LMFDB - Embedded newform 43.11.d.a.37.19

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			37.19
Character	$\chi$	$=$	43.37
Dual form			43.11.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)

$f(q)$	$=$	$q+0.266107i q^{2} +(-177.112 - 102.255i) q^{3} +1023.93 q^{4} +(-1112.32 - 642.200i) q^{5} +(27.2109 - 47.1306i) q^{6} +(-3824.38 + 2208.01i) q^{7} +544.968i q^{8} +(-8612.15 - 14916.7i) q^{9} +O(q^{10})$	\(q+0.266107i q^{2} +(-177.112 - 102.255i) q^{3} +1023.93 q^{4} +(-1112.32 - 642.200i) q^{5} +(27.2109 - 47.1306i) q^{6} +(-3824.38 + 2208.01i) q^{7} +544.968i q^{8} +(-8612.15 - 14916.7i) q^{9} +(170.894 - 295.997i) q^{10} +14253.7 q^{11} +(-181350. - 104702. i) q^{12} +(3665.36 + 6348.59i) q^{13} +(-587.566 - 1017.69i) q^{14} +(131337. + 227482. i) q^{15} +1.04836e6 q^{16} +(-920395. - 1.59417e6i) q^{17} +(3969.43 - 2291.75i) q^{18} +(1.53898e6 + 888533. i) q^{19} +(-1.13894e6 - 657567. i) q^{20} +903123. q^{21} +3793.01i q^{22} +(-4.35030e6 + 7.53494e6i) q^{23} +(55725.9 - 96520.1i) q^{24} +(-4.05797e6 - 7.02861e6i) q^{25} +(-1689.40 + 975.377i) q^{26} +1.55987e7i q^{27} +(-3.91590e6 + 2.26084e6i) q^{28} +(-2.56868e7 + 1.48303e7i) q^{29} +(-60534.5 + 34949.6i) q^{30} +(-1.70168e7 + 2.94739e7i) q^{31} +837022. i q^{32} +(-2.52450e6 - 1.45752e6i) q^{33} +(424219. - 244923. i) q^{34} +5.67193e6 q^{35} +(-8.81823e6 - 1.52736e7i) q^{36} +(-5.50278e7 - 3.17703e7i) q^{37} +(-236445. + 409534. i) q^{38} -1.49921e6i q^{39} +(349978. - 606180. i) q^{40} +3.59255e7 q^{41} +240327. i q^{42} +(-7.80094e7 + 1.24603e8i) q^{43} +1.45948e7 q^{44} +2.21229e7i q^{45} +(-2.00510e6 - 1.15764e6i) q^{46} -1.70031e8 q^{47} +(-1.85676e8 - 1.07200e8i) q^{48} +(-1.31487e8 + 2.27742e8i) q^{49} +(1.87036e6 - 1.07985e6i) q^{50} +3.76461e8i q^{51} +(3.75307e6 + 6.50050e6i) q^{52} +(-2.99025e8 + 5.17926e8i) q^{53} -4.15092e6 q^{54} +(-1.58547e7 - 9.15374e6i) q^{55} +(-1.20329e6 - 2.08416e6i) q^{56} +(-1.81715e8 - 3.14739e8i) q^{57} +(-3.94644e6 - 6.83543e6i) q^{58} -5.02875e8 q^{59} +(1.34480e8 + 2.32926e8i) q^{60} +(1.11055e9 - 6.41176e8i) q^{61} +(-7.84321e6 - 4.52828e6i) q^{62} +(6.58723e7 + 3.80314e7i) q^{63} +1.07330e9 q^{64} -9.41557e6i q^{65} +(387856. - 671787. i) q^{66} +(8.47364e8 - 1.46768e9i) q^{67} +(-9.42419e8 - 1.63232e9i) q^{68} +(1.54098e9 - 8.89684e8i) q^{69} +1.50934e6i q^{70} +(1.93037e9 - 1.11450e9i) q^{71} +(8.12911e6 - 4.69334e6i) q^{72} +(-1.99850e9 + 1.15383e9i) q^{73} +(8.45430e6 - 1.46433e7i) q^{74} +1.65980e9i q^{75} +(1.57581e9 + 9.09795e8i) q^{76} +(-5.45117e7 + 3.14723e7i) q^{77} +398950. q^{78} +(-3.14722e8 - 5.45115e8i) q^{79} +(-1.16611e9 - 6.73256e8i) q^{80} +(1.08652e9 - 1.88190e9i) q^{81} +9.56003e6i q^{82} +(4.84483e8 - 8.39150e8i) q^{83} +9.24734e8 q^{84} +2.36431e9i q^{85} +(-3.31578e7 - 2.07588e7i) q^{86} +6.06591e9 q^{87} +7.76782e6i q^{88} +(-5.24422e9 - 3.02775e9i) q^{89} -5.88705e6 q^{90} +(-2.80355e7 - 1.61863e7i) q^{91} +(-4.45440e9 + 7.71525e9i) q^{92} +(6.02774e9 - 3.48012e9i) q^{93} -4.52465e7i q^{94} +(-1.14123e9 - 1.97667e9i) q^{95} +(8.55901e7 - 1.48246e8i) q^{96} +9.46864e9 q^{97} +(-6.06037e7 - 3.49896e7i) q^{98} +(-1.22755e8 - 2.12618e8i) 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 $

$2$			0.266107i			0.00831584i	0.999991	+	0.00415792i	$0.00132351\pi$
$2$			0.266107i			0.00831584i	−0.999991	+	0.00415792i	$0.998676\pi$
$3$	−177.112	−	102.255i	−0.728854	−	0.420804i	0.0891485	−	0.996018i	$-0.471585\pi$
$3$	−177.112	−	102.255i	−0.728854	−	0.420804i	−0.818003	+	0.575214i	$0.804919\pi$
$4$	1023.93			0.999931
$5$	−1112.32	−	642.200i	−0.355943	−	0.205504i	0.311356	−	0.950293i	$-0.399217\pi$
$5$	−1112.32	−	642.200i	−0.355943	−	0.205504i	−0.667300	+	0.744789i	$0.732550\pi$
$6$	27.2109	−	47.1306i	0.00349934	−	0.00606103i
$7$	−3824.38	+	2208.01i	−0.227547	+	0.131374i	−0.609440	−	0.792832i	$-0.708606\pi$
$7$	−3824.38	+	2208.01i	−0.227547	+	0.131374i	0.381893	+	0.924207i	$0.375272\pi$
$8$			544.968i			0.0166311i
$9$	−8612.15	−	14916.7i	−0.145848	−	0.252615i
$10$	170.894	−	295.997i	0.00170894	−	0.00295997i
$11$	14253.7			0.0885044			0.0442522	−	0.999020i	$-0.485909\pi$
$11$	14253.7			0.0885044			0.0442522	+	0.999020i	$0.485909\pi$
$12$	−181350.	−	104702.i	−0.728804	−	0.420775i
$13$	3665.36	+	6348.59i	0.00987188	+	0.0170986i	0.870919	−	0.491426i	$-0.163524\pi$
$13$	3665.36	+	6348.59i	0.00987188	+	0.0170986i	−0.861047	+	0.508525i	$0.830191\pi$
$14$	−587.566	−	1017.69i	−0.00109249	−	0.00189224i
$15$	131337.	+	227482.i	0.172954	+	0.299565i
$16$	1.04836e6			0.999793
$17$	−920395.	−	1.59417e6i	−0.648230	−	1.12277i	−0.983545	−	0.180662i	$-0.942176\pi$
$17$	−920395.	−	1.59417e6i	−0.648230	−	1.12277i	0.335315	−	0.942106i	$-0.391157\pi$
$18$	3969.43	−	2291.75i	0.00210071	−	0.00121284i
$19$	1.53898e6	+	888533.i	0.621536	+	0.358844i	0.777467	−	0.628924i	$-0.216504\pi$
$19$	1.53898e6	+	888533.i	0.621536	+	0.358844i	−0.155931	+	0.987768i	$0.549838\pi$
$20$	−1.13894e6	−	657567.i	−0.355919	−	0.205490i
$21$	903123.			0.221131
$22$			3793.01i			0.000735988i
$23$	−4.35030e6	+	7.53494e6i	−0.675896	+	1.17069i	0.300310	+	0.953842i	$0.402910\pi$
$23$	−4.35030e6	+	7.53494e6i	−0.675896	+	1.17069i	−0.976206	+	0.216845i	$0.930423\pi$
$24$	55725.9	−	96520.1i	0.00699844	−	0.0121216i
$25$	−4.05797e6	−	7.02861e6i	−0.415536	−	0.719730i
$26$	−1689.40	+	975.377i	−0.000142189	+	8.20929e-5i
$27$			1.55987e7i			1.08710i
$28$	−3.91590e6	+	2.26084e6i	−0.227531	+	0.131365i
$29$	−2.56868e7	+	1.48303e7i	−1.25233	+	0.723035i	−0.971572	−	0.236742i	$-0.923920\pi$
$29$	−2.56868e7	+	1.48303e7i	−1.25233	+	0.723035i	−0.280761	+	0.959778i	$0.590587\pi$
$30$	−60534.5	+	34949.6i	−0.00249113	+	0.00143826i
$31$	−1.70168e7	+	2.94739e7i	−0.594387	+	1.02951i	0.399247	+	0.916844i	$0.369272\pi$
$31$	−1.70168e7	+	2.94739e7i	−0.594387	+	1.02951i	−0.993633	+	0.112664i	$0.964062\pi$
$32$			837022.i			0.0249452i
$33$	−2.52450e6	−	1.45752e6i	−0.0645068	−	0.0372430i
$34$	424219.	−	244923.i	0.00933676	−	0.00539058i
$35$	5.67193e6			0.107992
$36$	−8.81823e6	−	1.52736e7i	−0.145837	−	0.252598i
$37$	−5.50278e7	−	3.17703e7i	−0.793549	−	0.458156i	0.0476616	−	0.998864i	$-0.484823\pi$
$37$	−5.50278e7	−	3.17703e7i	−0.793549	−	0.458156i	−0.841210	+	0.540708i	$0.818156\pi$
$38$	−236445.	+	409534.i	−0.00298409	+	0.00516859i
$39$		−	1.49921e6i		−	0.0166165i
$40$	349978.	−	606180.i	0.00341776	−	0.00591973i
$41$	3.59255e7			0.310087			0.155044	−	0.987908i	$-0.450448\pi$
$41$	3.59255e7			0.310087			0.155044	+	0.987908i	$0.450448\pi$
$42$			240327.i			0.00183889i
$43$	−7.80094e7	+	1.24603e8i	−0.530646	+	0.847594i
$43$	−7.80094e7	+	1.24603e8i	−0.530646	+	0.847594i
$44$	1.45948e7			0.0884983
$45$			2.21229e7i			0.119889i
$46$	−2.00510e6	−	1.15764e6i	−0.00973524	−	0.00562064i
$47$	−1.70031e8			−0.741378			−0.370689	−	0.928757i	$-0.620878\pi$
$47$	−1.70031e8			−0.741378			−0.370689	+	0.928757i	$0.620878\pi$
$48$	−1.85676e8	−	1.07200e8i	−0.728703	−	0.420717i
$49$	−1.31487e8	+	2.27742e8i	−0.465482	+	0.806238i
$50$	1.87036e6	−	1.07985e6i	0.00598516	−	0.00345553i
$51$			3.76461e8i			1.09111i
$52$	3.75307e6	+	6.50050e6i	0.00987119	+	0.0170974i
$53$	−2.99025e8	+	5.17926e8i	−0.715036	+	1.23848i	0.247910	+	0.968783i	$0.420256\pi$
$53$	−2.99025e8	+	5.17926e8i	−0.715036	+	1.23848i	−0.962946	+	0.269695i	$0.913077\pi$
$54$	−4.15092e6			−0.00904016
$55$	−1.58547e7	−	9.15374e6i	−0.0315026	−	0.0181880i
$56$	−1.20329e6	−	2.08416e6i	−0.00218490	−	0.00378436i
$57$	−1.81715e8	−	3.14739e8i	−0.302006	−	0.523090i
$58$	−3.94644e6	−	6.83543e6i	−0.00601264	−	0.0104142i
$59$	−5.02875e8			−0.703396			−0.351698	−	0.936113i	$-0.614396\pi$
$59$	−5.02875e8			−0.703396			−0.351698	+	0.936113i	$0.614396\pi$
$60$	1.34480e8	+	2.32926e8i	0.172942	+	0.299544i
$61$	1.11055e9	−	6.41176e8i	1.31489	−	0.759151i	0.331987	−	0.943284i	$-0.392281\pi$
$61$	1.11055e9	−	6.41176e8i	1.31489	−	0.759151i	0.982901	+	0.184133i	$0.0589476\pi$
$62$	−7.84321e6	−	4.52828e6i	−0.00856122	−	0.00494282i
$63$	6.58723e7	+	3.80314e7i	0.0663743	+	0.0383212i
$64$	1.07330e9			0.999585
$65$		−	9.41557e6i		−	0.00811484i
$66$	387856.	−	671787.i	0.000309707	−	0.000536428i
$67$	8.47364e8	−	1.46768e9i	0.627619	−	1.08707i	−0.360409	−	0.932794i	$-0.617363\pi$
$67$	8.47364e8	−	1.46768e9i	0.627619	−	1.08707i	0.988028	−	0.154274i	$-0.0493037\pi$
$68$	−9.42419e8	−	1.63232e9i	−0.648186	−	1.12269i
$69$	1.54098e9	−	8.89684e8i	0.985260	−	0.568840i
$70$			1.50934e6i			0.000898042i
$71$	1.93037e9	−	1.11450e9i	1.06992	−	0.617716i	0.141758	−	0.989901i	$-0.454725\pi$
$71$	1.93037e9	−	1.11450e9i	1.06992	−	0.617716i	0.928159	+	0.372185i	$0.121391\pi$
$72$	8.12911e6	−	4.69334e6i	0.00420127	−	0.00242560i
$73$	−1.99850e9	+	1.15383e9i	−0.964026	+	0.556581i	−0.897410	−	0.441198i	$-0.854554\pi$
$73$	−1.99850e9	+	1.15383e9i	−0.964026	+	0.556581i	−0.0666165	+	0.997779i	$0.521220\pi$
$74$	8.45430e6	−	1.46433e7i	0.00380995	−	0.00659902i
$75$			1.65980e9i			0.699438i
$76$	1.57581e9	+	9.09795e8i	0.621493	+	0.358819i
$77$	−5.45117e7	+	3.14723e7i	−0.0201389	+	0.0116272i
$78$	398950.			0.000138180
$79$	−3.14722e8	−	5.45115e8i	−0.102280	−	0.177155i	0.810343	−	0.585955i	$-0.199281\pi$
$79$	−3.14722e8	−	5.45115e8i	−0.102280	−	0.177155i	−0.912624	+	0.408800i	$0.865947\pi$
