LMFDB - Embedded newform 357.2.i.f.205.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(205,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("357.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.5743021975227.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 2x^{8} + 10x^{7} - 8x^{6} - 12x^{5} - 24x^{4} + 90x^{3} + 54x^{2} - 324x + 243 $ x^10 - 4x^9 + 2x^8 + 10x^7 - 8x^6 - 12x^5 - 24x^4 + 90x^3 + 54x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			205.5
Root			$1.66532 + 0.476133i$ of defining polynomial
Character	$\chi$	$=$	357.205
Dual form			357.2.i.f.256.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24500 - 2.15641i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.10007 - 3.63743i) q^{4} +(1.16532 - 2.01840i) q^{5} +2.49001 q^{6} +(-1.62628 - 2.08692i) q^{7} -5.47838 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.24500 - 2.15641i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.10007 - 3.63743i) q^{4} +(1.16532 - 2.01840i) q^{5} +2.49001 q^{6} +(-1.62628 - 2.08692i) q^{7} -5.47838 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.90166 - 5.02583i) q^{10} +(2.57387 + 4.45807i) q^{11} +(2.10007 - 3.63743i) q^{12} -0.596965 q^{13} +(-6.52497 + 0.908700i) q^{14} +2.33064 q^{15} +(-2.62046 + 4.53877i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(1.24500 + 2.15641i) q^{18} +(-0.946522 + 1.63942i) q^{19} -9.78904 q^{20} +(0.994185 - 2.45186i) q^{21} +12.8179 q^{22} +(2.07968 - 3.60212i) q^{23} +(-2.73919 - 4.74442i) q^{24} +(-0.215950 - 0.374037i) q^{25} +(-0.743224 + 1.28730i) q^{26} -1.00000 q^{27} +(-4.17572 + 10.2981i) q^{28} -2.90140 q^{29} +(2.90166 - 5.02583i) q^{30} +(3.22053 + 5.57813i) q^{31} +(1.04659 + 1.81275i) q^{32} +(-2.57387 + 4.45807i) q^{33} -2.49001 q^{34} +(-6.10736 + 0.850541i) q^{35} +4.20014 q^{36} +(4.70193 - 8.14397i) q^{37} +(2.35685 + 4.08218i) q^{38} +(-0.298482 - 0.516987i) q^{39} +(-6.38408 + 11.0575i) q^{40} -2.09319 q^{41} +(-4.04944 - 5.19644i) q^{42} +11.3362 q^{43} +(10.8106 - 18.7245i) q^{44} +(1.16532 + 2.01840i) q^{45} +(-5.17843 - 8.96930i) q^{46} +(-2.19153 + 3.79584i) q^{47} -5.24092 q^{48} +(-1.71045 + 6.78781i) q^{49} -1.07544 q^{50} +(0.500000 - 0.866025i) q^{51} +(1.25367 + 2.17142i) q^{52} +(5.46554 + 9.46659i) q^{53} +(-1.24500 + 2.15641i) q^{54} +11.9975 q^{55} +(8.90936 + 11.4329i) q^{56} -1.89304 q^{57} +(-3.61225 + 6.25660i) q^{58} +(-1.60603 - 2.78172i) q^{59} +(-4.89452 - 8.47756i) q^{60} +(-5.29160 + 9.16532i) q^{61} +16.0383 q^{62} +(2.62046 - 0.364938i) q^{63} -5.26979 q^{64} +(-0.695656 + 1.20491i) q^{65} +(6.40895 + 11.1006i) q^{66} +(7.38448 + 12.7903i) q^{67} +(-2.10007 + 3.63743i) q^{68} +4.15937 q^{69} +(-5.76958 + 14.2289i) q^{70} -6.91028 q^{71} +(2.73919 - 4.74442i) q^{72} +(-0.217019 - 0.375888i) q^{73} +(-11.7078 - 20.2786i) q^{74} +(0.215950 - 0.374037i) q^{75} +7.95106 q^{76} +(5.11780 - 12.6215i) q^{77} -1.48645 q^{78} +(3.07982 - 5.33441i) q^{79} +(6.10736 + 10.5783i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.60603 + 4.51377i) q^{82} -5.17802 q^{83} +(-11.0063 + 1.53279i) q^{84} -2.33064 q^{85} +(14.1137 - 24.4456i) q^{86} +(-1.45070 - 2.51268i) q^{87} +(-14.1006 - 24.4230i) q^{88} +(-0.197342 + 0.341806i) q^{89} +5.80332 q^{90} +(0.970830 + 1.24582i) q^{91} -17.4699 q^{92} +(-3.22053 + 5.57813i) q^{93} +(5.45692 + 9.45166i) q^{94} +(2.20601 + 3.82091i) q^{95} +(-1.04659 + 1.81275i) q^{96} -17.4653 q^{97} +(12.5078 + 12.1393i) q^{98} -5.14774 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 5 q^{3} - 8 q^{4} - q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 - q^5 + 4 * q^6 - 5 * q^7 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 8 q^{4} - q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{9} - 13 q^{10} + 11 q^{11} + 8 q^{12} + 14 q^{13} + 3 q^{14} - 2 q^{15} + 2 q^{16} - 5 q^{17} + 2 q^{18} - 9 q^{19} + 24 q^{20} - 7 q^{21} + 10 q^{22} + 23 q^{23} - 14 q^{25} - 18 q^{26} - 10 q^{27} + 7 q^{28} - 36 q^{29} + 13 q^{30} - 9 q^{31} - 3 q^{32} - 11 q^{33} - 4 q^{34} - 5 q^{35} + 16 q^{36} + 7 q^{39} - 31 q^{40} + 6 q^{41} - 3 q^{42} + 24 q^{43} + 33 q^{44} - q^{45} - 13 q^{46} - 11 q^{47} + 4 q^{48} + 3 q^{49} + 48 q^{50} + 5 q^{51} - 5 q^{52} + 3 q^{53} - 2 q^{54} - 20 q^{55} - 27 q^{56} - 18 q^{57} + 34 q^{58} + 14 q^{59} + 12 q^{60} - 29 q^{61} - 10 q^{62} - 2 q^{63} + 8 q^{65} + 5 q^{66} - 16 q^{67} - 8 q^{68} + 46 q^{69} + 18 q^{70} - 38 q^{71} - 11 q^{73} - 45 q^{74} + 14 q^{75} + 18 q^{76} + 21 q^{77} - 36 q^{78} - q^{79} + 5 q^{80} - 5 q^{81} + 4 q^{82} + 10 q^{83} - 28 q^{84} + 2 q^{85} + 3 q^{86} - 18 q^{87} - 37 q^{88} - 8 q^{89} + 26 q^{90} - 33 q^{91} - 96 q^{92} + 9 q^{93} + 18 q^{94} + 21 q^{95} + 3 q^{96} + 38 q^{97} - 17 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 - q^5 + 4 * q^6 - 5 * q^7 - 5 * q^9 - 13 * q^10 + 11 * q^11 + 8 * q^12 + 14 * q^13 + 3 * q^14 - 2 * q^15 + 2 * q^16 - 5 * q^17 + 2 * q^18 - 9 * q^19 + 24 * q^20 - 7 * q^21 + 10 * q^22 + 23 * q^23 - 14 * q^25 - 18 * q^26 - 10 * q^27 + 7 * q^28 - 36 * q^29 + 13 * q^30 - 9 * q^31 - 3 * q^32 - 11 * q^33 - 4 * q^34 - 5 * q^35 + 16 * q^36 + 7 * q^39 - 31 * q^40 + 6 * q^41 - 3 * q^42 + 24 * q^43 + 33 * q^44 - q^45 - 13 * q^46 - 11 * q^47 + 4 * q^48 + 3 * q^49 + 48 * q^50 + 5 * q^51 - 5 * q^52 + 3 * q^53 - 2 * q^54 - 20 * q^55 - 27 * q^56 - 18 * q^57 + 34 * q^58 + 14 * q^59 + 12 * q^60 - 29 * q^61 - 10 * q^62 - 2 * q^63 + 8 * q^65 + 5 * q^66 - 16 * q^67 - 8 * q^68 + 46 * q^69 + 18 * q^70 - 38 * q^71 - 11 * q^73 - 45 * q^74 + 14 * q^75 + 18 * q^76 + 21 * q^77 - 36 * q^78 - q^79 + 5 * q^80 - 5 * q^81 + 4 * q^82 + 10 * q^83 - 28 * q^84 + 2 * q^85 + 3 * q^86 - 18 * q^87 - 37 * q^88 - 8 * q^89 + 26 * q^90 - 33 * q^91 - 96 * q^92 + 9 * q^93 + 18 * q^94 + 21 * q^95 + 3 * q^96 + 38 * q^97 - 17 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	1.24500	−	2.15641i	0.880351	−	1.52481i	0.0294001	−	0.999568i	$-0.490640\pi$
$2$	1.24500	−	2.15641i	0.880351	−	1.52481i	0.850951	−	0.525245i	$-0.176026\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−2.10007	−	3.63743i	−1.05004	−	1.81872i
$5$	1.16532	−	2.01840i	0.521148	−	0.902654i	−0.478550	−	0.878060i	$-0.658837\pi$
$5$	1.16532	−	2.01840i	0.521148	−	0.902654i	0.999698	−	0.0245940i	$-0.00782931\pi$
$6$	2.49001			1.01654
$7$	−1.62628	−	2.08692i	−0.614675	−	0.788781i
$7$	−1.62628	−	2.08692i	−0.614675	−	0.788781i
$8$	−5.47838			−1.93690
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.90166	−	5.02583i	−0.917586	−	1.58931i
$11$	2.57387	+	4.45807i	0.776050	+	1.34416i	0.934202	+	0.356744i	$0.116113\pi$
$11$	2.57387	+	4.45807i	0.776050	+	1.34416i	−0.158152	+	0.987415i	$0.550554\pi$
$12$	2.10007	−	3.63743i	0.606239	−	1.05004i
$13$	−0.596965			−0.165568			−0.0827841	−	0.996568i	$-0.526381\pi$
$13$	−0.596965			−0.165568			−0.0827841	+	0.996568i	$0.526381\pi$
$14$	−6.52497	+	0.908700i	−1.74387	+	0.242860i
$15$	2.33064			0.601770
$16$	−2.62046	+	4.53877i	−0.655115	+	1.13469i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$	1.24500	+	2.15641i	0.293450	+	0.508271i
$19$	−0.946522	+	1.63942i	−0.217147	+	0.376110i	−0.953935	−	0.300015i	$-0.903008\pi$
$19$	−0.946522	+	1.63942i	−0.217147	+	0.376110i	0.736788	+	0.676124i	$0.236342\pi$
$20$	−9.78904			−2.18890
$21$	0.994185	−	2.45186i	0.216949	−	0.535039i
$22$	12.8179			2.73279
$23$	2.07968	−	3.60212i	0.433644	−	0.751093i	−0.563540	−	0.826089i	$-0.690561\pi$
$23$	2.07968	−	3.60212i	0.433644	−	0.751093i	0.997184	+	0.0749957i	$0.0238943\pi$
$24$	−2.73919	−	4.74442i	−0.559135	−	0.968450i
$25$	−0.215950	−	0.374037i	−0.0431901	−	0.0748074i
$26$	−0.743224	+	1.28730i	−0.145758	+	0.252461i
$27$	−1.00000			−0.192450
$28$	−4.17572	+	10.2981i	−0.789137	+	1.94617i
$29$	−2.90140			−0.538776			−0.269388	−	0.963032i	$-0.586821\pi$
$29$	−2.90140			−0.538776			−0.269388	+	0.963032i	$0.586821\pi$
$30$	2.90166	−	5.02583i	0.529769	−	0.917586i
$31$	3.22053	+	5.57813i	0.578425	+	1.00186i	0.995660	+	0.0930629i	$0.0296658\pi$
$31$	3.22053	+	5.57813i	0.578425	+	1.00186i	−0.417235	+	0.908799i	$0.637001\pi$
$32$	1.04659	+	1.81275i	0.185013	+	0.320453i
$33$	−2.57387	+	4.45807i	−0.448053	+	0.776050i
$34$	−2.49001			−0.427033
$35$	−6.10736	+	0.850541i	−1.03233	+	0.143768i
$36$	4.20014			0.700024
$37$	4.70193	−	8.14397i	0.772992	−	1.33886i	−0.162925	−	0.986639i	$-0.552093\pi$
$37$	4.70193	−	8.14397i	0.772992	−	1.33886i	0.935916	−	0.352222i	$-0.114574\pi$
$38$	2.35685	+	4.08218i	0.382331	+	0.662217i
$39$	−0.298482	−	0.516987i	−0.0477954	−	0.0827841i
$40$	−6.38408	+	11.0575i	−1.00941	+	1.74835i
$41$	−2.09319			−0.326901			−0.163451	−	0.986552i	$-0.552262\pi$
$41$	−2.09319			−0.326901			−0.163451	+	0.986552i	$0.552262\pi$
$42$	−4.04944	−	5.19644i	−0.624843	−	0.801829i
$43$	11.3362			1.72876			0.864381	−	0.502838i	$-0.167711\pi$
$43$	11.3362			1.72876			0.864381	+	0.502838i	$0.167711\pi$
$44$	10.8106	−	18.7245i	1.62976	−	2.82283i
$45$	1.16532	+	2.01840i	0.173716	+	0.300885i
$46$	−5.17843	−	8.96930i	−0.763518	−	1.32245i
