LMFDB - Embedded newform 43.11.d.a.37.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,11,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, 11, names="a")

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 11 $
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:	$27.3203618650$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.25
Character	$\chi$	$=$	43.37
Dual form			43.11.d.a.7.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+25.0169i q^{2} +(171.910 + 99.2521i) q^{3} +398.154 q^{4} +(3482.07 + 2010.37i) q^{5} +(-2482.98 + 4300.65i) q^{6} +(-9759.68 + 5634.76i) q^{7} +35577.9i q^{8} +(-9822.54 - 17013.1i) q^{9} +O(q^{10})$	\(q+25.0169i q^{2} +(171.910 + 99.2521i) q^{3} +398.154 q^{4} +(3482.07 + 2010.37i) q^{5} +(-2482.98 + 4300.65i) q^{6} +(-9759.68 + 5634.76i) q^{7} +35577.9i q^{8} +(-9822.54 - 17013.1i) q^{9} +(-50293.3 + 87110.6i) q^{10} -142767. q^{11} +(68446.5 + 39517.6i) q^{12} +(126077. + 218372. i) q^{13} +(-140964. - 244157. i) q^{14} +(399068. + 691205. i) q^{15} -482341. q^{16} +(86105.3 + 149139. i) q^{17} +(425616. - 245730. i) q^{18} +(2.68849e6 + 1.55220e6i) q^{19} +(1.38640e6 + 800437. i) q^{20} -2.23705e6 q^{21} -3.57158e6i q^{22} +(-3.89319e6 + 6.74320e6i) q^{23} +(-3.53118e6 + 6.11619e6i) q^{24} +(3.20039e6 + 5.54323e6i) q^{25} +(-5.46299e6 + 3.15406e6i) q^{26} -1.56211e7i q^{27} +(-3.88585e6 + 2.24350e6i) q^{28} +(1.54996e7 - 8.94872e6i) q^{29} +(-1.72918e7 + 9.98344e6i) q^{30} +(6.98509e6 - 1.20985e7i) q^{31} +2.43651e7i q^{32} +(-2.45430e7 - 1.41699e7i) q^{33} +(-3.73099e6 + 2.15409e6i) q^{34} -4.53118e7 q^{35} +(-3.91088e6 - 6.77384e6i) q^{36} +(-5.98155e7 - 3.45345e7i) q^{37} +(-3.88313e7 + 6.72579e7i) q^{38} +5.00536e7i q^{39} +(-7.15249e7 + 1.23885e8i) q^{40} -3.51986e7 q^{41} -5.59640e7i q^{42} +(-6.89182e7 + 1.29853e8i) q^{43} -5.68430e7 q^{44} -7.89878e7i q^{45} +(-1.68694e8 - 9.73955e7i) q^{46} +2.13330e8 q^{47} +(-8.29190e7 - 4.78733e7i) q^{48} +(-7.77367e7 + 1.34644e8i) q^{49} +(-1.38675e8 + 8.00638e7i) q^{50} +3.41845e7i q^{51} +(5.01980e7 + 8.69454e7i) q^{52} +(1.26765e8 - 2.19563e8i) q^{53} +3.90792e8 q^{54} +(-4.97123e8 - 2.87014e8i) q^{55} +(-2.00473e8 - 3.47229e8i) q^{56} +(3.08119e8 + 5.33677e8i) q^{57} +(2.23870e8 + 3.87753e8i) q^{58} +9.65755e8 q^{59} +(1.58890e8 + 2.75206e8i) q^{60} +(-8.29005e8 + 4.78626e8i) q^{61} +(3.02668e8 + 1.74745e8i) q^{62} +(1.91730e8 + 1.10695e8i) q^{63} -1.10346e9 q^{64} +1.01385e9i q^{65} +(3.54487e8 - 6.13989e8i) q^{66} +(9.47058e8 - 1.64035e9i) q^{67} +(3.42831e7 + 5.93801e7i) q^{68} +(-1.33855e9 + 7.72814e8i) q^{69} -1.13356e9i q^{70} +(8.93528e8 - 5.15879e8i) q^{71} +(6.05292e8 - 3.49465e8i) q^{72} +(1.07096e9 - 6.18320e8i) q^{73} +(8.63947e8 - 1.49640e9i) q^{74} +1.27058e9i q^{75} +(1.07043e9 + 6.18015e8i) q^{76} +(1.39336e9 - 8.04455e8i) q^{77} -1.25219e9 q^{78} +(7.32800e8 + 1.26925e9i) q^{79} +(-1.67954e9 - 9.69684e8i) q^{80} +(9.70417e8 - 1.68081e9i) q^{81} -8.80561e8i q^{82} +(3.37652e9 - 5.84830e9i) q^{83} -8.90688e8 q^{84} +6.92415e8i q^{85} +(-3.24852e9 - 1.72412e9i) q^{86} +3.55272e9 q^{87} -5.07934e9i q^{88} +(-2.21219e9 - 1.27721e9i) q^{89} +1.97603e9 q^{90} +(-2.46094e9 - 1.42082e9i) q^{91} +(-1.55009e9 + 2.68483e9i) q^{92} +(2.40161e9 - 1.38657e9i) q^{93} +5.33686e9i q^{94} +(6.24101e9 + 1.08098e10i) q^{95} +(-2.41829e9 + 4.18860e9i) q^{96} +3.85226e9 q^{97} +(-3.36838e9 - 1.94473e9i) q^{98} +(1.40233e9 + 2.42891e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) $ 72 * q - 246 * q^3 - 38122 * q^4 - 3 * q^5 + 8511 * q^6 + 31377 * q^7 + 675876 * q^9	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9} - 127061 q^{10} + 521524 q^{11} - 606618 q^{12} + 796742 q^{13} - 865794 q^{14} - 433513 q^{15} + 22423366 q^{16} - 1768471 q^{17} - 11957547 q^{18} - 122844 q^{19} + 419841 q^{20} - 26778860 q^{21} + 16414886 q^{23} + 8684578 q^{24} + 70516989 q^{25} + 3069 q^{26} - 97624092 q^{28} + 118701393 q^{29} - 1455921 q^{30} + 10824883 q^{31} + 315141798 q^{33} + 47529561 q^{34} - 333788722 q^{35} - 597728908 q^{36} - 169881246 q^{37} - 88887452 q^{38} + 570788831 q^{40} - 543049070 q^{41} + 408159179 q^{43} - 754130886 q^{44} + 270181896 q^{46} + 348527658 q^{47} + 175039227 q^{48} + 781091547 q^{49} - 663244398 q^{50} - 1853993086 q^{52} + 219922736 q^{53} + 3104867360 q^{54} + 2154394182 q^{55} + 2010912675 q^{56} + 349107351 q^{57} + 2023447828 q^{58} + 2247595680 q^{59} - 2906780465 q^{60} + 508093974 q^{61} - 3451752063 q^{62} + 158921973 q^{63} - 13473879716 q^{64} + 1277847051 q^{66} - 2812410281 q^{67} + 13614613118 q^{68} - 5113655829 q^{69} + 2418191196 q^{71} + 26243329290 q^{72} - 6537901611 q^{73} - 2632816966 q^{74} - 10170994206 q^{76} - 16936463889 q^{77} - 24146069696 q^{78} + 5397136602 q^{79} + 7242149661 q^{80} - 15745886176 q^{81} + 4998656042 q^{83} + 44726677232 q^{84} - 27688564866 q^{86} + 37895576172 q^{87} - 12151857357 q^{89} - 96024912764 q^{90} + 36633770214 q^{91} - 31643971023 q^{92} + 59768940153 q^{93} - 19802964089 q^{95} - 3289705262 q^{96} - 40329658574 q^{97} + 19243888221 q^{98} + 18506221111 q^{99}+O(q^{100}) \) 72 * q - 246 * q^3 - 38122 * q^4 - 3 * q^5 + 8511 * q^6 + 31377 * q^7 + 675876 * q^9 - 127061 * q^10 + 521524 * q^11 - 606618 * q^12 + 796742 * q^13 - 865794 * q^14 - 433513 * q^15 + 22423366 * q^16 - 1768471 * q^17 - 11957547 * q^18 - 122844 * q^19 + 419841 * q^20 - 26778860 * q^21 + 16414886 * q^23 + 8684578 * q^24 + 70516989 * q^25 + 3069 * q^26 - 97624092 * q^28 + 118701393 * q^29 - 1455921 * q^30 + 10824883 * q^31 + 315141798 * q^33 + 47529561 * q^34 - 333788722 * q^35 - 597728908 * q^36 - 169881246 * q^37 - 88887452 * q^38 + 570788831 * q^40 - 543049070 * q^41 + 408159179 * q^43 - 754130886 * q^44 + 270181896 * q^46 + 348527658 * q^47 + 175039227 * q^48 + 781091547 * q^49 - 663244398 * q^50 - 1853993086 * q^52 + 219922736 * q^53 + 3104867360 * q^54 + 2154394182 * q^55 + 2010912675 * q^56 + 349107351 * q^57 + 2023447828 * q^58 + 2247595680 * q^59 - 2906780465 * q^60 + 508093974 * q^61 - 3451752063 * q^62 + 158921973 * q^63 - 13473879716 * q^64 + 1277847051 * q^66 - 2812410281 * q^67 + 13614613118 * q^68 - 5113655829 * q^69 + 2418191196 * q^71 + 26243329290 * q^72 - 6537901611 * q^73 - 2632816966 * q^74 - 10170994206 * q^76 - 16936463889 * q^77 - 24146069696 * q^78 + 5397136602 * q^79 + 7242149661 * q^80 - 15745886176 * q^81 + 4998656042 * q^83 + 44726677232 * q^84 - 27688564866 * q^86 + 37895576172 * q^87 - 12151857357 * q^89 - 96024912764 * q^90 + 36633770214 * q^91 - 31643971023 * q^92 + 59768940153 * q^93 - 19802964089 * q^95 - 3289705262 * q^96 - 40329658574 * q^97 + 19243888221 * q^98 + 18506221111 * 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 $

$2$			25.0169i			0.781779i	0.920438	+	0.390889i	$0.127833\pi$
$2$			25.0169i			0.781779i	−0.920438	+	0.390889i	$0.872167\pi$
$3$	171.910	+	99.2521i	0.707447	+	0.408445i	0.810115	−	0.586271i	$-0.199405\pi$
$3$	171.910	+	99.2521i	0.707447	+	0.408445i	−0.102668	+	0.994716i	$0.532738\pi$
$4$	398.154			0.388822
$5$	3482.07	+	2010.37i	1.11426	+	0.643319i	0.939930	−	0.341368i	$-0.110890\pi$
$5$	3482.07	+	2010.37i	1.11426	+	0.643319i	0.174332	+	0.984687i	$0.444223\pi$
$6$	−2482.98	+	4300.65i	−0.319314	+	0.553067i
$7$	−9759.68	+	5634.76i	−0.580692	+	0.335262i	−0.761408	−	0.648273i	$-0.775492\pi$
$7$	−9759.68	+	5634.76i	−0.580692	+	0.335262i	0.180717	+	0.983535i	$0.442158\pi$
$8$			35577.9i			1.08575i
$9$	−9822.54	−	17013.1i	−0.166346	−	0.288119i
$10$	−50293.3	+	87110.6i	−0.502933	+	0.871106i
$11$	−142767.			−0.886468			−0.443234	−	0.896406i	$-0.646169\pi$
$11$	−142767.			−0.886468			−0.443234	+	0.896406i	$0.646169\pi$
$12$	68446.5	+	39517.6i	0.275071	+	0.158812i
$13$	126077.	+	218372.i	0.339562	+	0.588138i	0.984350	−	0.176223i	$-0.0563879\pi$
$13$	126077.	+	218372.i	0.339562	+	0.588138i	−0.644789	+	0.764361i	$0.723055\pi$
$14$	−140964.	−	244157.i	−0.262101	−	0.453972i
$15$	399068.	+	691205.i	0.525521	+	0.910229i
$16$	−482341.			−0.459996
$17$	86105.3	+	149139.i	0.0606436	+	0.105038i	0.894753	−	0.446561i	$-0.147351\pi$
$17$	86105.3	+	149139.i	0.0606436	+	0.105038i	−0.834110	+	0.551599i	$0.814018\pi$
$18$	425616.	−	245730.i	0.225245	−	0.130045i
$19$	2.68849e6	+	1.55220e6i	1.08578	+	0.626874i	0.932449	−	0.361301i	$-0.117667\pi$
$19$	2.68849e6	+	1.55220e6i	1.08578	+	0.626874i	0.153329	+	0.988175i	$0.451001\pi$
$20$	1.38640e6	+	800437.i	0.433249	+	0.250137i
$21$	−2.23705e6			−0.547745
$22$		−	3.57158e6i		−	0.693022i
$23$	−3.89319e6	+	6.74320e6i	−0.604875	+	1.04767i	0.387196	+	0.921998i	$0.373444\pi$
$23$	−3.89319e6	+	6.74320e6i	−0.604875	+	1.04767i	−0.992071	+	0.125677i	$0.959890\pi$
$24$	−3.53118e6	+	6.11619e6i	−0.443470	+	0.768112i
$25$	3.20039e6	+	5.54323e6i	0.327720	+	0.567627i
$26$	−5.46299e6	+	3.15406e6i	−0.459794	+	0.265462i
$27$		−	1.56211e7i		−	1.08866i
$28$	−3.88585e6	+	2.24350e6i	−0.225786	+	0.130357i
$29$	1.54996e7	−	8.94872e6i	0.755669	−	0.436286i	−0.0720695	−	0.997400i	$-0.522960\pi$
$29$	1.54996e7	−	8.94872e6i	0.755669	−	0.436286i	0.827739	+	0.561114i	$0.189627\pi$
$30$	−1.72918e7	+	9.98344e6i	−0.711598	+	0.410841i
$31$	6.98509e6	−	1.20985e7i	0.243985	−	0.422595i	−0.717861	−	0.696187i	$-0.754878\pi$
$31$	6.98509e6	−	1.20985e7i	0.243985	−	0.422595i	0.961846	+	0.273592i	$0.0882118\pi$
$32$			2.43651e7i			0.726137i
$33$	−2.45430e7	−	1.41699e7i	−0.627129	−	0.362073i
$34$	−3.73099e6	+	2.15409e6i	−0.0821164	+	0.0474099i
$35$	−4.53118e7			−0.862723
$36$	−3.91088e6	−	6.77384e6i	−0.0646788	−	0.112027i
$37$	−5.98155e7	−	3.45345e7i	−0.862591	−	0.498017i	0.00228780	−	0.999997i	$-0.499272\pi$
$37$	−5.98155e7	−	3.45345e7i	−0.862591	−	0.498017i	−0.864879	+	0.501980i	$0.832605\pi$
$38$	−3.88313e7	+	6.72579e7i	−0.490077	+	0.848838i
$39$			5.00536e7i			0.554769i
$40$	−7.15249e7	+	1.23885e8i	−0.698485	+	1.20981i
$41$	−3.51986e7			−0.303813			−0.151907	−	0.988395i	$-0.548541\pi$
