LMFDB - Embedded newform 630.2.i.h.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 0, 2]))

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

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

chi := DirichletCharacter("630.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} + 14 x^{10} - 28 x^{9} + 36 x^{8} - 24 x^{7} + 33 x^{6} + 42 x^{5} + 114 x^{4} + \cdots + 79 $ x^12 - 5x^11 + 14x^10 - 28x^9 + 36x^8 - 24x^7 + 33x^6 + 42x^5 + 114x^4 + 104x^3 + 197x^2 + 166*x + 79
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$-0.633121 + 0.576989i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.h.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.0335666 + 1.73173i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.0335666 + 1.73173i) q^{6} +(2.64400 - 0.0963576i) q^{7} +1.00000 q^{8} +(-2.99775 + 0.116256i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.0335666 + 1.73173i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.0335666 + 1.73173i) q^{6} +(2.64400 - 0.0963576i) q^{7} +1.00000 q^{8} +(-2.99775 + 0.116256i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.03999 + 3.53336i) q^{11} +(0.0335666 + 1.73173i) q^{12} +(1.66295 - 2.88032i) q^{13} +(2.64400 - 0.0963576i) q^{14} +(-1.48293 + 0.894932i) q^{15} +1.00000 q^{16} +(2.10964 + 3.65400i) q^{17} +(-2.99775 + 0.116256i) q^{18} +(1.15581 - 2.00193i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.255615 + 4.57544i) q^{21} +(-2.03999 + 3.53336i) q^{22} +(-0.365460 - 0.632996i) q^{23} +(0.0335666 + 1.73173i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.66295 - 2.88032i) q^{26} +(-0.301948 - 5.18737i) q^{27} +(2.64400 - 0.0963576i) q^{28} +(0.513393 + 0.889223i) q^{29} +(-1.48293 + 0.894932i) q^{30} -10.5185 q^{31} +1.00000 q^{32} +(-6.18728 - 3.41409i) q^{33} +(2.10964 + 3.65400i) q^{34} +(1.40545 + 2.24159i) q^{35} +(-2.99775 + 0.116256i) q^{36} +(0.647932 - 1.12225i) q^{37} +(1.15581 - 2.00193i) q^{38} +(5.04374 + 2.78310i) q^{39} +(0.500000 + 0.866025i) q^{40} +(3.29918 - 5.71435i) q^{41} +(0.255615 + 4.57544i) q^{42} +(1.24480 + 2.15606i) q^{43} +(-2.03999 + 3.53336i) q^{44} +(-1.59955 - 2.53800i) q^{45} +(-0.365460 - 0.632996i) q^{46} -5.50389 q^{47} +(0.0335666 + 1.73173i) q^{48} +(6.98143 - 0.509538i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-6.25691 + 3.77596i) q^{51} +(1.66295 - 2.88032i) q^{52} +(2.65456 + 4.59783i) q^{53} +(-0.301948 - 5.18737i) q^{54} -4.07997 q^{55} +(2.64400 - 0.0963576i) q^{56} +(3.50558 + 1.93435i) q^{57} +(0.513393 + 0.889223i) q^{58} +5.96758 q^{59} +(-1.48293 + 0.894932i) q^{60} +0.903244 q^{61} -10.5185 q^{62} +(-7.91483 + 0.596237i) q^{63} +1.00000 q^{64} +3.32591 q^{65} +(-6.18728 - 3.41409i) q^{66} +1.10788 q^{67} +(2.10964 + 3.65400i) q^{68} +(1.08391 - 0.654125i) q^{69} +(1.40545 + 2.24159i) q^{70} +2.91752 q^{71} +(-2.99775 + 0.116256i) q^{72} +(-5.73968 - 9.94141i) q^{73} +(0.647932 - 1.12225i) q^{74} +(-1.51650 - 0.836793i) q^{75} +(1.15581 - 2.00193i) q^{76} +(-5.05325 + 9.53876i) q^{77} +(5.04374 + 2.78310i) q^{78} +12.8375 q^{79} +(0.500000 + 0.866025i) q^{80} +(8.97297 - 0.697014i) q^{81} +(3.29918 - 5.71435i) q^{82} +(-6.86528 - 11.8910i) q^{83} +(0.255615 + 4.57544i) q^{84} +(-2.10964 + 3.65400i) q^{85} +(1.24480 + 2.15606i) q^{86} +(-1.52266 + 0.918904i) q^{87} +(-2.03999 + 3.53336i) q^{88} +(7.27583 - 12.6021i) q^{89} +(-1.59955 - 2.53800i) q^{90} +(4.11930 - 7.77579i) q^{91} +(-0.365460 - 0.632996i) q^{92} +(-0.353071 - 18.2152i) q^{93} -5.50389 q^{94} +2.31162 q^{95} +(0.0335666 + 1.73173i) q^{96} +(-7.36150 - 12.7505i) q^{97} +(6.98143 - 0.509538i) q^{98} +(5.70458 - 10.8293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} + 2 q^{13} + 8 q^{14} + 7 q^{15} + 12 q^{16} + 7 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} + 17 q^{21} - 7 q^{22} - 9 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 8 q^{28} - 9 q^{29} + 7 q^{30} - 18 q^{31} + 12 q^{32} + 3 q^{33} + 7 q^{34} + 4 q^{35} - 4 q^{36} - 12 q^{37} + 14 q^{38} - 14 q^{39} + 6 q^{40} + q^{41} + 17 q^{42} + 7 q^{43} - 7 q^{44} - 5 q^{45} - 9 q^{46} - 14 q^{47} + 2 q^{48} - 24 q^{49} - 6 q^{50} - 3 q^{51} + 2 q^{52} + 2 q^{53} + 11 q^{54} - 14 q^{55} + 8 q^{56} - 14 q^{57} - 9 q^{58} - 58 q^{59} + 7 q^{60} + 22 q^{61} - 18 q^{62} - 13 q^{63} + 12 q^{64} + 4 q^{65} + 3 q^{66} + 44 q^{67} + 7 q^{68} - 18 q^{69} + 4 q^{70} + 10 q^{71} - 4 q^{72} + 6 q^{73} - 12 q^{74} + 5 q^{75} + 14 q^{76} - 23 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} - 4 q^{81} + q^{82} - 26 q^{83} + 17 q^{84} - 7 q^{85} + 7 q^{86} - 12 q^{87} - 7 q^{88} + 2 q^{89} - 5 q^{90} - 4 q^{91} - 9 q^{92} - 26 q^{93} - 14 q^{94} + 28 q^{95} + 2 q^{96} + 6 q^{97} - 24 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 + 2 * q^13 + 8 * q^14 + 7 * q^15 + 12 * q^16 + 7 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 + 17 * q^21 - 7 * q^22 - 9 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 8 * q^28 - 9 * q^29 + 7 * q^30 - 18 * q^31 + 12 * q^32 + 3 * q^33 + 7 * q^34 + 4 * q^35 - 4 * q^36 - 12 * q^37 + 14 * q^38 - 14 * q^39 + 6 * q^40 + q^41 + 17 * q^42 + 7 * q^43 - 7 * q^44 - 5 * q^45 - 9 * q^46 - 14 * q^47 + 2 * q^48 - 24 * q^49 - 6 * q^50 - 3 * q^51 + 2 * q^52 + 2 * q^53 + 11 * q^54 - 14 * q^55 + 8 * q^56 - 14 * q^57 - 9 * q^58 - 58 * q^59 + 7 * q^60 + 22 * q^61 - 18 * q^62 - 13 * q^63 + 12 * q^64 + 4 * q^65 + 3 * q^66 + 44 * q^67 + 7 * q^68 - 18 * q^69 + 4 * q^70 + 10 * q^71 - 4 * q^72 + 6 * q^73 - 12 * q^74 + 5 * q^75 + 14 * q^76 - 23 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 - 4 * q^81 + q^82 - 26 * q^83 + 17 * q^84 - 7 * q^85 + 7 * q^86 - 12 * q^87 - 7 * q^88 + 2 * q^89 - 5 * q^90 - 4 * q^91 - 9 * q^92 - 26 * q^93 - 14 * q^94 + 28 * q^95 + 2 * q^96 + 6 * q^97 - 24 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.0335666	+	1.73173i	0.0193797	+	0.999812i
$3$	0.0335666	+	1.73173i	0.0193797	+	0.999812i
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.0335666	+	1.73173i	0.0137035	+	0.706974i
$7$	2.64400	−	0.0963576i	0.999337	−	0.0364197i
$7$	2.64400	−	0.0963576i	0.999337	−	0.0364197i
$8$	1.00000			0.353553
$9$	−2.99775	+	0.116256i	−0.999249	+	0.0387521i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−2.03999	+	3.53336i	−0.615079	+	1.06535i	0.375292	+	0.926907i	$0.377543\pi$
$11$	−2.03999	+	3.53336i	−0.615079	+	1.06535i	−0.990371	+	0.138441i	$0.955791\pi$
$12$	0.0335666	+	1.73173i	0.00968985	+	0.499906i
$13$	1.66295	−	2.88032i	0.461220	−	0.798857i	−0.537802	−	0.843071i	$-0.680745\pi$
$13$	1.66295	−	2.88032i	0.461220	−	0.798857i	0.999022	+	0.0442145i	$0.0140785\pi$
$14$	2.64400	−	0.0963576i	0.706638	−	0.0257526i
$15$	−1.48293	+	0.894932i	−0.382892	+	0.231071i
$16$	1.00000			0.250000
$17$	2.10964	+	3.65400i	0.511662	+	0.886225i	0.999909	+	0.0135190i	$0.00430335\pi$
$17$	2.10964	+	3.65400i	0.511662	+	0.886225i	−0.488247	+	0.872706i	$0.662363\pi$
$18$	−2.99775	+	0.116256i	−0.706576	+	0.0274019i
$19$	1.15581	−	2.00193i	0.265162	−	0.459273i	−0.702444	−	0.711739i	$-0.747908\pi$
$19$	1.15581	−	2.00193i	0.265162	−	0.459273i	0.967606	+	0.252465i	$0.0812414\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	0.255615	+	4.57544i	0.0557798	+	0.998443i
$22$	−2.03999	+	3.53336i	−0.434926	+	0.753315i
$23$	−0.365460	−	0.632996i	−0.0762038	−	0.131989i	0.825405	−	0.564541i	$-0.190947\pi$
$23$	−0.365460	−	0.632996i	−0.0762038	−	0.131989i	−0.901609	+	0.432552i	$0.857613\pi$
$24$	0.0335666	+	1.73173i	0.00685176	+	0.353487i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.66295	−	2.88032i	0.326132	−	0.564877i
$27$	−0.301948	−	5.18737i	−0.0581100	−	0.998310i
$28$	2.64400	−	0.0963576i	0.499668	−	0.0182099i
$29$	0.513393	+	0.889223i	0.0953347	+	0.165124i	0.909748	−	0.415160i	$-0.136275\pi$
$29$	0.513393	+	0.889223i	0.0953347	+	0.165124i	−0.814414	+	0.580285i	$0.802941\pi$
$30$	−1.48293	+	0.894932i	−0.270746	+	0.163392i
$31$	−10.5185			−1.88918			−0.944591	−	0.328250i	$-0.893541\pi$
$31$	−10.5185			−1.88918			−0.944591	+	0.328250i	$0.893541\pi$
$32$	1.00000			0.176777
$33$	−6.18728	−	3.41409i	−1.07707	−	0.594317i
$34$	2.10964	+	3.65400i	0.361800	+	0.626655i
$35$	1.40545	+	2.24159i	0.237564	+	0.378898i
$36$	−2.99775	+	0.116256i	−0.499624	+	0.0193761i
$37$	0.647932	−	1.12225i	0.106519	−	0.184497i	−0.807839	−	0.589404i	$-0.799363\pi$
$37$	0.647932	−	1.12225i	0.106519	−	0.184497i	0.914358	+	0.404907i	$0.132696\pi$
$38$	1.15581	−	2.00193i	0.187498	−	0.324755i
$39$	5.04374	+	2.78310i	0.807645	+	0.445652i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	3.29918	−	5.71435i	0.515246	−	0.892432i	−0.484598	−	0.874737i	$-0.661034\pi$
$41$	3.29918	−	5.71435i	0.515246	−	0.892432i	0.999843	−	0.0176946i	$-0.00563267\pi$
$42$	0.255615	+	4.57544i	0.0394422	+	0.706006i
$43$	1.24480	+	2.15606i	0.189831	+	0.328796i	0.945194	−	0.326510i	$-0.105873\pi$
$43$	1.24480	+	2.15606i	0.189831	+	0.328796i	−0.755363	+	0.655307i	$0.772539\pi$
$44$	−2.03999	+	3.53336i	−0.307539	+	0.532674i
$45$	−1.59955	−	2.53800i	−0.238447	−	0.378342i
$46$	−0.365460	−	0.632996i	−0.0538842	−	0.0933302i
$47$	−5.50389			−0.802824			−0.401412	−	0.915898i	$-0.631480\pi$
$47$	−5.50389			−0.802824			−0.401412	+	0.915898i	$0.631480\pi$
$48$	0.0335666	+	1.73173i	0.00484493	+	0.249953i
$49$	6.98143	−	0.509538i	0.997347	−	0.0727912i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−6.25691	+	3.77596i	−0.876142	+	0.528741i
