LMFDB - Embedded newform 350.2.x.a.33.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(3,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("350.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.x (of order $60$, degree $16$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$20$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			33.15
Character	$\chi$	$=$	350.33
Dual form			350.2.x.a.297.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.838671 - 0.544639i) q^{2} +(-0.977539 + 0.375242i) q^{3} +(0.406737 - 0.913545i) q^{4} +(1.20732 + 1.88212i) q^{5} +(-0.615462 + 0.847110i) q^{6} +(2.05296 + 1.66893i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.41466 + 1.27376i) q^{9} +O(q^{10})$	\(q+(0.838671 - 0.544639i) q^{2} +(-0.977539 + 0.375242i) q^{3} +(0.406737 - 0.913545i) q^{4} +(1.20732 + 1.88212i) q^{5} +(-0.615462 + 0.847110i) q^{6} +(2.05296 + 1.66893i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.41466 + 1.27376i) q^{9} +(2.03762 + 0.920926i) q^{10} +(-1.84406 + 2.04804i) q^{11} +(-0.0548003 + 1.04565i) q^{12} +(0.551987 + 1.08333i) q^{13} +(2.63073 + 0.281560i) q^{14} +(-1.88645 - 1.38681i) q^{15} +(-0.669131 - 0.743145i) q^{16} +(0.714934 - 0.578942i) q^{17} +(-0.492691 + 1.83875i) q^{18} +(7.58312 - 3.37622i) q^{19} +(2.21046 - 0.337414i) q^{20} +(-2.63311 - 0.861088i) q^{21} +(-0.431119 + 2.72198i) q^{22} +(-1.25274 - 1.92905i) q^{23} +(0.523543 + 0.906803i) q^{24} +(-2.08476 + 4.54464i) q^{25} +(1.05296 + 0.607927i) q^{26} +(2.33102 - 4.57488i) q^{27} +(2.35966 - 1.19666i) q^{28} +(3.05991 + 4.21160i) q^{29} +(-2.33742 - 0.135640i) q^{30} +(1.82183 + 0.191482i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(1.03413 - 2.69401i) q^{33} +(0.284280 - 0.874923i) q^{34} +(-0.662548 + 5.87886i) q^{35} +(0.588248 + 1.81044i) q^{36} +(0.812696 + 0.0425916i) q^{37} +(4.52091 - 6.96160i) q^{38} +(-0.946101 - 0.851873i) q^{39} +(1.67008 - 1.48688i) q^{40} +(-9.01749 - 2.92996i) q^{41} +(-2.67729 + 0.711923i) q^{42} +(-6.42548 - 6.42548i) q^{43} +(1.12093 + 2.51765i) q^{44} +(-4.10532 - 1.12472i) q^{45} +(-2.10128 - 0.935549i) q^{46} +(6.03032 - 7.44683i) q^{47} +(0.932961 + 0.475367i) q^{48} +(1.42933 + 6.85252i) q^{49} +(0.726766 + 4.94690i) q^{50} +(-0.481632 + 0.834212i) q^{51} +(1.21419 - 0.0636329i) q^{52} +(-2.66748 - 6.94902i) q^{53} +(-0.536702 - 5.10638i) q^{54} +(-6.08103 - 0.998110i) q^{55} +(1.32723 - 2.28877i) q^{56} +(-6.14589 + 6.14589i) q^{57} +(4.86006 + 1.86560i) q^{58} +(-7.97398 + 1.69492i) q^{59} +(-2.03420 + 1.15929i) q^{60} +(-0.775505 + 3.64847i) q^{61} +(1.63221 - 0.831651i) q^{62} +(-5.03007 + 0.254023i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-1.37254 + 2.34684i) q^{65} +(-0.599965 - 2.82261i) q^{66} +(-8.29271 - 10.2406i) q^{67} +(-0.238100 - 0.888602i) q^{68} +(1.94847 + 1.41564i) q^{69} +(2.64620 + 5.29128i) q^{70} +(-4.41328 + 3.20643i) q^{71} +(1.47938 + 1.19798i) q^{72} +(-0.0695984 - 1.32802i) q^{73} +(0.704781 - 0.406906i) q^{74} +(0.332590 - 5.22486i) q^{75} -8.30075i q^{76} +(-7.20383 + 1.12693i) q^{77} +(-1.25743 - 0.199157i) q^{78} +(12.9888 - 1.36518i) q^{79} +(0.590834 - 2.15660i) q^{80} +(0.0349716 - 0.332733i) q^{81} +(-9.15847 + 2.45401i) q^{82} +(7.98452 - 1.26462i) q^{83} +(-1.85762 + 2.05523i) q^{84} +(1.95279 + 0.646624i) q^{85} +(-8.88843 - 1.88929i) q^{86} +(-4.57155 - 2.96880i) q^{87} +(2.31130 + 1.50097i) q^{88} +(11.8738 + 2.52386i) q^{89} +(-4.05558 + 1.29265i) q^{90} +(-0.674804 + 3.14528i) q^{91} +(-2.27182 + 0.359820i) q^{92} +(-1.85277 + 0.496447i) q^{93} +(1.00162 - 9.52978i) q^{94} +(15.5097 + 10.1962i) q^{95} +(1.04135 - 0.109450i) q^{96} +(-0.462945 - 0.0733233i) q^{97} +(4.93088 + 4.96854i) q^{98} -5.24617i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 12 q^{5} - 8 q^{7}+O(q^{10}) $ 320 * q + 12 * q^5 - 8 * q^7	$ 320 q + 12 q^{5} - 8 q^{7} + 12 q^{10} - 16 q^{15} - 40 q^{16} + 36 q^{17} + 8 q^{18} - 72 q^{22} + 44 q^{23} - 12 q^{25} - 24 q^{28} - 80 q^{29} + 20 q^{30} - 48 q^{33} - 28 q^{35} + 80 q^{36} - 4 q^{37} - 24 q^{38} - 40 q^{39} - 36 q^{42} + 88 q^{43} - 228 q^{45} - 12 q^{47} + 32 q^{50} - 52 q^{53} + 152 q^{57} + 32 q^{58} - 120 q^{59} - 8 q^{60} + 136 q^{63} + 8 q^{65} - 32 q^{67} - 144 q^{68} + 92 q^{70} + 8 q^{72} + 12 q^{73} - 432 q^{75} + 144 q^{77} - 16 q^{78} + 12 q^{80} - 40 q^{81} - 192 q^{82} + 60 q^{84} - 24 q^{85} + 24 q^{87} + 4 q^{88} - 300 q^{89} - 8 q^{92} - 68 q^{93} + 20 q^{95} - 40 q^{98}+O(q^{100}) $ 320 * q + 12 * q^5 - 8 * q^7 + 12 * q^10 - 16 * q^15 - 40 * q^16 + 36 * q^17 + 8 * q^18 - 72 * q^22 + 44 * q^23 - 12 * q^25 - 24 * q^28 - 80 * q^29 + 20 * q^30 - 48 * q^33 - 28 * q^35 + 80 * q^36 - 4 * q^37 - 24 * q^38 - 40 * q^39 - 36 * q^42 + 88 * q^43 - 228 * q^45 - 12 * q^47 + 32 * q^50 - 52 * q^53 + 152 * q^57 + 32 * q^58 - 120 * q^59 - 8 * q^60 + 136 * q^63 + 8 * q^65 - 32 * q^67 - 144 * q^68 + 92 * q^70 + 8 * q^72 + 12 * q^73 - 432 * q^75 + 144 * q^77 - 16 * q^78 + 12 * q^80 - 40 * q^81 - 192 * q^82 + 60 * q^84 - 24 * q^85 + 24 * q^87 + 4 * q^88 - 300 * q^89 - 8 * q^92 - 68 * q^93 + 20 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	0.838671	−	0.544639i	0.593030	−	0.385118i
$2$	0.838671	−	0.544639i	0.593030	−	0.385118i
$3$	−0.977539	+	0.375242i	−0.564382	+	0.216646i	−0.623796	−	0.781587i	$-0.714410\pi$
$3$	−0.977539	+	0.375242i	−0.564382	+	0.216646i	0.0594134	+	0.998233i	$0.481077\pi$
$4$	0.406737	−	0.913545i	0.203368	−	0.456773i
$5$	1.20732	+	1.88212i	0.539930	+	0.841710i
$5$	1.20732	+	1.88212i	0.539930	+	0.841710i
$6$	−0.615462	+	0.847110i	−0.251261	+	0.345831i
$7$	2.05296	+	1.66893i	0.775948	+	0.630797i
$7$	2.05296	+	1.66893i	0.775948	+	0.630797i
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	−1.41466	+	1.27376i	−0.471553	+	0.424588i
$10$	2.03762	+	0.920926i	0.644352	+	0.291222i
$11$	−1.84406	+	2.04804i	−0.556005	+	0.617507i	−0.953973	−	0.299893i	$-0.903049\pi$
$11$	−1.84406	+	2.04804i	−0.556005	+	0.617507i	0.397967	+	0.917400i	$0.369716\pi$
$12$	−0.0548003	+	1.04565i	−0.0158195	+	0.301853i
$13$	0.551987	+	1.08333i	0.153094	+	0.300463i	0.954797	−	0.297259i	$-0.0960726\pi$
$13$	0.551987	+	1.08333i	0.153094	+	0.300463i	−0.801703	+	0.597722i	$0.796073\pi$
$14$	2.63073	+	0.281560i	0.703091	+	0.0752502i
$15$	−1.88645	−	1.38681i	−0.487080	−	0.358073i
$16$	−0.669131	−	0.743145i	−0.167283	−	0.185786i
$17$	0.714934	−	0.578942i	0.173397	−	0.140414i	−0.538694	−	0.842502i	$-0.681082\pi$
$17$	0.714934	−	0.578942i	0.173397	−	0.140414i	0.712090	+	0.702088i	$0.247749\pi$
$18$	−0.492691	+	1.83875i	−0.116128	+	0.433397i
$19$	7.58312	−	3.37622i	1.73969	−	0.774558i	0.745547	−	0.666454i	$-0.232189\pi$
$19$	7.58312	−	3.37622i	1.73969	−	0.774558i	0.994140	−	0.108105i	$-0.0344782\pi$
$20$	2.21046	−	0.337414i	0.494275	−	0.0754481i
$21$	−2.63311	−	0.861088i	−0.574591	−	0.187905i
$22$	−0.431119	+	2.72198i	−0.0919148	+	0.580327i
$23$	−1.25274	−	1.92905i	−0.261215	−	0.402236i	0.683592	−	0.729865i	$-0.260417\pi$
$23$	−1.25274	−	1.92905i	−0.261215	−	0.402236i	−0.944806	+	0.327629i	$0.893750\pi$
$24$	0.523543	+	0.906803i	0.106868	+	0.185100i
$25$	−2.08476	+	4.54464i	−0.416951	+	0.908929i
$26$	1.05296	+	0.607927i	0.206503	+	0.119224i
$27$	2.33102	−	4.57488i	0.448604	−	0.880435i
$28$	2.35966	−	1.19666i	0.445934	−	0.226148i
$29$	3.05991	+	4.21160i	0.568211	+	0.782075i	0.992341	−	0.123526i	$-0.0394203\pi$
$29$	3.05991	+	4.21160i	0.568211	+	0.782075i	−0.424131	+	0.905601i	$0.639420\pi$
$30$	−2.33742	−	0.135640i	−0.426753	−	0.0247644i
$31$	1.82183	+	0.191482i	0.327211	+	0.0343913i	0.266710	−	0.963777i	$-0.414063\pi$
$31$	1.82183	+	0.191482i	0.327211	+	0.0343913i	0.0605011	+	0.998168i	$0.480730\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	1.03413	−	2.69401i	0.180019	−	0.468966i
$34$	0.284280	−	0.874923i	0.0487535	−	0.150048i
$35$	−0.662548	+	5.87886i	−0.111991	+	0.993709i
$36$	0.588248	+	1.81044i	0.0980413	+	0.301740i
$37$	0.812696	+	0.0425916i	0.133606	+	0.00700201i	0.119022	−	0.992892i	$-0.462024\pi$
$37$	0.812696	+	0.0425916i	0.133606	+	0.00700201i	0.0145845	+	0.999894i	$0.495357\pi$
$38$	4.52091	−	6.96160i	0.733389	−	1.12932i
$39$	−0.946101	−	0.851873i	−0.151497	−	0.136409i
$40$	1.67008	−	1.48688i	0.264063	−	0.235097i
$41$	−9.01749	−	2.92996i	−1.40830	−	0.457583i	−0.496432	−	0.868076i	$-0.665357\pi$
$41$	−9.01749	−	2.92996i	−1.40830	−	0.457583i	−0.911864	+	0.410493i	$0.865357\pi$
$42$	−2.67729	+	0.711923i	−0.413115	+	0.109852i
$43$	−6.42548	−	6.42548i	−0.979877	−	0.979877i	0.0199245	−	0.999801i	$-0.493657\pi$
$43$	−6.42548	−	6.42548i	−0.979877	−	0.979877i	−0.999801	+	0.0199245i	$0.993657\pi$
$44$	1.12093	+	2.51765i	0.168986	+	0.379549i
$45$	−4.10532	−	1.12472i	−0.611985	−	0.167663i
$46$	−2.10128	−	0.935549i	−0.309816	−	0.137939i
$47$	6.03032	−	7.44683i	0.879613	−	1.08623i	−0.116054	−	0.993243i	$-0.537025\pi$
$47$	6.03032	−	7.44683i	0.879613	−	1.08623i	0.995667	−	0.0929884i	$-0.0296419\pi$
$48$	0.932961	+	0.475367i	0.134661	+	0.0686133i
$49$	1.42933	+	6.85252i	0.204189	+	0.978931i
$50$	0.726766	+	4.94690i	0.102780	+	0.699597i
$51$	−0.481632	+	0.834212i	−0.0674420	+	0.116813i
$52$	1.21419	−	0.0636329i	0.168378	−	0.00882430i
$53$	−2.66748	−	6.94902i	−0.366407	−	0.954522i	−0.985571	−	0.169261i	$-0.945862\pi$
$53$	−2.66748	−	6.94902i	−0.366407	−	0.954522i	0.619165	−	0.785261i	$-0.287471\pi$
$54$	−0.536702	−	5.10638i	−0.0730358	−	0.694890i
$55$	−6.08103	−	0.998110i	−0.819966	−	0.134585i
$56$	1.32723	−	2.28877i	0.177359	−	0.305849i
$57$	−6.14589	+	6.14589i	−0.814043	+	0.814043i
$58$	4.86006	+	1.86560i	0.638157	+	0.244965i
$59$	−7.97398	+	1.69492i	−1.03812	+	0.220660i	−0.695285	−	0.718734i	$-0.744722\pi$
$59$	−7.97398	+	1.69492i	−1.03812	+	0.220660i	−0.342839	+	0.939394i	$0.611388\pi$
$60$	−2.03420	+	1.15929i	−0.262614	+	0.149664i
