LMFDB - Embedded newform 670.2.e.j.431.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(171,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("670.171");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.e (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:	$5.34997693543$
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} - 2 x^{11} + 17 x^{10} - 18 x^{9} + 172 x^{8} - 170 x^{7} + 887 x^{6} - 312 x^{5} + 2516 x^{4} + \cdots + 289 $ x^12 - 2x^11 + 17x^10 - 18x^9 + 172x^8 - 170x^7 + 887x^6 - 312x^5 + 2516x^4 - 1220x^3 + 3001x^2 + 816*x + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			431.6
Root			$-1.42828 - 2.47386i$ of defining polynomial
Character	$\chi$	$=$	670.431
Dual form			670.2.e.j.171.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +2.85656 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.42828 - 2.47386i) q^{6} +(2.24706 + 3.89203i) q^{7} -1.00000 q^{8} +5.15996 q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +2.85656 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.42828 - 2.47386i) q^{6} +(2.24706 + 3.89203i) q^{7} -1.00000 q^{8} +5.15996 q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.57998 - 2.73660i) q^{11} +(-1.42828 - 2.47386i) q^{12} +(0.503666 - 0.872375i) q^{13} +4.49412 q^{14} -2.85656 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.38990 - 4.13942i) q^{17} +(2.57998 - 4.46866i) q^{18} +(1.11836 - 1.93706i) q^{19} +(0.500000 + 0.866025i) q^{20} +(6.41888 + 11.1178i) q^{21} -3.15996 q^{22} +(-1.98966 + 3.44620i) q^{23} -2.85656 q^{24} +1.00000 q^{25} +(-0.503666 - 0.872375i) q^{26} +6.17006 q^{27} +(2.24706 - 3.89203i) q^{28} +(2.41428 + 4.18166i) q^{29} +(-1.42828 + 2.47386i) q^{30} +(3.72420 + 6.45050i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.51331 - 7.81729i) q^{33} +(-2.38990 - 4.13942i) q^{34} +(-2.24706 - 3.89203i) q^{35} +(-2.57998 - 4.46866i) q^{36} +(0.280396 - 0.485660i) q^{37} +(-1.11836 - 1.93706i) q^{38} +(1.43875 - 2.49199i) q^{39} +1.00000 q^{40} +(-2.45574 - 4.25347i) q^{41} +12.8378 q^{42} -9.06529 q^{43} +(-1.57998 + 2.73660i) q^{44} -5.15996 q^{45} +(1.98966 + 3.44620i) q^{46} +(-6.34989 - 10.9983i) q^{47} +(-1.42828 + 2.47386i) q^{48} +(-6.59858 + 11.4291i) q^{49} +(0.500000 - 0.866025i) q^{50} +(6.82690 - 11.8245i) q^{51} -1.00733 q^{52} -3.55346 q^{53} +(3.08503 - 5.34343i) q^{54} +(1.57998 + 2.73660i) q^{55} +(-2.24706 - 3.89203i) q^{56} +(3.19468 - 5.53334i) q^{57} +4.82856 q^{58} -3.55022 q^{59} +(1.42828 + 2.47386i) q^{60} +(-6.68053 + 11.5710i) q^{61} +7.44840 q^{62} +(11.5947 + 20.0827i) q^{63} +1.00000 q^{64} +(-0.503666 + 0.872375i) q^{65} -9.02662 q^{66} +(4.23827 - 7.00265i) q^{67} -4.77980 q^{68} +(-5.68361 + 9.84429i) q^{69} -4.49412 q^{70} +(-1.95128 - 3.37972i) q^{71} -5.15996 q^{72} +(-6.32323 + 10.9522i) q^{73} +(-0.280396 - 0.485660i) q^{74} +2.85656 q^{75} -2.23673 q^{76} +(7.10062 - 12.2986i) q^{77} +(-1.43875 - 2.49199i) q^{78} +(-6.08596 - 10.5412i) q^{79} +(0.500000 - 0.866025i) q^{80} +2.14530 q^{81} -4.91148 q^{82} +(-6.82278 + 11.8174i) q^{83} +(6.41888 - 11.1178i) q^{84} +(-2.38990 + 4.13942i) q^{85} +(-4.53264 + 7.85077i) q^{86} +(6.89655 + 11.9452i) q^{87} +(1.57998 + 2.73660i) q^{88} -3.52240 q^{89} +(-2.57998 + 4.46866i) q^{90} +4.52707 q^{91} +3.97933 q^{92} +(10.6384 + 18.4263i) q^{93} -12.6998 q^{94} +(-1.11836 + 1.93706i) q^{95} +(1.42828 + 2.47386i) q^{96} +(0.642699 - 1.11319i) q^{97} +(6.59858 + 11.4291i) q^{98} +(-8.15263 - 14.1208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9} - 6 q^{10} + 2 q^{12} + 6 q^{14} + 4 q^{15} - 6 q^{16} + 13 q^{17} + 12 q^{18} - 9 q^{19} + 6 q^{20} + 11 q^{21} - 3 q^{23} + 4 q^{24} + 12 q^{25} - 16 q^{27} + 3 q^{28} - 5 q^{29} + 2 q^{30} + 14 q^{31} + 6 q^{32} + 10 q^{33} - 13 q^{34} - 3 q^{35} - 12 q^{36} + 2 q^{37} + 9 q^{38} + 14 q^{39} + 12 q^{40} + 15 q^{41} + 22 q^{42} + 4 q^{43} - 24 q^{45} + 3 q^{46} - 11 q^{47} + 2 q^{48} - 43 q^{49} + 6 q^{50} + 15 q^{51} - 52 q^{53} - 8 q^{54} - 3 q^{56} + 3 q^{57} - 10 q^{58} + 54 q^{59} - 2 q^{60} - 6 q^{61} + 28 q^{62} - 4 q^{63} + 12 q^{64} + 20 q^{66} - 5 q^{67} - 26 q^{68} + 13 q^{69} - 6 q^{70} - 6 q^{71} - 24 q^{72} - 15 q^{73} - 2 q^{74} - 4 q^{75} + 18 q^{76} - 10 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} + 12 q^{81} + 30 q^{82} - 15 q^{83} + 11 q^{84} - 13 q^{85} + 2 q^{86} + 5 q^{87} - 14 q^{89} - 12 q^{90} + 4 q^{91} + 6 q^{92} + 28 q^{93} - 22 q^{94} + 9 q^{95} - 2 q^{96} + 21 q^{97} + 43 q^{98} - 72 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9 - 6 * q^10 + 2 * q^12 + 6 * q^14 + 4 * q^15 - 6 * q^16 + 13 * q^17 + 12 * q^18 - 9 * q^19 + 6 * q^20 + 11 * q^21 - 3 * q^23 + 4 * q^24 + 12 * q^25 - 16 * q^27 + 3 * q^28 - 5 * q^29 + 2 * q^30 + 14 * q^31 + 6 * q^32 + 10 * q^33 - 13 * q^34 - 3 * q^35 - 12 * q^36 + 2 * q^37 + 9 * q^38 + 14 * q^39 + 12 * q^40 + 15 * q^41 + 22 * q^42 + 4 * q^43 - 24 * q^45 + 3 * q^46 - 11 * q^47 + 2 * q^48 - 43 * q^49 + 6 * q^50 + 15 * q^51 - 52 * q^53 - 8 * q^54 - 3 * q^56 + 3 * q^57 - 10 * q^58 + 54 * q^59 - 2 * q^60 - 6 * q^61 + 28 * q^62 - 4 * q^63 + 12 * q^64 + 20 * q^66 - 5 * q^67 - 26 * q^68 + 13 * q^69 - 6 * q^70 - 6 * q^71 - 24 * q^72 - 15 * q^73 - 2 * q^74 - 4 * q^75 + 18 * q^76 - 10 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 + 12 * q^81 + 30 * q^82 - 15 * q^83 + 11 * q^84 - 13 * q^85 + 2 * q^86 + 5 * q^87 - 14 * q^89 - 12 * q^90 + 4 * q^91 + 6 * q^92 + 28 * q^93 - 22 * q^94 + 9 * q^95 - 2 * q^96 + 21 * q^97 + 43 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	2.85656			1.64924			0.824619	−	0.565688i	$-0.191390\pi$
$3$	2.85656			1.64924			0.824619	+	0.565688i	$0.191390\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.42828	−	2.47386i	0.583094	−	1.00995i
$7$	2.24706	+	3.89203i	0.849310	+	1.47105i	0.881825	+	0.471576i	$0.156315\pi$
$7$	2.24706	+	3.89203i	0.849310	+	1.47105i	−0.0325157	+	0.999471i	$0.510352\pi$
$8$	−1.00000			−0.353553
$9$	5.15996			1.71999
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−1.57998	−	2.73660i	−0.476382	−	0.825117i	0.523252	−	0.852178i	$-0.324719\pi$
$11$	−1.57998	−	2.73660i	−0.476382	−	0.825117i	−0.999634	+	0.0270607i	$0.991385\pi$
$12$	−1.42828	−	2.47386i	−0.412310	−	0.714141i
$13$	0.503666	−	0.872375i	0.139692	−	0.241953i	−0.787688	−	0.616074i	$-0.788722\pi$
$13$	0.503666	−	0.872375i	0.139692	−	0.241953i	0.927380	+	0.374121i	$0.122056\pi$
$14$	4.49412			1.20111
$15$	−2.85656			−0.737562
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.38990	−	4.13942i	0.579635	−	1.00396i	−0.415886	−	0.909417i	$-0.636528\pi$
$17$	2.38990	−	4.13942i	0.579635	−	1.00396i	0.995521	−	0.0945409i	$-0.0301383\pi$
$18$	2.57998	−	4.46866i	0.608107	−	1.05327i
$19$	1.11836	−	1.93706i	0.256570	−	0.444393i	−0.708751	−	0.705459i	$-0.750741\pi$
$19$	1.11836	−	1.93706i	0.256570	−	0.444393i	0.965321	+	0.261067i	$0.0840742\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	6.41888	+	11.1178i	1.40071	+	2.42611i
$22$	−3.15996			−0.673705
$23$	−1.98966	+	3.44620i	−0.414874	+	0.718583i	−0.995415	−	0.0956482i	$-0.969508\pi$
$23$	−1.98966	+	3.44620i	−0.414874	+	0.718583i	0.580541	+	0.814231i	$0.302841\pi$
$24$	−2.85656			−0.583094
$25$	1.00000			0.200000
$26$	−0.503666	−	0.872375i	−0.0987770	−	0.171087i
$27$	6.17006			1.18743
$28$	2.24706	−	3.89203i	0.424655	−	0.735524i
$29$	2.41428	+	4.18166i	0.448321	+	0.776514i	0.998277	−	0.0586792i	$-0.0186889\pi$
$29$	2.41428	+	4.18166i	0.448321	+	0.776514i	−0.549956	+	0.835194i	$0.685356\pi$
$30$	−1.42828	+	2.47386i	−0.260767	+	0.451662i
$31$	3.72420	+	6.45050i	0.668886	+	1.15854i	0.978216	+	0.207590i	$0.0665619\pi$
$31$	3.72420	+	6.45050i	0.668886	+	1.15854i	−0.309330	+	0.950955i	$0.600105\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−4.51331	−	7.81729i	−0.785667	−	1.36081i
$34$	−2.38990	−	4.13942i	−0.409864	−	0.709905i
$35$	−2.24706	−	3.89203i	−0.379823	−	0.657872i
$36$	−2.57998	−	4.46866i	−0.429997	−	0.744776i
$37$	0.280396	−	0.485660i	0.0460968	−	0.0798419i	−0.842056	−	0.539389i	$-0.818655\pi$
$37$	0.280396	−	0.485660i	0.0460968	−	0.0798419i	0.888153	+	0.459548i	$0.151988\pi$
$38$	−1.11836	−	1.93706i	−0.181423	−	0.314233i
$39$	1.43875	−	2.49199i	0.230385	−	0.399038i
$40$	1.00000			0.158114
$41$	−2.45574	−	4.25347i	−0.383522	−	0.664280i	0.608041	−	0.793906i	$-0.291956\pi$
$41$	−2.45574	−	4.25347i	−0.383522	−	0.664280i	−0.991563	+	0.129626i	$0.958622\pi$
$42$	12.8378			1.98091
$43$	−9.06529			−1.38244			−0.691222	−	0.722643i	$-0.742927\pi$
$43$	−9.06529			−1.38244			−0.691222	+	0.722643i	$0.742927\pi$
$44$	−1.57998	+	2.73660i	−0.238191	+	0.412559i
$45$	−5.15996			−0.769201
$46$	1.98966	+	3.44620i	0.293360	+	0.508115i
$47$	−6.34989	−	10.9983i	−0.926227	−	1.60427i	−0.789575	−	0.613654i	$-0.789699\pi$
