LMFDB - Embedded newform 276.2.o.a.71.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(35,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 20]))

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

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

chi := DirichletCharacter("276.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.o (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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$44$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			71.31
Character	$\chi$	$=$	276.71
Dual form			276.2.o.a.35.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.774443 + 1.18332i) q^{2} +(-1.33549 + 1.10293i) q^{3} +(-0.800475 + 1.83282i) q^{4} +(-0.168792 + 0.574851i) q^{5} +(-2.33938 - 0.726151i) q^{6} +(2.73269 + 2.36789i) q^{7} +(-2.78873 + 0.472203i) q^{8} +(0.567081 - 2.94592i) q^{9} +O(q^{10})$	\(q+(0.774443 + 1.18332i) q^{2} +(-1.33549 + 1.10293i) q^{3} +(-0.800475 + 1.83282i) q^{4} +(-0.168792 + 0.574851i) q^{5} +(-2.33938 - 0.726151i) q^{6} +(2.73269 + 2.36789i) q^{7} +(-2.78873 + 0.472203i) q^{8} +(0.567081 - 2.94592i) q^{9} +(-0.810951 + 0.245456i) q^{10} +(-2.81832 + 1.81123i) q^{11} +(-0.952452 - 3.33059i) q^{12} +(-2.47007 - 2.85062i) q^{13} +(-0.685649 + 5.06744i) q^{14} +(-0.408602 - 0.953876i) q^{15} +(-2.71848 - 2.93426i) q^{16} +(1.55064 + 0.708152i) q^{17} +(3.92512 - 1.61041i) q^{18} +(0.386731 - 0.176614i) q^{19} +(-0.918488 - 0.769519i) q^{20} +(-6.26112 - 0.148327i) q^{21} +(-4.32588 - 1.93227i) q^{22} +(-3.51470 + 3.26296i) q^{23} +(3.20352 - 3.70641i) q^{24} +(3.90430 + 2.50914i) q^{25} +(1.46025 - 5.13052i) q^{26} +(2.49181 + 4.55970i) q^{27} +(-6.52738 + 3.11311i) q^{28} +(0.0545631 + 0.0249181i) q^{29} +(0.812297 - 1.22223i) q^{30} +(7.54204 + 1.08438i) q^{31} +(1.36684 - 5.48924i) q^{32} +(1.76619 - 5.52730i) q^{33} +(0.362913 + 2.38332i) q^{34} +(-1.82244 + 1.17121i) q^{35} +(4.94541 + 3.39749i) q^{36} +(9.04804 - 2.65674i) q^{37} +(0.508491 + 0.320847i) q^{38} +(6.44280 + 1.08265i) q^{39} +(0.199268 - 1.68281i) q^{40} +(-2.14166 + 7.29381i) q^{41} +(-4.67337 - 7.52376i) q^{42} +(-3.74007 + 0.537741i) q^{43} +(-1.06366 - 6.61533i) q^{44} +(1.59775 + 0.823233i) q^{45} +(-6.58305 - 1.63203i) q^{46} +8.85011 q^{47} +(6.86680 + 0.920378i) q^{48} +(0.864497 + 6.01271i) q^{49} +(0.0545521 + 6.56322i) q^{50} +(-2.85191 + 0.764516i) q^{51} +(7.20191 - 2.24536i) q^{52} +(2.10780 + 1.82642i) q^{53} +(-3.46580 + 6.47983i) q^{54} +(-0.565477 - 1.92584i) q^{55} +(-8.73888 - 5.31303i) q^{56} +(-0.321683 + 0.662404i) q^{57} +(0.0127700 + 0.0838631i) q^{58} +(-3.59218 - 4.14560i) q^{59} +(2.07536 + 0.0146576i) q^{60} +(-1.40855 + 9.79667i) q^{61} +(4.55772 + 9.76441i) q^{62} +(8.52527 - 6.70750i) q^{63} +(7.55405 - 2.63370i) q^{64} +(2.05561 - 0.938765i) q^{65} +(7.90836 - 2.19062i) q^{66} +(4.30433 - 6.69767i) q^{67} +(-2.53916 + 2.27519i) q^{68} +(1.09504 - 8.23413i) q^{69} +(-2.79729 - 1.24949i) q^{70} +(-11.2331 - 7.21909i) q^{71} +(-0.190366 + 8.48315i) q^{72} +(-0.421746 - 0.923494i) q^{73} +(10.1510 + 8.64919i) q^{74} +(-7.98158 + 0.955240i) q^{75} +(0.0141341 + 0.850184i) q^{76} +(-11.9904 - 1.72396i) q^{77} +(3.70846 + 8.46232i) q^{78} +(-9.95979 + 8.63021i) q^{79} +(2.14562 - 1.06744i) q^{80} +(-8.35684 - 3.34115i) q^{81} +(-10.2895 + 3.11439i) q^{82} +(8.26280 - 2.42618i) q^{83} +(5.28372 - 11.3568i) q^{84} +(-0.668817 + 0.771856i) q^{85} +(-3.53279 - 4.00923i) q^{86} +(-0.100352 + 0.0269014i) q^{87} +(7.00428 - 6.38184i) q^{88} +(14.9047 - 2.14298i) q^{89} +(0.263218 + 2.52819i) q^{90} -13.6387i q^{91} +(-3.16699 - 9.05374i) q^{92} +(-11.2683 + 6.87017i) q^{93} +(6.85391 + 10.4725i) q^{94} +(0.0362499 + 0.252124i) q^{95} +(4.22885 + 8.83837i) q^{96} +(6.21222 + 1.82407i) q^{97} +(-6.44543 + 5.67948i) q^{98} +(3.73750 + 9.32965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$-1$	$-1$

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 $

$2$	0.774443	+	1.18332i	0.547614	+	0.836731i
$2$	0.774443	+	1.18332i	0.547614	+	0.836731i
$3$	−1.33549	+	1.10293i	−0.771047	+	0.636778i
$3$	−1.33549	+	1.10293i	−0.771047	+	0.636778i
$4$	−0.800475	+	1.83282i	−0.400237	+	0.916412i
$5$	−0.168792	+	0.574851i	−0.0754859	+	0.257081i	−0.988587	−	0.150652i	$-0.951863\pi$
$5$	−0.168792	+	0.574851i	−0.0754859	+	0.257081i	0.913101	+	0.407734i	$0.133681\pi$
$6$	−2.33938	−	0.726151i	−0.955048	−	0.296450i
$7$	2.73269	+	2.36789i	1.03286	+	0.894980i	0.994547	−	0.104286i	$-0.0332558\pi$
$7$	2.73269	+	2.36789i	1.03286	+	0.894980i	0.0383142	+	0.999266i	$0.487801\pi$
$8$	−2.78873	+	0.472203i	−0.985966	+	0.166949i
$9$	0.567081	−	2.94592i	0.189027	−	0.981972i
$10$	−0.810951	+	0.245456i	−0.256445	+	0.0776200i
$11$	−2.81832	+	1.81123i	−0.849756	+	0.546105i	−0.891499	−	0.453023i	$-0.850345\pi$
$11$	−2.81832	+	1.81123i	−0.849756	+	0.546105i	0.0417424	+	0.999128i	$0.486709\pi$
$12$	−0.952452	−	3.33059i	−0.274949	−	0.961459i
$13$	−2.47007	−	2.85062i	−0.685075	−	0.790619i	0.301581	−	0.953441i	$-0.402486\pi$
$13$	−2.47007	−	2.85062i	−0.685075	−	0.790619i	−0.986655	+	0.162822i	$0.947940\pi$
$14$	−0.685649	+	5.06744i	−0.183247	+	1.35433i
$15$	−0.408602	−	0.953876i	−0.105501	−	0.246290i
$16$	−2.71848	−	2.93426i	−0.679620	−	0.733564i
$17$	1.55064	+	0.708152i	0.376085	+	0.171752i	0.594484	−	0.804107i	$-0.297356\pi$
$17$	1.55064	+	0.708152i	0.376085	+	0.171752i	−0.218399	+	0.975859i	$0.570084\pi$
$18$	3.92512	−	1.61041i	0.925160	−	0.379577i
$19$	0.386731	−	0.176614i	0.0887221	−	0.0405180i	−0.370560	−	0.928809i	$-0.620834\pi$
$19$	0.386731	−	0.176614i	0.0887221	−	0.0405180i	0.459282	+	0.888291i	$0.348107\pi$
$20$	−0.918488	−	0.769519i	−0.205380	−	0.172070i
$21$	−6.26112	−	0.148327i	−1.36629	−	0.0323676i
$22$	−4.32588	−	1.93227i	−0.922282	−	0.411962i
$23$	−3.51470	+	3.26296i	−0.732866	+	0.680374i
$23$	−3.51470	+	3.26296i	−0.732866	+	0.680374i
$24$	3.20352	−	3.70641i	0.653916	−	0.756567i
$25$	3.90430	+	2.50914i	0.780861	+	0.501829i
$26$	1.46025	−	5.13052i	0.286378	−	1.00618i
$27$	2.49181	+	4.55970i	0.479550	+	0.877515i
$28$	−6.52738	+	3.11311i	−1.23356	+	0.588322i
$29$	0.0545631	+	0.0249181i	0.0101321	+	0.00462718i	0.420475	−	0.907304i	$-0.361864\pi$
$29$	0.0545631	+	0.0249181i	0.0101321	+	0.00462718i	−0.410343	+	0.911931i	$0.634591\pi$
$30$	0.812297	−	1.22223i	0.148304	−	0.223147i
$31$	7.54204	+	1.08438i	1.35459	+	0.194761i	0.781076	−	0.624435i	$-0.214671\pi$
$31$	7.54204	+	1.08438i	1.35459	+	0.194761i	0.573513	+	0.819196i	$0.305580\pi$
$32$	1.36684	−	5.48924i	0.241626	−	0.970369i
$33$	1.76619	−	5.52730i	0.307454	−	0.962179i
$34$	0.362913	+	2.38332i	0.0622390	+	0.408736i
$35$	−1.82244	+	1.17121i	−0.308049	+	0.197971i
$36$	4.94541	+	3.39749i	0.824235	+	0.566248i
$37$	9.04804	−	2.65674i	1.48749	−	0.436766i	0.565750	−	0.824577i	$-0.308587\pi$
$37$	9.04804	−	2.65674i	1.48749	−	0.436766i	0.921739	+	0.387811i	$0.126769\pi$
$38$	0.508491	+	0.320847i	0.0824882	+	0.0520483i
$39$	6.44280	+	1.08265i	1.03167	+	0.173363i
$40$	0.199268	−	1.68281i	0.0315070	−	0.266076i
$41$	−2.14166	+	7.29381i	−0.334471	+	1.13910i	0.604930	+	0.796279i	$0.293201\pi$
$41$	−2.14166	+	7.29381i	−0.334471	+	1.13910i	−0.939400	+	0.342823i	$0.888617\pi$
$42$	−4.67337	−	7.52376i	−0.721116	−	1.16094i
$43$	−3.74007	+	0.537741i	−0.570355	+	0.0820047i	−0.421458	−	0.906848i	$-0.638481\pi$
$43$	−3.74007	+	0.537741i	−0.570355	+	0.0820047i	−0.148897	+	0.988853i	$0.547572\pi$
$44$	−1.06366	−	6.61533i	−0.160353	−	0.997298i
$45$	1.59775	+	0.823233i	0.238178	+	0.122720i
$46$	−6.58305	−	1.63203i	−0.970617	−	0.240629i
$47$	8.85011			1.29092			0.645461	−	0.763793i	$-0.276665\pi$
$47$	8.85011			1.29092			0.645461	+	0.763793i	$0.276665\pi$
$48$	6.86680	+	0.920378i	0.991137	+	0.132845i
$49$	0.864497	+	6.01271i	0.123500	+	0.858959i
$50$	0.0545521	+	6.56322i	0.00771483	+	0.928179i
$51$	−2.85191	+	0.764516i	−0.399347	+	0.107054i
$52$	7.20191	−	2.24536i	0.998725	−	0.311375i
$53$	2.10780	+	1.82642i	0.289529	+	0.250878i	0.787499	−	0.616316i	$-0.211376\pi$
$53$	2.10780	+	1.82642i	0.289529	+	0.250878i	−0.497970	+	0.867194i	$0.665921\pi$
$54$	−3.46580	+	6.47983i	−0.471636	+	0.881794i
$55$	−0.565477	−	1.92584i	−0.0762489	−	0.259680i
$56$	−8.73888	−	5.31303i	−1.16778	−	0.709984i
$57$	−0.321683	+	0.662404i	−0.0426079	+	0.0877376i
$58$	0.0127700	+	0.0838631i	0.00167678	+	0.0110118i
$59$	−3.59218	−	4.14560i	−0.467662	−	0.539711i	0.472098	−	0.881546i	$-0.343497\pi$
$59$	−3.59218	−	4.14560i	−0.467662	−	0.539711i	−0.939760	+	0.341835i	$0.888952\pi$
$60$	2.07536	+	0.0146576i	0.267928	+	0.00189229i
$61$	−1.40855	+	9.79667i	−0.180346	+	1.25434i	0.675599	+	0.737269i	$0.263885\pi$
$61$	−1.40855	+	9.79667i	−0.180346	+	1.25434i	−0.855945	+	0.517066i	$0.827024\pi$
$62$	4.55772	+	9.76441i	0.578830	+	1.24008i
$63$	8.52527	−	6.70750i	1.07408	−	0.845066i
$64$	7.55405	−	2.63370i	0.944256	−	0.329212i
$65$	2.05561	−	0.938765i	0.254967	−	0.116439i
$66$	7.90836	−	2.19062i	0.973451	−	0.269647i
$67$	4.30433	−	6.69767i	0.525857	−	0.818250i	−0.472139	−	0.881524i	$-0.656518\pi$
$67$	4.30433	−	6.69767i	0.525857	−	0.818250i	0.997996	+	0.0632741i	$0.0201542\pi$
$68$	−2.53916	+	2.27519i	−0.307919	+	0.275907i
$69$	1.09504	−	8.23413i	0.131827	−	0.991273i
$70$	−2.79729	−	1.24949i	−0.334341	−	0.149342i
$71$	−11.2331	−	7.21909i	−1.33313	−	0.856749i	−0.336733	−	0.941600i	$-0.609322\pi$
$71$	−11.2331	−	7.21909i	−1.33313	−	0.856749i	−0.996394	+	0.0848515i	$0.972958\pi$
$72$	−0.190366	+	8.48315i	−0.0224348	+	0.999748i
