LMFDB - Embedded newform 220.2.l.c.23.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(23,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.l (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [28,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.7
Character	$\chi$	$=$	220.23
Dual form			220.2.l.c.67.7

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.00742634 - 1.41419i) q^{2} +(-0.373449 + 0.373449i) q^{3} +(-1.99989 - 0.0210046i) q^{4} +(1.17859 + 1.90025i) q^{5} +(0.525356 + 0.530903i) q^{6} +(2.76139 + 2.76139i) q^{7} +(-0.0445564 + 2.82808i) q^{8} +2.72107i q^{9} +(2.69607 - 1.65264i) q^{10} -1.00000i q^{11} +(0.754701 - 0.739013i) q^{12} +(-3.64993 - 3.64993i) q^{13} +(3.92566 - 3.88464i) q^{14} +(-1.14979 - 0.269503i) q^{15} +(3.99912 + 0.0840136i) q^{16} +(1.81518 - 1.81518i) q^{17} +(3.84812 + 0.0202076i) q^{18} +4.29288 q^{19} +(-2.31713 - 3.82504i) q^{20} -2.06248 q^{21} +(-1.41419 - 0.00742634i) q^{22} +(0.0710973 - 0.0710973i) q^{23} +(-1.03950 - 1.07278i) q^{24} +(-2.22187 + 4.47921i) q^{25} +(-5.18881 + 5.13460i) q^{26} +(-2.13653 - 2.13653i) q^{27} +(-5.46448 - 5.58049i) q^{28} +2.00711i q^{29} +(-0.389668 + 1.62402i) q^{30} +5.16327i q^{31} +(0.148510 - 5.65490i) q^{32} +(0.373449 + 0.373449i) q^{33} +(-2.55353 - 2.58049i) q^{34} +(-1.99279 + 8.50187i) q^{35} +(0.0571549 - 5.44184i) q^{36} +(2.56818 - 2.56818i) q^{37} +(0.0318804 - 6.07096i) q^{38} +2.72612 q^{39} +(-5.42655 + 3.24846i) q^{40} -5.55249 q^{41} +(-0.0153167 + 2.91675i) q^{42} +(6.95400 - 6.95400i) q^{43} +(-0.0210046 + 1.99989i) q^{44} +(-5.17070 + 3.20702i) q^{45} +(-0.100017 - 0.101073i) q^{46} +(-6.82018 - 6.82018i) q^{47} +(-1.52484 + 1.46209i) q^{48} +8.25060i q^{49} +(6.31797 + 3.17542i) q^{50} +1.35575i q^{51} +(7.22279 + 7.37612i) q^{52} +(-6.31623 - 6.31623i) q^{53} +(-3.03733 + 3.00560i) q^{54} +(1.90025 - 1.17859i) q^{55} +(-7.93247 + 7.68640i) q^{56} +(-1.60317 + 1.60317i) q^{57} +(2.83844 + 0.0149055i) q^{58} +3.52907 q^{59} +(2.29379 + 0.563127i) q^{60} +10.1471 q^{61} +(7.30186 + 0.0383442i) q^{62} +(-7.51395 + 7.51395i) q^{63} +(-7.99603 - 0.252018i) q^{64} +(2.63400 - 11.2375i) q^{65} +(0.530903 - 0.525356i) q^{66} +(-2.03423 - 2.03423i) q^{67} +(-3.66828 + 3.59203i) q^{68} +0.0531025i q^{69} +(12.0085 + 2.88132i) q^{70} -2.60807i q^{71} +(-7.69540 - 0.121241i) q^{72} +(3.23564 + 3.23564i) q^{73} +(-3.61284 - 3.65098i) q^{74} +(-0.843002 - 2.50251i) q^{75} +(-8.58528 - 0.0901701i) q^{76} +(2.76139 - 2.76139i) q^{77} +(0.0202451 - 3.85527i) q^{78} -5.62911 q^{79} +(4.55366 + 7.69832i) q^{80} -6.56744 q^{81} +(-0.0412347 + 7.85231i) q^{82} +(-2.63327 + 2.63327i) q^{83} +(4.12474 + 0.0433215i) q^{84} +(5.58863 + 1.30994i) q^{85} +(-9.78266 - 9.88595i) q^{86} +(-0.749553 - 0.749553i) q^{87} +(2.82808 + 0.0445564i) q^{88} -8.67975i q^{89} +(4.49695 + 7.33620i) q^{90} -20.1578i q^{91} +(-0.143680 + 0.140693i) q^{92} +(-1.92822 - 1.92822i) q^{93} +(-9.69571 + 9.59441i) q^{94} +(5.05953 + 8.15752i) q^{95} +(2.05636 + 2.16728i) q^{96} +(12.7838 - 12.7838i) q^{97} +(11.6680 + 0.0612718i) q^{98} +2.72107 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100})$ 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$ .

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.00742634	−	1.41419i	0.00525121	−	0.999986i
$2$	0.00742634	−	1.41419i	0.00525121	−	0.999986i
$3$	−0.373449	+	0.373449i	−0.215611	+	0.215611i	−0.806646	−	0.591035i	$-0.798720\pi$
$3$	−0.373449	+	0.373449i	−0.215611	+	0.215611i	0.591035	+	0.806646i	$0.298720\pi$
$4$	−1.99989	−	0.0210046i	−0.999945	−	0.0105023i
$5$	1.17859	+	1.90025i	0.527080	+	0.849816i
$5$	1.17859	+	1.90025i	0.527080	+	0.849816i
$6$	0.525356	+	0.530903i	0.214476	+	0.216740i
$7$	2.76139	+	2.76139i	1.04371	+	1.04371i	0.999000	+	0.0447091i	$0.0142361\pi$
$7$	2.76139	+	2.76139i	1.04371	+	1.04371i	0.0447091	+	0.999000i	$0.485764\pi$
$8$	−0.0445564	+	2.82808i	−0.0157531	+	0.999876i
$9$			2.72107i			0.907024i
$10$	2.69607	−	1.65264i	0.852572	−	0.522610i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	0.754701	−	0.739013i	0.217864	−	0.213335i
$13$	−3.64993	−	3.64993i	−1.01231	−	1.01231i	−0.999923	−	0.0123843i	$-0.996058\pi$
$13$	−3.64993	−	3.64993i	−1.01231	−	1.01231i	−0.0123843	−	0.999923i	$-0.503942\pi$
$14$	3.92566	−	3.88464i	1.04918	−	1.03821i
$15$	−1.14979	−	0.269503i	−0.296874	−	0.0695854i
$16$	3.99912	+	0.0840136i	0.999779	+	0.0210034i
$17$	1.81518	−	1.81518i	0.440245	−	0.440245i	−0.451849	−	0.892094i	$-0.649235\pi$
$17$	1.81518	−	1.81518i	0.440245	−	0.440245i	0.892094	+	0.451849i	$0.149235\pi$
$18$	3.84812	+	0.0202076i	0.907011	+	0.00476298i
$19$	4.29288			0.984854			0.492427	−	0.870354i	$-0.336110\pi$
$19$	4.29288			0.984854			0.492427	+	0.870354i	$0.336110\pi$
$20$	−2.31713	−	3.82504i	−0.518126	−	0.855304i
$21$	−2.06248			−0.450070
$22$	−1.41419	−	0.00742634i	−0.301507	−	0.00158330i
$23$	0.0710973	−	0.0710973i	0.0148248	−	0.0148248i	−0.699656	−	0.714480i	$-0.746663\pi$
$23$	0.0710973	−	0.0710973i	0.0148248	−	0.0148248i	0.714480	+	0.699656i	$0.246663\pi$
$24$	−1.03950	−	1.07278i	−0.212188	−	0.218981i
$25$	−2.22187	+	4.47921i	−0.444373	+	0.895842i
$26$	−5.18881	+	5.13460i	−1.01761	+	1.00698i
$27$	−2.13653	−	2.13653i	−0.411175	−	0.411175i
$28$	−5.46448	−	5.58049i	−1.03269	−	1.05461i
$29$			2.00711i			0.372711i	0.982482	+	0.186355i	$0.0596675\pi$
$29$			2.00711i			0.372711i	−0.982482	+	0.186355i	$0.940332\pi$
$30$	−0.389668	+	1.62402i	−0.0711434	+	0.296504i
$31$			5.16327i			0.927350i	0.886005	+	0.463675i	$0.153470\pi$
$31$			5.16327i			0.927350i	−0.886005	+	0.463675i	$0.846530\pi$
$32$	0.148510	−	5.65490i	0.0262532	−	0.999655i
$33$	0.373449	+	0.373449i	0.0650092	+	0.0650092i
$34$	−2.55353	−	2.58049i	−0.437927	−	0.442551i
$35$	−1.99279	+	8.50187i	−0.336842	+	1.43708i
$36$	0.0571549	−	5.44184i	0.00952582	−	0.906974i
$37$	2.56818	−	2.56818i	0.422207	−	0.422207i	−0.463756	−	0.885963i	$-0.653499\pi$
$37$	2.56818	−	2.56818i	0.422207	−	0.422207i	0.885963	+	0.463756i	$0.153499\pi$
$38$	0.0318804	−	6.07096i	0.00517168	−	0.984840i
$39$	2.72612			0.436529
$40$	−5.42655	+	3.24846i	−0.858013	+	0.513627i
$41$	−5.55249			−0.867154			−0.433577	−	0.901117i	$-0.642749\pi$
$41$	−5.55249			−0.867154			−0.433577	+	0.901117i	$0.642749\pi$
$42$	−0.0153167	+	2.91675i	−0.00236342	+	0.450064i
$43$	6.95400	−	6.95400i	1.06047	−	1.06047i	0.0624251	−	0.998050i	$-0.480117\pi$
$43$	6.95400	−	6.95400i	1.06047	−	1.06047i	0.998050	−	0.0624251i	$-0.0198834\pi$
$44$	−0.0210046	+	1.99989i	−0.00316656	+	0.301495i
$45$	−5.17070	+	3.20702i	−0.770803	+	0.478074i
$46$	−0.100017	−	0.101073i	−0.0147468	−	0.0149025i
$47$	−6.82018	−	6.82018i	−0.994825	−	0.994825i	0.00516121	−	0.999987i	$-0.498357\pi$
$47$	−6.82018	−	6.82018i	−0.994825	−	0.994825i	−0.999987	+	0.00516121i	$0.998357\pi$
$48$	−1.52484	+	1.46209i	−0.220092	+	0.211035i
$49$			8.25060i			1.17866i
$50$	6.31797	+	3.17542i	0.893496	+	0.449072i
$51$			1.35575i			0.189843i
$52$	7.22279	+	7.37612i	1.00162	+	1.02288i
$53$	−6.31623	−	6.31623i	−0.867601	−	0.867601i	0.124605	−	0.992206i	$-0.460233\pi$
$53$	−6.31623	−	6.31623i	−0.867601	−	0.867601i	−0.992206	+	0.124605i	$0.960233\pi$
$54$	−3.03733	+	3.00560i	−0.413329	+	0.409010i
$55$	1.90025	−	1.17859i	0.256229	−	0.158921i
$56$	−7.93247	+	7.68640i	−1.06002	+	1.02714i
$57$	−1.60317	+	1.60317i	−0.212345	+	0.212345i
$58$	2.83844	+	0.0149055i	0.372705	+	0.00195718i
$59$	3.52907			0.459446			0.229723	−	0.973256i	$-0.426218\pi$
$59$	3.52907			0.459446			0.229723	+	0.973256i	$0.426218\pi$
$60$	2.29379	+	0.563127i	0.296127	+	0.0726994i
$61$	10.1471			1.29920			0.649598	−	0.760278i	$-0.274937\pi$
$61$	10.1471			1.29920			0.649598	+	0.760278i	$0.274937\pi$
$62$	7.30186	+	0.0383442i	0.927338	+	0.00486972i
$63$	−7.51395	+	7.51395i	−0.946669	+	0.946669i
$64$	−7.99603	−	0.252018i	−0.999504	−	0.0315022i
$65$	2.63400	−	11.2375i	0.326708	−	1.39384i
$66$	0.530903	−	0.525356i	0.0653496	−	0.0646669i
$67$	−2.03423	−	2.03423i	−0.248520	−	0.248520i	0.571843	−	0.820363i	$-0.306229\pi$
$67$	−2.03423	−	2.03423i	−0.248520	−	0.248520i	−0.820363	+	0.571843i	$0.806229\pi$
$68$	−3.66828	+	3.59203i	−0.444845	+	0.435597i
$69$			0.0531025i			0.00639278i
$70$	12.0085	+	2.88132i	1.43529	+	0.344384i
$71$		−	2.60807i		−	0.309521i	−0.987952	−	0.154760i	$-0.950539\pi$
$71$		−	2.60807i		−	0.309521i	0.987952	−	0.154760i	$-0.0494605\pi$
$72$	−7.69540	−	0.121241i	−0.906911	−	0.0142884i
