LMFDB - Embedded newform 220.2.l.c.23.3

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			23.3
Character	$\chi$	$=$	220.23
Dual form			220.2.l.c.67.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38283 + 0.296256i) q^{2} +(-0.668480 + 0.668480i) q^{3} +(1.82447 - 0.819345i) q^{4} +(-0.500108 + 2.17942i) q^{5} +(0.726357 - 1.12244i) q^{6} +(-1.29641 - 1.29641i) q^{7} +(-2.28020 + 1.67353i) q^{8} +2.10627i q^{9} +(0.0459001 - 3.16194i) q^{10} -1.00000i q^{11} +(-0.671903 + 1.76733i) q^{12} +(-0.367075 - 0.367075i) q^{13} +(2.17679 + 1.40865i) q^{14} +(-1.12259 - 1.79121i) q^{15} +(2.65735 - 2.98973i) q^{16} +(-4.85390 + 4.85390i) q^{17} +(-0.623994 - 2.91262i) q^{18} -5.29151 q^{19} +(0.873272 + 4.38605i) q^{20} +1.73325 q^{21} +(0.296256 + 1.38283i) q^{22} +(-1.85759 + 1.85759i) q^{23} +(0.405548 - 2.64299i) q^{24} +(-4.49978 - 2.17990i) q^{25} +(0.616353 + 0.398857i) q^{26} +(-3.41344 - 3.41344i) q^{27} +(-3.42746 - 1.30305i) q^{28} -1.93692i q^{29} +(2.08301 + 2.14438i) q^{30} +10.6576i q^{31} +(-2.78895 + 4.92156i) q^{32} +(0.668480 + 0.668480i) q^{33} +(5.27415 - 8.15014i) q^{34} +(3.47377 - 2.17708i) q^{35} +(1.72576 + 3.84281i) q^{36} +(3.70433 - 3.70433i) q^{37} +(7.31728 - 1.56764i) q^{38} +0.490765 q^{39} +(-2.50698 - 5.80647i) q^{40} +8.12416 q^{41} +(-2.39680 + 0.513485i) q^{42} +(2.42576 - 2.42576i) q^{43} +(-0.819345 - 1.82447i) q^{44} +(-4.59045 - 1.05336i) q^{45} +(2.01842 - 3.11906i) q^{46} +(5.93375 + 5.93375i) q^{47} +(0.222194 + 3.77496i) q^{48} -3.63864i q^{49} +(6.86826 + 1.68135i) q^{50} -6.48947i q^{51} +(-0.970478 - 0.368955i) q^{52} +(5.03769 + 5.03769i) q^{53} +(5.73147 + 3.70897i) q^{54} +(2.17942 + 0.500108i) q^{55} +(5.12565 + 0.786495i) q^{56} +(3.53727 - 3.53727i) q^{57} +(0.573822 + 2.67844i) q^{58} -9.15604 q^{59} +(-3.51575 - 2.34822i) q^{60} +4.48236 q^{61} +(-3.15738 - 14.7377i) q^{62} +(2.73059 - 2.73059i) q^{63} +(2.39861 - 7.63195i) q^{64} +(0.983590 - 0.616436i) q^{65} +(-1.12244 - 0.726357i) q^{66} +(6.03756 + 6.03756i) q^{67} +(-4.87875 + 12.8328i) q^{68} -2.48352i q^{69} +(-4.15868 + 4.03967i) q^{70} +4.69476i q^{71} +(-3.52490 - 4.80271i) q^{72} +(3.33887 + 3.33887i) q^{73} +(-4.02505 + 6.21990i) q^{74} +(4.46523 - 1.55080i) q^{75} +(-9.65417 + 4.33557i) q^{76} +(-1.29641 + 1.29641i) q^{77} +(-0.678647 + 0.145392i) q^{78} -1.35636 q^{79} +(5.18694 + 7.28668i) q^{80} -1.75517 q^{81} +(-11.2344 + 2.40683i) q^{82} +(7.25746 - 7.25746i) q^{83} +(3.16225 - 1.42013i) q^{84} +(-8.15123 - 13.0062i) q^{85} +(-2.63578 + 4.07307i) q^{86} +(1.29479 + 1.29479i) q^{87} +(1.67353 + 2.28020i) q^{88} +2.98804i q^{89} +(6.65990 + 0.0966780i) q^{90} +0.951760i q^{91} +(-1.86710 + 4.91112i) q^{92} +(-7.12440 - 7.12440i) q^{93} +(-9.96331 - 6.44749i) q^{94} +(2.64633 - 11.5324i) q^{95} +(-1.42561 - 5.15432i) q^{96} +(-5.42928 + 5.42928i) q^{97} +(1.07797 + 5.03164i) q^{98} +2.10627 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

)

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

$2$	−1.38283	+	0.296256i	−0.977812	+	0.209484i
$2$	−1.38283	+	0.296256i	−0.977812	+	0.209484i
$3$	−0.668480	+	0.668480i	−0.385947	+	0.385947i	−0.873239	−	0.487292i	$-0.837985\pi$
$3$	−0.668480	+	0.668480i	−0.385947	+	0.385947i	0.487292	+	0.873239i	$0.337985\pi$
$4$	1.82447	−	0.819345i	0.912233	−	0.409673i
$5$	−0.500108	+	2.17942i	−0.223655	+	0.974668i
$5$	−0.500108	+	2.17942i	−0.223655	+	0.974668i
$6$	0.726357	−	1.12244i	0.296534	−	0.458234i
$7$	−1.29641	−	1.29641i	−0.489997	−	0.489997i	0.418308	−	0.908305i	$-0.362623\pi$
$7$	−1.29641	−	1.29641i	−0.489997	−	0.489997i	−0.908305	+	0.418308i	$0.862623\pi$
$8$	−2.28020	+	1.67353i	−0.806172	+	0.591681i
$9$			2.10627i			0.702090i
$10$	0.0459001	−	3.16194i	0.0145149	−	0.999895i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−0.671903	+	1.76733i	−0.193962	+	0.510186i
$13$	−0.367075	−	0.367075i	−0.101808	−	0.101808i	0.654368	−	0.756176i	$-0.272935\pi$
$13$	−0.367075	−	0.367075i	−0.101808	−	0.101808i	−0.756176	+	0.654368i	$0.772935\pi$
$14$	2.17679	+	1.40865i	0.581772	+	0.376478i
$15$	−1.12259	−	1.79121i	−0.289851	−	0.462490i
$16$	2.65735	−	2.98973i	0.664337	−	0.747433i
$17$	−4.85390	+	4.85390i	−1.17724	+	1.17724i	−0.196800	+	0.980444i	$0.563055\pi$
$17$	−4.85390	+	4.85390i	−1.17724	+	1.17724i	−0.980444	+	0.196800i	$0.936945\pi$
$18$	−0.623994	−	2.91262i	−0.147077	−	0.686512i
$19$	−5.29151			−1.21395			−0.606977	−	0.794719i	$-0.707618\pi$
$19$	−5.29151			−1.21395			−0.606977	+	0.794719i	$0.707618\pi$
$20$	0.873272	+	4.38605i	0.195269	+	0.980750i
$21$	1.73325			0.378226
$22$	0.296256	+	1.38283i	0.0631619	+	0.294821i
$23$	−1.85759	+	1.85759i	−0.387334	+	0.387334i	−0.873736	−	0.486401i	$-0.838309\pi$
$23$	−1.85759	+	1.85759i	−0.387334	+	0.387334i	0.486401	+	0.873736i	$0.338309\pi$
$24$	0.405548	−	2.64299i	0.0827821	−	0.539498i
$25$	−4.49978	−	2.17990i	−0.899957	−	0.435979i
$26$	0.616353	+	0.398857i	0.120877	+	0.0782222i
$27$	−3.41344	−	3.41344i	−0.656917	−	0.656917i
$28$	−3.42746	−	1.30305i	−0.647729	−	0.246253i
$29$		−	1.93692i		−	0.359676i	−0.983696	−	0.179838i	$-0.942443\pi$
$29$		−	1.93692i		−	0.359676i	0.983696	−	0.179838i	$-0.0575574\pi$
$30$	2.08301	+	2.14438i	0.380305	+	0.391509i
$31$			10.6576i			1.91416i	0.289818	+	0.957082i	$0.406405\pi$
$31$			10.6576i			1.91416i	−0.289818	+	0.957082i	$0.593595\pi$
$32$	−2.78895	+	4.92156i	−0.493021	+	0.870018i
$33$	0.668480	+	0.668480i	0.116367	+	0.116367i
$34$	5.27415	−	8.15014i	0.904509	−	1.39774i
$35$	3.47377	−	2.17708i	0.587175	−	0.367994i
$36$	1.72576	+	3.84281i	0.287627	+	0.640469i
$37$	3.70433	−	3.70433i	0.608988	−	0.608988i	−0.333694	−	0.942682i	$-0.608295\pi$
$37$	3.70433	−	3.70433i	0.608988	−	0.608988i	0.942682	+	0.333694i	$0.108295\pi$
$38$	7.31728	−	1.56764i	1.18702	−	0.254305i
$39$	0.490765			0.0785853
$40$	−2.50698	−	5.80647i	−0.396389	−	0.918083i
$41$	8.12416			1.26878			0.634390	−	0.773013i	$-0.281251\pi$
$41$	8.12416			1.26878			0.634390	+	0.773013i	$0.281251\pi$
$42$	−2.39680	+	0.513485i	−0.369834	+	0.0792324i
$43$	2.42576	−	2.42576i	0.369925	−	0.369925i	−0.497525	−	0.867450i	$-0.665758\pi$
$43$	2.42576	−	2.42576i	0.369925	−	0.369925i	0.867450	+	0.497525i	$0.165758\pi$
$44$	−0.819345	−	1.82447i	−0.123521	−	0.275048i
$45$	−4.59045	−	1.05336i	−0.684304	−	0.157026i
$46$	2.01842	−	3.11906i	0.297600	−	0.459881i
$47$	5.93375	+	5.93375i	0.865527	+	0.865527i	0.991973	−	0.126447i	$-0.0403573\pi$
$47$	5.93375	+	5.93375i	0.865527	+	0.865527i	−0.126447	+	0.991973i	$0.540357\pi$
$48$	0.222194	+	3.77496i	0.0320710	+	0.544869i
$49$		−	3.63864i		−	0.519806i
$50$	6.86826	+	1.68135i	0.971319	+	0.237779i
$51$		−	6.48947i		−	0.908708i
$52$	−0.970478	−	0.368955i	−0.134581	−	0.0511648i
$53$	5.03769	+	5.03769i	0.691980	+	0.691980i	0.962667	−	0.270687i	$-0.0872510\pi$
$53$	5.03769	+	5.03769i	0.691980	+	0.691980i	−0.270687	+	0.962667i	$0.587251\pi$
$54$	5.73147	+	3.70897i	0.779955	+	0.504727i
$55$	2.17942	+	0.500108i	0.293874	+	0.0674346i
$56$	5.12565	+	0.786495i	0.684944	+	0.105100i
$57$	3.53727	−	3.53727i	0.468523	−	0.468523i
$58$	0.573822	+	2.67844i	0.0753466	+	0.351696i
$59$	−9.15604			−1.19201			−0.596007	−	0.802979i	$-0.703247\pi$
$59$	−9.15604			−1.19201			−0.596007	+	0.802979i	$0.703247\pi$
$60$	−3.51575	−	2.34822i	−0.453881	−	0.303154i
$61$	4.48236			0.573908			0.286954	−	0.957944i	$-0.407357\pi$
$61$	4.48236			0.573908			0.286954	+	0.957944i	$0.407357\pi$
$62$	−3.15738	−	14.7377i	−0.400987	−	1.87169i
$63$	2.73059	−	2.73059i	0.344022	−	0.344022i
$64$	2.39861	−	7.63195i	0.299827	−	0.953994i
$65$	0.983590	−	0.616436i	0.121999	−	0.0764594i
$66$	−1.12244	−	0.726357i	−0.138163	−	0.0894083i
$67$	6.03756	+	6.03756i	0.737605	+	0.737605i	0.972114	−	0.234509i	$-0.0753482\pi$
$67$	6.03756	+	6.03756i	0.737605	+	0.737605i	−0.234509	+	0.972114i	$0.575348\pi$
$68$	−4.87875	+	12.8328i	−0.591636	+	1.55620i
$69$		−	2.48352i		−	0.298981i
$70$	−4.15868	+	4.03967i	−0.497058	+	0.482833i
$71$			4.69476i			0.557166i	0.960412	+	0.278583i	$0.0898647\pi$
$71$			4.69476i			0.557166i	−0.960412	+	0.278583i	$0.910135\pi$
$72$	−3.52490	−	4.80271i	−0.415413	−	0.566005i
$73$	3.33887	+	3.33887i	0.390785	+	0.390785i	0.874967	−	0.484182i	$-0.160883\pi$
$73$	3.33887	+	3.33887i	0.390785	+	0.390785i	−0.484182	+	0.874967i	$0.660883\pi$
