LMFDB - Embedded newform 43.7.d.a.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, 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:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	43.37
Dual form			43.7.d.a.7.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-12.2048i q^{2} +(14.4234 + 8.32735i) q^{3} -84.9566 q^{4} +(131.217 + 75.7580i) q^{5} +(101.633 - 176.034i) q^{6} +(221.781 - 128.045i) q^{7} +255.771i q^{8} +(-225.811 - 391.115i) q^{9} +O(q^{10})$	\(q-12.2048i q^{2} +(14.4234 + 8.32735i) q^{3} -84.9566 q^{4} +(131.217 + 75.7580i) q^{5} +(101.633 - 176.034i) q^{6} +(221.781 - 128.045i) q^{7} +255.771i q^{8} +(-225.811 - 391.115i) q^{9} +(924.609 - 1601.47i) q^{10} +1824.55 q^{11} +(-1225.36 - 707.463i) q^{12} +(-765.515 - 1325.91i) q^{13} +(-1562.76 - 2706.79i) q^{14} +(1261.73 + 2185.37i) q^{15} -2315.60 q^{16} +(3552.05 + 6152.33i) q^{17} +(-4773.48 + 2755.97i) q^{18} +(-6455.24 - 3726.93i) q^{19} +(-11147.7 - 6436.14i) q^{20} +4265.11 q^{21} -22268.2i q^{22} +(3152.25 - 5459.85i) q^{23} +(-2129.89 + 3689.08i) q^{24} +(3666.04 + 6349.78i) q^{25} +(-16182.4 + 9342.94i) q^{26} -19662.9i q^{27} +(-18841.8 + 10878.3i) q^{28} +(9268.73 - 5351.31i) q^{29} +(26672.0 - 15399.1i) q^{30} +(-9135.02 + 15822.3i) q^{31} +44630.7i q^{32} +(26316.1 + 15193.6i) q^{33} +(75087.8 - 43352.0i) q^{34} +38801.8 q^{35} +(19184.1 + 33227.8i) q^{36} +(64833.0 + 37431.4i) q^{37} +(-45486.4 + 78784.8i) q^{38} -25498.8i q^{39} +(-19376.7 + 33561.4i) q^{40} -89516.6 q^{41} -52054.7i q^{42} +(77674.7 + 16970.8i) q^{43} -155007. q^{44} -68427.8i q^{45} +(-66636.3 - 38472.5i) q^{46} -56266.6 q^{47} +(-33398.8 - 19282.8i) q^{48} +(-26033.3 + 45091.0i) q^{49} +(77497.6 - 44743.3i) q^{50} +118317. i q^{51} +(65035.5 + 112645. i) q^{52} +(-21290.3 + 36875.9i) q^{53} -239981. q^{54} +(239411. + 138224. i) q^{55} +(32750.3 + 56725.1i) q^{56} +(-62071.0 - 107510. i) q^{57} +(-65311.5 - 113123. i) q^{58} +244984. q^{59} +(-107192. - 185662. i) q^{60} +(-125603. + 72517.1i) q^{61} +(193108. + 111491. i) q^{62} +(-100161. - 57828.0i) q^{63} +396509. q^{64} -231975. i q^{65} +(185435. - 321183. i) q^{66} +(-96785.8 + 167638. i) q^{67} +(-301770. - 522681. i) q^{68} +(90932.1 - 52499.7i) q^{69} -473568. i q^{70} +(-421906. + 243587. i) q^{71} +(100036. - 57755.8i) q^{72} +(-507399. + 292947. i) q^{73} +(456842. - 791273. i) q^{74} +122114. i q^{75} +(548415. + 316628. i) q^{76} +(404649. - 233624. i) q^{77} -311208. q^{78} +(-20262.4 - 35095.5i) q^{79} +(-303845. - 175425. i) q^{80} +(-876.143 + 1517.52i) q^{81} +1.09253e6i q^{82} +(-193531. + 335206. i) q^{83} -362349. q^{84} +1.07638e6i q^{85} +(207125. - 948002. i) q^{86} +178249. q^{87} +466666. i q^{88} +(679613. + 392375. i) q^{89} -835146. q^{90} +(-339553. - 196041. i) q^{91} +(-267804. + 463850. i) q^{92} +(-263516. + 152141. i) q^{93} +686722. i q^{94} +(-564690. - 978072. i) q^{95} +(-371655. + 643726. i) q^{96} +60332.1 q^{97} +(550326. + 317731. i) q^{98} +(-412002. - 713608. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) $ 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	12.2048i		−	1.52560i	−0.646636	−	0.762799i	$-0.723825\pi$
$2$		−	12.2048i		−	1.52560i	0.646636	−	0.762799i	$-0.276175\pi$
$3$	14.4234	+	8.32735i	0.534200	+	0.308420i	0.742725	−	0.669597i	$-0.233533\pi$
$3$	14.4234	+	8.32735i	0.534200	+	0.308420i	−0.208525	+	0.978017i	$0.566866\pi$
$4$	−84.9566			−1.32745
$5$	131.217	+	75.7580i	1.04973	+	0.606064i	0.922575	−	0.385818i	$-0.126081\pi$
$5$	131.217	+	75.7580i	1.04973	+	0.606064i	0.127159	+	0.991882i	$0.459414\pi$
$6$	101.633	−	176.034i	0.470525	−	0.814974i
$7$	221.781	−	128.045i	0.646592	−	0.373310i	−0.140557	−	0.990073i	$-0.544889\pi$
$7$	221.781	−	128.045i	0.646592	−	0.373310i	0.787149	+	0.616763i	$0.211556\pi$
$8$			255.771i			0.499553i
$9$	−225.811	−	391.115i	−0.309754	−	0.536509i
$10$	924.609	−	1601.47i	0.924609	−	1.60147i
$11$	1824.55			1.37081			0.685404	−	0.728163i	$-0.259626\pi$
$11$	1824.55			1.37081			0.685404	+	0.728163i	$0.259626\pi$
$12$	−1225.36	−	707.463i	−0.709122	−	0.409412i
$13$	−765.515	−	1325.91i	−0.348436	−	0.603510i	0.637535	−	0.770421i	$-0.279954\pi$
$13$	−765.515	−	1325.91i	−0.348436	−	0.603510i	−0.985972	+	0.166911i	$0.946621\pi$
$14$	−1562.76	−	2706.79i	−0.569521	−	0.986439i
$15$	1261.73	+	2185.37i	0.373845	+	0.647518i
$16$	−2315.60			−0.565331
$17$	3552.05	+	6152.33i	0.722989	+	1.25225i	0.959796	+	0.280698i	$0.0905658\pi$
$17$	3552.05	+	6152.33i	0.722989	+	1.25225i	−0.236807	+	0.971557i	$0.576101\pi$
$18$	−4773.48	+	2755.97i	−0.818497	+	0.472560i
$19$	−6455.24	−	3726.93i	−0.941134	−	0.543364i	−0.0508186	−	0.998708i	$-0.516183\pi$
$19$	−6455.24	−	3726.93i	−0.941134	−	0.543364i	−0.890316	+	0.455344i	$0.849516\pi$
$20$	−11147.7	−	6436.14i	−1.39347	−	0.804518i
$21$	4265.11			0.460545
$22$		−	22268.2i		−	2.09130i
$23$	3152.25	−	5459.85i	0.259082	−	0.448742i	−0.706915	−	0.707299i	$-0.749913\pi$
$23$	3152.25	−	5459.85i	0.259082	−	0.448742i	0.965996	+	0.258556i	$0.0832468\pi$
$24$	−2129.89	+	3689.08i	−0.154072	+	0.266861i
$25$	3666.04	+	6349.78i	0.234627	+	0.406386i
$26$	−16182.4	+	9342.94i	−0.920713	+	0.531574i
$27$		−	19662.9i		−	0.998978i
$28$	−18841.8	+	10878.3i	−0.858316	+	0.495549i
$29$	9268.73	−	5351.31i	0.380037	−	0.219415i	−0.297797	−	0.954629i	$-0.596252\pi$
$29$	9268.73	−	5351.31i	0.380037	−	0.219415i	0.677835	+	0.735214i	$0.262919\pi$
$30$	26672.0	−	15399.1i	0.987852	−	0.570337i
$31$	−9135.02	+	15822.3i	−0.306637	+	0.531111i	−0.977624	−	0.210358i	$-0.932537\pi$
$31$	−9135.02	+	15822.3i	−0.306637	+	0.531111i	0.670987	+	0.741469i	$0.265870\pi$
$32$			44630.7i			1.36202i
$33$	26316.1	+	15193.6i	0.732285	+	0.422785i
$34$	75087.8	−	43352.0i	1.91044	−	1.10299i
$35$	38801.8			0.904999
$36$	19184.1	+	33227.8i	0.411182	+	0.712188i
$37$	64833.0	+	37431.4i	1.27994	+	0.738976i	0.976838	−	0.213980i	$-0.0686428\pi$
$37$	64833.0	+	37431.4i	1.27994	+	0.738976i	0.303107	+	0.952957i	$0.401976\pi$
$38$	−45486.4	+	78784.8i	−0.828955	+	1.43579i
$39$		−	25498.8i		−	0.429859i
$40$	−19376.7	+	33561.4i	−0.302761	+	0.524397i
$41$	−89516.6			−1.29883			−0.649415	−	0.760435i	$-0.724986\pi$
$41$	−89516.6			−1.29883			−0.649415	+	0.760435i	$0.724986\pi$
$42$		−	52054.7i		−	0.702607i
$43$	77674.7	+	16970.8i	0.976954	+	0.213450i
$43$	77674.7	+	16970.8i	0.976954	+	0.213450i
$44$	−155007.			−1.81968
$45$		−	68427.8i		−	0.750922i
$46$	−66636.3	−	38472.5i	−0.684600	−	0.395254i
$47$	−56266.6			−0.541947			−0.270974	−	0.962587i	$-0.587346\pi$
$47$	−56266.6			−0.541947			−0.270974	+	0.962587i	$0.587346\pi$
$48$	−33398.8	−	19282.8i	−0.302000	−	0.174360i
$49$	−26033.3	+	45091.0i	−0.221279	+	0.383267i
$50$	77497.6	−	44743.3i	0.619981	−	0.357946i
$51$			118317.i			0.891939i
$52$	65035.5	+	112645.i	0.462531	+	0.801127i
$53$	−21290.3	+	36875.9i	−0.143006	+	0.247694i	−0.928627	−	0.371014i	$-0.879010\pi$
$53$	−21290.3	+	36875.9i	−0.143006	+	0.247694i	0.785621	+	0.618708i	$0.212344\pi$
$54$	−239981.			−1.52404
$55$	239411.	+	138224.i	1.43898	+	0.830797i
$56$	32750.3	+	56725.1i	0.186488	+	0.323007i
$57$	−62071.0	−	107510.i	−0.335169	−	0.580530i
$58$	−65311.5	−	113123.i	−0.334739	−	0.579784i
$59$	244984.			1.19284			0.596419	−	0.802673i	$-0.296590\pi$
$59$	244984.			1.19284			0.596419	+	0.802673i	$0.296590\pi$
$60$	−107192.	−	185662.i	−0.496259	−	0.859546i
$61$	−125603.	+	72517.1i	−0.553365	+	0.319485i	−0.750478	−	0.660895i	$-0.770177\pi$
$61$	−125603.	+	72517.1i	−0.553365	+	0.319485i	0.197113	+	0.980381i	$0.436843\pi$
$62$	193108.	+	111491.i	0.810261	+	0.467805i
$63$	−100161.	−	57828.0i	−0.400568	−	0.231268i
$64$	396509.			1.51256
$65$		−	231975.i		−	0.844699i
$66$	185435.	−	321183.i	0.645000	−	1.11717i
$67$	−96785.8	+	167638.i	−0.321801	+	0.557375i	−0.980860	−	0.194716i	$-0.937621\pi$
$67$	−96785.8	+	167638.i	−0.321801	+	0.557375i	0.659059	+	0.752091i	$0.270955\pi$
$68$	−301770.	−	522681.i	−0.959730	−	1.66230i
$69$	90932.1	−	52499.7i	0.276803	−	0.159812i
$70$		−	473568.i		−	1.38066i
$71$	−421906.	+	243587.i	−1.17880	+	0.680581i	−0.955737	−	0.294223i	$-0.904939\pi$
$71$	−421906.	+	243587.i	−1.17880	+	0.680581i	−0.223063	+	0.974804i	$0.571606\pi$
$72$	100036.	−	57755.8i	0.268015	−	0.154738i
$73$	−507399.	+	292947.i	−1.30431	+	0.753044i	−0.981140	−	0.193297i	$-0.938082\pi$
$73$	−507399.	+	292947.i	−1.30431	+	0.753044i	−0.323170	+	0.946341i	$0.604749\pi$
$74$	456842.	−	791273.i	1.12738	−	1.95268i
$75$			122114.i			0.289455i
$76$	548415.	+	316628.i	1.24931	+	0.721287i
$77$	404649.	−	233624.i	0.886353	−	0.511736i
$78$	−311208.			−0.655792
$79$	−20262.4	−	35095.5i	−0.0410969	−	0.0711820i	0.844745	−	0.535169i	$-0.179752\pi$
$79$	−20262.4	−	35095.5i	−0.0410969	−	0.0711820i	−0.885842	+	0.463987i	$0.846419\pi$
$80$	−303845.	−	175425.i	−0.593447	−	0.342627i
$81$	−876.143	+	1517.52i	−0.00164862	+	0.00285549i
$82$			1.09253e6i			1.98149i
$83$	−193531.	+	335206.i	−0.338467	+	0.586242i	−0.984145	−	0.177368i	$-0.943242\pi$
$83$	−193531.	+	335206.i	−0.338467	+	0.586242i	0.645677	+	0.763610i	$0.276575\pi$
$84$	−362349.			−0.611350