$47$	−6.34989	−	10.9983i	−0.926227	−	1.60427i	−0.136652	−	0.990619i	$-0.543634\pi$
$48$	−1.42828	+	2.47386i	−0.206155	+	0.357071i
$49$	−6.59858	+	11.4291i	−0.942654	+	1.63272i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	6.82690	−	11.8245i	0.955957	−	1.65577i
$52$	−1.00733			−0.139692
$53$	−3.55346			−0.488105			−0.244053	−	0.969762i	$-0.578477\pi$
$53$	−3.55346			−0.488105			−0.244053	+	0.969762i	$0.578477\pi$
$54$	3.08503	−	5.34343i	0.419819	−	0.727148i
$55$	1.57998	+	2.73660i	0.213044	+	0.369004i
$56$	−2.24706	−	3.89203i	−0.300276	−	0.520094i
$57$	3.19468	−	5.53334i	0.423145	−	0.732909i
$58$	4.82856			0.634021
$59$	−3.55022			−0.462200			−0.231100	−	0.972930i	$-0.574232\pi$
$59$	−3.55022			−0.462200			−0.231100	+	0.972930i	$0.574232\pi$
$60$	1.42828	+	2.47386i	0.184390	+	0.319374i
$61$	−6.68053	+	11.5710i	−0.855354	+	1.48152i	0.0209616	+	0.999780i	$0.493327\pi$
$61$	−6.68053	+	11.5710i	−0.855354	+	1.48152i	−0.876316	+	0.481737i	$0.840006\pi$
$62$	7.44840			0.945948
$63$	11.5947	+	20.0827i	1.46080	+	2.53018i
$64$	1.00000			0.125000
$65$	−0.503666	+	0.872375i	−0.0624720	+	0.108205i
$66$	−9.02662			−1.11110
$67$	4.23827	−	7.00265i	0.517787	−	0.855509i
$67$	4.23827	−	7.00265i	0.517787	−	0.855509i
$68$	−4.77980			−0.579635
$69$	−5.68361	+	9.84429i	−0.684226	+	1.18511i
$70$	−4.49412			−0.537151
$71$	−1.95128	−	3.37972i	−0.231574	−	0.401099i	0.726697	−	0.686958i	$-0.241054\pi$
$71$	−1.95128	−	3.37972i	−0.231574	−	0.401099i	−0.958272	+	0.285859i	$0.907721\pi$
$72$	−5.15996			−0.608107
$73$	−6.32323	+	10.9522i	−0.740078	+	1.28185i	0.212381	+	0.977187i	$0.431878\pi$
$73$	−6.32323	+	10.9522i	−0.740078	+	1.28185i	−0.952459	+	0.304666i	$0.901455\pi$
$74$	−0.280396	−	0.485660i	−0.0325953	−	0.0564568i
$75$	2.85656			0.329848
$76$	−2.23673			−0.256570
$77$	7.10062	−	12.2986i	0.809191	−	1.40156i
$78$	−1.43875	−	2.49199i	−0.162907	−	0.282163i
$79$	−6.08596	−	10.5412i	−0.684724	−	1.18598i	−0.973523	−	0.228587i	$-0.926589\pi$
$79$	−6.08596	−	10.5412i	−0.684724	−	1.18598i	0.288800	−	0.957390i	$-0.406744\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	2.14530			0.238366
$82$	−4.91148			−0.542382
$83$	−6.82278	+	11.8174i	−0.748897	+	1.29713i	0.199455	+	0.979907i	$0.436083\pi$
$83$	−6.82278	+	11.8174i	−0.748897	+	1.29713i	−0.948352	+	0.317220i	$0.897250\pi$
$84$	6.41888	−	11.1178i	0.700357	−	1.21305i
$85$	−2.38990	+	4.13942i	−0.259221	+	0.448984i
$86$	−4.53264	+	7.85077i	−0.488768	+	0.846570i
$87$	6.89655	+	11.9452i	0.739388	+	1.28066i
$88$	1.57998	+	2.73660i	0.168426	+	0.291723i
$89$	−3.52240			−0.373373			−0.186687	−	0.982419i	$-0.559775\pi$
$89$	−3.52240			−0.373373			−0.186687	+	0.982419i	$0.559775\pi$
$90$	−2.57998	+	4.46866i	−0.271954	+	0.471038i
$91$	4.52707			0.474566
$92$	3.97933			0.414874
$93$	10.6384	+	18.4263i	1.10315	+	1.91072i
$94$	−12.6998			−1.30988
$95$	−1.11836	+	1.93706i	−0.114742	+	0.198738i
$96$	1.42828	+	2.47386i	0.145773	+	0.252487i
$97$	0.642699	−	1.11319i	0.0652562	−	0.113027i	−0.831551	−	0.555448i	$-0.812547\pi$
$97$	0.642699	−	1.11319i	0.0652562	−	0.113027i	0.896808	+	0.442421i	$0.145880\pi$
$98$	6.59858	+	11.4291i	0.666557	+	1.15451i
$99$	−8.15263	−	14.1208i	−0.819370	−	1.41919i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−3.72580	−	6.45328i	−0.370731	−	0.642125i	0.618947	−	0.785433i	$-0.287559\pi$
$101$	−3.72580	−	6.45328i	−0.370731	−	0.642125i	−0.989678	+	0.143308i	$0.954226\pi$
$102$	−6.82690	−	11.8245i	−0.675963	−	1.17080i
$103$	−4.74340	−	8.21580i	−0.467381	−	0.809527i	0.531925	−	0.846792i	$-0.321469\pi$
$103$	−4.74340	−	8.21580i	−0.467381	−	0.809527i	−0.999305	+	0.0372645i	$0.988136\pi$
$104$	−0.503666	+	0.872375i	−0.0493885	+	0.0855434i
$105$	−6.41888	−	11.1178i	−0.626418	−	1.08499i
$106$	−1.77673	+	3.07739i	−0.172571	+	0.298902i
$107$	9.34497			0.903412			0.451706	−	0.892167i	$-0.350816\pi$
$107$	9.34497			0.903412			0.451706	+	0.892167i	$0.350816\pi$
$108$	−3.08503	−	5.34343i	−0.296857	−	0.514172i
$109$	13.3672			1.28035			0.640173	−	0.768231i	$-0.278863\pi$
$109$	13.3672			1.28035			0.640173	+	0.768231i	$0.278863\pi$
$110$	3.15996			0.301290
$111$	0.800968	−	1.38732i	0.0760245	−	0.131678i
$112$	−4.49412			−0.424655
$113$	3.75547	+	6.50466i	0.353285	+	0.611907i	0.986823	−	0.161804i	$-0.0517314\pi$
$113$	3.75547	+	6.50466i	0.353285	+	0.611907i	−0.633538	+	0.773711i	$0.718398\pi$
$114$	−3.19468	−	5.53334i	−0.299209	−	0.518245i
$115$	1.98966	−	3.44620i	0.185537	−	0.321360i
$116$	2.41428	−	4.18166i	0.224160	−	0.388257i
$117$	2.59889	−	4.50142i	0.240268	−	0.416156i
$118$	−1.77511	+	3.07458i	−0.163412	+	0.283038i
$119$	21.4810			1.96916
$120$	2.85656			0.260767
$121$	0.507331	−	0.878724i	0.0461210	−	0.0798840i
$122$	6.68053	+	11.5710i	0.604827	+	1.04759i
$123$	−7.01498	−	12.1503i	−0.632519	−	1.09556i
$124$	3.72420	−	6.45050i	0.334443	−	0.579272i
$125$	−1.00000			−0.0894427
$126$	23.1895			2.06588
$127$	−0.0732391	−	0.126854i	−0.00649892	−	0.0112565i	0.862758	−	0.505618i	$-0.168735\pi$
$127$	−0.0732391	−	0.126854i	−0.00649892	−	0.0112565i	−0.869257	+	0.494361i	$0.835402\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−25.8956			−2.27998
$130$	0.503666	+	0.872375i	0.0441744	+	0.0765123i
$131$	11.0212			0.962922			0.481461	−	0.876467i	$-0.340106\pi$
$131$	11.0212			0.962922			0.481461	+	0.876467i	$0.340106\pi$
$132$	−4.51331	+	7.81729i	−0.392833	+	0.680407i
$133$	10.0521			0.871630
$134$	−3.94533	−	7.17177i	−0.340825	−	0.619547i
$135$	−6.17006			−0.531034
$136$	−2.38990	+	4.13942i	−0.204932	+	0.354953i
$137$	−14.8683			−1.27028			−0.635141	−	0.772396i	$-0.719058\pi$
$137$	−14.8683			−1.27028			−0.635141	+	0.772396i	$0.719058\pi$
$138$	5.68361	+	9.84429i	0.483821	+	0.838002i
$139$	6.42920			0.545318			0.272659	−	0.962111i	$-0.412097\pi$
$139$	6.42920			0.545318			0.272659	+	0.962111i	$0.412097\pi$
$140$	−2.24706	+	3.89203i	−0.189911	+	0.328936i
$141$	−18.1389	−	31.4175i	−1.52757	−	2.64583i
$142$	−3.90256			−0.327496
$143$	−3.18313			−0.266186
$144$	−2.57998	+	4.46866i	−0.214998	+	0.372388i
$145$	−2.41428	−	4.18166i	−0.200495	−	0.347268i
$146$	6.32323	+	10.9522i	0.523314	+	0.906407i
$147$	−18.8493	+	32.6479i	−1.55466	+	2.69275i
$148$	−0.560791			−0.0460968
$149$	14.1698			1.16083			0.580417	−	0.814319i	$-0.302890\pi$
$149$	14.1698			1.16083			0.580417	+	0.814319i	$0.302890\pi$
$150$	1.42828	−	2.47386i	0.116619	−	0.201990i
$151$	−3.43807	+	5.95492i	−0.279786	+	0.484604i	−0.971332	−	0.237729i	$-0.923597\pi$
$151$	−3.43807	+	5.95492i	−0.279786	+	0.484604i	0.691545	+	0.722333i	$0.256930\pi$
$152$	−1.11836	+	1.93706i	−0.0907113	+	0.157117i
$153$	12.3318	−	21.3593i	0.996965	−	1.72679i
$154$	−7.10062	−	12.2986i	−0.572184	−	0.991053i
$155$	−3.72420	−	6.45050i	−0.299135	−	0.518117i
$156$	−2.87751			−0.230385
$157$	10.0454	−	17.3991i	0.801707	−	1.38860i	−0.116785	−	0.993157i	$-0.537259\pi$
$157$	10.0454	−	17.3991i	0.801707	−	1.38860i	0.918492	−	0.395440i	$-0.129408\pi$
$158$	−12.1719			−0.968346
$159$	−10.1507			−0.805002
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−17.8836			−1.40943
$162$	1.07265	−	1.85788i	0.0842752	−	0.145969i
$163$	2.03273	+	3.52080i	0.159216	+	0.275770i	0.934586	−	0.355737i	$-0.115770\pi$
$163$	2.03273	+	3.52080i	0.159216	+	0.275770i	−0.775370	+	0.631507i	$0.782437\pi$
$164$	−2.45574	+	4.25347i	−0.191761	+	0.332140i
$165$	4.51331	+	7.81729i	0.351361	+	0.608575i
$166$	6.82278	+	11.8174i	0.529550	+	0.917208i
$167$	8.13469	+	14.0897i	0.629481	+	1.09029i	0.987656	+	0.156639i	$0.0500660\pi$
$167$	8.13469	+	14.0897i	0.629481	+	1.09029i	−0.358174	+	0.933655i	$0.616601\pi$
$168$	−6.41888	−	11.1178i	−0.495227	−	0.857758i
$169$	5.99264	+	10.3796i	0.460972	+	0.798428i
$170$	2.38990	+	4.13942i	0.183297	+	0.317479i
$171$	5.77071	−	9.99516i	0.441297	−	0.764349i
$172$	4.53264	+	7.85077i	0.345611	+	0.598616i
$173$	7.64982	−	13.2499i	0.581605	−	1.00737i	−0.413685	−	0.910420i	$-0.635758\pi$
$173$	7.64982	−	13.2499i	0.581605	−	1.00737i	0.995289	−	0.0969488i	$-0.0309083\pi$
$174$	13.7931			1.04565
$175$	2.24706	+	3.89203i	0.169862	+	0.294209i
$176$	3.15996			0.238191
$177$	−10.1414			−0.762277
$178$	−1.76120	+	3.05049i	−0.132007	+	0.228644i
$179$	−0.218731			−0.0163488			−0.00817438	−	0.999967i	$-0.502602\pi$
$179$	−0.218731			−0.0163488			−0.00817438	+	0.999967i	$0.502602\pi$
$180$	2.57998	+	4.46866i	0.192300	+	0.333074i
$181$	11.3277	+	19.6202i	0.841984	+	1.45836i	0.888215	+	0.459428i	$0.151946\pi$
$181$	11.3277	+	19.6202i	0.841984	+	1.45836i	−0.0462307	+	0.998931i	$0.514721\pi$
$182$	2.26354	−	3.92056i	0.167784	−	0.290611i
$183$	−19.0834	+	33.0534i	−1.41068	+	2.44337i
$184$	1.98966	−	3.44620i	0.146680	−	0.254057i
$185$	−0.280396	+	0.485660i	−0.0206151	+	0.0357064i
$186$	21.2768			1.56009
$187$	−15.1040			−1.10451
$188$	−6.34989	+	10.9983i	−0.463114	+	0.802136i
