LMFDB - Embedded newform 630.2.t.c.311.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("630.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.16
Character	$\chi$	$=$	630.311
Dual form			630.2.t.c.551.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(1.71699 - 0.227927i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.60092 + 0.661104i) q^{6} +(0.778946 - 2.52849i) q^{7} +1.00000i q^{8} +(2.89610 - 0.782695i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(1.71699 - 0.227927i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.60092 + 0.661104i) q^{6} +(0.778946 - 2.52849i) q^{7} +1.00000i q^{8} +(2.89610 - 0.782695i) q^{9} +(0.866025 + 0.500000i) q^{10} +2.90825i q^{11} +(1.05588 + 1.37299i) q^{12} +(-1.69585 - 0.979098i) q^{13} +(1.93883 - 1.80026i) q^{14} +(1.71699 - 0.227927i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.68420 - 2.91713i) q^{17} +(2.89944 + 0.770216i) q^{18} +(-6.97993 + 4.02986i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.761131 - 4.51892i) q^{21} +(-1.45413 + 2.51862i) q^{22} -2.85531i q^{23} +(0.227927 + 1.71699i) q^{24} +1.00000 q^{25} +(-0.979098 - 1.69585i) q^{26} +(4.79417 - 2.00398i) q^{27} +(2.57921 - 0.589657i) q^{28} +(1.87671 - 1.08352i) q^{29} +(1.60092 + 0.661104i) q^{30} +(-1.90977 + 1.10260i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.662868 + 4.99343i) q^{33} +(2.91713 - 1.68420i) q^{34} +(0.778946 - 2.52849i) q^{35} +(2.12588 + 2.11675i) q^{36} +(1.68075 + 2.91115i) q^{37} -8.05973 q^{38} +(-3.13491 - 1.29457i) q^{39} +1.00000i q^{40} +(-4.24814 + 7.35799i) q^{41} +(2.91862 - 3.53294i) q^{42} +(0.991430 + 1.71721i) q^{43} +(-2.51862 + 1.45413i) q^{44} +(2.89610 - 0.782695i) q^{45} +(1.42766 - 2.47278i) q^{46} +(-0.323599 + 0.560490i) q^{47} +(-0.661104 + 1.60092i) q^{48} +(-5.78649 - 3.93911i) q^{49} +(0.866025 + 0.500000i) q^{50} +(2.22687 - 5.39255i) q^{51} -1.95820i q^{52} +(-9.25368 - 5.34261i) q^{53} +(5.15386 + 0.661591i) q^{54} +2.90825i q^{55} +(2.52849 + 0.778946i) q^{56} +(-11.0659 + 8.51014i) q^{57} +2.16704 q^{58} +(4.55827 + 7.89516i) q^{59} +(1.05588 + 1.37299i) q^{60} +(2.63086 + 1.51893i) q^{61} -2.20521 q^{62} +(0.276870 - 7.93242i) q^{63} -1.00000 q^{64} +(-1.69585 - 0.979098i) q^{65} +(-1.92266 + 4.65587i) q^{66} +(7.56956 + 13.1109i) q^{67} +3.36841 q^{68} +(-0.650802 - 4.90254i) q^{69} +(1.93883 - 1.80026i) q^{70} -7.94202i q^{71} +(0.782695 + 2.89610i) q^{72} +(-12.5756 - 7.26053i) q^{73} +3.36151i q^{74} +(1.71699 - 0.227927i) q^{75} +(-6.97993 - 4.02986i) q^{76} +(7.35347 + 2.26537i) q^{77} +(-2.06763 - 2.68859i) q^{78} +(-2.14752 + 3.71962i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(7.77478 - 4.53352i) q^{81} +(-7.35799 + 4.24814i) q^{82} +(-6.87362 - 11.9055i) q^{83} +(4.29407 - 1.60030i) q^{84} +(1.68420 - 2.91713i) q^{85} +1.98286i q^{86} +(2.97532 - 2.28814i) q^{87} -2.90825 q^{88} +(-8.43872 - 14.6163i) q^{89} +(2.89944 + 0.770216i) q^{90} +(-3.79661 + 3.52526i) q^{91} +(2.47278 - 1.42766i) q^{92} +(-3.02774 + 2.32845i) q^{93} +(-0.560490 + 0.323599i) q^{94} +(-6.97993 + 4.02986i) q^{95} +(-1.37299 + 1.05588i) q^{96} +(-5.21536 + 3.01109i) q^{97} +(-3.04169 - 6.30461i) q^{98} +(2.27627 + 8.42258i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.71699	−	0.227927i	0.991304	−	0.131594i
$3$	1.71699	−	0.227927i	0.991304	−	0.131594i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.60092	+	0.661104i	0.653572	+	0.269895i
$7$	0.778946	−	2.52849i	0.294414	−	0.955678i
$7$	0.778946	−	2.52849i	0.294414	−	0.955678i
$8$			1.00000i			0.353553i
$9$	2.89610	−	0.782695i	0.965366	−	0.260898i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$			2.90825i			0.876870i	0.898763	+	0.438435i	$0.144467\pi$
$11$			2.90825i			0.876870i	−0.898763	+	0.438435i	$0.855533\pi$
$12$	1.05588	+	1.37299i	0.304808	+	0.396349i
$13$	−1.69585	−	0.979098i	−0.470344	−	0.271553i	0.246040	−	0.969260i	$-0.420871\pi$
$13$	−1.69585	−	0.979098i	−0.470344	−	0.271553i	−0.716384	+	0.697707i	$0.754204\pi$
$14$	1.93883	−	1.80026i	0.518174	−	0.481140i
$15$	1.71699	−	0.227927i	0.443325	−	0.0588504i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.68420	−	2.91713i	0.408479	−	0.707507i	−0.586240	−	0.810137i	$-0.699393\pi$
$17$	1.68420	−	2.91713i	0.408479	−	0.707507i	0.994720	+	0.102630i	$0.0327258\pi$
$18$	2.89944	+	0.770216i	0.683405	+	0.181542i
$19$	−6.97993	+	4.02986i	−1.60131	+	0.924514i	−0.610079	+	0.792341i	$0.708862\pi$
$19$	−6.97993	+	4.02986i	−1.60131	+	0.924514i	−0.991227	+	0.132173i	$0.957804\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	0.761131	−	4.51892i	0.166092	−	0.986110i
$22$	−1.45413	+	2.51862i	−0.310020	+	0.536971i
$23$		−	2.85531i		−	0.595374i	−0.954663	−	0.297687i	$-0.903785\pi$
$23$		−	2.85531i		−	0.595374i	0.954663	−	0.297687i	$-0.0962152\pi$
$24$	0.227927	+	1.71699i	0.0465253	+	0.350479i
$25$	1.00000			0.200000
$26$	−0.979098	−	1.69585i	−0.192017	−	0.332583i
$27$	4.79417	−	2.00398i	0.922639	−	0.385665i
$28$	2.57921	−	0.589657i	0.487424	−	0.111435i
$29$	1.87671	−	1.08352i	0.348496	−	0.201204i	−0.315527	−	0.948917i	$-0.602181\pi$
$29$	1.87671	−	1.08352i	0.348496	−	0.201204i	0.664023	+	0.747712i	$0.268848\pi$
$30$	1.60092	+	0.661104i	0.292286	+	0.120701i
$31$	−1.90977	+	1.10260i	−0.343004	+	0.198034i	−0.661600	−	0.749857i	$-0.730122\pi$
$31$	−1.90977	+	1.10260i	−0.343004	+	0.198034i	0.318595	+	0.947891i	$0.396789\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.662868	+	4.99343i	0.115390	+	0.869245i
$34$	2.91713	−	1.68420i	0.500283	−	0.288839i
$35$	0.778946	−	2.52849i	0.131666	−	0.427392i
$36$	2.12588	+	2.11675i	0.354314	+	0.352791i
$37$	1.68075	+	2.91115i	0.276314	+	0.478590i	0.970466	−	0.241239i	$-0.0775537\pi$
$37$	1.68075	+	2.91115i	0.276314	+	0.478590i	−0.694152	+	0.719829i	$0.744220\pi$
$38$	−8.05973			−1.30746
$39$	−3.13491	−	1.29457i	−0.501988	−	0.207297i
$40$			1.00000i			0.158114i
$41$	−4.24814	+	7.35799i	−0.663448	+	1.14912i	0.316256	+	0.948674i	$0.397574\pi$
$41$	−4.24814	+	7.35799i	−0.663448	+	1.14912i	−0.979704	+	0.200451i	$0.935759\pi$
$42$	2.91862	−	3.53294i	0.450353	−	0.545144i
$43$	0.991430	+	1.71721i	0.151192	+	0.261872i	0.931666	−	0.363316i	$-0.118356\pi$
$43$	0.991430	+	1.71721i	0.151192	+	0.261872i	−0.780474	+	0.625188i	$0.785022\pi$
$44$	−2.51862	+	1.45413i	−0.379696	+	0.219218i
$45$	2.89610	−	0.782695i	0.431725	−	0.116677i
$46$	1.42766	−	2.47278i	0.210497	−	0.364591i
$47$	−0.323599	+	0.560490i	−0.0472018	+	0.0817558i	−0.888661	−	0.458565i	$-0.848364\pi$
$47$	−0.323599	+	0.560490i	−0.0472018	+	0.0817558i	0.841459	+	0.540321i	$0.181697\pi$
$48$	−0.661104	+	1.60092i	−0.0954221	+	0.231073i
$49$	−5.78649	−	3.93911i	−0.826641	−	0.562730i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	2.22687	−	5.39255i	0.311824	−	0.755108i
$52$		−	1.95820i		−	0.271553i
$53$	−9.25368	−	5.34261i	−1.27109	−	0.733865i	−0.295897	−	0.955220i	$-0.595619\pi$
$53$	−9.25368	−	5.34261i	−1.27109	−	0.733865i	−0.975193	+	0.221355i	$0.928952\pi$
$54$	5.15386	+	0.661591i	0.701352	+	0.0900312i
$55$			2.90825i			0.392148i
$56$	2.52849	+	0.778946i	0.337883	+	0.104091i
$57$	−11.0659	+	8.51014i	−1.46572	+	1.12720i
$58$	2.16704			0.284546
$59$	4.55827	+	7.89516i	0.593437	+	1.02786i	0.993765	+	0.111491i	$0.0355626\pi$
$59$	4.55827	+	7.89516i	0.593437	+	1.02786i	−0.400329	+	0.916372i	$0.631104\pi$
$60$	1.05588	+	1.37299i	0.136314	+	0.177253i
$61$	2.63086	+	1.51893i	0.336847	+	0.194478i	0.658877	−	0.752251i	$-0.271032\pi$
$61$	2.63086	+	1.51893i	0.336847	+	0.194478i	−0.322030	+	0.946729i	$0.604365\pi$
$62$	−2.20521			−0.280062
$63$	0.276870	−	7.93242i	0.0348824	−	0.999391i
$64$	−1.00000			−0.125000
$65$	−1.69585	−	0.979098i	−0.210344	−	0.121442i
$66$	−1.92266	+	4.65587i	−0.236663	+	0.573098i
$67$	7.56956	+	13.1109i	0.924769	+	1.60175i	0.791932	+	0.610609i	$0.209075\pi$
$67$	7.56956	+	13.1109i	0.924769	+	1.60175i	0.132837	+	0.991138i	$0.457591\pi$
$68$	3.36841			0.408479
$69$	−0.650802	−	4.90254i	−0.0783474	−	0.590197i
$70$	1.93883	−	1.80026i	0.231734	−	0.215172i
$71$		−	7.94202i		−	0.942544i	−0.881988	−	0.471272i	$-0.843795\pi$
$71$		−	7.94202i		−	0.942544i	0.881988	−	0.471272i	$-0.156205\pi$
$72$	0.782695	+	2.89610i	0.0922415	+	0.341309i
$73$	−12.5756	−	7.26053i	−1.47186	−	0.849780i	−0.472363	−	0.881404i	$-0.656599\pi$
$73$	−12.5756	−	7.26053i	−1.47186	−	0.849780i	−0.999500	+	0.0316238i	$0.989932\pi$
$74$			3.36151i			0.390767i
$75$	1.71699	−	0.227927i	0.198261	−	0.0263187i
$76$	−6.97993	−	4.02986i	−0.800653	−	0.462257i
$77$	7.35347	+	2.26537i	0.838006	+	0.258163i
$78$	−2.06763	−	2.68859i	−0.234113	−	0.304423i
$79$	−2.14752	+	3.71962i	−0.241615	+	0.418490i	−0.961175	−	0.275941i	$-0.911010\pi$