$85$			1.07638e6i			1.75271i
$86$	207125.	−	948002.i	0.325639	−	1.49044i
$87$	178249.			0.270688
$88$			466666.i			0.684791i
$89$	679613.	+	392375.i	0.964032	+	0.556584i	0.897412	−	0.441194i	$-0.145445\pi$
$89$	679613.	+	392375.i	0.964032	+	0.556584i	0.0666203	+	0.997778i	$0.478778\pi$
$90$	−835146.			−1.14561
$91$	−339553.	−	196041.i	−0.450592	−	0.260150i
$92$	−267804.	+	463850.i	−0.343917	+	0.595682i
$93$	−263516.	+	152141.i	−0.327611	+	0.189146i
$94$			686722.i			0.826794i
$95$	−564690.	−	978072.i	−0.658627	−	1.14078i
$96$	−371655.	+	643726.i	−0.420075	+	0.727591i
$97$	60332.1			0.0661049			0.0330524	−	0.999454i	$-0.489477\pi$
$97$	60332.1			0.0661049			0.0330524	+	0.999454i	$0.489477\pi$
$98$	550326.	+	317731.i	0.584711	+	0.337583i
$99$	−412002.	−	713608.i	−0.424613	−	0.735451i
$100$	−311455.	−	539455.i	−0.311455	−	0.539455i
$101$	−205732.	−	356339.i	−0.199682	−	0.345859i	0.748743	−	0.662860i	$-0.230658\pi$
$101$	−205732.	−	356339.i	−0.199682	−	0.345859i	−0.948425	+	0.317001i	$0.897324\pi$
$102$	1.44403e6			1.36074
$103$	843106.	+	1.46030e6i	0.771561	+	1.33638i	0.936707	+	0.350114i	$0.113857\pi$
$103$	843106.	+	1.46030e6i	0.771561	+	1.33638i	−0.165146	+	0.986269i	$0.552809\pi$
$104$	339129.	−	195796.i	0.301485	−	0.174062i
$105$	559654.	+	323116.i	0.483450	+	0.279120i
$106$	450063.	+	259844.i	0.377881	+	0.218170i
$107$	−921373.			−0.752115			−0.376057	−	0.926596i	$-0.622720\pi$
$107$	−921373.			−0.752115			−0.376057	+	0.926596i	$0.622720\pi$
$108$			1.67049e6i			1.32609i
$109$	867532.	−	1.50261e6i	0.669894	−	1.16029i	−0.308039	−	0.951374i	$-0.599673\pi$
$109$	867532.	−	1.50261e6i	0.669894	−	1.16029i	0.977933	−	0.208917i	$-0.0669938\pi$
$110$	1.68699e6	−	2.92196e6i	1.26746	−	2.19531i
$111$	623408.	+	1.07977e6i	0.455831	+	0.789522i
$112$	−513555.	+	296501.i	−0.365538	+	0.211044i
$113$			1.01345e6i			0.702374i	0.936305	+	0.351187i	$0.114222\pi$
$113$			1.01345e6i			0.702374i	−0.936305	+	0.351187i	$0.885778\pi$
$114$	−1.31214e6	+	757563.i	−0.885655	+	0.511333i
$115$	827254.	−	477616.i	0.543933	−	0.314040i
$116$	−787440.	+	454629.i	−0.504480	+	0.291261i
$117$	−345723.	+	598809.i	−0.215859	+	0.373879i
$118$		−	2.98998e6i		−	1.81979i
$119$	1.57555e6	+	909646.i	0.934958	+	0.539798i
$120$	−558955.	+	322713.i	−0.323469	+	0.186755i
$121$	1.55740e6			0.879114
$122$	885056.	+	1.53296e6i	0.487406	+	0.844212i
$123$	−1.29113e6	−	745436.i	−0.693834	−	0.400585i
$124$	776081.	−	1.34421e6i	0.407044	−	0.705022i
$125$		−	1.25651e6i		−	0.643332i
$126$	−705777.	+	1.22244e6i	−0.352822	+	0.611106i
$127$	−2.46871e6			−1.20520			−0.602601	−	0.798043i	$-0.705869\pi$
$127$	−2.46871e6			−1.20520			−0.602601	+	0.798043i	$0.705869\pi$
$128$		−	1.98295e6i		−	0.945542i
$129$	979011.	+	891601.i	0.456056	+	0.415338i
$130$	−2.83121e6			−1.28867
$131$		−	487446.i		−	0.216827i	−0.994106	−	0.108413i	$-0.965423\pi$
$131$		−	487446.i		−	0.216827i	0.994106	−	0.108413i	$-0.0345770\pi$
$132$	−2.23573e6	−	1.29080e6i	−0.972070	−	0.561225i
$133$	−1.90887e6			−0.811373
$134$	2.04598e6	+	1.18125e6i	0.850330	+	0.490938i
$135$	1.48962e6	−	2.58010e6i	0.605445	−	1.04866i
$136$	−1.57359e6	+	908510.i	−0.625567	+	0.361171i
$137$		−	2.10439e6i		−	0.818399i	−0.912445	−	0.409199i	$-0.865808\pi$
$137$		−	2.10439e6i		−	0.818399i	0.912445	−	0.409199i	$-0.134192\pi$
$138$	−640747.	−	1.10981e6i	−0.243809	−	0.422289i
$139$	1.92136e6	−	3.32790e6i	0.715426	−	1.23915i	−0.247369	−	0.968921i	$-0.579566\pi$
$139$	1.92136e6	−	3.32790e6i	0.715426	−	1.23915i	0.962795	−	0.270233i	$-0.0871006\pi$
$140$	−3.29647e6			−1.20134
$141$	−811555.	−	468552.i	−0.289508	−	0.167148i
$142$	2.97293e6	+	5.14926e6i	1.03829	+	1.79837i
$143$	−1.39672e6	−	2.41918e6i	−0.477639	−	0.827296i
$144$	522886.	+	905665.i	0.175113	+	0.303305i
$145$	1.62162e6			0.531917
$146$	3.57535e6	+	6.19269e6i	1.14884	+	1.98985i
$147$	−750977.	+	433577.i	−0.236415	+	0.136494i
$148$	−5.50800e6	−	3.18004e6i	−1.69906	−	0.980952i
$149$	−3.41329e6	−	1.97067e6i	−1.03185	−	0.595737i	−0.114333	−	0.993442i	$-0.536473\pi$
$149$	−3.41329e6	−	1.97067e6i	−1.03185	−	0.595737i	−0.917513	+	0.397706i	$0.869806\pi$
$150$	1.49037e6			0.441591
$151$			5.04282e6i			1.46468i	0.680939	+	0.732340i	$0.261572\pi$
$151$			5.04282e6i			1.46468i	−0.680939	+	0.732340i	$0.738428\pi$
$152$	953242.	−	1.65106e6i	0.271439	−	0.470146i
$153$	1.60418e6	−	2.77852e6i	0.447897	−	0.775781i
$154$	−2.85133e6	−	4.93866e6i	−0.780703	−	1.35222i
$155$	−2.39734e6	+	1.38410e6i	−0.643774	+	0.371683i
$156$			2.16629e6i			0.570616i
$157$	38946.5	−	22485.8i	0.0100640	−	0.00581044i	−0.494960	−	0.868916i	$-0.664817\pi$
$157$	38946.5	−	22485.8i	0.0100640	−	0.00581044i	0.505024	+	0.863106i	$0.331484\pi$
$158$	−428333.	+	247298.i	−0.108595	+	0.0626974i
$159$	−614157.	+	354584.i	−0.152788	+	0.0882120i
$160$	−3.38113e6	+	5.85629e6i	−0.825471	+	1.42976i
$161$		−	1.61452e6i		−	0.386871i
$162$	18521.0	+	10693.1i	0.00435633	+	0.00251513i
$163$	1.13834e6	−	657218.i	0.262850	−	0.151756i	−0.362784	−	0.931873i	$-0.618174\pi$
$163$	1.13834e6	−	657218.i	0.262850	−	0.151756i	0.625634	+	0.780117i	$0.284840\pi$
$164$	7.60503e6			1.72413
$165$	2.30208e6	+	3.98731e6i	0.512469	+	0.887623i
$166$	4.09111e6	+	2.36200e6i	0.894370	+	0.516365i
$167$	4.28790e6	−	7.42687e6i	0.920652	−	1.59462i	0.122244	−	0.992500i	$-0.460991\pi$
$167$	4.28790e6	−	7.42687e6i	0.920652	−	1.59462i	0.798408	−	0.602116i	$-0.205676\pi$
$168$			1.09089e6i			0.230067i
$169$	1.24138e6	−	2.15013e6i	0.257184	−	0.445456i
$170$	1.31370e7			2.67393
$171$			3.36632e6i			0.673236i
$172$	−6.59898e6	−	1.44178e6i	−1.29685	−	0.283344i
$173$	−530452.			−0.102449			−0.0512245	−	0.998687i	$-0.516312\pi$
$173$	−530452.			−0.102449			−0.0512245	+	0.998687i	$0.516312\pi$
$174$		−	2.17549e6i		−	0.412961i
$175$	1.62612e6	+	938840.i	0.303416	+	0.175177i
$176$	−4.22491e6			−0.774960
$177$	3.53350e6	+	2.04007e6i	0.637214	+	0.367896i
$178$	4.78884e6	−	8.29452e6i	0.849123	−	1.47072i
$179$	−6.58390e6	+	3.80122e6i	−1.14795	+	0.662771i	−0.948388	−	0.317114i	$-0.897286\pi$
$179$	−6.58390e6	+	3.80122e6i	−1.14795	+	0.662771i	−0.199565	+	0.979885i	$0.563953\pi$
$180$			5.81339e6i			0.996810i
$181$	−5.25655e6	−	9.10462e6i	−0.886473	−	1.53542i	−0.844016	−	0.536318i	$-0.819815\pi$
$181$	−5.25655e6	−	9.10462e6i	−0.886473	−	1.53542i	−0.0424568	−	0.999098i	$-0.513518\pi$
$182$	−2.39264e6	+	4.14417e6i	−0.396883	+	0.687422i
$183$	−2.41550e6			−0.394143
$184$	1.39647e6	+	806253.i	0.224170	+	0.129425i
$185$	5.67145e6	+	9.82324e6i	0.895734	+	1.55146i
$186$	1.85685e6	+	3.21616e6i	0.288561	+	0.499802i
$187$	6.48087e6	+	1.12252e7i	0.991080	+	1.71660i
$188$	4.78022e6			0.719407
$189$	−2.51774e6	−	4.36085e6i	−0.372928	−	0.645931i
$190$	−1.19372e7	+	6.89192e6i	−1.74036	+	1.00480i
$191$	4.98943e6	+	2.88065e6i	0.716062	+	0.413419i	0.813302	−	0.581842i	$-0.197668\pi$
$191$	4.98943e6	+	2.88065e6i	0.716062	+	0.413419i	−0.0972393	+	0.995261i	$0.531001\pi$
$192$	5.71901e6	+	3.30187e6i	0.808011	+	0.466505i
$193$	−1.24172e7			−1.72723			−0.863616	−	0.504150i	$-0.831806\pi$
$193$	−1.24172e7			−1.72723			−0.863616	+	0.504150i	$0.831806\pi$
$194$		−	736341.i		−	0.100849i
$195$	1.93174e6	−	3.34587e6i	0.260522	−	0.451238i
$196$	2.21170e6	−	3.83078e6i	0.293737	−	0.508767i
$197$	−4.13998e6	−	7.17066e6i	−0.541502	−	0.937909i	−0.998818	−	0.0486045i	$-0.984523\pi$
$197$	−4.13998e6	−	7.17066e6i	−0.541502	−	0.937909i	0.457316	−	0.889304i	$-0.348811\pi$
$198$	−8.70942e6	+	5.02839e6i	−1.12200	+	0.647788i
$199$			3.87228e6i			0.491369i	0.969350	+	0.245684i	$0.0790126\pi$
$199$			3.87228e6i			0.491369i	−0.969350	+	0.245684i	$0.920987\pi$
$200$	−1.62409e6	+	937668.i	−0.203011	+	0.117208i
$201$	−2.79196e6	+	1.61194e6i	−0.343812	+	0.198500i
$202$	−4.34904e6	+	2.51092e6i	−0.527642	+	0.304634i
$203$	1.37042e6	−	2.37364e6i	0.163819	−	0.283744i
$204$		−	1.00518e7i		−	1.18400i
$205$	−1.17461e7	−	6.78160e6i	−1.36342	−	0.787174i
$206$	1.78227e7	−	1.02899e7i	2.03878	−	1.17709i
$207$	−2.84724e6			−0.321006
$208$	1.77262e6	+	3.07027e6i	0.196982	+	0.341183i
$209$	−1.17779e7	−	6.79996e6i	−1.29011	−	0.744848i
$210$	3.94356e6	−	6.83045e6i	0.425825	−	0.737550i
$211$			1.28313e7i			1.36591i	0.730459	+	0.682957i	$0.239306\pi$
$211$			1.28313e7i			1.36591i	−0.730459	+	0.682957i	$0.760694\pi$
$212$	1.80875e6	−	3.13285e6i	0.189833	−	0.328801i
$213$	−8.11374e6			−0.839620
$214$			1.12452e7i			1.14742i
$215$	8.90654e6	+	8.11133e6i	0.896177	+	0.816162i
$216$	5.02919e6			0.499042
$217$			4.67879e6i			0.457883i
$218$	−1.83390e7	−	1.05880e7i	−1.77014	−	1.02199i
$219$	−9.75789e6			−0.929017
$220$	−2.03395e7	−	1.17430e7i	−1.91017	−	1.10284i
$221$	5.43829e6	−	9.41939e6i	0.503832	−	0.872662i
$222$	1.31784e7	−	7.60856e6i	1.20449	−	0.695414i
$223$		−	1.02113e7i		−	0.920802i	−0.887711	−	0.460401i	$-0.847706\pi$
$223$		−	1.02113e7i		−	0.920802i	0.887711	−	0.460401i	$-0.152294\pi$
$224$	5.71475e6	+	9.89824e6i	0.508456	+	0.880671i
$225$	1.65566e6	−	2.86769e6i	0.145353	−	0.251759i
$226$	1.23690e7			1.07154
$227$	1.40345e7	+	8.10281e6i	1.19983	+	0.692720i	0.960517	−	0.278223i	$-0.0897454\pi$
