LMFDB - Embedded newform 630.2.l.i.571.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(331,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 0, 2]))

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

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

chi := DirichletCharacter("630.331");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + \cdots + 6561 $ x^16 - x^15 + 2x^14 - 4x^13 + 5x^12 + 2x^11 - 35x^10 + 81x^9 - 66x^8 + 243x^7 - 315x^6 + 54x^5 + 405x^4 - 972x^3 + 1458x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			571.7
Root			$1.52536 - 0.820531i$ of defining polynomial
Character	$\chi$	$=$	630.571
Dual form			630.2.l.i.331.7

$q$-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} +(1.47328 - 0.910737i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.0520808 - 1.73127i) q^{6} +(2.16962 + 1.51418i) q^{7} -1.00000 q^{8} +(1.34112 - 2.68354i) q^{9} +(-0.500000 + 0.866025i) q^{10} +5.14142 q^{11} +(-1.52536 - 0.820531i) q^{12} +(1.62366 - 2.81226i) q^{13} +(2.39613 - 1.12185i) q^{14} +(-1.47328 + 0.910737i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.89695 + 5.01766i) q^{17} +(-1.65346 - 2.50321i) q^{18} +(-2.34980 - 4.06997i) q^{19} +(0.500000 + 0.866025i) q^{20} +(4.57548 + 0.254868i) q^{21} +(2.57071 - 4.45260i) q^{22} -2.66925 q^{23} +(-1.47328 + 0.910737i) q^{24} +1.00000 q^{25} +(-1.62366 - 2.81226i) q^{26} +(-0.468162 - 5.17502i) q^{27} +(0.226513 - 2.63604i) q^{28} +(0.227646 + 0.394295i) q^{29} +(0.0520808 + 1.73127i) q^{30} +(-3.57071 - 6.18465i) q^{31} +(0.500000 + 0.866025i) q^{32} +(7.57475 - 4.68248i) q^{33} +(2.89695 + 5.01766i) q^{34} +(-2.16962 - 1.51418i) q^{35} +(-2.99458 + 0.180332i) q^{36} +(2.00070 + 3.46531i) q^{37} -4.69959 q^{38} +(-0.169123 - 5.62199i) q^{39} +1.00000 q^{40} +(-3.71105 + 6.42773i) q^{41} +(2.50846 - 3.83505i) q^{42} +(-1.80497 - 3.12631i) q^{43} +(-2.57071 - 4.45260i) q^{44} +(-1.34112 + 2.68354i) q^{45} +(-1.33463 + 2.31164i) q^{46} +(1.57921 - 2.73527i) q^{47} +(0.0520808 + 1.73127i) q^{48} +(2.41449 + 6.57041i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.301751 + 10.0308i) q^{51} -3.24732 q^{52} +(-1.63008 + 2.82338i) q^{53} +(-4.71578 - 2.18207i) q^{54} -5.14142 q^{55} +(-2.16962 - 1.51418i) q^{56} +(-7.16858 - 3.85616i) q^{57} +0.455293 q^{58} +(5.56657 + 9.64157i) q^{59} +(1.52536 + 0.820531i) q^{60} +(-2.99783 + 5.19239i) q^{61} -7.14142 q^{62} +(6.97309 - 3.79157i) q^{63} +1.00000 q^{64} +(-1.62366 + 2.81226i) q^{65} +(-0.267769 - 8.90117i) q^{66} +(5.88868 + 10.1995i) q^{67} +5.79389 q^{68} +(-3.93256 + 2.43099i) q^{69} +(-2.39613 + 1.12185i) q^{70} -4.38588 q^{71} +(-1.34112 + 2.68354i) q^{72} +(6.94143 - 12.0229i) q^{73} +4.00140 q^{74} +(1.47328 - 0.910737i) q^{75} +(-2.34980 + 4.06997i) q^{76} +(11.1549 + 7.78505i) q^{77} +(-4.95334 - 2.66453i) q^{78} +(-1.47595 + 2.55642i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-5.40282 - 7.19789i) q^{81} +(3.71105 + 6.42773i) q^{82} +(6.13291 + 10.6225i) q^{83} +(-2.06702 - 4.08992i) q^{84} +(2.89695 - 5.01766i) q^{85} -3.60995 q^{86} +(0.694486 + 0.373581i) q^{87} -5.14142 q^{88} +(-4.83214 - 8.36951i) q^{89} +(1.65346 + 2.50321i) q^{90} +(7.78102 - 3.64302i) q^{91} +(1.33463 + 2.31164i) q^{92} +(-10.8932 - 5.85975i) q^{93} +(-1.57921 - 2.73527i) q^{94} +(2.34980 + 4.06997i) q^{95} +(1.52536 + 0.820531i) q^{96} +(3.91728 + 6.78493i) q^{97} +(6.89738 + 1.19419i) q^{98} +(6.89523 - 13.7972i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - q^{3} - 8 q^{4} - 16 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} + 9 q^{9} - 8 q^{10} - 2 q^{11} - q^{12} + 2 q^{13} + 8 q^{14} + q^{15} - 8 q^{16} + 11 q^{17} + 3 q^{18} - 2 q^{19} + 8 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - q^3 - 8 * q^4 - 16 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 + 9 * q^9 - 8 * q^10 - 2 * q^11 - q^12 + 2 * q^13 + 8 * q^14 + q^15 - 8 * q^16 + 11 * q^17 + 3 * q^18 - 2 * q^19 + 8 * q^20 - q^22 - 22 * q^23 + q^24 + 16 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 + 2 * q^30 - 15 * q^31 + 8 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 - 4 * q^38 + 33 * q^39 + 16 * q^40 + 7 * q^41 - 9 * q^42 - 13 * q^43 + q^44 - 9 * q^45 - 11 * q^46 - 5 * q^47 + 2 * q^48 + 10 * q^49 + 8 * q^50 + 30 * q^51 - 4 * q^52 + 18 * q^53 + q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 + 34 * q^58 + q^59 + q^60 - 27 * q^61 - 30 * q^62 + 14 * q^63 + 16 * q^64 - 2 * q^65 + 10 * q^66 - 10 * q^67 - 22 * q^68 - 14 * q^69 - 8 * q^70 - 38 * q^71 - 9 * q^72 - 8 * q^73 - 4 * q^74 - q^75 - 2 * q^76 - 19 * q^77 - 25 * q^79 + 8 * q^80 + 9 * q^81 - 7 * q^82 + 2 * q^83 - 9 * q^84 - 11 * q^85 - 26 * q^86 + 58 * q^87 + 2 * q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 + 3 * q^93 + 5 * q^94 + 2 * q^95 + q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.47328	−	0.910737i	0.850599	−	0.525814i
$3$	1.47328	−	0.910737i	0.850599	−	0.525814i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.0520808	−	1.73127i	−0.0212619	−	0.706787i
$7$	2.16962	+	1.51418i	0.820039	+	0.572308i
$7$	2.16962	+	1.51418i	0.820039	+	0.572308i
$8$	−1.00000			−0.353553
$9$	1.34112	−	2.68354i	0.447039	−	0.894515i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	5.14142			1.55019			0.775097	−	0.631842i	$-0.217701\pi$
$11$	5.14142			1.55019			0.775097	+	0.631842i	$0.217701\pi$
$12$	−1.52536	−	0.820531i	−0.440334	−	0.236867i
$13$	1.62366	−	2.81226i	0.450323	−	0.779982i	−0.548083	−	0.836424i	$-0.684642\pi$
$13$	1.62366	−	2.81226i	0.450323	−	0.779982i	0.998406	+	0.0564419i	$0.0179756\pi$
$14$	2.39613	−	1.12185i	0.640393	−	0.299828i
$15$	−1.47328	+	0.910737i	−0.380400	+	0.235151i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.89695	+	5.01766i	−0.702613	+	1.21696i	0.264933	+	0.964267i	$0.414650\pi$
$17$	−2.89695	+	5.01766i	−0.702613	+	1.21696i	−0.967546	+	0.252694i	$0.918683\pi$
$18$	−1.65346	−	2.50321i	−0.389724	−	0.590013i
$19$	−2.34980	−	4.06997i	−0.539080	−	0.933715i	−0.998954	−	0.0457301i	$-0.985439\pi$
$19$	−2.34980	−	4.06997i	−0.539080	−	0.933715i	0.459873	−	0.887984i	$-0.347895\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	4.57548	+	0.254868i	0.998452	+	0.0556167i
$22$	2.57071	−	4.45260i	0.548077	−	0.949297i
$23$	−2.66925			−0.556578			−0.278289	−	0.960497i	$-0.589767\pi$
