LMFDB - Embedded newform 630.2.j.f.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(211,630)]

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, 0]))

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

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

chi := DirichletCharacter("630.211");

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.j (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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			421.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	630.421
Dual form			630.2.j.f.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.866025 + 1.50000i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.866025 + 1.50000i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-1.50000 - 2.59808i) q^{9} -1.00000 q^{10} +(-1.86603 + 3.23205i) q^{11} +1.73205 q^{12} +(-2.36603 - 4.09808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +1.73205 q^{15} +(-0.500000 + 0.866025i) q^{16} +1.00000 q^{17} -3.00000 q^{18} -6.46410 q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.866025 + 1.50000i) q^{21} +(1.86603 + 3.23205i) q^{22} +(-0.633975 - 1.09808i) q^{23} +(0.866025 - 1.50000i) q^{24} +(-0.500000 + 0.866025i) q^{25} -4.73205 q^{26} +5.19615 q^{27} -1.00000 q^{28} +(4.09808 - 7.09808i) q^{29} +(0.866025 - 1.50000i) q^{30} +(-4.46410 - 7.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.23205 - 5.59808i) q^{33} +(0.500000 - 0.866025i) q^{34} -1.00000 q^{35} +(-1.50000 + 2.59808i) q^{36} -9.66025 q^{37} +(-3.23205 + 5.59808i) q^{38} +8.19615 q^{39} +(0.500000 + 0.866025i) q^{40} +(-2.86603 - 4.96410i) q^{41} +1.73205 q^{42} +(-5.69615 + 9.86603i) q^{43} +3.73205 q^{44} +(-1.50000 + 2.59808i) q^{45} -1.26795 q^{46} +(-2.00000 + 3.46410i) q^{47} +(-0.866025 - 1.50000i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.866025 + 1.50000i) q^{51} +(-2.36603 + 4.09808i) q^{52} +10.1962 q^{53} +(2.59808 - 4.50000i) q^{54} +3.73205 q^{55} +(-0.500000 + 0.866025i) q^{56} +(5.59808 - 9.69615i) q^{57} +(-4.09808 - 7.09808i) q^{58} +(-4.23205 - 7.33013i) q^{59} +(-0.866025 - 1.50000i) q^{60} +(0.366025 - 0.633975i) q^{61} -8.92820 q^{62} -3.00000 q^{63} +1.00000 q^{64} +(-2.36603 + 4.09808i) q^{65} -6.46410 q^{66} +(4.50000 + 7.79423i) q^{67} +(-0.500000 - 0.866025i) q^{68} +2.19615 q^{69} +(-0.500000 + 0.866025i) q^{70} +8.73205 q^{71} +(1.50000 + 2.59808i) q^{72} -1.92820 q^{73} +(-4.83013 + 8.36603i) q^{74} +(-0.866025 - 1.50000i) q^{75} +(3.23205 + 5.59808i) q^{76} +(1.86603 + 3.23205i) q^{77} +(4.09808 - 7.09808i) q^{78} +(7.00000 - 12.1244i) q^{79} +1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -5.73205 q^{82} +(-0.732051 + 1.26795i) q^{83} +(0.866025 - 1.50000i) q^{84} +(-0.500000 - 0.866025i) q^{85} +(5.69615 + 9.86603i) q^{86} +(7.09808 + 12.2942i) q^{87} +(1.86603 - 3.23205i) q^{88} -0.535898 q^{89} +(1.50000 + 2.59808i) q^{90} -4.73205 q^{91} +(-0.633975 + 1.09808i) q^{92} +15.4641 q^{93} +(2.00000 + 3.46410i) q^{94} +(3.23205 + 5.59808i) q^{95} -1.73205 q^{96} +(0.500000 - 0.866025i) q^{97} -1.00000 q^{98} +11.1962 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} + 2 q^{7} - 4 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 + 2 * q^7 - 4 * q^8 - 6 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} + 2 q^{7} - 4 q^{8} - 6 q^{9} - 4 q^{10} - 4 q^{11} - 6 q^{13} - 2 q^{14} - 2 q^{16} + 4 q^{17} - 12 q^{18} - 12 q^{19} - 2 q^{20} + 4 q^{22} - 6 q^{23} - 2 q^{25} - 12 q^{26} - 4 q^{28} + 6 q^{29} - 4 q^{31} + 2 q^{32} - 6 q^{33} + 2 q^{34} - 4 q^{35} - 6 q^{36} - 4 q^{37} - 6 q^{38} + 12 q^{39} + 2 q^{40} - 8 q^{41} - 2 q^{43} + 8 q^{44} - 6 q^{45} - 12 q^{46} - 8 q^{47} - 2 q^{49} + 2 q^{50} - 6 q^{52} + 20 q^{53} + 8 q^{55} - 2 q^{56} + 12 q^{57} - 6 q^{58} - 10 q^{59} - 2 q^{61} - 8 q^{62} - 12 q^{63} + 4 q^{64} - 6 q^{65} - 12 q^{66} + 18 q^{67} - 2 q^{68} - 12 q^{69} - 2 q^{70} + 28 q^{71} + 6 q^{72} + 20 q^{73} - 2 q^{74} + 6 q^{76} + 4 q^{77} + 6 q^{78} + 28 q^{79} + 4 q^{80} - 18 q^{81} - 16 q^{82} + 4 q^{83} - 2 q^{85} + 2 q^{86} + 18 q^{87} + 4 q^{88} - 16 q^{89} + 6 q^{90} - 12 q^{91} - 6 q^{92} + 48 q^{93} + 8 q^{94} + 6 q^{95} + 2 q^{97} - 4 q^{98} + 24 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 + 2 * q^7 - 4 * q^8 - 6 * q^9 - 4 * q^10 - 4 * q^11 - 6 * q^13 - 2 * q^14 - 2 * q^16 + 4 * q^17 - 12 * q^18 - 12 * q^19 - 2 * q^20 + 4 * q^22 - 6 * q^23 - 2 * q^25 - 12 * q^26 - 4 * q^28 + 6 * q^29 - 4 * q^31 + 2 * q^32 - 6 * q^33 + 2 * q^34 - 4 * q^35 - 6 * q^36 - 4 * q^37 - 6 * q^38 + 12 * q^39 + 2 * q^40 - 8 * q^41 - 2 * q^43 + 8 * q^44 - 6 * q^45 - 12 * q^46 - 8 * q^47 - 2 * q^49 + 2 * q^50 - 6 * q^52 + 20 * q^53 + 8 * q^55 - 2 * q^56 + 12 * q^57 - 6 * q^58 - 10 * q^59 - 2 * q^61 - 8 * q^62 - 12 * q^63 + 4 * q^64 - 6 * q^65 - 12 * q^66 + 18 * q^67 - 2 * q^68 - 12 * q^69 - 2 * q^70 + 28 * q^71 + 6 * q^72 + 20 * q^73 - 2 * q^74 + 6 * q^76 + 4 * q^77 + 6 * q^78 + 28 * q^79 + 4 * q^80 - 18 * q^81 - 16 * q^82 + 4 * q^83 - 2 * q^85 + 2 * q^86 + 18 * q^87 + 4 * q^88 - 16 * q^89 + 6 * q^90 - 12 * q^91 - 6 * q^92 + 48 * q^93 + 8 * q^94 + 6 * q^95 + 2 * q^97 - 4 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.866025	+	1.50000i	0.353553	+	0.612372i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−1.00000			−0.353553
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	−1.00000			−0.316228
$11$	−1.86603	+	3.23205i	−0.562628	+	0.974500i	0.434638	+	0.900605i	$0.356876\pi$
$11$	−1.86603	+	3.23205i	−0.562628	+	0.974500i	−0.997266	+	0.0738948i	$0.976457\pi$
$12$	1.73205			0.500000
$13$	−2.36603	−	4.09808i	−0.656217	−	1.13660i	−0.981587	−	0.191015i	$-0.938822\pi$
$13$	−2.36603	−	4.09808i	−0.656217	−	1.13660i	0.325370	−	0.945587i	$-0.394511\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	1.73205			0.447214
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000			0.242536			0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000			0.242536			0.121268	+	0.992620i	$0.461304\pi$
$18$	−3.00000			−0.707107
$19$	−6.46410			−1.48297			−0.741483	−	0.670971i	$-0.765877\pi$
$19$	−6.46410			−1.48297			−0.741483	+	0.670971i	$0.765877\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	0.866025	+	1.50000i	0.188982	+	0.327327i
$22$	1.86603	+	3.23205i	0.397838	+	0.689076i
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	0.792329	−	0.610094i	$-0.208868\pi$
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	−0.924522	+	0.381130i	$0.875535\pi$
$24$	0.866025	−	1.50000i	0.176777	−	0.306186i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−4.73205			−0.928032
$27$	5.19615			1.00000
$28$	−1.00000			−0.188982
$29$	4.09808	−	7.09808i	0.760994	−	1.31808i	−0.181345	−	0.983419i	$-0.558045\pi$
$29$	4.09808	−	7.09808i	0.760994	−	1.31808i	0.942339	−	0.334660i	$-0.108622\pi$
$30$	0.866025	−	1.50000i	0.158114	−	0.273861i
$31$	−4.46410	−	7.73205i	−0.801776	−	1.38872i	−0.918446	−	0.395547i	$-0.870555\pi$
$31$	−4.46410	−	7.73205i	−0.801776	−	1.38872i	0.116670	−	0.993171i	$-0.462778\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.23205	−	5.59808i	−0.562628	−	0.974500i
$34$	0.500000	−	0.866025i	0.0857493	−	0.148522i
$35$	−1.00000			−0.169031
$36$	−1.50000	+	2.59808i	−0.250000	+	0.433013i
$37$	−9.66025			−1.58814			−0.794068	−	0.607829i	$-0.792041\pi$
$37$	−9.66025			−1.58814			−0.794068	+	0.607829i	$0.792041\pi$
$38$	−3.23205	+	5.59808i	−0.524308	+	0.908128i
$39$	8.19615			1.31243
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−2.86603	−	4.96410i	−0.447598	−	0.775262i	0.550631	−	0.834749i	$-0.314387\pi$
$41$	−2.86603	−	4.96410i	−0.447598	−	0.775262i	−0.998229	+	0.0594862i	$0.981054\pi$
$42$	1.73205			0.267261
$43$	−5.69615	+	9.86603i	−0.868655	+	1.50455i	−0.00528357	+	0.999986i	$0.501682\pi$
$43$	−5.69615	+	9.86603i	−0.868655	+	1.50455i	−0.863372	+	0.504569i	$0.831652\pi$
$44$	3.73205			0.562628
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$	−1.26795			−0.186949
$47$	−2.00000	+	3.46410i	−0.291730	+	0.505291i	−0.974219	−	0.225605i	$-0.927564\pi$
$47$	−2.00000	+	3.46410i	−0.291730	+	0.505291i	0.682489	+	0.730896i	$0.260898\pi$
$48$	−0.866025	−	1.50000i	−0.125000	−	0.216506i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−0.866025	+	1.50000i	−0.121268	+	0.210042i
$52$	−2.36603	+	4.09808i	−0.328109	+	0.568301i
$53$	10.1962			1.40055			0.700275	−	0.713874i	$-0.253061\pi$
$53$	10.1962			1.40055			0.700275	+	0.713874i	$0.253061\pi$
$54$	2.59808	−	4.50000i	0.353553	−	0.612372i
$55$	3.73205			0.503230
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	5.59808	−	9.69615i	0.741483	−	1.28429i
$58$	−4.09808	−	7.09808i	−0.538104	−	0.932023i
$59$	−4.23205	−	7.33013i	−0.550966	−	0.954301i	−0.998205	−	0.0598868i	$-0.980926\pi$
