LMFDB - Embedded newform 220.2.l.d.23.6

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			23.6
Character	$\chi$	$=$	220.23
Dual form			220.2.l.d.67.6

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.296256 + 1.38283i) 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} +(1.67353 - 2.28020i) q^{8} +2.10627i q^{9} +(-2.86562 - 1.33723i) q^{10} +1.00000i q^{11} +(-1.76733 + 0.671903i) 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} +(-2.91262 - 0.623994i) q^{18} +5.29151 q^{19} +(2.69813 - 3.56652i) q^{20} +1.73325 q^{21} +(-1.38283 - 0.296256i) 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} +(-1.30305 - 3.42746i) q^{28} -1.93692i q^{29} +(-2.80953 + 1.02170i) q^{30} -10.6576i q^{31} +(-4.92156 + 2.78895i) 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} +(-1.56764 + 7.31728i) q^{38} -0.490765 q^{39} +(4.13258 + 4.78767i) q^{40} +8.12416 q^{41} +(-0.513485 + 2.39680i) 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} +(3.77496 + 0.222194i) q^{48} -3.63864i q^{49} +(4.34752 - 5.57665i) q^{50} +6.48947i q^{51} +(0.368955 + 0.970478i) 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} +(2.67844 + 0.573822i) q^{58} +9.15604 q^{59} +(-0.580503 - 4.18780i) q^{60} +4.48236 q^{61} +(14.7377 + 3.15738i) 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} +(12.8328 - 4.87875i) q^{68} -2.48352i q^{69} +(-1.98142 - 5.44863i) q^{70} -4.69476i q^{71} +(4.80271 + 3.52490i) 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} +(0.145392 - 0.678647i) q^{78} +1.35636 q^{79} +(-7.84486 + 4.29630i) q^{80} -1.75517 q^{81} +(-2.40683 + 11.2344i) 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} +(2.28020 + 1.67353i) q^{88} +2.98804i q^{89} +(2.81657 - 6.03578i) q^{90} -0.951760i q^{91} +(-4.91112 + 1.86710i) 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} +(5.03164 + 1.07797i) q^{98} -2.10627 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q + 2 q^{2} + 4 q^{3} - 4 q^{4} + 2 q^{5} - 12 q^{6} + 2 q^{7} + 2 q^{8} - 6 q^{10} + 8 q^{12} + 6 q^{13} + 20 q^{14} - 8 q^{15} + 8 q^{16} - 14 q^{17} - 6 q^{18} - 4 q^{19} + 8 q^{20} - 16 q^{21} - 2 q^{22}+ \cdots + 20 q^{99}+O(q^{100})$ 28 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 + 2 * q^5 - 12 * q^6 + 2 * q^7 + 2 * q^8 - 6 * q^10 + 8 * q^12 + 6 * q^13 + 20 * q^14 - 8 * q^15 + 8 * q^16 - 14 * q^17 - 6 * 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 + 8 * q^28 - 24 * q^30 - 38 * q^32 + 4 * q^33 + 52 * q^34 + 10 * q^35 - 4 * q^36 + 20 * q^37 - 48 * q^38 - 32 * q^39 + 46 * q^40 + 12 * q^41 + 32 * q^42 - 2 * q^43 - 10 * q^45 + 4 * q^46 + 44 * q^47 + 44 * q^48 - 18 * q^50 - 52 * q^52 - 28 * q^53 + 40 * q^54 + 2 * q^55 + 4 * q^56 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 20 * q^62 + 10 * q^63 - 28 * q^64 - 30 * q^65 - 16 * q^67 + 68 * q^68 - 40 * q^70 - 38 * q^72 + 22 * q^73 + 20 * q^74 + 56 * q^75 + 4 * q^76 - 2 * q^77 - 40 * q^78 + 20 * q^79 + 12 * q^80 + 12 * q^81 + 12 * q^82 - 2 * q^83 - 120 * q^84 - 14 * q^85 - 20 * q^86 + 48 * q^87 + 14 * q^88 - 10 * q^90 + 4 * q^92 - 20 * q^93 + 20 * q^94 - 92 * q^95 + 40 * q^96 + 16 * q^97 - 82 * 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

)

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

$2$	−0.296256	+	1.38283i	−0.209484	+	0.977812i
$2$	−0.296256	+	1.38283i	−0.209484	+	0.977812i
$3$	0.668480	−	0.668480i	0.385947	−	0.385947i	−0.487292	−	0.873239i	$-0.662015\pi$
$3$	0.668480	−	0.668480i	0.385947	−	0.385947i	0.873239	+	0.487292i	$0.162015\pi$
$4$	−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	0.908305	−	0.418308i	$-0.137377\pi$
$7$	1.29641	+	1.29641i	0.489997	+	0.489997i	−0.418308	+	0.908305i	$0.637377\pi$
$8$	1.67353	−	2.28020i	0.591681	−	0.806172i
$9$			2.10627i			0.702090i
$10$	−2.86562	−	1.33723i	−0.906190	−	0.422870i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	−1.76733	+	0.671903i	−0.510186	+	0.193962i
$13$	−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	$0.936945\pi$
$18$	−2.91262	−	0.623994i	−0.686512	−	0.147077i
$19$	5.29151			1.21395			0.606977	−	0.794719i	$-0.292382\pi$
$19$	5.29151			1.21395			0.606977	+	0.794719i	$0.292382\pi$
$20$	2.69813	−	3.56652i	0.603320	−	0.797499i
$21$	1.73325			0.378226
$22$	−1.38283	−	0.296256i	−0.294821	−	0.0631619i
$23$	1.85759	−	1.85759i	0.387334	−	0.387334i	−0.486401	−	0.873736i	$-0.661691\pi$
$23$	1.85759	−	1.85759i	0.387334	−	0.387334i	0.873736	+	0.486401i	$0.161691\pi$
$24$	−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
$28$	−1.30305	−	3.42746i	−0.246253	−	0.647729i
$29$		−	1.93692i		−	0.359676i	−0.983696	−	0.179838i	$-0.942443\pi$
$29$		−	1.93692i		−	0.359676i	0.983696	−	0.179838i	$-0.0575574\pi$
$30$	−2.80953	+	1.02170i	−0.512947	+	0.186536i
$31$		−	10.6576i		−	1.91416i	−0.289818	−	0.957082i	$-0.593595\pi$
$31$		−	10.6576i		−	1.91416i	0.289818	−	0.957082i	$-0.406405\pi$
$32$	−4.92156	+	2.78895i	−0.870018	+	0.493021i
$33$	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	$0.108295\pi$
$38$	−1.56764	+	7.31728i	−0.254305	+	1.18702i
$39$	−0.490765			−0.0785853
$40$	4.13258	+	4.78767i	0.653418	+	0.756997i
$41$	8.12416			1.26878			0.634390	−	0.773013i	$-0.281251\pi$
$41$	8.12416			1.26878			0.634390	+	0.773013i	$0.281251\pi$
$42$	−0.513485	+	2.39680i	−0.0792324	+	0.369834i
$43$	−2.42576	+	2.42576i	−0.369925	+	0.369925i	−0.867450	−	0.497525i	$-0.834242\pi$
$43$	−2.42576	+	2.42576i	−0.369925	+	0.369925i	0.497525	+	0.867450i	$0.334242\pi$
$44$	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	0.126447	−	0.991973i	$-0.459643\pi$
