LMFDB - Embedded newform 85.2.l.a.66.5

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			66.5
Character	$\chi$	$=$	85.66
Dual form			85.2.l.a.76.5

$q$ -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 $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$ .

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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	0.979011	−	0.203806i	$-0.0653312\pi$
$2$	1.09631	+	1.09631i	0.775205	+	0.775205i	−0.203806	+	0.979011i	$0.565331\pi$
$3$	0.436412	+	1.05359i	0.251962	+	0.608291i	0.998362	−	0.0572066i	$-0.0182194\pi$
$3$	0.436412	+	1.05359i	0.251962	+	0.608291i	−0.746400	+	0.665498i	$0.768219\pi$
$4$			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	−0.382635	−	0.923900i	$-0.624983\pi$
$7$	−3.45666	−	1.43180i	−1.30649	−	0.541168i	−0.923859	+	0.382732i	$0.874983\pi$
$8$	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	−0.817111	−	0.576481i	$-0.804425\pi$
$11$	0.558213	−	1.34764i	0.168307	−	0.406330i	0.985418	+	0.170151i	$0.0544255\pi$
$12$	−0.425411	+	0.176211i	−0.122805	+	0.0508677i
$13$			6.71314i			1.86189i	0.365160	+	0.930945i	$0.381014\pi$
$13$			6.71314i			1.86189i	−0.365160	+	0.930945i	$0.618986\pi$
$14$	−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	0.538414	−	0.842680i	$-0.319024\pi$
$19$	−1.32627	−	1.32627i	−0.304266	−	0.304266i	−0.842680	+	0.538414i	$0.819024\pi$
$20$	−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	−0.660303	−	0.750999i	$-0.729572\pi$
$23$	1.61926	−	3.90923i	0.337639	−	0.815132i	0.997941	−	0.0641322i	$-0.0204279\pi$
$24$	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	−0.922784	−	0.385318i	$-0.874092\pi$
$29$	−7.01595	+	2.90610i	−1.30283	+	0.539650i	−0.380046	+	0.924968i	$0.624092\pi$
$30$		−	1.76809i		−	0.322807i
$31$	0.495602	+	1.19649i	0.0890128	+	0.214896i	0.962116	−	0.272639i	$-0.0878964\pi$
$31$	0.495602	+	1.19649i	0.0890128	+	0.214896i	−0.873104	+	0.487534i	$0.837896\pi$
$32$	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	0.999924	−	0.0123104i	$-0.00391861\pi$
$37$	1.72852	+	4.17301i	0.284166	+	0.686038i	−0.715758	+	0.698348i	$0.753919\pi$
$38$		−	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	0.493141	−	0.869949i	$-0.335849\pi$
$41$	1.45157	+	0.601260i	0.226697	+	0.0939011i	−0.266444	+	0.963850i	$0.585849\pi$
$42$	4.67767	−	4.67767i	0.721780	−	0.721780i
$43$	−4.56902	+	4.56902i	−0.696770	+	0.696770i	−0.963712	−	0.266943i	$-0.913987\pi$
$43$	−4.56902	+	4.56902i	−0.696770	+	0.696770i	0.266943	+	0.963712i	$0.413987\pi$
$44$	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	$-0.944757\pi$
$47$		−	2.36770i		−	0.345364i	0.984978	−	0.172682i	$-0.0552434\pi$
$48$	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	0.936140	−	0.351627i	$-0.114372\pi$
$53$	4.25532	+	4.25532i	0.584513	+	0.584513i	−0.351627	+	0.936140i	$0.614372\pi$
$54$	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	−0.0495099	−	0.998774i	$-0.515766\pi$
$59$	7.29143	−	7.29143i	0.949264	−	0.949264i	0.998774	+	0.0495099i	$0.0157659\pi$
$60$	0.325595	−	0.325595i	0.0420342	−	0.0420342i
$61$	2.90180	+	1.20197i	0.371537	+	0.153896i	0.560636	−	0.828062i	$-0.310557\pi$
$61$	2.90180	+	1.20197i	0.371537	+	0.153896i	−0.189099	+	0.981958i	$0.560557\pi$
$62$	−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	0.812679	−	0.582712i	$-0.198008\pi$
$71$	−1.46625	−	3.53983i	−0.174011	−	0.420101i	−0.986690	+	0.162611i	$0.948008\pi$
$72$		−	4.20591i		−	0.495672i
$73$	12.9392	−	5.35957i	1.51441	−	0.627291i	0.537951	−	0.842976i	$-0.319199\pi$
$73$	12.9392	−	5.35957i	1.51441	−	0.627291i	0.976463	+	0.215686i	$0.0691987\pi$
