LMFDB - Embedded newform 630.2.bk.b.131.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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([1, 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("630.101");

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.bk (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			131.5
Character	$\chi$	$=$	630.131
Dual form			630.2.bk.b.101.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.361836 + 1.69383i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.69383 - 0.361836i) q^{6} +(-1.96242 - 1.77452i) q^{7} +1.00000i q^{8} +(-2.73815 + 1.22578i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.361836 + 1.69383i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.69383 - 0.361836i) q^{6} +(-1.96242 - 1.77452i) q^{7} +1.00000i q^{8} +(-2.73815 + 1.22578i) q^{9} +(-0.866025 + 0.500000i) q^{10} +(3.53173 + 2.03904i) q^{11} +(-0.361836 - 1.69383i) q^{12} +(5.20173 + 3.00322i) q^{13} +(-1.77452 + 1.96242i) q^{14} +(1.28599 - 1.16028i) q^{15} +1.00000 q^{16} +(0.641724 + 1.11150i) q^{17} +(1.22578 + 2.73815i) q^{18} +(2.90701 + 1.67836i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.29566 - 3.96610i) q^{21} +(2.03904 - 3.53173i) q^{22} +(1.89542 - 1.09432i) q^{23} +(-1.69383 + 0.361836i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.00322 - 5.20173i) q^{26} +(-3.06703 - 4.19444i) q^{27} +(1.96242 + 1.77452i) q^{28} +(6.21856 - 3.59029i) q^{29} +(-1.16028 - 1.28599i) q^{30} +7.84355i q^{31} -1.00000i q^{32} +(-2.17589 + 6.71996i) q^{33} +(1.11150 - 0.641724i) q^{34} +(-0.555567 + 2.58676i) q^{35} +(2.73815 - 1.22578i) q^{36} +(-2.90160 + 5.02572i) q^{37} +(1.67836 - 2.90701i) q^{38} +(-3.20478 + 9.89754i) q^{39} +(0.866025 - 0.500000i) q^{40} +(-1.36925 + 2.37162i) q^{41} +(-3.96610 - 2.29566i) q^{42} +(-2.43768 - 4.22219i) q^{43} +(-3.53173 - 2.03904i) q^{44} +(2.43063 + 1.75842i) q^{45} +(-1.09432 - 1.89542i) q^{46} +8.27225 q^{47} +(0.361836 + 1.69383i) q^{48} +(0.702180 + 6.96469i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-1.65050 + 1.48916i) q^{51} +(-5.20173 - 3.00322i) q^{52} +(7.48689 - 4.32256i) q^{53} +(-4.19444 + 3.06703i) q^{54} -4.07809i q^{55} +(1.77452 - 1.96242i) q^{56} +(-1.79100 + 5.53128i) q^{57} +(-3.59029 - 6.21856i) q^{58} -1.26116 q^{59} +(-1.28599 + 1.16028i) q^{60} -2.96707i q^{61} +7.84355 q^{62} +(7.54857 + 2.45339i) q^{63} -1.00000 q^{64} -6.00644i q^{65} +(6.71996 + 2.17589i) q^{66} -8.62197 q^{67} +(-0.641724 - 1.11150i) q^{68} +(2.53943 + 2.81456i) q^{69} +(2.58676 + 0.555567i) q^{70} +14.1375i q^{71} +(-1.22578 - 2.73815i) q^{72} +(-6.02332 + 3.47757i) q^{73} +(5.02572 + 2.90160i) q^{74} +(-1.64782 - 0.533558i) q^{75} +(-2.90701 - 1.67836i) q^{76} +(-3.31241 - 10.2686i) q^{77} +(9.89754 + 3.20478i) q^{78} -12.1855 q^{79} +(-0.500000 - 0.866025i) q^{80} +(5.99492 - 6.71275i) q^{81} +(2.37162 + 1.36925i) q^{82} +(-6.87948 - 11.9156i) q^{83} +(-2.29566 + 3.96610i) q^{84} +(0.641724 - 1.11150i) q^{85} +(-4.22219 + 2.43768i) q^{86} +(8.33146 + 9.23412i) q^{87} +(-2.03904 + 3.53173i) q^{88} +(7.29497 - 12.6353i) q^{89} +(1.75842 - 2.43063i) q^{90} +(-4.87871 - 15.1241i) q^{91} +(-1.89542 + 1.09432i) q^{92} +(-13.2857 + 2.83808i) q^{93} -8.27225i q^{94} -3.35672i q^{95} +(1.69383 - 0.361836i) q^{96} +(16.8723 - 9.74120i) q^{97} +(6.96469 - 0.702180i) q^{98} +(-12.1698 - 1.25408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9	$ 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9 - 2 * q^12 + 2 * q^15 + 28 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 + 14 * q^20 + 16 * q^21 - 6 * q^22 + 30 * q^23 - 8 * q^24 - 14 * q^25 - 12 * q^26 - 28 * q^27 - 8 * q^28 - 4 * q^30 - 20 * q^33 - 4 * q^35 - 6 * q^36 + 4 * q^37 - 6 * q^38 - 42 * q^39 - 18 * q^41 + 28 * q^43 - 12 * q^45 - 18 * q^46 + 60 * q^47 + 2 * q^48 - 20 * q^49 - 74 * q^51 + 42 * q^53 + 10 * q^54 - 30 * q^57 + 6 * q^58 - 48 * q^59 - 2 * q^60 + 12 * q^62 - 28 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^67 - 6 * q^68 - 8 * q^69 + 6 * q^70 - 8 * q^72 + 6 * q^73 - 4 * q^75 + 6 * q^76 - 18 * q^77 + 14 * q^78 - 4 * q^79 - 14 * q^80 + 38 * q^81 + 24 * q^82 + 18 * q^83 - 16 * q^84 + 6 * q^85 - 96 * q^86 + 52 * q^87 + 6 * q^88 - 6 * q^89 - 4 * q^90 + 66 * q^91 - 30 * q^92 + 22 * q^93 + 8 * 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.361836	+	1.69383i	0.208906	+	0.977936i
$3$	0.361836	+	1.69383i	0.208906	+	0.977936i
$4$	−1.00000			−0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.69383	−	0.361836i	0.691505	−	0.147719i
$7$	−1.96242	−	1.77452i	−0.741725	−	0.670704i
$7$	−1.96242	−	1.77452i	−0.741725	−	0.670704i
$8$			1.00000i			0.353553i
$9$	−2.73815	+	1.22578i	−0.912716	+	0.408594i
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$	3.53173	+	2.03904i	1.06486	+	0.614795i	0.926771	−	0.375626i	$-0.122572\pi$
$11$	3.53173	+	2.03904i	1.06486	+	0.614795i	0.138084	+	0.990420i	$0.455906\pi$
$12$	−0.361836	−	1.69383i	−0.104453	−	0.488968i
$13$	5.20173	+	3.00322i	1.44270	+	0.832943i	0.998029	−	0.0627507i	$-0.0199873\pi$
$13$	5.20173	+	3.00322i	1.44270	+	0.832943i	0.444671	+	0.895694i	$0.353321\pi$
$14$	−1.77452	+	1.96242i	−0.474260	+	0.524479i
$15$	1.28599	−	1.16028i	0.332040	−	0.299582i
$16$	1.00000			0.250000
$17$	0.641724	+	1.11150i	0.155641	+	0.269578i	0.933292	−	0.359118i	$-0.116922\pi$
$17$	0.641724	+	1.11150i	0.155641	+	0.269578i	−0.777651	+	0.628696i	$0.783589\pi$
$18$	1.22578	+	2.73815i	0.288920	+	0.645388i
$19$	2.90701	+	1.67836i	0.666913	+	0.385043i	0.794906	−	0.606733i	$-0.207520\pi$
$19$	2.90701	+	1.67836i	0.666913	+	0.385043i	−0.127993	+	0.991775i	$0.540853\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	2.29566	−	3.96610i	0.500955	−	0.865474i
$22$	2.03904	−	3.53173i	0.434726	−	0.752967i
$23$	1.89542	−	1.09432i	0.395222	−	0.228182i	−0.289198	−	0.957269i	$-0.593389\pi$
$23$	1.89542	−	1.09432i	0.395222	−	0.228182i	0.684420	+	0.729088i	$0.260055\pi$
$24$	−1.69383	+	0.361836i	−0.345752	+	0.0738596i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.00322	−	5.20173i	0.588980	−	1.02014i
$27$	−3.06703	−	4.19444i	−0.590251	−	0.807220i
$28$	1.96242	+	1.77452i	0.370862	+	0.335352i
$29$	6.21856	−	3.59029i	1.15476	−	0.666700i	0.204716	−	0.978821i	$-0.434373\pi$
$29$	6.21856	−	3.59029i	1.15476	−	0.666700i	0.950042	+	0.312122i	$0.101040\pi$
$30$	−1.16028	−	1.28599i	−0.211837	−	0.234788i
$31$			7.84355i			1.40874i	0.709831	+	0.704372i	$0.248771\pi$
$31$			7.84355i			1.40874i	−0.709831	+	0.704372i	$0.751229\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−2.17589	+	6.71996i	−0.378775	+	1.16979i
$34$	1.11150	−	0.641724i	0.190621	−	0.110055i
$35$	−0.555567	+	2.58676i	−0.0939079	+	0.437243i
$36$	2.73815	−	1.22578i	0.456358	−	0.204297i
$37$	−2.90160	+	5.02572i	−0.477020	+	0.826223i	−0.999653	−	0.0263347i	$-0.991616\pi$
$37$	−2.90160	+	5.02572i	−0.477020	+	0.826223i	0.522633	+	0.852558i	$0.324950\pi$
$38$	1.67836	−	2.90701i	0.272266	−	0.471579i
$39$	−3.20478	+	9.89754i	−0.513176	+	1.58488i
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	−1.36925	+	2.37162i	−0.213842	+	0.370384i	−0.952914	−	0.303242i	$-0.901931\pi$
$41$	−1.36925	+	2.37162i	−0.213842	+	0.370384i	0.739072	+	0.673626i	$0.235264\pi$
$42$	−3.96610	−	2.29566i	−0.611982	−	0.354228i
$43$	−2.43768	−	4.22219i	−0.371743	−	0.643878i	0.618091	−	0.786107i	$-0.287906\pi$
$43$	−2.43768	−	4.22219i	−0.371743	−	0.643878i	−0.989834	+	0.142229i	$0.954573\pi$
$44$	−3.53173	−	2.03904i	−0.532428	−	0.307397i
$45$	2.43063	+	1.75842i	0.362337	+	0.262129i
$46$	−1.09432	−	1.89542i	−0.161349	−	0.279464i
$47$	8.27225			1.20663			0.603316	−	0.797502i	$-0.293846\pi$
$47$	8.27225			1.20663			0.603316	+	0.797502i	$0.293846\pi$
$48$	0.361836	+	1.69383i	0.0522266	+	0.244484i
$49$	0.702180	+	6.96469i	0.100311	+	0.994956i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	−1.65050	+	1.48916i	−0.231116	+	0.208523i
$52$	−5.20173	−	3.00322i	−0.721350	−	0.416472i
$53$	7.48689	−	4.32256i	1.02840	−	0.593749i	0.111877	−	0.993722i	$-0.464314\pi$
$53$	7.48689	−	4.32256i	1.02840	−	0.593749i	0.916527	+	0.399973i	$0.130980\pi$
$54$	−4.19444	+	3.06703i	−0.570791	+	0.417370i
$55$		−	4.07809i		−	0.549889i
$56$	1.77452	−	1.96242i	0.237130	−	0.262239i
$57$	−1.79100	+	5.53128i	−0.237224	+	0.732636i
$58$	−3.59029	−	6.21856i	−0.471428	−	0.816537i
$59$	−1.26116			−0.164189			−0.0820944	−	0.996625i	$-0.526161\pi$
$59$	−1.26116			−0.164189			−0.0820944	+	0.996625i	$0.526161\pi$
$60$	−1.28599	+	1.16028i	−0.166020	+	0.149791i
$61$		−	2.96707i		−	0.379894i	−0.981794	−	0.189947i	$-0.939168\pi$
$61$		−	2.96707i		−	0.379894i	0.981794	−	0.189947i	$-0.0608316\pi$
$62$	7.84355			0.996132
$63$	7.54857	+	2.45339i	0.951030	+	0.309098i
$64$	−1.00000			−0.125000
$65$		−	6.00644i		−	0.745007i
$66$	6.71996	+	2.17589i	0.827170	+	0.267834i
$67$	−8.62197			−1.05334			−0.526670	−	0.850070i	$-0.676560\pi$
$67$	−8.62197			−1.05334			−0.526670	+	0.850070i	$0.676560\pi$
$68$	−0.641724	−	1.11150i	−0.0778205	−	0.134789i
$69$	2.53943	+	2.81456i	0.305711	+	0.338833i