$79$	−2.14752	+	3.71962i	−0.241615	+	0.418490i	0.719559	+	0.694431i	$0.244344\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	7.77478	−	4.53352i	0.863864	−	0.503725i
$82$	−7.35799	+	4.24814i	−0.812554	+	0.469128i
$83$	−6.87362	−	11.9055i	−0.754477	−	1.30679i	−0.945634	−	0.325233i	$-0.894557\pi$
$83$	−6.87362	−	11.9055i	−0.754477	−	1.30679i	0.191156	−	0.981560i	$-0.438776\pi$
$84$	4.29407	−	1.60030i	0.468521	−	0.174607i
$85$	1.68420	−	2.91713i	0.182678	−	0.316407i
$86$			1.98286i			0.213817i
$87$	2.97532	−	2.28814i	0.318988	−	0.245314i
$88$	−2.90825			−0.310020
$89$	−8.43872	−	14.6163i	−0.894502	−	1.54932i	−0.834420	−	0.551130i	$-0.814197\pi$
$89$	−8.43872	−	14.6163i	−0.894502	−	1.54932i	−0.0600826	−	0.998193i	$-0.519136\pi$
$90$	2.89944	+	0.770216i	0.305628	+	0.0811879i
$91$	−3.79661	+	3.52526i	−0.397993	+	0.369548i
$92$	2.47278	−	1.42766i	0.257805	−	0.148844i
$93$	−3.02774	+	2.32845i	−0.313962	+	0.241449i
$94$	−0.560490	+	0.323599i	−0.0578101	+	0.0333767i
$95$	−6.97993	+	4.02986i	−0.716126	+	0.413455i
$96$	−1.37299	+	1.05588i	−0.140130	+	0.107766i
$97$	−5.21536	+	3.01109i	−0.529539	+	0.305730i	−0.740829	−	0.671694i	$-0.765567\pi$
$97$	−5.21536	+	3.01109i	−0.529539	+	0.305730i	0.211289	+	0.977424i	$0.432234\pi$
$98$	−3.04169	−	6.30461i	−0.307257	−	0.636862i
$99$	2.27627	+	8.42258i	0.228774	+	0.846501i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	15.6759			1.55981			0.779907	−	0.625895i	$-0.215266\pi$
$101$	15.6759			1.55981			0.779907	+	0.625895i	$0.215266\pi$
$102$	4.62480	−	3.55665i	0.457923	−	0.352161i
$103$			3.68960i			0.363547i	0.983340	+	0.181774i	$0.0581838\pi$
$103$			3.68960i			0.363547i	−0.983340	+	0.181774i	$0.941816\pi$
$104$	0.979098	−	1.69585i	0.0960085	−	0.166292i
$105$	0.761131	−	4.51892i	0.0742788	−	0.441002i
$106$	−5.34261	−	9.25368i	−0.518921	−	0.898797i
$107$	10.6841	−	6.16845i	1.03287	−	0.596327i	0.115063	−	0.993358i	$-0.463293\pi$
$107$	10.6841	−	6.16845i	1.03287	−	0.596327i	0.917805	+	0.397031i	$0.129960\pi$
$108$	4.13258	+	3.14989i	0.397658	+	0.303098i
$109$	−3.48038	+	6.02819i	−0.333360	+	0.577396i	−0.983168	−	0.182702i	$-0.941516\pi$
$109$	−3.48038	+	6.02819i	−0.333360	+	0.577396i	0.649809	+	0.760098i	$0.274849\pi$
$110$	−1.45413	+	2.51862i	−0.138645	+	0.240141i
$111$	3.54936	+	4.61532i	0.336890	+	0.438067i
$112$	1.80026	+	1.93883i	0.170109	+	0.183202i
$113$	2.35912	+	1.36204i	0.221927	+	0.128130i	0.606842	−	0.794822i	$-0.292436\pi$
$113$	2.35912	+	1.36204i	0.221927	+	0.128130i	−0.384915	+	0.922952i	$0.625769\pi$
$114$	−13.8385	+	1.83703i	−1.29609	+	0.172053i
$115$		−	2.85531i		−	0.266259i
$116$	1.87671	+	1.08352i	0.174248	+	0.100602i
$117$	−5.67768	−	1.50823i	−0.524901	−	0.139436i
$118$			9.11655i			0.839246i
$119$	−6.06401	−	6.53077i	−0.555887	−	0.598675i
$120$	0.227927	+	1.71699i	0.0208068	+	0.156739i
$121$	2.54208			0.231098
$122$	1.51893	+	2.63086i	0.137517	+	0.238187i
$123$	−5.61692	+	13.6018i	−0.506461	+	1.22644i
$124$	−1.90977	−	1.10260i	−0.171502	−	0.0990168i
$125$	1.00000			0.0894427
$126$	4.20599	−	6.73125i	0.374699	−	0.599667i
$127$	−6.59858			−0.585529			−0.292765	−	0.956185i	$-0.594575\pi$
$127$	−6.59858			−0.585529			−0.292765	+	0.956185i	$0.594575\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	2.09367	+	2.72245i	0.184337	+	0.239699i
$130$	−0.979098	−	1.69585i	−0.0858726	−	0.148736i
$131$	−4.41012			−0.385314			−0.192657	−	0.981266i	$-0.561710\pi$
$131$	−4.41012			−0.385314			−0.192657	+	0.981266i	$0.561710\pi$
$132$	−3.99300	+	3.07078i	−0.347546	+	0.267277i
$133$	4.75247	+	20.7877i	0.412091	+	1.80252i
$134$			15.1391i			1.30782i
$135$	4.79417	−	2.00398i	0.412617	−	0.172475i
$136$	2.91713	+	1.68420i	0.250142	+	0.144419i
$137$			4.89178i			0.417933i	0.977923	+	0.208966i	$0.0670099\pi$
$137$			4.89178i			0.417933i	−0.977923	+	0.208966i	$0.932990\pi$
$138$	1.88766	−	4.57113i	0.160688	−	0.389120i
$139$	−13.7982	−	7.96639i	−1.17035	−	0.675701i	−0.216586	−	0.976264i	$-0.569492\pi$
$139$	−13.7982	−	7.96639i	−1.17035	−	0.675701i	−0.953762	+	0.300563i	$0.902825\pi$
$140$	2.57921	−	0.589657i	0.217983	−	0.0498351i
$141$	−0.427865	+	1.03611i	−0.0360327	+	0.0872563i
$142$	3.97101	−	6.87799i	0.333240	−	0.577188i
$143$	2.84746	−	4.93195i	0.238117	−	0.412430i
$144$	−0.770216	+	2.89944i	−0.0641846	+	0.241620i
$145$	1.87671	−	1.08352i	0.155852	−	0.0899813i
$146$	−7.26053	−	12.5756i	−0.600885	−	1.04076i
$147$	−10.8332	−	5.44451i	−0.893504	−	0.449055i
$148$	−1.68075	+	2.91115i	−0.138157	+	0.239295i
$149$		−	7.16643i		−	0.587097i	−0.955944	−	0.293548i	$-0.905164\pi$
$149$		−	7.16643i		−	0.587097i	0.955944	−	0.293548i	$-0.0948362\pi$
$150$	1.60092	+	0.661104i	0.130714	+	0.0539789i
$151$	−6.76696			−0.550687			−0.275343	−	0.961346i	$-0.588792\pi$
$151$	−6.76696			−0.550687			−0.275343	+	0.961346i	$0.588792\pi$
$152$	−4.02986	−	6.97993i	−0.326865	−	0.566147i
$153$	2.59440	−	9.76650i	0.209745	−	0.789575i
$154$	5.23561	+	5.63860i	0.421897	+	0.454372i
$155$	−1.90977	+	1.10260i	−0.153396	+	0.0885634i
$156$	−0.446325	−	3.36220i	−0.0357346	−	0.269191i
$157$	8.74085	−	5.04653i	0.697596	−	0.402757i	−0.108856	−	0.994058i	$-0.534719\pi$
$157$	8.74085	−	5.04653i	0.697596	−	0.402757i	0.806451	+	0.591300i	$0.201385\pi$
$158$	−3.71962	+	2.14752i	−0.295917	+	0.170848i
$159$	−17.1062	−	7.06405i	−1.35661	−	0.560215i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−7.21962	−	2.22413i	−0.568986	−	0.175286i
$162$	8.99992	−	0.0387579i	0.707100	−	0.00304511i
$163$	11.7073	+	20.2777i	0.916989	+	1.58827i	0.803963	+	0.594679i	$0.202721\pi$
$163$	11.7073	+	20.2777i	0.916989	+	1.58827i	0.113026	+	0.993592i	$0.463946\pi$
$164$	−8.49627			−0.663448
$165$	0.662868	+	4.99343i	0.0516042	+	0.388738i
$166$		−	13.7472i		−	1.06699i
$167$	5.38906	−	9.33412i	0.417018	−	0.722296i	−0.578620	−	0.815597i	$-0.696409\pi$
$167$	5.38906	−	9.33412i	0.417018	−	0.722296i	0.995638	+	0.0933010i	$0.0297419\pi$
$168$	4.51892	+	0.761131i	0.348643	+	0.0587225i
$169$	−4.58273	−	7.93753i	−0.352518	−	0.610579i
$170$	2.91713	−	1.68420i	0.223733	−	0.129173i
$171$	−17.0604	+	17.1340i	−1.30464	+	1.31027i
$172$	−0.991430	+	1.71721i	−0.0755958	+	0.130936i
$173$	1.28943	−	2.23335i	0.0980333	−	0.169799i	−0.812837	−	0.582491i	$-0.802078\pi$
$173$	1.28943	−	2.23335i	0.0980333	−	0.169799i	0.910871	+	0.412692i	$0.135412\pi$
$174$	3.72078	−	0.493925i	0.282071	−	0.0374444i
$175$	0.778946	−	2.52849i	0.0588828	−	0.191136i
$176$	−2.51862	−	1.45413i	−0.189848	−	0.109609i
$177$	9.62602	+	12.5170i	0.723536	+	0.940832i
$178$		−	16.8774i		−	1.26502i
$179$	−0.461274	−	0.266316i	−0.0344772	−	0.0199054i	0.482662	−	0.875807i	$-0.339670\pi$
$179$	−0.461274	−	0.266316i	−0.0344772	−	0.0199054i	−0.517140	+	0.855901i	$0.673003\pi$
$180$	2.12588	+	2.11675i	0.158454	+	0.157773i
$181$		−	25.2946i		−	1.88013i	−0.340993	−	0.940066i	$-0.610763\pi$
$181$		−	25.2946i		−	1.88013i	0.340993	−	0.940066i	$-0.389237\pi$
$182$	−5.05059	+	1.15466i	−0.374375	+	0.0855893i
$183$	4.86335	+	2.00834i	0.359509	+	0.148460i
$184$	2.85531			0.210497
$185$	1.68075	+	2.91115i	0.123571	+	0.214032i
$186$	−3.78632	+	0.502626i	−0.277626	+	0.0368543i
$187$	8.48373	+	4.89809i	0.620392	+	0.358183i
$188$	−0.647198			−0.0472018
$189$	−1.33263	−	13.6830i	−0.0969344	−	0.995291i
$190$	−8.05973			−0.584714
$191$	20.2194	+	11.6737i	1.46302	+	0.844677i	0.999150	−	0.0412239i	$-0.0131257\pi$
$191$	20.2194	+	11.6737i	1.46302	+	0.844677i	0.463874	+	0.885901i	$0.346459\pi$
$192$	−1.71699	+	0.227927i	−0.123913	+	0.0164492i
$193$	−2.08929	−	3.61875i	−0.150390	−	0.260483i	0.780981	−	0.624555i	$-0.214720\pi$
$193$	−2.08929	−	3.61875i	−0.150390	−	0.260483i	−0.931371	+	0.364072i	$0.881386\pi$
$194$	−6.02218			−0.432367
$195$	−3.13491	−	1.29457i	−0.224496	−	0.0927062i
$196$	0.518123	−	6.98080i	0.0370088	−	0.498628i
$197$		−	2.79573i		−	0.199187i	−0.995028	−	0.0995936i	$-0.968246\pi$
$197$		−	2.79573i		−	0.199187i	0.995028	−	0.0995936i	$-0.0317543\pi$
$198$	−2.23998	+	8.43230i	−0.159188	+	0.599258i
$199$	−3.02178	−	1.74463i	−0.214208	−	0.123673i	0.389057	−	0.921214i	$-0.372801\pi$
$199$	−3.02178	−	1.74463i	−0.214208	−	0.123673i	−0.603266	+	0.797540i	$0.706134\pi$
$200$			1.00000i			0.0707107i
$201$	15.9852	+	20.7859i	1.12751	+	1.46612i
$202$	13.5758	+	7.83797i	0.955187	+	0.551477i
$203$	−1.27781	−	5.58923i	−0.0896845	−	0.392287i
$204$	5.78352	−	0.767750i	0.404927	−	0.0537532i
$205$	−4.24814	+	7.35799i	−0.296703	+	0.513904i
$206$	−1.84480	+	3.19529i	−0.128533	+	0.222626i
$207$	−2.23484	−	8.26927i	−0.155332	−	0.574754i
$208$	1.69585	−	0.979098i	0.117586	−	0.0678882i
$209$	−11.7199	−	20.2994i	−0.810679	−	1.40414i
$210$	2.91862	−	3.53294i	0.201404	−	0.243796i
$211$	−4.69846	+	8.13798i	−0.323455	+	0.560241i	−0.981199	−	0.193001i	$-0.938178\pi$
$211$	−4.69846	+	8.13798i	−0.323455	+	0.560241i	0.657743	+	0.753242i	$0.271511\pi$
$212$		−	10.6852i		−	0.733865i
