LMFDB - Embedded newform 85.2.l.a.76.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [85,2,Mod(26,85)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("85.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(85, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$85 = 5 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	85.l (of order $8$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			76.5
Character	$\chi$	$=$	85.76
Dual form			85.2.l.a.66.5

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09631 - 1.09631i) q^{2} +(0.436412 - 1.05359i) q^{3} -0.403772i q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.676617 - 1.63350i) q^{6} +(-3.45666 + 1.43180i) q^{7} +(1.74995 + 1.74995i) q^{8} +(1.20172 + 1.20172i) q^{9} +(-1.43239 + 0.593316i) q^{10} +(0.558213 + 1.34764i) q^{11} +(-0.425411 - 0.176211i) q^{12} -6.71314i q^{13} +(-2.21987 + 5.35924i) q^{14} +(-0.806384 + 0.806384i) q^{15} +4.64451 q^{16} +(-4.12042 + 0.148752i) q^{17} +2.63491 q^{18} +(-1.32627 + 1.32627i) q^{19} +(-0.154517 + 0.373037i) q^{20} +4.26676i q^{21} +(2.08940 + 0.865459i) q^{22} +(1.61926 + 3.90923i) q^{23} +(2.60744 - 1.08004i) q^{24} +(0.707107 + 0.707107i) q^{25} +(-7.35965 - 7.35965i) q^{26} +(4.95134 - 2.05091i) q^{27} +(0.578119 + 1.39570i) q^{28} +(-7.01595 - 2.90610i) q^{29} +1.76809i q^{30} +(0.495602 - 1.19649i) q^{31} +(1.59190 - 1.59190i) q^{32} +1.66348 q^{33} +(-4.35416 + 4.68032i) q^{34} +3.74146 q^{35} +(0.485222 - 0.485222i) q^{36} +(1.72852 - 4.17301i) q^{37} +2.90799i q^{38} +(-7.07290 - 2.92969i) q^{39} +(-0.947068 - 2.28642i) q^{40} +(1.45157 - 0.601260i) q^{41} +(4.67767 + 4.67767i) q^{42} +(-4.56902 - 4.56902i) q^{43} +(0.544141 - 0.225391i) q^{44} +(-0.650367 - 1.57012i) q^{45} +(6.06092 + 2.51051i) q^{46} +2.36770i q^{47} +(2.02692 - 4.89342i) q^{48} +(4.94871 - 4.94871i) q^{49} +1.55041 q^{50} +(-1.64148 + 4.40616i) q^{51} -2.71058 q^{52} +(4.25532 - 4.25532i) q^{53} +(3.17976 - 7.67661i) q^{54} -1.45868i q^{55} +(-8.55457 - 3.54342i) q^{56} +(0.818544 + 1.97614i) q^{57} +(-10.8776 + 4.50565i) q^{58} +(7.29143 + 7.29143i) q^{59} +(0.325595 + 0.325595i) q^{60} +(2.90180 - 1.20197i) q^{61} +(-0.768386 - 1.85505i) q^{62} +(-5.87456 - 2.43332i) q^{63} +5.79861i q^{64} +(-2.56901 + 6.20213i) q^{65} +(1.82368 - 1.82368i) q^{66} +6.08039 q^{67} +(0.0600619 + 1.66371i) q^{68} +4.82540 q^{69} +(4.10179 - 4.10179i) q^{70} +(-1.46625 + 3.53983i) q^{71} +4.20591i q^{72} +(12.9392 + 5.35957i) q^{73} +(-2.67991 - 6.46987i) q^{74} +(1.05359 - 0.436412i) q^{75} +(0.535509 + 0.535509i) q^{76} +(-3.85910 - 3.85910i) q^{77} +(-10.9659 + 4.54222i) q^{78} +(-0.916355 - 2.21228i) q^{79} +(-4.29097 - 1.77738i) q^{80} -1.01326i q^{81} +(0.932200 - 2.25053i) q^{82} +(-11.9378 + 11.9378i) q^{83} +1.72280 q^{84} +(3.86370 + 1.43939i) q^{85} -10.0181 q^{86} +(-6.12369 + 6.12369i) q^{87} +(-1.38147 + 3.33516i) q^{88} -1.59370i q^{89} +(-2.43434 - 1.00834i) q^{90} +(9.61184 + 23.2050i) q^{91} +(1.57844 - 0.653811i) q^{92} +(-1.04432 - 1.04432i) q^{93} +(2.59572 + 2.59572i) q^{94} +(1.73285 - 0.717770i) q^{95} +(-0.982486 - 2.37193i) q^{96} +(-12.5670 - 5.20542i) q^{97} -10.8506i q^{98} +(-0.948677 + 2.29031i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100})$ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$ .

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.09631	−	1.09631i	0.775205	−	0.775205i	−0.203806	−	0.979011i	$-0.565331\pi$
$2$	1.09631	−	1.09631i	0.775205	−	0.775205i	0.979011	+	0.203806i	$0.0653312\pi$
$3$	0.436412	−	1.05359i	0.251962	−	0.608291i	−0.746400	−	0.665498i	$-0.768219\pi$
$3$	0.436412	−	1.05359i	0.251962	−	0.608291i	0.998362	+	0.0572066i	$0.0182194\pi$
$4$		−	0.403772i		−	0.201886i
$5$	−0.923880	−	0.382683i	−0.413171	−	0.171141i
$5$	−0.923880	−	0.382683i	−0.413171	−	0.171141i
$6$	−0.676617	−	1.63350i	−0.276228	−	0.666873i
$7$	−3.45666	+	1.43180i	−1.30649	+	0.541168i	−0.923859	−	0.382732i	$-0.874983\pi$
$7$	−3.45666	+	1.43180i	−1.30649	+	0.541168i	−0.382635	+	0.923900i	$0.624983\pi$
$8$	1.74995	+	1.74995i	0.618702	+	0.618702i
$9$	1.20172	+	1.20172i	0.400574	+	0.400574i
$10$	−1.43239	+	0.593316i	−0.452962	+	0.187623i
$11$	0.558213	+	1.34764i	0.168307	+	0.406330i	0.985418	−	0.170151i	$-0.0544255\pi$
$11$	0.558213	+	1.34764i	0.168307	+	0.406330i	−0.817111	+	0.576481i	$0.804425\pi$
$12$	−0.425411	−	0.176211i	−0.122805	−	0.0508677i
$13$		−	6.71314i		−	1.86189i	−0.365160	−	0.930945i	$-0.618986\pi$
$13$		−	6.71314i		−	1.86189i	0.365160	−	0.930945i	$-0.381014\pi$
$14$	−2.21987	+	5.35924i	−0.593285	+	1.43232i
$15$	−0.806384	+	0.806384i	−0.208207	+	0.208207i
$16$	4.64451			1.16113
$17$	−4.12042	+	0.148752i	−0.999349	+	0.0360777i
$17$	−4.12042	+	0.148752i	−0.999349	+	0.0360777i
$18$	2.63491			0.621054
$19$	−1.32627	+	1.32627i	−0.304266	+	0.304266i	−0.842680	−	0.538414i	$-0.819024\pi$
$19$	−1.32627	+	1.32627i	−0.304266	+	0.304266i	0.538414	+	0.842680i	$0.319024\pi$
$20$	−0.154517	+	0.373037i	−0.0345510	+	0.0834135i
$21$			4.26676i			0.931083i
$22$	2.08940	+	0.865459i	0.445462	+	0.184516i
$23$	1.61926	+	3.90923i	0.337639	+	0.815132i	0.997941	+	0.0641322i	$0.0204279\pi$
$23$	1.61926	+	3.90923i	0.337639	+	0.815132i	−0.660303	+	0.750999i	$0.729572\pi$
$24$	2.60744	−	1.08004i	0.532241	−	0.220461i
$25$	0.707107	+	0.707107i	0.141421	+	0.141421i
$26$	−7.35965	−	7.35965i	−1.44335	−	1.44335i
$27$	4.95134	−	2.05091i	0.952886	−	0.394698i
$28$	0.578119	+	1.39570i	0.109254	+	0.263763i
$29$	−7.01595	−	2.90610i	−1.30283	−	0.539650i	−0.380046	−	0.924968i	$-0.624092\pi$
$29$	−7.01595	−	2.90610i	−1.30283	−	0.539650i	−0.922784	+	0.385318i	$0.874092\pi$
$30$			1.76809i			0.322807i
$31$	0.495602	−	1.19649i	0.0890128	−	0.214896i	−0.873104	−	0.487534i	$-0.837896\pi$
$31$	0.495602	−	1.19649i	0.0890128	−	0.214896i	0.962116	+	0.272639i	$0.0878964\pi$
$32$	1.59190	−	1.59190i	0.281410	−	0.281410i
$33$	1.66348			0.289574
$34$	−4.35416	+	4.68032i	−0.746733	+	0.802668i
$35$	3.74146			0.632422
$36$	0.485222	−	0.485222i	0.0808703	−	0.0808703i
$37$	1.72852	−	4.17301i	0.284166	−	0.686038i	−0.715758	−	0.698348i	$-0.753919\pi$
$37$	1.72852	−	4.17301i	0.284166	−	0.686038i	0.999924	+	0.0123104i	$0.00391861\pi$
$38$			2.90799i			0.471738i
$39$	−7.07290	−	2.92969i	−1.13257	−	0.469126i
$40$	−0.947068	−	2.28642i	−0.149745	−	0.361515i
$41$	1.45157	−	0.601260i	0.226697	−	0.0939011i	−0.266444	−	0.963850i	$-0.585849\pi$
$41$	1.45157	−	0.601260i	0.226697	−	0.0939011i	0.493141	+	0.869949i	$0.335849\pi$
$42$	4.67767	+	4.67767i	0.721780	+	0.721780i
$43$	−4.56902	−	4.56902i	−0.696770	−	0.696770i	0.266943	−	0.963712i	$-0.413987\pi$
$43$	−4.56902	−	4.56902i	−0.696770	−	0.696770i	−0.963712	+	0.266943i	$0.913987\pi$
$44$	0.544141	−	0.225391i	0.0820324	−	0.0339789i
$45$	−0.650367	−	1.57012i	−0.0969510	−	0.234060i
$46$	6.06092	+	2.51051i	0.893633	+	0.370155i
$47$			2.36770i			0.345364i	0.984978	+	0.172682i	$0.0552434\pi$
$47$			2.36770i			0.345364i	−0.984978	+	0.172682i	$0.944757\pi$
$48$	2.02692	−	4.89342i	0.292561	−	0.706304i
$49$	4.94871	−	4.94871i	0.706959	−	0.706959i
$50$	1.55041			0.219261
$51$	−1.64148	+	4.40616i	−0.229853	+	0.616985i
$52$	−2.71058			−0.375889
$53$	4.25532	−	4.25532i	0.584513	−	0.584513i	−0.351627	−	0.936140i	$-0.614372\pi$
$53$	4.25532	−	4.25532i	0.584513	−	0.584513i	0.936140	+	0.351627i	$0.114372\pi$
$54$	3.17976	−	7.67661i	0.432710	−	1.04465i
$55$		−	1.45868i		−	0.196688i
$56$	−8.55457	−	3.54342i	−1.14315	−	0.473509i
$57$	0.818544	+	1.97614i	0.108419	+	0.261746i
$58$	−10.8776	+	4.50565i	−1.42830	+	0.591621i
$59$	7.29143	+	7.29143i	0.949264	+	0.949264i	0.998774	−	0.0495099i	$-0.0157659\pi$
$59$	7.29143	+	7.29143i	0.949264	+	0.949264i	−0.0495099	+	0.998774i	$0.515766\pi$
$60$	0.325595	+	0.325595i	0.0420342	+	0.0420342i
$61$	2.90180	−	1.20197i	0.371537	−	0.153896i	−0.189099	−	0.981958i	$-0.560557\pi$
$61$	2.90180	−	1.20197i	0.371537	−	0.153896i	0.560636	+	0.828062i	$0.310557\pi$
$62$	−0.768386	−	1.85505i	−0.0975852	−	0.235591i
$63$	−5.87456	−	2.43332i	−0.740125	−	0.306570i
$64$			5.79861i			0.724827i
$65$	−2.56901	+	6.20213i	−0.318646	+	0.769280i
$66$	1.82368	−	1.82368i	0.224479	−	0.224479i
$67$	6.08039			0.742838			0.371419	−	0.928465i	$-0.378871\pi$
$67$	6.08039			0.742838			0.371419	+	0.928465i	$0.378871\pi$
$68$	0.0600619	+	1.66371i	0.00728357	+	0.201755i
$69$	4.82540			0.580909
$70$	4.10179	−	4.10179i	0.490257	−	0.490257i
$71$	−1.46625	+	3.53983i	−0.174011	+	0.420101i	−0.986690	−	0.162611i	$-0.948008\pi$
