LMFDB - Embedded newform 276.2.o.a.71.19

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			71.19
Character	$\chi$	$=$	276.71
Dual form			276.2.o.a.35.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.351967 + 1.36972i) q^{2} +(-0.954066 + 1.44560i) q^{3} +(-1.75224 - 0.964188i) q^{4} +(0.982607 - 3.34645i) q^{5} +(-1.64426 - 1.81560i) q^{6} +(-0.453842 - 0.393256i) q^{7} +(1.93739 - 2.06071i) q^{8} +(-1.17952 - 2.75839i) q^{9} +O(q^{10})$	\(q+(-0.351967 + 1.36972i) q^{2} +(-0.954066 + 1.44560i) q^{3} +(-1.75224 - 0.964188i) q^{4} +(0.982607 - 3.34645i) q^{5} +(-1.64426 - 1.81560i) q^{6} +(-0.453842 - 0.393256i) q^{7} +(1.93739 - 2.06071i) q^{8} +(-1.17952 - 2.75839i) q^{9} +(4.23784 + 2.52373i) q^{10} +(3.29933 - 2.12035i) q^{11} +(3.06558 - 1.61314i) q^{12} +(-1.84189 - 2.12565i) q^{13} +(0.698386 - 0.483221i) q^{14} +(3.90016 + 4.61319i) q^{15} +(2.14068 + 3.37898i) q^{16} +(-0.320532 - 0.146382i) q^{17} +(4.19337 - 0.644740i) q^{18} +(-1.79903 + 0.821588i) q^{19} +(-4.94837 + 4.91636i) q^{20} +(1.00149 - 0.280881i) q^{21} +(1.74302 + 5.26543i) q^{22} +(-2.93332 - 3.79416i) q^{23} +(1.13056 + 4.76674i) q^{24} +(-6.02696 - 3.87329i) q^{25} +(3.55982 - 1.77470i) q^{26} +(5.11287 + 0.926578i) q^{27} +(0.416066 + 1.12667i) q^{28} +(8.75025 + 3.99611i) q^{29} +(-7.69148 + 3.71842i) q^{30} +(-0.519891 - 0.0747490i) q^{31} +(-5.38168 + 1.74284i) q^{32} +(-0.0825988 + 6.79246i) q^{33} +(0.313318 - 0.387516i) q^{34} +(-1.76196 + 1.13234i) q^{35} +(-0.592815 + 5.97064i) q^{36} +(2.52234 - 0.740626i) q^{37} +(-0.492144 - 2.75332i) q^{38} +(4.83012 - 0.634621i) q^{39} +(-4.99236 - 8.50826i) q^{40} +(2.81995 - 9.60386i) q^{41} +(0.0322378 + 1.47061i) q^{42} +(-6.92362 + 0.995467i) q^{43} +(-7.82563 + 0.534185i) q^{44} +(-10.3898 + 1.23678i) q^{45} +(6.22935 - 2.68239i) q^{46} +5.45483 q^{47} +(-6.92700 - 0.129197i) q^{48} +(-0.944882 - 6.57180i) q^{49} +(7.42659 - 6.89194i) q^{50} +(0.517418 - 0.323703i) q^{51} +(1.17790 + 5.50057i) q^{52} +(1.30216 + 1.12832i) q^{53} +(-3.06871 + 6.67705i) q^{54} +(-3.85371 - 13.1245i) q^{55} +(-1.68966 + 0.173342i) q^{56} +(0.528702 - 3.38452i) q^{57} +(-8.55332 + 10.5789i) q^{58} +(-5.67755 - 6.55224i) q^{59} +(-2.38602 - 11.8439i) q^{60} +(-0.700298 + 4.87068i) q^{61} +(0.285369 - 0.685793i) q^{62} +(-0.549441 + 1.71573i) q^{63} +(-0.493014 - 7.98479i) q^{64} +(-8.92324 + 4.07511i) q^{65} +(-9.27467 - 2.50386i) q^{66} +(-3.97263 + 6.18154i) q^{67} +(0.420509 + 0.565549i) q^{68} +(8.28341 - 0.620527i) q^{69} +(-0.930836 - 2.81193i) q^{70} +(8.86761 + 5.69886i) q^{71} +(-7.96943 - 2.91346i) q^{72} +(4.20379 + 9.20502i) q^{73} +(0.126666 + 3.71556i) q^{74} +(11.3493 - 5.01719i) q^{75} +(3.94449 + 0.294982i) q^{76} +(-2.33121 - 0.335178i) q^{77} +(-0.830792 + 6.83925i) q^{78} +(12.2257 - 10.5936i) q^{79} +(13.4110 - 3.84348i) q^{80} +(-6.21748 + 6.50715i) q^{81} +(12.1620 + 7.24277i) q^{82} +(-16.3057 + 4.78777i) q^{83} +(-2.02567 - 0.473450i) q^{84} +(-0.804817 + 0.928809i) q^{85} +(1.07338 - 9.83376i) q^{86} +(-14.1251 + 8.83681i) q^{87} +(2.02268 - 10.9069i) q^{88} +(-8.07202 + 1.16058i) q^{89} +(1.96284 - 14.6664i) q^{90} +1.68904i q^{91} +(1.48159 + 9.47654i) q^{92} +(0.604067 - 0.680239i) q^{93} +(-1.91992 + 7.47156i) q^{94} +(0.981668 + 6.82765i) q^{95} +(2.61504 - 9.44254i) q^{96} +(9.68868 + 2.84485i) q^{97} +(9.33406 + 1.01884i) q^{98} +(-9.74038 - 6.59986i) 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 $

$2$	−0.351967	+	1.36972i	−0.248878	+	0.968535i
$2$	−0.351967	+	1.36972i	−0.248878	+	0.968535i
$3$	−0.954066	+	1.44560i	−0.550830	+	0.834617i
$3$	−0.954066	+	1.44560i	−0.550830	+	0.834617i
$4$	−1.75224	−	0.964188i	−0.876119	−	0.482094i
$5$	0.982607	−	3.34645i	0.439435	−	1.49658i	−0.380857	−	0.924634i	$-0.624371\pi$
$5$	0.982607	−	3.34645i	0.439435	−	1.49658i	0.820292	−	0.571945i	$-0.193811\pi$
$6$	−1.64426	−	1.81560i	−0.671267	−	0.741216i
$7$	−0.453842	−	0.393256i	−0.171536	−	0.148637i	0.564862	−	0.825185i	$-0.308929\pi$
$7$	−0.453842	−	0.393256i	−0.171536	−	0.148637i	−0.736398	+	0.676549i	$0.763475\pi$
$8$	1.93739	−	2.06071i	0.684972	−	0.728569i
$9$	−1.17952	−	2.75839i	−0.393173	−	0.919465i
$10$	4.23784	+	2.52373i	1.34012	+	0.798074i
$11$	3.29933	−	2.12035i	0.994785	−	0.639310i	0.0613728	−	0.998115i	$-0.480452\pi$
$11$	3.29933	−	2.12035i	0.994785	−	0.639310i	0.933412	+	0.358805i	$0.116816\pi$
$12$	3.06558	−	1.61314i	0.884957	−	0.465673i
$13$	−1.84189	−	2.12565i	−0.510847	−	0.589549i	0.440468	−	0.897768i	$-0.354813\pi$
$13$	−1.84189	−	2.12565i	−0.510847	−	0.589549i	−0.951315	+	0.308219i	$0.900267\pi$
$14$	0.698386	−	0.483221i	0.186652	−	0.129146i
$15$	3.90016	+	4.61319i	1.00702	+	1.19112i
$16$	2.14068	+	3.37898i	0.535170	+	0.844744i
$17$	−0.320532	−	0.146382i	−0.0777404	−	0.0355029i	0.376165	−	0.926553i	$-0.377242\pi$
$17$	−0.320532	−	0.146382i	−0.0777404	−	0.0355029i	−0.453906	+	0.891050i	$0.649970\pi$
$18$	4.19337	−	0.644740i	0.988386	−	0.151967i
$19$	−1.79903	+	0.821588i	−0.412725	+	0.188485i	−0.610946	−	0.791672i	$-0.709211\pi$
$19$	−1.79903	+	0.821588i	−0.412725	+	0.188485i	0.198221	+	0.980157i	$0.436484\pi$
$20$	−4.94837	+	4.91636i	−1.10649	+	1.09933i
$21$	1.00149	−	0.280881i	0.218542	−	0.0612934i
$22$	1.74302	+	5.26543i	0.371613	+	1.12259i
$23$	−2.93332	−	3.79416i	−0.611639	−	0.791137i
$23$	−2.93332	−	3.79416i	−0.611639	−	0.791137i
$24$	1.13056	+	4.76674i	0.230774	+	0.973007i
$25$	−6.02696	−	3.87329i	−1.20539	−	0.774658i
$26$	3.55982	−	1.77470i	0.698138	−	0.348048i
$27$	5.11287	+	0.926578i	0.983973	+	0.178320i
$28$	0.416066	+	1.12667i	0.0786291	+	0.212920i
$29$	8.75025	+	3.99611i	1.62488	+	0.742058i	0.999275	−	0.0380809i	$-0.0121244\pi$
$29$	8.75025	+	3.99611i	1.62488	+	0.742058i	0.625606	+	0.780139i	$0.284852\pi$
$30$	−7.69148	+	3.71842i	−1.40427	+	0.678887i
$31$	−0.519891	−	0.0747490i	−0.0933751	−	0.0134253i	0.0954689	−	0.995432i	$-0.469565\pi$
$31$	−0.519891	−	0.0747490i	−0.0933751	−	0.0134253i	−0.188844	+	0.982007i	$0.560474\pi$
$32$	−5.38168	+	1.74284i	−0.951356	+	0.308093i
$33$	−0.0825988	+	6.79246i	−0.0143786	+	1.18242i
$34$	0.313318	−	0.387516i	0.0537336	−	0.0664584i
$35$	−1.76196	+	1.13234i	−0.297826	+	0.191401i
$36$	−0.592815	+	5.97064i	−0.0988025	+	0.995107i
$37$	2.52234	−	0.740626i	0.414670	−	0.121758i	−0.0677412	−	0.997703i	$-0.521579\pi$
$37$	2.52234	−	0.740626i	0.414670	−	0.121758i	0.482411	+	0.875945i	$0.339761\pi$
$38$	−0.492144	−	2.75332i	−0.0798362	−	0.446648i
$39$	4.83012	−	0.634621i	0.773438	−	0.101621i
$40$	−4.99236	−	8.50826i	−0.789361	−	1.34527i
$41$	2.81995	−	9.60386i	0.440402	−	1.49987i	−0.378316	−	0.925676i	$-0.623497\pi$
$41$	2.81995	−	9.60386i	0.440402	−	1.49987i	0.818718	−	0.574195i	$-0.194685\pi$
$42$	0.0322378	+	1.47061i	0.00497440	+	0.226920i
$43$	−6.92362	+	0.995467i	−1.05584	+	0.151807i	−0.648305	−	0.761381i	$-0.724522\pi$
$43$	−6.92362	+	0.995467i	−1.05584	+	0.151807i	−0.407538	+	0.913188i	$0.633613\pi$
$44$	−7.82563	+	0.534185i	−1.17976	+	0.0805314i
$45$	−10.3898	+	1.23678i	−1.54883	+	0.184369i
$46$	6.22935	−	2.68239i	0.918467	−	0.395497i
$47$	5.45483			0.795668			0.397834	−	0.917457i	$-0.369762\pi$
$47$	5.45483			0.795668			0.397834	+	0.917457i	$0.369762\pi$
$48$	−6.92700	−	0.129197i	−0.999826	−	0.0186480i
$49$	−0.944882	−	6.57180i	−0.134983	−	0.938828i
$50$	7.42659	−	6.89194i	1.05028	−	0.974668i
$51$	0.517418	−	0.323703i	0.0724531	−	0.0453275i
$52$	1.17790	+	5.50057i	0.163345	+	0.762792i
$53$	1.30216	+	1.12832i	0.178865	+	0.154987i	0.739692	−	0.672946i	$-0.234971\pi$
$53$	1.30216	+	1.12832i	0.178865	+	0.154987i	−0.560827	+	0.827933i	$0.689517\pi$
$54$	−3.06871	+	6.67705i	−0.417598	+	0.908632i
$55$	−3.85371	−	13.1245i	−0.519634	−	1.76971i
$56$	−1.68966	+	0.173342i	−0.225790	+	0.0231639i
$57$	0.528702	−	3.38452i	0.0700283	−	0.448291i
$58$	−8.55332	+	10.5789i	−1.12311	+	1.38907i
$59$	−5.67755	−	6.55224i	−0.739154	−	0.853029i	0.254317	−	0.967121i	$-0.418149\pi$
$59$	−5.67755	−	6.55224i	−0.739154	−	0.853029i	−0.993470	+	0.114092i	$0.963604\pi$
$60$	−2.38602	−	11.8439i	−0.308034	−	1.52904i
$61$	−0.700298	+	4.87068i	−0.0896640	+	0.623627i	0.894593	+	0.446882i	$0.147466\pi$
$61$	−0.700298	+	4.87068i	−0.0896640	+	0.623627i	−0.984257	+	0.176745i	$0.943443\pi$
$62$	0.285369	−	0.685793i	0.0362419	−	0.0870958i
$63$	−0.549441	+	1.71573i	−0.0692231	+	0.216161i
$64$	−0.493014	−	7.98479i	−0.0616268	−	0.998099i
$65$	−8.92324	+	4.07511i	−1.10679	+	0.505455i
$66$	−9.27467	−	2.50386i	−1.14163	−	0.308204i
$67$	−3.97263	+	6.18154i	−0.485335	+	0.755195i	−0.994417	−	0.105523i	$-0.966348\pi$
$67$	−3.97263	+	6.18154i	−0.485335	+	0.755195i	0.509082	+	0.860718i	$0.329985\pi$
$68$	0.420509	+	0.565549i	0.0509942	+	0.0685829i
$69$	8.28341	−	0.620527i	0.997206	−	0.0747026i
$70$	−0.930836	−	2.81193i	−0.111256	−	0.336090i
$71$	8.86761	+	5.69886i	1.05239	+	0.676331i	0.948021	−	0.318208i	$-0.103081\pi$
$71$	8.86761	+	5.69886i	1.05239	+	0.676331i	0.104370	+	0.994539i	$0.466717\pi$
$72$	−7.96943	−	2.91346i	−0.939206	−	0.343354i
$73$	4.20379	+	9.20502i	0.492017	+	1.07737i	0.978982	+	0.203945i	$0.0653764\pi$
$73$	4.20379	+	9.20502i	0.492017	+	1.07737i	−0.486966	+	0.873421i	$0.661896\pi$
$74$	0.126666	+	3.71556i	0.0147247	+	0.431925i
$75$	11.3493	−	5.01719i	1.31051	−	0.579336i
$76$	3.94449	+	0.294982i	0.452464	+	0.0338368i
$77$	−2.33121	−	0.335178i	−0.265667	−	0.0381971i