$41$	−3.51986e7			−0.303813			−0.151907	+	0.988395i	$0.548541\pi$
$42$		−	5.59640e7i		−	0.428215i
$43$	−6.89182e7	+	1.29853e8i	−0.468805	+	0.883302i
$43$	−6.89182e7	+	1.29853e8i	−0.468805	+	0.883302i
$44$	−5.68430e7			−0.344678
$45$		−	7.89878e7i		−	0.428053i
$46$	−1.68694e8	−	9.73955e7i	−0.819050	−	0.472879i
$47$	2.13330e8			0.930171			0.465086	−	0.885266i	$-0.346024\pi$
$47$	2.13330e8			0.930171			0.465086	+	0.885266i	$0.346024\pi$
$48$	−8.29190e7	−	4.78733e7i	−0.325423	−	0.187883i
$49$	−7.77367e7	+	1.34644e8i	−0.275198	+	0.476657i
$50$	−1.38675e8	+	8.00638e7i	−0.443759	+	0.256204i
$51$			3.41845e7i			0.0990783i
$52$	5.01980e7	+	8.69454e7i	0.132029	+	0.228681i
$53$	1.26765e8	−	2.19563e8i	0.303124	−	0.525026i	−0.673718	−	0.738989i	$-0.735304\pi$
$53$	1.26765e8	−	2.19563e8i	0.303124	−	0.525026i	0.976842	+	0.213963i	$0.0686371\pi$
$54$	3.90792e8			0.851093
$55$	−4.97123e8	−	2.87014e8i	−0.987757	−	0.570282i
$56$	−2.00473e8	−	3.47229e8i	−0.364012	−	0.630487i
$57$	3.08119e8	+	5.33677e8i	0.512087	+	0.886961i
$58$	2.23870e8	+	3.87753e8i	0.341079	+	0.590766i
$59$	9.65755e8			1.35085			0.675424	−	0.737429i	$-0.263960\pi$
$59$	9.65755e8			1.35085			0.675424	+	0.737429i	$0.263960\pi$
$60$	1.58890e8	+	2.75206e8i	0.204334	+	0.353917i
$61$	−8.29005e8	+	4.78626e8i	−0.981540	+	0.566692i	−0.902735	−	0.430198i	$-0.858444\pi$
$61$	−8.29005e8	+	4.78626e8i	−0.981540	+	0.566692i	−0.0788051	+	0.996890i	$0.525110\pi$
$62$	3.02668e8	+	1.74745e8i	0.330376	+	0.190743i
$63$	1.91730e8	+	1.10695e8i	0.193191	+	0.111539i
$64$	−1.10346e9			−1.02767
$65$			1.01385e9i			0.873787i
$66$	3.54487e8	−	6.13989e8i	0.283061	−	0.490277i
$67$	9.47058e8	−	1.64035e9i	0.701460	−	1.21496i	−0.266495	−	0.963836i	$-0.585865\pi$
$67$	9.47058e8	−	1.64035e9i	0.701460	−	1.21496i	0.967954	−	0.251127i	$-0.0808012\pi$
$68$	3.42831e7	+	5.93801e7i	0.0235796	+	0.0408410i
$69$	−1.33855e9	+	7.72814e8i	−0.855835	+	0.494117i
$70$		−	1.13356e9i		−	0.674459i
$71$	8.93528e8	−	5.15879e8i	0.495241	−	0.285927i	−0.231505	−	0.972834i	$-0.574365\pi$
$71$	8.93528e8	−	5.15879e8i	0.495241	−	0.285927i	0.726746	+	0.686906i	$0.241032\pi$
$72$	6.05292e8	−	3.49465e8i	0.312826	−	0.180610i
$73$	1.07096e9	−	6.18320e8i	0.516606	−	0.298263i	−0.218939	−	0.975739i	$-0.570259\pi$
$73$	1.07096e9	−	6.18320e8i	0.516606	−	0.298263i	0.735545	+	0.677476i	$0.236926\pi$
$74$	8.63947e8	−	1.49640e9i	0.389339	−	0.674356i
$75$			1.27058e9i			0.535422i
$76$	1.07043e9	+	6.18015e8i	0.422174	+	0.243742i
$77$	1.39336e9	−	8.04455e8i	0.514764	−	0.297199i
$78$	−1.25219e9			−0.433707
$79$	7.32800e8	+	1.26925e9i	0.238150	+	0.412488i	0.960183	−	0.279370i	$-0.0901257\pi$
$79$	7.32800e8	+	1.26925e9i	0.238150	+	0.412488i	−0.722034	+	0.691858i	$0.756792\pi$
$80$	−1.67954e9	−	9.69684e8i	−0.512556	−	0.295924i
$81$	9.70417e8	−	1.68081e9i	0.278313	−	0.482052i
$82$		−	8.80561e8i		−	0.237515i
$83$	3.37652e9	−	5.84830e9i	0.857192	−	1.48470i	−0.0174038	−	0.999849i	$-0.505540\pi$
$83$	3.37652e9	−	5.84830e9i	0.857192	−	1.48470i	0.874596	−	0.484852i	$-0.161127\pi$
$84$	−8.90688e8			−0.212975
$85$			6.92415e8i			0.156053i
$86$	−3.24852e9	−	1.72412e9i	−0.690547	−	0.366502i
$87$	3.55272e9			0.712795
$88$		−	5.07934e9i		−	0.962484i
$89$	−2.21219e9	−	1.27721e9i	−0.396161	−	0.228724i	0.288665	−	0.957430i	$-0.406789\pi$
$89$	−2.21219e9	−	1.27721e9i	−0.396161	−	0.228724i	−0.684826	+	0.728706i	$0.740122\pi$
$90$	1.97603e9			0.334643
$91$	−2.46094e9	−	1.42082e9i	−0.394361	−	0.227685i
$92$	−1.55009e9	+	2.68483e9i	−0.235189	+	0.407359i
$93$	2.40161e9	−	1.38657e9i	0.345213	−	0.199309i
$94$			5.33686e9i			0.727188i
$95$	6.24101e9	+	1.08098e10i	0.806561	+	1.39700i
$96$	−2.41829e9	+	4.18860e9i	−0.296587	+	0.513703i
$97$	3.85226e9			0.448598			0.224299	−	0.974520i	$-0.427991\pi$
$97$	3.85226e9			0.448598			0.224299	+	0.974520i	$0.427991\pi$
$98$	−3.36838e9	−	1.94473e9i	−0.372641	−	0.215144i
$99$	1.40233e9	+	2.42891e9i	0.147460	+	0.255408i
$100$	1.27425e9	+	2.20706e9i	0.127425	+	0.220706i
$101$	1.34924e9	+	2.33694e9i	0.128375	+	0.222352i	0.923047	−	0.384687i	$-0.125691\pi$
$101$	1.34924e9	+	2.33694e9i	0.128375	+	0.222352i	−0.794672	+	0.607039i	$0.792357\pi$
$102$	−8.55191e8			−0.0774573
$103$	2.13552e9	+	3.69882e9i	0.184212	+	0.319064i	0.943311	−	0.331911i	$-0.107694\pi$
$103$	2.13552e9	+	3.69882e9i	0.184212	+	0.319064i	−0.759099	+	0.650975i	$0.774360\pi$
$104$	−7.76920e9	+	4.48555e9i	−0.638572	+	0.368680i
$105$	−7.78955e9	−	4.49730e9i	−0.610331	−	0.352375i
$106$	5.49280e9	+	3.17127e9i	0.410454	+	0.236976i
$107$	−6.25523e9			−0.445990			−0.222995	−	0.974820i	$-0.571583\pi$
$107$	−6.25523e9			−0.445990			−0.222995	+	0.974820i	$0.571583\pi$
$108$		−	6.21960e9i		−	0.423295i
$109$	−4.20411e9	+	7.28174e9i	−0.273239	+	0.473263i	−0.969689	−	0.244342i	$-0.921428\pi$
$109$	−4.20411e9	+	7.28174e9i	−0.273239	+	0.473263i	0.696451	+	0.717605i	$0.254761\pi$
$110$	7.18021e9	−	1.24365e10i	0.445834	−	0.772208i
$111$	−6.85524e9	−	1.18736e10i	−0.406825	−	0.704642i
$112$	4.70749e9	−	2.71787e9i	0.267116	−	0.154219i
$113$			3.16772e10i			1.71931i	0.510874	+	0.859656i	$0.329322\pi$
$113$			3.16772e10i			1.71931i	−0.510874	+	0.859656i	$0.670678\pi$
$114$	−1.33510e10	+	7.70818e9i	−0.693407	+	0.400339i
$115$	−2.71127e10	+	1.56535e10i	−1.34798	+	0.778256i
$116$	6.17124e9	−	3.56297e9i	0.293821	−	0.169637i
$117$	2.47679e9	−	4.28993e9i	0.112969	−	0.195668i
$118$			2.41602e10i			1.05607i
$119$	−1.68072e9	−	9.70364e8i	−0.0704305	−	0.0406631i
$120$	−2.45916e10	+	1.41980e10i	−0.988283	+	0.570585i
$121$	−5.55514e9			−0.214175
$122$	−1.19738e10	−	2.07392e10i	−0.443028	−	0.767347i
$123$	−6.05099e9	−	3.49354e9i	−0.214932	−	0.124091i
$124$	2.78114e9	−	4.81707e9i	0.0948668	−	0.164314i
$125$		−	1.35292e10i		−	0.443325i
$126$	−2.76925e9	+	4.79649e9i	−0.0871987	+	0.151033i
$127$	6.43736e10			1.94845			0.974225	−	0.225579i	$-0.0724272\pi$
$127$	6.43736e10			1.94845			0.974225	+	0.225579i	$0.0724272\pi$
$128$		−	2.65523e9i		−	0.0772773i
$129$	−2.47359e10	+	1.54827e10i	−0.692435	+	0.433409i
$130$	−2.53633e10			−0.683108
$131$		−	4.00483e10i		−	1.03807i	−0.854752	−	0.519036i	$-0.826291\pi$
$131$		−	4.00483e10i		−	1.03807i	0.854752	−	0.519036i	$-0.173709\pi$
$132$	−9.77186e9	−	5.64179e9i	−0.243842	−	0.140782i
$133$	−3.49851e10			−0.840670
$134$	4.10366e10	+	2.36925e10i	0.949833	+	0.548386i
$135$	3.14043e10	−	5.43938e10i	0.700357	−	1.21305i
$136$	−5.30604e9	+	3.06344e9i	−0.114045	+	0.0658439i
$137$		−	3.50832e10i		−	0.726937i	−0.931607	−	0.363468i	$-0.881593\pi$
$137$		−	3.50832e10i		−	0.726937i	0.931607	−	0.363468i	$-0.118407\pi$
$138$	−1.93334e10	−	3.34865e10i	−0.386290	−	0.669074i
$139$	1.78783e10	−	3.09661e10i	0.344550	−	0.596778i	−0.640722	−	0.767773i	$-0.721365\pi$
$139$	1.78783e10	−	3.09661e10i	0.344550	−	0.596778i	0.985272	+	0.170995i	$0.0546981\pi$
$140$	−1.80411e10			−0.335446
$141$	3.66735e10	+	2.11735e10i	0.658047	+	0.379924i
$142$	1.29057e10	+	2.23533e10i	0.223532	+	0.387169i
$143$	−1.79996e10	−	3.11762e10i	−0.301011	−	0.521366i
$144$	4.73781e9	+	8.20612e9i	0.0765182	+	0.132533i
$145$	7.19611e10			1.12268
$146$	1.54685e10	+	2.67922e10i	0.233176	+	0.403872i
$147$	−2.67274e10	+	1.54311e10i	−0.389376	+	0.224807i
$148$	−2.38158e10	−	1.37500e10i	−0.335394	−	0.193640i
$149$	4.50823e10	+	2.60283e10i	0.613867	+	0.354416i	0.774478	−	0.632601i	$-0.218013\pi$
$149$	4.50823e10	+	2.60283e10i	0.613867	+	0.354416i	−0.160610	+	0.987018i	$0.551346\pi$
$150$	−3.17860e10			−0.418581
$151$			5.73516e10i			0.730569i	0.930896	+	0.365284i	$0.119028\pi$
$151$			5.73516e10i			0.730569i	−0.930896	+	0.365284i	$0.880972\pi$
$152$	−5.52241e10	+	9.56510e10i	−0.680630	+	1.17889i
$153$	1.69154e9	−	2.92984e9i	0.0201756	−	0.0349451i
$154$	2.01250e10	+	3.48575e10i	0.232344	+	0.402432i
$155$	4.86451e10	−	2.80853e10i	0.543727	−	0.313921i
$156$			1.99290e10i			0.215706i
$157$	3.53306e10	−	2.03981e10i	0.370384	−	0.213841i	−0.303242	−	0.952914i	$-0.598069\pi$
$157$	3.53306e10	−	2.03981e10i	0.370384	−	0.213841i	0.673626	+	0.739072i	$0.264736\pi$
$158$	−3.17527e10	+	1.83324e10i	−0.322474	+	0.186181i
$159$	4.35843e10	−	2.51634e10i	0.428888	−	0.247619i
$160$	−4.89829e10	+	8.48409e10i	−0.467138	+	0.809106i
$161$		−	8.77486e10i		−	0.811168i
$162$	4.20487e10	+	2.42768e10i	0.376858	+	0.217579i
$163$	1.14713e11	−	6.62297e10i	0.996955	−	0.575592i	0.0896089	−	0.995977i	$-0.471438\pi$
$163$	1.14713e11	−	6.62297e10i	0.996955	−	0.575592i	0.907346	+	0.420385i	$0.138105\pi$
$164$	−1.40145e10			−0.118129
$165$	−5.69735e10	−	9.86810e10i	−0.465858	−	0.806889i
$166$	1.46306e11	+	8.44700e10i	1.16071	+	0.670135i
$167$	2.90581e10	−	5.03301e10i	0.223710	−	0.387477i	−0.732222	−	0.681066i	$-0.761517\pi$
$167$	2.90581e10	−	5.03301e10i	0.223710	−	0.387477i	0.955932	+	0.293590i	$0.0948499\pi$
$168$		−	7.95894e10i		−	0.594715i
$169$	3.71385e10	−	6.43257e10i	0.269396	−	0.466607i
$170$	−1.73221e10			−0.121999
$171$		−	6.09863e10i		−	0.417111i
$172$	−2.74400e10	+	5.17014e10i	−0.182281	+	0.343447i
$173$	1.62528e11			1.04881			0.524406	−	0.851469i	$-0.324288\pi$
$173$	1.62528e11			1.04881			0.524406	+	0.851469i	$0.324288\pi$
$174$			8.88781e10i			0.557248i
$175$	−6.24695e10	−	3.60668e10i	−0.380608	−	0.219744i
$176$	6.88621e10			0.407772
$177$	1.66023e11	+	9.58532e10i	0.955654	+	0.551747i
$178$	3.19518e10	−	5.53422e10i	0.178812	−	0.309711i
$179$	1.26809e11	−	7.32134e10i	0.690059	−	0.398406i	−0.113575	−	0.993529i	$-0.536230\pi$
$179$	1.26809e11	−	7.32134e10i	0.690059	−	0.398406i	0.803634	+	0.595124i	$0.202897\pi$
$180$		−	3.14493e10i		−	0.166436i
$181$	−6.23387e10	−	1.07974e11i	−0.320897	−	0.555809i	0.659777	−	0.751462i	$-0.270651\pi$
$181$	−6.23387e10	−	1.07974e11i	−0.320897	−	0.555809i	−0.980673	+	0.195653i	$0.937318\pi$
$182$	3.55447e10	−	6.15652e10i	0.177999	−	0.308303i
$183$	−1.90019e11			−0.925850
$184$	−2.39909e11	−	1.38511e11i	−1.13751	−	0.656744i
$185$	−1.38854e11	−	2.40503e11i	−0.640768	−	1.10984i
$186$	3.46877e10	+	6.00809e10i	0.155816	+	0.269881i