$73$	−0.421746	−	0.923494i	−0.0493616	−	0.108087i	0.883344	−	0.468725i	$-0.155286\pi$
$73$	−0.421746	−	0.923494i	−0.0493616	−	0.108087i	−0.932706	+	0.360638i	$0.882559\pi$
$74$	10.1510	+	8.64919i	1.18003	+	1.00545i
$75$	−7.98158	+	0.955240i	−0.921634	+	0.110302i
$76$	0.0141341	+	0.850184i	0.00162129	+	0.0975228i
$77$	−11.9904	−	1.72396i	−1.36643	−	0.196463i
$78$	3.70846	+	8.46232i	0.419901	+	0.958170i
$79$	−9.95979	+	8.63021i	−1.12056	+	0.970974i	−0.999764	−	0.0217029i	$-0.993091\pi$
$79$	−9.95979	+	8.63021i	−1.12056	+	0.970974i	−0.120799	+	0.992677i	$0.538546\pi$
$80$	2.14562	−	1.06744i	0.239887	−	0.119344i
$81$	−8.35684	−	3.34115i	−0.928538	−	0.371238i
$82$	−10.2895	+	3.11439i	−1.13628	+	0.343927i
$83$	8.26280	−	2.42618i	0.906961	−	0.266308i	0.205200	−	0.978720i	$-0.434216\pi$
$83$	8.26280	−	2.42618i	0.906961	−	0.266308i	0.701761	+	0.712412i	$0.252397\pi$
$84$	5.28372	−	11.3568i	0.576502	−	1.23913i
$85$	−0.668817	+	0.771856i	−0.0725434	+	0.0837195i
$86$	−3.53279	−	4.00923i	−0.380950	−	0.432327i
$87$	−0.100352	+	0.0269014i	−0.0107588	+	0.00288414i
$88$	7.00428	−	6.38184i	0.746659	−	0.680307i
$89$	14.9047	−	2.14298i	1.57990	−	0.227155i	0.704195	−	0.710006i	$-0.251308\pi$
$89$	14.9047	−	2.14298i	1.57990	−	0.227155i	0.875702	+	0.482851i	$0.160399\pi$
$90$	0.263218	+	2.52819i	0.0277456	+	0.266494i
$91$		−	13.6387i		−	1.42973i
$92$	−3.16699	−	9.05374i	−0.330182	−	0.943917i
$93$	−11.2683	+	6.87017i	−1.16847	+	0.712404i
$94$	6.85391	+	10.4725i	0.706927	+	1.08015i
$95$	0.0362499	+	0.252124i	0.00371916	+	0.0258673i
$96$	4.22885	+	8.83837i	0.431605	+	0.902063i
$97$	6.21222	+	1.82407i	0.630755	+	0.185206i	0.581456	−	0.813578i	$-0.302483\pi$
$97$	6.21222	+	1.82407i	0.630755	+	0.185206i	0.0492990	+	0.998784i	$0.484301\pi$
$98$	−6.44543	+	5.67948i	−0.651087	+	0.573714i
$99$	3.73750	+	9.32965i	0.375633	+	0.937665i
$100$	−7.72411	+	5.14739i	−0.772411	+	0.514739i
$101$	−0.0668407	−	0.227638i	−0.00665090	−	0.0226509i	0.956101	−	0.293038i	$-0.0946664\pi$
$101$	−0.0668407	−	0.227638i	−0.00665090	−	0.0226509i	−0.962752	+	0.270387i	$0.912848\pi$
$102$	−3.11331	−	2.78264i	−0.308263	−	0.275522i
$103$	−4.94024	−	7.68716i	−0.486776	−	0.757439i	0.507797	−	0.861477i	$-0.330460\pi$
$103$	−4.94024	−	7.68716i	−0.486776	−	0.757439i	−0.994573	+	0.104038i	$0.966824\pi$
$104$	8.23444	+	6.78323i	0.807453	+	0.665150i
$105$	1.14209	−	3.57418i	0.111457	−	0.348804i
$106$	−0.528860	+	3.90865i	−0.0513674	+	0.379642i
$107$	0.0820034	−	0.570346i	0.00792757	−	0.0551375i	−0.985474	−	0.169828i	$-0.945679\pi$
$107$	0.0820034	−	0.570346i	0.00792757	−	0.0551375i	0.993401	+	0.114691i	$0.0365878\pi$
$108$	−10.3518	+	0.917127i	−0.996098	+	0.0882506i
$109$	3.03415	−	6.64386i	0.290619	−	0.636366i	−0.706858	−	0.707355i	$-0.749888\pi$
$109$	3.03415	−	6.64386i	0.290619	−	0.636366i	0.997477	+	0.0709887i	$0.0226154\pi$
$110$	1.84094	−	2.16059i	0.175527	−	0.206004i
$111$	−9.15338	+	13.5274i	−0.868800	+	1.28397i
$112$	−0.480771	−	14.4555i	−0.0454286	−	1.36592i
$113$	3.04806	−	4.74287i	0.286737	−	0.446171i	−0.667767	−	0.744371i	$-0.732750\pi$
$113$	3.04806	−	4.74287i	0.286737	−	0.446171i	0.954504	+	0.298199i	$0.0963860\pi$
$114$	−1.03296	+	0.132342i	−0.0967455	+	0.0123950i
$115$	−1.28246	−	2.57119i	−0.119590	−	0.239765i
$116$	−0.0893469	+	0.0800582i	−0.00829565	+	0.00743322i
$117$	−9.79841	+	5.66010i	−0.905863	+	0.523276i
$118$	2.12361	−	7.46122i	0.195494	−	0.686861i
$119$	2.56059	+	5.60691i	0.234729	+	0.513985i
$120$	1.58991	+	2.46716i	0.145138	+	0.225220i
$121$	0.0928381	−	0.203287i	0.00843983	−	0.0184806i
$122$	−12.6834	+	5.92021i	−1.14830	+	0.535991i
$123$	−5.18441	−	12.1029i	−0.467463	−	1.09128i
$124$	−8.02469	+	12.9552i	−0.720638	+	1.16341i
$125$	−4.36532	+	3.78257i	−0.390446	+	0.338324i
$126$	14.5394	+	4.89351i	1.29528	+	0.435949i
$127$	−8.37991	−	13.0394i	−0.743597	−	1.15706i	−0.982545	−	0.186026i	$-0.940439\pi$
$127$	−8.37991	−	13.0394i	−0.743597	−	1.15706i	0.238948	−	0.971032i	$-0.423197\pi$
$128$	8.96668	+	6.89918i	0.792550	+	0.609807i
$129$	4.40174	−	4.84319i	0.387552	−	0.426419i
$130$	2.70281	+	1.70541i	0.237052	+	0.149575i
$131$	8.68672	−	10.0250i	0.758962	−	0.875889i	−0.236443	−	0.971645i	$-0.575982\pi$
$131$	8.68672	−	10.0250i	0.758962	−	0.875889i	0.995405	+	0.0957567i	$0.0305271\pi$
$132$	8.71677	+	7.66157i	0.758697	+	0.666854i
$133$	1.47502	+	0.433105i	0.127900	+	0.0375550i
$134$	11.2589	−	0.0935818i	0.972622	−	0.00808424i
$135$	−3.04175	+	0.662783i	−0.261792	+	0.0570433i
$136$	−4.65870	−	1.24263i	−0.399481	−	0.106555i
$137$		−	18.0918i		−	1.54568i	−0.634599	−	0.772841i	$-0.718835\pi$
$137$		−	18.0918i		−	1.54568i	0.634599	−	0.772841i	$-0.281165\pi$
$138$	10.5916	−	5.08110i	0.901619	−	0.432532i
$139$			12.0588i			1.02281i	0.859339	+	0.511406i	$0.170875\pi$
$139$			12.0588i			1.02281i	−0.859339	+	0.511406i	$0.829125\pi$
$140$	−0.687807	−	4.27774i	−0.0581303	−	0.361535i
$141$	−11.8193	+	9.76107i	−0.995361	+	0.822031i
$142$	−0.156953	−	18.8831i	−0.0131712	−	1.58464i
$143$	12.1246	+	3.56010i	1.01391	+	0.297710i
$144$	−10.1857	+	6.34445i	−0.848806	+	0.528704i
$145$	−0.0235340	+	0.0271597i	−0.00195439	+	0.00225549i
$146$	0.766168	−	1.21425i	0.0634085	−	0.100492i
$147$	−7.78614	−	7.07645i	−0.642190	−	0.583656i
$148$	−2.37338	+	18.7101i	−0.195091	+	1.53796i
$149$	1.84514	+	2.87109i	0.151160	+	0.235209i	0.908572	−	0.417727i	$-0.137173\pi$
$149$	1.84514	+	2.87109i	0.151160	+	0.235209i	−0.757413	+	0.652936i	$0.773537\pi$
$150$	−7.31164	−	8.70496i	−0.596993	−	0.710757i
$151$	10.1324	−	8.77976i	0.824562	−	0.714487i	−0.136554	−	0.990633i	$-0.543603\pi$
$151$	10.1324	−	8.77976i	0.824562	−	0.714487i	0.961116	+	0.276146i	$0.0890573\pi$
$152$	−0.995090	+	0.675144i	−0.0807125	+	0.0547614i
$153$	2.96549	−	4.16647i	0.239746	−	0.336839i
$154$	−7.24590	−	15.5236i	−0.583891	−	1.25092i
$155$	−1.89639	+	4.15252i	−0.152322	+	0.333538i
$156$	−7.14161	+	10.9419i	−0.571786	+	0.876051i
$157$	−5.46999	−	11.9776i	−0.436553	−	0.955917i	−0.992218	−	0.124511i	$-0.960264\pi$
$157$	−5.46999	−	11.9776i	−0.436553	−	0.955917i	0.555666	−	0.831406i	$-0.312463\pi$
$158$	−17.9256	−	5.10197i	−1.42608	−	0.405891i
$159$	−4.82937	−	0.114409i	−0.382994	−	0.00907320i
$160$	2.92478	+	1.71227i	0.231225	+	0.135367i
$161$	−17.3309	+	0.594231i	−1.36587	+	0.0468319i
$162$	−2.51827	−	12.4763i	−0.197854	−	0.980232i
$163$	−0.0383352	+	0.0596507i	−0.00300265	+	0.00467221i	−0.842752	−	0.538303i	$-0.819066\pi$
$163$	−0.0383352	+	0.0596507i	−0.00300265	+	0.00467221i	0.839749	+	0.542975i	$0.182702\pi$
$164$	−11.6539	−	9.76379i	−0.910019	−	0.762424i
$165$	2.87926	+	1.94826i	0.224150	+	0.151672i
$166$	9.27001	+	7.89857i	0.719492	+	0.613048i
$167$	−7.85796	+	17.2065i	−0.608067	+	1.33148i	0.315821	+	0.948819i	$0.397720\pi$
$167$	−7.85796	+	17.2065i	−0.608067	+	1.33148i	−0.923888	+	0.382663i	$0.875007\pi$
$168$	17.5306	−	2.54288i	1.35252	−	0.196187i
$169$	−0.174659	+	1.21478i	−0.0134353	+	0.0934445i
$170$	−1.43131	−	0.193663i	−0.109777	−	0.0148533i
$171$	−0.300982	−	1.23943i	−0.0230167	−	0.0947816i
$172$	2.00825	−	7.28533i	0.153127	−	0.555501i
$173$	−6.36987	−	9.91171i	−0.484292	−	0.753573i	0.510010	−	0.860168i	$-0.329642\pi$
$173$	−6.36987	−	9.91171i	−0.484292	−	0.753573i	−0.994303	+	0.106595i	$0.966005\pi$
$174$	−0.109550	−	0.0979141i	−0.00830493	−	0.00742285i
$175$	4.72789	+	16.1017i	0.357395	+	1.21717i
$176$	12.9762	+	3.34590i	0.978115	+	0.252207i
$177$	9.36965	+	1.57448i	0.704266	+	0.118345i
$178$	14.0787	+	15.9774i	1.05524	+	1.19756i
$179$	5.84903	+	1.71743i	0.437177	+	0.128367i	0.492913	−	0.870079i	$-0.335932\pi$
$179$	5.84903	+	1.71743i	0.437177	+	0.128367i	−0.0557355	+	0.998446i	$0.517750\pi$
$180$	−2.78780	+	2.26941i	−0.207790	+	0.169152i
$181$	2.23672	+	15.5567i	0.166254	+	1.15632i	0.886542	+	0.462648i	$0.153101\pi$
$181$	2.23672	+	15.5567i	0.166254	+	1.15632i	−0.720288	+	0.693675i	$0.755990\pi$
$182$	16.1389	−	10.5624i	1.19630	−	0.782939i
$183$	−8.92396	−	14.6369i	−0.659678	−	1.08199i
$184$	8.26078	−	10.7592i	0.608992	−	0.793176i
$185$			5.64971i			0.415375i
$186$	−16.8563	−	8.01344i	−1.23596	−	0.587574i
$187$	−5.65282	+	0.812753i	−0.413375	+	0.0594344i
$188$	−7.08429	+	16.2207i	−0.516675	+	1.18302i
$189$	−3.98752	+	18.3606i	−0.290050	+	1.33554i
$190$	−0.270268	+	0.238151i	−0.0196073	+	0.0172773i
$191$	5.05600	−	5.83494i	0.365840	−	0.422201i	−0.542748	−	0.839896i	$-0.682616\pi$
$191$	5.05600	−	5.83494i	0.365840	−	0.422201i	0.908588	+	0.417694i	$0.137162\pi$
$192$	−7.18359	+	11.8489i	−0.518431	+	0.855120i
$193$	−18.3695	+	5.39376i	−1.32226	+	0.388252i	−0.865309	−	0.501239i	$-0.832878\pi$
$193$	−18.3695	+	5.39376i	−1.32226	+	0.388252i	−0.456954	+	0.889490i	$0.651060\pi$
$194$	2.65256	+	8.76366i	0.190443	+	0.629194i
$195$	−1.70986	+	3.52091i	−0.122445	+	0.252138i
$196$	−11.7122	−	3.22855i	−0.836589	−	0.230611i
$197$	−12.0613	+	10.4512i	−0.859331	+	0.744614i	−0.968395	−	0.249420i	$-0.919760\pi$
$197$	−12.0613	+	10.4512i	−0.859331	+	0.744614i	0.109065	+	0.994035i	$0.465214\pi$
$198$	−8.14545	+	11.6479i	−0.578872	+	0.827783i
$199$	−3.59602	−	0.517029i	−0.254915	−	0.0366512i	0.0136725	−	0.999907i	$-0.495648\pi$
$199$	−3.59602	−	0.517029i	−0.254915	−	0.0366512i	−0.268588	+	0.963255i	$0.586557\pi$
$200$	−12.0729	−	5.15370i	−0.853682	−	0.364422i
$201$	1.63867	+	13.6921i	0.115583	+	0.965764i
$202$	0.217604	−	0.255387i	0.0153106	−	0.0179690i
$203$	0.0901008	+	0.197293i	0.00632384	+	0.0138473i
$204$	0.881659	−	5.83902i	0.0617285	−	0.408813i
