100}) \) 42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9 + 10028 * q^10 + 14876 * q^11 - 4836 * q^12 - 5922 * q^13 + 20176 * q^14 - 8460 * q^15 - 36726 * q^16 - 19095 * q^17 - 7338 * q^18 - 34334 * q^19 - 75668 * q^20 - 32764 * q^21 + 18526 * q^22 - 99896 * q^23 - 203760 * q^24 - 322660 * q^25 + 101516 * q^26 + 846616 * q^27 - 73490 * q^28 + 168186 * q^29 - 88790 * q^30 - 38052 * q^31 - 172292 * q^32 - 54536 * q^33 + 90724 * q^34 - 247046 * q^35 + 352004 * q^36 + 740185 * q^37 + 1994976 * q^38 - 591380 * q^39 - 38962 * q^40 - 292827 * q^41 - 1499386 * q^42 + 630980 * q^43 - 1727390 * q^44 - 994286 * q^45 + 576988 * q^46 + 3394668 * q^47 - 79840 * q^48 + 728851 * q^49 - 69656 * q^50 - 3970200 * q^51 - 2043140 * q^52 + 584438 * q^53 - 2160774 * q^54 + 2019874 * q^55 - 658986 * q^56 + 4295748 * q^57 - 5684872 * q^58 - 1773152 * q^59 + 20208544 * q^60 - 3596569 * q^61 - 1538738 * q^62 + 11795092 * q^63 - 9622852 * q^64 - 5027290 * q^65 - 17464952 * q^66 - 3249754 * q^67 + 5608668 * q^68 + 9599384 * q^69 - 5102080 * q^70 - 1162530 * q^71 - 4730172 * q^72 - 5266532 * q^73 + 4052290 * q^74 + 35543072 * q^75 - 13781226 * q^76 + 121180 * q^77 - 7012890 * q^78 - 13545718 * q^79 - 17840888 * q^80 - 16689077 * q^81 - 43173544 * q^82 + 7359048 * q^83 + 41186680 * q^84 + 21047382 * q^85 + 6732838 * q^86 + 7672800 * q^87 + 42023140 * q^88 + 2955725 * q^89 - 14596808 * q^90 - 19887752 * q^91 + 13352900 * q^92 + 9156784 * q^93 + 690474 * q^94 - 5667270 * q^95 + 29986904 * q^96 + 52065982 * q^97 - 53664462 * q^98 - 35534038 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.32071	−	4.01959i	0.205124	−	0.355285i	−0.745048	−	0.667011i	$-0.767574\pi$
$2$	2.32071	−	4.01959i	0.205124	−	0.355285i	0.950172	+	0.311725i	$0.100907\pi$
$3$	−46.0982	−	79.8444i	−0.985733	−	1.70734i	−0.638632	−	0.769513i	$-0.720499\pi$
$3$	−46.0982	−	79.8444i	−0.985733	−	1.70734i	−0.347102	−	0.937827i	$-0.612834\pi$
$4$	53.2286	+	92.1946i	0.415848	+	0.720270i
$5$	217.309	+	376.390i	0.777468	+	1.34661i	0.933397	+	0.358845i	$0.116829\pi$
$5$	217.309	+	376.390i	0.777468	+	1.34661i	−0.155930	+	0.987768i	$0.549837\pi$
$6$	−427.923			−0.808790
$7$	19.1096	+	33.0988i	0.0210576	+	0.0364728i	0.876362	−	0.481653i	$-0.159963\pi$
$7$	19.1096	+	33.0988i	0.0210576	+	0.0364728i	−0.855305	+	0.518126i	$0.826630\pi$
$8$	1088.22			0.751450
$9$	−3156.59	+	5467.37i	−1.44334	+	2.49994i
$10$	2017.24			0.637909
$11$	3754.11			0.850417			0.425209	−	0.905095i	$-0.360201\pi$
$11$	3754.11			0.850417			0.425209	+	0.905095i	$0.360201\pi$
$12$	4907.48	−	8500.01i	0.819831	−	1.41999i
$13$	−378.244	−	655.137i	−0.0477496	−	0.0827048i	0.841163	−	0.540782i	$-0.181872\pi$
$13$	−378.244	−	655.137i	−0.0477496	−	0.0827048i	−0.888912	+	0.458077i	$0.848538\pi$
$14$	177.392			0.0172777
$15$	20035.1	−	34701.8i	1.53275	−	2.65480i
$16$	−4287.82	+	7426.73i	−0.261708	+	0.453292i
$17$	12968.1	−	22461.4i	0.640185	−	1.10883i	−0.345206	−	0.938527i	$-0.612191\pi$
$17$	12968.1	−	22461.4i	0.640185	−	1.10883i	0.985391	−	0.170306i	$-0.0544757\pi$
$18$	14651.1	+	25376.4i	0.592127	+	1.02559i
$19$	22820.0	+	39525.4i	0.763270	+	1.32202i	0.941157	+	0.337971i	$0.109741\pi$
$19$	22820.0	+	39525.4i	0.763270	+	1.32202i	−0.177887	+	0.984051i	$0.556926\pi$
$20$	−23134.1	+	40069.4i	−0.646617	+	1.11997i
$21$	1761.84	−	3051.59i	0.0415143	−	0.0719049i
$22$	8712.20	−	15090.0i	0.174441	−	0.302141i
$23$	−32866.3			−0.563253			−0.281626	−	0.959524i	$-0.590874\pi$
$23$	−32866.3			−0.563253			−0.281626	+	0.959524i	$0.590874\pi$
$24$	−50164.8	−	86887.9i	−0.740729	−	1.28298i
$25$	−55383.7	+	95927.4i	−0.708912	+	1.22787i
$26$	−3511.18			−0.0391784
$27$	380418.			3.71953
$28$	−2034.35	+	3523.61i	−0.0175135	+	0.0303343i
$29$	−36050.0			−0.274481			−0.137240	−	0.990538i	$-0.543823\pi$
$29$	−36050.0			−0.274481			−0.137240	+	0.990538i	$0.543823\pi$
$30$	−92991.3	−	161066.i	−0.628808	−	1.08913i
$31$	105484.			0.635945			0.317973	−	0.948100i	$-0.396998\pi$
$31$	105484.			0.635945			0.317973	+	0.948100i	$0.396998\pi$
$32$	89547.4	+	155101.i	0.483090	+	0.836736i
$33$	−173057.	−	299744.i	−0.838285	−	1.45195i
$34$	−60190.5	−	104253.i	−0.262635	−	0.454896i
$35$	−8305.37	+	14385.3i	−0.0327432	+	0.0567129i
$36$	−672082.			−2.40084
$37$	78562.1	+	297926.i	0.254981	+	0.966946i
$37$	78562.1	+	297926.i	0.254981	+	0.966946i
$38$	211835.			0.626260
$39$	−34872.7	+	60401.3i	−0.0941368	+	0.163050i
$40$	236479.	+	409593.i	0.584228	+	1.01191i
$41$	−40301.6	−	69804.5i	−0.0913228	−	0.158176i	0.816745	−	0.576999i	$-0.195776\pi$
$41$	−40301.6	−	69804.5i	−0.0913228	−	0.158176i	−0.908068	+	0.418823i	$0.862443\pi$
$42$	−8177.43	−	14163.7i	−0.0170312	−	0.0294988i
$43$	73110.0			0.140229			0.0701144	−	0.997539i	$-0.477664\pi$
$43$	73110.0			0.140229			0.0701144	+	0.997539i	$0.477664\pi$
$44$	199826.	+	346108.i	0.353645	+	0.612530i
$45$	−2.74381e6			−4.48860
$46$	−76273.2	+	132109.i	−0.115537	+	0.200115i
$47$	597754.			0.839808			0.419904	−	0.907569i	$-0.362064\pi$
$47$	597754.			0.839808			0.419904	+	0.907569i	$0.362064\pi$
$48$	790644.			1.03190
$49$	411041.	−	711944.i	0.499113	−	0.864489i
$50$	257059.	+	445240.i	0.290830	+	0.503732i
$51$	−2.39123e6			−2.52421
$52$	40266.8	−	69744.1i	0.0397132	−	0.0687853i
$53$	−45453.6	+	78728.0i	−0.0419375	+	0.0726379i	−0.886232	−	0.463241i	$-0.846686\pi$
$53$	−45453.6	+	78728.0i	−0.0419375	+	0.0726379i	0.844295	+	0.535879i	$0.180020\pi$
$54$	882841.	−	1.52912e6i	0.762964	−	1.32149i
$55$	815800.	+	1.41301e6i	0.661172	+	1.14518i
$56$	20795.4	+	36018.6i	0.0158237	+	0.0274075i
$57$	2.10392e6	−	3.64410e6i	1.50476	−	2.60632i
$58$	−83661.6	+	144906.i	−0.0563026	+	0.0975189i
$59$	−1.34523e6	+	2.33001e6i	−0.852736	+	1.47698i	0.0259931	+	0.999662i	$0.491725\pi$
$59$	−1.34523e6	+	2.33001e6i	−0.852736	+	1.47698i	−0.878729	+	0.477320i	$0.841608\pi$
$60$	4.26576e6			2.54957
$61$	−688007.	−	1.19166e6i	−0.388096	−	0.672201i	0.604098	−	0.796910i	$-0.293534\pi$
$61$	−688007.	−	1.19166e6i	−0.388096	−	0.672201i	−0.992193	+	0.124709i	$0.960200\pi$
$62$	244797.	−	424002.i	0.130448	−	0.225942i
$63$	−241284.			−0.121573
$64$	−266428.			−0.127043
$65$	164391.	−	284734.i	0.0742476	−	0.128601i
$66$	−1.60647e6			−0.687809
$67$	−753583.	−	1.30524e6i	−0.306104	−	0.530188i	0.671402	−	0.741093i	$-0.265692\pi$
$67$	−753583.	−	1.30524e6i	−0.306104	−	0.530188i	−0.977507	+	0.210905i	$0.932359\pi$
$68$	2.76110e6			1.06488
$69$	1.51508e6	+	2.62419e6i	0.555217	+	0.961664i
$70$	38548.8	+	66768.4i	0.0134328	+	0.0232663i
$71$	2.30564e6	+	3.99348e6i	0.764516	+	1.32418i	0.940502	+	0.339788i	$0.110355\pi$
$71$	2.30564e6	+	3.99348e6i	0.764516	+	1.32418i	−0.175986	+	0.984393i	$0.556311\pi$
$72$	−3.43504e6	+	5.94967e6i	−1.08460	+	1.87858i
$73$	−3.68666e6			−1.10918			−0.554592	−	0.832122i	$-0.687126\pi$
$73$	−3.68666e6			−1.10918			−0.554592	+	0.832122i	$0.687126\pi$
$74$	1.37986e6	+	375613.i	0.395844	+	0.107753i
$75$	1.02124e7			2.79519
$76$	−2.42935e6	+	4.20776e6i	−0.634809	+	1.09952i
$77$	71739.5	+	124256.i	0.0179077	+	0.0310171i
$78$	161859.	+	280348.i	0.0386194	+	0.0668908i
$79$	−2.38032e6	−	4.12283e6i	−0.543176	−	0.940808i	−0.998719	−	0.0505943i	$-0.983888\pi$
$79$	−2.38032e6	−	4.12283e6i	−0.543176	−	0.940808i	0.455544	−	0.890213i	$-0.349445\pi$
$80$	−3.72713e6			−0.813878
$81$	−1.06331e7	−	1.84171e7i	−2.22312	−	3.85056i
$82$	−374114.			−0.0749299
$83$	3.58337e6	−	6.20658e6i	0.687889	−	1.19146i	−0.284630	−	0.958637i	$-0.591871\pi$
$83$	3.58337e6	−	6.20658e6i	0.687889	−	1.19146i	0.972519	−	0.232822i	$-0.0747959\pi$
$84$	375120.			0.0690547
$85$	1.12723e7			1.99089
$86$	169667.	−	293872.i	0.0287643	−	0.0498212i
$87$	1.66184e6	+	2.87839e6i	0.270565	+	0.468632i
$88$	4.08528e6			0.639046
$89$	−255548.	+	442622.i	−0.0384244	+	0.0665530i	−0.884598	−	0.466354i	$-0.845567\pi$
$89$	−255548.	+	442622.i	−0.0384244	+	0.0665530i	0.846174	+	0.532907i	$0.178901\pi$
$90$	−6.36761e6	+	1.10290e7i	−0.920720	+	1.59473i
$91$	14456.2	−	25038.8i	0.00201098	−	0.00348313i
$92$	−1.74943e6	−	3.03009e6i	−0.234228	−	0.405694i
$93$	−4.86261e6	−	8.42229e6i	−0.626872	−	1.08577i
$94$	1.38721e6	−	2.40273e6i	0.172265	−	0.298371i
$95$	−9.91797e6	+	1.71784e7i	−1.18684	+	2.05566i
$96$	8.25594e6	−	1.42997e7i	0.952396	−	1.64960i
$97$	−8.13277e6			−0.904768			−0.452384	−	0.891823i	$-0.649426\pi$
$97$	−8.13277e6			−0.904768			−0.452384	+	0.891823i	$0.649426\pi$
$98$	−1.90782e6	−	3.30444e6i	−0.204760	−	0.354655i
$99$	−1.18502e7	+	2.05251e7i	−1.22744	+	2.12599i
$100$	−1.17920e7			−1.17920
$101$	−3.54173e6			−0.342051			−0.171025	−	0.985267i	$-0.554708\pi$
$101$	−3.54173e6			−0.342051			−0.171025	+	0.985267i	$0.554708\pi$
$102$	−5.54935e6	+	9.61175e6i	−0.517775	+	0.896813i
$103$	4.40943e6			0.397606			0.198803	−	0.980040i	$-0.436295\pi$
$103$	4.40943e6			0.397606			0.198803	+	0.980040i	$0.436295\pi$
$104$	−411611.	−	712931.i	−0.0358815	−	0.0621485i
$105$	1.53145e6			0.129104
$106$	210970.	+	365410.i	0.0172048	+	0.0297996i
$107$	−4.10706e6	−	7.11363e6i	−0.324106	−	0.561368i	0.657225	−	0.753695i	$-0.271730\pi$