$187$	−1.22930e10	−	2.12920e10i	−0.0537586	−	0.0931127i
$188$	8.49381e10			0.361671
$189$	8.80211e10	+	1.52457e11i	0.364987	+	0.632177i
$190$	−2.70427e11	+	1.56131e11i	−1.09215	+	0.630552i
$191$	−2.00528e11	−	1.15775e11i	−0.788875	−	0.455457i	0.0506910	−	0.998714i	$-0.483858\pi$
$191$	−2.00528e11	−	1.15775e11i	−0.788875	−	0.455457i	−0.839567	+	0.543257i	$0.817191\pi$
$192$	−1.89695e11	−	1.09520e11i	−0.727025	−	0.419748i
$193$	−2.43304e11			−0.908580			−0.454290	−	0.890854i	$-0.650107\pi$
$193$	−2.43304e11			−0.908580			−0.454290	+	0.890854i	$0.650107\pi$
$194$			9.63717e10i			0.350704i
$195$	−1.00626e11	+	1.74290e11i	−0.356894	+	0.618158i
$196$	−3.09511e10	+	5.36089e10i	−0.107003	+	0.185335i
$197$	1.71039e11	+	2.96248e11i	0.576452	+	0.998444i	0.995882	+	0.0906564i	$0.0288965\pi$
$197$	1.71039e11	+	2.96248e11i	0.576452	+	0.998444i	−0.419430	+	0.907788i	$0.637770\pi$
$198$	−6.07638e10	+	3.50820e10i	−0.199673	+	0.115281i
$199$			5.68969e11i			1.82315i	0.411128	+	0.911577i	$0.365135\pi$
$199$			5.68969e11i			1.82315i	−0.411128	+	0.911577i	$0.634865\pi$
$200$	−1.97217e11	+	1.13863e11i	−0.616302	+	0.355822i
$201$	3.25617e11	−	1.87995e11i	0.992491	−	0.573015i
$202$	−5.84632e10	+	3.37537e10i	−0.173830	+	0.100361i
$203$	−1.00848e11	+	1.74673e11i	−0.292540	+	0.506695i
$204$			1.36107e10i			0.0385238i
$205$	−1.22564e11	−	7.07624e10i	−0.338527	−	0.195449i
$206$	−9.25332e10	+	5.34241e10i	−0.249437	+	0.144013i
$207$	1.52964e11			0.402473
$208$	−6.08120e10	−	1.05329e11i	−0.156197	−	0.270541i
$209$	−3.83827e11	−	2.21603e11i	−0.962508	−	0.555704i
$210$	1.12509e11	−	1.94870e11i	0.275479	−	0.477144i
$211$			1.87935e11i			0.449362i	0.974432	+	0.224681i	$0.0721339\pi$
$211$			1.87935e11i			0.449362i	−0.974432	+	0.224681i	$0.927866\pi$
$212$	5.04719e10	−	8.74200e10i	0.117861	−	0.204142i
$213$	2.04808e11			0.467142
$214$		−	1.56487e11i		−	0.348665i
$215$	−5.01031e11	+	3.13605e11i	−1.09062	+	0.682638i
$216$	5.55766e11			1.18202
$217$			1.57437e11i			0.327196i
$218$	−1.82167e11	−	1.05174e11i	−0.369987	−	0.213612i
$219$	2.45478e11			0.487296
$220$	−1.97931e11	−	1.14276e11i	−0.384062	−	0.221738i
$221$	−2.17118e10	+	3.76059e10i	−0.0411845	+	0.0713336i
$222$	2.97042e11	−	1.71497e11i	0.550874	−	0.318047i
$223$			9.59786e11i			1.74040i	0.492695	+	0.870202i	$0.336012\pi$
$223$			9.59786e11i			1.74040i	−0.492695	+	0.870202i	$0.663988\pi$
$224$	−1.37291e11	−	2.37796e11i	−0.243446	−	0.421661i
$225$	6.28718e10	−	1.08897e11i	0.109029	−	0.188844i
$226$	−7.92466e11			−1.34412
$227$	−2.16992e11	−	1.25281e11i	−0.360010	−	0.207852i	0.309075	−	0.951038i	$-0.399981\pi$
$227$	−2.16992e11	−	1.25281e11i	−0.360010	−	0.207852i	−0.669085	+	0.743186i	$0.733314\pi$
$228$	1.22679e11	+	2.12486e11i	0.199111	+	0.344870i
$229$	−1.54346e11	−	2.67335e11i	−0.245085	−	0.424500i	0.717070	−	0.697001i	$-0.245483\pi$
$229$	−1.54346e11	−	2.67335e11i	−0.245085	−	0.424500i	−0.962156	+	0.272500i	$0.912149\pi$
$230$	−3.91603e11	−	6.78276e11i	−0.608424	−	1.05382i
$231$	3.19375e11			0.485558
$232$	3.18377e11	+	5.51445e11i	0.473698	+	0.820469i
$233$	1.15109e12	−	6.64581e11i	1.67621	−	0.967762i	0.712174	−	0.702003i	$-0.247711\pi$
$233$	1.15109e12	−	6.64581e11i	1.67621	−	0.967762i	0.964040	−	0.265759i	$-0.0856225\pi$
$234$	1.07321e11	+	6.19617e10i	0.152969	+	0.0883169i
$235$	7.42830e11	+	4.28873e11i	1.03645	+	0.598397i
$236$	3.84519e11			0.525240
$237$			2.90928e11i			0.389084i
$238$	2.42755e10	−	4.20464e10i	0.0317895	−	0.0550611i
$239$	1.25760e11	−	2.17822e11i	0.161269	−	0.279326i	−0.774055	−	0.633118i	$-0.781775\pi$
$239$	1.25760e11	−	2.17822e11i	0.161269	−	0.279326i	0.935324	+	0.353792i	$0.115108\pi$
$240$	−1.92486e11	−	3.33396e11i	−0.241737	−	0.418702i
$241$	−4.68369e11	+	2.70413e11i	−0.576107	+	0.332615i	−0.759585	−	0.650408i	$-0.774598\pi$
$241$	−4.68369e11	+	2.70413e11i	−0.576107	+	0.332615i	0.183478	+	0.983024i	$0.441264\pi$
$242$		−	1.38972e11i		−	0.167437i
$243$	−4.65183e11	+	2.68573e11i	−0.549025	+	0.316980i
$244$	−3.30071e11	+	1.90567e11i	−0.381644	+	0.220342i
$245$	−5.41369e11	+	3.12559e11i	−0.613286	+	0.354081i
$246$	8.73976e10	−	1.51377e11i	0.0970116	−	0.168029i
$247$			7.82788e11i			0.851450i
$248$	4.30440e11	+	2.48515e11i	0.458833	+	0.264907i
$249$	1.16091e12	−	6.70253e11i	1.21284	−	0.700232i
$250$	3.38459e11			0.346582
$251$	−2.58237e11	−	4.47279e11i	−0.259209	−	0.448963i	0.706821	−	0.707392i	$-0.250128\pi$
$251$	−2.58237e11	−	4.47279e11i	−0.259209	−	0.448963i	−0.966030	+	0.258429i	$0.916795\pi$
$252$	7.63378e10	+	4.40737e10i	0.0751168	+	0.0433687i
$253$	5.55817e11	−	9.62703e11i	0.536203	−	0.928730i
$254$			1.61043e12i			1.52326i
$255$	−6.87236e10	+	1.19033e11i	−0.0637390	+	0.110399i
$256$	−1.06351e12			−0.967260
$257$		−	1.53682e12i		−	1.37074i	−0.728194	−	0.685372i	$-0.759640\pi$
$257$		−	1.53682e12i		−	1.37074i	0.728194	−	0.685372i	$-0.240360\pi$
$258$	−3.87329e11	−	6.18816e11i	−0.338830	−	0.541331i
$259$	7.78374e11			0.667866
$260$			4.03666e11i			0.339747i
$261$	−3.04492e11	−	1.75798e11i	−0.251404	−	0.145148i
$262$	1.00189e12			0.811543
$263$	−1.54435e12	−	8.91633e11i	−1.22735	−	0.708610i	−0.260875	−	0.965373i	$-0.584011\pi$
$263$	−1.54435e12	−	8.91633e11i	−1.22735	−	0.708610i	−0.966475	+	0.256762i	$0.917344\pi$
$264$	5.04135e11	−	8.73187e11i	0.393122	−	0.680907i
$265$	8.82809e11	−	5.09690e11i	0.675519	−	0.390011i
$266$		−	8.75220e11i		−	0.657218i
$267$	−2.53531e11	−	4.39129e11i	−0.186842	−	0.323620i
$268$	3.77075e11	−	6.53112e11i	0.272743	−	0.472404i
$269$	−7.02700e11			−0.498894			−0.249447	−	0.968388i	$-0.580249\pi$
$269$	−7.02700e11			−0.498894			−0.249447	+	0.968388i	$0.580249\pi$
$270$	1.36076e12	+	7.85638e11i	0.948340	+	0.547524i
$271$	−2.92972e11	−	5.07442e11i	−0.200438	−	0.347168i	0.748232	−	0.663437i	$-0.230903\pi$
$271$	−2.92972e11	−	5.07442e11i	−0.200438	−	0.347168i	−0.948670	+	0.316269i	$0.897570\pi$
$272$	−4.15321e10	−	7.19356e10i	−0.0278958	−	0.0483170i
$273$	−2.82040e11	−	4.88507e11i	−0.185993	−	0.322150i
$274$	8.77674e11			0.568304
$275$	−4.56908e11	−	7.91388e11i	−0.290513	−	0.503183i
$276$	−5.32950e11	+	3.07699e11i	−0.332767	+	0.192123i
$277$	1.26587e12	+	7.30848e11i	0.776227	+	0.448155i	0.835091	−	0.550111i	$-0.185415\pi$
$277$	1.26587e12	+	7.30848e11i	0.776227	+	0.448155i	−0.0588645	+	0.998266i	$0.518748\pi$
$278$	7.74677e11	+	4.47260e11i	0.466549	+	0.269362i
$279$	−2.74445e11			−0.162343
$280$		−	1.61210e12i		−	0.936703i
$281$	−1.25297e12	+	2.17020e12i	−0.715168	+	1.23871i	0.247727	+	0.968830i	$0.420316\pi$
$281$	−1.25297e12	+	2.17020e12i	−0.715168	+	1.23871i	−0.962895	+	0.269877i	$0.913017\pi$
$282$	−5.29695e11	+	9.17459e11i	−0.297016	+	0.514447i
$283$	1.18597e11	+	2.05415e11i	0.0653341	+	0.113162i	0.896842	−	0.442351i	$-0.145855\pi$
$283$	1.18597e11	+	2.05415e11i	0.0653341	+	0.113162i	−0.831508	+	0.555513i	$0.812522\pi$
$284$	3.55761e11	−	2.05399e11i	0.192560	−	0.111175i
$285$			2.47774e12i			1.31774i
$286$	7.79932e11	−	4.50294e11i	0.407593	−	0.235324i
$287$	3.43527e11	−	1.98336e11i	0.176422	−	0.101857i
$288$	4.14527e11	−	2.39327e11i	0.209214	−	0.120790i
$289$	9.93169e11	−	1.72022e12i	0.492645	−	0.853286i
$290$			1.80024e12i			0.877691i
$291$	6.62241e11	+	3.82345e11i	0.317359	+	0.183227i
$292$	4.26407e11	−	2.46186e11i	0.200868	−	0.115971i
$293$	−3.53595e12			−1.63745			−0.818725	−	0.574185i	$-0.805319\pi$
$293$	−3.53595e12			−1.63745			−0.818725	+	0.574185i	$0.805319\pi$
$294$	−3.86038e11	−	6.68637e11i	−0.175749	−	0.304406i
$295$	3.36282e12	+	1.94153e12i	1.50520	+	0.869027i
$296$	1.22867e12	−	2.12811e12i	0.540723	−	0.936560i
$297$			2.23017e12i			0.965064i
$298$	−6.51147e11	+	1.12782e12i	−0.277075	+	0.479908i
$299$	−1.96336e12			−0.821570
$300$			5.05886e11i			0.208184i
$301$	−5.90687e10	−	1.65566e12i	−0.0239070	−	0.670099i
$302$	−1.43476e12			−0.571143
$303$			5.35658e11i			0.209737i
$304$	−1.29677e12	−	7.48690e11i	−0.499453	−	0.288360i
$305$	−3.84887e12			−1.45826
$306$	7.32956e10	+	4.23172e10i	0.0273194	+	0.0157728i
$307$	1.90128e12	−	3.29312e12i	0.697197	−	1.20758i	−0.272238	−	0.962230i	$-0.587764\pi$
$307$	1.90128e12	−	3.29312e12i	0.697197	−	1.20758i	0.969435	−	0.245350i	$-0.0789029\pi$
$308$	5.54770e11	−	3.20296e11i	0.200152	−	0.115558i
$309$			8.47818e11i			0.300961i
$310$	7.02607e11	+	1.21695e12i	0.245417	+	0.425074i
$311$	−1.35761e12	+	2.35146e12i	−0.466632	+	0.808230i	−0.999274	−	0.0381110i	$-0.987866\pi$
$311$	−1.35761e12	+	2.35146e12i	−0.466632	+	0.808230i	0.532642	+	0.846341i	$0.321199\pi$
$312$	−1.78080e12			−0.602341
$313$	1.72600e11	+	9.96505e10i	0.0574537	+	0.0331709i	0.528452	−	0.848963i	$-0.322773\pi$
$313$	1.72600e11	+	9.96505e10i	0.0574537	+	0.0331709i	−0.470998	+	0.882134i	$0.656106\pi$
$314$	5.10298e11	+	8.83862e11i	0.167177	+	0.289558i
$315$	4.45077e11	+	7.70896e11i	0.143510	+	0.248567i
$316$	2.91767e11	+	5.05355e11i	0.0925979	+	0.160384i
$317$	4.53151e11			0.141562			0.0707809	−	0.997492i	$-0.477451\pi$
$317$	4.53151e11			0.141562			0.0707809	+	0.997492i	$0.477451\pi$
$318$	6.29511e11	+	1.09034e12i	0.193583	+	0.335296i
$319$	−2.21283e12	+	1.27758e12i	−0.669876	+	0.386753i
$320$	−3.84231e12	−	2.21836e12i	−1.14510	−	0.661123i
$321$	−1.07534e12	−	6.20845e11i	−0.315514	−	0.182162i
$322$	2.19520e12			0.634154
$323$			5.34611e11i			0.152064i
$324$	3.86375e11	−	6.69221e11i	0.108214	−	0.187432i
$325$	−8.06990e11	+	1.39775e12i	−0.222562	+	0.385489i
$326$	1.65686e12	+	2.86977e12i	0.449986	+	0.779398i
$327$	−1.44546e12	+	8.34534e11i	−0.386604	+	0.223206i
$328$		−	1.25229e12i		−	0.329866i
$329$	−2.08203e12	+	1.20206e12i	−0.540143	+	0.311851i
$330$	2.46869e12	−	1.42530e12i	0.630809	−	0.364198i
$331$	−5.96516e12	+	3.44399e12i	−1.50135	+	0.866806i	−0.501353	+	0.865243i	$0.667164\pi$
$331$	−5.96516e12	+	3.44399e12i	−1.50135	+	0.866806i	−0.999999	+	0.00156260i	$0.999503\pi$
$332$	1.34437e12	−	2.32852e12i	0.333295	−	0.577284i
$333$			1.35687e12i			0.331372i
$334$	1.25910e12	+	7.26944e11i	0.302921	+	0.174892i
$335$	6.59544e12	−	3.80788e12i	1.56322	−	0.902525i
