LMFDB - Embedded newform 552.2.bf.a.5.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(5,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 11, 1]))

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

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

chi := DirichletCharacter("552.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bf (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$92$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	552.5
Dual form			552.2.bf.a.221.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26313 - 0.636012i) q^{2} +(-0.135402 - 1.72675i) q^{3} +(1.19098 + 1.60673i) q^{4} +(-2.37700 - 0.341761i) q^{5} +(-0.927205 + 2.26722i) q^{6} +(-3.17635 + 1.45059i) q^{7} +(-0.482454 - 2.78698i) q^{8} +(-2.96333 + 0.467611i) q^{9} +O(q^{10})$	\(q+(-1.26313 - 0.636012i) q^{2} +(-0.135402 - 1.72675i) q^{3} +(1.19098 + 1.60673i) q^{4} +(-2.37700 - 0.341761i) q^{5} +(-0.927205 + 2.26722i) q^{6} +(-3.17635 + 1.45059i) q^{7} +(-0.482454 - 2.78698i) q^{8} +(-2.96333 + 0.467611i) q^{9} +(2.78509 + 1.94349i) q^{10} +(-0.202007 - 0.687974i) q^{11} +(2.61316 - 2.27407i) q^{12} +(0.701110 + 0.320186i) q^{13} +(4.93472 + 0.187919i) q^{14} +(-0.268285 + 4.15076i) q^{15} +(-1.16315 + 3.82715i) q^{16} +(3.19070 - 2.05054i) q^{17} +(4.04047 + 1.29406i) q^{18} +(4.82433 + 3.10041i) q^{19} +(-2.28184 - 4.22623i) q^{20} +(2.93489 + 5.28834i) q^{21} +(-0.182399 + 0.997477i) q^{22} +(4.78573 + 0.311055i) q^{23} +(-4.74709 + 1.21044i) q^{24} +(0.735873 + 0.216072i) q^{25} +(-0.681948 - 0.850350i) q^{26} +(1.20869 + 5.05362i) q^{27} +(-6.11365 - 3.37591i) q^{28} +(-5.77426 + 3.71089i) q^{29} +(2.97882 - 5.07231i) q^{30} +(2.41802 + 2.79055i) q^{31} +(3.90332 - 4.09440i) q^{32} +(-1.16061 + 0.441969i) q^{33} +(-5.33443 + 0.560765i) q^{34} +(8.04594 - 2.36250i) q^{35} +(-4.28058 - 4.20436i) q^{36} +(0.875967 + 6.09248i) q^{37} +(-4.12184 - 6.98454i) q^{38} +(0.457950 - 1.25400i) q^{39} +(0.194314 + 6.78953i) q^{40} +(-1.10017 - 0.158180i) q^{41} +(-0.343682 - 8.54647i) q^{42} +(1.88655 - 2.17720i) q^{43} +(0.864801 - 1.14393i) q^{44} +(7.20366 - 0.0987602i) q^{45} +(-5.84715 - 3.43669i) q^{46} +2.15429i q^{47} +(6.76603 + 1.49027i) q^{48} +(3.40094 - 3.92489i) q^{49} +(-0.792076 - 0.740951i) q^{50} +(-3.97280 - 5.23190i) q^{51} +(0.320553 + 1.50783i) q^{52} +(0.627086 - 0.286381i) q^{53} +(1.68744 - 7.15210i) q^{54} +(0.245049 + 1.70435i) q^{55} +(5.57520 + 8.15256i) q^{56} +(4.70041 - 8.75022i) q^{57} +(9.65379 - 1.01482i) q^{58} +(-4.29555 + 9.40595i) q^{59} +(-6.98867 + 4.51240i) q^{60} +(-6.36967 - 7.35099i) q^{61} +(-1.27944 - 5.06270i) q^{62} +(8.73426 - 5.78387i) q^{63} +(-7.53448 + 2.68918i) q^{64} +(-1.55711 - 1.00070i) q^{65} +(1.74709 + 0.179897i) q^{66} +(14.9889 + 4.40115i) q^{67} +(7.09471 + 2.68445i) q^{68} +(-0.110884 - 8.30588i) q^{69} +(-11.6656 - 2.13318i) q^{70} +(-3.38562 + 11.5303i) q^{71} +(2.73289 + 8.03314i) q^{72} +(0.474838 + 0.305160i) q^{73} +(2.76844 - 8.25270i) q^{74} +(0.273463 - 1.29993i) q^{75} +(0.764148 + 11.4439i) q^{76} +(1.63961 + 1.89221i) q^{77} +(-1.37601 + 1.29269i) q^{78} +(4.87560 + 2.22661i) q^{79} +(4.07278 - 8.69962i) q^{80} +(8.56268 - 2.77137i) q^{81} +(1.28905 + 0.899522i) q^{82} +(0.236116 - 0.0339484i) q^{83} +(-5.00155 + 11.0139i) q^{84} +(-8.28511 + 3.78368i) q^{85} +(-3.76768 + 1.55021i) q^{86} +(7.18963 + 9.46824i) q^{87} +(-1.81991 + 0.894906i) q^{88} +(-1.80166 + 2.07923i) q^{89} +(-9.16194 - 4.45687i) q^{90} -2.69143 q^{91} +(5.19991 + 8.05983i) q^{92} +(4.49117 - 4.55316i) q^{93} +(1.37016 - 2.72114i) q^{94} +(-10.4078 - 9.01845i) q^{95} +(-7.59852 - 6.18567i) q^{96} +(-1.67421 - 0.240715i) q^{97} +(-6.79210 + 2.79460i) q^{98} +(0.920319 + 1.94423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) $ 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9	$ 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) $ 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9 - 22 * q^10 - 12 * q^12 - 22 * q^15 - 30 * q^16 - 10 * q^18 - 14 * q^24 + 40 * q^25 - 22 * q^28 - 11 * q^30 - 20 * q^31 - 22 * q^33 - 18 * q^36 - 42 * q^39 - 176 * q^40 - 11 * q^42 + 90 * q^46 - 64 * q^48 + 32 * q^49 - 90 * q^52 + 21 * q^54 - 76 * q^55 - 22 * q^57 + 76 * q^58 - 11 * q^60 - 22 * q^63 - 28 * q^64 - 44 * q^66 - 116 * q^70 - 79 * q^72 - 36 * q^73 - 22 * q^76 - 134 * q^78 - 44 * q^79 - 34 * q^81 - 40 * q^82 - 165 * q^84 - 18 * q^87 - 22 * q^88 - 198 * q^90 + 88 * q^94 - 231 * q^96 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.26313	−	0.636012i	−0.893165	−	0.449729i
$2$	−1.26313	−	0.636012i	−0.893165	−	0.449729i
$3$	−0.135402	−	1.72675i	−0.0781744	−	0.996940i
$3$	−0.135402	−	1.72675i	−0.0781744	−	0.996940i
$4$	1.19098	+	1.60673i	0.595488	+	0.803364i
$5$	−2.37700	−	0.341761i	−1.06303	−	0.152840i	−0.411458	−	0.911429i	$-0.634980\pi$
$5$	−2.37700	−	0.341761i	−1.06303	−	0.152840i	−0.651570	+	0.758589i	$0.725889\pi$
$6$	−0.927205	+	2.26722i	−0.378530	+	0.925589i
$7$	−3.17635	+	1.45059i	−1.20055	+	0.548271i	−0.912394	−	0.409314i	$-0.865768\pi$
$7$	−3.17635	+	1.45059i	−1.20055	+	0.548271i	−0.288152	+	0.957585i	$0.593041\pi$
$8$	−0.482454	−	2.78698i	−0.170573	−	0.985345i
$9$	−2.96333	+	0.467611i	−0.987778	+	0.155870i
$10$	2.78509	+	1.94349i	0.880723	+	0.614586i
$11$	−0.202007	−	0.687974i	−0.0609075	−	0.207432i	0.923417	−	0.383798i	$-0.125384\pi$
$11$	−0.202007	−	0.687974i	−0.0609075	−	0.207432i	−0.984325	+	0.176366i	$0.943566\pi$
$12$	2.61316	−	2.27407i	0.754354	−	0.656468i
$13$	0.701110	+	0.320186i	0.194453	+	0.0888036i	0.510262	−	0.860019i	$-0.329549\pi$
$13$	0.701110	+	0.320186i	0.194453	+	0.0888036i	−0.315809	+	0.948823i	$0.602276\pi$
$14$	4.93472	+	0.187919i	1.31886	+	0.0502235i
$15$	−0.268285	+	4.15076i	−0.0692710	+	1.07172i
$16$	−1.16315	+	3.82715i	−0.290788	+	0.956788i
$17$	3.19070	−	2.05054i	0.773859	−	0.497329i	−0.0931311	−	0.995654i	$-0.529688\pi$
$17$	3.19070	−	2.05054i	0.773859	−	0.497329i	0.866991	+	0.498325i	$0.166051\pi$
$18$	4.04047	+	1.29406i	0.952348	+	0.305014i
$19$	4.82433	+	3.10041i	1.10678	+	0.711283i	0.960589	−	0.277974i	$-0.0896629\pi$
$19$	4.82433	+	3.10041i	1.10678	+	0.711283i	0.146189	+	0.989257i	$0.453299\pi$
$20$	−2.28184	−	4.22623i	−0.510234	−	0.945013i
$21$	2.93489	+	5.28834i	0.640445	+	1.15401i
$22$	−0.182399	+	0.997477i	−0.0388876	+	0.212663i
$23$	4.78573	+	0.311055i	0.997894	+	0.0648594i
$23$	4.78573	+	0.311055i	0.997894	+	0.0648594i
$24$	−4.74709	+	1.21044i	−0.968995	+	0.247080i
$25$	0.735873	+	0.216072i	0.147175	+	0.0432144i
$26$	−0.681948	−	0.850350i	−0.133741	−	0.166767i
$27$	1.20869	+	5.05362i	0.232612	+	0.972570i
$28$	−6.11365	−	3.37591i	−1.15537	−	0.637987i
$29$	−5.77426	+	3.71089i	−1.07225	+	0.689095i	−0.952755	−	0.303740i	$-0.901765\pi$
$29$	−5.77426	+	3.71089i	−1.07225	+	0.689095i	−0.119498	+	0.992834i	$0.538128\pi$
$30$	2.97882	−	5.07231i	0.543855	−	0.926072i
$31$	2.41802	+	2.79055i	0.434289	+	0.501197i	0.930137	−	0.367213i	$-0.119688\pi$
$31$	2.41802	+	2.79055i	0.434289	+	0.501197i	−0.495847	+	0.868410i	$0.665142\pi$
$32$	3.90332	−	4.09440i	0.690016	−	0.723794i
$33$	−1.16061	+	0.441969i	−0.202036	+	0.0769370i
$34$	−5.33443	+	0.560765i	−0.914848	+	0.0961703i
$35$	8.04594	−	2.36250i	1.36001	−	0.399335i
$36$	−4.28058	−	4.20436i	−0.713430	−	0.700726i
$37$	0.875967	+	6.09248i	0.144008	+	1.00160i	0.925788	+	0.378043i	$0.123403\pi$
$37$	0.875967	+	6.09248i	0.144008	+	1.00160i	−0.781780	+	0.623554i	$0.785688\pi$
$38$	−4.12184	−	6.98454i	−0.668651	−	1.13304i
$39$	0.457950	−	1.25400i	0.0733306	−	0.200800i
$40$	0.194314	+	6.78953i	0.0307237	+	1.07352i
$41$	−1.10017	−	0.158180i	−0.171817	−	0.0247036i	0.0558692	−	0.998438i	$-0.482207\pi$
$41$	−1.10017	−	0.158180i	−0.171817	−	0.0247036i	−0.227686	+	0.973735i	$0.573116\pi$
$42$	−0.343682	−	8.54647i	−0.0530312	−	1.31875i
$43$	1.88655	−	2.17720i	0.287697	−	0.332020i	−0.593443	−	0.804876i	$-0.702232\pi$
$43$	1.88655	−	2.17720i	0.287697	−	0.332020i	0.881139	+	0.472856i	$0.156777\pi$
$44$	0.864801	−	1.14393i	0.130374	−	0.172454i
$45$	7.20366	−	0.0987602i	1.07386	−	0.0147223i
$46$	−5.84715	−	3.43669i	−0.862115	−	0.506712i
$47$			2.15429i			0.314236i	0.987580	+	0.157118i	$0.0502203\pi$
$47$			2.15429i			0.314236i	−0.987580	+	0.157118i	$0.949780\pi$
$48$	6.76603	+	1.49027i	0.976592	+	0.215102i
$49$	3.40094	−	3.92489i	0.485849	−	0.560699i
$50$	−0.792076	−	0.740951i	−0.112017	−	0.104786i
$51$	−3.97280	−	5.23190i	−0.556303	−	0.732613i
$52$	0.320553	+	1.50783i	0.0444527	+	0.209098i
$53$	0.627086	−	0.286381i	0.0861369	−	0.0393374i	−0.371881	−	0.928281i	$-0.621287\pi$
$53$	0.627086	−	0.286381i	0.0861369	−	0.0393374i	0.458018	+	0.888943i	$0.348560\pi$
$54$	1.68744	−	7.15210i	0.229631	−	0.973278i
$55$	0.245049	+	1.70435i	0.0330424	+	0.229815i
$56$	5.57520	+	8.15256i	0.745017	+	1.08943i
$57$	4.70041	−	8.75022i	0.622584	−	1.15899i
$58$	9.65379	−	1.01482i	1.26760	−	0.133253i
$59$	−4.29555	+	9.40595i	−0.559234	+	1.22455i	0.393101	+	0.919495i	$0.371402\pi$
$59$	−4.29555	+	9.40595i	−0.559234	+	1.22455i	−0.952335	+	0.305055i	$0.901325\pi$
$60$	−6.98867	+	4.51240i	−0.902234	+	0.582548i
$61$	−6.36967	−	7.35099i	−0.815552	−	0.941198i	0.183573	−	0.983006i	$-0.441234\pi$
$61$	−6.36967	−	7.35099i	−0.815552	−	0.941198i	−0.999126	+	0.0418084i	$0.986688\pi$
$62$	−1.27944	−	5.06270i	−0.162490	−	0.642964i
$63$	8.73426	−	5.78387i	1.10041	−	0.728699i
$64$	−7.53448	+	2.68918i	−0.941809	+	0.336147i
$65$	−1.55711	−	1.00070i	−0.193136	−	0.124121i
$66$	1.74709	+	0.179897i	0.215052	+	0.0221438i
$67$	14.9889	+	4.40115i	1.83119	+	0.537686i	0.999837	−	0.0180572i	$-0.00574810\pi$
$67$	14.9889	+	4.40115i	1.83119	+	0.537686i	0.831354	+	0.555743i	$0.187566\pi$