$47$	−2.19153	+	3.79584i	−0.319667	+	0.553679i	−0.980419	−	0.196925i	$-0.936904\pi$
$47$	−2.19153	+	3.79584i	−0.319667	+	0.553679i	0.660752	+	0.750605i	$0.270238\pi$
$48$	−5.24092			−0.756462
$49$	−1.71045	+	6.78781i	−0.244350	+	0.969687i
$50$	−1.07544			−0.152090
$51$	0.500000	−	0.866025i	0.0700140	−	0.121268i
$52$	1.25367	+	2.17142i	0.173853	+	0.301122i
$53$	5.46554	+	9.46659i	0.750749	+	1.30034i	0.947460	+	0.319875i	$0.103641\pi$
$53$	5.46554	+	9.46659i	0.750749	+	1.30034i	−0.196710	+	0.980462i	$0.563026\pi$
$54$	−1.24500	+	2.15641i	−0.169424	+	0.293450i
$55$	11.9975			1.61775
$56$	8.90936	+	11.4329i	1.19056	+	1.52779i
$57$	−1.89304			−0.250740
$58$	−3.61225	+	6.25660i	−0.474312	+	0.821532i
$59$	−1.60603	−	2.78172i	−0.209087	−	0.362150i	0.742340	−	0.670023i	$-0.233716\pi$
$59$	−1.60603	−	2.78172i	−0.209087	−	0.362150i	−0.951427	+	0.307874i	$0.900383\pi$
$60$	−4.89452	−	8.47756i	−0.631880	−	1.09445i
$61$	−5.29160	+	9.16532i	−0.677520	+	1.17350i	0.298206	+	0.954502i	$0.403612\pi$
$61$	−5.29160	+	9.16532i	−0.677520	+	1.17350i	−0.975726	+	0.218997i	$0.929721\pi$
$62$	16.0383			2.03687
$63$	2.62046	−	0.364938i	0.330147	−	0.0459779i
$64$	−5.26979			−0.658724
$65$	−0.695656	+	1.20491i	−0.0862855	+	0.149451i
$66$	6.40895	+	11.1006i	0.788888	+	1.36639i
$67$	7.38448	+	12.7903i	0.902158	+	1.56258i	0.824687	+	0.565589i	$0.191351\pi$
$67$	7.38448	+	12.7903i	0.902158	+	1.56258i	0.0774709	+	0.996995i	$0.475316\pi$
$68$	−2.10007	+	3.63743i	−0.254671	+	0.441103i
$69$	4.15937			0.500729
$70$	−5.76958	+	14.2289i	−0.689596	+	1.70068i
$71$	−6.91028			−0.820099			−0.410050	−	0.912063i	$-0.634489\pi$
$71$	−6.91028			−0.820099			−0.410050	+	0.912063i	$0.634489\pi$
$72$	2.73919	−	4.74442i	0.322817	−	0.559135i
$73$	−0.217019	−	0.375888i	−0.0254002	−	0.0439944i	0.853046	−	0.521836i	$-0.174753\pi$
$73$	−0.217019	−	0.375888i	−0.0254002	−	0.0439944i	−0.878446	+	0.477842i	$0.841419\pi$
$74$	−11.7078	−	20.2786i	−1.36101	−	2.35734i
$75$	0.215950	−	0.374037i	0.0249358	−	0.0431901i
$76$	7.95106			0.912049
$77$	5.11780	−	12.6215i	0.583228	−	1.43835i
$78$	−1.48645			−0.168307
$79$	3.07982	−	5.33441i	0.346507	−	0.600168i	−0.639119	−	0.769108i	$-0.720701\pi$
$79$	3.07982	−	5.33441i	0.346507	−	0.600168i	0.985626	+	0.168939i	$0.0540342\pi$
$80$	6.10736	+	10.5783i	0.682824	+	1.18269i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.60603	+	4.51377i	−0.287788	+	0.498463i
$83$	−5.17802			−0.568362			−0.284181	−	0.958771i	$-0.591722\pi$
$83$	−5.17802			−0.568362			−0.284181	+	0.958771i	$0.591722\pi$
$84$	−11.0063	+	1.53279i	−1.20089	+	0.167242i
$85$	−2.33064			−0.252794
$86$	14.1137	−	24.4456i	1.52192	−	2.63604i
$87$	−1.45070	−	2.51268i	−0.155531	−	0.269388i
$88$	−14.1006	−	24.4230i	−1.50313	−	2.60350i
$89$	−0.197342	+	0.341806i	−0.0209182	+	0.0362313i	−0.876295	−	0.481775i	$-0.839992\pi$
$89$	−0.197342	+	0.341806i	−0.0209182	+	0.0362313i	0.855377	+	0.518006i	$0.173326\pi$
$90$	5.80332			0.611724
$91$	0.970830	+	1.24582i	0.101771	+	0.130597i
$92$	−17.4699			−1.82137
$93$	−3.22053	+	5.57813i	−0.333954	+	0.578425i
$94$	5.45692	+	9.45166i	0.562838	+	0.974865i
$95$	2.20601	+	3.82091i	0.226331	+	0.392018i
$96$	−1.04659	+	1.81275i	−0.106818	+	0.185013i
$97$	−17.4653			−1.77334			−0.886668	−	0.462407i	$-0.846986\pi$
$97$	−17.4653			−1.77334			−0.886668	+	0.462407i	$0.846986\pi$
$98$	12.5078	+	12.1393i	1.26348	+	1.22625i
$99$	−5.14774			−0.517367
$100$	−0.907023	+	1.57101i	−0.0907023	+	0.157101i
$101$	−7.58116	−	13.1310i	−0.754353	−	1.30658i	−0.945695	−	0.325055i	$-0.894617\pi$
$101$	−7.58116	−	13.1310i	−0.754353	−	1.30658i	0.191342	−	0.981523i	$-0.438716\pi$
$102$	−1.24500	−	2.15641i	−0.123274	−	0.213517i
$103$	6.89030	−	11.9343i	0.678921	−	1.17593i	−0.296385	−	0.955069i	$-0.595781\pi$
$103$	6.89030	−	11.9343i	0.678921	−	1.17593i	0.975306	−	0.220857i	$-0.0708855\pi$
$104$	3.27040			0.320689
$105$	−3.79027	−	4.86386i	−0.369893	−	0.474664i
$106$	27.2185			2.64369
$107$	0.440707	−	0.763327i	0.0426048	−	0.0737936i	−0.843937	−	0.536443i	$-0.819768\pi$
$107$	0.440707	−	0.763327i	0.0426048	−	0.0737936i	0.886541	+	0.462649i	$0.153101\pi$
$108$	2.10007	+	3.63743i	0.202080	+	0.350012i
$109$	−6.94356	−	12.0266i	−0.665072	−	1.15194i	−0.979266	−	0.202580i	$-0.935067\pi$
$109$	−6.94356	−	12.0266i	−0.665072	−	1.15194i	0.314194	−	0.949359i	$-0.398266\pi$
$110$	14.9370	−	25.8716i	1.42419	−	2.46676i
$111$	9.40385			0.892574
$112$	13.7336	−	1.91261i	1.29771	−	0.180725i
$113$	−16.4092			−1.54365			−0.771823	−	0.635838i	$-0.780655\pi$
$113$	−16.4092			−1.54365			−0.771823	+	0.635838i	$0.780655\pi$
$114$	−2.35685	+	4.08218i	−0.220739	+	0.382331i
$115$	−4.84700	−	8.39525i	−0.451985	−	0.782861i
$116$	6.09314	+	10.5536i	0.565734	+	0.979880i
$117$	0.298482	−	0.516987i	0.0275947	−	0.0477954i
$118$	−7.99805			−0.736280
$119$	−0.994185	+	2.45186i	−0.0911368	+	0.224761i
$120$	−12.7682			−1.16557
$121$	−7.74959	+	13.4227i	−0.704508	+	1.22024i
$122$	13.1761	+	22.8217i	1.19291	+	2.06618i
$123$	−1.04659	−	1.81275i	−0.0943682	−	0.163451i
$124$	13.5267	−	23.4289i	1.21473	−	2.10398i
$125$	10.6466			0.952262
$126$	2.47553	−	6.10514i	0.220538	−	0.543889i
$127$	5.62184			0.498858			0.249429	−	0.968393i	$-0.419757\pi$
$127$	5.62184			0.498858			0.249429	+	0.968393i	$0.419757\pi$
$128$	−8.65410	+	14.9893i	−0.764922	+	1.32488i
$129$	5.66812	+	9.81748i	0.499051	+	0.864381i
$130$	1.73219	+	3.00024i	0.151923	+	0.263138i
$131$	−4.22187	+	7.31249i	−0.368866	+	0.638895i	−0.989389	−	0.145294i	$-0.953587\pi$
$131$	−4.22187	+	7.31249i	−0.368866	+	0.638895i	0.620522	+	0.784189i	$0.286921\pi$
$132$	21.6212			1.88189
$133$	4.96065	−	0.690844i	0.430143	−	0.0599038i
$134$	36.7749			3.17686
$135$	−1.16532	+	2.01840i	−0.100295	+	0.173716i
$136$	2.73919	+	4.74442i	0.234884	+	0.406830i
$137$	0.435865	+	0.754941i	0.0372385	+	0.0644990i	0.884044	−	0.467404i	$-0.154811\pi$
$137$	0.435865	+	0.754941i	0.0372385	+	0.0644990i	−0.846805	+	0.531903i	$0.821477\pi$
$138$	5.17843	−	8.96930i	0.440817	−	0.763518i
$139$	−12.3738			−1.04954			−0.524768	−	0.851245i	$-0.675848\pi$
$139$	−12.3738			−1.04954			−0.524768	+	0.851245i	$0.675848\pi$
$140$	15.9197	+	20.4289i	1.34546	+	1.72656i
$141$	−4.38305			−0.369120
$142$	−8.60333	+	14.9014i	−0.721975	+	1.25050i
$143$	−1.53651	−	2.66131i	−0.128489	−	0.222550i
$144$	−2.62046	−	4.53877i	−0.218372	−	0.378231i
$145$	−3.38106	+	5.85617i	−0.280782	+	0.486328i
$146$	−1.08076			−0.0894442
$147$	−6.73364	+	1.91261i	−0.555381	+	0.157750i
$148$	−39.4975			−3.24668
$149$	2.56134	−	4.43637i	0.209833	−	0.363442i	−0.741829	−	0.670589i	$-0.766041\pi$
$149$	2.56134	−	4.43637i	0.209833	−	0.363442i	0.951662	+	0.307148i	$0.0993746\pi$
$150$	−0.537718	−	0.931356i	−0.0439045	−	0.0760449i
$151$	1.86857	+	3.23646i	0.152062	+	0.263380i	0.931985	−	0.362496i	$-0.118075\pi$
$151$	1.86857	+	3.23646i	0.152062	+	0.263380i	−0.779923	+	0.625875i	$0.784742\pi$
$152$	5.18541	−	8.98139i	0.420592	−	0.728487i
$153$	1.00000			0.0808452
$154$	−20.8455	−	26.7499i	−1.67978	−	2.15557i
$155$	15.0118			1.20578
$156$	−1.25367	+	2.17142i	−0.100374	+	0.173853i
$157$	1.80862	+	3.13261i	0.144343	+	0.250010i	0.929128	−	0.369759i	$-0.120560\pi$
$157$	1.80862	+	3.13261i	0.144343	+	0.250010i	−0.784785	+	0.619769i	$0.787226\pi$
$158$	−7.66879	−	13.2827i	−0.610096	−	1.05672i
$159$	−5.46554	+	9.46659i	−0.433445	+	0.750749i
$160$	4.87848			0.385677
$161$	−10.8995	+	1.51791i	−0.858998	+	0.119628i
$162$	−2.49001			−0.195634
$163$	2.86964	−	4.97037i	0.224768	−	0.389309i	−0.731482	−	0.681861i	$-0.761171\pi$
$163$	2.86964	−	4.97037i	0.224768	−	0.389309i	0.956250	+	0.292552i	$0.0945043\pi$
$164$	4.39585	+	7.61383i	0.343258	+	0.594540i
$165$	5.99877	+	10.3902i	0.467003	+	0.808874i
$166$	−6.44666	+	11.1659i	−0.500358	+	0.866646i
$167$	−25.0743			−1.94031			−0.970154	−	0.242490i	$-0.922036\pi$
$167$	−25.0743			−1.94031			−0.970154	+	0.242490i	$0.922036\pi$
$168$	−5.44652	+	13.4322i	−0.420208	+	1.03632i
$169$	−12.6436			−0.972587
$170$	−2.90166	+	5.02583i	−0.222547	+	0.385463i
$171$	−0.946522	−	1.63942i	−0.0723824	−	0.125370i
$172$	−23.8069	−	41.2348i	−1.81526	−	3.14413i
$173$	−8.26656	+	14.3181i	−0.628495	+	1.08858i	0.359359	+	0.933199i	$0.382995\pi$
$173$	−8.26656	+	14.3181i	−0.628495	+	1.08858i	−0.987854	+	0.155386i	$0.950338\pi$
$174$	−7.22450			−0.547688
$175$	−0.429389	+	1.05896i	−0.0324588	+	0.0800497i
$176$	−26.9789			−2.03361
$177$	1.60603	−	2.78172i	0.120717	−	0.209087i
$178$	0.491382	+	0.851099i	0.0368307	+	0.0637926i
$179$	−2.28512	−	3.95794i	−0.170798	−	0.295830i	0.767901	−	0.640568i	$-0.221301\pi$
$179$	−2.28512	−	3.95794i	−0.170798	−	0.295830i	−0.938699	+	0.344738i	$0.887968\pi$
$180$	4.89452	−	8.47756i	0.364816	−	0.631880i
$181$	23.3136			1.73289			0.866444	−	0.499275i	$-0.166400\pi$
$181$	23.3136			1.73289			0.866444	+	0.499275i	$0.166400\pi$
$182$	3.89518	−	0.542462i	0.288730	−	0.0402099i
$183$	−10.5832			−0.782332
$184$	−11.3933	+	19.7338i	−0.839924	+	1.45479i
$185$	−10.9585	−	18.9807i	−0.805686	−	1.39549i
$186$	8.01916	+	13.8896i	0.587993	+	1.01843i
$187$	2.57387	−	4.45807i	0.188220	−	0.326006i