$59$	−4.23205	−	7.33013i	−0.550966	−	0.954301i	0.447239	−	0.894414i	$-0.352407\pi$
$60$	−0.866025	−	1.50000i	−0.111803	−	0.193649i
$61$	0.366025	−	0.633975i	0.0468648	−	0.0811721i	−0.841641	−	0.540037i	$-0.818410\pi$
$61$	0.366025	−	0.633975i	0.0468648	−	0.0811721i	0.888506	+	0.458865i	$0.151744\pi$
$62$	−8.92820			−1.13388
$63$	−3.00000			−0.377964
$64$	1.00000			0.125000
$65$	−2.36603	+	4.09808i	−0.293469	+	0.508304i
$66$	−6.46410			−0.795676
$67$	4.50000	+	7.79423i	0.549762	+	0.952217i	0.998290	+	0.0584478i	$0.0186151\pi$
$67$	4.50000	+	7.79423i	0.549762	+	0.952217i	−0.448528	+	0.893769i	$0.648052\pi$
$68$	−0.500000	−	0.866025i	−0.0606339	−	0.105021i
$69$	2.19615			0.264386
$70$	−0.500000	+	0.866025i	−0.0597614	+	0.103510i
$71$	8.73205			1.03630			0.518152	−	0.855289i	$-0.326620\pi$
$71$	8.73205			1.03630			0.518152	+	0.855289i	$0.326620\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	−1.92820			−0.225679			−0.112840	−	0.993613i	$-0.535995\pi$
$73$	−1.92820			−0.225679			−0.112840	+	0.993613i	$0.535995\pi$
$74$	−4.83013	+	8.36603i	−0.561491	+	0.972531i
$75$	−0.866025	−	1.50000i	−0.100000	−	0.173205i
$76$	3.23205	+	5.59808i	0.370742	+	0.642143i
$77$	1.86603	+	3.23205i	0.212653	+	0.368326i
$78$	4.09808	−	7.09808i	0.464016	−	0.803699i
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	−0.139895	−	0.990166i	$-0.544677\pi$
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	0.927457	−	0.373930i	$-0.121990\pi$
$80$	1.00000			0.111803
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−5.73205			−0.632999
$83$	−0.732051	+	1.26795i	−0.0803530	+	0.139176i	−0.903402	−	0.428795i	$-0.858938\pi$
$83$	−0.732051	+	1.26795i	−0.0803530	+	0.139176i	0.823049	+	0.567971i	$0.192271\pi$
$84$	0.866025	−	1.50000i	0.0944911	−	0.163663i
$85$	−0.500000	−	0.866025i	−0.0542326	−	0.0939336i
$86$	5.69615	+	9.86603i	0.614232	+	1.06388i
$87$	7.09808	+	12.2942i	0.760994	+	1.31808i
$88$	1.86603	−	3.23205i	0.198919	−	0.344538i
$89$	−0.535898			−0.0568051			−0.0284026	−	0.999597i	$-0.509042\pi$
$89$	−0.535898			−0.0568051			−0.0284026	+	0.999597i	$0.509042\pi$
$90$	1.50000	+	2.59808i	0.158114	+	0.273861i
$91$	−4.73205			−0.496054
$92$	−0.633975	+	1.09808i	−0.0660964	+	0.114482i
$93$	15.4641			1.60355
$94$	2.00000	+	3.46410i	0.206284	+	0.357295i
$95$	3.23205	+	5.59808i	0.331601	+	0.574351i
$96$	−1.73205			−0.176777
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	−0.839525	−	0.543321i	$-0.817167\pi$
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	0.890292	+	0.455389i	$0.150500\pi$
$98$	−1.00000			−0.101015
$99$	11.1962			1.12526
$100$	1.00000			0.100000
$101$	−4.73205	+	8.19615i	−0.470857	+	0.815548i	−0.999444	−	0.0333310i	$-0.989388\pi$
$101$	−4.73205	+	8.19615i	−0.470857	+	0.815548i	0.528588	+	0.848879i	$0.322722\pi$
$102$	0.866025	+	1.50000i	0.0857493	+	0.148522i
$103$	3.36603	+	5.83013i	0.331664	+	0.574459i	0.982838	−	0.184469i	$-0.0590565\pi$
$103$	3.36603	+	5.83013i	0.331664	+	0.574459i	−0.651174	+	0.758928i	$0.725723\pi$
$104$	2.36603	+	4.09808i	0.232008	+	0.401849i
$105$	0.866025	−	1.50000i	0.0845154	−	0.146385i
$106$	5.09808	−	8.83013i	0.495169	−	0.857658i
$107$	18.4641			1.78499			0.892496	−	0.451055i	$-0.148952\pi$
$107$	18.4641			1.78499			0.892496	+	0.451055i	$0.148952\pi$
$108$	−2.59808	−	4.50000i	−0.250000	−	0.433013i
$109$	−4.73205			−0.453248			−0.226624	−	0.973982i	$-0.572769\pi$
$109$	−4.73205			−0.453248			−0.226624	+	0.973982i	$0.572769\pi$
$110$	1.86603	−	3.23205i	0.177919	−	0.308164i
$111$	8.36603	−	14.4904i	0.794068	−	1.37537i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	4.92820	+	8.53590i	0.463606	+	0.802990i	0.999137	−	0.0415258i	$-0.0132219\pi$
$113$	4.92820	+	8.53590i	0.463606	+	0.802990i	−0.535531	+	0.844516i	$0.679889\pi$
$114$	−5.59808	−	9.69615i	−0.524308	−	0.908128i
$115$	−0.633975	+	1.09808i	−0.0591184	+	0.102396i
$116$	−8.19615			−0.760994
$117$	−7.09808	+	12.2942i	−0.656217	+	1.13660i
$118$	−8.46410			−0.779184
$119$	0.500000	−	0.866025i	0.0458349	−	0.0793884i
$120$	−1.73205			−0.158114
$121$	−1.46410	−	2.53590i	−0.133100	−	0.230536i
$122$	−0.366025	−	0.633975i	−0.0331384	−	0.0573974i
$123$	9.92820			0.895196
$124$	−4.46410	+	7.73205i	−0.400888	+	0.694359i
$125$	1.00000			0.0894427
$126$	−1.50000	+	2.59808i	−0.133631	+	0.231455i
$127$	−1.66025			−0.147324			−0.0736619	−	0.997283i	$-0.523469\pi$
$127$	−1.66025			−0.147324			−0.0736619	+	0.997283i	$0.523469\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−9.86603	−	17.0885i	−0.868655	−	1.50455i
$130$	2.36603	+	4.09808i	0.207514	+	0.359425i
$131$	7.92820	+	13.7321i	0.692690	+	1.19977i	0.970953	+	0.239270i	$0.0769081\pi$
$131$	7.92820	+	13.7321i	0.692690	+	1.19977i	−0.278263	+	0.960505i	$0.589759\pi$
$132$	−3.23205	+	5.59808i	−0.281314	+	0.487250i
$133$	−3.23205	+	5.59808i	−0.280254	+	0.485415i
$134$	9.00000			0.777482
$135$	−2.59808	−	4.50000i	−0.223607	−	0.387298i
$136$	−1.00000			−0.0857493
$137$	−2.13397	+	3.69615i	−0.182318	+	0.315784i	−0.942669	−	0.333728i	$-0.891693\pi$
$137$	−2.13397	+	3.69615i	−0.182318	+	0.315784i	0.760352	+	0.649512i	$0.225027\pi$
$138$	1.09808	−	1.90192i	0.0934745	−	0.161903i
$139$	1.23205	+	2.13397i	0.104501	+	0.181001i	0.913534	−	0.406762i	$-0.133342\pi$
$139$	1.23205	+	2.13397i	0.104501	+	0.181001i	−0.809033	+	0.587763i	$0.800009\pi$
$140$	0.500000	+	0.866025i	0.0422577	+	0.0731925i
$141$	−3.46410	−	6.00000i	−0.291730	−	0.505291i
$142$	4.36603	−	7.56218i	0.366389	−	0.634604i
$143$	17.6603			1.47682
$144$	3.00000			0.250000
$145$	−8.19615			−0.680653
$146$	−0.964102	+	1.66987i	−0.0797896	+	0.138200i
$147$	1.73205			0.142857
$148$	4.83013	+	8.36603i	0.397034	+	0.687683i
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	0.508413	−	0.861113i	$-0.330232\pi$
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	−0.999953	+	0.00974235i	$0.996899\pi$
$150$	−1.73205			−0.141421
$151$	5.92820	−	10.2679i	0.482430	−	0.835594i	−0.517366	−	0.855764i	$-0.673087\pi$
$151$	5.92820	−	10.2679i	0.482430	−	0.835594i	0.999797	+	0.0201702i	$0.00642082\pi$
$152$	6.46410			0.524308
$153$	−1.50000	−	2.59808i	−0.121268	−	0.210042i
$154$	3.73205			0.300737
$155$	−4.46410	+	7.73205i	−0.358565	+	0.621053i
$156$	−4.09808	−	7.09808i	−0.328109	−	0.568301i
$157$	−10.0263	−	17.3660i	−0.800184	−	1.38596i	−0.919495	−	0.393103i	$-0.871402\pi$
$157$	−10.0263	−	17.3660i	−0.800184	−	1.38596i	0.119310	−	0.992857i	$-0.461932\pi$
$158$	−7.00000	−	12.1244i	−0.556890	−	0.964562i
$159$	−8.83013	+	15.2942i	−0.700275	+	1.21291i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−1.26795			−0.0999284
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	−2.39230			−0.187380			−0.0936899	−	0.995601i	$-0.529866\pi$
$163$	−2.39230			−0.187380			−0.0936899	+	0.995601i	$0.529866\pi$
$164$	−2.86603	+	4.96410i	−0.223799	+	0.387631i
$165$	−3.23205	+	5.59808i	−0.251615	+	0.435810i
$166$	0.732051	+	1.26795i	0.0568182	+	0.0984119i
$167$	−4.56218	−	7.90192i	−0.353032	−	0.611469i	0.633747	−	0.773540i	$-0.281516\pi$
$167$	−4.56218	−	7.90192i	−0.353032	−	0.611469i	−0.986779	+	0.162071i	$0.948183\pi$
$168$	−0.866025	−	1.50000i	−0.0668153	−	0.115728i
$169$	−4.69615	+	8.13397i	−0.361242	+	0.625690i
$170$	−1.00000			−0.0766965
$171$	9.69615	+	16.7942i	0.741483	+	1.28429i
$172$	11.3923			0.868655
$173$	−1.53590	+	2.66025i	−0.116772	+	0.202255i	−0.918487	−	0.395452i	$-0.870588\pi$
$173$	−1.53590	+	2.66025i	−0.116772	+	0.202255i	0.801715	+	0.597707i	$0.203921\pi$
$174$	14.1962			1.07621
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	−1.86603	−	3.23205i	−0.140657	−	0.243625i
$177$	14.6603			1.10193
$178$	−0.267949	+	0.464102i	−0.0200836	+	0.0347859i
$179$	−24.2487			−1.81243			−0.906217	−	0.422813i	$-0.861043\pi$
$179$	−24.2487			−1.81243			−0.906217	+	0.422813i	$0.861043\pi$
$180$	3.00000			0.223607
$181$	17.8564			1.32726			0.663628	−	0.748063i	$-0.269016\pi$
$181$	17.8564			1.32726			0.663628	+	0.748063i	$0.269016\pi$
$182$	−2.36603	+	4.09808i	−0.175381	+	0.303770i
$183$	0.633975	+	1.09808i	0.0468648	+	0.0811721i
$184$	0.633975	+	1.09808i	0.0467372	+	0.0809513i
$185$	4.83013	+	8.36603i	0.355118	+	0.615082i
$186$	7.73205	−	13.3923i	0.566941	−	0.981971i
$187$	−1.86603	+	3.23205i	−0.136457	+	0.236351i
$188$	4.00000			0.291730
$189$	2.59808	−	4.50000i	0.188982	−	0.327327i
$190$	6.46410			0.468955
$191$	1.26795	−	2.19615i	0.0917456	−	0.158908i	−0.816500	−	0.577345i	$-0.804089\pi$
$191$	1.26795	−	2.19615i	0.0917456	−	0.158908i	0.908246	+	0.418437i	$0.137422\pi$
$192$	−0.866025	+	1.50000i	−0.0625000	+	0.108253i
$193$	−13.0622	−	22.6244i	−0.940236	−	1.62854i	−0.765020	−	0.644007i	$-0.777271\pi$
$193$	−13.0622	−	22.6244i	−0.940236	−	1.62854i	−0.175216	−	0.984530i	$-0.556062\pi$
