LMFDB - Embedded newform 966.2.r.a.113.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(113,966)]

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([11, 0, 13]))

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

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

chi := DirichletCharacter("966.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.r (of order $22$, 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:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.16
Character	$\chi$	$=$	966.113
Dual form			966.2.r.a.701.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540641 - 0.841254i) q^{2} +(-0.980063 + 1.42810i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-3.32190 - 0.975398i) q^{5} +(0.671534 + 1.59657i) q^{6} +(0.755750 + 0.654861i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-1.07895 - 2.79926i) q^{9} +O(q^{10})$	\(q+(0.540641 - 0.841254i) q^{2} +(-0.980063 + 1.42810i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-3.32190 - 0.975398i) q^{5} +(0.671534 + 1.59657i) q^{6} +(0.755750 + 0.654861i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-1.07895 - 2.79926i) q^{9} +(-2.61651 + 2.26722i) q^{10} +(-0.766971 + 0.492902i) q^{11} +(1.70618 + 0.298241i) q^{12} +(0.355818 + 0.410636i) q^{13} +(0.959493 - 0.281733i) q^{14} +(4.64864 - 3.78806i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.668172 + 1.46309i) q^{17} +(-2.93821 - 0.605721i) q^{18} +(3.68342 - 1.68216i) q^{19} +(0.492714 + 3.42690i) q^{20} +(-1.67589 + 0.437483i) q^{21} +0.911700i q^{22} +(4.73011 + 0.791263i) q^{23} +(1.17333 - 1.27409i) q^{24} +(5.87736 + 3.77715i) q^{25} +(0.537819 - 0.0773267i) q^{26} +(5.05507 + 1.20259i) q^{27} +(0.281733 - 0.959493i) q^{28} +(5.77107 + 2.63556i) q^{29} +(-0.673478 - 5.95867i) q^{30} +(-0.691534 + 4.80972i) q^{31} +(0.281733 + 0.959493i) q^{32} +(0.0477647 - 1.57839i) q^{33} +(0.869591 + 1.35311i) q^{34} +(-1.87178 - 2.91254i) q^{35} +(-2.09808 + 2.14431i) q^{36} +(-1.16324 - 3.96162i) q^{37} +(0.576284 - 4.00814i) q^{38} +(-0.935155 + 0.105696i) q^{39} +(3.14928 + 1.43823i) q^{40} +(-2.24367 + 7.64123i) q^{41} +(-0.538020 + 1.64637i) q^{42} +(7.14148 - 1.02679i) q^{43} +(0.766971 + 0.492902i) q^{44} +(0.853784 + 10.3513i) q^{45} +(3.22294 - 3.55143i) q^{46} +8.42749i q^{47} +(-0.437483 - 1.67589i) q^{48} +(0.142315 + 0.989821i) q^{49} +(6.35508 - 2.90227i) q^{50} +(-1.43460 - 2.38814i) q^{51} +(0.225716 - 0.494248i) q^{52} +(2.86890 - 3.31089i) q^{53} +(3.74467 - 3.60243i) q^{54} +(3.02858 - 0.889271i) q^{55} +(-0.654861 - 0.755750i) q^{56} +(-1.20769 + 6.90893i) q^{57} +(5.33725 - 3.43004i) q^{58} +(4.28197 - 3.71035i) q^{59} +(-5.37686 - 2.65493i) q^{60} +(2.71855 + 0.390868i) q^{61} +(3.67232 + 3.18209i) q^{62} +(1.01771 - 2.82210i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-0.781460 - 1.71116i) q^{65} +(-1.30200 - 0.893524i) q^{66} +(-0.576184 + 0.896559i) q^{67} +1.60845 q^{68} +(-5.76581 + 5.97959i) q^{69} -3.46214 q^{70} +(8.00891 - 12.4621i) q^{71} +(0.669595 + 2.92432i) q^{72} +(-1.48144 - 3.24389i) q^{73} +(-3.96162 - 1.16324i) q^{74} +(-11.1543 + 4.69163i) q^{75} +(-3.06030 - 2.65176i) q^{76} +(-0.902421 - 0.129748i) q^{77} +(-0.416666 + 0.843846i) q^{78} +(-2.58437 + 2.23937i) q^{79} +(2.91254 - 1.87178i) q^{80} +(-6.67172 + 6.04054i) q^{81} +(5.21520 + 6.01866i) q^{82} +(3.32868 - 0.977389i) q^{83} +(1.09414 + 1.34271i) q^{84} +(3.64670 - 4.20852i) q^{85} +(2.99719 - 6.56292i) q^{86} +(-9.41986 + 5.65867i) q^{87} +(0.829312 - 0.378734i) q^{88} +(1.51569 + 10.5419i) q^{89} +(9.16964 + 4.87807i) q^{90} +0.543350i q^{91} +(-1.24520 - 4.63136i) q^{92} +(-6.19103 - 5.70141i) q^{93} +(7.08966 + 4.55625i) q^{94} +(-13.8768 + 1.99518i) q^{95} +(-1.64637 - 0.538020i) q^{96} +(-0.996754 + 3.39463i) q^{97} +(0.909632 + 0.415415i) q^{98} +(2.20729 + 1.61513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^9	$ 240 q - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} + 24 q^{14} + 18 q^{15} - 24 q^{16} + 32 q^{17} - 4 q^{18} + 4 q^{20} - 8 q^{23} + 12 q^{25} - 148 q^{27} + 40 q^{30} + 16 q^{31} + 42 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} + 154 q^{41} + 4 q^{42} + 22 q^{43} + 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} + 88 q^{50} + 24 q^{51} + 8 q^{52} - 108 q^{53} + 12 q^{54} - 16 q^{55} - 24 q^{56} - 62 q^{57} - 4 q^{58} + 22 q^{59} - 18 q^{60} - 4 q^{63} + 24 q^{64} - 100 q^{66} - 44 q^{67} - 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} - 16 q^{74} - 26 q^{75} - 78 q^{78} - 4 q^{80} + 52 q^{81} + 8 q^{82} + 16 q^{83} - 28 q^{85} + 16 q^{86} - 196 q^{87} + 24 q^{89} + 126 q^{90} + 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} + 172 q^{99}+O(q^{100}) $ 240 * q - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 + 24 * q^14 + 18 * q^15 - 24 * q^16 + 32 * q^17 - 4 * q^18 + 4 * q^20 - 8 * q^23 + 12 * q^25 - 148 * q^27 + 40 * q^30 + 16 * q^31 + 42 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 + 154 * q^41 + 4 * q^42 + 22 * q^43 + 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 + 88 * q^50 + 24 * q^51 + 8 * q^52 - 108 * q^53 + 12 * q^54 - 16 * q^55 - 24 * q^56 - 62 * q^57 - 4 * q^58 + 22 * q^59 - 18 * q^60 - 4 * q^63 + 24 * q^64 - 100 * q^66 - 44 * q^67 - 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 - 16 * q^74 - 26 * q^75 - 78 * q^78 - 4 * q^80 + 52 * q^81 + 8 * q^82 + 16 * q^83 - 28 * q^85 + 16 * q^86 - 196 * q^87 + 24 * q^89 + 126 * q^90 + 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$3$	−0.980063	+	1.42810i	−0.565840	+	0.824515i
$3$	−0.980063	+	1.42810i	−0.565840	+	0.824515i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	−3.32190	−	0.975398i	−1.48560	−	0.436211i	−0.564466	−	0.825457i	$-0.690918\pi$
$5$	−3.32190	−	0.975398i	−1.48560	−	0.436211i	−0.921134	+	0.389245i	$0.872736\pi$
$6$	0.671534	+	1.59657i	0.274153	+	0.651798i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$8$	−0.989821	−	0.142315i	−0.349955	−	0.0503159i
$9$	−1.07895	−	2.79926i	−0.359651	−	0.933087i
$10$	−2.61651	+	2.26722i	−0.827414	+	0.716958i
$11$	−0.766971	+	0.492902i	−0.231250	+	0.148616i	−0.651135	−	0.758962i	$-0.725707\pi$
$11$	−0.766971	+	0.492902i	−0.231250	+	0.148616i	0.419885	+	0.907577i	$0.362071\pi$
$12$	1.70618	+	0.298241i	0.492532	+	0.0860948i
$13$	0.355818	+	0.410636i	0.0986862	+	0.113890i	0.802944	−	0.596054i	$-0.203266\pi$
$13$	0.355818	+	0.410636i	0.0986862	+	0.113890i	−0.704258	+	0.709944i	$0.748720\pi$
$14$	0.959493	−	0.281733i	0.256435	−	0.0752962i
$15$	4.64864	−	3.78806i	1.20027	−	0.978074i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−0.668172	+	1.46309i	−0.162056	+	0.354852i	−0.973188	−	0.230010i	$-0.926124\pi$
$17$	−0.668172	+	1.46309i	−0.162056	+	0.354852i	0.811133	+	0.584862i	$0.198851\pi$
$18$	−2.93821	−	0.605721i	−0.692544	−	0.142770i
$19$	3.68342	−	1.68216i	0.845036	−	0.385915i	0.0546359	−	0.998506i	$-0.482600\pi$
$19$	3.68342	−	1.68216i	0.845036	−	0.385915i	0.790400	+	0.612592i	$0.209873\pi$
$20$	0.492714	+	3.42690i	0.110174	+	0.766279i
$21$	−1.67589	+	0.437483i	−0.365709	+	0.0954667i
$22$			0.911700i			0.194375i
$23$	4.73011	+	0.791263i	0.986295	+	0.164990i
$23$	4.73011	+	0.791263i	0.986295	+	0.164990i
$24$	1.17333	−	1.27409i	0.239504	−	0.260072i
$25$	5.87736	+	3.77715i	1.17547	+	0.755430i
$26$	0.537819	−	0.0773267i	0.105475	−	0.0151650i
$27$	5.05507	+	1.20259i	0.972849	+	0.231439i
$28$	0.281733	−	0.959493i	0.0532424	−	0.181327i
$29$	5.77107	+	2.63556i	1.07166	+	0.489411i	0.871522	−	0.490356i	$-0.163133\pi$
$29$	5.77107	+	2.63556i	1.07166	+	0.489411i	0.200139	+	0.979767i	$0.435861\pi$
$30$	−0.673478	−	5.95867i	−0.122960	−	1.08790i
$31$	−0.691534	+	4.80972i	−0.124203	+	0.863852i	0.828509	+	0.559976i	$0.189190\pi$
$31$	−0.691534	+	4.80972i	−0.124203	+	0.863852i	−0.952712	+	0.303875i	$0.901719\pi$
$32$	0.281733	+	0.959493i	0.0498038	+	0.169616i
$33$	0.0477647	−	1.57839i	0.00831477	−	0.274762i
$34$	0.869591	+	1.35311i	0.149134	+	0.232057i
$35$	−1.87178	−	2.91254i	−0.316388	−	0.492309i
$36$	−2.09808	+	2.14431i	−0.349681	+	0.357384i
$37$	−1.16324	−	3.96162i	−0.191235	−	0.651287i	−0.998160	−	0.0606330i	$-0.980688\pi$
$37$	−1.16324	−	3.96162i	−0.191235	−	0.651287i	0.806925	−	0.590654i	$-0.201130\pi$
$38$	0.576284	−	4.00814i	0.0934855	−	0.650206i
$39$	−0.935155	+	0.105696i	−0.149745	+	0.0169249i
$40$	3.14928	+	1.43823i	0.497944	+	0.227404i
$41$	−2.24367	+	7.64123i	−0.350402	+	1.19336i	0.576197	+	0.817311i	$0.304536\pi$
$41$	−2.24367	+	7.64123i	−0.350402	+	1.19336i	−0.926600	+	0.376050i	$0.877282\pi$
$42$	−0.538020	+	1.64637i	−0.0830184	+	0.254040i
$43$	7.14148	−	1.02679i	1.08907	−	0.156584i	0.425689	−	0.904870i	$-0.360032\pi$
$43$	7.14148	−	1.02679i	1.08907	−	0.156584i	0.663377	+	0.748286i	$0.269123\pi$
$44$	0.766971	+	0.492902i	0.115625	+	0.0743078i
$45$	0.853784	+	10.3513i	0.127275	+	1.54308i
$46$	3.22294	−	3.55143i	0.475197	−	0.523630i
$47$			8.42749i			1.22928i	0.788809	+	0.614638i	$0.210698\pi$
$47$			8.42749i			1.22928i	−0.788809	+	0.614638i	$0.789302\pi$
$48$	−0.437483	−	1.67589i	−0.0631453	−	0.241894i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	6.35508	−	2.90227i	0.898745	−	0.410443i
$51$	−1.43460	−	2.38814i	−0.200884	−	0.334407i
$52$	0.225716	−	0.494248i	0.0313011	−	0.0685399i
$53$	2.86890	−	3.31089i	0.394074	−	0.454785i	−0.523692	−	0.851908i	$-0.675446\pi$
$53$	2.86890	−	3.31089i	0.394074	−	0.454785i	0.917766	+	0.397122i	$0.129991\pi$
$54$	3.74467	−	3.60243i	0.509584	−	0.490228i
$55$	3.02858	−	0.889271i	0.408374	−	0.119909i
$56$	−0.654861	−	0.755750i	−0.0875094	−	0.100991i
$57$	−1.20769	+	6.90893i	−0.159962	+	0.915111i
$58$	5.33725	−	3.43004i	0.700815	−	0.450387i
$59$	4.28197	−	3.71035i	0.557465	−	0.483046i	−0.329962	−	0.943994i	$-0.607036\pi$
