LMFDB - Embedded newform 690.2.w.b.217.6

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			217.6
Character	$\chi$	$=$	690.217
Dual form			690.2.w.b.283.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0713392 + 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(2.23462 - 0.0804541i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-3.44079 + 1.87882i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.0713392 + 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(2.23462 - 0.0804541i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-3.44079 + 1.87882i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-0.0791669 + 2.23467i) q^{10} +(0.512771 + 0.444318i) q^{11} +(-0.997452 + 0.0713392i) q^{12} +(-3.12851 + 5.72944i) q^{13} +(-1.62857 - 3.56606i) q^{14} +(2.16645 - 0.553618i) q^{15} +(0.959493 + 0.281733i) q^{16} +(3.18196 + 2.38199i) q^{17} +(0.349464 + 0.936950i) q^{18} +(-0.239171 + 1.66347i) q^{19} +(-2.22332 - 0.238384i) q^{20} +(-2.96279 + 2.56727i) q^{21} +(-0.479767 + 0.479767i) q^{22} +(-1.34539 + 4.60325i) q^{23} -1.00000i q^{24} +(4.98705 - 0.359569i) q^{25} +(-5.49166 - 3.52927i) q^{26} +(0.800541 - 0.599278i) q^{27} +(3.67316 - 1.37002i) q^{28} +(2.45679 - 0.353233i) q^{29} +(0.397655 + 2.20043i) q^{30} +(5.47061 - 3.51575i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(0.595499 + 0.325167i) q^{33} +(-2.60292 + 3.00393i) q^{34} +(-7.53771 + 4.47527i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(4.77064 + 1.77936i) q^{37} +(-1.64217 - 0.357233i) q^{38} +(-1.83913 + 6.26352i) q^{39} +(0.396387 - 2.20065i) q^{40} +(-2.24845 + 4.92341i) q^{41} +(-2.34937 - 3.13839i) q^{42} +(-2.33542 - 10.7358i) q^{43} +(-0.444318 - 0.512771i) q^{44} +(1.99926 - 1.00148i) q^{45} +(-4.49554 - 1.67035i) q^{46} +(4.55955 + 4.55955i) q^{47} +(0.997452 + 0.0713392i) q^{48} +(4.52463 - 7.04047i) q^{49} +(0.00288011 + 5.00000i) q^{50} +(3.61557 + 1.65118i) q^{51} +(3.91205 - 5.22589i) q^{52} +(-2.23792 - 4.09845i) q^{53} +(0.540641 + 0.841254i) q^{54} +(1.18159 + 0.951628i) q^{55} +(1.10449 + 3.76153i) q^{56} +(0.119891 + 1.67630i) q^{57} +(0.177068 + 2.47573i) q^{58} +(-3.74486 - 12.7538i) q^{59} +(-2.22319 + 0.239665i) q^{60} +(6.18829 + 9.62916i) q^{61} +(3.11652 + 5.70748i) q^{62} +(-2.34937 + 3.13839i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-6.53008 + 13.0548i) q^{65} +(-0.366821 + 0.570784i) q^{66} +(-4.78621 - 0.342317i) q^{67} +(-2.81058 - 2.81058i) q^{68} +(-0.336152 + 4.78404i) q^{69} +(-3.92613 - 7.83777i) q^{70} +(-7.81093 - 9.01429i) q^{71} +(-0.212565 - 0.977147i) q^{72} +(-3.48068 - 4.64964i) q^{73} +(-2.11516 + 4.63155i) q^{74} +(4.79665 - 1.41143i) q^{75} +(0.473474 - 1.61250i) q^{76} +(-2.59913 - 0.565406i) q^{77} +(-6.11636 - 2.28128i) q^{78} +(-1.48297 + 0.435439i) q^{79} +(2.16677 + 0.552370i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-4.75046 - 2.59395i) q^{82} +(-4.16868 + 11.1767i) q^{83} +(3.29799 - 2.11949i) q^{84} +(7.30212 + 5.06684i) q^{85} +(10.8750 - 1.56359i) q^{86} +(2.32556 - 0.867389i) q^{87} +(0.543161 - 0.406606i) q^{88} +(1.40078 + 0.900224i) q^{89} +(0.856301 + 2.06561i) q^{90} -25.5917i q^{91} +(1.98681 - 4.36493i) q^{92} +(4.59826 - 4.59826i) q^{93} +(-4.87320 + 4.22266i) q^{94} +(-0.400624 + 3.73647i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-3.39372 - 9.09892i) q^{97} +(6.69975 + 5.01537i) q^{98} +(0.651009 + 0.191153i) 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} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * 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
$5$	2.23462	−	0.0804541i	0.999353	−	0.0359802i
$5$	2.23462	−	0.0804541i	0.999353	−	0.0359802i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	−3.44079	+	1.87882i	−1.30050	+	0.710126i	−0.972134	−	0.234425i	$-0.924679\pi$
$7$	−3.44079	+	1.87882i	−1.30050	+	0.710126i	−0.328364	+	0.944551i	$0.606497\pi$
$8$	0.212565	−	0.977147i	0.0751532	−	0.345474i
$9$	0.909632	−	0.415415i	0.303211	−	0.138472i
$10$	−0.0791669	+	2.23467i	−0.0250348	+	0.706663i
$11$	0.512771	+	0.444318i	0.154606	+	0.133967i	0.728729	−	0.684802i	$-0.240111\pi$
$11$	0.512771	+	0.444318i	0.154606	+	0.133967i	−0.574123	+	0.818769i	$0.694657\pi$
$12$	−0.997452	+	0.0713392i	−0.287940	+	0.0205938i
$13$	−3.12851	+	5.72944i	−0.867693	+	1.58906i	−0.0609635	+	0.998140i	$0.519417\pi$
$13$	−3.12851	+	5.72944i	−0.867693	+	1.58906i	−0.806729	+	0.590921i	$0.798764\pi$
$14$	−1.62857	−	3.56606i	−0.435252	−	0.953070i
$15$	2.16645	−	0.553618i	0.559375	−	0.142944i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	3.18196	+	2.38199i	0.771740	+	0.577717i	0.910936	−	0.412548i	$-0.135361\pi$
$17$	3.18196	+	2.38199i	0.771740	+	0.577717i	−0.139196	+	0.990265i	$0.544452\pi$
$18$	0.349464	+	0.936950i	0.0823695	+	0.220841i
$19$	−0.239171	+	1.66347i	−0.0548697	+	0.381627i	0.943820	+	0.330459i	$0.107204\pi$
$19$	−0.239171	+	1.66347i	−0.0548697	+	0.381627i	−0.998690	+	0.0511681i	$0.983706\pi$
$20$	−2.22332	−	0.238384i	−0.497151	−	0.0533044i
$21$	−2.96279	+	2.56727i	−0.646534	+	0.560225i
$22$	−0.479767	+	0.479767i	−0.102287	+	0.102287i
$23$	−1.34539	+	4.60325i	−0.280533	+	0.959844i
$23$	−1.34539	+	4.60325i	−0.280533	+	0.959844i
$24$		−	1.00000i		−	0.204124i
$25$	4.98705	−	0.359569i	0.997411	−	0.0719137i
$26$	−5.49166	−	3.52927i	−1.07700	−	0.692148i
$27$	0.800541	−	0.599278i	0.154064	−	0.115331i
$28$	3.67316	−	1.37002i	0.694161	−	0.258909i
$29$	2.45679	−	0.353233i	0.456214	−	0.0655937i	0.0896229	−	0.995976i	$-0.471434\pi$
$29$	2.45679	−	0.353233i	0.456214	−	0.0655937i	0.366591	+	0.930382i	$0.380525\pi$
$30$	0.397655	+	2.20043i	0.0726015	+	0.401741i
$31$	5.47061	−	3.51575i	0.982551	−	0.631447i	0.0524005	−	0.998626i	$-0.483313\pi$
$31$	5.47061	−	3.51575i	0.982551	−	0.631447i	0.930150	+	0.367179i	$0.119676\pi$
$32$	−0.349464	+	0.936950i	−0.0617771	+	0.165631i
$33$	0.595499	+	0.325167i	0.103663	+	0.0566043i
$34$	−2.60292	+	3.00393i	−0.446397	+	0.515169i
$35$	−7.53771	+	4.47527i	−1.27411	+	0.756458i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	4.77064	+	1.77936i	0.784289	+	0.292525i	0.709528	−	0.704677i	$-0.248908\pi$
$37$	4.77064	+	1.77936i	0.784289	+	0.292525i	0.0747604	+	0.997202i	$0.476181\pi$
$38$	−1.64217	−	0.357233i	−0.266396	−	0.0579508i
$39$	−1.83913	+	6.26352i	−0.294497	+	1.00297i
$40$	0.396387	−	2.20065i	0.0626743	−	0.347954i
$41$	−2.24845	+	4.92341i	−0.351148	+	0.768907i	0.648820	+	0.760942i	$0.275263\pi$
$41$	−2.24845	+	4.92341i	−0.351148	+	0.768907i	−0.999968	+	0.00796540i	$0.997465\pi$
$42$	−2.34937	−	3.13839i	−0.362515	−	0.484264i
$43$	−2.33542	−	10.7358i	−0.356148	−	1.63719i	−0.711666	−	0.702518i	$-0.752059\pi$
$43$	−2.33542	−	10.7358i	−0.356148	−	1.63719i	0.355517	−	0.934670i	$-0.384305\pi$
$44$	−0.444318	−	0.512771i	−0.0669835	−	0.0773031i
$45$	1.99926	−	1.00148i	0.298032	−	0.149292i
$46$	−4.49554	−	1.67035i	−0.662832	−	0.246280i
$47$	4.55955	+	4.55955i	0.665078	+	0.665078i	0.956573	−	0.291494i	$-0.0941524\pi$
$47$	4.55955	+	4.55955i	0.665078	+	0.665078i	−0.291494	+	0.956573i	$0.594152\pi$
$48$	0.997452	+	0.0713392i	0.143970	+	0.0102969i
$49$	4.52463	−	7.04047i	0.646376	−	1.00578i
$50$	0.00288011	+	5.00000i	0.000407309	+	0.707107i
$51$	3.61557	+	1.65118i	0.506282	+	0.231211i
$52$	3.91205	−	5.22589i	0.542504	−	0.724701i
$53$	−2.23792	−	4.09845i	−0.307402	−	0.562965i	0.677616	−	0.735416i	$-0.263013\pi$
$53$	−2.23792	−	4.09845i	−0.307402	−	0.562965i	−0.985018	+	0.172451i	$0.944831\pi$
$54$	0.540641	+	0.841254i	0.0735719	+	0.114480i
$55$	1.18159	+	0.951628i	0.159326	+	0.128317i
$56$	1.10449	+	3.76153i	0.147593	+	0.502656i
$57$	0.119891	+	1.67630i	0.0158800	+	0.222031i
$58$	0.177068	+	2.47573i	0.0232501	+	0.325079i
$59$	−3.74486	−	12.7538i	−0.487539	−	1.66041i	−0.724799	−	0.688960i	$-0.758068\pi$
$59$	−3.74486	−	12.7538i	−0.487539	−	1.66041i	0.237260	−	0.971446i	$-0.423751\pi$
$60$	−2.22319	+	0.239665i	−0.287012	+	0.0309406i
$61$	6.18829	+	9.62916i	0.792329	+	1.23289i	0.968619	+	0.248550i	$0.0799539\pi$
$61$	6.18829	+	9.62916i	0.792329	+	1.23289i	−0.176290	+	0.984338i	$0.556410\pi$
$62$	3.11652	+	5.70748i	0.395799	+	0.724851i
$63$	−2.34937	+	3.13839i	−0.295993	+	0.395400i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	−6.53008	+	13.0548i	−0.809956	+	1.61925i
$66$	−0.366821	+	0.570784i	−0.0451525	+	0.0702587i
$67$	−4.78621	−	0.342317i	−0.584729	−	0.0418206i	−0.224159	−	0.974553i	$-0.571963\pi$
$67$	−4.78621	−	0.342317i	−0.584729	−	0.0418206i	−0.360570	+	0.932732i	$0.617418\pi$
$68$	−2.81058	−	2.81058i	−0.340833	−	0.340833i
$69$	−0.336152	+	4.78404i	−0.0404680	+	0.575930i
$70$	−3.92613	−	7.83777i	−0.469262	−	0.936792i
$71$	−7.81093	−	9.01429i	−0.926987	−	1.06980i	−0.997384	−	0.0722809i	$-0.976972\pi$
$71$	−7.81093	−	9.01429i	−0.926987	−	1.06980i	0.0703974	−	0.997519i	$-0.477573\pi$
$72$	−0.212565	−	0.977147i	−0.0250511	−	0.115158i
$73$	−3.48068	−	4.64964i	−0.407383	−	0.544199i	0.549189	−	0.835698i	$-0.314937\pi$
$73$	−3.48068	−	4.64964i	−0.407383	−	0.544199i	−0.956571	+	0.291499i	$0.905846\pi$
$74$	−2.11516	+	4.63155i	−0.245882	+	0.538407i
$75$	4.79665	−	1.41143i	0.553870	−	0.162977i
$76$	0.473474	−	1.61250i	0.0543112	−	0.184967i
$77$	−2.59913	−	0.565406i	−0.296198	−	0.0644340i
$78$	−6.11636	−	2.28128i	−0.692541	−	0.258304i
$79$	−1.48297	+	0.435439i	−0.166847	+	0.0489907i	−0.364089	−	0.931364i	$-0.618620\pi$