$74$	−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	−0.967008	−	0.254745i	$-0.918008\pi$
$79$	−0.916355	+	2.21228i	−0.103098	+	0.248901i	0.863910	+	0.503646i	$0.168008\pi$
$80$	−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	−0.921158	−	0.389189i	$-0.872755\pi$
$83$	−11.9378	−	11.9378i	−1.31035	−	1.31035i	−0.389189	−	0.921158i	$-0.627245\pi$
$84$	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	$0.0269184\pi$
$89$			1.59370i			0.168931i	−0.996426	+	0.0844657i	$0.973082\pi$
$90$	−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	−0.914779	−	0.403955i	$-0.867635\pi$
$97$	−12.5670	+	5.20542i	−1.27599	+	0.528531i	−0.361207	+	0.932486i	$0.617635\pi$
$98$			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	−0.306399	−	0.951903i	$-0.599124\pi$
$107$	1.55204	−	0.642876i	0.150041	−	0.0621492i	0.456440	+	0.889754i	$0.349124\pi$
$108$	−0.828101	+	1.99921i	−0.0796841	+	0.192374i
$109$	5.77839	+	2.39349i	0.553469	+	0.229254i	0.641847	−	0.766833i	$-0.278168\pi$
$109$	5.77839	+	2.39349i	0.553469	+	0.229254i	−0.0883780	+	0.996087i	$0.528168\pi$
$110$	−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	−0.576998	−	0.816746i	$-0.695776\pi$
$113$	4.34271	−	10.4842i	0.408527	−	0.986273i	0.985526	−	0.169527i	$-0.0542240\pi$
$114$	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	−0.988213	−	0.153086i	$-0.951079\pi$
$127$	−9.41141	+	9.41141i	−0.835127	+	0.835127i	0.153086	+	0.988213i	$0.451079\pi$
$128$	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	−0.408900	−	0.912579i	$-0.634088\pi$
$131$	−0.603703	+	0.250062i	−0.0527458	+	0.0218480i	0.356155	+	0.934427i	$0.384088\pi$
$132$			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	0.979735	+	0.200296i	$0.0641904\pi$
$139$	5.05298	+	12.1990i	0.428589	+	1.03470i	−0.551147	+	0.834408i	$0.685810\pi$
$140$			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	$-0.611557\pi$
$149$		−	22.9291i		−	1.87842i	0.343336	−	0.939212i	$-0.388443\pi$
$150$	0.676617	+	1.63350i	0.0552456	+	0.133375i
$151$	−0.110126	−	0.110126i	−0.00896193	−	0.00896193i	0.702612	−	0.711574i	$-0.252017\pi$
$151$	−0.110126	−	0.110126i	−0.00896193	−	0.00896193i	−0.711574	+	0.702612i	$0.752017\pi$
$152$	−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	$-0.834354\pi$
$157$		−	12.4603i		−	0.994443i	0.867624	−	0.497221i	$-0.165646\pi$
$158$	−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	−0.555729	−	0.831364i	$-0.687561\pi$
$163$	−19.6174	−	8.12578i	−1.53655	−	0.636460i	−0.980822	+	0.194903i	$0.937561\pi$
$164$	−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	0.943682	−	0.330854i	$-0.107337\pi$
$167$	0.548558	+	1.32434i	0.0424487	+	0.102480i	−0.901233	+	0.433335i	$0.857337\pi$
$168$	−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	0.942704	−	0.333630i	$-0.108274\pi$
$173$	0.528746	+	1.27651i	0.0401998	+	0.0970509i	−0.902504	+	0.430681i	$0.858274\pi$
$174$		−	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	−0.907127	−	0.420858i	$-0.861729\pi$
$179$	−6.50583	+	6.50583i	−0.486269	+	0.486269i	0.420858	+	0.907127i	$0.361729\pi$
$180$	−0.633972	−	0.262600i	−0.0472535	−	0.0195730i
$181$	−5.27107	+	12.7255i	−0.391795	+	0.945878i	0.597754	+	0.801680i	$0.296060\pi$
$181$	−5.27107	+	12.7255i	−0.391795	+	0.945878i	−0.989549	+	0.144198i	$0.953940\pi$
$182$	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	$0.118658\pi$
$191$			10.0667i			0.728401i	−0.931321	+	0.364200i	$0.881342\pi$
$192$	6.10937	−	2.53058i	0.440905	−	0.182629i
$193$	0.678267	−	1.63748i	0.0488227	−	0.117869i	−0.897587	−	0.440838i	$-0.854681\pi$