$70$	2.58676	+	0.555567i	0.309177	+	0.0664029i
$71$			14.1375i			1.67781i	0.544277	+	0.838906i	$0.316804\pi$
$71$			14.1375i			1.67781i	−0.544277	+	0.838906i	$0.683196\pi$
$72$	−1.22578	−	2.73815i	−0.144460	−	0.322694i
$73$	−6.02332	+	3.47757i	−0.704977	+	0.407018i	−0.809198	−	0.587536i	$-0.800098\pi$
$73$	−6.02332	+	3.47757i	−0.704977	+	0.407018i	0.104222	+	0.994554i	$0.466765\pi$
$74$	5.02572	+	2.90160i	0.584228	+	0.337304i
$75$	−1.64782	−	0.533558i	−0.190274	−	0.0616099i
$76$	−2.90701	−	1.67836i	−0.333457	−	0.192521i
$77$	−3.31241	−	10.2686i	−0.377484	−	1.17021i
$78$	9.89754	+	3.20478i	1.12068	+	0.362870i
$79$	−12.1855			−1.37098			−0.685490	−	0.728082i	$-0.740412\pi$
$79$	−12.1855			−1.37098			−0.685490	+	0.728082i	$0.740412\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	5.99492	−	6.71275i	0.666102	−	0.745861i
$82$	2.37162	+	1.36925i	0.261901	+	0.151209i
$83$	−6.87948	−	11.9156i	−0.755121	−	1.30791i	−0.945314	−	0.326161i	$-0.894245\pi$
$83$	−6.87948	−	11.9156i	−0.755121	−	1.30791i	0.190194	−	0.981747i	$-0.439088\pi$
$84$	−2.29566	+	3.96610i	−0.250477	+	0.432737i
$85$	0.641724	−	1.11150i	0.0696048	−	0.120559i
$86$	−4.22219	+	2.43768i	−0.455291	+	0.262862i
$87$	8.33146	+	9.23412i	0.893226	+	0.990001i
$88$	−2.03904	+	3.53173i	−0.217363	+	0.376483i
$89$	7.29497	−	12.6353i	0.773265	−	1.33933i	−0.162499	−	0.986709i	$-0.551955\pi$
$89$	7.29497	−	12.6353i	0.773265	−	1.33933i	0.935764	−	0.352626i	$-0.114711\pi$
$90$	1.75842	−	2.43063i	0.185353	−	0.256211i
$91$	−4.87871	−	15.1241i	−0.511428	−	1.58544i
$92$	−1.89542	+	1.09432i	−0.197611	+	0.114091i
$93$	−13.2857	+	2.83808i	−1.37766	+	0.294295i
$94$		−	8.27225i		−	0.853218i
$95$		−	3.35672i		−	0.344392i
$96$	1.69383	−	0.361836i	0.172876	−	0.0369298i
$97$	16.8723	−	9.74120i	1.71312	−	0.989069i	0.782832	−	0.622233i	$-0.213774\pi$
$97$	16.8723	−	9.74120i	1.71312	−	0.989069i	0.930285	−	0.366837i	$-0.119559\pi$
$98$	6.96469	−	0.702180i	0.703540	−	0.0709309i
$99$	−12.1698	−	1.25408i	−1.22311	−	0.126039i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	4.26859	−	7.39341i	0.424740	−	0.735672i	−0.571656	−	0.820493i	$-0.693699\pi$
$101$	4.26859	−	7.39341i	0.424740	−	0.735672i	0.996396	+	0.0848218i	$0.0270321\pi$
$102$	1.48916	+	1.65050i	0.147448	+	0.163423i
$103$	−3.12850	+	1.80624i	−0.308260	+	0.177974i	−0.646147	−	0.763213i	$-0.723621\pi$
$103$	−3.12850	+	1.80624i	−0.308260	+	0.177974i	0.337888	+	0.941186i	$0.390288\pi$
$104$	−3.00322	+	5.20173i	−0.294490	+	0.510072i
$105$	−4.58257	−	0.00505279i	−0.447213	−	0.000493102i
$106$	−4.32256	−	7.48689i	−0.419844	−	0.727191i
$107$	−11.5596	−	6.67392i	−1.11751	−	0.645192i	−0.176743	−	0.984257i	$-0.556556\pi$
$107$	−11.5596	−	6.67392i	−1.11751	−	0.645192i	−0.940763	+	0.339065i	$0.889889\pi$
$108$	3.06703	+	4.19444i	0.295125	+	0.403610i
$109$	5.38583	+	9.32854i	0.515869	+	0.893512i	0.999830	+	0.0184222i	$0.00586429\pi$
$109$	5.38583	+	9.32854i	0.515869	+	0.893512i	−0.483961	+	0.875090i	$0.660802\pi$
$110$	−4.07809			−0.388830
$111$	−9.56264	−	3.09634i	−0.907646	−	0.293892i
$112$	−1.96242	−	1.77452i	−0.185431	−	0.167676i
$113$	−2.45659	−	1.41832i	−0.231097	−	0.133424i	0.379981	−	0.924994i	$-0.375930\pi$
$113$	−2.45659	−	1.41832i	−0.231097	−	0.133424i	−0.611078	+	0.791570i	$0.709264\pi$
$114$	5.53128	+	1.79100i	0.518052	+	0.167743i
$115$	−1.89542	−	1.09432i	−0.176749	−	0.102046i
$116$	−6.21856	+	3.59029i	−0.577379	+	0.333350i
$117$	−17.9244	−	1.84708i	−1.65711	−	0.170762i
$118$			1.26116i			0.116099i
$119$	0.713041	−	3.31998i	0.0653644	−	0.304342i
$120$	1.16028	+	1.28599i	0.105918	+	0.117394i
$121$	2.81540	+	4.87641i	0.255945	+	0.443310i
$122$	−2.96707			−0.268626
$123$	−4.51257	−	1.46115i	−0.406885	−	0.131748i
$124$		−	7.84355i		−	0.704372i
$125$	1.00000			0.0894427
$126$	2.45339	−	7.54857i	0.218566	−	0.672480i
$127$	−10.9625			−0.972768			−0.486384	−	0.873745i	$-0.661684\pi$
$127$	−10.9625			−0.972768			−0.486384	+	0.873745i	$0.661684\pi$
$128$			1.00000i			0.0883883i
$129$	6.26965	−	5.65677i	0.552012	−	0.498051i
$130$	−6.00644			−0.526800
$131$	10.3656	+	17.9538i	0.905647	+	1.56863i	0.820046	+	0.572297i	$0.193948\pi$
$131$	10.3656	+	17.9538i	0.905647	+	1.56863i	0.0856007	+	0.996330i	$0.472719\pi$
$132$	2.17589	−	6.71996i	0.189387	−	0.584897i
$133$	−2.72649	−	8.45218i	−0.236416	−	0.732897i
$134$			8.62197i			0.744825i
$135$	−2.09897	+	4.75335i	−0.180651	+	0.409103i
$136$	−1.11150	+	0.641724i	−0.0953103	+	0.0550274i
$137$	−8.37821	−	4.83716i	−0.715799	−	0.413267i	0.0974057	−	0.995245i	$-0.468946\pi$
$137$	−8.37821	−	4.83716i	−0.715799	−	0.413267i	−0.813204	+	0.581978i	$0.802279\pi$
$138$	2.81456	−	2.53943i	0.239591	−	0.216170i
$139$	4.57137	+	2.63928i	0.387739	+	0.223861i	0.681180	−	0.732116i	$-0.261467\pi$
$139$	4.57137	+	2.63928i	0.387739	+	0.223861i	−0.293441	+	0.955977i	$0.594800\pi$
$140$	0.555567	−	2.58676i	0.0469540	−	0.218621i
$141$	2.99320	+	14.0118i	0.252073	+	1.18001i
$142$	14.1375			1.18639
$143$	12.2474	+	21.2131i	1.02418	+	1.77393i
$144$	−2.73815	+	1.22578i	−0.228179	+	0.102149i
$145$	−6.21856	−	3.59029i	−0.516423	−	0.298157i
$146$	3.47757	+	6.02332i	0.287806	+	0.498494i
$147$	−11.5430	+	3.70946i	−0.952047	+	0.305951i
$148$	2.90160	−	5.02572i	0.238510	−	0.413112i
$149$	−3.79127	+	2.18889i	−0.310593	+	0.179321i	−0.647192	−	0.762327i	$-0.724057\pi$
$149$	−3.79127	+	2.18889i	−0.310593	+	0.179321i	0.336599	+	0.941648i	$0.390723\pi$
$150$	−0.533558	+	1.64782i	−0.0435648	+	0.134544i
$151$	2.78658	−	4.82650i	0.226769	−	0.392775i	−0.730080	−	0.683362i	$-0.760517\pi$
$151$	2.78658	−	4.82650i	0.226769	−	0.392775i	0.956849	+	0.290587i	$0.0938505\pi$
$152$	−1.67836	+	2.90701i	−0.136133	+	0.235789i
$153$	−3.11959	−	2.25684i	−0.252204	−	0.182454i
$154$	−10.2686	+	3.31241i	−0.827465	+	0.266922i
$155$	6.79271	−	3.92178i	0.545604	−	0.315005i
$156$	3.20478	−	9.89754i	0.256588	−	0.792438i
$157$			0.281341i			0.0224535i	0.999937	+	0.0112267i	$0.00357366\pi$
$157$			0.281341i			0.0224535i	−0.999937	+	0.0112267i	$0.996426\pi$
$158$			12.1855i			0.969429i
$159$	10.0307	+	11.1175i	0.795489	+	0.881675i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−5.66149	−	1.21594i	−0.446188	−	0.0958292i
$162$	−6.71275	−	5.99492i	−0.527403	−	0.471005i
$163$	−3.76577	+	6.52251i	−0.294958	+	0.510882i	−0.974975	−	0.222314i	$-0.928639\pi$
$163$	−3.76577	+	6.52251i	−0.294958	+	0.510882i	0.680017	+	0.733196i	$0.261972\pi$
$164$	1.36925	−	2.37162i	0.106921	−	0.185192i
$165$	6.90760	−	1.47560i	0.537756	−	0.114875i
$166$	−11.9156	+	6.87948i	−0.924830	+	0.533951i
$167$	4.87241	−	8.43926i	0.377039	−	0.653050i	−0.613591	−	0.789624i	$-0.710276\pi$
$167$	4.87241	−	8.43926i	0.377039	−	0.653050i	0.990630	+	0.136574i	$0.0436091\pi$
$168$	3.96610	+	2.29566i	0.305991	+	0.177114i
$169$	11.5387	+	19.9855i	0.887589	+	1.53735i
$170$	−1.11150	−	0.641724i	−0.0852481	−	0.0492180i
$171$	−10.0171	−	1.03225i	−0.766029	−	0.0789378i
$172$	2.43768	+	4.22219i	0.185872	+	0.321939i
$173$	14.2669			1.08469			0.542346	−	0.840155i	$-0.317536\pi$
$173$	14.2669			1.08469			0.542346	+	0.840155i	$0.317536\pi$
$174$	9.23412	−	8.33146i	0.700036	−	0.631606i
$175$	2.51799	−	0.812247i	0.190342	−	0.0614001i
$176$	3.53173	+	2.03904i	0.266214	+	0.153699i
$177$	−0.456333	−	2.13619i	−0.0343001	−	0.160566i
$178$	−12.6353	−	7.29497i	−0.947053	−	0.546781i
$179$	−7.42444	+	4.28650i	−0.554928	+	0.320388i	−0.751107	−	0.660180i	$-0.770480\pi$
$179$	−7.42444	+	4.28650i	−0.554928	+	0.320388i	0.196179	+	0.980568i	$0.437147\pi$
$180$	−2.43063	−	1.75842i	−0.181169	−	0.131065i
$181$		−	1.70947i		−	0.127064i	−0.997980	−	0.0635319i	$-0.979764\pi$
$181$		−	1.70947i		−	0.127064i	0.997980	−	0.0635319i	$-0.0202365\pi$
$182$	−15.1241	+	4.87871i	−1.12108	+	0.361634i
$183$	5.02572	−	1.07359i	0.371512	−	0.0793623i
$184$	1.09432	+	1.89542i	0.0806744	+	0.139732i
$185$	5.80320			0.426660
$186$	2.83808	+	13.2857i	0.208098	+	0.974153i
$187$			5.23401i			0.382749i
$188$	−8.27225			−0.603316
$189$	−1.42429	+	13.6737i	−0.103602	+	0.994619i
$190$	−3.35672			−0.243522
$191$			9.26150i			0.670138i	0.942194	+	0.335069i	$0.108760\pi$
$191$			9.26150i			0.670138i	−0.942194	+	0.335069i	$0.891240\pi$
$192$	−0.361836	−	1.69383i	−0.0261133	−	0.122242i
$193$	−24.2494			−1.74551			−0.872756	−	0.488157i	$-0.837670\pi$
$193$	−24.2494			−1.74551			−0.872756	+	0.488157i	$0.837670\pi$
$194$	−9.74120	−	16.8723i	−0.699377	−	1.21136i
$195$	10.1739	−	2.17335i	0.728569	−	0.155637i
$196$	−0.702180	−	6.96469i	−0.0501557	−	0.497478i
$197$		−	18.8947i		−	1.34619i	−0.739554	−	0.673097i	$-0.764964\pi$
$197$		−	18.8947i		−	1.34619i	0.739554	−	0.673097i	$-0.235036\pi$
$198$	−1.25408	+	12.1698i	−0.0891234	+	0.864871i
$199$	2.25502	−	1.30194i	0.159854	−	0.0922919i	−0.417939	−	0.908475i	$-0.637247\pi$
$199$	2.25502	−	1.30194i	0.159854	−	0.0922919i	0.577793	+	0.816183i	$0.303914\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	−3.11974	−	14.6042i	−0.220050	−	1.03010i
$202$	−7.39341	−	4.26859i	−0.520198	−	0.300337i
$203$	−18.5745	−	3.98929i	−1.30367	−	0.279993i