$213$	−1.81020	−	13.6364i	−0.124033	−	0.934347i
$214$	12.3369			0.843334
$215$	0.991430	+	1.71721i	0.0676150	+	0.117113i
$216$	2.00398	+	4.79417i	0.136353	+	0.326202i
$217$	1.30032	+	5.68769i	0.0882712	+	0.386106i
$218$	−6.02819	+	3.48038i	−0.408281	+	0.235721i
$219$	−23.2470	−	9.59993i	−1.57089	−	0.648703i
$220$	−2.51862	+	1.45413i	−0.169805	+	0.0980371i
$221$	−5.71231	+	3.29800i	−0.384251	+	0.221848i
$222$	0.766177	+	5.77167i	0.0514224	+	0.387369i
$223$	−14.4132	+	8.32148i	−0.965181	+	0.557248i	−0.897764	−	0.440477i	$-0.854809\pi$
$223$	−14.4132	+	8.32148i	−0.965181	+	0.557248i	−0.0674174	+	0.997725i	$0.521476\pi$
$224$	0.589657	+	2.57921i	0.0393981	+	0.172330i
$225$	2.89610	−	0.782695i	0.193073	−	0.0521797i
$226$	1.36204	+	2.35912i	0.0906013	+	0.156926i
$227$	−1.53015			−0.101559			−0.0507796	−	0.998710i	$-0.516171\pi$
$227$	−1.53015			−0.101559			−0.0507796	+	0.998710i	$0.516171\pi$
$228$	−12.9030	−	5.32832i	−0.854520	−	0.352876i
$229$			22.5827i			1.49231i	0.665773	+	0.746154i	$0.268102\pi$
$229$			22.5827i			1.49231i	−0.665773	+	0.746154i	$0.731898\pi$
$230$	1.42766	−	2.47278i	0.0941369	−	0.163050i
$231$	13.1422	+	2.21356i	0.864691	+	0.145642i
$232$	1.08352	+	1.87671i	0.0711365	+	0.123212i
$233$	1.52031	−	0.877750i	0.0995986	−	0.0575033i	−0.449373	−	0.893344i	$-0.648353\pi$
$233$	1.52031	−	0.877750i	0.0995986	−	0.0575033i	0.548972	+	0.835841i	$0.315019\pi$
$234$	−4.16290	−	4.14501i	−0.272137	−	0.270968i
$235$	−0.323599	+	0.560490i	−0.0211093	+	0.0365623i
$236$	−4.55827	+	7.89516i	−0.296718	+	0.513931i
$237$	−2.83947	+	6.87602i	−0.184443	+	0.446645i
$238$	−1.98620	−	8.68782i	−0.128746	−	0.563148i
$239$	13.5333	+	7.81348i	0.875399	+	0.505412i	0.869139	−	0.494568i	$-0.164674\pi$
$239$	13.5333	+	7.81348i	0.875399	+	0.505412i	0.00626059	+	0.999980i	$0.498007\pi$
$240$	−0.661104	+	1.60092i	−0.0426741	+	0.103339i
$241$		−	7.81032i		−	0.503107i	−0.967843	−	0.251553i	$-0.919059\pi$
$241$		−	7.81032i		−	0.503107i	0.967843	−	0.251553i	$-0.0809414\pi$
$242$	2.20151	+	1.27104i	0.141518	+	0.0817056i
$243$	12.3159	−	9.55609i	0.790065	−	0.613023i
$244$			3.03785i			0.194478i
$245$	−5.78649	−	3.93911i	−0.369685	−	0.251660i
$246$	−11.6653	+	8.97108i	−0.743754	+	0.571975i
$247$	15.7825			1.00422
$248$	−1.10260	−	1.90977i	−0.0700155	−	0.121270i
$249$	−14.5155	−	18.8748i	−0.919882	−	1.19614i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	−12.4166			−0.783726			−0.391863	−	0.920024i	$-0.628169\pi$
$251$	−12.4166			−0.783726			−0.391863	+	0.920024i	$0.628169\pi$
$252$	7.00812	−	3.72644i	0.441470	−	0.234743i
$253$	8.30397			0.522066
$254$	−5.71454	−	3.29929i	−0.358562	−	0.207016i
$255$	2.22687	−	5.39255i	0.139452	−	0.337694i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	29.4130			1.83473			0.917367	−	0.398042i	$-0.130310\pi$
$257$	29.4130			1.83473			0.917367	+	0.398042i	$0.130310\pi$
$258$	0.451947	+	3.40455i	0.0281370	+	0.211958i
$259$	8.67001	−	1.98213i	0.538729	−	0.123164i
$260$		−	1.95820i		−	0.121442i
$261$	4.58707	−	4.60687i	0.283933	−	0.285158i
$262$	−3.81928	−	2.20506i	−0.235956	−	0.136229i
$263$			26.0968i			1.60920i	0.593820	+	0.804598i	$0.297619\pi$
$263$			26.0968i			1.60920i	−0.593820	+	0.804598i	$0.702381\pi$
$264$	−4.99343	+	0.662868i	−0.307324	+	0.0407967i
$265$	−9.25368	−	5.34261i	−0.568449	−	0.328194i
$266$	−6.27809	+	20.3789i	−0.384934	+	1.24951i
$267$	−17.8206	−	23.1726i	−1.09060	−	1.41814i
$268$	−7.56956	+	13.1109i	−0.462385	+	0.800873i
$269$	7.78339	−	13.4812i	0.474562	−	0.821965i	−0.525014	−	0.851094i	$-0.675940\pi$
$269$	7.78339	−	13.4812i	0.474562	−	0.821965i	0.999576	+	0.0291286i	$0.00927325\pi$
$270$	5.15386	+	0.661591i	0.313654	+	0.0402632i
$271$	10.2838	−	5.93737i	0.624698	−	0.360670i	−0.153998	−	0.988071i	$-0.549215\pi$
$271$	10.2838	−	5.93737i	0.624698	−	0.360670i	0.778696	+	0.627402i	$0.215882\pi$
$272$	1.68420	+	2.91713i	0.102120	+	0.176877i
$273$	−5.71523	+	6.91819i	−0.345902	+	0.418708i
$274$	−2.44589	+	4.23640i	−0.147762	+	0.255931i
$275$			2.90825i			0.175374i
$276$	3.92033	−	3.01488i	0.235976	−	0.181475i
$277$	27.4557			1.64965			0.824825	−	0.565388i	$-0.191273\pi$
$277$	27.4557			1.64965			0.824825	+	0.565388i	$0.191273\pi$
$278$	−7.96639	−	13.7982i	−0.477793	−	0.827561i
$279$	−4.66787	+	4.68802i	−0.279458	+	0.280664i
$280$	2.52849	+	0.778946i	0.151106	+	0.0465509i
$281$	−22.5302	+	13.0078i	−1.34404	+	0.775980i	−0.987397	−	0.158263i	$-0.949411\pi$
$281$	−22.5302	+	13.0078i	−1.34404	+	0.775980i	−0.356639	+	0.934242i	$0.616077\pi$
$282$	−0.888598	+	0.683366i	−0.0529152	+	0.0406939i
$283$	0.749194	−	0.432547i	0.0445349	−	0.0257123i	−0.477567	−	0.878595i	$-0.658481\pi$
$283$	0.749194	−	0.432547i	0.0445349	−	0.0257123i	0.522102	+	0.852883i	$0.325148\pi$
$284$	6.87799	−	3.97101i	0.408133	−	0.235636i
$285$	−11.0659	+	8.51014i	−0.655490	+	0.504097i
$286$	4.93195	−	2.84746i	0.291632	−	0.168374i
$287$	15.2955	+	16.4728i	0.902865	+	0.972360i
$288$	−2.11675	+	2.12588i	−0.124731	+	0.125269i
$289$	2.82692	+	4.89636i	0.166289	+	0.288021i
$290$	2.16704			0.127253
$291$	−8.26840	+	6.35872i	−0.484702	+	0.372755i
$292$		−	14.5211i		−	0.849780i
$293$	11.3934	−	19.7339i	0.665608	−	1.15287i	−0.313512	−	0.949584i	$-0.601505\pi$
$293$	11.3934	−	19.7339i	0.665608	−	1.15287i	0.979120	−	0.203283i	$-0.0651612\pi$
$294$	−6.65954	−	10.1317i	−0.388392	−	0.590890i
$295$	4.55827	+	7.89516i	0.265393	+	0.459674i
$296$	−2.91115	+	1.68075i	−0.169207	+	0.0976918i
$297$	5.82806	+	13.9426i	0.338179	+	0.809035i
$298$	3.58321	−	6.20631i	0.207570	−	0.359522i
$299$	−2.79563	+	4.84218i	−0.161676	+	0.280030i
$300$	1.05588	+	1.37299i	0.0609615	+	0.0792697i
$301$	5.11421	−	1.16921i	0.294778	−	0.0673919i
$302$	−5.86035	−	3.38348i	−0.337226	−	0.194697i
$303$	26.9154	−	3.57296i	1.54625	−	0.205261i
$304$		−	8.05973i		−	0.462257i
$305$	2.63086	+	1.51893i	0.150642	+	0.0869734i
$306$	7.13007	−	7.16084i	0.407599	−	0.409358i
$307$			19.5794i			1.11745i	0.829352	+	0.558726i	$0.188710\pi$
$307$			19.5794i			1.11745i	−0.829352	+	0.558726i	$0.811290\pi$
$308$	1.71487	+	7.50098i	0.0977137	+	0.427408i
$309$	0.840958	+	6.33500i	0.0478404	+	0.360386i
$310$	−2.20521			−0.125247
$311$	12.3801	+	21.4429i	0.702010	+	1.21592i	0.967760	+	0.251876i	$0.0810474\pi$
$311$	12.3801	+	21.4429i	0.702010	+	1.21592i	−0.265749	+	0.964042i	$0.585619\pi$
$312$	1.29457	−	3.13491i	0.0732907	−	0.177480i
$313$	25.7274	+	14.8537i	1.45420	+	0.839582i	0.998716	−	0.0506624i	$-0.0161333\pi$
$313$	25.7274	+	14.8537i	1.45420	+	0.839582i	0.455483	+	0.890244i	$0.349467\pi$
$314$	10.0931			0.569585
$315$	0.276870	−	7.93242i	0.0155999	−	0.446941i
$316$	−4.29504			−0.241615
$317$	5.18529	+	2.99373i	0.291235	+	0.168144i	0.638499	−	0.769623i	$-0.279556\pi$
$317$	5.18529	+	2.99373i	0.291235	+	0.168144i	−0.347264	+	0.937767i	$0.612889\pi$
$318$	−11.2824	−	14.6707i	−0.632684	−	0.822694i
$319$	3.15114	+	5.45794i	0.176430	+	0.305586i
$320$	−1.00000			−0.0559017
$321$	16.9385	−	13.0263i	0.945414	−	0.727060i
$322$	−5.14031	−	5.53597i	−0.286458	−	0.308508i
$323$			27.1484i			1.51058i
$324$	7.81354	+	4.46639i	0.434085	+	0.248133i
$325$	−1.69585	−	0.979098i	−0.0940687	−	0.0543106i
$326$			23.4147i			1.29682i
$327$	−4.60178	+	11.1436i	−0.254479	+	0.616243i
$328$	−7.35799	−	4.24814i	−0.406277	−	0.234564i
$329$	1.16513	+	1.25481i	0.0642354	+	0.0691797i
$330$	−1.92266	+	4.65587i	−0.105839	+	0.256297i
$331$	−3.85334	+	6.67419i	−0.211799	+	0.366846i	−0.952278	−	0.305233i	$-0.901266\pi$
$331$	−3.85334	+	6.67419i	−0.211799	+	0.366846i	0.740479	+	0.672080i	$0.234599\pi$
$332$	6.87362	−	11.9055i	0.377239	−	0.653396i
$333$	7.14617	+	7.11546i	0.391608	+	0.389925i
$334$	9.33412	−	5.38906i	0.510741	−	0.294876i
$335$	7.56956	+	13.1109i	0.413569	+	0.716323i
$336$	3.53294	+	2.91862i	0.192738	+	0.159224i
$337$	3.29935	−	5.71465i	0.179727	−	0.311297i	−0.762060	−	0.647507i	$-0.775812\pi$
$337$	3.29935	−	5.71465i	0.179727	−	0.311297i	0.941787	+	0.336210i	$0.109145\pi$
$338$		−	9.16547i		−	0.498536i
$339$	4.36102	+	1.80090i	0.236858	+	0.0978112i
$340$	3.36841			0.182678
$341$	−3.20665	−	5.55408i	−0.173650	−	0.300770i
$342$	−23.3418	+	6.30831i	−1.26218	+	0.341114i
$343$	−14.4673	+	11.5627i	−0.781163	+	0.624327i
$344$	−1.71721	+	0.991430i	−0.0925856	+	0.0534543i
$345$	−0.650802	−	4.90254i	−0.0350380	−	0.263944i
$346$	2.23335	−	1.28943i	0.120066	−	0.0693200i
$347$	10.4929	−	6.05810i	0.563290	−	0.325216i	−0.191175	−	0.981556i	$-0.561230\pi$
$347$	10.4929	−	6.05810i	0.563290	−	0.325216i	0.754465	+	0.656340i	$0.227896\pi$
$348$	3.46925	+	1.43264i	0.185971	+	0.0767974i
$349$	0.214315	−	0.123735i	0.0114720	−	0.00662337i	−0.494253	−	0.869318i	$-0.664558\pi$
$349$	0.214315	−	0.123735i	0.0114720	−	0.00662337i	0.505725	+	0.862695i	$0.331225\pi$
$350$	1.93883	−	1.80026i	0.103635	−	0.0962280i