$68$	7.09471	+	2.68445i	0.860361	+	0.325537i
$69$	−0.110884	−	8.30588i	−0.0133489	−	0.999911i
$70$	−11.6656	−	2.13318i	−1.39431	−	0.254964i
$71$	−3.38562	+	11.5303i	−0.401799	+	1.36840i	0.471780	+	0.881717i	$0.343612\pi$
$71$	−3.38562	+	11.5303i	−0.401799	+	1.36840i	−0.873578	+	0.486684i	$0.838206\pi$
$72$	2.73289	+	8.03314i	0.322075	+	0.946714i
$73$	0.474838	+	0.305160i	0.0555756	+	0.0357163i	0.568134	−	0.822936i	$-0.307666\pi$
$73$	0.474838	+	0.305160i	0.0555756	+	0.0357163i	−0.512558	+	0.858653i	$0.671302\pi$
$74$	2.76844	−	8.25270i	0.321824	−	0.959357i
$75$	0.273463	−	1.29993i	0.0315768	−	0.150103i
$76$	0.764148	+	11.4439i	0.0876538	+	1.31271i
$77$	1.63961	+	1.89221i	0.186851	+	0.215638i
$78$	−1.37601	+	1.29269i	−0.155802	+	0.146369i
$79$	4.87560	+	2.22661i	0.548547	+	0.250513i	0.670355	−	0.742041i	$-0.266142\pi$
$79$	4.87560	+	2.22661i	0.548547	+	0.250513i	−0.121808	+	0.992554i	$0.538869\pi$
$80$	4.07278	−	8.69962i	0.455351	−	0.972648i
$81$	8.56268	−	2.77137i	0.951409	−	0.307930i
$82$	1.28905	+	0.899522i	0.142351	+	0.0993355i
$83$	0.236116	−	0.0339484i	0.0259171	−	0.00372632i	−0.129344	−	0.991600i	$-0.541287\pi$
$83$	0.236116	−	0.0339484i	0.0259171	−	0.00372632i	0.155261	+	0.987873i	$0.450378\pi$
$84$	−5.00155	+	11.0139i	−0.545714	+	1.20171i
$85$	−8.28511	+	3.78368i	−0.898646	+	0.410398i
$86$	−3.76768	+	1.55021i	−0.406280	+	0.167163i
$87$	7.18963	+	9.46824i	0.770809	+	1.01510i
$88$	−1.81991	+	0.894906i	−0.194003	+	0.0953973i
$89$	−1.80166	+	2.07923i	−0.190976	+	0.220398i	−0.843160	−	0.537663i	$-0.819307\pi$
$89$	−1.80166	+	2.07923i	−0.190976	+	0.220398i	0.652184	+	0.758061i	$0.273853\pi$
$90$	−9.16194	−	4.45687i	−0.965754	−	0.469795i
$91$	−2.69143			−0.282138
$92$	5.19991	+	8.05983i	0.542129	+	0.840296i
$93$	4.49117	−	4.55316i	0.465713	−	0.472141i
$94$	1.37016	−	2.72114i	0.141321	−	0.280665i
$95$	−10.4078	−	9.01845i	−1.06782	−	0.925273i
$96$	−7.59852	−	6.18567i	−0.775520	−	0.631323i
$97$	−1.67421	−	0.240715i	−0.169990	−	0.0244409i	0.0567940	−	0.998386i	$-0.481912\pi$
$97$	−1.67421	−	0.240715i	−0.169990	−	0.0244409i	−0.226784	+	0.973945i	$0.572821\pi$
$98$	−6.79210	+	2.79460i	−0.686105	+	0.282297i
$99$	0.920319	+	1.94423i	0.0924956	+	0.195403i
$100$	0.529239	+	1.43968i	0.0529239	+	0.143968i
$101$	1.26530	+	8.80039i	0.125903	+	0.875671i	0.950671	+	0.310201i	$0.100396\pi$
$101$	1.26530	+	8.80039i	0.125903	+	0.875671i	−0.824768	+	0.565471i	$0.808695\pi$
$102$	1.69059	+	9.13530i	0.167394	+	0.904530i
$103$	−4.57735	−	15.5890i	−0.451020	−	1.53603i	−0.800643	−	0.599142i	$-0.795509\pi$
$103$	−4.57735	−	15.5890i	−0.451020	−	1.53603i	0.349623	−	0.936890i	$-0.386310\pi$
$104$	0.554098	−	2.10845i	0.0543338	−	0.206751i
$105$	−5.16888	−	13.5734i	−0.504431	−	1.32463i
$106$	−0.974230	−	0.0370997i	−0.0946256	−	0.00360344i
$107$	−11.5929	+	10.0453i	−1.12073	+	0.971117i	−0.999768	−	0.0215401i	$-0.993143\pi$
$107$	−11.5929	+	10.0453i	−1.12073	+	0.971117i	−0.120961	+	0.992657i	$0.538598\pi$
$108$	−6.68027	+	7.96078i	−0.642810	+	0.766026i
$109$	−1.17325	+	0.754005i	−0.112377	+	0.0722206i	−0.595622	−	0.803265i	$-0.703094\pi$
$109$	−1.17325	+	0.754005i	−0.112377	+	0.0722206i	0.483245	+	0.875485i	$0.339458\pi$
$110$	0.774462	−	2.30867i	0.0738421	−	0.220123i
$111$	10.4016	−	2.33751i	0.987275	−	0.221867i
$112$	−1.85705	−	13.8436i	−0.175475	−	1.30810i
$113$	−15.9101	−	4.67163i	−1.49670	−	0.439470i	−0.572026	−	0.820236i	$-0.693842\pi$
$113$	−15.9101	−	4.67163i	−1.49670	−	0.439470i	−0.924671	+	0.380766i	$0.875660\pi$
$114$	−11.5025	+	8.06311i	−1.07730	+	0.755180i
$115$	−11.2694	−	2.37496i	−1.05088	−	0.221466i
$116$	−12.8394	−	4.85808i	−1.19211	−	0.451061i
$117$	−2.22734	−	0.620971i	−0.205918	−	0.0574088i
$118$	11.4081	−	9.14888i	1.05020	−	0.842223i
$119$	−7.16029	+	11.1416i	−0.656383	+	1.02135i
$120$	11.6975	−	1.25485i	1.06783	−	0.114551i
$121$	8.82129	−	5.66910i	0.801935	−	0.515372i
$122$	3.37037	+	13.3364i	0.305139	+	1.20742i
$123$	−0.124173	+	1.92113i	−0.0111963	+	0.173223i
$124$	−1.60384	+	7.20858i	−0.144029	+	0.647349i
$125$	9.24683	+	4.22289i	0.827062	+	0.377706i
$126$	−14.7111	+	1.75066i	−1.31057	+	0.155961i
$127$	−1.80761	+	0.530761i	−0.160399	+	0.0470974i	−0.360946	−	0.932587i	$-0.617546\pi$
$127$	−1.80761	+	0.530761i	−0.160399	+	0.0470974i	0.200547	+	0.979684i	$0.435728\pi$
$128$	11.2273	+	1.39525i	0.992366	+	0.123324i
$129$	−4.01492	−	2.96281i	−0.353494	−	0.260861i
$130$	1.33037	+	2.25435i	0.116682	+	0.197719i
$131$	3.29555	+	7.21625i	0.287934	+	0.630487i	0.997226	−	0.0744272i	$-0.0237129\pi$
$131$	3.29555	+	7.21625i	0.287934	+	0.630487i	−0.709293	+	0.704914i	$0.750986\pi$
$132$	−2.09238	−	1.33840i	−0.182118	−	0.116493i
$133$	−19.8212	−	2.84985i	−1.71871	−	0.247114i
$134$	−16.1337	−	15.0924i	−1.39374	−	1.30378i
$135$	−1.14592	−	12.4255i	−0.0986255	−	1.06942i
$136$	−7.25418	−	7.90313i	−0.622041	−	0.677687i
$137$	−12.7939			−1.09306			−0.546529	−	0.837440i	$-0.684051\pi$
$137$	−12.7939			−1.09306			−0.546529	+	0.837440i	$0.684051\pi$
$138$	−5.14258	+	10.5619i	−0.437766	+	0.899089i
$139$			19.3443i			1.64076i	0.571819	+	0.820380i	$0.306238\pi$
$139$			19.3443i			1.64076i	−0.571819	+	0.820380i	$0.693762\pi$
$140$	13.3784	+	10.1140i	1.13068	+	0.854785i
$141$	3.71992	−	0.291696i	0.313274	−	0.0245652i
$142$	11.6099	−	12.4110i	0.974282	−	1.04151i
$143$	0.0786504	−	0.547025i	0.00657707	−	0.0457445i
$144$	1.65719	−	11.8850i	0.138099	−	0.990418i
$145$	14.9937	−	6.84738i	1.24516	−	0.568644i
$146$	−0.405695	−	0.687458i	−0.0335755	−	0.0568945i
$147$	−7.23780	−	5.34113i	−0.596964	−	0.440529i
$148$	−8.74571	+	8.66344i	−0.718893	+	0.712130i
$149$	−3.06341	−	10.4330i	−0.250965	−	0.854707i	−0.984549	−	0.175109i	$-0.943972\pi$
$149$	−3.06341	−	10.4330i	−0.250965	−	0.854707i	0.733584	−	0.679598i	$-0.237846\pi$
$150$	−1.17219	+	1.46804i	−0.0957087	+	0.119865i
$151$	−9.73585	+	21.3185i	−0.792292	+	1.73488i	−0.122322	+	0.992490i	$0.539034\pi$
$151$	−9.73585	+	21.3185i	−0.792292	+	1.73488i	−0.669970	+	0.742388i	$0.733693\pi$
$152$	6.31325	−	14.9411i	0.512072	−	1.21188i
$153$	−8.49626	+	7.56844i	−0.686882	+	0.611872i
$154$	−0.867566	−	3.43292i	−0.0699105	−	0.276632i
$155$	−4.79394	−	7.45952i	−0.385059	−	0.599163i
$156$	2.56024	−	0.757678i	0.204983	−	0.0606628i
$157$	5.90365	+	3.79404i	0.471162	+	0.302798i	0.754591	−	0.656196i	$-0.227835\pi$
$157$	5.90365	+	3.79404i	0.471162	+	0.302798i	−0.283428	+	0.958993i	$0.591472\pi$
$158$	−4.74234	−	5.91343i	−0.377280	−	0.470447i
$159$	−0.579416	−	1.04404i	−0.0459507	−	0.0827981i
$160$	−10.6775	+	8.39838i	−0.844131	+	0.663950i
$161$	−15.6524	+	5.95411i	−1.23358	+	0.469250i
$162$	−12.5784	−	1.94538i	−0.988250	−	0.152843i
$163$	6.33018	−	21.5586i	0.495818	−	1.68860i	−0.207925	−	0.978145i	$-0.566671\pi$
$163$	6.33018	−	21.5586i	0.495818	−	1.68860i	0.703743	−	0.710455i	$-0.251511\pi$
$164$	−1.05612	−	1.95606i	−0.0824692	−	0.152743i
$165$	2.90981	−	0.653912i	0.226529	−	0.0509069i
$166$	−0.319836	−	0.107292i	−0.0248241	−	0.00832745i
$167$	12.0828	+	18.8013i	0.934999	+	1.45489i	0.890032	+	0.455898i	$0.150682\pi$
$167$	12.0828	+	18.8013i	0.934999	+	1.45489i	0.0449665	+	0.998988i	$0.485682\pi$
$168$	13.3225	−	10.7308i	1.02786	−	0.827903i
$169$	−8.12415	−	9.37577i	−0.624935	−	0.721213i
$170$	12.8716	+	0.490164i	0.987207	+	0.0375938i
$171$	−15.7459	−	6.93163i	−1.20412	−	0.530075i
$172$	5.74501	+	0.438187i	0.438053	+	0.0334114i
$173$	18.7884	−	5.51676i	1.42845	−	0.419431i	0.526097	−	0.850425i	$-0.323655\pi$
$173$	18.7884	−	5.51676i	1.42845	−	0.419431i	0.902355	+	0.430993i	$0.141837\pi$
$174$	−3.05949	−	16.5323i	−0.231939	−	1.25331i
$175$	−2.65082	+	0.381130i	−0.200383	+	0.0288107i
$176$	2.86794	+	0.0271052i	0.216179	+	0.00204313i
$177$	16.8234	+	6.14376i	1.26452	+	0.461794i
$178$	3.59815	−	1.48045i	0.269692	−	0.110964i
$179$	1.84149	−	12.8078i	0.137639	−	0.957303i	−0.797575	−	0.603220i	$-0.793884\pi$
$179$	1.84149	−	12.8078i	0.137639	−	0.957303i	0.935214	−	0.354083i	$-0.115207\pi$
$180$	8.73807	+	11.4567i	0.651297	+	0.853932i
$181$	−8.91899	+	10.2931i	−0.662943	+	0.765077i	−0.983255	−	0.182235i	$-0.941667\pi$
$181$	−8.91899	+	10.2931i	−0.662943	+	0.765077i	0.320312	+	0.947312i	$0.396212\pi$
$182$	3.39961	+	1.71178i	0.251996	+	0.126886i
$183$	−11.8309	+	11.9942i	−0.874562	+	0.886634i
$184$	−1.44199	−	13.4878i	−0.106305	−	0.994334i
$185$		−	14.7812i		−	1.08674i
$186$	−8.56878	+	2.89478i	−0.628294	+	0.212256i
$187$	−2.05526	−	1.78090i	−0.150296	−	0.130232i
$188$	−3.46136	+	2.56571i	−0.252446	+	0.187124i
$189$	−11.1699	−	14.2987i	−0.812493	−	1.04008i
$190$	7.41058	+	18.0110i	0.537620	+	1.30665i
$191$	−1.72050	−	3.76737i	−0.124491	−	0.272598i	0.837117	−	0.547024i	$-0.184239\pi$
$191$	−1.72050	−	3.76737i	−0.124491	−	0.272598i	−0.961608	+	0.274426i	$0.911512\pi$
$192$	5.66372	+	12.6460i	0.408744	+	0.912649i
$193$	2.94515	+	20.4840i	0.211997	+	1.47447i	0.766477	+	0.642272i	$0.222008\pi$
$193$	2.94515	+	20.4840i	0.211997	+	1.47447i	−0.554480	+	0.832197i	$0.687083\pi$
$194$	1.96164	+	1.36887i	0.140838	+	0.0982794i
$195$	−1.51711	+	2.82424i	−0.108643	+	0.202248i
$196$	10.3567	+	0.789931i	0.739763	+	0.0564236i
$197$	−0.429484	+	0.940439i	−0.0305995	+	0.0670035i	−0.924315	−	0.381631i	$-0.875362\pi$
$197$	−0.429484	+	0.940439i	−0.0305995	+	0.0670035i	0.893715	+	0.448635i	$0.148090\pi$
$198$	0.0740780	−	3.04115i	0.00526450	−	0.216125i
$199$	−13.4008	+	11.6118i	−0.949956	+	0.823141i	−0.984342	−	0.176267i	$-0.943598\pi$
$199$	−13.4008	+	11.6118i	−0.949956	+	0.823141i	0.0343865	+	0.999409i	$0.489052\pi$
$200$	0.247162	−	2.15511i	0.0174770	−	0.152389i
$201$	5.57015	−	26.4781i	0.392888	−	1.86762i
$202$	3.99892	−	11.9208i	0.281363	−	0.838741i
