LMFDB - Embedded newform 630.2.i.g.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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([2, 0, 2]))

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

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

chi := DirichletCharacter("630.121");

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.i (of order $3$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 3 x^{9} - 2 x^{8} + 24 x^{7} - 21 x^{6} + 72 x^{5} - 18 x^{4} + \cdots + 729 $ x^12 - 3x^11 + 7x^10 - 3x^9 - 2x^8 + 24x^7 - 21x^6 + 72x^5 - 18x^4 - 81x^3 + 567x^2 - 729*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.628063 - 1.61417i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.g.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.71194 - 0.263165i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.71194 - 0.263165i) q^{6} +(-2.25729 + 1.38008i) q^{7} +1.00000 q^{8} +(2.86149 + 0.901046i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.71194 - 0.263165i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.71194 - 0.263165i) q^{6} +(-2.25729 + 1.38008i) q^{7} +1.00000 q^{8} +(2.86149 + 0.901046i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.64454 - 4.58047i) q^{11} +(-1.71194 - 0.263165i) q^{12} +(-1.04535 + 1.81060i) q^{13} +(-2.25729 + 1.38008i) q^{14} +(0.628063 + 1.61417i) q^{15} +1.00000 q^{16} +(-2.66689 - 4.61919i) q^{17} +(2.86149 + 0.901046i) q^{18} +(4.21311 - 7.29732i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(4.22755 - 1.76858i) q^{21} +(2.64454 - 4.58047i) q^{22} +(-2.71224 - 4.69774i) q^{23} +(-1.71194 - 0.263165i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.04535 + 1.81060i) q^{26} +(-4.66158 - 2.29558i) q^{27} +(-2.25729 + 1.38008i) q^{28} +(0.582710 + 1.00928i) q^{29} +(0.628063 + 1.61417i) q^{30} -6.77682 q^{31} +1.00000 q^{32} +(-5.73271 + 7.14555i) q^{33} +(-2.66689 - 4.61919i) q^{34} +(2.32383 + 1.26483i) q^{35} +(2.86149 + 0.901046i) q^{36} +(1.59659 - 2.76537i) q^{37} +(4.21311 - 7.29732i) q^{38} +(2.26607 - 2.82455i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-1.51734 + 2.62811i) q^{41} +(4.22755 - 1.76858i) q^{42} +(-1.77230 - 3.06971i) q^{43} +(2.64454 - 4.58047i) q^{44} +(-0.650416 - 2.92864i) q^{45} +(-2.71224 - 4.69774i) q^{46} +9.36786 q^{47} +(-1.71194 - 0.263165i) q^{48} +(3.19076 - 6.23049i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.34995 + 8.60961i) q^{51} +(-1.04535 + 1.81060i) q^{52} +(3.71311 + 6.43129i) q^{53} +(-4.66158 - 2.29558i) q^{54} -5.28907 q^{55} +(-2.25729 + 1.38008i) q^{56} +(-9.13300 + 11.3838i) q^{57} +(0.582710 + 1.00928i) q^{58} +10.2030 q^{59} +(0.628063 + 1.61417i) q^{60} -14.7350 q^{61} -6.77682 q^{62} +(-7.70274 + 1.91516i) q^{63} +1.00000 q^{64} +2.09071 q^{65} +(-5.73271 + 7.14555i) q^{66} +8.39063 q^{67} +(-2.66689 - 4.61919i) q^{68} +(3.40692 + 8.75602i) q^{69} +(2.32383 + 1.26483i) q^{70} +2.28907 q^{71} +(2.86149 + 0.901046i) q^{72} +(6.16188 + 10.6727i) q^{73} +(1.59659 - 2.76537i) q^{74} +(1.08388 - 1.35100i) q^{75} +(4.21311 - 7.29732i) q^{76} +(0.351920 + 13.9891i) q^{77} +(2.26607 - 2.82455i) q^{78} -5.25613 q^{79} +(-0.500000 - 0.866025i) q^{80} +(7.37623 + 5.15667i) q^{81} +(-1.51734 + 2.62811i) q^{82} +(-3.46154 - 5.99556i) q^{83} +(4.22755 - 1.76858i) q^{84} +(-2.66689 + 4.61919i) q^{85} +(-1.77230 - 3.06971i) q^{86} +(-0.731958 - 1.88118i) q^{87} +(2.64454 - 4.58047i) q^{88} +(6.37499 - 11.0418i) q^{89} +(-0.650416 - 2.92864i) q^{90} +(-0.139110 - 5.52974i) q^{91} +(-2.71224 - 4.69774i) q^{92} +(11.6015 + 1.78342i) q^{93} +9.36786 q^{94} -8.42622 q^{95} +(-1.71194 - 0.263165i) q^{96} +(3.09361 + 5.35829i) q^{97} +(3.19076 - 6.23049i) q^{98} +(11.6945 - 10.7241i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 12 * q^16 + q^17 + 4 * q^18 + 8 * q^19 - 6 * q^20 + 5 * q^21 + 3 * q^22 + 11 * q^23 - 6 * q^25 - 2 * q^26 - 27 * q^27 + 4 * q^28 + 13 * q^29 + 3 * q^30 - 42 * q^31 + 12 * q^32 + 17 * q^33 + q^34 + 4 * q^35 + 4 * q^36 + 18 * q^37 + 8 * q^38 - 24 * q^39 - 6 * q^40 + 5 * q^41 + 5 * q^42 - 11 * q^43 + 3 * q^44 + q^45 + 11 * q^46 + 46 * q^47 - 6 * q^50 - 27 * q^51 - 2 * q^52 + 2 * q^53 - 27 * q^54 - 6 * q^55 + 4 * q^56 - 44 * q^57 + 13 * q^58 - 2 * q^59 + 3 * q^60 + 2 * q^61 - 42 * q^62 + 9 * q^63 + 12 * q^64 + 4 * q^65 + 17 * q^66 - 4 * q^67 + q^68 - 24 * q^69 + 4 * q^70 - 30 * q^71 + 4 * q^72 + 22 * q^73 + 18 * q^74 - 3 * q^75 + 8 * q^76 - 31 * q^77 - 24 * q^78 - 54 * q^79 - 6 * q^80 + 52 * q^81 + 5 * q^82 + 6 * q^83 + 5 * q^84 + q^85 - 11 * q^86 - 28 * q^87 + 3 * q^88 - 18 * q^89 + q^90 + 14 * q^91 + 11 * q^92 - 38 * q^93 + 46 * q^94 - 16 * q^95 - 4 * q^97 + 63 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.71194	−	0.263165i	−0.988390	−	0.151938i
$3$	−1.71194	−	0.263165i	−0.988390	−	0.151938i
$4$	1.00000			0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.71194	−	0.263165i	−0.698897	−	0.107437i
$7$	−2.25729	+	1.38008i	−0.853177	+	0.521621i
$7$	−2.25729	+	1.38008i	−0.853177	+	0.521621i
$8$	1.00000			0.353553
$9$	2.86149	+	0.901046i	0.953829	+	0.300349i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	2.64454	−	4.58047i	0.797358	−	1.38106i	−0.123974	−	0.992285i	$-0.539564\pi$
$11$	2.64454	−	4.58047i	0.797358	−	1.38106i	0.921331	−	0.388778i	$-0.127103\pi$
$12$	−1.71194	−	0.263165i	−0.494195	−	0.0759692i
$13$	−1.04535	+	1.81060i	−0.289929	+	0.502171i	−0.973792	−	0.227438i	$-0.926965\pi$
$13$	−1.04535	+	1.81060i	−0.289929	+	0.502171i	0.683864	+	0.729610i	$0.260298\pi$
$14$	−2.25729	+	1.38008i	−0.603287	+	0.368842i
$15$	0.628063	+	1.61417i	0.162165	+	0.416776i
$16$	1.00000			0.250000
$17$	−2.66689	−	4.61919i	−0.646815	−	1.12032i	−0.983879	−	0.178835i	$-0.942767\pi$
$17$	−2.66689	−	4.61919i	−0.646815	−	1.12032i	0.337064	−	0.941482i	$-0.390566\pi$
$18$	2.86149	+	0.901046i	0.674459	+	0.212379i
$19$	4.21311	−	7.29732i	0.966554	−	1.67412i	0.261172	−	0.965292i	$-0.415891\pi$
$19$	4.21311	−	7.29732i	0.966554	−	1.67412i	0.705382	−	0.708828i	$-0.250776\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	4.22755	−	1.76858i	0.922526	−	0.385935i
$22$	2.64454	−	4.58047i	0.563817	−	0.976560i
$23$	−2.71224	−	4.69774i	−0.565541	−	0.979546i	−0.996999	−	0.0774131i	$-0.975334\pi$
$23$	−2.71224	−	4.69774i	−0.565541	−	0.979546i	0.431458	−	0.902133i	$-0.357999\pi$
$24$	−1.71194	−	0.263165i	−0.349449	−	0.0537183i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.04535	+	1.81060i	−0.205011	+	0.355089i
$27$	−4.66158	−	2.29558i	−0.897121	−	0.441785i
$28$	−2.25729	+	1.38008i	−0.426589	+	0.260811i
$29$	0.582710	+	1.00928i	0.108207	+	0.187419i	0.915044	−	0.403355i	$-0.132156\pi$
$29$	0.582710	+	1.00928i	0.108207	+	0.187419i	−0.806837	+	0.590774i	$0.798823\pi$
$30$	0.628063	+	1.61417i	0.114668	+	0.294705i
$31$	−6.77682			−1.21715			−0.608576	−	0.793495i	$-0.708259\pi$
$31$	−6.77682			−1.21715			−0.608576	+	0.793495i	$0.708259\pi$
$32$	1.00000			0.176777
$33$	−5.73271	+	7.14555i	−0.997937	+	1.24388i
$34$	−2.66689	−	4.61919i	−0.457368	−	0.792184i
$35$	2.32383	+	1.26483i	0.392799	+	0.213796i
$36$	2.86149	+	0.901046i	0.476915	+	0.150174i
$37$	1.59659	−	2.76537i	0.262477	−	0.454624i	−0.704422	−	0.709781i	$-0.748794\pi$
$37$	1.59659	−	2.76537i	0.262477	−	0.454624i	0.966900	+	0.255157i	$0.0821273\pi$
$38$	4.21311	−	7.29732i	0.683457	−	1.18378i
$39$	2.26607	−	2.82455i	0.362862	−	0.452290i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−1.51734	+	2.62811i	−0.236969	+	0.410442i	−0.959843	−	0.280538i	$-0.909487\pi$
$41$	−1.51734	+	2.62811i	−0.236969	+	0.410442i	0.722874	+	0.690980i	$0.242821\pi$
$42$	4.22755	−	1.76858i	0.652324	−	0.272897i
$43$	−1.77230	−	3.06971i	−0.270273	−	0.468127i	0.698659	−	0.715455i	$-0.253781\pi$
$43$	−1.77230	−	3.06971i	−0.270273	−	0.468127i	−0.968932	+	0.247328i	$0.920447\pi$
$44$	2.64454	−	4.58047i	0.398679	−	0.690532i
$45$	−0.650416	−	2.92864i	−0.0969582	−	0.436577i
$46$	−2.71224	−	4.69774i	−0.399898	−	0.692644i
$47$	9.36786			1.36644			0.683221	−	0.730211i	$-0.260578\pi$
$47$	9.36786			1.36644			0.683221	+	0.730211i	$0.260578\pi$
$48$	−1.71194	−	0.263165i	−0.247097	−	0.0379846i
$49$	3.19076	−	6.23049i	0.455822	−	0.890071i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	3.34995	+	8.60961i	0.469087	+	1.20559i
$52$	−1.04535	+	1.81060i	−0.144964	+	0.251086i
$53$	3.71311	+	6.43129i	0.510035	+	0.883406i	0.999932	+	0.0116262i	$0.00370083\pi$
$53$	3.71311	+	6.43129i	0.510035	+	0.883406i	−0.489898	+	0.871780i	$0.662966\pi$
$54$	−4.66158	−	2.29558i	−0.634360	−	0.312389i
$55$	−5.28907			−0.713178
$56$	−2.25729	+	1.38008i	−0.301644	+	0.184421i
$57$	−9.13300	+	11.3838i	−1.20969	+	1.50783i
$58$	0.582710	+	1.00928i	0.0765136	+	0.132525i
$59$	10.2030			1.32832			0.664161	−	0.747589i	$-0.268789\pi$
$59$	10.2030			1.32832			0.664161	+	0.747589i	$0.268789\pi$
$60$	0.628063	+	1.61417i	0.0810826	+	0.208388i
$61$	−14.7350			−1.88663			−0.943313	−	0.331904i	$-0.892309\pi$
$61$	−14.7350			−1.88663			−0.943313	+	0.331904i	$0.892309\pi$
$62$	−6.77682			−0.860657