$194$	−0.500000	−	0.866025i	−0.0358979	−	0.0621770i
$195$	−4.09808	−	7.09808i	−0.293469	−	0.508304i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	2.73205			0.194651			0.0973253	−	0.995253i	$-0.468971\pi$
$197$	2.73205			0.194651			0.0973253	+	0.995253i	$0.468971\pi$
$198$	5.59808	−	9.69615i	0.397838	−	0.689076i
$199$	−11.2679			−0.798764			−0.399382	−	0.916785i	$-0.630775\pi$
$199$	−11.2679			−0.798764			−0.399382	+	0.916785i	$0.630775\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−15.5885			−1.09952
$202$	4.73205	+	8.19615i	0.332946	+	0.576679i
$203$	−4.09808	−	7.09808i	−0.287629	−	0.498187i
$204$	1.73205			0.121268
$205$	−2.86603	+	4.96410i	−0.200172	+	0.346708i
$206$	6.73205			0.469044
$207$	−1.90192	+	3.29423i	−0.132193	+	0.228965i
$208$	4.73205			0.328109
$209$	12.0622	−	20.8923i	0.834358	−	1.44515i
$210$	−0.866025	−	1.50000i	−0.0597614	−	0.103510i
$211$	−4.19615	−	7.26795i	−0.288875	−	0.500346i	0.684666	−	0.728857i	$-0.259948\pi$
$211$	−4.19615	−	7.26795i	−0.288875	−	0.500346i	−0.973542	+	0.228510i	$0.926615\pi$
$212$	−5.09808	−	8.83013i	−0.350137	−	0.606456i
$213$	−7.56218	+	13.0981i	−0.518152	+	0.897465i
$214$	9.23205	−	15.9904i	0.631090	−	1.09308i
$215$	11.3923			0.776949
$216$	−5.19615			−0.353553
$217$	−8.92820			−0.606086
$218$	−2.36603	+	4.09808i	−0.160247	+	0.277557i
$219$	1.66987	−	2.89230i	0.112840	−	0.195444i
$220$	−1.86603	−	3.23205i	−0.125807	−	0.217905i
$221$	−2.36603	−	4.09808i	−0.159156	−	0.275666i
$222$	−8.36603	−	14.4904i	−0.561491	−	0.972531i
$223$	13.2942	−	23.0263i	0.890247	−	1.54195i	0.0506688	−	0.998716i	$-0.483865\pi$
$223$	13.2942	−	23.0263i	0.890247	−	1.54195i	0.839579	−	0.543238i	$-0.182802\pi$
$224$	1.00000			0.0668153
$225$	3.00000			0.200000
$226$	9.85641			0.655638
$227$	−3.66987	+	6.35641i	−0.243578	+	0.421890i	−0.961731	−	0.273996i	$-0.911655\pi$
$227$	−3.66987	+	6.35641i	−0.243578	+	0.421890i	0.718153	+	0.695885i	$0.244988\pi$
$228$	−11.1962			−0.741483
$229$	−6.09808	−	10.5622i	−0.402972	−	0.697968i	0.591111	−	0.806590i	$-0.298690\pi$
$229$	−6.09808	−	10.5622i	−0.402972	−	0.697968i	−0.994083	+	0.108622i	$0.965356\pi$
$230$	0.633975	+	1.09808i	0.0418030	+	0.0724050i
$231$	−6.46410			−0.425307
$232$	−4.09808	+	7.09808i	−0.269052	+	0.466012i
$233$	27.5885			1.80738			0.903690	−	0.428187i	$-0.140848\pi$
$233$	27.5885			1.80738			0.903690	+	0.428187i	$0.140848\pi$
$234$	7.09808	+	12.2942i	0.464016	+	0.803699i
$235$	4.00000			0.260931
$236$	−4.23205	+	7.33013i	−0.275483	+	0.477151i
$237$	12.1244	+	21.0000i	0.787562	+	1.36410i
$238$	−0.500000	−	0.866025i	−0.0324102	−	0.0561361i
$239$	−3.19615	−	5.53590i	−0.206742	−	0.358087i	0.743944	−	0.668242i	$-0.232953\pi$
$239$	−3.19615	−	5.53590i	−0.206742	−	0.358087i	−0.950686	+	0.310154i	$0.899619\pi$
$240$	−0.866025	+	1.50000i	−0.0559017	+	0.0968246i
$241$	9.25833	−	16.0359i	0.596381	−	1.03296i	−0.396969	−	0.917832i	$-0.629938\pi$
$241$	9.25833	−	16.0359i	0.596381	−	1.03296i	0.993350	−	0.115131i	$-0.0367288\pi$
$242$	−2.92820			−0.188232
$243$	−7.79423	−	13.5000i	−0.500000	−	0.866025i
$244$	−0.732051			−0.0468648
$245$	−0.500000	+	0.866025i	−0.0319438	+	0.0553283i
$246$	4.96410	−	8.59808i	0.316500	−	0.548193i
$247$	15.2942	+	26.4904i	0.973148	+	1.68554i
$248$	4.46410	+	7.73205i	0.283471	+	0.490986i
$249$	−1.26795	−	2.19615i	−0.0803530	−	0.139176i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−10.8564			−0.685250			−0.342625	−	0.939472i	$-0.611316\pi$
$251$	−10.8564			−0.685250			−0.342625	+	0.939472i	$0.611316\pi$
$252$	1.50000	+	2.59808i	0.0944911	+	0.163663i
$253$	4.73205			0.297501
$254$	−0.830127	+	1.43782i	−0.0520868	+	0.0902170i
$255$	1.73205			0.108465
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.03590	−	5.25833i	−0.189374	−	0.328006i	0.755668	−	0.654955i	$-0.227313\pi$
$257$	−3.03590	−	5.25833i	−0.189374	−	0.328006i	−0.945042	+	0.326950i	$0.893979\pi$
$258$	−19.7321			−1.22846
$259$	−4.83013	+	8.36603i	−0.300129	+	0.519840i
$260$	4.73205			0.293469
$261$	−24.5885			−1.52199
$262$	15.8564			0.979612
$263$	−6.90192	+	11.9545i	−0.425591	+	0.737145i	−0.996475	−	0.0838854i	$-0.973267\pi$
$263$	−6.90192	+	11.9545i	−0.425591	+	0.737145i	0.570885	+	0.821030i	$0.306600\pi$
$264$	3.23205	+	5.59808i	0.198919	+	0.344538i
$265$	−5.09808	−	8.83013i	−0.313172	−	0.542430i
$266$	3.23205	+	5.59808i	0.198170	+	0.343240i
$267$	0.464102	−	0.803848i	0.0284026	−	0.0491947i
$268$	4.50000	−	7.79423i	0.274881	−	0.476108i
$269$	−19.2679			−1.17479			−0.587394	−	0.809301i	$-0.699846\pi$
$269$	−19.2679			−1.17479			−0.587394	+	0.809301i	$0.699846\pi$
$270$	−5.19615			−0.316228
$271$	16.0526			0.975124			0.487562	−	0.873089i	$-0.337886\pi$
$271$	16.0526			0.975124			0.487562	+	0.873089i	$0.337886\pi$
$272$	−0.500000	+	0.866025i	−0.0303170	+	0.0525105i
$273$	4.09808	−	7.09808i	0.248027	−	0.429595i
$274$	2.13397	+	3.69615i	0.128918	+	0.223293i
$275$	−1.86603	−	3.23205i	−0.112526	−	0.194900i
$276$	−1.09808	−	1.90192i	−0.0660964	−	0.114482i
$277$	−15.9282	+	27.5885i	−0.957033	+	1.65763i	−0.227387	+	0.973804i	$0.573018\pi$
$277$	−15.9282	+	27.5885i	−0.957033	+	1.65763i	−0.729646	+	0.683825i	$0.760315\pi$
$278$	2.46410			0.147787
$279$	−13.3923	+	23.1962i	−0.801776	+	1.38872i
$280$	1.00000			0.0597614
$281$	−10.1962	+	17.6603i	−0.608251	+	1.05352i	0.383277	+	0.923633i	$0.374795\pi$
$281$	−10.1962	+	17.6603i	−0.608251	+	1.05352i	−0.991529	+	0.129889i	$0.958538\pi$
$282$	−6.92820			−0.412568
$283$	12.3923	+	21.4641i	0.736646	+	1.27591i	0.953997	+	0.299815i	$0.0969249\pi$
$283$	12.3923	+	21.4641i	0.736646	+	1.27591i	−0.217351	+	0.976093i	$0.569742\pi$
$284$	−4.36603	−	7.56218i	−0.259076	−	0.448733i
$285$	−11.1962			−0.663203
$286$	8.83013	−	15.2942i	0.522136	−	0.904367i
$287$	−5.73205			−0.338352
$288$	1.50000	−	2.59808i	0.0883883	−	0.153093i
$289$	−16.0000			−0.941176
$290$	−4.09808	+	7.09808i	−0.240647	+	0.416813i
$291$	0.866025	+	1.50000i	0.0507673	+	0.0879316i
$292$	0.964102	+	1.66987i	0.0564198	+	0.0977219i
$293$	−10.2942	−	17.8301i	−0.601395	−	1.04165i	−0.992610	−	0.121348i	$-0.961278\pi$
$293$	−10.2942	−	17.8301i	−0.601395	−	1.04165i	0.391215	−	0.920299i	$-0.372055\pi$
$294$	0.866025	−	1.50000i	0.0505076	−	0.0874818i
$295$	−4.23205	+	7.33013i	−0.246400	+	0.426776i
$296$	9.66025			0.561491
$297$	−9.69615	+	16.7942i	−0.562628	+	0.974500i
$298$	−12.0000			−0.695141
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$	−0.866025	+	1.50000i	−0.0500000	+	0.0866025i
$301$	5.69615	+	9.86603i	0.328321	+	0.568668i
$302$	−5.92820	−	10.2679i	−0.341130	−	0.590854i
$303$	−8.19615	−	14.1962i	−0.470857	−	0.815548i
$304$	3.23205	−	5.59808i	0.185371	−	0.321072i
$305$	−0.732051			−0.0419171
$306$	−3.00000			−0.171499
$307$	−6.26795			−0.357731			−0.178865	−	0.983874i	$-0.557243\pi$
$307$	−6.26795			−0.357731			−0.178865	+	0.983874i	$0.557243\pi$
$308$	1.86603	−	3.23205i	0.106327	−	0.184163i
$309$	−11.6603			−0.663329
$310$	4.46410	+	7.73205i	0.253544	+	0.439151i
$311$	−4.26795	−	7.39230i	−0.242013	−	0.419179i	0.719274	−	0.694726i	$-0.244474\pi$
$311$	−4.26795	−	7.39230i	−0.242013	−	0.419179i	−0.961288	+	0.275547i	$0.911141\pi$
$312$	−8.19615			−0.464016
$313$	−8.50000	+	14.7224i	−0.480448	+	0.832161i	−0.999748	−	0.0224310i	$-0.992859\pi$
$313$	−8.50000	+	14.7224i	−0.480448	+	0.832161i	0.519300	+	0.854592i	$0.326193\pi$
$314$	−20.0526			−1.13163
$315$	1.50000	+	2.59808i	0.0845154	+	0.146385i
$316$	−14.0000			−0.787562
$317$	−4.63397	+	8.02628i	−0.260270	+	0.450801i	−0.966314	−	0.257368i	$-0.917145\pi$
$317$	−4.63397	+	8.02628i	−0.260270	+	0.450801i	0.706044	+	0.708168i	$0.250478\pi$
$318$	8.83013	+	15.2942i	0.495169	+	0.857658i
$319$	15.2942	+	26.4904i	0.856312	+	1.48318i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−15.9904	+	27.6962i	−0.892496	+	1.54585i
$322$	−0.633975	+	1.09808i	−0.0353300	+	0.0611934i
$323$	−6.46410			−0.359672
$324$	9.00000			0.500000
$325$	4.73205			0.262487
$326$	−1.19615	+	2.07180i	−0.0662488	+	0.114746i
$327$	4.09808	−	7.09808i	0.226624	−	0.392525i
$328$	2.86603	+	4.96410i	0.158250	+	0.274097i
$329$	2.00000	+	3.46410i	0.110264	+	0.190982i
$330$	3.23205	+	5.59808i	0.177919	+	0.308164i
$331$	11.2679	−	19.5167i	0.619343	−	1.07273i	−0.370263	−	0.928927i	$-0.620733\pi$
$331$	11.2679	−	19.5167i	0.619343	−	1.07273i	0.989606	−	0.143806i	$-0.0459341\pi$
$332$	1.46410			0.0803530
$333$	14.4904	+	25.0981i	0.794068	+	1.37537i
$334$	−9.12436			−0.499263
$335$	4.50000	−	7.79423i	0.245861	−	0.425844i
$336$	−1.73205			−0.0944911
$337$	−9.66987	−	16.7487i	−0.526752	−	0.912360i	−0.999514	−	0.0311706i	$-0.990076\pi$
$337$	−9.66987	−	16.7487i	−0.526752	−	0.912360i	0.472763	−	0.881190i	$-0.343257\pi$
$338$	4.69615	+	8.13397i	0.255437	+	0.442430i