$107$	−4.10706e6	−	7.11363e6i	−0.324106	−	0.561368i	−0.981331	+	0.192326i	$0.938397\pi$
$108$	2.02491e7	+	3.50725e7i	1.54676	+	2.67907i
$109$	−2.96788e6	+	5.14052e6i	−0.219509	+	0.380202i	−0.954658	−	0.297704i	$-0.903779\pi$
$109$	−2.96788e6	+	5.14052e6i	−0.219509	+	0.380202i	0.735149	+	0.677906i	$0.237112\pi$
$110$	7.57295e6			0.542489
$111$	2.01661e7	−	2.00066e7i	1.39956	−	1.38849i
$112$	−327754.			−0.0220438
$113$	−1.07270e6	+	1.85798e6i	−0.0699367	+	0.121134i	−0.898873	−	0.438209i	$-0.855613\pi$
$113$	−1.07270e6	+	1.85798e6i	−0.0699367	+	0.121134i	0.828937	+	0.559343i	$0.188946\pi$
$114$	−9.76519e6	−	1.69138e7i	−0.617325	−	1.06924i
$115$	−7.14213e6	−	1.23705e7i	−0.437911	−	0.758484i
$116$	−1.91889e6	−	3.32361e6i	−0.114142	−	0.197700i
$117$	4.77584e6			0.275676
$118$	6.24379e6	+	1.08146e7i	0.349833	+	0.605929i
$119$	991262.			0.0539230
$120$	2.18025e7	−	3.77630e7i	1.15179	−	1.99495i
$121$	−5.39386e6			−0.276790
$122$	−6.38667e6			−0.318431
$123$	−3.71566e6	+	6.43572e6i	−0.180040	+	0.311838i
$124$	5.61475e6	+	9.72504e6i	0.264457	+	0.458053i
$125$	−1.41870e7			−0.649688
$126$	−559952.	+	969865.i	−0.0249375	+	0.0431931i
$127$	1.77662e7	−	3.07719e7i	0.769629	−	1.33304i	−0.168136	−	0.985764i	$-0.553775\pi$
$127$	1.77662e7	−	3.07719e7i	0.769629	−	1.33304i	0.937764	−	0.347272i	$-0.112892\pi$
$128$	−1.20804e7	+	2.09238e7i	−0.509150	+	0.881873i
$129$	−3.37024e6	−	5.83742e6i	−0.138228	−	0.239418i
$130$	−763010.	−	1.32157e6i	−0.0304599	−	0.0527581i
$131$	4.65040e6	−	8.05474e6i	0.180735	−	0.313041i	−0.761396	−	0.648287i	$-0.775486\pi$
$131$	4.65040e6	−	8.05474e6i	0.180735	−	0.313041i	0.942131	+	0.335245i	$0.108819\pi$
$132$	1.84232e7	−	3.19099e7i	0.697199	−	1.20758i
$133$	−872162.	+	1.51063e6i	−0.0321452	+	0.0556772i
$134$	−6.99539e6			−0.251157
$135$	8.26682e7	+	1.43185e8i	2.89181	+	5.00877i
$136$	1.41121e7	−	2.44429e7i	0.481067	−	0.833232i
$137$	−1.44885e7			−0.481395			−0.240697	−	0.970600i	$-0.577376\pi$
$137$	−1.44885e7			−0.481395			−0.240697	+	0.970600i	$0.577376\pi$
$138$	1.40642e7			0.455553
$139$	6.29705e6	−	1.09068e7i	0.198877	−	0.344466i	−0.749287	−	0.662245i	$-0.769604\pi$
$139$	6.29705e6	−	1.09068e7i	0.198877	−	0.344466i	0.948165	+	0.317779i	$0.102937\pi$
$140$	−1.76833e6			−0.0544648
$141$	−2.75554e7	−	4.77273e7i	−0.827826	−	1.43384i
$142$	2.14029e7			0.627282
$143$	−1.41997e6	−	2.45946e6i	−0.0406071	−	0.0703336i
$144$	−2.70698e7	−	4.68862e7i	−0.755467	−	1.30851i
$145$	−7.83398e6	−	1.35688e7i	−0.213400	−	0.369619i
$146$	−8.55569e6	+	1.48189e7i	−0.227520	+	0.394077i
$147$	−7.57930e7			−1.96797
$148$	−2.32854e7	+	2.31012e7i	−0.590429	+	0.585758i
$149$	−5.19802e6			−0.128732			−0.0643659	−	0.997926i	$-0.520502\pi$
$149$	−5.19802e6			−0.128732			−0.0643659	+	0.997926i	$0.520502\pi$
$150$	2.36999e7	−	4.10495e7i	0.573361	−	0.993090i
$151$	−3.07492e7	−	5.32591e7i	−0.726799	−	1.25885i	−0.958229	−	0.286001i	$-0.907674\pi$
$151$	−3.07492e7	−	5.32591e7i	−0.726799	−	1.25885i	0.231431	−	0.972851i	$-0.425659\pi$
$152$	2.48331e7	+	4.30121e7i	0.573559	+	0.993433i
$153$	8.18699e7	+	1.41803e8i	1.84801	+	3.20085i
$154$	665947.			0.0146932
$155$	2.29226e7	+	3.97030e7i	0.494427	+	0.856372i
$156$	−7.42490e6			−0.156587
$157$	1.74380e6	−	3.02036e6i	0.0359624	−	0.0622887i	−0.847484	−	0.530821i	$-0.821884\pi$
$157$	1.74380e6	−	3.02036e6i	0.0359624	−	0.0622887i	0.883446	+	0.468532i	$0.155217\pi$
$158$	−2.20961e7			−0.445673
$159$	8.38132e6			0.165357
$160$	−3.89189e7	+	6.74095e7i	−0.751174	+	1.30107i
$161$	−628062.	−	1.08783e6i	−0.0118607	−	0.0205434i
$162$	−9.87057e7			−1.82406
$163$	2.75819e7	−	4.77733e7i	0.498848	−	0.864029i	−0.501152	−	0.865360i	$-0.667090\pi$
$163$	2.75819e7	−	4.77733e7i	0.498848	−	0.864029i	0.999999	+	0.00133027i	$0.000423437\pi$
$164$	4.29040e6	−	7.43119e6i	0.0759528	−	0.131554i
$165$	7.52138e7	−	1.30274e8i	1.30348	−	2.25769i
$166$	−1.66320e7	−	2.88074e7i	−0.282205	−	0.488794i
$167$	3.39096e7	+	5.87332e7i	0.563398	+	0.975834i	0.997197	+	0.0748241i	$0.0238395\pi$
$167$	3.39096e7	+	5.87332e7i	0.563398	+	0.975834i	−0.433799	+	0.901010i	$0.642827\pi$
$168$	1.91726e6	−	3.32079e6i	0.0311959	−	0.0540329i
$169$	3.10881e7	−	5.38462e7i	0.495440	−	0.858127i
$170$	2.61599e7	−	4.53102e7i	0.408380	−	0.707334i
$171$	−2.88133e8			−4.40663
$172$	3.89154e6	+	6.74035e6i	0.0583139	+	0.101003i
$173$	−5.00925e7	+	8.67628e7i	−0.735549	+	1.27401i	0.218933	+	0.975740i	$0.429742\pi$
$173$	−5.00925e7	+	8.67628e7i	−0.735549	+	1.27401i	−0.954482	+	0.298269i	$0.903591\pi$
$174$	1.54266e7			0.221997
$175$	−4.23344e6			−0.0597119
$176$	−1.60969e7	+	2.78807e7i	−0.222561	+	0.385487i
$177$	2.48051e8			3.36228
$178$	1.18611e6	+	2.05440e6i	0.0157635	+	0.0273032i
$179$	8.42615e7			1.09810			0.549052	−	0.835788i	$-0.314989\pi$
$179$	8.42615e7			1.09810			0.549052	+	0.835788i	$0.314989\pi$
$180$	−1.46049e8	−	2.52965e8i	−1.86658	−	3.23301i
$181$	−1.38013e7	−	2.39046e7i	−0.173000	−	0.299645i	0.766467	−	0.642283i	$-0.222013\pi$
$181$	−1.38013e7	−	2.39046e7i	−0.173000	−	0.299645i	−0.939467	+	0.342639i	$0.888679\pi$
$182$	−67097.3	−	116216.i	−0.000825002	−	0.00142895i
$183$	−6.34318e7	+	1.09867e8i	−0.765118	+	1.32522i
$184$	−3.57656e7			−0.423256
$185$	−9.50641e7	+	9.43119e7i	−1.10386	+	1.09513i
$186$	−4.51389e7			−0.514346
$187$	4.86837e7	−	8.43226e7i	0.544424	−	0.942971i
$188$	3.18176e7	+	5.51097e7i	0.349233	+	0.604889i
$189$	7.26964e6	+	1.25914e7i	0.0783243	+	0.135662i
$190$	4.60335e7	+	7.97324e7i	0.486897	+	0.843330i
$191$	−8.90580e7			−0.924818			−0.462409	−	0.886667i	$-0.653015\pi$
$191$	−8.90580e7			−0.924818			−0.462409	+	0.886667i	$0.653015\pi$
$192$	1.22818e7	+	2.12728e7i	0.125230	+	0.216905i
$193$	1.00395e8			1.00522			0.502610	−	0.864514i	$-0.332373\pi$
$193$	1.00395e8			1.00522			0.502610	+	0.864514i	$0.332373\pi$
$194$	−1.88738e7	+	3.26904e7i	−0.185590	+	0.321451i
$195$	−3.03126e7			−0.292753
$196$	8.75166e7			0.830222
$197$	−1.29173e7	+	2.23735e7i	−0.120376	+	0.208498i	−0.919916	−	0.392115i	$-0.871743\pi$
$197$	−1.29173e7	+	2.23735e7i	−0.120376	+	0.208498i	0.799540	+	0.600613i	$0.205077\pi$
$198$	5.50016e7	+	9.52656e7i	0.503555	+	0.872183i
$199$	4.03652e7			0.363096			0.181548	−	0.983382i	$-0.441889\pi$
$199$	4.03652e7			0.363096			0.181548	+	0.983382i	$0.441889\pi$
$200$	−6.02694e7	+	1.04390e8i	−0.532711	+	0.922683i
$201$	−6.94776e7	+	1.20339e8i	−0.603474	+	1.04525i
$202$	−8.21933e6	+	1.42363e7i	−0.0701628	+	0.121526i
$203$	−688901.	−	1.19321e6i	−0.00577990	−	0.0100111i
$204$	−1.27282e8	−	2.20458e8i	−1.04969	−	1.81811i
$205$	1.75158e7	−	3.03382e7i	0.142001	−	0.245953i
$206$	1.02330e7	−	1.77241e7i	0.0815584	−	0.141263i
$207$	1.03745e8	−	1.79692e8i	0.812965	−	1.40810i
$208$	6.48737e6			0.0499859
$209$	8.56687e7	+	1.48383e8i	0.649098	+	1.12427i
$210$	3.55405e6	−	6.15580e6i	0.0264824	−	0.0458688i
$211$	4.35017e7			0.318800			0.159400	−	0.987214i	$-0.449044\pi$
$211$	4.35017e7			0.318800			0.159400	+	0.987214i	$0.449044\pi$
$212$	−9.67773e6			−0.0697586
$213$	2.12571e8	−	3.68184e8i	1.50722	−	2.61058i
$214$	−3.81252e7			−0.265928
$215$	1.58874e7	+	2.75179e7i	0.109023	+	0.188834i
$216$	4.13977e8			2.79504
$217$	2.01575e6	+	3.49139e6i	0.0133915	+	0.0231947i
$218$	1.37752e7	+	2.38593e7i	0.0900533	+	0.155977i
$219$	1.69949e8	+	2.94360e8i	1.09336	+	1.89375i
$220$	−8.68478e7	+	1.50425e8i	−0.549894	+	0.952445i
$221$	−1.96204e7			−0.122274
$222$	−3.36185e7	−	1.27489e8i	−0.206226	−	0.782056i
$223$	9.76474e7			0.589649			0.294824	−	0.955551i	$-0.404739\pi$
$223$	9.76474e7			0.589649			0.294824	+	0.955551i	$0.404739\pi$
$224$	−3.42243e6	+	5.92782e6i	−0.0203454	+	0.0352393i
$225$	−3.49647e8	−	6.05606e8i	−2.04640	−	3.54447i
$226$	4.97887e6	+	8.62366e6i	0.0286914	+	0.0496949i
$227$	−1.15704e8	−	2.00406e8i	−0.656537	−	1.13715i	−0.981506	−	0.191430i	$-0.938687\pi$
$227$	−1.15704e8	−	2.00406e8i	−0.656537	−	1.13715i	0.324970	−	0.945724i	$-0.394646\pi$
$228$	4.47955e8			2.50301
$229$	−3.07777e7	−	5.33086e7i	−0.169361	−	0.293341i	0.768835	−	0.639448i	$-0.220837\pi$
$229$	−3.07777e7	−	5.33086e7i	−0.169361	−	0.293341i	−0.938195	+	0.346107i	$0.887504\pi$
$230$	−6.62994e7			−0.359304
$231$	6.61412e6	−	1.14560e7i	0.0353045	−	0.0611492i
$232$	−3.92301e7			−0.206258
$233$	−1.79620e8			−0.930270			−0.465135	−	0.885240i	$-0.653994\pi$
$233$	−1.79620e8			−0.930270			−0.465135	+	0.885240i	$0.653994\pi$
$234$	1.10833e7	−	1.91969e7i	0.0565477	−	0.0979435i
$235$	1.29897e8	+	2.24988e8i	0.652923	+	1.13090i
$236$	−2.86419e8			−1.41844
$237$	−2.19457e8	+	3.80110e8i	−1.07085	+	1.85477i
$238$	2.30043e6	−	3.98447e6i	0.0110609	−	0.0191580i
$239$	1.62171e8	−	2.80888e8i	0.768387	−	1.33089i	−0.170050	−	0.985435i	$-0.554393\pi$
$239$	1.62171e8	−	2.80888e8i	0.768387	−	1.33089i	0.938437	−	0.345450i	$-0.112274\pi$
$240$	1.71814e8	+	2.97590e8i	0.802267	+	1.38957i
$241$	1.34802e8	+	2.33484e8i	0.620350	+	1.07448i	0.989420	+	0.145077i	$0.0463430\pi$
$241$	1.34802e8	+	2.33484e8i	0.620350	+	1.07448i	−0.369070	+	0.929402i	$0.620324\pi$
$242$	−1.25176e7	+	2.16811e7i	−0.0567763	+	0.0983395i