$189$	13.8645	+	24.0140i	1.00849	+	1.74676i
$190$	1.11836	+	1.93706i	0.0811346	+	0.140529i
$191$	−0.588841	+	1.01990i	−0.0426070	+	0.0737975i	−0.886542	−	0.462647i	$-0.846900\pi$
$191$	−0.588841	+	1.01990i	−0.0426070	+	0.0737975i	0.843935	+	0.536445i	$0.180233\pi$
$192$	2.85656			0.206155
$193$	−8.71036			−0.626985			−0.313493	−	0.949591i	$-0.601499\pi$
$193$	−8.71036			−0.626985			−0.313493	+	0.949591i	$0.601499\pi$
$194$	−0.642699	−	1.11319i	−0.0461431	−	0.0799222i
$195$	−1.43875	+	2.49199i	−0.103031	+	0.178455i
$196$	13.1972			0.942654
$197$	8.00919	+	13.8723i	0.570631	+	0.988362i	0.996501	+	0.0835779i	$0.0266348\pi$
$197$	8.00919	+	13.8723i	0.570631	+	0.988362i	−0.425870	+	0.904784i	$0.640032\pi$
$198$	−16.3053			−1.15876
$199$	−6.98114	+	12.0917i	−0.494880	+	0.857157i	−0.999983	−	0.00590199i	$-0.998121\pi$
$199$	−6.98114	+	12.0917i	−0.494880	+	0.857157i	0.505103	+	0.863059i	$0.331455\pi$
$200$	−1.00000			−0.0707107
$201$	12.1069	−	20.0035i	0.853954	−	1.41094i
$202$	−7.45160			−0.524293
$203$	−10.8501	+	18.7929i	−0.761526	+	1.31900i
$204$	−13.6538			−0.955957
$205$	2.45574	+	4.25347i	0.171516	+	0.297075i
$206$	−9.48679			−0.660976
$207$	−10.2666	+	17.7823i	−0.713577	+	1.23595i
$208$	0.503666	+	0.872375i	0.0349229	+	0.0604883i
$209$	−7.06796			−0.488901
$210$	−12.8378			−0.885889
$211$	8.38955	−	14.5311i	0.577560	−	1.00036i	−0.418198	−	0.908356i	$-0.637338\pi$
$211$	8.38955	−	14.5311i	0.577560	−	1.00036i	0.995758	−	0.0920078i	$-0.0293285\pi$
$212$	1.77673	+	3.07739i	0.122026	+	0.211356i
$213$	−5.57396	−	9.65438i	−0.381921	−	0.661507i
$214$	4.67249	−	8.09298i	0.319405	−	0.553225i
$215$	9.06529			0.618248
$216$	−6.17006			−0.419819
$217$	−16.7370	+	28.9894i	−1.13618	+	1.96793i
$218$	6.68361	−	11.5763i	0.452671	−	0.784049i
$219$	−18.0627	+	31.2855i	−1.22057	+	2.11408i
$220$	1.57998	−	2.73660i	0.106522	−	0.184502i
$221$	−2.40742	−	4.16977i	−0.161941	−	0.280489i
$222$	−0.800968	−	1.38732i	−0.0537575	−	0.0931107i
$223$	−16.4544			−1.10187			−0.550933	−	0.834549i	$-0.685728\pi$
$223$	−16.4544			−1.10187			−0.550933	+	0.834549i	$0.685728\pi$
$224$	−2.24706	+	3.89203i	−0.150138	+	0.260047i
$225$	5.15996			0.343997
$226$	7.51094			0.499620
$227$	−5.76358	−	9.98282i	−0.382543	−	0.662583i	0.608882	−	0.793260i	$-0.291618\pi$
$227$	−5.76358	−	9.98282i	−0.382543	−	0.662583i	−0.991425	+	0.130677i	$0.958285\pi$
$228$	−6.38935			−0.423145
$229$	14.1846	−	24.5685i	0.937345	−	1.62353i	0.166947	−	0.985966i	$-0.446609\pi$
$229$	14.1846	−	24.5685i	0.937345	−	1.62353i	0.770398	−	0.637564i	$-0.220058\pi$
$230$	−1.98966	−	3.44620i	−0.131195	−	0.227236i
$231$	20.2834	−	35.1319i	1.33455	−	2.31151i
$232$	−2.41428	−	4.18166i	−0.158505	−	0.274539i
$233$	−1.39110	−	2.40945i	−0.0911339	−	0.157848i	0.816855	−	0.576844i	$-0.195716\pi$
$233$	−1.39110	−	2.40945i	−0.0911339	−	0.157848i	−0.907989	+	0.418995i	$0.862382\pi$
$234$	−2.59889	−	4.50142i	−0.169895	−	0.294267i
$235$	6.34989	+	10.9983i	0.414221	+	0.717453i
$236$	1.77511	+	3.07458i	0.115550	+	0.200138i
$237$	−17.3849	−	30.1116i	−1.12927	−	1.95596i
$238$	10.7405	−	18.6031i	0.696203	−	1.20586i
$239$	−12.1378	−	21.0233i	−0.785130	−	1.35989i	−0.928921	−	0.370277i	$-0.879263\pi$
$239$	−12.1378	−	21.0233i	−0.785130	−	1.35989i	0.143791	−	0.989608i	$-0.454071\pi$
$240$	1.42828	−	2.47386i	0.0921952	−	0.159687i
$241$	6.93147			0.446495			0.223248	−	0.974762i	$-0.428334\pi$
$241$	6.93147			0.446495			0.223248	+	0.974762i	$0.428334\pi$
$242$	−0.507331	−	0.878724i	−0.0326125	−	0.0564865i
$243$	−12.3820			−0.794306
$244$	13.3611			0.855354
$245$	6.59858	−	11.4291i	0.421568	−	0.730176i
$246$	−14.0300			−0.894517
$247$	−1.12656	−	1.95126i	−0.0716815	−	0.124156i
$248$	−3.72420	−	6.45050i	−0.236487	−	0.409607i
$249$	−19.4897	+	33.7571i	−1.23511	+	2.13927i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	5.02058	−	8.69590i	0.316896	−	0.548880i	−0.662942	−	0.748670i	$-0.730693\pi$
$251$	5.02058	−	8.69590i	0.316896	−	0.548880i	0.979839	+	0.199790i	$0.0640260\pi$
$252$	11.5947	−	20.0827i	0.730400	−	1.26509i
$253$	12.5745			0.790553
$254$	−0.146478			−0.00919086
$255$	−6.82690	+	11.8245i	−0.427517	+	0.740481i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.76190	+	16.9081i	0.608930	+	1.05470i	0.991417	+	0.130737i	$0.0417344\pi$
$257$	9.76190	+	16.9081i	0.608930	+	1.05470i	−0.382487	+	0.923961i	$0.624932\pi$
$258$	−12.9478	+	22.4262i	−0.806094	+	1.39620i
$259$	2.52027			0.156602
$260$	1.00733			0.0624720
$261$	12.4576	+	21.5772i	0.771105	+	1.33559i
$262$	5.51058	−	9.54460i	0.340445	−	0.589667i
$263$	2.78647			0.171821			0.0859105	−	0.996303i	$-0.472620\pi$
$263$	2.78647			0.171821			0.0859105	+	0.996303i	$0.472620\pi$
$264$	4.51331	+	7.81729i	0.277775	+	0.481121i
$265$	3.55346			0.218287
$266$	5.02606	−	8.70540i	0.308168	−	0.533762i
$267$	−10.0620			−0.615782
$268$	−8.18361	−	0.169127i	−0.499893	−	0.0103311i
$269$	24.1857			1.47463			0.737313	−	0.675551i	$-0.236094\pi$
$269$	24.1857			1.47463			0.737313	+	0.675551i	$0.236094\pi$
$270$	−3.08503	+	5.34343i	−0.187749	+	0.325191i
$271$	−27.6341			−1.67865			−0.839325	−	0.543630i	$-0.817050\pi$
$271$	−27.6341			−1.67865			−0.839325	+	0.543630i	$0.817050\pi$
$272$	2.38990	+	4.13942i	0.144909	+	0.250989i
$273$	12.9319			0.782673
$274$	−7.43414	+	12.8763i	−0.449113	+	0.777886i
$275$	−1.57998	−	2.73660i	−0.0952763	−	0.165023i
$276$	11.3672			0.684226
$277$	27.2038			1.63452			0.817258	−	0.576272i	$-0.195493\pi$
$277$	27.2038			1.63452			0.817258	+	0.576272i	$0.195493\pi$
$278$	3.21460	−	5.56785i	0.192799	−	0.333938i
$279$	19.2167	+	33.2843i	1.15047	+	1.99268i
$280$	2.24706	+	3.89203i	0.134288	+	0.232593i
$281$	15.4913	−	26.8317i	0.924133	−	1.60065i	0.131183	−	0.991358i	$-0.458122\pi$
$281$	15.4913	−	26.8317i	0.924133	−	1.60065i	0.792950	−	0.609287i	$-0.208544\pi$
$282$	−36.2778			−2.16031
$283$	−4.86433			−0.289154			−0.144577	−	0.989494i	$-0.546182\pi$
$283$	−4.86433			−0.289154			−0.144577	+	0.989494i	$0.546182\pi$
$284$	−1.95128	+	3.37972i	−0.115787	+	0.200549i
$285$	−3.19468	+	5.53334i	−0.189236	+	0.327767i
$286$	−1.59156	+	2.75667i	−0.0941111	+	0.163005i
$287$	11.0364	−	19.1156i	0.651458	−	1.12836i
$288$	2.57998	+	4.46866i	0.152027	+	0.263318i
$289$	−2.92322	−	5.06317i	−0.171954	−	0.297834i
$290$	−4.82856			−0.283543
$291$	1.83591	−	3.17989i	0.107623	−	0.186409i
$292$	12.6465			0.740078
$293$	7.34574			0.429143			0.214571	−	0.976708i	$-0.431165\pi$
$293$	7.34574			0.429143			0.214571	+	0.976708i	$0.431165\pi$
$294$	18.8493	+	32.6479i	1.09931	+	1.90406i
$295$	3.55022			0.206702
$296$	−0.280396	+	0.485660i	−0.0162977	+	0.0282284i
$297$	−9.74857	−	16.8850i	−0.565669	−	0.979768i
$298$	7.08489	−	12.2714i	0.410417	−	0.710863i
$299$	2.00425	+	3.47147i	0.115909	+	0.200760i
$300$	−1.42828	−	2.47386i	−0.0824619	−	0.142828i
$301$	−20.3703	−	35.2823i	−1.17412	−	2.03364i
$302$	3.43807	+	5.95492i	0.197839	+	0.342667i
$303$	−10.6430	−	18.4342i	−0.611424	−	1.05902i
$304$	1.11836	+	1.93706i	0.0641425	+	0.111098i
$305$	6.68053	−	11.5710i	0.382526	−	0.662555i
$306$	−12.3318	−	21.3593i	−0.704961	−	1.22103i
$307$	−3.21456	+	5.56779i	−0.183465	+	0.317770i	−0.943058	−	0.332628i	$-0.892065\pi$
$307$	−3.21456	+	5.56779i	−0.183465	+	0.317770i	0.759593	+	0.650398i	$0.225398\pi$
$308$	−14.2012			−0.809191
$309$	−13.5498	−	23.4690i	−0.770822	−	1.33510i
$310$	−7.44840			−0.423041
$311$	22.7484			1.28994			0.644970	−	0.764208i	$-0.276870\pi$
$311$	22.7484			1.28994			0.644970	+	0.764208i	$0.276870\pi$
$312$	−1.43875	+	2.49199i	−0.0814534	+	0.141081i
$313$	−10.4667			−0.591611			−0.295806	−	0.955248i	$-0.595588\pi$
$313$	−10.4667			−0.591611			−0.295806	+	0.955248i	$0.595588\pi$
$314$	−10.0454	−	17.3991i	−0.566892	−	0.981886i
$315$	−11.5947	−	20.0827i	−0.653290	−	1.13153i
$316$	−6.08596	+	10.5412i	−0.342362	+	0.592988i
$317$	−16.6592	+	28.8545i	−0.935673	+	1.62063i	−0.162243	+	0.986751i	$0.551873\pi$
$317$	−16.6592	+	28.8545i	−0.935673	+	1.62063i	−0.773430	+	0.633882i	$0.781460\pi$
$318$	−5.07534	+	8.79075i	−0.284611	+	0.492961i
$319$	7.62903	−	13.2139i	0.427144	−	0.739834i
$320$	−1.00000			−0.0559017
$321$	26.6945			1.48994
$322$	−8.94180	+	15.4877i	−0.498307	+	0.863093i
$323$	−5.34555	−	9.25876i	−0.297434	−	0.515171i
$324$	−1.07265	−	1.85788i	−0.0595915	−	0.103216i
$325$	0.503666	−	0.872375i	0.0279383	−	0.0483906i
$326$	4.06547			0.225165
$327$	38.1843			2.11160
$328$	2.45574	+	4.25347i	0.135596	+	0.234858i
$329$	28.5372	−	49.4279i	1.57331	−	2.72505i
$330$	9.02662			0.496899
$331$	10.8376	+	18.7713i	0.595691	+	1.03177i	0.993449	+	0.114276i	$0.0364549\pi$
$331$	10.8376	+	18.7713i	0.595691	+	1.03177i	−0.397758	+	0.917490i	$0.630212\pi$
$332$	13.6456			0.748897
$333$	1.44683	−	2.50598i	0.0792858	−	0.137327i
$334$	16.2694			0.890221
$335$	−4.23827	+	7.00265i	−0.231561	+	0.382595i