$204$	1.65050	−	1.48916i	0.115558	−	0.104262i
$205$	2.73851			0.191266
$206$	1.80624	+	3.12850i	0.125847	+	0.217973i
$207$	−3.84854	+	5.31978i	−0.267492	+	0.369750i
$208$	5.20173	+	3.00322i	0.360675	+	0.208236i
$209$	6.84450	+	11.8550i	0.473444	+	0.820029i
$210$	−0.00505279	+	4.58257i	−0.000348676	+	0.316228i
$211$	−3.12513	+	5.41288i	−0.215143	+	0.372638i	−0.953317	−	0.301972i	$-0.902355\pi$
$211$	−3.12513	+	5.41288i	−0.215143	+	0.372638i	0.738174	+	0.674610i	$0.235688\pi$
$212$	−7.48689	+	4.32256i	−0.514202	+	0.296875i
$213$	−23.9466	+	5.11546i	−1.64079	+	0.350505i
$214$	−6.67392	+	11.5596i	−0.456220	+	0.790196i
$215$	−2.43768	+	4.22219i	−0.166249	+	0.287951i
$216$	4.19444	−	3.06703i	0.285395	−	0.208685i
$217$	13.9185	−	15.3923i	0.944850	−	1.04490i
$218$	9.32854	−	5.38583i	0.631808	−	0.364775i
$219$	−8.06988	−	8.94420i	−0.545312	−	0.604393i
$220$			4.07809i			0.274945i
$221$			7.70896i			0.518560i
$222$	−3.09634	+	9.56264i	−0.207813	+	0.641802i
$223$	−4.24320	+	2.44981i	−0.284145	+	0.164051i	−0.635299	−	0.772267i	$-0.719123\pi$
$223$	−4.24320	+	2.44981i	−0.284145	+	0.164051i	0.351153	+	0.936318i	$0.385790\pi$
$224$	−1.77452	+	1.96242i	−0.118565	+	0.131120i
$225$	0.307516	−	2.98420i	0.0205011	−	0.198946i
$226$	−1.41832	+	2.45659i	−0.0943449	+	0.163410i
$227$	8.74040	−	15.1388i	0.580121	−	1.00480i	−0.415344	−	0.909665i	$-0.636339\pi$
$227$	8.74040	−	15.1388i	0.580121	−	1.00480i	0.995464	−	0.0951340i	$-0.0303280\pi$
$228$	1.79100	−	5.53128i	0.118612	−	0.366318i
$229$	12.6374	−	7.29619i	0.835102	−	0.482146i	−0.0204946	−	0.999790i	$-0.506524\pi$
$229$	12.6374	−	7.29619i	0.835102	−	0.482146i	0.855596	+	0.517644i	$0.173191\pi$
$230$	−1.09432	+	1.89542i	−0.0721573	+	0.124980i
$231$	16.1947	−	9.32622i	1.06553	−	0.613620i
$232$	3.59029	+	6.21856i	0.235714	+	0.408269i
$233$	−3.42360	−	1.97662i	−0.224288	−	0.129493i	0.383646	−	0.923480i	$-0.374668\pi$
$233$	−3.42360	−	1.97662i	−0.224288	−	0.129493i	−0.607934	+	0.793988i	$0.708002\pi$
$234$	−1.84708	+	17.9244i	−0.120747	+	1.17175i
$235$	−4.13613	−	7.16398i	−0.269811	−	0.467327i
$236$	1.26116			0.0820944
$237$	−4.40917	−	20.6403i	−0.286406	−	1.34073i
$238$	−3.31998	−	0.713041i	−0.215202	−	0.0462196i
$239$	16.0317	+	9.25590i	1.03700	+	0.598714i	0.918983	−	0.394297i	$-0.129012\pi$
$239$	16.0317	+	9.25590i	1.03700	+	0.598714i	0.118021	+	0.993011i	$0.462345\pi$
$240$	1.28599	−	1.16028i	0.0830100	−	0.0748955i
$241$	−18.9977	−	10.9683i	−1.22375	−	0.706532i	−0.258034	−	0.966136i	$-0.583075\pi$
$241$	−18.9977	−	10.9683i	−1.22375	−	0.706532i	−0.965715	+	0.259604i	$0.916408\pi$
$242$	4.87641	−	2.81540i	0.313468	−	0.180981i
$243$	13.5395	+	7.72548i	0.868557	+	0.495590i
$244$			2.96707i			0.189947i
$245$	5.68051	−	4.09045i	0.362915	−	0.261329i
$246$	−1.46115	+	4.51257i	−0.0931596	+	0.287711i
$247$	10.0810	+	17.4608i	0.641437	+	1.11100i
$248$	−7.84355			−0.498066
$249$	17.6938	−	15.9642i	1.12130	−	1.01169i
$250$		−	1.00000i		−	0.0632456i
$251$	−15.6773			−0.989540			−0.494770	−	0.869024i	$-0.664748\pi$
$251$	−15.6773			−0.989540			−0.494770	+	0.869024i	$0.664748\pi$
$252$	−7.54857	−	2.45339i	−0.475515	−	0.154549i
$253$	8.92547			0.561139
$254$			10.9625i			0.687851i
$255$	2.11489	+	0.684794i	0.132440	+	0.0428834i
$256$	1.00000			0.0625000
$257$	−5.29360	−	9.16878i	−0.330206	−	0.571933i	0.652346	−	0.757921i	$-0.273785\pi$
$257$	−5.29360	−	9.16878i	−0.330206	−	0.571933i	−0.982552	+	0.185988i	$0.940451\pi$
$258$	−5.65677	−	6.26965i	−0.352175	−	0.390331i
$259$	14.6124	−	4.71363i	0.907969	−	0.292891i
$260$			6.00644i			0.372504i
$261$	−12.6264	+	17.4533i	−0.781557	+	1.08033i
$262$	17.9538	−	10.3656i	1.10919	−	0.640389i
$263$	−21.0140	−	12.1325i	−1.29578	−	0.748120i	−0.316109	−	0.948723i	$-0.602377\pi$
$263$	−21.0140	−	12.1325i	−1.29578	−	0.748120i	−0.979673	+	0.200603i	$0.935710\pi$
$264$	−6.71996	−	2.17589i	−0.413585	−	0.133917i
$265$	−7.48689	−	4.32256i	−0.459916	−	0.265533i
$266$	−8.45218	+	2.72649i	−0.518237	+	0.167172i
$267$	24.0416	+	7.78457i	1.47132	+	0.476408i
$268$	8.62197			0.526670
$269$	9.04616	+	15.6684i	0.551554	+	0.955320i	0.998163	+	0.0605906i	$0.0192984\pi$
$269$	9.04616	+	15.6684i	0.551554	+	0.955320i	−0.446608	+	0.894730i	$0.647368\pi$
$270$	4.75335	+	2.09897i	0.289280	+	0.127739i
$271$	−3.07389	−	1.77471i	−0.186725	−	0.107806i	0.403723	−	0.914881i	$-0.367716\pi$
$271$	−3.07389	−	1.77471i	−0.186725	−	0.107806i	−0.590449	+	0.807075i	$0.701049\pi$
$272$	0.641724	+	1.11150i	0.0389102	+	0.0673945i
$273$	23.8525	−	13.7362i	1.44362	−	0.831352i
$274$	−4.83716	+	8.37821i	−0.292224	+	0.506146i
$275$	−3.53173	+	2.03904i	−0.212971	+	0.122959i
$276$	−2.53943	−	2.81456i	−0.152856	−	0.169417i
$277$	−1.15448	+	1.99961i	−0.0693658	+	0.120145i	−0.898622	−	0.438723i	$-0.855431\pi$
$277$	−1.15448	+	1.99961i	−0.0693658	+	0.120145i	0.829257	+	0.558868i	$0.188764\pi$
$278$	2.63928	−	4.57137i	0.158294	−	0.274173i
$279$	−9.61448	−	21.4768i	−0.575604	−	1.28578i
$280$	−2.58676	−	0.555567i	−0.154589	−	0.0332015i
$281$	−0.186637	+	0.107755i	−0.0111338	+	0.00642812i	−0.505557	−	0.862793i	$-0.668713\pi$
$281$	−0.186637	+	0.107755i	−0.0111338	+	0.00642812i	0.494423	+	0.869222i	$0.335379\pi$
$282$	14.0118	−	2.99320i	0.834392	−	0.178243i
$283$		−	15.4484i		−	0.918313i	−0.888355	−	0.459157i	$-0.848152\pi$
$283$		−	15.4484i		−	0.918313i	0.888355	−	0.459157i	$-0.151848\pi$
$284$		−	14.1375i		−	0.838906i
$285$	5.68573	−	1.21458i	0.336794	−	0.0719458i
$286$	21.2131	−	12.2474i	1.25436	−	0.724203i
$287$	6.89553	−	2.22434i	0.407030	−	0.131299i
$288$	1.22578	+	2.73815i	0.0722299	+	0.161347i
$289$	7.67638	−	13.2959i	0.451552	−	0.782111i
$290$	−3.59029	+	6.21856i	−0.210829	+	0.365167i
$291$	22.6050	+	25.0541i	1.32513	+	1.46870i
$292$	6.02332	−	3.47757i	0.352488	−	0.203509i
$293$	−0.347292	+	0.601528i	−0.0202890	+	0.0351417i	−0.875992	−	0.482326i	$-0.839792\pi$
$293$	−0.347292	+	0.601528i	−0.0202890	+	0.0351417i	0.855703	+	0.517468i	$0.173125\pi$
$294$	3.70946	+	11.5430i	0.216340	+	0.673199i
$295$	0.630579	+	1.09220i	0.0367137	+	0.0635901i
$296$	−5.02572	−	2.90160i	−0.292114	−	0.168652i
$297$	−2.27929	−	21.0674i	−0.132258	−	1.22246i
$298$	2.18889	+	3.79127i	0.126799	+	0.219623i
$299$	13.1459			0.760249
$300$	1.64782	+	0.533558i	0.0951370	+	0.0308050i
$301$	−2.70859	+	12.6114i	−0.156121	+	0.726910i
$302$	−4.82650	−	2.78658i	−0.277734	−	0.160350i
$303$	14.0677	+	4.55507i	0.808170	+	0.261682i
$304$	2.90701	+	1.67836i	0.166728	+	0.0962606i
$305$	−2.56956	+	1.48353i	−0.147132	+	0.0849469i
$306$	−2.25684	+	3.11959i	−0.129015	+	0.178335i
$307$			34.0796i			1.94502i	0.232853	+	0.972512i	$0.425194\pi$
$307$			34.0796i			1.94502i	−0.232853	+	0.972512i	$0.574806\pi$
$308$	3.31241	+	10.2686i	0.188742	+	0.585106i
$309$	−4.19147	−	4.64559i	−0.238444	−	0.264278i
$310$	−3.92178	−	6.79271i	−0.222742	−	0.385800i
$311$	−8.48761			−0.481288			−0.240644	−	0.970613i	$-0.577359\pi$
$311$	−8.48761			−0.481288			−0.240644	+	0.970613i	$0.577359\pi$
$312$	−9.89754	−	3.20478i	−0.560338	−	0.181435i
$313$			27.2798i			1.54195i	0.636868	+	0.770973i	$0.280230\pi$
$313$			27.2798i			1.54195i	−0.636868	+	0.770973i	$0.719770\pi$
$314$	0.281341			0.0158770
$315$	−1.64958	−	7.76395i	−0.0929435	−	0.437449i
$316$	12.1855			0.685490
$317$		−	0.0451228i		−	0.00253435i	−0.999999	−	0.00126717i	$-0.999597\pi$
$317$		−	0.0451228i		−	0.00253435i	0.999999	−	0.00126717i	$-0.000403354\pi$
$318$	11.1175	−	10.0307i	0.623438	−	0.562495i
$319$	29.2830			1.63953
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	7.12184	−	21.9949i	0.397503	−	1.22763i
$322$	−1.21594	+	5.66149i	−0.0677615	+	0.315503i
$323$			4.30818i			0.239714i
$324$	−5.99492	+	6.71275i	−0.333051	+	0.372930i
$325$	−5.20173	+	3.00322i	−0.288540	+	0.166589i
$326$	6.52251	+	3.76577i	0.361248	+	0.208567i
$327$	−13.8522	+	12.4981i	−0.766029	+	0.691147i
$328$	−2.37162	−	1.36925i	−0.130951	−	0.0756044i
$329$	−16.2336	−	14.6793i	−0.894989	−	0.809293i
$330$	−1.47560	−	6.90760i	−0.0812291	−	0.380251i
$331$	18.4652			1.01494			0.507468	−	0.861670i	$-0.330581\pi$
$331$	18.4652			1.01494			0.507468	+	0.861670i	$0.330581\pi$
$332$	6.87948	+	11.9156i	0.377560	+	0.653954i
$333$	1.78458	−	17.3179i	0.0977942	−	0.949015i
$334$	−8.43926	−	4.87241i	−0.461776	−	0.266607i
$335$	4.31098	+	7.46684i	0.235534	+	0.407957i
$336$	2.29566	−	3.96610i	0.125239	−	0.216368i
$337$	11.5293	−	19.9693i	0.628041	−	1.08780i	−0.359903	−	0.932990i	$-0.617190\pi$
$337$	11.5293	−	19.9693i	0.628041	−	1.08780i	0.987944	−	0.154810i	$-0.0494764\pi$
$338$	19.9855	−	11.5387i	1.08707	−	0.627620i
$339$	1.51351	−	4.67426i	0.0822023	−	0.253871i
$340$	−0.641724	+	1.11150i	−0.0348024	+	0.0602795i
$341$	−15.9933	+	27.7013i	−0.866088	+	1.50011i
$342$	−1.03225	+	10.0171i	−0.0558175	+	0.541664i
$343$	10.9810	−	14.9137i	0.592918	−	0.805263i
$344$	4.22219	−	2.43768i	0.227645	−	0.131431i
$345$	1.16777	−	3.60649i	0.0628704	−	0.194167i
$346$		−	14.2669i		−	0.766993i
$347$		−	22.3311i		−	1.19880i	−0.800451	−	0.599398i	$-0.795407\pi$
$347$		−	22.3311i		−	1.19880i	0.800451	−	0.599398i	$-0.204593\pi$
