LMFDB - Embedded newform 690.2.w.a.217.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.1
Character	$\chi$	$=$	690.217
Dual form			690.2.w.a.283.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0713392 + 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-2.18304 - 0.484099i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-4.31814 + 2.35788i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.0713392 + 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-2.18304 - 0.484099i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-4.31814 + 2.35788i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(0.638602 - 2.14294i) q^{10} +(0.567261 + 0.491535i) q^{11} +(0.997452 - 0.0713392i) q^{12} +(3.03681 - 5.56150i) q^{13} +(-2.04382 - 4.47535i) q^{14} +(2.23605 + 0.00899852i) q^{15} +(0.959493 + 0.281733i) q^{16} +(1.12074 + 0.838978i) q^{17} +(0.349464 + 0.936950i) q^{18} +(-0.534494 + 3.71749i) q^{19} +(2.09192 + 0.789850i) q^{20} +(3.71825 - 3.22189i) q^{21} +(-0.530750 + 0.530750i) q^{22} +(-4.38521 - 1.94164i) q^{23} +1.00000i q^{24} +(4.53130 + 2.11361i) q^{25} +(5.33069 + 3.42583i) q^{26} +(-0.800541 + 0.599278i) q^{27} +(4.60975 - 1.71935i) q^{28} +(6.83863 - 0.983246i) q^{29} +(-0.168494 + 2.22971i) q^{30} +(6.38294 - 4.10207i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(-0.658781 - 0.359721i) q^{33} +(-0.916793 + 1.05804i) q^{34} +(10.5681 - 3.05694i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(3.61778 + 1.34936i) q^{37} +(-3.66989 - 0.798335i) q^{38} +(-1.78523 + 6.07993i) q^{39} +(-0.937074 + 2.03024i) q^{40} +(-0.469073 + 1.02713i) q^{41} +(2.94842 + 3.93863i) q^{42} +(0.555199 + 2.55221i) q^{43} +(-0.491535 - 0.567261i) q^{44} +(-2.18686 + 0.466514i) q^{45} +(2.24953 - 4.23552i) q^{46} +(-8.63275 - 8.63275i) q^{47} +(-0.997452 - 0.0713392i) q^{48} +(9.30224 - 14.4746i) q^{49} +(-2.43149 + 4.36897i) q^{50} +(-1.27347 - 0.581573i) q^{51} +(-3.79739 + 5.07271i) q^{52} +(-5.03848 - 9.22729i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-1.00040 - 1.34765i) q^{55} +(1.38611 + 4.72066i) q^{56} +(-0.267930 - 3.74615i) q^{57} +(0.492879 + 6.89135i) q^{58} +(-1.73187 - 5.89822i) q^{59} +(-2.21201 - 0.327130i) q^{60} +(-0.0184279 - 0.0286744i) q^{61} +(3.63626 + 6.65932i) q^{62} +(-2.94842 + 3.93863i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-9.32179 + 10.6708i) q^{65} +(0.405802 - 0.631440i) q^{66} +(7.55814 + 0.540569i) q^{67} +(-0.989936 - 0.989936i) q^{68} +(4.69772 + 0.965123i) q^{69} +(2.29523 + 10.7593i) q^{70} +(2.93682 + 3.38928i) q^{71} +(-0.212565 - 0.977147i) q^{72} +(5.79995 + 7.74782i) q^{73} +(-1.60401 + 3.51230i) q^{74} +(-4.87702 - 1.10211i) q^{75} +(1.05811 - 3.60358i) q^{76} +(-3.60850 - 0.784980i) q^{77} +(-5.93708 - 2.21442i) q^{78} +(11.4802 - 3.37088i) q^{79} +(-1.95822 - 1.07952i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-0.991045 - 0.541152i) q^{82} +(-0.141720 + 0.379967i) q^{83} +(-4.13893 + 2.65993i) q^{84} +(-2.04047 - 2.37407i) q^{85} +(-2.58531 + 0.371712i) q^{86} +(-6.47334 + 2.41443i) q^{87} +(0.600882 - 0.449814i) q^{88} +(-10.9546 - 7.04011i) q^{89} +(-0.309316 - 2.21457i) q^{90} +31.1758i q^{91} +(4.06425 + 2.54596i) q^{92} +(-5.36512 + 5.36512i) q^{93} +(9.22661 - 7.99490i) q^{94} +(2.96646 - 7.85667i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-1.10685 - 2.96757i) q^{97} +(13.7741 + 10.3111i) q^{98} +(0.720190 + 0.211467i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.0713392	+	0.997452i	−0.0504444	+	0.705305i
$2$	−0.0713392	+	0.997452i	−0.0504444	+	0.705305i
$3$	−0.977147	+	0.212565i	−0.564156	+	0.122725i
$3$	−0.977147	+	0.212565i	−0.564156	+	0.122725i
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	−2.18304	−	0.484099i	−0.976284	−	0.216496i
$5$	−2.18304	−	0.484099i	−0.976284	−	0.216496i
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	−4.31814	+	2.35788i	−1.63210	+	0.891196i	−0.639638	+	0.768676i	$0.720916\pi$
$7$	−4.31814	+	2.35788i	−1.63210	+	0.891196i	−0.992466	+	0.122520i	$0.960902\pi$
$8$	0.212565	−	0.977147i	0.0751532	−	0.345474i
$9$	0.909632	−	0.415415i	0.303211	−	0.138472i
$10$	0.638602	−	2.14294i	0.201944	−	0.677657i
$11$	0.567261	+	0.491535i	0.171036	+	0.148203i	0.736173	−	0.676794i	$-0.236631\pi$
$11$	0.567261	+	0.491535i	0.171036	+	0.148203i	−0.565137	+	0.824997i	$0.691177\pi$
$12$	0.997452	−	0.0713392i	0.287940	−	0.0205938i
$13$	3.03681	−	5.56150i	0.842260	−	1.54248i	0.00219532	−	0.999998i	$-0.499301\pi$
$13$	3.03681	−	5.56150i	0.842260	−	1.54248i	0.840065	−	0.542486i	$-0.182517\pi$
$14$	−2.04382	−	4.47535i	−0.546235	−	1.19609i
$15$	2.23605	+	0.00899852i	0.577346	+	0.00232341i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	1.12074	+	0.838978i	0.271820	+	0.203482i	0.726488	−	0.687179i	$-0.241151\pi$
$17$	1.12074	+	0.838978i	0.271820	+	0.203482i	−0.454668	+	0.890661i	$0.650242\pi$
$18$	0.349464	+	0.936950i	0.0823695	+	0.220841i
$19$	−0.534494	+	3.71749i	−0.122621	+	0.852851i	0.831946	+	0.554856i	$0.187227\pi$
$19$	−0.534494	+	3.71749i	−0.122621	+	0.852851i	−0.954568	+	0.297994i	$0.903682\pi$
$20$	2.09192	+	0.789850i	0.467768	+	0.176616i
$21$	3.71825	−	3.22189i	0.811390	−	0.703073i
$22$	−0.530750	+	0.530750i	−0.113156	+	0.113156i
$23$	−4.38521	−	1.94164i	−0.914379	−	0.404860i
$23$	−4.38521	−	1.94164i	−0.914379	−	0.404860i
$24$			1.00000i			0.204124i
$25$	4.53130	+	2.11361i	0.906259	+	0.422723i
$26$	5.33069	+	3.42583i	1.04543	+	0.671860i
$27$	−0.800541	+	0.599278i	−0.154064	+	0.115331i
$28$	4.60975	−	1.71935i	0.871161	−	0.324926i
$29$	6.83863	−	0.983246i	1.26990	−	0.182584i	0.525775	−	0.850623i	$-0.323775\pi$
$29$	6.83863	−	0.983246i	1.26990	−	0.182584i	0.744126	+	0.668039i	$0.232866\pi$
$30$	−0.168494	+	2.22971i	−0.0307626	+	0.407088i
$31$	6.38294	−	4.10207i	1.14641	−	0.736753i	0.177489	−	0.984123i	$-0.443202\pi$
$31$	6.38294	−	4.10207i	1.14641	−	0.736753i	0.968921	+	0.247369i	$0.0795661\pi$
$32$	−0.349464	+	0.936950i	−0.0617771	+	0.165631i
$33$	−0.658781	−	0.359721i	−0.114679	−	0.0626195i
$34$	−0.916793	+	1.05804i	−0.157229	+	0.181452i
$35$	10.5681	−	3.05694i	1.78634	−	0.516716i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	3.61778	+	1.34936i	0.594759	+	0.221834i	0.628775	−	0.777587i	$-0.283557\pi$
$37$	3.61778	+	1.34936i	0.594759	+	0.221834i	−0.0340153	+	0.999421i	$0.510829\pi$
$38$	−3.66989	−	0.798335i	−0.595334	−	0.129507i
$39$	−1.78523	+	6.07993i	−0.285865	+	0.973568i
$40$	−0.937074	+	2.03024i	−0.148164	+	0.321010i
$41$	−0.469073	+	1.02713i	−0.0732568	+	0.160410i	−0.942718	−	0.333592i	$-0.891739\pi$
$41$	−0.469073	+	1.02713i	−0.0732568	+	0.160410i	0.869461	+	0.494002i	$0.164466\pi$
$42$	2.94842	+	3.93863i	0.454951	+	0.607743i
$43$	0.555199	+	2.55221i	0.0846670	+	0.389208i	0.999906	−	0.0137032i	$-0.00436201\pi$
$43$	0.555199	+	2.55221i	0.0846670	+	0.389208i	−0.915239	+	0.402911i	$0.867998\pi$
$44$	−0.491535	−	0.567261i	−0.0741016	−	0.0855178i
$45$	−2.18686	+	0.466514i	−0.325998	+	0.0695438i
$46$	2.24953	−	4.23552i	0.331675	−	0.624493i
$47$	−8.63275	−	8.63275i	−1.25922	−	1.25922i	−0.951468	−	0.307748i	$-0.900425\pi$
$47$	−8.63275	−	8.63275i	−1.25922	−	1.25922i	−0.307748	−	0.951468i	$-0.599575\pi$
$48$	−0.997452	−	0.0713392i	−0.143970	−	0.0102969i
$49$	9.30224	−	14.4746i	1.32889	−	2.06780i
$50$	−2.43149	+	4.36897i	−0.343864	+	0.617865i
$51$	−1.27347	−	0.581573i	−0.178321	−	0.0814366i
$52$	−3.79739	+	5.07271i	−0.526603	+	0.703459i
$53$	−5.03848	−	9.22729i	−0.692088	−	1.26747i	−0.953254	−	0.302171i	$-0.902289\pi$
$53$	−5.03848	−	9.22729i	−0.692088	−	1.26747i	0.261165	−	0.965294i	$-0.415893\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	−1.00040	−	1.34765i	−0.134894	−	0.181717i
$56$	1.38611	+	4.72066i	0.185227	+	0.630825i
$57$	−0.267930	−	3.74615i	−0.0354882	−	0.496189i
$58$	0.492879	+	6.89135i	0.0647182	+	0.904878i
$59$	−1.73187	−	5.89822i	−0.225471	−	0.767883i	−0.992062	−	0.125748i	$-0.959867\pi$
$59$	−1.73187	−	5.89822i	−0.225471	−	0.767883i	0.766591	−	0.642135i	$-0.221951\pi$
$60$	−2.21201	−	0.327130i	−0.285569	−	0.0422323i
$61$	−0.0184279	−	0.0286744i	−0.00235946	−	0.00367138i	0.840072	−	0.542475i	$-0.182513\pi$
$61$	−0.0184279	−	0.0286744i	−0.00235946	−	0.00367138i	−0.842431	+	0.538804i	$0.818876\pi$
$62$	3.63626	+	6.65932i	0.461806	+	0.845734i
$63$	−2.94842	+	3.93863i	−0.371466	+	0.496220i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	−9.32179	+	10.6708i	−1.15623	+	1.32356i
$66$	0.405802	−	0.631440i	0.0499507	−	0.0777249i
$67$	7.55814	+	0.540569i	0.923374	+	0.0660410i	0.524924	−	0.851149i	$-0.324094\pi$
$67$	7.55814	+	0.540569i	0.923374	+	0.0660410i	0.398450	+	0.917190i	$0.369548\pi$
$68$	−0.989936	−	0.989936i	−0.120047	−	0.120047i
$69$	4.69772	+	0.965123i	0.565539	+	0.116187i
$70$	2.29523	+	10.7593i	0.274332	+	1.28598i
$71$	2.93682	+	3.38928i	0.348537	+	0.402233i	0.902767	−	0.430131i	$-0.141533\pi$
$71$	2.93682	+	3.38928i	0.348537	+	0.402233i	−0.554230	+	0.832364i	$0.686987\pi$
$72$	−0.212565	−	0.977147i	−0.0250511	−	0.115158i
$73$	5.79995	+	7.74782i	0.678832	+	0.906814i	0.999180	−	0.0404861i	$-0.0128907\pi$
$73$	5.79995	+	7.74782i	0.678832	+	0.906814i	−0.320348	+	0.947300i	$0.603800\pi$
$74$	−1.60401	+	3.51230i	−0.186463	+	0.408297i
$75$	−4.87702	−	1.10211i	−0.563150	−	0.127261i
$76$	1.05811	−	3.60358i	0.121373	−	0.413359i
$77$	−3.60850	−	0.784980i	−0.411226	−	0.0894568i
$78$	−5.93708	−	2.21442i	−0.672242	−	0.250733i