$336$	1.07902e12			0.251960
$337$	2.27833e12	+	3.94618e12i	0.524163	+	0.907877i	0.999604	+	0.0281298i	$0.00895517\pi$
$337$	2.27833e12	+	3.94618e12i	0.524163	+	0.907877i	−0.475441	+	0.879748i	$0.657711\pi$
$338$	1.60923e12	+	9.29091e11i	0.364784	+	0.210608i
$339$	−3.14403e12	+	5.44562e12i	−0.702244	+	1.21632i
$340$			2.75687e11i			0.0606768i
$341$	−9.97237e11	+	1.72727e12i	−0.216285	+	0.374617i
$342$	1.52569e12			0.326088
$343$		−	4.93547e12i		−	1.03958i
$344$	−4.61989e12	−	2.45197e12i	−0.959046	−	0.509005i
$345$	−6.21458e12			−1.27150
$346$			4.06595e12i			0.819939i
$347$	−7.88760e12	−	4.55391e12i	−1.56783	−	0.905184i	−0.996422	−	0.0845147i	$-0.973066\pi$
$347$	−7.88760e12	−	4.55391e12i	−1.56783	−	0.905184i	−0.571403	−	0.820670i	$-0.693601\pi$
$348$	1.41453e12			0.277150
$349$	−5.91408e12	−	3.41450e12i	−1.14225	−	0.659477i	−0.195261	−	0.980751i	$-0.562556\pi$
$349$	−5.91408e12	−	3.41450e12i	−1.14225	−	0.659477i	−0.946986	+	0.321274i	$0.895889\pi$
$350$	9.02280e11	−	1.56280e12i	0.171791	−	0.297551i
$351$	3.41121e12	−	1.96946e12i	0.640283	−	0.369668i
$352$		−	3.47852e12i		−	0.643697i
$353$	−3.55829e12	−	6.16313e12i	−0.649183	−	1.12442i	−0.983318	−	0.181893i	$-0.941777\pi$
$353$	−3.55829e12	−	6.16313e12i	−0.649183	−	1.12442i	0.334135	−	0.942525i	$-0.391556\pi$
$354$	−2.39795e12	+	4.15337e12i	−0.431344	+	0.747110i
$355$	4.14843e12			0.735770
$356$	−8.80791e11	−	5.08525e11i	−0.154036	−	0.0889328i
$357$	−1.92621e11	−	3.33630e11i	−0.0332172	−	0.0575339i
$358$	1.83157e12	+	3.17238e12i	0.311465	+	0.539473i
$359$	−9.24935e11	−	1.60203e12i	−0.155110	−	0.268658i	0.777989	−	0.628278i	$-0.216240\pi$
$359$	−9.24935e11	−	1.60203e12i	−0.155110	−	0.268658i	−0.933099	+	0.359620i	$0.882906\pi$
$360$	2.81022e12			0.464759
$361$	1.75313e12	+	3.03652e12i	0.285943	+	0.495267i
$362$	2.70117e12	−	1.55952e12i	0.434520	−	0.250870i
$363$	−9.54982e11	−	5.51359e11i	−0.151517	−	0.0874785i
$364$	−9.79832e11	−	5.65706e11i	−0.153336	−	0.0885287i
$365$	4.97222e12			0.767513
$366$		−	4.75368e12i		−	0.723810i
$367$	6.42333e12	−	1.11255e13i	0.964783	−	1.67105i	0.254588	−	0.967050i	$-0.418060\pi$
$367$	6.42333e12	−	1.11255e13i	0.964783	−	1.67105i	0.710196	−	0.704004i	$-0.248606\pi$
$368$	1.87784e12	−	3.25252e12i	0.278240	−	0.481926i
$369$	3.45740e11	+	5.98839e11i	0.0505379	+	0.0875343i
$370$	6.01664e12	−	3.47371e12i	0.867652	−	0.500939i
$371$			2.85716e12i			0.406504i
$372$	9.56209e11	−	5.52068e11i	0.134227	−	0.0774957i
$373$	8.57319e11	−	4.94973e11i	0.118740	−	0.0685548i	−0.439453	−	0.898265i	$-0.644828\pi$
$373$	8.57319e11	−	4.94973e11i	0.118740	−	0.0685548i	0.558194	+	0.829711i	$0.311495\pi$
$374$	5.32661e11	−	3.07532e11i	0.0727935	−	0.0420274i
$375$	1.34280e12	−	2.32580e12i	0.181074	−	0.313629i
$376$			7.58984e12i			1.00993i
$377$	3.90829e12	+	2.25645e12i	0.513193	+	0.296292i
$378$	−3.81401e12	+	2.20202e12i	−0.494222	+	0.285339i
$379$	3.78512e12			0.484043			0.242022	−	0.970271i	$-0.422190\pi$
$379$	3.78512e12			0.484043			0.242022	+	0.970271i	$0.422190\pi$
$380$	2.48488e12	+	4.30394e12i	0.313608	+	0.543186i
$381$	1.10664e13	+	6.38922e12i	1.37843	+	0.795834i
$382$	2.89633e12	−	5.01660e12i	0.356067	−	0.616726i
$383$		−	1.17928e12i		−	0.143094i	−0.997437	−	0.0715471i	$-0.977206\pi$
$383$		−	1.17928e12i		−	0.143094i	0.997437	−	0.0715471i	$-0.0227936\pi$
$384$	2.63537e11	−	4.56459e11i	0.0315635	−	0.0546696i
$385$	6.46902e12			0.764777
$386$		−	6.08673e12i		−	0.710309i
$387$	2.88616e12	−	1.02969e11i	0.332479	−	0.0118618i
$388$	1.53379e12			0.174425
$389$			6.47848e12i			0.727320i	0.931532	+	0.363660i	$0.118473\pi$
$389$			6.47848e12i			0.727320i	−0.931532	+	0.363660i	$0.881527\pi$
$390$	−4.36020e12	−	2.51736e12i	−0.483263	−	0.279012i
$391$	−1.34090e12			−0.146727
$392$	−4.79035e12	−	2.76571e12i	−0.517531	−	0.298797i
$393$	3.97488e12	−	6.88469e12i	0.423995	−	0.734381i
$394$	−7.41120e12	+	4.27886e12i	−0.780562	+	0.450658i
$395$			5.89281e12i			0.612826i
$396$	5.58342e11	+	9.67078e11i	0.0573357	+	0.0993083i
$397$	−7.49705e12	+	1.29853e13i	−0.760217	+	1.31674i	0.182521	+	0.983202i	$0.441574\pi$
$397$	−7.49705e12	+	1.29853e13i	−0.760217	+	1.31674i	−0.942738	+	0.333533i	$0.891759\pi$
$398$	−1.42339e13			−1.42530
$399$	−6.01428e12	−	3.47235e12i	−0.594729	−	0.343367i
$400$	−1.54368e12	−	2.67373e12i	−0.150750	−	0.261106i
$401$	1.17834e12	+	2.04094e12i	0.113644	+	0.196838i	0.917237	−	0.398342i	$-0.130414\pi$
$401$	1.17834e12	+	2.04094e12i	0.113644	+	0.196838i	−0.803593	+	0.595180i	$0.797081\pi$
$402$	4.70306e12	+	8.14593e12i	0.447971	+	0.775909i
$403$	3.52263e12			0.331392
$404$	5.37203e11	+	9.30463e11i	0.0499150	+	0.0864554i
$405$	6.75812e12	−	3.90180e12i	0.620227	−	0.358088i
$406$	−4.36979e12	−	2.52290e12i	−0.396123	−	0.228702i
$407$	8.53965e12	+	4.93037e12i	0.764660	+	0.441476i
$408$	−1.21621e12			−0.107574
$409$			1.38422e13i			1.20945i	0.796435	+	0.604725i	$0.206717\pi$
$409$			1.38422e13i			1.20945i	−0.796435	+	0.604725i	$0.793283\pi$
$410$	1.77026e12	−	3.06617e12i	0.152798	−	0.264653i
$411$	3.48208e12	−	6.03114e12i	0.296914	−	0.514269i
$412$	8.50264e11	+	1.47270e12i	0.0716255	+	0.124059i
$413$	−9.42546e12	+	5.44179e12i	−0.784427	+	0.452889i
$414$			3.82668e12i			0.314645i
$415$	2.35145e13	−	1.35761e13i	1.91027	−	1.10290i
$416$	−5.32065e12	+	3.07188e12i	−0.427069	+	0.246568i
$417$	6.14691e12	−	3.54892e12i	0.487502	−	0.281459i
$418$	5.54382e12	−	9.60217e12i	0.434438	−	0.752468i
$419$		−	6.34310e12i		−	0.491170i	−0.969375	−	0.245585i	$-0.921020\pi$
$419$		−	6.34310e12i		−	0.491170i	0.969375	−	0.245585i	$-0.0789800\pi$
$420$	−3.10144e12	−	1.79061e12i	−0.237310	−	0.137011i
$421$	−1.69115e13	+	9.76388e12i	−1.27871	+	0.738264i	−0.976611	−	0.215012i	$-0.931021\pi$
$421$	−1.69115e13	+	9.76388e12i	−1.27871	+	0.738264i	−0.302100	+	0.953276i	$0.597688\pi$
$422$	−4.70156e12			−0.351301
$423$	−2.09544e12	−	3.62941e12i	−0.154730	−	0.268000i
$424$	7.81161e12	+	4.51003e12i	0.570048	+	0.329117i
$425$	−5.51140e11	+	9.54603e11i	−0.0397482	+	0.0688459i
$426$			5.12367e12i			0.365202i
$427$	5.39388e12	−	9.34248e12i	0.379981	−	0.658147i
$428$	−2.49054e12			−0.173410
$429$		−	7.14598e12i		−	0.491785i
$430$	−7.84543e12	−	1.25342e13i	−0.533672	−	0.852621i
$431$	8.73202e11			0.0587122			0.0293561	−	0.999569i	$-0.490654\pi$
$431$	8.73202e11			0.0587122			0.0293561	+	0.999569i	$0.490654\pi$
$432$			7.53469e12i			0.500780i
$433$	−1.55877e13	−	8.99954e12i	−1.02410	−	0.591263i	−0.108809	−	0.994063i	$-0.534704\pi$
$433$	−1.55877e13	−	8.99954e12i	−1.02410	−	0.591263i	−0.915288	+	0.402800i	$0.868037\pi$
$434$	−3.93859e12			−0.255795
$435$	1.23708e13	+	7.14229e12i	0.794240	+	0.458555i
$436$	−1.67388e12	+	2.89925e12i	−0.106241	+	0.184015i
$437$	−2.09336e13	+	1.20860e13i	−1.31352	+	0.758362i
$438$			6.14111e12i			0.380958i
$439$	−7.14203e12	−	1.23704e13i	−0.438025	−	0.758682i	0.559512	−	0.828822i	$-0.310989\pi$
$439$	−7.14203e12	−	1.23704e13i	−0.438025	−	0.758682i	−0.997537	+	0.0701405i	$0.977655\pi$
$440$	1.02114e13	−	1.76866e13i	0.619185	−	1.07246i
$441$	3.05429e12			0.183112
$442$	−9.40784e11	−	5.43162e11i	−0.0557671	−	0.0321972i
$443$	1.97586e12	+	3.42230e12i	0.115808	+	0.200585i	0.918102	−	0.396343i	$-0.129721\pi$
$443$	1.97586e12	+	3.42230e12i	0.115808	+	0.200585i	−0.802294	+	0.596928i	$0.796388\pi$
$444$	−2.72944e12	−	4.72753e12i	−0.158183	−	0.273980i
$445$	−5.13533e12	−	8.89465e12i	−0.294285	−	0.509717i
$446$	−2.40109e13			−1.36061
$447$	5.16672e12	+	8.94902e12i	0.289519	+	0.501462i
$448$	1.07694e13	−	6.21771e12i	0.596762	−	0.344540i
$449$	−1.63028e13	−	9.41243e12i	−0.893369	−	0.515787i	−0.0183259	−	0.999832i	$-0.505834\pi$
$449$	−1.63028e13	−	9.41243e12i	−0.893369	−	0.515787i	−0.875043	+	0.484045i	$0.839167\pi$
$450$	2.72427e12	+	1.57286e12i	0.147635	+	0.0852369i
$451$	5.02519e12			0.269321
$452$			1.26124e13i			0.668506i
$453$	−5.69227e12	+	9.85930e12i	−0.298397	+	0.516839i
$454$	3.13413e12	−	5.42848e12i	0.162494	−	0.281448i
$455$	−5.71278e12	−	9.89482e12i	−0.292948	−	0.507400i
$456$	−1.89871e13	+	1.09622e13i	−0.963019	+	0.555999i
$457$			8.53486e12i			0.428169i	0.976815	+	0.214085i	$0.0686768\pi$
$457$			8.53486e12i			0.428169i	−0.976815	+	0.214085i	$0.931323\pi$
$458$	6.68790e12	−	3.86126e12i	0.331866	−	0.191603i
$459$	2.32971e12	−	1.34506e12i	0.114351	−	0.0660204i
$460$	−1.07950e13	+	6.23250e12i	−0.524124	+	0.302603i
$461$	−6.90460e11	+	1.19591e12i	−0.0331615	+	0.0574374i	−0.882130	−	0.471006i	$-0.843891\pi$
$461$	−6.90460e11	+	1.19591e12i	−0.0331615	+	0.0574374i	0.848968	+	0.528444i	$0.177224\pi$
$462$			7.98979e12i			0.379599i
$463$	9.25586e12	+	5.34387e12i	0.435022	+	0.251160i	0.701484	−	0.712685i	$-0.252521\pi$
$463$	9.25586e12	+	5.34387e12i	0.435022	+	0.251160i	−0.266462	+	0.963846i	$0.585855\pi$
$464$	−7.47611e12	+	4.31633e12i	−0.347605	+	0.200690i
$465$	1.11501e13			0.512878
$466$	1.66258e13	+	2.87967e13i	0.756576	+	1.31043i
$467$	−3.69095e13	−	2.13097e13i	−1.66170	−	0.959385i	−0.971902	−	0.235386i	$-0.924365\pi$
$467$	−3.69095e13	−	2.13097e13i	−1.66170	−	0.959385i	−0.689801	−	0.723999i	$-0.742302\pi$
$468$	9.86143e11	−	1.70805e12i	0.0439249	−	0.0760801i
$469$			2.13458e13i			0.940692i
$470$	−1.07291e13	+	1.85833e13i	−0.467814	+	0.810278i
$471$	8.09822e12			0.349370
$472$			3.43595e13i			1.46669i
$473$	9.83922e12	−	1.85386e13i	0.415580	−	0.783019i
$474$	−7.27812e12			−0.304178
$475$			1.98706e13i			0.821756i
$476$	−6.69185e11	−	3.86354e11i	−0.0273849	−	0.0158107i
$477$	−4.98062e12			−0.201693
$478$	5.44923e12	+	3.14612e12i	0.218372	+	0.126077i
$479$	1.64313e13	−	2.84599e13i	0.651620	−	1.12864i	−0.331109	−	0.943592i	$-0.607423\pi$
$479$	1.64313e13	−	2.84599e13i	0.651620	−	1.12864i	0.982730	−	0.185047i	$-0.0592438\pi$
$480$	−1.68413e13	+	9.72332e12i	−0.660951	+	0.381600i
$481$		−	1.74160e13i		−	0.676431i
$482$	−6.76490e12	−	1.17172e13i	−0.260032	−	0.450388i
$483$	8.70923e12	−	1.50848e13i	0.331317	−	0.573859i
$484$	−2.21180e12			−0.0832757