$336$	−12.8378			−0.700357
$337$	11.0932	−	19.2140i	0.604286	−	1.04665i	−0.387878	−	0.921711i	$-0.626792\pi$
$337$	11.0932	−	19.2140i	0.604286	−	1.04665i	0.992164	−	0.124944i	$-0.0398750\pi$
$338$	11.9853			0.651913
$339$	10.7277	+	18.5810i	0.582651	+	1.00918i
$340$	4.77980			0.259221
$341$	11.7683	−	20.3833i	0.637290	−	1.10382i
$342$	−5.77071	−	9.99516i	−0.312044	−	0.540476i
$343$	−27.8508			−1.50380
$344$	9.06529			0.488768
$345$	5.68361	−	9.84429i	0.305995	−	0.529999i
$346$	−7.64982	−	13.2499i	−0.411257	−	0.712317i
$347$	−8.82651	−	15.2880i	−0.473832	−	0.820701i	0.525719	−	0.850658i	$-0.323796\pi$
$347$	−8.82651	−	15.2880i	−0.473832	−	0.820701i	−0.999551	+	0.0299571i	$0.990463\pi$
$348$	6.89655	−	11.9452i	0.369694	−	0.640328i
$349$	−23.0772			−1.23530			−0.617648	−	0.786455i	$-0.711914\pi$
$349$	−23.0772			−1.23530			−0.617648	+	0.786455i	$0.711914\pi$
$350$	4.49412			0.240221
$351$	3.10765	−	5.38260i	0.165874	−	0.287302i
$352$	1.57998	−	2.73660i	0.0842132	−	0.145861i
$353$	13.5950	−	23.5472i	0.723587	−	1.25329i	−0.235967	−	0.971761i	$-0.575826\pi$
$353$	13.5950	−	23.5472i	0.723587	−	1.25329i	0.959553	−	0.281528i	$-0.0908411\pi$
$354$	−5.07072	+	8.78274i	−0.269506	+	0.466798i
$355$	1.95128	+	3.37972i	0.103563	+	0.179377i
$356$	1.76120	+	3.05049i	0.0933434	+	0.161675i
$357$	61.3618			3.24761
$358$	−0.109366	+	0.189427i	−0.00578016	+	0.0100115i
$359$	−26.9813			−1.42402			−0.712010	−	0.702170i	$-0.752215\pi$
$359$	−26.9813			−1.42402			−0.712010	+	0.702170i	$0.752215\pi$
$360$	5.15996			0.271954
$361$	6.99853	+	12.1218i	0.368343	+	0.637990i
$362$	22.6555			1.19075
$363$	1.44922	−	2.51013i	0.0760646	−	0.131748i
$364$	−2.26354	−	3.92056i	−0.118642	−	0.205493i
$365$	6.32323	−	10.9522i	0.330973	−	0.573262i
$366$	19.0834	+	33.0534i	0.997503	+	1.72773i
$367$	13.3557	+	23.1327i	0.697161	+	1.20752i	0.969447	+	0.245301i	$0.0788869\pi$
$367$	13.3557	+	23.1327i	0.697161	+	1.20752i	−0.272286	+	0.962216i	$0.587780\pi$
$368$	−1.98966	−	3.44620i	−0.103718	−	0.179646i
$369$	−12.6715	−	21.9477i	−0.659653	−	1.14255i
$370$	0.280396	+	0.485660i	0.0145771	+	0.0252482i
$371$	−7.98484	−	13.8302i	−0.414552	−	0.718026i
$372$	10.6384	−	18.4263i	0.551576	−	0.955358i
$373$	−2.35596	−	4.08065i	−0.121987	−	0.211288i	0.798564	−	0.601910i	$-0.205593\pi$
$373$	−2.35596	−	4.08065i	−0.121987	−	0.211288i	−0.920551	+	0.390622i	$0.872260\pi$
$374$	−7.55198	+	13.0804i	−0.390503	+	0.676372i
$375$	−2.85656			−0.147512
$376$	6.34989	+	10.9983i	0.327471	+	0.567196i
$377$	4.86396			0.250507
$378$	27.7290			1.42623
$379$	9.10210	−	15.7653i	0.467544	−	0.809809i	−0.531769	−	0.846890i	$-0.678472\pi$
$379$	9.10210	−	15.7653i	0.467544	−	0.809809i	0.999312	+	0.0370802i	$0.0118057\pi$
$380$	2.23673			0.114742
$381$	−0.209212	−	0.362366i	−0.0107183	−	0.0185646i
$382$	0.588841	+	1.01990i	0.0301277	+	0.0521827i
$383$	−3.84384	+	6.65773i	−0.196411	+	0.340194i	−0.947362	−	0.320164i	$-0.896262\pi$
$383$	−3.84384	+	6.65773i	−0.196411	+	0.340194i	0.750951	+	0.660358i	$0.229595\pi$
$384$	1.42828	−	2.47386i	0.0728867	−	0.126243i
$385$	−7.10062	+	12.2986i	−0.361881	+	0.626797i
$386$	−4.35518	+	7.54339i	−0.221673	+	0.383949i
$387$	−46.7765			−2.37778
$388$	−1.28540			−0.0652562
$389$	−9.94332	+	17.2223i	−0.504146	+	0.873207i	0.495842	+	0.868413i	$0.334859\pi$
$389$	−9.94332	+	17.2223i	−0.504146	+	0.873207i	−0.999989	+	0.00479424i	$0.998474\pi$
$390$	1.43875	+	2.49199i	0.0728541	+	0.126187i
$391$	9.51019	+	16.4721i	0.480951	+	0.833032i
$392$	6.59858	−	11.4291i	0.333278	−	0.577255i
$393$	31.4826			1.58809
$394$	16.0184			0.806994
$395$	6.08596	+	10.5412i	0.306218	+	0.530385i
$396$	−8.15263	+	14.1208i	−0.409685	+	0.709595i
$397$	−31.5129			−1.58159			−0.790793	−	0.612083i	$-0.790332\pi$
$397$	−31.5129			−1.58159			−0.790793	+	0.612083i	$0.790332\pi$
$398$	6.98114	+	12.0917i	0.349933	+	0.606102i
$399$	28.7145			1.43753
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−8.92203			−0.445545			−0.222772	−	0.974870i	$-0.571511\pi$
$401$	−8.92203			−0.445545			−0.222772	+	0.974870i	$0.571511\pi$
$402$	−11.2701	−	20.4866i	−0.562101	−	1.02178i
$403$	7.50301			0.373751
$404$	−3.72580	+	6.45328i	−0.185365	+	0.321062i
$405$	−2.14530			−0.106601
$406$	10.8501	+	18.7929i	0.538480	+	0.932675i
$407$	−1.77208			−0.0878386
$408$	−6.82690	+	11.8245i	−0.337982	+	0.585402i
$409$	−9.88689	−	17.1246i	−0.488875	−	0.846757i	0.511043	−	0.859555i	$-0.329259\pi$
$409$	−9.88689	−	17.1246i	−0.488875	−	0.846757i	−0.999918	+	0.0127982i	$0.995926\pi$
$410$	4.91148			0.242561
$411$	−42.4722			−2.09500
$412$	−4.74340	+	8.21580i	−0.233690	+	0.404764i
$413$	−7.97757	−	13.8176i	−0.392551	−	0.679918i
$414$	10.2666	+	17.7823i	0.504575	+	0.873950i
$415$	6.82278	−	11.8174i	0.334917	−	0.580093i
$416$	1.00733			0.0493885
$417$	18.3654			0.899359
$418$	−3.53398	+	6.12104i	−0.172853	+	0.299390i
$419$	7.41294	−	12.8396i	0.362146	−	0.627255i	−0.626168	−	0.779688i	$-0.715378\pi$
$419$	7.41294	−	12.8396i	0.362146	−	0.627255i	0.988314	+	0.152433i	$0.0487110\pi$
$420$	−6.41888	+	11.1178i	−0.313209	+	0.542494i
$421$	3.25445	−	5.63687i	0.158612	−	0.274724i	−0.775756	−	0.631033i	$-0.782631\pi$
$421$	3.25445	−	5.63687i	0.158612	−	0.274724i	0.934368	+	0.356308i	$0.115965\pi$
$422$	−8.38955	−	14.5311i	−0.408397	−	0.707364i
$423$	−32.7652	−	56.7510i	−1.59310	−	2.75933i
$424$	3.55346			0.172571
$425$	2.38990	−	4.13942i	0.115927	−	0.200792i
$426$	−11.1479			−0.540118
$427$	−60.0463			−2.90584
$428$	−4.67249	−	8.09298i	−0.225853	−	0.391189i
$429$	−9.09280			−0.439005
$430$	4.53264	−	7.85077i	0.218584	−	0.378598i
$431$	1.51593	+	2.62567i	0.0730198	+	0.126474i	0.900223	−	0.435428i	$-0.143403\pi$
$431$	1.51593	+	2.62567i	0.0730198	+	0.126474i	−0.827204	+	0.561902i	$0.810070\pi$
$432$	−3.08503	+	5.34343i	−0.148429	+	0.257086i
$433$	9.74939	+	16.8864i	0.468526	+	0.811510i	0.999353	−	0.0359697i	$-0.0114520\pi$
$433$	9.74939	+	16.8864i	0.468526	+	0.811510i	−0.530827	+	0.847480i	$0.678119\pi$
$434$	16.7370	+	28.9894i	0.803402	+	1.39153i
$435$	−6.89655	−	11.9452i	−0.330664	−	0.572727i
$436$	−6.68361	−	11.5763i	−0.320087	−	0.554406i
$437$	4.45034	+	7.70821i	0.212888	+	0.368734i
$438$	18.0627	+	31.2855i	0.863070	+	1.49488i
$439$	−2.73228	+	4.73244i	−0.130404	+	0.225867i	−0.923833	−	0.382797i	$-0.874961\pi$
$439$	−2.73228	+	4.73244i	−0.130404	+	0.225867i	0.793428	+	0.608664i	$0.208294\pi$
$440$	−1.57998	−	2.73660i	−0.0753226	−	0.130462i
$441$	−34.0484	+	58.9735i	−1.62135	+	2.80826i
$442$	−4.81484			−0.229019
$443$	14.2350	+	24.6557i	0.676324	+	1.17143i	0.976080	+	0.217412i	$0.0697614\pi$
$443$	14.2350	+	24.6557i	0.676324	+	1.17143i	−0.299756	+	0.954016i	$0.596905\pi$
$444$	−1.60194			−0.0760245
$445$	3.52240			0.166978
$446$	−8.22719	+	14.2499i	−0.389569	+	0.674752i
$447$	40.4769			1.91449
$448$	2.24706	+	3.89203i	0.106164	+	0.183881i
$449$	−8.24126	−	14.2743i	−0.388929	−	0.673645i	0.603377	−	0.797456i	$-0.293822\pi$
$449$	−8.24126	−	14.2743i	−0.388929	−	0.673645i	−0.992306	+	0.123811i	$0.960488\pi$
$450$	2.57998	−	4.46866i	0.121621	−	0.210654i
$451$	−7.76004	+	13.4408i	−0.365406	+	0.632901i
$452$	3.75547	−	6.50466i	0.176642	−	0.305954i
$453$	−9.82108	+	17.0106i	−0.461434	+	0.799228i
$454$	−11.5272			−0.540997
$455$	−4.52707			−0.212232
$456$	−3.19468	+	5.53334i	−0.149604	+	0.259123i
$457$	7.52000	+	13.0250i	0.351771	+	0.609285i	0.986560	−	0.163400i	$-0.0522463\pi$
$457$	7.52000	+	13.0250i	0.351771	+	0.609285i	−0.634789	+	0.772686i	$0.718913\pi$
$458$	−14.1846	−	24.5685i	−0.662803	−	1.14801i
$459$	14.7458	−	25.5405i	0.688276	−	1.19213i
$460$	−3.97933			−0.185537
$461$	−3.06250			−0.142635			−0.0713175	−	0.997454i	$-0.522720\pi$
$461$	−3.06250			−0.142635			−0.0713175	+	0.997454i	$0.522720\pi$
$462$	−20.2834	−	35.1319i	−0.943668	−	1.63448i
$463$	−20.9244	+	36.2422i	−0.972440	+	1.68432i	−0.284304	+	0.958734i	$0.591762\pi$
$463$	−20.9244	+	36.2422i	−0.972440	+	1.68432i	−0.688136	+	0.725581i	$0.741571\pi$
$464$	−4.82856			−0.224160
$465$	−10.6384	−	18.4263i	−0.493345	−	0.854498i
$466$	−2.78220			−0.128883
$467$	3.88008	−	6.72050i	0.179549	−	0.310988i	−0.762177	−	0.647368i	$-0.775870\pi$
$467$	3.88008	−	6.72050i	0.179549	−	0.310988i	0.941726	+	0.336381i	$0.109203\pi$
$468$	−5.19779			−0.240268
$469$	36.7781	+	0.760080i	1.69826	+	0.0350972i
$470$	12.6998			0.585798
$471$	28.6952	−	49.7016i	1.32221	−	2.29013i
$472$	3.55022			0.163412
$473$	14.3230	+	24.8081i	0.658571	+	1.14068i
$474$	−34.7699			−1.59703
$475$	1.11836	−	1.93706i	0.0513140	−	0.0888785i
$476$	−10.7405	−	18.6031i	−0.492290	−	0.852671i
$477$	−18.3357			−0.839534
$478$	−24.2756			−1.11034
$479$	−2.69733	+	4.67192i	−0.123244	+	0.213465i	−0.921045	−	0.389455i	$-0.872663\pi$
$479$	−2.69733	+	4.67192i	−0.123244	+	0.213465i	0.797801	+	0.602921i	$0.205997\pi$