$227$	1.40345e7	+	8.10281e6i	1.19983	+	0.692720i	0.239310	+	0.970943i	$0.423079\pi$
$228$	5.27334e6	+	9.13369e6i	0.444919	+	0.770623i
$229$	−150445.	−	260579.i	−0.0125277	−	0.0216986i	0.859694	−	0.510810i	$-0.170654\pi$
$229$	−150445.	−	260579.i	−0.0125277	−	0.0216986i	−0.872221	+	0.489111i	$0.837321\pi$
$230$	−5.82919e6	−	1.00965e7i	−0.479099	−	0.829823i
$231$	7.78189e6			0.631319
$232$	1.36871e6	+	2.37067e6i	0.109609	+	0.189849i
$233$	1.62777e7	−	9.39794e6i	1.28684	−	0.742959i	0.308753	−	0.951142i	$-0.400088\pi$
$233$	1.62777e7	−	9.39794e6i	1.28684	−	0.742959i	0.978090	+	0.208183i	$0.0667550\pi$
$234$	7.30833e6	+	4.21947e6i	0.570388	+	0.329314i
$235$	−7.38312e6	−	4.26265e6i	−0.568900	−	0.328455i
$236$	−2.08130e7			−1.58343
$237$		−	674928.i		−	0.0507005i
$238$	1.11020e7	−	1.92293e7i	0.823515	−	1.42637i
$239$	2.57203e6	−	4.45488e6i	0.188401	−	0.326319i	−0.756317	−	0.654206i	$-0.773003\pi$
$239$	2.57203e6	−	4.45488e6i	0.188401	−	0.326319i	0.944717	+	0.327887i	$0.106336\pi$
$240$	−2.92165e6	−	5.06044e6i	−0.211346	−	0.366062i
$241$	2.02777e7	−	1.17073e7i	1.44866	−	0.836385i	0.450259	−	0.892898i	$-0.351332\pi$
$241$	2.02777e7	−	1.17073e7i	1.44866	−	0.836385i	0.998402	+	0.0565131i	$0.0179983\pi$
$242$		−	1.90078e7i		−	1.34117i
$243$	−1.24391e7	+	7.18171e6i	−0.866902	+	0.500506i
$244$	1.06708e7	−	6.16081e6i	0.734563	−	0.424100i
$245$	−6.83201e6	+	3.94446e6i	−0.464569	+	0.268219i
$246$	−9.09788e6	+	1.57580e7i	−0.611132	+	1.05851i
$247$			1.14121e7i			0.757311i
$248$	−4.04689e6	−	2.33647e6i	−0.265318	−	0.153181i
$249$	−5.58275e6	+	3.22320e6i	−0.361618	+	0.208780i
$250$	−1.53354e7			−0.981466
$251$	1.13327e7	+	1.96289e7i	0.716660	+	1.24129i	0.962316	+	0.271935i	$0.0876635\pi$
$251$	1.13327e7	+	1.96289e7i	0.716660	+	1.24129i	−0.245656	+	0.969357i	$0.579003\pi$
$252$	8.50934e6	+	4.91287e6i	0.531734	+	0.306996i
$253$	5.75142e6	−	9.96174e6i	0.355151	−	0.615140i
$254$			3.01301e7i			1.83865i
$255$	−8.96342e6	+	1.55251e7i	−0.540572	+	0.936298i
$256$	1.17519e6			0.0700466
$257$		−	1.63248e7i		−	0.961718i	−0.876798	−	0.480859i	$-0.840325\pi$
$257$		−	1.63248e7i		−	0.961718i	0.876798	−	0.480859i	$-0.159675\pi$
$258$	1.08818e7	−	1.19486e7i	0.633638	−	0.695758i
$259$	1.91716e7			1.10347
$260$			1.97078e7i			1.12129i
$261$	−4.18595e6	−	2.41676e6i	−0.235436	−	0.135929i
$262$	−5.94917e6			−0.330790
$263$	−1.74308e7	−	1.00637e7i	−0.958186	−	0.553209i	−0.0625716	−	0.998040i	$-0.519930\pi$
$263$	−1.74308e7	−	1.00637e7i	−0.958186	−	0.553209i	−0.895614	+	0.444832i	$0.853264\pi$
$264$	−3.88609e6	+	6.73090e6i	−0.211203	+	0.365815i
$265$	−5.58729e6	+	3.22582e6i	−0.300237	+	0.173342i
$266$			2.32973e7i			1.23783i
$267$	6.53488e6	+	1.13187e7i	0.343324	+	0.594654i
$268$	8.22259e6	−	1.42419e7i	0.427173	−	0.739886i
$269$	−1.85343e6			−0.0952180			−0.0476090	−	0.998866i	$-0.515160\pi$
$269$	−1.85343e6			−0.0952180			−0.0476090	+	0.998866i	$0.515160\pi$
$270$	−3.14895e7	−	1.81805e7i	−1.59983	−	0.923665i
$271$	9.48380e6	+	1.64264e7i	0.476513	+	0.825344i	0.999638	−	0.0269118i	$-0.00856734\pi$
$271$	9.48380e6	+	1.64264e7i	0.476513	+	0.825344i	−0.523125	+	0.852256i	$0.675234\pi$
$272$	−8.22511e6	−	1.42463e7i	−0.408728	−	0.707938i
$273$	−3.26501e6	−	5.65516e6i	−0.160471	−	0.277944i
$274$	−2.56836e7			−1.24855
$275$	6.68886e6	+	1.15855e7i	0.321628	+	0.557077i
$276$	−7.72529e6	+	4.46020e6i	−0.367441	+	0.212142i
$277$	3.20293e7	+	1.84921e7i	1.50698	+	0.870057i	0.999967	+	0.00812030i	$0.00258480\pi$
$277$	3.20293e7	+	1.84921e7i	1.50698	+	0.870057i	0.507016	+	0.861937i	$0.330749\pi$
$278$	−4.06162e7	−	2.34498e7i	−1.89045	−	1.09145i
$279$	8.25114e6			0.379928
$280$			9.92438e6i			0.452094i
$281$	−1.53110e7	+	2.65194e7i	−0.690057	+	1.19521i	0.281762	+	0.959484i	$0.409081\pi$
$281$	−1.53110e7	+	2.65194e7i	−0.690057	+	1.19521i	−0.971819	+	0.235729i	$0.924252\pi$
$282$	−5.71857e6	+	9.90485e6i	−0.255000	+	0.441673i
$283$	1.24793e6	+	2.16148e6i	0.0550593	+	0.0953655i	0.892241	−	0.451559i	$-0.149132\pi$
$283$	1.24793e6	+	2.16148e6i	0.0550593	+	0.0953655i	−0.837182	+	0.546924i	$0.815799\pi$
$284$	3.58437e7	−	2.06944e7i	1.56479	−	0.903435i
$285$		−	1.88095e7i		−	0.812536i
$286$	−2.95256e7	+	1.70466e7i	−1.26212	+	0.728685i
$287$	−1.98531e7	+	1.14622e7i	−0.839812	+	0.484866i
$288$	1.74557e7	−	1.00781e7i	0.730737	−	0.421891i
$289$	−1.31653e7	+	2.28030e7i	−0.545428	+	0.944708i
$290$		−	1.97915e7i		−	0.811492i
$291$	870194.	+	502407.i	0.0353132	+	0.0203881i
$292$	4.31069e7	−	2.48878e7i	1.73140	−	0.999626i
$293$	1.80623e7			0.718076			0.359038	−	0.933323i	$-0.383105\pi$
$293$	1.80623e7			0.718076			0.359038	+	0.933323i	$0.383105\pi$
$294$	5.29171e6	+	9.16551e6i	0.208235	+	0.360674i
$295$	3.21460e7	+	1.85595e7i	1.25216	+	0.722936i
$296$	−9.57386e6	+	1.65824e7i	−0.369158	+	0.639400i
$297$		−	3.58758e7i		−	1.36941i
$298$	−2.40515e7	+	4.16585e7i	−0.908854	+	1.57418i
$299$	−9.65236e6			−0.361094
$300$		−	1.03744e7i		−	0.384236i
$301$	1.93998e7	−	6.18208e6i	0.711373	−	0.226691i
$302$	6.15465e7			2.23451
$303$		−	6.85282e6i		−	0.246344i
$304$	1.49477e7	+	8.63008e6i	0.532053	+	0.307181i
$305$	−2.19750e7			−0.774514
$306$	−3.39112e7	−	1.95787e7i	−1.18353	−	0.683311i
$307$	2.30700e7	−	3.99585e7i	0.797321	−	1.38100i	−0.124034	−	0.992278i	$-0.539583\pi$
$307$	2.30700e7	−	3.99585e7i	0.797321	−	1.38100i	0.921355	−	0.388722i	$-0.127083\pi$
$308$	−3.43776e7	+	1.98479e7i	−1.17659	+	0.679303i
$309$			2.80833e7i			0.951861i
$310$	1.68927e7	+	2.92589e7i	0.567039	+	0.982140i
$311$	−9.54344e6	+	1.65297e7i	−0.317266	+	0.549521i	−0.979917	−	0.199408i	$-0.936098\pi$
$311$	−9.54344e6	+	1.65297e7i	−0.317266	+	0.549521i	0.662650	+	0.748929i	$0.269432\pi$
$312$	6.52186e6			0.214737
$313$	4.86336e7	+	2.80786e7i	1.58600	+	0.915678i	0.993957	+	0.109771i	$0.0350118\pi$
$313$	4.86336e7	+	2.80786e7i	1.58600	+	0.915678i	0.592043	+	0.805906i	$0.298322\pi$
$314$	−274434.	−	475334.i	−0.00886439	−	0.0153536i
$315$	−8.76186e6	−	1.51760e7i	−0.280327	−	0.485540i
$316$	1.72142e6	+	2.98160e6i	0.0545540	+	0.0944903i
$317$	−2.49276e7			−0.782534			−0.391267	−	0.920277i	$-0.627963\pi$
$317$	−2.49276e7			−0.782534			−0.391267	+	0.920277i	$0.627963\pi$
$318$	4.32762e6	+	7.49566e6i	0.134576	+	0.233092i
$319$	1.69112e7	−	9.76370e6i	0.520958	−	0.300775i
$320$	5.20286e7	+	3.00388e7i	1.58779	+	0.916710i
$321$	−1.32893e7	−	7.67259e6i	−0.401779	−	0.231967i
$322$	−1.97049e7			−0.590209
$323$		−	5.29530e7i		−	1.57139i
$324$	74434.1	−	128924.i	0.00218845	−	0.00379051i
$325$	5.61282e6	−	9.72169e6i	0.163505	−	0.283199i
$326$	−8.02120e6	−	1.38931e7i	−0.231519	−	0.401003i
$327$	2.50255e7	−	1.44485e7i	0.715714	−	0.413218i
$328$		−	2.28957e7i		−	0.648833i
$329$	−1.24789e7	+	7.20468e6i	−0.350419	+	0.202314i
$330$	4.86643e7	−	2.80963e7i	1.35416	−	0.781822i
$331$	2.01275e6	−	1.16206e6i	0.0555016	−	0.0320439i	−0.471992	−	0.881603i	$-0.656465\pi$
$331$	2.01275e6	−	1.16206e6i	0.0555016	−	0.0320439i	0.527494	+	0.849559i	$0.323132\pi$
$332$	1.64417e7	−	2.84779e7i	0.449297	−	0.778206i
$333$		−	3.38096e7i		−	0.915603i
$334$	−9.06433e7	−	5.23329e7i	−2.43274	−	1.40454i
$335$	−2.53998e7	+	1.46646e7i	−0.675610	+	0.390064i
$336$	−9.87628e6			−0.260361
$337$	−3.73122e7	−	6.46266e7i	−0.974901	−	1.68858i	−0.680260	−	0.732971i	$-0.738133\pi$
$337$	−3.73122e7	−	6.46266e7i	−0.974901	−	1.68858i	−0.294642	−	0.955608i	$-0.595200\pi$
$338$	−2.62419e7	−	1.51508e7i	−0.679587	−	0.392359i
$339$	−8.43938e6	+	1.46174e7i	−0.216626	+	0.375208i
$340$		−	9.14459e7i		−	2.32663i
$341$	−1.66673e7	+	2.88686e7i	−0.420340	+	0.728051i
$342$	4.10852e7			1.02709
$343$			4.34626e7i			1.07704i
$344$	−4.34063e6	+	1.98669e7i	−0.106630	+	0.488040i
$345$	1.59091e7			0.387425
$346$			6.47405e6i			0.156296i
$347$	−6.61233e7	−	3.81763e7i	−1.58258	−	0.913703i	−0.994481	−	0.104915i	$-0.966543\pi$
$347$	−6.61233e7	−	3.81763e7i	−1.58258	−	0.913703i	−0.588099	−	0.808789i	$-0.700124\pi$
$348$	−1.51434e7			−0.359324
$349$	1.12563e7	+	6.49883e6i	0.264801	+	0.152883i	0.626523	−	0.779403i	$-0.284478\pi$
$349$	1.12563e7	+	6.49883e6i	0.264801	+	0.152883i	−0.361722	+	0.932286i	$0.617811\pi$
$350$	1.14583e7	−	1.98464e7i	0.267250	−	0.462890i
$351$	−2.60712e7	+	1.50522e7i	−0.602893	+	0.348080i
$352$			8.14307e7i			1.86707i
$353$	9.59845e6	+	1.66250e7i	0.218211	+	0.377953i	0.954261	−	0.298974i	$-0.0966445\pi$
$353$	9.59845e6	+	1.66250e7i	0.218211	+	0.377953i	−0.736050	+	0.676927i	$0.763311\pi$
$354$	2.48986e7	−	4.31256e7i	0.561261	−	0.972132i
$355$	−7.38147e7			−1.64990
$356$	−5.77376e7	−	3.33348e7i	−1.27970	−	0.738836i
$357$	1.51499e7	+	2.62404e7i	0.332970	+	0.576720i
$358$	4.63930e7	+	8.03550e7i	1.01112	+	1.75131i
$359$	8.08127e6	+	1.39972e7i	0.174661	+	0.302522i	0.940044	−	0.341053i	$-0.110784\pi$
$359$	8.08127e6	+	1.39972e7i	0.174661	+	0.302522i	−0.765383	+	0.643575i	$0.777450\pi$
$360$	1.75018e7			0.375125
$361$	4.25715e6	+	7.37360e6i	0.0904893	+	0.156732i
$362$	−1.11120e8	+	6.41551e7i	−2.34243	+	1.35240i
$363$	2.24631e7	+	1.29691e7i	0.469623	+	0.271137i
$364$	2.88473e7	+	1.66550e7i	0.598137	+	0.345335i
$365$	−8.87723e7			−1.82557
$366$			2.94807e7i			0.601304i