$71$	−1.46625	+	3.53983i	−0.174011	+	0.420101i	0.812679	+	0.582712i	$0.198008\pi$
$72$			4.20591i			0.495672i
$73$	12.9392	+	5.35957i	1.51441	+	0.627291i	0.976463	−	0.215686i	$-0.0691987\pi$
$73$	12.9392	+	5.35957i	1.51441	+	0.627291i	0.537951	+	0.842976i	$0.319199\pi$
$74$	−2.67991	−	6.46987i	−0.311533	−	0.752107i
$75$	1.05359	−	0.436412i	0.121658	−	0.0503925i
$76$	0.535509	+	0.535509i	0.0614271	+	0.0614271i
$77$	−3.85910	−	3.85910i	−0.439785	−	0.439785i
$78$	−10.9659	+	4.54222i	−1.24164	+	0.514306i
$79$	−0.916355	−	2.21228i	−0.103098	−	0.248901i	0.863910	−	0.503646i	$-0.168008\pi$
$79$	−0.916355	−	2.21228i	−0.103098	−	0.248901i	−0.967008	+	0.254745i	$0.918008\pi$
$80$	−4.29097	−	1.77738i	−0.479745	−	0.198717i
$81$		−	1.01326i		−	0.112584i
$82$	0.932200	−	2.25053i	0.102944	−	0.248529i
$83$	−11.9378	+	11.9378i	−1.31035	+	1.31035i	−0.389189	+	0.921158i	$0.627245\pi$
$83$	−11.9378	+	11.9378i	−1.31035	+	1.31035i	−0.921158	+	0.389189i	$0.872755\pi$
$84$	1.72280			0.187973
$85$	3.86370	+	1.43939i	0.419077	+	0.156124i
$86$	−10.0181			−1.08028
$87$	−6.12369	+	6.12369i	−0.656528	+	0.656528i
$88$	−1.38147	+	3.33516i	−0.147265	+	0.355529i
$89$		−	1.59370i		−	0.168931i	−0.996426	−	0.0844657i	$-0.973082\pi$
$89$		−	1.59370i		−	0.168931i	0.996426	−	0.0844657i	$-0.0269184\pi$
$90$	−2.43434	−	1.00834i	−0.256602	−	0.106288i
$91$	9.61184	+	23.2050i	1.00759	+	2.43255i
$92$	1.57844	−	0.653811i	0.164564	−	0.0681645i
$93$	−1.04432	−	1.04432i	−0.108291	−	0.108291i
$94$	2.59572	+	2.59572i	0.267728	+	0.267728i
$95$	1.73285	−	0.717770i	0.177787	−	0.0736417i
$96$	−0.982486	−	2.37193i	−0.100275	−	0.242084i
$97$	−12.5670	−	5.20542i	−1.27599	−	0.528531i	−0.361207	−	0.932486i	$-0.617635\pi$
$97$	−12.5670	−	5.20542i	−1.27599	−	0.528531i	−0.914779	+	0.403955i	$0.867635\pi$
$98$		−	10.8506i		−	1.09608i
$99$	−0.948677	+	2.29031i	−0.0953457	+	0.230185i
$100$	0.285510	−	0.285510i	0.0285510	−	0.0285510i
$101$	−0.0696369			−0.00692913			−0.00346456	−	0.999994i	$-0.501103\pi$
$101$	−0.0696369			−0.00692913			−0.00346456	+	0.999994i	$0.501103\pi$
$102$	3.03093	+	6.63005i	0.300107	+	0.656473i
$103$	−7.83693			−0.772196			−0.386098	−	0.922458i	$-0.626177\pi$
$103$	−7.83693			−0.772196			−0.386098	+	0.922458i	$0.626177\pi$
$104$	11.7477	−	11.7477i	1.15195	−	1.15195i
$105$	1.63282	−	3.94197i	0.159347	−	0.384697i
$106$		−	9.33025i		−	0.906234i
$107$	1.55204	+	0.642876i	0.150041	+	0.0621492i	0.456440	−	0.889754i	$-0.349124\pi$
$107$	1.55204	+	0.642876i	0.150041	+	0.0621492i	−0.306399	+	0.951903i	$0.599124\pi$
$108$	−0.828101	−	1.99921i	−0.0796841	−	0.192374i
$109$	5.77839	−	2.39349i	0.553469	−	0.229254i	−0.0883780	−	0.996087i	$-0.528168\pi$
$109$	5.77839	−	2.39349i	0.553469	−	0.229254i	0.641847	+	0.766833i	$0.278168\pi$
$110$	−1.59916	−	1.59916i	−0.152474	−	0.152474i
$111$	−3.64230	−	3.64230i	−0.345712	−	0.345712i
$112$	−16.0545	+	6.64999i	−1.51701	+	0.628365i
$113$	4.34271	+	10.4842i	0.408527	+	0.986273i	0.985526	+	0.169527i	$0.0542240\pi$
$113$	4.34271	+	10.4842i	0.408527	+	0.986273i	−0.576998	+	0.816746i	$0.695776\pi$
$114$	3.06383	+	1.26908i	0.286954	+	0.118860i
$115$		−	4.23132i		−	0.394573i
$116$	−1.17340	+	2.83284i	−0.108948	+	0.263023i
$117$	8.06732	−	8.06732i	0.745824	−	0.745824i
$118$	15.9873			1.47175
$119$	14.0299	−	6.41378i	1.28612	−	0.587951i
$120$	−2.82227			−0.257637
$121$	6.27363	−	6.27363i	0.570330	−	0.570330i
$122$	1.86354	−	4.49898i	0.168717	−	0.407319i
$123$		−	1.79176i		−	0.161557i
$124$	−0.483109	−	0.200110i	−0.0433845	−	0.0179704i
$125$	−0.382683	−	0.923880i	−0.0342282	−	0.0826343i
$126$	−9.10798	+	3.77265i	−0.811403	+	0.336094i
$127$	−9.41141	−	9.41141i	−0.835127	−	0.835127i	0.153086	−	0.988213i	$-0.451079\pi$
$127$	−9.41141	−	9.41141i	−0.835127	−	0.835127i	−0.988213	+	0.153086i	$0.951079\pi$
$128$	9.54085	+	9.54085i	0.843300	+	0.843300i
$129$	−6.80786	+	2.81991i	−0.599399	+	0.248279i
$130$	3.98301	+	9.61585i	0.349333	+	0.843366i
$131$	−0.603703	−	0.250062i	−0.0527458	−	0.0218480i	0.356155	−	0.934427i	$-0.384088\pi$
$131$	−0.603703	−	0.250062i	−0.0527458	−	0.0218480i	−0.408900	+	0.912579i	$0.634088\pi$
$132$		−	0.671665i		−	0.0584610i
$133$	2.68551	−	6.48339i	0.232863	−	0.562182i
$134$	6.66597	−	6.66597i	0.575852	−	0.575852i
$135$	−5.35929			−0.461255
$136$	−7.47086	−	6.95024i	−0.640621	−	0.595978i
$137$	0.627983			0.0536522			0.0268261	−	0.999640i	$-0.491460\pi$
$137$	0.627983			0.0536522			0.0268261	+	0.999640i	$0.491460\pi$
$138$	5.29011	−	5.29011i	0.450324	−	0.450324i
$139$	5.05298	−	12.1990i	0.428589	−	1.03470i	−0.551147	−	0.834408i	$-0.685810\pi$
$139$	5.05298	−	12.1990i	0.428589	−	1.03470i	0.979735	−	0.200296i	$-0.0641904\pi$
$140$		−	1.51070i		−	0.127677i
$141$	2.49459	+	1.03329i	0.210082	+	0.0870188i
$142$	2.27328	+	5.48819i	0.190770	+	0.460559i
$143$	9.04692	−	3.74736i	0.756542	−	0.313370i
$144$	5.58141	+	5.58141i	0.465118	+	0.465118i
$145$	5.36978	+	5.36978i	0.445936	+	0.445936i
$146$	20.0610	−	8.30954i	1.66026	−	0.687702i
$147$	−3.05424	−	7.37359i	−0.251910	−	0.608164i
$148$	−1.68494	−	0.697926i	−0.138501	−	0.0573692i
$149$			22.9291i			1.87842i	0.343336	+	0.939212i	$0.388443\pi$
$149$			22.9291i			1.87842i	−0.343336	+	0.939212i	$0.611557\pi$
$150$	0.676617	−	1.63350i	0.0552456	−	0.133375i
$151$	−0.110126	+	0.110126i	−0.00896193	+	0.00896193i	−0.711574	−	0.702612i	$-0.752017\pi$
$151$	−0.110126	+	0.110126i	−0.00896193	+	0.00896193i	0.702612	+	0.711574i	$0.252017\pi$
$152$	−4.64181			−0.376500
$153$	−5.13036	−	4.77284i	−0.414765	−	0.385861i
$154$	−8.46151			−0.681848
$155$	−0.915753	+	0.915753i	−0.0735551	+	0.0735551i
$156$	−1.18293	+	2.85584i	−0.0947100	+	0.228650i
$157$			12.4603i			0.994443i	0.867624	+	0.497221i	$0.165646\pi$
$157$			12.4603i			0.994443i	−0.867624	+	0.497221i	$0.834354\pi$
$158$	−3.42994	−	1.42073i	−0.272871	−	0.113027i
$159$	−2.62629	−	6.34043i	−0.208279	−	0.502829i
$160$	−2.07991	+	0.861529i	−0.164432	+	0.0681098i
$161$	−11.1944	−	11.1944i	−0.882246	−	0.882246i
$162$	−1.11084	−	1.11084i	−0.0872759	−	0.0872759i
$163$	−19.6174	+	8.12578i	−1.53655	+	0.636460i	−0.980822	−	0.194903i	$-0.937561\pi$
$163$	−19.6174	+	8.12578i	−1.53655	+	0.636460i	−0.555729	+	0.831364i	$0.687561\pi$
$164$	−0.242772	−	0.586104i	−0.0189573	−	0.0457670i
$165$	−1.53685	−	0.636585i	−0.119644	−	0.0495581i
$166$			26.1750i			2.03158i
$167$	0.548558	−	1.32434i	0.0424487	−	0.102480i	−0.901233	−	0.433335i	$-0.857337\pi$
$167$	0.548558	−	1.32434i	0.0424487	−	0.102480i	0.943682	+	0.330854i	$0.107337\pi$
$168$	−7.46663	+	7.46663i	−0.576063	+	0.576063i
$169$	−32.0662			−2.46663
$170$	5.81380	−	2.65778i	0.445898	−	0.203843i
$171$	−3.18761			−0.243762
$172$	−1.84484	+	1.84484i	−0.140668	+	0.140668i
$173$	0.528746	−	1.27651i	0.0401998	−	0.0970509i	−0.902504	−	0.430681i	$-0.858274\pi$
$173$	0.528746	−	1.27651i	0.0401998	−	0.0970509i	0.942704	+	0.333630i	$0.108274\pi$
$174$			13.4269i			1.01789i
$175$	−3.45666	−	1.43180i	−0.261299	−	0.108234i
$176$	2.59263	+	6.25915i	0.195426	+	0.471801i
$177$	10.8643	−	4.50012i	0.816607	−	0.338250i
$178$	−1.74718	−	1.74718i	−0.130957	−	0.130957i
$179$	−6.50583	−	6.50583i	−0.486269	−	0.486269i	0.420858	−	0.907127i	$-0.361729\pi$
$179$	−6.50583	−	6.50583i	−0.486269	−	0.486269i	−0.907127	+	0.420858i	$0.861729\pi$
$180$	−0.633972	+	0.262600i	−0.0472535	+	0.0195730i
$181$	−5.27107	−	12.7255i	−0.391795	−	0.945878i	−0.989549	−	0.144198i	$-0.953940\pi$
$181$	−5.27107	−	12.7255i	−0.391795	−	0.945878i	0.597754	−	0.801680i	$-0.296060\pi$
$182$	35.9773	+	14.9023i	2.66682	+	1.10463i
$183$		−	3.58186i		−	0.264779i
$184$	−4.00735	+	9.67460i	−0.295426	+	0.713221i
$185$	−3.19388	+	3.19388i	−0.234819	+	0.234819i
$186$	−2.28980			−0.167896
$187$	−2.50054	−	5.46983i	−0.182857	−	0.399993i
$188$	0.956011			0.0697242
$189$	−14.1786	+	14.1786i	−1.03134	+	1.03134i
$190$	1.11284	−	2.68663i	0.0807338	−	0.194909i
$191$		−	10.0667i		−	0.728401i	−0.931321	−	0.364200i	$-0.881342\pi$
$191$		−	10.0667i		−	0.728401i	0.931321	−	0.364200i	$-0.118658\pi$
$192$	6.10937	+	2.53058i	0.440905	+	0.182629i
$193$	0.678267	+	1.63748i	0.0488227	+	0.117869i	0.946409	−	0.322970i	$-0.104681\pi$
$193$	0.678267	+	1.63748i	0.0488227	+	0.117869i	−0.897587	+	0.440838i	$0.854681\pi$
$194$	−19.4840	+	8.07054i	−1.39887	+	0.579431i
$195$	5.41336	+	5.41336i	0.387659	+	0.387659i
$196$	−1.99815	−	1.99815i	−0.142725	−	0.142725i
$197$	10.1354	−	4.19823i	0.722119	−	0.299112i	0.00881014	−	0.999961i	$-0.497196\pi$