$339$	−17.0718			−0.927213
$340$	−0.500000	+	0.866025i	−0.0271163	+	0.0469668i
$341$	33.3205			1.80441
$342$	19.3923			1.04862
$343$	−1.00000			−0.0539949
$344$	5.69615	−	9.86603i	0.307116	−	0.531940i
$345$	−1.09808	−	1.90192i	−0.0591184	−	0.102396i
$346$	1.53590	+	2.66025i	0.0825704	+	0.143016i
$347$	−13.3564	−	23.1340i	−0.717009	−	1.24190i	−0.962179	−	0.272417i	$-0.912177\pi$
$347$	−13.3564	−	23.1340i	−0.717009	−	1.24190i	0.245170	−	0.969480i	$-0.421156\pi$
$348$	7.09808	−	12.2942i	0.380497	−	0.659040i
$349$	4.29423	−	7.43782i	0.229865	−	0.398137i	−0.727903	−	0.685680i	$-0.759505\pi$
$349$	4.29423	−	7.43782i	0.229865	−	0.398137i	0.957768	+	0.287543i	$0.0928383\pi$
$350$	1.00000			0.0534522
$351$	−12.2942	−	21.2942i	−0.656217	−	1.13660i
$352$	−3.73205			−0.198919
$353$	10.9641	−	18.9904i	0.583560	−	1.01076i	−0.411493	−	0.911413i	$-0.634993\pi$
$353$	10.9641	−	18.9904i	0.583560	−	1.01076i	0.995053	−	0.0993431i	$-0.0316741\pi$
$354$	7.33013	−	12.6962i	0.389592	−	0.674793i
$355$	−4.36603	−	7.56218i	−0.231725	−	0.401359i
$356$	0.267949	+	0.464102i	0.0142013	+	0.0245973i
$357$	0.866025	+	1.50000i	0.0458349	+	0.0793884i
$358$	−12.1244	+	21.0000i	−0.640792	+	1.10988i
$359$	14.0526			0.741666			0.370833	−	0.928700i	$-0.379072\pi$
$359$	14.0526			0.741666			0.370833	+	0.928700i	$0.379072\pi$
$360$	1.50000	−	2.59808i	0.0790569	−	0.136931i
$361$	22.7846			1.19919
$362$	8.92820	−	15.4641i	0.469256	−	0.812775i
$363$	5.07180			0.266200
$364$	2.36603	+	4.09808i	0.124013	+	0.214798i
$365$	0.964102	+	1.66987i	0.0504634	+	0.0874051i
$366$	1.26795			0.0662768
$367$	−7.36603	+	12.7583i	−0.384503	+	0.665979i	−0.991700	−	0.128572i	$-0.958961\pi$
$367$	−7.36603	+	12.7583i	−0.384503	+	0.665979i	0.607197	+	0.794551i	$0.292294\pi$
$368$	1.26795			0.0660964
$369$	−8.59808	+	14.8923i	−0.447598	+	0.775262i
$370$	9.66025			0.502213
$371$	5.09808	−	8.83013i	0.264679	−	0.458437i
$372$	−7.73205	−	13.3923i	−0.400888	−	0.694359i
$373$	−3.19615	−	5.53590i	−0.165490	−	0.286638i	0.771339	−	0.636425i	$-0.219587\pi$
$373$	−3.19615	−	5.53590i	−0.165490	−	0.286638i	−0.936829	+	0.349787i	$0.886254\pi$
$374$	1.86603	+	3.23205i	0.0964899	+	0.167125i
$375$	−0.866025	+	1.50000i	−0.0447214	+	0.0774597i
$376$	2.00000	−	3.46410i	0.103142	−	0.178647i
$377$	−38.7846			−1.99751
$378$	−2.59808	−	4.50000i	−0.133631	−	0.231455i
$379$	0.803848			0.0412909			0.0206454	−	0.999787i	$-0.493428\pi$
$379$	0.803848			0.0412909			0.0206454	+	0.999787i	$0.493428\pi$
$380$	3.23205	−	5.59808i	0.165801	−	0.287175i
$381$	1.43782	−	2.49038i	0.0736619	−	0.127586i
$382$	−1.26795	−	2.19615i	−0.0648739	−	0.112365i
$383$	1.26795	+	2.19615i	0.0647892	+	0.112218i	0.896600	−	0.442840i	$-0.146029\pi$
$383$	1.26795	+	2.19615i	0.0647892	+	0.112218i	−0.831811	+	0.555059i	$0.812696\pi$
$384$	0.866025	+	1.50000i	0.0441942	+	0.0765466i
$385$	1.86603	−	3.23205i	0.0951015	−	0.164721i
$386$	−26.1244			−1.32969
$387$	34.1769			1.73731
$388$	−1.00000			−0.0507673
$389$	−4.53590	+	7.85641i	−0.229979	+	0.398336i	−0.957802	−	0.287430i	$-0.907199\pi$
$389$	−4.53590	+	7.85641i	−0.229979	+	0.398336i	0.727822	+	0.685766i	$0.240532\pi$
$390$	−8.19615			−0.415028
$391$	−0.633975	−	1.09808i	−0.0320615	−	0.0555321i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$	−27.4641			−1.38538
$394$	1.36603	−	2.36603i	0.0688194	−	0.119199i
$395$	−14.0000			−0.704416
$396$	−5.59808	−	9.69615i	−0.281314	−	0.487250i
$397$	4.33975			0.217806			0.108903	−	0.994052i	$-0.465266\pi$
$397$	4.33975			0.217806			0.108903	+	0.994052i	$0.465266\pi$
$398$	−5.63397	+	9.75833i	−0.282406	+	0.489141i
$399$	−5.59808	−	9.69615i	−0.280254	−	0.485415i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	10.4282	+	18.0622i	0.520760	+	0.901982i	0.999709	+	0.0241394i	$0.00768455\pi$
$401$	10.4282	+	18.0622i	0.520760	+	0.901982i	−0.478949	+	0.877843i	$0.658982\pi$
$402$	−7.79423	+	13.5000i	−0.388741	+	0.673319i
$403$	−21.1244	+	36.5885i	−1.05228	+	1.82260i
$404$	9.46410			0.470857
$405$	9.00000			0.447214
$406$	−8.19615			−0.406768
$407$	18.0263	−	31.2224i	0.893529	−	1.54764i
$408$	0.866025	−	1.50000i	0.0428746	−	0.0742611i
$409$	−14.1340	−	24.4808i	−0.698880	−	1.21050i	−0.968855	−	0.247628i	$-0.920349\pi$
$409$	−14.1340	−	24.4808i	−0.698880	−	1.21050i	0.269975	−	0.962867i	$-0.412985\pi$
$410$	2.86603	+	4.96410i	0.141543	+	0.245160i
$411$	−3.69615	−	6.40192i	−0.182318	−	0.315784i
$412$	3.36603	−	5.83013i	0.165832	−	0.287230i
$413$	−8.46410			−0.416491
$414$	1.90192	+	3.29423i	0.0934745	+	0.161903i
$415$	1.46410			0.0718699
$416$	2.36603	−	4.09808i	0.116004	−	0.200925i
$417$	−4.26795			−0.209002
$418$	−12.0622	−	20.8923i	−0.589980	−	1.02188i
$419$	−2.66025	−	4.60770i	−0.129962	−	0.225101i	0.793700	−	0.608310i	$-0.208152\pi$
$419$	−2.66025	−	4.60770i	−0.129962	−	0.225101i	−0.923662	+	0.383209i	$0.874819\pi$
$420$	−1.73205			−0.0845154
$421$	11.7583	−	20.3660i	0.573066	−	0.992579i	−0.423183	−	0.906044i	$-0.639087\pi$
$421$	11.7583	−	20.3660i	0.573066	−	0.992579i	0.996249	−	0.0865350i	$-0.0275795\pi$
$422$	−8.39230			−0.408531
$423$	12.0000			0.583460
$424$	−10.1962			−0.495169
$425$	−0.500000	+	0.866025i	−0.0242536	+	0.0420084i
$426$	7.56218	+	13.0981i	0.366389	+	0.634604i
$427$	−0.366025	−	0.633975i	−0.0177132	−	0.0306802i
$428$	−9.23205	−	15.9904i	−0.446248	−	0.772924i
$429$	−15.2942	+	26.4904i	−0.738412	+	1.27897i
$430$	5.69615	−	9.86603i	0.274693	−	0.475782i
$431$	−18.2487			−0.879009			−0.439505	−	0.898240i	$-0.644846\pi$
$431$	−18.2487			−0.879009			−0.439505	+	0.898240i	$0.644846\pi$
$432$	−2.59808	+	4.50000i	−0.125000	+	0.216506i
$433$	22.3205			1.07266			0.536328	−	0.844010i	$-0.319811\pi$
$433$	22.3205			1.07266			0.536328	+	0.844010i	$0.319811\pi$
$434$	−4.46410	+	7.73205i	−0.214284	+	0.371150i
$435$	7.09808	−	12.2942i	0.340327	−	0.589463i
$436$	2.36603	+	4.09808i	0.113312	+	0.196262i
$437$	4.09808	+	7.09808i	0.196038	+	0.339547i
$438$	−1.66987	−	2.89230i	−0.0797896	−	0.138200i
$439$	−8.63397	+	14.9545i	−0.412077	+	0.713739i	−0.995117	−	0.0987052i	$-0.968530\pi$
$439$	−8.63397	+	14.9545i	−0.412077	+	0.713739i	0.583040	+	0.812444i	$0.301863\pi$
$440$	−3.73205			−0.177919
$441$	−1.50000	+	2.59808i	−0.0714286	+	0.123718i
$442$	−4.73205			−0.225081
$443$	15.6244	−	27.0622i	0.742336	−	1.28576i	−0.209094	−	0.977896i	$-0.567051\pi$
$443$	15.6244	−	27.0622i	0.742336	−	1.28576i	0.951429	−	0.307867i	$-0.0996153\pi$
$444$	−16.7321			−0.794068
$445$	0.267949	+	0.464102i	0.0127020	+	0.0220005i
$446$	−13.2942	−	23.0263i	−0.629500	−	1.09033i
$447$	20.7846			0.983078
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	23.7846			1.12247			0.561233	−	0.827658i	$-0.310327\pi$
$449$	23.7846			1.12247			0.561233	+	0.827658i	$0.310327\pi$
$450$	1.50000	−	2.59808i	0.0707107	−	0.122474i
$451$	21.3923			1.00732
$452$	4.92820	−	8.53590i	0.231803	−	0.401495i
$453$	10.2679	+	17.7846i	0.482430	+	0.835594i
$454$	3.66987	+	6.35641i	0.172236	+	0.298321i
$455$	2.36603	+	4.09808i	0.110921	+	0.192121i
$456$	−5.59808	+	9.69615i	−0.262154	+	0.454064i
$457$	−8.99038	+	15.5718i	−0.420552	+	0.728418i	−0.995994	−	0.0894252i	$-0.971497\pi$
$457$	−8.99038	+	15.5718i	−0.420552	+	0.728418i	0.575441	+	0.817843i	$0.304830\pi$
$458$	−12.1962			−0.569889
$459$	5.19615			0.242536
$460$	1.26795			0.0591184
$461$	−3.36603	+	5.83013i	−0.156771	+	0.271536i	−0.933703	−	0.358049i	$-0.883442\pi$
$461$	−3.36603	+	5.83013i	−0.156771	+	0.271536i	0.776931	+	0.629585i	$0.216775\pi$
$462$	−3.23205	+	5.59808i	−0.150369	+	0.260446i
$463$	0.392305	+	0.679492i	0.0182320	+	0.0315787i	0.874997	−	0.484128i	$-0.160863\pi$
$463$	0.392305	+	0.679492i	0.0182320	+	0.0315787i	−0.856765	+	0.515706i	$0.827530\pi$
$464$	4.09808	+	7.09808i	0.190248	+	0.329520i
$465$	−7.73205	−	13.3923i	−0.358565	−	0.621053i
$466$	13.7942	−	23.8923i	0.639005	−	1.10679i
$467$	2.26795			0.104948			0.0524741	−	0.998622i	$-0.483289\pi$
$467$	2.26795			0.104948			0.0524741	+	0.998622i	$0.483289\pi$
$468$	14.1962			0.656217
$469$	9.00000			0.415581
$470$	2.00000	−	3.46410i	0.0922531	−	0.159787i
$471$	34.7321			1.60037
$472$	4.23205	+	7.33013i	0.194796	+	0.337396i
$473$	−21.2583	−	36.8205i	−0.977459	−	1.69301i
$474$	24.2487			1.11378
$475$	3.23205	−	5.59808i	0.148297	−	0.256857i
$476$	−1.00000			−0.0458349
$477$	−15.2942	−	26.4904i	−0.700275	−	1.21291i
$478$	−6.39230			−0.292377
$479$	13.5622	−	23.4904i	0.619672	−	1.07330i	−0.369874	−	0.929082i	$-0.620599\pi$
$479$	13.5622	−	23.4904i	0.619672	−	1.07330i	0.989546	−	0.144221i	$-0.0460676\pi$
$480$	0.866025	+	1.50000i	0.0395285	+	0.0684653i
$481$	22.8564	+	39.5885i	1.04216	+	1.80508i
$482$	−9.25833	−	16.0359i	−0.421705	−	0.730415i
$483$	1.09808	−	1.90192i	0.0499642	−	0.0865405i
$484$	−1.46410	+	2.53590i	−0.0665501	+	0.115268i