$367$	−1.83324e7	+	3.17526e7i	−0.370869	+	0.642364i	−0.989699	−	0.143161i	$-0.954273\pi$
$367$	−1.83324e7	+	3.17526e7i	−0.370869	+	0.642364i	0.618831	+	0.785524i	$0.287607\pi$
$368$	−7.29933e6	+	1.26428e7i	−0.146467	+	0.253688i
$369$	2.02138e7	+	3.50113e7i	0.402317	+	0.696834i
$370$	1.19890e8	−	6.92188e7i	2.36690	−	1.36653i
$371$			1.09045e7i			0.213542i
$372$	2.23874e7	−	1.29254e7i	0.434886	−	0.251082i
$373$	1.34444e6	−	776212.i	0.0259068	−	0.0149573i	−0.486991	−	0.873407i	$-0.661905\pi$
$373$	1.34444e6	−	776212.i	0.0259068	−	0.0149573i	0.512897	+	0.858450i	$0.328572\pi$
$374$	1.37001e8	−	7.90976e7i	2.61884	−	1.51199i
$375$	1.04634e7	−	1.81231e7i	0.198417	−	0.343668i
$376$		−	1.43914e7i		−	0.270731i
$377$	−1.41907e7	−	8.19301e6i	−0.264838	−	0.152904i
$378$	−5.32233e7	+	3.07285e7i	−0.985431	+	0.568939i
$379$	−2.87626e7			−0.528337			−0.264169	−	0.964477i	$-0.585098\pi$
$379$	−2.87626e7			−0.528337			−0.264169	+	0.964477i	$0.585098\pi$
$380$	4.79742e7	+	8.30937e7i	0.874292	+	1.51432i
$381$	−3.56072e7	−	2.05578e7i	−0.643818	−	0.371709i
$382$	3.51577e7	−	6.08949e7i	0.630711	−	1.09242i
$383$			8.23029e6i			0.146494i	0.997314	+	0.0732468i	$0.0233361\pi$
$383$			8.23029e6i			0.146494i	−0.997314	+	0.0732468i	$0.976664\pi$
$384$	1.65127e7	−	2.86008e7i	0.291624	−	0.505108i
$385$	7.07957e7			1.24058
$386$			1.51549e8i			2.63506i
$387$	−1.09022e7	−	3.42119e7i	−0.188097	−	0.590262i
$388$	−5.12562e6			−0.0877507
$389$		−	6.78277e7i		−	1.15228i	−0.817351	−	0.576140i	$-0.804558\pi$
$389$		−	6.78277e7i		−	1.15228i	0.817351	−	0.576140i	$-0.195442\pi$
$390$	−4.08356e7	−	2.35765e7i	−0.688407	−	0.397452i
$391$	4.47877e7			0.749253
$392$	−1.15330e7	−	6.65856e6i	−0.191462	−	0.110541i
$393$	4.05913e6	−	7.03063e6i	0.0668738	−	0.115829i
$394$	−8.75163e7	+	5.05276e7i	−1.43087	+	0.826114i
$395$		−	6.14015e6i		−	0.0996295i
$396$	3.50023e7	+	6.06257e7i	0.563651	+	0.976273i
$397$	3.00205e7	−	5.19971e7i	0.479785	−	0.831012i	−0.519946	−	0.854199i	$-0.674048\pi$
$397$	3.00205e7	−	5.19971e7i	0.479785	−	0.831012i	0.999731	+	0.0231870i	$0.00738132\pi$
$398$	4.72603e7			0.749631
$399$	−2.75323e7	−	1.58958e7i	−0.433435	−	0.250244i
$400$	−8.48908e6	−	1.47035e7i	−0.132642	−	0.229742i
$401$	−2.40289e7	−	4.16193e7i	−0.372650	−	0.645449i	0.617322	−	0.786710i	$-0.288218\pi$
$401$	−2.40289e7	−	4.16193e7i	−0.372650	−	0.645449i	−0.989972	+	0.141261i	$0.954884\pi$
$402$	1.96733e7	+	3.40752e7i	0.302831	+	0.524518i
$403$	2.79720e7			0.427374
$404$	1.74783e7	+	3.02734e7i	0.265067	+	0.459110i
$405$	−229929.	+	132750.i	−0.00346122	+	0.00199833i
$406$	−2.89697e7	−	1.67257e7i	−0.432878	−	0.249922i
$407$	1.18291e8	+	6.82952e7i	1.75456	+	1.01299i
$408$	−3.02619e7			−0.445570
$409$		−	1.06781e8i		−	1.56071i	−0.625335	−	0.780356i	$-0.715038\pi$
$409$		−	1.06781e8i		−	1.56071i	0.625335	−	0.780356i	$-0.284962\pi$
$410$	−8.27679e7	+	1.43358e8i	−1.20091	+	2.08004i
$411$	1.75240e7	−	3.03525e7i	0.252411	−	0.437188i
$412$	−7.16274e7	−	1.24062e8i	−1.02421	−	1.77398i
$413$	5.43328e7	−	3.13690e7i	0.771280	−	0.445298i
$414$			3.47499e7i			0.489726i
$415$	−5.07890e7	+	2.93231e7i	−0.710601	+	0.410265i
$416$	5.91763e7	−	3.41654e7i	0.821992	−	0.474577i
$417$	5.54251e7	−	3.19997e7i	0.764361	−	0.441304i
$418$	−8.29920e7	+	1.43746e8i	−1.13634	+	1.96820i
$419$		−	5.52509e6i		−	0.0751099i	−0.999295	−	0.0375549i	$-0.988043\pi$
$419$		−	5.52509e6i		−	0.0751099i	0.999295	−	0.0375549i	$-0.0119569\pi$
$420$	−4.75463e7	−	2.74509e7i	−0.641754	−	0.370517i
$421$	−5.71866e6	+	3.30167e6i	−0.0766386	+	0.0442473i	−0.537830	−	0.843054i	$-0.680756\pi$
$421$	−5.71866e6	+	3.30167e6i	−0.0766386	+	0.0442473i	0.461191	+	0.887301i	$0.347422\pi$
$422$	1.56603e8			2.08383
$423$	1.27056e7	+	2.20067e7i	0.167870	+	0.290760i
$424$	−9.43179e6	−	5.44545e6i	−0.123736	−	0.0714391i
$425$	−2.60439e7	+	4.51094e7i	−0.339266	+	0.587625i
$426$			9.90265e7i			1.28092i
$427$	−1.85710e7	+	3.21658e7i	−0.238534	+	0.413153i
$428$	7.82767e7			0.998393
$429$		−	4.65238e7i		−	0.589255i
$430$	9.89970e7	−	1.08702e8i	1.24514	−	1.36720i
$431$	4.98044e7			0.622065			0.311032	−	0.950399i	$-0.399325\pi$
$431$	4.98044e7			0.622065			0.311032	+	0.950399i	$0.399325\pi$
$432$			4.55313e7i			0.564753i
$433$	−1.16571e8	−	6.73021e7i	−1.43590	−	0.829020i	−0.438343	−	0.898808i	$-0.644434\pi$
$433$	−1.16571e8	−	6.73021e7i	−1.43590	−	0.829020i	−0.997562	+	0.0697879i	$0.977768\pi$
$434$	5.71036e7			0.698544
$435$	2.33892e7	+	1.35038e7i	0.284150	+	0.164054i
$436$	−7.37026e7	+	1.27657e8i	−0.889249	+	1.54022i
$437$	−4.06970e7	+	2.34964e7i	−0.487661	+	0.281551i
$438$			1.19093e8i			1.41731i
$439$	6.04326e7	+	1.04672e8i	0.714295	+	1.23720i	0.963231	+	0.268676i	$0.0865859\pi$
$439$	6.04326e7	+	1.04672e8i	0.714295	+	1.23720i	−0.248936	+	0.968520i	$0.580081\pi$
$440$	−3.53536e7	+	6.12343e7i	−0.415027	+	0.718848i
$441$	2.35144e7			0.274169
$442$	−1.14962e8	−	6.63731e7i	−1.33133	−	0.768644i
$443$	1.59862e6	+	2.76889e6i	0.0183880	+	0.0318490i	0.875073	−	0.483991i	$-0.160813\pi$
$443$	1.59862e6	+	2.76889e6i	0.0183880	+	0.0318490i	−0.856685	+	0.515840i	$0.827480\pi$
$444$	−5.29626e7	−	9.17340e7i	−0.605091	−	1.04805i
$445$	5.94510e7	+	1.02972e8i	0.674651	+	1.16853i
$446$	−1.24627e8			−1.40477
$447$	−3.28209e7	−	5.68474e7i	−0.367475	−	0.636485i
$448$	8.79382e7	−	5.07712e7i	0.978011	−	0.564655i
$449$	−8.85064e7	−	5.10992e7i	−0.977768	−	0.564515i	−0.0761725	−	0.997095i	$-0.524270\pi$
$449$	−8.85064e7	−	5.10992e7i	−0.977768	−	0.564515i	−0.901596	+	0.432580i	$0.857603\pi$
$450$	−3.49995e7	−	2.02070e7i	−0.384083	−	0.221750i
$451$	−1.63327e8			−1.78045
$452$		−	8.60995e7i		−	0.932364i
$453$	−4.19934e7	+	7.27346e7i	−0.451737	+	0.782432i
$454$	9.88930e7	−	1.71288e8i	1.05681	−	1.83045i
$455$	−2.97034e7	−	5.14477e7i	−0.315334	−	0.546175i
$456$	2.74980e7	−	1.58759e7i	0.290005	−	0.167435i
$457$		−	1.61189e7i		−	0.168884i	−0.996428	−	0.0844419i	$-0.973089\pi$
$457$		−	1.61189e7i		−	0.168884i	0.996428	−	0.0844419i	$-0.0269107\pi$
$458$	−3.18030e6	+	1.83615e6i	−0.0331034	+	0.0191122i
$459$	1.20972e8	−	6.98435e7i	1.25097	−	0.722251i
$460$	−7.02807e7	+	4.05766e7i	−0.722043	+	0.416871i
$461$	−2.23123e7	+	3.86460e7i	−0.227741	+	0.394459i	−0.957138	−	0.289631i	$-0.906467\pi$
$461$	−2.23123e7	+	3.86460e7i	−0.227741	+	0.394459i	0.729397	+	0.684090i	$0.239801\pi$
$462$		−	9.49762e7i		−	0.963139i
$463$	4.43822e7	+	2.56241e7i	0.447163	+	0.258170i	0.706631	−	0.707582i	$-0.250214\pi$
$463$	4.43822e7	+	2.56241e7i	0.447163	+	0.258170i	−0.259468	+	0.965752i	$0.583547\pi$
$464$	−2.14626e7	+	1.23915e7i	−0.214847	+	0.124042i
$465$	−4.61036e7			−0.458539
$466$	−1.14700e8	−	1.98666e8i	−1.13346	−	1.96320i
$467$	3.45832e7	+	1.99666e7i	0.339558	+	0.196044i	0.660077	−	0.751198i	$-0.270524\pi$
$467$	3.45832e7	+	1.99666e7i	0.339558	+	0.196044i	−0.320518	+	0.947242i	$0.603857\pi$
$468$	2.93714e7	−	5.08728e7i	0.286541	−	0.496304i
$469$			4.95718e7i			0.480526i
$470$	−5.20246e7	+	9.01093e7i	−0.501090	+	0.867913i
$471$	748988.			0.00716823
$472$			6.26598e7i			0.595886i
$473$	1.41721e8	+	3.09640e7i	1.33922	+	0.292599i
$474$	−8.23735e6			−0.0773486
$475$		−	5.46524e7i		−	0.509951i
$476$	−1.33854e8	−	7.72804e7i	−1.24111	−	0.716554i
$477$	1.92303e7			0.177187
$478$	−5.43709e7	−	3.13910e7i	−0.497832	−	0.287423i
$479$	3.49917e7	−	6.06074e7i	0.318389	−	0.551467i	−0.661763	−	0.749713i	$-0.730191\pi$
$479$	3.49917e7	−	6.06074e7i	0.318389	−	0.551467i	0.980152	+	0.198247i	$0.0635247\pi$
$480$	−9.75347e7	+	5.63117e7i	−0.881933	+	0.509184i
$481$		−	1.14617e8i		−	1.02995i
$482$	−1.42885e8	−	2.47484e8i	−1.27599	−	2.21007i
$483$	1.34447e7	−	2.32869e7i	0.119319	−	0.206666i
$484$	−1.32312e8			−1.16698
$485$	7.91658e6	+	4.57064e6i	0.0693925	+	0.0400638i
$486$	8.76512e7	+	1.51816e8i	0.763571	+	1.32254i
$487$	4.94502e7	+	8.56503e7i	0.428135	+	0.741552i	0.996708	−	0.0810811i	$-0.0258373\pi$
$487$	4.94502e7	+	8.56503e7i	0.428135	+	0.741552i	−0.568572	+	0.822633i	$0.692504\pi$
$488$	−1.85478e7	−	3.21257e7i	−0.159600	−	0.276435i
$489$	2.18915e7			0.187219
$490$	4.81413e7	+	8.33831e7i	0.409194	+	0.708745i
$491$	4.69445e7	−	2.71034e7i	0.396589	−	0.228971i	−0.288422	−	0.957503i	$-0.593131\pi$
$491$	4.69445e7	−	2.71034e7i	0.396589	−	0.228971i	0.685011	+	0.728533i	$0.259797\pi$
$492$	1.09690e8	+	6.33297e7i	0.921028	+	0.531756i
$493$	6.58460e7	+	3.80162e7i	0.549526	+	0.317269i
$494$	1.39282e8			1.15535
$495$		−	1.24850e8i		−	1.02937i
$496$	2.11530e7	−	3.66381e7i	0.173351	−	0.300254i
$497$	−6.23804e7	+	1.08046e8i	−0.508135	+	0.880116i
$498$	3.93385e7	+	6.81362e7i	0.318515	+	0.551684i
$499$	1.12455e8	−	6.49258e7i	0.905058	−	0.522535i	0.0262201	−	0.999656i	$-0.491653\pi$
$499$	1.12455e8	−	6.49258e7i	0.905058	−	0.522535i	0.878838	+	0.477121i	$0.158320\pi$
$500$			1.06749e8i			0.853990i
$501$	1.23692e8	−	7.14137e7i	0.983624	−	0.567896i
$502$	2.39566e8	−	1.38313e8i	1.89371	−	1.09333i
$503$	2.91336e7	−	1.68203e7i	0.228923	−	0.132169i	−0.381152	−	0.924512i	$-0.624473\pi$
$503$	2.91336e7	−	1.68203e7i	0.228923	−	0.132169i	0.610075	+	0.792343i	$0.291139\pi$
$504$	1.47907e7	−	2.56183e7i	0.115531	−	0.200105i
$505$		−	6.23435e7i		−	0.484080i