$52$	1.66295	−	2.88032i	0.230610	−	0.399428i
$53$	2.65456	+	4.59783i	0.364632	+	0.631561i	0.988717	−	0.149795i	$-0.0478615\pi$
$53$	2.65456	+	4.59783i	0.364632	+	0.631561i	−0.624085	+	0.781356i	$0.714528\pi$
$54$	−0.301948	−	5.18737i	−0.0410900	−	0.705912i
$55$	−4.07997			−0.550143
$56$	2.64400	−	0.0963576i	0.353319	−	0.0128763i
$57$	3.50558	+	1.93435i	0.464326	+	0.256211i
$58$	0.513393	+	0.889223i	0.0674118	+	0.116761i
$59$	5.96758			0.776913			0.388456	−	0.921467i	$-0.373008\pi$
$59$	5.96758			0.776913			0.388456	+	0.921467i	$0.373008\pi$
$60$	−1.48293	+	0.894932i	−0.191446	+	0.115535i
$61$	0.903244			0.115648			0.0578242	−	0.998327i	$-0.481584\pi$
$61$	0.903244			0.115648			0.0578242	+	0.998327i	$0.481584\pi$
$62$	−10.5185			−1.33585
$63$	−7.91483	+	0.596237i	−0.997175	+	0.0751188i
$64$	1.00000			0.125000
$65$	3.32591			0.412528
$66$	−6.18728	−	3.41409i	−0.761602	−	0.420246i
$67$	1.10788			0.135350			0.0676748	−	0.997707i	$-0.478442\pi$
$67$	1.10788			0.135350			0.0676748	+	0.997707i	$0.478442\pi$
$68$	2.10964	+	3.65400i	0.255831	+	0.443112i
$69$	1.08391	−	0.654125i	0.130487	−	0.0787473i
$70$	1.40545	+	2.24159i	0.167983	+	0.267921i
$71$	2.91752			0.346246			0.173123	−	0.984900i	$-0.444614\pi$
$71$	2.91752			0.346246			0.173123	+	0.984900i	$0.444614\pi$
$72$	−2.99775	+	0.116256i	−0.353288	+	0.0137009i
$73$	−5.73968	−	9.94141i	−0.671778	−	1.16355i	−0.977399	−	0.211401i	$-0.932197\pi$
$73$	−5.73968	−	9.94141i	−0.671778	−	1.16355i	0.305621	−	0.952153i	$-0.401136\pi$
$74$	0.647932	−	1.12225i	0.0753206	−	0.130459i
$75$	−1.51650	−	0.836793i	−0.175111	−	0.0966246i
$76$	1.15581	−	2.00193i	0.132581	−	0.229637i
$77$	−5.05325	+	9.53876i	−0.575871	+	1.08704i
$78$	5.04374	+	2.78310i	0.571091	+	0.315123i
$79$	12.8375			1.44433			0.722167	−	0.691718i	$-0.243146\pi$
$79$	12.8375			1.44433			0.722167	+	0.691718i	$0.243146\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	8.97297	−	0.697014i	0.996997	−	0.0774460i
$82$	3.29918	−	5.71435i	0.364334	−	0.631045i
$83$	−6.86528	−	11.8910i	−0.753562	−	1.30521i	−0.946086	−	0.323916i	$-0.895001\pi$
$83$	−6.86528	−	11.8910i	−0.753562	−	1.30521i	0.192524	−	0.981292i	$-0.438333\pi$
$84$	0.255615	+	4.57544i	0.0278899	+	0.499222i
$85$	−2.10964	+	3.65400i	−0.228822	+	0.396332i
$86$	1.24480	+	2.15606i	0.134230	+	0.232494i
$87$	−1.52266	+	0.918904i	−0.163246	+	0.0985168i
$88$	−2.03999	+	3.53336i	−0.217463	+	0.376657i
$89$	7.27583	−	12.6021i	0.771237	−	1.33582i	−0.165649	−	0.986185i	$-0.552972\pi$
$89$	7.27583	−	12.6021i	0.771237	−	1.33582i	0.936886	−	0.349636i	$-0.113695\pi$
$90$	−1.59955	−	2.53800i	−0.168608	−	0.267528i
$91$	4.11930	−	7.77579i	0.431820	−	0.815124i
$92$	−0.365460	−	0.632996i	−0.0381019	−	0.0659944i
$93$	−0.353071	−	18.2152i	−0.0366118	−	1.88883i
$94$	−5.50389			−0.567682
$95$	2.31162			0.237168
$96$	0.0335666	+	1.73173i	0.00342588	+	0.176743i
$97$	−7.36150	−	12.7505i	−0.747447	−	1.29462i	−0.949043	−	0.315147i	$-0.897946\pi$
$97$	−7.36150	−	12.7505i	−0.747447	−	1.29462i	0.201596	−	0.979469i	$-0.435387\pi$
$98$	6.98143	−	0.509538i	0.705231	−	0.0514711i
$99$	5.70458	−	10.8293i	0.573332	−	1.08838i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	2.25643	−	3.90825i	0.224523	−	0.388886i	−0.731653	−	0.681677i	$-0.761251\pi$
$101$	2.25643	−	3.90825i	0.224523	−	0.388886i	0.956176	+	0.292792i	$0.0945842\pi$
$102$	−6.25691	+	3.77596i	−0.619526	+	0.373876i
$103$	2.18230	+	3.77985i	0.215028	+	0.372440i	0.953281	−	0.302084i	$-0.0976823\pi$
$103$	2.18230	+	3.77985i	0.215028	+	0.372440i	−0.738253	+	0.674524i	$0.764349\pi$
$104$	1.66295	−	2.88032i	0.163066	−	0.282438i
$105$	−3.83464	+	2.50909i	−0.374223	+	0.244862i
$106$	2.65456	+	4.59783i	0.257834	+	0.446581i
$107$	0.637368	−	1.10395i	0.0616167	−	0.106723i	−0.833571	−	0.552412i	$-0.813708\pi$
$107$	0.637368	−	1.10395i	0.0616167	−	0.106723i	0.895188	+	0.445688i	$0.147041\pi$
$108$	−0.301948	−	5.18737i	−0.0290550	−	0.499155i
$109$	−8.63456	−	14.9555i	−0.827041	−	1.43248i	−0.900350	−	0.435167i	$-0.856689\pi$
$109$	−8.63456	−	14.9555i	−0.827041	−	1.43248i	0.0733089	−	0.997309i	$-0.476644\pi$
$110$	−4.07997			−0.389010
$111$	1.96518	+	1.08437i	0.186527	+	0.102924i
$112$	2.64400	−	0.0963576i	0.249834	−	0.00910494i
$113$	−9.68504	+	16.7750i	−0.911092	+	1.57806i	−0.0985672	+	0.995130i	$0.531426\pi$
$113$	−9.68504	+	16.7750i	−0.911092	+	1.57806i	−0.812525	+	0.582927i	$0.801907\pi$
$114$	3.50558	+	1.93435i	0.328328	+	0.181169i
$115$	0.365460	−	0.632996i	0.0340794	−	0.0590272i
$116$	0.513393	+	0.889223i	0.0476673	+	0.0825622i
$117$	−4.65026	+	8.82779i	−0.429916	+	0.816130i
$118$	5.96758			0.549360
$119$	5.92996	+	9.45788i	0.543599	+	0.867002i
$120$	−1.48293	+	0.894932i	−0.135373	+	0.0816958i
$121$	−2.82308	−	4.88972i	−0.256644	−	0.444520i
$122$	0.903244			0.0817758
$123$	10.0064	+	5.52147i	0.902249	+	0.497854i
$124$	−10.5185			−0.944591
$125$	−1.00000			−0.0894427
$126$	−7.91483	+	0.596237i	−0.705109	+	0.0531170i
$127$	−13.8367			−1.22781			−0.613903	−	0.789381i	$-0.710402\pi$
$127$	−13.8367			−1.22781			−0.613903	+	0.789381i	$0.710402\pi$
$128$	1.00000			0.0883883
$129$	−3.69192	+	2.22803i	−0.325056	+	0.196167i
$130$	3.32591			0.291701
$131$	6.74013	+	11.6742i	0.588888	+	1.01998i	0.994378	+	0.105884i	$0.0337673\pi$
$131$	6.74013	+	11.6742i	0.588888	+	1.01998i	−0.405491	+	0.914099i	$0.632899\pi$
$132$	−6.18728	−	3.41409i	−0.538534	−	0.297159i
$133$	2.86306	−	5.40446i	0.248259	−	0.468626i
$134$	1.10788			0.0957066
$135$	4.34142	−	2.85518i	0.373650	−	0.245735i
$136$	2.10964	+	3.65400i	0.180900	+	0.313328i
$137$	8.11165	−	14.0498i	0.693025	−	1.20035i	−0.277817	−	0.960634i	$-0.589611\pi$
$137$	8.11165	−	14.0498i	0.693025	−	1.20035i	0.970842	−	0.239721i	$-0.0770559\pi$
$138$	1.08391	−	0.654125i	0.0922684	−	0.0556828i
$139$	8.37410	−	14.5044i	0.710282	−	1.23024i	−0.254469	−	0.967081i	$-0.581901\pi$
$139$	8.37410	−	14.5044i	0.710282	−	1.23024i	0.964751	−	0.263164i	$-0.0847660\pi$
$140$	1.40545	+	2.24159i	0.118782	+	0.189449i
$141$	−0.184747	−	9.53122i	−0.0155585	−	0.802673i
$142$	2.91752			0.244833
$143$	6.78480	+	11.7516i	0.567373	+	0.982720i
$144$	−2.99775	+	0.116256i	−0.249812	+	0.00968803i
$145$	−0.513393	+	0.889223i	−0.0426350	+	0.0738459i
$146$	−5.73968	−	9.94141i	−0.475019	−	0.822757i
$147$	1.11672	+	12.0728i	0.0921058	+	0.995749i
$148$	0.647932	−	1.12225i	0.0532597	−	0.0922485i
$149$	−3.17404	−	5.49760i	−0.260028	−	0.450381i	0.706221	−	0.707991i	$-0.250398\pi$
$149$	−3.17404	−	5.49760i	−0.260028	−	0.450381i	−0.966249	+	0.257610i	$0.917065\pi$
$150$	−1.51650	−	0.836793i	−0.123822	−	0.0683239i
$151$	−8.74873	+	15.1532i	−0.711961	+	1.23315i	0.252159	+	0.967686i	$0.418860\pi$
$151$	−8.74873	+	15.1532i	−0.711961	+	1.23315i	−0.964120	+	0.265467i	$0.914474\pi$
$152$	1.15581	−	2.00193i	0.0937488	−	0.162378i
$153$	−6.74896	−	10.7085i	−0.545621	−	0.865731i
$154$	−5.05325	+	9.53876i	−0.407202	+	0.768655i
$155$	−5.25926	−	9.10930i	−0.422434	−	0.731677i
$156$	5.04374	+	2.78310i	0.403822	+	0.222826i
$157$	13.9358			1.11220			0.556099	−	0.831116i	$-0.312297\pi$
$157$	13.9358			1.11220			0.556099	+	0.831116i	$0.312297\pi$
$158$	12.8375			1.02130
$159$	−7.87308	+	4.75130i	−0.624376	+	0.376803i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−1.02727	−	1.63842i	−0.0809602	−	0.129126i
$162$	8.97297	−	0.697014i	0.704983	−	0.0547626i
$163$	7.83322	−	13.5675i	0.613545	−	1.06269i	−0.377093	−	0.926176i	$-0.623076\pi$
$163$	7.83322	−	13.5675i	0.613545	−	1.06269i	0.990638	−	0.136516i	$-0.0435905\pi$
$164$	3.29918	−	5.71435i	0.257623	−	0.446216i
$165$	−0.136951	−	7.06539i	−0.0106616	−	0.550040i
$166$	−6.86528	−	11.8910i	−0.532849	−	0.922922i
$167$	−11.6266	+	20.1379i	−0.899693	+	1.55831i	−0.0718065	+	0.997419i	$0.522876\pi$
$167$	−11.6266	+	20.1379i	−0.899693	+	1.55831i	−0.827887	+	0.560896i	$0.810457\pi$
$168$	0.255615	+	4.57544i	0.0197211	+	0.353003i
$169$	0.969176	+	1.67866i	0.0745520	+	0.129128i
$170$	−2.10964	+	3.65400i	−0.161802	+	0.280249i
$171$	−3.23210	+	6.13564i	−0.247165	+	0.469204i
$172$	1.24480	+	2.15606i	0.0949153	+	0.164398i
$173$	−1.66145			−0.126318			−0.0631589	−	0.998003i	$-0.520117\pi$
$173$	−1.66145			−0.126318			−0.0631589	+	0.998003i	$0.520117\pi$
$174$	−1.52266	+	0.918904i	−0.115432	+	0.0696619i
$175$	−1.23855	+	2.33795i	−0.0936256	+	0.176732i
$176$	−2.03999	+	3.53336i	−0.153770	+	0.266337i
$177$	0.200312	+	10.3342i	0.0150563	+	0.776767i
$178$	7.27583	−	12.6021i	0.545347	−	0.944568i
$179$	3.21357	+	5.56606i	0.240193	+	0.416027i	0.960769	−	0.277349i	$-0.0894559\pi$
$179$	3.21357	+	5.56606i	0.240193	+	0.416027i	−0.720576	+	0.693376i	$0.756123\pi$
$180$	−1.59955	−	2.53800i	−0.119224	−	0.189171i
$181$	3.64852			0.271193			0.135596	−	0.990764i	$-0.456705\pi$
$181$	3.64852			0.271193			0.135596	+	0.990764i	$0.456705\pi$
$182$	4.11930	−	7.77579i	0.305343	−	0.576380i
$183$	0.0303188	+	1.56417i	0.00224123	+	0.115627i
$184$	−0.365460	−	0.632996i	−0.0269421	−	0.0466651i
$185$	1.29586			0.0952739
$186$	−0.353071	−	18.2152i	−0.0258884	−	1.33560i
$187$	−17.2145			−1.25885
$188$	−5.50389			−0.401412
$189$	−1.29819	−	13.6863i	−0.0944297	−	0.995532i
$190$	2.31162			0.167703
$191$	−10.4457			−0.755826			−0.377913	−	0.925841i	$-0.623358\pi$
$191$	−10.4457			−0.755826			−0.377913	+	0.925841i	$0.623358\pi$
$192$	0.0335666	+	1.73173i	0.00242246	+	0.124977i