$79$	−1.48297	+	0.435439i	−0.166847	+	0.0489907i	0.197242	+	0.980355i	$0.436802\pi$
$80$	2.16677	+	0.552370i	0.242252	+	0.0617569i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−4.75046	−	2.59395i	−0.524601	−	0.286454i
$83$	−4.16868	+	11.1767i	−0.457572	+	1.22680i	0.479463	+	0.877562i	$0.340831\pi$
$83$	−4.16868	+	11.1767i	−0.457572	+	1.22680i	−0.937035	+	0.349235i	$0.886441\pi$
$84$	3.29799	−	2.11949i	0.359841	−	0.231256i
$85$	7.30212	+	5.06684i	0.792026	+	0.549576i
$86$	10.8750	−	1.56359i	1.17268	−	0.168606i
$87$	2.32556	−	0.867389i	0.249326	−	0.0929938i
$88$	0.543161	−	0.406606i	0.0579012	−	0.0433443i
$89$	1.40078	+	0.900224i	0.148482	+	0.0954236i	0.612772	−	0.790259i	$-0.290054\pi$
$89$	1.40078	+	0.900224i	0.148482	+	0.0954236i	−0.464290	+	0.885683i	$0.653691\pi$
$90$	0.856301	+	2.06561i	0.0902621	+	0.217735i
$91$		−	25.5917i		−	2.68274i
$92$	1.98681	−	4.36493i	0.207139	−	0.455075i
$93$	4.59826	−	4.59826i	0.476818	−	0.476818i
$94$	−4.87320	+	4.22266i	−0.502633	+	0.435534i
$95$	−0.400624	+	3.73647i	−0.0411031	+	0.383354i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	−3.39372	−	9.09892i	−0.344580	−	0.923856i	−0.987457	−	0.157886i	$-0.949532\pi$
$97$	−3.39372	−	9.09892i	−0.344580	−	0.923856i	0.642877	−	0.765969i	$-0.277741\pi$
$98$	6.69975	+	5.01537i	0.676776	+	0.506629i
$99$	0.651009	+	0.191153i	0.0654289	+	0.0192116i
$100$	−4.98747	−	0.353823i	−0.498747	−	0.0353823i
$101$	2.64440	+	5.79044i	0.263128	+	0.576170i	0.994372	−	0.105946i	$-0.0337871\pi$
$101$	2.64440	+	5.79044i	0.263128	+	0.576170i	−0.731244	+	0.682116i	$0.761060\pi$
$102$	−1.90490	+	3.48857i	−0.188613	+	0.345420i
$103$	−7.38713	+	0.528338i	−0.727876	+	0.0520587i	−0.430359	−	0.902658i	$-0.641613\pi$
$103$	−7.38713	+	0.528338i	−0.727876	+	0.0520587i	−0.297517	+	0.954717i	$0.596158\pi$
$104$	4.93349	+	4.27490i	0.483769	+	0.419188i
$105$	−6.41416	+	5.97525i	−0.625958	+	0.583125i
$106$	4.24766	−	1.93984i	0.412569	−	0.188414i
$107$	2.21389	−	10.1771i	0.214025	−	0.983857i	−0.737276	−	0.675592i	$-0.763888\pi$
$107$	2.21389	−	10.1771i	0.214025	−	0.983857i	0.951301	−	0.308265i	$-0.0997483\pi$
$108$	−0.877679	+	0.479249i	−0.0844547	+	0.0461158i
$109$	−1.29119	−	8.98042i	−0.123674	−	0.860168i	−0.953338	−	0.301906i	$-0.902377\pi$
$109$	−1.29119	−	8.98042i	−0.123674	−	0.860168i	0.829664	−	0.558263i	$-0.188532\pi$
$110$	−1.03350	+	1.11070i	−0.0985401	+	0.105901i
$111$	5.03985	+	0.724621i	0.478361	+	0.0687780i
$112$	−3.83074	+	0.833327i	−0.361971	+	0.0787420i
$113$	−0.285271	+	3.98860i	−0.0268360	+	0.375216i	0.966232	+	0.257674i	$0.0829561\pi$
$113$	−0.285271	+	3.98860i	−0.0268360	+	0.375216i	−0.993068	+	0.117542i	$0.962498\pi$
$114$	−1.68058			−0.157401
$115$	−2.63609	+	10.3948i	−0.245816	+	0.969316i
$116$	−2.48205			−0.230453
$117$	−0.465698	+	6.51131i	−0.0430538	+	0.601971i
$118$	12.9885	−	2.82547i	1.19569	−	0.260106i
$119$	−15.4238	−	2.21761i	−1.41390	−	0.203288i
$120$	−0.0804541	−	2.23462i	−0.00734442	−	0.203992i
$121$	−1.49995	−	10.4324i	−0.136359	−	0.948397i
$122$	−10.0461	+	5.48558i	−0.909531	+	0.496641i
$123$	−1.15052	+	5.28883i	−0.103738	+	0.476878i
$124$	−5.91527	+	2.70141i	−0.531207	+	0.242594i
$125$	11.1152	−	1.20473i	0.994178	−	0.107754i
$126$	−2.96279	−	2.56727i	−0.263946	−	0.228711i
$127$	13.8639	−	0.991568i	1.23023	−	0.0879875i	0.558954	−	0.829199i	$-0.311203\pi$
$127$	13.8639	−	0.991568i	1.23023	−	0.0879875i	0.671272	+	0.741211i	$0.265748\pi$
$128$	0.479249	−	0.877679i	0.0423600	−	0.0775766i
$129$	−4.56410	−	9.99398i	−0.401847	−	0.879921i
$130$	−12.5557	−	7.44476i	−1.10121	−	0.652949i
$131$	−5.52602	−	1.62259i	−0.482811	−	0.141766i	0.0312645	−	0.999511i	$-0.490047\pi$
$131$	−5.52602	−	1.62259i	−0.482811	−	0.141766i	−0.514075	+	0.857745i	$0.671865\pi$
$132$	−0.543161	−	0.406606i	−0.0472761	−	0.0353905i
$133$	−2.30242	−	6.17303i	−0.199645	−	0.535270i
$134$	0.682889	−	4.74960i	0.0589926	−	0.410303i
$135$	1.74069	−	1.40356i	0.149815	−	0.120800i
$136$	3.00393	−	2.60292i	0.257585	−	0.223198i
$137$	2.25904	−	2.25904i	0.193003	−	0.193003i	−0.603989	−	0.796992i	$-0.706423\pi$
$137$	2.25904	−	2.25904i	0.193003	−	0.193003i	0.796992	+	0.603989i	$0.206423\pi$
$138$	−4.74787	−	0.676585i	−0.404165	−	0.0575947i
$139$			12.0020i			1.01800i	0.860766	+	0.509000i	$0.169985\pi$
$139$			12.0020i			1.01800i	−0.860766	+	0.509000i	$0.830015\pi$
$140$	8.09788	−	3.35699i	0.684396	−	0.283717i
$141$	5.42455	+	3.48615i	0.456829	+	0.293586i
$142$	9.54855	−	7.14796i	0.801297	−	0.599843i
$143$	−4.14990	+	1.54783i	−0.347032	+	0.129436i
$144$	0.989821	−	0.142315i	0.0824851	−	0.0118596i
$145$	5.46157	−	0.987000i	0.453559	−	0.0819659i
$146$	4.88610	−	3.14011i	0.404377	−	0.259877i
$147$	2.92467	−	7.84135i	0.241223	−	0.646744i
$148$	−4.46885	−	2.44018i	−0.367338	−	0.200582i
$149$	5.00101	−	5.77147i	0.409698	−	0.472817i	−0.512973	−	0.858405i	$-0.671456\pi$
$149$	5.00101	−	5.77147i	0.409698	−	0.472817i	0.922671	+	0.385588i	$0.126001\pi$
$150$	1.06564	+	4.88512i	0.0870092	+	0.398868i
$151$	22.7294	−	6.67394i	1.84969	−	0.543118i	0.849818	−	0.527076i	$-0.176712\pi$
$151$	22.7294	−	6.67394i	1.84969	−	0.543118i	0.999871	−	0.0160417i	$-0.00510645\pi$
$152$	1.57462	+	0.587302i	0.127718	+	0.0476365i
$153$	3.88393	+	0.844897i	0.313997	+	0.0683059i
$154$	0.749386	−	2.55217i	0.0603872	−	0.205660i
$155$	11.9419	−	8.29649i	0.959195	−	0.666390i
$156$	2.71181	−	5.93803i	0.217118	−	0.475423i
$157$	10.8150	+	14.4471i	0.863131	+	1.15301i	0.987002	+	0.160709i	$0.0513782\pi$
$157$	10.8150	+	14.4471i	0.863131	+	1.15301i	−0.123871	+	0.992298i	$0.539531\pi$
$158$	−0.328536	−	1.51026i	−0.0261369	−	0.120149i
$159$	−3.05797	−	3.52908i	−0.242513	−	0.279874i
$160$	−0.705538	+	2.12184i	−0.0557777	+	0.167746i
$161$	−4.01945	−	18.3666i	−0.316777	−	1.44749i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	13.4728	+	0.963591i	1.05527	+	0.0754743i	0.588175	−	0.808734i	$-0.299847\pi$
$163$	13.4728	+	0.963591i	1.05527	+	0.0754743i	0.467093	+	0.884208i	$0.345301\pi$
$164$	2.92623	−	4.55331i	0.228500	−	0.355554i
$165$	1.35687	+	0.678714i	0.105633	+	0.0528378i
$166$	−10.8508	−	4.95539i	−0.842184	−	0.384613i
$167$	7.34061	−	9.80590i	0.568033	−	0.758804i	−0.420909	−	0.907103i	$-0.638289\pi$
$167$	7.34061	−	9.80590i	0.568033	−	0.758804i	0.988943	+	0.148299i	$0.0473799\pi$
$168$	1.87882	+	3.44079i	0.144954	+	0.265463i
$169$	−16.0106	−	24.9129i	−1.23158	−	1.91638i
$170$	−5.57485	+	6.92205i	−0.427572	+	0.530897i
$171$	0.473474	+	1.61250i	0.0362075	+	0.123311i
$172$	0.783792	+	10.9588i	0.0597636	+	0.835604i
$173$	0.818698	+	11.4469i	0.0622444	+	0.870291i	0.928652	+	0.370953i	$0.120969\pi$
$173$	0.818698	+	11.4469i	0.0622444	+	0.870291i	−0.866407	+	0.499338i	$0.833577\pi$
$174$	0.699275	+	2.38151i	0.0530119	+	0.180542i
$175$	−16.4839	+	10.6070i	−1.24606	+	0.801811i
$176$	0.366821	+	0.570784i	0.0276502	+	0.0430245i
$177$	−6.37030	−	11.6663i	−0.478821	−	0.876895i
$178$	−0.997861	+	1.33299i	−0.0747928	+	0.0999115i
$179$	4.26821	+	1.94923i	0.319021	+	0.145692i	0.568489	−	0.822691i	$-0.307528\pi$
$179$	4.26821	+	1.94923i	0.319021	+	0.145692i	−0.249468	+	0.968383i	$0.580256\pi$
$180$	−2.12144	+	0.706760i	−0.158122	+	0.0526788i
$181$	7.97765	−	12.4135i	0.592974	−	0.922686i	−0.406983	−	0.913436i	$-0.633419\pi$
$181$	7.97765	−	12.4135i	0.592974	−	0.922686i	0.999957	−	0.00924997i	$-0.00294440\pi$
$182$	25.5265	+	1.82569i	1.89215	+	0.135329i
$183$	8.09369	+	8.09369i	0.598303	+	0.598303i
$184$	4.21207	+	2.29314i	0.310518	+	0.169052i
$185$	10.8037	+	3.59237i	0.794306	+	0.264116i
$186$	4.25851	+	4.91458i	0.312249	+	0.360355i
$187$	0.573257	+	2.63522i	0.0419207	+	0.192706i
$188$	−3.86425	−	5.16203i	−0.281829	−	0.376480i
$189$	−1.62857	+	3.56606i	−0.118461	+	0.259393i
$190$	−3.69837	−	0.666160i	−0.268308	−	0.0483283i
$191$	−4.28220	+	14.5838i	−0.309849	+	1.05525i	0.646474	+	0.762936i	$0.276243\pi$
$191$	−4.28220	+	14.5838i	−0.309849	+	1.05525i	−0.956323	+	0.292312i	$0.905575\pi$
$192$	−0.977147	−	0.212565i	−0.0705195	−	0.0153406i
$193$	18.7842	+	7.00614i	1.35211	+	0.504313i	0.918013	−	0.396551i	$-0.129793\pi$
$193$	18.7842	+	7.00614i	1.35211	+	0.504313i	0.434102	+	0.900864i	$0.357066\pi$
$194$	9.31785	−	2.73597i	0.668982	−	0.196431i
$195$	−3.60584	+	14.1445i	−0.258220	+	1.01291i
$196$	−5.48054	+	6.32488i	−0.391467	+	0.451777i
$197$	−0.928691	−	0.507104i	−0.0661665	−	0.0361297i	0.445825	−	0.895120i	$-0.352910\pi$
$197$	−0.928691	−	0.507104i	−0.0661665	−	0.0361297i	−0.511992	+	0.858990i	$0.671092\pi$
$198$	−0.237109	+	0.635714i	−0.0168506	+	0.0451782i
$199$	−0.938963	+	0.603435i	−0.0665613	+	0.0427764i	−0.573498	−	0.819207i	$-0.694414\pi$
$199$	−0.938963	+	0.603435i	−0.0665613	+	0.0427764i	0.506937	+	0.861983i	$0.330778\pi$
$200$	0.708723	−	4.94952i	0.0501143	−	0.349984i
$201$	−4.74960	+	0.682889i	−0.335011	+	0.0481673i
$202$	−5.96433	+	2.22458i	−0.419649	+	0.156521i
$203$	−7.78965	+	5.83126i	−0.546726	+	0.409274i
$204$	−3.34379	−	2.14892i	−0.234112	−	0.150455i
$205$	−4.62831	+	11.1828i	−0.323255	+	0.781044i
$206$		−	7.40600i		−	0.516001i
$207$	0.688450	+	4.74616i	0.0478506	+	0.329881i
$208$	−4.61595	+	4.61595i	−0.320059	+	0.320059i
$209$	−0.861752	+	0.746712i	−0.0596086	+	0.0516512i
$210$	−5.50244	−	6.82409i	−0.379705	−	0.470907i
$211$	0.273262	−	1.90058i	0.0188121	−	0.130841i	−0.978251	−	0.207424i	$-0.933492\pi$