$485$	−1.00000			−0.0454077
$486$	−15.5885			−0.707107
$487$	−14.3923			−0.652178			−0.326089	−	0.945339i	$-0.605731\pi$
$487$	−14.3923			−0.652178			−0.326089	+	0.945339i	$0.605731\pi$
$488$	−0.366025	+	0.633975i	−0.0165692	+	0.0286987i
$489$	2.07180	−	3.58846i	0.0936899	−	0.162276i
$490$	0.500000	+	0.866025i	0.0225877	+	0.0391230i
$491$	−12.8660	−	22.2846i	−0.580636	−	1.00569i	−0.995404	−	0.0957634i	$-0.969471\pi$
$491$	−12.8660	−	22.2846i	−0.580636	−	1.00569i	0.414769	−	0.909927i	$-0.363863\pi$
$492$	−4.96410	−	8.59808i	−0.223799	−	0.387631i
$493$	4.09808	−	7.09808i	0.184568	−	0.319681i
$494$	30.5885			1.37624
$495$	−5.59808	−	9.69615i	−0.251615	−	0.435810i
$496$	8.92820			0.400888
$497$	4.36603	−	7.56218i	0.195843	−	0.339210i
$498$	−2.53590			−0.113636
$499$	−5.59808	−	9.69615i	−0.250604	−	0.434059i	0.713088	−	0.701074i	$-0.247296\pi$
$499$	−5.59808	−	9.69615i	−0.250604	−	0.434059i	−0.963692	+	0.267015i	$0.913963\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	15.8038			0.706064
$502$	−5.42820	+	9.40192i	−0.242273	+	0.419628i
$503$	−21.7128			−0.968126			−0.484063	−	0.875033i	$-0.660840\pi$
$503$	−21.7128			−0.968126			−0.484063	+	0.875033i	$0.660840\pi$
$504$	3.00000			0.133631
$505$	9.46410			0.421147
$506$	2.36603	−	4.09808i	0.105183	−	0.182182i
$507$	−8.13397	−	14.0885i	−0.361242	−	0.625690i
$508$	0.830127	+	1.43782i	0.0368309	+	0.0637930i
$509$	8.63397	+	14.9545i	0.382694	+	0.662846i	0.991446	−	0.130515i	$-0.0416630\pi$
$509$	8.63397	+	14.9545i	0.382694	+	0.662846i	−0.608752	+	0.793360i	$0.708330\pi$
$510$	0.866025	−	1.50000i	0.0383482	−	0.0664211i
$511$	−0.964102	+	1.66987i	−0.0426493	+	0.0738708i
$512$	−1.00000			−0.0441942
$513$	−33.5885			−1.48297
$514$	−6.07180			−0.267815
$515$	3.36603	−	5.83013i	0.148325	−	0.256906i
$516$	−9.86603	+	17.0885i	−0.434328	+	0.752277i
$517$	−7.46410	−	12.9282i	−0.328271	−	0.568582i
$518$	4.83013	+	8.36603i	0.212224	+	0.367582i
$519$	−2.66025	−	4.60770i	−0.116772	−	0.202255i
$520$	2.36603	−	4.09808i	0.103757	−	0.179713i
$521$	23.7321			1.03972			0.519860	−	0.854251i	$-0.325984\pi$
$521$	23.7321			1.03972			0.519860	+	0.854251i	$0.325984\pi$
$522$	−12.2942	+	21.2942i	−0.538104	+	0.932023i
$523$	24.5359			1.07288			0.536440	−	0.843938i	$-0.319769\pi$
$523$	24.5359			1.07288			0.536440	+	0.843938i	$0.319769\pi$
$524$	7.92820	−	13.7321i	0.346345	−	0.599887i
$525$	−1.73205			−0.0755929
$526$	6.90192	+	11.9545i	0.300938	+	0.521240i
$527$	−4.46410	−	7.73205i	−0.194459	−	0.336813i
$528$	6.46410			0.281314
$529$	10.6962	−	18.5263i	0.465050	−	0.805490i
$530$	−10.1962			−0.442893
$531$	−12.6962	+	21.9904i	−0.550966	+	0.954301i
$532$	6.46410			0.280254
$533$	−13.5622	+	23.4904i	−0.587443	+	1.01748i
$534$	−0.464102	−	0.803848i	−0.0200836	−	0.0347859i
$535$	−9.23205	−	15.9904i	−0.399136	−	0.691324i
$536$	−4.50000	−	7.79423i	−0.194370	−	0.336659i
$537$	21.0000	−	36.3731i	0.906217	−	1.56961i
$538$	−9.63397	+	16.6865i	−0.415350	+	0.719408i
$539$	3.73205			0.160751
$540$	−2.59808	+	4.50000i	−0.111803	+	0.193649i
$541$	−16.3923			−0.704760			−0.352380	−	0.935857i	$-0.614628\pi$
$541$	−16.3923			−0.704760			−0.352380	+	0.935857i	$0.614628\pi$
$542$	8.02628	−	13.9019i	0.344758	−	0.597139i
$543$	−15.4641	+	26.7846i	−0.663628	+	1.14944i
$544$	0.500000	+	0.866025i	0.0214373	+	0.0371305i
$545$	2.36603	+	4.09808i	0.101349	+	0.175542i
$546$	−4.09808	−	7.09808i	−0.175381	−	0.303770i
$547$	−14.0885	+	24.4019i	−0.602379	+	1.04335i	0.390081	+	0.920781i	$0.372447\pi$
$547$	−14.0885	+	24.4019i	−0.602379	+	1.04335i	−0.992460	+	0.122570i	$0.960886\pi$
$548$	4.26795			0.182318
$549$	−2.19615			−0.0937295
$550$	−3.73205			−0.159135
$551$	−26.4904	+	45.8827i	−1.12853	+	1.95467i
$552$	−2.19615			−0.0934745
$553$	−7.00000	−	12.1244i	−0.297670	−	0.515580i
$554$	15.9282	+	27.5885i	0.676725	+	1.17212i
$555$	−16.7321			−0.710236
$556$	1.23205	−	2.13397i	0.0522506	−	0.0905007i
$557$	40.7846			1.72810			0.864050	−	0.503407i	$-0.167920\pi$
$557$	40.7846			1.72810			0.864050	+	0.503407i	$0.167920\pi$
$558$	13.3923	+	23.1962i	0.566941	+	0.981971i
$559$	53.9090			2.28011
$560$	0.500000	−	0.866025i	0.0211289	−	0.0365963i
$561$	−3.23205	−	5.59808i	−0.136457	−	0.236351i
$562$	10.1962	+	17.6603i	0.430099	+	0.744953i
$563$	6.93782	+	12.0167i	0.292394	+	0.506442i	0.974375	−	0.224928i	$-0.0722147\pi$
$563$	6.93782	+	12.0167i	0.292394	+	0.506442i	−0.681981	+	0.731370i	$0.738881\pi$
$564$	−3.46410	+	6.00000i	−0.145865	+	0.252646i
$565$	4.92820	−	8.53590i	0.207331	−	0.359108i
$566$	24.7846			1.04177
$567$	4.50000	+	7.79423i	0.188982	+	0.327327i
$568$	−8.73205			−0.366389
$569$	8.89230	−	15.4019i	0.372785	−	0.645682i	−0.617208	−	0.786800i	$-0.711736\pi$
$569$	8.89230	−	15.4019i	0.372785	−	0.645682i	0.989993	+	0.141118i	$0.0450696\pi$
$570$	−5.59808	+	9.69615i	−0.234478	+	0.406127i
$571$	3.06218	+	5.30385i	0.128148	+	0.221959i	0.922959	−	0.384898i	$-0.125763\pi$
$571$	3.06218	+	5.30385i	0.128148	+	0.221959i	−0.794811	+	0.606857i	$0.792430\pi$
$572$	−8.83013	−	15.2942i	−0.369206	−	0.639484i
$573$	2.19615	+	3.80385i	0.0917456	+	0.158908i
$574$	−2.86603	+	4.96410i	−0.119626	+	0.207198i
$575$	1.26795			0.0528771
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$	−11.2487			−0.468290			−0.234145	−	0.972202i	$-0.575229\pi$
$577$	−11.2487			−0.468290			−0.234145	+	0.972202i	$0.575229\pi$
$578$	−8.00000	+	13.8564i	−0.332756	+	0.576351i
$579$	45.2487			1.88047
$580$	4.09808	+	7.09808i	0.170163	+	0.294732i
$581$	0.732051	+	1.26795i	0.0303706	+	0.0526034i
$582$	1.73205			0.0717958
$583$	−19.0263	+	32.9545i	−0.787988	+	1.36484i
$584$	1.92820			0.0797896
$585$	14.1962			0.586939
$586$	−20.5885			−0.850501
$587$	−2.99038	+	5.17949i	−0.123426	+	0.213781i	−0.921117	−	0.389287i	$-0.872722\pi$
$587$	−2.99038	+	5.17949i	−0.123426	+	0.213781i	0.797690	+	0.603067i	$0.206055\pi$
$588$	−0.866025	−	1.50000i	−0.0357143	−	0.0618590i
$589$	28.8564	+	49.9808i	1.18901	+	2.05942i
$590$	4.23205	+	7.33013i	0.174231	+	0.301777i
$591$	−2.36603	+	4.09808i	−0.0973253	+	0.168572i
$592$	4.83013	−	8.36603i	0.198517	−	0.343842i
$593$	2.53590			0.104137			0.0520684	−	0.998644i	$-0.483419\pi$
$593$	2.53590			0.104137			0.0520684	+	0.998644i	$0.483419\pi$
$594$	9.69615	+	16.7942i	0.397838	+	0.689076i
$595$	−1.00000			−0.0409960
$596$	−6.00000	+	10.3923i	−0.245770	+	0.425685i
$597$	9.75833	−	16.9019i	0.399382	−	0.691750i
$598$	3.00000	+	5.19615i	0.122679	+	0.212486i
$599$	−17.3205	−	30.0000i	−0.707697	−	1.22577i	−0.965709	−	0.259625i	$-0.916401\pi$
$599$	−17.3205	−	30.0000i	−0.707697	−	1.22577i	0.258013	−	0.966142i	$-0.416932\pi$
$600$	0.866025	+	1.50000i	0.0353553	+	0.0612372i
$601$	3.06218	−	5.30385i	0.124909	−	0.216348i	−0.796788	−	0.604258i	$-0.793469\pi$
$601$	3.06218	−	5.30385i	0.124909	−	0.216348i	0.921697	+	0.387910i	$0.126803\pi$
$602$	11.3923			0.464316
$603$	13.5000	−	23.3827i	0.549762	−	0.952217i
$604$	−11.8564			−0.482430
$605$	−1.46410	+	2.53590i	−0.0595242	+	0.103099i
$606$	−16.3923			−0.665892
$607$	−21.8564	−	37.8564i	−0.887124	−	1.53654i	−0.843260	−	0.537507i	$-0.819366\pi$
$607$	−21.8564	−	37.8564i	−0.887124	−	1.53654i	−0.0438647	−	0.999037i	$-0.513967\pi$
$608$	−3.23205	−	5.59808i	−0.131077	−	0.227032i
$609$	14.1962			0.575257
$610$	−0.366025	+	0.633975i	−0.0148199	+	0.0256689i
$611$	18.9282			0.765753
$612$	−1.50000	+	2.59808i	−0.0606339	+	0.105021i
$613$	30.0000			1.21169			0.605844	−	0.795583i	$-0.292835\pi$
$613$	30.0000			1.21169			0.605844	+	0.795583i	$0.292835\pi$
$614$	−3.13397	+	5.42820i	−0.126477	+	0.219064i
$615$	−4.96410	−	8.59808i	−0.200172	−	0.346708i
$616$	−1.86603	−	3.23205i	−0.0751843	−	0.130223i
$617$	−7.13397	−	12.3564i	−0.287203	−	0.497450i	0.685938	−	0.727660i	$-0.259392\pi$
$617$	−7.13397	−	12.3564i	−0.287203	−	0.497450i	−0.973141	+	0.230210i	$0.926059\pi$
$618$	−5.83013	+	10.0981i	−0.234522	+	0.406204i
$619$	−22.3564	+	38.7224i	−0.898580	+	1.55639i	−0.0692693	+	0.997598i	$0.522067\pi$
$619$	−22.3564	+	38.7224i	−0.898580	+	1.55639i	−0.829311	+	0.558788i	$0.811267\pi$
$620$	8.92820			0.358565
$621$	−3.29423	−	5.70577i	−0.132193	−	0.228965i
$622$	−8.53590			−0.342258
$623$	−0.267949	+	0.464102i	−0.0107352	+	0.0185938i
$624$	−4.09808	+	7.09808i	−0.164054	+	0.284150i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	8.50000	+	14.7224i	0.339728	+	0.588427i
$627$	20.8923	+	36.1865i	0.834358	+	1.44515i
$628$	−10.0263	+	17.3660i	−0.400092	+	0.692980i
$629$	−9.66025			−0.385180
$630$	3.00000			0.119523
$631$	−27.6603			−1.10114			−0.550569	−	0.834790i	$-0.685589\pi$
$631$	−27.6603			−1.10114			−0.550569	+	0.834790i	$0.685589\pi$
$632$	−7.00000	+	12.1244i	−0.278445	+	0.482281i
$633$	14.5359			0.577750
$634$	4.63397	+	8.02628i	0.184039	+	0.318764i
