LMFDB - Embedded newform 460.2.o.b.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.7
Character	$\chi$	$=$	460.19
Dual form			460.2.o.b.339.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34217 - 0.445613i) q^{2} +(-0.610817 + 0.179352i) q^{3} +(1.60286 + 1.19618i) q^{4} +(-1.58117 + 1.58110i) q^{5} +(0.899744 + 0.0314662i) q^{6} +(0.165059 - 0.0237318i) q^{7} +(-1.61828 - 2.31973i) q^{8} +(-2.18283 + 1.40282i) q^{9} +O(q^{10})$	\(q+(-1.34217 - 0.445613i) q^{2} +(-0.610817 + 0.179352i) q^{3} +(1.60286 + 1.19618i) q^{4} +(-1.58117 + 1.58110i) q^{5} +(0.899744 + 0.0314662i) q^{6} +(0.165059 - 0.0237318i) q^{7} +(-1.61828 - 2.31973i) q^{8} +(-2.18283 + 1.40282i) q^{9} +(2.82677 - 1.41752i) q^{10} +(0.155946 - 0.341474i) q^{11} +(-1.19359 - 0.443170i) q^{12} +(-0.436998 - 0.0628308i) q^{13} +(-0.232112 - 0.0417000i) q^{14} +(0.682234 - 1.24935i) q^{15} +(1.13831 + 3.83461i) q^{16} +(-3.78762 - 4.37115i) q^{17} +(3.55485 - 0.910131i) q^{18} +(4.29795 - 4.96009i) q^{19} +(-4.42568 + 0.642918i) q^{20} +(-0.0965642 + 0.0440994i) q^{21} +(-0.361472 + 0.388826i) q^{22} +(0.455648 + 4.77414i) q^{23} +(1.40452 + 1.12669i) q^{24} +(0.000223800 - 5.00000i) q^{25} +(0.558529 + 0.279062i) q^{26} +(2.33237 - 2.69170i) q^{27} +(0.292953 + 0.159401i) q^{28} +(-4.39311 - 5.06992i) q^{29} +(-1.47240 + 1.37283i) q^{30} +(1.68294 - 5.73157i) q^{31} +(0.180939 - 5.65396i) q^{32} +(-0.0340104 + 0.236547i) q^{33} +(3.13581 + 7.55466i) q^{34} +(-0.223464 + 0.298499i) q^{35} +(-5.17679 - 0.362533i) q^{36} +(-6.05320 + 3.89015i) q^{37} +(-7.97887 + 4.74209i) q^{38} +(0.278195 - 0.0399983i) q^{39} +(6.22652 + 1.10923i) q^{40} +(1.31023 + 0.842037i) q^{41} +(0.149257 - 0.0161588i) q^{42} +(-1.96116 - 6.67910i) q^{43} +(0.658424 - 0.360796i) q^{44} +(1.23343 - 5.66938i) q^{45} +(1.51586 - 6.61076i) q^{46} -4.34479 q^{47} +(-1.38305 - 2.13809i) q^{48} +(-6.68977 + 1.96429i) q^{49} +(-2.22836 + 6.71077i) q^{50} +(3.09752 + 1.99066i) q^{51} +(-0.625289 - 0.623437i) q^{52} +(-0.634266 - 4.41142i) q^{53} +(-4.32990 + 2.57339i) q^{54} +(0.293328 + 0.786497i) q^{55} +(-0.322163 - 0.344487i) q^{56} +(-1.73565 + 3.80055i) q^{57} +(3.63710 + 8.76234i) q^{58} +(-10.8996 - 1.56713i) q^{59} +(2.58797 - 1.18646i) q^{60} +(0.745275 - 2.53817i) q^{61} +(-4.81286 + 6.94282i) q^{62} +(-0.327003 + 0.283350i) q^{63} +(-2.76233 + 7.50797i) q^{64} +(0.790312 - 0.591593i) q^{65} +(0.151056 - 0.302332i) q^{66} +(-6.30252 + 2.87826i) q^{67} +(-0.842348 - 11.5370i) q^{68} +(-1.13457 - 2.83440i) q^{69} +(0.432942 - 0.301059i) q^{70} +(5.27714 - 2.40999i) q^{71} +(6.78660 + 2.79343i) q^{72} +(8.73205 + 7.56636i) q^{73} +(9.85794 - 2.52388i) q^{74} +(0.896623 + 3.05412i) q^{75} +(12.8222 - 2.80922i) q^{76} +(0.0176364 - 0.0600641i) q^{77} +(-0.391209 - 0.0702823i) q^{78} +(1.05496 - 7.33742i) q^{79} +(-7.86279 - 4.26340i) q^{80} +(2.29179 - 5.01831i) q^{81} +(-1.38334 - 1.71402i) q^{82} +(-2.34239 - 3.64482i) q^{83} +(-0.207530 - 0.0448230i) q^{84} +(12.9001 + 0.922926i) q^{85} +(-0.344074 + 9.83843i) q^{86} +(3.59269 + 2.30888i) q^{87} +(-1.04449 + 0.190848i) q^{88} +(1.45112 + 4.94205i) q^{89} +(-4.18183 + 7.05966i) q^{90} -0.0736214 q^{91} +(-4.98038 + 8.19730i) q^{92} +3.80278i q^{93} +(5.83146 + 1.93609i) q^{94} +(1.04662 + 14.6383i) q^{95} +(0.903529 + 3.48599i) q^{96} +(-0.696736 - 0.447765i) q^{97} +(9.85414 + 0.344623i) q^{98} +(0.138623 + 0.964144i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.34217	−	0.445613i	−0.949060	−	0.315096i
$2$	−1.34217	−	0.445613i	−0.949060	−	0.315096i
$3$	−0.610817	+	0.179352i	−0.352655	+	0.103549i	−0.453262	−	0.891377i	$-0.649740\pi$
$3$	−0.610817	+	0.179352i	−0.352655	+	0.103549i	0.100607	+	0.994926i	$0.467922\pi$
$4$	1.60286	+	1.19618i	0.801429	+	0.598089i
$5$	−1.58117	+	1.58110i	−0.707123	+	0.707091i
$5$	−1.58117	+	1.58110i	−0.707123	+	0.707091i
$6$	0.899744	+	0.0314662i	0.367319	+	0.0128460i
$7$	0.165059	−	0.0237318i	0.0623863	−	0.00896979i	−0.111051	−	0.993815i	$-0.535422\pi$
$7$	0.165059	−	0.0237318i	0.0623863	−	0.00896979i	0.173437	+	0.984845i	$0.444513\pi$
$8$	−1.61828	−	2.31973i	−0.572149	−	0.820150i
$9$	−2.18283	+	1.40282i	−0.727610	+	0.467607i
$10$	2.82677	−	1.41752i	0.893903	−	0.448260i
$11$	0.155946	−	0.341474i	0.0470195	−	0.102958i	−0.884664	−	0.466228i	$-0.845612\pi$
$11$	0.155946	−	0.341474i	0.0470195	−	0.102958i	0.931684	+	0.363270i	$0.118340\pi$
$12$	−1.19359	−	0.443170i	−0.344560	−	0.127932i
$13$	−0.436998	−	0.0628308i	−0.121201	−	0.0174261i	0.0814471	−	0.996678i	$-0.474046\pi$
$13$	−0.436998	−	0.0628308i	−0.121201	−	0.0174261i	−0.202649	+	0.979252i	$0.564955\pi$
$14$	−0.232112	−	0.0417000i	−0.0620347	−	0.0111448i
$15$	0.682234	−	1.24935i	0.176152	−	0.322581i
$16$	1.13831	+	3.83461i	0.284578	+	0.958653i
$17$	−3.78762	−	4.37115i	−0.918634	−	1.06016i	−0.997994	−	0.0633140i	$-0.979833\pi$
$17$	−3.78762	−	4.37115i	−0.918634	−	1.06016i	0.0793598	−	0.996846i	$-0.474712\pi$
$18$	3.55485	−	0.910131i	0.837886	−	0.214520i
$19$	4.29795	−	4.96009i	0.986016	−	1.13792i	−0.00442525	−	0.999990i	$-0.501409\pi$
$19$	4.29795	−	4.96009i	0.986016	−	1.13792i	0.990442	−	0.137933i	$-0.0440459\pi$
$20$	−4.42568	+	0.642918i	−0.989612	+	0.143761i
$21$	−0.0965642	+	0.0440994i	−0.0210720	+	0.00962328i
$22$	−0.361472	+	0.388826i	−0.0770660	+	0.0828980i
$23$	0.455648	+	4.77414i	0.0950091	+	0.995476i
$23$	0.455648	+	4.77414i	0.0950091	+	0.995476i
$24$	1.40452	+	1.12669i	0.286697	+	0.229985i
$25$	0.000223800	−	5.00000i	4.47600e−5	−	1.00000i
$26$	0.558529	+	0.279062i	0.109537	+	0.0547285i
$27$	2.33237	−	2.69170i	0.448865	−	0.518018i
$28$	0.292953	+	0.159401i	0.0553629	+	0.0301239i
$29$	−4.39311	−	5.06992i	−0.815781	−	0.941461i	0.183354	−	0.983047i	$-0.441304\pi$
$29$	−4.39311	−	5.06992i	−0.815781	−	0.941461i	−0.999135	+	0.0415857i	$0.986759\pi$
$30$	−1.47240	+	1.37283i	−0.268823	+	0.250644i
$31$	1.68294	−	5.73157i	0.302265	−	1.02942i	−0.658621	−	0.752475i	$-0.728860\pi$
$31$	1.68294	−	5.73157i	0.302265	−	1.02942i	0.960886	−	0.276945i	$-0.0893219\pi$
$32$	0.180939	−	5.65396i	0.0319858	−	0.999488i
$33$	−0.0340104	+	0.236547i	−0.00592045	+	0.0411776i
$34$	3.13581	+	7.55466i	0.537787	+	1.29561i
$35$	−0.223464	+	0.298499i	−0.0377723	+	0.0504555i
$36$	−5.17679	−	0.362533i	−0.862799	−	0.0604222i
$37$	−6.05320	+	3.89015i	−0.995139	+	0.639537i	−0.933506	−	0.358562i	$-0.883267\pi$
$37$	−6.05320	+	3.89015i	−0.995139	+	0.639537i	−0.0616332	+	0.998099i	$0.519631\pi$
$38$	−7.97887	+	4.74209i	−1.29434	+	0.769268i
$39$	0.278195	−	0.0399983i	0.0445468	−	0.00640486i
$40$	6.22652	+	1.10923i	0.984500	+	0.175385i
$41$	1.31023	+	0.842037i	0.204624	+	0.131504i	0.638940	−	0.769257i	$-0.279373\pi$
$41$	1.31023	+	0.842037i	0.204624	+	0.131504i	−0.434315	+	0.900761i	$0.643010\pi$
$42$	0.149257	−	0.0161588i	0.0230309	−	0.00249336i
$43$	−1.96116	−	6.67910i	−0.299074	−	1.01855i	−0.962719	−	0.270505i	$-0.912809\pi$
$43$	−1.96116	−	6.67910i	−0.299074	−	1.01855i	0.663645	−	0.748048i	$-0.269009\pi$
$44$	0.658424	−	0.360796i	0.0992611	−	0.0543920i
$45$	1.23343	−	5.66938i	0.183869	−	0.845142i
$46$	1.51586	−	6.61076i	0.223501	−	0.974704i
$47$	−4.34479			−0.633753			−0.316876	−	0.948467i	$-0.602634\pi$
$47$	−4.34479			−0.633753			−0.316876	+	0.948467i	$0.602634\pi$
$48$	−1.38305	−	2.13809i	−0.199625	−	0.308606i
$49$	−6.68977	+	1.96429i	−0.955681	+	0.280613i
$50$	−2.22836	+	6.71077i	−0.315138	+	0.949046i
$51$	3.09752	+	1.99066i	0.433740	+	0.278747i
$52$	−0.625289	−	0.623437i	−0.0867120	−	0.0864551i
$53$	−0.634266	−	4.41142i	−0.0871232	−	0.605955i	−0.985873	−	0.167494i	$-0.946433\pi$
$53$	−0.634266	−	4.41142i	−0.0871232	−	0.605955i	0.898750	−	0.438461i	$-0.144476\pi$
$54$	−4.32990	+	2.57339i	−0.589225	+	0.350195i
$55$	0.293328	+	0.786497i	0.0395524	+	0.106051i
$56$	−0.322163	−	0.344487i	−0.0430508	−	0.0460340i
$57$	−1.73565	+	3.80055i	−0.229893	+	0.503396i
$58$	3.63710	+	8.76234i	0.477574	+	1.15055i
$59$	−10.8996	−	1.56713i	−1.41901	−	0.204023i	−0.610272	−	0.792192i	$-0.708940\pi$
$59$	−10.8996	−	1.56713i	−1.41901	−	0.204023i	−0.808738	+	0.588169i	$0.799849\pi$
$60$	2.58797	−	1.18646i	0.334106	−	0.153171i
$61$	0.745275	−	2.53817i	0.0954227	−	0.324980i	−0.897923	−	0.440153i	$-0.854924\pi$
$61$	0.745275	−	2.53817i	0.0954227	−	0.324980i	0.993345	+	0.115173i	$0.0367423\pi$
$62$	−4.81286	+	6.94282i	−0.611233	+	0.881739i
$63$	−0.327003	+	0.283350i	−0.0411986	+	0.0356988i
$64$	−2.76233	+	7.50797i	−0.345291	+	0.938496i
$65$	0.790312	−	0.591593i	0.0980262	−	0.0733780i
$66$	0.151056	−	0.302332i	0.0185938	−	0.0372145i
$67$	−6.30252	+	2.87826i	−0.769975	+	0.351636i	−0.761362	−	0.648327i	$-0.775469\pi$
$67$	−6.30252	+	2.87826i	−0.769975	+	0.351636i	−0.00861328	+	0.999963i	$0.502742\pi$
$68$	−0.842348	−	11.5370i	−0.102150	−	1.39907i
$69$	−1.13457	−	2.83440i	−0.136586	−	0.341222i
$70$	0.432942	−	0.301059i	0.0517465	−	0.0359834i
$71$	5.27714	−	2.40999i	0.626281	−	0.286013i	−0.0768837	−	0.997040i	$-0.524497\pi$
$71$	5.27714	−	2.40999i	0.626281	−	0.286013i	0.703164	+	0.711027i	$0.251770\pi$
$72$	6.78660	+	2.79343i	0.799809	+	0.329209i
$73$	8.73205	+	7.56636i	1.02201	+	0.885576i	0.993479	−	0.114017i	$-0.0363718\pi$
$73$	8.73205	+	7.56636i	1.02201	+	0.885576i	0.0285304	+	0.999593i	$0.490917\pi$
$74$	9.85794	−	2.52388i	1.14596	−	0.293395i
$75$	0.896623	+	3.05412i	0.103533	+	0.352660i
$76$	12.8222	−	2.80922i	1.47080	−	0.322239i
$77$	0.0176364	−	0.0600641i	0.00200986	−	0.00684494i