$203$	12.9581	−	20.1631i	0.909478	−	1.41518i
$204$	3.67473	−	12.6143i	0.257283	−	0.883176i
$205$	2.56104	+	0.751989i	0.178871	+	0.0525212i
$206$	−4.13304	+	22.6022i	−0.287963	+	1.57477i
$207$	−14.3272	+	1.31610i	−0.995807	+	0.0914755i
$208$	−2.04090	+	2.31083i	−0.141511	+	0.160227i
$209$	1.15845	−	3.94532i	0.0801317	−	0.272904i
$210$	−2.10392	+	20.4324i	−0.145184	+	1.40997i
$211$	−4.12781	+	6.42299i	−0.284170	+	0.442177i	−0.953767	−	0.300548i	$-0.902831\pi$
$211$	−4.12781	+	6.42299i	−0.284170	+	0.442177i	0.669597	+	0.742725i	$0.266467\pi$
$212$	1.20698	+	0.666484i	0.0828957	+	0.0457743i
$213$	20.3684	+	4.28488i	1.39562	+	0.293595i
$214$	21.0323	−	5.31526i	1.43774	−	0.363344i
$215$	−5.22843	+	4.53046i	−0.356576	+	0.308975i
$216$	13.5012	−	5.80673i	0.918639	−	0.395098i
$217$	−11.7284	−	5.35618i	−0.796176	−	0.363601i
$218$	1.96152	−	0.206199i	0.132851	−	0.0139655i
$219$	0.462641	−	0.861246i	0.0312624	−	0.0581976i
$220$	−2.44659	+	2.42357i	−0.164949	+	0.163397i
$221$	2.89359	−	0.416035i	0.194644	−	0.0279856i
$222$	−14.6252	−	3.66297i	−0.981579	−	0.245842i
$223$	6.45833	+	14.1418i	0.432482	+	0.947003i	0.992918	+	0.118805i	$0.0379065\pi$
$223$	6.45833	+	14.1418i	0.432482	+	0.947003i	−0.560436	+	0.828198i	$0.689366\pi$
$224$	−6.45902	+	18.6673i	−0.431561	+	1.24726i
$225$	−2.28167	−	0.296190i	−0.152112	−	0.0197460i
$226$	17.1253	+	16.0199i	1.13916	+	1.06563i
$227$	7.07074	+	6.12683i	0.469302	+	0.406652i	0.857147	−	0.515072i	$-0.172235\pi$
$227$	7.07074	+	6.12683i	0.469302	+	0.406652i	−0.387845	+	0.921725i	$0.626780\pi$
$228$	19.6573	−	2.86902i	1.30184	−	0.190006i
$229$	5.06536			0.334728			0.167364	−	0.985895i	$-0.446474\pi$
$229$	5.06536			0.334728			0.167364	+	0.985895i	$0.446474\pi$
$230$	12.7242	+	10.1673i	0.839007	+	0.670415i
$231$	3.04537	−	3.08741i	0.200371	−	0.203137i
$232$	13.1280	+	14.3024i	0.861894	+	0.938998i
$233$	16.9956	+	14.7267i	1.11342	+	0.964781i	0.999588	−	0.0287197i	$-0.00914303\pi$
$233$	16.9956	+	14.7267i	1.11342	+	0.964781i	0.113829	+	0.993500i	$0.463688\pi$
$234$	2.41847	+	2.20098i	0.158100	+	0.143883i
$235$	0.736254	−	5.12076i	0.0480279	−	0.334041i
$236$	−20.2287	+	4.30048i	−1.31678	+	0.279937i
$237$	3.18463	−	8.72042i	0.206864	−	0.566452i
$238$	16.1306	−	9.51925i	1.04559	−	0.617041i
$239$	8.04319	−	1.15644i	0.520271	−	0.0748036i	0.122823	−	0.992429i	$-0.460805\pi$
$239$	8.04319	−	1.15644i	0.520271	−	0.0748036i	0.397447	+	0.917625i	$0.369896\pi$
$240$	−15.5735	−	5.85474i	−1.00527	−	0.377922i
$241$	4.06070	+	13.8295i	0.261573	+	0.890834i	0.980628	+	0.195881i	$0.0627567\pi$
$241$	4.06070	+	13.8295i	0.261573	+	0.890834i	−0.719055	+	0.694953i	$0.755425\pi$
$242$	−14.7480	+	1.55034i	−0.948038	+	0.0996594i
$243$	−5.94488	−	14.4104i	−0.381364	−	0.924425i
$244$	4.22492	−	18.9892i	0.270473	−	1.21566i
$245$	−9.42542	+	8.16717i	−0.602168	+	0.521781i
$246$	1.37871	−	2.34766i	0.0879033	−	0.149681i
$247$	2.38968	+	3.71841i	0.152052	+	0.236597i
$248$	6.61060	−	8.08528i	0.419774	−	0.513416i
$249$	−0.0905910	−	0.403117i	−0.00574097	−	0.0255465i
$250$	−8.99411	−	11.2151i	−0.568837	−	0.709308i
$251$	−1.07029	+	3.64508i	−0.0675563	+	0.230076i	−0.986350	−	0.164663i	$-0.947346\pi$
$251$	−1.07029	+	3.64508i	−0.0675563	+	0.230076i	0.918794	+	0.394738i	$0.129165\pi$
$252$	19.6954	+	7.14513i	1.24069	+	0.450101i
$253$	−0.752756	−	3.35530i	−0.0473254	−	0.210946i
$254$	2.62081	+	0.479242i	0.164444	+	0.0300703i
$255$	7.65529	+	13.7940i	0.479393	+	0.863813i
$256$	−13.2942	−	8.90311i	−0.830885	−	0.556444i
$257$	1.10713	−	1.72273i	0.0690610	−	0.107461i	−0.805005	−	0.593268i	$-0.797838\pi$
$257$	1.10713	−	1.72273i	0.0690610	−	0.107461i	0.874066	+	0.485806i	$0.161474\pi$
$258$	3.18697	+	6.29595i	0.198412	+	0.391968i
$259$	−11.6201	−	18.0812i	−0.722035	−	1.12351i
$260$	−0.246638	−	3.69366i	−0.0152959	−	0.229071i
$261$	15.3758	−	13.6967i	0.951738	−	0.847805i
$262$	0.426928	−	11.2110i	0.0263757	−	0.692621i
$263$	11.2397	−	24.6115i	0.693070	−	1.51761i	−0.155107	−	0.987898i	$-0.549572\pi$
$263$	11.2397	−	24.6115i	0.693070	−	1.51761i	0.848177	−	0.529714i	$-0.177701\pi$
$264$	1.79170	+	3.02135i	0.110271	+	0.185952i
$265$	−1.58846	+	0.466413i	−0.0975782	+	0.0286516i
$266$	23.2241	+	16.2062i	1.42396	+	0.993668i
$267$	3.83426	+	2.82949i	0.234653	+	0.173162i
$268$	10.7800	+	29.3248i	0.658495	+	1.79130i
$269$	−0.982687	−	2.15178i	−0.0599155	−	0.131197i	0.877306	−	0.479932i	$-0.159339\pi$
$269$	−0.982687	−	2.15178i	−0.0599155	−	0.131197i	−0.937221	+	0.348735i	$0.886611\pi$
$270$	−6.45536	+	16.4239i	−0.392860	+	0.999524i
$271$	4.37283	−	30.4137i	0.265630	−	1.84750i	−0.222757	−	0.974874i	$-0.571506\pi$
$271$	4.37283	−	30.4137i	0.265630	−	1.84750i	0.488388	−	0.872627i	$-0.337585\pi$
$272$	4.13646	+	14.5964i	0.250810	+	0.885036i
$273$	0.364425	+	4.64742i	0.0220560	+	0.281275i
$274$	16.1603	+	8.13709i	0.976281	+	0.491579i
$275$		−	0.549910i		−	0.0331608i
$276$	13.2132	−	10.0703i	0.795343	−	0.606159i
$277$		−	11.9541i		−	0.718251i	−0.933289	−	0.359126i	$-0.883075\pi$
$277$		−	11.9541i		−	0.718251i	0.933289	−	0.359126i	$-0.116925\pi$
$278$	12.3032	−	24.4343i	0.737897	−	1.46547i
$279$	−8.47029	−	7.13862i	−0.507103	−	0.427378i
$280$	−10.4660	−	21.2840i	−0.625465	−	1.27196i
$281$	−2.46015	+	17.1107i	−0.146760	+	1.02074i	0.774717	+	0.632309i	$0.217893\pi$
$281$	−2.46015	+	17.1107i	−0.146760	+	1.02074i	−0.921477	+	0.388433i	$0.873017\pi$
$282$	−4.88426	−	1.99747i	−0.290853	−	0.118948i
$283$	6.10788	+	13.3744i	0.363076	+	0.795025i	0.999715	+	0.0238635i	$0.00759672\pi$
$283$	6.10788	+	13.3744i	0.363076	+	0.795025i	−0.636639	+	0.771162i	$0.719676\pi$
$284$	−22.5583	+	8.29261i	−1.33859	+	0.492076i
$285$	−14.1634	+	19.1929i	−0.838965	+	1.13689i
$286$	−0.447260	+	0.640939i	−0.0264471	+	0.0378995i
$287$	3.72397	−	1.09345i	0.219819	−	0.0645446i
$288$	−9.65226	+	13.9583i	−0.568765	+	0.822500i
$289$	−1.08618	+	2.37841i	−0.0638930	+	0.139906i
$290$	−23.2939	−	0.887055i	−1.36787	−	0.0520897i
$291$	−0.188963	+	2.92354i	−0.0110772	+	0.171381i
$292$	0.0752118	+	1.12637i	0.00440144	+	0.0659160i
$293$	−9.97410	−	15.5200i	−0.582693	−	0.906689i	0.417304	−	0.908767i	$-0.362975\pi$
$293$	−9.97410	−	15.5200i	−0.582693	−	0.906689i	−0.999998	+	0.00207808i	$0.999339\pi$
$294$	5.74523	+	11.3499i	0.335069	+	0.661937i
$295$	13.4251	−	20.8899i	0.781641	−	1.21626i
$296$	16.5570	−	5.38064i	0.962355	−	0.312743i
$297$	3.23259	−	1.85241i	0.187574	−	0.107488i
$298$	−2.76606	+	15.1266i	−0.160233	+	0.876261i
$299$	3.25573	+	1.75041i	0.188284	+	0.101229i
$300$	2.41432	−	1.10880i	0.139391	−	0.0640166i
$301$	−2.83413	+	9.65215i	−0.163356	+	0.556341i
$302$	25.8565	−	20.7359i	1.48787	−	1.19322i
$303$	15.0247	−	3.37646i	0.863149	−	0.193972i
$304$	−17.4772	+	14.8572i	−1.00238	+	0.852119i
$305$	12.6284	+	19.6502i	0.723102	+	1.12517i
$306$	15.5455	−	4.15617i	0.888676	−	0.237593i
$307$	12.8475	−	11.1324i	0.733247	−	0.635362i	−0.206020	−	0.978548i	$-0.566051\pi$
$307$	12.8475	−	11.1324i	0.733247	−	0.635362i	0.939268	+	0.343185i	$0.111506\pi$
$308$	−1.08753	+	4.88799i	−0.0619680	+	0.278519i
$309$	−26.2986	+	10.0147i	−1.49607	+	0.569718i
$310$	1.31101	+	12.4713i	0.0744602	+	0.708323i
$311$	2.67431	+	9.10788i	0.151646	+	0.516460i	0.999914	−	0.0131074i	$-0.00417233\pi$
$311$	2.67431	+	9.10788i	0.151646	+	0.516460i	−0.848268	+	0.529568i	$0.822354\pi$
$312$	−3.71580	−	0.671300i	−0.210365	−	0.0380049i
$313$	−32.5997	+	4.68713i	−1.84264	+	0.264932i	−0.973344	−	0.229352i	$-0.926339\pi$
$313$	−32.5997	+	4.68713i	−1.84264	+	0.264932i	−0.869301	+	0.494284i	$0.835430\pi$
$314$	−5.04399	−	8.54715i	−0.284649	−	0.482344i
$315$	−22.7381	+	10.7632i	−1.28114	+	0.606440i
$316$	2.22916	+	10.4856i	0.125400	+	0.589861i
$317$	−2.08241	+	14.4835i	−0.116960	+	0.813475i	0.843912	+	0.536482i	$0.180247\pi$
$317$	−2.08241	+	14.4835i	−0.116960	+	0.813475i	−0.960872	+	0.276993i	$0.910662\pi$
$318$	0.0678509	+	1.68728i	0.00380489	+	0.0946177i
$319$	3.71944	+	3.22291i	0.208249	+	0.180448i
$320$	18.8285	−	3.81719i	1.05255	−	0.213387i
$321$	18.9155	+	18.6579i	1.05576	+	1.04138i
$322$	23.5578	+	2.43430i	1.31282	+	0.135658i
$323$	21.7505			1.21023
$324$	14.6508	+	10.4573i	0.813933	+	0.580959i
$325$	0.446745	+	0.387106i	0.0247809	+	0.0214728i
$326$	−21.7073	+	23.2052i	−1.20226	+	1.28522i
$327$	1.46084	+	1.92382i	0.0807846	+	0.106388i
$328$	0.0899358	+	3.14245i	0.00496588	+	0.173513i
$329$	−3.12499	−	6.84278i	−0.172286	−	0.377255i
$330$	−4.09136	−	1.02470i	−0.225222	−	0.0564081i
$331$	19.6541	−	2.82583i	1.08029	−	0.155322i	0.420886	−	0.907114i	$-0.361719\pi$
$331$	19.6541	−	2.82583i	1.08029	−	0.155322i	0.659400	+	0.751792i	$0.270810\pi$
$332$	0.335755	+	0.338943i	0.0184269	+	0.0186019i
$333$	−5.44469	−	17.6444i	−0.298367	−	0.966909i
$334$	−3.30431	−	31.4332i	−0.180804	−	1.71995i
$335$	−34.1246	−	15.5842i	−1.86443	−	0.851455i
$336$	−23.6530	+	5.08111i	−1.29038	+	0.277197i
$337$	3.53158	−	3.06013i	0.192377	−	0.166696i	−0.553346	−	0.832951i	$-0.686649\pi$
$337$	3.53158	−	3.06013i	0.192377	−	0.166696i	0.745724	+	0.666255i	$0.232104\pi$
$338$	4.29872	+	17.0098i	0.233820	+	0.925214i
$339$	−5.91248	+	28.1053i	−0.321122	+	1.52647i
$340$	−15.9467	−	8.80564i	−0.864832	−	0.477553i
$341$	1.43136	−	2.22725i	0.0775127	−	0.120612i
$342$	15.4804	+	18.7701i	0.837086	+	1.01497i
$343$	1.77732	−	6.05301i	0.0959664	−	0.326832i
$344$	−6.97798	−	4.20738i	−0.376228	−	0.226847i
$345$	−2.57506	+	19.7810i	−0.138636	+	1.06497i
$346$	−27.2408	−	4.98127i	−1.46447	−	0.267794i
$347$	−27.0398	−	7.93959i	−1.45157	−	0.426220i	−0.541510	−	0.840694i	$-0.682147\pi$
$347$	−27.0398	−	7.93959i	−1.45157	−	0.426220i	−0.910061	+	0.414475i	$0.863965\pi$
$348$	−6.65021	+	22.8282i	−0.356489	+	1.22372i
