LMFDB - Embedded newform 966.2.q.i.169.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.4
Character	$\chi$	$=$	966.169
Dual form			966.2.q.i.463.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.39800 + 2.76744i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.39800 + 2.76744i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-3.08054 + 1.97974i) q^{10} +(-0.108460 - 0.754355i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(-0.436975 + 0.280827i) q^{13} +(-0.654861 + 0.755750i) q^{14} +(-1.52119 + 3.33093i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-6.86156 + 2.01474i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(5.98820 + 1.75829i) q^{19} +(-1.52119 - 3.33093i) q^{20} +(-0.142315 + 0.989821i) q^{21} +0.762112 q^{22} +(-1.59862 + 4.52155i) q^{23} +1.00000 q^{24} +(-1.19674 + 8.32354i) q^{25} +(-0.215780 - 0.472493i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(-0.654861 - 0.755750i) q^{28} +(3.14018 - 0.922039i) q^{29} +(-3.08054 - 1.97974i) q^{30} +(1.74594 - 3.82308i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(0.641129 - 0.412029i) q^{33} +(-1.01773 - 7.07845i) q^{34} +(0.521135 + 3.62458i) q^{35} +(0.841254 - 0.540641i) q^{36} +(3.97506 - 4.58747i) q^{37} +(-2.59261 + 5.67702i) q^{38} +(-0.436975 - 0.280827i) q^{39} +(3.51352 - 1.03166i) q^{40} +(-1.12807 - 1.30186i) q^{41} +(-0.959493 - 0.281733i) q^{42} +(0.540642 + 1.18384i) q^{43} +(-0.108460 + 0.754355i) q^{44} -3.66185 q^{45} +(-4.24802 - 2.22583i) q^{46} -5.35754 q^{47} +(-0.142315 + 0.989821i) q^{48} +(0.415415 + 0.909632i) q^{49} +(-8.06850 - 2.36913i) q^{50} +(-4.68306 - 5.40454i) q^{51} +(0.498392 - 0.146341i) q^{52} +(0.863075 + 0.554665i) q^{53} +(0.415415 - 0.909632i) q^{54} +(1.82754 - 2.10910i) q^{55} +(0.841254 - 0.540641i) q^{56} +(0.888187 + 6.17748i) q^{57} +(0.465760 + 3.23944i) q^{58} +(2.75528 - 1.77071i) q^{59} +(2.39800 - 2.76744i) q^{60} +(4.09668 - 8.97047i) q^{61} +(3.53569 + 2.27225i) q^{62} +(-0.959493 + 0.281733i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-1.82504 - 0.535879i) q^{65} +(0.316593 + 0.693241i) q^{66} +(-0.796863 + 5.54230i) q^{67} +7.15124 q^{68} +(-4.77704 + 0.424166i) q^{69} -3.66185 q^{70} +(-2.13016 + 14.8156i) q^{71} +(0.415415 + 0.909632i) q^{72} +(-14.9578 - 4.39202i) q^{73} +(3.97506 + 4.58747i) q^{74} +(-8.06850 + 2.36913i) q^{75} +(-5.25027 - 3.37414i) q^{76} +(0.316593 - 0.693241i) q^{77} +(0.340156 - 0.392561i) q^{78} +(-6.84738 + 4.40055i) q^{79} +(0.521135 + 3.62458i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(1.44915 - 0.931311i) q^{82} +(9.70967 - 11.2056i) q^{83} +(0.415415 - 0.909632i) q^{84} +(-22.0297 - 14.1576i) q^{85} +(-1.24873 + 0.366661i) q^{86} +(2.14319 + 2.47338i) q^{87} +(-0.731241 - 0.214712i) q^{88} +(-0.0160233 - 0.0350861i) q^{89} +(0.521135 - 3.62458i) q^{90} -0.519433 q^{91} +(2.80773 - 3.88801i) q^{92} +4.20288 q^{93} +(0.762458 - 5.30301i) q^{94} +(9.49373 + 20.7884i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(2.90219 + 3.34930i) q^{97} +(-0.959493 + 0.281733i) q^{98} +(0.641129 + 0.412029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 7 q^{15} - 4 q^{16} - 7 q^{17} - 4 q^{18} + 20 q^{19} - 7 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{23} + 40 q^{24} - 22 q^{25} + 14 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 4 q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 7 q^{34} - 7 q^{35} - 4 q^{36} - 16 q^{37} - 13 q^{38} - 8 q^{39} + 4 q^{40} - 17 q^{41} - 4 q^{42} + 26 q^{43} - q^{44} + 4 q^{45} - 20 q^{46} + 72 q^{47} - 4 q^{48} - 4 q^{49} + 11 q^{50} - 7 q^{51} - 19 q^{52} + 6 q^{53} - 4 q^{54} + 49 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} - 51 q^{59} + 4 q^{60} - 42 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{64} + 8 q^{65} - 12 q^{66} + 54 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{70} - 59 q^{71} - 4 q^{72} - 27 q^{73} - 16 q^{74} + 11 q^{75} - 2 q^{76} - 12 q^{77} - 8 q^{78} - 6 q^{79} - 7 q^{80} - 4 q^{81} - 6 q^{82} - 24 q^{83} - 4 q^{84} + 35 q^{85} - 7 q^{86} - 29 q^{87} - q^{88} + 22 q^{89} - 7 q^{90} + 36 q^{91} - 9 q^{92} + 50 q^{93} - 16 q^{94} + 22 q^{95} - 4 q^{96} + 16 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 7 * q^15 - 4 * q^16 - 7 * q^17 - 4 * q^18 + 20 * q^19 - 7 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^23 + 40 * q^24 - 22 * q^25 + 14 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 4 * q^30 - 16 * q^31 - 4 * q^32 - q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 - 16 * q^37 - 13 * q^38 - 8 * q^39 + 4 * q^40 - 17 * q^41 - 4 * q^42 + 26 * q^43 - q^44 + 4 * q^45 - 20 * q^46 + 72 * q^47 - 4 * q^48 - 4 * q^49 + 11 * q^50 - 7 * q^51 - 19 * q^52 + 6 * q^53 - 4 * q^54 + 49 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 - 51 * q^59 + 4 * q^60 - 42 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^64 + 8 * q^65 - 12 * q^66 + 54 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^70 - 59 * q^71 - 4 * q^72 - 27 * q^73 - 16 * q^74 + 11 * q^75 - 2 * q^76 - 12 * q^77 - 8 * q^78 - 6 * q^79 - 7 * q^80 - 4 * q^81 - 6 * q^82 - 24 * q^83 - 4 * q^84 + 35 * q^85 - 7 * q^86 - 29 * q^87 - q^88 + 22 * q^89 - 7 * q^90 + 36 * q^91 - 9 * q^92 + 50 * q^93 - 16 * q^94 + 22 * q^95 - 4 * q^96 + 16 * q^97 - 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	2.39800	+	2.76744i	1.07242	+	1.23764i	0.970054	+	0.242890i	$0.0780954\pi$
$5$	2.39800	+	2.76744i	1.07242	+	1.23764i	0.102365	+	0.994747i	$0.467359\pi$
$6$	−0.959493	+	0.281733i	−0.391711	+	0.115017i
$7$	0.841254	+	0.540641i	0.317964	+	0.204343i
$7$	0.841254	+	0.540641i	0.317964	+	0.204343i
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	−3.08054	+	1.97974i	−0.974153	+	0.626050i
$11$	−0.108460	−	0.754355i	−0.0327019	−	0.227446i	0.966916	−	0.255096i	$-0.0821070\pi$
$11$	−0.108460	−	0.754355i	−0.0327019	−	0.227446i	−0.999618	+	0.0276492i	$0.991198\pi$
$12$	−0.142315	−	0.989821i	−0.0410828	−	0.285737i
$13$	−0.436975	+	0.280827i	−0.121195	+	0.0778873i	−0.599834	−	0.800125i	$-0.704767\pi$
$13$	−0.436975	+	0.280827i	−0.121195	+	0.0778873i	0.478639	+	0.878012i	$0.341130\pi$
$14$	−0.654861	+	0.755750i	−0.175019	+	0.201983i
$15$	−1.52119	+	3.33093i	−0.392769	+	0.860044i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−6.86156	+	2.01474i	−1.66417	+	0.488645i	−0.972371	−	0.233442i	$-0.925001\pi$
$17$	−6.86156	+	2.01474i	−1.66417	+	0.488645i	−0.691802	+	0.722087i	$0.743183\pi$
$18$	−0.654861	−	0.755750i	−0.154352	−	0.178132i
$19$	5.98820	+	1.75829i	1.37379	+	0.403380i	0.883602	−	0.468238i	$-0.155111\pi$
$19$	5.98820	+	1.75829i	1.37379	+	0.403380i	0.490185	+	0.871619i	$0.336929\pi$
$20$	−1.52119	−	3.33093i	−0.340148	−	0.744820i
$21$	−0.142315	+	0.989821i	−0.0310556	+	0.215997i
$22$	0.762112			0.162483
$23$	−1.59862	+	4.52155i	−0.333335	+	0.942808i
$23$	−1.59862	+	4.52155i	−0.333335	+	0.942808i
$24$	1.00000			0.204124
$25$	−1.19674	+	8.32354i	−0.239349	+	1.66471i
$26$	−0.215780	−	0.472493i	−0.0423180	−	0.0926635i
$27$	−0.959493	−	0.281733i	−0.184655	−	0.0542195i
$28$	−0.654861	−	0.755750i	−0.123757	−	0.142823i
$29$	3.14018	−	0.922039i	0.583116	−	0.171218i	0.0231475	−	0.999732i	$-0.492631\pi$
$29$	3.14018	−	0.922039i	0.583116	−	0.171218i	0.559969	+	0.828514i	$0.310813\pi$
$30$	−3.08054	−	1.97974i	−0.562428	−	0.361450i
$31$	1.74594	−	3.82308i	0.313580	−	0.686645i	−0.685564	−	0.728012i	$-0.740444\pi$
$31$	1.74594	−	3.82308i	0.313580	−	0.686645i	0.999144	+	0.0413678i	$0.0131716\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	0.641129	−	0.412029i	0.111606	−	0.0717250i
$34$	−1.01773	−	7.07845i	−0.174539	−	1.21394i
$35$	0.521135	+	3.62458i	0.0880880	+	0.612665i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	3.97506	−	4.58747i	0.653496	−	0.754175i	−0.328204	−	0.944607i	$-0.606443\pi$
$37$	3.97506	−	4.58747i	0.653496	−	0.754175i	0.981700	+	0.190432i	$0.0609889\pi$
$38$	−2.59261	+	5.67702i	−0.420576	+	0.920934i
$39$	−0.436975	−	0.280827i	−0.0699720	−	0.0449683i
$40$	3.51352	−	1.03166i	0.555536	−	0.163120i
$41$	−1.12807	−	1.30186i	−0.176175	−	0.203316i	0.660794	−	0.750567i	$-0.270220\pi$
$41$	−1.12807	−	1.30186i	−0.176175	−	0.203316i	−0.836968	+	0.547251i	$0.815674\pi$
$42$	−0.959493	−	0.281733i	−0.148053	−	0.0434723i
$43$	0.540642	+	1.18384i	0.0824472	+	0.180534i	0.946366	−	0.323097i	$-0.104724\pi$
$43$	0.540642	+	1.18384i	0.0824472	+	0.180534i	−0.863918	+	0.503632i	$0.831997\pi$
$44$	−0.108460	+	0.754355i	−0.0163509	+	0.113723i
$45$	−3.66185			−0.545876
$46$	−4.24802	−	2.22583i	−0.626336	−	0.328181i
$47$	−5.35754			−0.781478			−0.390739	−	0.920501i	$-0.627781\pi$
$47$	−5.35754			−0.781478			−0.390739	+	0.920501i	$0.627781\pi$
$48$	−0.142315	+	0.989821i	−0.0205414	+	0.142868i
$49$	0.415415	+	0.909632i	0.0593450	+	0.129947i
$50$	−8.06850	−	2.36913i	−1.14106	−	0.335045i
$51$	−4.68306	−	5.40454i	−0.655760	−	0.756788i
$52$	0.498392	−	0.146341i	0.0691146	−	0.0202939i
$53$	0.863075	+	0.554665i	0.118552	+	0.0761890i	0.598573	−	0.801068i	$-0.295735\pi$
$53$	0.863075	+	0.554665i	0.118552	+	0.0761890i	−0.480021	+	0.877257i	$0.659371\pi$
$54$	0.415415	−	0.909632i	0.0565308	−	0.123785i
$55$	1.82754	−	2.10910i	0.246426	−	0.284391i
$56$	0.841254	−	0.540641i	0.112417	−	0.0722462i
$57$	0.888187	+	6.17748i	0.117643	+	0.818227i
$58$	0.465760	+	3.23944i	0.0611573	+	0.425359i
$59$	2.75528	−	1.77071i	0.358707	−	0.230527i	−0.348858	−	0.937176i	$-0.613430\pi$
$59$	2.75528	−	1.77071i	0.358707	−	0.230527i	0.707564	+	0.706649i	$0.249794\pi$
$60$	2.39800	−	2.76744i	0.309581	−	0.357275i
$61$	4.09668	−	8.97047i	0.524526	−	1.14855i	−0.443171	−	0.896437i	$-0.646147\pi$