$61$	−0.775505	+	3.64847i	−0.0992933	+	0.467138i	0.900205	+	0.435466i	$0.143417\pi$
$61$	−0.775505	+	3.64847i	−0.0992933	+	0.467138i	−0.999498	+	0.0316719i	$0.989917\pi$
$62$	1.63221	−	0.831651i	0.207291	−	0.105620i
$63$	−5.03007	+	0.254023i	−0.633729	+	0.0320038i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	−1.37254	+	2.34684i	−0.170243	+	0.291089i
$66$	−0.599965	−	2.82261i	−0.0738506	−	0.347440i
$67$	−8.29271	−	10.2406i	−1.01312	−	1.25109i	−0.967694	−	0.252126i	$-0.918870\pi$
$67$	−8.29271	−	10.2406i	−1.01312	−	1.25109i	−0.0454212	−	0.998968i	$-0.514463\pi$
$68$	−0.238100	−	0.888602i	−0.0288739	−	0.107759i
$69$	1.94847	+	1.41564i	0.234568	+	0.170424i
$70$	2.64620	+	5.29128i	0.316281	+	0.632429i
$71$	−4.41328	+	3.20643i	−0.523759	+	0.380534i	−0.818018	−	0.575192i	$-0.804927\pi$
$71$	−4.41328	+	3.20643i	−0.523759	+	0.380534i	0.294259	+	0.955726i	$0.404927\pi$
$72$	1.47938	+	1.19798i	0.174347	+	0.141183i
$73$	−0.0695984	−	1.32802i	−0.00814588	−	0.155433i	−0.999674	−	0.0255391i	$-0.991870\pi$
$73$	−0.0695984	−	1.32802i	−0.00814588	−	0.155433i	0.991528	−	0.129894i	$-0.0414636\pi$
$74$	0.704781	−	0.406906i	0.0819291	−	0.0473018i
$75$	0.332590	−	5.22486i	0.0384042	−	0.603314i
$76$		−	8.30075i		−	0.952162i
$77$	−7.20383	+	1.12693i	−0.820953	+	0.128426i
$78$	−1.25743	−	0.199157i	−0.142376	−	0.0225501i
$79$	12.9888	−	1.36518i	1.46135	−	0.153595i	0.659766	−	0.751471i	$-0.270655\pi$
$79$	12.9888	−	1.36518i	1.46135	−	0.153595i	0.801588	+	0.597876i	$0.203989\pi$
$80$	0.590834	−	2.15660i	0.0660572	−	0.241115i
$81$	0.0349716	−	0.332733i	0.00388574	−	0.0369703i
$82$	−9.15847	+	2.45401i	−1.01138	+	0.271000i
$83$	7.98452	−	1.26462i	0.876415	−	0.138811i	0.298013	−	0.954562i	$-0.403676\pi$
$83$	7.98452	−	1.26462i	0.876415	−	0.138811i	0.578403	+	0.815751i	$0.303676\pi$
$84$	−1.85762	+	2.05523i	−0.202683	+	0.224244i
$85$	1.95279	+	0.646624i	0.211810	+	0.0701362i
$86$	−8.88843	−	1.88929i	−0.958464	−	0.203728i
$87$	−4.57155	−	2.96880i	−0.490122	−	0.318289i
$88$	2.31130	+	1.50097i	0.246385	+	0.160004i
$89$	11.8738	+	2.52386i	1.25862	+	0.267529i	0.788479	−	0.615061i	$-0.210869\pi$
$89$	11.8738	+	2.52386i	1.25862	+	0.267529i	0.470144	+	0.882590i	$0.344202\pi$
$90$	−4.05558	+	1.29265i	−0.427496	+	0.136257i
$91$	−0.674804	+	3.14528i	−0.0707387	+	0.329715i
$92$	−2.27182	+	0.359820i	−0.236853	+	0.0375138i
$93$	−1.85277	+	0.496447i	−0.192123	+	0.0514792i
$94$	1.00162	−	9.52978i	0.103309	−	0.982922i
$95$	15.5097	+	10.1962i	1.59126	+	1.04610i
$96$	1.04135	−	0.109450i	0.106282	−	0.0111707i
$97$	−0.462945	−	0.0733233i	−0.0470049	−	0.00744485i	0.132888	−	0.991131i	$-0.457575\pi$
$97$	−0.462945	−	0.0733233i	−0.0470049	−	0.00744485i	−0.179893	+	0.983686i	$0.557575\pi$
$98$	4.93088	+	4.96854i	0.498094	+	0.501898i
$99$		−	5.24617i		−	0.527260i
$100$	3.30379	+	3.75299i	0.330379	+	0.375299i
$101$	2.65959	−	1.53551i	0.264639	−	0.152789i	−0.361810	−	0.932252i	$-0.617841\pi$
$101$	2.65959	−	1.53551i	0.264639	−	0.152789i	0.626449	+	0.779463i	$0.284508\pi$
$102$	0.0504134	+	0.961945i	0.00499167	+	0.0952467i
$103$	3.89900	+	3.15735i	0.384180	+	0.311103i	0.801883	−	0.597481i	$-0.203832\pi$
$103$	3.89900	+	3.15735i	0.384180	+	0.311103i	−0.417703	+	0.908583i	$0.637165\pi$
$104$	0.983647	−	0.714662i	0.0964546	−	0.0700783i
$105$	−1.55833	−	5.99543i	−0.152077	−	0.585094i
$106$	−6.02185	−	4.37513i	−0.584893	−	0.424950i
$107$	−3.60736	−	13.4629i	−0.348737	−	1.30150i	−0.888186	−	0.459485i	$-0.848034\pi$
$107$	−3.60736	−	13.4629i	−0.348737	−	1.30150i	0.539449	−	0.842018i	$-0.318633\pi$
$108$	−3.23125	−	3.99026i	−0.310927	−	0.383963i
$109$	1.30454	+	6.13738i	0.124952	+	0.587854i	0.995418	+	0.0956241i	$0.0304847\pi$
$109$	1.30454	+	6.13738i	0.124952	+	0.587854i	−0.870465	+	0.492230i	$0.836182\pi$
$110$	−5.64359	+	2.47488i	−0.538095	+	0.235970i
$111$	−0.810424	+	0.263323i	−0.0769220	+	0.0249935i
$112$	−0.133442	−	2.64238i	−0.0126091	−	0.249682i
$113$	−16.0217	+	8.16347i	−1.50720	+	0.767955i	−0.995814	−	0.0913994i	$-0.970866\pi$
$113$	−16.0217	+	8.16347i	−1.50720	+	0.767955i	−0.511381	+	0.859354i	$0.670866\pi$
$114$	−1.80709	+	8.50167i	−0.169249	+	0.796254i
$115$	2.11825	−	4.68680i	0.197528	−	0.437046i
$116$	5.09207	−	1.08235i	0.472786	−	0.100494i
$117$	−2.16079	−	0.829448i	−0.199765	−	0.0766825i
$118$	−5.76442	+	5.76442i	−0.530658	+	0.530658i
$119$	2.43395	+	0.00462925i	0.223120	+	0.000424363i
$120$	−1.07463	+	2.08017i	−0.0980998	+	0.189893i
$121$	0.355917	+	3.38632i	0.0323561	+	0.307848i
$122$	1.33670	+	3.48223i	0.121019	+	0.315266i
$123$	9.91439	−	0.519591i	0.893951	−	0.0468500i
$124$	0.915935	−	1.58645i	0.0822533	−	0.142467i
$125$	−11.0705	+	1.56307i	−0.990179	+	0.139806i
$126$	−4.08022	+	2.95261i	−0.363495	+	0.263040i
$127$	14.4643	+	7.36990i	1.28349	+	0.653973i	0.956687	−	0.291118i	$-0.0940271\pi$
$127$	14.4643	+	7.36990i	1.28349	+	0.653973i	0.326807	+	0.945091i	$0.394027\pi$
$128$	−0.629320	+	0.777146i	−0.0556246	+	0.0686906i
$129$	8.69227	+	3.87005i	0.765312	+	0.340739i
$130$	0.127068	+	2.71576i	0.0111446	+	0.238188i
$131$	5.19941	+	11.6781i	0.454274	+	1.02032i	0.984965	+	0.172752i	$0.0552658\pi$
$131$	5.19941	+	11.6781i	0.454274	+	1.02032i	−0.530691	+	0.847565i	$0.678068\pi$
$132$	−2.04048	−	2.04048i	−0.177601	−	0.177601i
$133$	21.2026	+	5.72445i	1.83849	+	0.496373i
$134$	−12.5323	−	4.07199i	−1.08263	−	0.351767i
$135$	11.4247	−	1.13609i	0.983286	−	0.0977787i
$136$	−0.683655	−	0.615565i	−0.0586229	−	0.0527843i
$137$	0.559879	−	0.862138i	0.0478337	−	0.0736575i	−0.813945	−	0.580942i	$-0.802684\pi$
$137$	0.559879	−	0.862138i	0.0478337	−	0.0736575i	0.861778	+	0.507285i	$0.169351\pi$
$138$	2.40514	+	0.126048i	0.204739	+	0.0107299i
$139$	−5.94754	−	18.3047i	−0.504464	−	1.55258i	−0.801670	−	0.597767i	$-0.796055\pi$
$139$	−5.94754	−	18.3047i	−0.504464	−	1.55258i	0.297206	−	0.954813i	$-0.403945\pi$
$140$	5.10113	+	2.99642i	0.431124	+	0.253243i
$141$	−3.10051	+	9.54239i	−0.261110	+	0.803615i
$142$	−1.95494	+	5.09278i	−0.164055	+	0.427377i
$143$	−3.23661	−	0.867246i	−0.270659	−	0.0725228i
$144$	1.89318	+	0.198981i	0.157765	+	0.0165818i
$145$	−4.23246	+	10.8439i	−0.351486	+	0.900534i
$146$	−0.781660	−	1.07586i	−0.0646906	−	0.0890390i
$147$	−3.96858	−	6.16226i	−0.327323	−	0.508255i
$148$	0.369463	−	0.725111i	0.0303696	−	0.0596038i
$149$	−5.98187	−	3.45363i	−0.490054	−	0.282933i	0.234543	−	0.972106i	$-0.424641\pi$
$149$	−5.98187	−	3.45363i	−0.490054	−	0.282933i	−0.724597	+	0.689173i	$0.757974\pi$
$150$	−2.56673	−	4.56307i	−0.209572	−	0.372573i
$151$	−1.11983	−	1.93960i	−0.0911304	−	0.157843i	0.816857	−	0.576841i	$-0.195715\pi$
$151$	−1.11983	−	1.93960i	−0.0911304	−	0.157843i	−0.907987	+	0.418998i	$0.862381\pi$
$152$	−4.52091	−	6.96160i	−0.366695	−	0.564660i
$153$	−0.273952	+	1.72966i	−0.0221477	+	0.139835i
$154$	−5.42787	+	4.86861i	−0.437390	+	0.392324i
$155$	1.83914	+	3.66009i	0.147724	+	0.293986i
$156$	−1.16304	+	0.517818i	−0.0931177	+	0.0414587i
$157$	4.73222	−	17.6609i	0.377672	−	1.40949i	−0.471728	−	0.881744i	$-0.656370\pi$
$157$	4.73222	−	17.6609i	0.377672	−	1.40949i	0.849401	−	0.527748i	$-0.176964\pi$
$158$	10.1498	−	8.21915i	0.807475	−	0.653880i
$159$	5.21513	+	5.79199i	0.413587	+	0.459335i
$160$	−0.679053	−	2.13047i	−0.0536838	−	0.168428i
$161$	0.647626	−	6.05102i	0.0510401	−	0.476887i
$162$	−0.151890	−	0.298100i	−0.0119336	−	0.0234210i
$163$	0.879691	−	16.7855i	0.0689027	−	1.31474i	−0.717296	−	0.696768i	$-0.754621\pi$
$163$	0.879691	−	16.7855i	0.0689027	−	1.31474i	0.786199	−	0.617974i	$-0.212046\pi$
$164$	−6.34440	+	7.04616i	−0.495414	+	0.550213i
$165$	6.31897	−	1.30617i	0.491931	−	0.101685i
$166$	6.00762	−	5.40929i	0.466282	−	0.419842i
$167$	1.30505	+	8.23974i	0.100987	+	0.637610i	0.985315	+	0.170744i	$0.0546170\pi$
$167$	1.30505	+	8.23974i	0.100987	+	0.637610i	−0.884328	+	0.466866i	$0.845383\pi$
$168$	−0.438578	+	2.73539i	−0.0338371	+	0.211040i
$169$	6.77228	−	9.32125i	0.520945	−	0.717019i
$170$	1.98993	−	0.521263i	0.152620	−	0.0399790i
$171$	−6.42701	+	14.4353i	−0.491486	+	1.10390i
$172$	−8.48345	+	3.25649i	−0.646857	+	0.248305i
$173$	−7.21927	+	4.68825i	−0.548871	+	0.356441i	−0.789090	−	0.614278i	$-0.789447\pi$
$173$	−7.21927	+	4.68825i	−0.548871	+	0.356441i	0.240219	+	0.970719i	$0.422781\pi$
$174$	−5.45095			−0.413235
$175$	−11.8646	+	5.85067i	−0.896882	+	0.442269i
$176$	2.75591			0.207734
$177$	7.15887	−	4.64903i	0.538094	−	0.349442i
$178$	11.3328	−	4.35026i	0.849431	−	0.326066i
$179$	−2.85206	+	6.40583i	−0.213173	+	0.478794i	−0.988207	−	0.153125i	$-0.951066\pi$
$179$	−2.85206	+	6.40583i	−0.213173	+	0.478794i	0.775034	+	0.631920i	$0.217733\pi$
$180$	−2.69727	+	3.29294i	−0.201042	+	0.245441i
$181$	10.8269	−	14.9020i	0.804759	−	1.10766i	−0.187352	−	0.982293i	$-0.559991\pi$
$181$	10.8269	−	14.9020i	0.804759	−	1.10766i	0.992111	−	0.125363i	$-0.0400095\pi$
$182$	1.14710	+	3.00538i	0.0850288	+	0.222773i
$183$	−0.610971	−	3.85752i	−0.0451643	−	0.285156i
$184$	−1.70933	+	1.53909i	−0.126014	+	0.113463i
$185$	0.901021	+	1.58101i	0.0662444	+	0.116238i
$186$	−1.28348	+	1.42544i	−0.0941090	+	0.104519i
$187$	−0.132687	+	2.53182i	−0.00970303	+	0.185145i
$188$	−4.35026	−	8.53787i	−0.317275	−	0.622688i
$189$	12.4207	−	5.50175i	0.903469	−	0.400193i
$190$	18.5608	+	0.104031i	1.34654	+	0.00754723i
$191$	−5.06007	−	5.61977i	−0.366134	−	0.406632i	0.531725	−	0.846917i	$-0.321544\pi$
$191$	−5.06007	−	5.61977i	−0.366134	−	0.406632i	−0.897858	+	0.440285i	$0.854877\pi$
$192$	0.813739	−	0.658953i	0.0587265	−	0.0475558i
$193$	−0.801214	+	2.99017i	−0.0576726	+	0.215237i	−0.988748	−	0.149589i	$-0.952205\pi$
$193$	−0.801214	+	2.99017i	−0.0576726	+	0.215237i	0.931076	+	0.364826i	$0.118872\pi$
$194$	−0.428193	+	0.190644i	−0.0307425	+	0.0136874i
$195$	0.461082	−	2.80916i	0.0330187	−	0.201168i
$196$	6.84145	+	1.48142i	0.488675	+	0.105815i
