LMFDB - Embedded newform 750.2.o.b.469.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

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

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$14$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			469.7
Character	$\chi$	$=$	750.469
Dual form			750.2.o.b.379.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.91983 + 1.14641i) q^{5} +(0.876307 - 0.481754i) q^{6} +(-2.52498 - 3.47534i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})$	\(q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.91983 + 1.14641i) q^{5} +(0.876307 - 0.481754i) q^{6} +(-2.52498 - 3.47534i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(-1.98802 - 1.02360i) q^{10} +(0.285325 + 4.53512i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(2.47411 + 2.04676i) q^{13} +(2.73822 + 3.30994i) q^{14} +(-2.22523 - 0.219884i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.753874 - 5.96753i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(1.30094 - 2.76463i) q^{19} +(2.04837 + 0.896756i) q^{20} +(3.76440 + 2.06950i) q^{21} +(-0.569524 - 4.50825i) q^{22} +(1.28305 + 3.24062i) q^{23} +(0.809017 - 0.587785i) q^{24} +(2.37147 + 4.40183i) q^{25} +(-2.59775 - 1.88737i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(-2.94065 - 3.13147i) q^{28} +(2.77387 - 2.60484i) q^{29} +(2.23465 + 0.0797267i) q^{30} +(-0.837425 - 0.105791i) q^{31} +(-0.951057 + 0.309017i) q^{32} +(-2.18913 - 3.98201i) q^{33} +(-0.377682 + 6.00309i) q^{34} +(-0.863350 - 9.56672i) q^{35} +(0.535827 - 0.844328i) q^{36} +(0.598617 + 2.33146i) q^{37} +(-1.12478 + 2.84086i) q^{38} +(-3.11011 - 0.798542i) q^{39} +(-2.10064 - 0.766368i) q^{40} +(11.5602 + 4.57702i) q^{41} +(-3.88692 - 1.82904i) q^{42} +(-6.17066 - 2.00497i) q^{43} +(0.851476 + 4.46359i) q^{44} +(2.10707 - 0.748500i) q^{45} +(-1.48400 - 3.15366i) q^{46} +(7.50430 + 1.43152i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(-3.53933 + 10.8929i) q^{49} +(-2.64318 - 4.24424i) q^{50} +(1.85872 + 5.72056i) q^{51} +(2.71113 + 1.72054i) q^{52} +(5.07269 - 9.22719i) q^{53} +(0.187381 - 0.982287i) q^{54} +(-4.65134 + 9.03374i) q^{55} +(3.13147 + 2.94065i) q^{56} +3.05542i q^{57} +(-2.60484 + 2.77387i) q^{58} +(5.43267 + 8.56052i) q^{59} +(-2.23524 + 0.0607452i) q^{60} +(-1.52149 + 0.602401i) q^{61} +(0.842415 + 0.0530003i) q^{62} +(-4.28728 - 0.269733i) q^{63} +(0.929776 - 0.368125i) q^{64} +(2.40343 + 6.76579i) q^{65} +(2.43484 + 3.83670i) q^{66} +(4.84568 - 5.16013i) q^{67} -6.01496i q^{68} +(-2.54073 - 2.38590i) q^{69} +(1.46235 + 9.49363i) q^{70} +(-1.36849 + 7.17389i) q^{71} +(-0.481754 + 0.876307i) q^{72} +(10.8378 + 6.87785i) q^{73} +(-0.743829 - 2.28927i) q^{74} +(-4.01998 - 2.97317i) q^{75} +(0.944178 - 2.90588i) q^{76} +(15.0406 - 12.4427i) q^{77} +(3.15412 + 0.601680i) q^{78} +(2.86722 + 6.09316i) q^{79} +(2.14461 + 0.632956i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(-11.8248 - 3.84211i) q^{82} +(2.25593 + 1.06156i) q^{83} +(3.99409 + 1.58137i) q^{84} +(8.28856 - 10.5924i) q^{85} +(6.28438 + 1.61355i) q^{86} +(-1.40079 + 3.53798i) q^{87} +(-1.13007 - 4.40132i) q^{88} +(4.91603 - 7.74643i) q^{89} +(-2.05591 + 0.879327i) q^{90} +(0.866110 - 13.7664i) q^{91} +(1.67909 + 3.05426i) q^{92} +(0.802768 - 0.260835i) q^{93} +(-7.57938 - 0.957498i) q^{94} +(5.66698 - 3.81620i) q^{95} +(0.728969 - 0.684547i) q^{96} +(-0.275110 - 0.292962i) q^{97} +(2.84837 - 11.0937i) q^{98} +(3.67624 + 2.67094i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q+O(q^{10}) $ 280 * q	$ 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) $ 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{49}{50}\right)$	$1$

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 $

$2$	−0.998027	+	0.0627905i	−0.705711	+	0.0443996i
$2$	−0.998027	+	0.0627905i	−0.705711	+	0.0443996i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$4$	0.992115	−	0.125333i	0.496057	−	0.0626666i
$5$	1.91983	+	1.14641i	0.858573	+	0.512692i
$5$	1.91983	+	1.14641i	0.858573	+	0.512692i
$6$	0.876307	−	0.481754i	0.357751	−	0.196675i
$7$	−2.52498	−	3.47534i	−0.954353	−	1.31355i	−0.949566	−	0.313566i	$-0.898476\pi$
$7$	−2.52498	−	3.47534i	−0.954353	−	1.31355i	−0.00478692	−	0.999989i	$-0.501524\pi$
$8$	−0.982287	+	0.187381i	−0.347291	+	0.0662493i
$9$	0.637424	−	0.770513i	0.212475	−	0.256838i
$10$	−1.98802	−	1.02360i	−0.628668	−	0.323692i
$11$	0.285325	+	4.53512i	0.0860288	+	1.36739i	0.770077	+	0.637951i	$0.220218\pi$
$11$	0.285325	+	4.53512i	0.0860288	+	1.36739i	−0.684048	+	0.729437i	$0.739782\pi$
$12$	−0.844328	+	0.535827i	−0.243736	+	0.154680i
$13$	2.47411	+	2.04676i	0.686195	+	0.567670i	0.913840	−	0.406074i	$-0.133102\pi$
$13$	2.47411	+	2.04676i	0.686195	+	0.567670i	−0.227645	+	0.973744i	$0.573102\pi$
$14$	2.73822	+	3.30994i	0.731819	+	0.884618i
$15$	−2.22523	−	0.219884i	−0.574552	−	0.0567738i
$16$	0.968583	−	0.248690i	0.242146	−	0.0621725i
$17$	0.753874	−	5.96753i	0.182841	−	1.44734i	−0.587251	−	0.809405i	$-0.699790\pi$
$17$	0.753874	−	5.96753i	0.182841	−	1.44734i	0.770092	−	0.637933i	$-0.220210\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	1.30094	−	2.76463i	0.298455	−	0.634250i	−0.698206	−	0.715897i	$-0.746018\pi$
$19$	1.30094	−	2.76463i	0.298455	−	0.634250i	0.996661	+	0.0816472i	$0.0260181\pi$
$20$	2.04837	+	0.896756i	0.458030	+	0.200521i
$21$	3.76440	+	2.06950i	0.821459	+	0.451601i
$22$	−0.569524	−	4.50825i	−0.121423	−	0.961162i
$23$	1.28305	+	3.24062i	0.267535	+	0.675716i	0.999987	−	0.00510269i	$-0.00162425\pi$
$23$	1.28305	+	3.24062i	0.267535	+	0.675716i	−0.732452	+	0.680818i	$0.761624\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	2.37147	+	4.40183i	0.474294	+	0.880367i
$26$	−2.59775	−	1.88737i	−0.509460	−	0.370145i
$27$	−0.248690	+	0.968583i	−0.0478604	+	0.186404i
$28$	−2.94065	−	3.13147i	−0.555730	−	0.591792i
$29$	2.77387	−	2.60484i	0.515095	−	0.483706i	−0.382852	−	0.923810i	$-0.625058\pi$
$29$	2.77387	−	2.60484i	0.515095	−	0.483706i	0.897947	+	0.440103i	$0.145058\pi$
$30$	2.23465	+	0.0797267i	0.407989	+	0.0145560i
$31$	−0.837425	−	0.105791i	−0.150406	−	0.0190007i	0.0497697	−	0.998761i	$-0.484151\pi$
$31$	−0.837425	−	0.105791i	−0.150406	−	0.0190007i	−0.200176	+	0.979760i	$0.564151\pi$
$32$	−0.951057	+	0.309017i	−0.168125	+	0.0546270i
$33$	−2.18913	−	3.98201i	−0.381078	−	0.693179i
$34$	−0.377682	+	6.00309i	−0.0647720	+	1.02952i
$35$	−0.863350	−	9.56672i	−0.145933	−	1.61707i
$36$	0.535827	−	0.844328i	0.0893045	−	0.140721i
$37$	0.598617	+	2.33146i	0.0984120	+	0.383289i	0.998640	−	0.0521287i	$-0.0166006\pi$
$37$	0.598617	+	2.33146i	0.0984120	+	0.383289i	−0.900228	+	0.435418i	$0.856601\pi$
$38$	−1.12478	+	2.84086i	−0.182463	+	0.460849i
$39$	−3.11011	−	0.798542i	−0.498017	−	0.127869i
$40$	−2.10064	−	0.766368i	−0.332140	−	0.121173i
$41$	11.5602	+	4.57702i	1.80540	+	0.714810i	0.990891	+	0.134664i	$0.0429955\pi$
$41$	11.5602	+	4.57702i	1.80540	+	0.714810i	0.814513	+	0.580146i	$0.197005\pi$
$42$	−3.88692	−	1.82904i	−0.599764	−	0.282228i
$43$	−6.17066	−	2.00497i	−0.941017	−	0.305755i	−0.201957	−	0.979394i	$-0.564730\pi$
$43$	−6.17066	−	2.00497i	−0.941017	−	0.305755i	−0.739060	+	0.673640i	$0.764730\pi$
$44$	0.851476	+	4.46359i	0.128365	+	0.672912i
$45$	2.10707	−	0.748500i	0.314104	−	0.111580i
$46$	−1.48400	−	3.15366i	−0.218804	−	0.464982i
$47$	7.50430	+	1.43152i	1.09461	+	0.208809i	0.702908	−	0.711281i	$-0.251885\pi$
$47$	7.50430	+	1.43152i	1.09461	+	0.208809i	0.391707	+	0.920090i	$0.371885\pi$
$48$	−0.770513	+	0.637424i	−0.111214	+	0.0920042i
$49$	−3.53933	+	10.8929i	−0.505619	+	1.55613i
$50$	−2.64318	−	4.24424i	−0.373803	−	0.600226i
$51$	1.85872	+	5.72056i	0.260273	+	0.801039i
$52$	2.71113	+	1.72054i	0.375966	+	0.238595i
$53$	5.07269	−	9.22719i	0.696787	−	1.26745i	−0.256838	−	0.966455i	$-0.582681\pi$
$53$	5.07269	−	9.22719i	0.696787	−	1.26745i	0.953625	−	0.300997i	$-0.0973194\pi$
$54$	0.187381	−	0.982287i	0.0254994	−	0.133672i
$55$	−4.65134	+	9.03374i	−0.627187	+	1.21811i
$56$	3.13147	+	2.94065i	0.418460	+	0.392960i
$57$			3.05542i			0.404701i
$58$	−2.60484	+	2.77387i	−0.342032	+	0.364227i
$59$	5.43267	+	8.56052i	0.707274	+	1.11449i	0.987964	+	0.154687i	$0.0494368\pi$
$59$	5.43267	+	8.56052i	0.707274	+	1.11449i	−0.280690	+	0.959799i	$0.590563\pi$
$60$	−2.23524	+	0.0607452i	−0.288569	+	0.00784218i
$61$	−1.52149	+	0.602401i	−0.194807	+	0.0771296i	−0.463502	−	0.886096i	$-0.653407\pi$
$61$	−1.52149	+	0.602401i	−0.194807	+	0.0771296i	0.268695	+	0.963225i	$0.413407\pi$
$62$	0.842415	+	0.0530003i	0.106987	+	0.00673104i
$63$	−4.28728	−	0.269733i	−0.540146	−	0.0339831i
$64$	0.929776	−	0.368125i	0.116222	−	0.0460156i
$65$	2.40343	+	6.76579i	0.298109	+	0.839193i
$66$	2.43484	+	3.83670i	0.299708	+	0.472265i
$67$	4.84568	−	5.16013i	0.591994	−	0.630410i	−0.361301	−	0.932449i	$-0.617667\pi$
$67$	4.84568	−	5.16013i	0.591994	−	0.630410i	0.953296	+	0.302039i	$0.0976673\pi$
$68$		−	6.01496i		−	0.729421i
$69$	−2.54073	−	2.38590i	−0.305868	−	0.287229i
$70$	1.46235	+	9.49363i	0.174784	+	1.13471i
$71$	−1.36849	+	7.17389i	−0.162410	+	0.851384i	0.804049	+	0.594563i	$0.202675\pi$
$71$	−1.36849	+	7.17389i	−0.162410	+	0.851384i	−0.966459	+	0.256821i	$0.917325\pi$
$72$	−0.481754	+	0.876307i	−0.0567752	+	0.103274i
$73$	10.8378	+	6.87785i	1.26846	+	0.804992i	0.987937	−	0.154855i	$-0.0494910\pi$
$73$	10.8378	+	6.87785i	1.26846	+	0.804992i	0.280526	+	0.959846i	$0.409491\pi$