$349$	−4.42736	+	6.88910i	−0.236991	+	0.368765i	−0.939294	−	0.343113i	$-0.888519\pi$
$349$	−4.42736	+	6.88910i	−0.236991	+	0.368765i	0.702303	+	0.711878i	$0.252155\pi$
$350$	3.59072	+	1.20454i	0.191932	+	0.0643853i
$351$	−0.770675	+	3.93015i	−0.0411356	+	0.209776i
$352$	−3.60534	−	1.85829i	−0.192165	−	0.0990470i
$353$	−17.1607	+	14.8698i	−0.913369	+	0.791439i	−0.978459	−	0.206440i	$-0.933812\pi$
$353$	−17.1607	+	14.8698i	−0.913369	+	0.791439i	0.0650898	+	0.997879i	$0.479267\pi$
$354$	−17.3425	−	18.4602i	−0.921744	−	0.981149i
$355$	11.9882	−	26.2506i	0.636270	−	1.39324i
$356$	−5.48650	−	0.418470i	−0.290784	−	0.0221788i
$357$	20.2083	+	10.8554i	1.06954	+	0.574530i
$358$	−10.4720	+	15.0067i	−0.553461	+	0.793129i
$359$	−0.511695	−	3.55892i	−0.0270062	−	0.187832i	0.971853	−	0.235589i	$-0.0757019\pi$
$359$	−0.511695	−	3.55892i	−0.0270062	−	0.187832i	−0.998859	+	0.0477566i	$0.984793\pi$
$360$	−3.75068	−	20.0288i	−0.197678	−	1.05561i
$361$	5.76875	+	12.6318i	0.303618	+	0.664832i
$362$	17.8123	−	7.32885i	0.936195	−	0.385196i
$363$	−10.9835	−	14.4646i	−0.576486	−	0.759192i
$364$	−3.20542	−	4.32439i	−0.168010	−	0.226660i
$365$	−1.02440	−	0.887647i	−0.0536195	−	0.0464616i
$366$	22.5723	−	7.62557i	1.17987	−	0.398595i
$367$		−	17.0765i		−	0.891388i	−0.895185	−	0.445694i	$-0.852957\pi$
$367$		−	17.0765i		−	0.891388i	0.895185	−	0.445694i	$-0.147043\pi$
$368$	−6.75699	+	17.9539i	−0.352232	+	0.935913i
$369$	3.33413	−	0.0457100i	0.173568	−	0.00237957i
$370$	−9.40104	+	18.6705i	−0.488737	+	0.970635i
$371$	−1.57642	+	1.81929i	−0.0818437	+	0.0944527i
$372$	12.6646	+	1.79338i	0.656628	+	0.0929824i
$373$	5.09607	−	35.4439i	0.263864	−	1.83522i	−0.239202	−	0.970970i	$-0.576886\pi$
$373$	5.09607	−	35.4439i	0.263864	−	1.83522i	0.503067	−	0.864248i	$-0.332205\pi$
$374$	1.46339	+	3.55667i	0.0756699	+	0.183911i
$375$	6.03983	−	16.5388i	0.311895	−	0.854058i
$376$	6.00396	−	1.03935i	0.309631	−	0.0536002i
$377$	−5.23656	+	0.752904i	−0.269697	+	0.0387765i
$378$	5.01487	+	25.1653i	0.257937	+	1.29436i
$379$	17.2621	−	5.06860i	0.886694	−	0.260357i	0.193493	−	0.981102i	$-0.438018\pi$
$379$	17.2621	−	5.06860i	0.886694	−	0.260357i	0.693200	+	0.720745i	$0.256200\pi$
$380$	2.09470	−	27.4633i	0.107456	−	1.40884i
$381$	1.16125	+	3.04942i	0.0594924	+	0.156226i
$382$	−0.222885	+	5.85293i	−0.0114038	+	0.299462i
$383$	−8.90596	−	10.2780i	−0.455073	−	0.525183i	0.481126	−	0.876651i	$-0.340228\pi$
$383$	−8.90596	−	10.2780i	−0.455073	−	0.525183i	−0.936200	+	0.351469i	$0.885682\pi$
$384$	0.889044	−	19.5757i	0.0453688	−	0.998970i
$385$	−3.25068	−	5.05815i	−0.165670	−	0.257787i
$386$	9.30796	−	27.7470i	0.473763	−	1.41228i
$387$	−4.57241	+	7.33394i	−0.232428	+	0.372805i
$388$	−1.60718	−	2.97669i	−0.0815923	−	0.151118i
$389$	1.72217	−	5.86516i	0.0873173	−	0.297375i	−0.904244	−	0.427017i	$-0.859564\pi$
$389$	1.72217	−	5.86516i	0.0873173	−	0.297375i	0.991561	+	0.129642i	$0.0413827\pi$
$390$	3.71256	−	2.60247i	0.187993	−	0.131781i
$391$	15.9077	−	8.82086i	0.804486	−	0.446090i
$392$	−12.5794	−	7.58476i	−0.635355	−	0.383088i
$393$	12.0144	−	6.66769i	0.606048	−	0.336340i
$394$	1.14062	−	0.914736i	0.0574638	−	0.0460837i
$395$	−10.8283	−	6.95895i	−0.544832	−	0.350143i
$396$	−2.02778	+	3.79424i	−0.101900	+	0.190668i
$397$	3.74452	+	5.82659i	0.187932	+	0.292428i	0.922416	−	0.386198i	$-0.126212\pi$
$397$	3.74452	+	5.82659i	0.187932	+	0.292428i	−0.734484	+	0.678626i	$0.762576\pi$
$398$	24.3121	−	6.14416i	1.21866	−	0.307979i
$399$	−2.23716	+	34.6121i	−0.111998	+	1.73277i
$400$	−1.68287	+	2.56497i	−0.0841436	+	0.128249i
$401$	14.8363	−	32.4870i	0.740891	−	1.62232i	−0.0411928	−	0.999151i	$-0.513116\pi$
$401$	14.8363	−	32.4870i	0.740891	−	1.62232i	0.782084	−	0.623173i	$-0.214157\pi$
$402$	−23.8762	+	29.9025i	−1.19084	+	1.49140i
$403$	0.801805	+	2.73070i	0.0399407	+	0.136026i
$404$	−12.6329	+	12.5141i	−0.628510	+	0.622597i
$405$	−21.3007	+	3.66117i	−1.05844	+	0.181925i
$406$	−29.1917	+	17.2271i	−1.44876	+	0.854967i
$407$	4.01452	−	1.83337i	0.198992	−	0.0908767i
$408$	−12.6645	+	13.5963i	−0.626986	+	0.673115i
$409$	2.65558	−	18.4700i	0.131310	−	0.913281i	−0.812540	−	0.582906i	$-0.801916\pi$
$409$	2.65558	−	18.4700i	0.131310	−	0.913281i	0.943850	−	0.330375i	$-0.107175\pi$
$410$	−2.75664	−	2.57871i	−0.136141	−	0.127353i
$411$	1.73232	+	22.0919i	0.0854492	+	1.08971i
$412$	19.5958	−	25.9207i	0.965416	−	1.27702i
$413$		−	36.1076i		−	1.77674i
$414$	18.9341	+	7.44986i	0.930560	+	0.366140i
$415$	−0.572851			−0.0281201
$416$	4.04763	−	1.62083i	0.198451	−	0.0794678i
$417$	33.4027	−	2.61925i	1.63574	−	0.128265i
$418$	−3.97254	+	4.24665i	−0.194303	+	0.207710i
$419$	14.6886	+	2.11190i	0.717584	+	0.103173i	0.491428	−	0.870918i	$-0.336475\pi$
$419$	14.6886	+	2.11190i	0.717584	+	0.103173i	0.226156	+	0.974091i	$0.427384\pi$
$420$	15.6528	−	24.4706i	0.763778	−	1.19404i
$421$	−9.75248	−	21.3549i	−0.475307	−	1.04078i	−0.983727	−	0.179668i	$-0.942498\pi$
$421$	−9.75248	−	21.3549i	−0.475307	−	1.04078i	0.508421	−	0.861109i	$-0.330230\pi$
$422$	9.29904	−	5.48771i	0.452670	−	0.267138i
$423$	−1.00737	−	6.38388i	−0.0489801	−	0.310395i
$424$	−1.10068	−	1.60951i	−0.0534536	−	0.0781646i
$425$	2.79102	−	0.819517i	0.135384	−	0.0397524i
$426$	−23.0027	−	18.3669i	−1.11448	−	0.889881i
$427$	30.8955	+	14.1095i	1.49514	+	0.682807i
$428$	−29.9470	−	6.66293i	−1.44754	−	0.322065i
$429$	−0.955225	−	0.0617412i	−0.0461187	−	0.00298089i
$430$	9.48559	−	2.39720i	0.457436	−	0.115603i
$431$	22.4339	−	14.4174i	1.08060	−	0.694462i	0.125907	−	0.992042i	$-0.459816\pi$
$431$	22.4339	−	14.4174i	1.08060	−	0.694462i	0.954697	+	0.297580i	$0.0961795\pi$
$432$	−20.7468	−	1.25229i	−0.998183	−	0.0602508i
$433$	−16.6069	+	25.8408i	−0.798075	+	1.24183i	0.168565	+	0.985691i	$0.446087\pi$
$433$	−16.6069	+	25.8408i	−0.798075	+	1.24183i	−0.966640	+	0.256139i	$0.917550\pi$
$434$	11.4079	+	14.2249i	0.547595	+	0.682819i
$435$	−13.8539	−	24.9632i	−0.664243	−	1.19689i
$436$	−2.60880	−	0.987099i	−0.124939	−	0.0472735i
$437$	22.1236	+	16.3384i	1.05831	+	0.781570i
$438$	−1.13214	+	0.793617i	−0.0540956	+	0.0379205i
$439$	−19.9579	−	5.86017i	−0.952539	−	0.279691i	−0.231696	−	0.972788i	$-0.574427\pi$
$439$	−19.9579	−	5.86017i	−0.952539	−	0.279691i	−0.720844	+	0.693098i	$0.756246\pi$
$440$	4.63177	−	1.50522i	0.220811	−	0.0717585i
$441$	−8.24279	+	13.2211i	−0.392514	+	0.629575i
$442$	−3.91957	−	1.31485i	−0.186435	−	0.0625412i
$443$	−6.12520	+	3.93642i	−0.291017	+	0.187025i	−0.678001	−	0.735061i	$-0.737153\pi$
$443$	−6.12520	+	3.93642i	−0.291017	+	0.187025i	0.386984	+	0.922087i	$0.373517\pi$
$444$	16.1438	+	13.9286i	0.766150	+	0.661022i
$445$	4.99316	−	4.32660i	0.236698	−	0.205100i
$446$	0.836656	−	21.9704i	0.0396168	−	1.04033i
$447$	−17.6004	+	6.70240i	−0.832472	+	0.317013i
$448$	20.0312	−	19.4712i	0.946386	−	0.919927i
$449$	5.97984	+	20.3655i	0.282206	+	0.961106i	0.971582	+	0.236702i	$0.0760667\pi$
$449$	5.97984	+	20.3655i	0.282206	+	0.961106i	−0.689376	+	0.724404i	$0.742115\pi$
$450$	2.69366	+	1.82530i	0.126980	+	0.0860454i
$451$	0.113418	+	0.788840i	0.00534065	+	0.0371450i
$452$	−11.4425	−	31.1270i	−0.538211	−	1.46409i
$453$	38.1301	+	13.9248i	1.79151	+	0.654245i
$454$	−5.03450	−	12.2360i	−0.236281	−	0.574266i
$455$	6.39752	+	0.919825i	0.299921	+	0.0431221i
$456$	−26.6544	−	8.87835i	−1.24821	−	0.415767i
$457$	18.5846	+	16.1037i	0.869352	+	0.753298i	0.970379	−	0.241586i	$-0.0776675\pi$
$457$	18.5846	+	16.1037i	0.869352	+	0.753298i	−0.101027	+	0.994884i	$0.532213\pi$
$458$	−6.39818	−	3.22163i	−0.298968	−	0.150537i
$459$	14.2192	+	13.6461i	0.663696	+	0.636947i
$460$	−9.60567	−	20.9354i	−0.447867	−	0.976117i
$461$	−31.0100			−1.44428			−0.722140	−	0.691747i	$-0.756841\pi$
$461$	−31.0100			−1.44428			−0.722140	+	0.691747i	$0.756841\pi$
$462$	−5.81032	+	1.96289i	−0.270321	+	0.0913221i
$463$	−16.0987	+	18.5788i	−0.748168	+	0.863432i	−0.994389	−	0.105782i	$-0.966266\pi$
$463$	−16.0987	+	18.5788i	−0.748168	+	0.863432i	0.246221	+	0.969214i	$0.420811\pi$
$464$	−7.48580	−	26.4153i	−0.347519	−	1.22630i
$465$	−12.2316	+	9.28797i	−0.567228	+	0.430719i
$466$	−12.1012	−	29.4111i	−0.560575	−	1.36244i
$467$	−5.42614	+	2.47803i	−0.251092	+	0.114670i	−0.536985	−	0.843592i	$-0.680437\pi$
$467$	−5.42614	+	2.47803i	−0.251092	+	0.114670i	0.285894	+	0.958261i	$0.407710\pi$
$468$	−1.65498	−	4.31830i	−0.0765016	−	0.199613i
$469$	−53.9943	+	7.76321i	−2.49323	+	0.358472i
$470$	−4.18685	+	5.99990i	−0.193125	+	0.276755i
$471$	5.75200	−	10.7078i	0.265038	−	0.493392i
$472$	28.2866	+	7.43367i	1.30200	+	0.342162i
$473$	−1.87895	−	0.858090i	−0.0863944	−	0.0394550i
$474$	−9.56889	+	8.98953i	−0.439514	+	0.412903i
$475$	2.88019	+	3.32391i	0.132152	+	0.152511i
$476$	−26.4293	+	1.76477i	−1.21138	+	0.0808883i
$477$	−1.72435	+	1.14187i	−0.0789525	+	0.0522828i
$478$	−10.8951	−	3.65484i	−0.498329	−	0.167169i
$479$	−6.25703	−	4.02115i	−0.285891	−	0.183731i	0.389833	−	0.920885i	$-0.372533\pi$
$479$	−6.25703	−	4.02115i	−0.285891	−	0.183731i	−0.675724	+	0.737154i	$0.736169\pi$
$480$	15.9477	+	17.3002i	0.727908	+	0.789644i
$481$	−1.33658	+	4.55197i	−0.0609428	+	0.207552i
$482$	3.66654	−	20.0510i	0.167006	−	0.913299i
$483$	12.4006	+	26.2215i	0.564248	+	1.19312i
$484$	19.6146	+	7.42165i	0.891575	+	0.337348i
$485$	3.89734	+	1.14436i	0.176969	+	0.0519628i
$486$	−1.65604	+	21.9831i	−0.0751195	+	0.997175i
$487$	−9.32575	−	5.99330i	−0.422590	−	0.271582i	0.312015	−	0.950077i	$-0.398996\pi$
$487$	−9.32575	−	5.99330i	−0.422590	−	0.271582i	−0.734605	+	0.678495i	$0.762632\pi$
$488$	−17.4140	+	21.2986i	−0.788293	+	0.964144i
$489$	−38.0834	−	8.01155i	−1.72219	−	0.362295i
$490$	17.0999	−	4.32148i	0.772495	−	0.195225i