$63$	−7.70274	+	1.91516i	−0.970454	+	0.241287i
$64$	1.00000			0.125000
$65$	2.09071			0.259320
$66$	−5.73271	+	7.14555i	−0.705648	+	0.879556i
$67$	8.39063			1.02508			0.512539	−	0.858664i	$-0.328705\pi$
$67$	8.39063			1.02508			0.512539	+	0.858664i	$0.328705\pi$
$68$	−2.66689	−	4.61919i	−0.323408	−	0.560159i
$69$	3.40692	+	8.75602i	0.410145	+	1.05410i
$70$	2.32383	+	1.26483i	0.277751	+	0.151177i
$71$	2.28907			0.271663			0.135831	−	0.990732i	$-0.456629\pi$
$71$	2.28907			0.271663			0.135831	+	0.990732i	$0.456629\pi$
$72$	2.86149	+	0.901046i	0.337230	+	0.106189i
$73$	6.16188	+	10.6727i	0.721193	+	1.24914i	0.960522	+	0.278205i	$0.0897393\pi$
$73$	6.16188	+	10.6727i	0.721193	+	1.24914i	−0.239329	+	0.970939i	$0.576927\pi$
$74$	1.59659	−	2.76537i	0.185599	−	0.321467i
$75$	1.08388	−	1.35100i	0.125155	−	0.156000i
$76$	4.21311	−	7.29732i	0.483277	−	0.837060i
$77$	0.351920	+	13.9891i	0.0401050	+	1.59421i
$78$	2.26607	−	2.82455i	0.256582	−	0.319817i
$79$	−5.25613			−0.591360			−0.295680	−	0.955287i	$-0.595546\pi$
$79$	−5.25613			−0.591360			−0.295680	+	0.955287i	$0.595546\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	7.37623	+	5.15667i	0.819581	+	0.572963i
$82$	−1.51734	+	2.62811i	−0.167562	+	0.290226i
$83$	−3.46154	−	5.99556i	−0.379953	−	0.658099i	0.611102	−	0.791552i	$-0.290727\pi$
$83$	−3.46154	−	5.99556i	−0.379953	−	0.658099i	−0.991055	+	0.133454i	$0.957393\pi$
$84$	4.22755	−	1.76858i	0.461263	−	0.192967i
$85$	−2.66689	+	4.61919i	−0.289265	+	0.501021i
$86$	−1.77230	−	3.06971i	−0.191112	−	0.331016i
$87$	−0.731958	−	1.88118i	−0.0784741	−	0.201684i
$88$	2.64454	−	4.58047i	0.281908	−	0.488280i
$89$	6.37499	−	11.0418i	0.675747	−	1.17043i	−0.300503	−	0.953781i	$-0.597154\pi$
$89$	6.37499	−	11.0418i	0.675747	−	1.17043i	0.976250	−	0.216648i	$-0.0695122\pi$
$90$	−0.650416	−	2.92864i	−0.0685598	−	0.308706i
$91$	−0.139110	−	5.52974i	−0.0145827	−	0.579674i
$92$	−2.71224	−	4.69774i	−0.282771	−	0.489773i
$93$	11.6015	+	1.78342i	1.20302	+	0.184932i
$94$	9.36786			0.966221
$95$	−8.42622			−0.864512
$96$	−1.71194	−	0.263165i	−0.174724	−	0.0268592i
$97$	3.09361	+	5.35829i	0.314109	+	0.544052i	0.979248	−	0.202667i	$-0.0649611\pi$
$97$	3.09361	+	5.35829i	0.314109	+	0.544052i	−0.665139	+	0.746720i	$0.731628\pi$
$98$	3.19076	−	6.23049i	0.322315	−	0.629375i
$99$	11.6945	−	10.7241i	1.17534	−	1.07781i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−8.21774	+	14.2335i	−0.817696	+	1.41629i	0.0896797	+	0.995971i	$0.471416\pi$
$101$	−8.21774	+	14.2335i	−0.817696	+	1.41629i	−0.907376	+	0.420320i	$0.861918\pi$
$102$	3.34995	+	8.60961i	0.331694	+	0.852478i
$103$	−2.21281	−	3.83270i	−0.218035	−	0.377647i	0.736172	−	0.676794i	$-0.236631\pi$
$103$	−2.21281	−	3.83270i	−0.218035	−	0.377647i	−0.954207	+	0.299147i	$0.903298\pi$
$104$	−1.04535	+	1.81060i	−0.102505	+	0.177544i
$105$	−3.64540	−	2.77687i	−0.355755	−	0.270995i
$106$	3.71311	+	6.43129i	0.360649	+	0.624663i
$107$	−0.919326	+	1.59232i	−0.0888746	+	0.153935i	−0.907036	−	0.421054i	$-0.861660\pi$
$107$	−0.919326	+	1.59232i	−0.0888746	+	0.153935i	0.818161	+	0.574989i	$0.194994\pi$
$108$	−4.66158	−	2.29558i	−0.448561	−	0.220892i
$109$	2.06001	+	3.56804i	0.197313	+	0.341756i	0.947656	−	0.319292i	$-0.103445\pi$
$109$	2.06001	+	3.56804i	0.197313	+	0.341756i	−0.750343	+	0.661048i	$0.770112\pi$
$110$	−5.28907			−0.504293
$111$	−3.46101	+	4.31398i	−0.328504	+	0.409465i
$112$	−2.25729	+	1.38008i	−0.213294	+	0.130405i
$113$	0.259747	−	0.449896i	0.0244350	−	0.0423226i	−0.853549	−	0.521012i	$-0.825555\pi$
$113$	0.259747	−	0.449896i	0.0244350	−	0.0423226i	0.877984	+	0.478689i	$0.158888\pi$
$114$	−9.13300	+	11.3838i	−0.855383	+	1.06619i
$115$	−2.71224	+	4.69774i	−0.252918	+	0.438066i
$116$	0.582710	+	1.00928i	0.0541033	+	0.0937097i
$117$	−4.62270	+	4.23911i	−0.427369	+	0.391906i
$118$	10.2030			0.939266
$119$	12.3948	+	6.74634i	1.13623	+	0.618436i
$120$	0.628063	+	1.61417i	0.0573341	+	0.147353i
$121$	−8.48714	−	14.7002i	−0.771558	−	1.33638i
$122$	−14.7350			−1.33405
$123$	3.28923	−	4.09986i	0.296580	−	0.369672i
$124$	−6.77682			−0.608576
$125$	1.00000			0.0894427
$126$	−7.70274	+	1.91516i	−0.686214	+	0.170616i
$127$	−21.4515			−1.90351			−0.951754	−	0.306861i	$-0.900721\pi$
$127$	−21.4515			−1.90351			−0.951754	+	0.306861i	$0.900721\pi$
$128$	1.00000			0.0883883
$129$	2.22623	+	5.72158i	0.196009	+	0.503757i
$130$	2.09071			0.183367
$131$	6.44187	+	11.1577i	0.562829	+	0.974848i	0.997248	+	0.0741376i	$0.0236204\pi$
$131$	6.44187	+	11.1577i	0.562829	+	0.974848i	−0.434419	+	0.900711i	$0.643046\pi$
$132$	−5.73271	+	7.14555i	−0.498968	+	0.621940i
$133$	0.560657	+	22.2866i	0.0486152	+	1.93250i
$134$	8.39063			0.724840
$135$	0.342757	+	5.18484i	0.0294998	+	0.446240i
$136$	−2.66689	−	4.61919i	−0.228684	−	0.396092i
$137$	3.36628	−	5.83057i	0.287601	−	0.498139i	−0.685636	−	0.727945i	$-0.740476\pi$
$137$	3.36628	−	5.83057i	0.287601	−	0.498139i	0.973237	+	0.229806i	$0.0738091\pi$
$138$	3.40692	+	8.75602i	0.290016	+	0.745362i
$139$	−0.149027	+	0.258123i	−0.0126403	+	0.0218937i	−0.872276	−	0.489013i	$-0.837357\pi$
$139$	−0.149027	+	0.258123i	−0.0126403	+	0.0218937i	0.859636	+	0.510907i	$0.170690\pi$
$140$	2.32383	+	1.26483i	0.196400	+	0.106898i
$141$	−16.0372	−	2.46529i	−1.35058	−	0.207615i
$142$	2.28907			0.192095
$143$	5.52895	+	9.57642i	0.462354	+	0.800820i
$144$	2.86149	+	0.901046i	0.238457	+	0.0750872i
$145$	0.582710	−	1.00928i	0.0483915	−	0.0838165i
$146$	6.16188	+	10.6727i	0.509961	+	0.883278i
$147$	−7.10204	+	9.82655i	−0.585766	+	0.810480i
$148$	1.59659	−	2.76537i	0.131239	−	0.227312i
$149$	−1.09461	−	1.89593i	−0.0896743	−	0.155320i	0.817699	−	0.575646i	$-0.195249\pi$
$149$	−1.09461	−	1.89593i	−0.0896743	−	0.155320i	−0.907373	+	0.420325i	$0.861916\pi$
$150$	1.08388	−	1.35100i	0.0884983	−	0.110309i
$151$	−0.336307	+	0.582502i	−0.0273683	+	0.0474033i	−0.879385	−	0.476111i	$-0.842046\pi$
$151$	−0.336307	+	0.582502i	−0.0273683	+	0.0474033i	0.852017	+	0.523514i	$0.175379\pi$
$152$	4.21311	−	7.29732i	0.341728	−	0.591891i
$153$	−3.46917	−	15.6207i	−0.280466	−	1.26286i
$154$	0.351920	+	13.9891i	0.0283585	+	1.12728i
$155$	3.38841	+	5.86890i	0.272164	+	0.471401i
$156$	2.26607	−	2.82455i	0.181431	−	0.226145i
$157$	2.86316			0.228505			0.114252	−	0.993452i	$-0.463553\pi$
$157$	2.86316			0.228505			0.114252	+	0.993452i	$0.463553\pi$
$158$	−5.25613			−0.418155
$159$	−4.66414	−	11.9872i	−0.369890	−	0.950644i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	12.6056	+	6.86107i	0.993459	+	0.540728i
$162$	7.37623	+	5.15667i	0.579532	+	0.405146i
$163$	−1.90458	+	3.29883i	−0.149178	+	0.258385i	−0.930924	−	0.365213i	$-0.880996\pi$
$163$	−1.90458	+	3.29883i	−0.149178	+	0.258385i	0.781746	+	0.623597i	$0.214330\pi$
$164$	−1.51734	+	2.62811i	−0.118484	+	0.205221i
$165$	9.05458	+	1.39190i	0.704898	+	0.108359i
$166$	−3.46154	−	5.99556i	−0.268668	−	0.465346i
$167$	3.00516	−	5.20508i	0.232546	−	0.402781i	−0.726011	−	0.687683i	$-0.758628\pi$
$167$	3.00516	−	5.20508i	0.232546	−	0.402781i	0.958557	+	0.284902i	$0.0919611\pi$
$168$	4.22755	−	1.76858i	0.326162	−	0.136449i
$169$	4.31447	+	7.47289i	0.331883	+	0.574838i
$170$	−2.66689	+	4.61919i	−0.204541	+	0.354275i
$171$	18.6310	−	17.0850i	1.42475	−	1.30652i
$172$	−1.77230	−	3.06971i	−0.135137	−	0.234063i
$173$	−11.4510			−0.870605			−0.435302	−	0.900284i	$-0.643359\pi$
$173$	−11.4510			−0.870605			−0.435302	+	0.900284i	$0.643359\pi$
$174$	−0.731958	−	1.88118i	−0.0554896	−	0.142612i
$175$	−0.0665372	−	2.64491i	−0.00502974	−	0.199937i
$176$	2.64454	−	4.58047i	0.199339	−	0.345266i
$177$	−17.4670	−	2.68508i	−1.31290	−	0.201823i
$178$	6.37499	−	11.0418i	0.477825	−	0.827618i
$179$	1.22849	+	2.12781i	0.0918218	+	0.159040i	0.908278	−	0.418368i	$-0.137398\pi$
$179$	1.22849	+	2.12781i	0.0918218	+	0.159040i	−0.816456	+	0.577408i	$0.804064\pi$
$180$	−0.650416	−	2.92864i	−0.0484791	−	0.218288i
$181$	15.2271			1.13182			0.565910	−	0.824467i	$-0.308525\pi$
$181$	15.2271			1.13182			0.565910	+	0.824467i	$0.308525\pi$
$182$	−0.139110	−	5.52974i	−0.0103115	−	0.409891i
$183$	25.2255	+	3.87774i	1.86472	+	0.286651i
$184$	−2.71224	−	4.69774i	−0.199949	−	0.346322i
$185$	−3.19317			−0.234767
$186$	11.6015	+	1.78342i	0.850665	+	0.130767i
$187$	−28.2107			−2.06297
$188$	9.36786			0.683221
$189$	13.6906	−	1.25155i	0.995848	−	0.0910367i
$190$	−8.42622			−0.611302
$191$	−4.40589			−0.318799			−0.159399	−	0.987214i	$-0.550956\pi$
$191$	−4.40589			−0.318799			−0.159399	+	0.987214i	$0.550956\pi$
$192$	−1.71194	−	0.263165i	−0.123549	−	0.0189923i
$193$	−5.03320			−0.362298			−0.181149	−	0.983456i	$-0.557982\pi$
$193$	−5.03320			−0.362298			−0.181149	+	0.983456i	$0.557982\pi$
$194$	3.09361	+	5.35829i	0.222108	+	0.384703i
$195$	−3.57917	−	0.550200i	−0.256309	−	0.0394007i
$196$	3.19076	−	6.23049i	0.227911	−	0.445035i
$197$	14.0137			0.998431			0.499216	−	0.866478i	$-0.333622\pi$
$197$	14.0137			0.998431			0.499216	+	0.866478i	$0.333622\pi$
$198$	11.6945	−	10.7241i	0.831094	−	0.762130i
