LMFDB - Embedded newform 671.2.f.a.538.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(538,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("671.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.f (of order $4$, degree $2$, 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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			538.19
Character	$\chi$	$=$	671.538
Dual form			671.2.f.a.560.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.774186 - 0.774186i) q^{2} -1.40798i q^{3} -0.801272i q^{4} -0.371549i q^{5} +(-1.09004 + 1.09004i) q^{6} +(3.30218 + 3.30218i) q^{7} +(-2.16871 + 2.16871i) q^{8} +1.01760 q^{9} +O(q^{10})$	\(q+(-0.774186 - 0.774186i) q^{2} -1.40798i q^{3} -0.801272i q^{4} -0.371549i q^{5} +(-1.09004 + 1.09004i) q^{6} +(3.30218 + 3.30218i) q^{7} +(-2.16871 + 2.16871i) q^{8} +1.01760 q^{9} +(-0.287648 + 0.287648i) q^{10} +(1.91820 - 2.70565i) q^{11} -1.12817 q^{12} +0.101215i q^{13} -5.11300i q^{14} -0.523133 q^{15} +1.75542 q^{16} +(3.81724 - 3.81724i) q^{17} +(-0.787811 - 0.787811i) q^{18} +5.24033 q^{19} -0.297712 q^{20} +(4.64940 - 4.64940i) q^{21} +(-3.57971 + 0.609630i) q^{22} +(-1.70544 + 1.70544i) q^{23} +(3.05349 + 3.05349i) q^{24} +4.86195 q^{25} +(0.0783590 - 0.0783590i) q^{26} -5.65669i q^{27} +(2.64595 - 2.64595i) q^{28} +(-6.52012 + 6.52012i) q^{29} +(0.405002 + 0.405002i) q^{30} +(2.43475 + 2.43475i) q^{31} +(2.97839 + 2.97839i) q^{32} +(-3.80949 - 2.70078i) q^{33} -5.91051 q^{34} +(1.22692 - 1.22692i) q^{35} -0.815374i q^{36} +(-7.09244 - 7.09244i) q^{37} +(-4.05699 - 4.05699i) q^{38} +0.142508 q^{39} +(0.805780 + 0.805780i) q^{40} -10.8623 q^{41} -7.19899 q^{42} +(-2.48056 + 2.48056i) q^{43} +(-2.16796 - 1.53700i) q^{44} -0.378088i q^{45} +2.64066 q^{46} +0.313001 q^{47} -2.47159i q^{48} +14.8088i q^{49} +(-3.76405 - 3.76405i) q^{50} +(-5.37459 - 5.37459i) q^{51} +0.0811006 q^{52} +(8.16523 - 8.16523i) q^{53} +(-4.37933 + 4.37933i) q^{54} +(-1.00528 - 0.712704i) q^{55} -14.3229 q^{56} -7.37827i q^{57} +10.0956 q^{58} +(-1.43992 - 1.43992i) q^{59} +0.419172i q^{60} +(-0.344328 + 7.80266i) q^{61} -3.76990i q^{62} +(3.36029 + 3.36029i) q^{63} -8.12249i q^{64} +0.0376062 q^{65} +(0.858346 + 5.04016i) q^{66} +(-4.72154 - 4.72154i) q^{67} +(-3.05865 - 3.05865i) q^{68} +(2.40123 + 2.40123i) q^{69} -1.89973 q^{70} +(-0.00273624 - 0.00273624i) q^{71} +(-2.20687 + 2.20687i) q^{72} +2.00110i q^{73} +10.9817i q^{74} -6.84552i q^{75} -4.19893i q^{76} +(15.2688 - 2.60029i) q^{77} +(-0.110328 - 0.110328i) q^{78} +(2.66214 + 2.66214i) q^{79} -0.652224i q^{80} -4.91170 q^{81} +(8.40943 + 8.40943i) q^{82} -9.69784i q^{83} +(-3.72543 - 3.72543i) q^{84} +(-1.41829 - 1.41829i) q^{85} +3.84083 q^{86} +(9.18018 + 9.18018i) q^{87} +(1.70774 + 10.0278i) q^{88} +(7.96667 + 7.96667i) q^{89} +(-0.292710 + 0.292710i) q^{90} +(-0.334229 + 0.334229i) q^{91} +(1.36653 + 1.36653i) q^{92} +(3.42808 - 3.42808i) q^{93} +(-0.242321 - 0.242321i) q^{94} -1.94704i q^{95} +(4.19351 - 4.19351i) q^{96} +2.97817i q^{97} +(11.4648 - 11.4648i) q^{98} +(1.95196 - 2.75326i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 120 q^{9}+O(q^{10}) $ 120 * q - 120 * q^9	$ 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) $ 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.774186	−	0.774186i	−0.547432	−	0.547432i	0.378265	−	0.925697i	$-0.376521\pi$
$2$	−0.774186	−	0.774186i	−0.547432	−	0.547432i	−0.925697	+	0.378265i	$0.876521\pi$
$3$		−	1.40798i		−	0.812896i	−0.913674	−	0.406448i	$-0.866767\pi$
$3$		−	1.40798i		−	0.812896i	0.913674	−	0.406448i	$-0.133233\pi$
$4$		−	0.801272i		−	0.400636i
$5$		−	0.371549i		−	0.166162i	−0.996543	−	0.0830809i	$-0.973524\pi$
$5$		−	0.371549i		−	0.166162i	0.996543	−	0.0830809i	$-0.0264760\pi$
$6$	−1.09004	+	1.09004i	−0.445006	+	0.445006i
$7$	3.30218	+	3.30218i	1.24811	+	1.24811i	0.956555	+	0.291552i	$0.0941715\pi$
$7$	3.30218	+	3.30218i	1.24811	+	1.24811i	0.291552	+	0.956555i	$0.405829\pi$
$8$	−2.16871	+	2.16871i	−0.766753	+	0.766753i
$9$	1.01760			0.339200
$10$	−0.287648	+	0.287648i	−0.0909623	+	0.0909623i
$11$	1.91820	−	2.70565i	0.578359	−	0.815783i
$11$	1.91820	−	2.70565i	0.578359	−	0.815783i
$12$	−1.12817			−0.325676
$13$			0.101215i			0.0280719i	0.999901	+	0.0140360i	$0.00446793\pi$
$13$			0.101215i			0.0280719i	−0.999901	+	0.0140360i	$0.995532\pi$
$14$		−	5.11300i		−	1.36651i
$15$	−0.523133			−0.135072
$16$	1.75542			0.438855
$17$	3.81724	−	3.81724i	0.925817	−	0.925817i	−0.0716157	−	0.997432i	$-0.522816\pi$
$17$	3.81724	−	3.81724i	0.925817	−	0.925817i	0.997432	+	0.0716157i	$0.0228155\pi$
$18$	−0.787811	−	0.787811i	−0.185689	−	0.185689i
$19$	5.24033			1.20222			0.601108	−	0.799168i	$-0.294726\pi$
$19$	5.24033			1.20222			0.601108	+	0.799168i	$0.294726\pi$
$20$	−0.297712			−0.0665704
$21$	4.64940	−	4.64940i	1.01458	−	1.01458i
$22$	−3.57971	+	0.609630i	−0.763198	+	0.129974i
$23$	−1.70544	+	1.70544i	−0.355610	+	0.355610i	−0.862192	−	0.506582i	$-0.830909\pi$
$23$	−1.70544	+	1.70544i	−0.355610	+	0.355610i	0.506582	+	0.862192i	$0.330909\pi$
$24$	3.05349	+	3.05349i	0.623291	+	0.623291i
$25$	4.86195			0.972390
$26$	0.0783590	−	0.0783590i	0.0153675	−	0.0153675i
$27$		−	5.65669i		−	1.08863i
$28$	2.64595	−	2.64595i	0.500037	−	0.500037i
$29$	−6.52012	+	6.52012i	−1.21076	+	1.21076i	−0.239977	+	0.970778i	$0.577140\pi$
$29$	−6.52012	+	6.52012i	−1.21076	+	1.21076i	−0.970778	+	0.239977i	$0.922860\pi$
$30$	0.405002	+	0.405002i	0.0739429	+	0.0739429i
$31$	2.43475	+	2.43475i	0.437295	+	0.437295i	0.891101	−	0.453806i	$-0.149934\pi$
$31$	2.43475	+	2.43475i	0.437295	+	0.437295i	−0.453806	+	0.891101i	$0.649934\pi$
$32$	2.97839	+	2.97839i	0.526510	+	0.526510i
$33$	−3.80949	−	2.70078i	−0.663147	−	0.470146i
$34$	−5.91051			−1.01364
$35$	1.22692	−	1.22692i	0.207388	−	0.207388i
$36$		−	0.815374i		−	0.135896i
$37$	−7.09244	−	7.09244i	−1.16599	−	1.16599i	−0.983141	−	0.182849i	$-0.941468\pi$
$37$	−7.09244	−	7.09244i	−1.16599	−	1.16599i	−0.182849	−	0.983141i	$-0.558532\pi$
$38$	−4.05699	−	4.05699i	−0.658131	−	0.658131i
$39$	0.142508			0.0228196
$40$	0.805780	+	0.805780i	0.127405	+	0.127405i
$41$	−10.8623			−1.69640			−0.848202	−	0.529673i	$-0.822314\pi$
$41$	−10.8623			−1.69640			−0.848202	+	0.529673i	$0.822314\pi$
$42$	−7.19899			−1.11083
$43$	−2.48056	+	2.48056i	−0.378281	+	0.378281i	−0.870482	−	0.492200i	$-0.836193\pi$
$43$	−2.48056	+	2.48056i	−0.378281	+	0.378281i	0.492200	+	0.870482i	$0.336193\pi$
$44$	−2.16796	−	1.53700i	−0.326832	−	0.231711i
$45$		−	0.378088i		−	0.0563620i
$46$	2.64066			0.389344
$47$	0.313001			0.0456559			0.0228279	−	0.999739i	$-0.492733\pi$
$47$	0.313001			0.0456559			0.0228279	+	0.999739i	$0.492733\pi$
$48$		−	2.47159i		−	0.356743i
$49$			14.8088i			2.11554i
$50$	−3.76405	−	3.76405i	−0.532318	−	0.532318i
$51$	−5.37459	−	5.37459i	−0.752593	−	0.752593i
$52$	0.0811006			0.0112466
$53$	8.16523	−	8.16523i	1.12158	−	1.12158i	0.130076	−	0.991504i	$-0.458478\pi$
$53$	8.16523	−	8.16523i	1.12158	−	1.12158i	0.991504	−	0.130076i	$-0.0415222\pi$
$54$	−4.37933	+	4.37933i	−0.595951	+	0.595951i
$55$	−1.00528	−	0.712704i	−0.135552	−	0.0961011i
$56$	−14.3229			−1.91398
$57$		−	7.37827i		−	0.977276i
$58$	10.0956			1.32561
$59$	−1.43992	−	1.43992i	−0.187461	−	0.187461i	0.607136	−	0.794598i	$-0.292318\pi$
$59$	−1.43992	−	1.43992i	−0.187461	−	0.187461i	−0.794598	+	0.607136i	$0.792318\pi$
$60$			0.419172i			0.0541148i
$61$	−0.344328	+	7.80266i	−0.0440867	+	0.999028i
$61$	−0.344328	+	7.80266i	−0.0440867	+	0.999028i
$62$		−	3.76990i		−	0.478778i
$63$	3.36029	+	3.36029i	0.423357	+	0.423357i
$64$		−	8.12249i		−	1.01531i
$65$	0.0376062			0.00466448
$66$	0.858346	+	5.04016i	0.105655	+	0.620401i
$67$	−4.72154	−	4.72154i	−0.576828	−	0.576828i	0.357200	−	0.934028i	$-0.383731\pi$
$67$	−4.72154	−	4.72154i	−0.576828	−	0.576828i	−0.934028	+	0.357200i	$0.883731\pi$
$68$	−3.05865	−	3.05865i	−0.370916	−	0.370916i
$69$	2.40123	+	2.40123i	0.289074	+	0.289074i
$70$	−1.89973			−0.227061
$71$	−0.00273624	−	0.00273624i	−0.000324732	−	0.000324732i	0.706944	−	0.707269i	$-0.250073\pi$
$71$	−0.00273624	−	0.00273624i	−0.000324732	−	0.000324732i	−0.707269	+	0.706944i	$0.750073\pi$