$61$	4.09668	−	8.97047i	0.524526	−	1.14855i	0.967697	−	0.252115i	$-0.0811260\pi$
$62$	3.53569	+	2.27225i	0.449033	+	0.288576i
$63$	−0.959493	+	0.281733i	−0.120885	+	0.0354950i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−1.82504	−	0.535879i	−0.226368	−	0.0664676i
$66$	0.316593	+	0.693241i	0.0389699	+	0.0853321i
$67$	−0.796863	+	5.54230i	−0.0973523	+	0.677100i	0.881448	+	0.472282i	$0.156569\pi$
$67$	−0.796863	+	5.54230i	−0.0973523	+	0.677100i	−0.978800	+	0.204818i	$0.934340\pi$
$68$	7.15124			0.867215
$69$	−4.77704	+	0.424166i	−0.575088	+	0.0510636i
$70$	−3.66185			−0.437675
$71$	−2.13016	+	14.8156i	−0.252803	+	1.75828i	0.328412	+	0.944535i	$0.393487\pi$
$71$	−2.13016	+	14.8156i	−0.252803	+	1.75828i	−0.581215	+	0.813750i	$0.697423\pi$
$72$	0.415415	+	0.909632i	0.0489571	+	0.107201i
$73$	−14.9578	−	4.39202i	−1.75068	−	0.514047i	−0.759963	−	0.649966i	$-0.774783\pi$
$73$	−14.9578	−	4.39202i	−1.75068	−	0.514047i	−0.990720	+	0.135920i	$0.956601\pi$
$74$	3.97506	+	4.58747i	0.462092	+	0.533282i
$75$	−8.06850	+	2.36913i	−0.931671	+	0.273563i
$76$	−5.25027	−	3.37414i	−0.602247	−	0.387041i
$77$	0.316593	−	0.693241i	0.0360791	−	0.0790022i
$78$	0.340156	−	0.392561i	0.0385151	−	0.0444488i
$79$	−6.84738	+	4.40055i	−0.770391	+	0.495100i	−0.865832	−	0.500335i	$-0.833210\pi$
$79$	−6.84738	+	4.40055i	−0.770391	+	0.495100i	0.0954412	+	0.995435i	$0.469574\pi$
$80$	0.521135	+	3.62458i	0.0582647	+	0.405240i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	1.44915	−	0.931311i	0.160032	−	0.102846i
$83$	9.70967	−	11.2056i	1.06577	−	1.22997i	0.0936251	−	0.995608i	$-0.470154\pi$
$83$	9.70967	−	11.2056i	1.06577	−	1.22997i	0.972149	−	0.234362i	$-0.0753001\pi$
$84$	0.415415	−	0.909632i	0.0453255	−	0.0992490i
$85$	−22.0297	−	14.1576i	−2.38946	−	1.53561i
$86$	−1.24873	+	0.366661i	−0.134654	+	0.0395381i
$87$	2.14319	+	2.47338i	0.229774	+	0.265174i
$88$	−0.731241	−	0.214712i	−0.0779505	−	0.0228883i
$89$	−0.0160233	−	0.0350861i	−0.00169847	−	0.00371912i	0.908781	−	0.417274i	$-0.137014\pi$
$89$	−0.0160233	−	0.0350861i	−0.00169847	−	0.00371912i	−0.910479	+	0.413555i	$0.864287\pi$
$90$	0.521135	−	3.62458i	0.0549325	−	0.382064i
$91$	−0.519433			−0.0544514
$92$	2.80773	−	3.88801i	0.292726	−	0.405353i
$93$	4.20288			0.435819
$94$	0.762458	−	5.30301i	0.0786415	−	0.546964i
$95$	9.49373	+	20.7884i	0.974036	+	2.13284i
$96$	−0.959493	−	0.281733i	−0.0979278	−	0.0287542i
$97$	2.90219	+	3.34930i	0.294673	+	0.340070i	0.883709	−	0.468036i	$-0.155038\pi$
$97$	2.90219	+	3.34930i	0.294673	+	0.340070i	−0.589037	+	0.808106i	$0.700493\pi$
$98$	−0.959493	+	0.281733i	−0.0969234	+	0.0284593i
$99$	0.641129	+	0.412029i	0.0644359	+	0.0414104i
$100$	3.49328	−	7.64922i	0.349328	−	0.764922i
$101$	3.41482	−	3.94092i	0.339788	−	0.392136i	−0.559979	−	0.828507i	$-0.689191\pi$
$101$	3.41482	−	3.94092i	0.339788	−	0.392136i	0.899767	+	0.436371i	$0.143736\pi$
$102$	6.01600	−	3.86625i	0.595673	−	0.382816i
$103$	0.462117	+	3.21410i	0.0455338	+	0.316694i	0.999840	+	0.0178652i	$0.00568698\pi$
$103$	0.462117	+	3.21410i	0.0455338	+	0.316694i	−0.954307	+	0.298829i	$0.903404\pi$
$104$	0.0739230	+	0.514146i	0.00724875	+	0.0504162i
$105$	−3.08054	+	1.97974i	−0.300630	+	0.193203i
$106$	−0.671847	+	0.775353i	−0.0652556	+	0.0753089i
$107$	−6.51100	+	14.2571i	−0.629442	+	1.37828i	0.279007	+	0.960289i	$0.409995\pi$
$107$	−6.51100	+	14.2571i	−0.629442	+	1.37828i	−0.908449	+	0.417996i	$0.862733\pi$
$108$	0.841254	+	0.540641i	0.0809497	+	0.0520232i
$109$	8.59890	−	2.52487i	0.823626	−	0.241838i	0.157349	−	0.987543i	$-0.449705\pi$
$109$	8.59890	−	2.52487i	0.823626	−	0.241838i	0.666277	+	0.745705i	$0.267887\pi$
$110$	1.82754	+	2.10910i	0.174250	+	0.201095i
$111$	5.82421	+	1.71014i	0.552809	+	0.162319i
$112$	0.415415	+	0.909632i	0.0392530	+	0.0859521i
$113$	1.95492	−	13.5968i	0.183904	−	1.27908i	−0.663519	−	0.748159i	$-0.730938\pi$
$113$	1.95492	−	13.5968i	0.183904	−	1.27908i	0.847423	−	0.530919i	$-0.178153\pi$
$114$	−6.24100			−0.584524
$115$	−16.3466	+	6.41860i	−1.52433	+	0.598538i
$116$	−3.27275			−0.303867
$117$	0.0739230	−	0.514146i	0.00683419	−	0.0475328i
$118$	1.36057	+	2.97923i	0.125251	+	0.274261i
$119$	−6.86156	−	2.01474i	−0.628998	−	0.184691i
$120$	2.39800	+	2.76744i	0.218907	+	0.252632i
$121$	9.99714	−	2.93542i	0.908830	−	0.266857i
$122$	8.29615	+	5.33161i	0.751098	+	0.482701i
$123$	0.715597	−	1.56694i	0.0645232	−	0.141286i
$124$	−2.75230	+	3.17633i	−0.247164	+	0.285242i
$125$	−10.5020	+	6.74921i	−0.939326	+	0.603668i
$126$	−0.142315	−	0.989821i	−0.0126784	−	0.0881803i
$127$	−2.63745	−	18.3439i	−0.234036	−	1.62776i	−0.680356	−	0.732882i	$-0.738175\pi$
$127$	−2.63745	−	18.3439i	−0.234036	−	1.62776i	0.446320	−	0.894873i	$-0.352734\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	−0.852269	+	0.983571i	−0.0750381	+	0.0865986i
$130$	0.790155	−	1.73020i	0.0693012	−	0.151748i
$131$	9.25638	+	5.94872i	0.808734	+	0.519742i	0.878455	−	0.477825i	$-0.158575\pi$
$131$	9.25638	+	5.94872i	0.808734	+	0.519742i	−0.0697212	+	0.997567i	$0.522211\pi$
$132$	−0.731241	+	0.214712i	−0.0636464	+	0.0186883i
$133$	4.08699	+	4.71664i	0.354387	+	0.408984i
$134$	−5.37248	−	1.57750i	−0.464112	−	0.136276i
$135$	−1.52119	−	3.33093i	−0.130923	−	0.286681i
$136$	−1.01773	+	7.07845i	−0.0872694	+	0.606972i
$137$	11.8199			1.00984			0.504920	−	0.863166i	$-0.331522\pi$
$137$	11.8199			1.00984			0.504920	+	0.863166i	$0.331522\pi$
$138$	0.259995	−	4.78878i	0.0221322	−	0.407648i
$139$	5.72696			0.485754			0.242877	−	0.970057i	$-0.421909\pi$
$139$	5.72696			0.485754			0.242877	+	0.970057i	$0.421909\pi$
$140$	0.521135	−	3.62458i	0.0440440	−	0.306333i
$141$	−2.22560	−	4.87339i	−0.187430	−	0.410414i
$142$	−14.3616	−	4.21695i	−1.20520	−	0.353879i
$143$	0.259237	+	0.299176i	0.0216785	+	0.0250183i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	10.0818	+	6.47920i	0.837251	+	0.538069i
$146$	6.47604	−	14.1805i	0.535961	−	1.17359i
$147$	−0.654861	+	0.755750i	−0.0540120	+	0.0623332i
$148$	−5.10648	+	3.28174i	−0.419750	+	0.269757i
$149$	−1.00762	−	7.00813i	−0.0825472	−	0.574128i	−0.988554	−	0.150866i	$-0.951794\pi$
$149$	−1.00762	−	7.00813i	−0.0825472	−	0.574128i	0.906007	−	0.423262i	$-0.139115\pi$
$150$	−1.19674	−	8.32354i	−0.0977138	−	0.679614i
$151$	10.9928	−	7.06467i	0.894585	−	0.574915i	−0.0105950	−	0.999944i	$-0.503373\pi$
$151$	10.9928	−	7.06467i	0.894585	−	0.574915i	0.905180	+	0.425029i	$0.139736\pi$
$152$	4.08699	−	4.71664i	0.331499	−	0.382570i
$153$	2.97073	−	6.50499i	0.240169	−	0.525898i
$154$	0.641129	+	0.412029i	0.0516637	+	0.0332022i
$155$	14.7669	−	4.33595i	1.18611	−	0.348272i
$156$	0.340156	+	0.392561i	0.0272343	+	0.0314301i
$157$	−5.37910	−	1.57945i	−0.429299	−	0.126054i	0.0599426	−	0.998202i	$-0.480908\pi$
$157$	−5.37910	−	1.57945i	−0.429299	−	0.126054i	−0.489242	+	0.872148i	$0.662726\pi$
$158$	−3.38127	−	7.40395i	−0.268999	−	0.589027i
$159$	−0.146006	+	1.01550i	−0.0115791	+	0.0805341i
$160$	−3.66185			−0.289495
$161$	−3.78938	+	2.93949i	−0.298645	+	0.231664i
$162$	1.00000			0.0785674
$163$	1.54556	−	10.7496i	0.121057	−	0.841972i	−0.835305	−	0.549787i	$-0.814709\pi$
$163$	1.54556	−	10.7496i	0.121057	−	0.841972i	0.956362	−	0.292185i	$-0.0943822\pi$
$164$	0.715597	+	1.56694i	0.0558787	+	0.122357i
$165$	2.67769	+	0.786242i	0.208458	+	0.0612088i
$166$	9.70967	+	11.2056i	0.753616	+	0.869720i
$167$	−12.5254	+	3.67779i	−0.969246	+	0.284596i	−0.727778	−	0.685813i	$-0.759447\pi$
$167$	−12.5254	+	3.67779i	−0.969246	+	0.284596i	−0.241468	+	0.970409i	$0.577629\pi$
$168$	0.841254	+	0.540641i	0.0649041	+	0.0417113i
$169$	−5.28831	+	11.5798i	−0.406793	+	0.890753i
$170$	17.1487	−	19.7906i	1.31524	−	1.51787i
$171$	−5.25027	+	3.37414i	−0.401498	+	0.258027i
$172$	−0.185216	−	1.28820i	−0.0141226	−	0.0982247i
$173$	−1.89565	−	13.1845i	−0.144124	−	1.00240i	−0.925610	−	0.378479i	$-0.876447\pi$
$173$	−1.89565	−	13.1845i	−0.144124	−	1.00240i	0.781486	−	0.623922i	$-0.214462\pi$
$174$	−2.75321	+	1.76938i	−0.208720	+	0.134136i
$175$	−5.50681	+	6.35520i	−0.416276	+	0.480408i
$176$	0.316593	−	0.693241i	0.0238641	−	0.0522550i
$177$	2.75528	+	1.77071i	0.207100	+	0.133095i
$178$	0.0370094	−	0.0108669i	0.00277397	−	0.000814511i
$179$	11.2152	+	12.9431i	0.838267	+	0.967411i	0.999811	−	0.0194543i	$-0.00619288\pi$
$179$	11.2152	+	12.9431i	0.838267	+	0.967411i	−0.161544	+	0.986865i	$0.551647\pi$
$180$	3.51352	+	1.03166i	0.261882	+	0.0768955i
$181$	4.53575	+	9.93192i	0.337140	+	0.738233i	0.999944	−	0.0105592i	$-0.00336116\pi$
$181$	4.53575	+	9.93192i	0.337140	+	0.738233i	−0.662804	+	0.748793i	$0.730634\pi$
$182$	0.0739230	−	0.514146i	0.00547954	−	0.0381110i
$183$	9.86165			0.728994
$184$	3.44886	+	3.33247i	0.254253	+	0.245673i
$185$	22.2277			1.63422
$186$	−0.598132	+	4.16010i	−0.0438572	+	0.305033i
$187$	2.26403	+	4.95753i	0.165562	+	0.362531i
$188$	5.14053	+	1.50939i	0.374911	+	0.110084i
$189$	−0.654861	−	0.755750i	−0.0476341	−	0.0549727i
$190$	−21.9279	+	6.43861i	−1.59082	+	0.467106i
$191$	8.47966	+	5.44955i	0.613567	+	0.394316i	0.810193	−	0.586163i	$-0.199362\pi$
$191$	8.47966	+	5.44955i	0.613567	+	0.394316i	−0.196626	+	0.980479i	$0.562999\pi$
$192$	0.415415	−	0.909632i	0.0299800	−	0.0656470i
$193$	8.93232	−	10.3084i	0.642963	−	0.742018i	−0.336933	−	0.941529i	$-0.609390\pi$
$193$	8.93232	−	10.3084i	0.642963	−	0.742018i	0.979896	+	0.199510i	$0.0639351\pi$
$194$	−3.72824	+	2.39599i	−0.267672	+	0.172022i
$195$	−0.270695	−	1.88272i	−0.0193849	−	0.134825i
$196$	−0.142315	−	0.989821i	−0.0101653	−	0.0707015i
$197$	8.46121	−	5.43769i	0.602836	−	0.387419i	−0.203328	−	0.979111i	$-0.565176\pi$
$197$	8.46121	−	5.43769i	0.602836	−	0.387419i	0.806165	+	0.591691i	$0.201540\pi$