$193$	18.1442			1.30605			0.653023	−	0.757338i	$-0.273500\pi$
$193$	18.1442			1.30605			0.653023	+	0.757338i	$0.273500\pi$
$194$	−7.36150	−	12.7505i	−0.528525	−	0.915432i
$195$	0.111639	+	5.75956i	0.00799467	+	0.412450i
$196$	6.98143	−	0.509538i	0.498674	−	0.0363956i
$197$	−8.53501			−0.608095			−0.304047	−	0.952657i	$-0.598338\pi$
$197$	−8.53501			−0.608095			−0.304047	+	0.952657i	$0.598338\pi$
$198$	5.70458	−	10.8293i	0.405407	−	0.769603i
$199$	−3.48948	−	6.04396i	−0.247363	−	0.428445i	0.715430	−	0.698684i	$-0.246231\pi$
$199$	−3.48948	−	6.04396i	−0.247363	−	0.428445i	−0.962793	+	0.270239i	$0.912897\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	0.0371879	+	1.91855i	0.00262304	+	0.135324i
$202$	2.25643	−	3.90825i	0.158762	−	0.274984i
$203$	1.44309	+	2.30163i	0.101285	+	0.161543i
$204$	−6.25691	+	3.77596i	−0.438071	+	0.264370i
$205$	6.59836			0.460850
$206$	2.18230	+	3.77985i	0.152048	+	0.263355i
$207$	1.16915	+	1.85507i	0.0812614	+	0.128937i
$208$	1.66295	−	2.88032i	0.115305	−	0.199714i
$209$	4.71568	+	8.16780i	0.326191	+	0.564979i
$210$	−3.83464	+	2.50909i	−0.264615	+	0.173144i
$211$	−10.4514	+	18.1024i	−0.719507	+	1.24622i	0.241688	+	0.970354i	$0.422299\pi$
$211$	−10.4514	+	18.1024i	−0.719507	+	1.24622i	−0.961195	+	0.275869i	$0.911034\pi$
$212$	2.65456	+	4.59783i	0.182316	+	0.315780i
$213$	0.0979315	+	5.05235i	0.00671015	+	0.346181i
$214$	0.637368	−	1.10395i	0.0435696	−	0.0754648i
$215$	−1.24480	+	2.15606i	−0.0848948	+	0.147042i
$216$	−0.301948	−	5.18737i	−0.0205450	−	0.352956i
$217$	−27.8109	+	1.01354i	−1.88793	+	0.0688035i
$218$	−8.63456	−	14.9555i	−0.584806	−	1.01291i
$219$	17.0231	−	10.2732i	1.15032	−	0.694201i
$220$	−4.07997			−0.275072
$221$	14.0329			0.943955
$222$	1.96518	+	1.08437i	0.131894	+	0.0727782i
$223$	−3.45757	−	5.98869i	−0.231536	−	0.401032i	0.726724	−	0.686929i	$-0.241042\pi$
$223$	−3.45757	−	5.98869i	−0.231536	−	0.401032i	−0.958260	+	0.285897i	$0.907709\pi$
$224$	2.64400	−	0.0963576i	0.176659	−	0.00643816i
$225$	1.39819	−	2.65425i	0.0932128	−	0.176950i
$226$	−9.68504	+	16.7750i	−0.644239	+	1.11586i
$227$	−11.9738	+	20.7393i	−0.794731	+	1.37651i	0.128279	+	0.991738i	$0.459055\pi$
$227$	−11.9738	+	20.7393i	−0.794731	+	1.37651i	−0.923010	+	0.384777i	$0.874278\pi$
$228$	3.50558	+	1.93435i	0.232163	+	0.128106i
$229$	−6.70677	−	11.6165i	−0.443196	−	0.767638i	0.554729	−	0.832031i	$-0.312822\pi$
$229$	−6.70677	−	11.6165i	−0.443196	−	0.767638i	−0.997925	+	0.0643937i	$0.979489\pi$
$230$	0.365460	−	0.632996i	0.0240977	−	0.0417385i
$231$	−16.6881	−	8.43066i	−1.09800	−	0.554696i
$232$	0.513393	+	0.889223i	0.0337059	+	0.0583803i
$233$	−4.48461	+	7.76757i	−0.293797	+	0.508870i	−0.974704	−	0.223499i	$-0.928252\pi$
$233$	−4.48461	+	7.76757i	−0.293797	+	0.508870i	0.680908	+	0.732369i	$0.261585\pi$
$234$	−4.65026	+	8.82779i	−0.303997	+	0.577091i
$235$	−2.75194	−	4.76650i	−0.179517	−	0.310932i
$236$	5.96758			0.388456
$237$	0.430913	+	22.2311i	0.0279908	+	1.44406i
$238$	5.92996	+	9.45788i	0.384382	+	0.613063i
$239$	−10.2832	+	17.8110i	−0.665163	+	1.15210i	0.314079	+	0.949397i	$0.398304\pi$
$239$	−10.2832	+	17.8110i	−0.665163	+	1.15210i	−0.979241	+	0.202699i	$0.935029\pi$
$240$	−1.48293	+	0.894932i	−0.0957230	+	0.0577676i
$241$	−8.06952	+	13.9768i	−0.519803	+	0.900326i	0.479932	+	0.877306i	$0.340661\pi$
$241$	−8.06952	+	13.9768i	−0.519803	+	0.900326i	−0.999735	+	0.0230200i	$0.992672\pi$
$242$	−2.82308	−	4.88972i	−0.181475	−	0.314323i
$243$	1.50823	+	15.5153i	0.0967530	+	0.995308i
$244$	0.903244			0.0578242
$245$	3.93199	+	5.79133i	0.251206	+	0.369994i
$246$	10.0064	+	5.52147i	0.637987	+	0.352036i
$247$	−3.84412	−	6.65822i	−0.244596	−	0.423652i
$248$	−10.5185			−0.667927
$249$	20.3615	−	12.2879i	1.29036	−	0.778715i
$250$	−1.00000			−0.0632456
$251$	16.8254			1.06201			0.531005	−	0.847369i	$-0.321815\pi$
$251$	16.8254			1.06201			0.531005	+	0.847369i	$0.321815\pi$
$252$	−7.91483	+	0.596237i	−0.498587	+	0.0375594i
$253$	2.98214			0.187485
$254$	−13.8367			−0.868190
$255$	−6.39854	−	3.53066i	−0.400692	−	0.221098i
$256$	1.00000			0.0625000
$257$	−5.79416	−	10.0358i	−0.361430	−	0.626014i	0.626767	−	0.779207i	$-0.284378\pi$
$257$	−5.79416	−	10.0358i	−0.361430	−	0.626014i	−0.988196	+	0.153193i	$0.951045\pi$
$258$	−3.69192	+	2.22803i	−0.229849	+	0.138711i
$259$	1.60499	−	3.02966i	0.0997294	−	0.188254i
$260$	3.32591			0.206264
$261$	−1.64240	−	2.60598i	−0.101662	−	0.161306i
$262$	6.74013	+	11.6742i	0.416406	+	0.721237i
$263$	−11.9076	+	20.6246i	−0.734255	+	1.27177i	0.220794	+	0.975321i	$0.429135\pi$
$263$	−11.9076	+	20.6246i	−0.734255	+	1.27177i	−0.955049	+	0.296447i	$0.904198\pi$
$264$	−6.18728	−	3.41409i	−0.380801	−	0.210123i
$265$	−2.65456	+	4.59783i	−0.163068	+	0.282443i
$266$	2.86306	−	5.40446i	0.175546	−	0.331368i
$267$	22.0676	+	12.1767i	1.35052	+	0.745204i
$268$	1.10788			0.0676748
$269$	−9.01902	−	15.6214i	−0.549899	−	0.952454i	−0.998281	−	0.0586113i	$-0.981333\pi$
$269$	−9.01902	−	15.6214i	−0.549899	−	0.952454i	0.448382	−	0.893842i	$-0.352001\pi$
$270$	4.34142	−	2.85518i	0.264211	−	0.173761i
$271$	−9.61907	+	16.6607i	−0.584317	+	1.01207i	0.410644	+	0.911796i	$0.365304\pi$
$271$	−9.61907	+	16.6607i	−0.584317	+	1.01207i	−0.994960	+	0.100270i	$0.968029\pi$
$272$	2.10964	+	3.65400i	0.127916	+	0.221556i
$273$	13.6038	+	6.87249i	0.823340	+	0.415942i
$274$	8.11165	−	14.0498i	0.490043	−	0.848779i
$275$	−2.03999	−	3.53336i	−0.123016	−	0.213070i
$276$	1.08391	−	0.654125i	0.0652436	−	0.0393737i
$277$	8.98842	−	15.5684i	0.540062	−	0.935414i	−0.458838	−	0.888520i	$-0.651734\pi$
$277$	8.98842	−	15.5684i	0.540062	−	0.935414i	0.998900	−	0.0468942i	$-0.0149324\pi$
$278$	8.37410	−	14.5044i	0.502245	−	0.869914i
$279$	31.5319	−	1.22285i	1.88776	−	0.0732098i
$280$	1.40545	+	2.24159i	0.0839915	+	0.133961i
$281$	−6.06170	−	10.4992i	−0.361610	−	0.626328i	0.626616	−	0.779329i	$-0.284440\pi$
$281$	−6.06170	−	10.4992i	−0.361610	−	0.626328i	−0.988226	+	0.153001i	$0.951106\pi$
$282$	−0.184747	−	9.53122i	−0.0110015	−	0.567576i
$283$	−1.24188			−0.0738222			−0.0369111	−	0.999319i	$-0.511752\pi$
$283$	−1.24188			−0.0738222			−0.0369111	+	0.999319i	$0.511752\pi$
$284$	2.91752			0.173123
$285$	0.0775935	+	4.00310i	0.00459624	+	0.237123i
$286$	6.78480	+	11.7516i	0.401194	+	0.694888i
$287$	8.17240	−	15.4266i	0.482402	−	0.910605i
$288$	−2.99775	+	0.116256i	−0.176644	+	0.00685047i
$289$	−0.401134	+	0.694785i	−0.0235961	+	0.0408697i
$290$	−0.513393	+	0.889223i	−0.0301475	+	0.0522169i
$291$	21.8332	−	13.1761i	1.27989	−	0.772396i
$292$	−5.73968	−	9.94141i	−0.335889	−	0.581777i
$293$	−3.66402	+	6.34628i	−0.214055	+	0.370753i	−0.952980	−	0.303034i	$-0.902000\pi$
$293$	−3.66402	+	6.34628i	−0.214055	+	0.370753i	0.738925	+	0.673788i	$0.235334\pi$
$294$	1.11672	+	12.0728i	0.0651286	+	0.704101i
$295$	2.98379	+	5.16808i	0.173723	+	0.300897i
$296$	0.647932	−	1.12225i	0.0376603	−	0.0652296i
$297$	18.9448	+	9.51527i	1.09929	+	0.552132i
$298$	−3.17404	−	5.49760i	−0.183867	−	0.318468i
$299$	−2.43097			−0.140587
$300$	−1.51650	−	0.836793i	−0.0875553	−	0.0483123i
$301$	3.49901	+	5.58067i	0.201679	+	0.321665i
$302$	−8.74873	+	15.1532i	−0.503433	+	0.871971i
$303$	6.84376	+	3.77633i	0.393164	+	0.216945i
$304$	1.15581	−	2.00193i	0.0662904	−	0.114818i
$305$	0.451622	+	0.782232i	0.0258598	+	0.0447905i
$306$	−6.74896	−	10.7085i	−0.385812	−	0.612164i
$307$	22.6002			1.28986			0.644930	−	0.764242i	$-0.276886\pi$
$307$	22.6002			1.28986			0.644930	+	0.764242i	$0.276886\pi$
$308$	−5.05325	+	9.53876i	−0.287936	+	0.543521i
$309$	−6.47241	+	3.90602i	−0.368203	+	0.222206i
$310$	−5.25926	−	9.10930i	−0.298706	−	0.517374i
$311$	22.6835			1.28626			0.643131	−	0.765756i	$-0.277635\pi$
$311$	22.6835			1.28626			0.643131	+	0.765756i	$0.277635\pi$
$312$	5.04374	+	2.78310i	0.285546	+	0.157562i
$313$	−15.9517			−0.901646			−0.450823	−	0.892613i	$-0.648869\pi$
$313$	−15.9517			−0.901646			−0.450823	+	0.892613i	$0.648869\pi$
$314$	13.9358			0.786443
$315$	−4.47377	−	6.55632i	−0.252068	−	0.369407i
$316$	12.8375			0.722167
$317$	−12.9819			−0.729135			−0.364568	−	0.931177i	$-0.618783\pi$
$317$	−12.9819			−0.729135			−0.364568	+	0.931177i	$0.618783\pi$
$318$	−7.87308	+	4.75130i	−0.441500	+	0.266440i
$319$	−4.18926			−0.234553
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	1.93314	+	1.06669i	0.107897	+	0.0595369i
$322$	−1.02727	−	1.63842i	−0.0572475	−	0.0913058i
$323$	9.75338			0.542692
$324$	8.97297	−	0.697014i	0.498498	−	0.0387230i
$325$	1.66295	+	2.88032i	0.0922440	+	0.159771i
$326$	7.83322	−	13.5675i	0.433842	−	0.751436i
$327$	25.6090	−	15.4547i	1.41618	−	0.854646i
$328$	3.29918	−	5.71435i	0.182167	−	0.315522i
$329$	−14.5523	+	0.530341i	−0.802292	+	0.0292387i
$330$	−0.136951	−	7.06539i	−0.00753890	−	0.388937i
$331$	−20.2758			−1.11446			−0.557230	−	0.830358i	$-0.688136\pi$
$331$	−20.2758			−1.11446			−0.557230	+	0.830358i	$0.688136\pi$
$332$	−6.86528	−	11.8910i	−0.376781	−	0.652604i
$333$	−1.81187	+	3.43955i	−0.0992898	+	0.188486i
$334$	−11.6266	+	20.1379i	−0.636179	+	1.10189i
$335$	0.553942	+	0.959456i	0.0302651	+	0.0524207i
$336$	0.255615	+	4.57544i	0.0139449	+	0.249611i
$337$	−17.2070	+	29.8034i	−0.937326	+	1.62350i	−0.166892	+	0.985975i	$0.553373\pi$
$337$	−17.2070	+	29.8034i	−0.937326	+	1.62350i	−0.770433	+	0.637521i	$0.779960\pi$
$338$	0.969176	+	1.67866i	0.0527162	+	0.0913072i