$197$	−1.37644	+	8.69048i	−0.0980671	+	0.619171i	0.888882	+	0.458137i	$0.151483\pi$
$197$	−1.37644	+	8.69048i	−0.0980671	+	0.619171i	−0.986949	+	0.161034i	$0.948517\pi$
$198$	−2.85727	−	4.39981i	−0.203057	−	0.312681i
$199$	1.25027	+	2.16553i	0.0886292	+	0.153510i	0.906932	−	0.421277i	$-0.138418\pi$
$199$	1.25027	+	2.16553i	0.0886292	+	0.153510i	−0.818303	+	0.574787i	$0.805085\pi$
$200$	4.81482	+	1.34815i	0.340459	+	0.0953287i
$201$	11.9492	+	6.89886i	0.842829	+	0.486608i
$202$	1.39422	−	2.73630i	0.0980967	−	0.192526i
$203$	−0.746999	+	13.7530i	−0.0524290	+	0.965275i
$204$	0.566193	+	0.779298i	0.0396414	+	0.0545617i
$205$	−5.37246	−	20.5094i	−0.375229	−	1.43244i
$206$	4.98959	+	0.524427i	0.347641	+	0.0365386i
$207$	4.22936	+	1.13325i	0.293961	+	0.0787666i
$208$	0.435723	−	1.13510i	0.0302120	−	0.0787049i
$209$	−7.06910	+	21.7565i	−0.488980	+	1.50493i
$210$	−4.57227	−	4.17947i	−0.315517	−	0.288411i
$211$	2.84223	+	8.74749i	0.195667	+	0.602202i	0.999968	+	0.00797979i	$0.00254007\pi$
$211$	2.84223	+	8.74749i	0.195667	+	0.602202i	−0.804301	+	0.594222i	$0.797460\pi$
$212$	−7.43321	−	0.389558i	−0.510515	−	0.0267550i
$213$	3.11096	−	4.79046i	0.213160	−	0.328237i
$214$	−10.3578	−	9.32619i	−0.708044	−	0.637525i
$215$	4.33592	−	19.8511i	0.295707	−	1.35384i
$216$	−4.88320	−	1.58665i	−0.332260	−	0.107958i
$217$	3.42059	+	3.43363i	0.232205	+	0.233090i
$218$	4.43673	+	4.43673i	0.300493	+	0.300493i
$219$	0.566363	+	1.27207i	0.0382713	+	0.0859587i
$220$	−3.38520	+	5.14933i	−0.228230	+	0.347168i
$221$	1.02182	+	0.454944i	0.0687352	+	0.0306029i
$222$	−0.536263	+	0.662230i	−0.0359916	+	0.0444459i
$223$	14.2086	+	7.23966i	0.951481	+	0.484804i	0.859601	−	0.510966i	$-0.170712\pi$
$223$	14.2086	+	7.23966i	0.951481	+	0.484804i	0.0918801	+	0.995770i	$0.470712\pi$
$224$	−1.55106	−	2.14341i	−0.103635	−	0.143213i
$225$	−2.83959	−	9.08461i	−0.189306	−	0.605641i
$226$	−8.99079	+	15.5725i	−0.598059	+	1.03587i
$227$	0.407885	−	0.0213763i	0.0270723	−	0.00141880i	−0.0387950	−	0.999247i	$-0.512352\pi$
$227$	0.407885	−	0.0213763i	0.0270723	−	0.00141880i	0.0658673	+	0.997828i	$0.479019\pi$
$228$	3.11479	+	8.11431i	0.206282	+	0.537383i
$229$	−2.02059	−	19.2246i	−0.133524	−	1.27040i	−0.832005	−	0.554768i	$-0.812807\pi$
$229$	−2.02059	−	19.2246i	−0.133524	−	1.27040i	0.698481	−	0.715629i	$-0.253860\pi$
$230$	−0.776098	−	5.08436i	−0.0511744	−	0.335253i
$231$	6.61915	−	3.80480i	0.435508	−	0.250338i
$232$	3.68107	−	3.68107i	0.241674	−	0.241674i
$233$	1.16564	+	0.447445i	0.0763633	+	0.0293131i	0.396250	−	0.918143i	$-0.370311\pi$
$233$	1.16564	+	0.447445i	0.0763633	+	0.0293131i	−0.319886	+	0.947456i	$0.603645\pi$
$234$	−2.26394	+	0.481215i	−0.147998	+	0.0314580i
$235$	21.2964	+	2.35909i	1.38922	+	0.153890i
$236$	−1.69492	+	7.97398i	−0.110330	+	0.519062i
$237$	−12.1848	+	6.20846i	−0.791487	+	0.403283i
$238$	2.04380	−	1.32174i	0.132480	−	0.0856758i
$239$	−19.0535	+	6.19087i	−1.23247	+	0.400454i	−0.851609	−	0.524178i	$-0.824373\pi$
$239$	−19.0535	+	6.19087i	−1.23247	+	0.400454i	−0.380862	+	0.924632i	$0.624373\pi$
$240$	0.231683	+	2.32986i	0.0149551	+	0.150392i
$241$	4.77325	+	22.4564i	0.307472	+	1.44654i	0.812259	+	0.583297i	$0.198238\pi$
$241$	4.77325	+	22.4564i	0.307472	+	1.44654i	−0.504787	+	0.863244i	$0.668429\pi$
$242$	2.14282	+	2.64616i	0.137746	+	0.170102i
$243$	4.07739	+	15.2170i	0.261565	+	0.976173i
$244$	3.01761	+	2.19242i	0.193183	+	0.140356i
$245$	−11.1716	+	10.9633i	−0.713728	+	0.700423i
$246$	8.03192	−	5.83553i	0.512097	−	0.372060i
$247$	7.84336	+	6.35142i	0.499061	+	0.404131i
$248$	−0.0958726	−	1.82936i	−0.00608792	−	0.116164i
$249$	−7.33064	+	4.23235i	−0.464561	+	0.268214i
$250$	−8.43322	+	7.34035i	−0.533364	+	0.464245i
$251$			10.0268i			0.632887i	0.948611	+	0.316444i	$0.102489\pi$
$251$			10.0268i			0.632887i	−0.948611	+	0.316444i	$0.897511\pi$
$252$	−1.81385	+	4.69852i	−0.114262	+	0.295979i
$253$	6.26091	+	0.991631i	0.393620	+	0.0623433i
$254$	16.1447	−	1.69687i	1.01301	−	0.106471i
$255$	−2.15157	+	0.100670i	−0.134737	+	0.00630421i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	27.6452	−	7.40751i	1.72446	−	0.462068i	0.745565	−	0.666433i	$-0.232180\pi$
$257$	27.6452	−	7.40751i	1.72446	−	0.462068i	0.978895	+	0.204365i	$0.0655130\pi$
$258$	9.39773	−	1.48845i	0.585077	−	0.0926671i
$259$	1.59735	+	1.44377i	0.0992547	+	0.0897117i
$260$	1.58568	+	2.20842i	0.0983396	+	0.136961i
$261$	−9.69331	−	2.06038i	−0.600001	−	0.127534i
$262$	10.7209	+	6.96225i	0.662340	+	0.430129i
$263$	−19.9986	−	12.9872i	−1.23316	−	0.800826i	−0.247392	−	0.968915i	$-0.579574\pi$
$263$	−19.9986	−	12.9872i	−1.23316	−	0.800826i	−0.985772	+	0.168089i	$0.946240\pi$
$264$	−2.82261	−	0.599965i	−0.173720	−	0.0369253i
$265$	9.85840	−	13.4102i	0.605597	−	0.823783i
$266$	20.8997	−	6.74681i	1.28144	−	0.413673i
$267$	−12.5542	+	1.98839i	−0.768304	+	0.121687i
$268$	−12.7282	+	3.41052i	−0.777501	+	0.208331i
$269$	−2.03414	+	19.3536i	−0.124024	+	1.18001i	0.738593	+	0.674152i	$0.235491\pi$
$269$	−2.03414	+	19.3536i	−0.124024	+	1.18001i	−0.862617	+	0.505858i	$0.831176\pi$
$270$	8.96284	−	7.17517i	0.545461	−	0.436667i
$271$	−0.527252	+	0.0554165i	−0.0320283	+	0.00336631i	−0.120529	−	0.992710i	$-0.538459\pi$
$271$	−0.527252	+	0.0554165i	−0.0320283	+	0.00336631i	0.0885008	+	0.996076i	$0.471792\pi$
$272$	−0.908622	−	0.143912i	−0.0550933	−	0.00872592i
$273$	−0.520593	−	3.32785i	−0.0315077	−	0.201410i
$274$		−	1.02798i		−	0.0621027i
$275$	−5.46318	−	12.6503i	−0.329442	−	0.762840i
$276$	2.08577	−	1.20422i	0.125549	−	0.0724855i
$277$	0.766200	+	14.6200i	0.0460365	+	0.878429i	0.919875	+	0.392212i	$0.128290\pi$
$277$	0.766200	+	14.6200i	0.0460365	+	0.878429i	−0.873838	+	0.486217i	$0.838377\pi$
$278$	−14.9575	−	12.1123i	−0.897089	−	0.726448i
$279$	−2.82118	+	2.04970i	−0.168899	+	0.122713i
$280$	5.91013	−	0.265265i	0.353198	−	0.0158526i
$281$	−6.00959	−	4.36622i	−0.358502	−	0.260467i	0.393925	−	0.919143i	$-0.371117\pi$
$281$	−6.00959	−	4.36622i	−0.358502	−	0.260467i	−0.752427	+	0.658676i	$0.771117\pi$
$282$	2.59685	+	9.69158i	0.154640	+	0.577125i
$283$	−0.486871	−	0.601236i	−0.0289415	−	0.0357398i	0.762470	−	0.647024i	$-0.223987\pi$
$283$	−0.486871	−	0.601236i	−0.0289415	−	0.0357398i	−0.791411	+	0.611284i	$0.790653\pi$
$284$	1.13418	+	5.33590i	0.0673013	+	0.316627i
$285$	−18.9874	−	4.14725i	−1.12471	−	0.245662i
$286$	−3.18678	+	1.03545i	−0.188438	+	0.0612274i
$287$	−13.6227	−	21.0647i	−0.804121	−	1.24341i
$288$	1.69613	−	0.864221i	0.0999454	−	0.0509247i
$289$	−3.35854	+	15.8007i	−0.197561	+	0.929453i
$290$	2.35636	+	11.3996i	0.138370	+	0.669407i
$291$	0.480061	−	0.102040i	0.0281417	−	0.00598170i
$292$	−1.24151	−	0.476572i	−0.0726540	−	0.0278893i
$293$	−10.8939	+	10.8939i	−0.636430	+	0.636430i	−0.949673	−	0.313243i	$-0.898585\pi$
$293$	−10.8939	+	10.8939i	−0.636430	+	0.636430i	0.313243	+	0.949673i	$0.398585\pi$
$294$	−6.68454	−	3.00667i	−0.389850	−	0.175352i
$295$	−12.8172	−	12.9617i	−0.746246	−	0.754658i
$296$	−0.0850664	−	0.809353i	−0.00494439	−	0.0470427i
$297$	5.07098	+	13.2104i	0.294248	+	0.766543i
$298$	−6.89780	+	0.361498i	−0.399579	+	0.0209410i
$299$	1.39831	−	2.42195i	0.0808666	−	0.140065i
$300$	−4.63787	−	2.42898i	−0.267767	−	0.140237i
$301$	−2.46759	−	23.9150i	−0.142229	−	1.37844i
$302$	−1.99555	−	1.01678i	−0.114831	−	0.0585093i
$303$	−2.02366	+	2.49901i	−0.116256	+	0.143564i
$304$	−7.58312	−	3.37622i	−0.434922	−	0.193640i
$305$	−7.80314	+	2.94527i	−0.446806	+	0.168646i
$306$	0.712287	+	1.59982i	0.0407187	+	0.0914557i
$307$	1.69145	+	1.69145i	0.0965363	+	0.0965363i	0.753726	−	0.657189i	$-0.228255\pi$
$307$	1.69145	+	1.69145i	0.0965363	+	0.0965363i	−0.657189	+	0.753726i	$0.728255\pi$
$308$	−1.90056	+	7.03939i	−0.108294	+	0.401107i
$309$	−4.99620	−	1.62336i	−0.284224	−	0.0923499i
$310$	3.53586	+	2.06794i	0.200824	+	0.117451i
$311$	−14.3804	−	12.9482i	−0.815439	−	0.734225i	0.151713	−	0.988425i	$-0.451521\pi$
$311$	−14.3804	−	12.9482i	−0.815439	−	0.734225i	−0.967152	+	0.254200i	$0.918188\pi$
$312$	−0.693383	+	1.06772i	−0.0392551	+	0.0604475i
$313$	−11.3047	−	0.592453i	−0.638978	−	0.0334874i	−0.269904	−	0.962887i	$-0.586992\pi$
$313$	−11.3047	−	0.592453i	−0.638978	−	0.0334874i	−0.369074	+	0.929400i	$0.620325\pi$
$314$	−5.65003	−	17.3890i	−0.318850	−	0.981319i
$315$	−6.55101	−	9.16051i	−0.369107	−	0.516136i
$316$	4.03587	−	12.4211i	0.227035	−	0.698743i
$317$	6.51050	−	16.9604i	0.365666	−	0.952592i	−0.620108	−	0.784516i	$-0.712911\pi$
$317$	6.51050	−	16.9604i	0.365666	−	0.952592i	0.985774	−	0.168076i	$-0.0537554\pi$
$318$	7.52832	+	2.01721i	0.422167	+	0.113119i
$319$	−14.2682	−	1.49965i	−0.798865	−	0.0839640i
$320$	−1.72984	−	1.41692i	−0.0967008	−	0.0792083i
$321$	8.57817	+	11.8068i	0.478787	+	0.658993i
$322$	−2.75248	−	5.42754i	−0.153390	−	0.302465i
$323$	3.46679	−	6.80396i	0.192897	−	0.378582i
$324$	−0.289742	−	0.167283i	−0.0160968	−	0.00929349i
$325$	−6.07413	+	0.250093i	−0.336932	+	0.0138726i
$326$	−8.40427	−	14.5566i	−0.465469	−	0.806217i
$327$	−3.57824	−	5.51001i	−0.197877	−	0.304704i
$328$	−1.48324	+	9.36482i	−0.0818983	+	0.517085i
$329$	24.8083	−	5.22387i	1.36773	−	0.288001i
$330$	4.58815	−	4.53700i	0.252569	−	0.249754i
$331$	−19.8636	+	8.84385i	−1.09180	+	0.486102i	−0.872031	−	0.489450i	$-0.837198\pi$
$331$	−19.8636	+	8.84385i	−1.09180	+	0.486102i	−0.219771	+	0.975552i	$0.570531\pi$
$332$	2.09231	−	7.80859i	0.114830	−	0.428552i
$333$	−1.20394	+	0.974930i	−0.0659754	+	0.0534258i
$334$	5.58218	+	6.19964i	0.305444	+	0.339229i
$335$	9.26217	−	27.9716i	0.506047	−	1.52825i
$336$	1.12198	+	2.53296i	0.0612090	+	0.138184i
$337$	8.66113	+	16.9984i	0.471802	+	0.925963i	0.997177	+	0.0750920i	$0.0239250\pi$
$337$	8.66113	+	16.9984i	0.471802	+	0.925963i	−0.525375	+	0.850871i	$0.676075\pi$
$338$	0.602999	−	11.5059i	0.0327988	−	0.625839i
$339$	12.5986	−	13.9921i	0.684260	−	0.759948i