$193$	0.678267	−	1.63748i	0.0488227	−	0.117869i	0.946409	+	0.322970i	$0.104681\pi$
$194$	−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	0.713309	−	0.700850i	$-0.247196\pi$
$197$	10.1354	+	4.19823i	0.722119	+	0.299112i	0.00881014	+	0.999961i	$0.497196\pi$
$198$	1.47084	−	3.55092i	0.104528	−	0.252353i
$199$	3.63307	−	1.50487i	0.257542	−	0.106677i	−0.250177	−	0.968200i	$-0.580489\pi$
$199$	3.63307	−	1.50487i	0.257542	−	0.106677i	0.507719	+	0.861523i	$0.330489\pi$
$200$		−	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	0.997294	+	0.0735168i	$0.0234223\pi$
$211$	25.4852	+	10.5563i	1.75447	+	0.726726i	0.757178	+	0.653209i	$0.226578\pi$
$212$	−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	0.0355918	−	0.999366i	$-0.488668\pi$
$223$	−14.3922	−	14.3922i	−0.963775	−	0.963775i	−0.999366	+	0.0355918i	$0.988668\pi$
$224$	−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	−0.814520	−	0.580136i	$-0.802999\pi$
$227$	2.58618	−	6.24359i	0.171651	−	0.414402i	0.986170	+	0.165734i	$0.0529994\pi$
$228$	0.797910	+	0.330505i	0.0528429	+	0.0218882i
$229$	−17.3101	+	17.3101i	−1.14388	+	1.14388i	−0.156150	+	0.987733i	$0.549908\pi$
$229$	−17.3101	+	17.3101i	−1.14388	+	1.14388i	−0.987733	+	0.156150i	$0.950092\pi$
$230$	−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	−0.816659	−	0.577121i	$-0.804176\pi$
$233$	−15.0512	+	6.23442i	−0.986038	+	0.408430i	−0.169379	+	0.985551i	$0.554176\pi$
$234$			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	0.904916	−	0.425589i	$-0.139933\pi$
$241$	−0.557214	−	1.34523i	−0.0358933	−	0.0866541i	−0.940810	+	0.338935i	$0.889933\pi$
$242$			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	$0.261115\pi$
$251$			23.1739i			1.46272i	−0.681990	+	0.731361i	$0.738885\pi$
$252$	−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	0.923039	−	0.384706i	$-0.125697\pi$
$257$	8.63013	+	8.63013i	0.538332	+	0.538332i	−0.384706	+	0.923039i	$0.625697\pi$
$258$	−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	−0.945355	−	0.326043i	$-0.894284\pi$
$263$	−10.0435	+	10.0435i	−0.619312	+	0.619312i	0.326043	+	0.945355i	$0.394284\pi$
$264$	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	−0.999904	−	0.0138358i	$-0.995596\pi$
$269$	−4.96381	−	11.9837i	−0.302649	−	0.730658i	0.697256	−	0.716822i	$-0.254404\pi$
$270$	−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	−0.555742	−	0.831355i	$-0.687566\pi$
$277$	−6.00580	+	2.48768i	−0.360853	+	0.149470i	0.194888	+	0.980825i	$0.437566\pi$
$278$	−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	−0.823185	−	0.567774i	$-0.807805\pi$
$281$	−4.28147	+	4.28147i	−0.255411	+	0.255411i	0.567774	+	0.823185i	$0.307805\pi$
$282$	3.86763	+	1.60203i	0.230314	+	0.0953992i
$283$	5.38173	−	12.9927i	0.319911	−	0.772333i	−0.679347	−	0.733817i	$-0.737737\pi$
$283$	5.38173	−	12.9927i	0.319911	−	0.772333i	0.999258	−	0.0385160i	$-0.0122631\pi$
$284$	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	$-0.981549\pi$
$293$		−	1.98335i		−	0.115869i	0.998320	−	0.0579343i	$-0.0184514\pi$
$294$	−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	−0.475210	−	0.879872i	$-0.657628\pi$
$311$	−3.33429	+	1.38111i	−0.189070	+	0.0783155i	0.286140	+	0.958188i	$0.407628\pi$
$312$	−7.25042	+	17.5041i	−0.410474	+	0.990973i
$313$	−7.55002	−	3.12732i	−0.426753	−	0.176767i	0.158961	−	0.987285i	$-0.449186\pi$
$313$	−7.55002	−	3.12732i	−0.426753	−	0.176767i	−0.585713	+	0.810518i	$0.699186\pi$
$314$	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	−0.551198	−	0.834375i	$-0.685829\pi$
$317$	7.63011	−	18.4207i	0.428550	−	1.03461i	0.979748	−	0.200236i	$-0.0641710\pi$