$198$	−0.499077	+	0.575966i	−0.0354679	+	0.0409321i
$199$	3.51785	−	7.70301i	0.249374	−	0.546052i	−0.743004	−	0.669287i	$-0.766600\pi$
$199$	3.51785	−	7.70301i	0.249374	−	0.546052i	0.992378	+	0.123235i	$0.0393269\pi$
$200$	7.07421	+	4.54632i	0.500222	+	0.321473i
$201$	−5.37248	+	1.57750i	−0.378946	+	0.111269i
$202$	3.41482	+	3.94092i	0.240266	+	0.277282i
$203$	3.14018	+	0.922039i	0.220397	+	0.0647145i
$204$	2.97073	+	6.50499i	0.207993	+	0.455441i
$205$	0.897711	−	6.24372i	0.0626989	−	0.436080i
$206$	−3.24715			−0.226240
$207$	−2.37029	−	4.16914i	−0.164746	−	0.289775i
$208$	−0.519433			−0.0360162
$209$	0.676898	−	4.70793i	0.0468220	−	0.325654i
$210$	−1.52119	−	3.33093i	−0.104972	−	0.229856i
$211$	10.5389	+	3.09451i	0.725530	+	0.213035i	0.623586	−	0.781755i	$-0.285675\pi$
$211$	10.5389	+	3.09451i	0.725530	+	0.213035i	0.101945	+	0.994790i	$0.467493\pi$
$212$	−0.671847	−	0.775353i	−0.0461427	−	0.0532515i
$213$	−14.3616	+	4.21695i	−0.984042	+	0.288941i
$214$	−13.1854	−	8.47372i	−0.901333	−	0.579251i
$215$	−1.97975	+	4.33505i	−0.135018	+	0.295648i
$216$	−0.654861	+	0.755750i	−0.0445576	+	0.0514222i
$217$	3.53569	−	2.27225i	0.240018	−	0.154250i
$218$	1.27542	+	8.87071i	0.0863820	+	0.600800i
$219$	−2.21859	−	15.4306i	−0.149919	−	1.04271i
$220$	−2.34772	+	1.50879i	−0.158283	+	0.101722i
$221$	2.43254	−	2.80730i	0.163630	−	0.188839i
$222$	−2.52161	+	5.52155i	−0.169239	+	0.370582i
$223$	−17.5796	−	11.2977i	−1.17722	−	0.756553i	−0.202346	−	0.979314i	$-0.564857\pi$
$223$	−17.5796	−	11.2977i	−1.17722	−	0.756553i	−0.974873	+	0.222761i	$0.928493\pi$
$224$	−0.959493	+	0.281733i	−0.0641088	+	0.0188240i
$225$	−5.50681	−	6.35520i	−0.367121	−	0.423680i
$226$	13.1802	+	3.87005i	0.876732	+	0.257432i
$227$	12.0523	+	26.3909i	0.799940	+	1.75162i	0.645702	+	0.763590i	$0.276565\pi$
$227$	12.0523	+	26.3909i	0.799940	+	1.75162i	0.154238	+	0.988034i	$0.450708\pi$
$228$	0.888187	−	6.17748i	0.0588216	−	0.409114i
$229$	15.7619			1.04158			0.520789	−	0.853685i	$-0.325638\pi$
$229$	15.7619			1.04158			0.520789	+	0.853685i	$0.325638\pi$
$230$	−4.02690	−	17.0937i	−0.265526	−	1.12712i
$231$	0.762112			0.0501433
$232$	0.465760	−	3.23944i	0.0305787	−	0.212679i
$233$	10.1713	+	22.2721i	0.666347	+	1.45910i	0.876487	+	0.481426i	$0.159881\pi$
$233$	10.1713	+	22.2721i	0.666347	+	1.45910i	−0.210140	+	0.977671i	$0.567392\pi$
$234$	0.498392	+	0.146341i	0.0325809	+	0.00956662i
$235$	−12.8474	−	14.8267i	−0.838072	−	0.967186i
$236$	−3.14254	+	0.922733i	−0.204562	+	0.0600648i
$237$	−6.84738	−	4.40055i	−0.444785	−	0.285846i
$238$	2.97073	−	6.50499i	0.192564	−	0.421656i
$239$	−12.8496	+	14.8292i	−0.831171	+	0.959222i	−0.999649	−	0.0264834i	$-0.991569\pi$
$239$	−12.8496	+	14.8292i	−0.831171	+	0.959222i	0.168479	+	0.985705i	$0.446115\pi$
$240$	−3.08054	+	1.97974i	−0.198848	+	0.127792i
$241$	−0.120703	−	0.839508i	−0.00777516	−	0.0540775i	0.985564	−	0.169300i	$-0.0541508\pi$
$241$	−0.120703	−	0.839508i	−0.00777516	−	0.0540775i	−0.993340	+	0.115223i	$0.963242\pi$
$242$	1.48280	+	10.3131i	0.0953183	+	0.662953i
$243$	0.841254	−	0.540641i	0.0539664	−	0.0346821i
$244$	−6.45801	+	7.45294i	−0.413432	+	0.477126i
$245$	−1.52119	+	3.33093i	−0.0971851	+	0.212806i
$246$	1.44915	+	0.931311i	0.0923943	+	0.0593782i
$247$	−3.11047	+	0.913316i	−0.197914	+	0.0581129i
$248$	−2.75230	−	3.17633i	−0.174771	−	0.201697i
$249$	14.2265	+	4.17727i	0.901566	+	0.264724i
$250$	−5.18593	−	11.3556i	−0.327987	−	0.718191i
$251$	0.723592	−	5.03269i	0.0456727	−	0.317661i	−0.954159	−	0.299301i	$-0.903246\pi$
$251$	0.723592	−	5.03269i	0.0456727	−	0.317661i	0.999831	−	0.0183598i	$-0.00584442\pi$
$252$	1.00000			0.0629941
$253$	3.58424	+	0.715518i	0.225339	+	0.0449843i
$254$	18.5325			1.16283
$255$	3.72676	−	25.9202i	0.233379	−	1.62319i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−21.6625	−	6.36068i	−1.35127	−	0.396768i	−0.475592	−	0.879666i	$-0.657766\pi$
$257$	−21.6625	−	6.36068i	−1.35127	−	0.396768i	−0.875677	+	0.482898i	$0.839584\pi$
$258$	−0.852269	−	0.983571i	−0.0530600	−	0.0612345i
$259$	5.82421	−	1.71014i	0.361899	−	0.106263i
$260$	1.60014	+	1.02834i	0.0992362	+	0.0637752i
$261$	−1.35955	+	2.97700i	−0.0841539	+	0.184271i
$262$	−7.20549	+	8.31558i	−0.445157	+	0.513738i
$263$	1.89977	−	1.22091i	0.117145	−	0.0752845i	−0.480756	−	0.876854i	$-0.659638\pi$
$263$	1.89977	−	1.22091i	0.117145	−	0.0752845i	0.597901	+	0.801570i	$0.296001\pi$
$264$	−0.108460	−	0.754355i	−0.00667524	−	0.0464273i
$265$	0.534653	+	3.71859i	0.0328435	+	0.228431i
$266$	−5.25027	+	3.37414i	−0.321914	+	0.206882i
$267$	0.0252592	−	0.0291506i	0.00154584	−	0.00178399i
$268$	2.32603	−	5.09330i	0.142085	−	0.311123i
$269$	12.4264	+	7.98593i	0.757648	+	0.486911i	0.861547	−	0.507677i	$-0.169496\pi$
$269$	12.4264	+	7.98593i	0.757648	+	0.486911i	−0.103899	+	0.994588i	$0.533132\pi$
$270$	3.51352	−	1.03166i	0.213826	−	0.0627849i
$271$	15.6997	+	18.1185i	0.953692	+	1.10062i	0.994839	+	0.101466i	$0.0323533\pi$
$271$	15.6997	+	18.1185i	0.953692	+	1.10062i	−0.0411472	+	0.999153i	$0.513101\pi$
$272$	−6.86156	−	2.01474i	−0.416043	−	0.122161i
$273$	−0.215780	−	0.472493i	−0.0130596	−	0.0285966i
$274$	−1.68214	+	11.6996i	−0.101622	+	0.706797i
$275$	6.40870			0.386459
$276$	4.70303	+	0.938863i	0.283089	+	0.0565129i
$277$	20.8449			1.25245			0.626223	−	0.779644i	$-0.284600\pi$
$277$	20.8449			1.25245			0.626223	+	0.779644i	$0.284600\pi$
$278$	−0.815031	+	5.66867i	−0.0488823	+	0.339984i
$279$	1.74594	+	3.82308i	0.104527	+	0.228882i
$280$	3.51352	+	1.03166i	0.209973	+	0.0616536i
$281$	11.6032	+	13.3908i	0.692187	+	0.798827i	0.987675	−	0.156520i	$-0.0500275\pi$
$281$	11.6032	+	13.3908i	0.692187	+	0.798827i	−0.295488	+	0.955347i	$0.595482\pi$
$282$	5.14053	−	1.50939i	0.306114	−	0.0898831i
$283$	−15.4510	−	9.92975i	−0.918466	−	0.590263i	−0.00625420	−	0.999980i	$-0.501991\pi$
$283$	−15.4510	−	9.92975i	−0.918466	−	0.590263i	−0.912212	+	0.409718i	$0.865627\pi$
$284$	6.21790	−	13.6153i	0.368964	−	0.807919i
$285$	−14.9659	+	17.2716i	−0.886505	+	1.02308i
$286$	−0.333024	+	0.214021i	−0.0196921	+	0.0126553i
$287$	−0.245152	−	1.70507i	−0.0144709	−	0.100647i
$288$	−0.142315	−	0.989821i	−0.00838598	−	0.0583258i
$289$	28.7205	−	18.4576i	1.68944	−	1.08574i
$290$	−7.84805	+	9.05713i	−0.460853	+	0.531853i
$291$	−1.84102	+	4.03127i	−0.107923	+	0.236317i
$292$	13.1146	+	8.42822i	0.767472	+	0.493224i
$293$	−13.3590	+	3.92254i	−0.780439	+	0.229157i	−0.647600	−	0.761980i	$-0.724227\pi$
$293$	−13.3590	+	3.92254i	−0.780439	+	0.229157i	−0.132838	+	0.991138i	$0.542409\pi$
$294$	−0.654861	−	0.755750i	−0.0381923	−	0.0440762i
$295$	11.5075	+	3.37891i	0.669993	+	0.196728i
$296$	−2.52161	−	5.52155i	−0.146565	−	0.320933i
$297$	−0.108460	+	0.754355i	−0.00629348	+	0.0437721i
$298$	7.08019			0.410145
$299$	−0.571216	−	2.42474i	−0.0330343	−	0.140226i
$300$	8.40913			0.485502
$301$	−0.185216	+	1.28820i	−0.0106757	+	0.0742509i
$302$	5.42832	+	11.8864i	0.312365	+	0.683983i
$303$	5.00335	+	1.46912i	0.287435	+	0.0843986i
$304$	4.08699	+	4.71664i	0.234405	+	0.270518i
$305$	34.6491	−	10.1739i	1.98400	−	0.582555i
$306$	6.01600	+	3.86625i	0.343912	+	0.221019i
$307$	−12.4198	+	27.1956i	−0.708837	+	1.55214i	0.120079	+	0.992764i	$0.461685\pi$
$307$	−12.4198	+	27.1956i	−0.708837	+	1.55214i	−0.828916	+	0.559372i	$0.811042\pi$
$308$	−0.499077	+	0.575966i	−0.0284376	+	0.0328187i
$309$	−2.73168	+	1.75554i	−0.155400	+	0.0998692i
$310$	2.19027	+	15.2337i	0.124399	+	0.865214i
$311$	−1.64136	−	11.4159i	−0.0930727	−	0.647335i	−0.981943	−	0.189176i	$-0.939418\pi$
$311$	−1.64136	−	11.4159i	−0.0930727	−	0.647335i	0.888870	−	0.458159i	$-0.151491\pi$
$312$	−0.436975	+	0.280827i	−0.0247388	+	0.0158987i
$313$	5.95296	−	6.87009i	0.336481	−	0.388320i	−0.562142	−	0.827041i	$-0.690023\pi$
$313$	5.95296	−	6.87009i	0.336481	−	0.388320i	0.898624	+	0.438720i	$0.144568\pi$
$314$	2.32890	−	5.09957i	0.131427	−	0.287786i
$315$	−3.08054	−	1.97974i	−0.173569	−	0.111546i
$316$	7.80979	−	2.29316i	0.439335	−	0.129000i
$317$	−2.59232	−	2.99169i	−0.145599	−	0.168030i	0.678266	−	0.734817i	$-0.262732\pi$
$317$	−2.59232	−	2.99169i	−0.145599	−	0.168030i	−0.823865	+	0.566787i	$0.808186\pi$
$318$	−0.984381	−	0.289040i	−0.0552014	−	0.0162086i
$319$	−1.03613	−	2.26880i	−0.0580120	−	0.127029i
$320$	0.521135	−	3.62458i	0.0291324	−	0.202620i
$321$	−15.6735			−0.874808
$322$	−2.37029	−	4.16914i	−0.132091	−	0.232337i
$323$	−44.6309			−2.48333
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	−1.81453	−	3.97326i	−0.100652	−	0.220397i
$326$	10.4202	+	3.05965i	0.577122	+	0.169458i
$327$	5.86881	+	6.77297i	0.324546	+	0.374546i
$328$	−1.65283	+	0.485314i	−0.0912622	+	0.0267970i
$329$	−4.50705	−	2.89651i	−0.248482	−	0.159690i
$330$	−1.15931	+	2.53854i	−0.0638182	+	0.139742i
$331$	−2.08688	+	2.40838i	−0.114705	+	0.132377i	−0.810198	−	0.586156i	$-0.800641\pi$
$331$	−2.08688	+	2.40838i	−0.114705	+	0.132377i	0.695493	+	0.718533i	$0.255186\pi$
$332$	−12.4733	+	8.01612i	−0.684563	+	0.439942i
$333$	0.863864	+	6.00830i	0.0473394	+	0.329253i
$334$	−1.85781	−	12.9213i	−0.101655	−	0.707024i
$335$	−17.2489	+	11.0852i	−0.942406	+	0.605648i
$336$	−0.654861	+	0.755750i	−0.0357256	+	0.0412295i
$337$	8.04879	−	17.6244i	0.438446	−	0.960062i	−0.553435	−	0.832892i	$-0.686683\pi$
$337$	8.04879	−	17.6244i	0.438446	−	0.960062i	0.991881	−	0.127170i	$-0.0405894\pi$
$338$	−10.7093	−	6.88246i	−0.582510	−	0.374356i
$339$	13.1802	−	3.87005i	0.715849	−	0.210192i
$340$	17.1487	+	19.7906i	0.930017	+	1.07330i
$341$	−3.07332	−	0.902408i	−0.166430	−	0.0488681i
$342$	−2.59261	−	5.67702i	−0.140192	−	0.306978i
$343$	−0.142315	+	0.989821i	−0.00768428	+	0.0534453i