$340$	1.38499	−	1.52096i	0.0751118	−	0.0824856i
$341$	−3.75174	+	3.37808i	−0.203168	+	0.182933i
$342$	2.47188	+	15.6069i	0.133664	+	0.843922i
$343$	−8.50204	+	16.4534i	−0.459067	+	0.888402i
$344$	−5.34121	+	7.35154i	−0.287979	+	0.396369i
$345$	−0.311990	+	5.37639i	−0.0167970	+	0.289455i
$346$	−3.50119	+	7.86379i	−0.188225	+	0.422760i
$347$	9.60093	−	3.68545i	0.515405	−	0.197845i	−0.0867420	−	0.996231i	$-0.527646\pi$
$347$	9.60093	−	3.68545i	0.515405	−	0.197845i	0.602147	+	0.798385i	$0.294312\pi$
$348$	−4.57155	+	2.96880i	−0.245061	+	0.159144i
$349$	−23.3283			−1.24874			−0.624368	−	0.781130i	$-0.714643\pi$
$349$	−23.3283			−1.24874			−0.624368	+	0.781130i	$0.714643\pi$
$350$	−6.76402	+	11.3687i	−0.361552	+	0.607684i
$351$	6.24281			0.333217
$352$	2.31130	−	1.50097i	0.123193	−	0.0800022i
$353$	−18.1368	+	6.96206i	−0.965324	+	0.370553i	−0.789419	−	0.613854i	$-0.789618\pi$
$353$	−18.1368	+	6.96206i	−0.965324	+	0.370553i	−0.175904	+	0.984407i	$0.556285\pi$
$354$	3.47189	−	7.79800i	0.184529	−	0.414459i
$355$	−11.3631	−	4.43513i	−0.603092	−	0.235392i
$356$	7.13518	−	9.82073i	0.378164	−	0.520498i
$357$	−2.38102	+	0.908795i	−0.126017	+	0.0480985i
$358$	1.09693	+	6.92573i	0.0579744	+	0.366036i
$359$	12.6352	−	11.3768i	0.666861	−	0.600445i	−0.264568	−	0.964367i	$-0.585229\pi$
$359$	12.6352	−	11.3768i	0.666861	−	0.600445i	0.931429	+	0.363922i	$0.118563\pi$
$360$	−0.468656	+	4.23072i	−0.0247003	+	0.222979i
$361$	33.3913	−	37.0848i	1.75744	−	1.95183i
$362$	0.964021	−	18.3946i	0.0506678	−	0.966800i
$363$	−1.61861	−	3.17671i	−0.0849552	−	0.166734i
$364$	2.59889	+	1.89576i	0.136219	+	0.0993650i
$365$	2.41546	−	1.73433i	0.126431	−	0.0907792i
$366$	−2.61336	−	2.90243i	−0.136603	−	0.151712i
$367$	−9.50181	+	7.69441i	−0.495990	+	0.401645i	−0.844413	−	0.535692i	$-0.820051\pi$
$367$	−9.50181	+	7.69441i	−0.495990	+	0.401645i	0.348423	+	0.937337i	$0.386717\pi$
$368$	−0.595318	+	2.22176i	−0.0310331	+	0.115817i
$369$	16.4887	−	7.34126i	0.858370	−	0.382171i
$370$	1.61674	+	0.835218i	0.0840504	+	0.0434209i
$371$	6.12121	−	18.7179i	0.317797	−	0.971787i
$372$	−0.300061	+	1.89451i	−0.0155574	+	0.0982257i
$373$	−9.32972	−	14.3665i	−0.483075	−	0.743870i	0.510149	−	0.860086i	$-0.329590\pi$
$373$	−9.32972	−	14.3665i	−0.483075	−	0.743870i	−0.993224	+	0.116216i	$0.962924\pi$
$374$	1.26765	+	2.19563i	0.0655484	+	0.113533i
$375$	10.2354	−	5.68210i	0.528551	−	0.293422i
$376$	−8.29849	−	4.79114i	−0.427962	−	0.247084i
$377$	−2.87355	+	5.63965i	−0.147995	+	0.290457i
$378$	7.42037	−	11.3789i	0.381663	−	0.585269i
$379$	−1.23482	−	1.69959i	−0.0634286	−	0.0873020i	0.776124	−	0.630580i	$-0.217183\pi$
$379$	−1.23482	−	1.69959i	−0.0634286	−	0.0873020i	−0.839553	+	0.543278i	$0.817183\pi$
$380$	15.6230	−	10.0217i	0.801444	−	0.514101i
$381$	−16.9049	−	1.77677i	−0.866063	−	0.0910269i
$382$	−7.30448	−	1.95723i	−0.373730	−	0.100141i
$383$	−11.9872	+	31.2277i	−0.612516	+	1.59566i	0.178551	+	0.983931i	$0.442859\pi$
$383$	−11.9872	+	31.2277i	−0.612516	+	1.59566i	−0.791067	+	0.611729i	$0.790474\pi$
$384$	0.323567	−	0.995838i	0.0165120	−	0.0508186i
$385$	−10.8184	−	12.1979i	−0.551354	−	0.621663i
$386$	0.956609	+	2.94414i	0.0486901	+	0.149853i
$387$	17.2744	+	0.905314i	0.878108	+	0.0460197i
$388$	−0.255281	+	0.393098i	−0.0129599	+	0.0199565i
$389$	−21.8201	−	19.6469i	−1.10632	−	0.996135i	−0.999998	−	0.00180375i	$-0.999426\pi$
$389$	−21.8201	−	19.6469i	−1.10632	−	0.996135i	−0.106322	−	0.994332i	$-0.533907\pi$
$390$	−1.14328	−	2.60708i	−0.0578924	−	0.132015i
$391$	−2.01244	−	0.653881i	−0.101773	−	0.0330682i
$392$	6.54456	−	2.48370i	0.330550	−	0.125446i
$393$	−9.46472	−	9.46472i	−0.477432	−	0.477432i
$394$	3.57880	+	8.03811i	0.180297	+	0.404954i
$395$	18.2511	+	22.7983i	0.918311	+	1.14711i
$396$	−4.79262	−	2.13381i	−0.240838	−	0.107228i
$397$	1.38587	−	1.71141i	0.0695550	−	0.0858932i	−0.741181	−	0.671305i	$-0.765734\pi$
$397$	1.38587	−	1.71141i	0.0695550	−	0.0858932i	0.810736	+	0.585412i	$0.199067\pi$
$398$	2.22800	+	1.13522i	0.111679	+	0.0569034i
$399$	−22.8744	+	2.36022i	−1.14515	+	0.118159i
$400$	4.77230	−	1.49168i	0.238615	−	0.0745842i
$401$	−14.9311	+	25.8614i	−0.745622	+	1.29146i	0.204281	+	0.978912i	$0.434514\pi$
$401$	−14.9311	+	25.8614i	−0.745622	+	1.29146i	−0.949904	+	0.312543i	$0.898819\pi$
$402$	13.7788	−	0.722116i	0.687224	−	0.0360159i
$403$	0.798188	+	2.07935i	0.0397606	+	0.103580i
$404$	−0.321009	−	3.05420i	−0.0159708	−	0.151952i
$405$	0.668465	−	0.335894i	0.0332163	−	0.0166907i
$406$	6.86396	+	11.9411i	0.340653	+	0.592628i
$407$	−1.58589	+	1.58589i	−0.0786097	+	0.0786097i
$408$	0.899285	+	0.345203i	0.0445213	+	0.0170901i
$409$	−15.8398	+	3.36686i	−0.783229	+	0.166480i	−0.582136	−	0.813092i	$-0.697783\pi$
$409$	−15.8398	+	3.36686i	−0.783229	+	0.166480i	−0.201093	+	0.979572i	$0.564449\pi$
$410$	−15.6759	−	14.2746i	−0.774180	−	0.704971i
$411$	−0.223793	+	1.05286i	−0.0110389	+	0.0519340i
$412$	4.47025	−	2.27771i	0.220233	−	0.112215i
$413$	−19.1990	−	9.82842i	−0.944721	−	0.483625i
$414$	4.16426	−	1.35305i	0.204662	−	0.0664987i
$415$	12.0200	+	13.5010i	0.590041	+	0.662739i
$416$	−0.252790	−	1.18929i	−0.0123941	−	0.0583095i
$417$	12.6826	+	15.6617i	0.621071	+	0.766959i
$418$	5.92077	+	22.0966i	0.289594	+	1.08078i
$419$	−7.75392	−	5.63355i	−0.378804	−	0.275217i	0.382048	−	0.924142i	$-0.375219\pi$
$419$	−7.75392	−	5.63355i	−0.378804	−	0.275217i	−0.760852	+	0.648925i	$0.775219\pi$
$420$	−6.11093	−	1.01496i	−0.298183	−	0.0495249i
$421$	13.6123	−	9.88991i	0.663423	−	0.482005i	−0.204394	−	0.978889i	$-0.565523\pi$
$421$	13.6123	−	9.88991i	0.663423	−	0.482005i	0.867817	+	0.496884i	$0.165523\pi$
$422$	7.14792	+	5.78827i	0.347955	+	0.281769i
$423$	0.954656	+	18.2159i	0.0464170	+	0.885688i
$424$	−6.44618	+	3.72171i	−0.313054	+	0.180742i
$425$	1.14062	+	4.45607i	0.0553283	+	0.216151i
$426$		−	5.71197i		−	0.276746i
$427$	−7.68113	+	6.19590i	−0.371716	+	0.299841i
$428$	−13.7662	−	2.18035i	−0.665413	−	0.105391i
$429$	3.48934	−	0.366744i	0.168467	−	0.0177066i
$430$	−7.17530	−	19.0101i	−0.346024	−	0.916748i
$431$	−1.28096	+	12.1875i	−0.0617016	+	0.587052i	0.919368	+	0.393398i	$0.128701\pi$
$431$	−1.28096	+	12.1875i	−0.0617016	+	0.587052i	−0.981070	+	0.193654i	$0.937966\pi$
$432$	−4.95955	+	1.32891i	−0.238616	+	0.0639371i
$433$	7.00269	−	1.10912i	0.336528	−	0.0533007i	0.0141162	−	0.999900i	$-0.495507\pi$
$433$	7.00269	−	1.10912i	0.336528	−	0.0533007i	0.322411	+	0.946600i	$0.395507\pi$
$434$	4.73883	+	1.01669i	0.227471	+	0.0488029i
$435$	0.0683154	−	12.1885i	0.00327547	−	0.584394i
$436$	6.13738	+	1.30454i	0.293927	+	0.0624761i
$437$	−16.0126	−	10.3987i	−0.765987	−	0.497438i
$438$	1.16781	+	0.758386i	0.0558002	+	0.0362371i
$439$	−31.7526	−	6.74922i	−1.51547	−	0.322123i	−0.626256	−	0.779617i	$-0.715414\pi$
$439$	−31.7526	−	6.74922i	−1.51547	−	0.322123i	−0.889212	+	0.457494i	$0.848747\pi$
$440$	−0.0345391	+	6.16230i	−0.00164659	+	0.293776i
$441$	−10.7505	−	7.87335i	−0.511929	−	0.374921i
$442$	1.10475	−	0.174976i	0.0525477	−	0.00832274i
$443$	−33.2124	+	8.89924i	−1.57797	+	0.422816i	−0.938297	−	0.345831i	$-0.887597\pi$
$443$	−33.2124	+	8.89924i	−1.57797	+	0.422816i	−0.639673	+	0.768647i	$0.720930\pi$
$444$	−0.0890719	+	0.847462i	−0.00422716	+	0.0402188i
$445$	9.58530	+	25.3951i	0.454387	+	1.20384i
$446$	15.8594	−	1.66689i	0.750963	−	0.0789294i
$447$	7.14346	+	1.13141i	0.337874	+	0.0535140i
$448$	−2.46821	−	0.952849i	−0.116612	−	0.0450179i
$449$			8.60748i			0.406212i	0.979157	+	0.203106i	$0.0651036\pi$
$449$			8.60748i			0.406212i	−0.979157	+	0.203106i	$0.934896\pi$
$450$	−7.32931	−	6.07244i	−0.345507	−	0.286258i
$451$	22.6295	−	13.0651i	1.06558	−	0.615213i
$452$	0.941083	+	17.9569i	0.0442648	+	0.844623i
$453$	1.82250	+	1.47583i	0.0856284	+	0.0693405i
$454$	0.330439	−	0.240078i	0.0155082	−	0.0112674i
$455$	−6.73449	+	2.52729i	−0.315718	+	0.118481i
$456$	7.03166	+	5.10880i	0.329287	+	0.239241i
$457$	7.62424	+	28.4540i	0.356647	+	1.33102i	0.878399	+	0.477927i	$0.158612\pi$
$457$	7.62424	+	28.4540i	0.356647	+	1.33102i	−0.521753	+	0.853097i	$0.674722\pi$
$458$	−12.1651	−	15.0226i	−0.568436	−	0.701961i
$459$	−0.982066	−	4.62026i	−0.0458389	−	0.215655i
$460$	−3.42003	−	3.84141i	−0.159460	−	0.179107i
$461$	34.7155	−	11.2798i	1.61686	−	0.525351i	0.645664	−	0.763622i	$-0.276581\pi$
$461$	34.7155	−	11.2798i	1.61686	−	0.525351i	0.971199	+	0.238271i	$0.0765807\pi$
$462$	3.47904	−	6.79603i	0.161860	−	0.316180i
$463$	22.8557	−	11.6456i	1.06220	−	0.541216i	0.166573	−	0.986029i	$-0.446730\pi$
$463$	22.8557	−	11.6456i	1.06220	−	0.541216i	0.895623	+	0.444813i	$0.146730\pi$
$464$	1.08235	−	5.09207i	0.0502469	−	0.236393i
$465$	−3.17126	−	2.88776i	−0.147063	−	0.133917i
$466$	1.22128	−	0.259591i	0.0565747	−	0.0120253i
$467$	0.267754	+	0.102781i	0.0123902	+	0.00475614i	0.364555	−	0.931182i	$-0.381221\pi$
$467$	0.267754	+	0.102781i	0.0123902	+	0.00475614i	−0.352165	+	0.935938i	$0.614554\pi$
$468$	−1.63661	+	1.63661i	−0.0756523	+	0.0756523i
$469$	0.0663090	−	34.8637i	0.00306186	−	1.60985i
$470$	19.1455	−	9.62033i	0.883115	−	0.443753i
$471$	2.00118	+	19.0399i	0.0922094	+	0.877314i
$472$	2.92146	+	7.61066i	0.134471	+	0.350309i
$473$	25.0086	−	1.31065i	1.14990	−	0.0602636i
$474$	−6.83766	+	11.8432i	−0.314064	+	0.543975i
$475$	−0.465235	+	41.5012i	−0.0213464	+	1.90420i
$476$	0.994205	−	2.22164i	0.0455693	−	0.101829i
$477$	12.6250	+	6.43275i	0.578059	+	0.294536i
$478$	−12.6078	+	15.5694i	−0.576670	+	0.712128i
$479$	11.7040	+	5.21096i	0.534770	+	0.238095i	0.656310	−	0.754492i	$-0.272117\pi$
$479$	11.7040	+	5.21096i	0.534770	+	0.238095i	−0.121540	+	0.992587i	$0.538783\pi$
$480$	1.46324	+	1.82781i	0.0667875	+	0.0834275i
$481$	0.402456	+	0.903932i	0.0183504	+	0.0412157i
$482$	16.2338	+	16.2338i	0.739429	+	0.739429i
$483$	1.63752	+	6.15813i	0.0745097	+	0.280205i