$23$	−2.66925			−0.556578			−0.278289	+	0.960497i	$0.589767\pi$
$24$	−1.47328	+	0.910737i	−0.300732	+	0.185903i
$25$	1.00000			0.200000
$26$	−1.62366	−	2.81226i	−0.318426	−	0.551531i
$27$	−0.468162	−	5.17502i	−0.0900979	−	0.995933i
$28$	0.226513	−	2.63604i	0.0428069	−	0.498164i
$29$	0.227646	+	0.394295i	0.0422728	+	0.0732187i	0.886388	−	0.462944i	$-0.153207\pi$
$29$	0.227646	+	0.394295i	0.0422728	+	0.0732187i	−0.844115	+	0.536162i	$0.819873\pi$
$30$	0.0520808	+	1.73127i	0.00950861	+	0.316085i
$31$	−3.57071	−	6.18465i	−0.641318	−	1.11080i	−0.985139	−	0.171760i	$-0.945055\pi$
$31$	−3.57071	−	6.18465i	−0.641318	−	1.11080i	0.343821	−	0.939035i	$-0.388279\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	7.57475	−	4.68248i	1.31859	−	0.815115i
$34$	2.89695	+	5.01766i	0.496822	+	0.860521i
$35$	−2.16962	−	1.51418i	−0.366732	−	0.255944i
$36$	−2.99458	+	0.180332i	−0.499096	+	0.0300553i
$37$	2.00070	+	3.46531i	0.328913	+	0.569694i	0.982296	−	0.187333i	$-0.0599844\pi$
$37$	2.00070	+	3.46531i	0.328913	+	0.569694i	−0.653384	+	0.757027i	$0.726651\pi$
$38$	−4.69959			−0.762375
$39$	−0.169123	−	5.62199i	−0.0270814	−	0.900238i
$40$	1.00000			0.158114
$41$	−3.71105	+	6.42773i	−0.579569	+	1.00384i	0.415960	+	0.909383i	$0.363446\pi$
$41$	−3.71105	+	6.42773i	−0.579569	+	1.00384i	−0.995529	+	0.0944596i	$0.969888\pi$
$42$	2.50846	−	3.83505i	0.387064	−	0.591761i
$43$	−1.80497	−	3.12631i	−0.275256	−	0.476757i	0.694944	−	0.719064i	$-0.255429\pi$
$43$	−1.80497	−	3.12631i	−0.275256	−	0.476757i	−0.970200	+	0.242307i	$0.922096\pi$
$44$	−2.57071	−	4.45260i	−0.387549	−	0.671254i
$45$	−1.34112	+	2.68354i	−0.199922	+	0.400039i
$46$	−1.33463	+	2.31164i	−0.196780	+	0.340833i
$47$	1.57921	−	2.73527i	0.230352	−	0.398981i	−0.727560	−	0.686044i	$-0.759346\pi$
$47$	1.57921	−	2.73527i	0.230352	−	0.398981i	0.957912	+	0.287063i	$0.0926790\pi$
$48$	0.0520808	+	1.73127i	0.00751722	+	0.249887i
$49$	2.41449	+	6.57041i	0.344927	+	0.938629i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	0.301751	+	10.0308i	0.0422535	+	1.40459i
$52$	−3.24732			−0.450323
$53$	−1.63008	+	2.82338i	−0.223909	+	0.387821i	−0.955991	−	0.293395i	$-0.905215\pi$
$53$	−1.63008	+	2.82338i	−0.223909	+	0.387821i	0.732083	+	0.681216i	$0.238548\pi$
$54$	−4.71578	−	2.18207i	−0.641736	−	0.296942i
$55$	−5.14142			−0.693268
$56$	−2.16962	−	1.51418i	−0.289927	−	0.202341i
$57$	−7.16858	−	3.85616i	−0.949502	−	0.510761i
$58$	0.455293			0.0597828
$59$	5.56657	+	9.64157i	0.724705	+	1.25523i	0.959095	+	0.283083i	$0.0913573\pi$
$59$	5.56657	+	9.64157i	0.724705	+	1.25523i	−0.234390	+	0.972143i	$0.575309\pi$
$60$	1.52536	+	0.820531i	0.196923	+	0.105930i
$61$	−2.99783	+	5.19239i	−0.383833	+	0.664818i	−0.991606	−	0.129293i	$-0.958729\pi$
$61$	−2.99783	+	5.19239i	−0.383833	+	0.664818i	0.607774	+	0.794110i	$0.292063\pi$
$62$	−7.14142			−0.906961
$63$	6.97309	−	3.79157i	0.878527	−	0.477693i
$64$	1.00000			0.125000
$65$	−1.62366	+	2.81226i	−0.201390	+	0.348819i
$66$	−0.267769	−	8.90117i	−0.0329601	−	1.09566i
$67$	5.88868	+	10.1995i	0.719417	+	1.24607i	0.961231	+	0.275744i	$0.0889241\pi$
$67$	5.88868	+	10.1995i	0.719417	+	1.24607i	−0.241815	+	0.970322i	$0.577743\pi$
$68$	5.79389			0.702613
$69$	−3.93256	+	2.43099i	−0.473425	+	0.292657i
$70$	−2.39613	+	1.12185i	−0.286393	+	0.134087i
$71$	−4.38588			−0.520508			−0.260254	−	0.965540i	$-0.583806\pi$
$71$	−4.38588			−0.520508			−0.260254	+	0.965540i	$0.583806\pi$
$72$	−1.34112	+	2.68354i	−0.158052	+	0.316259i
$73$	6.94143	−	12.0229i	0.812433	−	1.40718i	−0.0987235	−	0.995115i	$-0.531476\pi$
$73$	6.94143	−	12.0229i	0.812433	−	1.40718i	0.911157	−	0.412060i	$-0.135191\pi$
$74$	4.00140			0.465153
$75$	1.47328	−	0.910737i	0.170120	−	0.105163i
$76$	−2.34980	+	4.06997i	−0.269540	+	0.466857i
$77$	11.1549	+	7.78505i	1.27122	+	0.887189i
$78$	−4.95334	−	2.66453i	−0.560856	−	0.301698i
$79$	−1.47595	+	2.55642i	−0.166057	+	0.287619i	−0.937030	−	0.349248i	$-0.886437\pi$
$79$	−1.47595	+	2.55642i	−0.166057	+	0.287619i	0.770973	+	0.636868i	$0.219770\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−5.40282	−	7.19789i	−0.600313	−	0.799765i
$82$	3.71105	+	6.42773i	0.409817	+	0.709824i
$83$	6.13291	+	10.6225i	0.673174	+	1.16597i	0.976999	+	0.213244i	$0.0684030\pi$
$83$	6.13291	+	10.6225i	0.673174	+	1.16597i	−0.303824	+	0.952728i	$0.598264\pi$
$84$	−2.06702	−	4.08992i	−0.225530	−	0.446247i
$85$	2.89695	−	5.01766i	0.314218	−	0.544242i
$86$	−3.60995			−0.389271
$87$	0.694486	+	0.373581i	0.0744567	+	0.0400521i
$88$	−5.14142			−0.548077
$89$	−4.83214	−	8.36951i	−0.512206	−	0.887166i	−0.999900	−	0.0141515i	$-0.995495\pi$
$89$	−4.83214	−	8.36951i	−0.512206	−	0.887166i	0.487694	−	0.873014i	$-0.337838\pi$
$90$	1.65346	+	2.50321i	0.174290	+	0.263862i
$91$	7.78102	−	3.64302i	0.815672	−	0.381892i
$92$	1.33463	+	2.31164i	0.139144	+	0.241005i
$93$	−10.8932	−	5.85975i	−1.12958	−	0.607628i
$94$	−1.57921	−	2.73527i	−0.162883	−	0.282122i
$95$	2.34980	+	4.06997i	0.241084	+	0.417570i
$96$	1.52536	+	0.820531i	0.155682	+	0.0837450i
$97$	3.91728	+	6.78493i	0.397740	+	0.688905i	0.993447	−	0.114296i	$-0.0364614\pi$
$97$	3.91728	+	6.78493i	0.397740	+	0.688905i	−0.595707	+	0.803202i	$0.703128\pi$
$98$	6.89738	+	1.19419i	0.696741	+	0.120632i
$99$	6.89523	−	13.7972i	0.692997	−	1.38667i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−5.72942			−0.570099			−0.285049	−	0.958513i	$-0.592010\pi$
$101$	−5.72942			−0.570099			−0.285049	+	0.958513i	$0.592010\pi$
$102$	8.83779	+	4.75407i	0.875071	+	0.470723i
$103$	−14.0309			−1.38250			−0.691252	−	0.722614i	$-0.742941\pi$
$103$	−14.0309			−1.38250			−0.691252	+	0.722614i	$0.742941\pi$
$104$	−1.62366	+	2.81226i	−0.159213	+	0.275765i
$105$	−4.57548	−	0.254868i	−0.446521	−	0.0248725i
$106$	1.63008	+	2.82338i	0.158327	+	0.274231i
$107$	7.30355	+	12.6501i	0.706061	+	1.22293i	0.966307	+	0.257391i	$0.0828627\pi$
$107$	7.30355	+	12.6501i	0.706061	+	1.22293i	−0.260247	+	0.965542i	$0.583804\pi$
$108$	−4.24762	+	2.99295i	−0.408727	+	0.287997i
$109$	1.60392	−	2.77806i	0.153627	−	0.266090i	−0.778931	−	0.627110i	$-0.784238\pi$
$109$	1.60392	−	2.77806i	0.153627	−	0.266090i	0.932558	+	0.361019i	$0.117571\pi$
$110$	−2.57071	+	4.45260i	−0.245107	+	0.424538i
$111$	6.10358	+	3.28327i	0.579326	+	0.311634i
$112$	−2.39613	+	1.12185i	−0.226413	+	0.106005i
$113$	1.14968	−	1.99131i	0.108153	−	0.187327i	−0.806869	−	0.590731i	$-0.798840\pi$