$211$	0.273262	−	1.90058i	0.0188121	−	0.130841i	0.997063	+	0.0765830i	$0.0244010\pi$
$212$	1.63187	+	4.37522i	0.112078	+	0.300492i
$213$	−9.54855	−	7.14796i	−0.654256	−	0.489770i
$214$	9.99323	+	2.93428i	0.683123	+	0.200583i
$215$	−6.08252	−	23.8024i	−0.414824	−	1.62331i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	−12.2178	+	22.3752i	−0.829399	+	1.51893i
$218$	9.04965	−	0.647244i	0.612920	−	0.0438369i
$219$	−4.38949	−	3.80351i	−0.296614	−	0.257017i
$220$	−1.03414	−	1.11010i	−0.0697215	−	0.0748429i
$221$	−23.6023	+	10.7788i	−1.58766	+	0.725060i
$222$	−1.08231	+	4.97531i	−0.0726401	+	0.333921i
$223$	−6.23045	+	3.40209i	−0.417222	+	0.227820i	−0.674126	−	0.738617i	$-0.735479\pi$
$223$	−6.23045	+	3.40209i	−0.417222	+	0.227820i	0.256904	+	0.966437i	$0.417298\pi$
$224$	−0.557922	−	3.88043i	−0.0372777	−	0.259272i
$225$	4.38701	−	2.39877i	0.292468	−	0.159918i
$226$	−3.95809	−	0.569087i	−0.263288	−	0.0378551i
$227$	16.2499	−	3.53495i	1.07854	−	0.234623i	0.362009	−	0.932175i	$-0.382091\pi$
$227$	16.2499	−	3.53495i	1.07854	−	0.234623i	0.716534	+	0.697552i	$0.245727\pi$
$228$	0.119891	−	1.67630i	0.00793999	−	0.111016i
$229$	18.7338			1.23797			0.618983	−	0.785404i	$-0.287545\pi$
$229$	18.7338			1.23797			0.618983	+	0.785404i	$0.287545\pi$
$230$	−10.1802	−	3.37092i	−0.671264	−	0.222272i
$231$	−2.65992			−0.175010
$232$	0.177068	−	2.47573i	0.0116251	−	0.162540i
$233$	19.3953	−	4.21918i	1.27063	−	0.276408i	0.473809	−	0.880628i	$-0.342879\pi$
$233$	19.3953	−	4.21918i	1.27063	−	0.276408i	0.796818	+	0.604220i	$0.206515\pi$
$234$	−6.46150	−	0.929024i	−0.422402	−	0.0607322i
$235$	10.5557	+	9.82202i	0.688577	+	0.640718i
$236$	1.89168	+	13.1570i	0.123138	+	0.856445i
$237$	−1.35652	+	0.740716i	−0.0881155	+	0.0481147i
$238$	3.31228	−	15.2263i	0.214703	−	0.986975i
$239$	−24.4595	+	11.1703i	−1.58216	+	0.722547i	−0.996142	−	0.0877542i	$-0.972031\pi$
$239$	−24.4595	+	11.1703i	−1.58216	+	0.722547i	−0.586014	+	0.810301i	$0.699304\pi$
$240$	2.23467	+	0.0791669i	0.144247	+	0.00511020i
$241$	−17.8086	−	15.4312i	−1.14715	−	0.994012i	−0.999988	−	0.00489987i	$-0.998440\pi$
$241$	−17.8086	−	15.4312i	−1.14715	−	0.994012i	−0.147163	−	0.989112i	$-0.547014\pi$
$242$	10.5128	−	0.751890i	0.675788	−	0.0483333i
$243$	0.479249	−	0.877679i	0.0307438	−	0.0563031i
$244$	−4.75493	−	10.4118i	−0.304403	−	0.666550i
$245$	9.54440	−	16.0968i	0.609770	−	1.02839i
$246$	−5.19328	−	1.52489i	−0.331112	−	0.0972231i
$247$	−8.78252	−	6.57451i	−0.558819	−	0.418326i
$248$	−2.27254	−	6.09292i	−0.144306	−	0.386901i
$249$	−1.69764	+	11.8073i	−0.107584	+	0.748260i
$250$	0.408706	+	11.1729i	0.0258489	+	0.706634i
$251$	−18.6168	+	16.1315i	−1.17508	+	1.01821i	−0.175652	+	0.984452i	$0.556203\pi$
$251$	−18.6168	+	16.1315i	−1.17508	+	1.01821i	−0.999430	+	0.0337616i	$0.989251\pi$
$252$	2.77209	−	2.77209i	0.174626	−	0.174626i
$253$	−2.73518	+	1.76263i	−0.171960	+	0.110816i
$254$			13.8994i			0.872123i
$255$	8.21228	+	3.39887i	0.514273	+	0.212845i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	15.0896	−	11.2959i	0.941264	−	0.704622i	−0.0141470	−	0.999900i	$-0.504503\pi$
$257$	15.0896	−	11.2959i	0.941264	−	0.704622i	0.955411	+	0.295278i	$0.0954124\pi$
$258$	10.2941	−	3.83951i	0.640884	−	0.239037i
$259$	−19.7579	+	2.84076i	−1.22770	+	0.176516i
$260$	8.32151	−	11.9926i	0.516078	−	0.743751i
$261$	2.08804	−	1.34190i	0.129246	−	0.0830615i
$262$	2.01267	−	5.39619i	0.124343	−	0.333377i
$263$	0.317129	+	0.173166i	0.0195550	+	0.0106778i	0.488997	−	0.872286i	$-0.337363\pi$
$263$	0.317129	+	0.173166i	0.0195550	+	0.0106778i	−0.469442	+	0.882963i	$0.655545\pi$
$264$	0.444318	−	0.512771i	0.0273459	−	0.0315588i
$265$	−5.33065	−	8.97843i	−0.327459	−	0.551541i
$266$	6.32155	−	1.85618i	0.387599	−	0.113809i
$267$	1.56012	+	0.581895i	0.0954778	+	0.0356114i
$268$	4.68878	+	1.01998i	0.286413	+	0.0623053i
$269$	6.76273	−	23.0318i	0.412331	−	1.40427i	−0.447771	−	0.894148i	$-0.647782\pi$
$269$	6.76273	−	23.0318i	0.412331	−	1.40427i	0.860102	−	0.510122i	$-0.170400\pi$
$270$	1.27581	+	1.83639i	0.0776433	+	0.111759i
$271$	4.66151	−	10.2073i	0.283166	−	0.620048i	−0.713587	−	0.700567i	$-0.752931\pi$
$271$	4.66151	−	10.2073i	0.283166	−	0.620048i	0.996753	+	0.0805191i	$0.0256578\pi$
$272$	2.38199	+	3.18196i	0.144429	+	0.192935i
$273$	−5.43991	−	25.0069i	−0.329239	−	1.51349i
$274$	2.09213	+	2.41444i	0.126390	+	0.145862i
$275$	2.71698	+	2.03146i	0.163840	+	0.122502i
$276$	1.01357	−	4.68750i	0.0610097	−	0.282154i
$277$	−14.4213	−	14.4213i	−0.866493	−	0.866493i	0.125589	−	0.992082i	$-0.459918\pi$
$277$	−14.4213	−	14.4213i	−0.866493	−	0.866493i	−0.992082	+	0.125589i	$0.959918\pi$
$278$	−11.9715	−	0.856216i	−0.718001	−	0.0513524i
$279$	3.51575	−	5.47061i	0.210482	−	0.327517i
$280$	2.77074	+	8.31674i	0.165583	+	0.497020i
$281$	1.66393	+	0.759890i	0.0992616	+	0.0453313i	0.464427	−	0.885611i	$-0.346260\pi$
$281$	1.66393	+	0.759890i	0.0992616	+	0.0453313i	−0.365165	+	0.930943i	$0.618988\pi$
$282$	−3.86425	+	5.16203i	−0.230112	+	0.307394i
$283$	5.54977	+	10.1636i	0.329900	+	0.604166i	0.989005	−	0.147885i	$-0.0472465\pi$
$283$	5.54977	+	10.1636i	0.329900	+	0.604166i	−0.659105	+	0.752051i	$0.729065\pi$
$284$	6.44856	+	10.0342i	0.382652	+	0.595417i
$285$	0.402776	+	3.73624i	0.0238584	+	0.221316i
$286$	−1.24784	−	4.24975i	−0.0737863	−	0.251293i
$287$	−1.51374	−	21.1649i	−0.0893533	−	1.24932i
$288$	0.0713392	+	0.997452i	0.00420370	+	0.0587754i
$289$	−0.338428	−	1.15258i	−0.0199075	−	0.0677988i
$290$	0.594861	+	5.51807i	0.0349315	+	0.324032i
$291$	−5.25028	−	8.16960i	−0.307777	−	0.478910i
$292$	2.78354	+	5.09767i	0.162894	+	0.298318i
$293$	−13.7444	+	18.3604i	−0.802957	+	1.07263i	0.192857	+	0.981227i	$0.438225\pi$
$293$	−13.7444	+	18.3604i	−0.802957	+	1.07263i	−0.995814	+	0.0913986i	$0.970866\pi$
$294$	7.61273	+	3.47662i	0.443983	+	0.202760i
$295$	−9.39444	−	28.1987i	−0.546965	−	1.64179i
$296$	2.75277	−	4.28339i	0.160001	−	0.248967i
$297$	0.676764	+	0.0484031i	0.0392698	+	0.00280863i
$298$	5.40000	+	5.40000i	0.312813	+	0.312813i
$299$	−22.1650	−	22.1097i	−1.28183	−	1.27863i
$300$	−4.94870	+	0.714425i	−0.285713	+	0.0412473i
$301$	28.2062	+	32.5517i	1.62578	+	1.87625i
$302$	5.03544	+	23.1476i	0.289757	+	1.33199i
$303$	3.81482	+	5.09600i	0.219155	+	0.292757i
$304$	−0.698138	+	1.52871i	−0.0400410	+	0.0876775i
$305$	14.6032	+	21.0196i	0.836175	+	1.20358i
$306$	−1.11982	+	3.81376i	−0.0640159	+	0.218018i
$307$	−7.18847	−	1.56376i	−0.410268	−	0.0892482i	0.00269472	−	0.999996i	$-0.499142\pi$
$307$	−7.18847	−	1.56376i	−0.410268	−	0.0892482i	−0.412962	+	0.910748i	$0.635506\pi$
$308$	2.49221	+	0.929546i	0.142007	+	0.0529658i
$309$	−7.10601	+	2.08651i	−0.404247	+	0.118698i
$310$	7.42343	+	12.5033i	0.421623	+	0.710141i
$311$	11.1725	−	12.8937i	0.633532	−	0.731135i	−0.344686	−	0.938718i	$-0.612014\pi$
$311$	11.1725	−	12.8937i	0.633532	−	0.731135i	0.978217	+	0.207584i	$0.0665599\pi$
$312$	5.72944	+	3.12851i	0.324366	+	0.177117i
$313$	−6.36291	+	17.0596i	−0.359653	+	0.964267i	0.623555	+	0.781779i	$0.285688\pi$
$313$	−6.36291	+	17.0596i	−0.359653	+	0.964267i	−0.983208	+	0.182488i	$0.941585\pi$
$314$	−15.1819	+	9.75680i	−0.856762	+	0.550608i
$315$	−4.99745	+	7.20212i	−0.281574	+	0.405794i
$316$	1.52984	−	0.219958i	0.0860605	−	0.0123736i
$317$	−23.2988	+	8.69000i	−1.30859	+	0.488079i	−0.904435	−	0.426611i	$-0.859707\pi$
$317$	−23.2988	+	8.69000i	−1.30859	+	0.488079i	−0.404156	+	0.914690i	$0.632435\pi$
$318$	3.73824	−	2.79841i	0.209630	−	0.156927i
$319$	1.41672	+	0.910469i	0.0793209	+	0.0509765i
$320$	−2.06610	−	0.855111i	−0.115499	−	0.0478022i
$321$		−	10.4151i		−	0.581315i
$322$	18.6065	−	2.69895i	1.03690	−	0.150407i
$323$	−4.72341	+	4.72341i	−0.262818	+	0.262818i
$324$	−0.755750	+	0.654861i	−0.0419861	+	0.0363812i
$325$	−13.5419	+	29.6979i	−0.751171	+	1.64735i
$326$	−1.92227	+	13.3697i	−0.106465	+	0.740479i
$327$	−3.17061	−	8.50073i	−0.175335	−	0.470091i
$328$	4.33295	+	3.24361i	0.239247	+	0.179098i
$329$	−24.2550	−	7.12191i	−1.33722	−	0.392644i
$330$	−0.773783	+	1.30500i	−0.0425954	+	0.0718378i
$331$	−0.736628	−	1.61299i	−0.0404887	−	0.0886580i	0.888307	−	0.459250i	$-0.151882\pi$
$331$	−0.736628	−	1.61299i	−0.0404887	−	0.0886580i	−0.928796	+	0.370592i	$0.879155\pi$
$332$	5.71685	−	10.4696i	0.313753	−	0.574595i
$333$	5.07870	−	0.363236i	0.278311	−	0.0199052i
$334$	9.25725	+	8.02145i	0.506534	+	0.438914i
$335$	−10.7229	−	0.379877i	−0.585855	−	0.0207549i
$336$	−3.56606	+	1.62857i	−0.194545	+	0.0888455i
$337$	−2.24923	+	10.3396i	−0.122524	+	0.563232i	0.874424	+	0.485162i	$0.161239\pi$
$337$	−2.24923	+	10.3396i	−0.122524	+	0.563232i	−0.996948	+	0.0780697i	$0.975124\pi$
$338$	25.9917	−	14.1925i	1.41376	−	0.771971i
$339$	0.569087	+	3.95809i	0.0309086	+	0.214974i
$340$	−6.50671	−	6.05446i	−0.352876	−	0.328349i
$341$	4.36728	+	0.627920i	0.236501	+	0.0340038i
$342$	−1.64217	+	0.357233i	−0.0887985	+	0.0193169i
$343$	−0.382878	+	5.35334i	−0.0206735	+	0.289053i
$344$	−10.9868			−0.592371
$345$	−0.366277	+	10.7175i	−0.0197197	+	0.577013i
$346$	−11.4761			−0.616960
$347$	−0.195099	+	2.72784i	−0.0104735	+	0.146438i	0.989524	+	0.144366i	$0.0461142\pi$
$347$	−0.195099	+	2.72784i	−0.0104735	+	0.146438i	−0.999998	+	0.00207227i	$0.999340\pi$
$348$	−2.42533	+	0.527598i	−0.130011	+	0.0282822i
$349$	−5.08131	−	0.730582i	−0.271996	−	0.0391072i	0.00496701	−	0.999988i	$-0.498419\pi$