$78$	−0.830792	+	6.83925i	−0.0940687	+	0.774393i
$79$	12.2257	−	10.5936i	1.37550	−	1.19188i	0.416270	−	0.909241i	$-0.363337\pi$
$79$	12.2257	−	10.5936i	1.37550	−	1.19188i	0.959228	−	0.282635i	$-0.0912085\pi$
$80$	13.4110	−	3.84348i	1.49940	−	0.429714i
$81$	−6.21748	+	6.50715i	−0.690831	+	0.723017i
$82$	12.1620	+	7.24277i	1.34307	+	0.799830i
$83$	−16.3057	+	4.78777i	−1.78978	+	0.525526i	−0.996520	−	0.0833581i	$-0.973435\pi$
$83$	−16.3057	+	4.78777i	−1.78978	+	0.525526i	−0.793259	+	0.608884i	$0.791617\pi$
$84$	−2.02567	−	0.473450i	−0.221018	−	0.0516576i
$85$	−0.804817	+	0.928809i	−0.0872947	+	0.100743i
$86$	1.07338	−	9.83376i	0.115746	−	1.06040i
$87$	−14.1251	+	8.83681i	−1.51437	+	0.947406i
$88$	2.02268	−	10.9069i	0.215619	−	1.16268i
$89$	−8.07202	+	1.16058i	−0.855633	+	0.123021i	−0.556152	−	0.831081i	$-0.687723\pi$
$89$	−8.07202	+	1.16058i	−0.855633	+	0.123021i	−0.299481	+	0.954102i	$0.596814\pi$
$90$	1.96284	−	14.6664i	0.206901	−	1.54598i
$91$			1.68904i			0.177060i
$92$	1.48159	+	9.47654i	0.154466	+	0.987998i
$93$	0.604067	−	0.680239i	0.0626388	−	0.0705375i
$94$	−1.91992	+	7.47156i	−0.198024	+	0.770632i
$95$	0.981668	+	6.82765i	0.100717	+	0.700502i
$96$	2.61504	−	9.44254i	0.266896	−	0.963725i
$97$	9.68868	+	2.84485i	0.983736	+	0.288851i	0.733766	−	0.679403i	$-0.237761\pi$
$97$	9.68868	+	2.84485i	0.983736	+	0.288851i	0.249970	+	0.968254i	$0.419579\pi$
$98$	9.33406	+	1.01884i	0.942882	+	0.102918i
$99$	−9.74038	−	6.59986i	−0.978945	−	0.663311i
$100$	6.82608	+	12.5980i	0.682608	+	1.25980i
$101$	3.23156	+	11.0057i	0.321553	+	1.09511i	0.948692	+	0.316201i	$0.102407\pi$
$101$	3.23156	+	11.0057i	0.321553	+	1.09511i	−0.627140	+	0.778907i	$0.715775\pi$
$102$	0.261267	+	0.822648i	0.0258692	+	0.0814543i
$103$	−3.37596	−	5.25310i	−0.332643	−	0.517603i	0.634134	−	0.773223i	$-0.281357\pi$
$103$	−3.37596	−	5.25310i	−0.332643	−	0.517603i	−0.966777	+	0.255620i	$0.917720\pi$
$104$	−7.94880	−	0.322635i	−0.779444	−	0.0316370i
$105$	0.0441107	−	3.62742i	0.00430477	−	0.354000i
$106$	−2.00380	+	1.38645i	−0.194626	+	0.134664i
$107$	−1.11284	+	7.73994i	−0.107582	+	0.748249i	0.862603	+	0.505882i	$0.168833\pi$
$107$	−1.11284	+	7.73994i	−0.107582	+	0.748249i	−0.970185	+	0.242367i	$0.922076\pi$
$108$	−8.06557	−	6.55336i	−0.776110	−	0.630597i
$109$	−1.54804	+	3.38975i	−0.148276	+	0.324679i	−0.969167	−	0.246407i	$-0.920750\pi$
$109$	−1.54804	+	3.38975i	−0.148276	+	0.324679i	0.820891	+	0.571085i	$0.193477\pi$
$110$	19.3332	−	0.659085i	1.84335	−	0.0628413i
$111$	−1.33583	+	4.35290i	−0.126791	+	0.413159i
$112$	0.357273	−	2.37536i	0.0337591	−	0.224450i
$113$	−2.93458	+	4.56629i	−0.276062	+	0.429560i	−0.951405	−	0.307943i	$-0.900359\pi$
$113$	−2.93458	+	4.56629i	−0.276062	+	0.429560i	0.675343	+	0.737504i	$0.263996\pi$
$114$	4.44974	+	1.91541i	0.416757	+	0.179395i
$115$	−15.5793	+	6.08804i	−1.45277	+	0.567713i
$116$	−11.4795	−	15.4390i	−1.06585	−	1.43348i
$117$	−3.69084	+	7.58789i	−0.341219	+	0.701501i
$118$	10.9730	−	5.47045i	1.01015	−	0.503596i
$119$	0.0879052	+	0.192485i	0.00805825	+	0.0176451i
$120$	17.0626	+	0.900487i	1.55759	+	0.0822028i
$121$	1.82012	−	3.98552i	0.165466	−	0.362320i
$122$	−6.42496	−	2.67353i	−0.581689	−	0.242050i
$123$	11.1929	+	13.2392i	1.00923	+	1.19374i
$124$	0.838901	+	0.632251i	0.0753355	+	0.0567778i
$125$	−5.70465	+	4.94311i	−0.510240	+	0.442125i
$126$	−2.15667	−	1.35646i	−0.192132	−	0.120843i
$127$	2.61416	+	4.06771i	0.231969	+	0.360951i	0.937651	−	0.347578i	$-0.112996\pi$
$127$	2.61416	+	4.06771i	0.231969	+	0.360951i	−0.705682	+	0.708529i	$0.749359\pi$
$128$	11.1104	+	2.13509i	0.982031	+	0.188717i
$129$	5.16655	−	10.9585i	0.454889	−	0.964845i
$130$	−2.44105	−	13.6566i	−0.214094	−	1.19776i
$131$	11.6519	−	13.4470i	1.01803	−	1.17487i	0.0335397	−	0.999437i	$-0.489322\pi$
$131$	11.6519	−	13.4470i	1.01803	−	1.17487i	0.984491	−	0.175433i	$-0.0561326\pi$
$132$	6.69395	−	11.8224i	0.582633	−	1.02901i
$133$	1.13957	+	0.334607i	0.0988131	+	0.0290141i
$134$	−7.06871	−	7.61707i	−0.610644	−	0.658015i
$135$	8.12469	−	16.1995i	0.699262	−	1.39423i
$136$	−0.922647	+	0.376922i	−0.0791163	+	0.0323208i
$137$		−	8.69528i		−	0.742888i	−0.928455	−	0.371444i	$-0.878863\pi$
$137$		−	8.69528i		−	0.742888i	0.928455	−	0.371444i	$-0.121137\pi$
$138$	−2.06554	+	11.5643i	−0.175831	+	0.984420i
$139$			11.0744i			0.939319i	0.882848	+	0.469660i	$0.155623\pi$
$139$			11.0744i			0.939319i	−0.882848	+	0.469660i	$0.844377\pi$
$140$	4.17917	−	0.285274i	0.353204	−	0.0241100i
$141$	−5.20426	+	7.88550i	−0.438278	+	0.664079i
$142$	−10.9269	+	10.1403i	−0.916967	+	0.850954i
$143$	−10.5841	−	3.10778i	−0.885088	−	0.259885i
$144$	6.79558	−	9.89041i	0.566298	−	0.824200i
$145$	21.9708	−	25.3557i	1.82458	−	2.10568i
$146$	−14.0879	+	2.51814i	−1.16592	+	0.208402i
$147$	10.4017	+	4.90401i	0.857915	+	0.404476i
$148$	−5.13385	−	1.13426i	−0.421999	−	0.0932354i
$149$	6.27379	+	9.76220i	0.513969	+	0.799751i	0.997124	−	0.0757837i	$-0.0241459\pi$
$149$	6.27379	+	9.76220i	0.513969	+	0.799751i	−0.483156	+	0.875534i	$0.660510\pi$
$150$	2.87754	+	17.3112i	0.234950	+	1.41346i
$151$	−4.90449	+	4.24977i	−0.399122	+	0.345841i	−0.831179	−	0.556005i	$-0.812333\pi$
$151$	−4.90449	+	4.24977i	−0.399122	+	0.345841i	0.432057	+	0.901846i	$0.357788\pi$
$152$	−1.79237	+	5.29900i	−0.145380	+	0.429806i
$153$	−0.0257063	+	1.05681i	−0.00207823	+	0.0854383i
$154$	1.27961	−	3.07513i	0.103114	−	0.247801i
$155$	−0.760992	+	1.66634i	−0.0611244	+	0.133844i
$156$	−9.07542	−	3.54514i	−0.726615	−	0.283838i
$157$	8.01598	+	17.5525i	0.639745	+	1.40085i	0.900250	+	0.435373i	$0.143384\pi$
$157$	8.01598	+	17.5525i	0.639745	+	1.40085i	−0.260505	+	0.965472i	$0.583889\pi$
$158$	10.2072	+	20.4743i	0.812042	+	1.62885i
$159$	−2.87345	+	0.805900i	−0.227879	+	0.0639121i
$160$	0.544236	+	19.7221i	0.0430257	+	1.55917i
$161$	−0.160814	+	2.87549i	−0.0126739	+	0.226621i
$162$	−6.72459	−	10.8065i	−0.528334	−	0.849037i
$163$	0.366445	−	0.570200i	0.0287022	−	0.0446615i	−0.826606	−	0.562781i	$-0.809731\pi$
$163$	0.366445	−	0.570200i	0.0287022	−	0.0446615i	0.855308	+	0.518120i	$0.173368\pi$
$164$	−14.2012	+	14.1093i	−1.10892	+	1.10175i
$165$	22.6495	+	6.95073i	1.76326	+	0.541114i
$166$	−0.818835	−	24.0192i	−0.0635539	−	1.86425i
$167$	2.28507	−	5.00361i	0.176824	−	0.387191i	−0.800380	−	0.599493i	$-0.795369\pi$
$167$	2.28507	−	5.00361i	0.176824	−	0.387191i	0.977204	+	0.212302i	$0.0680961\pi$
$168$	1.36146	−	2.60795i	0.105039	−	0.201207i
$169$	0.724250	−	5.03727i	0.0557115	−	0.387482i
$170$	−0.988934	−	1.42928i	−0.0758478	−	0.109621i
$171$	4.38825	+	3.99335i	0.335578	+	0.305379i
$172$	13.0917	+	4.93138i	0.998230	+	0.376014i
$173$	−6.56351	−	10.2130i	−0.499015	−	0.776482i	0.496801	−	0.867864i	$-0.334508\pi$
$173$	−6.56351	−	10.2130i	−0.499015	−	0.776482i	−0.995816	+	0.0913823i	$0.970871\pi$
$174$	−7.13236	−	22.4576i	−0.540703	−	1.70251i
$175$	1.21209	+	4.12800i	0.0916254	+	0.312047i
$176$	14.2274	+	6.60936i	1.07243	+	0.498199i
$177$	14.8887	−	1.95620i	1.11910	−	0.147037i
$178$	1.25142	−	11.4649i	0.0937977	−	0.859327i
$179$	16.2407	+	4.76870i	1.21389	+	0.356429i	0.825147	−	0.564918i	$-0.191092\pi$
$179$	16.2407	+	4.76870i	1.21389	+	0.356429i	0.388740	+	0.921348i	$0.372910\pi$
$180$	19.3980	+	7.85062i	1.44584	+	0.585151i
$181$	2.76411	+	19.2248i	0.205455	+	1.42897i	0.787751	+	0.615994i	$0.211245\pi$
$181$	2.76411	+	19.2248i	0.205455	+	1.42897i	−0.582296	+	0.812977i	$0.697846\pi$
$182$	−2.31351	−	0.594487i	−0.171489	−	0.0440663i
$183$	−6.37292	−	5.65930i	−0.471100	−	0.418347i
$184$	−13.5016	−	1.30607i	−0.995354	−	0.0962851i
$185$		−	9.16863i		−	0.674091i
$186$	0.719122	+	1.06682i	0.0527285	+	0.0782231i
$187$	−1.36792	+	0.196677i	−0.100032	+	0.0143825i
$188$	−9.55816	−	5.25948i	−0.697100	−	0.383587i
$189$	−1.95605	−	2.43119i	−0.142282	−	0.176843i
$190$	−9.69745	−	1.05850i	−0.703527	−	0.0767917i
$191$	12.6982	−	14.6546i	0.918813	−	1.06037i	−0.0791688	−	0.996861i	$-0.525227\pi$
$191$	12.6982	−	14.6546i	0.918813	−	1.06037i	0.997982	−	0.0635052i	$-0.0202279\pi$
$192$	12.0132	+	6.90532i	0.866977	+	0.498348i
$193$	−10.0032	+	2.93722i	−0.720049	+	0.211425i	−0.621172	−	0.783674i	$-0.713343\pi$
$193$	−10.0032	+	2.93722i	−0.720049	+	0.211425i	−0.0988768	+	0.995100i	$0.531525\pi$
$194$	−7.30673	+	12.2694i	−0.524593	+	0.880894i
$195$	2.62238	−	16.7873i	0.187793	−	1.20217i
$196$	−4.68079	+	12.4264i	−0.334342	+	0.887600i
$197$	10.0535	−	8.71145i	0.716285	−	0.620665i	−0.218517	−	0.975833i	$-0.570122\pi$
$197$	10.0535	−	8.71145i	0.716285	−	0.620665i	0.934802	+	0.355168i	$0.115576\pi$
$198$	12.4682	−	11.0186i	0.886078	−	0.783059i
$199$	−12.6819	−	1.82338i	−0.898993	−	0.129256i	−0.322702	−	0.946500i	$-0.604591\pi$
$199$	−12.6819	−	1.82338i	−0.898993	−	0.129256i	−0.576291	+	0.817245i	$0.695500\pi$
$200$	−19.6583	+	4.91570i	−1.39005	+	0.347592i
$201$	−5.14588	−	11.6404i	−0.362962	−	0.821053i
$202$	−16.2121	+	0.552682i	−1.14068	+	0.0388866i
$203$	−2.39974	−	5.25469i	−0.168428	−	0.368807i
$204$	−1.21875	+	0.0683159i	−0.0853296	+	0.00478307i
$205$	−29.3680	−	18.8736i	−2.05115	−	1.31819i
$206$	8.38347	−	2.77519i	0.584104	−	0.193357i
$207$	−7.00589	+	12.5665i	−0.486943	+	0.873434i
$208$	3.23963	−	10.7740i	0.224628	−	0.747045i
$209$	−4.19353	+	6.52525i	−0.290072	+	0.451361i
$210$	4.95301	+	1.33715i	0.341790	+	0.0922722i
$211$	23.8241	−	10.8801i	1.64012	−	0.749018i	0.640302	−	0.768123i	$-0.278809\pi$