$79$	11.4802	−	3.37088i	1.29162	−	0.379254i	0.437448	−	0.899244i	$-0.355882\pi$
$79$	11.4802	−	3.37088i	1.29162	−	0.379254i	0.854173	+	0.519989i	$0.174064\pi$
$80$	−1.95822	−	1.07952i	−0.218936	−	0.120694i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−0.991045	−	0.541152i	−0.109443	−	0.0597602i
$83$	−0.141720	+	0.379967i	−0.0155558	+	0.0417068i	−0.944496	−	0.328524i	$-0.893449\pi$
$83$	−0.141720	+	0.379967i	−0.0155558	+	0.0417068i	0.928940	+	0.370231i	$0.120721\pi$
$84$	−4.13893	+	2.65993i	−0.451594	+	0.290222i
$85$	−2.04047	−	2.37407i	−0.221320	−	0.257504i
$86$	−2.58531	+	0.371712i	−0.278781	+	0.0400827i
$87$	−6.47334	+	2.41443i	−0.694015	+	0.258854i
$88$	0.600882	−	0.449814i	0.0640542	−	0.0479504i
$89$	−10.9546	−	7.04011i	−1.16119	−	0.746250i	−0.189352	−	0.981909i	$-0.560639\pi$
$89$	−10.9546	−	7.04011i	−1.16119	−	0.746250i	−0.971836	+	0.235659i	$0.924275\pi$
$90$	−0.309316	−	2.21457i	−0.0326048	−	0.233436i
$91$			31.1758i			3.26811i
$92$	4.06425	+	2.54596i	0.423727	+	0.265434i
$93$	−5.36512	+	5.36512i	−0.556337	+	0.556337i
$94$	9.22661	−	7.99490i	0.951652	−	0.824611i
$95$	2.96646	−	7.85667i	0.304352	−	0.806077i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	−1.10685	−	2.96757i	−0.112383	−	0.301311i	0.868567	−	0.495572i	$-0.165042\pi$
$97$	−1.10685	−	2.96757i	−0.112383	−	0.301311i	−0.980950	+	0.194262i	$0.937769\pi$
$98$	13.7741	+	10.3111i	1.39139	+	1.04158i
$99$	0.720190	+	0.211467i	0.0723818	+	0.0212532i
$100$	−4.18437	−	2.73697i	−0.418437	−	0.273697i
$101$	1.39059	+	3.04497i	0.138369	+	0.302986i	0.966113	−	0.258120i	$-0.0831031\pi$
$101$	1.39059	+	3.04497i	0.138369	+	0.302986i	−0.827744	+	0.561106i	$0.810376\pi$
$102$	0.670940	−	1.22873i	0.0664329	−	0.121663i
$103$	−12.6314	+	0.903417i	−1.24461	+	0.0890163i	−0.678057	−	0.735009i	$-0.737178\pi$
$103$	−12.6314	+	0.903417i	−1.24461	+	0.0890163i	−0.566553	+	0.824025i	$0.691723\pi$
$104$	−4.78889	−	4.14959i	−0.469589	−	0.406901i
$105$	−9.67680	+	5.23349i	−0.944359	+	0.510736i
$106$	9.56322	−	4.36737i	0.928862	−	0.424197i
$107$	2.78010	−	12.7799i	0.268763	−	1.23548i	−0.622726	−	0.782440i	$-0.713975\pi$
$107$	2.78010	−	12.7799i	0.268763	−	1.23548i	0.891489	−	0.453043i	$-0.149661\pi$
$108$	0.877679	−	0.479249i	0.0844547	−	0.0461158i
$109$	−0.234240	−	1.62918i	−0.0224361	−	0.156047i	0.975523	−	0.219895i	$-0.0705716\pi$
$109$	−0.234240	−	1.62918i	−0.0224361	−	0.156047i	−0.997960	+	0.0638487i	$0.979663\pi$
$110$	1.41558	−	0.901711i	0.134971	−	0.0859748i
$111$	−3.82193	−	0.549511i	−0.362762	−	0.0521572i
$112$	−4.80752	+	1.04581i	−0.454268	+	0.0988199i
$113$	−0.354705	+	4.95942i	−0.0333678	+	0.466543i	0.953107	+	0.302632i	$0.0978655\pi$
$113$	−0.354705	+	4.95942i	−0.0333678	+	0.466543i	−0.986475	+	0.163911i	$0.947589\pi$
$114$	3.75572			0.351755
$115$	8.63312	+	6.36154i	0.805043	+	0.593217i
$116$	−6.90895			−0.641480
$117$	0.452048	−	6.32046i	0.0417919	−	0.584327i
$118$	6.00675	−	1.30669i	0.552966	−	0.120290i
$119$	−6.81774	−	0.980243i	−0.624981	−	0.0898587i
$120$	0.484099	−	2.18304i	0.0441920	−	0.199283i
$121$	−1.48528	−	10.3304i	−0.135026	−	0.939125i
$122$	0.0299160	−	0.0163354i	0.00270847	−	0.00147894i
$123$	0.240022	−	1.10336i	0.0216420	−	0.0994867i
$124$	−6.90176	+	3.15193i	−0.619796	+	0.283051i
$125$	−8.86878	−	6.80769i	−0.793248	−	0.608899i
$126$	−3.71825	−	3.22189i	−0.331248	−	0.287028i
$127$	11.1701	−	0.798904i	0.991190	−	0.0708913i	0.433685	−	0.901065i	$-0.357213\pi$
$127$	11.1701	−	0.798904i	0.991190	−	0.0708913i	0.557505	+	0.830173i	$0.311759\pi$
$128$	0.479249	−	0.877679i	0.0423600	−	0.0775766i
$129$	−1.08502	−	2.37586i	−0.0955308	−	0.209183i
$130$	−9.97865	−	10.0593i	−0.875186	−	0.882258i
$131$	−0.777663	−	0.228343i	−0.0679448	−	0.0199504i	0.247584	−	0.968867i	$-0.420364\pi$
$131$	−0.777663	−	0.228343i	−0.0679448	−	0.0199504i	−0.315528	+	0.948916i	$0.602182\pi$
$132$	0.600882	+	0.449814i	0.0523000	+	0.0391513i
$133$	−6.45739	−	17.3129i	−0.559926	−	1.50122i
$134$	−1.07838	+	7.50032i	−0.0931581	+	0.647929i
$135$	2.03772	−	0.920703i	0.175379	−	0.0792415i
$136$	1.05804	−	0.916793i	0.0907258	−	0.0786143i
$137$	5.44313	−	5.44313i	0.465038	−	0.465038i	−0.435265	−	0.900302i	$-0.643345\pi$
$137$	5.44313	−	5.44313i	0.465038	−	0.465038i	0.900302	+	0.435265i	$0.143345\pi$
$138$	−1.29780	+	4.61690i	−0.110476	+	0.393016i
$139$			0.149384i			0.0126706i	0.999980	+	0.00633530i	$0.00201660\pi$
$139$			0.149384i			0.0126706i	−0.999980	+	0.00633530i	$0.997983\pi$
$140$	−10.8956	+	1.52182i	−0.920845	+	0.128617i
$141$	10.2705	+	6.60044i	0.864931	+	0.555858i
$142$	−3.59015	+	2.68755i	−0.301279	+	0.225535i
$143$	4.45634	−	1.66213i	0.372658	−	0.138994i
$144$	0.989821	−	0.142315i	0.0824851	−	0.0118596i
$145$	−15.4050	−	1.16411i	−1.27931	−	0.0966744i
$146$	−8.14184	+	5.23245i	−0.673824	+	0.433040i
$147$	−6.01287	+	16.1211i	−0.495933	+	1.32965i
$148$	−3.38892	−	1.85049i	−0.278568	−	0.152109i
$149$	−8.99761	+	10.3838i	−0.737113	+	0.850674i	−0.993253	−	0.115966i	$-0.963004\pi$
$149$	−8.99761	+	10.3838i	−0.737113	+	0.850674i	0.256140	+	0.966640i	$0.417549\pi$
$150$	1.44723	−	4.78597i	0.118166	−	0.390773i
$151$	−18.4094	+	5.40549i	−1.49814	+	0.439892i	−0.925127	−	0.379657i	$-0.876042\pi$
$151$	−18.4094	+	5.40549i	−1.49814	+	0.439892i	−0.573008	+	0.819550i	$0.694224\pi$
$152$	3.51892	+	1.31249i	0.285422	+	0.106457i
$153$	1.36799	+	0.297587i	0.110595	+	0.0240585i
$154$	1.04041	−	3.54330i	0.0838384	−	0.285527i
$155$	−15.9200	+	5.86499i	−1.27873	+	0.471087i
$156$	2.63232	−	5.76398i	0.210754	−	0.461488i
$157$	2.78397	+	3.71894i	0.222185	+	0.296804i	0.897758	−	0.440489i	$-0.145195\pi$
$157$	2.78397	+	3.71894i	0.222185	+	0.296804i	−0.675573	+	0.737293i	$0.736104\pi$
$158$	2.54331	+	11.6914i	0.202335	+	0.930118i
$159$	6.88473	+	7.94541i	0.545995	+	0.630112i
$160$	1.21647	−	1.87622i	0.0961704	−	0.148328i
$161$	23.5141	−	1.95554i	1.85317	−	0.154118i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−11.4600	−	0.819633i	−0.897614	−	0.0641986i	−0.385097	−	0.922876i	$-0.625832\pi$
$163$	−11.4600	−	0.819633i	−0.897614	−	0.0641986i	−0.512516	+	0.858677i	$0.671287\pi$
$164$	0.610473	−	0.949915i	0.0476700	−	0.0741759i
$165$	1.26400	+	1.10420i	0.0984024	+	0.0859619i
$166$	−0.368889	−	0.168466i	−0.0286313	−	0.0130755i
$167$	8.99282	−	12.0130i	0.695886	−	0.929594i	−0.303847	−	0.952721i	$-0.598271\pi$
$167$	8.99282	−	12.0130i	0.695886	−	0.929594i	0.999733	+	0.0231265i	$0.00736207\pi$
$168$	−2.35788	−	4.31814i	−0.181915	−	0.333152i
$169$	−14.6798	−	22.8422i	−1.12921	−	1.75709i
$170$	2.51359	−	1.86591i	0.192783	−	0.143109i
$171$	1.05811	+	3.60358i	0.0809155	+	0.275573i
$172$	−0.186331	−	2.60524i	−0.0142076	−	0.198648i
$173$	0.525534	+	7.34793i	0.0399556	+	0.558653i	0.977520	+	0.210842i	$0.0676204\pi$
$173$	0.525534	+	7.34793i	0.0399556	+	0.558653i	−0.937565	+	0.347811i	$0.886925\pi$
$174$	−1.94648	−	6.62909i	−0.147562	−	0.502550i
$175$	−24.5504	+	1.55739i	−1.85584	+	0.117727i
$176$	0.405802	+	0.631440i	0.0305885	+	0.0475966i
$177$	2.94605	+	5.39529i	0.221439	+	0.405535i
$178$	7.80367	−	10.4245i	0.584910	−	0.781348i
$179$	14.4095	+	6.58058i	1.07701	+	0.491856i	0.873304	−	0.487175i	$-0.161973\pi$
$179$	14.4095	+	6.58058i	1.07701	+	0.491856i	0.203710	+	0.979031i	$0.434700\pi$
$180$	2.23099	−	0.150542i	0.166289	−	0.0112208i
$181$	13.4906	−	20.9918i	1.00275	−	1.56031i	0.186626	−	0.982431i	$-0.440245\pi$
$181$	13.4906	−	20.9918i	1.00275	−	1.56031i	0.816123	−	0.577878i	$-0.196119\pi$
$182$	−31.0964	−	2.22406i	−2.30502	−	0.164858i
$183$	0.0241020	+	0.0241020i	0.00178167	+	0.00178167i
$184$	−2.82941	+	3.87227i	−0.208587	+	0.285467i
$185$	−7.24452	−	4.69707i	−0.532628	−	0.345336i
$186$	−4.96870	−	5.73419i	−0.364323	−	0.420451i
$187$	0.223367	+	1.02680i	0.0163342	+	0.0750873i
$188$	7.31631	+	9.77345i	0.533597	+	0.712802i
$189$	2.04382	−	4.47535i	0.148666	−	0.325534i
$190$	7.62502	+	3.51939i	0.553177	+	0.255323i
$191$	4.29162	−	14.6159i	0.310530	−	1.05757i	−0.645368	−	0.763872i	$-0.723296\pi$
$191$	4.29162	−	14.6159i	0.310530	−	1.05757i	0.955898	−	0.293698i	$-0.0948859\pi$
$192$	0.977147	+	0.212565i	0.0705195	+	0.0153406i
$193$	10.0915	+	3.76392i	0.726400	+	0.270933i	0.685340	−	0.728223i	$-0.259654\pi$
$193$	10.0915	+	3.76392i	0.726400	+	0.270933i	0.0410603	+	0.999157i	$0.486926\pi$
$194$	3.03897	−	0.892321i	0.218185	−	0.0640649i
$195$	6.84051	−	12.4085i	0.489859	−	0.888589i
$196$	−11.2675	+	13.0034i	−0.804822	+	0.928814i
$197$	14.3810	+	7.85260i	1.02460	+	0.559475i	0.901436	−	0.432911i	$-0.142514\pi$
$197$	14.3810	+	7.85260i	1.02460	+	0.559475i	0.123165	+	0.992386i	$0.460696\pi$
$198$	−0.262306	+	0.703269i	−0.0186413	+	0.0499791i
$199$	20.5702	−	13.2196i	1.45818	−	0.937116i	0.459376	−	0.888242i	$-0.348073\pi$
$199$	20.5702	−	13.2196i	1.45818	−	0.937116i	0.998805	−	0.0488743i	$-0.0155634\pi$
$200$	3.02851	−	3.97846i	0.214148	−	0.281320i
$201$	−7.50032	+	1.07838i	−0.529032	+	0.0760633i
$202$	−3.13642	+	1.16982i	−0.220678	+	0.0823085i
$203$	−27.2118	+	20.3705i	−1.90989	+	1.42973i
$204$	1.17774	+	0.756887i	0.0824582	+	0.0529927i
$205$	1.52123	−	2.01517i	0.106248	−	0.140746i
$206$		−	12.6637i		−	0.882320i
$207$	−4.79551	+	0.0555044i	−0.333311	+	0.00385782i
$208$	4.48066	−	4.48066i	0.310678	−	0.310678i
$209$	−2.13047	+	1.84607i	−0.147368	+	0.127695i
$210$	−4.52982	−	10.0255i	−0.312587	−	0.691825i
$211$	−0.683538	+	4.75411i	−0.0470567	+	0.327287i	0.952672	+	0.304000i	$0.0983222\pi$