$72$	−2.20687	+	2.20687i	−0.260082	+	0.260082i
$73$			2.00110i			0.234211i	0.993119	+	0.117106i	$0.0373616\pi$
$73$			2.00110i			0.234211i	−0.993119	+	0.117106i	$0.962638\pi$
$74$			10.9817i			1.27660i
$75$		−	6.84552i		−	0.790452i
$76$		−	4.19893i		−	0.481651i
$77$	15.2688	−	2.60029i	1.74004	−	0.296331i
$78$	−0.110328	−	0.110328i	−0.0124922	−	0.0124922i
$79$	2.66214	+	2.66214i	0.299514	+	0.299514i	0.840824	−	0.541309i	$-0.182071\pi$
$79$	2.66214	+	2.66214i	0.299514	+	0.299514i	−0.541309	+	0.840824i	$0.682071\pi$
$80$		−	0.652224i		−	0.0729208i
$81$	−4.91170			−0.545744
$82$	8.40943	+	8.40943i	0.928666	+	0.928666i
$83$		−	9.69784i		−	1.06448i	−0.846595	−	0.532238i	$-0.821351\pi$
$83$		−	9.69784i		−	1.06448i	0.846595	−	0.532238i	$-0.178649\pi$
$84$	−3.72543	−	3.72543i	−0.406478	−	0.406478i
$85$	−1.41829	−	1.41829i	−0.153835	−	0.153835i
$86$	3.84083			0.414167
$87$	9.18018	+	9.18018i	0.984219	+	0.984219i
$88$	1.70774	+	10.0278i	0.182046	+	1.06896i
$89$	7.96667	+	7.96667i	0.844465	+	0.844465i	0.989436	−	0.144971i	$-0.0463089\pi$
$89$	7.96667	+	7.96667i	0.844465	+	0.844465i	−0.144971	+	0.989436i	$0.546309\pi$
$90$	−0.292710	+	0.292710i	−0.0308544	+	0.0308544i
$91$	−0.334229	+	0.334229i	−0.0350367	+	0.0350367i
$92$	1.36653	+	1.36653i	0.142470	+	0.142470i
$93$	3.42808	−	3.42808i	0.355475	−	0.355475i
$94$	−0.242321	−	0.242321i	−0.0249935	−	0.0249935i
$95$		−	1.94704i		−	0.199762i
$96$	4.19351	−	4.19351i	0.427998	−	0.427998i
$97$			2.97817i			0.302387i	0.988504	+	0.151193i	$0.0483117\pi$
$97$			2.97817i			0.302387i	−0.988504	+	0.151193i	$0.951688\pi$
$98$	11.4648	−	11.4648i	1.15811	−	1.15811i
$99$	1.95196	−	2.75326i	0.196179	−	0.276713i
$100$		−	3.89575i		−	0.389575i
$101$	−1.16321	−	1.16321i	−0.115744	−	0.115744i	0.646862	−	0.762607i	$-0.276081\pi$
$101$	−1.16321	−	1.16321i	−0.115744	−	0.115744i	−0.762607	+	0.646862i	$0.776081\pi$
$102$			8.32186i			0.823987i
$103$	−3.95148			−0.389351			−0.194676	−	0.980868i	$-0.562365\pi$
$103$	−3.95148			−0.389351			−0.194676	+	0.980868i	$0.562365\pi$
$104$	−0.219505	−	0.219505i	−0.0215242	−	0.0215242i
$105$	−1.72748	−	1.72748i	−0.168585	−	0.168585i
$106$	−12.6428			−1.22798
$107$	−6.73882			−0.651466			−0.325733	−	0.945462i	$-0.605611\pi$
$107$	−6.73882			−0.651466			−0.325733	+	0.945462i	$0.605611\pi$
$108$	−4.53255			−0.436145
$109$	3.79794			0.363777			0.181888	−	0.983319i	$-0.441779\pi$
$109$	3.79794			0.363777			0.181888	+	0.983319i	$0.441779\pi$
$110$	0.226507	+	1.33004i	0.0215966	+	0.126814i
$111$	−9.98600	+	9.98600i	−0.947829	+	0.947829i
$112$	5.79671	+	5.79671i	0.547737	+	0.547737i
$113$		−	10.8764i		−	1.02317i	−0.859233	−	0.511584i	$-0.829059\pi$
$113$		−	10.8764i		−	1.02317i	0.859233	−	0.511584i	$-0.170941\pi$
$114$	−5.71216	+	5.71216i	−0.534992	+	0.534992i
$115$	0.633656	+	0.633656i	0.0590887	+	0.0590887i
$116$	5.22439	+	5.22439i	0.485073	+	0.485073i
$117$			0.102996i			0.00952198i
$118$			2.22953i			0.205245i
$119$	25.2104			2.31104
$120$	1.13452	−	1.13452i	0.103567	−	0.103567i
$121$	−3.64103	−	10.3799i	−0.331003	−	0.943630i
$122$	6.30728	−	5.77413i	0.571034	−	0.522765i
$123$			15.2938i			1.37900i
$124$	1.95090	−	1.95090i	0.175196	−	0.175196i
$125$		−	3.66420i		−	0.327736i
$126$		−	5.20298i		−	0.463519i
$127$	−18.7251			−1.66158			−0.830790	−	0.556586i	$-0.812111\pi$
$127$	−18.7251			−1.66158			−0.830790	+	0.556586i	$0.812111\pi$
$128$	−0.331537	+	0.331537i	−0.0293040	+	0.0293040i
$129$	3.49257	+	3.49257i	0.307504	+	0.307504i
$130$	−0.0291142	−	0.0291142i	−0.00255348	−	0.00255348i
$131$		−	0.675068i		−	0.0589809i	−0.999565	−	0.0294905i	$-0.990612\pi$
$131$		−	0.675068i		−	0.0589809i	0.999565	−	0.0294905i	$-0.00938847\pi$
$132$	−2.16406	+	3.05244i	−0.188357	+	0.265681i
$133$	17.3045	+	17.3045i	1.50049	+	1.50049i
$134$			7.31070i			0.631548i
$135$	−2.10174			−0.180889
$136$			16.5569i			1.41975i
$137$	−17.6554			−1.50840			−0.754202	−	0.656642i	$-0.771976\pi$
$137$	−17.6554			−1.50840			−0.754202	+	0.656642i	$0.771976\pi$
$138$		−	3.71799i		−	0.316497i
$139$	−2.93614	+	2.93614i	−0.249040	+	0.249040i	−0.820577	−	0.571536i	$-0.806348\pi$
$139$	−2.93614	+	2.93614i	−0.249040	+	0.249040i	0.571536	+	0.820577i	$0.306348\pi$
$140$	−0.983098	−	0.983098i	−0.0830870	−	0.0830870i
$141$		−	0.440699i		−	0.0371135i
$142$			0.00423672i			0.000355538i
$143$	0.273851	+	0.194150i	0.0229006	+	0.0162356i
$144$	1.78631			0.148859
$145$	2.42254	+	2.42254i	0.201181	+	0.201181i
$146$	1.54923	−	1.54923i	0.128215	−	0.128215i
$147$	20.8504			1.71972
$148$	−5.68298	+	5.68298i	−0.467138	+	0.467138i
$149$	−6.60297			−0.540936			−0.270468	−	0.962729i	$-0.587178\pi$
$149$	−6.60297			−0.540936			−0.270468	+	0.962729i	$0.587178\pi$
$150$	−5.29970	+	5.29970i	−0.432719	+	0.432719i
$151$	8.34867	−	8.34867i	0.679405	−	0.679405i	−0.280461	−	0.959866i	$-0.590487\pi$
$151$	8.34867	−	8.34867i	0.679405	−	0.679405i	0.959866	+	0.280461i	$0.0904872\pi$
$152$	−11.3647	+	11.3647i	−0.921802	+	0.921802i
$153$	3.88442	−	3.88442i	0.314037	−	0.314037i
$154$	−13.8340	−	9.80775i	−1.11477	−	0.790331i
$155$	0.904630	−	0.904630i	0.0726616	−	0.0726616i
$156$		−	0.114188i		−	0.00914234i
$157$	6.38943	+	6.38943i	0.509932	+	0.509932i	0.914505	−	0.404573i	$-0.132580\pi$
$157$	6.38943	+	6.38943i	0.509932	+	0.509932i	−0.404573	+	0.914505i	$0.632580\pi$
$158$		−	4.12199i		−	0.327928i
$159$	−11.4965	−	11.4965i	−0.911729	−	0.911729i
$160$	1.10662	−	1.10662i	0.0874858	−	0.0874858i
$161$	−11.2634			−0.887678
$162$	3.80257	+	3.80257i	0.298758	+	0.298758i
$163$			18.8035i			1.47281i	0.676544	+	0.736403i	$0.263477\pi$
$163$			18.8035i			1.47281i	−0.676544	+	0.736403i	$0.736523\pi$
$164$			8.70365i			0.679640i
$165$	−1.00347	+	1.41541i	−0.0781202	+	0.110190i
$166$	−7.50793	+	7.50793i	−0.582728	+	0.582728i
$167$	0.398192			0.0308130			0.0154065	−	0.999881i	$-0.495096\pi$
$167$	0.398192			0.0308130			0.0154065	+	0.999881i	$0.495096\pi$
$168$			20.1663i			1.55587i
$169$	12.9898			0.999212
$170$			2.19604i			0.168429i
$171$	5.33256			0.407791
$172$	1.98760	+	1.98760i	0.151553	+	0.151553i
$173$	3.94306	+	3.94306i	0.299785	+	0.299785i	0.840930	−	0.541144i	$-0.182009\pi$
$173$	3.94306	+	3.94306i	0.299785	+	0.299785i	−0.541144	+	0.840930i	$0.682009\pi$
$174$		−	14.2143i		−	1.07759i
$175$	16.0550	+	16.0550i	1.21365	+	1.21365i
$176$	3.36724	−	4.74954i	0.253815	−	0.358010i
$177$	−2.02737	+	2.02737i	−0.152387	+	0.152387i
$178$		−	12.3354i		−	0.924574i
$179$	−7.38239			−0.551786			−0.275893	−	0.961188i	$-0.588974\pi$
$179$	−7.38239			−0.551786			−0.275893	+	0.961188i	$0.588974\pi$
$180$	−0.302951			−0.0225806
$181$	8.15194	+	8.15194i	0.605929	+	0.605929i	0.941880	−	0.335951i	$-0.109058\pi$
$181$	8.15194	+	8.15194i	0.605929	+	0.605929i	−0.335951	+	0.941880i	$0.609058\pi$
$182$	0.517511			0.0383605
$183$	10.9860	+	0.484806i	0.812106	+	0.0358379i
$184$		−	7.39721i		−	0.545330i
$185$	−2.63519	+	2.63519i	−0.193743	+	0.193743i
$186$	−5.30794			−0.389197
$187$	−3.00587	−	17.6503i	−0.219811	−	1.29072i
$188$		−	0.250799i		−	0.0182914i
$189$	18.6794	−	18.6794i	1.35873	−	1.35873i
$190$	−1.50737	+	1.50737i	−0.109356	+	0.109356i
$191$	10.6613	+	10.6613i	0.771424	+	0.771424i	0.978356	−	0.206931i	$-0.0663476\pi$
$191$	10.6613	+	10.6613i	0.771424	+	0.771424i	−0.206931	+	0.978356i	$0.566348\pi$
$192$	−11.4363			−0.825343
$193$	11.9410	−	11.9410i	0.859529	−	0.859529i	−0.131754	−	0.991282i	$-0.542061\pi$
$193$	11.9410	−	11.9410i	0.859529	−	0.859529i	0.991282	+	0.131754i	$0.0420608\pi$
$194$	2.30565	−	2.30565i	0.165536	−	0.165536i
$195$		−	0.0529487i		−	0.00379174i
$196$	11.8659			0.847562
$197$	1.97250			0.140535			0.0702673	−	0.997528i	$-0.477615\pi$
$197$	1.97250			0.140535			0.0702673	+	0.997528i	$0.477615\pi$
$198$	−3.64271	+	0.620359i	−0.258876	+	0.0440870i
$199$	11.8670			0.841228			0.420614	−	0.907240i	$-0.361815\pi$
$199$	11.8670			0.841228			0.420614	+	0.907240i	$0.361815\pi$
$200$	−10.5441	+	10.5441i	−0.745583	+	0.745583i
$201$	−6.64782	+	6.64782i	−0.468901	+	0.468901i
$202$			1.80109i			0.126724i
$203$	−43.0612			−3.02231
$204$	−4.30651	+	4.30651i	−0.301516	+	0.301516i
