LMFDB - Embedded newform 690.2.q.b.191.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 9]))

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

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

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			191.4
Character	$\chi$	$=$	690.191
Dual form			690.2.q.b.401.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.755750 - 0.654861i) q^{2} +(-0.340196 - 1.69831i) q^{3} +(0.142315 + 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.855055 + 1.50628i) q^{6} +(0.680617 + 2.31797i) q^{7} +(0.540641 - 0.841254i) q^{8} +(-2.76853 + 1.15552i) q^{9} +O(q^{10})$	\(q+(-0.755750 - 0.654861i) q^{2} +(-0.340196 - 1.69831i) q^{3} +(0.142315 + 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.855055 + 1.50628i) q^{6} +(0.680617 + 2.31797i) q^{7} +(0.540641 - 0.841254i) q^{8} +(-2.76853 + 1.15552i) q^{9} +(-0.281733 + 0.959493i) q^{10} +(-0.197716 - 0.228176i) q^{11} +(1.63261 - 0.578429i) q^{12} +(-3.04922 - 0.895332i) q^{13} +(1.00357 - 2.19751i) q^{14} +(-1.40352 + 1.01496i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.999648 + 6.95270i) q^{17} +(2.84902 + 0.939720i) q^{18} +(-1.79753 + 0.258446i) q^{19} +(0.841254 - 0.540641i) q^{20} +(3.70510 - 1.94447i) q^{21} +0.301920i q^{22} +(-1.84372 + 4.42727i) q^{23} +(-1.61264 - 0.631986i) q^{24} +(-0.654861 + 0.755750i) q^{25} +(1.71813 + 2.67346i) q^{26} +(2.90428 + 4.30873i) q^{27} +(-2.19751 + 1.00357i) q^{28} +(-7.72531 - 1.11073i) q^{29} +(1.72536 + 0.152054i) q^{30} +(-7.01862 - 4.51059i) q^{31} +(0.909632 + 0.415415i) q^{32} +(-0.320252 + 0.413408i) q^{33} +(5.30854 - 4.59987i) q^{34} +(1.82576 - 1.58203i) q^{35} +(-1.53776 - 2.57591i) q^{36} +(7.17744 + 3.27783i) q^{37} +(1.52773 + 0.981811i) q^{38} +(-0.483220 + 5.48312i) q^{39} +(-0.989821 - 0.142315i) q^{40} +(-0.173851 + 0.0793950i) q^{41} +(-4.07348 - 0.956792i) q^{42} +(6.41114 + 9.97593i) q^{43} +(0.197716 - 0.228176i) q^{44} +(2.20119 + 2.03833i) q^{45} +(4.29264 - 2.13852i) q^{46} -3.46094i q^{47} +(0.804886 + 1.53367i) q^{48} +(0.979029 - 0.629184i) q^{49} +(0.989821 - 0.142315i) q^{50} +(12.1479 - 0.667569i) q^{51} +(0.452269 - 3.14560i) q^{52} +(5.11778 - 1.50272i) q^{53} +(0.626712 - 5.15822i) q^{54} +(-0.125422 + 0.274636i) q^{55} +(2.31797 + 0.680617i) q^{56} +(1.05043 + 2.96485i) q^{57} +(5.11103 + 5.89844i) q^{58} +(-1.23944 + 4.22115i) q^{59} +(-1.20437 - 1.24479i) q^{60} +(-1.19755 + 1.86342i) q^{61} +(2.35051 + 8.00510i) q^{62} +(-4.56277 - 5.63091i) q^{63} +(-0.415415 - 0.909632i) q^{64} +(0.452269 + 3.14560i) q^{65} +(0.512755 - 0.102712i) q^{66} +(-2.64500 - 2.29191i) q^{67} -7.02420 q^{68} +(8.14611 + 1.62508i) q^{69} -2.41583 q^{70} +(-1.82861 - 1.58450i) q^{71} +(-0.524697 + 2.95376i) q^{72} +(-0.876688 - 6.09750i) q^{73} +(-3.27783 - 7.17744i) q^{74} +(1.50628 + 0.855055i) q^{75} +(-0.511630 - 1.74245i) q^{76} +(0.394337 - 0.613600i) q^{77} +(3.95587 - 3.82742i) q^{78} +(0.776230 - 2.64360i) q^{79} +(0.654861 + 0.755750i) q^{80} +(6.32955 - 6.39819i) q^{81} +(0.183380 + 0.0538453i) q^{82} +(-4.25560 + 9.31846i) q^{83} +(2.45196 + 3.39066i) q^{84} +(6.73967 - 1.97895i) q^{85} +(1.68763 - 11.7377i) q^{86} +(0.741752 + 13.4979i) q^{87} +(-0.298847 + 0.0429677i) q^{88} +(-11.8648 + 7.62507i) q^{89} +(-0.328727 - 2.98194i) q^{90} -7.67738i q^{91} +(-4.64459 - 1.19489i) q^{92} +(-5.27269 + 13.4543i) q^{93} +(-2.26644 + 2.61561i) q^{94} +(0.981811 + 1.52773i) q^{95} +(0.396051 - 1.68616i) q^{96} +(-7.80601 + 3.56489i) q^{97} +(-1.15193 - 0.165622i) q^{98} +(0.811044 + 0.403249i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9	$ 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9} + 12 q^{11} + 12 q^{14} - 16 q^{16} - 8 q^{18} - 16 q^{20} + 70 q^{21} - 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} + 2 q^{30} - 4 q^{31} - 16 q^{33} + 2 q^{36} - 72 q^{38} + 140 q^{39} - 44 q^{41} + 44 q^{43} - 12 q^{44} + 2 q^{45} + 4 q^{46} + 70 q^{49} + 2 q^{51} + 52 q^{53} - 62 q^{54} + 10 q^{55} + 54 q^{56} - 94 q^{57} - 36 q^{58} - 44 q^{61} + 16 q^{64} - 54 q^{66} - 44 q^{67} - 30 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} + 24 q^{74} + 88 q^{77} - 54 q^{78} - 44 q^{79} + 16 q^{80} - 66 q^{81} - 28 q^{82} - 4 q^{83} - 4 q^{84} - 158 q^{86} + 156 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} + 88 q^{98} - 58 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9 + 12 * q^11 + 12 * q^14 - 16 * q^16 - 8 * q^18 - 16 * q^20 + 70 * q^21 - 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 + 2 * q^30 - 4 * q^31 - 16 * q^33 + 2 * q^36 - 72 * q^38 + 140 * q^39 - 44 * q^41 + 44 * q^43 - 12 * q^44 + 2 * q^45 + 4 * q^46 + 70 * q^49 + 2 * q^51 + 52 * q^53 - 62 * q^54 + 10 * q^55 + 54 * q^56 - 94 * q^57 - 36 * q^58 - 44 * q^61 + 16 * q^64 - 54 * q^66 - 44 * q^67 - 30 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 + 24 * q^74 + 88 * q^77 - 54 * q^78 - 44 * q^79 + 16 * q^80 - 66 * q^81 - 28 * q^82 - 4 * q^83 - 4 * q^84 - 158 * q^86 + 156 * q^87 - 80 * q^89 + 8 * q^90 + 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 + 88 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−0.755750	−	0.654861i	−0.534396	−	0.463056i
$2$	−0.755750	−	0.654861i	−0.534396	−	0.463056i
$3$	−0.340196	−	1.69831i	−0.196412	−	0.980521i
$3$	−0.340196	−	1.69831i	−0.196412	−	0.980521i
$4$	0.142315	+	0.989821i	0.0711574	+	0.494911i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$5$	−0.415415	−	0.909632i	−0.185779	−	0.406800i
$6$	−0.855055	+	1.50628i	−0.349075	+	0.614936i
$7$	0.680617	+	2.31797i	0.257249	+	0.876110i	0.982284	+	0.187398i	$0.0600055\pi$
$7$	0.680617	+	2.31797i	0.257249	+	0.876110i	−0.725035	+	0.688712i	$0.758176\pi$
$8$	0.540641	−	0.841254i	0.191145	−	0.297428i
$9$	−2.76853	+	1.15552i	−0.922844	+	0.385173i
$10$	−0.281733	+	0.959493i	−0.0890917	+	0.303418i
$11$	−0.197716	−	0.228176i	−0.0596135	−	0.0687977i	0.725160	−	0.688581i	$-0.241766\pi$
$11$	−0.197716	−	0.228176i	−0.0596135	−	0.0687977i	−0.784773	+	0.619783i	$0.787221\pi$
$12$	1.63261	−	0.578429i	0.471294	−	0.166978i
$13$	−3.04922	−	0.895332i	−0.845702	−	0.248320i	−0.169953	−	0.985452i	$-0.554362\pi$
$13$	−3.04922	−	0.895332i	−0.845702	−	0.248320i	−0.675749	+	0.737132i	$0.736180\pi$
$14$	1.00357	−	2.19751i	0.268216	−	0.587310i
$15$	−1.40352	+	1.01496i	−0.362387	+	0.262061i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−0.999648	+	6.95270i	−0.242450	+	1.68628i	0.397295	+	0.917691i	$0.369949\pi$
$17$	−0.999648	+	6.95270i	−0.242450	+	1.68628i	−0.639745	+	0.768587i	$0.720960\pi$
$18$	2.84902	+	0.939720i	0.671521	+	0.221494i
$19$	−1.79753	+	0.258446i	−0.412382	+	0.0592915i	−0.345384	−	0.938462i	$-0.612251\pi$
$19$	−1.79753	+	0.258446i	−0.412382	+	0.0592915i	−0.0669980	+	0.997753i	$0.521342\pi$
$20$	0.841254	−	0.540641i	0.188110	−	0.120891i
$21$	3.70510	−	1.94447i	0.808518	−	0.424317i
$22$			0.301920i			0.0643696i
$23$	−1.84372	+	4.42727i	−0.384443	+	0.923149i
$23$	−1.84372	+	4.42727i	−0.384443	+	0.923149i
$24$	−1.61264	−	0.631986i	−0.329178	−	0.129004i
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	1.71813	+	2.67346i	0.336953	+	0.524309i
$27$	2.90428	+	4.30873i	0.558929	+	0.829216i
$28$	−2.19751	+	1.00357i	−0.415291	+	0.189657i
$29$	−7.72531	−	1.11073i	−1.43455	−	0.206258i	−0.619206	−	0.785228i	$-0.712546\pi$
$29$	−7.72531	−	1.11073i	−1.43455	−	0.206258i	−0.815348	+	0.578971i	$0.803455\pi$
$30$	1.72536	+	0.152054i	0.315007	+	0.0277612i
$31$	−7.01862	−	4.51059i	−1.26058	−	0.810127i	−0.272218	−	0.962236i	$-0.587757\pi$
$31$	−7.01862	−	4.51059i	−1.26058	−	0.810127i	−0.988364	+	0.152109i	$0.951394\pi$
$32$	0.909632	+	0.415415i	0.160802	+	0.0734357i
$33$	−0.320252	+	0.413408i	−0.0557488	+	0.0719651i
$34$	5.30854	−	4.59987i	0.910406	−	0.788872i
$35$	1.82576	−	1.58203i	0.308610	−	0.267412i
$36$	−1.53776	−	2.57591i	−0.256294	−	0.429318i
$37$	7.17744	+	3.27783i	1.17996	+	0.538871i	0.906169	−	0.422917i	$-0.138994\pi$
$37$	7.17744	+	3.27783i	1.17996	+	0.538871i	0.273795	+	0.961788i	$0.411721\pi$
$38$	1.52773	+	0.981811i	0.247830	+	0.159271i
$39$	−0.483220	+	5.48312i	−0.0773772	+	0.878002i
$40$	−0.989821	−	0.142315i	−0.156505	−	0.0225020i
$41$	−0.173851	+	0.0793950i	−0.0271509	+	0.0123994i	−0.428944	−	0.903331i	$-0.641114\pi$
$41$	−0.173851	+	0.0793950i	−0.0271509	+	0.0123994i	0.401793	+	0.915730i	$0.368387\pi$
$42$	−4.07348	−	0.956792i	−0.628551	−	0.147636i
$43$	6.41114	+	9.97593i	0.977690	+	1.52132i	0.848160	+	0.529740i	$0.177710\pi$
$43$	6.41114	+	9.97593i	0.977690	+	1.52132i	0.129530	+	0.991576i	$0.458653\pi$
$44$	0.197716	−	0.228176i	0.0298068	−	0.0343988i
$45$	2.20119	+	2.03833i	0.328134	+	0.303856i
$46$	4.29264	−	2.13852i	0.632915	−	0.315308i
$47$		−	3.46094i		−	0.504830i	−0.967619	−	0.252415i	$-0.918775\pi$
$47$		−	3.46094i		−	0.504830i	0.967619	−	0.252415i	$-0.0812249\pi$
$48$	0.804886	+	1.53367i	0.116175	+	0.221367i
$49$	0.979029	−	0.629184i	0.139861	−	0.0898834i
$50$	0.989821	−	0.142315i	0.139982	−	0.0201264i
$51$	12.1479	−	0.667569i	1.70105	−	0.0934783i
$52$	0.452269	−	3.14560i	0.0627185	−	0.436217i
$53$	5.11778	−	1.50272i	0.702982	−	0.206414i	0.0893428	−	0.996001i	$-0.471523\pi$
$53$	5.11778	−	1.50272i	0.702982	−	0.206414i	0.613639	+	0.789587i	$0.289705\pi$
$54$	0.626712	−	5.15822i	0.0852848	−	0.701945i
$55$	−0.125422	+	0.274636i	−0.0169119	+	0.0370320i
$56$	2.31797	+	0.680617i	0.309752	+	0.0909513i
$57$	1.05043	+	2.96485i	0.139133	+	0.392703i
$58$	5.11103	+	5.89844i	0.671111	+	0.774503i
$59$	−1.23944	+	4.22115i	−0.161361	+	0.549547i	0.838627	+	0.544706i	$0.183359\pi$
$59$	−1.23944	+	4.22115i	−0.161361	+	0.549547i	−0.999988	+	0.00484034i	$0.998459\pi$
$60$	−1.20437	−	1.24479i	−0.155483	−	0.160701i