$47$	−5.93375	−	5.93375i	−0.865527	−	0.865527i	−0.991973	+	0.126447i	$0.959643\pi$
$48$	3.77496	+	0.222194i	0.544869	+	0.0320710i
$49$		−	3.63864i		−	0.519806i
$50$	4.34752	−	5.57665i	0.614832	−	0.788658i
$51$			6.48947i			0.908708i
$52$	0.368955	+	0.970478i	0.0511648	+	0.134581i
$53$	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
$58$	2.67844	+	0.573822i	0.351696	+	0.0753466i
$59$	9.15604			1.19201			0.596007	−	0.802979i	$-0.296753\pi$
$59$	9.15604			1.19201			0.596007	+	0.802979i	$0.296753\pi$
$60$	−0.580503	−	4.18780i	−0.0749426	−	0.540642i
$61$	4.48236			0.573908			0.286954	−	0.957944i	$-0.407357\pi$
$61$	4.48236			0.573908			0.286954	+	0.957944i	$0.407357\pi$
$62$	14.7377	+	3.15738i	1.87169	+	0.400987i
$63$	−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	0.234509	−	0.972114i	$-0.424652\pi$
$67$	−6.03756	−	6.03756i	−0.737605	−	0.737605i	−0.972114	+	0.234509i	$0.924652\pi$
$68$	12.8328	−	4.87875i	1.55620	−	0.591636i
$69$		−	2.48352i		−	0.298981i
$70$	−1.98142	−	5.44863i	−0.236825	−	0.651236i
$71$		−	4.69476i		−	0.557166i	−0.960412	−	0.278583i	$-0.910135\pi$
$71$		−	4.69476i		−	0.557166i	0.960412	−	0.278583i	$-0.0898647\pi$
$72$	4.80271	+	3.52490i	0.566005	+	0.415413i
$73$	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
$78$	0.145392	−	0.678647i	0.0164624	−	0.0768417i
$79$	1.35636			0.152602			0.0763009	−	0.997085i	$-0.475689\pi$
$79$	1.35636			0.152602			0.0763009	+	0.997085i	$0.475689\pi$
$80$	−7.84486	+	4.29630i	−0.877082	+	0.480341i
$81$	−1.75517			−0.195019
$82$	−2.40683	+	11.2344i	−0.265790	+	1.24063i
$83$	−7.25746	+	7.25746i	−0.796609	+	0.796609i	−0.982559	−	0.185950i	$-0.940464\pi$
$83$	−7.25746	+	7.25746i	−0.796609	+	0.796609i	0.185950	+	0.982559i	$0.440464\pi$
$84$	−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
$88$	2.28020	+	1.67353i	0.243070	+	0.178399i
$89$			2.98804i			0.316732i	0.987381	+	0.158366i	$0.0506225\pi$
$89$			2.98804i			0.316732i	−0.987381	+	0.158366i	$0.949377\pi$
$90$	2.81657	−	6.03578i	0.296893	−	0.636227i
$91$		−	0.951760i		−	0.0997716i
$92$	−4.91112	+	1.86710i	−0.512019	+	0.194659i
$93$	−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	$0.377456\pi$
$98$	5.03164	+	1.07797i	0.508273	+	0.108891i
$99$	−2.10627			−0.211688
$100$	6.42361	+	7.66402i	0.642361	+	0.766402i
$101$	−7.54185			−0.750442			−0.375221	−	0.926935i	$-0.622433\pi$
$101$	−7.54185			−0.750442			−0.375221	+	0.926935i	$0.622433\pi$
$102$	−8.97387	−	1.92254i	−0.888545	−	0.190360i
$103$	−1.50798	+	1.50798i	−0.148586	+	0.148586i	−0.777486	−	0.628900i	$-0.783505\pi$
$103$	−1.50798	+	1.50798i	−0.148586	+	0.148586i	0.628900	+	0.777486i	$0.283505\pi$
$104$	−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	0.975686	−	0.219171i	$-0.0703352\pi$
$107$	7.82546	+	7.82546i	0.756516	+	0.756516i	−0.219171	+	0.975686i	$0.570335\pi$
$108$	−3.43092	−	9.02449i	−0.330140	−	0.868382i
$109$			10.8635i			1.04053i	0.854004	+	0.520266i	$0.174167\pi$
$109$			10.8635i			1.04053i	−0.854004	+	0.520266i	$0.825833\pi$
$110$	1.33723	−	2.86562i	0.127500	−	0.273227i
$111$		−	4.95254i		−	0.470074i
$112$	−0.430910	+	7.32093i	−0.0407172	+	0.691763i
$113$	−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
$118$	−2.71253	+	12.6613i	−0.249708	+	1.16557i
$119$	−12.5853			−1.15369
$120$	5.96301	+	0.437918i	0.544346	+	0.0399763i
$121$	−1.00000			−0.0909091
$122$	−1.32793	+	6.19837i	−0.120225	+	0.561174i
$123$	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	$-0.886840\pi$
$127$	−14.4872	−	14.4872i	−1.28553	−	1.28553i	−0.348062	−	0.937471i	$-0.613160\pi$
$128$	11.2643	−	1.05588i	0.995635	−	0.0933273i
$129$			3.24314i			0.285543i
$130$	0.561035	+	1.54277i	0.0492060	+	0.135310i
$131$		−	15.9254i		−	1.39141i	−0.718327	−	0.695706i	$-0.755092\pi$
$131$		−	15.9254i		−	1.39141i	0.718327	−	0.695706i	$-0.244908\pi$
$132$	−0.671903	−	1.76733i	−0.0584816	−	0.153827i
$133$	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	$0.196191\pi$
$138$	3.43430	+	0.735758i	0.292347	+	0.0626319i
$139$	9.60303			0.814519			0.407259	−	0.913313i	$-0.366485\pi$
$139$	9.60303			0.814519			0.407259	+	0.913313i	$0.366485\pi$
$140$	8.12156	−	1.12579i	0.686397	−	0.0951468i
$141$	−7.93319			−0.668095
$142$	6.49208	+	1.39085i	0.544804	+	0.116718i
$143$	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
$148$	−9.79354	+	3.72329i	−0.805024	+	0.306053i
$149$			17.8000i			1.45823i	0.684389	+	0.729117i	$0.260069\pi$
$149$			17.8000i			1.45823i	−0.684389	+	0.729117i	$0.739931\pi$
$150$	−0.821649	−	6.63411i	−0.0670874	−	0.541673i
$151$		−	0.874494i		−	0.0711653i	−0.999367	−	0.0355827i	$-0.988671\pi$
$151$		−	0.874494i		−	0.0711653i	0.999367	−	0.0355827i	$-0.0113287\pi$
$152$	8.85548	−	12.0657i	0.718274	−	0.978657i
$153$	−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	$0.0923962\pi$
$158$	−0.401828	+	1.87562i	−0.0319677	+	0.149216i
$159$	6.73519			0.534135
$160$	−3.61699	−	12.1209i	−0.285948	−	0.958245i
$161$	4.81640			0.379585
$162$	0.519980	−	2.42711i	0.0408535	−	0.190692i
$163$	−5.64237	+	5.64237i	−0.441945	+	0.441945i	−0.892665	−	0.450721i	$-0.851167\pi$
$163$	−5.64237	+	5.64237i	−0.441945	+	0.441945i	0.450721	+	0.892665i	$0.351167\pi$
$164$	−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	0.913386	−	0.407093i	$-0.133458\pi$
$167$	6.54275	+	6.54275i	0.506293	+	0.506293i	−0.407093	+	0.913386i	$0.633458\pi$
$168$	2.90064	−	3.95215i	0.223789	−	0.304915i
$169$		−	12.7305i		−	0.979270i
$170$	20.4003	−	7.41866i	1.56463	−	0.568985i
$171$			11.1453i			0.852305i
$172$	6.41325	−	2.43818i	0.489006	−	0.185909i