$74$	−0.743829	−	2.28927i	−0.0864683	−	0.266122i
$75$	−4.01998	−	2.97317i	−0.464187	−	0.343313i
$76$	0.944178	−	2.90588i	0.108305	−	0.333327i
$77$	15.0406	−	12.4427i	1.71404	−	1.41798i
$78$	3.15412	+	0.601680i	0.357133	+	0.0681269i
$79$	2.86722	+	6.09316i	0.322588	+	0.685534i	0.998684	−	0.0512793i	$-0.0163299\pi$
$79$	2.86722	+	6.09316i	0.322588	+	0.685534i	−0.676097	+	0.736813i	$0.736330\pi$
$80$	2.14461	+	0.632956i	0.239775	+	0.0707666i
$81$	−0.187381	−	0.982287i	−0.0208201	−	0.109143i
$82$	−11.8248	−	3.84211i	−1.30583	−	0.424290i
$83$	2.25593	+	1.06156i	0.247620	+	0.116521i	0.545585	−	0.838056i	$-0.316308\pi$
$83$	2.25593	+	1.06156i	0.247620	+	0.116521i	−0.297964	+	0.954577i	$0.596308\pi$
$84$	3.99409	+	1.58137i	0.435791	+	0.172542i
$85$	8.28856	−	10.5924i	0.899021	−	1.14890i
$86$	6.28438	+	1.61355i	0.677662	+	0.173994i
$87$	−1.40079	+	3.53798i	−0.150180	+	0.379312i
$88$	−1.13007	−	4.40132i	−0.120466	−	0.469182i
$89$	4.91603	−	7.74643i	0.521098	−	0.821119i	−0.477238	−	0.878774i	$-0.658362\pi$
$89$	4.91603	−	7.74643i	0.521098	−	0.821119i	0.998337	+	0.0576545i	$0.0183622\pi$
$90$	−2.05591	+	0.879327i	−0.216712	+	0.0926892i
$91$	0.866110	−	13.7664i	0.0907930	−	1.44311i
$92$	1.67909	+	3.05426i	0.175057	+	0.318428i
$93$	0.802768	−	0.260835i	0.0832432	−	0.0270474i
$94$	−7.57938	−	0.957498i	−0.781753	−	0.0987584i
$95$	5.66698	−	3.81620i	0.581420	−	0.391534i
$96$	0.728969	−	0.684547i	0.0744000	−	0.0698663i
$97$	−0.275110	−	0.292962i	−0.0279331	−	0.0297458i	0.714850	−	0.699277i	$-0.246495\pi$
$97$	−0.275110	−	0.292962i	−0.0279331	−	0.0297458i	−0.742783	+	0.669532i	$0.766495\pi$
$98$	2.84837	−	11.0937i	0.287729	−	1.12063i
$99$	3.67624	+	2.67094i	0.369476	+	0.268440i
$100$	2.90447	+	4.06990i	0.290447	+	0.406990i
$101$	9.27438	−	6.73823i	0.922836	−	0.670479i	−0.0213926	−	0.999771i	$-0.506810\pi$
$101$	9.27438	−	6.73823i	0.922836	−	0.670479i	0.944228	+	0.329292i	$0.106810\pi$
$102$	−2.21425	−	5.59256i	−0.219244	−	0.553746i
$103$	−0.0404745	−	0.320389i	−0.00398807	−	0.0315689i	0.989995	−	0.141102i	$-0.0450645\pi$
$103$	−0.0404745	−	0.320389i	−0.00398807	−	0.0315689i	−0.993983	+	0.109533i	$0.965064\pi$
$104$	−2.81381	−	1.54691i	−0.275917	−	0.151687i
$105$	4.85449	+	8.28863i	0.473750	+	0.808888i
$106$	−4.48330	+	9.52749i	−0.435456	+	0.925392i
$107$	2.48060	−	3.41425i	0.239808	−	0.330068i	−0.672101	−	0.740459i	$-0.734608\pi$
$107$	2.48060	−	3.41425i	0.239808	−	0.330068i	0.911909	+	0.410391i	$0.134608\pi$
$108$	−0.125333	+	0.992115i	−0.0120602	+	0.0954663i
$109$	−2.32961	+	0.598143i	−0.223136	+	0.0572917i	−0.358603	−	0.933490i	$-0.616747\pi$
$109$	−2.32961	+	0.598143i	−0.223136	+	0.0572917i	0.135466	+	0.990782i	$0.456747\pi$
$110$	4.07493	−	9.30797i	0.388530	−	0.887480i
$111$	−1.53433	−	1.85469i	−0.145632	−	0.176039i
$112$	−3.30994	−	2.73822i	−0.312760	−	0.258737i
$113$	−15.9835	+	10.1435i	−1.50360	+	0.954216i	−0.507921	+	0.861404i	$0.669586\pi$
$113$	−15.9835	+	10.1435i	−1.50360	+	0.954216i	−0.995684	+	0.0928128i	$0.970414\pi$
$114$	−0.191852	−	3.04939i	−0.0179686	−	0.285602i
$115$	−1.25185	+	7.69234i	−0.116736	+	0.717314i
$116$	2.42552	−	2.93196i	0.225204	−	0.272225i
$117$	3.15412	−	0.601680i	0.291598	−	0.0556253i
$118$	−5.95947	−	8.20251i	−0.548614	−	0.755102i
$119$	−22.6427	+	12.4479i	−2.07565	+	1.14110i
$120$	2.22702	−	0.200977i	0.203298	−	0.0183466i
$121$	−9.57260	+	1.20930i	−0.870236	+	0.109936i
$122$	1.48066	−	0.696748i	0.134053	−	0.0630806i
$123$	−12.4088	+	0.780696i	−1.11886	+	0.0703930i
$124$	−0.844081			−0.0758007
$125$	−0.493512	+	11.1694i	−0.0441410	+	0.999025i
$126$	4.29576			0.382696
$127$	−1.43992	+	0.0905922i	−0.127772	+	0.00803876i	−0.126548	−	0.991960i	$-0.540390\pi$
$127$	−1.43992	+	0.0905922i	−0.127772	+	0.00803876i	−0.00122445	+	0.999999i	$0.500390\pi$
$128$	−0.904827	+	0.425779i	−0.0799762	+	0.0376339i
$129$	6.43705	−	0.813189i	0.566751	−	0.0715973i
$130$	−2.82351	−	6.60153i	−0.247639	−	0.578992i
$131$	3.59357	−	1.97558i	0.313972	−	0.172608i	−0.316974	−	0.948434i	$-0.602667\pi$
$131$	3.59357	−	1.97558i	0.313972	−	0.172608i	0.630946	+	0.775827i	$0.282667\pi$
$132$	−2.67094	−	3.67624i	−0.232476	−	0.319976i
$133$	−12.8929	+	2.45945i	−1.11795	+	0.213261i
$134$	−4.51211	+	5.45421i	−0.389787	+	0.471172i
$135$	−1.58784	+	1.57441i	−0.136659	+	0.135504i
$136$	0.377682	+	6.00309i	0.0323860	+	0.514760i
$137$	−17.8423	+	11.3231i	−1.52437	+	0.967396i	−0.531651	+	0.846964i	$0.678428\pi$
$137$	−17.8423	+	11.3231i	−1.52437	+	0.967396i	−0.992722	+	0.120432i	$0.961572\pi$
$138$	2.68553	+	2.22166i	0.228607	+	0.189120i
$139$	−11.3658	−	13.7389i	−0.964034	−	1.16532i	−0.986199	−	0.165562i	$-0.947056\pi$
$139$	−11.3658	−	13.7389i	−0.964034	−	1.16532i	0.0221659	−	0.999754i	$-0.492944\pi$
$140$	−2.05557	−	9.38308i	−0.173727	−	0.793015i
$141$	−7.39961	+	1.89990i	−0.623159	+	0.160000i
$142$	0.915340	−	7.24566i	0.0768136	−	0.608043i
$143$	−8.57638	+	11.8044i	−0.717193	+	0.987132i
$144$	0.425779	−	0.904827i	0.0354816	−	0.0754023i
$145$	8.31157	−	1.82083i	0.690238	−	0.151212i
$146$	−11.2482	−	6.18377i	−0.930911	−	0.511772i
$147$	−1.43551	−	11.3632i	−0.118399	−	0.937221i
$148$	0.886105	+	2.23805i	0.0728374	+	0.183966i
$149$	−3.42283	+	2.48683i	−0.280409	+	0.203729i	−0.719096	−	0.694911i	$-0.755444\pi$
$149$	−3.42283	+	2.48683i	−0.280409	+	0.203729i	0.438687	+	0.898640i	$0.355444\pi$
$150$	4.19873	+	2.71489i	0.342825	+	0.221670i
$151$	−3.70662	−	2.69302i	−0.301640	−	0.219155i	0.426661	−	0.904412i	$-0.359690\pi$
$151$	−3.70662	−	2.69302i	−0.301640	−	0.219155i	−0.728301	+	0.685257i	$0.759690\pi$
$152$	−0.759853	+	2.95943i	−0.0616322	+	0.240042i
$153$	−4.11752	−	4.38471i	−0.332882	−	0.354483i
$154$	−14.2297	+	13.3625i	−1.14666	+	1.07678i
$155$	−1.48643	−	1.16314i	−0.119393	−	0.0934254i
$156$	−3.18567	−	0.402444i	−0.255058	−	0.0322213i
$157$	−1.55213	+	0.504317i	−0.123873	+	0.0402489i	−0.370298	−	0.928913i	$-0.620744\pi$
$157$	−1.55213	+	0.504317i	−0.123873	+	0.0402489i	0.246424	+	0.969162i	$0.420744\pi$
$158$	−3.24416	−	5.90110i	−0.258091	−	0.469466i
$159$	−0.661161	+	10.5089i	−0.0524335	+	0.833406i
$160$	−2.18013	−	0.497045i	−0.172354	−	0.0392949i
$161$	8.02257	−	12.6415i	0.632267	−	0.996293i
$162$	0.248690	+	0.968583i	0.0195389	+	0.0760991i
$163$	5.66380	−	14.3051i	0.443623	−	1.12046i	−0.520230	−	0.854026i	$-0.674154\pi$
$163$	5.66380	−	14.3051i	0.443623	−	1.12046i	0.963852	−	0.266437i	$-0.0858463\pi$
$164$	12.0427	+	3.09205i	0.940379	+	0.241448i
$165$	0.362285	−	10.1544i	0.0282038	−	0.790520i
$166$	−2.31813	−	0.917813i	−0.179922	−	0.0712361i
$167$	1.63487	+	0.769311i	0.126510	+	0.0595311i	0.487993	−	0.872848i	$-0.337729\pi$
$167$	1.63487	+	0.769311i	0.126510	+	0.0595311i	−0.361483	+	0.932379i	$0.617729\pi$
$168$	−4.08551	−	1.32746i	−0.315204	−	0.102416i
$169$	−0.503966	−	2.64188i	−0.0387666	−	0.203222i
$170$	−7.60711	+	11.0919i	−0.583438	+	0.850710i
$171$	−1.30094	−	2.76463i	−0.0994851	−	0.211417i
$172$	−6.37329	−	1.21577i	−0.485959	−	0.0927016i
$173$	−18.2699	+	15.1142i	−1.38904	+	1.14911i	−0.418481	+	0.908225i	$0.637437\pi$
$173$	−18.2699	+	15.1142i	−1.38904	+	1.14911i	−0.970554	+	0.240884i	$0.922563\pi$
$174$	1.17587	−	3.61896i	0.0891425	−	0.274352i
$175$	9.30994	−	19.3562i	0.703766	−	1.46319i
$176$	1.40420	+	4.32168i	0.105845	+	0.325759i
$177$	−8.56052	−	5.43267i	−0.643448	−	0.408345i
$178$	−4.41993	+	8.03982i	−0.331288	+	0.602610i
$179$	2.15129	−	11.2775i	0.160795	−	0.842919i	−0.806879	−	0.590716i	$-0.798845\pi$
$179$	2.15129	−	11.2775i	0.160795	−	0.842919i	0.967675	−	0.252202i	$-0.0811548\pi$
$180$	1.99664	−	1.00668i	0.148821	−	0.0750338i
$181$	1.43410	+	1.34671i	0.106596	+	0.100100i	0.736013	−	0.676968i	$-0.236706\pi$
$181$	1.43410	+	1.34671i	0.106596	+	0.100100i	−0.629417	+	0.777068i	$0.716706\pi$
$182$			13.7936i			1.02245i
$183$	1.12020	−	1.19289i	0.0828073	−	0.0881809i
$184$	−1.86756	−	2.94280i	−0.137678	−	0.216946i
$185$	−1.52358	+	5.16226i	−0.112015	+	0.379537i
$186$	−0.784806	+	0.310727i	−0.0575448	+	0.0227836i
$187$	27.2785	+	1.71622i	1.99480	+	0.125502i
$188$	7.62455	+	0.479696i	0.556077	+	0.0349854i
$189$	3.99409	−	1.58137i	0.290527	−	0.115028i
$190$	−5.41618	+	4.16450i	−0.392931	+	0.302125i
$191$	−13.3078	−	20.9697i	−0.962919	−	1.51732i	−0.852035	−	0.523484i	$-0.824632\pi$
$191$	−13.3078	−	20.9697i	−0.962919	−	1.51732i	−0.110884	−	0.993833i	$-0.535368\pi$
$192$	−0.684547	+	0.728969i	−0.0494029	+	0.0526088i
$193$		−	21.7936i		−	1.56874i	−0.620294	−	0.784370i	$-0.712987\pi$
$193$		−	21.7936i		−	1.56874i	0.620294	−	0.784370i	$-0.287013\pi$
$194$	0.292962	+	0.275110i	0.0210334	+	0.0197517i
$195$	−5.05542	−	5.09854i	−0.362026	−	0.365114i
$196$	−2.14617	+	11.2506i	−0.153298	+	0.803617i
$197$	4.70096	−	8.55101i	0.334929	−	0.609234i	−0.654193	−	0.756327i	$-0.726992\pi$
$197$	4.70096	−	8.55101i	0.334929	−	0.609234i	0.989123	+	0.147093i	$0.0469917\pi$
$198$	−3.83670	−	2.43484i	−0.272662	−	0.173037i
$199$	4.03577	+	12.4208i	0.286088	+	0.880489i	0.986070	+	0.166328i	$0.0531912\pi$
$199$	4.03577	+	12.4208i	0.286088	+	0.880489i	−0.699982	+	0.714160i	$0.746809\pi$
$200$	−3.15429	−	3.87950i	−0.223042	−	0.274322i
$201$	−2.18743	+	6.73222i	−0.154289	+	0.474854i
$202$	−8.83298	+	7.30728i	−0.621487	+	0.514138i
$203$	−16.0567	−	3.06297i	−1.12696	−	0.214978i
$204$	2.56104	+	5.44249i	0.179309	+	0.381051i
$205$	16.9465	+	22.0399i	1.18359	+	1.53933i