$199$	−4.47788	−	7.75591i	−0.317428	−	0.549802i	0.662522	−	0.749042i	$-0.269486\pi$
$199$	−4.47788	−	7.75591i	−0.317428	−	0.549802i	−0.979951	+	0.199240i	$0.936153\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−14.3643	−	2.20812i	−1.01318	−	0.155749i
$202$	−8.21774	+	14.2335i	−0.578198	+	1.00147i
$203$	−2.70824	−	1.47406i	−0.190081	−	0.103459i
$204$	3.34995	+	8.60961i	0.234543	+	0.602793i
$205$	3.03468			0.211951
$206$	−2.21281	−	3.83270i	−0.154174	−	0.267037i
$207$	−3.52817	−	15.8864i	−0.245225	−	1.10418i
$208$	−1.04535	+	1.81060i	−0.0724822	+	0.125543i
$209$	−22.2834	−	38.5960i	−1.54138	−	2.66974i
$210$	−3.64540	−	2.77687i	−0.251557	−	0.191622i
$211$	−14.4945	+	25.1052i	−0.997843	+	1.72832i	−0.442075	+	0.896978i	$0.645757\pi$
$211$	−14.4945	+	25.1052i	−0.997843	+	1.72832i	−0.555768	+	0.831337i	$0.687576\pi$
$212$	3.71311	+	6.43129i	0.255017	+	0.441703i
$213$	−3.91876	−	0.602403i	−0.268509	−	0.0412760i
$214$	−0.919326	+	1.59232i	−0.0628438	+	0.108849i
$215$	−1.77230	+	3.06971i	−0.120870	+	0.209353i
$216$	−4.66158	−	2.29558i	−0.317180	−	0.156195i
$217$	15.2973	−	9.35255i	1.03845	−	0.634893i
$218$	2.06001	+	3.56804i	0.139521	+	0.241658i
$219$	−7.74010	−	19.8926i	−0.523027	−	1.34422i
$220$	−5.28907			−0.356589
$221$	11.1514			0.750121
$222$	−3.46101	+	4.31398i	−0.232288	+	0.289536i
$223$	−7.16502	−	12.4102i	−0.479805	−	0.831047i	0.519927	−	0.854211i	$-0.325959\pi$
$223$	−7.16502	−	12.4102i	−0.479805	−	0.831047i	−0.999732	+	0.0231643i	$0.992626\pi$
$224$	−2.25729	+	1.38008i	−0.150822	+	0.0922105i
$225$	−2.21107	+	2.02760i	−0.147405	+	0.135173i
$226$	0.259747	−	0.449896i	0.0172781	−	0.0299266i
$227$	2.93565	−	5.08469i	0.194846	−	0.337482i	−0.752004	−	0.659158i	$-0.770913\pi$
$227$	2.93565	−	5.08469i	0.194846	−	0.337482i	0.946850	+	0.321676i	$0.104246\pi$
$228$	−9.13300	+	11.3838i	−0.604847	+	0.753913i
$229$	0.943042	+	1.63340i	0.0623180	+	0.107938i	0.895501	−	0.445059i	$-0.146817\pi$
$229$	0.943042	+	1.63340i	0.0623180	+	0.107938i	−0.833183	+	0.552997i	$0.813484\pi$
$230$	−2.71224	+	4.69774i	−0.178840	+	0.309760i
$231$	3.07898	−	24.0412i	0.202582	−	1.58180i
$232$	0.582710	+	1.00928i	0.0382568	+	0.0662627i
$233$	11.0050	−	19.0612i	0.720962	−	1.24874i	−0.239652	−	0.970859i	$-0.577033\pi$
$233$	11.0050	−	19.0612i	0.720962	−	1.24874i	0.960615	−	0.277884i	$-0.0896332\pi$
$234$	−4.62270	+	4.23911i	−0.302196	+	0.277119i
$235$	−4.68393	−	8.11280i	−0.305546	−	0.529221i
$236$	10.2030			0.664161
$237$	8.99818	+	1.38323i	0.584495	+	0.0898503i
$238$	12.3948	+	6.74634i	0.803435	+	0.437300i
$239$	−5.18227	+	8.97595i	−0.335213	+	0.580606i	−0.983526	−	0.180768i	$-0.942142\pi$
$239$	−5.18227	+	8.97595i	−0.335213	+	0.580606i	0.648313	+	0.761374i	$0.275475\pi$
$240$	0.628063	+	1.61417i	0.0405413	+	0.104194i
$241$	8.24738	−	14.2849i	0.531260	−	0.920170i	−0.468074	−	0.883689i	$-0.655052\pi$
$241$	8.24738	−	14.2849i	0.531260	−	0.920170i	0.999334	−	0.0364805i	$-0.0116147\pi$
$242$	−8.48714	−	14.7002i	−0.545574	−	0.944962i
$243$	−11.2706	−	10.7691i	−0.723011	−	0.690837i
$244$	−14.7350			−0.943313
$245$	−6.99115	+	0.351971i	−0.446648	+	0.0224866i
$246$	3.28923	−	4.09986i	0.209713	−	0.261398i
$247$	8.80837	+	15.2565i	0.560463	+	0.970751i
$248$	−6.77682			−0.430328
$249$	4.34813	+	11.1750i	0.275552	+	0.708187i
$250$	1.00000			0.0632456
$251$	15.2937			0.965333			0.482666	−	0.875804i	$-0.339668\pi$
$251$	15.2937			0.965333			0.482666	+	0.875804i	$0.339668\pi$
$252$	−7.70274	+	1.91516i	−0.485227	+	0.120644i
$253$	−28.6905			−1.80375
$254$	−21.4515			−1.34598
$255$	5.78116	−	7.20594i	0.362031	−	0.451254i
$256$	1.00000			0.0625000
$257$	9.57653	+	16.5870i	0.597368	+	1.03467i	0.993208	+	0.116352i	$0.0371200\pi$
$257$	9.57653	+	16.5870i	0.597368	+	1.03467i	−0.395841	+	0.918319i	$0.629547\pi$
$258$	2.22623	+	5.72158i	0.138599	+	0.356210i
$259$	0.212465	+	8.44567i	0.0132019	+	0.524788i
$260$	2.09071			0.129660
$261$	0.758008	+	3.41310i	0.0469195	+	0.211266i
$262$	6.44187	+	11.1577i	0.397980	+	0.689322i
$263$	7.94110	−	13.7544i	0.489669	−	0.848132i	−0.510260	−	0.860020i	$-0.670451\pi$
$263$	7.94110	−	13.7544i	0.489669	−	0.848132i	0.999929	+	0.0118883i	$0.00378427\pi$
$264$	−5.73271	+	7.14555i	−0.352824	+	0.439778i
$265$	3.71311	−	6.43129i	0.228095	−	0.395071i
$266$	0.560657	+	22.2866i	0.0343761	+	1.36648i
$267$	−13.8194	+	17.2252i	−0.845735	+	1.05417i
$268$	8.39063			0.512539
$269$	12.4222	+	21.5160i	0.757398	+	1.31185i	0.944173	+	0.329449i	$0.106863\pi$
$269$	12.4222	+	21.5160i	0.757398	+	1.31185i	−0.186775	+	0.982403i	$0.559804\pi$
$270$	0.342757	+	5.18484i	0.0208595	+	0.315539i
$271$	13.9586	−	24.1771i	0.847927	−	1.46865i	−0.0351276	−	0.999383i	$-0.511184\pi$
$271$	13.9586	−	24.1771i	0.847927	−	1.46865i	0.883055	−	0.469270i	$-0.155483\pi$
$272$	−2.66689	−	4.61919i	−0.161704	−	0.280079i
$273$	−1.21709	+	9.50320i	−0.0736613	+	0.575160i
$274$	3.36628	−	5.83057i	0.203364	−	0.352237i
$275$	2.64454	+	4.58047i	0.159472	+	0.276213i
$276$	3.40692	+	8.75602i	0.205072	+	0.527051i
$277$	9.85930	−	17.0768i	0.592388	−	1.02605i	−0.401522	−	0.915849i	$-0.631519\pi$
$277$	9.85930	−	17.0768i	0.592388	−	1.02605i	0.993910	−	0.110196i	$-0.0351480\pi$
$278$	−0.149027	+	0.258123i	−0.00893807	+	0.0154812i
$279$	−19.3918	−	6.10622i	−1.16096	−	0.365570i
$280$	2.32383	+	1.26483i	0.138876	+	0.0755883i
$281$	4.54841	+	7.87807i	0.271335	+	0.469966i	0.969204	−	0.246259i	$-0.0792015\pi$
$281$	4.54841	+	7.87807i	0.271335	+	0.469966i	−0.697869	+	0.716226i	$0.745868\pi$
$282$	−16.0372	−	2.46529i	−0.955003	−	0.146806i
$283$	0.959660			0.0570459			0.0285229	−	0.999593i	$-0.490920\pi$
$283$	0.959660			0.0570459			0.0285229	+	0.999593i	$0.490920\pi$
$284$	2.28907			0.135831
$285$	14.4252	+	2.21749i	0.854475	+	0.131352i
$286$	5.52895	+	9.57642i	0.326933	+	0.566265i
$287$	−0.201919	−	8.02647i	−0.0119189	−	0.473788i
$288$	2.86149	+	0.901046i	0.168615	+	0.0530946i
$289$	−5.72458	+	9.91527i	−0.336740	+	0.583251i
$290$	0.582710	−	1.00928i	0.0342179	−	0.0592672i
$291$	−3.88597	−	9.98721i	−0.227799	−	0.585461i
$292$	6.16188	+	10.6727i	0.360597	+	0.624572i
$293$	12.9193	−	22.3769i	0.754753	−	1.30727i	−0.190744	−	0.981640i	$-0.561090\pi$
$293$	12.9193	−	22.3769i	0.754753	−	1.30727i	0.945497	−	0.325630i	$-0.105577\pi$
$294$	−7.10204	+	9.82655i	−0.414199	+	0.573096i
$295$	−5.10152	−	8.83609i	−0.297022	−	0.514457i
$296$	1.59659	−	2.76537i	0.0927997	−	0.160734i
$297$	−22.8426	+	15.2815i	−1.32546	+	0.886721i
$298$	−1.09461	−	1.89593i	−0.0634093	−	0.109828i
$299$	11.3410			0.655867
$300$	1.08388	−	1.35100i	0.0625777	−	0.0780002i
$301$	8.23705	+	4.48333i	0.474776	+	0.258415i
$302$	−0.336307	+	0.582502i	−0.0193523	+	0.0335192i
$303$	17.8141	−	22.2044i	1.02339	−	1.27561i
$304$	4.21311	−	7.29732i	0.241638	−	0.418530i
$305$	7.36751	+	12.7609i	0.421863	+	0.730687i
$306$	−3.46917	−	15.6207i	−0.198319	−	0.892978i
$307$	23.6397			1.34919			0.674595	−	0.738188i	$-0.264318\pi$
$307$	23.6397			1.34919			0.674595	+	0.738188i	$0.264318\pi$
$308$	0.351920	+	13.9891i	0.0200525	+	0.797105i
$309$	2.77957	+	7.14369i	0.158124	+	0.406390i
$310$	3.38841	+	5.86890i	0.192449	+	0.333331i
$311$	−13.2270			−0.750032			−0.375016	−	0.927018i	$-0.622363\pi$
$311$	−13.2270			−0.750032			−0.375016	+	0.927018i	$0.622363\pi$
$312$	2.26607	−	2.82455i	0.128291	−	0.159909i
$313$	4.82630			0.272799			0.136399	−	0.990654i	$-0.456447\pi$
$313$	4.82630			0.272799			0.136399	+	0.990654i	$0.456447\pi$
$314$	2.86316			0.161577
$315$	5.50994	+	5.71319i	0.310450	+	0.321902i
$316$	−5.25613			−0.295680
$317$	−15.6665			−0.879919			−0.439960	−	0.898018i	$-0.645007\pi$
$317$	−15.6665			−0.879919			−0.439960	+	0.898018i	$0.645007\pi$
$318$	−4.66414	−	11.9872i	−0.261552	−	0.672207i
$319$	6.16399			0.345117
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	1.99288	−	2.48402i	0.111231	−	0.138645i
$322$	12.6056	+	6.86107i	0.702482	+	0.382353i
$323$	−44.9436			−2.50073
$324$	7.37623	+	5.15667i	0.409791	+	0.286481i
$325$	−1.04535	−	1.81060i	−0.0579857	−	0.100434i
$326$	−1.90458	+	3.29883i	−0.105485	+	0.182705i
$327$	−2.58763	−	6.65040i	−0.143096	−	0.367768i
$328$	−1.51734	+	2.62811i	−0.0837811	+	0.145113i
$329$	−21.1460	+	12.9284i	−1.16582	+	0.712766i
$330$	9.05458	+	1.39190i	0.498438	+	0.0766215i
$331$	−19.0551			−1.04736			−0.523682	−	0.851914i	$-0.675442\pi$
$331$	−19.0551			−1.04736			−0.523682	+	0.851914i	$0.675442\pi$
$332$	−3.46154	−	5.99556i	−0.189977	−	0.329049i
$333$	7.06033	−	6.47447i	0.386904	−	0.354799i
$334$	3.00516	−	5.20508i	0.164435	−	0.284809i
$335$	−4.19531	−	7.26650i	−0.229215	−	0.397011i
$336$	4.22755	−	1.76858i	0.230632	−	0.0964837i
$337$	−6.71208	+	11.6257i	−0.365631	+	0.633291i	−0.988877	−	0.148735i	$-0.952480\pi$
$337$	−6.71208	+	11.6257i	−0.365631	+	0.633291i	0.623247	+	0.782025i	$0.285813\pi$
$338$	4.31447	+	7.47289i	0.234676	+	0.406472i
$339$	−0.563069	+	0.701839i	−0.0305817	+	0.0381187i
$340$	−2.66689	+	4.61919i	−0.144632	+	0.250510i
$341$	−17.9215	+	31.0410i	−0.970506	+	1.68097i
$342$	18.6310	−	17.0850i	1.00745	−	0.923851i
$343$	1.39610	+	18.4676i	0.0753825	+	0.997155i