$59$	4.28197	−	3.71035i	0.557465	−	0.483046i	0.887427	+	0.460948i	$0.152491\pi$
$60$	−5.37686	−	2.65493i	−0.694150	−	0.342751i
$61$	2.71855	+	0.390868i	0.348074	+	0.0500455i	0.314135	−	0.949378i	$-0.398286\pi$
$61$	2.71855	+	0.390868i	0.348074	+	0.0500455i	0.0339393	+	0.999424i	$0.489195\pi$
$62$	3.67232	+	3.18209i	0.466386	+	0.404126i
$63$	1.01771	−	2.82210i	0.128219	−	0.355552i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−0.781460	−	1.71116i	−0.0969281	−	0.212243i
$66$	−1.30200	−	0.893524i	−0.160265	−	0.109985i
$67$	−0.576184	+	0.896559i	−0.0703920	+	0.109532i	−0.874665	−	0.484728i	$-0.838919\pi$
$67$	−0.576184	+	0.896559i	−0.0703920	+	0.109532i	0.804273	+	0.594260i	$0.202555\pi$
$68$	1.60845			0.195053
$69$	−5.76581	+	5.97959i	−0.694121	+	0.719858i
$70$	−3.46214			−0.413805
$71$	8.00891	−	12.4621i	0.950482	−	1.47898i	0.0741644	−	0.997246i	$-0.476371\pi$
$71$	8.00891	−	12.4621i	0.950482	−	1.47898i	0.876318	−	0.481733i	$-0.159993\pi$
$72$	0.669595	+	2.92432i	0.0789125	+	0.344634i
$73$	−1.48144	−	3.24389i	−0.173389	−	0.379669i	0.802908	−	0.596102i	$-0.203285\pi$
$73$	−1.48144	−	3.24389i	−0.173389	−	0.379669i	−0.976297	+	0.216434i	$0.930558\pi$
$74$	−3.96162	−	1.16324i	−0.460529	−	0.135224i
$75$	−11.1543	+	4.69163i	−1.28799	+	0.541743i
$76$	−3.06030	−	2.65176i	−0.351040	−	0.304178i
$77$	−0.902421	−	0.129748i	−0.102840	−	0.0147862i
$78$	−0.416666	+	0.843846i	−0.0471781	+	0.0955467i
$79$	−2.58437	+	2.23937i	−0.290764	+	0.251948i	−0.788012	−	0.615660i	$-0.788889\pi$
$79$	−2.58437	+	2.23937i	−0.290764	+	0.251948i	0.497248	+	0.867609i	$0.334344\pi$
$80$	2.91254	−	1.87178i	0.325632	−	0.209271i
$81$	−6.67172	+	6.04054i	−0.741302	+	0.671172i
$82$	5.21520	+	6.01866i	0.575922	+	0.664649i
$83$	3.32868	−	0.977389i	0.365370	−	0.107282i	−0.0938938	−	0.995582i	$-0.529931\pi$
$83$	3.32868	−	0.977389i	0.365370	−	0.107282i	0.459264	+	0.888300i	$0.348113\pi$
$84$	1.09414	+	1.34271i	0.119380	+	0.146501i
$85$	3.64670	−	4.20852i	0.395540	−	0.456478i
$86$	2.99719	−	6.56292i	0.323195	−	0.707698i
$87$	−9.41986	+	5.65867i	−1.00992	+	0.606673i
$88$	0.829312	−	0.378734i	0.0884049	−	0.0403732i
$89$	1.51569	+	10.5419i	0.160663	+	1.11744i	0.897388	+	0.441243i	$0.145462\pi$
$89$	1.51569	+	10.5419i	0.160663	+	1.11744i	−0.736725	+	0.676193i	$0.763629\pi$
$90$	9.16964	+	4.87807i	0.966565	+	0.514194i
$91$			0.543350i			0.0569585i
$92$	−1.24520	−	4.63136i	−0.129821	−	0.482852i
$93$	−6.19103	−	5.70141i	−0.641980	−	0.591209i
$94$	7.08966	+	4.55625i	0.731242	+	0.469941i
$95$	−13.8768	+	1.99518i	−1.42372	+	0.204701i
$96$	−1.64637	−	0.538020i	−0.168032	−	0.0549115i
$97$	−0.996754	+	3.39463i	−0.101205	+	0.344673i	−0.994492	−	0.104815i	$-0.966575\pi$
$97$	−0.996754	+	3.39463i	−0.101205	+	0.344673i	0.893287	+	0.449487i	$0.148393\pi$
$98$	0.909632	+	0.415415i	0.0918867	+	0.0419633i
$99$	2.20729	+	1.61513i	0.221841	+	0.162327i
$100$	0.994273	−	6.91532i	0.0994273	−	0.691532i
$101$	1.43870	+	4.89975i	0.143156	+	0.487543i	0.999588	−	0.0287165i	$-0.00914201\pi$
$101$	1.43870	+	4.89975i	0.143156	+	0.487543i	−0.856432	+	0.516260i	$0.827324\pi$
$102$	−2.78463	−	0.0842678i	−0.275720	−	0.00834375i
$103$	−1.73361	−	2.69755i	−0.170817	−	0.265797i	0.745281	−	0.666750i	$-0.232315\pi$
$103$	−1.73361	−	2.69755i	−0.170817	−	0.265797i	−0.916098	+	0.400953i	$0.868679\pi$
$104$	−0.293757	−	0.457095i	−0.0288052	−	0.0448218i
$105$	5.99386	+	0.181384i	0.584941	+	0.0177013i
$106$	−1.23425	−	4.20347i	−0.119881	−	0.408277i
$107$	2.18177	−	15.1745i	0.210919	−	1.46698i	−0.559177	−	0.829048i	$-0.688883\pi$
$107$	2.18177	−	15.1745i	0.210919	−	1.46698i	0.770096	−	0.637928i	$-0.220208\pi$
$108$	−1.00603	−	5.09783i	−0.0968057	−	0.490539i
$109$	6.13606	+	2.80225i	0.587728	+	0.268407i	0.687004	−	0.726653i	$-0.258925\pi$
$109$	6.13606	+	2.80225i	0.587728	+	0.268407i	−0.0992758	+	0.995060i	$0.531653\pi$
$110$	0.889271	−	3.02858i	0.0847887	−	0.288764i
$111$	6.79765	+	2.22142i	0.645204	+	0.210848i
$112$	−0.989821	+	0.142315i	−0.0935293	+	0.0134475i
$113$	13.9097	+	8.93924i	1.30852	+	0.840933i	0.994112	−	0.108356i	$-0.0345586\pi$
$113$	13.9097	+	8.93924i	1.30852	+	0.840933i	0.314405	+	0.949289i	$0.398195\pi$
$114$	5.15924	+	4.75122i	0.483207	+	0.444993i
$115$	−14.9412	−	7.24224i	−1.39327	−	0.675342i
$116$		−	6.34440i		−	0.589063i
$117$	0.765566	−	1.43909i	0.0707766	−	0.133044i
$118$	−0.806336	−	5.60819i	−0.0742292	−	0.516276i
$119$	−1.46309	+	0.668172i	−0.134122	+	0.0612513i
$120$	−5.14042	+	3.08794i	−0.469254	+	0.281889i
$121$	−4.22427	+	9.24987i	−0.384025	+	0.840897i
$122$	1.79858	−	2.07567i	0.162835	−	0.187922i
$123$	−8.71353	−	10.6931i	−0.785672	−	0.964162i
$124$	4.66235	−	1.36899i	0.418691	−	0.122939i
$125$	−4.50369	−	5.19753i	−0.402822	−	0.464881i
$126$	−1.82389	−	2.38189i	−0.162485	−	0.212196i
$127$	−13.9094	+	8.93902i	−1.23426	+	0.793210i	−0.984549	−	0.175111i	$-0.943971\pi$
$127$	−13.9094	+	8.93902i	−1.23426	+	0.793210i	−0.249709	+	0.968321i	$0.580335\pi$
$128$	0.755750	−	0.654861i	0.0667995	−	0.0578821i
$129$	−5.53274	+	11.2051i	−0.487130	+	0.986553i
$130$	−1.86201	−	0.267716i	−0.163309	−	0.0234803i
$131$	4.27163	+	3.70138i	0.373214	+	0.323391i	0.821191	−	0.570653i	$-0.193310\pi$
$131$	4.27163	+	3.70138i	0.373214	+	0.323391i	−0.447977	+	0.894045i	$0.647855\pi$
$132$	−1.45560	+	0.612238i	−0.126693	+	0.0532885i
$133$	3.88533	+	1.14084i	0.336901	+	0.0989230i
$134$	0.442725	+	0.969433i	0.0382456	+	0.0837463i
$135$	−15.6194	−	8.92561i	−1.34431	−	0.768194i
$136$	0.869591	−	1.35311i	0.0745668	−	0.116028i
$137$	−8.36258			−0.714464			−0.357232	−	0.934016i	$-0.616279\pi$
$137$	−8.36258			−0.714464			−0.357232	+	0.934016i	$0.616279\pi$
$138$	1.91312	+	8.08331i	0.162856	+	0.688097i
$139$	−4.59586			−0.389816			−0.194908	−	0.980822i	$-0.562441\pi$
$139$	−4.59586			−0.389816			−0.194908	+	0.980822i	$0.562441\pi$
$140$	−1.87178	+	2.91254i	−0.158194	+	0.246155i
$141$	−12.0353	−	8.25947i	−1.01356	−	0.695573i
$142$	−6.15385	−	13.4750i	−0.516419	−	1.13080i
$143$	−0.475306	−	0.139562i	−0.0397471	−	0.0116708i
$144$	2.82210	+	1.01771i	0.235175	+	0.0848089i
$145$	−16.6002	−	14.3842i	−1.37857	−	1.19454i
$146$	−3.52986	−	0.507517i	−0.292133	−	0.0420024i
$147$	−1.55304	−	0.766847i	−0.128093	−	0.0632485i
$148$	−3.12039	+	2.70384i	−0.256495	+	0.222254i
$149$	−13.0727	+	8.40129i	−1.07095	+	0.688261i	−0.952451	−	0.304693i	$-0.901446\pi$
$149$	−13.0727	+	8.40129i	−1.07095	+	0.688261i	−0.118504	+	0.992954i	$0.537810\pi$
$150$	−2.08364	+	11.9201i	−0.170129	+	0.973274i
$151$	−8.78372	−	10.1369i	−0.714809	−	0.824933i	0.275864	−	0.961197i	$-0.411036\pi$
$151$	−8.78372	−	10.1369i	−0.714809	−	0.824933i	−0.990673	+	0.136264i	$0.956491\pi$
$152$	−3.88533	+	1.14084i	−0.315142	+	0.0925340i
$153$	4.81651	+	0.291778i	0.389391	+	0.0235889i
$154$	−0.597037	+	0.689017i	−0.0481106	+	0.0555226i
$155$	6.98860	−	15.3029i	0.561338	−	1.22916i
$156$	0.484622	+	0.806739i	0.0388008	+	0.0645908i
$157$	19.5573	−	8.93153i	1.56084	−	0.712814i	0.567013	−	0.823709i	$-0.308099\pi$
$157$	19.5573	−	8.93153i	1.56084	−	0.712814i	0.993832	+	0.110895i	$0.0353717\pi$
$158$	0.486661	+	3.38480i	0.0387166	+	0.269280i
$159$	1.91658	+	7.34196i	0.151995	+	0.582255i
$160$		−	3.46214i		−	0.273706i
$161$	3.05661	+	3.69556i	0.240894	+	0.291251i
$162$	1.47463	+	8.87837i	0.115858	+	0.697551i
$163$	−0.125899	−	0.0809106i	−0.00986120	−	0.00633741i	0.535701	−	0.844408i	$-0.320047\pi$
$163$	−0.125899	−	0.0809106i	−0.00986120	−	0.00633741i	−0.545562	+	0.838070i	$0.683684\pi$
$164$	7.88276	−	1.13337i	0.615540	−	0.0885013i
$165$	−1.69823	+	5.19666i	−0.132207	+	0.404560i
$166$	0.977389	−	3.32868i	0.0758601	−	0.258356i
$167$	−6.30806	−	2.88080i	−0.488133	−	0.222923i	0.156116	−	0.987739i	$-0.450103\pi$
$167$	−6.30806	−	2.88080i	−0.488133	−	0.222923i	−0.644249	+	0.764816i	$0.722830\pi$
$168$	1.72109	−	0.194526i	0.132785	−	0.0150080i
$169$	1.80808	−	12.5755i	0.139083	−	0.967343i
$170$	−1.56888	−	5.34310i	−0.120327	−	0.409797i
$171$	−8.68306	−	8.49589i	−0.664010	−	0.649697i
$172$	−3.90068	−	6.06958i	−0.297424	−	0.462801i
$173$	−12.5797	−	19.5744i	−0.956419	−	1.48822i	−0.870651	−	0.491902i	$-0.836302\pi$
$173$	−12.5797	−	19.5744i	−0.956419	−	1.48822i	−0.0857679	−	0.996315i	$-0.527334\pi$
$174$	−0.332388	+	10.9838i	−0.0251983	+	0.832680i
$175$	1.96831	+	6.70343i	0.148790	+	0.506732i
$176$	0.129748	−	0.902421i	0.00978016	−	0.0680225i
$177$	1.10216	+	9.75147i	0.0828433	+	0.732965i
$178$	9.68782	+	4.42428i	0.726133	+	0.331614i
$179$	−3.42465	+	11.6633i	−0.255971	+	0.871756i	0.726788	+	0.686862i	$0.241012\pi$
$179$	−3.42465	+	11.6633i	−0.255971	+	0.871756i	−0.982759	+	0.184894i	$0.940806\pi$
$180$	9.06118	−	5.07671i	0.675380	−	0.378395i
$181$	−2.44538	+	0.351593i	−0.181764	+	0.0261337i	−0.232596	−	0.972574i	$-0.574722\pi$
$181$	−2.44538	+	0.351593i	−0.181764	+	0.0261337i	0.0508317	+	0.998707i	$0.483813\pi$
$182$	0.457095	+	0.293757i	0.0338821	+	0.0217747i
$183$	−3.22254	+	3.49929i	−0.238217	+	0.258675i
$184$	−4.56935	−	1.45637i	−0.336857	−	0.107365i
$185$			14.2947i			1.05097i
$186$	−8.14346	+	2.12581i	−0.597107	+	0.155872i
$187$	−0.208693	−	1.45149i	−0.0152612	−	0.106144i
$188$	7.66592	−	3.50091i	0.559094	−	0.255330i
$189$	3.03284	+	4.21923i	0.220606	+	0.306904i
$190$	−5.82389	+	12.7525i	−0.422509	+	0.925167i
$191$	−10.3065	+	11.8943i	−0.745752	+	0.860644i	−0.994149	−	0.108014i	$-0.965551\pi$
$191$	−10.3065	+	11.8943i	−0.745752	+	0.860644i	0.248397	+	0.968658i	$0.420096\pi$
$192$	−1.34271	+	1.09414i	−0.0969015	+	0.0789627i
$193$	26.5354	−	7.79150i	1.91006	−	0.560844i	0.927888	−	0.372858i	$-0.121622\pi$
$193$	26.5354	−	7.79150i	1.91006	−	0.560844i	0.982172	−	0.187986i	$-0.0601959\pi$
$194$	2.31686	+	2.67380i	0.166341	+	0.191968i