$78$	−0.391209	−	0.0702823i	−0.0442957	−	0.00795791i
$79$	1.05496	−	7.33742i	0.118692	−	0.825524i	−0.840306	−	0.542113i	$-0.817625\pi$
$79$	1.05496	−	7.33742i	0.118692	−	0.825524i	0.958998	−	0.283412i	$-0.0914663\pi$
$80$	−7.86279	−	4.26340i	−0.879086	−	0.476663i
$81$	2.29179	−	5.01831i	0.254643	−	0.557590i
$82$	−1.38334	−	1.71402i	−0.152764	−	0.189281i
$83$	−2.34239	−	3.64482i	−0.257110	−	0.400071i	0.688570	−	0.725170i	$-0.258239\pi$
$83$	−2.34239	−	3.64482i	−0.257110	−	0.400071i	−0.945680	+	0.325099i	$0.894602\pi$
$84$	−0.207530	−	0.0448230i	−0.0226433	−	0.00489059i
$85$	12.9001	+	0.922926i	1.39922	+	0.100105i
$86$	−0.344074	+	9.83843i	−0.0371024	+	1.06090i
$87$	3.59269	+	2.30888i	0.385177	+	0.247538i
$88$	−1.04449	+	0.190848i	−0.111343	+	0.0203445i
$89$	1.45112	+	4.94205i	0.153818	+	0.523856i	0.999959	−	0.00910368i	$-0.00289783\pi$
$89$	1.45112	+	4.94205i	0.153818	+	0.523856i	−0.846140	+	0.532960i	$0.821080\pi$
$90$	−4.18183	+	7.05966i	−0.440803	+	0.744154i
$91$	−0.0736214			−0.00771762
$92$	−4.98038	+	8.19730i	−0.519241	+	0.854628i
$93$			3.80278i			0.394330i
$94$	5.83146	+	1.93609i	0.601469	+	0.199693i
$95$	1.04662	+	14.6383i	0.107381	+	1.50185i
$96$	0.903529	+	3.48599i	0.0922160	+	0.355787i
$97$	−0.696736	−	0.447765i	−0.0707428	−	0.0454636i	0.504791	−	0.863241i	$-0.331569\pi$
$97$	−0.696736	−	0.447765i	−0.0707428	−	0.0454636i	−0.575534	+	0.817778i	$0.695206\pi$
$98$	9.85414	+	0.344623i	0.995419	+	0.0348122i
$99$	0.138623	+	0.964144i	0.0139321	+	0.0969002i
$100$	5.98125	−	8.01403i	0.598125	−	0.801403i
$101$	−1.27529	+	0.819581i	−0.126896	+	0.0815514i	−0.602549	−	0.798082i	$-0.705848\pi$
$101$	−1.27529	+	0.819581i	−0.126896	+	0.0815514i	0.475653	+	0.879633i	$0.342212\pi$
$102$	−3.27035	−	4.05210i	−0.323813	−	0.401218i
$103$	17.4068	+	7.94940i	1.71514	+	0.783278i	0.996093	+	0.0883149i	$0.0281482\pi$
$103$	17.4068	+	7.94940i	1.71514	+	0.783278i	0.719046	+	0.694963i	$0.244579\pi$
$104$	0.561435	+	1.11540i	0.0550533	+	0.109374i
$105$	0.0829591	−	0.222407i	0.00809598	−	0.0217047i
$106$	−1.11449	+	6.20353i	−0.108249	+	0.602540i
$107$	3.32867	−	11.3364i	0.321795	−	1.09593i	−0.626731	−	0.779235i	$-0.715608\pi$
$107$	3.32867	−	11.3364i	0.321795	−	1.09593i	0.948526	−	0.316698i	$-0.102574\pi$
$108$	6.95822	−	1.52448i	0.669555	−	0.146693i
$109$	−9.43758	+	8.17771i	−0.903956	+	0.783283i	−0.976821	−	0.214059i	$-0.931331\pi$
$109$	−9.43758	+	8.17771i	−0.903956	+	0.783283i	0.0728644	+	0.997342i	$0.476786\pi$
$110$	−0.0432242	−	1.18633i	−0.00412127	−	0.113112i
$111$	2.99969	−	3.46182i	0.284718	−	0.328582i
$112$	0.278891	+	0.605921i	0.0263527	+	0.0572542i
$113$	3.30529	+	7.23757i	0.310935	+	0.680853i	0.998996	−	0.0447998i	$-0.0142650\pi$
$113$	3.30529	+	7.23757i	0.310935	+	0.680853i	−0.688061	+	0.725653i	$0.741538\pi$
$114$	4.02312	−	4.32757i	0.376800	−	0.405314i
$115$	−8.26886	−	6.82832i	−0.771075	−	0.636744i
$116$	−0.977006	−	13.3813i	−0.0907127	−	1.24242i
$117$	1.04203	−	0.475881i	0.0963360	−	0.0439952i
$118$	13.9308	+	6.96037i	1.28244	+	0.640754i
$119$	−0.728916	−	0.631609i	−0.0668196	−	0.0578995i
$120$	−4.00221	+	0.439202i	−0.365350	+	0.0400935i
$121$	7.11118	+	8.20674i	0.646471	+	0.746067i
$122$	−2.13133	+	3.07457i	−0.192962	+	0.278358i
$123$	−0.951335	−	0.279337i	−0.0857790	−	0.0251870i
$124$	9.55349	−	7.17379i	0.857929	−	0.644226i
$125$	7.90516	+	7.90622i	0.707059	+	0.707154i
$126$	0.565160	−	0.234588i	0.0503484	−	0.0208988i
$127$	−3.98217	+	8.71973i	−0.353360	+	0.773751i	0.646580	+	0.762846i	$0.276199\pi$
$127$	−3.98217	+	8.71973i	−0.353360	+	0.773751i	−0.999941	+	0.0109053i	$0.996529\pi$
$128$	7.05317	−	8.84606i	0.623418	−	0.781889i
$129$	2.39582	+	3.72797i	0.210940	+	0.328229i
$130$	−1.32436	+	0.441847i	−0.116154	+	0.0387525i
$131$	−14.6540	+	2.10692i	−1.28032	+	0.184083i	−0.748706	−	0.662902i	$-0.769325\pi$
$131$	−14.6540	+	2.10692i	−1.28032	+	0.184083i	−0.531617	+	0.846985i	$0.678416\pi$
$132$	−0.337467	+	0.338470i	−0.0293727	+	0.0294600i
$133$	0.591701	−	0.920704i	0.0513070	−	0.0798352i
$134$	9.74166	−	1.05465i	0.841552	−	0.0911076i
$135$	0.567971	+	7.94377i	0.0488831	+	0.683691i
$136$	−4.01046	+	15.8600i	−0.343894	+	1.35999i
$137$	−18.4374			−1.57521			−0.787606	−	0.616179i	$-0.788680\pi$
$137$	−18.4374			−1.57521			−0.787606	+	0.616179i	$0.788680\pi$
$138$	0.259742	+	4.30984i	0.0221107	+	0.366878i
$139$		−	9.04931i		−	0.767553i	−0.923426	−	0.383776i	$-0.874623\pi$
$139$		−	9.04931i		−	0.767553i	0.923426	−	0.383776i	$-0.125377\pi$
$140$	−0.715239	+	0.211149i	−0.0604487	+	0.0178453i
$141$	2.65387	−	0.779247i	0.223496	−	0.0656244i
$142$	−8.15675	+	0.883062i	−0.684499	+	0.0741049i
$143$	−0.0896032	+	0.139425i	−0.00749300	+	0.0116593i
$144$	−7.86401	−	6.77346i	−0.655334	−	0.564455i
$145$	14.9624	+	1.07047i	1.24256	+	0.0888973i
$146$	−8.34826	−	14.0465i	−0.690907	−	1.16250i
$147$	3.73392	−	2.39965i	0.307969	−	0.197920i
$148$	−14.3557	−	1.00534i	−1.18003	−	0.0826384i
$149$	8.58679	+	3.92146i	0.703457	+	0.321258i	0.734832	−	0.678249i	$-0.237261\pi$
$149$	8.58679	+	3.92146i	0.703457	+	0.321258i	−0.0313743	+	0.999508i	$0.509988\pi$
$150$	0.157532	−	4.49871i	0.0128625	−	0.367318i
$151$	2.21563	+	0.318560i	0.180306	+	0.0259241i	0.231876	−	0.972745i	$-0.425514\pi$
$151$	2.21563	+	0.318560i	0.180306	+	0.0259241i	−0.0515704	+	0.998669i	$0.516423\pi$
$152$	−18.4614	−	1.94326i	−1.49742	−	0.157619i
$153$	14.3997	+	4.22813i	1.16415	+	0.341824i
$154$	−0.0504365	+	0.0727575i	−0.00406429	+	0.00586296i
$155$	6.40118	+	11.7235i	0.514155	+	0.941655i
$156$	0.493752	+	0.268659i	0.0395318	+	0.0215099i
$157$	2.09819	−	2.42144i	0.167454	−	0.193252i	−0.665820	−	0.746112i	$-0.731918\pi$
$157$	2.09819	−	2.42144i	0.167454	−	0.193252i	0.833274	+	0.552860i	$0.186464\pi$
$158$	−4.68559	+	9.37799i	−0.372766	+	0.746073i
$159$	1.17862	+	2.58081i	0.0934705	+	0.204672i
$160$	8.65340	+	9.22598i	0.684111	+	0.729378i
$161$	0.188508	+	0.777199i	0.0148565	+	0.0612519i
$162$	−5.31220	+	5.71420i	−0.417366	+	0.448950i
$163$	−7.71488	−	16.8932i	−0.604276	−	1.32318i	−0.926421	−	0.376489i	$-0.877131\pi$
$163$	−7.71488	−	16.8932i	−0.604276	−	1.32318i	0.322145	−	0.946690i	$-0.395596\pi$
$164$	1.09289	+	2.91694i	0.0853407	+	0.227775i
$165$	−0.320230	−	0.427797i	−0.0249298	−	0.0333039i
$166$	1.51971	+	5.93578i	0.117952	+	0.460706i
$167$	10.9028	+	12.5825i	0.843685	+	0.973665i	0.999901	−	0.0140582i	$-0.00447502\pi$
$167$	10.9028	+	12.5825i	0.843685	+	0.973665i	−0.156216	+	0.987723i	$0.549930\pi$
$168$	0.258567	+	0.152638i	0.0199489	+	0.0117763i
$169$	−12.2864	−	3.60761i	−0.945107	−	0.277508i
$170$	−16.9030	−	6.98719i	−1.29640	−	0.535893i
$171$	−2.42357	+	16.8563i	−0.185335	+	1.28903i
$172$	4.84593	−	13.0515i	0.369499	−	0.995171i
$173$	−2.01010	−	0.917980i	−0.152825	−	0.0697928i	0.337534	−	0.941313i	$-0.390407\pi$
$173$	−2.01010	−	0.917980i	−0.152825	−	0.0697928i	−0.490359	+	0.871520i	$0.663134\pi$
$174$	−3.79315	−	4.69987i	−0.287558	−	0.356296i
$175$	−0.118622	−	0.825298i	−0.00896700	−	0.0623867i
$176$	1.48694	+	0.209288i	0.112082	+	0.0157757i
$177$	6.93874	−	0.997640i	0.521548	−	0.0749872i
$178$	0.254590	−	7.27972i	0.0190823	−	0.545638i
$179$	−1.67731	+	2.60994i	−0.125368	+	0.195076i	−0.898264	−	0.439457i	$-0.855171\pi$
$179$	−1.67731	+	2.60994i	−0.125368	+	0.195076i	0.772896	+	0.634533i	$0.218807\pi$
$180$	8.75861	−	7.61182i	0.652829	−	0.567351i
$181$	−2.18697	−	7.44814i	−0.162556	−	0.553616i	−0.999975	−	0.00705412i	$-0.997755\pi$
$181$	−2.18697	−	7.44814i	−0.162556	−	0.553616i	0.837419	−	0.546562i	$-0.184064\pi$
$182$	0.0988127	+	0.0328066i	0.00732448	+	0.00243179i
$183$			1.68403i			0.124487i
$184$	10.3374	−	8.78288i	0.762080	−	0.647483i
$185$	3.42042	−	15.7217i	0.251475	−	1.15589i
$186$	1.69457	−	5.10398i	0.124252	−	0.374242i
$187$	−2.08330	+	0.611712i	−0.152346	+	0.0447328i
$188$	−6.96408	−	5.19715i	−0.507908	−	0.379041i
$189$	0.321099	−	0.499640i	0.0233565	−	0.0363434i
$190$	5.11825	−	20.1135i	0.371317	−	1.45919i
$191$	2.31013	+	16.0673i	0.167155	+	1.16259i	0.884729	+	0.466105i	$0.154343\pi$
$191$	2.31013	+	16.0673i	0.167155	+	1.16259i	−0.717574	+	0.696482i	$0.754748\pi$
$192$	0.340707	−	5.08142i	0.0245884	−	0.366720i
$193$	−11.2787	−	17.5499i	−0.811855	−	1.26327i	−0.961575	−	0.274543i	$-0.911473\pi$
$193$	−11.2787	−	17.5499i	−0.811855	−	1.26327i	0.149719	−	0.988729i	$-0.452163\pi$
$194$	0.735611	+	0.911453i	0.0528138	+	0.0654385i
$195$	−0.376633	+	0.503099i	−0.0269712	+	0.0360277i
$196$	−13.0724	−	4.85368i	−0.933743	−	0.346691i
$197$	−17.2002	−	2.47301i	−1.22546	−	0.176195i	−0.500962	−	0.865470i	$-0.667020\pi$
$197$	−17.2002	−	2.47301i	−1.22546	−	0.176195i	−0.724500	+	0.689275i	$0.757929\pi$
$198$	0.243579	−	1.35582i	0.0173104	−	0.0963540i
$199$	−18.0542	−	5.30120i	−1.27983	−	0.375792i	−0.429991	−	0.902833i	$-0.641483\pi$
$199$	−18.0542	−	5.30120i	−1.27983	−	0.375792i	−0.849840	+	0.527041i	$0.823302\pi$
$200$	−11.5990	+	8.09089i	−0.820175	+	0.572112i
$201$	3.33346	−	2.88846i	0.235124	−	0.203736i
$202$	2.07688	−	0.531733i	0.146129	−	0.0374126i
$203$	−0.845440	−	0.732578i	−0.0593383	−	0.0514169i
$204$	2.58371	+	6.89593i	0.180896	+	0.482811i
$205$	−3.40306	+	0.740210i	−0.237680	+	0.0516985i
$206$	−19.8205	−	18.4261i	−1.38096	−	1.28381i
$207$	−7.69186	−	9.78194i	−0.534621	−	0.679892i
$208$	−0.256508	−	1.74724i	−0.0177857	−	0.121149i
$209$	−1.02350	−	2.24114i	−0.0707967	−	0.155023i
$210$	−0.210453	+	0.261541i	−0.0145226	+	0.0180480i
$211$	4.74023	+	4.10744i	0.326331	+	0.282768i	0.802582	−	0.596542i	$-0.203459\pi$