$243$	−5.64348e8	+	9.77480e8i	−2.52305	+	4.37004i
$244$	7.32433e7	−	1.26861e8i	0.322778	−	0.559068i
$245$	3.57291e8			1.55218
$246$	1.72460e7	+	2.98709e7i	0.0738609	+	0.127931i
$247$	1.72630e7	−	2.99005e7i	0.0728917	−	0.126252i
$248$	1.14789e8			0.477881
$249$	−6.60748e8			−2.71230
$250$	−3.29239e7	+	5.70259e7i	−0.133267	+	0.230825i
$251$	1.77999e8			0.710494			0.355247	−	0.934772i	$-0.384397\pi$
$251$	1.77999e8			0.710494			0.355247	+	0.934772i	$0.384397\pi$
$252$	−1.28432e7	−	2.22451e7i	−0.0505559	−	0.0875655i
$253$	−1.23384e8			−0.479000
$254$	−8.24604e7	−	1.42826e8i	−0.315738	−	0.546875i
$255$	−5.19634e8	−	9.00033e8i	−1.96249	−	3.39913i
$256$	3.90187e7	+	6.75824e7i	0.145356	+	0.251764i
$257$	−1.64412e8	+	2.84769e8i	−0.604180	+	1.04647i	0.388000	+	0.921659i	$0.373166\pi$
$257$	−1.64412e8	+	2.84769e8i	−0.604180	+	1.04647i	−0.992180	+	0.124812i	$0.960167\pi$
$258$	−3.12854e7			−0.113416
$259$	−8.35970e6	+	8.29356e6i	−0.0298980	+	0.0296614i
$260$	3.50013e7			0.123503
$261$	1.13795e8	−	1.97098e8i	0.396169	−	0.686185i
$262$	−2.15845e7	−	3.73854e7i	−0.0741460	−	0.128425i
$263$	−2.71208e8	−	4.69747e8i	−0.919302	−	1.59228i	−0.800478	−	0.599362i	$-0.795421\pi$
$263$	−2.71208e8	−	4.69747e8i	−0.919302	−	1.59228i	−0.118824	−	0.992915i	$-0.537912\pi$
$264$	−1.88324e8	−	3.26186e8i	−0.629929	−	1.09107i
$265$	−3.95099e7			−0.130420
$266$	4.04808e6	+	7.01147e6i	0.0131875	+	0.0228414i
$267$	4.71212e7			0.151505
$268$	8.02243e7	−	1.38953e8i	0.254586	−	0.440955i
$269$	4.84072e8			1.51627			0.758135	−	0.652097i	$-0.226111\pi$
$269$	4.84072e8			1.51627			0.758135	+	0.652097i	$0.226111\pi$
$270$	7.67396e8			2.37272
$271$	1.37927e8	−	2.38896e8i	0.420975	−	0.729149i	−0.575061	−	0.818111i	$-0.695022\pi$
$271$	1.37927e8	−	2.38896e8i	0.420975	−	0.729149i	0.996035	+	0.0889616i	$0.0283548\pi$
$272$	1.11210e8	+	1.92621e8i	0.335083	+	0.580381i
$273$	−2.66561e6			−0.00792918
$274$	−3.36237e7	+	5.82379e7i	−0.0987456	+	0.171032i
$275$	−2.07916e8	+	3.60122e8i	−0.602871	+	1.04420i
$276$	−1.61291e8	+	2.79364e8i	−0.461772	+	0.799813i
$277$	−1.89819e8	−	3.28776e8i	−0.536612	−	0.929440i	−0.999083	−	0.0428055i	$-0.986370\pi$
$277$	−1.89819e8	−	3.28776e8i	−0.536612	−	0.929440i	0.462471	−	0.886634i	$-0.346963\pi$
$278$	−2.92273e7	−	5.06231e7i	−0.0815890	−	0.141316i
$279$	−3.32968e8	+	5.76718e8i	−0.917885	+	1.58982i
$280$	−9.03803e6	+	1.56543e7i	−0.0246049	+	0.0426169i
$281$	1.18413e8	−	2.05097e8i	0.318366	−	0.551425i	−0.661782	−	0.749697i	$-0.730199\pi$
$281$	1.18413e8	−	2.05097e8i	0.318366	−	0.551425i	0.980147	+	0.198271i	$0.0635327\pi$
$282$	−2.55792e8			−0.679228
$283$	−1.64953e8	−	2.85708e8i	−0.432622	−	0.749323i	0.564476	−	0.825449i	$-0.309078\pi$
$283$	−1.64953e8	−	2.85708e8i	−0.432622	−	0.749323i	−0.997098	+	0.0761261i	$0.975745\pi$
$284$	−2.45452e8	+	4.25135e8i	−0.635846	+	1.10132i
$285$	1.82880e9			4.67961
$286$	−1.31813e7			−0.0333180
$287$	1.54030e6	−	2.66787e6i	0.00384607	−	0.00666160i
$288$	−1.13066e9			−2.78905
$289$	−1.31174e8	−	2.27201e8i	−0.319674	−	0.553691i
$290$	−7.27216e7			−0.175094
$291$	3.74906e8	+	6.49356e8i	0.891860	+	1.54475i
$292$	−1.96236e8	−	3.39891e8i	−0.461252	−	0.798913i
$293$	−2.65485e8	−	4.59833e8i	−0.616599	−	1.06798i	−0.990102	−	0.140352i	$-0.955177\pi$
$293$	−2.65485e8	−	4.59833e8i	−0.616599	−	1.06798i	0.373503	−	0.927629i	$-0.378157\pi$
$294$	−1.75894e8	+	3.04657e8i	−0.403678	+	0.699190i
$295$	−1.16932e9			−2.65190
$296$	8.54925e7	+	3.24208e8i	0.191605	+	0.726611i
$297$	1.42813e9			3.16315
$298$	−1.20631e7	+	2.08939e7i	−0.0264060	+	0.0457365i
$299$	1.24315e7	+	2.15319e7i	0.0268951	+	0.0465837i
$300$	5.43589e8	+	9.41524e8i	1.16238	+	2.01329i
$301$	1.39710e6	+	2.41985e6i	0.00295288	+	0.00511454i
$302$	−2.85440e8			−0.596335
$303$	1.63267e8	+	2.82787e8i	0.337171	+	0.583997i
$304$	−3.91393e8			−0.799015
$305$	2.99020e8	−	5.17918e8i	0.603464	−	1.04523i
$306$	7.59986e8			1.51628
$307$	7.51368e7			0.148207			0.0741035	−	0.997251i	$-0.476390\pi$
$307$	7.51368e7			0.148207			0.0741035	+	0.997251i	$0.476390\pi$
$308$	−7.63718e6	+	1.32280e7i	−0.0148938	+	0.0257968i
$309$	−2.03267e8	−	3.52069e8i	−0.391933	−	0.678848i
$310$	2.12787e8			0.405675
$311$	−1.50258e8	+	2.60254e8i	−0.283253	+	0.490609i	−0.972184	−	0.234218i	$-0.924747\pi$
$311$	−1.50258e8	+	2.60254e8i	−0.283253	+	0.490609i	0.688931	+	0.724827i	$0.258080\pi$
$312$	−3.79490e7	+	6.57296e7i	−0.0707391	+	0.122524i
$313$	−2.06645e8	+	3.57919e8i	−0.380907	+	0.659750i	−0.991192	−	0.132432i	$-0.957722\pi$
$313$	−2.06645e8	+	3.57919e8i	−0.380907	+	0.659750i	0.610285	+	0.792182i	$0.291055\pi$
$314$	−8.09373e6	−	1.40188e7i	−0.0147535	−	0.0255538i
$315$	−5.24332e7	−	9.08170e7i	−0.0945191	−	0.163712i
$316$	2.53402e8	−	4.38905e8i	0.451757	−	0.782467i
$317$	6.45484e7	−	1.11801e8i	0.113809	−	0.197124i	−0.803494	−	0.595313i	$-0.797028\pi$
$317$	6.45484e7	−	1.11801e8i	0.113809	−	0.197124i	0.917303	+	0.398190i	$0.130361\pi$
$318$	1.94506e7	−	3.36895e7i	0.0339187	−	0.0587488i
$319$	−1.35335e8			−0.233423
$320$	−5.78971e7	−	1.00281e8i	−0.0987716	−	0.171077i
$321$	−3.78656e8	+	6.55851e8i	−0.638965	+	1.10672i
$322$	−5.83020e6			−0.00973169
$323$	1.18373e9			1.95454
$324$	1.13197e9	−	1.96063e9i	1.84896	−	3.20250i
$325$	8.37942e7			0.135401
$326$	−1.28019e8	−	2.21736e8i	−0.204651	−	0.354466i
$327$	5.47255e8			0.865511
$328$	−4.38568e7	−	7.59623e7i	−0.0686245	−	0.118861i
$329$	1.14228e7	+	1.97849e7i	0.0176843	+	0.0306301i
$330$	−3.49099e8	−	6.04658e8i	−0.534749	−	0.926213i
$331$	−1.89716e8	+	3.28597e8i	−0.287545	+	0.498042i	−0.973223	−	0.229863i	$-0.926172\pi$
$331$	−1.89716e8	+	3.28597e8i	−0.287545	+	0.498042i	0.685678	+	0.727905i	$0.259506\pi$
$332$	7.62951e8			1.14423
$333$	−1.87686e9	−	5.10901e8i	−2.78533	−	0.758196i
$334$	3.14778e8			0.462266
$335$	3.27520e8	−	5.67282e8i	0.475972	−	0.824408i
$336$	1.51089e7	+	2.61694e7i	0.0217293	+	0.0376362i
$337$	−4.90327e8	−	8.49272e8i	−0.697881	−	1.20877i	−0.969200	−	0.246276i	$-0.920793\pi$
$337$	−4.90327e8	−	8.49272e8i	−0.697881	−	1.20877i	0.271319	−	0.962490i	$-0.412540\pi$
$338$	−1.44293e8	−	2.49923e8i	−0.203253	−	0.352045i
$339$	1.97799e8			0.275756
$340$	6.00011e8	+	1.03925e9i	0.827909	+	1.43398i
$341$	3.95997e8			0.540819
$342$	−6.68674e8	+	1.15818e9i	−0.903906	+	1.56561i
$343$	6.28945e7			0.0841556
$344$	7.95594e7			0.105375
$345$	−6.58479e8	+	1.14052e9i	−0.863326	+	1.49532i
$346$	2.32501e8	+	4.02703e8i	0.301757	+	0.522659i
$347$	−5.31351e8			−0.682698			−0.341349	−	0.939937i	$-0.610884\pi$
$347$	−5.31351e8			−0.682698			−0.341349	+	0.939937i	$0.610884\pi$
$348$	−1.76915e8	+	3.06425e8i	−0.225028	+	0.389760i
$349$	6.13478e8	−	1.06258e9i	0.772521	−	1.33805i	−0.163656	−	0.986517i	$-0.552329\pi$
$349$	6.13478e8	−	1.06258e9i	0.772521	−	1.33805i	0.936177	−	0.351528i	$-0.114338\pi$
$350$	−9.82461e6	+	1.70167e7i	−0.0122483	+	0.0212147i
$351$	−1.43891e8	−	2.49226e8i	−0.177606	−	0.307623i
$352$	3.36170e8	+	5.82264e8i	0.410828	+	0.711575i
$353$	1.88898e8	−	3.27181e8i	0.228568	−	0.395891i	−0.728816	−	0.684710i	$-0.759929\pi$
$353$	1.88898e8	−	3.27181e8i	0.228568	−	0.395891i	0.957384	+	0.288818i	$0.0932624\pi$
$354$	5.75654e8	−	9.97063e8i	0.689685	−	1.19457i
$355$	−1.00207e9	+	1.73564e9i	−1.18877	+	2.05902i
$356$	−5.44098e7			−0.0639149
$357$	−4.56954e7	−	7.91467e7i	−0.0531537	−	0.0920649i
$358$	1.95547e8	−	3.38697e8i	0.225248	−	0.390140i
$359$	4.77893e8			0.545130			0.272565	−	0.962137i	$-0.412128\pi$
$359$	4.77893e8			0.545130			0.272565	+	0.962137i	$0.412128\pi$
$360$	−2.98586e9			−3.37296
$361$	−5.94569e8	+	1.02982e9i	−0.665161	+	1.15209i
$362$	−1.28116e8			−0.141946
$363$	2.48647e8	+	4.30670e8i	0.272841	+	0.472575i
$364$	3.07793e6			0.00334506
$365$	−8.01145e8	−	1.38762e9i	−0.862355	−	1.49364i
$366$	2.94414e8	+	5.09940e8i	0.313888	+	0.543670i
$367$	6.34528e8	+	1.09903e9i	0.670069	+	1.16059i	0.977884	+	0.209147i	$0.0670688\pi$
$367$	6.34528e8	+	1.09903e9i	0.670069	+	1.16059i	−0.307815	+	0.951446i	$0.599598\pi$
$368$	1.40925e8	−	2.44089e8i	0.147408	−	0.255318i
$369$	5.08862e8			0.527239
$370$	1.58479e8	+	6.00990e8i	0.162654	+	0.616824i
$371$	−3.47440e6			−0.00353241
$372$	5.17660e8	−	8.96613e8i	0.521368	−	0.903035i
$373$	−2.26172e8	−	3.91742e8i	−0.225662	−	0.390858i	0.730856	−	0.682532i	$-0.239121\pi$
$373$	−2.26172e8	−	3.91742e8i	−0.225662	−	0.390858i	−0.956518	+	0.291674i	$0.905788\pi$
$374$	−2.25962e8	−	3.91377e8i	−0.223349	−	0.386852i
$375$	6.53994e8	+	1.13275e9i	0.640419	+	1.10924i
$376$	6.50485e8			0.631073
$377$	1.36357e7	+	2.36177e7i	0.0131064	+	0.0227009i
$378$	6.74829e7			0.0642647
$379$	−4.77018e8	+	8.26219e8i	−0.450088	+	0.779575i	−0.998391	−	0.0567047i	$-0.981941\pi$
$379$	−4.77018e8	+	8.26219e8i	−0.450088	+	0.779575i	0.548303	+	0.836280i	$0.315274\pi$
$380$	−2.11168e9			−1.97417
$381$	−3.27596e9			−3.03459
$382$	−2.06678e8	+	3.57977e8i	−0.189702	+	0.328574i
$383$	3.16566e8	+	5.48308e8i	0.287918	+	0.498688i	0.973313	−	0.229484i	$-0.0737037\pi$
$383$	3.16566e8	+	5.48308e8i	0.287918	+	0.498688i	−0.685395	+	0.728172i	$0.740370\pi$
$384$	2.22753e9			2.00754