$211$	23.8241	−	10.8801i	1.64012	−	0.749018i	0.999817	+	0.0191055i	$0.00608182\pi$
$212$	−1.19377	−	3.23262i	−0.0819885	−	0.222017i
$213$	−16.6986	+	7.38192i	−1.14417	+	0.505801i
$214$	−10.2098	−	4.24847i	−0.697930	−	0.290420i
$215$	−3.47192	+	24.1477i	−0.236783	+	1.64686i
$216$	11.8150	−	8.74098i	0.803912	−	0.594748i
$217$	0.206553	+	0.238375i	0.0140217	+	0.0161819i
$218$	−4.09813	−	3.31346i	−0.277560	−	0.224416i
$219$	−17.3175	−	2.70519i	−1.17021	−	0.182800i
$220$	−5.90190	+	26.7130i	−0.397906	+	1.80099i
$221$	0.279226	+	0.950958i	0.0187828	+	0.0639683i
$222$	−5.49207	−	3.36178i	−0.368603	−	0.225628i
$223$	4.98752	+	4.32171i	0.333989	+	0.289403i	0.805668	−	0.592367i	$-0.201807\pi$
$223$	4.98752	+	4.32171i	0.333989	+	0.289403i	−0.471679	+	0.881770i	$0.656352\pi$
$224$	3.12781	+	1.32541i	0.208986	+	0.0885576i
$225$	−3.57516	+	21.1933i	−0.238344	+	1.41289i
$226$	−5.22164	−	5.62672i	−0.347339	−	0.374284i
$227$	−0.591735	−	4.11561i	−0.0392748	−	0.273163i	0.960716	−	0.277535i	$-0.0895174\pi$
$227$	−0.591735	−	4.11561i	−0.0392748	−	0.273163i	−0.999990	+	0.00437220i	$0.998608\pi$
$228$	−4.18973	+	5.42072i	−0.277471	+	0.358996i
$229$	−20.0204			−1.32298			−0.661492	−	0.749952i	$-0.730076\pi$
$229$	−20.0204			−1.32298			−0.661492	+	0.749952i	$0.730076\pi$
$230$	−2.85549	−	23.4819i	−0.188286	−	1.54835i
$231$	2.70866	−	3.05022i	0.178217	−	0.200690i
$232$	25.1875	−	10.2897i	1.65364	−	0.675549i
$233$	0.753500	−	0.108337i	0.0493634	−	0.00709739i	−0.117589	−	0.993062i	$-0.537517\pi$
$233$	0.753500	−	0.108337i	0.0493634	−	0.00709739i	0.166952	+	0.985965i	$0.446607\pi$
$234$	−9.09419	−	7.72609i	−0.594506	−	0.505070i
$235$	5.35995	−	18.2543i	0.349645	−	1.19078i
$236$	3.63082	+	16.9553i	0.236347	+	1.10370i
$237$	3.65003	+	27.7805i	0.237095	+	1.80454i
$238$	−0.294590	+	0.0526565i	−0.0190954	+	0.00341322i
$239$	−12.6260	+	3.70732i	−0.816706	+	0.239806i	−0.663297	−	0.748356i	$-0.730843\pi$
$239$	−12.6260	+	3.70732i	−0.816706	+	0.239806i	−0.153409	+	0.988163i	$0.549025\pi$
$240$	−7.23887	+	23.0539i	−0.467267	+	1.48812i
$241$	−6.19492	+	3.98123i	−0.399050	+	0.256454i	−0.724740	−	0.689023i	$-0.758040\pi$
$241$	−6.19492	+	3.98123i	−0.399050	+	0.256454i	0.325690	+	0.945477i	$0.394404\pi$
$242$	4.81840	+	3.89582i	0.309738	+	0.250433i
$243$	−3.47485	−	15.1962i	−0.222912	−	0.974839i
$244$	5.92334	−	7.85938i	0.379203	−	0.503145i
$245$	−22.9207	−	3.29549i	−1.46435	−	0.210541i
$246$	−22.0735	+	10.6714i	−1.40736	+	0.680381i
$247$	5.06001	+	2.31083i	0.321961	+	0.147035i
$248$	−1.16127	+	0.926524i	−0.0737406	+	0.0588343i
$249$	8.63546	−	28.1393i	0.547250	−	1.78326i
$250$	−4.76280	−	9.55356i	−0.301226	−	0.604220i
$251$	−7.55357	−	4.85438i	−0.476777	−	0.306406i	0.280091	−	0.959973i	$-0.409635\pi$
$251$	−7.55357	−	4.85438i	−0.476777	−	0.306406i	−0.756868	+	0.653567i	$0.773272\pi$
$252$	2.61704	−	2.47660i	0.164858	−	0.156011i
$253$	−17.7229	−	6.29852i	−1.11423	−	0.395985i
$254$	−6.49170	+	2.14895i	−0.407326	+	0.134837i
$255$	−0.574837	−	2.04959i	−0.0359977	−	0.128350i
$256$	−6.83497	+	14.4666i	−0.427185	+	0.904164i
$257$	8.03036	−	3.66734i	0.500920	−	0.228763i	−0.148898	−	0.988853i	$-0.547572\pi$
$257$	8.03036	−	3.66734i	0.500920	−	0.228763i	0.649818	+	0.760090i	$0.274845\pi$
$258$	13.1916	+	10.9337i	0.821274	+	0.680705i
$259$	−1.43600	−	0.655799i	−0.0892287	−	0.0407494i
$260$	19.5648	+	1.46312i	1.21336	+	0.0907391i
$261$	0.701759	−	28.8501i	0.0434378	−	1.78578i
$262$	14.3175	+	20.6927i	0.884537	+	1.27840i
$263$	16.6504	+	19.2156i	1.02671	+	1.18488i	0.982577	+	0.185858i	$0.0595064\pi$
$263$	16.6504	+	19.2156i	1.02671	+	1.18488i	0.0441307	+	0.999026i	$0.485948\pi$
$264$	13.8372	+	13.3299i	0.851623	+	0.820398i
$265$	5.05539	−	3.24890i	0.310550	−	0.199578i
$266$	−0.859407	+	1.44311i	−0.0526936	+	0.0884829i
$267$	6.02350	−	12.7762i	0.368632	−	0.781890i
$268$	12.9212	−	7.00117i	0.789286	−	0.427664i
$269$	2.42388	+	2.10030i	0.147786	+	0.128058i	0.725616	−	0.688100i	$-0.241555\pi$
$269$	2.42388	+	2.10030i	0.147786	+	0.128058i	−0.577830	+	0.816157i	$0.696100\pi$
$270$	19.3291	+	16.8302i	1.17633	+	1.02425i
$271$	1.80484	−	6.14671i	0.109636	−	0.373386i	−0.886337	−	0.463041i	$-0.846758\pi$
$271$	1.80484	−	6.14671i	0.109636	−	0.373386i	0.995973	+	0.0896551i	$0.0285765\pi$
$272$	−0.191535	−	1.39643i	−0.0116135	−	0.0846708i
$273$	−2.44168	−	1.61146i	−0.147777	−	0.0975298i
$274$	11.9101	+	3.06045i	0.719512	+	0.184888i
$275$	−28.0976			−1.69435
$276$	−15.1128	−	6.89946i	−0.909685	−	0.415299i
$277$	10.5558			0.634234			0.317117	−	0.948386i	$-0.397285\pi$
$277$	10.5558			0.634234			0.317117	+	0.948386i	$0.397285\pi$
$278$	−15.1688	−	3.89783i	−0.909764	−	0.233776i
$279$	0.407033	+	1.52223i	0.0243684	+	0.0911336i
$280$	−1.08018	+	5.82468i	−0.0645534	+	0.348091i
$281$	1.59444	−	5.43016i	0.0951162	−	0.323936i	−0.898165	−	0.439658i	$-0.855100\pi$
$281$	1.59444	−	5.43016i	0.0951162	−	0.323936i	0.993282	+	0.115721i	$0.0369180\pi$
$282$	−8.96916	−	9.90379i	−0.534106	−	0.589762i
$283$	14.5403	+	12.5993i	0.864333	+	0.748949i	0.969392	−	0.245517i	$-0.0789577\pi$
$283$	14.5403	+	12.5993i	0.864333	+	0.748949i	−0.105059	+	0.994466i	$0.533503\pi$
$284$	−10.0434	−	18.5358i	−0.595965	−	1.09990i
$285$	−10.8066	−	5.09493i	−0.640129	−	0.301798i
$286$	7.98202	−	13.4034i	0.471987	−	0.792559i
$287$	−5.05659	+	3.24967i	−0.298481	+	0.191822i
$288$	11.1552	+	12.7891i	0.657328	+	0.753605i
$289$	−11.0513	−	12.7539i	−0.650078	−	0.750230i
$290$	26.9971	+	39.0181i	1.58532	+	2.29122i
$291$	−13.3562	+	11.2918i	−0.782951	+	0.661935i
$292$	1.50933	−	20.1826i	0.0883267	−	1.18110i
$293$	9.39826	+	4.29204i	0.549052	+	0.250744i	0.670571	−	0.741845i	$-0.266049\pi$
$293$	9.39826	+	4.29204i	0.549052	+	0.250744i	−0.121519	+	0.992589i	$0.538776\pi$
$294$	−10.3781	+	12.5213i	−0.605265	+	0.730256i
$295$	−27.5055	+	12.5614i	−1.60143	+	0.731351i
$296$	3.36055	−	6.63268i	0.195328	−	0.385517i
$297$	18.8337	−	7.78399i	1.09284	−	0.451673i
$298$	−15.5796	+	5.15733i	−0.902502	+	0.298756i
$299$	−2.66222	+	13.2236i	−0.153960	+	0.764742i
$300$	−24.7243	−	2.15158i	−1.42746	−	0.124221i
$301$	3.53370	+	2.27097i	0.203679	+	0.130897i
$302$	−4.09475	−	8.21354i	−0.235627	−	0.472636i
$303$	−18.9930	−	5.82861i	−1.09112	−	0.334845i
$304$	−6.62727	−	4.32011i	−0.380100	−	0.247775i
$305$	15.6114	+	7.12948i	0.893905	+	0.408233i
$306$	−1.43849	−	0.407174i	−0.0822328	−	0.0232766i
$307$	−7.20952	−	1.03657i	−0.411469	−	0.0591603i	−0.0665276	−	0.997785i	$-0.521192\pi$
$307$	−7.20952	−	1.03657i	−0.411469	−	0.0591603i	−0.344941	+	0.938624i	$0.612101\pi$
$308$	3.76167	+	2.83504i	0.214341	+	0.161542i
$309$	10.8148	+	0.131511i	0.615230	+	0.00748142i
$310$	−2.01457	−	1.62884i	−0.114420	−	0.0925118i
$311$	−1.70175	+	1.09365i	−0.0964975	+	0.0620152i	−0.588000	−	0.808861i	$-0.700084\pi$
$311$	−1.70175	+	1.09365i	−0.0964975	+	0.0620152i	0.491502	+	0.870876i	$0.336448\pi$
$312$	8.05008	−	11.1830i	0.455746	−	0.633111i
$313$	17.1897	−	5.04736i	0.971620	−	0.285293i	0.242859	−	0.970062i	$-0.421915\pi$
$313$	17.1897	−	5.04736i	0.971620	−	0.285293i	0.728761	+	0.684768i	$0.240097\pi$
$314$	−26.8633	+	4.80169i	−1.51599	+	0.270975i
$315$	5.20171	+	3.52456i	0.293083	+	0.198587i
$316$	−31.6366	+	6.77469i	−1.77970	+	0.381106i
$317$	−0.680179	+	2.31648i	−0.0382027	+	0.130106i	−0.976386	−	0.216031i	$-0.930689\pi$
$317$	−0.680179	+	2.31648i	−0.0382027	+	0.130106i	0.938184	+	0.346137i	$0.112507\pi$
$318$	−0.0924961	−	4.21945i	−0.00518692	−	0.236615i
$319$	37.3431	−	5.36913i	2.09081	−	0.300613i
$320$	−27.2052	−	6.19606i	−1.52082	−	0.346371i
$321$	−10.1271	−	8.99313i	−0.565242	−	0.501948i
$322$	−3.88201	−	1.23235i	−0.216336	−	0.0686761i
$323$	0.696911			0.0387772
$324$	17.1686	−	5.40726i	0.953812	−	0.300403i
$325$	2.86771	+	19.9454i	0.159072	+	1.10637i
$326$	0.652035	+	0.702617i	0.0361129	+	0.0389143i
$327$	−3.42328	−	5.47189i	−0.189308	−	0.302596i
$328$	−14.3274	−	24.4175i	−0.791098	−	1.34823i
$329$	−2.47563	−	2.14514i	−0.136486	−	0.118266i
$330$	−17.4924	+	28.5769i	−0.962925	+	1.57311i
$331$	5.47735	+	18.6541i	0.301062	+	1.02532i	0.961582	+	0.274516i	$0.0885177\pi$
$331$	5.47735	+	18.6541i	0.301062	+	1.02532i	−0.660520	+	0.750808i	$0.729664\pi$
$332$	33.1877	+	7.33241i	1.82141	+	0.402418i
$333$	−5.01808	−	6.08403i	−0.274989	−	0.333403i
$334$	6.04925	+	4.89100i	0.331000	+	0.267624i
$335$	16.7827	+	19.3683i	0.916936	+	1.05820i
$336$	3.09295	+	2.78272i	0.168734	+	0.151810i
$337$	−2.15322	+	14.9759i	−0.117293	+	0.815792i	0.843222	+	0.537565i	$0.180656\pi$
$337$	−2.15322	+	14.9759i	−0.117293	+	0.815792i	−0.960515	+	0.278227i	$0.910253\pi$
$338$	6.64471	+	2.76497i	0.361424	+	0.150394i
$339$	−3.80125	−	8.59876i	−0.206456	−	0.467021i
$340$	2.30578	−	0.851499i	0.125048	−	0.0461790i
$341$	−1.87379	+	0.855729i	−0.101471	+	0.0463403i
$342$	−7.01426	+	4.60512i	−0.379288	+	0.249016i
$343$	−4.42823	+	6.89046i	−0.239102	+	0.372050i
$344$	−11.3624	+	16.1962i	−0.612621	+	0.873239i
$345$	6.06278	−	28.3298i	0.326409	−	1.52522i
$346$	16.2991	−	5.39550i	0.876244	−	0.290064i
$347$	23.2279	+	14.9276i	1.24694	+	0.801357i	0.986441	−	0.164118i	$-0.0524776\pi$
$347$	23.2279	+	14.9276i	1.24694	+	0.801357i	0.260496	+	0.965475i	$0.416114\pi$
$348$	33.2709	−	1.86497i	1.78351	−	0.0999727i
$349$	−9.01754	−	19.7457i	−0.482698	−	1.05696i	−0.981713	−	0.190368i	$-0.939032\pi$
$349$	−9.01754	−	19.7457i	−0.482698	−	1.05696i	0.499015	−	0.866593i	$-0.333695\pi$