$205$			4.03587i			0.281877i
$206$	3.05918	+	3.05918i	0.213143	+	0.213143i
$207$	−1.73546	+	1.73546i	−0.120623	+	0.120623i
$208$			0.177674i			0.0123195i
$209$	10.0520	−	14.1785i	0.695311	−	0.980746i
$210$			2.67478i			0.184577i
$211$	8.97962	−	8.97962i	0.618183	−	0.618183i	−0.326882	−	0.945065i	$-0.605998\pi$
$211$	8.97962	−	8.97962i	0.618183	−	0.618183i	0.945065	+	0.326882i	$0.105998\pi$
$212$	−6.54257	−	6.54257i	−0.449346	−	0.449346i
$213$	−0.00385257	+	0.00385257i	−0.000263974	+	0.000263974i
$214$	5.21710	+	5.21710i	0.356634	+	0.356634i
$215$	0.921648	+	0.921648i	0.0628559	+	0.0628559i
$216$	12.2677	+	12.2677i	0.834711	+	0.834711i
$217$			16.0800i			1.09158i
$218$	−2.94031	−	2.94031i	−0.199143	−	0.199143i
$219$	2.81751			0.190390
$220$	−0.571070	+	0.805503i	−0.0385016	+	0.0543070i
$221$	0.386361	+	0.386361i	0.0259894	+	0.0259894i
$222$	15.4620			1.03774
$223$	−11.3700	+	11.3700i	−0.761391	+	0.761391i	−0.976574	−	0.215183i	$-0.930965\pi$
$223$	−11.3700	+	11.3700i	−0.761391	+	0.761391i	0.215183	+	0.976574i	$0.430965\pi$
$224$			19.6704i			1.31428i
$225$	4.94752			0.329834
$226$	−8.42038	+	8.42038i	−0.560115	+	0.560115i
$227$	−9.40500	−	9.40500i	−0.624232	−	0.624232i	0.322379	−	0.946611i	$-0.395517\pi$
$227$	−9.40500	−	9.40500i	−0.624232	−	0.624232i	−0.946611	+	0.322379i	$0.895517\pi$
$228$	−5.91201			−0.391532
$229$			16.6539i			1.10052i	0.834994	+	0.550259i	$0.185471\pi$
$229$			16.6539i			1.10052i	−0.834994	+	0.550259i	$0.814529\pi$
$230$		−	0.981135i		−	0.0646941i
$231$	−3.66115	−	21.4981i	−0.240886	−	1.41447i
$232$		−	28.2804i		−	1.85670i
$233$	20.9415	+	20.9415i	1.37192	+	1.37192i	0.857591	+	0.514331i	$0.171960\pi$
$233$	20.9415	+	20.9415i	1.37192	+	1.37192i	0.514331	+	0.857591i	$0.328040\pi$
$234$	0.0797380	−	0.0797380i	0.00521264	−	0.00521264i
$235$		−	0.116295i		−	0.00758626i
$236$	−1.15377	+	1.15377i	−0.0751038	+	0.0751038i
$237$	3.74824	−	3.74824i	0.243474	−	0.243474i
$238$	−19.5176	−	19.5176i	−1.26514	−	1.26514i
$239$			11.8169i			0.764369i	0.924086	+	0.382185i	$0.124828\pi$
$239$			11.8169i			0.764369i	−0.924086	+	0.382185i	$0.875172\pi$
$240$	−0.918316			−0.0592771
$241$			13.0195i			0.838661i	0.907834	+	0.419331i	$0.137735\pi$
$241$			13.0195i			0.838661i	−0.907834	+	0.419331i	$0.862265\pi$
$242$	−5.21716	+	10.8548i	−0.335372	+	0.697775i
$243$		−	10.0545i		−	0.644997i
$244$	6.25205	+	0.275900i	0.400247	+	0.0176627i
$245$	5.50219			0.351522
$246$	11.8403	−	11.8403i	0.754909	−	0.754909i
$247$			0.530399i			0.0337485i
$248$	−10.5605			−0.670594
$249$	−13.6543			−0.865309
$250$	−2.83677	+	2.83677i	−0.179413	+	0.179413i
$251$	7.62879	−	7.62879i	0.481525	−	0.481525i	−0.424093	−	0.905618i	$-0.639407\pi$
$251$	7.62879	−	7.62879i	0.481525	−	0.481525i	0.905618	+	0.424093i	$0.139407\pi$
$252$	2.69251	−	2.69251i	0.169612	−	0.169612i
$253$	1.34295	+	7.88571i	0.0844303	+	0.495770i
$254$	14.4967	+	14.4967i	0.909603	+	0.909603i
$255$	−1.99692	+	1.99692i	−0.125052	+	0.125052i
$256$	−15.7316			−0.983228
$257$	−12.3023			−0.767398			−0.383699	−	0.923458i	$-0.625350\pi$
$257$	−12.3023			−0.767398			−0.383699	+	0.923458i	$0.625350\pi$
$258$		−	5.40780i		−	0.336675i
$259$		−	46.8410i		−	2.91056i
$260$		−	0.0301328i		−	0.00186876i
$261$	−6.63487	+	6.63487i	−0.410688	+	0.410688i
$262$	−0.522628	+	0.522628i	−0.0322881	+	0.0322881i
$263$	2.87240			0.177120			0.0885599	−	0.996071i	$-0.471774\pi$
$263$	2.87240			0.177120			0.0885599	+	0.996071i	$0.471774\pi$
$264$	14.1189	−	2.40446i	0.868956	−	0.147984i
$265$	−3.03378	−	3.03378i	−0.186364	−	0.186364i
$266$		−	26.7938i		−	1.64284i
$267$	11.2169	−	11.2169i	0.686462	−	0.686462i
$268$	−3.78324	+	3.78324i	−0.231098	+	0.231098i
$269$	0.741235			0.0451939			0.0225969	−	0.999745i	$-0.492807\pi$
$269$	0.741235			0.0451939			0.0225969	+	0.999745i	$0.492807\pi$
$270$	1.62714	+	1.62714i	0.0990243	+	0.0990243i
$271$	−30.1489			−1.83142			−0.915708	−	0.401845i	$-0.868369\pi$
$271$	−30.1489			−1.83142			−0.915708	+	0.401845i	$0.868369\pi$
$272$	6.70085	−	6.70085i	0.406299	−	0.406299i
$273$	0.470587	+	0.470587i	0.0284812	+	0.0284812i
$274$	13.6686	+	13.6686i	0.825749	+	0.825749i
$275$	9.32619	−	13.1547i	0.562390	−	0.793259i
$276$	1.92404	−	1.92404i	0.115813	−	0.115813i
$277$	3.91585	+	3.91585i	0.235281	+	0.235281i	0.814893	−	0.579612i	$-0.196796\pi$
$277$	3.91585	+	3.91585i	0.235281	+	0.235281i	−0.579612	+	0.814893i	$0.696796\pi$
$278$	4.54624			0.272665
$279$	2.47760	+	2.47760i	0.148330	+	0.148330i
$280$			5.32166i			0.318030i
$281$	−15.5157	+	15.5157i	−0.925586	+	0.925586i	−0.997417	−	0.0718307i	$-0.977116\pi$
$281$	−15.5157	+	15.5157i	−0.925586	+	0.925586i	0.0718307	+	0.997417i	$0.477116\pi$
$282$	−0.341183	+	0.341183i	−0.0203171	+	0.0203171i
$283$	−16.0724			−0.955403			−0.477702	−	0.878522i	$-0.658530\pi$
$283$	−16.0724			−0.955403			−0.477702	+	0.878522i	$0.658530\pi$
$284$	−0.00219247	+	0.00219247i	−0.000130099	+	0.000130099i
$285$	−2.74139			−0.162386
$286$	−0.0617036	−	0.362320i	−0.00364861	−	0.0214244i
$287$	−35.8692	−	35.8692i	−2.11729	−	2.11729i
$288$	3.03081	+	3.03081i	0.178592	+	0.178592i
$289$		−	12.1426i		−	0.714273i
$290$		−	3.75100i		−	0.220266i
$291$	4.19319			0.245809
$292$	1.60343			0.0938335
$293$	−25.8643			−1.51101			−0.755504	−	0.655144i	$-0.772608\pi$
$293$	−25.8643			−1.51101			−0.755504	+	0.655144i	$0.772608\pi$
$294$	−16.1421	−	16.1421i	−0.941427	−	0.941427i
$295$	−0.535000	+	0.535000i	−0.0311489	+	0.0311489i
$296$	30.7628			1.78805
$297$	−15.3050	−	10.8507i	−0.888086	−	0.629619i
$298$	5.11193	+	5.11193i	0.296126	+	0.296126i
$299$	−0.172616	−	0.172616i	−0.00998264	−	0.00998264i
$300$	−5.48513			−0.316684
$301$	−16.3825			−0.944271
$302$	−12.9268			−0.743856
$303$	−1.63778	+	1.63778i	−0.0940880	+	0.0940880i
$304$	9.19898			0.527597
$305$	2.89907	+	0.127935i	0.166000	+	0.00732551i
$306$	−6.01452			−0.343827
$307$	−21.2916	−	21.2916i	−1.21518	−	1.21518i	−0.969301	−	0.245876i	$-0.920924\pi$
$307$	−21.2916	−	21.2916i	−1.21518	−	1.21518i	−0.245876	−	0.969301i	$-0.579076\pi$
$308$	−2.08354	−	12.2344i	−0.118721	−	0.697122i
$309$			5.56360i			0.316502i
$310$	−1.40070			−0.0795546
$311$	−14.1881	−	14.1881i	−0.804535	−	0.804535i	0.179265	−	0.983801i	$-0.442628\pi$
$311$	−14.1881	−	14.1881i	−0.804535	−	0.804535i	−0.983801	+	0.179265i	$0.942628\pi$
$312$	−0.309058	+	0.309058i	−0.0174970	+	0.0174970i
$313$	12.1335	+	12.1335i	0.685827	+	0.685827i	0.961307	−	0.275480i	$-0.0888368\pi$
$313$	12.1335	+	12.1335i	0.685827	+	0.685827i	−0.275480	+	0.961307i	$0.588837\pi$
$314$		−	9.89321i		−	0.558306i
$315$	1.24851	−	1.24851i	0.0703458	−	0.0703458i
$316$	2.13310	−	2.13310i	0.119996	−	0.119996i
$317$	16.2792			0.914330			0.457165	−	0.889382i	$-0.348865\pi$
$317$	16.2792			0.914330			0.457165	+	0.889382i	$0.348865\pi$
$318$			17.8008i			0.998219i
$319$	5.13425	+	30.1480i	0.287463	+	1.68796i
$320$	−3.01790			−0.168706
$321$			9.48811i			0.529575i
$322$	8.71994	+	8.71994i	0.485943	+	0.485943i
$323$	20.0036	−	20.0036i	1.11303	−	1.11303i
$324$			3.93561i			0.218645i
$325$			0.492101i			0.0272969i
$326$	14.5574	−	14.5574i	0.806261	−	0.806261i
$327$		−	5.34742i		−	0.295713i
$328$	23.5571	−	23.5571i	1.30072	−	1.30072i
$329$	1.03359	+	1.03359i	0.0569834	+	0.0569834i
$330$	1.87267	−	0.318917i	0.103087	−	0.0175558i
$331$	18.4239	−	18.4239i	1.01267	−	1.01267i	0.0127498	−	0.999919i	$-0.495942\pi$
$331$	18.4239	−	18.4239i	1.01267	−	1.01267i	0.999919	−	0.0127498i	$-0.00405849\pi$
$332$	−7.77061			−0.426468
$333$	−7.21726	−	7.21726i	−0.395503	−	0.395503i
$334$	−0.308275	−	0.308275i	−0.0168680	−	0.0168680i
$335$	−1.75428	+	1.75428i	−0.0958467	+	0.0958467i
$336$	8.16163	−	8.16163i	0.445254	−	0.445254i
$337$	12.9156	+	12.9156i	0.703557	+	0.703557i	0.965172	−	0.261616i	$-0.0842553\pi$
$337$	12.9156	+	12.9156i	0.703557	+	0.703557i	−0.261616	+	0.965172i	$0.584255\pi$
$338$	−10.0565	−	10.0565i	−0.547001	−	0.547001i
$339$	−15.3138			−0.831730
$340$	−1.13644	+	1.13644i	−0.0616320	+	0.0616320i
$341$	11.2579	−	1.91724i	0.609650	−	0.103824i
$342$	−4.12839	−	4.12839i	−0.223238	−	0.223238i
$343$	−25.7860	+	25.7860i	−1.39231	+	1.39231i