$197$	10.1354	−	4.19823i	0.722119	−	0.299112i	0.713309	+	0.700850i	$0.247196\pi$
$198$	1.47084	+	3.55092i	0.104528	+	0.252353i
$199$	3.63307	+	1.50487i	0.257542	+	0.106677i	0.507719	−	0.861523i	$-0.330489\pi$
$199$	3.63307	+	1.50487i	0.257542	+	0.106677i	−0.250177	+	0.968200i	$0.580489\pi$
$200$			2.47481i			0.174995i
$201$	2.65355	−	6.40625i	0.187167	−	0.451862i
$202$	−0.0763433	+	0.0763433i	−0.00537150	+	0.00537150i
$203$	28.4127			1.99418
$204$	1.77908	+	0.662782i	0.124561	+	0.0464040i
$205$	−1.57117			−0.109735
$206$	−8.59167	+	8.59167i	−0.598610	+	0.598610i
$207$	−2.75191	+	6.64371i	−0.191271	+	0.461770i
$208$		−	31.1792i		−	2.16189i
$209$	−2.52767	−	1.04700i	−0.174843	−	0.0724223i
$210$	−2.53154	−	6.11167i	−0.174693	−	0.421745i
$211$	25.4852	−	10.5563i	1.75447	−	0.726726i	0.757178	−	0.653209i	$-0.226578\pi$
$211$	25.4852	−	10.5563i	1.75447	−	0.726726i	0.997294	−	0.0735168i	$-0.0234223\pi$
$212$	−1.71818	−	1.71818i	−0.118005	−	0.118005i
$213$	3.08965	+	3.08965i	0.211699	+	0.211699i
$214$	2.40630	−	0.996722i	0.164491	−	0.0681345i
$215$	2.47274	+	5.96972i	0.168639	+	0.407131i
$216$	12.2536	+	5.07562i	0.833753	+	0.345352i
$217$			4.84546i			0.328931i
$218$	3.71089	−	8.95887i	0.251333	−	0.606771i
$219$	11.2936	−	11.2936i	0.763151	−	0.763151i
$220$	−0.588974			−0.0397086
$221$	0.998592	+	27.6610i	0.0671726	+	1.86068i
$222$	−7.98614			−0.535995
$223$	−14.3922	+	14.3922i	−0.963775	+	0.963775i	−0.999366	−	0.0355918i	$-0.988668\pi$
$223$	−14.3922	+	14.3922i	−0.963775	+	0.963775i	0.0355918	+	0.999366i	$0.488668\pi$
$224$	−3.22338	+	7.78192i	−0.215371	+	0.519951i
$225$			1.69949i			0.113299i
$226$	16.2548	+	6.73298i	1.08126	+	0.447871i
$227$	2.58618	+	6.24359i	0.171651	+	0.414402i	0.986170	−	0.165734i	$-0.0529994\pi$
$227$	2.58618	+	6.24359i	0.171651	+	0.414402i	−0.814520	+	0.580136i	$0.802999\pi$
$228$	0.797910	−	0.330505i	0.0528429	−	0.0218882i
$229$	−17.3101	−	17.3101i	−1.14388	−	1.14388i	−0.987733	−	0.156150i	$-0.950092\pi$
$229$	−17.3101	−	17.3101i	−1.14388	−	1.14388i	−0.156150	−	0.987733i	$-0.549908\pi$
$230$	−4.63882	−	4.63882i	−0.305875	−	0.305875i
$231$	−5.75007	+	2.38176i	−0.378327	+	0.156708i
$232$	−7.19205	−	17.3631i	−0.472181	−	1.13995i
$233$	−15.0512	−	6.23442i	−0.986038	−	0.408430i	−0.169379	−	0.985551i	$-0.554176\pi$
$233$	−15.0512	−	6.23442i	−0.986038	−	0.408430i	−0.816659	+	0.577121i	$0.804176\pi$
$234$		−	17.6885i		−	1.15633i
$235$	0.906079	−	2.18747i	0.0591061	−	0.142695i
$236$	2.94408	−	2.94408i	0.191643	−	0.191643i
$237$	−2.73074			−0.177381
$238$	8.34960	−	22.4125i	0.541224	−	1.45279i
$239$	11.7800			0.761984			0.380992	−	0.924578i	$-0.375583\pi$
$239$	11.7800			0.761984			0.380992	+	0.924578i	$0.375583\pi$
$240$	−3.74526	+	3.74526i	−0.241755	+	0.241755i
$241$	−0.557214	+	1.34523i	−0.0358933	+	0.0866541i	−0.940810	−	0.338935i	$-0.889933\pi$
$241$	−0.557214	+	1.34523i	−0.0358933	+	0.0866541i	0.904916	+	0.425589i	$0.139933\pi$
$242$		−	13.7556i		−	0.884246i
$243$	13.7865	+	5.71054i	0.884402	+	0.366331i
$244$	−0.485320	−	1.17167i	−0.0310694	−	0.0750082i
$245$	−6.46580	+	2.67822i	−0.413085	+	0.171105i
$246$	−1.96431	−	1.96431i	−0.125240	−	0.125240i
$247$	8.90341	+	8.90341i	0.566510	+	0.566510i
$248$	2.96108	−	1.22652i	0.188029	−	0.0778841i
$249$	7.36778	+	17.7874i	0.466914	+	1.12723i
$250$	−1.43239	−	0.593316i	−0.0905924	−	0.0375246i
$251$		−	23.1739i		−	1.46272i	−0.681990	−	0.731361i	$-0.738885\pi$
$251$		−	23.1739i		−	1.46272i	0.681990	−	0.731361i	$-0.261115\pi$
$252$	−0.982508	+	2.37198i	−0.0618922	+	0.149421i
$253$	−4.36437	+	4.36437i	−0.274385	+	0.274385i
$254$	−20.6356			−1.29479
$255$	3.20269	−	3.44259i	0.200560	−	0.215583i
$256$	9.32214			0.582634
$257$	8.63013	−	8.63013i	0.538332	−	0.538332i	−0.384706	−	0.923039i	$-0.625697\pi$
$257$	8.63013	−	8.63013i	0.538332	−	0.538332i	0.923039	+	0.384706i	$0.125697\pi$
$258$	−4.37201	+	10.5550i	−0.272190	+	0.657124i
$259$			16.8995i			1.05009i
$260$	2.50425	+	1.03729i	0.155307	+	0.0643302i
$261$	−4.93889	−	11.9235i	−0.305710	−	0.738049i
$262$	−0.935988	+	0.387699i	−0.0578255	+	0.0239521i
$263$	−10.0435	−	10.0435i	−0.619312	−	0.619312i	0.326043	−	0.945355i	$-0.394284\pi$
$263$	−10.0435	−	10.0435i	−0.619312	−	0.619312i	−0.945355	+	0.326043i	$0.894284\pi$
$264$	2.91101	+	2.91101i	0.179160	+	0.179160i
$265$	−5.55984	+	2.30296i	−0.341538	+	0.141470i
$266$	−4.16364	−	10.0519i	−0.255289	−	0.616323i
$267$	−1.67910	−	0.695508i	−0.102760	−	0.0425644i
$268$		−	2.45509i		−	0.149969i
$269$	−4.96381	+	11.9837i	−0.302649	+	0.730658i	0.697256	+	0.716822i	$0.254404\pi$
$269$	−4.96381	+	11.9837i	−0.302649	+	0.730658i	−0.999904	+	0.0138358i	$0.995596\pi$
$270$	−5.87542	+	5.87542i	−0.357567	+	0.357567i
$271$	−26.5159			−1.61073			−0.805364	−	0.592780i	$-0.798030\pi$
$271$	−26.5159			−1.61073			−0.805364	+	0.592780i	$0.798030\pi$
$272$	−19.1373	+	0.690880i	−1.16037	+	0.0418908i
$273$	28.6433			1.73357
$274$	0.688461	−	0.688461i	0.0415915	−	0.0415915i
$275$	−0.558213	+	1.34764i	−0.0336615	+	0.0812660i
$276$		−	1.94836i		−	0.117277i
$277$	−6.00580	−	2.48768i	−0.360853	−	0.149470i	0.194888	−	0.980825i	$-0.437566\pi$
$277$	−6.00580	−	2.48768i	−0.360853	−	0.149470i	−0.555742	+	0.831355i	$0.687566\pi$
$278$	−7.83420	−	18.9134i	−0.469864	−	1.13435i
$279$	2.03342	−	0.842271i	0.121738	−	0.0504255i
$280$	6.54738	+	6.54738i	0.391281	+	0.391281i
$281$	−4.28147	−	4.28147i	−0.255411	−	0.255411i	0.567774	−	0.823185i	$-0.307805\pi$
$281$	−4.28147	−	4.28147i	−0.255411	−	0.255411i	−0.823185	+	0.567774i	$0.807805\pi$
$282$	3.86763	−	1.60203i	0.230314	−	0.0953992i
$283$	5.38173	+	12.9927i	0.319911	+	0.772333i	0.999258	+	0.0385160i	$0.0122631\pi$
$283$	5.38173	+	12.9927i	0.319911	+	0.772333i	−0.679347	+	0.733817i	$0.737737\pi$
$284$	1.42928	+	0.592029i	0.0848124	+	0.0351305i
$285$		−	2.13896i		−	0.126701i
$286$	5.80994	−	14.0264i	0.343549	−	0.829401i
$287$	−4.15670	+	4.15670i	−0.245362	+	0.245362i
$288$	3.82603			0.225451
$289$	16.9557	−	1.22584i	0.997397	−	0.0721083i
$290$	11.7738			0.691383
$291$	−10.9688	+	10.9688i	−0.643001	+	0.643001i
$292$	2.16405	−	5.22447i	0.126641	−	0.305739i
$293$			1.98335i			0.115869i	0.998320	+	0.0579343i	$0.0184514\pi$
$293$			1.98335i			0.115869i	−0.998320	+	0.0579343i	$0.981549\pi$
$294$	−11.4321	−	4.73533i	−0.666733	−	0.276170i
$295$	−3.94610	−	9.52672i	−0.229751	−	0.554667i
$296$	10.3274	−	4.27775i	0.600267	−	0.248639i
$297$	5.52780	+	5.52780i	0.320756	+	0.320756i
$298$	25.1373	+	25.1373i	1.45616	+	1.45616i
$299$	26.2432	−	10.8703i	1.51768	−	0.628646i
$300$	−0.176211	−	0.425411i	−0.0101735	−	0.0245611i
$301$	22.3355	+	9.25165i	1.28740	+	0.533257i
$302$			0.241463i			0.0138947i
$303$	−0.0303903	+	0.0733688i	−0.00174588	+	0.00421493i
$304$	−6.15986	+	6.15986i	−0.353292	+	0.353292i
$305$	−3.14089			−0.179847
$306$	−10.8569	+	0.391948i	−0.620649	+	0.0224062i
$307$	−3.54695			−0.202435			−0.101218	−	0.994864i	$-0.532274\pi$
$307$	−3.54695			−0.202435			−0.101218	+	0.994864i	$0.532274\pi$
$308$	−1.55820	+	1.55820i	−0.0887865	+	0.0887865i
$309$	−3.42013	+	8.25692i	−0.194564	+	0.469720i
$310$			2.00789i			0.114041i
$311$	−3.33429	−	1.38111i	−0.189070	−	0.0783155i	0.286140	−	0.958188i	$-0.407628\pi$
$311$	−3.33429	−	1.38111i	−0.189070	−	0.0783155i	−0.475210	+	0.879872i	$0.657628\pi$
$312$	−7.25042	−	17.5041i	−0.410474	−	0.990973i
$313$	−7.55002	+	3.12732i	−0.426753	+	0.176767i	−0.585713	−	0.810518i	$-0.699186\pi$
$313$	−7.55002	+	3.12732i	−0.426753	+	0.176767i	0.158961	+	0.987285i	$0.449186\pi$
$314$	13.6603	+	13.6603i	0.770897	+	0.770897i
$315$	4.49619	+	4.49619i	0.253332	+	0.253332i
$316$	−0.893255	+	0.369998i	−0.0502495	+	0.0208140i
$317$	7.63011	+	18.4207i	0.428550	+	1.03461i	0.979748	+	0.200236i	$0.0641710\pi$
$317$	7.63011	+	18.4207i	0.428550	+	1.03461i	−0.551198	+	0.834375i	$0.685829\pi$
$318$	−9.83027	−	4.07183i	−0.551254	−	0.228337i
$319$		−	11.0772i		−	0.620206i
$320$	2.21903	−	5.35722i	0.124048	−	0.299478i
$321$	1.35466	−	1.35466i	0.0756096	−	0.0756096i
$322$	−24.5451			−1.36784
$323$	5.26749	−	5.66206i	0.293091	−	0.315046i
$324$	−0.409125			−0.0227292
$325$	4.74691	−	4.74691i	0.263311	−	0.263311i
$326$	−12.5983	+	30.4150i	−0.697755	+	1.68453i
$327$		−	7.13260i		−	0.394434i
$328$	3.59236	+	1.48800i	0.198355	+	0.0821613i
$329$	−3.39006	−	8.18433i	−0.186900	−	0.451217i
$330$	−2.38275	+	0.986968i	−0.131166	+	0.0543308i
$331$	9.85914	+	9.85914i	0.541907	+	0.541907i	0.924088	−	0.382180i	$-0.124827\pi$
$331$	9.85914	+	9.85914i	0.541907	+	0.541907i	−0.382180	+	0.924088i	$0.624827\pi$