$73$	3.23564	+	3.23564i	0.378703	+	0.378703i	0.870634	−	0.491931i	$-0.163709\pi$
$73$	3.23564	+	3.23564i	0.378703	+	0.378703i	−0.491931	+	0.870634i	$0.663709\pi$
$74$	−3.61284	−	3.65098i	−0.419984	−	0.424418i
$75$	−0.843002	−	2.50251i	−0.0973415	−	0.288965i
$76$	−8.58528	−	0.0901701i	−0.984799	−	0.0103432i
$77$	2.76139	−	2.76139i	0.314690	−	0.314690i
$78$	0.0202451	−	3.85527i	0.00229231	−	0.436523i
$79$	−5.62911			−0.633324			−0.316662	−	0.948538i	$-0.602562\pi$
$79$	−5.62911			−0.633324			−0.316662	+	0.948538i	$0.602562\pi$
$80$	4.55366	+	7.69832i	0.509115	+	0.860699i
$81$	−6.56744			−0.729716
$82$	−0.0412347	+	7.85231i	−0.00455361	+	0.867142i
$83$	−2.63327	+	2.63327i	−0.289039	+	0.289039i	−0.836700	−	0.547661i	$-0.815518\pi$
$83$	−2.63327	+	2.63327i	−0.289039	+	0.289039i	0.547661	+	0.836700i	$0.315518\pi$
$84$	4.12474	+	0.0433215i	0.450046	+	0.00472677i
$85$	5.58863	+	1.30994i	0.606172	+	0.142083i
$86$	−9.78266	−	9.88595i	−1.05489	−	1.06603i
$87$	−0.749553	−	0.749553i	−0.0803605	−	0.0803605i
$88$	2.82808	+	0.0445564i	0.301474	+	0.00474973i
$89$		−	8.67975i		−	0.920051i	−0.887906	−	0.460026i	$-0.847840\pi$
$89$		−	8.67975i		−	0.920051i	0.887906	−	0.460026i	$-0.152160\pi$
$90$	4.49695	+	7.33620i	0.474020	+	0.773303i
$91$		−	20.1578i		−	2.11311i
$92$	−0.143680	+	0.140693i	−0.0149797	+	0.0146683i
$93$	−1.92822	−	1.92822i	−0.199947	−	0.199947i
$94$	−9.69571	+	9.59441i	−1.00004	+	0.989588i
$95$	5.05953	+	8.15752i	0.519097	+	0.836944i
$96$	2.05636	+	2.16728i	0.209876	+	0.221197i
$97$	12.7838	−	12.7838i	1.29800	−	1.29800i	0.368289	−	0.929711i	$-0.379944\pi$
$97$	12.7838	−	12.7838i	1.29800	−	1.29800i	0.929711	−	0.368289i	$-0.120056\pi$
$98$	11.6680	+	0.0612718i	1.17864	+	0.00618938i
$99$	2.72107			0.273478
$100$	4.53757	−	8.91125i	0.453757	−	0.891125i
$101$	13.9161			1.38470			0.692352	−	0.721560i	$-0.256575\pi$
$101$	13.9161			1.38470			0.692352	+	0.721560i	$0.256575\pi$
$102$	1.91730	+	0.0100683i	0.189841	+	0.000996909i
$103$	−9.01983	+	9.01983i	−0.888751	+	0.888751i	−0.994403	−	0.105652i	$-0.966307\pi$
$103$	−9.01983	+	9.01983i	−0.888751	+	0.888751i	0.105652	+	0.994403i	$0.466307\pi$
$104$	10.4849	−	10.1596i	1.02813	−	0.996235i
$105$	−2.43081	−	3.91922i	−0.237223	−	0.382477i
$106$	−8.97928	+	8.88547i	−0.872145	+	0.863033i
$107$	−10.2858	−	10.2858i	−0.994363	−	0.994363i	0.00562102	−	0.999984i	$-0.498211\pi$
$107$	−10.2858	−	10.2858i	−0.994363	−	0.994363i	−0.999984	+	0.00562102i	$0.998211\pi$
$108$	4.22795	+	4.31770i	0.406834	+	0.415471i
$109$			16.5775i			1.58784i	0.608023	+	0.793919i	$0.291963\pi$
$109$			16.5775i			1.58784i	−0.608023	+	0.793919i	$0.708037\pi$
$110$	−1.65264	−	2.69607i	−0.157573	−	0.257060i
$111$			1.91817i			0.182065i
$112$	10.8111	+	11.2751i	1.02156	+	1.06540i
$113$	−4.11182	−	4.11182i	−0.386808	−	0.386808i	0.486739	−	0.873547i	$-0.338186\pi$
$113$	−4.11182	−	4.11182i	−0.386808	−	0.386808i	−0.873547	+	0.486739i	$0.838186\pi$
$114$	2.25529	+	2.27910i	0.211227	+	0.213457i
$115$	0.218897	+	0.0513080i	0.0204122	+	0.00478450i
$116$	0.0421584	−	4.01399i	0.00391431	−	0.372690i
$117$	9.93171	−	9.93171i	0.918187	−	0.918187i
$118$	0.0262081	−	4.99079i	0.00241265	−	0.459439i
$119$	10.0248			0.918976
$120$	0.813405	−	3.23968i	0.0742534	−	0.295741i
$121$	−1.00000			−0.0909091
$122$	0.0753554	−	14.3499i	0.00682236	−	1.29918i
$123$	2.07357	−	2.07357i	0.186968	−	0.186968i
$124$	0.108452	−	10.3260i	0.00973930	−	0.927299i
$125$	−11.1303	+	1.05704i	−0.995521	+	0.0945447i
$126$	10.5704	+	10.6820i	0.941685	+	0.951627i
$127$	8.12197	+	8.12197i	0.720708	+	0.720708i	0.968749	−	0.248041i	$-0.0797869\pi$
$127$	8.12197	+	8.12197i	0.720708	+	0.720708i	−0.248041	+	0.968749i	$0.579787\pi$
$128$	−0.415783	+	11.3061i	−0.0367504	+	0.999324i
$129$			5.19393i			0.457300i
$130$	−15.8725	−	3.80844i	−1.39211	−	0.334023i
$131$		−	20.7524i		−	1.81315i	−0.422049	−	0.906573i	$-0.638689\pi$
$131$		−	20.7524i		−	1.81315i	0.422049	−	0.906573i	$-0.361311\pi$
$132$	−0.739013	−	0.754701i	−0.0643228	−	0.0656883i
$133$	11.8543	+	11.8543i	1.02790	+	1.02790i
$134$	−2.89190	+	2.86169i	−0.249822	+	0.247212i
$135$	1.54185	−	6.57802i	0.132701	−	0.566146i
$136$	5.05258	+	5.21434i	0.433256	+	0.447126i
$137$	1.42774	−	1.42774i	0.121980	−	0.121980i	−0.643482	−	0.765462i	$-0.722511\pi$
$137$	1.42774	−	1.42774i	0.121980	−	0.121980i	0.765462	+	0.643482i	$0.222511\pi$
$138$	0.0750972		0.000394357i	0.00639270		3.35699e-5i
$139$	−2.35976			−0.200152			−0.100076	−	0.994980i	$-0.531909\pi$
$139$	−2.35976			−0.200152			−0.100076	+	0.994980i	$0.531909\pi$
$140$	4.16393	−	16.9609i	0.351916	−	1.43346i
$141$	5.09398			0.428991
$142$	−3.68831	−	0.0193684i	−0.309516	−	0.00162536i
$143$	−3.64993	+	3.64993i	−0.305222	+	0.305222i
$144$	−0.228607	+	10.8819i	−0.0190506	+	0.906824i
$145$	−3.81400	+	2.36555i	−0.316735	+	0.196448i
$146$	4.59985	−	4.55179i	0.380686	−	0.376709i
$147$	−3.08118	−	3.08118i	−0.254132	−	0.254132i
$148$	−5.19002	+	5.08214i	−0.426617	+	0.417749i
$149$		−	9.71539i		−	0.795916i	−0.917404	−	0.397958i	$-0.869719\pi$
$149$		−	9.71539i		−	0.795916i	0.917404	−	0.397958i	$-0.130281\pi$
$150$	−3.54530	+	1.17358i	−0.289472	+	0.0958228i
$151$			4.26641i			0.347196i	0.984817	+	0.173598i	$0.0555393\pi$
$151$			4.26641i			0.347196i	−0.984817	+	0.173598i	$0.944461\pi$
$152$	−0.191275	+	12.1406i	−0.0155145	+	0.984732i
$153$	4.93923	+	4.93923i	0.399313	+	0.399313i
$154$	−3.88464	−	3.92566i	−0.313033	−	0.316338i
$155$	−9.81148	+	6.08536i	−0.788077	+	0.488788i
$156$	−5.45195	−	0.0572611i	−0.436505	−	0.00458456i
$157$	−7.97125	+	7.97125i	−0.636175	+	0.636175i	−0.949610	−	0.313434i	$-0.898520\pi$
$157$	−7.97125	+	7.97125i	−0.636175	+	0.636175i	0.313434	+	0.949610i	$0.398520\pi$
$158$	−0.0418037	+	7.96065i	−0.00332572	+	0.633315i
$159$	4.71758			0.374129
$160$	10.9207	−	6.38259i	0.863360	−	0.504588i
$161$	0.392655			0.0309456
$162$	−0.0487721	+	9.28764i	−0.00383190	+	0.729706i
$163$	8.23045	−	8.23045i	0.644659	−	0.644659i	−0.307038	−	0.951697i	$-0.599338\pi$
$163$	8.23045	−	8.23045i	0.644659	−	0.644659i	0.951697	+	0.307038i	$0.0993380\pi$
$164$	11.1044	+	0.116628i	0.867106	+	0.00910710i
$165$	−0.269503	+	1.14979i	−0.0209808	+	0.0895108i
$166$	3.70440	+	3.74351i	0.287517	+	0.290553i
$167$	13.5779	+	13.5779i	1.05069	+	1.05069i	0.998645	+	0.0520448i	$0.0165738\pi$
$167$	13.5779	+	13.5779i	1.05069	+	1.05069i	0.0520448	+	0.998645i	$0.483426\pi$
$168$	0.0918967	−	5.83285i	0.00708999	−	0.450015i
$169$			13.6439i			1.04953i
$170$	1.89401	−	7.89368i	0.145264	−	0.605417i
$171$			11.6812i			0.893286i
$172$	−14.0533	+	13.7612i	−1.07155	+	1.04928i
$173$	−5.98721	−	5.98721i	−0.455199	−	0.455199i	0.441877	−	0.897076i	$-0.354313\pi$
$173$	−5.98721	−	5.98721i	−0.455199	−	0.455199i	−0.897076	+	0.441877i	$0.854313\pi$
$174$	−1.06558	+	1.05445i	−0.0807814	+	0.0799374i
$175$	−18.5043	+	6.23341i	−1.39879	+	0.471202i
$176$	0.0840136	−	3.99912i	0.00633277	−	0.301445i
$177$	−1.31793	+	1.31793i	−0.0990615	+	0.0990615i
$178$	−12.2748	−	0.0644587i	−0.920039	−	0.00483139i
$179$	−21.1301			−1.57934			−0.789668	−	0.613534i	$-0.789747\pi$
$179$	−21.1301			−1.57934			−0.789668	+	0.613534i	$0.789747\pi$
$180$	10.4082	−	6.30507i	0.775781	−	0.469953i
$181$	−12.5532			−0.933069			−0.466534	−	0.884503i	$-0.654498\pi$
$181$	−12.5532			−0.933069			−0.466534	+	0.884503i	$0.654498\pi$
$182$	−28.5070	−	0.149699i	−2.11308	−	0.0110964i
$183$	−3.78941	+	3.78941i	−0.280121	+	0.280121i
$184$	0.197901	+	0.204236i	0.0145894	+	0.0150565i
$185$	7.90700	+	1.85335i	0.581334	+	0.136261i
$186$	−2.74119	+	2.71256i	−0.200994	+	0.198894i
$187$	−1.81518	−	1.81518i	−0.132739	−	0.132739i
$188$	13.4964	+	13.7829i	0.984323	+	1.00522i
$189$		−	11.7996i		−	0.858295i
$190$	11.5739	−	7.09458i	0.839659	−	0.514695i
$191$			15.8745i			1.14864i	0.818630	+	0.574321i	$0.194734\pi$
$191$			15.8745i			1.14864i	−0.818630	+	0.574321i	$0.805266\pi$
$192$	3.08023	−	2.89200i	0.222296	−	0.208712i
$193$	−6.27991	−	6.27991i	−0.452037	−	0.452037i	0.443993	−	0.896030i	$-0.353562\pi$
$193$	−6.27991	−	6.27991i	−0.452037	−	0.452037i	−0.896030	+	0.443993i	$0.853562\pi$
$194$	−17.9839	−	18.1737i	−1.29117	−	1.30480i
$195$	3.21297	+	5.18031i	0.230086	+	0.370969i
$196$	0.173300	−	16.5003i	0.0123786	−	1.17859i
$197$	−11.7319	+	11.7319i	−0.835862	+	0.835862i	−0.988311	−	0.152450i	$-0.951284\pi$
$197$	−11.7319	+	11.7319i	−0.835862	+	0.835862i	0.152450	+	0.988311i	$0.451284\pi$
$198$	0.0202076	−	3.84812i	0.00143609	−	0.273474i