$484$	3.23833	+	1.05220i	0.147197	+	0.0478271i
$485$	−0.420919	−	0.959843i	−0.0191130	−	0.0435842i
$486$	11.7074	+	10.5414i	0.531057	+	0.478166i
$487$	−18.1530	+	27.9532i	−0.822593	+	1.26668i	0.138474	+	0.990366i	$0.455780\pi$
$487$	−18.1530	+	27.9532i	−0.822593	+	1.26668i	−0.961067	+	0.276316i	$0.910886\pi$
$488$	3.72486	+	0.195212i	0.168617	+	0.00883682i
$489$	5.43869	+	16.7386i	0.245946	+	0.756945i
$490$	−3.39824	+	15.2791i	−0.153517	+	0.690241i
$491$	−0.363458	+	1.11861i	−0.0164026	+	0.0504821i	−0.958923	−	0.283667i	$-0.908449\pi$
$491$	−0.363458	+	1.11861i	−0.0164026	+	0.0504821i	0.942520	+	0.334149i	$0.108449\pi$
$492$	3.55788	−	9.26859i	0.160401	−	0.417860i
$493$	4.62591	+	1.23951i	0.208340	+	0.0558246i
$494$	10.0372	+	1.05495i	0.451596	+	0.0474647i
$495$	9.87393	−	6.33381i	0.443800	−	0.284684i
$496$	−1.07675	−	1.48201i	−0.0483473	−	0.0665444i
$497$	−14.4116	−	0.782769i	−0.646449	−	0.0351120i
$498$	−3.84289	+	7.54210i	−0.172204	+	0.337970i
$499$	28.3992	+	16.3963i	1.27132	+	0.733998i	0.975237	−	0.221164i	$-0.0709855\pi$
$499$	28.3992	+	16.3963i	1.27132	+	0.733998i	0.296085	+	0.955162i	$0.404319\pi$
$500$	−3.07485	+	10.7492i	−0.137512	+	0.480719i
$501$	−4.36763	−	7.56496i	−0.195131	−	0.337977i
$502$	5.46100	+	8.40920i	0.243736	+	0.375321i
$503$	−2.29930	+	14.5172i	−0.102521	+	0.647290i	0.881897	+	0.471443i	$0.156267\pi$
$503$	−2.29930	+	14.5172i	−0.102521	+	0.647290i	−0.984417	+	0.175847i	$0.943733\pi$
$504$	1.03777	+	4.92840i	0.0462260	+	0.219529i
$505$	6.10099	+	3.15181i	0.271490	+	0.140254i
$506$	5.79092	−	2.57828i	0.257438	−	0.114619i
$507$	−3.12245	+	11.6531i	−0.138673	+	0.517534i
$508$	12.6159	−	10.2161i	0.559739	−	0.453268i
$509$	12.5359	+	13.9225i	0.555642	+	0.617103i	0.953883	−	0.300178i	$-0.0970460\pi$
$509$	12.5359	+	13.9225i	0.555642	+	0.617103i	−0.398241	+	0.917281i	$0.630379\pi$
$510$	−1.74963	+	1.25626i	−0.0774750	+	0.0556281i
$511$	2.07349	−	2.84253i	0.0917257	−	0.125746i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	2.23057	−	42.5618i	0.0984821	−	1.87915i
$514$	19.1508	−	21.2691i	0.844705	−	0.938140i
$515$	−1.23517	+	11.1503i	−0.0544281	+	0.491342i
$516$	7.07093	−	6.36670i	0.311280	−	0.280278i
$517$	4.13110	+	26.0827i	0.181686	+	1.14712i
$518$	2.12599	+	0.340870i	0.0934106	+	0.0149770i
$519$	5.29789	−	7.29192i	0.232552	−	0.320080i
$520$	2.53266	+	0.988518i	0.111064	+	0.0433494i
$521$	14.7303	−	33.0848i	0.645346	−	1.44947i	−0.233495	−	0.972358i	$-0.575016\pi$
$521$	14.7303	−	33.0848i	0.645346	−	1.44947i	0.878842	−	0.477114i	$-0.158317\pi$
$522$	−9.25166	+	3.55138i	−0.404934	+	0.155440i
$523$	−4.38897	+	2.85023i	−0.191916	+	0.124632i	−0.637020	−	0.770847i	$-0.719833\pi$
$523$	−4.38897	+	2.85023i	−0.191916	+	0.124632i	0.445104	+	0.895479i	$0.353167\pi$
$524$	12.7832			0.558438
$525$	9.40273	−	10.1714i	0.410369	−	0.443915i
$526$	−23.8456			−1.03972
$527$	1.41335	−	0.917839i	0.0615664	−	0.0399817i
$528$	−2.69401	+	1.03413i	−0.117242	+	0.0450048i
$529$	7.20306	−	16.1783i	0.313176	−	0.703406i
$530$	0.964223	−	16.6160i	0.0418832	−	0.721754i
$531$	9.12153	−	12.5547i	0.395841	−	0.544828i
$532$	13.8534	−	17.0412i	0.600621	−	0.738828i
$533$	−1.80341	−	11.3863i	−0.0781142	−	0.493194i
$534$	−9.44587	+	8.50510i	−0.408763	+	0.368052i
$535$	20.9835	−	23.0435i	0.907195	−	0.996256i
$536$	−8.81730	+	9.79260i	−0.380849	+	0.422976i
$537$	0.384263	−	7.33217i	0.0165822	−	0.316406i
$538$	8.83474	+	17.3392i	0.380893	+	0.747544i
$539$	−16.6700	−	9.70915i	−0.718027	−	0.418203i
$540$	3.60900	−	10.8991i	0.155307	−	0.469023i
$541$	8.90601	+	9.89113i	0.382899	+	0.425253i	0.903527	−	0.428531i	$-0.140969\pi$
$541$	8.90601	+	9.89113i	0.382899	+	0.425253i	−0.520628	+	0.853784i	$0.674302\pi$
$542$	−0.412009	+	0.333638i	−0.0176973	+	0.0143310i
$543$	−4.99189	+	18.6300i	−0.214222	+	0.799489i
$544$	−0.840414	+	0.374177i	−0.0360325	+	0.0160427i
$545$	−9.97628	+	9.86508i	−0.427337	+	0.422573i
$546$	−2.24908	−	2.50743i	−0.0962517	−	0.107308i
$547$	2.20141	−	13.8991i	0.0941254	−	0.594284i	−0.894869	−	0.446329i	$-0.852731\pi$
$547$	2.20141	−	13.8991i	0.0941254	−	0.594284i	0.988994	−	0.147955i	$-0.0472690\pi$
$548$	−0.559879	−	0.862138i	−0.0239169	−	0.0368287i
$549$	−3.55021	−	6.14914i	−0.151519	−	0.262439i
$550$	−11.4716	−	7.63394i	−0.489152	−	0.325512i
$551$	37.4229	+	21.6061i	1.59427	+	0.920452i
$552$	1.09341	−	2.14593i	0.0465385	−	0.0913370i
$553$	28.9439	+	18.8748i	1.23082	+	0.802637i
$554$	8.60520	+	11.8440i	0.365600	+	0.503205i
$555$	−1.47405	−	1.20740i	−0.0625698	−	0.0512513i
$556$	−19.1412	−	2.01182i	−0.811769	−	0.0853203i
$557$	−23.9936	−	6.42908i	−1.01664	−	0.272409i	−0.288241	−	0.957558i	$-0.593070\pi$
$557$	−23.9936	−	6.42908i	−1.01664	−	0.272409i	−0.728403	+	0.685149i	$0.759737\pi$
$558$	−1.24969	+	3.25555i	−0.0529035	+	0.137818i
$559$	3.41417	−	10.5077i	0.144404	−	0.444430i
$560$	4.81218	−	3.44136i	0.203352	−	0.145424i
$561$	−0.820338	−	2.52474i	−0.0346347	−	0.106595i
$562$	−7.41808	−	0.388765i	−0.312913	−	0.0163991i
$563$	4.42219	−	6.80958i	0.186373	−	0.286990i	−0.733117	−	0.680103i	$-0.761935\pi$
$563$	4.42219	−	6.80958i	0.186373	−	0.286990i	0.919490	+	0.393113i	$0.128602\pi$
$564$	7.45632	+	6.71370i	0.313968	+	0.282698i
$565$	−34.7080	−	20.2989i	−1.46017	−	0.853980i
$566$	−0.735781	−	0.239070i	−0.0309272	−	0.0100489i
$567$	0.627104	−	0.624723i	0.0263359	−	0.0262359i
$568$	3.85734	+	3.85734i	0.161851	+	0.161851i
$569$	15.5008	+	34.8153i	0.649827	+	1.45953i	0.874463	+	0.485092i	$0.161214\pi$
$569$	15.5008	+	34.8153i	0.649827	+	1.45953i	−0.224636	+	0.974443i	$0.572119\pi$
$570$	−18.1829	+	6.86308i	−0.761598	+	0.287463i
$571$	−26.1945	−	11.6626i	−1.09621	−	0.488063i	−0.222706	−	0.974886i	$-0.571489\pi$
$571$	−26.1945	−	11.6626i	−1.09621	−	0.488063i	−0.873501	+	0.486823i	$0.838156\pi$
$572$	−2.10872	+	2.60405i	−0.0881698	+	0.108881i
$573$	7.05519	+	3.59480i	0.294735	+	0.150175i
$574$	−22.8976	−	10.2469i	−0.955727	−	0.427697i
$575$	11.3785	−	1.67166i	0.474517	−	0.0697130i
$576$	0.951805	−	1.64858i	0.0396586	−	0.0686906i
$577$	−17.9093	+	0.938585i	−0.745573	+	0.0390738i	−0.421339	−	0.906903i	$-0.638440\pi$
$577$	−17.9093	+	0.938585i	−0.745573	+	0.0390738i	−0.324234	+	0.945977i	$0.605106\pi$
$578$	5.78897	+	15.0808i	0.240789	+	0.627278i
$579$	−0.338820	−	3.22366i	−0.0140809	−	0.133971i
$580$	8.18487	+	8.27714i	0.339858	+	0.343689i
$581$	18.5025	+	10.7294i	0.767614	+	0.445131i
$582$	0.347038	−	0.347038i	0.0143852	−	0.0143852i
$583$	19.1509	+	7.35133i	0.793148	+	0.304461i
$584$	−1.30078	+	0.276489i	−0.0538266	+	0.0114412i
$585$	−1.04764	−	5.06827i	−0.0433145	−	0.209547i
$586$	−3.20316	+	15.0697i	−0.132321	+	0.622523i
$587$	18.0895	−	9.21707i	0.746634	−	0.380429i	−0.0389033	−	0.999243i	$-0.512386\pi$
$587$	18.0895	−	9.21707i	0.746634	−	0.380429i	0.785538	+	0.618814i	$0.212386\pi$
$588$	−7.24367	+	1.11906i	−0.298724	+	0.0461491i
$589$	14.4617	−	4.69888i	0.595883	−	0.193614i
$590$	−17.8088	−	3.88984i	−0.733178	−	0.160142i
$591$	−1.91551	−	9.01178i	−0.0787937	−	0.370695i
$592$	−0.512148	−	0.632450i	−0.0210491	−	0.0259935i
$593$	−3.82019	−	14.2572i	−0.156877	−	0.585471i	−0.998937	−	0.0460886i	$-0.985324\pi$
$593$	−3.82019	−	14.2572i	−0.156877	−	0.585471i	0.842061	−	0.539383i	$-0.181342\pi$
$594$	11.4478	+	8.31729i	0.469707	+	0.341262i
$595$	2.92984	+	4.58658i	0.120112	+	0.188031i
$596$	−5.58810	+	4.05999i	−0.228897	+	0.166304i
$597$	−2.03478	−	1.64774i	−0.0832782	−	0.0674373i
$598$	−0.146364	−	2.79280i	−0.00598528	−	0.114206i
$599$	−37.3946	+	21.5898i	−1.52790	+	0.882136i	−0.528454	+	0.848962i	$0.677228\pi$
$599$	−37.3946	+	21.5898i	−1.52790	+	0.882136i	−0.999450	+	0.0331739i	$0.989438\pi$
$600$	−5.21256	+	0.488852i	−0.212802	+	0.0199573i
$601$			5.02543i			0.204992i	0.994733	+	0.102496i	$0.0326828\pi$
$601$			5.02543i			0.204992i	−0.994733	+	0.102496i	$0.967317\pi$
$602$	−15.0945	−	18.7129i	−0.615207	−	0.762679i
$603$	24.7755	+	3.92406i	1.00894	+	0.159800i
$604$	−2.22739	+	0.234108i	−0.0906312	+	0.00952573i
$605$	−5.94377	+	4.75826i	−0.241648	+	0.193451i
$606$	−0.336125	+	3.19801i	−0.0136541	+	0.129910i
$607$	−15.3710	+	4.11866i	−0.623891	+	0.167171i	−0.556896	−	0.830582i	$-0.688008\pi$
$607$	−15.3710	+	4.11866i	−0.623891	+	0.167171i	−0.0669952	+	0.997753i	$0.521341\pi$
$608$	−8.19856	+	1.29852i	−0.332495	+	0.0526621i
$609$	−4.43050	−	13.7244i	−0.179533	−	0.556143i
$610$	−4.94015	+	6.72001i	−0.200021	+	0.272085i
$611$	11.3961	+	2.42231i	0.461035	+	0.0979961i
$612$	1.46870	+	0.953784i	0.0593686	+	0.0385544i
$613$	−30.8080	−	20.0070i	−1.24432	−	0.808074i	−0.256942	−	0.966427i	$-0.582715\pi$
$613$	−30.8080	−	20.0070i	−1.24432	−	0.808074i	−0.987383	+	0.158353i	$0.949382\pi$
$614$	2.33980	+	0.497340i	0.0944268	+	0.0200710i
$615$	12.9478	+	18.0328i	0.522105	+	0.727152i
$616$	2.23999	+	6.93885i	0.0902516	+	0.279574i
$617$	42.1822	−	6.68100i	1.69819	−	0.268967i	0.769183	−	0.639028i	$-0.220663\pi$
$617$	42.1822	−	6.68100i	1.69819	−	0.268967i	0.929007	+	0.370061i	$0.120663\pi$
$618$	−5.07431	+	1.35966i	−0.204119	+	0.0546934i
$619$	−3.68281	+	35.0396i	−0.148024	+	1.40836i	0.628273	+	0.777993i	$0.283762\pi$
$619$	−3.68281	+	35.0396i	−0.148024	+	1.40836i	−0.776298	+	0.630366i	$0.782905\pi$
$620$	4.09171	−	0.191447i	0.164327	−	0.00768871i
$621$	−11.7453	+	1.23449i	−0.471324	+	0.0495382i
$622$	−19.1125	−	3.02713i	−0.766343	−	0.121377i
$623$	20.1644	+	24.9980i	0.807869	+	1.00152i
$624$			1.27310i			0.0509650i
$625$	−16.3076	−	18.9490i	−0.652303	−	0.757958i
$626$	−9.80357	+	5.66010i	−0.391830	+	0.226223i
$627$	−1.25362	−	23.9204i	−0.0500646	−	0.955290i
$628$	−14.2093	−	11.5064i	−0.567011	−	0.459156i
$629$	0.605682	−	0.440054i	0.0241501	−	0.0175461i
$630$	−10.4833	−	4.11472i	−0.417665	−	0.163934i
$631$	−26.8697	−	19.5220i	−1.06966	−	0.777157i	−0.0938124	−	0.995590i	$-0.529905\pi$