$385$	−3.11792e7	+	5.40040e7i	−0.0278454	+	0.0482296i
$386$	2.32988e8	−	4.03546e8i	0.206195	−	0.357139i
$387$	−2.30778e8	+	3.99719e8i	−0.202398	+	0.350563i
$388$	−4.32896e8	−	7.49798e8i	−0.376246	−	0.651678i
$389$	2.17307e8	+	3.76387e8i	0.187176	+	0.324198i	0.944308	−	0.329064i	$-0.106733\pi$
$389$	2.17307e8	+	3.76387e8i	0.187176	+	0.324198i	−0.757132	+	0.653262i	$0.773400\pi$
$390$	−7.03468e7	+	1.21844e8i	−0.0600507	+	0.104011i
$391$	−4.26214e8	+	7.38224e8i	−0.360586	+	0.624553i
$392$	4.47301e8	−	7.74749e8i	0.375058	−	0.649620i
$393$	−8.57501e8			−0.712624
$394$	5.99548e7	+	1.03845e8i	0.0493841	+	0.0855358i
$395$	1.03453e9	−	1.79186e9i	0.844603	−	1.46289i
$396$	−2.52307e9			−2.04172
$397$	2.05663e9			1.64964			0.824820	−	0.565396i	$-0.191277\pi$
$397$	2.05663e9			1.64964			0.824820	+	0.565396i	$0.191277\pi$
$398$	9.36760e7	−	1.62252e8i	0.0744796	−	0.129002i
$399$	1.60820e8			0.126747
$400$	−4.74951e8	−	8.22640e8i	−0.371056	−	0.642687i
$401$	−7.95118e7			−0.0615781			−0.0307891	−	0.999526i	$-0.509802\pi$
$401$	−7.95118e7			−0.0615781			−0.0307891	+	0.999526i	$0.509802\pi$
$402$	3.22475e8	+	5.58543e8i	0.247574	+	0.428811i
$403$	−3.98986e7	−	6.91064e7i	−0.0303662	−	0.0525957i
$404$	−1.88521e8	−	3.26528e8i	−0.142241	−	0.246369i
$405$	4.62134e9	−	8.00440e9i	3.45681	−	5.98737i
$406$	−6.39496e6			−0.00474238
$407$	2.94931e8	+	1.11845e9i	0.216840	+	0.822308i
$408$	−2.60217e9			−1.89681
$409$	−6.34541e8	+	1.09906e9i	−0.458594	+	0.794308i	−0.998887	−	0.0471692i	$-0.984980\pi$
$409$	−6.34541e8	+	1.09906e9i	−0.458594	+	0.794308i	0.540293	+	0.841477i	$0.318313\pi$
$410$	−8.12982e7	−	1.40813e8i	−0.0582556	−	0.100902i
$411$	6.67894e8	+	1.15683e9i	0.474527	+	0.821905i
$412$	2.34708e8	+	4.06526e8i	0.165344	+	0.286384i
$413$	−1.02827e8			−0.0718263
$414$	−4.81526e8	−	8.34027e8i	−0.333517	−	0.577669i
$415$	3.11479e9			2.13925
$416$	6.77415e7	−	1.17332e8i	0.0461347	−	0.0799077i
$417$	−1.16113e9			−0.784160
$418$	7.95250e8			0.532582
$419$	−3.39046e8	+	5.87244e8i	−0.225169	+	0.390005i	−0.956370	−	0.292157i	$-0.905627\pi$
$419$	−3.39046e8	+	5.87244e8i	−0.225169	+	0.390005i	0.731201	+	0.682162i	$0.238960\pi$
$420$	8.15169e7	+	1.41191e8i	0.0536878	+	0.0929899i
$421$	2.23426e9			1.45930			0.729652	−	0.683819i	$-0.239682\pi$
$421$	2.23426e9			1.45930			0.729652	+	0.683819i	$0.239682\pi$
$422$	1.00955e8	−	1.74859e8i	0.0653935	−	0.113265i
$423$	−1.88686e9	+	3.26814e9i	−1.21213	+	2.09947i
$424$	−4.94633e7	+	8.56730e7i	−0.0315139	+	0.0545838i
$425$	1.43644e9	+	2.48800e9i	0.907669	+	1.57213i
$426$	−9.86634e8	−	1.70890e9i	−0.618333	−	1.07098i
$427$	2.62951e7	−	4.55445e7i	0.0163447	−	0.0283099i
$428$	4.37226e8	−	7.57297e8i	0.269558	−	0.466888i
$429$	−1.30916e8	+	2.26753e8i	−0.0800556	+	0.138660i
$430$	1.47481e8			0.0894532
$431$	−7.62371e7	−	1.32047e8i	−0.0458665	−	0.0794432i	0.842181	−	0.539195i	$-0.181272\pi$
$431$	−7.62371e7	−	1.32047e8i	−0.0458665	−	0.0794432i	−0.888047	+	0.459752i	$0.847938\pi$
$432$	−1.63117e9	+	2.82526e9i	−0.973430	+	1.68603i
$433$	−3.45601e8			−0.204582			−0.102291	−	0.994755i	$-0.532617\pi$
$433$	−3.45601e8			−0.204582			−0.102291	+	0.994755i	$0.532617\pi$
$434$	1.87119e7			0.0109876
$435$	−7.22264e8	+	1.25100e9i	−0.420711	+	0.728692i
$436$	−6.31904e8			−0.365131
$437$	−7.50009e8	−	1.29905e9i	−0.429914	−	0.744632i
$438$	1.57761e9			0.897097
$439$	−1.34293e9	−	2.32602e9i	−0.757579	−	1.31216i	−0.944082	−	0.329710i	$-0.893049\pi$
$439$	−1.34293e9	−	2.32602e9i	−0.757579	−	1.31216i	0.186503	−	0.982454i	$-0.440284\pi$
$440$	8.87766e8	+	1.53766e9i	0.496837	+	0.860548i
$441$	2.59497e9	+	4.49462e9i	1.44078	+	2.49550i
$442$	−4.55334e7	+	7.88661e7i	−0.0250814	+	0.0434423i
$443$	1.90553e9			1.04137			0.520683	−	0.853750i	$-0.325677\pi$
$443$	1.90553e9			1.04137			0.520683	+	0.853750i	$0.325677\pi$
$444$	2.91792e9	+	7.94288e8i	1.58209	+	0.430663i
$445$	−2.22131e8			−0.119495
$446$	2.26611e8	−	3.92503e8i	0.120951	−	0.209493i
$447$	2.39619e8	+	4.15033e8i	0.126895	+	0.219789i
$448$	−5.09133e6	−	8.81845e6i	−0.00267521	−	0.00463361i
$449$	−1.15527e9	−	2.00098e9i	−0.602311	−	1.04323i	−0.992470	−	0.122486i	$-0.960913\pi$
$449$	−1.15527e9	−	2.00098e9i	−0.602311	−	1.04323i	0.390159	−	0.920747i	$-0.372420\pi$
$450$	−3.24572e9			−1.67906
$451$	−1.51297e8	−	2.62053e8i	−0.0776625	−	0.134515i
$452$	−2.28394e8			−0.116332
$453$	−2.83496e9	+	4.91030e9i	−1.43286	+	2.48178i
$454$	−1.07407e9			−0.538686
$455$	1.25658e7			0.00625390
$456$	2.28952e9	−	3.96556e9i	1.13075	−	1.95852i
$457$	−6.56835e7	−	1.13767e8i	−0.0321921	−	0.0557584i	0.849480	−	0.527620i	$-0.176916\pi$
$457$	−6.56835e7	−	1.13767e8i	−0.0321921	−	0.0557584i	−0.881673	+	0.471862i	$0.843582\pi$
$458$	−2.85705e8			−0.138960
$459$	4.93330e9	−	8.54473e9i	2.38119	−	4.12433i
$460$	7.60331e8	−	1.31693e9i	0.364209	−	0.630828i
$461$	−8.88898e8	+	1.53962e9i	−0.422570	+	0.731913i	−0.996190	−	0.0872087i	$-0.972205\pi$
$461$	−8.88898e8	+	1.53962e9i	−0.422570	+	0.731913i	0.573620	+	0.819122i	$0.305539\pi$
$462$	−3.06989e7	−	5.31721e7i	−0.0144836	−	0.0250863i
$463$	2.76890e8	+	4.79588e8i	0.129651	+	0.224561i	0.923541	−	0.383499i	$-0.125281\pi$
$463$	2.76890e8	+	4.79588e8i	0.129651	+	0.224561i	−0.793891	+	0.608061i	$0.791948\pi$
$464$	1.54576e8	−	2.67733e8i	0.0718338	−	0.124420i
$465$	2.11338e9	−	3.66047e9i	0.974746	−	1.68831i
$466$	−4.16846e8	+	7.21999e8i	−0.190821	+	0.330511i
$467$	8.95283e8			0.406772			0.203386	−	0.979099i	$-0.434805\pi$
$467$	8.95283e8			0.406772			0.203386	+	0.979099i	$0.434805\pi$
$468$	2.54211e8	+	4.40306e8i	0.114639	+	0.198561i
$469$	2.88013e7	−	4.98854e7i	0.0128916	−	0.0223289i
$470$	1.20582e9			0.535721
$471$	−3.21545e8			−0.141797
$472$	−1.46390e9	+	2.53555e9i	−0.640788	+	1.10988i
$473$	2.74463e8			0.119253
$474$	1.01859e9	+	1.76425e9i	0.439315	+	0.760916i
$475$	−5.05543e9			−2.16436
$476$	5.27635e7	+	9.13890e7i	0.0224238	+	0.0388391i
$477$	−2.86956e8	−	4.97023e8i	−0.121060	−	0.209683i
$478$	−7.52704e8	−	1.30372e9i	−0.315229	−	0.545993i
$479$	−1.33482e9	+	2.31197e9i	−0.554941	+	0.961186i	0.442967	+	0.896538i	$0.353926\pi$
$479$	−1.33482e9	+	2.31197e9i	−0.554941	+	0.961186i	−0.997908	+	0.0646481i	$0.979408\pi$
$480$	7.17636e9			2.96183
$481$	1.65467e8	−	1.64158e8i	0.0677959	−	0.0672595i
$482$	1.25135e9			0.508995
$483$	−5.79050e7	+	1.00294e8i	−0.0233831	+	0.0405006i
$484$	−2.87108e8	−	4.97285e8i	−0.115103	−	0.199364i
$485$	−1.76732e9	−	3.06109e9i	−0.703428	−	1.21837i
$486$	2.61938e9	+	4.53690e9i	1.03507	+	1.79280i
$487$	−1.50932e9			−0.592148			−0.296074	−	0.955165i	$-0.595678\pi$
$487$	−1.50932e9			−0.592148			−0.296074	+	0.955165i	$0.595678\pi$
$488$	−7.48700e8	−	1.29679e9i	−0.291634	−	0.505125i
$489$	−5.08590e9			−1.96692
$490$	8.29171e8	−	1.43617e9i	0.318389	−	0.551465i
$491$	−2.78651e8			−0.106237			−0.0531184	−	0.998588i	$-0.516916\pi$
$491$	−2.78651e8			−0.106237			−0.0531184	+	0.998588i	$0.516916\pi$
$492$	−7.91118e8			−0.299477
$493$	−4.67500e8	+	8.09734e8i	−0.175718	+	0.304353i
$494$	−8.01251e7	−	1.38781e8i	−0.0299037	−	0.0517947i
$495$	−1.03006e10			−3.81718
$496$	−4.52296e8	+	7.83399e8i	−0.166432	+	0.288269i
$497$	−8.81196e7	+	1.52628e8i	−0.0321977	+	0.0557681i
$498$	−1.53341e9	+	2.65594e9i	−0.556358	+	0.963640i
$499$	−1.88579e9	−	3.26628e9i	−0.679424	−	1.17680i	−0.975155	−	0.221525i	$-0.928896\pi$
$499$	−1.88579e9	−	3.26628e9i	−0.679424	−	1.17680i	0.295731	−	0.955271i	$-0.404437\pi$
$500$	−7.55153e8	−	1.30796e9i	−0.270172	−	0.467951i
$501$	3.12634e9	−	5.41499e9i	1.11072	−	1.92382i
$502$	4.13086e8	−	7.15485e8i	0.145739	−	0.252428i
$503$	−1.81403e9	+	3.14200e9i	−0.635561	+	1.10082i	0.350835	+	0.936437i	$0.385898\pi$
$503$	−1.81403e9	+	3.14200e9i	−0.635561	+	1.10082i	−0.986396	+	0.164387i	$0.947436\pi$
$504$	−2.62569e8			−0.0913560
$505$	−7.69649e8	−	1.33307e9i	−0.265933	−	0.460610i
$506$	−2.86338e8	+	4.95951e8i	−0.0982543	+	0.170181i
$507$	−5.73242e9			−1.95349
$508$	3.78268e9			1.28020
$509$	−1.62879e9	+	2.82115e9i	−0.547461	+	0.948230i	0.450986	+	0.892531i	$0.351072\pi$
$509$	−1.62879e9	+	2.82115e9i	−0.547461	+	0.948230i	−0.998448	+	0.0556997i	$0.982261\pi$
$510$	−4.82369e9			−1.61021
$511$	−7.04507e7	−	1.22024e8i	−0.0233567	−	0.0404551i
$512$	−2.73037e9			−0.899035
$513$	8.68114e9	+	1.50362e10i	2.83900	+	4.91730i
$514$	7.63104e8	+	1.32174e9i	0.247864	+	0.429313i
$515$	9.58209e8	+	1.65967e9i	0.309125	+	0.535421i
$516$	3.58786e8	−	6.21436e8i	0.114964	−	0.199123i
$517$	2.24403e9			0.714187
$518$	1.39363e7	+	5.28496e7i	0.00440547	+	0.0167066i
$519$	9.23670e9			2.90022
$520$	1.78893e8	−	3.09852e8i	0.0557933	−	0.0966369i
$521$	2.84788e9	+	4.93267e9i	0.882245	+	1.52809i	0.848840	+	0.528650i	$0.177302\pi$
$521$	2.84788e9	+	4.93267e9i	0.882245	+	1.52809i	0.0334049	+	0.999442i	$0.489365\pi$
$522$	−5.28170e8	−	9.14817e8i	−0.162528	−	0.281506i
$523$	−2.27285e9	−	3.93668e9i	−0.694727	−	1.20330i	−0.970273	−	0.242014i	$-0.922192\pi$
$523$	−2.27285e9	−	3.93668e9i	−0.694727	−	1.20330i	0.275546	−	0.961288i	$-0.411141\pi$
$524$	9.90138e8			0.300633