$332$	4.82016	+	4.82016i	0.264541	+	0.264541i
$333$	7.09199	−	2.93760i	0.388639	−	0.160979i
$334$	−0.850490	−	2.05327i	−0.0465368	−	0.112350i
$335$	−5.61755	−	2.32687i	−0.306920	−	0.127130i
$336$			19.8170i			1.08111i
$337$	−7.67782	+	18.5359i	−0.418237	+	1.00971i	0.564621	+	0.825350i	$0.309022\pi$
$337$	−7.67782	+	18.5359i	−0.418237	+	1.00971i	−0.982858	+	0.184364i	$0.940978\pi$
$338$	−35.1544	+	35.1544i	−1.91215	+	1.91215i
$339$	12.9413			0.702874
$340$	0.581185	−	1.56005i	0.0315192	−	0.0846058i
$341$	1.88909			0.102300
$342$	−3.49459	+	3.49459i	−0.188966	+	0.188966i
$343$	0.00209978	−	0.00506933i	0.000113378	−	0.000273718i
$344$		−	15.9912i		−	0.862186i
$345$	−4.45809	−	1.84660i	−0.240015	−	0.0994176i
$346$	−0.819773	−	1.97911i	−0.0440713	−	0.106397i
$347$	−19.9229	+	8.25234i	−1.06952	+	0.443009i	−0.846820	−	0.531879i	$-0.821486\pi$
$347$	−19.9229	+	8.25234i	−1.06952	+	0.443009i	−0.222697	+	0.974888i	$0.571486\pi$
$348$	2.47257	+	2.47257i	0.132544	+	0.132544i
$349$	7.75970	+	7.75970i	0.415367	+	0.415367i	0.883603	−	0.468236i	$-0.155110\pi$
$349$	7.75970	+	7.75970i	0.415367	+	0.415367i	−0.468236	+	0.883603i	$0.655110\pi$
$350$	−5.35924	+	2.21987i	−0.286463	+	0.118657i
$351$	−13.7681	−	33.2390i	−0.734885	−	1.77417i
$352$	3.03393	+	1.25669i	0.161709	+	0.0669820i
$353$		−	23.3210i		−	1.24125i	−0.784108	−	0.620625i	$-0.786879\pi$
$353$		−	23.3210i		−	1.24125i	0.784108	−	0.620625i	$-0.213121\pi$
$354$	6.97703	−	16.8441i	0.370825	−	0.895251i
$355$	2.70927	−	2.70927i	0.143793	−	0.143793i
$356$	−0.643490			−0.0341049
$357$	−0.634689	−	17.5808i	−0.0335913	−	0.930477i
$358$	−14.2648			−0.753916
$359$	1.38736	−	1.38736i	0.0732222	−	0.0732222i	−0.669547	−	0.742769i	$-0.733512\pi$
$359$	1.38736	−	1.38736i	0.0732222	−	0.0732222i	0.742769	+	0.669547i	$0.233512\pi$
$360$	1.60953	−	3.88576i	0.0848299	−	0.204797i
$361$			15.4820i			0.814844i
$362$	−19.7297	−	8.17232i	−1.03697	−	0.429527i
$363$	−3.87195	−	9.34773i	−0.203225	−	0.490628i
$364$	9.36954	−	3.88099i	0.491097	−	0.203419i
$365$	−9.90320	−	9.90320i	−0.518357	−	0.518357i
$366$	−3.92682	−	3.92682i	−0.205258	−	0.205258i
$367$	30.4997	−	12.6334i	1.59207	−	0.659457i	0.601804	−	0.798644i	$-0.294449\pi$
$367$	30.4997	−	12.6334i	1.59207	−	0.659457i	0.990266	+	0.139187i	$0.0444488\pi$
$368$	7.52066	+	18.1565i	0.392042	+	0.946472i
$369$	2.46693	+	1.02184i	0.128423	+	0.0531947i
$370$			7.00294i			0.364066i
$371$	−8.61644	+	20.8019i	−0.447343	+	1.07998i
$372$	−0.421669	+	0.421669i	−0.0218625	+	0.0218625i
$373$	10.2773			0.532141			0.266070	−	0.963954i	$-0.414275\pi$
$373$	10.2773			0.532141			0.266070	+	0.963954i	$0.414275\pi$
$374$	−8.73795	−	3.25525i	−0.451829	−	0.168325i
$375$	−1.14040			−0.0588899
$376$	−4.14336	+	4.14336i	−0.213678	+	0.213678i
$377$	−19.5091	+	47.0990i	−1.00477	+	2.42572i
$378$			31.0882i			1.59900i
$379$	22.2204	+	9.20401i	1.14139	+	0.472778i	0.871637	−	0.490152i	$-0.163059\pi$
$379$	22.2204	+	9.20401i	1.14139	+	0.472778i	0.269751	+	0.962930i	$0.413059\pi$
$380$	−0.289816	−	0.699677i	−0.0148672	−	0.0358927i
$381$	−14.0230	+	5.80853i	−0.718421	+	0.297580i
$382$	−11.0362	−	11.0362i	−0.564660	−	0.564660i
$383$	−1.97435	−	1.97435i	−0.100884	−	0.100884i	0.654863	−	0.755748i	$-0.272726\pi$
$383$	−1.97435	−	1.97435i	−0.100884	−	0.100884i	−0.755748	+	0.654863i	$0.772726\pi$
$384$	14.2159	−	5.88841i	0.725451	−	0.300492i
$385$	2.08853	+	5.04216i	0.106441	+	0.256972i
$386$	2.53877	+	1.05159i	0.129220	+	0.0535247i
$387$		−	10.9814i		−	0.558215i
$388$	−2.10180	+	5.07420i	−0.106703	+	0.257604i
$389$	−3.02275	+	3.02275i	−0.153260	+	0.153260i	−0.779572	−	0.626313i	$-0.784563\pi$
$389$	−3.02275	+	3.02275i	−0.153260	+	0.153260i	0.626313	+	0.779572i	$0.284563\pi$
$390$	11.8694			0.601031
$391$	−7.25353	−	15.8668i	−0.366827	−	0.802420i
$392$	17.3200			0.874794
$393$	−0.526926	+	0.526926i	−0.0265799	+	0.0265799i
$394$	6.50898	−	15.7141i	0.327918	−	0.791663i
$395$			2.39455i			0.120483i
$396$	0.924763	+	0.383049i	0.0464711	+	0.0192490i
$397$	5.93808	+	14.3358i	0.298023	+	0.719492i	0.999974	+	0.00726623i	$0.00231293\pi$
$397$	5.93808	+	14.3358i	0.298023	+	0.719492i	−0.701950	+	0.712226i	$0.747687\pi$
$398$	5.63276	−	2.33316i	0.282345	−	0.116951i
$399$	−5.65886	−	5.65886i	−0.283297	−	0.283297i
$400$	3.28417	+	3.28417i	0.164208	+	0.164208i
$401$	19.3924	−	8.03258i	0.968409	−	0.401128i	0.158289	−	0.987393i	$-0.449402\pi$
$401$	19.3924	−	8.03258i	0.968409	−	0.401128i	0.810120	+	0.586265i	$0.199402\pi$
$402$	−4.11410	−	9.93231i	−0.205193	−	0.495379i
$403$	−8.03220	−	3.32704i	−0.400112	−	0.165732i
$404$			0.0281174i			0.00139889i
$405$	−0.387757	+	0.936128i	−0.0192678	+	0.0465166i
$406$	31.1490	−	31.1490i	1.54590	−	1.54590i
$407$	6.58861			0.326585
$408$	−10.5831	+	4.83806i	−0.523940	+	0.239520i
$409$	−8.86633			−0.438412			−0.219206	−	0.975679i	$-0.570347\pi$
$409$	−8.86633			−0.438412			−0.219206	+	0.975679i	$0.570347\pi$
$410$	−1.72248	+	1.72248i	−0.0850673	+	0.0850673i
$411$	0.274059	−	0.661637i	0.0135183	−	0.0326362i
$412$			3.16433i			0.155896i
$413$	−35.6438	−	14.7642i	−1.75392	−	0.726497i
$414$	4.26660	+	10.3005i	0.209692	+	0.506241i
$415$	15.5975	−	6.46071i	0.765652	−	0.317144i
$416$	−10.6866	−	10.6866i	−0.523955	−	0.523955i
$417$	−10.6476	−	10.6476i	−0.521413	−	0.521413i
$418$	−3.91893	+	1.62327i	−0.191681	+	0.0793970i
$419$	−12.3812	−	29.8909i	−0.604861	−	1.46026i	−0.868523	−	0.495649i	$-0.834930\pi$
$419$	−12.3812	−	29.8909i	−0.604861	−	1.46026i	0.263662	−	0.964615i	$-0.415070\pi$
$420$	−1.59166	−	0.659286i	−0.0776649	−	0.0321699i
$421$		−	3.62096i		−	0.176475i	−0.996099	−	0.0882374i	$-0.971877\pi$
$421$		−	3.62096i		−	0.176475i	0.996099	−	0.0882374i	$-0.0281234\pi$
$422$	16.3666	−	39.5125i	0.796714	−	1.92344i
$423$	−2.84531	+	2.84531i	−0.138344	+	0.138344i
$424$	14.8932			0.723278
$425$	−3.01876	−	2.80839i	−0.146431	−	0.136227i
$426$	6.77440			0.328221
$427$	−8.30957	+	8.30957i	−0.402128	+	0.402128i
$428$	0.259575	−	0.626670i	0.0125470	−	0.0302913i
$429$		−	11.1671i		−	0.539155i
$430$	9.25551	+	3.83376i	0.446340	+	0.184880i
$431$	6.69733	+	16.1688i	0.322599	+	0.778823i	0.999101	+	0.0423823i	$0.0134948\pi$
$431$	6.69733	+	16.1688i	0.322599	+	0.778823i	−0.676503	+	0.736440i	$0.736505\pi$
$432$	22.9966	−	9.52549i	1.10642	−	0.458295i
$433$	6.46703	+	6.46703i	0.310785	+	0.310785i	0.845214	−	0.534428i	$-0.179473\pi$
$433$	6.46703	+	6.46703i	0.310785	+	0.310785i	−0.534428	+	0.845214i	$0.679473\pi$
$434$	5.31210	+	5.31210i	0.254989	+	0.254989i
$435$	8.00098	−	3.31411i	0.383618	−	0.158900i
$436$	−0.966423	−	2.33315i	−0.0462833	−	0.111738i
$437$	−7.33225	−	3.03712i	−0.350749	−	0.145285i
$438$		−	24.7625i		−	1.18320i
$439$	2.07310	−	5.00491i	0.0989438	−	0.238872i	−0.866655	−	0.498908i	$-0.833735\pi$
$439$	2.07310	−	5.00491i	0.0989438	−	0.238872i	0.965599	+	0.260036i	$0.0837346\pi$
$440$	2.55262	−	2.55262i	0.121691	−	0.121691i
$441$	11.8939			0.566378
$442$	31.4196	+	29.2301i	1.49448	+	1.39033i
$443$	−6.91215			−0.328406			−0.164203	−	0.986427i	$-0.552505\pi$
$443$	−6.91215			−0.328406			−0.164203	+	0.986427i	$0.552505\pi$
$444$	−1.47066	+	1.47066i	−0.0697943	+	0.0697943i
$445$	−0.609881	+	1.47238i	−0.0289111	+	0.0697977i
$446$			31.5566i			1.49425i
$447$	24.1579	+	10.0065i	1.14263	+	0.473292i
$448$	−8.30243	−	20.0438i	−0.392253	−	0.946982i
$449$	16.5362	−	6.84953i	0.780392	−	0.323249i	0.0433186	−	0.999061i	$-0.486207\pi$
$449$	16.5362	−	6.84953i	0.780392	−	0.323249i	0.737074	+	0.675812i	$0.236207\pi$
$450$	1.86316	+	1.86316i	0.0878303	+	0.0878303i
$451$	1.62057	+	1.62057i	0.0763097	+	0.0763097i
$452$	4.23324	−	1.75346i	0.199115	−	0.0824760i
$453$	0.0679675	+	0.164088i	0.00319339	+	0.00770953i
$454$	9.68013	+	4.00964i	0.454311	+	0.188182i
$455$		−	25.1169i		−	1.17750i
$456$	−2.02574	+	4.89057i	−0.0948640	+	0.229022i
$457$	28.3676	−	28.3676i	1.32698	−	1.32698i	0.418988	−	0.907992i	$-0.362385\pi$
$457$	28.3676	−	28.3676i	1.32698	−	1.32698i	0.907992	−	0.418988i	$-0.137615\pi$
$458$	−37.9543			−1.77349
$459$	−20.0965	+	9.18715i	−0.938026	+	0.428819i
$460$	−1.70849			−0.0796588
$461$	−17.9742	+	17.9742i	−0.837140	+	0.837140i	−0.988482	−	0.151341i	$-0.951641\pi$
$461$	−17.9742	+	17.9742i	−0.837140	+	0.837140i	0.151341	+	0.988482i	$0.451641\pi$
$462$	−3.69270	+	8.91497i	−0.171800	+	0.414762i
$463$			3.16361i			0.147025i	0.997294	+	0.0735126i	$0.0234209\pi$
$463$			3.16361i			0.147025i	−0.997294	+	0.0735126i	$0.976579\pi$