$113$	1.14968	−	1.99131i	0.108153	−	0.187327i	0.915022	+	0.403404i	$0.132173\pi$
$114$	−6.92382	+	4.28009i	−0.648475	+	0.400868i
$115$	2.66925			0.248909
$116$	0.227646	−	0.394295i	0.0211364	−	0.0366094i
$117$	−5.36932	−	8.12874i	−0.496394	−	0.751502i
$118$	11.1331			1.02489
$119$	−13.8829	+	6.49989i	−1.27265	+	0.595844i
$120$	1.47328	−	0.910737i	0.134492	−	0.0831385i
$121$	15.4341			1.40310
$122$	2.99783	+	5.19239i	0.271411	+	0.470097i
$123$	0.386549	+	12.8496i	0.0348540	+	1.15861i
$124$	−3.57071	+	6.18465i	−0.320659	+	0.555398i
$125$	−1.00000			−0.0894427
$126$	0.202949	−	7.93466i	0.0180801	−	0.706876i
$127$	−2.31880			−0.205760			−0.102880	−	0.994694i	$-0.532806\pi$
$127$	−2.31880			−0.205760			−0.102880	+	0.994694i	$0.532806\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−5.50648	−	2.96207i	−0.484818	−	0.260796i
$130$	1.62366	+	2.81226i	0.142405	+	0.246652i
$131$	−18.7621			−1.63925			−0.819626	−	0.572899i	$-0.805819\pi$
$131$	−18.7621			−1.63925			−0.819626	+	0.572899i	$0.805819\pi$
$132$	−7.84252	−	4.21869i	−0.682604	−	0.367190i
$133$	1.06452	−	12.3883i	0.0923055	−	1.07420i
$134$	11.7774			1.01741
$135$	0.468162	+	5.17502i	0.0402930	+	0.445395i
$136$	2.89695	−	5.01766i	0.248411	−	0.430261i
$137$	−6.39791			−0.546610			−0.273305	−	0.961927i	$-0.588117\pi$
$137$	−6.39791			−0.546610			−0.273305	+	0.961927i	$0.588117\pi$
$138$	0.139017	+	4.62119i	0.0118339	+	0.393382i
$139$	10.4744	−	18.1422i	0.888429	−	1.53880i	0.0466966	−	0.998909i	$-0.485131\pi$
$139$	10.4744	−	18.1422i	0.888429	−	1.53880i	0.841732	−	0.539895i	$-0.181536\pi$
$140$	−0.226513	+	2.63604i	−0.0191438	+	0.222786i
$141$	−0.164493	−	5.46807i	−0.0138528	−	0.460495i
$142$	−2.19294	+	3.79828i	−0.184027	+	0.318745i
$143$	8.34792	−	14.4590i	0.698088	−	1.20912i
$144$	1.65346	+	2.50321i	0.137788	+	0.208601i
$145$	−0.227646	−	0.394295i	−0.0189050	−	0.0327444i
$146$	−6.94143	−	12.0229i	−0.574477	−	0.995023i
$147$	9.54114	+	7.48109i	0.786940	+	0.617030i
$148$	2.00070	−	3.46531i	0.164456	−	0.284847i
$149$	−12.3598			−1.01255			−0.506276	−	0.862372i	$-0.668978\pi$
$149$	−12.3598			−1.01255			−0.506276	+	0.862372i	$0.668978\pi$
$150$	−0.0520808	−	1.73127i	−0.00425238	−	0.141357i
$151$	19.4157			1.58002			0.790012	−	0.613091i	$-0.210074\pi$
$151$	19.4157			1.58002			0.790012	+	0.613091i	$0.210074\pi$
$152$	2.34980	+	4.06997i	0.190594	+	0.330118i
$153$	9.57997	+	14.5033i	0.774494	+	1.17253i
$154$	12.3195	−	5.76791i	0.992734	−	0.464791i
$155$	3.57071	+	6.18465i	0.286806	+	0.496763i
$156$	−4.78422	+	2.95746i	−0.383044	+	0.236786i
$157$	1.23050	+	2.13128i	0.0982043	+	0.170095i	0.910941	−	0.412536i	$-0.135357\pi$
$157$	1.23050	+	2.13128i	0.0982043	+	0.170095i	−0.812737	+	0.582631i	$0.802023\pi$
$158$	1.47595	+	2.55642i	0.117420	+	0.203378i
$159$	0.169792	+	5.64421i	0.0134654	+	0.447615i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−5.79126	−	4.04174i	−0.456415	−	0.318534i
$162$	−8.93496	+	1.08003i	−0.701997	+	0.0848554i
$163$	4.96118	+	8.59301i	0.388589	+	0.673057i	0.992260	−	0.124177i	$-0.0396291\pi$
$163$	4.96118	+	8.59301i	0.388589	+	0.673057i	−0.603671	+	0.797234i	$0.706296\pi$
$164$	7.42210			0.579569
$165$	−7.57475	+	4.68248i	−0.589694	+	0.364530i
$166$	12.2658			0.952012
$167$	−3.26841	+	5.66106i	−0.252917	+	0.438066i	−0.964328	−	0.264711i	$-0.914723\pi$
$167$	−3.26841	+	5.66106i	−0.252917	+	0.438066i	0.711410	+	0.702777i	$0.248057\pi$
$168$	−4.57548	−	0.254868i	−0.353006	−	0.0196635i
$169$	1.22744	+	2.12600i	0.0944188	+	0.163538i
$170$	−2.89695	−	5.01766i	−0.222186	−	0.384837i
$171$	−14.0733	+	0.847485i	−1.07621	+	0.0648088i
$172$	−1.80497	+	3.12631i	−0.137628	+	0.238379i
$173$	−6.36448	+	11.0236i	−0.483883	+	0.838109i	−0.999829	−	0.0185118i	$-0.994107\pi$
$173$	−6.36448	+	11.0236i	−0.483883	+	0.838109i	0.515946	+	0.856621i	$0.327441\pi$
$174$	0.670774	−	0.414652i	0.0508512	−	0.0314347i
$175$	2.16962	+	1.51418i	0.164008	+	0.114462i
$176$	−2.57071	+	4.45260i	−0.193774	+	0.335627i
$177$	16.9821	+	9.13507i	1.27645	+	0.686634i
$178$	−9.66427			−0.724368
$179$	11.6182	−	20.1233i	0.868386	−	1.50409i	0.00474023	−	0.999989i	$-0.498491\pi$
$179$	11.6182	−	20.1233i	0.868386	−	1.50409i	0.863646	−	0.504100i	$-0.168176\pi$
$180$	2.99458	−	0.180332i	0.223202	−	0.0134411i
$181$	−19.0687			−1.41737			−0.708683	−	0.705527i	$-0.750710\pi$
$181$	−19.0687			−1.41737			−0.708683	+	0.705527i	$0.750710\pi$
$182$	0.735561	−	8.56007i	0.0545234	−	0.634514i
$183$	0.312259	+	10.3801i	0.0230828	+	0.767318i
$184$	2.66925			0.196780
$185$	−2.00070	−	3.46531i	−0.147094	−	0.254775i
$186$	−10.5213	+	6.50395i	−0.771460	+	0.476893i
$187$	−14.8944	+	25.7979i	−1.08919	+	1.88653i
$188$	−3.15842			−0.230352
$189$	6.82020	−	11.9367i	0.496097	−	0.868267i
$190$	4.69959			0.340944
$191$	−13.1495	+	22.7755i	−0.951462	+	1.64798i	−0.209197	+	0.977874i	$0.567085\pi$
$191$	−13.1495	+	22.7755i	−0.951462	+	1.64798i	−0.742265	+	0.670107i	$0.766248\pi$
$192$	1.47328	−	0.910737i	0.106325	−	0.0657268i
$193$	−2.34431	−	4.06047i	−0.168747	−	0.292279i	0.769232	−	0.638969i	$-0.220639\pi$
$193$	−2.34431	−	4.06047i	−0.168747	−	0.292279i	−0.937980	+	0.346690i	$0.887305\pi$
$194$	7.83456			0.562489
$195$	0.169123	+	5.62199i	0.0121112	+	0.402599i
$196$	4.48289	−	5.37621i	0.320207	−	0.384015i
$197$	10.4576			0.745076			0.372538	−	0.928017i	$-0.378488\pi$
$197$	10.4576			0.745076			0.372538	+	0.928017i	$0.378488\pi$
$198$	−8.50112	−	12.8701i	−0.604148	−	0.914635i
$199$	−8.16053	+	14.1345i	−0.578485	+	1.00197i	0.417168	+	0.908829i	$0.363023\pi$
$199$	−8.16053	+	14.1345i	−0.578485	+	1.00197i	−0.995653	+	0.0931362i	$0.970311\pi$
$200$	−1.00000			−0.0707107
$201$	17.9647	+	9.66368i	1.26713	+	0.681624i
$202$	−2.86471	+	4.96182i	−0.201560	+	0.349113i
$203$	−0.103130	+	1.20017i	−0.00723828	+	0.0842353i
$204$	8.53604	−	5.27671i	0.597642	−	0.369444i
$205$	3.71105	−	6.42773i	0.259191	−	0.448932i
$206$	−7.01544	+	12.1511i	−0.488789	+	0.846608i
$207$	−3.57978	+	7.16306i	−0.248812	+	0.497867i
$208$	1.62366	+	2.81226i	0.112581	+	0.194995i
$209$	−12.0813	−	20.9254i	−0.835680	−	1.44744i
$210$	−2.50846	+	3.83505i	−0.173100	+	0.264644i
$211$	−2.17495	+	3.76713i	−0.149730	+	0.259340i	−0.931128	−	0.364693i	$-0.881174\pi$
$211$	−2.17495	+	3.76713i	−0.149730	+	0.259340i	0.781398	+	0.624033i	$0.214507\pi$
$212$	3.26016			0.223909