$480$	−1.42828	−	2.47386i	−0.0651919	−	0.112916i
$481$	−0.282451	−	0.489220i	−0.0128787	−	0.0223065i
$482$	3.46574	−	6.00283i	0.157860	−	0.273421i
$483$	−51.0857			−2.32448
$484$	−1.01466			−0.0461210
$485$	−0.642699	+	1.11319i	−0.0291835	+	0.0505473i
$486$	−6.19100	+	10.7231i	−0.280830	+	0.486411i
$487$	0.707213	−	1.22493i	0.0320469	−	0.0555069i	−0.849557	−	0.527497i	$-0.823131\pi$
$487$	0.707213	−	1.22493i	0.0320469	−	0.0555069i	0.881604	+	0.471990i	$0.156464\pi$
$488$	6.68053	−	11.5710i	0.302413	−	0.523795i
$489$	5.80663	+	10.0574i	0.262585	+	0.454811i
$490$	−6.59858	−	11.4291i	−0.298093	−	0.516313i
$491$	−39.4245			−1.77920			−0.889601	−	0.456739i	$-0.849017\pi$
$491$	−39.4245			−1.77920			−0.889601	+	0.456739i	$0.849017\pi$
$492$	−7.01498	+	12.1503i	−0.316260	+	0.547778i
$493$	23.0795			1.03945
$494$	−2.25313			−0.101373
$495$	8.15263	+	14.1208i	0.366433	+	0.634681i
$496$	−7.44840			−0.334443
$497$	8.76930	−	15.1889i	0.393357	−	0.681314i
$498$	19.4897	+	33.7571i	0.873354	+	1.51269i
$499$	11.6957	−	20.2575i	0.523570	−	0.906851i	−0.476053	−	0.879416i	$-0.657933\pi$
$499$	11.6957	−	20.2575i	0.523570	−	0.906851i	0.999624	−	0.0274341i	$-0.00873364\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	23.2373	+	40.2481i	1.03816	+	1.79815i
$502$	−5.02058	−	8.69590i	−0.224080	−	0.388117i
$503$	10.6927	+	18.5203i	0.476765	+	0.825781i	0.999645	−	0.0266247i	$-0.00847591\pi$
$503$	10.6927	+	18.5203i	0.476765	+	0.825781i	−0.522880	+	0.852406i	$0.675143\pi$
$504$	−11.5947	−	20.0827i	−0.516471	−	0.894554i
$505$	3.72580	+	6.45328i	0.165796	+	0.287167i
$506$	6.28726	−	10.8899i	0.279503	−	0.484113i
$507$	17.1184	+	29.6499i	0.760253	+	1.31680i
$508$	−0.0732391	+	0.126854i	−0.00324946	+	0.00562823i
$509$	15.8720			0.703514			0.351757	−	0.936091i	$-0.385584\pi$
$509$	15.8720			0.703514			0.351757	+	0.936091i	$0.385584\pi$
$510$	6.82690	+	11.8245i	0.302300	+	0.523599i
$511$	−56.8348			−2.51422
$512$	−1.00000			−0.0441942
$513$	6.90037	−	11.9518i	0.304659	−	0.527684i
$514$	19.5238			0.861157
$515$	4.74340	+	8.21580i	0.209019	+	0.362032i
$516$	12.9478	+	22.4262i	0.569995	+	0.987260i
$517$	−20.0654	+	34.7543i	−0.882475	+	1.52849i
$518$	1.26013	−	2.18261i	0.0553671	−	0.0958986i
$519$	21.8522	−	37.8491i	0.959205	−	1.66139i
$520$	0.503666	−	0.872375i	0.0220872	−	0.0382562i
$521$	−15.6199			−0.684322			−0.342161	−	0.939641i	$-0.611159\pi$
$521$	−15.6199			−0.684322			−0.342161	+	0.939641i	$0.611159\pi$
$522$	24.9152			1.09051
$523$	14.2957	−	24.7608i	0.625105	−	1.08271i	−0.363415	−	0.931627i	$-0.618389\pi$
$523$	14.2957	−	24.7608i	0.625105	−	1.08271i	0.988521	−	0.151087i	$-0.0482773\pi$
$524$	−5.51058	−	9.54460i	−0.240731	−	0.416958i
$525$	6.41888	+	11.1178i	0.280143	+	0.485221i
$526$	1.39323	−	2.41315i	0.0607479	−	0.105218i
$527$	35.6018			1.55084
$528$	9.02662			0.392833
$529$	3.58247	+	6.20502i	0.155759	+	0.269783i
$530$	1.77673	−	3.07739i	0.0771762	−	0.133673i
$531$	−18.3190			−0.794977
$532$	−5.02606	−	8.70540i	−0.217908	−	0.377427i
$533$	−4.94749			−0.214299
$534$	−5.03098	+	8.71391i	−0.217712	+	0.377088i
$535$	−9.34497			−0.404018
$536$	−4.23827	+	7.00265i	−0.183065	+	0.302468i
$537$	−0.624820			−0.0269630
$538$	12.0928	−	20.9454i	0.521359	−	0.903021i
$539$	41.7024			1.79625
$540$	3.08503	+	5.34343i	0.132759	+	0.229945i
$541$	5.96241			0.256344			0.128172	−	0.991752i	$-0.459089\pi$
$541$	5.96241			0.256344			0.128172	+	0.991752i	$0.459089\pi$
$542$	−13.8170	+	23.9318i	−0.593493	+	1.02796i
$543$	32.3584	+	56.0464i	1.38863	+	2.40518i
$544$	4.77980			0.204932
$545$	−13.3672			−0.572588
$546$	6.46594	−	11.1993i	0.276717	−	0.479287i
$547$	4.02806	+	6.97681i	0.172228	+	0.298307i	0.939198	−	0.343375i	$-0.111570\pi$
$547$	4.02806	+	6.97681i	0.172228	+	0.298307i	−0.766971	+	0.641682i	$0.778237\pi$
$548$	7.43414	+	12.8763i	0.317571	+	0.550049i
$549$	−34.4713	+	59.7060i	−1.47120	+	2.54819i
$550$	−3.15996			−0.134741
$551$	10.8002			0.460103
$552$	5.68361	−	9.84429i	0.241910	−	0.419001i
$553$	27.3511	−	47.3734i	1.16309	−	2.01452i
$554$	13.6019	−	23.5592i	0.577889	−	1.00093i
$555$	−0.800968	+	1.38732i	−0.0339992	+	0.0588884i
$556$	−3.21460	−	5.56785i	−0.136329	−	0.236130i
$557$	−10.2351	−	17.7276i	−0.433673	−	0.751144i	0.563513	−	0.826107i	$-0.309449\pi$
$557$	−10.2351	−	17.7276i	−0.433673	−	0.751144i	−0.997186	+	0.0749630i	$0.976116\pi$
$558$	38.4334			1.62702
$559$	−4.56588	+	7.90833i	−0.193116	+	0.334487i
$560$	4.49412			0.189911
$561$	−43.1454			−1.82160
$562$	−15.4913	−	26.8317i	−0.653461	−	1.13183i
$563$	22.9616			0.967716			0.483858	−	0.875146i	$-0.339235\pi$
$563$	22.9616			0.967716			0.483858	+	0.875146i	$0.339235\pi$
$564$	−18.1389	+	31.4175i	−0.763785	+	1.32291i
$565$	−3.75547	−	6.50466i	−0.157994	−	0.273653i
$566$	−2.43216	+	4.21263i	−0.102231	+	0.177070i
$567$	4.82061	+	8.34954i	0.202447	+	0.350648i
$568$	1.95128	+	3.37972i	0.0818739	+	0.141810i
$569$	−13.5246	−	23.4252i	−0.566979	−	0.982036i	−0.996863	−	0.0791521i	$-0.974779\pi$
$569$	−13.5246	−	23.4252i	−0.566979	−	0.982036i	0.429884	−	0.902884i	$-0.358555\pi$
$570$	3.19468	+	5.53334i	0.133810	+	0.231766i
$571$	3.51800	+	6.09335i	0.147224	+	0.254999i	0.930200	−	0.367052i	$-0.119633\pi$
$571$	3.51800	+	6.09335i	0.147224	+	0.254999i	−0.782977	+	0.622051i	$0.786300\pi$
$572$	1.59156	+	2.75667i	0.0665466	+	0.115262i
$573$	−1.68206	+	2.91341i	−0.0702691	+	0.121710i
$574$	−11.0364	−	19.1156i	−0.460650	−	0.797870i
$575$	−1.98966	+	3.44620i	−0.0829748	+	0.143717i
$576$	5.15996			0.214998
$577$	20.0029	+	34.6461i	0.832733	+	1.44234i	0.895863	+	0.444330i	$0.146558\pi$
$577$	20.0029	+	34.6461i	0.832733	+	1.44234i	−0.0631308	+	0.998005i	$0.520109\pi$
$578$	−5.84645			−0.243180
$579$	−24.8817			−1.03405
$580$	−2.41428	+	4.18166i	−0.100248	+	0.173634i
$581$	−61.3248			−2.54418
$582$	−1.83591	−	3.17989i	−0.0761010	−	0.131811i
$583$	5.61439	+	9.72441i	0.232524	+	0.402744i
$584$	6.32323	−	10.9522i	0.261657	−	0.453203i
$585$	−2.59889	+	4.50142i	−0.107451	+	0.186111i
$586$	3.67287	−	6.36160i	0.151725	−	0.262795i
$587$	17.3079	−	29.9782i	0.714375	−	1.23733i	−0.248825	−	0.968548i	$-0.580044\pi$
$587$	17.3079	−	29.9782i	0.714375	−	1.23733i	0.963200	−	0.268786i	$-0.0866223\pi$
$588$	37.6985			1.55466
$589$	16.6600			0.686465
$590$	1.77511	−	3.07458i	0.0730802	−	0.126579i
$591$	22.8788	+	39.6272i	0.941107	+	1.63004i
$592$	0.280396	+	0.485660i	0.0115242	+	0.0199605i
$593$	5.11485	−	8.85918i	0.210042	−	0.363803i	−0.741686	−	0.670748i	$-0.765973\pi$
$593$	5.11485	−	8.85918i	0.210042	−	0.363803i	0.951727	+	0.306945i	$0.0993067\pi$
$594$	−19.4971			−0.799977
$595$	−21.4810			−0.880635
$596$	−7.08489	−	12.2714i	−0.290209	−	0.502656i
$597$	−19.9421	+	34.5407i	−0.816175	+	1.41366i
$598$	4.00850			0.163920
$599$	9.96932	+	17.2674i	0.407336	+	0.705526i	0.994590	−	0.103876i	$-0.0331246\pi$
$599$	9.96932	+	17.2674i	0.407336	+	0.705526i	−0.587255	+	0.809402i	$0.699791\pi$
$600$	−2.85656			−0.116619
$601$	11.4181	−	19.7767i	0.465752	−	0.806707i	−0.533483	−	0.845811i	$-0.679117\pi$
$601$	11.4181	−	19.7767i	0.465752	−	0.806707i	0.999235	+	0.0391041i	$0.0124504\pi$
$602$	−40.7405			−1.66046
$603$	21.8693	−	36.1334i	0.890587	−	1.47146i
$604$	6.87615			0.279786
$605$	−0.507331	+	0.878724i	−0.0206260	+	0.0357252i
$606$	−21.2860			−0.864684
$607$	6.11278	+	10.5877i	0.248110	+	0.429740i	0.963001	−	0.269496i	$-0.0868571\pi$
$607$	6.11278	+	10.5877i	0.248110	+	0.429740i	−0.714891	+	0.699236i	$0.753524\pi$
$608$	2.23673			0.0907113
$609$	−30.9939	+	53.6831i	−1.25594	+	2.17535i
$610$	−6.68053	−	11.5710i	−0.270487	−	0.468497i
$611$	−12.7929			−0.517545
$612$	−24.6635			−0.996965
$613$	5.64908	−	9.78449i	0.228164	−	0.395192i	−0.729100	−	0.684407i	$-0.760061\pi$
$613$	5.64908	−	9.78449i	0.228164	−	0.395192i	0.957264	+	0.289215i	$0.0933944\pi$
$614$	3.21456	+	5.56779i	0.129729	+	0.224698i
$615$	7.01498	+	12.1503i	0.282871	+	0.489947i
$616$	−7.10062	+	12.2986i	−0.286092	+	0.495526i
$617$	14.7010			0.591838			0.295919	−	0.955213i	$-0.404374\pi$
$617$	14.7010			0.591838			0.295919	+	0.955213i	$0.404374\pi$
$618$	−27.0996			−1.09011
$619$	−5.29906	+	9.17825i	−0.212987	+	0.368905i	−0.952648	−	0.304075i	$-0.901653\pi$
$619$	−5.29906	+	9.17825i	−0.212987	+	0.368905i	0.739661	+	0.672980i	$0.234986\pi$
$620$	−3.72420	+	6.45050i	−0.149567	+	0.259058i
$621$	−12.2764	+	21.2633i	−0.492633	+	0.853265i
$622$	11.3742	−	19.7006i	0.456063	−	0.789924i
$623$	−7.91505	−	13.7093i	−0.317110	−	0.549250i
$624$	1.43875	+	2.49199i	0.0575962	+	0.0997596i
$625$	1.00000			0.0400000
$626$	−5.23333	+	9.06440i	−0.209166	+	0.362286i
$627$	−20.1901			−0.806315
$628$	−20.0907			−0.801707
$629$	−1.34023	−	2.32135i	−0.0534386	−	0.0925584i
$630$	−23.1895			−0.923892
$631$	5.99862	−	10.3899i	0.238801	−	0.413616i	−0.721569	−	0.692342i	$-0.756579\pi$