$61$	−1.19755	+	1.86342i	−0.153330	+	0.238587i	−0.909418	−	0.415884i	$-0.863472\pi$
$61$	−1.19755	+	1.86342i	−0.153330	+	0.238587i	0.756087	+	0.654471i	$0.227109\pi$
$62$	2.35051	+	8.00510i	0.298515	+	1.01665i
$63$	−4.56277	−	5.63091i	−0.574855	−	0.709428i
$64$	−0.415415	−	0.909632i	−0.0519269	−	0.113704i
$65$	0.452269	+	3.14560i	0.0560971	+	0.390164i
$66$	0.512755	−	0.102712i	0.0631158	−	0.0126430i
$67$	−2.64500	−	2.29191i	−0.323138	−	0.280001i	0.478151	−	0.878277i	$-0.341307\pi$
$67$	−2.64500	−	2.29191i	−0.323138	−	0.280001i	−0.801290	+	0.598276i	$0.795852\pi$
$68$	−7.02420			−0.851809
$69$	8.14611	+	1.62508i	0.980676	+	0.195637i
$70$	−2.41583			−0.288747
$71$	−1.82861	−	1.58450i	−0.217016	−	0.188046i	0.539568	−	0.841942i	$-0.318588\pi$
$71$	−1.82861	−	1.58450i	−0.217016	−	0.188046i	−0.756584	+	0.653897i	$0.773133\pi$
$72$	−0.524697	+	2.95376i	−0.0618362	+	0.348104i
$73$	−0.876688	−	6.09750i	−0.102609	−	0.713658i	−0.974570	−	0.224084i	$-0.928061\pi$
$73$	−0.876688	−	6.09750i	−0.102609	−	0.713658i	0.871961	−	0.489575i	$-0.162848\pi$
$74$	−3.27783	−	7.17744i	−0.381040	−	0.834360i
$75$	1.50628	+	0.855055i	0.173930	+	0.0987333i
$76$	−0.511630	−	1.74245i	−0.0586880	−	0.199873i
$77$	0.394337	−	0.613600i	0.0449388	−	0.0699262i
$78$	3.95587	−	3.82742i	0.447914	−	0.433370i
$79$	0.776230	−	2.64360i	0.0873327	−	0.297428i	−0.904232	−	0.427042i	$-0.859556\pi$
$79$	0.776230	−	2.64360i	0.0873327	−	0.297428i	0.991565	+	0.129614i	$0.0413738\pi$
$80$	0.654861	+	0.755750i	0.0732157	+	0.0844954i
$81$	6.32955	−	6.39819i	0.703283	−	0.710910i
$82$	0.183380	+	0.0538453i	0.0202510	+	0.00594622i
$83$	−4.25560	+	9.31846i	−0.467113	+	1.02283i	0.518696	+	0.854959i	$0.326418\pi$
$83$	−4.25560	+	9.31846i	−0.467113	+	1.02283i	−0.985808	+	0.167875i	$0.946310\pi$
$84$	2.45196	+	3.39066i	0.267531	+	0.369951i
$85$	6.73967	−	1.97895i	0.731020	−	0.214647i
$86$	1.68763	−	11.7377i	0.181982	−	1.26571i
$87$	0.741752	+	13.4979i	0.0795241	+	1.44712i
$88$	−0.298847	+	0.0429677i	−0.0318572	+	0.00458038i
$89$	−11.8648	+	7.62507i	−1.25767	+	0.808256i	−0.987964	−	0.154686i	$-0.950563\pi$
$89$	−11.8648	+	7.62507i	−1.25767	+	0.808256i	−0.269708	+	0.962942i	$0.586927\pi$
$90$	−0.328727	−	2.98194i	−0.0346508	−	0.314324i
$91$		−	7.67738i		−	0.804808i
$92$	−4.64459	−	1.19489i	−0.484232	−	0.124576i
$93$	−5.27269	+	13.4543i	−0.546753	+	1.39515i
$94$	−2.26644	+	2.61561i	−0.233765	+	0.269779i
$95$	0.981811	+	1.52773i	0.100732	+	0.156742i
$96$	0.396051	−	1.68616i	0.0404218	−	0.172093i
$97$	−7.80601	+	3.56489i	−0.792581	+	0.361959i	−0.770210	−	0.637790i	$-0.779849\pi$
$97$	−7.80601	+	3.56489i	−0.792581	+	0.361959i	−0.0223706	+	0.999750i	$0.507121\pi$
$98$	−1.15193	−	0.165622i	−0.116362	−	0.0167304i
$99$	0.811044	+	0.403249i	0.0815130	+	0.0405280i
$100$	−0.841254	−	0.540641i	−0.0841254	−	0.0540641i
$101$	15.9919	+	7.30326i	1.59125	+	0.726701i	0.996987	−	0.0775666i	$-0.0247150\pi$
$101$	15.9919	+	7.30326i	1.59125	+	0.726701i	0.594267	+	0.804268i	$0.297442\pi$
$102$	−9.61797	−	7.45069i	−0.952321	−	0.737729i
$103$	−10.2268	+	8.86157i	−1.00768	+	0.873156i	−0.991939	−	0.126720i	$-0.959555\pi$
$103$	−10.2268	+	8.86157i	−1.00768	+	0.873156i	−0.0157373	+	0.999876i	$0.505010\pi$
$104$	−2.40173	+	2.08111i	−0.235509	+	0.204070i
$105$	−3.30790	−	2.56251i	−0.322818	−	0.250076i
$106$	−4.85183	−	2.21576i	−0.471252	−	0.215213i
$107$	−12.3415	−	7.93138i	−1.19309	−	0.766755i	−0.215346	−	0.976538i	$-0.569088\pi$
$107$	−12.3415	−	7.93138i	−1.19309	−	0.766755i	−0.977748	+	0.209783i	$0.932724\pi$
$108$	−3.85155	+	3.48791i	−0.370616	+	0.335625i
$109$	8.91766	+	1.28217i	0.854157	+	0.122809i	0.555464	−	0.831540i	$-0.312540\pi$
$109$	8.91766	+	1.28217i	0.854157	+	0.122809i	0.298692	+	0.954349i	$0.403450\pi$
$110$	0.274636	−	0.125422i	0.0261855	−	0.0119585i
$111$	3.12504	−	13.3046i	0.296615	−	1.26282i
$112$	−1.30610	−	2.03232i	−0.123414	−	0.192037i
$113$	5.05791	−	5.83713i	0.475808	−	0.549111i	−0.466210	−	0.884674i	$-0.654381\pi$
$113$	5.05791	−	5.83713i	0.475808	−	0.549111i	0.942018	+	0.335563i	$0.108926\pi$
$114$	1.14770	−	2.92857i	0.107492	−	0.274286i
$115$	4.79309	−	0.162043i	0.446958	−	0.0151106i
$116$		−	7.80475i		−	0.724653i
$117$	9.47644	−	1.04468i	0.876097	−	0.0965805i
$118$	3.70097	−	2.37847i	0.340702	−	0.218956i
$119$	−16.7965	+	2.41498i	−1.53974	+	0.221381i
$120$	0.0950384	+	1.72944i	0.00867578	+	0.157876i
$121$	1.55249	−	10.7978i	0.141135	−	0.981619i
$122$	2.12533	−	0.624053i	0.192418	−	0.0564991i
$123$	0.193981	+	0.268243i	0.0174907	+	0.0241867i
$124$	3.46583	−	7.58911i	0.311241	−	0.681522i
$125$	0.959493	+	0.281733i	0.0858197	+	0.0251989i
$126$	−0.239150	+	7.24354i	−0.0213051	+	0.645306i
$127$	−2.05090	−	2.36687i	−0.181988	−	0.210026i	0.657424	−	0.753521i	$-0.271646\pi$
$127$	−2.05090	−	2.36687i	−0.181988	−	0.210026i	−0.839412	+	0.543495i	$0.817101\pi$
$128$	−0.281733	+	0.959493i	−0.0249019	+	0.0848080i
$129$	14.7612	−	14.2819i	1.29965	−	1.25745i
$130$	1.71813	−	2.67346i	0.150690	−	0.234478i
$131$	0.563111	+	1.91778i	0.0491992	+	0.167557i	0.980428	−	0.196878i	$-0.0630803\pi$
$131$	0.563111	+	1.91778i	0.0491992	+	0.167557i	−0.931229	+	0.364435i	$0.881262\pi$
$132$	−0.454777	−	0.258158i	−0.0395832	−	0.0224698i
$133$	−1.82250	−	3.99072i	−0.158031	−	0.346039i
$134$	0.498079	+	3.46422i	0.0430275	+	0.299263i
$135$	2.71288	−	4.43174i	0.233488	−	0.381423i
$136$	5.30854	+	4.59987i	0.455203	+	0.394436i
$137$	−16.1151			−1.37681			−0.688403	−	0.725328i	$-0.741688\pi$
$137$	−16.1151			−1.37681			−0.688403	+	0.725328i	$0.741688\pi$
$138$	−5.09222	−	6.56272i	−0.433478	−	0.558656i
$139$	−16.1232			−1.36755			−0.683775	−	0.729693i	$-0.739663\pi$
$139$	−16.1232			−1.36755			−0.683775	+	0.729693i	$0.739663\pi$
$140$	1.82576	+	1.58203i	0.154305	+	0.133706i
$141$	−5.87776	+	1.17740i	−0.494997	+	0.0991549i
$142$	0.344345	+	2.39497i	0.0288968	+	0.200981i
$143$	0.398586	+	0.872781i	0.0333314	+	0.0729856i
$144$	2.33084	−	1.88870i	0.194237	−	0.157392i
$145$	2.19885	+	7.48861i	0.182605	+	0.621895i
$146$	−3.33046	+	5.18229i	−0.275631	+	0.428890i
$147$	−1.40161	−	1.44865i	−0.115603	−	0.119483i
$148$	−2.22301	+	7.57087i	−0.182730	+	0.622321i
$149$	6.61952	+	7.63933i	0.542292	+	0.625838i	0.959070	−	0.283170i	$-0.0913861\pi$
$149$	6.61952	+	7.63933i	0.542292	+	0.625838i	−0.416778	+	0.909008i	$0.636841\pi$
$150$	−0.578429	−	1.63261i	−0.0472285	−	0.133302i
$151$	−13.5633	−	3.98256i	−1.10377	−	0.324096i	−0.321420	−	0.946937i	$-0.604160\pi$
$151$	−13.5633	−	3.98256i	−1.10377	−	0.324096i	−0.782349	+	0.622841i	$0.785978\pi$
$152$	−0.754399	+	1.65190i	−0.0611899	+	0.133987i
$153$	−5.26642	−	20.4039i	−0.425765	−	1.64956i
$154$	−0.699842	+	0.205492i	−0.0563949	+	0.0165590i
$155$	−1.18734	+	8.25813i	−0.0953694	+	0.663309i
$156$	−5.49608	+	0.302027i	−0.440038	+	0.0241815i
$157$	15.1663	−	2.18059i	1.21041	−	0.174030i	0.492589	−	0.870262i	$-0.336051\pi$
$157$	15.1663	−	2.18059i	1.21041	−	0.174030i	0.717817	+	0.696232i	$0.245142\pi$
$158$	−2.31782	+	1.48957i	−0.184396	+	0.118504i
$159$	−4.29313	−	8.18038i	−0.340468	−	0.648746i
$160$		−	1.00000i		−	0.0790569i
$161$	−11.5171	−	1.26042i	−0.907678	−	0.0993350i
$162$	−8.97348	+	0.690453i	−0.705023	+	0.0542471i
$163$	−3.61872	+	4.17622i	−0.283440	+	0.327107i	−0.879560	−	0.475788i	$-0.842163\pi$
$163$	−3.61872	+	4.17622i	−0.283440	+	0.327107i	0.596120	+	0.802895i	$0.296708\pi$
$164$	−0.103328	−	0.160782i	−0.00806859	−	0.0125550i
$165$	0.509087	+	0.119576i	0.0396323	+	0.00930897i
$166$	9.31846	−	4.25560i	0.723253	−	0.330298i
$167$	−18.0826	−	2.59988i	−1.39927	−	0.201185i	−0.598965	−	0.800775i	$-0.704421\pi$
$167$	−18.0826	−	2.59988i	−1.39927	−	0.201185i	−0.800307	+	0.599590i	$0.795330\pi$
$168$	0.367337	−	4.16818i	0.0283406	−	0.321582i
$169$	−2.44017	−	1.56820i	−0.187705	−	0.120631i
$170$	−6.38944	−	2.91796i	−0.490047	−	0.223797i
$171$	4.67788	−	2.79260i	0.357727	−	0.213555i
$172$	−8.96199	+	7.76561i	−0.683345	+	0.592122i
$173$	9.71815	−	8.42082i	0.738857	−	0.640223i	−0.201860	−	0.979414i	$-0.564699\pi$
$173$	9.71815	−	8.42082i	0.738857	−	0.640223i	0.940718	+	0.339191i	$0.110153\pi$
$174$	8.27864	−	10.6868i	0.627602	−	0.810160i
$175$	−2.19751	−	1.00357i	−0.166116	−	0.0758629i
$176$	0.253991	+	0.163230i	0.0191453	+	0.0123040i
$177$	7.59048	+	0.668940i	0.570536	+	0.0502806i
$178$	13.9602	+	2.00718i	1.04636	+	0.150444i
$179$	−12.8190	+	5.85422i	−0.958134	+	0.437565i	−0.832201	−	0.554474i	$-0.812920\pi$
$179$	−12.8190	+	5.85422i	−0.958134	+	0.437565i	−0.125933	+	0.992039i	$0.540192\pi$
$180$	−1.70432	+	2.46887i	−0.127032	+	0.184018i
$181$	−10.5746	−	16.4543i	−0.786001	−	1.22304i	−0.970712	−	0.240248i	$-0.922771\pi$
$181$	−10.5746	−	16.4543i	−0.786001	−	1.22304i	0.184711	−	0.982793i	$-0.440865\pi$
$182$	−5.02762	+	5.80218i	−0.372672	+	0.430086i
$183$	3.57207	+	1.39988i	0.264055	+	0.103482i
$184$	2.72766	+	3.94460i	0.201086	+	0.290800i
$185$		−	7.89049i		−	0.580120i
$186$	12.7955	−	6.71520i	0.938214	−	0.492383i
$187$	1.78409	−	1.14656i	0.130465	−	0.0838450i
$188$	3.42571	−	0.492543i	0.249846	−	0.0359224i
$189$	−8.01081	+	9.66463i	−0.582701	+	0.702998i
$190$	0.258446	−	1.79753i	0.0187496	−	0.130407i
$191$	19.9363	−	5.85382i	1.44254	−	0.423568i	0.535472	−	0.844553i	$-0.320134\pi$
$191$	19.9363	−	5.85382i	1.44254	−	0.423568i	0.907067	+	0.420986i	$0.138316\pi$
$192$	−1.40352	+	1.01496i	−0.101290	+	0.0732483i
$193$	2.40172	−	5.25904i	0.172880	−	0.378554i	−0.803282	−	0.595599i	$-0.796915\pi$
$193$	2.40172	−	5.25904i	0.172880	−	0.378554i	0.976162	+	0.217045i	$0.0696419\pi$
$194$	8.23390	+	2.41769i	0.591159	+	0.173580i
$195$	5.18836	−	1.83822i	0.371546	−	0.131637i
$196$	0.762110	+	0.879522i	0.0544364	+	0.0628230i
$197$	−1.33265	+	4.53859i	−0.0949474	+	0.323361i	−0.993246	−	0.116023i	$-0.962985\pi$