$485$	1.34138e13	+	7.74448e12i	0.499855	+	0.288592i
$486$	−6.71888e12	−	1.16374e13i	−0.247808	−	0.429216i
$487$	2.31296e13	+	4.00617e13i	0.844352	+	1.46246i	0.886183	+	0.463336i	$0.153348\pi$
$487$	2.31296e13	+	4.00617e13i	0.844352	+	1.46246i	−0.0418305	+	0.999125i	$0.513319\pi$
$488$	−1.70285e13	−	2.94943e13i	−0.615287	−	1.06571i
$489$	2.62938e13			0.940391
$490$	−7.81928e12	−	1.35434e13i	−0.276813	−	0.479454i
$491$	−2.18759e12	+	1.26301e12i	−0.0766582	+	0.0442586i	−0.537839	−	0.843047i	$-0.680759\pi$
$491$	−2.18759e12	+	1.26301e12i	−0.0766582	+	0.0442586i	0.461181	+	0.887306i	$0.347426\pi$
$492$	−2.40922e12	−	1.39096e12i	−0.0835702	−	0.0482492i
$493$	2.66920e12	+	1.54106e12i	0.0916530	+	0.0529159i
$494$	−1.95829e13			−0.665646
$495$			1.12768e13i			0.379455i
$496$	−3.36919e12	+	5.83561e12i	−0.112232	+	0.194392i
$497$	−5.81370e12	+	1.00696e13i	−0.191721	+	0.332071i
$498$	1.67677e13	+	2.90424e13i	0.547426	+	0.948170i
$499$	−3.36734e12	+	1.94414e12i	−0.108839	+	0.0628382i	−0.553431	−	0.832895i	$-0.686682\pi$
$499$	−3.36734e12	+	1.94414e12i	−0.108839	+	0.0628382i	0.444592	+	0.895733i	$0.353349\pi$
$500$		−	5.38670e12i		−	0.172375i
$501$	9.99074e12	−	5.76816e12i	0.316526	−	0.182746i
$502$	1.11896e13	−	6.46029e12i	0.350990	−	0.202644i
$503$	2.67026e13	−	1.54168e13i	0.829305	−	0.478799i	−0.0243100	−	0.999704i	$-0.507739\pi$
$503$	2.67026e13	−	1.54168e13i	0.829305	−	0.478799i	0.853614	+	0.520905i	$0.174406\pi$
$504$	−3.93830e12	+	6.82134e12i	−0.121103	+	0.209757i
$505$			1.08499e13i			0.330345i
$506$	2.40839e13	+	1.39048e13i	0.726062	+	0.419192i
$507$	1.27689e13	−	7.37215e12i	0.381167	−	0.220067i
$508$	2.56306e13			0.757600
$509$	−1.21569e13	−	2.10564e13i	−0.355824	−	0.616305i	0.631435	−	0.775429i	$-0.282466\pi$
$509$	−1.21569e13	−	2.10564e13i	−0.355824	−	0.616305i	−0.987259	+	0.159124i	$0.949133\pi$
$510$	−2.97783e12	−	1.71925e12i	−0.0863077	−	0.0498298i
$511$	−6.96817e12	+	1.20692e13i	−0.199993	+	0.346397i
$512$		−	2.93248e13i		−	0.833461i
$513$	2.42471e13	−	4.19973e13i	0.682454	−	1.18205i
$514$	3.84464e13			1.07162
$515$			1.71727e13i			0.474028i
$516$	−9.84868e12	+	6.16448e12i	−0.269234	+	0.168519i
$517$	−3.04564e13			−0.824567
$518$			1.94725e13i			0.522124i
$519$	2.79401e13	+	1.61312e13i	0.741979	+	0.428382i
$520$	−3.60705e13			−0.948715
$521$	−3.00421e13	−	1.73448e13i	−0.782603	−	0.451836i	0.0547491	−	0.998500i	$-0.482564\pi$
$521$	−3.00421e13	−	1.73448e13i	−0.782603	−	0.451836i	−0.837352	+	0.546664i	$0.815897\pi$
$522$	4.39793e12	−	7.61744e12i	0.113474	−	0.196543i
$523$	−2.59700e12	+	1.49938e12i	−0.0663688	+	0.0383181i	−0.532817	−	0.846230i	$-0.678867\pi$
$523$	−2.59700e12	+	1.49938e12i	−0.0663688	+	0.0383181i	0.466448	+	0.884548i	$0.345533\pi$
$524$		−	1.59454e13i		−	0.403625i
$525$	−7.15941e12	−	1.24005e13i	−0.179507	−	0.310915i
$526$	2.23059e13	−	3.86350e13i	0.553977	−	0.959516i
$527$	2.40581e12			0.0591846
$528$	1.18381e13	+	6.83471e12i	0.288477	+	0.166552i
$529$	−9.60053e12	−	1.66286e13i	−0.231749	−	0.401400i
$530$	1.27509e13	+	2.20852e13i	0.304902	+	0.528106i
$531$	−9.48616e12	−	1.64305e13i	−0.224708	−	0.389205i
$532$	−1.39295e13			−0.326871
$533$	−4.43773e12	−	7.68638e12i	−0.103163	−	0.178684i
$534$	1.09857e13	−	6.34257e12i	0.252999	−	0.146069i
$535$	−2.17812e13	−	1.25754e13i	−0.496949	−	0.286914i
$536$	5.83603e13	+	3.36943e13i	1.31915	+	0.761611i
$537$	2.90663e13			0.650907
$538$		−	1.75794e13i		−	0.390025i
$539$	1.10982e13	−	1.92226e13i	0.243954	−	0.422541i
$540$	1.25037e13	−	2.16571e13i	0.272314	−	0.471662i
$541$	−1.14187e13	−	1.97777e13i	−0.246394	−	0.426766i	0.716129	−	0.697968i	$-0.245912\pi$
$541$	−1.14187e13	−	1.97777e13i	−0.246394	−	0.426766i	−0.962523	+	0.271202i	$0.912579\pi$
$542$	1.26946e13	−	7.32926e12i	0.271409	−	0.156698i
$543$		−	2.47490e13i		−	0.524274i
$544$	−3.63378e12	+	2.09796e12i	−0.0762718	+	0.0440355i
$545$	−2.92780e13	+	1.69037e13i	−0.608918	+	0.351559i
$546$	1.22209e13	−	7.05577e12i	0.251850	−	0.145406i
$547$	−1.52205e13	+	2.63627e13i	−0.310808	+	0.538336i	−0.978538	−	0.206068i	$-0.933933\pi$
$547$	−1.52205e13	+	2.63627e13i	−0.310808	+	0.538336i	0.667729	+	0.744404i	$0.267266\pi$
$548$		−	1.39685e13i		−	0.282649i
$549$	1.62859e13	+	9.40265e12i	0.326549	+	0.188533i
$550$	1.97981e13	−	1.14304e13i	0.393378	−	0.227117i
$551$	5.55609e13			1.09399
$552$	−2.74951e13	−	4.76229e13i	−0.536488	−	0.929224i
$553$	−1.43038e13	−	8.25830e12i	−0.276583	−	0.159685i
$554$	−1.82836e13	+	3.16681e13i	−0.350358	+	0.606838i
$555$		−	5.51264e13i		−	1.04687i
$556$	7.11831e12	−	1.23293e13i	0.133969	−	0.232040i
$557$	4.31783e13			0.805359			0.402679	−	0.915341i	$-0.368079\pi$
$557$	4.31783e13			0.805359			0.402679	+	0.915341i	$0.368079\pi$
$558$		−	6.86577e12i		−	0.126917i
$559$	−3.70452e13	+	1.32165e12i	−0.678692	+	0.0242136i
$560$	2.18557e13			0.396849
$561$		−	4.88041e12i		−	0.0878297i
$562$	−5.42918e13	−	3.13454e13i	−0.968395	−	0.559103i
$563$	6.38973e13			1.12964			0.564821	−	0.825214i	$-0.308945\pi$
$563$	6.38973e13			1.12964			0.564821	+	0.825214i	$0.308945\pi$
$564$	1.46017e13	+	8.43029e12i	0.255863	+	0.147723i
$565$	−6.36830e13	+	1.10302e14i	−1.10607	+	1.91576i
$566$	−5.13886e12	+	2.96692e12i	−0.0884676	+	0.0510768i
$567$			2.18722e13i			0.373231i
$568$	1.83539e13	+	3.17899e13i	0.310446	+	0.537708i
$569$	−8.70973e12	+	1.50857e13i	−0.146030	+	0.252932i	−0.929757	−	0.368174i	$-0.879983\pi$
$569$	−8.70973e12	+	1.50857e13i	−0.146030	+	0.252932i	0.783726	+	0.621106i	$0.213316\pi$
$570$	−6.19853e13			−1.03018
$571$	−3.64593e12	−	2.10498e12i	−0.0600659	−	0.0346791i	0.469666	−	0.882844i	$-0.344374\pi$
$571$	−3.64593e12	−	2.10498e12i	−0.0600659	−	0.0346791i	−0.529732	+	0.848165i	$0.677708\pi$
$572$	−7.16659e12	−	1.24129e13i	−0.117039	−	0.202718i
$573$	−2.29818e13	−	3.98057e13i	−0.372059	−	0.644424i
$574$	4.96175e12	+	8.59400e12i	0.0796297	+	0.137923i
$575$	−4.98388e13			−0.792918
$576$	1.08387e13	+	1.87733e13i	0.170949	+	0.296092i
$577$	−6.80572e13	+	3.92929e13i	−1.06413	+	0.614377i	−0.926572	−	0.376117i	$-0.877259\pi$
$577$	−6.80572e13	+	3.92929e13i	−1.06413	+	0.614377i	−0.137559	+	0.990494i	$0.543926\pi$
$578$	4.30346e13	+	2.48460e13i	0.667081	+	0.385139i
$579$	−4.18264e13	−	2.41485e13i	−0.642773	−	0.371105i
$580$	2.86516e13			0.436524
$581$			7.61034e13i			1.14954i
$582$	−9.56510e12	+	1.65672e13i	−0.143243	+	0.248105i
$583$	−1.80978e13	+	3.13463e13i	−0.268710	+	0.465419i
$584$	2.19985e13	+	3.81026e13i	0.323839	+	0.560906i
$585$	1.72487e13	−	9.95854e12i	0.251754	−	0.145350i
$586$		−	8.84586e13i		−	1.28012i
$587$	−3.48542e13	+	2.01231e13i	−0.500110	+	0.288738i	−0.728759	−	0.684770i	$-0.759902\pi$
$587$	−3.48542e13	+	2.01231e13i	−0.500110	+	0.288738i	0.228649	+	0.973509i	$0.426569\pi$
$588$	−1.06416e13	+	6.14393e12i	−0.151398	+	0.0874097i
$589$	3.75587e13	−	2.16846e13i	0.529828	−	0.305896i
$590$	−4.85710e13	+	8.41275e13i	−0.679387	+	1.17673i
$591$			6.79038e13i			0.941795i
$592$	2.88514e13	+	1.66574e13i	0.396788	+	0.229086i
$593$	1.05610e14	−	6.09742e13i	1.44023	−	0.831520i	0.442369	−	0.896833i	$-0.354138\pi$
$593$	1.05610e14	−	6.09742e13i	1.44023	−	0.831520i	0.997865	+	0.0653133i	$0.0208047\pi$
$594$	−5.57920e13			−0.754466
$595$	−3.90159e12	−	6.75775e12i	−0.0523187	−	0.0906186i
$596$	1.79497e13	+	1.03632e13i	0.238685	+	0.137805i
$597$	−5.64714e13	+	9.78114e13i	−0.744658	+	1.28979i
$598$		−	4.91173e13i		−	0.642286i
$599$	3.96835e13	−	6.87339e13i	0.514607	−	0.891326i	−0.485249	−	0.874376i	$-0.661271\pi$
$599$	3.96835e13	−	6.87339e13i	0.514607	−	0.891326i	0.999856	−	0.0169500i	$-0.00539562\pi$
$600$	−4.52046e13			−0.581335
$601$			5.51159e13i			0.702918i	0.936203	+	0.351459i	$0.114314\pi$
$601$			5.51159e13i			0.702918i	−0.936203	+	0.351459i	$0.885686\pi$
$602$	4.14195e13	−	1.47772e12i	0.523869	−	0.0186900i
$603$	−3.72101e13			−0.466739
$604$			2.28348e13i			0.284061i
$605$	−1.93434e13	−	1.11679e13i	−0.238647	−	0.137783i
$606$	−1.34005e13			−0.163968
$607$	8.19623e12	+	4.73210e12i	0.0994651	+	0.0574262i	0.548907	−	0.835883i	$-0.315044\pi$
$607$	8.19623e12	+	4.73210e12i	0.0994651	+	0.0574262i	−0.449442	+	0.893309i	$0.648377\pi$
$608$	−3.78196e13	+	6.55054e13i	−0.455196	+	0.788423i
$609$	−3.46734e13	+	2.00187e13i	−0.413914	+	0.238973i
$610$		−	9.62869e13i		−	1.14003i
$611$	2.68960e13	+	4.65852e13i	0.315851	+	0.547069i
$612$	6.73494e11	−	1.16653e12i	0.00784471	−	0.0135874i
$613$	−3.36706e13			−0.388999			−0.194499	−	0.980903i	$-0.562308\pi$
$613$	−3.36706e13			−0.388999			−0.194499	+	0.980903i	$0.562308\pi$
$614$	8.23838e13	+	4.75643e13i	0.944060	+	0.545054i
$615$	−1.40466e13	−	2.43295e13i	−0.159660	−	0.276540i
$616$	2.86208e13	+	4.95727e13i	0.322685	+	0.558906i
$617$	−7.99841e13	−	1.38536e14i	−0.894495	−	1.54931i	−0.834429	−	0.551116i	$-0.814202\pi$
$617$	−7.99841e13	−	1.38536e14i	−0.894495	−	1.54931i	−0.0600656	−	0.998194i	$-0.519131\pi$
$618$	−2.12098e13			−0.235285
$619$	−6.18767e12	−	1.07174e13i	−0.0680885	−	0.117933i	0.829971	−	0.557806i	$-0.188357\pi$
$619$	−6.18767e12	−	1.07174e13i	−0.0680885	−	0.117933i	−0.898060	+	0.439873i	$0.855023\pi$
$620$	1.93682e13	−	1.11823e13i	0.211413	−	0.122059i
$621$	1.05336e14	+	6.08159e13i	1.14056	+	0.658505i
$622$	−5.88262e13	−	3.39633e13i	−0.631857	−	0.364803i
$623$	2.87870e13			0.306730
$624$		−	2.41429e13i		−	0.255191i
$625$	5.84525e13	−	1.01243e14i	0.612919	−	1.06161i
$626$	−2.49295e12	+	4.31791e12i	−0.0259323	+	0.0449161i
$627$	−4.39891e13	−	7.61913e13i	−0.453949	−	0.786263i
$628$	1.40670e13	−	8.12158e12i	0.144013	−	0.0831462i
$629$		−	1.18944e13i		−	0.120806i
$630$	−1.92855e13	+	1.11345e13i	−0.194324	+	0.112193i
$631$	−1.28434e14	+	7.41514e13i	−1.28391	+	0.741263i	−0.977560	−	0.210657i	$-0.932440\pi$
$631$	−1.28434e14	+	7.41514e13i	−1.28391	+	0.741263i	−0.306345	+	0.951920i	$0.599106\pi$
$632$	−4.51572e13	+	2.60715e13i	−0.447859	+	0.258572i
$633$	−1.86530e13	+	3.23079e13i	−0.183539	+	0.317900i
$634$			1.13364e13i			0.110670i
$635$	2.24153e14	+	1.29415e14i	2.17108	+	1.25348i