$195$	3.20959	+	0.561038i	0.229843	+	0.0401767i
$196$	0.841254	−	0.540641i	0.0600895	−	0.0386172i
$197$	4.74982	−	4.11574i	0.338411	−	0.293234i	−0.469031	−	0.883182i	$-0.655397\pi$
$197$	4.74982	−	4.11574i	0.338411	−	0.293234i	0.807442	+	0.589947i	$0.200851\pi$
$198$	2.55209	−	0.983682i	0.181369	−	0.0699073i
$199$	18.6021	+	2.67458i	1.31867	+	0.189596i	0.765480	−	0.643460i	$-0.222502\pi$
$199$	18.6021	+	2.67458i	1.31867	+	0.189596i	0.553189	+	0.833056i	$0.313411\pi$
$200$	−5.27999	−	4.57514i	−0.373352	−	0.323511i
$201$	−0.715682	−	1.70153i	−0.0504803	−	0.120017i
$202$	4.89975	+	1.43870i	0.344745	+	0.101226i
$203$	2.63556	+	5.77107i	0.184980	+	0.405050i
$204$	−1.57638	+	2.29702i	−0.110369	+	0.160824i
$205$	14.9065	−	23.1950i	1.04111	−	1.62001i
$206$	−3.20658			−0.223413
$207$	−2.88861	−	14.0945i	−0.200773	−	0.979638i
$208$	−0.543350			−0.0376745
$209$	−1.99594	+	3.10574i	−0.138062	+	0.214829i
$210$	3.39312	−	4.94430i	0.234147	−	0.341189i
$211$	5.37298	+	11.7652i	0.369891	+	0.809949i	0.999455	+	0.0330004i	$0.0105063\pi$
$211$	5.37298	+	11.7652i	0.369891	+	0.809949i	−0.629564	+	0.776949i	$0.716766\pi$
$212$	−4.20347	−	1.23425i	−0.288696	−	0.0847687i
$213$	9.94793	+	23.6512i	0.681621	+	1.62055i
$214$	−11.5861	−	10.0394i	−0.792007	−	0.686278i
$215$	−24.7248	−	3.55489i	−1.68622	−	0.242442i
$216$	−4.83247	−	1.90977i	−0.328808	−	0.129943i
$217$	−3.67232	+	3.18209i	−0.249294	+	0.216014i
$218$	5.67481	−	3.64698i	0.384346	−	0.247004i
$219$	6.08451	+	1.06358i	0.411153	+	0.0718698i
$220$	−2.06703	−	2.38548i	−0.139359	−	0.160829i
$221$	−0.838547	+	0.246220i	−0.0564068	+	0.0165625i
$222$	5.54386	−	4.51756i	0.372080	−	0.303199i
$223$	−14.1777	+	16.3620i	−0.949410	+	1.09568i	0.0459006	+	0.998946i	$0.485384\pi$
$223$	−14.1777	+	16.3620i	−0.949410	+	1.09568i	−0.995311	+	0.0967314i	$0.969161\pi$
$224$	−0.415415	+	0.909632i	−0.0277561	+	0.0607773i
$225$	4.23183	−	20.5276i	0.282122	−	1.36851i
$226$	15.0403	−	6.86869i	1.00047	−	0.456899i
$227$	0.237715	+	1.65334i	0.0157777	+	0.109736i	0.996188	−	0.0872279i	$-0.0278008\pi$
$227$	0.237715	+	1.65334i	0.0157777	+	0.109736i	−0.980411	+	0.196964i	$0.936892\pi$
$228$	6.78628	−	1.77153i	0.449432	−	0.117322i
$229$		−	19.9090i		−	1.31562i	−0.753182	−	0.657812i	$-0.771482\pi$
$229$		−	19.9090i		−	1.31562i	0.753182	−	0.657812i	$-0.228518\pi$
$230$	−14.1704	+	8.65385i	−0.934365	+	0.570618i
$231$	1.06972	−	1.16159i	0.0703826	−	0.0764268i
$232$	−5.33725	−	3.43004i	−0.350408	−	0.225193i
$233$	15.2824	−	2.19727i	1.00118	−	0.143948i	0.377817	−	0.925880i	$-0.376675\pi$
$233$	15.2824	−	2.19727i	1.00118	−	0.143948i	0.623363	+	0.781932i	$0.285766\pi$
$234$	−0.796739	−	1.42206i	−0.0520845	−	0.0929632i
$235$	8.22016	−	27.9953i	0.536224	−	1.82621i
$236$	−5.15385	−	2.35368i	−0.335487	−	0.153212i
$237$	−0.665203	−	5.88546i	−0.0432096	−	0.382302i
$238$	−0.228906	+	1.59207i	−0.0148377	+	0.103199i
$239$	7.07377	+	24.0910i	0.457564	+	1.55832i	0.788726	+	0.614745i	$0.210741\pi$
$239$	7.07377	+	24.0910i	0.457564	+	1.55832i	−0.331162	+	0.943574i	$0.607441\pi$
$240$	−0.181384	+	5.99386i	−0.0117083	+	0.386902i
$241$	2.61288	+	4.06572i	0.168310	+	0.261896i	0.915155	−	0.403103i	$-0.132068\pi$
$241$	2.61288	+	4.06572i	0.168310	+	0.261896i	−0.746844	+	0.664999i	$0.768432\pi$
$242$	5.49767	+	8.55454i	0.353404	+	0.549907i
$243$	−2.08781	−	15.4480i	−0.133933	−	0.990990i
$244$	−0.773779	−	2.63525i	−0.0495361	−	0.168704i
$245$	0.492714	−	3.42690i	0.0314784	−	0.218937i
$246$	−13.7065	+	1.54917i	−0.873893	+	0.0987716i
$247$	2.00139	+	0.914003i	0.127345	+	0.0581566i
$248$	1.36899	−	4.66235i	0.0869309	−	0.296060i
$249$	−1.86650	+	5.71160i	−0.118285	+	0.361958i
$250$	−6.80732	+	0.978745i	−0.430533	+	0.0619012i
$251$	7.00574	+	4.50232i	0.442199	+	0.284184i	0.742734	−	0.669587i	$-0.233529\pi$
$251$	7.00574	+	4.50232i	0.442199	+	0.284184i	−0.300535	+	0.953771i	$0.597165\pi$
$252$	−2.98985	+	0.246606i	−0.188343	+	0.0155347i
$253$	−4.01787	+	1.72460i	−0.252601	+	0.108425i
$254$			16.5341i			1.03744i
$255$	2.43620	+	9.33248i	0.152561	+	0.584422i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−20.2175	+	9.23301i	−1.26113	+	0.575939i	−0.929970	−	0.367635i	$-0.880168\pi$
$257$	−20.2175	+	9.23301i	−1.26113	+	0.575939i	−0.331161	+	0.943574i	$0.607440\pi$
$258$	6.43509	+	10.7124i	0.400631	+	0.666923i
$259$	1.71520	−	3.75575i	0.106577	−	0.233371i
$260$	−1.23189	+	1.42168i	−0.0763988	+	0.0881689i
$261$	1.15090	−	18.9984i	0.0712389	−	1.17597i
$262$	5.42322	−	1.59240i	0.335048	−	0.0983788i
$263$	−9.24919	−	10.6741i	−0.570329	−	0.658195i	0.395168	−	0.918609i	$-0.370686\pi$
$263$	−9.24919	−	10.6741i	−0.570329	−	0.658195i	−0.965497	+	0.260414i	$0.916141\pi$
$264$	−0.271907	+	1.55553i	−0.0167347	+	0.0957360i
$265$	−12.7596	+	8.20012i	−0.783818	+	0.503730i
$266$	3.06030	−	2.65176i	0.187639	−	0.162590i
$267$	−16.5403	−	8.16712i	−1.01225	−	0.499820i
$268$	1.05489	+	0.151671i	0.0644379	+	0.00926477i
$269$	7.40093	+	6.41294i	0.451242	+	0.391004i	0.850619	−	0.525783i	$-0.176228\pi$
$269$	7.40093	+	6.41294i	0.451242	+	0.391004i	−0.399376	+	0.916787i	$0.630773\pi$
$270$	−15.9532	+	8.31437i	−0.970882	+	0.505996i
$271$	−22.0394	−	6.47135i	−1.33880	−	0.393106i	−0.467557	−	0.883963i	$-0.654866\pi$
$271$	−22.0394	−	6.47135i	−1.33880	−	0.393106i	−0.871241	+	0.490856i	$0.836684\pi$
$272$	−0.668172	−	1.46309i	−0.0405139	−	0.0887131i
$273$	−0.775959	−	0.532517i	−0.0469632	−	0.0322294i
$274$	−4.52115	+	7.03505i	−0.273133	+	0.425003i
$275$	−6.36953			−0.384097
$276$	7.83443	+	2.76075i	0.471577	+	0.166178i
$277$	15.8885			0.954646			0.477323	−	0.878728i	$-0.341607\pi$
$277$	15.8885			0.954646			0.477323	+	0.878728i	$0.341607\pi$
$278$	−2.48471	+	3.86628i	−0.149023	+	0.231884i
$279$	14.2098	−	3.25368i	0.850718	−	0.194793i
$280$	1.43823	+	3.14928i	0.0859505	+	0.188205i
$281$	5.07748	+	1.49088i	0.302897	+	0.0889386i	0.429649	−	0.902996i	$-0.358637\pi$
$281$	5.07748	+	1.49088i	0.302897	+	0.0889386i	−0.126752	+	0.991934i	$0.540455\pi$
$282$	−13.4551	+	5.65935i	−0.801239	+	0.337009i
$283$	8.26970	+	7.16574i	0.491583	+	0.425959i	0.865051	−	0.501684i	$-0.167286\pi$
$283$	8.26970	+	7.16574i	0.491583	+	0.425959i	−0.373468	+	0.927643i	$0.621831\pi$
$284$	−14.6629	−	2.10821i	−0.870086	−	0.125099i
$285$	10.7508	−	21.7728i	0.636821	−	1.28971i
$286$	−0.374377	+	0.324400i	−0.0221374	+	0.0191822i
$287$	−6.69959	+	4.30557i	−0.395465	+	0.254150i
$288$	2.38189	−	1.82389i	0.140354	−	0.107474i
$289$	9.43844	+	10.8925i	0.555203	+	0.640738i
$290$	−21.0755	+	6.18832i	−1.23760	+	0.363391i
$291$	−3.87100	−	4.75042i	−0.226922	−	0.278474i
$292$	−2.33534	+	2.69512i	−0.136665	+	0.157720i
$293$	1.27345	−	2.78846i	0.0743956	−	0.162904i	−0.868780	−	0.495198i	$-0.835095\pi$
$293$	1.27345	−	2.78846i	0.0743956	−	0.162904i	0.943176	+	0.332294i	$0.107823\pi$
$294$	−1.48475	+	0.891915i	−0.0865925	+	0.0520175i
$295$	−17.8434	+	8.14879i	−1.03888	+	0.474441i
$296$	0.587600	+	4.08685i	0.0341535	+	0.237543i
$297$	−4.46986	+	1.56930i	−0.259367	+	0.0910602i
$298$			15.5395i			0.900180i
$299$	1.35814	+	2.22390i	0.0785431	+	0.128611i
$300$	8.90134	+	8.19737i	0.513919	+	0.473276i
$301$	6.06958	+	3.90068i	0.349845	+	0.224831i
$302$	−13.2766	+	1.90888i	−0.763981	+	0.109844i
$303$	−8.40736	−	2.74746i	−0.482990	−	0.157837i
$304$	−1.14084	+	3.88533i	−0.0654314	+	0.222839i
$305$	−8.64949	−	3.95009i	−0.495268	−	0.226181i
$306$	2.84946	−	3.89416i	0.162893	−	0.222614i
$307$	0.117334	−	0.816074i	0.00669659	−	0.0465758i	−0.986199	−	0.165563i	$-0.947056\pi$
$307$	0.117334	−	0.816074i	0.00669659	−	0.0465758i	0.992896	+	0.118988i	$0.0379649\pi$
$308$	0.256856	+	0.874770i	0.0146357	+	0.0498447i
$309$	5.55142	+	0.167995i	0.315809	+	0.00955691i
$310$	−9.09530	−	14.1526i	−0.516578	−	0.803812i
$311$	7.67054	+	11.9356i	0.434957	+	0.676806i	0.987667	−	0.156568i	$-0.0500429\pi$
$311$	7.67054	+	11.9356i	0.434957	+	0.676806i	−0.552711	+	0.833373i	$0.686407\pi$
$312$	0.940678	+	0.0284665i	0.0532554	+	0.00161160i
$313$	0.290417	+	0.989069i	0.0164153	+	0.0559055i	0.967293	−	0.253660i	$-0.0816345\pi$
$313$	0.290417	+	0.989069i	0.0164153	+	0.0559055i	−0.950878	+	0.309566i	$0.899816\pi$
$314$	3.05981	−	21.2814i	0.172675	−	1.20098i
$315$	−6.13340	+	8.38208i	−0.345578	+	0.472277i
$316$	3.11058	+	1.42056i	0.174984	+	0.0799125i
$317$	−7.31197	+	24.9023i	−0.410681	+	1.39865i	0.451599	+	0.892221i	$0.350854\pi$
$317$	−7.31197	+	24.9023i	−0.410681	+	1.39865i	−0.862280	+	0.506431i	$0.830964\pi$
$318$	7.21263	+	2.35703i	0.404464	+	0.132176i
$319$	−5.72532	+	0.823177i	−0.320556	+	0.0460890i
$320$	−2.91254	−	1.87178i	−0.162816	−	0.104635i
$321$	19.5325	+	17.9878i	1.09020	+	1.00398i
$322$	4.76143	−	0.573413i	0.265344	−	0.0319551i
$323$			6.51317i			0.362402i
$324$	8.26620	+	3.55948i	0.459234	+	0.197749i
$325$	0.540238	+	3.75744i	0.0299670	+	0.208425i
$326$	−0.136133	+	0.0621697i	−0.00753969	+	0.00344326i
$327$	−10.0156	+	6.01655i	−0.553865	+	0.332716i
$328$	3.30829	−	7.24415i	0.182670	−	0.399991i
$329$	−5.51883	+	6.36907i	−0.304263	+	0.351138i
$330$	3.45358	+	4.23817i	0.190113	+	0.233303i
$331$	30.3255	−	8.90437i	1.66684	−	0.489428i	0.693820	−	0.720149i	$-0.255926\pi$
$331$	30.3255	−	8.90437i	1.66684	−	0.489428i	0.973020	+	0.230720i	$0.0741082\pi$
$332$	−2.27185	−	2.62185i	−0.124684	−	0.143893i
$333$	−9.83454	+	7.53061i	−0.538929	+	0.412675i
$334$	−5.83388	+	3.74920i	−0.319215	+	0.205147i
$335$	2.78853	−	2.41627i	0.152354	−	0.132015i
$336$	0.766847	−	1.55304i	0.0418349	−	0.0847255i
$337$	10.8824	+	1.56466i	0.592804	+	0.0852323i	0.432186	−	0.901784i	$-0.357742\pi$
$337$	10.8824	+	1.56466i	0.592804	+	0.0852323i	0.160617	+	0.987017i	$0.448651\pi$
$338$	−9.60163	−	8.31986i	−0.522260	−	0.452540i
$339$	−26.3986	+	11.1035i	−1.43377	+	0.603060i
$340$	−5.34310	−	1.56888i	−0.289770	−	0.0850842i