$339$	−29.3748	−	16.2087i	−1.59542	−	0.880338i
$340$	−2.10964	+	3.65400i	−0.114411	+	0.198166i
$341$	21.4576	−	37.1657i	1.16200	−	2.01264i
$342$	−3.23210	+	6.13564i	−0.174772	+	0.331777i
$343$	18.4098	−	2.01993i	0.994035	−	0.109066i
$344$	1.24480	+	2.15606i	0.0671152	+	0.116247i
$345$	1.10844	+	0.611630i	0.0596765	+	0.0329290i
$346$	−1.66145			−0.0893201
$347$	−21.9857			−1.18025			−0.590127	−	0.807311i	$-0.700922\pi$
$347$	−21.9857			−1.18025			−0.590127	+	0.807311i	$0.700922\pi$
$348$	−1.52266	+	0.918904i	−0.0816230	+	0.0492584i
$349$	9.29786	+	16.1044i	0.497703	+	0.862047i	0.999996	−	0.00265023i	$-0.000843597\pi$
$349$	9.29786	+	16.1044i	0.497703	+	0.862047i	−0.502293	+	0.864697i	$0.667510\pi$
$350$	−1.23855	+	2.33795i	−0.0662033	+	0.124969i
$351$	−15.4434	−	7.75665i	−0.824308	−	0.414019i
$352$	−2.03999	+	3.53336i	−0.108732	+	0.188329i
$353$	−10.4601	+	18.1174i	−0.556733	+	0.964290i	0.441033	+	0.897491i	$0.354612\pi$
$353$	−10.4601	+	18.1174i	−0.556733	+	0.964290i	−0.997766	+	0.0667993i	$0.978721\pi$
$354$	0.200312	+	10.3342i	0.0106464	+	0.549257i
$355$	1.45876	+	2.52665i	0.0774231	+	0.134101i
$356$	7.27583	−	12.6021i	0.385618	−	0.667911i
$357$	−16.1794	+	10.5865i	−0.856305	+	0.560299i
$358$	3.21357	+	5.56606i	0.169842	+	0.294175i
$359$	−2.70799	+	4.69038i	−0.142922	+	0.247549i	−0.928596	−	0.371093i	$-0.878983\pi$
$359$	−2.70799	+	4.69038i	−0.142922	+	0.247549i	0.785674	+	0.618641i	$0.212317\pi$
$360$	−1.59955	−	2.53800i	−0.0843039	−	0.133764i
$361$	6.82820	+	11.8268i	0.359379	+	0.622462i
$362$	3.64852			0.191762
$363$	8.37290	−	5.05294i	0.439463	−	0.265210i
$364$	4.11930	−	7.77579i	0.215910	−	0.407562i
$365$	5.73968	−	9.94141i	0.300428	−	0.520357i
$366$	0.0303188	+	1.56417i	0.00158479	+	0.0817605i
$367$	7.15846	−	12.3988i	0.373669	−	0.647213i	−0.616458	−	0.787388i	$-0.711433\pi$
$367$	7.15846	−	12.3988i	0.373669	−	0.647213i	0.990127	+	0.140175i	$0.0447664\pi$
$368$	−0.365460	−	0.632996i	−0.0190509	−	0.0329972i
$369$	−9.22578	+	17.5137i	−0.480275	+	0.911728i
$370$	1.29586			0.0673688
$371$	7.46168	+	11.9009i	0.387391	+	0.617862i
$372$	−0.353071	−	18.2152i	−0.0183059	−	0.944413i
$373$	12.9244	+	22.3857i	0.669199	+	1.15909i	0.978129	+	0.208001i	$0.0666958\pi$
$373$	12.9244	+	22.3857i	0.669199	+	1.15909i	−0.308930	+	0.951085i	$0.599971\pi$
$374$	−17.2145			−0.890141
$375$	−0.0335666	−	1.73173i	−0.00173337	−	0.0894259i
$376$	−5.50389			−0.283841
$377$	3.41499			0.175881
$378$	−1.29819	−	13.6863i	−0.0667718	−	0.703947i
$379$	19.9647			1.02552			0.512758	−	0.858533i	$-0.328624\pi$
$379$	19.9647			1.02552			0.512758	+	0.858533i	$0.328624\pi$
$380$	2.31162			0.118584
$381$	−0.464451	−	23.9613i	−0.0237945	−	1.22758i
$382$	−10.4457			−0.534450
$383$	−5.09805	−	8.83007i	−0.260498	−	0.451196i	0.705876	−	0.708335i	$-0.250553\pi$
$383$	−5.09805	−	8.83007i	−0.260498	−	0.451196i	−0.966374	+	0.257139i	$0.917220\pi$
$384$	0.0335666	+	1.73173i	0.00171294	+	0.0883717i
$385$	−10.7874	+	0.393136i	−0.549778	+	0.0200361i
$386$	18.1442			0.923515
$387$	−3.98226	−	6.31861i	−0.202430	−	0.321193i
$388$	−7.36150	−	12.7505i	−0.373723	−	0.647308i
$389$	11.6171	−	20.1214i	0.589009	−	1.02019i	−0.405354	−	0.914160i	$-0.632852\pi$
$389$	11.6171	−	20.1214i	0.589009	−	1.02019i	0.994363	−	0.106033i	$-0.0338150\pi$
$390$	0.111639	+	5.75956i	0.00565308	+	0.291646i
$391$	1.54198	−	2.67078i	0.0779811	−	0.135067i
$392$	6.98143	−	0.509538i	0.352615	−	0.0257356i
$393$	−19.9903	+	12.0639i	−1.00838	+	0.608544i
$394$	−8.53501			−0.429988
$395$	6.41876	+	11.1176i	0.322963	+	0.559388i
$396$	5.70458	−	10.8293i	0.286666	−	0.544192i
$397$	−16.2529	+	28.1508i	−0.815708	+	1.41285i	0.0931112	+	0.995656i	$0.470319\pi$
$397$	−16.2529	+	28.1508i	−0.815708	+	1.41285i	−0.908819	+	0.417191i	$0.863015\pi$
$398$	−3.48948	−	6.04396i	−0.174912	−	0.302957i
$399$	9.45514	+	4.77663i	0.473349	+	0.239131i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	4.14576	+	7.18067i	0.207029	+	0.358586i	0.950777	−	0.309875i	$-0.100287\pi$
$401$	4.14576	+	7.18067i	0.207029	+	0.358586i	−0.743748	+	0.668460i	$0.766954\pi$
$402$	0.0371879	+	1.91855i	0.00185477	+	0.0956886i
$403$	−17.4918	+	30.2967i	−0.871329	+	1.50919i
$404$	2.25643	−	3.90825i	0.112262	−	0.194443i
$405$	5.09012	+	7.42231i	0.252930	+	0.368818i
$406$	1.44309	+	2.30163i	0.0716195	+	0.114228i
$407$	2.64355	+	4.57876i	0.131036	+	0.226961i
$408$	−6.25691	+	3.77596i	−0.309763	+	0.186938i
$409$	17.4619			0.863437			0.431718	−	0.902008i	$-0.357907\pi$
$409$	17.4619			0.863437			0.431718	+	0.902008i	$0.357907\pi$
$410$	6.59836			0.325870
$411$	24.6027	+	13.5755i	1.21356	+	0.669632i
$412$	2.18230	+	3.77985i	0.107514	+	0.186220i
$413$	15.7783	−	0.575022i	0.776397	−	0.0282950i
$414$	1.16915	+	1.85507i	0.0574605	+	0.0911719i
$415$	6.86528	−	11.8910i	0.337003	−	0.583707i
$416$	1.66295	−	2.88032i	0.0815330	−	0.141219i
$417$	25.3987	+	14.0148i	1.24378	+	0.686307i
$418$	4.71568	+	8.16780i	0.230652	+	0.399500i
$419$	−11.3255	+	19.6163i	−0.553286	+	0.958319i	0.444749	+	0.895655i	$0.353293\pi$
$419$	−11.3255	+	19.6163i	−0.553286	+	0.958319i	−0.998035	+	0.0626640i	$0.980040\pi$
$420$	−3.83464	+	2.50909i	−0.187111	+	0.122431i
$421$	4.80724	+	8.32639i	0.234291	+	0.405803i	0.959066	−	0.283182i	$-0.0913899\pi$
$421$	4.80724	+	8.32639i	0.234291	+	0.405803i	−0.724776	+	0.688985i	$0.758057\pi$
$422$	−10.4514	+	18.1024i	−0.508768	+	0.881213i
$423$	16.4993	−	0.639862i	0.802221	−	0.0311111i
$424$	2.65456	+	4.59783i	0.128917	+	0.223291i
$425$	−4.21927			−0.204665
$426$	0.0979315	+	5.05235i	0.00474480	+	0.244787i
$427$	2.38817	−	0.0870344i	0.115572	−	0.00421189i
$428$	0.637368	−	1.10395i	0.0308084	−	0.0533616i
$429$	−20.1228	+	12.1439i	−0.971540	+	0.586312i
$430$	−1.24480	+	2.15606i	−0.0600297	+	0.103974i
$431$	−3.40302	−	5.89421i	−0.163918	−	0.283914i	0.772353	−	0.635194i	$-0.219080\pi$
$431$	−3.40302	−	5.89421i	−0.163918	−	0.283914i	−0.936270	+	0.351280i	$0.885747\pi$
$432$	−0.301948	−	5.18737i	−0.0145275	−	0.249578i
$433$	−30.4675			−1.46417			−0.732087	−	0.681211i	$-0.761454\pi$
$433$	−30.4675			−1.46417			−0.732087	+	0.681211i	$0.761454\pi$
$434$	−27.8109	+	1.01354i	−1.33497	+	0.0486514i
$435$	−1.55712	−	0.859207i	−0.0746583	−	0.0411958i
$436$	−8.63456	−	14.9555i	−0.413520	−	0.716238i
$437$	−1.68961			−0.0808252
$438$	17.0231	−	10.2732i	0.813397	−	0.490875i
$439$	−13.9802			−0.667239			−0.333620	−	0.942708i	$-0.608270\pi$
$439$	−13.9802			−0.667239			−0.333620	+	0.942708i	$0.608270\pi$
$440$	−4.07997			−0.194505
$441$	−20.8693	+	2.33910i	−0.993777	+	0.111386i
$442$	14.0329			0.667477
$443$	−8.00349			−0.380257			−0.190129	−	0.981759i	$-0.560891\pi$
$443$	−8.00349			−0.380257			−0.190129	+	0.981759i	$0.560891\pi$
$444$	1.96518	+	1.08437i	0.0932634	+	0.0514620i
$445$	14.5517			0.689815
$446$	−3.45757	−	5.98869i	−0.163721	−	0.283573i
$447$	9.41380	−	5.68111i	0.445257	−	0.268707i
$448$	2.64400	−	0.0963576i	0.124917	−	0.00455247i
$449$	−37.4636			−1.76801			−0.884007	−	0.467473i	$-0.845165\pi$
$449$	−37.4636			−1.76801			−0.884007	+	0.467473i	$0.845165\pi$
$450$	1.39819	−	2.65425i	0.0659114	−	0.125123i
$451$	13.4606	+	23.3144i	0.633834	+	1.09783i
$452$	−9.68504	+	16.7750i	−0.455546	+	0.789029i
$453$	−26.5349	−	14.6418i	−1.24672	−	0.687929i
$454$	−11.9738	+	20.7393i	−0.561960	+	0.973343i
$455$	8.79368	−	0.320476i	0.412254	−	0.0150242i
$456$	3.50558	+	1.93435i	0.164164	+	0.0905843i
$457$	9.06266			0.423933			0.211967	−	0.977277i	$-0.432013\pi$
$457$	9.06266			0.423933			0.211967	+	0.977277i	$0.432013\pi$
$458$	−6.70677	−	11.6165i	−0.313387	−	0.542802i
$459$	18.3176	−	12.0468i	0.854994	−	0.562296i
$460$	0.365460	−	0.632996i	0.0170397	−	0.0295136i
$461$	−14.7896	−	25.6163i	−0.688818	−	1.19307i	−0.972221	−	0.234067i	$-0.924797\pi$
$461$	−14.7896	−	25.6163i	−0.688818	−	1.19307i	0.283402	−	0.959001i	$-0.408537\pi$
$462$	−16.6881	−	8.43066i	−0.776402	−	0.392230i
$463$	−8.49546	+	14.7146i	−0.394817	+	0.683844i	−0.993078	−	0.117458i	$-0.962525\pi$
$463$	−8.49546	+	14.7146i	−0.394817	+	0.683844i	0.598261	+	0.801302i	$0.295859\pi$
$464$	0.513393	+	0.889223i	0.0238337	+	0.0412811i
$465$	15.5983	−	9.41336i	0.723353	−	0.436534i
$466$	−4.48461	+	7.76757i	−0.207746	+	0.359826i
$467$	18.5392	−	32.1108i	0.857891	−	1.48591i	−0.0160450	−	0.999871i	$-0.505108\pi$
$467$	18.5392	−	32.1108i	0.857891	−	1.48591i	0.873936	−	0.486040i	$-0.161559\pi$
$468$	−4.65026	+	8.82779i	−0.214958	+	0.408065i
$469$	2.92924	−	0.106753i	0.135260	−	0.00492940i
$470$	−2.75194	−	4.76650i	−0.126938	−	0.219862i
$471$	0.467778	+	24.1330i	0.0215541	+	1.11199i
$472$	5.96758			0.274680
$473$	−10.1575			−0.467043
$474$	0.430913	+	22.2311i	0.0197925	+	1.02111i
$475$	1.15581	+	2.00193i	0.0530323	+	0.0918547i
$476$	5.92996	+	9.45788i	0.271799	+	0.433501i
$477$	−8.49223	−	13.4745i	−0.388832	−	0.616956i
$478$	−10.2832	+	17.8110i	−0.470341	+	0.814655i
$479$	−1.95565	+	3.38729i	−0.0893560	+	0.154769i	−0.907239	−	0.420615i	$-0.861814\pi$
$479$	−1.95565	+	3.38729i	−0.0893560	+	0.154769i	0.817883	+	0.575384i	$0.195148\pi$
$480$	−1.48293	+	0.894932i	−0.0676864	+	0.0408479i
$481$	−2.15496	−	3.73250i	−0.0982578	−	0.170188i
$482$	−8.06952	+	13.9768i	−0.367556	+	0.636627i
$483$	2.80282	−	1.83395i	0.127533	−	0.0834474i
$484$	−2.82308	−	4.88972i	−0.128322	−	0.222260i
$485$	7.36150	−	12.7505i	0.334268	−	0.578970i
$486$	1.50823	+	15.5153i	0.0684147	+	0.703789i