$74$	−4.02505	+	6.21990i	−0.467902	+	0.723049i
$75$	4.46523	−	1.55080i	0.515601	−	0.179071i
$76$	−9.65417	+	4.33557i	−1.10741	+	0.497324i
$77$	−1.29641	+	1.29641i	−0.147740	+	0.147740i
$78$	−0.678647	+	0.145392i	−0.0768417	+	0.0164624i
$79$	−1.35636			−0.152602			−0.0763009	−	0.997085i	$-0.524311\pi$
$79$	−1.35636			−0.152602			−0.0763009	+	0.997085i	$0.524311\pi$
$80$	5.18694	+	7.28668i	0.579917	+	0.814675i
$81$	−1.75517			−0.195019
$82$	−11.2344	+	2.40683i	−1.24063	+	0.265790i
$83$	7.25746	−	7.25746i	0.796609	−	0.796609i	−0.185950	−	0.982559i	$-0.559536\pi$
$83$	7.25746	−	7.25746i	0.796609	−	0.796609i	0.982559	+	0.185950i	$0.0595363\pi$
$84$	3.16225	−	1.42013i	0.345030	−	0.154949i
$85$	−8.15123	−	13.0062i	−0.884125	−	1.41072i
$86$	−2.63578	+	4.07307i	−0.284224	+	0.439210i
$87$	1.29479	+	1.29479i	0.138816	+	0.138816i
$88$	1.67353	+	2.28020i	0.178399	+	0.243070i
$89$			2.98804i			0.316732i	0.987381	+	0.158366i	$0.0506225\pi$
$89$			2.98804i			0.316732i	−0.987381	+	0.158366i	$0.949377\pi$
$90$	6.65990	+	0.0966780i	0.702016	+	0.0101908i
$91$			0.951760i			0.0997716i
$92$	−1.86710	+	4.91112i	−0.194659	+	0.512019i
$93$	−7.12440	−	7.12440i	−0.738766	−	0.738766i
$94$	−9.96331	−	6.44749i	−1.02764	−	0.665008i
$95$	2.64633	−	11.5324i	0.271507	−	1.18320i
$96$	−1.42561	−	5.15432i	−0.145501	−	0.526061i
$97$	−5.42928	+	5.42928i	−0.551260	+	0.551260i	−0.926804	−	0.375545i	$-0.877456\pi$
$97$	−5.42928	+	5.42928i	−0.551260	+	0.551260i	0.375545	+	0.926804i	$0.377456\pi$
$98$	1.07797	+	5.03164i	0.108891	+	0.508273i
$99$	2.10627			0.211688
$100$	−9.99579	−	0.290267i	−0.999579	−	0.0290267i
$101$	−7.54185			−0.750442			−0.375221	−	0.926935i	$-0.622433\pi$
$101$	−7.54185			−0.750442			−0.375221	+	0.926935i	$0.622433\pi$
$102$	1.92254	+	8.97387i	0.190360	+	0.888545i
$103$	1.50798	−	1.50798i	0.148586	−	0.148586i	−0.628900	−	0.777486i	$-0.716495\pi$
$103$	1.50798	−	1.50798i	0.148586	−	0.148586i	0.777486	+	0.628900i	$0.216495\pi$
$104$	1.45132	+	0.222694i	0.142313	+	0.0218370i
$105$	−0.866812	+	3.77748i	−0.0845922	+	0.368645i
$106$	−8.45874	−	5.47385i	−0.821585	−	0.531667i
$107$	−7.82546	−	7.82546i	−0.756516	−	0.756516i	0.219171	−	0.975686i	$-0.429665\pi$
$107$	−7.82546	−	7.82546i	−0.756516	−	0.756516i	−0.975686	+	0.219171i	$0.929665\pi$
$108$	−9.02449	−	3.43092i	−0.868382	−	0.330140i
$109$			10.8635i			1.04053i	0.854004	+	0.520266i	$0.174167\pi$
$109$			10.8635i			1.04053i	−0.854004	+	0.520266i	$0.825833\pi$
$110$	−3.16194	−	0.0459001i	−0.301480	−	0.00437640i
$111$			4.95254i			0.470074i
$112$	−7.32093	+	0.430910i	−0.691763	+	0.0407172i
$113$	−5.25469	−	5.25469i	−0.494320	−	0.494320i	0.415344	−	0.909664i	$-0.363661\pi$
$113$	−5.25469	−	5.25469i	−0.494320	−	0.494320i	−0.909664	+	0.415344i	$0.863661\pi$
$114$	−3.84352	+	5.93939i	−0.359979	+	0.556275i
$115$	−3.11948	−	4.97747i	−0.290893	−	0.464152i
$116$	−1.58700	−	3.53384i	−0.147350	−	0.328108i
$117$	0.773159	−	0.773159i	0.0714786	−	0.0714786i
$118$	12.6613	−	2.71253i	1.16557	−	0.249708i
$119$	12.5853			1.15369
$120$	5.55737	+	2.20564i	0.507317	+	0.201346i
$121$	−1.00000			−0.0909091
$122$	−6.19837	+	1.32793i	−0.561174	+	0.120225i
$123$	−5.43084	+	5.43084i	−0.489682	+	0.489682i
$124$	8.73226	+	19.4444i	0.784180	+	1.74616i
$125$	7.00130	−	8.71676i	0.626215	−	0.779650i
$126$	−2.96700	+	4.58490i	−0.264321	+	0.408456i
$127$	14.4872	+	14.4872i	1.28553	+	1.28553i	0.937471	+	0.348062i	$0.113160\pi$
$127$	14.4872	+	14.4872i	1.28553	+	1.28553i	0.348062	+	0.937471i	$0.386840\pi$
$128$	−1.05588	+	11.2643i	−0.0933273	+	0.995635i
$129$			3.24314i			0.285543i
$130$	−1.17752	+	1.14382i	−0.103275	+	0.100320i
$131$			15.9254i			1.39141i	0.718327	+	0.695706i	$0.244908\pi$
$131$			15.9254i			1.39141i	−0.718327	+	0.695706i	$0.755092\pi$
$132$	1.76733	+	0.671903i	0.153827	+	0.0584816i
$133$	6.85996	+	6.85996i	0.594834	+	0.594834i
$134$	−10.1376	−	6.56029i	−0.875756	−	0.566723i
$135$	9.14642	−	5.73225i	0.787199	−	0.493353i
$136$	2.94472	−	19.1910i	0.252508	−	1.64561i
$137$	2.78490	−	2.78490i	0.237930	−	0.237930i	−0.578063	−	0.815992i	$-0.696191\pi$
$137$	2.78490	−	2.78490i	0.237930	−	0.237930i	0.815992	+	0.578063i	$0.196191\pi$
$138$	0.735758	+	3.43430i	0.0626319	+	0.292347i
$139$	−9.60303			−0.814519			−0.407259	−	0.913313i	$-0.633515\pi$
$139$	−9.60303			−0.814519			−0.407259	+	0.913313i	$0.633515\pi$
$140$	4.55400	−	6.81823i	0.384883	−	0.576246i
$141$	−7.93319			−0.668095
$142$	−1.39085	−	6.49208i	−0.116718	−	0.544804i
$143$	−0.367075	+	0.367075i	−0.0306964	+	0.0306964i
$144$	6.29718	+	5.59709i	0.524765	+	0.466424i
$145$	4.22136	+	0.968667i	0.350565	+	0.0804434i
$146$	−5.60626	−	3.62794i	−0.463977	−	0.300251i
$147$	2.43236	+	2.43236i	0.200618	+	0.200618i
$148$	3.72329	−	9.79354i	0.306053	−	0.805024i
$149$			17.8000i			1.45823i	0.684389	+	0.729117i	$0.260069\pi$
$149$			17.8000i			1.45823i	−0.684389	+	0.729117i	$0.739931\pi$
$150$	−5.71525	+	3.46735i	−0.466648	+	0.283108i
$151$			0.874494i			0.0711653i	0.999367	+	0.0355827i	$0.0113287\pi$
$151$			0.874494i			0.0711653i	−0.999367	+	0.0355827i	$0.988671\pi$
$152$	12.0657	−	8.85548i	0.978657	−	0.718274i
$153$	−10.2236	−	10.2236i	−0.826530	−	0.826530i
$154$	1.40865	−	2.17679i	0.113512	−	0.175411i
$155$	−23.2275	−	5.32996i	−1.86567	−	0.428113i
$156$	0.895384	−	0.402106i	0.0716881	−	0.0321943i
$157$	8.41956	−	8.41956i	0.671954	−	0.671954i	−0.286212	−	0.958166i	$-0.592396\pi$
$157$	8.41956	−	8.41956i	0.671954	−	0.671954i	0.958166	+	0.286212i	$0.0923962\pi$
$158$	1.87562	−	0.401828i	0.149216	−	0.0319677i
$159$	−6.73519			−0.534135
$160$	−9.33140	−	8.53961i	−0.737712	−	0.675116i
$161$	4.81640			0.379585
$162$	2.42711	−	0.519980i	0.190692	−	0.0408535i
$163$	5.64237	−	5.64237i	0.441945	−	0.441945i	−0.450721	−	0.892665i	$-0.648833\pi$
$163$	5.64237	−	5.64237i	0.441945	−	0.441945i	0.892665	+	0.450721i	$0.148833\pi$
$164$	14.8222	−	6.65649i	1.15742	−	0.519785i
$165$	−1.79121	+	1.12259i	−0.139446	+	0.0873935i
$166$	−7.88580	+	12.1859i	−0.612057	+	0.945811i
$167$	−6.54275	−	6.54275i	−0.506293	−	0.506293i	0.407093	−	0.913386i	$-0.366542\pi$
$167$	−6.54275	−	6.54275i	−0.506293	−	0.506293i	−0.913386	+	0.407093i	$0.866542\pi$
$168$	−3.95215	+	2.90064i	−0.304915	+	0.223789i
$169$		−	12.7305i		−	0.979270i
$170$	15.1250	+	15.5706i	1.16003	+	1.19421i
$171$		−	11.1453i		−	0.852305i
$172$	2.43818	−	6.41325i	0.185909	−	0.489006i
$173$	−10.2127	−	10.2127i	−0.776459	−	0.776459i	0.202768	−	0.979227i	$-0.435006\pi$
$173$	−10.2127	−	10.2127i	−0.776459	−	0.776459i	−0.979227	+	0.202768i	$0.935006\pi$
$174$	−2.17407	−	1.40689i	−0.164816	−	0.106656i
$175$	3.00753	+	8.65960i	0.227348	+	0.654604i
$176$	−2.98973	−	2.65735i	−0.225360	−	0.200305i
$177$	6.12063	−	6.12063i	0.460055	−	0.460055i
$178$	−0.885224	−	4.13197i	−0.0663503	−	0.309704i
$179$	−13.4491			−1.00523			−0.502615	−	0.864511i	$-0.667629\pi$
$179$	−13.4491			−1.00523			−0.502615	+	0.864511i	$0.667629\pi$
$180$	−9.23819	+	1.83934i	−0.688574	+	0.137097i
$181$	12.9203			0.960359			0.480179	−	0.877170i	$-0.340572\pi$
$181$	12.9203			0.960359			0.480179	+	0.877170i	$0.340572\pi$
$182$	−0.281964	−	1.31613i	−0.0209006	−	0.0975579i
$183$	−2.99637	+	2.99637i	−0.221498	+	0.221498i
$184$	1.12695	−	7.34440i	0.0830796	−	0.541437i
$185$	6.22074	+	9.92587i	0.457358	+	0.729764i
$186$	11.9625	+	7.74123i	0.877134	+	0.567614i
$187$	4.85390	+	4.85390i	0.354952	+	0.354952i
$188$	15.6877	+	5.96413i	1.14414	+	0.434979i
$189$			8.85043i			0.643774i
$190$	−0.242881	+	16.7315i	−0.0176204	+	1.21383i
$191$		−	8.60539i		−	0.622664i	−0.950301	−	0.311332i	$-0.899225\pi$
$191$		−	8.60539i		−	0.622664i	0.950301	−	0.311332i	$-0.100775\pi$
$192$	3.49838	+	6.70523i	0.252474	+	0.483908i
$193$	7.88625	+	7.88625i	0.567665	+	0.567665i	0.931474	−	0.363809i	$-0.118524\pi$
$193$	7.88625	+	7.88625i	0.567665	+	0.567665i	−0.363809	+	0.931474i	$0.618524\pi$
$194$	5.89934	−	9.11625i	0.423548	−	0.654509i
$195$	−0.245436	+	1.06959i	−0.0175760	+	0.0765946i
$196$	−2.98130	−	6.63858i	−0.212950	−	0.474184i
$197$	0.119539	−	0.119539i	0.00851678	−	0.00851678i	−0.702836	−	0.711352i	$-0.748083\pi$
$197$	0.119539	−	0.119539i	0.00851678	−	0.00851678i	0.711352	+	0.702836i	$0.248083\pi$
$198$	−2.91262	+	0.623994i	−0.206991	+	0.0443453i
$199$	19.0177			1.34813			0.674065	−	0.738672i	$-0.264547\pi$