$631$	5.99862	−	10.3899i	0.238801	−	0.413616i	0.960371	+	0.278726i	$0.0899122\pi$
$632$	6.08596	+	10.5412i	0.242086	+	0.419306i
$633$	23.9653	−	41.5091i	0.952534	−	1.64984i
$634$	16.6592	+	28.8545i	0.661621	+	1.14596i
$635$	0.0732391	+	0.126854i	0.00290641	+	0.00503404i
$636$	5.07534	+	8.79075i	0.201250	+	0.348576i
$637$	6.64695	+	11.5129i	0.263362	+	0.456156i
$638$	−7.62903	−	13.2139i	−0.302036	−	0.523142i
$639$	−10.0685	−	17.4392i	−0.398305	−	0.689884i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	10.9639	+	18.9901i	0.433049	+	0.750062i	0.997134	−	0.0756541i	$-0.0241045\pi$
$641$	10.9639	+	18.9901i	0.433049	+	0.750062i	−0.564085	+	0.825716i	$0.690771\pi$
$642$	13.3473	−	23.1181i	0.526774	−	0.912400i
$643$	−10.7513			−0.423990			−0.211995	−	0.977271i	$-0.567996\pi$
$643$	−10.7513			−0.423990			−0.211995	+	0.977271i	$0.567996\pi$
$644$	8.94180	+	15.4877i	0.352356	+	0.610299i
$645$	25.8956			1.01964
$646$	−10.6911			−0.420636
$647$	−10.6281	+	18.4085i	−0.417835	+	0.723712i	−0.995721	−	0.0924055i	$-0.970544\pi$
$647$	−10.6281	+	18.4085i	−0.417835	+	0.723712i	0.577886	+	0.816117i	$0.303878\pi$
$648$	−2.14530			−0.0842752
$649$	5.60928	+	9.71555i	0.220183	+	0.381369i
$650$	−0.503666	−	0.872375i	−0.0197554	−	0.0342173i
$651$	−47.8104	+	82.8100i	−1.87384	+	3.24558i
$652$	2.03273	−	3.52080i	0.0796080	−	0.137885i
$653$	17.3614	−	30.0708i	0.679402	−	1.17676i	−0.295759	−	0.955263i	$-0.595572\pi$
$653$	17.3614	−	30.0708i	0.679402	−	1.17676i	0.975161	−	0.221497i	$-0.0710942\pi$
$654$	19.0921	−	33.0686i	0.746562	−	1.29308i
$655$	−11.0212			−0.430632
$656$	4.91148			0.191761
$657$	−32.6276	+	56.5127i	−1.27292	+	2.20477i
$658$	−28.5372	−	49.4279i	−1.11250	−	1.92690i
$659$	7.23113	+	12.5247i	0.281685	+	0.487893i	0.971800	−	0.235807i	$-0.0757734\pi$
$659$	7.23113	+	12.5247i	0.281685	+	0.487893i	−0.690115	+	0.723700i	$0.742440\pi$
$660$	4.51331	−	7.81729i	0.175680	−	0.304287i
$661$	36.1436			1.40582			0.702912	−	0.711277i	$-0.251883\pi$
$661$	36.1436			1.40582			0.702912	+	0.711277i	$0.251883\pi$
$662$	21.6753			0.842434
$663$	−6.87695	−	11.9112i	−0.267079	−	0.462594i
$664$	6.82278	−	11.8174i	0.264775	−	0.458604i
$665$	−10.0521			−0.389805
$666$	−1.44683	−	2.50598i	−0.0560635	−	0.0971049i
$667$	−19.2144			−0.743986
$668$	8.13469	−	14.0897i	0.314741	−	0.545147i
$669$	−47.0030			−1.81724
$670$	3.94533	+	7.17177i	0.152422	+	0.277070i
$671$	42.2204			1.62990
$672$	−6.41888	+	11.1178i	−0.247614	+	0.428879i
$673$	−32.6383			−1.25811			−0.629057	−	0.777359i	$-0.716559\pi$
$673$	−32.6383			−1.25811			−0.629057	+	0.777359i	$0.716559\pi$
$674$	−11.0932	−	19.2140i	−0.427295	−	0.740096i
$675$	6.17006			0.237486
$676$	5.99264	−	10.3796i	0.230486	−	0.399214i
$677$	22.0062	+	38.1158i	0.845767	+	1.46491i	0.884954	+	0.465679i	$0.154190\pi$
$677$	22.0062	+	38.1158i	0.845767	+	1.46491i	−0.0391873	+	0.999232i	$0.512477\pi$
$678$	21.4555			0.823992
$679$	5.77674			0.221691
$680$	2.38990	−	4.13942i	0.0916484	−	0.158740i
$681$	−16.4640	−	28.5166i	−0.630904	−	1.09276i
$682$	−11.7683	−	20.3833i	−0.450632	−	0.780518i
$683$	−17.4542	+	30.2315i	−0.667866	+	1.15678i	0.310634	+	0.950530i	$0.399459\pi$
$683$	−17.4542	+	30.2315i	−0.667866	+	1.15678i	−0.978500	+	0.206248i	$0.933875\pi$
$684$	−11.5414			−0.441297
$685$	14.8683			0.568088
$686$	−13.9254	+	24.1195i	−0.531674	+	0.920886i
$687$	40.5192	−	70.1814i	1.54591	−	2.67759i
$688$	4.53264	−	7.85077i	0.172805	−	0.299308i
$689$	−1.78976	+	3.09995i	−0.0681843	+	0.118099i
$690$	−5.68361	−	9.84429i	−0.216371	−	0.374766i
$691$	1.76647	+	3.05961i	0.0671995	+	0.116393i	0.897668	−	0.440673i	$-0.145260\pi$
$691$	1.76647	+	3.05961i	0.0671995	+	0.116393i	−0.830468	+	0.557066i	$0.811927\pi$
$692$	−15.2996			−0.581605
$693$	36.6389	−	63.4605i	1.39180	−	2.41066i
$694$	−17.6530			−0.670100
$695$	−6.42920			−0.243874
$696$	−6.89655	−	11.9452i	−0.261413	−	0.452781i
$697$	−23.4759			−0.889212
$698$	−11.5386	+	19.9855i	−0.436743	+	0.756461i
$699$	−3.97376	−	6.88276i	−0.150301	−	0.260330i
$700$	2.24706	−	3.89203i	0.0849310	−	0.147105i
$701$	−0.779963	−	1.35094i	−0.0294588	−	0.0510242i	0.850920	−	0.525295i	$-0.176045\pi$
$701$	−0.779963	−	1.35094i	−0.0294588	−	0.0510242i	−0.880379	+	0.474271i	$0.842712\pi$
$702$	−3.10765	−	5.38260i	−0.117291	−	0.203153i
$703$	−0.627169	−	1.08629i	−0.0236541	−	0.0409701i
$704$	−1.57998	−	2.73660i	−0.0595477	−	0.103140i
$705$	18.1389	+	31.4175i	0.683150	+	1.18325i
$706$	−13.5950	−	23.5472i	−0.511653	−	0.886209i
$707$	16.7442	−	29.0018i	0.629731	−	1.09073i
$708$	5.07072	+	8.78274i	0.190569	+	0.330076i
$709$	−10.0334	+	17.3783i	−0.376812	+	0.652657i	−0.990596	−	0.136816i	$-0.956313\pi$
$709$	−10.0334	+	17.3783i	−0.376812	+	0.652657i	0.613785	+	0.789474i	$0.289646\pi$
$710$	3.90256			0.146461
$711$	−31.4033	−	54.3921i	−1.17772	−	2.03986i
$712$	3.52240			0.132007
$713$	−29.6396			−1.11001
$714$	30.6809	−	53.1409i	1.14820	−	1.98875i
$715$	3.18313			0.119042
$716$	0.109366	+	0.189427i	0.00408719	+	0.00707922i
$717$	−34.6724	−	60.0544i	−1.29487	−	2.24277i
$718$	−13.4907	+	23.3665i	−0.503467	+	0.872030i
$719$	6.76392	−	11.7154i	0.252252	−	0.436912i	−0.711894	−	0.702287i	$-0.752162\pi$
$719$	6.76392	−	11.7154i	0.252252	−	0.436912i	0.964145	+	0.265375i	$0.0854956\pi$
$720$	2.57998	−	4.46866i	0.0961501	−	0.166537i
$721$	21.3174	−	36.9228i	0.793902	−	1.37508i
$722$	13.9971			0.520916
$723$	19.8002			0.736377
$724$	11.3277	−	19.6202i	0.420992	−	0.729180i
$725$	2.41428	+	4.18166i	0.0896642	+	0.155303i
$726$	−1.44922	−	2.51013i	−0.0537858	−	0.0931597i
$727$	7.73333	−	13.3945i	0.286813	−	0.496775i	−0.686234	−	0.727381i	$-0.740737\pi$
$727$	7.73333	−	13.3945i	0.286813	−	0.496775i	0.973047	+	0.230606i	$0.0740707\pi$
$728$	−4.52707			−0.167784
$729$	−41.8059			−1.54837
$730$	−6.32323	−	10.9522i	−0.234033	−	0.405357i
$731$	−21.6651	+	37.5251i	−0.801313	+	1.38792i
$732$	38.1667			1.41068
$733$	−14.8715	−	25.7581i	−0.549290	−	0.951398i	−0.998323	−	0.0578832i	$-0.981565\pi$
$733$	−14.8715	−	25.7581i	−0.549290	−	0.951398i	0.449033	−	0.893515i	$-0.351768\pi$
$734$	26.7114			0.985934
$735$	18.8493	−	32.6479i	0.695265	−	1.20423i
$736$	−3.97933			−0.146680
$737$	−25.8599	−	0.534436i	−0.952560	−	0.0196862i
$738$	−25.3430			−0.932890
$739$	−11.4606	+	19.8504i	−0.421586	+	0.730208i	−0.996095	−	0.0882902i	$-0.971860\pi$
$739$	−11.4606	+	19.8504i	−0.421586	+	0.730208i	0.574509	+	0.818498i	$0.305193\pi$
$740$	0.560791			0.0206151
$741$	−3.21810	−	5.57391i	−0.118220	−	0.204763i
$742$	−15.9697			−0.586266
$743$	−25.0187	+	43.3336i	−0.917845	+	1.58975i	−0.115164	+	0.993346i	$0.536739\pi$
$743$	−25.0187	+	43.3336i	−0.917845	+	1.58975i	−0.802681	+	0.596408i	$0.796594\pi$
$744$	−10.6384	−	18.4263i	−0.390023	−	0.675540i
$745$	−14.1698			−0.519141
$746$	−4.71193			−0.172516
$747$	−35.2052	+	60.9773i	−1.28809	+	2.23104i
$748$	7.55198	+	13.0804i	0.276128	+	0.478267i
$749$	20.9987	+	36.3709i	0.767277	+	1.32896i
$750$	−1.42828	+	2.47386i	−0.0521535	+	0.0903325i
$751$	2.20927			0.0806174			0.0403087	−	0.999187i	$-0.487166\pi$
$751$	2.20927			0.0806174			0.0403087	+	0.999187i	$0.487166\pi$
$752$	12.6998			0.463114
$753$	14.3416	−	24.8404i	0.522637	−	0.905235i
$754$	2.43198	−	4.21232i	0.0885675	−	0.153403i
$755$	3.43807	−	5.95492i	0.125124	−	0.216722i
$756$	13.8645	−	24.0140i	0.504247	−	0.873382i
$757$	−19.9564	−	34.5655i	−0.725329	−	1.25631i	−0.958839	−	0.283952i	$-0.908354\pi$
$757$	−19.9564	−	34.5655i	−0.725329	−	1.25631i	0.233510	−	0.972354i	$-0.424979\pi$
$758$	−9.10210	−	15.7653i	−0.330603	−	0.572622i
$759$	35.9199			1.30381
$760$	1.11836	−	1.93706i	0.0405673	−	0.0702646i
$761$	−7.91877			−0.287055			−0.143528	−	0.989646i	$-0.545845\pi$
$761$	−7.91877			−0.287055			−0.143528	+	0.989646i	$0.545845\pi$
$762$	−0.418425			−0.0151579
$763$	30.0370	+	52.0255i	1.08741	+	1.88345i
$764$	1.17768			0.0426070
$765$	−12.3318	+	21.3593i	−0.445856	+	0.772246i
$766$	3.84384	+	6.65773i	0.138884	+	0.240554i
$767$	−1.78813	+	3.09712i	−0.0645655	+	0.111831i
$768$	−1.42828	−	2.47386i	−0.0515387	−	0.0892676i
$769$	−16.8633	−	29.2081i	−0.608106	−	1.05327i	−0.991552	−	0.129708i	$-0.958596\pi$
$769$	−16.8633	−	29.2081i	−0.608106	−	1.05327i	0.383446	−	0.923563i	$-0.374737\pi$
$770$	7.10062	+	12.2986i	0.255889	+	0.443212i
$771$	27.8855	+	48.2991i	1.00427	+	1.73945i
$772$	4.35518	+	7.54339i	0.156746	+	0.271493i
$773$	7.89567	+	13.6757i	0.283988	+	0.491881i	0.972363	−	0.233474i	$-0.0750092\pi$
$773$	7.89567	+	13.6757i	0.283988	+	0.491881i	−0.688376	+	0.725354i	$0.741676\pi$
$774$	−23.3883	+	40.5097i	−0.840674	+	1.45609i
$775$	3.72420	+	6.45050i	0.133777	+	0.231709i
$776$	−0.642699	+	1.11319i	−0.0230716	+	0.0399611i
$777$	7.19930			0.258274
$778$	9.94332	+	17.2223i	0.356485	+	0.617450i
$779$	−10.9856			−0.393601
$780$	2.87751			0.103031