$205$	−3.83136	−	2.46227i	−0.267594	−	0.171972i
$206$	5.27041	−	11.7991i	0.367207	−	0.822085i
$207$	7.61928	+	12.2044i	0.529576	+	0.848262i
$208$	−1.64959	+	14.9972i	−0.114379	+	1.03987i
$209$	−0.770044	+	1.19821i	−0.0532650	+	0.0828820i
$210$	5.11387	−	1.41654i	0.352890	−	0.0977508i
$211$	−8.60045	+	3.92769i	−0.592079	+	0.270394i	−0.688839	−	0.724914i	$-0.741879\pi$
$211$	−8.60045	+	3.92769i	−0.592079	+	0.270394i	0.0967598	+	0.995308i	$0.469152\pi$
$212$	−5.03475	+	2.40122i	−0.345788	+	0.164917i
$213$	22.9639	−	2.74833i	1.57346	−	0.188313i
$214$	0.738407	−	0.344665i	0.0504765	−	0.0235608i
$215$	0.322171	−	2.24075i	0.0219719	−	0.152818i
$216$	−9.10210	−	11.5391i	−0.619320	−	0.785139i
$217$	18.0424	+	20.8220i	1.22480	+	1.41349i
$218$	10.2116	−	1.55494i	0.691614	−	0.105314i
$219$	1.58179	+	0.768163i	0.106887	+	0.0519076i
$220$	3.98237	+	0.505165i	0.268491	+	0.0340582i
$221$	−1.81152	−	6.16946i	−0.121856	−	0.415003i
$222$	−23.0960	−	0.355110i	−1.55010	−	0.0238334i
$223$	6.09435	+	5.28078i	0.408108	+	0.353627i	0.834593	−	0.550867i	$-0.185703\pi$
$223$	6.09435	+	5.28078i	0.408108	+	0.353627i	−0.426485	+	0.904495i	$0.640248\pi$
$224$	16.7331	−	11.7639i	1.11803	−	0.786007i
$225$	9.60578	−	10.0789i	0.640386	−	0.671924i
$226$	7.97286	−	0.0662688i	0.530347	−	0.00440813i
$227$	−3.59451	−	25.0004i	−0.238576	−	1.65933i	−0.659103	−	0.752053i	$-0.729064\pi$
$227$	−3.59451	−	25.0004i	−0.238576	−	1.65933i	0.420527	−	0.907280i	$-0.361845\pi$
$228$	−0.956571	−	1.11983i	−0.0633505	−	0.0741622i
$229$	−14.8882			−0.983839			−0.491920	−	0.870641i	$-0.663705\pi$
$229$	−14.8882			−0.983839			−0.491920	+	0.870641i	$0.663705\pi$
$230$	2.04934	−	3.50880i	0.135129	−	0.231364i
$231$	17.9145	−	10.9223i	1.17869	−	0.718633i
$232$	−0.163928	−	0.0437251i	−0.0107624	−	0.00287069i
$233$	17.4378	−	2.50718i	1.14239	−	0.164251i	0.454968	−	0.890508i	$-0.349651\pi$
$233$	17.4378	−	2.50718i	1.14239	−	0.164251i	0.687423	+	0.726257i	$0.258742\pi$
$234$	−14.2860	−	7.21119i	−0.933905	−	0.471410i
$235$	−1.49382	+	5.08750i	−0.0974464	+	0.331872i
$236$	10.4736	−	3.26539i	0.681773	−	0.212559i
$237$	3.78269	−	22.5105i	0.245712	−	1.46222i
$238$	−4.65171	+	7.37222i	−0.301526	+	0.477870i
$239$	−5.39705	+	1.58472i	−0.349106	+	0.102507i	−0.451584	−	0.892228i	$-0.649141\pi$
$239$	−5.39705	+	1.58472i	−0.349106	+	0.102507i	0.102478	+	0.994735i	$0.467323\pi$
$240$	−1.68814	+	3.79204i	−0.108969	+	0.244775i
$241$	25.3309	−	16.2792i	1.63171	−	1.04864i	0.684009	−	0.729474i	$-0.260235\pi$
$241$	25.3309	−	16.2792i	1.63171	−	1.04864i	0.947700	−	0.319162i	$-0.103401\pi$
$242$	0.312451	−	0.0475775i	0.0200851	−	0.00305840i
$243$	14.8456	−	4.75495i	0.952343	−	0.305030i
$244$	−16.8281	−	10.4236i	−1.07731	−	0.667303i
$245$	−3.60234	−	0.517938i	−0.230145	−	0.0330898i
$246$	10.3066	−	15.5078i	0.657122	−	0.988744i
$247$	−1.45871	−	0.666171i	−0.0928156	−	0.0423875i
$248$	−21.5448	+	0.537326i	−1.36809	+	0.0341202i
$249$	−8.35900	+	12.3535i	−0.529730	+	0.782868i
$250$	−7.85668	−	2.23617i	−0.496900	−	0.141428i
$251$	16.3944	+	10.5360i	1.03481	+	0.665029i	0.943697	−	0.330812i	$-0.107323\pi$
$251$	16.3944	+	10.5360i	1.03481	+	0.665029i	0.0911084	+	0.995841i	$0.470959\pi$
$252$	5.46940	+	20.9945i	0.344540	+	1.32253i
$253$	3.99561	−	15.5620i	0.251202	−	0.978373i
$254$	8.93996	−	20.0144i	0.560943	−	1.25581i
$255$	0.0418954	−	1.76847i	0.00262359	−	0.110746i
$256$	−1.21972	+	15.9534i	−0.0762328	+	0.997090i
$257$	18.7173	−	8.54791i	1.16755	−	0.533204i	0.265198	−	0.964194i	$-0.414563\pi$
$257$	18.7173	−	8.54791i	1.16755	−	0.533204i	0.902357	+	0.430990i	$0.141836\pi$
$258$	9.13993	+	1.45788i	0.569027	+	0.0907634i
$259$	31.0164	+	14.1647i	1.92727	+	0.880153i
$260$	0.0751276	+	4.51902i	0.00465922	+	0.280258i
$261$	0.104348	−	0.146608i	0.00645901	−	0.00907479i
$262$	18.5901	+	2.51533i	1.14850	+	0.155398i
$263$	−11.2286	−	12.9585i	−0.692385	−	0.799055i	0.295317	−	0.955399i	$-0.404575\pi$
$263$	−11.2286	−	12.9585i	−0.692385	−	0.799055i	−0.987703	+	0.156344i	$0.950029\pi$
$264$	−2.31542	+	16.2482i	−0.142504	+	1.00000i
$265$	−1.40570	+	0.903388i	−0.0863514	+	0.0554947i
$266$	0.629819	+	2.08083i	0.0386167	+	0.127584i
$267$	−17.5416	+	19.3008i	−1.07353	+	1.18119i
$268$	8.83013	+	13.2504i	0.539386	+	0.809396i
$269$	17.9579	+	15.5606i	1.09491	+	0.948745i	0.998912	−	0.0466360i	$-0.0148501\pi$
$269$	17.9579	+	15.5606i	1.09491	+	0.948745i	0.0959986	+	0.995381i	$0.469396\pi$
$270$	−3.13994	−	3.08606i	−0.191091	−	0.187812i
$271$	−2.45342	+	8.35559i	−0.149035	+	0.507566i	−0.999839	−	0.0179162i	$-0.994297\pi$
$271$	−2.45342	+	8.35559i	−0.149035	+	0.507566i	0.850805	+	0.525482i	$0.176115\pi$
$272$	−2.13748	−	6.47507i	−0.129604	−	0.392609i
$273$	15.0426	+	18.2144i	0.910419	+	1.10239i
$274$	21.4083	−	14.0110i	1.29332	−	0.846438i
$275$	−15.5482			−0.937593
$276$	14.2152	+	8.59822i	0.855652	+	0.517552i
$277$	−25.8264			−1.55176			−0.775880	−	0.630881i	$-0.782694\pi$
$277$	−25.8264			−1.55176			−0.775880	+	0.630881i	$0.782694\pi$
$278$	−14.2694	+	9.33884i	−0.855819	+	0.560107i
$279$	7.47144	−	21.6033i	0.447304	−	1.29335i
$280$	4.52925	−	4.12676i	0.270675	−	0.246621i
$281$	8.75598	−	29.8201i	0.522338	−	1.77892i	−0.0986741	−	0.995120i	$-0.531460\pi$
$281$	8.75598	−	29.8201i	0.522338	−	1.77892i	0.621012	−	0.783801i	$-0.286722\pi$
$282$	−20.7038	−	6.42652i	−1.23289	−	0.382694i
$283$	15.5191	+	13.4474i	0.922513	+	0.799362i	0.980003	−	0.198984i	$-0.0637641\pi$
$283$	15.5191	+	13.4474i	0.922513	+	0.799362i	−0.0574896	+	0.998346i	$0.518310\pi$
$284$	22.2232	−	14.8096i	1.31870	−	0.878790i
$285$	−0.326487	−	0.296728i	−0.0193394	−	0.0175767i
$286$	5.17708	+	17.1043i	0.306127	+	1.01140i
$287$	−23.1235	+	14.8605i	−1.36493	+	0.877190i
$288$	−15.3957	−	7.13945i	−0.907202	−	0.420696i
$289$	−9.22964	−	10.6516i	−0.542920	−	0.626563i
$290$	−0.0503643	−	0.00681453i	−0.00295749	−	0.000400163i
$291$	−10.3082	+	4.41562i	−0.604277	+	0.258848i
$292$	2.03020	−	0.0337515i	0.118808	−	0.00197516i
$293$	15.9216	+	7.27115i	0.930149	+	0.424785i	0.822089	−	0.569359i	$-0.192809\pi$
$293$	15.9216	+	7.27115i	0.930149	+	0.424785i	0.108060	+	0.994144i	$0.465536\pi$
$294$	2.34375	−	14.6938i	0.136690	−	0.856959i
$295$	2.98943	−	1.36523i	0.174052	−	0.0794867i
$296$	−23.9780	+	11.6815i	−1.39369	+	0.678971i
$297$	−15.2814	−	8.33747i	−0.886716	−	0.483789i
$298$	−1.96845	+	4.40688i	−0.114029	+	0.255284i
$299$	17.9830	+	1.95932i	1.03998	+	0.113310i
$300$	4.63827	−	15.3935i	0.267791	−	0.888743i
$301$	−11.4938	−	7.38660i	−0.662490	−	0.425757i
$302$	18.2362	+	5.19039i	1.04937	+	0.298673i
$303$	0.340335	+	0.230289i	0.0195517	+	0.0132297i
$304$	−1.56955	−	0.654645i	−0.0900199	−	0.0375465i
$305$	−5.39388	−	2.46330i	−0.308853	−	0.141048i
$306$	7.22686	+	0.282424i	0.413132	+	0.0161451i
$307$	−8.89079	−	1.27830i	−0.507424	−	0.0729566i	−0.116152	−	0.993231i	$-0.537056\pi$
$307$	−8.89079	−	1.27830i	−0.507424	−	0.0729566i	−0.391272	+	0.920275i	$0.627965\pi$
$308$	12.7577	−	20.5963i	0.726939	−	1.17358i
$309$	15.0761	+	4.81740i	0.857648	+	0.274052i
$310$	−6.38239	+	0.971859i	−0.362495	+	0.0551979i
$311$	−4.27612	+	2.74810i	−0.242477	+	0.155830i	−0.656235	−	0.754556i	$-0.727852\pi$
$311$	−4.27612	+	2.74810i	−0.242477	+	0.155830i	0.413759	+	0.910387i	$0.364216\pi$
$312$	−18.4785	+	0.0230805i	−1.04614	+	0.00130668i
$313$	0.668165	−	0.196191i	0.0377669	−	0.0110894i	−0.262795	−	0.964852i	$-0.584644\pi$
$313$	0.668165	−	0.196191i	0.0377669	−	0.0110894i	0.300561	+	0.953762i	$0.402826\pi$
$314$	9.93709	−	15.7487i	0.560783	−	0.888751i
$315$	2.41682	+	6.03294i	0.136172	+	0.339917i
$316$	−7.84508	−	25.1628i	−0.441320	−	1.41552i
$317$	−1.96751	+	6.70072i	−0.110506	+	0.376350i	−0.996113	−	0.0880862i	$-0.971925\pi$
$317$	−1.96751	+	6.70072i	−0.110506	+	0.376350i	0.885606	+	0.464436i	$0.153743\pi$
$318$	−3.60469	−	5.80328i	−0.202141	−	0.325432i
$319$	−0.198909	+	0.0285988i	−0.0111368	+	0.00160122i
$320$	0.238924	+	4.78700i	0.0133563	+	0.267602i
$321$	0.519538	+	0.852137i	0.0289978	+	0.0475617i
$322$	−14.1250	−	20.0478i	−0.787155	−	1.11722i
$323$	0.724749			0.0403261
$324$	12.8132	−	12.6421i	0.711843	−	0.702339i
$325$	−2.49131	−	17.3274i	−0.138193	−	0.961153i
$326$	−0.100274		0.000833458i	−0.00555367		4.61610e-5i
$327$	3.27564	+	12.2193i	0.181144	+	0.675728i
$328$	2.52834	−	21.3518i	0.139604	−	1.17895i
$329$	24.1847	+	20.9561i	1.33334	+	1.15535i
$330$	−0.0755836	+	4.91589i	−0.00416074	+	0.270611i
$331$	2.26908	+	7.72776i	0.124720	+	0.424756i	0.998053	−	0.0623663i	$-0.0198647\pi$
$331$	2.26908	+	7.72776i	0.124720	+	0.424756i	−0.873334	+	0.487122i	$0.838047\pi$
$332$	−2.16741	+	17.0864i	−0.118952	+	0.937735i
$333$	−2.69557	−	28.1613i	−0.147716	−	1.54323i
$334$	−26.4463	+	4.02703i	−1.44708	+	0.220350i
$335$	3.12363	+	3.60486i	0.170662	+	0.196955i
$336$	16.5855	+	18.7750i	0.904813	+	1.02426i
$337$	2.37879	−	16.5448i	0.129581	−	0.901255i	−0.816505	−	0.577339i	$-0.804091\pi$
$337$	2.37879	−	16.5448i	0.129581	−	0.901255i	0.946086	−	0.323917i	$-0.105000\pi$
$338$	−1.57273	+	0.734101i	−0.0855453	+	0.0399298i
$339$	1.16041	+	9.69586i	0.0630246	+	0.526607i
$340$	−0.879305	−	1.84367i	−0.0476870	−	0.0999873i
$341$	−23.2200	+	10.6042i	−1.25743	+	0.574250i
$342$	1.23354	−	1.31603i	0.0667024	−	0.0711625i
$343$	1.80917	−	2.81512i	0.0976860	−	0.152002i
$344$	10.1761	−	3.26569i	0.548660	−	0.176074i
$345$	4.54857	+	2.01933i	0.244887	+	0.108717i
$346$	6.79558	−	15.2136i	0.365333	−	0.817890i
$347$	15.0519	+	9.67324i	0.808026	+	0.519287i	0.878226	−	0.478246i	$-0.158727\pi$