$318$	−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	−0.382180	−	0.924088i	$-0.624827\pi$
$331$	9.85914	−	9.85914i	0.541907	−	0.541907i	0.924088	+	0.382180i	$0.124827\pi$
$332$	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	−0.982858	−	0.184364i	$-0.940978\pi$
$337$	−7.67782	−	18.5359i	−0.418237	−	1.00971i	0.564621	−	0.825350i	$-0.309022\pi$
$338$	−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	−0.222697	−	0.974888i	$-0.571486\pi$
$347$	−19.9229	−	8.25234i	−1.06952	−	0.443009i	−0.846820	+	0.531879i	$0.821486\pi$
$348$	2.47257	−	2.47257i	0.132544	−	0.132544i
$349$	7.75970	−	7.75970i	0.415367	−	0.415367i	−0.468236	−	0.883603i	$-0.655110\pi$
$349$	7.75970	−	7.75970i	0.415367	−	0.415367i	0.883603	+	0.468236i	$0.155110\pi$
$350$	−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	$0.213121\pi$
$353$			23.3210i			1.24125i	−0.784108	+	0.620625i	$0.786879\pi$
$354$	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	0.742769	−	0.669547i	$-0.233512\pi$
$359$	1.38736	+	1.38736i	0.0732222	+	0.0732222i	−0.669547	+	0.742769i	$0.733512\pi$
$360$	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	0.990266	−	0.139187i	$-0.0444488\pi$
$367$	30.4997	+	12.6334i	1.59207	+	0.659457i	0.601804	+	0.798644i	$0.294449\pi$
$368$	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	0.269751	−	0.962930i	$-0.413059\pi$
$379$	22.2204	−	9.20401i	1.14139	−	0.472778i	0.871637	+	0.490152i	$0.163059\pi$
$380$	−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	−0.755748	−	0.654863i	$-0.772726\pi$
$383$	−1.97435	+	1.97435i	−0.100884	+	0.100884i	0.654863	+	0.755748i	$0.272726\pi$
$384$	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	0.626313	−	0.779572i	$-0.284563\pi$
$389$	−3.02275	−	3.02275i	−0.153260	−	0.153260i	−0.779572	+	0.626313i	$0.784563\pi$
$390$	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	−0.701950	−	0.712226i	$-0.747687\pi$
$397$	5.93808	−	14.3358i	0.298023	−	0.719492i	0.999974	−	0.00726623i	$-0.00231293\pi$
$398$	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	0.810120	−	0.586265i	$-0.199402\pi$
$401$	19.3924	+	8.03258i	0.968409	+	0.401128i	0.158289	+	0.987393i	$0.449402\pi$
$402$	−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	0.263662	+	0.964615i	$0.415070\pi$
$419$	−12.3812	+	29.8909i	−0.604861	+	1.46026i	−0.868523	+	0.495649i	$0.834930\pi$
$420$	−1.59166	+	0.659286i	−0.0776649	+	0.0321699i
$421$			3.62096i			0.176475i	0.996099	+	0.0882374i	$0.0281234\pi$
$421$			3.62096i			0.176475i	−0.996099	+	0.0882374i	$0.971877\pi$
$422$	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	−0.676503	−	0.736440i	$-0.736505\pi$
$431$	6.69733	−	16.1688i	0.322599	−	0.778823i	0.999101	−	0.0423823i	$-0.0134948\pi$
$432$	22.9966	+	9.52549i	1.10642	+	0.458295i
$433$	6.46703	−	6.46703i	0.310785	−	0.310785i	−0.534428	−	0.845214i	$-0.679473\pi$
$433$	6.46703	−	6.46703i	0.310785	−	0.310785i	0.845214	+	0.534428i	$0.179473\pi$
$434$	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	0.965599	−	0.260036i	$-0.0837346\pi$
$439$	2.07310	+	5.00491i	0.0989438	+	0.238872i	−0.866655	+	0.498908i	$0.833735\pi$
$440$	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	0.737074	−	0.675812i	$-0.236207\pi$
$449$	16.5362	+	6.84953i	0.780392	+	0.323249i	0.0433186	+	0.999061i	$0.486207\pi$
$450$	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	0.907992	+	0.418988i	$0.137615\pi$
$457$	28.3676	+	28.3676i	1.32698	+	1.32698i	0.418988	+	0.907992i	$0.362385\pi$
$458$	−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	0.151341	−	0.988482i	$-0.451641\pi$
$461$	−17.9742	−	17.9742i	−0.837140	−	0.837140i	−0.988482	+	0.151341i	$0.951641\pi$