$487$	−2.95611	−	5.12014i	−0.133954	−	0.232016i	0.791243	−	0.611502i	$-0.209434\pi$
$487$	−2.95611	−	5.12014i	−0.133954	−	0.232016i	−0.925198	+	0.379486i	$0.876101\pi$
$488$	0.903244			0.0408879
$489$	23.7582	+	13.1096i	1.07438	+	0.592835i
$490$	3.93199	+	5.79133i	0.177629	+	0.261625i
$491$	2.72890	−	4.72659i	0.123153	−	0.213308i	−0.797856	−	0.602848i	$-0.794033\pi$
$491$	2.72890	−	4.72659i	0.123153	−	0.213308i	0.921010	+	0.389540i	$0.127366\pi$
$492$	10.0064	+	5.52147i	0.451125	+	0.248927i
$493$	−2.16614	+	3.75187i	−0.0975583	+	0.168976i
$494$	−3.84412	−	6.65822i	−0.172955	−	0.299567i
$495$	12.2307	−	0.474323i	0.549730	−	0.0213192i
$496$	−10.5185			−0.472295
$497$	7.71392	−	0.281126i	0.346017	−	0.0126102i
$498$	20.3615	−	12.2879i	0.912422	−	0.550635i
$499$	19.0494	+	32.9945i	0.852768	+	1.47704i	0.878701	+	0.477373i	$0.158411\pi$
$499$	19.0494	+	32.9945i	0.852768	+	1.47704i	−0.0259328	+	0.999664i	$0.508256\pi$
$500$	−1.00000			−0.0447214
$501$	−35.2635	−	19.4581i	−1.57546	−	0.869324i
$502$	16.8254			0.750954
$503$	−32.2093			−1.43614			−0.718070	−	0.695971i	$-0.754974\pi$
$503$	−32.2093			−1.43614			−0.718070	+	0.695971i	$0.754974\pi$
$504$	−7.91483	+	0.596237i	−0.352554	+	0.0265585i
$505$	4.51286			0.200820
$506$	2.98214			0.132572
$507$	−2.87445	+	1.73469i	−0.127659	+	0.0770405i
$508$	−13.8367			−0.613903
$509$	−2.01259	−	3.48591i	−0.0892066	−	0.154510i	0.817969	−	0.575262i	$-0.195100\pi$
$509$	−2.01259	−	3.48591i	−0.0892066	−	0.154510i	−0.907176	+	0.420751i	$0.861766\pi$
$510$	−6.39854	−	3.53066i	−0.283332	−	0.156340i
$511$	−16.1336	−	25.7320i	−0.713709	−	1.13832i
$512$	1.00000			0.0441942
$513$	−10.7337	−	5.39115i	−0.473906	−	0.238025i
$514$	−5.79416	−	10.0358i	−0.255569	−	0.442659i
$515$	−2.18230	+	3.77985i	−0.0961636	+	0.166560i
$516$	−3.69192	+	2.22803i	−0.162528	+	0.0980835i
$517$	11.2278	−	19.4472i	0.493800	−	0.855287i
$518$	1.60499	−	3.02966i	0.0705194	−	0.133116i
$519$	−0.0557693	−	2.87718i	−0.00244800	−	0.126294i
$520$	3.32591			0.145851
$521$	15.5722	+	26.9719i	0.682232	+	1.18166i	0.974298	+	0.225262i	$0.0723239\pi$
$521$	15.5722	+	26.9719i	0.682232	+	1.18166i	−0.292066	+	0.956398i	$0.594343\pi$
$522$	−1.64240	−	2.60598i	−0.0718859	−	0.114061i
$523$	11.9779	−	20.7464i	0.523759	−	0.907177i	−0.475859	−	0.879522i	$-0.657863\pi$
$523$	11.9779	−	20.7464i	0.523759	−	0.907177i	0.999618	−	0.0276550i	$-0.00880398\pi$
$524$	6.74013	+	11.6742i	0.294444	+	0.509992i
$525$	−4.09026	−	2.06635i	−0.178513	−	0.0901830i
$526$	−11.9076	+	20.6246i	−0.519197	+	0.899276i
$527$	−22.1903	−	38.4346i	−0.966623	−	1.67424i
$528$	−6.18728	−	3.41409i	−0.269267	−	0.148579i
$529$	11.2329	−	19.4559i	0.488386	−	0.845909i
$530$	−2.65456	+	4.59783i	−0.115307	+	0.199717i
$531$	−17.8893	+	0.693769i	−0.776329	+	0.0301070i
$532$	2.86306	−	5.40446i	0.124130	−	0.234313i
$533$	−10.9728	−	19.0054i	−0.475283	−	0.823215i
$534$	22.0676	+	12.1767i	0.954959	+	0.526939i
$535$	1.27474			0.0551117
$536$	1.10788			0.0478533
$537$	−9.53102	+	5.75185i	−0.411294	+	0.248211i
$538$	−9.01902	−	15.6214i	−0.388838	−	0.673486i
$539$	−12.4416	+	25.7074i	−0.535899	+	1.10729i
$540$	4.34142	−	2.85518i	0.186825	−	0.122867i
$541$	12.7810	−	22.1374i	0.549499	−	0.951760i	−0.448810	−	0.893627i	$-0.648152\pi$
$541$	12.7810	−	22.1374i	0.549499	−	0.951760i	0.998309	−	0.0581329i	$-0.0185147\pi$
$542$	−9.61907	+	16.6607i	−0.413174	+	0.715639i
$543$	0.122469	+	6.31824i	0.00525563	+	0.271142i
$544$	2.10964	+	3.65400i	0.0904499	+	0.156664i
$545$	8.63456	−	14.9555i	0.369864	−	0.640623i
$546$	13.6038	+	6.87249i	0.582189	+	0.294115i
$547$	−3.70248	−	6.41288i	−0.158306	−	0.274195i	0.775952	−	0.630792i	$-0.217270\pi$
$547$	−3.70248	−	6.41288i	−0.158306	−	0.274195i	−0.934258	+	0.356598i	$0.883937\pi$
$548$	8.11165	−	14.0498i	0.346513	−	0.600177i
$549$	−2.70770	+	0.105008i	−0.115562	+	0.00448163i
$550$	−2.03999	−	3.53336i	−0.0869853	−	0.150663i
$551$	2.37354			0.101116
$552$	1.08391	−	0.654125i	0.0461342	−	0.0278414i
$553$	33.9424	−	1.23699i	1.44338	−	0.0526023i
$554$	8.98842	−	15.5684i	0.381881	−	0.661438i
$555$	0.0434978	+	2.24408i	0.00184638	+	0.0952560i
$556$	8.37410	−	14.5044i	0.355141	−	0.615122i
$557$	−23.3296	−	40.4080i	−0.988506	−	1.71214i	−0.625180	−	0.780480i	$-0.714975\pi$
$557$	−23.3296	−	40.4080i	−0.988506	−	1.71214i	−0.363326	−	0.931662i	$-0.618359\pi$
$558$	31.5319	−	1.22285i	1.33485	−	0.0517672i
$559$	8.28019			0.350215
$560$	1.40545	+	2.24159i	0.0593909	+	0.0947244i
$561$	−0.577833	−	29.8108i	−0.0243961	−	1.25861i
$562$	−6.06170	−	10.4992i	−0.255697	−	0.442881i
$563$	16.4907			0.694999			0.347500	−	0.937680i	$-0.387031\pi$
$563$	16.4907			0.694999			0.347500	+	0.937680i	$0.387031\pi$
$564$	−0.184747	−	9.53122i	−0.00777925	−	0.401337i
$565$	−19.3701			−0.814905
$566$	−1.24188			−0.0522002
$567$	23.6573	−	2.70752i	0.993515	−	0.113705i
$568$	2.91752			0.122417
$569$	19.4327			0.814661			0.407330	−	0.913281i	$-0.366460\pi$
$569$	19.4327			0.814661			0.407330	+	0.913281i	$0.366460\pi$
$570$	0.0775935	+	4.00310i	0.00325003	+	0.167671i
$571$	−23.1170			−0.967418			−0.483709	−	0.875229i	$-0.660711\pi$
$571$	−23.1170			−0.967418			−0.483709	+	0.875229i	$0.660711\pi$
$572$	6.78480	+	11.7516i	0.283687	+	0.491360i
$573$	−0.350628	−	18.0891i	−0.0146477	−	0.755684i
$574$	8.17240	−	15.4266i	0.341110	−	0.643895i
$575$	0.730921			0.0304815
$576$	−2.99775	+	0.116256i	−0.124906	+	0.00484402i
$577$	4.92535	+	8.53096i	0.205045	+	0.355149i	0.950147	−	0.311802i	$-0.100933\pi$
$577$	4.92535	+	8.53096i	0.205045	+	0.355149i	−0.745102	+	0.666951i	$0.767599\pi$
$578$	−0.401134	+	0.694785i	−0.0166850	+	0.0288993i
$579$	0.609039	+	31.4207i	0.0253108	+	1.30580i
$580$	−0.513393	+	0.889223i	−0.0213175	+	0.0369230i
$581$	−19.2976	−	30.7783i	−0.800598	−	1.27690i
$582$	21.8332	−	13.1761i	0.905017	−	0.546166i
$583$	−21.6611			−0.897109
$584$	−5.73968	−	9.94141i	−0.237510	−	0.411379i
$585$	−9.97022	+	0.386658i	−0.412218	+	0.0159863i
$586$	−3.66402	+	6.34628i	−0.151359	+	0.262162i
$587$	−21.0981	−	36.5429i	−0.870811	−	1.50829i	−0.861160	−	0.508335i	$-0.830261\pi$
$587$	−21.0981	−	36.5429i	−0.870811	−	1.50829i	−0.00965097	−	0.999953i	$-0.503072\pi$
$588$	1.11672	+	12.0728i	0.0460529	+	0.497875i
$589$	−12.1574	+	21.0573i	−0.500938	+	0.867651i
$590$	2.98379	+	5.16808i	0.122841	+	0.212766i
$591$	−0.286492	−	14.7803i	−0.0117847	−	0.607980i
$592$	0.647932	−	1.12225i	0.0266299	−	0.0461243i
$593$	19.0345	−	32.9687i	0.781652	−	1.35386i	−0.149326	−	0.988788i	$-0.547711\pi$
$593$	19.0345	−	32.9687i	0.781652	−	1.35386i	0.930979	−	0.365074i	$-0.118956\pi$
$594$	18.9448	+	9.51527i	0.777315	+	0.390416i
$595$	−5.22578	+	9.86444i	−0.214236	+	0.404402i
$596$	−3.17404	−	5.49760i	−0.130014	−	0.225191i
$597$	10.3494	−	6.24570i	0.423571	−	0.255620i
$598$	−2.43097			−0.0994099
$599$	10.2606			0.419238			0.209619	−	0.977783i	$-0.432778\pi$
$599$	10.2606			0.419238			0.209619	+	0.977783i	$0.432778\pi$
$600$	−1.51650	−	0.836793i	−0.0619109	−	0.0341619i
$601$	23.8726	+	41.3486i	0.973785	+	1.68664i	0.683889	+	0.729586i	$0.260287\pi$
$601$	23.8726	+	41.3486i	0.973785	+	1.68664i	0.289896	+	0.957058i	$0.406379\pi$
$602$	3.49901	+	5.58067i	0.142609	+	0.227451i
$603$	−3.32116	+	0.128799i	−0.135248	+	0.00524508i
$604$	−8.74873	+	15.1532i	−0.355981	+	0.616577i
$605$	2.82308	−	4.88972i	0.114775	−	0.198796i
$606$	6.84376	+	3.77633i	0.278009	+	0.153403i
$607$	−19.8095	−	34.3110i	−0.804042	−	1.39264i	−0.916936	−	0.399034i	$-0.869346\pi$
$607$	−19.8095	−	34.3110i	−0.804042	−	1.39264i	0.112895	−	0.993607i	$-0.463988\pi$
$608$	1.15581	−	2.00193i	0.0468744	−	0.0811888i
$609$	−3.93735	+	2.57630i	−0.159550	+	0.104397i
$610$	0.451622	+	0.782232i	0.0182856	+	0.0316716i
$611$	−9.15270	+	15.8529i	−0.370279	+	0.641341i
$612$	−6.74896	−	10.7085i	−0.272810	−	0.432866i
$613$	8.09836	+	14.0268i	0.327090	+	0.566536i	0.981933	−	0.189229i	$-0.0605988\pi$
$613$	8.09836	+	14.0268i	0.327090	+	0.566536i	−0.654843	+	0.755765i	$0.727265\pi$
$614$	22.6002			0.912069
$615$	0.221485	+	11.4266i	0.00893113	+	0.460763i
$616$	−5.05325	+	9.53876i	−0.203601	+	0.384327i
$617$	10.7676	−	18.6501i	0.433488	−	0.750824i	−0.563683	−	0.825991i	$-0.690616\pi$
$617$	10.7676	−	18.6501i	0.433488	−	0.750824i	0.997171	+	0.0751677i	$0.0239492\pi$
$618$	−6.47241	+	3.90602i	−0.260359	+	0.157123i
$619$	7.11161	−	12.3177i	0.285840	−	0.495089i	−0.686973	−	0.726683i	$-0.741061\pi$
$619$	7.11161	−	12.3177i	0.285840	−	0.495089i	0.972813	+	0.231594i	$0.0743941\pi$
$620$	−5.25926	−	9.10930i	−0.211217	−	0.365838i
$621$	−3.17324	+	2.08691i	−0.127338	+	0.0837449i
$622$	22.6835			0.909525
$623$	18.0230	−	34.0210i	0.722075	−	1.36302i
$624$	5.04374	+	2.78310i	0.201911	+	0.111413i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−15.9517			−0.637560
$627$	−13.9861	+	8.44043i	−0.558551	+	0.337078i
$628$	13.9358			0.556099
$629$	5.46761			0.218008
$630$	−4.47377	−	6.55632i	−0.178239	−	0.261210i
$631$	−3.76778			−0.149993			−0.0749965	−	0.997184i	$-0.523895\pi$
$631$	−3.76778			−0.149993			−0.0749965	+	0.997184i	$0.523895\pi$
$632$	12.8375			0.510649
$633$	−31.6993	−	17.4914i	−1.25993	−	0.695221i
$634$	−12.9819			−0.515577
$635$	−6.91834	−	11.9829i	−0.274546	−	0.475527i
$636$	−7.87308	+	4.75130i	−0.312188	+	0.188401i
$637$	10.1422	−	20.9561i	0.401847	−	0.830310i
$638$	−4.18926			−0.165854