$199$	25.3575			1.79755			0.898774	−	0.438412i	$-0.144459\pi$
$199$	25.3575			1.79755			0.898774	+	0.438412i	$0.144459\pi$
$200$	−12.5685	−	6.48319i	−0.888730	−	0.458431i
$201$	1.51936			0.107168
$202$	0.103346	−	19.6801i	0.00727138	−	1.38468i
$203$	−5.54242	+	5.54242i	−0.389001	+	0.389001i
$204$	0.0284770	−	2.71136i	0.00199379	−	0.189833i
$205$	−6.54410	−	10.5511i	−0.457060	−	0.736921i
$206$	12.6888	+	12.8228i	0.884071	+	0.893405i
$207$	0.193461	+	0.193461i	0.0134465	+	0.0134465i
$208$	−14.2898	−	14.9031i	−0.990822	−	1.03335i
$209$		−	4.29288i		−	0.296945i
$210$	−5.56059	+	3.40854i	−0.383717	+	0.235211i
$211$		−	20.2950i		−	1.39717i	−0.715528	−	0.698584i	$-0.753814\pi$
$211$		−	20.2950i		−	1.39717i	0.715528	−	0.698584i	$-0.246186\pi$
$212$	12.4991	+	12.7644i	0.858441	+	0.876665i
$213$	0.973981	+	0.973981i	0.0667360	+	0.0667360i
$214$	−14.6225	+	14.4697i	−0.999571	+	0.989128i
$215$	21.4102	+	5.01842i	1.46016	+	0.342253i
$216$	6.13746	−	5.94707i	0.417602	−	0.404647i
$217$	−14.2578	+	14.2578i	−0.967884	+	0.967884i
$218$	23.4438	+	0.123110i	1.58782	+	0.00833808i
$219$	−2.41669			−0.163305
$220$	−3.82504	+	2.31713i	−0.257884	+	0.156221i
$221$	−13.2505			−0.891327
$222$	2.71267	+	0.0142450i	0.182062	+	0.000956061i
$223$	10.2651	−	10.2651i	0.687403	−	0.687403i	−0.274254	−	0.961657i	$-0.588431\pi$
$223$	10.2651	−	10.2651i	0.687403	−	0.687403i	0.961657	+	0.274254i	$0.0884309\pi$
$224$	16.0255	−	15.2053i	1.07075	−	1.01595i
$225$	−12.1882	−	6.04586i	−0.812550	−	0.403057i
$226$	−5.84545	+	5.78438i	−0.388834	+	0.384771i
$227$	16.1323	+	16.1323i	1.07074	+	1.07074i	0.997300	+	0.0734361i	$0.0233965\pi$
$227$	16.1323	+	16.1323i	1.07074	+	1.07074i	0.0734361	+	0.997300i	$0.476603\pi$
$228$	3.23984	−	3.17249i	0.214564	−	0.210104i
$229$			2.39301i			0.158135i	0.996869	+	0.0790673i	$0.0251942\pi$
$229$			2.39301i			0.158135i	−0.996869	+	0.0790673i	$0.974806\pi$
$230$	0.0741851	−	0.309181i	0.00489162	−	0.0203868i
$231$			2.06248i			0.135701i
$232$	−5.67625	−	0.0894295i	−0.372664	−	0.00587133i
$233$	4.46532	+	4.46532i	0.292533	+	0.292533i	0.838080	−	0.545547i	$-0.183678\pi$
$233$	4.46532	+	4.46532i	0.292533	+	0.292533i	−0.545547	+	0.838080i	$0.683678\pi$
$234$	−13.9716	−	14.1191i	−0.913353	−	0.922996i
$235$	4.92184	−	20.9982i	0.321066	−	1.36977i
$236$	−7.05775	−	0.0741266i	−0.459420	−	0.00482523i
$237$	2.10219	−	2.10219i	0.136552	−	0.136552i
$238$	0.0744479	−	14.1771i	0.00482574	−	0.918963i
$239$	3.25515			0.210558			0.105279	−	0.994443i	$-0.466426\pi$
$239$	3.25515			0.210558			0.105279	+	0.994443i	$0.466426\pi$
$240$	−4.57549	−	1.17437i	−0.295347	−	0.0758054i
$241$	7.36685			0.474540			0.237270	−	0.971444i	$-0.423747\pi$
$241$	7.36685			0.474540			0.237270	+	0.971444i	$0.423747\pi$
$242$	−0.00742634	+	1.41419i	−0.000477383	+	0.0909078i
$243$	8.86220	−	8.86220i	0.568510	−	0.568510i
$244$	−20.2930	−	0.213134i	−1.29913	−	0.0136445i
$245$	−15.6782	+	9.72405i	−1.00164	+	0.621247i
$246$	−2.91704	−	2.94784i	−0.185984	−	0.187947i
$247$	−15.6687	−	15.6687i	−0.996975	−	0.996975i
$248$	−14.6021	−	0.230057i	−0.927235	−	0.0146086i
$249$		−	1.96679i		−	0.124640i
$250$	1.41221	+	15.7482i	0.0893157	+	0.996003i
$251$			14.5727i			0.919820i	0.887966	+	0.459910i	$0.152118\pi$
$251$			14.5727i			0.919820i	−0.887966	+	0.459910i	$0.847882\pi$
$252$	15.1849	−	14.8692i	0.956559	−	0.936675i
$253$	−0.0710973	−	0.0710973i	−0.00446985	−	0.00446985i
$254$	11.5464	−	11.4257i	0.724483	−	0.716913i
$255$	−2.57627	+	1.59787i	−0.161332	+	0.100063i
$256$	15.9859	+	0.671961i	0.999118	+	0.0419976i
$257$	−12.6144	+	12.6144i	−0.786867	+	0.786867i	−0.980979	−	0.194113i	$-0.937817\pi$
$257$	−12.6144	+	12.6144i	−0.786867	+	0.786867i	0.194113	+	0.980979i	$0.437817\pi$
$258$	7.34523	+	0.0385719i	0.457294	+	0.00240138i
$259$	14.1835			0.881322
$260$	−5.50375	+	22.4185i	−0.341328	+	1.39033i
$261$	−5.46148			−0.338057
$262$	−29.3479	−	0.154114i	−1.81312	−	0.00952122i
$263$	−6.23856	+	6.23856i	−0.384686	+	0.384686i	−0.872787	−	0.488101i	$-0.837690\pi$
$263$	−6.23856	+	6.23856i	−0.384686	+	0.384686i	0.488101	+	0.872787i	$0.337690\pi$
$264$	−1.07278	+	1.03950i	−0.0660252	+	0.0639770i
$265$	4.55816	−	19.4466i	0.280006	−	1.19460i
$266$	16.8524	−	16.6763i	1.03328	−	1.02249i
$267$	3.24144	+	3.24144i	0.198373	+	0.198373i
$268$	4.02550	+	4.11096i	0.245897	+	0.251117i
$269$			4.08503i			0.249069i	0.992215	+	0.124534i	$0.0397437\pi$
$269$			4.08503i			0.249069i	−0.992215	+	0.124534i	$0.960256\pi$
$270$	−9.29114	−	2.22932i	−0.565441	−	0.135672i
$271$			11.6838i			0.709740i	0.934916	+	0.354870i	$0.115475\pi$
$271$			11.6838i			0.709740i	−0.934916	+	0.354870i	$0.884525\pi$
$272$	7.41161	−	7.10661i	0.449395	−	0.430902i
$273$	7.52791	+	7.52791i	0.455610	+	0.455610i
$274$	−2.00850	−	2.02970i	−0.121338	−	0.122619i
$275$	4.47921	+	2.22187i	0.270106	+	0.133984i
$276$	0.00111539	−	0.106199i	6.71388e−5	−	0.00639243i
$277$	−9.55074	+	9.55074i	−0.573849	+	0.573849i	−0.933202	−	0.359353i	$-0.882997\pi$
$277$	−9.55074	+	9.55074i	−0.573849	+	0.573849i	0.359353	+	0.933202i	$0.382997\pi$
$278$	−0.0175244	+	3.33716i	−0.00105104	+	0.200150i
$279$	−14.0496			−0.841129
$280$	−23.9551	−	6.01456i	−1.43159	−	0.359439i
$281$	13.7102			0.817883			0.408942	−	0.912560i	$-0.365898\pi$
$281$	13.7102			0.817883			0.408942	+	0.912560i	$0.365898\pi$
$282$	0.0378296	−	7.20388i	0.00225272	−	0.428985i
$283$	2.11194	−	2.11194i	0.125542	−	0.125542i	−0.641544	−	0.767086i	$-0.721706\pi$
$283$	2.11194	−	2.11194i	0.125542	−	0.125542i	0.767086	+	0.641544i	$0.221706\pi$
$284$	−0.0547813	+	5.21585i	−0.00325067	+	0.309504i
$285$	−4.93590	−	1.15694i	−0.292377	−	0.0685314i
$286$	5.13460	+	5.18881i	0.303615	+	0.306821i
$287$	−15.3326	−	15.3326i	−0.905057	−	0.905057i
$288$	15.3874	+	0.404107i	0.906711	+	0.0238123i
$289$			10.4103i			0.612368i
$290$	3.31702	+	5.41130i	0.194782	+	0.317762i
$291$			9.54822i			0.559726i
$292$	−6.40296	−	6.53888i	−0.374705	−	0.382659i
$293$	−1.35979	−	1.35979i	−0.0794396	−	0.0794396i	0.666271	−	0.745710i	$-0.267890\pi$
$293$	−1.35979	−	1.35979i	−0.0794396	−	0.0794396i	−0.745710	+	0.666271i	$0.767890\pi$
$294$	−4.38027	+	4.33451i	−0.255463	+	0.252794i
$295$	4.15931	+	6.70610i	0.242165	+	0.390444i
$296$	7.14859	+	7.37744i	0.415503	+	0.428805i
$297$	−2.13653	+	2.13653i	−0.123974	+	0.123974i
$298$	−13.7394	−	0.0721498i	−0.795905	−	0.00417953i
$299$	−0.519000			−0.0300145
$300$	1.63335	+	5.02245i	0.0943014	+	0.289972i
$301$	38.4055			2.21365
$302$	6.03354	+	0.0316838i	0.347191	+	0.00182320i
$303$	−5.19696	+	5.19696i	−0.298557	+	0.298557i
$304$	17.1677	+	0.360660i	0.984637	+	0.0206853i
$305$	11.9592	+	19.2819i	0.684781	+	1.10408i
$306$	7.02171	−	6.94835i	0.401404	−	0.397211i
$307$	14.9365	+	14.9365i	0.852469	+	0.852469i	0.990437	−	0.137967i	$-0.0440569\pi$
$307$	14.9365	+	14.9365i	0.852469	+	0.852469i	−0.137967	+	0.990437i	$0.544057\pi$
$308$	−5.58049	+	5.46448i	−0.317978	+	0.311368i
$309$		−	6.73690i		−	0.383249i
$310$	8.53301	+	13.9205i	0.484643	+	0.790633i
$311$			11.2749i			0.639341i	0.947529	+	0.319670i	$0.103572\pi$
$311$			11.2749i			0.639341i	−0.947529	+	0.319670i	$0.896428\pi$
$312$	−0.121466	+	7.70969i	−0.00687668	+	0.436475i
$313$	2.04043	+	2.04043i	0.115332	+	0.115332i	0.762417	−	0.647086i	$-0.224012\pi$
$313$	2.04043	+	2.04043i	0.115332	+	0.115332i	−0.647086	+	0.762417i	$0.724012\pi$
$314$	11.2137	+	11.3321i	0.632826	+	0.639507i
$315$	−23.1342	−	5.42251i	−1.30346	−	0.305524i
$316$	11.2576	+	0.118237i	0.633289	+	0.00665135i
$317$	3.69718	−	3.69718i	0.207654	−	0.207654i	−0.595615	−	0.803270i	$-0.703092\pi$
$317$	3.69718	−	3.69718i	0.207654	−	0.207654i	0.803270	+	0.595615i	$0.203092\pi$
$318$	0.0350344	−	6.67158i	0.00196463	−	0.374123i
$319$	2.00711			0.112376
$320$	−8.94512	−	15.4914i	−0.500047	−	0.865998i
$321$	7.68243			0.428791
$322$	0.00291599	−	0.555291i	0.000162502	−	0.0309452i
$323$	7.79234	−	7.79234i	0.433577	−	0.433577i
$324$	13.1342	+	0.137946i	0.729676	+	0.00766368i
$325$	24.4584	−	8.23913i	1.35671	−	0.457025i
$326$	−11.5783	−	11.7006i	−0.641265	−	0.648035i
$327$	−6.19086	−	6.19086i	−0.342355	−	0.342355i
$328$	0.247399	−	15.7029i	0.0136603	−	0.867046i
$329$		−	37.6664i		−	2.07662i
$330$	1.62402	+	0.389668i	0.0893994	+	0.0214505i
$331$			9.75396i			0.536126i	0.963401	+	0.268063i	$0.0863836\pi$
$331$			9.75396i			0.536126i	−0.963401	+	0.268063i	$0.913616\pi$
$332$	5.32156	−	5.21094i	0.292059	−	0.285988i