$80$	−1.16611e9	−	6.73256e8i	−0.355870	−	0.205461i
$81$	1.08652e9	−	1.88190e9i	0.311609	−	0.539723i
$82$			9.56003e6i			0.00257864i
$83$	4.84483e8	−	8.39150e8i	0.122995	−	0.213034i	−0.797952	−	0.602721i	$-0.794083\pi$
$83$	4.84483e8	−	8.39150e8i	0.122995	−	0.213034i	0.920948	+	0.389687i	$0.127417\pi$
$84$	9.24734e8			0.221116
$85$			2.36431e9i			0.532856i
$86$	−3.31578e7	−	2.07588e7i	−0.00704845	−	0.00441276i
$87$	6.06591e9			1.21703
$88$			7.76782e6i			0.00147193i
$89$	−5.24422e9	−	3.02775e9i	−0.939141	−	0.542213i	−0.0494502	−	0.998777i	$-0.515747\pi$
$89$	−5.24422e9	−	3.02775e9i	−0.939141	−	0.542213i	−0.889691	+	0.456563i	$0.849080\pi$
$90$	−5.88705e6			−0.000996977
$91$	−2.80355e7	−	1.61863e7i	−0.00449263	−	0.00259382i
$92$	−4.45440e9	+	7.71525e9i	−0.675850	+	1.17061i
$93$	6.02774e9	−	3.48012e9i	0.866443	−	0.500241i
$94$		−	4.52465e7i		−	0.00616518i
$95$	−1.14123e9	−	1.97667e9i	−0.147488	−	0.255456i
$96$	8.55901e7	−	1.48246e8i	0.0104971	−	0.0181814i
$97$	9.46864e9			1.10263			0.551314	−	0.834298i	$-0.314127\pi$
$97$	9.46864e9			1.10263			0.551314	+	0.834298i	$0.314127\pi$
$98$	−6.06037e7	−	3.49896e7i	−0.00670454	−	0.00387087i
$99$	−1.22755e8	−	2.12618e8i	−0.0129081	−	0.0223576i
$100$	−4.15507e9	−	7.19680e9i	−0.415507	−	0.719680i
$101$	−8.47026e8	−	1.46709e9i	−0.0805916	−	0.139589i	0.822913	−	0.568168i	$-0.192348\pi$
$101$	−8.47026e8	−	1.46709e9i	−0.0805916	−	0.139589i	−0.903504	+	0.428579i	$0.859014\pi$
$102$	−1.00179e8			−0.00907351
$103$	5.12615e7	+	8.87875e7i	0.00442186	+	0.00765889i	0.868228	−	0.496166i	$-0.165259\pi$
$103$	5.12615e7	+	8.87875e7i	0.00442186	+	0.00765889i	−0.863806	+	0.503825i	$0.831926\pi$
$104$	−3.45978e6	+	1.99750e6i	−0.000284368	+	0.000164180i
$105$	−1.00456e9	−	5.79986e8i	−0.0787103	−	0.0454434i
$106$	−1.37824e8	−	7.95725e7i	−0.0102990	−	0.00594612i
$107$	−2.20448e10			−1.57176			−0.785882	−	0.618377i	$-0.787790\pi$
$107$	−2.20448e10			−1.57176			−0.785882	+	0.618377i	$0.787790\pi$
$108$			1.59720e10i			1.08703i
$109$	−8.30185e9	+	1.43792e10i	−0.539563	+	0.934551i	0.459364	+	0.888248i	$0.348077\pi$
$109$	−8.30185e9	+	1.43792e10i	−0.539563	+	0.934551i	−0.998927	+	0.0463028i	$0.985256\pi$
$110$	2.43587e6	−	4.21906e6i	0.000151249	−	0.000261970i
$111$	6.49738e9	+	1.12538e10i	0.385588	+	0.667857i
$112$	−4.00932e9	+	2.31478e9i	−0.227500	+	0.131347i
$113$		−	2.41284e10i		−	1.30959i	−0.755806	−	0.654795i	$-0.772755\pi$
$113$		−	2.41284e10i		−	1.30959i	0.755806	−	0.654795i	$-0.227245\pi$
$114$	8.37542e7	−	4.83555e7i	0.00434993	−	0.00251143i
$115$	9.67788e9	−	5.58753e9i	0.481162	−	0.277799i
$116$	−2.63015e10	+	1.51852e10i	−1.25225	+	0.722985i
$117$	6.31332e7	−	1.09350e8i	0.00287958	−	0.00498757i
$118$		−	1.33818e8i		−	0.00584933i
$119$	7.03988e9	+	4.06448e9i	0.295006	+	0.170322i
$120$	−1.23970e8	+	7.15744e7i	−0.00498210	+	0.00287641i
$121$	−2.57343e10			−0.992167
$122$	1.70621e8	+	2.95525e8i	0.00631298	+	0.0109344i
$123$	−6.36283e9	−	3.67358e9i	−0.226009	−	0.130486i
$124$	−1.74240e10	+	3.01792e10i	−0.594346	+	1.02944i
$125$			2.29671e10i			0.752585i
$126$	−1.01204e7	+	1.75291e7i	−0.000318673	+	0.000551958i
$127$	6.39937e9			0.193695			0.0968475	−	0.995299i	$-0.469124\pi$
$127$	6.39937e9			0.193695			0.0968475	+	0.995299i	$0.469124\pi$
$128$			1.14272e9i			0.0332576i
$129$	2.65578e10	−	1.40918e10i	0.743435	−	0.394474i
$130$	2.50555e6			6.74817e−5
$131$			6.41907e9i			0.166386i	0.996533	+	0.0831928i	$0.0265117\pi$
$131$			6.41907e9i			0.166386i	−0.996533	+	0.0831928i	$0.973488\pi$
$132$	−2.58491e9	−	1.49240e9i	−0.0645024	−	0.0372405i
$133$	−7.84755e9			−0.188571
$134$	3.90559e8	+	2.25489e8i	0.00903988	+	0.00521918i
$135$	1.00175e10	−	1.73508e10i	0.223404	−	0.386947i
$136$	8.68771e8	−	5.01585e8i	0.0186729	−	0.0107808i
$137$		−	3.23629e10i		−	0.670571i	−0.942117	−	0.335286i	$-0.891167\pi$
$137$		−	3.23629e10i		−	0.670571i	0.942117	−	0.335286i	$-0.108833\pi$
$138$	2.36751e8	+	4.10065e8i	0.00473038	+	0.00819326i
$139$	−1.20210e10	+	2.08210e10i	−0.231668	+	0.401261i	−0.958299	−	0.285767i	$-0.907752\pi$
$139$	−1.20210e10	+	2.08210e10i	−0.231668	+	0.401261i	0.726631	+	0.687028i	$0.241085\pi$
$140$	5.80766e9			0.107984
$141$	3.01145e10	+	1.73866e10i	0.540357	+	0.311975i
$142$	2.96577e8	+	5.13686e8i	0.00513683	+	0.00889725i
$143$	5.22450e7	+	9.04910e7i	0.000873705	+	0.00151330i
$144$	−9.02862e9	−	1.56380e10i	−0.145817	−	0.252563i
$145$	3.80960e10			0.594347
$146$	−3.07043e8	−	5.31813e8i	−0.00462844	−	0.00801669i
$147$	4.65758e10	−	2.68905e10i	0.678537	−	0.391753i
$148$	−5.63446e10	−	3.25306e10i	−0.793494	−	0.458124i
$149$	4.77308e10	+	2.75574e10i	0.649931	+	0.375238i	0.788430	−	0.615125i	$-0.210894\pi$
$149$	4.77308e10	+	2.75574e10i	0.649931	+	0.375238i	−0.138499	+	0.990363i	$0.544228\pi$
$150$	−4.41684e8			−0.00581641
$151$		−	1.09151e11i		−	1.39041i	−0.718813	−	0.695203i	$-0.755314\pi$
$151$		−	1.09151e11i		−	1.39041i	0.718813	−	0.695203i	$-0.244686\pi$
$152$	−4.84222e8	+	8.38697e8i	−0.00596797	+	0.0103368i
$153$	−1.58532e10	+	2.74585e10i	−0.189086	+	0.327506i
$154$	−8.37500e6	−	1.45059e7i	−9.66899e−5	−	0.000167472i
$155$	3.78563e10	−	2.18564e10i	0.423136	−	0.244298i
$156$		−	1.53509e9i		−	0.0166154i
$157$	−5.95956e10	+	3.44075e10i	−0.624763	+	0.360707i	−0.778721	−	0.627370i	$-0.784131\pi$
$157$	−5.95956e10	+	3.44075e10i	−0.624763	+	0.360707i	0.153958	+	0.988077i	$0.450798\pi$
$158$	1.45059e8	−	8.37498e7i	0.00147319	−	0.000850547i
$159$	1.05922e11	−	6.11538e10i	1.04231	−	0.601780i
$160$	5.37536e8	−	9.31039e8i	0.00512634	−	0.00887908i
$161$		−	3.84220e10i		−	0.355182i
$162$	5.00786e8	+	2.89129e8i	0.00448825	+	0.00259129i
$163$	7.73469e10	−	4.46562e10i	0.672210	−	0.388100i	−0.124704	−	0.992194i	$-0.539798\pi$
$163$	7.73469e10	−	4.46562e10i	0.672210	−	0.388100i	0.796913	+	0.604094i	$0.206465\pi$
$164$	3.67852e10			0.310066
$165$	1.87204e9	+	3.24247e9i	0.0153072	+	0.0265128i
$166$	2.23303e8	+	1.28924e8i	0.00177156	+	0.00102281i
$167$	−1.00526e10	+	1.74116e10i	−0.0773921	+	0.134047i	−0.902124	−	0.431477i	$-0.857993\pi$
$167$	−1.00526e10	+	1.74116e10i	−0.0773921	+	0.134047i	0.824732	+	0.565524i	$0.191326\pi$
$168$			4.92173e8i			0.00367766i
$169$	6.89024e10	−	1.19342e11i	0.499805	−	0.865688i
$170$	−6.29159e8			−0.00443114
$171$		−	3.06087e10i		−	0.209346i
$172$	−7.98761e10	+	1.27585e11i	−0.530609	+	0.847535i
$173$	9.74864e10			0.629091			0.314546	−	0.949242i	$-0.398148\pi$
$173$	9.74864e10			0.629091			0.314546	+	0.949242i	$0.398148\pi$
$174$			1.61418e9i			0.0101206i
$175$	3.10385e10	+	1.79201e10i	0.189108	+	0.109182i
$176$	1.49430e10			0.0884860
$177$	8.90650e10	+	5.14217e10i	0.512673	+	0.295992i
$178$	8.05705e8	−	1.39552e9i	0.00450896	−	0.00780975i
$179$	−7.73211e10	+	4.46414e10i	−0.420759	+	0.242925i	−0.695402	−	0.718621i	$-0.744774\pi$
$179$	−7.73211e10	+	4.46414e10i	−0.420759	+	0.242925i	0.274643	+	0.961546i	$0.411440\pi$
$180$			2.26523e10i			0.119881i
$181$	4.37756e10	+	7.58216e10i	0.225341	+	0.390301i	0.956422	−	0.291989i	$-0.0943172\pi$
$181$	4.37756e10	+	7.58216e10i	0.225341	+	0.390301i	−0.731081	+	0.682291i	$0.760984\pi$
$182$	4.30728e6	−	7.46043e6i	2.15698e−5	−	3.73600e-5i
$183$	−2.62255e11			−1.27782
$184$	−4.10630e9	−	2.37077e9i	−0.0194698	−	0.0112409i
$185$	4.08058e10	+	7.06777e10i	0.188306	+	0.326155i
$186$	9.26083e8	+	1.60402e9i	0.00415992	+	0.00720519i
$187$	−1.31191e10	−	2.27229e10i	−0.0573713	−	0.0993699i
$188$	−1.74100e11			−0.741327
$189$	−3.44421e10	−	5.96555e10i	−0.142817	−	0.247367i
$190$	5.26006e8	−	3.03690e8i	0.00212433	−	0.00122648i
$191$	1.29292e11	+	7.46465e10i	0.508632	+	0.293659i	0.732271	−	0.681013i	$-0.238460\pi$
$191$	1.29292e11	+	7.46465e10i	0.508632	+	0.293659i	−0.223639	+	0.974672i	$0.571794\pi$
$192$	−1.90093e11	−	1.09750e11i	−0.728552	−	0.420630i
$193$	1.61486e11			0.603044			0.301522	−	0.953459i	$-0.402505\pi$
$193$	1.61486e11			0.603044			0.301522	+	0.953459i	$0.402505\pi$
$194$			2.51967e9i			0.00916927i
$195$	−9.62794e8	+	1.66761e9i	−0.00341476	+	0.00591454i
$196$	−1.34633e11	+	2.33192e11i	−0.465449	+	0.806182i
$197$	−1.73238e11	−	3.00057e11i	−0.583865	−	1.01128i	−0.995016	−	0.0997164i	$-0.968206\pi$
$197$	−1.73238e11	−	3.00057e11i	−0.583865	−	1.01128i	0.411151	−	0.911567i	$-0.365127\pi$
$198$	5.65792e7	−	3.26660e7i	0.000185922	−	0.000107342i
$199$			4.06486e10i			0.130251i	0.997877	+	0.0651254i	$0.0207448\pi$
$199$			4.06486e10i			0.130251i	−0.997877	+	0.0651254i	$0.979255\pi$
$200$	3.83037e9	−	2.21146e9i	0.0119699	−	0.00691082i
$201$	−3.00156e11	+	1.73295e11i	−0.914886	+	0.528209i
$202$	3.90403e8	−	2.25399e8i	0.00116080	−	0.000670187i
$203$	6.54908e10	−	1.13433e11i	0.189976	−	0.329049i
$204$			3.85470e11i			1.09104i
$205$	−3.99608e10	−	2.30714e10i	−0.110374	−	0.0637242i
$206$	−2.36270e7	+	1.36410e7i	−6.36901e−5	+	3.67715e-5i
$207$	1.49862e11			0.394311
$208$	3.84261e9	+	6.65560e9i	0.00986983	+	0.0170950i
$209$	2.19363e10	+	1.26649e10i	0.0550087	+	0.0317593i
$210$	1.54338e8	−	2.67322e8i	0.000377900	−	0.000654542i
$211$		−	3.39157e11i		−	0.810940i	−0.914108	−	0.405470i	$-0.867108\pi$
$211$		−	3.39157e11i		−	0.810940i	0.914108	−	0.405470i	$-0.132892\pi$
$212$	−3.06180e11	+	5.30320e11i	−0.714986	+	1.23839i
$213$	−4.55856e11			−1.03975
$214$		−	5.86627e9i		−	0.0130705i
$215$	1.66792e11	−	8.85016e10i	0.363064	−	0.192645i