$639$	−8.74600	+	0.339181i	−0.345986	+	0.0134178i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−7.54040	+	13.0604i	−0.297828	+	0.515853i	−0.975639	−	0.219383i	$-0.929596\pi$
$641$	−7.54040	+	13.0604i	−0.297828	+	0.515853i	0.677811	+	0.735236i	$0.262929\pi$
$642$	1.93314	+	1.06669i	0.0762949	+	0.0420989i
$643$	−3.00458	+	5.20409i	−0.118489	+	0.205229i	−0.919169	−	0.393863i	$-0.871138\pi$
$643$	−3.00458	+	5.20409i	−0.118489	+	0.205229i	0.800680	+	0.599092i	$0.204472\pi$
$644$	−1.02727	−	1.63842i	−0.0404801	−	0.0645629i
$645$	−3.77549	−	2.08328i	−0.148660	−	0.0820292i
$646$	9.75338			0.383741
$647$	22.3007	+	38.6259i	0.876731	+	1.51854i	0.854908	+	0.518780i	$0.173614\pi$
$647$	22.3007	+	38.6259i	0.876731	+	1.51854i	0.0218228	+	0.999762i	$0.493053\pi$
$648$	8.97297	−	0.697014i	0.352492	−	0.0273813i
$649$	−12.1738	+	21.0856i	−0.477863	+	0.827682i
$650$	1.66295	+	2.88032i	0.0652264	+	0.112975i
$651$	−2.68869	−	48.1269i	−0.105378	−	1.88624i
$652$	7.83322	−	13.5675i	0.306773	−	0.531346i
$653$	3.45339	+	5.98145i	0.135142	+	0.234072i	0.925652	−	0.378377i	$-0.123518\pi$
$653$	3.45339	+	5.98145i	0.135142	+	0.234072i	−0.790510	+	0.612449i	$0.790184\pi$
$654$	25.6090	−	15.4547i	1.00139	−	0.604326i
$655$	−6.74013	+	11.6742i	−0.263359	+	0.456150i
$656$	3.29918	−	5.71435i	0.128811	−	0.223108i
$657$	18.3618	+	29.1346i	0.716364	+	1.13665i
$658$	−14.5523	+	0.530341i	−0.567306	+	0.0206748i
$659$	−14.8057	−	25.6441i	−0.576746	−	0.998954i	−0.995849	−	0.0910154i	$-0.970989\pi$
$659$	−14.8057	−	25.6441i	−0.576746	−	0.998954i	0.419103	−	0.907939i	$-0.362345\pi$
$660$	−0.136951	−	7.06539i	−0.00533081	−	0.275020i
$661$	−29.7228			−1.15608			−0.578041	−	0.816007i	$-0.696183\pi$
$661$	−29.7228			−1.15608			−0.578041	+	0.816007i	$0.696183\pi$
$662$	−20.2758			−0.788042
$663$	0.471037	+	24.3011i	0.0182936	+	0.943778i
$664$	−6.86528	−	11.8910i	−0.266425	−	0.461461i
$665$	6.11193	−	0.222743i	0.237010	−	0.00863759i
$666$	−1.81187	+	3.43955i	−0.0702085	+	0.133280i
$667$	0.375250	−	0.649951i	0.0145297	−	0.0251662i
$668$	−11.6266	+	20.1379i	−0.449847	+	0.779157i
$669$	10.2547	−	6.18859i	0.396470	−	0.239265i
$670$	0.553942	+	0.959456i	0.0214006	+	0.0370670i
$671$	−1.84260	+	3.19148i	−0.0711329	+	0.123206i
$672$	0.255615	+	4.57544i	0.00986056	+	0.176501i
$673$	18.6415	+	32.2880i	0.718575	+	1.24461i	0.961564	+	0.274580i	$0.0885389\pi$
$673$	18.6415	+	32.2880i	0.718575	+	1.24461i	−0.242989	+	0.970029i	$0.578128\pi$
$674$	−17.2070	+	29.8034i	−0.662789	+	1.14798i
$675$	4.64337	+	2.33219i	0.178723	+	0.0897661i
$676$	0.969176	+	1.67866i	0.0372760	+	0.0645639i
$677$	10.5715			0.406296			0.203148	−	0.979148i	$-0.434883\pi$
$677$	10.5715			0.406296			0.203148	+	0.979148i	$0.434883\pi$
$678$	−29.3748	−	16.2087i	−1.12813	−	0.622493i
$679$	−20.6924	−	33.0029i	−0.794101	−	1.26654i
$680$	−2.10964	+	3.65400i	−0.0809009	+	0.140124i
$681$	−36.3167	−	20.0392i	−1.39166	−	0.767906i
$682$	21.4576	−	37.1657i	0.821655	−	1.42315i
$683$	1.44233	+	2.49820i	0.0551894	+	0.0955909i	0.892300	−	0.451443i	$-0.149090\pi$
$683$	1.44233	+	2.49820i	0.0551894	+	0.0955909i	−0.837111	+	0.547033i	$0.815757\pi$
$684$	−3.23210	+	6.13564i	−0.123582	+	0.234602i
$685$	16.2233			0.619861
$686$	18.4098	−	2.01993i	0.702889	−	0.0771213i
$687$	19.8914	−	12.0042i	0.758904	−	0.457989i
$688$	1.24480	+	2.15606i	0.0474576	+	0.0821991i
$689$	17.6576			0.672702
$690$	1.10844	+	0.611630i	0.0421977	+	0.0232843i
$691$	50.7600			1.93100			0.965501	−	0.260401i	$-0.0838548\pi$
$691$	50.7600			1.93100			0.965501	+	0.260401i	$0.0838548\pi$
$692$	−1.66145			−0.0631589
$693$	14.0394	−	29.1822i	0.533313	−	1.10854i
$694$	−21.9857			−0.834565
$695$	16.7482			0.635296
$696$	−1.52266	+	0.918904i	−0.0577161	+	0.0348310i
$697$	27.8403			1.05453
$698$	9.29786	+	16.1044i	0.351929	+	0.609559i
$699$	−13.6018	−	7.50538i	−0.514469	−	0.283880i
$700$	−1.23855	+	2.33795i	−0.0468128	+	0.0883661i
$701$	21.1533			0.798949			0.399474	−	0.916744i	$-0.369193\pi$
$701$	21.1533			0.798949			0.399474	+	0.916744i	$0.369193\pi$
$702$	−15.4434	−	7.75665i	−0.582874	−	0.292756i
$703$	−1.49778	−	2.59423i	−0.0564897	−	0.0978431i
$704$	−2.03999	+	3.53336i	−0.0768849	+	0.133168i
$705$	8.16190	−	4.92561i	0.307395	−	0.185509i
$706$	−10.4601	+	18.1174i	−0.393670	+	0.681856i
$707$	5.58940	−	10.5508i	0.210211	−	0.396805i
$708$	0.200312	+	10.3342i	0.00752817	+	0.388383i
$709$	−8.68577			−0.326201			−0.163101	−	0.986609i	$-0.552149\pi$
$709$	−8.68577			−0.326201			−0.163101	+	0.986609i	$0.552149\pi$
$710$	1.45876	+	2.52665i	0.0547464	+	0.0948235i
$711$	−38.4837	+	1.49244i	−1.44325	+	0.0559711i
$712$	7.27583	−	12.6021i	0.272673	−	0.472284i
$713$	3.84410	+	6.65818i	0.143963	+	0.249351i
$714$	−16.1794	+	10.5865i	−0.605499	+	0.396191i
$715$	−6.78480	+	11.7516i	−0.253737	+	0.439486i
$716$	3.21357	+	5.56606i	0.120097	+	0.208013i
$717$	−31.1889	−	17.2098i	−1.16477	−	0.642710i
$718$	−2.70799	+	4.69038i	−0.101061	+	0.175043i
$719$	−15.4039	+	26.6804i	−0.574470	+	0.995011i	0.421629	+	0.906768i	$0.361458\pi$
$719$	−15.4039	+	26.6804i	−0.574470	+	0.995011i	−0.996099	+	0.0882427i	$0.971875\pi$
$720$	−1.59955	−	2.53800i	−0.0596119	−	0.0945855i
$721$	6.13421	+	9.78363i	0.228450	+	0.364362i
$722$	6.82820	+	11.8268i	0.254119	+	0.440147i
$723$	−24.4749	−	13.5050i	−0.910230	−	0.502258i
$724$	3.64852			0.135596
$725$	−1.02679			−0.0381339
$726$	8.37290	−	5.05294i	0.310747	−	0.187532i
$727$	−22.6843	−	39.2904i	−0.841315	−	1.45720i	−0.888784	−	0.458327i	$-0.848449\pi$
$727$	−22.6843	−	39.2904i	−0.841315	−	1.45720i	0.0474691	−	0.998873i	$-0.484884\pi$
$728$	4.11930	−	7.77579i	0.152671	−	0.288190i
$729$	−26.8177	+	3.13264i	−0.993246	+	0.116024i
$730$	5.73968	−	9.94141i	0.212435	−	0.367948i
$731$	−5.25216	+	9.09701i	−0.194258	+	0.336465i
$732$	0.0303188	+	1.56417i	0.00112062	+	0.0578134i
$733$	−6.93863	−	12.0181i	−0.256284	−	0.443897i	0.708959	−	0.705249i	$-0.249165\pi$
$733$	−6.93863	−	12.0181i	−0.256284	−	0.443897i	−0.965244	+	0.261352i	$0.915832\pi$
$734$	7.15846	−	12.3988i	0.264224	−	0.457649i
$735$	−9.89701	+	7.00352i	−0.365057	+	0.258329i
$736$	−0.365460	−	0.632996i	−0.0134710	−	0.0233325i
$737$	−2.26007	+	3.91455i	−0.0832507	+	0.144194i
$738$	−9.22578	+	17.5137i	−0.339606	+	0.644689i
$739$	−15.4756	−	26.8045i	−0.569278	−	0.986018i	−0.996638	−	0.0819362i	$-0.973890\pi$
$739$	−15.4756	−	26.8045i	−0.569278	−	0.986018i	0.427360	−	0.904082i	$-0.359444\pi$
$740$	1.29586			0.0476369
$741$	11.4012	−	6.88046i	0.418832	−	0.252760i
$742$	7.46168	+	11.9009i	0.273927	+	0.436895i
$743$	−11.5004	+	19.9193i	−0.421909	+	0.730768i	−0.996126	−	0.0879349i	$-0.971973\pi$
$743$	−11.5004	+	19.9193i	−0.421909	+	0.730768i	0.574217	+	0.818703i	$0.305307\pi$
$744$	−0.353071	−	18.2152i	−0.0129442	−	0.667801i
$745$	3.17404	−	5.49760i	0.116288	−	0.201417i
$746$	12.9244	+	22.3857i	0.473195	+	0.819597i
$747$	21.9628	+	34.8481i	0.803576	+	1.27503i
$748$	−17.2145			−0.629425
$749$	1.57882	−	2.98027i	0.0576890	−	0.108897i
$750$	−0.0335666	−	1.73173i	−0.00122568	−	0.0632337i
$751$	−5.07227	−	8.78543i	−0.185090	−	0.320585i	0.758517	−	0.651653i	$-0.225924\pi$
$751$	−5.07227	−	8.78543i	−0.185090	−	0.320585i	−0.943607	+	0.331068i	$0.892591\pi$
$752$	−5.50389			−0.200706
$753$	0.564772	+	29.1370i	0.0205814	+	1.06181i
$754$	3.41499			0.124367
$755$	−17.4975			−0.636798
$756$	−1.29819	−	13.6863i	−0.0472148	−	0.497766i
$757$	30.7997			1.11943			0.559717	−	0.828684i	$-0.310910\pi$
$757$	30.7997			1.11943			0.559717	+	0.828684i	$0.310910\pi$
$758$	19.9647			0.725149
$759$	0.100100	+	5.16424i	0.00363341	+	0.187450i
$760$	2.31162			0.0838514
$761$	4.67014	+	8.08893i	0.169293	+	0.293223i	0.938171	−	0.346171i	$-0.112518\pi$
$761$	4.67014	+	8.08893i	0.169293	+	0.293223i	−0.768879	+	0.639395i	$0.779185\pi$
$762$	−0.464451	−	23.9613i	−0.0168253	−	0.868027i
$763$	−24.2708	−	38.7103i	−0.878662	−	1.40141i
$764$	−10.4457			−0.377913
$765$	5.89936	−	11.1990i	0.213292	−	0.404901i
$766$	−5.09805	−	8.83007i	−0.184200	−	0.319044i
$767$	9.92380	−	17.1885i	0.358328	−	0.620642i
$768$	0.0335666	+	1.73173i	0.00121123	+	0.0624883i
$769$	18.0682	−	31.2950i	0.651555	−	1.12853i	−0.331191	−	0.943564i	$-0.607450\pi$
$769$	18.0682	−	31.2950i	0.651555	−	1.12853i	0.982746	−	0.184962i	$-0.0592162\pi$
$770$	−10.7874	+	0.393136i	−0.388752	+	0.0141676i
$771$	17.1847	−	10.3708i	0.618892	−	0.373494i
$772$	18.1442			0.653023
$773$	−9.23468	−	15.9949i	−0.332148	−	0.575298i	0.650784	−	0.759263i	$-0.274440\pi$
$773$	−9.23468	−	15.9949i	−0.332148	−	0.575298i	−0.982933	+	0.183965i	$0.941107\pi$
$774$	−3.98226	−	6.31861i	−0.143139	−	0.227118i
$775$	5.25926	−	9.10930i	0.188918	−	0.327216i
$776$	−7.36150	−	12.7505i	−0.264262	−	0.457716i
$777$	5.30042	+	2.67771i	0.190151	+	0.0960624i
$778$	11.6171	−	20.1214i	0.416492	−	0.721386i
$779$	−7.62647	−	13.2094i	−0.273247	−	0.473277i
$780$	0.111639	+	5.75956i	0.00399733	+	0.206225i
$781$	−5.95171	+	10.3087i	−0.212969	+	0.368873i
$782$	1.54198	−	2.67078i	0.0551410	−	0.0955070i
$783$	4.45771	−	2.93166i	0.159306	−	0.104769i
$784$	6.98143	−	0.509538i	0.249337	−	0.0181978i
$785$	6.96791	+	12.0688i	0.248695	+	0.430753i
$786$	−19.9903	+	12.0639i	−0.713032	+	0.430306i
$787$	4.83666			0.172408			0.0862041	−	0.996277i	$-0.472526\pi$
$787$	4.83666			0.172408			0.0862041	+	0.996277i	$0.472526\pi$
$788$	−8.53501			−0.304047
$789$	−36.1159	−	19.9284i	−1.28576	−	0.709471i