$341$	−1.84034	−	4.02978i	−0.0996599	−	0.218225i
$342$	−11.8416	+	2.71143i	−0.640321	+	0.146617i
$343$	−0.540641	+	0.841254i	−0.0291919	+	0.0454234i
$344$	−7.21492			−0.389002
$345$	24.9859	−	14.2396i	1.34520	−	0.766637i
$346$	−23.2682			−1.25090
$347$	−16.5763	+	25.7932i	−0.889862	+	1.38465i	0.0329720	+	0.999456i	$0.489503\pi$
$347$	−16.5763	+	25.7932i	−0.889862	+	1.38465i	−0.922834	+	0.385197i	$0.874134\pi$
$348$	9.06046	+	6.21791i	0.485692	+	0.333315i
$349$	7.94680	+	17.4011i	0.425383	+	0.931458i	0.994053	+	0.108893i	$0.0347305\pi$
$349$	7.94680	+	17.4011i	0.425383	+	0.931458i	−0.568671	+	0.822565i	$0.692542\pi$
$350$	6.70343	+	1.96831i	0.358314	+	0.105210i
$351$	1.30486	+	2.50370i	0.0696482	+	0.133638i
$352$	−0.689017	−	0.597037i	−0.0367247	−	0.0318222i
$353$	15.3692	+	2.20976i	0.818020	+	0.117613i	0.538606	−	0.842557i	$-0.318951\pi$
$353$	15.3692	+	2.20976i	0.818020	+	0.117613i	0.279413	+	0.960171i	$0.409860\pi$
$354$	8.79933	+	4.34485i	0.467679	+	0.230926i
$355$	−38.7603	+	33.5860i	−2.05718	+	1.78256i
$356$	8.95957	−	5.75797i	0.474856	−	0.305172i
$357$	0.479705	−	2.74430i	0.0253887	−	0.145244i
$358$	7.96028	+	9.18665i	0.420714	+	0.485530i
$359$	33.3524	−	9.79316i	1.76027	−	0.516863i	0.767948	−	0.640512i	$-0.221278\pi$
$359$	33.3524	−	9.79316i	1.76027	−	0.516863i	0.992326	+	0.123649i	$0.0394597\pi$
$360$	0.628047	−	10.3674i	0.0331010	−	0.546411i
$361$	−1.70441	+	1.96700i	−0.0897059	+	0.103526i
$362$	−1.02630	+	2.24727i	−0.0539409	+	0.118114i
$363$	−9.06971	−	15.0981i	−0.476036	−	0.792447i
$364$	0.494248	−	0.225716i	0.0259056	−	0.0118307i
$365$	1.75710	+	12.2209i	0.0919707	+	0.639670i
$366$	1.20155	+	4.60283i	0.0628059	+	0.240594i
$367$		−	16.9266i		−	0.883563i	−0.897123	−	0.441781i	$-0.854347\pi$
$367$		−	16.9266i		−	0.883563i	0.897123	−	0.441781i	$-0.145653\pi$
$368$	−3.69556	+	3.05661i	−0.192644	+	0.159337i
$369$	23.8106	−	1.96392i	1.23953	−	0.102238i
$370$	12.0255	+	7.72832i	0.625176	+	0.401776i
$371$	4.33634	−	0.623472i	0.225132	−	0.0323690i
$372$	−2.61434	+	8.00001i	−0.135547	+	0.414781i
$373$	−4.25280	+	14.4837i	−0.220201	+	0.749937i	0.773090	+	0.634297i	$0.218710\pi$
$373$	−4.25280	+	14.4837i	−0.220201	+	0.749937i	−0.993291	+	0.115640i	$0.963108\pi$
$374$	−1.33390	−	0.609173i	−0.0689745	−	0.0314996i
$375$	11.8365	−	1.33782i	0.611234	−	0.0690847i
$376$	1.19936	−	8.34171i	0.0618521	−	0.430191i
$377$	0.971197	+	3.30759i	0.0500192	+	0.170350i
$378$	5.18912	−	0.270298i	0.266899	−	0.0139026i
$379$	−9.98113	−	15.5309i	−0.512696	−	0.797771i	0.484326	−	0.874888i	$-0.339065\pi$
$379$	−9.98113	−	15.5309i	−0.512696	−	0.797771i	−0.997022	+	0.0771167i	$0.975429\pi$
$380$	7.57949	+	11.7939i	0.388820	+	0.605015i
$381$	0.866236	−	28.6248i	0.0443786	−	1.46649i
$382$	4.43404	+	15.1009i	0.226865	+	0.772632i
$383$	3.42274	−	23.8057i	0.174894	−	1.21641i	−0.693470	−	0.720486i	$-0.743919\pi$
$383$	3.42274	−	23.8057i	0.174894	−	1.21641i	0.868364	−	0.495928i	$-0.165172\pi$
$384$	0.194526	+	1.72109i	0.00992687	+	0.0878291i
$385$	2.87120	+	1.31123i	0.146330	+	0.0668265i
$386$	7.79150	−	26.5354i	0.396577	−	1.35062i
$387$	−10.5796	−	18.8830i	−0.537790	−	0.959877i
$388$	3.50193	−	0.503502i	0.177784	−	0.0255614i
$389$	12.3030	+	7.90669i	0.623789	+	0.400885i	0.814006	−	0.580857i	$-0.197283\pi$
$389$	12.3030	+	7.90669i	0.623789	+	0.400885i	−0.190216	+	0.981742i	$0.560919\pi$
$390$	2.20721	−	2.39676i	0.111766	−	0.121365i
$391$	−4.31822	+	6.39189i	−0.218382	+	0.323252i
$392$		−	1.00000i		−	0.0505076i
$393$	−9.47242	+	2.47273i	−0.477820	+	0.124733i
$394$	−0.894436	−	6.22094i	−0.0450610	−	0.313406i
$395$	10.7693	−	4.91817i	0.541861	−	0.247460i
$396$	0.552236	−	2.67877i	0.0277509	−	0.134613i
$397$	−0.149197	+	0.326696i	−0.00748799	+	0.0163964i	−0.913339	−	0.407200i	$-0.866505\pi$
$397$	−0.149197	+	0.326696i	−0.00748799	+	0.0163964i	0.905851	+	0.423596i	$0.139232\pi$
$398$	12.3071	−	14.2031i	0.616897	−	0.711937i
$399$	−5.43710	+	4.43056i	−0.272195	+	0.221805i
$400$	−6.70343	+	1.96831i	−0.335172	+	0.0984153i
$401$	8.79603	+	10.1512i	0.439253	+	0.506925i	0.931605	−	0.363471i	$-0.118408\pi$
$401$	8.79603	+	10.1512i	0.439253	+	0.506925i	−0.492353	+	0.870396i	$0.663863\pi$
$402$	−1.81835	−	0.317848i	−0.0906910	−	0.0158528i
$403$	−2.22111	+	1.42742i	−0.110641	+	0.0711048i
$404$	3.85931	−	3.34411i	0.192008	−	0.166376i
$405$	28.0547	−	13.5585i	1.39405	−	0.673728i
$406$	6.27983	+	0.902903i	0.311663	+	0.0448103i
$407$	2.84486	+	2.46509i	0.141015	+	0.122190i
$408$	1.08013	+	2.56800i	0.0534742	+	0.127135i
$409$	26.7106	+	7.84293i	1.32075	+	0.387808i	0.864764	−	0.502178i	$-0.167468\pi$
$409$	26.7106	+	7.84293i	1.32075	+	0.387808i	0.455988	+	0.889986i	$0.349286\pi$
$410$	−11.4538	−	25.0803i	−0.565662	−	1.23863i
$411$	8.19586	−	11.9426i	0.404272	−	0.589086i
$412$	−1.73361	+	2.69755i	−0.0854087	+	0.132899i
$413$	5.66586			0.278799
$414$	−13.4188	−	5.19002i	−0.659497	−	0.255076i
$415$	−12.0109			−0.589591
$416$	−0.293757	+	0.457095i	−0.0144026	+	0.0224109i
$417$	4.50423	−	6.56336i	0.220573	−	0.321409i
$418$	1.53363	+	3.35818i	0.0750123	+	0.164254i
$419$	−0.0273122	−	0.00801959i	−0.00133429	−	0.000391783i	0.281065	−	0.959689i	$-0.409312\pi$
$419$	−0.0273122	−	0.00801959i	−0.00133429	−	0.000391783i	−0.282400	+	0.959297i	$0.591130\pi$
$420$	−2.32495	−	5.52756i	−0.113446	−	0.269717i
$421$	−22.5821	−	19.5675i	−1.10058	−	0.953661i	−0.101432	−	0.994843i	$-0.532342\pi$
$421$	−22.5821	−	19.5675i	−1.10058	−	0.953661i	−0.999152	+	0.0411816i	$0.986888\pi$
$422$	12.8024	+	1.84070i	0.623209	+	0.0896039i
$423$	23.5907	−	9.09287i	1.14702	−	0.442111i
$424$	−3.31089	+	2.86890i	−0.160791	+	0.139326i
$425$	−9.45342	+	6.07534i	−0.458558	+	0.294697i
$426$	25.2749	+	4.41807i	1.22457	+	0.214056i
$427$	1.79858	+	2.07567i	0.0870392	+	0.100449i
$428$	−14.7096	+	4.31912i	−0.711014	+	0.208772i
$429$	0.665139	−	0.542006i	0.0321132	−	0.0261683i
$430$	−16.3578	+	18.8779i	−0.788844	+	0.910375i
$431$	12.1543	−	26.6141i	0.585450	−	1.28196i	−0.352702	−	0.935736i	$-0.614737\pi$
$431$	12.1543	−	26.6141i	0.585450	−	1.28196i	0.938153	−	0.346222i	$-0.112536\pi$
$432$	−4.21923	+	3.03284i	−0.202998	+	0.145917i
$433$	−25.5338	+	11.6609i	−1.22708	+	0.560387i	−0.920232	−	0.391372i	$-0.872000\pi$
$433$	−25.5338	+	11.6609i	−1.22708	+	0.560387i	−0.306845	+	0.951760i	$0.599273\pi$
$434$	0.691534	+	4.80972i	0.0331947	+	0.230874i
$435$	36.8113	−	9.60942i	1.76497	−	0.460736i
$436$		−	6.74566i		−	0.323058i
$437$	18.7540	−	5.04225i	0.897127	−	0.241204i
$438$	4.18427	−	4.54360i	0.199932	−	0.217102i
$439$	4.39289	+	2.82314i	0.209661	+	0.134741i	0.641257	−	0.767326i	$-0.278413\pi$
$439$	4.39289	+	2.82314i	0.209661	+	0.134741i	−0.431596	+	0.902067i	$0.642049\pi$
$440$	−3.12431	+	0.449208i	−0.148946	+	0.0214151i
$441$	2.61722	−	1.46635i	0.124629	−	0.0698261i
$442$	−0.246220	+	0.838547i	−0.0117115	+	0.0398856i
$443$	−34.1116	−	15.5782i	−1.62069	−	0.740145i	−0.621624	−	0.783316i	$-0.713527\pi$
$443$	−34.1116	−	15.5782i	−1.62069	−	0.740145i	−0.999068	+	0.0431710i	$0.986254\pi$
$444$	−0.803174	−	7.10617i	−0.0381169	−	0.337244i
$445$	5.24754	−	36.4974i	0.248757	−	1.73014i
$446$	6.09950	+	20.7730i	0.288820	+	0.983630i
$447$	0.814127	−	26.9029i	0.0385069	−	1.27246i
$448$	0.540641	+	0.841254i	0.0255429	+	0.0397455i
$449$	20.4028	+	31.7473i	0.962866	+	1.49825i	0.864212	+	0.503127i	$0.167817\pi$
$449$	20.4028	+	31.7473i	0.962866	+	1.49825i	0.0986541	+	0.995122i	$0.468546\pi$
$450$	−14.9810	−	14.6581i	−0.706213	−	0.690990i
$451$	−2.04555	−	6.96651i	−0.0963213	−	0.328040i
$452$	2.35311	−	16.3662i	0.110681	−	0.769803i
$453$	23.0852	−	2.60920i	1.08464	−	0.122591i
$454$	1.51940	+	0.693886i	0.0713089	+	0.0325657i
$455$	0.529982	−	1.80495i	0.0248460	−	0.0846175i
$456$	2.17864	−	6.66674i	0.102024	−	0.312199i
$457$	17.9503	−	2.58087i	0.839681	−	0.120728i	0.290962	−	0.956735i	$-0.406025\pi$
$457$	17.9503	−	2.58087i	0.839681	−	0.120728i	0.548719	+	0.836007i	$0.315116\pi$
$458$	−16.7485	−	10.7636i	−0.782607	−	0.502951i
$459$	−5.13717	+	6.59250i	−0.239782	+	0.307712i
$460$	−0.380991	+	16.5995i	−0.0177638	+	0.773955i
$461$		−	19.1455i		−	0.891695i	−0.895109	−	0.445847i	$-0.852902\pi$
$461$		−	19.1455i		−	0.891695i	0.895109	−	0.445847i	$-0.147098\pi$
$462$	−0.398854	−	1.52791i	−0.0185563	−	0.0710848i
$463$	2.54692	+	17.7142i	0.118365	+	0.823248i	0.959356	+	0.282199i	$0.0910637\pi$
$463$	2.54692	+	17.7142i	0.118365	+	0.823248i	−0.840991	+	0.541049i	$0.818027\pi$
$464$	−5.77107	+	2.63556i	−0.267915	+	0.122353i
$465$	15.0048	+	24.9783i	0.695833	+	1.15834i
$466$	6.41380	−	14.0443i	0.297114	−	0.650588i
$467$	16.5918	−	19.1480i	0.767777	−	0.886062i	−0.228387	−	0.973570i	$-0.573345\pi$
$467$	16.5918	−	19.1480i	0.767777	−	0.886062i	0.996164	+	0.0875086i	$0.0278905\pi$
$468$	−1.62707	−	0.0985658i	−0.0752111	−	0.00455621i
$469$	−1.02257	+	0.300254i	−0.0472180	+	0.0138645i
$470$	−19.1070	−	22.0506i	−0.881340	−	1.01712i
$471$	−6.41227	+	36.6833i	−0.295462	+	1.69028i
$472$	−4.76642	+	3.06319i	−0.219392	+	0.140995i
$473$	−4.97120	+	4.30757i	−0.228576	+	0.198062i
$474$	−5.31080	−	2.62231i	−0.243933	−	0.120447i
$475$	28.0026	+	4.02617i	1.28485	+	0.184733i
$476$	1.21558	+	1.05331i	0.0557161	+	0.0482783i
$477$	−12.3634	−	4.45851i	−0.566083	−	0.204141i
$478$	24.0910	+	7.07377i	1.10190	+	0.323547i
$479$	−15.8669	−	34.7437i	−0.724978	−	1.58748i	−0.806795	−	0.590832i	$-0.798800\pi$
$479$	−15.8669	−	34.7437i	−0.724978	−	1.58748i	0.0818169	−	0.996647i	$-0.473928\pi$
$480$	4.94430	+	3.39312i	0.225675	+	0.154874i
$481$	1.21288	−	1.88729i	0.0553028	−	0.0860528i
$482$	4.83293			0.220134
$483$	−8.27330	+	0.743272i	−0.376448	+	0.0338200i
$484$	10.1688			0.462218
$485$	6.62224	−	10.3044i	0.300700	−	0.467899i
$486$	−14.1245	−	6.59544i	−0.640698	−	0.299175i