$491$	9.47255	+	10.9319i	0.427490	+	0.493350i	0.928104	−	0.372321i	$-0.121438\pi$
$491$	9.47255	+	10.9319i	0.427490	+	0.493350i	−0.500614	+	0.865671i	$0.666892\pi$
$492$	−3.23462	+	2.08851i	−0.145828	+	0.0941573i
$493$	−10.8146	+	23.6807i	−0.487066	+	1.06653i
$494$	−0.653509	−	6.21669i	−0.0294028	−	0.279702i
$495$	−1.52314	−	4.93598i	−0.0684599	−	0.221856i
$496$	−13.4924	+	6.00830i	−0.605825	+	0.269781i
$497$	−5.97190	−	41.5355i	−0.267876	−	1.86312i
$498$	−0.141960	+	0.566805i	−0.00636136	+	0.0253991i
$499$	−12.4279	+	5.67565i	−0.556351	+	0.254077i	−0.673689	−	0.739015i	$-0.735291\pi$
$499$	−12.4279	+	5.67565i	−0.556351	+	0.254077i	0.117338	+	0.993092i	$0.462564\pi$
$500$	4.22772	+	19.8865i	0.189070	+	0.889351i
$501$	30.8291	−	23.4098i	1.37734	−	1.04587i
$502$	3.67023	−	3.92348i	0.163811	−	0.175113i
$503$	−10.3003	+	11.8872i	−0.459268	+	0.530023i	−0.937395	−	0.348267i	$-0.886770\pi$
$503$	−10.3003	+	11.8872i	−0.459268	+	0.530023i	0.478128	+	0.878290i	$0.341316\pi$
$504$	−20.3334	−	21.5517i	−0.905721	−	0.959990i
$505$		−	21.3510i		−	0.950106i
$506$	−1.18318	+	4.71692i	−0.0525989	+	0.209693i
$507$	−15.0896	+	15.2979i	−0.670152	+	0.679403i
$508$	−3.00561	−	2.27221i	−0.133352	−	0.100813i
$509$	−21.5793	+	24.9039i	−0.956487	+	1.10385i	0.0380305	+	0.999277i	$0.487892\pi$
$509$	−21.5793	+	24.9039i	−0.956487	+	1.10385i	−0.994518	+	0.104568i	$0.966654\pi$
$510$	−0.896451	−	22.2924i	−0.0396955	−	0.987125i
$511$	−1.95091	−	0.280499i	−0.0863032	−	0.0124085i
$512$	11.1297	+	19.7010i	0.491868	+	0.870670i
$513$	−9.83717	+	28.1278i	−0.434322	+	1.24187i
$514$	−2.49413	+	1.47188i	−0.110011	+	0.0649218i
$515$	5.55265	+	38.6195i	0.244679	+	1.70178i
$516$	−0.0212467	−	9.97953i	−0.000935333	−	0.439324i
$517$	1.48210	−	0.435183i	0.0651826	−	0.0191393i
$518$	3.17775	+	30.2293i	0.139623	+	1.32820i
$519$	−12.0700	−	31.6958i	−0.529816	−	1.39129i
$520$	−2.03768	+	4.82242i	−0.0893581	+	0.211477i
$521$	28.1099	+	32.4406i	1.23152	+	1.42125i	0.872997	+	0.487725i	$0.162173\pi$
$521$	28.1099	+	32.4406i	1.23152	+	1.42125i	0.358521	+	0.933522i	$0.383281\pi$
$522$	−28.1328	+	7.52148i	−1.23134	+	0.329206i
$523$	−18.9992	+	12.2100i	−0.830777	+	0.533908i	−0.885525	−	0.464592i	$-0.846201\pi$
$523$	−18.9992	+	12.2100i	−0.830777	+	0.533908i	0.0547477	+	0.998500i	$0.482565\pi$
$524$	−7.66963	+	13.8894i	−0.335049	+	0.606763i
$525$	1.01704	+	4.52570i	0.0443874	+	0.197518i
$526$	−29.8504	+	23.9389i	−1.30154	+	1.04378i
$527$	13.4373	+	3.94555i	0.585339	+	0.171871i
$528$	−0.341522	−	4.95589i	−0.0148628	−	0.215678i
$529$	22.8065	+	2.97725i	0.991587	+	0.129446i
$530$	2.30307	+	0.421140i	0.100039	+	0.0182932i
$531$	8.33083	−	29.8816i	0.361527	−	1.29675i
$532$	−19.0276	−	35.2413i	−0.824951	−	1.52791i
$533$	−0.720691	−	0.463160i	−0.0312166	−	0.0200617i
$534$	−3.04356	−	6.01264i	−0.131708	−	0.260192i
$535$	30.9895	−	19.9157i	1.33979	−	0.861032i
$536$	5.03443	−	43.8972i	0.217454	−	1.89607i
$537$	−22.3653	−	1.44558i	−0.965133	−	0.0623816i
$538$	−0.127304	+	3.34298i	−0.00548846	+	0.144126i
$539$	−3.38724	−	1.54690i	−0.145899	−	0.0666297i
$540$	18.5997	−	16.6397i	0.800404	−	0.716060i
$541$	1.56480	+	5.32922i	0.0672760	+	0.229121i	0.986267	−	0.165157i	$-0.0528130\pi$
$541$	1.56480	+	5.32922i	0.0672760	+	0.229121i	−0.918991	+	0.394278i	$0.870995\pi$
$542$	−24.8669	+	35.6352i	−1.06813	+	1.53066i
$543$	18.9812	+	14.0072i	0.814561	+	0.601105i
$544$	4.05862	−	21.0679i	0.174012	−	0.903280i
$545$	3.04652	−	1.39130i	0.130498	−	0.0595967i
$546$	2.49550	−	6.10206i	0.106798	−	0.261144i
$547$	14.1483	+	2.03422i	0.604937	+	0.0869769i	0.437976	−	0.898987i	$-0.355695\pi$
$547$	14.1483	+	2.03422i	0.604937	+	0.0869769i	0.166961	+	0.985963i	$0.446605\pi$
$548$	−15.2372	−	20.5563i	−0.650903	−	0.878123i
$549$	22.3128	+	18.8049i	0.952289	+	0.802573i
$550$	−0.349749	+	0.694605i	−0.0149134	+	0.0296181i
$551$	−39.3622			−1.67689
$552$	−23.0948	+	4.31624i	−0.982980	+	0.183711i
$553$	−18.7165			−0.795905
$554$	−7.60295	+	15.0995i	−0.323018	+	0.641517i
$555$	−25.5235	+	2.00141i	−1.08341	+	0.0849550i
$556$	−31.0810	+	23.0386i	−1.31813	+	0.977053i
$557$	−1.19217	−	0.171408i	−0.0505139	−	0.00726281i	0.117012	−	0.993131i	$-0.462669\pi$
$557$	−1.19217	−	0.171408i	−0.0505139	−	0.00726281i	−0.167525	+	0.985868i	$0.553578\pi$
$558$	6.15880	+	14.4042i	0.260723	+	0.609778i
$559$	2.01979	−	0.922408i	0.0854281	−	0.0390137i
$560$	−0.316999	+	33.5409i	−0.0133956	+	1.41736i
$561$	−2.79688	+	3.79007i	−0.118084	+	0.160017i
$562$	13.9901	−	20.0483i	0.590138	−	0.845688i
$563$	−5.58028	−	19.0047i	−0.235181	−	0.800952i	−0.989511	−	0.144457i	$-0.953856\pi$
$563$	−5.58028	−	19.0047i	−0.235181	−	0.800952i	0.754330	−	0.656495i	$-0.227962\pi$
$564$	4.89902	+	5.62951i	0.206286	+	0.237045i
$565$	36.2218	+	16.5419i	1.52386	+	0.695924i
$566$	0.791256	−	20.7782i	0.0332590	−	0.873374i
$567$	−23.1779	+	21.2238i	−0.973381	+	0.891314i
$568$	33.7682	+	3.87277i	1.41688	+	0.162498i
$569$	29.7838	−	19.1409i	1.24860	−	0.802429i	0.261922	−	0.965089i	$-0.415644\pi$
$569$	29.7838	−	19.1409i	1.24860	−	0.802429i	0.986682	+	0.162660i	$0.0520074\pi$
$570$	30.0970	−	15.2349i	1.26063	−	0.638121i
$571$	32.4924	+	20.8816i	1.35977	+	0.873869i	0.998287	−	0.0585112i	$-0.0186353\pi$
$571$	32.4924	+	20.8816i	1.35977	+	0.873869i	0.361480	+	0.932380i	$0.382272\pi$
$572$	0.972592	−	0.525124i	0.0406661	−	0.0219565i
$573$	−6.27235	+	3.48099i	−0.262031	+	0.145420i
$574$	−5.39929	−	0.987317i	−0.225362	−	0.0412098i
$575$	3.45448	+	1.26296i	0.144062	+	0.0526690i
$576$	21.0697	−	11.4921i	0.877903	−	0.478839i
$577$	−28.8488	−	8.47077i	−1.20099	−	0.352643i	−0.380760	−	0.924674i	$-0.624337\pi$
$577$	−28.8488	−	8.47077i	−1.20099	−	0.352643i	−0.820232	+	0.572031i	$0.806156\pi$
$578$	2.88468	−	2.31340i	0.119987	−	0.0962248i
$579$	34.9719	−	7.85911i	1.45338	−	0.326614i
$580$	28.8590	+	15.9357i	1.19830	+	0.661693i
$581$	−0.700741	+	0.450339i	−0.0290717	+	0.0186832i
$582$	2.09809	−	3.57262i	0.0869687	−	0.148090i
$583$	−0.323698	−	0.373568i	−0.0134062	−	0.0154716i
$584$	0.621386	−	1.47059i	0.0257131	−	0.0608534i
$585$	5.08218	+	2.23727i	0.210122	+	0.0924997i
$586$	2.72763	+	25.9474i	0.112678	+	1.07188i
$587$	−37.8842	+	11.1238i	−1.56365	+	0.459129i	−0.945145	−	0.326652i	$-0.894079\pi$
$587$	−37.8842	+	11.1238i	−1.56365	+	0.459129i	−0.618505	+	0.785781i	$0.712261\pi$
$588$	−0.0383019	−	17.9903i	−0.00157954	−	0.741910i
$589$	3.01350	+	20.9594i	0.124169	+	0.863616i
$590$	−30.2439	+	17.8480i	−1.24512	+	0.734793i
$591$	1.68206	+	0.614274i	0.0691905	+	0.0252679i
$592$	−24.3357	−	3.73402i	−1.00019	−	0.153467i
$593$	20.4769	+	2.94414i	0.840887	+	0.120901i	0.549281	−	0.835637i	$-0.314902\pi$
$593$	20.4769	+	2.94414i	0.840887	+	0.120901i	0.291605	+	0.956539i	$0.405811\pi$
$594$	−5.26133	+	0.283864i	−0.215875	+	0.0116471i
$595$	20.8278	−	24.0366i	0.853856	−	0.985403i
$596$	13.1146	−	17.3476i	0.537195	−	0.710584i
$597$	21.8652	+	21.5675i	0.894885	+	0.882700i
$598$	−2.99912	−	4.28167i	−0.122643	−	0.175091i
$599$		−	2.58196i		−	0.105496i	−0.998608	−	0.0527481i	$-0.983202\pi$
$599$		−	2.58196i		−	0.105496i	0.998608	−	0.0527481i	$-0.0167980\pi$
$600$	−3.75480	−	0.134981i	−0.153289	−	0.00551059i
$601$	−7.37235	+	8.50814i	−0.300724	+	0.347054i	−0.885920	−	0.463838i	$-0.846472\pi$
$601$	−7.37235	+	8.50814i	−0.300724	+	0.347054i	0.585196	+	0.810892i	$0.301018\pi$
$602$	9.71875	−	10.3893i	0.396107	−	0.423438i
$603$	−46.4753	−	6.03308i	−1.89262	−	0.245686i
$604$	−45.8483	+	9.74701i	−1.86554	+	0.396600i
$605$	−22.9057	+	10.4607i	−0.931249	+	0.425287i
$606$	−21.1256	−	5.29104i	−0.858170	−	0.214934i
$607$	−4.93983	−	34.3573i	−0.200501	−	1.39452i	−0.802800	−	0.596248i	$-0.796658\pi$
$607$	−4.93983	−	34.3573i	−0.200501	−	1.39452i	0.602299	−	0.798271i	$-0.294252\pi$
$608$	31.5252	−	7.65082i	1.27852	−	0.310282i
$609$	−36.5713	−	19.6452i	−1.48194	−	0.796064i
$610$	−3.45352	−	32.8525i	−0.139829	−	1.33016i
$611$	−0.689774	+	1.51040i	−0.0279053	+	0.0611041i
$612$	−22.2793	−	4.63735i	−0.900586	−	0.187454i
$613$	−1.95844	−	2.26016i	−0.0791008	−	0.0912871i	0.714820	−	0.699309i	$-0.246509\pi$
$613$	−1.95844	−	2.26016i	−0.0791008	−	0.0912871i	−0.793920	+	0.608022i	$0.791963\pi$
$614$	−23.3084	+	5.89050i	−0.940652	+	0.237721i
$615$	0.951727	−	4.52410i	0.0383774	−	0.182429i
$616$	4.48252	−	5.48247i	0.180606	−	0.220895i
$617$	1.92231	+	1.23539i	0.0773893	+	0.0497351i	0.578763	−	0.815496i	$-0.303536\pi$
$617$	1.92231	+	1.23539i	0.0773893	+	0.0497351i	−0.501374	+	0.865231i	$0.667172\pi$
$618$	39.5879	+	4.07635i	1.59246	+	0.163975i
$619$	−32.4899	−	9.53990i	−1.30588	−	0.383441i	−0.446503	−	0.894782i	$-0.647331\pi$
$619$	−32.4899	−	9.53990i	−1.30588	−	0.383441i	−0.859378	+	0.511341i	$0.829149\pi$
$620$	6.27595	−	16.5867i	0.252048	−	0.666137i
$621$	4.21251	+	24.5612i	0.169042	+	0.985609i
$622$	2.41473	−	13.2053i	0.0968217	−	0.529484i
$623$	2.70660	−	9.21783i	0.108438	−	0.369304i
$624$	4.26656	+	3.21123i	0.170799	+	0.128552i
$625$	−23.7625	−	15.2712i	−0.950499	−	0.610848i
$626$	44.1586	+	14.8134i	1.76493	+	0.592062i
$627$	−6.96944	−	1.46615i	−0.278333	−	0.0585524i
$628$	0.935106	+	14.0042i	0.0373148	+	0.558827i
$629$	15.2878	+	17.6431i	0.609566	+	0.703476i
$630$	35.5666	+	0.866351i	1.41701	+	0.0345163i
$631$	40.6428	+	18.5609i	1.61796	+	0.738900i	0.998920	−	0.0464563i	$-0.0147928\pi$
$631$	40.6428	+	18.5609i	1.61796	+	0.738900i	0.619044	+	0.785356i	$0.287520\pi$
$632$	3.85326	−	14.6624i	0.153274	−	0.583239i
$633$	11.6498	+	6.25800i	0.463038	+	0.248733i
$634$	11.8420	−	16.9701i	0.470308	−	0.673967i
$635$	4.47808	−	0.643850i	0.177707	−	0.0255504i
$636$	0.987424	−	2.17440i	0.0391539	−	0.0862204i
$637$	3.64113	−	1.66285i	0.144267	−	0.0658844i