$790$	6.41876	+	11.1176i	0.228369	+	0.395547i
$791$	−23.9908	+	45.2862i	−0.853015	+	1.61019i
$792$	5.70458	−	10.8293i	0.202704	−	0.384802i
$793$	1.50205	−	2.60163i	0.0533394	−	0.0923866i
$794$	−16.2529	+	28.1508i	−0.576792	+	0.999034i
$795$	−8.05129	−	4.44264i	−0.285550	−	0.157564i
$796$	−3.48948	−	6.04396i	−0.123681	−	0.214223i
$797$	−6.12627	+	10.6110i	−0.217003	+	0.375861i	−0.953890	−	0.300155i	$-0.902962\pi$
$797$	−6.12627	+	10.6110i	−0.217003	+	0.375861i	0.736887	+	0.676016i	$0.236295\pi$
$798$	9.45514	+	4.77663i	0.334708	+	0.169091i
$799$	−11.6112	−	20.1112i	−0.410775	−	0.711483i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−20.3460	+	38.6238i	−0.718891	+	1.36470i
$802$	4.14576	+	7.18067i	0.146392	+	0.253558i
$803$	46.8354			1.65279
$804$	0.0371879	+	1.91855i	0.00131152	+	0.0676621i
$805$	0.905282	−	1.70885i	0.0319070	−	0.0602292i
$806$	−17.4918	+	30.2967i	−0.616122	+	1.06716i
$807$	26.7492	−	16.1428i	0.941618	−	0.568254i
$808$	2.25643	−	3.90825i	0.0793810	−	0.137492i
$809$	−5.90000	−	10.2191i	−0.207433	−	0.359284i	0.743472	−	0.668767i	$-0.233178\pi$
$809$	−5.90000	−	10.2191i	−0.207433	−	0.359284i	−0.950905	+	0.309483i	$0.899844\pi$
$810$	5.09012	+	7.42231i	0.178848	+	0.260793i
$811$	−17.2258			−0.604880			−0.302440	−	0.953168i	$-0.597801\pi$
$811$	−17.2258			−0.604880			−0.302440	+	0.953168i	$0.597801\pi$
$812$	1.44309	+	2.30163i	0.0506426	+	0.0807714i
$813$	−29.1747	−	16.0983i	−1.02320	−	0.564593i
$814$	2.64355	+	4.57876i	0.0926562	+	0.160485i
$815$	15.6664			0.548772
$816$	−6.25691	+	3.77596i	−0.219036	+	0.132185i
$817$	5.75503			0.201343
$818$	17.4619			0.610542
$819$	−11.4446	+	23.7887i	−0.399908	+	0.831246i
$820$	6.59836			0.230425
$821$	2.92926			0.102232			0.0511160	−	0.998693i	$-0.483722\pi$
$821$	2.92926			0.102232			0.0511160	+	0.998693i	$0.483722\pi$
$822$	24.6027	+	13.5755i	0.858116	+	0.473502i
$823$	−42.6205			−1.48566			−0.742829	−	0.669482i	$-0.766516\pi$
$823$	−42.6205			−1.48566			−0.742829	+	0.669482i	$0.766516\pi$
$824$	2.18230	+	3.77985i	0.0760240	+	0.131677i
$825$	6.05033	−	3.65130i	0.210646	−	0.127122i
$826$	15.7783	−	0.575022i	0.548996	−	0.0200076i
$827$	34.5649			1.20194			0.600969	−	0.799272i	$-0.294781\pi$
$827$	34.5649			1.20194			0.600969	+	0.799272i	$0.294781\pi$
$828$	1.16915	+	1.85507i	0.0406307	+	0.0644683i
$829$	7.48696	+	12.9678i	0.260033	+	0.450390i	0.966250	−	0.257605i	$-0.0829332\pi$
$829$	7.48696	+	12.9678i	0.260033	+	0.450390i	−0.706217	+	0.707995i	$0.749600\pi$
$830$	6.86528	−	11.8910i	0.238297	−	0.412743i
$831$	27.2619	+	15.0429i	0.945705	+	0.521832i
$832$	1.66295	−	2.88032i	0.0576525	−	0.0998571i
$833$	16.5901	+	24.4352i	0.574814	+	0.846629i
$834$	25.3987	+	14.0148i	0.879484	+	0.485292i
$835$	−23.2532			−0.804710
$836$	4.71568	+	8.16780i	0.163095	+	0.282489i
$837$	3.17605	+	54.5635i	0.109780	+	1.88599i
$838$	−11.3255	+	19.6163i	−0.391232	+	0.677634i
$839$	14.4123	+	24.9628i	0.497566	+	0.861810i	0.999996	−	0.00280774i	$-0.000893733\pi$
$839$	14.4123	+	24.9628i	0.497566	+	0.861810i	−0.502430	+	0.864618i	$0.667560\pi$
$840$	−3.83464	+	2.50909i	−0.132308	+	0.0865718i
$841$	13.9729	−	24.2017i	0.481823	−	0.834541i
$842$	4.80724	+	8.32639i	0.165669	+	0.286946i
$843$	17.9782	−	10.8496i	0.619202	−	0.373681i
$844$	−10.4514	+	18.1024i	−0.359754	+	0.623111i
$845$	−0.969176	+	1.67866i	−0.0333407	+	0.0577477i
$846$	16.4993	−	0.639862i	0.567256	−	0.0219989i
$847$	−7.93538	−	12.6564i	−0.272663	−	0.434879i
$848$	2.65456	+	4.59783i	0.0911580	+	0.157890i
$849$	−0.0416858	−	2.15060i	−0.00143065	−	0.0738083i
$850$	−4.21927			−0.144720
$851$	−0.947175			−0.0324687
$852$	0.0979315	+	5.05235i	0.00335508	+	0.173091i
$853$	1.03687	+	1.79592i	0.0355019	+	0.0614911i	0.883230	−	0.468939i	$-0.155364\pi$
$853$	1.03687	+	1.79592i	0.0355019	+	0.0614911i	−0.847729	+	0.530430i	$0.822030\pi$
$854$	2.38817	−	0.0870344i	0.0817216	−	0.00297825i
$855$	−6.92967	+	0.268741i	−0.236990	+	0.00919075i
$856$	0.637368	−	1.10395i	0.0217848	−	0.0377324i
$857$	−3.77130	+	6.53208i	−0.128825	+	0.223131i	−0.923222	−	0.384268i	$-0.874454\pi$
$857$	−3.77130	+	6.53208i	−0.128825	+	0.223131i	0.794397	+	0.607399i	$0.207787\pi$
$858$	−20.1228	+	12.1439i	−0.686982	+	0.414585i
$859$	14.0694	+	24.3690i	0.480043	+	0.831459i	0.999738	−	0.0228930i	$-0.00728772\pi$
$859$	14.0694	+	24.3690i	0.480043	+	0.831459i	−0.519695	+	0.854352i	$0.673954\pi$
$860$	−1.24480	+	2.15606i	−0.0424474	+	0.0735211i
$861$	26.9890	+	13.6345i	0.919783	+	0.464664i
$862$	−3.40302	−	5.89421i	−0.115907	−	0.200758i
$863$	−18.1524	+	31.4410i	−0.617916	+	1.07026i	0.371949	+	0.928253i	$0.378690\pi$
$863$	−18.1524	+	31.4410i	−0.617916	+	1.07026i	−0.989865	+	0.142009i	$0.954644\pi$
$864$	−0.301948	−	5.18737i	−0.0102725	−	0.176478i
$865$	−0.830725	−	1.43886i	−0.0282455	−	0.0489226i
$866$	−30.4675			−1.03533
$867$	−1.21664	−	0.671333i	−0.0413193	−	0.0227997i
$868$	−27.8109	+	1.01354i	−0.943964	+	0.0344018i
$869$	−26.1884	+	45.3596i	−0.888380	+	1.53872i
$870$	−1.55712	−	0.859207i	−0.0527914	−	0.0291299i
$871$	1.84236	−	3.19106i	0.0624260	−	0.108125i
$872$	−8.63456	−	14.9555i	−0.292403	−	0.506457i
$873$	23.5502	+	37.3669i	0.797055	+	1.26468i
$874$	−1.68961			−0.0571521
$875$	−2.64400	+	0.0963576i	−0.0893834	+	0.00325748i
$876$	17.0231	−	10.2732i	0.575158	−	0.347101i
$877$	6.05818	+	10.4931i	0.204570	+	0.354326i	0.949996	−	0.312263i	$-0.101087\pi$
$877$	6.05818	+	10.4931i	0.204570	+	0.354326i	−0.745425	+	0.666589i	$0.767754\pi$
$878$	−13.9802			−0.471809
$879$	−11.1130	−	6.13206i	−0.374832	−	0.206829i
$880$	−4.07997			−0.137536
$881$	−45.2200			−1.52350			−0.761750	−	0.647871i	$-0.775660\pi$
$881$	−45.2200			−1.52350			−0.761750	+	0.647871i	$0.775660\pi$
$882$	−20.8693	+	2.33910i	−0.702707	+	0.0787617i
$883$	15.8733			0.534180			0.267090	−	0.963672i	$-0.413938\pi$
$883$	15.8733			0.534180			0.267090	+	0.963672i	$0.413938\pi$
$884$	14.0329			0.471978
$885$	−8.84953	+	5.34058i	−0.297474	+	0.179522i
$886$	−8.00349			−0.268883
$887$	12.7670	+	22.1130i	0.428673	+	0.742483i	0.996756	−	0.0804883i	$-0.0256480\pi$
$887$	12.7670	+	22.1130i	0.428673	+	0.742483i	−0.568083	+	0.822971i	$0.692315\pi$
$888$	1.96518	+	1.08437i	0.0659472	+	0.0363891i
$889$	−36.5841	+	1.33327i	−1.22699	+	0.0447164i
$890$	14.5517			0.487773
$891$	−15.8419	+	33.1266i	−0.530725	+	1.10978i
$892$	−3.45757	−	5.98869i	−0.115768	−	0.200516i
$893$	−6.36146	+	11.0184i	−0.212878	+	0.368716i
$894$	9.41380	−	5.68111i	0.314845	−	0.190005i
$895$	−3.21357	+	5.56606i	−0.107418	+	0.186053i
$896$	2.64400	−	0.0963576i	0.0883297	−	0.00321908i
$897$	−0.0815996	−	4.20978i	−0.00272453	−	0.140560i
$898$	−37.4636			−1.25018
$899$	−5.40013	−	9.35330i	−0.180104	−	0.311950i
$900$	1.39819	−	2.65425i	0.0466064	−	0.0884751i
$901$	−11.2003	+	19.3995i	−0.373137	+	0.646292i
$902$	13.4606	+	23.3144i	0.448188	+	0.776284i
$903$	−9.54674	+	6.24664i	−0.317696	+	0.207875i
$904$	−9.68504	+	16.7750i	−0.322120	+	0.557928i
$905$	1.82426	+	3.15971i	0.0606405	+	0.105032i
$906$	−26.5349	−	14.6418i	−0.881564	−	0.486440i
$907$	−11.2373	+	19.4636i	−0.373129	+	0.646278i	−0.990045	−	0.140751i	$-0.955048\pi$
$907$	−11.2373	+	19.4636i	−0.373129	+	0.646278i	0.616916	+	0.787029i	$0.288382\pi$
$908$	−11.9738	+	20.7393i	−0.397366	+	0.688257i
$909$	−6.30985	+	11.9783i	−0.209284	+	0.397294i
$910$	8.79368	−	0.320476i	0.291508	−	0.0106237i
$911$	−17.7313	−	30.7115i	−0.587464	−	1.01752i	−0.994563	−	0.104133i	$-0.966793\pi$
$911$	−17.7313	−	30.7115i	−0.587464	−	1.01752i	0.407099	−	0.913384i	$-0.366540\pi$
$912$	3.50558	+	1.93435i	0.116081	+	0.0640528i
$913$	56.0203			1.85400
$914$	9.06266			0.299766
$915$	−1.33945	+	0.808342i	−0.0442809	+	0.0267230i
$916$	−6.70677	−	11.6165i	−0.221598	−	0.383819i
$917$	18.9458	+	30.2172i	0.625644	+	0.997859i
$918$	18.3176	−	12.0468i	0.604572	−	0.397603i
$919$	27.2696	−	47.2323i	0.899541	−	1.55805i	0.0714595	−	0.997444i	$-0.477234\pi$
$919$	27.2696	−	47.2323i	0.899541	−	1.55805i	0.828082	−	0.560607i	$-0.189432\pi$
$920$	0.365460	−	0.632996i	0.0120489	−	0.0208693i
$921$	0.758612	+	39.1373i	0.0249971	+	1.28962i
$922$	−14.7896	−	25.6163i	−0.487068	−	0.843626i
$923$	4.85171	−	8.40340i	0.159696	−	0.276601i
$924$	−16.6881	−	8.43066i	−0.548999	−	0.277348i
$925$	0.647932	+	1.12225i	0.0213039	+	0.0368994i
$926$	−8.49546	+	14.7146i	−0.279178	+	0.483551i
$927$	−6.98141	−	11.0773i	−0.229300	−	0.363827i
$928$	0.513393	+	0.889223i	0.0168529	+	0.0291902i
$929$	22.9601			0.753297			0.376648	−	0.926356i	$-0.377076\pi$
$929$	22.9601			0.753297			0.376648	+	0.926356i	$0.377076\pi$
$930$	15.5983	−	9.41336i	0.511488	−	0.308676i
$931$	7.04917	−	14.5652i	0.231027	−	0.477356i
$932$	−4.48461	+	7.76757i	−0.146898	+	0.254435i
$933$	0.761408	+	39.2816i	0.0249274	+	1.28602i
$934$	18.5392	−	32.1108i	0.606621	−	1.05070i
$935$	−8.60726	−	14.9082i	−0.281487	−	0.487551i
$936$	−4.65026	+	8.82779i	−0.151998	+	0.288545i
$937$	−46.9601			−1.53412			−0.767059	−	0.641576i	$-0.778281\pi$
$937$	−46.9601			−1.53412			−0.767059	+	0.641576i	$0.778281\pi$
$938$	2.92924	−	0.106753i	0.0956431	−	0.00348561i
$939$	−0.535446	−	27.6240i	−0.0174736	−	0.901477i
$940$	−2.75194	−	4.76650i	−0.0897585	−	0.155466i
$941$	53.8045			1.75398			0.876988	−	0.480513i	$-0.159550\pi$
$941$	53.8045			1.75398			0.876988	+	0.480513i	$0.159550\pi$
$942$	0.467778	+	24.1330i	0.0152410	+	0.786296i
$943$	−4.82288			−0.157055