$462$	−3.69270	−	8.91497i	−0.171800	−	0.414762i
$463$		−	3.16361i		−	0.147025i	−0.997294	−	0.0735126i	$-0.976579\pi$
$463$		−	3.16361i		−	0.147025i	0.997294	−	0.0735126i	$-0.0234209\pi$
$464$	−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	−0.336215	−	0.941785i	$-0.609147\pi$
$467$	13.0865	−	13.0865i	0.605571	−	0.605571i	0.941785	+	0.336215i	$0.109147\pi$
$468$	−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	−0.840780	−	0.541377i	$-0.817903\pi$
$479$	−13.7679	−	33.2386i	−0.629070	−	1.51871i	0.211710	−	0.977332i	$-0.432097\pi$
$480$		−	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	−0.961916	−	0.273344i	$-0.911870\pi$
$487$	−1.95204	+	4.71263i	−0.0884552	+	0.213550i	0.873461	+	0.486894i	$0.161870\pi$
$488$	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	0.962397	−	0.271646i	$-0.0875680\pi$
$491$	15.3060	+	15.3060i	0.690751	+	0.690751i	−0.271646	+	0.962397i	$0.587568\pi$
$492$	−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	0.490047	+	0.871696i	$0.336979\pi$
$499$	−10.5627	+	25.5006i	−0.472850	+	1.14156i	−0.962898	+	0.269866i	$0.913021\pi$
$500$	−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	−0.205018	−	0.978758i	$-0.565725\pi$
$503$	−23.3713	−	9.68071i	−1.04207	−	0.431642i	−0.837056	+	0.547117i	$0.815725\pi$
$504$	−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	−0.869341	−	0.494213i	$-0.835456\pi$
$521$	2.16471	−	5.22606i	0.0948375	−	0.228958i	0.964178	+	0.265255i	$0.0854562\pi$
$522$	−18.4864	+	7.65731i	−0.809127	+	0.335151i
$523$		−	21.6359i		−	0.946074i	−0.881043	−	0.473037i	$-0.843158\pi$
$523$		−	21.6359i		−	0.946074i	0.881043	−	0.473037i	$-0.156842\pi$
$524$	−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	0.974830	−	0.222951i	$-0.0715692\pi$
$541$	2.97419	+	7.18033i	0.127870	+	0.308707i	−0.846959	+	0.531658i	$0.821569\pi$
$542$	−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	0.847159	+	0.531340i	$0.178311\pi$
$547$	14.5904	+	35.2244i	0.623841	+	1.50609i	−0.223318	+	0.974746i	$0.571689\pi$
$548$			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	$0.0322155\pi$
$557$			4.76903i			0.202070i	−0.994883	+	0.101035i	$0.967785\pi$
$558$	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	0.994806	+	0.101785i	$0.0324554\pi$
$563$	26.0195	+	26.0195i	1.09659	+	1.09659i	0.101785	+	0.994806i	$0.467545\pi$
$564$	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	−0.689465	−	0.724319i	$-0.742154\pi$
$569$	0.831415	−	0.831415i	0.0348547	−	0.0348547i	0.724319	+	0.689465i	$0.242154\pi$
$570$	−2.34495	+	2.34495i	−0.0982193	+	0.0982193i
$571$	−31.8053	−	13.1742i	−1.33101	−	0.551323i	−0.400068	−	0.916485i	$-0.631014\pi$
$571$	−31.8053	−	13.1742i	−1.33101	−	0.551323i	−0.930944	+	0.365162i	$0.881014\pi$
$572$	−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	−0.968363	−	0.249546i	$-0.919719\pi$
$587$	−17.4156	+	17.4156i	−0.718817	+	0.718817i	0.249546	+	0.968363i	$0.419719\pi$
$588$	−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	0.898337	+	0.439307i	$0.144776\pi$
$593$	32.5738	+	32.5738i	1.33764	+	1.33764i	0.439307	+	0.898337i	$0.355224\pi$
$594$	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	$0.0128262\pi$
$599$			1.97185i			0.0805677i	−0.999188	+	0.0402839i	$0.987174\pi$
$600$	2.60744	−	1.08004i	0.106448	−	0.0440923i
$601$	1.26765	−	3.06037i	0.0517084	−	0.124835i	−0.895914	−	0.444227i	$-0.853479\pi$
$601$	1.26765	−	3.06037i	0.0517084	−	0.124835i	0.947623	+	0.319392i	$0.103479\pi$
$602$	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	0.0449760	−	0.998988i	$-0.485679\pi$