$333$	6.98821	+	6.98821i	0.382951	+	0.382951i
$334$	19.3026	−	19.1010i	1.05619	−	1.04516i
$335$	1.46802	−	6.26305i	0.0802064	−	0.342187i
$336$	−8.24811	−	0.173277i	−0.449971	−	0.00945301i
$337$	−1.86886	+	1.86886i	−0.101803	+	0.101803i	−0.756174	−	0.654371i	$-0.772934\pi$
$337$	−1.86886	+	1.86886i	−0.101803	+	0.101803i	0.654371	+	0.756174i	$0.272934\pi$
$338$	19.2952	+	0.101324i	1.04952	+	0.00551133i
$339$	3.07111			0.166800
$340$	−11.1491	−	2.73712i	−0.604646	−	0.148441i
$341$	5.16327			0.279607
$342$	16.5195	+	0.0867488i	0.893274	+	0.00469084i
$343$	−3.45341	+	3.45341i	−0.186466	+	0.186466i
$344$	19.3566	+	19.9763i	1.04364	+	1.07705i
$345$	−0.100908	+	0.0625858i	−0.00543269	+	0.00336951i
$346$	−8.51154	+	8.42261i	−0.457583	+	0.452802i
$347$	−7.79835	−	7.79835i	−0.418637	−	0.418637i	0.466097	−	0.884734i	$-0.345660\pi$
$347$	−7.79835	−	7.79835i	−0.418637	−	0.418637i	−0.884734	+	0.466097i	$0.845660\pi$
$348$	1.48328	+	1.51477i	0.0795121	+	0.0812000i
$349$		−	13.7734i		−	0.737272i	−0.929574	−	0.368636i	$-0.879825\pi$
$349$		−	13.7734i		−	0.737272i	0.929574	−	0.368636i	$-0.120175\pi$
$350$	8.67783	+	26.2150i	0.463850	+	1.40125i
$351$			15.5964i			0.832472i
$352$	−5.65490	−	0.148510i	−0.301407	−	0.00791563i
$353$	8.18700	+	8.18700i	0.435750	+	0.435750i	0.890579	−	0.454829i	$-0.150300\pi$
$353$	8.18700	+	8.18700i	0.435750	+	0.435750i	−0.454829	+	0.890579i	$0.650300\pi$
$354$	1.85402	+	1.87359i	0.0985400	+	0.0995803i
$355$	4.95597	−	3.07383i	0.263035	−	0.163142i
$356$	−0.182314	+	17.3585i	−0.00966264	+	0.920001i
$357$	−3.74377	+	3.74377i	−0.198141	+	0.198141i
$358$	−0.156919	+	29.8820i	−0.00829343	+	1.57931i
$359$	−13.2739			−0.700567			−0.350284	−	0.936644i	$-0.613915\pi$
$359$	−13.2739			−0.700567			−0.350284	+	0.936644i	$0.613915\pi$
$360$	−8.83930	−	14.7660i	−0.465872	−	0.778239i
$361$	−0.571197			−0.0300630
$362$	−0.0932240	+	17.7526i	−0.00489974	+	0.933056i
$363$	0.373449	−	0.373449i	0.0196010	−	0.0196010i
$364$	−0.423405	+	40.3133i	−0.0221925	+	2.11299i
$365$	−2.33503	+	9.96199i	−0.122221	+	0.521434i
$366$	5.33082	+	5.38710i	0.278646	+	0.281588i
$367$	−23.6854	−	23.6854i	−1.23637	−	1.23637i	−0.961476	−	0.274891i	$-0.911358\pi$
$367$	−23.6854	−	23.6854i	−1.23637	−	1.23637i	−0.274891	−	0.961476i	$-0.588642\pi$
$368$	0.290300	−	0.278353i	0.0151329	−	0.0145102i
$369$		−	15.1087i		−	0.786529i
$370$	2.67972	−	11.1683i	0.139312	−	0.580611i
$371$		−	34.8832i		−	1.81105i
$372$	3.81572	+	3.89673i	0.197836	+	0.202036i
$373$	−12.7401	−	12.7401i	−0.659659	−	0.659659i	0.295641	−	0.955299i	$-0.404467\pi$
$373$	−12.7401	−	12.7401i	−0.659659	−	0.659659i	−0.955299	+	0.295641i	$0.904467\pi$
$374$	−2.58049	+	2.55353i	−0.133434	+	0.132040i
$375$	3.76184	−	4.55134i	0.194260	−	0.235030i
$376$	19.5919	−	18.9841i	1.01037	−	0.979030i
$377$	7.32580	−	7.32580i	0.377298	−	0.377298i
$378$	−16.6869	−	0.0876279i	−0.858283	−	0.00450709i
$379$	−26.4361			−1.35793			−0.678964	−	0.734171i	$-0.737571\pi$
$379$	−26.4361			−1.35793			−0.678964	+	0.734171i	$0.737571\pi$
$380$	−9.94715	−	16.4204i	−0.510278	−	0.842350i
$381$	−6.06628			−0.310785
$382$	22.4497	+	0.117890i	1.14863	+	0.00603176i
$383$	−0.141503	+	0.141503i	−0.00723044	+	0.00723044i	−0.710713	−	0.703482i	$-0.751627\pi$
$383$	−0.141503	+	0.141503i	−0.00723044	+	0.00723044i	0.703482	+	0.710713i	$0.251627\pi$
$384$	−4.06697	−	4.37752i	−0.207542	−	0.223389i
$385$	8.50187	+	1.99279i	0.433295	+	0.101562i
$386$	−8.92764	+	8.83437i	−0.454405	+	0.449658i
$387$	18.9223	+	18.9223i	0.961876	+	0.961876i
$388$	−25.8347	+	25.2977i	−1.31156	+	1.28430i
$389$			17.4243i			0.883448i	0.897151	+	0.441724i	$0.145633\pi$
$389$			17.4243i			0.883448i	−0.897151	+	0.441724i	$0.854367\pi$
$390$	7.34982	−	4.50530i	0.372173	−	0.228135i
$391$		−	0.258108i		−	0.0130531i
$392$	−23.3333	−	0.367617i	−1.17851	−	0.0185675i
$393$	7.74997	+	7.74997i	0.390934	+	0.390934i
$394$	16.5040	+	16.6783i	0.831461	+	0.840239i
$395$	−6.63439	−	10.6967i	−0.333812	−	0.538209i
$396$	−5.44184	−	0.0571549i	−0.273463	−	0.00287214i
$397$	3.57654	−	3.57654i	0.179501	−	0.179501i	−0.611637	−	0.791138i	$-0.709489\pi$
$397$	3.57654	−	3.57654i	0.179501	−	0.179501i	0.791138	+	0.611637i	$0.209489\pi$
$398$	0.188314	−	35.8605i	0.00943931	−	1.79752i
$399$	−8.85398			−0.443254
$400$	−9.26182	+	17.7262i	−0.463091	+	0.886311i
$401$	−7.18608			−0.358855			−0.179428	−	0.983771i	$-0.557425\pi$
$401$	−7.18608			−0.358855			−0.179428	+	0.983771i	$0.557425\pi$
$402$	0.0112833	−	2.14867i	0.000562760	−	0.107166i
$403$	18.8456	−	18.8456i	0.938764	−	0.938764i
$404$	−27.8307	−	0.292302i	−1.38463	−	0.0145426i
$405$	−7.74030	−	12.4798i	−0.384619	−	0.620124i
$406$	7.79689	+	7.87921i	0.386953	+	0.391039i
$407$	−2.56818	−	2.56818i	−0.127300	−	0.127300i
$408$	−3.83417	−	0.0604075i	−0.189820	−	0.00299062i
$409$		−	8.87575i		−	0.438878i	−0.975626	−	0.219439i	$-0.929577\pi$
$409$		−	8.87575i		−	0.438878i	0.975626	−	0.219439i	$-0.0704227\pi$
$410$	−14.9699	+	9.17627i	−0.739311	+	0.453183i
$411$			1.06638i			0.0526004i
$412$	18.2281	−	17.8492i	0.898036	−	0.879368i
$413$	9.74515	+	9.74515i	0.479527	+	0.479527i
$414$	0.275028	−	0.272154i	0.0135169	−	0.0133757i
$415$	−8.10740	−	1.90032i	−0.397977	−	0.0932832i
$416$	−21.1820	+	20.0979i	−1.03853	+	0.985382i
$417$	0.881251	−	0.881251i	0.0431550	−	0.0431550i
$418$	−6.07096	−	0.0318804i	−0.296941	−	0.00155932i
$419$	−11.4747			−0.560576			−0.280288	−	0.959916i	$-0.590430\pi$
$419$	−11.4747			−0.560576			−0.280288	+	0.959916i	$0.590430\pi$
$420$	4.77904	+	7.88907i	0.233193	+	0.384947i
$421$	−13.8391			−0.674478			−0.337239	−	0.941419i	$-0.609493\pi$
$421$	−13.8391			−0.674478			−0.337239	+	0.941419i	$0.609493\pi$
$422$	−28.7011	−	0.150718i	−1.39715	−	0.00733683i
$423$	18.5582	−	18.5582i	0.902330	−	0.902330i
$424$	18.1442	−	17.5814i	0.881161	−	0.853826i
$425$	4.09748	+	12.1636i	0.198757	+	0.590023i
$426$	1.38463	−	1.37016i	0.0670856	−	0.0663847i
$427$	28.0200	+	28.0200i	1.35598	+	1.35598i
$428$	20.3544	+	20.7865i	0.983865	+	1.00475i
$429$		−	2.72612i		−	0.131619i
$430$	7.25601	−	30.2409i	0.349916	−	1.45835i
$431$		−	33.5657i		−	1.61680i	−0.588632	−	0.808401i	$-0.700333\pi$
$431$		−	33.5657i		−	1.61680i	0.588632	−	0.808401i	$-0.299667\pi$
$432$	−8.36474	−	8.72373i	−0.402449	−	0.419721i
$433$	−24.6599	−	24.6599i	−1.18508	−	1.18508i	−0.978412	−	0.206665i	$-0.933739\pi$
$433$	−24.6599	−	24.6599i	−1.18508	−	1.18508i	−0.206665	−	0.978412i	$-0.566261\pi$
$434$	20.0574	+	20.2692i	0.962788	+	0.972953i
$435$	0.540922	−	2.30775i	0.0259352	−	0.110648i
$436$	0.348204	−	33.1532i	0.0166759	−	1.58775i
$437$	0.305212	−	0.305212i	0.0146003	−	0.0146003i
$438$	−0.0179472	+	3.41767i	−0.000857550	+	0.163303i
$439$	3.75583			0.179256			0.0896280	−	0.995975i	$-0.471432\pi$
$439$	3.75583			0.179256			0.0896280	+	0.995975i	$0.471432\pi$
$440$	3.24846	+	5.42655i	0.154864	+	0.258701i
$441$	−22.4505			−1.06907
$442$	−0.0984030	+	18.7388i	−0.00468055	+	0.891315i
$443$	−22.6474	+	22.6474i	−1.07601	+	1.07601i	−0.0791461	+	0.996863i	$0.525219\pi$
$443$	−22.6474	+	22.6474i	−1.07601	+	1.07601i	−0.996863	+	0.0791461i	$0.974781\pi$
$444$	0.0402904	−	3.83613i	0.00191210	−	0.182055i
$445$	16.4937	−	10.2298i	0.781874	−	0.484941i
$446$	−14.4406	−	14.5931i	−0.683784	−	0.691003i
$447$	3.62821	+	3.62821i	0.171608	+	0.171608i
$448$	−21.3843	−	22.7761i	−1.01031	−	1.07607i
$449$		−	6.32076i		−	0.298295i	−0.988815	−	0.149148i	$-0.952347\pi$
$449$		−	6.32076i		−	0.298295i	0.988815	−	0.149148i	$-0.0476530\pi$
$450$	−8.64053	+	17.1916i	−0.407319	+	0.810422i
$451$			5.55249i			0.261457i
$452$	8.13683	+	8.30956i	0.382724	+	0.390849i
$453$	−1.59329	−	1.59329i	−0.0748592	−	0.0748592i
$454$	22.9340	−	22.6944i	1.07634	−	1.06510i
$455$	38.3047	−	23.7577i	1.79575	−	1.11378i
$456$	−4.46246	−	4.60532i	−0.208974	−	0.215664i
$457$	4.36570	−	4.36570i	0.204219	−	0.204219i	−0.597586	−	0.801805i	$-0.703873\pi$
$457$	4.36570	−	4.36570i	0.204219	−	0.204219i	0.801805	+	0.597586i	$0.203873\pi$
$458$	3.38418	+	0.0177713i	0.158132	+	0.000830399i
$459$	−7.75636			−0.362036
$460$	−0.436691	−	0.107208i	−0.0203608	−	0.00499861i
$461$	−9.08427			−0.423097			−0.211548	−	0.977368i	$-0.567851\pi$
$461$	−9.08427			−0.423097			−0.211548	+	0.977368i	$0.567851\pi$
$462$	2.91675	+	0.0153167i	0.135699	+	0.000712597i
$463$	−16.3736	+	16.3736i	−0.760946	+	0.760946i	−0.976493	−	0.215547i	$-0.930847\pi$
$463$	−16.3736	+	16.3736i	−0.760946	+	0.760946i	0.215547	+	0.976493i	$0.430847\pi$