$211$	−0.683538	+	4.75411i	−0.0470567	+	0.327287i	−0.999729	+	0.0232869i	$0.992587\pi$
$212$	3.67402	+	9.85042i	0.252332	+	0.676529i
$213$	−3.59015	−	2.68755i	−0.245993	−	0.184148i
$214$	12.5490	+	3.68473i	0.857835	+	0.251883i
$215$	0.0235032	−	5.84033i	0.00160291	−	0.398307i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	−17.8903	+	32.7635i	−1.21447	+	2.22413i
$218$	1.64173	−	0.117419i	0.111192	−	0.00795263i
$219$	−7.31432	−	6.33789i	−0.494256	−	0.428275i
$220$	0.798427	+	1.47630i	0.0538299	+	0.0995324i
$221$	8.06946	−	3.68520i	0.542811	−	0.247893i
$222$	0.820764	−	3.77299i	0.0550861	−	0.253227i
$223$	10.1606	−	5.54810i	0.680403	−	0.371528i	−0.101580	−	0.994827i	$-0.532390\pi$
$223$	10.1606	−	5.54810i	0.680403	−	0.371528i	0.781984	+	0.623299i	$0.214208\pi$
$224$	−0.700183	−	4.86988i	−0.0467829	−	0.325382i
$225$	4.99984	+	0.0402423i	0.333323	+	0.00268282i
$226$	−4.92148	−	0.707602i	−0.327372	−	0.0470690i
$227$	−10.1169	+	2.20080i	−0.671482	+	0.146072i	−0.535365	−	0.844621i	$-0.679826\pi$
$227$	−10.1169	+	2.20080i	−0.671482	+	0.146072i	−0.136117	+	0.990693i	$0.543462\pi$
$228$	−0.267930	+	3.74615i	−0.0177441	+	0.248095i
$229$	21.3745			1.41247			0.706234	−	0.707978i	$-0.250393\pi$
$229$	21.3745			1.41247			0.706234	+	0.707978i	$0.250393\pi$
$230$	−6.96121	+	8.15730i	−0.459009	+	0.537876i
$231$	3.69289			0.242974
$232$	0.492879	−	6.89135i	0.0323591	−	0.452439i
$233$	−17.2722	+	3.75734i	−1.13154	+	0.246152i	−0.739081	−	0.673617i	$-0.764740\pi$
$233$	−17.2722	+	3.75734i	−1.13154	+	0.246152i	−0.392461	+	0.919769i	$0.628376\pi$
$234$	6.27211	+	0.901793i	0.410020	+	0.0589520i
$235$	14.6665	+	23.0247i	0.956737	+	1.50197i
$236$	0.874842	+	6.08466i	0.0569474	+	0.396078i
$237$	−10.5013	+	5.73414i	−0.682132	+	0.372472i
$238$	1.46412	−	6.73044i	0.0949046	−	0.436269i
$239$	13.0099	−	5.94141i	0.841539	−	0.384318i	0.0524698	−	0.998623i	$-0.483291\pi$
$239$	13.0099	−	5.94141i	0.841539	−	0.384318i	0.789069	+	0.614305i	$0.210563\pi$
$240$	2.14294	+	0.638602i	0.138326	+	0.0412216i
$241$	−13.1576	−	11.4011i	−0.847553	−	0.734409i	0.118444	−	0.992961i	$-0.462209\pi$
$241$	−13.1576	−	11.4011i	−0.847553	−	0.734409i	−0.965997	+	0.258551i	$0.916755\pi$
$242$	10.4100	−	0.744539i	0.669181	−	0.0478608i
$243$	−0.479249	+	0.877679i	−0.0307438	+	0.0563031i
$244$	0.0141596	+	0.0310051i	0.000906473	+	0.00198490i
$245$	−27.3143	+	27.0953i	−1.74504	+	1.73106i
$246$	1.08343	+	0.318123i	0.0690768	+	0.0202828i
$247$	19.0517	+	14.2619i	1.21223	+	0.907463i
$248$	−2.65153	−	7.10903i	−0.168372	−	0.451424i
$249$	0.0577138	−	0.401408i	0.00365746	−	0.0254382i
$250$	7.42304	−	8.36053i	0.469474	−	0.528766i
$251$	−11.8975	+	10.3093i	−0.750965	+	0.650715i	−0.943800	−	0.330516i	$-0.892777\pi$
$251$	−11.8975	+	10.3093i	−0.750965	+	0.650715i	0.192835	+	0.981231i	$0.438232\pi$
$252$	3.47893	−	3.47893i	0.219152	−	0.219152i
$253$	−1.53318	−	3.25690i	−0.0963899	−	0.204759i
$254$			11.1987i			0.702667i
$255$	2.49849	+	1.88608i	0.156461	+	0.118111i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	3.81487	−	2.85577i	0.237965	−	0.178138i	−0.473639	−	0.880719i	$-0.657060\pi$
$257$	3.81487	−	2.85577i	0.237965	−	0.178138i	0.711604	+	0.702581i	$0.247969\pi$
$258$	2.44722	−	0.912764i	0.152357	−	0.0568262i
$259$	−18.8037	+	2.70357i	−1.16841	+	0.167992i
$260$	10.7455	−	9.23561i	0.666409	−	0.572768i
$261$	5.81218	−	3.73526i	0.359765	−	0.231207i
$262$	0.283239	−	0.759392i	0.0174985	−	0.0469154i
$263$	4.35541	+	2.37823i	0.268566	+	0.146648i	0.607890	−	0.794022i	$-0.292016\pi$
$263$	4.35541	+	2.37823i	0.268566	+	0.146648i	−0.339324	+	0.940670i	$0.610198\pi$
$264$	−0.491535	+	0.567261i	−0.0302519	+	0.0349125i
$265$	6.53226	+	22.5826i	0.401273	+	1.38724i
$266$	17.7295	−	5.20584i	1.08706	−	0.319191i
$267$	12.2008	+	4.55065i	0.746674	+	0.278495i
$268$	−7.40428	−	1.61070i	−0.452288	−	0.0983893i
$269$	3.22334	−	10.9777i	0.196530	−	0.669321i	−0.800973	−	0.598701i	$-0.795684\pi$
$269$	3.22334	−	10.9777i	0.196530	−	0.669321i	0.997503	−	0.0706205i	$-0.0224979\pi$
$270$	0.772988	+	2.09821i	0.0470426	+	0.127693i
$271$	0.0408956	−	0.0895489i	0.00248423	−	0.00543971i	−0.908386	−	0.418133i	$-0.862685\pi$
$271$	0.0408956	−	0.0895489i	0.00248423	−	0.00543971i	0.910870	+	0.412693i	$0.135412\pi$
$272$	0.838978	+	1.12074i	0.0508705	+	0.0679550i
$273$	−6.62690	−	30.4633i	−0.401078	−	1.84373i
$274$	5.04095	+	5.81757i	0.304535	+	0.351452i
$275$	1.53151	+	3.42626i	0.0923538	+	0.206611i
$276$	−4.51255	−	1.62385i	−0.271624	−	0.0977445i
$277$	1.92518	+	1.92518i	0.115673	+	0.115673i	0.762574	−	0.646901i	$-0.223935\pi$
$277$	1.92518	+	1.92518i	0.115673	+	0.115673i	−0.646901	+	0.762574i	$0.723935\pi$
$278$	−0.149004	−	0.0106569i	−0.00893664	−	0.000639161i
$279$	4.10207	−	6.38294i	0.245584	−	0.382137i
$280$	−0.740662	−	10.9764i	−0.0442630	−	0.655965i
$281$	9.63694	+	4.40104i	0.574892	+	0.262544i	0.681574	−	0.731749i	$-0.261296\pi$
$281$	9.63694	+	4.40104i	0.574892	+	0.262544i	−0.106683	+	0.994293i	$0.534023\pi$
$282$	−7.31631	+	9.77345i	−0.435680	+	0.582001i
$283$	−1.68514	−	3.08610i	−0.100171	−	0.183450i	0.822787	−	0.568349i	$-0.192418\pi$
$283$	−1.68514	−	3.08610i	−0.100171	−	0.183450i	−0.922958	+	0.384900i	$0.874236\pi$
$284$	−2.42459	−	3.77273i	−0.143873	−	0.223870i
$285$	−1.22861	+	8.30768i	−0.0727764	+	0.492105i
$286$	1.33998	+	4.56356i	0.0792348	+	0.269849i
$287$	−0.396321	−	5.54129i	−0.0233941	−	0.327092i
$288$	0.0713392	+	0.997452i	0.00420370	+	0.0587754i
$289$	−4.23727	−	14.4308i	−0.249251	−	0.848872i
$290$	2.26013	−	15.2827i	0.132719	−	0.897429i
$291$	1.71235	+	2.66447i	0.100380	+	0.156194i
$292$	−4.63828	−	8.49438i	−0.271435	−	0.497096i
$293$	15.1633	−	20.2558i	0.885849	−	1.18336i	−0.0963189	−	0.995351i	$-0.530707\pi$
$293$	15.1633	−	20.2558i	0.885849	−	1.18336i	0.982168	−	0.188005i	$-0.0602022\pi$
$294$	−15.6511	−	7.14761i	−0.912790	−	0.416857i
$295$	0.925418	+	13.7144i	0.0538799	+	0.798485i
$296$	2.08754	−	3.24828i	0.121336	−	0.188802i
$297$	−0.748682	−	0.0535468i	−0.0434429	−	0.00310710i
$298$	−9.71546	−	9.71546i	−0.562801	−	0.562801i
$299$	−24.1155	+	18.4920i	−1.39463	+	1.06942i
$300$	4.67053	+	1.78497i	0.269653	+	0.103055i
$301$	−8.41523	−	9.71170i	−0.485046	−	0.559773i
$302$	−4.07840	−	18.7481i	−0.234686	−	1.07883i
$303$	−2.00607	−	2.67979i	−0.115246	−	0.153950i
$304$	−1.56018	+	3.41632i	−0.0894825	+	0.195939i
$305$	0.0263476	+	0.0715183i	0.00150866	+	0.00409512i
$306$	−0.394420	+	1.34327i	−0.0225475	+	0.0767898i
$307$	5.50300	+	1.19711i	0.314073	+	0.0683224i	0.366839	−	0.930285i	$-0.380440\pi$
$307$	5.50300	+	1.19711i	0.314073	+	0.0683224i	−0.0527658	+	0.998607i	$0.516804\pi$
$308$	3.46005	+	1.29053i	0.197155	+	0.0735349i
$309$	12.1507	−	3.56777i	0.691230	−	0.202963i
$310$	−4.71432	−	16.2978i	−0.267755	−	0.925656i
$311$	−5.40438	+	6.23699i	−0.306454	+	0.353667i	−0.887997	−	0.459848i	$-0.847904\pi$
$311$	−5.40438	+	6.23699i	−0.306454	+	0.353667i	0.581543	+	0.813516i	$0.302449\pi$
$312$	5.56150	+	3.03681i	0.314858	+	0.171926i
$313$	−3.75335	+	10.0631i	−0.212152	+	0.568802i	−0.998820	−	0.0485754i	$-0.984532\pi$
$313$	−3.75335	+	10.0631i	−0.212152	+	0.568802i	0.786668	+	0.617377i	$0.211805\pi$
$314$	−3.90807	+	2.51157i	−0.220545	+	0.141736i
$315$	8.34319	−	7.17084i	0.470086	−	0.404031i
$316$	−11.8431	+	1.70277i	−0.666224	+	0.0957885i
$317$	−5.16661	+	1.92705i	−0.290186	+	0.108234i	−0.490342	−	0.871530i	$-0.663128\pi$
$317$	−5.16661	+	1.92705i	−0.290186	+	0.108234i	0.200156	+	0.979764i	$0.435855\pi$
$318$	−8.41632	+	6.30037i	−0.471964	+	0.353307i
$319$	4.36259	+	2.80367i	0.244258	+	0.156975i
$320$	1.78466	+	1.34722i	0.0997654	+	0.0753118i
$321$			13.0788i			0.729989i
$322$	0.273079	+	23.5937i	0.0152181	+	1.31483i
$323$	−3.71792	+	3.71792i	−0.206871	+	0.206871i
$324$	−0.755750	+	0.654861i	−0.0419861	+	0.0363812i
$325$	25.5156	−	18.7822i	1.41535	−	1.04185i
$326$	1.63509	−	11.3723i	0.0905592	−	0.629853i
$327$	0.575193	+	1.54215i	0.0318082	+	0.0852812i
$328$	0.903944	+	0.676684i	0.0499120	+	0.0373636i
$329$	57.6325	+	16.9224i	3.17738	+	0.932963i
$330$	−1.19156	+	1.18201i	−0.0655932	+	0.0650674i
$331$	2.21340	+	4.84666i	0.121659	+	0.266397i	0.960657	−	0.277739i	$-0.0895850\pi$
$331$	2.21340	+	4.84666i	0.121659	+	0.266397i	−0.838997	+	0.544136i	$0.816858\pi$
$332$	0.194353	−	0.355931i	0.0106665	−	0.0195342i
$333$	3.85139	−	0.275457i	0.211055	−	0.0150950i
$334$	11.3409	+	9.82691i	0.620544	+	0.537705i
$335$	−16.2380	−	4.83897i	−0.887177	−	0.264381i
$336$	4.47535	−	2.04382i	0.244150	−	0.111500i
$337$	−2.10050	+	9.65584i	−0.114422	+	0.525987i	0.883879	+	0.467715i	$0.154923\pi$
$337$	−2.10050	+	9.65584i	−0.114422	+	0.525987i	−0.998301	+	0.0582720i	$0.981441\pi$
$338$	23.8312	−	13.0128i	1.29625	−	0.707805i
$339$	−0.707602	−	4.92148i	−0.0384317	−	0.267298i
$340$	1.68184	+	2.64029i	0.0912105	+	0.143190i
$341$	5.63710	+	0.810493i	0.305266	+	0.0438907i
$342$	−3.66989	+	0.798335i	−0.198445	+	0.0431690i
$343$	−3.58214	+	50.0849i	−0.193418	+	2.70433i
$344$	2.61190			0.140824
$345$	−9.78807	−	4.38106i	−0.526972	−	0.235868i
$346$	−7.36670			−0.396036
$347$	−2.57265	+	35.9704i	−0.138107	+	1.93099i	0.181405	+	0.983409i	$0.441936\pi$
$347$	−2.57265	+	35.9704i	−0.138107	+	1.93099i	−0.319512	+	0.947582i	$0.603519\pi$
$348$	6.75106	−	1.46860i	0.361895	−	0.0787254i
$349$	−22.7925	−	3.27706i	−1.22005	−	0.175417i	−0.497952	−	0.867204i	$-0.665915\pi$