$636$	1.73532e13	−	1.00189e13i	0.166761	−	0.0962796i
$637$	−3.92032e13			−0.373787
$638$	−3.19611e13	−	5.53582e13i	−0.302356	−	0.523695i
$639$	−1.75534e13	−	1.01345e13i	−0.164762	−	0.0951255i
$640$	5.33800e12	−	9.24568e12i	0.0497140	−	0.0861071i
$641$			2.02938e14i			1.87531i	0.347564	+	0.937656i	$0.387009\pi$
$641$			2.02938e14i			1.87531i	−0.347564	+	0.937656i	$0.612991\pi$
$642$	1.55316e13	−	2.69016e13i	0.142411	−	0.246662i
$643$	9.71468e13			0.883840			0.441920	−	0.897054i	$-0.354298\pi$
$643$	9.71468e13			0.883840			0.441920	+	0.897054i	$0.354298\pi$
$644$		−	3.49374e13i		−	0.315400i
$645$	−1.17258e14	+	4.18340e12i	−1.05037	+	0.0374740i
$646$	−1.33743e13			−0.118880
$647$		−	2.03352e14i		−	1.79361i	−0.442430	−	0.896803i	$-0.645884\pi$
$647$		−	2.03352e14i		−	1.79361i	0.442430	−	0.896803i	$-0.354116\pi$
$648$	5.97997e13	+	3.45254e13i	0.523389	+	0.302179i
$649$	−1.37877e14			−1.19748
$650$	−3.49673e13	−	2.01884e13i	−0.301367	−	0.173994i
$651$	−1.56260e13	+	2.70650e13i	−0.133642	+	0.231474i
$652$	4.56735e13	−	2.63696e13i	0.387638	−	0.223803i
$653$			4.13670e13i			0.348408i	0.984710	+	0.174204i	$0.0557352\pi$
$653$			4.13670e13i			0.348408i	−0.984710	+	0.174204i	$0.944265\pi$
$654$	−2.08775e13	−	3.61609e13i	−0.174498	−	0.302239i
$655$	8.05120e13	−	1.39451e14i	0.667812	−	1.15668i
$656$	1.69777e13			0.139753
$657$	−2.10391e13	−	1.21469e13i	−0.171870	−	0.0992294i
$658$	−3.00719e13	−	5.20861e13i	−0.243799	−	0.422272i
$659$	1.55917e13	+	2.70056e13i	0.125449	+	0.217283i	0.921908	−	0.387408i	$-0.126630\pi$
$659$	1.55917e13	+	2.70056e13i	0.125449	+	0.217283i	−0.796460	+	0.604692i	$0.793296\pi$
$660$	−2.26842e13	−	3.92902e13i	−0.181136	−	0.313736i
$661$	−1.27954e14			−1.01402			−0.507008	−	0.861941i	$-0.669249\pi$
$661$	−1.27954e14			−1.01402			−0.507008	+	0.861941i	$0.669249\pi$
$662$	−8.61580e13	−	1.49230e14i	−0.677650	−	1.17372i
$663$	−7.46493e12	+	4.30988e12i	−0.0582717	+	0.0336432i
$664$	2.08070e14	+	1.20129e14i	1.61202	+	0.930698i
$665$	−1.21821e14	−	7.03332e13i	−0.936726	−	0.540819i
$666$	−3.39446e13			−0.259059
$667$			1.39356e14i			1.05559i
$668$	1.15696e13	−	2.00391e13i	0.0869832	−	0.150659i
$669$	−9.52608e13	+	1.64997e14i	−0.710859	+	1.23124i
$670$	9.52615e13	+	1.64998e14i	0.705575	+	1.22209i
$671$	1.18354e14	−	6.83318e13i	0.870104	−	0.502355i
$672$		−	5.45058e13i		−	0.397738i
$673$	7.12588e13	−	4.11413e13i	0.516135	−	0.297990i	−0.219217	−	0.975676i	$-0.570350\pi$
$673$	7.12588e13	−	4.11413e13i	0.516135	−	0.297990i	0.735352	+	0.677686i	$0.237017\pi$
$674$	−9.87212e13	+	5.69967e13i	−0.709759	+	0.409780i
$675$	8.65914e13	−	4.99936e13i	0.617954	−	0.356776i
$676$	1.47868e13	−	2.56115e13i	0.104747	−	0.181427i
$677$			1.84933e14i			1.30038i	0.759770	+	0.650192i	$0.225312\pi$
$677$			1.84933e14i			1.30038i	−0.759770	+	0.650192i	$0.774688\pi$
$678$	−1.36233e14	−	7.86539e13i	−0.950895	−	0.549000i
$679$	−3.75969e13	+	2.17066e13i	−0.260497	+	0.150398i
$680$	−2.46347e13			−0.169435
$681$	−2.48687e13	−	4.30739e13i	−0.169792	−	0.294089i
$682$	−4.32109e13	−	2.49478e13i	−0.292867	−	0.169087i
$683$	−1.29263e14	+	2.23890e14i	−0.869701	+	1.50637i	−0.00739798	+	0.999973i	$0.502355\pi$
$683$	−1.29263e14	+	2.23890e14i	−0.869701	+	1.50637i	−0.862303	+	0.506393i	$0.830978\pi$
$684$		−	2.42819e13i		−	0.162182i
$685$	7.05303e13	−	1.22162e14i	0.467652	−	0.809998i
$686$	1.23470e14			0.812721
$687$		−	6.12766e13i		−	0.400416i
$688$	3.32421e13	−	6.26333e13i	0.215648	−	0.406315i
$689$	6.39286e13			0.411717
$690$		−	1.55470e14i		−	0.994031i
$691$	2.17407e14	+	1.25520e14i	1.38001	+	0.796751i	0.992160	−	0.124971i	$-0.0398838\pi$
$691$	2.17407e14	+	1.25520e14i	1.38001	+	0.796751i	0.387852	+	0.921722i	$0.373217\pi$
$692$	6.47111e13			0.407801
$693$	−2.73726e13	−	1.58036e13i	−0.171258	−	0.0988756i
$694$	1.13925e14	−	1.97324e14i	0.707654	−	1.22569i
$695$	1.24507e14	−	7.18841e13i	0.767838	−	0.443311i
$696$			1.26398e14i			0.773918i
$697$	−3.03079e12	−	5.24948e12i	−0.0184243	−	0.0319119i
$698$	8.54202e13	−	1.47952e14i	0.515565	−	0.892985i
$699$	2.63844e14			1.58111
$700$	−2.48725e13	−	1.43601e13i	−0.147989	−	0.0854413i
$701$	−7.01816e13	−	1.21558e14i	−0.414604	−	0.718115i	0.580783	−	0.814058i	$-0.302746\pi$
$701$	−7.01816e13	−	1.21558e14i	−0.414604	−	0.718115i	−0.995387	+	0.0959436i	$0.969413\pi$
$702$	4.92698e13	+	8.53379e13i	0.288999	+	0.500560i
$703$	−1.07209e14	−	1.85692e14i	−0.624389	−	1.08147i
$704$	1.57537e14			0.911000
$705$	8.51331e13	+	1.47455e14i	0.488825	+	0.846669i
$706$	1.54183e14	−	8.90174e13i	0.879047	−	0.507518i
$707$	−2.63362e13	−	1.52052e13i	−0.149093	−	0.0860787i
$708$	6.61025e13	+	3.81643e13i	0.371579	+	0.214531i
$709$	−1.72608e14			−0.963452			−0.481726	−	0.876322i	$-0.659990\pi$
$709$	−1.72608e14			−0.963452			−0.481726	+	0.876322i	$0.659990\pi$
$710$			1.03781e14i			0.575210i
$711$	1.43959e13	−	2.49345e13i	0.0792303	−	0.137231i
$712$	4.54404e13	−	7.87050e13i	0.248337	−	0.430133i
$713$	5.43885e13	+	9.42037e13i	0.295161	+	0.511234i
$714$	8.34640e12	−	4.81879e12i	0.0449788	−	0.0259685i
$715$		−	1.44743e14i		−	0.774584i
$716$	5.04896e13	−	2.91502e13i	0.268310	−	0.154909i
$717$	4.32386e13	−	2.49638e13i	0.228179	−	0.131739i
$718$	4.00780e13	−	2.31390e13i	0.210031	−	0.121262i
$719$	−7.87135e12	+	1.36336e13i	−0.0409642	+	0.0709521i	−0.885781	−	0.464104i	$-0.846376\pi$
$719$	−7.87135e12	+	1.36336e13i	−0.0409642	+	0.0709521i	0.844816	+	0.535056i	$0.179710\pi$
$720$			3.80990e13i			0.196903i
$721$	−4.16839e13	−	2.40662e13i	−0.213940	−	0.123518i
$722$	−7.59643e13	+	4.38580e13i	−0.387190	+	0.223544i
$723$	−1.07356e14			−0.543420
$724$	−2.48204e13	−	4.29902e13i	−0.124772	−	0.216111i
$725$	9.92097e13	+	5.72788e13i	0.495295	+	0.285959i
$726$	1.37933e13	−	2.38907e13i	0.0683888	−	0.118453i
$727$		−	2.65385e14i		−	1.30679i	−0.757019	−	0.653393i	$-0.773345\pi$
$727$		−	2.65385e14i		−	1.30679i	0.757019	−	0.653393i	$-0.226655\pi$
$728$	5.05500e13	−	8.75551e13i	0.247209	−	0.428178i
$729$	−2.21230e14			−1.07450
$730$			1.24390e14i			0.600026i
$731$	−2.53003e13	+	9.02635e11i	−0.121210	+	0.00432440i
$732$	−7.56566e13			−0.359991
$733$			2.93185e14i			1.38555i	0.721154	+	0.692775i	$0.243612\pi$
$733$			2.93185e14i			1.38555i	−0.721154	+	0.692775i	$0.756388\pi$
$734$	2.78327e14	+	1.60692e14i	1.30639	+	0.754247i
$735$	−1.24089e14			−0.578490
$736$	−1.64299e14	−	9.48579e13i	−0.760755	−	0.439222i
$737$	−1.35208e14	+	2.34188e14i	−0.621821	+	1.07703i
$738$	−1.49811e13	+	8.64935e12i	−0.0684325	+	0.0395095i
$739$		−	2.24724e14i		−	1.01960i	−0.860294	−	0.509798i	$-0.829720\pi$
$739$		−	2.24724e14i		−	1.01960i	0.860294	−	0.509798i	$-0.170280\pi$
$740$	−5.52854e13	−	9.57571e13i	−0.249145	−	0.431531i
$741$	−7.76933e13	+	1.34569e14i	−0.347770	+	0.602356i
$742$	−7.14774e13			−0.317796
$743$	1.41160e14	+	8.14987e13i	0.623401	+	0.359921i	0.778192	−	0.628027i	$-0.216137\pi$
$743$	1.41160e14	+	8.14987e13i	0.623401	+	0.359921i	−0.154791	+	0.987947i	$0.549470\pi$
$744$	4.93313e13	+	8.54442e13i	0.216400	+	0.374816i
$745$	1.04653e14	+	1.81264e14i	0.456006	+	0.789825i
$746$	1.23827e13	+	2.14475e13i	0.0535947	+	0.0928287i
$747$	−1.32664e14			−0.570360
$748$	−4.89448e12	−	8.47749e12i	−0.0209025	−	0.0362042i
$749$	6.10491e13	−	3.52467e13i	0.258982	−	0.149524i
$750$	5.81844e13	+	3.35928e13i	0.245189	+	0.141560i
$751$	1.38082e14	+	7.97218e13i	0.578013	+	0.333716i	0.760343	−	0.649521i	$-0.225031\pi$
$751$	1.38082e14	+	7.97218e13i	0.578013	+	0.333716i	−0.182330	+	0.983237i	$0.558364\pi$
$752$	−1.02898e14			−0.427875
$753$		−	1.02522e14i		−	0.423490i
$754$	−5.64495e13	+	9.77735e13i	−0.231635	+	0.401203i
$755$	−1.15298e14	+	1.99702e14i	−0.469989	+	0.814045i
$756$	3.50459e13	+	6.07013e13i	0.141915	+	0.245804i
$757$	−1.46875e14	+	8.47984e13i	−0.590839	+	0.341121i	−0.765429	−	0.643520i	$-0.777473\pi$
$757$	−1.46875e14	+	8.47984e13i	−0.590839	+	0.341121i	0.174590	+	0.984641i	$0.444140\pi$
$758$			9.46921e13i			0.378415i
$759$	1.91101e14	−	1.10332e14i	0.758670	−	0.438019i
$760$	−3.84588e14	+	2.22042e14i	−1.51680	+	0.875725i
$761$	−1.69184e14	+	9.76784e13i	−0.662881	+	0.382715i	−0.793374	−	0.608735i	$-0.791677\pi$
$761$	−1.69184e14	+	9.76784e13i	−0.662881	+	0.382715i	0.130493	+	0.991449i	$0.458344\pi$
$762$	−1.59839e14	+	2.76848e14i	−0.622167	+	1.07762i
$763$		−	9.47566e13i		−	0.366426i
$764$	−7.98410e13	−	4.60962e13i	−0.306732	−	0.177092i
$765$	1.17801e13	−	6.80127e12i	0.0449618	−	0.0259587i
$766$	2.95019e13			0.111868
$767$	1.21759e14	+	2.10893e14i	0.458697	+	0.794486i
$768$	−1.82828e14	−	1.05556e14i	−0.684286	−	0.395073i
$769$	1.33021e14	−	2.30398e14i	0.494638	−	0.856738i	−0.505343	−	0.862919i	$-0.668634\pi$
$769$	1.33021e14	−	2.30398e14i	0.494638	−	0.856738i	0.999981	+	0.00618071i	$0.00196739\pi$
$770$			1.61835e14i			0.597886i
$771$	1.52532e14	−	2.64193e14i	0.559873	−	0.969729i
$772$	−9.68725e13			−0.353276
$773$		−	3.07043e14i		−	1.11251i	−0.831013	−	0.556253i	$-0.812239\pi$
$773$		−	3.07043e14i		−	1.11251i	0.831013	−	0.556253i	$-0.187761\pi$
$774$	2.57597e12	+	7.22027e13i	0.00927332	+	0.259925i
$775$	8.94200e13			0.319835
$776$			1.37055e14i			0.487066i
$777$	1.33810e14	+	7.72552e13i	0.472480	+	0.272787i
$778$	−1.62072e14			−0.568603
$779$	−9.46313e13	−	5.46354e13i	−0.329874	−	0.190453i
$780$	−4.00648e13	+	6.93942e13i	−0.138768	+	0.240353i
$781$	−1.27566e14	+	7.36502e13i	−0.439015	+	0.253465i
$782$		−	3.35451e13i		−	0.114708i
$783$	−1.39789e14	−	2.42122e14i	−0.474968	−	0.822668i
$784$	3.74956e13	−	6.49442e13i	0.126590	−	0.219260i
$785$	1.64031e14			0.550273
$786$	1.72234e14	+	9.94392e13i	0.574124	+	0.331471i
$787$	−1.82297e14	−	3.15748e14i	−0.603819	−	1.04584i	−0.992237	−	0.124361i	$-0.960312\pi$
$787$	−1.82297e14	−	3.15748e14i	−0.603819	−	1.04584i	0.388418	−	0.921483i	$-0.373022\pi$
$788$	6.80996e13	+	1.17952e14i	0.224137	+	0.388217i
$789$	−1.76993e14	−	3.06561e14i	−0.578857	−	1.00261i
$790$	−1.47420e14			−0.479094
$791$	−1.78493e14	−	3.09159e14i	−0.576421	−	0.998390i