$173$	−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
$178$	−4.13197	−	0.885224i	−0.309704	−	0.0663503i
$179$	13.4491			1.00523			0.502615	−	0.864511i	$-0.332371\pi$
$179$	13.4491			1.00523			0.502615	+	0.864511i	$0.332371\pi$
$180$	7.51206	+	5.68299i	0.559916	+	0.423585i
$181$	12.9203			0.960359			0.480179	−	0.877170i	$-0.340572\pi$
$181$	12.9203			0.960359			0.480179	+	0.877170i	$0.340572\pi$
$182$	1.31613	+	0.281964i	0.0975579	+	0.0209006i
$183$	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
$188$	5.96413	+	15.6877i	0.434979	+	1.14414i
$189$			8.85043i			0.643774i
$190$	−15.1635	−	7.07598i	−1.10007	−	0.513346i
$191$			8.60539i			0.622664i	0.950301	+	0.311332i	$0.100775\pi$
$191$			8.60539i			0.622664i	−0.950301	+	0.311332i	$0.899225\pi$
$192$	−6.70523	−	3.49838i	−0.483908	−	0.252474i
$193$	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	$0.248083\pi$
$198$	0.623994	−	2.91262i	0.0443453	−	0.206991i
$199$	−19.0177			−1.34813			−0.674065	−	0.738672i	$-0.735453\pi$
$199$	−19.0177			−1.34813			−0.674065	+	0.738672i	$0.735453\pi$
$200$	−12.5011	+	6.61229i	−0.883962	+	0.467559i
$201$	−8.07198			−0.569353
$202$	2.23432	−	10.4291i	0.157206	−	0.733791i
$203$	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
$208$	0.122011	−	2.07290i	0.00845995	−	0.143730i
$209$			5.29151i			0.366021i
$210$	−4.96684	−	2.31776i	−0.342745	−	0.159941i
$211$			22.3887i			1.54131i	0.637256	+	0.770653i	$0.280070\pi$
$211$			22.3887i			1.54131i	−0.637256	+	0.770653i	$0.719930\pi$
$212$	−5.06348	−	13.3187i	−0.347761	−	0.914732i
$213$	−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
$218$	−15.0224	−	3.21837i	−1.01745	−	0.217975i
$219$	4.46393			0.301645
$220$	3.56652	+	2.69813i	0.240455	+	0.181908i
$221$	3.56349			0.239707
$222$	6.84854	+	1.46722i	0.459644	+	0.0984732i
$223$	18.6892	−	18.6892i	1.25152	−	1.25152i	0.296482	−	0.955038i	$-0.404186\pi$
$223$	18.6892	−	18.6892i	1.25152	−	1.25152i	0.955038	−	0.296482i	$-0.0958136\pi$
$224$	−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	0.593130	−	0.805107i	$-0.297892\pi$
$227$	−3.19376	−	3.19376i	−0.211978	−	0.211978i	−0.805107	+	0.593130i	$0.797892\pi$
$228$	−9.35186	+	3.55538i	−0.619342	+	0.235461i
$229$			16.8873i			1.11594i	0.829860	+	0.557972i	$0.188421\pi$
$229$			16.8873i			1.11594i	−0.829860	+	0.557972i	$0.811579\pi$
$230$	−7.80719	+	2.83912i	−0.514791	+	0.187206i
$231$			1.73325i			0.114039i
$232$	−4.41655	−	3.24148i	−0.289961	−	0.212814i
$233$	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
$238$	3.72846	−	17.4034i	0.241680	−	1.12809i
$239$	4.23222			0.273759			0.136880	−	0.990588i	$-0.456293\pi$
$239$	4.23222			0.273759			0.136880	+	0.990588i	$0.456293\pi$
$240$	−2.37214	+	8.11612i	−0.153121	+	0.523893i
$241$	−10.5664			−0.680641			−0.340321	−	0.940309i	$-0.610536\pi$
$241$	−10.5664			−0.680641			−0.340321	+	0.940309i	$0.610536\pi$
$242$	0.296256	−	1.38283i	0.0190440	−	0.0888920i
$243$	−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
$248$	−24.3015	−	17.8358i	−1.54315	−	1.13257i
$249$			9.70293i			0.614898i
$250$	9.97966	+	12.2640i	0.631169	+	0.775645i
$251$		−	7.97831i		−	0.503587i	−0.967781	−	0.251793i	$-0.918980\pi$
$251$		−	7.97831i		−	0.503587i	0.967781	−	0.251793i	$-0.0810203\pi$
$252$	7.21916	−	2.74457i	0.454764	−	0.172892i
$253$	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	$0.959096\pi$
$258$	−4.48473	−	0.960800i	−0.279207	−	0.0598168i
$259$	9.60465			0.596804
$260$	−2.29960	+	0.318765i	−0.142615	+	0.0197690i
$261$	4.07967			0.252525
$262$	22.0222	+	4.71800i	1.36054	+	0.291479i
$263$	−9.67785	+	9.67785i	−0.596762	+	0.596762i	−0.939449	−	0.342687i	$-0.888663\pi$
$263$	−9.67785	+	9.67785i	−0.596762	+	0.596762i	0.342687	+	0.939449i	$0.388663\pi$
$264$	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
$268$	6.06847	+	15.9622i	0.370691	+	0.975044i
$269$		−	26.4122i		−	1.61038i	−0.593018	−	0.805189i	$-0.702064\pi$
$269$		−	26.4122i		−	1.61038i	0.593018	−	0.805189i	$-0.297936\pi$
$270$	−5.21707	−	14.3462i	−0.317501	−	0.873082i
$271$		−	31.3605i		−	1.90501i	−0.304518	−	0.952506i	$-0.598495\pi$
$271$		−	31.3605i		−	1.90501i	0.304518	−	0.952506i	$-0.401505\pi$
$272$	−27.4104	−	1.61337i	−1.66200	−	0.0978251i
$273$	−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	$0.209358\pi$
$278$	−2.84495	+	13.2794i	−0.170629	+	0.796446i
$279$	22.4478			1.34391
$280$	−0.849273	+	11.5643i	−0.0507537	+	0.691099i
$281$	−8.14685			−0.486000			−0.243000	−	0.970026i	$-0.578132\pi$
$281$	−8.14685			−0.486000			−0.243000	+	0.970026i	$0.578132\pi$
$282$	2.35025	−	10.9703i	0.139955	−	0.653271i
$283$	17.7814	−	17.7814i	1.05699	−	1.05699i	0.0587187	−	0.998275i	$-0.481299\pi$
$283$	17.7814	−	17.7814i	1.05699	−	1.05699i	0.998275	−	0.0587187i	$-0.0187015\pi$
$284$	−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
$288$	−5.87427	−	10.3661i	−0.346145	−	0.610830i
$289$		−	30.1207i		−	1.77180i
$290$	−2.59011	+	5.55048i	−0.152096	+	0.325935i
$291$			7.25873i			0.425514i
$292$	−3.35596	−	8.82733i	−0.196393	−	0.516581i
$293$	−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
$298$	−24.6145	−	5.27335i	−1.42588	−	0.305477i
$299$	−1.36375			−0.0788678
$300$	9.41730	+	0.829188i	0.543708	+	0.0478732i
$301$	−6.28956			−0.362524
$302$	1.20928	+	0.259074i	0.0695863	+	0.0149080i
$303$	−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	0.903901	−	0.427742i	$-0.140691\pi$
$307$	8.34298	+	8.34298i	0.476159	+	0.476159i	−0.427742	+	0.903901i	$0.640691\pi$
$308$	3.42746	−	1.30305i	0.195298	−	0.0742480i
$309$			2.01612i			0.114693i