$188$	18.4095			1.34265
$189$	1.62628	+	2.08692i	0.118294	+	0.151801i
$190$	10.9859			0.797005
$191$	−9.13188	+	15.8169i	−0.660760	+	1.14447i	0.319657	+	0.947533i	$0.396432\pi$
$191$	−9.13188	+	15.8169i	−0.660760	+	1.14447i	−0.980416	+	0.196936i	$0.936901\pi$
$192$	−2.63489	−	4.56377i	−0.190157	−	0.329362i
$193$	0.0449554	+	0.0778650i	0.00323596	+	0.00560484i	0.867639	−	0.497195i	$-0.165637\pi$
$193$	0.0449554	+	0.0778650i	0.00323596	+	0.00560484i	−0.864403	+	0.502800i	$0.832303\pi$
$194$	−21.7444	+	37.6624i	−1.56116	+	2.70401i
$195$	−1.39131			−0.0996339
$196$	28.2823	−	8.03326i	2.02016	−	0.573804i
$197$	4.49561			0.320299			0.160150	−	0.987093i	$-0.448802\pi$
$197$	4.49561			0.320299			0.160150	+	0.987093i	$0.448802\pi$
$198$	−6.40895	+	11.1006i	−0.455464	+	0.788888i
$199$	7.16288	+	12.4065i	0.507763	+	0.879471i	0.999960	+	0.00898737i	$0.00286081\pi$
$199$	7.16288	+	12.4065i	0.507763	+	0.879471i	−0.492197	+	0.870484i	$0.663806\pi$
$200$	1.18306	+	2.04912i	0.0836548	+	0.144894i
$201$	−7.38448	+	12.7903i	−0.520861	+	0.902158i
$202$	−37.7543			−2.65638
$203$	4.71847	+	6.05497i	0.331172	+	0.424976i
$204$	−4.20014			−0.294069
$205$	−2.43924	+	4.22489i	−0.170364	+	0.295079i
$206$	−17.1569	−	29.7166i	−1.19538	−	2.07046i
$207$	2.07968	+	3.60212i	0.144548	+	0.250364i
$208$	1.56432	−	2.70949i	0.108466	−	0.187869i
$209$	−9.74489			−0.674068
$210$	−15.2074	+	2.11786i	−1.04941	+	0.146146i
$211$	17.5551			1.20854			0.604270	−	0.796780i	$-0.293465\pi$
$211$	17.5551			1.20854			0.604270	+	0.796780i	$0.293465\pi$
$212$	22.9560	−	39.7610i	1.57663	−	2.73080i
$213$	−3.45514	−	5.98448i	−0.236742	−	0.410050i
$214$	−1.09736	−	1.90069i	−0.0750143	−	0.129929i
$215$	13.2104	−	22.8810i	0.900940	−	1.56047i
$216$	5.47838			0.372756
$217$	6.40361	−	15.7926i	0.434706	−	1.07207i
$218$	−34.5790			−2.34199
$219$	0.217019	−	0.375888i	0.0146648	−	0.0254002i
$220$	−25.1957	−	43.6402i	−1.69869	−	2.94222i
$221$	0.298482	+	0.516987i	0.0200781	+	0.0347763i
$222$	11.7078	−	20.2786i	0.785778	−	1.36101i
$223$	24.8716			1.66553			0.832764	−	0.553628i	$-0.186757\pi$
$223$	24.8716			1.66553			0.832764	+	0.553628i	$0.186757\pi$
$224$	2.08102	−	5.13220i	0.139044	−	0.342909i
$225$	0.431901			0.0287934
$226$	−20.4295	+	35.3849i	−1.35895	+	2.35377i
$227$	4.16368	+	7.21171i	0.276353	+	0.478658i	0.970476	−	0.241199i	$-0.0775407\pi$
$227$	4.16368	+	7.21171i	0.276353	+	0.478658i	−0.694122	+	0.719857i	$0.744207\pi$
$228$	3.97553	+	6.88582i	0.263286	+	0.456025i
$229$	−8.51284	+	14.7447i	−0.562544	+	0.974355i	0.434729	+	0.900561i	$0.356844\pi$
$229$	−8.51284	+	14.7447i	−0.562544	+	0.974355i	−0.997273	+	0.0737941i	$0.976489\pi$
$230$	−24.1381			−1.59162
$231$	13.4894	−	1.87861i	0.887540	−	0.123603i
$232$	15.8949			1.04355
$233$	7.69984	−	13.3365i	0.504433	−	0.873704i	−0.495554	−	0.868577i	$-0.665035\pi$
$233$	7.69984	−	13.3365i	0.504433	−	0.873704i	0.999987	−	0.00512668i	$-0.00163188\pi$
$234$	−0.743224	−	1.28730i	−0.0485861	−	0.0841535i
$235$	5.10767	+	8.84674i	0.333188	+	0.577098i
$236$	−6.74555	+	11.6836i	−0.439098	+	0.760540i
$237$	6.15965			0.400112
$238$	4.04944	+	5.19644i	0.262486	+	0.336835i
$239$	12.0954			0.782388			0.391194	−	0.920308i	$-0.372062\pi$
$239$	12.0954			0.782388			0.391194	+	0.920308i	$0.372062\pi$
$240$	−6.10736	+	10.5783i	−0.394229	+	0.682824i
$241$	−7.39732	−	12.8125i	−0.476503	−	0.825328i	0.523134	−	0.852250i	$-0.324763\pi$
$241$	−7.39732	−	12.8125i	−0.476503	−	0.825328i	−0.999638	+	0.0269222i	$0.991429\pi$
$242$	19.2965	+	33.4226i	1.24043	+	2.14849i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	44.4510			2.84568
$245$	11.7073	+	11.3623i	0.747950	+	0.725914i
$246$	−5.21206			−0.332309
$247$	0.565040	−	0.978678i	0.0359527	−	0.0622718i
$248$	−17.6433	−	30.5591i	−1.12035	−	1.94050i
$249$	−2.58901	−	4.48430i	−0.164072	−	0.284181i
$250$	13.2551	−	22.9585i	0.838325	−	1.45202i
$251$	−11.4881			−0.725121			−0.362560	−	0.931960i	$-0.618097\pi$
$251$	−11.4881			−0.725121			−0.362560	+	0.931960i	$0.618097\pi$
$252$	−6.83060	−	8.76535i	−0.430287	−	0.552165i
$253$	21.4113			1.34612
$254$	6.99922	−	12.1230i	0.439170	−	0.760664i
$255$	−1.16532	−	2.01840i	−0.0729753	−	0.126397i
$256$	16.2790	+	28.1960i	1.01744	+	1.76225i
$257$	−3.92761	+	6.80282i	−0.244997	+	0.424348i	−0.962131	−	0.272588i	$-0.912120\pi$
$257$	−3.92761	+	6.80282i	−0.244997	+	0.424348i	0.717133	+	0.696936i	$0.245454\pi$
$258$	28.2274			1.75736
$259$	−24.6424	+	3.43183i	−1.53121	+	0.213243i
$260$	5.84371			0.362412
$261$	1.45070	−	2.51268i	0.0897960	−	0.155531i
$262$	10.5125	+	18.2082i	0.649464	+	1.12490i
$263$	−7.82870	−	13.5597i	−0.482738	−	0.836127i	0.517065	−	0.855946i	$-0.327024\pi$
$263$	−7.82870	−	13.5597i	−0.482738	−	0.836127i	−0.999804	+	0.0198187i	$0.993691\pi$
$264$	14.1006	−	24.4230i	0.867833	−	1.50313i
$265$	25.4764			1.56501
$266$	4.68629	−	11.5573i	0.287335	−	0.708624i
$267$	−0.394683			−0.0241542
$268$	31.0159	−	53.7211i	1.89460	−	3.28154i
$269$	−14.3835	−	24.9129i	−0.876975	−	1.51897i	−0.854644	−	0.519215i	$-0.826224\pi$
$269$	−14.3835	−	24.9129i	−0.876975	−	1.51897i	−0.0223313	−	0.999751i	$-0.507109\pi$
$270$	2.90166	+	5.02583i	0.176590	+	0.305862i
$271$	2.43463	−	4.21690i	0.147893	−	0.256158i	−0.782556	−	0.622581i	$-0.786084\pi$
$271$	2.43463	−	4.21690i	0.147893	−	0.256158i	0.930449	+	0.366423i	$0.119418\pi$
$272$	5.24092			0.317778
$273$	−0.593493	+	1.46367i	−0.0359198	+	0.0885854i
$274$	2.17062			0.131132
$275$	1.11166	−	1.92544i	0.0670353	−	0.116109i
$276$	−8.73497	−	15.1294i	−0.525783	−	0.910683i
$277$	−9.62936	−	16.6785i	−0.578572	−	1.00212i	−0.995643	−	0.0932428i	$-0.970277\pi$
$277$	−9.62936	−	16.6785i	−0.578572	−	1.00212i	0.417071	−	0.908874i	$-0.363057\pi$
$278$	−15.4055	+	26.6831i	−0.923960	+	1.60035i
$279$	−6.44107			−0.385617
$280$	33.4584	−	4.65959i	1.99952	−	0.278464i
$281$	14.6294			0.872716			0.436358	−	0.899773i	$-0.356268\pi$
$281$	14.6294			0.872716			0.436358	+	0.899773i	$0.356268\pi$
$282$	−5.45692	+	9.45166i	−0.324955	+	0.562838i
$283$	−5.99015	−	10.3752i	−0.356078	−	0.616744i	0.631224	−	0.775600i	$-0.282553\pi$
$283$	−5.99015	−	10.3752i	−0.356078	−	0.616744i	−0.987302	+	0.158856i	$0.949219\pi$
$284$	14.5121	+	25.1357i	0.861134	+	1.49153i
$285$	−2.20601	+	3.82091i	−0.130673	+	0.226331i
$286$	−7.65184			−0.452463
$287$	3.40410	+	4.36831i	0.200938	+	0.257853i
$288$	−2.09319			−0.123342
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	8.41887	+	14.5819i	0.494373	+	0.856279i
$291$	−8.73267	−	15.1254i	−0.511918	−	0.886668i
$292$	−0.911511	+	1.57878i	−0.0533422	+	0.0923913i
$293$	−7.08802			−0.414087			−0.207043	−	0.978332i	$-0.566384\pi$
$293$	−7.08802			−0.414087			−0.207043	+	0.978332i	$0.566384\pi$
$294$	−4.25903	+	16.9017i	−0.248392	+	0.985728i
$295$	−7.48616			−0.435861
$296$	−25.7589	+	44.6158i	−1.49721	+	2.59324i
$297$	−2.57387	−	4.45807i	−0.149351	−	0.258683i
$298$	−6.37776	−	11.0466i	−0.369454	−	0.639912i
$299$	−1.24150	+	2.15034i	−0.0717976	+	0.124357i
$300$	−1.81405			−0.104734
$301$	−18.4359	−	23.6578i	−1.06263	−	1.36361i
$302$	9.30553			0.535473
$303$	7.58116	−	13.1310i	0.435526	−	0.754353i
$304$	−4.96065	−	8.59210i	−0.284513	−	0.492791i
$305$	12.3328	+	21.3611i	0.706176	+	1.22313i
$306$	1.24500	−	2.15641i	0.0711722	−	0.123274i
$307$	30.7472			1.75484			0.877418	−	0.479726i	$-0.159264\pi$
$307$	30.7472			1.75484			0.877418	+	0.479726i	$0.159264\pi$
$308$	−56.6576	+	7.89042i	−3.22837	+	0.449598i
$309$	13.7806			0.783951
$310$	18.6898	−	32.3717i	1.06151	−	1.83859i
$311$	−16.4415	−	28.4776i	−0.932313	−	1.61481i	−0.779356	−	0.626581i	$-0.784454\pi$
$311$	−16.4415	−	28.4776i	−0.932313	−	1.61481i	−0.152957	−	0.988233i	$-0.548880\pi$
$312$	1.63520	+	2.83225i	0.0925749	+	0.160344i
$313$	1.17705	−	2.03871i	0.0665306	−	0.115234i	−0.830841	−	0.556509i	$-0.812140\pi$
$313$	1.17705	−	2.03871i	0.0665306	−	0.115234i	0.897372	+	0.441275i	$0.145474\pi$
$314$	9.00694			0.508291
$315$	2.31709	−	5.71440i	0.130553	−	0.321970i
$316$	−25.8714			−1.45538
$317$	−15.2899	+	26.4828i	−0.858765	+	1.48742i	0.0143426	+	0.999897i	$0.495434\pi$
$317$	−15.2899	+	26.4828i	−0.858765	+	1.48742i	−0.873108	+	0.487527i	$0.837899\pi$
$318$	13.6092	+	23.5719i	0.763168	+	1.32185i
$319$	−7.46781	−	12.9346i	−0.418117	−	0.724200i
$320$	−6.14100	+	10.6365i	−0.343292	+	0.594600i
$321$	0.881414			0.0491957
$322$	−10.2966	+	25.3935i	−0.573809	+	1.41513i
$323$	1.89304			0.105332
$324$	−2.10007	+	3.63743i	−0.116671	+	0.202080i
$325$	0.128915	+	0.223287i	0.00715090	+	0.0123857i
$326$	−7.14543	−	12.3763i	−0.395749	−	0.685457i
$327$	6.94356	−	12.0266i	0.383980	−	0.665072i
$328$	11.4673			0.633175
$329$	11.4856	−	1.59954i	0.633223	−	0.0881857i
$330$	29.8740			1.64451
$331$	2.00378	−	3.47065i	0.110138	−	0.190764i	−0.805688	−	0.592340i	$-0.798204\pi$
$331$	2.00378	−	3.47065i	0.110138	−	0.190764i	0.915826	+	0.401576i	$0.131537\pi$
$332$	10.8742	+	18.8347i	0.596801	+	1.03369i
$333$	4.70193	+	8.14397i	0.257664	+	0.446287i
$334$	−31.2176	+	54.0705i	−1.70815	+	2.95861i
$335$	34.4212			1.88063