$792$	−8.64154e13	+	4.98920e13i	−0.277310	+	0.160105i
$793$	−2.09037e14	−	1.20687e14i	−0.666587	−	0.384854i
$794$	−3.24851e14	−	1.87553e14i	−1.02940	−	0.594322i
$795$	2.02351e14			0.637192
$796$			2.26537e14i			0.708882i
$797$	9.60810e13	−	1.66417e14i	0.298776	−	0.517496i	−0.677080	−	0.735909i	$-0.736755\pi$
$797$	9.60810e13	−	1.66417e14i	0.298776	−	0.517496i	0.975856	+	0.218414i	$0.0700882\pi$
$798$	8.68675e13	−	1.50459e14i	0.268437	−	0.464947i
$799$	1.83688e13	+	3.18158e13i	0.0564089	+	0.0977032i
$800$	−1.35061e14	+	7.79777e13i	−0.412175	+	0.237969i
$801$			5.01817e13i			0.152189i
$802$	−5.10581e13	+	2.94784e13i	−0.153884	+	0.0888448i
$803$	−1.52898e14	+	8.82755e13i	−0.457955	+	0.264400i
$804$	1.29646e14	−	7.48509e13i	0.385902	−	0.222801i
$805$	1.76407e14	−	3.05547e14i	0.521840	−	0.903854i
$806$			8.81255e13i			0.259075i
$807$	−1.20801e14	−	6.97445e13i	−0.352941	−	0.203771i
$808$	−8.31436e13	+	4.80030e13i	−0.241419	+	0.139383i
$809$	−1.21812e14			−0.351517			−0.175758	−	0.984433i	$-0.556238\pi$
$809$	−1.21812e14			−0.351517			−0.175758	+	0.984433i	$0.556238\pi$
$810$	9.76110e13	+	1.69067e14i	0.279946	+	0.484880i
$811$	5.66563e14	+	3.27105e14i	1.61489	+	0.932359i	0.988213	+	0.153083i	$0.0489202\pi$
$811$	5.66563e14	+	3.27105e14i	1.61489	+	0.932359i	0.626680	+	0.779276i	$0.284413\pi$
$812$	−4.01529e13	+	6.95468e13i	−0.113746	+	0.197014i
$813$		−	1.16312e14i		−	0.327471i
$814$	−1.23343e14	+	2.13636e14i	−0.345137	+	0.597795i
$815$	5.32586e14			1.48116
$816$		−	1.64886e13i		−	0.0455756i
$817$	−3.86844e14	+	2.42133e14i	−1.06274	+	0.665188i
$818$	−3.46289e14			−0.945522
$819$			5.58244e13i			0.151497i
$820$	−4.87993e13	−	2.81743e13i	−0.131627	−	0.0759948i
$821$	6.16992e14			1.65411			0.827054	−	0.562122i	$-0.190015\pi$
$821$	6.16992e14			1.65411			0.827054	+	0.562122i	$0.190015\pi$
$822$	1.50881e14	+	8.71110e13i	0.402045	+	0.232121i
$823$	−1.85488e14	+	3.21274e14i	−0.491266	+	0.850897i	−0.999949	−	0.0100563i	$-0.996799\pi$
$823$	−1.85488e14	+	3.21274e14i	−0.491266	+	0.850897i	0.508684	+	0.860953i	$0.330132\pi$
$824$	−1.31596e14	+	7.59772e13i	−0.346424	+	0.200008i
$825$		−	1.81396e14i		−	0.474634i
$826$	−1.36137e14	−	2.35796e14i	−0.354059	−	0.613248i
$827$	−5.04134e13	+	8.73185e13i	−0.130322	+	0.225725i	−0.923801	−	0.382874i	$-0.874934\pi$
$827$	−5.04134e13	+	8.73185e13i	−0.130322	+	0.225725i	0.793479	+	0.608598i	$0.208268\pi$
$828$	6.09031e13			0.156490
$829$	−4.91438e14	−	2.83732e14i	−1.25515	−	0.724661i	−0.283022	−	0.959113i	$-0.591337\pi$
$829$	−4.91438e14	−	2.83732e14i	−1.25515	−	0.724661i	−0.972128	+	0.234452i	$0.924670\pi$
$830$	3.39633e14	+	5.88261e14i	0.862221	+	1.49341i
$831$	1.45076e14	+	2.51280e14i	0.366093	+	0.634092i
$832$	−1.39120e14	−	2.40964e14i	−0.348959	−	0.604414i
$833$	−2.67741e13			−0.0667561
$834$	8.87830e13	+	1.53777e14i	0.220039	+	0.381119i
$835$	2.02365e14	−	1.16835e14i	0.498542	−	0.287834i
$836$	−1.52822e14	−	8.82319e13i	−0.374244	−	0.216070i
$837$	−1.88992e14	−	1.09115e14i	−0.460063	−	0.265617i
$838$	1.58685e14			0.383986
$839$			6.36036e14i			1.52993i	0.644071	+	0.764966i	$0.277244\pi$
$839$			6.36036e14i			1.52993i	−0.644071	+	0.764966i	$0.722756\pi$
$840$	1.60004e14	−	2.77136e14i	0.382592	−	0.662668i
$841$	−5.01943e13	+	8.69392e13i	−0.119309	+	0.206650i
$842$	−2.44262e14	−	4.23075e14i	−0.577160	−	0.999670i
$843$	−4.30794e14	+	2.48719e14i	−1.01189	+	0.584213i
$844$			7.48271e13i			0.174722i
$845$	2.58637e14	−	1.49324e14i	0.600355	−	0.346615i
$846$	9.07968e13	−	5.24215e13i	0.209517	−	0.120964i
$847$	5.42164e13	−	3.13018e13i	0.124369	−	0.0718047i
$848$	−6.11439e13	+	1.05904e14i	−0.139436	+	0.241510i
$849$			4.70838e13i			0.106742i
$850$	−2.38812e13	−	1.37878e13i	−0.0538223	−	0.0310743i
$851$	4.65746e14	−	2.68898e14i	1.04352	−	0.602477i
$852$	8.15451e13			0.181635
$853$	2.67905e14	+	4.64025e14i	0.593247	+	1.02753i	0.993792	+	0.111257i	$0.0354876\pi$
$853$	2.67905e14	+	4.64025e14i	0.593247	+	1.02753i	−0.400545	+	0.916277i	$0.631179\pi$
$854$	2.33720e14	+	1.34938e14i	0.514525	+	0.297061i
$855$	1.22605e14	−	2.12358e14i	0.268336	−	0.464771i
$856$		−	2.22548e14i		−	0.484234i
$857$	1.34257e14	−	2.32541e14i	0.290425	−	0.503031i	−0.683485	−	0.729964i	$-0.739537\pi$
$857$	1.34257e14	−	2.32541e14i	0.290425	−	0.503031i	0.973910	+	0.226933i	$0.0728699\pi$
$858$	1.78770e14			0.384467
$859$		−	1.87561e14i		−	0.401030i	−0.979691	−	0.200515i	$-0.935738\pi$
$859$		−	1.87561e14i		−	0.401030i	0.979691	−	0.200515i	$-0.0642616\pi$
$860$	−1.99487e14	+	1.24863e14i	−0.424055	+	0.265425i
$861$	7.87409e13			0.166412
$862$			2.18448e13i			0.0458999i
$863$	−3.54508e14	−	2.04675e14i	−0.740580	−	0.427574i	0.0817002	−	0.996657i	$-0.473965\pi$
$863$	−3.54508e14	−	2.04675e14i	−0.740580	−	0.427574i	−0.822280	+	0.569083i	$0.807298\pi$
$864$	3.80610e14			0.790517
$865$	5.65933e14	+	3.26742e14i	1.16865	+	0.674721i
$866$	2.25141e14	−	3.89955e14i	0.462237	−	0.800618i
$867$	3.41471e14	−	1.97148e14i	0.697040	−	0.402436i
$868$			6.26841e13i			0.127221i
$869$	−1.04619e14	−	1.81206e14i	−0.211112	−	0.365657i
$870$	−1.78678e14	+	3.09480e14i	−0.358488	+	0.620920i
$871$	4.77609e14			0.952755
$872$	−2.59069e14	−	1.49574e14i	−0.513846	−	0.296669i
$873$	−3.78390e13	−	6.55390e13i	−0.0746222	−	0.129249i
$874$	−3.02355e14	−	5.23695e14i	−0.592871	−	1.02688i
$875$	7.62338e13	+	1.32041e14i	0.148630	+	0.257435i
$876$	9.77381e13			0.189471
$877$	−1.62842e14	−	2.82051e14i	−0.313884	−	0.543663i	0.665316	−	0.746562i	$-0.268297\pi$
$877$	−1.62842e14	−	2.82051e14i	−0.313884	−	0.543663i	−0.979200	+	0.202899i	$0.934964\pi$
$878$	3.09468e14	−	1.78672e14i	0.593121	−	0.342439i
$879$	−6.07864e14	−	3.50951e14i	−1.15841	−	0.668808i
$880$	2.39783e14	+	1.38439e14i	0.454364	+	0.262327i
$881$	5.87171e14			1.10633			0.553165	−	0.833071i	$-0.313420\pi$
$881$	5.87171e14			1.10633			0.553165	+	0.833071i	$0.313420\pi$
$882$			7.64088e13i			0.143153i
$883$	−4.28223e14	+	7.41704e14i	−0.797749	+	1.38174i	0.123330	+	0.992366i	$0.460643\pi$
$883$	−4.28223e14	+	7.41704e14i	−0.797749	+	1.38174i	−0.921079	+	0.389376i	$0.872691\pi$
$884$	−8.64462e12	+	1.49729e13i	−0.0160134	+	0.0277361i
$885$	3.85401e14	+	6.67535e14i	0.709900	+	1.22958i
$886$	−8.56154e13	+	4.94301e13i	−0.156813	+	0.0905363i
$887$		−	3.01348e14i		−	0.548845i	−0.961609	−	0.274423i	$-0.911513\pi$
$887$		−	3.01348e14i		−	0.548845i	0.961609	−	0.274423i	$-0.0884867\pi$
$888$	4.22439e14	−	2.43895e14i	0.765066	−	0.441711i
$889$	−6.28266e14	+	3.62730e14i	−1.13145	+	0.653242i
$890$	2.22517e14	−	1.28470e14i	0.398486	−	0.230066i
$891$	−1.38543e14	+	2.39964e14i	−0.246715	+	0.427324i
$892$			3.82142e14i			0.676707i
$893$	5.73537e14	+	3.31132e14i	1.00996	+	0.583100i
$894$	−2.23877e14	+	1.29255e14i	−0.392032	+	0.226340i
$895$	5.88745e14			1.02521
$896$	1.49616e13	+	2.59142e13i	0.0259082	+	0.0448743i
$897$	−3.37521e14	−	1.94868e14i	−0.581218	−	0.335566i
$898$	2.35470e14	−	4.07846e14i	0.403231	−	0.698417i
$899$		−	2.50031e14i		−	0.425789i
$900$	2.50326e13	−	4.33578e13i	0.0423930	−	0.0734268i
$901$	4.36605e13			0.0735301
$902$			1.25715e14i			0.210549i
$903$	1.54173e14	−	2.90487e14i	0.256785	−	0.483824i
$904$	−1.12701e15			−1.86675
$905$		−	5.01296e14i		−	0.825756i
$906$	−2.46649e14	−	1.42403e14i	−0.404054	−	0.233281i
$907$	1.59624e14			0.260053			0.130027	−	0.991510i	$-0.458494\pi$
$907$	1.59624e14			0.260053			0.130027	+	0.991510i	$0.458494\pi$
$908$	−8.63962e13	−	4.98809e13i	−0.139980	−	0.0808174i
$909$	2.65058e13	−	4.59094e13i	0.0427092	−	0.0739746i
$910$	2.47538e14	−	1.42916e14i	0.396675	−	0.229020i
$911$		−	8.37742e14i		−	1.33511i	−0.744559	−	0.667557i	$-0.767340\pi$
$911$		−	8.37742e14i		−	1.33511i	0.744559	−	0.667557i	$-0.232660\pi$
$912$	−1.48618e14	−	2.57414e14i	−0.235558	−	0.407998i
$913$	−4.82053e14	+	8.34941e14i	−0.759874	+	1.31614i
$914$	−2.13516e14			−0.334734
$915$	−6.61658e14	−	3.82008e14i	−1.03164	−	0.595617i
$916$	−6.14533e13	−	1.06440e14i	−0.0952946	−	0.165055i
$917$	2.25662e14	+	3.90859e14i	0.348027	+	0.602800i
$918$	3.36492e13	+	5.82822e13i	0.0516133	+	0.0893969i
$919$	1.25200e15			1.90997			0.954984	−	0.296657i	$-0.0958718\pi$
$919$	1.25200e15			1.90997			0.954984	+	0.296657i	$0.0958718\pi$
$920$	−5.56919e14	−	9.64612e14i	−0.844993	−	1.46357i
$921$	6.53699e14	−	3.77413e14i	0.986460	−	0.569533i
$922$	−2.99181e13	−	1.72732e13i	−0.0449033	−	0.0259250i
$923$	2.25306e14	+	1.30081e14i	0.336330	+	0.194180i
$924$	1.27160e14			0.188796
$925$		−	4.42095e14i		−	0.652840i
$926$	−1.33687e14	+	2.31553e14i	−0.196352	+	0.340091i
$927$	4.19524e13	−	7.26637e13i	0.0612855	−	0.106150i
$928$	2.18037e14	+	3.77650e14i	0.316803	+	0.548719i
$929$	−1.08512e15	+	6.26492e14i	−1.56818	+	0.905392i	−0.571804	+	0.820390i	$0.693756\pi$
$929$	−1.08512e15	+	6.26492e14i	−1.56818	+	0.905392i	−0.996381	+	0.0850018i	$0.972910\pi$
$930$			2.78941e14i			0.400957i
$931$	−4.17989e14	+	2.41326e14i	−0.597608	+	0.345029i
$932$	4.58310e14	−	2.64605e14i	0.651748	−	0.376287i
$933$	−4.66774e14	+	2.69492e14i	−0.660235	+	0.381187i
$934$	5.33103e14	−	9.23361e14i	0.750027	−	1.29908i
$935$		−	9.88537e13i		−	0.138336i
$936$	1.52627e14	+	8.81190e13i	0.212447	+	0.122656i
$937$	4.11790e14	−	2.37747e14i	0.570136	−	0.329168i	−0.187068	−	0.982347i	$-0.559898\pi$
$937$	4.11790e14	−	2.37747e14i	0.570136	−	0.329168i	0.757203	+	0.653179i	$0.226565\pi$
$938$	−5.34005e14			−0.735413
$939$	1.97810e13	+	3.42618e13i	0.0270970	+	0.0469334i
$940$	2.95760e14	+	1.70757e14i	0.402996	+	0.232670i
$941$	−1.68444e12	+	2.91754e12i	−0.00228301	+	0.00395430i	−0.867165	−	0.498022i	$-0.834060\pi$
$941$	−1.68444e12	+	2.91754e12i	−0.00228301	+	0.00395430i	0.864882	+	0.501976i	$0.167393\pi$
$942$			2.02593e14i			0.273130i
$943$	1.37035e14	−	2.37351e14i	0.183769	−	0.318297i
$944$	−4.65823e14			−0.621385
$945$			7.07821e14i			0.939214i
$946$	4.63780e14	+	2.46147e14i	0.612148	+	0.324892i
$947$	−4.13792e14			−0.543291			−0.271645	−	0.962397i	$-0.587568\pi$