$211$	4.74023	+	4.10744i	0.326331	+	0.282768i	−0.476251	+	0.879310i	$0.658005\pi$
$212$	4.26021	−	7.82958i	0.292592	−	0.537738i
$213$	−2.79113	+	2.41853i	−0.191245	+	0.165715i
$214$	−9.51931	+	13.7321i	−0.650727	+	0.938710i
$215$	13.6613	+	7.46002i	0.931692	+	0.508769i
$216$	−10.0185	−	1.05455i	−0.681670	−	0.0717531i
$217$	0.141763	−	0.985984i	0.00962350	−	0.0669329i
$218$	16.3110	−	6.77040i	1.10472	−	0.458549i
$219$	−6.69073	−	3.05555i	−0.452117	−	0.206475i
$220$	−0.470627	+	1.61152i	−0.0317297	+	0.108648i
$221$	1.38054	+	2.14816i	0.0928653	+	0.144501i
$222$	−5.56873	+	3.30967i	−0.373749	+	0.222130i
$223$	1.25308	+	8.71536i	0.0839124	+	0.583624i	0.987785	+	0.155822i	$0.0498027\pi$
$223$	1.25308	+	8.71536i	0.0839124	+	0.583624i	−0.903873	+	0.427801i	$0.859288\pi$
$224$	−0.104313	−	0.937529i	−0.00696973	−	0.0626413i
$225$	7.01361	+	10.9145i	0.467574	+	0.727631i
$226$	−1.21112	−	11.1870i	−0.0805623	−	0.744145i
$227$	−1.68083	−	5.72440i	−0.111561	−	0.379942i	0.884718	−	0.466126i	$-0.154351\pi$
$227$	−1.68083	−	5.72440i	−0.111561	−	0.379942i	−0.996279	+	0.0861845i	$0.972533\pi$
$228$	−7.32815	+	4.01560i	−0.485319	+	0.265939i
$229$			4.56149i			0.301432i	0.988577	+	0.150716i	$0.0481579\pi$
$229$			4.56149i			0.301432i	−0.988577	+	0.150716i	$0.951842\pi$
$230$	8.05546	+	12.8495i	0.531162	+	0.847271i
$231$			0.0398513i			0.00262202i
$232$	−4.65158	+	18.3954i	−0.305391	+	1.20772i
$233$	−7.38403	−	25.1477i	−0.483744	−	1.64748i	−0.733887	−	0.679272i	$-0.762296\pi$
$233$	−7.38403	−	25.1477i	−0.483744	−	1.64748i	0.250143	−	0.968209i	$-0.419522\pi$
$234$	−1.61065	+	0.174371i	−0.105291	+	0.0113990i
$235$	6.86987	−	6.86956i	0.448141	−	0.448121i
$236$	−15.5960	−	15.5498i	−1.01521	−	1.01220i
$237$	0.671593	+	4.67103i	0.0436246	+	0.303416i
$238$	0.696878	+	1.17254i	0.0451719	+	0.0760046i
$239$	−15.1891	−	23.6347i	−0.982502	−	1.52880i	−0.842531	−	0.538647i	$-0.818936\pi$
$239$	−15.1891	−	23.6347i	−0.982502	−	1.52880i	−0.139971	−	0.990156i	$-0.544701\pi$
$240$	5.56737	+	1.19395i	0.359372	+	0.0770691i
$241$	−11.0668	−	5.05405i	−0.712877	−	0.325560i	0.0257553	−	0.999668i	$-0.491801\pi$
$241$	−11.0668	−	5.05405i	−0.712877	−	0.325560i	−0.738633	+	0.674108i	$0.764528\pi$
$242$	−5.88741	−	14.1837i	−0.378457	−	0.911763i
$243$	−2.02044	+	14.0524i	−0.129611	+	0.901464i
$244$	4.23068	−	3.17685i	0.270842	−	0.203377i
$245$	7.47194	−	13.6831i	0.477365	−	0.874182i
$246$	1.15238	+	0.798845i	0.0734731	+	0.0509325i
$247$	−2.18984	+	1.89751i	−0.139336	+	0.120736i
$248$	−16.0192	+	5.37132i	−1.01722	+	0.341079i
$249$	2.08447	+	1.80621i	0.132098	+	0.114464i
$250$	−7.08699	−	14.1342i	−0.448220	−	0.893923i
$251$	6.02704	+	13.1974i	0.380423	+	0.833011i	0.998886	+	0.0471966i	$0.0150287\pi$
$251$	6.02704	+	13.1974i	0.380423	+	0.833011i	−0.618462	+	0.785815i	$0.712244\pi$
$252$	−0.863078	+	0.0630156i	−0.0543688	+	0.00396961i
$253$	1.70130	+	0.588916i	0.106960	+	0.0370248i
$254$	9.23039	−	9.92889i	0.579166	−	0.622994i
$255$	−8.04515	+	1.74993i	−0.503807	+	0.109585i
$256$	−13.4085	+	8.72997i	−0.838031	+	0.545623i
$257$	4.85313	+	4.20526i	0.302730	+	0.262317i	0.792957	−	0.609278i	$-0.208541\pi$
$257$	4.85313	+	4.20526i	0.302730	+	0.262317i	−0.490227	+	0.871595i	$0.663086\pi$
$258$	−1.55438	−	6.07119i	−0.0967712	−	0.377976i
$259$	−0.906812	+	0.785757i	−0.0563465	+	0.0488245i
$260$	1.97441	−	0.00288482i	0.122448	−	0.000178909i
$261$	16.7016	+	4.90404i	1.03380	+	0.303552i
$262$	20.6070	+	3.70214i	1.27311	+	0.228719i
$263$	28.2585	+	4.06296i	1.74249	+	0.250533i	0.938788	−	0.344495i	$-0.111950\pi$
$263$	28.2585	+	4.06296i	1.74249	+	0.250533i	0.803705	+	0.595028i	$0.202859\pi$
$264$	0.603765	−	0.303905i	0.0371592	−	0.0187041i
$265$	7.97780	+	5.97238i	0.490072	+	0.366881i
$266$	−1.20444	+	0.972075i	−0.0738491	+	0.0596018i
$267$	−1.77273	−	2.75843i	−0.108490	−	0.168813i
$268$	−13.5450	−	2.92549i	−0.827391	−	0.178703i
$269$	2.07171	+	14.4091i	0.126315	+	0.878537i	0.950169	+	0.311736i	$0.100910\pi$
$269$	2.07171	+	14.4091i	0.126315	+	0.878537i	−0.823854	+	0.566802i	$0.808181\pi$
$270$	2.77753	−	10.9150i	0.169035	−	0.664266i
$271$	−13.8575	+	21.5627i	−0.841782	+	1.30984i	0.107114	+	0.994247i	$0.465839\pi$
$271$	−13.8575	+	21.5627i	−0.841782	+	1.30984i	−0.948895	+	0.315591i	$0.897797\pi$
$272$	12.4502	−	19.4998i	0.754902	−	1.18235i
$273$	0.0449692	−	0.0132041i	0.00272166	−	0.000799151i
$274$	24.7462	+	8.21593i	1.49497	+	0.496343i
$275$	−1.70734	−	0.779807i	−0.102956	−	0.0470241i
$276$	1.57190	−	5.90029i	0.0946172	−	0.355156i
$277$		−	6.05587i		−	0.363862i	−0.983311	−	0.181931i	$-0.941765\pi$
$277$		−	6.05587i		−	0.363862i	0.983311	−	0.181931i	$-0.0582348\pi$
$278$	−4.03249	+	12.1457i	−0.241853	+	0.728453i
$279$	4.36678	+	14.8719i	0.261432	+	0.890357i
$280$	1.05407	+	0.0353213i	0.0629925	+	0.00211085i
$281$	−4.65237	+	7.23923i	−0.277537	+	0.431856i	−0.951838	−	0.306600i	$-0.900809\pi$
$281$	−4.65237	+	7.23923i	−0.277537	+	0.431856i	0.674301	+	0.738456i	$0.264445\pi$
$282$	−3.90920	−	0.136714i	−0.232789	−	0.00814121i
$283$	−20.2214	+	2.90740i	−1.20204	+	0.172827i	−0.714096	−	0.700048i	$-0.753162\pi$
$283$	−20.2214	+	2.90740i	−1.20204	+	0.172827i	−0.487944	+	0.872875i	$0.662253\pi$
$284$	11.3413	+	2.44953i	0.672981	+	0.145353i
$285$	−3.26470	−	8.75359i	−0.193384	−	0.518518i
$286$	0.182393	−	0.147205i	0.0107851	−	0.00870439i
$287$	0.236249	+	0.107891i	0.0139453	+	0.00636861i
$288$	7.53653	+	12.5955i	0.444094	+	0.742195i
$289$	−2.34152	+	16.2856i	−0.137736	+	0.957976i
$290$	−19.6051	−	8.10416i	−1.15125	−	0.475893i
$291$	0.505886	+	0.148541i	0.0296555	+	0.00870765i
$292$	4.94552	+	22.5729i	0.289415	+	1.32098i
$293$	0.399869	+	0.461474i	0.0233606	+	0.0269596i	0.767310	−	0.641277i	$-0.221595\pi$
$293$	0.399869	+	0.461474i	0.0233606	+	0.0269596i	−0.743949	+	0.668236i	$0.767049\pi$
$294$	−6.08089	+	1.55686i	−0.354645	+	0.0907979i
$295$	19.7120	−	14.7555i	1.14768	−	0.859100i
$296$	18.8199	+	7.74644i	1.09388	+	0.450252i
$297$	−0.555422	−	1.21620i	−0.0322289	−	0.0705713i
$298$	−9.77751	−	9.08966i	−0.566396	−	0.526550i
$299$	0.100846	−	2.11492i	0.00583207	−	0.122309i
$300$	−2.21612	+	5.96785i	−0.127948	+	0.344554i
$301$	−0.482214	−	1.05590i	−0.0277943	−	0.0608611i
$302$	−2.83181	−	1.41488i	−0.162952	−	0.0814171i
$303$	0.631977	−	0.729341i	0.0363061	−	0.0418995i
$304$	23.9124	+	10.8348i	1.37147	+	0.621419i
$305$	2.83471	+	5.19165i	0.162315	+	0.297273i
$306$	−17.4428	−	12.0916i	−0.997136	−	0.691228i
$307$	9.55231	+	2.80481i	0.545179	+	0.160079i	0.542714	−	0.839918i	$-0.317397\pi$
$307$	9.55231	+	2.80481i	0.545179	+	0.160079i	0.00246579	+	0.999997i	$0.499215\pi$
$308$	0.100116	−	0.0751780i	0.00570465	−	0.00428366i
$309$	−12.0581	−	1.73369i	−0.685960	−	0.0986262i
$310$	−3.36735	−	18.5874i	−0.191253	−	1.05569i
$311$	−0.0168123	−	0.00767792i	−0.000953338	−	0.000435375i	0.414938	−	0.909850i	$-0.363803\pi$
$311$	−0.0168123	−	0.00767792i	−0.000953338	−	0.000435375i	−0.415892	+	0.909414i	$0.636530\pi$
$312$	−0.542983	−	0.580609i	−0.0307404	−	0.0328705i
$313$	−20.7588	+	13.3409i	−1.17336	+	0.754071i	−0.974154	−	0.225887i	$-0.927472\pi$
$313$	−20.7588	+	13.3409i	−1.17336	+	0.754071i	−0.199204	+	0.979958i	$0.563836\pi$
$314$	−3.89516	+	2.31501i	−0.219816	+	0.130644i
$315$	0.0690436	−	0.965052i	0.00389017	−	0.0543745i
$316$	10.4678	−	10.4989i	0.588861	−	0.590611i
$317$	11.1269	−	17.3138i	0.624950	−	0.972441i	−0.374036	−	0.927414i	$-0.622026\pi$
$317$	11.1269	−	17.3138i	0.624950	−	0.972441i	0.998986	−	0.0450266i	$-0.0143373\pi$
$318$	−0.431866	−	3.98910i	−0.0242179	−	0.223698i
$319$	−2.41634	+	0.709500i	−0.135289	+	0.0397244i
$320$	−7.50315	−	16.2389i	−0.419439	−	0.907784i
$321$			7.52148i			0.419808i
$322$	0.0933198	−	1.12714i	0.00520051	−	0.0628129i
$323$	−37.9603			−2.11217
$324$	9.67621	−	5.30226i	0.537567	−	0.294570i
$325$	−0.314252	+	2.18498i	−0.0174316	+	0.121201i
$326$	2.82687	+	26.1115i	0.156566	+	1.44618i
$327$	4.29795	−	6.68773i	0.237677	−	0.369832i
$328$	−0.167028	−	4.40205i	−0.00922260	−	0.243062i
$329$	−0.717145	+	0.103110i	−0.0395375	+	0.00568463i
$330$	0.239172	+	0.716876i	0.0131660	+	0.0394627i
$331$	−11.3632	−	17.6815i	−0.624580	−	0.971865i	−0.999005	−	0.0446081i	$-0.985796\pi$
$331$	−11.3632	−	17.6815i	−0.624580	−	0.971865i	0.374425	−	0.927257i	$-0.377840\pi$
$332$	0.605347	−	8.64405i	0.0332227	−	0.474404i
$333$	7.75592	−	16.9831i	0.425022	−	0.930667i
$334$	−9.02654	−	21.7464i	−0.493910	−	1.18991i
$335$	5.41455	−	14.5160i	0.295828	−	0.793092i
$336$	−0.279024	−	0.320087i	−0.0152220	−	0.0174622i
$337$	28.2132	+	8.28414i	1.53687	+	0.451266i	0.937145	−	0.348939i	$-0.113458\pi$
$337$	28.2132	+	8.28414i	1.53687	+	0.451266i	0.599726	+	0.800205i	$0.295276\pi$
$338$	14.8829	+	10.3170i	0.809521	+	0.561171i
$339$	−3.31700	−	3.82802i	−0.180155	−	0.207910i
$340$	19.5731	+	16.9102i	1.06150	+	0.917084i
$341$	−1.69473	−	1.46850i	−0.0917750	−	0.0795235i
$342$	10.7642	−	21.5441i	0.582063	−	1.16497i
$343$	−2.11939	+	0.967895i	−0.114436	+	0.0522614i
$344$	−12.3200	+	15.3580i	−0.664251	+	0.828050i
$345$	6.27543	+	2.68781i	0.337858	+	0.144707i
$346$	2.28883	+	2.12781i	0.123049	+	0.114392i
$347$	−6.41888	−	14.0554i	−0.344584	−	0.754533i	0.655416	−	0.755268i	$-0.272493\pi$
$347$	−6.41888	−	14.0554i	−0.344584	−	0.754533i	−1.00000		0.000734935i	$0.999766\pi$
$348$	2.99674	+	7.99831i	0.160642	+	0.428754i
$349$	−2.47881	+	2.86070i	−0.132688	+	0.153130i	−0.818205	−	0.574927i	$-0.805031\pi$