$944$	5.96758			0.194228
$945$	11.2036	−	7.96742i	0.364453	−	0.259180i
$946$	−10.1575			−0.330249
$947$	−7.68899			−0.249859			−0.124929	−	0.992166i	$-0.539870\pi$
$947$	−7.68899			−0.249859			−0.124929	+	0.992166i	$0.539870\pi$
$948$	0.430913	+	22.2311i	0.0139954	+	0.722032i
$949$	−38.1792			−1.23935
$950$	1.15581	+	2.00193i	0.0374995	+	0.0649510i
$951$	−0.435758	−	22.4811i	−0.0141304	−	0.728998i
$952$	5.92996	+	9.45788i	0.192191	+	0.306532i
$953$	8.60696			0.278807			0.139403	−	0.990236i	$-0.455482\pi$
$953$	8.60696			0.278807			0.139403	+	0.990236i	$0.455482\pi$
$954$	−8.49223	−	13.4745i	−0.274946	−	0.436254i
$955$	−5.22286	−	9.04626i	−0.169008	−	0.292730i
$956$	−10.2832	+	17.8110i	−0.332581	+	0.576048i
$957$	−0.140619	−	7.25464i	−0.00454557	−	0.234509i
$958$	−1.95565	+	3.38729i	−0.0631842	+	0.109438i
$959$	20.0934	−	37.9292i	0.648849	−	1.22480i
$960$	−1.48293	+	0.894932i	−0.0478615	+	0.0288838i
$961$	79.6392			2.56901
$962$	−2.15496	−	3.73250i	−0.0694788	−	0.120341i
$963$	−1.78233	+	3.38347i	−0.0574347	+	0.109031i
$964$	−8.06952	+	13.9768i	−0.259902	+	0.450163i
$965$	9.07209	+	15.7133i	0.292041	+	0.505830i
$966$	2.80282	−	1.83395i	0.0901792	−	0.0590062i
$967$	9.16552	−	15.8752i	0.294743	−	0.510510i	−0.680182	−	0.733043i	$-0.738099\pi$
$967$	9.16552	−	15.8752i	0.294743	−	0.510510i	0.974925	+	0.222533i	$0.0714325\pi$
$968$	−2.82308	−	4.88972i	−0.0907374	−	0.157162i
$969$	0.327388	+	16.8902i	0.0105172	+	0.542590i
$970$	7.36150	−	12.7505i	0.236363	−	0.409394i
$971$	−9.84994	+	17.0606i	−0.316100	+	0.547500i	−0.979671	−	0.200613i	$-0.935707\pi$
$971$	−9.84994	+	17.0606i	−0.316100	+	0.547500i	0.663571	+	0.748113i	$0.269040\pi$
$972$	1.50823	+	15.5153i	0.0483765	+	0.497654i
$973$	20.7435	−	39.1564i	0.665006	−	1.25530i
$974$	−2.95611	−	5.12014i	−0.0947200	−	0.164060i
$975$	−4.93210	+	2.97646i	−0.157954	+	0.0953230i
$976$	0.903244			0.0289121
$977$	24.4888			0.783467			0.391734	−	0.920079i	$-0.371876\pi$
$977$	24.4888			0.783467			0.391734	+	0.920079i	$0.371876\pi$
$978$	23.7582	+	13.1096i	0.759703	+	0.419198i
$979$	29.6852	+	51.4163i	0.948743	+	1.64327i
$980$	3.93199	+	5.79133i	0.125603	+	0.184997i
$981$	27.6229	+	43.8290i	0.881931	+	1.39935i
$982$	2.72890	−	4.72659i	0.0870827	−	0.150832i
$983$	18.1559	−	31.4470i	0.579084	−	1.00300i	−0.416500	−	0.909136i	$-0.636743\pi$
$983$	18.1559	−	31.4470i	0.579084	−	1.00300i	0.995585	−	0.0938681i	$-0.0299232\pi$
$984$	10.0064	+	5.52147i	0.318993	+	0.176018i
$985$	−4.26751	−	7.39154i	−0.135974	−	0.235514i
$986$	−2.16614	+	3.75187i	−0.0689841	+	0.119484i
$987$	−1.40688	−	25.1827i	−0.0447813	−	0.801574i
$988$	−3.84412	−	6.65822i	−0.122298	−	0.211826i
$989$	0.909852	−	1.57591i	0.0289316	−	0.0501110i
$990$	12.2307	−	0.474323i	0.388718	−	0.0150750i
$991$	13.0056	+	22.5264i	0.413137	+	0.715575i	0.995231	−	0.0975469i	$-0.0310996\pi$
$991$	13.0056	+	22.5264i	0.413137	+	0.715575i	−0.582094	+	0.813122i	$0.697766\pi$
$992$	−10.5185			−0.333963
$993$	−0.680591	−	35.1121i	−0.0215979	−	1.11425i
$994$	7.71392	−	0.281126i	0.244671	−	0.00891676i
$995$	3.48948	−	6.04396i	0.110624	−	0.191607i
$996$	20.3615	−	12.2879i	0.645180	−	0.389358i
$997$	−18.2634	+	31.6331i	−0.578407	+	1.00183i	0.417255	+	0.908789i	$0.362992\pi$
$997$	−18.2634	+	31.6331i	−0.578407	+	1.00183i	−0.995662	+	0.0930412i	$0.970341\pi$
$998$	19.0494	+	32.9945i	0.602998	+	1.04442i
$999$	−6.01718	−	3.02220i	−0.190375	−	0.0956183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.h.121.3	✓	12
3.2	odd	2		1890.2.i.f.1171.6		12
7.4	even	3		630.2.l.f.571.6	yes	12
9.2	odd	6		1890.2.l.h.1801.3		12
9.7	even	3		630.2.l.f.331.6	yes	12
21.11	odd	6		1890.2.l.h.361.3		12
63.11	odd	6		1890.2.i.f.991.6		12
63.25	even	3	inner	630.2.i.h.151.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.h.121.3	✓	12	1.1	even	1	trivial
630.2.i.h.151.3	yes	12	63.25	even	3	inner
630.2.l.f.331.6	yes	12	9.7	even	3
630.2.l.f.571.6	yes	12	7.4	even	3
1890.2.i.f.991.6		12	63.11	odd	6
1890.2.i.f.1171.6		12	3.2	odd	2
1890.2.l.h.361.3		12	21.11	odd	6
1890.2.l.h.1801.3		12	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.0335666 + 1.73173i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.0335666 + 1.73173i) q^{6} +(2.64400 - 0.0963576i) q^{7} +1.00000 q^{8} +(-2.99775 + 0.116256i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.0335666 + 1.73173i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.0335666 + 1.73173i) q^{6} +(2.64400 - 0.0963576i) q^{7} +1.00000 q^{8} +(-2.99775 + 0.116256i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-2.03999 + 3.53336i) q^{11} +(0.0335666 + 1.73173i) q^{12} +(1.66295 - 2.88032i) q^{13} +(2.64400 - 0.0963576i) q^{14} +(-1.48293 + 0.894932i) q^{15} +1.00000 q^{16} +(2.10964 + 3.65400i) q^{17} +(-2.99775 + 0.116256i) q^{18} +(1.15581 - 2.00193i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.255615 + 4.57544i) q^{21} +(-2.03999 + 3.53336i) q^{22} +(-0.365460 - 0.632996i) q^{23} +(0.0335666 + 1.73173i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.66295 - 2.88032i) q^{26} +(-0.301948 - 5.18737i) q^{27} +(2.64400 - 0.0963576i) q^{28} +(0.513393 + 0.889223i) q^{29} +(-1.48293 + 0.894932i) q^{30} -10.5185 q^{31} +1.00000 q^{32} +(-6.18728 - 3.41409i) q^{33} +(2.10964 + 3.65400i) q^{34} +(1.40545 + 2.24159i) q^{35} +(-2.99775 + 0.116256i) q^{36} +(0.647932 - 1.12225i) q^{37} +(1.15581 - 2.00193i) q^{38} +(5.04374 + 2.78310i) q^{39} +(0.500000 + 0.866025i) q^{40} +(3.29918 - 5.71435i) q^{41} +(0.255615 + 4.57544i) q^{42} +(1.24480 + 2.15606i) q^{43} +(-2.03999 + 3.53336i) q^{44} +(-1.59955 - 2.53800i) q^{45} +(-0.365460 - 0.632996i) q^{46} -5.50389 q^{47} +(0.0335666 + 1.73173i) q^{48} +(6.98143 - 0.509538i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-6.25691 + 3.77596i) q^{51} +(1.66295 - 2.88032i) q^{52} +(2.65456 + 4.59783i) q^{53} +(-0.301948 - 5.18737i) q^{54} -4.07997 q^{55} +(2.64400 - 0.0963576i) q^{56} +(3.50558 + 1.93435i) q^{57} +(0.513393 + 0.889223i) q^{58} +5.96758 q^{59} +(-1.48293 + 0.894932i) q^{60} +0.903244 q^{61} -10.5185 q^{62} +(-7.91483 + 0.596237i) q^{63} +1.00000 q^{64} +3.32591 q^{65} +(-6.18728 - 3.41409i) q^{66} +1.10788 q^{67} +(2.10964 + 3.65400i) q^{68} +(1.08391 - 0.654125i) q^{69} +(1.40545 + 2.24159i) q^{70} +2.91752 q^{71} +(-2.99775 + 0.116256i) q^{72} +(-5.73968 - 9.94141i) q^{73} +(0.647932 - 1.12225i) q^{74} +(-1.51650 - 0.836793i) q^{75} +(1.15581 - 2.00193i) q^{76} +(-5.05325 + 9.53876i) q^{77} +(5.04374 + 2.78310i) q^{78} +12.8375 q^{79} +(0.500000 + 0.866025i) q^{80} +(8.97297 - 0.697014i) q^{81} +(3.29918 - 5.71435i) q^{82} +(-6.86528 - 11.8910i) q^{83} +(0.255615 + 4.57544i) q^{84} +(-2.10964 + 3.65400i) q^{85} +(1.24480 + 2.15606i) q^{86} +(-1.52266 + 0.918904i) q^{87} +(-2.03999 + 3.53336i) q^{88} +(7.27583 - 12.6021i) q^{89} +(-1.59955 - 2.53800i) q^{90} +(4.11930 - 7.77579i) q^{91} +(-0.365460 - 0.632996i) q^{92} +(-0.353071 - 18.2152i) q^{93} -5.50389 q^{94} +2.31162 q^{95} +(0.0335666 + 1.73173i) q^{96} +(-7.36150 - 12.7505i) q^{97} +(6.98143 - 0.509538i) q^{98} +(5.70458 - 10.8293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9	\( 12 q + 12 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} + 2 q^{13} + 8 q^{14} + 7 q^{15} + 12 q^{16} + 7 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{20} + 17 q^{21} - 7 q^{22} - 9 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 8 q^{28} - 9 q^{29} + 7 q^{30} - 18 q^{31} + 12 q^{32} + 3 q^{33} + 7 q^{34} + 4 q^{35} - 4 q^{36} - 12 q^{37} + 14 q^{38} - 14 q^{39} + 6 q^{40} + q^{41} + 17 q^{42} + 7 q^{43} - 7 q^{44} - 5 q^{45} - 9 q^{46} - 14 q^{47} + 2 q^{48} - 24 q^{49} - 6 q^{50} - 3 q^{51} + 2 q^{52} + 2 q^{53} + 11 q^{54} - 14 q^{55} + 8 q^{56} - 14 q^{57} - 9 q^{58} - 58 q^{59} + 7 q^{60} + 22 q^{61} - 18 q^{62} - 13 q^{63} + 12 q^{64} + 4 q^{65} + 3 q^{66} + 44 q^{67} + 7 q^{68} - 18 q^{69} + 4 q^{70} + 10 q^{71} - 4 q^{72} + 6 q^{73} - 12 q^{74} + 5 q^{75} + 14 q^{76} - 23 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} - 4 q^{81} + q^{82} - 26 q^{83} + 17 q^{84} - 7 q^{85} + 7 q^{86} - 12 q^{87} - 7 q^{88} + 2 q^{89} - 5 q^{90} - 4 q^{91} - 9 q^{92} - 26 q^{93} - 14 q^{94} + 28 q^{95} + 2 q^{96} + 6 q^{97} - 24 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 + 2 * q^13 + 8 * q^14 + 7 * q^15 + 12 * q^16 + 7 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^20 + 17 * q^21 - 7 * q^22 - 9 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 8 * q^28 - 9 * q^29 + 7 * q^30 - 18 * q^31 + 12 * q^32 + 3 * q^33 + 7 * q^34 + 4 * q^35 - 4 * q^36 - 12 * q^37 + 14 * q^38 - 14 * q^39 + 6 * q^40 + q^41 + 17 * q^42 + 7 * q^43 - 7 * q^44 - 5 * q^45 - 9 * q^46 - 14 * q^47 + 2 * q^48 - 24 * q^49 - 6 * q^50 - 3 * q^51 + 2 * q^52 + 2 * q^53 + 11 * q^54 - 14 * q^55 + 8 * q^56 - 14 * q^57 - 9 * q^58 - 58 * q^59 + 7 * q^60 + 22 * q^61 - 18 * q^62 - 13 * q^63 + 12 * q^64 + 4 * q^65 + 3 * q^66 + 44 * q^67 + 7 * q^68 - 18 * q^69 + 4 * q^70 + 10 * q^71 - 4 * q^72 + 6 * q^73 - 12 * q^74 + 5 * q^75 + 14 * q^76 - 23 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 - 4 * q^81 + q^82 - 26 * q^83 + 17 * q^84 - 7 * q^85 + 7 * q^86 - 12 * q^87 - 7 * q^88 + 2 * q^89 - 5 * q^90 - 4 * q^91 - 9 * q^92 - 26 * q^93 - 14 * q^94 + 28 * q^95 + 2 * q^96 + 6 * q^97 - 24 * q^98 - 27 * q^99

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