$349$	−5.08131	−	0.730582i	−0.271996	−	0.0391072i	−0.276963	+	0.960881i	$0.589328\pi$
$350$	−9.40399	−	17.1986i	−0.502664	−	0.919302i
$351$	0.929024	+	6.46150i	0.0495876	+	0.344889i
$352$	−0.595499	+	0.325167i	−0.0317402	+	0.0173315i
$353$	−3.83056	+	17.6088i	−0.203880	+	0.937221i	0.755510	+	0.655137i	$0.227389\pi$
$353$	−3.83056	+	17.6088i	−0.203880	+	0.937221i	−0.959390	+	0.282084i	$0.908974\pi$
$354$	12.0911	−	5.52180i	0.642632	−	0.293480i
$355$	−18.1797	−	19.5151i	−0.964878	−	1.03575i
$356$	−1.25840	−	1.09041i	−0.0666952	−	0.0577917i
$357$	−15.5427	+	1.11164i	−0.822607	+	0.0588340i
$358$	−2.24875	+	4.11828i	−0.118850	+	0.217658i
$359$	−2.99950	−	6.56798i	−0.158307	−	0.346645i	0.813813	−	0.581127i	$-0.197388\pi$
$359$	−2.99950	−	6.56798i	−0.158307	−	0.346645i	−0.972121	+	0.234482i	$0.924661\pi$
$360$	−0.553618	−	2.16645i	−0.0291782	−	0.114182i
$361$	15.5204	+	4.55721i	0.816864	+	0.239853i
$362$	11.8127	+	8.84289i	0.620863	+	0.464772i
$363$	−3.68323	−	9.87512i	−0.193319	−	0.518309i
$364$	−3.64208	+	25.3312i	−0.190897	+	1.32772i
$365$	−8.15208	−	10.1101i	−0.426699	−	0.529189i
$366$	−8.65047	+	7.49567i	−0.452167	+	0.391805i
$367$	−10.0139	+	10.0139i	−0.522721	+	0.522721i	−0.918392	−	0.395671i	$-0.870512\pi$
$367$	−10.0139	+	10.0139i	−0.522721	+	0.522721i	0.395671	+	0.918392i	$0.370512\pi$
$368$	−2.58778	+	4.03775i	−0.134897	+	0.210482i
$369$			5.41253i			0.281765i
$370$	−4.35395	+	10.5199i	−0.226351	+	0.546905i
$371$	15.4005	+	9.89728i	0.799552	+	0.513841i
$372$	−5.20586	+	3.89706i	−0.269911	+	0.202053i
$373$	−11.0468	+	4.12025i	−0.571983	+	0.213339i	−0.618778	−	0.785566i	$-0.712372\pi$
$373$	−11.0468	+	4.12025i	−0.571983	+	0.213339i	0.0467949	+	0.998905i	$0.485099\pi$
$374$	−2.66940	+	0.383802i	−0.138031	+	0.0198459i
$375$	10.6051	−	3.53991i	0.547647	−	0.182800i
$376$	5.42455	−	3.48615i	0.279750	−	0.179784i
$377$	−5.66227	+	15.1811i	−0.291621	+	0.781867i
$378$	−3.44079	−	1.87882i	−0.176975	−	0.0966359i
$379$	8.46392	−	9.76789i	0.434762	−	0.501743i	−0.495515	−	0.868599i	$-0.665021\pi$
$379$	8.46392	−	9.76789i	0.434762	−	0.501743i	0.930277	+	0.366857i	$0.119566\pi$
$380$	0.928302	−	3.64143i	0.0476209	−	0.186801i
$381$	13.3363	−	3.91590i	0.683241	−	0.200618i
$382$	−14.2412	−	5.31168i	−0.728642	−	0.271769i
$383$	−34.1609	−	7.43125i	−1.74554	−	0.379719i	−0.777181	−	0.629277i	$-0.783351\pi$
$383$	−34.1609	−	7.43125i	−1.74554	−	0.379719i	−0.968360	+	0.249557i	$0.919715\pi$
$384$	0.281733	−	0.959493i	0.0143771	−	0.0489639i
$385$	−5.85356	−	1.05436i	−0.298325	−	0.0537350i
$386$	−8.32833	+	18.2365i	−0.423901	+	0.928214i
$387$	−6.58417	−	8.79542i	−0.334692	−	0.447096i
$388$	2.06427	+	9.48929i	0.104797	+	0.481746i
$389$	25.0250	+	28.8803i	1.26882	+	1.46429i	0.821812	+	0.569759i	$0.192963\pi$
$389$	25.0250	+	28.8803i	1.26882	+	1.46429i	0.447003	+	0.894532i	$0.352491\pi$
$390$	−13.8513	−	4.60572i	−0.701386	−	0.233219i
$391$	−15.2459	+	11.4427i	−0.771017	+	0.578681i
$392$	−5.91779	−	5.91779i	−0.298894	−	0.298894i
$393$	−5.74464	−	0.410865i	−0.289779	−	0.0207254i
$394$	0.572064	−	0.890149i	0.0288202	−	0.0448450i
$395$	−3.27884	+	1.09235i	−0.164976	+	0.0549622i
$396$	−0.617179	−	0.281856i	−0.0310144	−	0.0141638i
$397$	9.70381	−	12.9628i	0.487020	−	0.650583i	−0.487962	−	0.872865i	$-0.662260\pi$
$397$	9.70381	−	12.9628i	0.487020	−	0.650583i	0.974982	+	0.222282i	$0.0713506\pi$
$398$	−0.534912	−	0.979619i	−0.0268127	−	0.0491039i
$399$	−3.56198	−	5.54254i	−0.178322	−	0.277474i
$400$	4.88635	+	1.06001i	0.244317	+	0.0530006i
$401$	9.99312	+	34.0334i	0.499033	+	1.69955i	0.695061	+	0.718951i	$0.255377\pi$
$401$	9.99312	+	34.0334i	0.499033	+	1.69955i	−0.196028	+	0.980598i	$0.562804\pi$
$402$	−0.342317	−	4.78621i	−0.0170732	−	0.238715i
$403$	3.02840	+	42.3426i	0.150855	+	2.10924i
$404$	−1.79342	−	6.10784i	−0.0892261	−	0.303876i
$405$	1.40256	−	1.74150i	0.0696939	−	0.0865358i
$406$	−5.26069	−	8.18580i	−0.261084	−	0.406254i
$407$	1.65564	+	3.03209i	0.0820672	+	0.150295i
$408$	2.38199	−	3.18196i	0.117926	−	0.157531i
$409$	22.5399	+	10.2936i	1.11452	+	0.508986i	0.885596	−	0.464457i	$-0.153750\pi$
$409$	22.5399	+	10.2936i	1.11452	+	0.508986i	0.228929	+	0.973443i	$0.426478\pi$
$410$	−10.8242	−	5.41430i	−0.534568	−	0.267393i
$411$	1.72722	−	2.68761i	0.0851976	−	0.132570i
$412$	7.38713	+	0.528338i	0.363938	+	0.0260294i
$413$	36.8474	+	36.8474i	1.81314	+	1.81314i
$414$	−4.78318	+	0.348109i	−0.235081	+	0.0171086i
$415$	−8.41620	+	25.3110i	−0.413135	+	1.24247i
$416$	−4.27490	−	4.93349i	−0.209594	−	0.241884i
$417$	2.55122	+	11.7278i	0.124934	+	0.574311i
$418$	−0.683333	−	0.912826i	−0.0334229	−	0.0446478i
$419$	−4.46772	+	9.78295i	−0.218263	+	0.477928i	−0.986814	−	0.161860i	$-0.948251\pi$
$419$	−4.46772	+	9.78295i	−0.218263	+	0.477928i	0.768551	+	0.639788i	$0.220978\pi$
$420$	7.19924	−	5.00160i	0.351287	−	0.244053i
$421$	−3.57125	+	12.1626i	−0.174052	+	0.592767i	0.825544	+	0.564338i	$0.190869\pi$
$421$	−3.57125	+	12.1626i	−0.174052	+	0.592767i	−0.999596	+	0.0284286i	$0.990950\pi$
$422$	1.87624	+	0.408152i	0.0913341	+	0.0198685i
$423$	6.04161	+	2.25341i	0.293753	+	0.109564i
$424$	−4.48049	+	1.31559i	−0.217592	+	0.0638908i
$425$	16.7251	+	10.7350i	0.811287	+	0.520723i
$426$	7.81093	−	9.01429i	0.378441	−	0.436744i
$427$	−39.3841	−	21.5053i	−1.90593	−	1.04072i
$428$	−3.63971	+	9.75844i	−0.175932	+	0.471692i
$429$	−3.72605	+	2.39459i	−0.179895	+	0.115612i
$430$	24.1757	−	4.36897i	1.16586	−	0.210690i
$431$	12.2317	−	1.75865i	0.589180	−	0.0847113i	0.158724	−	0.987323i	$-0.449262\pi$
$431$	12.2317	−	1.75865i	0.589180	−	0.0847113i	0.430456	+	0.902612i	$0.358353\pi$
$432$	0.936950	−	0.349464i	0.0450790	−	0.0168136i
$433$	0.728957	−	0.545690i	0.0350314	−	0.0262242i	−0.581618	−	0.813462i	$-0.697580\pi$
$433$	0.728957	−	0.545690i	0.0350314	−	0.0262242i	0.616650	+	0.787237i	$0.288489\pi$
$434$	−21.4466	−	13.7829i	−1.02947	−	0.661601i
$435$	5.12696	−	2.12538i	0.245819	−	0.101904i
$436$			9.07277i			0.434507i
$437$	−7.33561	−	3.33899i	−0.350910	−	0.159725i
$438$	4.10696	−	4.10696i	0.196238	−	0.196238i
$439$	−18.4670	+	16.0017i	−0.881380	+	0.763720i	−0.972691	−	0.232102i	$-0.925440\pi$
$439$	−18.4670	+	16.0017i	−0.881380	+	0.763720i	0.0913114	+	0.995822i	$0.470894\pi$
$440$	1.18105	−	0.952308i	0.0563042	−	0.0453995i
$441$	1.19104	−	8.28383i	0.0567160	−	0.394468i
$442$	−9.06757	−	24.3111i	−0.431300	−	1.15636i
$443$	−14.7722	−	11.0583i	−0.701848	−	0.525397i	0.187707	−	0.982225i	$-0.439894\pi$
$443$	−14.7722	−	11.0583i	−0.701848	−	0.525397i	−0.889555	+	0.456828i	$0.848985\pi$
$444$	−4.88542	−	1.43449i	−0.231852	−	0.0680779i
$445$	3.20263	+	1.89896i	0.151819	+	0.0900194i
$446$	−2.94894	−	6.45728i	−0.139636	−	0.305761i
$447$	3.65990	−	6.70261i	0.173107	−	0.317023i
$448$	3.91035	−	0.279673i	0.184746	−	0.0132133i
$449$	−21.7839	−	18.8759i	−1.02805	−	0.890807i	−0.0339625	−	0.999423i	$-0.510813\pi$
$449$	−21.7839	−	18.8759i	−1.02805	−	0.890807i	−0.994084	+	0.108616i	$0.965358\pi$
$450$	2.07969	+	4.54696i	0.0980377	+	0.214346i
$451$	−3.34050	+	1.52555i	−0.157298	+	0.0718355i
$452$	0.850004	−	3.90741i	0.0399808	−	0.183789i
$453$	20.7913	−	11.3529i	0.976859	−	0.533406i
$454$	2.36669	+	16.4607i	0.111074	+	0.772537i
$455$	−2.05896	−	57.1878i	−0.0965255	−	2.68101i
$456$	1.66347	+	0.239171i	0.0778993	+	0.0112002i
$457$	−16.6054	+	3.61228i	−0.776767	+	0.168975i	−0.583437	−	0.812159i	$-0.698292\pi$
$457$	−16.6054	+	3.61228i	−0.776767	+	0.168975i	−0.193330	+	0.981134i	$0.561929\pi$
$458$	−1.33646	+	18.6861i	−0.0624485	+	0.873144i
$459$	3.97477			0.185526
$460$	4.08858	−	9.91380i	0.190631	−	0.462233i
$461$	16.2965			0.759003			0.379502	−	0.925191i	$-0.376095\pi$
$461$	16.2965			0.759003			0.379502	+	0.925191i	$0.376095\pi$
$462$	0.189756	−	2.65314i	0.00882827	−	0.123435i
$463$	30.0720	−	6.54177i	1.39757	−	0.304022i	0.550201	−	0.835033i	$-0.314551\pi$
$463$	30.0720	−	6.54177i	1.39757	−	0.304022i	0.847365	+	0.531011i	$0.178188\pi$
$464$	2.45679	+	0.353233i	0.114054	+	0.0163984i
$465$	9.90542	−	10.6453i	0.459353	−	0.493665i
$466$	2.82479	+	19.6469i	0.130856	+	0.910123i
$467$	0.0401712	−	0.0219352i	0.00185890	−	0.00101504i	−0.478319	−	0.878186i	$-0.658754\pi$
$467$	0.0401712	−	0.0219352i	0.00185890	−	0.00101504i	0.480178	+	0.877171i	$0.340572\pi$
$468$	1.38761	−	6.37876i	0.0641425	−	0.294858i
$469$	17.1115	−	7.81457i	0.790137	−	0.360843i
$470$	−10.5500	+	9.82810i	−0.486637	+	0.453336i
$471$	13.6388	+	11.8181i	0.628443	+	0.544549i
$472$	−13.2584	+	0.948258i	−0.610267	+	0.0436471i
$473$	3.57256	−	6.54265i	0.164266	−	0.300831i
$474$	−0.642056	−	1.40591i	−0.0294906	−	0.0645754i
$475$	−0.594628	+	8.38183i	−0.0272834	+	0.384585i
$476$	14.9512	+	4.39007i	0.685288	+	0.201219i
$477$	−3.73824	−	2.79841i	−0.171162	−	0.128131i
$478$	−9.39691	−	25.1941i	−0.429805	−	1.15235i
$479$	−1.46571	+	10.1943i	−0.0669702	+	0.465788i	0.928548	+	0.371213i	$0.121058\pi$
$479$	−1.46571	+	10.1943i	−0.0669702	+	0.465788i	−0.995518	+	0.0945746i	$0.969851\pi$
$480$	−0.238384	+	2.22332i	−0.0108807	+	0.101480i
$481$	−25.1197	+	21.7664i	−1.14536	+	0.992461i
$482$	16.6623	−	16.6623i	0.758949	−	0.758949i
$483$	−7.83169	−	17.0925i	−0.356354	−	0.777734i
$484$			10.5396i			0.479075i
$485$	−8.31573	−	20.0596i	−0.377598	−	0.910859i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	−8.34698	+	6.24847i	−0.378238	+	0.283145i	−0.771434	−	0.636309i	$-0.780460\pi$