$607$	19.2952	−	7.99235i	0.783170	−	0.324400i	0.738194	+	0.674588i	$0.235679\pi$
$608$		−	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	−0.476349	−	0.879256i	$-0.658040\pi$
$617$	−4.75553	+	1.96980i	−0.191450	+	0.0793013i	0.284899	+	0.958558i	$0.408040\pi$
$618$	5.30260	−	12.8016i	0.213302	−	0.514957i
$619$	7.81974	+	3.23904i	0.314302	+	0.130188i	0.534258	−	0.845322i	$-0.320591\pi$
$619$	7.81974	+	3.23904i	0.314302	+	0.130188i	−0.219956	+	0.975510i	$0.570591\pi$
$620$	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	0.553114	−	0.833106i	$-0.313439\pi$
$631$	−7.03331	−	7.03331i	−0.279992	−	0.279992i	−0.833106	+	0.553114i	$0.813439\pi$
$632$	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	−0.570658	−	0.821188i	$-0.693312\pi$
$641$	−9.96278	+	4.12672i	−0.393506	+	0.162996i	0.177152	+	0.984184i	$0.443312\pi$
$642$			2.97024i			0.117226i
$643$	−1.11381	−	2.68897i	−0.0439243	−	0.106043i	0.900395	−	0.435074i	$-0.143278\pi$
$643$	−1.11381	−	2.68897i	−0.0439243	−	0.106043i	−0.944319	+	0.329031i	$0.893278\pi$
$644$	−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	−0.234100	−	0.972212i	$-0.575214\pi$
$653$	−27.7794	−	11.5066i	−1.08709	−	0.450288i	−0.852992	+	0.521924i	$0.825214\pi$
$654$	−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	$0.0791860\pi$
$659$			12.6410i			0.492424i	−0.969216	+	0.246212i	$0.920814\pi$
$660$	−0.257035	−	0.620538i	−0.0100051	−	0.0241544i
$661$	10.8422	+	10.8422i	0.421712	+	0.421712i	0.885793	−	0.464081i	$-0.153615\pi$
$661$	10.8422	+	10.8422i	0.421712	+	0.421712i	−0.464081	+	0.885793i	$0.653615\pi$
$662$	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	−0.135788	−	0.990738i	$-0.543357\pi$
$673$	−24.1876	−	10.0188i	−0.932362	−	0.386197i	−0.796574	+	0.604541i	$0.793357\pi$
$674$	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	0.994505	−	0.104686i	$-0.0333837\pi$
$677$	5.65293	+	13.6474i	0.217260	+	0.524512i	−0.777245	+	0.629198i	$0.783384\pi$
$678$	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	0.990103	+	0.140341i	$0.0448198\pi$
$683$	10.1723	+	24.5580i	0.389230	+	0.939685i	−0.600873	+	0.799345i	$0.705180\pi$
$684$		−	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	0.173540	−	0.984827i	$-0.444479\pi$
$691$	19.6417	−	47.4193i	0.747206	−	1.80392i	0.573667	−	0.819089i	$-0.305521\pi$
$692$	−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	$-0.954931\pi$
$701$		−	7.47248i		−	0.282232i	0.989993	−	0.141116i	$-0.0450690\pi$
$702$	−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	−0.473559	−	0.880762i	$-0.657031\pi$
$709$	−4.94262	+	2.04730i	−0.185624	+	0.0768880i	0.287936	+	0.957650i	$0.407031\pi$
$710$			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	−0.0281782	−	0.999603i	$-0.508971\pi$
$719$	17.6631	−	7.31630i	0.658723	−	0.272852i	0.686901	+	0.726751i	$0.258971\pi$
$720$	−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	$-0.617619\pi$
$727$		−	50.2861i		−	1.86501i	0.361159	−	0.932504i	$-0.382381\pi$
$728$	−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	0.570571	−	0.821248i	$-0.306722\pi$
$733$	−6.78681	−	6.78681i	−0.250677	−	0.250677i	−0.821248	+	0.570571i	$0.806722\pi$
$734$	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	−0.903489	−	0.428612i	$-0.859003\pi$
$739$	−12.9093	+	12.9093i	−0.474877	+	0.474877i	0.428612	+	0.903489i	$0.359003\pi$
$740$	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	−0.173938	−	0.984757i	$-0.555649\pi$
$743$	10.8868	−	4.50945i	0.399397	−	0.165436i	0.573335	+	0.819321i	$0.305649\pi$
$744$			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	0.931522	−	0.363684i	$-0.118481\pi$