$216$	−8.50080e9			−0.0180797
$217$		−	1.50293e11i		−	0.312348i
$218$	−3.82641e9	−	2.20918e9i	−0.00777157	−	0.00448692i
$219$	4.71942e11			0.936846
$220$	−1.62341e10	−	9.37278e9i	−0.0315004	−	0.0181868i
$221$	6.74715e9	−	1.16864e10i	0.0127985	−	0.0221677i
$222$	−2.99471e9	+	1.72900e9i	−0.00555379	+	0.00320648i
$223$			5.17413e10i			0.0938238i	0.998899	+	0.0469119i	$0.0149380\pi$
$223$			5.17413e10i			0.0938238i	−0.998899	+	0.0469119i	$0.985062\pi$
$224$	−1.84815e9	−	3.20109e9i	−0.00327716	−	0.00567621i
$225$	−6.98957e10	+	1.21063e11i	−0.121210	+	0.209942i
$226$	6.42072e9			0.0108903
$227$	−3.99807e11	−	2.30828e11i	−0.663316	−	0.382966i	0.130223	−	0.991485i	$-0.458431\pi$
$227$	−3.99807e11	−	2.30828e11i	−0.663316	−	0.382966i	−0.793539	+	0.608519i	$0.791764\pi$
$228$	−1.86063e11	−	3.22270e11i	−0.301985	−	0.523054i
$229$	5.96679e11	+	1.03348e12i	0.947465	+	1.64106i	0.750739	+	0.660599i	$0.229698\pi$
$229$	5.96679e11	+	1.03348e12i	0.947465	+	1.64106i	0.196727	+	0.980458i	$0.436969\pi$
$230$	1.48688e9	+	2.57535e9i	0.00231013	+	0.00400126i
$231$	1.28729e10			0.0195711
$232$	−8.08203e9	−	1.39985e10i	−0.0120249	−	0.0208277i
$233$	−6.49516e11	+	3.74998e11i	−0.945824	+	0.546072i	−0.891781	−	0.452467i	$-0.850544\pi$
$233$	−6.49516e11	+	3.74998e11i	−0.945824	+	0.546072i	−0.0540428	+	0.998539i	$0.517211\pi$
$234$	2.90988e7	+	1.68002e7i	4.14759e−5	+	2.39461e-5i
$235$	1.89130e11	+	1.09194e11i	0.263889	+	0.152356i
$236$	−5.14909e11			−0.703348
$237$			1.28728e11i			0.172160i
$238$	−1.08158e9	+	1.87336e9i	−0.00141637	+	0.00245322i
$239$	2.82042e11	−	4.88511e11i	0.361680	−	0.626448i	−0.626558	−	0.779375i	$-0.715537\pi$
$239$	2.82042e11	−	4.88511e11i	0.361680	−	0.626448i	0.988237	+	0.152927i	$0.0488700\pi$
$240$	1.37688e11	+	2.38483e11i	0.172918	+	0.299503i
$241$	−3.56101e11	+	2.05595e11i	−0.438014	+	0.252888i	−0.702755	−	0.711432i	$-0.748047\pi$
$241$	−3.56101e11	+	2.05595e11i	−0.438014	+	0.252888i	0.264741	+	0.964320i	$0.414714\pi$
$242$		−	6.84806e9i		−	0.00825070i
$243$	4.12817e11	−	2.38340e11i	0.487222	−	0.281298i
$244$	1.13712e12	−	6.56519e11i	1.31480	−	0.759099i
$245$	2.92512e11	−	1.68882e11i	0.331370	−	0.191317i
$246$	9.77565e8	−	1.69319e9i	0.00108510	−	0.00187945i
$247$			1.30272e10i			0.0141699i
$248$	−1.60623e10	−	9.27360e9i	−0.0171218	−	0.00988530i
$249$	−1.71615e11	+	9.90821e10i	−0.179291	+	0.103514i
$250$	−6.11170e9			−0.00625838
$251$	−7.23749e11	−	1.25357e12i	−0.726472	−	1.25829i	−0.958365	−	0.285546i	$-0.907825\pi$
$251$	−7.23749e11	−	1.25357e12i	−0.726472	−	1.25829i	0.231893	−	0.972741i	$-0.425508\pi$
$252$	6.74486e10	+	3.89414e10i	0.0663697	+	0.0383186i
$253$	−6.20080e10	+	1.07401e11i	−0.0598198	+	0.103611i
$254$			1.70292e9i			0.00161074i
$255$	2.41764e11	−	4.18747e11i	0.224228	−	0.388374i
$256$	1.09875e12			0.999309
$257$		−	9.16511e10i		−	0.0817470i	−0.999164	−	0.0408735i	$-0.986986\pi$
$257$		−	9.16511e10i		−	0.0817470i	0.999164	−	0.0408735i	$-0.0130141\pi$
$258$	3.74993e9	+	7.06720e9i	0.00328038	+	0.00618228i
$259$	2.80596e11			0.240759
$260$		−	9.64088e9i		−	0.00811428i
$261$	4.42437e11	+	2.55441e11i	0.365300	+	0.210906i
$262$	−1.70816e9			−0.00138364
$263$	−5.28544e11	−	3.05155e11i	−0.420051	−	0.242517i	0.275048	−	0.961430i	$-0.411306\pi$
$263$	−5.28544e11	−	3.05155e11i	−0.420051	−	0.242517i	−0.695099	+	0.718914i	$0.744640\pi$
$264$	7.94302e8	−	1.37577e9i	0.000619393	−	0.00107282i
$265$	6.65224e11	−	3.84067e11i	0.509025	−	0.293886i
$266$		−	2.08829e9i		−	0.00156813i
$267$	6.19208e11	+	1.07250e12i	0.456331	+	0.790389i
$268$	8.67641e11	−	1.50280e12i	0.627576	−	1.08699i
$269$	1.12493e12			0.798662			0.399331	−	0.916807i	$-0.369242\pi$
$269$	1.12493e12			0.798662			0.399331	+	0.916807i	$0.369242\pi$
$270$	4.61717e9	+	2.66572e9i	0.00321779	+	0.00185779i
$271$	−4.34374e11	−	7.52358e11i	−0.297179	−	0.514728i	0.678311	−	0.734775i	$-0.262712\pi$
$271$	−4.34374e11	−	7.52358e11i	−0.297179	−	0.514728i	−0.975489	+	0.220047i	$0.929379\pi$
$272$	−9.64903e11	−	1.67126e12i	−0.648096	−	1.12254i
$273$	3.31027e9	+	5.73356e9i	0.00218298	+	0.00378104i
$274$	8.61199e9			0.00557636
$275$	−5.78412e10	−	1.00184e11i	−0.0367768	−	0.0636993i
$276$	1.57785e12	−	9.10973e11i	0.985192	−	0.568801i
$277$	−3.10457e11	−	1.79242e11i	−0.190371	−	0.109911i	0.401785	−	0.915734i	$-0.368390\pi$
$277$	−3.10457e11	−	1.79242e11i	−0.190371	−	0.109911i	−0.592156	+	0.805823i	$0.701723\pi$
$278$	−5.54060e9	−	3.19887e9i	−0.00333682	−	0.00192651i
$279$	5.86204e11			0.346759
$280$			3.09102e9i			0.00179602i
$281$	−9.47152e11	+	1.64052e12i	−0.540615	+	0.936373i	0.458254	+	0.888822i	$0.348475\pi$
$281$	−9.47152e11	+	1.64052e12i	−0.540615	+	0.936373i	−0.998869	+	0.0475516i	$0.984858\pi$
$282$	−4.62670e9	+	8.01368e9i	−0.00259433	+	0.00449352i
$283$	1.07117e12	+	1.85533e12i	0.590104	+	1.02209i	0.994218	+	0.107381i	$0.0342464\pi$
$283$	1.07117e12	+	1.85533e12i	0.590104	+	1.02209i	−0.404114	+	0.914708i	$0.632420\pi$
$284$	1.97657e12	−	1.14117e12i	1.06984	−	0.617674i
$285$			4.66789e11i			0.248254i
$286$	−2.40803e7	+	1.39028e7i	−1.25844e−5	+	7.26558e-6i
$287$	−1.37393e11	+	7.93239e10i	−0.0705594	+	0.0407375i
$288$	1.24856e10	−	7.20856e9i	0.00630154	−	0.00363820i
$289$	−6.86255e11	+	1.18863e12i	−0.340406	+	0.589600i
$290$			1.01376e10i			0.00494249i
$291$	−1.67701e12	−	9.68220e11i	−0.803655	−	0.463991i
$292$	−2.04632e12	+	1.18144e12i	−0.963960	+	0.556542i
$293$	−3.57938e12			−1.65756			−0.828781	−	0.559573i	$-0.810965\pi$
$293$	−3.57938e12			−1.65756			−0.828781	+	0.559573i	$0.810965\pi$
$294$	7.15575e9	+	1.23941e10i	0.00325776	+	0.00564260i
$295$	5.59360e11	+	3.22946e11i	0.250369	+	0.144551i
$296$	1.73138e10	−	2.99884e10i	0.00761963	−	0.0131976i
$297$			2.22340e11i			0.0962133i
$298$	−7.33320e9	+	1.27015e10i	−0.00312042	+	0.00540472i
$299$	−6.37817e10			−0.0266895
$300$			1.69952e12i			0.699389i
$301$	2.32125e10	−	6.48776e11i	0.00939485	−	0.262581i
$302$	2.90457e10			0.0115624
$303$			3.46452e11i			0.135653i
$304$	1.61341e12	+	9.31501e11i	0.621407	+	0.358769i
$305$	−1.64705e12			−0.624035
$306$	−7.30688e9	−	4.21863e9i	−0.00272349	−	0.00157240i
$307$	−1.41337e12	+	2.44802e12i	−0.518278	+	0.897685i	0.481496	+	0.876448i	$0.340094\pi$
$307$	−1.41337e12	+	2.44802e12i	−0.518278	+	0.897685i	−0.999774	+	0.0212363i	$0.993240\pi$
$308$	−5.58161e10	+	3.22254e10i	−0.0201375	+	0.0116264i
$309$		−	2.09671e10i		−	0.00744295i
$310$	5.81613e9	+	1.00738e10i	0.00203154	+	0.00351873i
$311$	−1.64963e12	+	2.85724e12i	−0.567001	+	0.982074i	0.429860	+	0.902896i	$0.358563\pi$
$311$	−1.64963e12	+	2.85724e12i	−0.567001	+	0.982074i	−0.996860	+	0.0791786i	$0.974770\pi$
$312$	8.17022e8			0.000276351
$313$	−2.99480e11	−	1.72905e11i	−0.0996888	−	0.0575554i	0.449327	−	0.893367i	$-0.351664\pi$
$313$	−2.99480e11	−	1.72905e11i	−0.0996888	−	0.0575554i	−0.549016	+	0.835812i	$0.684997\pi$
$314$	−9.15607e9	−	1.58588e10i	−0.00299958	−	0.00519543i
$315$	−4.88475e10	−	8.46064e10i	−0.0157503	−	0.0272804i
$316$	−3.22253e11	−	5.58159e11i	−0.102273	−	0.177143i
$317$	−5.34909e12			−1.67103			−0.835513	−	0.549471i	$-0.814829\pi$
$317$	−5.34909e12			−1.67103			−0.835513	+	0.549471i	$0.814829\pi$
$318$	1.62734e10	+	2.81864e10i	0.00500431	+	0.00866771i
$319$	−3.66133e11	+	2.11387e11i	−0.110837	+	0.0639918i
$320$	−1.19385e12	−	6.89271e11i	−0.355796	−	0.205419i
$321$	3.90439e12	+	2.25420e12i	1.14559	+	0.661405i
$322$	1.02244e10			0.00295363
$323$		−	3.27120e12i		−	0.930454i
$324$	1.11251e12	−	1.92693e12i	0.311588	−	0.539686i
$325$	2.97478e10	−	5.15248e10i	0.00820424	−	0.0142102i
$326$	1.18833e10	+	2.05825e10i	0.00322738	+	0.00558998i
$327$	2.94071e12	−	1.69782e12i	0.786526	−	0.454101i
$328$			1.95783e10i			0.00515709i
$329$	6.50265e11	−	3.75430e11i	0.168698	−	0.0973980i
$330$	−8.62843e8	+	4.98162e8i	−0.000220476	+	0.000127292i
$331$	1.75998e12	−	1.01612e12i	0.442962	−	0.255745i	−0.261891	−	0.965097i	$-0.584346\pi$
$331$	1.75998e12	−	1.01612e12i	0.442962	−	0.255745i	0.704853	+	0.709353i	$0.251013\pi$
$332$	4.96077e11	−	8.59230e11i	0.122987	−	0.213019i
$333$			1.09444e12i			0.267283i
$334$	−4.63335e9	−	2.67507e9i	−0.00111471	−	0.000643580i
$335$	−1.88509e12	+	1.08835e12i	−0.446794	+	0.257956i
$336$	9.46797e11			0.221086
$337$	−1.76421e12	−	3.05569e12i	−0.405882	−	0.703008i	0.588542	−	0.808467i	$-0.299702\pi$
$337$	−1.76421e12	−	3.05569e12i	−0.405882	−	0.703008i	−0.994424	+	0.105459i	$0.966369\pi$
$338$	3.17578e10	+	1.83354e10i	0.00719892	+	0.00415630i
$339$	−2.46726e12	+	4.27341e12i	−0.551081	+	0.954501i
$340$			2.42089e12i			0.532819i
$341$	−2.42553e11	+	4.20113e11i	−0.0526058	+	0.0911160i
$342$	8.14519e9			0.00174089
$343$		−	2.40871e12i		−	0.507358i
$344$	−6.79048e10	−	4.25126e10i	−0.0140964	−	0.00882522i
$345$	−2.28542e12			−0.467596
$346$			2.59418e10i			0.00523142i
$347$	−5.59016e12	−	3.22748e12i	−1.11116	−	0.641529i	−0.172031	−	0.985092i	$-0.555033\pi$
$347$	−5.59016e12	−	3.22748e12i	−1.11116	−	0.641529i	−0.939130	+	0.343563i	$0.888366\pi$
$348$	6.21106e12			1.21694
$349$	4.75017e12	+	2.74251e12i	0.917449	+	0.529690i	0.882820	−	0.469711i	$-0.155642\pi$
$349$	4.75017e12	+	2.74251e12i	0.917449	+	0.529690i	0.0346288	+	0.999400i	$0.488975\pi$
$350$	−4.76865e9	+	8.25954e9i	−0.000907936	+	0.00157259i