$487$	−9.47301	−	20.7430i	−0.429263	−	0.939955i	−0.993446	−	0.114305i	$-0.963536\pi$
$487$	−9.47301	−	20.7430i	−0.429263	−	0.939955i	0.564183	−	0.825650i	$-0.309191\pi$
$488$	−2.63525	−	0.773779i	−0.119292	−	0.0350273i
$489$	0.238938	−	0.100500i	0.0108051	−	0.00454476i
$490$	−2.61651	−	2.26722i	−0.118202	−	0.102423i
$491$	8.64537	+	1.24302i	0.390160	+	0.0560965i	0.334603	−	0.942359i	$-0.391398\pi$
$491$	8.64537	+	1.24302i	0.390160	+	0.0560965i	0.0555564	+	0.998456i	$0.482307\pi$
$492$	−6.10703	+	12.3682i	−0.275326	+	0.557600i
$493$	−7.71214	+	6.68261i	−0.347337	+	0.300970i
$494$	1.85094	−	1.18953i	0.0832777	−	0.0535193i
$495$	−5.75700	−	7.51830i	−0.258758	−	0.337922i
$496$	−3.18209	−	3.67232i	−0.142880	−	0.164892i
$497$	14.2137	−	4.17351i	0.637570	−	0.187207i
$498$	3.79579	+	4.65813i	0.170094	+	0.208736i
$499$	−23.9022	+	27.5846i	−1.07001	+	1.23486i	−0.0991857	+	0.995069i	$0.531624\pi$
$499$	−23.9022	+	27.5846i	−1.07001	+	1.23486i	−0.970825	+	0.239789i	$0.922922\pi$
$500$	−2.85694	+	6.25583i	−0.127766	+	0.279769i
$501$	10.2964	−	6.18520i	0.460008	−	0.276334i
$502$	7.57518	−	3.45947i	0.338097	−	0.154404i
$503$	−5.38512	−	37.4544i	−0.240111	−	1.67001i	−0.651577	−	0.758582i	$-0.725892\pi$
$503$	−5.38512	−	37.4544i	−0.240111	−	1.67001i	0.411466	−	0.911425i	$-0.365017\pi$
$504$	−1.40898	+	2.64854i	−0.0627608	+	0.117976i
$505$		−	17.6798i		−	0.786741i
$506$	−0.721395	+	4.31244i	−0.0320699	+	0.191711i
$507$	16.1870	+	14.9069i	0.718890	+	0.662037i
$508$	13.9094	+	8.93902i	0.617129	+	0.396605i
$509$	−19.1810	+	2.75780i	−0.850181	+	0.122238i	−0.553613	−	0.832774i	$-0.686751\pi$
$509$	−19.1810	+	2.75780i	−0.850181	+	0.122238i	−0.296568	+	0.955012i	$0.595842\pi$
$510$	9.16809	+	2.99606i	0.405970	+	0.132668i
$511$	1.00470	−	3.42170i	0.0444454	−	0.151367i
$512$	−0.909632	−	0.415415i	−0.0402004	−	0.0183589i
$513$	20.6429	−	4.07379i	0.911408	−	0.179862i
$514$	−3.16309	+	21.9998i	−0.139518	+	0.970368i
$515$	3.12769	+	10.6519i	0.137823	+	0.469380i
$516$	12.4909	+	0.377995i	0.549881	+	0.0166403i
$517$	−4.15393	−	6.46364i	−0.182690	−	0.284271i
$518$	−2.23224	−	3.47343i	−0.0980788	−	0.152614i
$519$	40.2832	+	1.21904i	1.76824	+	0.0535098i
$520$	0.529982	+	1.80495i	0.0232413	+	0.0791525i
$521$	5.45760	−	37.9584i	0.239102	−	1.66299i	−0.417444	−	0.908703i	$-0.637074\pi$
$521$	5.45760	−	37.9584i	0.239102	−	1.66299i	0.656545	−	0.754286i	$-0.272017\pi$
$522$	−15.3602	−	11.2395i	−0.672299	−	0.491940i
$523$	16.0488	+	7.32924i	0.701764	+	0.320485i	0.734147	−	0.678990i	$-0.237582\pi$
$523$	16.0488	+	7.32924i	0.701764	+	0.320485i	−0.0323826	+	0.999476i	$0.510310\pi$
$524$	1.59240	−	5.42322i	0.0695643	−	0.236914i
$525$	−11.5023	−	3.75884i	−0.502000	−	0.164049i
$526$	−13.9801	+	2.01004i	−0.609563	+	0.0876419i
$527$	−6.57501	−	4.22550i	−0.286412	−	0.184066i
$528$	1.16159	+	1.06972i	0.0505516	+	0.0465537i
$529$	21.7478	+	7.48552i	0.945557	+	0.325457i
$530$			15.1674i			0.658830i
$531$	−15.0063	−	7.98306i	−0.651217	−	0.346435i
$532$	−0.576284	−	4.00814i	−0.0249851	−	0.173775i
$533$	−3.93611	+	1.79756i	−0.170492	+	0.0778609i
$534$	−15.8130	+	9.49913i	−0.684295	+	0.411068i
$535$	−22.0488	+	48.2802i	−0.953253	+	2.08733i
$536$	0.697913	−	0.805434i	0.0301452	−	0.0347895i
$537$	−13.3000	−	16.3215i	−0.573938	−	0.704325i
$538$	9.39615	−	2.75896i	0.405097	−	0.118947i
$539$	−0.597037	−	0.689017i	−0.0257162	−	0.0296781i
$540$	−1.63047	+	17.9158i	−0.0701642	+	0.770973i
$541$	−20.1072	+	12.9221i	−0.864474	+	0.555564i	−0.896058	−	0.443937i	$-0.853581\pi$
$541$	−20.1072	+	12.9221i	−0.864474	+	0.555564i	0.0315837	+	0.999501i	$0.489945\pi$
$542$	−17.3594	+	15.0420i	−0.745652	+	0.646111i
$543$	1.89452	−	3.83684i	0.0813016	−	0.164655i
$544$	−1.59207	−	0.228906i	−0.0682596	−	0.00981425i
$545$	−17.6501	−	15.2939i	−0.756047	−	0.655119i
$546$	−0.867497	+	0.364878i	−0.0371254	+	0.0156153i
$547$	23.6652	+	6.94873i	1.01185	+	0.297106i	0.745311	−	0.666717i	$-0.232301\pi$
$547$	23.6652	+	6.94873i	1.01185	+	0.297106i	0.266541	+	0.963824i	$0.414119\pi$
$548$	3.47394	+	7.60687i	0.148399	+	0.324949i
$549$	−1.83904	−	8.03165i	−0.0784885	−	0.342782i
$550$	−3.44363	+	5.35839i	−0.146837	+	0.228483i
$551$	25.6908			1.09446
$552$	6.55810	−	5.09817i	0.279131	−	0.216992i
$553$	−3.41961			−0.145416
$554$	8.58996	−	13.3662i	0.364952	−	0.567877i
$555$	−20.4144	−	14.0097i	−0.866541	−	0.594681i
$556$	1.90919	+	4.18054i	0.0809676	+	0.177294i
$557$	−2.92249	−	0.858121i	−0.123830	−	0.0363598i	0.219230	−	0.975673i	$-0.429645\pi$
$557$	−2.92249	−	0.858121i	−0.123830	−	0.0363598i	−0.343060	+	0.939313i	$0.611464\pi$
$558$	4.94522	−	13.7131i	0.209348	−	0.580523i
$559$	2.96271	+	2.56720i	0.125309	+	0.108581i
$560$	3.42690	+	0.492714i	0.144813	+	0.0208210i
$561$	2.27742	+	1.12452i	0.0961525	+	0.0474773i
$562$	3.99930	−	3.46542i	0.168700	−	0.146180i
$563$	30.4832	−	19.5904i	1.28472	−	0.825636i	0.293253	−	0.956035i	$-0.405262\pi$
$563$	30.4832	−	19.5904i	1.28472	−	0.825636i	0.991462	+	0.130398i	$0.0416257\pi$
$564$	−2.51343	+	14.3788i	−0.105834	+	0.605458i
$565$	−37.4874	−	43.2628i	−1.57711	−	1.82008i
$566$	10.4991	−	3.08283i	0.441312	−	0.129581i
$567$	−8.99786	+	0.196093i	−0.377875	+	0.00823513i
$568$	−9.70093	+	11.1955i	−0.407042	+	0.469751i
$569$	−6.35640	+	13.9186i	−0.266474	+	0.583497i	−0.994813	−	0.101720i	$-0.967565\pi$
$569$	−6.35640	+	13.9186i	−0.266474	+	0.583497i	0.728339	+	0.685217i	$0.240293\pi$
$570$	−12.5042	−	20.8154i	−0.523742	−	0.871861i
$571$	−7.58703	+	3.46488i	−0.317507	+	0.145001i	−0.567793	−	0.823171i	$-0.692203\pi$
$571$	−7.58703	+	3.46488i	−0.317507	+	0.145001i	0.250286	+	0.968172i	$0.419475\pi$
$572$	0.0704988	+	0.490330i	0.00294770	+	0.0205017i
$573$	−6.88531	−	26.3759i	−0.287638	−	1.10187i
$574$			7.96382i			0.332404i
$575$	24.8118	+	22.5169i	1.03472	+	0.939018i
$576$	−0.246606	−	2.98985i	−0.0102752	−	0.124577i
$577$	−10.6155	−	6.82214i	−0.441927	−	0.284009i	0.300694	−	0.953721i	$-0.402782\pi$
$577$	−10.6155	−	6.82214i	−0.441927	−	0.284009i	−0.742622	+	0.669711i	$0.766418\pi$
$578$	14.2662	−	2.05117i	0.593396	−	0.0853174i
$579$	−14.8793	+	45.5314i	−0.618363	+	1.89222i
$580$	−6.18832	+	21.0755i	−0.256956	+	0.875112i
$581$	3.15570	+	1.44116i	0.130921	+	0.0597894i
$582$	−6.08913	+	0.688223i	−0.252402	+	0.0285277i
$583$	−0.568419	+	3.95344i	−0.0235415	+	0.163735i
$584$	1.00470	+	3.42170i	0.0415749	+	0.141591i
$585$	−3.94682	+	4.03377i	−0.163181	+	0.166776i
$586$	−1.65733	−	2.57885i	−0.0684635	−	0.106531i
$587$	−11.3064	−	17.5932i	−0.466667	−	0.726148i	0.525537	−	0.850771i	$-0.323864\pi$
$587$	−11.3064	−	17.5932i	−0.466667	−	0.726148i	−0.992204	+	0.124623i	$0.960228\pi$
$588$	−0.0523908	+	1.73126i	−0.00216056	+	0.0713959i
$589$	5.54353	+	18.8795i	0.228417	+	0.777917i
$590$	−2.79165	+	19.4163i	−0.114930	+	0.799358i
$591$	1.22258	+	10.8169i	0.0502902	+	0.444948i
$592$	3.75575	+	1.71520i	0.154361	+	0.0704941i
$593$	−11.2498	+	38.3132i	−0.461973	+	1.57334i	0.318358	+	0.947970i	$0.396868\pi$
$593$	−11.2498	+	38.3132i	−0.461973	+	1.57334i	−0.780332	+	0.625366i	$0.784950\pi$
$594$	−1.09641	+	4.60871i	−0.0449861	+	0.189098i
$595$	5.51199	−	0.792504i	0.225969	−	0.0324895i
$596$	13.0727	+	8.40129i	0.535477	+	0.344130i
$597$	−22.0508	+	23.9445i	−0.902480	+	0.979982i
$598$	2.60513	+	0.0597929i	0.106532	+	0.00244511i
$599$		−	43.6936i		−	1.78527i	−0.450777	−	0.892637i	$-0.648853\pi$
$599$		−	43.6936i		−	1.78527i	0.450777	−	0.892637i	$-0.351147\pi$
$600$	11.7085	−	3.05645i	0.477997	−	0.124779i
$601$	1.91816	+	13.3411i	0.0782433	+	0.544194i	0.990809	+	0.135265i	$0.0431886\pi$
$601$	1.91816	+	13.3411i	0.0782433	+	0.544194i	−0.912566	+	0.408929i	$0.865902\pi$
$602$	6.56292	−	2.99719i	0.267485	−	0.122156i
$603$	3.13138	+	0.645542i	0.127520	+	0.0262885i
$604$	−5.57201	+	12.2010i	−0.226722	+	0.496451i
$605$	23.0549	−	26.6068i	0.937316	−	1.08172i
$606$	−6.85667	+	5.58733i	−0.278533	+	0.226970i
$607$	−11.6583	+	3.42320i	−0.473198	+	0.138943i	−0.509632	−	0.860393i	$-0.670218\pi$
$607$	−11.6583	+	3.42320i	−0.473198	+	0.138943i	0.0364340	+	0.999336i	$0.488400\pi$
$608$	2.65176	+	3.06030i	0.107543	+	0.124112i
$609$	−10.8247	−	1.89216i	−0.438639	−	0.0766743i
$610$	−7.99929	+	5.14083i	−0.323882	+	0.208146i
$611$	−3.46063	+	2.99866i	−0.140002	+	0.121313i
$612$	−1.73544	−	4.50246i	−0.0701509	−	0.182001i
$613$	−27.6108	−	3.96983i	−1.11519	−	0.160340i	−0.440010	−	0.897993i	$-0.645025\pi$
$613$	−27.6108	−	3.96983i	−1.11519	−	0.160340i	−0.675180	+	0.737653i	$0.735934\pi$
$614$	−0.623090	−	0.539910i	−0.0251458	−	0.0217890i
$615$	18.5155	+	44.0205i	0.746616	+	1.77508i
$616$	0.874770	+	0.256856i	0.0352455	+	0.0103490i
$617$	3.07632	+	6.73621i	0.123848	+	0.271190i	0.961393	−	0.275179i	$-0.0887371\pi$
$617$	3.07632	+	6.73621i	0.123848	+	0.271190i	−0.837545	+	0.546368i	$0.816010\pi$
$618$	3.14265	−	4.57932i	0.126416	−	0.184207i
$619$	25.1448	−	39.1261i	1.01066	−	1.57261i	0.206279	−	0.978493i	$-0.433865\pi$
$619$	25.1448	−	39.1261i	1.01066	−	1.57261i	0.804378	−	0.594118i	$-0.202499\pi$
$620$	−16.8232			−0.675635
$621$	22.9595	+	9.68829i	0.921332	+	0.388778i
$622$	14.1879			0.568882
$623$	−5.75797	+	8.95957i	−0.230688	+	0.358958i
$624$	0.532517	−	0.775959i	0.0213177	−	0.0310632i
$625$	−4.62021	−	10.1168i	−0.184808	−	0.404674i
$626$	0.989069	+	0.290417i	0.0395311	+	0.0116074i
$627$	−2.47917	−	5.89422i	−0.0990085	−	0.235393i
$628$	−16.2488	−	14.0797i	−0.648398	−	0.561840i
$629$	6.57347	+	0.945122i	0.262101	+	0.0376845i
$630$	3.73549	+	9.69144i	0.148826	+	0.386116i
$631$	−23.4148	+	20.2890i	−0.932128	+	0.807693i	−0.981574	−	0.191083i	$-0.938800\pi$
$631$	−23.4148	+	20.2890i	−0.932128	+	0.807693i	0.0494458	+	0.998777i	$0.484254\pi$
$632$	2.87676	−	1.84878i	0.114431	−	0.0735405i