$348$	−8.33146	−	9.23412i	−0.446613	−	0.495001i
$349$	8.01876	−	4.62963i	0.429235	−	0.247819i	−0.269786	−	0.962920i	$-0.586953\pi$
$349$	8.01876	−	4.62963i	0.429235	−	0.247819i	0.699020	+	0.715102i	$0.253620\pi$
$350$	−0.812247	−	2.51799i	−0.0434164	−	0.134592i
$351$	−3.35706	−	31.0293i	−0.179187	−	1.65622i
$352$	2.03904	−	3.53173i	0.108681	−	0.188242i
$353$	6.59338	−	11.4201i	0.350930	−	0.607829i	−0.635483	−	0.772115i	$-0.719199\pi$
$353$	6.59338	−	11.4201i	0.350930	−	0.607829i	0.986413	+	0.164286i	$0.0525321\pi$
$354$	−2.13619	+	0.456333i	−0.113537	+	0.0242538i
$355$	12.2434	−	7.06874i	0.649813	−	0.375170i
$356$	−7.29497	+	12.6353i	−0.386633	+	0.669667i
$357$	5.88150	+	0.00648500i	0.311282	+	0.000343222i
$358$	4.28650	+	7.42444i	0.226549	+	0.392394i
$359$	−9.81294	−	5.66550i	−0.517907	−	0.299014i	0.218171	−	0.975911i	$-0.429991\pi$
$359$	−9.81294	−	5.66550i	−0.517907	−	0.299014i	−0.736078	+	0.676897i	$0.763324\pi$
$360$	−1.75842	+	2.43063i	−0.0926766	+	0.128106i
$361$	−3.86621	−	6.69647i	−0.203485	−	0.352446i
$362$	−1.70947			−0.0898477
$363$	−7.24112	+	6.53328i	−0.380060	+	0.342908i
$364$	4.87871	+	15.1241i	0.255714	+	0.792720i
$365$	6.02332	+	3.47757i	0.315275	+	0.182024i
$366$	−1.07359	−	5.02572i	−0.0561176	−	0.262699i
$367$	−21.0854	−	12.1737i	−1.10065	−	0.635461i	−0.164259	−	0.986417i	$-0.552523\pi$
$367$	−21.0854	−	12.1737i	−1.10065	−	0.635461i	−0.936392	+	0.350956i	$0.885857\pi$
$368$	1.89542	−	1.09432i	0.0988055	−	0.0570454i
$369$	0.842135	−	8.17225i	0.0438398	−	0.425430i
$370$		−	5.80320i		−	0.301694i
$371$	−22.3629	−	4.80294i	−1.16102	−	0.249356i
$372$	13.2857	−	2.83808i	0.688830	−	0.147148i
$373$	13.7313	+	23.7833i	0.710979	+	1.23145i	0.964490	+	0.264119i	$0.0850811\pi$
$373$	13.7313	+	23.7833i	0.710979	+	1.23145i	−0.253512	+	0.967332i	$0.581586\pi$
$374$	5.23401			0.270644
$375$	0.361836	+	1.69383i	0.0186852	+	0.0874692i
$376$			8.27225i			0.426609i
$377$	43.1297			2.22129
$378$	13.6737	+	1.42429i	0.703302	+	0.0732577i
$379$	32.0033			1.64390			0.821948	−	0.569562i	$-0.192887\pi$
$379$	32.0033			1.64390			0.821948	+	0.569562i	$0.192887\pi$
$380$			3.35672i			0.172196i
$381$	−3.96665	−	18.5687i	−0.203217	−	0.951304i
$382$	9.26150			0.473859
$383$	7.13527	+	12.3587i	0.364595	+	0.631498i	0.988711	−	0.149834i	$-0.0478740\pi$
$383$	7.13527	+	12.3587i	0.364595	+	0.631498i	−0.624116	+	0.781332i	$0.714541\pi$
$384$	−1.69383	+	0.361836i	−0.0864381	+	0.0184649i
$385$	−7.23663	+	8.00292i	−0.368813	+	0.407866i
$386$			24.2494i			1.23426i
$387$	11.8502	+	8.57292i	0.602381	+	0.435786i
$388$	−16.8723	+	9.74120i	−0.856559	+	0.494535i
$389$	−9.31929	−	5.38049i	−0.472507	−	0.272802i	0.244782	−	0.969578i	$-0.421284\pi$
$389$	−9.31929	−	5.38049i	−0.472507	−	0.272802i	−0.717288	+	0.696776i	$0.754617\pi$
$390$	−2.17335	−	10.1739i	−0.110052	−	0.515176i
$391$	2.43267	+	1.40450i	0.123025	+	0.0710288i
$392$	−6.96469	+	0.702180i	−0.351770	+	0.0354655i
$393$	−26.6600	+	24.0539i	−1.34482	+	1.21336i
$394$	−18.8947			−0.951903
$395$	6.09277	+	10.5530i	0.306560	+	0.530978i
$396$	12.1698	+	1.25408i	0.611556	+	0.0630197i
$397$	19.3500	+	11.1717i	0.971150	+	0.560694i	0.899587	−	0.436742i	$-0.143868\pi$
$397$	19.3500	+	11.1717i	0.971150	+	0.560694i	0.0715634	+	0.997436i	$0.477201\pi$
$398$	−1.30194	−	2.25502i	−0.0652602	−	0.113034i
$399$	13.3301	−	7.67653i	0.667337	−	0.384307i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−16.4405	+	9.49194i	−0.821000	+	0.474005i	−0.850761	−	0.525552i	$-0.823859\pi$
$401$	−16.4405	+	9.49194i	−0.821000	+	0.474005i	0.0297611	+	0.999557i	$0.490525\pi$
$402$	−14.6042	+	3.11974i	−0.728390	+	0.155599i
$403$	−23.5559	+	40.8000i	−1.17340	+	2.03239i
$404$	−4.26859	+	7.39341i	−0.212370	+	0.367836i
$405$	−8.81087	−	1.83538i	−0.437816	−	0.0912006i
$406$	−3.98929	+	18.5745i	−0.197985	+	0.921835i
$407$	−20.4953	+	11.8330i	−1.01592	+	0.586539i
$408$	−1.48916	−	1.65050i	−0.0737242	−	0.0817117i
$409$		−	26.0187i		−	1.28654i	−0.765639	−	0.643270i	$-0.777577\pi$
$409$		−	26.0187i		−	1.28654i	0.765639	−	0.643270i	$-0.222423\pi$
$410$		−	2.73851i		−	0.135245i
$411$	5.16181	−	15.9416i	0.254613	−	0.786339i
$412$	3.12850	−	1.80624i	0.154130	−	0.0889869i
$413$	2.47492	+	2.23795i	0.121783	+	0.110122i
$414$	5.31978	+	3.84854i	0.261453	+	0.189145i
$415$	−6.87948	+	11.9156i	−0.337700	+	0.584914i
$416$	3.00322	−	5.20173i	0.147245	−	0.255036i
$417$	−2.81642	+	8.69813i	−0.137921	+	0.425949i
$418$	11.8550	−	6.84450i	0.579848	−	0.334776i
$419$	−3.75114	+	6.49717i	−0.183255	+	0.317407i	−0.942987	−	0.332829i	$-0.891997\pi$
$419$	−3.75114	+	6.49717i	−0.183255	+	0.317407i	0.759732	+	0.650236i	$0.225330\pi$
$420$	4.58257	+	0.00505279i	0.223607	+	0.000246551i
$421$	−7.94926	−	13.7685i	−0.387423	−	0.671037i	0.604679	−	0.796469i	$-0.293301\pi$
$421$	−7.94926	−	13.7685i	−0.387423	−	0.671037i	−0.992102	+	0.125433i	$0.959968\pi$
$422$	5.41288	+	3.12513i	0.263495	+	0.152129i
$423$	−22.6507	+	10.1400i	−1.10131	+	0.493023i
$424$	4.32256	+	7.48689i	0.209922	+	0.363596i
$425$	−1.28345			−0.0622564
$426$	5.11546	+	23.9466i	0.247845	+	1.16021i
$427$	−5.26511	+	5.82263i	−0.254797	+	0.281777i
$428$	11.5596	+	6.67392i	0.558753	+	0.322596i
$429$	−31.4999	+	28.4207i	−1.52083	+	1.37217i
$430$	4.22219	+	2.43768i	0.203612	+	0.117556i
$431$	19.4232	−	11.2140i	0.935581	−	0.540158i	0.0470087	−	0.998894i	$-0.485031\pi$
$431$	19.4232	−	11.2140i	0.935581	−	0.540158i	0.888572	+	0.458737i	$0.151698\pi$
$432$	−3.06703	−	4.19444i	−0.147563	−	0.201805i
$433$		−	1.97195i		−	0.0947659i	−0.998877	−	0.0473830i	$-0.984912\pi$
$433$		−	1.97195i		−	0.0947659i	0.998877	−	0.0473830i	$-0.0150881\pi$
$434$	−15.3923	−	13.9185i	−0.738856	−	0.668110i
$435$	3.83125	−	11.8323i	0.183694	−	0.567316i
$436$	−5.38583	−	9.32854i	−0.257935	−	0.446756i
$437$	7.34666			0.351438
$438$	−8.94420	+	8.06988i	−0.427370	+	0.385594i
$439$			10.5670i			0.504336i	0.967683	+	0.252168i	$0.0811436\pi$
$439$			10.5670i			0.504336i	−0.967683	+	0.252168i	$0.918856\pi$
$440$	4.07809			0.194415
$441$	−10.4599	−	18.2096i	−0.498089	−	0.867126i
$442$	7.70896			0.366678
$443$			6.76147i			0.321247i	0.987016	+	0.160624i	$0.0513505\pi$
$443$			6.76147i			0.321247i	−0.987016	+	0.160624i	$0.948649\pi$
$444$	9.56264	+	3.09634i	0.453823	+	0.146946i
$445$	−14.5899			−0.691629
$446$	2.44981	+	4.24320i	0.116002	+	0.200921i
$447$	−5.07944	−	5.62977i	−0.240249	−	0.266279i
$448$	1.96242	+	1.77452i	0.0927156	+	0.0838380i
$449$		−	3.97534i		−	0.187608i	−0.995591	−	0.0938039i	$-0.970097\pi$
$449$		−	3.97534i		−	0.187608i	0.995591	−	0.0938039i	$-0.0299027\pi$
$450$	−2.98420	−	0.307516i	−0.140676	−	0.0144964i
$451$	−9.67166	+	5.58394i	−0.455421	+	0.262937i
$452$	2.45659	+	1.41832i	0.115548	+	0.0667119i
$453$	9.18358	+	2.97360i	0.431482	+	0.139712i
$454$	−15.1388	−	8.74040i	−0.710500	−	0.410207i
$455$	−10.6585	+	11.7872i	−0.499680	+	0.552590i
$456$	−5.53128	−	1.79100i	−0.259026	−	0.0838715i
$457$	−6.52028			−0.305006			−0.152503	−	0.988303i	$-0.548733\pi$
$457$	−6.52028			−0.305006			−0.152503	+	0.988303i	$0.548733\pi$
$458$	−7.29619	−	12.6374i	−0.340929	−	0.590506i
$459$	2.69392	−	6.10068i	0.125742	−	0.284755i
$460$	1.89542	+	1.09432i	0.0883743	+	0.0510229i
$461$	−4.69303	−	8.12857i	−0.218576	−	0.378585i	0.735797	−	0.677203i	$-0.236808\pi$
$461$	−4.69303	−	8.12857i	−0.218576	−	0.378585i	−0.954373	+	0.298617i	$0.903475\pi$
$462$	−9.32622	−	16.1947i	−0.433895	−	0.753446i
$463$	16.8709	−	29.2212i	0.784056	−	1.35803i	−0.145505	−	0.989357i	$-0.546481\pi$
$463$	16.8709	−	29.2212i	0.784056	−	1.35803i	0.929561	−	0.368668i	$-0.120186\pi$
$464$	6.21856	−	3.59029i	0.288689	−	0.166675i
$465$	9.10069	+	10.0867i	0.422034	+	0.467759i
$466$	−1.97662	+	3.42360i	−0.0915651	+	0.158595i
$467$	−17.9147	+	31.0293i	−0.828996	+	1.43586i	0.0698312	+	0.997559i	$0.477754\pi$
$467$	−17.9147	+	31.0293i	−0.828996	+	1.43586i	−0.898827	+	0.438304i	$0.855579\pi$
$468$	17.9244	+	1.84708i	0.828556	+	0.0853811i
$469$	16.9199	+	15.2998i	0.781289	+	0.706480i
$470$	−7.16398	+	4.13613i	−0.330450	+	0.190785i
$471$	−0.476545	+	0.101800i	−0.0219581	+	0.00469067i
$472$		−	1.26116i		−	0.0580495i
$473$		−	19.8822i		−	0.914183i
$474$	−20.6403	+	4.40917i	−0.948039	+	0.202520i
$475$	−2.90701	+	1.67836i	−0.133383	+	0.0770085i
$476$	−0.713041	+	3.31998i	−0.0326822	+	0.152171i
$477$	−15.2017	+	21.0131i	−0.696039	+	0.962124i
$478$	9.25590	−	16.0317i	0.423355	−	0.733272i
$479$	−6.93894	+	12.0186i	−0.317048	+	0.549144i	−0.979871	−	0.199633i	$-0.936025\pi$
$479$	−6.93894	+	12.0186i	−0.317048	+	0.549144i	0.662823	+	0.748776i	$0.269358\pi$
$480$	−1.16028	−	1.28599i	−0.0529591	−	0.0586969i
$481$	−30.1867	+	17.4283i	−1.37639	+	0.794661i
$482$	−10.9683	+	18.9977i	−0.499593	+	0.865321i
$483$	0.0110587	−	10.0296i	0.000503190	−	0.456363i
$484$	−2.81540	−	4.87641i	−0.127973	−	0.221655i
$485$	−16.8723	−	9.74120i	−0.766130	−	0.442325i
$486$	7.72548	−	13.5395i	0.350435	−	0.614162i
$487$	13.8002	+	23.9026i	0.625345	+	1.08313i	0.988474	+	0.151390i	$0.0483750\pi$