$506$	−1.21581e8	−	7.01947e7i	−0.938456	−	0.541818i
$507$	3.58098e7	−	2.06748e7i	0.274775	−	0.158642i
$508$	2.09734e8			1.59984
$509$	1.09957e8	+	1.90451e8i	0.833813	+	1.44421i	0.894993	+	0.446080i	$0.147180\pi$
$509$	1.09957e8	+	1.90451e8i	0.833813	+	1.44421i	−0.0611798	+	0.998127i	$0.519486\pi$
$510$	1.89480e8	+	1.09397e8i	1.42841	+	0.824695i
$511$	−7.50210e7	+	1.29940e8i	−0.562238	+	0.973824i
$512$		−	1.41251e8i		−	1.05241i
$513$	−7.32823e7	+	1.26929e8i	−0.542809	+	0.940173i
$514$	−1.99240e8			−1.46719
$515$			2.55488e8i			1.87046i
$516$	−8.31734e7	−	7.57474e7i	−0.605390	−	0.551339i
$517$	−1.02661e8			−0.742906
$518$		−	2.33986e8i		−	1.68345i
$519$	−7.65092e6	−	4.41726e6i	−0.0547282	−	0.0315974i
$520$	5.93326e7			0.421971
$521$	−1.71803e8	−	9.91905e7i	−1.21484	−	0.701386i	−0.251027	−	0.967980i	$-0.580768\pi$
$521$	−1.71803e8	−	9.91905e7i	−1.21484	−	0.701386i	−0.963809	+	0.266594i	$0.914102\pi$
$522$	−2.94960e7	+	5.10887e7i	−0.207373	+	0.359181i
$523$	−4.84491e7	+	2.79721e7i	−0.338673	+	0.195533i	−0.659685	−	0.751542i	$-0.729310\pi$
$523$	−4.84491e7	+	2.79721e7i	−0.338673	+	0.195533i	0.321012	+	0.947075i	$0.395977\pi$
$524$			4.14118e7i			0.287826i
$525$	1.56361e7	+	2.70825e7i	0.108056	+	0.187159i
$526$	−1.22825e8	+	2.12739e8i	−0.843974	+	1.46181i
$527$	−1.29792e8			−0.886781
$528$	−6.09375e7	−	3.51823e7i	−0.413984	−	0.239014i
$529$	5.41446e7	+	9.37813e7i	0.365753	+	0.633504i
$530$	3.93705e7	+	6.81917e7i	0.264450	+	0.458040i
$531$	−5.53200e7	−	9.58170e7i	−0.369486	−	0.639969i
$532$	1.62171e8			1.07705
$533$	6.85263e7	+	1.18691e8i	0.452559	+	0.783856i
$534$	1.38143e8	−	7.97568e7i	0.907203	−	0.523774i
$535$	−1.20900e8	−	6.98014e7i	−0.789520	−	0.455830i
$536$	−4.28769e7	−	2.47550e7i	−0.278438	−	0.160756i
$537$	−1.26616e8			−0.817648
$538$			2.26207e7i			0.145264i
$539$	−4.74989e7	+	8.22706e7i	−0.303332	+	0.525386i
$540$	−1.26553e8	+	2.19196e8i	−0.803696	+	1.39204i
$541$	−6.90958e6	−	1.19678e7i	−0.0436375	−	0.0755824i	0.843382	−	0.537315i	$-0.180561\pi$
$541$	−6.90958e6	−	1.19678e7i	−0.0436375	−	0.0755824i	−0.887019	+	0.461733i	$0.847228\pi$
$542$	2.00481e8	−	1.15748e8i	1.25914	−	0.726966i
$543$		−	1.75093e8i		−	1.09363i
$544$	−2.74583e8	+	1.58530e8i	−1.70560	+	0.984726i
$545$	2.27669e8	−	1.31445e8i	1.40642	−	0.811997i
$546$	−6.90199e7	+	3.98487e7i	−0.424030	+	0.244814i
$547$	8.89896e7	−	1.54134e8i	0.543722	−	0.941755i	−0.454964	−	0.890510i	$-0.650348\pi$
$547$	8.89896e7	−	1.54134e8i	0.543722	−	0.941755i	0.998686	−	0.0512447i	$-0.0163188\pi$
$548$			1.78782e8i			1.08638i
$549$	5.67251e7	+	3.27503e7i	0.342814	+	0.197924i
$550$	1.41398e8	−	8.16361e7i	0.849875	−	0.490675i
$551$	−7.97759e7			−0.476888
$552$	1.34279e7	+	2.32578e7i	0.0798345	+	0.138277i
$553$	−8.98763e6	−	5.18901e6i	−0.0531459	−	0.0306838i
$554$	2.25692e8	−	3.90911e8i	1.32736	−	2.29905i
$555$			1.88913e8i			1.10505i
$556$	−1.63232e8	+	2.82727e8i	−0.949690	+	1.64491i
$557$	−2.05210e8			−1.18750			−0.593749	−	0.804650i	$-0.702353\pi$
$557$	−2.05210e8			−1.18750			−0.593749	+	0.804650i	$0.702353\pi$
$558$		−	1.00703e8i		−	0.579617i
$559$	−3.69594e7	−	1.15981e8i	−0.211587	−	0.663975i
$560$	−8.98493e7			−0.511624
$561$			2.15874e8i			1.22268i
$562$	3.23664e8	+	1.86867e8i	1.82341	+	1.05275i
$563$	−1.61619e8			−0.905666			−0.452833	−	0.891595i	$-0.649587\pi$
$563$	−1.61619e8			−0.905666			−0.452833	+	0.891595i	$0.649587\pi$
$564$	6.89470e7	+	3.98066e7i	0.384307	+	0.221880i
$565$	−7.67771e7	+	1.32982e8i	−0.425683	+	0.737305i
$566$	2.63803e7	−	1.52307e7i	0.145489	−	0.0839983i
$567$			448744.i			0.00246178i
$568$	−6.23025e7	−	1.07911e8i	−0.339986	−	0.588873i
$569$	−9.86242e7	+	1.70822e8i	−0.535361	+	0.927273i	0.463785	+	0.885948i	$0.346491\pi$
$569$	−9.86242e7	+	1.70822e8i	−0.535361	+	0.927273i	−0.999146	+	0.0413246i	$0.986842\pi$
$570$	−2.29566e8			−1.23960
$571$	2.19840e7	+	1.26925e7i	0.118086	+	0.0681770i	0.557880	−	0.829922i	$-0.311615\pi$
$571$	2.19840e7	+	1.26925e7i	0.118086	+	0.0681770i	−0.439794	+	0.898099i	$0.644948\pi$
$572$	1.18660e8	+	2.05526e8i	0.634041	+	1.09819i
$573$	4.79763e7	+	8.30975e7i	0.255014	+	0.441696i
$574$	1.39893e8	+	2.42302e8i	0.739710	+	1.28122i
$575$	4.62251e7			0.243150
$576$	−8.95360e7	−	1.55081e8i	−0.468522	−	0.811504i
$577$	−7.83811e7	+	4.52533e7i	−0.408022	+	0.235572i	−0.689940	−	0.723867i	$-0.742363\pi$
$577$	−7.83811e7	+	4.52533e7i	−0.408022	+	0.235572i	0.281917	+	0.959439i	$0.409030\pi$
$578$	2.78305e8	+	1.60680e8i	1.44124	+	0.832103i
$579$	−1.79098e8	−	1.03402e8i	−0.922687	−	0.532713i
$580$	−1.37767e8			−0.706092
$581$			9.91230e7i			0.505413i
$582$	6.13176e6	−	1.06205e7i	0.0311040	−	0.0538737i
$583$	−3.88452e7	+	6.72818e7i	−0.196034	+	0.339541i
$584$	−7.49273e7	−	1.29778e8i	−0.376185	−	0.651572i
$585$	−9.07291e7	+	5.23825e7i	−0.453189	+	0.261649i
$586$		−	2.20447e8i		−	1.09550i
$587$	−8.11189e7	+	4.68340e7i	−0.401059	+	0.231551i	−0.686941	−	0.726713i	$-0.741047\pi$
$587$	−8.11189e7	+	4.68340e7i	−0.401059	+	0.231551i	0.285882	+	0.958265i	$0.407713\pi$
$588$	6.38005e7	−	3.68352e7i	0.313828	−	0.181189i
$589$	1.17938e8	−	6.80913e7i	0.577173	−	0.333231i
$590$	2.26515e8	−	3.92335e8i	1.10291	−	1.91030i
$591$		−	1.37900e8i		−	0.668041i
$592$	−1.50127e8	−	8.66759e7i	−0.723593	−	0.417766i
$593$	1.39072e8	−	8.02930e7i	0.666921	−	0.385047i	−0.127988	−	0.991776i	$-0.540852\pi$
$593$	1.39072e8	−	8.02930e7i	0.666921	−	0.385047i	0.794909	+	0.606729i	$0.207519\pi$
$594$	−4.37857e8			−2.08916
$595$	1.37826e8	+	2.38721e8i	0.654305	+	1.13329i
$596$	2.89982e8	+	1.67421e8i	1.36972	+	0.790809i
$597$	−3.22458e7	+	5.58514e7i	−0.151548	+	0.262489i
$598$			1.17805e8i			0.550884i
$599$	1.52271e8	−	2.63742e8i	0.708497	−	1.22715i	−0.256918	−	0.966433i	$-0.582707\pi$
$599$	1.52271e8	−	2.63742e8i	0.708497	−	1.22715i	0.965415	−	0.260719i	$-0.0839596\pi$
$600$	−3.12331e7			−0.144598
$601$		−	3.07887e8i		−	1.41830i	−0.705058	−	0.709149i	$-0.749079\pi$
$601$		−	3.07887e8i		−	1.41830i	0.705058	−	0.709149i	$-0.250921\pi$
$602$	−7.54509e7	−	2.36770e8i	−0.345840	−	1.08527i
$603$	8.74210e7			0.398716
$604$		−	4.28421e8i		−	1.94429i
$605$	2.04357e8	+	1.17986e8i	0.922836	+	0.532799i
$606$	−8.36372e7			−0.375821
$607$	4.78001e7	+	2.75974e7i	0.213729	+	0.123396i	0.603043	−	0.797709i	$-0.293955\pi$
$607$	4.78001e7	+	2.75974e7i	0.213729	+	0.123396i	−0.389314	+	0.921105i	$0.627288\pi$
$608$	1.66336e8	−	2.88102e8i	0.740073	−	1.28184i
$609$	3.95322e7	−	2.28239e7i	0.175025	−	0.101050i
$610$			2.68200e8i			1.18160i
$611$	4.30729e7	+	7.46045e7i	0.188834	+	0.327070i
$612$	−1.36286e8	+	2.36054e8i	−0.594560	+	1.02981i
$613$	2.23884e8			0.971944			0.485972	−	0.873974i	$-0.338466\pi$
$613$	2.23884e8			0.971944			0.485972	+	0.873974i	$0.338466\pi$
$614$	−4.87684e8	−	2.81565e8i	−2.10685	−	1.21639i
$615$	−1.12945e8	−	1.95627e8i	−0.485561	−	0.841016i
$616$	5.97543e7	+	1.03498e8i	0.255639	+	0.442780i
$617$	−1.86075e8	−	3.22292e8i	−0.792196	−	1.37212i	−0.924604	−	0.380929i	$-0.875604\pi$
$617$	−1.86075e8	−	3.22292e8i	−0.792196	−	1.37212i	0.132408	−	0.991195i	$-0.457729\pi$
$618$	3.42751e8			1.45216
$619$	1.73207e8	+	3.00003e8i	0.730285	+	1.26489i	0.956761	+	0.290875i	$0.0939463\pi$
$619$	1.73207e8	+	3.00003e8i	0.730285	+	1.26489i	−0.226476	+	0.974017i	$0.572720\pi$
$620$	2.03669e8	−	1.17589e8i	0.854576	−	0.493390i
$621$	−1.07356e8	−	6.19822e7i	−0.448284	−	0.258817i
$622$	2.01742e8	+	1.16476e8i	0.838348	+	0.484021i
$623$	2.00967e8			0.831113
$624$			5.90450e7i			0.243013i
$625$	1.52472e8	−	2.64090e8i	0.624527	−	1.08171i
$626$	3.42693e8	−	5.93562e8i	1.39696	−	2.41960i
$627$	−1.13251e8	−	1.96157e8i	−0.459452	−	0.795795i
$628$	−3.30877e6	+	1.91032e6i	−0.0133594	+	0.00771305i
$629$			5.31832e8i			2.13709i
$630$	−1.85220e8	+	1.06937e8i	−0.740739	+	0.427666i
$631$	−3.45368e8	+	1.99398e8i	−1.37466	+	0.793659i	−0.991510	−	0.130029i	$-0.958493\pi$
$631$	−3.45368e8	+	1.99398e8i	−1.37466	+	0.793659i	−0.383147	+	0.923687i	$0.625160\pi$
$632$	8.97641e6	−	5.18253e6i	0.0355591	−	0.0205301i
$633$	−1.06851e8	+	1.85071e8i	−0.421275	+	0.729670i
$634$			3.04236e8i			1.19383i
$635$	−3.23937e8	−	1.87025e8i	−1.26514	−	0.730429i
$636$	5.21767e7	−	3.01243e7i	0.202818	−	0.117097i
$637$	7.97155e7			0.308407
$638$	−1.19164e8	−	2.06398e8i	−0.458862	−	0.794773i
$639$	1.90541e8	+	1.10009e8i	0.730276	+	0.421625i
$640$	1.50224e8	−	2.60196e8i	0.573059	−	0.992567i
$641$			6.70622e7i			0.254627i	0.991863	+	0.127313i	$0.0406354\pi$
$641$			6.70622e7i			0.254627i	−0.991863	+	0.127313i	$0.959365\pi$
$642$	−9.36423e7	+	1.62193e8i	−0.353889	+	0.612954i
$643$	−1.90178e7			−0.0715365			−0.0357682	−	0.999360i	$-0.511388\pi$
$643$	−1.90178e7			−0.0715365			−0.0357682	+	0.999360i	$0.511388\pi$
$644$			1.37164e8i			0.513551i
$645$	6.09167e7	+	1.91161e8i	0.227016	+	0.712393i
$646$	−6.46280e8			−2.39730
$647$		−	2.39490e8i		−	0.884249i	−0.896954	−	0.442125i	$-0.854225\pi$
$647$		−	2.39490e8i		−	0.884249i	0.896954	−	0.442125i	$-0.145775\pi$
$648$	−388138.	−	224092.i	−0.00142647	−	0.000823571i
$649$	4.46984e8			1.63515
$650$	−1.18651e8	−	6.85033e7i	−0.432048	−	0.249443i