$344$		−	10.7592i		−	0.580097i
$345$	0.892173	−	0.892173i	0.0480330	−	0.0480330i
$346$		−	6.10532i		−	0.328224i
$347$			8.76864i			0.470725i	0.971908	+	0.235363i	$0.0756278\pi$
$347$			8.76864i			0.470725i	−0.971908	+	0.235363i	$0.924372\pi$
$348$	7.35583	−	7.35583i	0.394314	−	0.394314i
$349$	7.63209	+	7.63209i	0.408536	+	0.408536i	0.881228	−	0.472692i	$-0.156718\pi$
$349$	7.63209	+	7.63209i	0.408536	+	0.408536i	−0.472692	+	0.881228i	$0.656718\pi$
$350$		−	24.8592i		−	1.32878i
$351$	0.572540			0.0305599
$352$	13.7716	−	2.34532i	0.734030	−	0.125006i
$353$			35.5183i			1.89045i	0.326420	+	0.945225i	$0.394158\pi$
$353$			35.5183i			1.89045i	−0.326420	+	0.945225i	$0.605842\pi$
$354$	3.13913			0.166843
$355$	−0.00101665	+	0.00101665i	−5.39581e−5	+	5.39581e-5i
$356$	6.38347	−	6.38347i	0.338323	−	0.338323i
$357$		−	35.4957i		−	1.87863i
$358$	5.71534	+	5.71534i	0.302065	+	0.302065i
$359$	−6.05423	+	6.05423i	−0.319530	+	0.319530i	−0.848587	−	0.529056i	$-0.822546\pi$
$359$	−6.05423	+	6.05423i	−0.319530	+	0.319530i	0.529056	+	0.848587i	$0.322546\pi$
$360$	0.819961	+	0.819961i	0.0432157	+	0.0432157i
$361$	8.46110			0.445321
$362$		−	12.6222i		−	0.663410i
$363$	−14.6147	+	5.12649i	−0.767073	+	0.269071i
$364$	0.267809	+	0.267809i	0.0140370	+	0.0140370i
$365$	0.743507			0.0389170
$366$	−8.12985	−	8.88051i	−0.424954	−	0.464192i
$367$	−0.686135			−0.0358160			−0.0179080	−	0.999840i	$-0.505701\pi$
$367$	−0.686135			−0.0358160			−0.0179080	+	0.999840i	$0.505701\pi$
$368$	−2.99377	+	2.99377i	−0.156061	+	0.156061i
$369$	−11.0534			−0.575419
$370$	4.08025			0.212122
$371$	53.9261			2.79970
$372$	−2.74682	−	2.74682i	−0.142416	−	0.142416i
$373$	9.74552	+	9.74552i	0.504604	+	0.504604i	0.912865	−	0.408261i	$-0.133865\pi$
$373$	9.74552	+	9.74552i	0.504604	+	0.504604i	−0.408261	+	0.912865i	$0.633865\pi$
$374$	−11.3375	+	15.9917i	−0.586249	+	0.826913i
$375$	−5.15911			−0.266415
$376$	−0.678807	+	0.678807i	−0.0350068	+	0.0350068i
$377$	−0.659932	−	0.659932i	−0.0339882	−	0.0339882i
$378$	−28.9227			−1.48762
$379$	−17.4821			−0.897993			−0.448997	−	0.893534i	$-0.648218\pi$
$379$	−17.4821			−0.897993			−0.448997	+	0.893534i	$0.648218\pi$
$380$	−1.56011			−0.0800319
$381$			26.3645i			1.35069i
$382$		−	16.5077i		−	0.844605i
$383$	−4.51442	−	4.51442i	−0.230676	−	0.230676i	0.582299	−	0.812975i	$-0.302153\pi$
$383$	−4.51442	−	4.51442i	−0.230676	−	0.230676i	−0.812975	+	0.582299i	$0.802153\pi$
$384$	0.466797	+	0.466797i	0.0238212	+	0.0238212i
$385$	−0.966135	−	5.67309i	−0.0492388	−	0.289128i
$386$	−18.4890			−0.941067
$387$	−2.52421	+	2.52421i	−0.128313	+	0.128313i
$388$	2.38632			0.121147
$389$	−0.826144	+	0.826144i	−0.0418871	+	0.0418871i	−0.727740	−	0.685853i	$-0.759429\pi$
$389$	−0.826144	+	0.826144i	−0.0418871	+	0.0418871i	0.685853	+	0.727740i	$0.259429\pi$
$390$	−0.0409922	+	0.0409922i	−0.00207572	+	0.00207572i
$391$			13.0202i			0.658459i
$392$	−32.1159	−	32.1159i	−1.62210	−	1.62210i
$393$	−0.950480			−0.0479454
$394$	−1.52708	−	1.52708i	−0.0769331	−	0.0769331i
$395$	0.989116	−	0.989116i	0.0497678	−	0.0497678i
$396$	−2.20611	−	1.56405i	−0.110861	−	0.0785964i
$397$	−13.6344	−	13.6344i	−0.684292	−	0.684292i	0.276672	−	0.960964i	$-0.410768\pi$
$397$	−13.6344	−	13.6344i	−0.684292	−	0.684292i	−0.960964	+	0.276672i	$0.910768\pi$
$398$	−9.18725	−	9.18725i	−0.460515	−	0.460515i
$399$	24.3644	−	24.3644i	1.21974	−	1.21974i
$400$	8.53476			0.426738
$401$	17.5886	+	17.5886i	0.878335	+	0.878335i	0.993362	−	0.115027i	$-0.0366955\pi$
$401$	17.5886	+	17.5886i	0.878335	+	0.878335i	−0.115027	+	0.993362i	$0.536696\pi$
$402$	10.2933			0.513383
$403$	−0.246433	+	0.246433i	−0.0122757	+	0.0122757i
$404$	−0.932052	+	0.932052i	−0.0463713	+	0.0463713i
$405$			1.82494i			0.0906818i
$406$	33.3374	+	33.3374i	1.65451	+	1.65451i
$407$	−32.7943	+	5.58492i	−1.62555	+	0.276834i
$408$	23.3118			1.15411
$409$	15.3408	−	15.3408i	0.758554	−	0.758554i	−0.217505	−	0.976059i	$-0.569792\pi$
$409$	15.3408	−	15.3408i	0.758554	−	0.758554i	0.976059	+	0.217505i	$0.0697920\pi$
$410$	3.12451	−	3.12451i	0.154309	−	0.154309i
$411$			24.8584i			1.22618i
$412$			3.16621i			0.155988i
$413$		−	9.50974i		−	0.467944i
$414$	2.68713			0.132065
$415$	−3.60322			−0.176875
$416$	−0.301457	+	0.301457i	−0.0147801	+	0.0147801i
$417$	4.13402	+	4.13402i	0.202444	+	0.202444i
$418$	−18.7589	+	3.19467i	−0.917528	+	0.156256i
$419$	15.0409	−	15.0409i	0.734798	−	0.734798i	−0.236768	−	0.971566i	$-0.576088\pi$
$419$	15.0409	−	15.0409i	0.734798	−	0.734798i	0.971566	+	0.236768i	$0.0760882\pi$
$420$	−1.38418	+	1.38418i	−0.0675411	+	0.0675411i
$421$	−27.1119	+	27.1119i	−1.32135	+	1.32135i	−0.408668	+	0.912683i	$0.634007\pi$
$421$	−27.1119	+	27.1119i	−1.32135	+	1.32135i	−0.912683	+	0.408668i	$0.865993\pi$
$422$	−13.9038			−0.676826
$423$	0.318509			0.0154865
$424$			35.4160i			1.71995i
$425$	18.5592	−	18.5592i	0.900255	−	0.900255i
$426$	0.00596521			0.000289015
$427$	−26.9028	+	24.6287i	−1.30192	+	1.19187i
$428$			5.39963i			0.261001i
$429$	0.273359	−	0.385576i	0.0131979	−	0.0186158i
$430$		−	1.42705i		−	0.0688187i
$431$	35.0315			1.68741			0.843705	−	0.536807i	$-0.180370\pi$
$431$	35.0315			1.68741			0.843705	+	0.536807i	$0.180370\pi$
$432$		−	9.92985i		−	0.477750i
$433$	−20.7608	−	20.7608i	−0.997701	−	0.997701i	0.00229682	−	0.999997i	$-0.499269\pi$
$433$	−20.7608	−	20.7608i	−0.997701	−	0.997701i	−0.999997	+	0.00229682i	$0.999269\pi$
$434$	12.4489	−	12.4489i	0.597566	−	0.597566i
$435$	3.41089	−	3.41089i	0.163540	−	0.163540i
$436$		−	3.04318i		−	0.145742i
$437$	−8.93710	+	8.93710i	−0.427519	+	0.427519i
$438$	−2.18127	−	2.18127i	−0.104225	−	0.104225i
$439$		−	16.7524i		−	0.799550i	−0.916613	−	0.399775i	$-0.869088\pi$
$439$		−	16.7524i		−	0.799550i	0.916613	−	0.399775i	$-0.130912\pi$
$440$	3.72580	−	0.634509i	0.177621	−	0.0302490i
$441$			15.0694i			0.717590i
$442$		−	0.598230i		−	0.0284549i
$443$	18.7976			0.893101			0.446551	−	0.894758i	$-0.352652\pi$
$443$	18.7976			0.893101			0.446551	+	0.894758i	$0.352652\pi$
$444$	8.00150	+	8.00150i	0.379735	+	0.379735i
$445$	2.96001	−	2.96001i	0.140318	−	0.140318i
$446$	17.6050			0.833619
$447$			9.29683i			0.439725i
$448$	26.8219	−	26.8219i	1.26722	−	1.26722i
$449$	−23.1028			−1.09029			−0.545144	−	0.838342i	$-0.683525\pi$
$449$	−23.1028			−1.09029			−0.545144	+	0.838342i	$0.683525\pi$
$450$	−3.83030	−	3.83030i	−0.180562	−	0.180562i
$451$	−20.8360	+	29.3895i	−0.981129	+	1.38390i
$452$	−8.71498			−0.409918
$453$	−11.7547	−	11.7547i	−0.552286	−	0.552286i
$454$			14.5624i			0.683449i
$455$	0.124182	+	0.124182i	0.00582177	+	0.00582177i
$456$	16.0013	+	16.0013i	0.749330	+	0.749330i
$457$	−9.33343	−	9.33343i	−0.436599	−	0.436599i	0.454266	−	0.890866i	$-0.349901\pi$
$457$	−9.33343	−	9.33343i	−0.436599	−	0.436599i	−0.890866	+	0.454266i	$0.849901\pi$
$458$	12.8932	−	12.8932i	0.602459	−	0.602459i
$459$	−21.5929	−	21.5929i	−1.00787	−	1.00787i
$460$	0.507731	−	0.507731i	0.0236731	−	0.0236731i
$461$		−	4.13901i		−	0.192773i	−0.995344	−	0.0963864i	$-0.969272\pi$
$461$		−	4.13901i		−	0.192773i	0.995344	−	0.0963864i	$-0.0307285\pi$
$462$	−13.8091	+	19.4779i	−0.642457	+	0.906195i
$463$			6.23782i			0.289896i	0.989439	+	0.144948i	$0.0463015\pi$
$463$			6.23782i			0.289896i	−0.989439	+	0.144948i	$0.953698\pi$
$464$	−11.4455	+	11.4455i	−0.531346	+	0.531346i
$465$	−1.27370	−	1.27370i	−0.0590664	−	0.0590664i
$466$		−	32.4252i		−	1.50207i
$467$	8.43180	−	8.43180i	0.390177	−	0.390177i	−0.484573	−	0.874751i	$-0.661025\pi$
$467$	8.43180	−	8.43180i	0.390177	−	0.390177i	0.874751	+	0.484573i	$0.161025\pi$
$468$	0.0825278			0.00381485
$469$		−	31.1828i		−	1.43989i
$470$	−0.0900341	+	0.0900341i	−0.00415296	+	0.00415296i
$471$	8.99617	−	8.99617i	0.414522	−	0.414522i
$472$	6.24552			0.287473
$473$	1.95331	+	11.4697i	0.0898132	+	0.527378i
$474$	−5.80367			−0.266571
$475$	25.4782			1.16902
$476$		−	20.2004i		−	0.925884i
$477$	8.30893	−	8.30893i	0.380440	−	0.380440i
$478$	9.14845	−	9.14845i	0.418440	−	0.418440i
$479$	−43.3725			−1.98174			−0.990871	−	0.134812i	$-0.956957\pi$
$479$	−43.3725			−1.98174			−0.990871	+	0.134812i	$0.956957\pi$