$206$	0.0605121	+	0.317215i	0.00421607	+	0.0221014i
$207$	3.31479	+	1.07704i	0.230394	+	0.0748594i
$208$	2.90539	+	1.36717i	0.201453	+	0.0947965i
$209$	12.9091	+	5.11108i	0.892942	+	0.353541i
$210$	−5.36536	−	7.96746i	−0.370245	−	0.549807i
$211$	−15.8067	−	4.05848i	−1.08818	−	0.279397i	−0.338346	−	0.941022i	$-0.609867\pi$
$211$	−15.8067	−	4.05848i	−1.08818	−	0.279397i	−0.749835	+	0.661624i	$0.769867\pi$
$212$	3.87622	−	9.79020i	0.266220	−	0.672394i
$213$	−1.81624	−	7.07381i	−0.124447	−	0.484689i
$214$	−2.26132	+	3.56327i	−0.154581	+	0.243580i
$215$	−9.54807	−	10.9233i	−0.651173	−	0.744965i
$216$	0.0627905	−	0.998027i	0.00427235	−	0.0679071i
$217$	1.74682	+	3.17746i	0.118582	+	0.215700i
$218$	2.28746	−	0.743240i	0.154926	−	0.0503386i
$219$	−12.7347	−	1.60877i	−0.860534	−	0.108711i
$220$	−3.48244	+	9.54547i	−0.234786	+	0.643556i
$221$	14.0793	−	13.2213i	0.947075	−	0.889363i
$222$	1.64776	+	1.75469i	0.110590	+	0.117767i
$223$	−3.66988	+	14.2932i	−0.245753	+	0.957146i	0.719217	+	0.694786i	$0.244501\pi$
$223$	−3.66988	+	14.2932i	−0.245753	+	0.957146i	−0.964970	+	0.262360i	$0.915499\pi$
$224$	3.47534	+	2.52498i	0.232206	+	0.168707i
$225$	4.90330	+	0.978585i	0.326887	+	0.0652390i
$226$	15.3151	−	11.1271i	1.01874	−	0.740161i
$227$	−8.90172	−	22.4832i	−0.590828	−	1.49226i	−0.850187	−	0.526480i	$-0.823511\pi$
$227$	−8.90172	−	22.4832i	−0.590828	−	1.49226i	0.259359	−	0.965781i	$-0.416489\pi$
$228$	0.382946	+	3.03133i	0.0253612	+	0.200755i
$229$	−8.41272	−	4.62493i	−0.555928	−	0.305624i	0.178911	−	0.983865i	$-0.442742\pi$
$229$	−8.41272	−	4.62493i	−0.555928	−	0.305624i	−0.734839	+	0.678241i	$0.762742\pi$
$230$	0.766378	−	7.75576i	0.0505335	−	0.511400i
$231$	−8.31132	+	17.6625i	−0.546845	+	1.16210i
$232$	−2.23664	+	3.07847i	−0.146843	+	0.202111i
$233$	−2.92752	+	23.1737i	−0.191788	+	1.51816i	0.542923	+	0.839782i	$0.317317\pi$
$233$	−2.92752	+	23.1737i	−0.191788	+	1.51816i	−0.734712	+	0.678379i	$0.762683\pi$
$234$	−3.11011	+	0.798542i	−0.203315	+	0.0522023i
$235$	12.7658	+	11.3513i	0.832752	+	0.740478i
$236$	6.46275	+	7.81213i	0.420689	+	0.508526i
$237$	−5.18868	−	4.29245i	−0.337041	−	0.278824i
$238$	21.8164	−	13.8451i	1.41415	−	0.897445i
$239$	−0.831654	−	13.2188i	−0.0537952	−	0.855050i	−0.928718	−	0.370787i	$-0.879088\pi$
$239$	−0.831654	−	13.2188i	−0.0537952	−	0.855050i	0.874923	−	0.484263i	$-0.160912\pi$
$240$	−2.21000	+	0.340416i	−0.142655	+	0.0219738i
$241$	12.8295	−	15.5082i	0.826422	−	0.998973i	−0.173478	−	0.984838i	$-0.555501\pi$
$241$	12.8295	−	15.5082i	0.826422	−	0.998973i	0.999900	−	0.0141351i	$-0.00449950\pi$
$242$	9.47778	−	1.80798i	0.609255	−	0.116222i
$243$	0.587785	+	0.809017i	0.0377064	+	0.0518985i
$244$	−1.43399	+	0.788345i	−0.0918020	+	0.0504686i
$245$	−19.2827	+	16.8550i	−1.23193	+	1.07683i
$246$	12.3353	−	1.55831i	0.786470	−	0.0993542i
$247$	8.87721	−	4.17730i	0.564843	−	0.265795i
$248$	0.842415	−	0.0530003i	0.0534934	−	0.00336552i
$249$	−2.49321			−0.158001
$250$	−0.208797	−	11.1784i	−0.0132055	−	0.706983i
$251$	12.7139			0.802495			0.401247	−	0.915970i	$-0.368577\pi$
$251$	12.7139			0.802495			0.401247	+	0.915970i	$0.368577\pi$
$252$	−4.28728	+	0.269733i	−0.270073	+	0.0169916i
$253$	−14.3305	+	6.74342i	−0.900950	+	0.423955i
$254$	1.43139	−	0.180827i	0.0898135	−	0.0113461i
$255$	−2.98971	+	13.1134i	−0.187223	+	0.821190i
$256$	0.876307	−	0.481754i	0.0547692	−	0.0301096i
$257$	−2.14560	−	2.95316i	−0.133839	−	0.184213i	0.736837	−	0.676070i	$-0.236318\pi$
$257$	−2.14560	−	2.95316i	−0.133839	−	0.184213i	−0.870676	+	0.491857i	$0.836318\pi$
$258$	−6.37329	+	1.21577i	−0.396784	+	0.0756906i
$259$	6.59111	−	7.96728i	0.409552	−	0.495063i
$260$	3.23246	+	6.41121i	0.200468	+	0.397606i
$261$	−0.238930	−	3.79769i	−0.0147894	−	0.235071i
$262$	−3.46244	+	2.19733i	−0.213910	+	0.135751i
$263$	22.9177	+	18.9591i	1.41316	+	1.16907i	0.960802	+	0.277235i	$0.0894181\pi$
$263$	22.9177	+	18.9591i	1.41316	+	1.16907i	0.452361	+	0.891835i	$0.350582\pi$
$264$	2.89651	+	3.50128i	0.178268	+	0.215489i
$265$	20.3169	−	11.8992i	1.24805	−	0.730962i
$266$	12.7130	−	3.26414i	0.779484	−	0.200137i
$267$	−1.14989	+	9.10232i	−0.0703721	+	0.557053i
$268$	4.16074	−	5.72677i	0.254158	−	0.349818i
$269$	−11.7154	+	24.8965i	−0.714302	+	1.51797i	0.135449	+	0.990784i	$0.456752\pi$
$269$	−11.7154	+	24.8965i	−0.714302	+	1.51797i	−0.849751	+	0.527184i	$0.823248\pi$
$270$	1.48585	−	1.67100i	0.0904258	−	0.101694i
$271$	−9.97193	−	5.48212i	−0.605752	−	0.333015i	0.149188	−	0.988809i	$-0.452334\pi$
$271$	−9.97193	−	5.48212i	−0.605752	−	0.333015i	−0.754940	+	0.655794i	$0.772334\pi$
$272$	−0.753874	−	5.96753i	−0.0457103	−	0.361834i
$273$	5.07778	+	12.8250i	0.307321	+	0.776204i
$274$	17.0961	−	12.4211i	1.03282	−	0.750384i
$275$	−19.2862	+	12.0108i	−1.16300	+	0.724281i
$276$	−2.81973	−	2.04865i	−0.169728	−	0.123314i
$277$	4.53832	−	17.6756i	0.272681	−	1.06202i	−0.673709	−	0.738997i	$-0.735300\pi$
$277$	4.53832	−	17.6756i	0.272681	−	1.06202i	0.946390	−	0.323026i	$-0.104700\pi$
$278$	12.2060	+	12.9981i	0.732069	+	0.779574i
$279$	−0.615308	+	0.577813i	−0.0368375	+	0.0345928i
$280$	2.64068	+	9.23549i	0.157811	+	0.551926i
$281$	20.8347	+	2.63203i	1.24289	+	0.157014i	0.719145	−	0.694860i	$-0.244533\pi$
$281$	20.8347	+	2.63203i	1.24289	+	0.157014i	0.523748	+	0.851873i	$0.324533\pi$
$282$	7.26571	−	2.36077i	0.432667	−	0.140582i
$283$	−7.35749	−	13.3832i	−0.437357	−	0.795550i	0.562147	−	0.827037i	$-0.309976\pi$
$283$	−7.35749	−	13.3832i	−0.437357	−	0.795550i	−0.999504	+	0.0314874i	$0.989976\pi$
$284$	−0.458575	+	7.28884i	−0.0272114	+	0.432513i
$285$	−3.50278	+	5.86589i	−0.207487	+	0.347465i
$286$	7.81826	−	12.3196i	0.462303	−	0.728473i
$287$	−13.2827	−	51.7326i	−0.784051	−	3.05368i
$288$	−0.368125	+	0.929776i	−0.0216919	+	0.0547876i
$289$	−18.5771	−	4.76980i	−1.09277	−	0.280576i
$290$	−8.18084	+	2.33913i	−0.480395	+	0.137358i
$291$	0.373664	+	0.147944i	0.0219045	+	0.00867262i
$292$	11.6143	+	5.46529i	0.679677	+	0.319832i
$293$	−10.3158	−	3.35180i	−0.602654	−	0.195814i	−0.00823015	−	0.999966i	$-0.502620\pi$
$293$	−10.3158	−	3.35180i	−0.602654	−	0.195814i	−0.594424	+	0.804152i	$0.702620\pi$
$294$	2.14617	+	11.2506i	0.125167	+	0.656151i
$295$	0.615887	+	22.6628i	0.0358584	+	1.31948i
$296$	−1.02488	−	2.17799i	−0.0595702	−	0.126593i
$297$	−4.46359	−	0.851476i	−0.259004	−	0.0494077i
$298$	3.25992	−	2.69684i	0.188842	−	0.156224i
$299$	−3.45837	+	10.6438i	−0.200003	+	0.615545i
$300$	−4.36092	−	2.44589i	−0.251778	−	0.141214i
$301$	8.61286	+	26.5076i	0.496437	+	1.52788i
$302$	3.86840	+	2.45496i	0.222601	+	0.141267i
$303$	−5.52271	+	10.0458i	−0.317272	+	0.577115i
$304$	0.572529	−	3.00130i	0.0328368	−	0.172137i
$305$	−3.61160	−	0.587754i	−0.206800	−	0.0336547i
$306$	4.38471	+	4.11752i	0.250657	+	0.235383i
$307$			10.3301i			0.589568i	0.955564	+	0.294784i	$0.0952476\pi$
$307$			10.3301i			0.589568i	−0.955564	+	0.294784i	$0.904752\pi$
$308$	13.3625	−	14.2297i	0.761401	−	0.810810i
$309$	0.173037	+	0.272663i	0.00984376	+	0.0155113i
$310$	1.55653	+	1.06751i	0.0884050	+	0.0606304i
$311$	6.47753	−	2.56464i	0.367307	−	0.145427i	−0.177218	−	0.984172i	$-0.556710\pi$
$311$	6.47753	−	2.56464i	0.367307	−	0.145427i	0.544525	+	0.838744i	$0.316710\pi$
$312$	3.20466	+	0.201620i	0.181428	+	0.0114145i
$313$	−18.2584	−	1.14872i	−1.03203	−	0.0649297i	−0.462268	−	0.886740i	$-0.652964\pi$
$313$	−18.2584	−	1.14872i	−1.03203	−	0.0649297i	−0.569761	+	0.821811i	$0.692964\pi$
$314$	1.51740	−	0.600781i	0.0856318	−	0.0339040i
$315$	−7.92161	−	5.43284i	−0.446332	−	0.306106i
$316$	3.60829	+	5.68575i	0.202982	+	0.319848i
$317$	−4.73844	+	5.04593i	−0.266137	+	0.283408i	−0.848132	−	0.529785i	$-0.822273\pi$
$317$	−4.73844	+	5.04593i	−0.266137	+	0.283408i	0.581994	+	0.813193i	$0.302273\pi$
$318$		−	10.5296i		−	0.590472i
$319$	12.6047	+	11.8366i	0.705727	+	0.662722i
$320$	2.20703	+	0.359173i	0.123377	+	0.0200784i
$321$	−0.790795	+	4.14549i	−0.0441379	+	0.231379i
$322$	−7.21297	+	13.1203i	−0.401963	+	0.731168i
$323$	−15.5173	−	9.84755i	−0.863404	−	0.547933i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	−3.14223	+	15.7445i	−0.174300	+	0.873346i
$326$	−4.75439	+	14.6325i	−0.263321	+	0.810420i
$327$	1.85322	−	1.53312i	0.102483	−	0.0847816i
$328$	−12.2131	−	2.32978i	−0.674356	−	0.128640i
$329$	−13.9732	−	29.6946i	−0.770367	−	1.63711i
$330$	0.276031	+	10.1571i	0.0151950	+	0.559131i
$331$	−1.79838	−	9.42746i	−0.0988482	−	0.518180i	−0.996926	−	0.0783444i	$-0.975037\pi$
$331$	−1.79838	−	9.42746i	−0.0988482	−	0.518180i	0.898078	−	0.439836i	$-0.144963\pi$
$332$	2.37119	+	0.770446i	0.130136	+	0.0422837i
$333$	2.17799	+	1.02488i	0.119353	+	0.0561633i
$334$	−1.67995	−	0.665139i	−0.0919227	−	0.0363948i
$335$	15.2185	−	4.35139i	0.831476	−	0.237742i
$336$	4.16080	+	1.06831i	0.226990	+	0.0582811i
$337$	−13.0925	+	33.0679i	−0.713194	+	1.80132i	−0.125742	+	0.992063i	$0.540131\pi$
$337$	−13.0925	+	33.0679i	−0.713194	+	1.80132i	−0.587452	+	0.809259i	$0.699869\pi$
$338$	0.668857	+	2.60503i	0.0363810	+	0.141695i
$339$	10.1435	−	15.9835i	0.550917	−	0.868106i
$340$	6.89563	−	11.5477i	0.373968	−	0.626260i
$341$	0.240838	−	3.82800i	0.0130421	−	0.207298i
$342$	1.47196	+	2.67749i	0.0795946	+	0.144782i
$343$	18.1948	−	5.91186i	0.982430	−	0.319211i
$344$	6.43705	+	0.813189i	0.347063	+	0.0438442i
$345$	−2.14253	−	7.49325i	−0.115350	−	0.403423i
$346$	17.2848	−	16.2315i	0.929238	−	0.872613i