$947$	−4.13792e14			−0.543291			−0.271645	+	0.962397i	$0.587568\pi$
$948$			1.15834e14i			0.151284i
$949$	2.70047e14	+	1.55912e14i	0.350840	+	0.202557i
$950$	−4.97101e14			−0.642431
$951$	7.79010e13	+	4.49762e13i	0.100148	+	0.0578202i
$952$	3.45235e13	−	5.97965e13i	0.0441500	−	0.0764700i
$953$	−4.68133e14	+	2.70277e14i	−0.595531	+	0.343830i	−0.767282	−	0.641310i	$-0.778391\pi$
$953$	−4.68133e14	+	2.70277e14i	−0.595531	+	0.343830i	0.171750	+	0.985141i	$0.445058\pi$
$954$		−	1.24600e14i		−	0.157679i
$955$	−4.65502e14	−	8.06273e14i	−0.586009	−	1.01500i
$956$	5.00716e13	−	8.67266e13i	0.0627050	−	0.108608i
$957$	−5.07209e14			−0.631870
$958$	7.11978e14	+	4.11061e14i	0.882347	+	0.509423i
$959$	1.97685e14	+	3.42401e14i	0.243715	+	0.422126i
$960$	−4.40354e14	−	7.62715e14i	−0.540064	−	0.935419i
$961$	3.12231e14	+	5.40800e14i	0.380942	+	0.659812i
$962$	4.35695e14			0.528819
$963$	6.14423e13	+	1.06421e14i	0.0741884	+	0.128498i
$964$	−1.86483e14	+	1.07666e14i	−0.224003	+	0.129328i
$965$	−8.47202e14	−	4.89133e14i	−1.01240	−	0.584507i
$966$	3.77376e14	+	2.17878e14i	0.448631	+	0.259017i
$967$	−3.16323e14			−0.374109			−0.187054	−	0.982350i	$-0.559894\pi$
$967$	−3.16323e14			−0.374109			−0.187054	+	0.982350i	$0.559894\pi$
$968$		−	1.97640e14i		−	0.232540i
$969$	−5.30613e13	+	9.19049e13i	−0.0621096	+	0.107577i
$970$	−1.93743e14	+	3.35573e14i	−0.225615	+	0.390776i
$971$	−2.45178e14	−	4.24661e14i	−0.284044	−	0.491979i	0.688333	−	0.725395i	$-0.258343\pi$
$971$	−2.45178e14	−	4.24661e14i	−0.284044	−	0.491979i	−0.972377	+	0.233416i	$0.925010\pi$
$972$	−1.85214e14	+	1.06933e14i	−0.213473	+	0.123249i
$973$			4.02960e14i			0.462059i
$974$	−1.00222e15	+	5.78632e14i	−1.14332	+	0.660097i
$975$	−2.77459e14	+	1.60191e14i	−0.314902	+	0.181809i
$976$	3.99863e14	−	2.30861e14i	0.451504	−	0.260676i
$977$	6.81105e14	−	1.17971e15i	0.765141	−	1.32526i	−0.175031	−	0.984563i	$-0.556003\pi$
$977$	6.81105e14	−	1.17971e15i	0.765141	−	1.32526i	0.940172	−	0.340700i	$-0.110664\pi$
$978$			6.57789e14i			0.735178i
$979$	3.15827e14	+	1.82343e14i	0.351184	+	0.202756i
$980$	−2.15548e14	+	1.24447e14i	−0.238459	+	0.137674i
$981$	1.65180e14			0.181808
$982$	−3.15965e13	−	5.47268e13i	−0.0346004	−	0.0599297i
$983$	2.03892e14	+	1.17717e14i	0.222143	+	0.128254i	0.606942	−	0.794746i	$-0.292396\pi$
$983$	2.03892e14	+	1.17717e14i	0.222143	+	0.128254i	−0.384799	+	0.923000i	$0.625729\pi$
$984$	1.24293e14	−	2.15281e14i	0.134732	−	0.233362i
$985$			1.37541e15i			1.48337i
$986$	−3.85527e13	+	6.67752e13i	−0.0413685	+	0.0716524i
$987$	−4.77229e14			−0.509497
$988$			3.11670e14i			0.331062i
$989$	−6.07311e14	−	9.70270e14i	−0.641845	−	1.02544i
$990$	−2.82111e14			−0.296650
$991$		−	2.79658e14i		−	0.292590i	−0.989241	−	0.146295i	$-0.953265\pi$
$991$		−	2.79658e14i		−	0.292590i	0.989241	−	0.146295i	$-0.0467348\pi$
$992$	2.94782e14	+	1.70192e14i	0.306862	+	0.177167i
$993$	−1.36729e15			−1.41617
$994$	−2.51911e14	−	1.45441e14i	−0.259606	−	0.149884i
$995$	−1.14384e15	+	1.98119e15i	−1.17287	+	2.03147i
$996$	4.62221e14	−	2.66863e14i	0.471577	−	0.272265i
$997$			4.28901e14i			0.435393i	0.976017	+	0.217696i	$0.0698542\pi$
$997$			4.28901e14i			0.435393i	−0.976017	+	0.217696i	$0.930146\pi$
$998$	−4.86363e13	−	8.42405e13i	−0.0491256	−	0.0850880i
$999$	−5.39467e14	+	9.34384e14i	−0.542172	+	0.939070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.37.25	yes	72
43.7	odd	6	inner	43.11.d.a.7.12	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.12	✓	72	43.7	odd	6	inner
43.11.d.a.37.25	yes	72	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+25.0169i q^{2} +(171.910 + 99.2521i) q^{3} +398.154 q^{4} +(3482.07 + 2010.37i) q^{5} +(-2482.98 + 4300.65i) q^{6} +(-9759.68 + 5634.76i) q^{7} +35577.9i q^{8} +(-9822.54 - 17013.1i) q^{9} +O(q^{10})\)	\(q+25.0169i q^{2} +(171.910 + 99.2521i) q^{3} +398.154 q^{4} +(3482.07 + 2010.37i) q^{5} +(-2482.98 + 4300.65i) q^{6} +(-9759.68 + 5634.76i) q^{7} +35577.9i q^{8} +(-9822.54 - 17013.1i) q^{9} +(-50293.3 + 87110.6i) q^{10} -142767. q^{11} +(68446.5 + 39517.6i) q^{12} +(126077. + 218372. i) q^{13} +(-140964. - 244157. i) q^{14} +(399068. + 691205. i) q^{15} -482341. q^{16} +(86105.3 + 149139. i) q^{17} +(425616. - 245730. i) q^{18} +(2.68849e6 + 1.55220e6i) q^{19} +(1.38640e6 + 800437. i) q^{20} -2.23705e6 q^{21} -3.57158e6i q^{22} +(-3.89319e6 + 6.74320e6i) q^{23} +(-3.53118e6 + 6.11619e6i) q^{24} +(3.20039e6 + 5.54323e6i) q^{25} +(-5.46299e6 + 3.15406e6i) q^{26} -1.56211e7i q^{27} +(-3.88585e6 + 2.24350e6i) q^{28} +(1.54996e7 - 8.94872e6i) q^{29} +(-1.72918e7 + 9.98344e6i) q^{30} +(6.98509e6 - 1.20985e7i) q^{31} +2.43651e7i q^{32} +(-2.45430e7 - 1.41699e7i) q^{33} +(-3.73099e6 + 2.15409e6i) q^{34} -4.53118e7 q^{35} +(-3.91088e6 - 6.77384e6i) q^{36} +(-5.98155e7 - 3.45345e7i) q^{37} +(-3.88313e7 + 6.72579e7i) q^{38} +5.00536e7i q^{39} +(-7.15249e7 + 1.23885e8i) q^{40} -3.51986e7 q^{41} -5.59640e7i q^{42} +(-6.89182e7 + 1.29853e8i) q^{43} -5.68430e7 q^{44} -7.89878e7i q^{45} +(-1.68694e8 - 9.73955e7i) q^{46} +2.13330e8 q^{47} +(-8.29190e7 - 4.78733e7i) q^{48} +(-7.77367e7 + 1.34644e8i) q^{49} +(-1.38675e8 + 8.00638e7i) q^{50} +3.41845e7i q^{51} +(5.01980e7 + 8.69454e7i) q^{52} +(1.26765e8 - 2.19563e8i) q^{53} +3.90792e8 q^{54} +(-4.97123e8 - 2.87014e8i) q^{55} +(-2.00473e8 - 3.47229e8i) q^{56} +(3.08119e8 + 5.33677e8i) q^{57} +(2.23870e8 + 3.87753e8i) q^{58} +9.65755e8 q^{59} +(1.58890e8 + 2.75206e8i) q^{60} +(-8.29005e8 + 4.78626e8i) q^{61} +(3.02668e8 + 1.74745e8i) q^{62} +(1.91730e8 + 1.10695e8i) q^{63} -1.10346e9 q^{64} +1.01385e9i q^{65} +(3.54487e8 - 6.13989e8i) q^{66} +(9.47058e8 - 1.64035e9i) q^{67} +(3.42831e7 + 5.93801e7i) q^{68} +(-1.33855e9 + 7.72814e8i) q^{69} -1.13356e9i q^{70} +(8.93528e8 - 5.15879e8i) q^{71} +(6.05292e8 - 3.49465e8i) q^{72} +(1.07096e9 - 6.18320e8i) q^{73} +(8.63947e8 - 1.49640e9i) q^{74} +1.27058e9i q^{75} +(1.07043e9 + 6.18015e8i) q^{76} +(1.39336e9 - 8.04455e8i) q^{77} -1.25219e9 q^{78} +(7.32800e8 + 1.26925e9i) q^{79} +(-1.67954e9 - 9.69684e8i) q^{80} +(9.70417e8 - 1.68081e9i) q^{81} -8.80561e8i q^{82} +(3.37652e9 - 5.84830e9i) q^{83} -8.90688e8 q^{84} +6.92415e8i q^{85} +(-3.24852e9 - 1.72412e9i) q^{86} +3.55272e9 q^{87} -5.07934e9i q^{88} +(-2.21219e9 - 1.27721e9i) q^{89} +1.97603e9 q^{90} +(-2.46094e9 - 1.42082e9i) q^{91} +(-1.55009e9 + 2.68483e9i) q^{92} +(2.40161e9 - 1.38657e9i) q^{93} +5.33686e9i q^{94} +(6.24101e9 + 1.08098e10i) q^{95} +(-2.41829e9 + 4.18860e9i) q^{96} +3.85226e9 q^{97} +(-3.36838e9 - 1.94473e9i) q^{98} +(1.40233e9 + 2.42891e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9}+O(q^{10}) \) 72 * q - 246 * q^3 - 38122 * q^4 - 3 * q^5 + 8511 * q^6 + 31377 * q^7 + 675876 * q^9	\( 72 q - 246 q^{3} - 38122 q^{4} - 3 q^{5} + 8511 q^{6} + 31377 q^{7} + 675876 q^{9} - 127061 q^{10} + 521524 q^{11} - 606618 q^{12} + 796742 q^{13} - 865794 q^{14} - 433513 q^{15} + 22423366 q^{16} - 1768471 q^{17} - 11957547 q^{18} - 122844 q^{19} + 419841 q^{20} - 26778860 q^{21} + 16414886 q^{23} + 8684578 q^{24} + 70516989 q^{25} + 3069 q^{26} - 97624092 q^{28} + 118701393 q^{29} - 1455921 q^{30} + 10824883 q^{31} + 315141798 q^{33} + 47529561 q^{34} - 333788722 q^{35} - 597728908 q^{36} - 169881246 q^{37} - 88887452 q^{38} + 570788831 q^{40} - 543049070 q^{41} + 408159179 q^{43} - 754130886 q^{44} + 270181896 q^{46} + 348527658 q^{47} + 175039227 q^{48} + 781091547 q^{49} - 663244398 q^{50} - 1853993086 q^{52} + 219922736 q^{53} + 3104867360 q^{54} + 2154394182 q^{55} + 2010912675 q^{56} + 349107351 q^{57} + 2023447828 q^{58} + 2247595680 q^{59} - 2906780465 q^{60} + 508093974 q^{61} - 3451752063 q^{62} + 158921973 q^{63} - 13473879716 q^{64} + 1277847051 q^{66} - 2812410281 q^{67} + 13614613118 q^{68} - 5113655829 q^{69} + 2418191196 q^{71} + 26243329290 q^{72} - 6537901611 q^{73} - 2632816966 q^{74} - 10170994206 q^{76} - 16936463889 q^{77} - 24146069696 q^{78} + 5397136602 q^{79} + 7242149661 q^{80} - 15745886176 q^{81} + 4998656042 q^{83} + 44726677232 q^{84} - 27688564866 q^{86} + 37895576172 q^{87} - 12151857357 q^{89} - 96024912764 q^{90} + 36633770214 q^{91} - 31643971023 q^{92} + 59768940153 q^{93} - 19802964089 q^{95} - 3289705262 q^{96} - 40329658574 q^{97} + 19243888221 q^{98} + 18506221111 q^{99}+O(q^{100}) \) 72 * q - 246 * q^3 - 38122 * q^4 - 3 * q^5 + 8511 * q^6 + 31377 * q^7 + 675876 * q^9 - 127061 * q^10 + 521524 * q^11 - 606618 * q^12 + 796742 * q^13 - 865794 * q^14 - 433513 * q^15 + 22423366 * q^16 - 1768471 * q^17 - 11957547 * q^18 - 122844 * q^19 + 419841 * q^20 - 26778860 * q^21 + 16414886 * q^23 + 8684578 * q^24 + 70516989 * q^25 + 3069 * q^26 - 97624092 * q^28 + 118701393 * q^29 - 1455921 * q^30 + 10824883 * q^31 + 315141798 * q^33 + 47529561 * q^34 - 333788722 * q^35 - 597728908 * q^36 - 169881246 * q^37 - 88887452 * q^38 + 570788831 * q^40 - 543049070 * q^41 + 408159179 * q^43 - 754130886 * q^44 + 270181896 * q^46 + 348527658 * q^47 + 175039227 * q^48 + 781091547 * q^49 - 663244398 * q^50 - 1853993086 * q^52 + 219922736 * q^53 + 3104867360 * q^54 + 2154394182 * q^55 + 2010912675 * q^56 + 349107351 * q^57 + 2023447828 * q^58 + 2247595680 * q^59 - 2906780465 * q^60 + 508093974 * q^61 - 3451752063 * q^62 + 158921973 * q^63 - 13473879716 * q^64 + 1277847051 * q^66 - 2812410281 * q^67 + 13614613118 * q^68 - 5113655829 * q^69 + 2418191196 * q^71 + 26243329290 * q^72 - 6537901611 * q^73 - 2632816966 * q^74 - 10170994206 * q^76 - 16936463889 * q^77 - 24146069696 * q^78 + 5397136602 * q^79 + 7242149661 * q^80 - 15745886176 * q^81 + 4998656042 * q^83 + 44726677232 * q^84 - 27688564866 * q^86 + 37895576172 * q^87 - 12151857357 * q^89 - 96024912764 * q^90 + 36633770214 * q^91 - 31643971023 * q^92 + 59768940153 * q^93 - 19802964089 * q^95 - 3289705262 * q^96 - 40329658574 * q^97 + 19243888221 * q^98 + 18506221111 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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