$347$	15.0519	+	9.67324i	0.808026	+	0.519287i	−0.0702000	+	0.997533i	$0.522364\pi$
$348$	0.0310234	−	0.205461i	0.00166303	−	0.0110138i
$349$	0.562820	+	1.23240i	0.0301271	+	0.0659691i	0.924097	−	0.382157i	$-0.124819\pi$
$349$	0.562820	+	1.23240i	0.0301271	+	0.0659691i	−0.893970	+	0.448126i	$0.852091\pi$
$350$	−15.3919	+	18.0644i	−0.822733	+	0.965585i
$351$	6.84300	−	18.3660i	0.365252	−	0.980304i
$352$	6.09004	+	17.9461i	0.324600	+	0.956531i
$353$	−23.7738	−	3.41816i	−1.26535	−	0.181930i	−0.523229	−	0.852192i	$-0.675273\pi$
$353$	−23.7738	−	3.41816i	−1.26535	−	0.181930i	−0.742125	+	0.670262i	$0.766182\pi$
$354$	5.39315	+	12.3066i	0.286643	+	0.654089i
$355$	6.04596	−	5.23886i	0.320886	−	0.278050i
$356$	−8.00316	+	29.0331i	−0.424167	+	1.53875i
$357$	−9.60369	−	4.66383i	−0.508281	−	0.246836i
$358$	2.49748	+	8.25131i	0.131996	+	0.436095i
$359$	−0.0674153	+	0.0197949i	−0.00355804	+	0.00104474i	−0.283511	−	0.958969i	$-0.591499\pi$
$359$	−0.0674153	+	0.0197949i	−0.00355804	+	0.00104474i	0.279953	+	0.960014i	$0.409681\pi$
$360$	−4.84442	−	1.54132i	−0.255323	−	0.0812345i
$361$	−12.3240	+	14.2226i	−0.648631	+	0.748560i
$362$	−16.6763	+	14.6946i	−0.876488	+	0.772329i
$363$	0.100227	+	0.373882i	0.00526057	+	0.0196237i
$364$	24.9974	+	10.9175i	1.31022	+	0.572230i
$365$	0.602059	−	0.0865631i	0.0315132	−	0.00453092i
$366$	10.4090	−	21.8953i	0.544087	−	1.14449i
$367$		−	29.5553i		−	1.54277i	−0.636366	−	0.771387i	$-0.719563\pi$
$367$		−	29.5553i		−	1.54277i	0.636366	−	0.771387i	$-0.280437\pi$
$368$	19.1290	+	1.44275i	0.997168	+	0.0752083i
$369$	20.2725	+	10.4453i	1.05534	+	0.543762i
$370$	−6.68540	+	4.37538i	−0.347557	+	0.227465i
$371$	1.43521	+	9.98210i	0.0745123	+	0.518245i
$372$	−3.57180	−	26.1523i	−0.185189	−	1.35593i
$373$	3.31581	+	0.973610i	0.171686	+	0.0504116i	0.366446	−	0.930439i	$-0.380575\pi$
$373$	3.31581	+	0.973610i	0.171686	+	0.0504116i	−0.194760	+	0.980851i	$0.562393\pi$
$374$	−5.33953	−	6.05964i	−0.276101	−	0.313337i
$375$	1.65793	−	9.86625i	0.0856153	−	0.509491i
$376$	−24.6806	+	4.17905i	−1.27280	+	0.215518i
$377$	−0.0637428	−	0.217088i	−0.00328292	−	0.0111806i
$378$	−24.8145	+	9.50076i	−1.27632	+	0.488666i
$379$	5.60208	+	8.71701i	0.287760	+	0.447763i	0.954796	−	0.297263i	$-0.0960737\pi$
$379$	5.60208	+	8.71701i	0.287760	+	0.447763i	−0.667036	+	0.745025i	$0.732437\pi$
$380$	−0.491115	−	0.135379i	−0.0251937	−	0.00694479i
$381$	25.5729	+	8.17154i	1.31014	+	0.418641i
$382$	10.8202	+	1.46402i	0.553608	+	0.0749058i
$383$	0.253054	−	1.76003i	0.0129305	−	0.0899334i	−0.982334	−	0.187135i	$-0.940080\pi$
$383$	0.253054	−	1.76003i	0.0129305	−	0.0899334i	0.995265	+	0.0972012i	$0.0309890\pi$
$384$	−19.5843	+	0.675836i	−0.999405	+	0.0344886i
$385$	3.01490	−	6.60171i	0.153654	−	0.336454i
$386$	−20.6086	−	17.5597i	−1.04895	−	0.893767i
$387$	−0.536783	+	11.3229i	−0.0272862	+	0.575574i
$388$	−8.31593	+	9.92578i	−0.422177	+	0.503905i
$389$	−15.1683	+	23.6023i	−0.769063	+	1.19669i	0.206817	+	0.978380i	$0.433689\pi$
$389$	−15.1683	+	23.6023i	−0.769063	+	1.19669i	−0.975880	+	0.218306i	$0.929947\pi$
$390$	−5.49054	+	0.703446i	−0.278024	+	0.0356204i
$391$	−7.76070	+	2.57072i	−0.392475	+	0.130007i
$392$	−5.25007	−	16.3596i	−0.265169	−	0.826285i
$393$	−0.544144	+	22.9692i	−0.0274484	+	1.15864i
$394$	−21.7078	−	6.17848i	−1.09362	−	0.311267i
$395$	−3.27996	−	7.18211i	−0.165033	−	0.361371i
$396$	−20.0914	−	0.617971i	−1.00963	−	0.0310542i
$397$	−1.11296	+	2.43705i	−0.0558580	+	0.122312i	−0.935503	−	0.353319i	$-0.885053\pi$
$397$	−1.11296	+	2.43705i	−0.0558580	+	0.122312i	0.879645	+	0.475631i	$0.157780\pi$
$398$	−2.17310	−	4.65564i	−0.108928	−	0.233366i
$399$	−2.44756	+	1.04844i	−0.122531	+	0.0524876i
$400$	−3.25130	−	18.2773i	−0.162565	−	0.913864i
$401$	−26.8694	+	23.2825i	−1.34179	+	1.16267i	−0.369413	+	0.929265i	$0.620441\pi$
$401$	−26.8694	+	23.2825i	−1.34179	+	1.16267i	−0.972380	+	0.233405i	$0.925013\pi$
$402$	−14.9330	+	12.5428i	−0.744790	+	0.625578i
$403$	−15.5382	−	24.1780i	−0.774014	−	1.20439i
$404$	0.470725	+	0.0597117i	0.0234195	+	0.00297077i
$405$	3.33123	−	4.23998i	0.165530	−	0.210686i
$406$	−0.163682	+	0.259410i	−0.00812342	+	0.0128743i
$407$	−20.6883	+	23.8756i	−1.02548	+	1.18347i
$408$	7.59220	−	3.47871i	0.375870	−	0.172222i
$409$	−3.00140	−	0.881289i	−0.148409	−	0.0435770i	0.206684	−	0.978408i	$-0.433733\pi$
$409$	−3.00140	−	0.881289i	−0.148409	−	0.0435770i	−0.355094	+	0.934831i	$0.615551\pi$
$410$	−0.0535330	−	6.44060i	−0.00264381	−	0.318079i
$411$	19.9540	+	24.1614i	0.984257	+	1.19179i
$412$	18.0437	−	2.90121i	0.888952	−	0.142932i
$413$		−	19.8346i		−	0.975995i
$414$	−8.54093	+	18.4676i	−0.419764	+	0.907633i
$415$			5.15940i			0.253265i
$416$	−19.0239	+	9.66247i	−0.932724	+	0.473742i
$417$	−13.3000	−	16.1044i	−0.651305	−	0.788637i
$418$	−2.01422	+	0.0167418i	−0.0985187	+	0.000818867i
$419$	−27.0142	−	7.93210i	−1.31973	−	0.387508i	−0.455336	−	0.890320i	$-0.650481\pi$
$419$	−27.0142	−	7.93210i	−1.31973	−	0.387508i	−0.864396	+	0.502812i	$0.832299\pi$
$420$	5.63662	+	4.95429i	0.275039	+	0.241745i
$421$	−2.56922	+	2.96503i	−0.125216	+	0.144507i	−0.814896	−	0.579608i	$-0.803206\pi$
$421$	−2.56922	+	2.96503i	−0.125216	+	0.144507i	0.689680	+	0.724114i	$0.257751\pi$
$422$	−11.3083	−	7.13527i	−0.550478	−	0.347340i
$423$	5.01873	−	26.0717i	0.244019	−	1.26765i
$424$	−6.74053	−	4.09808i	−0.327349	−	0.199021i
$425$	4.27730	+	6.65562i	0.207480	+	0.322845i
$426$	21.0364	+	25.0452i	1.01922	+	1.21344i
$427$	−27.0466	+	23.4360i	−1.30888	+	1.13415i
$428$	0.979702	+	0.606846i	0.0473557	+	0.0293330i
$429$	−20.1188	+	8.61810i	−0.971346	+	0.416086i
$430$	2.90102	−	1.35410i	0.139900	−	0.0653007i
$431$	−7.21986	+	15.8093i	−0.347769	+	0.761507i	0.652225	+	0.758025i	$0.273836\pi$
$431$	−7.21986	+	15.8093i	−0.347769	+	0.761507i	−0.999994	+	0.00348181i	$0.998892\pi$
$432$	6.60539	−	19.7071i	0.317802	−	0.948157i
$433$	1.26608	+	2.77233i	0.0608439	+	0.133230i	0.937611	−	0.347685i	$-0.113032\pi$
$433$	1.26608	+	2.77233i	0.0608439	+	0.133230i	−0.876768	+	0.480914i	$0.840305\pi$
$434$	−10.6662	+	37.4753i	−0.511995	+	1.79887i
$435$	0.00147419	−	0.0622280i	7.06822e−5	−	0.00298361i
$436$	9.74826	+	10.8793i	0.466857	+	0.521024i
$437$	−0.782958	+	1.88263i	−0.0374540	+	0.0900584i
$438$	0.316027	+	2.46666i	0.0151004	+	0.117861i
$439$	−8.75428	+	13.6219i	−0.417819	+	0.650139i	−0.984820	−	0.173578i	$-0.944467\pi$
$439$	−8.75428	+	13.6219i	−0.417819	+	0.650139i	0.567001	+	0.823717i	$0.308104\pi$
$440$	2.48635	+	5.10362i	0.118532	+	0.243306i
$441$	18.2032	+	0.862958i	0.866818	+	0.0410932i
$442$	5.89751	−	6.92150i	0.280516	−	0.329222i
$443$	13.8651	−	30.3604i	0.658752	−	1.44247i	−0.224929	−	0.974375i	$-0.572215\pi$
$443$	13.8651	−	30.3604i	0.658752	−	1.44247i	0.883681	−	0.468090i	$-0.155058\pi$
$444$	−17.4663	−	27.6049i	−0.828916	−	1.31007i
$445$	−1.28390	+	8.92972i	−0.0608627	+	0.423309i
$446$	−1.52911	+	11.3012i	−0.0724054	+	0.535128i
$447$	−5.63079	−	1.79926i	−0.266327	−	0.0851020i
$448$	26.8792	+	10.6901i	1.26992	+	0.505059i
$449$	−11.8697	−	18.4697i	−0.560168	−	0.871638i	0.439478	−	0.898253i	$-0.355163\pi$
$449$	−11.8697	−	18.4697i	−0.560168	−	0.871638i	−0.999646	+	0.0266153i	$0.991527\pi$
$450$	19.3656	+	3.56117i	0.912904	+	0.167875i
$451$	−7.17486	−	24.4353i	−0.337851	−	1.15062i
$452$	6.25294	+	9.38309i	0.294114	+	0.441343i
$453$	−3.84824	+	22.9006i	−0.180806	+	1.07597i
$454$	26.7996	−	23.6148i	1.25777	−	1.10830i
$455$	7.84025	+	2.30210i	0.367556	+	0.107924i
$456$	0.584297	−	1.99917i	0.0273622	−	0.0936196i
$457$	2.45217	+	17.0552i	0.114708	+	0.797809i	0.963236	+	0.268658i	$0.0865803\pi$
$457$	2.45217	+	17.0552i	0.114708	+	0.797809i	−0.848528	+	0.529151i	$0.822511\pi$
$458$	−11.5301	−	17.6174i	−0.538764	−	0.823209i
$459$	0.634935	+	8.83503i	0.0296362	+	0.412384i
$460$	5.73912	−	0.292357i	0.267588	−	0.0136312i
$461$			24.6025i			1.14585i	0.819607	+	0.572927i	$0.194192\pi$
$461$			24.6025i			1.14585i	−0.819607	+	0.572927i	$0.805808\pi$
$462$	26.7983	+	12.7399i	1.24677	+	0.592711i
$463$	−31.7070	+	4.55878i	−1.47355	+	0.211864i	−0.831811	−	0.555060i	$-0.812695\pi$
$463$	−31.7070	+	4.55878i	−1.47355	+	0.211864i	−0.641738	+	0.766924i	$0.721786\pi$
$464$	−0.0752125	−	0.227842i	−0.00349165	−	0.0105773i
$465$	−2.04733	−	7.63725i	−0.0949426	−	0.354169i
$466$	16.4714	+	18.6928i	0.763024	+	0.865928i
$467$	3.89243	−	4.49211i	0.180120	−	0.207870i	−0.658508	−	0.752573i	$-0.728812\pi$
$467$	3.89243	−	4.49211i	0.180120	−	0.207870i	0.838629	+	0.544703i	$0.183358\pi$
$468$	−2.53058	−	22.4895i	−0.116976	−	1.03958i
$469$	27.6218	−	8.11049i	1.27546	−	0.374507i
$470$	−7.17700	+	2.17231i	−0.331051	+	0.100201i
$471$	20.5156	+	9.96297i	0.945309	+	0.459070i
$472$	11.9752	+	9.86473i	0.551203	+	0.454061i
$473$	9.56675	−	8.28964i	0.439880	−	0.381158i
$474$	29.5666	−	12.9570i	1.35804	−	0.595136i
$475$	1.95306	+	0.280808i	0.0896127	+	0.0128844i
$476$	−12.3262	+	0.204919i	−0.564969	+	0.00939246i
$477$	6.57577	−	5.17368i	0.301084	−	0.236886i
$478$	−6.05493	−	5.15914i	−0.276946	−	0.235974i
$479$	1.59617	+	3.49513i	0.0729309	+	0.159696i	0.942586	−	0.333963i	$-0.108386\pi$
$479$	1.59617	+	3.49513i	0.0729309	+	0.159696i	−0.869655	+	0.493660i	$0.835659\pi$
$480$	−5.79455	+	0.939116i	−0.264484	+	0.0428646i
$481$	−29.9227	−	19.2301i	−1.36436	−	0.876819i
$482$	38.8808	+	17.3672i	1.77097	+	0.791054i
$483$	22.4899	−	19.9084i	1.02333	−	0.905865i
$484$	0.298275	+	0.332882i	0.0135579	+	0.0151310i