$310$	−14.2517	+	30.5407i	−0.809443	+	1.73460i
$311$			7.13322i			0.404488i	0.979335	+	0.202244i	$0.0648233\pi$
$311$			7.13322i			0.404488i	−0.979335	+	0.202244i	$0.935177\pi$
$312$	−0.821309	+	1.11904i	−0.0464975	+	0.0633533i
$313$	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	$0.366660\pi$
$318$	−1.99534	+	9.31366i	−0.111893	+	0.522284i
$319$	1.93692			0.108446
$320$	17.8328	−	1.41080i	0.996885	−	0.0788659i
$321$	10.4623			0.583950
$322$	−1.42688	+	6.66028i	−0.0795172	+	0.371163i
$323$	−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
$328$	13.5960	−	18.5247i	0.750714	−	1.02286i
$329$		−	15.3852i		−	0.848211i
$330$	−1.02170	−	2.80953i	−0.0562427	−	0.154659i
$331$			17.2364i			0.947398i	0.880687	+	0.473699i	$0.157082\pi$
$331$			17.2364i			0.947398i	−0.880687	+	0.473699i	$0.842918\pi$
$332$	19.1873	−	7.29461i	1.05304	−	0.400344i
$333$	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	$0.225562\pi$
$338$	17.6042	+	3.77149i	0.957542	+	0.205142i
$339$	−7.02532			−0.381563
$340$	4.21509	+	30.4080i	0.228595	+	1.64911i
$341$	10.6576			0.577142
$342$	−15.4122	−	3.30187i	−0.833394	−	0.178545i
$343$	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	0.297027	−	0.954869i	$-0.404005\pi$
$347$	−12.2542	−	12.2542i	−0.657842	−	0.657842i	−0.954869	+	0.297027i	$0.904005\pi$
$348$	1.30142	+	3.42318i	0.0697634	+	0.183502i
$349$			16.0748i			0.860464i	0.902718	+	0.430232i	$0.141568\pi$
$349$			16.0748i			0.860464i	−0.902718	+	0.430232i	$0.858432\pi$
$350$	12.8658	−	1.59346i	0.687706	−	0.0851738i
$351$		−	2.50598i		−	0.133759i
$352$	−2.78895	−	4.92156i	−0.148651	−	0.262320i
$353$	−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
$358$	−3.98436	+	18.5978i	−0.210580	+	0.982925i
$359$	−36.1440			−1.90761			−0.953804	−	0.300429i	$-0.902870\pi$
$359$	−36.1440			−1.90761			−0.953804	+	0.300429i	$0.902870\pi$
$360$	−10.0841	+	8.70432i	−0.531480	+	0.458758i
$361$	9.00005			0.473687
$362$	−3.82771	+	17.8667i	−0.201180	+	0.939051i
$363$	−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	0.267920	−	0.963441i	$-0.413664\pi$
$367$	−13.3243	−	13.3243i	−0.695521	−	0.695521i	−0.963441	+	0.267920i	$0.913664\pi$
$368$	10.4900	+	0.617439i	0.546827	+	0.0321862i
$369$			17.1117i			0.890798i
$370$	−15.5688	+	5.66166i	−0.809382	+	0.294336i
$371$			13.0618i			0.678136i
$372$	7.16088	+	18.8356i	0.371274	+	0.976579i
$373$	−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
$378$	−12.2387	−	2.62199i	−0.629490	−	0.134861i
$379$	−24.6120			−1.26423			−0.632116	−	0.774874i	$-0.717813\pi$
$379$	−24.6120			−1.26423			−0.632116	+	0.774874i	$0.717813\pi$
$380$	14.2772	−	18.8723i	0.732404	−	0.968128i
$381$	−19.3689			−0.992296
$382$	−11.8998	−	2.54939i	−0.608848	−	0.130438i
$383$	−4.11209	+	4.11209i	−0.210118	+	0.210118i	−0.804318	−	0.594200i	$-0.797469\pi$
$383$	−4.11209	+	4.11209i	−0.210118	+	0.210118i	0.594200	+	0.804318i	$0.297469\pi$
$384$	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
$388$	14.3540	−	5.45708i	0.728713	−	0.277041i
$389$		−	35.8237i		−	1.81633i	−0.418609	−	0.908167i	$-0.637482\pi$
$389$		−	35.8237i		−	1.81633i	0.418609	−	0.908167i	$-0.362518\pi$
$390$	1.40635	+	0.656268i	0.0712132	+	0.0332314i
$391$			18.0331i			0.911974i
$392$	−8.29683	−	6.08937i	−0.419053	−	0.307560i
$393$	−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	$0.0993780\pi$
$398$	5.63410	−	26.2984i	0.282412	−	1.31822i
$399$	9.17150			0.459149
$400$	−5.44018	−	19.2459i	−0.272009	−	0.962295i
$401$	−37.6622			−1.88076			−0.940379	−	0.340128i	$-0.889530\pi$
$401$	−37.6622			−1.88076			−0.940379	+	0.340128i	$0.889530\pi$
$402$	2.39137	−	11.1622i	0.119271	−	0.556721i
$403$	−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
$408$	14.7973	+	10.8603i	0.732575	+	0.537665i
$409$			0.683799i			0.0338117i	0.999857	+	0.0169059i	$0.00538156\pi$
$409$			0.683799i			0.0338117i	−0.999857	+	0.0169059i	$0.994618\pi$
$410$	−23.2808	−	10.8639i	−1.14976	−	0.536530i
$411$		−	3.72330i		−	0.183657i
$412$	3.98683	−	1.51571i	0.196417	−	0.0746735i
$413$	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
$418$	−7.31728	−	1.56764i	−0.357900	−	0.0766757i
$419$	−10.8056			−0.527890			−0.263945	−	0.964538i	$-0.585024\pi$
$419$	−10.8056			−0.527890			−0.263945	+	0.964538i	$0.585024\pi$
$420$	4.67653	−	6.18167i	0.228191	−	0.301635i
$421$	−8.45471			−0.412058			−0.206029	−	0.978546i	$-0.566054\pi$
$421$	−8.45471			−0.412058			−0.206029	+	0.978546i	$0.566054\pi$
$422$	−30.9599	−	6.63279i	−1.50711	−	0.322879i
$423$	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
$428$	−7.86552	−	20.6890i	−0.380194	−	1.00004i
$429$		−	0.490765i		−	0.0236944i
$430$	10.1951	−	3.70751i	0.491653	−	0.178792i
$431$		−	21.3584i		−	1.02880i	−0.857550	−	0.514400i	$-0.828015\pi$
$431$		−	21.3584i		−	1.02880i	0.857550	−	0.514400i	$-0.171985\pi$
$432$	−1.13458	+	19.2760i	−0.0545877	+	0.927415i
$433$	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
$438$	−1.32247	+	6.17288i	−0.0631898	+	0.294952i
$439$	−14.5992			−0.696784			−0.348392	−	0.937349i	$-0.613272\pi$
$439$	−14.5992			−0.696784			−0.348392	+	0.937349i	$0.613272\pi$
$440$	−4.78767	+	4.13258i	−0.228243	+	0.197013i
$441$	7.66396			0.364950
$442$	−1.05571	+	4.92772i	−0.0502148	+	0.234388i
$443$	−4.09243	+	4.09243i	−0.194437	+	0.194437i	−0.797610	−	0.603173i	$-0.793903\pi$
$443$	−4.09243	+	4.09243i	−0.194437	+	0.194437i	0.603173	+	0.797610i	$0.293903\pi$
$444$	−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
$448$	6.78455	−	13.0037i	0.320540	−	0.614368i
$449$		−	24.1892i		−	1.14156i	−0.821103	−	0.570781i	$-0.806641\pi$