$347$	15.2368	+	16.2255i	0.817953	+	0.871032i	0.993546	−	0.113431i	$-0.0361842\pi$
$347$	15.2368	+	16.2255i	0.817953	+	0.871032i	−0.175593	+	0.984463i	$0.556184\pi$
$348$	−0.946314	+	3.68565i	−0.0507278	+	0.197572i
$349$	−28.9979	−	21.0682i	−1.55222	−	1.12776i	−0.942043	−	0.335493i	$-0.891097\pi$
$349$	−28.9979	−	21.0682i	−1.55222	−	1.12776i	−0.610180	−	0.792263i	$-0.708903\pi$
$350$	−8.07619	+	19.9026i	−0.431690	+	1.06384i
$351$	−2.59775	+	1.88737i	−0.138658	+	0.100741i
$352$	−1.67279	−	4.22498i	−0.0891599	−	0.225192i
$353$	1.84405	+	14.5972i	0.0981489	+	0.776929i	0.961975	+	0.273138i	$0.0880616\pi$
$353$	1.84405	+	14.5972i	0.0981489	+	0.776929i	−0.863826	+	0.503790i	$0.831938\pi$
$354$	8.88475	+	4.88443i	0.472219	+	0.259605i
$355$	−10.8515	+	12.2038i	−0.575939	+	0.647709i
$356$	3.90638	−	8.30148i	0.207038	−	0.439978i
$357$	15.1877	−	20.9040i	0.803816	−	1.10636i
$358$	−1.43893	+	11.3903i	−0.0760498	+	0.601997i
$359$	0.992081	−	0.254723i	0.0523601	−	0.0134438i	−0.222419	−	0.974951i	$-0.571395\pi$
$359$	0.992081	−	0.254723i	0.0523601	−	0.0134438i	0.274779	+	0.961507i	$0.411395\pi$
$360$	−1.92949	+	1.13007i	−0.101693	+	0.0595598i
$361$	6.16031	+	7.44654i	0.324227	+	0.391923i
$362$	−1.51583	−	1.25400i	−0.0796701	−	0.0659089i
$363$	8.14665	−	5.17002i	0.427588	−	0.271356i
$364$	−0.866110	−	13.7664i	−0.0453965	−	0.721557i
$365$	12.9218	+	25.6288i	0.676356	+	1.34147i
$366$	−1.04308	+	1.26087i	−0.0545229	+	0.0659069i
$367$	−21.3133	+	4.06574i	−1.11255	+	0.212230i	−0.710712	−	0.703483i	$-0.751627\pi$
$367$	−21.3133	+	4.06574i	−1.11255	+	0.212230i	−0.401834	+	0.915712i	$0.631627\pi$
$368$	2.04865	+	2.81973i	0.106793	+	0.146988i
$369$	10.8954	−	5.98981i	0.567193	−	0.311817i
$370$	1.19643	−	5.24774i	0.0621993	−	0.272817i
$371$	−44.8760	+	5.66916i	−2.32985	+	0.294328i
$372$	0.763747	−	0.359392i	0.0395984	−	0.0186336i
$373$	24.9898	−	1.57223i	1.29392	−	0.0814068i	0.599151	−	0.800636i	$-0.295505\pi$
$373$	24.9898	−	1.57223i	1.29392	−	0.0814068i	0.694773	+	0.719229i	$0.255505\pi$
$374$	−27.3325			−1.41333
$375$	−4.30917	−	10.3165i	−0.222525	−	0.532744i
$376$	−7.63962			−0.393983
$377$	12.1944	−	0.767204i	0.628041	−	0.0395130i
$378$	−3.88692	+	1.82904i	−0.199921	+	0.0940758i
$379$	14.7743	−	1.86643i	0.758907	−	0.0958723i	0.263650	−	0.964619i	$-0.415074\pi$
$379$	14.7743	−	1.86643i	0.758907	−	0.0958723i	0.495257	+	0.868746i	$0.335074\pi$
$380$	5.14400	−	4.49637i	0.263882	−	0.230659i
$381$	1.26431	−	0.695059i	0.0647724	−	0.0356090i
$382$	14.5982	+	20.0928i	0.746911	+	1.02804i
$383$	6.03830	−	1.15187i	0.308543	−	0.0588577i	−0.0307846	−	0.999526i	$-0.509801\pi$
$383$	6.03830	−	1.15187i	0.308543	−	0.0588577i	0.339327	+	0.940668i	$0.389801\pi$
$384$	0.637424	−	0.770513i	0.0325284	−	0.0393201i
$385$	43.1399	−	6.64502i	2.19861	−	0.338662i
$386$	1.36843	+	21.7506i	0.0696514	+	1.10708i
$387$	−5.47818	+	3.47656i	−0.278472	+	0.176723i
$388$	−0.309658	−	0.256171i	−0.0157205	−	0.0130051i
$389$	9.94304	+	12.0191i	0.504132	+	0.609391i	0.959775	−	0.280772i	$-0.0905904\pi$
$389$	9.94304	+	12.0191i	0.504132	+	0.609391i	−0.455642	+	0.890163i	$0.650590\pi$
$390$	5.36558	+	4.77105i	0.271697	+	0.241591i
$391$	20.3057	−	5.21363i	1.02691	−	0.263664i
$392$	1.43551	−	11.3632i	0.0725040	−	0.573928i
$393$	−2.41040	+	3.31763i	−0.121589	+	0.167352i
$394$	−4.15476	+	8.82932i	−0.209314	+	0.444814i
$395$	−1.48071	+	14.9848i	−0.0745026	+	0.753968i
$396$	3.98201	+	2.18913i	0.200103	+	0.110008i
$397$	3.92438	+	31.0647i	0.196959	+	1.55909i	0.712157	+	0.702020i	$0.247718\pi$
$397$	3.92438	+	31.0647i	0.196959	+	1.55909i	−0.515198	+	0.857071i	$0.672282\pi$
$398$	−4.80771	−	12.1429i	−0.240989	−	0.608669i
$399$	10.6186	−	7.71489i	0.531597	−	0.386228i
$400$	3.39166	+	3.67378i	0.169583	+	0.183689i
$401$	−19.6384	−	14.2681i	−0.980692	−	0.712515i	−0.0228292	−	0.999739i	$-0.507267\pi$
$401$	−19.6384	−	14.2681i	−0.980692	−	0.712515i	−0.957863	+	0.287225i	$0.907267\pi$
$402$	1.76039	−	6.85628i	0.0878005	−	0.341960i
$403$	−1.85535	−	1.97575i	−0.0924217	−	0.0984191i
$404$	8.35673	−	7.84749i	0.415763	−	0.390427i
$405$	0.766368	−	2.10064i	0.0380811	−	0.104382i
$406$	16.2173	+	2.04872i	0.804851	+	0.101676i
$407$	−10.4026	+	3.38002i	−0.515639	+	0.167541i
$408$	−2.89773	−	5.27095i	−0.143459	−	0.260951i
$409$	1.58643	−	25.2155i	0.0784437	−	1.24683i	−0.740145	−	0.672447i	$-0.765243\pi$
$409$	1.58643	−	25.2155i	0.0784437	−	1.24683i	0.818589	−	0.574380i	$-0.194757\pi$
$410$	−18.2969	−	20.9323i	−0.903621	−	1.03377i
$411$	11.3231	−	17.8423i	0.558526	−	0.880097i
$412$	−0.0803108	−	0.312790i	−0.00395663	−	0.0154100i
$413$	16.0333	−	40.4955i	0.788948	−	1.99266i
$414$	−3.37587	−	0.866777i	−0.165915	−	0.0425998i
$415$	3.11400	+	4.62424i	0.152860	+	0.226995i
$416$	−2.98551	−	1.18205i	−0.146376	−	0.0579545i
$417$	16.1338	+	7.59199i	0.790076	+	0.371781i
$418$	−13.2046	−	4.29042i	−0.645856	−	0.209851i
$419$	2.61593	+	13.7132i	0.127797	+	0.669934i	0.987308	+	0.158817i	$0.0507680\pi$
$419$	2.61593	+	13.7132i	0.127797	+	0.669934i	−0.859511	+	0.511117i	$0.829232\pi$
$420$	5.85506	+	7.61485i	0.285698	+	0.371566i
$421$	−14.7101	−	31.2606i	−0.716927	−	1.52355i	−0.846738	−	0.532009i	$-0.821437\pi$
$421$	−14.7101	−	31.2606i	−0.716927	−	1.52355i	0.129811	−	0.991539i	$-0.458563\pi$
$422$	16.0304	+	3.05796i	0.780347	+	0.148859i
$423$	5.88643	−	4.86968i	0.286208	−	0.236772i
$424$	−3.25383	+	10.0143i	−0.158020	+	0.486336i
$425$	28.0558	−	10.8334i	1.36091	−	0.525496i
$426$	2.25683	+	6.94581i	0.109344	+	0.336525i
$427$	5.93529	+	3.76665i	0.287229	+	0.182281i
$428$	2.03312	−	3.69823i	0.0982745	−	0.178761i
$429$	2.73408	−	14.3326i	0.132003	−	0.691983i
$430$	10.2151	+	10.3022i	0.492617	+	0.496818i
$431$	18.7440	+	17.6018i	0.902867	+	0.847848i	0.988921	−	0.148442i	$-0.0474258\pi$
$431$	18.7440	+	17.6018i	0.902867	+	0.847848i	−0.0860542	+	0.996290i	$0.527426\pi$
$432$			1.00000i			0.0481125i
$433$	12.2631	−	13.0589i	0.589326	−	0.627569i	−0.363314	−	0.931667i	$-0.618355\pi$
$433$	12.2631	−	13.0589i	0.589326	−	0.627569i	0.952641	+	0.304098i	$0.0983549\pi$
$434$	−1.94289	−	3.06150i	−0.0932616	−	0.146957i
$435$	−6.74526	+	5.18643i	−0.323411	+	0.248670i
$436$	−2.23628	+	0.885404i	−0.107098	+	0.0424032i
$437$	10.6283	+	0.668675i	0.508420	+	0.0319871i
$438$	12.8106	+	0.805976i	0.612116	+	0.0385110i
$439$	−11.9744	+	4.74099i	−0.571506	+	0.226275i	−0.636061	−	0.771639i	$-0.719437\pi$
$439$	−11.9744	+	4.74099i	−0.571506	+	0.226275i	0.0645550	+	0.997914i	$0.479437\pi$
$440$	2.87620	−	9.74530i	0.137118	−	0.464589i
$441$	6.13710	+	9.67052i	0.292243	+	0.460501i
$442$	−13.2213	+	14.0793i	−0.628875	+	0.669683i
$443$			28.4370i			1.35108i	0.737322	+	0.675541i	$0.236090\pi$
$443$			28.4370i			1.35108i	−0.737322	+	0.675541i	$0.763910\pi$
$444$	−1.75469	−	1.64776i	−0.0832737	−	0.0781992i
$445$	18.3185	−	9.23599i	0.868382	−	0.437828i
$446$	2.76516	−	14.4955i	0.130934	−	0.686380i
$447$	2.03823	−	3.70752i	0.0964048	−	0.175360i
$448$	−3.62703	−	2.30178i	−0.171361	−	0.108749i
$449$	6.31353	+	19.4310i	0.297954	+	0.917008i	0.982213	+	0.187769i	$0.0601256\pi$
$449$	6.31353	+	19.4310i	0.297954	+	0.917008i	−0.684259	+	0.729239i	$0.739874\pi$
$450$	−4.95507	−	0.668773i	−0.233584	−	0.0315263i
$451$	−17.4589	+	53.7329i	−0.822106	+	2.53018i
$452$	−14.5862	+	12.0667i	−0.686077	+	0.567572i
$453$	4.50048	+	0.858512i	0.211451	+	0.0403364i
$454$	10.2959	+	21.8799i	0.483210	+	1.02687i
$455$	17.4448	−	25.4362i	0.817825	−	1.19247i
$456$	−0.572529	−	3.00130i	−0.0268111	−	0.140549i
$457$	7.01294	+	2.27864i	0.328052	+	0.106590i	0.468412	−	0.883510i	$-0.344826\pi$
$457$	7.01294	+	2.27864i	0.328052	+	0.106590i	−0.140361	+	0.990100i	$0.544826\pi$
$458$	8.68652	+	4.08756i	0.405894	+	0.190999i
$459$	5.59256	+	2.21425i	0.261039	+	0.103352i
$460$	−0.277877	+	7.78858i	−0.0129561	+	0.363144i
$461$	−30.9882	−	7.95641i	−1.44326	−	0.370567i	−0.555749	−	0.831350i	$-0.687569\pi$
$461$	−30.9882	−	7.95641i	−1.44326	−	0.370567i	−0.887513	+	0.460783i	$0.847569\pi$
$462$	7.18589	−	18.1495i	0.334318	−	0.844390i
$463$	5.63268	+	21.9379i	0.261773	+	1.01954i	0.954469	+	0.298309i	$0.0964227\pi$
$463$	5.63268	+	21.9379i	0.261773	+	1.01954i	−0.692696	+	0.721229i	$0.743577\pi$
$464$	2.03893	−	3.21283i	0.0946548	−	0.149152i
$465$	1.84020	+	0.419546i	0.0853373	+	0.0194560i
$466$	1.46666	−	23.3118i	0.0679415	−	1.07990i
$467$	−4.32676	−	7.87035i	−0.200219	−	0.364196i	0.757068	−	0.653336i	$-0.226631\pi$
$467$	−4.32676	−	7.87035i	−0.200219	−	0.364196i	−0.957287	+	0.289139i	$0.906631\pi$
$468$	3.05384	−	0.992251i	0.141164	−	0.0458668i
$469$	−30.1685	−	3.81116i	−1.39305	−	0.175983i
$470$	−13.4534	−	10.5273i	−0.620559	−	0.485590i
$471$	1.18968	−	1.11718i	0.0548175	−	0.0514771i
$472$	−6.94053	−	7.39091i	−0.319464	−	0.340194i
$473$	7.33212	−	28.5567i	0.337131	−	1.31304i
$474$	5.44797	+	3.95818i	0.250233	+	0.181805i
$475$	15.2546	−	0.829733i	0.699928	−	0.0380708i
$476$	−20.9040	+	15.1877i	−0.958134	+	0.696125i
$477$	−3.87622	−	9.79020i	−0.177480	−	0.448263i
$478$	1.66003	+	13.1405i	0.0759278	+	0.601030i
$479$	3.34487	+	1.83886i	0.152831	+	0.0840196i	0.556334	−	0.830959i	$-0.312207\pi$
$479$	3.34487	+	1.83886i	0.152831	+	0.0840196i	−0.403503	+	0.914978i	$0.632207\pi$
$480$	2.18427	−	0.478512i	0.0996977	−	0.0218410i
$481$	−3.29090	+	6.99352i	−0.150052	+	0.318877i
$482$	−11.8304	+	16.2832i	−0.538862	+	0.741679i
$483$	−1.87653	+	14.8543i	−0.0853850	+	0.675892i