$344$	1.30145			0.0701696
$345$	−12.6292	−	12.2030i	−0.679933	−	0.656988i
$346$	13.3201			0.716094
$347$	4.11571	−	28.6254i	0.220943	−	1.53669i	−0.513542	−	0.858065i	$-0.671667\pi$
$347$	4.11571	−	28.6254i	0.220943	−	1.53669i	0.734484	−	0.678626i	$-0.237424\pi$
$348$	−1.35955	−	2.97700i	−0.0728794	−	0.159584i
$349$	−12.6644	−	3.71861i	−0.677911	−	0.199052i	−0.0753879	−	0.997154i	$-0.524020\pi$
$349$	−12.6644	−	3.71861i	−0.677911	−	0.199052i	−0.602523	+	0.798102i	$0.705838\pi$
$350$	−5.50681	−	6.35520i	−0.294351	−	0.339700i
$351$	0.498392	−	0.146341i	0.0266022	−	0.00781112i
$352$	0.641129	+	0.412029i	0.0341723	+	0.0219612i
$353$	11.3694	−	24.8956i	0.605134	−	1.32506i	−0.320719	−	0.947174i	$-0.603924\pi$
$353$	11.3694	−	24.8956i	0.605134	−	1.32506i	0.925853	−	0.377884i	$-0.123348\pi$
$354$	−2.14480	+	2.47524i	−0.113995	+	0.131557i
$355$	−46.1093	+	29.6327i	−2.44723	+	1.57274i
$356$	0.00548934	+	0.0381792i	0.000290934	+	0.00202349i
$357$	−1.01773	−	7.07845i	−0.0538638	−	0.374631i
$358$	−14.4074	+	9.25910i	−0.761457	+	0.489358i
$359$	4.65121	−	5.36779i	0.245482	−	0.283301i	−0.619615	−	0.784906i	$-0.712711\pi$
$359$	4.65121	−	5.36779i	0.245482	−	0.283301i	0.865097	+	0.501605i	$0.167257\pi$
$360$	−1.52119	+	3.33093i	−0.0801736	+	0.175556i
$361$	16.7831	+	10.7859i	0.883322	+	0.567676i
$362$	−10.4763	+	3.07613i	−0.550624	+	0.161678i
$363$	6.82312	+	7.87430i	0.358121	+	0.413293i
$364$	0.498392	+	0.146341i	0.0261229	+	0.00767036i
$365$	−23.7143	−	51.9270i	−1.24126	−	2.71798i
$366$	−1.40346	+	9.76128i	−0.0733600	+	0.510230i
$367$	26.0493			1.35976			0.679880	−	0.733323i	$-0.262032\pi$
$367$	26.0493			1.35976			0.679880	+	0.733323i	$0.262032\pi$
$368$	−3.78938	+	2.93949i	−0.197535	+	0.153232i
$369$	1.72261			0.0896753
$370$	−3.16334	+	22.0015i	−0.164454	+	1.14380i
$371$	0.426190	+	0.933227i	0.0221267	+	0.0484507i
$372$	−4.03264	−	1.18409i	−0.209082	−	0.0613921i
$373$	−19.3189	−	22.2952i	−1.00029	−	1.15440i	−0.987997	−	0.154475i	$-0.950631\pi$
$373$	−19.3189	−	22.2952i	−1.00029	−	1.15440i	−0.0122960	−	0.999924i	$-0.503914\pi$
$374$	−5.22928	+	1.53545i	−0.270399	+	0.0793964i
$375$	−10.5020	−	6.74921i	−0.542320	−	0.348528i
$376$	−2.22560	+	4.87339i	−0.114777	+	0.251326i
$377$	−1.11325	+	1.28475i	−0.0573351	+	0.0661682i
$378$	0.841254	−	0.540641i	0.0432694	−	0.0278076i
$379$	−3.82119	−	26.5769i	−0.196281	−	1.36517i	−0.814958	−	0.579520i	$-0.803240\pi$
$379$	−3.82119	−	26.5769i	−0.196281	−	1.36517i	0.618677	−	0.785646i	$-0.287669\pi$
$380$	−3.25241	−	22.6210i	−0.166845	−	1.16043i
$381$	15.5905	−	10.0194i	0.798727	−	0.513311i
$382$	−6.60086	+	7.61780i	−0.337729	+	0.389761i
$383$	−6.63110	+	14.5201i	−0.338834	+	0.741942i	−0.999965	−	0.00832779i	$-0.997349\pi$
$383$	−6.63110	+	14.5201i	−0.338834	+	0.741942i	0.661132	+	0.750270i	$0.270076\pi$
$384$	0.841254	+	0.540641i	0.0429300	+	0.0275895i
$385$	2.67769	−	0.786242i	0.136468	−	0.0400706i
$386$	8.93232	+	10.3084i	0.454643	+	0.524686i
$387$	−1.24873	−	0.366661i	−0.0634767	−	0.0186384i
$388$	−1.84102	−	4.03127i	−0.0934637	−	0.204657i
$389$	−3.23308	+	22.4865i	−0.163924	+	1.14011i	0.727224	+	0.686400i	$0.240810\pi$
$389$	−3.23308	+	22.4865i	−0.163924	+	1.14011i	−0.891148	+	0.453713i	$0.850099\pi$
$390$	1.90209			0.0963158
$391$	1.85928	−	34.2457i	0.0940281	−	1.73188i
$392$	1.00000			0.0505076
$393$	−1.56590	+	10.8911i	−0.0789893	+	0.549383i
$394$	4.17819	+	9.14895i	0.210494	+	0.460918i
$395$	−28.5983	−	8.39721i	−1.43894	−	0.422510i
$396$	−0.499077	−	0.575966i	−0.0250796	−	0.0289434i
$397$	−2.11193	+	0.620119i	−0.105995	+	0.0311229i	−0.334300	−	0.942467i	$-0.608500\pi$
$397$	−2.11193	+	0.620119i	−0.105995	+	0.0311229i	0.228305	+	0.973590i	$0.426682\pi$
$398$	7.12396	+	4.57829i	0.357092	+	0.229489i
$399$	−2.59261	+	5.67702i	−0.129793	+	0.284206i
$400$	−5.50681	+	6.35520i	−0.275341	+	0.317760i
$401$	−28.4714	+	18.2975i	−1.42180	+	0.913732i	−0.421820	+	0.906679i	$0.638609\pi$
$401$	−28.4714	+	18.2975i	−1.42180	+	0.913732i	−0.999975	+	0.00705294i	$0.997755\pi$
$402$	−0.796863	−	5.54230i	−0.0397439	−	0.276425i
$403$	0.310690	+	2.16089i	0.0154766	+	0.107642i
$404$	−4.38678	+	2.81921i	−0.218251	+	0.140261i
$405$	2.39800	−	2.76744i	0.119158	−	0.137515i
$406$	−1.35955	+	2.97700i	−0.0674733	+	0.147746i
$407$	−3.89171	−	2.50105i	−0.192905	−	0.123972i
$408$	−6.86156	+	2.01474i	−0.339698	+	0.0997443i
$409$	−14.0388	−	16.2017i	−0.694175	−	0.801121i	0.293778	−	0.955874i	$-0.405087\pi$
$409$	−14.0388	−	16.2017i	−0.694175	−	0.801121i	−0.987953	+	0.154753i	$0.950542\pi$
$410$	6.05241	+	1.77715i	0.298907	+	0.0877671i
$411$	4.91016	+	10.7517i	0.242200	+	0.530344i
$412$	0.462117	−	3.21410i	0.0227669	−	0.158347i
$413$	3.27521			0.161162
$414$	4.46403	−	1.75283i	0.219395	−	0.0861469i
$415$	54.2945			2.66521
$416$	0.0739230	−	0.514146i	0.00362437	−	0.0252081i
$417$	2.37906	+	5.20942i	0.116503	+	0.255107i
$418$	4.56368	+	1.34002i	0.223217	+	0.0655423i
$419$	−7.11744	−	8.21397i	−0.347710	−	0.401279i	0.554775	−	0.832001i	$-0.312804\pi$
$419$	−7.11744	−	8.21397i	−0.347710	−	0.401279i	−0.902485	+	0.430722i	$0.858259\pi$
$420$	3.51352	−	1.03166i	0.171442	−	0.0503399i
$421$	−15.0239	−	9.65527i	−0.732220	−	0.470569i	0.120648	−	0.992695i	$-0.461503\pi$
$421$	−15.0239	−	9.65527i	−0.732220	−	0.470569i	−0.852868	+	0.522126i	$0.825139\pi$
$422$	−4.56286	+	9.99127i	−0.222117	+	0.486367i
$423$	3.50845	−	4.04896i	0.170586	−	0.196867i
$424$	0.863075	−	0.554665i	0.0419146	−	0.0269369i
$425$	−8.55820	−	59.5236i	−0.415134	−	2.88732i
$426$	−2.13016	−	14.8156i	−0.103206	−	0.717817i
$427$	8.29615	−	5.33161i	0.401479	−	0.258015i
$428$	10.2639	−	11.8452i	0.496126	−	0.572560i
$429$	−0.164449	+	0.360092i	−0.00793966	+	0.0173854i
$430$	−4.00918	−	2.57654i	−0.193340	−	0.124252i
$431$	18.9122	−	5.55314i	0.910971	−	0.267485i	0.207521	−	0.978230i	$-0.433460\pi$
$431$	18.9122	−	5.55314i	0.910971	−	0.267485i	0.703449	+	0.710745i	$0.251642\pi$
$432$	−0.654861	−	0.755750i	−0.0315070	−	0.0363610i
$433$	−18.2200	−	5.34987i	−0.875596	−	0.257098i	−0.187102	−	0.982340i	$-0.559910\pi$
$433$	−18.2200	−	5.34987i	−0.875596	−	0.257098i	−0.688494	+	0.725242i	$0.741728\pi$
$434$	1.74594	+	3.82308i	0.0838078	+	0.183513i
$435$	−1.70554	+	11.8623i	−0.0817746	+	0.568755i
$436$	−8.96193			−0.429198
$437$	−17.5231	+	24.2651i	−0.838242	+	1.16076i
$438$	15.5893			0.744886
$439$	−4.16701	+	28.9822i	−0.198881	+	1.38325i	0.608659	+	0.793432i	$0.291708\pi$
$439$	−4.16701	+	28.9822i	−0.198881	+	1.38325i	−0.807539	+	0.589814i	$0.799201\pi$
$440$	−1.15931	−	2.53854i	−0.0552681	−	0.121020i
$441$	−0.959493	−	0.281733i	−0.0456901	−	0.0134158i
$442$	2.43254	+	2.80730i	0.115704	+	0.133530i
$443$	4.19882	−	1.23289i	0.199492	−	0.0585762i	−0.180460	−	0.983582i	$-0.557759\pi$
$443$	4.19882	−	1.23289i	0.199492	−	0.0585762i	0.379952	+	0.925006i	$0.375940\pi$
$444$	−5.10648	−	3.28174i	−0.242343	−	0.155744i
$445$	0.0586749	−	0.128480i	0.00278146	−	0.00609054i
$446$	13.6846	−	15.7929i	0.647984	−	0.747814i
$447$	5.95624	−	3.82784i	0.281720	−	0.181051i
$448$	−0.142315	−	0.989821i	−0.00672374	−	0.0467647i
$449$	−2.19775	−	15.2857i	−0.103718	−	0.721375i	−0.973624	−	0.228158i	$-0.926730\pi$
$449$	−2.19775	−	15.2857i	−0.103718	−	0.721375i	0.869906	−	0.493217i	$-0.164179\pi$
$450$	7.07421	−	4.54632i	0.333482	−	0.214316i
$451$	−0.859713	+	0.992162i	−0.0404823	+	0.0467191i
$452$	−5.70639	+	12.4953i	−0.268406	+	0.587727i
$453$	10.9928	+	7.06467i	0.516489	+	0.331927i
$454$	−27.8375	+	8.17382i	−1.30648	+	0.383616i
$455$	−1.24560	−	1.43750i	−0.0583947	−	0.0673910i
$456$	5.98820	+	1.75829i	0.280423	+	0.0823397i
$457$	−1.85099	−	4.05309i	−0.0865855	−	0.189596i	0.861386	−	0.507951i	$-0.169597\pi$
$457$	−1.85099	−	4.05309i	−0.0865855	−	0.189596i	−0.947972	+	0.318355i	$0.896870\pi$
$458$	−2.24316	+	15.6015i	−0.104816	+	0.729010i
$459$	7.15124			0.333791
$460$	17.4928	−	1.55323i	0.815605	−	0.0724198i
$461$	−27.2041			−1.26702			−0.633510	−	0.773734i	$-0.718387\pi$
$461$	−27.2041			−1.26702			−0.633510	+	0.773734i	$0.718387\pi$
$462$	−0.108460	+	0.754355i	−0.00504601	+	0.0350958i
$463$	6.71095	+	14.6949i	0.311884	+	0.682931i	0.999050	−	0.0435690i	$-0.0138728\pi$
$463$	6.71095	+	14.6949i	0.311884	+	0.682931i	−0.687166	+	0.726500i	$0.741146\pi$
$464$	3.14018	+	0.922039i	0.145779	+	0.0428046i
$465$	10.0785	+	11.6312i	0.467380	+	0.539385i
$466$	−23.4930	+	6.89816i	−1.08829	+	0.319551i
$467$	20.6875	+	13.2951i	0.957303	+	0.615222i	0.923251	−	0.384198i	$-0.125522\pi$
$467$	20.6875	+	13.2951i	0.957303	+	0.615222i	0.0340529	+	0.999420i	$0.489159\pi$
$468$	−0.215780	+	0.472493i	−0.00997445	+	0.0218410i
$469$	−3.66676	+	4.23167i	−0.169315	+	0.195400i
$470$	16.5041	−	10.6066i	0.761279	−	0.489245i
$471$	−0.797844	−	5.54913i	−0.0367627	−	0.255690i
$472$	−0.466111	−	3.24187i	−0.0214545	−	0.149219i
$473$	0.834399	−	0.536235i	0.0383657	−	0.0246561i
$474$	5.33024	−	6.15142i	0.244826	−	0.282544i
$475$	−21.8016	+	47.7388i	−1.00032	+	2.19041i
$476$	6.01600	+	3.86625i	0.275743	+	0.177209i
$477$	−0.984381	+	0.289040i	−0.0450717	+	0.0132343i
$478$	−12.8496	−	14.8292i	−0.587726	−	0.678272i
$479$	−22.5097	−	6.60945i	−1.02850	−	0.301994i	−0.276397	−	0.961044i	$-0.589140\pi$
$479$	−22.5097	−	6.60945i	−1.02850	−	0.301994i	−0.752099	+	0.659050i	$0.770958\pi$
$480$	−1.52119	−	3.33093i	−0.0694324	−	0.152036i
$481$	−0.448719	+	3.12091i	−0.0204598	+	0.142301i
$482$	0.848141			0.0386318
$483$	−4.24802	−	2.22583i	−0.193292	−	0.101279i
$484$	−10.4192			−0.473599
$485$	−2.30955	+	16.0633i	−0.104871	+	0.729395i
$486$	0.415415	+	0.909632i	0.0188436	+	0.0412617i
$487$	14.3702	+	4.21947i	0.651175	+	0.191202i	0.590604	−	0.806962i	$-0.298890\pi$