$349$	−2.47881	+	2.86070i	−0.132688	+	0.153130i	0.685517	+	0.728056i	$0.259576\pi$
$350$	−0.208552	+	1.16055i	−0.0111476	+	0.0620342i
$351$	−1.18836	+	1.02972i	−0.0634302	+	0.0549625i
$352$	−1.90246	−	0.943498i	−0.101402	−	0.0502886i
$353$	−2.56041	+	8.71995i	−0.136277	+	0.464116i	−0.999146	−	0.0413106i	$-0.986847\pi$
$353$	−2.56041	+	8.71995i	−0.136277	+	0.464116i	0.862870	+	0.505427i	$0.168665\pi$
$354$	−9.75755	−	1.75298i	−0.518608	−	0.0931701i
$355$	−4.53363	+	12.1543i	−0.240620	+	0.645084i
$356$	−3.58564	+	9.65720i	−0.190039	+	0.511831i
$357$	0.558514	+	0.255065i	0.0295597	+	0.0134995i
$358$	3.41426	−	2.75556i	0.180449	−	0.145636i
$359$	27.1780	−	17.4662i	1.43440	−	0.921832i	0.434623	−	0.900612i	$-0.356882\pi$
$359$	27.1780	−	17.4662i	1.43440	−	0.921832i	0.999775	−	0.0212191i	$-0.00675474\pi$
$360$	−15.1475	+	6.31343i	−0.798343	+	0.332747i
$361$	−3.42621	−	23.8298i	−0.180327	−	1.25420i
$362$	−0.383691	+	10.9712i	−0.0201663	+	0.576635i
$363$	−5.81553	−	3.73741i	−0.305236	−	0.196163i
$364$	−0.118005	−	0.0880643i	−0.00618513	−	0.00461583i
$365$	−25.7701	+	1.84253i	−1.34887	+	0.0964426i
$366$	0.750423	−	2.26026i	0.0392253	−	0.118145i
$367$			18.0778i			0.943653i	0.881692	+	0.471826i	$0.156405\pi$
$367$			18.0778i			0.943653i	−0.881692	+	0.471826i	$0.843595\pi$
$368$	−17.7883	+	7.18169i	−0.927279	+	0.374372i
$369$	−4.04125			−0.210379
$370$	−11.5966	+	19.5771i	−0.602879	+	1.01777i
$371$	−0.209382	−	0.713090i	−0.0108706	−	0.0370218i
$372$	−4.54880	+	6.09531i	−0.235844	+	0.316027i
$373$	16.5944	+	10.6646i	0.859228	+	0.552192i	0.894440	−	0.447188i	$-0.147574\pi$
$373$	16.5944	+	10.6646i	0.859228	+	0.552192i	−0.0352123	+	0.999380i	$0.511211\pi$
$374$	3.06874	+	0.107321i	0.158681	+	0.00554945i
$375$	−6.24660	−	3.41145i	−0.322573	−	0.176166i
$376$	7.03109	+	10.0788i	0.362601	+	0.519772i
$377$	1.60123	+	2.49157i	0.0824678	+	0.128322i
$378$	−0.653616	+	0.527517i	−0.0336184	+	0.0271326i
$379$	9.12709	−	19.9855i	0.468827	−	1.02659i	−0.516559	−	0.856252i	$-0.672787\pi$
$379$	9.12709	−	19.9855i	0.468827	−	1.02659i	0.985386	−	0.170336i	$-0.0544854\pi$
$380$	−15.8324	+	24.7150i	−0.812185	+	1.26785i
$381$	0.868474	−	6.04037i	0.0444933	−	0.309458i
$382$	4.05919	−	22.5945i	0.207686	−	1.15603i
$383$	5.51797	−	18.7925i	0.281955	−	0.960250i	−0.689749	−	0.724048i	$-0.742279\pi$
$383$	5.51797	−	18.7925i	0.281955	−	0.960250i	0.971704	−	0.236202i	$-0.0759026\pi$
$384$	−2.72163	+	6.66832i	−0.138888	+	0.340292i
$385$	0.0670814	+	0.122857i	0.00341878	+	0.00626137i
$386$	7.31744	+	28.5810i	0.372448	+	1.45473i
$387$	13.6505	+	11.8282i	0.693891	+	0.601260i
$388$	−0.581162	−	1.55112i	−0.0295040	−	0.0787464i
$389$	4.22929	−	1.93145i	0.214434	−	0.0979285i	−0.305302	−	0.952255i	$-0.598758\pi$
$389$	4.22929	−	1.93145i	0.214434	−	0.0979285i	0.519736	+	0.854327i	$0.326030\pi$
$390$	0.729694	−	0.507414i	0.0369495	−	0.0256939i
$391$	19.1427	−	20.0743i	0.968086	−	1.01520i
$392$	15.3826	+	12.3397i	0.776937	+	0.623249i
$393$	8.57301	−	3.91516i	0.432451	−	0.197494i
$394$	21.9836	+	10.9838i	1.10752	+	0.553357i
$395$	9.93314	+	13.2697i	0.499791	+	0.667673i
$396$	−0.931096	+	1.71121i	−0.0467893	+	0.0859913i
$397$	−3.71921	+	3.22272i	−0.186662	+	0.161743i	−0.743179	−	0.669093i	$-0.766683\pi$
$397$	−3.71921	+	3.22272i	−0.186662	+	0.161743i	0.556517	+	0.830836i	$0.312137\pi$
$398$	21.8696	+	15.1603i	1.09623	+	0.759919i
$399$	−0.196291	+	0.668504i	−0.00982682	+	0.0334671i
$400$	19.1733	−	5.69070i	0.958666	−	0.284535i
$401$	5.02156	+	0.721991i	0.250765	+	0.0360545i	0.266551	−	0.963821i	$-0.414116\pi$
$401$	5.02156	+	0.721991i	0.250765	+	0.0360545i	−0.0157861	+	0.999875i	$0.505025\pi$
$402$	−5.76122	+	2.39138i	−0.287344	+	0.119271i
$403$	−1.09556	+	2.39894i	−0.0545738	+	0.119500i
$404$	−3.02448	−	0.211806i	−0.150474	−	0.0105377i
$405$	4.31076	+	11.5584i	0.214203	+	0.574340i
$406$	0.808281	+	1.35999i	0.0401143	+	0.0674949i
$407$	0.384415	+	2.67366i	0.0190547	+	0.132529i
$408$	−0.394871	−	10.4069i	−0.0195490	−	0.515216i
$409$	−31.8808	−	20.4885i	−1.57640	−	1.01309i	−0.977154	−	0.212532i	$-0.931829\pi$
$409$	−31.8808	−	20.4885i	−1.57640	−	1.01309i	−0.599250	−	0.800562i	$-0.704534\pi$
$410$	4.89734	+	0.522955i	0.241862	+	0.0258269i
$411$	11.2619	−	3.30678i	0.555507	−	0.163112i
$412$	18.3917	+	33.5634i	0.906092	+	1.65355i
$413$	−1.83627			−0.0903568
$414$	5.96485	+	16.5566i	0.293156	+	0.813715i
$415$	9.46656	+	2.05955i	0.464695	+	0.101099i
$416$	−0.434313	+	2.45940i	−0.0212939	+	0.120582i
$417$	1.62301	+	5.52747i	0.0794792	+	0.270681i
$418$	0.375027	+	3.46409i	0.0183432	+	0.169434i
$419$	26.9640	+	17.3287i	1.31728	+	0.846564i	0.994980	−	0.100074i	$-0.0319080\pi$
$419$	26.9640	+	17.3287i	1.31728	+	0.846564i	0.322299	+	0.946638i	$0.395544\pi$
$420$	0.399010	−	0.257253i	0.0194697	−	0.0125527i
$421$	−15.6704	+	2.25307i	−0.763730	+	0.109808i	−0.513163	−	0.858291i	$-0.671526\pi$
$421$	−15.6704	+	2.25307i	−0.763730	+	0.109808i	−0.250567	+	0.968099i	$0.580617\pi$
$422$	−4.53189	−	7.62520i	−0.220609	−	0.371189i
$423$	9.48394	−	6.09496i	0.461125	−	0.296347i
$424$	−9.20690	+	8.61025i	−0.447126	+	0.418151i
$425$	−21.8566	+	18.9371i	−1.06020	+	0.918586i
$426$	4.82390	−	2.00232i	0.233719	−	0.0970127i
$427$	0.0627785	−	0.436634i	0.00303807	−	0.0211302i
$428$	18.8958	−	14.1890i	0.913362	−	0.685851i
$429$	0.0297249	−	0.101234i	0.00143513	−	0.00488762i
$430$	−15.0115	−	16.1003i	−0.723920	−	0.776424i
$431$	−4.42640	−	5.10834i	−0.213212	−	0.246060i	0.639062	−	0.769155i	$-0.279323\pi$
$431$	−4.42640	−	5.10834i	−0.213212	−	0.246060i	−0.852274	+	0.523095i	$0.824777\pi$
$432$	12.9766	+	5.87974i	0.624337	+	0.282889i
$433$	−15.5055	+	17.8943i	−0.745148	+	0.859946i	−0.994089	−	0.108572i	$-0.965372\pi$
$433$	−15.5055	+	17.8943i	−0.745148	+	0.859946i	0.248941	+	0.968519i	$0.419918\pi$
$434$	−0.629637	+	1.26019i	−0.0302236	+	0.0604910i
$435$	−9.33125	+	2.02967i	−0.447399	+	0.0973152i
$436$	−24.9091	+	1.81868i	−1.19293	+	0.0870990i
$437$	25.6385	+	18.2589i	1.22646	+	0.873443i
$438$	7.61852	+	7.08255i	0.364027	+	0.338417i
$439$	4.75260	−	2.17044i	0.226829	−	0.103589i	−0.298759	−	0.954329i	$-0.596573\pi$
$439$	4.75260	−	2.17044i	0.226829	−	0.103589i	0.525588	+	0.850739i	$0.323845\pi$
$440$	1.34978	−	1.95322i	0.0643480	−	0.0931160i
$441$	11.8471	−	13.6723i	0.564147	−	0.651060i
$442$	−0.895677	−	3.49840i	−0.0426030	−	0.166402i
$443$	8.47538	+	9.78111i	0.402677	+	0.464715i	0.920482	−	0.390784i	$-0.127796\pi$
$443$	8.47538	+	9.78111i	0.402677	+	0.464715i	−0.517805	+	0.855499i	$0.673251\pi$
$444$	8.94904	−	1.96065i	0.424702	−	0.0930484i
$445$	−10.1084	−	5.51988i	−0.479182	−	0.261667i
$446$	2.20182	−	12.2559i	0.104259	−	0.580334i
$447$	−5.94828	−	0.855233i	−0.281344	−	0.0404511i
$448$	−0.277768	+	1.30481i	−0.0131233	+	0.0616465i
$449$	13.6295	−	29.8444i	0.643216	−	1.40845i	−0.254153	−	0.967164i	$-0.581797\pi$
$449$	13.6295	−	29.8444i	0.643216	−	1.40845i	0.897368	−	0.441282i	$-0.145476\pi$
$450$	−4.54986	−	17.7745i	−0.214482	−	0.837896i
$451$	0.491860	−	0.316099i	0.0231608	−	0.0148845i
$452$	−3.35952	+	15.5545i	−0.158018	+	0.731623i
$453$	−1.41048	+	0.202797i	−0.0662702	+	0.00952821i
$454$	−0.294892	+	8.43214i	−0.0138400	+	0.395740i
$455$	0.116408	−	0.116403i	0.00545730	−	0.00545706i
$456$	11.6251	−	2.12411i	0.544393	−	0.0994706i
$457$	4.85268	−	1.42487i	0.226999	−	0.0666528i	−0.166255	−	0.986083i	$-0.553168\pi$
$457$	4.85268	−	1.42487i	0.226999	−	0.0666528i	0.393254	+	0.919430i	$0.371349\pi$
$458$	2.03266	−	6.12231i	0.0949799	−	0.286077i
$459$	−20.6000			−0.961525
$460$	−5.08593	−	20.8359i	−0.237133	−	0.971477i
$461$	−10.8092			−0.503434			−0.251717	−	0.967801i	$-0.580995\pi$
$461$	−10.8092			−0.503434			−0.251717	+	0.967801i	$0.580995\pi$
$462$	0.0177583	−	0.0534874i	0.000826189	−	0.00248846i
$463$	−4.14534	+	1.21718i	−0.192650	+	0.0565672i	−0.376634	−	0.926362i	$-0.622919\pi$
$463$	−4.14534	+	1.21718i	−0.192650	+	0.0565672i	0.183984	+	0.982929i	$0.441101\pi$
$464$	14.4405	−	22.6170i	0.670381	−	1.04997i
$465$	−6.01258	−	6.01285i	−0.278827	−	0.278839i
$466$	−1.29548	+	37.0430i	−0.0600121	+	1.71598i
$467$	9.44028	−	1.35731i	0.436844	−	0.0628087i	0.0796154	−	0.996826i	$-0.474631\pi$
$467$	9.44028	−	1.35731i	0.436844	−	0.0628087i	0.357229	+	0.934017i	$0.383722\pi$
$468$	2.23947	+	0.483689i	0.103520	+	0.0223585i
$469$	−0.971979	+	0.624653i	−0.0448818	+	0.0288438i
$470$	−12.2817	+	6.15884i	−0.566513	+	0.284086i
$471$	−0.847319	+	1.85537i	−0.0390424	+	0.0854909i
$472$	14.0033	+	27.8203i	0.644556	+	1.28053i
$473$	−2.58657	−	0.371893i	−0.118931	−	0.0170997i
$474$	1.18008	−	6.56860i	0.0542027	−	0.301706i
$475$	−24.7995	−	21.4908i	−1.13788	−	0.986067i
$476$	−0.412831	−	1.88429i	−0.0189221	−	0.0863664i
$477$	7.57292	+	8.73962i	0.346740	+	0.400160i
$478$	9.85449	+	38.4904i	0.450734	+	1.76051i
$479$	11.9888	−	13.8359i	0.547784	−	0.632176i	−0.412582	−	0.910921i	$-0.635373\pi$
$479$	11.9888	−	13.8359i	0.547784	−	0.632176i	0.960365	+	0.278745i	$0.0899183\pi$
$480$	−6.94034	−	4.08338i	−0.316782	−	0.186380i
$481$	2.88966	−	1.31966i	0.131757	−	0.0601714i
$482$	12.6015	+	11.7149i	0.573981	+	0.533601i
$483$	−0.254536	−	0.440917i	−0.0115818	−	0.0200624i
$484$	1.58149	+	21.6605i	0.0718859	+	0.984568i
$485$	1.80962	−	0.393617i	0.0821708	−	0.0178732i
$486$	8.97372	−	17.9605i	0.407056	−	0.814704i
$487$	6.39163	−	7.37634i	0.289632	−	0.334254i	−0.592222	−	0.805774i	$-0.701749\pi$
$487$	6.39163	−	7.37634i	0.289632	−	0.334254i	0.881855	+	0.471521i	$0.156295\pi$