$351$	−10.0923	−	1.29553i	−0.538686	−	0.0691500i
$352$	−1.45413	−	2.51862i	−0.0775051	−	0.134243i
$353$	−0.130520			−0.00694685			−0.00347343	−	0.999994i	$-0.501106\pi$
$353$	−0.130520			−0.00694685			−0.00347343	+	0.999994i	$0.501106\pi$
$354$	2.07790	+	15.6530i	0.110439	+	0.831948i
$355$		−	7.94202i		−	0.421518i
$356$	8.43872	−	14.6163i	0.447251	−	0.774662i
$357$	−11.9004	−	9.83111i	−0.629835	−	0.520317i
$358$	−0.266316	−	0.461274i	−0.0140753	−	0.0243791i
$359$	8.88009	−	5.12692i	0.468673	−	0.270589i	−0.247011	−	0.969013i	$-0.579448\pi$
$359$	8.88009	−	5.12692i	0.468673	−	0.270589i	0.715684	+	0.698424i	$0.246115\pi$
$360$	0.782695	+	2.89610i	0.0412516	+	0.152638i
$361$	22.9796	−	39.8018i	1.20945	−	2.09483i
$362$	12.6473	−	21.9057i	0.664727	−	1.15134i
$363$	4.36473	−	0.579408i	0.229089	−	0.0304110i
$364$	−4.95127	−	1.52533i	−0.259517	−	0.0799489i
$365$	−12.5756	−	7.26053i	−0.658237	−	0.380033i
$366$	3.20762	+	4.17095i	0.167665	+	0.218019i
$367$			0.432258i			0.0225637i	0.999936	+	0.0112818i	$0.00359120\pi$
$367$			0.432258i			0.0225637i	−0.999936	+	0.0112818i	$0.996409\pi$
$368$	2.47278	+	1.42766i	0.128902	+	0.0744218i
$369$	−6.54396	+	24.6345i	−0.340665	+	1.28242i
$370$			3.36151i			0.174756i
$371$	−20.7168	+	19.2362i	−1.07556	+	0.998694i
$372$	−3.53036	−	1.45787i	−0.183041	−	0.0755872i
$373$	3.09282			0.160140			0.0800700	−	0.996789i	$-0.474486\pi$
$373$	3.09282			0.160140			0.0800700	+	0.996789i	$0.474486\pi$
$374$	4.89809	+	8.48373i	0.253274	+	0.438683i
$375$	1.71699	−	0.227927i	0.0886649	−	0.0117701i
$376$	−0.560490	−	0.323599i	−0.0289051	−	0.0166883i
$377$	−4.24348			−0.218550
$378$	5.68740	−	12.5161i	0.292528	−	0.643760i
$379$	−9.20781			−0.472973			−0.236487	−	0.971635i	$-0.575996\pi$
$379$	−9.20781			−0.472973			−0.236487	+	0.971635i	$0.575996\pi$
$380$	−6.97993	−	4.02986i	−0.358063	−	0.206728i
$381$	−11.3297	+	1.50399i	−0.580437	+	0.0770518i
$382$	11.6737	+	20.2194i	0.597277	+	1.03451i
$383$	24.4921			1.25149			0.625743	−	0.780029i	$-0.284796\pi$
$383$	24.4921			1.25149			0.625743	+	0.780029i	$0.284796\pi$
$384$	−1.60092	−	0.661104i	−0.0816966	−	0.0337368i
$385$	7.35347	+	2.26537i	0.374768	+	0.115454i
$386$		−	4.17857i		−	0.212684i
$387$	4.21533	+	4.19721i	0.214277	+	0.213356i
$388$	−5.21536	−	3.01109i	−0.264770	−	0.152865i
$389$			5.21951i			0.264640i	0.991207	+	0.132320i	$0.0422426\pi$
$389$			5.21951i			0.264640i	−0.991207	+	0.132320i	$0.957757\pi$
$390$	−2.06763	−	2.68859i	−0.104698	−	0.136142i
$391$	−8.32931	−	4.80893i	−0.421232	−	0.243198i
$392$	3.93911	−	5.78649i	0.198955	−	0.292262i
$393$	−7.57213	+	1.00518i	−0.381963	+	0.0507048i
$394$	1.39786	−	2.42117i	0.0704233	−	0.121977i
$395$	−2.14752	+	3.71962i	−0.108054	+	0.187154i
$396$	−6.15603	+	6.18260i	−0.309352	+	0.310687i
$397$	8.32819	−	4.80828i	0.417980	−	0.241321i	−0.276233	−	0.961091i	$-0.589086\pi$
$397$	8.32819	−	4.80828i	0.417980	−	0.241321i	0.694213	+	0.719770i	$0.255753\pi$
$398$	−1.74463	−	3.02178i	−0.0874502	−	0.151468i
$399$	12.8980	+	34.6090i	0.645708	+	1.73262i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	18.2870i		−	0.913207i	−0.889670	−	0.456604i	$-0.849066\pi$
$401$		−	18.2870i		−	0.913207i	0.889670	−	0.456604i	$-0.150934\pi$
$402$	3.45061	+	25.9937i	0.172101	+	1.29645i
$403$	4.31823			0.215107
$404$	7.83797	+	13.5758i	0.389953	+	0.675419i
$405$	7.77478	−	4.53352i	0.386332	−	0.225273i
$406$	1.68800	−	5.47932i	0.0837742	−	0.271934i
$407$	−8.46635	+	4.88805i	−0.419661	+	0.242292i
$408$	5.39255	+	2.22687i	0.266971	+	0.110246i
$409$	3.51981	−	2.03216i	0.174043	−	0.100484i	−0.410448	−	0.911884i	$-0.634628\pi$
$409$	3.51981	−	2.03216i	0.174043	−	0.100484i	0.584491	+	0.811400i	$0.301294\pi$
$410$	−7.35799	+	4.24814i	−0.363385	+	0.209801i
$411$	1.11497	+	8.39913i	0.0549973	+	0.414298i
$412$	−3.19529	+	1.84480i	−0.157421	+	0.0908868i
$413$	23.5135	−	5.37563i	1.15702	−	0.264518i
$414$	2.19921	−	8.27882i	0.108085	−	0.406882i
$415$	−6.87362	−	11.9055i	−0.337412	−	0.584416i
$416$	1.95820			0.0960085
$417$	−25.5071	−	10.5332i	−1.24909	−	0.515814i
$418$		−	23.4397i		−	1.14647i
$419$	−6.00474	+	10.4005i	−0.293351	+	0.508098i	−0.974600	−	0.223953i	$-0.928104\pi$
$419$	−6.00474	+	10.4005i	−0.293351	+	0.508098i	0.681249	+	0.732052i	$0.261437\pi$
$420$	4.29407	−	1.60030i	0.209529	−	0.0780868i
$421$	−6.01384	−	10.4163i	−0.293097	−	0.507658i	0.681444	−	0.731871i	$-0.261352\pi$
$421$	−6.01384	−	10.4163i	−0.293097	−	0.507658i	−0.974540	+	0.224212i	$0.928019\pi$
$422$	−8.13798	+	4.69846i	−0.396150	+	0.228718i
$423$	−0.498482	+	1.87651i	−0.0242370	+	0.0912392i
$424$	5.34261	−	9.25368i	0.259460	−	0.449398i
$425$	1.68420	−	2.91713i	0.0816959	−	0.141501i
$426$	5.25050	−	12.7145i	0.254387	−	0.616021i
$427$	5.88988	−	5.46892i	0.285031	−	0.264660i
$428$	10.6841	+	6.16845i	0.516434	+	0.298163i
$429$	3.76494	−	9.11711i	0.181773	−	0.440178i
$430$			1.98286i			0.0956220i
$431$	8.15790	+	4.70997i	0.392952	+	0.226871i	0.683439	−	0.730008i	$-0.260484\pi$
$431$	8.15790	+	4.70997i	0.392952	+	0.226871i	−0.290486	+	0.956879i	$0.593817\pi$
$432$	−0.661591	+	5.15386i	−0.0318308	+	0.247965i
$433$		−	28.8287i		−	1.38542i	−0.721216	−	0.692710i	$-0.756417\pi$
$433$		−	28.8287i		−	1.38542i	0.721216	−	0.692710i	$-0.243583\pi$
$434$	−1.71774	+	5.57584i	−0.0824541	+	0.267649i
$435$	2.97532	−	2.28814i	0.142656	−	0.109708i
$436$	−6.96076			−0.333360
$437$	11.5065	+	19.9299i	0.550432	+	0.953376i
$438$	−15.3326	−	19.9373i	−0.732618	−	0.952641i
$439$	−30.5223	−	17.6221i	−1.45675	−	0.841055i	−0.457901	−	0.889003i	$-0.651398\pi$
$439$	−30.5223	−	17.6221i	−1.45675	−	0.841055i	−0.998850	+	0.0479482i	$0.984732\pi$
$440$	−2.90825			−0.138645
$441$	−19.8414	−	6.87899i	−0.944827	−	0.327571i
$442$	−6.59600			−0.313740
$443$	18.3956	+	10.6207i	0.874001	+	0.504605i	0.868676	−	0.495381i	$-0.164972\pi$
$443$	18.3956	+	10.6207i	0.874001	+	0.504605i	0.00532541	+	0.999986i	$0.498305\pi$
$444$	−2.22230	+	5.38150i	−0.105466	+	0.255395i
$445$	−8.43872	−	14.6163i	−0.400034	−	0.692878i
$446$	−16.6430			−0.788067
$447$	−1.63342	−	12.3047i	−0.0772581	−	0.581991i
$448$	−0.778946	+	2.52849i	−0.0368017	+	0.119460i
$449$		−	16.9305i		−	0.799002i	−0.916733	−	0.399501i	$-0.869183\pi$
$449$		−	16.9305i		−	0.799002i	0.916733	−	0.399501i	$-0.130817\pi$
$450$	2.89944	+	0.770216i	0.136681	+	0.0363083i
$451$	−21.3989	−	12.3546i	−1.00763	−	0.581757i
$452$			2.72407i			0.128130i
$453$	−11.6188	+	1.54237i	−0.545898	+	0.0724668i
$454$	−1.32514	−	0.765073i	−0.0621921	−	0.0359066i
$455$	−3.79661	+	3.52526i	−0.177988	+	0.165267i
$456$	−8.51014	−	11.0659i	−0.398524	−	0.518210i
$457$	−16.6175	+	28.7824i	−0.777335	+	1.34638i	0.156137	+	0.987735i	$0.450096\pi$
$457$	−16.6175	+	28.7824i	−0.777335	+	1.34638i	−0.933473	+	0.358649i	$0.883238\pi$
$458$	−11.2914	+	19.5572i	−0.527610	+	0.913848i
$459$	2.22851	−	17.3603i	0.104018	−	0.810310i
$460$	2.47278	−	1.42766i	0.115294	−	0.0665649i
$461$	13.2679	+	22.9806i	0.617946	+	1.07031i	0.989860	+	0.142047i	$0.0453684\pi$
$461$	13.2679	+	22.9806i	0.617946	+	1.07031i	−0.371914	+	0.928267i	$0.621298\pi$
$462$	10.2747	+	8.48808i	0.478021	+	0.394901i
$463$	−5.25467	+	9.10135i	−0.244205	+	0.422976i	−0.961908	−	0.273374i	$-0.911860\pi$
$463$	−5.25467	+	9.10135i	−0.244205	+	0.422976i	0.717703	+	0.696350i	$0.245194\pi$
$464$			2.16704i			0.100602i
$465$	−3.02774	+	2.32845i	−0.140408	+	0.107979i
$466$	1.75550			0.0813220
$467$	6.14519	+	10.6438i	0.284366	+	0.492536i	0.972455	−	0.233090i	$-0.0748837\pi$
$467$	6.14519	+	10.6438i	0.284366	+	0.492536i	−0.688089	+	0.725626i	$0.741550\pi$
$468$	−1.53267	−	5.67113i	−0.0708477	−	0.262148i
$469$	39.0469	−	8.92688i	1.80302	−	0.412205i
$470$	−0.560490	+	0.323599i	−0.0258535	+	0.0149265i
$471$	13.8577	−	10.6571i	0.638529	−	0.491054i
$472$	−7.89516	+	4.55827i	−0.363404	+	0.209812i
$473$	−4.99407	+	2.88333i	−0.229628	+	0.132576i
$474$	−5.89706	+	4.53507i	−0.270861	+	0.208303i
$475$	−6.97993	+	4.02986i	−0.320261	+	0.184903i
$476$	2.62381	−	8.51697i	0.120262	−	0.390375i
$477$	−30.9812	−	8.22993i	−1.41853	−	0.376823i
$478$	7.81348	+	13.5333i	0.357380	+	0.619001i
$479$	31.7392			1.45020			0.725100	−	0.688643i	$-0.241793\pi$
$479$	31.7392			1.45020			0.725100	+	0.688643i	$0.241793\pi$
$480$	−1.37299	+	1.05588i	−0.0626682	+	0.0481943i
$481$		−	6.58249i		−	0.300136i
$482$	3.90516	−	6.76393i	0.177875	−	0.308089i
$483$	−12.9030	−	2.17327i	−0.587105	−	0.0988872i
$484$	1.27104	+	2.20151i	0.0577746	+	0.100069i
$485$	−5.21536	+	3.01109i	−0.236817	+	0.136726i
$486$	15.4439	−	2.11787i	0.700550	−	0.0960684i
$487$	20.7358	−	35.9155i	0.939630	−	1.62749i	0.173468	−	0.984840i	$-0.444503\pi$
$487$	20.7358	−	35.9155i	0.939630	−	1.62749i	0.766162	−	0.642647i	$-0.222164\pi$
$488$	−1.51893	+	2.63086i	−0.0687585	+	0.119093i