$480$	−1.55809	−	1.55809i	−0.0711169	−	0.0711169i
$481$	0.717859	−	0.717859i	0.0327316	−	0.0327316i
$482$	10.0795	−	10.0795i	0.459110	−	0.459110i
$483$			15.8586i			0.721590i
$484$	−8.31715	+	2.91746i	−0.378052	+	0.132612i
$485$	1.10653			0.0502451
$486$	−7.78406	+	7.78406i	−0.353092	+	0.353092i
$487$		−	19.2988i		−	0.874514i	−0.899337	−	0.437257i	$-0.855950\pi$
$487$		−	19.2988i		−	0.874514i	0.899337	−	0.437257i	$-0.144050\pi$
$488$	−16.1749	−	17.6684i	−0.732204	−	0.799811i
$489$	26.4749			1.19724
$490$	−4.25972	−	4.25972i	−0.192434	−	0.192434i
$491$	−26.7014			−1.20502			−0.602508	−	0.798113i	$-0.705832\pi$
$491$	−26.7014			−1.20502			−0.602508	+	0.798113i	$0.705832\pi$
$492$	12.2545			0.552477
$493$			49.7777i			2.24188i
$494$	0.410627	−	0.410627i	0.0184750	−	0.0184750i
$495$	−1.02297	−	0.725247i	−0.0459791	−	0.0325974i
$496$	4.27401	+	4.27401i	0.191909	+	0.191909i
$497$		−	0.0180711i		−	0.000810601i
$498$	10.5710	+	10.5710i	0.473698	+	0.473698i
$499$	−3.57867	−	3.57867i	−0.160203	−	0.160203i	0.622453	−	0.782657i	$-0.286136\pi$
$499$	−3.57867	−	3.57867i	−0.160203	−	0.160203i	−0.782657	+	0.622453i	$0.786136\pi$
$500$	−2.93602			−0.131303
$501$		−	0.560646i		−	0.0250478i
$502$	−11.8122			−0.527205
$503$			26.4120i			1.17765i	0.808260	+	0.588826i	$0.200410\pi$
$503$			26.4120i			1.17765i	−0.808260	+	0.588826i	$0.799590\pi$
$504$	−14.5750			−0.649221
$505$	−0.432191	+	0.432191i	−0.0192323	+	0.0192323i
$506$	5.06531	−	7.14469i	0.225181	−	0.317620i
$507$		−	18.2893i		−	0.812256i
$508$			15.0039i			0.665689i
$509$	8.86713	+	8.86713i	0.393029	+	0.393029i	0.875766	−	0.482737i	$-0.160357\pi$
$509$	8.86713	+	8.86713i	0.393029	+	0.393029i	−0.482737	+	0.875766i	$0.660357\pi$
$510$	3.09198			0.136915
$511$	−6.60800	+	6.60800i	−0.292321	+	0.292321i
$512$	12.8423	+	12.8423i	0.567554	+	0.567554i
$513$		−	29.6429i		−	1.30877i
$514$	9.52429	+	9.52429i	0.420099	+	0.420099i
$515$			1.46817i			0.0646953i
$516$	2.79850	−	2.79850i	0.123197	−	0.123197i
$517$	0.600398	−	0.846870i	0.0264055	−	0.0372453i
$518$	−36.2637	+	36.2637i	−1.59333	+	1.59333i
$519$	5.55174	−	5.55174i	0.243694	−	0.243694i
$520$	−0.0815568	+	0.0815568i	−0.00357650	+	0.00357650i
$521$	−25.3979	+	25.3979i	−1.11270	+	1.11270i	−0.119918	+	0.992784i	$0.538263\pi$
$521$	−25.3979	+	25.3979i	−1.11270	+	1.11270i	−0.992784	+	0.119918i	$0.961737\pi$
$522$	10.2732			0.449647
$523$	−20.7611	+	20.7611i	−0.907820	+	0.907820i	−0.996096	−	0.0882759i	$-0.971864\pi$
$523$	−20.7611	+	20.7611i	−0.907820	+	0.907820i	0.0882759	+	0.996096i	$0.471864\pi$
$524$	−0.540913			−0.0236299
$525$	22.6051	−	22.6051i	0.986569	−	0.986569i
$526$	−2.22377	−	2.22377i	−0.0969611	−	0.0969611i
$527$	18.5881			0.809709
$528$	−6.68724	−	4.74100i	−0.291025	−	0.206325i
$529$			17.1829i			0.747084i
$530$			4.69742i			0.204043i
$531$	−1.46526	−	1.46526i	−0.0635868	−	0.0635868i
$532$	13.8656	−	13.8656i	0.601152	−	0.601152i
$533$		−	1.09942i		−	0.0476213i
$534$	−17.3679			−0.751583
$535$			2.50380i			0.108249i
$536$	20.4793			0.884570
$537$			10.3942i			0.448545i
$538$	−0.573854	−	0.573854i	−0.0247406	−	0.0247406i
$539$	40.0673	+	28.4062i	1.72582	+	1.22354i
$540$			1.68406i			0.0724706i
$541$	17.4782	+	17.4782i	0.751448	+	0.751448i	0.974749	−	0.223301i	$-0.0716834\pi$
$541$	17.4782	+	17.4782i	0.751448	+	0.751448i	−0.223301	+	0.974749i	$0.571683\pi$
$542$	23.3409	+	23.3409i	1.00258	+	1.00258i
$543$	11.4777	−	11.4777i	0.492557	−	0.492557i
$544$	22.7385			0.974904
$545$		−	1.41112i		−	0.0604458i
$546$		−	0.728644i		−	0.0311831i
$547$	−2.72553	+	2.72553i	−0.116535	+	0.116535i	−0.762970	−	0.646434i	$-0.776259\pi$
$547$	−2.72553	+	2.72553i	−0.116535	+	0.116535i	0.646434	+	0.762970i	$0.276259\pi$
$548$			14.1468i			0.604321i
$549$	−0.350387	+	7.93997i	−0.0149542	+	0.338870i
$550$	−17.4044	+	2.96399i	−0.742126	+	0.126385i
$551$	−34.1676	+	34.1676i	−1.45559	+	1.45559i
$552$	−10.4151			−0.443297
$553$			17.5818i			0.747652i
$554$		−	6.06320i		−	0.257601i
$555$	3.71029	+	3.71029i	0.157493	+	0.157493i
$556$	2.35265	+	2.35265i	0.0997746	+	0.0997746i
$557$	4.46681	−	4.46681i	0.189265	−	0.189265i	−0.606113	−	0.795378i	$-0.707272\pi$
$557$	4.46681	−	4.46681i	0.189265	−	0.189265i	0.795378	+	0.606113i	$0.207272\pi$
$558$		−	3.83625i		−	0.162401i
$559$	−0.251069	−	0.251069i	−0.0106191	−	0.0106191i
$560$	2.15376	−	2.15376i	0.0910130	−	0.0910130i
$561$	−24.8513	+	4.23220i	−1.04922	+	0.178684i
$562$	24.0240			1.01339
$563$	31.2116			1.31541			0.657706	−	0.753275i	$-0.271527\pi$
$563$	31.2116			1.31541			0.657706	+	0.753275i	$0.271527\pi$
$564$	−0.353120			−0.0148690
$565$	−4.04113			−0.170011
$566$	12.4430	+	12.4430i	0.523018	+	0.523018i
$567$	−16.2193	−	16.2193i	−0.681147	−	0.681147i
$568$	0.0118682			0.000497979
$569$		−	32.4834i		−	1.36178i	−0.732387	−	0.680888i	$-0.761594\pi$
$569$		−	32.4834i		−	1.36178i	0.732387	−	0.680888i	$-0.238406\pi$
$570$	2.12235	+	2.12235i	0.0888953	+	0.0888953i
$571$		−	6.01592i		−	0.251759i	−0.992046	−	0.125879i	$-0.959825\pi$
$571$		−	6.01592i		−	0.251759i	0.992046	−	0.125879i	$-0.0401752\pi$
$572$	0.155567	−	0.219429i	0.00650458	−	0.00917480i
$573$	15.0109	−	15.0109i	0.627088	−	0.627088i
$574$			55.5389i			2.31815i
$575$	−8.29179	+	8.29179i	−0.345791	+	0.345791i
$576$		−	8.26544i		−	0.344393i
$577$	1.06769	+	1.06769i	0.0444486	+	0.0444486i	0.728982	−	0.684533i	$-0.239994\pi$
$577$	1.06769	+	1.06769i	0.0444486	+	0.0444486i	−0.684533	+	0.728982i	$0.739994\pi$
$578$	−9.40066	+	9.40066i	−0.391016	+	0.391016i
$579$	−16.8126	−	16.8126i	−0.698708	−	0.698708i
$580$	1.94112	−	1.94112i	0.0806005	−	0.0806005i
$581$	32.0240	−	32.0240i	1.32858	−	1.32858i
$582$	−3.24631	−	3.24631i	−0.134564	−	0.134564i
$583$	−6.42968	−	37.7547i	−0.266290	−	1.56364i
$584$	−4.33980	−	4.33980i	−0.179582	−	0.179582i
$585$	0.0382680			0.00158219
$586$	20.0238	+	20.0238i	0.827175	+	0.827175i
$587$	−30.9361	−	30.9361i	−1.27687	−	1.27687i	−0.942410	−	0.334461i	$-0.891446\pi$
$587$	−30.9361	−	30.9361i	−1.27687	−	1.27687i	−0.334461	−	0.942410i	$-0.608554\pi$
$588$		−	16.7069i		−	0.688980i
$589$	12.7589	+	12.7589i	0.525722	+	0.525722i
$590$	0.828379			0.0341038
$591$		−	2.77723i		−	0.114240i
$592$	−12.4502	−	12.4502i	−0.511700	−	0.511700i
$593$	24.9251	+	24.9251i	1.02355	+	1.02355i	0.999716	+	0.0238359i	$0.00758792\pi$
$593$	24.9251	+	24.9251i	1.02355	+	1.02355i	0.0238359	+	0.999716i	$0.492412\pi$
$594$	3.44849	+	20.2493i	0.141493	+	0.830840i
$595$		−	9.36691i		−	0.384006i
$596$			5.29078i			0.216719i
$597$		−	16.7084i		−	0.683831i
$598$			0.267274i			0.0109296i
$599$	−18.3099	+	18.3099i	−0.748123	+	0.748123i	−0.974126	−	0.226003i	$-0.927434\pi$
$599$	−18.3099	+	18.3099i	−0.748123	+	0.748123i	0.226003	+	0.974126i	$0.427434\pi$
$600$	14.8459	+	14.8459i	0.606082	+	0.606082i
$601$	40.5098			1.65243			0.826215	−	0.563355i	$-0.190490\pi$
$601$	40.5098			1.65243			0.826215	+	0.563355i	$0.190490\pi$
$602$	12.6831	+	12.6831i	0.516924	+	0.516924i
$603$	−4.80463	−	4.80463i	−0.195660	−	0.195660i
$604$	−6.68956	−	6.68956i	−0.272194	−	0.272194i
$605$	−3.85665	+	1.35282i	−0.156795	+	0.0550000i
$606$	2.53589			0.103014
$607$		−	21.4136i		−	0.869151i	−0.900636	−	0.434575i	$-0.856898\pi$
$607$		−	21.4136i		−	0.869151i	0.900636	−	0.434575i	$-0.143102\pi$
$608$	15.6078	+	15.6078i	0.632978	+	0.632978i
$609$			60.6292i			2.45682i
$610$	−2.14537	−	2.34346i	−0.0868636	−	0.0948840i
$611$			0.0316803i			0.00128165i
$612$	−3.11248	−	3.11248i	−0.125814	−	0.125814i
$613$	−43.3814			−1.75216			−0.876079	−	0.482168i	$-0.839849\pi$
$613$	−43.3814			−1.75216			−0.876079	+	0.482168i	$0.839849\pi$
$614$			32.9674i			1.33045i
$615$	5.68241			0.229137
$616$	−27.4742	+	38.7527i	−1.10697	+	1.56139i
$617$	−15.9654	+	15.9654i	−0.642742	+	0.642742i	−0.951229	−	0.308486i	$-0.900178\pi$
$617$	−15.9654	+	15.9654i	−0.642742	+	0.642742i	0.308486	+	0.951229i	$0.400178\pi$
$618$	4.30726	−	4.30726i	0.173263	−	0.173263i
$619$	26.4246			1.06210			0.531048	−	0.847342i	$-0.321798\pi$
$619$	26.4246			1.06210			0.531048	+	0.847342i	$0.321798\pi$
$620$	−0.724855	−	0.724855i	−0.0291109	−	0.0291109i
$621$	9.64717	+	9.64717i	0.387127	+	0.387127i