$197$	−1.33265	+	4.53859i	−0.0949474	+	0.323361i	0.898299	+	0.439384i	$0.144803\pi$
$198$	−0.348875	−	0.835876i	−0.0247934	−	0.0594031i
$199$	−9.60329	+	14.9430i	−0.680759	+	1.05928i	0.313216	+	0.949682i	$0.398593\pi$
$199$	−9.60329	+	14.9430i	−0.680759	+	1.05928i	−0.993976	+	0.109600i	$0.965043\pi$
$200$	0.281733	+	0.959493i	0.0199215	+	0.0678464i
$201$	−2.99256	+	5.27174i	−0.211079	+	0.371840i
$202$	−7.30326	−	15.9919i	−0.513855	−	1.12519i
$203$	−2.68334	−	18.6630i	−0.188333	−	1.30989i
$204$	2.38961	+	11.9293i	0.167306	+	0.835217i
$205$	0.144440	+	0.125158i	0.0100882	+	0.00874144i
$206$	13.5320			0.942818
$207$	−0.0113836	−	14.3875i	−0.000791216	−	1.00000i
$208$	3.17795			0.220351
$209$	0.414371	+	0.359055i	0.0286626	+	0.0248363i
$210$	0.821856	+	4.10283i	0.0567134	+	0.283122i
$211$	−1.22410	−	8.51377i	−0.0842702	−	0.586112i	−0.987579	−	0.157122i	$-0.949778\pi$
$211$	−1.22410	−	8.51377i	−0.0842702	−	0.586112i	0.903309	−	0.428991i	$-0.141131\pi$
$212$	2.21576	+	4.85183i	0.152179	+	0.333225i
$213$	−2.06889	+	3.64459i	−0.141758	+	0.249723i
$214$	4.13311	+	14.0761i	0.282533	+	0.962221i
$215$	6.41114	−	9.97593i	0.437236	−	0.680353i
$216$	5.19491	−	0.113758i	0.353469	−	0.00774024i
$217$	5.67843	−	19.3389i	0.385477	−	1.31281i
$218$	−5.89988	−	6.80882i	−0.399590	−	0.461151i
$219$	−10.0572	+	3.56324i	−0.679604	+	0.240781i
$220$	−0.289690	−	0.0850608i	−0.0195309	−	0.00573480i
$221$	9.27312	−	20.3053i	0.623778	−	1.36588i
$222$	−11.0744	+	8.00851i	−0.743267	+	0.537496i
$223$	3.33719	−	0.979887i	0.223475	−	0.0656181i	−0.168078	−	0.985774i	$-0.553756\pi$
$223$	3.33719	−	0.979887i	0.223475	−	0.0656181i	0.391553	+	0.920156i	$0.371938\pi$
$224$	−0.343808	+	2.39124i	−0.0229717	+	0.159771i
$225$	0.939720	−	2.84902i	0.0626480	−	0.189935i
$226$	−7.64502	+	1.09919i	−0.508539	+	0.0731169i
$227$	−6.49425	+	4.17360i	−0.431039	+	0.277012i	−0.738117	−	0.674672i	$-0.764285\pi$
$227$	−6.49425	+	4.17360i	−0.431039	+	0.277012i	0.307079	+	0.951684i	$0.400649\pi$
$228$	−2.78518	+	1.46168i	−0.184453	+	0.0968024i
$229$		−	16.7304i		−	1.10558i	−0.833322	−	0.552788i	$-0.813564\pi$
$229$		−	16.7304i		−	1.10558i	0.833322	−	0.552788i	$-0.186436\pi$
$230$	−3.72849	−	3.01634i	−0.245850	−	0.198892i
$231$	−1.17624	−	0.460963i	−0.0773907	−	0.0303291i
$232$	−5.11103	+	5.89844i	−0.335555	+	0.387252i
$233$	15.8877	+	24.7217i	1.04084	+	1.61957i	0.748350	+	0.663304i	$0.230846\pi$
$233$	15.8877	+	24.7217i	1.04084	+	1.61957i	0.292486	+	0.956270i	$0.405517\pi$
$234$	−7.84594	−	5.41624i	−0.512905	−	0.354070i
$235$	−3.14818	+	1.43773i	−0.205365	+	0.0937870i
$236$	−4.35457	−	0.626093i	−0.283459	−	0.0407552i
$237$	−4.75373	−	0.418940i	−0.308788	−	0.0272131i
$238$	14.2754	+	9.17427i	0.925340	+	0.594680i
$239$	−8.28568	−	3.78394i	−0.535956	−	0.244763i	0.129001	−	0.991644i	$-0.458823\pi$
$239$	−8.28568	−	3.78394i	−0.535956	−	0.244763i	−0.664957	+	0.746882i	$0.731550\pi$
$240$	1.06072	−	1.36926i	0.0684691	−	0.0883855i
$241$	−5.82168	+	5.04452i	−0.375008	+	0.324946i	−0.821889	−	0.569647i	$-0.807080\pi$
$241$	−5.82168	+	5.04452i	−0.375008	+	0.324946i	0.446882	+	0.894593i	$0.352534\pi$
$242$	−8.24435	+	7.14377i	−0.529967	+	0.459219i
$243$	−13.0194	−	8.57292i	−0.835196	−	0.549953i
$244$	−2.01488	−	0.920167i	−0.128990	−	0.0589076i
$245$	−0.979029	−	0.629184i	−0.0625479	−	0.0401971i
$246$	0.0290609	−	0.329755i	0.00185285	−	0.0210244i
$247$	5.71246	+	0.821328i	0.363475	+	0.0522598i
$248$	−7.58911	+	3.46583i	−0.481909	+	0.220080i
$249$	17.2734	+	4.05723i	1.09466	+	0.257117i
$250$	−0.540641	−	0.841254i	−0.0341931	−	0.0532055i
$251$	−2.98059	+	3.43979i	−0.188133	+	0.217118i	−0.841979	−	0.539511i	$-0.818609\pi$
$251$	−2.98059	+	3.43979i	−0.188133	+	0.217118i	0.653845	+	0.756628i	$0.273155\pi$
$252$	4.92425	−	5.31769i	0.310198	−	0.334983i
$253$	1.37473	−	0.454647i	0.0864285	−	0.0285834i
$254$			3.13182i			0.196508i
$255$	−5.65368	−	10.7728i	−0.354047	−	0.674621i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	15.9637	−	2.29523i	0.995786	−	0.143172i	0.374893	−	0.927068i	$-0.377679\pi$
$257$	15.9637	−	2.29523i	0.995786	−	0.143172i	0.620893	+	0.783896i	$0.286770\pi$
$258$	−20.5084	+	1.12701i	−1.27680	+	0.0701643i
$259$	−2.71281	+	18.8680i	−0.168566	+	1.17240i
$260$	−3.04922	+	0.895332i	−0.189105	+	0.0555261i
$261$	22.6713	−	5.85165i	1.40332	−	0.362208i
$262$	0.830307	−	1.81812i	0.0512966	−	0.112324i
$263$	1.17228	+	0.344213i	0.0722860	+	0.0212251i	0.317676	−	0.948199i	$-0.397098\pi$
$263$	1.17228	+	0.344213i	0.0722860	+	0.0212251i	−0.245390	+	0.969425i	$0.578916\pi$
$264$	0.174639	+	0.492918i	0.0107483	+	0.0303370i
$265$	−3.49292	−	4.03105i	−0.214569	−	0.247625i
$266$	−1.23601	+	4.20947i	−0.0757847	+	0.258099i
$267$	16.9861	+	17.5562i	1.03953	+	1.07442i
$268$	1.89216	−	2.94425i	0.115582	−	0.179849i
$269$	5.85379	+	19.9362i	0.356912	+	1.21553i	0.920917	+	0.389758i	$0.127441\pi$
$269$	5.85379	+	19.9362i	0.356912	+	1.21553i	−0.564006	+	0.825771i	$0.690740\pi$
$270$	−4.95243	+	1.57272i	−0.301395	+	0.0957129i
$271$	13.2625	+	29.0409i	0.805642	+	1.76411i	0.625104	+	0.780541i	$0.285056\pi$
$271$	13.2625	+	29.0409i	0.805642	+	1.76411i	0.180537	+	0.983568i	$0.442216\pi$
$272$	−0.999648	−	6.95270i	−0.0606125	−	0.421570i
$273$	−13.0386	+	2.61182i	−0.789132	+	0.158074i
$274$	12.1790	+	10.5532i	0.735760	+	0.637539i
$275$	0.301920			0.0182065
$276$	−0.449226	+	8.29447i	−0.0270402	+	0.499268i
$277$	−5.30825			−0.318942			−0.159471	−	0.987203i	$-0.550979\pi$
$277$	−5.30825			−0.318942			−0.159471	+	0.987203i	$0.550979\pi$
$278$	12.1851	+	10.5584i	0.730813	+	0.633253i
$279$	24.6434	+	4.37758i	1.47536	+	0.262079i
$280$	−0.343808	−	2.39124i	−0.0205465	−	0.142904i
$281$	5.53629	+	12.1228i	0.330267	+	0.723184i	0.999808	−	0.0195911i	$-0.00623643\pi$
$281$	5.53629	+	12.1228i	0.330267	+	0.723184i	−0.669541	+	0.742775i	$0.733509\pi$
$282$	5.21315	+	2.95930i	0.310439	+	0.176224i
$283$	2.86448	+	9.75552i	0.170276	+	0.579905i	0.999771	+	0.0213921i	$0.00680983\pi$
$283$	2.86448	+	9.75552i	0.170276	+	0.579905i	−0.829496	+	0.558513i	$0.811372\pi$
$284$	1.30813	−	2.03550i	0.0776234	−	0.120784i
$285$	2.26055	−	2.18715i	0.133904	−	0.129556i
$286$	0.270319	−	0.920622i	0.0159843	−	0.0544375i
$287$	−0.302361	−	0.348943i	−0.0178478	−	0.0205975i
$288$	−2.99837	−	0.0989928i	−0.176680	−	0.00583321i
$289$	−31.0294	−	9.11105i	−1.82526	−	0.535944i
$290$	3.24221	−	7.09945i	0.190389	−	0.416894i
$291$	8.70987	+	12.0443i	0.510582	+	0.706049i
$292$	5.91067	−	1.73553i	0.345896	−	0.101564i
$293$	2.12776	−	14.7989i	0.124305	−	0.864561i	−0.828286	−	0.560306i	$-0.810683\pi$
$293$	2.12776	−	14.7989i	0.124305	−	0.864561i	0.952591	−	0.304255i	$-0.0984074\pi$
$294$	0.110603	+	2.01268i	0.00645051	+	0.117382i
$295$	4.35457	−	0.626093i	0.253533	−	0.0364526i
$296$	6.63790	−	4.26592i	0.385820	−	0.247952i
$297$	0.408928	−	1.51459i	0.0237284	−	0.0878855i
$298$		−	10.1083i		−	0.585557i
$299$	9.58579	−	11.8490i	0.554361	−	0.685244i
$300$	−0.631986	+	1.61264i	−0.0364877	+	0.0931056i
$301$	−18.7604	+	21.6506i	−1.08133	+	1.24792i
$302$	7.64247	+	11.8919i	0.439775	+	0.684303i
$303$	6.96283	−	29.6438i	0.400004	−	1.70299i
$304$	1.65190	−	0.754399i	0.0947432	−	0.0432678i
$305$	2.19251	+	0.315235i	0.125543	+	0.0180503i
$306$	−9.38161	+	18.8690i	−0.536311	+	1.07867i
$307$	−0.0855540	−	0.0549822i	−0.00488282	−	0.00313800i	0.538197	−	0.842819i	$-0.319106\pi$
$307$	−0.0855540	−	0.0549822i	−0.00488282	−	0.00313800i	−0.543080	+	0.839681i	$0.682742\pi$
$308$	0.663474	+	0.302999i	0.0378050	+	0.0172649i
$309$	18.5288	+	14.3536i	1.05407	+	0.816549i
$310$	6.30526	−	5.46354i	0.358115	−	0.310308i
$311$	9.74661	−	8.44548i	0.552679	−	0.478899i	−0.333174	−	0.942866i	$-0.608120\pi$
$311$	9.74661	−	8.44548i	0.552679	−	0.478899i	0.885853	+	0.463966i	$0.153574\pi$
$312$	4.35145	+	3.37091i	0.246352	+	0.190840i
$313$	−1.25691	−	0.574011i	−0.0710447	−	0.0324450i	0.379576	−	0.925161i	$-0.376070\pi$
$313$	−1.25691	−	0.574011i	−0.0710447	−	0.0324450i	−0.450621	+	0.892716i	$0.648797\pi$
$314$	−12.8899	−	8.28386i	−0.727421	−	0.467485i
$315$	−3.22661	+	6.48961i	−0.181799	+	0.365648i
$316$	2.72716	+	0.392106i	0.153415	+	0.0220577i
$317$	23.9106	−	10.9196i	1.34296	−	0.613307i	0.391240	−	0.920289i	$-0.372046\pi$
$317$	23.9106	−	10.9196i	1.34296	−	0.613307i	0.951715	+	0.306982i	$0.0993190\pi$
$318$	−2.11247	+	8.99372i	−0.118462	+	0.504343i
$319$	1.27397	+	1.98234i	0.0713288	+	0.110990i
$320$	−0.654861	+	0.755750i	−0.0366078	+	0.0422477i
$321$	−9.27144	+	23.6579i	−0.517481	+	1.32045i
$322$	7.87867	+	8.49469i	0.439061	+	0.473390i
$323$		−	12.7560i		−	0.709765i
$324$	7.23385	+	5.35457i	0.401881	+	0.297476i
$325$	2.67346	−	1.71813i	0.148297	−	0.0953047i
$326$	5.46969	−	0.786422i	0.302938	−	0.0435559i
$327$	−0.856236	−	15.5812i	−0.0473499	−	0.861640i
$328$	−0.0271995	+	0.189177i	−0.00150184	+	0.0104455i
$329$	8.02236	−	2.35558i	0.442287	−	0.129867i
$330$	−0.306436	−	0.423750i	−0.0168688	−	0.0233267i
$331$	8.34509	−	18.2732i	0.458688	−	1.00439i	−0.529097	−	0.848561i	$-0.677469\pi$
$331$	8.34509	−	18.2732i	0.458688	−	1.00439i	0.987785	−	0.155824i	$-0.0498034\pi$
$332$	−9.82925	−	2.88613i	−0.539450	−	0.158397i
$333$	−23.6586	−	0.781101i	−1.29648	−	0.0428041i
$334$	11.9633	+	13.8064i	0.654605	+	0.755454i
$335$	−0.986019	+	3.35807i	−0.0538720	+	0.183471i
$336$	−3.00719	+	2.90955i	−0.164056	+	0.158729i
$337$	−8.69122	+	13.5238i	−0.473441	+	0.736688i	−0.993047	−	0.117718i	$-0.962442\pi$
$337$	−8.69122	+	13.5238i	−0.473441	+	0.736688i	0.519606	+	0.854406i	$0.326079\pi$
$338$	0.817202	+	2.78314i	0.0444499	+	0.151383i
$339$	−11.6340	−	6.60414i	−0.631870	−	0.358687i
$340$	2.91796	+	6.38944i	0.158248	+	0.346516i