$489$	24.7232	+	32.1481i	1.11802	+	1.45379i
$490$	−3.04169	−	6.30461i	−0.137410	−	0.284813i
$491$	9.34197	+	5.39359i	0.421597	+	0.243409i	0.695760	−	0.718274i	$-0.255068\pi$
$491$	9.34197	+	5.39359i	0.421597	+	0.243409i	−0.274163	+	0.961683i	$0.588401\pi$
$492$	−14.5880	+	1.93653i	−0.657678	+	0.0873054i
$493$		−	7.29946i		−	0.328751i
$494$	13.6681	+	7.89126i	0.614956	+	0.355045i
$495$	2.27627	+	8.42258i	0.102311	+	0.378567i
$496$		−	2.20521i		−	0.0990168i
$497$	−20.0813	−	6.18640i	−0.900769	−	0.277498i
$498$	−3.13336	−	23.6038i	−0.140409	−	1.05771i
$499$	26.8670			1.20273			0.601365	−	0.798974i	$-0.294624\pi$
$499$	26.8670			1.20273			0.601365	+	0.798974i	$0.294624\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	7.12546	−	17.2549i	0.318342	−	0.770892i
$502$	−10.7530	−	6.20828i	−0.479932	−	0.277089i
$503$	−36.7424			−1.63826			−0.819131	−	0.573606i	$-0.805544\pi$
$503$	−36.7424			−1.63826			−0.819131	+	0.573606i	$0.805544\pi$
$504$	7.93242	+	0.276870i	0.353338	+	0.0123328i
$505$	15.6759			0.697570
$506$	7.19145	+	4.15198i	0.319699	+	0.184578i
$507$	−9.67768	−	12.5841i	−0.429801	−	0.558880i
$508$	−3.29929	−	5.71454i	−0.146382	−	0.253542i
$509$	−12.2706			−0.543885			−0.271942	−	0.962314i	$-0.587666\pi$
$509$	−12.2706			−0.543885			−0.271942	+	0.962314i	$0.587666\pi$
$510$	4.62480	−	3.55665i	0.204789	−	0.157491i
$511$	−28.1539	+	26.1417i	−1.24545	+	1.15644i
$512$		−	1.00000i		−	0.0441942i
$513$	−25.3872	+	33.3075i	−1.12087	+	1.47056i
$514$	25.4724	+	14.7065i	1.12354	+	0.648676i
$515$			3.68960i			0.162583i
$516$	−1.31088	+	3.17440i	−0.0577081	+	0.139745i
$517$	−1.63004	−	0.941107i	−0.0716893	−	0.0413898i
$518$	8.49952	+	2.61843i	0.373447	+	0.115047i
$519$	1.70489	−	4.12853i	0.0748363	−	0.181223i
$520$	0.979098	−	1.69585i	0.0429363	−	0.0743678i
$521$	−14.0346	+	24.3087i	−0.614868	+	1.06498i	0.375540	+	0.926806i	$0.377457\pi$
$521$	−14.0346	+	24.3087i	−0.614868	+	1.06498i	−0.990408	+	0.138176i	$0.955876\pi$
$522$	6.27595	−	1.69613i	0.274691	−	0.0742375i
$523$	−15.2468	+	8.80274i	−0.666696	+	0.384917i	−0.794824	−	0.606841i	$-0.792437\pi$
$523$	−15.2468	+	8.80274i	−0.666696	+	0.384917i	0.128128	+	0.991758i	$0.459103\pi$
$524$	−2.20506	−	3.81928i	−0.0963285	−	0.166846i
$525$	0.761131	−	4.51892i	0.0332185	−	0.197222i
$526$	−13.0484	+	22.6005i	−0.568937	+	0.985427i
$527$			7.42805i			0.323571i
$528$	−4.65587	−	1.92266i	−0.202621	−	0.0836728i
$529$	14.8472			0.645529
$530$	−5.34261	−	9.25368i	−0.232068	−	0.401954i
$531$	19.3807	+	19.2974i	0.841051	+	0.837437i
$532$	−15.6264	+	14.5096i	−0.677492	+	0.629071i
$533$	14.4084	−	8.31869i	0.624096	−	0.360322i
$534$	−3.84682	−	28.9784i	−0.166468	−	1.25402i
$535$	10.6841	−	6.16845i	0.461913	−	0.266685i
$536$	−13.1109	+	7.56956i	−0.566303	+	0.326955i
$537$	−0.852702	−	0.352126i	−0.0367968	−	0.0151953i
$538$	13.4812	−	7.78339i	0.581217	−	0.335566i
$539$	11.4559	−	16.8286i	0.493441	−	0.724857i
$540$	4.13258	+	3.14989i	0.177838	+	0.135550i
$541$	−11.8477	−	20.5208i	−0.509372	−	0.882258i	−0.999941	−	0.0108558i	$-0.996544\pi$
$541$	−11.8477	−	20.5208i	−0.509372	−	0.882258i	0.490569	−	0.871402i	$-0.336789\pi$
$542$	11.8747			0.510064
$543$	−5.76531	−	43.4305i	−0.247413	−	1.86378i
$544$			3.36841i			0.144419i
$545$	−3.48038	+	6.02819i	−0.149083	+	0.258219i
$546$	−8.40863	+	3.13371i	−0.359856	+	0.134110i
$547$	−16.4082	−	28.4199i	−0.701566	−	1.21515i	−0.967917	−	0.251271i	$-0.919151\pi$
$547$	−16.4082	−	28.4199i	−0.701566	−	1.21515i	0.266351	−	0.963876i	$-0.414182\pi$
$548$	−4.23640	+	2.44589i	−0.180970	+	0.104483i
$549$	8.80808	+	2.33980i	0.375920	+	0.0998603i
$550$	−1.45413	+	2.51862i	−0.0620041	+	0.107394i
$551$	−8.73286	+	15.1258i	−0.372032	+	0.644379i
$552$	4.90254	−	0.650802i	0.208666	−	0.0277000i
$553$	7.73220	+	8.32736i	0.328807	+	0.354115i
$554$	23.7773	+	13.7278i	1.01020	+	0.583240i
$555$	3.54936	+	4.61532i	0.150662	+	0.195909i
$556$		−	15.9328i		−	0.675701i
$557$	−20.6283	−	11.9097i	−0.874048	−	0.504632i	−0.00535689	−	0.999986i	$-0.501705\pi$
$557$	−20.6283	−	11.9097i	−0.874048	−	0.504632i	−0.868691	+	0.495354i	$0.835038\pi$
$558$	−6.38651	+	1.72601i	−0.270362	+	0.0730677i
$559$		−	3.88283i		−	0.164226i
$560$	1.80026	+	1.93883i	0.0760749	+	0.0819305i
$561$	15.6829	+	6.47629i	0.662132	+	0.273429i
$562$	−26.0156			−1.09740
$563$	−9.00650	−	15.5997i	−0.379579	−	0.657450i	0.611422	−	0.791304i	$-0.290598\pi$
$563$	−9.00650	−	15.5997i	−0.379579	−	0.657450i	−0.991001	+	0.133855i	$0.957264\pi$
$564$	−1.11123	+	0.147514i	−0.0467913	+	0.00621145i
$565$	2.35912	+	1.36204i	0.0992488	+	0.0573013i
$566$	0.865094			0.0363626
$567$	−5.40682	−	23.1898i	−0.227065	−	0.973880i
$568$	7.94202			0.333240
$569$	−13.7736	−	7.95220i	−0.577420	−	0.333374i	0.182687	−	0.983171i	$-0.441520\pi$
$569$	−13.7736	−	7.95220i	−0.577420	−	0.333374i	−0.760107	+	0.649797i	$0.774854\pi$
$570$	−13.8385	+	1.83703i	−0.579629	+	0.0769446i
$571$	−13.7635	−	23.8391i	−0.575985	−	0.997635i	−0.995934	−	0.0900870i	$-0.971285\pi$
$571$	−13.7635	−	23.8391i	−0.575985	−	0.997635i	0.419949	−	0.907548i	$-0.362048\pi$
$572$	5.69492			0.238117
$573$	37.3772	+	15.4350i	1.56146	+	0.644807i
$574$	5.00988	+	21.9136i	0.209108	+	0.914658i
$575$		−	2.85531i		−	0.119075i
$576$	−2.89610	+	0.782695i	−0.120671	+	0.0326123i
$577$	−17.2512	−	9.95997i	−0.718176	−	0.414639i	0.0959051	−	0.995390i	$-0.469425\pi$
$577$	−17.2512	−	9.95997i	−0.718176	−	0.414639i	−0.814081	+	0.580752i	$0.802759\pi$
$578$			5.65383i			0.235168i
$579$	−4.41209	−	5.73714i	−0.183360	−	0.238428i
$580$	1.87671	+	1.08352i	0.0779261	+	0.0449907i
$581$	−35.4569	+	8.10614i	−1.47100	+	0.336300i
$582$	−10.3400	+	1.37261i	−0.428607	+	0.0568967i
$583$	15.5377	−	26.9120i	0.643504	−	1.11458i
$584$	7.26053	−	12.5756i	0.300443	−	0.520382i
$585$	−5.67768	−	1.50823i	−0.234743	−	0.0623578i
$586$	19.7339	−	11.3934i	0.815200	−	0.470656i
$587$	−17.0018	−	29.4479i	−0.701739	−	1.21545i	−0.967856	−	0.251506i	$-0.919074\pi$
$587$	−17.0018	−	29.4479i	−0.701739	−	1.21545i	0.266117	−	0.963941i	$-0.414259\pi$
$588$	−0.701499	−	12.1040i	−0.0289293	−	0.499162i
$589$	8.88669	−	15.3922i	0.366170	−	0.634225i
$590$			9.11655i			0.375322i
$591$	−0.637221	−	4.80023i	−0.0262118	−	0.197455i
$592$	−3.36151			−0.138157
$593$	−5.23235	−	9.06270i	−0.214867	−	0.372160i	0.738364	−	0.674402i	$-0.235598\pi$
$593$	−5.23235	−	9.06270i	−0.214867	−	0.372160i	−0.953231	+	0.302241i	$0.902265\pi$
$594$	−1.92407	+	14.9887i	−0.0789457	+	0.614995i
$595$	−6.06401	−	6.53077i	−0.248600	−	0.267735i
$596$	6.20631	−	3.58321i	0.254220	−	0.146774i
$597$	−5.58601	−	2.30676i	−0.228620	−	0.0944094i
$598$	−4.84218	+	2.79563i	−0.198011	+	0.114322i
$599$	−13.8125	+	7.97466i	−0.564364	+	0.325836i	−0.754895	−	0.655845i	$-0.772312\pi$
$599$	−13.8125	+	7.97466i	−0.564364	+	0.325836i	0.190531	+	0.981681i	$0.438979\pi$
$600$	0.227927	+	1.71699i	0.00930507	+	0.0700958i
$601$	−14.6089	+	8.43447i	−0.595911	+	0.344049i	−0.767431	−	0.641131i	$-0.778465\pi$
$601$	−14.6089	+	8.43447i	−0.595911	+	0.344049i	0.171520	+	0.985181i	$0.445132\pi$
$602$	5.01364	+	1.54454i	0.204341	+	0.0629508i
$603$	32.1840	+	32.0457i	1.31063	+	1.30500i
$604$	−3.38348	−	5.86035i	−0.137672	−	0.238454i
$605$	2.54208			0.103350
$606$	25.0959	+	10.3634i	1.01945	+	0.420985i
$607$			9.56645i			0.388290i	0.980973	+	0.194145i	$0.0621933\pi$
$607$			9.56645i			0.388290i	−0.980973	+	0.194145i	$0.937807\pi$
$608$	4.02986	−	6.97993i	0.163433	−	0.283073i
$609$	−3.46792	−	9.30541i	−0.140527	−	0.377074i
$610$	1.51893	+	2.63086i	0.0614995	+	0.106520i
$611$	1.09755	−	0.633670i	0.0444021	−	0.0256356i
$612$	9.75524	−	2.63644i	0.394332	−	0.106572i
$613$	−19.3430	+	33.5030i	−0.781255	+	1.35317i	0.149956	+	0.988693i	$0.452087\pi$
$613$	−19.3430	+	33.5030i	−0.781255	+	1.35317i	−0.931211	+	0.364480i	$0.881247\pi$
$614$	−9.78968	+	16.9562i	−0.395079	+	0.684297i
$615$	−5.61692	+	13.6018i	−0.226496	+	0.548479i
$616$	−2.26537	+	7.35347i	−0.0912743	+	0.296280i
$617$	−26.6003	−	15.3577i	−1.07089	−	0.618277i	−0.142464	−	0.989800i	$-0.545502\pi$
$617$	−26.6003	−	15.3577i	−1.07089	−	0.618277i	−0.928424	+	0.371523i	$0.878836\pi$
$618$	−2.43921	+	5.90675i	−0.0981194	+	0.237604i
$619$			3.61536i			0.145314i	0.997357	+	0.0726569i	$0.0231478\pi$
$619$			3.61536i			0.145314i	−0.997357	+	0.0726569i	$0.976852\pi$
$620$	−1.90977	−	1.10260i	−0.0766981	−	0.0442817i
$621$	−5.72198	−	13.6889i	−0.229615	−	0.549315i
$622$			24.7602i			0.992793i
$623$	−43.5304	+	9.95189i	−1.74401	+	0.398714i
$624$	2.68859	−	2.06763i	0.107630	−	0.0827714i
$625$	1.00000			0.0400000
$626$	14.8537	+	25.7274i	0.593674	+	1.02827i
$627$	−24.7496	−	32.1825i	−0.988405	−	1.28525i
$628$	8.74085	+	5.04653i	0.348798	+	0.201379i
$629$	11.3229			0.451474
$630$	4.20599	−	6.73125i	0.167571	−	0.268179i
$631$	40.5503			1.61428			0.807142	−	0.590358i	$-0.201013\pi$