$464$	−32.5857	−	13.4974i	−1.51275	−	0.626602i
$465$	0.565184	+	1.36447i	0.0262098	+	0.0632760i
$466$	−23.3356	+	9.66591i	−1.08100	+	0.447764i
$467$	13.0865	+	13.0865i	0.605571	+	0.605571i	0.941785	−	0.336215i	$-0.109147\pi$
$467$	13.0865	+	13.0865i	0.605571	+	0.605571i	−0.336215	+	0.941785i	$0.609147\pi$
$468$	−3.25736	−	3.25736i	−0.150571	−	0.150571i
$469$	−21.0178	+	8.70588i	−0.970514	+	0.402000i
$470$	−1.40479	−	3.39147i	−0.0647983	−	0.156437i
$471$	13.1281	+	5.43783i	0.604910	+	0.250562i
$472$			25.5193i			1.17462i
$473$	3.60693	−	8.70791i	0.165847	−	0.400390i
$474$	−2.99373	+	2.99373i	−0.137506	+	0.137506i
$475$	−1.87562			−0.0860595
$476$	−2.58971	−	5.66489i	−0.118699	−	0.259650i
$477$	10.2274			0.468281
$478$	12.9145	−	12.9145i	0.590694	−	0.590694i
$479$	−13.7679	+	33.2386i	−0.629070	+	1.51871i	0.211710	+	0.977332i	$0.432097\pi$
$479$	−13.7679	+	33.2386i	−0.629070	+	1.51871i	−0.840780	+	0.541377i	$0.817903\pi$
$480$			2.56736i			0.117183i
$481$	−28.0140	−	11.6038i	−1.27733	−	0.529086i
$482$	0.863910	+	2.08566i	0.0393500	+	0.0949994i
$483$	−16.6798	+	6.90898i	−0.758955	+	0.314369i
$484$	−2.53312	−	2.53312i	−0.115142	−	0.115142i
$485$	9.61837	+	9.61837i	0.436748	+	0.436748i
$486$	21.3747	−	8.85368i	0.969575	−	0.401611i
$487$	−1.95204	−	4.71263i	−0.0884552	−	0.213550i	0.873461	−	0.486894i	$-0.161870\pi$
$487$	−1.95204	−	4.71263i	−0.0884552	−	0.213550i	−0.961916	+	0.273344i	$0.911870\pi$
$488$	7.18140	+	2.97463i	0.325087	+	0.134655i
$489$			24.2149i			1.09503i
$490$	−4.15234	+	10.0246i	−0.187584	+	0.452867i
$491$	15.3060	−	15.3060i	0.690751	−	0.690751i	−0.271646	−	0.962397i	$-0.587568\pi$
$491$	15.3060	−	15.3060i	0.690751	−	0.690751i	0.962397	+	0.271646i	$0.0875680\pi$
$492$	−0.723462			−0.0326162
$493$	29.3410	+	10.9307i	1.32145	+	0.492295i
$494$	19.5217			0.878323
$495$	1.75293	−	1.75293i	0.0787882	−	0.0787882i
$496$	2.30183	−	5.55711i	0.103355	−	0.249522i
$497$		−	14.3354i		−	0.643029i
$498$	27.5778	+	11.4231i	1.23579	+	0.511881i
$499$	−10.5627	−	25.5006i	−0.472850	−	1.14156i	−0.962898	−	0.269866i	$-0.913021\pi$
$499$	−10.5627	−	25.5006i	−0.472850	−	1.14156i	0.490047	−	0.871696i	$-0.336979\pi$
$500$	−0.373037	+	0.154517i	−0.0166827	+	0.00691020i
$501$	−1.15591	−	1.15591i	−0.0516423	−	0.0516423i
$502$	−25.4057	−	25.4057i	−1.13391	−	1.13391i
$503$	−23.3713	+	9.68071i	−1.04207	+	0.431642i	−0.837056	−	0.547117i	$-0.815725\pi$
$503$	−23.3713	+	9.68071i	−1.04207	+	0.431642i	−0.205018	+	0.978758i	$0.565725\pi$
$504$	−6.02201	−	14.5384i	−0.268242	−	0.647592i
$505$	0.0643361	+	0.0266489i	0.00286292	+	0.00118586i
$506$			9.56936i			0.425410i
$507$	−13.9941	+	33.7847i	−0.621498	+	1.50043i
$508$	−3.80006	+	3.80006i	−0.168601	+	0.168601i
$509$	12.5871			0.557913			0.278957	−	0.960304i	$-0.410011\pi$
$509$	12.5871			0.557913			0.278957	+	0.960304i	$0.410011\pi$
$510$	−0.263006	−	7.28526i	−0.0116461	−	0.322597i
$511$	−52.4001			−2.31804
$512$	−8.86178	+	8.86178i	−0.391639	+	0.391639i
$513$	−3.84674	+	9.28685i	−0.169838	+	0.410025i
$514$		−	18.9225i		−	0.834636i
$515$	7.24038	+	2.99906i	0.319049	+	0.132155i
$516$	1.13860	+	2.74882i	0.0501241	+	0.121010i
$517$	−3.19082	+	1.32168i	−0.140332	+	0.0581274i
$518$	18.5271	+	18.5271i	0.814033	+	0.814033i
$519$	−1.11416	−	1.11416i	−0.0489064	−	0.0489064i
$520$	−15.3491	+	6.35780i	−0.673102	+	0.278808i
$521$	2.16471	+	5.22606i	0.0948375	+	0.228958i	0.964178	−	0.265255i	$-0.0854562\pi$
$521$	2.16471	+	5.22606i	0.0948375	+	0.228958i	−0.869341	+	0.494213i	$0.835456\pi$
$522$	−18.4864	−	7.65731i	−0.809127	−	0.335151i
$523$			21.6359i			0.946074i	0.881043	+	0.473037i	$0.156842\pi$
$523$			21.6359i			0.946074i	−0.881043	+	0.473037i	$0.843158\pi$
$524$	−0.100968	+	0.243758i	−0.00441081	+	0.0106486i
$525$	−3.01705	+	3.01705i	−0.131675	+	0.131675i
$526$	−22.0216			−0.960187
$527$	−1.86411	+	5.00376i	−0.0812019	+	0.217967i
$528$	7.72604			0.336233
$529$	3.60334	−	3.60334i	0.156667	−	0.156667i
$530$	−3.57053	+	8.62003i	−0.155094	+	0.374430i
$531$			17.5245i			0.760500i
$532$	−2.61781	−	1.08433i	−0.113497	−	0.0470118i
$533$	−4.03634	−	9.74459i	−0.174833	−	0.422085i
$534$	−2.60330	+	1.07832i	−0.112656	+	0.0466636i
$535$	−1.18788	−	1.18788i	−0.0513565	−	0.0513565i
$536$	10.6404	+	10.6404i	0.459595	+	0.459595i
$537$	−9.69371	+	4.01526i	−0.418314	+	0.173271i
$538$	7.69593	+	18.5796i	0.331795	+	0.801025i
$539$	9.43153	+	3.90667i	0.406245	+	0.168272i
$540$			2.16393i			0.0931208i
$541$	2.97419	−	7.18033i	0.127870	−	0.308707i	−0.846959	−	0.531658i	$-0.821569\pi$
$541$	2.97419	−	7.18033i	0.127870	−	0.308707i	0.974830	+	0.222951i	$0.0715692\pi$
$542$	−29.0696	+	29.0696i	−1.24864	+	1.24864i
$543$	−15.7078			−0.674087
$544$	−6.32249	+	6.79609i	−0.271075	+	0.291380i
$545$	−6.25448			−0.267913
$546$	31.4018	−	31.4018i	1.34387	−	1.34387i
$547$	14.5904	−	35.2244i	0.623841	−	1.50609i	−0.223318	−	0.974746i	$-0.571689\pi$
$547$	14.5904	−	35.2244i	0.623841	−	1.50609i	0.847159	−	0.531340i	$-0.178311\pi$
$548$		−	0.253562i		−	0.0108316i
$549$	4.93158	+	2.04273i	0.210475	+	0.0871815i
$550$	0.865459	+	2.08940i	0.0369033	+	0.0890924i
$551$	13.1593	−	5.45075i	0.560604	−	0.232210i
$552$	8.44422	+	8.44422i	0.359410	+	0.359410i
$553$	6.33505	+	6.33505i	0.269394	+	0.269394i
$554$	−9.31145	+	3.85693i	−0.395606	+	0.163865i
$555$	1.97120	+	4.75889i	0.0836727	+	0.202004i
$556$	−4.92561	−	2.04025i	−0.208892	−	0.0865260i
$557$		−	4.76903i		−	0.202070i	−0.994883	−	0.101035i	$-0.967785\pi$
$557$		−	4.76903i		−	0.202070i	0.994883	−	0.101035i	$-0.0322155\pi$
$558$	1.30587	−	3.15264i	0.0552817	−	0.133462i
$559$	−30.6725	+	30.6725i	−1.29731	+	1.29731i
$560$	17.3773			0.734323
$561$	−6.85422	+	0.247445i	−0.289386	+	0.0104472i
$562$	−9.38760			−0.395992
$563$	26.0195	−	26.0195i	1.09659	−	1.09659i	0.101785	−	0.994806i	$-0.467545\pi$
$563$	26.0195	−	26.0195i	1.09659	−	1.09659i	0.994806	−	0.101785i	$-0.0324554\pi$
$564$	0.417214	−	1.00724i	0.0175679	−	0.0424126i
$565$		−	11.3480i		−	0.477416i
$566$	20.1439	+	8.34389i	0.846713	+	0.350720i
$567$	1.45078	+	3.50249i	0.0609269	+	0.147091i
$568$	−8.76040	+	3.62868i	−0.367578	+	0.152256i
$569$	0.831415	+	0.831415i	0.0348547	+	0.0348547i	0.724319	−	0.689465i	$-0.242154\pi$
$569$	0.831415	+	0.831415i	0.0348547	+	0.0348547i	−0.689465	+	0.724319i	$0.742154\pi$
$570$	−2.34495	−	2.34495i	−0.0982193	−	0.0982193i
$571$	−31.8053	+	13.1742i	−1.33101	+	0.551323i	−0.930944	−	0.365162i	$-0.881014\pi$
$571$	−31.8053	+	13.1742i	−1.33101	+	0.551323i	−0.400068	+	0.916485i	$0.631014\pi$
$572$	−1.51308	−	3.65289i	−0.0632650	−	0.152735i
$573$	−10.6062	−	4.39323i	−0.443080	−	0.183530i
$574$			9.11403i			0.380412i
$575$	−1.61926	+	3.90923i	−0.0675277	+	0.163026i
$576$	−6.96832	+	6.96832i	−0.290347	+	0.290347i
$577$	−2.18297			−0.0908782			−0.0454391	−	0.998967i	$-0.514469\pi$
$577$	−2.18297			−0.0908782			−0.0454391	+	0.998967i	$0.514469\pi$
$578$	17.2448	−	19.9326i	0.717288	−	0.829086i
$579$	2.02124			0.0839999
$580$	2.16817	−	2.16817i	0.0900282	−	0.0900282i
$581$	24.1725	−	58.3575i	1.00284	−	2.42108i
$582$			24.0503i			0.996915i
$583$	8.11002	+	3.35928i	0.335883	+	0.139127i
$584$	13.2639	+	32.0219i	0.548865	+	1.32508i
$585$	−10.5405	+	4.36600i	−0.435795	+	0.180512i
$586$	2.17436	+	2.17436i	0.0898220	+	0.0898220i
$587$	−17.4156	−	17.4156i	−0.718817	−	0.718817i	0.249546	−	0.968363i	$-0.419719\pi$
$587$	−17.4156	−	17.4156i	−0.718817	−	0.718817i	−0.968363	+	0.249546i	$0.919719\pi$
$588$	−2.97725	+	1.23322i	−0.122780	+	0.0508570i
$589$	0.929563	+	2.24416i	0.0383020	+	0.0924692i
$590$	−14.7703	−	6.11807i	−0.608084	−	0.251877i
$591$		−	12.5108i		−	0.514623i
$592$	8.02811	−	19.3816i	0.329953	−	0.796578i
$593$	32.5738	−	32.5738i	1.33764	−	1.33764i	0.439307	−	0.898337i	$-0.355224\pi$
$593$	32.5738	−	32.5738i	1.33764	−	1.33764i	0.898337	−	0.439307i	$-0.144776\pi$
$594$	12.1203			0.497303
$595$	−15.4164	+	0.556550i	−0.632011	+	0.0228163i
$596$	9.25813			0.379228
$597$	3.17103	−	3.17103i	0.129782	−	0.129782i
$598$	16.8534	−	40.6878i	0.689188	−	1.66385i
$599$		−	1.97185i		−	0.0805677i	−0.999188	−	0.0402839i	$-0.987174\pi$
$599$		−	1.97185i		−	0.0805677i	0.999188	−	0.0402839i	$-0.0128262\pi$
$600$	2.60744	+	1.08004i	0.106448	+	0.0440923i
$601$	1.26765	+	3.06037i	0.0517084	+	0.124835i	0.947623	−	0.319392i	$-0.103479\pi$
$601$	1.26765	+	3.06037i	0.0517084	+	0.124835i	−0.895914	+	0.444227i	$0.853479\pi$
$602$	34.6291	−	14.3439i	1.41138	−	0.584612i
$603$	7.30694	+	7.30694i	0.297562	+	0.297562i