$487$	13.8002	+	23.9026i	0.625345	+	1.08313i	−0.363129	+	0.931739i	$0.618292\pi$
$488$	2.96707			0.134313
$489$	−12.4106	−	4.01851i	−0.561229	−	0.181723i
$490$	−4.09045	−	5.68051i	−0.184788	−	0.256619i
$491$	−18.1949	−	10.5048i	−0.821122	−	0.474075i	0.0296811	−	0.999559i	$-0.490551\pi$
$491$	−18.1949	−	10.5048i	−0.821122	−	0.474075i	−0.850803	+	0.525484i	$0.823884\pi$
$492$	4.51257	+	1.46115i	0.203443	+	0.0658738i
$493$	7.98120	+	4.60795i	0.359455	+	0.207532i
$494$	17.4608	−	10.0810i	0.785597	−	0.453565i
$495$	4.99885	+	11.1664i	0.224681	+	0.501893i
$496$			7.84355i			0.352186i
$497$	25.0872	−	27.7437i	1.12532	−	1.24447i
$498$	−15.9642	−	17.6938i	−0.715372	−	0.792878i
$499$	−0.197663	−	0.342363i	−0.00884862	−	0.0153263i	0.861567	−	0.507644i	$-0.169483\pi$
$499$	−0.197663	−	0.342363i	−0.00884862	−	0.0153263i	−0.870416	+	0.492317i	$0.836150\pi$
$500$	−1.00000			−0.0447214
$501$	16.0577	+	5.19942i	0.717407	+	0.232293i
$502$			15.6773i			0.699710i
$503$	10.3934			0.463418			0.231709	−	0.972785i	$-0.425568\pi$
$503$	10.3934			0.463418			0.231709	+	0.972785i	$0.425568\pi$
$504$	−2.45339	+	7.54857i	−0.109283	+	0.336240i
$505$	−8.53717			−0.379899
$506$		−	8.92547i		−	0.396785i
$507$	−29.6771	+	26.7761i	−1.31801	+	1.18917i
$508$	10.9625			0.486384
$509$	−20.2673	−	35.1041i	−0.898334	−	1.55596i	−0.829624	−	0.558323i	$-0.811445\pi$
$509$	−20.2673	−	35.1041i	−0.898334	−	1.55596i	−0.0687103	−	0.997637i	$-0.521888\pi$
$510$	0.684794	−	2.11489i	0.0303232	−	0.0936491i
$511$	17.9913	+	3.86404i	0.795888	+	0.170935i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.87611	−	17.3409i	−0.0828322	−	0.765617i
$514$	−9.16878	+	5.29360i	−0.404417	+	0.233491i
$515$	3.12850	+	1.80624i	0.137858	+	0.0795923i
$516$	−6.26965	+	5.65677i	−0.276006	+	0.249026i
$517$	29.2153	+	16.8675i	1.28489	+	0.741831i
$518$	−4.71363	−	14.6124i	−0.207105	−	0.642031i
$519$	5.16228	+	24.1657i	0.226599	+	1.06076i
$520$	6.00644			0.263400
$521$	−4.80694	−	8.32586i	−0.210596	−	0.364763i	0.741305	−	0.671168i	$-0.234207\pi$
$521$	−4.80694	−	8.32586i	−0.210596	−	0.364763i	−0.951901	+	0.306405i	$0.900874\pi$
$522$	17.4533	+	12.6264i	0.763912	+	0.552644i
$523$	−14.2342	−	8.21809i	−0.622416	−	0.359352i	0.155393	−	0.987853i	$-0.450336\pi$
$523$	−14.2342	−	8.21809i	−0.622416	−	0.359352i	−0.777809	+	0.628501i	$0.783669\pi$
$524$	−10.3656	−	17.9538i	−0.452824	−	0.784313i
$525$	2.28691	+	3.97115i	0.0998090	+	0.173315i
$526$	−12.1325	+	21.0140i	−0.529001	+	0.916256i
$527$	−8.71810	+	5.03340i	−0.379766	+	0.219258i
$528$	−2.17589	+	6.71996i	−0.0946936	+	0.292449i
$529$	−9.10493	+	15.7702i	−0.395866	+	0.685661i
$530$	−4.32256	+	7.48689i	−0.187760	+	0.325210i
$531$	3.45324	−	1.54591i	0.149858	−	0.0670866i
$532$	2.72649	+	8.45218i	0.118208	+	0.366449i
$533$	−14.2450	+	8.22434i	−0.617019	+	0.356236i
$534$	7.78457	−	24.0416i	0.336871	−	1.04038i
$535$			13.3478i			0.577078i
$536$		−	8.62197i		−	0.372412i
$537$	−9.94705	−	11.0248i	−0.429247	−	0.475753i
$538$	15.6684	−	9.04616i	0.675513	−	0.390008i
$539$	−11.7214	+	26.0292i	−0.504877	+	1.12116i
$540$	2.09897	−	4.75335i	0.0903254	−	0.204552i
$541$	16.1578	−	27.9861i	0.694678	−	1.20322i	−0.275612	−	0.961269i	$-0.588880\pi$
$541$	16.1578	−	27.9861i	0.694678	−	1.20322i	0.970289	−	0.241948i	$-0.0777863\pi$
$542$	−1.77471	+	3.07389i	−0.0762303	+	0.132035i
$543$	2.89556	−	0.618548i	0.124260	−	0.0265444i
$544$	1.11150	−	0.641724i	0.0476551	−	0.0275137i
$545$	5.38583	−	9.32854i	0.230704	−	0.399591i
$546$	−13.7362	−	23.8525i	−0.587855	−	1.02079i
$547$	−3.41985	−	5.92335i	−0.146222	−	0.253264i	0.783606	−	0.621258i	$-0.213378\pi$
$547$	−3.41985	−	5.92335i	−0.146222	−	0.253264i	−0.929828	+	0.367994i	$0.880045\pi$
$548$	8.37821	+	4.83716i	0.357899	+	0.206633i
$549$	3.63698	+	8.12427i	0.155222	+	0.346736i
$550$	2.03904	+	3.53173i	0.0869451	+	0.150593i
$551$	24.1032			1.02683
$552$	−2.81456	+	2.53943i	−0.119796	+	0.108085i
$553$	23.9131	+	21.6234i	1.01689	+	0.919522i
$554$	1.99961	+	1.15448i	0.0849554	+	0.0490490i
$555$	2.09981	+	9.82966i	0.0891319	+	0.417246i
$556$	−4.57137	−	2.63928i	−0.193869	−	0.111931i
$557$	5.91206	−	3.41333i	0.250502	−	0.144627i	−0.369492	−	0.929234i	$-0.620468\pi$
$557$	5.91206	−	3.41333i	0.250502	−	0.144627i	0.619994	+	0.784607i	$0.287135\pi$
$558$	−21.4768	+	9.61448i	−0.909186	+	0.407014i
$559$		−	29.2836i		−	1.23856i
$560$	−0.555567	+	2.58676i	−0.0234770	+	0.109311i
$561$	−8.86555	+	1.89386i	−0.374304	+	0.0799587i
$562$	0.107755	+	0.186637i	0.00454537	+	0.00787281i
$563$	−10.8371			−0.456731			−0.228366	−	0.973575i	$-0.573338\pi$
$563$	−10.8371			−0.456731			−0.228366	+	0.973575i	$0.573338\pi$
$564$	−2.99320	−	14.0118i	−0.126037	−	0.590004i
$565$			2.83663i			0.119338i
$566$	−15.4484			−0.649346
$567$	−23.6764	+	2.53515i	−0.994316	+	0.106466i
$568$	−14.1375			−0.593196
$569$			13.9500i			0.584816i	0.956294	+	0.292408i	$0.0944564\pi$
$569$			13.9500i			0.584816i	−0.956294	+	0.292408i	$0.905544\pi$
$570$	−1.21458	−	5.68573i	−0.0508734	−	0.238149i
$571$	−27.2120			−1.13879			−0.569393	−	0.822066i	$-0.692822\pi$
$571$	−27.2120			−1.13879			−0.569393	+	0.822066i	$0.692822\pi$
$572$	−12.2474	−	21.2131i	−0.512089	−	0.886964i
$573$	−15.6874	+	3.35115i	−0.655352	+	0.139996i
$574$	−2.22434	−	6.89553i	−0.0928423	−	0.287814i
$575$			2.18864i			0.0912726i
$576$	2.73815	−	1.22578i	0.114090	−	0.0510743i
$577$	13.2438	−	7.64631i	0.551346	−	0.318320i	−0.198318	−	0.980138i	$-0.563548\pi$
$577$	13.2438	−	7.64631i	0.551346	−	0.318320i	0.749665	+	0.661818i	$0.230215\pi$
$578$	−13.2959	−	7.67638i	−0.553036	−	0.319295i
$579$	−8.77433	−	41.0745i	−0.364649	−	1.70700i
$580$	6.21856	+	3.59029i	0.258212	+	0.149079i
$581$	−7.64402	+	35.5912i	−0.317127	+	1.47657i
$582$	25.0541	−	22.6050i	1.03853	−	0.937006i
$583$	35.2556			1.46014
$584$	−3.47757	−	6.02332i	−0.143903	−	0.249247i
$585$	7.36259	+	16.4465i	0.304405	+	0.679980i
$586$	0.601528	+	0.347292i	0.0248489	+	0.0143465i
$587$	7.16231	+	12.4055i	0.295620	+	0.512029i	0.975129	−	0.221638i	$-0.0711404\pi$
$587$	7.16231	+	12.4055i	0.295620	+	0.512029i	−0.679509	+	0.733667i	$0.737807\pi$
$588$	11.5430	−	3.70946i	0.476024	−	0.152975i
$589$	−13.1643	+	22.8013i	−0.542426	+	0.939509i
$590$	1.09220	−	0.630579i	0.0449650	−	0.0259605i
$591$	32.0045	−	6.83680i	1.31649	−	0.281228i
$592$	−2.90160	+	5.02572i	−0.119255	+	0.206556i
$593$	−0.594674	+	1.03001i	−0.0244203	+	0.0422973i	−0.877977	−	0.478702i	$-0.841107\pi$
$593$	−0.594674	+	1.03001i	−0.0244203	+	0.0422973i	0.853557	+	0.521000i	$0.174441\pi$
$594$	−21.0674	+	2.27929i	−0.864407	+	0.0935202i
$595$	−3.23171	+	1.04248i	−0.132487	+	0.0427374i
$596$	3.79127	−	2.18889i	0.155297	−	0.0896606i
$597$	3.02121	+	3.34854i	0.123650	+	0.137047i
$598$		−	13.1459i		−	0.537577i
$599$		−	45.9639i		−	1.87803i	−0.343872	−	0.939016i	$-0.611739\pi$
$599$		−	45.9639i		−	1.87803i	0.343872	−	0.939016i	$-0.388261\pi$
$600$	0.533558	−	1.64782i	0.0217824	−	0.0672720i
$601$	14.0543	−	8.11427i	0.573288	−	0.330988i	−0.185173	−	0.982706i	$-0.559285\pi$
$601$	14.0543	−	8.11427i	0.573288	−	0.330988i	0.758462	+	0.651718i	$0.225951\pi$
$602$	12.6114	+	2.70859i	0.514003	+	0.110394i
$603$	23.6082	−	10.5687i	0.961401	−	0.430389i
$604$	−2.78658	+	4.82650i	−0.113384	+	0.196387i
$605$	2.81540	−	4.87641i	0.114462	−	0.198254i
$606$	4.55507	−	14.0677i	0.185037	−	0.571463i
$607$	6.02151	−	3.47652i	0.244406	−	0.141108i	−0.372794	−	0.927914i	$-0.621600\pi$
$607$	6.02151	−	3.47652i	0.244406	−	0.141108i	0.617200	+	0.786806i	$0.288267\pi$
$608$	1.67836	−	2.90701i	0.0680665	−	0.117895i
$609$	0.0362819	−	32.9055i	0.00147022	−	1.33340i
$610$	1.48353	+	2.56956i	0.0600665	+	0.104038i
$611$	43.0300	+	24.8434i	1.74081	+	1.00506i
$612$	3.11959	+	2.25684i	0.126102	+	0.0912272i
$613$	−20.0114	−	34.6608i	−0.808253	−	1.39993i	−0.914073	−	0.405549i	$-0.867080\pi$
$613$	−20.0114	−	34.6608i	−0.808253	−	1.39993i	0.105821	−	0.994385i	$-0.466253\pi$
$614$	34.0796			1.37534
$615$	0.990892	+	4.63858i	0.0399566	+	0.187046i
$616$	10.2686	−	3.31241i	0.413732	−	0.133461i
$617$	7.94775	+	4.58864i	0.319964	+	0.184732i	0.651377	−	0.758754i	$-0.274192\pi$
$617$	7.94775	+	4.58864i	0.319964	+	0.184732i	−0.331412	+	0.943486i	$0.607525\pi$
$618$	−4.64559	+	4.19147i	−0.186873	+	0.168606i
$619$	−33.1913	−	19.1630i	−1.33407	−	0.770227i	−0.348151	−	0.937438i	$-0.613190\pi$
$619$	−33.1913	−	19.1630i	−1.33407	−	0.770227i	−0.985921	+	0.167212i	$0.946524\pi$
$620$	−6.79271	+	3.92178i	−0.272802	+	0.157502i
$621$	−10.4034	−	4.59390i	−0.417473	−	0.184347i
$622$			8.48761i			0.340322i
$623$	−36.7373	+	11.8506i	−1.47185	+	0.474785i
$624$	−3.20478	+	9.89754i	−0.128294	+	0.396219i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	27.2798			1.09032
$627$	−17.6039	+	15.8830i	−0.703031	+	0.634307i
$628$		−	0.281341i		−	0.0112267i
$629$	−7.44811			−0.296976
$630$	−7.76395	+	1.64958i	−0.309323	+	0.0657210i
$631$	−21.4220			−0.852797			−0.426399	−	0.904535i	$-0.640218\pi$
$631$	−21.4220			−0.852797			−0.426399	+	0.904535i	$0.640218\pi$
$632$		−	12.1855i		−	0.484714i
$633$	−10.2993	−	3.33487i	−0.409360	−	0.132549i