$488$	−7.09395	+	2.37864i	−0.321128	+	0.107676i
$489$	7.74221	+	8.93499i	0.350115	+	0.404054i
$490$	−16.1260	+	15.0355i	−0.728499	+	0.679235i
$491$	6.56124	−	22.3455i	0.296104	−	1.00844i	−0.668275	−	0.743915i	$-0.732967\pi$
$491$	6.56124	−	22.3455i	0.296104	−	1.00844i	0.964379	−	0.264524i	$-0.0852150\pi$
$492$	−1.19072	−	1.58570i	−0.0536817	−	0.0714891i
$493$	−5.52194	+	38.4059i	−0.248696	+	1.72972i
$494$	3.78470	−	1.57096i	0.170282	−	0.0706810i
$495$	−1.74360	−	1.30530i	−0.0783690	−	0.0586690i
$496$	23.8940	−	0.0708930i	1.07287	−	0.00318319i
$497$	0.813843	−	0.523025i	0.0365059	−	0.0234609i
$498$	−1.99286	−	3.35311i	−0.0893021	−	0.150257i
$499$	−32.5014	+	4.67300i	−1.45496	+	0.209192i	−0.823986	−	0.566610i	$-0.808255\pi$
$499$	−32.5014	+	4.67300i	−1.45496	+	0.209192i	−0.630977	+	0.775802i	$0.717346\pi$
$500$	3.21360	+	22.1286i	0.143717	+	0.989619i
$501$	−8.91633	−	5.73017i	−0.398352	−	0.256005i
$502$	−2.20842	−	20.3989i	−0.0985664	−	0.910447i
$503$	4.01406	+	13.6706i	0.178978	+	0.609544i	0.999292	+	0.0376298i	$0.0119808\pi$
$503$	4.01406	+	13.6706i	0.178978	+	0.609544i	−0.820313	+	0.571914i	$0.806201\pi$
$504$	1.18648	+	0.300021i	0.0528500	+	0.0133640i
$505$	0.720618	−	3.31227i	0.0320671	−	0.147394i
$506$	−2.02101	−	1.54855i	−0.0898450	−	0.0688414i
$507$	8.15177			0.362033
$508$	−16.8132	+	9.21312i	−0.745966	+	0.408766i
$509$	12.6019	−	3.70025i	0.558569	−	0.164011i	0.00975098	−	0.999952i	$-0.496896\pi$
$509$	12.6019	−	3.70025i	0.558569	−	0.164011i	0.548818	+	0.835942i	$0.315078\pi$
$510$	11.5778	+	1.23632i	0.512673	+	0.0547450i
$511$	1.62086	+	1.04167i	0.0717028	+	0.0460806i
$512$	21.8867	−	5.74214i	0.967265	−	0.253769i
$513$	−3.32668	−	23.1376i	−0.146876	−	1.02155i
$514$	−4.63983	−	7.80681i	−0.204654	−	0.344344i
$515$	−40.0919	+	14.9525i	−1.76666	+	0.658886i
$516$	−0.619156	+	8.84123i	−0.0272568	+	0.389214i
$517$	−0.677553	+	1.48363i	−0.0297987	+	0.0652501i
$518$	1.56724	−	0.650535i	0.0688606	−	0.0285829i
$519$	1.39244	+	0.200203i	0.0611215	+	0.00878794i
$520$	−2.65129	−	0.875950i	−0.116267	−	0.0384129i
$521$	−4.64391	+	15.8157i	−0.203454	+	0.692899i	0.793035	+	0.609175i	$0.208499\pi$
$521$	−4.64391	+	15.8157i	−0.203454	+	0.692899i	−0.996489	+	0.0837236i	$0.973319\pi$
$522$	−20.2312	−	14.0245i	−0.885494	−	0.613836i
$523$	20.0367	−	17.3619i	0.876144	−	0.759183i	−0.0955505	−	0.995425i	$-0.530461\pi$
$523$	20.0367	−	17.3619i	0.876144	−	0.759183i	0.971694	+	0.236242i	$0.0759157\pi$
$524$	−26.0085	−	14.1517i	−1.13619	−	0.618219i
$525$	0.220475	+	0.482831i	0.00962234	+	0.0210725i
$526$	−36.1173	−	18.0455i	−1.57479	−	0.786823i
$527$	−31.4279	+	14.3526i	−1.36902	+	0.625211i
$528$	−0.945782	+	0.138848i	−0.0411599	+	0.00604259i
$529$	−22.5848	+	4.35065i	−0.981947	+	0.189159i
$530$	−8.04622	−	11.5710i	−0.349505	−	0.502611i
$531$	25.9904	−	11.8694i	1.12789	−	0.515089i
$532$	2.04974	−	0.767979i	0.0888675	−	0.0332961i
$533$	−0.519664	−	0.450292i	−0.0225092	−	0.0195043i
$534$	1.15013	+	4.49224i	0.0497708	+	0.194398i
$535$	12.6608	+	23.1878i	0.547376	+	1.00250i
$536$	16.8761	+	9.96232i	0.728935	+	0.430307i
$537$	0.556429	−	1.89502i	0.0240117	−	0.0817763i
$538$	3.64027	−	20.2627i	0.156943	−	0.873586i
$539$	−0.372487	+	2.59071i	−0.0160442	+	0.111590i
$540$	−8.59179	+	13.4121i	−0.369732	+	0.577166i
$541$	−9.84316	+	21.5535i	−0.423191	+	0.926658i	0.571192	+	0.820816i	$0.306481\pi$
$541$	−9.84316	+	21.5535i	−0.423191	+	0.926658i	−0.994383	+	0.105842i	$0.966246\pi$
$542$	28.2077	−	22.7658i	1.21163	−	0.977873i
$543$	2.67168	+	4.15721i	0.114653	+	0.178403i
$544$	−25.3996	+	20.6242i	−1.08900	+	0.884254i
$545$	1.99265	−	27.8522i	0.0853559	−	1.19306i
$546$	−0.0662404	−	0.00231659i	−0.00283483	−	9.91407e-5i
$547$	−23.1375	−	14.8696i	−0.989288	−	0.635777i	−0.0573347	−	0.998355i	$-0.518260\pi$
$547$	−23.1375	−	14.8696i	−0.989288	−	0.635777i	−0.931953	+	0.362578i	$0.881897\pi$
$548$	−29.5525	−	22.0544i	−1.26242	−	0.942118i
$549$	1.93379	+	6.58589i	0.0825322	+	0.281079i
$550$	1.94405	+	1.80745i	0.0828945	+	0.0770698i
$551$	−44.0287			−1.87568
$552$	−4.73901	+	7.21876i	−0.201705	+	0.307251i
$553$		−	1.23614i		−	0.0525661i
$554$	−2.69857	+	8.12803i	−0.114651	+	0.345327i
$555$	0.730473	+	10.2166i	0.0310069	+	0.433669i
$556$	10.8246	−	14.5048i	0.459065	−	0.615139i
$557$	−2.85212	−	1.83294i	−0.120848	−	0.0776643i	0.478820	−	0.877913i	$-0.341064\pi$
$557$	−2.85212	−	1.83294i	−0.120848	−	0.0776643i	−0.599668	+	0.800249i	$0.704701\pi$
$558$	0.766126	−	21.9066i	0.0324327	−	0.927379i
$559$	0.437370	+	3.04197i	0.0184988	+	0.128662i
$560$	−1.39900	−	0.517112i	−0.0591185	−	0.0218520i
$561$	1.16280	−	0.747288i	0.0490936	−	0.0315505i
$562$	9.47018	−	7.64314i	0.399475	−	0.322407i
$563$	−8.32554	−	3.80215i	−0.350880	−	0.160241i	0.232176	−	0.972674i	$-0.425416\pi$
$563$	−8.32554	−	3.80215i	−0.350880	−	0.160241i	−0.583055	+	0.812433i	$0.698143\pi$
$564$	5.18590	+	1.92548i	0.218366	+	0.0810774i
$565$	−16.6696	−	6.21786i	−0.701295	−	0.261587i
$566$	28.4363	+	5.10869i	1.19527	+	0.214734i
$567$	0.259185	−	0.882704i	0.0108848	−	0.0370701i
$568$	−14.1304	−	8.34151i	−0.592899	−	0.350002i
$569$	−7.82890	+	6.78378i	−0.328204	+	0.284391i	−0.803339	−	0.595523i	$-0.796945\pi$
$569$	−7.82890	+	6.78378i	−0.328204	+	0.284391i	0.475134	+	0.879913i	$0.342400\pi$
$570$	0.481079	+	13.2036i	0.0201502	+	0.553039i
$571$	13.2895	−	15.3369i	0.556150	−	0.641831i	−0.406155	−	0.913804i	$-0.633131\pi$
$571$	13.2895	−	15.3369i	0.556150	−	0.641831i	0.962305	+	0.271973i	$0.0876762\pi$
$572$	−0.310399	+	0.116298i	−0.0129784	+	0.00486265i
$573$	−4.29276	−	9.39984i	−0.179333	−	0.392684i
$574$	−0.269009	−	0.250084i	−0.0112282	−	0.0104383i
$575$	23.8708	−	2.27717i	0.995481	−	0.0949646i
$576$	−4.50263	−	20.2637i	−0.187610	−	0.844319i
$577$	34.5366	−	15.7723i	1.43778	−	0.656611i	0.464360	−	0.885647i	$-0.346284\pi$
$577$	34.5366	−	15.7723i	1.43778	−	0.656611i	0.973418	+	0.229036i	$0.0735572\pi$
$578$	10.3998	−	20.8147i	0.432574	−	0.865777i
$579$	10.0368	+	8.69694i	0.417116	+	0.361433i
$580$	22.7021	+	19.6135i	0.942652	+	0.814404i
$581$	−0.473129	−	0.546020i	−0.0196287	−	0.0226527i
$582$	−0.612794	−	0.424797i	−0.0254011	−	0.0176084i
$583$	−1.60530	−	0.471358i	−0.0664846	−	0.0195216i
$584$	3.42103	−	32.5005i	0.141563	−	1.34488i
$585$	−0.895219	+	2.40001i	−0.0370128	+	0.0992283i
$586$	−0.331055	−	0.797564i	−0.0136758	−	0.0329471i
$587$	−0.781803	+	1.71191i	−0.0322685	+	0.0706581i	−0.925080	−	0.379773i	$-0.876002\pi$
$587$	−0.781803	+	1.71191i	−0.0322685	+	0.0706581i	0.892811	+	0.450431i	$0.148730\pi$
$588$	8.85536	+	0.620145i	0.365189	+	0.0255744i
$589$	−21.1959	−	32.9815i	−0.873363	−	1.35898i
$590$	−33.0322	+	11.0206i	−1.35991	+	0.453709i
$591$	10.9497	−	1.57433i	0.450410	−	0.0647592i
$592$	−21.8077	−	18.7834i	−0.896289	−	0.771995i
$593$	16.5408	−	25.7380i	0.679250	−	1.05693i	−0.314921	−	0.949118i	$-0.601978\pi$
$593$	16.5408	−	25.7380i	0.679250	−	1.05693i	0.994171	−	0.107816i	$-0.0343857\pi$
$594$	0.203517	+	1.87986i	0.00835038	+	0.0771316i
$595$	2.15118	−	0.153807i	0.0881898	−	0.00630548i
$596$	9.07265	+	16.5569i	0.371630	+	0.678196i
$597$	11.9786			0.490252
$598$	−1.07779	+	2.79365i	−0.0440740	+	0.114241i
$599$			4.60956i			0.188341i	0.995556	+	0.0941707i	$0.0300200\pi$
$599$			4.60956i			0.188341i	−0.995556	+	0.0941707i	$0.969980\pi$
$600$	5.63377	−	7.02236i	0.229998	−	0.286687i
$601$	−2.44538	+	0.718027i	−0.0997490	+	0.0292889i	−0.331226	−	0.943551i	$-0.607462\pi$
$601$	−2.44538	+	0.718027i	−0.0997490	+	0.0292889i	0.231477	+	0.972840i	$0.425644\pi$
$602$	0.176692	+	1.63208i	0.00720142	+	0.0665187i
$603$	9.71965	−	15.1241i	0.395815	−	0.615899i
$604$	3.17029	+	3.16090i	0.128997	+	0.128615i
$605$	−24.2197	−	1.73277i	−0.984672	−	0.0704473i
$606$	−1.17323	+	0.697284i	−0.0476591	+	0.0283252i
$607$	−32.7030	+	21.0169i	−1.32737	+	0.853050i	−0.995904	−	0.0904162i	$-0.971180\pi$
$607$	−32.7030	+	21.0169i	−1.32737	+	0.853050i	−0.331468	+	0.943466i	$0.607544\pi$
$608$	−27.2665	−	25.1979i	−1.10580	−	1.02191i
$609$	0.647798	+	0.295840i	0.0262501	+	0.0119880i
$610$	−1.49120	−	8.23128i	−0.0603770	−	0.333275i
$611$	1.89866	+	0.272987i	0.0768118	+	0.0110439i
$612$	18.0231	+	24.0017i	0.728539	+	0.970211i
$613$	−25.5017	−	7.48798i	−1.03000	−	0.302437i	−0.277292	−	0.960786i	$-0.589437\pi$
$613$	−25.5017	−	7.48798i	−1.03000	−	0.302437i	−0.752713	+	0.658349i	$0.771255\pi$
$614$	−11.5710	−	8.02118i	−0.466968	−	0.323708i
$615$	1.94589	−	1.06248i	0.0784657	−	0.0428432i
$616$	−0.167873	+	0.0562889i	−0.00676382	+	0.00226794i
$617$	−4.42404	+	5.10562i	−0.178105	+	0.205544i	−0.837782	−	0.546005i	$-0.816148\pi$
$617$	−4.42404	+	5.10562i	−0.178105	+	0.205544i	0.659676	+	0.751550i	$0.270693\pi$
$618$	15.4115	+	7.70015i	0.619941	+	0.309745i
$619$	1.24979	+	2.73665i	0.0502332	+	0.109995i	0.933084	−	0.359657i	$-0.117106\pi$
$619$	1.24979	+	2.73665i	0.0502332	+	0.109995i	−0.882851	+	0.469653i	$0.844379\pi$
$620$	−3.76323	+	26.4481i	−0.151135	+	1.06218i
$621$	13.9133	+	9.90859i	0.558321	+	0.397618i
$622$	0.0191436	+	0.0177969i	0.000767590	+	0.000713589i
$623$	0.356803	+	0.781290i	0.0142950	+	0.0313017i
$624$	0.470051	+	1.02124i	0.0188171	+	0.0408822i
$625$	−25.0000	−	0.00223800i	−1.00000	−	8.95201e-5i
$626$	33.8068	−	8.65539i	1.35119	−	0.345939i
$627$	1.02712	+	1.18536i	0.0410193	+	0.0473388i
$628$	6.25957	−	1.37142i	0.249784	−	0.0547254i
$629$	39.9317	+	11.7250i	1.59218	+	0.467506i
$630$	−0.522708	+	1.26450i	−0.0208252	+	0.0503789i