$336$	8.52319	+	10.9374i	0.464978	+	0.596683i
$337$	−23.1664			−1.26195			−0.630977	−	0.775801i	$-0.717346\pi$
$337$	−23.1664			−1.26195			−0.630977	+	0.775801i	$0.717346\pi$
$338$	−15.7414	+	27.2649i	−0.856218	+	1.48301i
$339$	−8.20459	−	14.2108i	−0.445612	−	0.771823i
$340$	4.89452	+	8.47756i	0.265443	+	0.459760i
$341$	−16.5785	+	28.7147i	−0.897774	+	1.55499i
$342$	−4.71370			−0.254888
$343$	16.9473	−	7.46930i	0.915066	−	0.403304i
$344$	−62.1043			−3.34844
$345$	4.84700	−	8.39525i	0.260954	−	0.451985i
$346$	20.5838	+	35.6522i	1.10659	+	1.91667i
$347$	2.95625	+	5.12037i	0.158700	+	0.274876i	0.934400	−	0.356225i	$-0.115937\pi$
$347$	2.95625	+	5.12037i	0.158700	+	0.274876i	−0.775700	+	0.631101i	$0.782603\pi$
$348$	−6.09314	+	10.5536i	−0.326627	+	0.565734i
$349$	26.4483			1.41575			0.707874	−	0.706339i	$-0.249655\pi$
$349$	26.4483			1.41575			0.707874	+	0.706339i	$0.249655\pi$
$350$	1.74896	+	2.24435i	0.0934857	+	0.119965i
$351$	0.596965			0.0318636
$352$	−5.38759	+	9.33158i	−0.287160	+	0.497375i
$353$	2.16542	+	3.75061i	0.115254	+	0.199625i	0.917881	−	0.396856i	$-0.129899\pi$
$353$	2.16542	+	3.75061i	0.115254	+	0.199625i	−0.802628	+	0.596481i	$0.796565\pi$
$354$	−3.99903	−	6.92652i	−0.212546	−	0.368140i
$355$	−8.05270	+	13.9477i	−0.427393	+	0.740266i
$356$	1.65773			0.0878593
$357$	−2.62046	+	0.364938i	−0.138690	+	0.0193146i
$358$	−11.3799			−0.601448
$359$	−0.698715	+	1.21021i	−0.0368768	+	0.0638724i	−0.883875	−	0.467724i	$-0.845074\pi$
$359$	−0.698715	+	1.21021i	−0.0368768	+	0.0638724i	0.846998	+	0.531596i	$0.178408\pi$
$360$	−6.38408	−	11.0575i	−0.336470	−	0.582784i
$361$	7.70819	+	13.3510i	0.405694	+	0.702683i
$362$	29.0256	−	50.2737i	1.52555	−	2.64233i
$363$	−15.4992			−0.813496
$364$	2.49276	−	6.14763i	0.130656	−	0.322223i
$365$	−1.01159			−0.0529489
$366$	−13.1761	+	22.8217i	−0.688727	+	1.19291i
$367$	0.829833	+	1.43731i	0.0433169	+	0.0750272i	0.886871	−	0.462017i	$-0.152874\pi$
$367$	0.829833	+	1.43731i	0.0433169	+	0.0750272i	−0.843554	+	0.537044i	$0.819541\pi$
$368$	10.8995	+	18.8784i	0.568173	+	0.984105i
$369$	1.04659	−	1.81275i	0.0544835	−	0.0943682i
$370$	−54.5736			−2.83715
$371$	10.8675	−	26.8014i	0.564213	−	1.39146i
$372$	27.0534			1.40265
$373$	−0.920052	+	1.59358i	−0.0476385	+	0.0825123i	−0.888861	−	0.458176i	$-0.848503\pi$
$373$	−0.920052	+	1.59358i	−0.0476385	+	0.0825123i	0.841223	+	0.540688i	$0.181836\pi$
$374$	−6.40895	−	11.1006i	−0.331399	−	0.574000i
$375$	5.32331	+	9.22024i	0.274894	+	0.476131i
$376$	12.0060	−	20.7950i	0.619163	−	1.07242i
$377$	1.73203			0.0892041
$378$	6.52497	−	0.908700i	0.335608	−	0.0467385i
$379$	−4.60612			−0.236600			−0.118300	−	0.992978i	$-0.537745\pi$
$379$	−4.60612			−0.236600			−0.118300	+	0.992978i	$0.537745\pi$
$380$	9.26554	−	16.0484i	0.475312	−	0.823265i
$381$	2.81092	+	4.86866i	0.144008	+	0.249429i
$382$	22.7385	+	39.3842i	1.16340	+	2.01507i
$383$	5.68567	−	9.84787i	0.290524	−	0.503203i	−0.683410	−	0.730035i	$-0.739504\pi$
$383$	5.68567	−	9.84787i	0.290524	−	0.503203i	0.973934	+	0.226832i	$0.0728370\pi$
$384$	−17.3082			−0.883255
$385$	−19.5113	−	25.0379i	−0.994389	−	1.27605i
$386$	0.223879			0.0113951
$387$	−5.66812	+	9.81748i	−0.288127	+	0.499051i
$388$	36.6785	+	63.5290i	1.86207	+	3.22519i
$389$	−1.62680	−	2.81770i	−0.0824821	−	0.142863i	0.821833	−	0.569728i	$-0.192951\pi$
$389$	−1.62680	−	2.81770i	−0.0824821	−	0.142863i	−0.904315	+	0.426865i	$0.859618\pi$
$390$	−1.73219	+	3.00024i	−0.0877128	+	0.151923i
$391$	−4.15937			−0.210348
$392$	9.37048	−	37.1862i	0.473281	−	1.87819i
$393$	−8.44374			−0.425930
$394$	5.59706	−	9.69439i	0.281976	−	0.488396i
$395$	−7.17797	−	12.4326i	−0.361163	−	0.625553i
$396$	10.8106	+	18.7245i	0.543254	+	0.940943i
$397$	−0.0664812	+	0.115149i	−0.00333660	+	0.00577916i	−0.867689	−	0.497108i	$-0.834395\pi$
$397$	−0.0664812	+	0.115149i	−0.00333660	+	0.00577916i	0.864352	+	0.502887i	$0.167729\pi$
$398$	35.6713			1.78804
$399$	3.07861	+	3.95063i	0.154123	+	0.197779i
$400$	2.26356			0.113178
$401$	5.09167	−	8.81904i	0.254266	−	0.440402i	−0.710430	−	0.703768i	$-0.751499\pi$
$401$	5.09167	−	8.81904i	0.254266	−	0.440402i	0.964696	+	0.263366i	$0.0848328\pi$
$402$	18.3874	+	31.8480i	0.917082	+	1.58843i
$403$	−1.92254	−	3.32995i	−0.0957688	−	0.165876i
$404$	−31.8420	+	55.1519i	−1.58420	+	2.74391i
$405$	−2.33064			−0.115811
$406$	18.9315	−	2.63650i	0.939556	−	0.130847i
$407$	48.4085			2.39952
$408$	−2.73919	+	4.74442i	−0.135610	+	0.234884i
$409$	7.03167	+	12.1792i	0.347694	+	0.602223i	0.985839	−	0.167693i	$-0.0536316\pi$
$409$	7.03167	+	12.1792i	0.347694	+	0.602223i	−0.638146	+	0.769916i	$0.720298\pi$
$410$	6.07373	+	10.5200i	0.299960	+	0.519546i
$411$	−0.435865	+	0.754941i	−0.0214997	+	0.0372385i
$412$	−57.8805			−2.85157
$413$	−3.19338	+	7.87550i	−0.157136	+	0.387528i
$414$	10.3569			0.509012
$415$	−6.03407	+	10.4513i	−0.296201	+	0.513035i
$416$	−0.624780	−	1.08215i	−0.0306323	−	0.0530568i
$417$	−6.18692	−	10.7161i	−0.302975	−	0.524768i
$418$	−12.1324	+	21.0140i	−0.593417	+	1.02783i
$419$	26.5734			1.29820			0.649098	−	0.760704i	$-0.275146\pi$
$419$	26.5734			1.29820			0.649098	+	0.760704i	$0.275146\pi$
$420$	−9.73212	+	24.0013i	−0.474879	+	1.17114i
$421$	−11.0420			−0.538155			−0.269077	−	0.963119i	$-0.586719\pi$
$421$	−11.0420			−0.538155			−0.269077	+	0.963119i	$0.586719\pi$
$422$	21.8561	−	37.8559i	1.06394	−	1.84280i
$423$	−2.19153	−	3.79584i	−0.106556	−	0.184560i
$424$	−29.9423	−	51.8616i	−1.45413	−	2.51862i
$425$	−0.215950	+	0.374037i	−0.0104751	+	0.0181435i
$426$	−17.2067			−0.833665
$427$	27.7329	−	3.86221i	1.34209	−	0.186906i
$428$	−3.70207			−0.178946
$429$	1.53651	−	2.66131i	0.0741833	−	0.128489i
$430$	−32.8940	−	56.9740i	−1.58629	−	2.74753i
$431$	3.20784	+	5.55614i	0.154516	+	0.267630i	0.932883	−	0.360180i	$-0.117285\pi$
$431$	3.20784	+	5.55614i	0.154516	+	0.267630i	−0.778367	+	0.627810i	$0.783951\pi$
$432$	2.62046	−	4.53877i	0.126077	−	0.218372i
$433$	−20.9787			−1.00817			−0.504086	−	0.863654i	$-0.668170\pi$
$433$	−20.9787			−1.00817			−0.504086	+	0.863654i	$0.668170\pi$
$434$	−26.0827	−	33.4706i	−1.25201	−	1.60664i
$435$	−6.76212			−0.324219
$436$	−29.1639	+	50.5134i	−1.39670	+	2.41915i
$437$	3.93693	+	6.81896i	0.188329	+	0.326195i
$438$	−0.540379	−	0.935964i	−0.0258203	−	0.0447221i
$439$	3.56767	−	6.17939i	0.170276	−	0.294926i	−0.768241	−	0.640161i	$-0.778868\pi$
$439$	3.56767	−	6.17939i	0.170276	−	0.294926i	0.938516	+	0.345235i	$0.112201\pi$
$440$	−65.7271			−3.13341
$441$	−5.02319	−	4.87520i	−0.239200	−	0.232152i
$442$	1.48645			0.0707031
$443$	−11.9249	+	20.6545i	−0.566569	+	0.981327i	0.430332	+	0.902671i	$0.358396\pi$
$443$	−11.9249	+	20.6545i	−0.566569	+	0.981327i	−0.996902	+	0.0786566i	$0.974937\pi$
$444$	−19.7488	−	34.2059i	−0.937235	−	1.62334i
$445$	0.459933	+	0.796627i	0.0218029	+	0.0377638i
$446$	30.9653	−	53.6335i	1.46625	−	2.53962i
$447$	5.12268			0.242294
$448$	8.57014	+	10.9976i	0.404901	+	0.519588i
$449$	31.7250			1.49720			0.748598	−	0.663025i	$-0.230727\pi$
$449$	31.7250			1.49720			0.748598	+	0.663025i	$0.230727\pi$
$450$	0.537718	−	0.931356i	0.0253483	−	0.0439045i
$451$	−5.38759	−	9.33158i	−0.253692	−	0.439407i
$452$	34.4604	+	59.6872i	1.62088	+	2.80745i
$453$	−1.86857	+	3.23646i	−0.0877933	+	0.152062i
$454$	20.7352			0.973152
$455$	3.64588	−	0.507743i	0.170921	−	0.0238034i
$456$	10.3708			0.485658
$457$	−13.8608	+	24.0076i	−0.648379	+	1.12303i	0.335130	+	0.942172i	$0.391220\pi$
$457$	−13.8608	+	24.0076i	−0.648379	+	1.12303i	−0.983510	+	0.180854i	$0.942114\pi$
$458$	21.1970	+	36.7144i	0.990473	+	1.71555i
$459$	0.500000	+	0.866025i	0.0233380	+	0.0404226i
$460$	−20.3581	+	35.2613i	−0.949201	+	1.64406i
$461$	−22.6069			−1.05291			−0.526453	−	0.850204i	$-0.676478\pi$
$461$	−22.6069			−1.05291			−0.526453	+	0.850204i	$0.676478\pi$
$462$	12.7434	−	31.4277i	0.592875	−	1.46215i
$463$	7.23081			0.336044			0.168022	−	0.985783i	$-0.446262\pi$
$463$	7.23081			0.336044			0.168022	+	0.985783i	$0.446262\pi$
$464$	7.60300	−	13.1688i	0.352960	−	0.611345i
$465$	7.50592	+	13.0006i	0.348079	+	0.602890i
$466$	−19.1727	−	33.2080i	−0.888157	−	1.53833i
$467$	15.4473	−	26.7556i	0.714818	−	1.23810i	−0.248212	−	0.968706i	$-0.579843\pi$
$467$	15.4473	−	26.7556i	0.714818	−	1.23810i	0.963030	−	0.269395i	$-0.0868236\pi$
$468$	−2.50734			−0.115902
$469$	14.6831	−	36.2114i	0.678002	−	1.67209i
$470$	25.4363			1.17329
$471$	−1.80862	+	3.13261i	−0.0833366	+	0.144343i
$472$	8.79844	+	15.2393i	0.404981	+	0.701447i
$473$	29.1780	+	50.5378i	1.34161	+	2.32373i
$474$	7.66879	−	13.2827i	0.352239	−	0.610096i
$475$	0.817607			0.0375144
$476$	11.0063	−	1.53279i	0.504474	−	0.0702555i
$477$	−10.9311			−0.500500
$478$	15.0589	−	26.0827i	0.688776	−	1.19300i
$479$	10.9056	+	18.8890i	0.498289	+	0.863061i	0.999998	−	0.00197495i	$-0.000628647\pi$
$479$	10.9056	+	18.8890i	0.498289	+	0.863061i	−0.501709	+	0.865036i	$0.667295\pi$
$480$	2.43924	+	4.22489i	0.111335	+	0.192839i
$481$	−2.80688	+	4.86166i	−0.127983	+	0.221673i
$482$	−36.8388			−1.67796
$483$	−6.76428	−	8.68025i	−0.307785	−	0.394965i
$484$	65.0988			2.95904