$350$	−6.08080	+	0.207299i	−0.325032	+	0.0110806i
$351$	−7.44775	−	12.5748i	−0.397531	−	0.671195i
$352$	−14.0605	+	17.1612i	−0.749429	+	0.914697i
$353$	−15.5532	−	2.23621i	−0.827813	−	0.119022i	−0.284632	−	0.958637i	$-0.591871\pi$
$353$	−15.5532	−	2.23621i	−0.827813	−	0.119022i	−0.543181	+	0.839615i	$0.682780\pi$
$354$	−2.56089	+	21.0817i	−0.136110	+	1.12048i
$355$	27.7843	−	24.0753i	1.47464	−	1.27778i
$356$	15.2631	+	5.74934i	0.808944	+	0.304714i
$357$	−0.362124	−	0.0565681i	−0.0191656	−	0.00299390i
$358$	−12.2479	+	20.5667i	−0.647324	+	1.08698i
$359$	5.07481	−	1.49010i	0.267838	−	0.0786443i	−0.145056	−	0.989423i	$-0.546336\pi$
$359$	5.07481	−	1.49010i	0.267838	−	0.0786443i	0.412894	+	0.910779i	$0.364518\pi$
$360$	−17.5806	+	23.8065i	−0.926577	+	1.25471i
$361$	−9.88087	+	11.4031i	−0.520046	+	0.600165i
$362$	−27.3054	−	2.98045i	−1.43514	−	0.156649i
$363$	4.02494	+	6.43361i	0.211255	+	0.337677i
$364$	1.62855	−	2.95961i	0.0853595	−	0.155125i
$365$	34.9348	−	5.02287i	1.82857	−	0.262909i
$366$	9.99469	−	6.73721i	0.522431	−	0.352159i
$367$		−	8.83580i		−	0.461225i	−0.973046	−	0.230613i	$-0.925927\pi$
$367$		−	8.83580i		−	0.461225i	0.973046	−	0.230613i	$-0.0740730\pi$
$368$	6.54108	−	18.0337i	0.340977	−	0.940072i
$369$	−29.8174	+	3.54940i	−1.55223	+	0.184774i
$370$	12.5584	+	3.22705i	0.652881	+	0.167767i
$371$	−0.147252	−	1.02416i	−0.00764495	−	0.0531718i
$372$	−1.71435	+	0.609506i	−0.0888848	+	0.0316014i
$373$	18.9959	+	5.57770i	0.983570	+	0.288802i	0.733697	−	0.679477i	$-0.237793\pi$
$373$	18.9959	+	5.57770i	0.983570	+	0.288802i	0.249873	+	0.968279i	$0.419611\pi$
$374$	0.212071	−	1.94289i	0.0109659	−	0.100464i
$375$	−1.70315	−	12.9627i	−0.0879501	−	0.669391i
$376$	10.5681	−	11.2408i	0.545010	−	0.579700i
$377$	−7.62265	−	25.9603i	−0.392586	−	1.33703i
$378$	4.01850	−	1.82354i	0.206689	−	0.0937926i
$379$	2.80724	+	4.36814i	0.144198	+	0.224377i	0.905838	−	0.423623i	$-0.139242\pi$
$379$	2.80724	+	4.36814i	0.144198	+	0.224377i	−0.761640	+	0.648000i	$0.775606\pi$
$380$	4.86303	−	12.9102i	0.249468	−	0.662279i
$381$	−8.37436	−	0.101835i	−0.429032	−	0.00521718i
$382$	15.6032	+	22.5509i	0.798329	+	1.15380i
$383$	5.34445	−	37.1715i	0.273089	−	1.89937i	−0.142458	−	0.989801i	$-0.545501\pi$
$383$	5.34445	−	37.1715i	0.273089	−	1.89937i	0.415547	−	0.909572i	$-0.363590\pi$
$384$	−13.6866	+	14.0242i	−0.698439	+	0.715669i
$385$	−3.41232	+	7.47195i	−0.173908	+	0.380806i
$386$	−0.502341	−	14.7354i	−0.0255685	−	0.750011i
$387$	10.9124	+	17.9239i	0.554710	+	0.911124i
$388$	−14.2339	−	14.3266i	−0.722617	−	0.727321i
$389$	5.23715	−	8.14916i	0.265534	−	0.413179i	−0.682726	−	0.730675i	$-0.739206\pi$
$389$	5.23715	−	8.14916i	0.265534	−	0.413179i	0.948260	+	0.317496i	$0.102842\pi$
$390$	22.0709	+	9.50050i	1.11760	+	0.481077i
$391$	0.384825	+	1.64553i	0.0194615	+	0.0832182i
$392$	−15.3731	−	10.7850i	−0.776461	−	0.544726i
$393$	8.32232	+	29.6733i	0.419805	+	1.49682i
$394$	8.39369	+	16.8366i	0.422868	+	0.848217i
$395$	−23.4380	−	51.3221i	−1.17929	−	2.58229i
$396$	10.7040	+	20.9561i	0.537894	+	1.05308i
$397$	6.44643	−	14.1157i	0.323537	−	0.708448i	−0.676059	−	0.736847i	$-0.736314\pi$
$397$	6.44643	−	14.1157i	0.323537	−	0.708448i	0.999597	+	0.0283994i	$0.00904101\pi$
$398$	6.96110	−	16.7288i	0.348928	−	0.838537i
$399$	−1.57093	+	1.32812i	−0.0786449	+	0.0664892i
$400$	0.185963	−	28.6564i	0.00929814	−	1.43282i
$401$	−3.16775	+	2.74487i	−0.158190	+	0.137072i	−0.730359	−	0.683063i	$-0.760647\pi$
$401$	−3.16775	+	2.74487i	−0.158190	+	0.137072i	0.572169	+	0.820135i	$0.306102\pi$
$402$	17.7553	−	2.95134i	0.885552	−	0.147200i
$403$	0.798690	+	1.24279i	0.0397856	+	0.0619075i
$404$	4.94909	−	22.4004i	0.246227	−	1.11446i
$405$	15.6665	+	27.2005i	0.778476	+	1.35160i
$406$	8.04206	−	1.43748i	0.399121	−	0.0713409i
$407$	6.75165	−	7.79181i	0.334667	−	0.386226i
$408$	0.335387	−	1.69339i	0.0166041	−	0.0838351i
$409$	5.36573	+	1.57552i	0.265318	+	0.0779045i	0.411686	−	0.911326i	$-0.364940\pi$
$409$	5.36573	+	1.57552i	0.265318	+	0.0779045i	−0.146368	+	0.989230i	$0.546758\pi$
$410$	36.1881	−	33.5829i	1.78720	−	1.65854i
$411$	12.5699	+	8.29586i	0.620027	+	0.409205i
$412$	0.850513	+	12.4597i	0.0419018	+	0.613847i
$413$			5.20641i			0.256191i
$414$	−14.7467	−	14.0191i	−0.724762	−	0.689000i
$415$			59.2706i			2.90948i
$416$	13.6171	+	8.22947i	0.667634	+	0.403483i
$417$	−16.0092	−	10.5657i	−0.783972	−	0.517405i
$418$	−7.46176	−	8.04061i	−0.364966	−	0.393279i
$419$	−6.34771	−	1.86386i	−0.310106	−	0.0910553i	0.122977	−	0.992410i	$-0.460756\pi$
$419$	−6.34771	−	1.86386i	−0.310106	−	0.0910553i	−0.433083	+	0.901354i	$0.642574\pi$
$420$	−3.57481	+	6.31358i	−0.174433	+	0.308071i
$421$	4.11692	−	4.75118i	0.200647	−	0.231559i	−0.646505	−	0.762910i	$-0.723770\pi$
$421$	4.11692	−	4.75118i	0.200647	−	0.231559i	0.847152	+	0.531351i	$0.178316\pi$
$422$	6.51735	+	36.4617i	0.317260	+	1.77493i
$423$	−6.43406	−	15.0466i	−0.312835	−	0.731589i
$424$	4.84793	−	0.497351i	0.235436	−	0.0241535i
$425$	1.36485	+	2.12375i	0.0662050	+	0.103017i
$426$	−4.23379	−	25.4705i	−0.205128	−	1.23405i
$427$	2.23325	−	1.93512i	0.108075	−	0.0936471i
$428$	9.41272	−	12.4892i	0.454981	−	0.603690i
$429$	14.5905	−	12.3354i	0.704438	−	0.595557i
$430$	−31.8535	−	13.2547i	−1.53611	−	0.639200i
$431$	8.45883	−	18.5222i	0.407447	−	0.892185i	−0.589013	−	0.808123i	$-0.700483\pi$
$431$	8.45883	−	18.5222i	0.407447	−	0.892185i	0.996461	−	0.0840619i	$-0.0267893\pi$
$432$	7.81414	+	19.2598i	0.375958	+	0.926637i
$433$	0.417975	+	0.915238i	0.0200866	+	0.0439836i	0.919409	−	0.393302i	$-0.128667\pi$
$433$	0.417975	+	0.915238i	0.0200866	+	0.0439836i	−0.899323	+	0.437285i	$0.855940\pi$
$434$	−0.399205	+	0.199018i	−0.0191624	+	0.00955319i
$435$	15.6926	+	55.9520i	0.752401	+	2.68269i
$436$	5.98090	−	4.44704i	0.286433	−	0.212974i
$437$	8.39435	+	4.41581i	0.401556	+	0.211237i
$438$	9.80052	−	22.7679i	0.468287	−	1.08789i
$439$	9.49129	−	14.7687i	0.452995	−	0.704873i	−0.537372	−	0.843345i	$-0.680583\pi$
$439$	9.49129	−	14.7687i	0.452995	−	0.704873i	0.990366	+	0.138472i	$0.0442191\pi$
$440$	−34.5119	−	17.4860i	−1.64529	−	0.833612i
$441$	−17.0131	+	10.3579i	−0.810148	+	0.493234i
$442$	−1.40082	+	0.0477550i	−0.0666302	+	0.00227148i
$443$	−1.11372	+	2.43870i	−0.0529142	+	0.115866i	−0.934242	−	0.356639i	$-0.883923\pi$
$443$	−1.11372	+	2.43870i	−0.0529142	+	0.115866i	0.881328	+	0.472505i	$0.156650\pi$
$444$	6.53771	−	6.33933i	0.310266	−	0.300851i
$445$	−4.04780	+	28.1530i	−0.191884	+	1.33458i
$446$	−7.67495	+	5.31038i	−0.363419	+	0.251454i
$447$	−20.0978	−	0.244397i	−0.950595	−	0.0115596i
$448$	−2.91632	+	3.81771i	−0.137783	+	0.180370i
$449$	−9.22360	−	14.3522i	−0.435288	−	0.677322i	0.552431	−	0.833558i	$-0.313700\pi$
$449$	−9.22360	−	14.3522i	−0.435288	−	0.677322i	−0.987720	+	0.156236i	$0.950064\pi$
$450$	−27.7705	−	12.3563i	−1.30911	−	0.582481i
$451$	−11.0596	−	37.6656i	−0.520777	−	1.77360i
$452$	9.54484	−	5.17175i	0.448952	−	0.243258i
$453$	−1.46425	−	11.1445i	−0.0687967	−	0.523614i
$454$	5.84548	+	0.638049i	0.274342	+	0.0299451i
$455$	5.65230	+	1.65966i	0.264984	+	0.0778063i
$456$	−5.95020	−	7.64665i	−0.278643	−	0.358087i
$457$	2.97790	+	20.7118i	0.139300	+	0.968855i	0.932828	+	0.360321i	$0.117333\pi$
$457$	2.97790	+	20.7118i	0.139300	+	0.968855i	−0.793528	+	0.608534i	$0.791758\pi$
$458$	7.04651	−	27.4222i	0.329262	−	1.28136i
$459$	−1.50320	−	1.04543i	−0.0701636	−	0.0487965i
$460$	33.1686	+	4.35365i	1.54649	+	0.202990i
$461$			27.8083i			1.29516i	0.761996	+	0.647582i	$0.224220\pi$
$461$			27.8083i			1.29516i	−0.761996	+	0.647582i	$0.775780\pi$
$462$	3.22457	+	4.78368i	0.150021	+	0.222557i
$463$	−3.20439	+	0.460722i	−0.148921	+	0.0214116i	−0.216372	−	0.976311i	$-0.569422\pi$
$463$	−3.20439	+	0.460722i	−0.148921	+	0.0214116i	0.0674512	+	0.997723i	$0.478513\pi$
$464$	5.22875	+	38.1213i	0.242739	+	1.76974i
$465$	−1.68283	−	2.68989i	−0.0780391	−	0.124741i
$466$	−0.116816	+	1.07021i	−0.00541141	+	0.0495766i
$467$	4.85354	−	5.60129i	0.224595	−	0.259197i	−0.632257	−	0.774759i	$-0.717871\pi$
$467$	4.85354	−	5.60129i	0.224595	−	0.259197i	0.856852	+	0.515562i	$0.172417\pi$
$468$	13.7834	−	9.73713i	0.637138	−	0.450099i
$469$	4.23388	−	1.24318i	0.195502	−	0.0574046i
$470$	23.1167	+	13.7665i	1.06629	+	0.635002i
$471$	−33.0217	−	5.15838i	−1.52156	−	0.237686i
$472$	−24.5019	−	0.994510i	−1.12779	−	0.0457761i
$473$	−20.7326	+	17.9649i	−0.953285	+	0.826026i
$474$	−39.3360	−	4.77831i	−1.80676	−	0.219475i
$475$	14.0249	+	2.01648i	0.643506	+	0.0925223i
$476$	0.0315614	−	0.422038i	0.00144662	−	0.0193441i
$477$	1.57645	−	4.92274i	0.0721806	−	0.225397i
$478$	−0.634049	−	18.5988i	−0.0290007	−	0.850691i
$479$	10.9905	+	24.0658i	0.502168	+	1.09960i	0.975759	+	0.218850i	$0.0702306\pi$
$479$	10.9905	+	24.0658i	0.502168	+	1.09960i	−0.473590	+	0.880745i	$0.657042\pi$
$480$	−29.0295	−	18.0294i	−1.32501	−	0.822926i
$481$	−6.22018	−	3.99746i	−0.283616	−	0.182269i
$482$	−3.27275	−	9.88654i	−0.149070	−	0.450319i
$483$	−4.00339	−	2.97588i	−0.182160	−	0.135407i
$484$	−7.03208	+	5.22863i	−0.319640	+	0.237665i
$485$	19.0403	−	29.6273i	0.864576	−	1.34531i
$486$	22.0375	+	0.589010i	0.999643	+	0.0267180i
$487$	−22.6111	+	10.3262i	−1.02461	+	0.467923i	−0.855570	−	0.517687i	$-0.826793\pi$
$487$	−22.6111	+	10.3262i	−1.02461	+	0.467923i	−0.169038	+	0.985610i	$0.554066\pi$
$488$	8.68029	+	10.8795i	0.392938	+	0.492493i