$485$	−2.09714	+	3.26322i	−0.0952263	+	0.148175i
$486$	17.1237	+	13.8845i	0.776745	+	0.629816i
$487$	7.49586	−	3.42325i	0.339670	−	0.155122i	−0.238275	−	0.971198i	$-0.576582\pi$
$487$	7.49586	−	3.42325i	0.339670	−	0.155122i	0.577945	+	0.816076i	$0.303855\pi$
$488$	−0.697956	−	27.9854i	−0.0315950	−	1.26684i
$489$	−0.0145943	−	0.121944i	−0.000659979	−	0.00551451i
$490$	−2.17692	−	4.66382i	−0.0983433	−	0.210690i
$491$	0.190903	−	1.32776i	0.00861534	−	0.0599210i	−0.985060	−	0.172210i	$-0.944909\pi$
$491$	0.190903	−	1.32776i	0.00861534	−	0.0599210i	0.993676	+	0.112289i	$0.0358183\pi$
$492$	26.3325	+	0.185978i	1.18716	+	0.00838454i
$493$	0.0669618	+	0.0772780i	0.00301581	+	0.00348043i
$494$	−0.341398	−	2.24203i	−0.0153602	−	0.100874i
$495$	−5.99402	+	0.573741i	−0.269411	+	0.0257877i
$496$	−17.3210	−	25.0781i	−0.777737	−	1.12604i
$497$	−13.6027	−	46.3264i	−0.610163	−	2.07802i
$498$	−21.0916	−	0.324292i	−0.945138	−	0.0145319i
$499$	−3.85303	−	3.33867i	−0.172485	−	0.149459i	0.564340	−	0.825542i	$-0.309131\pi$
$499$	−3.85303	−	3.33867i	−0.172485	−	0.149459i	−0.736826	+	0.676083i	$0.763676\pi$
$500$	−3.43846	−	11.0287i	−0.153773	−	0.493219i
$501$	−8.48339	−	31.6460i	−0.379010	−	1.41384i
$502$	0.229067	+	27.5593i	0.0102238	+	1.23003i
$503$	−3.63258	−	25.2651i	−0.161969	−	1.12652i	−0.894917	−	0.446232i	$-0.852766\pi$
$503$	−3.63258	−	25.2651i	−0.161969	−	1.12652i	0.732949	−	0.680284i	$-0.238144\pi$
$504$	−20.6074	+	22.7311i	−0.917926	+	1.01252i
$505$	0.142140			0.00632517
$506$	21.5091	−	7.32381i	0.956197	−	0.325583i
$507$	−1.10656	−	1.81497i	−0.0491442	−	0.0806054i
$508$	30.6068	−	4.92119i	1.35796	−	0.218342i
$509$	−15.4769	+	2.22524i	−0.686001	+	0.0986320i	−0.476497	−	0.879176i	$-0.658094\pi$
$509$	−15.4769	+	2.22524i	−0.686001	+	0.0986320i	−0.209504	+	0.977808i	$0.567185\pi$
$510$	2.12510	−	1.32000i	0.0941011	−	0.0584507i
$511$	1.03423	−	3.52228i	0.0457518	−	0.155816i
$512$	−19.8226	+	10.9117i	−0.876042	+	0.482234i
$513$	1.76897	+	1.32329i	0.0781018	+	0.0584245i
$514$	24.6104	+	15.5286i	1.08552	+	0.684939i
$515$	5.25285	−	1.54238i	0.231468	−	0.0679652i
$516$	5.35323	+	11.9445i	0.235663	+	0.525826i
$517$	−24.9425	+	16.0296i	−1.09697	+	0.704979i
$518$	7.25911	+	47.6720i	0.318947	+	2.09459i
$519$	19.4389	+	6.21148i	0.853271	+	0.272654i
$520$	−5.28925	+	3.58863i	−0.231949	+	0.157372i
$521$	35.4738	+	5.10037i	1.55414	+	0.223451i	0.865221	−	0.501391i	$-0.167178\pi$
$521$	35.4738	+	5.10037i	1.55414	+	0.223451i	0.688915	+	0.724842i	$0.258087\pi$
$522$	0.254295	+	0.00993781i	0.0111302	+	0.000434966i
$523$	−9.74343	−	4.44968i	−0.426051	−	0.194571i	0.190838	−	0.981622i	$-0.438880\pi$
$523$	−9.74343	−	4.44968i	−0.426051	−	0.194571i	−0.616888	+	0.787051i	$0.711607\pi$
$524$	11.4206	+	23.9460i	0.498910	+	1.04608i
$525$	−24.0731	−	16.2892i	−1.05064	−	0.710917i
$526$	6.63808	−	23.3226i	0.289434	−	1.01691i
$527$	10.9271	+	7.02239i	0.475990	+	0.305900i
$528$	−21.0199	+	9.84340i	−0.914772	+	0.428379i
$529$	1.70623	−	22.9366i	0.0741837	−	0.997245i
$530$	−2.15763	−	0.963764i	−0.0937214	−	0.0418632i
$531$	−14.2496	+	8.23138i	−0.618382	+	0.357211i
$532$	−1.97452	+	2.35676i	−0.0856063	+	0.102179i
$533$	26.0819	−	11.9112i	1.12973	−	0.515932i
$534$	−36.4240	−	5.80985i	−1.57622	−	0.251417i
$535$	0.314023	+	0.143409i	0.0135764	+	0.00620013i
$536$	−8.84096	+	20.7105i	−0.381871	+	0.894558i
$537$	−9.70555	+	4.15747i	−0.418825	+	0.179408i
$538$	−4.50573	+	33.3006i	−0.194256	+	1.43569i
$539$	−13.3268	−	15.3800i	−0.574026	−	0.662462i
$540$	1.22008	−	6.10553i	0.0525038	−	0.262740i
$541$	7.39265	−	4.75097i	0.317835	−	0.204260i	−0.371989	−	0.928237i	$-0.621324\pi$
$541$	7.39265	−	4.75097i	0.317835	−	0.204260i	0.689824	+	0.723977i	$0.257688\pi$
$542$	−11.7873	+	3.56776i	−0.506309	+	0.153248i
$543$	−20.1452	−	18.3090i	−0.864511	−	0.785713i
$544$	6.00670	−	7.54389i	0.257535	−	0.323441i
$545$	3.30709	+	2.86561i	0.141660	+	0.122749i
$546$	−9.90379	+	31.9062i	−0.423843	+	1.36546i
$547$	1.99062	−	6.77942i	0.0851127	−	0.289867i	−0.905927	−	0.423433i	$-0.860825\pi$
$547$	1.99062	−	6.77942i	0.0851127	−	0.289867i	0.991040	+	0.133566i	$0.0426429\pi$
$548$	33.1590	+	14.4820i	1.41648	+	0.618640i
$549$	28.0614	+	9.70497i	1.19763	+	0.414198i
$550$	−12.0412	−	18.3985i	−0.513439	−	0.784513i
$551$	0.0255021			0.00108643
$552$	0.834424	+	23.4799i	0.0355154	+	0.999369i
$553$	−47.6525			−2.02639
$554$	−20.0011	−	30.5608i	−0.849766	−	1.29841i
$555$	−6.23125	−	7.54515i	−0.264502	−	0.320274i
$556$	−22.1016	−	9.65275i	−0.937317	−	0.409368i
$557$	5.56632	−	18.9571i	0.235852	−	0.803240i	−0.753468	−	0.657484i	$-0.771621\pi$
$557$	5.56632	−	18.9571i	0.235852	−	0.803240i	0.989321	−	0.145755i	$-0.0465612\pi$
$558$	31.3497	−	7.88944i	1.32714	−	0.333986i
$559$	10.7711	+	9.33324i	0.455570	+	0.394754i
$560$	8.39092	+	2.16360i	0.354581	+	0.0914286i
$561$	6.65289	−	7.32010i	0.280885	−	0.309055i
$562$	42.0677	−	12.7329i	1.77452	−	0.537106i
$563$	4.15326	−	2.66914i	0.175039	−	0.112491i	−0.450188	−	0.892934i	$-0.648643\pi$
$563$	4.15326	−	2.66914i	0.175039	−	0.112491i	0.625227	+	0.780443i	$0.285007\pi$
$564$	−8.42930	−	29.4761i	−0.354938	−	1.24117i
$565$	2.21196	+	2.55273i	0.0930577	+	0.107394i
$566$	−3.89383	+	28.7782i	−0.163670	+	1.20964i
$567$	−14.9252	−	28.9184i	−0.626800	−	1.21446i
$568$	34.7351	+	14.8278i	1.45745	+	0.622160i
$569$	−1.79226	−	0.818499i	−0.0751355	−	0.0343132i	0.377493	−	0.926013i	$-0.376786\pi$
$569$	−1.79226	−	0.818499i	−0.0751355	−	0.0343132i	−0.452628	+	0.891699i	$0.649514\pi$
$570$	0.0982776	−	0.616136i	0.00411639	−	0.0258071i
$571$	8.05903	−	3.68044i	0.337260	−	0.154021i	−0.239584	−	0.970876i	$-0.577011\pi$
$571$	8.05903	−	3.68044i	0.337260	−	0.154021i	0.576844	+	0.816854i	$0.304284\pi$
$572$	−16.2304	+	19.3724i	−0.678629	+	0.810002i
$573$	−0.316713	+	13.3689i	−0.0132309	+	0.558496i
$574$	−35.4925	−	15.8537i	−1.48143	−	0.661721i
$575$	−21.9097	+	3.92069i	−0.913697	+	0.163504i
$576$	−3.47489	−	23.7471i	−0.144787	−	0.989463i
$577$	22.7927	+	14.6480i	0.948872	+	0.609803i	0.920897	−	0.389806i	$-0.127458\pi$
$577$	22.7927	+	14.6480i	0.948872	+	0.609803i	0.0279748	+	0.999609i	$0.491094\pi$
$578$	5.45634	−	19.1706i	0.226954	−	0.797392i
$579$	18.5833	−	27.4636i	0.772297	−	1.14135i
$580$	−0.0309406	−	0.0648744i	−0.00128474	−	0.00269376i
$581$	28.3247	+	12.9354i	1.17510	+	0.536652i
$582$	−13.2082	−	8.77821i	−0.547497	−	0.363869i
$583$	−9.24852	−	1.32974i	−0.383035	−	0.0550721i
$584$	1.61221	+	2.37623i	0.0667138	+	0.0983290i
$585$	−1.59983	−	6.58800i	−0.0661446	−	0.272380i
$586$	3.72631	+	24.4714i	0.153932	+	1.01090i
$587$	37.6386	−	24.1888i	1.55351	−	0.998380i	0.569145	−	0.822237i	$-0.307274\pi$
$587$	37.6386	−	24.1888i	1.55351	−	0.998380i	0.984365	−	0.176143i	$-0.0563622\pi$
$588$	19.2025	−	8.60610i	0.791897	−	0.354910i
$589$	3.10825	−	0.912666i	0.128073	−	0.0376057i
$590$	3.93065	+	2.48015i	0.161822	+	0.102106i
$591$	4.58083	−	27.2602i	0.188430	−	1.12134i
$592$	−32.3925	−	19.3270i	−1.33132	−	0.794333i
$593$	−12.2300	+	41.6516i	−0.502226	+	1.71042i	0.183903	+	0.982944i	$0.441127\pi$
$593$	−12.2300	+	41.6516i	−0.502226	+	1.71042i	−0.686129	+	0.727480i	$0.740691\pi$
$594$	−1.96870	−	24.5396i	−0.0807768	−	1.00687i
$595$	−3.65535	+	0.525559i	−0.149855	+	0.0215458i
$596$	−6.73919	+	1.08358i	−0.276048	+	0.0443850i
$597$	5.37271	−	3.27568i	0.219890	−	0.134064i
$598$	11.6083	+	22.7970i	0.474700	+	0.932237i
$599$	−7.33899			−0.299863			−0.149931	−	0.988696i	$-0.547905\pi$
$599$	−7.33899			−0.299863			−0.149931	+	0.988696i	$0.547905\pi$
$600$	21.8074	−	6.43284i	0.890285	−	0.262619i
$601$	0.405873	+	2.82291i	0.0165559	+	0.115149i	0.996424	−	0.0844994i	$-0.0269291\pi$
$601$	0.405873	+	2.82291i	0.0165559	+	0.115149i	−0.979868	+	0.199648i	$0.936020\pi$
$602$	−0.160595	−	19.3213i	−0.00654535	−	0.787477i
$603$	−17.2899	−	16.4783i	−0.704097	−	0.671049i
$604$	7.98103	+	25.5988i	0.324744	+	1.04160i
$605$	0.101190	+	0.0876813i	0.00411394	+	0.00356475i
$606$	−0.00893416	+	0.581070i	−0.000362926	+	0.0236043i
$607$	−0.695016	−	2.36701i	−0.0282098	−	0.0960739i	0.944185	−	0.329416i	$-0.106852\pi$
$607$	−0.695016	−	2.36701i	−0.0282098	−	0.0960739i	−0.972395	+	0.233342i	$0.925034\pi$
$608$	−0.440876	−	2.36426i	−0.0178799	−	0.0958834i
$609$	−0.337930	−	0.164109i	−0.0136936	−	0.00665002i
$610$	−1.26239	−	8.29035i	−0.0511126	−	0.335667i
$611$	−21.8604	−	25.2283i	−0.884378	−	1.02063i
$612$	5.26260	+	8.77038i	0.212728	+	0.354522i
$613$	−5.00236	+	34.7922i	−0.202044	+	1.40524i	0.596165	+	0.802862i	$0.296691\pi$
$613$	−5.00236	+	34.7922i	−0.202044	+	1.40524i	−0.798208	+	0.602382i	$0.794219\pi$
$614$	−5.37278	−	11.5106i	−0.216828	−	0.464530i
$615$	7.83247	−	0.937394i	0.315836	−	0.0377994i
$616$	34.2521	−	0.854246i	1.38006	−	0.0344186i
$617$	−9.27982	+	4.23795i	−0.373591	+	0.170613i	−0.593357	−	0.804939i	$-0.702198\pi$
$617$	−9.27982	+	4.23795i	−0.373591	+	0.170613i	0.219766	+	0.975553i	$0.429471\pi$
$618$	5.97506	+	21.5706i	0.240352	+	0.867695i
$619$	9.46240	−	14.7238i	0.380326	−	0.591799i	−0.597334	−	0.801993i	$-0.703773\pi$
$619$	9.46240	−	14.7238i	0.380326	−	0.591799i	0.977660	+	0.210194i	$0.0674096\pi$
$620$	−6.09282	−	6.79973i	−0.244693	−	0.273084i
$621$	−23.6361	−	7.89530i	−0.948483	−	0.316827i
$622$	−6.56348	−	2.93176i	−0.263172	−	0.117553i
$623$	45.8044	+	29.4367i	1.83511	+	1.17936i
$624$	−14.3378	−	21.8480i	−0.573973	−	0.874620i
$625$	8.20223	+	17.9604i	0.328089	+	0.718415i
$626$	0.749612	+	0.638712i	0.0299605	+	0.0255281i
