LMFDB - Embedded newform 630.2.t.b.311.2

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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.2
Character	$\chi$	$=$	630.311
Dual form			630.2.t.b.551.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.18136 - 1.26664i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.389766 + 1.68763i) q^{6} +(2.05946 + 1.66090i) q^{7} -1.00000i q^{8} +(-0.208774 + 2.99273i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.18136 - 1.26664i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.389766 + 1.68763i) q^{6} +(2.05946 + 1.66090i) q^{7} -1.00000i q^{8} +(-0.208774 + 2.99273i) q^{9} +(0.866025 + 0.500000i) q^{10} -3.95684i q^{11} +(0.506266 - 1.65641i) q^{12} +(-2.82686 - 1.63209i) q^{13} +(-0.953096 - 2.46812i) q^{14} +(1.18136 + 1.26664i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.497322 - 0.861388i) q^{17} +(1.67717 - 2.48739i) q^{18} +(-4.90846 + 2.83390i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.329195 - 4.57074i) q^{21} +(-1.97842 + 3.42673i) q^{22} -7.70987i q^{23} +(-1.26664 + 1.18136i) q^{24} +1.00000 q^{25} +(1.63209 + 2.82686i) q^{26} +(4.03736 - 3.27105i) q^{27} +(-0.408654 + 2.61400i) q^{28} +(-4.10273 + 2.36871i) q^{29} +(-0.389766 - 1.68763i) q^{30} +(-4.83278 + 2.79020i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.01191 + 4.67446i) q^{33} +(-0.861388 + 0.497322i) q^{34} +(-2.05946 - 1.66090i) q^{35} +(-2.69616 + 1.31556i) q^{36} +(-5.05548 - 8.75634i) q^{37} +5.66780 q^{38} +(1.27227 + 5.50871i) q^{39} +1.00000i q^{40} +(-5.16567 + 8.94721i) q^{41} +(-2.00028 + 4.12297i) q^{42} +(5.10292 + 8.83852i) q^{43} +(3.42673 - 1.97842i) q^{44} +(0.208774 - 2.99273i) q^{45} +(-3.85494 + 6.67695i) q^{46} +(-2.36963 + 4.10432i) q^{47} +(1.68763 - 0.389766i) q^{48} +(1.48279 + 6.84115i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-1.67859 + 0.387679i) q^{51} -3.26418i q^{52} +(-8.82289 - 5.09390i) q^{53} +(-5.13198 + 0.814131i) q^{54} +3.95684i q^{55} +(1.66090 - 2.05946i) q^{56} +(9.38820 + 2.86941i) q^{57} +4.73743 q^{58} +(-1.70360 - 2.95072i) q^{59} +(-0.506266 + 1.65641i) q^{60} +(5.45543 + 3.14969i) q^{61} +5.58041 q^{62} +(-5.40060 + 5.81666i) q^{63} -1.00000 q^{64} +(2.82686 + 1.63209i) q^{65} +(6.67767 - 1.54224i) q^{66} +(-4.61095 - 7.98640i) q^{67} +0.994645 q^{68} +(-9.76567 + 9.10814i) q^{69} +(0.953096 + 2.46812i) q^{70} +2.74965i q^{71} +(2.99273 + 0.208774i) q^{72} +(-12.7539 - 7.36348i) q^{73} +10.1110i q^{74} +(-1.18136 - 1.26664i) q^{75} +(-4.90846 - 2.83390i) q^{76} +(6.57194 - 8.14898i) q^{77} +(1.65254 - 5.40682i) q^{78} +(0.920736 - 1.59476i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.91283 - 1.24961i) q^{81} +(8.94721 - 5.16567i) q^{82} +(0.789829 + 1.36802i) q^{83} +(3.79378 - 2.57046i) q^{84} +(-0.497322 + 0.861388i) q^{85} -10.2058i q^{86} +(7.84713 + 2.39840i) q^{87} -3.95684 q^{88} +(-6.92781 - 11.9993i) q^{89} +(-1.67717 + 2.48739i) q^{90} +(-3.11107 - 8.05637i) q^{91} +(6.67695 - 3.85494i) q^{92} +(9.24345 + 2.82517i) q^{93} +(4.10432 - 2.36963i) q^{94} +(4.90846 - 2.83390i) q^{95} +(-1.65641 - 0.506266i) q^{96} +(0.776974 - 0.448586i) q^{97} +(2.13644 - 6.66600i) q^{98} +(11.8417 + 0.826087i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * 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
$3$	−1.18136	−	1.26664i	−0.682059	−	0.731297i
$3$	−1.18136	−	1.26664i	−0.682059	−	0.731297i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.389766	+	1.68763i	0.159121	+	0.688971i
$7$	2.05946	+	1.66090i	0.778404	+	0.627763i
$7$	2.05946	+	1.66090i	0.778404	+	0.627763i
$8$		−	1.00000i		−	0.353553i
$9$	−0.208774	+	2.99273i	−0.0695914	+	0.997576i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$		−	3.95684i		−	1.19303i	−0.802601	−	0.596516i	$-0.796551\pi$
$11$		−	3.95684i		−	1.19303i	0.802601	−	0.596516i	$-0.203449\pi$
$12$	0.506266	−	1.65641i	0.146146	−	0.478164i
$13$	−2.82686	−	1.63209i	−0.784030	−	0.452660i	0.0538267	−	0.998550i	$-0.482858\pi$
$13$	−2.82686	−	1.63209i	−0.784030	−	0.452660i	−0.837857	+	0.545890i	$0.816191\pi$
$14$	−0.953096	−	2.46812i	−0.254726	−	0.659632i
$15$	1.18136	+	1.26664i	0.305026	+	0.327046i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.497322	−	0.861388i	0.120618	−	0.208917i	−0.799393	−	0.600808i	$-0.794846\pi$
$17$	0.497322	−	0.861388i	0.120618	−	0.208917i	0.920012	+	0.391891i	$0.128179\pi$
$18$	1.67717	−	2.48739i	0.395312	−	0.586284i
$19$	−4.90846	+	2.83390i	−1.12608	+	0.650141i	−0.942945	−	0.332947i	$-0.891957\pi$
$19$	−4.90846	+	2.83390i	−1.12608	+	0.650141i	−0.183132	+	0.983088i	$0.558624\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−0.329195	−	4.57074i	−0.0718363	−	0.997416i
$22$	−1.97842	+	3.42673i	−0.421801	+	0.730580i
$23$		−	7.70987i		−	1.60762i	−0.594886	−	0.803810i	$-0.702803\pi$
$23$		−	7.70987i		−	1.60762i	0.594886	−	0.803810i	$-0.297197\pi$
$24$	−1.26664	+	1.18136i	−0.258553	+	0.241144i
$25$	1.00000			0.200000
$26$	1.63209	+	2.82686i	0.320079	+	0.554393i
$27$	4.03736	−	3.27105i	0.776990	−	0.629513i
$28$	−0.408654	+	2.61400i	−0.0772283	+	0.494000i
$29$	−4.10273	+	2.36871i	−0.761858	+	0.439859i	−0.829963	−	0.557819i	$-0.811638\pi$
$29$	−4.10273	+	2.36871i	−0.761858	+	0.439859i	0.0681041	+	0.997678i	$0.478305\pi$
$30$	−0.389766	−	1.68763i	−0.0711613	−	0.308117i
$31$	−4.83278	+	2.79020i	−0.867992	+	0.501135i	−0.866680	−	0.498864i	$-0.833751\pi$
$31$	−4.83278	+	2.79020i	−0.867992	+	0.501135i	−0.00131164	+	0.999999i	$0.500418\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−5.01191	+	4.67446i	−0.872462	+	0.813719i
$34$	−0.861388	+	0.497322i	−0.147727	+	0.0852901i
$35$	−2.05946	−	1.66090i	−0.348113	−	0.280744i
$36$	−2.69616	+	1.31556i	−0.449361	+	0.219260i
$37$	−5.05548	−	8.75634i	−0.831115	−	1.43953i	−0.897155	−	0.441717i	$-0.854370\pi$
$37$	−5.05548	−	8.75634i	−0.831115	−	1.43953i	0.0660393	−	0.997817i	$-0.478964\pi$
$38$	5.66780			0.919438
$39$	1.27227	+	5.50871i	0.203726	+	0.882100i
$40$			1.00000i			0.158114i
$41$	−5.16567	+	8.94721i	−0.806743	+	1.39732i	0.108365	+	0.994111i	$0.465438\pi$
$41$	−5.16567	+	8.94721i	−0.806743	+	1.39732i	−0.915108	+	0.403208i	$0.867895\pi$
$42$	−2.00028	+	4.12297i	−0.308649	+	0.636188i
$43$	5.10292	+	8.83852i	0.778188	+	1.34786i	0.932985	+	0.359915i	$0.117194\pi$
$43$	5.10292	+	8.83852i	0.778188	+	1.34786i	−0.154797	+	0.987946i	$0.549472\pi$
$44$	3.42673	−	1.97842i	0.516598	−	0.298258i
$45$	0.208774	−	2.99273i	0.0311222	−	0.446129i
$46$	−3.85494	+	6.67695i	−0.568379	+	0.984462i
$47$	−2.36963	+	4.10432i	−0.345646	+	0.598677i	−0.985471	−	0.169844i	$-0.945674\pi$
$47$	−2.36963	+	4.10432i	−0.345646	+	0.598677i	0.639825	+	0.768521i	$0.279007\pi$
$48$	1.68763	−	0.389766i	0.243588	−	0.0562579i
$49$	1.48279	+	6.84115i	0.211827	+	0.977307i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$	−1.67859	+	0.387679i	−0.235049	+	0.0542859i
$52$		−	3.26418i		−	0.452660i
$53$	−8.82289	−	5.09390i	−1.21192	−	0.699701i	−0.248741	−	0.968570i	$-0.580017\pi$
$53$	−8.82289	−	5.09390i	−1.21192	−	0.699701i	−0.963177	+	0.268869i	$0.913350\pi$
$54$	−5.13198	+	0.814131i	−0.698374	+	0.110789i
$55$			3.95684i			0.533540i
$56$	1.66090	−	2.05946i	0.221948	−	0.275208i
$57$	9.38820	+	2.86941i	1.24350	+	0.380063i
$58$	4.73743			0.622055
$59$	−1.70360	−	2.95072i	−0.221790	−	0.384152i	0.733562	−	0.679623i	$-0.237857\pi$
$59$	−1.70360	−	2.95072i	−0.221790	−	0.384152i	−0.955352	+	0.295471i	$0.904523\pi$
$60$	−0.506266	+	1.65641i	−0.0653586	+	0.213842i
$61$	5.45543	+	3.14969i	0.698496	+	0.403277i	0.806787	−	0.590842i	$-0.201204\pi$
$61$	5.45543	+	3.14969i	0.698496	+	0.403277i	−0.108291	+	0.994119i	$0.534538\pi$
$62$	5.58041			0.708713
$63$	−5.40060	+	5.81666i	−0.680411	+	0.732830i
$64$	−1.00000			−0.125000
$65$	2.82686	+	1.63209i	0.350629	+	0.202436i
$66$	6.67767	−	1.54224i	0.821964	−	0.189837i
$67$	−4.61095	−	7.98640i	−0.563317	−	0.975694i	−0.997204	−	0.0747267i	$-0.976192\pi$
$67$	−4.61095	−	7.98640i	−0.563317	−	0.975694i	0.433887	−	0.900967i	$-0.357142\pi$
$68$	0.994645			0.120618
$69$	−9.76567	+	9.10814i	−1.17565	+	1.09649i
$70$	0.953096	+	2.46812i	0.113917	+	0.294997i
$71$			2.74965i			0.326324i	0.986599	+	0.163162i	$0.0521693\pi$
$71$			2.74965i			0.326324i	−0.986599	+	0.163162i	$0.947831\pi$
$72$	2.99273	+	0.208774i	0.352696	+	0.0246043i
$73$	−12.7539	−	7.36348i	−1.49273	−	0.861830i	−0.492767	−	0.870161i	$-0.664015\pi$
$73$	−12.7539	−	7.36348i	−1.49273	−	0.861830i	−0.999965	+	0.00833139i	$0.997348\pi$
$74$			10.1110i			1.17537i
$75$	−1.18136	−	1.26664i	−0.136412	−	0.146259i
$76$	−4.90846	−	2.83390i	−0.563039	−	0.325071i
$77$	6.57194	−	8.14898i	0.748942	−	0.928662i
$78$	1.65254	−	5.40682i	0.187113	−	0.612201i
$79$	0.920736	−	1.59476i	0.103591	−	0.179425i	−0.809571	−	0.587022i	$-0.800300\pi$