$213$	−6.46164	+	3.99438i	−0.442744	+	0.273691i
$214$	14.6071			0.998520
$215$	1.80497	+	3.12631i	0.123098	+	0.213212i
$216$	0.468162	+	5.17502i	0.0318544	+	0.352115i
$217$	1.61762	−	18.8250i	0.109811	−	1.27793i
$218$	−1.60392	−	2.77806i	−0.108631	−	0.188154i
$219$	−0.723031	−	24.0349i	−0.0488579	−	1.62413i
$220$	2.57071	+	4.45260i	0.173317	+	0.300194i
$221$	9.40732	+	16.2940i	0.632805	+	1.09605i
$222$	5.89519	−	3.64422i	0.395659	−	0.244584i
$223$	1.72717	+	2.99154i	0.115660	+	0.200328i	0.918043	−	0.396480i	$-0.129768\pi$
$223$	1.72717	+	2.99154i	0.115660	+	0.200328i	−0.802384	+	0.596809i	$0.796435\pi$
$224$	−0.226513	+	2.63604i	−0.0151345	+	0.176128i
$225$	1.34112	−	2.68354i	0.0894077	−	0.178903i
$226$	−1.14968	−	1.99131i	−0.0764758	−	0.132460i
$227$	−19.2095			−1.27498			−0.637491	−	0.770458i	$-0.720028\pi$
$227$	−19.2095			−1.27498			−0.637491	+	0.770458i	$0.720028\pi$
$228$	0.244759	+	8.13625i	0.0162095	+	0.538837i
$229$	−21.6622			−1.43148			−0.715739	−	0.698368i	$-0.753910\pi$
$229$	−21.6622			−1.43148			−0.715739	+	0.698368i	$0.753910\pi$
$230$	1.33463	−	2.31164i	0.0880027	−	0.152425i
$231$	23.5245	+	1.31038i	1.54780	+	0.0862167i
$232$	−0.227646	−	0.394295i	−0.0149457	−	0.0258867i
$233$	−1.36959	−	2.37220i	−0.0897248	−	0.155408i	0.817670	−	0.575687i	$-0.195265\pi$
$233$	−1.36959	−	2.37220i	−0.0897248	−	0.155408i	−0.907395	+	0.420279i	$0.861932\pi$
$234$	−9.72436	+	0.585595i	−0.635701	+	0.0382816i
$235$	−1.57921	+	2.73527i	−0.103016	+	0.178430i
$236$	5.56657	−	9.64157i	0.362353	−	0.627613i
$237$	0.153737	+	5.11052i	0.00998630	+	0.331964i
$238$	−1.31239	+	15.2729i	−0.0850697	+	0.989996i
$239$	11.2181	−	19.4304i	0.725641	−	1.25685i	−0.233068	−	0.972460i	$-0.574877\pi$
$239$	11.2181	−	19.4304i	0.725641	−	1.25685i	0.958710	−	0.284387i	$-0.0917901\pi$
$240$	−0.0520808	−	1.73127i	−0.00336180	−	0.111753i
$241$	21.8355			1.40655			0.703273	−	0.710920i	$-0.251721\pi$
$241$	21.8355			1.40655			0.703273	+	0.710920i	$0.251721\pi$
$242$	7.71707	−	13.3664i	0.496072	−	0.859222i
$243$	−14.5153	−	5.68397i	−0.931154	−	0.364627i
$244$	5.99566			0.383833
$245$	−2.41449	−	6.57041i	−0.154256	−	0.419768i
$246$	11.3214	+	6.09006i	0.721826	+	0.388288i
$247$	−15.2611			−0.971041
$248$	3.57071	+	6.18465i	0.226740	+	0.392725i
$249$	18.7098	+	10.0645i	1.18569	+	0.637811i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−5.65826			−0.357146			−0.178573	−	0.983927i	$-0.557148\pi$
$251$	−5.65826			−0.357146			−0.178573	+	0.983927i	$0.557148\pi$
$252$	−6.77014	−	4.14309i	−0.426479	−	0.260990i
$253$	−13.7237			−0.862804
$254$	−1.15940	+	2.00814i	−0.0727471	+	0.126002i
$255$	−0.301751	−	10.0308i	−0.0188964	−	0.628152i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.76277			0.484228			0.242114	−	0.970248i	$-0.422159\pi$
$257$	7.76277			0.484228			0.242114	+	0.970248i	$0.422159\pi$
$258$	−5.31847	+	3.28771i	−0.331113	+	0.204684i
$259$	−0.906368	+	10.5478i	−0.0563190	+	0.655411i
$260$	3.24732			0.201390
$261$	1.36341	−	0.0821036i	0.0843928	−	0.00508209i
$262$	−9.38105	+	16.2485i	−0.579563	+	1.00383i
$263$	9.18265			0.566227			0.283113	−	0.959086i	$-0.408633\pi$
$263$	9.18265			0.566227			0.283113	+	0.959086i	$0.408633\pi$
$264$	−7.57475	+	4.68248i	−0.466194	+	0.288187i
$265$	1.63008	−	2.82338i	0.100135	−	0.173439i
$266$	−10.1963	−	7.11605i	−0.625177	−	0.436313i
$267$	−14.7415	−	7.92983i	−0.902166	−	0.485298i
$268$	5.88868	−	10.1995i	0.359708	−	0.623033i
$269$	9.03012	−	15.6406i	0.550576	−	0.953626i	−0.447657	−	0.894205i	$-0.647741\pi$
$269$	9.03012	−	15.6406i	0.550576	−	0.953626i	0.998233	−	0.0594206i	$-0.0189253\pi$
$270$	4.71578	+	2.18207i	0.286993	+	0.132797i
$271$	−12.2464	−	21.2114i	−0.743917	−	1.28850i	−0.950699	−	0.310115i	$-0.899632\pi$
$271$	−12.2464	−	21.2114i	−0.743917	−	1.28850i	0.206782	−	0.978387i	$-0.433701\pi$
$272$	−2.89695	−	5.01766i	−0.175653	−	0.304240i
$273$	8.14579	−	12.4537i	0.493006	−	0.753729i
$274$	−3.19895	+	5.54075i	−0.193256	+	0.334729i
$275$	5.14142			0.310039
$276$	4.07158	+	2.19020i	0.245080	+	0.131835i
$277$	−13.1167			−0.788104			−0.394052	−	0.919088i	$-0.628927\pi$
$277$	−13.1167			−0.788104			−0.394052	+	0.919088i	$0.628927\pi$
$278$	−10.4744	−	18.1422i	−0.628214	−	1.08810i
$279$	−21.3855	+	1.28782i	−1.28032	+	0.0770999i
$280$	2.16962	+	1.51418i	0.129660	+	0.0904898i
$281$	1.06057	+	1.83696i	0.0632684	+	0.109584i	0.895925	−	0.444206i	$-0.146514\pi$
$281$	1.06057	+	1.83696i	0.0632684	+	0.109584i	−0.832656	+	0.553790i	$0.813181\pi$
$282$	−4.81774	−	2.59158i	−0.286892	−	0.154326i
$283$	5.62680	+	9.74590i	0.334478	+	0.579334i	0.983385	−	0.181535i	$-0.0581065\pi$
$283$	5.62680	+	9.74590i	0.334478	+	0.579334i	−0.648906	+	0.760869i	$0.724773\pi$
$284$	2.19294	+	3.79828i	0.130127	+	0.225387i
$285$	7.16858	+	3.85616i	0.424630	+	0.228419i
$286$	−8.34792	−	14.4590i	−0.493623	−	0.854980i
$287$	−17.7843	+	8.32650i	−1.04978	+	0.491498i
$288$	2.99458	−	0.180332i	0.176457	−	0.0106261i
$289$	−8.28460	−	14.3493i	−0.487329	−	0.844079i
$290$	−0.455293			−0.0267357
$291$	11.9505	+	6.42850i	0.700553	+	0.376845i
$292$	−13.8829			−0.812433
$293$	4.80935	−	8.33003i	0.280965	−	0.486646i	−0.690658	−	0.723182i	$-0.742679\pi$
$293$	4.80935	−	8.33003i	0.280965	−	0.486646i	0.971623	+	0.236536i	$0.0760121\pi$
$294$	11.2494	−	4.52232i	0.656077	−	0.263747i
$295$	−5.56657	−	9.64157i	−0.324098	−	0.561354i
$296$	−2.00070	−	3.46531i	−0.116288	−	0.201417i
$297$	−2.40702	−	26.6069i	−0.139669	−	1.54389i
$298$	−6.17989	+	10.7039i	−0.357991	+	0.620059i
$299$	−4.33397	+	7.50665i	−0.250640	+	0.434121i
$300$	−1.52536	−	0.820531i	−0.0880668	−	0.0473734i
$301$	0.817700	−	9.51595i	0.0471314	−	0.548490i
$302$	9.70783	−	16.8145i	0.558623	−	0.967563i
$303$	−8.44105	+	5.21800i	−0.484925	+	0.299766i
$304$	4.69959			0.269540
$305$	2.99783	−	5.19239i	0.171655	−	0.297315i
$306$	17.3502	−	1.04482i	0.991848	−	0.0597285i
$307$	−9.13535			−0.521382			−0.260691	−	0.965422i	$-0.583950\pi$
$307$	−9.13535			−0.521382			−0.260691	+	0.965422i	$0.583950\pi$
$308$	1.16460	−	13.5530i	0.0663591	−	0.772252i
$309$	−20.6714	+	12.7784i	−1.17596	+	0.726941i
$310$	7.14142			0.405605
$311$	−10.2974	−	17.8356i	−0.583911	−	1.01136i	−0.995010	−	0.0997726i	$-0.968188\pi$
$311$	−10.2974	−	17.8356i	−0.583911	−	1.01136i	0.411100	−	0.911590i	$-0.365145\pi$
$312$	0.169123	+	5.62199i	0.00957472	+	0.318282i