$464$	−0.168624	+	8.02666i	−0.00782819	+	0.372628i
$465$	1.39152	−	5.93666i	0.0645300	−	0.275306i
$466$	6.34799	−	6.28167i	0.294065	−	0.290993i
$467$	4.73129	+	4.73129i	0.218938	+	0.218938i	0.808051	−	0.589113i	$-0.200523\pi$
$467$	4.73129	+	4.73129i	0.218938	+	0.218938i	−0.589113	+	0.808051i	$0.700523\pi$
$468$	−20.0709	+	19.6537i	−0.927780	+	0.908493i
$469$		−	11.2346i		−	0.518766i
$470$	−29.6590	−	7.11638i	−1.36807	−	0.328254i
$471$		−	5.95372i		−	0.274333i
$472$	−0.157243	+	9.98047i	−0.00723768	+	0.459389i
$473$	−6.95400	−	6.95400i	−0.319745	−	0.319745i
$474$	−2.95729	−	2.98851i	−0.135833	−	0.137267i
$475$	−9.53820	+	19.2287i	−0.437643	+	0.882273i
$476$	−20.0486	−	0.210568i	−0.918925	−	0.00965135i
$477$	17.1869	−	17.1869i	0.786935	−	0.786935i
$478$	0.0241739	−	4.60341i	0.00110569	−	0.210555i
$479$	−12.6523			−0.578099			−0.289050	−	0.957314i	$-0.593339\pi$
$479$	−12.6523			−0.578099			−0.289050	+	0.957314i	$0.593339\pi$
$480$	−1.69477	+	6.46191i	−0.0773553	+	0.294945i
$481$	−18.7474			−0.854806
$482$	0.0547087	−	10.4182i	0.00249191	−	0.474534i
$483$	−0.146637	+	0.146637i	−0.00667221	+	0.00667221i
$484$	1.99989	+	0.0210046i	0.0909041	+	0.000954753i
$485$	39.3592	+	9.22556i	1.78721	+	0.418911i
$486$	−12.4671	−	12.5987i	−0.565517	−	0.571488i
$487$	12.9846	+	12.9846i	0.588386	+	0.588386i	0.937194	−	0.348808i	$-0.113413\pi$
$487$	12.9846	+	12.9846i	0.588386	+	0.588386i	−0.348808	+	0.937194i	$0.613413\pi$
$488$	−0.452116	+	28.6966i	−0.0204663	+	1.29904i
$489$			6.14731i			0.277991i
$490$	13.6353	+	22.2442i	0.615978	+	1.00489i
$491$		−	26.9597i		−	1.21667i	−0.793679	−	0.608337i	$-0.791837\pi$
$491$		−	26.9597i		−	1.21667i	0.793679	−	0.608337i	$-0.208163\pi$
$492$	−4.19048	+	4.10337i	−0.188921	+	0.184994i
$493$	3.64326	+	3.64326i	0.164084	+	0.164084i
$494$	−22.2749	+	22.0422i	−1.00220	+	0.991726i
$495$	3.20702	+	5.17070i	0.144145	+	0.232406i
$496$	−0.433785	+	20.6485i	−0.0194775	+	0.927146i
$497$	7.20190	−	7.20190i	0.323049	−	0.323049i
$498$	−2.78142	−	0.0146060i	−0.124638	−	0.000654511i
$499$	−6.07788			−0.272083			−0.136042	−	0.990703i	$-0.543438\pi$
$499$	−6.07788			−0.272083			−0.136042	+	0.990703i	$0.543438\pi$
$500$	22.2815	−	1.88018i	0.996459	−	0.0840842i
$501$	−10.1413			−0.453080
$502$	20.6086	+	0.108222i	0.919807	+	0.00483017i
$503$	−2.06402	+	2.06402i	−0.0920302	+	0.0920302i	−0.751623	−	0.659593i	$-0.770729\pi$
$503$	−2.06402	+	2.06402i	−0.0920302	+	0.0920302i	0.659593	+	0.751623i	$0.270729\pi$
$504$	−20.9152	−	21.5848i	−0.931639	−	0.961464i
$505$	16.4013	+	26.4440i	0.729850	+	1.17674i
$506$	−0.101073	+	0.100017i	−0.00449326	+	0.00444631i
$507$	−5.09532	−	5.09532i	−0.226291	−	0.226291i
$508$	−16.0724	−	16.4136i	−0.713099	−	0.728237i
$509$			16.2229i			0.719066i	0.933132	+	0.359533i	$0.117064\pi$
$509$			16.2229i			0.719066i	−0.933132	+	0.359533i	$0.882936\pi$
$510$	2.24057	+	3.65521i	0.0992141	+	0.161855i
$511$			17.8698i			0.790511i
$512$	1.06900	−	22.6022i	0.0472436	−	0.998883i
$513$	−9.17186	−	9.17186i	−0.404948	−	0.404948i
$514$	17.7456	+	17.9329i	0.782724	+	0.790988i
$515$	−27.7706	−	6.50924i	−1.22372	−	0.286832i
$516$	0.109096	−	10.3873i	0.00480270	−	0.457275i
$517$	−6.82018	+	6.82018i	−0.299951	+	0.299951i
$518$	0.105332	−	20.0583i	0.00462801	−	0.881309i
$519$	4.47184			0.196292
$520$	31.6632	+	7.94986i	1.38852	+	0.348625i
$521$	−29.3949			−1.28782			−0.643908	−	0.765103i	$-0.722688\pi$
$521$	−29.3949			−1.28782			−0.643908	+	0.765103i	$0.722688\pi$
$522$	−0.0405588	+	7.72360i	−0.00177521	+	0.338053i
$523$	3.29734	−	3.29734i	0.144183	−	0.144183i	−0.631331	−	0.775513i	$-0.717491\pi$
$523$	3.29734	−	3.29734i	0.144183	−	0.144183i	0.775513	+	0.631331i	$0.217491\pi$
$524$	−0.435895	+	41.5025i	−0.0190422	+	1.81305i
$525$	4.58256	−	9.23828i	0.199999	−	0.403192i
$526$	8.77620	+	8.86886i	0.382660	+	0.386701i
$527$	9.37225	+	9.37225i	0.408262	+	0.408262i
$528$	1.46209	+	1.52484i	0.0636294	+	0.0663602i
$529$			22.9899i			0.999560i
$530$	−27.4674	−	6.59055i	−1.19311	−	0.286275i
$531$			9.60285i			0.416728i
$532$	−23.4584	−	23.9564i	−1.01705	−	1.03864i
$533$	20.2662	+	20.2662i	0.877827	+	0.877827i
$534$	4.60810	−	4.55996i	0.199412	−	0.197329i
$535$	7.42282	−	31.6682i	0.320917	−	1.36913i
$536$	5.84359	−	5.66231i	0.252405	−	0.244575i
$537$	7.89101	−	7.89101i	0.340522	−	0.340522i
$538$	5.77703	+	0.0303368i	0.249065	+	0.00130791i
$539$	8.25060			0.355379
$540$	−3.22169	+	13.1229i	−0.138639	+	0.564721i
$541$	−43.5693			−1.87319			−0.936596	−	0.350412i	$-0.886042\pi$
$541$	−43.5693			−1.87319			−0.936596	+	0.350412i	$0.886042\pi$
$542$	16.5232	+	0.0867678i	0.709730	+	0.00372700i
$543$	4.68797	−	4.68797i	0.201180	−	0.201180i
$544$	−9.99509	−	10.5342i	−0.428536	−	0.451651i
$545$	−31.5014	+	19.5380i	−1.34937	+	0.836918i
$546$	10.7018	−	10.5900i	0.457996	−	0.453211i
$547$	2.03097	+	2.03097i	0.0868382	+	0.0868382i	0.749192	−	0.662353i	$-0.230442\pi$
$547$	2.03097	+	2.03097i	0.0868382	+	0.0868382i	−0.662353	+	0.749192i	$0.730442\pi$
$548$	−2.88531	+	2.82533i	−0.123254	+	0.120692i
$549$			27.6109i			1.17840i
$550$	3.17542	−	6.31797i	0.135400	−	0.269399i
$551$			8.61627i			0.367065i
$552$	−0.150178	−	0.00236605i	−0.00639199	−	0.000100706i
$553$	−15.5442	−	15.5442i	−0.661006	−	0.661006i
$554$	13.4357	+	13.5775i	0.570827	+	0.576854i
$555$	−3.64500	+	2.26073i	−0.154721	+	0.0959627i
$556$	4.71926	+	0.0495658i	0.200141	+	0.00210206i
$557$	1.12071	−	1.12071i	0.0474861	−	0.0474861i	−0.682965	−	0.730451i	$-0.739310\pi$
$557$	1.12071	−	1.12071i	0.0474861	−	0.0474861i	0.730451	+	0.682965i	$0.239310\pi$
$558$	−0.104337	+	19.8689i	−0.00441695	+	0.841117i
$559$	−50.7632			−2.14705
$560$	−8.68366	+	33.8326i	−0.366951	+	1.42969i
$561$	1.35575			0.0572400
$562$	0.101817	−	19.3889i	0.00429488	−	0.817872i
$563$	7.47972	−	7.47972i	0.315233	−	0.315233i	−0.531700	−	0.846933i	$-0.678447\pi$
$563$	7.47972	−	7.47972i	0.315233	−	0.315233i	0.846933	+	0.531700i	$0.178447\pi$
$564$	−10.1874	−	0.106997i	−0.428967	−	0.00450538i
$565$	2.96733	−	12.6596i	0.124837	−	0.532594i
$566$	−2.97101	−	3.00238i	−0.124881	−	0.126199i
$567$	−18.1353	−	18.1353i	−0.761611	−	0.761611i
$568$	7.37581	+	0.116206i	0.309482	+	0.00487590i
$569$		−	44.4756i		−	1.86452i	−0.361795	−	0.932258i	$-0.617836\pi$
$569$		−	44.4756i		−	1.86452i	0.361795	−	0.932258i	$-0.382164\pi$
$570$	−1.67280	+	6.97173i	−0.0700658	+	0.292013i
$571$			23.9328i			1.00155i	0.865576	+	0.500777i	$0.166952\pi$
$571$			23.9328i			1.00155i	−0.865576	+	0.500777i	$0.833048\pi$
$572$	7.37612	−	7.22279i	0.308411	−	0.302000i
$573$	−5.92833	−	5.92833i	−0.247660	−	0.247660i
$574$	−21.7972	+	21.5694i	−0.909797	+	0.900291i
$575$	0.160491	+	0.476428i	0.00669293	+	0.0198684i
$576$	0.685758	−	21.7578i	0.0285733	−	0.906574i
$577$	3.63715	−	3.63715i	0.151416	−	0.151416i	−0.627334	−	0.778750i	$-0.715854\pi$
$577$	3.63715	−	3.63715i	0.151416	−	0.151416i	0.778750	+	0.627334i	$0.215854\pi$
$578$	14.7221	+	0.0773101i	0.612360	+	0.00321568i
$579$	4.69045			0.194929
$580$	7.67726	−	4.65073i	0.318781	−	0.193111i
$581$	−14.5430			−0.603345
$582$	13.5030	+	0.0709083i	0.559719	+	0.00293924i
$583$	−6.31623	+	6.31623i	−0.261592	+	0.261592i
$584$	−9.29480	+	9.00647i	−0.384622	+	0.372690i
$585$	30.5781	+	7.16731i	1.26425	+	0.296332i
$586$	−1.93310	+	1.91290i	−0.0798556	+	0.0790213i
$587$	9.27813	+	9.27813i	0.382950	+	0.382950i	0.872164	−	0.489214i	$-0.162716\pi$
$587$	9.27813	+	9.27813i	0.382950	+	0.382950i	−0.489214	+	0.872164i	$0.662716\pi$
$588$	6.09730	+	6.22674i	0.251449	+	0.256786i
$589$			22.1653i			0.913304i
$590$	9.51461	−	5.83227i	0.391710	−	0.240111i
$591$		−	8.76252i		−	0.360442i
$592$	10.4862	−	10.0547i	0.430981	−	0.413246i
$593$	11.5723	+	11.5723i	0.475218	+	0.475218i	0.903598	−	0.428381i	$-0.140916\pi$
$593$	11.5723	+	11.5723i	0.475218	+	0.475218i	−0.428381	+	0.903598i	$0.640916\pi$
$594$	3.00560	+	3.03733i	0.123321	+	0.124623i
$595$	11.8152	+	19.0497i	0.484374	+	0.780960i
$596$	−0.204068	+	19.4297i	−0.00835894	+	0.795872i
$597$	−9.46976	+	9.46976i	−0.387571	+	0.387571i
$598$	−0.00385427	+	0.733966i	−0.000157613	+	0.0300141i
$599$	12.4306			0.507899			0.253949	−	0.967217i	$-0.418270\pi$
$599$	12.4306			0.507899			0.253949	+	0.967217i	$0.418270\pi$
$600$	7.11485	−	2.27257i	0.290463	−	0.0927774i
$601$	42.1302			1.71853			0.859264	−	0.511533i	$-0.170922\pi$
$601$	42.1302			1.71853			0.859264	+	0.511533i	$0.170922\pi$