$199$	19.0177			1.34813			0.674065	+	0.738672i	$0.264547\pi$
$200$	13.9085	−	2.55992i	0.983481	−	0.181013i
$201$	−8.07198			−0.569353
$202$	10.4291	−	2.23432i	0.733791	−	0.157206i
$203$	−2.51104	+	2.51104i	−0.176240	+	0.176240i
$204$	−5.31712	−	11.8398i	−0.372273	−	0.828953i
$205$	−4.06296	+	17.7060i	−0.283769	+	1.23664i
$206$	−1.63855	+	2.53204i	−0.114163	+	0.176416i
$207$	−3.91258	−	3.91258i	−0.271943	−	0.271943i
$208$	−2.07290	+	0.122011i	−0.143730	+	0.00845995i
$209$			5.29151i			0.366021i
$210$	0.0795563	−	5.48044i	0.00548991	−	0.378186i
$211$		−	22.3887i		−	1.54131i	−0.637256	−	0.770653i	$-0.719930\pi$
$211$		−	22.3887i		−	1.54131i	0.637256	−	0.770653i	$-0.280070\pi$
$212$	13.3187	+	5.06348i	0.914732	+	0.347761i
$213$	−3.13836	−	3.13836i	−0.215037	−	0.215037i
$214$	13.1397	+	8.50298i	0.898208	+	0.581252i
$215$	4.07362	+	6.49990i	0.277818	+	0.443290i
$216$	13.4958	+	2.07084i	0.918273	+	0.140903i
$217$	13.8166	−	13.8166i	0.937934	−	0.937934i
$218$	−3.21837	−	15.0224i	−0.217975	−	1.01745i
$219$	−4.46393			−0.301645
$220$	4.38605	−	0.873272i	0.295707	−	0.0588760i
$221$	3.56349			0.239707
$222$	−1.46722	−	6.84854i	−0.0984732	−	0.459644i
$223$	−18.6892	+	18.6892i	−1.25152	+	1.25152i	−0.296482	+	0.955038i	$0.595814\pi$
$223$	−18.6892	+	18.6892i	−1.25152	+	1.25152i	−0.955038	+	0.296482i	$0.904186\pi$
$224$	9.99598	−	2.76474i	0.667885	−	0.184727i
$225$	4.59145	−	9.47775i	0.306096	−	0.631850i
$226$	8.82311	+	5.70964i	0.586904	+	0.379800i
$227$	3.19376	+	3.19376i	0.211978	+	0.211978i	0.805107	−	0.593130i	$-0.202108\pi$
$227$	3.19376	+	3.19376i	0.211978	+	0.211978i	−0.593130	+	0.805107i	$0.702108\pi$
$228$	3.55538	−	9.35186i	0.235461	−	0.619342i
$229$			16.8873i			1.11594i	0.829860	+	0.557972i	$0.188421\pi$
$229$			16.8873i			1.11594i	−0.829860	+	0.557972i	$0.811579\pi$
$230$	5.78833	+	5.95886i	0.381671	+	0.392916i
$231$		−	1.73325i		−	0.114039i
$232$	3.24148	+	4.41655i	0.212814	+	0.289961i
$233$	1.11453	+	1.11453i	0.0730150	+	0.0730150i	0.742671	−	0.669656i	$-0.233559\pi$
$233$	1.11453	+	1.11453i	0.0730150	+	0.0730150i	−0.669656	+	0.742671i	$0.733559\pi$
$234$	−0.840099	+	1.29820i	−0.0549190	+	0.0848663i
$235$	−15.8997	+	9.96465i	−1.03718	+	0.650022i
$236$	−16.7049	+	7.50196i	−1.08739	+	0.488336i
$237$	0.906696	−	0.906696i	0.0588963	−	0.0588963i
$238$	−17.4034	+	3.72846i	−1.12809	+	0.241680i
$239$	−4.23222			−0.273759			−0.136880	−	0.990588i	$-0.543707\pi$
$239$	−4.23222			−0.273759			−0.136880	+	0.990588i	$0.543707\pi$
$240$	−8.33836	−	1.40363i	−0.538239	−	0.0906041i
$241$	−10.5664			−0.680641			−0.340321	−	0.940309i	$-0.610536\pi$
$241$	−10.5664			−0.680641			−0.340321	+	0.940309i	$0.610536\pi$
$242$	1.38283	−	0.296256i	0.0888920	−	0.0190440i
$243$	11.4136	−	11.4136i	0.732184	−	0.732184i
$244$	8.17792	−	3.67260i	0.523537	−	0.235114i
$245$	7.93015	+	1.81971i	0.506639	+	0.116257i
$246$	5.90104	−	9.11887i	0.376236	−	0.581398i
$247$	1.94238	+	1.94238i	0.123591	+	0.123591i
$248$	−17.8358	−	24.3015i	−1.13257	−	1.54315i
$249$			9.70293i			0.614898i
$250$	−7.09925	+	14.1280i	−0.448996	+	0.893534i
$251$			7.97831i			0.503587i	0.967781	+	0.251793i	$0.0810203\pi$
$251$			7.97831i			0.503587i	−0.967781	+	0.251793i	$0.918980\pi$
$252$	2.74457	−	7.21916i	0.172892	−	0.454764i
$253$	1.85759	+	1.85759i	0.116786	+	0.116786i
$254$	−24.3254	−	15.7415i	−1.52631	−	0.987711i
$255$	14.1433	+	3.24544i	0.885689	+	0.203237i
$256$	−1.87702	−	15.8895i	−0.117314	−	0.993095i
$257$	−17.9535	+	17.9535i	−1.11991	+	1.11991i	−0.128151	+	0.991755i	$0.540904\pi$
$257$	−17.9535	+	17.9535i	−1.11991	+	1.11991i	−0.991755	+	0.128151i	$0.959096\pi$
$258$	−0.960800	−	4.48473i	−0.0598168	−	0.279207i
$259$	−9.60465			−0.596804
$260$	1.28945	−	1.93057i	0.0799685	−	0.119729i
$261$	4.07967			0.252525
$262$	−4.71800	−	22.0222i	−0.291479	−	1.36054i
$263$	9.67785	−	9.67785i	0.596762	−	0.596762i	−0.342687	−	0.939449i	$-0.611337\pi$
$263$	9.67785	−	9.67785i	0.596762	−	0.596762i	0.939449	+	0.342687i	$0.111337\pi$
$264$	−2.64299	−	0.405548i	−0.162665	−	0.0249597i
$265$	−13.4987	+	8.45988i	−0.829216	+	0.519686i
$266$	−11.5185	−	7.45389i	−0.706244	−	0.457028i
$267$	−1.99745	−	1.99745i	−0.122242	−	0.122242i
$268$	15.9622	+	6.06847i	0.975044	+	0.370691i
$269$		−	26.4122i		−	1.61038i	−0.593018	−	0.805189i	$-0.702064\pi$
$269$		−	26.4122i		−	1.61038i	0.593018	−	0.805189i	$-0.297936\pi$
$270$	−10.9498	+	10.6364i	−0.666383	+	0.647312i
$271$			31.3605i			1.90501i	0.304518	+	0.952506i	$0.401505\pi$
$271$			31.3605i			1.90501i	−0.304518	+	0.952506i	$0.598495\pi$
$272$	1.61337	+	27.4104i	0.0978251	+	1.66200i
$273$	−0.636233	−	0.636233i	−0.0385066	−	0.0385066i
$274$	−3.02601	+	4.67609i	−0.182808	+	0.282493i
$275$	−2.17990	+	4.49978i	−0.131453	+	0.271347i
$276$	−2.03486	−	4.53110i	−0.122484	−	0.272740i
$277$	2.99711	−	2.99711i	0.180079	−	0.180079i	−0.611311	−	0.791390i	$-0.709358\pi$
$277$	2.99711	−	2.99711i	0.180079	−	0.180079i	0.791390	+	0.611311i	$0.209358\pi$
$278$	13.2794	−	2.84495i	0.796446	−	0.170629i
$279$	−22.4478			−1.34391
$280$	−4.27749	+	10.7776i	−0.255629	+	0.644087i
$281$	−8.14685			−0.486000			−0.243000	−	0.970026i	$-0.578132\pi$
$281$	−8.14685			−0.486000			−0.243000	+	0.970026i	$0.578132\pi$
$282$	10.9703	−	2.35025i	0.653271	−	0.139955i
$283$	−17.7814	+	17.7814i	−1.05699	+	1.05699i	−0.0587187	+	0.998275i	$0.518701\pi$
$283$	−17.7814	+	17.7814i	−1.05699	+	1.05699i	−0.998275	+	0.0587187i	$0.981299\pi$
$284$	3.84663	+	8.56543i	0.228256	+	0.508265i
$285$	5.94019	+	9.47822i	0.351867	+	0.561442i
$286$	0.398857	−	0.616353i	0.0235849	−	0.0364457i
$287$	−10.5322	−	10.5322i	−0.621699	−	0.621699i
$288$	−10.3661	−	5.87427i	−0.610830	−	0.346145i
$289$		−	30.1207i		−	1.77180i
$290$	−6.12442	−	0.0889047i	−0.359638	−	0.00522066i
$291$		−	7.25873i		−	0.425514i
$292$	8.82733	+	3.35596i	0.516581	+	0.196393i
$293$	−7.56643	−	7.56643i	−0.442036	−	0.442036i	0.450660	−	0.892696i	$-0.351189\pi$
$293$	−7.56643	−	7.56643i	−0.442036	−	0.442036i	−0.892696	+	0.450660i	$0.851189\pi$
$294$	−4.08415	−	2.64295i	−0.238193	−	0.154140i
$295$	4.57901	−	19.9549i	0.266600	−	1.16182i
$296$	−2.24731	+	14.6459i	−0.130622	+	0.851275i
$297$	−3.41344	+	3.41344i	−0.198068	+	0.198068i
$298$	−5.27335	−	24.6145i	−0.305477	−	1.42588i
$299$	1.36375			0.0788678
$300$	6.87602	−	6.48795i	0.396987	−	0.374582i
$301$	−6.28956			−0.362524
$302$	−0.259074	−	1.20928i	−0.0149080	−	0.0695863i
$303$	5.04158	−	5.04158i	0.289631	−	0.289631i
$304$	−14.0614	+	15.8202i	−0.806475	+	0.907351i
$305$	−2.24167	+	9.76897i	−0.128357	+	0.559370i
$306$	17.1664	+	11.1088i	0.981336	+	0.635046i
$307$	−8.34298	−	8.34298i	−0.476159	−	0.476159i	0.427742	−	0.903901i	$-0.359309\pi$
$307$	−8.34298	−	8.34298i	−0.476159	−	0.476159i	−0.903901	+	0.427742i	$0.859309\pi$
$308$	−1.30305	+	3.42746i	−0.0742480	+	0.195298i
$309$			2.01612i			0.114693i
$310$	33.6988	+	0.489186i	1.91396	+	0.0277839i
$311$		−	7.13322i		−	0.404488i	−0.979335	−	0.202244i	$-0.935177\pi$
$311$		−	7.13322i		−	0.404488i	0.979335	−	0.202244i	$-0.0648233\pi$
$312$	−1.11904	+	0.821309i	−0.0633533	+	0.0464975i
$313$	16.1315	+	16.1315i	0.911808	+	0.911808i	0.996414	−	0.0846064i	$-0.0269633\pi$
$313$	16.1315	+	16.1315i	0.911808	+	0.911808i	−0.0846064	+	0.996414i	$0.526963\pi$
$314$	−9.14852	+	14.1372i	−0.516281	+	0.797809i
$315$	4.58552	+	7.31670i	0.258365	+	0.412249i
$316$	−2.47462	+	1.11132i	−0.139208	+	0.0625168i
$317$	−9.02301	+	9.02301i	−0.506783	+	0.506783i	−0.913537	−	0.406755i	$-0.866660\pi$
$317$	−9.02301	+	9.02301i	−0.506783	+	0.506783i	0.406755	+	0.913537i	$0.366660\pi$
$318$	9.31366	−	1.99534i	0.522284	−	0.111893i
$319$	−1.93692			−0.108446
$320$	15.4337	+	9.04439i	0.862770	+	0.505597i
$321$	10.4623			0.583950
$322$	−6.66028	+	1.42688i	−0.371163	+	0.0795172i
$323$	25.6844	−	25.6844i	1.42912	−	1.42912i
$324$	−3.20225	+	1.43809i	−0.177903	+	0.0798940i
$325$	0.851574	+	2.45195i	0.0472368	+	0.136009i
$326$	−6.13088	+	9.47405i	−0.339558	+	0.524719i
$327$	−7.26202	−	7.26202i	−0.401591	−	0.401591i
$328$	−18.5247	+	13.5960i	−1.02286	+	0.750714i
$329$		−	15.3852i		−	0.848211i
$330$	2.14438	−	2.08301i	0.118044	−	0.114666i
$331$		−	17.2364i		−	0.947398i	−0.880687	−	0.473699i	$-0.842918\pi$
$331$		−	17.2364i		−	0.947398i	0.880687	−	0.473699i	$-0.157082\pi$