$79$	0.920736	−	1.59476i	0.103591	−	0.179425i	0.913162	+	0.407598i	$0.133633\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−8.91283	−	1.24961i	−0.990314	−	0.138845i
$82$	8.94721	−	5.16567i	0.988054	−	0.570453i
$83$	0.789829	+	1.36802i	0.0866950	+	0.150160i	0.906112	−	0.423037i	$-0.139036\pi$
$83$	0.789829	+	1.36802i	0.0866950	+	0.150160i	−0.819417	+	0.573198i	$0.805703\pi$
$84$	3.79378	−	2.57046i	0.413935	−	0.280460i
$85$	−0.497322	+	0.861388i	−0.0539422	+	0.0934306i
$86$		−	10.2058i		−	1.10052i
$87$	7.84713	+	2.39840i	0.841300	+	0.257135i
$88$	−3.95684			−0.421801
$89$	−6.92781	−	11.9993i	−0.734347	−	1.27193i	−0.955009	−	0.296576i	$-0.904155\pi$
$89$	−6.92781	−	11.9993i	−0.734347	−	1.27193i	0.220663	−	0.975350i	$-0.429178\pi$
$90$	−1.67717	+	2.48739i	−0.176789	+	0.262194i
$91$	−3.11107	−	8.05637i	−0.326129	−	0.844537i
$92$	6.67695	−	3.85494i	0.696120	−	0.401905i
$93$	9.24345	+	2.82517i	0.958501	+	0.292956i
$94$	4.10432	−	2.36963i	0.423329	−	0.244409i
$95$	4.90846	−	2.83390i	0.503597	−	0.290752i
$96$	−1.65641	−	0.506266i	−0.169057	−	0.0516705i
$97$	0.776974	−	0.448586i	0.0788897	−	0.0455470i	−0.460036	−	0.887900i	$-0.652164\pi$
$97$	0.776974	−	0.448586i	0.0788897	−	0.0455470i	0.538926	+	0.842353i	$0.318830\pi$
$98$	2.13644	−	6.66600i	0.215813	−	0.673368i
$99$	11.8417	+	0.826087i	1.19014	+	0.0830249i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−0.215695			−0.0214624			−0.0107312	−	0.999942i	$-0.503416\pi$
$101$	−0.215695			−0.0214624			−0.0107312	+	0.999942i	$0.503416\pi$
$102$	1.64754	+	0.503554i	0.163131	+	0.0498593i
$103$			11.3535i			1.11869i	0.828934	+	0.559346i	$0.188948\pi$
$103$			11.3535i			1.11869i	−0.828934	+	0.559346i	$0.811052\pi$
$104$	−1.63209	+	2.82686i	−0.160039	+	0.277196i
$105$	0.329195	+	4.57074i	0.0321261	+	0.446058i
$106$	5.09390	+	8.82289i	0.494763	+	0.856955i
$107$	−5.53564	+	3.19600i	−0.535151	+	0.308969i	−0.743111	−	0.669168i	$-0.766651\pi$
$107$	−5.53564	+	3.19600i	−0.535151	+	0.308969i	0.207961	+	0.978137i	$0.433317\pi$
$108$	4.85149	+	1.86093i	0.466835	+	0.179068i
$109$	0.615666	−	1.06636i	0.0589701	−	0.102139i	−0.835033	−	0.550199i	$-0.814552\pi$
$109$	0.615666	−	1.06636i	0.0589701	−	0.102139i	0.894003	+	0.448060i	$0.147885\pi$
$110$	1.97842	−	3.42673i	0.188635	−	0.326725i
$111$	−5.11883	+	16.7479i	−0.485858	+	1.58964i
$112$	−2.46812	+	0.953096i	−0.233215	+	0.0900591i
$113$	−7.32005	−	4.22623i	−0.688612	−	0.397571i	0.114480	−	0.993426i	$-0.463480\pi$
$113$	−7.32005	−	4.22623i	−0.688612	−	0.397571i	−0.803092	+	0.595855i	$0.796813\pi$
$114$	−6.69571	−	7.17908i	−0.627111	−	0.672383i
$115$			7.70987i			0.718949i
$116$	−4.10273	−	2.36871i	−0.380929	−	0.219930i
$117$	5.47457	−	8.11928i	0.506124	−	0.750628i
$118$			3.40720i			0.313658i
$119$	2.45490	−	0.947992i	0.225040	−	0.0869023i
$120$	1.26664	−	1.18136i	0.115628	−	0.107843i
$121$	−4.65660			−0.423327
$122$	−3.14969	−	5.45543i	−0.285160	−	0.493911i
$123$	17.4355	−	4.02681i	1.57210	−	0.363085i
$124$	−4.83278	−	2.79020i	−0.433996	−	0.250568i
$125$	−1.00000			−0.0894427
$126$	7.58539	−	2.33708i	0.675760	−	0.208203i
$127$	20.5777			1.82598			0.912988	−	0.407985i	$-0.133769\pi$
$127$	20.5777			1.82598			0.912988	+	0.407985i	$0.133769\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	5.16687	−	16.9051i	0.454917	−	1.48841i
$130$	−1.63209	−	2.82686i	−0.143144	−	0.247932i
$131$	5.00917			0.437654			0.218827	−	0.975764i	$-0.429777\pi$
$131$	5.00917			0.437654			0.218827	+	0.975764i	$0.429777\pi$
$132$	−6.55415	−	2.00321i	−0.570466	−	0.174357i
$133$	−14.8156	−	2.31617i	−1.28468	−	0.200837i
$134$			9.22190i			0.796651i
$135$	−4.03736	+	3.27105i	−0.347480	+	0.281527i
$136$	−0.861388	−	0.497322i	−0.0738634	−	0.0426450i
$137$		−	9.23672i		−	0.789147i	−0.918864	−	0.394573i	$-0.870892\pi$
$137$		−	9.23672i		−	0.789147i	0.918864	−	0.394573i	$-0.129108\pi$
$138$	13.0114	−	3.00505i	1.10760	−	0.255807i
$139$	−11.2919	−	6.51936i	−0.957763	−	0.552965i	−0.0622791	−	0.998059i	$-0.519837\pi$
$139$	−11.2919	−	6.51936i	−0.957763	−	0.552965i	−0.895484	+	0.445094i	$0.853170\pi$
$140$	0.408654	−	2.61400i	0.0345375	−	0.220923i
$141$	7.99811	−	1.84721i	0.673562	−	0.155563i
$142$	1.37483	−	2.38127i	0.115373	−	0.199832i
$143$	−6.45792	+	11.1854i	−0.540038	+	0.935373i
$144$	−2.48739	−	1.67717i	−0.207283	−	0.139764i
$145$	4.10273	−	2.36871i	0.340713	−	0.196711i
$146$	7.36348	+	12.7539i	0.609406	+	1.05552i
$147$	6.91359	−	9.96003i	0.570224	−	0.821490i
$148$	5.05548	−	8.75634i	0.415558	−	0.719767i
$149$		−	22.0661i		−	1.80773i	−0.427821	−	0.903863i	$-0.640719\pi$
$149$		−	22.0661i		−	1.80773i	0.427821	−	0.903863i	$-0.359281\pi$
$150$	0.389766	+	1.68763i	0.0318243	+	0.137794i
$151$	5.53782			0.450661			0.225331	−	0.974282i	$-0.427654\pi$
$151$	5.53782			0.450661			0.225331	+	0.974282i	$0.427654\pi$
$152$	2.83390	+	4.90846i	0.229860	+	0.398128i
$153$	2.47407	+	1.66819i	0.200017	+	0.134865i
$154$	−9.76595	+	3.77125i	−0.786963	+	0.303896i
$155$	4.83278	−	2.79020i	0.388178	−	0.224115i
$156$	−4.13455	+	3.85617i	−0.331029	+	0.308741i
$157$	14.5468	−	8.39860i	1.16096	−	0.670281i	0.209427	−	0.977824i	$-0.432840\pi$
$157$	14.5468	−	8.39860i	1.16096	−	0.670281i	0.951534	+	0.307543i	$0.0995068\pi$
$158$	−1.59476	+	0.920736i	−0.126872	+	0.0732498i
$159$	3.97086	+	17.1932i	0.314910	+	1.36351i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	12.8054	−	15.8782i	1.00920	−	1.25138i
$162$	7.09393	+	5.53861i	0.557352	+	0.435154i
$163$	0.864749	+	1.49779i	0.0677324	+	0.117316i	0.897903	−	0.440194i	$-0.145090\pi$
$163$	0.864749	+	1.49779i	0.0677324	+	0.117316i	−0.830170	+	0.557510i	$0.811757\pi$
$164$	−10.3313			−0.806743
$165$	5.01191	−	4.67446i	0.390177	−	0.363906i
$166$		−	1.57966i		−	0.122605i
$167$	−0.371022	+	0.642629i	−0.0287105	+	0.0497281i	−0.880024	−	0.474930i	$-0.842473\pi$
$167$	−0.371022	+	0.642629i	−0.0287105	+	0.0497281i	0.851313	+	0.524658i	$0.175807\pi$
$168$	−4.57074	+	0.329195i	−0.352640	+	0.0253979i
$169$	−1.17257	−	2.03096i	−0.0901981	−	0.156228i
$170$	0.861388	−	0.497322i	0.0660654	−	0.0381429i
$171$	−7.45633	−	15.2813i	−0.570200	−	1.16859i
$172$	−5.10292	+	8.83852i	−0.389094	+	0.673930i
$173$	0.482119	−	0.835055i	0.0366548	−	0.0634881i	−0.847116	−	0.531408i	$-0.821663\pi$
$173$	0.482119	−	0.835055i	0.0366548	−	0.0634881i	0.883771	+	0.467920i	$0.154996\pi$
$174$	−5.59661	−	6.00064i	−0.424278	−	0.454907i
$175$	2.05946	+	1.66090i	0.155681	+	0.125553i
$176$	3.42673	+	1.97842i	0.258299	+	0.149129i
$177$	−1.72495	+	5.64373i	−0.129655	+	0.424208i
$178$			13.8556i			1.03852i
$179$	−0.186006	−	0.107391i	−0.0139028	−	0.00802676i	0.493033	−	0.870011i	$-0.335888\pi$
$179$	−0.186006	−	0.107391i	−0.0139028	−	0.00802676i	−0.506935	+	0.861984i	$0.669222\pi$
$180$	2.69616	−	1.31556i	0.200960	−	0.0980560i
$181$		−	11.1757i		−	0.830681i	−0.909666	−	0.415341i	$-0.863662\pi$
$181$		−	11.1757i		−	0.830681i	0.909666	−	0.415341i	$-0.136338\pi$
$182$	−1.33392	+	8.53256i	−0.0988765	+	0.632476i
$183$	−2.45529	−	10.6310i	−0.181500	−	0.785867i
$184$	−7.70987			−0.568379
$185$	5.05548	+	8.75634i	0.371686	+	0.643779i
$186$	−6.59247	−	7.06839i	−0.483384	−	0.518280i
$187$	−3.40837	−	1.96783i	−0.249245	−	0.143902i
$188$	−4.73926			−0.345646
$189$	13.7477	−	0.0309387i	0.999997	−	0.00225046i
$190$	−5.66780			−0.411185
$191$	16.3524	+	9.44109i	1.18322	+	0.683133i	0.956758	−	0.290886i	$-0.0939502\pi$
$191$	16.3524	+	9.44109i	1.18322	+	0.683133i	0.226464	+	0.974020i	$0.427284\pi$
$192$	1.18136	+	1.26664i	0.0852574	+	0.0914122i
$193$	2.94509	+	5.10105i	0.211992	+	0.367181i	0.952338	−	0.305045i	$-0.0986715\pi$
$193$	2.94509	+	5.10105i	0.211992	+	0.367181i	−0.740346	+	0.672226i	$0.765338\pi$
$194$	−0.897172			−0.0644132
$195$	−1.27227	−	5.50871i	−0.0911089	−	0.394487i
$196$	−5.18322	+	4.70471i	−0.370230	+	0.336051i
$197$			24.0786i			1.71553i	0.514043	+	0.857764i	$0.328147\pi$
$197$			24.0786i			1.71553i	−0.514043	+	0.857764i	$0.671853\pi$
$198$	−9.84221	−	6.63629i	−0.699455	−	0.471620i
$199$	13.1750	+	7.60658i	0.933950	+	0.539216i	0.888059	−	0.459730i	$-0.152054\pi$
$199$	13.1750	+	7.60658i	0.933950	+	0.539216i	0.0458914	+	0.998946i	$0.485387\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−4.66873	+	15.2753i	−0.329307	+	1.07743i
$202$	0.186797	+	0.107847i	0.0131430	+	0.00758812i
$203$	−12.3836	−	1.93597i	−0.869161	−	0.135878i
$204$	−1.17503	−	1.25986i	−0.0822688	−	0.0882079i
$205$	5.16567	−	8.94721i	0.360786	−	0.624900i
$206$	5.67674	−	9.83240i	0.395517	−	0.685056i
$207$	23.0735	+	1.60962i	1.60372	+	0.111877i
$208$	2.82686	−	1.63209i	0.196007	−	0.113165i
$209$	11.2133	+	19.4220i	0.775640	+	1.34345i
$210$	2.00028	−	4.12297i	0.138032	−	0.284512i
$211$	−3.11109	+	5.38856i	−0.214176	+	0.370964i	−0.953017	−	0.302916i	$-0.902040\pi$
$211$	−3.11109	+	5.38856i	−0.214176	+	0.370964i	0.738841	+	0.673879i	$0.235373\pi$