$484$	−9.34555	+	2.39953i	−0.424798	+	0.109070i
$485$	−0.192307	−	0.877825i	−0.00873221	−	0.0398600i
$486$	−0.637424	−	0.770513i	−0.0289141	−	0.0349512i
$487$	−28.8474	−	23.8647i	−1.30720	−	1.08141i	−0.991161	−	0.132665i	$-0.957647\pi$
$487$	−28.8474	−	23.8647i	−1.30720	−	1.08141i	−0.316040	−	0.948746i	$-0.602353\pi$
$488$	1.38166	−	0.876830i	0.0625450	−	0.0396922i
$489$	0.966066	+	15.3552i	0.0436870	+	0.694385i
$490$	18.1863	−	18.0325i	0.821575	−	0.814627i
$491$	−22.8214	+	27.5864i	−1.02992	+	1.24496i	−0.0608526	+	0.998147i	$0.519382\pi$
$491$	−22.8214	+	27.5864i	−1.02992	+	1.24496i	−0.969064	+	0.246809i	$0.920618\pi$
$492$	−12.2131	+	2.32978i	−0.550609	+	0.105034i
$493$	−13.4533	−	18.5169i	−0.605905	−	0.833957i
$494$	−8.59740	+	4.72646i	−0.386815	+	0.212653i
$495$	3.99573	+	9.34224i	0.179595	+	0.419903i
$496$	−0.837425	+	0.105791i	−0.0376015	+	0.00475017i
$497$	28.3871	−	13.3580i	1.27334	−	0.599187i
$498$	2.48829	−	0.156550i	0.111503	−	0.00701518i
$499$	8.88353			0.397681			0.198841	−	0.980032i	$-0.436282\pi$
$499$	8.88353			0.397681			0.198841	+	0.980032i	$0.436282\pi$
$500$	0.910282	+	11.1432i	0.0407090	+	0.498340i
$501$	−1.80683			−0.0807232
$502$	−12.6888	+	0.798313i	−0.566330	+	0.0356304i
$503$	−24.6146	+	11.5827i	−1.09751	+	0.516449i	−0.887293	−	0.461206i	$-0.847417\pi$
$503$	−24.6146	+	11.5827i	−1.09751	+	0.516449i	−0.210217	+	0.977655i	$0.567417\pi$
$504$	4.26188	−	0.538401i	0.189839	−	0.0239823i
$505$	25.5300	−	2.30396i	1.13607	−	0.102525i
$506$	13.8788	−	7.62993i	0.616988	−	0.339192i
$507$	1.58086	+	2.17587i	0.0702086	+	0.0966338i
$508$	−1.41721	+	0.270348i	−0.0628787	+	0.0119947i
$509$	5.00551	−	6.05063i	0.221866	−	0.268189i	−0.647822	−	0.761791i	$-0.724320\pi$
$509$	5.00551	−	6.05063i	0.221866	−	0.268189i	0.869688	+	0.493602i	$0.164320\pi$
$510$	2.16041	−	13.2752i	0.0956647	−	0.587836i
$511$	−3.46228	−	55.0313i	−0.153162	−	2.43444i
$512$	−0.844328	+	0.535827i	−0.0373144	+	0.0236804i
$513$	2.35424	+	1.94760i	0.103942	+	0.0859887i
$514$	2.32679	+	2.81261i	0.102631	+	0.124059i
$515$	0.289594	−	0.661492i	0.0127610	−	0.0291488i
$516$	6.28438	−	1.61355i	0.276654	−	0.0710327i
$517$	−4.35095	+	34.4413i	−0.191355	+	1.51473i
$518$	−6.07783	+	8.36542i	−0.267045	+	0.367555i
$519$	10.0958	−	21.4547i	0.443156	−	0.941755i
$520$	−3.62864	−	6.19559i	−0.159126	−	0.271695i
$521$	−37.7775	−	20.7684i	−1.65506	−	0.909879i	−0.986014	−	0.166660i	$-0.946702\pi$
$521$	−37.7775	−	20.7684i	−1.65506	−	0.909879i	−0.669049	−	0.743219i	$-0.733298\pi$
$522$	0.476918	+	3.77519i	0.0208741	+	0.165236i
$523$	−1.38019	−	3.48597i	−0.0603516	−	0.152431i	0.896472	−	0.443101i	$-0.146122\pi$
$523$	−1.38019	−	3.48597i	−0.0603516	−	0.152431i	−0.956823	+	0.290670i	$0.906122\pi$
$524$	3.31763	−	2.41040i	0.144931	−	0.105299i
$525$	−0.182417	+	21.4780i	−0.00796131	+	0.937377i
$526$	−24.0629	−	17.4827i	−1.04919	−	0.762282i
$527$	−1.26263	+	4.91760i	−0.0550008	+	0.214214i
$528$	−3.11064	−	3.31249i	−0.135373	−	0.144158i
$529$	7.91089	−	7.42882i	0.343952	−	0.322992i
$530$	−19.5296	+	13.1514i	−0.848312	+	0.571261i
$531$	10.0589	+	1.27074i	0.436520	+	0.0551453i
$532$	−12.4830	+	4.05596i	−0.541205	+	0.175848i
$533$	19.2332	+	34.9851i	0.833083	+	1.51537i
$534$	0.576082	−	9.15656i	0.0249295	−	0.396243i
$535$	8.67646	−	3.71098i	0.375116	−	0.160440i
$536$	−3.79294	+	5.97672i	−0.163830	+	0.258155i
$537$	2.85517	+	11.1201i	0.123210	+	0.479870i
$538$	10.1290	−	25.5830i	0.436694	−	1.10296i
$539$	−50.4106	−	12.9432i	−2.17134	−	0.557505i
$540$	−1.37799	+	1.76100i	−0.0592993	+	0.0757816i
$541$	11.4119	+	4.51831i	0.490638	+	0.194257i	0.600399	−	0.799701i	$-0.295009\pi$
$541$	11.4119	+	4.51831i	0.490638	+	0.194257i	−0.109761	+	0.993958i	$0.535009\pi$
$542$	10.2965	+	4.84516i	0.442272	+	0.208117i
$543$	−1.87101	−	0.607928i	−0.0802927	−	0.0260887i
$544$	1.12709	+	5.90841i	0.0483236	+	0.253321i
$545$	−5.15817	−	1.52237i	−0.220952	−	0.0652112i
$546$	−5.87305	−	12.4809i	−0.251343	−	0.534131i
$547$	32.4631	+	6.19267i	1.38802	+	0.264779i	0.826619	−	0.562763i	$-0.190261\pi$
$547$	32.4631	+	6.19267i	1.38802	+	0.264779i	0.561404	+	0.827542i	$0.310261\pi$
$548$	−16.2825	+	13.4700i	−0.695553	+	0.575411i
$549$	−0.505677	+	1.55631i	−0.0215818	+	0.0664219i
$550$	18.4940	−	13.1981i	0.788585	−	0.562770i
$551$	−3.59278	−	11.0575i	−0.153058	−	0.471063i
$552$	2.94280	+	1.86756i	0.125254	+	0.0794885i
$553$	13.9361	−	25.3497i	0.592623	−	1.07798i
$554$	−3.41950	+	17.9257i	−0.145281	+	0.761589i
$555$	−0.819410	−	5.31966i	−0.0347820	−	0.225807i
$556$	−12.9981	−	12.2060i	−0.551242	−	0.517651i
$557$			15.1047i			0.640007i	0.947416	+	0.320003i	$0.103684\pi$
$557$			15.1047i			0.640007i	−0.947416	+	0.320003i	$0.896316\pi$
$558$	0.577813	−	0.615308i	0.0244608	−	0.0260481i
$559$	−11.1632	−	17.5904i	−0.472153	−	0.743995i
$560$	−3.21537	−	9.05146i	−0.135874	−	0.382494i
$561$	−25.4131	+	10.0617i	−1.07294	+	0.424807i
$562$	−20.9588	−	1.31862i	−0.884095	−	0.0556226i
$563$	1.54688	+	0.0973216i	0.0651933	+	0.00410162i	0.0953537	−	0.995443i	$-0.469602\pi$
$563$	1.54688	+	0.0973216i	0.0651933	+	0.00410162i	−0.0301603	+	0.999545i	$0.509602\pi$
$564$	−7.10314	+	2.81233i	−0.299096	+	0.118421i
$565$	−42.3142	+	1.14994i	−1.78017	+	0.0483782i
$566$	8.18331	+	12.8948i	0.343970	+	0.542010i
$567$	−2.94065	+	3.13147i	−0.123496	+	0.131509i
$568$		−	7.30325i		−	0.306438i
$569$	−1.01547	−	0.953592i	−0.0425708	−	0.0399767i	0.662970	−	0.748646i	$-0.269296\pi$
$569$	−1.01547	−	0.953592i	−0.0425708	−	0.0399767i	−0.705541	+	0.708669i	$0.749296\pi$
$570$	3.12755	−	6.07425i	0.130999	−	0.254422i
$571$	0.910077	−	4.77079i	0.0380855	−	0.199651i	−0.958159	−	0.286237i	$-0.907596\pi$
$571$	0.910077	−	4.77079i	0.0380855	−	0.199651i	0.996244	+	0.0865855i	$0.0275956\pi$
$572$	−7.02928	+	12.7862i	−0.293909	+	0.534618i
$573$	20.9697	+	13.3078i	0.876024	+	0.555942i
$574$	16.5048	+	50.7965i	0.688896	+	2.12020i
$575$	−11.2219	+	13.3328i	−0.467987	+	0.556017i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−18.6223	+	15.4057i	−0.775256	+	0.641348i	−0.938516	−	0.345235i	$-0.887799\pi$
$577$	−18.6223	+	15.4057i	−0.775256	+	0.641348i	0.163260	+	0.986583i	$0.447799\pi$
$578$	18.8400	+	3.59392i	0.783639	+	0.149487i
$579$	9.27927	+	19.7195i	0.385633	+	0.819513i
$580$	8.01782	−	2.84819i	0.332922	−	0.118265i
$581$	−2.00690	−	10.5205i	−0.0832602	−	0.436465i
$582$	−0.382216	−	0.124189i	−0.0158434	−	0.00514782i
$583$	43.2937	+	20.3725i	1.79304	+	0.843742i
$584$	−11.9346	−	4.72523i	−0.493856	−	0.195531i
$585$	6.74513	+	2.46080i	0.278877	+	0.101742i
$586$	10.5059	+	2.69745i	0.433994	+	0.111431i
$587$	−9.24046	+	23.3387i	−0.381395	+	0.963293i	0.604602	+	0.796528i	$0.293332\pi$
$587$	−9.24046	+	23.3387i	−0.381395	+	0.963293i	−0.985997	+	0.166765i	$0.946668\pi$
$588$	−2.84837	−	11.0937i	−0.117465	−	0.457496i
$589$	−1.38191	+	2.17754i	−0.0569406	+	0.0897241i
$590$	−2.03768	−	22.5794i	−0.0838900	−	0.929580i
$591$	−0.612711	+	9.73876i	−0.0252036	+	0.400599i
$592$	1.15962	+	2.10934i	0.0476601	+	0.0866934i
$593$	−18.7419	+	6.08962i	−0.769639	+	0.250071i	−0.667410	−	0.744690i	$-0.732597\pi$
$593$	−18.7419	+	6.08962i	−0.769639	+	0.250071i	−0.102228	+	0.994761i	$0.532597\pi$
$594$	4.50825	+	0.569524i	0.184976	+	0.0233679i
$595$	−57.7405	−	2.06004i	−2.36713	−	0.0844534i
$596$	−3.08416	+	2.89621i	−0.126332	+	0.118634i
$597$	−8.94020	−	9.52035i	−0.365898	−	0.389642i
$598$	2.78322	−	10.8399i	0.113814	−	0.443277i
$599$	26.7502	+	19.4351i	1.09298	+	0.794098i	0.979900	−	0.199487i	$-0.0639277\pi$
$599$	26.7502	+	19.4351i	1.09298	+	0.794098i	0.113082	+	0.993586i	$0.463928\pi$
$600$	4.50589	+	2.16724i	0.183952	+	0.0884773i
$601$	−14.9430	+	10.8567i	−0.609538	+	0.442855i	−0.849251	−	0.527989i	$-0.822946\pi$
$601$	−14.9430	+	10.8567i	−0.609538	+	0.442855i	0.239714	+	0.970844i	$0.422946\pi$
$602$	−10.2603	−	25.9145i	−0.418178	−	1.05620i
$603$	−0.887193	−	7.02285i	−0.0361293	−	0.285993i
$604$	−4.01492	−	2.20722i	−0.163365	−	0.0898104i
$605$	−19.7641	−	8.65251i	−0.803524	−	0.351775i
$606$	4.88103	−	10.3727i	0.198278	−	0.421363i
$607$	−11.7777	+	16.2106i	−0.478043	+	0.657969i	−0.978127	−	0.208007i	$-0.933302\pi$
$607$	−11.7777	+	16.2106i	−0.478043	+	0.657969i	0.500085	+	0.865977i	$0.333302\pi$
$608$	−0.382946	+	3.03133i	−0.0155305	+	0.122937i
$609$	15.8327	−	4.06513i	0.641571	−	0.164728i
$610$	3.64138	+	0.359819i	0.147435	+	0.0145687i
$611$	15.6365	+	18.9013i	0.632585	+	0.764664i
$612$	−4.63460	−	3.83408i	−0.187343	−	0.154983i
$613$	38.5797	−	24.4834i	1.55822	−	0.988876i	0.572611	−	0.819827i	$-0.305931\pi$
$613$	38.5797	−	24.4834i	1.55822	−	0.988876i	0.985608	−	0.169048i	$-0.0540694\pi$
$614$	−0.648630	−	10.3097i	−0.0261766	−	0.416065i
$615$	−24.7178	−	12.7268i	−0.996716	−	0.513195i
$616$	−12.4427	+	15.0406i	−0.501330	+	0.606004i
$617$	2.67185	−	0.509682i	0.107565	−	0.0205190i	−0.133318	−	0.991073i	$-0.542563\pi$
$617$	2.67185	−	0.509682i	0.107565	−	0.0205190i	0.240883	+	0.970554i	$0.422563\pi$
$618$	−0.189817	−	0.261260i	−0.00763555	−	0.0105094i
$619$	22.8019	−	12.5355i	0.916487	−	0.503843i	0.0476072	−	0.998866i	$-0.484840\pi$
$619$	22.8019	−	12.5355i	0.916487	−	0.503843i	0.868880	+	0.495023i	$0.164840\pi$
$620$	−1.62049	−	0.967666i	−0.0650804	−	0.0388624i
$621$	−3.45789	+	0.436833i	−0.138760	+	0.0175295i
$622$	−6.30372	+	2.96630i	−0.252756	+	0.118938i
$623$	−39.3343	+	2.47471i	−1.57590	+	0.0991470i
$624$	−3.21099			−0.128543