$635$	0.830127	+	1.43782i	0.0329426	+	0.0570582i
$636$	17.6603			0.700275
$637$	−2.36603	+	4.09808i	−0.0937453	+	0.162372i
$638$	30.5885			1.21101
$639$	−13.0981	−	22.6865i	−0.518152	−	0.897465i
$640$	−1.00000			−0.0395285
$641$	−9.50000	+	16.4545i	−0.375227	+	0.649913i	−0.990361	−	0.138510i	$-0.955769\pi$
$641$	−9.50000	+	16.4545i	−0.375227	+	0.649913i	0.615134	+	0.788423i	$0.289102\pi$
$642$	15.9904	+	27.6962i	0.631090	+	1.09308i
$643$	10.0622	+	17.4282i	0.396814	+	0.687301i	0.993331	−	0.115299i	$-0.0367826\pi$
$643$	10.0622	+	17.4282i	0.396814	+	0.687301i	−0.596517	+	0.802600i	$0.703449\pi$
$644$	0.633975	+	1.09808i	0.0249821	+	0.0432703i
$645$	−9.86603	+	17.0885i	−0.388474	+	0.672857i
$646$	−3.23205	+	5.59808i	−0.127163	+	0.220253i
$647$	10.1962			0.400852			0.200426	−	0.979709i	$-0.435767\pi$
$647$	10.1962			0.400852			0.200426	+	0.979709i	$0.435767\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	31.5885			1.23996
$650$	2.36603	−	4.09808i	0.0928032	−	0.160740i
$651$	7.73205	−	13.3923i	0.303043	−	0.524886i
$652$	1.19615	+	2.07180i	0.0468449	+	0.0811378i
$653$	13.9282	+	24.1244i	0.545053	+	0.944059i	0.998604	+	0.0528286i	$0.0168237\pi$
$653$	13.9282	+	24.1244i	0.545053	+	0.944059i	−0.453551	+	0.891230i	$0.649843\pi$
$654$	−4.09808	−	7.09808i	−0.160247	−	0.277557i
$655$	7.92820	−	13.7321i	0.309781	−	0.536556i
$656$	5.73205			0.223799
$657$	2.89230	+	5.00962i	0.112840	+	0.195444i
$658$	4.00000			0.155936
$659$	0.732051	−	1.26795i	0.0285167	−	0.0493923i	−0.851415	−	0.524493i	$-0.824255\pi$
$659$	0.732051	−	1.26795i	0.0285167	−	0.0493923i	0.879932	+	0.475101i	$0.157588\pi$
$660$	6.46410			0.251615
$661$	−4.19615	−	7.26795i	−0.163211	−	0.282690i	0.772807	−	0.634641i	$-0.218852\pi$
$661$	−4.19615	−	7.26795i	−0.163211	−	0.282690i	−0.936019	+	0.351950i	$0.885519\pi$
$662$	−11.2679	−	19.5167i	−0.437941	−	0.758537i
$663$	8.19615			0.318312
$664$	0.732051	−	1.26795i	0.0284091	−	0.0492060i
$665$	6.46410			0.250667
$666$	28.9808			1.12298
$667$	−10.3923			−0.402392
$668$	−4.56218	+	7.90192i	−0.176516	+	0.305735i
$669$	23.0263	+	39.8827i	0.890247	+	1.54195i
$670$	−4.50000	−	7.79423i	−0.173850	−	0.301117i
$671$	1.36603	+	2.36603i	0.0527348	+	0.0913394i
$672$	−0.866025	+	1.50000i	−0.0334077	+	0.0578638i
$673$	2.85641	−	4.94744i	0.110106	−	0.190710i	−0.805707	−	0.592315i	$-0.798214\pi$
$673$	2.85641	−	4.94744i	0.110106	−	0.190710i	0.915813	+	0.401605i	$0.131548\pi$
$674$	−19.3397			−0.744939
$675$	−2.59808	+	4.50000i	−0.100000	+	0.173205i
$676$	9.39230			0.361242
$677$	8.70577	−	15.0788i	0.334590	−	0.579527i	−0.648816	−	0.760945i	$-0.724736\pi$
$677$	8.70577	−	15.0788i	0.334590	−	0.579527i	0.983406	+	0.181418i	$0.0580689\pi$
$678$	−8.53590	+	14.7846i	−0.327819	+	0.567800i
$679$	−0.500000	−	0.866025i	−0.0191882	−	0.0332350i
$680$	0.500000	+	0.866025i	0.0191741	+	0.0332106i
$681$	−6.35641	−	11.0096i	−0.243578	−	0.421890i
$682$	16.6603	−	28.8564i	0.637954	−	1.10497i
$683$	−10.3205			−0.394903			−0.197452	−	0.980313i	$-0.563267\pi$
$683$	−10.3205			−0.394903			−0.197452	+	0.980313i	$0.563267\pi$
$684$	9.69615	−	16.7942i	0.370742	−	0.642143i
$685$	4.26795			0.163070
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	21.1244			0.805944
$688$	−5.69615	−	9.86603i	−0.217164	−	0.376139i
$689$	−24.1244	−	41.7846i	−0.919065	−	1.59187i
$690$	−2.19615			−0.0836061
$691$	−5.46410	+	9.46410i	−0.207864	+	0.360031i	−0.951042	−	0.309063i	$-0.899985\pi$
$691$	−5.46410	+	9.46410i	−0.207864	+	0.360031i	0.743177	+	0.669095i	$0.233318\pi$
$692$	3.07180			0.116772
$693$	5.59808	−	9.69615i	0.212653	−	0.368326i
$694$	−26.7128			−1.01400
$695$	1.23205	−	2.13397i	0.0467344	−	0.0809463i
$696$	−7.09808	−	12.2942i	−0.269052	−	0.466012i
$697$	−2.86603	−	4.96410i	−0.108558	−	0.188029i
$698$	−4.29423	−	7.43782i	−0.162539	−	0.281526i
$699$	−23.8923	+	41.3827i	−0.903690	+	1.56524i
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	13.6603			0.515941			0.257970	−	0.966153i	$-0.416946\pi$
$701$	13.6603			0.515941			0.257970	+	0.966153i	$0.416946\pi$
$702$	−24.5885			−0.928032
$703$	62.4449			2.35515
$704$	−1.86603	+	3.23205i	−0.0703285	+	0.121812i
$705$	−3.46410	+	6.00000i	−0.130466	+	0.225973i
$706$	−10.9641	−	18.9904i	−0.412639	−	0.714712i
$707$	4.73205	+	8.19615i	0.177967	+	0.308248i
$708$	−7.33013	−	12.6962i	−0.275483	−	0.477151i
$709$	−0.437822	+	0.758330i	−0.0164428	+	0.0284797i	−0.874130	−	0.485693i	$-0.838567\pi$
$709$	−0.437822	+	0.758330i	−0.0164428	+	0.0284797i	0.857687	+	0.514172i	$0.171901\pi$
$710$	−8.73205			−0.327708
$711$	−42.0000			−1.57512
$712$	0.535898			0.0200836
$713$	−5.66025	+	9.80385i	−0.211978	+	0.367157i
$714$	1.73205			0.0648204
$715$	−8.83013	−	15.2942i	−0.330228	−	0.571972i
$716$	12.1244	+	21.0000i	0.453108	+	0.784807i
$717$	11.0718			0.413484
$718$	7.02628	−	12.1699i	0.262218	−	0.454176i
$719$	−34.9808			−1.30456			−0.652281	−	0.757977i	$-0.726188\pi$
$719$	−34.9808			−1.30456			−0.652281	+	0.757977i	$0.726188\pi$
$720$	−1.50000	−	2.59808i	−0.0559017	−	0.0968246i
$721$	6.73205			0.250715
$722$	11.3923	−	19.7321i	0.423978	−	0.734351i
$723$	16.0359	+	27.7750i	0.596381	+	1.03296i
$724$	−8.92820	−	15.4641i	−0.331814	−	0.574719i
$725$	4.09808	+	7.09808i	0.152199	+	0.263616i
$726$	2.53590	−	4.39230i	0.0941160	−	0.163014i
$727$	23.0263	−	39.8827i	0.853997	−	1.47917i	−0.0235746	−	0.999722i	$-0.507505\pi$
$727$	23.0263	−	39.8827i	0.853997	−	1.47917i	0.877572	−	0.479445i	$-0.159162\pi$
$728$	4.73205			0.175381
$729$	27.0000			1.00000
$730$	1.92820			0.0713660
$731$	−5.69615	+	9.86603i	−0.210680	+	0.364908i
$732$	0.633975	−	1.09808i	0.0234324	−	0.0405861i
$733$	−9.09808	−	15.7583i	−0.336045	−	0.582047i	0.647640	−	0.761947i	$-0.275756\pi$
$733$	−9.09808	−	15.7583i	−0.336045	−	0.582047i	−0.983685	+	0.179899i	$0.942423\pi$
$734$	7.36603	+	12.7583i	0.271885	+	0.470919i
$735$	−0.866025	−	1.50000i	−0.0319438	−	0.0553283i
$736$	0.633975	−	1.09808i	0.0233686	−	0.0404756i
$737$	−33.5885			−1.23725
$738$	8.59808	+	14.8923i	0.316500	+	0.548193i
$739$	22.1244			0.813858			0.406929	−	0.913460i	$-0.366600\pi$
$739$	22.1244			0.813858			0.406929	+	0.913460i	$0.366600\pi$
$740$	4.83013	−	8.36603i	0.177559	−	0.307541i
$741$	−52.9808			−1.94630
$742$	−5.09808	−	8.83013i	−0.187156	−	0.324164i
$743$	13.3923	+	23.1962i	0.491316	+	0.850984i	0.999950	−	0.00999854i	$-0.00318269\pi$
$743$	13.3923	+	23.1962i	0.491316	+	0.850984i	−0.508634	+	0.860983i	$0.669849\pi$
$744$	−15.4641			−0.566941
$745$	−6.00000	+	10.3923i	−0.219823	+	0.380745i
$746$	−6.39230			−0.234039
$747$	4.39230			0.160706
$748$	3.73205			0.136457
$749$	9.23205	−	15.9904i	0.337332	−	0.584276i
$750$	0.866025	+	1.50000i	0.0316228	+	0.0547723i
$751$	16.8301	+	29.1506i	0.614140	+	1.06372i	0.990535	+	0.137262i	$0.0438303\pi$
$751$	16.8301	+	29.1506i	0.614140	+	1.06372i	−0.376395	+	0.926459i	$0.622836\pi$
$752$	−2.00000	−	3.46410i	−0.0729325	−	0.126323i
$753$	9.40192	−	16.2846i	0.342625	−	0.593444i
$754$	−19.3923	+	33.5885i	−0.706226	+	1.22322i
$755$	−11.8564			−0.431499
$756$	−5.19615			−0.188982
$757$	15.6603			0.569182			0.284591	−	0.958649i	$-0.408142\pi$
$757$	15.6603			0.569182			0.284591	+	0.958649i	$0.408142\pi$
$758$	0.401924	−	0.696152i	0.0145985	−	0.0252854i
$759$	−4.09808	+	7.09808i	−0.148751	+	0.257644i
$760$	−3.23205	−	5.59808i	−0.117239	−	0.203064i
$761$	1.39230	+	2.41154i	0.0504710	+	0.0874184i	0.890157	−	0.455654i	$-0.150594\pi$
$761$	1.39230	+	2.41154i	0.0504710	+	0.0874184i	−0.839686	+	0.543072i	$0.817261\pi$
$762$	−1.43782	−	2.49038i	−0.0520868	−	0.0902170i
$763$	−2.36603	+	4.09808i	−0.0856559	+	0.148360i
$764$	−2.53590			−0.0917456
$765$	−1.50000	+	2.59808i	−0.0542326	+	0.0939336i
$766$	2.53590			0.0916257
$767$	−20.0263	+	34.6865i	−0.723107	+	1.25246i
$768$	1.73205			0.0625000
$769$	−15.8564	−	27.4641i	−0.571797	−	0.990381i	−0.996382	−	0.0849927i	$-0.972913\pi$
$769$	−15.8564	−	27.4641i	−0.571797	−	0.990381i	0.424585	−	0.905388i	$-0.360420\pi$
$770$	−1.86603	−	3.23205i	−0.0672469	−	0.116475i
$771$	10.5167			0.378748
$772$	−13.0622	+	22.6244i	−0.470118	+	0.814268i
$773$	−21.3731			−0.768736			−0.384368	−	0.923180i	$-0.625581\pi$
$773$	−21.3731			−0.768736			−0.384368	+	0.923180i	$0.625581\pi$
$774$	17.0885	−	29.5981i	0.614232	−	1.06388i
$775$	8.92820			0.320711
$776$	−0.500000	+	0.866025i	−0.0179490	+	0.0310885i
$777$	−8.36603	−	14.4904i	−0.300129	−	0.519840i
$778$	4.53590	+	7.85641i	0.162620	+	0.281666i
$779$	18.5263	+	32.0885i	0.663773	+	1.14969i
$780$	−4.09808	+	7.09808i	−0.146735	+	0.254152i
$781$	−16.2942	+	28.2224i	−0.583053	+	1.00988i
$782$	−1.26795			−0.0453418
$783$	21.2942	−	36.8827i	0.760994	−	1.31808i
$784$	1.00000			0.0357143
$785$	−10.0263	+	17.3660i	−0.357853	+	0.619820i