$487$	−8.34698	+	6.24847i	−0.378238	+	0.283145i	0.393196	+	0.919455i	$0.371369\pi$
$488$	10.7245	−	4.00004i	0.485476	−	0.181073i
$489$	13.3697	−	1.92227i	0.604598	−	0.0869281i
$490$	15.3749	+	10.6684i	0.694567	+	0.481950i
$491$	−13.2166	+	8.49379i	−0.596456	+	0.383319i	−0.803757	−	0.594958i	$-0.797169\pi$
$491$	−13.2166	+	8.49379i	−0.596456	+	0.383319i	0.207300	+	0.978277i	$0.433532\pi$
$492$	1.89148	−	5.07127i	0.0852747	−	0.228630i
$493$	8.65881	+	4.72807i	0.389973	+	0.212941i
$494$	7.18430	−	8.29113i	0.323237	−	0.373035i
$495$	1.47014	+	0.374779i	0.0660777	+	0.0168451i
$496$	6.23951	−	1.83209i	0.280162	−	0.0822631i
$497$	43.8120	+	16.3410i	1.96524	+	0.732996i
$498$	−11.6562	−	2.53564i	−0.522325	−	0.113625i
$499$	10.7082	−	36.4687i	0.479363	−	1.63256i	−0.264612	−	0.964355i	$-0.585244\pi$
$499$	10.7082	−	36.4687i	0.479363	−	1.63256i	0.743976	−	0.668207i	$-0.232938\pi$
$500$	−11.1736	−	0.389398i	−0.499697	−	0.0174144i
$501$	5.08846	−	11.1422i	0.227335	−	0.497795i
$502$	−14.7623	−	19.7202i	−0.658875	−	0.880154i
$503$	−4.76668	−	21.9121i	−0.212536	−	0.977011i	−0.952541	−	0.304410i	$-0.901541\pi$
$503$	−4.76668	−	21.9121i	−0.212536	−	0.977011i	0.740005	−	0.672601i	$-0.234823\pi$
$504$	2.56727	+	2.96279i	0.114355	+	0.131973i
$505$	6.37510	+	12.7267i	0.283688	+	0.566330i
$506$	−1.56301	−	2.85396i	−0.0694844	−	0.126874i
$507$	−20.9403	−	20.9403i	−0.929992	−	0.929992i
$508$	−13.8639	−	0.991568i	−0.615113	−	0.0439937i
$509$	21.2294	−	33.0336i	0.940976	−	1.46419i	0.0560650	−	0.998427i	$-0.482145\pi$
$509$	21.2294	−	33.0336i	0.940976	−	1.46419i	0.884911	−	0.465760i	$-0.154219\pi$
$510$	−3.97606	+	7.94888i	−0.176063	+	0.351982i
$511$	20.7121	+	9.45891i	0.916250	+	0.418437i
$512$	−0.599278	+	0.800541i	−0.0264846	+	0.0353793i
$513$	0.805416	+	1.47501i	0.0355600	+	0.0651232i
$514$	10.1907	+	15.8570i	0.449492	+	0.699423i
$515$	−16.4649	+	1.77496i	−0.725532	+	0.0782141i
$516$	3.09535	+	10.5418i	0.136265	+	0.464077i
$517$	0.312112	+	4.36389i	0.0137267	+	0.191924i
$518$	−1.42401	−	19.9102i	−0.0625672	−	0.874804i
$519$	3.23320	+	11.0113i	0.141922	+	0.483341i
$520$	11.3684	+	9.15585i	0.498538	+	0.401510i
$521$	−0.833831	−	1.29747i	−0.0365308	−	0.0568430i	0.822508	−	0.568754i	$-0.192574\pi$
$521$	−0.833831	−	1.29747i	−0.0365308	−	0.0568430i	−0.859039	+	0.511911i	$0.828938\pi$
$522$	1.18952	+	2.17845i	0.0520639	+	0.0953480i
$523$	9.85683	−	13.1672i	0.431009	−	0.575761i	−0.531484	−	0.847069i	$-0.678365\pi$
$523$	9.85683	−	13.1672i	0.431009	−	0.575761i	0.962493	+	0.271308i	$0.0874562\pi$
$524$	5.23885	+	2.39250i	0.228860	+	0.104517i
$525$	−13.8525	+	13.8685i	−0.604572	+	0.605269i
$526$	−0.195348	+	0.303967i	−0.00851758	+	0.0132536i
$527$	25.7818	+	1.84395i	1.12307	+	0.0803236i
$528$	0.479767	+	0.479767i	0.0208792	+	0.0208792i
$529$	−19.3799	−	12.3863i	−0.842602	−	0.538536i
$530$	9.33584	−	4.67655i	0.405523	−	0.203136i
$531$	−8.70457	−	10.0456i	−0.377746	−	0.435943i
$532$	1.40047	+	6.43787i	0.0607182	+	0.279117i
$533$	−21.1741	−	28.2853i	−0.917152	−	1.22517i
$534$	−0.691710	+	1.51463i	−0.0299332	+	0.0655446i
$535$	4.12842	−	22.9201i	0.178487	−	0.990921i
$536$	−1.35188	+	4.60407i	−0.0583921	+	0.198865i
$537$	4.58501	+	0.997408i	0.197858	+	0.0430413i
$538$	22.4906	+	8.38857i	0.969640	+	0.361657i
$539$	5.44831	−	1.59977i	0.234675	−	0.0689068i
$540$	−1.92272	+	1.14155i	−0.0827408	+	0.0491246i
$541$	8.56520	−	9.88477i	0.368247	−	0.424979i	−0.541139	−	0.840933i	$-0.682007\pi$
$541$	8.56520	−	9.88477i	0.368247	−	0.424979i	0.909386	+	0.415954i	$0.136552\pi$
$542$	9.84872	+	5.37781i	0.423039	+	0.230997i
$543$	5.15666	−	13.8256i	0.221294	−	0.593311i
$544$	−3.34379	+	2.14892i	−0.143364	+	0.0921342i
$545$	−3.60783	−	19.9639i	−0.154542	−	0.855161i
$546$	25.3312	−	3.64208i	1.08408	−	0.155867i
$547$	43.6033	−	16.2632i	1.86434	−	0.695364i	0.896922	−	0.442189i	$-0.145798\pi$
$547$	43.6033	−	16.2632i	1.86434	−	0.695364i	0.967421	−	0.253174i	$-0.0814746\pi$
$548$	−2.55754	+	1.91455i	−0.109253	+	0.0817857i
$549$	9.62916	+	6.18829i	0.410963	+	0.264110i
$550$	−2.22011	+	2.56513i	−0.0946660	+	0.109378i
$551$			4.17129i			0.177703i
$552$	4.60325	+	1.34539i	0.195927	+	0.0572636i
$553$	4.28448	−	4.28448i	0.182195	−	0.182195i
$554$	15.4134	−	13.3558i	0.654852	−	0.567432i
$555$	11.3204	+	1.21378i	0.480526	+	0.0515219i
$556$	1.70807	−	11.8799i	0.0724383	−	0.503819i
$557$	1.65833	+	4.44614i	0.0702655	+	0.188389i	0.967336	−	0.253499i	$-0.0815815\pi$
$557$	1.65833	+	4.44614i	0.0702655	+	0.188389i	−0.897070	+	0.441888i	$0.854309\pi$
$558$	5.20586	+	3.89706i	0.220382	+	0.164976i
$559$	68.8163	+	20.2063i	2.91062	+	0.854635i
$560$	−8.49321	+	2.17037i	−0.358904	+	0.0917148i
$561$	1.12031	+	2.45314i	0.0472996	+	0.103572i
$562$	−0.876658	+	1.60548i	−0.0369796	+	0.0677230i
$563$	1.59967	−	0.114411i	0.0674182	−	0.00482184i	−0.0375893	−	0.999293i	$-0.511968\pi$
$563$	1.59967	−	0.114411i	0.0674182	−	0.00482184i	0.105008	+	0.994471i	$0.466513\pi$
$564$	−4.87320	−	4.22266i	−0.205199	−	0.177806i
$565$	−0.316572	+	8.93597i	−0.0133183	+	0.375939i
$566$	−10.5337	+	4.81057i	−0.442763	+	0.202203i
$567$	−0.833327	+	3.83074i	−0.0349964	+	0.160876i
$568$	−10.4686	+	5.71630i	−0.439254	+	0.239851i
$569$	2.06937	+	14.3928i	0.0867526	+	0.603377i	0.986101	+	0.166145i	$0.0531321\pi$
$569$	2.06937	+	14.3928i	0.0867526	+	0.603377i	−0.899349	+	0.437232i	$0.855959\pi$
$570$	−3.75546	+	0.135209i	−0.157299	+	0.00566330i
$571$	−32.3897	−	4.65693i	−1.35547	−	0.194886i	−0.574010	−	0.818848i	$-0.694613\pi$
$571$	−32.3897	−	4.65693i	−1.35547	−	0.194886i	−0.781455	+	0.623962i	$0.785522\pi$
$572$	4.32794	−	0.941486i	0.180960	−	0.0393655i
$573$	−1.08432	+	15.1608i	−0.0452981	+	0.633351i
$574$	21.2189			0.885660
$575$	−5.05435	+	23.4404i	−0.210781	+	0.977533i
$576$	−1.00000			−0.0416667
$577$	3.09030	−	43.2080i	0.128651	−	1.79877i	−0.366968	−	0.930234i	$-0.619604\pi$
$577$	3.09030	−	43.2080i	0.128651	−	1.79877i	0.495619	−	0.868540i	$-0.334941\pi$
$578$	1.17379	−	0.255342i	0.0488231	−	0.0106208i
$579$	19.8442	+	2.85316i	0.824695	+	0.118573i
$580$	−5.54644	+	0.199691i	−0.230304	+	0.00829173i
$581$	−6.65532	−	46.2888i	−0.276109	−	1.92038i
$582$	8.52333	−	4.65409i	0.353304	−	0.192918i
$583$	0.673475	−	3.09591i	0.0278925	−	0.128220i
$584$	−5.28325	+	2.41278i	−0.218623	+	0.0998416i
$585$	−0.516797	+	14.5878i	−0.0213669	+	0.603130i
$586$	−17.3331	−	15.0192i	−0.716024	−	0.620438i
$587$	−22.6588	+	1.62059i	−0.935228	+	0.0668888i	−0.530628	−	0.847605i	$-0.678044\pi$
$587$	−22.6588	+	1.62059i	−0.935228	+	0.0668888i	−0.404600	+	0.914494i	$0.632589\pi$
$588$	−4.01084	+	7.34531i	−0.165404	+	0.302916i
$589$	4.53994	+	9.94108i	0.187065	+	0.409615i
$590$	28.7970	−	7.35883i	1.18555	−	0.302958i
$591$	−1.01526	−	0.298107i	−0.0417622	−	0.0122625i
$592$	4.07609	+	3.05133i	0.167526	+	0.125409i
$593$	−10.1963	−	27.3373i	−0.418711	−	1.12261i	−0.959564	−	0.281491i	$-0.909171\pi$
$593$	−10.1963	−	27.3373i	−0.418711	−	1.12261i	0.540853	−	0.841117i	$-0.318102\pi$
$594$	−0.0965596	+	0.671587i	−0.00396189	+	0.0275555i
$595$	−34.6448	−	3.71460i	−1.42030	−	0.152284i
$596$	−5.77147	+	5.00101i	−0.236409	+	0.204849i
$597$	−0.789235	+	0.789235i	−0.0323012	+	0.0323012i
$598$	23.6346	−	20.5312i	0.966489	−	0.839584i
$599$			24.6520i			1.00725i	0.863921	+	0.503627i	$0.168002\pi$
$599$			24.6520i			1.00725i	−0.863921	+	0.503627i	$0.831998\pi$
$600$	−0.359569	−	4.98705i	−0.0146793	−	0.203596i
$601$	11.9445	+	7.67624i	0.487225	+	0.313120i	0.761088	−	0.648648i	$-0.224665\pi$
$601$	11.9445	+	7.67624i	0.487225	+	0.313120i	−0.273864	+	0.961769i	$0.588302\pi$
$602$	−34.4810	+	25.8121i	−1.40534	+	1.05202i
$603$	−4.49589	+	1.67688i	−0.183087	+	0.0682879i
$604$	−23.4478	+	3.37129i	−0.954078	+	0.137176i
$605$	−4.19114	−	23.1917i	−0.170394	−	0.942877i
$606$	−5.35516	+	3.44155i	−0.217539	+	0.139804i
$607$	−0.238435	+	0.639270i	−0.00967780	+	0.0259472i	−0.941699	−	0.336457i	$-0.890771\pi$
$607$	−0.238435	+	0.639270i	−0.00967780	+	0.0259472i	0.932021	+	0.362404i	$0.118044\pi$
$608$	−1.47501	−	0.805416i	−0.0598195	−	0.0326639i
$609$	−6.37211	+	7.35380i	−0.258211	+	0.297991i
$610$	−22.0079	+	13.0664i	−0.891073	+	0.529045i
$611$	−40.3882	+	11.8591i	−1.63393	+	0.479766i
$612$	−3.72416	−	1.38904i	−0.150540	−	0.0561485i
$613$	−44.2343	−	9.62258i	−1.78661	−	0.388652i	−0.807156	−	0.590338i	$-0.798995\pi$
$613$	−44.2343	−	9.62258i	−1.78661	−	0.388652i	−0.979450	+	0.201685i	$0.935358\pi$
$614$	2.07259	−	7.05860i	0.0836430	−	0.284862i
$615$	−2.14546	+	11.9111i	−0.0865132	+	0.480302i
$616$	−1.10497	+	2.41955i	−0.0445205	+	0.0974863i
$617$	−7.27161	−	9.71374i	−0.292744	−	0.391060i	0.629923	−	0.776657i	$-0.283086\pi$
$617$	−7.27161	−	9.71374i	−0.292744	−	0.391060i	−0.922667	+	0.385597i	$0.873995\pi$
$618$	−1.57426	−	7.23675i	−0.0633260	−	0.291105i
$619$	12.0048	+	13.8542i	0.482512	+	0.556848i	0.943849	−	0.330377i	$-0.107176\pi$
$619$	12.0048	+	13.8542i	0.482512	+	0.556848i	−0.461337	+	0.887225i	$0.652630\pi$
$620$	−13.0010	+	6.51254i	−0.522134	+	0.261550i
$621$	1.68159	+	4.49135i	0.0674797	+	0.180232i
$622$	12.0638	+	12.0638i	0.483715	+	0.483715i
$623$	−6.51114	−	0.465686i	−0.260863	−	0.0186573i
$624$	−3.52927	+	5.49166i	−0.141284	+	0.219842i
$625$	24.7414	−	3.58638i	0.989657	−	0.143455i
$626$	−16.5622	−	7.56372i	−0.661960	−	0.302307i
$627$	−0.683333	+	0.912826i	−0.0272897	+	0.0364548i
$628$	−8.64887	−	15.8392i	−0.345128	−	0.632054i