$489$	0.474668	+	1.07374i	0.0214652	+	0.0485562i
$490$	12.5812	−	30.2349i	0.568360	−	1.36587i
$491$	1.26814	−	8.82011i	0.0572303	−	0.398046i	−0.940991	−	0.338431i	$-0.890104\pi$
$491$	1.26814	−	8.82011i	0.0572303	−	0.398046i	0.998221	−	0.0596146i	$-0.0189872\pi$
$492$	−6.84757	−	33.9904i	−0.308712	−	1.53241i
$493$	−2.21978	−	2.56176i	−0.0999737	−	0.115376i
$494$	−4.94613	+	6.11744i	−0.222537	+	0.275236i
$495$	−31.6571	+	26.1106i	−1.42288	+	1.17359i
$496$	−0.860345	−	1.91671i	−0.0386306	−	0.0860629i
$497$	−1.78338	−	6.07362i	−0.0799954	−	0.272439i
$498$	35.5034	+	21.7322i	1.59095	+	0.973844i
$499$	25.1151	+	21.7624i	1.12431	+	0.974218i	0.999838	−	0.0180055i	$-0.00573162\pi$
$499$	25.1151	+	21.7624i	1.12431	+	0.974218i	0.124470	+	0.992223i	$0.460277\pi$
$500$	14.7620	−	3.16115i	0.660177	−	0.141371i
$501$	5.05311	+	8.07708i	0.225756	+	0.360857i
$502$	9.30773	−	8.63766i	0.415424	−	0.385517i
$503$	−3.30836	−	23.0101i	−0.147512	−	1.02597i	−0.920274	−	0.391274i	$-0.872034\pi$
$503$	−3.30836	−	23.0101i	−0.147512	−	1.02597i	0.772762	−	0.634696i	$-0.218875\pi$
$504$	2.47113	+	4.45627i	0.110073	+	0.198498i
$505$	40.0054			1.78022
$506$	14.8651	−	22.0585i	0.660833	−	0.980620i
$507$	6.59089	+	5.85286i	0.292712	+	0.259935i
$508$	−0.658591	−	9.64815i	−0.0292203	−	0.428067i
$509$	−13.0074	+	1.87019i	−0.576545	+	0.0828946i	−0.424418	−	0.905466i	$-0.639521\pi$
$509$	−13.0074	+	1.87019i	−0.576545	+	0.0828946i	−0.152127	+	0.988361i	$0.548612\pi$
$510$	3.00968	−	0.0659761i	0.133271	−	0.00292147i
$511$	1.71207	−	5.83079i	0.0757377	−	0.257939i
$512$	−17.4095	−	14.4537i	−0.769397	−	0.638771i
$513$	−9.95945	+	2.53373i	−0.439721	+	0.111867i
$514$	2.19679	+	12.2901i	0.0968964	+	0.542093i
$515$	−20.8965	+	6.13576i	−0.920809	+	0.270374i
$516$	−19.6191	+	14.2204i	−0.863683	+	0.626020i
$517$	17.9973	−	11.5661i	0.791519	−	0.508678i
$518$	1.40368	−	1.73609i	0.0616742	−	0.0762794i
$519$	21.0260	+	0.255683i	0.922938	+	0.0112233i
$520$	−8.89023	+	26.2832i	−0.389862	+	1.15260i
$521$	20.7202	+	2.97912i	0.907771	+	0.130518i	0.580356	−	0.814363i	$-0.302913\pi$
$521$	20.7202	+	2.97912i	0.907771	+	0.130518i	0.327415	+	0.944881i	$0.393823\pi$
$522$	39.2694	+	11.1155i	1.71878	+	0.486512i
$523$	−37.2516	−	17.0123i	−1.62890	−	0.743894i	−0.629450	−	0.777041i	$-0.716720\pi$
$523$	−37.2516	−	17.0123i	−1.62890	−	0.743894i	−0.999450	+	0.0331467i	$0.989447\pi$
$524$	−33.3824	+	12.3277i	−1.45831	+	0.538540i
$525$	−7.12385	−	2.18618i	−0.310910	−	0.0954129i
$526$	−32.1803	+	16.0431i	−1.40313	+	0.699510i
$527$	0.155700	+	0.100062i	0.00678239	+	0.00435877i
$528$	−23.1284	+	14.2614i	−1.00653	+	0.620648i
$529$	−5.79129	+	22.2590i	−0.251795	+	0.967781i
$530$	2.67074	+	8.06795i	0.116010	+	0.350449i
$531$	−11.3769	+	23.3894i	−0.493715	+	1.01501i
$532$	−1.67417	−	1.68507i	−0.0725845	−	0.0730570i
$533$	−25.6085	+	11.6950i	−1.10923	+	0.506567i
$534$	15.3797	+	12.7473i	0.665543	+	0.551629i
$535$	24.8079	+	11.3294i	1.07254	+	0.489812i
$536$	5.04178	+	20.1625i	0.217772	+	0.870887i
$537$	−22.3883	+	18.9279i	−0.966128	+	0.816799i
$538$	−3.72994	+	2.58078i	−0.160809	+	0.111266i
$539$	−17.0520	−	19.6790i	−0.734481	−	0.847636i
$540$	−29.8558	+	20.5517i	−1.28479	+	0.884404i
$541$	9.85680	−	6.33458i	0.423777	−	0.272345i	−0.311322	−	0.950304i	$-0.600772\pi$
$541$	9.85680	−	6.33458i	0.423777	−	0.272345i	0.735099	+	0.677960i	$0.237136\pi$
$542$	7.78399	+	4.63555i	0.334351	+	0.199114i
$543$	−30.4286	−	14.3459i	−1.30581	−	0.615644i
$544$	1.98012	+	0.229147i	0.0848970	+	0.00982461i
$545$	9.82250	+	8.51124i	0.420750	+	0.364582i
$546$	3.06663	−	2.77723i	0.131240	−	0.118854i
$547$	0.315096	−	1.07312i	0.0134725	−	0.0458832i	−0.952482	−	0.304594i	$-0.901479\pi$
$547$	0.315096	−	1.07312i	0.0134725	−	0.0458832i	0.965955	+	0.258710i	$0.0832975\pi$
$548$	−8.38388	+	15.2362i	−0.358142	+	0.650858i
$549$	14.2613	−	3.81336i	0.608656	−	0.162750i
$550$	9.88944	−	38.4858i	0.421687	−	1.64104i
$551$	−19.0251			−0.810496
$552$	14.7695	−	18.2719i	0.628632	−	0.777703i
$553$	−9.71454			−0.413104
$554$	−3.71528	+	14.4584i	−0.157847	+	0.614278i
$555$	13.2542	+	8.74748i	0.562608	+	0.371310i
$556$	10.6778	−	19.4050i	0.452840	−	0.822956i
$557$	−10.0522	+	34.2347i	−0.425926	+	1.45057i	0.415200	+	0.909730i	$0.363711\pi$
$557$	−10.0522	+	34.2347i	−0.425926	+	1.45057i	−0.841126	+	0.540839i	$0.818107\pi$
$558$	−2.22829	+	0.0217445i	−0.0943309	+	0.000920517i
$559$	14.8685	+	12.8837i	0.628872	+	0.544921i
$560$	−7.59796	−	3.52964i	−0.321072	−	0.149154i
$561$	1.02077	−	2.16511i	0.0430969	−	0.0914110i
$562$	6.87658	+	4.09516i	0.290071	+	0.172744i
$563$	−18.0695	+	11.6126i	−0.761539	+	0.489411i	−0.862860	−	0.505443i	$-0.831329\pi$
$563$	−18.0695	+	11.6126i	−0.761539	+	0.489411i	0.101322	+	0.994854i	$0.467693\pi$
$564$	16.7222	−	8.79938i	0.704132	−	0.370521i
$565$	12.3973	+	14.3073i	0.521560	+	0.601912i
$566$	−22.3751	+	15.4816i	−0.940497	+	0.650740i
$567$	5.38073	−	0.508155i	0.225969	−	0.0213405i
$568$	28.9237	−	7.23258i	1.21361	−	0.303472i
$569$	35.3045	+	16.1230i	1.48004	+	0.675913i	0.981589	−	0.191004i	$-0.0611745\pi$
$569$	35.3045	+	16.1230i	1.48004	+	0.675913i	0.498453	+	0.866917i	$0.333902\pi$
$570$	10.7822	−	13.0088i	0.451616	−	0.544877i
$571$	−7.69626	+	3.51477i	−0.322079	+	0.147088i	−0.569892	−	0.821719i	$-0.693015\pi$
$571$	−7.69626	+	3.51477i	−0.322079	+	0.147088i	0.247814	+	0.968808i	$0.420288\pi$
$572$	15.5494	+	15.6506i	0.650154	+	0.654386i
$573$	9.06966	+	32.3380i	0.378891	+	1.35094i
$574$	−2.67137	−	8.06986i	−0.111501	−	0.336830i
$575$	2.98310	+	34.2288i	0.124404	+	1.42744i
$576$	−21.4437	+	10.7781i	−0.893487	+	0.449089i
$577$	−33.0103	−	21.2144i	−1.37424	−	0.883169i	−0.375196	−	0.926945i	$-0.622425\pi$
$577$	−33.0103	−	21.2144i	−1.37424	−	0.883169i	−0.999041	+	0.0437763i	$0.986061\pi$
$578$	21.3589	−	10.6482i	0.888414	−	0.442907i
$579$	5.29771	−	17.2630i	0.220165	−	0.717425i
$580$	−62.9458	+	23.2452i	−2.61368	+	0.965205i
$581$	9.28301	+	4.23941i	0.385124	+	0.175880i
$582$	−10.7656	−	22.2685i	−0.446248	−	0.923057i
$583$	6.68868	+	0.961687i	0.277017	+	0.0398290i
$584$	27.1132	+	9.17097i	1.12195	+	0.379497i
$585$	21.7659	+	19.8071i	0.899908	+	0.818925i
$586$	−9.18675	+	11.3623i	−0.379501	+	0.469371i
$587$	−23.9507	+	15.3922i	−0.988553	+	0.635305i	−0.931757	−	0.363081i	$-0.881725\pi$
$587$	−23.9507	+	15.3922i	−0.988553	+	0.635305i	−0.0567956	+	0.998386i	$0.518088\pi$
$588$	−13.4978	−	18.6222i	−0.556641	−	0.767965i
$589$	0.996710	−	0.292660i	0.0410687	−	0.0120589i
$590$	−7.52445	−	42.0959i	−0.309777	−	1.73306i
$591$	3.00152	+	22.8447i	0.123466	+	0.939705i
$592$	7.90208	+	6.93749i	0.324774	+	0.285129i
$593$	−1.11349	+	3.79221i	−0.0457256	+	0.155727i	−0.979191	−	0.202940i	$-0.934950\pi$
$593$	−1.11349	+	3.79221i	−0.0457256	+	0.155727i	0.933466	+	0.358667i	$0.116769\pi$
$594$	4.03301	+	28.5365i	0.165476	+	1.17087i
$595$	0.730519	−	0.105033i	0.0299484	−	0.00430593i
$596$	−1.58057	−	23.1548i	−0.0647426	−	0.948458i
$597$	14.7352	−	16.5933i	0.603071	−	0.679117i
$598$	−17.1756	−	8.30075i	−0.702362	−	0.339443i
$599$	12.5278			0.511872			0.255936	−	0.966694i	$-0.417616\pi$
$599$	12.5278			0.511872			0.255936	+	0.966694i	$0.417616\pi$
$600$	11.6492	−	33.1079i	0.475575	−	1.35163i
$601$	−0.00773076	−	0.0537686i	−0.000315344	−	0.00219327i	0.989663	−	0.143411i	$-0.0458072\pi$
$601$	−0.00773076	−	0.0537686i	−0.000315344	−	0.00219327i	−0.989979	+	0.141218i	$0.954898\pi$
$602$	−4.35433	+	4.04086i	−0.177469	+	0.164693i
$603$	21.7369	+	3.66686i	0.885196	+	0.149326i
$604$	12.6914	−	2.71775i	0.516407	−	0.110584i
$605$	−11.5489	−	10.0072i	−0.469528	−	0.406849i
$606$	14.6684	−	23.9635i	0.595864	−	0.973449i
$607$	−1.97614	−	6.73012i	−0.0802092	−	0.273167i	0.909617	−	0.415447i	$-0.136375\pi$
$607$	−1.97614	−	6.73012i	−0.0802092	−	0.273167i	−0.989826	+	0.142280i	$0.954557\pi$
$608$	8.24990	−	7.55693i	0.334578	−	0.306474i
$609$	9.88569	+	1.54426i	0.400588	+	0.0625766i
$610$	−15.2600	+	18.8738i	−0.617861	+	0.764178i
$611$	−10.0472	−	11.5951i	−0.406465	−	0.469086i
$612$	1.06401	−	1.82700i	0.0430101	−	0.0738523i
$613$	3.32713	−	23.1407i	0.134382	−	0.934645i	−0.805367	−	0.592777i	$-0.798031\pi$
$613$	3.32713	−	23.1407i	0.134382	−	0.934645i	0.939748	−	0.341868i	$-0.111059\pi$
$614$	3.95732	−	9.51014i	0.159704	−	0.383798i
$615$	55.3027	−	24.4476i	2.23002	−	0.985824i
$616$	−5.20718	+	4.15457i	−0.209803	+	0.167393i
$617$	−21.8796	+	9.99209i	−0.880841	+	0.402266i	−0.803897	−	0.594769i	$-0.797244\pi$
$617$	−21.8796	+	9.99209i	−0.880841	+	0.402266i	−0.0769440	+	0.997035i	$0.524516\pi$
$618$	−3.98657	+	14.7669i	−0.160363	+	0.594010i
$619$	−8.27493	+	12.8760i	−0.332598	+	0.517532i	−0.966766	−	0.255663i	$-0.917706\pi$
$619$	−8.27493	+	12.8760i	−0.332598	+	0.517532i	0.634168	+	0.773195i	$0.281343\pi$
$620$	2.94011	−	2.18609i	0.118078	−	0.0877954i
$621$	−11.4821	−	22.1170i	−0.460760	−	0.887525i
$622$	−0.899028	−	2.71584i	−0.0360477	−	0.108895i
$623$	4.11983	+	2.64765i	0.165057	+	0.106076i
$624$	12.4841	+	14.9623i	0.499765	+	0.598973i
$625$	−3.94425	−	8.63670i	−0.157770	−	0.345468i
$626$	0.863230	+	25.3215i	0.0345016	+	1.01205i
$627$	−5.43201	−	12.2877i	−0.216933	−	0.490723i
$628$	2.87805	−	38.4852i	0.114847	−	1.53573i
$629$	−0.916905	−	0.131831i	−0.0365594	−	0.00525645i
$630$	−6.65848	+	5.88434i	−0.265280	+	0.234438i
$631$	−35.1379	+	30.4472i	−1.39882	+	1.21208i	−0.451303	+	0.892371i	$0.649041\pi$