$638$	−2.64831	−	6.43655i	−0.104848	−	0.254826i
$639$	4.64099	−	35.7514i	0.183595	−	1.41430i
$640$	−26.2106	−	7.15359i	−1.03606	−	0.282770i
$641$	−0.214315	+	0.247333i	−0.00846495	+	0.00976907i	−0.759966	−	0.649963i	$-0.774785\pi$
$641$	−0.214315	+	0.247333i	−0.00846495	+	0.00976907i	0.751501	+	0.659732i	$0.229330\pi$
$642$	−12.0259	−	35.5978i	−0.474626	−	1.40493i
$643$	11.0132			0.434317			0.217159	−	0.976136i	$-0.430321\pi$
$643$	11.0132			0.434317			0.217159	+	0.976136i	$0.430321\pi$
$644$	−28.2082	−	18.0579i	−1.11156	−	0.711580i
$645$	8.53091	+	8.41475i	0.335904	+	0.331331i
$646$	−27.4737	−	13.8336i	−1.08094	−	0.544276i
$647$	−4.55055	−	3.94308i	−0.178901	−	0.155018i	0.560807	−	0.827946i	$-0.310491\pi$
$647$	−4.55055	−	3.94308i	−0.178901	−	0.155018i	−0.739708	+	0.672928i	$0.765036\pi$
$648$	−11.8549	−	22.5269i	−0.465703	−	0.884941i
$649$	7.33878	+	1.05516i	0.288072	+	0.0414186i
$650$	−0.318090	−	0.773100i	−0.0124765	−	0.0303235i
$651$	−7.66074	+	20.9773i	−0.300248	+	0.822164i
$652$	42.1779	−	15.5049i	1.65181	−	0.607219i
$653$	0.204414	+	1.42173i	0.00799935	+	0.0556367i	0.993430	−	0.114440i	$-0.0365075\pi$
$653$	0.204414	+	1.42173i	0.00799935	+	0.0556367i	−0.985431	+	0.170077i	$0.945598\pi$
$654$	−0.621648	−	3.35914i	−0.0243084	−	0.131353i
$655$	−5.36730	−	18.2793i	−0.209718	−	0.714233i
$656$	1.88504	−	4.02652i	0.0735985	−	0.157209i
$657$	−1.54980	−	0.682251i	−0.0604634	−	0.0266171i
$658$	−0.404833	+	10.6308i	−0.0157820	+	0.414433i
$659$	−6.23597	+	5.40350i	−0.242919	+	0.210491i	−0.767808	−	0.640680i	$-0.778652\pi$
$659$	−6.23597	+	5.40350i	−0.242919	+	0.210491i	0.524889	+	0.851171i	$0.324107\pi$
$660$	4.51618	+	3.89649i	0.175792	+	0.151671i
$661$	2.78196	−	1.78785i	0.108206	−	0.0695395i	−0.485419	−	0.874282i	$-0.661333\pi$
$661$	2.78196	−	1.78785i	0.108206	−	0.0695395i	0.593624	+	0.804742i	$0.297697\pi$
$662$	−26.6229	−	8.93086i	−1.03473	−	0.347108i
$663$	−1.11019	−	4.94017i	−0.0431161	−	0.191860i
$664$	−0.208529	−	0.641672i	−0.00809248	−	0.0249017i
$665$	46.1410	+	13.5482i	1.78927	+	0.525377i
$666$	−4.34475	+	25.7500i	−0.168356	+	0.997794i
$667$	−28.7883	+	15.9632i	−1.11469	+	0.618098i
$668$	−15.8182	+	41.8057i	−0.612023	+	1.61751i
$669$	23.5448	−	13.0668i	0.910296	−	0.505190i
$670$	33.1920	+	41.3885i	1.28232	+	1.59898i
$671$	−3.77057	+	5.86712i	−0.145561	+	0.226498i
$672$	33.1084	+	8.62552i	1.27718	+	0.332737i
$673$	15.7978	−	10.1526i	0.608960	−	0.391355i	−0.199507	−	0.979896i	$-0.563934\pi$
$673$	15.7978	−	10.1526i	0.608960	−	0.391355i	0.808467	+	0.588542i	$0.200298\pi$
$674$	−6.40711	+	1.61920i	−0.246793	+	0.0623693i
$675$	−0.202503	+	3.97999i	−0.00779435	+	0.153190i
$676$	5.38865	−	24.2196i	0.207256	−	0.931524i
$677$	31.7407	+	14.4955i	1.21990	+	0.557108i	0.918132	−	0.396275i	$-0.129697\pi$
$677$	31.7407	+	14.4955i	1.21990	+	0.557108i	0.301764	+	0.953383i	$0.402425\pi$
$678$	25.3435	−	31.7402i	0.973313	−	1.21897i
$679$	5.66705	−	1.66400i	0.217482	−	0.0638583i
$680$	14.5422	+	21.2649i	0.557668	+	0.815473i
$681$	9.62212	−	13.0390i	0.368720	−	0.499655i
$682$	−3.22455	+	1.90293i	−0.123474	+	0.0728669i
$683$	14.3059	+	31.3256i	0.547401	+	1.19864i	0.957985	+	0.286818i	$0.0925974\pi$
$683$	14.3059	+	31.3256i	0.547401	+	1.19864i	−0.410585	+	0.911823i	$0.634675\pi$
$684$	−7.61572	−	33.5548i	−0.291194	−	1.28300i
$685$	30.4112	+	4.37246i	1.16195	+	0.167063i
$686$	−6.09477	+	6.51531i	−0.232699	+	0.248756i
$687$	−0.685860	−	8.74660i	−0.0261672	−	0.333704i
$688$	6.13812	+	9.75254i	0.234014	+	0.371812i
$689$	0.531351			0.0202429
$690$	15.8336	−	23.3481i	0.602774	−	0.888848i
$691$			24.7610i			0.941952i	0.882146	+	0.470976i	$0.156098\pi$
$691$			24.7610i			0.941952i	−0.882146	+	0.470976i	$0.843902\pi$
$692$	31.2404	+	23.6175i	1.18758	+	0.897801i
$693$	−5.74354	−	4.84056i	−0.218179	−	0.183878i
$694$	29.1050	+	27.2263i	1.10481	+	1.03350i
$695$	6.61112	−	45.9814i	0.250774	−	1.74417i
$696$	22.9191	−	24.6053i	0.868746	−	0.932662i
$697$	−3.83466	+	1.75123i	−0.145248	+	0.0663326i
$698$	9.97387	−	5.88595i	0.377516	−	0.222787i
$699$	23.1282	−	31.3411i	0.874787	−	1.18543i
$700$	−3.76944	−	3.80523i	−0.142471	−	0.143824i
$701$	−4.51368	−	15.3722i	−0.170479	−	0.580599i	−0.999763	−	0.0217714i	$-0.993069\pi$
$701$	−4.51368	−	15.3722i	−0.170479	−	0.580599i	0.829284	−	0.558828i	$-0.188749\pi$
$702$	3.47308	−	4.47411i	0.131083	−	0.168865i
$703$	−14.6632	+	32.1080i	−0.553034	+	1.21098i
$704$	3.37210	+	4.64029i	0.127091	+	0.174888i
$705$	−8.94196	−	0.577965i	−0.336774	−	0.0217674i
$706$	31.1334	−	7.86803i	1.17172	−	0.296117i
$707$	−16.7848	−	26.1176i	−0.631257	−	0.982255i
$708$	10.1649	+	34.3476i	0.382019	+	1.29086i
$709$	2.81185	+	1.80707i	0.105601	+	0.0678659i	0.592376	−	0.805662i	$-0.298190\pi$
$709$	2.81185	+	1.80707i	0.105601	+	0.0678659i	−0.486774	+	0.873528i	$0.661827\pi$
$710$	−31.8384	+	25.5331i	−1.19487	+	0.958242i
$711$	−15.4892	−	4.31830i	−0.580890	−	0.161949i
$712$	6.66399	+	4.01806i	0.249743	+	0.150583i
$713$	10.7040	+	14.1069i	0.400868	+	0.528309i
$714$	−18.6215	−	26.5645i	−0.696891	−	0.994152i
$715$	−0.373904	+	1.27340i	−0.0139832	+	0.0476225i
$716$	22.7719	−	12.2951i	0.851026	−	0.459488i
$717$	−3.08594	−	13.7320i	−0.115247	−	0.512831i
$718$	−1.61718	+	4.82080i	−0.0603526	+	0.179911i
$719$	0.448956	+	0.698589i	0.0167432	+	0.0260530i	0.849524	−	0.527550i	$-0.176889\pi$
$719$	0.448956	+	0.698589i	0.0167432	+	0.0260530i	−0.832781	+	0.553602i	$0.813253\pi$
$720$	−8.00098	+	27.6844i	−0.298179	+	1.03174i
$721$	37.1525	+	42.8763i	1.38363	+	1.59680i
$722$	0.747323	−	19.6246i	0.0278125	−	0.730350i
$723$	23.3302	−	8.88435i	0.867660	−	0.330412i
$724$	−27.1604	−	2.07160i	−1.00941	−	0.0769904i
$725$	−5.05094	+	1.48309i	−0.187587	+	0.0550806i
$726$	4.67396	+	25.2562i	0.173467	+	0.937346i
$727$	2.49068	−	0.358106i	0.0923744	−	0.0132814i	−0.0959726	−	0.995384i	$-0.530596\pi$
$727$	2.49068	−	0.358106i	0.0923744	−	0.0132814i	0.188347	+	0.982103i	$0.439687\pi$
$728$	1.29849	+	7.50094i	0.0481252	+	0.278003i
$729$	−24.0781	+	12.2165i	−0.891783	+	0.452463i
$730$	0.729391	+	1.77274i	0.0269960	+	0.0656121i
$731$	1.55500	−	10.8153i	0.0575137	−	0.400017i
$732$	−33.3616	−	4.72420i	−1.23308	−	0.174612i
$733$	−13.9509	+	16.1002i	−0.515287	+	0.594673i	−0.952444	−	0.304712i	$-0.901440\pi$
$733$	−13.9509	+	16.1002i	−0.515287	+	0.594673i	0.437158	+	0.899385i	$0.355985\pi$
$734$	−10.8609	+	21.5698i	−0.400883	+	0.796157i
$735$	15.3789	+	15.1695i	0.567259	+	0.559535i
$736$	19.9538	−	18.3805i	0.735508	−	0.677516i
$737$		−	11.2011i		−	0.412597i
$738$	−4.24050	−	2.06281i	−0.156095	−	0.0759331i
$739$	−28.1559	−	24.3972i	−1.03573	−	0.897467i	−0.0409168	−	0.999163i	$-0.513028\pi$
$739$	−28.1559	−	24.3972i	−1.03573	−	0.897467i	−0.994816	+	0.101695i	$0.967573\pi$
$740$	23.7494	−	17.6041i	0.873045	−	0.647139i
$741$	6.09720	−	4.62986i	0.223986	−	0.170082i
$742$	3.14831	−	1.29537i	0.115578	−	0.0475544i
$743$	6.12727	+	13.4168i	0.224788	+	0.492216i	0.988100	−	0.153813i	$-0.0491555\pi$
$743$	6.12727	+	13.4168i	0.224788	+	0.492216i	−0.763312	+	0.646030i	$0.776428\pi$
$744$	−14.8563	−	10.3201i	−0.544660	−	0.378353i
$745$	3.71614	+	25.8463i	0.136149	+	0.946935i
$746$	−28.9798	+	41.5290i	−1.06102	+	1.52048i
$747$	−0.683816	+	0.211011i	−0.0250195	+	0.00772048i
$748$	0.413646	−	5.42326i	0.0151244	−	0.198294i
$749$	22.2515	−	48.7239i	0.813051	−	1.78033i
$750$	−18.1479	+	17.0491i	−0.662668	+	0.622546i
$751$	25.8087	−	22.3633i	0.941771	−	0.816049i	−0.0413237	−	0.999146i	$-0.513157\pi$
$751$	25.8087	−	22.3633i	0.941771	−	0.816049i	0.983095	+	0.183096i	$0.0586120\pi$
$752$	−8.24480	−	2.50577i	−0.300657	−	0.0913760i
$753$	6.43907	+	1.35458i	0.234653	+	0.0493635i
$754$	7.09330	+	2.37951i	0.258323	+	0.0866565i
$755$	30.4280	−	47.3469i	1.10739	−	1.72313i
$756$	9.67105	−	34.9765i	0.351733	−	1.27208i
$757$	−37.9194	−	11.1341i	−1.37820	−	0.404677i	−0.493061	−	0.869995i	$-0.664122\pi$
$757$	−37.9194	−	11.1341i	−1.37820	−	0.404677i	−0.885144	+	0.465317i	$0.845940\pi$
$758$	−25.0279	−	4.57661i	−0.909054	−	0.166230i
$759$	−5.69183	+	1.75414i	−0.206600	+	0.0636711i
$760$	−20.1129	+	33.3574i	−0.729572	+	1.21000i
$761$	−10.0965	+	34.3855i	−0.365998	+	1.24647i	0.546523	+	0.837444i	$0.315951\pi$
$761$	−10.0965	+	34.3855i	−0.365998	+	1.24647i	−0.912521	+	0.409031i	$0.865867\pi$
$762$	0.472668	−	4.59037i	0.0171230	−	0.166291i
$763$	2.63291	−	4.09689i	0.0953178	−	0.148317i
$764$	4.00407	−	7.25123i	0.144862	−	0.262340i
$765$	22.7822	−	15.0865i	0.823693	−	0.545454i
$766$	4.71240	+	18.6467i	0.170266	+	0.673734i
$767$	−6.02331	+	5.21923i	−0.217489	+	0.188455i
$768$	−13.5734	+	24.1612i	−0.489788	+	0.871842i
$769$	14.4343	+	6.59190i	0.520513	+	0.237710i	0.658305	−	0.752751i	$-0.271274\pi$
$769$	14.4343	+	6.59190i	0.520513	+	0.237710i	−0.137793	+	0.990461i	$0.544001\pi$
$770$	0.888968	+	8.45656i	0.0320362	+	0.304753i
$771$	−3.12464	−	1.67848i	−0.112531	−	0.0604490i
$772$	−29.4046	+	29.1280i	−1.05829	+	1.04834i
$773$	14.7981	−	2.12765i	0.532251	−	0.0765261i	0.129051	−	0.991638i	$-0.458807\pi$
$773$	14.7981	−	2.12765i	0.532251	−	0.0765261i	0.403200	+	0.915112i	$0.367898\pi$
$774$	10.4400	−	6.35559i	0.375258	−	0.228447i
$775$	1.17640	+	2.57595i	0.0422575	+	0.0925310i
$776$	0.136862	+	4.78212i	0.00491308	+	0.171668i
$777$	−29.6483	+	22.5132i	−1.06363	+	0.807655i
$778$	−5.90563	+	6.31312i	−0.211727	+	0.226336i
$779$	−4.81715	−	4.17408i	−0.172592	−	0.149552i
$780$	−6.34463	+	0.926012i	−0.227174	+	0.0331565i
$781$	8.61650			0.308323
$782$	−25.7036	+	1.02437i	−0.919159	+	0.0366314i
$783$	−25.7327	−	24.6956i	−0.919612	−	0.882548i
$784$	11.0653	+	17.5812i	0.395191	+	0.627898i
$785$	−12.7363	−	11.0361i	−0.454579	−	0.393895i