$344$	−1.77230	−	3.06971i	−0.0955560	−	0.165508i
$345$	5.87948	−	7.32849i	0.316540	−	0.394553i
$346$	−11.4510			−0.615610
$347$	0.855476			0.0459243			0.0229622	−	0.999736i	$-0.492690\pi$
$347$	0.855476			0.0459243			0.0229622	+	0.999736i	$0.492690\pi$
$348$	−0.731958	−	1.88118i	−0.0392371	−	0.100842i
$349$	5.98519	+	10.3666i	0.320380	+	0.554914i	0.980566	−	0.196188i	$-0.0628562\pi$
$349$	5.98519	+	10.3666i	0.320380	+	0.554914i	−0.660187	+	0.751102i	$0.729523\pi$
$350$	−0.0665372	−	2.64491i	−0.00355656	−	0.141377i
$351$	9.02938	−	6.04058i	0.481953	−	0.322422i
$352$	2.64454	−	4.58047i	0.140954	−	0.244140i
$353$	−8.55996	+	14.8263i	−0.455601	+	0.789123i	−0.998723	−	0.0505305i	$-0.983909\pi$
$353$	−8.55996	+	14.8263i	−0.455601	+	0.789123i	0.543122	+	0.839654i	$0.317242\pi$
$354$	−17.4670	−	2.68508i	−0.928361	−	0.142710i
$355$	−1.14454	−	1.98239i	−0.0607456	−	0.105215i
$356$	6.37499	−	11.0418i	0.337874	−	0.585214i
$357$	−19.4438	−	14.8112i	−1.02907	−	0.783893i
$358$	1.22849	+	2.12781i	0.0649278	+	0.112458i
$359$	14.0850	−	24.3960i	0.743380	−	1.28757i	−0.207567	−	0.978221i	$-0.566555\pi$
$359$	14.0850	−	24.3960i	0.743380	−	1.28757i	0.950948	−	0.309352i	$-0.100112\pi$
$360$	−0.650416	−	2.92864i	−0.0342799	−	0.154353i
$361$	−26.0006	−	45.0343i	−1.36845	−	2.37023i
$362$	15.2271			0.800317
$363$	10.6609	+	27.3993i	0.559553	+	1.43809i
$364$	−0.139110	−	5.52974i	−0.00729133	−	0.289837i
$365$	6.16188	−	10.6727i	0.322527	−	0.558634i
$366$	25.2255	+	3.87774i	1.31856	+	0.202693i
$367$	−5.26160	+	9.11336i	−0.274653	+	0.475714i	−0.970048	−	0.242915i	$-0.921896\pi$
$367$	−5.26160	+	9.11336i	−0.274653	+	0.475714i	0.695394	+	0.718628i	$0.255230\pi$
$368$	−2.71224	−	4.69774i	−0.141385	−	0.244887i
$369$	−6.70990	+	6.15312i	−0.349304	+	0.320319i
$370$	−3.19317			−0.166005
$371$	−17.2573	−	9.39294i	−0.895954	−	0.487657i
$372$	11.6015	+	1.78342i	0.601511	+	0.0924661i
$373$	8.18913	+	14.1840i	0.424017	+	0.734419i	0.996328	−	0.0856174i	$-0.0272863\pi$
$373$	8.18913	+	14.1840i	0.424017	+	0.734419i	−0.572311	+	0.820037i	$0.693953\pi$
$374$	−28.2107			−1.45874
$375$	−1.71194	−	0.263165i	−0.0884043	−	0.0135898i
$376$	9.36786			0.483110
$377$	−2.43655			−0.125489
$378$	13.6906	−	1.25155i	0.704171	−	0.0643727i
$379$	27.2786			1.40121			0.700603	−	0.713551i	$-0.252915\pi$
$379$	27.2786			1.40121			0.700603	+	0.713551i	$0.252915\pi$
$380$	−8.42622			−0.432256
$381$	36.7236	+	5.64527i	1.88141	+	0.289216i
$382$	−4.40589			−0.225425
$383$	11.2144	+	19.4239i	0.573030	+	0.992516i	0.996253	+	0.0864909i	$0.0275653\pi$
$383$	11.2144	+	19.4239i	0.573030	+	0.992516i	−0.423223	+	0.906026i	$0.639101\pi$
$384$	−1.71194	−	0.263165i	−0.0873622	−	0.0134296i
$385$	11.9390	−	7.29934i	0.608467	−	0.372009i
$386$	−5.03320			−0.256183
$387$	−2.30546	−	10.3809i	−0.117193	−	0.527689i
$388$	3.09361	+	5.35829i	0.157054	+	0.272026i
$389$	10.4413	−	18.0849i	0.529397	−	0.916942i	−0.470015	−	0.882658i	$-0.655752\pi$
$389$	10.4413	−	18.0849i	0.529397	−	0.916942i	0.999412	−	0.0342841i	$-0.0109151\pi$
$390$	−3.57917	−	0.550200i	−0.181238	−	0.0278605i
$391$	−14.4665	+	25.0567i	−0.731602	+	1.26717i
$392$	3.19076	−	6.23049i	0.161158	−	0.314688i
$393$	−8.09181	−	20.7965i	−0.408178	−	1.04905i
$394$	14.0137			0.705998
$395$	2.62806	+	4.55194i	0.132232	+	0.229033i
$396$	11.6945	−	10.7241i	0.587672	−	0.538907i
$397$	−4.23067	+	7.32774i	−0.212331	+	0.367769i	−0.952444	−	0.304715i	$-0.901439\pi$
$397$	−4.23067	+	7.32774i	−0.212331	+	0.367769i	0.740112	+	0.672483i	$0.234772\pi$
$398$	−4.47788	−	7.75591i	−0.224456	−	0.388769i
$399$	4.90525	−	38.3010i	0.245569	−	1.91745i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−9.69991	−	16.8007i	−0.484390	−	0.838989i	0.515449	−	0.856920i	$-0.327625\pi$
$401$	−9.69991	−	16.8007i	−0.484390	−	0.838989i	−0.999839	+	0.0179318i	$0.994292\pi$
$402$	−14.3643	−	2.20812i	−0.716425	−	0.110131i
$403$	7.08417	−	12.2701i	0.352887	−	0.611219i
$404$	−8.21774	+	14.2335i	−0.408848	+	0.708146i
$405$	0.777687	−	8.96634i	0.0386436	−	0.445541i
$406$	−2.70824	−	1.47406i	−0.134408	−	0.0731566i
$407$	−8.44446	−	14.6262i	−0.418576	−	0.724995i
$408$	3.34995	+	8.60961i	0.165847	+	0.426239i
$409$	14.7215			0.727933			0.363966	−	0.931412i	$-0.381422\pi$
$409$	14.7215			0.727933			0.363966	+	0.931412i	$0.381422\pi$
$410$	3.03468			0.149872
$411$	−7.29727	+	9.09570i	−0.359948	+	0.448658i
$412$	−2.21281	−	3.83270i	−0.109017	−	0.188824i
$413$	−23.0313	+	14.0810i	−1.13329	+	0.692881i
$414$	−3.52817	−	15.8864i	−0.173400	−	0.780773i
$415$	−3.46154	+	5.99556i	−0.169920	+	0.294311i
$416$	−1.04535	+	1.81060i	−0.0512526	+	0.0887722i
$417$	0.323055	−	0.402673i	0.0158201	−	0.0197190i
$418$	−22.2834	−	38.5960i	−1.08992	−	1.88779i
$419$	−3.17371	+	5.49702i	−0.155046	+	0.268547i	−0.933076	−	0.359680i	$-0.882886\pi$
$419$	−3.17371	+	5.49702i	−0.155046	+	0.268547i	0.778030	+	0.628227i	$0.216219\pi$
$420$	−3.64540	−	2.77687i	−0.177878	−	0.135498i
$421$	5.59699	+	9.69427i	0.272781	+	0.472470i	0.969573	−	0.244803i	$-0.0787234\pi$
$421$	5.59699	+	9.69427i	0.272781	+	0.472470i	−0.696792	+	0.717273i	$0.745390\pi$
$422$	−14.4945	+	25.1052i	−0.705582	+	1.22210i
$423$	26.8060	+	8.44087i	1.30335	+	0.410409i
$424$	3.71311	+	6.43129i	0.180325	+	0.312331i
$425$	5.33378			0.258726
$426$	−3.91876	−	0.602403i	−0.189864	−	0.0291865i
$427$	33.2613	−	20.3355i	1.60963	−	0.984105i
$428$	−0.919326	+	1.59232i	−0.0444373	+	0.0769677i
$429$	−6.94506	−	17.8493i	−0.335310	−	0.861772i
$430$	−1.77230	+	3.06971i	−0.0854679	+	0.148035i
$431$	5.82854	+	10.0953i	0.280751	+	0.486275i	0.971570	−	0.236753i	$-0.0760831\pi$
$431$	5.82854	+	10.0953i	0.280751	+	0.486275i	−0.690819	+	0.723028i	$0.742750\pi$
$432$	−4.66158	−	2.29558i	−0.224280	−	0.110446i
$433$	13.7382			0.660215			0.330108	−	0.943943i	$-0.392915\pi$
$433$	13.7382			0.660215			0.330108	+	0.943943i	$0.392915\pi$
$434$	15.2973	−	9.35255i	0.734293	−	0.448937i
$435$	−1.26317	+	1.57449i	−0.0605646	+	0.0754909i
$436$	2.06001	+	3.56804i	0.0986565	+	0.170878i
$437$	−45.7079			−2.18650
$438$	−7.74010	−	19.8926i	−0.369836	−	0.950505i
$439$	31.5330			1.50499			0.752494	−	0.658599i	$-0.228851\pi$
$439$	31.5330			1.50499			0.752494	+	0.658599i	$0.228851\pi$
$440$	−5.28907			−0.252147
$441$	14.7443	−	14.9535i	0.702108	−	0.712070i
$442$	11.1514			0.530416
$443$	−19.2607			−0.915103			−0.457552	−	0.889183i	$-0.651274\pi$
$443$	−19.2607			−0.915103			−0.457552	+	0.889183i	$0.651274\pi$
$444$	−3.46101	+	4.31398i	−0.164252	+	0.204733i
$445$	−12.7500			−0.604407
$446$	−7.16502	−	12.4102i	−0.339273	−	0.587639i
$447$	1.37497	+	3.53378i	0.0650341	+	0.167142i
$448$	−2.25729	+	1.38008i	−0.106647	+	0.0652027i
$449$	0.289535			0.0136640			0.00683199	−	0.999977i	$-0.497825\pi$
$449$	0.289535			0.0136640			0.00683199	+	0.999977i	$0.497825\pi$
$450$	−2.21107	+	2.02760i	−0.104231	+	0.0955819i
$451$	8.02533	+	13.9003i	0.377898	+	0.654538i
$452$	0.259747	−	0.449896i	0.0122175	−	0.0211613i
$453$	0.729033	−	0.908704i	0.0342529	−	0.0426947i
$454$	2.93565	−	5.08469i	0.137777	−	0.238636i
$455$	−4.71934	+	2.88534i	−0.221246	+	0.135267i
$456$	−9.13300	+	11.3838i	−0.427692	+	0.533097i
$457$	−6.69849			−0.313342			−0.156671	−	0.987651i	$-0.550076\pi$
$457$	−6.69849			−0.313342			−0.156671	+	0.987651i	$0.550076\pi$
$458$	0.943042	+	1.63340i	0.0440655	+	0.0763236i
$459$	1.82819	+	27.6547i	0.0853326	+	1.29081i
$460$	−2.71224	+	4.69774i	−0.126459	+	0.219033i
$461$	−7.64617	−	13.2436i	−0.356118	−	0.616814i	0.631191	−	0.775627i	$-0.282566\pi$
$461$	−7.64617	−	13.2436i	−0.356118	−	0.616814i	−0.987309	+	0.158814i	$0.949233\pi$
$462$	3.07898	−	24.0412i	0.143247	−	1.11850i
$463$	0.952273	−	1.64938i	0.0442559	−	0.0766534i	−0.843049	−	0.537837i	$-0.819242\pi$
$463$	0.952273	−	1.64938i	0.0442559	−	0.0766534i	0.887305	+	0.461183i	$0.152575\pi$
$464$	0.582710	+	1.00928i	0.0270517	+	0.0468548i
$465$	−4.25627	−	10.9389i	−0.197380	−	0.507280i
$466$	11.0050	−	19.0612i	0.509797	−	0.882995i
$467$	11.0803	−	19.1917i	0.512736	−	0.888085i	−0.487155	−	0.873316i	$-0.661965\pi$
$467$	11.0803	−	19.1917i	0.512736	−	0.888085i	0.999891	−	0.0147694i	$-0.00470141\pi$
$468$	−4.62270	+	4.23911i	−0.213685	+	0.195953i
$469$	−18.9401	+	11.5797i	−0.874574	+	0.534703i
$470$	−4.68393	−	8.11280i	−0.216054	−	0.374216i
$471$	−4.90156	−	0.753483i	−0.225852	−	0.0347187i
$472$	10.2030			0.469633
$473$	−18.7476			−0.862017
$474$	8.99818	+	1.38323i	0.413300	+	0.0635338i
$475$	4.21311	+	7.29732i	0.193311	+	0.334824i
$476$	12.3948	+	6.74634i	0.568115	+	0.309218i
$477$	4.83013	+	21.7488i	0.221156	+	0.995807i
$478$	−5.18227	+	8.97595i	−0.237031	+	0.410551i
$479$	7.77973	−	13.4749i	0.355465	−	0.615683i	−0.631733	−	0.775186i	$-0.717656\pi$
$479$	7.77973	−	13.4749i	0.355465	−	0.615683i	0.987197	+	0.159503i	$0.0509893\pi$
$480$	0.628063	+	1.61417i	0.0286670	+	0.0736763i
$481$	3.33799	+	5.78157i	0.152199	+	0.263617i
$482$	8.24738	−	14.2849i	0.375658	−	0.650658i
$483$	−19.7744	−	15.0631i	−0.899768	−	0.685395i
$484$	−8.48714	−	14.7002i	−0.385779	−	0.668189i