$485$	−20.3527	+	35.2520i	−0.924170	+	1.60071i
$486$	−1.24500	−	2.15641i	−0.0564745	−	0.0978168i
$487$	−2.27912	−	3.94755i	−0.103277	−	0.178880i	0.809756	−	0.586767i	$-0.199599\pi$
$487$	−2.27912	−	3.94755i	−0.103277	−	0.178880i	−0.913033	+	0.407886i	$0.866266\pi$
$488$	28.9894	−	50.2111i	1.31229	−	2.27295i
$489$	5.73928			0.259539
$490$	39.0775	−	11.0995i	1.76534	−	0.501425i
$491$	−1.59981			−0.0721983			−0.0360992	−	0.999348i	$-0.511493\pi$
$491$	−1.59981			−0.0721983			−0.0360992	+	0.999348i	$0.511493\pi$
$492$	−4.39585	+	7.61383i	−0.198180	+	0.343258i
$493$	1.45070	+	2.51268i	0.0653362	+	0.113166i
$494$	−1.40696	−	2.43692i	−0.0633019	−	0.109642i
$495$	−5.99877	+	10.3902i	−0.269625	+	0.467003i
$496$	−33.7571			−1.51574
$497$	11.2380	+	14.4212i	0.504094	+	0.646878i
$498$	−12.8933			−0.577764
$499$	12.5765	−	21.7832i	0.563003	−	0.975150i	−0.434229	−	0.900802i	$-0.642979\pi$
$499$	12.5765	−	21.7832i	0.563003	−	0.975150i	0.997232	−	0.0743474i	$-0.0236874\pi$
$500$	−22.3587	−	38.7263i	−0.999909	−	1.73189i
$501$	−12.5372	−	21.7150i	−0.560119	−	0.970154i
$502$	−14.3027	+	24.7730i	−0.638361	+	1.10567i
$503$	17.2499			0.769135			0.384568	−	0.923097i	$-0.374351\pi$
$503$	17.2499			0.769135			0.384568	+	0.923097i	$0.374351\pi$
$504$	−14.3559	+	1.99927i	−0.639462	+	0.0890546i
$505$	−35.3380			−1.57252
$506$	26.6572	−	46.1716i	1.18506	−	2.05258i
$507$	−6.32182	−	10.9497i	−0.280762	−	0.486294i
$508$	−11.8063	−	20.4491i	−0.523818	−	0.907280i
$509$	7.76030	−	13.4412i	0.343969	−	0.595772i	−0.641197	−	0.767377i	$-0.721562\pi$
$509$	7.76030	−	13.4412i	0.343969	−	0.595772i	0.985166	+	0.171604i	$0.0548951\pi$
$510$	−5.80332			−0.256976
$511$	−0.431514	+	1.06420i	−0.0190891	+	0.0470774i
$512$	46.4533			2.05296
$513$	0.946522	−	1.63942i	0.0417900	−	0.0723824i
$514$	9.77978	+	16.9391i	0.431368	+	0.747151i
$515$	−16.0588	−	27.8147i	−0.707637	−	1.22566i
$516$	23.8069	−	41.2348i	1.04804	−	1.81526i
$517$	−22.5628			−0.992311
$518$	−23.2795	+	57.4118i	−1.02284	+	2.52253i
$519$	−16.5331			−0.725723
$520$	3.81107	−	6.60096i	0.167126	−	0.289471i
$521$	−12.7448	−	22.0747i	−0.558361	−	0.967110i	−0.997633	−	0.0687562i	$-0.978097\pi$
$521$	−12.7448	−	22.0747i	−0.558361	−	0.967110i	0.439272	−	0.898354i	$-0.355236\pi$
$522$	−3.61225	−	6.25660i	−0.158104	−	0.273844i
$523$	−4.51439	+	7.81915i	−0.197400	+	0.341907i	−0.947685	−	0.319208i	$-0.896583\pi$
$523$	−4.51439	+	7.81915i	−0.197400	+	0.341907i	0.750284	+	0.661115i	$0.229917\pi$
$524$	35.4649			1.54929
$525$	−1.13178	+	0.157617i	−0.0493949	+	0.00687898i
$526$	−38.9871			−1.69992
$527$	3.22053	−	5.57813i	0.140289	−	0.242987i
$528$	−13.4894	−	23.3644i	−0.587053	−	1.01681i
$529$	2.84984	+	4.93607i	0.123906	+	0.214612i
$530$	31.7183	−	54.9377i	1.37775	−	2.38634i
$531$	3.21206			0.139391
$532$	−12.9306	−	16.5932i	−0.560614	−	0.719407i
$533$	1.24956			0.0541244
$534$	−0.491382	+	0.851099i	−0.0212642	+	0.0368307i
$535$	−1.02713	−	1.77904i	−0.0444068	−	0.0769148i
$536$	−40.4550	−	70.0701i	−1.74739	−	3.02657i
$537$	2.28512	−	3.95794i	0.0986101	−	0.170798i
$538$	−71.6299			−3.08818
$539$	−34.6630	+	9.84563i	−1.49304	+	0.424081i
$540$	9.78904			0.421253
$541$	17.1995	−	29.7904i	0.739464	−	1.28079i	−0.213273	−	0.976993i	$-0.568412\pi$
$541$	17.1995	−	29.7904i	0.739464	−	1.28079i	0.952737	−	0.303796i	$-0.0982543\pi$
$542$	−6.06224	−	10.5001i	−0.260396	−	0.451018i
$543$	11.6568	+	20.1902i	0.500241	+	0.866444i
$544$	1.04659	−	1.81275i	0.0448724	−	0.0777212i
$545$	−32.3659			−1.38640
$546$	2.41737	+	3.10209i	0.103454	+	0.132757i
$547$	−24.1154			−1.03110			−0.515551	−	0.856859i	$-0.672413\pi$
$547$	−24.1154			−1.03110			−0.515551	+	0.856859i	$0.672413\pi$
$548$	1.83070	−	3.17086i	0.0782035	−	0.135453i
$549$	−5.29160	−	9.16532i	−0.225840	−	0.391166i
$550$	−2.76803	−	4.79437i	−0.118029	−	0.204433i
$551$	2.74624	−	4.75662i	0.116994	−	0.202639i
$552$	−22.7866			−0.969861
$553$	−16.1411	+	2.24789i	−0.686390	+	0.0955901i
$554$	−47.9544			−2.03739
$555$	10.9585	−	18.9807i	0.465163	−	0.805686i
$556$	25.9860	+	45.0090i	1.10205	+	1.90881i
$557$	−9.19967	−	15.9343i	−0.389803	−	0.675158i	0.602620	−	0.798028i	$-0.294123\pi$
$557$	−9.19967	−	15.9343i	−0.389803	−	0.675158i	−0.992423	+	0.122870i	$0.960790\pi$
$558$	−8.01916	+	13.8896i	−0.339478	+	0.587993i
$559$	−6.76734			−0.286228
$560$	12.1437	−	29.9487i	0.513165	−	1.26557i
$561$	5.14774			0.217338
$562$	18.2137	−	31.5470i	0.768297	−	1.33073i
$563$	6.83677	+	11.8416i	0.288136	+	0.499065i	0.973365	−	0.229262i	$-0.0736313\pi$
$563$	6.83677	+	11.8416i	0.288136	+	0.499065i	−0.685229	+	0.728328i	$0.740298\pi$
$564$	9.20473	+	15.9431i	0.387589	+	0.671324i
$565$	−19.1220	+	33.1202i	−0.804467	+	1.39338i
$566$	−29.8311			−1.25389
$567$	−0.994185	+	2.45186i	−0.0417518	+	0.102968i
$568$	37.8571			1.58845
$569$	11.7978	−	20.4343i	0.494588	−	0.856652i	−0.505392	−	0.862890i	$-0.668652\pi$
$569$	11.7978	−	20.4343i	0.494588	−	0.856652i	0.999981	+	0.00623751i	$0.00198547\pi$
$570$	5.49297	+	9.51411i	0.230075	+	0.398502i
$571$	2.85804	+	4.95027i	0.119605	+	0.207162i	0.919611	−	0.392830i	$-0.128504\pi$
$571$	2.85804	+	4.95027i	0.119605	+	0.207162i	−0.800006	+	0.599992i	$0.795170\pi$
$572$	−6.45356	+	11.1779i	−0.269837	+	0.467371i
$573$	−18.2638			−0.762980
$574$	13.6580	−	1.90208i	0.570074	−	0.0793913i
$575$	−1.79643			−0.0749164
$576$	2.63489	−	4.56377i	0.109787	−	0.190157i
$577$	12.6215	+	21.8611i	0.525440	+	0.910089i	0.999561	+	0.0296294i	$0.00943272\pi$
$577$	12.6215	+	21.8611i	0.525440	+	0.910089i	−0.474121	+	0.880460i	$0.657234\pi$
$578$	1.24500	+	2.15641i	0.0517854	+	0.0896949i
$579$	−0.0449554	+	0.0778650i	−0.00186828	+	0.00323596i
$580$	28.4019			1.17932
$581$	8.42090	+	10.8061i	0.349358	+	0.448313i
$582$	−43.4888			−1.80267
$583$	−28.1351	+	48.7315i	−1.16524	+	2.01825i
$584$	1.18891	+	2.05926i	0.0491975	+	0.0852126i
$585$	−0.695656	−	1.20491i	−0.0287618	−	0.0498170i
$586$	−8.82462	+	15.2847i	−0.364542	+	0.631405i
$587$	10.1988			0.420950			0.210475	−	0.977599i	$-0.432499\pi$
$587$	10.1988			0.420950			0.210475	+	0.977599i	$0.432499\pi$
$588$	21.0981	+	20.4765i	0.870072	+	0.844438i
$589$	−12.1932			−0.502413
$590$	−9.32031	+	16.1432i	−0.383711	+	0.664607i
$591$	2.24781	+	3.89332i	0.0924624	+	0.160150i
$592$	24.6424	+	42.6819i	1.01280	+	1.75422i
$593$	1.62267	−	2.81054i	0.0666349	−	0.115415i	−0.830783	−	0.556596i	$-0.812107\pi$
$593$	1.62267	−	2.81054i	0.0666349	−	0.115415i	0.897418	+	0.441181i	$0.145440\pi$
$594$	−12.8179			−0.525925
$595$	3.79027	+	4.86386i	0.155386	+	0.199399i
$596$	−21.5160			−0.881329
$597$	−7.16288	+	12.4065i	−0.293157	+	0.507763i
$598$	3.09134	+	5.35436i	0.126414	+	0.218956i
$599$	10.5704	+	18.3085i	0.431895	+	0.748064i	0.997037	−	0.0769299i	$-0.0245118\pi$
$599$	10.5704	+	18.3085i	0.431895	+	0.748064i	−0.565142	+	0.824994i	$0.691178\pi$
$600$	−1.18306	+	2.04912i	−0.0482981	+	0.0836548i
$601$	8.77314			0.357864			0.178932	−	0.983861i	$-0.442736\pi$
$601$	8.77314			0.357864			0.178932	+	0.983861i	$0.442736\pi$
$602$	−73.9687	+	10.3012i	−3.01474	+	0.419847i
$603$	−14.7690			−0.601439
$604$	7.84828	−	13.5936i	0.319342	−	0.553116i
$605$	18.0615	+	31.2835i	0.734306	+	1.27185i
$606$	−18.8772	−	32.6962i	−0.766832	−	1.32819i
$607$	10.2399	−	17.7359i	0.415623	−	0.719880i	−0.579871	−	0.814708i	$-0.696897\pi$
$607$	10.2399	−	17.7359i	0.415623	−	0.719880i	0.995494	+	0.0948287i	$0.0302303\pi$
$608$	−3.96250			−0.160701
$609$	−2.88452	+	7.11381i	−0.116887	+	0.288266i
$610$	61.4177			2.48673
$611$	1.30826	−	2.26598i	0.0529267	−	0.0916717i
$612$	−2.10007	−	3.63743i	−0.0848904	−	0.147034i
$613$	−15.0441	−	26.0572i	−0.607626	−	1.05244i	−0.991631	−	0.129108i	$-0.958789\pi$
$613$	−15.0441	−	26.0572i	−0.607626	−	1.05244i	0.384005	−	0.923331i	$-0.374545\pi$
$614$	38.2804	−	66.3036i	1.54487	−	2.67580i
$615$	−4.87848			−0.196719
$616$	−28.0373	+	69.1454i	−1.12965	+	2.78595i
$617$	37.8597			1.52417			0.762086	−	0.647476i	$-0.224175\pi$
$617$	37.8597			1.52417			0.762086	+	0.647476i	$0.224175\pi$
$618$	17.1569	−	29.7166i	0.690152	−	1.19538i
$619$	5.54171	+	9.59852i	0.222740	+	0.385797i	0.955639	−	0.294540i	$-0.0951665\pi$
$619$	5.54171	+	9.59852i	0.222740	+	0.385797i	−0.732899	+	0.680338i	$0.761833\pi$
$620$	−31.5259	−	54.6045i	−1.26611	−	2.19297i
$621$	−2.07968	+	3.60212i	−0.0834548	+	0.144548i
$622$	−81.8791			−3.28305
$623$	1.03425	−	0.144035i	0.0414364	−	0.00577064i
$624$	3.12865			0.125246
$625$	13.4865	−	23.3593i	0.539459	−	0.934371i
$626$	−2.93086	−	5.07639i	−0.117141	−	0.202894i
$627$	−4.87245	−	8.43932i	−0.194587	−	0.337034i
$628$	7.59645	−	13.1574i	0.303131	−	0.525039i
$629$	−9.40385			−0.374956
$630$	−9.43781	−	12.1111i	−0.376011	−	0.482516i
$631$	−23.5684			−0.938243			−0.469122	−	0.883134i	$-0.655429\pi$
$631$	−23.5684			−0.938243			−0.469122	+	0.883134i	$0.655429\pi$
$632$	−16.8724	+	29.2239i	−0.671150	+	1.16247i
$633$	8.77753	+	15.2031i	0.348875	+	0.604270i
$634$	38.0719	+	65.9425i	1.51203	+	2.61891i
$635$	6.55125	−	11.3471i	0.259979	−	0.450296i
$636$	45.9121			1.82053