$349$	−22.7925	−	3.27706i	−1.22005	−	0.175417i	−0.722101	+	0.691787i	$0.756824\pi$
$350$	0.197990	−	24.5990i	0.0105830	−	1.31487i
$351$	0.901793	+	6.27211i	0.0481341	+	0.334780i
$352$	−0.658781	+	0.359721i	−0.0351131	+	0.0191732i
$353$	6.15333	−	28.2864i	0.327508	−	1.50553i	−0.459270	−	0.888297i	$-0.651889\pi$
$353$	6.15333	−	28.2864i	0.327508	−	1.50553i	0.786778	−	0.617235i	$-0.211747\pi$
$354$	−5.59172	+	2.55365i	−0.297196	+	0.135725i
$355$	−4.77045	−	8.82063i	−0.253189	−	0.468150i
$356$	9.84121	+	8.52746i	0.521583	+	0.451954i
$357$	6.87030	−	0.491373i	0.363615	−	0.0260062i
$358$	−7.59178	+	13.9033i	−0.401238	+	0.734812i
$359$	5.12912	+	11.2312i	0.270704	+	0.592760i	0.995346	−	0.0963661i	$-0.0307220\pi$
$359$	5.12912	+	11.2312i	0.270704	+	0.592760i	−0.724642	+	0.689126i	$0.757995\pi$
$360$	−0.00899852	+	2.23605i	−0.000474264	+	0.117850i
$361$	4.69632	+	1.37896i	0.247175	+	0.0725771i
$362$	19.9759	+	14.9538i	1.04991	+	0.785953i
$363$	3.64722	+	9.77858i	0.191429	+	0.513242i
$364$	4.43678	−	30.8585i	0.232550	−	1.61742i
$365$	−8.91078	−	19.7215i	−0.466411	−	1.03227i
$366$	−0.0257600	+	0.0223212i	−0.00134650	+	0.00116675i
$367$	19.4385	−	19.4385i	1.01468	−	1.01468i	0.0147888	−	0.999891i	$-0.495292\pi$
$367$	19.4385	−	19.4385i	1.01468	−	1.01468i	0.999891	−	0.0147888i	$-0.00470759\pi$
$368$	−3.66055	−	3.09844i	−0.190819	−	0.161518i
$369$			1.12917i			0.0587820i
$370$	5.20192	−	6.89098i	0.270435	−	0.358245i
$371$	43.5137	+	27.9646i	2.25912	+	1.45185i
$372$	6.07404	−	4.54697i	0.314924	−	0.235749i
$373$	−11.6442	+	4.34306i	−0.602913	+	0.224875i	−0.632339	−	0.774692i	$-0.717905\pi$
$373$	−11.6442	+	4.34306i	−0.602913	+	0.224875i	0.0294256	+	0.999567i	$0.490632\pi$
$374$	−1.04012	+	0.149547i	−0.0537834	+	0.00773289i
$375$	10.1132	+	4.76692i	0.522243	+	0.246163i
$376$	−10.2705	+	6.60044i	−0.529660	+	0.340392i
$377$	15.2993	−	41.0190i	0.787954	−	2.11259i
$378$	4.31814	+	2.35788i	0.222101	+	0.121276i
$379$	−22.1103	+	25.5167i	−1.13573	+	1.31070i	−0.191472	+	0.981498i	$0.561326\pi$
$379$	−22.1103	+	25.5167i	−1.13573	+	1.31070i	−0.944258	+	0.329205i	$0.893219\pi$
$380$	−4.05438	+	7.35453i	−0.207985	+	0.377279i
$381$	−10.7450	+	3.15503i	−0.550486	+	0.161637i
$382$	14.2725	+	5.32337i	0.730245	+	0.272367i
$383$	25.4556	+	5.53752i	1.30072	+	0.282954i	0.809004	−	0.587803i	$-0.200007\pi$
$383$	25.4556	+	5.53752i	1.30072	+	0.282954i	0.491714	+	0.870757i	$0.336371\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	7.49747	+	3.46051i	0.382106	+	0.176364i
$386$	−4.47425	+	9.79725i	−0.227733	+	0.498667i
$387$	1.56525	+	2.09093i	0.0795662	+	0.106288i
$388$	0.673250	+	3.09488i	0.0341791	+	0.157119i
$389$	0.632306	+	0.729720i	0.0320592	+	0.0369983i	0.771553	−	0.636165i	$-0.219480\pi$
$389$	0.632306	+	0.729720i	0.0320592	+	0.0369983i	−0.739494	+	0.673164i	$0.764935\pi$
$390$	11.8889	+	7.70829i	0.602016	+	0.390324i
$391$	−3.28570	−	5.85517i	−0.166165	−	0.296109i
$392$	−12.1664	−	12.1664i	−0.614499	−	0.614499i
$393$	0.808429	+	0.0578200i	0.0407799	+	0.00291663i
$394$	−8.85852	+	13.7841i	−0.446286	+	0.694434i
$395$	−26.6935	+	1.80122i	−1.34310	+	0.0906290i
$396$	−0.682764	−	0.311808i	−0.0343102	−	0.0156689i
$397$	−5.91172	+	7.89714i	−0.296701	+	0.396346i	−0.923975	−	0.382452i	$-0.875080\pi$
$397$	−5.91172	+	7.89714i	−0.296701	+	0.396346i	0.627274	+	0.778798i	$0.284171\pi$
$398$	11.7185	+	21.4608i	0.587396	+	1.07573i
$399$	9.98994	+	15.5446i	0.500123	+	0.778206i
$400$	3.75227	+	3.30461i	0.187614	+	0.165231i
$401$	6.46808	+	22.0282i	0.323000	+	1.10004i	0.947697	+	0.319171i	$0.103404\pi$
$401$	6.46808	+	22.0282i	0.323000	+	1.10004i	−0.624697	+	0.780867i	$0.714777\pi$
$402$	−0.540569	−	7.55814i	−0.0269611	−	0.376966i
$403$	−3.42988	−	47.9560i	−0.170854	−	2.38886i
$404$	−0.943094	−	3.21188i	−0.0469207	−	0.159797i
$405$	−1.79544	+	1.33281i	−0.0892163	+	0.0662279i
$406$	−18.3773	−	28.5957i	−0.912051	−	1.41918i
$407$	1.38897	+	2.54371i	0.0688486	+	0.126087i
$408$	−0.838978	+	1.12074i	−0.0415356	+	0.0554850i
$409$	−32.3656	−	14.7809i	−1.60037	−	0.730867i	−0.602632	−	0.798019i	$-0.705881\pi$
$409$	−32.3656	−	14.7809i	−1.60037	−	0.730867i	−0.997743	+	0.0671528i	$0.978609\pi$
$410$	1.90152	+	1.66112i	0.0939092	+	0.0820368i
$411$	−4.16171	+	6.47575i	−0.205282	+	0.319425i
$412$	12.6314	+	0.903417i	0.622305	+	0.0445081i
$413$	21.3858	+	21.3858i	1.05233	+	1.05233i
$414$	0.286745	−	4.78725i	0.0140927	−	0.235281i
$415$	0.493322	−	0.760875i	0.0242162	−	0.0373499i
$416$	4.14959	+	4.78889i	0.203451	+	0.234794i
$417$	−0.0317539	−	0.145970i	−0.00155499	−	0.00714820i
$418$	−1.68938	−	2.25674i	−0.0826300	−	0.110381i
$419$	8.32405	−	18.2271i	0.406656	−	0.890453i	−0.589896	−	0.807480i	$-0.700831\pi$
$419$	8.32405	−	18.2271i	0.406656	−	0.890453i	0.996552	−	0.0829734i	$-0.0264416\pi$
$420$	10.3231	−	3.80307i	0.503716	−	0.185571i
$421$	−8.95419	+	30.4952i	−0.436401	+	1.48624i	0.388756	+	0.921341i	$0.372905\pi$
$421$	−8.95419	+	30.4952i	−0.436401	+	1.48624i	−0.825157	+	0.564904i	$0.808913\pi$
$422$	−4.69324	−	1.02095i	−0.228463	−	0.0496991i
$423$	−11.4388	−	4.26645i	−0.556174	−	0.207442i
$424$	−10.0874	+	2.96193i	−0.489888	+	0.143844i
$425$	3.30514	+	6.17047i	0.160323	+	0.299312i
$426$	2.93682	−	3.38928i	0.142290	−	0.164211i
$427$	0.147185	+	0.0803693i	0.00712280	+	0.00388934i
$428$	−4.57058	+	12.2542i	−0.220927	+	0.592329i
$429$	−4.00119	+	2.57141i	−0.193179	+	0.124149i
$430$	5.82377	+	0.440088i	0.280847	+	0.0212229i
$431$	2.41040	−	0.346563i	0.116105	−	0.0166934i	−0.0840174	−	0.996464i	$-0.526775\pi$
$431$	2.41040	−	0.346563i	0.116105	−	0.0166934i	0.200122	+	0.979771i	$0.435866\pi$
$432$	−0.936950	+	0.349464i	−0.0450790	+	0.0168136i
$433$	19.8599	−	14.8669i	0.954406	−	0.714459i	−0.00396308	−	0.999992i	$-0.501261\pi$
$433$	19.8599	−	14.8669i	0.954406	−	0.714459i	0.958369	+	0.285533i	$0.0921706\pi$
$434$	−31.4038	−	20.1820i	−1.50743	−	0.968767i
$435$	15.3004	−	2.13705i	0.733596	−	0.102464i
$436$			1.64593i			0.0788257i
$437$	9.56189	−	15.2642i	0.457407	−	0.730184i
$438$	6.84354	−	6.84354i	0.326997	−	0.326997i
$439$	−3.49731	+	3.03044i	−0.166918	+	0.144635i	−0.734314	−	0.678810i	$-0.762496\pi$
$439$	−3.49731	+	3.03044i	−0.166918	+	0.144635i	0.567397	+	0.823445i	$0.307951\pi$
$440$	−1.52950	+	0.691075i	−0.0729161	+	0.0329457i
$441$	2.44866	−	17.0308i	0.116603	−	0.810992i
$442$	3.10014	+	8.31180i	0.147459	+	0.395352i
$443$	−9.48434	−	7.09989i	−0.450615	−	0.337326i	0.349746	−	0.936844i	$-0.386268\pi$
$443$	−9.48434	−	7.09989i	−0.450615	−	0.337326i	−0.800361	+	0.599519i	$0.795359\pi$
$444$	3.70483	+	1.08783i	0.175823	+	0.0516264i
$445$	20.5062	+	20.6719i	0.972089	+	0.979944i
$446$	4.80912	+	10.5305i	0.227718	+	0.498633i
$447$	6.58475	−	12.0591i	0.311448	−	0.570375i
$448$	4.90742	−	0.350986i	0.231854	−	0.0165825i
$449$	−3.55513	−	3.08054i	−0.167777	−	0.145380i	0.566925	−	0.823769i	$-0.308133\pi$
$449$	−3.55513	−	3.08054i	−0.167777	−	0.145380i	−0.734702	+	0.678389i	$0.762678\pi$
$450$	−0.396824	+	4.98423i	−0.0187065	+	0.234959i
$451$	−0.770955	+	0.352083i	−0.0363028	+	0.0165789i
$452$	1.05689	−	4.85846i	0.0497121	−	0.228523i
$453$	16.8397	−	9.19515i	0.791197	−	0.432026i
$454$	−1.47346	−	10.2481i	−0.0691528	−	0.480968i
$455$	15.0922	−	68.0579i	0.707533	−	3.19060i
$456$	−3.71749	−	0.534494i	−0.174087	−	0.0250300i
$457$	17.8759	−	3.88867i	0.836201	−	0.181904i	0.225976	−	0.974133i	$-0.427443\pi$
$457$	17.8759	−	3.88867i	0.836201	−	0.181904i	0.610224	+	0.792229i	$0.291079\pi$
$458$	−1.52484	+	21.3201i	−0.0712512	+	0.996221i
$459$	−1.39998			−0.0653455
$460$	−7.63991	−	7.52541i	−0.356212	−	0.350874i
$461$	−27.8588			−1.29751			−0.648756	−	0.760996i	$-0.724711\pi$
$461$	−27.8588			−1.29751			−0.648756	+	0.760996i	$0.724711\pi$
$462$	−0.263448	+	3.68348i	−0.0122567	+	0.171371i
$463$	−28.9039	+	6.28766i	−1.34328	+	0.292212i	−0.826032	−	0.563624i	$-0.809407\pi$
$463$	−28.9039	+	6.28766i	−1.34328	+	0.292212i	−0.517247	+	0.855836i	$0.673043\pi$
$464$	6.83863	+	0.983246i	0.317475	+	0.0456461i
$465$	14.3095	−	9.11499i	0.663587	−	0.422698i
$466$	−2.51558	−	17.4963i	−0.116532	−	0.810499i
$467$	15.1126	−	8.25213i	0.699330	−	0.381863i	−0.0899086	−	0.995950i	$-0.528657\pi$
$467$	15.1126	−	8.25213i	0.699330	−	0.381863i	0.789238	+	0.614087i	$0.210476\pi$
$468$	−1.34694	+	6.19179i	−0.0622624	+	0.286216i
$469$	−33.9117	+	15.4870i	−1.56590	+	0.715122i
$470$	−24.0124	+	12.9866i	−1.10761	+	0.599026i
$471$	−3.51086	−	3.04218i	−0.161772	−	0.140176i
$472$	−6.13157	+	0.438538i	−0.282228	+	0.0201854i
$473$	−0.939555	+	1.72067i	−0.0432008	+	0.0791164i
$474$	−4.97037	−	10.8836i	−0.228297	−	0.499900i
$475$	−10.2793	+	15.7153i	−0.471646	+	0.721069i
$476$	6.60884	+	1.94053i	0.302916	+	0.0889441i
$477$	−8.41632	−	6.30037i	−0.385357	−	0.288474i
$478$	4.99816	+	13.4006i	0.228610	+	0.612928i
$479$	3.77808	−	26.2771i	0.172625	−	1.20063i	−0.700686	−	0.713469i	$-0.747123\pi$
$479$	3.77808	−	26.2771i	0.172625	−	1.20063i	0.873311	−	0.487163i	$-0.161968\pi$
$480$	−0.789850	+	2.09192i	−0.0360516	+	0.0954827i
$481$	18.4910	−	16.0225i	0.843117	−	0.730565i
$482$	12.3107	−	12.3107i	0.560737	−	0.560737i
$483$	−22.5610	+	6.90913i	−1.02656	+	0.314376i
$484$			10.4366i			0.474391i
$485$	0.979686	+	7.01413i	0.0444852	+	0.318495i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	−8.69302	+	6.50751i	−0.393918	+	0.294884i	−0.777816	−	0.628492i	$-0.783672\pi$
$487$	−8.69302	+	6.50751i	−0.393918	+	0.294884i	0.383898	+	0.923376i	$0.374582\pi$