$525$	1.95154e8	+	3.38017e8i	0.0588600	+	0.101948i
$526$	−2.51759e9			−0.754283
$527$	1.36793e9	−	2.36932e9i	0.407123	−	0.705157i
$528$	2.96816e9			0.877543
$529$	−2.32463e9			−0.682746
$530$	−9.16911e7	+	1.58814e8i	−0.0267523	+	0.0463364i
$531$	−8.49267e9	−	1.47097e10i	−2.46158	−	4.26358i
$532$	−1.85696e8			−0.0534702
$533$	−3.04877e7	+	5.28062e7i	−0.00872126	+	0.0151057i
$534$	1.09355e8	−	1.89408e8i	0.0310773	−	0.0538274i
$535$	1.78500e9	−	3.09171e9i	0.503964	−	0.872892i
$536$	−8.20060e8	−	1.42039e9i	−0.230022	−	0.398409i
$537$	−3.88430e9	−	6.72781e9i	−1.08244	−	1.87484i
$538$	1.12339e9	−	1.94577e9i	0.311023	−	0.538708i
$539$	1.54309e9	−	2.67271e9i	0.424454	−	0.735177i
$540$	−8.80062e9	+	1.52431e10i	−2.40511	+	4.16577i
$541$	4.55362e9			1.23642			0.618210	−	0.786013i	$-0.287858\pi$
$541$	4.55362e9			1.23642			0.618210	+	0.786013i	$0.287858\pi$
$542$	−6.40176e8	−	1.10882e9i	−0.172704	−	0.299132i
$543$	−1.27243e9	+	2.20392e9i	−0.341064	+	0.590740i
$544$	4.64504e9			1.23707
$545$	−2.57978e9			−0.682646
$546$	−6.18612e6	+	1.07147e7i	−0.00162646	+	0.00281712i
$547$	−8.07820e6			−0.00211037			−0.00105519	−	0.999999i	$-0.500336\pi$
$547$	−8.07820e6			−0.00211037			−0.00105519	+	0.999999i	$0.500336\pi$
$548$	−7.71203e8	−	1.33576e9i	−0.200187	−	0.346735i
$549$	8.68702e9			2.24062
$550$	9.65028e8	+	1.67148e9i	0.247326	+	0.428382i
$551$	−8.22660e8	−	1.42489e9i	−0.209503	−	0.362870i
$552$	1.64873e9	+	2.85568e9i	0.417218	+	0.722642i
$553$	9.09739e7	−	1.57571e8i	0.0228759	−	0.0396223i
$554$	−1.76206e9			−0.440288
$555$	1.19126e10	+	3.24273e9i	2.95787	+	0.805165i
$556$	1.34073e9			0.330811
$557$	−8.82577e8	+	1.52867e9i	−0.216401	+	0.374817i	−0.953705	−	0.300744i	$-0.902765\pi$
$557$	−8.82577e8	+	1.52867e9i	−0.216401	+	0.374817i	0.737304	+	0.675561i	$0.236099\pi$
$558$	1.54545e9	+	2.67679e9i	0.376561	+	0.652222i
$559$	−2.76534e7	−	4.78971e7i	−0.00669588	−	0.0115976i
$560$	−7.12239e7	−	1.23363e8i	−0.0171383	−	0.0296844i
$561$	−8.97691e9			−2.14663
$562$	−5.49603e8	−	9.51941e8i	−0.130609	−	0.226221i
$563$	7.23416e9			1.70847			0.854237	−	0.519883i	$-0.174025\pi$
$563$	7.23416e9			1.70847			0.854237	+	0.519883i	$0.174025\pi$
$564$	2.93347e9	−	5.08091e9i	0.688500	−	1.19252i
$565$	−9.32431e8			−0.217494
$566$	−1.53124e9			−0.354964
$567$	4.06390e8	−	7.03887e8i	0.0936272	−	0.162167i
$568$	2.50903e9	+	4.34577e9i	0.574496	+	0.995055i
$569$	4.61901e8			0.105113			0.0525565	−	0.998618i	$-0.483263\pi$
$569$	4.61901e8			0.105113			0.0525565	+	0.998618i	$0.483263\pi$
$570$	4.24412e9	−	7.35104e9i	0.959900	−	1.66260i
$571$	−3.89569e9	+	6.74753e9i	−0.875705	+	1.51677i	−0.0196954	+	0.999806i	$0.506270\pi$
$571$	−3.89569e9	+	6.74753e9i	−0.875705	+	1.51677i	−0.856010	+	0.516960i	$0.827064\pi$
$572$	1.51166e8	−	2.61827e8i	0.0337728	−	0.0584962i
$573$	4.10541e9	+	7.11078e9i	0.911623	+	1.57898i
$574$	−7.14917e6	−	1.23827e7i	−0.00157784	−	0.00273291i
$575$	1.82026e9	−	3.15278e9i	0.399296	−	0.691602i
$576$	8.41002e8	−	1.45666e9i	0.183366	−	0.317599i
$577$	2.22605e9	−	3.85563e9i	0.482413	−	0.835565i	−0.517383	−	0.855754i	$-0.673094\pi$
$577$	2.22605e9	−	3.85563e9i	0.482413	−	0.835565i	0.999796	+	0.0201896i	$0.00642697\pi$
$578$	−1.21767e9			−0.262291
$579$	−4.62802e9	−	8.01596e9i	−0.990878	−	1.71625i
$580$	8.33983e8	−	1.44450e9i	0.177484	−	0.307411i
$581$	2.73907e8			0.0579412
$582$	3.48020e9			0.731768
$583$	−1.70638e8	+	2.95553e8i	−0.0356644	+	0.0617726i
$584$	−4.01189e9			−0.833496
$585$	1.03783e9	+	1.79758e9i	0.214329	+	0.371229i
$586$	−2.46445e9			−0.505917
$587$	1.17419e9	+	2.03376e9i	0.239610	+	0.415017i	0.960602	−	0.277926i	$-0.0896470\pi$
$587$	1.17419e9	+	2.03376e9i	0.239610	+	0.415017i	−0.720992	+	0.692943i	$0.756314\pi$
$588$	−4.03435e9	−	6.98771e9i	−0.818377	−	1.41747i
$589$	2.40714e9	+	4.16929e9i	0.485398	+	0.840734i
$590$	−2.71366e9	+	4.70020e9i	−0.543968	+	0.942180i
$591$	2.38186e9			0.474636
$592$	−2.54948e9	−	6.93994e8i	−0.505039	−	0.137477i
$593$	−9.24214e9			−1.82004			−0.910021	−	0.414562i	$-0.863935\pi$
$593$	−9.24214e9			−1.82004			−0.910021	+	0.414562i	$0.863935\pi$
$594$	3.31428e9	−	5.74050e9i	0.648838	−	1.12382i
$595$	2.15410e8	+	3.73101e8i	0.0419234	+	0.0726134i
$596$	−2.76683e8	−	4.79229e8i	−0.0535329	−	0.0927218i
$597$	−1.86076e9	−	3.22293e9i	−0.357916	−	0.619928i
$598$	1.15399e8			0.0220673
$599$	1.48592e9	+	2.57369e9i	0.282489	+	0.489285i	0.971997	−	0.234993i	$-0.0755066\pi$
$599$	1.48592e9	+	2.57369e9i	0.282489	+	0.489285i	−0.689508	+	0.724278i	$0.742173\pi$
$600$	1.11132e10			2.10045
$601$	−3.48290e9	+	6.03256e9i	−0.654456	+	1.13355i	0.327574	+	0.944826i	$0.393769\pi$
$601$	−3.48290e9	+	6.03256e9i	−0.654456	+	1.13355i	−0.982030	+	0.188725i	$0.939564\pi$
$602$	1.29691e7			0.00242283
$603$	9.51499e9			1.76725
$604$	3.27347e9	−	5.66982e9i	0.604476	−	1.04698i
$605$	−1.17213e9	−	2.03019e9i	−0.215196	−	0.372730i
$606$	1.51559e9			0.276647
$607$	−1.97196e9	+	3.41553e9i	−0.357880	+	0.619866i	−0.987606	−	0.156951i	$-0.949834\pi$
$607$	−1.97196e9	+	3.41553e9i	−0.357880	+	0.619866i	0.629727	+	0.776817i	$0.283167\pi$
$608$	−4.08694e9	+	7.07879e9i	−0.737456	+	1.27731i
$609$	−6.35141e7	+	1.10010e8i	−0.0113949	+	0.0197365i
$610$	−1.38788e9	−	2.40388e9i	−0.247570	−	0.428803i
$611$	−2.26097e8	−	3.91611e8i	−0.0401005	−	0.0694561i
$612$	−8.71564e9	+	1.50959e10i	−1.53698	+	2.66213i
$613$	−1.24091e8	+	2.14931e8i	−0.0217584	+	0.0376867i	−0.876700	−	0.481038i	$-0.840260\pi$
$613$	−1.24091e8	+	2.14931e8i	−0.0217584	+	0.0376867i	0.854941	+	0.518725i	$0.173593\pi$
$614$	1.74371e8	−	3.02019e8i	0.0304008	−	0.0526557i
$615$	−3.22979e9			−0.559900
$616$	7.80680e7	+	1.35218e8i	0.0134568	+	0.0233078i
$617$	−4.27718e8	+	7.40830e8i	−0.0733094	+	0.126976i	−0.900350	−	0.435167i	$-0.856689\pi$
$617$	−4.27718e8	+	7.40830e8i	−0.0733094	+	0.126976i	0.827040	+	0.562142i	$0.190023\pi$
$618$	−1.88690e9			−0.321579
$619$	−1.97271e8			−0.0334307			−0.0167154	−	0.999860i	$-0.505321\pi$
$619$	−1.97271e8			−0.0334307			−0.0167154	+	0.999860i	$0.505321\pi$
$620$	−2.44027e9	+	4.22667e9i	−0.411213	+	0.712242i
$621$	−1.25029e10			−2.09503
$622$	6.97410e8	+	1.20795e9i	0.116204	+	0.201271i
$623$	−1.95337e7			−0.00323650
$624$	−2.99056e8	−	5.17980e8i	−0.0492727	−	0.0853429i
$625$	1.24390e9	+	2.15449e9i	0.203800	+	0.352992i
$626$	9.59125e8	+	1.66125e9i	0.156266	+	0.270661i
$627$	7.89834e9	−	1.36803e10i	1.27967	−	2.21646i
$628$	3.71281e8			0.0598196
$629$	7.71064e9	+	2.09892e9i	1.23542	+	0.336294i
$630$	−4.86730e8			−0.0775525
$631$	3.04700e9	−	5.27756e9i	0.482803	−	0.836240i	−0.517002	−	0.855984i	$-0.672952\pi$
$631$	3.04700e9	−	5.27756e9i	0.482803	−	0.836240i	0.999805	+	0.0197445i	$0.00628529\pi$
$632$	−2.59030e9	−	4.48653e9i	−0.408169	−	0.706970i
$633$	−2.00535e9	−	3.47337e9i	−0.314252	−	0.544300i
$634$	−2.99596e8	−	5.18916e8i	−0.0466900	−	0.0808695i
$635$	1.54430e10			2.39345
$636$	4.46126e8	+	7.72712e8i	0.0687634	+	0.119102i
$637$	−6.21895e8			−0.0953299
$638$	−3.14075e8	+	5.43993e8i	−0.0478807	+	0.0829318i
$639$	−2.91118e10			−4.41383
$640$	−1.05007e10			−1.58339
$641$	−3.66208e9	+	6.34291e9i	−0.549193	+	0.951230i	0.449137	+	0.893463i	$0.351731\pi$
$641$	−3.66208e9	+	6.34291e9i	−0.549193	+	0.951230i	−0.998330	+	0.0577669i	$0.981602\pi$
$642$	1.75750e9	+	3.04408e9i	0.262134	+	0.454029i
$643$	1.61710e9			0.239882			0.119941	−	0.992781i	$-0.461729\pi$
$643$	1.61710e9			0.239882			0.119941	+	0.992781i	$0.461729\pi$
$644$	6.68617e7	−	1.15808e8i	0.00986454	−	0.0170859i
$645$	1.46477e9	−	2.53705e9i	0.214936	−	0.372280i
$646$	2.74710e9	−	4.75811e9i	0.400922	−	0.694417i
$647$	−2.39374e8	−	4.14608e8i	−0.0347466	−	0.0601829i	0.848129	−	0.529790i	$-0.177729\pi$
$647$	−2.39374e8	−	4.14608e8i	−0.0347466	−	0.0601829i	−0.882876	+	0.469607i	$0.844396\pi$
$648$	−1.15711e10	−	2.00418e10i	−1.67056	−	2.89350i
$649$	−5.05014e9	+	8.74710e9i	−0.725182	+	1.25605i
$650$	1.94462e8	−	3.36819e8i	0.0277740	−	0.0481060i
$651$	1.85845e8	−	3.21893e8i	0.0264008	−	0.0457276i
$652$	5.87259e9			0.829780
$653$	5.65413e9	+	9.79324e9i	0.794638	+	1.37635i	0.923069	+	0.384635i	$0.125673\pi$
$653$	5.65413e9	+	9.79324e9i	0.794638	+	1.37635i	−0.128430	+	0.991719i	$0.540994\pi$
$654$	1.27002e9	−	2.19974e9i	0.177537	−	0.307503i
$655$	4.04229e9			0.562061
$656$	6.91225e8			0.0955996
$657$	1.16373e10	−	2.01563e10i	1.60093	−	2.77289i
$658$	1.06036e8			0.0145099
$659$	3.95390e9	+	6.84836e9i	0.538179	+	0.932153i	0.999002	+	0.0446615i	$0.0142209\pi$
$659$	3.95390e9	+	6.84836e9i	0.538179	+	0.932153i	−0.460823	+	0.887492i	$0.652446\pi$
$660$	1.60141e10			2.16820
$661$	5.53655e7	+	9.58959e7i	0.00745649	+	0.0129150i	0.869730	−	0.493529i	$-0.164293\pi$
$661$	5.53655e7	+	9.58959e7i	0.00745649	+	0.0129150i	−0.862273	+	0.506444i	$0.830960\pi$
$662$	8.80551e8	+	1.52516e9i	0.117965	+	0.204321i
$663$	9.04466e8	+	1.56658e9i	0.120530	+	0.208764i
$664$	3.89948e9	−	6.75410e9i	0.516914	−	0.895322i
$665$	−7.58114e8			−0.0999675
$666$	−6.40926e9	+	6.35855e9i	−0.840714	+	0.834062i
$667$	1.18483e9			0.154602
$668$	−3.60992e9	+	6.25257e9i	−0.468576	+	0.811598i