$631$	40.5503			1.61428			0.807142	+	0.590358i	$0.201013\pi$
$632$	−3.71962	−	2.14752i	−0.147958	−	0.0854238i
$633$	−6.21234	+	15.0437i	−0.246919	+	0.597934i
$634$	2.99373	+	5.18529i	0.118896	+	0.205934i
$635$	−6.59858			−0.261857
$636$	−2.43545	−	18.3464i	−0.0965718	−	0.727483i
$637$	5.95623	+	12.3457i	0.235994	+	0.489153i
$638$			6.30228i			0.249510i
$639$	−6.21618	−	23.0009i	−0.245908	−	0.909900i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$		−	34.7592i		−	1.37291i	−0.727174	−	0.686453i	$-0.759167\pi$
$641$		−	34.7592i		−	1.37291i	0.727174	−	0.686453i	$-0.240833\pi$
$642$	21.1823	−	2.81191i	0.836000	−	0.110977i
$643$	0.969046	+	0.559479i	0.0382154	+	0.0220637i	0.518986	−	0.854783i	$-0.326310\pi$
$643$	0.969046	+	0.559479i	0.0382154	+	0.0220637i	−0.480771	+	0.876846i	$0.659643\pi$
$644$	−1.68365	−	7.36445i	−0.0663453	−	0.290200i
$645$	2.09367	+	2.72245i	0.0824382	+	0.107196i
$646$	−13.5742	+	23.5112i	−0.534071	+	0.925038i
$647$	−8.00562	+	13.8661i	−0.314734	+	0.545134i	−0.979381	−	0.202023i	$-0.935248\pi$
$647$	−8.00562	+	13.8661i	−0.314734	+	0.545134i	0.664647	+	0.747157i	$0.268582\pi$
$648$	4.53352	+	7.77478i	0.178094	+	0.305422i
$649$	−22.9611	+	13.2566i	−0.901302	+	0.520367i
$650$	−0.979098	−	1.69585i	−0.0384034	−	0.0665166i
$651$	3.52900	+	9.46932i	0.138313	+	0.371132i
$652$	−11.7073	+	20.2777i	−0.458494	+	0.794136i
$653$			20.8129i			0.814471i	0.913323	+	0.407235i	$0.133507\pi$
$653$			20.8129i			0.814471i	−0.913323	+	0.407235i	$0.866493\pi$
$654$	−9.55706	+	7.34975i	−0.373711	+	0.287398i
$655$	−4.41012			−0.172318
$656$	−4.24814	−	7.35799i	−0.165862	−	0.287281i
$657$	−42.1030	−	11.1843i	−1.64259	−	0.436343i
$658$	0.381624	+	1.66926i	0.0148773	+	0.0650744i
$659$	1.89741	−	1.09547i	0.0739127	−	0.0426735i	−0.462588	−	0.886573i	$-0.653079\pi$
$659$	1.89741	−	1.09547i	0.0739127	−	0.0426735i	0.536501	+	0.843900i	$0.319746\pi$
$660$	−3.99300	+	3.07078i	−0.155428	+	0.119530i
$661$	16.2877	−	9.40371i	0.633518	−	0.365762i	−0.148595	−	0.988898i	$-0.547475\pi$
$661$	16.2877	−	9.40371i	0.633518	−	0.365762i	0.782113	+	0.623136i	$0.214142\pi$
$662$	−6.67419	+	3.85334i	−0.259400	+	0.149764i
$663$	−9.05626	+	6.96462i	−0.351716	+	0.270483i
$664$	11.9055	−	6.87362i	0.462021	−	0.266748i
$665$	4.75247	+	20.7877i	0.184293	+	0.806112i
$666$	2.63103	+	9.73525i	0.101950	+	0.377233i
$667$	−3.09379	−	5.35859i	−0.119792	−	0.207486i
$668$	10.7781			0.417018
$669$	−22.8507	+	17.5730i	−0.883458	+	0.679413i
$670$			15.1391i			0.584875i
$671$	−4.41742	+	7.65119i	−0.170532	+	0.295371i
$672$	1.60030	+	4.29407i	0.0617330	+	0.165647i
$673$	−18.6100	−	32.2335i	−0.717364	−	1.24251i	−0.962041	−	0.272906i	$-0.912015\pi$
$673$	−18.6100	−	32.2335i	−0.717364	−	1.24251i	0.244676	−	0.969605i	$-0.421318\pi$
$674$	5.71465	−	3.29935i	0.220120	−	0.127086i
$675$	4.79417	−	2.00398i	0.184528	−	0.0771331i
$676$	4.58273	−	7.93753i	0.176259	−	0.305290i
$677$	−20.5046	+	35.5150i	−0.788056	+	1.36495i	0.139101	+	0.990278i	$0.455579\pi$
$677$	−20.5046	+	35.5150i	−0.788056	+	1.36495i	−0.927157	+	0.374674i	$0.877755\pi$
$678$	2.87631	+	3.74013i	0.110464	+	0.143639i
$679$	3.55102	+	15.5324i	0.136275	+	0.596080i
$680$	2.91713	+	1.68420i	0.111867	+	0.0645863i
$681$	−2.62724	+	0.348761i	−0.100676	+	0.0133645i
$682$		−	6.41330i		−	0.245578i
$683$	28.9807	+	16.7320i	1.10892	+	0.640233i	0.938549	−	0.345147i	$-0.112171\pi$
$683$	28.9807	+	16.7320i	1.10892	+	0.640233i	0.170368	+	0.985380i	$0.445504\pi$
$684$	−23.3687	−	6.20773i	−0.893525	−	0.237358i
$685$			4.89178i			0.186905i
$686$	−18.3104	+	2.77993i	−0.699096	+	0.106138i
$687$	5.14720	+	38.7743i	0.196378	+	1.47933i
$688$	−1.98286			−0.0755958
$689$	10.4619	+	18.1205i	0.398566	+	0.690337i
$690$	1.88766	−	4.57113i	0.0718620	−	0.174020i
$691$	−37.3917	−	21.5881i	−1.42245	−	0.821250i	−0.425939	−	0.904752i	$-0.640056\pi$
$691$	−37.3917	−	21.5881i	−1.42245	−	0.821250i	−0.996508	+	0.0835021i	$0.973389\pi$
$692$	2.57885			0.0980333
$693$	23.0695	+	0.805207i	0.876337	+	0.0305873i
$694$	12.1162			0.459924
$695$	−13.7982	−	7.96639i	−0.523395	−	0.302183i
$696$	2.28814	+	2.97532i	0.0867317	+	0.112779i
$697$	14.3095	+	24.7847i	0.542009	+	0.938788i
$698$	0.247470			0.00936687
$699$	2.41029	−	1.85360i	0.0911655	−	0.0701098i
$700$	2.57921	−	0.589657i	0.0974848	−	0.0222869i
$701$		−	23.1589i		−	0.874701i	−0.899291	−	0.437350i	$-0.855917\pi$
$701$		−	23.1589i		−	0.874701i	0.899291	−	0.437350i	$-0.144083\pi$
$702$	−8.09240	−	6.16809i	−0.305428	−	0.232800i
$703$	−23.4631	−	13.5464i	−0.884926	−	0.510912i
$704$		−	2.90825i		−	0.109609i
$705$	−0.427865	+	1.03611i	−0.0161143	+	0.0390222i
$706$	−0.113033	−	0.0652598i	−0.00425406	−	0.00245608i
$707$	12.2107	−	39.6364i	0.459231	−	1.49068i
$708$	−6.02699	+	14.5949i	−0.226508	+	0.548508i
$709$	−12.7416	+	22.0690i	−0.478519	+	0.828820i	−0.999697	−	0.0246288i	$-0.992160\pi$
$709$	−12.7416	+	22.0690i	−0.478519	+	0.828820i	0.521177	+	0.853448i	$0.325493\pi$
$710$	3.97101	−	6.87799i	0.149029	−	0.258126i
$711$	−3.30811	+	12.4532i	−0.124064	+	0.467033i
$712$	14.6163	−	8.43872i	0.547768	−	0.316254i
$713$	3.14828	+	5.45299i	0.117904	+	0.204216i
$714$	−5.39047	−	14.4642i	−0.201733	−	0.541308i
$715$	2.84746	−	4.93195i	0.106489	−	0.184444i
$716$		−	0.532633i		−	0.0199054i
$717$	25.0175	+	10.3310i	0.934296	+	0.385820i
$718$	10.2538			0.382670
$719$	−1.20759	−	2.09160i	−0.0450354	−	0.0780036i	0.842629	−	0.538495i	$-0.181007\pi$
$719$	−1.20759	−	2.09160i	−0.0450354	−	0.0780036i	−0.887664	+	0.460491i	$0.847673\pi$
$720$	−0.770216	+	2.89944i	−0.0287042	+	0.108056i
$721$	9.32911	+	2.87400i	0.347434	+	0.107033i
$722$	39.8018	−	22.9796i	1.48127	−	0.855212i
$723$	−1.78018	−	13.4102i	−0.0662056	−	0.498732i
$724$	21.9057	−	12.6473i	0.814121	−	0.470033i
$725$	1.87671	−	1.08352i	0.0696992	−	0.0402409i
$726$	4.06967	+	1.68058i	0.151040	+	0.0623722i
$727$	−23.7545	+	13.7147i	−0.881006	+	0.508649i	−0.870990	−	0.491301i	$-0.836522\pi$
$727$	−23.7545	+	13.7147i	−0.881006	+	0.508649i	−0.0100163	+	0.999950i	$0.503188\pi$
$728$	−3.52526	−	3.79661i	−0.130655	−	0.140712i
$729$	18.9682	−	19.2148i	0.702524	−	0.711660i
$730$	−7.26053	−	12.5756i	−0.268724	−	0.465444i
$731$	6.67908			0.247035
$732$	0.692407	+	5.21596i	0.0255921	+	0.192787i
$733$		−	42.5703i		−	1.57237i	−0.617992	−	0.786184i	$-0.712054\pi$
$733$		−	42.5703i		−	1.57237i	0.617992	−	0.786184i	$-0.287946\pi$
$734$	−0.216129	+	0.374347i	−0.00797747	+	0.0138174i
$735$	−10.8332	−	5.44451i	−0.399587	−	0.200824i
$736$	1.42766	+	2.47278i	0.0526241	+	0.0911477i
$737$	−38.1297	+	22.0142i	−1.40452	+	0.810903i
$738$	−17.9845	+	18.0621i	−0.662017	+	0.664875i
$739$	−17.3740	+	30.0927i	−0.639113	+	1.10698i	0.346514	+	0.938045i	$0.387365\pi$
$739$	−17.3740	+	30.0927i	−0.639113	+	1.10698i	−0.985628	+	0.168932i	$0.945968\pi$
$740$	−1.68075	+	2.91115i	−0.0617857	+	0.107016i
$741$	27.0984	−	3.59726i	0.995485	−	0.132149i
$742$	−27.5594	+	6.30062i	−1.01174	+	0.231303i
$743$	−30.6126	−	17.6742i	−1.12307	−	0.648404i	−0.180886	−	0.983504i	$-0.557897\pi$
$743$	−30.6126	−	17.6742i	−1.12307	−	0.648404i	−0.942183	+	0.335100i	$0.891230\pi$
$744$	−2.32845	−	3.02774i	−0.0853650	−	0.111002i
$745$		−	7.16643i		−	0.262558i
$746$	2.67846	+	1.54641i	0.0980654	+	0.0566181i
$747$	−29.2250	−	29.0994i	−1.06929	−	1.06469i
$748$			9.79617i			0.358183i
$749$	−7.27454	−	31.8194i	−0.265806	−	1.16266i
$750$	1.60092	+	0.661104i	0.0584573	+	0.0241401i
$751$	−34.6922			−1.26594			−0.632968	−	0.774178i	$-0.718163\pi$
$751$	−34.6922			−1.26594			−0.632968	+	0.774178i	$0.718163\pi$
$752$	−0.323599	−	0.560490i	−0.0118004	−	0.0204390i
$753$	−21.3191	+	2.83006i	−0.776910	+	0.103133i
$754$	−3.67496	−	2.12174i	−0.133834	−	0.0772693i
$755$	−6.76696			−0.246275
$756$	11.1835	−	7.99558i	0.406740	−	0.290797i
$757$	39.4586			1.43415			0.717074	−	0.696997i	$-0.245481\pi$
$757$	39.4586			1.43415			0.717074	+	0.696997i	$0.245481\pi$
$758$	−7.97419	−	4.60390i	−0.289636	−	0.167221i
$759$	14.2578	−	1.89270i	0.517526	−	0.0687005i
$760$	−4.02986	−	6.97993i	−0.146179	−	0.253189i
$761$	11.3522			0.411515			0.205758	−	0.978603i	$-0.434034\pi$
$761$	11.3522			0.411515			0.205758	+	0.978603i	$0.434034\pi$
$762$	−10.5638	−	4.36235i	−0.382686	−	0.158031i
$763$	12.5312	+	13.4957i	0.453659	+	0.488578i
$764$			23.3473i			0.844677i
$765$	2.59440	−	9.76650i	0.0938008	−	0.353109i
$766$	21.2108	+	12.2460i	0.766376	+	0.442467i
$767$		−	17.8520i		−	0.644598i
$768$	−1.05588	−	1.37299i	−0.0381010	−	0.0495436i
$769$	25.0365	+	14.4549i	0.902841	+	0.521255i	0.878121	−	0.478439i	$-0.158797\pi$
$769$	25.0365	+	14.4549i	0.902841	+	0.521255i	0.0247199	+	0.999694i	$0.492131\pi$
$770$	5.23561	+	5.63860i	0.188678	+	0.203201i
$771$	50.5018	−	6.70401i	1.81878	−	0.241439i
$772$	2.08929	−	3.61875i	0.0751950	−	0.130242i