$631$	−26.8697	−	19.5220i	−1.06966	−	0.777157i	−0.975852	+	0.218433i	$0.929905\pi$
$632$	−3.38027	−	12.6153i	−0.134460	−	0.501811i
$633$	−6.06082	−	7.48449i	−0.240896	−	0.297482i
$634$	−3.77715	−	17.7701i	−0.150010	−	0.705740i
$635$	3.59193	+	36.1213i	0.142541	+	1.43343i
$636$	7.41243	−	2.40845i	0.293922	−	0.0955011i
$637$	−6.63460	+	5.33094i	−0.262873	+	0.211219i
$638$	−12.7831	+	6.51330i	−0.506086	+	0.257864i
$639$	2.15904	−	10.1575i	0.0854103	−	0.401824i
$640$	−2.22247	−	0.246193i	−0.0878510	−	0.00973164i
$641$	46.0857	−	9.79581i	1.82027	−	0.386911i	0.833965	−	0.551817i	$-0.186065\pi$
$641$	46.0857	−	9.79581i	1.82027	−	0.386911i	0.986309	+	0.164905i	$0.0527318\pi$
$642$	13.6247	+	5.23004i	0.537725	+	0.206413i
$643$	−1.46249	+	1.46249i	−0.0576751	+	0.0576751i	−0.735356	−	0.677681i	$-0.762985\pi$
$643$	−1.46249	+	1.46249i	−0.0576751	+	0.0576751i	0.677681	+	0.735356i	$0.262985\pi$
$644$	−5.26447	−	3.05281i	−0.207449	−	0.120298i
$645$	3.21045	+	21.0323i	0.126412	+	0.828146i
$646$	−0.798207	−	7.59443i	−0.0314050	−	0.298799i
$647$	0.311675	+	0.811942i	0.0122532	+	0.0319207i	0.939571	−	0.342355i	$-0.111225\pi$
$647$	0.311675	+	0.811942i	0.0122532	+	0.0319207i	−0.927317	+	0.374276i	$0.877891\pi$
$648$	−0.334107	+	0.0175098i	−0.0131250	+	0.000687850i
$649$	11.2332	−	19.4566i	0.440943	−	0.763737i
$650$	−4.95798	+	3.51795i	−0.194468	+	0.137985i
$651$	−4.63220	−	2.07295i	−0.181550	−	0.0812455i
$652$	−14.9765	−	7.63092i	−0.586526	−	0.298850i
$653$	−1.07436	+	1.32672i	−0.0420429	+	0.0519186i	−0.797734	−	0.603010i	$-0.793968\pi$
$653$	−1.07436	+	1.32672i	−0.0420429	+	0.0519186i	0.755691	+	0.654929i	$0.227301\pi$
$654$	−6.00193	−	2.67223i	−0.234694	−	0.104492i
$655$	−15.7022	+	23.8851i	−0.613535	+	0.933267i
$656$	3.85649	+	8.66183i	0.150571	+	0.338188i
$657$	1.79004	+	1.79004i	0.0698360	+	0.0698360i
$658$	17.9609	−	17.8927i	0.700187	−	0.697529i
$659$	−22.6636	−	7.36386i	−0.882849	−	0.286855i	−0.167709	−	0.985836i	$-0.553637\pi$
$659$	−22.6636	−	7.36386i	−0.882849	−	0.286855i	−0.715140	+	0.698981i	$0.753637\pi$
$660$	1.37692	−	6.30394i	0.0535964	−	0.245380i
$661$	−33.2392	−	29.9287i	−1.29286	−	1.16409i	−0.976515	−	0.215448i	$-0.930879\pi$
$661$	−33.2392	−	29.9287i	−1.29286	−	1.16409i	−0.316341	−	0.948646i	$-0.602454\pi$
$662$	−11.8423	+	18.2356i	−0.460265	+	0.708745i
$663$	−1.16959	−	0.0612954i	−0.0454229	−	0.00238051i
$664$	−2.49811	−	7.68839i	−0.0969454	−	0.298367i
$665$	14.8242	+	46.8170i	0.574856	+	1.81549i
$666$	−0.478723	+	1.47336i	−0.0185501	+	0.0570914i
$667$	4.29113	−	11.1788i	0.166153	−	0.432844i
$668$	8.05818	+	2.15918i	0.311780	+	0.0835413i
$669$	−16.6061	−	1.74537i	−0.642030	−	0.0674801i
$670$	−7.46652	−	28.5035i	−0.288457	−	1.10119i
$671$	−6.04212	−	8.31626i	−0.233253	−	0.321046i
$672$	2.32052	+	1.51325i	0.0895160	+	0.0583747i
$673$	15.3848	−	30.1943i	0.593040	−	1.16391i	−0.378183	−	0.925731i	$-0.623451\pi$
$673$	15.3848	−	30.1943i	0.593040	−	1.16391i	0.971222	−	0.238175i	$-0.0765491\pi$
$674$	16.5218	+	9.53888i	0.636397	+	0.367424i
$675$	15.9316	+	20.1311i	0.613207	+	0.774848i
$676$	−5.76085	−	9.97808i	−0.221571	−	0.383772i
$677$	−13.6118	−	20.9604i	−0.523145	−	0.805573i	0.474044	−	0.880501i	$-0.342794\pi$
$677$	−13.6118	−	20.9604i	−0.523145	−	0.805573i	−0.997189	+	0.0749286i	$0.976127\pi$
$678$	2.94539	−	18.5965i	0.113117	−	0.714193i
$679$	−0.828038	−	0.923154i	−0.0317772	−	0.0354274i
$680$	0.333179	−	2.02991i	0.0127768	−	0.0778433i
$681$	−0.390702	+	0.173952i	−0.0149717	+	0.00666584i
$682$	−1.30664	+	4.87644i	−0.0500337	+	0.186728i
$683$	23.7390	−	19.2235i	0.908349	−	0.735567i	−0.0564910	−	0.998403i	$-0.517991\pi$
$683$	23.7390	−	19.2235i	0.908349	−	0.735567i	0.964840	+	0.262836i	$0.0846579\pi$
$684$	10.5732	+	11.7427i	0.404277	+	0.448995i
$685$	2.29860	+	0.0128835i	0.0878251	+	0.000492251i
$686$	1.83077	+	18.4295i	0.0698991	+	0.703643i
$687$	9.18908	+	18.0346i	0.350585	+	0.688062i
$688$	−0.475577	+	9.07455i	−0.0181312	+	0.345964i
$689$	6.05570	−	6.72554i	0.230704	−	0.256223i
$690$	2.66653	+	4.67894i	0.101513	+	0.178124i
$691$	−36.6012	+	32.9559i	−1.39237	+	1.25370i	−0.462104	+	0.886826i	$0.652905\pi$
$691$	−36.6012	+	32.9559i	−1.39237	+	1.25370i	−0.930271	+	0.366874i	$0.880428\pi$
$692$	1.34659	+	8.50201i	0.0511895	+	0.323198i
$693$	8.75551	−	10.7702i	0.332594	−	0.409126i
$694$	6.04477	−	8.31992i	0.229456	−	0.315820i
$695$	27.2710	−	33.2936i	1.03445	−	1.26290i
$696$	−2.21710	+	4.97969i	−0.0840390	+	0.188755i
$697$	−8.14319	+	3.12588i	−0.308445	+	0.118401i
$698$	−19.5648	+	12.7055i	−0.740537	+	0.480911i
$699$	−1.30735			−0.0494487
$700$	0.519072	+	13.2186i	0.0196191	+	0.499615i
$701$	40.8204			1.54176			0.770882	−	0.636978i	$-0.219816\pi$
$701$	40.8204			1.54176			0.770882	+	0.636978i	$0.219816\pi$
$702$	5.23566	−	3.40008i	0.197607	−	0.128328i
$703$	6.30656	−	2.42086i	0.237857	−	0.0913046i
$704$	1.12093	−	2.51765i	0.0422466	−	0.0948874i
$705$	−21.7032	+	5.68518i	−0.817392	+	0.214116i
$706$	−11.4190	+	15.7169i	−0.429759	+	0.591513i
$707$	8.02270	+	1.28632i	0.301725	+	0.0483769i
$708$	−1.33532	−	8.43088i	−0.0501844	−	0.316852i
$709$	−17.4722	+	15.7321i	−0.656183	+	0.590830i	−0.928479	−	0.371384i	$-0.878883\pi$
$709$	−17.4722	+	15.7321i	−0.656183	+	0.590830i	0.272297	+	0.962213i	$0.412217\pi$
$710$	−11.9455	+	2.46919i	−0.448305	+	0.0926671i
$711$	−16.6358	+	18.4759i	−0.623891	+	0.692902i
$712$	0.635311	−	12.1225i	0.0238093	−	0.454308i
$713$	−1.91291	−	3.75429i	−0.0716390	−	0.140599i
$714$	−1.50192	+	2.05897i	−0.0562081	+	0.0770552i
$715$	−2.27536	−	7.13873i	−0.0850936	−	0.266973i
$716$	4.69198	+	5.21097i	0.175348	+	0.194743i
$717$	16.3025	−	13.2015i	0.608828	−	0.493019i
$718$	4.40054	−	16.4230i	0.164227	−	0.612902i
$719$	15.7437	−	7.00953i	0.587139	−	0.261411i	−0.0915936	−	0.995796i	$-0.529196\pi$
$719$	15.7437	−	7.00953i	0.587139	−	0.261411i	0.678733	+	0.734385i	$0.262529\pi$
$720$	1.91117	+	3.80343i	0.0712251	+	0.141746i
$721$	2.73511	+	12.9891i	0.101861	+	0.483739i
$722$	7.80647	−	49.2881i	0.290527	−	1.83431i
$723$	−13.0926	−	20.1608i	−0.486919	−	0.749790i
$724$	−9.20993	−	15.9521i	−0.342284	−	0.592854i
$725$	−25.5194	+	5.12602i	−0.947766	+	0.190376i
$726$	−3.08764	−	1.78265i	−0.114593	−	0.0661604i
$727$	18.0723	−	35.4689i	0.670265	−	1.31547i	−0.265931	−	0.963992i	$-0.585679\pi$
$727$	18.0723	−	35.4689i	0.670265	−	1.31547i	0.936196	−	0.351477i	$-0.114321\pi$
$728$	3.21212	+	0.174467i	0.119049	+	0.00646616i
$729$	−9.10592	−	12.5332i	−0.337256	−	0.464193i
$730$	1.08119	−	2.77009i	0.0400166	−	0.102526i
$731$	−8.31378	−	0.873813i	−0.307496	−	0.0323192i
$732$	−3.77252	−	1.01084i	−0.139437	−	0.0373619i
$733$	−1.48210	+	3.86101i	−0.0547427	+	0.142609i	−0.958225	−	0.286016i	$-0.907669\pi$
$733$	−1.48210	+	3.86101i	−0.0547427	+	0.142609i	0.903482	+	0.428626i	$0.141002\pi$
$734$	−3.77821	+	11.6281i	−0.139456	+	0.429202i
$735$	6.80678	−	14.9092i	0.251072	−	0.549933i
$736$	0.710780	+	2.18756i	0.0261997	+	0.0806344i
$737$	36.2655	+	1.90059i	1.33586	+	0.0700093i
$738$	9.83029	−	15.1373i	0.361858	−	0.557212i
$739$	7.96011	+	7.16732i	0.292817	+	0.263654i	0.802425	−	0.596753i	$-0.203543\pi$
$739$	7.96011	+	7.16732i	0.292817	+	0.263654i	−0.509608	+	0.860407i	$0.670209\pi$
$740$	1.81081	−	0.180068i	0.0665665	−	0.00661943i
$741$	−10.0505	−	3.26561i	−0.369215	−	0.119965i
$742$	−5.06084	−	19.0320i	−0.185789	−	0.698688i
$743$	−4.57364	−	4.57364i	−0.167791	−	0.167791i	0.618217	−	0.786008i	$-0.287855\pi$
$743$	−4.57364	−	4.57364i	−0.167791	−	0.167791i	−0.786008	+	0.618217i	$0.787855\pi$
$744$	0.780172	+	1.75229i	0.0286025	+	0.0642422i
$745$	−0.721874	−	15.4282i	−0.0264474	−	0.565247i
$746$	−15.6491	−	6.96744i	−0.572955	−	0.255096i
$747$	−9.68454	+	11.9594i	−0.354339	+	0.437572i
$748$	2.25896	+	1.15100i	0.0825958	+	0.0420847i
$749$	15.0628	−	33.6592i	0.550383	−	1.22988i
$750$	5.48940	−	10.3400i	0.200444	−	0.377563i
$751$	−17.2204	+	29.8267i	−0.628382	+	1.08839i	0.359494	+	0.933147i	$0.382949\pi$
$751$	−17.2204	+	29.8267i	−0.628382	+	1.08839i	−0.987876	+	0.155243i	$0.950384\pi$
$752$	−9.56914	+	0.501498i	−0.348951	+	0.0182877i
$753$	−3.76248	−	9.80161i	−0.137113	−	0.357190i
$754$	0.661616	+	6.29486i	0.0240946	+	0.229245i
$755$	2.29857	−	4.44937i	0.0836536	−	0.161929i
$756$	0.0258372	−	13.5846i	0.000939691	−	0.494067i
$757$	−16.4707	+	16.4707i	−0.598636	+	0.598636i	−0.939950	−	0.341313i	$-0.889128\pi$
$757$	−16.4707	+	16.4707i	−0.598636	+	0.598636i	0.341313	+	0.939950i	$0.389128\pi$
$758$	−1.96127	−	0.752862i	−0.0712366	−	0.0273452i
$759$	−6.49239	+	1.38000i	−0.235659	+	0.0500908i
$760$	7.64438	−	16.9138i	0.277291	−	0.613527i
$761$	2.61792	−	12.3163i	0.0948995	−	0.446467i	−0.904884	−	0.425658i	$-0.860043\pi$
$761$	2.61792	−	12.3163i	0.0948995	−	0.446467i	0.999783	−	0.0208088i	$-0.00662414\pi$
$762$	−15.1453	+	7.71692i	−0.548657	+	0.279555i
$763$	−7.56469	+	14.7770i	−0.273860	+	0.534963i
$764$	−7.19203	+	2.33683i	−0.260199	+	0.0845436i
$765$	−3.58618	+	1.57265i	−0.129659	+	0.0568591i
$766$	6.95452	+	32.7184i	0.251277	+	1.18216i
$767$	−6.23770	−	7.70292i	−0.225230	−	0.278136i
$768$	−0.271006	−	1.01141i	−0.00977908	−	0.0364960i
$769$	18.7414	+	13.6164i	0.675833	+	0.491021i	0.871973	−	0.489555i	$-0.162841\pi$
$769$	18.7414	+	13.6164i	0.675833	+	0.491021i	−0.196140	+	0.980576i	$0.562841\pi$
$770$	−15.7165	−	4.33793i	−0.566383	−	0.156328i
$771$	−24.2446	+	17.6148i	−0.873150	+	0.634380i
$772$	2.40577	+	1.94816i	0.0865857	+	0.0701157i
$773$	2.49460	+	47.5997i	0.0897244	+	1.71204i	0.559147	+	0.829069i	$0.311129\pi$
$773$	2.49460	+	47.5997i	0.0897244	+	1.71204i	−0.469422	+	0.882974i	$0.655538\pi$
$774$	14.9806	−	8.64906i	0.538467	−	0.310884i
$775$	−4.66830	+	7.88039i	−0.167690	+	0.283072i
$776$			0.468716i			0.0168259i
$777$	−2.10324	−	0.811951i	−0.0754533	−	0.0291286i
$778$	−29.0003	−	4.59319i	−1.03971	−	0.164674i