$604$	0.0444658	+	0.0444658i	0.00180929	+	0.00180929i
$605$	−8.19689	+	3.39526i	−0.333251	+	0.138037i
$606$	0.0471175	+	0.113752i	0.00191402	+	0.00462085i
$607$	19.2952	+	7.99235i	0.783170	+	0.324400i	0.738194	−	0.674588i	$-0.235679\pi$
$607$	19.2952	+	7.99235i	0.783170	+	0.324400i	0.0449760	+	0.998988i	$0.485679\pi$
$608$			4.22256i			0.171247i
$609$	12.3996	−	29.9354i	0.502458	−	1.21304i
$610$	−3.44337	+	3.44337i	−0.139418	+	0.139418i
$611$	15.8947			0.643030
$612$	−1.92714	+	2.07149i	−0.0779000	+	0.0837352i
$613$	27.4926			1.11042			0.555208	−	0.831711i	$-0.312638\pi$
$613$	27.4926			1.11042			0.555208	+	0.831711i	$0.312638\pi$
$614$	−3.88854	+	3.88854i	−0.156929	+	0.156929i
$615$	−0.685676	+	1.65537i	−0.0276491	+	0.0667509i
$616$		−	13.5065i		−	0.544192i
$617$	−4.75553	−	1.96980i	−0.191450	−	0.0793013i	0.284899	−	0.958558i	$-0.408040\pi$
$617$	−4.75553	−	1.96980i	−0.191450	−	0.0793013i	−0.476349	+	0.879256i	$0.658040\pi$
$618$	5.30260	+	12.8016i	0.213302	+	0.514957i
$619$	7.81974	−	3.23904i	0.314302	−	0.130188i	−0.219956	−	0.975510i	$-0.570591\pi$
$619$	7.81974	−	3.23904i	0.314302	−	0.130188i	0.534258	+	0.845322i	$0.320591\pi$
$620$	0.369755	+	0.369755i	0.0148497	+	0.0148497i
$621$	16.0350	+	16.0350i	0.643462	+	0.643462i
$622$	−5.16952	+	2.14128i	−0.207279	+	0.0858577i
$623$	2.28185	+	5.50887i	0.0914203	+	0.220708i
$624$	−32.8502	−	13.6070i	−1.31506	−	0.544715i
$625$			1.00000i			0.0400000i
$626$	−4.84863	+	11.7056i	−0.193790	+	0.467851i
$627$	−2.20621	+	2.20621i	−0.0881077	+	0.0881077i
$628$	5.03113			0.200764
$629$	−6.50147	+	17.4517i	−0.259231	+	0.695844i
$630$	9.85841			0.392768
$631$	−7.03331	+	7.03331i	−0.279992	+	0.279992i	−0.833106	−	0.553114i	$-0.813439\pi$
$631$	−7.03331	+	7.03331i	−0.279992	+	0.279992i	0.553114	+	0.833106i	$0.313439\pi$
$632$	2.26780	−	5.47496i	0.0902083	−	0.217782i
$633$		−	31.4578i		−	1.25034i
$634$	28.5597	+	11.8298i	1.13425	+	0.469822i
$635$	5.09342	+	12.2966i	0.202126	+	0.487976i
$636$	−2.56009	+	1.06042i	−0.101514	+	0.0420485i
$637$	−33.2214	−	33.2214i	−1.31628	−	1.31628i
$638$	−12.1440	−	12.1440i	−0.480787	−	0.480787i
$639$	−6.01591	+	2.49187i	−0.237986	+	0.0985769i
$640$	−5.16347	−	12.4657i	−0.204104	−	0.492751i
$641$	−9.96278	−	4.12672i	−0.393506	−	0.162996i	0.177152	−	0.984184i	$-0.443312\pi$
$641$	−9.96278	−	4.12672i	−0.393506	−	0.162996i	−0.570658	+	0.821188i	$0.693312\pi$
$642$		−	2.97024i		−	0.117226i
$643$	−1.11381	+	2.68897i	−0.0439243	+	0.106043i	−0.944319	−	0.329031i	$-0.893278\pi$
$643$	−1.11381	+	2.68897i	−0.0439243	+	0.106043i	0.900395	+	0.435074i	$0.143278\pi$
$644$	−4.52000	+	4.52000i	−0.178113	+	0.178113i
$645$	7.36877			0.290145
$646$	−0.432569	−	11.9821i	−0.0170192	−	0.471431i
$647$	−30.6301			−1.20419			−0.602097	−	0.798423i	$-0.705668\pi$
$647$	−30.6301			−1.20419			−0.602097	+	0.798423i	$0.705668\pi$
$648$	1.77315	−	1.77315i	0.0696561	−	0.0696561i
$649$	−5.75609	+	13.8964i	−0.225946	+	0.545483i
$650$		−	10.4081i		−	0.408240i
$651$	5.10513	+	2.11461i	0.200086	+	0.0828782i
$652$	3.28096	+	7.92095i	0.128492	+	0.310208i
$653$	−27.7794	+	11.5066i	−1.08709	+	0.450288i	−0.852992	−	0.521924i	$-0.825214\pi$
$653$	−27.7794	+	11.5066i	−1.08709	+	0.450288i	−0.234100	+	0.972212i	$0.575214\pi$
$654$	−7.81951	−	7.81951i	−0.305767	−	0.305767i
$655$	0.462054	+	0.462054i	0.0180540	+	0.0180540i
$656$	6.74184	−	2.79256i	0.263224	−	0.109031i
$657$	9.10855	+	21.9900i	0.355358	+	0.857911i
$658$	−12.6891	−	5.25598i	−0.494671	−	0.204900i
$659$		−	12.6410i		−	0.492424i	−0.969216	−	0.246212i	$-0.920814\pi$
$659$		−	12.6410i		−	0.492424i	0.969216	−	0.246212i	$-0.0791860\pi$
$660$	−0.257035	+	0.620538i	−0.0100051	+	0.0241544i
$661$	10.8422	−	10.8422i	0.421712	−	0.421712i	−0.464081	−	0.885793i	$-0.653615\pi$
$661$	10.8422	−	10.8422i	0.421712	−	0.421712i	0.885793	+	0.464081i	$0.153615\pi$
$662$	21.6173			0.840179
$663$	29.5791	+	11.0195i	1.14876	+	0.427960i
$664$	−41.7813			−1.62143
$665$	−4.96217	+	4.96217i	−0.192425	+	0.192425i
$666$	4.55448	−	10.9955i	0.176483	−	0.426067i
$667$		−	32.1327i		−	1.24418i
$668$	−0.534730	−	0.221493i	−0.0206893	−	0.00856980i
$669$	8.88258	+	21.4445i	0.343421	+	0.829090i
$670$	−8.70951	+	3.60760i	−0.336478	+	0.139374i
$671$	3.23964	+	3.23964i	0.125065	+	0.125065i
$672$	6.79224	+	6.79224i	0.262016	+	0.262016i
$673$	−24.1876	+	10.0188i	−0.932362	+	0.386197i	−0.796574	−	0.604541i	$-0.793357\pi$
$673$	−24.1876	+	10.0188i	−0.932362	+	0.386197i	−0.135788	+	0.990738i	$0.543357\pi$
$674$	11.9038	+	28.7382i	0.458516	+	1.10696i
$675$	4.95134	+	2.05091i	0.190577	+	0.0789397i
$676$			12.9474i			0.497978i
$677$	5.65293	−	13.6474i	0.217260	−	0.524512i	−0.777245	−	0.629198i	$-0.783384\pi$
$677$	5.65293	−	13.6474i	0.217260	−	0.524512i	0.994505	+	0.104686i	$0.0333837\pi$
$678$	14.1876	−	14.1876i	0.544872	−	0.544872i
$679$	50.8929			1.95309
$680$	4.24243	+	9.28016i	0.162690	+	0.355878i
$681$	7.70683			0.295327
$682$	2.07102	−	2.07102i	0.0793036	−	0.0793036i
$683$	10.1723	−	24.5580i	0.389230	−	0.939685i	−0.600873	−	0.799345i	$-0.705180\pi$
$683$	10.1723	−	24.5580i	0.389230	−	0.939685i	0.990103	−	0.140341i	$-0.0448198\pi$
$684$			1.28707i			0.0492122i
$685$	−0.580181	−	0.240319i	−0.0221676	−	0.00918211i
$686$	−0.00325553	−	0.00785954i	−0.000124297	−	0.000300079i
$687$	−25.7921	+	10.6834i	−0.984029	+	0.407598i
$688$	−21.2209	−	21.2209i	−0.809039	−	0.809039i
$689$	−28.5665	−	28.5665i	−1.08830	−	1.08830i
$690$	−6.91186	+	2.86299i	−0.263130	+	0.108992i
$691$	19.6417	+	47.4193i	0.747206	+	1.80392i	0.573667	+	0.819089i	$0.305521\pi$
$691$	19.6417	+	47.4193i	0.747206	+	1.80392i	0.173540	+	0.984827i	$0.444479\pi$
$692$	−0.515417	−	0.213493i	−0.0195932	−	0.00811578i
$693$		−	9.27513i		−	0.352333i
$694$	−12.7945	+	30.8887i	−0.485673	+	1.17252i
$695$	−9.33670	+	9.33670i	−0.354161	+	0.354161i
$696$	−21.4323			−0.812390
$697$	−5.89164	+	2.69337i	−0.223162	+	0.102019i
$698$	17.0140			0.643990
$699$	−13.1371	+	13.1371i	−0.496889	+	0.496889i
$700$	−0.578119	+	1.39570i	−0.0218508	+	0.0527526i
$701$			7.47248i			0.282232i	0.989993	+	0.141116i	$0.0450690\pi$
$701$			7.47248i			0.282232i	−0.989993	+	0.141116i	$0.954931\pi$
$702$	−51.5341	−	21.3461i	−1.94503	−	0.805658i
$703$	3.24205	+	7.82699i	0.122276	+	0.295201i
$704$	−7.81447	+	3.23686i	−0.294519	+	0.121994i
$705$	−1.90927	−	1.90927i	−0.0719074	−	0.0719074i
$706$	−25.5669	−	25.5669i	−0.962223	−	0.962223i
$707$	0.240711	−	0.0997058i	0.00905287	−	0.00374982i
$708$	−1.81702	−	4.38668i	−0.0682879	−	0.164862i
$709$	−4.94262	−	2.04730i	−0.185624	−	0.0768880i	0.287936	−	0.957650i	$-0.407031\pi$
$709$	−4.94262	−	2.04730i	−0.185624	−	0.0768880i	−0.473559	+	0.880762i	$0.657031\pi$
$710$		−	5.94037i		−	0.222938i
$711$	1.55734	−	3.75974i	0.0584047	−	0.141001i
$712$	2.78889	−	2.78889i	0.104518	−	0.104518i
$713$	5.47986			0.205222
$714$	−19.9698	−	18.5782i	−0.747350	−	0.695270i
$715$	−9.79232			−0.366212
$716$	−2.62687	+	2.62687i	−0.0981708	+	0.0981708i
$717$	5.14092	−	12.4113i	0.191991	−	0.463508i
$718$		−	3.04195i		−	0.113524i
$719$	17.6631	+	7.31630i	0.658723	+	0.272852i	0.686901	−	0.726751i	$-0.258971\pi$
$719$	17.6631	+	7.31630i	0.658723	+	0.272852i	−0.0281782	+	0.999603i	$0.508971\pi$
$720$	−3.02064	−	7.29246i	−0.112573	−	0.271774i
$721$	27.0896	−	11.2209i	1.00887	−	0.417888i
$722$	16.9730	+	16.9730i	0.631671	+	0.631671i
$723$	1.17415	+	1.17415i	0.0436672	+	0.0436672i
$724$	−5.13819	+	2.12831i	−0.190959	+	0.0790980i
$725$	−2.90610	−	7.01595i	−0.107930	−	0.260566i
$726$	−14.4928	−	6.00312i	−0.537879	−	0.222797i
$727$			50.2861i			1.86501i	0.361159	+	0.932504i	$0.382381\pi$
$727$			50.2861i			1.86501i	−0.361159	+	0.932504i	$0.617619\pi$
$728$	−23.7875	+	57.4280i	−0.881622	+	2.12842i
$729$	14.1826	−	14.1826i	0.525281	−	0.525281i
$730$	−21.7139			−0.803666
$731$	19.5060	+	18.1467i	0.721454	+	0.671178i
$732$	−1.44626			−0.0534551
$733$	−6.78681	+	6.78681i	−0.250677	+	0.250677i	−0.821248	−	0.570571i	$-0.806722\pi$
$733$	−6.78681	+	6.78681i	−0.250677	+	0.250677i	0.570571	+	0.821248i	$0.306722\pi$
$734$	19.5869	−	47.2870i	0.722966	−	1.74540i
$735$			7.98112i			0.294388i
$736$	8.80079	+	3.64541i	0.324401	+	0.134371i
$737$	3.39415	+	8.19421i	0.125025	+	0.301837i
$738$	3.82475	−	1.58427i	0.140791	−	0.0583176i
$739$	−12.9093	−	12.9093i	−0.474877	−	0.474877i	0.428612	−	0.903489i	$-0.359003\pi$
$739$	−12.9093	−	12.9093i	−0.474877	−	0.474877i	−0.903489	+	0.428612i	$0.859003\pi$
$740$	1.28960	+	1.28960i	0.0474066	+	0.0474066i
$741$	13.2661	−	5.49500i	0.487342	−	0.201864i