$629$	10.9416	+	17.0255i	0.436270	+	0.678850i
$630$	−6.82726	−	5.49851i	−0.272005	−	0.219066i
$631$	9.36759	+	31.9031i	0.372918	+	1.27004i	0.905747	+	0.423819i	$0.139311\pi$
$631$	9.36759	+	31.9031i	0.372918	+	1.27004i	−0.532829	+	0.846223i	$0.678871\pi$
$632$	0.110260	+	1.54164i	0.00438591	+	0.0613231i
$633$	−0.136980	−	1.91523i	−0.00544447	−	0.0761236i
$634$	−7.00574	−	23.8594i	−0.278234	−	0.947577i
$635$	30.9009	−	3.33119i	1.22626	−	0.132194i
$636$	2.52460	+	3.92836i	0.100107	+	0.155769i
$637$	26.1826	+	47.9498i	1.03739	+	1.89984i
$638$	−1.00922	+	1.34816i	−0.0399553	+	0.0533740i
$639$	−10.8497	−	4.95491i	−0.429209	−	0.196013i
$640$	1.00033	−	1.99984i	0.0395414	−	0.0790505i
$641$	14.6239	−	22.7552i	0.577608	−	0.898776i	−0.422363	−	0.906427i	$-0.638799\pi$
$641$	14.6239	−	22.7552i	0.577608	−	0.898776i	0.999971	+	0.00765135i	$0.00243552\pi$
$642$	10.3886	+	0.743006i	0.410004	+	0.0293241i
$643$	−18.8269	−	18.8269i	−0.742460	−	0.742460i	0.230591	−	0.973051i	$-0.425934\pi$
$643$	−18.8269	−	18.8269i	−0.742460	−	0.742460i	−0.973051	+	0.230591i	$0.925934\pi$
$644$	1.36470	+	18.7517i	0.0537768	+	0.738919i
$645$	−11.0031	−	21.9656i	−0.433246	−	0.864893i
$646$	−4.37441	−	5.04834i	−0.172109	−	0.198624i
$647$	−0.837618	−	3.85047i	−0.0329301	−	0.151377i	0.957746	−	0.287615i	$-0.0928625\pi$
$647$	−0.837618	−	3.85047i	−0.0329301	−	0.151377i	−0.990676	+	0.136238i	$0.956499\pi$
$648$	−0.599278	−	0.800541i	−0.0235419	−	0.0314482i
$649$	3.74650	−	8.20369i	0.147063	−	0.322023i
$650$	−28.6562	−	15.6261i	−1.12399	−	0.612904i
$651$	−7.18239	+	24.4610i	−0.281500	+	0.958701i
$652$	−13.1985	−	2.87116i	−0.516893	−	0.112443i
$653$	−1.90449	−	0.710338i	−0.0745284	−	0.0277977i	0.311923	−	0.950107i	$-0.399027\pi$
$653$	−1.90449	−	0.710338i	−0.0745284	−	0.0277977i	−0.386452	+	0.922310i	$0.626299\pi$
$654$	8.70526	−	2.55609i	0.340402	−	0.0999512i
$655$	−12.4791	−	3.18127i	−0.487599	−	0.124303i
$656$	−3.54445	+	4.09052i	−0.138388	+	0.159708i
$657$	−5.09767	−	2.78354i	−0.198879	−	0.108596i
$658$	8.83410	−	23.6851i	0.344389	−	0.923343i
$659$	−3.28397	+	2.11048i	−0.127925	+	0.0822127i	−0.603039	−	0.797712i	$-0.706044\pi$
$659$	−3.28397	+	2.11048i	−0.127925	+	0.0822127i	0.475113	+	0.879925i	$0.342407\pi$
$660$	−1.24647	−	0.864909i	−0.0485189	−	0.0336665i
$661$	13.4896	−	1.93951i	0.524684	−	0.0754381i	0.125117	−	0.992142i	$-0.460070\pi$
$661$	13.4896	−	1.93951i	0.524684	−	0.0754381i	0.399567	+	0.916704i	$0.369160\pi$
$662$	1.66143	−	0.619682i	0.0645733	−	0.0240846i
$663$	−20.7717	+	15.5495i	−0.806705	+	0.603892i
$664$	10.0351	+	6.44918i	0.389438	+	0.250277i
$665$	−5.64168	−	13.6091i	−0.218775	−	0.527740i
$666$			5.09167i			0.197298i
$667$	−1.67932	+	11.7845i	−0.0650235	+	0.456296i
$668$	−8.66142	+	8.66142i	−0.335120	+	0.335120i
$669$	−5.36490	+	4.64872i	−0.207419	+	0.179730i
$670$	1.14387	−	10.6685i	0.0441917	−	0.412159i
$671$	−1.10524	+	7.68712i	−0.0426674	+	0.296758i
$672$	−1.37002	−	3.67316i	−0.0528495	−	0.141695i
$673$	−18.7107	−	14.0067i	−0.721245	−	0.539918i	0.174406	−	0.984674i	$-0.444199\pi$
$673$	−18.7107	−	14.0067i	−0.721245	−	0.539918i	−0.895652	+	0.444756i	$0.853290\pi$
$674$	−10.1528	−	2.98112i	−0.391069	−	0.114828i
$675$	3.77686	−	3.27648i	0.145371	−	0.126112i
$676$	12.3021	+	26.9379i	0.473159	+	1.03607i
$677$	−12.7060	+	23.2692i	−0.488330	+	0.894309i	0.511066	+	0.859542i	$0.329251\pi$
$677$	−12.7060	+	23.2692i	−0.488330	+	0.894309i	−0.999395	+	0.0347672i	$0.988931\pi$
$678$	−3.98860	+	0.285271i	−0.153181	+	0.0109558i
$679$	28.7723	+	24.9313i	1.10418	+	0.956777i
$680$	6.50322	−	6.05821i	0.249387	−	0.232322i
$681$	15.1271	−	6.90832i	0.579672	−	0.264727i
$682$	−0.937878	+	4.31136i	−0.0359132	+	0.165090i
$683$	15.9744	−	8.72266i	0.611242	−	0.333763i	−0.143634	−	0.989631i	$-0.545879\pi$
$683$	15.9744	−	8.72266i	0.611242	−	0.333763i	0.754876	+	0.655868i	$0.227697\pi$
$684$	−0.239171	−	1.66347i	−0.00914495	−	0.0636045i
$685$	4.86635	−	5.22985i	0.185934	−	0.199822i
$686$	−5.31238	−	0.763806i	−0.202828	−	0.0291622i
$687$	18.3057	−	3.98216i	0.698407	−	0.151929i
$688$	0.783792	−	10.9588i	0.0298818	−	0.417802i
$689$	30.4832			1.16132
$690$	−10.6641	−	1.12993i	−0.405976	−	0.0430155i
$691$	−9.47636			−0.360498			−0.180249	−	0.983621i	$-0.557690\pi$
$691$	−9.47636			−0.360498			−0.180249	+	0.983621i	$0.557690\pi$
$692$	0.818698	−	11.4469i	0.0311222	−	0.435145i
$693$	−2.59913	+	0.565406i	−0.0987328	+	0.0214780i
$694$	−2.70697	−	0.389203i	−0.102755	−	0.0147740i
$695$	0.965614	+	26.8200i	0.0366278	+	1.01734i
$696$	−0.353233	−	2.45679i	−0.0133893	−	0.0931243i
$697$	−18.8820	+	10.3103i	−0.715206	+	0.390532i
$698$	1.09122	−	5.01624i	0.0413032	−	0.189868i
$699$	18.0552	−	8.24553i	0.682910	−	0.311874i
$700$	17.8256	−	8.15310i	0.673745	−	0.308158i
$701$	−33.0736	−	28.6584i	−1.24917	−	1.08241i	−0.993283	−	0.115709i	$-0.963086\pi$
$701$	−33.0736	−	28.6584i	−1.24917	−	1.08241i	−0.255890	−	0.966706i	$-0.582368\pi$
$702$	−6.51131	+	0.465698i	−0.245754	+	0.0175767i
$703$	−4.10092	+	7.51027i	−0.154669	+	0.283255i
$704$	−0.281856	−	0.617179i	−0.0106228	−	0.0232608i
$705$	12.4023	+	7.35378i	0.467097	+	0.276960i
$706$	−17.2907	−	5.07699i	−0.650742	−	0.191075i
$707$	−19.9780	−	14.9554i	−0.751351	−	0.562454i
$708$	4.64517	+	12.4542i	0.174576	+	0.468056i
$709$	3.89851	−	27.1147i	0.146412	−	1.01831i	−0.775620	−	0.631200i	$-0.782563\pi$
$709$	3.89851	−	27.1147i	0.146412	−	1.01831i	0.922032	−	0.387114i	$-0.126528\pi$
$710$	20.7623	−	16.7412i	0.779195	−	0.628286i
$711$	−1.16807	+	1.01214i	−0.0438060	+	0.0379581i
$712$	1.17741	−	1.17741i	0.0441252	−	0.0441252i
$713$	8.82377	+	29.9127i	0.330453	+	1.12024i
$714$		−	15.5824i		−	0.583157i
$715$	−9.14893	+	3.79270i	−0.342151	+	0.141839i
$716$	−3.94736	−	2.53682i	−0.147520	−	0.0948053i
$717$	−21.5261	+	16.1143i	−0.803909	+	0.601799i
$718$	6.76523	−	2.52330i	0.252476	−	0.0941687i
$719$	0.877403	−	0.126151i	0.0327216	−	0.00470466i	−0.125935	−	0.992039i	$-0.540193\pi$
$719$	0.877403	−	0.126151i	0.0327216	−	0.00470466i	0.158656	+	0.987334i	$0.449284\pi$
$720$	2.20043	−	0.397655i	0.0820050	−	0.0148197i
$721$	24.4250	−	15.6970i	0.909633	−	0.584586i
$722$	−5.65281	+	15.1558i	−0.210376	+	0.564039i
$723$	−20.6817	−	11.2931i	−0.769162	−	0.419994i
$724$	−9.66307	+	11.1518i	−0.359125	+	0.414453i
$725$	12.1251	−	2.64498i	0.450316	−	0.0982319i
$726$	10.1127	−	2.96936i	0.375318	−	0.110203i
$727$	24.6280	+	9.18577i	0.913402	+	0.340681i	0.761839	−	0.647766i	$-0.224297\pi$
$727$	24.6280	+	9.18577i	0.913402	+	0.340681i	0.151563	+	0.988448i	$0.451569\pi$
$728$	−25.0069	−	5.43991i	−0.926817	−	0.201617i
$729$	0.281733	−	0.959493i	0.0104345	−	0.0355368i
$730$	10.6660	−	7.41006i	0.394765	−	0.274258i
$731$	18.1412	−	39.7237i	0.670977	−	1.46924i
$732$	−6.85946	−	9.16316i	−0.253533	−	0.338680i
$733$	−1.95394	−	8.98213i	−0.0721705	−	0.331763i	0.926879	−	0.375361i	$-0.122481\pi$
$733$	−1.95394	−	8.98213i	−0.0721705	−	0.331763i	−0.999049	+	0.0435987i	$0.986118\pi$
$734$	−9.27400	−	10.7028i	−0.342310	−	0.395046i
$735$	5.90466	−	17.7577i	0.217797	−	0.655004i
$736$	−3.84285	−	2.86923i	−0.141649	−	0.105761i
$737$	−2.30213	−	2.30213i	−0.0848001	−	0.0848001i
$738$	−5.39874	−	0.386125i	−0.198730	−	0.0142135i
$739$	7.41168	−	11.5328i	0.272643	−	0.424241i	−0.677750	−	0.735293i	$-0.737045\pi$
$739$	7.41168	−	11.5328i	0.272643	−	0.424241i	0.950393	+	0.311051i	$0.100681\pi$
$740$	−10.1825	−	5.09334i	−0.374317	−	0.187235i
$741$	−9.97933	−	4.55741i	−0.366600	−	0.167421i
$742$	−10.9707	+	14.6552i	−0.402748	+	0.538008i
$743$	19.6822	+	36.0453i	0.722070	+	1.32237i	0.938229	+	0.346014i	$0.112465\pi$
$743$	19.6822	+	36.0453i	0.722070	+	1.32237i	−0.216159	+	0.976358i	$0.569353\pi$
$744$	−3.51575	−	5.47061i	−0.128894	−	0.200562i
$745$	10.7110	−	13.2994i	0.392421	−	0.487252i
$746$	−3.32169	−	11.3126i	−0.121616	−	0.414184i
$747$	0.850988	+	11.8984i	0.0311360	+	0.435339i
$748$	−0.192391	−	2.68998i	−0.00703451	−	0.0983553i
$749$	11.5033	+	39.1768i	0.420323	+	1.43149i
$750$	2.77433	+	10.8307i	0.101304	+	0.395480i
$751$	−1.84076	−	2.86428i	−0.0671704	−	0.104519i	0.806044	−	0.591856i	$-0.201605\pi$
$751$	−1.84076	−	2.86428i	−0.0671704	−	0.104519i	−0.873214	+	0.487337i	$0.837968\pi$
$752$	3.09028	+	5.65943i	0.112691	+	0.206378i
$753$	−14.7623	+	19.7202i	−0.537969	+	0.718643i
$754$	−14.7385	−	6.73085i	−0.536744	−	0.245123i
$755$	50.2545	−	16.7424i	1.82895	−	0.609318i
$756$	2.11949	−	3.29799i	0.0770852	−	0.119947i
$757$	−20.8537	−	1.49149i	−0.757941	−	0.0542090i	−0.312981	−	0.949759i	$-0.601328\pi$
$757$	−20.8537	−	1.49149i	−0.757941	−	0.0542090i	−0.444960	+	0.895550i	$0.646782\pi$
$758$	9.13919	+	9.13919i	0.331950	+	0.331950i
$759$	−2.29800	+	2.30375i	−0.0834122	+	0.0836210i
$760$	3.56592	+	1.18571i	0.129350	+	0.0430103i
$761$	0.996455	+	1.14997i	0.0361215	+	0.0416864i	0.773523	−	0.633768i	$-0.218493\pi$
$761$	0.996455	+	1.14997i	0.0361215	+	0.0416864i	−0.737401	+	0.675455i	$0.763947\pi$
$762$	2.95452	+	13.5817i	0.107031	+	0.492013i
$763$	21.3153	+	28.4739i	0.771665	+	1.03082i
$764$	6.31411	−	13.8260i	0.228436	−	0.500206i
$765$	8.74708	+	1.57555i	0.316251	+	0.0569640i
$766$	9.84933	−	33.5437i	0.355871	−	1.21198i
$767$	84.7881	+	18.4445i	3.06152	+	0.665993i
$768$	0.936950	+	0.349464i	0.0338093	+	0.0126102i
$769$	−27.3934	+	8.04344i	−0.987832	+	0.290054i	−0.735454	−	0.677575i	$-0.763031\pi$