$341$	0.358482	+	2.49330i	0.0194129	+	0.135020i
$342$	−5.36407	−	0.952857i	−0.290056	−	0.0515246i
$343$	14.9051	+	12.9153i	0.804800	+	0.697363i
$344$	11.8584			0.639363
$345$	−1.90579	−	8.08505i	−0.102604	−	0.435284i
$346$	−12.8590			−0.691301
$347$	−7.33156	−	6.35283i	−0.393579	−	0.341038i	0.435481	−	0.900198i	$-0.356578\pi$
$347$	−7.33156	−	6.35283i	−0.393579	−	0.341038i	−0.829060	+	0.559160i	$0.811124\pi$
$348$	−13.2549	+	2.65515i	−0.710538	+	0.142331i
$349$	3.87778	+	26.9706i	0.207573	+	1.44370i	0.781045	+	0.624475i	$0.214687\pi$
$349$	3.87778	+	26.9706i	0.207573	+	1.44370i	−0.573472	+	0.819225i	$0.694404\pi$
$350$	1.00357	+	2.19751i	0.0536431	+	0.117462i
$351$	−4.99804	−	15.7386i	−0.266776	−	0.840063i
$352$	−0.0850608	−	0.289690i	−0.00453375	−	0.0154405i
$353$	−15.3824	+	23.9356i	−0.818725	+	1.27396i	0.140150	+	0.990130i	$0.455242\pi$
$353$	−15.3824	+	23.9356i	−0.818725	+	1.27396i	−0.958874	+	0.283831i	$0.908395\pi$
$354$	−5.29844	−	5.47626i	−0.281609	−	0.291060i
$355$	−0.681680	+	2.32159i	−0.0361798	+	0.123217i
$356$	−9.23601	−	10.6589i	−0.489507	−	0.564922i
$357$	9.81551	+	27.7042i	0.519492	+	1.46626i
$358$	13.5216	+	3.97031i	0.714640	+	0.209837i
$359$	9.82509	−	21.5139i	0.518548	−	1.13546i	−0.451438	−	0.892303i	$-0.649089\pi$
$359$	9.82509	−	21.5139i	0.518548	−	1.13546i	0.969986	−	0.243160i	$-0.0781840\pi$
$360$	2.90480	−	0.749755i	0.153096	−	0.0395155i
$361$	−15.0660	+	4.42379i	−0.792950	+	0.232831i
$362$	−2.78358	+	19.3602i	−0.146302	+	1.01755i
$363$	−18.8662	+	1.03676i	−0.990219	+	0.0544158i
$364$	7.59924	−	1.09261i	0.398308	−	0.0572681i
$365$	−5.18229	+	3.33046i	−0.271254	+	0.174324i
$366$	−1.78287	−	3.39717i	−0.0931919	−	0.177573i
$367$			25.7551i			1.34440i	0.740368	+	0.672201i	$0.234651\pi$
$367$			25.7551i			1.34440i	−0.740368	+	0.672201i	$0.765349\pi$
$368$	0.521734	−	4.76737i	0.0271973	−	0.248516i
$369$	0.389569	−	0.420695i	0.0202802	−	0.0219005i
$370$	−5.16717	+	5.96323i	−0.268628	+	0.310014i
$371$	6.96650	+	10.8401i	0.361683	+	0.562790i
$372$	−14.0677	−	3.30428i	−0.729378	−	0.171319i
$373$	13.0953	−	5.98043i	0.678050	−	0.309655i	−0.0464591	−	0.998920i	$-0.514794\pi$
$373$	13.0953	−	5.98043i	0.678050	−	0.309655i	0.724509	+	0.689265i	$0.242066\pi$
$374$	−2.09916	−	0.301814i	−0.108545	−	0.0156064i
$375$	0.152054	−	1.72536i	0.00785204	−	0.0890974i
$376$	−2.91153	−	1.87113i	−0.150151	−	0.0964960i
$377$	22.5617	+	10.3036i	1.16199	+	0.530662i
$378$	12.3832	−	2.05807i	0.636921	−	0.105856i
$379$	−3.91034	+	3.38832i	−0.200860	+	0.174047i	−0.749483	−	0.662024i	$-0.769698\pi$
$379$	−3.91034	+	3.38832i	−0.200860	+	0.174047i	0.548623	+	0.836070i	$0.315152\pi$
$380$	−1.37245	+	1.18924i	−0.0704053	+	0.0610065i
$381$	−3.32197	+	4.28828i	−0.170190	+	0.219695i
$382$	−18.9003	−	8.63147i	−0.967022	−	0.441624i
$383$	−9.05342	−	5.81828i	−0.462608	−	0.297300i	0.288499	−	0.957480i	$-0.406844\pi$
$383$	−9.05342	−	5.81828i	−0.462608	−	0.297300i	−0.751108	+	0.660180i	$0.770480\pi$
$384$	1.72536	+	0.152054i	0.0880471	+	0.00775948i
$385$	−0.721963	−	0.103803i	−0.0367947	−	0.00529027i
$386$	−5.25904	+	2.40172i	−0.267678	+	0.122245i
$387$	−29.2768	−	20.2105i	−1.48823	−	1.02736i
$388$	−4.63951	−	7.21922i	−0.235536	−	0.366501i
$389$	13.1607	−	15.1883i	0.667276	−	0.770077i	−0.316672	−	0.948535i	$-0.602565\pi$
$389$	13.1607	−	15.1883i	0.667276	−	0.770077i	0.983948	+	0.178458i	$0.0571108\pi$
$390$	−5.12488	−	2.00842i	−0.259508	−	0.101700i
$391$	−28.9384	−	17.2446i	−1.46348	−	0.872095i
$392$		−	1.16377i		−	0.0587795i
$393$	3.06542	−	1.60876i	0.154630	−	0.0811512i
$394$	3.97929	−	2.55734i	0.200474	−	0.128837i
$395$	−2.72716	+	0.392106i	−0.137218	+	0.0197290i
$396$	−0.283721	+	0.860177i	−0.0142575	+	0.0432255i
$397$	1.49359	−	10.3881i	0.0749611	−	0.521366i	−0.917397	−	0.397974i	$-0.869714\pi$
$397$	1.49359	−	10.3881i	0.0749611	−	0.521366i	0.992358	−	0.123392i	$-0.0393774\pi$
$398$	17.0433	−	5.00436i	0.854302	−	0.250846i
$399$	−6.15748	+	4.45280i	−0.308260	+	0.222919i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	17.9228	+	5.26262i	0.895024	+	0.262803i	0.696725	−	0.717339i	$-0.254640\pi$
$401$	17.9228	+	5.26262i	0.895024	+	0.262803i	0.198300	+	0.980141i	$0.436458\pi$
$402$	5.71388	−	2.02441i	0.284982	−	0.100968i
$403$	17.3628	+	20.0378i	0.864905	+	0.998154i
$404$	−4.95304	+	16.8685i	−0.246423	+	0.839239i
$405$	−8.44939	−	3.09966i	−0.419853	−	0.154023i
$406$	−10.1938	+	15.8618i	−0.505907	+	0.787207i
$407$	−0.671171	−	2.28580i	−0.0332687	−	0.113303i
$408$	6.00608	−	10.5804i	0.297345	−	0.523809i
$409$	−12.4130	−	27.1806i	−0.613782	−	1.34399i	−0.919957	−	0.392019i	$-0.871777\pi$
$409$	−12.4130	−	27.1806i	−0.613782	−	1.34399i	0.306175	−	0.951975i	$-0.400951\pi$
$410$	−0.0271995	−	0.189177i	−0.00134329	−	0.00934277i
$411$	5.48230	+	27.3685i	0.270422	+	1.34999i
$412$	−10.2268	−	8.86157i	−0.503838	−	0.436578i
$413$	−10.6281			−0.522974
$414$	−9.41320	+	10.8808i	−0.462633	+	0.534762i
$415$	10.2442			0.502868
$416$	−2.40173	−	2.08111i	−0.117755	−	0.102035i
$417$	5.48505	+	27.3822i	0.268604	+	1.34091i
$418$	−0.0780300	−	0.542711i	−0.00381657	−	0.0265448i
$419$	−5.83071	−	12.7675i	−0.284849	−	0.623732i	0.712075	−	0.702103i	$-0.247755\pi$
$419$	−5.83071	−	12.7675i	−0.284849	−	0.623732i	−0.996924	+	0.0783709i	$0.975028\pi$
$420$	2.06567	−	3.63891i	0.100794	−	0.177561i
$421$	5.05817	+	17.2266i	0.246520	+	0.839571i	0.986050	+	0.166447i	$0.0532296\pi$
$421$	5.05817	+	17.2266i	0.246520	+	0.839571i	−0.739530	+	0.673124i	$0.764952\pi$
$422$	−4.65023	+	7.23589i	−0.226369	+	0.352238i
$423$	3.99919	+	9.58173i	0.194447	+	0.465880i
$424$	1.50272	−	5.11778i	0.0729784	−	0.248541i
$425$	−4.59987	−	5.30854i	−0.223127	−	0.257502i
$426$	3.95026	−	1.39956i	0.191391	−	0.0678091i
$427$	−5.13443	−	1.50760i	−0.248472	−	0.0729581i
$428$	6.09427	−	13.3446i	0.294578	−	0.645035i
$429$	1.34666	−	0.973840i	0.0650172	−	0.0470174i
$430$	−11.3781	+	3.34090i	−0.548699	+	0.161113i
$431$	0.878593	−	6.11075i	0.0423203	−	0.294344i	−0.957659	−	0.287905i	$-0.907041\pi$
$431$	0.878593	−	6.11075i	0.0423203	−	0.294344i	0.999979	−	0.00643927i	$-0.00204970\pi$
$432$	−4.00054	−	3.31597i	−0.192476	−	0.159540i
$433$	−0.595725	+	0.0856523i	−0.0286287	+	0.00411619i	−0.156614	−	0.987660i	$-0.550058\pi$
$433$	−0.595725	+	0.0856523i	−0.0286287	+	0.00411619i	0.127986	+	0.991776i	$0.459149\pi$
$434$	−16.9558	+	10.8968i	−0.813904	+	0.523064i
$435$	11.9700	−	6.28194i	0.573915	−	0.301196i
$436$			9.00936i			0.431470i
$437$	2.16994	−	8.43464i	0.103802	−	0.403484i
$438$	9.93416	+	3.89316i	0.474673	+	0.186022i
$439$	3.39053	−	3.91289i	0.161821	−	0.186752i	−0.669048	−	0.743219i	$-0.733298\pi$
$439$	3.39053	−	3.91289i	0.161821	−	0.186752i	0.830870	+	0.556467i	$0.187843\pi$
$440$	0.163230	+	0.253991i	0.00778170	+	0.0121086i
$441$	−1.98344	+	2.87320i	−0.0944495	+	0.136819i
$442$	−20.3053	+	9.27312i	−0.965825	+	0.441078i
$443$	35.7477	+	5.13974i	1.69842	+	0.244196i	0.922325	−	0.386415i	$-0.126287\pi$
$443$	35.7477	+	5.13974i	1.69842	+	0.244196i	0.776099	+	0.630611i	$0.217196\pi$
$444$	13.6140	+	1.19978i	0.646090	+	0.0569391i
$445$	11.8648	+	7.62507i	0.562448	+	0.361463i
$446$	−3.16377	−	1.44484i	−0.149809	−	0.0684154i
$447$	10.7220	−	13.8409i	0.507135	−	0.654651i
$448$	1.82576	−	1.58203i	0.0862591	−	0.0747439i
$449$	22.2386	−	19.2698i	1.04950	−	0.909400i	0.0534865	−	0.998569i	$-0.482967\pi$
$449$	22.2386	−	19.2698i	1.04950	−	0.909400i	0.996017	+	0.0891691i	$0.0284211\pi$
$450$	−2.57591	+	1.53776i	−0.121429	+	0.0724908i
$451$	0.0524891	+	0.0239709i	0.00247161	+	0.00112875i
$452$	6.49754	+	4.17571i	0.305618	+	0.196409i
$453$	−2.14943	+	24.3896i	−0.100989	+	1.14593i
$454$	7.64115	+	1.09863i	0.358617	+	0.0515614i
$455$	−6.98359	+	3.18930i	−0.327396	+	0.149517i
$456$	3.06209	+	0.719235i	0.143396	+	0.0336812i
$457$	18.3638	+	28.5746i	0.859023	+	1.33667i	0.940431	+	0.339985i	$0.110422\pi$
$457$	18.3638	+	28.5746i	0.859023	+	1.33667i	−0.0814081	+	0.996681i	$0.525942\pi$
$458$	−10.9561	+	12.6440i	−0.511944	+	0.590815i
$459$	−32.8606	+	15.8854i	−1.53380	+	0.741465i
$460$	0.842522	+	4.72125i	0.0392828	+	0.220129i
$461$			9.73419i			0.453366i	0.973969	+	0.226683i	$0.0727882\pi$
$461$			9.73419i			0.453366i	−0.973969	+	0.226683i	$0.927212\pi$
$462$	0.587074	+	1.11864i	0.0273131	+	0.0520440i
$463$	−18.8057	+	12.0857i	−0.873973	+	0.561668i	−0.898965	−	0.438019i	$-0.855680\pi$
$463$	−18.8057	+	12.0857i	−0.873973	+	0.561668i	0.0249928	+	0.999688i	$0.492044\pi$
$464$	7.72531	−	1.11073i	0.358639	−	0.0515645i
$465$	14.4288	−	0.792911i	0.669120	−	0.0367703i
$466$	4.18217	−	29.0876i	0.193735	−	1.34746i
$467$	−2.61145	+	0.766792i	−0.120844	+	0.0354829i	−0.341595	−	0.939847i	$-0.610967\pi$
$467$	−2.61145	+	0.766792i	−0.120844	+	0.0354829i	0.220752	+	0.975330i	$0.429149\pi$
$468$	2.38268	+	9.23131i	0.110140	+	0.426718i
$469$	3.51234	−	7.69095i	0.162185	−	0.355135i
$470$	3.32075	+	0.975060i	0.153175	+	0.0449762i
$471$	−8.86285	−	25.0154i	−0.408379	−	1.15265i
$472$	2.88096	+	3.32481i	0.132607	+	0.153037i
$473$	1.00869	−	3.43527i	0.0463794	−	0.157954i
$474$	3.31828	+	3.42964i	0.152414	+	0.157529i
$475$	0.981811	−	1.52773i	0.0450486	−	0.0700970i
$476$	−4.78079	−	16.2819i	−0.219127	−	0.746279i
$477$	−12.4323	+	10.0740i	−0.569237	+	0.461258i
$478$	3.78394	+	8.28568i	0.173074	+	0.378978i
$479$	−1.28995	−	8.97178i	−0.0589392	−	0.409931i	−0.997837	−	0.0657352i	$-0.979061\pi$
$479$	−1.28995	−	8.97178i	−0.0589392	−	0.409931i	0.938898	−	0.344196i	$-0.111848\pi$
$480$	−1.69831	+	0.340196i	−0.0775170	+	0.0155278i
$481$	−18.9509	−	16.4210i	−0.864085	−	0.748734i
$482$	7.70319			0.350871
$483$	1.77750	+	19.9885i	0.0808791	+	0.909508i
$484$	10.9088			0.495857
$485$	6.48547	+	5.61969i	0.294490	+	0.255177i