$449$		−	24.1892i		−	1.14156i	0.821103	−	0.570781i	$-0.193359\pi$
$450$	11.7459	+	9.15705i	0.553708	+	0.431667i
$451$			8.12416i			0.382552i
$452$	5.28160	+	13.8924i	0.248425	+	0.653444i
$453$	−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	$0.430104\pi$
$458$	−23.3524	−	5.00296i	−1.09118	−	0.233773i
$459$	−33.1370			−1.54670
$460$	−1.61312	−	11.6372i	−0.0752120	−	0.542585i
$461$	27.9186			1.30030			0.650150	−	0.759806i	$-0.274706\pi$
$461$	27.9186			1.30030			0.650150	+	0.759806i	$0.274706\pi$
$462$	−2.39680	−	0.513485i	−0.111509	−	0.0238895i
$463$	0.269175	−	0.269175i	0.0125096	−	0.0125096i	−0.700824	−	0.713334i	$-0.747184\pi$
$463$	0.269175	−	0.269175i	0.0125096	−	0.0125096i	0.713334	+	0.700824i	$0.247184\pi$
$464$	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	0.523065	−	0.852293i	$-0.324788\pi$
$467$	−7.11467	−	7.11467i	−0.329227	−	0.329227i	−0.852293	+	0.523065i	$0.824788\pi$
$468$	−2.04409	+	0.777118i	−0.0944879	+	0.0359223i
$469$		−	15.6543i		−	0.722849i
$470$	9.06909	+	24.9387i	0.418326	+	1.15034i
$471$		−	11.2566i		−	0.518678i
$472$	15.3229	−	20.8776i	0.705293	−	0.960969i
$473$	−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
$478$	−1.25382	+	5.85246i	−0.0573483	+	0.267685i
$479$	−14.3186			−0.654231			−0.327116	−	0.944984i	$-0.606077\pi$
$479$	−14.3186			−0.654231			−0.327116	+	0.944984i	$0.606077\pi$
$480$	−10.5205	−	5.68473i	−0.480193	−	0.259471i
$481$	−2.71953			−0.124000
$482$	3.13035	−	14.6116i	0.142584	−	0.665539i
$483$	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	0.945873	−	0.324537i	$-0.105208\pi$
$487$	13.7117	+	13.7117i	0.621337	+	0.621337i	−0.324537	+	0.945873i	$0.605208\pi$
$488$	7.50136	−	10.2207i	0.339571	−	0.462668i
$489$			7.54363i			0.341135i
$490$	−4.86572	+	10.4270i	−0.219811	+	0.471043i
$491$		−	6.52789i		−	0.294599i	−0.989092	−	0.147300i	$-0.952942\pi$
$491$		−	6.52789i		−	0.294599i	0.989092	−	0.147300i	$-0.0470582\pi$
$492$	−14.3581	+	5.45865i	−0.647314	+	0.246095i
$493$	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
$498$	−13.4176	−	2.87455i	−0.601255	−	0.128812i
$499$	8.11300			0.363188			0.181594	−	0.983374i	$-0.441874\pi$
$499$	8.11300			0.363188			0.181594	+	0.983374i	$0.441874\pi$
$500$	−19.9157	+	10.1669i	−0.890655	+	0.454679i
$501$	8.74739			0.390805
$502$	11.0327	+	2.36362i	0.492413	+	0.105493i
$503$	−9.92654	+	9.92654i	−0.442602	+	0.442602i	−0.892886	−	0.450283i	$-0.851323\pi$
$503$	−9.92654	+	9.92654i	−0.442602	+	0.442602i	0.450283	+	0.892886i	$0.351323\pi$
$504$	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
$508$	14.5614	+	38.3015i	0.646058	+	1.69935i
$509$		−	7.00878i		−	0.310659i	−0.987863	−	0.155329i	$-0.950356\pi$
$509$		−	7.00878i		−	0.310659i	0.987863	−	0.155329i	$-0.0496439\pi$
$510$	8.67794	−	18.5964i	0.384266	−	0.823462i
$511$			8.65708i			0.382967i
$512$	−21.4165	−	7.30296i	−0.946485	−	0.322748i
$513$	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
$518$	−2.84543	+	13.2817i	−0.125021	+	0.583562i
$519$	−13.6540			−0.599344
$520$	0.240469	−	3.27440i	0.0105453	−	0.143592i
$521$	20.0023			0.876318			0.438159	−	0.898897i	$-0.355631\pi$
$521$	20.0023			0.876318			0.438159	+	0.898897i	$0.355631\pi$
$522$	−1.20862	+	5.64150i	−0.0529000	+	0.246922i
$523$	19.4284	−	19.4284i	0.849544	−	0.849544i	−0.140532	−	0.990076i	$-0.544881\pi$
$523$	19.4284	−	19.4284i	0.849544	−	0.849544i	0.990076	+	0.140532i	$0.0448813\pi$
$524$	−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
$528$	−0.222194	+	3.77496i	−0.00966976	+	0.164284i
$529$			16.0987i			0.699944i
$530$	−7.69956	−	21.1727i	−0.334448	−	0.919683i
$531$			19.2851i			0.836901i
$532$	−6.89509	−	18.1364i	−0.298940	−	0.786314i
$533$	−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
$538$	36.5237	+	7.82475i	1.57465	+	0.337349i
$539$	3.63864			0.156727
$540$	21.3840	−	2.96420i	0.920222	−	0.127559i
$541$	−25.8531			−1.11151			−0.555755	−	0.831346i	$-0.687571\pi$
$541$	−25.8531			−1.11151			−0.555755	+	0.831346i	$0.687571\pi$
$542$	43.3664	+	9.29072i	1.86274	+	0.399070i
$543$	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	0.638684	−	0.769469i	$-0.279479\pi$
$547$	−3.05881	−	3.05881i	−0.130785	−	0.130785i	−0.769469	+	0.638684i	$0.779479\pi$
$548$	−7.36274	+	2.79915i	−0.314521	+	0.119574i
$549$			9.44106i			0.402935i
$550$	5.57665	+	4.34752i	0.237789	+	0.185379i
$551$		−	10.2492i		−	0.436631i
$552$	−5.66293	−	4.15625i	−0.241030	−	0.176902i
$553$	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	$0.885786\pi$
$558$	−6.65028	+	31.0416i	−0.281529	+	1.31410i
$559$	1.78087			0.0753229
$560$	−15.7399	−	4.60039i	−0.665133	−	0.194402i
$561$	−6.48947			−0.273986
$562$	2.41355	−	11.2657i	0.101809	−	0.475217i
$563$	21.8066	−	21.8066i	0.919038	−	0.919038i	−0.0779218	−	0.996959i	$-0.524828\pi$
$563$	21.8066	−	21.8066i	0.919038	−	0.919038i	0.996959	+	0.0779218i	$0.0248285\pi$
$564$	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
$568$	−10.7050	−	7.85682i	−0.449172	−	0.329665i
$569$			18.9769i			0.795553i	0.917482	+	0.397776i	$0.130218\pi$
$569$			18.9769i			0.795553i	−0.917482	+	0.397776i	$0.869782\pi$
$570$	−14.8666	+	5.40633i	−0.622695	+	0.226446i
$571$			7.44095i			0.311394i	0.987805	+	0.155697i	$0.0497624\pi$
$571$			7.44095i			0.311394i	−0.987805	+	0.155697i	$0.950238\pi$
$572$	−0.970478	+	0.368955i	−0.0405777	+	0.0154268i
$573$	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	$0.110768\pi$
$578$	41.6519	+	8.92342i	1.73249	+	0.371165i
$579$	10.5436			0.438177
$580$	−6.90806	−	5.22605i	−0.286841	−	0.217000i