$351$	−9.90298e10	+	5.71749e10i	−0.0185879	+	0.0107317i
$352$			1.19307e10i			0.00220776i
$353$	1.22810e12	+	2.12714e12i	0.224059	+	0.388081i	0.956037	−	0.293247i	$-0.0947359\pi$
$353$	1.22810e12	+	2.12714e12i	0.224059	+	0.388081i	−0.731978	+	0.681328i	$0.761403\pi$
$354$	−1.36837e10	+	2.37008e10i	−0.00246142	+	0.00426331i
$355$	−2.86293e12			−0.507773
$356$	−5.36971e12	−	3.10020e12i	−0.939076	−	0.542176i
$357$	−8.31230e11	−	1.43973e12i	−0.143344	−	0.248279i
$358$	−1.18794e10	−	2.05757e10i	−0.00202013	−	0.00349896i
$359$	2.36064e12	+	4.08875e12i	0.395874	+	0.685675i	0.993212	−	0.116315i	$-0.0371082\pi$
$359$	2.36064e12	+	4.08875e12i	0.395874	+	0.685675i	−0.597338	+	0.801990i	$0.703775\pi$
$360$	−1.20563e10			−0.00199389
$361$	−1.48655e12	−	2.57478e12i	−0.242462	−	0.419957i
$362$	−2.01766e10	+	1.16490e10i	−0.00324568	+	0.00187390i
$363$	4.55784e12	+	2.63147e12i	0.723145	+	0.417508i
$364$	−2.87063e10	−	1.65736e10i	−0.00449232	−	0.00259364i
$365$	2.96396e12			0.457518
$366$		−	6.97879e10i		−	0.0106261i
$367$	−6.30218e12	+	1.09157e13i	−0.946588	+	1.63954i	−0.194046	+	0.980992i	$0.562161\pi$
$367$	−6.30218e12	+	1.09157e13i	−0.946588	+	1.63954i	−0.752541	+	0.658545i	$0.771172\pi$
$368$	−4.56067e12	+	7.89932e12i	−0.675756	+	1.17044i
$369$	−3.09396e11	−	5.35890e11i	−0.0452255	−	0.0783328i
$370$	−1.88078e10	+	1.08587e10i	−0.00271225	+	0.00156592i
$371$		−	2.64100e12i		−	0.375749i
$372$	6.17198e12	−	3.56339e12i	0.866383	−	0.500206i
$373$	4.98357e12	−	2.87726e12i	0.690234	−	0.398507i	−0.113466	−	0.993542i	$-0.536195\pi$
$373$	4.98357e12	−	2.87726e12i	0.690234	−	0.398507i	0.803700	+	0.595035i	$0.202862\pi$
$374$	6.04671e9	−	3.49107e9i	0.000826344	−	0.000477090i
$375$	2.34851e12	−	4.06774e12i	0.316691	−	0.548525i
$376$		−	9.26616e10i		−	0.0123299i
$377$	−1.88303e11	−	1.08717e11i	−0.0247258	−	0.0142754i
$378$	1.58747e10	−	9.16527e9i	0.00205706	−	0.00118764i
$379$	5.62870e12			0.719801			0.359900	−	0.932991i	$-0.382811\pi$
$379$	5.62870e12			0.719801			0.359900	+	0.932991i	$0.382811\pi$
$380$	−1.16854e12	−	2.02397e12i	−0.147478	−	0.255439i
$381$	−1.13340e12	−	6.54370e11i	−0.141176	−	0.0815077i
$382$	−1.98640e10	+	3.44054e10i	−0.00244202	+	0.00422970i
$383$		−	1.49154e13i		−	1.80984i	−0.425577	−	0.904922i	$-0.639929\pi$
$383$		−	1.49154e13i		−	1.80984i	0.425577	−	0.904922i	$-0.360071\pi$
$384$	1.16850e11	−	2.02389e11i	0.0139949	−	0.0242399i
$385$	8.08461e10			0.00955775
$386$			4.29726e10i			0.00501482i
$387$	2.53050e12	+	9.05385e10i	0.291509	+	0.0104299i
$388$	9.69522e12			1.10255
$389$		−	1.52200e13i		−	1.70870i	−0.519698	−	0.854350i	$-0.673955\pi$
$389$		−	1.52200e13i		−	1.70870i	0.519698	−	0.854350i	$-0.326045\pi$
$390$	−4.43762e8	−	2.56206e8i	−4.91843e−5	−	2.83966e-5i
$391$	1.60160e13			1.75255
$392$	−1.24112e11	−	7.16562e10i	−0.0134086	−	0.00774147i
$393$	6.56385e11	−	1.13689e12i	0.0700158	−	0.121271i
$394$	7.98473e10	−	4.60998e10i	0.00840967	−	0.00485532i
$395$			8.08459e11i			0.0840761i
$396$	−1.25693e11	−	2.17706e11i	−0.0129073	−	0.0223560i
$397$	−1.61006e12	+	2.78871e12i	−0.163264	+	0.282781i	−0.936037	−	0.351901i	$-0.885535\pi$
$397$	−1.61006e12	+	2.78871e12i	−0.163264	+	0.282781i	0.772774	+	0.634682i	$0.218869\pi$
$398$	−1.08169e10			−0.00108314
$399$	1.38989e12	+	8.02455e11i	0.137441	+	0.0793517i
$400$	−4.25421e12	−	7.36850e12i	−0.415450	−	0.719580i
$401$	5.98105e12	+	1.03595e13i	0.576840	+	0.999117i	0.995839	+	0.0911300i	$0.0290479\pi$
$401$	5.98105e12	+	1.03595e13i	0.576840	+	0.999117i	−0.418999	+	0.907987i	$0.637619\pi$
$402$	−4.61150e10	−	7.98736e10i	−0.00439250	−	0.00760804i
$403$	−2.49490e11			−0.0234708
$404$	−8.67295e11	−	1.50220e12i	−0.0805860	−	0.139579i
$405$	−2.41711e12	+	1.39552e12i	−0.221831	+	0.128074i
$406$	3.01854e10	+	1.74275e10i	0.00273632	+	0.00157981i
$407$	−7.84351e11	−	4.52845e11i	−0.0702326	−	0.0405488i
$408$	−2.05159e11			−0.0181464
$409$		−	2.15762e13i		−	1.88520i	−0.333918	−	0.942602i	$-0.608371\pi$
$409$		−	2.15762e13i		−	1.88520i	0.333918	−	0.942602i	$-0.391629\pi$
$410$	6.13945e9	−	1.06338e10i	0.000529920	−	0.000917849i
$411$	−3.30928e12	+	5.73185e12i	−0.282179	+	0.488749i
$412$	5.24881e10	+	9.09121e10i	0.00442155	+	0.00765836i
$413$	1.92319e12	−	1.11035e12i	0.160056	−	0.0924082i
$414$			3.98792e10i			0.00327903i
$415$	−1.07780e12	+	6.22271e11i	−0.0875587	+	0.0505520i
$416$	−5.31391e9	+	3.06799e9i	−0.000426528	+	0.000246256i
$417$	4.25811e12	−	2.45842e12i	0.337704	−	0.194974i
$418$	−3.37022e9	+	5.83739e9i	−0.000264105	+	0.000457443i
$419$			5.73630e12i			0.444183i	0.975026	+	0.222091i	$0.0712883\pi$
$419$			5.73630e12i			0.444183i	−0.975026	+	0.222091i	$0.928712\pi$
$420$	−1.02860e12	−	5.93864e11i	−0.0787048	−	0.0454403i
$421$	−4.54991e11	+	2.62689e11i	−0.0344027	+	0.0198624i	−0.517103	−	0.855923i	$-0.672989\pi$
$421$	−4.54991e11	+	2.62689e11i	−0.0344027	+	0.0198624i	0.482700	+	0.875786i	$0.339656\pi$
$422$	9.02520e10			0.00674365
$423$	1.46434e12	+	2.53630e12i	0.108128	+	0.187283i
$424$	−2.82253e11	−	1.62959e11i	−0.0205973	−	0.0118918i
$425$	−7.46987e12	+	1.29382e13i	−0.538726	+	0.933102i
$426$		−	1.21306e11i		−	0.00864640i
$427$	−2.83144e12	+	4.90421e12i	−0.199466	+	0.345485i
$428$	−2.25723e13			−1.57165
$429$		−	2.13693e10i		−	0.00147063i
$430$	2.35509e10	+	4.43845e10i	0.00160201	+	0.00301918i
$431$	−7.59348e12			−0.510569			−0.255285	−	0.966866i	$-0.582169\pi$
$431$	−7.59348e12			−0.510569			−0.255285	+	0.966866i	$0.582169\pi$
$432$			1.63530e13i			1.08688i
$433$	7.13150e12	+	4.11737e12i	0.468534	+	0.270508i	0.715626	−	0.698484i	$-0.246142\pi$
$433$	7.13150e12	+	4.11737e12i	0.468534	+	0.270508i	−0.247092	+	0.968992i	$0.579475\pi$
$434$	3.99939e10			0.00259744
$435$	−6.74725e12	−	3.89553e12i	−0.433192	−	0.250104i
$436$	−8.50050e12	+	1.47233e13i	−0.539526	+	0.934486i
$437$	−1.33901e13	+	7.73077e12i	−0.840188	+	0.485083i
$438$			1.25587e11i			0.00779066i
$439$	1.15834e13	+	2.00631e13i	0.710420	+	1.23048i	0.964700	+	0.263352i	$0.0848282\pi$
$439$	1.15834e13	+	2.00631e13i	0.710420	+	1.23048i	−0.254280	+	0.967131i	$0.581839\pi$
$440$	4.98849e9	−	8.64033e9i	0.000302487	−	0.000523922i
$441$	4.52954e12			0.271557
$442$	3.10983e9	+	1.79546e9i	0.000184343	+	0.000106430i
$443$	−4.52241e12	−	7.83304e12i	−0.265064	−	0.459104i	0.702516	−	0.711668i	$-0.252060\pi$
$443$	−4.52241e12	−	7.83304e12i	−0.265064	−	0.459104i	−0.967580	+	0.252563i	$0.918726\pi$
$444$	6.65285e12	+	1.15231e13i	0.385561	+	0.667811i
$445$	3.88885e12	+	6.73568e12i	0.222854	+	0.385995i
$446$	−1.37687e10			−0.000780224
$447$	−5.63578e12	−	9.76146e12i	−0.315803	−	0.546987i
$448$	−4.10469e12	+	2.36985e12i	−0.227453	+	0.131320i
$449$	−2.79057e13	−	1.61114e13i	−1.52919	−	0.882878i	−0.999396	−	0.0347523i	$-0.988936\pi$
$449$	−2.79057e13	−	1.61114e13i	−1.52919	−	0.882878i	−0.529794	−	0.848126i	$-0.677731\pi$
$450$	−3.22157e10	−	1.85997e10i	−0.00174584	−	0.00100796i
$451$	5.12073e11			0.0274441
$452$		−	2.47057e13i		−	1.30950i
$453$	−1.11612e13	+	1.93319e13i	−0.585089	+	1.01340i
$454$	6.14250e10	−	1.06391e11i	0.00318468	−	0.00551603i
$455$	2.07897e10	+	3.60088e10i	0.00106608	+	0.00184651i
$456$	1.71523e11	−	9.90286e10i	0.00869956	−	0.00502269i
$457$			1.29629e13i			0.650310i	0.945661	+	0.325155i	$0.105416\pi$
$457$			1.29629e13i			0.650310i	−0.945661	+	0.325155i	$0.894584\pi$
$458$	−2.75016e11	+	1.58780e11i	−0.0136468	+	0.00787897i
$459$	2.48670e13	−	1.43570e13i	1.22056	−	0.704692i
$460$	9.90946e12	−	5.72123e12i	0.481128	−	0.277780i
$461$	1.26227e13	−	2.18632e13i	0.606245	−	1.05005i	−0.385609	−	0.922662i	$-0.626009\pi$
$461$	1.26227e13	−	2.18632e13i	0.606245	−	1.05005i	0.991853	−	0.127384i	$-0.0406581\pi$
$462$			3.42556e9i			0.000162750i
$463$	1.64221e12	+	9.48128e11i	0.0771832	+	0.0445617i	0.538095	−	0.842884i	$-0.319144\pi$
$463$	1.64221e12	+	9.48128e11i	0.0771832	+	0.0445617i	−0.460912	+	0.887446i	$0.652478\pi$
$464$	−2.69290e13	+	1.55475e13i	−1.25207	+	0.722885i
$465$	−8.93973e12			−0.411206
$466$	−9.97896e10	−	1.72841e11i	−0.00454104	−	0.00786532i
$467$	7.88825e12	+	4.55428e12i	0.355137	+	0.205038i	0.666945	−	0.745107i	$-0.267601\pi$
$467$	7.88825e12	+	4.55428e12i	0.355137	+	0.205038i	−0.311808	+	0.950145i	$0.600935\pi$
$468$	6.46440e10	−	1.11967e11i	0.00287938	−	0.00498723i
$469$			7.48395e12i			0.329812i
$470$	−2.90573e10	+	5.03287e10i	−0.00126697	+	0.00219445i
$471$	1.40734e13			0.607149
$472$		−	2.74051e11i		−	0.0116983i
$473$	−1.11192e12	+	1.77606e12i	−0.0469645	+	0.0750158i
$474$	−3.42555e10			−0.00143165
$475$		−	1.44226e13i		−	0.596451i
$476$	7.20834e12	+	4.16174e12i	0.294985	+	0.170310i
$477$	1.03010e13			0.417145
$478$	1.29996e11	+	7.50533e10i	0.00520944	+	0.00300767i
$479$	−9.15214e12	+	1.58520e13i	−0.362949	+	0.628645i	−0.988445	−	0.151582i	$-0.951563\pi$
$479$	−9.15214e12	+	1.58520e13i	−0.362949	+	0.628645i	0.625496	+	0.780227i	$0.284897\pi$
$480$	−1.90408e11	+	1.09932e11i	−0.00747271	+	0.00431437i
$481$		−	4.65799e11i		−	0.0180914i
$482$	−5.47103e10	−	9.47610e10i	−0.00210297	−	0.00364246i
$483$	−3.92886e12	+	6.80498e12i	−0.149462	+	0.258876i
$484$	−2.63501e13			−0.992098
$485$	−1.05322e13	−	6.08076e12i	−0.392473	−	0.226595i
$486$	6.34239e10	+	1.09854e11i	0.00233922	+	0.00405166i
$487$	−2.42319e13	−	4.19709e13i	−0.884591	−	1.53216i	−0.846181	−	0.532895i	$-0.821104\pi$