$625$	−13.7523	+	20.8776i	−0.550091	+	0.835105i
$626$	18.2945			0.731197
$627$	−13.8567	+	0.871790i	−0.553383	+	0.0348159i
$628$	−1.47668	+	0.694873i	−0.0589260	+	0.0277285i
$629$	14.3643	−	1.81463i	0.572743	−	0.0723542i
$630$	8.24711	+	4.92471i	0.328573	+	0.196205i
$631$	−30.2534	+	16.6320i	−1.20437	+	0.662108i	−0.952171	−	0.305567i	$-0.901154\pi$
$631$	−30.2534	+	16.6320i	−1.20437	+	0.662108i	−0.252200	+	0.967675i	$0.581154\pi$
$632$	−3.95818	−	5.44797i	−0.157448	−	0.216708i
$633$	16.0304	−	3.05796i	0.637151	−	0.121543i
$634$	4.41225	−	5.33350i	0.175233	−	0.211820i
$635$	−2.86826	−	1.47683i	−0.113823	−	0.0586060i
$636$	0.661161	+	10.5089i	0.0262167	+	0.416703i
$637$	−31.0520	+	19.7062i	−1.23032	+	0.780787i
$638$	−13.3230	−	11.0218i	−0.527464	−	0.436356i
$639$	4.65527	+	5.62725i	0.184160	+	0.222611i
$640$	−2.22523	−	0.219884i	−0.0879600	−	0.00869168i
$641$	12.7394	−	3.27092i	0.503175	−	0.129193i	0.0114336	−	0.999935i	$-0.496360\pi$
$641$	12.7394	−	3.27092i	0.503175	−	0.129193i	0.491742	+	0.870741i	$0.336360\pi$
$642$	0.528937	−	4.18697i	0.0208755	−	0.165246i
$643$	17.0454	−	23.4609i	0.672204	−	0.925209i	−0.327604	−	0.944815i	$-0.606241\pi$
$643$	17.0454	−	23.4609i	0.672204	−	0.925209i	0.999808	+	0.0196059i	$0.00624116\pi$
$644$	6.37490	−	13.5474i	0.251206	−	0.533841i
$645$	13.2903	+	5.81835i	0.523304	+	0.229097i
$646$	16.1050	+	8.85379i	0.633642	+	0.348348i
$647$	−0.859256	−	6.80171i	−0.0337808	−	0.267403i	−0.999955	−	0.00951153i	$-0.996972\pi$
$647$	−0.859256	−	6.80171i	−0.0337808	−	0.267403i	0.966174	−	0.257891i	$-0.0830277\pi$
$648$	0.368125	+	0.929776i	0.0144613	+	0.0365251i
$649$	−37.2729	+	27.0803i	−1.46309	+	1.06300i
$650$	2.14743	−	15.9107i	0.0842290	−	0.624069i
$651$	−2.93347	−	2.13129i	−0.114972	−	0.0835318i
$652$	3.82623	−	14.9022i	0.149847	−	0.583614i
$653$	−25.8086	−	27.4834i	−1.00997	−	1.07551i	−0.997139	−	0.0755890i	$-0.975916\pi$
$653$	−25.8086	−	27.4834i	−1.00997	−	1.07551i	−0.0128290	−	0.999918i	$-0.504084\pi$
$654$	−1.75330	+	1.64646i	−0.0685594	+	0.0643815i
$655$	9.16388	+	0.326945i	0.358062	+	0.0127748i
$656$	12.3353	+	1.55831i	0.481612	+	0.0608418i
$657$	12.2077	−	3.96653i	0.476269	−	0.154749i
$658$	15.8102	+	28.7586i	0.616344	+	1.12113i
$659$	1.01826	−	16.1848i	0.0396658	−	0.630471i	−0.927101	−	0.374811i	$-0.877707\pi$
$659$	1.01826	−	16.1848i	0.0396658	−	0.630471i	0.966767	−	0.255659i	$-0.0822925\pi$
$660$	−0.913258	−	10.1198i	−0.0355485	−	0.393911i
$661$	13.1741	−	20.7590i	0.512412	−	0.807433i	−0.485348	−	0.874321i	$-0.661307\pi$
$661$	13.1741	−	20.7590i	0.512412	−	0.807433i	0.997760	+	0.0668883i	$0.0213071\pi$
$662$	2.38679	+	9.29594i	0.0927653	+	0.361297i
$663$	−7.10995	+	17.9577i	−0.276128	+	0.697419i
$664$	−2.41489	−	0.620037i	−0.0937157	−	0.0240621i
$665$	−27.5716	−	10.0589i	−1.06918	−	0.390066i
$666$	−2.23805	−	0.886105i	−0.0867225	−	0.0343359i
$667$	12.0003	+	5.64691i	0.464654	+	0.218649i
$668$	1.71840	+	0.558341i	0.0664868	+	0.0216029i
$669$	−2.76516	−	14.4955i	−0.106907	−	0.560427i
$670$	−14.9153	+	5.29839i	−0.576227	+	0.204695i
$671$	−3.16608	−	6.72826i	−0.122225	−	0.259742i
$672$	−4.21967	−	0.804944i	−0.162777	−	0.0310514i
$673$	29.9631	−	24.7876i	1.15499	−	0.955492i	0.155514	−	0.987834i	$-0.450297\pi$
$673$	29.9631	−	24.7876i	1.15499	−	0.955492i	0.999477	+	0.0323418i	$0.0102965\pi$
$674$	10.9903	−	33.8247i	0.423331	−	1.30288i
$675$	−4.85330	+	1.20227i	−0.186804	+	0.0462756i
$676$	−0.831108	−	2.55789i	−0.0319657	−	0.0983803i
$677$	−1.76020	−	1.11706i	−0.0676499	−	0.0429319i	0.501572	−	0.865116i	$-0.332755\pi$
$677$	−1.76020	−	1.11706i	−0.0676499	−	0.0429319i	−0.569222	+	0.822184i	$0.692755\pi$
$678$	−9.11983	+	16.5889i	−0.350245	+	0.637093i
$679$	−0.323495	+	1.69582i	−0.0124146	+	0.0650797i
$680$	−6.15694	+	11.9579i	−0.236108	+	0.458563i
$681$	17.6274	+	16.5532i	0.675483	+	0.634321i
$682$			3.83557i			0.146872i
$683$	33.4735	−	35.6457i	1.28083	−	1.36394i	0.382909	−	0.923786i	$-0.374922\pi$
$683$	33.4735	−	35.6457i	1.28083	−	1.36394i	0.897920	−	0.440158i	$-0.145078\pi$
$684$	−1.63718	−	2.57978i	−0.0625991	−	0.0986404i
$685$	−47.2351	+	1.28367i	−1.80476	+	0.0490464i
$686$	−17.7877	+	7.04266i	−0.679139	+	0.268890i
$687$	9.58125	+	0.602801i	0.365548	+	0.0229983i
$688$	−6.47541	−	0.407398i	−0.246873	−	0.0155319i
$689$	31.4363	−	12.4465i	1.19763	−	0.474174i
$690$	2.60880	+	7.34393i	0.0993154	+	0.279579i
$691$	−0.0488444	−	0.0769665i	−0.00185813	−	0.00292794i	0.843398	−	0.537290i	$-0.180552\pi$
$691$	−0.0488444	−	0.0769665i	−0.00185813	−	0.00292794i	−0.845256	+	0.534362i	$0.820552\pi$
$692$	−16.2315	+	17.2848i	−0.617030	+	0.657070i
$693$		−	19.5203i		−	0.741513i
$694$	−16.2255	−	15.2368i	−0.615912	−	0.578380i
$695$	−6.06990	−	39.4062i	−0.230244	−	1.49476i
$696$	0.713023	−	3.73780i	0.0270271	−	0.141681i
$697$	36.0284	−	65.5354i	1.36467	−	2.48233i
$698$	30.2636	+	19.2059i	1.14549	+	0.726952i
$699$	−7.21799	−	22.2147i	−0.273010	−	0.840237i
$700$	6.81056	−	20.3704i	0.257415	−	0.769930i
$701$	−1.46428	+	4.50659i	−0.0553050	+	0.170211i	−0.974894	−	0.222672i	$-0.928522\pi$
$701$	−1.46428	+	4.50659i	−0.0553050	+	0.170211i	0.919588	+	0.392883i	$0.128522\pi$
$702$	2.47411	−	2.04676i	0.0933794	−	0.0772501i
$703$	7.22438	+	1.37812i	0.272473	+	0.0519769i
$704$	1.93478	+	4.11161i	0.0729196	+	0.154962i
$705$	−16.3840	−	4.83554i	−0.617058	−	0.182117i
$706$	−2.75698	−	14.4526i	−0.103760	−	0.543930i
$707$	−46.8353	−	15.2177i	−1.76142	−	0.572321i
$708$	−9.17392	−	4.31692i	−0.344777	−	0.162240i
$709$	−5.89918	−	2.33565i	−0.221548	−	0.0877172i	0.254728	−	0.967013i	$-0.418014\pi$
$709$	−5.89918	−	2.33565i	−0.221548	−	0.0877172i	−0.476277	+	0.879295i	$0.658014\pi$
$710$	10.0638	−	12.8611i	0.377689	−	0.482667i
$711$	6.52249	+	1.67469i	0.244613	+	0.0628058i
$712$	−3.37742	+	8.53039i	−0.126574	+	0.319690i
$713$	−0.731630	−	2.84951i	−0.0273998	−	0.106715i
$714$	−13.8451	+	21.8164i	−0.518140	+	0.816458i
$715$	−29.9979	+	12.8303i	−1.12186	+	0.479825i
$716$	0.720888	−	11.4582i	0.0269408	−	0.428212i
$717$	6.38078	+	11.6066i	0.238294	+	0.433456i
$718$	−0.974130	+	0.316514i	−0.0363542	+	0.0118122i
$719$	−2.05479	−	0.259580i	−0.0766306	−	0.00968070i	0.0869244	−	0.996215i	$-0.472296\pi$
$719$	−2.05479	−	0.259580i	−0.0766306	−	0.00968070i	−0.163555	+	0.986534i	$0.552296\pi$
$720$	1.85473	−	1.24899i	0.0691217	−	0.0465472i
$721$	−1.01126	+	0.949639i	−0.0376614	+	0.0353664i
$722$	−6.61573	−	7.04503i	−0.246212	−	0.262189i
$723$	−5.00542	+	19.4948i	−0.186153	+	0.725020i
$724$	1.59158	+	1.15635i	0.0591504	+	0.0429753i
$725$	18.0442	+	6.03282i	0.670145	+	0.224053i
$726$	−7.80595	+	5.67135i	−0.289706	+	0.210484i
$727$	−2.78277	−	7.02847i	−0.103207	−	0.260671i	0.868992	−	0.494825i	$-0.164768\pi$
$727$	−2.78277	−	7.02847i	−0.103207	−	0.260671i	−0.972200	+	0.234154i	$0.924768\pi$
$728$	1.72880	+	13.6849i	0.0640736	+	0.507195i
$729$	−0.876307	−	0.481754i	−0.0324558	−	0.0178427i
$730$	−14.5055	−	24.7669i	−0.536873	−	0.916664i
$731$	−16.6166	+	35.3121i	−0.614587	+	1.30606i
$732$	0.961855	−	1.32388i	0.0355512	−	0.0489320i
$733$	−4.56073	+	36.1019i	−0.168455	+	1.33345i	0.650461	+	0.759540i	$0.274576\pi$
$733$	−4.56073	+	36.1019i	−0.168455	+	1.33345i	−0.818915	+	0.573915i	$0.805424\pi$
$734$	21.0160	−	5.39599i	0.775714	−	0.199170i
$735$	10.2710	−	23.4611i	0.378852	−	0.865374i
$736$	−2.22166	−	2.68553i	−0.0818915	−	0.0989898i
$737$	24.7844	+	20.5034i	0.912944	+	0.755253i
$738$	−10.4978	+	6.66212i	−0.386430	+	0.245236i
$739$	−0.412425	−	6.55530i	−0.0151713	−	0.241141i	−0.998303	−	0.0582397i	$-0.981451\pi$
$739$	−0.412425	−	6.55530i	−0.0151713	−	0.241141i	0.983131	−	0.182901i	$-0.0585488\pi$
$740$	−0.864559	+	5.31251i	−0.0317818	+	0.195292i
$741$	−6.25373	+	7.55946i	−0.229737	+	0.277704i
$742$	44.4315	−	8.47577i	1.63113	−	0.311155i
$743$	−19.6808	−	27.0883i	−0.722017	−	0.993772i	−0.999454	−	0.0330279i	$-0.989485\pi$
$743$	−19.6808	−	27.0883i	−0.722017	−	0.993772i	0.277437	−	0.960744i	$-0.410515\pi$
$744$	−0.739673	+	0.406639i	−0.0271177	+	0.0149081i
$745$	−9.42217	+	0.850305i	−0.345202	+	0.0311528i
$746$	−24.8418	+	3.13825i	−0.909523	+	0.114899i
$747$	2.25593	−	1.06156i	0.0825401	−	0.0388404i
$748$	27.2785	−	1.71622i	0.997401	−	0.0627512i
$749$	−18.1291			−0.662424
$750$	4.94845	+	10.0256i	0.180692	+	0.366083i
$751$	−6.66758			−0.243304			−0.121652	−	0.992573i	$-0.538819\pi$
$751$	−6.66758			−0.243304			−0.121652	+	0.992573i	$0.538819\pi$
$752$	7.62455	−	0.479696i	0.278039	−	0.0174927i
$753$	−11.5039	+	5.41332i	−0.419225	+	0.197272i
$754$	−12.1221	+	1.53138i	−0.441461	+	0.0557696i
$755$	−4.02875	−	9.41944i	−0.146621	−	0.342809i
$756$	3.76440	−	2.06950i	0.136910	−	0.0752668i
$757$	−6.35699	−	8.74965i	−0.231049	−	0.318012i	0.677713	−	0.735327i	$-0.262971\pi$
$757$	−6.35699	−	8.74965i	−0.231049	−	0.318012i	−0.908762	+	0.417315i	$0.862971\pi$
$758$	−14.6280	+	2.79044i	−0.531313	+	0.101353i
$759$	10.0954	−	12.2033i	0.366440	−	0.442950i
$760$	−4.85152	+	4.81049i	−0.175983	+	0.174495i
$761$	0.666705	+	10.5970i	0.0241681	+	0.384140i	0.991454	+	0.130453i	$0.0416433\pi$
$761$	0.666705	+	10.5970i	0.0241681	+	0.384140i	−0.967286	+	0.253687i	$0.918357\pi$
$762$	−1.21817	+	0.773074i	−0.0441296	+	0.0280055i
$763$	7.96098	+	6.58590i	0.288207	+	0.238425i
$764$	−15.8311	−	19.1365i	−0.572748	−	0.692334i
$765$	−2.87823	−	13.1383i	−0.104063	−	0.475015i
$766$	−5.95406	+	1.52874i	−0.215129	+	0.0552357i