$637$	1.02108	−	4.05208i	0.0404565	−	0.160549i
$638$	−37.1898			−1.47236
$639$	3.45514	−	5.98448i	0.136683	−	0.236742i
$640$	20.1696	+	34.9348i	0.797274	+	1.38092i
$641$	−12.4440	−	21.5537i	−0.491510	−	0.851320i	0.508442	−	0.861096i	$-0.330222\pi$
$641$	−12.4440	−	21.5537i	−0.491510	−	0.851320i	−0.999952	+	0.00977574i	$0.996888\pi$
$642$	1.09736	−	1.90069i	0.0433095	−	0.0750143i
$643$	21.5679			0.850557			0.425278	−	0.905063i	$-0.360176\pi$
$643$	21.5679			0.850557			0.425278	+	0.905063i	$0.360176\pi$
$644$	28.4109	+	36.4583i	1.11955	+	1.43666i
$645$	26.4208			1.04032
$646$	2.35685	−	4.08218i	0.0927290	−	0.160611i
$647$	11.1073	+	19.2384i	0.436674	+	0.756341i	0.997431	−	0.0716393i	$-0.0228231\pi$
$647$	11.1073	+	19.2384i	0.436674	+	0.756341i	−0.560757	+	0.827981i	$0.689490\pi$
$648$	2.73919	+	4.74442i	0.107606	+	0.186378i
$649$	8.26741	−	14.3196i	0.324524	−	0.562093i
$650$	0.641998			0.0251812
$651$	16.8786	−	2.35059i	0.661523	−	0.0921270i
$652$	−24.1058			−0.944057
$653$	11.2721	−	19.5239i	0.441112	−	0.764028i	−0.556660	−	0.830740i	$-0.687918\pi$
$653$	11.2721	−	19.5239i	0.441112	−	0.764028i	0.997772	+	0.0667120i	$0.0212509\pi$
$654$	−17.2895	−	29.9463i	−0.676074	−	1.17099i
$655$	9.83967	+	17.0428i	0.384468	+	0.665918i
$656$	5.48512	−	9.50051i	0.214158	−	0.370933i
$657$	0.434038			0.0169334
$658$	10.8504	−	26.7592i	0.422992	−	1.04318i
$659$	−38.3546			−1.49408			−0.747041	−	0.664778i	$-0.768526\pi$
$659$	−38.3546			−1.49408			−0.747041	+	0.664778i	$0.768526\pi$
$660$	25.1957	−	43.6402i	0.980741	−	1.69869i
$661$	−14.1377	−	24.4873i	−0.549895	−	0.952445i	−0.998281	−	0.0586056i	$-0.981335\pi$
$661$	−14.1377	−	24.4873i	−0.549895	−	0.952445i	0.448387	−	0.893840i	$-0.351999\pi$
$662$	−4.98943	−	8.64195i	−0.193920	−	0.335879i
$663$	−0.298482	+	0.516987i	−0.0115921	+	0.0200781i
$664$	28.3672			1.10086
$665$	4.38636	−	10.8176i	0.170096	−	0.419489i
$666$	23.4157			0.907339
$667$	−6.03398	+	10.4512i	−0.233637	+	0.404671i
$668$	52.6578	+	91.2061i	2.03739	+	3.52887i
$669$	12.4358	+	21.5395i	0.480797	+	0.832764i
$670$	42.8545	−	74.2262i	1.65562	−	2.86761i
$671$	−54.4795			−2.10316
$672$	5.48512	−	0.763885i	0.211593	−	0.0294675i
$673$	21.8417			0.841937			0.420969	−	0.907075i	$-0.361690\pi$
$673$	21.8417			0.841937			0.420969	+	0.907075i	$0.361690\pi$
$674$	−28.8423	+	49.9563i	−1.11096	+	1.92424i
$675$	0.215950	+	0.374037i	0.00831194	+	0.0143967i
$676$	26.5525	+	45.9904i	1.02125	+	1.76886i
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	−0.917899	−	0.396813i	$-0.870116\pi$
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	0.802600	+	0.596518i	$0.203449\pi$
$678$	−40.8590			−1.56918
$679$	28.4035	+	36.4487i	1.09002	+	1.39877i
$680$	12.7682			0.489636
$681$	−4.16368	+	7.21171i	−0.159553	+	0.276353i
$682$	41.2805	+	71.4999i	1.58071	+	2.73787i
$683$	−6.80646	−	11.7891i	−0.260442	−	0.451099i	0.705917	−	0.708294i	$-0.250535\pi$
$683$	−6.80646	−	11.7891i	−0.260442	−	0.451099i	−0.966359	+	0.257195i	$0.917202\pi$
$684$	−3.97553	+	6.88582i	−0.152008	+	0.263286i
$685$	2.03169			0.0776271
$686$	4.99254	−	45.8446i	0.190616	−	1.75035i
$687$	−17.0257			−0.649570
$688$	−29.7062	+	51.4527i	−1.13254	+	1.96161i
$689$	−3.26273	−	5.65122i	−0.124300	−	0.215294i
$690$	−12.0691	−	20.9042i	−0.459462	−	0.795811i
$691$	10.9400	−	18.9487i	0.416178	−	0.720842i	−0.579373	−	0.815062i	$-0.696703\pi$
$691$	10.9400	−	18.9487i	0.416178	−	0.720842i	0.995551	+	0.0942206i	$0.0300359\pi$
$692$	69.4415			2.63977
$693$	8.37164	+	10.7429i	0.318012	+	0.408089i
$694$	14.7222			0.558846
$695$	−14.4195	+	24.9753i	−0.546963	+	0.947368i
$696$	7.94747	+	13.7654i	0.301248	+	0.521777i
$697$	1.04659	+	1.81275i	0.0396426	+	0.0686630i
$698$	32.9283	−	57.0335i	1.24635	−	2.15875i
$699$	15.3997			0.582469
$700$	4.75364	−	0.662015i	0.179671	−	0.0250218i
$701$	−23.2153			−0.876829			−0.438414	−	0.898773i	$-0.644460\pi$
$701$	−23.2153			−0.876829			−0.438414	+	0.898773i	$0.644460\pi$
$702$	0.743224	−	1.28730i	0.0280512	−	0.0485861i
$703$	8.90095	+	15.4169i	0.335706	+	0.581459i
$704$	−13.5637	−	23.4931i	−0.511203	−	0.885429i
$705$	−5.10767	+	8.84674i	−0.192366	+	0.333188i
$706$	10.7838			0.405854
$707$	−15.0741	+	37.1758i	−0.566922	+	1.39814i
$708$	−13.4911			−0.507027
$709$	−1.28712	+	2.22935i	−0.0483387	+	0.0837251i	−0.889182	−	0.457553i	$-0.848726\pi$
$709$	−1.28712	+	2.22935i	−0.0483387	+	0.0837251i	0.840844	+	0.541278i	$0.182059\pi$
$710$	20.0513	+	34.7299i	0.752512	+	1.30339i
$711$	3.07982	+	5.33441i	0.115502	+	0.200056i
$712$	1.08111	−	1.87254i	0.0405164	−	0.0701764i
$713$	26.7908			1.00332
$714$	−2.47553	+	6.10514i	−0.0926444	+	0.228479i
$715$	−7.16211			−0.267848
$716$	−9.59783	+	16.6239i	−0.358688	+	0.621265i
$717$	6.04771	+	10.4749i	0.225856	+	0.391194i
$718$	1.73981	+	3.01343i	0.0649290	+	0.112460i
$719$	−9.41387	+	16.3053i	−0.351078	+	0.608085i	−0.986439	−	0.164130i	$-0.947518\pi$
$719$	−9.41387	+	16.3053i	−0.351078	+	0.608085i	0.635360	+	0.772216i	$0.280852\pi$
$720$	−12.2147			−0.455216
$721$	−36.1115	+	5.02907i	−1.34486	+	0.187292i
$722$	38.3869			1.42861
$723$	7.39732	−	12.8125i	0.275109	−	0.476503i
$724$	−48.9603	−	84.8017i	−1.81959	−	3.15163i
$725$	0.626558	+	1.08523i	0.0232698	+	0.0403044i
$726$	−19.2965	+	33.4226i	−0.716162	+	1.24043i
$727$	−16.5235			−0.612823			−0.306411	−	0.951899i	$-0.599128\pi$
$727$	−16.5235			−0.612823			−0.306411	+	0.951899i	$0.599128\pi$
$728$	−5.31857	−	6.82505i	−0.197119	−	0.252953i
$729$	1.00000			0.0370370
$730$	−1.25943	+	2.18140i	−0.0466137	+	0.0807372i
$731$	−5.66812	−	9.81748i	−0.209643	−	0.363113i
$732$	22.2255	+	38.4957i	0.821477	+	1.42284i
$733$	8.03661	−	13.9198i	0.296839	−	0.514140i	−0.678572	−	0.734534i	$-0.737401\pi$
$733$	8.03661	−	13.9198i	0.296839	−	0.514140i	0.975411	+	0.220394i	$0.0707342\pi$
$734$	4.13258			0.152536
$735$	−3.98644	+	15.8200i	−0.147042	+	0.583528i
$736$	8.70634			0.320920
$737$	−38.0134	+	65.8411i	−1.40024	+	2.42529i
$738$	−2.60603	−	4.51377i	−0.0959293	−	0.166154i
$739$	3.17347	+	5.49661i	0.116738	+	0.202196i	0.918473	−	0.395483i	$-0.129423\pi$
$739$	3.17347	+	5.49661i	0.116738	+	0.202196i	−0.801735	+	0.597679i	$0.796090\pi$
$740$	−46.0273	+	79.7217i	−1.69200	+	2.93063i
$741$	1.13008			0.0415145
$742$	−44.2648	−	56.8027i	−1.62501	−	2.08529i
$743$	8.14793			0.298918			0.149459	−	0.988768i	$-0.452247\pi$
$743$	8.14793			0.298918			0.149459	+	0.988768i	$0.452247\pi$
$744$	17.6433	−	30.5591i	0.646835	−	1.12035i
$745$	−5.96957	−	10.3396i	−0.218708	−	0.378814i
$746$	2.29094	+	3.96802i	0.0838772	+	0.145280i
$747$	2.58901	−	4.48430i	0.0947270	−	0.164072i
$748$	−21.6212			−0.790550
$749$	−2.30971	+	0.321662i	−0.0843951	+	0.0117533i
$750$	26.5102			0.968014
$751$	−18.5765	+	32.1754i	−0.677864	+	1.17410i	0.297758	+	0.954641i	$0.403761\pi$
$751$	−18.5765	+	32.1754i	−0.677864	+	1.17410i	−0.975623	+	0.219454i	$0.929572\pi$
$752$	−11.4856	−	19.8937i	−0.418838	−	0.725448i
$753$	−5.74404	−	9.94897i	−0.209324	−	0.362560i
$754$	2.15639	−	3.73497i	0.0785310	−	0.136020i
$755$	8.70996			0.316988
$756$	4.17572	−	10.2981i	0.151869	−	0.374540i
$757$	9.61543			0.349479			0.174739	−	0.984615i	$-0.444092\pi$
$757$	9.61543			0.349479			0.174739	+	0.984615i	$0.444092\pi$
$758$	−5.73464	+	9.93268i	−0.208291	+	0.360771i
$759$	10.7057	+	18.5427i	0.388591	+	0.673059i
$760$	−12.0853	−	20.9324i	−0.438381	−	0.759299i
$761$	0.0792099	−	0.137196i	0.00287136	−	0.00497334i	−0.864586	−	0.502485i	$-0.832419\pi$
$761$	0.0792099	−	0.137196i	0.00287136	−	0.00497334i	0.867458	+	0.497511i	$0.165753\pi$
$762$	13.9984			0.507110
$763$	−13.8064	+	34.0492i	−0.499824	+	1.23266i
$764$	76.7104			2.77529
$765$	1.16532	−	2.01840i	0.0421323	−	0.0729753i
$766$	−14.1574	−	24.5213i	−0.511527	−	0.885990i
$767$	0.958743	+	1.66059i	0.0346182	+	0.0599605i
$768$	−16.2790	+	28.1960i	−0.587418	+	1.01744i
$769$	25.6975			0.926674			0.463337	−	0.886182i	$-0.346652\pi$
$769$	25.6975			0.926674			0.463337	+	0.886182i	$0.346652\pi$
$770$	−78.2836	+	10.9022i	−2.82115	+	0.392887i
$771$	−7.85522			−0.282899
$772$	0.188819	−	0.327044i	0.00679575	−	0.0117706i
$773$	15.7495	+	27.2790i	0.566472	+	0.981158i	0.996911	+	0.0785385i	$0.0250254\pi$
$773$	15.7495	+	27.2790i	0.566472	+	0.981158i	−0.430439	+	0.902620i	$0.641641\pi$
$774$	14.1137	+	24.4456i	0.507306	+	0.878679i
$775$	1.39095	−	2.40920i	0.0499644	−	0.0865410i
$776$	95.6817			3.43477
$777$	−15.2933	−	19.6251i	−0.548643	−	0.704045i
$778$	−8.10150			−0.290453
$779$	1.98125	−	3.43162i	0.0709856	−	0.122951i
$780$	2.92186	+	5.06080i	0.104619	+	0.181206i
$781$	−17.7861	−	30.8065i	−0.636438	−	1.10234i
$782$	−5.17843	+	8.96930i	−0.185180	+	0.320742i
$783$	2.90140			0.103687
$784$	−26.3262	−	25.5505i	−0.940220	−	0.912519i
$785$	8.43048			0.300897
$786$	−10.5125	+	18.2082i	−0.374968	+	0.649464i
$787$	−17.6356	−	30.5458i	−0.628642	−	1.08884i	−0.987824	−	0.155573i	$-0.950278\pi$
$787$	−17.6356	−	30.5458i	−0.628642	−	1.08884i	0.359182	−	0.933267i	$-0.383056\pi$
$788$	−9.44111	−	16.3525i	−0.336326	−	0.582533i
$789$	7.82870	−	13.5597i	0.278709	−	0.482738i