$488$	−0.0319363	+	0.0119116i	−0.00144569	+	0.000539213i
$489$	11.3723	−	1.63509i	0.514273	−	0.0739413i
$490$	−25.0777	−	29.1776i	−1.13289	−	1.31811i
$491$	5.29304	−	3.40163i	0.238871	−	0.153513i	−0.415729	−	0.909489i	$-0.636473\pi$
$491$	5.29304	−	3.40163i	0.238871	−	0.153513i	0.654600	+	0.755975i	$0.272837\pi$
$492$	−0.394603	+	1.05797i	−0.0177901	+	0.0476971i
$493$	8.48927	+	4.63549i	0.382337	+	0.208772i
$494$	−15.5847	+	17.9857i	−0.701189	+	0.809215i
$495$	−1.46983	−	0.810283i	−0.0660639	−	0.0364195i
$496$	7.28008	−	2.13762i	0.326885	−	0.0959821i
$497$	−20.6731	−	7.71068i	−0.927317	−	0.345871i
$498$	0.396268	+	0.0862029i	0.0177572	+	0.00386284i
$499$	8.03873	−	27.3774i	0.359863	−	1.22558i	−0.558387	−	0.829580i	$-0.688580\pi$
$499$	8.03873	−	27.3774i	0.359863	−	1.22558i	0.918250	−	0.396000i	$-0.129602\pi$
$500$	7.80968	+	8.00056i	0.349259	+	0.357796i
$501$	−6.23376	+	13.6500i	−0.278504	+	0.609839i
$502$	−9.43424	−	12.6027i	−0.421071	−	0.562485i
$503$	−9.01756	−	41.4530i	−0.402073	−	1.84830i	−0.518469	−	0.855097i	$-0.673498\pi$
$503$	−9.01756	−	41.4530i	−0.402073	−	1.84830i	0.116396	−	0.993203i	$-0.462866\pi$
$504$	3.22189	+	3.71825i	0.143514	+	0.165624i
$505$	−1.56164	−	7.32047i	−0.0694923	−	0.325757i
$506$	3.35797	−	1.29692i	0.149280	−	0.0576553i
$507$	19.1998	+	19.1998i	0.852691	+	0.852691i
$508$	−11.1701	−	0.798904i	−0.495595	−	0.0354456i
$509$	−20.6803	+	32.1791i	−0.916637	+	1.42632i	−0.0120972	+	0.999927i	$0.503851\pi$
$509$	−20.6803	+	32.1791i	−0.916637	+	1.42632i	−0.904540	+	0.426389i	$0.859786\pi$
$510$	−2.05952	+	2.35757i	−0.0911969	+	0.104395i
$511$	−43.3134	−	19.7806i	−1.91607	−	0.875042i
$512$	−0.599278	+	0.800541i	−0.0264846	+	0.0353793i
$513$	−1.79992	−	3.29631i	−0.0794686	−	0.145536i
$514$	2.57635	+	4.00888i	0.113638	+	0.176824i
$515$	28.0122	+	4.14267i	1.23436	+	0.182548i
$516$	0.735856	+	2.50610i	0.0323943	+	0.110325i
$517$	−0.653729	−	9.14032i	−0.0287510	−	0.401991i
$518$	−1.35524	−	18.9487i	−0.0595457	−	0.832558i
$519$	−2.07544	−	7.06830i	−0.0911017	−	0.310264i
$520$	8.44550	+	11.3770i	0.370360	+	0.498915i
$521$	−6.92156	−	10.7702i	−0.303239	−	0.471849i	0.655875	−	0.754870i	$-0.272300\pi$
$521$	−6.92156	−	10.7702i	−0.303239	−	0.471849i	−0.959114	+	0.283021i	$0.908664\pi$
$522$	3.31111	+	6.06384i	0.144923	+	0.265407i
$523$	6.58047	−	8.79048i	0.287744	−	0.384381i	−0.633257	−	0.773942i	$-0.718282\pi$
$523$	6.58047	−	8.79048i	0.287744	−	0.384381i	0.921001	+	0.389561i	$0.127373\pi$
$524$	0.737251	+	0.336691i	0.0322070	+	0.0147084i
$525$	23.6583	−	6.74036i	1.03253	−	0.294174i
$526$	−2.68289	+	4.17465i	−0.116979	+	0.182023i
$527$	10.5952	+	0.757782i	0.461533	+	0.0330095i
$528$	−0.530750	−	0.530750i	−0.0230979	−	0.0230979i
$529$	15.4601	+	17.0290i	0.672177	+	0.740390i
$530$	−22.9911	+	4.90459i	−0.998669	+	0.213042i
$531$	−4.02558	−	4.64577i	−0.174695	−	0.201609i
$532$	3.92777	+	18.0557i	0.170291	+	0.782813i
$533$	4.28788	+	5.72794i	0.185729	+	0.248104i
$534$	−5.40945	+	11.8450i	−0.234090	+	0.512585i
$535$	−12.2558	+	26.5532i	−0.529866	+	1.14800i
$536$	2.13481	−	7.27051i	0.0922099	−	0.314038i
$537$	−15.4790	−	3.36724i	−0.667967	−	0.145307i
$538$	10.7198	+	3.99826i	0.462162	+	0.172377i
$539$	12.3916	−	3.63849i	0.533742	−	0.156721i
$540$	−2.14801	+	0.621334i	−0.0924356	+	0.0267380i
$541$	−1.04569	+	1.20679i	−0.0449578	+	0.0518840i	−0.777783	−	0.628533i	$-0.783656\pi$
$541$	−1.04569	+	1.20679i	−0.0449578	+	0.0518840i	0.732825	+	0.680417i	$0.238201\pi$
$542$	0.0864032	+	0.0471797i	0.00371134	+	0.00202654i
$543$	−8.72018	+	23.3797i	−0.374219	+	1.00332i
$544$	−1.17774	+	0.756887i	−0.0504952	+	0.0324513i
$545$	−0.277328	+	3.66994i	−0.0118794	+	0.157203i
$546$	30.8585	−	4.43678i	1.32062	−	0.189877i
$547$	15.5544	−	5.80148i	0.665057	−	0.248054i	0.00581380	−	0.999983i	$-0.498149\pi$
$547$	15.5544	−	5.80148i	0.665057	−	0.248054i	0.659243	+	0.751930i	$0.270877\pi$
$548$	−6.16236	+	4.61309i	−0.263243	+	0.197061i
$549$	−0.0286744	−	0.0184279i	−0.00122379	−	0.000786485i
$550$	−3.52679	+	1.28319i	−0.150383	+	0.0547152i
$551$			25.9481i			1.10542i
$552$	1.94164	−	4.38521i	0.0826416	−	0.186647i
$553$	−41.6249	+	41.6249i	−1.77007	+	1.77007i
$554$	−2.05761	+	1.78293i	−0.0874195	+	0.0757494i
$555$	8.07740	+	3.04980i	0.342866	+	0.129457i
$556$	0.0212596	−	0.147864i	0.000901607	−	0.00627082i
$557$	−13.9575	−	37.4216i	−0.591400	−	1.58560i	−0.795039	−	0.606558i	$-0.792550\pi$
$557$	−13.9575	−	37.4216i	−0.591400	−	1.58560i	0.203639	−	0.979046i	$-0.434723\pi$
$558$	6.07404	+	4.54697i	0.257135	+	0.192489i
$559$	15.8801	+	4.66283i	0.671659	+	0.197217i
$560$	11.0013	+	0.0442723i	0.464888	+	0.00187085i
$561$	−0.436526	−	0.955858i	−0.0184301	−	0.0403563i
$562$	−5.07732	+	9.29842i	−0.214174	+	0.392230i
$563$	6.23449	−	0.445899i	0.262752	−	0.0187924i	0.0606584	−	0.998159i	$-0.480680\pi$
$563$	6.23449	−	0.445899i	0.262752	−	0.0187924i	0.202094	+	0.979366i	$0.435225\pi$
$564$	−9.22661	−	7.99490i	−0.388510	−	0.336646i
$565$	3.17519	−	10.6549i	0.133581	−	0.448254i
$566$	3.19845	−	1.46068i	0.134441	−	0.0613971i
$567$	−1.04581	+	4.80752i	−0.0439200	+	0.201897i
$568$	3.93609	−	2.14927i	0.165155	−	0.0901812i
$569$	−2.54810	−	17.7224i	−0.106822	−	0.742963i	−0.970879	−	0.239569i	$-0.922994\pi$
$569$	−2.54810	−	17.7224i	−0.106822	−	0.742963i	0.864057	−	0.503394i	$-0.167915\pi$
$570$	−8.19887	−	1.81814i	−0.343413	−	0.0761535i
$571$	−6.19033	−	0.890035i	−0.259057	−	0.0372468i	0.0115625	−	0.999933i	$-0.496319\pi$
$571$	−6.19033	−	0.890035i	−0.259057	−	0.0372468i	−0.270620	+	0.962686i	$0.587229\pi$
$572$	−4.64752	+	1.01101i	−0.194323	+	0.0422723i
$573$	−1.08671	+	15.1941i	−0.0453978	+	0.634744i
$574$	5.55545			0.231880
$575$	−15.7668	−	18.0668i	−0.657521	−	0.753436i
$576$	−1.00000			−0.0416667
$577$	0.615489	−	8.60566i	0.0256231	−	0.358258i	−0.968424	−	0.249309i	$-0.919797\pi$
$577$	0.615489	−	8.60566i	0.0256231	−	0.358258i	0.994047	−	0.108950i	$-0.0347488\pi$
$578$	14.6963	−	3.19699i	0.611287	−	0.132977i
$579$	−10.6609	−	1.53281i	−0.443053	−	0.0637014i
$580$	15.0825	+	3.34462i	0.626266	+	0.138878i
$581$	−0.283949	−	1.97491i	−0.0117802	−	0.0819331i
$582$	−2.77984	+	1.51791i	−0.115228	+	0.0629193i
$583$	1.67740	−	7.71087i	0.0694707	−	0.319352i
$584$	8.80363	−	4.02048i	0.364297	−	0.166369i
$585$	−4.04657	+	13.5790i	−0.167305	+	0.561421i
$586$	19.1224	+	16.5697i	0.789941	+	0.684488i
$587$	−13.7770	+	0.985348i	−0.568636	+	0.0406697i	−0.352698	−	0.935737i	$-0.614736\pi$
$587$	−13.7770	+	0.985348i	−0.568636	+	0.0406697i	−0.215939	+	0.976407i	$0.569281\pi$
$588$	8.24594	−	15.1013i	0.340057	−	0.622767i
$589$	11.8378	+	25.9211i	0.487766	+	1.06806i
$590$	−13.7455	−	0.0553160i	−0.565894	−	0.00227732i
$591$	−15.7215	−	4.61625i	−0.646697	−	0.189887i
$592$	3.09108	+	2.31395i	0.127042	+	0.0951028i
$593$	−5.73890	−	15.3866i	−0.235668	−	0.631851i	0.764246	−	0.644925i	$-0.223111\pi$
$593$	−5.73890	−	15.3866i	−0.235668	−	0.631851i	−0.999915	+	0.0130734i	$0.995838\pi$
$594$	0.106821	−	0.742954i	0.00438291	−	0.0304838i
$595$	14.4088	+	5.44037i	0.590705	+	0.223033i
$596$	10.3838	−	8.99761i	0.425337	−	0.368556i
$597$	−17.2900	+	17.2900i	−0.707634	+	0.707634i
$598$	−16.7245	−	25.3732i	−0.683914	−	1.03759i
$599$		−	30.9444i		−	1.26435i	−0.774824	−	0.632177i	$-0.782161\pi$
$599$		−	30.9444i		−	1.26435i	0.774824	−	0.632177i	$-0.217839\pi$
$600$	−2.11361	+	4.53130i	−0.0862879	+	0.184989i
$601$	19.4352	+	12.4902i	0.792778	+	0.509487i	0.873252	−	0.487269i	$-0.162007\pi$
$601$	19.4352	+	12.4902i	0.792778	+	0.509487i	−0.0804740	+	0.996757i	$0.525643\pi$
$602$	10.2873	−	7.70097i	0.419279	−	0.313868i
$603$	7.09969	−	2.64805i	0.289122	−	0.107837i
$604$	18.9913	−	2.73054i	0.772745	−	0.111104i
$605$	−1.75850	+	23.2706i	−0.0714932	+	0.946085i
$606$	2.81608	−	1.80978i	0.114395	−	0.0735174i
$607$	2.99663	−	8.03428i	0.121630	−	0.326101i	−0.861839	−	0.507183i	$-0.830687\pi$
$607$	2.99663	−	8.03428i	0.121630	−	0.326101i	0.983468	+	0.181081i	$0.0579597\pi$
$608$	−3.29631	−	1.79992i	−0.133683	−	0.0729965i
$609$	22.2599	−	25.6892i	0.902015	−	1.04098i
$610$	−0.0732157	+	0.0211784i	−0.00296442	+	0.000857488i
$611$	−74.2271	+	21.7950i	−3.00291	+	0.881733i
$612$	−1.31171	−	0.489243i	−0.0530228	−	0.0197765i
$613$	−5.82362	−	1.26685i	−0.235214	−	0.0511676i	0.0934132	−	0.995627i	$-0.470222\pi$
$613$	−5.82362	−	1.26685i	−0.235214	−	0.0511676i	−0.328627	+	0.944460i	$0.606586\pi$
$614$	−1.58664	+	5.40358i	−0.0640314	+	0.218071i
$615$	−1.05811	+	2.29248i	−0.0426672	+	0.0924419i
$616$	−1.53408	+	3.35917i	−0.0618099	+	0.135345i
$617$	9.49624	+	12.6855i	0.382304	+	0.510699i	0.949877	−	0.312625i	$-0.101208\pi$
$617$	9.49624	+	12.6855i	0.382304	+	0.510699i	−0.567572	+	0.823323i	$0.692117\pi$
$618$	2.69186	+	12.3743i	0.108282	+	0.497766i
$619$	29.7685	+	34.3547i	1.19650	+	1.38083i	0.905631	+	0.424066i	$0.139398\pi$
$619$	29.7685	+	34.3547i	1.19650	+	1.38083i	0.290865	+	0.956764i	$0.406057\pi$
$620$	16.5926	−	3.53964i	0.666376	−	0.142155i
$621$	4.67412	−	1.07359i	0.187566	−	0.0430819i
$622$	−5.83555	−	5.83555i	−0.233984	−	0.233984i
$623$	63.9034	+	4.57046i	2.56023	+	0.183112i
$624$	−3.42583	+	5.33069i	−0.137143	+	0.213398i
$625$	16.0653	+	19.1548i	0.642611	+	0.766193i
$626$	−9.76973	−	4.46168i	−0.390477	−	0.178325i
$627$	1.68938	−	2.25674i	0.0674671	−	0.0901256i
$628$	−2.22637	−	4.07729i	−0.0888418	−	0.162702i