$486$	4.22535	+	15.0049i	0.191666	+	0.680635i
$487$	−2.92985	−	20.3776i	−0.132764	−	0.923395i	−0.941929	−	0.335813i	$-0.890989\pi$
$487$	−2.92985	−	20.3776i	−0.132764	−	0.923395i	0.809164	−	0.587582i	$-0.199920\pi$
$488$	0.920167	+	2.01488i	0.0416540	+	0.0912095i
$489$	8.32360	+	4.72498i	0.376406	+	0.213671i
$490$	0.327873	+	1.11663i	0.0148118	+	0.0504443i
$491$	−11.9223	+	18.5515i	−0.538047	+	0.837217i	−0.998732	−	0.0503464i	$-0.983967\pi$
$491$	−11.9223	+	18.5515i	−0.538047	+	0.837217i	0.460685	+	0.887564i	$0.347604\pi$
$492$	−0.237906	+	0.230181i	−0.0107256	+	0.0103774i
$493$	15.4452	−	52.6015i	0.695616	−	2.36905i
$494$	−3.77933	−	4.36158i	−0.170040	−	0.196237i
$495$	0.0298879	−	0.905268i	0.00134336	−	0.0406888i
$496$	8.00510	+	2.35051i	0.359440	+	0.105541i
$497$	2.42824	−	5.31710i	0.108921	−	0.238505i
$498$	−10.3974	−	14.3779i	−0.465921	−	0.644290i
$499$	0.729771	−	0.214280i	0.0326690	−	0.00959249i	−0.265357	−	0.964150i	$-0.585490\pi$
$499$	0.729771	−	0.214280i	0.0326690	−	0.00959249i	0.298026	+	0.954558i	$0.403672\pi$
$500$	−0.142315	+	0.989821i	−0.00636451	+	0.0442662i
$501$	1.73621	+	31.5943i	0.0775682	+	1.41153i
$502$	4.50516	−	0.647745i	0.201075	−	0.0289103i
$503$	−0.920882	+	0.591815i	−0.0410601	+	0.0263877i	−0.561010	−	0.827809i	$-0.689587\pi$
$503$	−0.920882	+	0.591815i	−0.0410601	+	0.0263877i	0.519950	+	0.854197i	$0.325951\pi$
$504$	−7.20384	+	0.794148i	−0.320885	+	0.0353741i
$505$		−	17.5806i		−	0.782328i
$506$	−1.33668	−	0.556657i	−0.0594227	−	0.0247464i
$507$	−1.83316	+	4.67766i	−0.0814134	+	0.207742i
$508$	2.05090	−	2.36687i	0.0909941	−	0.105013i
$509$	−11.7211	−	18.2384i	−0.519529	−	0.808403i	0.478022	−	0.878348i	$-0.341354\pi$
$509$	−11.7211	−	18.2384i	−0.519529	−	0.808403i	−0.997551	+	0.0699447i	$0.977718\pi$
$510$	−2.78194	+	11.8439i	−0.123186	+	0.524458i
$511$	13.5371	−	6.18220i	0.598848	−	0.273485i
$512$	−0.989821	−	0.142315i	−0.0437443	−	0.00628949i
$513$	−6.33410	−	6.99447i	−0.279657	−	0.308814i
$514$	−13.5676	−	8.71936i	−0.598440	−	0.384594i
$515$	12.3091	+	5.62139i	0.542405	+	0.247708i
$516$	16.2373	+	12.5784i	0.714806	+	0.553735i
$517$	−0.789704	+	0.684283i	−0.0347312	+	0.0300947i
$518$	14.4061	−	12.4830i	0.632970	−	0.548471i
$519$	−17.6073	−	13.6397i	−0.772873	−	0.598717i
$520$	2.89077	+	1.32017i	0.126768	+	0.0578932i
$521$	−3.10277	−	1.99403i	−0.135935	−	0.0873599i	0.470906	−	0.882183i	$-0.343927\pi$
$521$	−3.10277	−	1.99403i	−0.135935	−	0.0873599i	−0.606841	+	0.794823i	$0.707563\pi$
$522$	−20.9658	−	10.4241i	−0.917649	−	0.456252i
$523$	33.1775	+	4.77021i	1.45075	+	0.208587i	0.822208	−	0.569188i	$-0.192742\pi$
$523$	33.1775	+	4.77021i	1.45075	+	0.208587i	0.628544	+	0.777774i	$0.283651\pi$
$524$	−1.81812	+	0.830307i	−0.0794249	+	0.0362721i
$525$	−0.956792	+	4.07348i	−0.0417578	+	0.177781i
$526$	−0.660540	−	1.02782i	−0.0288009	−	0.0448151i
$527$	38.3770	−	44.2894i	1.67173	−	1.92928i
$528$	0.190809	−	0.486887i	0.00830391	−	0.0211891i
$529$	−16.2014	−	16.3253i	−0.704407	−	0.709796i
$530$			5.33384i			0.231687i
$531$	−1.44619	−	13.1186i	−0.0627591	−	0.569298i
$532$	3.69073	−	2.37189i	0.160013	−	0.102834i
$533$	0.601194	−	0.0864387i	0.0260406	−	0.00374407i
$534$	−1.34040	−	24.3916i	−0.0580048	−	1.05553i
$535$	−2.08781	+	14.5210i	−0.0902637	+	0.627798i
$536$	−3.35807	+	0.986019i	−0.145047	+	0.0425895i
$537$	14.3033	+	19.7790i	0.617231	+	0.853528i
$538$	8.63141	−	18.9002i	0.372127	−	0.814844i
$539$	−0.337134	−	0.0989915i	−0.0145214	−	0.00426387i
$540$	4.77271	+	2.05456i	0.205385	+	0.0884144i
$541$	12.8693	+	14.8520i	0.553296	+	0.638537i	0.961648	−	0.274287i	$-0.0884419\pi$
$541$	12.8693	+	14.8520i	0.553296	+	0.638537i	−0.408352	+	0.912824i	$0.633896\pi$
$542$	8.99459	−	30.6328i	0.386351	−	1.31579i
$543$	−24.3472	+	23.5566i	−1.04484	+	1.01091i
$544$	−3.79757	+	5.90913i	−0.162819	+	0.253352i
$545$	−2.53823	−	8.64442i	−0.108726	−	0.370286i
$546$	11.5643	+	6.56459i	0.494906	+	0.280938i
$547$	−0.387724	−	0.848996i	−0.0165779	−	0.0363005i	0.901162	−	0.433483i	$-0.142715\pi$
$547$	−0.387724	−	0.848996i	−0.0165779	−	0.0363005i	−0.917740	+	0.397182i	$0.869988\pi$
$548$	−2.29342	−	15.9511i	−0.0979700	−	0.681396i
$549$	1.16223	−	6.54274i	0.0496029	−	0.279237i
$550$	−0.228176	−	0.197716i	−0.00972946	−	0.00843063i
$551$	14.1735			0.603813
$552$	5.77122	−	5.97436i	0.245640	−	0.254286i
$553$	6.65610			0.283046
$554$	4.01171	+	3.47616i	0.170441	+	0.147688i
$555$	−13.4005	+	2.68431i	−0.568820	+	0.113943i
$556$	−2.29457	−	15.9591i	−0.0973114	−	0.676815i
$557$	−5.83464	−	12.7761i	−0.247221	−	0.541339i	0.744818	−	0.667268i	$-0.232536\pi$
$557$	−5.83464	−	12.7761i	−0.247221	−	0.541339i	−0.992039	+	0.125928i	$0.959809\pi$
$558$	−15.7575	−	19.4463i	−0.667069	−	0.823228i
$559$	−10.6172	−	36.1589i	−0.449060	−	1.52936i
$560$	−1.30610	+	2.03232i	−0.0551926	+	0.0858814i
$561$	−2.55416	−	2.63988i	−0.107837	−	0.111456i
$562$	3.75468	−	12.7873i	0.158382	−	0.539399i
$563$	1.85395	+	2.13957i	0.0781348	+	0.0901723i	0.793471	−	0.608608i	$-0.208272\pi$
$563$	1.85395	+	2.13957i	0.0781348	+	0.0901723i	−0.715336	+	0.698781i	$0.753726\pi$
$564$	−2.00191	−	5.65037i	−0.0842955	−	0.237924i
$565$	−7.41077	−	2.17600i	−0.311774	−	0.0915450i
$566$	4.22368	−	9.24856i	0.177534	−	0.388746i
$567$	19.1388	+	10.3170i	0.803754	+	0.433273i
$568$	−2.32159	+	0.681680i	−0.0974116	+	0.0286026i
$569$	−6.23482	+	43.3641i	−0.261377	+	1.81792i	0.261153	+	0.965297i	$0.415897\pi$
$569$	−6.23482	+	43.3641i	−0.261377	+	1.81792i	−0.522530	+	0.852621i	$0.675012\pi$
$570$	−3.14069	+	0.172591i	−0.131549	+	0.00722905i
$571$	24.1826	−	3.47693i	1.01201	−	0.145505i	0.383691	−	0.923462i	$-0.374653\pi$
$571$	24.1826	−	3.47693i	1.01201	−	0.145505i	0.628318	+	0.777957i	$0.283744\pi$
$572$	−0.807172	+	0.518738i	−0.0337496	+	0.0216895i
$573$	−16.7239	−	31.8666i	−0.698650	−	1.33125i
$574$			0.461718i			0.0192717i
$575$	−2.13852	−	4.29264i	−0.0891826	−	0.179015i
$576$	2.20119	+	2.03833i	0.0917161	+	0.0849303i
$577$	8.82105	−	10.1800i	0.367225	−	0.423800i	−0.541822	−	0.840493i	$-0.682265\pi$
$577$	8.82105	−	10.1800i	0.367225	−	0.423800i	0.909047	+	0.416693i	$0.136811\pi$
$578$	17.4840	+	27.2056i	0.727238	+	1.13160i
$579$	−9.74856	−	2.28977i	−0.405136	−	0.0951597i
$580$	−7.09945	+	3.24221i	−0.294789	+	0.134626i
$581$	−24.4963	−	3.52204i	−1.01628	−	0.146119i
$582$	1.30485	−	14.8062i	0.0540879	−	0.613738i
$583$	−1.35475	−	0.870645i	−0.0561080	−	0.0360584i
$584$	−5.60352	−	2.55904i	−0.231875	−	0.105894i
$585$	−4.88693	−	8.18610i	−0.202050	−	0.338454i
$586$	−11.2993	+	9.79087i	−0.466769	+	0.404457i
$587$	0.0382540	−	0.0331473i	0.00157891	−	0.00136814i	−0.654071	−	0.756433i	$-0.726940\pi$
$587$	0.0382540	−	0.0331473i	0.00157891	−	0.00136814i	0.655650	+	0.755065i	$0.272395\pi$
$588$	1.23444	−	1.59351i	0.0509073	−	0.0657153i
$589$	13.7819	+	6.29399i	0.567874	+	0.259339i
$590$	−3.70097	−	2.37847i	−0.152367	−	0.0979201i
$591$	8.16131	+	0.719246i	0.335711	+	0.0295858i
$592$	−7.81017	−	1.12293i	−0.320996	−	0.0461523i
$593$	−27.3172	+	12.4754i	−1.12178	+	0.512302i	−0.887934	−	0.459971i	$-0.847860\pi$
$593$	−27.3172	+	12.4754i	−1.12178	+	0.512302i	−0.233850	+	0.972273i	$0.575133\pi$
$594$	−1.30089	+	0.876860i	−0.0533763	+	0.0359780i
$595$	9.17427	+	14.2754i	0.376109	+	0.585236i
$596$	−6.61952	+	7.63933i	−0.271146	+	0.312919i
$597$	28.6449	+	11.2258i	1.17236	+	0.459443i
$598$	−15.0039	+	2.67749i	−0.613554	+	0.109491i
$599$		−	13.8095i		−	0.564240i	−0.959379	−	0.282120i	$-0.908962\pi$
$599$		−	13.8095i		−	0.564240i	0.959379	−	0.282120i	$-0.0910377\pi$
$600$	1.53367	−	0.804886i	0.0626120	−	0.0328593i
$601$	16.0809	−	10.3346i	0.655955	−	0.421557i	−0.169883	−	0.985464i	$-0.554339\pi$
$601$	16.0809	−	10.3346i	0.655955	−	0.421557i	0.825838	+	0.563908i	$0.190703\pi$
$602$	28.3563	−	4.07702i	1.15572	−	0.166167i
$603$	9.97112	+	3.28887i	0.406055	+	0.133933i
$604$	2.01175	−	13.9921i	0.0818571	−	0.569329i
$605$	−10.4670	+	3.07338i	−0.425542	+	0.124951i
$606$	−24.6747	+	17.8436i	−1.00234	+	0.724847i
$607$	−18.7703	+	41.1012i	−0.761863	+	1.66825i	−0.0180707	+	0.999837i	$0.505752\pi$
$607$	−18.7703	+	41.1012i	−0.761863	+	1.66825i	−0.743792	+	0.668411i	$0.766975\pi$
$608$	−1.74245	−	0.511630i	−0.0706658	−	0.0207493i
$609$	−30.7828	+	10.9062i	−1.24738	+	0.441943i
$610$	−1.45055	−	1.67403i	−0.0587311	−	0.0677793i
$611$	−3.09869	+	10.5532i	−0.125360	+	0.426936i
$612$	19.4467	−	8.11660i	0.786087	−	0.328094i
$613$	17.2763	−	26.8824i	0.697783	−	1.08577i	−0.293746	−	0.955884i	$-0.594902\pi$
$613$	17.2763	−	26.8824i	0.697783	−	1.08577i	0.991529	−	0.129888i	$-0.0414618\pi$
$614$	0.0286517	+	0.0975787i	0.00115629	+	0.00393796i
$615$	0.163420	−	0.287883i	0.00658973	−	0.0116086i
$616$	−0.302999	−	0.663474i	−0.0122082	−	0.0267321i
$617$	−6.17401	−	42.9412i	−0.248556	−	1.72875i	−0.606568	−	0.795031i	$-0.707454\pi$
$617$	−6.17401	−	42.9412i	−0.248556	−	1.72875i	0.358012	−	0.933717i	$-0.383455\pi$
$618$	−4.60353	−	22.9815i	−0.185181	−	0.924453i
$619$	0.679549	+	0.588833i	0.0273134	+	0.0236672i	0.668410	−	0.743793i	$-0.266975\pi$
$619$	0.679549	+	0.588833i	0.0273134	+	0.0236672i	−0.641097	+	0.767460i	$0.721520\pi$
$620$	−8.34305			−0.335065
$621$	−24.4306	+	4.91390i	−0.980366	+	0.197188i
$622$	−12.8966			−0.517107
$623$	−25.7501	−	22.3126i	−1.03166	−	0.893936i
$624$	−1.08113	−	5.39715i	−0.0432797	−	0.216059i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	0.574011	+	1.25691i	0.0229421	+	0.0502362i
$627$	0.468819	−	0.825881i	0.0187228	−	0.0329825i
$628$	4.31679	+	14.7016i	0.172259	+	0.586659i
$629$	−29.9647	+	46.6259i	−1.19477	+	1.85910i
$630$	6.68830	−	2.79154i	0.266468	−	0.111217i
$631$	5.45351	−	18.5730i	0.217101	−	0.739378i	−0.776863	−	0.629670i	$-0.783190\pi$