$786$	−13.7321	+	23.7846i	−0.489806	+	0.848369i
$787$	−14.9282	−	25.8564i	−0.532133	−	0.921681i	−0.999296	−	0.0375103i	$-0.988057\pi$
$787$	−14.9282	−	25.8564i	−0.532133	−	0.921681i	0.467163	−	0.884171i	$-0.345276\pi$
$788$	−1.36603	−	2.36603i	−0.0486626	−	0.0842862i
$789$	−11.9545	−	20.7058i	−0.425591	−	0.737145i
$790$	−7.00000	+	12.1244i	−0.249049	+	0.431365i
$791$	9.85641			0.350453
$792$	−11.1962			−0.397838
$793$	−3.46410			−0.123014
$794$	2.16987	−	3.75833i	0.0770059	−	0.133378i
$795$	17.6603			0.626345
$796$	5.63397	+	9.75833i	0.199691	+	0.345875i
$797$	9.46410	+	16.3923i	0.335236	+	0.580645i	0.983530	−	0.180745i	$-0.0578507\pi$
$797$	9.46410	+	16.3923i	0.335236	+	0.580645i	−0.648294	+	0.761390i	$0.724517\pi$
$798$	−11.1962			−0.396339
$799$	−2.00000	+	3.46410i	−0.0707549	+	0.122551i
$800$	−1.00000			−0.0353553
$801$	0.803848	+	1.39230i	0.0284026	+	0.0491947i
$802$	20.8564			0.736465
$803$	3.59808	−	6.23205i	0.126973	−	0.219924i
$804$	7.79423	+	13.5000i	0.274881	+	0.476108i
$805$	0.633975	+	1.09808i	0.0223447	+	0.0387021i
$806$	21.1244	+	36.5885i	0.744074	+	1.28877i
$807$	16.6865	−	28.9019i	0.587394	−	1.01740i
$808$	4.73205	−	8.19615i	0.166473	−	0.288340i
$809$	22.6077			0.794844			0.397422	−	0.917636i	$-0.369905\pi$
$809$	22.6077			0.794844			0.397422	+	0.917636i	$0.369905\pi$
$810$	4.50000	−	7.79423i	0.158114	−	0.273861i
$811$	−26.6077			−0.934323			−0.467161	−	0.884172i	$-0.654723\pi$
$811$	−26.6077			−0.934323			−0.467161	+	0.884172i	$0.654723\pi$
$812$	−4.09808	+	7.09808i	−0.143814	+	0.249094i
$813$	−13.9019	+	24.0788i	−0.487562	+	0.844482i
$814$	−18.0263	−	31.2224i	−0.631821	−	1.09435i
$815$	1.19615	+	2.07180i	0.0418994	+	0.0725719i
$816$	−0.866025	−	1.50000i	−0.0303170	−	0.0525105i
$817$	36.8205	−	63.7750i	1.28819	−	2.23120i
$818$	−28.2679			−0.988366
$819$	7.09808	+	12.2942i	0.248027	+	0.429595i
$820$	5.73205			0.200172
$821$	−6.16987	+	10.6865i	−0.215330	+	0.372963i	−0.953375	−	0.301789i	$-0.902416\pi$
$821$	−6.16987	+	10.6865i	−0.215330	+	0.372963i	0.738045	+	0.674752i	$0.235749\pi$
$822$	−7.39230			−0.257836
$823$	−8.16987	−	14.1506i	−0.284784	−	0.493260i	0.687773	−	0.725926i	$-0.258588\pi$
$823$	−8.16987	−	14.1506i	−0.284784	−	0.493260i	−0.972557	+	0.232666i	$0.925255\pi$
$824$	−3.36603	−	5.83013i	−0.117261	−	0.203102i
$825$	6.46410			0.225051
$826$	−4.23205	+	7.33013i	−0.147252	+	0.255048i
$827$	−12.1436			−0.422274			−0.211137	−	0.977456i	$-0.567717\pi$
$827$	−12.1436			−0.422274			−0.211137	+	0.977456i	$0.567717\pi$
$828$	3.80385			0.132193
$829$	−20.3923			−0.708254			−0.354127	−	0.935197i	$-0.615222\pi$
$829$	−20.3923			−0.708254			−0.354127	+	0.935197i	$0.615222\pi$
$830$	0.732051	−	1.26795i	0.0254099	−	0.0440112i
$831$	−27.5885	−	47.7846i	−0.957033	−	1.65763i
$832$	−2.36603	−	4.09808i	−0.0820272	−	0.142075i
$833$	−0.500000	−	0.866025i	−0.0173240	−	0.0300060i
$834$	−2.13397	+	3.69615i	−0.0738935	+	0.127987i
$835$	−4.56218	+	7.90192i	−0.157881	+	0.273457i
$836$	−24.1244			−0.834358
$837$	−23.1962	−	40.1769i	−0.801776	−	1.38872i
$838$	−5.32051			−0.183794
$839$	−28.1506	+	48.7583i	−0.971868	+	1.68332i	−0.281962	+	0.959426i	$0.590985\pi$
$839$	−28.1506	+	48.7583i	−0.971868	+	1.68332i	−0.689906	+	0.723899i	$0.742348\pi$
$840$	−0.866025	+	1.50000i	−0.0298807	+	0.0517549i
$841$	−19.0885	−	33.0622i	−0.658223	−	1.14008i
$842$	−11.7583	−	20.3660i	−0.405219	−	0.701860i
$843$	−17.6603	−	30.5885i	−0.608251	−	1.05352i
$844$	−4.19615	+	7.26795i	−0.144438	+	0.250173i
$845$	9.39230			0.323105
$846$	6.00000	−	10.3923i	0.206284	−	0.357295i
$847$	−2.92820			−0.100614
$848$	−5.09808	+	8.83013i	−0.175069	+	0.303228i
$849$	−42.9282			−1.47329
$850$	0.500000	+	0.866025i	0.0171499	+	0.0297044i
$851$	6.12436	+	10.6077i	0.209940	+	0.363627i
$852$	15.1244			0.518152
$853$	8.58846	−	14.8756i	0.294063	−	0.509332i	−0.680703	−	0.732559i	$-0.738326\pi$
$853$	8.58846	−	14.8756i	0.294063	−	0.509332i	0.974767	+	0.223227i	$0.0716591\pi$
$854$	−0.732051			−0.0250503
$855$	9.69615	−	16.7942i	0.331601	−	0.574351i
$856$	−18.4641			−0.631090
$857$	21.4641	−	37.1769i	0.733200	−	1.26994i	−0.222309	−	0.974976i	$-0.571359\pi$
$857$	21.4641	−	37.1769i	0.733200	−	1.26994i	0.955509	−	0.294963i	$-0.0953073\pi$
$858$	15.2942	+	26.4904i	0.522136	+	0.904367i
$859$	1.96410	+	3.40192i	0.0670143	+	0.116072i	0.897586	−	0.440840i	$-0.145319\pi$
$859$	1.96410	+	3.40192i	0.0670143	+	0.116072i	−0.830571	+	0.556912i	$0.811986\pi$
$860$	−5.69615	−	9.86603i	−0.194237	−	0.336429i
$861$	4.96410	−	8.59808i	0.169176	−	0.293022i
$862$	−9.12436	+	15.8038i	−0.310777	+	0.538281i
$863$	1.32051			0.0449506			0.0224753	−	0.999747i	$-0.492845\pi$
$863$	1.32051			0.0449506			0.0224753	+	0.999747i	$0.492845\pi$
$864$	2.59808	+	4.50000i	0.0883883	+	0.153093i
$865$	3.07180			0.104444
$866$	11.1603	−	19.3301i	0.379241	−	0.656864i
$867$	13.8564	−	24.0000i	0.470588	−	0.815083i
$868$	4.46410	+	7.73205i	0.151521	+	0.262443i
$869$	26.1244	+	45.2487i	0.886208	+	1.53496i
$870$	−7.09808	−	12.2942i	−0.240647	−	0.416813i
$871$	21.2942	−	36.8827i	0.721527	−	1.24972i
$872$	4.73205			0.160247
$873$	−3.00000			−0.101535
$874$	8.19615			0.277239
$875$	0.500000	−	0.866025i	0.0169031	−	0.0292770i
$876$	−3.33975			−0.112840
$877$	8.75833	+	15.1699i	0.295748	+	0.512250i	0.975159	−	0.221508i	$-0.0710979\pi$
$877$	8.75833	+	15.1699i	0.295748	+	0.512250i	−0.679411	+	0.733758i	$0.737765\pi$
$878$	8.63397	+	14.9545i	0.291383	+	0.504689i
$879$	35.6603			1.20279
$880$	−1.86603	+	3.23205i	−0.0629037	+	0.108952i
$881$	−11.2154			−0.377856			−0.188928	−	0.981991i	$-0.560501\pi$
$881$	−11.2154			−0.377856			−0.188928	+	0.981991i	$0.560501\pi$
$882$	1.50000	+	2.59808i	0.0505076	+	0.0874818i
$883$	−30.4641			−1.02520			−0.512599	−	0.858628i	$-0.671317\pi$
$883$	−30.4641			−1.02520			−0.512599	+	0.858628i	$0.671317\pi$
$884$	−2.36603	+	4.09808i	−0.0795780	+	0.137833i
$885$	−7.33013	−	12.6962i	−0.246400	−	0.426776i
$886$	−15.6244	−	27.0622i	−0.524910	−	0.909172i
$887$	28.7128	+	49.7321i	0.964082	+	1.66984i	0.712062	+	0.702117i	$0.247762\pi$
$887$	28.7128	+	49.7321i	0.964082	+	1.66984i	0.252020	+	0.967722i	$0.418905\pi$
$888$	−8.36603	+	14.4904i	−0.280745	+	0.486265i
$889$	−0.830127	+	1.43782i	−0.0278416	+	0.0482230i
$890$	0.535898			0.0179634
$891$	−16.7942	−	29.0885i	−0.562628	−	0.974500i
$892$	−26.5885			−0.890247
$893$	12.9282	−	22.3923i	0.432626	−	0.749330i
$894$	10.3923	−	18.0000i	0.347571	−	0.602010i
$895$	12.1244	+	21.0000i	0.405273	+	0.701953i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$	−5.19615	−	9.00000i	−0.173494	−	0.300501i
$898$	11.8923	−	20.5981i	0.396851	−	0.687367i
$899$	−73.1769			−2.44059
$900$	−1.50000	−	2.59808i	−0.0500000	−	0.0866025i
$901$	10.1962			0.339683
$902$	10.6962	−	18.5263i	0.356143	−	0.616858i
$903$	−19.7321			−0.656642
$904$	−4.92820	−	8.53590i	−0.163910	−	0.283900i
$905$	−8.92820	−	15.4641i	−0.296784	−	0.514044i
$906$	20.5359			0.682260
$907$	13.4282	−	23.2583i	0.445876	−	0.772280i	−0.552237	−	0.833687i	$-0.686226\pi$
$907$	13.4282	−	23.2583i	0.445876	−	0.772280i	0.998113	+	0.0614072i	$0.0195588\pi$
$908$	7.33975			0.243578
$909$	28.3923			0.941713
$910$	4.73205			0.156866
$911$	−7.68653	+	13.3135i	−0.254666	+	0.441095i	−0.964805	−	0.262967i	$-0.915299\pi$
$911$	−7.68653	+	13.3135i	−0.254666	+	0.441095i	0.710139	+	0.704062i	$0.248632\pi$
$912$	5.59808	+	9.69615i	0.185371	+	0.321072i
$913$	−2.73205	−	4.73205i	−0.0904177	−	0.156608i
$914$	8.99038	+	15.5718i	0.297375	+	0.515069i
$915$	0.633975	−	1.09808i	0.0209586	−	0.0363013i
$916$	−6.09808	+	10.5622i	−0.201486	+	0.348984i
$917$	15.8564			0.523625
$918$	2.59808	−	4.50000i	0.0857493	−	0.148522i
$919$	−44.0526			−1.45316			−0.726580	−	0.687082i	$-0.758891\pi$
$919$	−44.0526			−1.45316			−0.726580	+	0.687082i	$0.758891\pi$
$920$	0.633975	−	1.09808i	0.0209015	−	0.0362025i
$921$	5.42820	−	9.40192i	0.178865	−	0.309804i
$922$	3.36603	+	5.83013i	0.110854	+	0.192005i
$923$	−20.6603	−	35.7846i	−0.680041	−	1.17786i
$924$	3.23205	+	5.59808i	0.106327	+	0.184163i
$925$	4.83013	−	8.36603i	0.158814	−	0.275073i
$926$	0.784610			0.0257839
$927$	10.0981	−	17.4904i	0.331664	−	0.574459i
$928$	8.19615			0.269052
$929$	0.607695	−	1.05256i	0.0199378	−	0.0345333i	−0.855884	−	0.517167i	$-0.826987\pi$
$929$	0.607695	−	1.05256i	0.0199378	−	0.0345333i	0.875822	+	0.482634i	$0.160320\pi$
$930$	−15.4641			−0.507088
$931$	3.23205	+	5.59808i	0.105926	+	0.183470i
$932$	−13.7942	−	23.8923i	−0.451845	−	0.782618i
$933$	14.7846			0.484026
$934$	1.13397	−	1.96410i	0.0371048	−	0.0642674i
$935$	3.73205			0.122051
$936$	7.09808	−	12.2942i	0.232008	−	0.401849i
$937$	−25.4641			−0.831876			−0.415938	−	0.909393i	$-0.636547\pi$
$937$	−25.4641			−0.831876			−0.415938	+	0.909393i	$0.636547\pi$