$631$	4.00588	−	27.8615i	0.159472	−	1.10915i	−0.740138	−	0.672455i	$-0.765240\pi$
$631$	4.00588	−	27.8615i	0.159472	−	1.10915i	0.899610	−	0.436694i	$-0.143851\pi$
$632$	−18.7281	+	9.42679i	−0.744963	+	0.374977i
$633$	−3.63209	−	1.65872i	−0.144363	−	0.0659282i
$634$	−22.6495	+	18.2798i	−0.899527	+	0.725986i
$635$	−7.49030	−	20.0836i	−0.297243	−	0.796995i
$636$	−1.19796	+	5.54652i	−0.0475020	+	0.219934i
$637$	3.04683	−	0.438069i	0.120720	−	0.0173569i
$638$	3.55930	+	0.124478i	0.140914	+	0.00492811i
$639$	−8.13831	+	12.6635i	−0.321947	+	0.500959i
$640$	2.83426	+	25.1390i	0.112034	+	0.993704i
$641$	3.67310	+	12.5094i	0.145079	+	0.494093i	0.999683	−	0.0251875i	$-0.00801828\pi$
$641$	3.67310	+	12.5094i	0.145079	+	0.494093i	−0.854604	+	0.519280i	$0.826200\pi$
$642$	3.35167	−	10.0951i	0.132280	−	0.398423i
$643$		−	22.9418i		−	0.904738i	−0.891831	−	0.452369i	$-0.850579\pi$
$643$		−	22.9418i		−	0.904738i	0.891831	−	0.452369i	$-0.149421\pi$
$644$	−0.627518	+	1.47123i	−0.0247277	+	0.0579746i
$645$	−9.68251	−	2.10653i	−0.381248	−	0.0829445i
$646$	50.9493	+	16.9156i	2.00457	+	0.665535i
$647$	18.3916	−	5.40027i	0.723050	−	0.212307i	0.100556	−	0.994931i	$-0.467938\pi$
$647$	18.3916	−	5.40027i	0.723050	−	0.212307i	0.622494	+	0.782625i	$0.286120\pi$
$648$	−15.3499	+	2.80471i	−0.603001	+	0.110179i
$649$	−2.23489	+	3.47755i	−0.0877270	+	0.136506i
$650$	1.39543	−	2.79258i	0.0547334	−	0.109534i
$651$	0.0902469	+	0.627681i	0.00353705	+	0.0246008i
$652$	7.84146	−	36.3058i	0.307095	−	1.42185i
$653$	−4.06816	−	6.33019i	−0.159200	−	0.247719i	0.752486	−	0.658609i	$-0.228855\pi$
$653$	−4.06816	−	6.33019i	−0.159200	−	0.247719i	−0.911685	+	0.410889i	$0.865218\pi$
$654$	−8.74873	+	7.06088i	−0.342102	+	0.276102i
$655$	19.8392	−	26.5009i	0.775183	−	1.03547i
$656$	−1.73743	+	5.98274i	−0.0678351	+	0.233587i
$657$	−29.6748	−	4.26660i	−1.15773	−	0.166456i
$658$	1.00848	+	0.181178i	0.0393146	+	0.00706304i
$659$	−1.03516	−	0.303951i	−0.0403242	−	0.0118403i	0.261508	−	0.965201i	$-0.415780\pi$
$659$	−1.03516	−	0.303951i	−0.0403242	−	0.0118403i	−0.301832	+	0.953361i	$0.597598\pi$
$660$	−0.00156155	−	1.06875i	−6.07834e−5	−	0.0416010i
$661$	28.4338	−	24.6381i	1.10595	−	0.958310i	0.106597	−	0.994302i	$-0.466005\pi$
$661$	28.4338	−	24.6381i	1.10595	−	0.958310i	0.999352	+	0.0359925i	$0.0114592\pi$
$662$	7.37232	+	28.7953i	0.286533	+	1.11916i
$663$	−1.22854	−	1.06453i	−0.0477124	−	0.0413430i
$664$	−4.66438	+	11.3321i	−0.181013	+	0.439769i
$665$	0.520147	+	2.39133i	0.0201704	+	0.0927320i
$666$	−17.9777	+	19.3381i	−0.696620	+	0.749337i
$667$	22.2028	−	23.2834i	0.859696	−	0.901538i
$668$	2.42473	+	33.2097i	0.0938156	+	1.28492i
$669$	−2.32852	−	5.09875i	−0.0900257	−	0.197129i
$670$	−13.7358	+	17.0702i	−0.530659	+	0.659478i
$671$	−0.750498	−	0.650310i	−0.0289727	−	0.0251050i
$672$	0.231864	+	0.553950i	0.00894435	+	0.0213691i
$673$	−33.2827	+	28.8396i	−1.28295	+	1.11168i	−0.295237	+	0.955424i	$0.595398\pi$
$673$	−33.2827	+	28.8396i	−1.28295	+	1.11168i	−0.987716	+	0.156260i	$0.950056\pi$
$674$	−34.1755	−	23.6909i	−1.31639	−	0.912540i
$675$	−13.4580	−	11.6625i	−0.517998	−	0.448888i
$676$	−15.3780	−	20.4792i	−0.591462	−	0.787662i
$677$	−0.426050	+	2.96324i	−0.0163744	+	0.113887i	−0.996369	−	0.0851358i	$-0.972868\pi$
$677$	−0.426050	+	2.96324i	−0.0163744	+	0.113887i	0.979995	+	0.199022i	$0.0637767\pi$
$678$	2.74617	+	6.61596i	0.105466	+	0.254085i
$679$	−0.125629	−	0.0573726i	−0.00482118	−	0.00220176i
$680$	−18.7351	−	31.4184i	−0.718459	−	1.20484i
$681$	2.05336	+	3.19510i	0.0786851	+	0.122436i
$682$	1.62025	+	2.72617i	0.0620425	+	0.104390i
$683$	−0.393174	−	2.73459i	−0.0150444	−	0.104636i	0.980916	−	0.194434i	$-0.0622870\pi$
$683$	−0.393174	−	2.73459i	−0.0150444	−	0.104636i	−0.995960	+	0.0897978i	$0.971378\pi$
$684$	−24.0478	+	24.1192i	−0.919489	+	0.922222i
$685$	29.1527	−	29.1514i	1.11387	−	1.11382i
$686$	3.27590	−	0.354654i	0.125074	−	0.0135407i
$687$	−0.818113	−	2.78624i	−0.0312130	−	0.106302i
$688$	23.3793	−	15.1232i	0.891329	−	0.576566i
$689$			1.96763i			0.0749609i
$690$	−7.22500	−	6.40392i	−0.275051	−	0.243793i
$691$		−	8.48185i		−	0.322665i	−0.986900	−	0.161332i	$-0.948421\pi$
$691$		−	8.48185i		−	0.322665i	0.986900	−	0.161332i	$-0.0515791\pi$
$692$	−2.12383	−	3.87583i	−0.0807360	−	0.147337i
$693$	0.0457619	+	0.155851i	0.00173835	+	0.00592027i
$694$	2.35199	+	21.7251i	0.0892804	+	0.824674i
$695$	14.3079	+	14.3085i	0.542729	+	0.542754i
$696$	−0.457995	−	12.0705i	−0.0173603	−	0.457531i
$697$	−1.28201	−	8.91655i	−0.0485595	−	0.337739i
$698$	4.60176	−	2.73497i	0.174179	−	0.103520i
$699$	9.02058	+	14.0363i	0.341190	+	0.530902i
$700$	0.797070	−	1.46473i	0.0301264	−	0.0553616i
$701$	8.03007	+	3.66721i	0.303292	+	0.138509i	0.561247	−	0.827648i	$-0.310322\pi$
$701$	8.03007	+	3.66721i	0.303292	+	0.138509i	−0.257956	+	0.966157i	$0.583049\pi$
$702$	2.05385	−	0.852517i	0.0775175	−	0.0321762i
$703$	−6.72078	+	46.7441i	−0.253479	+	1.76299i
$704$	2.13300	+	2.11410i	0.0803905	+	0.0796782i
$705$	−2.96416	+	5.42817i	−0.111637	+	0.204437i
$706$	7.32223	−	10.5627i	0.275576	−	0.397534i
$707$	−0.191048	+	0.165544i	−0.00718510	+	0.00622592i
$708$	12.3152	+	6.70090i	0.462833	+	0.251835i
$709$	12.0908	+	10.4767i	0.454079	+	0.393462i	0.851651	−	0.524109i	$-0.175602\pi$
$709$	12.0908	+	10.4767i	0.454079	+	0.393462i	−0.397572	+	0.917571i	$0.630147\pi$
$710$	11.5010	−	14.2929i	0.431626	−	0.536405i
$711$	7.99028	+	17.4963i	0.299659	+	0.656161i
$712$	9.11592	−	11.3638i	0.341634	−	0.425878i
$713$	28.1301	+	5.42301i	1.05348	+	0.203093i
$714$	−0.635963	−	0.591222i	−0.0238003	−	0.0221259i
$715$	−0.0787676	−	0.362128i	−0.00294574	−	0.0135428i
$716$	−5.81044	+	2.17701i	−0.217146	+	0.0813586i
$717$	13.5167	+	11.7123i	0.504790	+	0.437403i
$718$	−44.2607	+	11.3318i	−1.65179	+	0.422901i
$719$	−4.07991	+	3.53526i	−0.152155	+	0.131843i	−0.727612	−	0.685989i	$-0.759370\pi$
$719$	−4.07991	+	3.53526i	−0.152155	+	0.131843i	0.575457	+	0.817832i	$0.304824\pi$
$720$	23.1439	−	1.72380i	0.862523	−	0.0642422i
$721$	3.06179	+	0.899022i	0.114027	+	0.0334813i
$722$	−6.02030	+	33.5105i	−0.224052	+	1.24713i
$723$	7.66626	+	1.10224i	0.285111	+	0.0409928i
$724$	5.40390	−	14.5543i	0.200834	−	0.540907i
$725$	−25.3506	+	21.9644i	−0.941498	+	0.815739i
$726$	6.14001	+	7.60773i	0.227877	+	0.282349i
$727$	4.92065	+	7.65668i	0.182497	+	0.283971i	0.920433	−	0.390899i	$-0.127836\pi$
$727$	4.92065	+	7.65668i	0.182497	+	0.283971i	−0.737937	+	0.674870i	$0.764200\pi$
$728$	0.119140	+	0.170782i	0.00441563	+	0.00632960i
$729$	1.06918	+	7.43628i	0.0395991	+	0.275418i
$730$	35.4090	+	9.01048i	1.31055	+	0.333493i
$731$	−21.7672	+	33.8704i	−0.805089	+	1.25274i
$732$	−2.01440	+	2.69926i	−0.0744542	+	0.0997674i
$733$	−0.272847	+	0.0801151i	−0.0100778	+	0.00295912i	−0.286768	−	0.958000i	$-0.592581\pi$
$733$	−0.272847	+	0.0801151i	−0.0100778	+	0.00295912i	0.276690	+	0.960959i	$0.410763\pi$
$734$	8.05569	−	24.2635i	0.297341	−	0.895583i
$735$	−2.10989	+	9.69798i	−0.0778246	+	0.357715i
$736$	27.0752	−	1.71239i	0.998006	−	0.0631194i
$737$			2.60100i			0.0958091i
$738$	5.42405	+	1.80083i	0.199662	+	0.0662895i
$739$	5.38398	+	18.3362i	0.198053	+	0.674507i	0.997295	+	0.0734978i	$0.0234162\pi$
$739$	5.38398	+	18.3362i	0.198053	+	0.674507i	−0.799242	+	0.601009i	$0.794766\pi$
$740$	24.2885	−	21.1083i	0.892862	−	0.775956i
$741$	0.997270	−	1.55178i	0.0366356	−	0.0570061i
$742$	−0.0367348	+	1.05039i	−0.00134858	+	0.0385612i
$743$	33.5074	−	4.81764i	1.22927	−	0.176742i	0.503081	−	0.864239i	$-0.332200\pi$
$743$	33.5074	−	4.81764i	1.22927	−	0.176742i	0.726187	+	0.687497i	$0.241291\pi$
$744$	8.82143	−	6.15396i	0.323409	−	0.225615i
$745$	−19.7774	+	7.37610i	−0.724589	+	0.270239i
$746$	−17.5203	−	21.7084i	−0.641465	−	0.794802i
$747$	10.2261	+	4.67008i	0.374152	+	0.170869i
$748$	−4.07095	−	1.51151i	−0.148849	−	0.0552663i
$749$	0.280392	−	1.95017i	0.0102453	−	0.0712577i
$750$	6.86384	+	7.36232i	0.250632	+	0.268834i
$751$	18.8573	+	5.53701i	0.688113	+	0.202048i	0.607053	−	0.794661i	$-0.292351\pi$
$751$	18.8573	+	5.53701i	0.688113	+	0.202048i	0.0810597	+	0.996709i	$0.474170\pi$
$752$	−4.94573	−	16.6606i	−0.180352	−	0.607549i
$753$	−6.04839	−	6.98022i	−0.220416	−	0.254373i
$754$	−1.03886	−	4.05765i	−0.0378330	−	0.147771i
$755$	−4.00698	+	2.99945i	−0.145829	+	0.109161i
$756$	1.11233	−	0.416760i	0.0404552	−	0.0151574i
$757$	−22.0121	−	48.1998i	−0.800044	−	1.75185i	−0.645347	−	0.763890i	$-0.723287\pi$
$757$	−22.0121	−	48.1998i	−0.800044	−	1.75185i	−0.154697	−	0.987962i	$-0.549440\pi$
$758$	−21.1559	+	22.7569i	−0.768418	+	0.826568i
$759$	−1.14481	−	0.0545879i	−0.0415538	−	0.00198142i
$760$	32.2632	−	26.1167i	1.17031	−	0.947353i
$761$	1.38960	+	3.04280i	0.0503730	+	0.110301i	0.933145	−	0.359500i	$-0.117053\pi$
$761$	1.38960	+	3.04280i	0.0503730	+	0.110301i	−0.882772	+	0.469801i	$0.844325\pi$
$762$	−3.85731	+	7.72022i	−0.139736	+	0.279674i
$763$	−1.36368	+	1.57377i	−0.0493686	+	0.0569744i
$764$	−15.5165	+	28.5169i	−0.561368	+	1.03171i
$765$	−29.4535	+	16.0820i	−1.06489	+	0.581445i
$766$	−15.7802	+	22.7639i	−0.570163	+	0.822492i
$767$	4.66465	+	1.36966i	0.168431	+	0.0494557i
$768$	6.62439	−	7.73725i	0.239037	−	0.279194i
$769$	24.8804	+	3.57726i	0.897211	+	0.128999i	0.575465	−	0.817827i	$-0.304821\pi$
$769$	24.8804	+	3.57726i	0.897211	+	0.128999i	0.321746	+	0.946826i	$0.395730\pi$
$770$	−0.0352882	−	0.194788i	−0.00127170	−	0.00701965i
$771$	−3.71860	−	1.69823i	−0.133922	−	0.0611601i