$631$	−35.1379	+	30.4472i	−1.39882	+	1.21208i	−0.947515	+	0.319711i	$0.896414\pi$
$632$	1.85564	−	45.7176i	0.0738133	−	1.81855i
$633$	−7.00149	+	44.8205i	−0.278284	+	1.78145i
$634$	−2.93351	−	1.74697i	−0.116505	−	0.0693812i
$635$	16.1811	−	4.75120i	0.642127	−	0.188546i
$636$	5.81200	+	1.35841i	0.230461	+	0.0538646i
$637$	−12.2290	+	14.1130i	−0.484530	+	0.559177i
$638$	−5.78936	+	53.0392i	−0.229203	+	2.09984i
$639$	5.26022	−	31.1823i	0.208091	−	1.23355i
$640$	18.0622	−	35.0825i	0.713970	−	1.38676i
$641$	−43.3925	+	6.23889i	−1.71390	+	0.246421i	−0.928172	−	0.372152i	$-0.878620\pi$
$641$	−43.3925	+	6.23889i	−1.71390	+	0.246421i	−0.785727	+	0.618573i	$0.787711\pi$
$642$	15.8824	−	10.7060i	0.626830	−	0.422533i
$643$		−	14.0091i		−	0.552463i	−0.961091	−	0.276232i	$-0.910914\pi$
$643$		−	14.0091i		−	0.552463i	0.961091	−	0.276232i	$-0.0890857\pi$
$644$	3.05430	−	4.88350i	0.120356	−	0.192437i
$645$	−31.5955	−	28.0575i	−1.24407	−	1.10476i
$646$	−0.245290	+	0.954569i	−0.00965079	+	0.0375570i
$647$	1.23820	+	8.61189i	0.0486788	+	0.338568i	0.999577	+	0.0290661i	$0.00925332\pi$
$647$	1.23820	+	8.61189i	0.0486788	+	0.338568i	−0.950899	+	0.309502i	$0.899838\pi$
$648$	1.36362	+	25.4193i	0.0535681	+	0.998564i
$649$	−32.6251	−	9.57960i	−1.28065	−	0.376032i
$650$	−28.3288	−	3.09216i	−1.11115	−	0.121284i
$651$	−0.541659	+	0.0711676i	−0.0212293	+	0.00278928i
$652$	−1.19188	+	0.645804i	−0.0466776	+	0.0252916i
$653$	5.71956	+	19.4790i	0.223824	+	0.762273i	0.992458	+	0.122585i	$0.0391184\pi$
$653$	5.71956	+	19.4790i	0.223824	+	0.762273i	−0.768634	+	0.639688i	$0.779063\pi$
$654$	8.69981	−	2.76299i	0.340190	−	0.108042i
$655$	−33.5505	−	52.2056i	−1.31093	−	2.03984i
$656$	38.4878	−	11.0303i	1.50270	−	0.430660i
$657$	20.4326	−	22.4532i	0.797153	−	0.875983i
$658$	3.80958	−	2.63589i	0.148513	−	0.102758i
$659$	−0.287152	+	1.99718i	−0.0111858	+	0.0777992i	−0.994650	−	0.103305i	$-0.967058\pi$
$659$	−0.287152	+	1.99718i	−0.0111858	+	0.0777992i	0.983464	+	0.181105i	$0.0579672\pi$
$660$	−32.9855	−	34.0177i	−1.28396	−	1.32414i
$661$	−8.09382	+	17.7230i	−0.314813	+	0.689344i	−0.999209	−	0.0397661i	$-0.987339\pi$
$661$	−8.09382	+	17.7230i	−0.314813	+	0.689344i	0.684396	+	0.729111i	$0.260066\pi$
$662$	−27.4787	+	0.936771i	−1.06799	+	0.0364086i
$663$	−1.64110	−	0.503627i	−0.0637352	−	0.0195592i
$664$	−21.7243	+	42.8770i	−0.843066	+	1.66395i
$665$	2.23949	−	3.48472i	0.0868439	−	0.135132i
$666$	10.0996	−	4.73197i	0.391351	−	0.183360i
$667$	−10.5054	−	44.9217i	−0.406771	−	1.73938i
$668$	−8.82842	+	6.56428i	−0.341582	+	0.253980i
$669$	−11.0059	+	3.08676i	−0.425512	+	0.119341i
$670$	−32.4359	+	16.1705i	−1.25311	+	0.624722i
$671$	8.01704	+	17.5549i	0.309494	+	0.677698i
$672$	−4.90015	+	3.25704i	−0.189027	+	0.125643i
$673$	3.97386	−	8.70155i	0.153181	−	0.335420i	−0.817447	−	0.576003i	$-0.804611\pi$
$673$	3.97386	−	8.70155i	0.153181	−	0.335420i	0.970628	+	0.240583i	$0.0773387\pi$
$674$	−19.7549	−	8.22033i	−0.760931	−	0.316635i
$675$	−27.2261	−	25.3881i	−1.04793	−	0.977188i
$676$	−6.12593	+	8.12818i	−0.235613	+	0.312622i
$677$	11.9982	−	10.3965i	0.461128	−	0.399570i	−0.393077	−	0.919505i	$-0.628590\pi$
$677$	11.9982	−	10.3965i	0.461128	−	0.399570i	0.854205	+	0.519936i	$0.174044\pi$
$678$	13.1158	−	2.18015i	0.503708	−	0.0837282i
$679$	−3.27837	−	5.10124i	−0.125812	−	0.195768i
$680$	0.354754	+	3.45796i	0.0136042	+	0.132607i
$681$	6.51408	+	3.07115i	0.249620	+	0.117687i
$682$	−0.512595	−	2.86774i	−0.0196283	−	0.109811i
$683$	13.0737	−	15.0878i	0.500250	−	0.577320i	−0.448325	−	0.893871i	$-0.647979\pi$
$683$	13.0737	−	15.0878i	0.500250	−	0.577320i	0.948576	+	0.316551i	$0.102525\pi$
$684$	−3.83892	−	11.2284i	−0.146785	−	0.429328i
$685$	−29.0983	−	8.54404i	−1.11179	−	0.326451i
$686$	−7.87937	−	8.49062i	−0.300836	−	0.324173i
$687$	19.1008	−	28.9415i	0.728739	−	1.10419i
$688$	−18.1849	−	21.2638i	−0.693294	−	0.810674i
$689$		−	4.84617i		−	0.184624i
$690$	36.6698	+	18.2754i	1.39600	+	0.695733i
$691$			14.6458i			0.557154i	0.960414	+	0.278577i	$0.0898627\pi$
$691$			14.6458i			0.557154i	−0.960414	+	0.278577i	$0.910137\pi$
$692$	1.65356	+	24.2241i	0.0628590	+	0.920863i
$693$	1.82516	+	6.82576i	0.0693319	+	0.259289i
$694$	−28.6220	+	26.5615i	−1.08648	+	1.00826i
$695$	37.0600	+	10.8818i	1.40577	+	0.412770i
$696$	−9.15577	+	46.2280i	−0.347049	+	1.75227i
$697$	−2.30972	+	2.66556i	−0.0874868	+	0.100965i
$698$	30.2198	−	5.40164i	1.14384	−	0.204455i
$699$	−0.562276	+	1.19262i	−0.0212672	+	0.0451090i
$700$	1.85630	−	8.40192i	0.0701615	−	0.317563i
$701$	7.27814	+	11.3250i	0.274891	+	0.427739i	0.951059	−	0.309008i	$-0.0999970\pi$
$701$	7.27814	+	11.3250i	0.274891	+	0.427739i	−0.676168	+	0.736747i	$0.736361\pi$
$702$	19.8453	−	5.77537i	0.749012	−	0.217977i
$703$	−3.92927	+	3.40473i	−0.148195	+	0.128412i
$704$	−18.5572	−	25.2991i	−0.699400	−	0.953496i
$705$	21.2747	+	25.1642i	0.801251	+	0.947737i
$706$	8.53718	−	20.5164i	0.321301	−	0.772144i
$707$	2.86144	−	6.26568i	0.107615	−	0.235645i
$708$	−27.9746	−	10.9278i	−1.05135	−	0.410690i
$709$	−12.1954	−	26.7041i	−0.458007	−	1.00289i	−0.987937	−	0.154854i	$-0.950509\pi$
$709$	−12.1954	−	26.7041i	−0.458007	−	1.00289i	0.529931	−	0.848041i	$-0.322218\pi$
$710$	23.1971	+	46.5303i	0.870572	+	1.74625i
$711$	−43.6418	−	21.2279i	−1.63670	−	0.796109i
$712$	−13.2471	+	18.8826i	−0.496455	+	0.707654i
$713$	1.24140	+	2.19181i	0.0464906	+	0.0820840i
$714$	0.204938	−	0.476097i	0.00766961	−	0.0178175i
$715$	−20.8000	+	32.3655i	−0.777878	+	1.21040i
$716$	−23.8597	−	24.0150i	−0.891677	−	0.897483i
$717$	6.68670	−	21.7891i	0.249719	−	0.813729i
$718$	0.254846	+	7.47550i	0.00951076	+	0.278983i
$719$	13.7336	−	30.0723i	0.512176	−	1.12151i	−0.460142	−	0.887845i	$-0.652201\pi$
$719$	13.7336	−	30.0723i	0.512176	−	1.12151i	0.972318	−	0.233663i	$-0.0750713\pi$
$720$	−26.4204	−	32.4595i	−0.984630	−	1.20969i
$721$	−0.533661	+	3.71169i	−0.0198746	+	0.138231i
$722$	−12.1413	−	17.5475i	−0.451852	−	0.653050i
$723$	0.155090	−	12.7537i	0.00576786	−	0.474316i
$724$	13.6930	−	36.3516i	0.508895	−	1.35100i
$725$	−37.2593	−	57.9766i	−1.38378	−	2.15320i
$726$	−10.2289	+	3.24861i	−0.379629	+	0.120567i
$727$	−6.47146	−	22.0398i	−0.240013	−	0.817410i	−0.988100	−	0.153810i	$-0.950846\pi$
$727$	−6.47146	−	22.0398i	−0.240013	−	0.817410i	0.748087	−	0.663600i	$-0.230972\pi$
$728$	3.48062	+	3.27234i	0.129000	+	0.121281i
$729$	25.2829	+	9.47495i	0.936404	+	0.350924i
$730$	−5.41600	+	49.6187i	−0.200455	+	1.83647i
$731$	2.36496	+	0.694415i	0.0874713	+	0.0256839i
$732$	5.71025	+	16.0611i	0.211057	+	0.593637i
$733$	0.886402	+	6.16506i	0.0327400	+	0.227712i	0.999621	−	0.0275144i	$-0.00875920\pi$
$733$	0.886402	+	6.16506i	0.0327400	+	0.227712i	−0.966881	+	0.255226i	$0.917850\pi$
$734$	12.1025	+	3.10991i	0.446713	+	0.114789i
$735$	26.6318	−	29.9900i	0.982328	−	1.10620i
$736$	22.3988	+	15.3067i	0.825630	+	0.564212i
$737$			28.8183i			1.06154i
$738$	5.63308	−	42.0906i	0.207357	−	1.54938i
$739$	3.56067	−	0.511948i	0.130982	−	0.0188323i	−0.0765122	−	0.997069i	$-0.524378\pi$
$739$	3.56067	−	0.511948i	0.130982	−	0.0188323i	0.207494	+	0.978236i	$0.433469\pi$
$740$	−8.84029	+	16.0656i	−0.324976	+	0.590585i
$741$	−8.16812	+	5.11007i	−0.300063	+	0.187723i
$742$	1.45464	+	0.158777i	0.0534014	+	0.00582890i
$743$	−25.5510	+	29.4875i	−0.937377	+	1.08179i	0.0591278	+	0.998250i	$0.481168\pi$
$743$	−25.5510	+	29.4875i	−0.937377	+	1.08179i	−0.996504	+	0.0835399i	$0.973377\pi$
$744$	−0.231456	−	2.56269i	−0.00848558	−	0.0939529i
$745$	38.8334	−	11.4025i	1.42275	−	0.417756i
$746$	−14.3258	+	24.0558i	−0.524504	+	0.880745i
$747$	32.4394	+	39.3302i	1.18689	+	1.43902i
$748$	2.58656	+	0.974308i	0.0945740	+	0.0356242i
$749$	3.54883	−	3.07508i	0.129672	−	0.112361i
$750$	18.3547	+	2.22961i	0.670217	+	0.0814140i
$751$	34.3996	+	4.94592i	1.25526	+	0.180479i	0.737677	−	0.675154i	$-0.235923\pi$
$751$	34.3996	+	4.94592i	1.25526	+	0.180479i	0.517583	+	0.855633i	$0.326832\pi$
$752$	11.6770	+	18.4317i	0.425818	+	0.672136i
$753$	14.2241	−	6.28804i	0.518355	−	0.229149i
$754$	38.2412	−	1.30367i	1.39266	−	0.0474770i
$755$	9.40245	+	20.5885i	0.342190	+	0.749292i
$756$	1.08335	+	6.14603i	0.0394009	+	0.223529i
$757$	−2.06396	−	1.32643i	−0.0750158	−	0.0482098i	0.502595	−	0.864522i	$-0.332379\pi$
$757$	−2.06396	−	1.32643i	−0.0750158	−	0.0482098i	−0.577611	+	0.816312i	$0.696015\pi$
$758$	−6.97117	+	2.30767i	−0.253204	+	0.0838184i
$759$	26.0140	−	19.6111i	0.944248	−	0.711836i
$760$	15.9717	+	11.2049i	0.579353	+	0.406445i
$761$	6.13535	−	9.54679i	0.222406	−	0.346071i	−0.712062	−	0.702116i	$-0.752239\pi$
$761$	6.13535	−	9.54679i	0.222406	−	0.346071i	0.934469	+	0.356045i	$0.115875\pi$
$762$	3.08698	−	11.4347i	0.111830	−	0.414234i
$763$	2.03561	−	0.929630i	0.0736939	−	0.0336549i
$764$	−36.3801	+	13.4348i	−1.31619	+	0.486053i
$765$	3.51132	+	1.12446i	0.126952	+	0.0406548i
$766$	49.0332	+	20.4035i	1.77164	+	0.737208i
$767$	−3.47037	+	24.1370i	−0.125308	+	0.871535i
$768$	−14.3919	−	23.6827i	−0.519324	−	0.854577i
$769$	−23.8047	−	27.4720i	−0.858418	−	0.990667i	−1.00000		0.000740736i	$-0.999764\pi$
$769$	−23.8047	−	27.4720i	−0.858418	−	0.990667i	0.141582	−	0.989927i	$-0.454781\pi$
$770$	−9.03342	−	7.30379i	−0.325542	−	0.263210i
$771$	−2.35998	+	15.1076i	−0.0849926	+	0.544086i
$772$	20.3601	+	4.49830i	0.732776	+	0.161897i
$773$	−15.4418	−	52.5901i	−0.555404	−	1.89153i	−0.439418	−	0.898283i	$-0.644815\pi$