$742$	13.3590	+	32.2515i	0.490425	+	1.18399i
$743$	10.8868	+	4.50945i	0.399397	+	0.165436i	0.573335	−	0.819321i	$-0.305649\pi$
$743$	10.8868	+	4.50945i	0.399397	+	0.165436i	−0.173938	+	0.984757i	$0.555649\pi$
$744$		−	3.65504i		−	0.134000i
$745$	8.77459	−	21.1837i	0.321476	−	0.776112i
$746$	11.2671	−	11.2671i	0.412518	−	0.412518i
$747$	−28.6919			−1.04978
$748$	−2.20856	+	1.00965i	−0.0807531	+	0.0369163i
$749$	−6.28534			−0.229661
$750$	−1.25023	+	1.25023i	−0.0456518	+	0.0456518i
$751$	0.429503	−	1.03691i	0.0156728	−	0.0378374i	−0.915849	−	0.401522i	$-0.868481\pi$
$751$	0.429503	−	1.03691i	0.0156728	−	0.0378374i	0.931522	+	0.363684i	$0.118481\pi$
$752$			10.9968i			0.401012i
$753$	−24.4158	−	10.1134i	−0.889761	−	0.368551i
$754$	30.2471	+	73.0228i	1.10153	+	2.65933i
$755$	0.143887	−	0.0595998i	0.00523657	−	0.00216906i
$756$	5.72493	+	5.72493i	0.208214	+	0.208214i
$757$	30.1857	+	30.1857i	1.09712	+	1.09712i	0.994746	+	0.102372i	$0.0326432\pi$
$757$	30.1857	+	30.1857i	1.09712	+	1.09712i	0.102372	+	0.994746i	$0.467357\pi$
$758$	34.4508	−	14.2700i	1.25131	−	0.518309i
$759$	2.69360	+	6.50292i	0.0977714	+	0.236041i
$760$	4.28847	+	1.77634i	0.155559	+	0.0644348i
$761$			45.3927i			1.64549i	0.568414	+	0.822743i	$0.307557\pi$
$761$			45.3927i			1.64549i	−0.568414	+	0.822743i	$0.692443\pi$
$762$	−9.00560	+	21.7414i	−0.326238	+	0.787609i
$763$	−16.5469	+	16.5469i	−0.599039	+	0.599039i
$764$	−4.06465			−0.147054
$765$	2.91335	+	6.37283i	0.105332	+	0.230410i
$766$	−4.32897			−0.156412
$767$	48.9484	−	48.9484i	1.76742	−	1.76742i
$768$	4.06829	−	9.82172i	0.146802	−	0.354411i
$769$		−	22.5224i		−	0.812177i	−0.913834	−	0.406089i	$-0.866892\pi$
$769$		−	22.5224i		−	0.812177i	0.913834	−	0.406089i	$-0.133108\pi$
$770$	7.81742	+	3.23808i	0.281720	+	0.116692i
$771$	−5.32634	−	12.8589i	−0.191823	−	0.463102i
$772$	0.661169	−	0.273865i	0.0237960	−	0.00985663i
$773$	31.7746	+	31.7746i	1.14285	+	1.14285i	0.987926	+	0.154926i	$0.0495140\pi$
$773$	31.7746	+	31.7746i	1.14285	+	1.14285i	0.154926	+	0.987926i	$0.450486\pi$
$774$	−12.0390	−	12.0390i	−0.432731	−	0.432731i
$775$	1.19649	−	0.495602i	0.0429792	−	0.0178026i
$776$	−12.8824	−	31.1009i	−0.462452	−	1.11646i
$777$	17.8052	+	7.37516i	0.638758	+	0.264582i
$778$			6.62772i			0.237615i
$779$	−1.12774	+	2.72260i	−0.0404054	+	0.0975473i
$780$	2.18577	−	2.18577i	0.0782629	−	0.0782629i
$781$	−5.58891			−0.199987
$782$	−25.3470	−	9.44280i	−0.906406	−	0.337674i
$783$	−40.6985			−1.45445
$784$	22.9843	−	22.9843i	0.820870	−	0.820870i
$785$	4.76836	−	11.5118i	0.170190	−	0.410875i
$786$			1.15534i			0.0412098i
$787$	11.1724	+	4.62777i	0.398254	+	0.164962i	0.572816	−	0.819684i	$-0.305851\pi$
$787$	11.1724	+	4.62777i	0.398254	+	0.164962i	−0.174562	+	0.984646i	$0.555851\pi$
$788$	−1.69513	−	4.09240i	−0.0603864	−	0.145786i
$789$	−14.9649	+	6.19867i	−0.532765	+	0.220678i
$790$	2.62516	+	2.62516i	0.0933990	+	0.0933990i
$791$	−30.0225	−	30.0225i	−1.06748	−	1.06748i
$792$	−5.66808	+	2.34779i	−0.201406	+	0.0834252i
$793$	−8.06896	−	19.4802i	−0.286537	−	0.691762i
$794$	22.2263	+	9.20645i	0.788784	+	0.326725i
$795$			6.86283i			0.243400i
$796$	0.607624	−	1.46693i	0.0215367	−	0.0519941i
$797$	12.2957	−	12.2957i	0.435536	−	0.435536i	−0.454971	−	0.890506i	$-0.650350\pi$
$797$	12.2957	−	12.2957i	0.435536	−	0.435536i	0.890506	+	0.454971i	$0.150350\pi$
$798$	−12.4077			−0.439227
$799$	−0.352200	−	9.75592i	−0.0124599	−	0.345140i
$800$	2.25128			0.0795949
$801$	1.91518	−	1.91518i	0.0676695	−	0.0676695i
$802$	12.4538	−	30.0661i	0.439759	−	1.06167i
$803$			20.4292i			0.720929i
$804$	−2.58666	−	1.07143i	−0.0912246	−	0.0377865i
$805$	6.05839	+	14.6262i	0.213530	+	0.515507i
$806$	−12.4532	+	5.15828i	−0.438645	+	0.181693i
$807$	10.4596	+	10.4596i	0.368197	+	0.368197i
$808$	−0.121861	−	0.121861i	−0.00428707	−	0.00428707i
$809$	−38.8774	+	16.1035i	−1.36686	+	0.566170i	−0.940934	−	0.338590i	$-0.890050\pi$
$809$	−38.8774	+	16.1035i	−1.36686	+	0.566170i	−0.425922	+	0.904760i	$0.640050\pi$
$810$	0.601182	+	1.45138i	0.0211234	+	0.0509964i
$811$	1.23386	+	0.511083i	0.0433268	+	0.0179465i	0.404242	−	0.914652i	$-0.367535\pi$
$811$	1.23386	+	0.511083i	0.0433268	+	0.0179465i	−0.360915	+	0.932599i	$0.617535\pi$
$812$		−	11.4723i		−	0.402597i
$813$	−11.5719	+	27.9370i	−0.405843	+	0.979792i
$814$	7.22313	−	7.22313i	0.253171	−	0.253171i
$815$	21.2337			0.743784
$816$	−7.62386	+	20.4644i	−0.266888	+	0.716399i
$817$	12.1195			0.424007
$818$	−9.72021	+	9.72021i	−0.339859	+	0.339859i
$819$	−16.3352	+	39.4367i	−0.570799	+	1.37803i
$820$			0.634394i			0.0221540i
$821$	−10.8502	−	4.49430i	−0.378675	−	0.156852i	0.185224	−	0.982696i	$-0.440699\pi$
$821$	−10.8502	−	4.49430i	−0.378675	−	0.156852i	−0.563898	+	0.825844i	$0.690699\pi$
$822$	−0.424904	−	1.02581i	−0.0148202	−	0.0357792i
$823$	44.5359	−	18.4474i	1.55243	−	0.643036i	0.568673	−	0.822564i	$-0.307457\pi$
$823$	44.5359	−	18.4474i	1.55243	−	0.643036i	0.983753	+	0.179528i	$0.0574571\pi$
$824$	−13.7143	−	13.7143i	−0.477759	−	0.477759i
$825$	1.17626	+	1.17626i	0.0409520	+	0.0409520i
$826$	−55.2626	+	22.8905i	−1.92283	+	0.796463i
$827$	−14.4623	−	34.9152i	−0.502905	−	1.21412i	−0.947894	−	0.318584i	$-0.896793\pi$
$827$	−14.4623	−	34.9152i	−0.502905	−	1.21412i	0.444989	−	0.895536i	$-0.353207\pi$
$828$	2.68254	+	1.11115i	0.0932248	+	0.0386150i
$829$		−	22.2052i		−	0.771219i	−0.922662	−	0.385610i	$-0.873991\pi$
$829$		−	22.2052i		−	0.771219i	0.922662	−	0.385610i	$-0.126009\pi$
$830$	10.0167	−	24.1826i	0.347686	−	0.839389i
$831$	−5.24200	+	5.24200i	−0.181843	+	0.181843i
$832$	38.9269			1.34955
$833$	−19.6546	+	21.1269i	−0.680993	+	0.732004i
$834$	−23.3460			−0.808404
$835$	−1.01360	+	1.01360i	−0.0350772	+	0.0350772i
$836$	−0.422748	+	1.02060i	−0.0146210	+	0.0352983i
$837$		−	6.94066i		−	0.239904i
$838$	−46.3431	−	19.1959i	−1.60090	−	0.663113i
$839$	−8.99769	−	21.7224i	−0.310635	−	0.749939i	−0.999682	−	0.0252223i	$-0.991971\pi$
$839$	−8.99769	−	21.7224i	−0.310635	−	0.749939i	0.689047	−	0.724717i	$-0.258029\pi$
$840$	9.75562	−	4.04091i	0.336601	−	0.139425i
$841$	20.2720	+	20.2720i	0.699036	+	0.699036i
$842$	−3.96968	−	3.96968i	−0.136804	−	0.136804i
$843$	−6.37940	+	2.64244i	−0.219718	+	0.0910103i
$844$	−4.26234	−	10.2902i	−0.146716	−	0.354203i
$845$	29.6253	+	12.2712i	1.01914	+	0.422142i
$846$			6.23867i			0.214490i
$847$	−12.7033	+	30.6684i	−0.436489	+	1.05378i
$848$	19.7639	−	19.7639i	0.678694	−	0.678694i
$849$	16.0376			0.550409
$850$	−6.38834	+	0.230627i	−0.219118	+	0.00791043i
$851$	19.1122			0.655157
$852$	1.24751	−	1.24751i	0.0427391	−	0.0427391i
$853$	5.32864	−	12.8645i	0.182449	−	0.440471i	−0.806021	−	0.591887i	$-0.798383\pi$
$853$	5.32864	−	12.8645i	0.182449	−	0.440471i	0.988470	+	0.151416i	$0.0483832\pi$
$854$			18.2197i			0.623464i
$855$	2.94496	+	1.21984i	0.100716	+	0.0417178i
$856$	1.59099	+	3.84100i	0.0543791	+	0.131283i
$857$	−48.0643	+	19.9089i	−1.64185	+	0.680075i	−0.996483	−	0.0838004i	$-0.973294\pi$
$857$	−48.0643	+	19.9089i	−1.64185	+	0.680075i	−0.645364	+	0.763875i	$0.723294\pi$
$858$	−12.2426	−	12.2426i	−0.417956	−	0.417956i
$859$	−34.4176	−	34.4176i	−1.17431	−	1.17431i	−0.981171	−	0.193144i	$-0.938132\pi$
$859$	−34.4176	−	34.4176i	−1.17431	−	1.17431i	−0.193144	−	0.981171i	$-0.561868\pi$
$860$	2.41041	−	0.998423i	0.0821941	−	0.0340459i
$861$	2.56543	+	6.19350i	0.0874297	+	0.211074i
$862$	25.0682	+	10.3836i	0.853828	+	0.353667i
$863$			45.2241i			1.53945i	0.638378	+	0.769723i	$0.279606\pi$
$863$			45.2241i			1.53945i	−0.638378	+	0.769723i	$0.720394\pi$
$864$	4.61718	−	11.1469i	0.157080	−	0.379224i
$865$	−0.976995	+	0.976995i	−0.0332188	+	0.0332188i
$866$	14.1797			0.481845
$867$	6.10815	−	18.3994i	0.207444	−	0.624876i
$868$	1.95646			0.0664066
$869$	2.46984	−	2.46984i	0.0837836	−	0.0837836i
$870$	5.13824	−	12.4048i	0.174203	−	0.420562i
$871$		−	40.8185i		−	1.38308i
$872$	14.3004	+	5.92342i	0.484273	+	0.200592i
$873$	−8.84657	−	21.3575i	−0.299411	−	0.722842i
$874$	−11.3680	+	4.70878i	−0.384528	+	0.159277i
$875$	2.64561	+	2.64561i	0.0894380	+	0.0894380i
$876$	−4.56004	−	4.56004i	−0.154069	−	0.154069i
$877$	10.6998	−	4.43201i	0.361308	−	0.149658i	−0.194642	−	0.980874i	$-0.562355\pi$
$877$	10.6998	−	4.43201i	0.361308	−	0.149658i	0.555950	+	0.831216i	$0.312355\pi$
$878$	−3.21416	−	7.75967i	−0.108473	−	0.261876i
$879$	2.08964	+	0.865558i	0.0704819	+	0.0291945i
$880$		−	6.77486i		−	0.228380i
$881$	7.67251	−	18.5231i	0.258493	−	0.624058i	−0.740346	−	0.672226i	$-0.765338\pi$