$938$	4.50000	−	7.79423i	0.146930	−	0.254491i
$939$	−14.7224	−	25.5000i	−0.480448	−	0.832161i
$940$	−2.00000	−	3.46410i	−0.0652328	−	0.112987i
$941$	14.7321	+	25.5167i	0.480251	+	0.831819i	0.999743	−	0.0226558i	$-0.00721219\pi$
$941$	14.7321	+	25.5167i	0.480251	+	0.831819i	−0.519492	+	0.854475i	$0.673879\pi$
$942$	17.3660	−	30.0788i	0.565816	−	0.980022i
$943$	−3.63397	+	6.29423i	−0.118338	+	0.204968i
$944$	8.46410			0.275483
$945$	−5.19615			−0.169031
$946$	−42.5167			−1.38234
$947$	−11.3564	+	19.6699i	−0.369034	+	0.639185i	−0.989415	−	0.145116i	$-0.953645\pi$
$947$	−11.3564	+	19.6699i	−0.369034	+	0.639185i	0.620381	+	0.784301i	$0.286978\pi$
$948$	12.1244	−	21.0000i	0.393781	−	0.682048i
$949$	4.56218	+	7.90192i	0.148095	+	0.256507i
$950$	−3.23205	−	5.59808i	−0.104862	−	0.181626i
$951$	−8.02628	−	13.9019i	−0.260270	−	0.450801i
$952$	−0.500000	+	0.866025i	−0.0162051	+	0.0280680i
$953$	−11.8756			−0.384690			−0.192345	−	0.981327i	$-0.561609\pi$
$953$	−11.8756			−0.384690			−0.192345	+	0.981327i	$0.561609\pi$
$954$	−30.5885			−0.990338
$955$	−2.53590			−0.0820597
$956$	−3.19615	+	5.53590i	−0.103371	+	0.179044i
$957$	−52.9808			−1.71262
$958$	−13.5622	−	23.4904i	−0.438174	−	0.758940i
$959$	2.13397	+	3.69615i	0.0689096	+	0.119355i
$960$	1.73205			0.0559017
$961$	−24.3564	+	42.1865i	−0.785691	+	1.36086i
$962$	45.7128			1.47384
$963$	−27.6962	−	47.9711i	−0.892496	−	1.54585i
$964$	−18.5167			−0.596381
$965$	−13.0622	+	22.6244i	−0.420486	+	0.728304i
$966$	−1.09808	−	1.90192i	−0.0353300	−	0.0611934i
$967$	16.4641	+	28.5167i	0.529450	+	0.917034i	0.999410	+	0.0343464i	$0.0109349\pi$
$967$	16.4641	+	28.5167i	0.529450	+	0.917034i	−0.469960	+	0.882688i	$0.655732\pi$
$968$	1.46410	+	2.53590i	0.0470580	+	0.0815069i
$969$	5.59808	−	9.69615i	0.179836	−	0.311485i
$970$	−0.500000	+	0.866025i	−0.0160540	+	0.0278064i
$971$	25.8564			0.829772			0.414886	−	0.909873i	$-0.363822\pi$
$971$	25.8564			0.829772			0.414886	+	0.909873i	$0.363822\pi$
$972$	−7.79423	+	13.5000i	−0.250000	+	0.433013i
$973$	2.46410			0.0789955
$974$	−7.19615	+	12.4641i	−0.230580	+	0.399376i
$975$	−4.09808	+	7.09808i	−0.131243	+	0.227320i
$976$	0.366025	+	0.633975i	0.0117162	+	0.0202930i
$977$	9.52628	+	16.5000i	0.304773	+	0.527882i	0.977211	−	0.212272i	$-0.0680862\pi$
$977$	9.52628	+	16.5000i	0.304773	+	0.527882i	−0.672438	+	0.740153i	$0.734753\pi$
$978$	−2.07180	−	3.58846i	−0.0662488	−	0.114746i
$979$	1.00000	−	1.73205i	0.0319601	−	0.0553566i
$980$	1.00000			0.0319438
$981$	7.09808	+	12.2942i	0.226624	+	0.392525i
$982$	−25.7321			−0.821143
$983$	−6.39230	+	11.0718i	−0.203883	+	0.353135i	−0.949776	−	0.312930i	$-0.898690\pi$
$983$	−6.39230	+	11.0718i	−0.203883	+	0.353135i	0.745893	+	0.666065i	$0.232023\pi$
$984$	−9.92820			−0.316500
$985$	−1.36603	−	2.36603i	−0.0435252	−	0.0753878i
$986$	−4.09808	−	7.09808i	−0.130509	−	0.226049i
$987$	−6.92820			−0.220527
$988$	15.2942	−	26.4904i	0.486574	−	0.842771i
$989$	14.4449			0.459320
$990$	−11.1962			−0.355837
$991$	−17.4641			−0.554765			−0.277383	−	0.960760i	$-0.589467\pi$
$991$	−17.4641			−0.554765			−0.277383	+	0.960760i	$0.589467\pi$
$992$	4.46410	−	7.73205i	0.141735	−	0.245493i
$993$	19.5167	+	33.8038i	0.619343	+	1.07273i
$994$	−4.36603	−	7.56218i	−0.138482	−	0.239858i
$995$	5.63397	+	9.75833i	0.178609	+	0.309360i
$996$	−1.26795	+	2.19615i	−0.0401765	+	0.0695878i
$997$	1.53590	−	2.66025i	0.0486424	−	0.0842511i	−0.840679	−	0.541534i	$-0.817844\pi$
$997$	1.53590	−	2.66025i	0.0486424	−	0.0842511i	0.889321	+	0.457283i	$0.151177\pi$
$998$	−11.1962			−0.354408
$999$	−50.1962			−1.58814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.f.421.1	yes	4
3.2	odd	2		1890.2.j.h.1261.2		4
9.2	odd	6		5670.2.a.be.1.1		2
9.4	even	3	inner	630.2.j.f.211.1	✓	4
9.5	odd	6		1890.2.j.h.631.2		4
9.7	even	3		5670.2.a.z.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.f.211.1	✓	4	9.4	even	3	inner
630.2.j.f.421.1	yes	4	1.1	even	1	trivial
1890.2.j.h.631.2		4	9.5	odd	6
1890.2.j.h.1261.2		4	3.2	odd	2
5670.2.a.z.1.2		2	9.7	even	3
5670.2.a.be.1.1		2	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.866025 + 1.50000i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.866025 + 1.50000i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-1.50000 - 2.59808i) q^{9} -1.00000 q^{10} +(-1.86603 + 3.23205i) q^{11} +1.73205 q^{12} +(-2.36603 - 4.09808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +1.73205 q^{15} +(-0.500000 + 0.866025i) q^{16} +1.00000 q^{17} -3.00000 q^{18} -6.46410 q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.866025 + 1.50000i) q^{21} +(1.86603 + 3.23205i) q^{22} +(-0.633975 - 1.09808i) q^{23} +(0.866025 - 1.50000i) q^{24} +(-0.500000 + 0.866025i) q^{25} -4.73205 q^{26} +5.19615 q^{27} -1.00000 q^{28} +(4.09808 - 7.09808i) q^{29} +(0.866025 - 1.50000i) q^{30} +(-4.46410 - 7.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.23205 - 5.59808i) q^{33} +(0.500000 - 0.866025i) q^{34} -1.00000 q^{35} +(-1.50000 + 2.59808i) q^{36} -9.66025 q^{37} +(-3.23205 + 5.59808i) q^{38} +8.19615 q^{39} +(0.500000 + 0.866025i) q^{40} +(-2.86603 - 4.96410i) q^{41} +1.73205 q^{42} +(-5.69615 + 9.86603i) q^{43} +3.73205 q^{44} +(-1.50000 + 2.59808i) q^{45} -1.26795 q^{46} +(-2.00000 + 3.46410i) q^{47} +(-0.866025 - 1.50000i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.866025 + 1.50000i) q^{51} +(-2.36603 + 4.09808i) q^{52} +10.1962 q^{53} +(2.59808 - 4.50000i) q^{54} +3.73205 q^{55} +(-0.500000 + 0.866025i) q^{56} +(5.59808 - 9.69615i) q^{57} +(-4.09808 - 7.09808i) q^{58} +(-4.23205 - 7.33013i) q^{59} +(-0.866025 - 1.50000i) q^{60} +(0.366025 - 0.633975i) q^{61} -8.92820 q^{62} -3.00000 q^{63} +1.00000 q^{64} +(-2.36603 + 4.09808i) q^{65} -6.46410 q^{66} +(4.50000 + 7.79423i) q^{67} +(-0.500000 - 0.866025i) q^{68} +2.19615 q^{69} +(-0.500000 + 0.866025i) q^{70} +8.73205 q^{71} +(1.50000 + 2.59808i) q^{72} -1.92820 q^{73} +(-4.83013 + 8.36603i) q^{74} +(-0.866025 - 1.50000i) q^{75} +(3.23205 + 5.59808i) q^{76} +(1.86603 + 3.23205i) q^{77} +(4.09808 - 7.09808i) q^{78} +(7.00000 - 12.1244i) q^{79} +1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -5.73205 q^{82} +(-0.732051 + 1.26795i) q^{83} +(0.866025 - 1.50000i) q^{84} +(-0.500000 - 0.866025i) q^{85} +(5.69615 + 9.86603i) q^{86} +(7.09808 + 12.2942i) q^{87} +(1.86603 - 3.23205i) q^{88} -0.535898 q^{89} +(1.50000 + 2.59808i) q^{90} -4.73205 q^{91} +(-0.633975 + 1.09808i) q^{92} +15.4641 q^{93} +(2.00000 + 3.46410i) q^{94} +(3.23205 + 5.59808i) q^{95} -1.73205 q^{96} +(0.500000 - 0.866025i) q^{97} -1.00000 q^{98} +11.1962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} + 2 q^{7} - 4 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 + 2 * q^7 - 4 * q^8 - 6 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} + 2 q^{7} - 4 q^{8} - 6 q^{9} - 4 q^{10} - 4 q^{11} - 6 q^{13} - 2 q^{14} - 2 q^{16} + 4 q^{17} - 12 q^{18} - 12 q^{19} - 2 q^{20} + 4 q^{22} - 6 q^{23} - 2 q^{25} - 12 q^{26} - 4 q^{28} + 6 q^{29} - 4 q^{31} + 2 q^{32} - 6 q^{33} + 2 q^{34} - 4 q^{35} - 6 q^{36} - 4 q^{37} - 6 q^{38} + 12 q^{39} + 2 q^{40} - 8 q^{41} - 2 q^{43} + 8 q^{44} - 6 q^{45} - 12 q^{46} - 8 q^{47} - 2 q^{49} + 2 q^{50} - 6 q^{52} + 20 q^{53} + 8 q^{55} - 2 q^{56} + 12 q^{57} - 6 q^{58} - 10 q^{59} - 2 q^{61} - 8 q^{62} - 12 q^{63} + 4 q^{64} - 6 q^{65} - 12 q^{66} + 18 q^{67} - 2 q^{68} - 12 q^{69} - 2 q^{70} + 28 q^{71} + 6 q^{72} + 20 q^{73} - 2 q^{74} + 6 q^{76} + 4 q^{77} + 6 q^{78} + 28 q^{79} + 4 q^{80} - 18 q^{81} - 16 q^{82} + 4 q^{83} - 2 q^{85} + 2 q^{86} + 18 q^{87} + 4 q^{88} - 16 q^{89} + 6 q^{90} - 12 q^{91} - 6 q^{92} + 48 q^{93} + 8 q^{94} + 6 q^{95} + 2 q^{97} - 4 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 + 2 * q^7 - 4 * q^8 - 6 * q^9 - 4 * q^10 - 4 * q^11 - 6 * q^13 - 2 * q^14 - 2 * q^16 + 4 * q^17 - 12 * q^18 - 12 * q^19 - 2 * q^20 + 4 * q^22 - 6 * q^23 - 2 * q^25 - 12 * q^26 - 4 * q^28 + 6 * q^29 - 4 * q^31 + 2 * q^32 - 6 * q^33 + 2 * q^34 - 4 * q^35 - 6 * q^36 - 4 * q^37 - 6 * q^38 + 12 * q^39 + 2 * q^40 - 8 * q^41 - 2 * q^43 + 8 * q^44 - 6 * q^45 - 12 * q^46 - 8 * q^47 - 2 * q^49 + 2 * q^50 - 6 * q^52 + 20 * q^53 + 8 * q^55 - 2 * q^56 + 12 * q^57 - 6 * q^58 - 10 * q^59 - 2 * q^61 - 8 * q^62 - 12 * q^63 + 4 * q^64 - 6 * q^65 - 12 * q^66 + 18 * q^67 - 2 * q^68 - 12 * q^69 - 2 * q^70 + 28 * q^71 + 6 * q^72 + 20 * q^73 - 2 * q^74 + 6 * q^76 + 4 * q^77 + 6 * q^78 + 28 * q^79 + 4 * q^80 - 18 * q^81 - 16 * q^82 + 4 * q^83 - 2 * q^85 + 2 * q^86 + 18 * q^87 + 4 * q^88 - 16 * q^89 + 6 * q^90 - 12 * q^91 - 6 * q^92 + 48 * q^93 + 8 * q^94 + 6 * q^95 + 2 * q^97 - 4 * q^98 + 24 * q^99

Introduction

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