$651$	−3.89619e7	+	6.74840e7i	−0.141220	+	0.244601i
$652$	−9.67091e7	+	5.58350e7i	−0.348919	+	0.201448i
$653$		−	1.74522e7i		−	0.0626775i	−0.999509	−	0.0313388i	$-0.990023\pi$
$653$		−	1.74522e7i		−	0.0626775i	0.999509	−	0.0313388i	$-0.00997707\pi$
$654$	−1.76341e8	−	3.05431e8i	−0.630404	−	1.09189i
$655$	3.69279e7	−	6.39611e7i	0.131411	−	0.227610i
$656$	2.07284e8			0.734269
$657$	2.29152e8	+	1.32301e8i	0.808030	+	0.466517i
$658$	8.79315e7	+	1.52302e8i	0.308650	+	0.534598i
$659$	−2.20170e8	−	3.81345e8i	−0.769310	−	1.33248i	−0.937938	−	0.346804i	$-0.887267\pi$
$659$	−2.20170e8	−	3.81345e8i	−0.769310	−	1.33248i	0.168628	−	0.985680i	$-0.446066\pi$
$660$	−1.95577e8	−	3.38749e8i	−0.680276	−	1.17827i
$661$	2.61688e8			0.906107			0.453053	−	0.891483i	$-0.350335\pi$
$661$	2.61688e8			0.906107			0.453053	+	0.891483i	$0.350335\pi$
$662$	−1.41827e7	−	2.45651e7i	−0.0488860	−	0.0846731i
$663$	1.56877e8	−	9.05731e7i	0.538293	−	0.310784i
$664$	−8.57359e7	−	4.94996e7i	−0.292859	−	0.169082i
$665$	−2.50475e8	−	1.44612e8i	−0.851725	−	0.491744i
$666$	−4.12639e8			−1.39684
$667$		−	6.74745e7i		−	0.227385i
$668$	−3.64286e8	+	6.30961e8i	−1.22212	+	2.11677i
$669$	8.50331e7	−	1.47282e8i	0.283994	−	0.491892i
$670$	1.78978e8	+	3.09999e8i	0.595080	+	1.03071i
$671$	−2.29169e8	+	1.32311e8i	−0.758557	+	0.437953i
$672$			1.90355e8i			0.627272i
$673$	−3.66228e8	+	2.11442e8i	−1.20145	+	0.693658i	−0.960878	−	0.276973i	$-0.910669\pi$
$673$	−3.66228e8	+	2.11442e8i	−1.20145	+	0.693658i	−0.240573	+	0.970631i	$0.577335\pi$
$674$	−7.88753e8	+	4.55387e8i	−2.57609	+	1.48731i
$675$	1.24855e8	−	7.20850e7i	0.405970	−	0.234387i
$676$	−1.05463e8	+	1.82668e8i	−0.341398	+	0.591319i
$677$			1.35947e8i			0.438129i	0.975710	+	0.219065i	$0.0703005\pi$
$677$			1.35947e8i			0.438129i	−0.975710	+	0.219065i	$0.929699\pi$
$678$	1.78402e8	+	1.03001e8i	0.572416	+	0.330485i
$679$	1.33805e7	−	7.72525e6i	0.0427429	−	0.0246776i
$680$	−2.75308e8			−0.875571
$681$	1.34950e8	+	2.33740e8i	0.427298	+	0.740102i
$682$	3.52334e8	+	2.03420e8i	1.11071	+	0.641270i
$683$	9.14614e7	−	1.58416e8i	0.287062	−	0.497206i	−0.686045	−	0.727559i	$-0.740655\pi$
$683$	9.14614e7	−	1.58416e8i	0.287062	−	0.497206i	0.973107	+	0.230353i	$0.0739880\pi$
$684$		−	2.85992e8i		−	0.893686i
$685$	1.59424e8	−	2.76131e8i	0.496002	−	0.859100i
$686$	5.30451e8			1.64313
$687$		−	5.01123e6i		−	0.0154552i
$688$	−1.79863e8	−	3.92975e7i	−0.552302	−	0.120670i
$689$	6.51922e7			0.199314
$690$		−	1.94167e8i		−	0.591055i
$691$	−1.50564e8	−	8.69280e7i	−0.456338	−	0.263467i	0.254165	−	0.967161i	$-0.418199\pi$
$691$	−1.50564e8	−	8.69280e7i	−0.456338	−	0.263467i	−0.710503	+	0.703694i	$0.751533\pi$
$692$	4.50654e7			0.135996
$693$	−1.82748e8	−	1.05510e8i	−0.549102	−	0.317024i
$694$	−4.65933e8	+	8.07020e8i	−1.39394	+	2.41438i
$695$	5.04229e8	−	2.91117e8i	1.50201	−	0.867188i
$696$			4.55908e7i			0.135223i
$697$	−3.17967e8	−	5.50735e8i	−0.939040	−	1.62646i
$698$	7.93168e7	−	1.37381e8i	0.233238	−	0.403980i
$699$	3.13040e8			0.916575
$700$	−1.38149e8	−	7.97606e7i	−0.402768	−	0.232538i
$701$	2.29131e8	+	3.96866e8i	0.665164	+	1.15210i	0.979241	+	0.202701i	$0.0649718\pi$
$701$	2.29131e8	+	3.96866e8i	0.665164	+	1.15210i	−0.314076	+	0.949398i	$0.601695\pi$
$702$	1.83709e8	+	3.18194e8i	0.531030	+	0.919772i
$703$	−2.79009e8	−	4.83257e8i	−0.803067	−	1.39095i
$704$	7.23449e8			2.07343
$705$	−7.09931e7	−	1.22964e8i	−0.202604	−	0.350921i
$706$	2.02904e8	−	1.17147e8i	0.576604	−	0.332902i
$707$	−9.12551e7	−	5.26861e7i	−0.258225	−	0.149086i
$708$	−3.00194e8	−	1.73317e8i	−0.845868	−	0.488362i
$709$	−3.39431e8			−0.952385			−0.476193	−	0.879341i	$-0.657984\pi$
$709$	−3.39431e8			−0.952385			−0.476193	+	0.879341i	$0.657984\pi$
$710$			9.00892e8i			2.51708i
$711$	−9.15092e6	+	1.58499e7i	−0.0254599	+	0.0440978i
$712$	−1.00358e8	+	1.73825e8i	−0.278043	+	0.481585i
$713$	5.75917e7	+	9.97517e7i	0.158888	+	0.275202i
$714$	3.20258e8	−	1.84901e8i	0.879843	−	0.507977i
$715$		−	4.23250e8i		−	1.15792i
$716$	5.59346e8	−	3.22938e8i	1.52385	−	0.879793i
$717$	7.41947e7	−	4.28364e7i	0.201287	−	0.116213i
$718$	1.70832e8	−	9.86301e7i	0.461526	−	0.266462i
$719$	−1.62600e8	+	2.81632e8i	−0.437456	+	0.757696i	−0.997493	−	0.0707718i	$-0.977454\pi$
$719$	−1.62600e8	+	2.81632e8i	−0.437456	+	0.757696i	0.560036	+	0.828468i	$0.310787\pi$
$720$			1.58451e8i			0.424520i
$721$	3.73970e8	+	2.15912e8i	0.997770	+	0.576063i
$722$	8.99931e7	−	5.19575e7i	0.239110	−	0.138050i
$723$	3.89964e8			1.03183
$724$	4.46579e8	+	7.73498e8i	1.17675	+	2.03818i
$725$	6.79592e7	+	3.92363e7i	0.178334	+	0.102961i
$726$	1.58284e8	−	2.74157e8i	0.413645	−	0.716455i
$727$			1.19403e8i			0.310750i	0.987856	+	0.155375i	$0.0496586\pi$
$727$			1.19403e8i			0.310750i	−0.987856	+	0.155375i	$0.950341\pi$
$728$	5.01416e7	−	8.68478e7i	0.129958	−	0.225094i
$729$	−2.37941e8			−0.614168
$730$			1.08345e9i			2.78509i
$731$	1.71494e8	+	5.38161e8i	0.439033	+	1.37772i
$732$	2.05213e8			0.523204
$733$		−	2.15521e8i		−	0.547240i	−0.961838	−	0.273620i	$-0.911779\pi$
$733$		−	2.15521e8i		−	0.547240i	0.961838	−	0.273620i	$-0.0882211\pi$
$734$	3.87533e8	+	2.23742e8i	0.979988	+	0.565796i
$735$	−1.31388e8			−0.330897
$736$	2.43677e8	+	1.40687e8i	0.611196	+	0.352874i
$737$	−1.76590e8	+	3.05863e8i	−0.441127	+	0.764054i
$738$	4.27305e8	−	2.46705e8i	1.06309	−	0.613774i
$739$		−	1.48063e8i		−	0.366871i	−0.983032	−	0.183435i	$-0.941278\pi$
$739$		−	1.48063e8i		−	0.366871i	0.983032	−	0.183435i	$-0.0587218\pi$
$740$	−4.81827e8	−	8.34549e8i	−1.18904	−	2.05948i
$741$	−9.50325e7	+	1.64601e8i	−0.233570	+	0.404556i
$742$	1.33087e8			0.325780
$743$	−4.89963e8	−	2.82880e8i	−1.19453	−	0.689662i	−0.235199	−	0.971947i	$-0.575574\pi$
$743$	−4.89963e8	−	2.82880e8i	−1.19453	−	0.689662i	−0.959331	+	0.282285i	$0.908908\pi$
$744$	−3.89133e7	−	6.73997e7i	−0.0944885	−	0.163659i
$745$	−2.98587e8	−	5.17169e8i	−0.722109	−	1.25073i
$746$	−9.47349e6	−	1.64086e7i	−0.0228188	−	0.0395234i
$747$	1.74805e8			0.419366
$748$	−5.50593e8	−	9.53655e8i	−1.31561	−	2.27870i
$749$	−2.04343e8	+	1.17977e8i	−0.486311	+	0.280772i
$750$	−2.21189e8	−	1.27703e8i	−0.524299	−	0.302704i
$751$	2.13089e8	+	1.23027e8i	0.503084	+	0.290456i	0.729986	−	0.683462i	$-0.239526\pi$
$751$	2.13089e8	+	1.23027e8i	0.503084	+	0.290456i	−0.226902	+	0.973918i	$0.572860\pi$
$752$	1.30291e8			0.306380
$753$			3.77486e8i			0.884130i
$754$	−9.99938e7	+	1.73194e8i	−0.233270	+	0.404036i
$755$	−3.82034e8	+	6.61703e8i	−0.887690	+	1.53752i
$756$	2.13899e8	+	3.70483e8i	0.495043	+	0.857439i
$757$	−4.49703e8	+	2.59636e8i	−1.03666	+	0.598518i	−0.918886	−	0.394522i	$-0.870910\pi$
$757$	−4.49703e8	+	2.59636e8i	−1.03666	+	0.598518i	−0.117777	+	0.993040i	$0.537577\pi$
$758$			3.51042e8i			0.806030i
$759$	1.65910e8	−	9.57881e7i	0.379443	−	0.219072i
$760$	2.50162e8	−	1.44431e8i	0.569877	−	0.329019i
$761$	1.22254e8	−	7.05834e7i	0.277402	−	0.160158i	−0.354845	−	0.934925i	$-0.615466\pi$
$761$	1.22254e8	−	7.05834e7i	0.277402	−	0.160158i	0.632247	+	0.774767i	$0.282133\pi$
$762$	−2.50904e8	+	4.34578e8i	−0.567078	+	0.982208i
$763$		−	4.44334e8i		−	1.00031i
$764$	−4.23885e8	−	2.44730e8i	−0.950535	−	0.548792i
$765$	4.20990e8	−	2.43059e8i	0.940346	−	0.542909i
$766$	1.00449e8			0.223490
$767$	−1.87539e8	−	3.24827e8i	−0.415628	−	0.719889i
$768$	1.69502e7	+	9.78619e6i	0.0374188	+	0.0216038i
$769$	1.68123e8	−	2.91197e8i	0.369698	−	0.640336i	−0.619820	−	0.784744i	$-0.712794\pi$
$769$	1.68123e8	−	2.91197e8i	0.369698	−	0.640336i	0.989518	+	0.144408i	$0.0461278\pi$
$770$		−	8.64046e8i		−	1.89262i
$771$	1.35942e8	−	2.35459e8i	0.296613	−	0.513749i
$772$	1.05492e9			2.29281
$773$		−	5.67268e8i		−	1.22814i	−0.789250	−	0.614072i	$-0.789530\pi$
$773$		−	5.67268e8i		−	1.22814i	0.789250	−	0.614072i	$-0.210470\pi$
$774$	−4.17549e8	+	1.33059e8i	−0.900502	+	0.286960i
$775$	−1.33958e8			−0.287781
$776$			1.54312e7i			0.0330229i
$777$	2.76520e8	+	1.59649e8i	0.589473	+	0.340332i
$778$	−8.27822e8			−1.75792
$779$	5.77851e8	+	3.33623e8i	1.22237	+	0.705737i
$780$	−1.64114e8	+	2.84254e8i	−0.345830	+	0.598994i
$781$	−7.69786e8	+	4.44436e8i	−1.61591	+	0.932945i
$782$		−	5.46624e8i		−	1.14306i
$783$	−1.05222e8	−	1.82250e8i	−0.219191	−	0.379649i
$784$	6.02826e7	−	1.04413e8i	0.125096	−	0.216673i
$785$	6.81391e6			0.0140860
$786$	−8.58072e7	−	4.95408e7i	−0.176708	−	0.102022i
$787$	−3.32132e8	−	5.75269e8i	−0.681375	−	1.18018i	−0.974561	−	0.224120i	$-0.928049\pi$
$787$	−3.32132e8	−	5.75269e8i	−0.681375	−	1.18018i	0.293187	−	0.956055i	$-0.405284\pi$
$788$	3.51719e8	+	6.09195e8i	0.718815	+	1.24502i
$789$	−1.67607e8	−	2.90304e8i	−0.341242	−	0.591048i
$790$	−7.49392e7			−0.151994
$791$	1.29768e8	+	2.24765e8i	0.262203	+	0.454149i
$792$	1.82520e8	−	1.05378e8i	0.367397	−	0.212116i
$793$	1.92302e8	+	1.11026e8i	0.385625	+	0.222641i
$794$	−6.34613e8	−	3.66394e8i	−1.26779	−	0.731959i
$795$	−1.07450e8			−0.213848
$796$		−	3.28976e8i		−	0.652266i
$797$	−4.04452e8	+	7.00532e8i	−0.798900	+	1.38374i	0.121433	+	0.992600i	$0.461251\pi$
$797$	−4.04452e8	+	7.00532e8i	−0.798900	+	1.38374i	−0.920333	+	0.391136i	$0.872082\pi$
$798$	−1.94005e8	+	3.36026e8i	−0.381771	+	0.661248i