$631$	5.45351	−	18.5730i	0.217101	−	0.739378i	0.993964	−	0.109708i	$-0.0349916\pi$
$632$	−1.80427	−	2.08224i	−0.0717702	−	0.0828272i
$633$	−14.0426	+	4.97525i	−0.558144	+	0.197749i
$634$	−25.2213	−	7.40564i	−1.00167	−	0.294115i
$635$	−1.30100	+	2.84880i	−0.0516287	+	0.113051i
$636$	7.48614	−	5.41362i	0.296845	−	0.214664i
$637$	−3.54860	+	1.04196i	−0.140601	+	0.0412841i
$638$	0.335353	−	2.33243i	0.0132767	−	0.0923417i
$639$	6.89349	+	2.27375i	0.272702	+	0.0899480i
$640$	0.989821	−	0.142315i	0.0391261	−	0.00562549i
$641$	−26.5988	+	17.0940i	−1.05059	+	0.675174i	−0.947584	−	0.319507i	$-0.896483\pi$
$641$	−26.5988	+	17.0940i	−1.05059	+	0.675174i	−0.103007	+	0.994681i	$0.532846\pi$
$642$	22.4995	−	11.8079i	0.887985	−	0.466022i
$643$		−	13.9735i		−	0.551061i	−0.961292	−	0.275530i	$-0.911147\pi$
$643$		−	13.9735i		−	0.551061i	0.961292	−	0.275530i	$-0.0888535\pi$
$644$	−0.391469	−	11.5793i	−0.0154260	−	0.456288i
$645$	−19.1233	−	7.49435i	−0.752979	−	0.295090i
$646$	−8.35343	+	9.64037i	−0.328661	+	0.379295i
$647$	15.2943	+	23.7984i	0.601282	+	0.935612i	0.999830	+	0.0184649i	$0.00587789\pi$
$647$	15.2943	+	23.7984i	0.601282	+	0.935612i	−0.398548	+	0.917148i	$0.630486\pi$
$648$	−1.96048	−	8.78388i	−0.0770151	−	0.345063i
$649$	1.20822	−	0.551777i	0.0474269	−	0.0216591i
$650$	−3.14560	−	0.452269i	−0.123381	−	0.0177395i
$651$	−34.7754	−	3.06471i	−1.36295	−	0.120115i
$652$	−4.64871	−	2.98754i	−0.182058	−	0.117001i
$653$	−13.1390	−	6.00036i	−0.514167	−	0.234812i	0.141395	−	0.989953i	$-0.454841\pi$
$653$	−13.1390	−	6.00036i	−0.514167	−	0.234812i	−0.655563	+	0.755141i	$0.727568\pi$
$654$	−9.55639	+	12.3362i	−0.373684	+	0.482382i
$655$	1.51055	−	1.30890i	0.0590220	−	0.0511429i
$656$	0.144440	−	0.125158i	0.00563945	−	0.00488661i
$657$	9.47292	+	15.8681i	0.369574	+	0.619074i
$658$	−7.60547	−	3.47330i	−0.296492	−	0.135403i
$659$	−12.6445	−	8.12612i	−0.492559	−	0.316549i	0.270675	−	0.962671i	$-0.412753\pi$
$659$	−12.6445	−	8.12612i	−0.492559	−	0.316549i	−0.763234	+	0.646122i	$0.776390\pi$
$660$	−0.0459082	+	0.520922i	−0.00178697	+	0.0202769i
$661$	−35.7489	−	5.13991i	−1.39047	−	0.199919i	−0.593935	−	0.804513i	$-0.702426\pi$
$661$	−35.7489	−	5.13991i	−1.39047	−	0.199919i	−0.796534	+	0.604594i	$0.793336\pi$
$662$	−18.2732	+	8.34509i	−0.710208	+	0.324341i
$663$	−37.6395	−	8.84088i	−1.46180	−	0.343351i
$664$	5.53844	+	8.61798i	0.214933	+	0.334442i
$665$	−2.87299	+	3.31561i	−0.111410	+	0.128574i
$666$	17.3684	+	16.0834i	0.673014	+	0.623219i
$667$	19.1608	−	32.1541i	0.741911	−	1.24501i
$668$		−	18.2685i		−	0.706830i
$669$	−2.79945	−	5.33424i	−0.108233	−	0.206234i
$670$	2.94425	−	1.89216i	0.113746	−	0.0731004i
$671$	0.661963	−	0.0951758i	0.0255548	−	0.00367422i
$672$	4.17803	−	0.229597i	0.161171	−	0.00885688i
$673$	−5.15877	+	35.8800i	−0.198856	+	1.38307i	0.608755	+	0.793358i	$0.291669\pi$
$673$	−5.15877	+	35.8800i	−0.198856	+	1.38307i	−0.807611	+	0.589715i	$0.799240\pi$
$674$	15.4246	−	4.52907i	0.594133	−	0.174453i
$675$	−5.15822	−	0.626712i	−0.198540	−	0.0241222i
$676$	1.20497	−	2.63851i	0.0463448	−	0.101481i
$677$	19.6574	+	5.77192i	0.755494	+	0.221833i	0.636727	−	0.771089i	$-0.280288\pi$
$677$	19.6574	+	5.77192i	0.755494	+	0.221833i	0.118767	+	0.992922i	$0.462106\pi$
$678$	4.46757	+	12.6097i	0.171576	+	0.484272i
$679$	−13.5762	−	15.6678i	−0.521007	−	0.601274i
$680$	1.97895	−	6.73967i	0.0758891	−	0.258455i
$681$	9.29740	+	9.60942i	0.356277	+	0.368234i
$682$	1.36184	−	2.11906i	0.0521475	−	0.0811432i
$683$	4.03406	+	13.7388i	0.154359	+	0.525699i	0.999967	−	0.00810539i	$-0.00258005\pi$
$683$	4.03406	+	13.7388i	0.154359	+	0.525699i	−0.845608	+	0.533804i	$0.820762\pi$
$684$	3.42990	+	4.23284i	0.131146	+	0.161847i
$685$	6.69446	+	14.6588i	0.255782	+	0.560085i
$686$	−2.80677	−	19.5215i	−0.107163	−	0.745336i
$687$	−28.4134	+	5.69162i	−1.08404	+	0.217149i
$688$	−8.96199	−	7.76561i	−0.341673	−	0.296061i
$689$	−16.9507			−0.645770
$690$	−3.85428	+	7.35830i	−0.146730	+	0.280126i
$691$	0.739344			0.0281260			0.0140630	−	0.999901i	$-0.495523\pi$
$691$	0.739344			0.0281260			0.0140630	+	0.999901i	$0.495523\pi$
$692$	9.71815	+	8.42082i	0.369429	+	0.320112i
$693$	−0.382708	+	2.15443i	−0.0145379	+	0.0818402i
$694$	1.38060	+	9.60230i	0.0524069	+	0.364498i
$695$	6.69781	+	14.6662i	0.254062	+	0.556319i
$696$	11.7561	+	6.67350i	0.445616	+	0.252958i
$697$	−0.378220	−	1.28810i	−0.0143261	−	0.0487902i
$698$	14.7313	−	22.9224i	0.557589	−	0.867625i
$699$	36.5803	−	35.3925i	1.38359	−	1.33867i
$700$	0.680617	−	2.31797i	0.0257249	−	0.0876110i
$701$	19.4907	+	22.4935i	0.736155	+	0.849568i	0.993150	−	0.116844i	$-0.0372779\pi$
$701$	19.4907	+	22.4935i	0.736155	+	0.849568i	−0.256995	+	0.966413i	$0.582732\pi$
$702$	−6.52930	+	15.1674i	−0.246433	+	0.572458i
$703$	−13.7488	−	4.03701i	−0.518546	−	0.152259i
$704$	−0.125422	+	0.274636i	−0.00472703	+	0.0103507i
$705$	3.51271	+	4.85749i	0.132296	+	0.182944i
$706$	27.2997	−	8.01592i	1.02744	−	0.301683i
$707$	−6.04437	+	42.0395i	−0.227322	+	1.58106i
$708$	0.418108	+	7.60842i	0.0157134	+	0.285942i
$709$	18.9663	−	2.72694i	0.712293	−	0.102412i	0.223363	−	0.974735i	$-0.428296\pi$
$709$	18.9663	−	2.72694i	0.712293	−	0.102412i	0.488930	+	0.872323i	$0.337387\pi$
$710$	2.03550	−	1.30813i	0.0763908	−	0.0490934i
$711$	0.905709	+	8.21584i	0.0339667	+	0.308118i
$712$			14.1038i			0.528561i
$713$	32.9100	−	22.7570i	1.23249	−	0.852257i
$714$	10.7243	−	27.3652i	0.401348	−	1.02412i
$715$	0.628331	−	0.725132i	0.0234982	−	0.0271184i
$716$	−7.61896	−	11.8553i	−0.284734	−	0.443055i
$717$	−3.60756	+	15.3590i	−0.134727	+	0.573591i
$718$	−21.5139	+	9.82509i	−0.802893	+	0.366669i
$719$	39.5169	+	5.68168i	1.47373	+	0.211891i	0.831888	−	0.554944i	$-0.187260\pi$
$719$	39.5169	+	5.68168i	1.47373	+	0.211891i	0.641845	+	0.766834i	$0.278169\pi$
$720$	−2.68629	−	1.33561i	−0.100112	−	0.0497754i
$721$	−27.5014	−	17.6741i	−1.02420	−	0.658217i
$722$	14.2831	+	6.52289i	0.531563	+	0.242757i
$723$	10.5477	+	8.17091i	0.392273	+	0.303880i
$724$	14.7819	−	12.8086i	0.549366	−	0.476029i
$725$	5.89844	−	5.11103i	0.219063	−	0.189819i
$726$	14.9371	+	11.5712i	0.554366	+	0.429448i
$727$	−34.9827	−	15.9761i	−1.29744	−	0.592520i	−0.357515	−	0.933908i	$-0.616376\pi$
$727$	−34.9827	−	15.9761i	−1.29744	−	0.592520i	−0.939922	+	0.341388i	$0.889103\pi$
$728$	−6.45862	−	4.15071i	−0.239373	−	0.153835i
$729$	−10.1303	+	25.0275i	−0.375198	+	0.926945i
$730$	6.09750	+	0.876688i	0.225679	+	0.0324477i
$731$	−75.7686	+	34.6023i	−2.80240	+	1.27981i
$732$	−0.877275	+	3.73494i	−0.0324250	+	0.138047i
$733$	10.0146	+	15.5830i	0.369897	+	0.575571i	0.975446	−	0.220237i	$-0.0706830\pi$
$733$	10.0146	+	15.5830i	0.369897	+	0.575571i	−0.605550	+	0.795808i	$0.707047\pi$
$734$	16.8660	−	19.4644i	0.622534	−	0.718443i
$735$	−0.735489	+	1.87674i	−0.0271289	+	0.0692247i
$736$	−3.51626	+	3.26127i	−0.129611	+	0.120212i
$737$			1.05667i			0.0389230i
$738$	−0.569914	+	0.0628269i	−0.0209788	+	0.00231269i
$739$	35.0780	−	22.5433i	1.29037	−	0.829268i	0.298238	−	0.954492i	$-0.403601\pi$
$739$	35.0780	−	22.5433i	1.29037	−	0.829268i	0.992129	+	0.125223i	$0.0399647\pi$
$740$	7.81017	−	1.12293i	0.287108	−	0.0412799i
$741$	−0.548486	−	9.98096i	−0.0201491	−	0.366660i
$742$	1.83382	−	12.7545i	0.0673216	−	0.468232i
$743$	−30.0444	+	8.82184i	−1.10222	+	0.323642i	−0.781735	−	0.623611i	$-0.785665\pi$
$743$	−30.0444	+	8.82184i	−1.10222	+	0.323642i	−0.320488	+	0.947253i	$0.603847\pi$
$744$	8.46785	+	11.7096i	0.310446	+	0.429295i
$745$	4.19913	−	9.19482i	0.153844	−	0.336872i
$746$	−13.8131	−	4.05590i	−0.505735	−	0.148497i
$747$	1.01410	−	30.7159i	0.0371041	−	1.12384i
$748$	1.38879	+	1.60275i	0.0507794	+	0.0586025i
$749$	9.98488	−	34.0054i	0.364840	−	1.24253i
$750$	−1.24479	+	1.20437i	−0.0454532	+	0.0439773i
$751$	5.95572	−	9.26728i	0.217327	−	0.338168i	−0.715423	−	0.698692i	$-0.753766\pi$
$751$	5.95572	−	9.26728i	0.217327	−	0.338168i	0.932750	+	0.360524i	$0.117402\pi$
$752$	0.975060	+	3.32075i	0.0355568	+	0.121095i
$753$	6.85582	+	3.89178i	0.249840	+	0.141824i
$754$	−10.3036	−	22.5617i	−0.375235	−	0.821649i
$755$	2.01175	+	13.9921i	0.0732152	+	0.509223i
$756$	−10.7063	−	6.55385i	−0.389385	−	0.238361i
$757$	−32.5642	−	28.2171i	−1.18357	−	1.02557i	−0.999087	−	0.0427305i	$-0.986394\pi$
$757$	−32.5642	−	28.2171i	−1.18357	−	1.02557i	−0.184480	−	0.982836i	$-0.559060\pi$
$758$	5.17412			0.187932
$759$	−1.23981	−	2.18005i	−0.0450023	−	0.0791309i
$760$	1.81601			0.0658738
$761$	−22.0988	−	19.1487i	−0.801080	−	0.694140i	0.154784	−	0.987948i	$-0.450532\pi$
$761$	−22.0988	−	19.1487i	−0.801080	−	0.694140i	−0.955864	+	0.293808i	$0.905077\pi$
$762$	5.31880	−	1.06543i	0.192680	−	0.0385965i
$763$	3.09749	+	21.5435i	0.112137	+	0.779928i
$764$	8.63147	+	18.9003i	0.312275	+	0.683788i
$765$	−16.3723	+	13.2666i	−0.591941	+	0.479655i
$766$	3.03196	+	10.3259i	0.109549	+	0.373090i
$767$	7.55866	−	11.7615i	0.272927	−	0.424683i
$768$	−1.20437	−	1.24479i	−0.0434589	−	0.0449174i
$769$	5.10201	−	17.3758i	0.183983	−	0.626589i	−0.814912	−	0.579585i	$-0.803215\pi$
$769$	5.10201	−	17.3758i	0.183983	−	0.626589i	0.998895	−	0.0470038i	$-0.0149673\pi$
$770$	0.477647	+	0.551234i	0.0172132	+	0.0198651i
$771$	−9.32879	−	26.3305i	−0.335968	−	0.948268i
$772$	5.54731	+	1.62884i	0.199652	+	0.0586232i
$773$	−0.0157385	+	0.0344626i	−0.000566076	+	0.00123953i	−0.909915	−	0.414795i	$-0.863853\pi$
$773$	−0.0157385	+	0.0344626i	−0.000566076	+	0.00123953i	0.909349	+	0.416035i	$0.136581\pi$
$774$	8.89090	+	34.4463i	0.319577	+	1.23815i
$775$	8.00510	−	2.35051i	0.287552	−	0.0844328i
$776$	−1.22128	+	8.49416i	−0.0438412	+	0.304923i
$777$	32.9667	−	1.81163i	1.18267	−	0.0649918i
$778$	−19.8924	+	2.86010i	−0.713179	+	0.102540i