$633$	−22.0678	−	3.85746i	−0.877115	−	0.153320i
$634$	16.9960	+	19.6144i	0.674997	+	0.778988i
$635$	54.9247	−	16.1273i	2.17962	−	0.639994i
$636$	5.88231	−	4.79335i	0.233249	−	0.190069i
$637$	−0.355818	+	0.410636i	−0.0140980	+	0.0162700i
$638$	−2.40284	+	5.26149i	−0.0951294	+	0.208304i
$639$	−43.5259	−	8.97298i	−1.72186	−	0.354966i
$640$	−3.14928	+	1.43823i	−0.124486	+	0.0568509i
$641$	3.04997	+	21.2130i	0.120467	+	0.837863i	0.957029	+	0.289992i	$0.0936526\pi$
$641$	3.04997	+	21.2130i	0.120467	+	0.837863i	−0.836563	+	0.547871i	$0.815438\pi$
$642$	25.6923	−	6.70686i	1.01400	−	0.264699i
$643$			16.7529i			0.660670i	0.943864	+	0.330335i	$0.107162\pi$
$643$			16.7529i			0.660670i	−0.943864	+	0.330335i	$0.892838\pi$
$644$	2.09184	−	4.31558i	0.0824299	−	0.170058i
$645$	29.3086	−	31.8256i	1.15403	−	1.25313i
$646$	5.47923	+	3.52129i	0.215577	+	0.138543i
$647$	−16.0336	+	2.30528i	−0.630345	+	0.0906300i	−0.450080	−	0.892988i	$-0.648605\pi$
$647$	−16.0336	+	2.30528i	−0.630345	+	0.0906300i	−0.180265	+	0.983618i	$0.557696\pi$
$648$	7.46347	−	5.02958i	0.293193	−	0.197580i
$649$	−1.45531	+	4.95632i	−0.0571258	+	0.194553i
$650$	3.45303	+	1.57695i	0.135439	+	0.0618529i
$651$	−0.945238	−	8.36310i	−0.0370468	−	0.327776i
$652$	−0.0212984	+	0.148134i	−0.000834110	+	0.00580136i
$653$	0.581208	+	1.97941i	0.0227444	+	0.0774604i	0.970083	−	0.242773i	$-0.0780569\pi$
$653$	0.581208	+	1.97941i	0.0227444	+	0.0774604i	−0.947339	+	0.320233i	$0.896239\pi$
$654$	−0.353410	+	11.6785i	−0.0138194	+	0.456664i
$655$	−10.5796	−	16.4622i	−0.413379	−	0.643230i
$656$	−4.30557	−	6.69959i	−0.168104	−	0.261575i
$657$	−7.48210	+	7.64693i	−0.291904	+	0.298335i
$658$	2.37430	+	8.08612i	0.0925598	+	0.315230i
$659$	−3.54876	+	24.6822i	−0.138240	+	0.961481i	0.796117	+	0.605143i	$0.206884\pi$
$659$	−3.54876	+	24.6822i	−0.138240	+	0.961481i	−0.934357	+	0.356338i	$0.884025\pi$
$660$	5.43252	−	0.614010i	0.211461	−	0.0239003i
$661$	−0.224622	−	0.102581i	−0.00873678	−	0.00398995i	0.411042	−	0.911616i	$-0.365165\pi$
$661$	−0.224622	−	0.102581i	−0.00873678	−	0.00398995i	−0.419779	+	0.907627i	$0.637892\pi$
$662$	8.90437	−	30.3255i	0.346078	−	1.17863i
$663$	0.470202	−	1.43884i	0.0182611	−	0.0558800i
$664$	−3.43390	+	0.493720i	−0.133261	+	0.0191600i
$665$	−11.7939	−	7.57949i	−0.457348	−	0.293920i
$666$	1.01820	+	12.3447i	0.0394546	+	0.478347i
$667$	25.2124	+	17.0329i	0.976227	+	0.659517i
$668$			6.93474i			0.268313i
$669$	−9.47150	−	36.2830i	−0.366189	−	1.40278i
$670$	−0.525106	−	3.65219i	−0.0202866	−	0.141097i
$671$	−2.27771	+	1.04019i	−0.0879299	+	0.0401562i
$672$	−0.891915	−	1.48475i	−0.0344064	−	0.0572755i
$673$	9.65440	−	21.1402i	0.372150	−	0.814895i	−0.627201	−	0.778858i	$-0.715799\pi$
$673$	9.65440	−	21.1402i	0.372150	−	0.814895i	0.999350	−	0.0360368i	$-0.0114733\pi$
$674$	7.19976	−	8.30896i	0.277324	−	0.320049i
$675$	25.1681	+	26.1619i	0.968721	+	1.00697i
$676$	−12.1901	+	3.57935i	−0.468851	+	0.137667i
$677$	3.06422	+	3.53630i	0.117768	+	0.135911i	0.811572	−	0.584252i	$-0.198612\pi$
$677$	3.06422	+	3.53630i	0.117768	+	0.135911i	−0.693804	+	0.720164i	$0.744067\pi$
$678$	−4.93128	+	28.2109i	−0.189385	+	1.08343i
$679$	−2.97631	+	1.91276i	−0.114220	+	0.0734049i
$680$	−4.20852	+	3.64670i	−0.161389	+	0.139845i
$681$	−2.59412	−	1.28090i	−0.0994068	−	0.0490841i
$682$	−4.38503	−	0.630472i	−0.167911	−	0.0241420i
$683$	−32.8896	−	28.4990i	−1.25849	−	1.09048i	−0.991946	−	0.126661i	$-0.959574\pi$
$683$	−32.8896	−	28.4990i	−1.25849	−	1.09048i	−0.266540	−	0.963824i	$-0.585881\pi$
$684$	−4.12106	+	11.4277i	−0.157573	+	0.436949i
$685$	27.7797	+	8.15685i	1.06141	+	0.311657i
$686$	0.415415	+	0.909632i	0.0158606	+	0.0347299i
$687$	28.4321	+	19.5121i	1.08475	+	0.744432i
$688$	−3.90068	+	6.06958i	−0.148712	+	0.231400i
$689$	2.38038			0.0906852
$690$	1.52925	−	28.7180i	0.0582177	−	1.09328i
$691$	22.5816			0.859045			0.429522	−	0.903056i	$-0.358682\pi$
$691$	22.5816			0.859045			0.429522	+	0.903056i	$0.358682\pi$
$692$	−12.5797	+	19.5744i	−0.478209	+	0.744108i
$693$	0.610470	+	2.66610i	0.0231898	+	0.101277i
$694$	12.7368	+	27.8897i	0.483483	+	1.05868i
$695$	15.2670	+	4.48279i	0.579110	+	0.170042i
$696$	10.1293	−	4.26048i	0.383950	−	0.161493i
$697$	−9.68068	−	8.38836i	−0.366682	−	0.317732i
$698$	18.9351	+	2.72245i	0.716703	+	0.103046i
$699$	−11.8397	+	23.9782i	−0.447820	+	0.906940i
$700$	5.27999	−	4.57514i	0.199565	−	0.172924i
$701$	−17.5096	+	11.2527i	−0.661328	+	0.425010i	−0.827790	−	0.561038i	$-0.810402\pi$
$701$	−17.5096	+	11.2527i	−0.661328	+	0.425010i	0.166462	+	0.986048i	$0.446766\pi$
$702$	2.81171	+	0.255886i	0.106121	+	0.00965780i
$703$	−10.9488	−	12.6356i	−0.412942	−	0.476560i
$704$	−0.874770	+	0.256856i	−0.0329691	+	0.00968061i
$705$	31.9239	+	39.1764i	1.20232	+	1.47547i
$706$	10.1682	−	11.7347i	0.382685	−	0.441641i
$707$	−2.12136	+	4.64513i	−0.0797820	+	0.174698i
$708$	8.41239	−	5.05346i	0.316157	−	0.189921i
$709$	−5.83376	+	2.66419i	−0.219092	+	0.100056i	−0.521937	−	0.852984i	$-0.674791\pi$
$709$	−5.83376	+	2.66419i	−0.219092	+	0.100056i	0.302846	+	0.953040i	$0.402063\pi$
$710$	7.29894	+	50.7652i	0.273924	+	1.90518i
$711$	9.05698	+	4.81814i	0.339663	+	0.180694i
$712$		−	10.6503i		−	0.399136i
$713$	−7.07678	+	22.2033i	−0.265028	+	0.831521i
$714$	−2.04930	−	1.88723i	−0.0766932	−	0.0706279i
$715$	1.44279	+	0.927225i	0.0539573	+	0.0346763i
$716$	12.0320	−	1.72993i	0.449655	−	0.0646507i
$717$	−41.3372	−	13.5087i	−1.54377	−	0.504490i
$718$	9.79316	−	33.3524i	0.365477	−	1.24470i
$719$	25.9101	+	11.8328i	0.966285	+	0.441287i	0.835117	−	0.550073i	$-0.185400\pi$
$719$	25.9101	+	11.8328i	0.966285	+	0.441287i	0.131168	+	0.991360i	$0.458127\pi$
$720$	−8.38208	−	6.13340i	−0.312382	−	0.228578i
$721$	0.456344	−	3.17394i	0.0169951	−	0.118204i
$722$	0.733268	+	2.49728i	0.0272894	+	0.0929392i
$723$	−8.36705	−	0.253201i	−0.311174	−	0.00941665i
$724$	1.33567	+	2.07834i	0.0496398	+	0.0772410i
$725$	23.9638	+	37.2884i	0.889992	+	1.38485i
$726$	−17.6048	−	0.532752i	−0.653376	−	0.0197723i
$727$	−1.98145	−	6.74820i	−0.0734879	−	0.250277i	0.914554	−	0.404465i	$-0.132542\pi$
$727$	−1.98145	−	6.74820i	−0.0734879	−	0.250277i	−0.988042	+	0.154188i	$0.950724\pi$
$728$	0.0773267	−	0.537819i	0.00286592	−	0.0199329i
$729$	24.1075	+	12.1584i	0.892872	+	0.450311i
$730$	11.2308	+	5.12894i	0.415671	+	0.189831i
$731$	−3.26945	+	11.1347i	−0.120925	+	0.411833i
$732$	4.52176	+	1.47767i	0.167129	+	0.0546164i
$733$	−44.2936	+	6.36846i	−1.63602	+	0.235225i	−0.898142	−	0.439706i	$-0.855082\pi$
$733$	−44.2936	+	6.36846i	−1.63602	+	0.235225i	−0.737881	+	0.674931i	$0.764173\pi$
$734$	−14.2396	−	9.15123i	−0.525593	−	0.337778i
$735$	4.41108	+	4.06223i	0.162705	+	0.149838i
$736$	0.573413	+	4.76143i	0.0211363	+	0.175509i
$737$		−	0.971637i		−	0.0357907i
$738$	11.2208	−	21.0925i	0.413045	−	0.776427i
$739$	−5.59945	−	38.9450i	−0.205979	−	1.43261i	−0.786107	−	0.618090i	$-0.787907\pi$
$739$	−5.59945	−	38.9450i	−0.205979	−	1.43261i	0.580128	−	0.814525i	$-0.303002\pi$
$740$	13.0030	−	5.93825i	0.477998	−	0.218294i
$741$	−3.26677	+	1.96241i	−0.120008	+	0.0720908i
$742$	1.81990	−	3.98504i	0.0668108	−	0.146295i
$743$	−25.7805	+	29.7522i	−0.945794	+	1.09150i	0.0498960	+	0.998754i	$0.484111\pi$
$743$	−25.7805	+	29.7522i	−0.945794	+	1.09150i	−0.995689	+	0.0927495i	$0.970434\pi$
$744$	5.31662	+	6.52446i	0.194917	+	0.239198i
$745$	51.6207	−	15.1572i	1.89124	−	0.555317i
$746$	9.88522	+	11.4082i	0.361924	+	0.417682i
$747$	−6.32746	−	8.26328i	−0.231510	−	0.302338i
$748$	−1.23363	+	0.792807i	−0.0451060	+	0.0289879i
$749$	11.5861	−	10.0394i	0.423346	−	0.366831i
$750$	5.27385	−	10.6808i	0.192574	−	0.390007i
$751$	−19.9523	−	2.86871i	−0.728071	−	0.104681i	−0.231695	−	0.972788i	$-0.574427\pi$
$751$	−19.9523	−	2.86871i	−0.728071	−	0.104681i	−0.496376	+	0.868108i	$0.665336\pi$
$752$	−6.36907	−	5.51883i	−0.232256	−	0.201251i
$753$	−13.2958	+	5.59237i	−0.484527	+	0.203797i
$754$	3.30759	+	0.971197i	0.120455	+	0.0353689i
$755$	19.2911	+	42.2416i	0.702074	+	1.53733i
$756$	2.57806	−	4.51150i	0.0937631	−	0.164082i
$757$	3.01386	−	4.68966i	0.109541	−	0.170449i	−0.782155	−	0.623084i	$-0.785880\pi$
$757$	3.01386	−	4.68966i	0.109541	−	0.170449i	0.891696	+	0.452635i	$0.149516\pi$
$758$	−18.4617			−0.670558
$759$	1.47485	−	7.42815i	0.0535338	−	0.269625i
$760$	14.0195			0.508539
$761$	2.19375	−	3.41355i	0.0795235	−	0.123741i	−0.799214	−	0.601047i	$-0.794750\pi$
$761$	2.19375	−	3.41355i	0.0795235	−	0.123741i	0.878737	+	0.477306i	$0.158387\pi$
$762$	−23.6124	−	16.2045i	−0.855387	−	0.587026i
$763$	2.80225	+	6.13606i	0.101448	+	0.222140i
$764$	15.1009	+	4.43404i	0.546333	+	0.160418i
$765$	−15.7154	−	5.66727i	−0.568190	−	0.204901i
$766$	−18.1762	−	15.7497i	−0.656731	−	0.569061i
$767$	3.04721	+	0.438122i	0.110028	+	0.0158197i
$768$	1.55304	+	0.766847i	0.0560406	+	0.0276712i
$769$	−33.4208	+	28.9593i	−1.20519	+	1.04430i	−0.207370	+	0.978263i	$0.566490\pi$
$769$	−33.4208	+	28.9593i	−1.20519	+	1.04430i	−0.997817	+	0.0660375i	$0.978964\pi$
$770$	2.65536	−	1.70650i	0.0956927	−	0.0614979i
$771$	6.62871	−	37.9216i	0.238727	−	1.36571i
$772$	−18.1106	−	20.9007i	−0.651815	−	0.752234i
$773$	0.913520	−	0.268234i	0.0328570	−	0.00964770i	−0.265263	−	0.964176i	$-0.585459\pi$
$773$	0.913520	−	0.268234i	0.0328570	−	0.00964770i	0.298120	+	0.954528i	$0.403641\pi$
$774$	−21.6051	−	1.30882i	−0.776581	−	0.0470444i
$775$	−22.2314	+	25.6565i	−0.798577	+	0.921607i
$776$	1.46971	−	3.21823i	0.0527597	−	0.115528i
$777$	3.68260	+	6.13035i	0.132113	+	0.219925i
$778$	13.3031	−	6.07530i	0.476938	−	0.217810i
$779$	4.58942	+	31.9201i	0.164433	+	1.14366i
$780$	−0.822973	−	3.15261i	−0.0294672	−	0.112881i
$781$			13.5057i			0.483271i
$782$	3.04259	+	7.08843i	0.108803	+	0.253482i
$783$	26.0037	+	20.2632i	0.929296	+	0.724148i