$627$	−0.293158	−	2.44951i	−0.0117076	−	0.0978240i
$628$	26.3314	−	0.437753i	1.05074	−	0.0174682i
$629$	15.9116	+	2.28774i	0.634437	+	0.0912183i
$630$	−5.26718	+	7.53203i	−0.209849	+	0.300083i
$631$	23.1571	−	20.0657i	0.921870	−	0.798805i	−0.0580261	−	0.998315i	$-0.518481\pi$
$631$	23.1571	−	20.0657i	0.921870	−	0.798805i	0.979896	+	0.199510i	$0.0639352\pi$
$632$	23.7000	−	28.7704i	0.942734	−	1.14442i
$633$	7.15386	−	14.7311i	0.284340	−	0.585509i
$634$	−9.45280	+	2.86115i	−0.375419	+	0.113631i
$635$	8.91017	−	2.61626i	0.353589	−	0.103823i
$636$	4.07548	−	8.75980i	0.161603	−	0.347349i
$637$	15.0046	−	17.3162i	0.594502	−	0.686092i
$638$	−0.187885	−	0.213224i	−0.00743844	−	0.00844162i
$639$	−27.6369	+	28.9980i	−1.09330	+	1.14714i
$640$	−5.47950	+	3.98998i	−0.216596	+	0.157718i
$641$	−3.88194	+	0.558138i	−0.153327	+	0.0220451i	−0.218551	−	0.975826i	$-0.570133\pi$
$641$	−3.88194	+	0.558138i	−0.153327	+	0.0220451i	0.0652237	+	0.997871i	$0.479224\pi$
$642$	−0.605995	+	1.27471i	−0.0239167	+	0.0503088i
$643$			42.3026i			1.66825i	0.551575	+	0.834125i	$0.314027\pi$
$643$			42.3026i			1.66825i	−0.551575	+	0.834125i	$0.685973\pi$
$644$	12.7839	−	32.2402i	0.503754	−	1.27044i
$645$	2.04114	+	3.34784i	0.0803697	+	0.131821i
$646$	0.561277	+	0.857607i	0.0220831	+	0.0337421i
$647$	4.16570	+	28.9731i	0.163771	+	1.13905i	0.891445	+	0.453128i	$0.149692\pi$
$647$	4.16570	+	28.9731i	0.163771	+	1.13905i	−0.727675	+	0.685922i	$0.759399\pi$
$648$	24.8827	+	5.37143i	0.977484	+	0.211010i
$649$	17.6325	+	5.17738i	0.692138	+	0.203230i
$650$	18.5745	−	16.3671i	0.728550	−	0.641972i
$651$	−47.0608	−	7.90813i	−1.84446	−	0.309944i
$652$	−0.0786429	−	0.118011i	−0.00307989	−	0.00462165i
$653$	−3.37936	−	11.5090i	−0.132245	−	0.450384i	0.866570	−	0.499055i	$-0.166319\pi$
$653$	−3.37936	−	11.5090i	−0.132245	−	0.450384i	−0.998815	+	0.0486714i	$0.984501\pi$
$654$	−11.9225	+	13.3393i	−0.466206	+	0.521607i
$655$	4.29664	+	6.68571i	0.167884	+	0.261232i
$656$	27.2240	−	13.5439i	1.06292	−	0.528801i
$657$	−2.95970	+	0.718731i	−0.115469	+	0.0280404i
$658$	−6.06807	+	44.8474i	−0.236558	+	1.74833i
$659$	−1.98147	+	13.7814i	−0.0771869	+	0.536847i	0.914137	+	0.405405i	$0.132870\pi$
$659$	−1.98147	+	13.7814i	−0.0771869	+	0.536847i	−0.991324	+	0.131442i	$0.958039\pi$
$660$	−5.87558	+	3.71764i	−0.228707	+	0.144709i
$661$	0.850184	−	1.86164i	0.0330683	−	0.0724095i	−0.892377	−	0.451291i	$-0.850964\pi$
$661$	0.850184	−	1.86164i	0.0330683	−	0.0724095i	0.925445	+	0.378881i	$0.123691\pi$
$662$	−7.38712	+	8.66975i	−0.287108	+	0.336959i
$663$	9.22376	+	6.24129i	0.358221	+	0.242392i
$664$	−21.8971	+	10.6677i	−0.849772	+	0.413986i
$665$	−0.497942	+	0.774813i	−0.0193094	+	0.0300459i
$666$	31.2362	−	24.9991i	1.21038	−	0.968695i
$667$	−0.273080	+	0.0904573i	−0.0105737	+	0.00350252i
$668$	−25.2464	−	28.1756i	−0.976814	−	1.09015i
$669$	−13.9633	−	0.330793i	−0.539852	−	0.0127892i
$670$	−1.84661	+	6.48800i	−0.0713410	+	0.250653i
$671$	−13.7742	−	30.1614i	−0.531749	−	1.16437i
$672$	−9.37218	+	34.1660i	−0.361540	+	1.31798i
$673$	−12.6798	+	27.7649i	−0.488771	+	1.07026i	0.491187	+	0.871054i	$0.336563\pi$
$673$	−12.6798	+	27.7649i	−0.488771	+	1.07026i	−0.979958	+	0.199205i	$0.936164\pi$
$674$	21.4200	−	9.99819i	0.825069	−	0.385116i
$675$	−1.71215	+	24.0548i	−0.0659007	+	0.925869i
$676$	−2.08666	−	1.29252i	−0.0802563	−	0.0497122i
$677$	20.4310	−	17.7035i	0.785226	−	0.680402i	−0.166946	−	0.985966i	$-0.553391\pi$
$677$	20.4310	−	17.7035i	0.785226	−	0.680402i	0.952171	+	0.305564i	$0.0988451\pi$
$678$	−10.5746	+	8.88202i	−0.406115	+	0.341112i
$679$	12.6569	+	19.6945i	0.485727	+	0.755806i
$680$	1.50068	−	2.46832i	0.0575484	−	0.0946556i
$681$	32.3742	+	29.4233i	1.24058	+	1.12750i
$682$	−30.5307	−	19.2642i	−1.16908	−	0.737664i
$683$	9.87008	−	11.3907i	0.377668	−	0.435852i	−0.534813	−	0.844970i	$-0.679618\pi$
$683$	9.87008	−	11.3907i	0.377668	−	0.435852i	0.912481	+	0.409118i	$0.134164\pi$
$684$	2.51258	+	0.440485i	0.0960711	+	0.0168424i
$685$	10.4001	+	3.05374i	0.397366	+	0.116677i
$686$	4.73228	−	0.0393338i	0.180679	−	0.00150177i
$687$	19.8831	−	16.4207i	0.758586	−	0.626487i
$688$	11.7452	+	9.51248i	0.447781	+	0.362660i
$689$		−	10.5199i		−	0.400777i
$690$	1.13310	+	6.94626i	0.0431363	+	0.264439i
$691$		−	5.33748i		−	0.203047i	−0.994833	−	0.101524i	$-0.967628\pi$
$691$		−	5.33748i		−	0.203047i	0.994833	−	0.101524i	$-0.0323717\pi$
$692$	23.2653	−	3.74077i	0.884415	−	0.142203i
$693$	−11.8782	+	34.3451i	−0.451214	+	1.30466i
$694$	0.210309	+	25.3025i	0.00798322	+	0.960469i
$695$	−6.93201	−	2.03542i	−0.262946	−	0.0772079i
$696$	0.267151	−	0.122407i	0.0101263	−	0.00463983i
$697$	−8.48606	+	9.79344i	−0.321433	+	0.370953i
$698$	−1.02245	+	1.62042i	−0.0387004	+	0.0613339i
$699$	−20.5229	+	22.5811i	−0.776246	+	0.854095i
$700$	−33.2961	−	4.22362i	−1.25848	−	0.159638i
$701$	−24.7762	−	38.5525i	−0.935783	−	1.45611i	−0.889372	−	0.457185i	$-0.848858\pi$
$701$	−24.7762	−	38.5525i	−0.935783	−	1.45611i	−0.0464120	−	0.998922i	$-0.514779\pi$
$702$	27.0323	−	6.12600i	1.02027	−	0.231211i
$703$	3.02994	−	2.62545i	0.114276	−	0.0990209i
$704$	−16.5195	+	21.1047i	−0.622603	+	0.795413i
$705$	−3.61618	−	8.44191i	−0.136193	−	0.317941i
$706$	−14.3667	−	30.7791i	−0.540699	−	1.15839i
$707$	0.356368	−	0.780338i	0.0134026	−	0.0293476i
$708$	−10.3859	+	15.9126i	−0.390327	+	0.598031i
$709$	6.57460	+	14.3964i	0.246914	+	0.540667i	0.991990	−	0.126313i	$-0.0403143\pi$
$709$	6.57460	+	14.3964i	0.246914	+	0.540667i	−0.745076	+	0.666979i	$0.767587\pi$
$710$	10.8815	+	3.09709i	0.408375	+	0.116232i
$711$	19.7759	+	34.2347i	0.741652	+	1.28390i
$712$	−40.5534	+	13.0142i	−1.51980	+	0.487729i
$713$	−30.0463	+	20.7981i	−1.12524	+	0.778894i
$714$	−1.91873	−	14.9761i	−0.0718067	−	0.560465i
$715$	−4.09305	+	6.36891i	−0.153071	+	0.238184i
$716$	−7.82975	+	9.34548i	−0.292611	+	0.349257i
$717$	5.45989	−	8.06896i	0.203903	−	0.301341i
$718$	−0.0756330	−	0.0644436i	−0.00282260	−	0.00240501i
$719$	−6.68188	+	14.6313i	−0.249192	+	0.545655i	−0.992349	−	0.123462i	$-0.960600\pi$
$719$	−6.68188	+	14.6313i	−0.249192	+	0.545655i	0.743157	+	0.669117i	$0.233327\pi$
$720$	−1.92786	−	6.92614i	−0.0718472	−	0.258122i
$721$	4.70222	−	32.7046i	0.175120	−	1.21798i
$722$	−26.3741	−	3.56854i	−0.981543	−	0.132807i
$723$	−15.8744	+	49.6791i	−0.590376	+	1.84758i
$724$	−30.3032	−	8.35326i	−1.12621	−	0.310446i
$725$	0.150508	+	0.234195i	0.00558972	+	0.00869777i
$726$	−0.364801	+	0.408151i	−0.0135390	+	0.0151479i
$727$	1.21663	+	4.14347i	0.0451224	+	0.153673i	0.978973	−	0.203991i	$-0.0653914\pi$
$727$	1.21663	+	4.14347i	0.0451224	+	0.153673i	−0.933850	+	0.357664i	$0.883573\pi$
$728$	6.44025	+	38.0348i	0.238692	+	1.40966i
$729$	−14.5817	+	22.7238i	−0.540064	+	0.841624i
$730$	0.568692	+	0.645388i	0.0210482	+	0.0238869i
$731$	−6.18029	−	1.81470i	−0.228586	−	0.0671190i
$732$	33.9703	−	4.63956i	1.25558	−	0.171483i
$733$	−6.34214	−	44.1106i	−0.234252	−	1.62926i	−0.679375	−	0.733792i	$-0.737749\pi$
$733$	−6.34214	−	44.1106i	−0.234252	−	1.62926i	0.445122	−	0.895470i	$-0.353160\pi$
$734$	34.9733	−	22.8889i	1.29089	−	0.844845i
$735$	5.38214	−	3.28143i	0.198523	−	0.121037i
$736$	13.1071	+	23.7530i	0.483134	+	0.875546i
$737$			26.6723i			0.982487i
$738$	3.33976	+	32.0780i	0.122938	+	1.18081i
$739$	11.0292	−	1.58575i	0.405714	−	0.0583329i	0.0635630	−	0.997978i	$-0.479754\pi$
$739$	11.0292	−	1.58575i	0.405714	−	0.0583329i	0.342151	+	0.939645i	$0.388845\pi$
$740$	−10.3549	−	4.52245i	−0.380655	−	0.166249i
$741$	2.68284	−	0.719193i	0.0985566	−	0.0264202i
$742$	−10.7005	+	9.42888i	−0.392827	+	0.346145i
$743$	−3.86230	+	4.45733i	−0.141694	+	0.163524i	−0.822161	−	0.569255i	$-0.807232\pi$
$743$	−3.86230	+	4.45733i	−0.141694	+	0.163524i	0.680467	+	0.732779i	$0.261777\pi$
$744$	28.1802	−	24.4800i	1.03314	−	0.897481i
$745$	−1.96190	+	0.576064i	−0.0718783	+	0.0211054i
$746$	1.41582	+	4.67766i	0.0518368	+	0.171261i
$747$	−2.46164	−	25.7174i	−0.0900666	−	0.940949i
$748$	3.03531	−	11.0112i	0.110982	−	0.402610i
$749$	1.57461	−	1.36441i	0.0575350	−	0.0498543i
$750$	12.9589	−	5.67900i	0.473191	−	0.207368i
$751$	7.06576	+	1.01590i	0.257833	+	0.0370708i	0.270019	−	0.962855i	$-0.412970\pi$
$751$	7.06576	+	1.01590i	0.257833	+	0.0370708i	−0.0121859	+	0.999926i	$0.503879\pi$
$752$	−24.0589	−	25.9685i	−0.877336	−	0.946974i
$753$	−33.5151	+	4.01111i	−1.22136	+	0.146173i
$754$	0.207519	−	0.243550i	0.00755738	−	0.00886958i
$755$	3.33680	+	7.30657i	0.121438	+	0.265913i
$756$	−30.4599	−	22.0056i	−1.10781	−	0.800337i
$757$	35.1466	+	22.5873i	1.27742	+	0.820951i	0.990568	−	0.137022i	$-0.0437533\pi$
$757$	35.1466	+	22.5873i	1.27742	+	0.820951i	0.286857	+	0.957973i	$0.407390\pi$
$758$	−5.97648	+	13.3799i	−0.217076	+	0.485978i
$759$	11.8277	+	25.1898i	0.429319	+	0.914332i
$760$	−0.220145	−	0.685988i	−0.00798549	−	0.0248834i
$761$	−7.01580	+	10.9168i	−0.254323	+	0.395734i	−0.944814	−	0.327607i	$-0.893758\pi$
$761$	−7.01580	+	10.9168i	−0.254323	+	0.395734i	0.690491	+	0.723341i	$0.257394\pi$
$762$	10.1352	+	36.5892i	0.367160	+	1.32549i
$763$	24.0234	−	10.9711i	0.869704	−	0.397181i
$764$	6.64721	+	13.9375i	0.240488	+	0.504240i
$765$	1.89455	+	2.40798i	0.0684976	+	0.0870608i
$766$	2.27865	−	1.06360i	0.0823310	−	0.0384295i
$767$	−2.94456	+	20.4799i	−0.106322	+	0.739485i
$768$	−15.9666	−	22.6510i	−0.576146	−	0.817347i
$769$	8.92586	+	10.3010i	0.321875	+	0.371463i	0.893509	−	0.449045i	$-0.148236\pi$
$769$	8.92586	+	10.3010i	0.321875	+	0.371463i	−0.571634	+	0.820509i	$0.693690\pi$