$332$	7.29461	−	19.1873i	0.400344	−	1.05304i
$333$	7.80231	+	7.80231i	0.427564	+	0.427564i
$334$	10.9859	+	7.10921i	0.601120	+	0.388999i
$335$	−16.1778	+	10.1390i	−0.883890	+	0.553951i
$336$	4.60584	−	5.18195i	0.251269	−	0.282699i
$337$	1.99124	−	1.99124i	0.108470	−	0.108470i	−0.650789	−	0.759259i	$-0.725562\pi$
$337$	1.99124	−	1.99124i	0.108470	−	0.108470i	0.759259	+	0.650789i	$0.225562\pi$
$338$	3.77149	+	17.6042i	0.205142	+	0.957542i
$339$	7.02532			0.381563
$340$	−25.5282	−	17.0507i	−1.38446	−	0.924702i
$341$	10.6576			0.577142
$342$	3.30187	+	15.4122i	0.178545	+	0.833394i
$343$	−13.7920	+	13.7920i	−0.744700	+	0.744700i
$344$	−1.47164	+	9.59079i	−0.0793455	+	0.517101i
$345$	5.41265	+	1.24203i	0.291408	+	0.0668687i
$346$	17.1481	+	11.0969i	0.921887	+	0.596575i
$347$	12.2542	+	12.2542i	0.657842	+	0.657842i	0.954869	−	0.297027i	$-0.0959953\pi$
$347$	12.2542	+	12.2542i	0.657842	+	0.657842i	−0.297027	+	0.954869i	$0.595995\pi$
$348$	3.42318	+	1.30142i	0.183502	+	0.0697634i
$349$			16.0748i			0.860464i	0.902718	+	0.430232i	$0.141568\pi$
$349$			16.0748i			0.860464i	−0.902718	+	0.430232i	$0.858432\pi$
$350$	−6.72437	−	11.0838i	−0.359433	−	0.592454i
$351$			2.50598i			0.133759i
$352$	4.92156	+	2.78895i	0.262320	+	0.148651i
$353$	−17.7559	−	17.7559i	−0.945051	−	0.945051i	0.0535158	−	0.998567i	$-0.482957\pi$
$353$	−17.7559	−	17.7559i	−0.945051	−	0.945051i	−0.998567	+	0.0535158i	$0.982957\pi$
$354$	−6.65055	+	10.2771i	−0.353473	+	0.546221i
$355$	−10.2319	−	2.34789i	−0.543052	−	0.124613i
$356$	2.44824	+	5.45158i	0.129756	+	0.288933i
$357$	−8.41302	+	8.41302i	−0.445264	+	0.445264i
$358$	18.5978	−	3.98436i	0.982925	−	0.210580i
$359$	36.1440			1.90761			0.953804	−	0.300429i	$-0.0971300\pi$
$359$	36.1440			1.90761			0.953804	+	0.300429i	$0.0971300\pi$
$360$	12.2300	−	5.28038i	0.644576	−	0.278300i
$361$	9.00005			0.473687
$362$	−17.8667	+	3.82771i	−0.939051	+	0.201180i
$363$	0.668480	−	0.668480i	0.0350861	−	0.0350861i
$364$	0.779820	+	1.73645i	0.0408737	+	0.0910149i
$365$	−8.94661	+	5.60702i	−0.468287	+	0.293485i
$366$	3.25579	−	5.03118i	0.170183	−	0.262984i
$367$	13.3243	+	13.3243i	0.695521	+	0.695521i	0.963441	−	0.267920i	$-0.0863363\pi$
$367$	13.3243	+	13.3243i	0.695521	+	0.695521i	−0.267920	+	0.963441i	$0.586336\pi$
$368$	0.617439	+	10.4900i	0.0321862	+	0.546827i
$369$			17.1117i			0.890798i
$370$	−11.5428	−	11.8829i	−0.600084	−	0.617763i
$371$		−	13.0618i		−	0.678136i
$372$	−18.8356	−	7.16088i	−0.976579	−	0.371274i
$373$	−5.64022	−	5.64022i	−0.292040	−	0.292040i	0.545846	−	0.837886i	$-0.316208\pi$
$373$	−5.64022	−	5.64022i	−0.292040	−	0.292040i	−0.837886	+	0.545846i	$0.816208\pi$
$374$	−8.15014	−	5.27415i	−0.421434	−	0.272720i
$375$	1.14675	+	10.5072i	0.0592180	+	0.542590i
$376$	−23.4604	−	3.59984i	−1.20988	−	0.185647i
$377$	−0.710994	+	0.710994i	−0.0366181	+	0.0366181i
$378$	−2.62199	−	12.2387i	−0.134861	−	0.629490i
$379$	24.6120			1.26423			0.632116	−	0.774874i	$-0.282187\pi$
$379$	24.6120			1.26423			0.632116	+	0.774874i	$0.282187\pi$
$380$	−4.62092	−	23.2088i	−0.237048	−	1.19059i
$381$	−19.3689			−0.992296
$382$	2.54939	+	11.8998i	0.130438	+	0.608848i
$383$	4.11209	−	4.11209i	0.210118	−	0.210118i	−0.594200	−	0.804318i	$-0.702531\pi$
$383$	4.11209	−	4.11209i	0.210118	−	0.210118i	0.804318	+	0.594200i	$0.202531\pi$
$384$	−6.82415	−	8.23581i	−0.348243	−	0.420282i
$385$	−2.17708	−	3.47377i	−0.110954	−	0.177040i
$386$	−13.2417	−	8.56904i	−0.673987	−	0.436153i
$387$	5.10930	+	5.10930i	0.259720	+	0.259720i
$388$	−5.45708	+	14.3540i	−0.277041	+	0.728713i
$389$		−	35.8237i		−	1.81633i	−0.418609	−	0.908167i	$-0.637482\pi$
$389$		−	35.8237i		−	1.81633i	0.418609	−	0.908167i	$-0.362518\pi$
$390$	0.0225262	−	1.55177i	0.00114066	−	0.0785770i
$391$		−	18.0331i		−	0.911974i
$392$	6.08937	+	8.29683i	0.307560	+	0.419053i
$393$	−10.6458	−	10.6458i	−0.537011	−	0.537011i
$394$	−0.129888	+	0.200716i	−0.00654367	+	0.0101119i
$395$	0.678324	−	2.95607i	0.0341302	−	0.148736i
$396$	3.84281	−	1.72576i	0.193109	−	0.0867228i
$397$	12.8416	−	12.8416i	0.644501	−	0.644501i	−0.307158	−	0.951659i	$-0.599378\pi$
$397$	12.8416	−	12.8416i	0.644501	−	0.644501i	0.951659	+	0.307158i	$0.0993780\pi$
$398$	−26.2984	+	5.63410i	−1.31822	+	0.282412i
$399$	−9.17150			−0.459149
$400$	−18.4748	+	7.66042i	−0.923740	+	0.383021i
$401$	−37.6622			−1.88076			−0.940379	−	0.340128i	$-0.889530\pi$
$401$	−37.6622			−1.88076			−0.940379	+	0.340128i	$0.889530\pi$
$402$	11.1622	−	2.39137i	0.556721	−	0.119271i
$403$	3.91215	−	3.91215i	0.194878	−	0.194878i
$404$	−13.7598	+	6.17938i	−0.684578	+	0.307436i
$405$	0.877776	−	3.82527i	0.0436170	−	0.190079i
$406$	2.72844	−	4.21626i	0.135410	−	0.209249i
$407$	−3.70433	−	3.70433i	−0.183617	−	0.183617i
$408$	10.8603	+	14.7973i	0.537665	+	0.732575i
$409$			0.683799i			0.0338117i	0.999857	+	0.0169059i	$0.00538156\pi$
$409$			0.683799i			0.0338117i	−0.999857	+	0.0169059i	$0.994618\pi$
$410$	0.372900	−	25.6881i	0.0184162	−	1.26865i
$411$			3.72330i			0.183657i
$412$	1.51571	−	3.98683i	0.0746735	−	0.196417i
$413$	11.8700	+	11.8700i	0.584084	+	0.584084i
$414$	6.56958	+	4.25133i	0.322877	+	0.208942i
$415$	12.1876	+	19.4466i	0.598264	+	0.954595i
$416$	2.83034	−	0.782831i	0.138769	−	0.0383814i
$417$	6.41944	−	6.41944i	0.314361	−	0.314361i
$418$	−1.56764	−	7.31728i	−0.0766757	−	0.357900i
$419$	10.8056			0.527890			0.263945	−	0.964538i	$-0.414976\pi$
$419$	10.8056			0.527890			0.263945	+	0.964538i	$0.414976\pi$
$420$	1.51360	+	7.60211i	0.0738560	+	0.370945i
$421$	−8.45471			−0.412058			−0.206029	−	0.978546i	$-0.566054\pi$
$421$	−8.45471			−0.412058			−0.206029	+	0.978546i	$0.566054\pi$
$422$	6.63279	+	30.9599i	0.322879	+	1.50711i
$423$	−12.4981	+	12.4981i	−0.607677	+	0.607677i
$424$	−19.9176	−	3.05622i	−0.967286	−	0.148423i
$425$	32.4225	−	11.2605i	1.57272	−	0.546215i
$426$	5.26959	+	3.41007i	0.255312	+	0.165219i
$427$	−5.81098	−	5.81098i	−0.281213	−	0.281213i
$428$	−20.6890	−	7.86552i	−1.00004	−	0.380194i
$429$		−	0.490765i		−	0.0236944i
$430$	−7.55878	−	7.78146i	−0.364517	−	0.375255i
$431$			21.3584i			1.02880i	0.857550	+	0.514400i	$0.171985\pi$
$431$			21.3584i			1.02880i	−0.857550	+	0.514400i	$0.828015\pi$
$432$	−19.2760	+	1.13458i	−0.927415	+	0.0545877i
$433$	14.4383	+	14.4383i	0.693859	+	0.693859i	0.963079	−	0.269220i	$-0.0867659\pi$
$433$	14.4383	+	14.4383i	0.693859	+	0.693859i	−0.269220	+	0.963079i	$0.586766\pi$
$434$	−15.0129	+	23.1994i	−0.720641	+	1.11361i
$435$	−3.46943	+	2.17436i	−0.166347	+	0.104253i
$436$	8.90094	+	19.8200i	0.426278	+	0.949208i
$437$	9.82945	−	9.82945i	0.470206	−	0.470206i
$438$	6.17288	−	1.32247i	0.294952	−	0.0631898i
$439$	14.5992			0.696784			0.348392	−	0.937349i	$-0.386728\pi$
$439$	14.5992			0.696784			0.348392	+	0.937349i	$0.386728\pi$
$440$	−5.80647	+	2.50698i	−0.276812	+	0.119516i
$441$	7.66396			0.364950
$442$	−4.92772	+	1.05571i	−0.234388	+	0.0502148i
$443$	4.09243	−	4.09243i	0.194437	−	0.194437i	−0.603173	−	0.797610i	$-0.706097\pi$
$443$	4.09243	−	4.09243i	0.194437	−	0.194437i	0.797610	+	0.603173i	$0.206097\pi$
$444$	4.05784	+	9.03574i	0.192577	+	0.428817i
$445$	−6.51221	−	1.49434i	−0.308708	−	0.0708387i
$446$	20.3073	−	31.3808i	0.961578	−	1.48593i
$447$	−11.8989	−	11.8989i	−0.562801	−	0.562801i
$448$	−13.0037	+	6.78455i	−0.614368	+	0.320540i
$449$		−	24.1892i		−	1.14156i	−0.821103	−	0.570781i	$-0.806641\pi$
$449$		−	24.1892i		−	1.14156i	0.821103	−	0.570781i	$-0.193359\pi$
$450$	−3.54137	+	14.4664i	−0.166942	+	0.681953i
$451$		−	8.12416i		−	0.382552i
$452$	−13.8924	−	5.28160i	−0.653444	−	0.248425i
$453$	−0.584582	−	0.584582i	−0.0274660	−	0.0274660i
$454$	−5.36262	−	3.47028i	−0.251680	−	0.162868i
$455$	−2.07429	−	0.475983i	−0.0972442	−	0.0223144i
$456$	−2.14596	+	13.9854i	−0.100494	+	0.654926i
$457$	−16.2077	+	16.2077i	−0.758164	+	0.758164i	−0.975988	−	0.217824i	$-0.930104\pi$
$457$	−16.2077	+	16.2077i	−0.758164	+	0.758164i	0.217824	+	0.975988i	$0.430104\pi$
$458$	−5.00296	−	23.3524i	−0.233773	−	1.09118i
$459$	33.1370			1.54670
$460$	−9.76966	−	6.52530i	−0.455513	−	0.304243i
$461$	27.9186			1.30030			0.650150	−	0.759806i	$-0.274706\pi$
$461$	27.9186			1.30030			0.650150	+	0.759806i	$0.274706\pi$
$462$	0.513485	+	2.39680i	0.0238895	+	0.111509i
$463$	−0.269175	+	0.269175i	−0.0125096	+	0.0125096i	−0.713334	−	0.700824i	$-0.752816\pi$