$773$	−15.4418	−	52.5901i	−0.555404	−	1.89153i	−0.115986	−	0.993251i	$-0.537003\pi$
$774$	−28.3915	+	8.63829i	−1.02051	+	0.310497i
$775$	2.84383	+	2.46420i	0.102154	+	0.0885166i
$776$	24.6332	−	14.4539i	0.884280	−	0.518865i
$777$	2.31806	−	1.45021i	0.0831599	−	0.0520258i
$778$	9.31872	+	10.0416i	0.334092	+	0.360010i
$779$	2.81725	+	19.5944i	0.100939	+	0.702044i
$780$	−20.7812	+	26.8870i	−0.744086	+	0.962708i
$781$	41.3407			1.47929
$782$	−2.38936	−	0.0520725i	−0.0854433	−	0.00186211i
$783$	41.0362	+	28.5394i	1.46651	+	1.01991i
$784$	20.1833	−	17.2609i	0.720831	−	0.616459i
$785$	66.6153	−	9.57783i	2.37760	−	0.341848i
$786$	−43.5732	+	0.955182i	−1.55420	+	0.0340702i
$787$	−2.25489	+	7.67944i	−0.0803781	+	0.273743i	−0.989870	−	0.141980i	$-0.954653\pi$
$787$	−2.25489	+	7.67944i	−0.0803781	+	0.273743i	0.909491	+	0.415723i	$0.136471\pi$
$788$	−26.0157	+	5.57102i	−0.926771	+	0.198459i
$789$	−43.6636	+	5.73688i	−1.55447	+	0.204238i
$790$	78.5460	−	14.0397i	2.79454	−	0.499511i
$791$	3.12756	−	0.918333i	0.111203	−	0.0326522i
$792$	−32.4713	+	7.28553i	−1.15382	+	0.258880i
$793$	11.6432	−	7.48265i	0.413463	−	0.265717i
$794$	17.0656	+	13.7980i	0.605635	+	0.489674i
$795$	−0.126562	+	10.4077i	−0.00448868	+	0.369124i
$796$	20.4636	+	15.4227i	0.725312	+	0.546643i
$797$	−50.6379	−	7.28063i	−1.79369	−	0.257893i	−0.836625	−	0.547777i	$-0.815474\pi$
$797$	−50.6379	−	7.28063i	−1.79369	−	0.257893i	−0.957062	+	0.289884i	$0.906383\pi$
$798$	−1.26623	−	2.61918i	−0.0448242	−	0.0927180i
$799$	−1.74845	−	0.798489i	−0.0618556	−	0.0282485i
$800$	39.1857	+	10.3408i	1.38542	+	0.365603i
$801$	12.7224	+	20.8969i	0.449525	+	0.738356i
$802$	−2.64475	−	5.30502i	−0.0933894	−	0.187327i
$803$	33.3876	+	21.4569i	1.17822	+	0.757197i
$804$	−2.20676	+	25.3584i	−0.0778265	+	0.894322i
$805$	9.46468	+	3.36364i	0.333586	+	0.118553i
$806$	−1.98337	+	0.656558i	−0.0698614	+	0.0231263i
$807$	−5.34873	+	1.50013i	−0.188284	+	0.0528071i
$808$	28.9403	+	14.6631i	1.01812	+	0.515845i
$809$	40.9240	−	18.6894i	1.43881	−	0.657083i	0.465181	−	0.885216i	$-0.345989\pi$
$809$	40.9240	−	18.6894i	1.43881	−	0.657083i	0.973630	+	0.228133i	$0.0732620\pi$
$810$	−42.7710	+	11.8850i	−1.50282	+	0.417597i
$811$	3.41096	+	1.55774i	0.119775	+	0.0546995i	0.474401	−	0.880309i	$-0.342665\pi$
$811$	3.41096	+	1.55774i	0.119775	+	0.0546995i	−0.354626	+	0.935008i	$0.615392\pi$
$812$	−0.861600	+	11.5213i	−0.0302362	+	0.404317i
$813$	7.16375	+	8.47343i	0.251244	+	0.297176i
$814$	8.29621	+	11.9903i	0.290782	+	0.420259i
$815$	−1.54807	−	1.78657i	−0.0542267	−	0.0625809i
$816$	2.20141	+	1.05540i	0.0770648	+	0.0369464i
$817$	11.6379	−	7.47924i	0.407159	−	0.261665i
$818$	−4.04657	+	6.79499i	−0.141485	+	0.237581i
$819$	4.65904	−	1.99226i	0.162800	−	0.0696150i
$820$	33.2619	+	61.3874i	1.16156	+	2.14374i
$821$	−9.52449	−	8.25302i	−0.332407	−	0.288032i	0.472625	−	0.881264i	$-0.343307\pi$
$821$	−9.52449	−	8.25302i	−0.332407	−	0.288032i	−0.805032	+	0.593231i	$0.797852\pi$
$822$	−15.7872	+	14.2973i	−0.550640	+	0.498676i
$823$	−3.84645	+	13.0998i	−0.134079	+	0.456631i	−0.998972	−	0.0453248i	$-0.985568\pi$
$823$	−3.84645	+	13.0998i	−0.134079	+	0.456631i	0.864893	+	0.501956i	$0.167386\pi$
$824$	−17.3656	−	3.22045i	−0.604961	−	0.112190i
$825$	26.8070	−	40.6179i	0.933300	−	1.41414i
$826$	−7.13130	−	1.83248i	−0.248130	−	0.0637602i
$827$	−26.5265			−0.922416			−0.461208	−	0.887292i	$-0.652584\pi$
$827$	−26.5265			−0.922416			−0.461208	+	0.887292i	$0.652584\pi$
$828$	24.3925	−	15.2646i	0.847697	−	0.530480i
$829$	15.1098			0.524784			0.262392	−	0.964961i	$-0.415489\pi$
$829$	15.1098			0.524784			0.262392	+	0.964961i	$0.415489\pi$
$830$	−81.1838	−	20.8613i	−2.81793	−	0.724106i
$831$	−10.0709	+	15.2594i	−0.349355	+	0.529343i
$832$	−16.0648	+	15.7551i	−0.556947	+	0.546208i
$833$	−0.659128	+	2.24478i	−0.0228374	+	0.0777772i
$834$	20.1067	−	18.2092i	0.696239	−	0.630534i
$835$	−14.4990	−	12.5635i	−0.501759	−	0.434777i
$836$	13.6396	−	7.39045i	0.471737	−	0.255604i
$837$	−2.58887	−	0.863902i	−0.0894846	−	0.0298608i
$838$	4.78714	−	8.03854i	0.165369	−	0.277687i
$839$	−21.0022	+	13.4973i	−0.725076	+	0.465978i	−0.850399	−	0.526138i	$-0.823640\pi$
$839$	−21.0022	+	13.4973i	−0.725076	+	0.465978i	0.125323	+	0.992116i	$0.460003\pi$
$840$	−7.38959	−	7.11864i	−0.254965	−	0.245616i
$841$	41.6071	+	48.0171i	1.43473	+	1.65576i
$842$	5.05875	+	7.31127i	0.174336	+	0.251963i
$843$	6.32864	+	7.48565i	0.217970	+	0.257819i
$844$	−52.2360	−	3.90639i	−1.79804	−	0.134463i
$845$	−16.1453	−	7.37332i	−0.555416	−	0.253650i
$846$	22.8741	−	3.51695i	0.786427	−	0.120915i
$847$	−2.39338	+	1.09302i	−0.0822374	+	0.0375566i
$848$	−1.02508	+	6.81533i	−0.0352014	+	0.234040i
$849$	−32.0859	+	8.99898i	−1.10119	+	0.308844i
$850$	−3.38932	+	1.12197i	−0.116253	+	0.0384832i
$851$	−10.2089	−	7.39767i	−0.349956	−	0.253589i
$852$	36.3774	+	3.16567i	1.24627	+	0.108454i
$853$	16.0894	+	10.3400i	0.550890	+	0.354036i	0.786285	−	0.617864i	$-0.212002\pi$
$853$	16.0894	+	10.3400i	0.550890	+	0.354036i	−0.235394	+	0.971900i	$0.575638\pi$
$854$	1.86454	+	3.74001i	0.0638031	+	0.127981i
$855$	17.6755	−	10.7612i	0.604488	−	0.368024i
$856$	13.7937	+	17.2885i	0.471460	+	0.590910i
$857$	−20.2605	−	9.25266i	−0.692085	−	0.316065i	0.0381387	−	0.999272i	$-0.487857\pi$
$857$	−20.2605	−	9.25266i	−0.692085	−	0.316065i	−0.730224	+	0.683208i	$0.760584\pi$
$858$	11.7606	+	24.3265i	0.401499	+	0.830494i
$859$	−25.0235	−	3.59784i	−0.853791	−	0.122757i	−0.298497	−	0.954411i	$-0.596485\pi$
$859$	−25.0235	−	3.59784i	−0.853791	−	0.122757i	−0.555294	+	0.831654i	$0.687394\pi$
$860$	29.3666	−	38.9650i	1.00139	−	1.32870i
$861$	0.126592	−	10.4102i	0.00431424	−	0.354779i
$862$	22.3930	+	18.1054i	0.762708	+	0.616672i
$863$	21.4101	−	13.7594i	0.728807	−	0.468376i	−0.122883	−	0.992421i	$-0.539214\pi$
$863$	21.4101	−	13.7594i	0.728807	−	0.468376i	0.851691	+	0.524045i	$0.175578\pi$
$864$	−29.1307	+	3.92434i	−0.991048	+	0.133509i
$865$	−40.6268	+	11.9291i	−1.38135	+	0.405601i
$866$	−1.40073	+	0.250374i	−0.0475987	+	0.00850804i
$867$	28.9807	−	3.80773i	0.984237	−	0.129317i
$868$	−0.132092	−	0.616845i	−0.00448348	−	0.0209371i
$869$	17.8744	−	60.8746i	0.606347	−	2.06503i
$870$	−82.1616	+	1.80109i	−2.78554	+	0.0610628i
$871$	20.4569	−	2.94126i	0.693157	−	0.0996609i
$872$	3.98610	+	9.75733i	0.134986	+	0.330425i
$873$	−3.58074	−	30.0807i	−0.121190	−	1.01808i
$874$	−9.00294	+	9.94365i	−0.304529	+	0.336349i
$875$	4.53292			0.153241
$876$	27.7360	+	21.4374i	0.937113	+	0.724304i
$877$	−4.99804	−	34.7621i	−0.168772	−	1.17383i	−0.881427	−	0.472320i	$-0.843417\pi$
$877$	−4.99804	−	34.7621i	−0.168772	−	1.17383i	0.712655	−	0.701514i	$-0.247492\pi$
$878$	16.8883	+	18.1985i	0.569954	+	0.614169i
$879$	−15.1711	+	9.49123i	−0.511709	+	0.320131i
$880$	36.0979	−	41.1170i	1.21686	−	1.38605i
$881$	10.5215	+	9.11694i	0.354479	+	0.307158i	0.813837	−	0.581094i	$-0.197375\pi$
$881$	10.5215	+	9.11694i	0.354479	+	0.307158i	−0.459358	+	0.888251i	$0.651920\pi$
$882$	−8.19934	−	26.9487i	−0.276086	−	0.907411i
$883$	8.91523	+	30.3625i	0.300021	+	1.02178i	0.962180	+	0.272415i	$0.0878223\pi$
$883$	8.91523	+	30.3625i	0.300021	+	1.02178i	−0.662159	+	0.749364i	$0.730359\pi$
$884$	0.427631	−	1.93553i	0.0143828	−	0.0650990i
$885$	8.08339	−	51.7464i	0.271720	−	1.73944i
$886$	−2.94833	−	2.38381i	−0.0990510	−	0.0800858i
$887$	14.9589	+	17.2634i	0.502269	+	0.579650i	0.949102	−	0.314968i	$-0.101994\pi$
$887$	14.9589	+	17.2634i	0.502269	+	0.579650i	−0.446833	+	0.894617i	$0.647448\pi$
$888$	6.38202	+	11.1860i	0.214167	+	0.375379i
$889$	0.413238	−	2.87413i	0.0138596	−	0.0963953i
$890$	−37.1369	−	15.4533i	−1.24483	−	0.517994i
$891$	−6.71607	+	34.6525i	−0.224997	+	1.16090i
$892$	−4.57238	−	12.3816i	−0.153095	−	0.414566i
$893$	−9.81338	+	4.48162i	−0.328392	+	0.149972i
$894$	7.40853	−	27.4423i	0.247778	−	0.917808i
$895$	31.9164	−	49.6630i	1.06685	−	1.66005i
$896$	−4.20273	−	5.33823i	−0.140403	−	0.178338i
$897$	−16.5761	−	16.4647i	−0.553461	−	0.549740i
$898$	22.9048	−	7.58220i	0.764344	−	0.253021i
$899$	−4.25047	−	2.73161i	−0.141761	−	0.0911043i
$900$	26.6989	−	33.6887i	0.889963	−	1.12296i
$901$	−0.252216	−	0.552276i	−0.00840253	−	0.0183990i
$902$	55.4837	−	1.89148i	1.84741	−	0.0629796i
$903$	−6.65430	+	2.94166i	−0.221441	+	0.0978924i
$904$	3.72435	+	14.8940i	0.123870	+	0.495367i
$905$	67.0510	+	9.64048i	2.22885	+	0.320460i
$906$	15.7801	+	1.91688i	0.524260	+	0.0636840i
$907$	18.2567	−	15.8195i	0.606202	−	0.525277i	−0.296785	−	0.954944i	$-0.595915\pi$
$907$	18.2567	−	15.8195i	0.606202	−	0.525277i	0.902987	+	0.429667i	$0.141369\pi$
$908$	−2.93136	+	7.78207i	−0.0972806	+	0.258257i
$909$	26.5464	−	21.8953i	0.880487	−	0.726222i
$910$	−4.26269	+	7.15789i	−0.141307	+	0.237282i
$911$	2.17190	−	0.637727i	0.0719582	−	0.0211288i	−0.245555	−	0.969383i	$-0.578970\pi$
$911$	2.17190	−	0.637727i	0.0719582	−	0.0211288i	0.317514	+	0.948254i	$0.397152\pi$
$912$	12.5680	−	5.45871i	0.416168	−	0.180756i
$913$	−43.6460	+	50.3701i	−1.44447	+	1.66701i
$914$	−29.4173	−	3.21097i	−0.973039	−	0.106210i
$915$	−25.2007	+	15.7658i	−0.833108	+	0.521202i
$916$	35.0805	+	19.3034i	1.15909	+	0.637803i
$917$	−10.5762	+	1.52063i	−0.349258	+	0.0502157i
$918$	1.96102	−	1.69100i	0.0647233	−	0.0558115i
$919$		−	11.1460i		−	0.367672i	−0.982957	−	0.183836i	$-0.941148\pi$
$919$		−	11.1460i		−	0.367672i	0.982957	−	0.183836i	$-0.0588516\pi$