$634$	−0.0451228			−0.00179205
$635$	5.48127	+	9.49383i	0.217517	+	0.376751i
$636$	−10.0307	−	11.1175i	−0.397744	−	0.440837i
$637$	−17.2640	+	38.3372i	−0.684023	+	1.51898i
$638$		−	29.2830i		−	1.15933i
$639$	−17.3295	−	38.7105i	−0.685544	−	1.53137i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$	−20.6416	−	11.9174i	−0.815294	−	0.470710i	0.0334967	−	0.999439i	$-0.489336\pi$
$641$	−20.6416	−	11.9174i	−0.815294	−	0.470710i	−0.848791	+	0.528728i	$0.822669\pi$
$642$	−21.9949	−	7.12184i	−0.868068	−	0.281077i
$643$	−10.6419	−	6.14411i	−0.419676	−	0.242300i	0.275263	−	0.961369i	$-0.411235\pi$
$643$	−10.6419	−	6.14411i	−0.419676	−	0.242300i	−0.694939	+	0.719069i	$0.744568\pi$
$644$	5.66149	+	1.21594i	0.223094	+	0.0479146i
$645$	−8.03373	−	2.60129i	−0.316328	−	0.102426i
$646$	4.30818			0.169503
$647$	−8.50175	−	14.7255i	−0.334238	−	0.578917i	0.649100	−	0.760703i	$-0.275146\pi$
$647$	−8.50175	−	14.7255i	−0.334238	−	0.578917i	−0.983338	+	0.181786i	$0.941812\pi$
$648$	6.71275	+	5.99492i	0.263702	+	0.235503i
$649$	−4.45407	−	2.57156i	−0.174837	−	0.100942i
$650$	3.00322	+	5.20173i	0.117796	+	0.204029i
$651$	31.1083	+	18.0061i	1.21923	+	0.705716i
$652$	3.76577	−	6.52251i	0.147479	−	0.255441i
$653$	9.60648	−	5.54631i	0.375931	−	0.217044i	−0.300116	−	0.953903i	$-0.597025\pi$
$653$	9.60648	−	5.54631i	0.375931	−	0.217044i	0.676046	+	0.736859i	$0.263692\pi$
$654$	12.4981	+	13.8522i	0.488715	+	0.541664i
$655$	10.3656	−	17.9538i	0.405018	−	0.701511i
$656$	−1.36925	+	2.37162i	−0.0534604	+	0.0925961i
$657$	12.2300	−	16.9054i	0.477138	−	0.659542i
$658$	−14.6793	+	16.2336i	−0.572257	+	0.632853i
$659$	−39.7712	+	22.9619i	−1.54927	+	0.894470i	−0.551069	+	0.834459i	$0.685780\pi$
$659$	−39.7712	+	22.9619i	−1.54927	+	0.894470i	−0.998198	+	0.0600103i	$0.980887\pi$
$660$	−6.90760	+	1.47560i	−0.268878	+	0.0574377i
$661$			20.8191i			0.809770i	0.914368	+	0.404885i	$0.132688\pi$
$661$			20.8191i			0.809770i	−0.914368	+	0.404885i	$0.867312\pi$
$662$		−	18.4652i		−	0.717669i
$663$	−13.0577	+	2.78938i	−0.507119	+	0.108331i
$664$	11.9156	−	6.87948i	0.462415	−	0.266975i
$665$	−5.95656	+	6.58730i	−0.230986	+	0.255444i
$666$	−17.3179	−	1.78458i	−0.671055	−	0.0691509i
$667$	7.85785	−	13.6102i	0.304257	−	0.526989i
$668$	−4.87241	+	8.43926i	−0.188519	+	0.326525i
$669$	−5.68491	−	6.30084i	−0.219792	−	0.243605i
$670$	7.46684	−	4.31098i	0.288469	−	0.166548i
$671$	6.04998	−	10.4789i	0.233557	−	0.404532i
$672$	−3.96610	−	2.29566i	−0.152996	−	0.0885571i
$673$	14.6307	+	25.3410i	0.563970	+	0.976825i	0.997145	+	0.0755149i	$0.0240600\pi$
$673$	14.6307	+	25.3410i	0.563970	+	0.976825i	−0.433175	+	0.901310i	$0.642607\pi$
$674$	−19.9693	−	11.5293i	−0.769190	−	0.444092i
$675$	5.16601	−	0.558910i	0.198840	−	0.0215125i
$676$	−11.5387	−	19.9855i	−0.443795	−	0.768675i
$677$	24.6115			0.945898			0.472949	−	0.881090i	$-0.343189\pi$
$677$	24.6115			0.945898			0.472949	+	0.881090i	$0.343189\pi$
$678$	−4.67426	−	1.51351i	−0.179514	−	0.0581258i
$679$	−50.3964	−	10.8238i	−1.93403	−	0.415378i
$680$	1.11150	+	0.641724i	0.0426240	+	0.0246090i
$681$	28.8052	+	9.32701i	1.10382	+	0.357412i
$682$	27.7013	+	15.9933i	1.06074	+	0.612417i
$683$	4.84830	−	2.79917i	0.185515	−	0.107107i	−0.404366	−	0.914597i	$-0.632508\pi$
$683$	4.84830	−	2.79917i	0.185515	−	0.107107i	0.589881	+	0.807490i	$0.299175\pi$
$684$	10.0171	+	1.03225i	0.383014	+	0.0394689i
$685$			9.67432i			0.369637i
$686$	−14.9137	−	10.9810i	−0.569407	−	0.419256i
$687$	16.9312	+	18.7656i	0.645966	+	0.715952i
$688$	−2.43768	−	4.22219i	−0.0929358	−	0.160970i
$689$	51.9264			1.97824
$690$	−3.60649	−	1.16777i	−0.137297	−	0.0444561i
$691$		−	33.0844i		−	1.25859i	−0.777167	−	0.629294i	$-0.783344\pi$
$691$		−	33.0844i		−	1.25859i	0.777167	−	0.629294i	$-0.216656\pi$
$692$	−14.2669			−0.542346
$693$	21.6569	+	24.0566i	0.822678	+	0.913833i
$694$	−22.3311			−0.847677
$695$		−	5.27856i		−	0.200227i
$696$	−9.23412	+	8.33146i	−0.350018	+	0.315803i
$697$	−3.51473			−0.133130
$698$	−4.62963	−	8.01876i	−0.175234	−	0.303515i
$699$	2.10928	−	6.51423i	0.0797803	−	0.246391i
$700$	−2.51799	+	0.812247i	−0.0951709	+	0.0307000i
$701$			3.12417i			0.117998i	0.998258	+	0.0589992i	$0.0187909\pi$
$701$			3.12417i			0.117998i	−0.998258	+	0.0589992i	$0.981209\pi$
$702$	−31.0293	+	3.35706i	−1.17113	+	0.126704i
$703$	−16.8699	+	9.73987i	−0.636262	+	0.367346i
$704$	−3.53173	−	2.03904i	−0.133107	−	0.0768493i
$705$	10.6380	−	9.59810i	0.400650	−	0.361485i
$706$	−11.4201	−	6.59338i	−0.429800	−	0.248145i
$707$	−21.4965	+	6.93429i	−0.808459	+	0.260791i
$708$	0.456333	+	2.13619i	0.0171500	+	0.0802831i
$709$	−43.4822			−1.63301			−0.816504	−	0.577340i	$-0.804091\pi$
$709$	−43.4822			−1.63301			−0.816504	+	0.577340i	$0.804091\pi$
$710$	−7.06874	−	12.2434i	−0.265285	−	0.459487i
$711$	33.3658	−	14.9368i	1.25132	−	0.560174i
$712$	12.6353	+	7.29497i	0.473526	+	0.273391i
$713$	8.58336	+	14.8668i	0.321449	+	0.556766i
$714$	0.00648500	−	5.88150i	0.000242695	−	0.220109i
$715$	12.2474	−	21.2131i	0.458026	−	0.793325i
$716$	7.42444	−	4.28650i	0.277464	−	0.160194i
$717$	−9.87711	+	30.5041i	−0.368867	+	1.13920i
$718$	−5.66550	+	9.81294i	−0.211435	+	0.366216i
$719$	2.21764	−	3.84106i	0.0827039	−	0.143247i	−0.821707	−	0.569911i	$-0.806978\pi$
$719$	2.21764	−	3.84106i	0.0827039	−	0.143247i	0.904411	+	0.426663i	$0.140311\pi$
$720$	2.43063	+	1.75842i	0.0905843	+	0.0655323i
$721$	9.34462	+	2.00697i	0.348012	+	0.0747435i
$722$	−6.69647	+	3.86621i	−0.249217	+	0.143885i
$723$	11.7045	−	36.1477i	0.435294	−	1.34435i
$724$			1.70947i			0.0635319i
$725$			7.18058i			0.266680i
$726$	6.53328	+	7.24112i	0.242473	+	0.268743i
$727$	−36.5068	+	21.0772i	−1.35396	+	0.781711i	−0.988802	−	0.149233i	$-0.952320\pi$
$727$	−36.5068	+	21.0772i	−1.35396	+	0.781711i	−0.365162	+	0.930944i	$0.618986\pi$
$728$	15.1241	−	4.87871i	0.560538	−	0.180817i
$729$	−8.18661	+	25.7290i	−0.303208	+	0.952924i
$730$	3.47757	−	6.02332i	0.128711	−	0.222933i
$731$	3.12864	−	5.41896i	0.115717	−	0.200428i
$732$	−5.02572	+	1.07359i	−0.185756	+	0.0396812i
$733$	40.0324	−	23.1127i	1.47863	−	0.853688i	0.478923	−	0.877857i	$-0.341027\pi$
$733$	40.0324	−	23.1127i	1.47863	−	0.853688i	0.999708	+	0.0241691i	$0.00769402\pi$
$734$	−12.1737	+	21.0854i	−0.449339	+	0.778278i
$735$	8.98396	+	8.14177i	0.331379	+	0.300314i
$736$	−1.09432	−	1.89542i	−0.0403372	−	0.0698660i
$737$	−30.4504	−	17.5806i	−1.12166	−	0.647589i
$738$	−8.17225	−	0.842135i	−0.300825	−	0.0309994i
$739$	−14.2820	−	24.7371i	−0.525371	−	0.909969i	−0.999563	−	0.0295478i	$-0.990593\pi$
$739$	−14.2820	−	24.7371i	−0.525371	−	0.909969i	0.474193	−	0.880421i	$-0.342740\pi$
$740$	−5.80320			−0.213330
$741$	−25.9280	+	23.3934i	−0.952488	+	0.859380i
$742$	−4.80294	+	22.3629i	−0.176322	+	0.820967i
$743$	3.36454	+	1.94252i	0.123433	+	0.0712640i	0.560445	−	0.828192i	$-0.310630\pi$
$743$	3.36454	+	1.94252i	0.123433	+	0.0712640i	−0.437012	+	0.899456i	$0.643963\pi$
$744$	−2.83808	−	13.2857i	−0.104049	−	0.487076i
$745$	3.79127	+	2.18889i	0.138902	+	0.0801948i
$746$	23.7833	−	13.7313i	0.870767	−	0.502738i
$747$	33.4430	+	24.1940i	1.22361	+	0.885210i
$748$		−	5.23401i		−	0.191375i
$749$	10.8417	+	33.6097i	0.396149	+	1.22807i
$750$	1.69383	−	0.361836i	0.0618501	−	0.0132124i
$751$	−10.6443	−	18.4364i	−0.388415	−	0.672754i	0.603822	−	0.797119i	$-0.293644\pi$
$751$	−10.6443	−	18.4364i	−0.388415	−	0.672754i	−0.992236	+	0.124365i	$0.960310\pi$
$752$	8.27225			0.301658
$753$	−5.67260	−	26.5547i	−0.206721	−	0.967706i
$754$		−	43.1297i		−	1.57069i
$755$	−5.57316			−0.202828
$756$	1.42429	−	13.6737i	0.0518010	−	0.497309i
$757$	−42.1251			−1.53106			−0.765531	−	0.643399i	$-0.777524\pi$
$757$	−42.1251			−1.53106			−0.765531	+	0.643399i	$0.777524\pi$
$758$		−	32.0033i		−	1.16241i
$759$	3.22956	+	15.1183i	0.117226	+	0.548758i
$760$	3.35672			0.121761
$761$	24.4190	+	42.2949i	0.885187	+	1.53319i	0.845499	+	0.533976i	$0.179303\pi$
$761$	24.4190	+	42.2949i	0.885187	+	1.53319i	0.0396873	+	0.999212i	$0.487364\pi$
$762$	−18.5687	+	3.96665i	−0.672674	+	0.143696i
$763$	5.98438	−	27.8638i	0.216649	−	1.00874i
$764$		−	9.26150i		−	0.335069i
$765$	−0.394681	+	3.83006i	−0.0142697	+	0.138476i
$766$	12.3587	−	7.13527i	0.446536	−	0.257808i
$767$	−6.56020	−	3.78754i	−0.236875	−	0.136760i
$768$	0.361836	+	1.69383i	0.0130566	+	0.0611210i
$769$	41.1583	+	23.7627i	1.48420	+	0.856906i	0.999839	−	0.0179596i	$-0.00571703\pi$
$769$	41.1583	+	23.7627i	1.48420	+	0.856906i	0.484366	+	0.874866i	$0.339050\pi$
$770$	8.00292	+	7.23663i	0.288405	+	0.260790i
$771$	13.6150	−	12.2841i	0.490331	−	0.442400i
$772$	24.2494			0.872756
$773$	−2.07497	−	3.59395i	−0.0746314	−	0.129265i	0.826295	−	0.563238i	$-0.190445\pi$
$773$	−2.07497	−	3.59395i	−0.0746314	−	0.129265i	−0.900926	+	0.433973i	$0.857111\pi$
$774$	8.57292	−	11.8502i	0.308147	−	0.425948i
$775$	−6.79271	−	3.92178i	−0.244001	−	0.140874i
$776$	9.74120	+	16.8723i	0.349689	+	0.605679i
$777$	13.2714	+	23.0454i	0.476109	+	0.826749i
$778$	−5.38049	+	9.31929i	−0.192900	+	0.334113i