$622$			21.9685i			0.880857i
$623$			52.6147i			2.10796i
$624$	0.250161			0.0100145
$625$	22.9483			0.917933
$626$		−	18.7872i		−	0.750887i
$627$	−19.9630	−	14.1530i	−0.797245	−	0.565216i
$628$	5.11967	−	5.11967i	0.204297	−	0.204297i
$629$	−54.1471			−2.15899
$630$	−1.93316			−0.0770191
$631$	11.6936	+	11.6936i	0.465514	+	0.465514i	0.900458	−	0.434944i	$-0.143232\pi$
$631$	11.6936	+	11.6936i	0.465514	+	0.465514i	−0.434944	+	0.900458i	$0.643232\pi$
$632$	−11.5468			−0.459307
$633$	−12.6431	−	12.6431i	−0.502519	−	0.502519i
$634$	−12.6031	−	12.6031i	−0.500534	−	0.500534i
$635$			6.95728i			0.276091i
$636$	−9.21179	+	9.21179i	−0.365271	+	0.365271i
$637$	−1.49887			−0.0593873
$638$	19.3653	−	27.3150i	0.766680	−	1.08141i
$639$	−0.00278440	−	0.00278440i	−0.000110149	−	0.000110149i
$640$	0.123182	+	0.123182i	0.00486921	+	0.00486921i
$641$	−2.40224	−	2.40224i	−0.0948829	−	0.0948829i	0.658072	−	0.752955i	$-0.271372\pi$
$641$	−2.40224	−	2.40224i	−0.0948829	−	0.0948829i	−0.752955	+	0.658072i	$0.771372\pi$
$642$	7.34556	−	7.34556i	0.289906	−	0.289906i
$643$	6.03230	−	6.03230i	0.237891	−	0.237891i	−0.578085	−	0.815976i	$-0.696200\pi$
$643$	6.03230	−	6.03230i	0.237891	−	0.237891i	0.815976	+	0.578085i	$0.196200\pi$
$644$			9.02502i			0.355636i
$645$	1.29766	−	1.29766i	0.0510953	−	0.0510953i
$646$	−30.9730			−1.21862
$647$	−11.7076	−	11.7076i	−0.460272	−	0.460272i	0.438473	−	0.898744i	$-0.355520\pi$
$647$	−11.7076	−	11.7076i	−0.460272	−	0.460272i	−0.898744	+	0.438473i	$0.855520\pi$
$648$	10.6520	−	10.6520i	0.418451	−	0.418451i
$649$	−6.65796	+	1.13386i	−0.261348	+	0.0445079i
$650$	0.380978	−	0.380978i	0.0149432	−	0.0149432i
$651$	22.6403			0.887342
$652$	15.0667			0.590059
$653$	29.7402	+	29.7402i	1.16382	+	1.16382i	0.983631	+	0.180193i	$0.0576721\pi$
$653$	29.7402	+	29.7402i	1.16382	+	1.16382i	0.180193	+	0.983631i	$0.442328\pi$
$654$	−4.13989	+	4.13989i	−0.161883	+	0.161883i
$655$	−0.250821			−0.00980037
$656$	−19.0678			−0.744474
$657$			2.03632i			0.0794444i
$658$		−	1.60038i		−	0.0623891i
$659$	16.2133			0.631581			0.315790	−	0.948829i	$-0.397730\pi$
$659$	16.2133			0.631581			0.315790	+	0.948829i	$0.397730\pi$
$660$	1.13413	+	0.804054i	0.0441459	+	0.0312978i
$661$	6.60403	−	6.60403i	0.256867	−	0.256867i	−0.566912	−	0.823779i	$-0.691862\pi$
$661$	6.60403	−	6.60403i	0.256867	−	0.256867i	0.823779	+	0.566912i	$0.191862\pi$
$662$	−28.5270			−1.10873
$663$	0.543987	−	0.543987i	0.0211267	−	0.0211267i
$664$	21.0318	+	21.0318i	0.816190	+	0.816190i
$665$	6.42948	−	6.42948i	0.249324	−	0.249324i
$666$			11.1750i			0.433022i
$667$		−	22.2394i		−	0.861113i
$668$		−	0.319060i		−	0.0123448i
$669$	16.0087	+	16.0087i	0.618932	+	0.618932i
$670$	2.71628			0.104939
$671$	20.4507	+	15.8987i	0.789492	+	0.613761i
$672$	27.6954			1.06837
$673$	−20.3560	−	20.3560i	−0.784665	−	0.784665i	0.195949	−	0.980614i	$-0.437221\pi$
$673$	−20.3560	−	20.3560i	−0.784665	−	0.784665i	−0.980614	+	0.195949i	$0.937221\pi$
$674$		−	19.9981i		−	0.770299i
$675$		−	27.5025i		−	1.05857i
$676$		−	10.4083i		−	0.400320i
$677$	30.5762	−	30.5762i	1.17514	−	1.17514i	0.194172	−	0.980967i	$-0.437798\pi$
$677$	30.5762	−	30.5762i	1.17514	−	1.17514i	0.980967	−	0.194172i	$-0.0622021\pi$
$678$	11.8557	+	11.8557i	0.455316	+	0.455316i
$679$	−9.83444	+	9.83444i	−0.377411	+	0.377411i
$680$	6.15171			0.235907
$681$	−13.2420	+	13.2420i	−0.507436	+	0.507436i
$682$	−10.2000	−	7.23142i	−0.390579	−	0.276905i
$683$	31.4368			1.20289			0.601447	−	0.798913i	$-0.294591\pi$
$683$	31.4368			1.20289			0.601447	+	0.798913i	$0.294591\pi$
$684$		−	4.27283i		−	0.163376i
$685$			6.55985i			0.250639i
$686$	39.9263			1.52439
$687$	23.4483			0.894607
$688$	−4.35442	+	4.35442i	−0.166011	+	0.166011i
$689$	0.826441	+	0.826441i	0.0314849	+	0.0314849i
$690$	−1.38142			−0.0525896
$691$	−27.9388			−1.06284			−0.531421	−	0.847108i	$-0.678342\pi$
$691$	−27.9388			−1.06284			−0.531421	+	0.847108i	$0.678342\pi$
$692$	3.15947	−	3.15947i	0.120105	−	0.120105i
$693$	15.5375	−	2.64605i	0.590220	−	0.100515i
$694$	6.78856	−	6.78856i	0.257690	−	0.257690i
$695$	1.09092	+	1.09092i	0.0413810	+	0.0413810i
$696$	−39.8182			−1.50931
$697$	−41.4639	+	41.4639i	−1.57056	+	1.57056i
$698$		−	11.8173i		−	0.447292i
$699$	29.4852	−	29.4852i	1.11523	−	1.11523i
$700$	12.8645	−	12.8645i	0.486231	−	0.486231i
$701$	−4.27638	−	4.27638i	−0.161516	−	0.161516i	0.621722	−	0.783238i	$-0.286433\pi$
$701$	−4.27638	−	4.27638i	−0.161516	−	0.161516i	−0.783238	+	0.621722i	$0.786433\pi$
$702$	−0.443253	−	0.443253i	−0.0167295	−	0.0167295i
$703$	−37.1668	−	37.1668i	−1.40177	−	1.40177i
$704$	−21.9766	−	15.5806i	−0.828274	−	0.587214i
$705$	−0.163741			−0.00616685
$706$	27.4978	−	27.4978i	1.03489	−	1.03489i
$707$		−	7.68229i		−	0.288922i
$708$	1.62448	+	1.62448i	0.0610516	+	0.0610516i
$709$	21.6911	+	21.6911i	0.814627	+	0.814627i	0.985324	−	0.170697i	$-0.0546018\pi$
$709$	21.6911	+	21.6911i	0.814627	+	0.814627i	−0.170697	+	0.985324i	$0.554602\pi$
$710$	0.00157415			5.90767e−5
$711$	2.70899	+	2.70899i	0.101595	+	0.101595i
$712$	−34.5547			−1.29499
$713$	−8.30467			−0.311012
$714$	−27.4803	+	27.4803i	−1.02842	+	1.02842i
$715$	0.0721362	−	0.101749i	0.00269774	−	0.00380520i
$716$			5.91531i			0.221065i
$717$	16.6379			0.621353
$718$	9.37420			0.349842
$719$			4.63293i			0.172779i	0.996261	+	0.0863895i	$0.0275330\pi$
$719$			4.63293i			0.172779i	−0.996261	+	0.0863895i	$0.972467\pi$
$720$		−	0.663702i		−	0.0247347i
$721$	−13.0485	−	13.0485i	−0.485952	−	0.485952i
$722$	−6.55046	−	6.55046i	−0.243783	−	0.243783i
$723$	18.3312			0.681745
$724$	6.53192	−	6.53192i	0.242757	−	0.242757i
$725$	−31.7005	+	31.7005i	−1.17733	+	1.17733i
$726$	15.2834	+	7.34564i	0.567219	+	0.272622i
$727$	−2.20500			−0.0817790			−0.0408895	−	0.999164i	$-0.513019\pi$
$727$	−2.20500			−0.0817790			−0.0408895	+	0.999164i	$0.513019\pi$
$728$		−	1.44969i		−	0.0537291i
$729$	−28.8916			−1.07006
$730$	−0.575613	−	0.575613i	−0.0213044	−	0.0213044i
$731$			18.9378i			0.700439i
$732$	0.388461	−	8.80275i	0.0143579	−	0.325359i
$733$		−	21.8166i		−	0.805814i	−0.915241	−	0.402907i	$-0.868000\pi$
$733$		−	21.8166i		−	0.805814i	0.915241	−	0.402907i	$-0.132000\pi$
$734$	0.531196	+	0.531196i	0.0196068	+	0.0196068i
$735$		−	7.74696i		−	0.285751i
$736$	−10.1590			−0.374464
$737$	−21.8317	+	3.71796i	−0.804180	+	0.136953i
$738$	8.55742	+	8.55742i	0.315003	+	0.315003i
$739$	−14.0665	−	14.0665i	−0.517445	−	0.517445i	0.399353	−	0.916797i	$-0.369235\pi$
$739$	−14.0665	−	14.0665i	−0.517445	−	0.517445i	−0.916797	+	0.399353i	$0.869235\pi$
$740$	2.11150	+	2.11150i	0.0776204	+	0.0776204i
$741$	0.746790			0.0274340
$742$	−41.7488	−	41.7488i	−1.53265	−	1.53265i
$743$	−23.1968	+	23.1968i	−0.851007	+	0.851007i	−0.990257	−	0.139251i	$-0.955531\pi$
$743$	−23.1968	+	23.1968i	−0.851007	+	0.851007i	0.139251	+	0.990257i	$0.455531\pi$
$744$			14.8690i			0.545123i
$745$			2.45333i			0.0898829i
$746$		−	15.0897i		−	0.552473i
$747$		−	9.86851i		−	0.361070i
$748$	−14.1427	+	2.40852i	−0.517109	+	0.0880643i
$749$	−22.2528	−	22.2528i	−0.813099	−	0.813099i
$750$	3.99411	+	3.99411i	0.145844	+	0.145844i
$751$		−	24.2630i		−	0.885368i	−0.896678	−	0.442684i	$-0.854026\pi$
$751$		−	24.2630i		−	0.885368i	0.896678	−	0.442684i	$-0.145974\pi$
$752$	0.549448			0.0200363
$753$	−10.7412	−	10.7412i	−0.391430	−	0.391430i
$754$			1.02182i			0.0372125i
$755$	−3.10194	−	3.10194i	−0.112891	−	0.112891i
$756$	−14.9673	−	14.9673i	−0.544355	−	0.544355i
$757$	−16.3715			−0.595031			−0.297515	−	0.954717i	$-0.596158\pi$
$757$	−16.3715			−0.595031			−0.297515	+	0.954717i	$0.596158\pi$
$758$	13.5344	+	13.5344i	0.491590	+	0.491590i
$759$	11.1029	−	1.89084i	0.403010	−	0.0686331i
$760$	4.22256	+	4.22256i	0.153168	+	0.153168i
$761$	6.20772	−	6.20772i	0.225030	−	0.225030i	−0.585583	−	0.810613i	$-0.699134\pi$
$761$	6.20772	−	6.20772i	0.225030	−	0.225030i	0.810613	+	0.585583i	$0.199134\pi$
$762$	20.4110	−	20.4110i	0.739413	−	0.739413i
$763$	12.5415	+	12.5415i	0.454032	+	0.454032i
$764$	8.54260	−	8.54260i	0.309060	−	0.309060i
$765$	−1.44325	−	1.44325i	−0.0521809	−	0.0521809i
$766$			6.99001i			0.252559i