$751$	0.429503	+	1.03691i	0.0156728	+	0.0378374i	−0.915849	+	0.401522i	$0.868481\pi$
$752$		−	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	0.102372	−	0.994746i	$-0.467357\pi$
$757$	30.1857	−	30.1857i	1.09712	−	1.09712i	0.994746	−	0.102372i	$-0.0326432\pi$
$758$	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	$-0.692443\pi$
$761$		−	45.3927i		−	1.64549i	0.568414	−	0.822743i	$-0.307557\pi$
$762$	−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	$0.133108\pi$
$769$			22.5224i			0.812177i	−0.913834	+	0.406089i	$0.866892\pi$
$770$	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	0.154926	−	0.987926i	$-0.450486\pi$
$773$	31.7746	−	31.7746i	1.14285	−	1.14285i	0.987926	−	0.154926i	$-0.0495140\pi$
$774$	−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	−0.174562	−	0.984646i	$-0.555851\pi$
$787$	11.1724	−	4.62777i	0.398254	−	0.164962i	0.572816	+	0.819684i	$0.305851\pi$
$788$	−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	0.890506	−	0.454971i	$-0.150350\pi$
$797$	12.2957	+	12.2957i	0.435536	+	0.435536i	−0.454971	+	0.890506i	$0.650350\pi$
$798$	−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	−0.425922	−	0.904760i	$-0.640050\pi$
$809$	−38.8774	−	16.1035i	−1.36686	−	0.566170i	−0.940934	+	0.338590i	$0.890050\pi$
$810$	0.601182	−	1.45138i	0.0211234	−	0.0509964i
$811$	1.23386	−	0.511083i	0.0433268	−	0.0179465i	−0.360915	−	0.932599i	$-0.617535\pi$
$811$	1.23386	−	0.511083i	0.0433268	−	0.0179465i	0.404242	+	0.914652i	$0.367535\pi$
$812$			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	−0.563898	−	0.825844i	$-0.690699\pi$
$821$	−10.8502	+	4.49430i	−0.378675	+	0.156852i	0.185224	+	0.982696i	$0.440699\pi$
$822$	−0.424904	+	1.02581i	−0.0148202	+	0.0357792i
$823$	44.5359	+	18.4474i	1.55243	+	0.643036i	0.983753	−	0.179528i	$-0.0574571\pi$
$823$	44.5359	+	18.4474i	1.55243	+	0.643036i	0.568673	+	0.822564i	$0.307457\pi$
$824$	−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	0.444989	+	0.895536i	$0.353207\pi$
$827$	−14.4623	+	34.9152i	−0.502905	+	1.21412i	−0.947894	+	0.318584i	$0.896793\pi$
$828$	2.68254	−	1.11115i	0.0932248	−	0.0386150i
$829$			22.2052i			0.771219i	0.922662	+	0.385610i	$0.126009\pi$
$829$			22.2052i			0.771219i	−0.922662	+	0.385610i	$0.873991\pi$
$830$	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	0.689047	+	0.724717i	$0.258029\pi$
$839$	−8.99769	+	21.7224i	−0.310635	+	0.749939i	−0.999682	+	0.0252223i	$0.991971\pi$
$840$	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	0.988470	−	0.151416i	$-0.0483832\pi$
$853$	5.32864	+	12.8645i	0.182449	+	0.440471i	−0.806021	+	0.591887i	$0.798383\pi$
$854$		−	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	−0.645364	−	0.763875i	$-0.723294\pi$
$857$	−48.0643	−	19.9089i	−1.64185	−	0.680075i	−0.996483	+	0.0838004i	$0.973294\pi$
$858$	−12.2426	+	12.2426i	−0.417956	+	0.417956i
$859$	−34.4176	+	34.4176i	−1.17431	+	1.17431i	−0.193144	+	0.981171i	$0.561868\pi$
$859$	−34.4176	+	34.4176i	−1.17431	+	1.17431i	−0.981171	+	0.193144i	$0.938132\pi$
$860$	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	$-0.720394\pi$
$863$		−	45.2241i		−	1.53945i	0.638378	−	0.769723i	$-0.279606\pi$
$864$	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	0.555950	−	0.831216i	$-0.312355\pi$
$877$	10.6998	+	4.43201i	0.361308	+	0.149658i	−0.194642	+	0.980874i	$0.562355\pi$
$878$	−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	0.998839	−	0.0481680i	$-0.0153383\pi$
$881$	7.67251	+	18.5231i	0.258493	+	0.624058i	−0.740346	+	0.672226i	$0.765338\pi$
$882$	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	0.846143	−	0.532957i	$-0.178919\pi$