$779$	−78.2729	+	8.22681i	−2.80442	+	0.294756i
$780$	−2.37876	−	1.56381i	−0.0851732	−	0.0559933i
$781$	1.57146	−	14.9514i	0.0562312	−	0.535004i
$782$	−2.04390	+	0.547662i	−0.0730898	+	0.0195844i
$783$	26.4002	−	4.18139i	0.943468	−	0.149431i
$784$	4.13601	−	5.64743i	0.147715	−	0.201694i
$785$	38.9532	−	12.4157i	1.39030	−	0.443136i
$786$	−13.0926	−	2.78293i	−0.466999	−	0.0992637i
$787$	11.3958	+	7.40051i	0.406216	+	0.263800i	0.731534	−	0.681805i	$-0.238805\pi$
$787$	11.3958	+	7.40051i	0.406216	+	0.263800i	−0.325318	+	0.945605i	$0.605471\pi$
$788$	7.37930	+	4.79218i	0.262877	+	0.170714i
$789$	24.4227	+	5.19121i	0.869472	+	0.184812i
$790$	27.7235	+	9.18001i	0.986357	+	0.326610i
$791$	−46.5163	−	9.97985i	−1.65393	−	0.354843i
$792$	−5.18158	+	0.820682i	−0.184120	+	0.0291617i
$793$	−4.38058	+	1.17377i	−0.155559	+	0.0416819i
$794$	0.230190	−	2.19011i	0.00816913	−	0.0777241i
$795$	−4.60489	+	16.8083i	−0.163319	+	0.596129i
$796$	2.48684	−	0.261377i	0.0881437	−	0.00926427i
$797$	−26.6940	−	4.22791i	−0.945549	−	0.149760i	−0.335426	−	0.942067i	$-0.608880\pi$
$797$	−26.6940	−	4.22791i	−0.945549	−	0.149760i	−0.610123	+	0.792306i	$0.708880\pi$
$798$	−17.8986	+	14.4377i	−0.633604	+	0.511090i
$799$		−	8.81520i		−	0.311859i
$800$	3.18996	−	3.85021i	0.112782	−	0.136126i
$801$	−20.0122	+	11.5541i	−0.707097	+	0.408242i
$802$	1.56286	+	29.8212i	0.0551866	+	1.05302i
$803$	2.84817	+	2.30640i	0.100510	+	0.0813912i
$804$	11.1626	−	8.11009i	0.393674	−	0.286021i
$805$	12.1706	−	6.08661i	0.428959	−	0.214525i
$806$	1.80191	+	1.30917i	0.0634697	+	0.0461134i
$807$	−5.27383	−	19.6822i	−0.185647	−	0.692846i
$808$	−1.93266	−	2.38663i	−0.0679907	−	0.0839615i
$809$	3.92661	+	18.4732i	0.138052	+	0.649485i	0.991694	+	0.128623i	$0.0410558\pi$
$809$	3.92661	+	18.4732i	0.138052	+	0.649485i	−0.853641	+	0.520861i	$0.825611\pi$
$810$	0.377681	−	0.645777i	0.0132704	−	0.0226903i
$811$	17.9067	−	5.81823i	0.628788	−	0.204306i	0.0227499	−	0.999741i	$-0.492758\pi$
$811$	17.9067	−	5.81823i	0.628788	−	0.204306i	0.606038	+	0.795436i	$0.292758\pi$
$812$	12.2602	+	6.27629i	0.430249	+	0.220254i
$813$	0.494615	−	0.252019i	0.0173469	−	0.00883869i
$814$	−0.466302	+	2.19378i	−0.0163439	+	0.0768919i
$815$	32.6544	−	18.6098i	1.14383	−	0.651872i
$816$	0.942215	−	0.200274i	0.0329841	−	0.00701099i
$817$	−70.4190	−	27.0313i	−2.46365	−	0.945707i
$818$	−11.4507	+	11.4507i	−0.400363	+	0.400363i
$819$	−3.05172	−	5.30903i	−0.106636	−	0.185513i
$820$	−20.9214	−	3.43394i	−0.730609	−	0.119918i
$821$	−2.83210	−	26.9457i	−0.0988411	−	0.940410i	−0.925766	−	0.378098i	$-0.876578\pi$
$821$	−2.83210	−	26.9457i	−0.0988411	−	0.940410i	0.826925	−	0.562313i	$-0.190088\pi$
$822$	0.385742	+	1.00489i	0.0134543	+	0.0350497i
$823$	25.7503	−	1.34952i	0.897599	−	0.0470412i	0.402046	−	0.915619i	$-0.368299\pi$
$823$	25.7503	−	1.34952i	0.897599	−	0.0470412i	0.495552	+	0.868578i	$0.334966\pi$
$824$	2.50854	−	4.34492i	0.0873891	−	0.151362i
$825$	10.0874	+	10.3161i	0.351198	+	0.359161i
$826$	−21.4546	+	2.21372i	−0.746501	+	0.0770252i
$827$	−5.88896	−	3.00057i	−0.204779	−	0.104340i	0.348593	−	0.937274i	$-0.386659\pi$
$827$	−5.88896	−	3.00057i	−0.204779	−	0.104340i	−0.553373	+	0.832934i	$0.686659\pi$
$828$	2.75552	−	3.40278i	0.0957608	−	0.118255i
$829$	9.86446	+	4.39194i	0.342607	+	0.152538i	0.570825	−	0.821072i	$-0.306623\pi$
$829$	9.86446	+	4.39194i	0.342607	+	0.152538i	−0.228218	+	0.973610i	$0.573290\pi$
$830$	17.4340	+	4.77633i	0.605145	+	0.165789i
$831$	−6.23502	−	14.0041i	−0.216290	−	0.485796i
$832$	−0.859739	−	0.859739i	−0.0298061	−	0.0298061i
$833$	4.98909	+	4.07160i	0.172862	+	0.141073i
$834$	19.1666	+	6.22759i	0.663683	+	0.215644i
$835$	−13.9326	+	12.4043i	−0.482156	+	0.429267i
$836$	17.0003	+	15.3071i	0.587966	+	0.529407i
$837$	5.12273	−	7.88831i	0.177067	−	0.272660i
$838$	−9.57123	−	0.501607i	−0.330633	−	0.0173277i
$839$	−2.83049	−	8.71135i	−0.0977193	−	0.300749i	0.890234	−	0.455504i	$-0.150541\pi$
$839$	−2.83049	−	8.71135i	−0.0977193	−	0.300749i	−0.987953	+	0.154755i	$0.950541\pi$
$840$	−5.67784	+	2.47704i	−0.195904	+	0.0854659i
$841$	0.586941	−	1.80642i	0.0202393	−	0.0622903i
$842$	6.02980	−	15.7082i	0.207801	−	0.541339i
$843$	7.51300	+	2.01310i	0.258761	+	0.0693349i
$844$	9.14727	+	0.961417i	0.314862	+	0.0330933i
$845$	25.7200	+	1.49253i	0.884796	+	0.0513445i
$846$	10.7217	+	14.7572i	0.368621	+	0.507363i
$847$	−4.92086	+	7.54601i	−0.169083	+	0.259284i
$848$	−3.37924	+	6.63213i	−0.116044	+	0.227748i
$849$	0.701545	+	0.405037i	0.0240770	+	0.0139008i
$850$	3.38356	+	3.11595i	0.116055	+	0.106876i
$851$	−0.935937	−	1.62109i	−0.0320835	−	0.0555703i
$852$	−3.11096	−	4.79046i	−0.106580	−	0.164118i
$853$	5.24531	−	33.1176i	0.179596	−	1.13392i	−0.718956	−	0.695056i	$-0.755380\pi$
$853$	5.24531	−	33.1176i	0.179596	−	1.13392i	0.898552	−	0.438868i	$-0.144620\pi$
$854$	−3.06741	+	9.37977i	−0.104964	+	0.320969i
$855$	−34.9284	+	5.33162i	−1.19453	+	0.182337i
$856$	−12.7328	+	5.66900i	−0.435198	+	0.193763i
$857$	−4.91443	+	18.3409i	−0.167874	+	0.626513i	0.829782	+	0.558087i	$0.188464\pi$
$857$	−4.91443	+	18.3409i	−0.167874	+	0.626513i	−0.997656	+	0.0684262i	$0.978202\pi$
$858$	2.72666	−	2.20801i	0.0930867	−	0.0753801i
$859$	−1.05742	−	1.17438i	−0.0360786	−	0.0400694i	0.724835	−	0.688922i	$-0.241916\pi$
$859$	−1.05742	−	1.17438i	−0.0360786	−	0.0400694i	−0.760914	+	0.648853i	$0.775249\pi$
$860$	−16.3713	−	12.0353i	−0.558258	−	0.410399i
$861$	21.2211	+	15.4798i	0.723212	+	0.527549i
$862$	5.56349	+	10.9190i	0.189493	+	0.371901i
$863$	0.974742	−	18.5992i	0.0331806	−	0.633123i	−0.930537	−	0.366199i	$-0.880659\pi$
$863$	0.974742	−	18.5992i	0.0331806	−	0.633123i	0.963717	−	0.266925i	$-0.0860076\pi$
$864$	−3.43565	+	3.81568i	−0.116883	+	0.129812i
$865$	−17.5398	−	7.92732i	−0.596372	−	0.269537i
$866$	5.26888	−	4.74412i	0.179044	−	0.161212i
$867$	−2.64598	−	16.7061i	−0.0898622	−	0.567368i
$868$	4.52805	−	1.72828i	0.153692	−	0.0586617i
$869$	−21.1562	+	29.1190i	−0.717676	+	0.987796i
$870$	−6.58104	−	10.2593i	−0.223118	−	0.347824i
$871$	6.51658	−	14.6365i	0.220806	−	0.495938i
$872$	5.85774	−	2.24858i	0.198368	−	0.0761464i
$873$	0.748306	−	0.485955i	0.0253263	−	0.0164471i
$874$	−19.0928			−0.645825
$875$	−25.3361	−	15.2670i	−0.856516	−	0.516120i
$876$	1.39246			0.0470467
$877$	−35.3299	+	22.9435i	−1.19301	+	0.774747i	−0.979352	−	0.202163i	$-0.935203\pi$
$877$	−35.3299	+	22.9435i	−1.19301	+	0.774747i	−0.213653	+	0.976910i	$0.568536\pi$
$878$	−30.3059	+	11.6333i	−1.02277	+	0.392606i
$879$	6.56138	−	14.7371i	0.221310	−	0.497070i
$880$	3.32726	+	5.18695i	0.112162	+	0.174852i
$881$	−18.9008	+	26.0147i	−0.636784	+	0.876458i	−0.998439	−	0.0558542i	$-0.982212\pi$
$881$	−18.9008	+	26.0147i	−0.636784	+	0.876458i	0.361655	+	0.932312i	$0.382212\pi$
$882$	−13.3043	−	0.748004i	−0.447978	−	0.0251866i
$883$	−2.32702	−	14.6922i	−0.0783105	−	0.494433i	−0.995404	−	0.0957616i	$-0.969471\pi$
$883$	−2.32702	−	14.6922i	−0.0783105	−	0.494433i	0.917094	−	0.398672i	$-0.130529\pi$
$884$	0.831225	−	0.748438i	0.0279571	−	0.0251727i
$885$	17.3931	+	7.86100i	0.584662	+	0.264245i
$886$	−23.0074	+	25.5523i	−0.772949	+	0.858447i
$887$	2.48005	−	47.3223i	0.0832721	−	1.58893i	−0.563417	−	0.826172i	$-0.690514\pi$
$887$	2.48005	−	47.3223i	0.0832721	−	1.58893i	0.646689	−	0.762753i	$-0.276153\pi$
$888$	0.386859	+	0.759254i	0.0129821	+	0.0254789i
$889$	17.3947	+	39.2700i	0.583400	+	1.31707i
$890$	21.8701	+	16.0776i	0.733086	+	0.538922i
$891$	0.616960	+	0.685203i	0.0206689	+	0.0229552i
$892$	12.3929	−	10.0356i	0.414946	−	0.336017i
$893$	20.5865	−	76.8298i	0.688901	−	2.57101i
$894$	6.60722	−	2.94172i	0.220978	−	0.0983860i
$895$	−15.4999	+	2.36597i	−0.518105	+	0.0790856i
$896$	−2.58898	+	0.545160i	−0.0864916	+	0.0182125i
$897$	−0.458089	+	2.89226i	−0.0152951	+	0.0965697i
$898$	4.68797	+	7.21884i	0.156440	+	0.240896i
$899$	4.76820	+	8.25876i	0.159028	+	0.275445i
$900$	−9.45417	−	1.10095i	−0.315139	−	0.0366984i
$901$	−5.93015	−	3.42378i	−0.197562	−	0.114063i
$902$	11.8629	−	23.2822i	0.394991	−	0.775214i
$903$	11.3861	+	22.4519i	0.378905	+	0.747152i
$904$	10.5693	+	14.5474i	0.351530	+	0.483840i
$905$	41.1189	+	2.38612i	1.36684	+	0.0793172i
$906$	2.33227	+	0.245131i	0.0774845	+	0.00814395i
$907$	11.7680	+	3.15324i	0.390751	+	0.104702i	0.448845	−	0.893610i	$-0.351836\pi$
$907$	11.7680	+	3.15324i	0.390751	+	0.104702i	−0.0580936	+	0.998311i	$0.518502\pi$
$908$	0.146373	−	0.381316i	0.00485757	−	0.0126544i
$909$	−1.80652	+	5.55991i	−0.0599186	+	0.184411i
$910$	−4.27156	+	5.78743i	−0.141601	+	0.191852i
$911$	−0.993780	−	3.05854i	−0.0329254	−	0.101334i	0.933243	−	0.359245i	$-0.116966\pi$
$911$	−0.993780	−	3.05854i	−0.0329254	−	0.101334i	−0.966169	+	0.257911i	$0.916966\pi$
$912$	8.67969	+	0.454883i	0.287413	+	0.0150627i
$913$	−12.1340	+	18.6846i	−0.401575	+	0.618372i
$914$	21.8914	+	19.7111i	0.724103	+	0.651986i
$915$	6.52268	−	5.80718i	0.215633	−	0.191980i
$916$	−18.3844	−	5.97345i	−0.607437	−	0.197368i
$917$	−8.81570	+	32.6521i	−0.291120	+	1.07827i
$918$	−3.34000	−	3.34000i	−0.110236	−	0.110236i
$919$	12.6580	+	28.4303i	0.417549	+	0.937830i	0.992792	+	0.119848i	$0.0382407\pi$
$919$	12.6580	+	28.4303i	0.417549	+	0.937830i	−0.575243	+	0.817982i	$0.695093\pi$
$920$	−4.96046	−	1.35900i	−0.163542	−	0.0448048i
$921$	−2.28817	−	1.01876i	−0.0753976	−	0.0335692i
$922$	22.9715	−	28.3674i	0.756526	−	0.934231i
$923$	−5.90971	−	3.01115i	−0.194520	−	0.0991131i
$924$	−0.783608	−	7.59445i	−0.0257788	−	0.249839i
$925$	−1.88784	+	3.60462i	−0.0620717	+	0.118519i
$926$	12.8258	−	22.2149i	0.421482	−	0.730028i
$927$	−9.53747	+	0.499838i	−0.313252	+	0.0164168i
$928$	−1.86560	−	4.86006i	−0.0612414	−	0.159539i
$929$	−1.30690	−	12.4343i	−0.0428779	−	0.407956i	−0.994818	−	0.101672i	$-0.967581\pi$
$929$	−1.30690	−	12.4343i	−0.0428779	−	0.407956i	0.951940	−	0.306284i	$-0.0990858\pi$