$767$	0.145741	−	0.145741i	0.00526240	−	0.00526240i
$768$			22.1498i			0.799262i
$769$	6.94438	−	6.94438i	0.250421	−	0.250421i	−0.570722	−	0.821143i	$-0.693337\pi$
$769$	6.94438	−	6.94438i	0.250421	−	0.250421i	0.821143	+	0.570722i	$0.193337\pi$
$770$	−3.64406	+	5.14000i	−0.131323	+	0.185233i
$771$			17.3214i			0.623815i
$772$	−9.56796	−	9.56796i	−0.344358	−	0.344358i
$773$		−	9.26801i		−	0.333347i	−0.986012	−	0.166674i	$-0.946697\pi$
$773$		−	9.26801i		−	0.333347i	0.986012	−	0.166674i	$-0.0533026\pi$
$774$	3.90842			0.140485
$775$	11.8377	+	11.8377i	0.425221	+	0.425221i
$776$	−6.45877	−	6.45877i	−0.231856	−	0.231856i
$777$	−65.9511			−2.36598
$778$	1.27918			0.0458607
$779$	−56.9220			−2.03944
$780$	−0.0424263			−0.00151911
$781$	−0.0126520	+	0.00215465i	−0.000452723	+	7.70993e-5i
$782$	10.0800	−	10.0800i	0.360461	−	0.360461i
$783$	36.8823	+	36.8823i	1.31807	+	1.31807i
$784$			25.9956i			0.928415i
$785$	2.37399	−	2.37399i	0.0847312	−	0.0847312i
$786$	0.735848	+	0.735848i	0.0262468	+	0.0262468i
$787$	16.7497	+	16.7497i	0.597064	+	0.597064i	0.939530	−	0.342466i	$-0.111262\pi$
$787$	16.7497	+	16.7497i	0.597064	+	0.597064i	−0.342466	+	0.939530i	$0.611262\pi$
$788$		−	1.58051i		−	0.0563032i
$789$		−	4.04428i		−	0.143980i
$790$	−1.53152			−0.0544890
$791$	35.9159	−	35.9159i	1.27702	−	1.27702i
$792$	1.73779	+	10.2042i	0.0617498	+	0.362592i
$793$	−0.789744	−	0.0348510i	−0.0280446	−	0.00123760i
$794$			21.1112i			0.749207i
$795$	−4.27150	+	4.27150i	−0.151494	+	0.151494i
$796$		−	9.50868i		−	0.337026i
$797$		−	8.89601i		−	0.315113i	−0.987510	−	0.157557i	$-0.949638\pi$
$797$		−	8.89601i		−	0.315113i	0.987510	−	0.157557i	$-0.0503616\pi$
$798$	−37.7251			−1.33546
$799$	1.19480	−	1.19480i	0.0422690	−	0.0422690i
$800$	14.4808	+	14.4808i	0.511973	+	0.511973i
$801$	8.10687	+	8.10687i	0.286442	+	0.286442i
$802$		−	27.2338i		−	0.961658i
$803$	5.41427	+	3.83851i	0.191066	+	0.135458i
$804$	5.32672	+	5.32672i	0.187859	+	0.187859i
$805$			4.18489i			0.147498i
$806$	0.381570			0.0134402
$807$		−	1.04364i		−	0.0367380i
$808$	5.04534			0.177494
$809$		−	16.4753i		−	0.579242i	−0.957141	−	0.289621i	$-0.906471\pi$
$809$		−	16.4753i		−	0.579242i	0.957141	−	0.289621i	$-0.0935293\pi$
$810$	1.41284	−	1.41284i	0.0496421	−	0.0496421i
$811$	−6.13134	−	6.13134i	−0.215300	−	0.215300i	0.591214	−	0.806515i	$-0.298649\pi$
$811$	−6.13134	−	6.13134i	−0.215300	−	0.215300i	−0.806515	+	0.591214i	$0.798649\pi$
$812$			34.5038i			1.21084i
$813$			42.4490i			1.48875i
$814$	29.7127	+	21.0651i	1.04143	+	0.738333i
$815$	6.98643			0.244724
$816$	−9.43465	−	9.43465i	−0.330279	−	0.330279i
$817$	−12.9989	+	12.9989i	−0.454776	+	0.454776i
$818$	−23.7533			−0.830513
$819$	−0.340111	+	0.340111i	−0.0118844	+	0.0118844i
$820$	3.23383			0.112930
$821$	−19.4502	+	19.4502i	−0.678817	+	0.678817i	−0.959732	−	0.280916i	$-0.909362\pi$
$821$	−19.4502	+	19.4502i	−0.678817	+	0.678817i	0.280916	+	0.959732i	$0.409362\pi$
$822$	19.2450	−	19.2450i	0.671248	−	0.671248i
$823$	23.2449	−	23.2449i	0.810267	−	0.810267i	−0.174407	−	0.984674i	$-0.555801\pi$
$823$	23.2449	−	23.2449i	0.810267	−	0.810267i	0.984674	+	0.174407i	$0.0558007\pi$
$824$	8.56960	−	8.56960i	0.298536	−	0.298536i
$825$	−18.5215	−	13.1311i	−0.644837	−	0.457165i
$826$	−7.36231	+	7.36231i	−0.256167	+	0.256167i
$827$			31.6216i			1.09959i	0.835299	+	0.549795i	$0.185294\pi$
$827$			31.6216i			1.09959i	−0.835299	+	0.549795i	$0.814706\pi$
$828$	1.39057	+	1.39057i	0.0483258	+	0.0483258i
$829$			10.0156i			0.347856i	0.984758	+	0.173928i	$0.0556461\pi$
$829$			10.0156i			0.347856i	−0.984758	+	0.173928i	$0.944354\pi$
$830$	2.78956	+	2.78956i	0.0968271	+	0.0968271i
$831$	5.51343	−	5.51343i	0.191259	−	0.191259i
$832$	0.822116			0.0285017
$833$	56.5287	+	56.5287i	1.95860	+	1.95860i
$834$		−	6.40101i		−	0.221649i
$835$		−	0.147948i		−	0.00511995i
$836$	−11.3608	−	8.05439i	−0.392922	−	0.278567i
$837$	13.7726	−	13.7726i	0.476052	−	0.476052i
$838$	−23.2890			−0.804504
$839$			31.5166i			1.08807i	0.839061	+	0.544037i	$0.183105\pi$
$839$			31.5166i			1.08807i	−0.839061	+	0.544037i	$0.816895\pi$
$840$	7.49278			0.258526
$841$		−	56.0239i		−	1.93186i
$842$	41.9792			1.44670
$843$	21.8457	+	21.8457i	0.752406	+	0.752406i
$844$	−7.19512	−	7.19512i	−0.247666	−	0.247666i
$845$		−	4.82633i		−	0.166031i
$846$	−0.246586	−	0.246586i	−0.00847779	−	0.00847779i
$847$	22.2530	−	46.2997i	0.764624	−	1.59088i
$848$	14.3334	−	14.3334i	0.492211	−	0.492211i
$849$			22.6295i			0.776644i
$850$	−28.7366			−0.985657
$851$	24.1915			0.829275
$852$	0.00308696	+	0.00308696i	0.000105757	+	0.000105757i
$853$	−44.9290			−1.53834			−0.769170	−	0.639044i	$-0.779330\pi$
$853$	−44.9290			−1.53834			−0.769170	+	0.639044i	$0.779330\pi$
$854$	39.8950	+	1.76055i	1.36518	+	0.0602447i
$855$		−	1.98131i		−	0.0677592i
$856$	14.6145	−	14.6145i	0.499514	−	0.499514i
$857$	−30.3273			−1.03596			−0.517981	−	0.855392i	$-0.673316\pi$
$857$	−30.3273			−1.03596			−0.517981	+	0.855392i	$0.673316\pi$
$858$	−0.510138	+	0.0868772i	−0.0174158	+	0.00296594i
$859$		−	45.1157i		−	1.53933i	−0.638449	−	0.769664i	$-0.720424\pi$
$859$		−	45.1157i		−	1.53933i	0.638449	−	0.769664i	$-0.279576\pi$
$860$	0.738491	−	0.738491i	0.0251823	−	0.0251823i
$861$	−50.5030	+	50.5030i	−1.72114	+	1.72114i
$862$	−27.1209	−	27.1209i	−0.923742	−	0.923742i
$863$	32.5838			1.10917			0.554583	−	0.832128i	$-0.312878\pi$
$863$	32.5838			1.10917			0.554583	+	0.832128i	$0.312878\pi$
$864$	16.8478	−	16.8478i	0.573175	−	0.573175i
$865$	1.46504	−	1.46504i	0.0498129	−	0.0498129i
$866$			32.1454i			1.09235i
$867$	−17.0966			−0.580630
$868$	12.8844			0.437327
$869$	12.3093	−	2.09630i	0.417565	−	0.0711120i
$870$	−5.28132			−0.179054
$871$	0.477889	−	0.477889i	0.0161927	−	0.0161927i
$872$	−8.23661	+	8.23661i	−0.278927	+	0.278927i
$873$			3.03058i			0.102570i
$874$	13.8379			0.468076
$875$	12.0998	−	12.0998i	0.409049	−	0.409049i
$876$		−	2.25759i		−	0.0762769i
$877$	21.3581	+	21.3581i	0.721212	+	0.721212i	0.968852	−	0.247640i	$-0.0796549\pi$
$877$	21.3581	+	21.3581i	0.721212	+	0.721212i	−0.247640	+	0.968852i	$0.579655\pi$
$878$	−12.9695	+	12.9695i	−0.437700	+	0.437700i
$879$			36.4164i			1.22829i
$880$	−1.76469	−	1.25109i	−0.0594875	−	0.0421744i
$881$		−	5.00296i		−	0.168554i	−0.996442	−	0.0842770i	$-0.973142\pi$
$881$		−	5.00296i		−	0.168554i	0.996442	−	0.0842770i	$-0.0268581\pi$
$882$	11.6665	−	11.6665i	0.392832	−	0.392832i
$883$	−28.5447	−	28.5447i	−0.960606	−	0.960606i	0.0386472	−	0.999253i	$-0.487695\pi$
$883$	−28.5447	−	28.5447i	−0.960606	−	0.960606i	−0.999253	+	0.0386472i	$0.987695\pi$
$884$	0.309580	−	0.309580i	0.0104123	−	0.0104123i
$885$	0.753268	+	0.753268i	0.0253208	+	0.0253208i
$886$	−14.5528	−	14.5528i	−0.488912	−	0.488912i
$887$	17.0540	+	17.0540i	0.572618	+	0.572618i	0.932859	−	0.360241i	$-0.117306\pi$
$887$	17.0540	+	17.0540i	0.572618	+	0.572618i	−0.360241	+	0.932859i	$0.617306\pi$
$888$		−	43.3134i		−	1.45350i
$889$	−61.8335	−	61.8335i	−2.07383	−	2.07383i
$890$	−4.58319			−0.153629
$891$	−9.42161	+	13.2893i	−0.315636	+	0.445209i
$892$	9.11046	+	9.11046i	0.305041	+	0.305041i
$893$	1.64023			0.0548882
$894$	7.19748	−	7.19748i	0.240720	−	0.240720i
$895$			2.74292i			0.0916857i
$896$	−2.18959			−0.0731492
$897$	−0.243040	+	0.243040i	−0.00811485	+	0.00811485i
$898$	17.8859	+	17.8859i	0.596859	+	0.596859i
$899$	−31.7498			−1.05891
$900$		−	3.96431i		−	0.132144i
$901$		−	62.3373i		−	2.07676i
$902$	38.8839	−	6.62197i	1.29469	−	0.220488i
$903$			23.0662i			0.767595i
$904$	23.5878	+	23.5878i	0.784518	+	0.784518i
$905$	3.02884	−	3.02884i	0.100682	−	0.100682i
$906$			18.2007i			0.604678i
$907$	13.3903	−	13.3903i	0.444618	−	0.444618i	−0.448942	−	0.893561i	$-0.648199\pi$
$907$	13.3903	−	13.3903i	0.444618	−	0.444618i	0.893561	+	0.448942i	$0.148199\pi$
$908$	−7.53596	+	7.53596i	−0.250090	+	0.250090i
$909$	−1.18369	−	1.18369i	−0.0392604	−	0.0392604i
$910$		−	0.192281i		−	0.00637404i
$911$	43.9362			1.45567			0.727835	−	0.685752i	$-0.240526\pi$
$911$	43.9362			1.45567			0.727835	+	0.685752i	$0.240526\pi$
$912$		−	12.9520i		−	0.428882i
$913$	−26.2389	−	18.6024i	−0.868381	−	0.615649i
$914$			14.4516i			0.478017i