$212$		−	10.1878i		−	0.699701i
$213$	3.48283	−	3.24833i	0.238640	−	0.222572i
$214$	6.39201			0.436949
$215$	−5.10292	−	8.83852i	−0.348016	−	0.602782i
$216$	−3.27105	−	4.03736i	−0.222567	−	0.274707i
$217$	−14.5872	−	2.28045i	−0.990243	−	0.154807i
$218$	−1.06636	+	0.615666i	−0.0722233	+	0.0416982i
$219$	5.74007	+	24.8536i	0.387878	+	1.67945i
$220$	−3.42673	+	1.97842i	−0.231030	+	0.133385i
$221$	−2.81172	+	1.62335i	−0.189137	+	0.109198i
$222$	12.8070	−	11.9447i	0.859548	−	0.801675i
$223$	−4.37102	+	2.52361i	−0.292705	+	0.168994i	−0.639161	−	0.769073i	$-0.720718\pi$
$223$	−4.37102	+	2.52361i	−0.292705	+	0.168994i	0.346456	+	0.938066i	$0.387385\pi$
$224$	2.61400	+	0.408654i	0.174655	+	0.0273043i
$225$	−0.208774	+	2.99273i	−0.0139183	+	0.199515i
$226$	4.22623	+	7.32005i	0.281125	+	0.486922i
$227$	−5.07962			−0.337146			−0.168573	−	0.985689i	$-0.553916\pi$
$227$	−5.07962			−0.337146			−0.168573	+	0.985689i	$0.553916\pi$
$228$	2.20912	+	9.56513i	0.146302	+	0.633466i
$229$		−	29.6559i		−	1.95972i	−0.199692	−	0.979859i	$-0.563994\pi$
$229$		−	29.6559i		−	1.95972i	0.199692	−	0.979859i	$-0.436006\pi$
$230$	3.85494	−	6.67695i	0.254187	−	0.440265i
$231$	−18.0857	+	1.30257i	−1.18995	+	0.0857030i
$232$	2.36871	+	4.10273i	0.155514	+	0.269358i
$233$	−15.8420	+	9.14639i	−1.03784	+	0.599200i	−0.919222	−	0.393740i	$-0.871181\pi$
$233$	−15.8420	+	9.14639i	−1.03784	+	0.599200i	−0.118622	+	0.992939i	$0.537848\pi$
$234$	−8.80076	+	4.29422i	−0.575324	+	0.280722i
$235$	2.36963	−	4.10432i	0.154578	−	0.267737i
$236$	1.70360	−	2.95072i	0.110895	−	0.192076i
$237$	−3.10772	+	0.717744i	−0.201868	+	0.0466225i
$238$	−2.60000	−	0.406465i	−0.168533	−	0.0263472i
$239$	6.05638	+	3.49665i	0.391755	+	0.226180i	0.682920	−	0.730493i	$-0.260710\pi$
$239$	6.05638	+	3.49665i	0.391755	+	0.226180i	−0.291165	+	0.956673i	$0.594043\pi$
$240$	−1.68763	+	0.389766i	−0.108936	+	0.0251593i
$241$			5.51586i			0.355308i	0.984093	+	0.177654i	$0.0568507\pi$
$241$			5.51586i			0.355308i	−0.984093	+	0.177654i	$0.943149\pi$
$242$	4.03273	+	2.32830i	0.259234	+	0.149669i
$243$	8.94645	+	12.7656i	0.573915	+	0.818915i
$244$			6.29939i			0.403277i
$245$	−1.48279	−	6.84115i	−0.0947319	−	0.437065i
$246$	−17.1130	−	5.23041i	−1.09108	−	0.333479i
$247$	18.5007			1.17717
$248$	2.79020	+	4.83278i	0.177178	+	0.306882i
$249$	0.799727	−	2.61656i	0.0506806	−	0.165818i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	0.276363			0.0174439			0.00872195	−	0.999962i	$-0.497224\pi$
$251$	0.276363			0.0174439			0.00872195	+	0.999962i	$0.497224\pi$
$252$	−7.73767	−	1.76872i	−0.487428	−	0.111419i
$253$	−30.5068			−1.91794
$254$	−17.8208	−	10.2889i	−1.11818	−	0.645580i
$255$	1.67859	−	0.387679i	0.105117	−	0.0242774i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−16.4912			−1.02870			−0.514348	−	0.857582i	$-0.671966\pi$
$257$	−16.4912			−1.02870			−0.514348	+	0.857582i	$0.671966\pi$
$258$	−12.9272	+	12.0568i	−0.804810	+	0.750622i
$259$	4.13188	−	26.4300i	0.256742	−	1.64228i
$260$			3.26418i			0.202436i
$261$	−6.23237	−	12.7729i	−0.385774	−	0.790622i
$262$	−4.33807	−	2.50459i	−0.268007	−	0.154734i
$263$			2.50928i			0.154729i	0.997003	+	0.0773646i	$0.0246505\pi$
$263$			2.50928i			0.154729i	−0.997003	+	0.0773646i	$0.975349\pi$
$264$	4.67446	+	5.01191i	0.287693	+	0.308462i
$265$	8.82289	+	5.09390i	0.541986	+	0.312916i
$266$	11.6726	+	9.41368i	0.715695	+	0.577189i
$267$	−7.01463	+	22.9506i	−0.429288	+	1.40455i
$268$	4.61095	−	7.98640i	0.281659	−	0.487847i
$269$	−13.3603	+	23.1408i	−0.814594	+	1.41092i	0.0950245	+	0.995475i	$0.469707\pi$
$269$	−13.3603	+	23.1408i	−0.814594	+	1.41092i	−0.909619	+	0.415444i	$0.863626\pi$
$270$	5.13198	−	0.814131i	0.312322	−	0.0495464i
$271$	12.9500	−	7.47668i	0.786656	−	0.454176i	−0.0521278	−	0.998640i	$-0.516600\pi$
$271$	12.9500	−	7.47668i	0.786656	−	0.454176i	0.838784	+	0.544464i	$0.183267\pi$
$272$	0.497322	+	0.861388i	0.0301546	+	0.0522293i
$273$	−6.52926	+	13.4581i	−0.395169	+	0.814522i
$274$	−4.61836	+	7.99924i	−0.279005	+	0.483252i
$275$		−	3.95684i		−	0.238607i
$276$	−12.7707	−	3.90324i	−0.768707	−	0.234948i
$277$	−14.2293			−0.854956			−0.427478	−	0.904026i	$-0.640598\pi$
$277$	−14.2293			−0.854956			−0.427478	+	0.904026i	$0.640598\pi$
$278$	6.51936	+	11.2919i	0.391005	+	0.677241i
$279$	−7.34136	−	15.0457i	−0.439516	−	0.900762i
$280$	−1.66090	+	2.05946i	−0.0992581	+	0.123077i
$281$	21.5588	−	12.4470i	1.28609	−	0.742524i	0.308135	−	0.951343i	$-0.400295\pi$
$281$	21.5588	−	12.4470i	1.28609	−	0.742524i	0.977954	+	0.208819i	$0.0669620\pi$
$282$	−7.85017	−	2.39933i	−0.467471	−	0.142878i
$283$	14.8780	−	8.58983i	0.884407	−	0.510612i	0.0122977	−	0.999924i	$-0.496085\pi$
$283$	14.8780	−	8.58983i	0.884407	−	0.510612i	0.872109	+	0.489312i	$0.162752\pi$
$284$	−2.38127	+	1.37483i	−0.141302	+	0.0815810i
$285$	−9.38820	−	2.86941i	−0.556109	−	0.169969i
$286$	11.1854	−	6.45792i	0.661409	−	0.381865i
$287$	−25.4990	+	9.84677i	−1.50516	+	0.581236i
$288$	1.31556	+	2.69616i	0.0775201	+	0.158873i
$289$	8.00534	+	13.8657i	0.470902	+	0.815627i
$290$	−4.73743			−0.278191
$291$	−1.48609	−	0.454207i	−0.0871159	−	0.0266261i
$292$		−	14.7270i		−	0.861830i
$293$	−3.98706	+	6.90578i	−0.232926	+	0.403440i	−0.958668	−	0.284527i	$-0.908163\pi$
$293$	−3.98706	+	6.90578i	−0.232926	+	0.403440i	0.725742	+	0.687967i	$0.241497\pi$
$294$	−10.9674	+	5.16884i	−0.639630	+	0.301453i
$295$	1.70360	+	2.95072i	0.0991875	+	0.171798i
$296$	−8.75634	+	5.05548i	−0.508952	+	0.293844i
$297$	−12.9430	−	15.9752i	−0.751030	−	0.926974i
$298$	−11.0331	+	19.1098i	−0.639128	+	1.10700i
$299$	−12.5832	+	21.7947i	−0.727705	+	1.26042i
$300$	0.506266	−	1.65641i	0.0292293	−	0.0956329i
$301$	−4.17065	+	26.6781i	−0.240392	+	1.53770i
$302$	−4.79589	−	2.76891i	−0.275973	−	0.159333i
$303$	0.254814	+	0.273209i	0.0146387	+	0.0156954i
$304$		−	5.66780i		−	0.325071i
$305$	−5.45543	−	3.14969i	−0.312377	−	0.180351i
$306$	−1.30851	−	2.68173i	−0.0748028	−	0.153304i
$307$		−	15.5665i		−	0.888429i	−0.895920	−	0.444215i	$-0.853483\pi$
$307$		−	15.5665i		−	0.888429i	0.895920	−	0.444215i	$-0.146517\pi$
$308$	10.3432	+	1.61698i	0.589358	+	0.0921358i
$309$	14.3808	−	13.4126i	0.818096	−	0.763014i
$310$	−5.58041			−0.316946
$311$	−10.0834	−	17.4650i	−0.571779	−	0.990350i	−0.996383	−	0.0849714i	$-0.972920\pi$
$311$	−10.0834	−	17.4650i	−0.571779	−	0.990350i	0.424604	−	0.905379i	$-0.360413\pi$
$312$	5.50871	−	1.27227i	0.311869	−	0.0720279i
$313$	−5.77815	−	3.33602i	−0.326600	−	0.188563i	0.327730	−	0.944771i	$-0.393716\pi$
$313$	−5.77815	−	3.33602i	−0.326600	−	0.188563i	−0.654331	+	0.756209i	$0.727050\pi$
$314$	−16.7972			−0.947921
$315$	5.40060	−	5.81666i	0.304289	−	0.327732i
$316$	1.84147			0.103591
$317$	22.1197	+	12.7708i	1.24236	+	0.717279i	0.969575	−	0.244795i	$-0.0787207\pi$
$317$	22.1197	+	12.7708i	1.24236	+	0.717279i	0.272789	+	0.962074i	$0.412054\pi$
$318$	5.15773	−	16.8752i	0.289231	−	0.946313i
$319$	9.37263	+	16.2339i	0.524766	+	0.908922i
$320$	1.00000			0.0559017
$321$	10.5878	+	3.23605i	0.590953	+	0.180619i
$322$	−19.0289	+	7.34825i	−1.06044	+	0.409502i
$323$			5.63745i			0.313676i
$324$	−3.37422	−	8.34354i	−0.187457	−	0.463530i
$325$	−2.82686	−	1.63209i	−0.156806	−	0.0905320i
$326$		−	1.72950i		−	0.0957881i
$327$	−2.07803	+	0.479932i	−0.114915	+	0.0265403i
$328$	8.94721	+	5.16567i	0.494027	+	0.285227i
$329$	−11.6971	+	4.51697i	−0.644880	+	0.249029i
$330$	−6.67767	+	1.54224i	−0.367594	+	0.0848977i
$331$	−0.906390	+	1.56991i	−0.0498197	+	0.0862903i	−0.889860	−	0.456234i	$-0.849198\pi$
$331$	−0.906390	+	1.56991i	−0.0498197	+	0.0862903i	0.840040	+	0.542524i	$0.182531\pi$
$332$	−0.789829	+	1.36802i	−0.0433475	+	0.0750801i
$333$	27.2608	−	13.3016i	1.49388	−	0.728921i
$334$	0.642629	−	0.371022i	0.0351631	−	0.0203014i
$335$	4.61095	+	7.98640i	0.251923	+	0.436344i
$336$	4.12297	+	2.00028i	0.224927	+	0.109124i
$337$	7.15488	−	12.3926i	0.389751	−	0.675069i	−0.602665	−	0.797995i	$-0.705894\pi$
$337$	7.15488	−	12.3926i	0.389751	−	0.675069i	0.992416	+	0.122926i	$0.0392277\pi$
$338$			2.34515i			0.127559i
$339$	3.29449	+	14.2646i	0.178932	+	0.774747i
$340$	−0.994645			−0.0539422
$341$	11.0404	+	19.1225i	0.597871	+	1.03554i
$342$	−1.18329	+	16.9622i	−0.0639850	+	0.917209i
$343$	−8.30875	+	16.5519i	−0.448630	+	0.893717i
$344$	8.83852	−	5.10292i	0.476541	−	0.275131i
$345$	9.76567	−	9.10814i	0.525766	−	0.490366i
$346$	−0.835055	+	0.482119i	−0.0448928	+	0.0259189i
$347$	−5.20049	+	3.00250i	−0.279177	+	0.161183i	−0.633051	−	0.774110i	$-0.718198\pi$
$347$	−5.20049	+	3.00250i	−0.279177	+	0.161183i	0.353874	+	0.935293i	$0.384864\pi$
$348$	1.84649	+	7.99501i	0.0989822	+	0.428577i
$349$	−11.6157	+	6.70633i	−0.621775	+	0.358982i	−0.777560	−	0.628809i	$-0.783543\pi$
$349$	−11.6157	+	6.70633i	−0.621775	+	0.358982i	0.155785	+	0.987791i	$0.450209\pi$