$463$	−0.269175	+	0.269175i	−0.0125096	+	0.0125096i	0.700824	+	0.713334i	$0.252816\pi$
$464$	−5.79086	−	5.14706i	−0.268834	−	0.238946i
$465$	19.0901	−	11.9641i	0.885281	−	0.554823i
$466$	−1.87139	−	1.21102i	−0.0866905	−	0.0560995i
$467$	7.11467	+	7.11467i	0.329227	+	0.329227i	0.852293	−	0.523065i	$-0.175212\pi$
$467$	7.11467	+	7.11467i	0.329227	+	0.329227i	−0.523065	+	0.852293i	$0.675212\pi$
$468$	0.777118	−	2.04409i	0.0359223	−	0.0944879i
$469$		−	15.6543i		−	0.722849i
$470$	19.0346	−	18.4898i	0.877999	−	0.852872i
$471$			11.2566i			0.518678i
$472$	20.8776	−	15.3229i	0.960969	−	0.705293i
$473$	−2.42576	−	2.42576i	−0.111537	−	0.111537i
$474$	−0.985198	+	1.52243i	−0.0452516	+	0.0699273i
$475$	23.8106	+	11.5349i	1.09251	+	0.529259i
$476$	22.9614	−	10.3117i	1.05243	−	0.472636i
$477$	−10.6107	+	10.6107i	−0.485832	+	0.485832i
$478$	5.85246	−	1.25382i	0.267685	−	0.0573483i
$479$	14.3186			0.654231			0.327116	−	0.944984i	$-0.393923\pi$
$479$	14.3186			0.654231			0.327116	+	0.944984i	$0.393923\pi$
$480$	11.9464	−	0.529295i	0.545277	−	0.0241589i
$481$	−2.71953			−0.124000
$482$	14.6116	−	3.13035i	0.665539	−	0.142584i
$483$	−3.21967	+	3.21967i	−0.146500	+	0.146500i
$484$	−1.82447	+	0.819345i	−0.0829302	+	0.0372430i
$485$	−9.11748	−	14.5479i	−0.414003	−	0.660588i
$486$	−12.4018	+	19.1645i	−0.562557	+	0.869319i
$487$	−13.7117	−	13.7117i	−0.621337	−	0.621337i	0.324537	−	0.945873i	$-0.394792\pi$
$487$	−13.7117	−	13.7117i	−0.621337	−	0.621337i	−0.945873	+	0.324537i	$0.894792\pi$
$488$	−10.2207	+	7.50136i	−0.462668	+	0.339571i
$489$			7.54363i			0.341135i
$490$	−11.5052	−	0.167014i	−0.519751	−	0.00754493i
$491$			6.52789i			0.294599i	0.989092	+	0.147300i	$0.0470582\pi$
$491$			6.52789i			0.294599i	−0.989092	+	0.147300i	$0.952942\pi$
$492$	−5.45865	+	14.3581i	−0.246095	+	0.647314i
$493$	9.40160	+	9.40160i	0.423427	+	0.423427i
$494$	−3.26144	−	2.11055i	−0.146739	−	0.0949582i
$495$	−1.05336	+	4.59045i	−0.0473451	+	0.206326i
$496$	31.8634	+	28.3210i	1.43071	+	1.27165i
$497$	6.08634	−	6.08634i	0.273010	−	0.273010i
$498$	−2.87455	−	13.4176i	−0.128812	−	0.601255i
$499$	−8.11300			−0.363188			−0.181594	−	0.983374i	$-0.558126\pi$
$499$	−8.11300			−0.363188			−0.181594	+	0.983374i	$0.558126\pi$
$500$	5.63159	−	21.6399i	0.251852	−	0.967766i
$501$	8.74739			0.390805
$502$	−2.36362	−	11.0327i	−0.105493	−	0.492413i
$503$	9.92654	−	9.92654i	0.442602	−	0.442602i	−0.450283	−	0.892886i	$-0.648677\pi$
$503$	9.92654	−	9.92654i	0.442602	−	0.442602i	0.892886	+	0.450283i	$0.148677\pi$
$504$	−1.65657	+	10.7960i	−0.0737895	+	0.480892i
$505$	3.77174	−	16.4369i	0.167840	−	0.731432i
$506$	−3.11906	−	2.01842i	−0.138659	−	0.0897297i
$507$	8.51009	+	8.51009i	0.377947	+	0.377947i
$508$	38.3015	+	14.5614i	1.69935	+	0.646058i
$509$		−	7.00878i		−	0.310659i	−0.987863	−	0.155329i	$-0.950356\pi$
$509$		−	7.00878i		−	0.310659i	0.987863	−	0.155329i	$-0.0496439\pi$
$510$	−20.5193	−	0.297868i	−0.908612	−	0.0131898i
$511$		−	8.65708i		−	0.382967i
$512$	7.30296	+	21.4165i	0.322748	+	0.946485i
$513$	18.0622	+	18.0622i	0.797467	+	0.797467i
$514$	19.5079	−	30.1455i	0.860455	−	1.32966i
$515$	2.53238	+	4.04069i	0.111590	+	0.178054i
$516$	2.65726	+	5.91700i	0.116979	+	0.260482i
$517$	5.93375	−	5.93375i	0.260966	−	0.260966i
$518$	13.2817	−	2.84543i	0.583562	−	0.125021i
$519$	13.6540			0.599344
$520$	−1.21116	+	3.05166i	−0.0531129	+	0.133824i
$521$	20.0023			0.876318			0.438159	−	0.898897i	$-0.355631\pi$
$521$	20.0023			0.876318			0.438159	+	0.898897i	$0.355631\pi$
$522$	−5.64150	+	1.20862i	−0.246922	+	0.0529000i
$523$	−19.4284	+	19.4284i	−0.849544	+	0.849544i	−0.990076	−	0.140532i	$-0.955119\pi$
$523$	−19.4284	+	19.4284i	−0.849544	+	0.849544i	0.140532	+	0.990076i	$0.455119\pi$
$524$	13.0484	+	29.0554i	0.570023	+	1.26929i
$525$	−7.79924	−	3.77830i	−0.340387	−	0.164899i
$526$	−10.5158	+	16.2500i	−0.458509	+	0.708533i
$527$	−51.7310	−	51.7310i	−2.25344	−	2.25344i
$528$	3.77496	−	0.222194i	0.164284	−	0.00966976i
$529$			16.0987i			0.699944i
$530$	16.1601	−	15.6977i	0.701951	−	0.681863i
$531$		−	19.2851i		−	0.836901i
$532$	18.1364	+	6.89509i	0.786314	+	0.298940i
$533$	−2.98218	−	2.98218i	−0.129173	−	0.129173i
$534$	3.35389	+	2.17038i	0.145137	+	0.0939217i
$535$	20.9686	−	13.1414i	0.906550	−	0.568153i
$536$	−23.8709	−	3.66281i	−1.03106	−	0.158209i
$537$	8.99042	−	8.99042i	0.387965	−	0.387965i
$538$	7.82475	+	36.5237i	0.337349	+	1.57465i
$539$	−3.63864			−0.156727
$540$	11.9906	−	17.9524i	0.515995	−	0.772547i
$541$	−25.8531			−1.11151			−0.555755	−	0.831346i	$-0.687571\pi$
$541$	−25.8531			−1.11151			−0.555755	+	0.831346i	$0.687571\pi$
$542$	−9.29072	−	43.3664i	−0.399070	−	1.86274i
$543$	−8.63697	+	8.63697i	−0.370648	+	0.370648i
$544$	−10.3515	−	37.4260i	−0.443817	−	1.60463i
$545$	−23.6761	−	5.43292i	−1.01417	−	0.232721i
$546$	1.06829	+	0.691318i	0.0457187	+	0.0295857i
$547$	3.05881	+	3.05881i	0.130785	+	0.130785i	0.769469	−	0.638684i	$-0.220521\pi$
$547$	3.05881	+	3.05881i	0.130785	+	0.130785i	−0.638684	+	0.769469i	$0.720521\pi$
$548$	2.79915	−	7.36274i	0.119574	−	0.314521i
$549$			9.44106i			0.402935i
$550$	1.68135	−	6.86826i	0.0716930	−	0.292864i
$551$			10.2492i			0.436631i
$552$	4.15625	+	5.66293i	0.176902	+	0.241030i
$553$	1.75839	+	1.75839i	0.0747744	+	0.0747744i
$554$	−3.25660	+	5.03242i	−0.138360	+	0.213807i
$555$	−10.7937	−	2.47680i	−0.458166	−	0.105134i
$556$	−17.5204	+	7.86820i	−0.743031	+	0.333686i
$557$	−30.3856	+	30.3856i	−1.28748	+	1.28748i	−0.351164	+	0.936314i	$0.614214\pi$
$557$	−30.3856	+	30.3856i	−1.28748	+	1.28748i	−0.936314	+	0.351164i	$0.885786\pi$
$558$	31.0416	−	6.65028i	1.31410	−	0.281529i
$559$	−1.78087			−0.0753229
$560$	2.72212	−	16.1709i	0.115031	−	0.683346i
$561$	−6.48947			−0.273986
$562$	11.2657	−	2.41355i	0.475217	−	0.101809i
$563$	−21.8066	+	21.8066i	−0.919038	+	0.919038i	−0.996959	−	0.0779218i	$-0.975172\pi$
$563$	−21.8066	+	21.8066i	−0.919038	+	0.919038i	0.0779218	+	0.996959i	$0.475172\pi$
$564$	−14.4738	+	6.50002i	−0.609458	+	0.273700i
$565$	14.0801	−	8.82430i	0.592355	−	0.371241i
$566$	19.3209	−	29.8565i	0.812117	−	1.25496i
$567$	2.27542	+	2.27542i	0.0955588	+	0.0955588i
$568$	−7.85682	−	10.7050i	−0.329665	−	0.449172i
$569$			18.9769i			0.795553i	0.917482	+	0.397776i	$0.130218\pi$
$569$			18.9769i			0.795553i	−0.917482	+	0.397776i	$0.869782\pi$
$570$	−11.0223	−	11.3470i	−0.461673	−	0.475274i
$571$		−	7.44095i		−	0.311394i	−0.987805	−	0.155697i	$-0.950238\pi$
$571$		−	7.44095i		−	0.311394i	0.987805	−	0.155697i	$-0.0497624\pi$
$572$	−0.368955	+	0.970478i	−0.0154268	+	0.0405777i
$573$	5.75253	+	5.75253i	0.240315	+	0.240315i
$574$	17.6846	+	11.4441i	0.738140	+	0.477668i
$575$	12.4081	−	4.30940i	0.517454	−	0.179714i
$576$	16.0749	+	5.05212i	0.669789	+	0.210505i
$577$	14.3898	−	14.3898i	0.599054	−	0.599054i	−0.341007	−	0.940061i	$-0.610768\pi$
$577$	14.3898	−	14.3898i	0.599054	−	0.599054i	0.940061	+	0.341007i	$0.110768\pi$
$578$	8.92342	+	41.6519i	0.371165	+	1.73249i
$579$	−10.5436			−0.438177
$580$	8.49540	−	1.69145i	0.352752	−	0.0702338i
$581$	−18.8173			−0.780672
$582$	2.15044	+	10.0376i	0.0891386	+	0.416073i
$583$	5.03769	−	5.03769i	0.208640	−	0.208640i
$584$	−13.2010	−	2.02560i	−0.546260	−	0.0838197i
$585$	1.29838	+	2.07171i	0.0536814	+	0.0856545i
$586$	12.7047	+	8.22153i	0.524827	+	0.339628i
$587$	29.2489	+	29.2489i	1.20723	+	1.20723i	0.971921	+	0.235309i	$0.0756101\pi$
$587$	29.2489	+	29.2489i	1.20723	+	1.20723i	0.235309	+	0.971921i	$0.424390\pi$
$588$	6.43070	+	2.44481i	0.265198	+	0.100822i
$589$		−	56.3948i		−	2.32371i
$590$	−0.420263	+	28.9509i	−0.0173020	+	1.19189i
$591$			0.159818i			0.00657405i
$592$	−1.23127	−	20.9186i	−0.0506049	−	0.859751i
$593$	17.5651	+	17.5651i	0.721313	+	0.721313i	0.968873	−	0.247559i	$-0.0796285\pi$
$593$	17.5651	+	17.5651i	0.721313	+	0.721313i	−0.247559	+	0.968873i	$0.579629\pi$
$594$	3.70897	−	5.73147i	0.152181	−	0.235165i
$595$	−6.29400	+	27.4287i	−0.258029	+	1.12447i
$596$	14.5843	+	32.4755i	0.597398	+	1.33025i
$597$	−12.7130	+	12.7130i	−0.520307	+	0.520307i
$598$	−1.88584	+	0.404019i	−0.0771179	+	0.0165216i
$599$	3.17816			0.129856			0.0649280	−	0.997890i	$-0.479318\pi$
$599$	3.17816			0.129856			0.0649280	+	0.997890i	$0.479318\pi$