$767$	−4.08032	+	32.2991i	−0.147332	+	1.16625i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	−6.92797	+	14.7227i	−0.249829	+	0.530913i	−0.989926	−	0.141587i	$-0.954780\pi$
$769$	−6.92797	+	14.7227i	−0.249829	+	0.530913i	0.740097	+	0.672500i	$0.234780\pi$
$770$	−42.6375	+	9.34068i	−1.53655	+	0.336615i
$771$	3.19879	+	1.75855i	0.115202	+	0.0633326i
$772$	−2.73147	−	21.6218i	−0.0983076	−	0.778185i
$773$	−6.65652	−	16.8125i	−0.239419	−	0.604702i	0.759534	−	0.650468i	$-0.225427\pi$
$773$	−6.65652	−	16.8125i	−0.239419	−	0.604702i	−0.998952	+	0.0457658i	$0.985427\pi$
$774$	5.24908	−	3.81368i	0.188674	−	0.137080i
$775$	−1.52025	−	3.93708i	−0.0546091	−	0.141424i
$776$	0.325132	+	0.236222i	0.0116716	+	0.00847989i
$777$	−2.57151	+	10.0154i	−0.0922524	+	0.359299i
$778$	−10.6781	−	11.3710i	−0.382829	−	0.407671i
$779$	27.6929	−	26.0053i	0.992200	−	0.931738i
$780$	−5.65457	−	4.42472i	−0.202466	−	0.158431i
$781$	−32.9249	−	4.15938i	−1.17815	−	0.148834i
$782$	−19.9383	+	6.47835i	−0.712992	+	0.231665i
$783$	1.83317	+	3.33452i	0.0655121	+	0.119166i
$784$	−0.719172	+	11.4309i	−0.0256847	+	0.408247i
$785$	−3.55797	−	0.811180i	−0.126989	−	0.0289523i
$786$	2.19733	−	3.46244i	0.0783761	−	0.123501i
$787$	3.11331	+	12.1255i	0.110978	+	0.432229i	0.999654	−	0.0263059i	$-0.00837439\pi$
$787$	3.11331	+	12.1255i	0.110978	+	0.432229i	−0.888676	+	0.458535i	$0.848374\pi$
$788$	3.59216	−	9.07277i	0.127966	−	0.323204i
$789$	−28.8089	−	7.39687i	−1.02562	−	0.263336i
$790$	0.536884	−	15.0482i	0.0191015	−	0.535392i
$791$	75.6101	+	29.9362i	2.68839	+	1.06441i
$792$	−4.11161	−	1.93478i	−0.146100	−	0.0687493i
$793$	−4.99732	−	1.62373i	−0.177460	−	0.0576602i
$794$	−5.86720	−	30.7570i	−0.208219	−	1.09152i
$795$	−13.3168	+	19.4172i	−0.472299	+	0.688658i
$796$	5.56069	+	11.8171i	0.197093	+	0.418845i
$797$	7.15376	+	1.36465i	0.253399	+	0.0483385i	0.312516	−	0.949913i	$-0.398828\pi$
$797$	7.15376	+	1.36465i	0.253399	+	0.0483385i	−0.0591165	+	0.998251i	$0.518828\pi$
$798$	−10.1133	+	8.36642i	−0.358005	+	0.296168i
$799$	14.1999	−	43.7029i	0.502358	−	1.54610i
$800$	−3.61564	−	3.45357i	−0.127832	−	0.122102i
$801$	−2.83513	−	8.72562i	−0.100174	−	0.308305i
$802$	20.4955	+	13.0068i	0.723721	+	0.459287i
$803$	−28.0996	+	51.1129i	−0.991612	+	1.80374i
$804$	−1.32641	+	6.95329i	−0.0467789	+	0.245224i
$805$	29.8944	−	15.0724i	1.05364	−	0.531232i
$806$	1.97575	+	1.85535i	0.0695928	+	0.0653520i
$807$		−	27.5152i		−	0.968582i
$808$	−7.84749	+	8.35673i	−0.276074	+	0.293989i
$809$	15.6311	+	24.6306i	0.549559	+	0.865967i	0.999635	−	0.0270234i	$-0.00860288\pi$
$809$	15.6311	+	24.6306i	0.549559	+	0.865967i	−0.450075	+	0.892991i	$0.648603\pi$
$810$	−0.632956	+	2.14461i	−0.0222398	+	0.0753540i
$811$	−4.38724	+	1.73703i	−0.154057	+	0.0609955i	−0.443888	−	0.896082i	$-0.646401\pi$
$811$	−4.38724	+	1.73703i	−0.154057	+	0.0609955i	0.289831	+	0.957078i	$0.406401\pi$
$812$	−16.3139	−	1.02639i	−0.572507	−	0.0360191i
$813$	11.3570	+	0.714525i	0.398309	+	0.0250595i
$814$	10.1699	−	4.02654i	0.356454	−	0.141130i
$815$	27.2731	−	20.9703i	0.955335	−	0.734557i
$816$	3.22297	+	5.07860i	0.112827	+	0.177786i
$817$	−13.5706	+	14.4513i	−0.474776	+	0.505586i
$818$			25.2654i			0.883383i
$819$	−10.0551	−	9.44240i	−0.351355	−	0.329944i
$820$	19.5752	+	19.7421i	0.683595	+	0.689425i
$821$	−3.64014	+	19.0823i	−0.127042	+	0.665977i	0.860604	+	0.509275i	$0.170086\pi$
$821$	−3.64014	+	19.0823i	−0.127042	+	0.665977i	−0.987646	+	0.156702i	$0.949914\pi$
$822$	−10.1804	+	18.5181i	−0.355083	+	0.645893i
$823$	−24.2053	−	15.3612i	−0.843745	−	0.535457i	0.0422736	−	0.999106i	$-0.486540\pi$
$823$	−24.2053	−	15.3612i	−0.843745	−	0.535457i	−0.886019	+	0.463649i	$0.846540\pi$
$824$	0.0997925	+	0.307130i	0.00347644	+	0.0106994i
$825$	12.3367	−	19.0794i	0.429508	−	0.664259i
$826$	−13.4589	+	41.4224i	−0.468297	+	1.44127i
$827$	2.79056	−	2.30856i	0.0970374	−	0.0802763i	−0.587640	−	0.809122i	$-0.699943\pi$
$827$	2.79056	−	2.30856i	0.0970374	−	0.0802763i	0.684678	+	0.728846i	$0.259943\pi$
$828$	3.42364	+	0.653094i	0.118980	+	0.0226966i
$829$	3.09522	+	6.57768i	0.107501	+	0.228452i	0.951339	−	0.308147i	$-0.0997088\pi$
$829$	3.09522	+	6.57768i	0.107501	+	0.228452i	−0.843837	+	0.536599i	$0.819709\pi$
$830$	−3.39822	−	4.41958i	−0.117954	−	0.153406i
$831$	3.41950	+	17.9257i	0.118621	+	0.621834i
$832$	3.05384	+	0.992251i	0.105873	+	0.0344001i
$833$	62.3357	+	29.3329i	2.15980	+	1.01633i
$834$	−16.5787	−	6.56396i	−0.574072	−	0.227291i
$835$	2.25672	+	3.35118i	0.0780969	+	0.115972i
$836$	13.4479	+	3.45283i	0.465105	+	0.119419i
$837$	0.310727	−	0.784806i	0.0107403	−	0.0271269i
$838$	−3.47183	−	13.5219i	−0.119932	−	0.467106i
$839$	20.3136	−	32.0091i	0.701302	−	1.10508i	−0.287778	−	0.957697i	$-0.592917\pi$
$839$	20.3136	−	32.0091i	0.701302	−	1.10508i	0.989080	−	0.147378i	$-0.0470835\pi$
$840$	−6.32164	−	7.23218i	−0.218117	−	0.249534i
$841$	−0.911748	+	14.4918i	−0.0314396	+	0.499718i
$842$	16.6440	+	30.2753i	0.573589	+	1.04335i
$843$	−19.9725	+	6.48944i	−0.687888	+	0.223508i
$844$	−16.1908	−	2.04537i	−0.557309	−	0.0704045i
$845$	2.06117	−	5.64971i	0.0709062	−	0.194356i
$846$	−5.56904	+	5.22968i	−0.191468	+	0.179800i
$847$	28.3734	+	30.2146i	0.974920	+	1.03818i
$848$	2.61861	−	10.1988i	0.0899235	−	0.350229i
$849$	12.3556	+	8.97684i	0.424042	+	0.308084i
$850$	−27.3202	+	12.5736i	−0.937077	+	0.431272i
$851$	−6.78731	+	4.93127i	−0.232666	+	0.169042i
$852$	−2.68851	−	6.79039i	−0.0921067	−	0.232635i
$853$	4.47547	+	35.4270i	0.153237	+	1.21300i	0.861763	+	0.507312i	$0.169361\pi$
$853$	4.47547	+	35.4270i	0.153237	+	1.21300i	−0.708525	+	0.705685i	$0.750639\pi$
$854$	−6.16008	−	3.38654i	−0.210794	−	0.115885i
$855$	0.671839	−	6.79902i	0.0229764	−	0.232522i
$856$	−1.79689	+	3.81859i	−0.0614165	+	0.130517i
$857$	−11.6141	+	15.9854i	−0.396729	+	0.546051i	−0.959919	−	0.280277i	$-0.909574\pi$
$857$	−11.6141	+	15.9854i	−0.396729	+	0.546051i	0.563190	+	0.826327i	$0.309574\pi$
$858$	−1.82874	+	14.4760i	−0.0624321	+	0.494201i
$859$	33.1236	−	8.50470i	1.13016	−	0.290177i	0.363101	−	0.931750i	$-0.381718\pi$
$859$	33.1236	−	8.50470i	1.13016	−	0.290177i	0.767062	+	0.641573i	$0.221718\pi$
$860$	−10.8418	−	9.64050i	−0.369704	−	0.328738i
$861$	34.0452	+	41.1536i	1.16026	+	1.40251i
$862$	−19.8122	−	16.3901i	−0.674808	−	0.558249i
$863$	−30.7447	+	19.5112i	−1.04656	+	0.664169i	−0.943793	−	0.330536i	$-0.892770\pi$
$863$	−30.7447	+	19.5112i	−1.04656	+	0.664169i	−0.102770	+	0.994705i	$0.532770\pi$
$864$	−0.0627905	−	0.998027i	−0.00213618	−	0.0339536i
$865$	−52.4022	+	8.07173i	−1.78173	+	0.274447i
$866$	−11.4189	+	13.8031i	−0.388031	+	0.469048i
$867$	18.8400	−	3.59392i	0.639839	−	0.122056i
$868$	2.13129	+	2.93347i	0.0723406	+	0.0995683i
$869$	−26.8151	+	14.7417i	−0.909639	+	0.500078i
$870$	6.40629	−	5.59974i	0.217194	−	0.189849i
$871$	22.5503	−	2.84877i	0.764089	−	0.0965269i
$872$	2.17627	−	1.02407i	0.0736977	−	0.0346795i
$873$	−0.401092	+	0.0252346i	−0.0135749	+	0.000854062i
$874$	−10.6493			−0.360218
$875$	40.0637	−	26.4875i	1.35440	−	0.895441i
$876$	−12.8360			−0.433687
$877$	−37.9591	+	2.38819i	−1.28179	+	0.0806433i	−0.689028	−	0.724735i	$-0.741962\pi$
$877$	−37.9591	+	2.38819i	−1.28179	+	0.0806433i	−0.592761	+	0.805378i	$0.701962\pi$
$878$	11.6531	−	5.48351i	0.393272	−	0.185060i
$879$	10.7611	−	1.35945i	0.362963	−	0.0458529i
$880$	−2.25862	+	9.90667i	−0.0761379	+	0.333954i
$881$	37.6598	−	20.7036i	1.26879	−	0.697523i	0.302051	−	0.953292i	$-0.402329\pi$
$881$	37.6598	−	20.7036i	1.26879	−	0.697523i	0.966738	+	0.255769i	$0.0823286\pi$
$882$	−6.73221	−	9.26609i	−0.226685	−	0.312005i
$883$	5.79433	−	1.10533i	0.194995	−	0.0371973i	−0.0889586	−	0.996035i	$-0.528354\pi$
$883$	5.79433	−	1.10533i	0.194995	−	0.0371973i	0.283953	+	0.958838i	$0.408354\pi$
$884$	12.3112	−	14.8817i	0.414070	−	0.500525i
$885$	−10.2066	−	20.2437i	−0.343092	−	0.680484i
$886$	−1.78557	−	28.3809i	−0.0599875	−	0.953475i
$887$	38.6715	−	24.5417i	1.29846	−	0.824029i	0.306660	−	0.951819i	$-0.400788\pi$
$887$	38.6715	−	24.5417i	1.29846	−	0.824029i	0.991801	+	0.127790i	$0.0407884\pi$
$888$	1.85469	+	1.53433i	0.0622392	+	0.0514888i
$889$	3.95061	+	4.77547i	0.132499	+	0.160164i
$890$	−17.7025	+	10.3680i	−0.593388	+	0.347536i
$891$	4.40132	−	1.13007i	0.147450	−	0.0378587i
$892$	−1.84952	+	14.6405i	−0.0619267	+	0.490200i
$893$	13.7202	−	18.8843i	0.459131	−	0.631939i
$894$	−1.80141	+	3.82819i	−0.0602481	+	0.128034i
$895$	17.0588	−	19.1845i	0.570212	−	0.641268i
$896$	3.76440	+	2.06950i	0.125760	+	0.0691370i
$897$	−1.40267	−	11.1033i	−0.0468337	−	0.370727i
$898$	−7.52116	−	18.9963i	−0.250984	−	0.633914i
$899$	−2.59848	+	1.88790i	−0.0866640	+	0.0629651i
$900$	4.98729	+	0.356322i	0.166243	+	0.0118774i
$901$	−51.2393	−	37.2275i	−1.70703	−	1.24023i
$902$	14.0505	−	54.7231i	0.467831	−	1.82208i
$903$	−19.0796	−	20.3177i	−0.634928	−	0.676129i
$904$	13.7997	−	12.9588i	0.458972	−	0.431004i
$905$	1.20933	+	4.22951i	0.0401996	+	0.140594i
$906$	−4.54551	−	0.574231i	−0.151014	−	0.0190775i
$907$	21.0460	−	6.83826i	0.698821	−	0.227061i	0.0620043	−	0.998076i	$-0.480251\pi$
$907$	21.0460	−	6.83826i	0.698821	−	0.227061i	0.636817	+	0.771015i	$0.280251\pi$
$908$	−11.6494	−	21.1902i	−0.386600	−	0.703222i
$909$	0.719816	−	11.4411i	0.0238748	−	0.379479i
$910$	−15.8132	+	26.4814i	−0.524203	+	0.877850i
$911$	−16.8109	+	26.4897i	−0.556969	+	0.877642i	−0.999820	−	0.0189525i	$-0.993967\pi$