$602$	0.285212	−	54.3128i	0.0116244	−	2.21362i
$603$	5.53528	−	5.53528i	0.225414	−	0.225414i
$604$	0.0896142	−	8.53236i	0.00364635	−	0.347177i
$605$	−1.17859	−	1.90025i	−0.0479164	−	0.0772560i
$606$	7.31091	+	7.38810i	0.296986	+	0.300121i
$607$	−25.2317	−	25.2317i	−1.02412	−	1.02412i	−0.999702	−	0.0244204i	$-0.992226\pi$
$607$	−25.2317	−	25.2317i	−1.02412	−	1.02412i	−0.0244204	−	0.999702i	$-0.507774\pi$
$608$	0.637537	−	24.2758i	0.0258555	−	0.984514i
$609$		−	4.13962i		−	0.167746i
$610$	27.3571	−	16.7694i	1.10766	−	0.678973i
$611$			49.7863i			2.01414i
$612$	−9.77417	−	9.98166i	−0.395097	−	0.403485i
$613$	12.8188	+	12.8188i	0.517746	+	0.517746i	0.916889	−	0.399143i	$-0.130692\pi$
$613$	12.8188	+	12.8188i	0.517746	+	0.517746i	−0.399143	+	0.916889i	$0.630692\pi$
$614$	21.2340	−	21.0121i	0.856934	−	0.847981i
$615$	6.38419	+	1.49641i	0.257435	+	0.0603412i
$616$	7.68640	+	7.93247i	0.309694	+	0.319608i
$617$	−26.2973	+	26.2973i	−1.05869	+	1.05869i	−0.0605224	+	0.998167i	$0.519277\pi$
$617$	−26.2973	+	26.2973i	−1.05869	+	1.05869i	−0.998167	+	0.0605224i	$0.980723\pi$
$618$	−9.52728	−	0.0500305i	−0.383244	−	0.00201252i
$619$	−18.9424			−0.761359			−0.380680	−	0.924707i	$-0.624310\pi$
$619$	−18.9424			−0.761359			−0.380680	+	0.924707i	$0.624310\pi$
$620$	19.7497	−	11.9640i	0.793167	−	0.480484i
$621$	−0.303803			−0.0121912
$622$	15.9449	+	0.0837312i	0.639332	+	0.00335732i
$623$	23.9682	−	23.9682i	0.960266	−	0.960266i
$624$	10.9021	+	0.229032i	0.436433	+	0.00916861i
$625$	−15.1266	−	19.9044i	−0.605065	−	0.796176i
$626$	2.90071	−	2.87041i	0.115936	−	0.114724i
$627$	1.60317	+	1.60317i	0.0640245	+	0.0640245i
$628$	16.1091	−	15.7742i	0.642822	−	0.629459i
$629$		−	9.32342i		−	0.371749i
$630$	−7.84029	+	32.6760i	−0.312364	+	1.30184i
$631$			38.9678i			1.55128i	0.631174	+	0.775641i	$0.282573\pi$
$631$			38.9678i			1.55128i	−0.631174	+	0.775641i	$0.717427\pi$
$632$	0.250813	−	15.9195i	0.00997680	−	0.633246i
$633$	7.57916	+	7.57916i	0.301245	+	0.301245i
$634$	−5.20108	−	5.25599i	−0.206561	−	0.208742i
$635$	−5.86129	+	25.0062i	−0.232598	+	0.992340i
$636$	−9.43464	−	0.0990908i	−0.374108	−	0.00392921i
$637$	30.1141	−	30.1141i	1.19316	−	1.19316i
$638$	0.0149055	−	2.83844i	0.000590113	−	0.112375i
$639$	7.09674			0.280743
$640$	−21.9743	+	12.5351i	−0.868612	+	0.495493i
$641$	46.4774			1.83575			0.917874	−	0.396872i	$-0.129904\pi$
$641$	46.4774			1.83575			0.917874	+	0.396872i	$0.129904\pi$
$642$	0.0570523	−	10.8644i	0.00225168	−	0.428785i
$643$	3.84474	−	3.84474i	0.151622	−	0.151622i	−0.627220	−	0.778842i	$-0.715807\pi$
$643$	3.84474	−	3.84474i	0.151622	−	0.151622i	0.778842	+	0.627220i	$0.215807\pi$
$644$	−0.785267	−	0.00824756i	−0.0309439	−	0.000324999i
$645$	−9.86974	+	6.12150i	−0.388621	+	0.241034i
$646$	−10.9620	−	11.0777i	−0.431295	−	0.435848i
$647$	31.7952	+	31.7952i	1.25000	+	1.25000i	0.955719	+	0.294281i	$0.0950802\pi$
$647$	31.7952	+	31.7952i	1.25000	+	1.25000i	0.294281	+	0.955719i	$0.404920\pi$
$648$	0.292622	−	18.5732i	0.0114953	−	0.729625i
$649$		−	3.52907i		−	0.138528i
$650$	−11.4701	−	34.6502i	−0.449894	−	1.35909i
$651$		−	10.6491i		−	0.417373i
$652$	−16.6329	+	16.2871i	−0.651394	+	0.637853i
$653$	−6.83041	−	6.83041i	−0.267295	−	0.267295i	0.560714	−	0.828009i	$-0.310527\pi$
$653$	−6.83041	−	6.83041i	−0.267295	−	0.267295i	−0.828009	+	0.560714i	$0.810527\pi$
$654$	−8.80106	+	8.70911i	−0.344149	+	0.340553i
$655$	39.4347	−	24.4585i	1.54084	−	0.955673i
$656$	−22.2051	−	0.466485i	−0.866963	−	0.0182132i
$657$	−8.80441	+	8.80441i	−0.343493	+	0.343493i
$658$	−53.2676	−	0.279724i	−2.07659	−	0.0109048i
$659$	13.0818			0.509595			0.254798	−	0.966994i	$-0.417991\pi$
$659$	13.0818			0.509595			0.254798	+	0.966994i	$0.417991\pi$
$660$	0.563127	−	2.29379i	0.0219197	−	0.0892856i
$661$	−15.4462			−0.600788			−0.300394	−	0.953815i	$-0.597118\pi$
$661$	−15.4462			−0.600788			−0.300394	+	0.953815i	$0.597118\pi$
$662$	13.7940	+	0.0724363i	0.536119	+	0.00281531i
$663$	4.94840	−	4.94840i	0.192180	−	0.192180i
$664$	−7.32976	−	7.56442i	−0.284450	−	0.293556i
$665$	−8.55478	+	36.4975i	−0.331740	+	1.41531i
$666$	9.93458	−	9.83078i	0.384957	−	0.380935i
$667$	0.142700	+	0.142700i	0.00552536	+	0.00552536i
$668$	−26.8691	−	27.4395i	−1.03960	−	1.06167i
$669$			7.66700i			0.296423i
$670$	−8.84626	−	2.12258i	−0.341761	−	0.0820022i
$671$		−	10.1471i		−	0.391723i
$672$	−0.306300	+	11.6631i	−0.0118158	+	0.449915i
$673$	13.2007	+	13.2007i	0.508850	+	0.508850i	0.914173	−	0.405323i	$-0.132841\pi$
$673$	13.2007	+	13.2007i	0.508850	+	0.508850i	−0.405323	+	0.914173i	$0.632841\pi$
$674$	2.62905	+	2.65680i	0.101267	+	0.102336i
$675$	14.3170	−	4.82288i	0.551063	−	0.185633i
$676$	0.286585	−	27.2864i	0.0110225	−	1.04948i
$677$	5.87620	−	5.87620i	0.225841	−	0.225841i	−0.585112	−	0.810953i	$-0.698949\pi$
$677$	5.87620	−	5.87620i	0.225841	−	0.225841i	0.810953	+	0.585112i	$0.198949\pi$
$678$	0.0228071	−	4.34315i	0.000875903	−	0.166798i
$679$	70.6023			2.70947
$680$	−3.95362	+	15.7467i	−0.151614	+	0.603858i
$681$	−12.0492			−0.461725
$682$	0.0383442	−	7.30186i	0.00146827	−	0.279603i
$683$	−11.1326	+	11.1326i	−0.425976	+	0.425976i	−0.887255	−	0.461279i	$-0.847391\pi$
$683$	−11.1326	+	11.1326i	−0.425976	+	0.425976i	0.461279	+	0.887255i	$0.347391\pi$
$684$	0.245359	−	23.3612i	0.00938154	−	0.893237i
$685$	4.39576	+	1.03034i	0.167954	+	0.0393673i
$686$	4.85814	+	4.90943i	0.185485	+	0.187443i
$687$	−0.893668	−	0.893668i	−0.0340956	−	0.0340956i
$688$	28.3941	−	27.2256i	1.08251	−	1.03797i
$689$			46.1076i			1.75656i
$690$	0.0877592	+	0.143168i	0.00334093	+	0.00545031i
$691$		−	14.6563i		−	0.557554i	−0.960356	−	0.278777i	$-0.910071\pi$
$691$		−	14.6563i		−	0.557554i	0.960356	−	0.278777i	$-0.0899290\pi$
$692$	11.8480	+	12.0995i	0.450393	+	0.459954i
$693$	7.51395	+	7.51395i	0.285431	+	0.285431i
$694$	−11.0863	+	10.9705i	−0.420830	+	0.416433i
$695$	−2.78118	−	4.48412i	−0.105496	−	0.170093i
$696$	2.15319	−	2.08639i	0.0816164	−	0.0790846i
$697$	−10.0788	+	10.0788i	−0.381761	+	0.381761i
$698$	−19.4782	−	0.102286i	−0.737261	−	0.00387157i
$699$	−3.33514			−0.126147
$700$	37.1375	−	12.0775i	1.40367	−	0.456485i
$701$	4.70503			0.177707			0.0888533	−	0.996045i	$-0.471680\pi$
$701$	4.70503			0.177707			0.0888533	+	0.996045i	$0.471680\pi$
$702$	22.0563	+	0.115824i	0.832460	+	0.00437149i
$703$	11.0249	−	11.0249i	0.415812	−	0.415812i
$704$	−0.252018	+	7.99603i	−0.00949828	+	0.301362i
$705$	6.00370	+	9.67982i	0.226112	+	0.364563i
$706$	11.6388	−	11.5172i	0.438032	−	0.433456i
$707$	38.4279	+	38.4279i	1.44523	+	1.44523i
$708$	2.66339	−	2.60803i	0.100096	−	0.0980157i
$709$		−	41.1641i		−	1.54595i	−0.634437	−	0.772974i	$-0.718768\pi$
$709$		−	41.1641i		−	1.54595i	0.634437	−	0.772974i	$-0.281232\pi$
$710$	−4.31019	−	7.03153i	−0.161759	−	0.263889i
$711$		−	15.3172i		−	0.574440i
$712$	24.5470	+	0.386738i	0.919937	+	0.0144936i
$713$	0.367094	+	0.367094i	0.0137478	+	0.0137478i
$714$	5.26662	+	5.32222i	0.197098	+	0.199179i
$715$	−11.2375	−	2.63400i	−0.420259	−	0.0985061i
$716$	42.2578	+	0.443828i	1.57925	+	0.0165866i
$717$	−1.21563	+	1.21563i	−0.0453987	+	0.0453987i
$718$	−0.0985761	+	18.7718i	−0.00367883	+	0.700557i
$719$	−5.22637			−0.194911			−0.0974554	−	0.995240i	$-0.531070\pi$
$719$	−5.22637			−0.194911			−0.0974554	+	0.995240i	$0.531070\pi$
$720$	−20.9477	+	12.3908i	−0.780674	+	0.461779i
$721$	−49.8146			−1.85519
$722$	−0.00424190	+	0.807783i	−0.000157867	+	0.0300626i
$723$	−2.75114	+	2.75114i	−0.102316	+	0.102316i
$724$	25.1049	+	0.263674i	0.933017	+	0.00979935i
$725$	−8.99025	−	4.45953i	−0.333890	−	0.165623i
$726$	−0.525356	−	0.530903i	−0.0194978	−	0.0197037i
$727$	−14.5427	−	14.5427i	−0.539361	−	0.539361i	0.383980	−	0.923341i	$-0.374553\pi$
$727$	−14.5427	−	14.5427i	−0.539361	−	0.539361i	−0.923341	+	0.383980i	$0.874553\pi$
$728$	57.0077	+	0.898158i	2.11285	+	0.0332879i
$729$		−	13.0832i		−	0.484562i
$730$	14.0708	+	3.37616i	0.520785	+	0.124957i
$731$		−	25.2455i		−	0.933738i
$732$	7.65799	−	7.49880i	0.283048	−	0.277164i
$733$	−1.22031	−	1.22031i	−0.0450734	−	0.0450734i	0.684211	−	0.729284i	$-0.260147\pi$
$733$	−1.22031	−	1.22031i	−0.0450734	−	0.0450734i	−0.729284	+	0.684211i	$0.760147\pi$
$734$	−33.6716	+	33.3198i	−1.24284	+	1.22986i
$735$	2.22356	−	9.48644i	0.0820173	−	0.349913i
$736$	−0.391490	−	0.412607i	−0.0144305	−	0.0152089i
$737$	−2.03423	+	2.03423i	−0.0749317	+	0.0749317i
$738$	−21.3667	−	0.112203i	−0.786518	−	0.00413023i