$781$	−6.16597	+	10.6798i	−0.220636	+	0.382152i
$782$	19.0204			0.680168
$783$	14.8963	+	25.8011i	0.532349	+	0.922055i
$784$	−6.59858	−	11.4291i	−0.235663	−	0.408181i
$785$	−10.0454	+	17.3991i	−0.358534	+	0.620999i
$786$	15.7413	−	27.2648i	0.561474	−	0.972502i
$787$	−6.50152	+	11.2610i	−0.231754	+	0.401410i	−0.958324	−	0.285682i	$-0.907780\pi$
$787$	−6.50152	+	11.2610i	−0.231754	+	0.401410i	0.726570	+	0.687092i	$0.241113\pi$
$788$	8.00919	−	13.8723i	0.285316	−	0.494181i
$789$	7.95972			0.283374
$790$	12.1719			0.433057
$791$	−16.8775	+	29.2328i	−0.600096	+	1.03940i
$792$	8.15263	+	14.1208i	0.289691	+	0.501760i
$793$	6.72951	+	11.6559i	0.238972	+	0.413911i
$794$	−15.7564	+	27.2910i	−0.559175	+	0.968520i
$795$	10.1507			0.360008
$796$	13.9623			0.494880
$797$	−24.9444	−	43.2049i	−0.883575	−	1.53040i	−0.847338	−	0.531053i	$-0.821796\pi$
$797$	−24.9444	−	43.2049i	−0.883575	−	1.53040i	−0.0362366	−	0.999343i	$-0.511537\pi$
$798$	14.3573	−	24.8675i	0.508242	−	0.880301i
$799$	−60.7024			−2.14750
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−18.1754			−0.642197
$802$	−4.46102	+	7.72671i	−0.157524	+	0.272839i
$803$	39.9623			1.41024
$804$	−23.3770	−	0.483123i	−0.824443	−	0.0170384i
$805$	17.8836			0.630314
$806$	3.75150	−	6.49780i	0.132141	−	0.228875i
$807$	69.0879			2.43201
$808$	3.72580	+	6.45328i	0.131073	+	0.227025i
$809$	14.9279			0.524835			0.262418	−	0.964954i	$-0.415480\pi$
$809$	14.9279			0.524835			0.262418	+	0.964954i	$0.415480\pi$
$810$	−1.07265	+	1.85788i	−0.0376890	+	0.0652793i
$811$	−11.1930	−	19.3868i	−0.393038	−	0.680761i	0.599811	−	0.800142i	$-0.295242\pi$
$811$	−11.1930	−	19.3868i	−0.393038	−	0.680761i	−0.992849	+	0.119381i	$0.961909\pi$
$812$	21.7002			0.761526
$813$	−78.9385			−2.76849
$814$	−0.886039	+	1.53466i	−0.0310556	+	0.0537900i
$815$	−2.03273	−	3.52080i	−0.0712035	−	0.123328i
$816$	6.82690	+	11.8245i	0.238989	+	0.413941i
$817$	−10.1383	+	17.5600i	−0.354694	+	0.614348i
$818$	−19.7738			−0.691374
$819$	23.3595			0.816247
$820$	2.45574	−	4.25347i	0.0857582	−	0.148537i
$821$	−9.21305	+	15.9575i	−0.321538	+	0.556919i	−0.980805	−	0.194989i	$-0.937533\pi$
$821$	−9.21305	+	15.9575i	−0.321538	+	0.556919i	0.659268	+	0.751908i	$0.270866\pi$
$822$	−21.2361	+	36.7820i	−0.740694	+	1.28292i
$823$	−22.3242	+	38.6666i	−0.778173	+	1.34783i	0.154821	+	0.987943i	$0.450520\pi$
$823$	−22.3242	+	38.6666i	−0.778173	+	1.34783i	−0.932994	+	0.359892i	$0.882813\pi$
$824$	4.74340	+	8.21580i	0.165244	+	0.286211i
$825$	−4.51331	−	7.81729i	−0.157133	−	0.272163i
$826$	−15.9551			−0.555150
$827$	6.54846	−	11.3423i	0.227712	−	0.394409i	−0.729418	−	0.684069i	$-0.760209\pi$
$827$	6.54846	−	11.3423i	0.227712	−	0.394409i	0.957130	+	0.289660i	$0.0935421\pi$
$828$	20.5332			0.713577
$829$	39.0237			1.35535			0.677675	−	0.735362i	$-0.262988\pi$
$829$	39.0237			1.35535			0.677675	+	0.735362i	$0.262988\pi$
$830$	−6.82278	−	11.8174i	−0.236822	−	0.410188i
$831$	77.7093			2.69571
$832$	0.503666	−	0.872375i	0.0174615	−	0.0302441i
$833$	31.5398	+	54.6286i	1.09279	+	1.89277i
$834$	9.18272	−	15.9049i	0.317971	−	0.550743i
$835$	−8.13469	−	14.0897i	−0.281513	−	0.487594i
$836$	3.53398	+	6.12104i	0.122225	+	0.211700i
$837$	22.9785	+	39.8000i	0.794254	+	1.37569i
$838$	−7.41294	−	12.8396i	−0.256076	−	0.443536i
$839$	−6.65497	−	11.5267i	−0.229755	−	0.397948i	0.727980	−	0.685598i	$-0.240459\pi$
$839$	−6.65497	−	11.5267i	−0.229755	−	0.397948i	−0.957735	+	0.287650i	$0.907126\pi$
$840$	6.41888	+	11.1178i	0.221472	+	0.383601i
$841$	2.84249	−	4.92334i	0.0980170	−	0.169770i
$842$	−3.25445	−	5.63687i	−0.112156	−	0.194259i
$843$	44.2519	−	76.6465i	1.52412	−	2.63984i
$844$	−16.7791			−0.577560
$845$	−5.99264	−	10.3796i	−0.206153	−	0.357068i
$846$	−65.5304			−2.25298
$847$	4.56002			0.156684
$848$	1.77673	−	3.07739i	0.0610132	−	0.105678i
$849$	−13.8953			−0.476884
$850$	−2.38990	−	4.13942i	−0.0819728	−	0.141981i
$851$	1.11579	+	1.93260i	0.0382487	+	0.0662487i
$852$	−5.57396	+	9.65438i	−0.190961	+	0.330754i
$853$	−3.80971	+	6.59861i	−0.130442	+	0.225932i	−0.923847	−	0.382762i	$-0.874973\pi$
$853$	−3.80971	+	6.59861i	−0.130442	+	0.225932i	0.793405	+	0.608694i	$0.208306\pi$
$854$	−30.0231	+	52.0016i	−1.02737	+	1.77946i
$855$	−5.77071	+	9.99516i	−0.197354	+	0.341827i
$856$	−9.34497			−0.319405
$857$	3.07051			0.104886			0.0524432	−	0.998624i	$-0.483299\pi$
$857$	3.07051			0.104886			0.0524432	+	0.998624i	$0.483299\pi$
$858$	−4.54640	+	7.87460i	−0.155212	+	0.268834i
$859$	17.8682	+	30.9487i	0.609656	+	1.05596i	0.991297	+	0.131644i	$0.0420257\pi$
$859$	17.8682	+	30.9487i	0.609656	+	1.05596i	−0.381641	+	0.924311i	$0.624641\pi$
$860$	−4.53264	−	7.85077i	−0.154562	−	0.267709i
$861$	31.5262	−	54.6049i	1.07441	−	1.86093i
$862$	3.03186			0.103266
$863$	−8.07597			−0.274909			−0.137455	−	0.990508i	$-0.543892\pi$
$863$	−8.07597			−0.274909			−0.137455	+	0.990508i	$0.543892\pi$
$864$	3.08503	+	5.34343i	0.104955	+	0.181787i
$865$	−7.64982	+	13.2499i	−0.260102	+	0.450509i
$866$	19.4988			0.662596
$867$	−8.35037	−	14.4633i	−0.283594	−	0.491198i
$868$	33.4740			1.13618
$869$	−19.2314	+	33.3097i	−0.652380	+	1.12996i
$870$	−13.7931			−0.467630
$871$	−3.97426	−	7.22435i	−0.134663	−	0.244788i
$872$	−13.3672			−0.452671
$873$	3.31630	−	5.74400i	0.112240	−	0.194405i
$874$	8.90067			0.301070
$875$	−2.24706	−	3.89203i	−0.0759646	−	0.131574i
$876$	36.1254			1.22057
$877$	−11.2332	+	19.4564i	−0.379317	+	0.656997i	−0.990963	−	0.134135i	$-0.957174\pi$
$877$	−11.2332	+	19.4564i	−0.379317	+	0.656997i	0.611646	+	0.791132i	$0.290508\pi$
$878$	2.73228	+	4.73244i	0.0922099	+	0.159712i
$879$	20.9836			0.707758
$880$	−3.15996			−0.106522
$881$	−16.2695	+	28.1796i	−0.548134	+	0.949395i	0.450269	+	0.892893i	$0.351328\pi$
$881$	−16.2695	+	28.1796i	−0.548134	+	0.949395i	−0.998402	+	0.0565023i	$0.982005\pi$
$882$	34.0484	+	58.9735i	1.14647	+	1.98574i
$883$	−9.77152	−	16.9248i	−0.328838	−	0.569564i	0.653444	−	0.756975i	$-0.273324\pi$
$883$	−9.77152	−	16.9248i	−0.328838	−	0.569564i	−0.982282	+	0.187411i	$0.939990\pi$
$884$	−2.40742	+	4.16977i	−0.0809703	+	0.140245i
$885$	10.1414			0.340901
$886$	28.4699			0.956467
$887$	−8.98005	+	15.5539i	−0.301520	+	0.522249i	−0.976481	−	0.215606i	$-0.930827\pi$
$887$	−8.98005	+	15.5539i	−0.301520	+	0.522249i	0.674960	+	0.737854i	$0.264161\pi$
$888$	−0.800968	+	1.38732i	−0.0268787	+	0.0465553i
$889$	0.329146	−	0.570097i	0.0110392	−	0.0191204i
$890$	1.76120	−	3.05049i	0.0590355	−	0.102253i
$891$	−3.38952	−	5.87082i	−0.113553	−	0.196680i
$892$	8.22719	+	14.2499i	0.275467	+	0.477122i
$893$	−28.4060			−0.950569
$894$	20.2385	−	35.0540i	0.676875	−	1.17238i
$895$	0.218731			0.00731139
$896$	4.49412			0.150138
$897$	5.72527	+	9.91647i	0.191161	+	0.331101i
$898$	−16.4825			−0.550029
$899$	−17.9825	+	31.1467i	−0.599751	+	1.03880i
$900$	−2.57998	−	4.46866i	−0.0859993	−	0.148955i
$901$	−8.49241	+	14.7093i	−0.282923	+	0.490037i
$902$	7.76004	+	13.4408i	0.258381	+	0.447529i
$903$	−58.1890	−	100.786i	−1.93641	−	3.35396i
$904$	−3.75547	−	6.50466i	−0.124905	−	0.216342i
$905$	−11.3277	−	19.6202i	−0.376547	−	0.652198i
$906$	9.82108	+	17.0106i	0.326283	+	0.565139i
$907$	7.17966	+	12.4355i	0.238397	+	0.412915i	0.960254	−	0.279126i	$-0.0900448\pi$
$907$	7.17966	+	12.4355i	0.238397	+	0.412915i	−0.721858	+	0.692041i	$0.756712\pi$
$908$	−5.76358	+	9.98282i	−0.191271	+	0.331292i
$909$	−19.2250	−	33.2986i	−0.637652	−	1.10445i
$910$	−2.26354	+	3.92056i	−0.0750355	+	0.129965i
$911$	−36.7883			−1.21885			−0.609425	−	0.792844i	$-0.708600\pi$
$911$	−36.7883			−1.21885			−0.609425	+	0.792844i	$0.708600\pi$
$912$	3.19468	+	5.53334i	0.105786	+	0.183227i
$913$	43.1194			1.42704
$914$	15.0400			0.497479
$915$	19.0834	−	33.0534i	0.630877	−	1.09271i
$916$	−28.3692			−0.937345
$917$	24.7652	+	42.8946i	0.817819	+	1.41650i
$918$	−14.7458	−	25.5405i	−0.486684	−	0.842962i
$919$	24.5733	−	42.5623i	0.810599	−	1.40400i	−0.101846	−	0.994800i	$-0.532475\pi$
$919$	24.5733	−	42.5623i	0.810599	−	1.40400i	0.912445	−	0.409199i	$-0.134192\pi$
$920$	−1.98966	+	3.44620i	−0.0655973	+	0.113618i
$921$	−9.18260	+	15.9047i	−0.302577	+	0.524079i
$922$	−1.53125	+	2.65220i	−0.0504291	+	0.0873457i
$923$	−3.93117			−0.129396
$924$	−40.5668			−1.33455
$925$	0.280396	−	0.485660i	0.00921935	−	0.0159684i
$926$	20.9244	+	36.2422i	0.687619	+	1.19099i
$927$	−24.4757	−	42.3932i	−0.803888	−	1.39238i
$928$	−2.41428	+	4.18166i	−0.0792527	+	0.137270i
$929$	−47.2750			−1.55104			−0.775521	−	0.631322i	$-0.782513\pi$
$929$	−47.2750			−1.55104			−0.775521	+	0.631322i	$0.782513\pi$
$930$	−21.2768			−0.697695
$931$	14.7592	+	25.5637i	0.483714	+	0.837817i
$932$	−1.39110	+	2.40945i	−0.0455669	+	0.0789242i
$933$	64.9821			2.12742
$934$	−3.88008	−	6.72050i	−0.126960	−	0.219902i
$935$	15.1040			0.493952