$790$	−35.7464			−1.27180
$791$	26.6859	+	34.2446i	0.948840	+	1.21760i
$792$	28.2012			1.00209
$793$	3.15890	−	5.47137i	0.112176	−	0.194294i
$794$	0.165539	+	0.286722i	0.00587476	+	0.0101754i
$795$	12.7382	+	22.0633i	0.451778	+	0.782503i
$796$	30.0851	−	52.1090i	1.06634	−	1.84695i
$797$	2.97165			0.105261			0.0526306	−	0.998614i	$-0.483239\pi$
$797$	2.97165			0.105261			0.0526306	+	0.998614i	$0.483239\pi$
$798$	12.3521	−	1.72021i	0.437258	−	0.0608947i
$799$	4.38305			0.155061
$800$	0.452025	−	0.782930i	0.0159815	−	0.0276808i
$801$	−0.197342	−	0.341806i	−0.00697272	−	0.0120771i
$802$	−12.6783	−	21.9595i	−0.447687	−	0.775416i
$803$	1.11716	−	1.93497i	0.0394236	−	0.0682837i
$804$	62.0318			2.18769
$805$	−9.63763	+	23.7683i	−0.339682	+	0.837722i
$806$	−9.57431			−0.337241
$807$	14.3835	−	24.9129i	0.506322	−	0.876975i
$808$	41.5325	+	71.9363i	1.46111	+	2.53071i
$809$	−23.0577	−	39.9371i	−0.810665	−	1.40411i	−0.912399	−	0.409302i	$-0.865772\pi$
$809$	−23.0577	−	39.9371i	−0.810665	−	1.40411i	0.101734	−	0.994812i	$-0.467561\pi$
$810$	−2.90166	+	5.02583i	−0.101954	+	0.176590i
$811$	−28.0004			−0.983227			−0.491614	−	0.870813i	$-0.663593\pi$
$811$	−28.0004			−0.983227			−0.491614	+	0.870813i	$0.663593\pi$
$812$	12.1154	−	29.8790i	0.425168	−	1.04855i
$813$	4.86925			0.170772
$814$	60.2688	−	104.389i	2.11242	−	3.65882i
$815$	−6.68811	−	11.5842i	−0.234274	−	0.405775i
$816$	2.62046	+	4.53877i	0.0917345	+	0.158889i
$817$	−10.7300	+	18.5849i	−0.375396	+	0.650204i
$818$	35.0178			1.22437
$819$	−1.56432	+	0.217855i	−0.0546619	+	0.00761248i
$820$	20.4903			0.715553
$821$	−7.06991	+	12.2454i	−0.246741	+	0.427369i	−0.962620	−	0.270856i	$-0.912693\pi$
$821$	−7.06991	+	12.2454i	−0.246741	+	0.427369i	0.715878	+	0.698225i	$0.246027\pi$
$822$	1.08531	+	1.87981i	0.0378545	+	0.0655659i
$823$	16.8643	+	29.2098i	0.587852	+	1.01819i	0.994513	+	0.104611i	$0.0333597\pi$
$823$	16.8643	+	29.2098i	0.587852	+	1.01819i	−0.406661	+	0.913579i	$0.633307\pi$
$824$	−37.7477	+	65.3809i	−1.31500	+	2.27765i
$825$	2.22331			0.0774058
$826$	13.0070	+	16.6913i	0.452573	+	0.580764i
$827$	−43.8428			−1.52456			−0.762282	−	0.647245i	$-0.775921\pi$
$827$	−43.8428			−1.52456			−0.762282	+	0.647245i	$0.775921\pi$
$828$	8.73497	−	15.1294i	0.303561	−	0.525783i
$829$	−15.4144	−	26.6986i	−0.535365	−	0.927279i	−0.999146	−	0.0413291i	$-0.986841\pi$
$829$	−15.4144	−	26.6986i	−0.535365	−	0.927279i	0.463781	−	0.885950i	$-0.346493\pi$
$830$	15.0249	+	26.0239i	0.521521	+	0.903301i
$831$	9.62936	−	16.6785i	0.334039	−	0.578572i
$832$	3.14588			0.109064
$833$	6.73364	−	1.91261i	0.233307	−	0.0662682i
$834$	−30.8110			−1.06690
$835$	−29.2196	+	50.6099i	−1.01119	+	1.75143i
$836$	20.4650	+	35.4464i	0.707796	+	1.22594i
$837$	−3.22053	−	5.57813i	−0.111318	−	0.192808i
$838$	33.0840	−	57.3032i	1.14287	−	1.97951i
$839$	−0.689347			−0.0237989			−0.0118995	−	0.999929i	$-0.503788\pi$
$839$	−0.689347			−0.0237989			−0.0118995	+	0.999929i	$0.503788\pi$
$840$	20.7645	+	26.6461i	0.716445	+	0.919377i
$841$	−20.5819			−0.709721
$842$	−13.7474	+	23.8111i	−0.473765	+	0.820586i
$843$	7.31470	+	12.6694i	0.251932	+	0.436358i
$844$	−36.8669	−	63.8553i	−1.26901	−	2.19799i
$845$	−14.7339	+	25.5199i	−0.506862	+	0.877910i
$846$	−10.9138			−0.375226
$847$	40.6150	−	5.65624i	1.39555	−	0.194351i
$848$	−57.2889			−1.96731
$849$	5.99015	−	10.3752i	0.205581	−	0.356078i
$850$	0.537718	+	0.931356i	0.0184436	+	0.0319452i
$851$	−19.5570	−	33.8738i	−0.670406	−	1.16118i
$852$	−14.5121	+	25.1357i	−0.497176	+	0.861134i
$853$	−8.18346			−0.280196			−0.140098	−	0.990138i	$-0.544742\pi$
$853$	−8.18346			−0.280196			−0.140098	+	0.990138i	$0.544742\pi$
$854$	26.1990	−	64.6119i	0.896512	−	2.21097i
$855$	−4.41201			−0.150888
$856$	−2.41436	+	4.18180i	−0.0825211	+	0.142931i
$857$	−25.5105	−	44.1855i	−0.871423	−	1.50935i	−0.860525	−	0.509408i	$-0.829864\pi$
$857$	−25.5105	−	44.1855i	−0.871423	−	1.50935i	−0.0108975	−	0.999941i	$-0.503469\pi$
$858$	−3.82592	−	6.62669i	−0.130615	−	0.226231i
$859$	−9.77387	+	16.9288i	−0.333480	+	0.577605i	−0.983192	−	0.182576i	$-0.941556\pi$
$859$	−9.77387	+	16.9288i	−0.333480	+	0.577605i	0.649712	+	0.760181i	$0.274890\pi$
$860$	−110.971			−3.78408
$861$	−2.08102	+	5.13220i	−0.0709209	+	0.174905i
$862$	15.9751			0.544114
$863$	0.427888	−	0.741123i	0.0145655	−	0.0252281i	−0.858651	−	0.512561i	$-0.828697\pi$
$863$	0.427888	−	0.741123i	0.0145655	−	0.0252281i	0.873216	+	0.487333i	$0.162030\pi$
$864$	−1.04659	−	1.81275i	−0.0356059	−	0.0616712i
$865$	19.2664	+	33.3704i	0.655077	+	1.13463i
$866$	−26.1186	+	45.2387i	−0.887545	+	1.53727i
$867$	−1.00000			−0.0339618
$868$	−70.8924	+	9.87283i	−2.40625	+	0.335106i
$869$	31.7082			1.07563
$870$	−8.41887	+	14.5819i	−0.285426	+	0.494373i
$871$	−4.40828	−	7.63536i	−0.149369	−	0.258714i
$872$	38.0394	+	65.8862i	1.28818	+	2.23119i
$873$	8.73267	−	15.1254i	0.295556	−	0.511918i
$874$	19.6060			0.663182
$875$	−17.3143	−	22.2186i	−0.585331	−	0.751126i
$876$	−1.82302			−0.0615942
$877$	5.01076	−	8.67889i	0.169201	−	0.293065i	−0.768938	−	0.639323i	$-0.779214\pi$
$877$	5.01076	−	8.67889i	0.169201	−	0.293065i	0.938139	+	0.346258i	$0.112548\pi$
$878$	−8.88353	−	15.3867i	−0.299805	−	0.519277i
$879$	−3.54401	−	6.13841i	−0.119537	−	0.207043i
$880$	−31.4391	+	54.4541i	−1.05981	+	1.83565i
$881$	32.1954			1.08469			0.542345	−	0.840156i	$-0.317537\pi$
$881$	32.1954			1.08469			0.542345	+	0.840156i	$0.317537\pi$
$882$	−16.7668	+	4.76243i	−0.564568	+	0.160359i
$883$	19.5142			0.656706			0.328353	−	0.944555i	$-0.393506\pi$
$883$	19.5142			0.656706			0.328353	+	0.944555i	$0.393506\pi$
$884$	1.25367	−	2.17142i	0.0421654	−	0.0730327i
$885$	−3.74308	−	6.48321i	−0.125822	−	0.217931i
$886$	29.6931	+	51.4300i	0.997560	+	1.72782i
$887$	−0.141967	+	0.245894i	−0.00476678	+	0.00825630i	−0.868399	−	0.495866i	$-0.834851\pi$
$887$	−0.141967	+	0.245894i	−0.00476678	+	0.00825630i	0.863632	+	0.504122i	$0.168184\pi$
$888$	−51.5179			−1.72883
$889$	−9.14267	−	11.7323i	−0.306635	−	0.393489i
$890$	2.29047			0.0767769
$891$	2.57387	−	4.45807i	0.0862278	−	0.149351i
$892$	−52.2323	−	90.4689i	−1.74887	−	3.02912i
$893$	−4.14866	−	7.18568i	−0.138830	−	0.240460i
$894$	6.37776	−	11.0466i	0.213304	−	0.369454i
$895$	−10.6516			−0.356044
$896$	45.3555	−	6.31643i	1.51522	−	0.211017i
$897$	−2.48299			−0.0829048
$898$	39.4978	−	68.4121i	1.31806	−	2.28294i
$899$	−9.34405	−	16.1844i	−0.311641	−	0.539779i
$900$	−0.907023	−	1.57101i	−0.0302341	−	0.0523670i
$901$	5.46554	−	9.46659i	0.182083	−	0.315378i
$902$	−26.8303			−0.893351
$903$	11.2703	−	27.7948i	0.375053	−	0.924955i
$904$	89.8957			2.98989
$905$	27.1679	−	47.0561i	0.903090	−	1.56420i
$906$	4.65277	+	8.05883i	0.154578	+	0.267737i
$907$	−6.85534	−	11.8738i	−0.227628	−	0.394263i	0.729477	−	0.684006i	$-0.239764\pi$
$907$	−6.85534	−	11.8738i	−0.227628	−	0.394263i	−0.957105	+	0.289743i	$0.906430\pi$
$908$	17.4881	−	30.2902i	0.580362	−	1.00522i
$909$	15.1623			0.502902
$910$	3.44423	−	8.49416i	0.114175	−	0.281579i
$911$	−24.6522			−0.816762			−0.408381	−	0.912811i	$-0.633907\pi$
$911$	−24.6522			−0.816762			−0.408381	+	0.912811i	$0.633907\pi$
$912$	4.96065	−	8.59210i	0.164264	−	0.284513i
$913$	−13.3276	−	23.0840i	−0.441078	−	0.763969i
$914$	34.5134	+	59.7790i	1.14160	+	1.97731i
$915$	−12.3328	+	21.3611i	−0.407711	+	0.706176i
$916$	71.5103			2.36277
$917$	22.1265	−	3.08144i	0.730681	−	0.101758i
$918$	2.49001			0.0821825
$919$	2.82238	−	4.88850i	0.0931017	−	0.161257i	−0.815713	−	0.578457i	$-0.803655\pi$
$919$	2.82238	−	4.88850i	0.0931017	−	0.161257i	0.908815	+	0.417200i	$0.136988\pi$
$920$	26.5537	+	45.9924i	0.875450	+	1.51632i
$921$	15.3736	+	26.6279i	0.506578	+	0.877418i
$922$	−28.1456	+	48.7497i	−0.926927	+	1.60548i
$923$	4.12519			0.135782
$924$	−35.1621	−	45.1217i	−1.15675	−	1.48440i
$925$	−4.06153			−0.133542
$926$	9.00239	−	15.5926i	0.295837	−	0.512404i
$927$	6.89030	+	11.9343i	0.226307	+	0.391975i
$928$	−3.03658	−	5.25952i	−0.0996808	−	0.172652i
$929$	−14.7322	+	25.5169i	−0.483348	+	0.837184i	−0.999817	−	0.0191223i	$-0.993913\pi$
$929$	−14.7322	+	25.5169i	−0.483348	+	0.837184i	0.516469	+	0.856306i	$0.327246\pi$
$930$	37.3796			1.22573
$931$	−9.50913	−	9.22896i	−0.311649	−	0.302467i
$932$	−64.6809			−2.11869
$933$	16.4415	−	28.4776i	0.538271	−	0.932313i
$934$	−38.4640	−	66.6216i	−1.25858	−	2.17993i
$935$	−5.99877	−	10.3902i	−0.196181	−	0.339795i
$936$	−1.63520	+	2.83225i	−0.0534482	+	0.0925749i
$937$	0.947116			0.0309409			0.0154705	−	0.999880i	$-0.495075\pi$
$937$	0.947116			0.0309409			0.0154705	+	0.999880i	$0.495075\pi$
$938$	−59.8061	−	76.7461i	−1.95274	−	2.50585i
$939$	2.35409			0.0768230
$940$	21.4529	−	37.1576i	0.699718	−	1.21195i
$941$	2.77876	+	4.81295i	0.0905850	+	0.156898i	0.907757	−	0.419495i	$-0.137793\pi$
$941$	2.77876	+	4.81295i	0.0905850	+	0.156898i	−0.817172	+	0.576393i	$0.804460\pi$
$942$	4.50347	+	7.80024i	0.146731	+	0.254145i
$943$	−4.35317	+	7.53991i	−0.141759	+	0.245533i
$944$	16.8342			0.547905
$945$	6.10736	−	0.850541i	0.198673	−	0.0276681i
$946$	145.307			4.72434