$786$	−19.4165	+	0.780801i	−0.692563	+	0.0278502i
$787$	−3.38395	+	23.5359i	−0.120625	+	0.838964i	0.836226	+	0.548385i	$0.184757\pi$
$787$	−3.38395	+	23.5359i	−0.120625	+	0.838964i	−0.956851	+	0.290579i	$0.906152\pi$
$788$	−2.02254	+	0.429976i	−0.0720498	+	0.0153173i
$789$	−44.0198	−	16.0757i	−1.56715	−	0.572310i
$790$	9.25157	+	15.6770i	0.329156	+	0.557762i
$791$	57.3126	−	8.24031i	2.03780	−	0.292992i
$792$	4.97452	−	3.50291i	0.176762	−	0.124471i
$793$	−2.11215	−	7.19333i	−0.0750047	−	0.255443i
$794$	−1.02402	−	9.74128i	−0.0363411	−	0.345705i
$795$	1.02046	+	2.67972i	0.0361920	+	0.0950398i
$796$	−34.6171	−	7.70198i	−1.22697	−	0.272990i
$797$	20.5925	−	17.8435i	0.729424	−	0.632049i	−0.208848	−	0.977948i	$-0.566971\pi$
$797$	20.5925	−	17.8435i	0.729424	−	0.632049i	0.938272	+	0.345899i	$0.112426\pi$
$798$	24.8395	−	42.2966i	0.879310	−	1.49728i
$799$	4.41746	+	6.87371i	0.156279	+	0.243174i
$800$	3.75703	−	2.16956i	0.132831	−	0.0767055i
$801$	4.36666	−	7.00393i	0.154288	−	0.247472i
$802$	−39.4023	+	31.5991i	−1.39134	+	1.11580i
$803$	0.114021	−	0.388321i	0.00402372	−	0.0137035i
$804$	49.1770	−	22.5850i	1.73434	−	0.796513i
$805$	39.2406	−	8.80357i	1.38305	−	0.310285i
$806$	0.723976	−	3.95917i	0.0255010	−	0.139456i
$807$	−3.58254	+	1.98821i	−0.126111	+	0.0699883i
$808$	23.9160	−	7.77216i	0.841363	−	0.273424i
$809$	6.40027	−	9.95901i	0.225021	−	0.350140i	−0.710325	−	0.703874i	$-0.751452\pi$
$809$	6.40027	−	9.95901i	0.225021	−	0.350140i	0.935346	+	0.353734i	$0.115088\pi$
$810$	29.2340	+	8.92296i	1.02718	+	0.313521i
$811$	−2.50716	−	3.90121i	−0.0880382	−	0.136990i	0.794441	−	0.607341i	$-0.207764\pi$
$811$	−2.50716	−	3.90121i	−0.0880382	−	0.136990i	−0.882480	+	0.470351i	$0.844127\pi$
$812$	47.8294	−	3.19373i	1.67848	−	0.112078i
$813$	−53.1089	−	3.43271i	−1.86261	−	0.120390i
$814$	−6.23689	−	0.237507i	−0.218603	−	0.00832462i
$815$	−22.4147	+	49.0814i	−0.785154	+	1.71925i
$816$	24.6442	−	9.11901i	0.862721	−	0.319229i
$817$	15.8516	−	4.65444i	0.554576	−	0.162838i
$818$	−15.1015	+	21.6409i	−0.528010	+	0.756657i
$819$	7.97559	−	1.25854i	0.278690	−	0.0439770i
$820$	1.84190	+	5.01050i	0.0643218	+	0.174974i
$821$	0.489754	+	1.07241i	0.0170925	+	0.0374274i	0.917986	−	0.396613i	$-0.129815\pi$
$821$	0.489754	+	1.07241i	0.0170925	+	0.0374274i	−0.900893	+	0.434041i	$0.857087\pi$
$822$	11.8626	−	29.0066i	0.413755	−	1.01172i
$823$	−1.64612	+	11.4490i	−0.0573801	+	0.399088i	0.940809	+	0.338937i	$0.110067\pi$
$823$	−1.64612	+	11.4490i	−0.0573801	+	0.399088i	−0.998189	+	0.0601508i	$0.980842\pi$
$824$	−41.2379	+	20.2780i	−1.43659	+	0.706416i
$825$	−0.949557	+	0.0744589i	−0.0330593	+	0.00259233i
$826$	−22.9649	+	45.6085i	−0.799051	+	1.58692i
$827$		−	15.0802i		−	0.524391i	−0.965015	−	0.262195i	$-0.915553\pi$
$827$		−	15.0802i		−	0.524391i	0.965015	−	0.262195i	$-0.0844465\pi$
$828$	−19.1779	−	21.4524i	−0.666480	−	0.745523i
$829$		−	16.7740i		−	0.582583i	−0.956634	−	0.291292i	$-0.905915\pi$
$829$		−	16.7740i		−	0.582583i	0.956634	−	0.291292i	$-0.0940850\pi$
$830$	0.723583	+	0.364340i	0.0251159	+	0.0126464i
$831$	−20.6417	+	1.61861i	−0.716053	+	0.0561489i
$832$	−6.14353	−	0.527026i	−0.212989	−	0.0182714i
$833$	2.80324	−	19.4969i	0.0971264	−	0.675529i
$834$	−43.8577	−	17.9361i	−1.51867	−	0.621076i
$835$	−22.2954	−	48.8201i	−0.771564	−	1.68949i
$836$	7.71874	−	2.83747i	0.266958	−	0.0981359i
$837$	−11.1797	+	15.5927i	−0.386428	+	0.538961i
$838$	−17.2103	−	12.0097i	−0.594521	−	0.414869i
$839$	16.9299	−	4.97108i	0.584487	−	0.171621i	0.0238969	−	0.999714i	$-0.492393\pi$
$839$	16.9299	−	4.97108i	0.584487	−	0.171621i	0.560590	+	0.828094i	$0.310574\pi$
$840$	−35.3351	+	20.9541i	−1.21918	+	0.722986i
$841$	7.52431	−	16.4759i	0.259459	−	0.568136i
$842$	−1.26340	+	33.1767i	−0.0435397	+	1.14334i
$843$	29.8791	+	1.93124i	1.02909	+	0.0665155i
$844$	−15.2361	+	1.01737i	−0.524449	+	0.0350192i
$845$	16.1069	+	25.0628i	0.554093	+	0.862185i
$846$	−2.78779	+	8.70435i	−0.0958463	+	0.299262i
$847$	−19.7959	+	30.8031i	−0.680196	+	1.05841i
$848$	0.366626	+	2.73306i	0.0125900	+	0.0938535i
$849$	22.2672	−	12.3577i	0.764209	−	0.424115i
$850$	−4.04663	−	0.739969i	−0.138798	−	0.0253807i
$851$	2.29705	+	29.4295i	0.0787418	+	1.00883i
$852$	17.3737	+	37.8298i	0.595213	+	1.29603i
$853$	−8.64134	+	29.4297i	−0.295874	+	1.00765i	0.668632	+	0.743593i	$0.266880\pi$
$853$	−8.64134	+	29.4297i	−0.295874	+	1.00765i	−0.964506	+	0.264060i	$0.914938\pi$
$854$	−30.0511	−	37.4720i	−1.02833	−	1.28227i
$855$	35.0590	+	21.8578i	1.19899	+	0.747522i
$856$	33.5891	+	27.4628i	1.14805	+	0.938658i
$857$	−18.5480	−	28.8612i	−0.633587	−	0.985881i	−0.998495	−	0.0548372i	$-0.982536\pi$
$857$	−18.5480	−	28.8612i	−0.633587	−	0.985881i	0.364908	−	0.931043i	$-0.381100\pi$
$858$	1.16730	+	0.685522i	0.0398510	+	0.0234033i
$859$	−31.3471	+	27.1624i	−1.06955	+	0.926769i	−0.997502	−	0.0706328i	$-0.977498\pi$
$859$	−31.3471	+	27.1624i	−1.06955	+	0.926769i	−0.0720455	+	0.997401i	$0.522953\pi$
$860$	−13.5061	−	3.00499i	−0.460556	−	0.102469i
$861$	−2.39236	−	6.28230i	−0.0815313	−	0.214100i
$862$	−37.5065	+	3.94275i	−1.27748	+	0.134291i
$863$	6.49391	+	22.1162i	0.221055	+	0.752845i	0.993099	+	0.117276i	$0.0374163\pi$
$863$	6.49391	+	22.1162i	0.221055	+	0.752845i	−0.772044	+	0.635569i	$0.780766\pi$
$864$	25.4094	+	14.7771i	0.864446	+	0.502726i
$865$	−46.5454	+	6.69221i	−1.58259	+	0.227542i
$866$	37.4116	−	22.0780i	1.27130	−	0.750241i
$867$	4.25398	+	1.55352i	0.144473	+	0.0527604i
$868$	−5.36232	−	25.2234i	−0.182009	−	0.856140i
$869$	0.546943	−	3.80407i	0.0185538	−	0.129044i
$870$	1.62232	+	40.3429i	0.0550018	+	1.36775i
$871$	9.09971	+	7.88494i	0.308332	+	0.267171i
$872$	2.66743	+	2.90606i	0.0903307	+	0.0984116i
$873$	5.07381	−	0.0695605i	0.171722	−	0.00235427i
$874$	−17.5535	−	34.7083i	−0.593755	−	1.17403i
$875$	−35.4968			−1.20001
$876$	1.93478	−	0.282385i	0.0653702	−	0.00954092i
$877$	5.37612	+	4.65843i	0.181539	+	0.157304i	0.740890	−	0.671627i	$-0.234404\pi$
$877$	5.37612	+	4.65843i	0.181539	+	0.157304i	−0.559351	+	0.828931i	$0.688950\pi$
$878$	21.4822	+	20.0956i	0.724990	+	0.678194i
$879$	−25.4487	+	19.3242i	−0.858362	+	0.651790i
$880$	−6.80785	−	1.04458i	−0.229492	−	0.0352128i
$881$	6.07634	+	13.3053i	0.204717	+	0.448268i	0.983945	−	0.178473i	$-0.0571158\pi$
$881$	6.07634	+	13.3053i	0.204717	+	0.448268i	−0.779228	+	0.626741i	$0.784388\pi$
$882$	18.8205	−	11.4574i	0.633718	−	0.385790i
$883$	−30.5860	+	4.39760i	−1.02930	+	0.147991i	−0.636216	−	0.771511i	$-0.719501\pi$
$883$	−30.5860	+	4.39760i	−1.02930	+	0.147991i	−0.393085	+	0.919502i	$0.628592\pi$
$884$	4.11465	+	4.15372i	0.138391	+	0.139705i
$885$	−37.8895	−	20.3533i	−1.27364	−	0.684169i
$886$	10.2405	−	1.07650i	0.344037	−	0.0361657i
$887$	−5.08094	−	2.32039i	−0.170601	−	0.0779110i	0.328284	−	0.944579i	$-0.393530\pi$
$887$	−5.08094	−	2.32039i	−0.170601	−	0.0779110i	−0.498885	+	0.866668i	$0.666257\pi$
$888$	−11.5329	−	27.8612i	−0.387018	−	0.934962i
$889$	4.97167	−	4.30797i	0.166744	−	0.144485i
$890$	−9.05876	+	2.28933i	−0.303650	+	0.0767384i
$891$	−3.63636	−	5.33106i	−0.121823	−	0.178597i
$892$	−15.0303	+	27.2193i	−0.503251	+	0.911370i
$893$	−6.67919	+	10.3930i	−0.223511	+	0.347789i
$894$	26.4944	+	2.72812i	0.886105	+	0.0912419i
$895$	−8.75445	+	29.8149i	−0.292629	+	0.996603i
$896$	−37.6859	+	11.8545i	−1.25900	+	0.396030i
$897$	2.58169	−	5.85884i	0.0862000	−	0.195621i
$898$	5.39940	−	29.5274i	0.180180	−	0.985343i
$899$	−24.3177	−	7.14032i	−0.811040	−	0.238143i
$900$	−2.24152	−	4.01879i	−0.0747174	−	0.133960i
$901$	1.41361	−	2.19962i	0.0470942	−	0.0732800i
$902$	0.358451	−	1.06854i	0.0119351	−	0.0355785i
$903$	17.0506	+	3.58691i	0.567409	+	0.119365i
$904$	−5.34382	+	46.5949i	−0.177733	+	1.54972i
$905$	24.7182	−	21.4185i	0.821661	−	0.711974i
$906$	−39.3067	−	41.8400i	−1.30588	−	1.39004i
$907$	6.08409	−	13.3223i	0.202019	−	0.442359i	−0.781323	−	0.624127i	$-0.785455\pi$
$907$	6.08409	−	13.3223i	0.202019	−	0.442359i	0.983341	+	0.181768i	$0.0581819\pi$
$908$	−1.42307	+	18.6577i	−0.0472262	+	0.619177i
$909$	−7.86468	−	25.4868i	−0.260855	−	0.845344i
$910$	−7.49586	−	5.23076i	−0.248485	−	0.173398i
$911$	4.11376	+	28.6119i	0.136295	+	0.947953i	0.937108	+	0.349039i	$0.113492\pi$
$911$	4.11376	+	28.6119i	0.136295	+	0.947953i	−0.800813	+	0.598914i	$0.795599\pi$
$912$	28.0211	+	28.1670i	0.927872	+	0.932702i
$913$	−0.0710528	−	0.155584i	−0.00235150	−	0.00514908i
$914$	−13.2326	−	32.1610i	−0.437695	−	1.06379i
$915$	32.2211	−	24.4668i	1.06520	−	0.808848i
$916$	6.03272	+	8.13865i	0.199327	+	0.268909i
$917$	−20.9356	−	18.1408i	−0.691355	−	0.599063i
$918$	−9.28156	−	26.2804i	−0.306337	−	0.867382i
$919$			19.5058i			0.643438i	0.946835	+	0.321719i	$0.104261\pi$
$919$			19.5058i			0.643438i	−0.946835	+	0.321719i	$0.895739\pi$
$920$	−1.18198	+	32.5533i	−0.0389688	+	1.07325i
$921$	−20.9625	−	20.6771i	−0.690739	−	0.681334i
$922$	39.1695	+	19.7227i	1.28998	+	0.649534i
$923$	−6.06554	+	7.00001i	−0.199650	+	0.230408i
$924$	8.58760	+	1.21605i	0.282511	+	0.0400053i
$925$	−0.671814	+	4.67257i	−0.0220891	+	0.153633i
$926$	32.1510	−	13.2285i	1.05655	−	0.434715i
$927$	20.8538	+	44.0550i	0.684929	+	1.44696i
$928$	−7.34494	+	38.1269i	−0.241109	+	1.25158i
$929$	−21.4765	+	3.08785i	−0.704621	+	0.101309i	−0.485305	−	0.874345i	$-0.661291\pi$
$929$	−21.4765	+	3.08785i	−0.704621	+	0.101309i	−0.219315	+	0.975654i	$0.570382\pi$
$930$	21.3573	−	3.95242i	0.700335	−	0.129605i
$931$	28.5760	−	8.39068i	0.936542	−	0.274993i
$932$	−3.42056	+	44.8464i	−0.112044	+	1.46899i
$933$	15.3649	−	5.85110i	0.503025	−	0.191556i
$934$	8.42996	+	0.321021i	0.275837	+	0.0105041i
$935$	4.27673	+	4.93561i	0.139864	+	0.161412i