$313$	0.275427	−	0.477053i	0.0155680	−	0.0269646i	−0.858136	−	0.513422i	$-0.828378\pi$
$313$	0.275427	−	0.477053i	0.0155680	−	0.0269646i	0.873704	+	0.486457i	$0.161711\pi$
$314$	2.46099			0.138882
$315$	−6.97309	+	3.79157i	−0.392889	+	0.213631i
$316$	2.95190			0.166057
$317$	13.4872	−	23.3605i	0.757517	−	1.31206i	−0.186596	−	0.982437i	$-0.559746\pi$
$317$	13.4872	−	23.3605i	0.757517	−	1.31206i	0.944113	−	0.329621i	$-0.106921\pi$
$318$	4.97292	+	2.67506i	0.278868	+	0.150010i
$319$	1.17042	+	2.02723i	0.0655312	+	0.113503i
$320$	−1.00000			−0.0559017
$321$	22.2811	+	11.9856i	1.24361	+	0.668969i
$322$	−6.39588	+	2.99451i	−0.356429	+	0.166877i
$323$	27.2289			1.51506
$324$	−3.53214	+	8.27792i	−0.196230	+	0.459884i
$325$	1.62366	−	2.81226i	0.0900646	−	0.155996i
$326$	9.92235			0.549548
$327$	−0.167066	−	5.55361i	−0.00923879	−	0.307115i
$328$	3.71105	−	6.42773i	0.204908	−	0.354912i
$329$	7.56800	−	3.54328i	0.417237	−	0.195348i
$330$	0.267769	+	8.90117i	0.0147402	+	0.489993i
$331$	8.44384	−	14.6252i	0.464115	−	0.803871i	−0.535046	−	0.844823i	$-0.679706\pi$
$331$	8.44384	−	14.6252i	0.464115	−	0.803871i	0.999161	+	0.0409516i	$0.0130390\pi$
$332$	6.13291	−	10.6225i	0.336587	−	0.582986i
$333$	11.9825	−	0.721579i	0.656636	−	0.0395423i
$334$	3.26841	+	5.66106i	0.178840	+	0.309759i
$335$	−5.88868	−	10.1995i	−0.321733	−	0.557258i
$336$	−2.50846	+	3.83505i	−0.136848	+	0.209219i
$337$	12.8294	−	22.2212i	0.698863	−	1.21047i	−0.269998	−	0.962861i	$-0.587023\pi$
$337$	12.8294	−	22.2212i	0.698863	−	1.21047i	0.968861	−	0.247606i	$-0.0796437\pi$
$338$	2.45489			0.133528
$339$	−0.119753	−	3.98082i	−0.00650409	−	0.216209i
$340$	−5.79389			−0.314218
$341$	−18.3585	−	31.7978i	−0.994168	−	1.72195i
$342$	−6.30270	+	12.6116i	−0.340811	+	0.681955i
$343$	−4.71028	+	17.9113i	−0.254331	+	0.967117i
$344$	1.80497	+	3.12631i	0.0973176	+	0.168559i
$345$	3.93256	−	2.43099i	0.211722	−	0.130880i
$346$	6.36448	+	11.0236i	0.342157	+	0.592633i
$347$	8.51177	+	14.7428i	0.456936	+	0.791436i	0.998797	−	0.0490321i	$-0.0156137\pi$
$347$	8.51177	+	14.7428i	0.456936	+	0.791436i	−0.541862	+	0.840468i	$0.682280\pi$
$348$	−0.0237120	−	0.788233i	−0.00127110	−	0.0422537i
$349$	−11.3156	−	19.5992i	−0.605709	−	1.04912i	−0.991939	−	0.126716i	$-0.959556\pi$
$349$	−11.3156	−	19.5992i	−0.605709	−	1.04912i	0.386230	−	0.922403i	$-0.373777\pi$
$350$	2.39613	−	1.12185i	0.128079	−	0.0599655i
$351$	−15.3137	−	7.08589i	−0.817383	−	0.378217i
$352$	2.57071	+	4.45260i	0.137019	+	0.237324i
$353$	−8.74841			−0.465631			−0.232815	−	0.972521i	$-0.574794\pi$
$353$	−8.74841			−0.465631			−0.232815	+	0.972521i	$0.574794\pi$
$354$	16.4022	−	10.1394i	0.871769	−	0.538901i
$355$	4.38588			0.232778
$356$	−4.83214	+	8.36951i	−0.256103	+	0.443583i
$357$	−14.5338	+	22.2199i	−0.769209	+	1.17600i
$358$	−11.6182	−	20.1233i	−0.614041	−	1.06355i
$359$	13.0119	+	22.5373i	0.686741	+	1.18947i	0.972886	+	0.231284i	$0.0742928\pi$
$359$	13.0119	+	22.5373i	0.686741	+	1.18947i	−0.286145	+	0.958186i	$0.592374\pi$
$360$	1.34112	−	2.68354i	0.0706830	−	0.141435i
$361$	−1.54309	+	2.67271i	−0.0812152	+	0.140669i
$362$	−9.53436	+	16.5140i	−0.501115	+	0.867956i
$363$	22.7388	−	14.0565i	1.19348	−	0.737772i
$364$	−7.04545	−	4.91705i	−0.369282	−	0.257723i
$365$	−6.94143	+	12.0229i	−0.363331	+	0.629308i
$366$	9.14555	+	4.91962i	0.478045	+	0.257153i
$367$	34.5588			1.80395			0.901976	−	0.431786i	$-0.142116\pi$
$367$	34.5588			1.80395			0.901976	+	0.431786i	$0.142116\pi$
$368$	1.33463	−	2.31164i	0.0695722	−	0.120503i
$369$	12.2721	+	18.5791i	0.638862	+	0.967189i
$370$	−4.00140			−0.208023
$371$	−7.81177	+	3.65742i	−0.405567	+	0.189884i
$372$	0.371931	+	12.3637i	0.0192837	+	0.641028i
$373$	8.97898			0.464914			0.232457	−	0.972607i	$-0.425324\pi$
$373$	8.97898			0.464914			0.232457	+	0.972607i	$0.425324\pi$
$374$	14.8944	+	25.7979i	0.770171	+	1.33398i
$375$	−1.47328	+	0.910737i	−0.0760799	+	0.0470303i
$376$	−1.57921	+	2.73527i	−0.0814416	+	0.141061i
$377$	1.47848			0.0761457
$378$	−6.92739	−	11.8748i	−0.356306	−	0.610775i
$379$	−21.2288			−1.09045			−0.545225	−	0.838290i	$-0.683556\pi$
$379$	−21.2288			−1.09045			−0.545225	+	0.838290i	$0.683556\pi$
$380$	2.34980	−	4.06997i	0.120542	−	0.208785i
$381$	−3.41624	+	2.11181i	−0.175019	+	0.108192i
$382$	13.1495	+	22.7755i	0.672785	+	1.16530i
$383$	0.216305			0.0110527			0.00552634	−	0.999985i	$-0.498241\pi$
$383$	0.216305			0.0110527			0.00552634	+	0.999985i	$0.498241\pi$
$384$	−0.0520808	−	1.73127i	−0.00265774	−	0.0883484i
$385$	−11.1549	−	7.78505i	−0.568507	−	0.396763i
$386$	−4.68862			−0.238645
$387$	−10.8103	+	0.650988i	−0.549516	+	0.0330916i
$388$	3.91728	−	6.78493i	0.198870	−	0.344453i
$389$	−11.6262			−0.589474			−0.294737	−	0.955578i	$-0.595232\pi$
$389$	−11.6262			−0.589474			−0.294737	+	0.955578i	$0.595232\pi$
$390$	4.95334	+	2.66453i	0.250822	+	0.134924i
$391$	7.73269	−	13.3934i	0.391059	−	0.677334i
$392$	−2.41449	−	6.57041i	−0.121950	−	0.331856i
$393$	−27.6419	+	17.0873i	−1.39435	+	0.861942i
$394$	5.22882	−	9.05658i	0.263424	−	0.456264i
$395$	1.47595	−	2.55642i	0.0742630	−	0.128627i
$396$	−15.3964	+	0.927160i	−0.773696	+	0.0465915i
$397$	−14.1667	−	24.5375i	−0.711007	−	1.23150i	−0.964479	−	0.264158i	$-0.914906\pi$
$397$	−14.1667	−	24.5375i	−0.711007	−	1.23150i	0.253472	−	0.967343i	$-0.418427\pi$
$398$	8.16053	+	14.1345i	0.409051	+	0.708496i
$399$	−9.71415	−	19.2210i	−0.486316	−	0.962251i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−6.82249			−0.340699			−0.170349	−	0.985384i	$-0.554490\pi$
$401$	−6.82249			−0.340699			−0.170349	+	0.985384i	$0.554490\pi$
$402$	17.3514	−	10.7261i	0.865407	−	0.534968i
$403$	−23.1905			−1.15520
$404$	2.86471	+	4.96182i	0.142525	+	0.246860i
$405$	5.40282	+	7.19789i	0.268468	+	0.357666i
$406$	0.987811	+	0.689397i	0.0490242	+	0.0342142i
$407$	10.2864	+	17.8166i	0.509879	+	0.883137i
$408$	−0.301751	−	10.0308i	−0.0149389	−	0.496598i
$409$	−5.58692	−	9.67683i	−0.276255	−	0.478489i	0.694196	−	0.719786i	$-0.255760\pi$
$409$	−5.58692	−	9.67683i	−0.276255	−	0.478489i	−0.970451	+	0.241298i	$0.922427\pi$
$410$	−3.71105	−	6.42773i	−0.183276	−	0.317443i
$411$	−9.42592	+	5.82681i	−0.464946	+	0.287415i
$412$	7.01544	+	12.1511i	0.345626	+	0.598642i
$413$	−2.52180	+	29.3473i	−0.124090	+	1.44409i
$414$	4.41350	+	6.68171i	0.216912	+	0.328388i