$911$	−16.8109	+	26.4897i	−0.556969	+	0.877642i	0.442852	+	0.896595i	$0.353967\pi$
$912$	0.759853	+	2.95943i	0.0251612	+	0.0979966i
$913$	−4.17062	+	10.5338i	−0.138027	+	0.348617i
$914$	−7.14218	−	1.83380i	−0.236242	−	0.0606567i
$915$	3.51813	−	1.00593i	0.116306	−	0.0332550i
$916$	−8.92604	−	3.53407i	−0.294925	−	0.116769i
$917$	−15.9395	−	7.50058i	−0.526370	−	0.247691i
$918$	−5.72056	−	1.85872i	−0.188807	−	0.0613470i
$919$	2.21805	+	11.6274i	0.0731668	+	0.383554i	0.999968	+	0.00800148i	$0.00254698\pi$
$919$	2.21805	+	11.6274i	0.0731668	+	0.383554i	−0.926801	+	0.375552i	$0.877453\pi$
$920$	−0.211720	−	7.79066i	−0.00698020	−	0.256850i
$921$	−4.39833	−	9.34692i	−0.144930	−	0.307991i
$922$	31.4266	+	5.99494i	1.03498	+	0.197433i
$923$	−18.0691	+	14.9480i	−0.594751	+	0.492021i
$924$	−6.03209	+	18.5649i	−0.198441	+	0.610739i
$925$	−8.84308	+	8.16399i	−0.290759	+	0.268430i
$926$	−6.99906	−	21.5409i	−0.230003	−	0.707878i
$927$	−0.272663	−	0.173037i	−0.00895544	−	0.00568329i
$928$	−1.83317	+	3.33452i	−0.0601767	+	0.109461i
$929$	−6.08671	+	31.9077i	−0.199699	+	1.04686i	0.731361	+	0.681990i	$0.238885\pi$
$929$	−6.08671	+	31.9077i	−0.199699	+	1.04686i	−0.931060	+	0.364866i	$0.881115\pi$
$930$	−1.86291	−	0.303171i	−0.0610873	−	0.00994138i
$931$	25.5105	+	23.9560i	0.836073	+	0.785125i
$932$			23.3579i			0.765114i
$933$	−4.76908	+	5.07855i	−0.156133	+	0.166264i
$934$	4.81241	+	7.58314i	0.157467	+	0.248128i
$935$	50.4025	+	34.5673i	1.64834	+	1.13047i
$936$	−2.98551	+	1.18205i	−0.0975843	+	0.0386364i
$937$	26.9778	+	1.69730i	0.881326	+	0.0554483i	0.497001	−	0.867750i	$-0.334434\pi$
$937$	26.9778	+	1.69730i	0.881326	+	0.0554483i	0.384324	+	0.923198i	$0.374434\pi$
$938$	30.3482	+	1.90935i	0.990905	+	0.0623425i
$939$	17.0098	−	6.73467i	0.555095	−	0.219778i
$940$	14.0879	+	9.66182i	0.459496	+	0.315134i
$941$	−24.7779	−	39.0438i	−0.807738	−	1.27279i	−0.958747	−	0.284259i	$-0.908252\pi$
$941$	−24.7779	−	39.0438i	−0.807738	−	1.27279i	0.151009	−	0.988532i	$-0.451748\pi$
$942$	−1.11718	+	1.18968i	−0.0363998	+	0.0387619i
$943$			43.3348i			1.41118i
$944$	7.39091	+	6.94053i	0.240554	+	0.225895i
$945$	9.48087	+	1.54292i	0.308413	+	0.0501912i
$946$	−5.52456	+	28.9608i	−0.179619	+	0.941596i
$947$	1.51361	−	2.75325i	0.0491857	−	0.0894685i	−0.850571	−	0.525860i	$-0.823744\pi$
$947$	1.51361	−	2.75325i	0.0491857	−	0.0894685i	0.899757	+	0.436391i	$0.143744\pi$
$948$	−5.68575	−	3.60829i	−0.184665	−	0.117192i
$949$	12.7365	+	39.1989i	0.413444	+	1.27245i
$950$	−15.1724	+	1.78594i	−0.492257	+	0.0579435i
$951$	2.13902	−	6.58322i	0.0693624	−	0.213476i
$952$	19.9091	−	16.4703i	0.645258	−	0.533804i
$953$	32.5321	+	6.20583i	1.05382	+	0.201027i	0.685051	−	0.728495i	$-0.259780\pi$
$953$	32.5321	+	6.20583i	1.05382	+	0.201027i	0.368767	+	0.929522i	$0.379780\pi$
$954$	4.48330	+	9.52749i	0.145152	+	0.308464i
$955$	−1.50867	−	55.5145i	−0.0488194	−	1.79641i
$956$	−2.48185	−	13.0103i	−0.0802686	−	0.420783i
$957$	−16.4448	−	5.34325i	−0.531586	−	0.172723i
$958$	−3.45374	−	1.62520i	−0.111585	−	0.0525080i
$959$	84.4031	+	33.4175i	2.72552	+	1.07911i
$960$	−2.14991	+	0.614719i	−0.0693881	+	0.0198400i
$961$	−29.3360	−	7.53220i	−0.946322	−	0.242974i
$962$	2.84528	−	7.18635i	0.0917355	−	0.231697i
$963$	−1.04953	−	4.08766i	−0.0338207	−	0.131723i
$964$	10.7847	−	16.9939i	0.347351	−	0.547337i
$965$	24.9845	−	41.8400i	0.804280	−	1.34688i
$966$	0.940119	−	14.9428i	0.0302478	−	0.480776i
$967$	−8.03068	−	14.6077i	−0.258249	−	0.469754i	0.715118	−	0.699003i	$-0.246373\pi$
$967$	−8.03068	−	14.6077i	−0.258249	−	0.469754i	−0.973368	+	0.229250i	$0.926373\pi$
$968$	9.17644	−	2.98161i	0.294942	−	0.0958325i
$969$	18.2333	+	2.30340i	0.585739	+	0.0739960i
$970$	0.247047	+	0.864018i	0.00793219	+	0.0277420i
$971$	−15.6630	+	14.7086i	−0.502651	+	0.472021i	−0.893901	−	0.448263i	$-0.852043\pi$
$971$	−15.6630	+	14.7086i	−0.502651	+	0.472021i	0.391250	+	0.920284i	$0.372043\pi$
$972$	0.684547	+	0.728969i	0.0219569	+	0.0233817i
$973$	−19.0489	+	74.1904i	−0.610678	+	2.37843i
$974$	30.2890	+	22.0062i	0.970521	+	0.705125i
$975$	−3.86049	−	15.5839i	−0.123635	−	0.499085i
$976$	−1.32388	+	0.961855i	−0.0423764	+	0.0307882i
$977$	−12.1870	−	30.7809i	−0.389897	−	0.984769i	−0.983645	−	0.180117i	$-0.942352\pi$
$977$	−12.1870	−	30.7809i	−0.389897	−	0.984769i	0.593748	−	0.804651i	$-0.297648\pi$
$978$	−1.92832	−	15.2642i	−0.0616609	−	0.488096i
$979$	36.5336	+	20.0845i	1.16762	+	0.641904i
$980$	−17.0182	+	19.1389i	−0.543626	+	0.611369i
$981$	−1.02407	+	2.17627i	−0.0326962	+	0.0694829i
$982$	21.0442	−	28.9649i	0.671549	−	0.924307i
$983$	−1.19480	+	9.45778i	−0.0381080	+	0.301656i	0.961529	+	0.274705i	$0.0885800\pi$
$983$	−1.19480	+	9.45778i	−0.0381080	+	0.301656i	−0.999637	+	0.0269517i	$0.991420\pi$
$984$	12.0427	−	3.09205i	0.383908	−	0.0985708i
$985$	18.8280	−	11.0272i	0.599911	−	0.351356i
$986$	14.5894	+	17.6356i	0.464622	+	0.561631i
$987$	25.2867	+	20.9189i	0.804883	+	0.665857i
$988$	8.28366	−	5.25697i	0.263538	−	0.167246i
$989$	−1.41994	−	22.5692i	−0.0451513	−	0.717660i
$990$	−4.57445	−	9.07291i	−0.145386	−	0.288356i
$991$	31.2888	−	37.8216i	0.993921	−	1.20144i	0.0144423	−	0.999896i	$-0.495403\pi$
$991$	31.2888	−	37.8216i	0.993921	−	1.20144i	0.979479	−	0.201548i	$-0.0645973\pi$
$992$	0.829130	−	0.158165i	0.0263249	−	0.00502174i
$993$	5.64125	+	7.76451i	0.179020	+	0.246399i
$994$	−27.4924	+	15.1140i	−0.872005	+	0.479389i
$995$	−6.49142	+	28.4725i	−0.205792	+	0.902638i
$996$	−2.47355	+	0.312483i	−0.0783776	+	0.00990139i
$997$	16.9781	−	7.98928i	0.537701	−	0.253023i	−0.137699	−	0.990474i	$-0.543971\pi$
$997$	16.9781	−	7.98928i	0.537701	−	0.253023i	0.675401	+	0.737451i	$0.263971\pi$
$998$	−8.86600	+	0.557801i	−0.280648	+	0.0176569i
$999$	−2.40708			−0.0761567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.469.7	yes	280
125.4	even	50	inner	750.2.o.b.379.7	✓	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.379.7	✓	280	125.4	even	50	inner
750.2.o.b.469.7	yes	280	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.91983 + 1.14641i) q^{5} +(0.876307 - 0.481754i) q^{6} +(-2.52498 - 3.47534i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})\)	\(q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.91983 + 1.14641i) q^{5} +(0.876307 - 0.481754i) q^{6} +(-2.52498 - 3.47534i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(-1.98802 - 1.02360i) q^{10} +(0.285325 + 4.53512i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(2.47411 + 2.04676i) q^{13} +(2.73822 + 3.30994i) q^{14} +(-2.22523 - 0.219884i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.753874 - 5.96753i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(1.30094 - 2.76463i) q^{19} +(2.04837 + 0.896756i) q^{20} +(3.76440 + 2.06950i) q^{21} +(-0.569524 - 4.50825i) q^{22} +(1.28305 + 3.24062i) q^{23} +(0.809017 - 0.587785i) q^{24} +(2.37147 + 4.40183i) q^{25} +(-2.59775 - 1.88737i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(-2.94065 - 3.13147i) q^{28} +(2.77387 - 2.60484i) q^{29} +(2.23465 + 0.0797267i) q^{30} +(-0.837425 - 0.105791i) q^{31} +(-0.951057 + 0.309017i) q^{32} +(-2.18913 - 3.98201i) q^{33} +(-0.377682 + 6.00309i) q^{34} +(-0.863350 - 9.56672i) q^{35} +(0.535827 - 0.844328i) q^{36} +(0.598617 + 2.33146i) q^{37} +(-1.12478 + 2.84086i) q^{38} +(-3.11011 - 0.798542i) q^{39} +(-2.10064 - 0.766368i) q^{40} +(11.5602 + 4.57702i) q^{41} +(-3.88692 - 1.82904i) q^{42} +(-6.17066 - 2.00497i) q^{43} +(0.851476 + 4.46359i) q^{44} +(2.10707 - 0.748500i) q^{45} +(-1.48400 - 3.15366i) q^{46} +(7.50430 + 1.43152i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(-3.53933 + 10.8929i) q^{49} +(-2.64318 - 4.24424i) q^{50} +(1.85872 + 5.72056i) q^{51} +(2.71113 + 1.72054i) q^{52} +(5.07269 - 9.22719i) q^{53} +(0.187381 - 0.982287i) q^{54} +(-4.65134 + 9.03374i) q^{55} +(3.13147 + 2.94065i) q^{56} +3.05542i q^{57} +(-2.60484 + 2.77387i) q^{58} +(5.43267 + 8.56052i) q^{59} +(-2.23524 + 0.0607452i) q^{60} +(-1.52149 + 0.602401i) q^{61} +(0.842415 + 0.0530003i) q^{62} +(-4.28728 - 0.269733i) q^{63} +(0.929776 - 0.368125i) q^{64} +(2.40343 + 6.76579i) q^{65} +(2.43484 + 3.83670i) q^{66} +(4.84568 - 5.16013i) q^{67} -6.01496i q^{68} +(-2.54073 - 2.38590i) q^{69} +(1.46235 + 9.49363i) q^{70} +(-1.36849 + 7.17389i) q^{71} +(-0.481754 + 0.876307i) q^{72} +(10.8378 + 6.87785i) q^{73} +(-0.743829 - 2.28927i) q^{74} +(-4.01998 - 2.97317i) q^{75} +(0.944178 - 2.90588i) q^{76} +(15.0406 - 12.4427i) q^{77} +(3.15412 + 0.601680i) q^{78} +(2.86722 + 6.09316i) q^{79} +(2.14461 + 0.632956i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(-11.8248 - 3.84211i) q^{82} +(2.25593 + 1.06156i) q^{83} +(3.99409 + 1.58137i) q^{84} +(8.28856 - 10.5924i) q^{85} +(6.28438 + 1.61355i) q^{86} +(-1.40079 + 3.53798i) q^{87} +(-1.13007 - 4.40132i) q^{88} +(4.91603 - 7.74643i) q^{89} +(-2.05591 + 0.879327i) q^{90} +(0.866110 - 13.7664i) q^{91} +(1.67909 + 3.05426i) q^{92} +(0.802768 - 0.260835i) q^{93} +(-7.57938 - 0.957498i) q^{94} +(5.66698 - 3.81620i) q^{95} +(0.728969 - 0.684547i) q^{96} +(-0.275110 - 0.292962i) q^{97} +(2.84837 - 11.0937i) q^{98} +(3.67624 + 2.67094i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q+O(q^{10}) \) 280 * q	\( 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) \) 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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