$772$	2.91476	−	41.6213i	0.104905	−	1.49799i
$773$	30.7883	−	19.7864i	1.10738	−	0.711669i	0.146658	−	0.989187i	$-0.453148\pi$
$773$	30.7883	−	19.7864i	1.10738	−	0.711669i	0.960720	+	0.277518i	$0.0895119\pi$
$774$	−13.0505	−	21.9583i	−0.469090	−	0.789274i
$775$	−28.6575	−	8.41598i	−1.02941	−	0.302311i
$776$	0.0888197	+	2.34085i	0.00318844	+	0.0840317i
$777$	0.412969	−	0.642592i	0.0148152	−	0.0230529i
$778$	−6.53712	+	0.707719i	−0.234367	+	0.0253729i
$779$	9.80790	−	2.87986i	0.351404	−	0.103182i
$780$	−1.20549	+	0.355876i	−0.0431633	+	0.0127424i
$781$		−	2.17783i		−	0.0779290i
$782$	−34.6381	+	18.4130i	−1.23866	+	0.658449i
$783$	−23.8931			−0.853869
$784$	−15.1474	−	23.4167i	−0.540977	−	0.836310i
$785$	0.510943	+	7.14617i	0.0182364	+	0.255058i
$786$	−13.2511	+	1.43459i	−0.472652	+	0.0511700i
$787$	10.8140	−	16.8269i	0.385477	−	0.599815i	−0.593240	−	0.805025i	$-0.702152\pi$
$787$	10.8140	−	16.8269i	0.385477	−	0.599815i	0.978718	+	0.205211i	$0.0657880\pi$
$788$	−24.6113	−	24.5384i	−0.876741	−	0.874143i
$789$	−17.9895	+	2.58649i	−0.640442	+	0.0920817i
$790$	−7.41884	−	22.2366i	−0.263950	−	0.791144i
$791$	0.717327	+	1.11618i	0.0255052	+	0.0396869i
$792$	2.01223	−	1.88183i	0.0715014	−	0.0668678i
$793$	−0.485159	+	1.06235i	−0.0172285	+	0.0377252i
$794$	6.42791	−	2.66812i	0.228118	−	0.0946879i
$795$	−5.94413	−	2.21720i	−0.210817	−	0.0786359i
$796$	−22.5972	−	30.0932i	−0.800937	−	1.06662i
$797$	27.1172	+	7.96232i	0.960540	+	0.282040i	0.724169	−	0.689623i	$-0.242224\pi$
$797$	27.1172	+	7.96232i	0.960540	+	0.282040i	0.236371	+	0.971663i	$0.424042\pi$
$798$	0.561350	−	0.809779i	0.0198716	−	0.0286659i
$799$	16.4564	+	18.9917i	0.582187	+	0.671879i
$800$	−28.2698	−	0.905959i	−0.999487	−	0.0320305i
$801$	−10.1003	−	8.75200i	−0.356878	−	0.309237i
$802$	−6.41807	−	3.20671i	−0.226630	−	0.113233i
$803$	3.94545	−	1.80182i	0.139232	−	0.0635850i
$804$	8.79819	−	0.642379i	0.310288	−	0.0226550i
$805$	−1.52690	−	0.930837i	−0.0538160	−	0.0328077i
$806$	2.53943	−	2.73160i	0.0894477	−	0.0962166i
$807$	−3.84974	−	8.42975i	−0.135517	−	0.296741i
$808$	3.96499	+	1.63203i	0.139488	+	0.0574145i
$809$	28.4879	−	32.8768i	1.00158	−	1.15589i	0.0138232	−	0.999904i	$-0.495600\pi$
$809$	28.4879	−	32.8768i	1.00158	−	1.15589i	0.987760	−	0.155984i	$-0.0498548\pi$
$810$	−0.635225	−	17.4343i	−0.0223195	−	0.612578i
$811$	−27.3588	+	23.7066i	−0.960699	+	0.832450i	−0.985918	−	0.167232i	$-0.946517\pi$
$811$	−27.3588	+	23.7066i	−0.960699	+	0.832450i	0.0252190	+	0.999682i	$0.491972\pi$
$812$	−0.478827	−	2.18552i	−0.0168035	−	0.0766966i
$813$	4.59707	−	15.6562i	0.161226	−	0.549087i
$814$	0.675467	−	3.75982i	0.0236751	−	0.131782i
$815$	38.9085	+	14.5131i	1.36291	+	0.508372i
$816$	−4.10744	+	14.1438i	−0.143789	+	0.495131i
$817$	−41.5579	−	18.9789i	−1.45393	−	0.663986i
$818$	33.6596	+	41.7057i	1.17688	+	1.45820i
$819$	0.160703	−	0.103278i	0.00561542	−	0.00360881i
$820$	−6.34004	−	2.88421i	−0.221404	−	0.100721i
$821$	3.35436	+	23.3301i	0.117068	+	0.814225i	0.960757	+	0.277392i	$0.0894702\pi$
$821$	3.35436	+	23.3301i	0.117068	+	0.814225i	−0.843689	+	0.536833i	$0.819621\pi$
$822$	−16.5889	−	0.580155i	−0.578605	−	0.0202352i
$823$	−31.8417	−	20.4634i	−1.10993	−	0.713311i	−0.148655	−	0.988889i	$-0.547494\pi$
$823$	−31.8417	−	20.4634i	−1.10993	−	0.713311i	−0.961279	+	0.275578i	$0.911131\pi$
$824$	−9.72855	−	53.2434i	−0.338910	−	1.85482i
$825$	1.18273	+	0.170105i	0.0411774	+	0.00592229i
$826$	2.46459	+	0.818264i	0.0857540	+	0.0284710i
$827$			15.0386i			0.522942i	0.965211	+	0.261471i	$0.0842077\pi$
$827$			15.0386i			0.522942i	−0.965211	+	0.261471i	$0.915792\pi$
$828$	−0.628010	−	24.8799i	−0.0218248	−	0.864636i
$829$	38.2205			1.32745			0.663727	−	0.747975i	$-0.268974\pi$
$829$	38.2205			1.32745			0.663727	+	0.747975i	$0.268974\pi$
$830$	−11.7880	−	6.98269i	−0.409168	−	0.242373i
$831$	1.08613	+	3.69903i	0.0376775	+	0.128318i
$832$	1.67886	−	3.10741i	0.0582041	−	0.107730i
$833$	33.9246	+	21.8020i	1.17542	+	0.755394i
$834$	0.284748	−	8.14206i	0.00986000	−	0.281936i
$835$	−37.1335	−	2.65668i	−1.28506	−	0.0919381i
$836$	1.04029	−	4.81652i	0.0359792	−	0.166583i
$837$	−11.5024	−	17.8981i	−0.397582	−	0.618649i
$838$	−28.4685	−	35.2737i	−0.983428	−	1.21851i
$839$	−18.8480	+	41.2714i	−0.650705	+	1.42485i	0.240230	+	0.970716i	$0.422777\pi$
$839$	−18.8480	+	41.2714i	−0.650705	+	1.42485i	−0.890935	+	0.454130i	$0.849950\pi$
$840$	−0.650176	+	0.167474i	−0.0224332	+	0.00577840i
$841$	−2.27755	+	15.8407i	−0.0785361	+	0.546230i
$842$	22.0364	+	3.95893i	0.759425	+	0.136434i
$843$	1.54338	−	5.25625i	0.0531567	−	0.181035i
$844$	2.68470	+	12.2538i	0.0924111	+	0.421793i
$845$	25.1309	−	13.7218i	0.864530	−	0.472044i
$846$	−15.4451	+	3.95433i	−0.531013	+	0.135953i
$847$	1.36852	+	1.18583i	0.0470230	+	0.0407457i
$848$	16.1941	−	7.45374i	0.556107	−	0.255962i
$849$	11.8301	−	5.40265i	0.406010	−	0.185418i
$850$	37.7740	−	15.6774i	1.29564	−	0.537729i
$851$	−21.3302	−	27.1262i	−0.731191	−	0.929876i
$852$	−7.36677	+	0.537867i	−0.252381	+	0.0184270i
$853$	−20.0539	+	9.15830i	−0.686632	+	0.313574i	−0.728007	−	0.685569i	$-0.759553\pi$
$853$	−20.0539	+	9.15830i	−0.686632	+	0.313574i	0.0413755	+	0.999144i	$0.486826\pi$
$854$	−0.278829	+	0.558064i	−0.00954135	+	0.0190966i
$855$	−22.8194	−	30.4846i	−0.780409	−	1.04255i
$856$	−31.6842	+	10.6239i	−1.08294	+	0.363117i
$857$	13.5944	−	11.7796i	0.464376	−	0.402384i	−0.391001	−	0.920390i	$-0.627871\pi$
$857$	13.5944	−	11.7796i	0.464376	−	0.402384i	0.855377	+	0.518006i	$0.173326\pi$
$858$	−0.0850071	+	0.122628i	−0.00290209	+	0.00418644i
$859$	−0.438810	+	1.49445i	−0.0149720	+	0.0509900i	−0.966640	−	0.256138i	$-0.917550\pi$
$859$	−0.438810	+	1.49445i	−0.0149720	+	0.0509900i	0.951668	+	0.307128i	$0.0993680\pi$
$860$	12.9736	+	28.2987i	0.442396	+	0.964977i
$861$	−0.163655	−	0.0235301i	−0.00557735	−	0.000801902i
$862$	3.66466	+	8.82874i	0.124819	+	0.300708i
$863$	−8.70763	+	19.0670i	−0.296411	+	0.649050i	−0.997978	−	0.0635534i	$-0.979757\pi$
$863$	−8.70763	+	19.0670i	−0.296411	+	0.649050i	0.701567	+	0.712603i	$0.252484\pi$
$864$	−14.7967	−	13.6742i	−0.503396	−	0.465205i
$865$	4.62974	−	1.72668i	0.157416	−	0.0587090i
$866$	28.7850	−	17.1078i	0.978155	−	0.581348i
$867$	−1.49062	−	10.3675i	−0.0506240	−	0.352098i
$868$	1.40664	−	1.41082i	0.0477444	−	0.0478863i
$869$	−2.34102	−	1.50448i	−0.0794138	−	0.0510361i
$870$	13.4286	+	1.43395i	0.455272	+	0.0486156i
$871$	2.93503	−	0.861803i	0.0994498	−	0.0292011i
$872$	34.2428	+	8.65883i	1.15961	+	0.293225i
$873$	2.14899			0.0727323
$874$	−26.2749	−	35.9315i	−0.888763	−	1.21540i
$875$	1.49244	+	1.11739i	0.0504538	+	0.0377746i
$876$	−7.06930	−	12.9009i	−0.238850	−	0.435882i
$877$	2.24318	+	7.63958i	0.0757469	+	0.257970i	0.988657	−	0.150190i	$-0.0479886\pi$
$877$	2.24318	+	7.63958i	0.0757469	+	0.257970i	−0.912910	+	0.408160i	$0.866170\pi$
$878$	−7.34598	+	0.795287i	−0.247915	+	0.0268396i
$879$	−0.327013	−	0.210158i	−0.0110299	−	0.00708847i
$880$	−2.68201	+	2.02008i	−0.0904106	+	0.0680968i
$881$	28.9235	−	4.15858i	0.974459	−	0.140106i	0.363350	−	0.931653i	$-0.381633\pi$
$881$	28.9235	−	4.15858i	0.974459	−	0.140106i	0.611109	+	0.791547i	$0.290724\pi$
$882$	−21.9934	+	13.0713i	−0.740555	+	0.440135i
$883$	−4.06702	+	2.61371i	−0.136866	+	0.0879585i	−0.607282	−	0.794486i	$-0.707740\pi$
$883$	−4.06702	+	2.61371i	−0.136866	+	0.0879585i	0.470416	+	0.882445i	$0.344104\pi$
$884$	−0.356776	+	5.09458i	−0.0119997	+	0.171349i
$885$	−9.39399	+	12.5483i	−0.315775	+	0.421807i
$886$	−7.01684	−	16.9047i	−0.235735	−	0.567924i
$887$	−7.70795	+	53.6100i	−0.258808	+	1.80005i	0.282548	+	0.959253i	$0.408821\pi$
$887$	−7.70795	+	53.6100i	−0.258808	+	1.80005i	−0.541355	+	0.840794i	$0.682089\pi$
$888$	−12.8848	−	1.35627i	−0.432387	−	0.0455134i
$889$	−0.450356	+	1.53377i	−0.0151045	+	0.0514410i
$890$	11.1074	+	11.9130i	0.372322	+	0.399326i
$891$	−1.35623	−	1.56517i	−0.0454354	−	0.0524352i
$892$	−8.41662	+	15.4684i	−0.281809	+	0.517920i
$893$	−18.6737	+	21.5506i	−0.624891	+	0.721162i
$894$	7.60252	+	3.79850i	0.254266	+	0.127041i
$895$	−1.47447	−	6.77877i	−0.0492861	−	0.226589i
$896$	0.954252	−	1.62750i	0.0318793	−	0.0543711i
$897$	0.317716	+	1.30991i	0.0106082	+	0.0437368i
$898$	−31.5922	+	33.9829i	−1.05425	+	1.13403i
$899$	−36.4519	+	16.6470i	−1.21574	+	0.555210i
$900$	−1.81383	+	25.8839i	−0.0604608	+	0.862796i
$901$	−16.8806	+	19.4813i	−0.562375	+	0.649015i
$902$	−0.801019	+	0.205081i	−0.0266710	+	0.00682844i
$903$	0.483922	+	0.558476i	0.0161039	+	0.0185849i
$904$	11.4403	−	19.3798i	0.380500	−	0.644563i
$905$	15.2343	+	8.31898i	0.506404	+	0.276532i
$906$	1.98348	+	0.356340i	0.0658967	+	0.0118386i
$907$	47.1774	+	6.78308i	1.56650	+	0.225229i	0.870264	−	0.492585i	$-0.163948\pi$
$907$	47.1774	+	6.78308i	1.56650	+	0.225229i	0.696235	+	0.717814i	$0.254857\pi$
$908$	4.15326	−	11.1860i	0.137831	−	0.371220i
$909$	1.63402	−	3.57801i	0.0541972	−	0.118675i
$910$	−0.208111	+	0.104360i	−0.00689880	+	0.00345950i
$911$	−13.6077	+	8.74514i	−0.450843	+	0.289740i	−0.746291	−	0.665619i	$-0.768167\pi$
$911$	−13.6077	+	8.74514i	−0.450843	+	0.289740i	0.295448	+	0.955359i	$0.404531\pi$
$912$	−16.5494	−	2.32934i	−0.548004	−	0.0771323i
$913$	−1.60990	+	0.231468i	−0.0532799	+	0.00766049i
$914$	−7.14807	−	0.249985i	−0.236437	−	0.00826878i
$915$	−2.66262	−	2.66274i	−0.0880235	−	0.0880274i
$916$	−5.45636	+	7.31143i	−0.180283	+	0.241576i
$917$	−2.36876	+	0.695532i	−0.0782235	+	0.0229685i
$918$	27.6487	+	9.17961i	0.912544	+	0.302972i