$784$	−0.841254	−	0.540641i	−0.0300448	−	0.0193086i
$785$	−73.6793	+	10.5935i	−2.62973	+	0.378098i
$786$	−3.04098	+	9.30556i	−0.108468	+	0.331918i
$787$	0.215385	−	0.733535i	0.00767766	−	0.0261477i	−0.955565	−	0.294780i	$-0.904754\pi$
$787$	0.215385	−	0.733535i	0.00767766	−	0.0261477i	0.963243	+	0.268633i	$0.0865717\pi$
$788$	−5.71696	−	2.61085i	−0.203658	−	0.0930076i
$789$	24.3085	−	2.74747i	0.865407	−	0.0978125i
$790$	1.68489	−	11.7187i	0.0599457	−	0.416931i
$791$	4.65832	+	15.8648i	0.165631	+	0.564086i
$792$	−1.95496	−	1.91282i	−0.0694666	−	0.0679692i
$793$	0.806804	+	1.25541i	0.0286504	+	0.0445810i
$794$	0.194172	+	0.302138i	0.00689091	+	0.0107225i
$795$	0.794633	−	26.2587i	0.0281827	−	0.931300i
$796$	−5.29471	−	18.0321i	−0.187666	−	0.639132i
$797$	0.544623	−	3.78794i	0.0192916	−	0.134176i	−0.977900	−	0.209075i	$-0.932955\pi$
$797$	0.544623	−	3.78794i	0.0192916	−	0.134176i	0.997191	+	0.0748997i	$0.0238637\pi$
$798$	0.787706	+	6.96932i	0.0278845	+	0.246711i
$799$	−12.3302	−	5.63102i	−0.436211	−	0.199211i
$800$	−1.96831	+	6.70343i	−0.0695901	+	0.237002i
$801$	27.8741	−	15.6170i	0.984881	−	0.551799i
$802$	13.2952	−	1.91156i	0.469469	−	0.0674995i
$803$	2.73514	+	1.75777i	0.0965210	+	0.0620303i
$804$	−1.25046	+	1.35785i	−0.0441005	+	0.0478877i
$805$	−6.54911	−	15.2577i	−0.230826	−	0.537763i
$806$			2.64023i			0.0929983i
$807$	−16.4117	+	4.28420i	−0.577719	+	0.150811i
$808$	−0.726746	−	5.05463i	−0.0255668	−	0.177821i
$809$	−2.65763	+	1.21370i	−0.0934371	+	0.0426713i	−0.461585	−	0.887096i	$-0.652719\pi$
$809$	−2.65763	+	1.21370i	−0.0934371	+	0.0426713i	0.368148	+	0.929767i	$0.379992\pi$
$810$	3.76138	−	30.9314i	0.132162	−	1.08682i
$811$	−1.90230	+	4.16545i	−0.0667987	+	0.146269i	−0.940087	−	0.340936i	$-0.889256\pi$
$811$	−1.90230	+	4.16545i	−0.0667987	+	0.146269i	0.873288	+	0.487205i	$0.161983\pi$
$812$	4.15470	−	4.79478i	0.145801	−	0.168264i
$813$	30.8417	−	25.1322i	1.08167	−	0.881424i
$814$	3.61181	−	1.06052i	0.126594	−	0.0371713i
$815$	0.339305	+	0.391579i	0.0118853	+	0.0137164i
$816$	2.74430	+	0.479705i	0.0960697	+	0.0167930i
$817$	24.5779	−	15.7952i	0.859871	−	0.552606i
$818$	21.0387	−	18.2302i	0.735602	−	0.637402i
$819$	1.52098	−	0.586249i	0.0531472	−	0.0204852i
$820$	−27.2913	−	3.92389i	−0.953052	−	0.137028i
$821$	−20.4734	−	17.7403i	−0.714528	−	0.619142i	0.219805	−	0.975544i	$-0.429458\pi$
$821$	−20.4734	−	17.7403i	−0.714528	−	0.619142i	−0.934333	+	0.356402i	$0.884003\pi$
$822$	−5.61576	−	13.3515i	−0.195872	−	0.465686i
$823$	29.3982	+	8.63209i	1.02476	+	0.300896i	0.750577	−	0.660783i	$-0.229775\pi$
$823$	29.3982	+	8.63209i	1.02476	+	0.300896i	0.274180	+	0.961678i	$0.411594\pi$
$824$	1.33206	+	2.91681i	0.0464045	+	0.101612i
$825$	6.24254	−	9.09635i	0.217337	−	0.316694i
$826$	3.06319	−	4.76642i	0.106582	−	0.165845i
$827$	3.00134			0.104367			0.0521834	−	0.998638i	$-0.483382\pi$
$827$	3.00134			0.104367			0.0521834	+	0.998638i	$0.483382\pi$
$828$	−11.6209	+	8.48266i	−0.403853	+	0.294793i
$829$	−43.7070			−1.51801			−0.759003	−	0.651087i	$-0.774313\pi$
$829$	−43.7070			−1.51801			−0.759003	+	0.651087i	$0.774313\pi$
$830$	−6.49358	+	10.1042i	−0.225395	+	0.350722i
$831$	−15.5717	+	22.6904i	−0.540176	+	0.787120i
$832$	0.225716	+	0.494248i	0.00782528	+	0.0171350i
$833$	−1.54329	−	0.453151i	−0.0534719	−	0.0157008i
$834$	−3.08628	−	7.33762i	−0.106869	−	0.254081i
$835$	18.1448	+	15.7226i	0.627928	+	0.544103i
$836$	3.65422	+	0.525398i	0.126384	+	0.0181713i
$837$	−9.27990	+	23.4819i	−0.320760	+	0.811652i
$838$	−0.0215126	+	0.0186408i	−0.000743141	+	0.000643935i
$839$	0.0523395	−	0.0336366i	0.00180696	−	0.00116126i	−0.539737	−	0.841834i	$-0.681476\pi$
$839$	0.0523395	−	0.0336366i	0.00180696	−	0.00116126i	0.541544	+	0.840672i	$0.317840\pi$
$840$	−5.90704	−	1.03255i	−0.203812	−	0.0356265i
$841$	7.36814	+	8.50328i	0.254074	+	0.293217i
$842$	−28.6700	+	8.41827i	−0.988034	+	0.290113i
$843$	−7.10538	+	5.79000i	−0.244722	+	0.199418i
$844$	8.46997	−	9.77487i	0.291549	−	0.336465i
$845$	−18.2723	+	40.0108i	−0.628587	+	1.37641i
$846$	5.10471	−	24.7618i	0.175503	−	0.851327i
$847$	−9.24987	+	4.22427i	−0.317829	+	0.145148i
$848$	0.623472	+	4.33634i	0.0214101	+	0.148911i
$849$	−18.3382	+	4.78711i	−0.629367	+	0.164293i
$850$			11.2373i			0.385436i
$851$	−2.36755	−	19.6593i	−0.0811586	−	0.673913i
$852$	17.3814	−	18.8740i	0.595475	−	0.646613i
$853$	−29.1320	−	18.7220i	−0.997461	−	0.641029i	−0.0633425	−	0.997992i	$-0.520176\pi$
$853$	−29.1320	−	18.7220i	−0.997461	−	0.641029i	−0.934119	+	0.356962i	$0.883812\pi$
$854$	2.71855	−	0.390868i	0.0930267	−	0.0133752i
$855$	20.5574	+	36.6919i	0.703048	+	1.25484i
$856$	−4.31912	+	14.7096i	−0.147624	+	0.502763i
$857$	−14.6048	−	6.66981i	−0.498892	−	0.227836i	0.150044	−	0.988679i	$-0.452058\pi$
$857$	−14.6048	−	6.66981i	−0.498892	−	0.227836i	−0.648936	+	0.760843i	$0.724786\pi$
$858$	−0.0963628	−	0.852581i	−0.00328977	−	0.0291066i
$859$	−0.878479	+	6.10996i	−0.0299733	+	0.208469i	−0.999305	−	0.0372890i	$-0.988128\pi$
$859$	−0.878479	+	6.10996i	−0.0299733	+	0.208469i	0.969331	+	0.245758i	$0.0790369\pi$
$860$	7.03742	+	23.9673i	0.239974	+	0.817276i
$861$	0.417231	−	13.7874i	0.0142192	−	0.469875i
$862$	−15.8181	−	24.6135i	−0.538768	−	0.838339i
$863$	−20.1052	−	31.2843i	−0.684389	−	1.06493i	−0.993492	−	0.113901i	$-0.963665\pi$
$863$	−20.1052	−	31.2843i	−0.684389	−	1.06493i	0.309103	−	0.951028i	$-0.399971\pi$
$864$	0.270298	+	5.18912i	0.00919571	+	0.176537i
$865$	22.6957	+	77.2946i	0.771678	+	2.62809i
$866$	−3.99485	+	27.7848i	−0.135750	+	0.944165i
$867$	−24.8059	+	2.80369i	−0.842454	+	0.0952182i
$868$	4.42007	+	2.01858i	0.150027	+	0.0685150i
$869$	0.878345	−	2.99137i	0.0297958	−	0.101475i
$870$	11.8177	−	36.1629i	0.400659	−	1.22604i
$871$	−0.573176	+	0.0824103i	−0.0194213	+	0.00279237i
$872$	−5.67481	−	3.64698i	−0.192173	−	0.123502i
$873$	10.5779	−	0.872477i	0.358008	−	0.0295289i
$874$	5.89738	−	18.5029i	0.199482	−	0.625871i
$875$		−	6.87732i		−	0.232496i
$876$	−1.56013	−	5.97649i	−0.0527121	−	0.201927i
$877$	−0.196168	−	1.36438i	−0.00662411	−	0.0460717i	0.986241	−	0.165312i	$-0.0528632\pi$
$877$	−0.196168	−	1.36438i	−0.00662411	−	0.0460717i	−0.992865	+	0.119240i	$0.961954\pi$
$878$	4.74995	−	2.16923i	0.160303	−	0.0732079i
$879$	2.73415	+	4.55148i	0.0922206	+	0.153518i
$880$	−1.31123	+	2.87120i	−0.0442016	+	0.0967880i
$881$	21.0023	−	24.2379i	0.707585	−	0.816597i	−0.282171	−	0.959364i	$-0.591055\pi$
$881$	21.0023	−	24.2379i	0.707585	−	0.816597i	0.989756	+	0.142767i	$0.0456000\pi$
$882$	0.181404	−	2.99451i	0.00610819	−	0.100830i
$883$	−43.9628	+	12.9087i	−1.47947	+	0.434411i	−0.919164	−	0.393876i	$-0.871134\pi$
$883$	−43.9628	+	12.9087i	−1.47947	+	0.434411i	−0.560304	+	0.828287i	$0.689316\pi$
$884$	0.572314	+	0.660486i	0.0192490	+	0.0222145i
$885$	5.85030	−	33.4685i	0.196656	−	1.12503i
$886$	−31.5474	+	20.2743i	−1.05986	+	0.681128i
$887$	−2.99999	+	2.59951i	−0.100730	+	0.0872829i	−0.703770	−	0.710428i	$-0.748501\pi$
$887$	−2.99999	+	2.59951i	−0.100730	+	0.0872829i	0.603040	+	0.797711i	$0.293956\pi$
$888$	−6.41232	−	3.16621i	−0.215183	−	0.106251i
$889$	−16.3658	−	2.35305i	−0.548892	−	0.0789188i
$890$	−27.8666	−	24.1465i	−0.934089	−	0.809393i
$891$	2.13962	−	7.92143i	0.0716798	−	0.265378i
$892$	20.7730	+	6.09950i	0.695531	+	0.204226i
$893$	14.1764	+	31.0420i	0.474396	+	1.03878i
$894$	−22.1920	−	15.2297i	−0.742212	−	0.509357i
$895$	22.7527	−	35.4039i	0.760540	−	1.18342i
$896$	1.00000			0.0334077
$897$	−4.50701	−	0.240002i	−0.150485	−	0.00801342i
$898$	37.7381			1.25934
$899$	−16.6672	+	25.9347i	−0.555882	+	0.864970i
$900$	−20.4306	+	4.67808i	−0.681019	+	0.155936i
$901$	2.92722	+	6.40971i	0.0975198	+	0.213538i
$902$	−6.96651	−	2.04555i	−0.231960	−	0.0681095i
$903$	−11.5191	+	4.84507i	−0.383333	+	0.161234i
$904$	−12.4960	−	10.8278i	−0.415610	−	0.360128i
$905$	8.46627	+	1.21727i	0.281428	+	0.0404633i
$906$	10.2858	−	20.8311i	0.341723	−	0.692068i
$907$	−13.9468	+	12.0849i	−0.463095	+	0.401274i	−0.854915	−	0.518768i	$-0.826391\pi$
$907$	−13.9468	+	12.0849i	−0.463095	+	0.401274i	0.391820	+	0.920042i	$0.371846\pi$
$908$	1.40518	−	0.903056i	0.0466326	−	0.0299690i
$909$	12.1634	−	9.31389i	0.403434	−	0.308922i
$910$	−1.23189	−	1.42168i	−0.0408369	−	0.0471283i
$911$	22.7948	−	6.69316i	0.755226	−	0.221754i	0.118616	−	0.992940i	$-0.462154\pi$
$911$	22.7948	−	6.69316i	0.755226	−	0.221754i	0.636610	+	0.771186i	$0.280336\pi$
$912$	−4.43056	−	5.43710i	−0.146710	−	0.180040i
$913$	−2.07124	+	2.39034i	−0.0685482	+	0.0791088i
$914$	7.53352	−	16.4961i	0.249187	−	0.545643i
$915$	14.1182	−	8.48102i	0.466733	−	0.280374i
$916$	−18.1099	+	8.27050i	−0.598367	+	0.273265i
$917$	0.804388	+	5.59464i	0.0265632	+	0.184751i
$918$	2.76860	+	7.88584i	0.0913776	+	0.260271i
$919$			34.0089i			1.12185i	0.827867	+	0.560925i	$0.189554\pi$
$919$			34.0089i			1.12185i	−0.827867	+	0.560925i	$0.810446\pi$
$920$	13.7584	+	9.29487i	0.453601	+	0.306443i
$921$	1.05044	+	0.967368i	0.0346133	+	0.0318759i
$922$	−16.1062	−	10.3508i	−0.530430	−	0.340887i
$923$	7.96711	−	1.14550i	0.262240	−	0.0377045i
$924$	−1.50100	−	0.490513i	−0.0493791	−	0.0161367i
$925$	8.12688	−	27.6776i	0.267210	−	0.910035i
$926$	16.2791	+	7.43441i	0.534964	+	0.244310i
$927$	−5.68065	+	7.76334i	−0.186577	+	0.254982i
$928$	−0.902903	+	6.27983i	−0.0296392	+	0.206145i
$929$	−4.09200	−	13.9361i	−0.134254	−	0.457228i	0.864733	−	0.502233i	$-0.167488\pi$
$929$	−4.09200	−	13.9361i	−0.134254	−	0.457228i	−0.998987	+	0.0450048i	$0.985670\pi$
$930$	29.1253	+	0.881380i	0.955055	+	0.0289016i
$931$	2.18925	+	3.40654i	0.0717497	+	0.111645i
$932$	−8.34723	−	12.9885i	−0.273423	−	0.425454i
$933$	−24.5629	−	0.743314i	−0.804152	−	0.0243350i
$934$	−7.13808	−	24.3101i	−0.233565	−	0.795450i