$350$	−0.953096	−	2.46812i	−0.0509451	−	0.131926i
$351$	−16.7517	+	2.65747i	−0.894139	+	0.141845i
$352$	−1.97842	−	3.42673i	−0.105450	−	0.182645i
$353$	−0.505383			−0.0268988			−0.0134494	−	0.999910i	$-0.504281\pi$
$353$	−0.505383			−0.0268988			−0.0134494	+	0.999910i	$0.504281\pi$
$354$	4.31571	−	4.02513i	0.229378	−	0.213933i
$355$		−	2.74965i		−	0.145937i
$356$	6.92781	−	11.9993i	0.367173	−	0.635963i
$357$	−4.10089	−	1.98956i	−0.217042	−	0.105299i
$358$	0.107391	+	0.186006i	0.00567578	+	0.00983073i
$359$	11.2748	−	6.50952i	0.595062	−	0.343559i	−0.172034	−	0.985091i	$-0.555034\pi$
$359$	11.2748	−	6.50952i	0.595062	−	0.343559i	0.767097	+	0.641532i	$0.221701\pi$
$360$	−2.99273	−	0.208774i	−0.157731	−	0.0110034i
$361$	6.56197	−	11.3657i	0.345367	−	0.598193i
$362$	−5.58784	+	9.67842i	−0.293690	+	0.508686i
$363$	5.50112	+	5.89826i	0.288734	+	0.309578i
$364$	5.42149	−	6.72246i	0.284163	−	0.352352i
$365$	12.7539	+	7.36348i	0.667570	+	0.385422i
$366$	−3.18916	+	10.4344i	−0.166700	+	0.545413i
$367$		−	32.0287i		−	1.67188i	−0.548819	−	0.835942i	$-0.684922\pi$
$367$		−	32.0287i		−	1.67188i	0.548819	−	0.835942i	$-0.315078\pi$
$368$	6.67695	+	3.85494i	0.348060	+	0.200952i
$369$	−25.6981	−	17.3274i	−1.33779	−	0.902028i
$370$		−	10.1110i		−	0.525643i
$371$	−9.70995	−	25.1447i	−0.504116	−	1.30545i
$372$	2.17506	+	9.41764i	0.112771	+	0.488282i
$373$	6.80077			0.352130			0.176065	−	0.984379i	$-0.443663\pi$
$373$	6.80077			0.352130			0.176065	+	0.984379i	$0.443663\pi$
$374$	1.96783	+	3.40837i	0.101754	+	0.176243i
$375$	1.18136	+	1.26664i	0.0610052	+	0.0654092i
$376$	4.10432	+	2.36963i	0.211664	+	0.122204i
$377$	15.4638			0.796426
$378$	−11.9213	−	6.84705i	−0.613167	−	0.352174i
$379$	2.14646			0.110256			0.0551281	−	0.998479i	$-0.482443\pi$
$379$	2.14646			0.110256			0.0551281	+	0.998479i	$0.482443\pi$
$380$	4.90846	+	2.83390i	0.251799	+	0.145376i
$381$	−24.3097	−	26.0646i	−1.24542	−	1.33533i
$382$	−9.44109	−	16.3524i	−0.483048	−	0.836664i
$383$	0.710547			0.0363072			0.0181536	−	0.999835i	$-0.494221\pi$
$383$	0.710547			0.0363072			0.0181536	+	0.999835i	$0.494221\pi$
$384$	−0.389766	−	1.68763i	−0.0198902	−	0.0861213i
$385$	−6.57194	+	8.14898i	−0.334937	+	0.415310i
$386$		−	5.89018i		−	0.299802i
$387$	−27.5166	+	13.4264i	−1.39875	+	0.682502i
$388$	0.776974	+	0.448586i	0.0394449	+	0.0227735i
$389$		−	19.6149i		−	0.994517i	−0.867603	−	0.497258i	$-0.834340\pi$
$389$		−	19.6149i		−	0.994517i	0.867603	−	0.497258i	$-0.165660\pi$
$390$	−1.65254	+	5.40682i	−0.0836796	+	0.273785i
$391$	−6.64119	−	3.83429i	−0.335859	−	0.193908i
$392$	6.84115	−	1.48279i	0.345530	−	0.0748922i
$393$	−5.91764	−	6.34484i	−0.298505	−	0.320055i
$394$	12.0393	−	20.8527i	0.606531	−	1.05054i
$395$	−0.920736	+	1.59476i	−0.0463273	+	0.0802412i
$396$	5.20546	+	10.6683i	0.261584	+	0.536102i
$397$	20.7322	−	11.9697i	1.04052	−	0.600743i	0.120538	−	0.992709i	$-0.461538\pi$
$397$	20.7322	−	11.9697i	1.04052	−	0.600743i	0.919980	+	0.391965i	$0.128205\pi$
$398$	−7.60658	−	13.1750i	−0.381284	−	0.660402i
$399$	14.5688	+	21.5024i	0.729355	+	1.07646i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			0.675625i			0.0337391i	0.999858	+	0.0168696i	$0.00537000\pi$
$401$			0.675625i			0.0337391i	−0.999858	+	0.0168696i	$0.994630\pi$
$402$	11.6809	−	10.8944i	0.582589	−	0.543363i
$403$	18.2154			0.907376
$404$	−0.107847	−	0.186797i	−0.00536561	−	0.00929351i
$405$	8.91283	+	1.24961i	0.442882	+	0.0620936i
$406$	9.75657	+	7.86842i	0.484210	+	0.390503i
$407$	−34.6475	+	20.0037i	−1.71741	+	0.991548i
$408$	0.387679	+	1.67859i	0.0191930	+	0.0831025i
$409$	−26.2888	+	15.1779i	−1.29990	+	0.750497i	−0.980386	−	0.197085i	$-0.936853\pi$
$409$	−26.2888	+	15.1779i	−1.29990	+	0.750497i	−0.319513	+	0.947582i	$0.603519\pi$
$410$	−8.94721	+	5.16567i	−0.441871	+	0.255114i
$411$	−11.6996	+	10.9119i	−0.577101	+	0.538244i
$412$	−9.83240	+	5.67674i	−0.484408	+	0.279673i
$413$	1.39237	−	8.90643i	0.0685138	−	0.438257i
$414$	−19.1775	−	12.9307i	−0.942521	−	0.635512i
$415$	−0.789829	−	1.36802i	−0.0387712	−	0.0671537i
$416$	−3.26418			−0.160039
$417$	5.08205	+	22.0045i	0.248869	+	1.07756i
$418$		−	22.4266i		−	1.09692i
$419$	−5.87786	+	10.1808i	−0.287152	+	0.497363i	−0.973129	−	0.230261i	$-0.926042\pi$
$419$	−5.87786	+	10.1808i	−0.287152	+	0.497363i	0.685976	+	0.727624i	$0.259375\pi$
$420$	−3.79378	+	2.57046i	−0.185117	+	0.125426i
$421$	14.4557	+	25.0380i	0.704526	+	1.22028i	0.966862	+	0.255299i	$0.0821739\pi$
$421$	14.4557	+	25.0380i	0.704526	+	1.22028i	−0.262336	+	0.964977i	$0.584493\pi$
$422$	5.38856	−	3.11109i	0.262311	−	0.151445i
$423$	−11.7884	−	7.94854i	−0.573172	−	0.386471i
$424$	−5.09390	+	8.82289i	−0.247382	+	0.428477i
$425$	0.497322	−	0.861388i	0.0241237	−	0.0417834i
$426$	−4.64039	+	1.07172i	−0.224828	+	0.0519251i
$427$	6.00392	+	15.5476i	0.290550	+	0.752402i
$428$	−5.53564	−	3.19600i	−0.267575	−	0.154485i
$429$	21.7971	−	5.03416i	1.05237	−	0.243051i
$430$			10.2058i			0.492169i
$431$	−17.2762	−	9.97444i	−0.832167	−	0.480452i	0.0224273	−	0.999748i	$-0.492861\pi$
$431$	−17.2762	−	9.97444i	−0.832167	−	0.480452i	−0.854594	+	0.519297i	$0.826194\pi$
$432$	0.814131	+	5.13198i	0.0391699	+	0.246912i
$433$		−	28.8157i		−	1.38479i	−0.721517	−	0.692397i	$-0.756555\pi$
$433$		−	28.8157i		−	1.38479i	0.721517	−	0.692397i	$-0.243445\pi$
$434$	11.4927	+	9.26853i	0.551665	+	0.444904i
$435$	−7.84713	−	2.39840i	−0.376241	−	0.114994i
$436$	1.23133			0.0589701
$437$	21.8490	+	37.8436i	1.04518	+	1.81030i
$438$	7.45575	−	24.3939i	0.356249	−	1.16558i
$439$	7.07993	+	4.08760i	0.337907	+	0.195091i	0.659346	−	0.751840i	$-0.270833\pi$
$439$	7.07993	+	4.08760i	0.337907	+	0.195091i	−0.321439	+	0.946930i	$0.604167\pi$
$440$	3.95684			0.188635
$441$	−20.7833	+	3.00933i	−0.989679	+	0.143301i
$442$	3.24670			0.154430
$443$	−22.7505	−	13.1350i	−1.08091	−	0.624063i	−0.149767	−	0.988721i	$-0.547852\pi$
$443$	−22.7505	−	13.1350i	−1.08091	−	0.624063i	−0.931141	+	0.364659i	$0.881186\pi$
$444$	−17.0635	+	3.94091i	−0.809798	+	0.187027i
$445$	6.92781	+	11.9993i	0.328410	+	0.568822i
$446$	5.04722			0.238993
$447$	−27.9499	+	26.0680i	−1.32199	+	1.23298i
$448$	−2.05946	−	1.66090i	−0.0973006	−	0.0784704i
$449$			6.39690i			0.301888i	0.988542	+	0.150944i	$0.0482314\pi$
$449$			6.39690i			0.301888i	−0.988542	+	0.150944i	$0.951769\pi$
$450$	1.67717	−	2.48739i	0.0790624	−	0.117257i
$451$	35.4027	+	20.4398i	1.66705	+	0.962471i
$452$		−	8.45246i		−	0.397571i
$453$	−6.54216	−	7.01444i	−0.307378	−	0.329567i
$454$	4.39908	+	2.53981i	0.206459	+	0.119199i
$455$	3.11107	+	8.05637i	0.145849	+	0.377689i
$456$	2.86941	−	9.38820i	0.134373	−	0.439643i
$457$	5.16337	−	8.94322i	0.241532	−	0.418346i	−0.719619	−	0.694369i	$-0.755683\pi$
$457$	5.16337	−	8.94322i	0.241532	−	0.418346i	0.961151	+	0.276023i	$0.0890167\pi$
$458$	−14.8280	+	25.6828i	−0.692865	+	1.20008i
$459$	−0.809771	−	5.10449i	−0.0377969	−	0.238257i
$460$	−6.67695	+	3.85494i	−0.311314	+	0.179737i
$461$	4.00379	+	6.93476i	0.186475	+	0.322984i	0.944073	−	0.329738i	$-0.106960\pi$
$461$	4.00379	+	6.93476i	0.186475	+	0.322984i	−0.757598	+	0.652722i	$0.773627\pi$
$462$	16.3139	+	7.91478i	0.758994	+	0.368229i
$463$	15.2865	−	26.4770i	0.710425	−	1.23049i	−0.254273	−	0.967132i	$-0.581836\pi$
$463$	15.2865	−	26.4770i	0.710425	−	1.23049i	0.964698	−	0.263359i	$-0.0848304\pi$
$464$		−	4.73743i		−	0.219930i
$465$	−9.24345	−	2.82517i	−0.428655	−	0.131014i
$466$	18.2928			0.847396
$467$	3.61017	+	6.25300i	0.167059	+	0.289354i	0.937385	−	0.348296i	$-0.113240\pi$
$467$	3.61017	+	6.25300i	0.167059	+	0.289354i	−0.770326	+	0.637651i	$0.779906\pi$
$468$	9.76879	+	0.681476i	0.451562	+	0.0315012i
$469$	3.76856	−	24.1061i	0.174016	−	1.11311i
$470$	−4.10432	+	2.36963i	−0.189318	+	0.109303i
$471$	−27.8231	−	8.50385i	−1.28202	−	0.391837i
$472$	−2.95072	+	1.70360i	−0.135818	+	0.0784146i
$473$	34.9726	−	20.1914i	1.60804	−	0.928404i
$474$	3.05023	+	0.932274i	0.140102	+	0.0428208i
$475$	−4.90846	+	2.83390i	−0.225215	+	0.130028i
$476$	2.04844	+	1.65201i	0.0938899	+	0.0757198i
$477$	17.0866	−	25.3410i	0.782344	−	1.16029i
$478$	−3.49665	−	6.05638i	−0.159933	−	0.277012i
$479$	18.2719			0.834864			0.417432	−	0.908708i	$-0.362930\pi$
$479$	18.2719			0.834864			0.417432	+	0.908708i	$0.362930\pi$
$480$	1.65641	+	0.506266i	0.0756044	+	0.0231078i
$481$			33.0039i			1.50485i
$482$	2.75793	−	4.77687i	0.125620	−	0.217581i
$483$	−35.2398	+	2.53805i	−1.60347	+	0.115485i
$484$	−2.32830	−	4.03273i	−0.105832	−	0.183306i
$485$	−0.776974	+	0.448586i	−0.0352806	+	0.0203692i
$486$	−1.36505	−	15.5286i	−0.0619198	−	0.704390i
$487$	−19.2868	+	33.4057i	−0.873967	+	1.51375i	−0.0161074	+	0.999870i	$0.505127\pi$
$487$	−19.2868	+	33.4057i	−0.873967	+	1.51375i	−0.857859	+	0.513885i	$0.828206\pi$