$600$	−7.58631	+	11.0088i	−0.309710	+	0.449433i
$601$	−25.3530			−1.03417			−0.517084	−	0.855935i	$-0.672983\pi$
$601$	−25.3530			−1.03417			−0.517084	+	0.855935i	$0.672983\pi$
$602$	8.69742	−	1.86332i	0.354480	−	0.0759431i
$603$	−12.7167	+	12.7167i	−0.517865	+	0.517865i
$604$	0.716512	+	1.59548i	0.0291545	+	0.0649193i
$605$	0.500108	−	2.17942i	0.0203323	−	0.0886062i
$606$	−5.47807	+	8.46526i	−0.222532	+	0.343878i
$607$	−30.5343	−	30.5343i	−1.23935	−	1.23935i	−0.960268	−	0.279079i	$-0.909971\pi$
$607$	−30.5343	−	30.5343i	−1.23935	−	1.23935i	−0.279079	−	0.960268i	$-0.590029\pi$
$608$	14.7577	−	26.0425i	0.598505	−	1.05616i
$609$		−	3.35716i		−	0.136039i
$610$	0.205741	−	14.1730i	0.00833021	−	0.573847i
$611$		−	4.35627i		−	0.176236i
$612$	−27.0293	−	10.2760i	−1.09259	−	0.415381i
$613$	−0.522024	−	0.522024i	−0.0210844	−	0.0210844i	0.696486	−	0.717570i	$-0.254746\pi$
$613$	−0.522024	−	0.522024i	−0.0210844	−	0.0210844i	−0.717570	+	0.696486i	$0.754746\pi$
$614$	14.0086	+	9.06531i	0.565342	+	0.365846i
$615$	−9.12010	−	14.5521i	−0.367758	−	0.586798i
$616$	0.786495	−	5.12565i	0.0316888	−	0.206518i
$617$	−31.4261	+	31.4261i	−1.26517	+	1.26517i	−0.316610	+	0.948556i	$0.602545\pi$
$617$	−31.4261	+	31.4261i	−1.26517	+	1.26517i	−0.948556	+	0.316610i	$0.897455\pi$
$618$	−0.597286	−	2.78796i	−0.0240263	−	0.112148i
$619$	−27.2472			−1.09516			−0.547579	−	0.836754i	$-0.684450\pi$
$619$	−27.2472			−1.09516			−0.547579	+	0.836754i	$0.684450\pi$
$620$	−46.7448	+	9.30699i	−1.87732	+	0.373778i
$621$	12.6815			0.508893
$622$	2.11326	+	9.86406i	0.0847338	+	0.395513i
$623$	3.87373	−	3.87373i	0.155198	−	0.155198i
$624$	1.30413	−	1.46726i	0.0522071	−	0.0587373i
$625$	15.4961	+	19.6181i	0.619844	+	0.784725i
$626$	−27.0863	−	17.5282i	−1.08259	−	0.700567i
$627$	−3.53727	−	3.53727i	−0.141265	−	0.141265i
$628$	8.46267	−	22.2597i	0.337697	−	0.888260i
$629$			35.9609i			1.43385i
$630$	−8.50863	−	8.75930i	−0.338992	−	0.348979i
$631$		−	11.2725i		−	0.448751i	−0.974503	−	0.224376i	$-0.927966\pi$
$631$		−	11.2725i		−	0.448751i	0.974503	−	0.224376i	$-0.0720343\pi$
$632$	3.09276	−	2.26990i	0.123023	−	0.0902917i
$633$	14.9664	+	14.9664i	0.594862	+	0.594862i
$634$	9.80422	−	15.1505i	0.389375	−	0.601701i
$635$	−38.8190	+	24.3286i	−1.54049	+	0.965453i
$636$	−12.2881	+	5.51845i	−0.487256	+	0.218821i
$637$	−1.33566	+	1.33566i	−0.0529206	+	0.0529206i
$638$	2.67844	−	0.573822i	0.106040	−	0.0227178i
$639$	−9.88843			−0.391180
$640$	−24.0217	−	7.93459i	−0.949541	−	0.313642i
$641$	−3.36250			−0.132811			−0.0664055	−	0.997793i	$-0.521153\pi$
$641$	−3.36250			−0.132811			−0.0664055	+	0.997793i	$0.521153\pi$
$642$	−14.4677	+	3.09952i	−0.570993	+	0.122328i
$643$	27.1699	−	27.1699i	1.07148	−	1.07148i	0.0742356	−	0.997241i	$-0.476348\pi$
$643$	27.1699	−	27.1699i	1.07148	−	1.07148i	0.997241	−	0.0742356i	$-0.0236517\pi$
$644$	8.78735	−	3.94629i	0.346270	−	0.155506i
$645$	−7.06819	−	1.62192i	−0.278310	−	0.0638631i
$646$	−27.9082	+	43.1265i	−1.09803	+	1.69679i
$647$	−9.89362	−	9.89362i	−0.388958	−	0.388958i	0.485357	−	0.874316i	$-0.338690\pi$
$647$	−9.89362	−	9.89362i	−0.388958	−	0.388958i	−0.874316	+	0.485357i	$0.838690\pi$
$648$	4.00214	−	2.93733i	0.157219	−	0.115389i
$649$			9.15604i			0.359406i
$650$	−1.90399	−	3.13835i	−0.0746806	−	0.123096i
$651$			18.4723i			0.723986i
$652$	5.67126	−	14.9174i	0.222104	−	0.584209i
$653$	7.52469	+	7.52469i	0.294464	+	0.294464i	0.838841	−	0.544377i	$-0.183234\pi$
$653$	7.52469	+	7.52469i	0.294464	+	0.294464i	−0.544377	+	0.838841i	$0.683234\pi$
$654$	12.1936	+	7.89076i	0.476807	+	0.308553i
$655$	−34.7083	−	7.96444i	−1.35617	−	0.311196i
$656$	21.5887	−	24.2891i	0.842898	−	0.948329i
$657$	−7.03255	+	7.03255i	−0.274366	+	0.274366i
$658$	4.55794	+	21.2751i	0.177687	+	0.829391i
$659$	3.72674			0.145173			0.0725865	−	0.997362i	$-0.476875\pi$
$659$	3.72674			0.145173			0.0725865	+	0.997362i	$0.476875\pi$
$660$	−2.34822	+	3.51575i	−0.0914043	+	0.136850i
$661$	19.5967			0.762225			0.381112	−	0.924529i	$-0.375541\pi$
$661$	19.5967			0.762225			0.381112	+	0.924529i	$0.375541\pi$
$662$	5.10638	+	23.8351i	0.198465	+	0.926377i
$663$	−2.38212	+	2.38212i	−0.0925141	+	0.0925141i
$664$	−4.40289	+	28.6940i	−0.170865	+	1.11354i
$665$	−18.3815	+	11.5200i	−0.712804	+	0.446728i
$666$	−13.1008	−	8.47783i	−0.507645	−	0.328509i
$667$	3.59800	+	3.59800i	0.139315	+	0.139315i
$668$	−17.2978	−	6.57625i	−0.669271	−	0.254443i
$669$		−	24.9867i		−	0.966042i
$670$	19.3676	−	18.8133i	0.748234	−	0.726821i
$671$		−	4.48236i		−	0.173040i
$672$	−4.83394	+	8.53029i	−0.186473	+	0.329063i
$673$	−12.1976	−	12.1976i	−0.470184	−	0.470184i	0.431790	−	0.901974i	$-0.357882\pi$
$673$	−12.1976	−	12.1976i	−0.470184	−	0.470184i	−0.901974	+	0.431790i	$0.857882\pi$
$674$	−2.16364	+	3.34347i	−0.0833404	+	0.128786i
$675$	7.91880	+	22.8007i	0.304795	+	0.877599i
$676$	−10.4307	−	23.2264i	−0.401180	−	0.893322i
$677$	0.509447	−	0.509447i	0.0195796	−	0.0195796i	−0.697249	−	0.716829i	$-0.745593\pi$
$677$	0.509447	−	0.509447i	0.0195796	−	0.0195796i	0.716829	+	0.697249i	$0.245593\pi$
$678$	−9.71486	+	2.08129i	−0.373097	+	0.0799315i
$679$	14.0771			0.540231
$680$	40.3526	+	16.0154i	1.54745	+	0.614161i
$681$	−4.26993			−0.163624
$682$	−14.7377	+	3.15738i	−0.564336	+	0.120902i
$683$	−19.5295	+	19.5295i	−0.747275	+	0.747275i	−0.973967	−	0.226692i	$-0.927209\pi$
$683$	−19.5295	+	19.5295i	−0.747275	+	0.747275i	0.226692	+	0.973967i	$0.427209\pi$
$684$	−9.13188	−	20.3343i	−0.349166	−	0.777500i
$685$	4.67672	+	7.46222i	0.178688	+	0.285117i
$686$	14.9861	−	23.1581i	0.572174	−	0.884180i
$687$	−11.2888	−	11.2888i	−0.430696	−	0.430696i
$688$	−0.806291	−	13.6985i	−0.0307396	−	0.522249i
$689$		−	3.69842i		−	0.140899i
$690$	−7.85277	−	0.113994i	−0.298950	−	0.00433968i
$691$		−	15.5219i		−	0.590481i	−0.955423	−	0.295240i	$-0.904600\pi$
$691$		−	15.5219i		−	0.590481i	0.955423	−	0.295240i	$-0.0953997\pi$
$692$	−27.0005	−	10.2650i	−1.02640	−	0.390217i
$693$	−2.73059	−	2.73059i	−0.103726	−	0.103726i
$694$	−20.5760	−	13.3152i	−0.781053	−	0.505438i
$695$	4.80255	−	20.9291i	0.182171	−	0.793886i
$696$	−5.11925	−	0.785512i	−0.194044	−	0.0297748i
$697$	−39.4339	+	39.4339i	−1.49366	+	1.49366i
$698$	−4.76225	−	22.2288i	−0.180254	−	0.841372i
$699$	−1.49008			−0.0563599
$700$	12.5823	+	13.3349i	0.475567	+	0.504013i
$701$	30.9689			1.16968			0.584839	−	0.811149i	$-0.301158\pi$
$701$	30.9689			1.16968			0.584839	+	0.811149i	$0.301158\pi$
$702$	−0.742410	−	3.46536i	−0.0280205	−	0.130791i
$703$	−19.6015	+	19.6015i	−0.739284	+	0.739284i
$704$	−7.63195	−	2.39861i	−0.287640	−	0.0904011i
$705$	3.96745	−	17.2898i	0.149423	−	0.651171i
$706$	29.8138	+	19.2932i	1.12206	+	0.726109i
$707$	9.77733	+	9.77733i	0.367714	+	0.367714i
$708$	6.15197	−	16.1818i	0.231205	−	0.608149i
$709$			28.8659i			1.08408i	0.840352	+	0.542041i	$0.182348\pi$
$709$			28.8659i			1.08408i	−0.840352	+	0.542041i	$0.817652\pi$
$710$	14.8446	+	0.215490i	0.557107	+	0.00808721i
$711$		−	2.85685i		−	0.107140i
$712$	−5.00057	−	6.81333i	−0.187404	−	0.255340i
$713$	−19.7975	−	19.7975i	−0.741421	−	0.741421i
$714$	9.14141	−	14.1262i	0.342109	−	0.528660i
$715$	−0.616436	−	0.983590i	−0.0230534	−	0.0367842i
$716$	−24.5373	+	11.0194i	−0.917003	+	0.411815i
$717$	2.82915	−	2.82915i	0.105657	−	0.105657i
$718$	−49.9812	+	10.7079i	−1.86528	+	0.399614i
$719$	−7.73510			−0.288471			−0.144235	−	0.989543i	$-0.546072\pi$
$719$	−7.73510			−0.288471			−0.144235	+	0.989543i	$0.546072\pi$
$720$	−15.3477	+	10.9251i	−0.571975	+	0.407154i
$721$	−3.90993			−0.145614
$722$	−12.4456	+	2.66631i	−0.463177	+	0.0992300i
$723$	7.06342	−	7.06342i	0.262692	−	0.262692i
$724$	23.5727	−	10.5862i	0.876071	−	0.393433i
$725$	−4.22228	+	8.71570i	−0.156811	+	0.323693i
$726$	−0.726357	+	1.12244i	−0.0269576	+	0.0416576i
$727$	−19.6820	−	19.6820i	−0.729965	−	0.729965i	0.240647	−	0.970613i	$-0.422640\pi$
$727$	−19.6820	−	19.6820i	−0.729965	−	0.729965i	−0.970613	+	0.240647i	$0.922640\pi$
$728$	−1.59280	−	2.17020i	−0.0590330	−	0.0804331i
$729$			9.99403i			0.370149i
$730$	10.7106	−	10.4041i	0.396416	−	0.385072i
$731$			23.5488i			0.870983i
$732$	−3.01171	+	7.92184i	−0.111316	+	0.292800i
$733$	−2.84694	−	2.84694i	−0.105154	−	0.105154i	0.652572	−	0.757726i	$-0.273690\pi$
$733$	−2.84694	−	2.84694i	−0.105154	−	0.105154i	−0.757726	+	0.652572i	$0.773690\pi$