$769$	−27.3934	+	8.04344i	−0.987832	+	0.290054i	−0.252378	+	0.967629i	$0.581213\pi$
$770$	1.46926	−	5.76343i	0.0529484	−	0.207700i
$771$	12.3436	−	14.2453i	0.444545	−	0.513033i
$772$	−17.5959	−	9.60809i	−0.633291	−	0.345803i
$773$	7.51708	−	20.1541i	0.270371	−	0.724892i	−0.728822	−	0.684704i	$-0.759932\pi$
$773$	7.51708	−	20.1541i	0.270371	−	0.724892i	0.999192	−	0.0401879i	$-0.0127957\pi$
$774$	9.24272	−	5.93994i	0.332223	−	0.213507i
$775$	26.0181	−	19.5003i	0.934597	−	0.700471i
$776$	−9.61237	+	1.38205i	−0.345064	+	0.0496127i
$777$	−18.7025	+	6.97568i	−0.670949	+	0.250251i
$778$	−30.5920	+	22.9009i	−1.09678	+	0.821037i
$779$	−7.65220	−	4.91777i	−0.274168	−	0.176197i
$780$	5.58212	−	13.4874i	0.199872	−	0.482927i
$781$		−	8.09280i		−	0.289583i
$782$	−10.3259	−	16.0233i	−0.369253	−	0.572993i
$783$	1.75508	−	1.75508i	0.0627213	−	0.0627213i
$784$	6.32488	−	5.48054i	0.225889	−	0.195734i
$785$	25.3297	+	31.4138i	0.904057	+	1.12121i
$786$	0.819636	−	5.70069i	0.0292354	−	0.203337i
$787$	−11.5999	−	31.1007i	−0.413494	−	1.10862i	−0.962138	−	0.272563i	$-0.912129\pi$
$787$	−11.5999	−	31.1007i	−0.413494	−	1.10862i	0.548644	−	0.836056i	$-0.315144\pi$
$788$	0.847070	+	0.634109i	0.0301756	+	0.0225892i
$789$	0.346691	+	0.101798i	0.0123425	+	0.00362409i
$790$	−0.855659	−	3.34841i	−0.0304430	−	0.119131i
$791$	−6.51230	−	14.2599i	−0.231551	−	0.507025i
$792$	0.325167	−	0.595499i	0.0115543	−	0.0211601i
$793$	−74.5298	+	5.33048i	−2.64663	+	0.189291i
$794$	12.2375	+	10.6038i	0.434292	+	0.376316i
$795$	−7.11733	−	7.64013i	−0.252426	−	0.270968i
$796$	1.01528	−	0.463664i	0.0359858	−	0.0164341i
$797$	−0.633300	+	2.91123i	−0.0224326	+	0.103121i	−0.987002	−	0.160709i	$-0.948622\pi$
$797$	−0.633300	+	2.91123i	−0.0224326	+	0.103121i	0.964569	+	0.263830i	$0.0849857\pi$
$798$	5.78253	−	3.15750i	0.204699	−	0.111774i
$799$	3.64753	+	25.3691i	0.129040	+	0.897494i
$800$	−1.40590	+	4.79828i	−0.0497060	+	0.169645i
$801$	1.64816	+	0.236969i	0.0582348	+	0.00837290i
$802$	−34.6596	+	7.53974i	−1.22387	+	0.266238i
$803$	0.281131	−	3.93073i	0.00992091	−	0.138712i
$804$	4.79844			0.169228
$805$	−10.4596	−	40.7190i	−0.368653	−	1.43515i
$806$	−42.4508			−1.49526
$807$	1.71243	−	23.9429i	0.0602805	−	0.842831i
$808$	6.22022	−	1.35312i	0.218826	−	0.0476028i
$809$	38.4765	+	5.53208i	1.35276	+	0.194498i	0.780285	−	0.625424i	$-0.215074\pi$
$809$	38.4765	+	5.53208i	1.35276	+	0.194498i	0.572475	+	0.819922i	$0.305983\pi$
$810$	1.63700	+	1.52323i	0.0575185	+	0.0535207i
$811$	5.87520	+	40.8629i	0.206306	+	1.43489i	0.785075	+	0.619400i	$0.212624\pi$
$811$	5.87520	+	40.8629i	0.206306	+	1.43489i	−0.578769	+	0.815492i	$0.696467\pi$
$812$	8.54023	−	4.66332i	0.299703	−	0.163650i
$813$	2.38526	−	10.9649i	0.0836549	−	0.384555i
$814$	−3.14247	+	1.43512i	−0.110144	+	0.0503009i
$815$	30.1840	+	1.06932i	1.05730	+	0.0374567i
$816$	3.00393	+	2.60292i	0.105158	+	0.0911204i
$817$	18.4172	−	1.31723i	0.644337	−	0.0460839i
$818$	−11.8754	+	21.7481i	−0.415212	+	0.760405i
$819$	−10.6312	−	23.2791i	−0.371484	−	0.813436i
$820$	6.17269	−	10.4103i	0.215560	−	0.363545i
$821$	−9.42076	−	2.76619i	−0.328787	−	0.0965405i	0.113173	−	0.993575i	$-0.463899\pi$
$821$	−9.42076	−	2.76619i	−0.328787	−	0.0965405i	−0.441960	+	0.897035i	$0.645717\pi$
$822$	2.55754	+	1.91455i	0.0892046	+	0.0667777i
$823$	1.19371	+	3.20047i	0.0416103	+	0.111561i	0.956093	−	0.293064i	$-0.0946748\pi$
$823$	1.19371	+	3.20047i	0.0416103	+	0.111561i	−0.914483	+	0.404625i	$0.867402\pi$
$824$	−1.05398	+	7.33062i	−0.0367173	+	0.255374i
$825$	3.08670	+	1.40750i	0.107465	+	0.0490029i
$826$	−39.3822	+	34.1248i	−1.37028	+	1.18736i
$827$	−36.6597	+	36.6597i	−1.27478	+	1.27478i	−0.331233	+	0.943549i	$0.607465\pi$
$827$	−36.6597	+	36.6597i	−1.27478	+	1.27478i	−0.943549	+	0.331233i	$0.892535\pi$
$828$	−0.00599354	−	4.79583i	−0.000208290	−	0.166667i
$829$			14.5303i			0.504658i	0.967642	+	0.252329i	$0.0811965\pi$
$829$			14.5303i			0.504658i	−0.967642	+	0.252329i	$0.918803\pi$
$830$	−24.6461	−	10.2004i	−0.855478	−	0.354062i
$831$	−17.1572	−	11.0263i	−0.595177	−	0.382497i
$832$	5.22589	−	3.91205i	0.181175	−	0.135626i
$833$	31.1675	−	11.6249i	1.07989	−	0.402778i
$834$	−11.8799	+	1.70807i	−0.411367	+	0.0591456i
$835$	15.6145	−	22.5030i	0.540364	−	0.778750i
$836$	0.959248	−	0.616472i	0.0331763	−	0.0213211i
$837$	2.27254	−	6.09292i	0.0785505	−	0.210602i
$838$	−9.43930	−	5.15425i	−0.326075	−	0.178051i
$839$	−4.71139	+	5.43724i	−0.162655	+	0.187714i	−0.831226	−	0.555934i	$-0.812361\pi$
$839$	−4.71139	+	5.43724i	−0.162655	+	0.187714i	0.668571	+	0.743648i	$0.266906\pi$
$840$	4.47527	+	7.53771i	0.154411	+	0.260076i
$841$	−21.9143	+	6.43461i	−0.755664	+	0.221883i
$842$	−11.8768	−	4.42982i	−0.409301	−	0.152662i
$843$	1.78743	+	0.388831i	0.0615623	+	0.0133921i
$844$	−0.540962	+	1.84235i	−0.0186207	+	0.0634162i
$845$	−37.7819	−	54.3829i	−1.29974	−	1.87083i
$846$	−2.67867	+	5.86546i	−0.0920945	+	0.201659i
$847$	24.7615	+	33.0775i	0.850816	+	1.13656i
$848$	−0.992605	−	4.56293i	−0.0340862	−	0.156692i
$849$	7.58338	+	8.75169i	0.260261	+	0.300357i
$850$	−11.9008	+	15.9167i	−0.408193	+	0.545938i
$851$	−14.6092	+	19.5665i	−0.500797	+	0.670732i
$852$	8.43410	+	8.43410i	0.288948	+	0.288948i
$853$	−10.7578	−	0.769413i	−0.368340	−	0.0263442i	−0.114057	−	0.993474i	$-0.536385\pi$
$853$	−10.7578	−	0.769413i	−0.368340	−	0.0263442i	−0.254283	+	0.967130i	$0.581839\pi$
$854$	24.2602	−	37.7495i	0.830165	−	1.29176i
$855$	1.18777	+	3.56524i	0.0406208	+	0.121929i
$856$	−9.47392	−	4.32660i	−0.323812	−	0.147880i
$857$	−2.76398	+	3.69225i	−0.0944159	+	0.126125i	−0.845261	−	0.534353i	$-0.820555\pi$
$857$	−2.76398	+	3.69225i	−0.0944159	+	0.126125i	0.750846	+	0.660478i	$0.229646\pi$
$858$	−2.12267	−	3.88738i	−0.0724668	−	0.132713i
$859$	−28.6372	−	44.5603i	−0.977088	−	1.52038i	−0.848849	−	0.528636i	$-0.822704\pi$
$859$	−28.6372	−	44.5603i	−0.977088	−	1.52038i	−0.128240	−	0.991743i	$-0.540933\pi$
$860$	2.63316	+	24.4258i	0.0897901	+	0.832913i
$861$	−5.97806	−	20.3594i	−0.203732	−	0.693847i
$862$	0.881572	+	12.3260i	0.0300265	+	0.419825i
$863$	1.27210	+	17.7862i	0.0433026	+	0.605450i	0.972056	+	0.234751i	$0.0754274\pi$
$863$	1.27210	+	17.7862i	0.0433026	+	0.605450i	−0.928753	+	0.370699i	$0.879118\pi$
$864$	0.281733	+	0.959493i	0.00958474	+	0.0326426i
$865$	2.75043	+	25.5136i	0.0935173	+	0.867488i
$866$	0.492297	+	0.766029i	0.0167289	+	0.0260307i
$867$	−0.575692	−	1.05430i	−0.0195515	−	0.0358060i
$868$	15.2778	−	20.4087i	0.518561	−	0.692717i
$869$	−0.953897	−	0.435630i	−0.0323587	−	0.0147777i
$870$	1.75422	+	5.26552i	0.0594735	+	0.178518i
$871$	16.9350	−	26.3514i	0.573821	−	0.892882i
$872$	−9.04965	−	0.647244i	−0.306460	−	0.0219184i
$873$	−6.86687	−	6.86687i	−0.232408	−	0.232408i
$874$	3.85380	−	7.07872i	0.130357	−	0.239441i
$875$	−35.9818	+	25.0287i	−1.21641	+	0.846125i
$876$	3.80351	+	4.38949i	0.128509	+	0.148307i
$877$	−2.38062	−	10.9435i	−0.0803879	−	0.369537i	0.919325	−	0.393499i	$-0.128736\pi$
$877$	−2.38062	−	10.9435i	−0.0803879	−	0.369537i	−0.999713	+	0.0239619i	$0.992372\pi$
$878$	−14.6435	−	19.5615i	−0.494195	−	0.660167i
$879$	−9.52753	+	20.8624i	−0.321356	+	0.703671i
$880$	0.865627	+	1.24597i	0.0291803	+	0.0420018i
$881$	−9.92788	+	33.8113i	−0.334479	+	1.13913i	0.604915	+	0.796290i	$0.293207\pi$
$881$	−9.92788	+	33.8113i	−0.334479	+	1.13913i	−0.939394	+	0.342840i	$0.888611\pi$
$882$	8.17776	+	1.77896i	0.275360	+	0.0599008i
$883$	25.1953	+	9.39737i	0.847890	+	0.316247i	0.735589	−	0.677428i	$-0.236905\pi$
$883$	25.1953	+	9.39737i	0.847890	+	0.316247i	0.112301	+	0.993674i	$0.464178\pi$
$884$	24.8960	−	7.31013i	0.837344	−	0.245866i
$885$	−15.1738	−	25.5573i	−0.510062	−	0.859099i
$886$	12.0840	−	13.9457i	0.405969	−	0.468514i
$887$	−10.8217	−	5.90910i	−0.363358	−	0.198408i	0.287190	−	0.957874i	$-0.407279\pi$
$887$	−10.8217	−	5.90910i	−0.363358	−	0.198408i	−0.650548	+	0.759465i	$0.725461\pi$
$888$	1.77936	−	4.77064i	0.0597113	−	0.160092i
$889$	−45.8400	+	29.4596i	−1.53742	+	0.988042i
$890$	−2.12260	+	3.05900i	−0.0711496	+	0.102538i
$891$	0.671587	−	0.0965596i	0.0224990	−	0.00323487i
$892$	6.65120	−	2.48077i	0.222699	−	0.0830624i
$893$	−8.67520	+	6.49417i	−0.290304	+	0.217319i
$894$	6.42444	+	4.12874i	0.214865	+	0.138086i
$895$	9.69466	+	4.01239i	0.324057	+	0.134119i
$896$			3.92033i			0.130969i
$897$	−26.3582	−	16.8929i	−0.880075	−	0.564037i
$898$	20.3818	−	20.3818i	0.680150	−	0.680150i
$899$	12.1983	−	10.5699i	0.406835	−	0.352524i
$900$	−4.68374	+	1.75002i	−0.156125	+	0.0583340i
$901$	2.64147	−	18.3718i	0.0880001	−	0.612054i
$902$	−1.28336	−	3.44082i	−0.0427312	−	0.114567i
$903$	34.4810	+	25.8121i	1.14746	+	0.858974i
$904$	3.83681	+	1.12659i	0.127611	+	0.0374698i
$905$	16.8283	−	28.3812i	0.559392	−	0.943423i
$906$	9.84074	+	21.5482i	0.326937	+	0.715891i
$907$	21.7152	−	39.7685i	0.721042	−	1.32049i	−0.217749	−	0.976005i	$-0.569871\pi$
$907$	21.7152	−	39.7685i	0.721042	−	1.32049i	0.938792	−	0.344486i	$-0.111947\pi$
$908$	−16.5876	+	1.18637i	−0.550477	+	0.0393709i
$909$	4.81087	+	4.16864i	0.159566	+	0.138265i
$910$	57.1890	+	2.02602i	1.89580	+	0.0671618i
$911$	−38.4689	+	17.5682i	−1.27453	+	0.582059i	−0.933697	−	0.358064i	$-0.883437\pi$
$911$	−38.4689	+	17.5682i	−1.27453	+	0.582059i	−0.340835	+	0.940123i	$0.610710\pi$
$912$	−0.357233	+	1.64217i	−0.0118292	+	0.0543778i
$913$	−7.10357	+	3.87884i	−0.235094	+	0.128371i