$485$	3.09361	−	5.35829i	0.140474	−	0.243307i
$486$	−11.2706	−	10.7691i	−0.511246	−	0.488495i
$487$	13.4645	+	23.3212i	0.610136	+	1.05679i	0.991217	+	0.132245i	$0.0422185\pi$
$487$	13.4645	+	23.3212i	0.610136	+	1.05679i	−0.381081	+	0.924542i	$0.624448\pi$
$488$	−14.7350			−0.667023
$489$	4.12867	−	5.14619i	0.186705	−	0.232719i
$490$	−6.99115	+	0.351971i	−0.315828	+	0.0159004i
$491$	1.17935	−	2.04269i	0.0532232	−	0.0921852i	−0.838186	−	0.545384i	$-0.816384\pi$
$491$	1.17935	−	2.04269i	0.0532232	−	0.0921852i	0.891410	+	0.453199i	$0.149717\pi$
$492$	3.28923	−	4.09986i	0.148290	−	0.184836i
$493$	3.10805	−	5.38330i	0.139979	−	0.242451i
$494$	8.80837	+	15.2565i	0.396307	+	0.686425i
$495$	−15.1346	−	4.76570i	−0.680250	−	0.214202i
$496$	−6.77682			−0.304288
$497$	−5.16711	+	3.15910i	−0.231776	+	0.141705i
$498$	4.34813	+	11.1750i	0.194844	+	0.500764i
$499$	9.37453	+	16.2372i	0.419662	+	0.726875i	0.995905	−	0.0904026i	$-0.0288154\pi$
$499$	9.37453	+	16.2372i	0.419662	+	0.726875i	−0.576244	+	0.817278i	$0.695482\pi$
$500$	1.00000			0.0447214
$501$	−6.51445	+	8.11994i	−0.291044	+	0.362772i
$502$	15.2937			0.682593
$503$	3.17851			0.141723			0.0708614	−	0.997486i	$-0.477425\pi$
$503$	3.17851			0.141723			0.0708614	+	0.997486i	$0.477425\pi$
$504$	−7.70274	+	1.91516i	−0.343107	+	0.0853079i
$505$	16.4355			0.731370
$506$	−28.6905			−1.27545
$507$	−5.41953	−	13.9286i	−0.240690	−	0.618589i
$508$	−21.4515			−0.951754
$509$	−2.69672	−	4.67085i	−0.119530	−	0.207032i	0.800052	−	0.599931i	$-0.204805\pi$
$509$	−2.69672	−	4.67085i	−0.119530	−	0.207032i	−0.919581	+	0.392899i	$0.871472\pi$
$510$	5.78116	−	7.20594i	0.255994	−	0.319085i
$511$	−28.6383	−	15.5875i	−1.26689	−	0.689551i
$512$	1.00000			0.0441942
$513$	−36.3913	+	24.3455i	−1.60672	+	1.07488i
$514$	9.57653	+	16.5870i	0.422403	+	0.731623i
$515$	−2.21281	+	3.83270i	−0.0975081	+	0.168889i
$516$	2.22623	+	5.72158i	0.0980044	+	0.251878i
$517$	24.7736	−	42.9092i	1.08954	−	1.88714i
$518$	0.212465	+	8.44567i	0.00933517	+	0.371081i
$519$	19.6035	+	3.01351i	0.860497	+	0.132278i
$520$	2.09071			0.0916835
$521$	14.5383	+	25.1810i	0.636934	+	1.10320i	0.986102	+	0.166141i	$0.0531308\pi$
$521$	14.5383	+	25.1810i	0.636934	+	1.10320i	−0.349168	+	0.937060i	$0.613536\pi$
$522$	0.758008	+	3.41310i	0.0331771	+	0.149387i
$523$	−17.6575	+	30.5837i	−0.772108	+	1.33733i	0.164297	+	0.986411i	$0.447464\pi$
$523$	−17.6575	+	30.5837i	−0.772108	+	1.33733i	−0.936406	+	0.350920i	$0.885869\pi$
$524$	6.44187	+	11.1577i	0.281415	+	0.487424i
$525$	−0.582141	+	4.54545i	−0.0254067	+	0.198380i
$526$	7.94110	−	13.7544i	0.346248	−	0.599720i
$527$	18.0730	+	31.3034i	0.787273	+	1.36360i
$528$	−5.73271	+	7.14555i	−0.249484	+	0.310970i
$529$	−3.21250	+	5.56421i	−0.139674	+	0.241922i
$530$	3.71311	−	6.43129i	0.161287	−	0.279358i
$531$	29.1959	+	9.19341i	1.26699	+	0.398960i
$532$	0.560657	+	22.2866i	0.0243076	+	0.966248i
$533$	−3.17231	−	5.49461i	−0.137408	−	0.237998i
$534$	−13.8194	+	17.2252i	−0.598025	+	0.745409i
$535$	1.83865			0.0794919
$536$	8.39063			0.362420
$537$	−1.54314	−	3.96598i	−0.0665915	−	0.171145i
$538$	12.4222	+	21.5160i	0.535561	+	0.927619i
$539$	−20.1005	−	31.0919i	−0.865791	−	1.33922i
$540$	0.342757	+	5.18484i	0.0147499	+	0.223120i
$541$	10.7671	−	18.6492i	0.462914	−	0.801790i	−0.536191	−	0.844097i	$-0.680137\pi$
$541$	10.7671	−	18.6492i	0.462914	−	0.801790i	0.999105	+	0.0423068i	$0.0134707\pi$
$542$	13.9586	−	24.1771i	0.599575	−	1.03849i
$543$	−26.0679	−	4.00723i	−1.11868	−	0.171967i
$544$	−2.66689	−	4.61919i	−0.114342	−	0.198046i
$545$	2.06001	−	3.56804i	0.0882411	−	0.152838i
$546$	−1.21709	+	9.50320i	−0.0520864	+	0.406699i
$547$	2.71862	+	4.70879i	0.116240	+	0.201333i	0.918275	−	0.395944i	$-0.129583\pi$
$547$	2.71862	+	4.70879i	0.116240	+	0.201333i	−0.802035	+	0.597277i	$0.796249\pi$
$548$	3.36628	−	5.83057i	0.143800	−	0.249069i
$549$	−42.1641	−	13.2769i	−1.79952	−	0.566646i
$550$	2.64454	+	4.58047i	0.112763	+	0.195312i
$551$	9.82009			0.418350
$552$	3.40692	+	8.75602i	0.145008	+	0.372681i
$553$	11.8646	−	7.25388i	0.504535	−	0.308466i
$554$	9.85930	−	17.0768i	0.418881	−	0.725524i
$555$	5.46652	+	0.840331i	0.232041	+	0.0356700i
$556$	−0.149027	+	0.258123i	−0.00632017	+	0.0109469i
$557$	−6.35938	−	11.0148i	−0.269456	−	0.466711i	0.699266	−	0.714862i	$-0.253510\pi$
$557$	−6.35938	−	11.0148i	−0.269456	−	0.466711i	−0.968721	+	0.248151i	$0.920177\pi$
$558$	−19.3918	−	6.10622i	−0.820920	−	0.258497i
$559$	7.41072			0.313440
$560$	2.32383	+	1.26483i	0.0981998	+	0.0534490i
$561$	48.2951	+	7.42407i	2.03902	+	0.313445i
$562$	4.54841	+	7.87807i	0.191863	+	0.332316i
$563$	11.0295			0.464840			0.232420	−	0.972616i	$-0.425336\pi$
$563$	11.0295			0.464840			0.232420	+	0.972616i	$0.425336\pi$
$564$	−16.0372	−	2.46529i	−0.675289	−	0.103808i
$565$	−0.519495			−0.0218553
$566$	0.959660			0.0403375
$567$	−23.7669	−	1.46032i	−0.998118	−	0.0613277i
$568$	2.28907			0.0960473
$569$	−41.3292			−1.73261			−0.866304	−	0.499517i	$-0.833511\pi$
$569$	−41.3292			−1.73261			−0.866304	+	0.499517i	$0.833511\pi$
$570$	14.4252	+	2.21749i	0.604205	+	0.0928802i
$571$	−26.5859			−1.11258			−0.556292	−	0.830987i	$-0.687776\pi$
$571$	−26.5859			−1.11258			−0.556292	+	0.830987i	$0.687776\pi$
$572$	5.52895	+	9.57642i	0.231177	+	0.400410i
$573$	7.54262	+	1.15947i	0.315097	+	0.0484377i
$574$	−0.201919	−	8.02647i	−0.00842795	−	0.335019i
$575$	5.42448			0.226217
$576$	2.86149	+	0.901046i	0.119229	+	0.0375436i
$577$	1.70143	+	2.94696i	0.0708313	+	0.122683i	0.899266	−	0.437402i	$-0.144101\pi$
$577$	1.70143	+	2.94696i	0.0708313	+	0.122683i	−0.828435	+	0.560086i	$0.810768\pi$
$578$	−5.72458	+	9.91527i	−0.238111	+	0.412421i
$579$	8.61654	+	1.32456i	0.358091	+	0.0550469i
$580$	0.582710	−	1.00928i	0.0241957	−	0.0419082i
$581$	16.0881	+	8.75655i	0.667446	+	0.363283i
$582$	−3.88597	−	9.98721i	−0.161079	−	0.413983i
$583$	39.2778			1.62672
$584$	6.16188	+	10.6727i	0.254980	+	0.441639i
$585$	5.98253	+	1.88382i	0.247347	+	0.0778865i
$586$	12.9193	−	22.3769i	0.533691	−	0.924380i
$587$	15.0871	+	26.1316i	0.622710	+	1.07856i	0.988979	+	0.148056i	$0.0473015\pi$
$587$	15.0871	+	26.1316i	0.622710	+	1.07856i	−0.366269	+	0.930509i	$0.619365\pi$
$588$	−7.10204	+	9.82655i	−0.292883	+	0.405240i
$589$	−28.5515	+	49.4526i	−1.17644	+	2.03766i
$590$	−5.10152	−	8.83609i	−0.210026	−	0.363776i
$591$	−23.9906	−	3.68790i	−0.986840	−	0.151700i
$592$	1.59659	−	2.76537i	0.0656193	−	0.113656i
$593$	−7.47128	+	12.9406i	−0.306808	+	0.531408i	−0.977662	−	0.210182i	$-0.932594\pi$
$593$	−7.47128	+	12.9406i	−0.306808	+	0.531408i	0.670854	+	0.741590i	$0.265928\pi$
$594$	−22.8426	+	15.2815i	−0.937241	+	0.627006i
$595$	−0.354895	−	14.1074i	−0.0145493	−	0.578346i
$596$	−1.09461	−	1.89593i	−0.0448372	−	0.0776602i
$597$	5.62478	+	14.4561i	0.230207	+	0.591648i
$598$	11.3410			0.463768
$599$	13.4535			0.549694			0.274847	−	0.961488i	$-0.411373\pi$
$599$	13.4535			0.549694			0.274847	+	0.961488i	$0.411373\pi$
$600$	1.08388	−	1.35100i	0.0442491	−	0.0551544i
$601$	8.22867	+	14.2525i	0.335655	+	0.581371i	0.983610	−	0.180307i	$-0.0577092\pi$
$601$	8.22867	+	14.2525i	0.335655	+	0.581371i	−0.647956	+	0.761678i	$0.724376\pi$
$602$	8.23705	+	4.48333i	0.335717	+	0.182727i
$603$	24.0097	+	7.56034i	0.977750	+	0.307881i
$604$	−0.336307	+	0.582502i	−0.0136842	+	0.0237017i
$605$	−8.48714	+	14.7002i	−0.345051	+	0.597646i
$606$	17.8141	−	22.2044i	0.723647	−	0.901991i
$607$	−1.02135	−	1.76903i	−0.0414553	−	0.0718026i	0.844553	−	0.535472i	$-0.179866\pi$
$607$	−1.02135	−	1.76903i	−0.0414553	−	0.0718026i	−0.886009	+	0.463669i	$0.846533\pi$
$608$	4.21311	−	7.29732i	0.170864	−	0.295945i
$609$	4.24843	+	3.23623i	0.172155	+	0.131139i
$610$	7.36751	+	12.7609i	0.298302	+	0.516674i
$611$	−9.79272	+	16.9615i	−0.396171	+	0.686188i
$612$	−3.46917	−	15.6207i	−0.140233	−	0.631431i
$613$	7.70128	+	13.3390i	0.311052	+	0.538758i	0.978590	−	0.205818i	$-0.0659854\pi$
$613$	7.70128	+	13.3390i	0.311052	+	0.538758i	−0.667539	+	0.744575i	$0.732652\pi$
$614$	23.6397			0.954022
$615$	−5.19520	−	0.798622i	−0.209491	−	0.0322035i
$616$	0.351920	+	13.9891i	0.0141793	+	0.563639i
$617$	23.1260	−	40.0554i	0.931019	−	1.61257i	0.149434	−	0.988772i	$-0.452255\pi$
$617$	23.1260	−	40.0554i	0.931019	−	1.61257i	0.781584	−	0.623800i	$-0.214412\pi$
$618$	2.77957	+	7.14369i	0.111811	+	0.287361i
$619$	−11.9991	+	20.7830i	−0.482284	+	0.835340i	−0.999793	−	0.0203377i	$-0.993526\pi$
$619$	−11.9991	+	20.7830i	−0.482284	+	0.835340i	0.517510	+	0.855677i	$0.326859\pi$
$620$	3.38841	+	5.86890i	0.136082	+	0.235701i
$621$	1.85928	+	28.1250i	0.0746103	+	1.12862i
$622$	−13.2270			−0.530353
$623$	0.848348	+	33.7226i	0.0339883	+	1.35107i
$624$	2.26607	−	2.82455i	0.0907154	−	0.113072i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.82630			0.192898
$627$	27.9908	+	71.9384i	1.11785	+	2.87294i
$628$	2.86316			0.114252
$629$	−17.0317			−0.679097
$630$	5.50994	+	5.71319i	0.219521	+	0.227619i
$631$	−40.3072			−1.60461			−0.802303	−	0.596918i	$-0.796392\pi$