$488$	3.14969	−	5.45543i	0.142580	−	0.246956i
$489$	0.875586	−	2.86476i	0.0395954	−	0.129549i
$490$	−2.13644	+	6.66600i	−0.0965146	+	0.301139i
$491$	21.3449	+	12.3235i	0.963282	+	0.556151i	0.897182	−	0.441662i	$-0.145611\pi$
$491$	21.3449	+	12.3235i	0.963282	+	0.556151i	0.0661005	+	0.997813i	$0.478944\pi$
$492$	12.2050	+	13.0861i	0.550246	+	0.589969i
$493$			4.71206i			0.212220i
$494$	−16.0221	−	9.25035i	−0.720867	−	0.416193i
$495$	−11.8417	−	0.826087i	−0.532247	−	0.0371298i
$496$		−	5.58041i		−	0.250568i
$497$	−4.56691	+	5.66282i	−0.204854	+	0.254012i
$498$	−2.00087	+	1.86615i	−0.0896609	+	0.0836240i
$499$	10.5180			0.470850			0.235425	−	0.971893i	$-0.424352\pi$
$499$	10.5180			0.470850			0.235425	+	0.971893i	$0.424352\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	1.25229	−	0.289224i	0.0559483	−	0.0129216i
$502$	−0.239338	−	0.138182i	−0.0106822	−	0.00616735i
$503$	19.4315			0.866406			0.433203	−	0.901296i	$-0.357383\pi$
$503$	19.4315			0.866406			0.433203	+	0.901296i	$0.357383\pi$
$504$	5.81666	+	5.40060i	0.259095	+	0.240562i
$505$	0.215695			0.00959830
$506$	26.4196	+	15.2534i	1.17450	+	0.678095i
$507$	−1.18727	+	3.88453i	−0.0527285	+	0.172518i
$508$	10.2889	+	17.8208i	0.456494	+	0.790671i
$509$	23.3328			1.03421			0.517105	−	0.855922i	$-0.327010\pi$
$509$	23.3328			1.03421			0.517105	+	0.855922i	$0.327010\pi$
$510$	−1.64754	−	0.503554i	−0.0729543	−	0.0222978i
$511$	−14.0362	−	36.3479i	−0.620925	−	1.60793i
$512$			1.00000i			0.0441942i
$513$	−10.5474	+	27.4973i	−0.465678	+	1.21403i
$514$	14.2818	+	8.24562i	0.629945	+	0.363699i
$515$		−	11.3535i		−	0.500294i
$516$	17.2236	−	3.97789i	0.758229	−	0.175117i
$517$	16.2402	+	9.37626i	0.714241	+	0.412367i
$518$	−16.7933	+	20.8232i	−0.737857	+	0.914917i
$519$	−1.62727	+	0.375828i	−0.0714294	+	0.0164970i
$520$	1.63209	−	2.82686i	0.0715718	−	0.123966i
$521$	−11.8637	+	20.5486i	−0.519759	+	0.900249i	0.479977	+	0.877281i	$0.340645\pi$
$521$	−11.8637	+	20.5486i	−0.519759	+	0.900249i	−0.999736	+	0.0229682i	$0.992688\pi$
$522$	−0.989053	+	14.1778i	−0.0432897	+	0.620547i
$523$	15.7239	−	9.07818i	0.687556	−	0.396961i	−0.115140	−	0.993349i	$-0.536732\pi$
$523$	15.7239	−	9.07818i	0.687556	−	0.396961i	0.802696	+	0.596388i	$0.203398\pi$
$524$	2.50459	+	4.33807i	0.109413	+	0.189510i
$525$	−0.329195	−	4.57074i	−0.0143673	−	0.199483i
$526$	1.25464	−	2.17310i	0.0547050	−	0.0947519i
$527$			5.55052i			0.241785i
$528$	−1.54224	−	6.67767i	−0.0671175	−	0.290608i
$529$	−36.4421			−1.58444
$530$	−5.09390	−	8.82289i	−0.221265	−	0.383242i
$531$	9.18638	−	4.48238i	0.398655	−	0.194519i
$532$	−5.40196	−	13.9888i	−0.234205	−	0.606491i
$533$	29.2053	−	16.8617i	1.26502	−	0.730360i
$534$	17.5501	−	16.3685i	0.759469	−	0.708334i
$535$	5.53564	−	3.19600i	0.239327	−	0.138175i
$536$	−7.98640	+	4.61095i	−0.344960	+	0.199163i
$537$	0.0837146	+	0.362471i	0.00361255	+	0.0156418i
$538$	23.1408	−	13.3603i	0.997670	−	0.576005i
$539$	27.0694	−	5.86716i	1.16596	−	0.252717i
$540$	−4.85149	−	1.86093i	−0.208775	−	0.0800817i
$541$	5.56494	+	9.63875i	0.239255	+	0.414402i	0.960501	−	0.278277i	$-0.0897634\pi$
$541$	5.56494	+	9.63875i	0.239255	+	0.414402i	−0.721245	+	0.692680i	$0.756430\pi$
$542$	−14.9534			−0.642302
$543$	−14.1556	+	13.2025i	−0.607475	+	0.566574i
$544$		−	0.994645i		−	0.0426450i
$545$	−0.615666	+	1.06636i	−0.0263722	+	0.0456781i
$546$	12.3836	−	8.39043i	0.529967	−	0.359077i
$547$	−15.8512	−	27.4550i	−0.677747	−	1.17389i	−0.975658	−	0.219299i	$-0.929623\pi$
$547$	−15.8512	−	27.4550i	−0.677747	−	1.17389i	0.297911	−	0.954594i	$-0.403710\pi$
$548$	7.99924	−	4.61836i	0.341711	−	0.197287i
$549$	−10.5651	+	15.6690i	−0.450908	+	0.668738i
$550$	−1.97842	+	3.42673i	−0.0843602	+	0.146116i
$551$	13.4254	−	23.2535i	0.571941	−	0.990631i
$552$	9.10814	+	9.76567i	0.387668	+	0.415654i
$553$	4.54497	−	1.75510i	0.193272	−	0.0746345i
$554$	12.3229	+	7.11465i	0.523552	+	0.302273i
$555$	5.11883	−	16.7479i	0.217282	−	0.710908i
$556$		−	13.0387i		−	0.552965i
$557$	−28.2949	−	16.3360i	−1.19889	−	0.692181i	−0.238584	−	0.971122i	$-0.576683\pi$
$557$	−28.2949	−	16.3360i	−1.19889	−	0.692181i	−0.960308	+	0.278941i	$0.910016\pi$
$558$	−1.16505	+	16.7006i	−0.0493203	+	0.706994i
$559$		−	33.3137i		−	1.40902i
$560$	2.46812	−	0.953096i	0.104297	−	0.0402757i
$561$	1.53398	+	6.64191i	0.0647649	+	0.280422i
$562$	−24.8939			−1.05009
$563$	−12.2498	−	21.2172i	−0.516267	−	0.894200i	−0.999822	−	0.0188863i	$-0.993988\pi$
$563$	−12.2498	−	21.2172i	−0.516267	−	0.894200i	0.483555	−	0.875314i	$-0.339345\pi$
$564$	5.59878	+	6.00296i	0.235751	+	0.252770i
$565$	7.32005	+	4.22623i	0.307957	+	0.177799i
$566$	−17.1797			−0.722115
$567$	−16.2802	−	17.3769i	−0.683703	−	0.729760i
$568$	2.74965			0.115373
$569$	18.5002	+	10.6811i	0.775567	+	0.447774i	0.834857	−	0.550467i	$-0.185550\pi$
$569$	18.5002	+	10.6811i	0.775567	+	0.447774i	−0.0592899	+	0.998241i	$0.518884\pi$
$570$	6.69571	+	7.17908i	0.280453	+	0.300699i
$571$	8.22432	+	14.2449i	0.344177	+	0.596132i	0.985204	−	0.171386i	$-0.0548246\pi$
$571$	8.22432	+	14.2449i	0.344177	+	0.596132i	−0.641027	+	0.767518i	$0.721491\pi$
$572$	−12.9158			−0.540038
$573$	−7.35963	−	31.8661i	−0.307453	−	1.33122i
$574$	27.0062	+	4.22194i	1.12722	+	0.176220i
$575$		−	7.70987i		−	0.321524i
$576$	0.208774	−	2.99273i	0.00869893	−	0.124697i
$577$	17.2606	+	9.96542i	0.718569	+	0.414866i	0.814226	−	0.580549i	$-0.197162\pi$
$577$	17.2606	+	9.96542i	0.718569	+	0.414866i	−0.0956570	+	0.995414i	$0.530495\pi$
$578$		−	16.0107i		−	0.665957i
$579$	2.98200	−	9.75656i	0.123928	−	0.405469i
$580$	4.10273	+	2.36871i	0.170357	+	0.0983555i
$581$	−0.645533	+	4.12923i	−0.0267812	+	0.171309i
$582$	1.05988	+	1.13640i	0.0439336	+	0.0471052i
$583$	−20.1558	+	34.9108i	−0.834766	+	1.44586i
$584$	−7.36348	+	12.7539i	−0.304703	+	0.527761i
$585$	−5.47457	+	8.11928i	−0.226346	+	0.335691i
$586$	6.90578	−	3.98706i	0.285275	−	0.164704i
$587$	1.94532	+	3.36939i	0.0802918	+	0.139070i	0.903375	−	0.428851i	$-0.141081\pi$
$587$	1.94532	+	3.36939i	0.0802918	+	0.139070i	−0.823083	+	0.567920i	$0.807748\pi$
$588$	12.0824	+	1.00733i	0.498271	+	0.0415416i
$589$	15.8143	−	27.3912i	0.651618	−	1.12863i
$590$		−	3.40720i		−	0.140272i
$591$	30.4990	−	28.4455i	1.25456	−	1.17009i
$592$	10.1110			0.415558
$593$	−7.52066	−	13.0262i	−0.308836	−	0.534920i	0.669272	−	0.743018i	$-0.266606\pi$
$593$	−7.52066	−	13.0262i	−0.308836	−	0.534920i	−0.978108	+	0.208097i	$0.933273\pi$
$594$	3.22139	+	20.3064i	0.132175	+	0.833183i
$595$	−2.45490	+	0.947992i	−0.100641	+	0.0388639i
$596$	19.1098	−	11.0331i	0.782769	−	0.451932i
$597$	−5.92958	−	25.6741i	−0.242681	−	1.05077i
$598$	21.7947	−	12.5832i	0.891253	−	0.514565i
$599$	23.6663	−	13.6638i	0.966979	−	0.558286i	0.0686653	−	0.997640i	$-0.478126\pi$
$599$	23.6663	−	13.6638i	0.966979	−	0.558286i	0.898314	+	0.439354i	$0.144793\pi$
$600$	−1.26664	+	1.18136i	−0.0517105	+	0.0482288i
$601$	−10.2307	+	5.90670i	−0.417319	+	0.240939i	−0.693930	−	0.720043i	$-0.744122\pi$
$601$	−10.2307	+	5.90670i	−0.417319	+	0.240939i	0.276610	+	0.960982i	$0.410789\pi$
$602$	16.9509	−	21.0186i	0.690868	−	0.856653i
$603$	24.8638	−	12.1320i	1.01253	−	0.494052i
$604$	2.76891	+	4.79589i	0.112665	+	0.195142i
$605$	4.65660			0.189318
$606$	−0.0840706	−	0.364012i	−0.00341514	−	0.0147870i
$607$		−	0.740209i		−	0.0300441i	−0.999887	−	0.0150221i	$-0.995218\pi$
$607$		−	0.740209i		−	0.0300441i	0.999887	−	0.0150221i	$-0.00478185\pi$
$608$	−2.83390	+	4.90846i	−0.114930	+	0.199064i
$609$	12.1774	+	17.9727i	0.493452	+	0.728292i
$610$	3.14969	+	5.45543i	0.127527	+	0.220884i
$611$	13.3972	−	7.73490i	0.541994	−	0.312920i
$612$	−0.207656	+	2.97670i	−0.00839400	+	0.120326i
$613$	8.29710	−	14.3710i	0.335117	−	0.580439i	−0.648390	−	0.761308i	$-0.724558\pi$
$613$	8.29710	−	14.3710i	0.335117	−	0.580439i	0.983507	+	0.180869i	$0.0578909\pi$
$614$	−7.78327	+	13.4810i	−0.314107	+	0.544050i
$615$	−17.4355	+	4.02681i	−0.703065	+	0.162377i
$616$	−8.14898	−	6.57194i	−0.328332	−	0.264791i
$617$	−40.0027	−	23.0956i	−1.61045	−	0.929793i	−0.989266	−	0.146128i	$-0.953319\pi$
$617$	−40.0027	−	23.0956i	−1.61045	−	0.929793i	−0.621184	−	0.783665i	$-0.713348\pi$
$618$	−19.1604	+	4.42520i	−0.770746	+	0.178008i
$619$			18.0967i			0.727366i	0.931523	+	0.363683i	$0.118481\pi$
$619$			18.0967i			0.727366i	−0.931523	+	0.363683i	$0.881519\pi$
$620$	4.83278	+	2.79020i	0.194089	+	0.112057i
$621$	−25.2194	−	31.1275i	−1.01202	−	1.24910i
$622$			20.1669i			0.808618i
$623$	5.66215	−	36.2186i	0.226849	−	1.45107i
$624$	−5.40682	−	1.65254i	−0.216446	−	0.0661546i
$625$	1.00000			0.0400000
$626$	3.33602	+	5.77815i	0.133334	+	0.230941i
$627$	11.3538	−	37.1476i	0.453427	−	1.48353i
$628$	14.5468	+	8.39860i	0.580481	+	0.335141i
$629$	−10.0568			−0.400991
$630$	−7.58539	+	2.33708i	−0.302209	+	0.0931114i