$415$	−6.13291	−	10.6225i	−0.301053	−	0.521439i
$416$	3.24732			0.159213
$417$	−1.09103	−	36.2681i	−0.0534281	−	1.77605i
$418$	−24.1626			−1.18183
$419$	−2.78160	+	4.81787i	−0.135890	+	0.235368i	−0.925937	−	0.377678i	$-0.876723\pi$
$419$	−2.78160	+	4.81787i	−0.135890	+	0.235368i	0.790047	+	0.613046i	$0.210056\pi$
$420$	2.06702	+	4.08992i	0.100860	+	0.199568i
$421$	−17.2899	−	29.9470i	−0.842658	−	1.45953i	−0.887640	−	0.460539i	$-0.847656\pi$
$421$	−17.2899	−	29.9470i	−0.842658	−	1.45953i	0.0449814	−	0.998988i	$-0.485677\pi$
$422$	2.17495	+	3.76713i	0.105875	+	0.183381i
$423$	−5.22232	−	7.90620i	−0.253918	−	0.384413i
$424$	1.63008	−	2.82338i	0.0791636	−	0.137115i
$425$	−2.89695	+	5.01766i	−0.140523	+	0.243392i
$426$	0.228420	+	7.59313i	0.0110670	+	0.367889i
$427$	−14.3664	+	6.72624i	−0.695238	+	0.325506i
$428$	7.30355	−	12.6501i	0.353030	−	0.611466i
$429$	−0.869533	−	28.9050i	−0.0419814	−	1.39554i
$430$	3.60995			0.174087
$431$	19.2277	−	33.3034i	0.926167	−	1.60417i	0.136495	−	0.990641i	$-0.456416\pi$
$431$	19.2277	−	33.3034i	0.926167	−	1.60417i	0.789673	−	0.613528i	$-0.210250\pi$
$432$	4.71578	+	2.18207i	0.226888	+	0.104985i
$433$	30.9550			1.48760			0.743800	−	0.668402i	$-0.233021\pi$
$433$	30.9550			1.48760			0.743800	+	0.668402i	$0.233021\pi$
$434$	−15.4941	−	10.8134i	−0.743743	−	0.519061i
$435$	−0.694486	−	0.373581i	−0.0332981	−	0.0179119i
$436$	−3.20783			−0.153627
$437$	6.27220	+	10.8638i	0.300040	+	0.519685i
$438$	−21.1764	−	11.3913i	−1.01185	−	0.544298i
$439$	−13.4194	+	23.2431i	−0.640474	+	1.10933i	0.344853	+	0.938657i	$0.387929\pi$
$439$	−13.4194	+	23.2431i	−0.640474	+	1.10933i	−0.985327	+	0.170676i	$0.945405\pi$
$440$	5.14142			0.245107
$441$	20.8701	+	2.33228i	0.993814	+	0.111061i
$442$	18.8146			0.894922
$443$	16.1258	−	27.9308i	0.766162	−	1.32703i	−0.173468	−	0.984840i	$-0.555497\pi$
$443$	16.1258	−	27.9308i	0.766162	−	1.32703i	0.939630	−	0.342192i	$-0.111169\pi$
$444$	−0.208396	−	6.92749i	−0.00989004	−	0.328764i
$445$	4.83214	+	8.36951i	0.229065	+	0.396753i
$446$	3.45434			0.163568
$447$	−18.2094	+	11.2565i	−0.861276	+	0.532414i
$448$	2.16962	+	1.51418i	0.102505	+	0.0715385i
$449$	−9.45029			−0.445987			−0.222993	−	0.974820i	$-0.571583\pi$
$449$	−9.45029			−0.445987			−0.222993	+	0.974820i	$0.571583\pi$
$450$	−1.65346	−	2.50321i	−0.0779448	−	0.118003i
$451$	−19.0801	+	33.0476i	−0.898445	+	1.55615i
$452$	−2.29937			−0.108153
$453$	28.6047	−	17.6826i	1.34397	−	0.830799i
$454$	−9.60477	+	16.6359i	−0.450774	+	0.780764i
$455$	−7.78102	+	3.64302i	−0.364780	+	0.170787i
$456$	7.16858	+	3.85616i	0.335700	+	0.180581i
$457$	−12.6657	+	21.9376i	−0.592474	+	1.02620i	0.401424	+	0.915892i	$0.368516\pi$
$457$	−12.6657	+	21.9376i	−0.592474	+	1.02620i	−0.993898	+	0.110303i	$0.964818\pi$
$458$	−10.8311	+	18.7600i	−0.506104	+	0.876598i
$459$	27.3227	+	12.6427i	1.27532	+	0.590110i
$460$	−1.33463	−	2.31164i	−0.0622273	−	0.107781i
$461$	0.0688453	+	0.119244i	0.00320645	+	0.00555373i	0.867624	−	0.497221i	$-0.165646\pi$
$461$	0.0688453	+	0.119244i	0.00320645	+	0.00555373i	−0.864418	+	0.502774i	$0.832313\pi$
$462$	12.8971	−	19.7176i	0.600025	−	0.917345i
$463$	−8.01422	+	13.8810i	−0.372452	+	0.645106i	−0.989942	−	0.141473i	$-0.954816\pi$
$463$	−8.01422	+	13.8810i	−0.372452	+	0.645106i	0.617490	+	0.786579i	$0.288150\pi$
$464$	−0.455293			−0.0211364
$465$	10.8932	+	5.85975i	0.505162	+	0.271739i
$466$	−2.73918			−0.126890
$467$	10.9032	+	18.8849i	0.504540	+	0.873888i	0.999986	+	0.00524984i	$0.00167108\pi$
$467$	10.9032	+	18.8849i	0.504540	+	0.873888i	−0.495447	+	0.868638i	$0.664996\pi$
$468$	−4.35504	+	8.71434i	−0.201312	+	0.402820i
$469$	−2.66772	+	31.0456i	−0.123184	+	1.43355i
$470$	1.57921	+	2.73527i	0.0728436	+	0.126169i
$471$	3.75391	+	2.01932i	0.172971	+	0.0930453i
$472$	−5.56657	−	9.64157i	−0.256222	−	0.443789i
$473$	−9.28012	−	16.0736i	−0.426700	−	0.739066i
$474$	4.50271	+	2.42212i	0.206816	+	0.111252i
$475$	−2.34980	−	4.06997i	−0.107816	−	0.186743i
$476$	12.5705	+	8.77302i	0.576170	+	0.402111i
$477$	5.39054	+	8.16087i	0.246816	+	0.373661i
$478$	−11.2181	−	19.4304i	−0.513106	−	0.888725i
$479$	−16.2660			−0.743213			−0.371606	−	0.928390i	$-0.621193\pi$
$479$	−16.2660			−0.743213			−0.371606	+	0.928390i	$0.621193\pi$
$480$	−1.52536	−	0.820531i	−0.0696229	−	0.0374519i
$481$	12.9938			0.592468
$482$	10.9177	−	18.9101i	0.497289	−	0.861330i
$483$	−12.2131	−	0.680306i	−0.555716	−	0.0309550i
$484$	−7.71707	−	13.3664i	−0.350776	−	0.607562i
$485$	−3.91728	−	6.78493i	−0.177875	−	0.308088i
$486$	−12.1801	+	9.72859i	−0.552500	+	0.441298i
$487$	−17.0685	+	29.5636i	−0.773449	+	1.33965i	0.162213	+	0.986756i	$0.448137\pi$
$487$	−17.0685	+	29.5636i	−0.773449	+	1.33965i	−0.935662	+	0.352897i	$0.885196\pi$
$488$	2.99783	−	5.19239i	0.135705	−	0.235048i
$489$	15.1352	+	8.14159i	0.684437	+	0.368176i
$490$	−6.89738	−	1.19419i	−0.311592	−	0.0539481i
$491$	21.6539	−	37.5057i	0.977228	−	1.69261i	0.304849	−	0.952401i	$-0.401394\pi$
$491$	21.6539	−	37.5057i	0.977228	−	1.69261i	0.672379	−	0.740207i	$-0.265273\pi$
$492$	10.9348	−	6.75958i	0.492981	−	0.304746i
$493$	−2.63792			−0.118806
$494$	−7.63055	+	13.2165i	−0.343315	+	0.594639i
$495$	−6.89523	+	13.7972i	−0.309918	+	0.620139i
$496$	7.14142			0.320659
$497$	−9.51569	−	6.64103i	−0.426837	−	0.297891i
$498$	18.0710	−	11.1709i	0.809781	−	0.500582i
$499$	6.64628			0.297528			0.148764	−	0.988873i	$-0.452470\pi$
$499$	6.64628			0.297528			0.148764	+	0.988873i	$0.452470\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	0.340443	+	11.3170i	0.0152099	+	0.505606i
$502$	−2.82913	+	4.90019i	−0.126270	+	0.218706i
$503$	35.8333			1.59773			0.798865	−	0.601510i	$-0.205434\pi$
$503$	35.8333			1.59773			0.798865	+	0.601510i	$0.205434\pi$
$504$	−6.97309	+	3.79157i	−0.310606	+	0.168890i
$505$	5.72942			0.254956
$506$	−6.86187	+	11.8851i	−0.305047	+	0.528358i
$507$	3.74459	+	2.01431i	0.166303	+	0.0894587i
$508$	1.15940	+	2.00814i	0.0514400	+	0.0890967i
$509$	13.8746			0.614981			0.307490	−	0.951551i	$-0.400511\pi$
$509$	13.8746			0.614981			0.307490	+	0.951551i	$0.400511\pi$
$510$	−8.83779	−	4.75407i	−0.391344	−	0.210514i
$511$	33.2652	−	15.5745i	1.47156	−	0.688976i
$512$	−1.00000			−0.0441942
$513$	−19.9621	+	14.0656i	−0.881347	+	0.621014i
$514$	3.88139	−	6.72276i	0.171201	−	0.296528i
$515$	14.0309			0.618275