$739$	−24.9876			−0.919183			−0.459591	−	0.888130i	$-0.652004\pi$
$739$	−24.9876			−0.919183			−0.459591	+	0.888130i	$0.652004\pi$
$740$	−15.7742	−	3.87258i	−0.579871	−	0.142359i
$741$	11.7029			0.429918
$742$	−49.3316	−	0.259055i	−1.81102	−	0.00951019i
$743$	−23.5454	+	23.5454i	−0.863797	+	0.863797i	−0.991777	−	0.127980i	$-0.959151\pi$
$743$	−23.5454	+	23.5454i	−0.863797	+	0.863797i	0.127980	+	0.991777i	$0.459151\pi$
$744$	5.53906	−	5.36723i	0.203072	−	0.196772i
$745$	18.4616	−	11.4504i	0.676382	−	0.419511i
$746$	−18.1116	+	17.9224i	−0.663113	+	0.656185i
$747$	−7.16532	−	7.16532i	−0.262165	−	0.262165i
$748$	3.59203	+	3.66828i	0.131338	+	0.134126i
$749$		−	56.8062i		−	2.07565i
$750$	−6.40854	−	5.35376i	−0.234007	−	0.195492i
$751$			41.1049i			1.49994i	0.661472	+	0.749970i	$0.269932\pi$
$751$			41.1049i			1.49994i	−0.661472	+	0.749970i	$0.730068\pi$
$752$	−26.7017	−	27.8477i	−0.973711	−	1.01550i
$753$	−5.44216	−	5.44216i	−0.198323	−	0.198323i
$754$	−10.3057	−	10.4145i	−0.375311	−	0.379274i
$755$	−8.10723	+	5.02834i	−0.295052	+	0.183000i
$756$	−0.247846	+	23.5979i	−0.00901406	+	0.858248i
$757$	−23.7617	+	23.7617i	−0.863633	+	0.863633i	−0.991758	−	0.128125i	$-0.959104\pi$
$757$	−23.7617	+	23.7617i	−0.863633	+	0.863633i	0.128125	+	0.991758i	$0.459104\pi$
$758$	−0.196323	+	37.3857i	−0.00713078	+	1.35791i
$759$	0.0531025			0.00192750
$760$	−23.2955	+	13.9453i	−0.845018	+	0.505848i
$761$	11.3929			0.412991			0.206495	−	0.978448i	$-0.433794\pi$
$761$	11.3929			0.412991			0.206495	+	0.978448i	$0.433794\pi$
$762$	−0.0450503	+	8.57890i	−0.00163200	+	0.310781i
$763$	−45.7771	+	45.7771i	−1.65724	+	1.65724i
$764$	0.333438	−	31.7473i	0.0120634	−	1.14858i
$765$	−3.56444	+	15.2071i	−0.128873	+	0.549812i
$766$	0.199061	+	0.201163i	0.00719238	+	0.00726831i
$767$	−12.8808	−	12.8808i	−0.465100	−	0.465100i
$768$	−6.22086	+	5.71897i	−0.224476	+	0.206366i
$769$		−	2.57827i		−	0.0929748i	−0.998919	−	0.0464874i	$-0.985197\pi$
$769$		−	2.57827i		−	0.0929748i	0.998919	−	0.0464874i	$-0.0148027\pi$
$770$	2.88132	−	12.0085i	0.103836	−	0.432756i
$771$		−	9.42170i		−	0.339314i
$772$	12.4272	+	12.6910i	0.447265	+	0.456760i
$773$	−1.68486	−	1.68486i	−0.0606002	−	0.0606002i	0.676157	−	0.736757i	$-0.263644\pi$
$773$	−1.68486	−	1.68486i	−0.0606002	−	0.0606002i	−0.736757	+	0.676157i	$0.763644\pi$
$774$	26.9004	−	26.6193i	0.966914	−	0.956812i
$775$	−23.1274	−	11.4721i	−0.830759	−	0.412090i
$776$	35.5840	+	36.7232i	1.27739	+	1.31829i
$777$	−5.29683	+	5.29683i	−0.190023	+	0.190023i
$778$	24.6414	+	0.129399i	0.883436	+	0.00463918i
$779$	−23.8362			−0.854020
$780$	−6.31678	−	10.4275i	−0.226177	−	0.373365i
$781$	−2.60807			−0.0933240
$782$	−0.365015	−	0.00191680i	−0.0130529	−	6.85447e-5i
$783$	4.28824	−	4.28824i	0.153249	−	0.153249i
$784$	−0.693163	+	32.9951i	−0.0247558	+	1.17840i
$785$	−24.5422	−	5.75253i	−0.875947	−	0.205317i
$786$	11.0175	−	10.9024i	0.392982	−	0.388876i
$787$	−21.6183	−	21.6183i	−0.770610	−	0.770610i	0.207604	−	0.978213i	$-0.433434\pi$
$787$	−21.6183	−	21.6183i	−0.770610	−	0.770610i	−0.978213	+	0.207604i	$0.933434\pi$
$788$	23.7089	−	23.2160i	0.844594	−	0.827037i
$789$		−	4.65957i		−	0.165885i
$790$	−15.1765	+	9.30288i	−0.539954	+	0.330982i
$791$		−	22.7087i		−	0.807430i
$792$	−0.121241	+	7.69540i	−0.00430812	+	0.273444i
$793$	−37.0360	−	37.0360i	−1.31519	−	1.31519i
$794$	−5.03136	−	5.08448i	−0.178556	−	0.180441i
$795$	5.56008	+	8.96457i	0.197196	+	0.317940i
$796$	−50.7123	−	0.532624i	−1.79745	−	0.0188784i
$797$	−4.68958	+	4.68958i	−0.166113	+	0.166113i	−0.785269	−	0.619155i	$-0.787475\pi$
$797$	−4.68958	+	4.68958i	−0.166113	+	0.166113i	0.619155	+	0.785269i	$0.287475\pi$
$798$	−0.0657527	+	12.5212i	−0.00232762	+	0.443247i
$799$	−24.7597			−0.875935
$800$	24.9995	+	13.2297i	0.883867	+	0.467739i
$801$	23.6182			0.834508
$802$	−0.0533662	+	10.1625i	−0.00188443	+	0.358851i
$803$	3.23564	−	3.23564i	0.114183	−	0.114183i
$804$	−3.03856	−	0.0319135i	−0.107162	−	0.00112550i
$805$	0.462778	+	0.746142i	0.0163108	+	0.0262980i
$806$	−26.5113	−	26.7912i	−0.933821	−	0.943680i
$807$	−1.52555	−	1.52555i	−0.0537020	−	0.0537020i
$808$	−0.620051	+	39.3558i	−0.0218133	+	1.38453i
$809$			13.0854i			0.460059i	0.973184	+	0.230030i	$0.0738823\pi$
$809$			13.0854i			0.460059i	−0.973184	+	0.230030i	$0.926118\pi$
$810$	−17.7063	+	10.8536i	−0.622135	+	0.381357i
$811$		−	7.78052i		−	0.273211i	−0.990626	−	0.136605i	$-0.956381\pi$
$811$		−	7.78052i		−	0.273211i	0.990626	−	0.136605i	$-0.0436193\pi$
$812$	11.2006	−	10.9678i	0.393065	−	0.384895i
$813$	−4.36330	−	4.36330i	−0.153028	−	0.153028i
$814$	−3.65098	+	3.61284i	−0.127967	+	0.126630i
$815$	25.3402	+	5.93958i	0.887628	+	0.208054i
$816$	−0.113902	+	5.42182i	−0.00398736	+	0.189802i
$817$	29.8527	−	29.8527i	1.04441	−	1.04441i
$818$	−12.5520	−	0.0659144i	−0.438872	−	0.00230464i
$819$	54.8508			1.91664
$820$	12.8658	+	21.2385i	0.449295	+	0.741681i
$821$	9.74066			0.339951			0.169976	−	0.985448i	$-0.445631\pi$
$821$	9.74066			0.339951			0.169976	+	0.985448i	$0.445631\pi$
$822$	1.50806	+	0.00791926i	0.0525997	+	0.000276216i
$823$	3.94689	−	3.94689i	0.137580	−	0.137580i	−0.634963	−	0.772543i	$-0.718985\pi$
$823$	3.94689	−	3.94689i	0.137580	−	0.137580i	0.772543	+	0.634963i	$0.218985\pi$
$824$	−25.1069	−	25.9107i	−0.874640	−	0.902641i
$825$	−2.50251	+	0.843002i	−0.0871263	+	0.0293496i
$826$	13.8539	−	13.7092i	0.482039	−	0.477003i
$827$	9.71577	+	9.71577i	0.337850	+	0.337850i	0.855558	−	0.517707i	$-0.173214\pi$
$827$	9.71577	+	9.71577i	0.337850	+	0.337850i	−0.517707	+	0.855558i	$0.673214\pi$
$828$	−0.382837	−	0.390964i	−0.0133045	−	0.0135869i
$829$			33.5680i			1.16586i	0.812521	+	0.582932i	$0.198094\pi$
$829$			33.5680i			1.16586i	−0.812521	+	0.582932i	$0.801906\pi$
$830$	−2.74763	+	11.4513i	−0.0953718	+	0.397481i
$831$		−	7.13344i		−	0.247456i
$832$	28.2651	+	30.1048i	0.979915	+	1.04370i
$833$	14.9763	+	14.9763i	0.518898	+	0.518898i
$834$	−1.23972	−	1.25280i	−0.0429278	−	0.0433811i
$835$	−9.79861	+	41.8041i	−0.339095	+	1.44669i
$836$	−0.0901701	+	8.58528i	−0.00311860	+	0.296928i
$837$	11.0315	−	11.0315i	0.381304	−	0.381304i
$838$	−0.0852150	+	16.2275i	−0.00294370	+	0.560568i
$839$	19.4509			0.671520			0.335760	−	0.941948i	$-0.391007\pi$
$839$	19.4509			0.671520			0.335760	+	0.941948i	$0.391007\pi$
$840$	11.1922	−	6.69990i	0.386166	−	0.231168i
$841$	24.9715			0.861087
$842$	−0.102774	+	19.5712i	−0.00354183	+	0.674468i
$843$	−5.12007	+	5.12007i	−0.176345	+	0.176345i
$844$	−0.426288	+	40.5878i	−0.0146735	+	1.39709i
$845$	−25.9268	+	16.0806i	−0.891910	+	0.553188i
$846$	−26.1071	−	26.3827i	−0.897580	−	0.907056i
$847$	−2.76139	−	2.76139i	−0.0948826	−	0.0948826i
$848$	−24.7287	−	25.7900i	−0.849187	−	0.885632i
$849$			1.57741i			0.0541364i
$850$	17.2322	−	5.70430i	0.591059	−	0.195656i
$851$		−	0.365182i		−	0.0125183i
$852$	−1.92740	−	1.96831i	−0.0660315	−	0.0674332i
$853$	−19.3877	−	19.3877i	−0.663822	−	0.663822i	0.292457	−	0.956279i	$-0.405527\pi$
$853$	−19.3877	−	19.3877i	−0.663822	−	0.663822i	−0.956279	+	0.292457i	$0.905527\pi$
$854$	39.8338	−	39.4177i	1.36309	−	1.34884i
$855$	−22.1972	+	13.7673i	−0.759128	+	0.470833i
$856$	29.5472	−	28.6307i	1.00990	−	0.978576i
$857$	−15.5713	+	15.5713i	−0.531906	+	0.531906i	−0.921139	−	0.389233i	$-0.872740\pi$
$857$	−15.5713	+	15.5713i	−0.531906	+	0.531906i	0.389233	+	0.921139i	$0.372740\pi$
$858$	−3.85527	−	0.0202451i	−0.131617	−	0.000691157i
$859$	54.5179			1.86013			0.930064	−	0.367397i	$-0.119751\pi$
$859$	54.5179			1.86013			0.930064	+	0.367397i	$0.119751\pi$
$860$	−42.7126	−	10.4860i	−1.45649	−	0.357569i
$861$	11.4519			0.390280
$862$	−47.4684	−	0.249270i	−1.61678	−	0.00849018i
$863$	−13.4361	+	13.4361i	−0.457371	+	0.457371i	−0.897792	−	0.440420i	$-0.854829\pi$
$863$	−13.4361	+	13.4361i	−0.457371	+	0.457371i	0.440420	+	0.897792i	$0.354829\pi$
$864$	−12.3992	+	11.7646i	−0.421828	+	0.400239i
$865$	4.32072	−	18.4336i	0.146909	−	0.626761i
$866$	−35.0569	+	34.6907i	−1.19128	+	1.17884i
$867$	−3.88770	−	3.88770i	−0.132033	−	0.132033i
$868$	28.8135	−	28.2146i	0.977996	−	0.957666i
$869$			5.62911i			0.190954i
$870$	−3.25959	−	0.782106i	−0.110510	−	0.0265159i
$871$			14.8496i			0.503158i
$872$	−46.8825	−	0.738635i	−1.58764	−	0.0250133i
$873$	34.7857	+	34.7857i	1.17732	+	1.17732i
$874$	−0.429362	−	0.433896i	−0.0145234	−	0.0146767i
$875$	−33.6539	−	27.8161i	−1.13771	−	0.940357i
$876$	4.83312	+	0.0507616i	0.163296	+	0.00171508i