$631$	8.36756			0.333107			0.166554	−	0.986032i	$-0.446736\pi$
$631$	8.36756			0.333107			0.166554	+	0.986032i	$0.446736\pi$
$632$	−1.59476	−	0.920736i	−0.0634362	−	0.0366249i
$633$	10.5007	−	2.42519i	0.417365	−	0.0963928i
$634$	−12.7708	−	22.1197i	−0.507193	−	0.878484i
$635$	−20.5777			−0.816602
$636$	−12.9043	+	12.0355i	−0.511689	+	0.477237i
$637$	6.97372	−	21.7590i	0.276309	−	0.862124i
$638$		−	18.7453i		−	0.742132i
$639$	−8.22896	−	0.574057i	−0.325533	−	0.0227093i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$		−	17.2032i		−	0.679485i	−0.940518	−	0.339743i	$-0.889660\pi$
$641$		−	17.2032i		−	0.679485i	0.940518	−	0.339743i	$-0.110340\pi$
$642$	−7.55127	−	8.09640i	−0.298025	−	0.319539i
$643$	−33.1046	−	19.1129i	−1.30552	−	0.753740i	−0.324172	−	0.945998i	$-0.605086\pi$
$643$	−33.1046	−	19.1129i	−1.30552	−	0.753740i	−0.981344	+	0.192258i	$0.938419\pi$
$644$	20.1536	+	3.15067i	0.794164	+	0.124154i
$645$	−5.16687	+	16.9051i	−0.203445	+	0.665636i
$646$	2.81872	−	4.88217i	0.110901	−	0.192086i
$647$	−7.26184	+	12.5779i	−0.285492	+	0.494487i	−0.972728	−	0.231947i	$-0.925490\pi$
$647$	−7.26184	+	12.5779i	−0.285492	+	0.494487i	0.687236	+	0.726434i	$0.258824\pi$
$648$	−1.24961	+	8.91283i	−0.0490893	+	0.350129i
$649$	−11.6755	+	6.74088i	−0.458305	+	0.264603i
$650$	1.63209	+	2.82686i	0.0640158	+	0.110879i
$651$	14.3442	+	21.1708i	0.562194	+	0.829750i
$652$	−0.864749	+	1.49779i	−0.0338662	+	0.0586580i
$653$			20.8516i			0.815987i	0.912985	+	0.407994i	$0.133771\pi$
$653$			20.8516i			0.815987i	−0.912985	+	0.407994i	$0.866229\pi$
$654$	2.03959	+	0.623381i	0.0797543	+	0.0243761i
$655$	−5.00917			−0.195725
$656$	−5.16567	−	8.94721i	−0.201686	−	0.349330i
$657$	24.6996	−	36.6317i	0.963622	−	1.42914i
$658$	12.3884	+	1.93672i	0.482952	+	0.0755011i
$659$	−19.3743	+	11.1857i	−0.754715	+	0.435735i	−0.827395	−	0.561621i	$-0.810178\pi$
$659$	−19.3743	+	11.1857i	−0.754715	+	0.435735i	0.0726801	+	0.997355i	$0.476845\pi$
$660$	6.55415	+	2.00321i	0.255120	+	0.0779750i
$661$	−38.5676	+	22.2670i	−1.50011	+	0.866086i	−0.500106	+	0.865964i	$0.666705\pi$
$661$	−38.5676	+	22.2670i	−1.50011	+	0.866086i	−1.00000		0.000121967i	$0.999961\pi$
$662$	1.56991	−	0.906390i	0.0610164	−	0.0352279i
$663$	5.37786	+	1.64369i	0.208859	+	0.0638357i
$664$	1.36802	−	0.789829i	0.0530896	−	0.0306513i
$665$	14.8156	+	2.31617i	0.574526	+	0.0898171i
$666$	−30.2593	−	2.11091i	−1.17252	−	0.0817960i
$667$	18.2625	+	31.6316i	0.707126	+	1.22478i
$668$	−0.742044			−0.0287105
$669$	8.36027	+	2.55524i	0.323227	+	0.0987911i
$670$		−	9.22190i		−	0.356273i
$671$	12.4628	−	21.5863i	0.481123	−	0.833329i
$672$	−2.57046	−	3.79378i	−0.0991576	−	0.146348i
$673$	−2.10536	−	3.64659i	−0.0811557	−	0.140566i	0.822591	−	0.568634i	$-0.192528\pi$
$673$	−2.10536	−	3.64659i	−0.0811557	−	0.140566i	−0.903747	+	0.428068i	$0.859194\pi$
$674$	−12.3926	+	7.15488i	−0.477346	+	0.275596i
$675$	4.03736	−	3.27105i	0.155398	−	0.125903i
$676$	1.17257	−	2.03096i	0.0450990	−	0.0781138i
$677$	−19.8282	+	34.3434i	−0.762059	+	1.31992i	0.179729	+	0.983716i	$0.442478\pi$
$677$	−19.8282	+	34.3434i	−0.762059	+	1.31992i	−0.941788	+	0.336209i	$0.890855\pi$
$678$	4.27919	−	14.0007i	0.164341	−	0.537696i
$679$	2.34521	+	0.366633i	0.0900009	+	0.0140701i
$680$	0.861388	+	0.497322i	0.0330327	+	0.0190714i
$681$	6.00086	+	6.43407i	0.229953	+	0.246554i
$682$		−	22.0808i		−	0.845517i
$683$	39.4682	+	22.7869i	1.51021	+	0.871918i	0.999929	+	0.0119087i	$0.00379073\pi$
$683$	39.4682	+	22.7869i	1.51021	+	0.871918i	0.510278	+	0.860010i	$0.329543\pi$
$684$	9.50585	−	14.0980i	0.363465	−	0.539052i
$685$			9.23672i			0.352917i
$686$	15.4715	−	10.1800i	0.590706	−	0.388673i
$687$	−37.5635	+	35.0343i	−1.43314	+	1.33664i
$688$	−10.2058			−0.389094
$689$	16.6274	+	28.7995i	0.633453	+	1.09717i
$690$	−13.0114	+	3.00505i	−0.495335	+	0.114400i
$691$	−17.0955	−	9.87010i	−0.650344	−	0.375476i	0.138244	−	0.990398i	$-0.455854\pi$
$691$	−17.0955	−	9.87010i	−0.650344	−	0.375476i	−0.788588	+	0.614922i	$0.789187\pi$
$692$	0.964238			0.0366548
$693$	23.0156	+	21.3693i	0.874291	+	0.811753i
$694$	6.00500			0.227947
$695$	11.2919	+	6.51936i	0.428325	+	0.247293i
$696$	2.39840	−	7.84713i	0.0909110	−	0.297445i
$697$	5.13801	+	8.89930i	0.194616	+	0.337085i
$698$	13.4127			0.507677
$699$	30.3003	+	9.26100i	1.14606	+	0.350283i
$700$	−0.408654	+	2.61400i	−0.0154457	+	0.0988000i
$701$		−	13.6845i		−	0.516855i	−0.966031	−	0.258427i	$-0.916796\pi$
$701$		−	13.6845i		−	0.516855i	0.966031	−	0.258427i	$-0.0832043\pi$
$702$	15.8361	+	6.07441i	0.597696	+	0.229264i
$703$	49.6292	+	28.6534i	1.87180	+	1.08068i
$704$			3.95684i			0.149129i
$705$	−7.99811	+	1.84721i	−0.301226	+	0.0695698i
$706$	0.437675	+	0.252692i	0.0164721	+	0.00951017i
$707$	−0.444216	−	0.358249i	−0.0167065	−	0.0134733i
$708$	−5.75008	+	1.32801i	−0.216101	+	0.0499098i
$709$	3.49061	−	6.04592i	0.131093	−	0.227059i	−0.793005	−	0.609215i	$-0.791485\pi$
$709$	3.49061	−	6.04592i	0.131093	−	0.227059i	0.924098	+	0.382155i	$0.124818\pi$
$710$	−1.37483	+	2.38127i	−0.0515963	+	0.0893675i
$711$	4.58046	+	3.08846i	0.171781	+	0.115826i
$712$	−11.9993	+	6.92781i	−0.449694	+	0.259631i
$713$	21.5121	+	37.2601i	0.805635	+	1.39540i
$714$	2.55669	+	3.77346i	0.0956819	+	0.141218i
$715$	6.45792	−	11.1854i	0.241512	−	0.418312i
$716$		−	0.214781i		−	0.00802676i
$717$	−2.72576	−	11.8021i	−0.101795	−	0.440757i
$718$	−13.0190			−0.485866
$719$	−7.49920	−	12.9890i	−0.279673	−	0.484408i	0.691630	−	0.722252i	$-0.256893\pi$
$719$	−7.49920	−	12.9890i	−0.279673	−	0.484408i	−0.971303	+	0.237844i	$0.923559\pi$
$720$	2.48739	+	1.67717i	0.0926996	+	0.0625043i
$721$	−18.8571	+	23.3821i	−0.702273	+	0.870795i
$722$	−11.3657	+	6.56197i	−0.422986	+	0.244211i
$723$	6.98663	−	6.51622i	0.259835	−	0.242341i
$724$	9.67842	−	5.58784i	0.359696	−	0.207670i
$725$	−4.10273	+	2.36871i	−0.152372	+	0.0879718i
$726$	−1.81499	−	7.85860i	−0.0673604	−	0.291660i
$727$	22.4642	−	12.9697i	0.833152	−	0.481020i	−0.0217788	−	0.999763i	$-0.506933\pi$
$727$	22.4642	−	12.9697i	0.833152	−	0.481020i	0.854931	+	0.518742i	$0.173600\pi$
$728$	−8.05637	+	3.11107i	−0.298589	+	0.115304i
$729$	5.60051	−	26.4128i	0.207426	−	0.978251i
$730$	−7.36348	−	12.7539i	−0.272534	−	0.472044i
$731$	10.1512			0.375455
$732$	7.97908	−	7.44185i	0.294915	−	0.275059i
$733$			22.7143i			0.838973i	0.907762	+	0.419486i	$0.137790\pi$
$733$			22.7143i			0.838973i	−0.907762	+	0.419486i	$0.862210\pi$
$734$	−16.0143	+	27.7376i	−0.591100	+	1.02382i
$735$	−6.91359	+	9.96003i	−0.255012	+	0.367381i
$736$	−3.85494	−	6.67695i	−0.142095	−	0.246116i
$737$	−31.6009	+	18.2448i	−1.16404	+	0.672056i
$738$	13.5915	+	27.8550i	0.500310	+	1.02536i
$739$	−6.74623	+	11.6848i	−0.248164	+	0.429833i	−0.963016	−	0.269443i	$-0.913161\pi$
$739$	−6.74623	+	11.6848i	−0.248164	+	0.429833i	0.714852	+	0.699275i	$0.246494\pi$
$740$	−5.05548	+	8.75634i	−0.185843	+	0.321890i
$741$	−21.8560	−	23.4338i	−0.802900	−	0.860862i
$742$	−4.16328	+	26.6309i	−0.152839	+	0.977652i
$743$	−32.3371	−	18.6698i	−1.18633	−	0.684930i	−0.228862	−	0.973459i	$-0.573500\pi$
$743$	−32.3371	−	18.6698i	−1.18633	−	0.684930i	−0.957471	+	0.288529i	$0.906834\pi$
$744$	2.82517	−	9.24345i	0.103576	−	0.338881i
$745$			22.0661i			0.808440i
$746$	−5.88964	−	3.40038i	−0.215635	−	0.124497i
$747$	−4.25902	+	2.07813i	−0.155829	+	0.0760350i
$748$		−	3.93565i		−	0.143902i
$749$	−16.7087	−	2.61212i	−0.610523	−	0.0954447i
$750$	−0.389766	−	1.68763i	−0.0142323	−	0.0616234i
$751$	−30.6698			−1.11916			−0.559579	−	0.828777i	$-0.689037\pi$
$751$	−30.6698			−1.11916			−0.559579	+	0.828777i	$0.689037\pi$
$752$	−2.36963	−	4.10432i	−0.0864116	−	0.149669i
$753$	−0.326485	−	0.350054i	−0.0118978	−	0.0127567i
$754$	−13.3920	−	7.73190i	−0.487710	−	0.281579i
$755$	−5.53782			−0.201542
$756$	6.90064	+	11.8904i	0.250974	+	0.432449i
$757$	−22.5697			−0.820308			−0.410154	−	0.912016i	$-0.634525\pi$
$757$	−22.5697			−0.820308			−0.410154	+	0.912016i	$0.634525\pi$
$758$	−1.85889	−	1.07323i	−0.0675179	−	0.0389815i
$759$	36.0395	+	38.6412i	1.30815	+	1.40259i
$760$	−2.83390	−	4.90846i	−0.102796	−	0.178048i
$761$	20.2312			0.733382			0.366691	−	0.930343i	$-0.380491\pi$
$761$	20.2312			0.733382			0.366691	+	0.930343i	$0.380491\pi$
$762$	8.02050	+	34.7275i	0.290552	+	1.25804i
$763$	3.03907	−	1.17358i	0.110022	−	0.0424864i
$764$			18.8822i			0.683133i
$765$	−2.47407	−	1.66819i	−0.0894502	−	0.0603134i
$766$	−0.615351	−	0.355273i	−0.0222335	−	0.0128365i
$767$			11.1217i			0.401582i
$768$	−0.506266	+	1.65641i	−0.0182683	+	0.0597706i
$769$	−29.9888	−	17.3140i	−1.08142	−	0.624359i	−0.150143	−	0.988664i	$-0.547973\pi$
$769$	−29.9888	−	17.3140i	−1.08142	−	0.624359i	−0.931280	+	0.364305i	$0.881307\pi$
$770$	9.76595	−	3.77125i	0.351941	−	0.135906i
$771$	19.4821	+	20.8885i	0.701631	+	0.752282i
$772$	−2.94509	+	5.10105i	−0.105996	+	0.183591i