$581$	−18.8173			−0.780672
$582$	−10.0376	−	2.15044i	−0.416073	−	0.0891386i
$583$	−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	$-0.924390\pi$
$587$	−29.2489	−	29.2489i	−1.20723	−	1.20723i	−0.235309	−	0.971921i	$-0.575610\pi$
$588$	2.44481	+	6.43070i	0.100822	+	0.265198i
$589$		−	56.3948i		−	2.32371i
$590$	−26.2378	−	12.2438i	−1.08019	−	0.504068i
$591$		−	0.159818i		−	0.00657405i
$592$	20.9186	+	1.23127i	0.859751	+	0.0506049i
$593$	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
$598$	0.404019	−	1.88584i	0.0165216	−	0.0771179i
$599$	−3.17816			−0.129856			−0.0649280	−	0.997890i	$-0.520682\pi$
$599$	−3.17816			−0.129856			−0.0649280	+	0.997890i	$0.520682\pi$
$600$	−3.93656	+	12.7769i	−0.160709	+	0.521616i
$601$	−25.3530			−1.03417			−0.517084	−	0.855935i	$-0.672983\pi$
$601$	−25.3530			−1.03417			−0.517084	+	0.855935i	$0.672983\pi$
$602$	1.86332	−	8.69742i	0.0759431	−	0.354480i
$603$	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	$0.0900291\pi$
$607$	30.5343	+	30.5343i	1.23935	+	1.23935i	0.279079	+	0.960268i	$0.409971\pi$
$608$	−26.0425	+	14.7577i	−1.05616	+	0.598505i
$609$		−	3.35716i		−	0.136039i
$610$	−12.8448	−	5.99397i	−0.520070	−	0.242689i
$611$			4.35627i			0.176236i
$612$	10.2760	+	27.0293i	0.415381	+	1.09259i
$613$	−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	$0.897455\pi$
$618$	−2.78796	−	0.597286i	−0.112148	−	0.0240263i
$619$	27.2472			1.09516			0.547579	−	0.836754i	$-0.315550\pi$
$619$	27.2472			1.09516			0.547579	+	0.836754i	$0.315550\pi$
$620$	−38.0106	−	28.7556i	−1.52654	−	1.15485i
$621$	12.6815			0.508893
$622$	−9.86406	−	2.11326i	−0.395513	−	0.0847338i
$623$	−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
$628$	−22.2597	+	8.46267i	−0.888260	+	0.337697i
$629$			35.9609i			1.43385i
$630$	11.4763	−	4.17341i	0.457226	−	0.166272i
$631$			11.2725i			0.448751i	0.974503	+	0.224376i	$0.0720343\pi$
$631$			11.2725i			0.448751i	−0.974503	+	0.224376i	$0.927966\pi$
$632$	2.26990	−	3.09276i	0.0902917	−	0.123023i
$633$	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
$638$	−0.573822	+	2.67844i	−0.0227178	+	0.106040i
$639$	9.88843			0.391180
$640$	−3.33218	+	25.0778i	−0.131716	+	0.991288i
$641$	−3.36250			−0.132811			−0.0664055	−	0.997793i	$-0.521153\pi$
$641$	−3.36250			−0.132811			−0.0664055	+	0.997793i	$0.521153\pi$
$642$	−3.09952	+	14.4677i	−0.122328	+	0.570993i
$643$	−27.1699	+	27.1699i	−1.07148	+	1.07148i	−0.0742356	+	0.997241i	$0.523652\pi$
$643$	−27.1699	+	27.1699i	−1.07148	+	1.07148i	−0.997241	+	0.0742356i	$0.976348\pi$
$644$	−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	0.874316	−	0.485357i	$-0.161310\pi$
$647$	9.89362	+	9.89362i	0.388958	+	0.388958i	−0.485357	+	0.874316i	$0.661310\pi$
$648$	−2.93733	+	4.00214i	−0.115389	+	0.157219i
$649$			9.15604i			0.359406i
$650$	−3.64292	+	0.451183i	−0.142887	+	0.0176969i
$651$		−	18.4723i		−	0.723986i
$652$	14.9174	−	5.67126i	0.584209	−	0.222104i
$653$	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
$658$	21.2751	+	4.55794i	0.829391	+	0.177687i
$659$	−3.72674			−0.145173			−0.0725865	−	0.997362i	$-0.523125\pi$
$659$	−3.72674			−0.145173			−0.0725865	+	0.997362i	$0.523125\pi$
$660$	4.18780	−	0.580503i	0.163010	−	0.0225961i
$661$	19.5967			0.762225			0.381112	−	0.924529i	$-0.375541\pi$
$661$	19.5967			0.762225			0.381112	+	0.924529i	$0.375541\pi$
$662$	−23.8351	−	5.10638i	−0.926377	−	0.198465i
$663$	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
$668$	−6.57625	−	17.2978i	−0.254443	−	0.669271i
$669$		−	24.9867i		−	0.966042i
$670$	9.22775	+	25.3750i	0.356499	+	0.980322i
$671$			4.48236i			0.173040i
$672$	−8.53029	+	4.83394i	−0.329063	+	0.186473i
$673$	−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	$0.245593\pi$
$678$	2.08129	−	9.71486i	0.0799315	−	0.373097i
$679$	−14.0771			−0.540231
$680$	−43.2980	−	3.17977i	−1.66040	−	0.121939i
$681$	−4.26993			−0.163624
$682$	−3.15738	+	14.7377i	−0.120902	+	0.564336i
$683$	19.5295	−	19.5295i	0.747275	−	0.747275i	−0.226692	−	0.973967i	$-0.572791\pi$
$683$	19.5295	−	19.5295i	0.747275	−	0.747275i	0.973967	+	0.226692i	$0.0727910\pi$
$684$	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
$688$	−13.6985	−	0.806291i	−0.522249	−	0.0307396i
$689$		−	3.69842i		−	0.140899i
$690$	−3.32105	+	7.11685i	−0.126430	+	0.270934i
$691$			15.5219i			0.590481i	0.955423	+	0.295240i	$0.0953997\pi$
$691$			15.5219i			0.590481i	−0.955423	+	0.295240i	$0.904600\pi$
$692$	10.2650	+	27.0005i	0.390217	+	1.02640i
$693$	−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
$698$	−22.2288	−	4.76225i	−0.841372	−	0.180254i
$699$	1.49008			0.0563599
$700$	−1.60808	+	18.2633i	−0.0607796	+	0.690290i
$701$	30.9689			1.16968			0.584839	−	0.811149i	$-0.301158\pi$
$701$	30.9689			1.16968			0.584839	+	0.811149i	$0.301158\pi$
$702$	3.46536	+	0.742410i	0.130791	+	0.0280205i
$703$	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
$708$	−16.1818	+	6.15197i	−0.608149	+	0.231205i
$709$			28.8659i			1.08408i	0.840352	+	0.542041i	$0.182348\pi$
$709$			28.8659i			1.08408i	−0.840352	+	0.542041i	$0.817652\pi$
$710$	−6.27800	+	13.4534i	−0.235609	+	0.504898i
$711$			2.85685i			0.107140i
$712$	6.81333	+	5.00057i	0.255340	+	0.187404i
$713$	−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
$718$	10.7079	−	49.9812i	0.399614	−	1.86528i
$719$	7.73510			0.288471			0.144235	−	0.989543i	$-0.453928\pi$
$719$	7.73510			0.288471			0.144235	+	0.989543i	$0.453928\pi$
$720$	−9.04916	−	16.5234i	−0.337242	−	0.615790i
$721$	−3.90993			−0.145614
$722$	−2.66631	+	12.4456i	−0.0992300	+	0.463177i