$669$	−4.50137e9	−	7.79659e9i	−0.581237	−	1.00673i
$670$	−1.52016e9	−	2.63300e9i	−0.195266	−	0.338211i
$671$	−2.58285e9	−	4.47363e9i	−0.330043	−	0.571652i
$672$	6.31071e8			0.0802206
$673$	6.17744e8	+	1.06996e9i	0.0781189	+	0.135306i	0.902438	−	0.430819i	$-0.141775\pi$
$673$	6.17744e8	+	1.06996e9i	0.0781189	+	0.135306i	−0.824319	+	0.566125i	$0.808442\pi$
$674$	−4.55163e9			−0.572608
$675$	−2.10690e10	+	3.64925e10i	−2.63682	+	4.56710i
$676$	6.61911e9			0.824112
$677$	4.77061e8			0.0590899			0.0295450	−	0.999563i	$-0.490594\pi$
$677$	4.77061e8			0.0590899			0.0295450	+	0.999563i	$0.490594\pi$
$678$	4.59034e8	−	7.95070e8i	0.0565641	−	0.0979719i
$679$	−1.55414e8	−	2.69185e8i	−0.0190522	−	0.0329994i
$680$	1.22667e10			1.49606
$681$	−1.06675e10	+	1.84767e10i	−1.29434	+	2.24186i
$682$	9.18996e8	−	1.59175e9i	0.110935	−	0.192145i
$683$	−6.60801e9	+	1.14454e10i	−0.793593	+	1.37454i	0.130135	+	0.991496i	$0.458459\pi$
$683$	−6.60801e9	+	1.14454e10i	−0.793593	+	1.37454i	−0.923729	+	0.383048i	$0.874874\pi$
$684$	−1.53369e10	−	2.65643e10i	−1.83249	−	3.17397i
$685$	−3.14848e9	−	5.45333e9i	−0.374269	−	0.648253i
$686$	1.45960e8	−	2.52810e8i	0.0172623	−	0.0298992i
$687$	−2.83759e9	+	4.91486e9i	−0.333889	+	0.578312i
$688$	−3.13483e8	+	5.42968e8i	−0.0366990	+	0.0635645i
$689$	6.87702e7			0.00801001
$690$	3.05628e9	+	5.29363e9i	0.354178	+	0.613454i
$691$	6.29549e9	−	1.09041e10i	0.725866	−	1.25724i	−0.232750	−	0.972536i	$-0.574773\pi$
$691$	6.29549e9	−	1.09041e10i	0.725866	−	1.25724i	0.958617	−	0.284700i	$-0.0918941\pi$
$692$	−1.06654e10			−1.22351
$693$	−9.05807e8			−0.103388
$694$	−1.23311e9	+	2.13581e9i	−0.140038	+	0.242552i
$695$	5.47362e9			0.618483
$696$	1.80844e9	+	3.13231e9i	0.203316	+	0.352153i
$697$	−2.09054e9			−0.233854
$698$	−2.84741e9	−	4.93187e9i	−0.316925	−	0.548930i
$699$	8.28015e9	+	1.43416e10i	0.916998	+	1.58829i
$700$	−2.25340e8	−	3.90301e8i	−0.0248311	−	0.0430087i
$701$	1.34064e9	−	2.32206e9i	0.146994	−	0.254601i	−0.783121	−	0.621869i	$-0.786374\pi$
$701$	1.34064e9	−	2.32206e9i	0.146994	−	0.254601i	0.930115	+	0.367268i	$0.119707\pi$
$702$	−1.33572e9			−0.145725
$703$	−9.98286e9	+	9.90387e9i	−1.08371	+	1.07513i
$704$	−1.00020e9			−0.108039
$705$	1.19760e10	−	2.07431e10i	1.28722	−	2.22952i
$706$	−8.76755e8	−	1.51858e9i	−0.0937695	−	0.162414i
$707$	−6.76810e7	−	1.17227e8i	−0.00720276	−	0.0124756i
$708$	1.32034e10	+	2.28689e10i	1.39820	+	2.42175i
$709$	−4.50987e9			−0.475228			−0.237614	−	0.971360i	$-0.576365\pi$
$709$	−4.50987e9			−0.475228			−0.237614	+	0.971360i	$0.576365\pi$
$710$	4.65103e9	+	8.05583e9i	0.487692	+	0.844707i
$711$	3.00547e10			3.13595
$712$	−2.78091e8	+	4.81668e8i	−0.0288740	+	0.0500112i
$713$	−3.46686e9			−0.358198
$714$	−4.24183e8			−0.0436124
$715$	6.17143e8	−	1.06892e9i	0.0631414	−	0.109364i
$716$	4.48512e9	+	7.76846e9i	0.456645	+	0.790932i
$717$	−2.99031e10			−3.02970
$718$	1.10905e9	−	1.92094e9i	0.111819	−	0.193677i
$719$	3.10494e9	−	5.37791e9i	0.311531	−	0.539588i	−0.667163	−	0.744912i	$-0.732491\pi$
$719$	3.10494e9	−	5.37791e9i	0.311531	−	0.539588i	0.978694	+	0.205324i	$0.0658248\pi$
$720$	1.17650e10	−	2.03776e10i	1.17470	−	2.03465i
$721$	8.42625e7	+	1.45947e8i	0.00837261	+	0.0145018i
$722$	2.75965e9	+	4.77985e9i	0.272881	+	0.472644i
$723$	1.24283e10	−	2.15264e10i	1.22300	−	2.11830i
$724$	1.46925e9	−	2.54482e9i	0.143883	−	0.249213i
$725$	1.99658e9	−	3.45818e9i	0.194583	−	0.337027i
$726$	2.30815e9			0.223865
$727$	1.87322e9	+	3.24451e9i	0.180808	+	0.313169i	0.942156	−	0.335175i	$-0.108795\pi$
$727$	1.87322e9	+	3.24451e9i	0.180808	+	0.313169i	−0.761348	+	0.648344i	$0.775462\pi$
$728$	1.57314e7	−	2.72476e7i	0.00151115	−	0.00261739i
$729$	5.75525e10			5.50196
$730$	−7.43691e9			−0.707558
$731$	9.48099e8	−	1.64216e9i	0.0897724	−	0.155490i
$732$	−1.35055e10			−1.27269
$733$	−5.29240e9	−	9.16671e9i	−0.496351	−	0.859705i	0.503640	−	0.863914i	$-0.331994\pi$
$733$	−5.29240e9	−	9.16671e9i	−0.496351	−	0.859705i	−0.999991	+	0.00420836i	$0.998660\pi$
$734$	5.89023e9			0.549789
$735$	−1.64705e10	−	2.85277e10i	−1.53003	−	2.65009i
$736$	−2.94309e9	−	5.09758e9i	−0.272102	−	0.471294i
$737$	−2.82903e9	−	4.90002e9i	−0.260316	−	0.450881i
$738$	1.18092e9	−	2.04542e9i	0.108149	−	0.187320i
$739$	−1.00868e10			−0.919387			−0.459693	−	0.888078i	$-0.652041\pi$
$739$	−1.00868e10			−0.919387			−0.459693	+	0.888078i	$0.652041\pi$
$740$	−1.37552e10	−	3.74431e9i	−1.24783	−	0.339672i
$741$	−3.18318e9			−0.287407
$742$	−8.06309e6	+	1.39657e7i	−0.000724582	+	0.00125501i
$743$	−6.69375e9	−	1.15939e10i	−0.598699	−	1.03698i	−0.993013	−	0.118002i	$-0.962351\pi$
$743$	−6.69375e9	−	1.15939e10i	−0.598699	−	1.03698i	0.394314	−	0.918976i	$-0.370982\pi$
$744$	−5.29157e9	−	9.16526e9i	−0.471063	−	0.815905i
$745$	−1.12958e9	−	1.95648e9i	−0.100085	−	0.173352i
$746$	−2.09952e9			−0.185155
$747$	2.26224e10	+	3.91832e10i	1.98572	+	3.43936i
$748$	1.03655e10			0.905592
$749$	1.56968e8	−	2.71877e8i	0.0136498	−	0.0236421i
$750$	6.07093e9			0.525461
$751$	1.78491e10			1.53772			0.768860	−	0.639417i	$-0.220824\pi$
$751$	1.78491e10			1.53772			0.768860	+	0.639417i	$0.220824\pi$
$752$	−2.56306e9	+	4.43936e9i	−0.219784	+	0.380678i
$753$	−8.20545e9	−	1.42123e10i	−0.700358	−	1.21306i
$754$	1.26578e8			0.0107537
$755$	1.33641e10	−	2.31474e10i	1.13012	−	1.95743i
$756$	−7.73905e8	+	1.34044e9i	−0.0651420	+	0.112829i
$757$	6.59359e9	−	1.14204e10i	0.552442	−	0.956857i	−0.445656	−	0.895204i	$-0.647030\pi$
$757$	6.59359e9	−	1.14204e10i	0.552442	−	0.956857i	0.998098	−	0.0616528i	$-0.0196371\pi$
$758$	2.21404e9	+	3.83483e9i	0.184648	+	0.319819i
$759$	5.68776e9	+	9.85148e9i	0.472166	+	0.817816i
$760$	−1.07929e10	+	1.86938e10i	−0.891847	+	1.54472i
$761$	−3.04576e9	+	5.27542e9i	−0.250524	+	0.433921i	−0.963670	−	0.267095i	$-0.913936\pi$
$761$	−3.04576e9	+	5.27542e9i	−0.250524	+	0.433921i	0.713146	+	0.701016i	$0.247270\pi$
$762$	−7.60255e9	+	1.31680e10i	−0.622468	+	1.07815i
$763$	−2.26860e8			−0.0184894
$764$	−4.74043e9	−	8.21067e9i	−0.384584	−	0.666119i
$765$	−3.55821e10	+	6.16300e10i	−2.87354	+	4.97711i
$766$	2.93863e9			0.236235
$767$	2.03530e9			0.162871
$768$	3.59739e9	−	6.23086e9i	0.286565	−	0.496345i
$769$	−7.95936e9			−0.631155			−0.315577	−	0.948900i	$-0.602198\pi$
$769$	−7.95936e9			−0.631155			−0.315577	+	0.948900i	$0.602198\pi$
$770$	1.44716e8	+	2.50656e8i	0.0114235	+	0.0197861i
$771$	3.03163e10			2.38224
$772$	5.34387e9	+	9.25586e9i	0.418019	+	0.724030i
$773$	−9.28968e9	−	1.60902e10i	−0.723390	−	1.25295i	−0.959633	−	0.281254i	$-0.909250\pi$
$773$	−9.28968e9	−	1.60902e10i	−0.723390	−	1.25295i	0.236243	−	0.971694i	$-0.424084\pi$
$774$	1.07114e9	+	1.85527e9i	0.0830333	+	0.143818i
$775$	−5.84208e9	+	1.01188e10i	−0.450829	+	0.780859i
$776$	−8.85021e9			−0.679888
$777$	1.04756e9	+	2.85157e8i	0.0801135	+	0.0218078i
$778$	2.01723e9			0.153577
$779$	1.83937e9	−	3.18588e9i	0.139408	−	0.241461i
$780$	−1.61350e9	−	2.79466e9i	−0.121741	−	0.210862i
$781$	8.65561e9	+	1.49919e10i	0.650158	+	1.12611i
$782$	1.97824e9	+	3.42641e9i	0.147930	+	0.256222i
$783$	−1.37141e10			−1.02094
$784$	3.52494e9	+	6.10538e9i	0.261244	+	0.452488i
$785$	1.51577e9			0.111838
$786$	−1.99001e9	+	3.44680e9i	−0.146176	+	0.253185i
$787$	2.20070e10			1.60935			0.804674	−	0.593716i	$-0.202340\pi$
$787$	2.20070e10			1.60935			0.804674	+	0.593716i	$0.202340\pi$
$788$	−2.75028e9			−0.200233
$789$	−2.50044e10	+	4.33090e10i	−1.81237	+	3.13912i
$790$	−4.80169e9	−	8.31676e9i	−0.346497	−	0.600150i
$791$	−8.19957e7			−0.00589079
$792$	−1.28955e10	+	2.23357e10i	−0.922361	+	1.59758i
$793$	−5.20469e8	+	9.01479e8i	−0.0370629	+	0.0641947i
$794$	4.77284e9	−	8.26681e9i	0.338381	−	0.586092i
$795$	1.82133e9	+	3.15464e9i	0.128560	+	0.222672i
$796$	2.14858e9	+	3.72145e9i	0.150993	+	0.261527i
$797$	8.36387e9	−	1.44867e10i	0.585199	−	1.01359i	−0.409652	−	0.912242i	$-0.634350\pi$
$797$	8.36387e9	−	1.44867e10i	0.585199	−	1.01359i	0.994851	−	0.101352i	$-0.0323168\pi$
$798$	3.73218e8	−	6.46432e8i	0.0259987	−	0.0450311i
$799$	7.75174e9	−	1.34264e10i	0.537632	−	0.931206i
$800$	−1.98379e10			−1.36987
$801$	−1.61332e9	−	2.79435e9i	−0.110919	−	0.192117i
$802$	−1.84524e8	+	3.19605e8i	−0.0126311	+	0.0218778i
$803$	−1.38401e10			−0.943269
$804$	−1.47928e10			−1.00381
$805$	2.72967e8	−	4.72792e8i	0.0184427	−	0.0319437i
$806$	−3.70373e8			−0.0249153
$807$	−2.23148e10	−	3.86504e10i	−1.49464	−	2.58879i
$808$	−3.85416e9			−0.257034
$809$	−1.47480e8	−	2.55443e8i	−0.00979296	−	0.0169619i	0.861087	−	0.508457i	$-0.169784\pi$
$809$	−1.47480e8	−	2.55443e8i	−0.00979296	−	0.0169619i	−0.870880	+	0.491495i	$0.836451\pi$
$810$	−2.14496e10	−	3.71518e10i	−1.41815	−	2.45631i
$811$	−9.11355e9	−	1.57851e10i	−0.599949	−	1.03914i	−0.992828	−	0.119552i	$-0.961854\pi$
$811$	−9.11355e9	−	1.57851e10i	−0.599949	−	1.03914i	0.392879	−	0.919590i	$-0.371479\pi$
$812$	7.33384e7	−	1.27026e8i	0.00480712	−	0.00832618i
$813$	−2.54327e10			−1.65987
$814$	5.18014e9	+	1.41009e9i	0.336633	+	0.0916350i
$815$	2.39752e10			1.55135
$816$	1.02532e10	−	1.77590e10i	0.660605	−	1.14420i