$914$	−2.41846	−	16.8208i	−0.0799956	−	0.556381i
$915$	18.7375	+	17.4352i	0.619443	+	0.576388i
$916$	−18.5432	−	2.66610i	−0.612683	−	0.0880905i
$917$	22.0624	−	4.79939i	0.728566	−	0.158490i
$918$	−0.283557	+	3.96464i	−0.00935876	+	0.130853i
$919$	−6.41720			−0.211684			−0.105842	−	0.994383i	$-0.533754\pi$
$919$	−6.41720			−0.211684			−0.105842	+	0.994383i	$0.533754\pi$
$920$	9.59687	+	4.78541i	0.316399	+	0.157770i
$921$	−7.35659			−0.242408
$922$	−1.16258	+	16.2550i	−0.0382875	+	0.535329i
$923$	76.0835	−	16.5509i	2.50432	−	0.544781i
$924$	2.63284	+	0.378546i	0.0866142	+	0.0124532i
$925$	24.4313	+	7.15838i	0.803295	+	0.235366i
$926$	4.37979	+	30.4621i	0.143929	+	1.00105i
$927$	−6.50009	+	3.54932i	−0.213491	+	0.116575i
$928$	−0.527598	+	2.42533i	−0.0173193	+	0.0796154i
$929$	4.96255	−	2.26632i	0.162816	−	0.0743555i	−0.332340	−	0.943160i	$-0.607838\pi$
$929$	4.96255	−	2.26632i	0.162816	−	0.0743555i	0.495156	+	0.868804i	$0.335111\pi$
$930$	9.91155	+	10.6396i	0.325013	+	0.348887i
$931$	10.6295	+	9.21049i	0.348367	+	0.301861i
$932$	−19.7983	+	1.41600i	−0.648515	+	0.0463827i
$933$	8.17638	−	14.9739i	0.267683	−	0.490224i
$934$	0.0190135	+	0.0416337i	0.000622140	+	0.00136230i
$935$	1.49302	+	5.84259i	0.0488271	+	0.191073i
$936$	6.26352	+	1.83913i	0.204729	+	0.0601140i
$937$	3.01815	+	2.25936i	0.0985986	+	0.0738100i	0.647440	−	0.762117i	$-0.275840\pi$
$937$	3.01815	+	2.25936i	0.0985986	+	0.0738100i	−0.548841	+	0.835927i	$0.684931\pi$
$938$	6.57394	+	17.6254i	0.214647	+	0.575490i
$939$	−2.59121	+	18.0223i	−0.0845611	+	0.588135i
$940$	−9.05043	−	11.2243i	−0.295192	−	0.366096i
$941$	−36.7322	+	31.8286i	−1.19744	+	1.03758i	−0.199096	+	0.979980i	$0.563801\pi$
$941$	−36.7322	+	31.8286i	−1.19744	+	1.03758i	−0.998340	+	0.0576041i	$0.981654\pi$
$942$	−12.7610	+	12.7610i	−0.415775	+	0.415775i
$943$	−19.6387	−	16.9741i	−0.639523	−	0.552752i
$944$		−	13.2923i		−	0.432626i
$945$	−3.35232	+	8.09982i	−0.109051	+	0.263487i
$946$	6.27112	+	4.03020i	0.203892	+	0.131033i
$947$	−37.0851	+	27.7615i	−1.20510	+	0.902128i	−0.997108	−	0.0760017i	$-0.975785\pi$
$947$	−37.0851	+	27.7615i	−1.20510	+	0.902128i	−0.207995	+	0.978130i	$0.566694\pi$
$948$	1.44813	−	0.540124i	0.0470330	−	0.0175424i
$949$	37.5292	−	5.39588i	1.21825	−	0.175158i
$950$	−8.31805	−	1.19107i	−0.269873	−	0.0386433i
$951$	−20.9192	+	13.4439i	−0.678350	+	0.435949i
$952$	−5.44549	+	14.5999i	−0.176489	+	0.473187i
$953$	6.81843	+	3.72315i	0.220871	+	0.120605i	0.585875	−	0.810401i	$-0.300751\pi$
$953$	6.81843	+	3.72315i	0.220871	+	0.120605i	−0.365005	+	0.931006i	$0.618933\pi$
$954$	3.05797	−	3.52908i	0.0990054	−	0.114258i
$955$	−8.39576	+	32.9338i	−0.271680	+	1.06571i
$956$	25.8003	−	7.57565i	0.834441	−	0.245014i
$957$	1.57787	+	0.588517i	0.0510054	+	0.0190240i
$958$	−10.0637	−	2.18923i	−0.325144	−	0.0707308i
$959$	−3.52858	+	12.0172i	−0.113944	+	0.388056i
$960$	−2.20065	−	0.396387i	−0.0710258	−	0.0127933i
$961$	4.68923	−	10.2680i	0.151266	−	0.331225i
$962$	−19.9189	−	26.6085i	−0.642211	−	0.857893i
$963$	−2.21389	−	10.1771i	−0.0713417	−	0.327952i
$964$	15.4312	+	17.8086i	0.497006	+	0.573576i
$965$	42.5392	+	14.1448i	1.36938	+	0.455337i
$966$	17.6076	−	6.59238i	0.566516	−	0.212106i
$967$	14.1429	+	14.1429i	0.454805	+	0.454805i	0.896946	−	0.442141i	$-0.145781\pi$
$967$	14.1429	+	14.1429i	0.454805	+	0.454805i	−0.442141	+	0.896946i	$0.645781\pi$
$968$	−10.5128	−	0.751890i	−0.337894	−	0.0241667i
$969$	−3.61143	+	5.61950i	−0.116016	+	0.180524i
$970$	20.6017	−	6.86350i	0.661482	−	0.220374i
$971$	23.3313	+	10.6550i	0.748736	+	0.341936i	0.752970	−	0.658055i	$-0.228620\pi$
$971$	23.3313	+	10.6550i	0.748736	+	0.341936i	−0.00423381	+	0.999991i	$0.501348\pi$
$972$	−0.599278	+	0.800541i	−0.0192218	+	0.0256774i
$973$	−22.5496	−	41.2966i	−0.722908	−	1.32391i
$974$	−5.63708	−	8.77147i	−0.180624	−	0.281056i
$975$	−6.91970	+	31.8978i	−0.221608	+	1.02155i
$976$	3.22477	+	10.9826i	0.103222	+	0.351543i
$977$	0.931001	+	13.0171i	0.0297853	+	0.416454i	0.990368	+	0.138459i	$0.0442150\pi$
$977$	0.931001	+	13.0171i	0.0297853	+	0.416454i	−0.960583	+	0.277994i	$0.910330\pi$
$978$	0.963591	+	13.4728i	0.0308122	+	0.430811i
$979$	0.318291	+	1.08400i	0.0101726	+	0.0346448i
$980$	−11.7381	+	14.5746i	−0.374959	+	0.465570i
$981$	−4.90511	−	7.63250i	−0.156608	−	0.243687i
$982$	−7.52928	−	13.7889i	−0.240269	−	0.440020i
$983$	12.0367	−	16.0792i	0.383911	−	0.512845i	−0.566407	−	0.824126i	$-0.691667\pi$
$983$	12.0367	−	16.0792i	0.383911	−	0.512845i	0.950318	+	0.311280i	$0.100758\pi$
$984$	4.92341	+	2.24845i	0.156953	+	0.0716778i
$985$	−2.11607	−	1.05847i	−0.0674236	−	0.0337256i
$986$	−5.33373	+	8.29945i	−0.169861	+	0.264308i
$987$	−25.2146	−	1.80338i	−0.802589	−	0.0574023i
$988$	7.75748	+	7.75748i	0.246798	+	0.246798i
$989$	52.5615	+	3.69325i	1.67136	+	0.117439i
$990$	−0.478703	+	1.43965i	−0.0152142	+	0.0457552i
$991$	23.4452	+	27.0572i	0.744762	+	0.859501i	0.994050	−	0.108928i	$-0.0347419\pi$
$991$	23.4452	+	27.0572i	0.744762	+	0.859501i	−0.249288	+	0.968429i	$0.580196\pi$
$992$	1.38230	+	6.35432i	0.0438880	+	0.201750i
$993$	−1.06266	−	1.41955i	−0.0337225	−	0.0450480i
$994$	−19.4249	+	42.5346i	−0.616121	+	1.34912i
$995$	−2.04968	+	1.42399i	−0.0649791	+	0.0451435i
$996$	3.36072	−	11.4456i	0.106489	−	0.362667i
$997$	−54.6106	−	11.8798i	−1.72954	−	0.376237i	−0.765796	−	0.643083i	$-0.777655\pi$
$997$	−54.6106	−	11.8798i	−1.72954	−	0.376237i	−0.963739	+	0.266846i	$0.914019\pi$
$998$	35.6118	+	13.2825i	1.12727	+	0.420451i
$999$	4.88542	−	1.43449i	0.154568	−	0.0453853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.217.6	yes	240
5.3	odd	4	inner	690.2.w.b.493.11	yes	240
23.7	odd	22	inner	690.2.w.b.7.11	✓	240
115.53	even	44	inner	690.2.w.b.283.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.11	✓	240	23.7	odd	22	inner
690.2.w.b.217.6	yes	240	1.1	even	1	trivial
690.2.w.b.283.6	yes	240	115.53	even	44	inner
690.2.w.b.493.11	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)

\(f(q)\)	\(=\)	\(q+(-0.0713392 + 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(2.23462 - 0.0804541i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-3.44079 + 1.87882i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.0713392 + 0.997452i) q^{2} +(0.977147 - 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(2.23462 - 0.0804541i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-3.44079 + 1.87882i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-0.0791669 + 2.23467i) q^{10} +(0.512771 + 0.444318i) q^{11} +(-0.997452 + 0.0713392i) q^{12} +(-3.12851 + 5.72944i) q^{13} +(-1.62857 - 3.56606i) q^{14} +(2.16645 - 0.553618i) q^{15} +(0.959493 + 0.281733i) q^{16} +(3.18196 + 2.38199i) q^{17} +(0.349464 + 0.936950i) q^{18} +(-0.239171 + 1.66347i) q^{19} +(-2.22332 - 0.238384i) q^{20} +(-2.96279 + 2.56727i) q^{21} +(-0.479767 + 0.479767i) q^{22} +(-1.34539 + 4.60325i) q^{23} -1.00000i q^{24} +(4.98705 - 0.359569i) q^{25} +(-5.49166 - 3.52927i) q^{26} +(0.800541 - 0.599278i) q^{27} +(3.67316 - 1.37002i) q^{28} +(2.45679 - 0.353233i) q^{29} +(0.397655 + 2.20043i) q^{30} +(5.47061 - 3.51575i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(0.595499 + 0.325167i) q^{33} +(-2.60292 + 3.00393i) q^{34} +(-7.53771 + 4.47527i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(4.77064 + 1.77936i) q^{37} +(-1.64217 - 0.357233i) q^{38} +(-1.83913 + 6.26352i) q^{39} +(0.396387 - 2.20065i) q^{40} +(-2.24845 + 4.92341i) q^{41} +(-2.34937 - 3.13839i) q^{42} +(-2.33542 - 10.7358i) q^{43} +(-0.444318 - 0.512771i) q^{44} +(1.99926 - 1.00148i) q^{45} +(-4.49554 - 1.67035i) q^{46} +(4.55955 + 4.55955i) q^{47} +(0.997452 + 0.0713392i) q^{48} +(4.52463 - 7.04047i) q^{49} +(0.00288011 + 5.00000i) q^{50} +(3.61557 + 1.65118i) q^{51} +(3.91205 - 5.22589i) q^{52} +(-2.23792 - 4.09845i) q^{53} +(0.540641 + 0.841254i) q^{54} +(1.18159 + 0.951628i) q^{55} +(1.10449 + 3.76153i) q^{56} +(0.119891 + 1.67630i) q^{57} +(0.177068 + 2.47573i) q^{58} +(-3.74486 - 12.7538i) q^{59} +(-2.22319 + 0.239665i) q^{60} +(6.18829 + 9.62916i) q^{61} +(3.11652 + 5.70748i) q^{62} +(-2.34937 + 3.13839i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-6.53008 + 13.0548i) q^{65} +(-0.366821 + 0.570784i) q^{66} +(-4.78621 - 0.342317i) q^{67} +(-2.81058 - 2.81058i) q^{68} +(-0.336152 + 4.78404i) q^{69} +(-3.92613 - 7.83777i) q^{70} +(-7.81093 - 9.01429i) q^{71} +(-0.212565 - 0.977147i) q^{72} +(-3.48068 - 4.64964i) q^{73} +(-2.11516 + 4.63155i) q^{74} +(4.79665 - 1.41143i) q^{75} +(0.473474 - 1.61250i) q^{76} +(-2.59913 - 0.565406i) q^{77} +(-6.11636 - 2.28128i) q^{78} +(-1.48297 + 0.435439i) q^{79} +(2.16677 + 0.552370i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-4.75046 - 2.59395i) q^{82} +(-4.16868 + 11.1767i) q^{83} +(3.29799 - 2.11949i) q^{84} +(7.30212 + 5.06684i) q^{85} +(10.8750 - 1.56359i) q^{86} +(2.32556 - 0.867389i) q^{87} +(0.543161 - 0.406606i) q^{88} +(1.40078 + 0.900224i) q^{89} +(0.856301 + 2.06561i) q^{90} -25.5917i q^{91} +(1.98681 - 4.36493i) q^{92} +(4.59826 - 4.59826i) q^{93} +(-4.87320 + 4.22266i) q^{94} +(-0.400624 + 3.73647i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-3.39372 - 9.09892i) q^{97} +(6.69975 + 5.01537i) q^{98} +(0.651009 + 0.191153i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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