$936$	−0.656041	+	6.50715i	−0.0214434	+	0.212693i
$937$	12.9980	+	20.2252i	0.424625	+	0.660729i	0.985983	−	0.166844i	$-0.0533575\pi$
$937$	12.9980	+	20.2252i	0.424625	+	0.660729i	−0.561359	+	0.827573i	$0.689721\pi$
$938$	73.1391	+	24.5351i	2.38808	+	0.801101i
$939$	12.5076	+	55.6569i	0.408169	+	1.81629i
$940$	9.10453	−	4.91574i	0.296957	−	0.160334i
$941$	−6.03993	+	20.5701i	−0.196896	+	0.670566i	0.800558	+	0.599255i	$0.204536\pi$
$941$	−6.03993	+	20.5701i	−0.196896	+	0.670566i	−0.997454	+	0.0713110i	$0.977282\pi$
$942$	−14.0758	+	9.86702i	−0.458615	+	0.321485i
$943$	−5.21590	−	1.09922i	−0.169853	−	0.0357955i
$944$	−31.0016	−	27.3803i	−1.00902	−	0.891152i
$945$	21.6642	+	37.8056i	0.704737	+	1.22982i
$946$	1.82760	+	2.27891i	0.0594204	+	0.0740939i
$947$	4.13582	+	2.65793i	0.134396	+	0.0863710i	0.606111	−	0.795380i	$-0.292729\pi$
$947$	4.13582	+	2.65793i	0.134396	+	0.0863710i	−0.471715	+	0.881751i	$0.656365\pi$
$948$	17.8042	−	5.26898i	0.578253	−	0.171128i
$949$	0.235206	+	0.365987i	0.00763510	+	0.0118804i
$950$	−1.52399	−	6.03035i	−0.0494447	−	0.195650i
$951$	25.2914	+	1.63471i	0.820129	+	0.0530092i
$952$	34.5060	+	14.5802i	1.11834	+	0.472548i
$953$	5.15630	−	11.2907i	0.167029	−	0.365742i	−0.807546	−	0.589805i	$-0.799205\pi$
$953$	5.15630	−	11.2907i	0.167029	−	0.365742i	0.974575	+	0.224062i	$0.0719320\pi$
$954$	2.90432	−	0.345622i	0.0940307	−	0.0111899i
$955$	2.80209	+	9.54305i	0.0906736	+	0.308806i
$956$	11.4373	+	11.5459i	0.369910	+	0.373422i
$957$	5.06154	−	6.85893i	0.163616	−	0.221718i
$958$	5.34592	+	9.05877i	0.172719	+	0.292675i
$959$	40.6379	−	18.5587i	1.31227	−	0.599292i
$960$	−9.14075	−	31.9953i	−0.295016	−	1.03264i
$961$	2.47144	−	17.1893i	0.0797240	−	0.554493i
$962$	4.58338	−	4.89963i	0.147774	−	0.157971i
$963$	29.6563	−	35.1886i	0.955663	−	1.13394i
$964$	−17.3840	+	22.9950i	−0.559901	+	0.740619i
$965$		−	49.6970i		−	1.59980i
$966$	1.01365	−	41.0080i	0.0326137	−	1.31941i
$967$	−0.871094			−0.0280125			−0.0140062	−	0.999902i	$-0.504458\pi$
$967$	−0.871094			−0.0280125			−0.0140062	+	0.999902i	$0.504458\pi$
$968$	−20.0555	−	21.8496i	−0.644608	−	0.702274i
$969$	−2.94507	−	37.5577i	−0.0946092	−	1.20653i
$970$	−4.19500	−	3.92423i	−0.134693	−	0.125999i
$971$	−0.524812	−	0.0754566i	−0.0168420	−	0.00242152i	0.133889	−	0.990996i	$-0.457254\pi$
$971$	−0.524812	−	0.0754566i	−0.0168420	−	0.00242152i	−0.150731	+	0.988575i	$0.548163\pi$
$972$	16.0733	−	26.7142i	0.515552	−	0.856858i
$973$	−28.0606	−	61.4441i	−0.899580	−	1.96981i
$974$	7.96779	+	13.5016i	0.255304	+	0.432619i
$975$	0.607946	−	0.823832i	0.0194699	−	0.0263837i
$976$	35.5422	−	15.8274i	1.13768	−	0.506622i
$977$	−14.4417	+	4.24048i	−0.462032	+	0.135665i	−0.504461	−	0.863435i	$-0.668309\pi$
$977$	−14.4417	+	4.24048i	−0.462032	+	0.135665i	0.0424284	+	0.999100i	$0.486491\pi$
$978$	43.0087	+	34.3411i	1.37527	+	1.09811i
$979$	1.79441	+	0.819478i	0.0573495	+	0.0261906i
$980$	−24.3479	−	5.41718i	−0.777764	−	0.173045i
$981$	3.12416	−	2.78299i	0.0997468	−	0.0888541i
$982$	−5.01220	−	19.8330i	−0.159946	−	0.632898i
$983$	−11.0864	+	7.12477i	−0.353600	+	0.227245i	−0.705366	−	0.708843i	$-0.749217\pi$
$983$	−11.0864	+	7.12477i	−0.353600	+	0.227245i	0.351767	+	0.936088i	$0.385581\pi$
$984$	5.41406	−	0.580792i	0.172594	−	0.0185150i
$985$	1.34229	−	2.08864i	0.0427689	−	0.0665497i
$986$	28.7214	−	23.0335i	0.914677	−	0.733536i
$987$	−11.3926	+	6.32261i	−0.362632	+	0.201251i
$988$	−3.12843	+	8.26810i	−0.0995285	+	0.263043i
$989$	9.70578	−	9.83268i	0.308626	−	0.312661i
$990$	−1.21543	+	7.20350i	−0.0386289	+	0.228942i
$991$	−12.0775	−	3.54628i	−0.383655	−	0.112651i	0.0842169	−	0.996447i	$-0.473161\pi$
$991$	−12.0775	−	3.54628i	−0.383655	−	0.112651i	−0.467872	+	0.883796i	$0.654979\pi$
$992$	20.8639	+	0.992063i	0.662430	+	0.0314980i
$993$	−7.54071	−	33.5551i	−0.239297	−	1.06484i
$994$	−18.8738	+	56.2628i	−0.598642	+	1.78455i
$995$	35.8222	−	23.0215i	1.13564	−	0.729831i
$996$	0.539808	−	0.625658i	0.0171045	−	0.0198247i
$997$	11.7471	−	10.1789i	0.372034	−	0.322369i	−0.448697	−	0.893684i	$-0.648112\pi$
$997$	11.7471	−	10.1789i	0.372034	−	0.322369i	0.820731	+	0.571314i	$0.193566\pi$
$998$	19.3079	+	0.735263i	0.611179	+	0.0232743i
$999$	−29.7303	+	11.7907i	−0.940625	+	0.373042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bf.a.5.13	yes	920
3.2	odd	2	inner	552.2.bf.a.5.80	yes	920
8.5	even	2	inner	552.2.bf.a.5.88	yes	920
23.14	odd	22	inner	552.2.bf.a.221.5	yes	920
24.5	odd	2	inner	552.2.bf.a.5.5	✓	920
69.14	even	22	inner	552.2.bf.a.221.88	yes	920
184.37	odd	22	inner	552.2.bf.a.221.80	yes	920
552.221	even	22	inner	552.2.bf.a.221.13	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bf.a.5.5	✓	920	24.5	odd	2	inner
552.2.bf.a.5.13	yes	920	1.1	even	1	trivial
552.2.bf.a.5.80	yes	920	3.2	odd	2	inner
552.2.bf.a.5.88	yes	920	8.5	even	2	inner
552.2.bf.a.221.5	yes	920	23.14	odd	22	inner
552.2.bf.a.221.13	yes	920	552.221	even	22	inner
552.2.bf.a.221.80	yes	920	184.37	odd	22	inner
552.2.bf.a.221.88	yes	920	69.14	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bf (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26313 - 0.636012i) q^{2} +(-0.135402 - 1.72675i) q^{3} +(1.19098 + 1.60673i) q^{4} +(-2.37700 - 0.341761i) q^{5} +(-0.927205 + 2.26722i) q^{6} +(-3.17635 + 1.45059i) q^{7} +(-0.482454 - 2.78698i) q^{8} +(-2.96333 + 0.467611i) q^{9} +O(q^{10})\)	\(q+(-1.26313 - 0.636012i) q^{2} +(-0.135402 - 1.72675i) q^{3} +(1.19098 + 1.60673i) q^{4} +(-2.37700 - 0.341761i) q^{5} +(-0.927205 + 2.26722i) q^{6} +(-3.17635 + 1.45059i) q^{7} +(-0.482454 - 2.78698i) q^{8} +(-2.96333 + 0.467611i) q^{9} +(2.78509 + 1.94349i) q^{10} +(-0.202007 - 0.687974i) q^{11} +(2.61316 - 2.27407i) q^{12} +(0.701110 + 0.320186i) q^{13} +(4.93472 + 0.187919i) q^{14} +(-0.268285 + 4.15076i) q^{15} +(-1.16315 + 3.82715i) q^{16} +(3.19070 - 2.05054i) q^{17} +(4.04047 + 1.29406i) q^{18} +(4.82433 + 3.10041i) q^{19} +(-2.28184 - 4.22623i) q^{20} +(2.93489 + 5.28834i) q^{21} +(-0.182399 + 0.997477i) q^{22} +(4.78573 + 0.311055i) q^{23} +(-4.74709 + 1.21044i) q^{24} +(0.735873 + 0.216072i) q^{25} +(-0.681948 - 0.850350i) q^{26} +(1.20869 + 5.05362i) q^{27} +(-6.11365 - 3.37591i) q^{28} +(-5.77426 + 3.71089i) q^{29} +(2.97882 - 5.07231i) q^{30} +(2.41802 + 2.79055i) q^{31} +(3.90332 - 4.09440i) q^{32} +(-1.16061 + 0.441969i) q^{33} +(-5.33443 + 0.560765i) q^{34} +(8.04594 - 2.36250i) q^{35} +(-4.28058 - 4.20436i) q^{36} +(0.875967 + 6.09248i) q^{37} +(-4.12184 - 6.98454i) q^{38} +(0.457950 - 1.25400i) q^{39} +(0.194314 + 6.78953i) q^{40} +(-1.10017 - 0.158180i) q^{41} +(-0.343682 - 8.54647i) q^{42} +(1.88655 - 2.17720i) q^{43} +(0.864801 - 1.14393i) q^{44} +(7.20366 - 0.0987602i) q^{45} +(-5.84715 - 3.43669i) q^{46} +2.15429i q^{47} +(6.76603 + 1.49027i) q^{48} +(3.40094 - 3.92489i) q^{49} +(-0.792076 - 0.740951i) q^{50} +(-3.97280 - 5.23190i) q^{51} +(0.320553 + 1.50783i) q^{52} +(0.627086 - 0.286381i) q^{53} +(1.68744 - 7.15210i) q^{54} +(0.245049 + 1.70435i) q^{55} +(5.57520 + 8.15256i) q^{56} +(4.70041 - 8.75022i) q^{57} +(9.65379 - 1.01482i) q^{58} +(-4.29555 + 9.40595i) q^{59} +(-6.98867 + 4.51240i) q^{60} +(-6.36967 - 7.35099i) q^{61} +(-1.27944 - 5.06270i) q^{62} +(8.73426 - 5.78387i) q^{63} +(-7.53448 + 2.68918i) q^{64} +(-1.55711 - 1.00070i) q^{65} +(1.74709 + 0.179897i) q^{66} +(14.9889 + 4.40115i) q^{67} +(7.09471 + 2.68445i) q^{68} +(-0.110884 - 8.30588i) q^{69} +(-11.6656 - 2.13318i) q^{70} +(-3.38562 + 11.5303i) q^{71} +(2.73289 + 8.03314i) q^{72} +(0.474838 + 0.305160i) q^{73} +(2.76844 - 8.25270i) q^{74} +(0.273463 - 1.29993i) q^{75} +(0.764148 + 11.4439i) q^{76} +(1.63961 + 1.89221i) q^{77} +(-1.37601 + 1.29269i) q^{78} +(4.87560 + 2.22661i) q^{79} +(4.07278 - 8.69962i) q^{80} +(8.56268 - 2.77137i) q^{81} +(1.28905 + 0.899522i) q^{82} +(0.236116 - 0.0339484i) q^{83} +(-5.00155 + 11.0139i) q^{84} +(-8.28511 + 3.78368i) q^{85} +(-3.76768 + 1.55021i) q^{86} +(7.18963 + 9.46824i) q^{87} +(-1.81991 + 0.894906i) q^{88} +(-1.80166 + 2.07923i) q^{89} +(-9.16194 - 4.45687i) q^{90} -2.69143 q^{91} +(5.19991 + 8.05983i) q^{92} +(4.49117 - 4.55316i) q^{93} +(1.37016 - 2.72114i) q^{94} +(-10.4078 - 9.01845i) q^{95} +(-7.59852 - 6.18567i) q^{96} +(-1.67421 - 0.240715i) q^{97} +(-6.79210 + 2.79460i) q^{98} +(0.920319 + 1.94423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9}+O(q^{10}) \) 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9	\( 920 q - 22 q^{4} - 2 q^{6} - 44 q^{7} - 18 q^{9} - 22 q^{10} - 12 q^{12} - 22 q^{15} - 30 q^{16} - 10 q^{18} - 14 q^{24} + 40 q^{25} - 22 q^{28} - 11 q^{30} - 20 q^{31} - 22 q^{33} - 18 q^{36} - 42 q^{39} - 176 q^{40} - 11 q^{42} + 90 q^{46} - 64 q^{48} + 32 q^{49} - 90 q^{52} + 21 q^{54} - 76 q^{55} - 22 q^{57} + 76 q^{58} - 11 q^{60} - 22 q^{63} - 28 q^{64} - 44 q^{66} - 116 q^{70} - 79 q^{72} - 36 q^{73} - 22 q^{76} - 134 q^{78} - 44 q^{79} - 34 q^{81} - 40 q^{82} - 165 q^{84} - 18 q^{87} - 22 q^{88} - 198 q^{90} + 88 q^{94} - 231 q^{96} - 44 q^{97}+O(q^{100}) \) 920 * q - 22 * q^4 - 2 * q^6 - 44 * q^7 - 18 * q^9 - 22 * q^10 - 12 * q^12 - 22 * q^15 - 30 * q^16 - 10 * q^18 - 14 * q^24 + 40 * q^25 - 22 * q^28 - 11 * q^30 - 20 * q^31 - 22 * q^33 - 18 * q^36 - 42 * q^39 - 176 * q^40 - 11 * q^42 + 90 * q^46 - 64 * q^48 + 32 * q^49 - 90 * q^52 + 21 * q^54 - 76 * q^55 - 22 * q^57 + 76 * q^58 - 11 * q^60 - 22 * q^63 - 28 * q^64 - 44 * q^66 - 116 * q^70 - 79 * q^72 - 36 * q^73 - 22 * q^76 - 134 * q^78 - 44 * q^79 - 34 * q^81 - 40 * q^82 - 165 * q^84 - 18 * q^87 - 22 * q^88 - 198 * q^90 + 88 * q^94 - 231 * q^96 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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