$779$	0.291983	−	0.187646i	0.0104614	−	0.00672311i
$780$	2.55789	+	4.87394i	0.0915871	+	0.174515i
$781$			0.730526i			0.0261403i
$782$	10.5774	+	31.9832i	0.378247	+	1.14372i
$783$	−17.6506	−	36.5122i	−0.630781	−	1.30484i
$784$	−0.762110	+	0.879522i	−0.0272182	+	0.0314115i
$785$	−8.28386	−	12.8899i	−0.295664	−	0.460062i
$786$	−3.37020	−	0.791604i	−0.120211	−	0.0282356i
$787$	−19.3101	+	8.81865i	−0.688332	+	0.314351i	−0.728699	−	0.684834i	$-0.759875\pi$
$787$	−19.3101	+	8.81865i	−0.688332	+	0.314351i	0.0403668	+	0.999185i	$0.487147\pi$
$788$	−4.68205	−	0.673177i	−0.166791	−	0.0239809i
$789$	0.185776	−	2.10800i	0.00661379	−	0.0750469i
$790$	2.31782	+	1.48957i	0.0824645	+	0.0529967i
$791$	16.9728	+	7.75122i	0.603483	+	0.275602i
$792$	0.777718	−	0.464281i	0.0276350	−	0.0164975i
$793$	5.31997	−	4.60978i	0.188918	−	0.163698i
$794$	−7.93157	+	6.87274i	−0.281481	+	0.243904i
$795$	−5.65770	+	7.30342i	−0.200658	+	0.259026i
$796$	−16.1576	−	7.37893i	−0.572691	−	0.261539i
$797$	−19.5127	−	12.5401i	−0.691176	−	0.444192i	0.147327	−	0.989088i	$-0.452933\pi$
$797$	−19.5127	−	12.5401i	−0.691176	−	0.444192i	−0.838504	+	0.544896i	$0.816569\pi$
$798$	7.56948	+	0.667088i	0.267957	+	0.0236147i
$799$	24.0629	+	3.45972i	0.851284	+	0.122396i
$800$	−0.909632	+	0.415415i	−0.0321603	+	0.0146871i
$801$	24.0373	−	34.8203i	0.849316	−	1.23032i
$802$	−10.0989	−	15.7142i	−0.356604	−	0.554887i
$803$	−1.21797	+	1.40561i	−0.0429812	+	0.0496029i
$804$	−5.64397	−	2.21185i	−0.199047	−	0.0780059i
$805$	3.63787	+	11.0000i	0.128218	+	0.387698i
$806$		−	26.5138i		−	0.933909i
$807$	31.8664	−	16.7238i	1.12175	−	0.588704i
$808$	14.7898	−	9.50481i	0.520302	−	0.334378i
$809$	16.4644	−	2.36723i	0.578858	−	0.0832273i	0.153334	−	0.988174i	$-0.450999\pi$
$809$	16.4644	−	2.36723i	0.578858	−	0.0832273i	0.425524	+	0.904947i	$0.360090\pi$
$810$	4.35578	+	7.87574i	0.153046	+	0.276725i
$811$	−2.71051	+	18.8520i	−0.0951787	+	0.661983i	0.885251	+	0.465114i	$0.153987\pi$
$811$	−2.71051	+	18.8520i	−0.0951787	+	0.661983i	−0.980430	+	0.196869i	$0.936923\pi$
$812$	18.0912	−	5.31205i	0.634876	−	0.186416i
$813$	44.8087	−	32.4035i	1.57151	−	1.13644i
$814$	−0.989642	+	2.16701i	−0.0346870	+	0.0759538i
$815$	5.30209	+	1.55684i	0.185724	+	0.0545336i
$816$	−11.4678	+	4.06300i	−0.401453	+	0.142233i
$817$	−14.1025	−	16.2751i	−0.493382	−	0.569394i
$818$	−8.41842	+	28.6705i	−0.294343	+	1.00244i
$819$	8.87136	+	21.2551i	0.309991	+	0.742713i
$820$	−0.103328	+	0.160782i	−0.00360838	+	0.00561475i
$821$	9.83438	+	33.4928i	0.343222	+	1.16891i	0.932558	+	0.361020i	$0.117571\pi$
$821$	9.83438	+	33.4928i	0.343222	+	1.16891i	−0.589336	+	0.807888i	$0.700611\pi$
$822$	13.7793	−	24.2739i	0.480609	−	0.846649i
$823$	19.4035	+	42.4878i	0.676364	+	1.48103i	0.866451	+	0.499263i	$0.166396\pi$
$823$	19.4035	+	42.4878i	0.676364	+	1.48103i	−0.190087	+	0.981767i	$0.560877\pi$
$824$	1.92580	+	13.3942i	0.0670885	+	0.466611i
$825$	−0.102712	−	0.512755i	−0.00357598	−	0.0178518i
$826$	8.03217	+	6.95991i	0.279475	+	0.242166i
$827$	5.44149			0.189219			0.0946096	−	0.995514i	$-0.469840\pi$
$827$	5.44149			0.189219			0.0946096	+	0.995514i	$0.469840\pi$
$828$	14.2394	−	2.05882i	0.494854	−	0.0715490i
$829$	−8.72208			−0.302930			−0.151465	−	0.988463i	$-0.548399\pi$
$829$	−8.72208			−0.302930			−0.151465	+	0.988463i	$0.548399\pi$
$830$	−7.74206	−	6.70853i	−0.268731	−	0.232856i
$831$	1.80585	+	9.01507i	0.0626441	+	0.312729i
$832$	0.452269	+	3.14560i	0.0156796	+	0.109054i
$833$	3.39584	+	7.43586i	0.117659	+	0.257637i
$834$	13.7862	−	24.2860i	0.477377	−	0.840957i
$835$	5.14684	+	17.5285i	0.178114	+	0.606599i
$836$	−0.296429	+	0.461252i	−0.0102522	+	0.0159527i
$837$	−0.949087	−	43.3414i	−0.0328053	−	1.49810i
$838$	−3.95436	+	13.4673i	−0.136601	+	0.465221i
$839$	4.25212	+	4.90721i	0.146800	+	0.169416i	0.824387	−	0.566026i	$-0.191520\pi$
$839$	4.25212	+	4.90721i	0.146800	+	0.169416i	−0.677588	+	0.735442i	$0.736975\pi$
$840$	−3.94411	+	1.39738i	−0.136085	+	0.0482143i
$841$	30.6214	+	8.99127i	1.05591	+	0.310044i
$842$	7.45828	−	16.3314i	0.257029	−	0.562816i
$843$	18.7048	−	13.5265i	0.644229	−	0.465876i
$844$	8.25291	−	2.42327i	0.284077	−	0.0834125i
$845$	−0.412803	+	2.87111i	−0.0142009	+	0.0987691i
$846$	3.25232	−	9.86030i	0.111817	−	0.339004i
$847$	26.0856	−	3.75055i	0.896313	−	0.128870i
$848$	−4.48711	+	2.88369i	−0.154088	+	0.0990264i
$849$	15.5934	−	8.18357i	0.535165	−	0.280859i
$850$			7.02420i			0.240928i
$851$	−27.7450	+	25.7330i	−0.951087	+	0.882117i
$852$	−3.90193	−	1.52915i	−0.133678	−	0.0523879i
$853$	−3.52592	+	4.06913i	−0.120725	+	0.139324i	−0.812895	−	0.582411i	$-0.802110\pi$
$853$	−3.52592	+	4.06913i	−0.120725	+	0.139324i	0.692170	+	0.721735i	$0.256655\pi$
$854$	2.89307	+	4.50171i	0.0989989	+	0.154045i
$855$	−4.48350	−	3.09506i	−0.153332	−	0.105849i
$856$	−13.3446	+	6.09427i	−0.456109	+	0.208298i
$857$	−0.452709	−	0.0650897i	−0.0154642	−	0.00222342i	0.134578	−	0.990903i	$-0.457032\pi$
$857$	−0.452709	−	0.0650897i	−0.0154642	−	0.00222342i	−0.150043	+	0.988680i	$0.547941\pi$
$858$	−1.65547	−	0.145894i	−0.0565166	−	0.00498074i
$859$	8.23626	+	5.29312i	0.281018	+	0.180599i	0.673555	−	0.739137i	$-0.264766\pi$
$859$	8.23626	+	5.29312i	0.281018	+	0.180599i	−0.392538	+	0.919736i	$0.628403\pi$
$860$	10.7868	+	4.92616i	0.367827	+	0.167981i
$861$	−0.489753	+	0.632213i	−0.0166907	+	0.0215458i
$862$	−4.66569	+	4.04284i	−0.158914	+	0.137700i
$863$	−16.7967	+	14.5544i	−0.571765	+	0.495437i	−0.892082	−	0.451873i	$-0.850756\pi$
$863$	−16.7967	+	14.5544i	−0.571765	+	0.495437i	0.320317	+	0.947310i	$0.396211\pi$
$864$	0.851912	+	5.12584i	0.0289826	+	0.174385i
$865$	−11.6969	−	5.34180i	−0.397707	−	0.181627i
$866$	0.506309	+	0.325385i	0.0172051	+	0.0110570i
$867$	−4.91733	+	55.7972i	−0.167001	+	1.89497i
$868$	19.9502	+	2.86841i	0.677155	+	0.0973602i
$869$	−0.756679	+	0.345564i	−0.0256686	+	0.0117224i
$870$	−13.1601	−	3.09108i	−0.446169	−	0.104798i
$871$	6.01318	+	9.35669i	0.203749	+	0.317039i
$872$	5.89988	−	6.80882i	0.199795	−	0.230576i
$873$	17.4919	−	18.8895i	0.592011	−	0.639313i
$874$	−7.16345	+	4.95347i	−0.242307	+	0.167554i
$875$			2.41583i			0.0816699i
$876$	−4.95826	−	9.44775i	−0.167524	−	0.319210i
$877$	42.8460	−	27.5355i	1.44681	−	0.929806i	0.447437	−	0.894316i	$-0.352337\pi$
$877$	42.8460	−	27.5355i	1.44681	−	0.929806i	0.999370	−	0.0354906i	$-0.0112994\pi$
$878$	−5.12479	+	0.736834i	−0.172953	+	0.0248669i
$879$	−25.8570	+	1.42093i	−0.872135	+	0.0479267i
$880$	0.0429677	−	0.298847i	0.00144844	−	0.0100741i
$881$	−32.8894	+	9.65719i	−1.10807	+	0.325359i	−0.784054	−	0.620692i	$-0.786852\pi$
$881$	−32.8894	+	9.65719i	−1.10807	+	0.325359i	−0.324017	+	0.946051i	$0.605034\pi$
$882$	3.38053	−	0.872545i	0.113828	−	0.0293801i
$883$	−21.1047	+	46.2128i	−0.710230	+	1.55519i	0.116880	+	0.993146i	$0.462711\pi$
$883$	−21.1047	+	46.2128i	−0.710230	+	1.55519i	−0.827110	+	0.562040i	$0.810017\pi$
$884$	21.4183	+	6.28899i	0.720377	+	0.211522i
$885$	−2.54471	−	7.18244i	−0.0855396	−	0.241435i
$886$	−23.6505	−	27.2941i	−0.794553	−	0.916964i
$887$	6.31720	−	21.5144i	0.212111	−	0.722383i	−0.782858	−	0.622200i	$-0.786239\pi$
$887$	6.31720	−	21.5144i	0.212111	−	0.722383i	0.994969	−	0.100183i	$-0.0319428\pi$
$888$	−9.50306	−	9.82198i	−0.318902	−	0.329604i
$889$	4.09045	−	6.36486i	0.137189	−	0.213471i
$890$	−3.97349	−	13.5325i	−0.133192	−	0.453609i
$891$	−2.71137	−	0.179230i	−0.0908341	−	0.00600443i
$892$	1.44484	+	3.16377i	0.0483770	+	0.105931i
$893$	0.894466	+	6.22115i	0.0299322	+	0.208183i
$894$	−17.1670	+	3.43880i	−0.574151	+	0.115011i
$895$	10.6504	+	9.22860i	0.356003	+	0.308478i
$896$	−2.41583			−0.0807072
$897$	−23.3843	−	12.2487i	−0.780779	−	0.408972i
$898$	−29.4258			−0.981953
$899$	49.2110	+	42.6416i	1.64128	+	1.42218i
$900$	2.95376	+	0.524697i	0.0984586	+	0.0174899i
$901$	5.33196	+	37.0846i	0.177633	+	1.23547i
$902$	−0.0239709	−	0.0524891i	−0.000798145	−	0.00174769i
$903$	43.1518	+	24.4955i	1.43600	+	0.815160i
$904$	−2.17600	−	7.41077i	−0.0723727	−	0.246479i
$905$	−10.5746	+	16.4543i	−0.351510	+	0.546961i
$906$	17.5962	−	17.0249i	0.584596	−	0.565614i
$907$	−14.9080	+	50.7720i	−0.495012	+	1.68586i	0.210860	+	0.977516i	$0.432374\pi$
$907$	−14.9080	+	50.7720i	−0.495012	+	1.68586i	−0.705872	+	0.708339i	$0.749445\pi$
$908$	−5.05535	−	5.83418i	−0.167768	−	0.193614i
$909$	−52.7132	−	1.74036i	−1.74839	−	0.0577240i
$910$	7.36639	+	2.16297i	0.244194	+	0.0717017i
$911$	−4.42780	+	9.69554i	−0.146700	+	0.321228i	−0.968690	−	0.248274i	$-0.920137\pi$
$911$	−4.42780	+	9.69554i	−0.146700	+	0.321228i	0.821990	+	0.569502i	$0.192864\pi$
$912$	−1.84318	−	2.54881i	−0.0610337	−	0.0843994i
$913$	2.96765	−	0.871380i	0.0982148	−	0.0288385i
$914$	4.83397	−	33.6210i	0.159894	−	1.11208i
$915$	−0.210515	−	3.83081i	−0.00695942	−	0.126643i
$916$	16.5601	−	2.38098i	0.547161	−	0.0786699i
$917$	−4.06209	+	2.61055i	−0.134142	+	0.0862079i
$918$	35.2371	+	9.51375i	1.16300	+	0.314000i
$919$			31.9507i			1.05396i	0.849879	+	0.526978i	$0.176675\pi$
$919$			31.9507i			1.05396i	−0.849879	+	0.526978i	$0.823325\pi$
$920$	2.45502	−	4.11981i	0.0809397	−	0.135826i
$921$	−0.0642718	+	0.164002i	−0.00211783	+	0.00540405i
$922$	6.37454	−	7.35661i	0.209934	−	0.242277i
$923$	4.15718	+	6.46870i	0.136835	+	0.212920i
$924$	0.288875	−	1.22987i	0.00950328	−	0.0404596i
$925$	−7.17744	+	3.27783i	−0.235993	+	0.107774i
$926$	22.1268	+	3.18135i	0.727131	+	0.104546i
$927$	18.0735	−	36.3508i	0.593612	−	1.19392i
$928$	−6.56578	−	4.21957i	−0.215532	−	0.138514i
$929$	24.8584	+	11.3524i	0.815577	+	0.372462i	0.779121	−	0.626873i	$-0.215666\pi$
$929$	24.8584	+	11.3524i	0.815577	+	0.372462i	0.0364564	+	0.999335i	$0.488393\pi$
$930$	−11.4238	−	8.84963i	−0.374602	−	0.290191i