$734$	−22.3726	−	14.4779i	−0.825790	−	0.534388i
$735$	−6.51759	+	4.08470i	−0.240405	+	0.150667i
$736$	−3.96153	−	14.3230i	−0.146024	−	0.527952i
$737$	6.03756	−	6.03756i	0.222396	−	0.222396i
$738$	−5.06943	−	23.6626i	−0.186608	−	0.871033i
$739$	47.7645			1.75704			0.878522	−	0.477702i	$-0.158530\pi$
$739$	47.7645			1.75704			0.878522	+	0.477702i	$0.158530\pi$
$740$	19.4822	+	13.0125i	0.716181	+	0.478348i
$741$	−2.59689			−0.0953990
$742$	3.86964	+	18.0623i	0.142059	+	0.663090i
$743$	10.2569	−	10.2569i	0.376290	−	0.376290i	−0.493472	−	0.869762i	$-0.664272\pi$
$743$	10.2569	−	10.2569i	0.376290	−	0.376290i	0.869762	+	0.493472i	$0.164272\pi$
$744$	28.1679	+	4.32217i	1.03269	+	0.158458i
$745$	−38.7938	−	8.90193i	−1.42129	−	0.326141i
$746$	9.47045	+	6.12855i	0.346738	+	0.224382i
$747$	15.2861	+	15.2861i	0.559291	+	0.559291i
$748$	12.8328	+	4.87875i	0.469213	+	0.178385i
$749$			20.2900i			0.741381i
$750$	−4.69859	−	14.1900i	−0.171568	−	0.518146i
$751$			0.255515i			0.00932386i	0.999989	+	0.00466193i	$0.00148394\pi$
$751$			0.255515i			0.00932386i	−0.999989	+	0.00466193i	$0.998516\pi$
$752$	33.5084	−	1.97230i	1.22192	−	0.0719225i
$753$	−5.33334	−	5.33334i	−0.194358	−	0.194358i
$754$	0.772552	−	1.19382i	0.0281347	−	0.0434765i
$755$	−1.90589	−	0.437341i	−0.0693626	−	0.0159165i
$756$	7.25156	+	16.1473i	0.263737	+	0.587272i
$757$	−9.15478	+	9.15478i	−0.332736	+	0.332736i	−0.853625	−	0.520888i	$-0.825601\pi$
$757$	−9.15478	+	9.15478i	−0.332736	+	0.332736i	0.520888	+	0.853625i	$0.325601\pi$
$758$	−34.0343	+	7.29144i	−1.23618	+	0.264837i
$759$	−2.48352			−0.0901462
$760$	13.2657	+	30.7250i	0.481198	+	1.11451i
$761$	41.5539			1.50633			0.753164	−	0.657833i	$-0.228527\pi$
$761$	41.5539			1.50633			0.753164	+	0.657833i	$0.228527\pi$
$762$	26.7839	−	5.73813i	0.970279	−	0.207871i
$763$	14.0835	−	14.0835i	0.509858	−	0.509858i
$764$	−7.05078	−	15.7002i	−0.255088	−	0.568014i
$765$	27.3945	−	17.1687i	0.990451	−	0.620735i
$766$	−4.46811	+	6.90457i	−0.161439	+	0.249472i
$767$	3.36096	+	3.36096i	0.121357	+	0.121357i
$768$	11.8766	+	9.36708i	0.428559	+	0.338005i
$769$			12.2677i			0.442383i	0.975230	+	0.221192i	$0.0709946\pi$
$769$			12.2677i			0.442383i	−0.975230	+	0.221192i	$0.929005\pi$
$770$	4.03967	+	4.15868i	0.145580	+	0.149868i
$771$		−	24.0031i		−	0.864449i
$772$	20.8498	+	7.92663i	0.750399	+	0.285286i
$773$	8.17596	+	8.17596i	0.294069	+	0.294069i	0.838685	−	0.544616i	$-0.183325\pi$
$773$	8.17596	+	8.17596i	0.294069	+	0.294069i	−0.544616	+	0.838685i	$0.683325\pi$
$774$	−8.57898	−	5.55166i	−0.308365	−	0.199550i
$775$	23.2325	−	47.9570i	0.834535	−	1.72266i
$776$	3.29379	−	21.4659i	0.118240	−	0.770580i
$777$	6.42052	−	6.42052i	0.230335	−	0.230335i
$778$	10.6130	+	49.5382i	0.380493	+	1.77603i
$779$	−42.9890			−1.54024
$780$	0.428571	+	2.15252i	0.0153453	+	0.0770725i
$781$	4.69476			0.167992
$782$	5.34241	+	24.9368i	0.191044	+	0.891739i
$783$	−6.61155	+	6.61155i	−0.236277	+	0.236277i
$784$	−10.8786	−	9.66913i	−0.388520	−	0.345326i
$785$	14.1391	+	22.5605i	0.504646	+	0.805218i
$786$	17.8753	+	11.5675i	0.637592	+	0.412601i
$787$	15.0777	+	15.0777i	0.537461	+	0.537461i	0.922783	−	0.385321i	$-0.125909\pi$
$787$	15.0777	+	15.0777i	0.537461	+	0.537461i	−0.385321	+	0.922783i	$0.625909\pi$
$788$	0.120151	−	0.316038i	0.00428019	−	0.0112584i
$789$			12.9389i			0.460637i
$790$	−0.0622569	+	4.28872i	−0.00221500	+	0.152586i
$791$			13.6245i			0.484431i
$792$	−4.80271	+	3.52490i	−0.170657	+	0.125252i
$793$	−1.64537	−	1.64537i	−0.0584286	−	0.0584286i
$794$	−13.9534	+	21.5622i	−0.495188	+	0.765213i
$795$	3.36832	−	14.6788i	0.119462	−	0.520605i
$796$	34.6972	−	15.5821i	1.22981	−	0.552292i
$797$	5.02505	−	5.02505i	0.177996	−	0.177996i	−0.612485	−	0.790482i	$-0.709830\pi$
$797$	5.02505	−	5.02505i	0.177996	−	0.177996i	0.790482	+	0.612485i	$0.209830\pi$
$798$	12.6827	−	2.71711i	0.448962	−	0.0961846i
$799$	−57.6037			−2.03787
$800$	23.2781	−	16.0664i	0.823007	−	0.568031i
$801$	−6.29362			−0.222374
$802$	52.0806	−	11.1576i	1.83903	−	0.393989i
$803$	3.33887	−	3.33887i	0.117826	−	0.117826i
$804$	−14.7270	+	6.61374i	−0.519383	+	0.233248i
$805$	−2.40872	+	10.4970i	−0.0848962	+	0.369970i
$806$	−4.25086	+	6.56885i	−0.149730	+	0.231378i
$807$	17.6560	+	17.6560i	0.621521	+	0.621521i
$808$	17.1969	−	12.6215i	0.604985	−	0.444023i
$809$		−	51.8541i		−	1.82309i	−0.411199	−	0.911546i	$-0.634890\pi$
$809$		−	51.8541i		−	1.82309i	0.411199	−	0.911546i	$-0.365110\pi$
$810$	−0.0805626	+	5.54976i	−0.00283068	+	0.194999i
$811$		−	8.52533i		−	0.299365i	−0.988734	−	0.149682i	$-0.952175\pi$
$811$		−	8.52533i		−	0.299365i	0.988734	−	0.149682i	$-0.0478251\pi$
$812$	−2.52389	+	6.63871i	−0.0885713	+	0.232973i
$813$	−20.9639	−	20.9639i	−0.735234	−	0.735234i
$814$	6.21990	+	4.02505i	0.218007	+	0.141078i
$815$	9.47533	+	15.1189i	0.331906	+	0.529593i
$816$	−19.4018	−	17.2448i	−0.679199	−	0.603688i
$817$	−12.8359	+	12.8359i	−0.449072	+	0.449072i
$818$	−0.202579	−	0.945582i	−0.00708302	−	0.0330615i
$819$	−2.00466			−0.0700486
$820$	7.09460	+	35.6329i	0.247754	+	1.24436i
$821$	5.85995			0.204514			0.102257	−	0.994758i	$-0.467394\pi$
$821$	5.85995			0.204514			0.102257	+	0.994758i	$0.467394\pi$
$822$	−1.10305	−	5.14870i	−0.0384732	−	0.179582i
$823$	−20.1439	+	20.1439i	−0.702173	+	0.702173i	−0.964877	−	0.262703i	$-0.915386\pi$
$823$	−20.1439	+	20.1439i	−0.702173	+	0.702173i	0.262703	+	0.964877i	$0.415386\pi$
$824$	−0.914851	+	5.96216i	−0.0318703	+	0.207702i
$825$	−1.55080	−	4.46523i	−0.0539919	−	0.155459i
$826$	−19.9308	−	12.8977i	−0.693480	−	0.448768i
$827$	−6.82747	−	6.82747i	−0.237415	−	0.237415i	0.578364	−	0.815779i	$-0.303691\pi$
$827$	−6.82747	−	6.82747i	−0.237415	−	0.237415i	−0.815779	+	0.578364i	$0.803691\pi$
$828$	−10.3441	−	3.93262i	−0.359483	−	0.136668i
$829$		−	3.96788i		−	0.137810i	−0.997623	−	0.0689051i	$-0.978049\pi$
$829$		−	3.96788i		−	0.137810i	0.997623	−	0.0689051i	$-0.0219506\pi$
$830$	−22.6146	−	23.2808i	−0.784963	−	0.808088i
$831$			4.00702i			0.139002i
$832$	−3.68197	+	1.92103i	−0.127649	+	0.0665997i
$833$	17.6616	+	17.6616i	0.611938	+	0.611938i
$834$	−6.97523	+	10.7788i	−0.241532	+	0.373240i
$835$	17.5315	−	10.9873i	0.606703	−	0.380233i
$836$	4.33557	+	9.65417i	0.149949	+	0.333896i
$837$	36.3791	−	36.3791i	1.25745	−	1.25745i
$838$	−14.9424	+	3.20123i	−0.516178	+	0.110585i
$839$	37.1348			1.28203			0.641017	−	0.767526i	$-0.278513\pi$
$839$	37.1348			1.28203			0.641017	+	0.767526i	$0.278513\pi$
$840$	−4.34522	−	10.0640i	−0.149924	−	0.347243i
$841$	25.2484			0.870633
$842$	11.6915	−	2.50476i	0.402915	−	0.0863196i
$843$	5.44601	−	5.44601i	0.187570	−	0.187570i
$844$	−18.3441	−	40.8475i	−0.631431	−	1.40603i
$845$	27.7452	+	6.36663i	0.954464	+	0.219019i
$846$	13.5802	−	20.9854i	0.466895	−	0.721493i
$847$	1.29641	+	1.29641i	0.0445452	+	0.0445452i
$848$	28.4482	−	1.67446i	0.976917	−	0.0575013i
$849$		−	23.7730i		−	0.815887i
$850$	−41.4990	+	25.1768i	−1.42340	+	0.863556i
$851$			13.7622i			0.471764i
$852$	−8.29722	−	3.15443i	−0.284258	−	0.108069i
$853$	−25.9386	−	25.9386i	−0.888121	−	0.888121i	0.106222	−	0.994342i	$-0.466125\pi$
$853$	−25.9386	−	25.9386i	−0.888121	−	0.888121i	−0.994342	+	0.106222i	$0.966125\pi$
$854$	9.75716	+	6.31409i	0.333883	+	0.216064i
$855$	24.2904	+	5.57387i	0.830715	+	0.190622i
$856$	30.9397	+	4.74748i	1.05750	+	0.162266i
$857$	16.8871	−	16.8871i	0.576852	−	0.576852i	−0.357183	−	0.934034i	$-0.616263\pi$
$857$	16.8871	−	16.8871i	0.576852	−	0.576852i	0.934034	+	0.357183i	$0.116263\pi$
$858$	0.145392	+	0.678647i	0.00496360	+	0.0231686i
$859$	9.25847			0.315895			0.157948	−	0.987448i	$-0.449512\pi$
$859$	9.25847			0.315895			0.157948	+	0.987448i	$0.449512\pi$
$860$	12.7578	+	8.52115i	0.435039	+	0.290569i
$861$	14.0812			0.479886
$862$	−6.32756	−	29.5352i	−0.215517	−	1.00597i
$863$	−17.9760	+	17.9760i	−0.611910	+	0.611910i	−0.943443	−	0.331534i	$-0.892434\pi$
$863$	−17.9760	+	17.9760i	−0.611910	+	0.611910i	0.331534	+	0.943443i	$0.392434\pi$
$864$	26.3194	−	7.27955i	0.895403	−	0.247655i
$865$	27.3653	−	17.1504i	0.930449	−	0.583131i
$866$	−24.2432	−	15.6883i	−0.823816	−	0.533111i
$867$	20.1351	+	20.1351i	0.683823	+	0.683823i
$868$	13.8874	−	36.5286i	0.471368	−	1.23986i
$869$			1.35636i			0.0460112i
$870$	4.15349	−	4.03462i	0.140816	−	0.136787i