$773$	15.3683	−	26.6187i	0.552761	−	0.957410i	−0.445313	−	0.895375i	$-0.646908\pi$
$773$	15.3683	−	26.6187i	0.552761	−	0.957410i	0.998074	−	0.0620349i	$-0.0197590\pi$
$774$	1.55197	+	5.74256i	0.0557846	+	0.206412i
$775$	−1.90977	+	1.10260i	−0.0686009	+	0.0396067i
$776$	−3.01109	−	5.21536i	−0.108092	−	0.187220i
$777$	14.4345	−	5.37943i	0.517836	−	0.192986i
$778$	−2.60976	+	4.52023i	−0.0935643	+	0.162058i
$779$		−	68.4776i		−	2.45347i
$780$	−0.446325	−	3.36220i	−0.0159810	−	0.120386i
$781$	23.0974			0.826489
$782$	−4.80893	−	8.32931i	−0.171967	−	0.297856i
$783$	6.82592	−	8.95545i	0.243938	−	0.320042i
$784$	6.30461	−	3.04169i	0.225165	−	0.108632i
$785$	8.74085	−	5.04653i	0.311974	−	0.180118i
$786$	−7.06025	−	2.91555i	−0.251831	−	0.103994i
$787$	−22.7404	+	13.1291i	−0.810606	+	0.468004i	−0.847166	−	0.531328i	$-0.821693\pi$
$787$	−22.7404	+	13.1291i	−0.810606	+	0.468004i	0.0365602	+	0.999331i	$0.488360\pi$
$788$	2.42117	−	1.39786i	0.0862506	−	0.0497968i
$789$	5.94815	+	44.8078i	0.211760	+	1.59520i
$790$	−3.71962	+	2.14752i	−0.132338	+	0.0764054i
$791$	5.28152	−	4.90404i	0.187789	−	0.174368i
$792$	−8.42258	+	2.27627i	−0.299283	+	0.0808838i
$793$	−2.97435	−	5.15173i	−0.105622	−	0.182943i
$794$	9.61657			0.341279
$795$	−17.1062	−	7.06405i	−0.606694	−	0.250536i
$796$		−	3.48925i		−	0.123673i
$797$	−5.45013	+	9.43990i	−0.193054	+	0.334379i	−0.946261	−	0.323405i	$-0.895172\pi$
$797$	−5.45013	+	9.43990i	−0.193054	+	0.334379i	0.753207	+	0.657783i	$0.228506\pi$
$798$	−6.13451	+	36.4213i	−0.217159	+	1.28930i
$799$	1.09001	+	1.88796i	0.0385619	+	0.0667912i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−35.8794	−	35.7253i	−1.26774	−	1.26229i
$802$	9.14348	−	15.8370i	0.322868	−	0.559223i
$803$	21.1154	−	36.5730i	0.745147	−	1.29063i
$804$	−10.0085	+	24.2365i	−0.352974	+	0.854756i
$805$	−7.21962	−	2.22413i	−0.254458	−	0.0783905i
$806$	3.73970	+	2.15912i	0.131725	+	0.0760516i
$807$	10.2913	−	24.9212i	0.362270	−	0.877266i
$808$			15.6759i			0.551477i
$809$	14.0577	+	8.11622i	0.494243	+	0.285351i	0.726333	−	0.687343i	$-0.241223\pi$
$809$	14.0577	+	8.11622i	0.494243	+	0.285351i	−0.232090	+	0.972694i	$0.574556\pi$
$810$	8.99992	−	0.0387579i	0.316225	−	0.00136181i
$811$			34.0263i			1.19482i	0.801934	+	0.597412i	$0.203804\pi$
$811$			34.0263i			1.19482i	−0.801934	+	0.597412i	$0.796196\pi$
$812$	4.20152	−	3.90123i	0.147444	−	0.136906i
$813$	16.3039	−	12.5384i	0.571804	−	0.439739i
$814$	−9.77610			−0.342652
$815$	11.7073	+	20.2777i	0.410090	+	0.710296i
$816$	3.55665	+	4.62480i	0.124508	+	0.161900i
$817$	−13.8402	−	7.99066i	−0.484208	−	0.279558i
$818$	4.06433			0.142106
$819$	−8.23615	+	13.1811i	−0.287794	+	0.460585i
$820$	−8.49627			−0.296703
$821$	30.2973	+	17.4922i	1.05738	+	0.610480i	0.924707	−	0.380679i	$-0.124310\pi$
$821$	30.2973	+	17.4922i	1.05738	+	0.610480i	0.132676	+	0.991159i	$0.457643\pi$
$822$	−3.23397	+	7.83134i	−0.112798	+	0.273149i
$823$	0.732942	+	1.26949i	0.0255487	+	0.0442517i	0.878517	−	0.477711i	$-0.158533\pi$
$823$	0.732942	+	1.26949i	0.0255487	+	0.0442517i	−0.852968	+	0.521963i	$0.825200\pi$
$824$	−3.68960			−0.128533
$825$	0.662868	+	4.99343i	0.0230781	+	0.173849i
$826$	23.0511	+	7.10130i	0.802049	+	0.247086i
$827$			3.05294i			0.106161i	0.998590	+	0.0530805i	$0.0169040\pi$
$827$			3.05294i			0.106161i	−0.998590	+	0.0530805i	$0.983096\pi$
$828$	6.04398	−	6.07007i	0.210043	−	0.210949i
$829$	−45.1011	−	26.0391i	−1.56643	−	0.904377i	−0.996581	−	0.0826248i	$-0.973670\pi$
$829$	−45.1011	−	26.0391i	−1.56643	−	0.904377i	−0.569846	−	0.821752i	$-0.692997\pi$
$830$		−	13.7472i		−	0.477173i
$831$	47.1410	−	6.25788i	1.63530	−	0.217083i
$832$	1.69585	+	0.979098i	0.0587929	+	0.0339441i
$833$	−21.2365	+	10.2457i	−0.735801	+	0.354991i
$834$	−16.8232	−	21.8756i	−0.582539	−	0.757490i
$835$	5.38906	−	9.33412i	0.186496	−	0.323021i
$836$	11.7199	−	20.2994i	0.405340	−	0.702069i
$837$	−6.94616	+	9.11321i	−0.240094	+	0.314998i
$838$	−10.4005	+	6.00474i	−0.359280	+	0.207430i
$839$	−1.17639	−	2.03757i	−0.0406135	−	0.0703447i	0.845004	−	0.534760i	$-0.179598\pi$
$839$	−1.17639	−	2.03757i	−0.0406135	−	0.0703447i	−0.885618	+	0.464415i	$0.846265\pi$
$840$	4.51892	+	0.761131i	0.155918	+	0.0262615i
$841$	−12.1520	+	21.0478i	−0.419034	+	0.725788i
$842$		−	12.0277i		−	0.414501i
$843$	−35.7192	+	27.4694i	−1.23023	+	0.946098i
$844$	−9.39692			−0.323455
$845$	−4.58273	−	7.93753i	−0.157651	−	0.273059i
$846$	−1.36995	+	1.37587i	−0.0471000	+	0.0473033i
$847$	1.98014	−	6.42762i	0.0680385	−	0.220856i
$848$	9.25368	−	5.34261i	0.317773	−	0.183466i
$849$	1.18777	−	0.913440i	0.0407641	−	0.0313492i
$850$	2.91713	−	1.68420i	0.100057	−	0.0577677i
$851$	8.31225	−	4.79908i	0.284940	−	0.164510i
$852$	10.9043	−	8.38585i	0.373576	−	0.287295i
$853$	24.1341	−	13.9338i	0.826334	−	0.477084i	−0.0262617	−	0.999655i	$-0.508360\pi$
$853$	24.1341	−	13.9338i	0.826334	−	0.477084i	0.852596	+	0.522571i	$0.175027\pi$
$854$	7.83525	−	1.79129i	0.268117	−	0.0612966i
$855$	−17.0604	+	17.1340i	−0.583454	+	0.585972i
$856$	6.16845	+	10.6841i	0.210833	+	0.365174i
$857$	−29.1560			−0.995951			−0.497975	−	0.867191i	$-0.665923\pi$
$857$	−29.1560			−0.995951			−0.497975	+	0.867191i	$0.665923\pi$
$858$	7.81909	−	6.01318i	0.266939	−	0.205287i
$859$			57.4463i			1.96004i	0.198890	+	0.980022i	$0.436266\pi$
$859$			57.4463i			1.96004i	−0.198890	+	0.980022i	$0.563734\pi$
$860$	−0.991430	+	1.71721i	−0.0338075	+	0.0585563i
$861$	30.0168	+	24.7974i	1.02297	+	0.845093i
$862$	4.70997	+	8.15790i	0.160422	+	0.277859i
$863$	−16.5615	+	9.56179i	−0.563761	+	0.325487i	−0.754653	−	0.656124i	$-0.772195\pi$
$863$	−16.5615	+	9.56179i	−0.563761	+	0.325487i	0.190893	+	0.981611i	$0.438862\pi$
$864$	−3.14989	+	4.13258i	−0.107161	+	0.140593i
$865$	1.28943	−	2.23335i	0.0438418	−	0.0759362i
$866$	14.4144	−	24.9664i	0.489820	−	0.848393i
$867$	5.96979	+	7.76267i	0.202745	+	0.263634i
$868$	−4.27553	+	3.96995i	−0.145121	+	0.134749i
$869$	−10.8176	−	6.24553i	−0.366961	−	0.211865i
$870$	3.72078	−	0.493925i	0.126146	−	0.0167456i
$871$		−	29.6454i		−	1.00450i
$872$	−6.02819	−	3.48038i	−0.204140	−	0.117860i
$873$	−12.7474	+	12.8024i	−0.431435	+	0.433297i
$874$			23.0131i			0.778428i
$875$	0.778946	−	2.52849i	0.0263332	−	0.0854784i
$876$	−3.30974	−	24.9325i	−0.111826	−	0.842390i
$877$	28.7546			0.970973			0.485487	−	0.874244i	$-0.338642\pi$
$877$	28.7546			0.970973			0.485487	+	0.874244i	$0.338642\pi$
$878$	−17.6221	−	30.5223i	−0.594716	−	1.03008i
$879$	15.0644	−	36.4798i	0.508110	−	1.23043i
$880$	−2.51862	−	1.45413i	−0.0849026	−	0.0490185i
$881$	9.79497			0.330001			0.165001	−	0.986293i	$-0.447237\pi$
$881$	9.79497			0.330001			0.165001	+	0.986293i	$0.447237\pi$
$882$	−13.7436	−	15.8781i	−0.462772	−	0.534642i
$883$	−22.0390			−0.741670			−0.370835	−	0.928699i	$-0.620929\pi$
$883$	−22.0390			−0.741670			−0.370835	+	0.928699i	$0.620929\pi$
$884$	−5.71231	−	3.29800i	−0.192126	−	0.110924i
$885$	9.62602	+	12.5170i	0.323575	+	0.420753i
$886$	10.6207	+	18.3956i	0.356810	+	0.618012i
$887$	47.6284			1.59921			0.799603	−	0.600529i	$-0.205043\pi$
$887$	47.6284			1.59921			0.799603	+	0.600529i	$0.205043\pi$
$888$	−4.61532	+	3.54936i	−0.154880	+	0.119109i
$889$	−5.13993	+	16.6844i	−0.172388	+	0.559577i
$890$		−	16.8774i		−	0.565733i
$891$	13.1846	+	22.6110i	0.441701	+	0.757497i
$892$	−14.4132	−	8.32148i	−0.482591	−	0.278624i
$893$		−	5.21624i		−	0.174555i
$894$	4.73776	−	11.4729i	0.158454	−	0.383710i
$895$	−0.461274	−	0.266316i	−0.0154187	−	0.00890198i
$896$	−1.93883	+	1.80026i	−0.0647718	+	0.0601425i
$897$	−3.69641	+	8.95116i	−0.123419	+	0.298871i
$898$	8.46527	−	14.6623i	0.282490	−	0.489287i
$899$	−2.38939	+	4.13854i	−0.0796905	+	0.138028i
$900$	2.12588	+	2.11675i	0.0708628	+	0.0705583i
$901$	−31.1702	+	17.9961i	−1.03843	+	0.599537i
$902$	−12.3546	−	21.3989i	−0.411365	−	0.712504i
$903$	8.51454	−	3.17318i	0.283346	−	0.105597i
$904$	−1.36204	+	2.35912i	−0.0453007	+	0.0784631i
$905$		−	25.2946i		−	0.840820i
$906$	−10.8333	−	4.47366i	−0.359914	−	0.148627i
$907$	−6.35186			−0.210910			−0.105455	−	0.994424i	$-0.533630\pi$
$907$	−6.35186			−0.210910			−0.105455	+	0.994424i	$0.533630\pi$
$908$	−0.765073	−	1.32514i	−0.0253898	−	0.0439765i
$909$	45.3991	−	12.2695i	1.50579	−	0.406953i
$910$	−5.05059	+	1.15466i	−0.167425	+	0.0382767i
$911$	23.4087	−	13.5150i	0.775563	−	0.447772i	−0.0592924	−	0.998241i	$-0.518884\pi$
$911$	23.4087	−	13.5150i	0.775563	−	0.447772i	0.834856	+	0.550469i	$0.185551\pi$
$912$	−1.83703	−	13.8385i	−0.0608300	−	0.458237i
$913$	34.6240	−	19.9902i	1.14589	−	0.661579i
$914$	−28.7824	+	16.6175i	−0.952037	+	0.549659i
$915$	4.86335	+	2.00834i	0.160778	+	0.0663935i
$916$	−19.5572	+	11.2914i	−0.646188	+	0.373077i
$917$	−3.43524	+	11.1509i	−0.113442	+	0.368236i