$930$	−4.23242	−	0.694689i	−0.138787	−	0.0227798i
$931$	33.9744	+	47.1377i	1.11346	+	1.54488i
$932$	0.882868	−	0.882868i	0.0289193	−	0.0289193i
$933$	18.9161	+	7.26122i	0.619286	+	0.237722i
$934$	0.280536	−	0.0596297i	0.00917941	−	0.00195114i
$935$	−4.92538	+	2.80698i	−0.161077	+	0.0917981i
$936$	−0.481215	+	2.26394i	−0.0157290	+	0.0739991i
$937$	−12.2344	+	6.23375i	−0.399681	+	0.203648i	−0.642265	−	0.766483i	$-0.722005\pi$
$937$	−12.2344	+	6.23375i	−0.399681	+	0.203648i	0.242584	+	0.970130i	$0.422005\pi$
$938$	−18.9325	−	29.2752i	−0.618168	−	0.955870i
$939$	11.2731	−	3.66285i	0.367883	−	0.119532i
$940$	10.8171	−	18.4957i	0.352816	−	0.603262i
$941$	1.73378	+	8.15677i	0.0565195	+	0.265903i	0.997330	−	0.0730306i	$-0.0232671\pi$
$941$	1.73378	+	8.15677i	0.0565195	+	0.265903i	−0.940810	+	0.338934i	$0.889934\pi$
$942$	12.0482	+	14.8783i	0.392552	+	0.484762i
$943$	5.64454	+	21.0657i	0.183812	+	0.685994i
$944$	6.59521	+	4.79170i	0.214656	+	0.155956i
$945$	25.3507	+	16.7348i	0.824657	+	0.544383i
$946$	20.2602	−	14.7199i	0.658715	−	0.478584i
$947$	15.3219	+	12.4074i	0.497895	+	0.403187i	0.845105	−	0.534600i	$-0.179538\pi$
$947$	15.3219	+	12.4074i	0.497895	+	0.403187i	−0.347210	+	0.937787i	$0.612871\pi$
$948$	0.715711	+	13.6566i	0.0232452	+	0.443545i
$949$	1.40027	−	0.808446i	0.0454547	−	0.0262433i
$950$	22.2130	+	35.0592i	0.720684	+	1.13747i
$951$			19.0225i			0.616846i
$952$	−0.376181	−	2.40471i	−0.0121921	−	0.0779370i
$953$	19.2473	+	3.04848i	0.623482	+	0.0987498i	0.460179	−	0.887826i	$-0.347785\pi$
$953$	19.2473	+	3.04848i	0.623482	+	0.0987498i	0.163303	+	0.986576i	$0.447785\pi$
$954$	14.0917	−	1.48110i	0.456237	−	0.0479524i
$955$	4.46797	−	16.3085i	0.144580	−	0.527731i
$956$	−2.09413	+	19.9243i	−0.0677290	+	0.644399i
$957$	14.5104	−	3.88806i	0.469056	−	0.125683i
$958$	12.6539	−	2.00418i	0.408829	−	0.0647522i
$959$	2.58826	−	0.835539i	0.0835794	−	0.0269809i
$960$	2.22267	+	0.735988i	0.0717364	+	0.0237539i
$961$	−27.0402	−	5.74756i	−0.872263	−	0.185405i
$962$	0.829845	+	0.538907i	0.0267553	+	0.0173751i
$963$	22.2517	+	14.4504i	0.717051	+	0.465658i
$964$	22.4564	+	4.77325i	0.723271	+	0.153736i
$965$	−6.59518	+	2.10211i	−0.212306	+	0.0676693i
$966$	4.72730	+	4.27278i	0.152098	+	0.137475i
$967$	−50.4847	+	7.99599i	−1.62348	+	0.257134i	−0.900859	−	0.434113i	$-0.857062\pi$
$967$	−50.4847	+	7.99599i	−1.62348	+	0.257134i	−0.722619	+	0.691246i	$0.757062\pi$
$968$	3.28896	−	0.881273i	0.105711	−	0.0283252i
$969$	−0.835791	+	7.95202i	−0.0268495	+	0.255456i
$970$	−0.875781	−	0.575743i	−0.0281196	−	0.0184860i
$971$	25.2494	−	2.65382i	0.810292	−	0.0851651i	0.309684	−	0.950839i	$-0.399777\pi$
$971$	25.2494	−	2.65382i	0.810292	−	0.0851651i	0.500607	+	0.865674i	$0.333110\pi$
$972$	15.5599	+	2.46444i	0.499083	+	0.0790470i
$973$	18.3391	−	47.5049i	0.587926	−	1.52294i
$974$			33.3304i			1.06798i
$975$	5.84385	−	2.52374i	0.187153	−	0.0808245i
$976$	3.23025	−	1.86499i	0.103398	−	0.0596968i
$977$	1.65931	+	31.6615i	0.0530860	+	1.01294i	0.887211	+	0.461365i	$0.152640\pi$
$977$	1.65931	+	31.6615i	0.0530860	+	1.01294i	−0.834125	+	0.551576i	$0.814027\pi$
$978$	13.6778	+	11.0760i	0.437366	+	0.354172i
$979$	−27.0650	+	19.6639i	−0.865002	+	0.628461i
$980$	5.47161	+	14.6650i	0.174784	+	0.468455i
$981$	−9.66305	−	7.02061i	−0.308517	−	0.224151i
$982$	0.304416	+	1.13610i	0.00971431	+	0.0362543i
$983$	−26.6634	−	32.9265i	−0.850429	−	1.05019i	−0.998128	−	0.0611601i	$-0.980520\pi$
$983$	−26.6634	−	32.9265i	−0.850429	−	1.05019i	0.147699	−	0.989032i	$-0.452813\pi$
$984$	−2.06415	−	9.71105i	−0.0658026	−	0.309577i
$985$	−18.0183	+	7.90157i	−0.574112	+	0.251765i
$986$	4.55469	−	1.47991i	0.145051	−	0.0471299i
$987$	−22.2909	+	14.4156i	−0.709526	+	0.458855i
$988$	8.99249	−	4.58190i	0.286089	−	0.145770i
$989$	−4.34563	+	20.4446i	−0.138183	+	0.650100i
$990$	4.83134	−	10.6897i	0.153550	−	0.339741i
$991$	−7.14112	+	1.51789i	−0.226845	+	0.0482174i	−0.319932	−	0.947441i	$-0.603660\pi$
$991$	−7.14112	+	1.51789i	−0.226845	+	0.0482174i	0.0930866	+	0.995658i	$0.470327\pi$
$992$	−1.71020	−	0.656483i	−0.0542988	−	0.0208434i
$993$	16.0989	−	16.0989i	0.510882	−	0.510882i
$994$	−12.5129	+	7.19264i	−0.396886	+	0.228137i
$995$	−2.56631	+	4.96764i	−0.0813576	+	0.157485i
$996$	0.884802	+	8.41833i	0.0280360	+	0.266745i
$997$	−10.0176	−	26.0968i	−0.317261	−	0.826493i	−0.995768	−	0.0918996i	$-0.970706\pi$
$997$	−10.0176	−	26.0968i	−0.317261	−	0.826493i	0.678507	−	0.734594i	$-0.262627\pi$
$998$	32.7476	−	1.71623i	1.03661	−	0.0543263i
$999$	2.08926	−	3.61870i	0.0661012	−	0.114491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.x.a.33.15	✓	320
7.3	odd	6	inner	350.2.x.a.283.15	yes	320
25.22	odd	20	inner	350.2.x.a.47.15	yes	320
175.122	even	60	inner	350.2.x.a.297.15	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.x.a.33.15	✓	320	1.1	even	1	trivial
350.2.x.a.47.15	yes	320	25.22	odd	20	inner
350.2.x.a.283.15	yes	320	7.3	odd	6	inner
350.2.x.a.297.15	yes	320	175.122	even	60	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.838671 - 0.544639i) q^{2} +(-0.977539 + 0.375242i) q^{3} +(0.406737 - 0.913545i) q^{4} +(1.20732 + 1.88212i) q^{5} +(-0.615462 + 0.847110i) q^{6} +(2.05296 + 1.66893i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.41466 + 1.27376i) q^{9} +O(q^{10})\)	\(q+(0.838671 - 0.544639i) q^{2} +(-0.977539 + 0.375242i) q^{3} +(0.406737 - 0.913545i) q^{4} +(1.20732 + 1.88212i) q^{5} +(-0.615462 + 0.847110i) q^{6} +(2.05296 + 1.66893i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.41466 + 1.27376i) q^{9} +(2.03762 + 0.920926i) q^{10} +(-1.84406 + 2.04804i) q^{11} +(-0.0548003 + 1.04565i) q^{12} +(0.551987 + 1.08333i) q^{13} +(2.63073 + 0.281560i) q^{14} +(-1.88645 - 1.38681i) q^{15} +(-0.669131 - 0.743145i) q^{16} +(0.714934 - 0.578942i) q^{17} +(-0.492691 + 1.83875i) q^{18} +(7.58312 - 3.37622i) q^{19} +(2.21046 - 0.337414i) q^{20} +(-2.63311 - 0.861088i) q^{21} +(-0.431119 + 2.72198i) q^{22} +(-1.25274 - 1.92905i) q^{23} +(0.523543 + 0.906803i) q^{24} +(-2.08476 + 4.54464i) q^{25} +(1.05296 + 0.607927i) q^{26} +(2.33102 - 4.57488i) q^{27} +(2.35966 - 1.19666i) q^{28} +(3.05991 + 4.21160i) q^{29} +(-2.33742 - 0.135640i) q^{30} +(1.82183 + 0.191482i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(1.03413 - 2.69401i) q^{33} +(0.284280 - 0.874923i) q^{34} +(-0.662548 + 5.87886i) q^{35} +(0.588248 + 1.81044i) q^{36} +(0.812696 + 0.0425916i) q^{37} +(4.52091 - 6.96160i) q^{38} +(-0.946101 - 0.851873i) q^{39} +(1.67008 - 1.48688i) q^{40} +(-9.01749 - 2.92996i) q^{41} +(-2.67729 + 0.711923i) q^{42} +(-6.42548 - 6.42548i) q^{43} +(1.12093 + 2.51765i) q^{44} +(-4.10532 - 1.12472i) q^{45} +(-2.10128 - 0.935549i) q^{46} +(6.03032 - 7.44683i) q^{47} +(0.932961 + 0.475367i) q^{48} +(1.42933 + 6.85252i) q^{49} +(0.726766 + 4.94690i) q^{50} +(-0.481632 + 0.834212i) q^{51} +(1.21419 - 0.0636329i) q^{52} +(-2.66748 - 6.94902i) q^{53} +(-0.536702 - 5.10638i) q^{54} +(-6.08103 - 0.998110i) q^{55} +(1.32723 - 2.28877i) q^{56} +(-6.14589 + 6.14589i) q^{57} +(4.86006 + 1.86560i) q^{58} +(-7.97398 + 1.69492i) q^{59} +(-2.03420 + 1.15929i) q^{60} +(-0.775505 + 3.64847i) q^{61} +(1.63221 - 0.831651i) q^{62} +(-5.03007 + 0.254023i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-1.37254 + 2.34684i) q^{65} +(-0.599965 - 2.82261i) q^{66} +(-8.29271 - 10.2406i) q^{67} +(-0.238100 - 0.888602i) q^{68} +(1.94847 + 1.41564i) q^{69} +(2.64620 + 5.29128i) q^{70} +(-4.41328 + 3.20643i) q^{71} +(1.47938 + 1.19798i) q^{72} +(-0.0695984 - 1.32802i) q^{73} +(0.704781 - 0.406906i) q^{74} +(0.332590 - 5.22486i) q^{75} -8.30075i q^{76} +(-7.20383 + 1.12693i) q^{77} +(-1.25743 - 0.199157i) q^{78} +(12.9888 - 1.36518i) q^{79} +(0.590834 - 2.15660i) q^{80} +(0.0349716 - 0.332733i) q^{81} +(-9.15847 + 2.45401i) q^{82} +(7.98452 - 1.26462i) q^{83} +(-1.85762 + 2.05523i) q^{84} +(1.95279 + 0.646624i) q^{85} +(-8.88843 - 1.88929i) q^{86} +(-4.57155 - 2.96880i) q^{87} +(2.31130 + 1.50097i) q^{88} +(11.8738 + 2.52386i) q^{89} +(-4.05558 + 1.29265i) q^{90} +(-0.674804 + 3.14528i) q^{91} +(-2.27182 + 0.359820i) q^{92} +(-1.85277 + 0.496447i) q^{93} +(1.00162 - 9.52978i) q^{94} +(15.5097 + 10.1962i) q^{95} +(1.04135 - 0.109450i) q^{96} +(-0.462945 - 0.0733233i) q^{97} +(4.93088 + 4.96854i) q^{98} -5.24617i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 12 q^{5} - 8 q^{7}+O(q^{10}) \) 320 * q + 12 * q^5 - 8 * q^7	\( 320 q + 12 q^{5} - 8 q^{7} + 12 q^{10} - 16 q^{15} - 40 q^{16} + 36 q^{17} + 8 q^{18} - 72 q^{22} + 44 q^{23} - 12 q^{25} - 24 q^{28} - 80 q^{29} + 20 q^{30} - 48 q^{33} - 28 q^{35} + 80 q^{36} - 4 q^{37} - 24 q^{38} - 40 q^{39} - 36 q^{42} + 88 q^{43} - 228 q^{45} - 12 q^{47} + 32 q^{50} - 52 q^{53} + 152 q^{57} + 32 q^{58} - 120 q^{59} - 8 q^{60} + 136 q^{63} + 8 q^{65} - 32 q^{67} - 144 q^{68} + 92 q^{70} + 8 q^{72} + 12 q^{73} - 432 q^{75} + 144 q^{77} - 16 q^{78} + 12 q^{80} - 40 q^{81} - 192 q^{82} + 60 q^{84} - 24 q^{85} + 24 q^{87} + 4 q^{88} - 300 q^{89} - 8 q^{92} - 68 q^{93} + 20 q^{95} - 40 q^{98}+O(q^{100}) \) 320 * q + 12 * q^5 - 8 * q^7 + 12 * q^10 - 16 * q^15 - 40 * q^16 + 36 * q^17 + 8 * q^18 - 72 * q^22 + 44 * q^23 - 12 * q^25 - 24 * q^28 - 80 * q^29 + 20 * q^30 - 48 * q^33 - 28 * q^35 + 80 * q^36 - 4 * q^37 - 24 * q^38 - 40 * q^39 - 36 * q^42 + 88 * q^43 - 228 * q^45 - 12 * q^47 + 32 * q^50 - 52 * q^53 + 152 * q^57 + 32 * q^58 - 120 * q^59 - 8 * q^60 + 136 * q^63 + 8 * q^65 - 32 * q^67 - 144 * q^68 + 92 * q^70 + 8 * q^72 + 12 * q^73 - 432 * q^75 + 144 * q^77 - 16 * q^78 + 12 * q^80 - 40 * q^81 - 192 * q^82 + 60 * q^84 - 24 * q^85 + 24 * q^87 + 4 * q^88 - 300 * q^89 - 8 * q^92 - 68 * q^93 + 20 * q^95 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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