$631$	−40.3072			−1.60461			−0.802303	+	0.596918i	$0.796392\pi$
$632$	−5.25613			−0.209077
$633$	31.4206	−	39.1642i	1.24886	−	1.55664i
$634$	−15.6665			−0.622197
$635$	10.7257	+	18.5775i	0.425638	+	0.737226i
$636$	−4.66414	−	11.9872i	−0.184945	−	0.475322i
$637$	7.94549	+	12.2903i	0.314812	+	0.486958i
$638$	6.16399			0.244035
$639$	6.55015	+	2.06256i	0.259120	+	0.0815935i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−11.3894	+	19.7269i	−0.449853	+	0.779167i	−0.998376	−	0.0569677i	$-0.981857\pi$
$641$	−11.3894	+	19.7269i	−0.449853	+	0.779167i	0.548523	+	0.836135i	$0.315190\pi$
$642$	1.99288	−	2.48402i	0.0786525	−	0.0980366i
$643$	−11.0662	+	19.1672i	−0.436408	+	0.755880i	−0.997409	−	0.0719343i	$-0.977083\pi$
$643$	−11.0662	+	19.1672i	−0.436408	+	0.755880i	0.561002	+	0.827815i	$0.310416\pi$
$644$	12.6056	+	6.86107i	0.496730	+	0.270364i
$645$	3.84191	−	4.78876i	0.151275	−	0.188557i
$646$	−44.9436			−1.76828
$647$	10.6320	+	18.4151i	0.417986	+	0.723973i	0.995737	−	0.0922404i	$-0.0294028\pi$
$647$	10.6320	+	18.4151i	0.417986	+	0.723973i	−0.577751	+	0.816213i	$0.696069\pi$
$648$	7.37623	+	5.15667i	0.289766	+	0.202573i
$649$	26.9823	−	46.7347i	1.05915	−	1.83450i
$650$	−1.04535	−	1.81060i	−0.0410021	−	0.0710177i
$651$	−28.6493	+	11.9853i	−1.12285	+	0.469742i
$652$	−1.90458	+	3.29883i	−0.0745892	+	0.129192i
$653$	3.73284	+	6.46547i	0.146077	+	0.253013i	0.929774	−	0.368130i	$-0.120002\pi$
$653$	3.73284	+	6.46547i	0.146077	+	0.253013i	−0.783697	+	0.621143i	$0.786669\pi$
$654$	−2.58763	−	6.65040i	−0.101184	−	0.260051i
$655$	6.44187	−	11.1577i	0.251705	−	0.435966i
$656$	−1.51734	+	2.62811i	−0.0592422	+	0.102611i
$657$	8.01556	+	36.0919i	0.312717	+	1.40808i
$658$	−21.1460	+	12.9284i	−0.824358	+	0.504001i
$659$	−6.26129	−	10.8449i	−0.243905	−	0.422456i	0.717918	−	0.696128i	$-0.245095\pi$
$659$	−6.26129	−	10.8449i	−0.243905	−	0.422456i	−0.961823	+	0.273671i	$0.911762\pi$
$660$	9.05458	+	1.39190i	0.352449	+	0.0541796i
$661$	16.4773			0.640894			0.320447	−	0.947266i	$-0.396167\pi$
$661$	16.4773			0.640894			0.320447	+	0.947266i	$0.396167\pi$
$662$	−19.0551			−0.740598
$663$	−19.0905	−	2.93465i	−0.741412	−	0.113972i
$664$	−3.46154	−	5.99556i	−0.134334	−	0.232673i
$665$	19.0205	−	11.6289i	0.737582	−	0.450948i
$666$	7.06033	−	6.47447i	0.273582	−	0.250881i
$667$	3.16090	−	5.47484i	0.122391	−	0.211987i
$668$	3.00516	−	5.20508i	0.116273	−	0.201391i
$669$	9.00017	+	23.1311i	0.347967	+	0.894299i
$670$	−4.19531	−	7.26650i	−0.162079	−	0.280729i
$671$	−38.9673	+	67.4933i	−1.50432	+	2.60555i
$672$	4.22755	−	1.76858i	0.163081	−	0.0682243i
$673$	4.80375	+	8.32034i	0.185171	+	0.320725i	0.943634	−	0.330990i	$-0.107383\pi$
$673$	4.80375	+	8.32034i	0.185171	+	0.320725i	−0.758463	+	0.651716i	$0.774049\pi$
$674$	−6.71208	+	11.6257i	−0.258540	+	0.447804i
$675$	4.31882	−	2.88925i	0.166231	−	0.111207i
$676$	4.31447	+	7.47289i	0.165941	+	0.287419i
$677$	27.2956			1.04906			0.524528	−	0.851393i	$-0.324242\pi$
$677$	27.2956			1.04906			0.524528	+	0.851393i	$0.324242\pi$
$678$	−0.563069	+	0.701839i	−0.0216245	+	0.0269540i
$679$	−14.3781	−	7.82581i	−0.551779	−	0.300327i
$680$	−2.66689	+	4.61919i	−0.102270	+	0.177138i
$681$	−6.36376	+	7.93213i	−0.243860	+	0.303960i
$682$	−17.9215	+	31.0410i	−0.686251	+	1.18862i
$683$	−3.58533	−	6.20998i	−0.137189	−	0.237618i	0.789243	−	0.614082i	$-0.210473\pi$
$683$	−3.58533	−	6.20998i	−0.137189	−	0.237618i	−0.926432	+	0.376463i	$0.877140\pi$
$684$	18.6310	−	17.0850i	0.712374	−	0.653261i
$685$	−6.73256			−0.257238
$686$	1.39610	+	18.4676i	0.0533035	+	0.705095i
$687$	−1.18458	−	3.04446i	−0.0451946	−	0.116153i
$688$	−1.77230	−	3.06971i	−0.0675683	−	0.117032i
$689$	−15.5260			−0.591495
$690$	5.87948	−	7.32849i	0.223828	−	0.278991i
$691$	−16.7983			−0.639038			−0.319519	−	0.947580i	$-0.603521\pi$
$691$	−16.7983			−0.639038			−0.319519	+	0.947580i	$0.603521\pi$
$692$	−11.4510			−0.435302
$693$	−11.5978	+	40.3469i	−0.440566	+	1.53265i
$694$	0.855476			0.0324734
$695$	0.298055			0.0113059
$696$	−0.731958	−	1.88118i	−0.0277448	−	0.0713061i
$697$	16.1863			0.613100
$698$	5.98519	+	10.3666i	0.226543	+	0.392383i
$699$	−23.8562	+	29.7356i	−0.902324	+	1.12470i
$700$	−0.0665372	−	2.64491i	−0.00251487	−	0.0999684i
$701$	−7.02750			−0.265425			−0.132712	−	0.991155i	$-0.542369\pi$
$701$	−7.02750			−0.265425			−0.132712	+	0.991155i	$0.542369\pi$
$702$	9.02938	−	6.04058i	0.340792	−	0.227987i
$703$	−13.4532	−	23.3016i	−0.507396	−	0.878836i
$704$	2.64454	−	4.58047i	0.0996697	−	0.172633i
$705$	5.88361	+	15.1213i	0.221590	+	0.569501i
$706$	−8.55996	+	14.8263i	−0.322158	+	0.557994i
$707$	−1.09357	−	43.4705i	−0.0411280	−	1.63487i
$708$	−17.4670	−	2.68508i	−0.656450	−	0.100912i
$709$	−11.5692			−0.434489			−0.217245	−	0.976117i	$-0.569707\pi$
$709$	−11.5692			−0.434489			−0.217245	+	0.976117i	$0.569707\pi$
$710$	−1.14454	−	1.98239i	−0.0429537	−	0.0743979i
$711$	−15.0403	−	4.73601i	−0.564057	−	0.177614i
$712$	6.37499	−	11.0418i	0.238913	−	0.413809i
$713$	18.3804	+	31.8357i	0.688350	+	1.19226i
$714$	−19.4438	−	14.8112i	−0.727665	−	0.554296i
$715$	5.52895	−	9.57642i	0.206771	−	0.358138i
$716$	1.22849	+	2.12781i	0.0459109	+	0.0795200i
$717$	11.2339	−	14.0025i	0.419538	−	0.522934i
$718$	14.0850	−	24.3960i	0.525649	−	0.910451i
$719$	−8.00664	+	13.8679i	−0.298597	+	0.517186i	−0.975815	−	0.218597i	$-0.929852\pi$
$719$	−8.00664	+	13.8679i	−0.298597	+	0.517186i	0.677218	+	0.735783i	$0.263185\pi$
$720$	−0.650416	−	2.92864i	−0.0242396	−	0.109144i
$721$	10.2844	+	5.59768i	0.383011	+	0.208468i
$722$	−26.0006	−	45.0343i	−0.967642	−	1.67600i
$723$	−17.8783	+	22.2845i	−0.664901	+	0.828768i
$724$	15.2271			0.565910
$725$	−1.16542			−0.0432826
$726$	10.6609	+	27.3993i	0.395664	+	1.01688i
$727$	−26.2866	−	45.5297i	−0.974917	−	1.68860i	−0.680210	−	0.733017i	$-0.738112\pi$
$727$	−26.2866	−	45.5297i	−0.974917	−	1.68860i	−0.294706	−	0.955588i	$-0.595222\pi$
$728$	−0.139110	−	5.52974i	−0.00515575	−	0.204946i
$729$	16.4606	+	21.4021i	0.609652	+	0.792669i
$730$	6.16188	−	10.6727i	0.228061	−	0.395014i
$731$	−9.45305	+	16.3732i	−0.349634	+	0.605583i
$732$	25.2255	+	3.87774i	0.932361	+	0.143325i
$733$	−8.65788	−	14.9959i	−0.319786	−	0.553886i	0.660657	−	0.750688i	$-0.270278\pi$
$733$	−8.65788	−	14.9959i	−0.319786	−	0.553886i	−0.980443	+	0.196802i	$0.936944\pi$
$734$	−5.26160	+	9.11336i	−0.194209	+	0.336380i
$735$	12.0611	+	1.23727i	0.444879	+	0.0456374i
$736$	−2.71224	−	4.69774i	−0.0999745	−	0.173161i
$737$	22.1893	−	38.4330i	0.817354	−	1.41570i
$738$	−6.70990	+	6.15312i	−0.246995	+	0.226499i
$739$	15.2716	+	26.4513i	0.561776	+	0.973025i	0.997342	+	0.0728681i	$0.0232152\pi$
$739$	15.2716	+	26.4513i	0.561776	+	0.973025i	−0.435565	+	0.900157i	$0.643451\pi$
$740$	−3.19317			−0.117383
$741$	−11.0644	−	28.4364i	−0.406462	−	1.04464i
$742$	−17.2573	−	9.39294i	−0.633535	−	0.344826i
$743$	24.7349	−	42.8421i	0.907436	−	1.57173i	0.0898229	−	0.995958i	$-0.471370\pi$
$743$	24.7349	−	42.8421i	0.907436	−	1.57173i	0.817613	−	0.575768i	$-0.195297\pi$
$744$	11.6015	+	1.78342i	0.425332	+	0.0653834i
$745$	−1.09461	+	1.89593i	−0.0401036	+	0.0694614i
$746$	8.18913	+	14.1840i	0.299825	+	0.519313i
$747$	−4.50288	−	20.2752i	−0.164752	−	0.741832i
$748$	−28.2107			−1.03149
$749$	−0.122339	−	4.86308i	−0.00447016	−	0.177693i
$750$	−1.71194	−	0.263165i	−0.0625113	−	0.00960942i
$751$	16.0957	+	27.8786i	0.587342	+	1.01731i	0.994579	+	0.103984i	$0.0331589\pi$
$751$	16.0957	+	27.8786i	0.587342	+	1.01731i	−0.407237	+	0.913322i	$0.633508\pi$
$752$	9.36786			0.341611
$753$	−26.1820	−	4.02478i	−0.954125	−	0.146671i
$754$	−2.43655			−0.0887340
$755$	0.672615			0.0244790
$756$	13.6906	−	1.25155i	0.497924	−	0.0455183i
$757$	−0.422668			−0.0153621			−0.00768107	−	0.999971i	$-0.502445\pi$
$757$	−0.422668			−0.0153621			−0.00768107	+	0.999971i	$0.502445\pi$
$758$	27.2786			0.990802
$759$	49.1164	+	7.55032i	1.78281	+	0.274059i
$760$	−8.42622			−0.305651
$761$	−21.0714	−	36.4967i	−0.763836	−	1.32300i	−0.940860	−	0.338796i	$-0.889980\pi$
$761$	−21.0714	−	36.4967i	−0.763836	−	1.32300i	0.177024	−	0.984207i	$-0.443353\pi$
$762$	36.7236	+	5.64527i	1.33036	+	0.204507i
$763$	−9.57423	−	5.21114i	−0.346610	−	0.188656i
$764$	−4.40589			−0.159399
$765$	−11.7934	+	10.8148i	−0.426390	+	0.391008i
$766$	11.2144	+	19.4239i	0.405193	+	0.701815i
$767$	−10.6658	+	18.4737i	−0.385119	+	0.667045i
$768$	−1.71194	−	0.263165i	−0.0617744	−	0.00949615i
$769$	−20.1910	+	34.9718i	−0.728105	+	1.26112i	0.229578	+	0.973290i	$0.426265\pi$
$769$	−20.1910	+	34.9718i	−0.728105	+	1.26112i	−0.957683	+	0.287825i	$0.907068\pi$
$770$	11.9390	−	7.29934i	0.430251	−	0.263050i
$771$	−12.0293	−	30.9162i	−0.433226	−	1.11342i
$772$	−5.03320			−0.181149
$773$	−18.2886	−	31.6767i	−0.657794	−	1.13933i	−0.981185	−	0.193068i	$-0.938156\pi$
$773$	−18.2886	−	31.6767i	−0.657794	−	1.13933i	0.323391	−	0.946265i	$-0.395177\pi$
$774$	−2.30546	−	10.3809i	−0.0828682	−	0.373133i
$775$	3.38841	−	5.86890i	0.121715	−	0.210817i
$776$	3.09361	+	5.35829i	0.111054	+	0.192351i
$777$	1.85888	−	14.5144i	0.0666868	−	0.520701i