$487$	14.3702	+	4.21947i	0.651175	+	0.191202i	0.0605712	+	0.998164i	$0.480708\pi$
$488$	−6.45801	−	7.45294i	−0.292340	−	0.337379i
$489$	10.4202	−	3.05965i	0.471218	−	0.138362i
$490$	−3.08054	−	1.97974i	−0.139165	−	0.0894357i
$491$	5.47945	−	11.9983i	0.247284	−	0.541476i	−0.744765	−	0.667326i	$-0.767439\pi$
$491$	5.47945	−	11.9983i	0.247284	−	0.541476i	0.992049	+	0.125850i	$0.0401659\pi$
$492$	−1.12807	+	1.30186i	−0.0508572	+	0.0586923i
$493$	−19.6889	+	12.6533i	−0.886742	+	0.569874i
$494$	−0.461354	−	3.20879i	−0.0207573	−	0.144370i
$495$	0.397163	+	2.76233i	0.0178512	+	0.124158i
$496$	3.53569	−	2.27225i	0.158757	−	0.102027i
$497$	−9.80190	+	11.3120i	−0.439675	+	0.507413i
$498$	−6.15939	+	13.4872i	−0.276009	+	0.604375i
$499$	−7.93300	−	5.09823i	−0.355130	−	0.228228i	0.350895	−	0.936415i	$-0.385877\pi$
$499$	−7.93300	−	5.09823i	−0.355130	−	0.228228i	−0.706025	+	0.708186i	$0.749514\pi$
$500$	11.9781	−	3.51707i	0.535675	−	0.157288i
$501$	−8.54869	−	9.86571i	−0.381927	−	0.440767i
$502$	4.87849	+	1.43245i	0.217738	+	0.0639336i
$503$	−6.60374	−	14.4602i	−0.294446	−	0.644748i	0.703368	−	0.710826i	$-0.251679\pi$
$503$	−6.60374	−	14.4602i	−0.294446	−	0.644748i	−0.997814	+	0.0660783i	$0.978951\pi$
$504$	−0.142315	+	0.989821i	−0.00633921	+	0.0440902i
$505$	19.0950			0.849716
$506$	−1.21833	+	3.44593i	−0.0541612	+	0.153190i
$507$	−12.7302			−0.565368
$508$	−2.63745	+	18.3439i	−0.117018	+	0.813878i
$509$	−5.75742	−	12.6070i	−0.255193	−	0.558795i	0.738063	−	0.674731i	$-0.235740\pi$
$509$	−5.75742	−	12.6070i	−0.255193	−	0.558795i	−0.993257	+	0.115936i	$0.963013\pi$
$510$	25.1260	+	7.37766i	1.11260	+	0.326688i
$511$	−10.2088	−	11.7816i	−0.451612	−	0.521188i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−5.25027	−	3.37414i	−0.231805	−	0.148972i
$514$	9.37883	−	20.5368i	0.413682	−	0.905838i
$515$	−7.78666	+	8.98629i	−0.343121	+	0.395983i
$516$	1.09485	−	0.703618i	0.0481981	−	0.0309750i
$517$	0.581078	+	4.04149i	0.0255558	+	0.177744i
$518$	0.863864	+	6.00830i	0.0379560	+	0.263990i
$519$	11.2056	−	7.20140i	0.491871	−	0.316106i
$520$	−1.24560	+	1.43750i	−0.0546232	+	0.0630385i
$521$	−2.82640	+	6.18895i	−0.123827	+	0.271143i	−0.961386	−	0.275204i	$-0.911255\pi$
$521$	−2.82640	+	6.18895i	−0.123827	+	0.271143i	0.837559	+	0.546347i	$0.183982\pi$
$522$	−2.75321	−	1.76938i	−0.120505	−	0.0774437i
$523$	−4.54704	+	1.33513i	−0.198828	+	0.0583813i	−0.379630	−	0.925138i	$-0.623949\pi$
$523$	−4.54704	+	1.33513i	−0.198828	+	0.0583813i	0.180802	+	0.983520i	$0.442131\pi$
$524$	−7.20549	−	8.31558i	−0.314773	−	0.363268i
$525$	−8.06850	−	2.36913i	−0.352138	−	0.103397i
$526$	0.938117	+	2.05419i	0.0409039	+	0.0895669i
$527$	−4.27739	+	29.7499i	−0.186326	+	1.29592i
$528$	0.762112			0.0331667
$529$	−17.8888	−	14.4565i	−0.777776	−	0.628542i
$530$	−3.75683			−0.163186
$531$	−0.466111	+	3.24187i	−0.0202275	+	0.140685i
$532$	−2.59261	−	5.67702i	−0.112404	−	0.246130i
$533$	0.858534	+	0.252088i	0.0371872	+	0.0109192i
$534$	0.0252592	+	0.0291506i	0.00109307	+	0.00126147i
$535$	−55.0690	+	16.1697i	−2.38084	+	0.699078i
$536$	4.71043	+	3.02721i	0.203459	+	0.130755i
$537$	−7.11446	+	15.5785i	−0.307012	+	0.672262i
$538$	−9.67310	+	11.1634i	−0.417037	+	0.481286i
$539$	0.641129	−	0.412029i	0.0276154	−	0.0177473i
$540$	0.521135	+	3.62458i	0.0224261	+	0.155977i
$541$	6.33478	+	44.0594i	0.272353	+	1.89426i	0.423738	+	0.905785i	$0.360718\pi$
$541$	6.33478	+	44.0594i	0.272353	+	1.89426i	−0.151385	+	0.988475i	$0.548373\pi$
$542$	−20.1684	+	12.9614i	−0.866305	+	0.556741i
$543$	−7.15017	+	8.25173i	−0.306843	+	0.354116i
$544$	2.97073	−	6.50499i	0.127369	−	0.278899i
$545$	27.6076	+	17.7423i	1.18258	+	0.759998i
$546$	0.498392	−	0.146341i	0.0213292	−	0.00626283i
$547$	20.2289	+	23.3454i	0.864927	+	0.998179i	0.999973	+	0.00733967i	$0.00233631\pi$
$547$	20.2289	+	23.3454i	0.864927	+	0.998179i	−0.135046	+	0.990839i	$0.543118\pi$
$548$	−11.3411	−	3.33004i	−0.484467	−	0.142252i
$549$	4.09668	+	8.97047i	0.174842	+	0.382851i
$550$	−0.912053	+	6.34347i	−0.0388901	+	0.270486i
$551$	20.4252			0.870144
$552$	−1.59862	+	4.52155i	−0.0680417	+	0.192450i
$553$	−8.13950			−0.346127
$554$	−2.96653	+	20.6327i	−0.126036	+	0.876599i
$555$	9.23374	+	20.2191i	0.391950	+	0.858252i
$556$	−5.49498	−	1.61347i	−0.233039	−	0.0684264i
$557$	−16.5966	−	19.1534i	−0.703218	−	0.811557i	0.285965	−	0.958240i	$-0.407686\pi$
$557$	−16.5966	−	19.1534i	−0.703218	−	0.811557i	−0.989184	+	0.146683i	$0.953140\pi$
$558$	−4.03264	+	1.18409i	−0.170715	+	0.0501265i
$559$	−0.568702	−	0.365482i	−0.0240535	−	0.0154583i
$560$	−1.52119	+	3.33093i	−0.0642819	+	0.140758i
$561$	−3.56902	+	4.11887i	−0.150684	+	0.173899i
$562$	−14.9058	+	9.57936i	−0.628762	+	0.404081i
$563$	−5.31349	−	36.9561i	−0.223937	−	1.55751i	−0.722938	−	0.690913i	$-0.757209\pi$
$563$	−5.31349	−	36.9561i	−0.223937	−	1.55751i	0.499001	−	0.866601i	$-0.333700\pi$
$564$	0.762458	+	5.30301i	0.0321053	+	0.223297i
$565$	42.3162	−	27.1950i	1.78026	−	1.14410i
$566$	12.0276	−	13.8806i	0.505557	−	0.583444i
$567$	0.415415	−	0.909632i	0.0174458	−	0.0382010i
$568$	12.5918	+	8.09227i	0.528341	+	0.339544i
$569$	2.93622	−	0.862152i	0.123093	−	0.0361433i	−0.219606	−	0.975589i	$-0.570477\pi$
$569$	2.93622	−	0.862152i	0.123093	−	0.0361433i	0.342699	+	0.939445i	$0.388659\pi$
$570$	−14.9659	−	17.2716i	−0.626854	−	0.723428i
$571$	−29.4608	−	8.65046i	−1.23289	−	0.362010i	−0.400553	−	0.916274i	$-0.631182\pi$
$571$	−29.4608	−	8.65046i	−1.23289	−	0.362010i	−0.832341	+	0.554263i	$0.813000\pi$
$572$	−0.164449	−	0.360092i	−0.00687595	−	0.0150562i
$573$	−1.43450	+	9.97720i	−0.0599273	+	0.416803i
$574$	1.72261			0.0719002
$575$	−35.7222	−	18.7173i	−1.48972	−	0.780566i
$576$	1.00000			0.0416667
$577$	−2.30754	+	16.0493i	−0.0960640	+	0.668140i	0.883710	+	0.468034i	$0.155038\pi$
$577$	−2.30754	+	16.0493i	−0.0960640	+	0.668140i	−0.979774	+	0.200106i	$0.935871\pi$
$578$	14.1823	+	31.0550i	0.589908	+	1.29172i
$579$	13.0875	+	3.84284i	0.543899	+	0.159703i
$580$	−7.84805	−	9.05713i	−0.325873	−	0.376077i
$581$	14.2265	−	4.17727i	0.590214	−	0.173302i
$582$	−3.72824	−	2.39599i	−0.154540	−	0.0993171i
$583$	0.324805	−	0.711223i	0.0134520	−	0.0294559i
$584$	−10.2088	+	11.7816i	−0.422444	+	0.487527i
$585$	1.60014	−	1.02834i	0.0661575	−	0.0425168i
$586$	−1.98144	−	13.7812i	−0.0818525	−	0.569297i
$587$	2.09370	+	14.5620i	0.0864162	+	0.601038i	0.986307	+	0.164922i	$0.0527372\pi$
$587$	2.09370	+	14.5620i	0.0864162	+	0.601038i	−0.899890	+	0.436116i	$0.856354\pi$
$588$	0.841254	−	0.540641i	0.0346927	−	0.0222957i
$589$	17.1771	−	19.8235i	0.707771	−	0.816811i
$590$	−4.98220	+	10.9095i	−0.205114	+	0.449137i
$591$	8.46121	+	5.43769i	0.348048	+	0.223677i
$592$	5.82421	−	1.71014i	0.239373	−	0.0702864i
$593$	−18.0545	−	20.8360i	−0.741408	−	0.855630i	0.252298	−	0.967650i	$-0.418814\pi$
$593$	−18.0545	−	20.8360i	−0.741408	−	0.855630i	−0.993706	+	0.112019i	$0.964268\pi$
$594$	−0.731241	−	0.214712i	−0.0300032	−	0.00880973i
$595$	−10.8784	−	23.8203i	−0.445970	−	0.976537i
$596$	−1.00762	+	7.00813i	−0.0412736	+	0.287064i
$597$	8.46827			0.346583
$598$	2.48135	−	0.220326i	0.101470	−	0.00900979i
$599$	−14.7688			−0.603435			−0.301718	−	0.953397i	$-0.597560\pi$
$599$	−14.7688			−0.603435			−0.301718	+	0.953397i	$0.597560\pi$
$600$	−1.19674	+	8.32354i	−0.0488569	+	0.339807i
$601$	−15.8923	−	34.7993i	−0.648262	−	1.41949i	−0.893067	−	0.449923i	$-0.851451\pi$
$601$	−15.8923	−	34.7993i	−0.648262	−	1.41949i	0.244806	−	0.969572i	$-0.421276\pi$
$602$	−1.24873	−	0.366661i	−0.0508946	−	0.0149440i
$603$	−3.66676	−	4.23167i	−0.149322	−	0.172327i
$604$	−12.5379	+	3.68146i	−0.510160	+	0.149796i
$605$	32.0967	+	20.6273i	1.30492	+	0.838620i
$606$	−2.16621	+	4.74335i	−0.0879965	+	0.192685i
$607$	−15.6023	+	18.0060i	−0.633277	+	0.730840i	−0.978171	−	0.207801i	$-0.933369\pi$
$607$	−15.6023	+	18.0060i	−0.633277	+	0.730840i	0.344895	+	0.938641i	$0.387915\pi$
$608$	−5.25027	+	3.37414i	−0.212926	+	0.136839i
$609$	0.465760	+	3.23944i	0.0188736	+	0.131269i
$610$	5.13926	+	35.7443i	0.208082	+	1.44724i
$611$	2.34111	−	1.50454i	0.0947113	−	0.0608672i
$612$	−4.68306	+	5.40454i	−0.189302	+	0.218466i
$613$	−5.47612	+	11.9910i	−0.221178	+	0.484313i	−0.987396	−	0.158268i	$-0.949409\pi$
$613$	−5.47612	+	11.9910i	−0.221178	+	0.484313i	0.766218	+	0.642581i	$0.222136\pi$
$614$	−25.1513	−	16.1638i	−1.01502	−	0.652316i
$615$	6.05241	−	1.77715i	0.244057	−	0.0716615i
$616$	−0.499077	−	0.575966i	−0.0201084	−	0.0232063i
$617$	−35.3654	−	10.3842i	−1.42376	−	0.418053i	−0.522983	−	0.852343i	$-0.675181\pi$
$617$	−35.3654	−	10.3842i	−1.42376	−	0.418053i	−0.900773	+	0.434290i	$0.856999\pi$
$618$	−1.34891	−	2.95371i	−0.0542613	−	0.118816i
$619$	1.09697	−	7.62960i	0.0440910	−	0.306660i	−0.955828	−	0.293927i	$-0.905038\pi$
$619$	1.09697	−	7.62960i	0.0440910	−	0.306660i	0.999919	−	0.0127328i	$-0.00405310\pi$
$620$	−15.3903			−0.618090
$621$	2.80773	−	3.88801i	0.112670	−	0.156021i
$622$	11.5333			0.462442
$623$	0.00548934	−	0.0381792i	0.000219926	−	0.00152962i
$624$	−0.215780	−	0.472493i	−0.00863813	−	0.0189149i
$625$	−3.51928	−	1.03335i	−0.140771	−	0.0413342i
$626$	5.95296	+	6.87009i	0.237928	+	0.274584i
$627$	4.56368	−	1.34002i	0.182256	−	0.0535151i
$628$	4.71623	+	3.03094i	0.188198	+	0.120948i
$629$	−18.0326	+	39.4859i	−0.719007	+	1.57441i
$630$	2.39800	−	2.76744i	0.0955386	−	0.110257i
$631$	22.5992	−	14.5236i	0.899659	−	0.578176i	−0.00703020	−	0.999975i	$-0.502238\pi$
$631$	22.5992	−	14.5236i	0.899659	−	0.578176i	0.906689	+	0.421800i	$0.138601\pi$
$632$	1.15837	+	8.05665i	0.0460775	+	0.320476i
$633$	1.56317	+	10.8721i	0.0621303	+	0.432126i