$629$	2.92252	+	4.54753i	0.116528	+	0.181322i
$630$	6.55737	+	8.83350i	0.261252	+	0.351935i
$631$	−13.3158	−	45.3496i	−0.530095	−	1.80534i	−0.590341	−	0.807154i	$-0.701007\pi$
$631$	−13.3158	−	45.3496i	−0.530095	−	1.80534i	0.0602459	−	0.998184i	$-0.480812\pi$
$632$	−0.853562	−	11.9344i	−0.0339529	−	0.474723i
$633$	−0.342642	−	4.79076i	−0.0136188	−	0.190416i
$634$	−1.55356	−	5.29092i	−0.0616996	−	0.210129i
$635$	−24.7716	−	3.66342i	−0.983030	−	0.145378i
$636$	−5.68391	−	8.84433i	−0.225382	−	0.350701i
$637$	−52.2513	−	95.6910i	−2.07027	−	3.79142i
$638$	−3.10775	+	4.15146i	−0.123037	+	0.164358i
$639$	4.07939	+	1.86299i	0.161378	+	0.0736989i
$640$	−1.47110	+	1.68400i	−0.0581504	+	0.0665660i
$641$	1.54625	−	2.40601i	0.0610731	−	0.0950316i	−0.809374	−	0.587294i	$-0.800193\pi$
$641$	1.54625	−	2.40601i	0.0610731	−	0.0950316i	0.870447	+	0.492262i	$0.163830\pi$
$642$	−13.0455	−	0.933033i	−0.514865	−	0.0368239i
$643$	−2.03772	−	2.03772i	−0.0803597	−	0.0803597i	0.665784	−	0.746144i	$-0.268097\pi$
$643$	−2.03772	−	2.03772i	−0.0803597	−	0.0803597i	−0.746144	+	0.665784i	$0.768097\pi$
$644$	−23.5531	−	1.41077i	−0.928121	−	0.0555922i
$645$	1.21849	+	5.71186i	0.0479778	+	0.224904i
$646$	−3.44321	−	3.97368i	−0.135471	−	0.156342i
$647$	−4.42519	−	20.3423i	−0.173972	−	0.799737i	−0.978570	−	0.205916i	$-0.933983\pi$
$647$	−4.42519	−	20.3423i	−0.173972	−	0.799737i	0.804598	−	0.593820i	$-0.202381\pi$
$648$	−0.599278	−	0.800541i	−0.0235419	−	0.0314482i
$649$	1.91676	−	4.19711i	0.0752392	−	0.164751i
$650$	16.9141	+	26.7905i	0.663424	+	1.05081i
$651$	10.5170	−	35.8176i	0.412194	−	1.40380i
$652$	11.2267	+	2.44221i	0.439670	+	0.0956445i
$653$	−2.97558	−	1.10983i	−0.116443	−	0.0434312i	0.290567	−	0.956855i	$-0.406156\pi$
$653$	−2.97558	−	1.10983i	−0.116443	−	0.0434312i	−0.407011	+	0.913423i	$0.633429\pi$
$654$	−1.57926	+	0.463712i	−0.0617538	+	0.0181326i
$655$	1.58713	+	0.874947i	0.0620142	+	0.0341870i
$656$	−0.739447	+	0.853367i	−0.0288705	+	0.0333184i
$657$	8.49438	+	4.63828i	0.331397	+	0.180957i
$658$	−20.9908	+	56.2784i	−0.818305	+	2.19396i
$659$	−39.7931	+	25.5735i	−1.55012	+	0.996202i	−0.564852	+	0.825193i	$0.691067\pi$
$659$	−39.7931	+	25.5735i	−1.55012	+	0.996202i	−0.985269	+	0.171010i	$0.945297\pi$
$660$	−1.09399	−	1.27285i	−0.0425836	−	0.0495455i
$661$	−27.9161	+	4.01373i	−1.08581	+	0.156116i	−0.661903	−	0.749589i	$-0.730251\pi$
$661$	−27.9161	+	4.01373i	−1.08581	+	0.156116i	−0.423908	+	0.905705i	$0.639342\pi$
$662$	−4.99222	+	1.86200i	−0.194028	+	0.0723687i
$663$	−7.10170	+	5.31627i	−0.275807	+	0.206467i
$664$	0.341159	+	0.219249i	0.0132395	+	0.00850853i
$665$	5.71553	+	40.9208i	0.221639	+	1.58684i
$666$			3.86123i			0.149620i
$667$	−31.8979	−	8.96641i	−1.23509	−	0.347181i
$668$	−10.6109	+	10.6109i	−0.410549	+	0.410549i
$669$	−8.74905	+	7.58110i	−0.338258	+	0.293102i
$670$	5.98505	−	15.8514i	0.231223	−	0.612394i
$671$	0.00364102	−	0.0253239i	0.000140560	−	0.000977617i
$672$	1.71935	+	4.60975i	0.0663253	+	0.177825i
$673$	8.40137	+	6.28919i	0.323849	+	0.242430i	0.748815	−	0.662779i	$-0.230623\pi$
$673$	8.40137	+	6.28919i	0.323849	+	0.242430i	−0.424966	+	0.905209i	$0.639714\pi$
$674$	−9.48139	−	2.78399i	−0.365210	−	0.107235i
$675$	−4.89413	+	1.02347i	−0.188375	+	0.0393934i
$676$	11.2796	+	24.6988i	0.433830	+	0.949955i
$677$	−8.71135	+	15.9536i	−0.334804	+	0.613148i	−0.989797	−	0.142487i	$-0.954490\pi$
$677$	−8.71135	+	15.9536i	−0.334804	+	0.613148i	0.654992	+	0.755635i	$0.272672\pi$
$678$	4.95942	−	0.354705i	0.190465	−	0.0136224i
$679$	11.7767	+	10.2046i	0.451948	+	0.391615i
$680$	−2.75355	+	1.48920i	−0.105594	+	0.0571081i
$681$	9.41788	−	4.30100i	0.360894	−	0.164815i
$682$	−1.21057	+	5.56492i	−0.0463553	+	0.213092i
$683$	−15.3046	+	8.35695i	−0.585614	+	0.319770i	−0.744600	−	0.667511i	$-0.767360\pi$
$683$	−15.3046	+	8.35695i	−0.585614	+	0.319770i	0.158985	+	0.987281i	$0.449178\pi$
$684$	−0.534494	−	3.71749i	−0.0204369	−	0.142142i
$685$	−14.5176	+	9.24753i	−0.554687	+	0.353330i
$686$	−49.7018	−	7.14603i	−1.89762	−	0.272837i
$687$	−20.8861	+	4.54348i	−0.796853	+	0.173345i
$688$	−0.186331	+	2.60524i	−0.00710379	+	0.0993239i
$689$	−66.6185			−2.53796
$690$	5.06817	−	9.45059i	0.192942	−	0.359778i
$691$	−28.9191			−1.10013			−0.550067	−	0.835121i	$-0.685398\pi$
$691$	−28.9191			−1.10013			−0.550067	+	0.835121i	$0.685398\pi$
$692$	0.525534	−	7.34793i	0.0199778	−	0.279326i
$693$	−3.60850	+	0.784980i	−0.137075	+	0.0298189i
$694$	−35.6952	−	5.13219i	−1.35497	−	0.194815i
$695$	0.0723168	−	0.326111i	0.00274313	−	0.0123701i
$696$	0.983246	+	6.83863i	0.0372699	+	0.259218i
$697$	−1.38745	+	0.757602i	−0.0525532	+	0.0286962i
$698$	4.89471	−	22.5006i	0.185268	−	0.851661i
$699$	16.0788	−	7.34295i	0.608157	−	0.277736i
$700$	24.5222	+	1.95236i	0.926851	+	0.0737922i
$701$	−16.8924	−	14.6373i	−0.638016	−	0.552844i	0.274653	−	0.961543i	$-0.411437\pi$
$701$	−16.8924	−	14.6373i	−0.638016	−	0.552844i	−0.912669	+	0.408700i	$0.865982\pi$
$702$	−6.32046	+	0.452048i	−0.238550	+	0.0170615i
$703$	−6.94992	+	12.7278i	−0.262121	+	0.480039i
$704$	−0.311808	−	0.682764i	−0.0117517	−	0.0257327i
$705$	−19.2256	−	19.3809i	−0.724077	−	0.729929i
$706$	27.7753	+	8.15558i	1.04534	+	0.306939i
$707$	−13.1845	−	9.86977i	−0.495853	−	0.371191i
$708$	−2.14824	−	5.75964i	−0.0807357	−	0.216461i
$709$	−6.31291	+	43.9073i	−0.237086	+	1.64897i	0.429151	+	0.903233i	$0.358813\pi$
$709$	−6.31291	+	43.9073i	−0.237086	+	1.64897i	−0.666237	+	0.745740i	$0.732096\pi$
$710$	9.13847	−	4.12904i	0.342961	−	0.154960i
$711$	9.04242	−	7.83530i	0.339117	−	0.293847i
$712$	−9.20779	+	9.20779i	−0.345077	+	0.345077i
$713$	−35.9553	+	5.59505i	−1.34654	+	0.209536i
$714$			6.88785i			0.257771i
$715$	−10.5330	+	1.47118i	−0.393911	+	0.0550188i
$716$	−13.3263	−	8.56428i	−0.498027	−	0.320062i
$717$	−11.4496	+	8.57108i	−0.427594	+	0.320093i
$718$	−11.5685	+	4.31482i	−0.431732	+	0.161028i
$719$	−1.41070	+	0.202828i	−0.0526103	+	0.00756422i	−0.168570	−	0.985690i	$-0.553915\pi$
$719$	−1.41070	+	0.202828i	−0.0526103	+	0.00756422i	0.115959	+	0.993254i	$0.463006\pi$
$720$	−2.22971	−	0.168494i	−0.0830964	−	0.00627938i
$721$	52.4141	−	33.6845i	1.95200	−	1.25448i
$722$	−1.71048	+	4.58598i	−0.0636576	+	0.170673i
$723$	15.2804	+	8.34370i	0.568282	+	0.310306i
$724$	−16.3407	+	18.8582i	−0.607299	+	0.700860i
$725$	33.0660	+	9.99884i	1.22804	+	0.371348i
$726$	−10.0139	+	2.94033i	−0.371649	+	0.109126i
$727$	−14.7186	−	5.48977i	−0.545884	−	0.203604i	0.0613656	−	0.998115i	$-0.480454\pi$
$727$	−14.7186	−	5.48977i	−0.545884	−	0.203604i	−0.607250	+	0.794511i	$0.707727\pi$
$728$	30.4633	+	6.62690i	1.12905	+	0.245609i
$729$	0.281733	−	0.959493i	0.0104345	−	0.0355368i
$730$	20.3070	−	7.48116i	0.751595	−	0.276890i
$731$	−1.51901	+	3.32617i	−0.0561826	+	0.123023i
$732$	−0.0204266	−	0.0272867i	−0.000754989	−	0.00100855i
$733$	−4.70837	−	21.6440i	−0.173908	−	0.799441i	−0.978604	−	0.205754i	$-0.934035\pi$
$733$	−4.70837	−	21.6440i	−0.173908	−	0.799441i	0.804696	−	0.593687i	$-0.202328\pi$
$734$	18.0022	+	20.7757i	0.664474	+	0.766844i
$735$	20.9305	−	32.2822i	0.772034	−	1.19075i
$736$	3.35169	−	3.43019i	0.123545	−	0.126438i
$737$	4.02173	+	4.02173i	0.148142	+	0.148142i
$738$	−1.12629	−	0.0805538i	−0.0414593	−	0.00296523i
$739$	26.9555	−	41.9435i	0.991573	−	1.54292i	0.160290	−	0.987070i	$-0.448757\pi$
$739$	26.9555	−	41.9435i	0.991573	−	1.54292i	0.831284	−	0.555848i	$-0.187606\pi$
$740$	6.50232	+	5.68027i	0.239030	+	0.208811i
$741$	−21.6479	−	9.88625i	−0.795255	−	0.363181i
$742$	−30.9976	+	41.4079i	−1.13796	+	1.52013i
$743$	13.6055	+	24.9166i	0.499137	+	0.914101i	0.998852	+	0.0479107i	$0.0152563\pi$
$743$	13.6055	+	24.9166i	0.499137	+	0.914101i	−0.499715	+	0.866190i	$0.666562\pi$
$744$	4.10207	+	6.38294i	0.150389	+	0.234010i
$745$	24.6689	−	18.3125i	0.903798	−	0.670917i
$746$	−3.50130	−	11.9243i	−0.128192	−	0.436581i
$747$	0.0289306	+	0.404503i	0.00105852	+	0.0148000i
$748$	−0.0749645	−	1.04814i	−0.00274097	−	0.0383238i
$749$	18.1287	+	61.7407i	0.662409	+	2.25596i
$750$	−5.47624	+	9.74735i	−0.199964	+	0.355923i
$751$	−2.28387	−	3.55377i	−0.0833395	−	0.129679i	0.797081	−	0.603872i	$-0.206376\pi$
$751$	−2.28387	−	3.55377i	−0.0833395	−	0.129679i	−0.880421	+	0.474193i	$0.842740\pi$
$752$	−5.85094	−	10.7152i	−0.213362	−	0.390743i
$753$	9.43424	−	12.6027i	0.343803	−	0.459267i
$754$	39.8230	+	18.1866i	1.45027	+	0.662316i
$755$	42.8052	−	2.88839i	1.55784	−	0.105119i
$756$	−2.65993	+	4.13893i	−0.0967407	+	0.150531i
$757$	−16.7135	−	1.19537i	−0.607462	−	0.0434466i	−0.235780	−	0.971806i	$-0.575764\pi$
$757$	−16.7135	−	1.19537i	−0.607462	−	0.0434466i	−0.371682	+	0.928360i	$0.621219\pi$
$758$	−23.8743	−	23.8743i	−0.867154	−	0.867154i
$759$	2.19044	+	2.85657i	0.0795080	+	0.103687i
$760$	−7.04655	−	4.56872i	−0.255605	−	0.165725i
$761$	24.1779	+	27.9027i	0.876447	+	1.01147i	0.999817	+	0.0191130i	$0.00608422\pi$
$761$	24.1779	+	27.9027i	0.876447	+	1.01147i	−0.123370	+	0.992361i	$0.539370\pi$
$762$	−2.38045	−	10.9427i	−0.0862346	−	0.396414i
$763$	4.85289	+	6.48270i	0.175686	+	0.234689i
$764$	−6.32799	+	13.8564i	−0.228939	+	0.501306i
$765$	−2.84230	−	1.31189i	−0.102764	−	0.0474313i
$766$	−7.33939	+	24.9957i	−0.265183	+	0.903130i
$767$	−38.0624	−	8.27996i	−1.37435	−	0.298972i
$768$	−0.936950	−	0.349464i	−0.0338093	−	0.0126102i
$769$	−10.0901	+	2.96273i	−0.363860	+	0.106839i	−0.458552	−	0.888668i	$-0.651632\pi$