$778$	10.4413	−	18.0849i	0.374340	−	0.648376i
$779$	12.7854	+	22.1450i	0.458086	+	0.793429i
$780$	−3.57917	−	0.550200i	−0.128155	−	0.0197003i
$781$	6.05353	−	10.4850i	0.216612	−	0.375184i
$782$	−14.4665	+	25.0567i	−0.517320	+	0.896025i
$783$	−0.399456	−	6.04252i	−0.0142754	−	0.215942i
$784$	3.19076	−	6.23049i	0.113956	−	0.222518i
$785$	−1.43158	−	2.47957i	−0.0510953	−	0.0884996i
$786$	−8.09181	−	20.7965i	−0.288625	−	0.741787i
$787$	31.6161			1.12699			0.563497	−	0.826118i	$-0.309456\pi$
$787$	31.6161			1.12699			0.563497	+	0.826118i	$0.309456\pi$
$788$	14.0137			0.499216
$789$	−17.2144	+	21.4569i	−0.612848	+	0.763885i
$790$	2.62806	+	4.55194i	0.0935023	+	0.161951i
$791$	0.0345658	+	1.37402i	0.00122902	+	0.0488545i
$792$	11.6945	−	10.7241i	0.415547	−	0.381065i
$793$	15.4033	−	26.6793i	0.546987	−	0.947410i
$794$	−4.23067	+	7.32774i	−0.150141	+	0.260052i
$795$	−8.04912	+	10.0328i	−0.285473	+	0.355828i
$796$	−4.47788	−	7.75591i	−0.158714	−	0.274901i
$797$	13.3101	−	23.0538i	0.471468	−	0.816606i	−0.527999	−	0.849245i	$-0.677058\pi$
$797$	13.3101	−	23.0538i	0.471468	−	0.816606i	0.999467	+	0.0326384i	$0.0103910\pi$
$798$	4.90525	−	38.3010i	0.173644	−	1.35584i
$799$	−24.9830	−	43.2719i	−0.883836	−	1.53085i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	28.1911	−	25.8518i	0.996084	−	0.913429i
$802$	−9.69991	−	16.8007i	−0.342516	−	0.593254i
$803$	65.1812			2.30019
$804$	−14.3643	−	2.20812i	−0.506589	−	0.0778744i
$805$	−0.360930	−	14.3473i	−0.0127211	−	0.505676i
$806$	7.08417	−	12.2701i	0.249529	−	0.432197i
$807$	−15.6039	−	40.1032i	−0.549284	−	1.41170i
$808$	−8.21774	+	14.2335i	−0.289099	+	0.500735i
$809$	−20.5037	−	35.5135i	−0.720873	−	1.24859i	−0.960650	−	0.277761i	$-0.910408\pi$
$809$	−20.5037	−	35.5135i	−0.720873	−	1.24859i	0.239777	−	0.970828i	$-0.422926\pi$
$810$	0.777687	−	8.96634i	0.0273251	−	0.315045i
$811$	10.2292			0.359196			0.179598	−	0.983740i	$-0.442520\pi$
$811$	10.2292			0.359196			0.179598	+	0.983740i	$0.442520\pi$
$812$	−2.70824	−	1.47406i	−0.0950407	−	0.0517295i
$813$	−30.2589	+	37.7163i	−1.06123	+	1.32277i
$814$	−8.44446	−	14.6262i	−0.295978	−	0.512649i
$815$	3.80916			0.133429
$816$	3.34995	+	8.60961i	0.117272	+	0.301397i
$817$	−29.8676			−1.04493
$818$	14.7215			0.514726
$819$	4.58449	−	15.9486i	0.160195	−	0.557290i
$820$	3.03468			0.105976
$821$	25.1305			0.877061			0.438530	−	0.898716i	$-0.355499\pi$
$821$	25.1305			0.877061			0.438530	+	0.898716i	$0.355499\pi$
$822$	−7.29727	+	9.09570i	−0.254522	+	0.317249i
$823$	−17.5508			−0.611781			−0.305891	−	0.952067i	$-0.598954\pi$
$823$	−17.5508			−0.611781			−0.305891	+	0.952067i	$0.598954\pi$
$824$	−2.21281	−	3.83270i	−0.0770869	−	0.133518i
$825$	−3.32187	−	8.53745i	−0.115653	−	0.297236i
$826$	−23.0313	+	14.0810i	−0.801360	+	0.489941i
$827$	−17.6521			−0.613824			−0.306912	−	0.951738i	$-0.599296\pi$
$827$	−17.6521			−0.613824			−0.306912	+	0.951738i	$0.599296\pi$
$828$	−3.52817	−	15.8864i	−0.122612	−	0.552090i
$829$	10.7975	+	18.7017i	0.375011	+	0.649538i	0.990329	−	0.138741i	$-0.0443056\pi$
$829$	10.7975	+	18.7017i	0.375011	+	0.649538i	−0.615318	+	0.788279i	$0.710972\pi$
$830$	−3.46154	+	5.99556i	−0.120152	+	0.208109i
$831$	−21.3726	+	26.6399i	−0.741406	+	0.924127i
$832$	−1.04535	+	1.81060i	−0.0362411	+	0.0627714i
$833$	−37.2892	+	1.87733i	−1.29199	+	0.0650457i
$834$	0.323055	−	0.402673i	0.0111865	−	0.0139434i
$835$	−6.01031			−0.207995
$836$	−22.2834	−	38.5960i	−0.770689	−	1.33487i
$837$	31.5907	+	15.5567i	1.09193	+	0.537720i
$838$	−3.17371	+	5.49702i	−0.109634	+	0.189891i
$839$	−12.4252	−	21.5211i	−0.428966	−	0.742991i	0.567816	−	0.823156i	$-0.307789\pi$
$839$	−12.4252	−	21.5211i	−0.428966	−	0.742991i	−0.996782	+	0.0801650i	$0.974455\pi$
$840$	−3.64540	−	2.77687i	−0.125778	−	0.0958112i
$841$	13.8209	−	23.9385i	0.476583	−	0.825465i
$842$	5.59699	+	9.69427i	0.192885	+	0.334087i
$843$	−5.71337	−	14.6838i	−0.196779	−	0.505736i
$844$	−14.4945	+	25.1052i	−0.498922	+	0.864158i
$845$	4.31447	−	7.47289i	0.148422	−	0.257075i
$846$	26.8060	+	8.44087i	0.921610	+	0.290203i
$847$	39.4454	+	21.4696i	1.35536	+	0.737706i
$848$	3.71311	+	6.43129i	0.127509	+	0.220852i
$849$	−1.64288	−	0.252549i	−0.0563836	−	0.00866746i
$850$	5.33378			0.182947
$851$	−17.3213			−0.593766
$852$	−3.91876	−	0.602403i	−0.134254	−	0.0206380i
$853$	10.8030	+	18.7114i	0.369889	+	0.640667i	0.989548	−	0.144205i	$-0.0460624\pi$
$853$	10.8030	+	18.7114i	0.369889	+	0.640667i	−0.619659	+	0.784871i	$0.712729\pi$
$854$	33.2613	−	20.3355i	1.13818	−	0.695867i
$855$	−24.1115	−	7.59241i	−0.824597	−	0.259655i
$856$	−0.919326	+	1.59232i	−0.0314219	+	0.0544244i
$857$	15.2419	−	26.3997i	0.520652	−	0.901795i	−0.479060	−	0.877782i	$-0.659022\pi$
$857$	15.2419	−	26.3997i	0.520652	−	0.901795i	0.999712	−	0.0240131i	$-0.00764434\pi$
$858$	−6.94506	−	17.8493i	−0.237100	−	0.609365i
$859$	5.38449	+	9.32621i	0.183716	+	0.318206i	0.943143	−	0.332387i	$-0.107854\pi$
$859$	5.38449	+	9.32621i	0.183716	+	0.318206i	−0.759427	+	0.650593i	$0.774521\pi$
$860$	−1.77230	+	3.06971i	−0.0604349	+	0.104676i
$861$	−1.76661	+	13.7940i	−0.0602060	+	0.470098i
$862$	5.82854	+	10.0953i	0.198521	+	0.343848i
$863$	14.6312	−	25.3420i	0.498052	−	0.862651i	−0.501946	−	0.864899i	$-0.667382\pi$
$863$	14.6312	−	25.3420i	0.498052	−	0.862651i	0.999997	+	0.00224819i	$0.000715621\pi$
$864$	−4.66158	−	2.29558i	−0.158590	−	0.0780973i
$865$	5.72551	+	9.91687i	0.194673	+	0.337184i
$866$	13.7382			0.466843
$867$	12.4095	−	15.4678i	0.421449	−	0.525316i
$868$	15.2973	−	9.35255i	0.519223	−	0.317446i
$869$	−13.9000	+	24.0755i	−0.471526	+	0.816706i
$870$	−1.26317	+	1.57449i	−0.0428256	+	0.0533801i
$871$	−8.77117	+	15.1921i	−0.297200	+	0.514765i
$872$	2.06001	+	3.56804i	0.0697607	+	0.120829i
$873$	4.02427	+	18.1202i	0.136201	+	0.613275i
$874$	−45.7079			−1.54609
$875$	−2.25729	+	1.38008i	−0.0763105	+	0.0466552i
$876$	−7.74010	−	19.8926i	−0.261514	−	0.672109i
$877$	21.0051	+	36.3819i	0.709291	+	1.22853i	0.965121	+	0.261806i	$0.0843181\pi$
$877$	21.0051	+	36.3819i	0.709291	+	1.22853i	−0.255830	+	0.966722i	$0.582349\pi$
$878$	31.5330			1.06419
$879$	−28.0059	+	34.9080i	−0.944615	+	1.17742i
$880$	−5.28907			−0.178295
$881$	3.22903			0.108789			0.0543944	−	0.998520i	$-0.482677\pi$
$881$	3.22903			0.108789			0.0543944	+	0.998520i	$0.482677\pi$
$882$	14.7443	−	14.9535i	0.496466	−	0.503510i
$883$	−34.0160			−1.14473			−0.572365	−	0.819999i	$-0.693974\pi$
$883$	−34.0160			−1.14473			−0.572365	+	0.819999i	$0.693974\pi$
$884$	11.1514			0.375061
$885$	6.40815	+	16.4694i	0.215408	+	0.553613i
$886$	−19.2607			−0.647076
$887$	−1.90383	−	3.29753i	−0.0639243	−	0.110720i	0.832292	−	0.554337i	$-0.187028\pi$
$887$	−1.90383	−	3.29753i	−0.0639243	−	0.110720i	−0.896216	+	0.443617i	$0.853695\pi$
$888$	−3.46101	+	4.31398i	−0.116144	+	0.144768i
$889$	48.4223	−	29.6047i	1.62403	−	0.992911i
$890$	−12.7500			−0.427380
$891$	43.1267	−	20.1496i	1.44480	−	0.675038i
$892$	−7.16502	−	12.4102i	−0.239902	−	0.415523i
$893$	39.4678	−	68.3603i	1.32074	−	2.28759i
$894$	1.37497	+	3.53378i	0.0459860	+	0.118187i
$895$	1.22849	−	2.12781i	0.0410640	−	0.0711249i
$896$	−2.25729	+	1.38008i	−0.0754109	+	0.0461052i
$897$	−19.4151	−	2.98455i	−0.648252	−	0.0996513i
$898$	0.289535			0.00966190
$899$	−3.94892	−	6.83973i	−0.131704	−	0.228118i
$900$	−2.21107	+	2.02760i	−0.0737024	+	0.0675866i
$901$	19.8049	−	34.3031i	0.659797	−	1.14280i
$902$	8.02533	+	13.9003i	0.267214	+	0.462828i
$903$	−12.9215	−	9.84291i	−0.430001	−	0.327551i
$904$	0.259747	−	0.449896i	0.00863907	−	0.0149633i
$905$	−7.61354	−	13.1870i	−0.253083	−	0.438352i
$906$	0.729033	−	0.908704i	0.0242205	−	0.0301897i
$907$	17.5162	−	30.3389i	0.581615	−	1.00739i	−0.413673	−	0.910425i	$-0.635754\pi$
$907$	17.5162	−	30.3389i	0.581615	−	1.00739i	0.995288	−	0.0969611i	$-0.0309123\pi$
$908$	2.93565	−	5.08469i	0.0974228	−	0.168741i
$909$	−36.3401	+	33.3246i	−1.20532	+	1.10531i
$910$	−4.71934	+	2.88534i	−0.156445	+	0.0956481i
$911$	18.6271	+	32.2631i	0.617144	+	1.06893i	0.990004	+	0.141038i	$0.0450438\pi$
$911$	18.6271	+	32.2631i	0.617144	+	1.06893i	−0.372860	+	0.927888i	$0.621623\pi$
$912$	−9.13300	+	11.3838i	−0.302424	+	0.376957i
$913$	−36.6167			−1.21183
$914$	−6.69849			−0.221566
$915$	−9.25453	−	23.7848i	−0.305945	−	0.786301i
$916$	0.943042	+	1.63340i	0.0311590	+	0.0539690i
$917$	−29.9397	−	16.2958i	−0.988695	−	0.538135i
$918$	1.82819	+	27.6547i	0.0603392	+	0.912743i
$919$	−8.85959	+	15.3453i	−0.292251	+	0.506194i	−0.974342	−	0.225074i	$-0.927738\pi$
$919$	−8.85959	+	15.3453i	−0.292251	+	0.506194i	0.682091	+	0.731268i	$0.261071\pi$
$920$	−2.71224	+	4.69774i	−0.0894199	+	0.154880i
$921$	−40.4698	−	6.22115i	−1.33353	−	0.204994i
$922$	−7.64617	−	13.2436i	−0.251813	−	0.436153i
$923$	−2.39289	+	4.14460i	−0.0787628	+	0.136421i
$924$	3.07898	−	24.0412i	0.101291	−	0.790898i
$925$	1.59659	+	2.76537i	0.0524954	+	0.0909247i
$926$	0.952273	−	1.64938i	0.0312936	−	0.0542021i
$927$	−2.87849	−	12.9611i	−0.0945421	−	0.425697i
$928$	0.582710	+	1.00928i	0.0191284	+	0.0331314i