$634$	3.33017	−	2.14017i	0.132258	−	0.0849969i
$635$	44.4410	−	51.2876i	1.76359	−	2.03529i
$636$	0.426190	−	0.933227i	0.0168996	−	0.0370049i
$637$	−0.436975	−	0.280827i	−0.0173136	−	0.0111268i
$638$	2.39317	−	0.702697i	0.0947464	−	0.0278200i
$639$	−9.80190	−	11.3120i	−0.387757	−	0.447496i
$640$	3.51352	+	1.03166i	0.138884	+	0.0407800i
$641$	−11.5761	−	25.3482i	−0.457230	−	1.00119i	−0.988110	−	0.153747i	$-0.950866\pi$
$641$	−11.5761	−	25.3482i	−0.457230	−	1.00119i	0.530881	−	0.847447i	$-0.321861\pi$
$642$	2.23057	−	15.5139i	0.0880335	−	0.612286i
$643$	−9.84673			−0.388317			−0.194159	−	0.980970i	$-0.562198\pi$
$643$	−9.84673			−0.388317			−0.194159	+	0.980970i	$0.562198\pi$
$644$	4.46403	−	1.75283i	0.175908	−	0.0690712i
$645$	−4.76572			−0.187650
$646$	6.35164	−	44.1766i	0.249902	−	1.73811i
$647$	10.3890	+	22.7488i	0.408435	+	0.894349i	0.996345	+	0.0854220i	$0.0272238\pi$
$647$	10.3890	+	22.7488i	0.408435	+	0.894349i	−0.587909	+	0.808927i	$0.700049\pi$
$648$	−0.959493	−	0.281733i	−0.0376924	−	0.0110675i
$649$	−1.63458	−	1.88641i	−0.0641629	−	0.0740480i
$650$	4.19105	−	1.23060i	0.164386	−	0.0482682i
$651$	3.53569	+	2.27225i	0.138575	+	0.0890565i
$652$	−4.51146	+	9.87871i	−0.176682	+	0.386880i
$653$	−26.5248	+	30.6112i	−1.03799	+	1.19791i	−0.0581175	+	0.998310i	$0.518510\pi$
$653$	−26.5248	+	30.6112i	−1.03799	+	1.19791i	−0.979877	+	0.199600i	$0.936036\pi$
$654$	−7.53925	+	4.84518i	−0.294808	+	0.189462i
$655$	5.73410	+	39.8815i	0.224050	+	1.55830i
$656$	−0.245152	−	1.70507i	−0.00957160	−	0.0665719i
$657$	13.1146	−	8.42822i	0.511648	−	0.328816i
$658$	3.50845	−	4.04896i	0.136773	−	0.157845i
$659$	10.0046	−	21.9070i	0.389724	−	0.853376i	−0.608486	−	0.793565i	$-0.708223\pi$
$659$	10.0046	−	21.9070i	0.389724	−	0.853376i	0.998210	−	0.0598112i	$-0.0190499\pi$
$660$	−2.34772	−	1.50879i	−0.0913848	−	0.0587294i
$661$	−19.8374	+	5.82478i	−0.771585	+	0.226558i	−0.643748	−	0.765237i	$-0.722622\pi$
$661$	−19.8374	+	5.82478i	−0.771585	+	0.226558i	−0.127837	+	0.991795i	$0.540803\pi$
$662$	−2.08688	−	2.40838i	−0.0811088	−	0.0936045i
$663$	3.56412	+	1.04652i	0.138419	+	0.0406435i
$664$	−6.15939	−	13.4872i	−0.239031	−	0.523404i
$665$	−3.25241	+	22.6210i	−0.126123	+	0.877204i
$666$	−6.07009			−0.235211
$667$	−0.850897	+	15.6725i	−0.0329469	+	0.606840i
$668$	13.0542			0.505082
$669$	2.97395	−	20.6842i	0.114979	−	0.799699i
$670$	−8.51757	−	18.6509i	−0.329063	−	0.720547i
$671$	−7.21124	−	2.11741i	−0.278387	−	0.0817418i
$672$	−0.654861	−	0.755750i	−0.0252618	−	0.0291537i
$673$	26.0188	−	7.63980i	1.00295	−	0.294493i	0.261284	−	0.965262i	$-0.415854\pi$
$673$	26.0188	−	7.63980i	1.00295	−	0.294493i	0.741666	+	0.670769i	$0.234036\pi$
$674$	16.2995	+	10.4751i	0.627835	+	0.403485i
$675$	3.49328	−	7.64922i	0.134456	−	0.294418i
$676$	8.33650	−	9.62084i	0.320635	−	0.370032i
$677$	7.66325	−	4.92487i	0.294523	−	0.189278i	−0.385032	−	0.922903i	$-0.625810\pi$
$677$	7.66325	−	4.92487i	0.294523	−	0.189278i	0.679554	+	0.733625i	$0.262173\pi$
$678$	1.95492	+	13.5968i	0.0750784	+	0.522181i
$679$	0.630706	+	4.38665i	0.0242043	+	0.168344i
$680$	−22.0297	+	14.1576i	−0.844800	+	0.542920i
$681$	−18.9993	+	21.9263i	−0.728054	+	0.840219i
$682$	1.33060	−	2.91361i	0.0509514	−	0.111568i
$683$	−10.1682	−	6.53472i	−0.389076	−	0.250044i	0.331449	−	0.943473i	$-0.392463\pi$
$683$	−10.1682	−	6.53472i	−0.389076	−	0.250044i	−0.720525	+	0.693429i	$0.756099\pi$
$684$	5.98820	−	1.75829i	0.228965	−	0.0672300i
$685$	28.3441	+	32.7108i	1.08297	+	1.24982i
$686$	−0.959493	−	0.281733i	−0.0366336	−	0.0107566i
$687$	6.54774	+	14.3376i	0.249812	+	0.547012i
$688$	−0.185216	+	1.28820i	−0.00706129	+	0.0491123i
$689$	−0.532907			−0.0203021
$690$	13.8761	−	10.7640i	0.528255	−	0.409778i
$691$	−14.5494			−0.553485			−0.276742	−	0.960944i	$-0.589255\pi$
$691$	−14.5494			−0.553485			−0.276742	+	0.960944i	$0.589255\pi$
$692$	−1.89565	+	13.1845i	−0.0720618	+	0.501201i
$693$	0.316593	+	0.693241i	0.0120264	+	0.0263341i
$694$	27.7483	+	8.14763i	1.05331	+	0.309280i
$695$	13.7332	+	15.8490i	0.520932	+	0.601187i
$696$	3.14018	−	0.922039i	0.119028	−	0.0349498i
$697$	10.3632	+	6.66003i	0.392534	+	0.252267i
$698$	5.48309	−	12.0063i	0.207538	−	0.454445i
$699$	−16.0341	+	18.5044i	−0.606466	+	0.699900i
$700$	7.07421	−	4.54632i	0.267380	−	0.171835i
$701$	−5.61101	−	39.0254i	−0.211925	−	1.47397i	−0.766719	−	0.641983i	$-0.778112\pi$
$701$	−5.61101	−	39.0254i	−0.211925	−	1.47397i	0.554794	−	0.831988i	$-0.312797\pi$
$702$	0.0739230	+	0.514146i	0.00279005	+	0.0194052i
$703$	31.8696	−	20.4813i	1.20198	−	0.772468i
$704$	−0.499077	+	0.575966i	−0.0188097	+	0.0217075i
$705$	8.14983	−	17.8456i	0.306940	−	0.672105i
$706$	23.0242	+	14.7967i	0.866525	+	0.556882i
$707$	5.00335	−	1.46912i	0.188170	−	0.0552518i
$708$	−2.14480	−	2.47524i	−0.0806067	−	0.0930251i
$709$	−12.6836	−	3.72423i	−0.476341	−	0.139866i	0.0347446	−	0.999396i	$-0.488938\pi$
$709$	−12.6836	−	3.72423i	−0.476341	−	0.139866i	−0.511085	+	0.859530i	$0.670756\pi$
$710$	−22.7690	−	49.8572i	−0.854505	−	1.87111i
$711$	1.15837	−	8.05665i	0.0434423	−	0.302148i
$712$	−0.0385718			−0.00144554
$713$	14.4951	+	14.0060i	0.542847	+	0.524529i
$714$	7.15124			0.267628
$715$	−0.206300	+	1.43485i	−0.00771518	+	0.0536602i
$716$	−7.11446	−	15.5785i	−0.265880	−	0.582196i
$717$	−18.8270	−	5.52812i	−0.703108	−	0.206451i
$718$	4.65121	+	5.36779i	0.173582	+	0.200324i
$719$	21.9088	−	6.43300i	0.817059	−	0.239910i	0.153610	−	0.988132i	$-0.450910\pi$
$719$	21.9088	−	6.43300i	0.817059	−	0.239910i	0.663449	+	0.748221i	$0.269092\pi$
$720$	−3.08054	−	1.97974i	−0.114805	−	0.0737807i
$721$	−1.34891	+	2.95371i	−0.0502362	+	0.110002i
$722$	−13.0646	+	15.0773i	−0.486212	+	0.561119i
$723$	0.713501	−	0.458540i	0.0265354	−	0.0170533i
$724$	−1.55388	−	10.8075i	−0.0577495	−	0.401657i
$725$	3.91664	+	27.2408i	0.145460	+	1.01170i
$726$	−8.76518	+	5.63304i	−0.325306	+	0.209062i
$727$	−17.5616	+	20.2671i	−0.651323	+	0.751666i	−0.981334	−	0.192311i	$-0.938402\pi$
$727$	−17.5616	+	20.2671i	−0.651323	+	0.751666i	0.330012	+	0.943977i	$0.392947\pi$
$728$	−0.215780	+	0.472493i	−0.00799735	+	0.0175118i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	54.7733	−	16.0829i	2.02725	−	0.595255i
$731$	−6.09478	−	7.03375i	−0.225424	−	0.260153i
$732$	−9.46219	−	2.77835i	−0.349732	−	0.102691i
$733$	−14.3414	−	31.4032i	−0.529710	−	1.15990i	−0.965631	−	0.259918i	$-0.916304\pi$
$733$	−14.3414	−	31.4032i	−0.529710	−	1.15990i	0.435921	−	0.899985i	$-0.356423\pi$
$734$	−3.70720	+	25.7841i	−0.136835	+	0.951709i
$735$	−3.66185			−0.135069
$736$	−2.37029	−	4.16914i	−0.0873700	−	0.153677i
$737$	4.26729			0.157188
$738$	−0.245152	+	1.70507i	−0.00902419	+	0.0627646i
$739$	−0.383482	−	0.839708i	−0.0141066	−	0.0308892i	0.902448	−	0.430800i	$-0.141768\pi$
$739$	−0.383482	−	0.839708i	−0.0141066	−	0.0308892i	−0.916554	+	0.399911i	$0.869041\pi$
$740$	−21.3274	−	6.26228i	−0.784009	−	0.230206i
$741$	−2.12292	−	2.44998i	−0.0779873	−	0.0900021i
$742$	−0.984381	+	0.289040i	−0.0361378	+	0.0106110i
$743$	27.8676	+	17.9094i	1.02236	+	0.657032i	0.940564	−	0.339617i	$-0.110297\pi$
$743$	27.8676	+	17.9094i	1.02236	+	0.657032i	0.0817980	+	0.996649i	$0.473934\pi$
$744$	1.74594	−	3.82308i	0.0640093	−	0.140161i
$745$	16.9783	−	19.5940i	0.622037	−	0.717869i
$746$	24.8176	−	15.9493i	0.908636	−	0.583945i
$747$	2.11011	+	14.6762i	0.0772050	+	0.536972i
$748$	−0.775622	−	5.39457i	−0.0283595	−	0.197245i
$749$	−13.1854	+	8.47372i	−0.481783	+	0.309623i
$750$	8.17510	−	9.43457i	0.298513	−	0.344502i
$751$	−4.67472	+	10.2362i	−0.170583	+	0.373525i	−0.975544	−	0.219802i	$-0.929459\pi$
$751$	−4.67472	+	10.2362i	−0.170583	+	0.373525i	0.804961	+	0.593327i	$0.202186\pi$
$752$	−4.50705	−	2.89651i	−0.164355	−	0.105625i
$753$	4.87849	−	1.43245i	0.177782	−	0.0522015i
$754$	−1.11325	−	1.28475i	−0.0405420	−	0.0467880i
$755$	45.9119	+	13.4809i	1.67090	+	0.490622i
$756$	0.415415	+	0.909632i	0.0151085	+	0.0330830i
$757$	0.0818706	−	0.569422i	0.00297564	−	0.0206960i	−0.988280	−	0.152655i	$-0.951218\pi$
$757$	0.0818706	−	0.569422i	0.00297564	−	0.0206960i	0.991255	+	0.131959i	$0.0421267\pi$
$758$	26.8502			0.975244
$759$	0.838088	+	3.55757i	0.0304207	+	0.129132i
$760$	22.8536			0.828987
$761$	6.23241	−	43.3474i	0.225925	−	1.57134i	−0.489091	−	0.872233i	$-0.662671\pi$
$761$	6.23241	−	43.3474i	0.225925	−	1.57134i	0.715015	−	0.699109i	$-0.246420\pi$
$762$	7.69868	+	16.8578i	0.278894	+	0.610692i
$763$	8.59890	+	2.52487i	0.311301	+	0.0914063i
$764$	−6.60086	−	7.61780i	−0.238811	−	0.275602i
$765$	25.1260	−	7.37766i	0.908432	−	0.266740i
$766$	−13.4286	−	8.63003i	−0.485195	−	0.311816i
$767$	−0.706725	+	1.54751i	−0.0255184	+	0.0558774i
$768$	−0.654861	+	0.755750i	−0.0236303	+	0.0272708i
$769$	27.2753	−	17.5288i	0.983573	−	0.632104i	0.0531484	−	0.998587i	$-0.483074\pi$
$769$	27.2753	−	17.5288i	0.983573	−	0.632104i	0.930425	+	0.366482i	$0.119438\pi$
$770$	0.397163	+	2.76233i	0.0143128	+	0.0995475i
$771$	−3.21304	−	22.3472i	−0.115715	−	0.804815i
$772$	−11.4747	+	7.37436i	−0.412984	+	0.265409i
$773$	12.6248	−	14.5698i	0.454083	−	0.524040i	−0.481833	−	0.876263i	$-0.660029\pi$
$773$	12.6248	−	14.5698i	0.454083	−	0.524040i	0.935916	+	0.352223i	$0.114574\pi$
$774$	0.540642	−	1.18384i	0.0194330	−	0.0425523i
$775$	29.7321	+	19.1076i	1.06801	+	0.686367i
$776$	4.25225	−	1.24857i	0.152647	−	0.0448211i
$777$	3.97506	+	4.58747i	0.142605	+	0.164574i
$778$	−21.7976	−	6.40034i	−0.781480	−	0.229463i
$779$	−4.46604	−	9.77926i	−0.160013	−	0.350379i
$780$	−0.270695	+	1.88272i	−0.00969243	+	0.0674124i
$781$	11.4072			0.408183
$782$	33.6325	+	6.71403i	1.20270	+	0.240093i
$783$	−3.27275			−0.116958