$516$	0.188009	+	6.24978i	0.00827663	+	0.275131i
$517$	8.11938	−	14.0632i	0.357090	−	0.618498i
$518$	8.68151	+	6.05886i	0.381444	+	0.266211i
$519$	0.662935	+	22.0372i	0.0290996	+	0.967328i
$520$	1.62366	−	2.81226i	0.0712023	−	0.123326i
$521$	−5.15160	+	8.92284i	−0.225696	+	0.390917i	−0.956528	−	0.291641i	$-0.905799\pi$
$521$	−5.15160	+	8.92284i	−0.225696	+	0.390917i	0.730832	+	0.682557i	$0.239132\pi$
$522$	0.610600	−	1.22180i	0.0267252	−	0.0534766i
$523$	6.16132	+	10.6717i	0.269416	+	0.466642i	0.968711	−	0.248191i	$-0.0798360\pi$
$523$	6.16132	+	10.6717i	0.269416	+	0.466642i	−0.699295	+	0.714833i	$0.746503\pi$
$524$	9.38105	+	16.2485i	0.409813	+	0.709817i
$525$	4.57548	+	0.254868i	0.199690	+	0.0111233i
$526$	4.59133	−	7.95241i	0.200191	−	0.346742i
$527$	41.3766			1.80239
$528$	0.267769	+	8.90117i	0.0116532	+	0.387374i
$529$	−15.8751			−0.690221
$530$	−1.63008	−	2.82338i	−0.0708061	−	0.122640i
$531$	33.3390	−	2.00766i	1.44679	−	0.0871248i
$532$	−11.2608	+	5.27225i	−0.488220	+	0.228581i
$533$	12.0510	+	20.8729i	0.521986	+	0.904106i
$534$	−14.2382	+	8.80161i	−0.616147	+	0.380883i
$535$	−7.30355	−	12.6501i	−0.315760	−	0.546912i
$536$	−5.88868	−	10.1995i	−0.254352	−	0.440551i
$537$	−1.21017	−	40.2285i	−0.0522228	−	1.73599i
$538$	−9.03012	−	15.6406i	−0.389316	−	0.674315i
$539$	12.4139	+	33.7812i	0.534704	+	1.45506i
$540$	4.24762	−	2.99295i	0.182788	−	0.128796i
$541$	13.9275	+	24.1231i	0.598789	+	1.03713i	0.993000	+	0.118113i	$0.0376847\pi$
$541$	13.9275	+	24.1231i	0.598789	+	1.03713i	−0.394211	+	0.919020i	$0.628982\pi$
$542$	−24.4928			−1.05206
$543$	−28.0936	+	17.3666i	−1.20561	+	0.745272i
$544$	−5.79389			−0.248411
$545$	−1.60392	+	2.77806i	−0.0687042	+	0.118999i
$546$	−6.71228	−	13.2813i	−0.287259	−	0.568387i
$547$	4.11573	+	7.12866i	0.175976	+	0.304799i	0.940499	−	0.339798i	$-0.110359\pi$
$547$	4.11573	+	7.12866i	0.175976	+	0.304799i	−0.764523	+	0.644597i	$0.777025\pi$
$548$	3.19895	+	5.54075i	0.136653	+	0.236689i
$549$	9.91357	+	15.0084i	0.423101	+	0.640543i
$550$	2.57071	−	4.45260i	0.109615	−	0.189859i
$551$	1.06984	−	1.85303i	0.0455769	−	0.0789415i
$552$	3.93256	−	2.43099i	0.167381	−	0.103470i
$553$	−7.07313	+	3.31159i	−0.300780	+	0.140823i
$554$	−6.55834	+	11.3594i	−0.278637	+	0.482613i
$555$	−6.10358	−	3.28327i	−0.259083	−	0.139367i
$556$	−20.9488			−0.888429
$557$	12.5376	−	21.7157i	0.531234	−	0.920125i	−0.468101	−	0.883675i	$-0.655062\pi$
$557$	12.5376	−	21.7157i	0.531234	−	0.920125i	0.999335	−	0.0364501i	$-0.0116050\pi$
$558$	−9.57746	+	19.1643i	−0.405446	+	0.811290i
$559$	−11.7227			−0.495816
$560$	2.39613	−	1.12185i	0.101255	−	0.0474069i
$561$	1.55143	+	51.5724i	0.0655012	+	2.17739i
$562$	2.12114			0.0894751
$563$	−8.20455	−	14.2107i	−0.345780	−	0.598909i	0.639715	−	0.768612i	$-0.279052\pi$
$563$	−8.20455	−	14.2107i	−0.345780	−	0.598909i	−0.985495	+	0.169703i	$0.945719\pi$
$564$	−4.65324	+	2.87649i	−0.195937	+	0.121122i
$565$	−1.14968	+	1.99131i	−0.0483676	+	0.0837751i
$566$	11.2536			0.473024
$567$	−0.823124	−	23.7975i	−0.0345679	−	0.999402i
$568$	4.38588			0.184027
$569$	15.8903	−	27.5227i	0.666154	−	1.15381i	−0.312817	−	0.949813i	$-0.601273\pi$
$569$	15.8903	−	27.5227i	0.666154	−	1.15381i	0.978971	−	0.203999i	$-0.0653940\pi$
$570$	6.92382	−	4.28009i	0.290007	−	0.179273i
$571$	−13.0878	−	22.6687i	−0.547708	−	0.948657i	−0.998431	−	0.0559938i	$-0.982167\pi$
$571$	−13.0878	−	22.6687i	−0.547708	−	0.948657i	0.450723	−	0.892664i	$-0.351166\pi$
$572$	−16.6958			−0.698088
$573$	1.36967	+	45.5305i	0.0572188	+	1.90206i
$574$	−1.68120	+	19.5649i	−0.0701720	+	0.816625i
$575$	−2.66925			−0.111316
$576$	1.34112	−	2.68354i	0.0558798	−	0.111814i
$577$	21.3065	−	36.9039i	0.887000	−	1.53633i	0.0435950	−	0.999049i	$-0.486119\pi$
$577$	21.3065	−	36.9039i	0.887000	−	1.53633i	0.843405	−	0.537279i	$-0.180548\pi$
$578$	−16.5692			−0.689188
$579$	−7.15185	−	3.84716i	−0.297221	−	0.159882i
$580$	−0.227646	+	0.394295i	−0.00945250	+	0.0163722i
$581$	−2.77837	+	32.3332i	−0.115266	+	1.34141i
$582$	11.5425	−	7.13523i	0.478453	−	0.295765i
$583$	−8.38091	+	14.5162i	−0.347102	+	0.601198i
$584$	−6.94143	+	12.0229i	−0.287238	+	0.497512i
$585$	5.36932	+	8.12874i	0.221994	+	0.336082i
$586$	−4.80935	−	8.33003i	−0.198672	−	0.344111i
$587$	9.85073	+	17.0620i	0.406583	+	0.704223i	0.994504	−	0.104695i	$-0.0333868\pi$
$587$	9.85073	+	17.0620i	0.406583	+	0.704223i	−0.587921	+	0.808918i	$0.700053\pi$
$588$	1.70825	−	12.0034i	0.0704469	−	0.495012i
$589$	−16.7809	+	29.0653i	−0.691444	+	1.19762i
$590$	−11.1331			−0.458344
$591$	15.4071	−	9.52416i	0.633761	−	0.391772i
$592$	−4.00140			−0.164456
$593$	−11.4796	−	19.8832i	−0.471411	−	0.816507i	0.528055	−	0.849210i	$-0.322922\pi$
$593$	−11.4796	−	19.8832i	−0.471411	−	0.816507i	−0.999465	+	0.0327034i	$0.989588\pi$
$594$	−24.2458	−	11.2189i	−0.994816	−	0.460318i
$595$	13.8829	−	6.49989i	0.569145	−	0.266470i
$596$	6.17989	+	10.7039i	0.253138	+	0.438448i
$597$	0.850014	+	28.2561i	0.0347888	+	1.15645i
$598$	4.33397	+	7.50665i	0.177229	+	0.306970i
$599$	4.31627	+	7.47600i	0.176358	+	0.305461i	0.940630	−	0.339432i	$-0.110235\pi$
$599$	4.31627	+	7.47600i	0.176358	+	0.305461i	−0.764272	+	0.644894i	$0.776902\pi$
$600$	−1.47328	+	0.910737i	−0.0601465	+	0.0371807i
$601$	10.2828	+	17.8104i	0.419445	+	0.726500i	0.995884	−	0.0906402i	$-0.0288913\pi$
$601$	10.2828	+	17.8104i	0.419445	+	0.726500i	−0.576439	+	0.817140i	$0.695558\pi$
$602$	−7.83221	−	5.46613i	−0.319217	−	0.222783i
$603$	35.2682	−	2.12383i	1.43623	−	0.0864890i
$604$	−9.70783	−	16.8145i	−0.395006	−	0.684171i
$605$	−15.4341			−0.627487
$606$	0.298393	+	9.91916i	0.0121214	+	0.402938i
$607$	−15.4125			−0.625573			−0.312786	−	0.949823i	$-0.601262\pi$
$607$	−15.4125			−0.625573			−0.312786	+	0.949823i	$0.601262\pi$
$608$	2.34980	−	4.06997i	0.0952968	−	0.165059i
$609$	0.941099	+	1.86211i	0.0381352	+	0.0754565i
$610$	−2.99783	−	5.19239i	−0.121379	−	0.210234i
$611$	−5.12821	−	8.88232i	−0.207465	−	0.359340i
$612$	7.77028	−	15.5482i	0.314095	−	0.628497i
$613$	−3.08756	+	5.34781i	−0.124705	+	0.215996i	−0.921618	−	0.388099i	$-0.873132\pi$
$613$	−3.08756	+	5.34781i	−0.124705	+	0.215996i	0.796912	+	0.604095i	$0.206465\pi$
$614$	−4.56767	+	7.91144i	−0.184336	+	0.319280i
$615$	−0.386549	−	12.8496i	−0.0155872	−	0.518148i
$616$	−11.1549	−	7.78505i	−0.449444	−	0.313669i
$617$	6.63619	−	11.4942i	0.267163	−	0.462740i	−0.700965	−	0.713196i	$-0.747247\pi$