$929$	13.4210			0.440330			0.220165	−	0.975463i	$-0.429340\pi$
$929$	13.4210			0.440330			0.220165	+	0.975463i	$0.429340\pi$
$930$	−4.25627	−	10.9389i	−0.139569	−	0.358701i
$931$	−32.0229	−	49.5337i	−1.04951	−	1.62340i
$932$	11.0050	−	19.0612i	0.360481	−	0.624372i
$933$	22.6438	+	3.48087i	0.741324	+	0.113959i
$934$	11.0803	−	19.1917i	0.362559	−	0.627971i
$935$	14.1054	+	24.4312i	0.461295	+	0.798986i
$936$	−4.62270	+	4.23911i	−0.151098	+	0.138560i
$937$	−41.9854			−1.37160			−0.685801	−	0.727789i	$-0.740548\pi$
$937$	−41.9854			−1.37160			−0.685801	+	0.727789i	$0.740548\pi$
$938$	−18.9401	+	11.5797i	−0.618417	+	0.378092i
$939$	−8.26234	−	1.27011i	−0.269631	−	0.0414486i
$940$	−4.68393	−	8.11280i	−0.152773	−	0.264611i
$941$	−14.9024			−0.485803			−0.242901	−	0.970051i	$-0.578099\pi$
$941$	−14.9024			−0.485803			−0.242901	+	0.970051i	$0.578099\pi$
$942$	−4.90156	−	0.753483i	−0.159701	−	0.0245498i
$943$	16.4616			0.536063
$944$	10.2030			0.332081
$945$	−7.92919	−	11.2307i	−0.257937	−	0.365334i
$946$	−18.7476			−0.609538
$947$	43.1891			1.40346			0.701729	−	0.712444i	$-0.252412\pi$
$947$	43.1891			1.40346			0.701729	+	0.712444i	$0.252412\pi$
$948$	8.99818	+	1.38323i	0.292247	+	0.0449252i
$949$	−25.7653			−0.836378
$950$	4.21311	+	7.29732i	0.136691	+	0.236756i
$951$	26.8202	+	4.12288i	0.869703	+	0.133693i
$952$	12.3948	+	6.74634i	0.401718	+	0.218650i
$953$	−14.8153			−0.479916			−0.239958	−	0.970783i	$-0.577134\pi$
$953$	−14.8153			−0.479916			−0.239958	+	0.970783i	$0.577134\pi$
$954$	4.83013	+	21.7488i	0.156381	+	0.704142i
$955$	2.20294	+	3.81561i	0.0712856	+	0.123470i
$956$	−5.18227	+	8.97595i	−0.167607	+	0.290303i
$957$	−10.5524	−	1.62215i	−0.341111	−	0.0524366i
$958$	7.77973	−	13.4749i	0.251352	−	0.435354i
$959$	0.447966	+	17.8070i	0.0144656	+	0.575019i
$960$	0.628063	+	1.61417i	0.0202707	+	0.0520970i
$961$	14.9253			0.481460
$962$	3.33799	+	5.78157i	0.107621	+	0.186405i
$963$	−4.06539	+	3.72805i	−0.131006	+	0.120135i
$964$	8.24738	−	14.2849i	0.265630	−	0.460085i
$965$	2.51660	+	4.35888i	0.0810122	+	0.140317i
$966$	−19.7744	−	15.0631i	−0.636232	−	0.484647i
$967$	1.79834	−	3.11481i	0.0578306	−	0.100166i	−0.835661	−	0.549246i	$-0.814915\pi$
$967$	1.79834	−	3.11481i	0.0578306	−	0.100166i	0.893491	+	0.449080i	$0.148248\pi$
$968$	−8.48714	−	14.7002i	−0.272787	−	0.472481i
$969$	76.9408	+	11.8276i	2.47169	+	0.379956i
$970$	3.09361	−	5.35829i	0.0993299	−	0.172044i
$971$	8.50573	−	14.7324i	0.272962	−	0.472784i	−0.696657	−	0.717404i	$-0.745330\pi$
$971$	8.50573	−	14.7324i	0.272962	−	0.472784i	0.969619	+	0.244620i	$0.0786633\pi$
$972$	−11.2706	−	10.7691i	−0.361506	−	0.345418i
$973$	−0.0198317	−	0.788329i	−0.000635776	−	0.0252727i
$974$	13.4645	+	23.3212i	0.431431	+	0.747261i
$975$	1.31310	+	3.37475i	0.0420527	+	0.108078i
$976$	−14.7350			−0.471657
$977$	−5.95822			−0.190620			−0.0953102	−	0.995448i	$-0.530384\pi$
$977$	−5.95822			−0.190620			−0.0953102	+	0.995448i	$0.530384\pi$
$978$	4.12867	−	5.14619i	0.132020	−	0.164557i
$979$	−33.7178	−	58.4009i	−1.07762	−	1.86650i
$980$	−6.99115	+	0.351971i	−0.223324	+	0.0112433i
$981$	2.67972	+	12.0661i	0.0855570	+	0.385240i
$982$	1.17935	−	2.04269i	0.0376345	−	0.0651848i
$983$	−16.1418	+	27.9585i	−0.514844	+	0.891737i	0.485007	+	0.874510i	$0.338817\pi$
$983$	−16.1418	+	27.9585i	−0.514844	+	0.891737i	−0.999852	+	0.0172265i	$0.994516\pi$
$984$	3.28923	−	4.09986i	0.104857	−	0.130699i
$985$	−7.00683	−	12.1362i	−0.223256	−	0.386691i
$986$	3.10805	−	5.38330i	0.0989804	−	0.171439i
$987$	39.6031	−	16.5678i	1.26058	−	0.527358i
$988$	8.80837	+	15.2565i	0.280232	+	0.485375i
$989$	−9.61381	+	16.6516i	−0.305701	+	0.529490i
$990$	−15.1346	−	4.76570i	−0.481010	−	0.151464i
$991$	5.28676	+	9.15694i	0.167940	+	0.290880i	0.937695	−	0.347459i	$-0.112955\pi$
$991$	5.28676	+	9.15694i	0.167940	+	0.290880i	−0.769756	+	0.638339i	$0.779622\pi$
$992$	−6.77682			−0.215164
$993$	32.6212	+	5.01464i	1.03520	+	0.159135i
$994$	−5.16711	+	3.15910i	−0.163891	+	0.100201i
$995$	−4.47788	+	7.75591i	−0.141958	+	0.245879i
$996$	4.34813	+	11.1750i	0.137776	+	0.354094i
$997$	21.8168	−	37.7878i	0.690946	−	1.19675i	−0.280583	−	0.959830i	$-0.590528\pi$
$997$	21.8168	−	37.7878i	0.690946	−	1.19675i	0.971528	−	0.236923i	$-0.0761390\pi$
$998$	9.37453	+	16.2372i	0.296746	+	0.513979i
$999$	−13.7907	+	9.22588i	−0.436320	+	0.291894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.g.121.1	✓	12
3.2	odd	2		1890.2.i.g.1171.1		12
7.4	even	3		630.2.l.g.571.3	yes	12
9.2	odd	6		1890.2.l.g.1801.6		12
9.7	even	3		630.2.l.g.331.3	yes	12
21.11	odd	6		1890.2.l.g.361.6		12
63.11	odd	6		1890.2.i.g.991.1		12
63.25	even	3	inner	630.2.i.g.151.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.g.121.1	✓	12	1.1	even	1	trivial
630.2.i.g.151.1	yes	12	63.25	even	3	inner
630.2.l.g.331.3	yes	12	9.7	even	3
630.2.l.g.571.3	yes	12	7.4	even	3
1890.2.i.g.991.1		12	63.11	odd	6
1890.2.i.g.1171.1		12	3.2	odd	2
1890.2.l.g.361.6		12	21.11	odd	6
1890.2.l.g.1801.6		12	9.2	odd	6

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.71194 - 0.263165i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.71194 - 0.263165i) q^{6} +(-2.25729 + 1.38008i) q^{7} +1.00000 q^{8} +(2.86149 + 0.901046i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.71194 - 0.263165i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.71194 - 0.263165i) q^{6} +(-2.25729 + 1.38008i) q^{7} +1.00000 q^{8} +(2.86149 + 0.901046i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.64454 - 4.58047i) q^{11} +(-1.71194 - 0.263165i) q^{12} +(-1.04535 + 1.81060i) q^{13} +(-2.25729 + 1.38008i) q^{14} +(0.628063 + 1.61417i) q^{15} +1.00000 q^{16} +(-2.66689 - 4.61919i) q^{17} +(2.86149 + 0.901046i) q^{18} +(4.21311 - 7.29732i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(4.22755 - 1.76858i) q^{21} +(2.64454 - 4.58047i) q^{22} +(-2.71224 - 4.69774i) q^{23} +(-1.71194 - 0.263165i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.04535 + 1.81060i) q^{26} +(-4.66158 - 2.29558i) q^{27} +(-2.25729 + 1.38008i) q^{28} +(0.582710 + 1.00928i) q^{29} +(0.628063 + 1.61417i) q^{30} -6.77682 q^{31} +1.00000 q^{32} +(-5.73271 + 7.14555i) q^{33} +(-2.66689 - 4.61919i) q^{34} +(2.32383 + 1.26483i) q^{35} +(2.86149 + 0.901046i) q^{36} +(1.59659 - 2.76537i) q^{37} +(4.21311 - 7.29732i) q^{38} +(2.26607 - 2.82455i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-1.51734 + 2.62811i) q^{41} +(4.22755 - 1.76858i) q^{42} +(-1.77230 - 3.06971i) q^{43} +(2.64454 - 4.58047i) q^{44} +(-0.650416 - 2.92864i) q^{45} +(-2.71224 - 4.69774i) q^{46} +9.36786 q^{47} +(-1.71194 - 0.263165i) q^{48} +(3.19076 - 6.23049i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.34995 + 8.60961i) q^{51} +(-1.04535 + 1.81060i) q^{52} +(3.71311 + 6.43129i) q^{53} +(-4.66158 - 2.29558i) q^{54} -5.28907 q^{55} +(-2.25729 + 1.38008i) q^{56} +(-9.13300 + 11.3838i) q^{57} +(0.582710 + 1.00928i) q^{58} +10.2030 q^{59} +(0.628063 + 1.61417i) q^{60} -14.7350 q^{61} -6.77682 q^{62} +(-7.70274 + 1.91516i) q^{63} +1.00000 q^{64} +2.09071 q^{65} +(-5.73271 + 7.14555i) q^{66} +8.39063 q^{67} +(-2.66689 - 4.61919i) q^{68} +(3.40692 + 8.75602i) q^{69} +(2.32383 + 1.26483i) q^{70} +2.28907 q^{71} +(2.86149 + 0.901046i) q^{72} +(6.16188 + 10.6727i) q^{73} +(1.59659 - 2.76537i) q^{74} +(1.08388 - 1.35100i) q^{75} +(4.21311 - 7.29732i) q^{76} +(0.351920 + 13.9891i) q^{77} +(2.26607 - 2.82455i) q^{78} -5.25613 q^{79} +(-0.500000 - 0.866025i) q^{80} +(7.37623 + 5.15667i) q^{81} +(-1.51734 + 2.62811i) q^{82} +(-3.46154 - 5.99556i) q^{83} +(4.22755 - 1.76858i) q^{84} +(-2.66689 + 4.61919i) q^{85} +(-1.77230 - 3.06971i) q^{86} +(-0.731958 - 1.88118i) q^{87} +(2.64454 - 4.58047i) q^{88} +(6.37499 - 11.0418i) q^{89} +(-0.650416 - 2.92864i) q^{90} +(-0.139110 - 5.52974i) q^{91} +(-2.71224 - 4.69774i) q^{92} +(11.6015 + 1.78342i) q^{93} +9.36786 q^{94} -8.42622 q^{95} +(-1.71194 - 0.263165i) q^{96} +(3.09361 + 5.35829i) q^{97} +(3.19076 - 6.23049i) q^{98} +(11.6945 - 10.7241i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 12 * q^16 + q^17 + 4 * q^18 + 8 * q^19 - 6 * q^20 + 5 * q^21 + 3 * q^22 + 11 * q^23 - 6 * q^25 - 2 * q^26 - 27 * q^27 + 4 * q^28 + 13 * q^29 + 3 * q^30 - 42 * q^31 + 12 * q^32 + 17 * q^33 + q^34 + 4 * q^35 + 4 * q^36 + 18 * q^37 + 8 * q^38 - 24 * q^39 - 6 * q^40 + 5 * q^41 + 5 * q^42 - 11 * q^43 + 3 * q^44 + q^45 + 11 * q^46 + 46 * q^47 - 6 * q^50 - 27 * q^51 - 2 * q^52 + 2 * q^53 - 27 * q^54 - 6 * q^55 + 4 * q^56 - 44 * q^57 + 13 * q^58 - 2 * q^59 + 3 * q^60 + 2 * q^61 - 42 * q^62 + 9 * q^63 + 12 * q^64 + 4 * q^65 + 17 * q^66 - 4 * q^67 + q^68 - 24 * q^69 + 4 * q^70 - 30 * q^71 + 4 * q^72 + 22 * q^73 + 18 * q^74 - 3 * q^75 + 8 * q^76 - 31 * q^77 - 24 * q^78 - 54 * q^79 - 6 * q^80 + 52 * q^81 + 5 * q^82 + 6 * q^83 + 5 * q^84 + q^85 - 11 * q^86 - 28 * q^87 + 3 * q^88 - 18 * q^89 + q^90 + 14 * q^91 + 11 * q^92 - 38 * q^93 + 46 * q^94 - 16 * q^95 - 4 * q^97 + 63 * q^99

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