$799$	−1.99862e8	−	3.46171e8i	−0.391822	−	0.678656i
$800$	−2.83395e8	+	1.63618e8i	−0.553505	+	0.319567i
$801$		−	3.54409e8i		−	0.689616i
$802$	−5.07955e8	+	2.93268e8i	−0.984695	+	0.568514i
$803$	−9.25773e8	+	5.34495e8i	−1.78796	+	1.03228i
$804$	2.37195e8	−	1.36945e8i	0.456392	−	0.263498i
$805$	1.22313e8	−	2.11852e8i	0.234468	−	0.406111i
$806$		−	3.41392e8i		−	0.652001i
$807$	−2.67327e7	−	1.54342e7i	−0.0508654	−	0.0293672i
$808$	9.11412e7	−	5.26204e7i	0.172775	−	0.0997516i
$809$	5.68187e8			1.07311			0.536556	−	0.843864i	$-0.319725\pi$
$809$	5.68187e8			1.07311			0.536556	+	0.843864i	$0.319725\pi$
$810$	1.62018e6	+	2.80623e6i	0.00304865	+	0.00528042i
$811$	−4.42976e8	−	2.55752e8i	−0.830457	−	0.479465i	0.0235520	−	0.999723i	$-0.492502\pi$
$811$	−4.42976e8	−	2.55752e8i	−0.830457	−	0.479465i	−0.854009	+	0.520258i	$0.825836\pi$
$812$	−1.16426e8	+	2.01656e8i	−0.217462	+	0.376655i
$813$			3.15900e8i			0.587865i
$814$	8.33528e8	−	1.44371e9i	1.54542	−	2.67675i
$815$	1.99158e8			0.367896
$816$		−	2.73973e8i		−	0.504241i
$817$	−4.38160e8	−	3.99039e8i	−0.803464	−	0.731727i
$818$	−1.30324e9			−2.38102
$819$			1.77073e8i			0.322329i
$820$	9.97907e8	+	5.76142e8i	1.80987	+	1.04493i
$821$	6.92301e8			1.25102			0.625512	−	0.780215i	$-0.284890\pi$
$821$	6.92301e8			1.25102			0.625512	+	0.780215i	$0.284890\pi$
$822$	−3.70445e8	−	2.13877e8i	−0.666973	−	0.385077i
$823$	−3.20231e8	+	5.54656e8i	−0.574465	+	0.995002i	0.421635	+	0.906766i	$0.361456\pi$
$823$	−3.20231e8	+	5.54656e8i	−0.574465	+	0.995002i	−0.996100	+	0.0882364i	$0.971877\pi$
$824$	−3.73503e8	+	2.15642e8i	−0.667594	+	0.385435i
$825$			2.22802e8i			0.396787i
$826$	−3.82852e8	−	6.63120e8i	−0.679346	−	1.17666i
$827$	5.47434e7	−	9.48184e7i	0.0967867	−	0.167639i	−0.813566	−	0.581472i	$-0.802477\pi$
$827$	5.47434e7	−	9.48184e7i	0.0967867	−	0.167639i	0.910353	+	0.413833i	$0.135810\pi$
$828$	2.41892e8			0.426119
$829$	3.19886e8	+	1.84686e8i	0.561477	+	0.324169i	0.753738	−	0.657175i	$-0.228249\pi$
$829$	3.19886e8	+	1.84686e8i	0.561477	+	0.324169i	−0.192261	+	0.981344i	$0.561582\pi$
$830$	3.57881e8	+	6.19869e8i	0.625900	+	1.08409i
$831$	3.07981e8	+	5.33439e8i	0.536687	+	0.929568i
$832$	−3.03534e8	−	5.25736e8i	−0.527032	−	0.912846i
$833$	−3.69886e8			−0.639931
$834$	−3.90549e8	−	6.76451e8i	−0.673252	−	1.16611i
$835$	1.12529e9	−	6.49686e8i	1.93288	−	1.11595i
$836$	1.00061e9	+	5.77702e8i	1.71256	+	0.988746i
$837$	3.11113e8	+	1.79621e8i	0.530568	+	0.306324i
$838$	−6.74325e7			−0.114587
$839$			1.01496e9i			1.71856i	0.511507	+	0.859279i	$0.329088\pi$
$839$			1.01496e9i			1.71856i	−0.511507	+	0.859279i	$0.670912\pi$
$840$	−8.26437e7	+	1.43143e8i	−0.139435	+	0.241509i
$841$	−2.40139e8	+	4.15932e8i	−0.403714	+	0.699254i
$842$	4.02961e7	+	6.97949e7i	0.0675036	+	0.116920i
$843$	−4.41673e8	+	2.55000e8i	−0.737256	+	0.425655i
$844$		−	1.09010e9i		−	1.81318i
$845$	3.25779e8	−	1.88089e8i	0.539950	−	0.311740i
$846$	2.68587e8	−	1.55069e8i	0.443582	−	0.256102i
$847$	3.45403e8	−	1.99418e8i	0.568428	−	0.328182i
$848$	4.92998e7	−	8.53898e7i	0.0808458	−	0.140029i
$849$			4.15678e7i			0.0679256i
$850$	5.50550e8	+	3.17860e8i	0.896479	+	0.517583i
$851$	4.08739e8	−	2.35986e8i	0.663220	−	0.382910i
$852$	6.89316e8			1.11455
$853$	2.82951e8	+	4.90086e8i	0.455895	+	0.789633i	0.998739	−	0.0502004i	$-0.0159860\pi$
$853$	2.82951e8	+	4.90086e8i	0.455895	+	0.789633i	−0.542844	+	0.839833i	$0.682653\pi$
$854$	3.92577e8	+	2.26654e8i	0.630306	+	0.363907i
$855$	−2.55026e8	+	4.41718e8i	−0.408024	+	0.706719i
$856$		−	2.35660e8i		−	0.375721i
$857$	1.04626e8	−	1.81217e8i	0.166225	−	0.287910i	−0.770865	−	0.636999i	$-0.780176\pi$
$857$	1.04626e8	−	1.81217e8i	0.166225	−	0.287910i	0.937090	+	0.349089i	$0.113509\pi$
$858$	−5.67812e8			−0.898966
$859$			2.12315e8i			0.334967i	0.985875	+	0.167484i	$0.0535641\pi$
$859$			2.12315e8i			0.334967i	−0.985875	+	0.167484i	$0.946436\pi$
$860$	−7.56670e8	−	6.89111e8i	−1.18963	−	1.08341i
$861$	−3.81798e8			−0.598170
$862$		−	6.07851e8i		−	0.949020i
$863$	−6.13167e8	−	3.54012e8i	−0.953996	−	0.550790i	−0.0596758	−	0.998218i	$-0.519007\pi$
$863$	−6.13167e8	−	3.54012e8i	−0.953996	−	0.550790i	−0.894320	+	0.447428i	$0.852340\pi$
$864$	8.77568e8			1.36063
$865$	−6.96041e7	−	4.01860e7i	−0.107544	−	0.0620906i
$866$	−8.21407e8	+	1.42272e9i	−1.26475	+	2.19061i
$867$	−3.79776e8	+	2.19264e8i	−0.582735	+	0.336442i
$868$		−	3.97494e8i		−	0.607815i
$869$	−3.69697e7	−	6.40333e7i	−0.0563360	−	0.0975768i
$870$	1.64810e8	−	2.85460e8i	0.250281	−	0.433499i
$871$	2.96364e8			0.448508
$872$	3.84324e8	+	2.21889e8i	0.579626	+	0.334647i
$873$	−1.36236e7	−	2.35968e7i	−0.0204762	−	0.0354659i
$874$	2.86769e8	+	4.96698e8i	0.429534	+	0.743975i
$875$	−1.60890e8	−	2.78670e8i	−0.240162	−	0.415973i
$876$	8.28997e8			1.23322
$877$	−9.83248e7	−	1.70304e8i	−0.145769	−	0.252479i	0.783891	−	0.620899i	$-0.213232\pi$
$877$	−9.83248e7	−	1.70304e8i	−0.145769	−	0.252479i	−0.929659	+	0.368420i	$0.879899\pi$
$878$	1.27750e9	−	7.37567e8i	1.88746	−	1.08973i
$879$	2.60520e8	+	1.50411e8i	0.383596	+	0.221469i
$880$	−5.54379e8	−	3.20071e8i	−0.813502	−	0.469676i
$881$	6.73557e8			0.985023			0.492512	−	0.870306i	$-0.336079\pi$
$881$	6.73557e8			0.985023			0.492512	+	0.870306i	$0.336079\pi$
$882$		−	2.86988e8i		−	0.418271i
$883$	3.76677e8	−	6.52424e8i	0.547126	−	0.947650i	−0.451344	−	0.892350i	$-0.649055\pi$
$883$	3.76677e8	−	6.52424e8i	0.547126	−	0.947650i	0.998470	−	0.0553000i	$-0.0176115\pi$
$884$	−4.62019e8	+	8.00240e8i	−0.668810	+	1.15841i
$885$	3.09103e8	+	5.35382e8i	0.445937	+	0.772385i
$886$	3.37937e7	−	1.95108e7i	0.0485887	−	0.0280527i
$887$			8.71133e7i			0.124828i	0.998050	+	0.0624142i	$0.0198800\pi$
$887$			8.71133e7i			0.124828i	−0.998050	+	0.0624142i	$0.980120\pi$
$888$	−2.76175e8	+	1.59450e8i	−0.394408	+	0.227711i
$889$	−5.47514e8	+	3.16107e8i	−0.779273	+	0.449914i
$890$	1.25675e9	−	7.25586e8i	1.78271	−	1.02925i
$891$	−1.59856e6	+	2.76879e6i	−0.00225994	+	0.00391433i
$892$			8.67517e8i			1.22232i
$893$	3.63215e8	+	2.09702e8i	0.510045	+	0.294475i
$894$	−6.93810e8	+	4.00571e8i	−0.971019	+	0.560618i
$895$	−1.15189e9			−1.60673
$896$	−2.53907e8	−	4.39780e8i	−0.352980	−	0.611380i
$897$	−1.39220e8	−	8.03786e7i	−0.192896	−	0.111369i
$898$	−6.23655e8	+	1.08020e9i	−0.861222	+	1.49168i
$899$			1.95537e8i			0.269123i
$900$	−1.40660e8	+	2.43629e8i	−0.192949	+	0.334197i
$901$	−3.02497e8			−0.413568
$902$			1.99337e9i			2.71624i
$903$	3.31291e8	+	7.23823e7i	0.449932	+	0.0983036i
$904$	−2.59212e8			−0.350873
$905$		−	1.59290e9i		−	2.14904i
$906$	8.87710e8	+	5.12520e8i	1.19368	+	0.689169i
$907$	1.95329e8			0.261785			0.130892	−	0.991397i	$-0.458216\pi$
$907$	1.95329e8			0.261785			0.130892	+	0.991397i	$0.458216\pi$
$908$	−1.19232e9	−	6.88387e8i	−1.59271	−	0.919550i
$909$	−9.29131e7	+	1.60930e8i	−0.123704	+	0.214262i
$910$	−6.27908e8	+	3.62523e8i	−0.833244	+	0.481073i
$911$		−	7.60525e8i		−	1.00591i	−0.864313	−	0.502954i	$-0.832247\pi$
$911$		−	7.60525e8i		−	1.00591i	0.864313	−	0.502954i	$-0.167753\pi$
$912$	1.43731e8	+	2.48950e8i	0.189482	+	0.328192i
$913$	−3.53106e8	+	6.11598e8i	−0.463973	+	0.803626i
$914$	−1.96728e8			−0.257649
$915$	−3.16954e8	−	1.82994e8i	−0.413745	−	0.238876i
$916$	1.27813e7	+	2.21379e7i	0.0166299	+	0.0288038i
$917$	−6.24152e7	−	1.08106e8i	−0.0809436	−	0.140198i
$918$	−8.52425e8	−	1.47644e9i	−1.10186	−	1.90848i
$919$	−1.09238e8			−0.140743			−0.0703717	−	0.997521i	$-0.522419\pi$
$919$	−1.09238e8			−0.140743			−0.0703717	+	0.997521i	$0.522419\pi$
$920$	1.22160e8	+	2.11588e8i	0.156879	+	0.271723i
$921$	6.65496e8	−	3.84224e8i	0.851857	−	0.491820i
$922$	4.71666e8	+	2.72317e8i	0.601786	+	0.347441i
$923$	6.45950e8	+	3.72939e8i	0.821474	+	0.474278i
$924$	−6.61123e8			−0.838043
$925$			5.48900e8i			0.693535i
$926$	3.12736e8	−	5.41675e8i	0.393863	−	0.682190i
$927$	3.80764e8	−	6.59503e8i	0.477988	−	0.827900i
$928$	2.38832e8	+	4.13670e8i	0.298847	+	0.517619i
$929$	4.79393e8	−	2.76778e8i	0.597922	−	0.345211i	−0.170301	−	0.985392i	$-0.554474\pi$
$929$	4.79393e8	−	2.76778e8i	0.597922	−	0.345211i	0.768224	+	0.640181i	$0.221141\pi$
$930$			5.62684e8i			0.699545i
$931$	3.36102e8	−	1.94049e8i	0.416507	−	0.240471i
$932$	−1.38290e9	+	7.98417e8i	−1.70822	+	0.986239i
$933$	−2.75298e8	+	1.58943e8i	−0.338967	+	0.195703i
$934$	2.43688e8	−	4.22080e8i	0.299084	−	0.518029i
$935$			1.96391e9i			2.40263i
$936$	−1.53158e8	−	8.84258e7i	−0.186772	−	0.107833i
$937$	−5.46399e7	+	3.15463e7i	−0.0664188	+	0.0383469i	−0.532842	−	0.846215i	$-0.678876\pi$
$937$	−5.46399e7	+	3.15463e7i	−0.0664188	+	0.0383469i	0.466423	+	0.884562i	$0.345543\pi$
$938$	6.05013e8			0.733089
$939$	4.67641e8	+	8.09978e8i	0.564827	+	0.978309i
$940$	6.27245e8	+	3.62140e8i	0.755185	+	0.436006i
$941$	−2.23372e8	+	3.86891e8i	−0.268077	+	0.464323i	−0.968365	−	0.249537i	$-0.919721\pi$
$941$	−2.23372e8	+	3.86891e8i	−0.268077	+	0.464323i	0.700288	+	0.713860i	$0.253055\pi$
$942$		−	9.14123e6i		−	0.0109358i
$943$	−2.82178e8	+	4.88747e8i	−0.336503	+	0.582840i
$944$	−5.67284e8			−0.674349
$945$		−	7.62956e8i		−	0.904074i
$946$	3.77908e8	−	1.72967e9i	0.446389	−	2.04310i