$770$	10.1468	−	1.54507i	0.365665	−	0.0556805i
$771$	−15.5691	+	32.0596i	−0.560706	+	1.15460i
$772$	4.81848	−	37.9856i	0.173421	−	1.36713i
$773$	−7.53798	−	25.6720i	−0.271122	−	0.923358i	−0.976679	−	0.214704i	$-0.931121\pi$
$773$	−7.53798	−	25.6720i	−0.271122	−	0.923358i	0.705557	−	0.708653i	$-0.250697\pi$
$774$	−13.8142	+	8.13374i	−0.496543	+	0.292361i
$775$	26.7255	+	23.1578i	0.960010	+	0.831853i
$776$	−18.1855	−	2.15342i	−0.652823	−	0.0773032i
$777$	−57.0449	+	15.2921i	−2.04648	+	0.548602i
$778$	−39.6760	+	0.329779i	−1.42245	+	0.0118231i
$779$	0.459945	+	3.19899i	0.0164792	+	0.114616i
$780$	−5.08451	−	5.95226i	−0.182055	−	0.213125i
$781$	44.7340			1.60071
$782$	−9.05220	−	7.19248i	−0.323706	−	0.257203i
$783$	0.0223418	+	0.310883i	0.000798431	+	0.0111100i
$784$	15.2927	−	18.8821i	0.546168	−	0.674361i
$785$	7.80863	−	1.12271i	0.278702	−	0.0400713i
$786$	−27.6012	+	17.1444i	−0.984503	+	0.611522i
$787$	14.0505	−	47.8517i	0.500847	−	1.70573i	−0.189179	−	0.981943i	$-0.560583\pi$
$787$	14.0505	−	47.8517i	0.500847	−	1.70573i	0.690026	−	0.723785i	$-0.257599\pi$
$788$	−9.50038	−	30.4721i	−0.338437	−	1.08552i
$789$	29.2881	+	4.92159i	1.04268	+	0.175213i
$790$	5.95856	−	9.44336i	0.211996	−	0.335980i
$791$	19.5600	−	5.74334i	0.695474	−	0.204210i
$792$	−14.8284	−	24.2530i	−0.526904	−	0.861794i
$793$	31.4058	−	20.1833i	1.11525	−	0.716729i
$794$	−3.74573	+	0.570370i	−0.132931	+	0.0202417i
$795$	0.880925	−	2.75686i	0.0312432	−	0.0977757i
$796$	3.82615	−	6.17700i	0.135614	−	0.218938i
$797$	−35.1694	−	5.05659i	−1.24576	−	0.179114i	−0.512278	−	0.858820i	$-0.671198\pi$
$797$	−35.1694	−	5.05659i	−1.24576	−	0.179114i	−0.733485	+	0.679706i	$0.762107\pi$
$798$	−3.13613	−	2.08429i	−0.111018	−	0.0737829i
$799$	13.7233	+	6.26723i	0.485496	+	0.221719i
$800$	19.1099	−	18.0020i	0.675636	−	0.636468i
$801$	2.13916	−	45.1233i	0.0755835	−	1.59435i
$802$	−48.3593	−	13.7640i	−1.70763	−	0.486025i
$803$	2.86127	+	1.83883i	0.100972	+	0.0648908i
$804$	−26.4069	−	7.95675i	−0.931298	−	0.280613i
$805$	2.58372	−	10.0630i	0.0910642	−	0.354675i
$806$	16.5767	−	37.1111i	0.583889	−	1.30718i
$807$	−41.1449	−	0.974730i	−1.44837	−	0.0343121i
$808$	0.293892	+	0.603260i	0.0103391	+	0.0212226i
$809$	−10.5789	+	4.83121i	−0.371933	+	0.169856i	−0.592607	−	0.805491i	$-0.701901\pi$
$809$	−10.5789	+	4.83121i	−0.371933	+	0.169856i	0.220674	+	0.975348i	$0.429174\pi$
$810$	7.59709	+	0.658267i	0.266934	+	0.0231292i
$811$	−13.9175	−	6.35593i	−0.488711	−	0.223187i	0.155790	−	0.987790i	$-0.450208\pi$
$811$	−13.9175	−	6.35593i	−0.488711	−	0.223187i	−0.644501	+	0.764603i	$0.722935\pi$
$812$	−0.433727	+	0.00721060i	−0.0152208	+	0.000253042i
$813$	−5.93912	−	13.8648i	−0.208294	−	0.486259i
$814$	−44.2743	−	5.99053i	−1.55181	−	0.209968i
$815$	−0.0278197	−	0.0321056i	−0.000974480	−	0.00112461i
$816$	9.99615	+	6.28991i	0.349935	+	0.220191i
$817$	−1.35143	+	0.868509i	−0.0472804	+	0.0303853i
$818$	−1.28157	−	4.23411i	−0.0448090	−	0.148042i
$819$	−40.1786	−	7.73427i	−1.40395	−	0.270257i
$820$	7.57981	−	5.05123i	0.264699	−	0.176397i
$821$	24.3408	+	21.0914i	0.849500	+	0.736096i	0.966399	−	0.257048i	$-0.0827498\pi$
$821$	24.3408	+	21.0914i	0.849500	+	0.736096i	−0.116899	+	0.993144i	$0.537295\pi$
$822$	−13.1374	+	42.3235i	−0.458218	+	1.47620i
$823$	7.80947	−	26.5966i	0.272221	−	0.927099i	−0.703978	−	0.710222i	$-0.748595\pi$
$823$	7.80947	−	26.5966i	0.272221	−	0.927099i	0.976199	−	0.216877i	$-0.0695872\pi$
$824$	17.4069	+	19.1046i	0.606398	+	0.665542i
$825$	20.7645	−	17.1486i	0.722928	−	0.597039i
$826$	23.4706	−	15.3608i	0.816645	−	0.534469i
$827$	45.3313			1.57632			0.788161	−	0.615469i	$-0.211033\pi$
$827$	45.3313			1.57632			0.788161	+	0.615469i	$0.211033\pi$
$828$	−28.4675	+	4.19550i	−0.989314	+	0.145804i
$829$	−0.873420			−0.0303351			−0.0151676	−	0.999885i	$-0.504828\pi$
$829$	−0.873420			−0.0303351			−0.0151676	+	0.999885i	$0.504828\pi$
$830$	−6.10521	+	3.99567i	−0.211915	+	0.138692i
$831$	34.4910	−	28.4848i	1.19648	−	0.988127i
$832$	−26.1667	−	15.0283i	−0.907167	−	0.521011i
$833$	−2.91739	+	9.93573i	−0.101082	+	0.344253i
$834$	8.75650	−	28.2101i	0.303213	−	0.976835i
$835$	−8.56484	−	7.42148i	−0.296399	−	0.256831i
$836$	−1.57971	−	2.37049i	−0.0546354	−	0.0819852i
$837$	13.8489	+	37.0915i	0.478688	+	1.28207i
$838$	−11.5348	−	38.1093i	−0.398464	−	1.31647i
$839$	−14.6609	+	9.42201i	−0.506151	+	0.325284i	−0.768673	−	0.639642i	$-0.779082\pi$
$839$	−14.6609	+	9.42201i	−0.506151	+	0.325284i	0.262521	+	0.964926i	$0.415446\pi$
$840$	−1.49725	+	10.5067i	−0.0516599	+	0.362516i
$841$	−18.9886	−	21.9140i	−0.654779	−	0.755656i
$842$	−5.49828	−	0.743944i	−0.189483	−	0.0256380i
$843$	21.1960	+	49.4818i	0.730031	+	1.70425i
$844$	−0.314326	−	18.9071i	−0.0108195	−	0.650810i
$845$	−0.668836	−	0.305447i	−0.0230087	−	0.0105077i
$846$	34.7378	−	14.2523i	1.19431	−	0.490004i
$847$	0.735060	−	0.335691i	0.0252570	−	0.0115345i
$848$	−0.370831	−	11.1499i	−0.0127344	−	0.382890i
$849$	−35.5571	−	0.842355i	−1.22032	−	0.0289096i
$850$	−4.56317	+	10.2158i	−0.156515	+	0.350399i
$851$	−23.1323	+	38.8610i	−0.792965	+	1.33214i
$852$	−13.3448	+	44.2888i	−0.457186	+	1.51731i
$853$	−16.2563	−	10.4473i	−0.556604	−	0.357708i	0.231898	−	0.972740i	$-0.425507\pi$
$853$	−16.2563	−	10.4473i	−0.556604	−	0.357708i	−0.788502	+	0.615033i	$0.789143\pi$
$854$	−48.6783	−	13.8548i	−1.66574	−	0.474102i
$855$	0.763291	+	0.0361854i	0.0261040	+	0.00123751i
$856$	0.0406338	+	1.62927i	0.00138884	+	0.0556871i
$857$	6.54509	+	2.98904i	0.223576	+	0.102104i	0.524054	−	0.851685i	$-0.324419\pi$
$857$	6.54509	+	2.98904i	0.223576	+	0.102104i	−0.300478	+	0.953789i	$0.597146\pi$
$858$	−25.7788	−	17.1327i	−0.880075	−	0.584901i
$859$	−41.0783	−	5.90617i	−1.40157	−	0.201516i	−0.600281	−	0.799789i	$-0.704945\pi$
$859$	−41.0783	−	5.90617i	−1.40157	−	0.201516i	−0.801292	+	0.598273i	$0.795854\pi$
$860$	3.84901	+	2.38415i	0.131250	+	0.0812987i
$861$	14.4910	−	45.3498i	0.493853	−	1.54552i
$862$	−24.2988	+	3.70002i	−0.827619	+	0.126023i
$863$	−21.4685	+	13.7970i	−0.730797	+	0.469655i	−0.852378	−	0.522927i	$-0.824840\pi$
$863$	−21.4685	+	13.7970i	−0.730797	+	0.469655i	0.121580	+	0.992582i	$0.461204\pi$
$864$	28.4352	−	7.44576i	0.967385	−	0.253310i
$865$	6.77294	−	1.98871i	0.230287	−	0.0676183i
$866$	−2.30003	+	3.64518i	−0.0781583	+	0.123868i
$867$	24.0741	+	4.04543i	0.817598	+	0.137390i
$868$	−52.6056	+	16.4010i	−1.78555	+	0.556686i
$869$	12.4386	−	42.3621i	0.421952	−	1.43704i
$870$	0.0747771	−	0.0464476i	0.00253518	−	0.00157472i
$871$	−29.7245	+	4.27373i	−1.00718	+	0.144810i
$872$	−5.32418	+	19.9607i	−0.180299	+	0.675954i
$873$	8.89640	−	17.2663i	0.301097	−	0.584375i
$874$	−2.83410	+	0.531504i	−0.0958650	+	0.0179784i
$875$	−20.8858			−0.706070
$876$	−2.67409	+	2.28425i	−0.0903491	+	0.0771775i
$877$	3.07148	+	21.3626i	0.103716	+	0.721364i	0.973626	+	0.228152i	$0.0732682\pi$
$877$	3.07148	+	21.3626i	0.103716	+	0.721364i	−0.869909	+	0.493212i	$0.835823\pi$
$878$	−22.8988	+	0.190330i	−0.772795	+	0.00642332i
$879$	−29.2827	+	7.84987i	−0.987683	+	0.264770i
$880$	−4.11366	+	6.89460i	−0.138672	+	0.232417i
$881$	−13.0312	−	11.2916i	−0.439032	−	0.380424i	0.407111	−	0.913378i	$-0.366536\pi$
$881$	−13.0312	−	11.2916i	−0.439032	−	0.380424i	−0.846144	+	0.532955i	$0.821082\pi$
$882$	13.0762	+	22.2084i	0.440298	+	0.747797i
$883$	5.77409	+	19.6647i	0.194313	+	0.661771i	0.997791	+	0.0664355i	$0.0211626\pi$
$883$	5.77409	+	19.6647i	0.194313	+	0.661771i	−0.803477	+	0.595335i	$0.797019\pi$
$884$	12.7576	+	1.61831i	0.429085	+	0.0544295i
$885$	−2.48661	+	5.12040i	−0.0835866	+	0.172120i
$886$	46.6637	−	7.10557i	1.56770	−	0.238716i
$887$	3.46255	+	3.99600i	0.116261	+	0.134173i	0.810897	−	0.585189i	$-0.198980\pi$
$887$	3.46255	+	3.99600i	0.116261	+	0.134173i	−0.694636	+	0.719362i	$0.744434\pi$
$888$	19.1386	−	42.0466i	0.642250	−	1.41099i
$889$	7.97616	−	55.4754i	0.267512	−	1.86059i
$890$	−11.5610	+	5.39630i	−0.387525	+	0.180885i
$891$	29.6038	−	5.71970i	0.991766	−	0.191617i
$892$	−14.5571	+	6.94273i	−0.487408	+	0.232460i
$893$	3.42261	−	1.56305i	0.114533	−	0.0523056i
$894$	−2.23164	−	8.05643i	−0.0746371	−	0.269447i
$895$	−1.97454	+	3.07244i	−0.0660014	+	0.102700i
$896$	8.16667	+	40.0855i	0.272829	+	1.33916i
$897$	−26.1772	+	17.2174i	−0.874030	+	0.574871i
$898$	12.6630	−	28.3494i	0.422571	−	0.946031i
$899$	0.384496	+	0.247101i	0.0128237	+	0.00824127i
$900$	10.7836	+	25.6736i	0.359453	+	0.855786i
$901$	1.97505	+	4.32476i	0.0657985	+	0.144079i
$902$	23.3582	−	27.4139i	0.777743	−	0.912784i
$903$	23.4968	−	2.81211i	0.781924	−	0.0935810i
$904$	−6.26061	+	14.6659i	−0.208225	+	0.487780i
$905$	−9.32035	−	1.34006i	−0.309819	−	0.0445453i
$906$	−30.0789	+	13.1816i	−0.999306	+	0.437928i
$907$	9.11640	−	7.89940i	0.302705	−	0.262295i	−0.490242	−	0.871587i	$-0.663091\pi$
$907$	9.11640	−	7.89940i	0.302705	−	0.262295i	0.792946	+	0.609291i	$0.208546\pi$
$908$	48.6986	+	13.4241i	1.61612	+	0.445493i
$909$	−0.708508	+	0.0678176i	−0.0234997	+	0.00224937i
$910$	3.34771	+	11.0603i	0.110976	+	0.366647i
$911$	−8.28222	+	2.43188i	−0.274402	+	0.0805717i	−0.416038	−	0.909347i	$-0.636582\pi$
$911$	−8.28222	+	2.43188i	−0.274402	+	0.0805717i	0.141636	+	0.989919i	$0.454764\pi$
$912$	2.81815	−	0.856834i	0.0933183	−	0.0283726i
$913$	−18.8929	+	21.8036i	−0.625263	+	0.721592i
$914$	−18.2826	+	16.1100i	−0.604736	+	0.532871i
$915$	9.92034	−	2.65936i	0.327956	−	0.0879158i
$916$	11.9176	−	27.2874i	0.393769	−	0.901602i
$917$	47.4763	−	6.82606i	1.56780	−	0.225416i