$773$	9.02636	−	15.6341i	0.324656	−	0.562320i	−0.656787	−	0.754076i	$-0.728085\pi$
$773$	9.02636	−	15.6341i	0.324656	−	0.562320i	0.981443	+	0.191756i	$0.0614183\pi$
$774$	30.5433	+	2.13072i	1.09786	+	0.0765870i
$775$	−4.83278	+	2.79020i	−0.173598	+	0.100227i
$776$	−0.448586	−	0.776974i	−0.0161033	−	0.0278917i
$777$	−38.3587	+	25.9898i	−1.37611	+	0.932379i
$778$	−9.80747	+	16.9870i	−0.351615	+	0.609015i
$779$		−	58.5560i		−	2.09799i
$780$	4.13455	−	3.85617i	0.148041	−	0.138073i
$781$	10.8799			0.389315
$782$	3.83429	+	6.64119i	0.137114	+	0.237488i
$783$	−8.81603	+	22.9836i	−0.315059	+	0.821366i
$784$	−6.66600	−	2.13644i	−0.238072	−	0.0763015i
$785$	−14.5468	+	8.39860i	−0.519198	+	0.299759i
$786$	1.95241	+	8.45361i	0.0696400	+	0.301530i
$787$	1.54781	−	0.893627i	0.0551734	−	0.0318544i	−0.472160	−	0.881513i	$-0.656525\pi$
$787$	1.54781	−	0.893627i	0.0551734	−	0.0318544i	0.527333	+	0.849659i	$0.323192\pi$
$788$	−20.8527	+	12.0393i	−0.742846	+	0.428882i
$789$	3.17837	−	2.96437i	0.113153	−	0.105534i
$790$	1.59476	−	0.920736i	0.0567391	−	0.0327583i
$791$	−8.05601	−	20.8617i	−0.286439	−	0.741756i
$792$	0.826087	−	11.8417i	0.0293537	−	0.420778i
$793$	−10.2812	−	17.8075i	−0.365094	−	0.632362i
$794$	−23.9395			−0.849580
$795$	−3.97086	−	17.1932i	−0.140832	−	0.609780i
$796$			15.2132i			0.539216i
$797$	21.5468	−	37.3202i	0.763227	−	1.32195i	−0.177951	−	0.984039i	$-0.556947\pi$
$797$	21.5468	−	37.3202i	0.763227	−	1.32195i	0.941179	−	0.337909i	$-0.109720\pi$
$798$	−1.86581	−	25.9060i	−0.0660490	−	0.917063i
$799$	2.35694	+	4.08234i	0.0833826	+	0.144423i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	37.3570	−	18.2279i	1.31995	−	0.644051i
$802$	0.337812	−	0.585108i	0.0119286	−	0.0206609i
$803$	−29.1361	+	50.4652i	−1.02819	+	1.78088i
$804$	−15.5631	+	3.59439i	−0.548869	+	0.126764i
$805$	−12.8054	+	15.8782i	−0.451330	+	0.559633i
$806$	−15.7750	−	9.10772i	−0.555652	−	0.320806i
$807$	45.0945	−	10.4148i	1.58740	−	0.366619i
$808$			0.215695i			0.00758812i
$809$	−31.6514	−	18.2739i	−1.11280	−	0.642478i	−0.173250	−	0.984878i	$-0.555427\pi$
$809$	−31.6514	−	18.2739i	−1.11280	−	0.642478i	−0.939554	+	0.342400i	$0.888760\pi$
$810$	−7.09393	−	5.53861i	−0.249255	−	0.194607i
$811$		−	0.856906i		−	0.0300900i	−0.999887	−	0.0150450i	$-0.995211\pi$
$811$		−	0.856906i		−	0.0300900i	0.999887	−	0.0150450i	$-0.00478916\pi$
$812$	−4.51523	−	11.6925i	−0.158453	−	0.410327i
$813$	−24.7689	−	7.57038i	−0.868684	−	0.265505i
$814$	40.0074			1.40226
$815$	−0.864749	−	1.49779i	−0.0302908	−	0.0524653i
$816$	0.503554	−	1.64754i	0.0176279	−	0.0576754i
$817$	−50.0949	−	28.9223i	−1.75260	−	1.01186i
$818$	30.3557			1.06136
$819$	24.7600	−	7.62863i	0.865186	−	0.266566i
$820$	10.3313			0.360786
$821$	−11.7056	−	6.75824i	−0.408529	−	0.235864i	0.281629	−	0.959523i	$-0.409125\pi$
$821$	−11.7056	−	6.75824i	−0.408529	−	0.235864i	−0.690157	+	0.723659i	$0.742459\pi$
$822$	15.5881	−	3.60016i	0.543699	−	0.125570i
$823$	7.48663	+	12.9672i	0.260968	+	0.452009i	0.966499	−	0.256669i	$-0.0826251\pi$
$823$	7.48663	+	12.9672i	0.260968	+	0.452009i	−0.705532	+	0.708678i	$0.749292\pi$
$824$	11.3535			0.395517
$825$	−5.01191	+	4.67446i	−0.174492	+	0.162744i
$826$	−5.65904	+	7.01701i	−0.196903	+	0.244153i
$827$			14.6192i			0.508361i	0.967157	+	0.254180i	$0.0818057\pi$
$827$			14.6192i			0.508361i	−0.967157	+	0.254180i	$0.918194\pi$
$828$	10.1428	+	20.7871i	0.352487	+	0.722401i
$829$	3.40972	+	1.96860i	0.118425	+	0.0683724i	0.558042	−	0.829813i	$-0.311553\pi$
$829$	3.40972	+	1.96860i	0.118425	+	0.0683724i	−0.439618	+	0.898185i	$0.644886\pi$
$830$			1.57966i			0.0548308i
$831$	16.8099	+	18.0235i	0.583130	+	0.625227i
$832$	2.82686	+	1.63209i	0.0980037	+	0.0565825i
$833$	6.63031	+	2.12500i	0.229726	+	0.0736269i
$834$	6.60105	−	21.5975i	0.228576	−	0.747859i
$835$	0.371022	−	0.642629i	0.0128397	−	0.0222391i
$836$	−11.2133	+	19.4220i	−0.387820	+	0.671724i
$837$	−10.3848	+	27.0733i	−0.358950	+	0.935790i
$838$	10.1808	−	5.87786i	0.351688	−	0.203047i
$839$	−16.9706	−	29.3940i	−0.585891	−	1.01479i	−0.994764	−	0.102202i	$-0.967411\pi$
$839$	−16.9706	−	29.3940i	−0.585891	−	1.01479i	0.408872	−	0.912592i	$-0.365922\pi$
$840$	4.57074	−	0.329195i	0.157705	−	0.0113583i
$841$	−3.27839	+	5.67833i	−0.113048	+	0.195804i
$842$		−	28.9113i		−	0.996351i
$843$	−41.2346	−	12.6029i	−1.42019	−	0.434068i
$844$	−6.22217			−0.214176
$845$	1.17257	+	2.03096i	0.0403378	+	0.0698671i
$846$	6.23478	+	12.7778i	0.214356	+	0.439311i
$847$	−9.59010	−	7.73417i	−0.329520	−	0.265749i
$848$	8.82289	−	5.09390i	0.302979	−	0.174925i
$849$	−28.4566	−	8.69747i	−0.976627	−	0.298496i
$850$	−0.861388	+	0.497322i	−0.0295453	+	0.0170580i
$851$	−67.5103	+	38.9771i	−2.31422	+	1.33612i
$852$	4.55456	+	1.39206i	0.156037	+	0.0476910i
$853$	−27.7997	+	16.0501i	−0.951843	+	0.549547i	−0.893653	−	0.448759i	$-0.851866\pi$
$853$	−27.7997	+	16.0501i	−0.951843	+	0.549547i	−0.0581898	+	0.998306i	$0.518533\pi$
$854$	2.57427	−	16.4666i	0.0880896	−	0.563476i
$855$	7.45633	+	15.2813i	0.255001	+	0.522610i
$856$	3.19600	+	5.53564i	0.109237	+	0.189204i
$857$	−14.7405			−0.503525			−0.251763	−	0.967789i	$-0.581010\pi$
$857$	−14.7405			−0.503525			−0.251763	+	0.967789i	$0.581010\pi$
$858$	−21.3939	−	6.53884i	−0.730376	−	0.223232i
$859$			1.58168i			0.0539661i	0.999636	+	0.0269831i	$0.00859002\pi$
$859$			1.58168i			0.0539661i	−0.999636	+	0.0269831i	$0.991410\pi$
$860$	5.10292	−	8.83852i	0.174008	−	0.301391i
$861$	42.5959	+	20.6656i	1.45166	+	0.704280i
$862$	9.97444	+	17.2762i	0.339731	+	0.588431i
$863$	−5.03980	+	2.90973i	−0.171557	+	0.0990483i	−0.583320	−	0.812243i	$-0.698247\pi$
$863$	−5.03980	+	2.90973i	−0.171557	+	0.0990483i	0.411763	+	0.911291i	$0.364913\pi$
$864$	1.86093	−	4.85149i	0.0633101	−	0.165051i
$865$	−0.482119	+	0.835055i	−0.0163925	+	0.0283927i
$866$	−14.4078	+	24.9551i	−0.489598	+	0.848009i
$867$	8.10566	−	26.5203i	0.275283	−	0.900675i
$868$	−5.31867	−	13.7731i	−0.180527	−	0.467490i
$869$	−6.31022	−	3.64321i	−0.214060	−	0.123587i
$870$	5.59661	+	6.00064i	0.189743	+	0.203441i
$871$			30.1019i			1.01996i
$872$	−1.06636	−	0.615666i	−0.0361117	−	0.0208491i
$873$	1.18028	+	2.41892i	0.0399465	+	0.0818682i
$874$		−	43.6980i		−	1.47811i
$875$	−2.05946	−	1.66090i	−0.0696226	−	0.0561488i
$876$	−18.6538	+	17.3978i	−0.630254	+	0.587819i
$877$	−48.1745			−1.62674			−0.813369	−	0.581748i	$-0.802369\pi$
$877$	−48.1745			−1.62674			−0.813369	+	0.581748i	$0.802369\pi$
$878$	−4.08760	−	7.07993i	−0.137950	−	0.238936i
$879$	13.4573	−	3.10804i	0.453904	−	0.104832i
$880$	−3.42673	−	1.97842i	−0.115515	−	0.0666926i
$881$	53.9354			1.81713			0.908566	−	0.417742i	$-0.137178\pi$
$881$	53.9354			1.81713			0.908566	+	0.417742i	$0.137178\pi$
$882$	19.5035	+	7.78548i	0.656717	+	0.262151i
$883$	−42.9089			−1.44400			−0.722000	−	0.691893i	$-0.756777\pi$
$883$	−42.9089			−1.44400			−0.722000	+	0.691893i	$0.756777\pi$
$884$	−2.81172	−	1.62335i	−0.0945684	−	0.0545991i
$885$	1.72495	−	5.64373i	0.0579835	−	0.189712i
$886$	13.1350	+	22.7505i	0.441279	+	0.764317i
$887$	19.1085			0.641600			0.320800	−	0.947147i	$-0.396048\pi$
$887$	19.1085			0.641600			0.320800	+	0.947147i	$0.396048\pi$
$888$	16.7479	+	5.11883i	0.562022	+	0.171777i
$889$	42.3791	+	34.1776i	1.42135	+	1.14628i
$890$		−	13.8556i		−	0.464442i
$891$	−4.94450	+	35.2666i	−0.165647	+	1.18148i
$892$	−4.37102	−	2.52361i	−0.146353	−	0.0844968i
$893$		−	26.8612i		−	0.898876i
$894$	37.2394	−	8.60063i	1.24547	−	0.287648i
$895$	0.186006	+	0.107391i	0.00621750	+	0.00358968i
$896$	0.953096	+	2.46812i	0.0318407	+	0.0824540i
$897$	42.4715	−	9.80901i	1.41808	−	0.327513i
$898$	3.19845	−	5.53988i	0.106734	−	0.184868i
$899$	13.2184	−	22.8949i	0.440858	−	0.763589i
$900$	−2.69616	+	1.31556i	−0.0898722	+	0.0438520i
$901$	−8.77564	+	5.06662i	−0.292359	+	0.168794i
$902$	−20.4398	−	35.4027i	−0.680570	−	1.17878i
$903$	38.7187	−	26.2337i	1.28848	−	0.873003i
$904$	−4.22623	+	7.32005i	−0.140562	+	0.243461i
$905$			11.1757i			0.371492i
$906$	2.15845	+	9.34577i	0.0717099	+	0.310492i
$907$	−27.0455			−0.898032			−0.449016	−	0.893524i	$-0.648225\pi$
$907$	−27.0455			−0.898032			−0.449016	+	0.893524i	$0.648225\pi$
$908$	−2.53981	−	4.39908i	−0.0842865	−	0.145989i
$909$	0.0450316	−	0.645516i	0.00149360	−	0.0214104i
$910$	1.33392	−	8.53256i	0.0442189	−	0.282852i
$911$	4.11941	−	2.37834i	0.136482	−	0.0787979i	−0.430204	−	0.902732i	$-0.641558\pi$
$911$	4.11941	−	2.37834i	0.136482	−	0.0787979i	0.566686	+	0.823934i	$0.308225\pi$
$912$	−7.17908	+	6.69571i	−0.237723	+	0.221717i
$913$	5.41306	−	3.12523i	0.179146	−	0.103430i
$914$	−8.94322	+	5.16337i	−0.295815	+	0.170789i
$915$	2.45529	+	10.6310i	0.0811693	+	0.351450i
$916$	25.6828	−	14.8280i	0.848582	−	0.489929i
$917$	10.3162	+	8.31976i	0.340671	+	0.274743i