$817$	1.66837e9	+	2.88970e9i	0.107032	+	0.185386i
$818$	2.94517e9	+	5.10119e9i	0.188137	+	0.325863i
$819$	9.12643e7	+	1.58074e8i	0.00580507	+	0.0100547i
$820$	3.72936e9			0.236203
$821$	−1.07526e10	−	1.86241e10i	−0.678131	−	1.17456i	−0.975543	−	0.219808i	$-0.929457\pi$
$821$	−1.07526e10	−	1.86241e10i	−0.678131	−	1.17456i	0.297413	−	0.954749i	$-0.403876\pi$
$822$	6.19996e9			0.389347
$823$	9.42534e8	−	1.63252e9i	0.0589383	−	0.102084i	−0.835051	−	0.550173i	$-0.814562\pi$
$823$	9.42534e8	−	1.63252e9i	0.0589383	−	0.102084i	0.893989	+	0.448089i	$0.147895\pi$
$824$	4.79841e9			0.298781
$825$	3.83383e10			2.37708
$826$	−2.38633e8	+	4.13324e8i	−0.0147333	+	0.0255188i
$827$	−3.37020e9	−	5.83736e9i	−0.207199	−	0.358878i	0.743632	−	0.668589i	$-0.233101\pi$
$827$	−3.37020e9	−	5.83736e9i	−0.207199	−	0.358878i	−0.950831	+	0.309710i	$0.899768\pi$
$828$	2.20888e10			1.35228
$829$	2.37809e9	−	4.11897e9i	0.144973	−	0.251101i	−0.784390	−	0.620268i	$-0.787024\pi$
$829$	2.37809e9	−	4.11897e9i	0.144973	−	0.251101i	0.929363	+	0.369168i	$0.120357\pi$
$830$	7.22854e9	−	1.25202e10i	0.438811	−	0.760042i
$831$	−1.75006e10	+	3.03120e10i	−1.05791	+	1.83236i
$832$	1.00775e8	+	1.74547e8i	0.00606624	+	0.0105070i
$833$	−1.06609e10	−	1.84651e10i	−0.639050	−	1.10687i
$834$	−2.69465e9	+	4.66727e9i	−0.160850	+	0.278600i
$835$	−1.47377e10	+	2.55265e10i	−0.876047	+	1.51736i
$836$	−9.12005e9	+	1.57964e10i	−0.539853	+	0.935052i
$837$	4.01279e10			2.36542
$838$	1.57366e9	+	2.72565e9i	0.0923752	+	0.159999i
$839$	−6.60494e9	+	1.14401e10i	−0.386102	+	0.668749i	−0.991921	−	0.126854i	$-0.959512\pi$
$839$	−6.60494e9	+	1.14401e10i	−0.386102	+	0.668749i	0.605819	+	0.795602i	$0.292845\pi$
$840$	1.66655e9			0.0970153
$841$	−1.59503e10			−0.924660
$842$	5.18507e9	−	8.98080e9i	0.299338	−	0.518469i
$843$	−2.18344e10			−1.25529
$844$	2.31554e9	+	4.01063e9i	0.132572	+	0.229622i
$845$	2.70229e10			1.54075
$846$	8.75772e9	+	1.51688e10i	0.497273	+	0.861302i
$847$	−1.03075e8	−	1.78530e8i	−0.00582854	−	0.0100953i
$848$	−3.89794e8	−	6.75143e8i	−0.0219508	−	0.0380199i
$849$	−1.52081e10	+	2.63412e10i	−0.852900	+	1.47727i
$850$	1.33343e10			0.744739
$851$	−2.58205e9	−	9.79172e9i	−0.143618	−	0.544635i
$852$	4.52595e10			2.50710
$853$	−3.31416e9	+	5.74030e9i	−0.182832	+	0.316674i	−0.942844	−	0.333235i	$-0.891860\pi$
$853$	−3.31416e9	+	5.74030e9i	−0.182832	+	0.316674i	0.760012	+	0.649909i	$0.225193\pi$
$854$	−1.22047e8	−	2.11391e8i	−0.00670538	−	0.0116141i
$855$	−6.26139e10	−	1.08450e11i	−3.42601	−	5.93403i
$856$	−4.46936e9	−	7.74116e9i	−0.243550	−	0.421840i
$857$	9.22050e9			0.500405			0.250203	−	0.968194i	$-0.419503\pi$
$857$	9.22050e9			0.500405			0.250203	+	0.968194i	$0.419503\pi$
$858$	6.07636e8	+	1.05246e9i	0.0328426	+	0.0568851i
$859$	−2.87653e10			−1.54844			−0.774219	−	0.632918i	$-0.781857\pi$
$859$	−2.87653e10			−1.54844			−0.774219	+	0.632918i	$0.781857\pi$
$860$	−1.69133e9	+	2.92947e9i	−0.0906744	+	0.157053i
$861$	−2.84019e8			−0.0151648
$862$	−7.07698e8			−0.0376333
$863$	1.49649e9	−	2.59200e9i	0.0792567	−	0.137277i	−0.823673	−	0.567065i	$-0.808079\pi$
$863$	1.49649e9	−	2.59200e9i	0.0792567	−	0.137277i	0.902929	+	0.429789i	$0.141412\pi$
$864$	3.40654e10	+	5.90031e10i	1.79687	+	3.11226i
$865$	−4.35422e10			−2.28746
$866$	−8.02039e8	+	1.38917e9i	−0.0419646	+	0.0726848i
$867$	−1.20938e10	+	2.09471e10i	−0.630226	+	1.09158i
$868$	−2.14591e8	+	3.71683e8i	−0.0111376	+	0.0192910i
$869$	−8.93597e9	−	1.54775e10i	−0.461926	−	0.800079i
$870$	3.35233e9	+	5.80641e9i	0.172596	+	0.298945i
$871$	−5.70076e8	+	9.87401e8i	−0.0292327	+	0.0506326i
$872$	−3.22969e9	+	5.59399e9i	−0.164950	+	0.285702i
$873$	2.56718e10	−	4.44648e10i	1.30589	−	2.26187i
$874$	−6.96222e9			−0.352742
$875$	−2.71108e8	−	4.69572e8i	−0.0136809	−	0.0236960i
$876$	−1.80922e10	+	3.13367e10i	−0.909344	+	1.57503i
$877$	3.25322e10			1.62860			0.814300	−	0.580444i	$-0.197121\pi$
$877$	3.25322e10			1.62860			0.814300	+	0.580444i	$0.197121\pi$
$878$	−1.24662e10			−0.621590
$879$	−2.44767e10	+	4.23949e10i	−1.21560	+	2.10549i
$880$	−1.39920e10			−0.692136
$881$	6.70718e9	+	1.16172e10i	0.330464	+	0.572381i	0.982603	−	0.185719i	$-0.0594613\pi$
$881$	6.70718e9	+	1.16172e10i	0.330464	+	0.572381i	−0.652139	+	0.758100i	$0.726128\pi$
$882$	2.40887e10			1.18215
$883$	1.24197e10	+	2.15116e10i	0.607085	+	1.05150i	0.991718	+	0.128433i	$0.0409946\pi$
$883$	1.24197e10	+	2.15116e10i	0.607085	+	1.05150i	−0.384633	+	0.923070i	$0.625672\pi$
$884$	−1.04437e9	−	1.80890e9i	−0.0508476	−	0.0880706i
$885$	5.39036e10	+	9.33638e10i	2.61407	+	4.52769i
$886$	4.42219e9	−	7.65946e9i	0.213609	−	0.369982i
$887$	8.91068e9			0.428724			0.214362	−	0.976754i	$-0.431233\pi$
$887$	8.91068e9			0.428724			0.214362	+	0.976754i	$0.431233\pi$
$888$	2.19451e10	−	2.17715e10i	1.05170	−	1.04338i
$889$	1.35802e9			0.0648261
$890$	−5.15502e8	+	8.92876e8i	−0.0245113	+	0.0424548i
$891$	−3.99179e10	−	6.91398e10i	−1.89058	−	3.27458i
$892$	5.19763e9	+	9.00256e9i	0.245205	+	0.424707i
$893$	1.36407e10	+	2.36265e10i	0.641000	+	1.11024i
$894$	2.22435e9			0.104117
$895$	1.83108e10	+	3.17152e10i	0.853741	+	1.47872i
$896$	−9.23404e8			−0.0428858
$897$	1.14614e9	−	1.98517e9i	0.0530228	−	0.0918382i
$898$	−1.07242e10			−0.494194
$899$	−3.80269e9			−0.174555
$900$	3.72224e10	−	6.44711e10i	1.70199	−	2.94793i
$901$	1.17890e9	+	2.04191e9i	0.0536956	+	0.0930035i
$902$	−1.40446e9			−0.0637217
$903$	1.28808e8	−	2.23102e8i	0.00582150	−	0.0100831i
$904$	−1.16733e9	+	2.02188e9i	−0.0525539	+	0.0910260i
$905$	5.99830e9	−	1.03894e10i	0.269004	−	0.465928i
$906$	1.31583e10	+	2.27908e10i	0.587827	+	1.01815i
$907$	−9.78533e9	−	1.69487e10i	−0.435462	−	0.754242i	0.561871	−	0.827225i	$-0.310082\pi$
$907$	−9.78533e9	−	1.69487e10i	−0.435462	−	0.754242i	−0.997333	+	0.0729826i	$0.976748\pi$
$908$	1.23176e10	−	2.13346e10i	0.546039	−	0.945768i
$909$	1.11798e10	−	1.93639e10i	0.493696	−	0.855106i
$910$	2.91617e7	−	5.05095e7i	0.00128282	−	0.00222192i
$911$	2.44524e10			1.07154			0.535769	−	0.844364i	$-0.320022\pi$
$911$	2.44524e10			1.07154			0.535769	+	0.844364i	$0.320022\pi$
$912$	1.80425e10	+	3.12505e10i	0.787616	+	1.36419i
$913$	1.34524e10	−	2.33002e10i	0.584993	−	1.01324i
$914$	−6.09730e8			−0.0264135
$915$	−5.51371e10			−2.37942
$916$	3.27651e9	−	5.67508e9i	0.140857	−	0.243971i
$917$	3.55469e8			0.0152233
$918$	−2.28975e10	−	3.96597e10i	−0.976876	−	1.69200i
$919$	−3.80616e9			−0.161764			−0.0808822	−	0.996724i	$-0.525774\pi$
$919$	−3.80616e9			−0.161764			−0.0808822	+	0.996724i	$0.525774\pi$
$920$	−7.77218e9	−	1.34618e10i	−0.329068	−	0.569962i
$921$	−3.46367e9	−	5.99926e9i	−0.146093	−	0.253040i
$922$	4.12575e9	+	7.14602e9i	0.173358	+	0.300266i
$923$	1.74419e9	−	3.02102e9i	0.0730108	−	0.126458i
$924$	1.40824e9			0.0587253
$925$	−3.29303e10	−	8.96399e9i	−1.36804	−	0.372396i
$926$	2.57033e9			0.106378
$927$	−1.39188e10	+	2.41080e10i	−0.573880	+	0.993990i
$928$	−3.22818e9	−	5.59137e9i	−0.132599	−	0.229668i
$929$	1.31702e10	+	2.28114e10i	0.538936	+	0.933464i	0.998962	+	0.0455586i	$0.0145068\pi$
$929$	1.31702e10	+	2.28114e10i	0.538936	+	0.933464i	−0.460026	+	0.887905i	$0.652160\pi$
$930$	−9.80908e9	−	1.69898e10i	−0.399887	−	0.692625i
$931$	3.75198e10			1.52383
$932$	−9.56092e9	−	1.65600e10i	−0.386851	−	0.670046i
$933$	2.77064e10			1.11685
$934$	2.07769e9	−	3.59867e9i	0.0834387	−	0.144520i
$935$	4.23176e10			1.69309
$936$	5.19714e9			0.207157
$937$	9.83787e9	−	1.70397e10i	0.390672	−	0.676664i	−0.601866	−	0.798597i	$-0.705576\pi$
$937$	9.83787e9	−	1.70397e10i	0.390672	−	0.676664i	0.992538	+	0.121933i	$0.0389093\pi$
$938$	−1.33679e8	−	2.31539e8i	−0.00528876	−	0.00916040i
$939$	3.81038e10			1.50189
$940$	−1.38285e10	+	2.39516e10i	−0.543034	+	0.940563i
$941$	−1.90139e10	+	3.29331e10i	−0.743890	+	1.28845i	0.206822	+	0.978379i	$0.433688\pi$
$941$	−1.90139e10	+	3.29331e10i	−0.743890	+	1.28845i	−0.950712	+	0.310076i	$0.899645\pi$
$942$	−7.46213e8	+	1.29248e9i	−0.0290860	+	0.0503785i
$943$	1.32456e9	+	2.29421e9i	0.0514378	+	0.0890929i
$944$	−1.15362e10	−	1.99813e10i	−0.446336	−	0.773076i
$945$	−3.15951e9	+	5.47243e9i	−0.121789	+	0.210945i
$946$	6.36949e8	−	1.10323e9i	0.0244616	−	0.0423688i
$947$	5.99911e9	−	1.03908e10i	0.229542	−	0.397578i	−0.728130	−	0.685439i	$-0.759611\pi$
$947$	5.99911e9	−	1.03908e10i	0.229542	−	0.397578i	0.957672	+	0.287860i	$0.0929438\pi$
$948$	−4.67255e10			−1.78125
$949$	1.39446e9	+	2.41527e9i	0.0529631	+	0.0917349i
$950$	−1.17322e10	+	2.03208e10i	−0.443963	+	0.768966i
$951$	−1.19022e10			−0.448743
$952$	1.07871e9			0.0405204
$953$	7.11633e9	−	1.23258e10i	0.266337	−	0.461308i	−0.701576	−	0.712594i	$-0.747520\pi$
$953$	7.11633e9	−	1.23258e10i	0.266337	−	0.461308i	0.967913	+	0.251286i	$0.0808534\pi$
$954$	−2.66377e9			−0.0993294
$955$	−1.93531e10	−	3.35205e10i	−0.719016	−	1.24537i
$956$	3.45285e10			1.27813
$957$	6.23872e9	+	1.08058e10i	0.230093	+	0.398533i
$958$	6.19544e9	+	1.07308e10i	0.227663	+	0.394325i
$959$	−2.76870e8	−	4.79552e8i	−0.0101370	−	0.0175578i
$960$	−5.33791e9	+	9.24552e9i	−0.194725	+	0.337273i