$779$	−7.96086	+	4.59621i	−0.285228	+	0.164676i
$780$	−10.1739	+	2.17335i	−0.364285	+	0.0778184i
$781$	−28.8270	+	49.9297i	−1.03151	+	1.78663i
$782$	1.40450	−	2.43267i	0.0502249	−	0.0869922i
$783$	−34.1318	−	15.0718i	−1.21977	−	0.538623i
$784$	0.702180	+	6.96469i	0.0250779	+	0.248739i
$785$	0.243649	−	0.140671i	0.00869619	−	0.00502075i
$786$	24.0539	+	26.6600i	0.857976	+	0.950932i
$787$		−	27.3237i		−	0.973984i	−0.873406	−	0.486992i	$-0.838094\pi$
$787$		−	27.3237i		−	0.973984i	0.873406	−	0.486992i	$-0.161906\pi$
$788$			18.8947i			0.673097i
$789$	12.9467	−	39.9843i	0.460916	−	1.42348i
$790$	10.5530	−	6.09277i	0.375458	−	0.216771i
$791$	2.30404	+	7.14260i	0.0819224	+	0.253961i
$792$	1.25408	−	12.1698i	0.0445617	−	0.432436i
$793$	8.91076	−	15.4339i	0.316430	−	0.548073i
$794$	11.1717	−	19.3500i	0.396470	−	0.686707i
$795$	4.61267	−	14.2456i	0.163594	−	0.505240i
$796$	−2.25502	+	1.30194i	−0.0799271	+	0.0461459i
$797$	−14.7404	+	25.5311i	−0.522132	+	0.904359i	0.477536	+	0.878612i	$0.341530\pi$
$797$	−14.7404	+	25.5311i	−0.522132	+	0.904359i	−0.999668	+	0.0257473i	$0.991803\pi$
$798$	−7.67653	−	13.3301i	−0.271746	−	0.471879i
$799$	5.30850	+	9.19460i	0.187801	+	0.325282i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	−4.48664	+	43.5393i	−0.158528	+	1.53838i
$802$	9.49194	+	16.4405i	0.335172	+	0.580535i
$803$	−28.3636			−1.00093
$804$	3.11974	+	14.6042i	0.110025	+	0.515050i
$805$	1.77772	+	5.51097i	0.0626563	+	0.194236i
$806$	40.8000	+	23.5559i	1.43712	+	0.829721i
$807$	−23.2665	+	20.9921i	−0.819018	+	0.738957i
$808$	7.39341	+	4.26859i	0.260099	+	0.150168i
$809$	−1.53294	+	0.885046i	−0.0538955	+	0.0311166i	−0.526706	−	0.850048i	$-0.676573\pi$
$809$	−1.53294	+	0.885046i	−0.0538955	+	0.0311166i	0.472810	+	0.881164i	$0.343240\pi$
$810$	−1.83538	+	8.81087i	−0.0644886	+	0.309582i
$811$		−	21.7821i		−	0.764872i	−0.923982	−	0.382436i	$-0.875085\pi$
$811$		−	21.7821i		−	0.764872i	0.923982	−	0.382436i	$-0.124915\pi$
$812$	18.5745	+	3.98929i	0.651836	+	0.139997i
$813$	1.89382	−	5.84881i	0.0664191	−	0.205127i
$814$	11.8330	+	20.4953i	0.414746	+	0.718361i
$815$	7.53154			0.263818
$816$	−1.65050	+	1.48916i	−0.0577789	+	0.0521309i
$817$		−	16.3653i		−	0.572548i
$818$	−26.0187			−0.909722
$819$	31.8975	+	35.4319i	1.11459	+	1.23809i
$820$	−2.73851			−0.0956329
$821$			24.8390i			0.866886i	0.901181	+	0.433443i	$0.142702\pi$
$821$			24.8390i			0.866886i	−0.901181	+	0.433443i	$0.857298\pi$
$822$	−15.9416	−	5.16181i	−0.556026	−	0.180039i
$823$	44.7079			1.55842			0.779210	−	0.626763i	$-0.215620\pi$
$823$	44.7079			1.55842			0.779210	+	0.626763i	$0.215620\pi$
$824$	−1.80624	−	3.12850i	−0.0629233	−	0.108986i
$825$	−4.73171	−	5.24436i	−0.164737	−	0.182585i
$826$	2.23795	−	2.47492i	0.0778681	−	0.0861135i
$827$		−	43.9883i		−	1.52962i	−0.644255	−	0.764811i	$-0.722832\pi$
$827$		−	43.9883i		−	1.52962i	0.644255	−	0.764811i	$-0.277168\pi$
$828$	3.84854	−	5.31978i	0.133746	−	0.184875i
$829$	23.3072	−	13.4564i	0.809492	−	0.467360i	−0.0372876	−	0.999305i	$-0.511872\pi$
$829$	23.3072	−	13.4564i	0.809492	−	0.467360i	0.846779	+	0.531944i	$0.178538\pi$
$830$	11.9156	+	6.87948i	0.413597	+	0.238790i
$831$	−3.80474	−	1.23196i	−0.131985	−	0.0427362i
$832$	−5.20173	−	3.00322i	−0.180338	−	0.104118i
$833$	−7.29064	+	5.24988i	−0.252606	+	0.181898i
$834$	8.69813	+	2.81642i	0.301192	+	0.0975246i
$835$	−9.74482			−0.337234
$836$	−6.84450	−	11.8550i	−0.236722	−	0.410015i
$837$	32.8993	−	24.0564i	1.13717	−	0.831512i
$838$	6.49717	+	3.75114i	0.224441	+	0.129581i
$839$	−7.52241	−	13.0292i	−0.259702	−	0.449818i	0.706460	−	0.707753i	$-0.250291\pi$
$839$	−7.52241	−	13.0292i	−0.259702	−	0.449818i	−0.966162	+	0.257935i	$0.916958\pi$
$840$	0.00505279	−	4.58257i	0.000174338	−	0.158114i
$841$	11.2803	−	19.5381i	0.388977	−	0.673728i
$842$	−13.7685	+	7.94926i	−0.474495	+	0.273950i
$843$	−0.250051	−	0.277143i	−0.00861222	−	0.00954530i
$844$	3.12513	−	5.41288i	0.107571	−	0.186319i
$845$	11.5387	−	19.9855i	0.396942	−	0.687524i
$846$	10.1400	+	22.6507i	0.348620	+	0.778746i
$847$	3.12828	−	14.5655i	0.107489	−	0.500478i
$848$	7.48689	−	4.32256i	0.257101	−	0.148437i
$849$	26.1671	−	5.58980i	0.898051	−	0.191842i
$850$			1.28345i			0.0440219i
$851$			12.7011i			0.435389i
$852$	23.9466	−	5.11546i	0.820396	−	0.175253i
$853$	−11.0905	+	6.40312i	−0.379732	+	0.219239i	−0.677702	−	0.735337i	$-0.737024\pi$
$853$	−11.0905	+	6.40312i	−0.379732	+	0.219239i	0.297970	+	0.954575i	$0.403691\pi$
$854$	5.82263	+	5.26511i	0.199246	+	0.180168i
$855$	4.11461	+	9.19121i	0.140717	+	0.314333i
$856$	6.67392	−	11.5596i	0.228110	−	0.395098i
$857$	−21.2608	+	36.8247i	−0.726254	+	1.25791i	0.232201	+	0.972668i	$0.425407\pi$
$857$	−21.2608	+	36.8247i	−0.726254	+	1.25791i	−0.958456	+	0.285241i	$0.907926\pi$
$858$	28.4207	+	31.4999i	0.970268	+	1.07539i
$859$	6.36498	−	3.67482i	0.217170	−	0.125383i	−0.387469	−	0.921883i	$-0.626651\pi$
$859$	6.36498	−	3.67482i	0.217170	−	0.125383i	0.604639	+	0.796499i	$0.293317\pi$
$860$	2.43768	−	4.22219i	0.0831243	−	0.143976i
$861$	6.26272	+	10.8750i	0.213433	+	0.370620i
$862$	−11.2140	−	19.4232i	−0.381949	−	0.661556i
$863$	−3.64790	−	2.10612i	−0.124176	−	0.0716930i	0.436625	−	0.899643i	$-0.356174\pi$
$863$	−3.64790	−	2.10612i	−0.124176	−	0.0716930i	−0.560801	+	0.827950i	$0.689507\pi$
$864$	−4.19444	+	3.06703i	−0.142698	+	0.104343i
$865$	−7.13345	−	12.3555i	−0.242544	−	0.420099i
$866$	−1.97195			−0.0670096
$867$	25.2986	+	8.19158i	0.859186	+	0.278201i
$868$	−13.9185	+	15.3923i	−0.472425	+	0.522450i
$869$	−43.0360	−	24.8468i	−1.45990	−	0.842871i
$870$	−11.8323	−	3.83125i	−0.401153	−	0.129892i
$871$	−44.8491	−	25.8937i	−1.51966	−	0.877373i
$872$	−9.32854	+	5.38583i	−0.315904	+	0.182387i
$873$	−34.2582	+	47.3546i	−1.15946	+	1.60271i
$874$		−	7.34666i		−	0.248504i
$875$	−1.96242	−	1.77452i	−0.0663419	−	0.0599896i
$876$	8.06988	+	8.94420i	0.272656	+	0.302197i
$877$	13.3618	+	23.1433i	0.451195	+	0.781493i	0.998461	−	0.0554662i	$-0.0176645\pi$
$877$	13.3618	+	23.1433i	0.451195	+	0.781493i	−0.547265	+	0.836959i	$0.684331\pi$
$878$	10.5670			0.356620
$879$	−1.14455	−	0.370601i	−0.0386048	−	0.0125001i
$880$		−	4.07809i		−	0.137472i
$881$	−5.40270			−0.182022			−0.0910109	−	0.995850i	$-0.529010\pi$
$881$	−5.40270			−0.182022			−0.0910109	+	0.995850i	$0.529010\pi$
$882$	−18.2096	+	10.4599i	−0.613151	+	0.352202i
$883$	−27.9671			−0.941169			−0.470584	−	0.882355i	$-0.655957\pi$
$883$	−27.9671			−0.941169			−0.470584	+	0.882355i	$0.655957\pi$
$884$		−	7.70896i		−	0.259280i
$885$	−1.62183	+	1.46329i	−0.0545173	+	0.0491880i
$886$	6.76147			0.227156
$887$	10.7276	+	18.5807i	0.360198	+	0.623880i	0.987993	−	0.154498i	$-0.0493760\pi$
$887$	10.7276	+	18.5807i	0.360198	+	0.623880i	−0.627796	+	0.778378i	$0.716043\pi$
$888$	3.09634	−	9.56264i	0.103906	−	0.320901i
$889$	21.5131	+	19.4532i	0.721526	+	0.652439i
$890$			14.5899i			0.489056i
$891$	34.8600	−	11.4837i	1.16785	−	0.384718i
$892$	4.24320	−	2.44981i	0.142073	−	0.0820257i
$893$	24.0475	+	13.8838i	0.804719	+	0.464605i
$894$	−5.62977	+	5.07944i	−0.188288	+	0.169882i
$895$	7.42444	+	4.28650i	0.248172	+	0.143282i
$896$	1.77452	−	1.96242i	0.0592824	−	0.0655598i
$897$	4.75668	+	22.2670i	0.158821	+	0.743475i
$898$	−3.97534			−0.132659
$899$	28.1606	+	48.7756i	0.939209	+	1.62676i
$900$	−0.307516	+	2.98420i	−0.0102505	+	0.0994732i
$901$	9.60904	+	5.54778i	0.320124	+	0.184823i
$902$	5.58394	+	9.67166i	0.185925	+	0.322031i
$903$	−22.3417	−	0.0246342i	−0.743486	−	0.000819775i
$904$	1.41832	−	2.45659i	0.0471725	−	0.0817051i
$905$	−1.48044	+	0.854734i	−0.0492116	+	0.0284123i
$906$	2.97360	−	9.18358i	0.0987913	−	0.305104i
$907$	10.5503	−	18.2736i	0.350317	−	0.606766i	−0.635988	−	0.771699i	$-0.719407\pi$
$907$	10.5503	−	18.2736i	0.350317	−	0.606766i	0.986305	+	0.164932i	$0.0527406\pi$
$908$	−8.74040	+	15.1388i	−0.290060	+	0.502399i
$909$	−2.62532	+	25.4766i	−0.0870763	+	0.845006i
$910$	11.7872	+	10.6585i	0.390740	+	0.353327i
$911$	18.9423	−	10.9363i	0.627585	−	0.362337i	−0.152231	−	0.988345i	$-0.548646\pi$
$911$	18.9423	−	10.9363i	0.627585	−	0.362337i	0.779816	+	0.626008i	$0.215312\pi$
$912$	−1.79100	+	5.53128i	−0.0593061	+	0.183159i
$913$		−	56.1102i		−	1.85698i
$914$			6.52028i			0.215672i
$915$	−3.44262	−	3.81561i	−0.113809	−	0.126140i
$916$	−12.6374	+	7.29619i	−0.417551	+	0.241073i
$917$	11.5176	−	53.6267i	0.380344	−	1.77091i
$918$	−6.10068	−	2.69392i	−0.201352	−	0.0889127i
$919$	−10.9564	+	18.9770i	−0.361418	+	0.625994i	−0.988194	−	0.153205i	$-0.951040\pi$
$919$	−10.9564	+	18.9770i	−0.361418	+	0.625994i	0.626777	+	0.779199i	$0.284374\pi$
$920$	1.09432	−	1.89542i	0.0360787	−	0.0624901i
$921$	−57.7251	+	12.3312i	−1.90211	+	0.406328i
$922$	−8.12857	+	4.69303i	−0.267700	+	0.154557i
$923$	−42.4580	+	73.5394i	−1.39752	+	2.42058i
$924$	−16.1947	+	9.32622i	−0.532766	+	0.306810i
$925$	−2.90160	−	5.02572i	−0.0954040	−	0.165245i
$926$	−29.2212	−	16.8709i	−0.960269	−	0.554411i
$927$	6.35223	−	8.78060i	0.208635	−	0.288393i
$928$	−3.59029	−	6.21856i	−0.117857	−	0.204134i
$929$	24.2160			0.794502			0.397251	−	0.917710i	$-0.369964\pi$