$918$	−1.85096	+	4.82551i	−0.0610909	+	0.159265i
$919$	−17.3173	−	29.9945i	−0.571245	−	0.989426i	−0.996438	−	0.0843232i	$-0.973127\pi$
$919$	−17.3173	−	29.9945i	−0.571245	−	0.989426i	0.425193	−	0.905103i	$-0.360206\pi$
$920$	7.70987			0.254187
$921$	−19.7173	+	18.3897i	−0.649706	+	0.605961i
$922$		−	8.00758i		−	0.263715i
$923$	4.48768	−	7.77289i	0.147714	−	0.255848i
$924$	−10.1709	−	15.0114i	−0.334598	−	0.493838i
$925$	−5.05548	−	8.75634i	−0.166223	−	0.287907i
$926$	−26.4770	+	15.2865i	−0.870089	+	0.502346i
$927$	−33.9779	−	2.37032i	−1.11598	−	0.0778514i
$928$	−2.36871	+	4.10273i	−0.0777569	+	0.134679i
$929$	−14.6395	+	25.3564i	−0.480307	+	0.831917i	−0.999745	−	0.0225917i	$-0.992808\pi$
$929$	−14.6395	+	25.3564i	−0.480307	+	0.831917i	0.519437	+	0.854509i	$0.326142\pi$
$930$	6.59247	+	7.06839i	0.216176	+	0.231782i
$931$	−26.6653	−	29.3774i	−0.873921	−	0.962806i
$932$	−15.8420	−	9.14639i	−0.518922	−	0.299600i
$933$	−10.2098	+	33.4046i	−0.334254	+	1.09362i
$934$		−	7.22034i		−	0.236257i
$935$	3.40837	+	1.96783i	0.111466	+	0.0643548i
$936$	−8.11928	−	5.47457i	−0.265387	−	0.178942i
$937$			25.3740i			0.828932i	0.910065	+	0.414466i	$0.136032\pi$
$937$			25.3740i			0.828932i	−0.910065	+	0.414466i	$0.863968\pi$
$938$	−15.3167	+	18.9922i	−0.500108	+	0.620117i
$939$	2.60053	+	11.2599i	0.0848652	+	0.367453i
$940$	4.73926			0.154578
$941$	−6.09522	−	10.5572i	−0.198699	−	0.344156i	0.749408	−	0.662108i	$-0.230338\pi$
$941$	−6.09522	−	10.5572i	−0.198699	−	0.344156i	−0.948107	+	0.317952i	$0.897005\pi$
$942$	19.8436	+	21.2761i	0.646538	+	0.693212i
$943$	68.9819	+	39.8267i	2.24636	+	1.29694i
$944$	3.40720			0.110895
$945$	−13.7477	+	0.0309387i	−0.447212	+	0.00100644i
$946$	−40.3829			−1.31296
$947$	14.1104	+	8.14666i	0.458527	+	0.264731i	0.711425	−	0.702762i	$-0.248050\pi$
$947$	14.1104	+	8.14666i	0.458527	+	0.264731i	−0.252898	+	0.967493i	$0.581384\pi$
$948$	−2.17544	−	2.33249i	−0.0706551	−	0.0757558i
$949$	24.0357	+	41.6310i	0.780231	+	1.35140i
$950$	5.66780			0.183888
$951$	−9.95524	−	43.1046i	−0.322821	−	1.39776i
$952$	−0.947992	−	2.45490i	−0.0307246	−	0.0795638i
$953$			58.2513i			1.88695i	0.331449	+	0.943473i	$0.392462\pi$
$953$			58.2513i			1.88695i	−0.331449	+	0.943473i	$0.607538\pi$
$954$	−27.4680	+	13.4027i	−0.889309	+	0.433927i
$955$	−16.3524	−	9.44109i	−0.529153	−	0.305506i
$956$			6.99331i			0.226180i
$957$	9.49008	−	31.0498i	0.306771	−	1.00370i
$958$	−15.8239	−	9.13594i	−0.511248	−	0.295169i
$959$	15.3413	−	19.0227i	0.495397	−	0.614275i
$960$	−1.18136	−	1.26664i	−0.0381282	−	0.0408808i
$961$	0.0704801	−	0.122075i	0.00227355	−	0.00393791i
$962$	16.5020	−	28.5822i	0.532045	−	0.921529i
$963$	−8.40907	−	17.2339i	−0.270978	−	0.555355i
$964$	−4.77687	+	2.75793i	−0.153853	+	0.0888269i
$965$	−2.94509	−	5.10105i	−0.0948058	−	0.164209i
$966$	31.7876	+	15.4219i	1.02275	+	0.496191i
$967$	5.61342	−	9.72273i	0.180515	−	0.312662i	−0.761541	−	0.648117i	$-0.775557\pi$
$967$	5.61342	−	9.72273i	0.180515	−	0.312662i	0.942056	+	0.335455i	$0.108890\pi$
$968$			4.65660i			0.149669i
$969$	7.14064	−	6.65986i	0.229390	−	0.213945i
$970$	0.897172			0.0288065
$971$	−8.18607	−	14.1787i	−0.262704	−	0.455016i	0.704256	−	0.709946i	$-0.251281\pi$
$971$	−8.18607	−	14.1787i	−0.262704	−	0.455016i	−0.966959	+	0.254930i	$0.917947\pi$
$972$	−6.58212	+	14.1307i	−0.211122	+	0.453241i
$973$	−12.4272	−	32.1811i	−0.398396	−	1.03168i
$974$	33.4057	−	19.2868i	1.07039	−	0.617988i
$975$	1.27227	+	5.50871i	0.0407451	+	0.176420i
$976$	−5.45543	+	3.14969i	−0.174624	+	0.100819i
$977$	−50.6299	+	29.2312i	−1.61979	+	0.935189i	−0.632823	+	0.774297i	$0.718104\pi$
$977$	−50.6299	+	29.2312i	−1.61979	+	0.935189i	−0.986972	+	0.160892i	$0.948563\pi$
$978$	−2.19066	+	2.04316i	−0.0700496	+	0.0653331i
$979$	−47.4794	+	27.4123i	−1.51745	+	0.876100i
$980$	5.18322	−	4.70471i	0.165572	−	0.150286i
$981$	3.06280	+	2.06515i	0.0977878	+	0.0659352i
$982$	−12.3235	−	21.3449i	−0.393258	−	0.681143i
$983$	−25.3666			−0.809070			−0.404535	−	0.914522i	$-0.632567\pi$
$983$	−25.3666			−0.809070			−0.404535	+	0.914522i	$0.632567\pi$
$984$	−4.02681	−	17.4355i	−0.128370	−	0.555822i
$985$		−	24.0786i		−	0.767208i
$986$	2.35603	−	4.08076i	0.0750312	−	0.129958i
$987$	19.5398	+	9.47984i	0.621960	+	0.301747i
$988$	9.25035	+	16.0221i	0.294293	+	0.509730i
$989$	68.1438	−	39.3429i	2.16685	−	1.25103i
$990$	9.84221	+	6.63629i	0.312806	+	0.210915i
$991$	−11.2022	+	19.4028i	−0.355850	+	0.616349i	−0.987263	−	0.159097i	$-0.949142\pi$
$991$	−11.2022	+	19.4028i	−0.355850	+	0.616349i	0.631413	+	0.775446i	$0.282475\pi$
$992$	−2.79020	+	4.83278i	−0.0885891	+	0.153441i
$993$	3.05930	−	0.706561i	0.0970838	−	0.0224220i
$994$	6.78647	−	2.62069i	0.215254	−	0.0831231i
$995$	−13.1750	−	7.60658i	−0.417675	−	0.241145i
$996$	2.66587	−	0.615698i	0.0844714	−	0.0195091i
$997$			24.3980i			0.772693i	0.922354	+	0.386346i	$0.126263\pi$
$997$			24.3980i			0.772693i	−0.922354	+	0.386346i	$0.873737\pi$
$998$	−9.10884	−	5.25899i	−0.288335	−	0.166470i
$999$	−49.0532	−	18.8158i	−1.55197	−	0.595305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.b.311.2	✓	28
3.2	odd	2		1890.2.t.b.1151.9		28
7.5	odd	6		630.2.bk.b.131.8	yes	28
9.2	odd	6		630.2.bk.b.101.1	yes	28
9.7	even	3		1890.2.bk.b.521.12		28
21.5	even	6		1890.2.bk.b.341.12		28
63.47	even	6	inner	630.2.t.b.551.2	yes	28
63.61	odd	6		1890.2.t.b.1601.9		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.2	✓	28	1.1	even	1	trivial
630.2.t.b.551.2	yes	28	63.47	even	6	inner
630.2.bk.b.101.1	yes	28	9.2	odd	6
630.2.bk.b.131.8	yes	28	7.5	odd	6
1890.2.t.b.1151.9		28	3.2	odd	2
1890.2.t.b.1601.9		28	63.61	odd	6
1890.2.bk.b.341.12		28	21.5	even	6
1890.2.bk.b.521.12		28	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.18136 - 1.26664i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.389766 + 1.68763i) q^{6} +(2.05946 + 1.66090i) q^{7} -1.00000i q^{8} +(-0.208774 + 2.99273i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.18136 - 1.26664i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.389766 + 1.68763i) q^{6} +(2.05946 + 1.66090i) q^{7} -1.00000i q^{8} +(-0.208774 + 2.99273i) q^{9} +(0.866025 + 0.500000i) q^{10} -3.95684i q^{11} +(0.506266 - 1.65641i) q^{12} +(-2.82686 - 1.63209i) q^{13} +(-0.953096 - 2.46812i) q^{14} +(1.18136 + 1.26664i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.497322 - 0.861388i) q^{17} +(1.67717 - 2.48739i) q^{18} +(-4.90846 + 2.83390i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.329195 - 4.57074i) q^{21} +(-1.97842 + 3.42673i) q^{22} -7.70987i q^{23} +(-1.26664 + 1.18136i) q^{24} +1.00000 q^{25} +(1.63209 + 2.82686i) q^{26} +(4.03736 - 3.27105i) q^{27} +(-0.408654 + 2.61400i) q^{28} +(-4.10273 + 2.36871i) q^{29} +(-0.389766 - 1.68763i) q^{30} +(-4.83278 + 2.79020i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.01191 + 4.67446i) q^{33} +(-0.861388 + 0.497322i) q^{34} +(-2.05946 - 1.66090i) q^{35} +(-2.69616 + 1.31556i) q^{36} +(-5.05548 - 8.75634i) q^{37} +5.66780 q^{38} +(1.27227 + 5.50871i) q^{39} +1.00000i q^{40} +(-5.16567 + 8.94721i) q^{41} +(-2.00028 + 4.12297i) q^{42} +(5.10292 + 8.83852i) q^{43} +(3.42673 - 1.97842i) q^{44} +(0.208774 - 2.99273i) q^{45} +(-3.85494 + 6.67695i) q^{46} +(-2.36963 + 4.10432i) q^{47} +(1.68763 - 0.389766i) q^{48} +(1.48279 + 6.84115i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-1.67859 + 0.387679i) q^{51} -3.26418i q^{52} +(-8.82289 - 5.09390i) q^{53} +(-5.13198 + 0.814131i) q^{54} +3.95684i q^{55} +(1.66090 - 2.05946i) q^{56} +(9.38820 + 2.86941i) q^{57} +4.73743 q^{58} +(-1.70360 - 2.95072i) q^{59} +(-0.506266 + 1.65641i) q^{60} +(5.45543 + 3.14969i) q^{61} +5.58041 q^{62} +(-5.40060 + 5.81666i) q^{63} -1.00000 q^{64} +(2.82686 + 1.63209i) q^{65} +(6.67767 - 1.54224i) q^{66} +(-4.61095 - 7.98640i) q^{67} +0.994645 q^{68} +(-9.76567 + 9.10814i) q^{69} +(0.953096 + 2.46812i) q^{70} +2.74965i q^{71} +(2.99273 + 0.208774i) q^{72} +(-12.7539 - 7.36348i) q^{73} +10.1110i q^{74} +(-1.18136 - 1.26664i) q^{75} +(-4.90846 - 2.83390i) q^{76} +(6.57194 - 8.14898i) q^{77} +(1.65254 - 5.40682i) q^{78} +(0.920736 - 1.59476i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-8.91283 - 1.24961i) q^{81} +(8.94721 - 5.16567i) q^{82} +(0.789829 + 1.36802i) q^{83} +(3.79378 - 2.57046i) q^{84} +(-0.497322 + 0.861388i) q^{85} -10.2058i q^{86} +(7.84713 + 2.39840i) q^{87} -3.95684 q^{88} +(-6.92781 - 11.9993i) q^{89} +(-1.67717 + 2.48739i) q^{90} +(-3.11107 - 8.05637i) q^{91} +(6.67695 - 3.85494i) q^{92} +(9.24345 + 2.82517i) q^{93} +(4.10432 - 2.36963i) q^{94} +(4.90846 - 2.83390i) q^{95} +(-1.65641 - 0.506266i) q^{96} +(0.776974 - 0.448586i) q^{97} +(2.13644 - 6.66600i) q^{98} +(11.8417 + 0.826087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

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