$487$	−2.42319e13	−	4.19709e13i	−0.884591	−	1.53216i	−0.0384103	−	0.999262i	$-0.512229\pi$
$488$	3.49420e11	+	6.05214e11i	0.0126255	+	0.0218680i
$489$	−1.82654e13			−0.653257
$490$	4.49406e10	+	7.78395e10i	0.00159096	+	0.00275562i
$491$	3.82059e13	−	2.20582e13i	1.33882	−	0.772969i	0.352189	−	0.935929i	$-0.385437\pi$
$491$	3.82059e13	−	2.20582e13i	1.33882	−	0.772969i	0.986633	+	0.162960i	$0.0521040\pi$
$492$	−6.51509e12	−	3.76149e12i	−0.225993	−	0.130477i
$493$	4.72840e13	+	2.72994e13i	1.62360	+	0.937387i
$494$	−3.46662e9			−0.000117834
$495$			3.15334e11i			0.0106107i
$496$	−1.78397e13	+	3.08992e13i	−0.594263	+	1.02929i
$497$	−4.92166e12	+	8.52456e12i	−0.162304	+	0.281119i
$498$	−2.63664e10	−	4.56680e10i	−0.000860804	−	0.00149096i
$499$	2.87412e13	−	1.65937e13i	0.928970	−	0.536341i	0.0424847	−	0.999097i	$-0.486473\pi$
$499$	2.87412e13	−	1.65937e13i	0.928970	−	0.536341i	0.886486	+	0.462756i	$0.153139\pi$
$500$			2.35167e13i			0.752533i
$501$	3.56087e12	−	2.05587e12i	0.112815	−	0.0651338i
$502$	3.33583e11	−	1.92594e11i	0.0104637	−	0.00604123i
$503$	1.00695e13	−	5.81365e12i	0.312730	−	0.180555i	−0.335417	−	0.942070i	$-0.608877\pi$
$503$	1.00695e13	−	5.81365e12i	0.312730	−	0.180555i	0.648148	+	0.761515i	$0.275544\pi$
$504$	−2.07259e10	+	3.58983e10i	−0.000637324	+	0.00110388i
$505$			2.17584e12i			0.0662476i
$506$	−2.85801e10	−	1.65007e10i	−0.000861612	−	0.000497452i
$507$	−2.44068e13	+	1.40913e13i	−0.728570	+	0.420640i
$508$	6.55250e12			0.193682
$509$	−3.06068e13	−	5.30125e13i	−0.895837	−	1.55163i	−0.832766	−	0.553625i	$-0.813244\pi$
$509$	−3.06068e13	−	5.30125e13i	−0.895837	−	1.55163i	−0.0630706	−	0.998009i	$-0.520089\pi$
$510$	1.11431e11	+	6.43349e10i	0.00322966	+	0.00186464i
$511$	5.09534e12	−	8.82539e12i	0.146241	−	0.253297i
$512$			1.46253e12i			0.0415677i
$513$	−1.38600e13	+	2.40062e13i	−0.390100	+	0.675673i
$514$	2.43890e10			0.000679795
$515$		−	1.31681e11i		−	0.00363484i
$516$	2.71933e13	−	1.44290e13i	0.743383	−	0.394447i
$517$	−2.42358e12			−0.0656152
$518$			7.46686e10i			0.00200212i
$519$	−1.72660e13	−	9.96852e12i	−0.458516	−	0.264724i
$520$	5.13119e9			0.000134959
$521$	3.17049e13	+	1.83049e13i	0.825921	+	0.476846i	0.852454	−	0.522802i	$-0.175113\pi$
$521$	3.17049e13	+	1.83049e13i	0.825921	+	0.476846i	−0.0265332	+	0.999648i	$0.508447\pi$
$522$	−6.79746e10	+	1.17736e11i	−0.00175386	+	0.00303777i
$523$	5.32832e13	−	3.07631e13i	1.36170	−	0.786179i	0.371852	−	0.928292i	$-0.378723\pi$
$523$	5.32832e13	−	3.07631e13i	1.36170	−	0.786179i	0.989850	+	0.142113i	$0.0453897\pi$
$524$			6.57268e12i			0.166374i
$525$	−3.66485e12	−	6.34770e12i	−0.0918881	−	0.159155i
$526$	8.12038e10	−	1.40649e11i	0.00201673	−	0.00349308i
$527$	6.26486e13			1.54120
$528$	−2.64658e12	−	1.52800e12i	−0.0644934	−	0.0372353i
$529$	−1.71370e13	−	2.96821e13i	−0.413672	−	0.716501i
$530$	1.02203e11	+	1.77021e11i	0.00244390	+	0.00423297i
$531$	4.33084e12	+	7.50123e12i	0.102589	+	0.177689i
$532$	−8.03534e12			−0.188558
$533$	1.31680e11	+	2.28076e11i	0.00306114	+	0.00530206i
$534$	−2.85400e11	+	1.64776e11i	−0.00657275	+	0.00379478i
$535$	2.45209e13	+	1.41572e13i	0.559459	+	0.323004i
$536$	7.99837e11	+	4.61786e11i	0.0180791	+	0.0104380i
$537$	1.82593e13			0.408896
$538$			2.99351e11i			0.00664154i
$539$	−1.87418e12	+	3.24617e12i	−0.0411972	+	0.0713556i
$540$	1.02572e13	−	1.77660e13i	0.223388	−	0.386920i
$541$	1.95588e13	+	3.38768e13i	0.422042	+	0.730998i	0.996139	−	0.0877892i	$-0.0279802\pi$
$541$	1.95588e13	+	3.38768e13i	0.422042	+	0.730998i	−0.574097	+	0.818787i	$0.694647\pi$
$542$	2.00208e11	−	1.15590e11i	0.00428040	−	0.00247129i
$543$		−	1.79052e13i		−	0.379297i
$544$	1.33436e12	−	7.70391e11i	0.0280077	−	0.0161702i
$545$	1.84687e13	−	1.06629e13i	0.384108	−	0.221765i
$546$	−1.52574e9	+	8.80885e8i	−3.14425e−5	+	1.81533e-5i
$547$	2.67111e13	−	4.62650e13i	0.545450	−	0.944748i	−0.453128	−	0.891445i	$-0.649692\pi$
$547$	2.67111e13	−	4.62650e13i	0.545450	−	0.944748i	0.998578	−	0.0533024i	$-0.0169747\pi$
$548$		−	3.31373e13i		−	0.670525i
$549$	−1.91284e13	−	1.10438e13i	−0.383546	−	0.221441i
$550$	2.66596e10	−	1.53919e10i	0.000529713	−	0.000305830i
$551$	−5.27088e13			−1.03783
$552$	4.84849e11	+	8.39783e11i	0.00946044	+	0.0163860i
$553$	2.40724e12	+	1.38982e12i	0.0465472	+	0.0268740i
$554$	4.76975e10	−	8.26146e10i	0.000914002	−	0.00158310i
$555$		−	1.66905e13i		−	0.316959i
$556$	−1.23086e13	+	2.13192e13i	−0.231652	+	0.401233i
$557$	−3.33861e13			−0.622715			−0.311358	−	0.950293i	$-0.600784\pi$
$557$	−3.33861e13			−0.622715			−0.311358	+	0.950293i	$0.600784\pi$
$558$			1.55993e11i			0.00288359i
$559$	−1.07699e12	−	3.85335e10i	−0.0197311	−	0.000705959i
$560$	5.94622e12			0.107969
$561$			5.36598e12i			0.0965683i
$562$	−4.36552e11	−	2.52044e11i	−0.00778673	−	0.00449567i
$563$	7.65278e13			1.35294			0.676468	−	0.736472i	$-0.263510\pi$
$563$	7.65278e13			1.35294			0.676468	+	0.736472i	$0.263510\pi$
$564$	3.08351e13	+	1.78027e13i	0.540319	+	0.311953i
$565$	−1.54952e13	+	2.68385e13i	−0.269126	+	0.466140i
$566$	−4.93716e11	+	2.85047e11i	−0.00849953	+	0.00490720i
$567$			9.59614e12i			0.163750i
$568$	6.07368e11	+	1.05199e12i	0.0102733	+	0.0177939i
$569$	−4.63572e13	+	8.02931e13i	−0.777242	+	1.34622i	0.156284	+	0.987712i	$0.450048\pi$
$569$	−4.63572e13	+	8.02931e13i	−0.777242	+	1.34622i	−0.933526	+	0.358510i	$0.883285\pi$
$570$	−1.24216e11			−0.00206444
$571$	−1.04652e14	−	6.04207e13i	−1.72411	−	0.995418i	−0.909866	−	0.414902i	$-0.863816\pi$
$571$	−1.04652e14	−	6.04207e13i	−1.72411	−	0.995418i	−0.814249	−	0.580516i	$-0.802851\pi$
$572$	5.34952e10	+	9.26564e10i	0.000873644	+	0.00151320i
$573$	−1.52660e13	−	2.64415e13i	−0.247146	−	0.428069i
$574$	−2.11086e10	−	3.65612e10i	−0.000338766	−	0.000586761i
$575$	7.06136e13			1.12344
$576$	−9.24339e12	−	1.60100e13i	−0.145787	−	0.252510i
$577$	−5.28763e13	+	3.05282e13i	−0.826765	+	0.477333i	−0.852744	−	0.522329i	$-0.825063\pi$
$577$	−5.28763e13	+	3.05282e13i	−0.826765	+	0.477333i	0.0259785	+	0.999663i	$0.491730\pi$
$578$	−3.16302e11	−	1.82617e11i	−0.00490301	−	0.00283076i
$579$	−2.86011e13	−	1.65129e13i	−0.439532	−	0.253764i
$580$	3.90076e13			0.594305
$581$			4.27897e12i			0.0646337i
$582$	2.57650e11	−	4.46263e11i	0.00385847	−	0.00668307i
$583$	−4.26222e12	+	7.38238e12i	−0.0632838	+	0.109611i
$584$	−6.28801e11	−	1.08912e12i	−0.00925655	−	0.0160328i
$585$	−1.40449e11	+	8.10883e10i	−0.00204993	+	0.00118353i
$586$		−	9.52497e11i		−	0.0137840i
$587$	1.37666e13	−	7.94817e12i	0.197532	−	0.114045i	−0.397972	−	0.917398i	$-0.630286\pi$
$587$	1.37666e13	−	7.94817e12i	0.197532	−	0.114045i	0.595504	+	0.803353i	$0.296952\pi$
$588$	4.76903e13	−	2.75340e13i	0.678490	−	0.391726i
$589$	−5.23771e13	+	3.02399e13i	−0.738865	+	0.426584i
$590$	−8.59382e10	+	1.48849e11i	−0.00120206	+	0.00208203i
$591$			7.08582e13i			0.982771i
$592$	−5.76889e13	−	3.33067e13i	−0.793384	−	0.458061i
$593$	−6.72396e13	+	3.88208e13i	−0.916963	+	0.529409i	−0.882665	−	0.470003i	$-0.844253\pi$
$593$	−6.72396e13	+	3.88208e13i	−0.916963	+	0.529409i	−0.0342978	+	0.999412i	$0.510919\pi$
$594$	−5.91661e10			−0.000800094
$595$	−5.22041e12	−	9.04202e12i	−0.0700036	−	0.121250i
$596$	4.88729e13	+	2.82168e13i	0.649886	+	0.375212i
$597$	4.15654e12	−	7.19935e12i	0.0548101	−	0.0949339i
$598$		−	1.69727e10i		−	0.000221945i
$599$	−7.66134e12	+	1.32698e13i	−0.0993506	+	0.172080i	−0.911416	−	0.411486i	$-0.865010\pi$
$599$	−7.66134e12	+	1.32698e13i	−0.0993506	+	0.172080i	0.812065	+	0.583566i	$0.198343\pi$
$600$	−9.04537e11			−0.0116324
$601$			6.99972e13i			0.892706i	0.894857	+	0.446353i	$0.147277\pi$
$601$			6.99972e13i			0.892706i	−0.894857	+	0.446353i	$0.852723\pi$
$602$	1.72644e11	+	6.17701e9i	0.00218358	+	7.81261e-5i
$603$	−2.91905e13			−0.366147
$604$		−	1.11763e14i		−	1.39031i
$605$	2.86248e13	+	1.65265e13i	0.353155	+	0.203894i
$606$	−9.21932e10			−0.00112807
$607$	3.09820e13	+	1.78875e13i	0.375981	+	0.217073i	0.676068	−	0.736839i	$-0.263682\pi$
$607$	3.09820e13	+	1.78875e13i	0.375981	+	0.217073i	−0.300087	+	0.953912i	$0.597016\pi$
$608$	−7.43722e11	+	1.28816e12i	−0.00895144	+	0.0155043i
$609$	−2.31983e13	+	1.33936e13i	−0.276930	+	0.159886i
$610$		−	4.38292e11i		−	0.00518937i
$611$	−6.23226e11	−	1.07946e12i	−0.00731879	−	0.0126765i
$612$	−1.62325e13	+	2.81155e13i	−0.189073	+	0.327483i
$613$	−1.42063e14			−1.64126			−0.820632	−	0.571458i	$-0.806378\pi$
$613$	−1.42063e14			−1.64126			−0.820632	+	0.571458i	$0.806378\pi$
$614$	−6.51436e11	−	3.76107e11i	−0.00746500	−	0.00430992i
$615$	4.71835e12	+	8.17242e12i	0.0536308	+	0.0928913i
$616$	−1.71514e10	−	2.97071e10i	−0.000193373	−	0.000334932i
$617$	6.85456e13	+	1.18724e14i	0.766573	+	1.32774i	0.939411	+	0.342794i	$0.111373\pi$
$617$	6.85456e13	+	1.18724e14i	0.766573	+	1.32774i	−0.172837	+	0.984950i	$0.555293\pi$
$618$	5.57948e9			6.18944e−5
$619$	2.02094e13	+	3.50036e13i	0.222382	+	0.385176i	0.955531	−	0.294892i	$-0.0952835\pi$
$619$	2.02094e13	+	3.50036e13i	0.222382	+	0.385176i	−0.733149	+	0.680068i	$0.761950\pi$
$620$	3.87622e13	−	2.23794e13i	0.423107	−	0.244281i
$621$	−1.17535e14	−	6.78591e13i	−1.27266	−	0.734768i
$622$	−7.60330e11	−	4.38977e11i	−0.00816677	−	0.00471509i
$623$	2.67412e13			0.284932
$624$		−	1.57171e12i		−	0.0166131i