$936$	−2.59889	+	4.50142i	−0.0849475	+	0.147133i
$937$	−35.0244			−1.14420			−0.572098	−	0.820185i	$-0.693870\pi$
$937$	−35.0244			−1.14420			−0.572098	+	0.820185i	$0.693870\pi$
$938$	19.0473	−	31.4708i	0.621917	−	1.02756i
$939$	−29.8987			−0.975708
$940$	6.34989	−	10.9983i	0.207111	−	0.358726i
$941$	55.6740			1.81492			0.907460	−	0.420139i	$-0.138019\pi$
$941$	55.6740			1.81492			0.907460	+	0.420139i	$0.138019\pi$
$942$	−28.6952	−	49.7016i	−0.934940	−	1.61936i
$943$	19.5444			0.636453
$944$	1.77511	−	3.07458i	0.0577749	−	0.100069i
$945$	−13.8645	−	24.0140i	−0.451012	−	0.781176i
$946$	28.6459			0.931360
$947$	17.4537			0.567168			0.283584	−	0.958947i	$-0.408476\pi$
$947$	17.4537			0.567168			0.283584	+	0.958947i	$0.408476\pi$
$948$	−17.3849	+	30.1116i	−0.564636	+	0.977979i
$949$	6.36959	+	11.0325i	0.206766	+	0.358129i
$950$	−1.11836	−	1.93706i	−0.0362845	−	0.0628466i
$951$	−47.5880	+	82.4249i	−1.54315	+	2.67281i
$952$	−21.4810			−0.696203
$953$	−7.64184			−0.247543			−0.123772	−	0.992311i	$-0.539499\pi$
$953$	−7.64184			−0.247543			−0.123772	+	0.992311i	$0.539499\pi$
$954$	−9.16785	+	15.8792i	−0.296820	+	0.514108i
$955$	0.588841	−	1.01990i	0.0190544	−	0.0330032i
$956$	−12.1378	+	21.0233i	−0.392565	+	0.679943i
$957$	21.7928	−	37.7463i	0.704461	−	1.22016i
$958$	2.69733	+	4.67192i	0.0871469	+	0.150943i
$959$	−33.4099	−	57.8677i	−1.07886	−	1.86865i
$960$	−2.85656			−0.0921952
$961$	−12.2393	+	21.1991i	−0.394817	+	0.683843i
$962$	−0.564903			−0.0182132
$963$	48.2197			1.55386
$964$	−3.46574	−	6.00283i	−0.111624	−	0.193338i
$965$	8.71036			0.280396
$966$	−25.5428	+	44.2415i	−0.821827	+	1.42345i
$967$	3.89292	+	6.74274i	0.125188	+	0.216832i	0.921806	−	0.387651i	$-0.126713\pi$
$967$	3.89292	+	6.74274i	0.125188	+	0.216832i	−0.796618	+	0.604482i	$0.793380\pi$
$968$	−0.507331	+	0.878724i	−0.0163063	+	0.0282433i
$969$	−15.2699	−	26.4482i	−0.490540	−	0.849640i
$970$	0.642699	+	1.11319i	0.0206358	+	0.0357423i
$971$	−17.9921	−	31.1632i	−0.577394	−	1.00008i	−0.995777	−	0.0918054i	$-0.970736\pi$
$971$	−17.9921	−	31.1632i	−0.577394	−	1.00008i	0.418383	−	0.908271i	$-0.362597\pi$
$972$	6.19100	+	10.7231i	0.198576	+	0.343945i
$973$	14.4468	+	25.0226i	0.463144	+	0.802189i
$974$	−0.707213	−	1.22493i	−0.0226606	−	0.0392493i
$975$	1.43875	−	2.49199i	0.0460770	−	0.0798077i
$976$	−6.68053	−	11.5710i	−0.213839	−	0.370379i
$977$	9.67400	−	16.7559i	0.309499	−	0.536067i	−0.668754	−	0.743484i	$-0.733172\pi$
$977$	9.67400	−	16.7559i	0.309499	−	0.536067i	0.978253	+	0.207416i	$0.0665054\pi$
$978$	11.6133			0.371351
$979$	5.56532	+	9.63941i	0.177868	+	0.308077i
$980$	−13.1972			−0.421568
$981$	68.9743			2.20218
$982$	−19.7122	+	34.1426i	−0.629043	+	1.08953i
$983$	−48.9508			−1.56129			−0.780643	−	0.624977i	$-0.785108\pi$
$983$	−48.9508			−1.56129			−0.780643	+	0.624977i	$0.785108\pi$
$984$	7.01498	+	12.1503i	0.223629	+	0.387337i
$985$	−8.00919	−	13.8723i	−0.255194	−	0.442009i
$986$	11.5398	−	19.9875i	0.367501	−	0.636531i
$987$	81.5184	−	141.194i	2.59476	−	4.49425i
$988$	−1.12656	+	1.95126i	−0.0358407	+	0.0620780i
$989$	18.0369	−	31.2408i	0.573540	−	0.993400i
$990$	16.3053			0.518215
$991$	−7.45780			−0.236905			−0.118452	−	0.992960i	$-0.537793\pi$
$991$	−7.45780			−0.236905			−0.118452	+	0.992960i	$0.537793\pi$
$992$	−3.72420	+	6.45050i	−0.118243	+	0.204804i
$993$	30.9584	+	53.6215i	0.982436	+	1.70163i
$994$	−8.76930	−	15.1889i	−0.278145	−	0.481762i
$995$	6.98114	−	12.0917i	0.221317	−	0.383332i
$996$	38.9794			1.23511
$997$	−39.7859			−1.26003			−0.630017	−	0.776582i	$-0.716952\pi$
$997$	−39.7859			−1.26003			−0.630017	+	0.776582i	$0.716952\pi$
$998$	−11.6957	−	20.2575i	−0.370220	−	0.641240i
$999$	1.73006	−	2.99655i	0.0547366	−	0.0948066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.j.431.6	yes	12
67.37	even	3	inner	670.2.e.j.171.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.j.171.6	✓	12	67.37	even	3	inner
670.2.e.j.431.6	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +2.85656 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.42828 - 2.47386i) q^{6} +(2.24706 + 3.89203i) q^{7} -1.00000 q^{8} +5.15996 q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +2.85656 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(1.42828 - 2.47386i) q^{6} +(2.24706 + 3.89203i) q^{7} -1.00000 q^{8} +5.15996 q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.57998 - 2.73660i) q^{11} +(-1.42828 - 2.47386i) q^{12} +(0.503666 - 0.872375i) q^{13} +4.49412 q^{14} -2.85656 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.38990 - 4.13942i) q^{17} +(2.57998 - 4.46866i) q^{18} +(1.11836 - 1.93706i) q^{19} +(0.500000 + 0.866025i) q^{20} +(6.41888 + 11.1178i) q^{21} -3.15996 q^{22} +(-1.98966 + 3.44620i) q^{23} -2.85656 q^{24} +1.00000 q^{25} +(-0.503666 - 0.872375i) q^{26} +6.17006 q^{27} +(2.24706 - 3.89203i) q^{28} +(2.41428 + 4.18166i) q^{29} +(-1.42828 + 2.47386i) q^{30} +(3.72420 + 6.45050i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.51331 - 7.81729i) q^{33} +(-2.38990 - 4.13942i) q^{34} +(-2.24706 - 3.89203i) q^{35} +(-2.57998 - 4.46866i) q^{36} +(0.280396 - 0.485660i) q^{37} +(-1.11836 - 1.93706i) q^{38} +(1.43875 - 2.49199i) q^{39} +1.00000 q^{40} +(-2.45574 - 4.25347i) q^{41} +12.8378 q^{42} -9.06529 q^{43} +(-1.57998 + 2.73660i) q^{44} -5.15996 q^{45} +(1.98966 + 3.44620i) q^{46} +(-6.34989 - 10.9983i) q^{47} +(-1.42828 + 2.47386i) q^{48} +(-6.59858 + 11.4291i) q^{49} +(0.500000 - 0.866025i) q^{50} +(6.82690 - 11.8245i) q^{51} -1.00733 q^{52} -3.55346 q^{53} +(3.08503 - 5.34343i) q^{54} +(1.57998 + 2.73660i) q^{55} +(-2.24706 - 3.89203i) q^{56} +(3.19468 - 5.53334i) q^{57} +4.82856 q^{58} -3.55022 q^{59} +(1.42828 + 2.47386i) q^{60} +(-6.68053 + 11.5710i) q^{61} +7.44840 q^{62} +(11.5947 + 20.0827i) q^{63} +1.00000 q^{64} +(-0.503666 + 0.872375i) q^{65} -9.02662 q^{66} +(4.23827 - 7.00265i) q^{67} -4.77980 q^{68} +(-5.68361 + 9.84429i) q^{69} -4.49412 q^{70} +(-1.95128 - 3.37972i) q^{71} -5.15996 q^{72} +(-6.32323 + 10.9522i) q^{73} +(-0.280396 - 0.485660i) q^{74} +2.85656 q^{75} -2.23673 q^{76} +(7.10062 - 12.2986i) q^{77} +(-1.43875 - 2.49199i) q^{78} +(-6.08596 - 10.5412i) q^{79} +(0.500000 - 0.866025i) q^{80} +2.14530 q^{81} -4.91148 q^{82} +(-6.82278 + 11.8174i) q^{83} +(6.41888 - 11.1178i) q^{84} +(-2.38990 + 4.13942i) q^{85} +(-4.53264 + 7.85077i) q^{86} +(6.89655 + 11.9452i) q^{87} +(1.57998 + 2.73660i) q^{88} -3.52240 q^{89} +(-2.57998 + 4.46866i) q^{90} +4.52707 q^{91} +3.97933 q^{92} +(10.6384 + 18.4263i) q^{93} -12.6998 q^{94} +(-1.11836 + 1.93706i) q^{95} +(1.42828 + 2.47386i) q^{96} +(0.642699 - 1.11319i) q^{97} +(6.59858 + 11.4291i) q^{98} +(-8.15263 - 14.1208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9} - 6 q^{10} + 2 q^{12} + 6 q^{14} + 4 q^{15} - 6 q^{16} + 13 q^{17} + 12 q^{18} - 9 q^{19} + 6 q^{20} + 11 q^{21} - 3 q^{23} + 4 q^{24} + 12 q^{25} - 16 q^{27} + 3 q^{28} - 5 q^{29} + 2 q^{30} + 14 q^{31} + 6 q^{32} + 10 q^{33} - 13 q^{34} - 3 q^{35} - 12 q^{36} + 2 q^{37} + 9 q^{38} + 14 q^{39} + 12 q^{40} + 15 q^{41} + 22 q^{42} + 4 q^{43} - 24 q^{45} + 3 q^{46} - 11 q^{47} + 2 q^{48} - 43 q^{49} + 6 q^{50} + 15 q^{51} - 52 q^{53} - 8 q^{54} - 3 q^{56} + 3 q^{57} - 10 q^{58} + 54 q^{59} - 2 q^{60} - 6 q^{61} + 28 q^{62} - 4 q^{63} + 12 q^{64} + 20 q^{66} - 5 q^{67} - 26 q^{68} + 13 q^{69} - 6 q^{70} - 6 q^{71} - 24 q^{72} - 15 q^{73} - 2 q^{74} - 4 q^{75} + 18 q^{76} - 10 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} + 12 q^{81} + 30 q^{82} - 15 q^{83} + 11 q^{84} - 13 q^{85} + 2 q^{86} + 5 q^{87} - 14 q^{89} - 12 q^{90} + 4 q^{91} + 6 q^{92} + 28 q^{93} - 22 q^{94} + 9 q^{95} - 2 q^{96} + 21 q^{97} + 43 q^{98} - 72 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9 - 6 * q^10 + 2 * q^12 + 6 * q^14 + 4 * q^15 - 6 * q^16 + 13 * q^17 + 12 * q^18 - 9 * q^19 + 6 * q^20 + 11 * q^21 - 3 * q^23 + 4 * q^24 + 12 * q^25 - 16 * q^27 + 3 * q^28 - 5 * q^29 + 2 * q^30 + 14 * q^31 + 6 * q^32 + 10 * q^33 - 13 * q^34 - 3 * q^35 - 12 * q^36 + 2 * q^37 + 9 * q^38 + 14 * q^39 + 12 * q^40 + 15 * q^41 + 22 * q^42 + 4 * q^43 - 24 * q^45 + 3 * q^46 - 11 * q^47 + 2 * q^48 - 43 * q^49 + 6 * q^50 + 15 * q^51 - 52 * q^53 - 8 * q^54 - 3 * q^56 + 3 * q^57 - 10 * q^58 + 54 * q^59 - 2 * q^60 - 6 * q^61 + 28 * q^62 - 4 * q^63 + 12 * q^64 + 20 * q^66 - 5 * q^67 - 26 * q^68 + 13 * q^69 - 6 * q^70 - 6 * q^71 - 24 * q^72 - 15 * q^73 - 2 * q^74 - 4 * q^75 + 18 * q^76 - 10 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 + 12 * q^81 + 30 * q^82 - 15 * q^83 + 11 * q^84 - 13 * q^85 + 2 * q^86 + 5 * q^87 - 14 * q^89 - 12 * q^90 + 4 * q^91 + 6 * q^92 + 28 * q^93 - 22 * q^94 + 9 * q^95 - 2 * q^96 + 21 * q^97 + 43 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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