$877$	−37.4787	+	37.4787i	−1.26556	+	1.26556i	−0.317208	+	0.948356i	$0.602745\pi$
$877$	−37.4787	+	37.4787i	−1.26556	+	1.26556i	−0.948356	+	0.317208i	$0.897255\pi$
$878$	0.0278921	−	5.31147i	0.000941312	−	0.179253i
$879$	1.01562			0.0342561
$880$	7.69832	−	4.55366i	0.259510	−	0.153504i
$881$	31.1422			1.04921			0.524604	−	0.851346i	$-0.324213\pi$
$881$	31.1422			1.04921			0.524604	+	0.851346i	$0.324213\pi$
$882$	−0.166725	+	31.7493i	−0.00561392	+	1.06906i
$883$	38.3255	−	38.3255i	1.28975	−	1.28975i	0.354820	−	0.934934i	$-0.384542\pi$
$883$	38.3255	−	38.3255i	1.28975	−	1.28975i	0.934934	−	0.354820i	$-0.115458\pi$
$884$	26.4996	+	0.278322i	0.891278	+	0.00936097i
$885$	−4.05768	−	0.951094i	−0.136397	−	0.0319707i
$886$	31.8596	+	32.1960i	1.07034	+	1.08164i
$887$	0.00334246	+	0.00334246i	0.000112229	+	0.000112229i	0.707163	−	0.707051i	$-0.249975\pi$
$887$	0.00334246	+	0.00334246i	0.000112229	+	0.000112229i	−0.707051	+	0.707163i	$0.749975\pi$
$888$	−5.42473	−	0.0854668i	−0.182042	−	0.00286808i
$889$			44.8559i			1.50442i
$890$	−14.3445	−	23.4012i	−0.480828	−	0.784410i
$891$			6.56744i			0.220018i
$892$	−20.7447	+	20.3135i	−0.694585	+	0.680146i
$893$	−29.2782	−	29.2782i	−0.979758	−	0.979758i
$894$	5.15793	−	5.10404i	0.172507	−	0.170705i
$895$	−24.9036	−	40.1523i	−0.832437	−	1.34214i
$896$	−32.3687	+	30.0724i	−1.08136	+	1.00465i
$897$	0.193820	−	0.193820i	0.00647146	−	0.00647146i
$898$	−8.93879	−	0.0469401i	−0.298291	−	0.00156641i
$899$	−10.3632			−0.345633
$900$	24.2482	+	12.3471i	0.808272	+	0.411569i
$901$	−22.9302			−0.763915
$902$	7.85231	+	0.0412347i	0.261453	+	0.00137297i
$903$	−14.3425	+	14.3425i	−0.477288	+	0.477288i
$904$	11.8118	−	11.4453i	0.392853	−	0.380666i
$905$	−14.7950	−	23.8541i	−0.491802	−	0.792936i
$906$	−2.26505	+	2.24139i	−0.0752513	+	0.0744651i
$907$	28.7419	+	28.7419i	0.954358	+	0.954358i	0.999003	−	0.0446445i	$-0.0142155\pi$
$907$	28.7419	+	28.7419i	0.954358	+	0.954358i	−0.0446445	+	0.999003i	$0.514216\pi$
$908$	−31.9239	−	32.6016i	−1.05943	−	1.08192i
$909$			37.8667i			1.25596i
$910$	−33.3135	−	54.3468i	−1.10433	−	1.80158i
$911$		−	42.2570i		−	1.40004i	−0.714125	−	0.700019i	$-0.753175\pi$
$911$		−	42.2570i		−	1.40004i	0.714125	−	0.700019i	$-0.246825\pi$
$912$	−6.54596	+	6.27659i	−0.216758	+	0.207839i
$913$	2.63327	+	2.63327i	0.0871485	+	0.0871485i
$914$	−6.14153	−	6.20637i	−0.203144	−	0.205288i
$915$	−11.6670	−	2.73466i	−0.385698	−	0.0904051i
$916$	0.0502642	−	4.78576i	0.00166078	−	0.158126i
$917$	57.3056	−	57.3056i	1.89240	−	1.89240i
$918$	−0.0576014	+	10.9690i	−0.00190113	+	0.362031i
$919$	5.94844			0.196221			0.0981105	−	0.995176i	$-0.468720\pi$
$919$	5.94844			0.196221			0.0981105	+	0.995176i	$0.468720\pi$
$920$	−0.154856	+	0.616770i	−0.00510546	+	0.0203343i
$921$	−11.1560			−0.367604
$922$	−0.0674629	+	12.8469i	−0.00222177	+	0.423091i
$923$	−9.51925	+	9.51925i	−0.313330	+	0.313330i
$924$	0.0433215	−	4.12474i	0.00142517	−	0.135694i
$925$	5.79726	+	17.2096i	0.190613	+	0.565848i
$926$	23.0339	+	23.2771i	0.756940	+	0.764932i
$927$	−24.5436	−	24.5436i	−0.806118	−	0.806118i
$928$	11.3500	+	0.298076i	0.372582	+	0.00978484i
$929$		−	35.6659i		−	1.17016i	−0.810976	−	0.585080i	$-0.801063\pi$
$929$		−	35.6659i		−	1.17016i	0.810976	−	0.585080i	$-0.198937\pi$
$930$	−8.38526	−	2.01196i	−0.274963	−	0.0659748i
$931$			35.4188i			1.16081i
$932$	−8.83636	−	9.02394i	−0.289445	−	0.295589i
$933$	−4.21060	−	4.21060i	−0.137849	−	0.137849i
$934$	6.72611	−	6.65583i	0.220085	−	0.217785i
$935$	1.30994	−	5.58863i	0.0428396	−	0.182768i
$936$	27.6451	+	28.5302i	0.903609	+	0.932537i
$937$	8.97236	−	8.97236i	0.293114	−	0.293114i	−0.545195	−	0.838309i	$-0.683544\pi$
$937$	8.97236	−	8.97236i	0.293114	−	0.293114i	0.838309	+	0.545195i	$0.183544\pi$
$938$	−15.8879	−	0.0834320i	−0.518759	−	0.00272415i
$939$	−1.52399			−0.0497336
$940$	−10.2842	+	41.8907i	−0.335434	+	1.36632i
$941$	52.8689			1.72348			0.861738	−	0.507353i	$-0.169376\pi$
$941$	52.8689			1.72348			0.861738	+	0.507353i	$0.169376\pi$
$942$	−8.41971	−	0.0442143i	−0.274329	−	0.00144058i
$943$	−0.394767	+	0.394767i	−0.0128554	+	0.0128554i
$944$	14.1132	+	0.296490i	0.459344	+	0.00964992i
$945$	22.4221	−	13.9069i	0.729392	−	0.452390i
$946$	−9.88595	+	9.78266i	−0.321420	+	0.318062i
$947$	−23.6748	−	23.6748i	−0.769329	−	0.769329i	0.208660	−	0.977988i	$-0.433090\pi$
$947$	−23.6748	−	23.6748i	−0.769329	−	0.769329i	−0.977988	+	0.208660i	$0.933090\pi$
$948$	−4.24830	+	4.15998i	−0.137978	+	0.135110i
$949$		−	23.6197i		−	0.766728i
$950$	27.1223	+	13.6317i	0.879963	+	0.442270i
$951$			2.76142i			0.0895452i
$952$	−0.446671	+	28.3510i	−0.0144767	+	0.918862i
$953$	−38.4689	−	38.4689i	−1.24613	−	1.24613i	−0.957415	−	0.288714i	$-0.906772\pi$
$953$	−38.4689	−	38.4689i	−1.24613	−	1.24613i	−0.288714	−	0.957415i	$-0.593228\pi$
$954$	−24.1780	−	24.4333i	−0.782791	−	0.791056i
$955$	−30.1655	+	18.7095i	−0.976133	+	0.605426i
$956$	−6.50994	−	0.0683730i	−0.210547	−	0.00221134i
$957$	−0.749553	+	0.749553i	−0.0242296	+	0.0242296i
$958$	−0.0939604	+	17.8928i	−0.00303572	+	0.578091i
$959$	7.88509			0.254623
$960$	9.12582	+	2.44472i	0.294534	+	0.0789030i
$961$	4.34066			0.140021
$962$	−0.139224	+	26.5124i	−0.00448877	+	0.854794i
$963$	27.9883	−	27.9883i	0.901911	−	0.901911i
$964$	−14.7329	−	0.154737i	−0.474514	−	0.00498376i
$965$	4.53195	−	19.3348i	0.145889	−	0.622408i
$966$	0.206284	+	0.208462i	0.00663708	+	0.00670715i
$967$	−30.8238	−	30.8238i	−0.991225	−	0.991225i	0.00873634	−	0.999962i	$-0.497219\pi$
$967$	−30.8238	−	30.8238i	−0.991225	−	0.991225i	−0.999962	+	0.00873634i	$0.997219\pi$
$968$	0.0445564	−	2.82808i	0.00143210	−	0.0908978i
$969$			5.82009i			0.186968i
$970$	13.3390	−	55.5931i	0.428290	−	1.78499i
$971$		−	15.1385i		−	0.485819i	−0.970049	−	0.242909i	$-0.921898\pi$
$971$		−	15.1385i		−	0.485819i	0.970049	−	0.242909i	$-0.0781017\pi$
$972$	−17.9096	+	17.5373i	−0.574449	+	0.562508i
$973$	−6.51623	−	6.51623i	−0.208901	−	0.208901i
$974$	18.4591	−	18.2663i	0.591468	−	0.585289i
$975$	−6.05709	+	12.2109i	−0.193982	+	0.391061i
$976$	40.5793	+	0.852491i	1.29891	+	0.0272876i
$977$	−13.9647	+	13.9647i	−0.446771	+	0.446771i	−0.894280	−	0.447508i	$-0.852311\pi$
$977$	−13.9647	+	13.9647i	−0.446771	+	0.446771i	0.447508	+	0.894280i	$0.352311\pi$
$978$	8.69349	+	0.0456520i	0.277987	+	0.00145979i
$979$	−8.67975			−0.277406
$980$	31.5589	−	19.1177i	1.00811	−	0.610693i
$981$	−45.1086			−1.44021
$982$	−38.1262	−	0.200212i	−1.21666	−	0.00638901i
$983$	31.5836	−	31.5836i	1.00736	−	1.00736i	0.00738854	−	0.999973i	$-0.497648\pi$
$983$	31.5836	−	31.5836i	1.00736	−	1.00736i	0.999973	−	0.00738854i	$-0.00235187\pi$
$984$	5.77184	+	5.95662i	0.183999	+	0.189890i
$985$	−36.1205	−	8.46641i	−1.15089	−	0.269762i
$986$	5.17933	−	5.12522i	0.164943	−	0.163220i
$987$	14.0665	+	14.0665i	0.447741	+	0.447741i
$988$	31.0065	+	31.6648i	0.986450	+	1.00739i
$989$		−	0.988821i		−	0.0314427i
$990$	7.33620	−	4.49695i	0.233160	−	0.142922i
$991$		−	38.1343i		−	1.21137i	−0.795703	−	0.605687i	$-0.792898\pi$
$991$		−	38.1343i		−	1.21137i	0.795703	−	0.605687i	$-0.207102\pi$
$992$	29.1978	+	0.766799i	0.927031	+	0.0243459i
$993$	−3.64261	−	3.64261i	−0.115595	−	0.115595i
$994$	−10.1314	−	10.2384i	−0.321349	−	0.324741i
$995$	29.8861	+	48.1856i	0.947452	+	1.52759i
$996$	−0.0413115	+	3.93336i	−0.00130900	+	0.124633i
$997$	−8.05395	+	8.05395i	−0.255071	+	0.255071i	−0.823046	−	0.567975i	$-0.807727\pi$
$997$	−8.05395	+	8.05395i	−0.255071	+	0.255071i	0.567975	+	0.823046i	$0.307727\pi$
$998$	−0.0451364	+	8.59531i	−0.00142877	+	0.272080i
$999$	−10.9740			−0.347202

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.c.23.7	✓	28
4.3	odd	2		220.2.l.d.23.14	yes	28
5.2	odd	4		220.2.l.d.67.14	yes	28
20.7	even	4	inner	220.2.l.c.67.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.7	✓	28	1.1	even	1	trivial
220.2.l.c.67.7	yes	28	20.7	even	4	inner
220.2.l.d.23.14	yes	28	4.3	odd	2
220.2.l.d.67.14	yes	28	5.2	odd	4

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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

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Modular forms

Varieties

Fields

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Groups

Database

Properties

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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	220.2.l.c.23.7

Level	$220$
Weight	$2$
Character	220.23
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$28$
Inner twists	$2$