$769$	−10.0901	+	2.96273i	−0.363860	+	0.106839i	0.0946919	+	0.995507i	$0.469813\pi$
$770$	−3.98656	+	7.23150i	−0.143666	+	0.260605i
$771$	−3.12065	+	3.60142i	−0.112387	+	0.129702i
$772$	−9.45309	−	5.16178i	−0.340224	−	0.185777i
$773$	0.988494	−	2.65025i	0.0355537	−	0.0953230i	−0.917960	−	0.396673i	$-0.870165\pi$
$773$	0.988494	−	2.65025i	0.0355537	−	0.0953230i	0.953514	+	0.301350i	$0.0974373\pi$
$774$	−2.19727	+	1.41210i	−0.0789791	+	0.0507568i
$775$	37.5932	−	5.09661i	1.35039	−	0.183076i
$776$	−3.13503	+	0.450749i	−0.112541	+	0.0161809i
$777$	17.7993	−	6.63880i	0.638547	−	0.238166i
$778$	−0.772969	+	0.578637i	−0.0277123	+	0.0207451i
$779$	−3.56761	−	2.29277i	−0.127823	−	0.0821468i
$780$	−8.53679	+	11.3087i	−0.305666	+	0.404915i
$781$			3.36616i			0.120451i
$782$	6.07465	−	2.85962i	0.217229	−	0.102260i
$783$	−4.88537	+	4.88537i	−0.174589	+	0.174589i
$784$	13.0034	−	11.2675i	0.464407	−	0.402411i
$785$	−4.27716	−	9.46631i	−0.152658	−	0.337867i
$786$	−0.115345	+	0.802245i	−0.00411423	+	0.0286151i
$787$	5.52019	+	14.8002i	0.196774	+	0.527571i	0.997438	−	0.0715432i	$-0.0227924\pi$
$787$	5.52019	+	14.8002i	0.196774	+	0.527571i	−0.800664	+	0.599114i	$0.795520\pi$
$788$	−13.1171	−	9.81930i	−0.467276	−	0.349798i
$789$	−4.76141	−	1.39807i	−0.169511	−	0.0497728i
$790$	0.107666	−	26.7540i	0.00383058	−	0.951864i
$791$	−10.1621	−	22.2518i	−0.361322	−	0.791184i
$792$	0.359721	−	0.658781i	0.0127821	−	0.0234088i
$793$	−0.215435	+	0.0154082i	−0.00765033	+	0.000547162i
$794$	−7.45528	−	6.46004i	−0.264578	−	0.229258i
$795$	−11.1833	−	20.6780i	−0.396629	−	0.733373i
$796$	−22.2422	+	10.1577i	−0.788352	+	0.360028i
$797$	2.40448	−	11.0532i	0.0851712	−	0.391526i	−0.914751	−	0.404019i	$-0.867613\pi$
$797$	2.40448	−	11.0532i	0.0851712	−	0.391526i	0.999922	+	0.0124929i	$0.00397672\pi$
$798$	−16.2177	+	8.85554i	−0.574101	+	0.313483i
$799$	−2.43241	−	16.9178i	−0.0860525	−	0.598508i
$800$	−3.56387	+	3.50696i	−0.126002	+	0.123990i
$801$	−12.8892	−	1.85319i	−0.455419	−	0.0654794i
$802$	−22.4335	+	4.88012i	−0.792156	+	0.172323i
$803$	−0.518238	+	7.24591i	−0.0182882	+	0.255703i
$804$	7.57745			0.267236
$805$	−52.2788	−	7.11415i	−1.84259	−	0.250741i
$806$	48.0785			1.69349
$807$	−0.816201	+	11.4120i	−0.0287316	+	0.401721i
$808$	3.27098	−	0.711558i	0.115073	−	0.0250325i
$809$	54.6947	+	7.86391i	1.92296	+	0.276481i	0.995293	−	0.0969162i	$-0.0308979\pi$
$809$	54.6947	+	7.86391i	1.92296	+	0.276481i	0.927672	+	0.373397i	$0.121807\pi$
$810$	−1.20133	−	1.88595i	−0.0422104	−	0.0662655i
$811$	−4.39299	−	30.5539i	−0.154259	−	1.07289i	−0.908978	−	0.416845i	$-0.863136\pi$
$811$	−4.39299	−	30.5539i	−0.154259	−	1.07289i	0.754719	−	0.656049i	$-0.227773\pi$
$812$	29.8338	−	16.2905i	1.04696	−	0.571685i
$813$	−0.0209260	+	0.0961954i	−0.000733908	+	0.00337372i
$814$	−2.63631	+	1.20396i	−0.0924027	+	0.0421989i
$815$	24.6207	+	7.33705i	0.862427	+	0.257006i
$816$	−1.05804	−	0.916793i	−0.0370386	−	0.0320942i
$817$	−9.78455	+	0.699805i	−0.342318	+	0.0244831i
$818$	17.0521	−	31.2287i	0.596214	−	1.09188i
$819$	12.9509	+	28.3585i	0.452541	+	0.990927i
$820$	−1.79254	+	1.77817i	−0.0625982	+	0.0620964i
$821$	−1.99355	−	0.585358i	−0.0695753	−	0.0204291i	0.246760	−	0.969077i	$-0.420634\pi$
$821$	−1.99355	−	0.585358i	−0.0695753	−	0.0204291i	−0.316335	+	0.948648i	$0.602452\pi$
$822$	−6.16236	−	4.61309i	−0.214937	−	0.160900i
$823$	−18.8458	−	50.5275i	−0.656922	−	1.76128i	−0.648384	−	0.761313i	$-0.724555\pi$
$823$	−18.8458	−	50.5275i	−0.656922	−	1.76128i	−0.00853804	−	0.999964i	$-0.502718\pi$
$824$	−1.80223	+	12.5348i	−0.0627836	+	0.436670i
$825$	−2.22482	−	3.02241i	−0.0774582	−	0.105227i
$826$	−22.8570	+	19.8057i	−0.795295	+	0.689127i
$827$	4.92833	−	4.92833i	0.171375	−	0.171375i	−0.616208	−	0.787583i	$-0.711332\pi$
$827$	4.92833	−	4.92833i	0.171375	−	0.171375i	0.787583	+	0.616208i	$0.211332\pi$
$828$	4.75460	+	0.627533i	0.165234	+	0.0218083i
$829$		−	2.87645i		−	0.0999034i	−0.998752	−	0.0499517i	$-0.984093\pi$
$829$		−	2.87645i		−	0.0999034i	0.998752	−	0.0499517i	$-0.0159067\pi$
$830$	0.723743	+	0.546346i	0.0251215	+	0.0189639i
$831$	−2.29040	−	1.47195i	−0.0794532	−	0.0510615i
$832$	−5.07271	+	3.79739i	−0.175865	+	0.131651i
$833$	22.5693	−	8.41790i	0.781979	−	0.291663i
$834$	0.147864	−	0.0212596i	0.00512010	−	0.000736159i
$835$	−25.4472	+	21.8714i	−0.880635	+	0.756891i
$836$	2.37151	−	1.52408i	0.0820204	−	0.0527113i
$837$	−2.65153	+	7.10903i	−0.0916503	+	0.245724i
$838$	17.5868	+	9.60314i	0.607528	+	0.331735i
$839$	−1.38206	+	1.59498i	−0.0477139	+	0.0550648i	−0.779105	−	0.626894i	$-0.784326\pi$
$839$	−1.38206	+	1.59498i	−0.0477139	+	0.0550648i	0.731391	+	0.681958i	$0.238872\pi$
$840$	3.05694	+	10.5681i	0.105474	+	0.364634i
$841$	17.9748	−	5.27787i	0.619820	−	0.181995i
$842$	−29.7787	−	11.1069i	−1.02624	−	0.382768i
$843$	−10.3522	−	2.25199i	−0.356549	−	0.0775626i
$844$	1.35316	−	4.60845i	0.0465777	−	0.158629i
$845$	20.9886	+	56.9718i	0.722030	+	1.95989i
$846$	5.07162	−	11.1053i	0.174366	−	0.381808i
$847$	30.7715	+	41.1059i	1.05732	+	1.41242i
$848$	−2.23476	−	10.2730i	−0.0767419	−	0.352777i
$849$	2.30262	+	2.65737i	0.0790259	+	0.0912007i
$850$	−6.39054	+	2.85653i	−0.219194	+	0.0979780i
$851$	−13.2447	−	12.9417i	−0.454024	−	0.443634i
$852$	3.17113	+	3.17113i	0.108641	+	0.108641i
$853$	41.7217	+	2.98399i	1.42852	+	0.102170i	0.764057	−	0.645149i	$-0.223205\pi$
$853$	41.7217	+	2.98399i	1.42852	+	0.102170i	0.664466	+	0.747319i	$0.268659\pi$
$854$	−0.0906646	+	0.141077i	−0.00310248	+	0.00482755i
$855$	−0.565395	−	8.37899i	−0.0193361	−	0.286555i
$856$	−11.8969	−	5.43314i	−0.406628	−	0.185701i
$857$	11.1838	−	14.9398i	0.382031	−	0.510333i	−0.567771	−	0.823187i	$-0.692194\pi$
$857$	11.1838	−	14.9398i	0.382031	−	0.510333i	0.949801	+	0.312853i	$0.101285\pi$
$858$	−2.27941	−	4.17443i	−0.0778179	−	0.142513i
$859$	−10.1155	−	15.7401i	−0.345138	−	0.537045i	0.624678	−	0.780882i	$-0.285230\pi$
$859$	−10.1155	−	15.7401i	−0.345138	−	0.537045i	−0.969816	+	0.243837i	$0.921594\pi$
$860$	−0.854430	+	5.77754i	−0.0291358	+	0.197012i
$861$	1.56515	+	5.33041i	0.0533402	+	0.181660i
$862$	0.173724	+	2.42898i	0.00591707	+	0.0827314i
$863$	1.11355	+	15.5695i	0.0379058	+	0.529992i	0.980560	+	0.196221i	$0.0628669\pi$
$863$	1.11355	+	15.5695i	0.0379058	+	0.529992i	−0.942654	+	0.333772i	$0.891679\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	2.40987	−	16.2952i	0.0819380	−	0.554054i
$866$	13.4123	+	20.8699i	0.455767	+	0.709188i
$867$	7.20793	+	13.2003i	0.244794	+	0.448307i
$868$	22.3709	−	29.8840i	0.759318	−	1.01433i
$869$	8.16917	+	3.73073i	0.277120	+	0.126556i
$870$	1.04009	+	15.4138i	0.0352624	+	0.522578i
$871$	25.9590	−	40.3930i	0.879588	−	1.36867i
$872$	−1.64173	−	0.117419i	−0.0555962	−	0.00397632i
$873$	−2.23959	−	2.23959i	−0.0757988	−	0.0757988i
$874$	14.5431	+	10.6265i	0.491929	+	0.359445i
$875$	54.3484	+	8.48502i	1.83731	+	0.286846i
$876$	6.33789	+	7.31432i	0.214138	+	0.247128i
$877$	9.73609	+	44.7561i	0.328764	+	1.51131i	0.783902	+	0.620884i	$0.213226\pi$
$877$	9.73609	+	44.7561i	0.328764	+	1.51131i	−0.455138	+	0.890421i	$0.650410\pi$
$878$	−2.77322	−	3.70459i	−0.0935917	−	0.125024i
$879$	−10.5111	+	23.0161i	−0.354530	+	0.776313i
$880$	−0.580200	−	1.57490i	−0.0195586	−	0.0530900i
$881$	−6.43699	+	21.9224i	−0.216868	+	0.738584i	0.777145	+	0.629321i	$0.216667\pi$
$881$	−6.43699	+	21.9224i	−0.216868	+	0.738584i	−0.994013	+	0.109263i	$0.965151\pi$
$882$	16.8127	+	3.65739i	0.566115	+	0.123151i
$883$	38.1346	+	14.2235i	1.28333	+	0.478657i	0.896316	−	0.443416i	$-0.146234\pi$
$883$	38.1346	+	14.2235i	1.28333	+	0.478657i	0.387015	+	0.922074i	$0.373506\pi$
$884$	−8.51179	+	2.49929i	−0.286282	+	0.0840601i
$885$	−3.81948	−	13.2043i	−0.128390	−	0.443858i
$886$	7.75840	−	8.95367i	0.260649	−	0.300805i
$887$	7.51586	+	4.10397i	0.252358	+	0.137798i	0.600449	−	0.799663i	$-0.294988\pi$
$887$	7.51586	+	4.10397i	0.252358	+	0.137798i	−0.348092	+	0.937461i	$0.613170\pi$
$888$	−1.34936	+	3.61778i	−0.0452816	+	0.121405i
$889$	−46.3505	+	29.7877i	−1.55455	+	0.999046i
$890$	−22.0822	+	18.9793i	−0.740196	+	0.636186i
$891$	0.742954	−	0.106821i	0.0248899	−	0.00357863i
$892$	−10.8467	+	4.04563i	−0.363176	+	0.135458i
$893$	36.7063	−	27.4780i	1.22833	−	0.919516i
$894$	11.5586	+	7.42826i	0.386577	+	0.248438i
$895$	−28.2707	−	21.3413i	−0.944987	−	0.713360i
$896$			4.91996i			0.164364i
$897$	19.6336	−	23.1955i	0.655547	−	0.774474i
$898$	3.32631	−	3.32631i	0.111000	−	0.111000i
$899$	39.6172	−	34.3285i	1.32131	−	1.14492i
$900$	−4.94322	−	0.751384i	−0.164774	−	0.0250461i
$901$	2.09465	−	14.5686i	0.0697828	−	0.485350i
$902$	−0.296187	−	0.794108i	−0.00986194	−	0.0264409i
$903$	10.2873	+	7.70097i	0.342339	+	0.256272i
$904$	4.77069	+	1.40080i	0.158671	+	0.0465899i
$905$	−39.6126	+	39.2951i	−1.31677	+	1.30621i
$906$	7.97040	+	17.4527i	0.264799	+	0.579828i
$907$	2.63660	−	4.82858i	0.0875469	−	0.160330i	−0.830237	−	0.557411i	$-0.811795\pi$
$907$	2.63660	−	4.82858i	0.0875469	−	0.160330i	0.917784	+	0.397081i	$0.129977\pi$
$908$	10.3271	−	0.738611i	0.342718	−	0.0245117i
$909$	2.52986	+	2.19213i	0.0839100	+	0.0727084i
$910$	66.8079	+	19.9089i	2.21466	+	0.659975i
$911$	9.02431	−	4.12126i	0.298989	−	0.136544i	−0.260272	−	0.965535i	$-0.583812\pi$
$911$	9.02431	−	4.12126i	0.298989	−	0.136544i	0.559261	+	0.828992i	$0.311085\pi$
$912$	0.798335	−	3.66989i	0.0264355	−	0.121522i
$913$	−0.267159	+	0.145880i	−0.00884168	+	0.00482792i