$918$	−9.96291	+	7.59356i	−0.328825	+	0.250625i
$919$			50.5053i			1.66602i	0.553261	+	0.833008i	$0.313383\pi$
$919$			50.5053i			1.66602i	−0.553261	+	0.833008i	$0.686617\pi$
$920$	4.79057	+	6.56477i	0.157940	+	0.216434i
$921$	13.2835	−	8.09877i	0.437705	−	0.266864i
$922$	−29.1126	+	19.0533i	−0.958771	+	0.627486i
$923$	7.16778	+	49.8530i	0.235930	+	1.64093i
$924$	5.67848	+	41.5771i	0.186808	+	1.36779i
$925$	41.9924	+	12.3301i	1.38070	+	0.405411i
$926$	−29.9497	−	33.9889i	−0.984210	−	1.11694i
$927$	−25.4473	+	10.1943i	−0.835797	+	0.334824i
$928$	0.211361	−	0.265451i	0.00693826	−	0.00871385i
$929$	−13.5234	−	46.0564i	−0.443688	−	1.51106i	−0.813283	−	0.581869i	$-0.802322\pi$
$929$	−13.5234	−	46.0564i	−0.443688	−	1.51106i	0.369595	−	0.929193i	$-0.379497\pi$
$930$	7.45174	−	8.33725i	0.244352	−	0.273389i
$931$	1.39626	+	2.17262i	0.0457604	+	0.0712046i
$932$	−9.36333	+	33.9674i	−0.306706	+	1.11264i
$933$	2.67976	−	8.38634i	0.0877316	−	0.274556i
$934$	8.33005	+	1.12710i	0.272568	+	0.0368797i
$935$	0.486937	−	3.38672i	0.0159245	−	0.110758i
$936$	24.6524	−	20.4113i	0.805789	−	0.667165i
$937$	−6.18981	+	13.5538i	−0.202212	+	0.442783i	−0.983385	−	0.181532i	$-0.941895\pi$
$937$	−6.18981	+	13.5538i	−0.202212	+	0.442783i	0.781173	+	0.624315i	$0.214622\pi$
$938$	30.9888	+	26.4042i	1.01182	+	0.862127i
$939$	−0.675944	+	0.998953i	−0.0220586	+	0.0325996i
$940$	−8.12872	−	6.81033i	−0.265130	−	0.222129i
$941$	3.35864	−	5.22614i	0.109488	−	0.170367i	−0.782185	−	0.623046i	$-0.785895\pi$
$941$	3.35864	−	5.22614i	0.109488	−	0.170367i	0.891674	+	0.452678i	$0.149531\pi$
$942$	4.09883	+	31.9922i	0.133547	+	1.04236i
$943$	−16.2721	−	32.6237i	−0.529893	−	1.06237i
$944$	−2.39897	+	21.8101i	−0.0780800	+	0.709859i
$945$	−9.88157	−	5.39135i	−0.321447	−	0.175381i
$946$	17.2182	+	4.90064i	0.559811	+	0.159333i
$947$	−12.5055	−	27.3832i	−0.406374	−	0.889835i	−0.996584	−	0.0825852i	$-0.973682\pi$
$947$	−12.5055	−	27.3832i	−0.406374	−	0.889835i	0.590210	−	0.807250i	$-0.299045\pi$
$948$	38.2299	+	24.9521i	1.24165	+	0.810407i
$949$	−1.59079	+	3.48333i	−0.0516391	+	0.113074i
$950$	1.18025	+	2.52856i	0.0382924	+	0.0820374i
$951$	−4.76285	−	11.1188i	−0.154446	−	0.360552i
$952$	−9.78840	−	14.4270i	−0.317244	−	0.467583i
$953$	4.21778	−	3.65472i	0.136627	−	0.118388i	−0.583866	−	0.811850i	$-0.698461\pi$
$953$	4.21778	−	3.65472i	0.136627	−	0.118388i	0.720493	+	0.693462i	$0.243915\pi$
$954$	11.2147	+	3.77450i	0.363088	+	0.122204i
$955$	2.50081	+	3.89134i	0.0809244	+	0.125921i
$956$	1.41570	−	11.1604i	0.0457869	−	0.360952i
$957$	0.234099	−	0.257576i	0.00756734	−	0.00832626i
$958$	−2.89969	+	4.59555i	−0.0936849	+	0.148476i
$959$	42.8393	−	49.4392i	1.38335	−	1.59648i
$960$	−5.59882	−	6.12949i	−0.180701	−	0.197828i
$961$	25.9622	+	7.62318i	0.837489	+	0.245909i
$962$	−0.418089	−	50.3006i	−0.0134797	−	1.62176i
$963$	−1.63369	−	0.565008i	−0.0526449	−	0.0182071i
$964$	9.56013	+	59.4582i	0.307911	+	1.91502i
$965$		−	11.4701i		−	0.369237i
$966$	40.9752	+	11.1948i	1.31835	+	0.360185i
$967$			28.8249i			0.926946i	0.886111	+	0.463473i	$0.153397\pi$
$967$			28.8249i			0.926946i	−0.886111	+	0.463473i	$0.846603\pi$
$968$	−0.162908	+	0.610752i	−0.00523605	+	0.0196303i
$969$	−0.967896	+	0.799349i	−0.0310933	+	0.0256788i
$970$	−5.48553	+	0.0455946i	−0.176130	+	0.00146396i
$971$	24.2241	+	7.11285i	0.777390	+	0.228262i	0.646275	−	0.763105i	$-0.276326\pi$
$971$	24.2241	+	7.11285i	0.777390	+	0.228262i	0.131115	+	0.991367i	$0.458144\pi$
$972$	−3.16851	+	31.0155i	−0.101630	+	0.994822i
$973$	−28.5539	+	32.9530i	−0.915396	+	1.05642i
$974$	9.85591	+	6.21887i	0.315804	+	0.199265i
$975$	22.4381	+	20.3929i	0.718595	+	0.653096i
$976$	32.5751	−	22.4990i	1.04270	−	0.720176i
$977$	17.6536	+	27.4696i	0.564790	+	0.878830i	0.999766	−	0.0216116i	$-0.00687973\pi$
$977$	17.6536	+	27.4696i	0.564790	+	0.878830i	−0.434977	+	0.900442i	$0.643243\pi$
$978$	0.132996	−	0.111709i	0.00425275	−	0.00357205i
$979$	−38.1249	+	33.0354i	−1.21848	+	1.05582i
$980$	3.83287	−	6.18785i	0.122436	−	0.197664i
$981$	−17.8516	−	12.7060i	−0.569959	−	0.405670i
$982$	1.71900	−	0.802376i	0.0548556	−	0.0256049i
$983$	3.37257	−	7.38489i	0.107568	−	0.235541i	−0.848192	−	0.529689i	$-0.822309\pi$
$983$	3.37257	−	7.38489i	0.107568	−	0.235541i	0.955760	+	0.294148i	$0.0950358\pi$
$984$	20.1730	+	31.3037i	0.643091	+	0.997927i
$985$	−3.97202	−	8.69751i	−0.126559	−	0.277126i
$986$	−0.0395862	+	0.139084i	−0.00126068	+	0.00442935i
$987$	−55.4116	−	1.31271i	−1.76377	−	0.0417841i
$988$	2.38864	−	2.14031i	0.0759926	−	0.0680922i
$989$	11.3906	−	14.0937i	0.362200	−	0.448153i
$990$	−5.32095	−	6.64850i	−0.169111	−	0.211303i
$991$	26.7983	−	41.6990i	0.851276	−	1.32461i	−0.0930700	−	0.995660i	$-0.529668\pi$
$991$	26.7983	−	41.6990i	0.851276	−	1.32461i	0.944346	−	0.328952i	$-0.106696\pi$
$992$	16.2612	−	39.9179i	0.516294	−	1.26739i
$993$	−11.5535	−	7.81773i	−0.366640	−	0.248088i
$994$	44.2843	−	51.9734i	1.40461	−	1.64850i
$995$	0.904193	−	1.97991i	0.0286648	−	0.0627673i
$996$	−15.9505	−	25.2092i	−0.505412	−	0.798784i
$997$	−3.87504	+	26.9515i	−0.122724	+	0.853563i	0.831725	+	0.555188i	$0.187354\pi$
$997$	−3.87504	+	26.9515i	−0.122724	+	0.853563i	−0.954449	+	0.298375i	$0.903555\pi$
$998$	0.966749	−	7.14497i	0.0306019	−	0.226170i
$999$	34.6600	+	34.6362i	1.09659	+	1.09584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.o.a.71.31	yes	440
3.2	odd	2	inner	276.2.o.a.71.14	yes	440
4.3	odd	2	inner	276.2.o.a.71.3	yes	440
12.11	even	2	inner	276.2.o.a.71.42	yes	440
23.12	even	11	inner	276.2.o.a.35.42	yes	440
69.35	odd	22	inner	276.2.o.a.35.3	✓	440
92.35	odd	22	inner	276.2.o.a.35.14	yes	440
276.35	even	22	inner	276.2.o.a.35.31	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.o.a.35.3	✓	440	69.35	odd	22	inner
276.2.o.a.35.14	yes	440	92.35	odd	22	inner
276.2.o.a.35.31	yes	440	276.35	even	22	inner
276.2.o.a.35.42	yes	440	23.12	even	11	inner
276.2.o.a.71.3	yes	440	4.3	odd	2	inner
276.2.o.a.71.14	yes	440	3.2	odd	2	inner
276.2.o.a.71.31	yes	440	1.1	even	1	trivial
276.2.o.a.71.42	yes	440	12.11	even	2	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.774443 + 1.18332i) q^{2} +(-1.33549 + 1.10293i) q^{3} +(-0.800475 + 1.83282i) q^{4} +(-0.168792 + 0.574851i) q^{5} +(-2.33938 - 0.726151i) q^{6} +(2.73269 + 2.36789i) q^{7} +(-2.78873 + 0.472203i) q^{8} +(0.567081 - 2.94592i) q^{9} +O(q^{10})\)	\(q+(0.774443 + 1.18332i) q^{2} +(-1.33549 + 1.10293i) q^{3} +(-0.800475 + 1.83282i) q^{4} +(-0.168792 + 0.574851i) q^{5} +(-2.33938 - 0.726151i) q^{6} +(2.73269 + 2.36789i) q^{7} +(-2.78873 + 0.472203i) q^{8} +(0.567081 - 2.94592i) q^{9} +(-0.810951 + 0.245456i) q^{10} +(-2.81832 + 1.81123i) q^{11} +(-0.952452 - 3.33059i) q^{12} +(-2.47007 - 2.85062i) q^{13} +(-0.685649 + 5.06744i) q^{14} +(-0.408602 - 0.953876i) q^{15} +(-2.71848 - 2.93426i) q^{16} +(1.55064 + 0.708152i) q^{17} +(3.92512 - 1.61041i) q^{18} +(0.386731 - 0.176614i) q^{19} +(-0.918488 - 0.769519i) q^{20} +(-6.26112 - 0.148327i) q^{21} +(-4.32588 - 1.93227i) q^{22} +(-3.51470 + 3.26296i) q^{23} +(3.20352 - 3.70641i) q^{24} +(3.90430 + 2.50914i) q^{25} +(1.46025 - 5.13052i) q^{26} +(2.49181 + 4.55970i) q^{27} +(-6.52738 + 3.11311i) q^{28} +(0.0545631 + 0.0249181i) q^{29} +(0.812297 - 1.22223i) q^{30} +(7.54204 + 1.08438i) q^{31} +(1.36684 - 5.48924i) q^{32} +(1.76619 - 5.52730i) q^{33} +(0.362913 + 2.38332i) q^{34} +(-1.82244 + 1.17121i) q^{35} +(4.94541 + 3.39749i) q^{36} +(9.04804 - 2.65674i) q^{37} +(0.508491 + 0.320847i) q^{38} +(6.44280 + 1.08265i) q^{39} +(0.199268 - 1.68281i) q^{40} +(-2.14166 + 7.29381i) q^{41} +(-4.67337 - 7.52376i) q^{42} +(-3.74007 + 0.537741i) q^{43} +(-1.06366 - 6.61533i) q^{44} +(1.59775 + 0.823233i) q^{45} +(-6.58305 - 1.63203i) q^{46} +8.85011 q^{47} +(6.86680 + 0.920378i) q^{48} +(0.864497 + 6.01271i) q^{49} +(0.0545521 + 6.56322i) q^{50} +(-2.85191 + 0.764516i) q^{51} +(7.20191 - 2.24536i) q^{52} +(2.10780 + 1.82642i) q^{53} +(-3.46580 + 6.47983i) q^{54} +(-0.565477 - 1.92584i) q^{55} +(-8.73888 - 5.31303i) q^{56} +(-0.321683 + 0.662404i) q^{57} +(0.0127700 + 0.0838631i) q^{58} +(-3.59218 - 4.14560i) q^{59} +(2.07536 + 0.0146576i) q^{60} +(-1.40855 + 9.79667i) q^{61} +(4.55772 + 9.76441i) q^{62} +(8.52527 - 6.70750i) q^{63} +(7.55405 - 2.63370i) q^{64} +(2.05561 - 0.938765i) q^{65} +(7.90836 - 2.19062i) q^{66} +(4.30433 - 6.69767i) q^{67} +(-2.53916 + 2.27519i) q^{68} +(1.09504 - 8.23413i) q^{69} +(-2.79729 - 1.24949i) q^{70} +(-11.2331 - 7.21909i) q^{71} +(-0.190366 + 8.48315i) q^{72} +(-0.421746 - 0.923494i) q^{73} +(10.1510 + 8.64919i) q^{74} +(-7.98158 + 0.955240i) q^{75} +(0.0141341 + 0.850184i) q^{76} +(-11.9904 - 1.72396i) q^{77} +(3.70846 + 8.46232i) q^{78} +(-9.95979 + 8.63021i) q^{79} +(2.14562 - 1.06744i) q^{80} +(-8.35684 - 3.34115i) q^{81} +(-10.2895 + 3.11439i) q^{82} +(8.26280 - 2.42618i) q^{83} +(5.28372 - 11.3568i) q^{84} +(-0.668817 + 0.771856i) q^{85} +(-3.53279 - 4.00923i) q^{86} +(-0.100352 + 0.0269014i) q^{87} +(7.00428 - 6.38184i) q^{88} +(14.9047 - 2.14298i) q^{89} +(0.263218 + 2.52819i) q^{90} -13.6387i q^{91} +(-3.16699 - 9.05374i) q^{92} +(-11.2683 + 6.87017i) q^{93} +(6.85391 + 10.4725i) q^{94} +(0.0362499 + 0.252124i) q^{95} +(4.22885 + 8.83837i) q^{96} +(6.21222 + 1.82407i) q^{97} +(-6.44543 + 5.67948i) q^{98} +(3.73750 + 9.32965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Introduction

L-functions

Modular forms

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