$918$	10.6101	−	13.9202i	0.350185	−	0.459436i
$919$	−18.7122	−	32.4104i	−0.617257	−	1.06912i	−0.989984	−	0.141179i	$-0.954911\pi$
$919$	−18.7122	−	32.4104i	−0.617257	−	1.06912i	0.372727	−	0.927941i	$-0.378423\pi$
$920$	2.85531			0.0941369
$921$	4.46266	+	33.6175i	0.147050	+	1.10774i
$922$			26.5357i			0.873908i
$923$	−7.77601	+	13.4684i	−0.255951	+	0.443319i
$924$	4.65408	+	12.4882i	0.153108	+	0.410832i
$925$	1.68075	+	2.91115i	0.0552628	+	0.0957180i
$926$	−9.10135	+	5.25467i	−0.299089	+	0.172679i
$927$	2.88783	+	10.6854i	0.0948488	+	0.350956i
$928$	−1.08352	+	1.87671i	−0.0355682	+	0.0616060i
$929$	−3.89744	+	6.75056i	−0.127871	+	0.221479i	−0.922851	−	0.385156i	$-0.874148\pi$
$929$	−3.89744	+	6.75056i	−0.127871	+	0.221479i	0.794981	+	0.606635i	$0.207481\pi$
$930$	−3.78632	+	0.502626i	−0.124158	+	0.0164818i
$931$	56.2633	+	4.17593i	1.84396	+	0.136861i
$932$	1.52031	+	0.877750i	0.0497993	+	0.0287517i
$933$	26.1439	+	33.9955i	0.855912	+	1.11296i
$934$			12.2904i			0.402154i
$935$	8.48373	+	4.89809i	0.277448	+	0.160185i
$936$	1.50823	−	5.67768i	0.0492982	−	0.185581i
$937$			55.3757i			1.80905i	0.426424	+	0.904523i	$0.359773\pi$
$937$			55.3757i			1.80905i	−0.426424	+	0.904523i	$0.640227\pi$
$938$	38.2791	+	11.7926i	1.24986	+	0.385040i
$939$	47.5592	+	19.6397i	1.55204	+	0.640918i
$940$	−0.647198			−0.0211093
$941$	−14.6362	−	25.3507i	−0.477128	−	0.826410i	0.522529	−	0.852622i	$-0.324989\pi$
$941$	−14.6362	−	25.3507i	−0.477128	−	0.826410i	−0.999656	+	0.0262121i	$0.991655\pi$
$942$	17.3297	−	2.30048i	0.564631	−	0.0749536i
$943$	21.0094	+	12.1298i	0.684159	+	0.395000i
$944$	−9.11655			−0.296718
$945$	−1.33263	−	13.6830i	−0.0433504	−	0.445108i
$946$	−5.76665			−0.187490
$947$	−37.7000	−	21.7661i	−1.22508	−	0.707303i	−0.259087	−	0.965854i	$-0.583422\pi$
$947$	−37.7000	−	21.7661i	−1.22508	−	0.707303i	−0.965997	+	0.258551i	$0.916755\pi$
$948$	−7.37454	+	0.978955i	−0.239514	+	0.0317950i
$949$	14.2175	+	24.6255i	0.461521	+	0.799377i
$950$	−8.05973			−0.261492
$951$	9.58543	+	3.95833i	0.310829	+	0.128358i
$952$	6.53077	−	6.06401i	0.211663	−	0.196536i
$953$			19.9323i			0.645672i	0.946455	+	0.322836i	$0.104636\pi$
$953$			19.9323i			0.645672i	−0.946455	+	0.322836i	$0.895364\pi$
$954$	−22.7155	−	22.6179i	−0.735443	−	0.732283i
$955$	20.2194	+	11.6737i	0.654284	+	0.377751i
$956$			15.6270i			0.505412i
$957$	6.65448	+	8.65299i	0.215109	+	0.279711i
$958$	27.4869	+	15.8696i	0.888063	+	0.512723i
$959$	12.3688	+	3.81043i	0.399409	+	0.123045i
$960$	−1.71699	+	0.227927i	−0.0554156	+	0.00735630i
$961$	−13.0685	+	22.6353i	−0.421565	+	0.730173i
$962$	3.29124	−	5.70060i	0.106114	−	0.183795i
$963$	26.1141	−	26.2268i	0.841516	−	0.845147i
$964$	6.76393	−	3.90516i	0.217852	−	0.125777i
$965$	−2.08929	−	3.61875i	−0.0672565	−	0.116492i
$966$	−10.0876	−	8.33358i	−0.324565	−	0.268129i
$967$	13.3577	−	23.1362i	0.429555	−	0.744011i	−0.567279	−	0.823526i	$-0.692004\pi$
$967$	13.3577	−	23.1362i	0.429555	−	0.744011i	0.996834	+	0.0795148i	$0.0253371\pi$
$968$			2.54208i			0.0817056i
$969$	6.18785	+	46.6136i	0.198783	+	1.49744i
$970$	−6.02218			−0.193360
$971$	1.77474	+	3.07394i	0.0569541	+	0.0986475i	0.893097	−	0.449865i	$-0.148528\pi$
$971$	1.77474	+	3.07394i	0.0569541	+	0.0986475i	−0.836143	+	0.548512i	$0.815194\pi$
$972$	14.4338	+	5.88783i	0.462963	+	0.188852i
$973$	−30.8910	+	28.6832i	−0.990319	+	0.919540i
$974$	35.9155	−	20.7358i	1.15081	−	0.664419i
$975$	−3.13491	−	1.29457i	−0.100398	−	0.0414595i
$976$	−2.63086	+	1.51893i	−0.0842117	+	0.0486196i
$977$	−44.4673	+	25.6732i	−1.42264	+	0.821360i	−0.996524	−	0.0833106i	$-0.973451\pi$
$977$	−44.4673	+	25.6732i	−1.42264	+	0.821360i	−0.426113	+	0.904670i	$0.640117\pi$
$978$	5.33682	+	40.2027i	0.170653	+	1.28554i
$979$	42.5078	−	24.5419i	1.35856	−	0.784362i
$980$	0.518123	−	6.98080i	0.0165508	−	0.222993i
$981$	−5.36128	+	20.1823i	−0.171173	+	0.644372i
$982$	5.39359	+	9.34197i	0.172116	+	0.298114i
$983$	41.4904			1.32334			0.661669	−	0.749796i	$-0.269848\pi$
$983$	41.4904			1.32334			0.661669	+	0.749796i	$0.269848\pi$
$984$	−13.6018	−	5.61692i	−0.433611	−	0.179061i
$985$		−	2.79573i		−	0.0890793i
$986$	3.64973	−	6.32152i	0.116231	−	0.201318i
$987$	2.28651	+	1.88893i	0.0727804	+	0.0601252i
$988$	7.89126	+	13.6681i	0.251055	+	0.434839i
$989$	4.90317	−	2.83085i	0.155912	−	0.0900156i
$990$	−2.23998	+	8.43230i	−0.0711912	+	0.267996i
$991$	12.9670	−	22.4595i	0.411911	−	0.713451i	−0.583188	−	0.812337i	$-0.698195\pi$
$991$	12.9670	−	22.4595i	0.411911	−	0.713451i	0.995099	+	0.0988866i	$0.0315281\pi$
$992$	1.10260	−	1.90977i	0.0350077	−	0.0606352i
$993$	−5.09492	+	12.3378i	−0.161682	+	0.391528i
$994$	−14.2977	−	15.3982i	−0.453495	−	0.488402i
$995$	−3.02178	−	1.74463i	−0.0957969	−	0.0553084i
$996$	9.08835	−	22.0082i	0.287975	−	0.697357i
$997$			21.2122i			0.671796i	0.941898	+	0.335898i	$0.109040\pi$
$997$			21.2122i			0.671796i	−0.941898	+	0.335898i	$0.890960\pi$
$998$	23.2675	+	13.4335i	0.736519	+	0.425229i
$999$	13.8917	+	10.5884i	0.439514	+	0.335001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.c.311.16	✓	32
3.2	odd	2		1890.2.t.c.1151.6		32
7.5	odd	6		630.2.bk.c.131.6	yes	32
9.2	odd	6		630.2.bk.c.101.14	yes	32
9.7	even	3		1890.2.bk.c.521.13		32
21.5	even	6		1890.2.bk.c.341.13		32
63.47	even	6	inner	630.2.t.c.551.16	yes	32
63.61	odd	6		1890.2.t.c.1601.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.16	✓	32	1.1	even	1	trivial
630.2.t.c.551.16	yes	32	63.47	even	6	inner
630.2.bk.c.101.14	yes	32	9.2	odd	6
630.2.bk.c.131.6	yes	32	7.5	odd	6
1890.2.t.c.1151.6		32	3.2	odd	2
1890.2.t.c.1601.6		32	63.61	odd	6
1890.2.bk.c.341.13		32	21.5	even	6
1890.2.bk.c.521.13		32	9.7	even	3

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.71699 - 0.227927i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.60092 + 0.661104i) q^{6} +(0.778946 - 2.52849i) q^{7} +1.00000i q^{8} +(2.89610 - 0.782695i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.71699 - 0.227927i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.60092 + 0.661104i) q^{6} +(0.778946 - 2.52849i) q^{7} +1.00000i q^{8} +(2.89610 - 0.782695i) q^{9} +(0.866025 + 0.500000i) q^{10} +2.90825i q^{11} +(1.05588 + 1.37299i) q^{12} +(-1.69585 - 0.979098i) q^{13} +(1.93883 - 1.80026i) q^{14} +(1.71699 - 0.227927i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.68420 - 2.91713i) q^{17} +(2.89944 + 0.770216i) q^{18} +(-6.97993 + 4.02986i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.761131 - 4.51892i) q^{21} +(-1.45413 + 2.51862i) q^{22} -2.85531i q^{23} +(0.227927 + 1.71699i) q^{24} +1.00000 q^{25} +(-0.979098 - 1.69585i) q^{26} +(4.79417 - 2.00398i) q^{27} +(2.57921 - 0.589657i) q^{28} +(1.87671 - 1.08352i) q^{29} +(1.60092 + 0.661104i) q^{30} +(-1.90977 + 1.10260i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.662868 + 4.99343i) q^{33} +(2.91713 - 1.68420i) q^{34} +(0.778946 - 2.52849i) q^{35} +(2.12588 + 2.11675i) q^{36} +(1.68075 + 2.91115i) q^{37} -8.05973 q^{38} +(-3.13491 - 1.29457i) q^{39} +1.00000i q^{40} +(-4.24814 + 7.35799i) q^{41} +(2.91862 - 3.53294i) q^{42} +(0.991430 + 1.71721i) q^{43} +(-2.51862 + 1.45413i) q^{44} +(2.89610 - 0.782695i) q^{45} +(1.42766 - 2.47278i) q^{46} +(-0.323599 + 0.560490i) q^{47} +(-0.661104 + 1.60092i) q^{48} +(-5.78649 - 3.93911i) q^{49} +(0.866025 + 0.500000i) q^{50} +(2.22687 - 5.39255i) q^{51} -1.95820i q^{52} +(-9.25368 - 5.34261i) q^{53} +(5.15386 + 0.661591i) q^{54} +2.90825i q^{55} +(2.52849 + 0.778946i) q^{56} +(-11.0659 + 8.51014i) q^{57} +2.16704 q^{58} +(4.55827 + 7.89516i) q^{59} +(1.05588 + 1.37299i) q^{60} +(2.63086 + 1.51893i) q^{61} -2.20521 q^{62} +(0.276870 - 7.93242i) q^{63} -1.00000 q^{64} +(-1.69585 - 0.979098i) q^{65} +(-1.92266 + 4.65587i) q^{66} +(7.56956 + 13.1109i) q^{67} +3.36841 q^{68} +(-0.650802 - 4.90254i) q^{69} +(1.93883 - 1.80026i) q^{70} -7.94202i q^{71} +(0.782695 + 2.89610i) q^{72} +(-12.5756 - 7.26053i) q^{73} +3.36151i q^{74} +(1.71699 - 0.227927i) q^{75} +(-6.97993 - 4.02986i) q^{76} +(7.35347 + 2.26537i) q^{77} +(-2.06763 - 2.68859i) q^{78} +(-2.14752 + 3.71962i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(7.77478 - 4.53352i) q^{81} +(-7.35799 + 4.24814i) q^{82} +(-6.87362 - 11.9055i) q^{83} +(4.29407 - 1.60030i) q^{84} +(1.68420 - 2.91713i) q^{85} +1.98286i q^{86} +(2.97532 - 2.28814i) q^{87} -2.90825 q^{88} +(-8.43872 - 14.6163i) q^{89} +(2.89944 + 0.770216i) q^{90} +(-3.79661 + 3.52526i) q^{91} +(2.47278 - 1.42766i) q^{92} +(-3.02774 + 2.32845i) q^{93} +(-0.560490 + 0.323599i) q^{94} +(-6.97993 + 4.02986i) q^{95} +(-1.37299 + 1.05588i) q^{96} +(-5.21536 + 3.01109i) q^{97} +(-3.04169 - 6.30461i) q^{98} +(2.27627 + 8.42258i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

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