$625$	−2.48792e13	+	4.30920e13i	−0.260877	+	0.451852i
$626$	4.60112e10	−	7.96937e10i	0.000478621	−	0.000828996i
$627$	−2.59011e12	−	4.48620e12i	−0.0267289	−	0.0462958i
$628$	−6.10216e13	+	3.52309e13i	−0.624720	+	0.360682i
$629$			1.16965e14i			1.18796i
$630$	2.25143e10	−	1.29987e10i	0.000226859	−	0.000130977i
$631$	4.06404e13	−	2.34638e13i	0.406267	−	0.234558i	−0.282918	−	0.959144i	$-0.591302\pi$
$631$	4.06404e13	−	2.34638e13i	0.406267	−	0.234558i	0.689185	+	0.724586i	$0.257969\pi$
$632$	2.97070e11	−	1.71514e11i	0.00294628	−	0.00170103i
$633$	−3.46807e13	+	6.00687e13i	−0.341247	+	0.591057i
$634$		−	1.42343e12i		−	0.0138960i
$635$	−7.11817e12	−	4.10968e12i	−0.0689445	−	0.0398051i
$636$	1.08456e14	−	6.26172e13i	1.04224	−	0.601739i
$637$	−1.92779e12			−0.0183807
$638$	−5.62514e10	−	9.74304e10i	−0.000532145	−	0.000921703i
$639$	−3.32493e13	−	1.91965e13i	−0.312089	−	0.180185i
$640$	7.33856e11	−	1.27108e12i	0.00683457	−	0.0118378i
$641$		−	8.75420e13i		−	0.808959i	−0.914547	−	0.404479i	$-0.867453\pi$
$641$		−	8.75420e13i		−	0.808959i	0.914547	−	0.404479i	$-0.132547\pi$
$642$	−5.99858e11	+	1.03898e12i	−0.00550013	+	0.00952651i
$643$	−1.16643e14			−1.06122			−0.530608	−	0.847617i	$-0.678037\pi$
$643$	−1.16643e14			−1.06122			−0.530608	+	0.847617i	$0.678037\pi$
$644$		−	3.93414e13i		−	0.355157i
$645$	−3.85906e13	−	1.38073e12i	−0.345687	−	0.0123683i
$646$	8.70490e11			0.00773751
$647$			2.48373e13i			0.219070i	0.993983	+	0.109535i	$0.0349361\pi$
$647$			2.48373e13i			0.219070i	−0.993983	+	0.109535i	$0.965064\pi$
$648$	1.02557e12	+	5.92116e11i	0.00897619	+	0.00518241i
$649$	−7.16784e12			−0.0622537
$650$	1.37111e10	+	7.91610e9i	0.000118169	+	6.82252e-5i
$651$	−1.53683e13	+	2.66186e13i	−0.131438	+	0.227657i
$652$	7.91977e13	−	4.57248e13i	0.672163	−	0.388074i
$653$			2.25493e13i			0.189918i	0.995481	+	0.0949590i	$0.0302720\pi$
$653$			2.25493e13i			0.189918i	−0.995481	+	0.0949590i	$0.969728\pi$
$654$	4.51801e11	+	7.82542e11i	0.00377623	+	0.00654062i
$655$	4.12233e12	−	7.14009e12i	0.0341929	−	0.0592239i
$656$	3.76629e13			0.310023
$657$	3.44227e13	+	1.98739e13i	0.281202	+	0.162352i
$658$	9.99046e10	+	1.73040e11i	0.000809946	+	0.00140287i
$659$	1.86362e13	+	3.22788e13i	0.149944	+	0.259711i	0.931207	−	0.364492i	$-0.118757\pi$
$659$	1.86362e13	+	3.22788e13i	0.149944	+	0.259711i	−0.781262	+	0.624203i	$0.785424\pi$
$660$	1.91684e12	+	3.32006e12i	0.0153061	+	0.0265110i
$661$	1.15783e14			0.917566			0.458783	−	0.888548i	$-0.348286\pi$
$661$	1.15783e14			0.917566			0.458783	+	0.888548i	$0.348286\pi$
$662$	2.70397e11	+	4.68342e11i	0.00212673	+	0.00368360i
$663$	−2.39000e12	+	1.37987e12i	−0.0186565	+	0.0107713i
$664$	4.57310e11	+	2.64028e11i	0.00354299	+	0.00204555i
$665$	8.72901e12	+	5.03970e12i	0.0671208	+	0.0387522i
$666$	−2.91239e11			−0.00222269
$667$		−	2.58065e14i		−	1.95479i
$668$	−1.02932e13	+	1.78283e13i	−0.0773867	+	0.134038i
$669$	5.29083e12	−	9.16399e12i	0.0394815	−	0.0683839i
$670$	−2.89619e11	−	5.01634e11i	−0.00214512	−	0.00371546i
$671$	1.58295e13	−	9.13915e12i	0.116373	−	0.0671882i
$672$			7.55934e11i			0.00551617i
$673$	−1.24605e14	+	7.19405e13i	−0.902524	+	0.521073i	−0.878018	−	0.478627i	$-0.841135\pi$
$673$	−1.24605e14	+	7.19405e13i	−0.902524	+	0.521073i	−0.0245060	+	0.999700i	$0.507801\pi$
$674$	8.13141e11	−	4.69467e11i	0.00584610	−	0.00337525i
$675$	1.09637e14	−	6.32991e13i	0.782419	−	0.451730i
$676$	7.05512e13	−	1.22198e14i	0.499771	−	0.865628i
$677$		−	1.37026e14i		−	0.963517i	−0.876304	−	0.481759i	$-0.839998\pi$
$677$		−	1.37026e14i		−	0.963517i	0.876304	−	0.481759i	$-0.160002\pi$
$678$	−1.13718e12	−	6.56554e11i	−0.00793747	−	0.00458270i
$679$	−3.62117e13	+	2.09068e13i	−0.250900	+	0.144857i
$680$	−1.28847e12			−0.00886198
$681$	4.72069e13	+	8.17648e13i	0.322307	+	0.558253i
$682$	−1.11795e11	−	6.45449e10i	−0.000757706	−	0.000437462i
$683$	8.52053e13	−	1.47580e14i	0.573275	−	0.992941i	−0.422952	−	0.906152i	$-0.639006\pi$
$683$	8.52053e13	−	1.47580e14i	0.573275	−	0.992941i	0.996227	−	0.0867890i	$-0.0276606\pi$
$684$		−	3.13412e13i		−	0.209331i
$685$	−2.07835e13	+	3.59980e13i	−0.137805	+	0.238685i
$686$	6.40975e11			0.00421910
$687$		−	2.44055e14i		−	1.59479i
$688$	−8.17818e13	+	1.30629e14i	−0.530536	+	0.847418i
$689$	−4.38413e12			−0.0282350
$690$		−	6.08166e11i		−	0.00388845i
$691$	2.55661e14	+	1.47606e14i	1.62283	+	0.936944i	0.986157	+	0.165813i	$0.0530247\pi$
$691$	2.55661e14	+	1.47606e14i	1.62283	+	0.936944i	0.636677	+	0.771131i	$0.280309\pi$
$692$	9.98192e13			0.629048
$693$	9.38925e11	+	5.42089e11i	0.00587442	+	0.00339160i
$694$	8.58854e11	−	1.48758e12i	0.00533485	−	0.00924023i
$695$	2.67424e13	−	1.54398e13i	0.164921	−	0.0952174i
$696$			3.30572e12i			0.0202405i
$697$	−3.30657e13	−	5.72714e13i	−0.201008	−	0.348156i
$698$	−7.29801e11	+	1.26405e12i	−0.00440481	+	0.00762936i
$699$	1.53382e14			0.919157
$700$	3.17812e13	+	1.83489e13i	0.189095	+	0.109174i
$701$	1.34216e14	+	2.32470e14i	0.792894	+	1.37333i	0.924168	+	0.381987i	$0.124760\pi$
$701$	1.34216e14	+	2.32470e14i	0.792894	+	1.37333i	−0.131273	+	0.991346i	$0.541907\pi$
$702$	−1.52146e10	−	2.63525e10i	−8.92433e−5	−	0.000154574i
$703$	−5.64580e13	−	9.77881e13i	−0.328813	−	0.569520i
$704$	1.52985e13			0.0884677
$705$	−2.23314e13	−	3.86791e13i	−0.128224	−	0.222091i
$706$	−5.66046e11	+	3.26807e11i	−0.00322722	+	0.00186324i
$707$	6.47870e12	+	3.74048e12i	0.0366767	+	0.0211753i
$708$	9.11963e13	+	5.26522e13i	0.512638	+	0.295972i
$709$	−1.29518e14			−0.722936			−0.361468	−	0.932385i	$-0.617724\pi$
$709$	−1.29518e14			−0.722936			−0.361468	+	0.932385i	$0.617724\pi$
$710$		−	7.61846e11i		−	0.00422256i
$711$	−5.42087e12	+	9.38923e12i	−0.0298347	+	0.0516752i
$712$	1.65003e12	−	2.85793e12i	0.00901761	−	0.0156190i
$713$	−1.48056e14	−	2.56441e14i	−0.803487	−	1.39168i
$714$	3.83122e11	−	2.21196e11i	0.00206465	−	0.00119203i
$715$		−	1.34207e11i		−	0.000718199i
$716$	−7.91714e13	+	4.57096e13i	−0.420729	+	0.242908i
$717$	−9.99058e13	+	5.76807e13i	−0.527224	+	0.304393i
$718$	−1.08804e12	+	6.28182e11i	−0.00570196	+	0.00329203i
$719$	3.35031e13	−	5.80291e13i	0.174358	−	0.301996i	−0.765581	−	0.643339i	$-0.777548\pi$
$719$	3.35031e13	−	5.80291e13i	0.174358	−	0.301996i	0.939939	+	0.341343i	$0.110882\pi$
$720$			2.31927e13i			0.119864i
$721$	−3.92087e11	−	2.26372e11i	−0.00201236	−	0.00116184i
$722$	6.85167e11	−	3.95581e11i	0.00349229	−	0.00201628i
$723$	8.40929e13			0.425665
$724$	4.48231e13	+	7.76359e13i	0.225325	+	0.390274i
$725$	2.08473e14	+	1.20362e14i	1.04078	+	0.600895i
$726$	−7.00251e11	+	1.21287e12i	−0.00347193	+	0.00601356i
$727$			3.53852e14i			1.74241i	0.490923	+	0.871203i	$0.336660\pi$
$727$			3.53852e14i			1.74241i	−0.490923	+	0.871203i	$0.663340\pi$
$728$	8.82100e9	−	1.52784e10i	4.31381e−5	−	7.47174e-5i
$729$	−2.25802e14			−1.09670
$730$			7.88731e11i			0.00380465i
$731$	2.70439e14	+	9.67600e12i	1.29563	+	0.0463563i
$732$	−2.68531e14			−1.27773
$733$		−	3.09036e14i		−	1.46046i	−0.683201	−	0.730230i	$-0.739413\pi$
$733$		−	3.09036e14i		−	1.46046i	0.683201	−	0.730230i	$-0.260587\pi$
$734$	−2.90474e12	−	1.67705e12i	−0.0136341	−	0.00787167i
$735$	−6.90764e13			−0.322028
$736$	−6.30691e12	−	3.64130e12i	−0.0292030	−	0.0168604i
$737$	1.20781e13	−	2.09199e13i	0.0555470	−	0.0962103i
$738$	1.42604e11	−	8.23324e10i	0.000651403	−	0.000376088i
$739$		−	1.86144e14i		−	0.844553i	−0.906467	−	0.422276i	$-0.861231\pi$
$739$		−	1.86144e14i		−	0.844553i	0.906467	−	0.422276i	$-0.138769\pi$
$740$	4.17823e13	+	7.23690e13i	0.188293	+	0.326132i
$741$	1.33210e12	−	2.30726e12i	0.00596273	−	0.0103278i
$742$	7.02787e11			0.00312467
$743$	7.84188e13	+	4.52751e13i	0.346319	+	0.199947i	0.663063	−	0.748564i	$-0.269256\pi$
$743$	7.84188e13	+	4.52751e13i	0.346319	+	0.199947i	−0.316744	+	0.948511i	$0.602590\pi$
$744$	1.89655e12	+	3.28492e12i	0.00831955	+	0.0144099i
$745$	−3.53947e13	−	6.13054e13i	−0.154226	−	0.267127i
$746$	7.65659e11	+	1.32616e12i	0.00331392	+	0.00573987i
$747$	−1.66898e13			−0.0717542
$748$	−1.34330e13	−	2.32666e13i	−0.0573673	−	0.0993631i
$749$	8.43077e13	−	4.86751e13i	0.357650	−	0.206489i
$750$	1.08245e12	+	6.24954e11i	0.00456145	+	0.00263355i
$751$	−1.80652e14	−	1.04299e14i	−0.756209	−	0.436598i	0.0717238	−	0.997425i	$-0.477150\pi$
$751$	−1.80652e14	−	1.04299e14i	−0.756209	−	0.436598i	−0.827933	+	0.560827i	$0.810483\pi$
$752$	−1.78254e14			−0.741224
$753$			2.96029e14i			1.22281i
$754$	2.89302e10	−	5.01086e10i	0.000118712	−	0.000205615i
$755$	−7.00966e13	+	1.21411e14i	−0.285734	+	0.494906i
$756$	−3.52663e13	−	6.10830e13i	−0.142807	−	0.247350i
$757$	−2.23889e14	+	1.29262e14i	−0.900644	+	0.519987i	−0.877409	−	0.479743i	$-0.840730\pi$
$757$	−2.23889e14	+	1.29262e14i	−0.900644	+	0.519987i	−0.0232347	+	0.999730i	$0.507396\pi$
$758$			1.49784e12i			0.00598575i
$759$	2.19647e13	−	1.26813e13i	0.0871999	−	0.0503449i
$760$	1.07722e12	−	6.21935e11i	0.00424852	−	0.00245288i
$761$	−2.46886e14	+	1.42540e14i	−0.967328	+	0.558487i	−0.898420	−	0.439136i	$-0.855285\pi$
$761$	−2.46886e14	+	1.42540e14i	−0.967328	+	0.558487i	−0.0689071	+	0.997623i	$0.521951\pi$
$762$	1.74132e11	−	3.01606e11i	0.000677805	−	0.00117399i
$763$		−	7.33222e13i		−	0.283539i
$764$	1.32385e14	+	7.64328e13i	0.508597	+	0.293638i