$723$	−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	0.970613	−	0.240647i	$-0.0773597\pi$
$727$	19.6820	+	19.6820i	0.729965	+	0.729965i	−0.240647	+	0.970613i	$0.577360\pi$
$728$	−2.17020	−	1.59280i	−0.0804331	−	0.0590330i
$729$			9.99403i			0.370149i
$730$	−5.10310	−	14.0328i	−0.188874	−	0.519377i
$731$		−	23.5488i		−	0.870983i
$732$	−7.92184	+	3.01171i	−0.292800	+	0.111316i
$733$	−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
$738$	−23.6626	−	5.06943i	−0.871033	−	0.186608i
$739$	−47.7645			−1.75704			−0.878522	−	0.477702i	$-0.841470\pi$
$739$	−47.7645			−1.75704			−0.878522	+	0.477702i	$0.841470\pi$
$740$	−3.21681	−	23.2063i	−0.118252	−	0.853082i
$741$	−2.59689			−0.0953990
$742$	−18.0623	−	3.86964i	−0.663090	−	0.142059i
$743$	−10.2569	+	10.2569i	−0.376290	+	0.376290i	−0.869762	−	0.493472i	$-0.835728\pi$
$743$	−10.2569	+	10.2569i	−0.376290	+	0.376290i	0.493472	+	0.869762i	$0.335728\pi$
$744$	−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
$748$	4.87875	+	12.8328i	0.178385	+	0.469213i
$749$			20.2900i			0.741381i
$750$	14.8695	+	1.52705i	0.542956	+	0.0557600i
$751$		−	0.255515i		−	0.00932386i	−0.999989	−	0.00466193i	$-0.998516\pi$
$751$		−	0.255515i		−	0.00932386i	0.999989	−	0.00466193i	$-0.00148394\pi$
$752$	1.97230	−	33.5084i	0.0719225	−	1.22192i
$753$	−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	$0.325601\pi$
$758$	7.29144	−	34.0343i	0.264837	−	1.23618i
$759$	2.48352			0.0901462
$760$	21.8676	+	25.3340i	0.793220	+	0.918961i
$761$	41.5539			1.50633			0.753164	−	0.657833i	$-0.228527\pi$
$761$	41.5539			1.50633			0.753164	+	0.657833i	$0.228527\pi$
$762$	5.73813	−	26.7839i	0.207871	−	0.970279i
$763$	−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
$768$	9.36708	+	11.8766i	0.338005	+	0.428559i
$769$			12.2677i			0.442383i	0.975230	+	0.221192i	$0.0709946\pi$
$769$			12.2677i			0.442383i	−0.975230	+	0.221192i	$0.929005\pi$
$770$	5.44863	−	1.98142i	0.196355	−	0.0714055i
$771$			24.0031i			0.864449i
$772$	−7.92663	−	20.8498i	−0.285286	−	0.750399i
$773$	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
$778$	49.5382	+	10.6130i	1.77603	+	0.380493i
$779$	42.9890			1.54024
$780$	−1.32415	+	1.75033i	−0.0474121	+	0.0626717i
$781$	4.69476			0.167992
$782$	−24.9368	−	5.34241i	−0.891739	−	0.191044i
$783$	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	0.385321	−	0.922783i	$-0.374091\pi$
$787$	−15.0777	−	15.0777i	−0.537461	−	0.537461i	−0.922783	+	0.385321i	$0.874091\pi$
$788$	−0.316038	+	0.120151i	−0.0112584	+	0.00428019i
$789$			12.9389i			0.460637i
$790$	−3.88680	−	1.81376i	−0.138286	−	0.0645308i
$791$		−	13.6245i		−	0.484431i
$792$	−3.52490	+	4.80271i	−0.125252	+	0.170657i
$793$	−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	$0.209830\pi$
$798$	−2.71711	+	12.6827i	−0.0961846	+	0.448962i
$799$	57.6037			2.03787
$800$	28.2256	−	1.82116i	0.997925	−	0.0643879i
$801$	−6.29362			−0.222374
$802$	11.1576	−	52.0806i	0.393989	−	1.83903i
$803$	−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
$808$	−12.6215	+	17.1969i	−0.444023	+	0.604985i
$809$		−	51.8541i		−	1.82309i	−0.411199	−	0.911546i	$-0.634890\pi$
$809$		−	51.8541i		−	1.82309i	0.411199	−	0.911546i	$-0.365110\pi$
$810$	5.02967	+	2.34708i	0.176724	+	0.0824679i
$811$			8.52533i			0.299365i	0.988734	+	0.149682i	$0.0478251\pi$
$811$			8.52533i			0.299365i	−0.988734	+	0.149682i	$0.952175\pi$
$812$	−6.63871	+	2.52389i	−0.232973	+	0.0885713i
$813$	−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
$818$	−0.945582	−	0.202579i	−0.0330615	−	0.00708302i
$819$	2.00466			0.0700486
$820$	21.9200	−	28.9750i	0.765481	−	1.01185i
$821$	5.85995			0.204514			0.102257	−	0.994758i	$-0.467394\pi$
$821$	5.85995			0.204514			0.102257	+	0.994758i	$0.467394\pi$
$822$	5.14870	+	1.10305i	0.179582	+	0.0384732i
$823$	20.1439	−	20.1439i	0.702173	−	0.702173i	−0.262703	−	0.964877i	$-0.584614\pi$
$823$	20.1439	−	20.1439i	0.702173	−	0.702173i	0.964877	+	0.262703i	$0.0846140\pi$
$824$	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	0.815779	−	0.578364i	$-0.196309\pi$
$827$	6.82747	+	6.82747i	0.237415	+	0.237415i	−0.578364	+	0.815779i	$0.696309\pi$
$828$	−3.93262	−	10.3441i	−0.136668	−	0.359483i
$829$		−	3.96788i		−	0.137810i	−0.997623	−	0.0689051i	$-0.978049\pi$
$829$		−	3.96788i		−	0.137810i	0.997623	−	0.0689051i	$-0.0219506\pi$
$830$	30.5021	−	11.0922i	1.05874	−	0.385017i
$831$		−	4.00702i		−	0.139002i
$832$	−1.92103	+	3.68197i	−0.0665997	+	0.127649i
$833$	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
$838$	3.20123	−	14.9424i	0.110585	−	0.516178i
$839$	−37.1348			−1.28203			−0.641017	−	0.767526i	$-0.721487\pi$
$839$	−37.1348			−1.28203			−0.641017	+	0.767526i	$0.721487\pi$
$840$	7.16278	+	8.29823i	0.247140	+	0.286316i
$841$	25.2484			0.870633
$842$	2.50476	−	11.6915i	0.0863196	−	0.402915i
$843$	−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
$848$	−1.67446	+	28.4482i	−0.0575013	+	0.976917i
$849$		−	23.7730i		−	0.815887i
$850$	5.96607	+	48.1709i	0.204635	+	1.65225i
$851$		−	13.7622i		−	0.471764i
$852$	3.15443	+	8.29722i	0.108069	+	0.284258i
$853$	−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	$0.116263\pi$
$858$	0.678647	+	0.145392i	0.0231686	+	0.00496360i
$859$	−9.25847			−0.315895			−0.157948	−	0.987448i	$-0.550488\pi$
$859$	−9.25847			−0.315895			−0.157948	+	0.987448i	$0.550488\pi$
$860$	2.10651	+	15.1965i	0.0718314	+	0.518198i
$861$	14.0812			0.479886
$862$	29.5352	+	6.32756i	1.00597	+	0.215517i
$863$	17.9760	−	17.9760i	0.611910	−	0.611910i	−0.331534	−	0.943443i	$-0.607566\pi$