$961$	−1.63858e10			−0.595574
$962$	−2.75846e8	−	1.04607e9i	−0.00998973	−	0.0378834i
$963$	5.18571e10			1.87118
$964$	−1.43507e10	+	2.48561e10i	−0.515943	+	0.893640i
$965$	2.18167e10	+	3.77876e10i	0.781525	+	1.35364i
$966$	2.68762e8	+	4.65509e8i	0.00959285	+	0.0166153i
$967$	6.37778e9	+	1.10466e10i	0.226818	+	0.392860i	0.956863	−	0.290539i	$-0.0938345\pi$
$967$	6.37778e9	+	1.10466e10i	0.226818	+	0.392860i	−0.730046	+	0.683398i	$0.760501\pi$
$968$	−5.86968e9			−0.207994
$969$	−5.45678e10	−	9.45142e10i	−1.92665	−	3.33706i
$970$	−1.64058e10			−0.577160
$971$	1.20449e10	−	2.08624e10i	0.422219	−	0.731304i	−0.573938	−	0.818899i	$-0.694585\pi$
$971$	1.20449e10	−	2.08624e10i	0.422219	−	0.731304i	0.996156	+	0.0875950i	$0.0279181\pi$
$972$	−1.20158e11			−4.19682
$973$	4.81336e8			0.0167515
$974$	−3.50270e9	+	6.06686e9i	−0.121464	+	0.210381i
$975$	−3.86276e9	−	6.69050e9i	−0.133469	−	0.231176i
$976$	1.18002e10			0.406271
$977$	3.32935e9	−	5.76660e9i	0.114216	−	0.197828i	−0.803250	−	0.595642i	$-0.796898\pi$
$977$	3.32935e9	−	5.76660e9i	0.114216	−	0.197828i	0.917466	+	0.397814i	$0.130231\pi$
$978$	−1.18029e10	+	2.04433e10i	−0.403463	+	0.698818i
$979$	−9.59353e8	+	1.66165e9i	−0.0326768	+	0.0565978i
$980$	1.90181e10	+	3.29403e10i	0.645470	+	1.11799i
$981$	−1.87367e10	−	3.24529e10i	−0.633654	−	1.09752i
$982$	−6.46668e8	+	1.12006e9i	−0.0217917	+	0.0377444i
$983$	5.40567e8	−	9.36289e8i	0.0181515	−	0.0314393i	−0.856807	−	0.515637i	$-0.827555\pi$
$983$	5.40567e8	−	9.36289e8i	0.0181515	−	0.0314393i	0.874958	+	0.484198i	$0.160889\pi$
$984$	−4.04344e9	+	7.00345e9i	−0.135291	+	0.234331i
$985$	−1.12282e10			−0.374355
$986$	2.16987e9	+	3.75832e9i	0.0720881	+	0.124860i
$987$	1.05314e9	−	1.82410e9i	0.0348640	−	0.0603863i
$988$	3.67555e9			0.121248
$989$	−2.40285e9			−0.0789842
$990$	−2.39047e10	+	4.14041e10i	−0.782996	+	1.35619i
$991$	−7.81850e8			−0.0255191			−0.0127596	−	0.999919i	$-0.504062\pi$
$991$	−7.81850e8			−0.0255191			−0.0127596	+	0.999919i	$0.504062\pi$
$992$	9.44580e9	+	1.63606e10i	0.307219	+	0.532119i
$993$	3.49822e10			1.13377
$994$	4.09001e8	+	7.08410e8i	0.0132091	+	0.0228787i
$995$	8.77171e9	+	1.51930e10i	0.282295	+	0.488950i
$996$	−3.51707e10	−	6.09174e10i	−1.12791	−	1.95359i
$997$	2.60867e10	−	4.51835e10i	0.833655	−	1.44393i	−0.0614652	−	0.998109i	$-0.519577\pi$
$997$	2.60867e10	−	4.51835e10i	0.833655	−	1.44393i	0.895121	−	0.445824i	$-0.147089\pi$
$998$	−1.75055e10			−0.557464
$999$	2.98864e10	+	1.13336e11i	0.948407	+	3.59658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.c.a.10.13	✓	42
37.26	even	3	inner	37.8.c.a.26.13	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.c.a.10.13	✓	42	1.1	even	1	trivial
37.8.c.a.26.13	yes	42	37.26	even	3	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.32071 - 4.01959i) q^{2} +(-46.0982 - 79.8444i) q^{3} +(53.2286 + 92.1946i) q^{4} +(217.309 + 376.390i) q^{5} -427.923 q^{6} +(19.1096 + 33.0988i) q^{7} +1088.22 q^{8} +(-3156.59 + 5467.37i) q^{9} +O(q^{10})\)	\(q+(2.32071 - 4.01959i) q^{2} +(-46.0982 - 79.8444i) q^{3} +(53.2286 + 92.1946i) q^{4} +(217.309 + 376.390i) q^{5} -427.923 q^{6} +(19.1096 + 33.0988i) q^{7} +1088.22 q^{8} +(-3156.59 + 5467.37i) q^{9} +2017.24 q^{10} +3754.11 q^{11} +(4907.48 - 8500.01i) q^{12} +(-378.244 - 655.137i) q^{13} +177.392 q^{14} +(20035.1 - 34701.8i) q^{15} +(-4287.82 + 7426.73i) q^{16} +(12968.1 - 22461.4i) q^{17} +(14651.1 + 25376.4i) q^{18} +(22820.0 + 39525.4i) q^{19} +(-23134.1 + 40069.4i) q^{20} +(1761.84 - 3051.59i) q^{21} +(8712.20 - 15090.0i) q^{22} -32866.3 q^{23} +(-50164.8 - 86887.9i) q^{24} +(-55383.7 + 95927.4i) q^{25} -3511.18 q^{26} +380418. q^{27} +(-2034.35 + 3523.61i) q^{28} -36050.0 q^{29} +(-92991.3 - 161066. i) q^{30} +105484. q^{31} +(89547.4 + 155101. i) q^{32} +(-173057. - 299744. i) q^{33} +(-60190.5 - 104253. i) q^{34} +(-8305.37 + 14385.3i) q^{35} -672082. q^{36} +(78562.1 + 297926. i) q^{37} +211835. q^{38} +(-34872.7 + 60401.3i) q^{39} +(236479. + 409593. i) q^{40} +(-40301.6 - 69804.5i) q^{41} +(-8177.43 - 14163.7i) q^{42} +73110.0 q^{43} +(199826. + 346108. i) q^{44} -2.74381e6 q^{45} +(-76273.2 + 132109. i) q^{46} +597754. q^{47} +790644. q^{48} +(411041. - 711944. i) q^{49} +(257059. + 445240. i) q^{50} -2.39123e6 q^{51} +(40266.8 - 69744.1i) q^{52} +(-45453.6 + 78728.0i) q^{53} +(882841. - 1.52912e6i) q^{54} +(815800. + 1.41301e6i) q^{55} +(20795.4 + 36018.6i) q^{56} +(2.10392e6 - 3.64410e6i) q^{57} +(-83661.6 + 144906. i) q^{58} +(-1.34523e6 + 2.33001e6i) q^{59} +4.26576e6 q^{60} +(-688007. - 1.19166e6i) q^{61} +(244797. - 424002. i) q^{62} -241284. q^{63} -266428. q^{64} +(164391. - 284734. i) q^{65} -1.60647e6 q^{66} +(-753583. - 1.30524e6i) q^{67} +2.76110e6 q^{68} +(1.51508e6 + 2.62419e6i) q^{69} +(38548.8 + 66768.4i) q^{70} +(2.30564e6 + 3.99348e6i) q^{71} +(-3.43504e6 + 5.94967e6i) q^{72} -3.68666e6 q^{73} +(1.37986e6 + 375613. i) q^{74} +1.02124e7 q^{75} +(-2.42935e6 + 4.20776e6i) q^{76} +(71739.5 + 124256. i) q^{77} +(161859. + 280348. i) q^{78} +(-2.38032e6 - 4.12283e6i) q^{79} -3.72713e6 q^{80} +(-1.06331e7 - 1.84171e7i) q^{81} -374114. q^{82} +(3.58337e6 - 6.20658e6i) q^{83} +375120. q^{84} +1.12723e7 q^{85} +(169667. - 293872. i) q^{86} +(1.66184e6 + 2.87839e6i) q^{87} +4.08528e6 q^{88} +(-255548. + 442622. i) q^{89} +(-6.36761e6 + 1.10290e7i) q^{90} +(14456.2 - 25038.8i) q^{91} +(-1.74943e6 - 3.03009e6i) q^{92} +(-4.86261e6 - 8.42229e6i) q^{93} +(1.38721e6 - 2.40273e6i) q^{94} +(-9.91797e6 + 1.71784e7i) q^{95} +(8.25594e6 - 1.42997e7i) q^{96} -8.13277e6 q^{97} +(-1.90782e6 - 3.30444e6i) q^{98} +(-1.18502e7 + 2.05251e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9}+O(q^{10}) \) 42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9	\( 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9} + 10028 q^{10} + 14876 q^{11} - 4836 q^{12} - 5922 q^{13} + 20176 q^{14} - 8460 q^{15} - 36726 q^{16} - 19095 q^{17} - 7338 q^{18} - 34334 q^{19} - 75668 q^{20} - 32764 q^{21} + 18526 q^{22} - 99896 q^{23} - 203760 q^{24} - 322660 q^{25} + 101516 q^{26} + 846616 q^{27} - 73490 q^{28} + 168186 q^{29} - 88790 q^{30} - 38052 q^{31} - 172292 q^{32} - 54536 q^{33} + 90724 q^{34} - 247046 q^{35} + 352004 q^{36} + 740185 q^{37} + 1994976 q^{38} - 591380 q^{39} - 38962 q^{40} - 292827 q^{41} - 1499386 q^{42} + 630980 q^{43} - 1727390 q^{44} - 994286 q^{45} + 576988 q^{46} + 3394668 q^{47} - 79840 q^{48} + 728851 q^{49} - 69656 q^{50} - 3970200 q^{51} - 2043140 q^{52} + 584438 q^{53} - 2160774 q^{54} + 2019874 q^{55} - 658986 q^{56} + 4295748 q^{57} - 5684872 q^{58} - 1773152 q^{59} + 20208544 q^{60} - 3596569 q^{61} - 1538738 q^{62} + 11795092 q^{63} - 9622852 q^{64} - 5027290 q^{65} - 17464952 q^{66} - 3249754 q^{67} + 5608668 q^{68} + 9599384 q^{69} - 5102080 q^{70} - 1162530 q^{71} - 4730172 q^{72} - 5266532 q^{73} + 4052290 q^{74} + 35543072 q^{75} - 13781226 q^{76} + 121180 q^{77} - 7012890 q^{78} - 13545718 q^{79} - 17840888 q^{80} - 16689077 q^{81} - 43173544 q^{82} + 7359048 q^{83} + 41186680 q^{84} + 21047382 q^{85} + 6732838 q^{86} + 7672800 q^{87} + 42023140 q^{88} + 2955725 q^{89} - 14596808 q^{90} - 19887752 q^{91} + 13352900 q^{92} + 9156784 q^{93} + 690474 q^{94} - 5667270 q^{95} + 29986904 q^{96} + 52065982 q^{97} - 53664462 q^{98} - 35534038 q^{99}+O(q^{100}) \) 42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9 + 10028 * q^10 + 14876 * q^11 - 4836 * q^12 - 5922 * q^13 + 20176 * q^14 - 8460 * q^15 - 36726 * q^16 - 19095 * q^17 - 7338 * q^18 - 34334 * q^19 - 75668 * q^20 - 32764 * q^21 + 18526 * q^22 - 99896 * q^23 - 203760 * q^24 - 322660 * q^25 + 101516 * q^26 + 846616 * q^27 - 73490 * q^28 + 168186 * q^29 - 88790 * q^30 - 38052 * q^31 - 172292 * q^32 - 54536 * q^33 + 90724 * q^34 - 247046 * q^35 + 352004 * q^36 + 740185 * q^37 + 1994976 * q^38 - 591380 * q^39 - 38962 * q^40 - 292827 * q^41 - 1499386 * q^42 + 630980 * q^43 - 1727390 * q^44 - 994286 * q^45 + 576988 * q^46 + 3394668 * q^47 - 79840 * q^48 + 728851 * q^49 - 69656 * q^50 - 3970200 * q^51 - 2043140 * q^52 + 584438 * q^53 - 2160774 * q^54 + 2019874 * q^55 - 658986 * q^56 + 4295748 * q^57 - 5684872 * q^58 - 1773152 * q^59 + 20208544 * q^60 - 3596569 * q^61 - 1538738 * q^62 + 11795092 * q^63 - 9622852 * q^64 - 5027290 * q^65 - 17464952 * q^66 - 3249754 * q^67 + 5608668 * q^68 + 9599384 * q^69 - 5102080 * q^70 - 1162530 * q^71 - 4730172 * q^72 - 5266532 * q^73 + 4052290 * q^74 + 35543072 * q^75 - 13781226 * q^76 + 121180 * q^77 - 7012890 * q^78 - 13545718 * q^79 - 17840888 * q^80 - 16689077 * q^81 - 43173544 * q^82 + 7359048 * q^83 + 41186680 * q^84 + 21047382 * q^85 + 6732838 * q^86 + 7672800 * q^87 + 42023140 * q^88 + 2955725 * q^89 - 14596808 * q^90 - 19887752 * q^91 + 13352900 * q^92 + 9156784 * q^93 + 690474 * q^94 - 5667270 * q^95 + 29986904 * q^96 + 52065982 * q^97 - 53664462 * q^98 - 35534038 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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