$947$	−7.56982e8			−0.891324			−0.445662	−	0.895201i	$-0.647032\pi$
$947$	−7.56982e8			−0.891324			−0.445662	+	0.895201i	$0.647032\pi$
$948$			5.73396e7i			0.0673023i
$949$	7.76843e8	+	4.48510e8i	0.908939	+	0.524776i
$950$	−6.67021e8			−0.777980
$951$	−3.59541e8	−	2.07581e8i	−0.418029	−	0.241349i
$952$	−2.32661e8	+	4.02981e8i	−0.269658	+	0.467061i
$953$	4.63656e8	−	2.67692e8i	0.535695	−	0.309284i	−0.207637	−	0.978206i	$-0.566577\pi$
$953$	4.63656e8	−	2.67692e8i	0.535695	−	0.309284i	0.743332	+	0.668922i	$0.233244\pi$
$954$		−	2.34702e8i		−	0.270316i
$955$	4.36464e8	+	7.55978e8i	0.501116	+	0.867959i
$956$	−2.18511e8	+	3.78472e8i	−0.250092	+	0.433172i
$957$	3.25223e8			0.371061
$958$	−7.39700e8	−	4.27066e8i	−0.841316	−	0.485734i
$959$	−2.69457e8	−	4.66714e8i	−0.305516	−	0.529170i
$960$	5.00286e8	+	8.66521e8i	0.565464	+	0.979412i
$961$	2.76855e8	+	4.79526e8i	0.311947	+	0.540309i
$962$	−1.39888e9			−1.57128
$963$	2.08056e8	+	3.60363e8i	0.232970	+	0.403517i
$964$	−1.72272e9	+	9.94614e8i	−1.92302	+	1.11026i
$965$	−1.62934e9	−	9.40700e8i	−1.81313	−	1.04681i
$966$	−2.84211e8	−	1.64089e8i	−0.315290	−	0.182033i
$967$	1.53765e9			1.70050			0.850252	−	0.526376i	$-0.176449\pi$
$967$	1.53765e9			1.70050			0.850252	+	0.526376i	$0.176449\pi$
$968$			3.98339e8i			0.439164i
$969$	4.40958e8	−	7.63762e8i	0.484648	−	0.839434i
$970$	5.57837e7	−	9.66202e7i	0.0611212	−	0.105865i
$971$	1.06417e8	+	1.84320e8i	0.116240	+	0.201333i	0.918275	−	0.395944i	$-0.129583\pi$
$971$	1.06417e8	+	1.84320e8i	0.116240	+	0.201333i	−0.802035	+	0.597277i	$0.796249\pi$
$972$	1.05678e9	−	6.10134e8i	1.15077	−	0.664395i
$973$		−	9.84085e8i		−	1.06830i
$974$	1.04534e9	−	6.03529e8i	1.13131	−	0.653162i
$975$	1.61912e8	−	9.34799e7i	0.174689	−	0.100857i
$976$	2.90847e8	−	1.67920e8i	0.312835	−	0.180615i
$977$	−6.26345e8	+	1.08486e9i	−0.671630	+	1.16330i	0.305812	+	0.952092i	$0.401072\pi$
$977$	−6.26345e8	+	1.08486e9i	−0.671630	+	1.16330i	−0.977442	+	0.211205i	$0.932261\pi$
$978$		−	2.67181e8i		−	0.285621i
$979$	1.23998e9	+	7.15905e8i	1.32150	+	0.762970i
$980$	5.80424e8	−	3.35108e8i	0.616691	−	0.356046i
$981$	−7.83591e8			−0.830009
$982$	−3.30791e8	−	5.72947e8i	−0.349317	−	0.605035i
$983$	6.01479e8	+	3.47264e8i	0.633228	+	0.365594i	0.782001	−	0.623277i	$-0.214199\pi$
$983$	6.01479e8	+	3.47264e8i	0.633228	+	0.365594i	−0.148773	+	0.988871i	$0.547532\pi$
$984$	1.90661e8	−	3.30234e8i	0.200113	−	0.346607i
$985$		−	1.25455e9i		−	1.31274i
$986$	4.63979e8	−	8.03635e8i	0.484025	−	0.838356i
$987$	−2.39983e8			−0.249591
$988$		−	9.69533e8i		−	1.00529i
$989$	3.37508e8	−	3.70596e8i	0.348895	−	0.383100i
$990$	−1.52376e9			−1.57040
$991$		−	4.57538e8i		−	0.470117i	−0.971981	−	0.235058i	$-0.924472\pi$
$991$		−	4.57538e8i		−	0.470117i	0.971981	−	0.235058i	$-0.0755281\pi$
$992$	−7.06161e8	−	4.07702e8i	−0.723384	−	0.417646i
$993$	3.87075e7			0.0395319
$994$	1.31868e9	+	7.61339e8i	1.34270	+	0.775209i
$995$	−2.93356e8	+	5.08108e8i	−0.297801	+	0.515806i
$996$	4.74292e8	−	2.73832e8i	0.480029	−	0.277145i
$997$			4.56275e8i			0.460407i	0.973143	+	0.230203i	$0.0739391\pi$
$997$			4.56275e8i			0.460407i	−0.973143	+	0.230203i	$0.926061\pi$
$998$	−7.92405e8	−	1.37249e9i	−0.797179	−	1.38075i
$999$	7.36009e8	−	1.27480e9i	0.738221	−	1.27864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.d.a.37.4	yes	42
43.7	odd	6	inner	43.7.d.a.7.18	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.d.a.7.18	✓	42	43.7	odd	6	inner
43.7.d.a.37.4	yes	42	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-12.2048i q^{2} +(14.4234 + 8.32735i) q^{3} -84.9566 q^{4} +(131.217 + 75.7580i) q^{5} +(101.633 - 176.034i) q^{6} +(221.781 - 128.045i) q^{7} +255.771i q^{8} +(-225.811 - 391.115i) q^{9} +O(q^{10})\)	\(q-12.2048i q^{2} +(14.4234 + 8.32735i) q^{3} -84.9566 q^{4} +(131.217 + 75.7580i) q^{5} +(101.633 - 176.034i) q^{6} +(221.781 - 128.045i) q^{7} +255.771i q^{8} +(-225.811 - 391.115i) q^{9} +(924.609 - 1601.47i) q^{10} +1824.55 q^{11} +(-1225.36 - 707.463i) q^{12} +(-765.515 - 1325.91i) q^{13} +(-1562.76 - 2706.79i) q^{14} +(1261.73 + 2185.37i) q^{15} -2315.60 q^{16} +(3552.05 + 6152.33i) q^{17} +(-4773.48 + 2755.97i) q^{18} +(-6455.24 - 3726.93i) q^{19} +(-11147.7 - 6436.14i) q^{20} +4265.11 q^{21} -22268.2i q^{22} +(3152.25 - 5459.85i) q^{23} +(-2129.89 + 3689.08i) q^{24} +(3666.04 + 6349.78i) q^{25} +(-16182.4 + 9342.94i) q^{26} -19662.9i q^{27} +(-18841.8 + 10878.3i) q^{28} +(9268.73 - 5351.31i) q^{29} +(26672.0 - 15399.1i) q^{30} +(-9135.02 + 15822.3i) q^{31} +44630.7i q^{32} +(26316.1 + 15193.6i) q^{33} +(75087.8 - 43352.0i) q^{34} +38801.8 q^{35} +(19184.1 + 33227.8i) q^{36} +(64833.0 + 37431.4i) q^{37} +(-45486.4 + 78784.8i) q^{38} -25498.8i q^{39} +(-19376.7 + 33561.4i) q^{40} -89516.6 q^{41} -52054.7i q^{42} +(77674.7 + 16970.8i) q^{43} -155007. q^{44} -68427.8i q^{45} +(-66636.3 - 38472.5i) q^{46} -56266.6 q^{47} +(-33398.8 - 19282.8i) q^{48} +(-26033.3 + 45091.0i) q^{49} +(77497.6 - 44743.3i) q^{50} +118317. i q^{51} +(65035.5 + 112645. i) q^{52} +(-21290.3 + 36875.9i) q^{53} -239981. q^{54} +(239411. + 138224. i) q^{55} +(32750.3 + 56725.1i) q^{56} +(-62071.0 - 107510. i) q^{57} +(-65311.5 - 113123. i) q^{58} +244984. q^{59} +(-107192. - 185662. i) q^{60} +(-125603. + 72517.1i) q^{61} +(193108. + 111491. i) q^{62} +(-100161. - 57828.0i) q^{63} +396509. q^{64} -231975. i q^{65} +(185435. - 321183. i) q^{66} +(-96785.8 + 167638. i) q^{67} +(-301770. - 522681. i) q^{68} +(90932.1 - 52499.7i) q^{69} -473568. i q^{70} +(-421906. + 243587. i) q^{71} +(100036. - 57755.8i) q^{72} +(-507399. + 292947. i) q^{73} +(456842. - 791273. i) q^{74} +122114. i q^{75} +(548415. + 316628. i) q^{76} +(404649. - 233624. i) q^{77} -311208. q^{78} +(-20262.4 - 35095.5i) q^{79} +(-303845. - 175425. i) q^{80} +(-876.143 + 1517.52i) q^{81} +1.09253e6i q^{82} +(-193531. + 335206. i) q^{83} -362349. q^{84} +1.07638e6i q^{85} +(207125. - 948002. i) q^{86} +178249. q^{87} +466666. i q^{88} +(679613. + 392375. i) q^{89} -835146. q^{90} +(-339553. - 196041. i) q^{91} +(-267804. + 463850. i) q^{92} +(-263516. + 152141. i) q^{93} +686722. i q^{94} +(-564690. - 978072. i) q^{95} +(-371655. + 643726. i) q^{96} +60332.1 q^{97} +(550326. + 317731. i) q^{98} +(-412002. - 713608. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9}+O(q^{10}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9	\( 42 q - 3 q^{3} - 1194 q^{4} - 3 q^{5} + 111 q^{6} - 147 q^{7} + 3852 q^{9} - 981 q^{10} - 4104 q^{11} + 918 q^{12} + 4843 q^{13} + 2814 q^{14} - 163 q^{15} + 36678 q^{16} + 3641 q^{17} - 507 q^{18} - 5229 q^{19} - 1599 q^{20} - 29990 q^{21} + 6575 q^{23} - 4622 q^{24} + 68484 q^{25} + 189 q^{26} + 48948 q^{28} + 95361 q^{29} - 85041 q^{30} - 79373 q^{31} - 79638 q^{33} - 184743 q^{34} - 80582 q^{35} + 59972 q^{36} - 66063 q^{37} - 69820 q^{38} + 189951 q^{40} + 40632 q^{41} - 368728 q^{43} + 130330 q^{44} + 34056 q^{46} - 247820 q^{47} + 326907 q^{48} - 21876 q^{49} - 28638 q^{50} - 617150 q^{52} + 11639 q^{53} + 655904 q^{54} - 43638 q^{55} + 553875 q^{56} - 422859 q^{57} + 587796 q^{58} - 649352 q^{59} + 875455 q^{60} - 52251 q^{61} + 1335249 q^{62} + 93690 q^{63} - 792420 q^{64} + 160395 q^{66} - 173603 q^{67} + 22286 q^{68} + 870417 q^{69} + 1670505 q^{71} - 2068518 q^{72} - 2646201 q^{73} - 1625030 q^{74} - 80622 q^{76} - 486066 q^{77} + 2835040 q^{78} + 1897639 q^{79} - 817059 q^{80} + 2215367 q^{81} + 1584059 q^{83} - 824560 q^{84} - 2333682 q^{86} - 5547198 q^{87} + 2736939 q^{89} + 1092196 q^{90} - 3724131 q^{91} + 470257 q^{92} + 488433 q^{93} - 1289839 q^{95} + 1697650 q^{96} + 5260848 q^{97} + 4722621 q^{98} + 1375834 q^{99}+O(q^{100}) \) 42 * q - 3 * q^3 - 1194 * q^4 - 3 * q^5 + 111 * q^6 - 147 * q^7 + 3852 * q^9 - 981 * q^10 - 4104 * q^11 + 918 * q^12 + 4843 * q^13 + 2814 * q^14 - 163 * q^15 + 36678 * q^16 + 3641 * q^17 - 507 * q^18 - 5229 * q^19 - 1599 * q^20 - 29990 * q^21 + 6575 * q^23 - 4622 * q^24 + 68484 * q^25 + 189 * q^26 + 48948 * q^28 + 95361 * q^29 - 85041 * q^30 - 79373 * q^31 - 79638 * q^33 - 184743 * q^34 - 80582 * q^35 + 59972 * q^36 - 66063 * q^37 - 69820 * q^38 + 189951 * q^40 + 40632 * q^41 - 368728 * q^43 + 130330 * q^44 + 34056 * q^46 - 247820 * q^47 + 326907 * q^48 - 21876 * q^49 - 28638 * q^50 - 617150 * q^52 + 11639 * q^53 + 655904 * q^54 - 43638 * q^55 + 553875 * q^56 - 422859 * q^57 + 587796 * q^58 - 649352 * q^59 + 875455 * q^60 - 52251 * q^61 + 1335249 * q^62 + 93690 * q^63 - 792420 * q^64 + 160395 * q^66 - 173603 * q^67 + 22286 * q^68 + 870417 * q^69 + 1670505 * q^71 - 2068518 * q^72 - 2646201 * q^73 - 1625030 * q^74 - 80622 * q^76 - 486066 * q^77 + 2835040 * q^78 + 1897639 * q^79 - 817059 * q^80 + 2215367 * q^81 + 1584059 * q^83 - 824560 * q^84 - 2333682 * q^86 - 5547198 * q^87 + 2736939 * q^89 + 1092196 * q^90 - 3724131 * q^91 + 470257 * q^92 + 488433 * q^93 - 1289839 * q^95 + 1697650 * q^96 + 5260848 * q^97 + 4722621 * q^98 + 1375834 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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