$881$	7.67251	−	18.5231i	0.258493	−	0.624058i	0.998839	+	0.0481680i	$0.0153383\pi$
$882$	13.0394	−	13.0394i	0.439059	−	0.439059i
$883$	−30.6207			−1.03047			−0.515234	−	0.857050i	$-0.672295\pi$
$883$	−30.6207			−1.03047			−0.515234	+	0.857050i	$0.672295\pi$
$884$	11.1687	−	0.403204i	0.375645	−	0.0135612i
$885$	−11.7594			−0.395287
$886$	−7.57783	+	7.57783i	−0.254582	+	0.254582i
$887$	−3.84278	+	9.27729i	−0.129028	+	0.311501i	−0.975170	−	0.221456i	$-0.928919\pi$
$887$	−3.84278	+	9.27729i	−0.129028	+	0.311501i	0.846143	+	0.532957i	$0.178919\pi$
$888$		−	12.7477i		−	0.427785i
$889$	46.0072	+	19.0568i	1.54303	+	0.639145i
$890$	0.945566	+	2.28280i	0.0316954	+	0.0765196i
$891$	1.36551	−	0.565613i	0.0457464	−	0.0189488i
$892$	5.81118	+	5.81118i	0.194573	+	0.194573i
$893$	−3.14020	−	3.14020i	−0.105083	−	0.105083i
$894$	37.4546	−	15.5142i	1.25267	−	0.518873i
$895$	3.52093	+	8.50028i	0.117692	+	0.284133i
$896$	−46.6400	−	19.3189i	−1.55813	−	0.645400i
$897$		−	32.3936i		−	1.08159i
$898$	10.6196	−	25.6379i	0.354380	−	0.855549i
$899$	−6.95424	+	6.95424i	−0.231937	+	0.231937i
$900$	0.686207			0.0228736
$901$	−16.9007	+	18.1667i	−0.563044	+	0.605220i
$902$	3.55328			0.118311
$903$	19.4949	−	19.4949i	0.648750	−	0.648750i
$904$	−10.7474	+	25.9464i	−0.357452	+	0.862966i
$905$			13.7740i			0.457862i
$906$	0.254404	+	0.105377i	0.00845200	+	0.00350093i
$907$	−0.723044	−	1.74558i	−0.0240083	−	0.0579611i	0.911421	−	0.411476i	$-0.134986\pi$
$907$	−0.723044	−	1.74558i	−0.0240083	−	0.0579611i	−0.935429	+	0.353515i	$0.884986\pi$
$908$	2.52099	−	1.04423i	0.0836619	−	0.0346539i
$909$	−0.0836841	−	0.0836841i	−0.00277563	−	0.00277563i
$910$	−27.5358	−	27.5358i	−0.912804	−	0.912804i
$911$	18.7844	−	7.78074i	0.622354	−	0.257787i	−0.0491465	−	0.998792i	$-0.515650\pi$
$911$	18.7844	−	7.78074i	0.622354	−	0.257787i	0.671500	+	0.741004i	$0.265650\pi$
$912$	3.80174	+	9.17821i	0.125888	+	0.303921i
$913$	−22.7518	−	9.42410i	−0.752974	−	0.311892i
$914$		−	62.1991i		−	2.05736i
$915$	−1.37072	+	3.30921i	−0.0453146	+	0.109399i
$916$	−6.98933	+	6.98933i	−0.230934	+	0.230934i
$917$	2.44483			0.0807355
$918$	−11.9600	+	32.1039i	−0.394740	+	1.05959i
$919$	51.7893			1.70837			0.854185	−	0.519969i	$-0.174057\pi$
$919$	51.7893			1.70837			0.854185	+	0.519969i	$0.174057\pi$
$920$	7.40462	−	7.40462i	0.244123	−	0.244123i
$921$	−1.54793	+	3.73704i	−0.0510061	+	0.123140i
$922$			39.4104i			1.29791i
$923$	23.7634	+	9.84311i	0.782181	+	0.323990i
$924$	0.961687	+	2.32172i	0.0316372	+	0.0763789i
$925$	4.17301	−	1.72852i	0.137208	−	0.0568333i
$926$	3.46828	+	3.46828i	0.113975	+	0.113975i
$927$	−9.41781	−	9.41781i	−0.309322	−	0.309322i
$928$	−15.7949	+	6.54246i	−0.518493	+	0.214767i
$929$	−3.23396	−	7.80748i	−0.106103	−	0.256155i	0.861907	−	0.507066i	$-0.169270\pi$
$929$	−3.23396	−	7.80748i	−0.106103	−	0.256155i	−0.968010	+	0.250911i	$0.919270\pi$
$930$	2.11550	+	0.876267i	0.0693698	+	0.0287339i
$931$			13.1266i			0.430208i
$932$	−2.51728	+	6.07726i	−0.0824564	+	0.199067i
$933$	−2.91025	+	2.91025i	−0.0952772	+	0.0952772i
$934$	28.6936			0.938883
$935$	0.216982	+	6.01038i	0.00709605	+	0.196560i
$936$	28.2349			0.922886
$937$	15.6827	−	15.6827i	0.512332	−	0.512332i	−0.402908	−	0.915240i	$-0.632001\pi$
$937$	15.6827	−	15.6827i	0.512332	−	0.512332i	0.915240	+	0.402908i	$0.132001\pi$
$938$	−13.4977	+	32.5863i	−0.440715	+	1.06398i
$939$			9.31944i			0.304128i
$940$	−0.883239	−	0.365849i	−0.0288081	−	0.0119327i
$941$	−18.5984	−	44.9006i	−0.606292	−	1.46372i	−0.867004	−	0.498302i	$-0.833957\pi$
$941$	−18.5984	−	44.9006i	−0.606292	−	1.46372i	0.260712	−	0.965417i	$-0.416043\pi$
$942$	20.3539	−	8.43087i	0.663167	−	0.274693i
$943$	4.70093	+	4.70093i	0.153083	+	0.153083i
$944$	33.8652	+	33.8652i	1.10222	+	1.10222i
$945$	18.5253	−	7.67341i	0.602626	−	0.249616i
$946$	−5.59223	−	13.5008i	−0.181819	−	0.438950i
$947$	−48.2759	−	19.9965i	−1.56875	−	0.649799i	−0.582172	−	0.813065i	$-0.697797\pi$
$947$	−48.2759	−	19.9965i	−1.56875	−	0.649799i	−0.986582	+	0.163266i	$0.947797\pi$
$948$			1.10260i			0.0358107i
$949$	35.9796	−	86.8623i	1.16795	−	2.81967i
$950$	−2.05626	+	2.05626i	−0.0667138	+	0.0667138i
$951$	22.7378			0.737323
$952$	35.7755	+	13.3279i	1.15949	+	0.431959i
$953$	20.2125			0.654748			0.327374	−	0.944895i	$-0.393836\pi$
$953$	20.2125			0.654748			0.327374	+	0.944895i	$0.393836\pi$
$954$	11.2124	−	11.2124i	0.363014	−	0.363014i
$955$	−3.85236	+	9.30042i	−0.124659	+	0.300954i
$956$		−	4.75643i		−	0.153834i
$957$	−11.6709	−	4.83423i	−0.377266	−	0.156269i
$958$	21.3458	+	51.5334i	0.689653	+	1.66497i
$959$	−2.17072	+	0.899143i	−0.0700963	+	0.0290348i
$960$	−4.67591	−	4.67591i	−0.150914	−	0.150914i
$961$	20.7343	+	20.7343i	0.668850	+	0.668850i
$962$	−43.4331	+	17.9906i	−1.40034	+	0.580040i
$963$	1.09256	+	2.63768i	0.0352073	+	0.0849980i
$964$	0.543168	+	0.224987i	0.0174943	+	0.00724636i
$965$		−	1.77240i		−	0.0570555i
$966$	−10.7118	+	25.8605i	−0.344645	+	0.832047i
$967$	−35.3479	+	35.3479i	−1.13671	+	1.13671i	−0.147678	+	0.989036i	$0.547180\pi$
$967$	−35.3479	+	35.3479i	−1.13671	+	1.13671i	−0.989036	+	0.147678i	$0.952820\pi$
$968$	21.9571			0.705729
$969$	−3.66670	−	8.02077i	−0.117791	−	0.257664i
$970$	21.0893			0.677138
$971$	−14.4144	+	14.4144i	−0.462580	+	0.462580i	−0.899500	−	0.436921i	$-0.856069\pi$
$971$	−14.4144	+	14.4144i	−0.462580	+	0.462580i	0.436921	+	0.899500i	$0.356069\pi$
$972$	2.30576	−	5.56659i	0.0739572	−	0.178548i
$973$			49.4026i			1.58377i
$974$	−7.30652	−	3.02646i	−0.234116	−	0.0969740i
$975$	−2.92969	−	7.07290i	−0.0938252	−	0.226514i
$976$	13.4774	−	5.58254i	0.431403	−	0.178693i
$977$	−16.4798	−	16.4798i	−0.527235	−	0.527235i	0.392512	−	0.919747i	$-0.371606\pi$
$977$	−16.4798	−	16.4798i	−0.527235	−	0.527235i	−0.919747	+	0.392512i	$0.871606\pi$
$978$	26.5469	+	26.5469i	0.848876	+	0.848876i
$979$	2.14774	−	0.889621i	0.0686419	−	0.0284324i
$980$	1.08139	+	2.61071i	0.0345438	+	0.0833961i
$981$	9.82032	+	4.06771i	0.313539	+	0.129872i
$982$		−	33.5602i		−	1.07095i
$983$	−18.0553	+	43.5894i	−0.575876	+	1.39029i	0.320609	+	0.947212i	$0.396113\pi$
$983$	−18.0553	+	43.5894i	−0.575876	+	1.39029i	−0.896484	+	0.443075i	$0.853887\pi$
$984$	3.13549	−	3.13549i	0.0999559	−	0.0999559i
$985$	−10.9705			−0.349549
$986$	44.1501	−	20.1832i	1.40603	−	0.642765i
$987$	−10.1024			−0.321563
$988$	3.59495	−	3.59495i	0.114371	−	0.114371i
$989$	10.4630	−	25.2598i	0.332703	−	0.803215i
$990$		−	3.84349i		−	0.122154i
$991$	−35.6588	−	14.7703i	−1.13274	−	0.469196i	−0.264027	−	0.964515i	$-0.585051\pi$
$991$	−35.6588	−	14.7703i	−1.13274	−	0.469196i	−0.868711	+	0.495320i	$0.835051\pi$
$992$	−1.11574	−	2.69364i	−0.0354248	−	0.0855230i
$993$	14.6901	−	6.08486i	0.466178	−	0.193097i
$994$	−15.7159	−	15.7159i	−0.498479	−	0.498479i
$995$	−2.78063	−	2.78063i	−0.0881520	−	0.0881520i
$996$	7.18205	−	2.97490i	0.227572	−	0.0942634i
$997$	−10.6032	−	25.5984i	−0.335807	−	0.810711i	−0.998109	−	0.0614733i	$-0.980420\pi$
$997$	−10.6032	−	25.5984i	−0.335807	−	0.810711i	0.662301	−	0.749238i	$-0.269580\pi$
$998$	−39.5363	−	16.3765i	−1.25150	−	0.518389i
$999$		−	24.2070i		−	0.765876i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.l.a.76.5	yes	24
3.2	odd	2		765.2.be.b.586.2		24
5.2	odd	4		425.2.n.f.399.5		24
5.3	odd	4		425.2.n.c.399.2		24
5.4	even	2		425.2.m.b.76.2		24
17.6	odd	16		1445.2.d.j.866.16		24
17.7	odd	16		1445.2.a.p.1.5		12
17.10	odd	16		1445.2.a.q.1.5		12
17.11	odd	16		1445.2.d.j.866.15		24
17.15	even	8	inner	85.2.l.a.66.5	✓	24
51.32	odd	8		765.2.be.b.406.2		24
85.24	odd	16		7225.2.a.bs.1.8		12
85.32	odd	8		425.2.n.c.49.2		24
85.44	odd	16		7225.2.a.bq.1.8		12
85.49	even	8		425.2.m.b.151.2		24
85.83	odd	8		425.2.n.f.49.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.5	✓	24	17.15	even	8	inner
85.2.l.a.76.5	yes	24	1.1	even	1	trivial
425.2.m.b.76.2		24	5.4	even	2
425.2.m.b.151.2		24	85.49	even	8
425.2.n.c.49.2		24	85.32	odd	8
425.2.n.c.399.2		24	5.3	odd	4
425.2.n.f.49.5		24	85.83	odd	8
425.2.n.f.399.5		24	5.2	odd	4
765.2.be.b.406.2		24	51.32	odd	8
765.2.be.b.586.2		24	3.2	odd	2
1445.2.a.p.1.5		12	17.7	odd	16
1445.2.a.q.1.5		12	17.10	odd	16
1445.2.d.j.866.15		24	17.11	odd	16
1445.2.d.j.866.16		24	17.6	odd	16
7225.2.a.bq.1.8		12	85.44	odd	16
7225.2.a.bs.1.8		12	85.24	odd	16

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	85.2.l.a.76.5

Level	$85$
Weight	$2$
Character	85.76
Analytic conductor	$0.679$
Analytic rank	$0$
Dimension	$24$
Inner twists	$2$