$919$	29.8992			0.986283			0.493141	−	0.869949i	$-0.335849\pi$
$919$	29.8992			0.986283			0.493141	+	0.869949i	$0.335849\pi$
$920$	−2.45852	+	30.2317i	−0.0810551	+	0.996710i
$921$	−6.33776			−0.208836
$922$	14.5078	+	4.81671i	0.477789	+	0.158630i
$923$	−2.45752	+	0.721593i	−0.0808902	+	0.0237515i
$924$	−0.0476693	+	0.0638760i	−0.00156820	+	0.00210137i
$925$	19.4494	+	30.2668i	0.639493	+	0.995168i
$926$	6.10616	+	0.213547i	0.200661	+	0.00701759i
$927$	−49.1476	+	7.06635i	−1.61422	+	0.232090i
$928$	−29.4600	+	23.9211i	−0.967073	+	0.785250i
$929$	3.18949	−	2.04976i	0.104644	−	0.0672505i	−0.487272	−	0.873250i	$-0.662008\pi$
$929$	3.18949	−	2.04976i	0.104644	−	0.0672505i	0.591916	+	0.806000i	$0.298372\pi$
$930$	5.39053	+	10.7496i	0.176762	+	0.352492i
$931$	−19.0092	+	41.6243i	−0.623001	+	1.36418i
$932$	18.2456	−	49.1408i	0.597654	−	1.60966i
$933$	0.0116463	+	0.00167448i	0.000381282	+	5.48201e-5i
$934$	−13.2753	−	2.38497i	−0.434382	−	0.0780385i
$935$	2.32688	−	4.26114i	0.0760971	−	0.139354i
$936$	−2.79022	−	1.64713i	−0.0912012	−	0.0538381i
$937$	30.9532	+	35.7220i	1.01120	+	1.16699i	0.985905	+	0.167305i	$0.0535066\pi$
$937$	30.9532	+	35.7220i	1.01120	+	1.16699i	0.0252934	+	0.999680i	$0.491948\pi$
$938$	1.58292	−	0.405266i	0.0516841	−	0.0132324i
$939$	10.2871	−	11.8720i	0.335708	−	0.387427i
$940$	19.2287	−	2.79335i	0.627170	−	0.0911089i
$941$	−36.7742	+	16.7942i	−1.19880	+	0.547475i	−0.911871	−	0.410476i	$-0.865363\pi$
$941$	−36.7742	+	16.7942i	−1.19880	+	0.547475i	−0.286932	+	0.957951i	$0.592635\pi$
$942$	1.96403	−	2.11265i	0.0639914	−	0.0688339i
$943$	−3.42299	+	6.63891i	−0.111468	+	0.216193i
$944$	−6.39784	−	43.5797i	−0.208232	−	1.41840i
$945$	0.282269	+	1.29771i	0.00918220	+	0.0422145i
$946$	3.30591	+	1.65176i	0.107484	+	0.0537032i
$947$	24.1141	−	27.8292i	0.783603	−	0.904326i	−0.213761	−	0.976886i	$-0.568571\pi$
$947$	24.1141	−	27.8292i	0.783603	−	0.904326i	0.997364	+	0.0725598i	$0.0231168\pi$
$948$	−4.51092	+	8.29035i	−0.146508	+	0.269258i
$949$	−3.34049	−	3.85513i	−0.108437	−	0.125143i
$950$	23.7086	+	39.8954i	0.769210	+	1.29438i
$951$	−3.69124	+	12.5712i	−0.119697	+	0.407649i
$952$	−0.285573	+	2.71301i	−0.00925549	+	0.0879292i
$953$	−7.75357	+	53.9272i	−0.251163	+	1.74687i	0.340094	+	0.940391i	$0.389541\pi$
$953$	−7.75357	+	53.9272i	−0.251163	+	1.74687i	−0.591257	+	0.806483i	$0.701368\pi$
$954$	−6.26969	−	15.1047i	−0.202989	−	0.489032i
$955$	−29.0567	−	21.7526i	−0.940254	−	0.703898i
$956$	3.92535	−	56.0520i	0.126955	−	1.81285i
$957$	1.34869	−	0.866750i	0.0435969	−	0.0280180i
$958$	−22.2565	+	13.2277i	−0.719076	+	0.427369i
$959$	−3.04325	+	0.437553i	−0.0982716	+	0.0141293i
$960$	7.49554	+	8.57331i	0.241917	+	0.276702i
$961$	−3.93971	−	2.53190i	−0.127087	−	0.0816740i
$962$	−4.46648	+	0.483548i	−0.144005	+	0.0155902i
$963$	8.63703	+	29.4150i	0.278324	+	0.947886i
$964$	−11.6930	−	21.3388i	−0.376607	−	0.687278i
$965$	45.5818	+	9.91678i	1.46733	+	0.319232i
$966$	0.145153	+	0.705212i	0.00467022	+	0.0226898i
$967$	8.44508			0.271575			0.135788	−	0.990738i	$-0.456643\pi$
$967$	8.44508			0.271575			0.135788	+	0.990738i	$0.456643\pi$
$968$	7.52956	−	29.7769i	0.242009	−	0.957065i
$969$	23.1868	−	6.80826i	0.744868	−	0.218713i
$970$	−2.60423	−	0.278089i	−0.0836168	−	0.00892889i
$971$	−24.4728	−	15.7277i	−0.785368	−	0.504725i	0.0854431	−	0.996343i	$-0.472769\pi$
$971$	−24.4728	−	15.7277i	−0.785368	−	0.504725i	−0.870811	+	0.491618i	$0.836406\pi$
$972$	−20.0477	+	20.1073i	−0.643030	+	0.644941i
$973$	−0.214757	−	1.49367i	−0.00688479	−	0.0478848i
$974$	−11.8657	+	7.05213i	−0.380200	+	0.225965i
$975$	−0.199929	−	1.39098i	−0.00640287	−	0.0445471i
$976$	10.5813	−	0.0313943i	0.338698	−	0.00100491i
$977$	−7.29119	+	15.9655i	−0.233266	+	0.510781i	−0.989677	−	0.143316i	$-0.954224\pi$
$977$	−7.29119	+	15.9655i	−0.233266	+	0.510781i	0.756411	+	0.654096i	$0.226951\pi$
$978$	−6.40985	−	15.4423i	−0.204964	−	0.493791i
$979$	1.91388	+	0.275174i	0.0611678	+	0.00879460i
$980$	28.3439	−	12.9943i	0.905413	−	0.415088i
$981$	9.12878	−	31.0898i	0.291460	−	0.992620i
$982$	−18.7638	+	27.0678i	−0.598776	+	0.863768i
$983$	7.62720	−	6.60901i	0.243270	−	0.210795i	−0.524689	−	0.851294i	$-0.675818\pi$
$983$	7.62720	−	6.60901i	0.243270	−	0.210795i	0.767958	+	0.640500i	$0.221273\pi$
$984$	0.891540	+	2.65889i	0.0284213	+	0.0847623i
$985$	31.1066	−	23.2850i	0.991137	−	0.741921i
$986$	24.5256	−	49.0868i	0.781053	−	1.56324i
$987$	0.419551	−	0.191603i	0.0133545	−	0.00609878i
$988$	−5.77976	+	0.421996i	−0.183879	+	0.0134255i
$989$	30.9933	−	12.4062i	0.985531	−	0.394493i
$990$	1.75855	+	2.52891i	0.0558905	+	0.0803741i
$991$	28.8886	−	13.1930i	0.917678	−	0.419090i	0.100146	−	0.994973i	$-0.468069\pi$
$991$	28.8886	−	13.1930i	0.917678	−	0.419090i	0.817532	+	0.575883i	$0.195342\pi$
$992$	−32.1015	−	10.5523i	−1.01922	−	0.335037i
$993$	10.1121	+	8.76216i	0.320897	+	0.278059i
$994$	−1.32539	+	0.339332i	−0.0420387	+	0.0107630i
$995$	36.9286	−	20.1635i	1.17072	−	0.639226i
$996$	1.18057	+	5.38850i	0.0374078	+	0.170741i
$997$	−15.5941	+	53.1087i	−0.493871	+	1.68197i	0.214985	+	0.976617i	$0.431030\pi$
$997$	−15.5941	+	53.1087i	−0.493871	+	1.68197i	−0.708856	+	0.705353i	$0.750788\pi$
$998$	45.7049	+	8.21107i	1.44676	+	0.259917i
$999$	−3.64718	+	25.3667i	−0.115392	+	0.802566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.b.19.7	✓	640
4.3	odd	2	inner	460.2.o.b.19.24	yes	640
5.4	even	2	inner	460.2.o.b.19.58	yes	640
20.19	odd	2	inner	460.2.o.b.19.41	yes	640
23.17	odd	22	inner	460.2.o.b.339.41	yes	640
92.63	even	22	inner	460.2.o.b.339.58	yes	640
115.109	odd	22	inner	460.2.o.b.339.24	yes	640
460.339	even	22	inner	460.2.o.b.339.7	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.b.19.7	✓	640	1.1	even	1	trivial
460.2.o.b.19.24	yes	640	4.3	odd	2	inner
460.2.o.b.19.41	yes	640	20.19	odd	2	inner
460.2.o.b.19.58	yes	640	5.4	even	2	inner
460.2.o.b.339.7	yes	640	460.339	even	22	inner
460.2.o.b.339.24	yes	640	115.109	odd	22	inner
460.2.o.b.339.41	yes	640	23.17	odd	22	inner
460.2.o.b.339.58	yes	640	92.63	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34217 - 0.445613i) q^{2} +(-0.610817 + 0.179352i) q^{3} +(1.60286 + 1.19618i) q^{4} +(-1.58117 + 1.58110i) q^{5} +(0.899744 + 0.0314662i) q^{6} +(0.165059 - 0.0237318i) q^{7} +(-1.61828 - 2.31973i) q^{8} +(-2.18283 + 1.40282i) q^{9} +O(q^{10})\)	\(q+(-1.34217 - 0.445613i) q^{2} +(-0.610817 + 0.179352i) q^{3} +(1.60286 + 1.19618i) q^{4} +(-1.58117 + 1.58110i) q^{5} +(0.899744 + 0.0314662i) q^{6} +(0.165059 - 0.0237318i) q^{7} +(-1.61828 - 2.31973i) q^{8} +(-2.18283 + 1.40282i) q^{9} +(2.82677 - 1.41752i) q^{10} +(0.155946 - 0.341474i) q^{11} +(-1.19359 - 0.443170i) q^{12} +(-0.436998 - 0.0628308i) q^{13} +(-0.232112 - 0.0417000i) q^{14} +(0.682234 - 1.24935i) q^{15} +(1.13831 + 3.83461i) q^{16} +(-3.78762 - 4.37115i) q^{17} +(3.55485 - 0.910131i) q^{18} +(4.29795 - 4.96009i) q^{19} +(-4.42568 + 0.642918i) q^{20} +(-0.0965642 + 0.0440994i) q^{21} +(-0.361472 + 0.388826i) q^{22} +(0.455648 + 4.77414i) q^{23} +(1.40452 + 1.12669i) q^{24} +(0.000223800 - 5.00000i) q^{25} +(0.558529 + 0.279062i) q^{26} +(2.33237 - 2.69170i) q^{27} +(0.292953 + 0.159401i) q^{28} +(-4.39311 - 5.06992i) q^{29} +(-1.47240 + 1.37283i) q^{30} +(1.68294 - 5.73157i) q^{31} +(0.180939 - 5.65396i) q^{32} +(-0.0340104 + 0.236547i) q^{33} +(3.13581 + 7.55466i) q^{34} +(-0.223464 + 0.298499i) q^{35} +(-5.17679 - 0.362533i) q^{36} +(-6.05320 + 3.89015i) q^{37} +(-7.97887 + 4.74209i) q^{38} +(0.278195 - 0.0399983i) q^{39} +(6.22652 + 1.10923i) q^{40} +(1.31023 + 0.842037i) q^{41} +(0.149257 - 0.0161588i) q^{42} +(-1.96116 - 6.67910i) q^{43} +(0.658424 - 0.360796i) q^{44} +(1.23343 - 5.66938i) q^{45} +(1.51586 - 6.61076i) q^{46} -4.34479 q^{47} +(-1.38305 - 2.13809i) q^{48} +(-6.68977 + 1.96429i) q^{49} +(-2.22836 + 6.71077i) q^{50} +(3.09752 + 1.99066i) q^{51} +(-0.625289 - 0.623437i) q^{52} +(-0.634266 - 4.41142i) q^{53} +(-4.32990 + 2.57339i) q^{54} +(0.293328 + 0.786497i) q^{55} +(-0.322163 - 0.344487i) q^{56} +(-1.73565 + 3.80055i) q^{57} +(3.63710 + 8.76234i) q^{58} +(-10.8996 - 1.56713i) q^{59} +(2.58797 - 1.18646i) q^{60} +(0.745275 - 2.53817i) q^{61} +(-4.81286 + 6.94282i) q^{62} +(-0.327003 + 0.283350i) q^{63} +(-2.76233 + 7.50797i) q^{64} +(0.790312 - 0.591593i) q^{65} +(0.151056 - 0.302332i) q^{66} +(-6.30252 + 2.87826i) q^{67} +(-0.842348 - 11.5370i) q^{68} +(-1.13457 - 2.83440i) q^{69} +(0.432942 - 0.301059i) q^{70} +(5.27714 - 2.40999i) q^{71} +(6.78660 + 2.79343i) q^{72} +(8.73205 + 7.56636i) q^{73} +(9.85794 - 2.52388i) q^{74} +(0.896623 + 3.05412i) q^{75} +(12.8222 - 2.80922i) q^{76} +(0.0176364 - 0.0600641i) q^{77} +(-0.391209 - 0.0702823i) q^{78} +(1.05496 - 7.33742i) q^{79} +(-7.86279 - 4.26340i) q^{80} +(2.29179 - 5.01831i) q^{81} +(-1.38334 - 1.71402i) q^{82} +(-2.34239 - 3.64482i) q^{83} +(-0.207530 - 0.0448230i) q^{84} +(12.9001 + 0.922926i) q^{85} +(-0.344074 + 9.83843i) q^{86} +(3.59269 + 2.30888i) q^{87} +(-1.04449 + 0.190848i) q^{88} +(1.45112 + 4.94205i) q^{89} +(-4.18183 + 7.05966i) q^{90} -0.0736214 q^{91} +(-4.98038 + 8.19730i) q^{92} +3.80278i q^{93} +(5.83146 + 1.93609i) q^{94} +(1.04662 + 14.6383i) q^{95} +(0.903529 + 3.48599i) q^{96} +(-0.696736 - 0.447765i) q^{97} +(9.85414 + 0.344623i) q^{98} +(0.138623 + 0.964144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Introduction

L-functions

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