$947$	−15.1118	+	26.1744i	−0.491068	+	0.850554i	−0.999947	−	0.0102836i	$-0.996727\pi$
$947$	−15.1118	+	26.1744i	−0.491068	+	0.850554i	0.508879	+	0.860838i	$0.330060\pi$
$948$	−12.9357	−	22.4053i	−0.420132	−	0.727690i
$949$	0.129553	+	0.224392i	0.00420546	+	0.00728407i
$950$	1.01792	−	1.76310i	0.0330258	−	0.0572024i
$951$	−30.5798			−0.991616
$952$	5.44652	−	13.4322i	0.176523	−	0.435340i
$953$	47.8740			1.55079			0.775395	−	0.631476i	$-0.217551\pi$
$953$	47.8740			1.55079			0.775395	+	0.631476i	$0.217551\pi$
$954$	−13.6092	+	23.5719i	−0.440615	+	0.763168i
$955$	21.2832	+	36.8635i	0.688707	+	1.19288i
$956$	−25.4013	−	43.9963i	−0.821536	−	1.42294i
$957$	7.46781	−	12.9346i	0.241400	−	0.418117i
$958$	54.3100			1.75468
$959$	0.866662	−	2.13736i	0.0279860	−	0.0690189i
$960$	−12.2820			−0.396400
$961$	−5.24368	+	9.08232i	−0.169151	+	0.292978i
$962$	6.98916	+	12.1056i	0.225340	+	0.390300i
$963$	0.440707	+	0.763327i	0.0142016	+	0.0245979i
$964$	−31.0698	+	53.8145i	−1.00069	+	1.73325i
$965$	0.209550			0.00674565
$966$	−27.1397	+	3.77961i	−0.873207	+	0.121607i
$967$	−32.5941			−1.04816			−0.524078	−	0.851671i	$-0.675590\pi$
$967$	−32.5941			−1.04816			−0.524078	+	0.851671i	$0.675590\pi$
$968$	42.4552	−	73.5345i	1.36456	−	2.36349i
$969$	0.946522	+	1.63942i	0.0304067	+	0.0526659i
$970$	50.6785	+	87.7777i	1.62719	+	2.81837i
$971$	30.2776	−	52.4423i	0.971654	−	1.68295i	0.281092	−	0.959681i	$-0.409303\pi$
$971$	30.2776	−	52.4423i	0.971654	−	1.68295i	0.690562	−	0.723273i	$-0.257363\pi$
$972$	−4.20014			−0.134720
$973$	20.1233	+	25.8232i	0.645123	+	0.827853i
$974$	−11.3500			−0.363679
$975$	−0.128915	+	0.223287i	−0.00412858	+	0.00715090i
$976$	−27.7329	−	48.0347i	−0.887707	−	1.53755i
$977$	1.11354	+	1.92871i	0.0356253	+	0.0617048i	0.883288	−	0.468830i	$-0.155324\pi$
$977$	1.11354	+	1.92871i	0.0356253	+	0.0617048i	−0.847663	+	0.530535i	$0.821991\pi$
$978$	7.14543	−	12.3763i	0.228486	−	0.395749i
$979$	−2.03172			−0.0649342
$980$	16.7436	−	66.4462i	0.534856	−	2.12254i
$981$	13.8871			0.443381
$982$	−1.99177	+	3.44984i	−0.0635599	+	0.110089i
$983$	16.4458	+	28.4850i	0.524541	+	0.908531i	0.999592	+	0.0285730i	$0.00909632\pi$
$983$	16.4458	+	28.4850i	0.524541	+	0.908531i	−0.475051	+	0.879958i	$0.657570\pi$
$984$	5.73364	+	9.93096i	0.182782	+	0.316587i
$985$	5.23884	−	9.07393i	0.166923	−	0.289120i
$986$	7.22450			0.230075
$987$	7.12806	+	9.14707i	0.226889	+	0.291154i
$988$	−4.74650			−0.151006
$989$	23.5758	−	40.8345i	0.749667	−	1.29846i
$990$	14.9370	+	25.8716i	0.474729	+	0.822254i
$991$	19.6589	+	34.0503i	0.624487	+	1.08164i	0.988640	+	0.150304i	$0.0480252\pi$
$991$	19.6589	+	34.0503i	0.624487	+	1.08164i	−0.364153	+	0.931339i	$0.618641\pi$
$992$	−6.74118	+	11.6761i	−0.214033	+	0.370716i
$993$	4.00756			0.127176
$994$	45.0894	−	6.27937i	1.43015	−	0.199170i
$995$	33.3882			1.05848
$996$	−10.8742	+	18.8347i	−0.344563	+	0.596801i
$997$	19.3188	+	33.4611i	0.611832	+	1.05972i	0.990931	+	0.134368i	$0.0429006\pi$
$997$	19.3188	+	33.4611i	0.611832	+	1.05972i	−0.379099	+	0.925356i	$0.623766\pi$
$998$	−31.3157	−	54.2403i	−0.991280	−	1.71695i
$999$	−4.70193	+	8.14397i	−0.148762	+	0.257664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.i.f.205.5	✓	10
3.2	odd	2		1071.2.i.g.919.1		10
7.2	even	3		2499.2.a.ba.1.1		5
7.4	even	3	inner	357.2.i.f.256.5	yes	10
7.5	odd	6		2499.2.a.bb.1.1		5
21.2	odd	6		7497.2.a.bv.1.5		5
21.5	even	6		7497.2.a.bw.1.5		5
21.11	odd	6		1071.2.i.g.613.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.i.f.205.5	✓	10	1.1	even	1	trivial
357.2.i.f.256.5	yes	10	7.4	even	3	inner
1071.2.i.g.613.1		10	21.11	odd	6
1071.2.i.g.919.1		10	3.2	odd	2
2499.2.a.ba.1.1		5	7.2	even	3
2499.2.a.bb.1.1		5	7.5	odd	6
7497.2.a.bv.1.5		5	21.2	odd	6
7497.2.a.bw.1.5		5	21.5	even	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24500 - 2.15641i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.10007 - 3.63743i) q^{4} +(1.16532 - 2.01840i) q^{5} +2.49001 q^{6} +(-1.62628 - 2.08692i) q^{7} -5.47838 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.24500 - 2.15641i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-2.10007 - 3.63743i) q^{4} +(1.16532 - 2.01840i) q^{5} +2.49001 q^{6} +(-1.62628 - 2.08692i) q^{7} -5.47838 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.90166 - 5.02583i) q^{10} +(2.57387 + 4.45807i) q^{11} +(2.10007 - 3.63743i) q^{12} -0.596965 q^{13} +(-6.52497 + 0.908700i) q^{14} +2.33064 q^{15} +(-2.62046 + 4.53877i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(1.24500 + 2.15641i) q^{18} +(-0.946522 + 1.63942i) q^{19} -9.78904 q^{20} +(0.994185 - 2.45186i) q^{21} +12.8179 q^{22} +(2.07968 - 3.60212i) q^{23} +(-2.73919 - 4.74442i) q^{24} +(-0.215950 - 0.374037i) q^{25} +(-0.743224 + 1.28730i) q^{26} -1.00000 q^{27} +(-4.17572 + 10.2981i) q^{28} -2.90140 q^{29} +(2.90166 - 5.02583i) q^{30} +(3.22053 + 5.57813i) q^{31} +(1.04659 + 1.81275i) q^{32} +(-2.57387 + 4.45807i) q^{33} -2.49001 q^{34} +(-6.10736 + 0.850541i) q^{35} +4.20014 q^{36} +(4.70193 - 8.14397i) q^{37} +(2.35685 + 4.08218i) q^{38} +(-0.298482 - 0.516987i) q^{39} +(-6.38408 + 11.0575i) q^{40} -2.09319 q^{41} +(-4.04944 - 5.19644i) q^{42} +11.3362 q^{43} +(10.8106 - 18.7245i) q^{44} +(1.16532 + 2.01840i) q^{45} +(-5.17843 - 8.96930i) q^{46} +(-2.19153 + 3.79584i) q^{47} -5.24092 q^{48} +(-1.71045 + 6.78781i) q^{49} -1.07544 q^{50} +(0.500000 - 0.866025i) q^{51} +(1.25367 + 2.17142i) q^{52} +(5.46554 + 9.46659i) q^{53} +(-1.24500 + 2.15641i) q^{54} +11.9975 q^{55} +(8.90936 + 11.4329i) q^{56} -1.89304 q^{57} +(-3.61225 + 6.25660i) q^{58} +(-1.60603 - 2.78172i) q^{59} +(-4.89452 - 8.47756i) q^{60} +(-5.29160 + 9.16532i) q^{61} +16.0383 q^{62} +(2.62046 - 0.364938i) q^{63} -5.26979 q^{64} +(-0.695656 + 1.20491i) q^{65} +(6.40895 + 11.1006i) q^{66} +(7.38448 + 12.7903i) q^{67} +(-2.10007 + 3.63743i) q^{68} +4.15937 q^{69} +(-5.76958 + 14.2289i) q^{70} -6.91028 q^{71} +(2.73919 - 4.74442i) q^{72} +(-0.217019 - 0.375888i) q^{73} +(-11.7078 - 20.2786i) q^{74} +(0.215950 - 0.374037i) q^{75} +7.95106 q^{76} +(5.11780 - 12.6215i) q^{77} -1.48645 q^{78} +(3.07982 - 5.33441i) q^{79} +(6.10736 + 10.5783i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.60603 + 4.51377i) q^{82} -5.17802 q^{83} +(-11.0063 + 1.53279i) q^{84} -2.33064 q^{85} +(14.1137 - 24.4456i) q^{86} +(-1.45070 - 2.51268i) q^{87} +(-14.1006 - 24.4230i) q^{88} +(-0.197342 + 0.341806i) q^{89} +5.80332 q^{90} +(0.970830 + 1.24582i) q^{91} -17.4699 q^{92} +(-3.22053 + 5.57813i) q^{93} +(5.45692 + 9.45166i) q^{94} +(2.20601 + 3.82091i) q^{95} +(-1.04659 + 1.81275i) q^{96} -17.4653 q^{97} +(12.5078 + 12.1393i) q^{98} -5.14774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 5 q^{3} - 8 q^{4} - q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 - q^5 + 4 * q^6 - 5 * q^7 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 8 q^{4} - q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{9} - 13 q^{10} + 11 q^{11} + 8 q^{12} + 14 q^{13} + 3 q^{14} - 2 q^{15} + 2 q^{16} - 5 q^{17} + 2 q^{18} - 9 q^{19} + 24 q^{20} - 7 q^{21} + 10 q^{22} + 23 q^{23} - 14 q^{25} - 18 q^{26} - 10 q^{27} + 7 q^{28} - 36 q^{29} + 13 q^{30} - 9 q^{31} - 3 q^{32} - 11 q^{33} - 4 q^{34} - 5 q^{35} + 16 q^{36} + 7 q^{39} - 31 q^{40} + 6 q^{41} - 3 q^{42} + 24 q^{43} + 33 q^{44} - q^{45} - 13 q^{46} - 11 q^{47} + 4 q^{48} + 3 q^{49} + 48 q^{50} + 5 q^{51} - 5 q^{52} + 3 q^{53} - 2 q^{54} - 20 q^{55} - 27 q^{56} - 18 q^{57} + 34 q^{58} + 14 q^{59} + 12 q^{60} - 29 q^{61} - 10 q^{62} - 2 q^{63} + 8 q^{65} + 5 q^{66} - 16 q^{67} - 8 q^{68} + 46 q^{69} + 18 q^{70} - 38 q^{71} - 11 q^{73} - 45 q^{74} + 14 q^{75} + 18 q^{76} + 21 q^{77} - 36 q^{78} - q^{79} + 5 q^{80} - 5 q^{81} + 4 q^{82} + 10 q^{83} - 28 q^{84} + 2 q^{85} + 3 q^{86} - 18 q^{87} - 37 q^{88} - 8 q^{89} + 26 q^{90} - 33 q^{91} - 96 q^{92} + 9 q^{93} + 18 q^{94} + 21 q^{95} + 3 q^{96} + 38 q^{97} - 17 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 - q^5 + 4 * q^6 - 5 * q^7 - 5 * q^9 - 13 * q^10 + 11 * q^11 + 8 * q^12 + 14 * q^13 + 3 * q^14 - 2 * q^15 + 2 * q^16 - 5 * q^17 + 2 * q^18 - 9 * q^19 + 24 * q^20 - 7 * q^21 + 10 * q^22 + 23 * q^23 - 14 * q^25 - 18 * q^26 - 10 * q^27 + 7 * q^28 - 36 * q^29 + 13 * q^30 - 9 * q^31 - 3 * q^32 - 11 * q^33 - 4 * q^34 - 5 * q^35 + 16 * q^36 + 7 * q^39 - 31 * q^40 + 6 * q^41 - 3 * q^42 + 24 * q^43 + 33 * q^44 - q^45 - 13 * q^46 - 11 * q^47 + 4 * q^48 + 3 * q^49 + 48 * q^50 + 5 * q^51 - 5 * q^52 + 3 * q^53 - 2 * q^54 - 20 * q^55 - 27 * q^56 - 18 * q^57 + 34 * q^58 + 14 * q^59 + 12 * q^60 - 29 * q^61 - 10 * q^62 - 2 * q^63 + 8 * q^65 + 5 * q^66 - 16 * q^67 - 8 * q^68 + 46 * q^69 + 18 * q^70 - 38 * q^71 - 11 * q^73 - 45 * q^74 + 14 * q^75 + 18 * q^76 + 21 * q^77 - 36 * q^78 - q^79 + 5 * q^80 - 5 * q^81 + 4 * q^82 + 10 * q^83 - 28 * q^84 + 2 * q^85 + 3 * q^86 - 18 * q^87 - 37 * q^88 - 8 * q^89 + 26 * q^90 - 33 * q^91 - 96 * q^92 + 9 * q^93 + 18 * q^94 + 21 * q^95 + 3 * q^96 + 38 * q^97 - 17 * q^98 - 22 * q^99

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