$935$	−0.722526	+	5.02528i	−0.0236291	+	0.164344i
$936$	−0.962577	+	1.31549i	−0.0314628	+	0.0429980i
$937$	−34.3450	−	15.6848i	−1.12200	−	0.512401i	−0.233998	−	0.972237i	$-0.575181\pi$
$937$	−34.3450	−	15.6848i	−1.12200	−	0.512401i	−0.888004	+	0.459836i	$0.847908\pi$
$938$	−0.300254	+	1.02257i	−0.00980365	+	0.0333882i
$939$	−1.69712	−	0.554604i	−0.0553834	−	0.0180988i
$940$	−28.8802	+	4.15235i	−0.941968	+	0.135435i
$941$	−31.9878	−	20.5573i	−1.04277	−	0.670148i	−0.0971003	−	0.995275i	$-0.530957\pi$
$941$	−31.9878	−	20.5573i	−1.04277	−	0.670148i	−0.945671	+	0.325126i	$0.894593\pi$
$942$	27.3933	+	25.2269i	0.892520	+	0.821935i
$943$	−16.6590	+	34.3685i	−0.542492	+	1.11919i
$944$			5.66586i			0.184408i
$945$	−5.95936	−	16.9741i	−0.193858	−	0.552167i
$946$	0.936125	+	6.51089i	0.0304360	+	0.211687i
$947$	−19.9873	+	9.12789i	−0.649500	+	0.296617i	−0.712789	−	0.701379i	$-0.752568\pi$
$947$	−19.9873	+	9.12789i	−0.649500	+	0.296617i	0.0632890	+	0.997995i	$0.479841\pi$
$948$	−5.07727	+	3.05000i	−0.164902	+	0.0990593i
$949$	0.804938	−	1.76257i	0.0261294	−	0.0572154i
$950$	18.5264	−	21.3806i	0.601075	−	0.693678i
$951$	−28.3968	−	34.8481i	−0.920830	−	1.13003i
$952$	1.54329	−	0.453151i	0.0500184	−	0.0146867i
$953$	−15.5143	−	17.9045i	−0.502559	−	0.579984i	0.446619	−	0.894724i	$-0.352628\pi$
$953$	−15.5143	−	17.9045i	−0.502559	−	0.579984i	−0.949178	+	0.314740i	$0.898083\pi$
$954$	−10.4349	+	7.99034i	−0.337843	+	0.258697i
$955$	45.8389	−	29.4589i	1.48331	−	0.953267i
$956$	18.9754	−	16.4423i	0.613709	−	0.531782i
$957$	4.43559	−	8.98311i	0.143382	−	0.290383i
$958$	−37.8065	−	5.43576i	−1.22147	−	0.175621i
$959$	−6.32002	−	5.47633i	−0.204084	−	0.176840i
$960$	5.52756	−	2.32495i	0.178401	−	0.0750374i
$961$	7.08907	+	2.08154i	0.228680	+	0.0671464i
$962$	−0.931951	−	2.04069i	−0.0300473	−	0.0657944i
$963$	−44.8315	+	10.2653i	−1.44467	+	0.330794i
$964$	2.61288	−	4.06572i	0.0841552	−	0.130948i
$965$	−95.7478			−3.08223
$966$	−3.84761	+	7.36179i	−0.123795	+	0.236862i
$967$	8.68607			0.279325			0.139663	−	0.990199i	$-0.455398\pi$
$967$	8.68607			0.279325			0.139663	+	0.990199i	$0.455398\pi$
$968$	5.49767	−	8.55454i	0.176702	−	0.274953i
$969$	−9.30147	−	6.38332i	−0.298806	−	0.205062i
$970$	−5.08836	−	11.1420i	−0.163377	−	0.357747i
$971$	−8.40014	−	2.46650i	−0.269573	−	0.0791538i	0.144152	−	0.989556i	$-0.453954\pi$
$971$	−8.40014	−	2.46650i	−0.269573	−	0.0791538i	−0.413725	+	0.910402i	$0.635773\pi$
$972$	−13.1847	+	8.31648i	−0.422899	+	0.266751i
$973$	−3.47332	−	3.00965i	−0.111349	−	0.0964848i
$974$	−22.5716	−	3.24531i	−0.723241	−	0.103986i
$975$	−5.89547	−	2.91101i	−0.188806	−	0.0932269i
$976$	−2.07567	+	1.79858i	−0.0664405	+	0.0575710i
$977$	−15.9520	+	10.2518i	−0.510351	+	0.327983i	−0.770345	−	0.637628i	$-0.779916\pi$
$977$	−15.9520	+	10.2518i	−0.510351	+	0.327983i	0.259994	+	0.965610i	$0.416279\pi$
$978$	0.0446339	−	0.255342i	0.00142723	−	0.00816493i
$979$	−6.35860	−	7.33822i	−0.203222	−	0.234530i
$980$	−3.32190	+	0.975398i	−0.106114	+	0.0311580i
$981$	1.22369	−	20.1999i	0.0390694	−	0.644934i
$982$	5.71973	−	6.60092i	0.182524	−	0.210644i
$983$	8.28568	−	18.1431i	0.264272	−	0.578675i	−0.730253	−	0.683177i	$-0.760598\pi$
$983$	8.28568	−	18.1431i	0.264272	−	0.578675i	0.994525	+	0.104502i	$0.0333249\pi$
$984$	7.10305	+	11.8243i	0.226437	+	0.376945i
$985$	−19.7929	+	9.03912i	−0.630655	+	0.288010i
$986$	1.45227	+	10.1008i	0.0462497	+	0.321674i
$987$	−3.68689	−	14.1236i	−0.117355	−	0.449558i
$988$		−	2.20022i		−	0.0699982i
$989$	34.5924	+	0.793965i	1.09998	+	0.0252466i
$990$	−9.43726	+	0.778395i	−0.299936	+	0.0247390i
$991$	−13.6994	−	8.80408i	−0.435176	−	0.279671i	0.304656	−	0.952463i	$-0.401459\pi$
$991$	−13.6994	−	8.80408i	−0.435176	−	0.279671i	−0.739832	+	0.672792i	$0.765095\pi$
$992$	−4.80972	+	0.691534i	−0.152709	+	0.0219562i
$993$	−17.0045	+	52.0348i	−0.539623	+	1.65127i
$994$	4.17351	−	14.2137i	0.132376	−	0.450830i
$995$	−59.1856	−	27.0292i	−1.87631	−	0.856882i
$996$	5.97083	−	0.674852i	0.189193	−	0.0213835i
$997$	1.00951	−	7.02133i	0.0319716	−	0.222368i	−0.967571	−	0.252598i	$-0.918715\pi$
$997$	1.00951	−	7.02133i	0.0319716	−	0.222368i	0.999543	+	0.0302303i	$0.00962408\pi$
$998$	10.2832	+	35.0212i	0.325508	+	1.10858i
$999$	−1.11602	−	21.4252i	−0.0353094	−	0.677863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.r.a.113.16	✓	240
3.2	odd	2		966.2.r.b.113.9	yes	240
23.11	odd	22		966.2.r.b.701.9	yes	240
69.11	even	22	inner	966.2.r.a.701.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.r.a.113.16	✓	240	1.1	even	1	trivial
966.2.r.a.701.16	yes	240	69.11	even	22	inner
966.2.r.b.113.9	yes	240	3.2	odd	2
966.2.r.b.701.9	yes	240	23.11	odd	22

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.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 - 0.841254i) q^{2} +(-0.980063 + 1.42810i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-3.32190 - 0.975398i) q^{5} +(0.671534 + 1.59657i) q^{6} +(0.755750 + 0.654861i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-1.07895 - 2.79926i) q^{9} +O(q^{10})\)	\(q+(0.540641 - 0.841254i) q^{2} +(-0.980063 + 1.42810i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-3.32190 - 0.975398i) q^{5} +(0.671534 + 1.59657i) q^{6} +(0.755750 + 0.654861i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-1.07895 - 2.79926i) q^{9} +(-2.61651 + 2.26722i) q^{10} +(-0.766971 + 0.492902i) q^{11} +(1.70618 + 0.298241i) q^{12} +(0.355818 + 0.410636i) q^{13} +(0.959493 - 0.281733i) q^{14} +(4.64864 - 3.78806i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.668172 + 1.46309i) q^{17} +(-2.93821 - 0.605721i) q^{18} +(3.68342 - 1.68216i) q^{19} +(0.492714 + 3.42690i) q^{20} +(-1.67589 + 0.437483i) q^{21} +0.911700i q^{22} +(4.73011 + 0.791263i) q^{23} +(1.17333 - 1.27409i) q^{24} +(5.87736 + 3.77715i) q^{25} +(0.537819 - 0.0773267i) q^{26} +(5.05507 + 1.20259i) q^{27} +(0.281733 - 0.959493i) q^{28} +(5.77107 + 2.63556i) q^{29} +(-0.673478 - 5.95867i) q^{30} +(-0.691534 + 4.80972i) q^{31} +(0.281733 + 0.959493i) q^{32} +(0.0477647 - 1.57839i) q^{33} +(0.869591 + 1.35311i) q^{34} +(-1.87178 - 2.91254i) q^{35} +(-2.09808 + 2.14431i) q^{36} +(-1.16324 - 3.96162i) q^{37} +(0.576284 - 4.00814i) q^{38} +(-0.935155 + 0.105696i) q^{39} +(3.14928 + 1.43823i) q^{40} +(-2.24367 + 7.64123i) q^{41} +(-0.538020 + 1.64637i) q^{42} +(7.14148 - 1.02679i) q^{43} +(0.766971 + 0.492902i) q^{44} +(0.853784 + 10.3513i) q^{45} +(3.22294 - 3.55143i) q^{46} +8.42749i q^{47} +(-0.437483 - 1.67589i) q^{48} +(0.142315 + 0.989821i) q^{49} +(6.35508 - 2.90227i) q^{50} +(-1.43460 - 2.38814i) q^{51} +(0.225716 - 0.494248i) q^{52} +(2.86890 - 3.31089i) q^{53} +(3.74467 - 3.60243i) q^{54} +(3.02858 - 0.889271i) q^{55} +(-0.654861 - 0.755750i) q^{56} +(-1.20769 + 6.90893i) q^{57} +(5.33725 - 3.43004i) q^{58} +(4.28197 - 3.71035i) q^{59} +(-5.37686 - 2.65493i) q^{60} +(2.71855 + 0.390868i) q^{61} +(3.67232 + 3.18209i) q^{62} +(1.01771 - 2.82210i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-0.781460 - 1.71116i) q^{65} +(-1.30200 - 0.893524i) q^{66} +(-0.576184 + 0.896559i) q^{67} +1.60845 q^{68} +(-5.76581 + 5.97959i) q^{69} -3.46214 q^{70} +(8.00891 - 12.4621i) q^{71} +(0.669595 + 2.92432i) q^{72} +(-1.48144 - 3.24389i) q^{73} +(-3.96162 - 1.16324i) q^{74} +(-11.1543 + 4.69163i) q^{75} +(-3.06030 - 2.65176i) q^{76} +(-0.902421 - 0.129748i) q^{77} +(-0.416666 + 0.843846i) q^{78} +(-2.58437 + 2.23937i) q^{79} +(2.91254 - 1.87178i) q^{80} +(-6.67172 + 6.04054i) q^{81} +(5.21520 + 6.01866i) q^{82} +(3.32868 - 0.977389i) q^{83} +(1.09414 + 1.34271i) q^{84} +(3.64670 - 4.20852i) q^{85} +(2.99719 - 6.56292i) q^{86} +(-9.41986 + 5.65867i) q^{87} +(0.829312 - 0.378734i) q^{88} +(1.51569 + 10.5419i) q^{89} +(9.16964 + 4.87807i) q^{90} +0.543350i q^{91} +(-1.24520 - 4.63136i) q^{92} +(-6.19103 - 5.70141i) q^{93} +(7.08966 + 4.55625i) q^{94} +(-13.8768 + 1.99518i) q^{95} +(-1.64637 - 0.538020i) q^{96} +(-0.996754 + 3.39463i) q^{97} +(0.909632 + 0.415415i) q^{98} +(2.20729 + 1.61513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^9	\( 240 q - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} + 24 q^{14} + 18 q^{15} - 24 q^{16} + 32 q^{17} - 4 q^{18} + 4 q^{20} - 8 q^{23} + 12 q^{25} - 148 q^{27} + 40 q^{30} + 16 q^{31} + 42 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} + 154 q^{41} + 4 q^{42} + 22 q^{43} + 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} + 88 q^{50} + 24 q^{51} + 8 q^{52} - 108 q^{53} + 12 q^{54} - 16 q^{55} - 24 q^{56} - 62 q^{57} - 4 q^{58} + 22 q^{59} - 18 q^{60} - 4 q^{63} + 24 q^{64} - 100 q^{66} - 44 q^{67} - 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} - 16 q^{74} - 26 q^{75} - 78 q^{78} - 4 q^{80} + 52 q^{81} + 8 q^{82} + 16 q^{83} - 28 q^{85} + 16 q^{86} - 196 q^{87} + 24 q^{89} + 126 q^{90} + 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} + 172 q^{99}+O(q^{100}) \) 240 * q - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 + 24 * q^14 + 18 * q^15 - 24 * q^16 + 32 * q^17 - 4 * q^18 + 4 * q^20 - 8 * q^23 + 12 * q^25 - 148 * q^27 + 40 * q^30 + 16 * q^31 + 42 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 + 154 * q^41 + 4 * q^42 + 22 * q^43 + 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 + 88 * q^50 + 24 * q^51 + 8 * q^52 - 108 * q^53 + 12 * q^54 - 16 * q^55 - 24 * q^56 - 62 * q^57 - 4 * q^58 + 22 * q^59 - 18 * q^60 - 4 * q^63 + 24 * q^64 - 100 * q^66 - 44 * q^67 - 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 - 16 * q^74 - 26 * q^75 - 78 * q^78 - 4 * q^80 + 52 * q^81 + 8 * q^82 + 16 * q^83 - 28 * q^85 + 16 * q^86 - 196 * q^87 + 24 * q^89 + 126 * q^90 + 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

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