$914$	2.60351	+	18.1078i	0.0861164	+	0.598953i
$915$	−0.0409478	−	0.0642833i	−0.00135369	−	0.00212514i
$916$	−21.1570	−	3.04191i	−0.699046	−	0.100508i
$917$	3.89647	−	0.847624i	0.128673	−	0.0279910i
$918$	0.0998735	−	1.39641i	0.00329632	−	0.0460885i
$919$	−26.3662			−0.869740			−0.434870	−	0.900493i	$-0.643206\pi$
$919$	−26.3662			−0.869740			−0.434870	+	0.900493i	$0.643206\pi$
$920$	8.05126	−	7.08358i	0.265442	−	0.233539i
$921$	−5.63171			−0.185571
$922$	1.98742	−	27.7878i	0.0654523	−	0.915142i
$923$	27.7681	−	6.04057i	0.913997	−	0.198828i
$924$	−3.65530	−	0.525553i	−0.120251	−	0.0172894i
$925$	13.5412	+	13.7609i	0.445232	+	0.452457i
$926$	−4.20966	−	29.2788i	−0.138338	−	0.962162i
$927$	−11.1146	+	6.06906i	−0.365053	+	0.199334i
$928$	−1.46860	+	6.75106i	−0.0482093	+	0.221614i
$929$	−54.6018	+	24.9358i	−1.79143	+	0.818117i	−0.823320	+	0.567577i	$0.807881\pi$
$929$	−54.6018	+	24.9358i	−1.79143	+	0.818117i	−0.968106	+	0.250540i	$0.919392\pi$
$930$	8.07094	+	14.9233i	0.264657	+	0.489354i
$931$	48.8371	+	42.3176i	1.60057	+	1.38690i
$932$	17.6312	−	1.26100i	0.577528	−	0.0413056i
$933$	3.95511	−	7.24324i	0.129484	−	0.237133i
$934$	7.15298	+	15.6628i	0.234053	+	0.512504i
$935$	0.00945581	−	2.34968i	0.000309238	−	0.0768428i
$936$	−6.07993	−	1.78523i	−0.198729	−	0.0583520i
$937$	−37.7481	−	28.2579i	−1.23318	−	0.923145i	−0.234379	−	0.972145i	$-0.575306\pi$
$937$	−37.7481	−	28.2579i	−1.23318	−	0.923145i	−0.998799	+	0.0489998i	$0.984397\pi$
$938$	−13.0283	−	34.9301i	−0.425388	−	1.14051i
$939$	1.52850	−	10.6310i	0.0498809	−	0.346929i
$940$	−11.2405	−	24.8776i	−0.366623	−	0.811419i
$941$	6.71997	−	5.82289i	0.219065	−	0.189821i	−0.538414	−	0.842680i	$-0.680976\pi$
$941$	6.71997	−	5.82289i	0.219065	−	0.189821i	0.757479	+	0.652860i	$0.226431\pi$
$942$	3.28489	−	3.28489i	0.107028	−	0.107028i
$943$	4.05129	−	3.59339i	0.131928	−	0.117017i
$944$		−	6.14723i		−	0.200075i
$945$	−6.62825	+	8.78043i	−0.215617	+	0.285628i
$946$	−1.64926	−	1.05991i	−0.0536219	−	0.0344607i
$947$	23.0485	−	17.2539i	0.748976	−	0.560676i	−0.155176	−	0.987887i	$-0.549595\pi$
$947$	23.0485	−	17.2539i	0.748976	−	0.560676i	0.904152	+	0.427211i	$0.140504\pi$
$948$	11.2105	−	4.18128i	0.364099	−	0.135802i
$949$	60.7029	−	8.72776i	1.97050	−	0.283315i
$950$	−14.9420	−	11.3742i	−0.484782	−	0.369028i
$951$	4.63892	−	2.98125i	0.150427	−	0.0966737i
$952$	−2.40706	+	6.45357i	−0.0780131	+	0.209161i
$953$	−0.367949	−	0.200916i	−0.0119191	−	0.00650829i	0.473278	−	0.880913i	$-0.343070\pi$
$953$	−0.367949	−	0.200916i	−0.0119191	−	0.00650829i	−0.485197	+	0.874405i	$0.661252\pi$
$954$	6.88473	−	7.94541i	0.222902	−	0.257242i
$955$	−16.4443	+	29.8295i	−0.532125	+	0.965259i
$956$	−13.7230	+	4.02944i	−0.443834	+	0.130321i
$957$	−4.85885	−	1.81226i	−0.157064	−	0.0585820i
$958$	25.9406	+	5.64304i	0.838104	+	0.182318i
$959$	−10.6699	+	36.3384i	−0.344550	+	1.17343i
$960$	−2.03024	−	0.937074i	−0.0655259	−	0.0302439i
$961$	11.0371	−	24.1680i	0.356037	−	0.779611i
$962$	14.6626	+	19.5869i	0.472741	+	0.631508i
$963$	−2.78010	−	12.7799i	−0.0895876	−	0.411828i
$964$	11.4011	+	13.1576i	0.367205	+	0.423777i
$965$	−20.2079	−	13.1021i	−0.650517	−	0.421770i
$966$	−5.28204	−	22.9965i	−0.169947	−	0.739899i
$967$	27.0511	+	27.0511i	0.869905	+	0.869905i	0.992462	−	0.122557i	$-0.0391093\pi$
$967$	27.0511	+	27.0511i	0.869905	+	0.869905i	−0.122557	+	0.992462i	$0.539109\pi$
$968$	−10.4100	−	0.744539i	−0.334591	−	0.0239304i
$969$	2.84265	−	4.42326i	0.0913192	−	0.142095i
$970$	−7.06615	+	0.476807i	−0.226880	+	0.0153094i
$971$	27.4344	+	12.5289i	0.880411	+	0.402070i	0.803736	−	0.594986i	$-0.202842\pi$
$971$	27.4344	+	12.5289i	0.880411	+	0.402070i	0.0766748	+	0.997056i	$0.475570\pi$
$972$	0.599278	−	0.800541i	0.0192218	−	0.0256774i
$973$	−0.352230	−	0.645062i	−0.0112920	−	0.0206797i
$974$	−5.87078	−	9.13511i	−0.188112	−	0.292708i
$975$	−20.9400	+	23.7767i	−0.670617	+	0.761463i
$976$	−0.00960295	−	0.0327047i	−0.000307383	−	0.00104685i
$977$	0.617577	+	8.63485i	0.0197580	+	0.276253i	0.997721	+	0.0674749i	$0.0214943\pi$
$977$	0.617577	+	8.63485i	0.0197580	+	0.276253i	−0.977963	+	0.208779i	$0.933051\pi$
$978$	0.819633	+	11.4600i	0.0262090	+	0.366449i
$979$	−2.75368	−	9.37816i	−0.0880079	−	0.299727i
$980$	30.8923	−	22.9323i	0.986819	−	0.732545i
$981$	−0.889856	−	1.38464i	−0.0284109	−	0.0442083i
$982$	3.01536	+	5.52222i	0.0962240	+	0.176221i
$983$	−26.9172	+	35.9572i	−0.858526	+	1.14686i	0.129348	+	0.991599i	$0.458712\pi$
$983$	−26.9172	+	35.9572i	−0.858526	+	1.14686i	−0.987874	+	0.155258i	$0.950379\pi$
$984$	−1.02713	−	0.469073i	−0.0327436	−	0.0149535i
$985$	−27.5927	−	24.1043i	−0.879178	−	0.768028i
$986$	−5.22930	+	8.13694i	−0.166535	+	0.259133i
$987$	−59.9125	−	4.28503i	−1.90704	−	0.136394i
$988$	−16.8281	−	16.8281i	−0.535372	−	0.535372i
$989$	2.52080	−	12.2699i	0.0801568	−	0.390162i
$990$	0.913075	−	1.40828i	0.0290194	−	0.0447581i
$991$	−19.9533	−	23.0274i	−0.633838	−	0.731488i	0.344435	−	0.938810i	$-0.388071\pi$
$991$	−19.9533	−	23.0274i	−0.633838	−	0.731488i	−0.978273	+	0.207322i	$0.933525\pi$
$992$	1.61282	+	7.41402i	0.0512072	+	0.235395i
$993$	−3.19305	−	4.26541i	−0.101328	−	0.135359i
$994$	9.16584	−	20.0704i	0.290723	−	0.636594i
$995$	−51.3051	+	18.9010i	−1.62648	+	0.599201i
$996$	−0.114253	+	0.389109i	−0.00362024	+	0.0123294i
$997$	−25.8551	−	5.62442i	−0.818838	−	0.178127i	−0.216412	−	0.976302i	$-0.569435\pi$
$997$	−25.8551	−	5.62442i	−0.818838	−	0.178127i	−0.602426	+	0.798175i	$0.705799\pi$
$998$	26.7342	+	9.97133i	0.846255	+	0.315637i
$999$	−3.70483	+	1.08783i	−0.117215	+	0.0344176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.217.1	yes	240
5.3	odd	4	inner	690.2.w.a.493.8	yes	240
23.7	odd	22	inner	690.2.w.a.7.8	✓	240
115.53	even	44	inner	690.2.w.a.283.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.8	✓	240	23.7	odd	22	inner
690.2.w.a.217.1	yes	240	1.1	even	1	trivial
690.2.w.a.283.1	yes	240	115.53	even	44	inner
690.2.w.a.493.8	yes	240	5.3	odd	4	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.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0713392 + 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-2.18304 - 0.484099i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-4.31814 + 2.35788i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.0713392 + 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-2.18304 - 0.484099i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-4.31814 + 2.35788i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(0.638602 - 2.14294i) q^{10} +(0.567261 + 0.491535i) q^{11} +(0.997452 - 0.0713392i) q^{12} +(3.03681 - 5.56150i) q^{13} +(-2.04382 - 4.47535i) q^{14} +(2.23605 + 0.00899852i) q^{15} +(0.959493 + 0.281733i) q^{16} +(1.12074 + 0.838978i) q^{17} +(0.349464 + 0.936950i) q^{18} +(-0.534494 + 3.71749i) q^{19} +(2.09192 + 0.789850i) q^{20} +(3.71825 - 3.22189i) q^{21} +(-0.530750 + 0.530750i) q^{22} +(-4.38521 - 1.94164i) q^{23} +1.00000i q^{24} +(4.53130 + 2.11361i) q^{25} +(5.33069 + 3.42583i) q^{26} +(-0.800541 + 0.599278i) q^{27} +(4.60975 - 1.71935i) q^{28} +(6.83863 - 0.983246i) q^{29} +(-0.168494 + 2.22971i) q^{30} +(6.38294 - 4.10207i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(-0.658781 - 0.359721i) q^{33} +(-0.916793 + 1.05804i) q^{34} +(10.5681 - 3.05694i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(3.61778 + 1.34936i) q^{37} +(-3.66989 - 0.798335i) q^{38} +(-1.78523 + 6.07993i) q^{39} +(-0.937074 + 2.03024i) q^{40} +(-0.469073 + 1.02713i) q^{41} +(2.94842 + 3.93863i) q^{42} +(0.555199 + 2.55221i) q^{43} +(-0.491535 - 0.567261i) q^{44} +(-2.18686 + 0.466514i) q^{45} +(2.24953 - 4.23552i) q^{46} +(-8.63275 - 8.63275i) q^{47} +(-0.997452 - 0.0713392i) q^{48} +(9.30224 - 14.4746i) q^{49} +(-2.43149 + 4.36897i) q^{50} +(-1.27347 - 0.581573i) q^{51} +(-3.79739 + 5.07271i) q^{52} +(-5.03848 - 9.22729i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-1.00040 - 1.34765i) q^{55} +(1.38611 + 4.72066i) q^{56} +(-0.267930 - 3.74615i) q^{57} +(0.492879 + 6.89135i) q^{58} +(-1.73187 - 5.89822i) q^{59} +(-2.21201 - 0.327130i) q^{60} +(-0.0184279 - 0.0286744i) q^{61} +(3.63626 + 6.65932i) q^{62} +(-2.94842 + 3.93863i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-9.32179 + 10.6708i) q^{65} +(0.405802 - 0.631440i) q^{66} +(7.55814 + 0.540569i) q^{67} +(-0.989936 - 0.989936i) q^{68} +(4.69772 + 0.965123i) q^{69} +(2.29523 + 10.7593i) q^{70} +(2.93682 + 3.38928i) q^{71} +(-0.212565 - 0.977147i) q^{72} +(5.79995 + 7.74782i) q^{73} +(-1.60401 + 3.51230i) q^{74} +(-4.87702 - 1.10211i) q^{75} +(1.05811 - 3.60358i) q^{76} +(-3.60850 - 0.784980i) q^{77} +(-5.93708 - 2.21442i) q^{78} +(11.4802 - 3.37088i) q^{79} +(-1.95822 - 1.07952i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-0.991045 - 0.541152i) q^{82} +(-0.141720 + 0.379967i) q^{83} +(-4.13893 + 2.65993i) q^{84} +(-2.04047 - 2.37407i) q^{85} +(-2.58531 + 0.371712i) q^{86} +(-6.47334 + 2.41443i) q^{87} +(0.600882 - 0.449814i) q^{88} +(-10.9546 - 7.04011i) q^{89} +(-0.309316 - 2.21457i) q^{90} +31.1758i q^{91} +(4.06425 + 2.54596i) q^{92} +(-5.36512 + 5.36512i) q^{93} +(9.22661 - 7.99490i) q^{94} +(2.96646 - 7.85667i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-1.10685 - 2.96757i) q^{97} +(13.7741 + 10.3111i) q^{98} +(0.720190 + 0.211467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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