$784$	−0.142315	+	0.989821i	−0.00508267	+	0.0353508i
$785$	−8.52807	−	18.6739i	−0.304380	−	0.666499i
$786$	−10.5574	−	3.09993i	−0.376569	−	0.110571i
$787$	11.1585	+	12.8776i	0.397759	+	0.459039i	0.918934	−	0.394411i	$-0.129051\pi$
$787$	11.1585	+	12.8776i	0.397759	+	0.459039i	−0.521175	+	0.853450i	$0.674506\pi$
$788$	−9.65045	+	2.83363i	−0.343783	+	0.100944i
$789$	1.89977	+	1.22091i	0.0676337	+	0.0434656i
$790$	12.3817	−	27.1121i	0.440521	−	0.964607i
$791$	8.99556	−	10.3814i	0.319845	−	0.369121i
$792$	0.641129	−	0.412029i	0.0227815	−	0.0146408i
$793$	0.729003	+	5.07033i	0.0258877	+	0.180053i
$794$	−0.313248	−	2.17869i	−0.0111168	−	0.0773187i
$795$	−3.16045	+	2.03110i	−0.112090	+	0.0720356i
$796$	−5.54554	+	6.39989i	−0.196556	+	0.226838i
$797$	14.8809	−	32.5845i	0.527107	−	1.15420i	−0.439571	−	0.898208i	$-0.644869\pi$
$797$	14.8809	−	32.5845i	0.527107	−	1.15420i	0.966678	−	0.255996i	$-0.0824033\pi$
$798$	−5.25027	−	3.37414i	−0.185857	−	0.119443i
$799$	36.7611	−	10.7940i	1.30051	−	0.381866i
$800$	−5.50681	−	6.35520i	−0.194695	−	0.224690i
$801$	0.0370094	+	0.0108669i	0.00130766	+	0.000383964i
$802$	−14.0593	−	30.7856i	−0.496452	−	1.08708i
$803$	−1.69081	+	11.7599i	−0.0596675	+	0.414997i
$804$	5.59930			0.197472
$805$	−17.2218	−	3.43797i	−0.606989	−	0.121173i
$806$	−2.18312			−0.0768970
$807$	−2.10217	+	14.6209i	−0.0739997	+	0.514679i
$808$	−2.16621	−	4.74335i	−0.0762072	−	0.166870i
$809$	−21.4591	−	6.30097i	−0.754463	−	0.221530i	−0.118187	−	0.992991i	$-0.537708\pi$
$809$	−21.4591	−	6.30097i	−0.754463	−	0.221530i	−0.636277	+	0.771461i	$0.719526\pi$
$810$	2.39800	+	2.76744i	0.0842572	+	0.0972379i
$811$	31.6240	−	9.28565i	1.11047	−	0.326063i	0.325465	−	0.945554i	$-0.394479\pi$
$811$	31.6240	−	9.28565i	1.11047	−	0.326063i	0.785004	+	0.619491i	$0.212661\pi$
$812$	−2.75321	−	1.76938i	−0.0966187	−	0.0620931i
$813$	−9.95923	+	21.8077i	−0.349286	+	0.764829i
$814$	3.02944	−	3.49616i	0.106182	−	0.122540i
$815$	33.4551	−	21.5003i	1.17188	−	0.753121i
$816$	−1.01773	−	7.07845i	−0.0356276	−	0.247795i
$817$	1.15593	+	8.03969i	0.0404410	+	0.281273i
$818$	18.0347	−	11.5902i	0.630568	−	0.405242i
$819$	0.340156	−	0.392561i	0.0118860	−	0.0137172i
$820$	−2.62041	+	5.73789i	−0.0915085	+	0.200376i
$821$	−1.63371	−	1.04992i	−0.0570169	−	0.0366425i	0.511822	−	0.859092i	$-0.328971\pi$
$821$	−1.63371	−	1.04992i	−0.0570169	−	0.0366425i	−0.568839	+	0.822449i	$0.692607\pi$
$822$	−11.3411	+	3.33004i	−0.395566	+	0.116149i
$823$	−28.4611	−	32.8459i	−0.992093	−	1.14494i	−0.989440	−	0.144940i	$-0.953701\pi$
$823$	−28.4611	−	32.8459i	−0.992093	−	1.14494i	−0.00265238	−	0.999996i	$-0.500844\pi$
$824$	3.11562	+	0.914827i	0.108538	+	0.0318695i
$825$	2.66227	+	5.82956i	0.0926883	+	0.202959i
$826$	−0.466111	+	3.24187i	−0.0162181	+	0.112799i
$827$	−8.78579			−0.305512			−0.152756	−	0.988264i	$-0.548815\pi$
$827$	−8.78579			−0.305512			−0.152756	+	0.988264i	$0.548815\pi$
$828$	1.09969	+	4.66805i	0.0382169	+	0.162226i
$829$	55.8982			1.94143			0.970713	−	0.240243i	$-0.0772272\pi$
$829$	55.8982			1.94143			0.970713	+	0.240243i	$0.0772272\pi$
$830$	−7.72691	+	53.7419i	−0.268205	+	1.86541i
$831$	8.65927	+	18.9612i	0.300387	+	0.657755i
$832$	0.498392	+	0.146341i	0.0172786	+	0.00507347i
$833$	−4.68306	−	5.40454i	−0.162259	−	0.187256i
$834$	−5.49498	+	1.61347i	−0.190275	+	0.0558699i
$835$	−40.2140	−	25.8440i	−1.39166	−	0.894368i
$836$	−1.97586	+	4.32652i	−0.0683364	+	0.149636i
$837$	−2.75230	+	3.17633i	−0.0951335	+	0.109790i
$838$	9.14328	−	5.87603i	0.315849	−	0.202984i
$839$	−7.21418	−	50.1757i	−0.249061	−	1.73226i	−0.603662	−	0.797240i	$-0.706292\pi$
$839$	−7.21418	−	50.1757i	−0.249061	−	1.73226i	0.354601	−	0.935018i	$-0.384617\pi$
$840$	0.521135	+	3.62458i	0.0179809	+	0.125060i
$841$	−15.3858	+	9.88785i	−0.530545	+	0.340960i
$842$	11.6951	−	13.4969i	0.403040	−	0.465133i
$843$	−7.36055	+	16.1173i	−0.253511	+	0.555111i
$844$	−9.24021	−	5.93832i	−0.318061	−	0.204406i
$845$	−44.7277	+	13.1333i	−1.53868	+	0.451798i
$846$	3.50845	+	4.04896i	0.120623	+	0.139206i
$847$	9.99714	+	2.93542i	0.343506	+	0.100862i
$848$	0.426190	+	0.933227i	0.0146354	+	0.0320471i
$849$	2.61384	−	18.1797i	0.0897069	−	0.623925i
$850$	60.1357			2.06264
$851$	14.3879	+	25.3071i	0.493209	+	0.867515i
$852$	14.9679			0.512793
$853$	−0.142865	+	0.993649i	−0.00489161	+	0.0340219i	−0.992121	−	0.125283i	$-0.960016\pi$
$853$	−0.142865	+	0.993649i	−0.00489161	+	0.0340219i	0.987229	+	0.159305i	$0.0509252\pi$
$854$	4.09668	+	8.97047i	0.140185	+	0.306963i
$855$	−21.9279	−	6.43861i	−0.749918	−	0.220196i
$856$	10.2639	+	11.8452i	0.350814	+	0.404861i
$857$	−38.2338	+	11.2265i	−1.30604	+	0.383488i	−0.859436	−	0.511243i	$-0.829185\pi$
$857$	−38.2338	+	11.2265i	−1.30604	+	0.383488i	−0.446605	+	0.894731i	$0.647367\pi$
$858$	−0.333024	−	0.214021i	−0.0113692	−	0.00730657i
$859$	−10.6665	+	23.3564i	−0.363937	+	0.796911i	0.635750	+	0.771895i	$0.280691\pi$
$859$	−10.6665	+	23.3564i	−0.363937	+	0.796911i	−0.999687	+	0.0250158i	$0.992036\pi$
$860$	3.12088	−	3.60169i	0.106421	−	0.122817i
$861$	1.44915	−	0.931311i	0.0493869	−	0.0317390i
$862$	2.80512	+	19.5100i	0.0955428	+	0.664515i
$863$	5.90117	+	41.0436i	0.200878	+	1.39714i	0.801686	+	0.597746i	$0.203937\pi$
$863$	5.90117	+	41.0436i	0.200878	+	1.39714i	−0.600807	+	0.799394i	$0.705154\pi$
$864$	0.841254	−	0.540641i	0.0286200	−	0.0183930i
$865$	31.9416	−	36.8626i	1.08605	−	1.25337i
$866$	7.88839	−	17.2732i	0.268058	−	0.586966i
$867$	28.7205	+	18.4576i	0.975401	+	0.626852i
$868$	−4.03264	+	1.18409i	−0.136877	+	0.0401906i
$869$	4.06224	+	4.68807i	0.137802	+	0.159032i
$870$	−11.4989	−	3.37637i	−0.389848	−	0.114470i
$871$	−1.20822	−	2.64563i	−0.0409389	−	0.0896437i
$872$	1.27542	−	8.87071i	0.0431910	−	0.300400i
$873$	−4.43176			−0.149992
$874$	−21.5243	−	20.7980i	−0.728071	−	0.703502i
$875$	−12.4837			−0.422027
$876$	−2.21859	+	15.4306i	−0.0749593	+	0.521353i
$877$	1.85833	+	4.06918i	0.0627514	+	0.137406i	0.938409	−	0.345525i	$-0.112299\pi$
$877$	1.85833	+	4.06918i	0.0627514	+	0.137406i	−0.875658	+	0.482932i	$0.839572\pi$
$878$	−28.0942	−	8.24920i	−0.948133	−	0.278397i
$879$	−9.11758	−	10.5222i	−0.307528	−	0.354907i
$880$	2.67769	−	0.786242i	0.0902650	−	0.0265042i
$881$	−35.5070	−	22.8189i	−1.19626	−	0.768789i	−0.217955	−	0.975959i	$-0.569938\pi$
$881$	−35.5070	−	22.8189i	−1.19626	−	0.768789i	−0.978305	+	0.207170i	$0.933575\pi$
$882$	0.415415	−	0.909632i	0.0139878	−	0.0306289i
$883$	27.7902	−	32.0716i	0.935214	−	1.07929i	−0.0614851	−	0.998108i	$-0.519584\pi$
$883$	27.7902	−	32.0716i	0.935214	−	1.07929i	0.996699	−	0.0811863i	$-0.0258709\pi$
$884$	−3.12491	+	2.00826i	−0.105102	+	0.0675450i
$885$	1.70683	+	11.8712i	0.0573743	+	0.399047i
$886$	0.622782	+	4.33154i	0.0209228	+	0.145521i
$887$	−2.61563	+	1.68096i	−0.0878241	+	0.0564411i	−0.583816	−	0.811886i	$-0.698441\pi$
$887$	−2.61563	+	1.68096i	−0.0878241	+	0.0564411i	0.495992	+	0.868327i	$0.334805\pi$
$888$	3.97506	−	4.58747i	0.133394	−	0.153945i
$889$	7.69868	−	16.8578i	0.258205	−	0.565391i
$890$	0.118822	+	0.0763623i	0.00398292	+	0.00255967i
$891$	−0.731241	+	0.214712i	−0.0244975	+	0.00719311i
$892$	13.6846	+	15.7929i	0.458194	+	0.528784i
$893$	−32.0820	−	9.42014i	−1.07358	−	0.315233i
$894$	2.94122	+	6.44037i	0.0983690	+	0.215398i
$895$	−8.92504	+	62.0750i	−0.298331	+	2.07494i
$896$	1.00000			0.0334077
$897$	1.96833	−	1.52687i	0.0657206	−	0.0509807i
$898$	15.4428			0.515334
$899$	1.95754	−	13.6150i	0.0652875	−	0.454084i
$900$	3.49328	+	7.64922i	0.116443	+	0.254974i
$901$	−7.03954	−	2.06700i	−0.234521	−	0.0688616i
$902$	−0.859713	−	0.992162i	−0.0286253	−	0.0330354i
$903$	−1.24873	+	0.366661i	−0.0415552	+	0.0122017i
$904$	−11.5560	−	7.42657i	−0.384346	−	0.247004i
$905$	−16.6092	+	36.3692i	−0.552110	+	1.20895i
$906$	−8.55720	+	9.87554i	−0.284294	+	0.328093i
$907$	10.4311	−	6.70369i	0.346360	−	0.222592i	−0.355881	−	0.934531i	$-0.615819\pi$
$907$	10.4311	−	6.70369i	0.346360	−	0.222592i	0.702241	+	0.711939i	$0.252183\pi$
$908$	−4.12894	−	28.7174i	−0.137024	−	0.953020i
$909$	0.742112	+	5.16150i	0.0246143	+	0.171196i
$910$	1.60014	−	1.02834i	0.0530440	−	0.0340893i
$911$	−28.2592	+	32.6129i	−0.936269	+	1.08051i	0.0603359	+	0.998178i	$0.480783\pi$
$911$	−28.2592	+	32.6129i	−0.936269	+	1.08051i	−0.996605	+	0.0823338i	$0.973763\pi$
$912$	−2.59261	+	5.67702i	−0.0858498	+	0.187985i
$913$	−9.50607	−	6.10918i	−0.314605	−	0.202184i
$914$	4.27526	−	1.25533i	0.141413	−	0.0415226i
$915$	23.6482	+	27.2915i	0.781787	+	0.902230i
$916$	−15.1235	−	4.44065i	−0.499693	−	0.146723i
$917$	4.57085	+	10.0088i	0.150943	+	0.330518i
$918$	−1.01773	+	7.07845i	−0.0335900	+	0.233624i
$919$	−44.4734			−1.46704			−0.733521	−	0.679666i	$-0.762125\pi$
$919$	−44.4734			−1.46704			−0.733521	+	0.679666i	$0.762125\pi$
$920$	−0.952062	+	17.5358i	−0.0313885	+	0.578138i
$921$	−29.8974			−0.985153
$922$	3.87155	−	26.9272i	0.127503	−	0.886800i
$923$	−3.22978	−	7.07224i	−0.106310	−	0.232786i
$924$	−0.731241	−	0.214712i	−0.0240561	−	0.00706350i
$925$	33.4268	+	38.5766i	1.09907	+	1.26839i
$926$	−15.5004	+	4.55133i	−0.509375	+	0.149566i
$927$	−2.73168	−	1.75554i	−0.0897200	−	0.0576595i
$928$	−1.35955	+	2.97700i	−0.0446294	+	0.0977247i
$929$	−30.0009	+	34.6229i	−0.984297	+	1.13594i	0.00641753	+	0.999979i	$0.497957\pi$
$929$	−30.0009	+	34.6229i	−0.984297	+	1.13594i	−0.990714	+	0.135960i	$0.956588\pi$
$930$	−12.9472	+	8.32063i	−0.424554	+	0.272844i
$931$	0.888187	+	6.17748i	0.0291092	+	0.202459i
$932$	−3.48455	−	24.2356i	−0.114140	−	0.793863i
$933$	9.70240	−	6.23536i	0.317642	−	0.204136i
$934$	−16.1039	+	18.5849i	−0.526935	+	0.608115i
$935$	−8.29053	+	18.1537i	−0.271129	+	0.593691i