$915$	0.180129	−	4.08182i	0.00595488	−	0.134941i
$916$	13.3443			0.440907
$917$	2.22919	−	2.22919i	0.0736145	−	0.0736145i
$918$			33.4339i			1.10348i
$919$	32.0997			1.05887			0.529436	−	0.848350i	$-0.322403\pi$
$919$	32.0997			1.05887			0.529436	+	0.848350i	$0.322403\pi$
$920$	−2.74843			−0.0906129
$921$	−29.9781	+	29.9781i	−0.987813	+	0.987813i
$922$	−3.20436	+	3.20436i	−0.105530	+	0.105530i
$923$	0.000276948	0	0.000276948i	9.11585e−6	0	9.11585e-6i
$924$	−17.2258	+	2.93358i	−0.566688	+	0.0965077i
$925$	−34.4831	−	34.4831i	−1.13380	−	1.13380i
$926$	4.82923	−	4.82923i	0.158698	−	0.158698i
$927$	−4.02102			−0.132068
$928$	−38.8389			−1.27495
$929$			36.9683i			1.21289i	0.795126	+	0.606445i	$0.207405\pi$
$929$			36.9683i			1.21289i	−0.795126	+	0.606445i	$0.792595\pi$
$930$			1.97216i			0.0646696i
$931$			77.6030i			2.54333i
$932$	16.7798	−	16.7798i	0.549642	−	0.549642i
$933$	−19.9766	+	19.9766i	−0.654004	+	0.654004i
$934$	−13.0556			−0.427191
$935$	−6.55796	+	1.11683i	−0.214468	+	0.0365242i
$936$	−0.223368	−	0.223368i	−0.00730101	−	0.00730101i
$937$		−	44.5901i		−	1.45670i	−0.685207	−	0.728348i	$-0.740288\pi$
$937$		−	44.5901i		−	1.45670i	0.685207	−	0.728348i	$-0.259712\pi$
$938$	−24.1413	+	24.1413i	−0.788240	+	0.788240i
$939$	17.0837	−	17.0837i	0.557506	−	0.557506i
$940$	−0.0931841			−0.00303933
$941$	−7.20655	−	7.20655i	−0.234927	−	0.234927i	0.579819	−	0.814745i	$-0.303123\pi$
$941$	−7.20655	−	7.20655i	−0.234927	−	0.234927i	−0.814745	+	0.579819i	$0.803123\pi$
$942$	−13.9294			−0.453845
$943$	18.5250	−	18.5250i	0.603257	−	0.603257i
$944$	−2.52766	−	2.52766i	−0.0822683	−	0.0822683i
$945$	−6.94031	−	6.94031i	−0.225768	−	0.225768i
$946$	7.36746	−	10.3919i	0.239537	−	0.337870i
$947$	26.4380	−	26.4380i	0.859121	−	0.859121i	−0.132114	−	0.991235i	$-0.542176\pi$
$947$	26.4380	−	26.4380i	0.859121	−	0.859121i	0.991235	+	0.132114i	$0.0421765\pi$
$948$	−3.00336	−	3.00336i	−0.0975446	−	0.0975446i
$949$	−0.202541			−0.00657476
$950$	−19.7249	−	19.7249i	−0.639960	−	0.639960i
$951$		−	22.9207i		−	0.743256i
$952$	−54.6740	+	54.6740i	−1.77199	+	1.77199i
$953$	−19.2773	+	19.2773i	−0.624453	+	0.624453i	−0.946667	−	0.322214i	$-0.895573\pi$
$953$	−19.2773	+	19.2773i	−0.624453	+	0.624453i	0.322214	+	0.946667i	$0.395573\pi$
$954$	−12.8653			−0.416530
$955$	3.96119	−	3.96119i	0.128181	−	0.128181i
$956$	9.46852			0.306234
$957$	42.4477	−	7.22891i	1.37214	−	0.233677i
$958$	33.5784	+	33.5784i	1.08487	+	1.08487i
$959$	−58.3014	−	58.3014i	−1.88265	−	1.88265i
$960$			4.24914i			0.137140i
$961$		−	19.1440i		−	0.617547i
$962$	−1.11151			−0.0358366
$963$	−6.85741			−0.220977
$964$	10.4322			0.335998
$965$	−4.43665	−	4.43665i	−0.142821	−	0.142821i
$966$	12.2775	−	12.2775i	0.395021	−	0.395021i
$967$	−19.8756			−0.639157			−0.319578	−	0.947560i	$-0.603541\pi$
$967$	−19.8756			−0.639157			−0.319578	+	0.947560i	$0.603541\pi$
$968$	30.4073	+	14.6147i	0.977329	+	0.469734i
$969$	−28.1646	−	28.1646i	−0.904778	−	0.904778i
$970$	−0.856663	−	0.856663i	−0.0275058	−	0.0275058i
$971$	−37.8034			−1.21317			−0.606585	−	0.795019i	$-0.707461\pi$
$971$	−37.8034			−1.21317			−0.606585	+	0.795019i	$0.707461\pi$
$972$	−8.05640			−0.258409
$973$	−19.3913			−0.621658
$974$	−14.9409	+	14.9409i	−0.478737	+	0.478737i
$975$	0.692867			0.0221895
$976$	−0.604439	+	13.6969i	−0.0193476	+	0.438428i
$977$	−6.31409			−0.202006			−0.101003	−	0.994886i	$-0.532205\pi$
$977$	−6.31409			−0.202006			−0.101003	+	0.994886i	$0.532205\pi$
$978$	−20.4965	−	20.4965i	−0.655406	−	0.655406i
$979$	36.8366	−	6.27333i	1.17730	−	0.200496i
$980$		−	4.40875i		−	0.140832i
$981$	3.86478			0.123393
$982$	20.6718	+	20.6718i	0.659664	+	0.659664i
$983$	15.1594	−	15.1594i	0.483509	−	0.483509i	−0.422741	−	0.906250i	$-0.638932\pi$
$983$	15.1594	−	15.1594i	0.483509	−	0.483509i	0.906250	+	0.422741i	$0.138932\pi$
$984$	−33.1679	−	33.1679i	−1.05735	−	1.05735i
$985$		−	0.732879i		−	0.0233515i
$986$	38.5372	−	38.5372i	1.22727	−	1.22727i
$987$	1.45527	−	1.45527i	0.0463216	−	0.0463216i
$988$	0.424994			0.0135209
$989$		−	8.46090i		−	0.269041i
$990$	0.230494	+	1.35345i	0.00732557	+	0.0430153i
$991$	40.6882			1.29250			0.646252	−	0.763124i	$-0.276336\pi$
$991$	40.6882			1.29250			0.646252	+	0.763124i	$0.276336\pi$
$992$			14.5033i			0.460480i
$993$	−25.9404	−	25.9404i	−0.823194	−	0.823194i
$994$	−0.0139904	+	0.0139904i	−0.000443749	+	0.000443749i
$995$		−	4.40916i		−	0.139780i
$996$			10.9408i			0.346674i
$997$	31.4316	−	31.4316i	0.995449	−	0.995449i	−0.00454033	−	0.999990i	$-0.501445\pi$
$997$	31.4316	−	31.4316i	0.995449	−	0.995449i	0.999990	+	0.00454033i	$0.00144524\pi$
$998$			5.54111i			0.175401i
$999$	−40.1197	+	40.1197i	−1.26933	+	1.26933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.f.a.538.19	✓	120
11.10	odd	2	inner	671.2.f.a.538.42	yes	120
61.11	odd	4	inner	671.2.f.a.560.42	yes	120
671.560	even	4	inner	671.2.f.a.560.19	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.f.a.538.19	✓	120	1.1	even	1	trivial
671.2.f.a.538.42	yes	120	11.10	odd	2	inner
671.2.f.a.560.19	yes	120	671.560	even	4	inner
671.2.f.a.560.42	yes	120	61.11	odd	4	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.774186 - 0.774186i) q^{2} -1.40798i q^{3} -0.801272i q^{4} -0.371549i q^{5} +(-1.09004 + 1.09004i) q^{6} +(3.30218 + 3.30218i) q^{7} +(-2.16871 + 2.16871i) q^{8} +1.01760 q^{9} +O(q^{10})\)	\(q+(-0.774186 - 0.774186i) q^{2} -1.40798i q^{3} -0.801272i q^{4} -0.371549i q^{5} +(-1.09004 + 1.09004i) q^{6} +(3.30218 + 3.30218i) q^{7} +(-2.16871 + 2.16871i) q^{8} +1.01760 q^{9} +(-0.287648 + 0.287648i) q^{10} +(1.91820 - 2.70565i) q^{11} -1.12817 q^{12} +0.101215i q^{13} -5.11300i q^{14} -0.523133 q^{15} +1.75542 q^{16} +(3.81724 - 3.81724i) q^{17} +(-0.787811 - 0.787811i) q^{18} +5.24033 q^{19} -0.297712 q^{20} +(4.64940 - 4.64940i) q^{21} +(-3.57971 + 0.609630i) q^{22} +(-1.70544 + 1.70544i) q^{23} +(3.05349 + 3.05349i) q^{24} +4.86195 q^{25} +(0.0783590 - 0.0783590i) q^{26} -5.65669i q^{27} +(2.64595 - 2.64595i) q^{28} +(-6.52012 + 6.52012i) q^{29} +(0.405002 + 0.405002i) q^{30} +(2.43475 + 2.43475i) q^{31} +(2.97839 + 2.97839i) q^{32} +(-3.80949 - 2.70078i) q^{33} -5.91051 q^{34} +(1.22692 - 1.22692i) q^{35} -0.815374i q^{36} +(-7.09244 - 7.09244i) q^{37} +(-4.05699 - 4.05699i) q^{38} +0.142508 q^{39} +(0.805780 + 0.805780i) q^{40} -10.8623 q^{41} -7.19899 q^{42} +(-2.48056 + 2.48056i) q^{43} +(-2.16796 - 1.53700i) q^{44} -0.378088i q^{45} +2.64066 q^{46} +0.313001 q^{47} -2.47159i q^{48} +14.8088i q^{49} +(-3.76405 - 3.76405i) q^{50} +(-5.37459 - 5.37459i) q^{51} +0.0811006 q^{52} +(8.16523 - 8.16523i) q^{53} +(-4.37933 + 4.37933i) q^{54} +(-1.00528 - 0.712704i) q^{55} -14.3229 q^{56} -7.37827i q^{57} +10.0956 q^{58} +(-1.43992 - 1.43992i) q^{59} +0.419172i q^{60} +(-0.344328 + 7.80266i) q^{61} -3.76990i q^{62} +(3.36029 + 3.36029i) q^{63} -8.12249i q^{64} +0.0376062 q^{65} +(0.858346 + 5.04016i) q^{66} +(-4.72154 - 4.72154i) q^{67} +(-3.05865 - 3.05865i) q^{68} +(2.40123 + 2.40123i) q^{69} -1.89973 q^{70} +(-0.00273624 - 0.00273624i) q^{71} +(-2.20687 + 2.20687i) q^{72} +2.00110i q^{73} +10.9817i q^{74} -6.84552i q^{75} -4.19893i q^{76} +(15.2688 - 2.60029i) q^{77} +(-0.110328 - 0.110328i) q^{78} +(2.66214 + 2.66214i) q^{79} -0.652224i q^{80} -4.91170 q^{81} +(8.40943 + 8.40943i) q^{82} -9.69784i q^{83} +(-3.72543 - 3.72543i) q^{84} +(-1.41829 - 1.41829i) q^{85} +3.84083 q^{86} +(9.18018 + 9.18018i) q^{87} +(1.70774 + 10.0278i) q^{88} +(7.96667 + 7.96667i) q^{89} +(-0.292710 + 0.292710i) q^{90} +(-0.334229 + 0.334229i) q^{91} +(1.36653 + 1.36653i) q^{92} +(3.42808 - 3.42808i) q^{93} +(-0.242321 - 0.242321i) q^{94} -1.94704i q^{95} +(4.19351 - 4.19351i) q^{96} +2.97817i q^{97} +(11.4648 - 11.4648i) q^{98} +(1.95196 - 2.75326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 120 q^{9}+O(q^{10}) \) 120 * q - 120 * q^9	\( 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) \) 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

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Database

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