$765$	3.52677e13	−	2.03618e13i	0.134608	−	0.0777157i
$766$	3.96909e12			0.0150504
$767$	−1.84322e12	−	3.19255e12i	−0.00694384	−	0.0120271i
$768$	−1.94602e14	−	1.12353e14i	−0.728350	−	0.420513i
$769$	1.12893e14	−	1.95536e14i	0.419793	−	0.727103i	−0.576125	−	0.817361i	$-0.695436\pi$
$769$	1.12893e14	−	1.95536e14i	0.419793	−	0.727103i	0.995918	+	0.0902587i	$0.0287694\pi$
$770$			2.15137e10i			7.94807e-5i
$771$	−9.37182e12	+	1.62325e13i	−0.0343995	+	0.0595817i
$772$	1.65351e14			0.603003
$773$			2.47369e14i			0.896288i	0.893961	+	0.448144i	$0.147915\pi$
$773$			2.47369e14i			0.896288i	−0.893961	+	0.448144i	$0.852085\pi$
$774$	−2.40929e10	+	6.73383e11i	−8.67330e−5	+	0.00242414i
$775$	2.76214e14			0.987957
$776$			5.16011e12i			0.0183379i
$777$	−4.96969e13	−	2.86925e13i	−0.175479	−	0.101313i
$778$	4.05014e12			0.0142093
$779$	5.52889e13	+	3.19210e13i	0.192730	+	0.111273i
$780$	−9.85833e11	+	1.70751e12i	−0.00341452	+	0.00591413i
$781$	2.75150e13	−	1.58858e13i	0.0946923	−	0.0546706i
$782$			4.26196e12i			0.0145739i
$783$	−2.31333e14	−	4.00681e14i	−0.786013	−	1.36141i
$784$	−1.37846e14	+	2.38755e14i	−0.465385	+	0.806071i
$785$	8.83860e13			0.296507
$786$	3.02535e11	+	1.74669e11i	0.00100847	+	0.000582240i
$787$	1.46168e13	+	2.53171e13i	0.0484150	+	0.0838572i	0.889217	−	0.457485i	$-0.151250\pi$
$787$	1.46168e13	+	2.53171e13i	0.0484150	+	0.0838572i	−0.840802	+	0.541342i	$0.817916\pi$
$788$	−1.77384e14	−	3.07237e14i	−0.583825	−	1.01121i
$789$	6.24075e13	+	1.08093e14i	0.204104	+	0.353519i
$790$	−2.15136e11			−0.000699163
$791$	5.32756e13	+	9.22761e13i	0.172047	+	0.297993i
$792$	1.15870e11	−	6.68976e10i	0.000371831	−	0.000214677i
$793$	8.14113e12	+	4.70028e12i	0.0259608	+	0.0149885i
$794$	−7.42094e11	−	4.28448e11i	−0.00235156	−	0.00135767i
$795$	−1.57092e14			−0.494673
$796$			4.16213e13i			0.130242i
$797$	−2.86544e13	+	4.96308e13i	−0.0891044	+	0.154333i	−0.907133	−	0.420844i	$-0.861734\pi$
$797$	−2.86544e13	+	4.96308e13i	−0.0891044	+	0.154333i	0.818028	+	0.575178i	$0.195067\pi$
$798$	−2.13539e11	+	3.69860e11i	−0.000659876	+	0.00114294i
$799$	1.56496e14	+	2.71059e14i	0.480584	+	0.832396i
$800$	5.88310e12	−	3.39661e12i	0.0179538	−	0.0103656i
$801$			1.04302e14i			0.316322i
$802$	−2.75673e12	+	1.59160e12i	−0.00830849	+	0.00479691i
$803$	−2.84860e13	+	1.64464e13i	−0.0853206	+	0.0492599i
$804$	−3.07339e14	+	1.77442e14i	−0.914822	+	0.528173i
$805$	−2.46746e13	+	4.27377e13i	−0.0729913	+	0.126425i
$806$		−	6.63911e10i		−	0.000195180i
$807$	−1.99238e14	−	1.15030e14i	−0.582108	−	0.336080i
$808$	7.99518e11	−	4.61602e11i	0.00232151	−	0.00134033i
$809$	1.25678e14			0.362674			0.181337	−	0.983421i	$-0.441958\pi$
$809$	1.25678e14			0.362674			0.181337	+	0.983421i	$0.441958\pi$
$810$	−3.71357e11	−	6.43210e11i	−0.00106504	−	0.00184471i
$811$	−3.24402e13	−	1.87294e13i	−0.0924655	−	0.0533850i	0.453054	−	0.891483i	$-0.350334\pi$
$811$	−3.24402e13	−	1.87294e13i	−0.0924655	−	0.0533850i	−0.545520	+	0.838098i	$0.683668\pi$
$812$	6.70579e13	−	1.16148e14i	0.189963	−	0.329026i
$813$			1.77668e14i			0.500216i
$814$	1.20505e11	−	2.08721e11i	0.000337197	−	0.000584042i
$815$	−1.14713e14			−0.319025
$816$			3.94667e14i			1.09089i
$817$	−2.30770e14	+	1.22449e14i	−0.633969	+	0.336391i
$818$	5.74157e12			0.0156770
$819$			5.57595e11i			0.00151321i
$820$	−4.09170e13	−	2.36235e13i	−0.110366	−	0.0637198i
$821$	6.31361e13			0.169263			0.0846314	−	0.996412i	$-0.473029\pi$
$821$	6.31361e13			0.169263			0.0846314	+	0.996412i	$0.473029\pi$
$822$	−1.52528e12	−	8.80623e11i	−0.00406435	−	0.00234656i
$823$	−1.98876e14	+	3.44463e14i	−0.526724	+	0.912313i	0.472791	+	0.881174i	$0.343246\pi$
$823$	−1.98876e14	+	3.44463e14i	−0.526724	+	0.912313i	−0.999515	+	0.0311380i	$0.990087\pi$
$824$	−4.83863e10	+	2.79359e10i	−0.000127376	+	7.35404e-5i
$825$			2.36583e13i			0.0619033i
$826$	2.95472e11	+	5.11773e11i	0.000768451	+	0.00133100i
$827$	1.57531e12	−	2.72851e12i	0.00407228	−	0.00705340i	−0.863982	−	0.503523i	$-0.832037\pi$
$827$	1.57531e12	−	2.72851e12i	0.00407228	−	0.00705340i	0.868054	+	0.496469i	$0.165370\pi$
$828$	1.53448e14			0.394284
$829$	−3.35357e14	−	1.93618e14i	−0.856514	−	0.494509i	0.00632904	−	0.999980i	$-0.497985\pi$
$829$	−3.35357e14	−	1.93618e14i	−0.856514	−	0.494509i	−0.862844	+	0.505471i	$0.831319\pi$
$830$	−1.65590e11	−	2.86811e11i	−0.000420383	−	0.000728124i
$831$	3.66570e13	+	6.34917e13i	0.0925021	+	0.160218i
$832$	3.93402e12	+	6.81392e12i	0.00986778	+	0.0170915i
$833$	4.84080e14			1.20696
$834$	6.54203e11	+	1.13311e12i	0.00162137	+	0.00280829i
$835$	2.23635e13	−	1.29116e13i	0.0550944	−	0.0318088i
$836$	2.24612e13	+	1.29680e13i	0.0550049	+	0.0317571i
$837$	−4.59756e14	−	2.65440e14i	−1.11918	−	0.646159i
$838$	−1.52647e12			−0.00369375
$839$			2.84222e14i			0.683673i	0.939759	+	0.341837i	$0.111049\pi$
$839$			2.84222e14i			0.683673i	−0.939759	+	0.341837i	$0.888951\pi$
$840$	3.16074e11	−	5.47456e11i	0.000755774	−	0.00130904i
$841$	2.29521e14	−	3.97542e14i	0.545560	−	0.944937i
$842$	−6.99033e10	−	1.21076e11i	−0.000165172	−	0.000286087i
$843$	3.35503e14	−	1.93703e14i	0.788060	−	0.454986i
$844$		−	3.47273e14i		−	0.810884i
$845$	−1.53283e14	+	8.84982e13i	−0.355805	+	0.205424i
$846$	−6.74927e11	+	3.89670e11i	−0.00155742	+	0.000899176i
$847$	9.84176e13	−	5.68214e13i	0.225765	−	0.130345i
$848$	−3.13485e14	+	5.42972e14i	−0.714888	+	1.23822i
$849$		−	4.38134e14i		−	0.993272i
$850$	−3.44294e12	−	1.98778e12i	−0.00775952	−	0.00447996i
$851$	4.78775e14	−	2.76421e14i	1.07271	−	0.619331i
$852$	−4.66764e14			−1.03968
$853$	2.80603e14	+	4.86019e14i	0.621366	+	1.07624i	0.989232	+	0.146358i	$0.0467553\pi$
$853$	2.80603e14	+	4.86019e14i	0.621366	+	1.07624i	−0.367866	+	0.929879i	$0.619911\pi$
$854$	−1.30504e12	−	7.53467e11i	−0.00287300	−	0.00165873i
$855$	−1.96569e13	+	3.40468e13i	−0.0430214	+	0.0745153i
$856$		−	1.20137e13i		−	0.0261401i
$857$	2.52322e14	−	4.37034e14i	0.545822	−	0.945391i	−0.452733	−	0.891646i	$-0.649551\pi$
$857$	2.52322e14	−	4.37034e14i	0.545822	−	0.945391i	0.998555	−	0.0537448i	$-0.0171157\pi$
$858$	5.68653e9			1.22296e−5
$859$		−	2.30854e14i		−	0.493597i	−0.969067	−	0.246798i	$-0.920621\pi$
$859$		−	2.30854e14i		−	0.493597i	0.969067	−	0.246798i	$-0.0793786\pi$
$860$	1.70783e14	−	9.06194e13i	0.363039	−	0.192632i
$861$	3.24452e13			0.0685701
$862$		−	2.02068e12i		−	0.00424581i
$863$	3.95421e14	+	2.28296e14i	0.826048	+	0.476919i	0.852498	−	0.522731i	$-0.175087\pi$
$863$	3.95421e14	+	2.28296e14i	0.826048	+	0.476919i	−0.0264493	+	0.999650i	$0.508420\pi$
$864$	−1.30565e13			−0.0271180
$865$	−1.08436e14	−	6.26058e13i	−0.223921	−	0.129281i
$866$	−1.09566e12	+	1.89774e12i	−0.00224950	+	0.00389626i
$867$	2.43088e14	−	1.40347e14i	0.496212	−	0.286488i
$868$		−	1.53889e14i		−	0.312327i
$869$	−4.48597e12	−	7.76992e12i	−0.00905226	−	0.0156790i
$870$	1.03663e12	−	1.79549e12i	0.00207982	−	0.00360235i
$871$	1.24236e13			0.0247831
$872$	−7.83621e12	−	4.52424e12i	−0.0155426	−	0.00897353i
$873$	−8.15454e13	−	1.41241e14i	−0.160816	−	0.278541i
$874$	−2.05721e12	−	3.56319e12i	−0.00403387	−	0.00698686i
$875$	−5.07115e13	−	8.78349e13i	−0.0988704	−	0.171249i
$876$	4.83236e14			0.936782
$877$	−9.81809e13	−	1.70054e14i	−0.189247	−	0.327785i	0.755752	−	0.654857i	$-0.227271\pi$
$877$	−9.81809e13	−	1.70054e14i	−0.189247	−	0.327785i	−0.944999	+	0.327072i	$0.893938\pi$
$878$	−5.33893e12	+	3.08243e12i	−0.0102325	+	0.00590773i
$879$	6.33950e14	+	3.66011e14i	1.20812	+	0.697509i
$880$	−1.66215e13	−	9.59640e12i	−0.0314960	−	0.0181842i
$881$	4.55542e14			0.858320			0.429160	−	0.903229i	$-0.358810\pi$
$881$	4.55542e14			0.858320			0.429160	+	0.903229i	$0.358810\pi$
$882$			1.20534e12i			0.00225823i
$883$	4.81856e14	−	8.34600e14i	0.897665	−	1.55480i	0.0671929	−	0.997740i	$-0.478596\pi$
$883$	4.81856e14	−	8.34600e14i	0.897665	−	1.55480i	0.830472	−	0.557061i	$-0.188071\pi$
$884$	6.90861e12	−	1.19661e13i	0.0127976	−	0.0221661i
$885$	−6.60461e13	−	1.14395e14i	−0.121655	−	0.210713i
$886$	2.08442e12	−	1.20344e12i	0.00381784	−	0.00220423i
$887$		−	2.46547e14i		−	0.449037i	−0.974470	−	0.224519i	$-0.927919\pi$
$887$		−	2.46547e14i		−	0.449037i	0.974470	−	0.224519i	$-0.0720810\pi$
$888$	−6.13295e12	+	3.54086e12i	−0.0111072	+	0.00641275i
$889$	−2.44736e13	+	1.41299e13i	−0.0440747	+	0.0254466i
$890$	−1.79241e12	+	1.03485e12i	−0.00320987	+	0.00185322i
$891$	1.54869e13	−	2.68241e13i	0.0275788	−	0.0477679i
$892$			5.29794e13i			0.0938173i
$893$	−2.61676e14	−	1.51078e14i	−0.460793	−	0.266039i
$894$	2.59759e12	−	1.49972e12i	0.00454866	−	0.00262617i
$895$	1.14675e14			0.199688
$896$	−2.52314e12	−	4.37021e12i	−0.00436919	−	0.00756766i
$897$	1.12965e13	+	6.52202e12i	0.0194527	+	0.0112310i
$898$	4.28735e12	−	7.42590e12i	0.00734187	−	0.0127165i
$899$		−	1.00945e15i		−	1.71905i
$900$	−7.15682e13	+	1.23960e14i	−0.121201	+	0.209927i
$901$	1.10088e15			1.85403
$902$			1.36266e11i			0.000228221i
$903$	−7.04521e13	+	1.12532e14i	−0.117343	+	0.187430i
$904$	1.31492e13			0.0217799
$905$		−	1.12451e14i		−	0.185234i
$906$	−5.14434e12	−	2.97008e12i	−0.00842730	−	0.00486550i
$907$	−9.40014e14			−1.53143			−0.765717	−	0.643178i	$-0.777615\pi$
$907$	−9.40014e14			−1.53143			−0.765717	+	0.643178i	$0.777615\pi$
$908$	−4.09374e14	−	2.36352e14i	−0.663270	−	0.382939i