$863$	17.9760	−	17.9760i	0.611910	−	0.611910i	0.943443	+	0.331534i	$0.107566\pi$
$864$	−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
$868$	−36.5286	+	13.8874i	−1.23986	+	0.471368i
$869$			1.35636i			0.0460112i
$870$	1.97895	+	5.44182i	0.0670925	+	0.184495i
$871$			4.43248i			0.150189i
$872$	24.7709	+	18.1803i	0.838849	+	0.615664i
$873$	−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	$0.259235\pi$
$878$	4.32511	−	20.1883i	0.145965	−	0.681324i
$879$	−10.1160			−0.341205
$880$	−4.29630	−	7.84486i	−0.144828	−	0.264450i
$881$	43.7931			1.47543			0.737713	−	0.675115i	$-0.235906\pi$
$881$	43.7931			1.47543			0.737713	+	0.675115i	$0.235906\pi$
$882$	−2.27049	+	10.5980i	−0.0764514	+	0.356853i
$883$	−30.5067	+	30.5067i	−1.02663	+	1.02663i	−0.0269967	+	0.999636i	$0.508594\pi$
$883$	−30.5067	+	30.5067i	−1.02663	+	1.02663i	−0.999636	+	0.0269967i	$0.991406\pi$
$884$	−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	0.596750	−	0.802427i	$-0.296458\pi$
$887$	−6.12557	−	6.12557i	−0.205677	−	0.205677i	−0.802427	+	0.596750i	$0.796458\pi$
$888$	−11.2928	−	8.28821i	−0.378961	−	0.278134i
$889$		−	37.5628i		−	1.25982i
$890$	3.99571	−	8.56261i	0.133936	−	0.287019i
$891$		−	1.75517i		−	0.0588005i
$892$	−49.4107	+	18.7849i	−1.65439	+	0.628964i
$893$	−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
$898$	33.4497	+	7.16620i	1.11623	+	0.239139i
$899$	−20.6429			−0.688479
$900$	−16.1425	+	13.5299i	−0.538083	+	0.450995i
$901$	−48.9049			−1.62926
$902$	−11.2344	−	2.40683i	−0.374064	−	0.0801386i
$903$	−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	0.125779	−	0.992058i	$-0.459857\pi$
$907$	−26.0892	−	26.0892i	−0.866279	−	0.866279i	−0.992058	+	0.125779i	$0.959857\pi$
$908$	3.21012	+	8.44370i	0.106531	+	0.280214i
$909$		−	15.8852i		−	0.526878i
$910$	−1.27273	+	2.72739i	−0.0421905	+	0.0904120i
$911$		−	19.5370i		−	0.647291i	−0.946178	−	0.323645i	$-0.895092\pi$
$911$		−	19.5370i		−	0.647291i	0.946178	−	0.323645i	$-0.104908\pi$
$912$	19.9752	+	1.17574i	0.661446	+	0.0389327i
$913$	−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
$918$	9.81702	−	45.8230i	0.324010	−	1.51238i
$919$	11.4181			0.376649			0.188325	−	0.982107i	$-0.439694\pi$
$919$	11.4181			0.376649			0.188325	+	0.982107i	$0.439694\pi$
$920$	16.5702	+	1.21690i	0.546302	+	0.0401200i
$921$	11.1542			0.367545
$922$	−8.27105	+	38.6068i	−0.272392	+	1.27145i
$923$	−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
$928$	5.40196	+	9.53265i	0.177328	+	0.312925i
$929$			27.1354i			0.890285i	0.895460	+	0.445142i	$0.146847\pi$
$929$			27.1354i			0.890285i	−0.895460	+	0.445142i	$0.853153\pi$
$930$	10.8889	+	29.9429i	0.357060	+	0.981865i
$931$		−	19.2539i		−	0.631021i
$932$	−1.12023	−	2.94660i	−0.0366944	−	0.0965189i
$933$	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	$-0.00124610\pi$
$938$	21.6473	+	4.63768i	0.706810	+	0.151425i
$939$	21.5672			0.703820
$940$	−37.1729	+	5.15283i	−1.21245	+	0.168067i
$941$	4.84496			0.157941			0.0789706	−	0.996877i	$-0.474837\pi$
$941$	4.84496			0.157941			0.0789706	+	0.996877i	$0.474837\pi$
$942$	15.5660	+	3.33484i	0.507169	+	0.108655i
$943$	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	0.715075	−	0.699048i	$-0.246393\pi$
$947$	0.493208	+	0.493208i	0.0160271	+	0.0160271i	−0.699048	+	0.715075i	$0.746393\pi$
$948$	−2.39713	+	0.911339i	−0.0778553	+	0.0295989i
$949$		−	2.45123i		−	0.0795704i
$950$	23.0049	−	29.5089i	0.746379	−	0.957395i
$951$			12.0634i			0.391183i
$952$	−21.0618	+	28.6970i	−0.682618	+	0.930074i
$953$	−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
$958$	4.24195	−	19.8002i	0.137051	−	0.639715i
$959$	7.22073			0.233170
$960$	10.9778	−	12.8640i	0.354307	−	0.415183i
$961$	−82.5847			−2.66402
$962$	0.805677	−	3.76067i	0.0259761	−	0.121249i
$963$	−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	$-0.978696\pi$
$967$	−33.1067	−	33.1067i	−1.06464	−	1.06464i	−0.0668797	−	0.997761i	$-0.521304\pi$
$968$	−1.67353	+	2.28020i	−0.0537892	+	0.0732884i
$969$			34.3391i			1.10313i
$970$	22.8185	−	8.29806i	0.732658	−	0.266435i
$971$		−	60.7857i		−	1.95071i	−0.220652	−	0.975353i	$-0.570818\pi$
$971$		−	60.7857i		−	1.95071i	0.220652	−	0.975353i	$-0.429182\pi$
$972$	30.1754	−	11.4721i	0.967878	−	0.367966i
$973$	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	$-0.121067\pi$
$978$	−10.4316	−	2.23484i	−0.333565	−	0.0714624i
$979$	−2.98804			−0.0954982
$980$	−12.9773	−	9.81753i	−0.414545	−	0.313610i
$981$	−22.8814			−0.730547
$982$	9.02699	+	1.93392i	0.288063	+	0.0617140i
$983$	−16.3582	+	16.3582i	−0.521747	+	0.521747i	−0.918099	−	0.396352i	$-0.870276\pi$
$983$	−16.3582	+	16.3582i	−0.521747	+	0.521747i	0.396352	+	0.918099i	$0.370276\pi$
$984$	−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
$988$	1.95233	+	5.13529i	0.0621118	+	0.163375i
$989$			9.01214i			0.286569i
$990$	6.03578	+	2.81657i	0.191830	+	0.0895166i
$991$			37.4154i			1.18854i	0.804266	+	0.594270i	$0.202559\pi$
$991$			37.4154i			1.18854i	−0.804266	+	0.594270i	$0.797441\pi$
$992$	29.7235	+	52.4521i	0.943722	+	1.66536i
$993$	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	$0.196953\pi$
$998$	−2.40352	+	11.2189i	−0.0760821	+	0.355129i
$999$	25.2890			0.800108

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Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

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Modular forms

Varieties

Fields

Representations

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.d.23.6

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