$871$		−	4.43248i		−	0.150189i
$872$	−18.1803	−	24.7709i	−0.615664	−	0.838849i
$873$	−11.4355	−	11.4355i	−0.387034	−	0.387034i
$874$	−10.6805	+	16.5045i	−0.361273	+	0.558274i
$875$	−20.3770	+	2.22394i	−0.688870	+	0.0751829i
$876$	−8.14429	+	3.65750i	−0.275170	+	0.123576i
$877$	−1.21487	+	1.21487i	−0.0410233	+	0.0410233i	−0.727321	−	0.686298i	$-0.759235\pi$
$877$	−1.21487	+	1.21487i	−0.0410233	+	0.0410233i	0.686298	+	0.727321i	$0.259235\pi$
$878$	−20.1883	+	4.32511i	−0.681324	+	0.145965i
$879$	10.1160			0.341205
$880$	7.28668	−	5.18694i	0.245634	−	0.174852i
$881$	43.7931			1.47543			0.737713	−	0.675115i	$-0.235906\pi$
$881$	43.7931			1.47543			0.737713	+	0.675115i	$0.235906\pi$
$882$	−10.5980	+	2.27049i	−0.356853	+	0.0764514i
$883$	30.5067	−	30.5067i	1.02663	−	1.02663i	0.0269967	−	0.999636i	$-0.491406\pi$
$883$	30.5067	−	30.5067i	1.02663	−	1.02663i	0.999636	−	0.0269967i	$-0.00859438\pi$
$884$	6.50147	−	2.91973i	0.218668	−	0.0982012i
$885$	10.2785	+	16.4004i	0.345507	+	0.551294i
$886$	−4.44675	+	6.87156i	−0.149392	+	0.230855i
$887$	6.12557	+	6.12557i	0.205677	+	0.205677i	0.802427	−	0.596750i	$-0.203542\pi$
$887$	6.12557	+	6.12557i	0.205677	+	0.205677i	−0.596750	+	0.802427i	$0.703542\pi$
$888$	−8.28821	−	11.2928i	−0.278134	−	0.378961i
$889$		−	37.5628i		−	1.25982i
$890$	9.44802	+	0.137151i	0.316698	+	0.00459733i
$891$			1.75517i			0.0588005i
$892$	−18.7849	+	49.4107i	−0.628964	+	1.65439i
$893$	−31.3985	−	31.3985i	−1.05071	−	1.05071i
$894$	19.9794	+	12.9292i	0.668212	+	0.432416i
$895$	6.72598	−	29.3112i	0.224825	−	0.979765i
$896$	15.9720	−	13.2343i	0.533588	−	0.442128i
$897$	−0.911641	+	0.911641i	−0.0304388	+	0.0304388i
$898$	7.16620	+	33.4497i	0.239139	+	1.11623i
$899$	20.6429			0.688479
$900$	0.611381	−	21.0538i	0.0203794	−	0.701794i
$901$	−48.9049			−1.62926
$902$	2.40683	+	11.2344i	0.0801386	+	0.374064i
$903$	4.20444	−	4.20444i	0.139915	−	0.139915i
$904$	20.7756	+	3.18787i	0.690987	+	0.106027i
$905$	−6.46155	+	28.1588i	−0.214789	+	0.936031i
$906$	0.981566	+	0.635195i	0.0326103	+	0.0211029i
$907$	26.0892	+	26.0892i	0.866279	+	0.866279i	0.992058	−	0.125779i	$-0.0401431\pi$
$907$	26.0892	+	26.0892i	0.866279	+	0.866279i	−0.125779	+	0.992058i	$0.540143\pi$
$908$	8.44370	+	3.21012i	0.280214	+	0.106531i
$909$		−	15.8852i		−	0.526878i
$910$	3.00941	+	0.0436859i	0.0997611	+	0.00144817i
$911$			19.5370i			0.647291i	0.946178	+	0.323645i	$0.104908\pi$
$911$			19.5370i			0.647291i	−0.946178	+	0.323645i	$0.895092\pi$
$912$	−1.17574	−	19.9752i	−0.0389327	−	0.661446i
$913$	−7.25746	−	7.25746i	−0.240187	−	0.240187i
$914$	17.6109	−	27.2142i	0.582518	−	0.900165i
$915$	−5.03186	−	8.02887i	−0.166348	−	0.265426i
$916$	13.8365	+	30.8103i	0.457172	+	1.01800i
$917$	20.6459	−	20.6459i	0.681787	−	0.681787i
$918$	−45.8230	+	9.81702i	−1.51238	+	0.324010i
$919$	−11.4181			−0.376649			−0.188325	−	0.982107i	$-0.560306\pi$
$919$	−11.4181			−0.376649			−0.188325	+	0.982107i	$0.560306\pi$
$920$	15.4430	+	6.12909i	0.509140	+	0.202070i
$921$	11.1542			0.367545
$922$	−38.6068	+	8.27105i	−1.27145	+	0.272392i
$923$	1.72333	−	1.72333i	0.0567242	−	0.0567242i
$924$	−1.42013	−	3.16225i	−0.0467188	−	0.104030i
$925$	−24.7437	+	8.59363i	−0.813569	+	0.282557i
$926$	0.292480	−	0.451969i	0.00961149	−	0.0148526i
$927$	3.17622	+	3.17622i	0.104321	+	0.104321i
$928$	9.53265	+	5.40196i	0.312925	+	0.177328i
$929$			27.1354i			0.890285i	0.895460	+	0.445142i	$0.146847\pi$
$929$			27.1354i			0.890285i	−0.895460	+	0.445142i	$0.853153\pi$
$930$	−22.8540	+	22.2000i	−0.749411	+	0.727965i
$931$			19.2539i			0.631021i
$932$	2.94660	+	1.12023i	0.0965189	+	0.0366944i
$933$	4.76841	+	4.76841i	0.156111	+	0.156111i
$934$	−11.9462	−	7.73065i	−0.390891	−	0.252955i
$935$	−13.0062	+	8.15123i	−0.425348	+	0.266574i
$936$	−0.469054	+	3.05686i	−0.0153315	+	0.0999166i
$937$	30.7301	−	30.7301i	1.00391	−	1.00391i	0.00391474	−	0.999992i	$-0.498754\pi$
$937$	30.7301	−	30.7301i	1.00391	−	1.00391i	0.999992	−	0.00391474i	$-0.00124610\pi$
$938$	4.63768	+	21.6473i	0.151425	+	0.706810i
$939$	−21.5672			−0.703820
$940$	−20.8439	+	31.2075i	−0.679854	+	1.01788i
$941$	4.84496			0.157941			0.0789706	−	0.996877i	$-0.474837\pi$
$941$	4.84496			0.157941			0.0789706	+	0.996877i	$0.474837\pi$
$942$	−3.33484	−	15.5660i	−0.108655	−	0.507169i
$943$	−15.0914	+	15.0914i	−0.491442	+	0.491442i
$944$	−24.3308	+	27.3741i	−0.791899	+	0.890952i
$945$	−19.2889	−	4.42617i	−0.627466	−	0.143983i
$946$	4.07307	+	2.63578i	0.132427	+	0.0856966i
$947$	−0.493208	−	0.493208i	−0.0160271	−	0.0160271i	0.699048	−	0.715075i	$-0.253607\pi$
$947$	−0.493208	−	0.493208i	−0.0160271	−	0.0160271i	−0.715075	+	0.699048i	$0.753607\pi$
$948$	0.911339	−	2.39713i	0.0295989	−	0.0778553i
$949$		−	2.45123i		−	0.0795704i
$950$	−36.3435	−	8.89687i	−1.17914	−	0.288653i
$951$		−	12.0634i		−	0.391183i
$952$	−28.6970	+	21.0618i	−0.930074	+	0.682618i
$953$	−19.6960	−	19.6960i	−0.638015	−	0.638015i	0.312050	−	0.950066i	$-0.398984\pi$
$953$	−19.6960	−	19.6960i	−0.638015	−	0.638015i	−0.950066	+	0.312050i	$0.898984\pi$
$954$	11.5294	−	17.8164i	0.373278	−	0.576826i
$955$	18.7548	+	4.30362i	0.606891	+	0.139262i
$956$	−7.72153	+	3.46765i	−0.249732	+	0.112152i
$957$	1.29479	−	1.29479i	0.0418546	−	0.0418546i
$958$	−19.8002	+	4.24195i	−0.639715	+	0.137051i
$959$	−7.22073			−0.233170
$960$	−16.3631	+	4.27112i	−0.528117	+	0.137850i
$961$	−82.5847			−2.66402
$962$	3.76067	−	0.805677i	0.121249	−	0.0259761i
$963$	16.4825	−	16.4825i	0.531142	−	0.531142i
$964$	−19.2780	+	8.65752i	−0.620903	+	0.278840i
$965$	−21.1315	+	13.2435i	−0.680246	+	0.426324i
$966$	3.49842	−	5.40611i	0.112560	−	0.173939i
$967$	33.1067	+	33.1067i	1.06464	+	1.06464i	0.997761	+	0.0668797i	$0.0213044\pi$
$967$	33.1067	+	33.1067i	1.06464	+	1.06464i	0.0668797	+	0.997761i	$0.478696\pi$
$968$	2.28020	−	1.67353i	0.0732884	−	0.0537892i
$969$			34.3391i			1.10313i
$970$	16.9179	+	17.4163i	0.543200	+	0.559203i
$971$			60.7857i			1.95071i	0.220652	+	0.975353i	$0.429182\pi$
$971$			60.7857i			1.95071i	−0.220652	+	0.975353i	$0.570818\pi$
$972$	11.4721	−	30.1754i	0.367966	−	0.967878i
$973$	12.4495	+	12.4495i	0.399112	+	0.399112i
$974$	23.0232	+	14.8989i	0.737711	+	0.477390i
$975$	−2.20834	−	1.06982i	−0.0707234	−	0.0342616i
$976$	11.9112	−	13.4011i	0.381268	−	0.428958i
$977$	40.6271	−	40.6271i	1.29978	−	1.29978i	0.371239	−	0.928537i	$-0.378933\pi$
$977$	40.6271	−	40.6271i	1.29978	−	1.29978i	0.928537	−	0.371239i	$-0.121067\pi$
$978$	−2.23484	−	10.4316i	−0.0714624	−	0.333565i
$979$	2.98804			0.0954982
$980$	15.9593	−	3.17752i	0.509800	−	0.101502i
$981$	−22.8814			−0.730547
$982$	−1.93392	−	9.02699i	−0.0617140	−	0.288063i
$983$	16.3582	−	16.3582i	0.521747	−	0.521747i	−0.396352	−	0.918099i	$-0.629724\pi$
$983$	16.3582	−	16.3582i	0.521747	−	0.521747i	0.918099	+	0.396352i	$0.129724\pi$
$984$	3.29474	−	21.4721i	0.105032	−	0.684504i
$985$	0.200743	+	0.320308i	0.00639621	+	0.0102059i
$986$	−15.7861	−	10.2156i	−0.502733	−	0.325330i
$987$	10.2847	+	10.2847i	0.327365	+	0.327365i
$988$	5.13529	+	1.95233i	0.163375	+	0.0621118i
$989$			9.01214i			0.286569i
$990$	0.0966780	−	6.65990i	0.00307263	−	0.211666i
$991$		−	37.4154i		−	1.18854i	−0.804266	−	0.594270i	$-0.797441\pi$
$991$		−	37.4154i		−	1.18854i	0.804266	−	0.594270i	$-0.202559\pi$
$992$	−52.4521	−	29.7235i	−1.66536	−	0.943722i
$993$	11.5222	+	11.5222i	0.365646	+	0.365646i
$994$	−6.61329	+	10.2195i	−0.209761	+	0.324143i
$995$	−9.51091	+	41.4477i	−0.301516	+	1.31398i
$996$	7.95005	+	17.7027i	0.251907	+	0.560930i
$997$	7.40737	−	7.40737i	0.234594	−	0.234594i	−0.580013	−	0.814607i	$-0.696953\pi$
$997$	7.40737	−	7.40737i	0.234594	−	0.234594i	0.814607	+	0.580013i	$0.196953\pi$
$998$	11.2189	−	2.40352i	0.355129	−	0.0760821i
$999$	−25.2890			−0.800108

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	220.2.l.c.23.3	✓	28
4.3	odd	2		220.2.l.d.23.6	yes	28
5.2	odd	4		220.2.l.d.67.6	yes	28
20.7	even	4	inner	220.2.l.c.67.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.3	✓	28	1.1	even	1	trivial
220.2.l.c.67.3	yes	28	20.7	even	4	inner
220.2.l.d.23.6	yes	28	4.3	odd	2
220.2.l.d.67.6	yes	28	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

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.23.3

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