$909$	−1.45894e13	+	2.52696e13i	−0.0235082	+	0.0407173i
$910$	−9.58217e9	+	5.53227e9i	−1.53553e−5	+	8.86536e-6i
$911$			7.37044e14i			1.17463i	0.809358	+	0.587316i	$0.199815\pi$
$911$			7.37044e14i			1.17463i	−0.809358	+	0.587316i	$0.800185\pi$
$912$	−1.90502e14	−	3.29959e14i	−0.301943	−	0.522981i
$913$	6.90569e12	−	1.19610e13i	0.0108856	−	0.0188545i
$914$	−3.44951e12			−0.00540787
$915$	2.91712e14	+	1.68420e14i	0.454830	+	0.262596i
$916$	6.10957e14	+	1.05821e15i	0.947400	+	1.64094i
$917$	−1.41734e13	−	2.45490e13i	−0.0218588	−	0.0378606i
$918$	3.82049e12	+	6.61728e12i	0.00586011	+	0.0101500i
$919$	−7.17113e14			−1.09398			−0.546991	−	0.837139i	$-0.684227\pi$
$919$	−7.17113e14			−1.09398			−0.546991	+	0.837139i	$0.684227\pi$
$920$	3.04502e12	+	5.27413e12i	0.00462010	+	0.00800225i
$921$	5.00648e14	−	2.89049e14i	0.755499	−	0.436188i
$922$	5.81794e12	+	3.35899e12i	0.00873201	+	0.00504143i
$923$	1.41510e13	+	8.17010e12i	0.0211242	+	0.0121960i
$924$	1.31809e13			0.0195698
$925$			5.15692e14i			0.761521i
$926$	−2.52303e11	+	4.37002e11i	−0.000370568	+	0.000641843i
$927$	8.82943e11	−	1.52930e12i	0.00128983	−	0.00223406i
$928$	−1.24133e13	−	2.15004e13i	−0.0180363	−	0.0312397i
$929$	−5.63871e14	+	3.25551e14i	−0.814895	+	0.470480i	−0.848653	−	0.528950i	$-0.822586\pi$
$929$	−5.63871e14	+	3.25551e14i	−0.814895	+	0.470480i	0.0337580	+	0.999430i	$0.489252\pi$
$930$		−	2.37892e12i		−	0.00341952i
$931$	−4.04713e14	+	2.33661e14i	−0.578627	+	0.334070i
$932$	−6.65059e14	+	3.83972e14i	−0.945759	+	0.546034i
$933$	5.84336e14	−	3.37367e14i	0.826522	−	0.477193i
$934$	−1.21192e12	+	2.09912e12i	−0.00170507	+	0.00295326i
$935$			3.37002e13i			0.0471601i
$936$	5.95922e10	+	3.44056e10i	8.29488e−5	+	4.78905e-5i
$937$	−1.70405e14	+	9.83833e13i	−0.235930	+	0.136214i	−0.613305	−	0.789846i	$-0.710160\pi$
$937$	−1.70405e14	+	9.83833e13i	−0.235930	+	0.136214i	0.377374	+	0.926061i	$0.376827\pi$
$938$	−1.99153e12			−0.00274266
$939$	3.53610e13	+	6.12470e13i	0.0484391	+	0.0838990i
$940$	1.93656e14	+	1.11807e14i	0.263870	+	0.152346i
$941$	4.39645e13	−	7.61487e13i	0.0595873	−	0.103208i	−0.834693	−	0.550716i	$-0.814355\pi$
$941$	4.39645e13	−	7.61487e13i	0.0595873	−	0.103208i	0.894280	+	0.447507i	$0.147688\pi$
$942$			3.74503e12i			0.00504895i
$943$	−1.56287e14	+	2.70697e14i	−0.209587	+	0.363015i
$944$	−5.27193e14			−0.703250
$945$			8.84749e13i			0.117398i
$946$	−4.72622e11	−	2.95891e11i	−0.000623819	−	0.000390549i
$947$	−1.33358e15			−1.75093			−0.875466	−	0.483280i	$-0.839445\pi$
$947$	−1.33358e15			−1.75093			−0.875466	+	0.483280i	$0.839445\pi$
$948$			1.31809e14i			0.172148i
$949$	−1.46504e13	−	8.45842e12i	−0.0190335	−	0.0109890i
$950$	3.83794e12			0.00495998
$951$	9.47385e14	+	5.46973e14i	1.21793	+	0.703175i
$952$	−2.21501e12	+	3.83651e12i	−0.00283264	+	0.00490627i
$953$	−5.26098e14	+	3.03743e14i	−0.669271	+	0.386404i	−0.795800	−	0.605559i	$-0.792950\pi$
$953$	−5.26098e14	+	3.03743e14i	−0.669271	+	0.386404i	0.126529	+	0.991963i	$0.459616\pi$
$954$			2.74116e12i			0.00346891i
$955$	−9.58760e13	−	1.66062e14i	−0.120696	−	0.209052i
$956$	2.88791e14	−	5.00201e14i	0.361655	−	0.626404i
$957$	8.64618e13			0.107712
$958$	−4.21832e12	−	2.43545e12i	−0.00522771	−	0.00301822i
$959$	7.14576e13	+	1.23768e14i	0.0880958	+	0.152586i
$960$	1.40963e14	+	2.44156e14i	0.172882	+	0.299441i
$961$	−1.69328e14	−	2.93284e14i	−0.206591	−	0.357826i
$962$	1.23952e11			0.000150445
$963$	1.89853e14	+	3.28835e14i	0.229238	+	0.397051i
$964$	−3.64623e14	+	2.10515e14i	−0.437984	+	0.252870i
$965$	−1.79625e14	−	1.03707e14i	−0.214650	−	0.123928i
$966$	−1.81085e12	−	1.04550e12i	−0.00215277	−	0.00124290i
$967$	−9.77710e14			−1.15632			−0.578160	−	0.815924i	$-0.696229\pi$
$967$	−9.77710e14			−1.15632			−0.578160	+	0.815924i	$0.696229\pi$
$968$		−	1.40243e13i		−	0.0165008i
$969$	−3.34498e14	+	5.79368e14i	−0.391539	+	0.678166i
$970$	1.61813e12	−	2.80269e12i	0.00188432	−	0.00326374i
$971$	−1.48496e14	−	2.57203e14i	−0.172036	−	0.297975i	0.767096	−	0.641533i	$-0.221701\pi$
$971$	−1.48496e14	−	2.57203e14i	−0.172036	−	0.297975i	−0.939131	+	0.343558i	$0.888368\pi$
$972$	4.22696e14	−	2.44044e14i	0.487188	−	0.281278i
$973$		−	1.06170e14i		−	0.121741i
$974$	1.11687e13	−	6.44827e12i	0.0127412	−	0.00735612i
$975$	−1.05374e13	+	6.08376e12i	−0.0119594	+	0.00690476i
$976$	1.16425e15	−	6.72183e14i	1.31462	−	0.758994i
$977$	−4.79774e14	+	8.30993e14i	−0.538969	+	0.933523i	0.459990	+	0.887924i	$0.347853\pi$
$977$	−4.79774e14	+	8.30993e14i	−0.538969	+	0.933523i	−0.998960	+	0.0455986i	$0.985480\pi$
$978$		−	4.86054e12i		−	0.00543238i
$979$	−7.47497e13	−	4.31567e13i	−0.0831181	−	0.0479883i
$980$	2.99512e14	−	1.72923e14i	0.331347	−	0.191303i
$981$	2.85987e14			0.314776
$982$	5.86983e12	+	1.01668e13i	0.00642789	+	0.0111334i
$983$	2.25111e14	+	1.29968e14i	0.245261	+	0.141602i	0.617592	−	0.786498i	$-0.288108\pi$
$983$	2.25111e14	+	1.29968e14i	0.245261	+	0.141602i	−0.372331	+	0.928100i	$0.621441\pi$
$984$	2.00198e12	−	3.46754e12i	0.00217013	−	0.00375877i
$985$			4.45014e14i			0.479946i
$986$	−7.26456e12	+	1.25826e13i	−0.00779516	+	0.0135016i
$987$	−1.53559e14			−0.163942
$988$			1.33389e13i			0.0141689i
$989$	−5.99515e14	−	1.12986e15i	−0.633605	−	1.19411i
$990$	−8.39124e10			−8.82369e−5
$991$		−	1.08746e14i		−	0.113775i	−0.998381	−	0.0568874i	$-0.981882\pi$
$991$		−	1.08746e14i		−	0.113775i	0.998381	−	0.0568874i	$-0.0181176\pi$
$992$	−2.46703e13	−	1.42434e13i	−0.0256813	−	0.0148271i
$993$	−4.15616e14			−0.430474
$994$	−2.26844e12	−	1.30969e12i	−0.00233774	−	0.00134969i
$995$	2.61046e13	−	4.52144e13i	0.0267671	−	0.0463619i
$996$	−1.75722e14	+	1.01453e14i	−0.179279	+	0.103507i
$997$		−	3.66687e14i		−	0.372237i	−0.982527	−	0.186118i	$-0.940409\pi$
$997$		−	3.66687e14i		−	0.372237i	0.982527	−	0.186118i	$-0.0595908\pi$
$998$	4.41570e12	+	7.64822e12i	0.00446013	+	0.00772517i
$999$	4.95576e14	−	8.58363e14i	0.498062	−	0.862668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.d.a.37.19	yes	72
43.7	odd	6	inner	43.11.d.a.7.18	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.d.a.7.18	✓	72	43.7	odd	6	inner
43.11.d.a.37.19	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)

\(f(q)\)	\(=\)	\(q+0.266107i q^{2} +(-177.112 - 102.255i) q^{3} +1023.93 q^{4} +(-1112.32 - 642.200i) q^{5} +(27.2109 - 47.1306i) q^{6} +(-3824.38 + 2208.01i) q^{7} +544.968i q^{8} +(-8612.15 - 14916.7i) q^{9} +O(q^{10})\)	\(q+0.266107i q^{2} +(-177.112 - 102.255i) q^{3} +1023.93 q^{4} +(-1112.32 - 642.200i) q^{5} +(27.2109 - 47.1306i) q^{6} +(-3824.38 + 2208.01i) q^{7} +544.968i q^{8} +(-8612.15 - 14916.7i) q^{9} +(170.894 - 295.997i) q^{10} +14253.7 q^{11} +(-181350. - 104702. i) q^{12} +(3665.36 + 6348.59i) q^{13} +(-587.566 - 1017.69i) q^{14} +(131337. + 227482. i) q^{15} +1.04836e6 q^{16} +(-920395. - 1.59417e6i) q^{17} +(3969.43 - 2291.75i) q^{18} +(1.53898e6 + 888533. i) q^{19} +(-1.13894e6 - 657567. i) q^{20} +903123. q^{21} +3793.01i q^{22} +(-4.35030e6 + 7.53494e6i) q^{23} +(55725.9 - 96520.1i) q^{24} +(-4.05797e6 - 7.02861e6i) q^{25} +(-1689.40 + 975.377i) q^{26} +1.55987e7i q^{27} +(-3.91590e6 + 2.26084e6i) q^{28} +(-2.56868e7 + 1.48303e7i) q^{29} +(-60534.5 + 34949.6i) q^{30} +(-1.70168e7 + 2.94739e7i) q^{31} +837022. i q^{32} +(-2.52450e6 - 1.45752e6i) q^{33} +(424219. - 244923. i) q^{34} +5.67193e6 q^{35} +(-8.81823e6 - 1.52736e7i) q^{36} +(-5.50278e7 - 3.17703e7i) q^{37} +(-236445. + 409534. i) q^{38} -1.49921e6i q^{39} +(349978. - 606180. i) q^{40} +3.59255e7 q^{41} +240327. i q^{42} +(-7.80094e7 + 1.24603e8i) q^{43} +1.45948e7 q^{44} +2.21229e7i q^{45} +(-2.00510e6 - 1.15764e6i) q^{46} -1.70031e8 q^{47} +(-1.85676e8 - 1.07200e8i) q^{48} +(-1.31487e8 + 2.27742e8i) q^{49} +(1.87036e6 - 1.07985e6i) q^{50} +3.76461e8i q^{51} +(3.75307e6 + 6.50050e6i) q^{52} +(-2.99025e8 + 5.17926e8i) q^{53} -4.15092e6 q^{54} +(-1.58547e7 - 9.15374e6i) q^{55} +(-1.20329e6 - 2.08416e6i) q^{56} +(-1.81715e8 - 3.14739e8i) q^{57} +(-3.94644e6 - 6.83543e6i) q^{58} -5.02875e8 q^{59} +(1.34480e8 + 2.32926e8i) q^{60} +(1.11055e9 - 6.41176e8i) q^{61} +(-7.84321e6 - 4.52828e6i) q^{62} +(6.58723e7 + 3.80314e7i) q^{63} +1.07330e9 q^{64} -9.41557e6i q^{65} +(387856. - 671787. i) q^{66} +(8.47364e8 - 1.46768e9i) q^{67} +(-9.42419e8 - 1.63232e9i) q^{68} +(1.54098e9 - 8.89684e8i) q^{69} +1.50934e6i q^{70} +(1.93037e9 - 1.11450e9i) q^{71} +(8.12911e6 - 4.69334e6i) q^{72} +(-1.99850e9 + 1.15383e9i) q^{73} +(8.45430e6 - 1.46433e7i) q^{74} +1.65980e9i q^{75} +(1.57581e9 + 9.09795e8i) q^{76} +(-5.45117e7 + 3.14723e7i) q^{77} +398950. q^{78} +(-3.14722e8 - 5.45115e8i) q^{79} +(-1.16611e9 - 6.73256e8i) q^{80} +(1.08652e9 - 1.88190e9i) q^{81} +9.56003e6i q^{82} +(4.84483e8 - 8.39150e8i) q^{83} +9.24734e8 q^{84} +2.36431e9i q^{85} +(-3.31578e7 - 2.07588e7i) q^{86} +6.06591e9 q^{87} +7.76782e6i q^{88} +(-5.24422e9 - 3.02775e9i) q^{89} -5.88705e6 q^{90} +(-2.80355e7 - 1.61863e7i) q^{91} +(-4.45440e9 + 7.71525e9i) q^{92} +(6.02774e9 - 3.48012e9i) q^{93} -4.52465e7i q^{94} +(-1.14123e9 - 1.97667e9i) q^{95} +(8.55901e7 - 1.48246e8i) q^{96} +9.46864e9 q^{97} +(-6.06037e7 - 3.49896e7i) q^{98} +(-1.22755e8 - 2.12618e8i) 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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