$920$	−17.6375	+	43.8992i	−0.581492	+	1.44731i
$921$	8.37682	−	9.43312i	0.276026	−	0.310832i
$922$	−38.0895	−	9.78762i	−1.25441	−	0.322338i
$923$	−4.21933	−	29.3461i	−0.138881	−	0.965938i
$924$	−7.68722	+	2.73305i	−0.252891	+	0.0899108i
$925$	−18.0707	−	5.30603i	−0.594161	−	0.174461i
$926$	0.496782	−	4.55126i	0.0163253	−	0.149564i
$927$	−10.5081	+	15.5083i	−0.345132	+	0.509361i
$928$	−54.0556	−	6.25553i	−1.77446	−	0.205348i
$929$	3.76805	+	12.8328i	0.123626	+	0.421031i	0.997927	−	0.0643526i	$-0.0204982\pi$
$929$	3.76805	+	12.8328i	0.123626	+	0.421031i	−0.874301	+	0.485383i	$0.838680\pi$
$930$	4.27668	−	1.35824i	0.140238	−	0.0445384i
$931$	7.09918	+	11.0465i	0.232666	+	0.362035i
$932$	−1.42477	−	0.536684i	−0.0466699	−	0.0175797i
$933$	0.0426034	−	3.50347i	0.00139477	−	0.114698i
$934$	5.96388	+	8.61944i	0.195144	+	0.282037i
$935$	−0.685958	+	4.77094i	−0.0224332	+	0.156026i
$936$	8.48579	+	22.3065i	0.277367	+	0.729110i
$937$	2.43838	−	5.33930i	0.0796583	−	0.174427i	−0.865612	−	0.500715i	$-0.833071\pi$
$937$	2.43838	−	5.33930i	0.0796583	−	0.174427i	0.945271	+	0.326288i	$0.105798\pi$
$938$	0.212616	+	6.23676i	0.00694216	+	0.203637i
$939$	−9.10366	+	29.6650i	−0.297087	+	0.968079i
$940$	−26.9925	+	26.8179i	−0.880399	+	0.874704i
$941$	−9.77757	+	15.2142i	−0.318740	+	0.495968i	−0.963243	−	0.268633i	$-0.913428\pi$
$941$	−9.77757	+	15.2142i	−0.318740	+	0.495968i	0.644503	+	0.764602i	$0.277064\pi$
$942$	18.6881	−	43.4148i	0.608890	−	1.41453i
$943$	−44.7104	+	17.4719i	−1.45597	+	0.568962i
$944$	9.98604	−	33.2105i	0.325018	−	1.08091i
$945$	−10.0579	+	4.15693i	−0.327183	+	0.135225i
$946$	−17.3096	−	34.7208i	−0.562783	−	1.12887i
$947$	1.23271	+	2.69925i	0.0400576	+	0.0877139i	0.928603	−	0.371075i	$-0.121011\pi$
$947$	1.23271	+	2.69925i	0.0400576	+	0.0877139i	−0.888545	+	0.458789i	$0.848283\pi$
$948$	20.3899	−	52.1973i	0.662233	−	1.69529i
$949$	11.8237	−	25.8904i	0.383815	−	0.840438i
$950$	−7.69830	+	18.5004i	−0.249766	+	0.600232i
$951$	−2.69976	−	3.19334i	−0.0875458	−	0.103551i
$952$	0.566963	+	0.191773i	0.0183754	+	0.00621541i
$953$	−24.1657	+	20.9397i	−0.782804	+	0.678303i	−0.951597	−	0.307348i	$-0.900558\pi$
$953$	−24.1657	+	20.9397i	−0.782804	+	0.678303i	0.168793	+	0.985651i	$0.446013\pi$
$954$	6.18789	+	3.89192i	0.200340	+	0.126006i
$955$	−36.5634	−	56.8937i	−1.18316	−	1.84104i
$956$	25.6983	+	5.67770i	0.831141	+	0.183630i
$957$	−27.8662	+	59.1057i	−0.900785	+	1.91062i
$958$	−36.8316	+	6.58347i	−1.18998	+	0.212702i
$959$	−3.41947	+	3.94628i	−0.110420	+	0.127432i
$960$	34.9125	−	33.4163i	1.12680	−	1.07851i
$961$	−29.4796	−	8.65599i	−0.950954	−	0.279225i
$962$	7.66468	−	7.11289i	0.247119	−	0.229329i
$963$	22.6624	−	6.05976i	0.730286	−	0.195273i
$964$	14.6936	−	1.00300i	0.473250	−	0.0323045i
$965$			36.3615i			1.17052i
$966$	5.48517	−	4.43609i	0.176482	−	0.142729i
$967$		−	36.8645i		−	1.18548i	−0.805393	−	0.592741i	$-0.798046\pi$
$967$		−	36.8645i		−	1.18548i	0.805393	−	0.592741i	$-0.201954\pi$
$968$	−4.68668	−	11.4723i	−0.150636	−	0.368732i
$969$	−0.664899	+	1.00745i	−0.0213596	+	0.0323641i
$970$	33.8794	+	36.5076i	1.08780	+	1.17219i
$971$	−34.4427	−	10.1133i	−1.10532	−	0.324551i	−0.322355	−	0.946619i	$-0.604474\pi$
$971$	−34.4427	−	10.1133i	−1.10532	−	0.324551i	−0.782963	+	0.622068i	$0.786293\pi$
$972$	−8.56326	+	29.9778i	−0.274667	+	0.961540i
$973$	4.35508	−	5.02603i	0.139618	−	0.161127i
$974$	−6.18553	−	34.6053i	−0.198197	−	1.10882i
$975$	−31.5690	−	14.8836i	−1.01102	−	0.476657i
$976$	−17.9570	+	8.06028i	−0.574791	+	0.258003i
$977$	−7.92670	−	12.3342i	−0.253598	−	0.394605i	0.690990	−	0.722864i	$-0.257175\pi$
$977$	−7.92670	−	12.3342i	−0.253598	−	0.394605i	−0.944588	+	0.328258i	$0.893538\pi$
$978$	−1.63779	+	0.272239i	−0.0523706	+	0.00870523i
$979$	−24.1714	+	20.9447i	−0.772522	+	0.669394i
$980$	36.9850	+	27.8743i	1.18144	+	0.890412i
$981$	11.1762	+	0.271853i	0.356829	+	0.00867961i
$982$	11.6347	+	4.84137i	0.371278	+	0.154494i
$983$	−2.52955	+	5.53893i	−0.0806800	+	0.176665i	−0.945673	−	0.325119i	$-0.894595\pi$
$983$	−2.52955	+	5.53893i	−0.0806800	+	0.176665i	0.864993	+	0.501784i	$0.167323\pi$
$984$	48.9673	+	2.58428i	1.56102	+	0.0823837i
$985$	−19.2738	−	42.2036i	−0.614113	−	1.34472i
$986$	4.29017	−	2.13881i	0.136627	−	0.0681135i
$987$	5.46293	−	1.53216i	0.173887	−	0.0487692i
$988$	−6.63827	−	8.92793i	−0.211192	−	0.284035i
$989$	24.0862	+	23.3493i	0.765895	+	0.742465i
$990$	−24.6219	−	52.5513i	−0.782535	−	1.67019i
$991$	−11.7055	+	18.2141i	−0.371837	+	0.578590i	−0.975865	−	0.218373i	$-0.929925\pi$
$991$	−11.7055	+	18.2141i	−0.371837	+	0.578590i	0.604028	+	0.796963i	$0.293561\pi$
$992$	2.92816	−	0.503809i	0.0929693	−	0.0159959i
$993$	−32.1922	−	9.87922i	−1.02159	−	0.313508i
$994$	8.94682	−	0.305004i	0.283776	−	0.00967415i
$995$	−18.5631	+	40.6476i	−0.588490	+	1.28861i
$996$	−42.2630	+	40.9806i	−1.33915	+	1.29852i
$997$	1.91231	−	13.3004i	0.0605636	−	0.421229i	−0.936873	−	0.349670i	$-0.886294\pi$
$997$	1.91231	−	13.3004i	0.0605636	−	0.421229i	0.997436	−	0.0715586i	$-0.0227973\pi$
$998$	−38.6480	+	26.7409i	−1.22338	+	0.846469i
$999$	13.5826	−	1.44958i	0.429736	−	0.0458626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.o.a.71.19	yes	440
3.2	odd	2	inner	276.2.o.a.71.26	yes	440
4.3	odd	2	inner	276.2.o.a.71.10	yes	440
12.11	even	2	inner	276.2.o.a.71.35	yes	440
23.12	even	11	inner	276.2.o.a.35.35	yes	440
69.35	odd	22	inner	276.2.o.a.35.10	✓	440
92.35	odd	22	inner	276.2.o.a.35.26	yes	440
276.35	even	22	inner	276.2.o.a.35.19	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.o.a.35.10	✓	440	69.35	odd	22	inner
276.2.o.a.35.19	yes	440	276.35	even	22	inner
276.2.o.a.35.26	yes	440	92.35	odd	22	inner
276.2.o.a.35.35	yes	440	23.12	even	11	inner
276.2.o.a.71.10	yes	440	4.3	odd	2	inner
276.2.o.a.71.19	yes	440	1.1	even	1	trivial
276.2.o.a.71.26	yes	440	3.2	odd	2	inner
276.2.o.a.71.35	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)

\(f(q)\)	\(=\)	\(q+(-0.351967 + 1.36972i) q^{2} +(-0.954066 + 1.44560i) q^{3} +(-1.75224 - 0.964188i) q^{4} +(0.982607 - 3.34645i) q^{5} +(-1.64426 - 1.81560i) q^{6} +(-0.453842 - 0.393256i) q^{7} +(1.93739 - 2.06071i) q^{8} +(-1.17952 - 2.75839i) q^{9} +O(q^{10})\)	\(q+(-0.351967 + 1.36972i) q^{2} +(-0.954066 + 1.44560i) q^{3} +(-1.75224 - 0.964188i) q^{4} +(0.982607 - 3.34645i) q^{5} +(-1.64426 - 1.81560i) q^{6} +(-0.453842 - 0.393256i) q^{7} +(1.93739 - 2.06071i) q^{8} +(-1.17952 - 2.75839i) q^{9} +(4.23784 + 2.52373i) q^{10} +(3.29933 - 2.12035i) q^{11} +(3.06558 - 1.61314i) q^{12} +(-1.84189 - 2.12565i) q^{13} +(0.698386 - 0.483221i) q^{14} +(3.90016 + 4.61319i) q^{15} +(2.14068 + 3.37898i) q^{16} +(-0.320532 - 0.146382i) q^{17} +(4.19337 - 0.644740i) q^{18} +(-1.79903 + 0.821588i) q^{19} +(-4.94837 + 4.91636i) q^{20} +(1.00149 - 0.280881i) q^{21} +(1.74302 + 5.26543i) q^{22} +(-2.93332 - 3.79416i) q^{23} +(1.13056 + 4.76674i) q^{24} +(-6.02696 - 3.87329i) q^{25} +(3.55982 - 1.77470i) q^{26} +(5.11287 + 0.926578i) q^{27} +(0.416066 + 1.12667i) q^{28} +(8.75025 + 3.99611i) q^{29} +(-7.69148 + 3.71842i) q^{30} +(-0.519891 - 0.0747490i) q^{31} +(-5.38168 + 1.74284i) q^{32} +(-0.0825988 + 6.79246i) q^{33} +(0.313318 - 0.387516i) q^{34} +(-1.76196 + 1.13234i) q^{35} +(-0.592815 + 5.97064i) q^{36} +(2.52234 - 0.740626i) q^{37} +(-0.492144 - 2.75332i) q^{38} +(4.83012 - 0.634621i) q^{39} +(-4.99236 - 8.50826i) q^{40} +(2.81995 - 9.60386i) q^{41} +(0.0322378 + 1.47061i) q^{42} +(-6.92362 + 0.995467i) q^{43} +(-7.82563 + 0.534185i) q^{44} +(-10.3898 + 1.23678i) q^{45} +(6.22935 - 2.68239i) q^{46} +5.45483 q^{47} +(-6.92700 - 0.129197i) q^{48} +(-0.944882 - 6.57180i) q^{49} +(7.42659 - 6.89194i) q^{50} +(0.517418 - 0.323703i) q^{51} +(1.17790 + 5.50057i) q^{52} +(1.30216 + 1.12832i) q^{53} +(-3.06871 + 6.67705i) q^{54} +(-3.85371 - 13.1245i) q^{55} +(-1.68966 + 0.173342i) q^{56} +(0.528702 - 3.38452i) q^{57} +(-8.55332 + 10.5789i) q^{58} +(-5.67755 - 6.55224i) q^{59} +(-2.38602 - 11.8439i) q^{60} +(-0.700298 + 4.87068i) q^{61} +(0.285369 - 0.685793i) q^{62} +(-0.549441 + 1.71573i) q^{63} +(-0.493014 - 7.98479i) q^{64} +(-8.92324 + 4.07511i) q^{65} +(-9.27467 - 2.50386i) q^{66} +(-3.97263 + 6.18154i) q^{67} +(0.420509 + 0.565549i) q^{68} +(8.28341 - 0.620527i) q^{69} +(-0.930836 - 2.81193i) q^{70} +(8.86761 + 5.69886i) q^{71} +(-7.96943 - 2.91346i) q^{72} +(4.20379 + 9.20502i) q^{73} +(0.126666 + 3.71556i) q^{74} +(11.3493 - 5.01719i) q^{75} +(3.94449 + 0.294982i) q^{76} +(-2.33121 - 0.335178i) q^{77} +(-0.830792 + 6.83925i) q^{78} +(12.2257 - 10.5936i) q^{79} +(13.4110 - 3.84348i) q^{80} +(-6.21748 + 6.50715i) q^{81} +(12.1620 + 7.24277i) q^{82} +(-16.3057 + 4.78777i) q^{83} +(-2.02567 - 0.473450i) q^{84} +(-0.804817 + 0.928809i) q^{85} +(1.07338 - 9.83376i) q^{86} +(-14.1251 + 8.83681i) q^{87} +(2.02268 - 10.9069i) q^{88} +(-8.07202 + 1.16058i) q^{89} +(1.96284 - 14.6664i) q^{90} +1.68904i q^{91} +(1.48159 + 9.47654i) q^{92} +(0.604067 - 0.680239i) q^{93} +(-1.91992 + 7.47156i) q^{94} +(0.981668 + 6.82765i) q^{95} +(2.61504 - 9.44254i) q^{96} +(9.68868 + 2.84485i) q^{97} +(9.33406 + 1.01884i) q^{98} +(-9.74038 - 6.59986i) 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

Varieties

Fields

Representations

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Database

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