$887$	−3.84278	−	9.27729i	−0.129028	−	0.311501i	−0.975170	+	0.221456i	$0.928919\pi$
$888$			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	−0.935429	−	0.353515i	$-0.884986\pi$
$907$	−0.723044	+	1.74558i	−0.0240083	+	0.0579611i	0.911421	+	0.411476i	$0.134986\pi$
$908$	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	0.671500	−	0.741004i	$-0.265650\pi$
$911$	18.7844	+	7.78074i	0.622354	+	0.257787i	−0.0491465	+	0.998792i	$0.515650\pi$
$912$	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	−0.968010	−	0.250911i	$-0.919270\pi$
$929$	−3.23396	+	7.80748i	−0.106103	+	0.256155i	0.861907	+	0.507066i	$0.169270\pi$
$930$	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	0.915240	−	0.402908i	$-0.132001\pi$
$937$	15.6827	+	15.6827i	0.512332	+	0.512332i	−0.402908	+	0.915240i	$0.632001\pi$
$938$	−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	0.260712	+	0.965417i	$0.416043\pi$
$941$	−18.5984	+	44.9006i	−0.606292	+	1.46372i	−0.867004	+	0.498302i	$0.833957\pi$
$942$	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	−0.986582	−	0.163266i	$-0.947797\pi$
$947$	−48.2759	+	19.9965i	−1.56875	+	0.649799i	−0.582172	+	0.813065i	$0.697797\pi$
$948$		−	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	−0.989036	−	0.147678i	$-0.952820\pi$
$967$	−35.3479	−	35.3479i	−1.13671	−	1.13671i	−0.147678	−	0.989036i	$-0.547180\pi$
$968$	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	0.436921	−	0.899500i	$-0.356069\pi$
$971$	−14.4144	−	14.4144i	−0.462580	−	0.462580i	−0.899500	+	0.436921i	$0.856069\pi$
$972$	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	−0.919747	−	0.392512i	$-0.871606\pi$
$977$	−16.4798	+	16.4798i	−0.527235	+	0.527235i	0.392512	+	0.919747i	$0.371606\pi$
$978$	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	−0.896484	−	0.443075i	$-0.853887\pi$
$983$	−18.0553	−	43.5894i	−0.575876	−	1.39029i	0.320609	−	0.947212i	$-0.396113\pi$
$984$	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	−0.868711	−	0.495320i	$-0.835051\pi$
$991$	−35.6588	+	14.7703i	−1.13274	+	0.469196i	−0.264027	+	0.964515i	$0.585051\pi$
$992$	−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	0.662301	+	0.749238i	$0.269580\pi$
$997$	−10.6032	+	25.5984i	−0.335807	+	0.810711i	−0.998109	+	0.0614733i	$0.980420\pi$
$998$	−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.66.5	✓	24
3.2	odd	2		765.2.be.b.406.2		24
5.2	odd	4		425.2.n.c.49.2		24
5.3	odd	4		425.2.n.f.49.5		24
5.4	even	2		425.2.m.b.151.2		24
17.3	odd	16		1445.2.d.j.866.15		24
17.5	odd	16		1445.2.a.p.1.5		12
17.8	even	8	inner	85.2.l.a.76.5	yes	24
17.12	odd	16		1445.2.a.q.1.5		12
17.14	odd	16		1445.2.d.j.866.16		24
51.8	odd	8		765.2.be.b.586.2		24
85.8	odd	8		425.2.n.c.399.2		24
85.29	odd	16		7225.2.a.bq.1.8		12
85.39	odd	16		7225.2.a.bs.1.8		12
85.42	odd	8		425.2.n.f.399.5		24
85.59	even	8		425.2.m.b.76.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.5	✓	24	1.1	even	1	trivial
85.2.l.a.76.5	yes	24	17.8	even	8	inner
425.2.m.b.76.2		24	85.59	even	8
425.2.m.b.151.2		24	5.4	even	2
425.2.n.c.49.2		24	5.2	odd	4
425.2.n.c.399.2		24	85.8	odd	8
425.2.n.f.49.5		24	5.3	odd	4
425.2.n.f.399.5		24	85.42	odd	8
765.2.be.b.406.2		24	3.2	odd	2
765.2.be.b.586.2		24	51.8	odd	8
1445.2.a.p.1.5		12	17.5	odd	16
1445.2.a.q.1.5		12	17.12	odd	16
1445.2.d.j.866.15		24	17.3	odd	16
1445.2.d.j.866.16		24	17.14	odd	16
7225.2.a.bq.1.8		12	85.29	odd	16
7225.2.a.bs.1.8		12	85.39	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.66.5

Level	$85$
Weight	$2$
Character	85.66
Analytic conductor	$0.679$
Analytic rank	$0$
Dimension	$24$
Inner twists	$2$