$929$	24.2160			0.794502			0.397251	+	0.917710i	$0.369964\pi$
$930$	10.0867	−	9.10069i	0.330756	−	0.298423i
$931$	−9.64803	+	21.4249i	−0.316201	+	0.702174i
$932$	3.42360	+	1.97662i	0.112144	+	0.0647463i
$933$	−3.07113	−	14.3766i	−0.100544	−	0.470669i
$934$	31.0293	+	17.9147i	1.01531	+	0.586188i
$935$	4.53279	−	2.61701i	0.148238	−	0.0855853i
$936$	1.84708	−	17.9244i	0.0603736	−	0.585877i
$937$			38.1815i			1.24733i	0.781690	+	0.623667i	$0.214358\pi$
$937$			38.1815i			1.24733i	−0.781690	+	0.623667i	$0.785642\pi$
$938$	15.2998	−	16.9199i	0.499557	−	0.552455i
$939$	−46.2075	+	9.87083i	−1.50792	+	0.322122i
$940$	4.13613	+	7.16398i	0.134906	+	0.233663i
$941$	7.93221			0.258583			0.129291	−	0.991607i	$-0.458730\pi$
$941$	7.93221			0.258583			0.129291	+	0.991607i	$0.458730\pi$
$942$	0.101800	+	0.476545i	0.00331681	+	0.0155267i
$943$			5.99361i			0.195179i
$944$	−1.26116			−0.0410472
$945$	12.5540	−	5.60340i	0.408380	−	0.182279i
$946$	−19.8822			−0.646425
$947$			3.30616i			0.107436i	0.998556	+	0.0537179i	$0.0171072\pi$
$947$			3.30616i			0.107436i	−0.998556	+	0.0537179i	$0.982893\pi$
$948$	4.40917	+	20.6403i	0.143203	+	0.670365i
$949$	−41.7756			−1.35609
$950$	1.67836	+	2.90701i	0.0544532	+	0.0943158i
$951$	0.0764305	−	0.0163271i	0.00247843	−	0.000529441i
$952$	3.31998	+	0.713041i	0.107601	+	0.0231098i
$953$		−	53.6699i		−	1.73854i	−0.494339	−	0.869269i	$-0.664590\pi$
$953$		−	53.6699i		−	1.73854i	0.494339	−	0.869269i	$-0.335410\pi$
$954$	21.0131	+	15.2017i	0.680325	+	0.492174i
$955$	8.02069	−	4.63075i	0.259543	−	0.149847i
$956$	−16.0317	−	9.25590i	−0.518502	−	0.299357i
$957$	10.5957	+	49.6006i	0.342509	+	1.60336i
$958$	12.0186	+	6.93894i	0.388303	+	0.224187i
$959$	7.85794	+	24.3598i	0.253746	+	0.786619i
$960$	−1.28599	+	1.16028i	−0.0415050	+	0.0374478i
$961$	−30.5213			−0.984557
$962$	17.4283	+	30.1867i	0.561910	+	0.973257i
$963$	39.8326	+	4.10468i	1.28359	+	0.132271i
$964$	18.9977	+	10.9683i	0.611874	+	0.353266i
$965$	12.1247	+	21.0006i	0.390308	+	0.676034i
$966$	−10.0296	−	0.0110587i	−0.322697	−	0.000355809i
$967$	8.76620	−	15.1835i	0.281902	−	0.488268i	−0.689951	−	0.723856i	$-0.742368\pi$
$967$	8.76620	−	15.1835i	0.281902	−	0.488268i	0.971853	+	0.235587i	$0.0757014\pi$
$968$	−4.87641	+	2.81540i	−0.156734	+	0.0904903i
$969$	−7.29734	+	1.55886i	−0.234424	+	0.0500777i
$970$	−9.74120	+	16.8723i	−0.312771	+	0.541735i
$971$	−1.13150	+	1.95981i	−0.0363115	+	0.0628933i	−0.883610	−	0.468224i	$-0.844894\pi$
$971$	−1.13150	+	1.95981i	−0.0363115	+	0.0628933i	0.847299	+	0.531117i	$0.178228\pi$
$972$	−13.5395	−	7.72548i	−0.434278	−	0.247795i
$973$	−4.28750	−	13.2914i	−0.137451	−	0.426101i
$974$	23.9026	−	13.8002i	0.765888	−	0.442186i
$975$	−6.96913	−	7.72419i	−0.223191	−	0.247372i
$976$		−	2.96707i		−	0.0949735i
$977$			45.2960i			1.44915i	0.689197	+	0.724574i	$0.257963\pi$
$977$			45.2960i			1.44915i	−0.689197	+	0.724574i	$0.742037\pi$
$978$	−4.01851	+	12.4106i	−0.128498	+	0.396849i
$979$	51.5277	−	29.7495i	1.64683	−	0.950799i
$980$	−5.68051	+	4.09045i	−0.181457	+	0.130665i
$981$	−26.1820	−	18.9411i	−0.835926	−	0.604742i
$982$	−10.5048	+	18.1949i	−0.335222	+	0.580621i
$983$	13.5937	−	23.5450i	0.433572	−	0.750970i	−0.563605	−	0.826044i	$-0.690586\pi$
$983$	13.5937	−	23.5450i	0.433572	−	0.750970i	0.997178	+	0.0750745i	$0.0239195\pi$
$984$	1.46115	−	4.51257i	0.0465798	−	0.143856i
$985$	−16.3633	+	9.44736i	−0.521379	+	0.301018i
$986$	4.60795	−	7.98120i	0.146747	−	0.254173i
$987$	18.9903	−	32.8086i	0.604468	−	1.04431i
$988$	−10.0810	−	17.4608i	−0.320719	−	0.555501i
$989$	−9.24086	−	5.33521i	−0.293842	−	0.169650i
$990$	11.1664	−	4.99885i	0.354892	−	0.158874i
$991$	−13.1793	−	22.8272i	−0.418654	−	0.725130i	0.577150	−	0.816638i	$-0.304165\pi$
$991$	−13.1793	−	22.8272i	−0.418654	−	0.725130i	−0.995804	+	0.0915077i	$0.970831\pi$
$992$	7.84355			0.249033
$993$	6.68137	+	31.2769i	0.212027	+	0.992543i
$994$	−27.7437	−	25.0872i	−0.879976	−	0.795718i
$995$	−2.25502	−	1.30194i	−0.0714890	−	0.0412742i
$996$	−17.6938	+	15.9642i	−0.560650	+	0.505845i
$997$	−44.4800	−	25.6806i	−1.40870	−	0.813312i	−0.413435	−	0.910534i	$-0.635671\pi$
$997$	−44.4800	−	25.6806i	−1.40870	−	0.813312i	−0.995263	+	0.0972221i	$0.969004\pi$
$998$	−0.342363	+	0.197663i	−0.0108373	+	0.00625692i
$999$	29.9794	−	3.24347i	0.948505	−	0.102619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.b.131.5	yes	28
3.2	odd	2		1890.2.bk.b.341.13		28
7.3	odd	6		630.2.t.b.311.9	✓	28
9.2	odd	6		630.2.t.b.551.9	yes	28
9.7	even	3		1890.2.t.b.1601.1		28
21.17	even	6		1890.2.t.b.1151.1		28
63.38	even	6	inner	630.2.bk.b.101.12	yes	28
63.52	odd	6		1890.2.bk.b.521.13		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.9	✓	28	7.3	odd	6
630.2.t.b.551.9	yes	28	9.2	odd	6
630.2.bk.b.101.12	yes	28	63.38	even	6	inner
630.2.bk.b.131.5	yes	28	1.1	even	1	trivial
1890.2.t.b.1151.1		28	21.17	even	6
1890.2.t.b.1601.1		28	9.7	even	3
1890.2.bk.b.341.13		28	3.2	odd	2
1890.2.bk.b.521.13		28	63.52	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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.361836 + 1.69383i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.69383 - 0.361836i) q^{6} +(-1.96242 - 1.77452i) q^{7} +1.00000i q^{8} +(-2.73815 + 1.22578i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.361836 + 1.69383i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.69383 - 0.361836i) q^{6} +(-1.96242 - 1.77452i) q^{7} +1.00000i q^{8} +(-2.73815 + 1.22578i) q^{9} +(-0.866025 + 0.500000i) q^{10} +(3.53173 + 2.03904i) q^{11} +(-0.361836 - 1.69383i) q^{12} +(5.20173 + 3.00322i) q^{13} +(-1.77452 + 1.96242i) q^{14} +(1.28599 - 1.16028i) q^{15} +1.00000 q^{16} +(0.641724 + 1.11150i) q^{17} +(1.22578 + 2.73815i) q^{18} +(2.90701 + 1.67836i) q^{19} +(0.500000 + 0.866025i) q^{20} +(2.29566 - 3.96610i) q^{21} +(2.03904 - 3.53173i) q^{22} +(1.89542 - 1.09432i) q^{23} +(-1.69383 + 0.361836i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.00322 - 5.20173i) q^{26} +(-3.06703 - 4.19444i) q^{27} +(1.96242 + 1.77452i) q^{28} +(6.21856 - 3.59029i) q^{29} +(-1.16028 - 1.28599i) q^{30} +7.84355i q^{31} -1.00000i q^{32} +(-2.17589 + 6.71996i) q^{33} +(1.11150 - 0.641724i) q^{34} +(-0.555567 + 2.58676i) q^{35} +(2.73815 - 1.22578i) q^{36} +(-2.90160 + 5.02572i) q^{37} +(1.67836 - 2.90701i) q^{38} +(-3.20478 + 9.89754i) q^{39} +(0.866025 - 0.500000i) q^{40} +(-1.36925 + 2.37162i) q^{41} +(-3.96610 - 2.29566i) q^{42} +(-2.43768 - 4.22219i) q^{43} +(-3.53173 - 2.03904i) q^{44} +(2.43063 + 1.75842i) q^{45} +(-1.09432 - 1.89542i) q^{46} +8.27225 q^{47} +(0.361836 + 1.69383i) q^{48} +(0.702180 + 6.96469i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-1.65050 + 1.48916i) q^{51} +(-5.20173 - 3.00322i) q^{52} +(7.48689 - 4.32256i) q^{53} +(-4.19444 + 3.06703i) q^{54} -4.07809i q^{55} +(1.77452 - 1.96242i) q^{56} +(-1.79100 + 5.53128i) q^{57} +(-3.59029 - 6.21856i) q^{58} -1.26116 q^{59} +(-1.28599 + 1.16028i) q^{60} -2.96707i q^{61} +7.84355 q^{62} +(7.54857 + 2.45339i) q^{63} -1.00000 q^{64} -6.00644i q^{65} +(6.71996 + 2.17589i) q^{66} -8.62197 q^{67} +(-0.641724 - 1.11150i) q^{68} +(2.53943 + 2.81456i) q^{69} +(2.58676 + 0.555567i) q^{70} +14.1375i q^{71} +(-1.22578 - 2.73815i) q^{72} +(-6.02332 + 3.47757i) q^{73} +(5.02572 + 2.90160i) q^{74} +(-1.64782 - 0.533558i) q^{75} +(-2.90701 - 1.67836i) q^{76} +(-3.31241 - 10.2686i) q^{77} +(9.89754 + 3.20478i) q^{78} -12.1855 q^{79} +(-0.500000 - 0.866025i) q^{80} +(5.99492 - 6.71275i) q^{81} +(2.37162 + 1.36925i) q^{82} +(-6.87948 - 11.9156i) q^{83} +(-2.29566 + 3.96610i) q^{84} +(0.641724 - 1.11150i) q^{85} +(-4.22219 + 2.43768i) q^{86} +(8.33146 + 9.23412i) q^{87} +(-2.03904 + 3.53173i) q^{88} +(7.29497 - 12.6353i) q^{89} +(1.75842 - 2.43063i) q^{90} +(-4.87871 - 15.1241i) q^{91} +(-1.89542 + 1.09432i) q^{92} +(-13.2857 + 2.83808i) q^{93} -8.27225i q^{94} -3.35672i q^{95} +(1.69383 - 0.361836i) q^{96} +(16.8723 - 9.74120i) q^{97} +(6.96469 - 0.702180i) q^{98} +(-12.1698 - 1.25408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9	\( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9 - 2 * q^12 + 2 * q^15 + 28 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 + 14 * q^20 + 16 * q^21 - 6 * q^22 + 30 * q^23 - 8 * q^24 - 14 * q^25 - 12 * q^26 - 28 * q^27 - 8 * q^28 - 4 * q^30 - 20 * q^33 - 4 * q^35 - 6 * q^36 + 4 * q^37 - 6 * q^38 - 42 * q^39 - 18 * q^41 + 28 * q^43 - 12 * q^45 - 18 * q^46 + 60 * q^47 + 2 * q^48 - 20 * q^49 - 74 * q^51 + 42 * q^53 + 10 * q^54 - 30 * q^57 + 6 * q^58 - 48 * q^59 - 2 * q^60 + 12 * q^62 - 28 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^67 - 6 * q^68 - 8 * q^69 + 6 * q^70 - 8 * q^72 + 6 * q^73 - 4 * q^75 + 6 * q^76 - 18 * q^77 + 14 * q^78 - 4 * q^79 - 14 * q^80 + 38 * q^81 + 24 * q^82 + 18 * q^83 - 16 * q^84 + 6 * q^85 - 96 * q^86 + 52 * q^87 + 6 * q^88 - 6 * q^89 - 4 * q^90 + 66 * q^91 - 30 * q^92 + 22 * q^93 + 8 * q^96 + 72 * q^97 + 24 * q^98 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more