$936$	−0.436975	−	0.280827i	−0.0142830	−	0.00917911i
$937$	43.1781	−	12.6782i	1.41057	−	0.414180i	0.514268	−	0.857630i	$-0.328064\pi$
$937$	43.1781	−	12.6782i	1.41057	−	0.414180i	0.896299	+	0.443450i	$0.146246\pi$
$938$	−3.66676	−	4.23167i	−0.119724	−	0.138169i
$939$	8.72220	+	2.56107i	0.284638	+	0.0835773i
$940$	8.14983	+	17.8456i	0.265818	+	0.582060i
$941$	0.861497	−	5.99184i	0.0280840	−	0.195328i	−0.970949	−	0.239285i	$-0.923087\pi$
$941$	0.861497	−	5.99184i	0.0280840	−	0.195328i	0.999033	+	0.0439562i	$0.0139962\pi$
$942$	5.60619			0.182660
$943$	7.68977	−	3.01944i	0.250413	−	0.0983264i
$944$	3.27521			0.106599
$945$	0.521135	−	3.62458i	0.0169525	−	0.117907i
$946$	0.412030	+	0.902220i	0.0133963	+	0.0293337i
$947$	30.5145	+	8.95986i	0.991587	+	0.291156i	0.736999	−	0.675893i	$-0.236242\pi$
$947$	30.5145	+	8.95986i	0.991587	+	0.291156i	0.254588	+	0.967050i	$0.418060\pi$
$948$	5.33024	+	6.15142i	0.173118	+	0.199789i
$949$	7.76960	−	2.28136i	0.252212	−	0.0740561i
$950$	−44.1502	−	28.3736i	−1.43242	−	0.920561i
$951$	1.64445	−	3.60085i	0.0533250	−	0.116765i
$952$	−4.68306	+	5.40454i	−0.151779	+	0.175162i
$953$	22.5483	−	14.4909i	0.730411	−	0.469407i	−0.121833	−	0.992551i	$-0.538877\pi$
$953$	22.5483	−	14.4909i	0.730411	−	0.469407i	0.852244	+	0.523144i	$0.175241\pi$
$954$	−0.146006	−	1.01550i	−0.00472713	−	0.0328779i
$955$	5.25294	+	36.5350i	0.169981	+	1.18224i
$956$	16.5070	−	10.6084i	0.533873	−	0.343099i
$957$	1.63335	−	1.88499i	0.0527988	−	0.0609331i
$958$	9.74564	−	21.3400i	0.314867	−	0.689464i
$959$	9.94352	+	6.39031i	0.321093	+	0.206354i
$960$	3.51352	−	1.03166i	0.113398	−	0.0332967i
$961$	8.73308	+	10.0785i	0.281712	+	0.325113i
$962$	−3.02529	−	0.888304i	−0.0975391	−	0.0286401i
$963$	−6.51100	−	14.2571i	−0.209814	−	0.459428i
$964$	−0.120703	+	0.839508i	−0.00388758	+	0.0270387i
$965$	49.9477			1.60787
$966$	2.80773	−	3.88801i	0.0903373	−	0.125095i
$967$	−6.12563			−0.196987			−0.0984936	−	0.995138i	$-0.531402\pi$
$967$	−6.12563			−0.196987			−0.0984936	+	0.995138i	$0.531402\pi$
$968$	1.48280	−	10.3131i	0.0476591	−	0.331477i
$969$	−18.5403	−	40.5977i	−0.595602	−	1.30419i
$970$	−15.5711	−	4.57208i	−0.499957	−	0.146801i
$971$	−22.5454	−	26.0188i	−0.723516	−	0.834982i	0.268209	−	0.963361i	$-0.413568\pi$
$971$	−22.5454	−	26.0188i	−0.723516	−	0.834982i	−0.991725	+	0.128379i	$0.959023\pi$
$972$	−0.959493	+	0.281733i	−0.0307758	+	0.00903658i
$973$	4.81782	+	3.09623i	0.154452	+	0.0992605i
$974$	−6.22161	+	13.6234i	−0.199353	+	0.436523i
$975$	2.86042	−	3.30110i	0.0916067	−	0.105720i
$976$	8.29615	−	5.33161i	0.265553	−	0.170661i
$977$	4.81076	+	33.4596i	0.153910	+	1.07047i	0.909584	+	0.415520i	$0.136400\pi$
$977$	4.81076	+	33.4596i	0.153910	+	1.07047i	−0.755674	+	0.654948i	$0.772691\pi$
$978$	1.54556	+	10.7496i	0.0494214	+	0.343734i
$979$	−0.0247295	+	0.0158927i	−0.000790358	+	0.000507932i
$980$	2.39800	−	2.76744i	0.0766013	−	0.0884026i
$981$	−3.72292	+	8.15205i	−0.118864	+	0.260275i
$982$	11.0964	+	7.13121i	0.354100	+	0.227566i
$983$	−8.35899	+	2.45442i	−0.266610	+	0.0782839i	−0.412305	−	0.911046i	$-0.635276\pi$
$983$	−8.35899	+	2.45442i	−0.266610	+	0.0782839i	0.145695	+	0.989330i	$0.453458\pi$
$984$	−1.12807	−	1.30186i	−0.0359615	−	0.0415018i
$985$	35.3385	+	10.3763i	1.12598	+	0.330617i
$986$	−9.72245	−	21.2892i	−0.309626	−	0.677986i
$987$	0.762458	−	5.30301i	0.0242693	−	0.168797i
$988$	3.24178			0.103135
$989$	−6.21708	+	0.552031i	−0.197692	+	0.0175536i
$990$	−2.79074			−0.0886955
$991$	−2.67873	+	18.6310i	−0.0850926	+	0.591832i	0.902007	+	0.431722i	$0.142094\pi$
$991$	−2.67873	+	18.6310i	−0.0850926	+	0.591832i	−0.987099	+	0.160110i	$0.948815\pi$
$992$	1.74594	+	3.82308i	0.0554337	+	0.121383i
$993$	−3.05766	−	0.897811i	−0.0970320	−	0.0284912i
$994$	−9.80190	−	11.3120i	−0.310897	−	0.358795i
$995$	29.7534	−	8.73639i	0.943247	−	0.276962i
$996$	−12.4733	−	8.01612i	−0.395233	−	0.254001i
$997$	−6.60311	+	14.4588i	−0.209123	+	0.457915i	−0.984907	−	0.173083i	$-0.944627\pi$
$997$	−6.60311	+	14.4588i	−0.209123	+	0.457915i	0.775785	+	0.630998i	$0.217354\pi$
$998$	6.17532	−	7.12670i	0.195476	−	0.225592i
$999$	−5.10648	+	3.28174i	−0.161562	+	0.103830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.i.169.4	✓	40
23.3	even	11	inner	966.2.q.i.463.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.i.169.4	✓	40	1.1	even	1	trivial
966.2.q.i.463.4	yes	40	23.3	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.39800 + 2.76744i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(0.415415 + 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.39800 + 2.76744i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-3.08054 + 1.97974i) q^{10} +(-0.108460 - 0.754355i) q^{11} +(-0.142315 - 0.989821i) q^{12} +(-0.436975 + 0.280827i) q^{13} +(-0.654861 + 0.755750i) q^{14} +(-1.52119 + 3.33093i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-6.86156 + 2.01474i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(5.98820 + 1.75829i) q^{19} +(-1.52119 - 3.33093i) q^{20} +(-0.142315 + 0.989821i) q^{21} +0.762112 q^{22} +(-1.59862 + 4.52155i) q^{23} +1.00000 q^{24} +(-1.19674 + 8.32354i) q^{25} +(-0.215780 - 0.472493i) q^{26} +(-0.959493 - 0.281733i) q^{27} +(-0.654861 - 0.755750i) q^{28} +(3.14018 - 0.922039i) q^{29} +(-3.08054 - 1.97974i) q^{30} +(1.74594 - 3.82308i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(0.641129 - 0.412029i) q^{33} +(-1.01773 - 7.07845i) q^{34} +(0.521135 + 3.62458i) q^{35} +(0.841254 - 0.540641i) q^{36} +(3.97506 - 4.58747i) q^{37} +(-2.59261 + 5.67702i) q^{38} +(-0.436975 - 0.280827i) q^{39} +(3.51352 - 1.03166i) q^{40} +(-1.12807 - 1.30186i) q^{41} +(-0.959493 - 0.281733i) q^{42} +(0.540642 + 1.18384i) q^{43} +(-0.108460 + 0.754355i) q^{44} -3.66185 q^{45} +(-4.24802 - 2.22583i) q^{46} -5.35754 q^{47} +(-0.142315 + 0.989821i) q^{48} +(0.415415 + 0.909632i) q^{49} +(-8.06850 - 2.36913i) q^{50} +(-4.68306 - 5.40454i) q^{51} +(0.498392 - 0.146341i) q^{52} +(0.863075 + 0.554665i) q^{53} +(0.415415 - 0.909632i) q^{54} +(1.82754 - 2.10910i) q^{55} +(0.841254 - 0.540641i) q^{56} +(0.888187 + 6.17748i) q^{57} +(0.465760 + 3.23944i) q^{58} +(2.75528 - 1.77071i) q^{59} +(2.39800 - 2.76744i) q^{60} +(4.09668 - 8.97047i) q^{61} +(3.53569 + 2.27225i) q^{62} +(-0.959493 + 0.281733i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-1.82504 - 0.535879i) q^{65} +(0.316593 + 0.693241i) q^{66} +(-0.796863 + 5.54230i) q^{67} +7.15124 q^{68} +(-4.77704 + 0.424166i) q^{69} -3.66185 q^{70} +(-2.13016 + 14.8156i) q^{71} +(0.415415 + 0.909632i) q^{72} +(-14.9578 - 4.39202i) q^{73} +(3.97506 + 4.58747i) q^{74} +(-8.06850 + 2.36913i) q^{75} +(-5.25027 - 3.37414i) q^{76} +(0.316593 - 0.693241i) q^{77} +(0.340156 - 0.392561i) q^{78} +(-6.84738 + 4.40055i) q^{79} +(0.521135 + 3.62458i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(1.44915 - 0.931311i) q^{82} +(9.70967 - 11.2056i) q^{83} +(0.415415 - 0.909632i) q^{84} +(-22.0297 - 14.1576i) q^{85} +(-1.24873 + 0.366661i) q^{86} +(2.14319 + 2.47338i) q^{87} +(-0.731241 - 0.214712i) q^{88} +(-0.0160233 - 0.0350861i) q^{89} +(0.521135 - 3.62458i) q^{90} -0.519433 q^{91} +(2.80773 - 3.88801i) q^{92} +4.20288 q^{93} +(0.762458 - 5.30301i) q^{94} +(9.49373 + 20.7884i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(2.90219 + 3.34930i) q^{97} +(-0.959493 + 0.281733i) q^{98} +(0.641129 + 0.412029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 7 q^{15} - 4 q^{16} - 7 q^{17} - 4 q^{18} + 20 q^{19} - 7 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{23} + 40 q^{24} - 22 q^{25} + 14 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 4 q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 7 q^{34} - 7 q^{35} - 4 q^{36} - 16 q^{37} - 13 q^{38} - 8 q^{39} + 4 q^{40} - 17 q^{41} - 4 q^{42} + 26 q^{43} - q^{44} + 4 q^{45} - 20 q^{46} + 72 q^{47} - 4 q^{48} - 4 q^{49} + 11 q^{50} - 7 q^{51} - 19 q^{52} + 6 q^{53} - 4 q^{54} + 49 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} - 51 q^{59} + 4 q^{60} - 42 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{64} + 8 q^{65} - 12 q^{66} + 54 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{70} - 59 q^{71} - 4 q^{72} - 27 q^{73} - 16 q^{74} + 11 q^{75} - 2 q^{76} - 12 q^{77} - 8 q^{78} - 6 q^{79} - 7 q^{80} - 4 q^{81} - 6 q^{82} - 24 q^{83} - 4 q^{84} + 35 q^{85} - 7 q^{86} - 29 q^{87} - q^{88} + 22 q^{89} - 7 q^{90} + 36 q^{91} - 9 q^{92} + 50 q^{93} - 16 q^{94} + 22 q^{95} - 4 q^{96} + 16 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 7 * q^15 - 4 * q^16 - 7 * q^17 - 4 * q^18 + 20 * q^19 - 7 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^23 + 40 * q^24 - 22 * q^25 + 14 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 4 * q^30 - 16 * q^31 - 4 * q^32 - q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 - 16 * q^37 - 13 * q^38 - 8 * q^39 + 4 * q^40 - 17 * q^41 - 4 * q^42 + 26 * q^43 - q^44 + 4 * q^45 - 20 * q^46 + 72 * q^47 - 4 * q^48 - 4 * q^49 + 11 * q^50 - 7 * q^51 - 19 * q^52 + 6 * q^53 - 4 * q^54 + 49 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 - 51 * q^59 + 4 * q^60 - 42 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^64 + 8 * q^65 - 12 * q^66 + 54 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^70 - 59 * q^71 - 4 * q^72 - 27 * q^73 - 16 * q^74 + 11 * q^75 - 2 * q^76 - 12 * q^77 - 8 * q^78 - 6 * q^79 - 7 * q^80 - 4 * q^81 - 6 * q^82 - 24 * q^83 - 4 * q^84 + 35 * q^85 - 7 * q^86 - 29 * q^87 - q^88 + 22 * q^89 - 7 * q^90 + 36 * q^91 - 9 * q^92 + 50 * q^93 - 16 * q^94 + 22 * q^95 - 4 * q^96 + 16 * q^97 - 4 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more