$931$	−1.59722	+	1.38400i	−0.0523469	+	0.0453588i
$932$	−22.2090	+	19.2442i	−0.727481	+	0.630366i
$933$	−17.6588	−	13.6797i	−0.578124	−	0.447852i
$934$	2.47575	+	1.13064i	0.0810089	+	0.0369955i
$935$	−1.78409	−	1.14656i	−0.0583459	−	0.0374966i
$936$	4.24451	−	8.53689i	0.138736	−	0.279037i
$937$	8.48575	+	1.22007i	0.277217	+	0.0398579i	0.279521	−	0.960139i	$-0.409824\pi$
$937$	8.48575	+	1.22007i	0.277217	+	0.0398579i	−0.00230382	+	0.999997i	$0.500733\pi$
$938$	−7.69095	+	3.51234i	−0.251118	+	0.114682i
$939$	−0.547255	+	2.32990i	−0.0178590	+	0.0760335i
$940$	−1.87113	−	2.91153i	−0.0610294	−	0.0949636i
$941$	22.6627	−	26.1542i	0.738783	−	0.852601i	−0.254648	−	0.967034i	$-0.581960\pi$
$941$	22.6627	−	26.1542i	0.738783	−	0.852601i	0.993431	+	0.114433i	$0.0365050\pi$
$942$	−9.68348	+	24.7093i	−0.315505	+	0.805072i
$943$	−0.0309701	−	0.916066i	−0.00100852	−	0.0298312i
$944$		−	4.39935i		−	0.143187i
$945$	12.1191	+	3.27206i	0.394233	+	0.106440i
$946$	−3.01194	+	1.93565i	−0.0979265	+	0.0629335i
$947$	−9.65302	+	1.38790i	−0.313681	+	0.0451005i	−0.297357	−	0.954766i	$-0.596105\pi$
$947$	−9.65302	+	1.38790i	−0.313681	+	0.0451005i	−0.0163236	+	0.999867i	$0.505196\pi$
$948$	−0.261850	−	4.76496i	−0.00850450	−	0.154759i
$949$	−2.78607	+	19.3776i	−0.0904397	+	0.629022i
$950$	−1.74245	+	0.511630i	−0.0565326	+	0.0165995i
$951$	−26.6792	−	36.8929i	−0.865134	−	1.19634i
$952$	−7.04928	+	15.4358i	−0.228469	+	0.500277i
$953$	36.1213	+	10.6062i	1.17008	+	0.343568i	0.808343	−	0.588711i	$-0.200365\pi$
$953$	36.1213	+	10.6062i	1.17008	+	0.343568i	0.361740	+	0.932279i	$0.382183\pi$
$954$	15.9928	+	0.528012i	0.517786	+	0.0170950i
$955$	−13.6067	−	15.7029i	−0.440301	−	0.508134i
$956$	2.56625	−	8.73986i	0.0829986	−	0.282667i
$957$	2.93323	−	2.83799i	0.0948180	−	0.0917392i
$958$	−4.90039	+	7.62515i	−0.158324	+	0.246357i
$959$	−10.9682	−	37.3543i	−0.354182	−	1.20623i
$960$	1.50628	+	0.855055i	0.0486150	+	0.0275968i
$961$	16.0377	+	35.1177i	0.517346	+	1.13283i
$962$	3.56863	+	24.8203i	0.115057	+	0.800240i
$963$	43.3326	+	7.69748i	1.39637	+	0.248048i
$964$	−5.82168	−	5.04452i	−0.187504	−	0.162473i
$965$	−5.78151			−0.186113
$966$	11.7463	−	16.2703i	0.377932	−	0.523489i
$967$	45.3584			1.45863			0.729313	−	0.684180i	$-0.239840\pi$
$967$	45.3584			1.45863			0.729313	+	0.684180i	$0.239840\pi$
$968$	−8.24435	−	7.14377i	−0.264984	−	0.229610i
$969$	−21.6638	+	4.33956i	−0.695940	+	0.139407i
$970$	−1.22128	−	8.49416i	−0.0392128	−	0.272731i
$971$	−4.53379	−	9.92761i	−0.145496	−	0.318592i	0.822827	−	0.568292i	$-0.192395\pi$
$971$	−4.53379	−	9.92761i	−0.145496	−	0.318592i	−0.968323	+	0.249699i	$0.919668\pi$
$972$	6.63280	−	14.1069i	0.212747	−	0.452481i
$973$	−10.9737	−	37.3731i	−0.351801	−	1.19813i
$974$	−11.1302	+	17.3190i	−0.356636	+	0.554936i
$975$	−3.82742	−	3.95587i	−0.122576	−	0.126689i
$976$	0.624053	−	2.12533i	0.0199754	−	0.0680301i
$977$	−13.9113	−	16.0545i	−0.445061	−	0.513628i	0.488247	−	0.872706i	$-0.337637\pi$
$977$	−13.9113	−	16.0545i	−0.445061	−	0.513628i	−0.933308	+	0.359078i	$0.883091\pi$
$978$	−3.19636	−	9.02170i	−0.102208	−	0.288482i
$979$	4.08573	+	1.19968i	0.130580	+	0.0383419i
$980$	0.483449	−	1.05861i	0.0154432	−	0.0338159i
$981$	−26.1704	+	6.75481i	−0.835556	+	0.215664i
$982$	21.1589	−	6.21282i	0.675209	−	0.198259i
$983$	−2.83968	+	19.7504i	−0.0905717	+	0.629940i	0.893085	+	0.449887i	$0.148536\pi$
$983$	−2.83968	+	19.7504i	−0.0905717	+	0.629940i	−0.983657	+	0.180052i	$0.942373\pi$
$984$	0.330534	−	0.0181639i	0.0105371	−	0.000579045i
$985$	4.68205	−	0.673177i	0.149182	−	0.0214492i
$986$	−46.1193	+	29.6391i	−1.46874	+	0.943901i
$987$	−6.72969	−	12.8231i	−0.214208	−	0.408164i
$988$			5.77120i			0.183606i
$989$	−55.9865	+	9.99098i	−1.78027	+	0.317695i
$990$	−0.615412	+	0.664583i	−0.0195591	+	0.0211218i
$991$	10.9841	−	12.6763i	0.348921	−	0.402676i	−0.553977	−	0.832532i	$-0.686890\pi$
$991$	10.9841	−	12.6763i	0.348921	−	0.402676i	0.902897	+	0.429856i	$0.141436\pi$
$992$	−4.51059	−	7.01862i	−0.143212	−	0.222841i
$993$	−33.8726	−	7.95610i	−1.07491	−	0.252479i
$994$	−5.31710	+	2.42824i	−0.168648	+	0.0770191i
$995$	17.5820	+	2.52791i	0.557387	+	0.0801401i
$996$	−1.55767	+	17.6750i	−0.0493568	+	0.560053i
$997$	4.16538	+	2.67693i	0.131919	+	0.0847791i	0.604936	−	0.796274i	$-0.293199\pi$
$997$	4.16538	+	2.67693i	0.131919	+	0.0847791i	−0.473017	+	0.881053i	$0.656835\pi$
$998$	−0.691847	−	0.315956i	−0.0219000	−	0.0100014i
$999$	6.72200	+	40.4454i	0.212675	+	1.27964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.b.191.4	yes	160
3.2	odd	2		690.2.q.a.191.14	✓	160
23.10	odd	22		690.2.q.a.401.14	yes	160
69.56	even	22	inner	690.2.q.b.401.4	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.191.14	✓	160	3.2	odd	2
690.2.q.a.401.14	yes	160	23.10	odd	22
690.2.q.b.191.4	yes	160	1.1	even	1	trivial
690.2.q.b.401.4	yes	160	69.56	even	22	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.755750 - 0.654861i) q^{2} +(-0.340196 - 1.69831i) q^{3} +(0.142315 + 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.855055 + 1.50628i) q^{6} +(0.680617 + 2.31797i) q^{7} +(0.540641 - 0.841254i) q^{8} +(-2.76853 + 1.15552i) q^{9} +O(q^{10})\)	\(q+(-0.755750 - 0.654861i) q^{2} +(-0.340196 - 1.69831i) q^{3} +(0.142315 + 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.855055 + 1.50628i) q^{6} +(0.680617 + 2.31797i) q^{7} +(0.540641 - 0.841254i) q^{8} +(-2.76853 + 1.15552i) q^{9} +(-0.281733 + 0.959493i) q^{10} +(-0.197716 - 0.228176i) q^{11} +(1.63261 - 0.578429i) q^{12} +(-3.04922 - 0.895332i) q^{13} +(1.00357 - 2.19751i) q^{14} +(-1.40352 + 1.01496i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.999648 + 6.95270i) q^{17} +(2.84902 + 0.939720i) q^{18} +(-1.79753 + 0.258446i) q^{19} +(0.841254 - 0.540641i) q^{20} +(3.70510 - 1.94447i) q^{21} +0.301920i q^{22} +(-1.84372 + 4.42727i) q^{23} +(-1.61264 - 0.631986i) q^{24} +(-0.654861 + 0.755750i) q^{25} +(1.71813 + 2.67346i) q^{26} +(2.90428 + 4.30873i) q^{27} +(-2.19751 + 1.00357i) q^{28} +(-7.72531 - 1.11073i) q^{29} +(1.72536 + 0.152054i) q^{30} +(-7.01862 - 4.51059i) q^{31} +(0.909632 + 0.415415i) q^{32} +(-0.320252 + 0.413408i) q^{33} +(5.30854 - 4.59987i) q^{34} +(1.82576 - 1.58203i) q^{35} +(-1.53776 - 2.57591i) q^{36} +(7.17744 + 3.27783i) q^{37} +(1.52773 + 0.981811i) q^{38} +(-0.483220 + 5.48312i) q^{39} +(-0.989821 - 0.142315i) q^{40} +(-0.173851 + 0.0793950i) q^{41} +(-4.07348 - 0.956792i) q^{42} +(6.41114 + 9.97593i) q^{43} +(0.197716 - 0.228176i) q^{44} +(2.20119 + 2.03833i) q^{45} +(4.29264 - 2.13852i) q^{46} -3.46094i q^{47} +(0.804886 + 1.53367i) q^{48} +(0.979029 - 0.629184i) q^{49} +(0.989821 - 0.142315i) q^{50} +(12.1479 - 0.667569i) q^{51} +(0.452269 - 3.14560i) q^{52} +(5.11778 - 1.50272i) q^{53} +(0.626712 - 5.15822i) q^{54} +(-0.125422 + 0.274636i) q^{55} +(2.31797 + 0.680617i) q^{56} +(1.05043 + 2.96485i) q^{57} +(5.11103 + 5.89844i) q^{58} +(-1.23944 + 4.22115i) q^{59} +(-1.20437 - 1.24479i) q^{60} +(-1.19755 + 1.86342i) q^{61} +(2.35051 + 8.00510i) q^{62} +(-4.56277 - 5.63091i) q^{63} +(-0.415415 - 0.909632i) q^{64} +(0.452269 + 3.14560i) q^{65} +(0.512755 - 0.102712i) q^{66} +(-2.64500 - 2.29191i) q^{67} -7.02420 q^{68} +(8.14611 + 1.62508i) q^{69} -2.41583 q^{70} +(-1.82861 - 1.58450i) q^{71} +(-0.524697 + 2.95376i) q^{72} +(-0.876688 - 6.09750i) q^{73} +(-3.27783 - 7.17744i) q^{74} +(1.50628 + 0.855055i) q^{75} +(-0.511630 - 1.74245i) q^{76} +(0.394337 - 0.613600i) q^{77} +(3.95587 - 3.82742i) q^{78} +(0.776230 - 2.64360i) q^{79} +(0.654861 + 0.755750i) q^{80} +(6.32955 - 6.39819i) q^{81} +(0.183380 + 0.0538453i) q^{82} +(-4.25560 + 9.31846i) q^{83} +(2.45196 + 3.39066i) q^{84} +(6.73967 - 1.97895i) q^{85} +(1.68763 - 11.7377i) q^{86} +(0.741752 + 13.4979i) q^{87} +(-0.298847 + 0.0429677i) q^{88} +(-11.8648 + 7.62507i) q^{89} +(-0.328727 - 2.98194i) q^{90} -7.67738i q^{91} +(-4.64459 - 1.19489i) q^{92} +(-5.27269 + 13.4543i) q^{93} +(-2.26644 + 2.61561i) q^{94} +(0.981811 + 1.52773i) q^{95} +(0.396051 - 1.68616i) q^{96} +(-7.80601 + 3.56489i) q^{97} +(-1.15193 - 0.165622i) q^{98} +(0.811044 + 0.403249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9	\( 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9} + 12 q^{11} + 12 q^{14} - 16 q^{16} - 8 q^{18} - 16 q^{20} + 70 q^{21} - 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} + 2 q^{30} - 4 q^{31} - 16 q^{33} + 2 q^{36} - 72 q^{38} + 140 q^{39} - 44 q^{41} + 44 q^{43} - 12 q^{44} + 2 q^{45} + 4 q^{46} + 70 q^{49} + 2 q^{51} + 52 q^{53} - 62 q^{54} + 10 q^{55} + 54 q^{56} - 94 q^{57} - 36 q^{58} - 44 q^{61} + 16 q^{64} - 54 q^{66} - 44 q^{67} - 30 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} + 24 q^{74} + 88 q^{77} - 54 q^{78} - 44 q^{79} + 16 q^{80} - 66 q^{81} - 28 q^{82} - 4 q^{83} - 4 q^{84} - 158 q^{86} + 156 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} + 88 q^{98} - 58 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9 + 12 * q^11 + 12 * q^14 - 16 * q^16 - 8 * q^18 - 16 * q^20 + 70 * q^21 - 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 + 2 * q^30 - 4 * q^31 - 16 * q^33 + 2 * q^36 - 72 * q^38 + 140 * q^39 - 44 * q^41 + 44 * q^43 - 12 * q^44 + 2 * q^45 + 4 * q^46 + 70 * q^49 + 2 * q^51 + 52 * q^53 - 62 * q^54 + 10 * q^55 + 54 * q^56 - 94 * q^57 - 36 * q^58 - 44 * q^61 + 16 * q^64 - 54 * q^66 - 44 * q^67 - 30 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 + 24 * q^74 + 88 * q^77 - 54 * q^78 - 44 * q^79 + 16 * q^80 - 66 * q^81 - 28 * q^82 - 4 * q^83 - 4 * q^84 - 158 * q^86 + 156 * q^87 - 80 * q^89 + 8 * q^90 + 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 + 88 * q^98 - 58 * q^99

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