$617$	6.63619	−	11.4942i	0.267163	−	0.462740i	0.968128	+	0.250456i	$0.0805804\pi$
$618$	0.730740	+	24.2912i	0.0293947	+	0.977136i
$619$	25.1378			1.01037			0.505187	−	0.863010i	$-0.331423\pi$
$619$	25.1378			1.01037			0.505187	+	0.863010i	$0.331423\pi$
$620$	3.57071	−	6.18465i	0.143403	−	0.248381i
$621$	1.24964	+	13.8134i	0.0501465	+	0.554314i
$622$	−20.5948			−0.825775
$623$	2.18908	−	25.4754i	0.0877038	−	1.02065i
$624$	4.95334	+	2.66453i	0.198292	+	0.106666i
$625$	1.00000			0.0400000
$626$	−0.275427	−	0.477053i	−0.0110083	−	0.0190669i
$627$	−36.8567	−	19.8261i	−1.47191	−	0.791779i
$628$	1.23050	−	2.13128i	0.0491021	−	0.0850474i
$629$	−23.1837			−0.924394
$630$	−0.202949	+	7.93466i	−0.00808569	+	0.316124i
$631$	−22.4313			−0.892978			−0.446489	−	0.894789i	$-0.647326\pi$
$631$	−22.4313			−0.892978			−0.446489	+	0.894789i	$0.647326\pi$
$632$	1.47595	−	2.55642i	0.0587101	−	0.101689i
$633$	0.226547	+	7.53086i	0.00900442	+	0.299325i
$634$	−13.4872	−	23.3605i	−0.535645	−	0.927765i
$635$	2.31880			0.0920187
$636$	4.80313	−	2.96915i	0.190457	−	0.117734i
$637$	22.3980	+	3.87793i	0.887443	+	0.153649i
$638$	2.34085			0.0926750
$639$	−5.88197	+	11.7697i	−0.232687	+	0.465602i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−39.1457			−1.54616			−0.773082	−	0.634306i	$-0.781286\pi$
$641$	−39.1457			−1.54616			−0.773082	+	0.634306i	$0.781286\pi$
$642$	21.5204	−	13.3032i	0.849341	−	0.525036i
$643$	−17.4010	+	30.1395i	−0.686230	+	1.18859i	0.286818	+	0.957985i	$0.407402\pi$
$643$	−17.4010	+	30.1395i	−0.686230	+	1.18859i	−0.973048	+	0.230601i	$0.925931\pi$
$644$	−0.604620	+	7.03625i	−0.0238254	+	0.277267i
$645$	5.50648	+	2.96207i	0.216817	+	0.116631i
$646$	13.6145	−	23.5810i	0.535654	−	0.927780i
$647$	15.2199	−	26.3617i	0.598357	−	1.03638i	−0.394707	−	0.918807i	$-0.629154\pi$
$647$	15.2199	−	26.3617i	0.598357	−	1.03638i	0.993064	−	0.117578i	$-0.0375129\pi$
$648$	5.40282	+	7.19789i	0.212243	+	0.282760i
$649$	28.6200	+	49.5713i	1.12343	+	1.94585i
$650$	−1.62366	−	2.81226i	−0.0636853	−	0.110306i
$651$	−14.7614	−	29.2078i	−0.578547	−	1.14474i
$652$	4.96118	−	8.59301i	0.194295	−	0.336528i
$653$	−13.5323			−0.529559			−0.264779	−	0.964309i	$-0.585299\pi$
$653$	−13.5323			−0.529559			−0.264779	+	0.964309i	$0.585299\pi$
$654$	−4.89310	−	2.63212i	−0.191335	−	0.102924i
$655$	18.7621			0.733096
$656$	−3.71105	−	6.42773i	−0.144892	−	0.250961i
$657$	−22.9547	−	34.7518i	−0.895550	−	1.35579i
$658$	0.715423	−	8.32572i	0.0278901	−	0.324570i
$659$	4.39992	+	7.62088i	0.171397	+	0.296867i	0.938908	−	0.344167i	$-0.111839\pi$
$659$	4.39992	+	7.62088i	0.171397	+	0.296867i	−0.767512	+	0.641035i	$0.778505\pi$
$660$	7.84252	+	4.21869i	0.305270	+	0.164212i
$661$	17.9543	+	31.0978i	0.698342	+	1.20956i	0.969041	+	0.246900i	$0.0794119\pi$
$661$	17.9543	+	31.0978i	0.698342	+	1.20956i	−0.270699	+	0.962664i	$0.587255\pi$
$662$	−8.44384	−	14.6252i	−0.328179	−	0.568423i
$663$	28.6992	+	15.4380i	1.11458	+	0.599562i
$664$	−6.13291	−	10.6225i	−0.238003	−	0.412234i
$665$	−1.06452	+	12.3883i	−0.0412803	+	0.480398i
$666$	5.36634	−	10.7379i	0.207941	−	0.416086i
$667$	−0.607646	−	1.05247i	−0.0235281	−	0.0407519i
$668$	6.53683			0.252917
$669$	5.26911	+	2.83439i	0.203716	+	0.109584i
$670$	−11.7774			−0.454999
$671$	−15.4131	+	26.6962i	−0.595015	+	1.03060i
$672$	2.06702	+	4.08992i	0.0797370	+	0.157772i
$673$	−11.4811	−	19.8858i	−0.442563	−	0.766541i	0.555316	−	0.831639i	$-0.312597\pi$
$673$	−11.4811	−	19.8858i	−0.442563	−	0.766541i	−0.997879	+	0.0650982i	$0.979264\pi$
$674$	−12.8294	−	22.2212i	−0.494171	−	0.855929i
$675$	−0.468162	−	5.17502i	−0.0180196	−	0.199187i
$676$	1.22744	−	2.12600i	0.0472094	−	0.0817691i
$677$	16.2831	−	28.2031i	0.625810	−	1.08393i	−0.362574	−	0.931955i	$-0.618102\pi$
$677$	16.2831	−	28.2031i	0.625810	−	1.08393i	0.988384	−	0.151980i	$-0.0485648\pi$
$678$	−3.50737	−	1.88670i	−0.134700	−	0.0724583i
$679$	−1.77463	+	20.6522i	−0.0681040	+	0.792559i
$680$	−2.89695	+	5.01766i	−0.111093	+	0.192418i
$681$	−28.3011	+	17.4948i	−1.08450	+	0.670404i
$682$	−36.7170			−1.40597
$683$	−25.6672	+	44.4569i	−0.982128	+	1.70110i	−0.328066	+	0.944655i	$0.606397\pi$
$683$	−25.6672	+	44.4569i	−0.982128	+	1.70110i	−0.654062	+	0.756441i	$0.726936\pi$
$684$	7.77059	+	11.7641i	0.297116	+	0.449811i
$685$	6.39791			0.244452
$686$	13.1565	+	13.0349i	0.502316	+	0.497673i
$687$	−31.9145	+	19.7286i	−1.21761	+	0.752692i
$688$	3.60995			0.137628
$689$	5.29339	+	9.16843i	0.201662	+	0.349289i
$690$	−0.139017	−	4.62119i	−0.00529228	−	0.175926i
$691$	−19.6397	+	34.0170i	−0.747130	+	1.29407i	0.202064	+	0.979372i	$0.435235\pi$
$691$	−19.6397	+	34.0170i	−0.747130	+	1.29407i	−0.949193	+	0.314694i	$0.898098\pi$
$692$	12.7290			0.483883
$693$	35.8516	−	19.4940i	1.36189	−	0.740517i
$694$	17.0235			0.646204
$695$	−10.4744	+	18.1422i	−0.397318	+	0.688174i
$696$	−0.694486	−	0.373581i	−0.0263244	−	0.0141606i
$697$	−21.5014	−	37.2416i	−0.814425	−	1.41063i
$698$	−22.6312			−0.856602
$699$	−4.17824	−	2.24758i	−0.158036	−	0.0850113i
$700$	0.226513	−	2.63604i	0.00856138	−	0.0996328i
$701$	−40.2576			−1.52051			−0.760254	−	0.649626i	$-0.774926\pi$
$701$	−40.2576			−1.52051			−0.760254	+	0.649626i	$0.774926\pi$
$702$	−13.7934	+	9.71908i	−0.520598	+	0.366823i
$703$	9.40247	−	16.2856i	0.354621	−	0.614222i
$704$	5.14142			0.193774
$705$	0.164493	+	5.46807i	0.00619517	+	0.205940i
$706$	−4.37421	+	7.57635i	−0.164625	+	0.285140i
$707$	−12.4307	−	8.67540i	−0.467503	−	0.326272i
$708$	−0.579822	−	19.2744i	−0.0217911	−	0.724377i
$709$	−6.62156	+	11.4689i	−0.248678	+	0.430722i	−0.963159	−	0.268932i	$-0.913329\pi$
$709$	−6.62156	+	11.4689i	−0.248678	+	0.430722i	0.714481	+	0.699654i	$0.246663\pi$
$710$	2.19294	−	3.79828i	0.0822996	−	0.142547i
$711$	4.88084	+	7.38922i	0.183046	+	0.277118i
$712$	4.83214	+	8.36951i	0.181092	+	0.313661i
$713$	9.53112	+	16.5084i	0.356943	+	0.618244i
$714$	11.9761	+	23.6965i	0.448194	+	0.886821i
$715$	−8.34792	+	14.4590i	−0.312194	+	0.540737i
$716$	−23.2364			−0.868386
$717$	−1.16850	−	38.8432i	−0.0436384	−	1.45063i
$718$	26.0238			0.971199
$719$	−22.7520	−	39.4076i	−0.848507	−	1.46966i	−0.882541	−	0.470236i	$-0.844169\pi$
$719$	−22.7520	−	39.4076i	−0.848507	−	1.46966i	0.0340340	−	0.999421i	$-0.489165\pi$
$720$	−1.65346	−	2.50321i	−0.0616208	−	0.0932892i
$721$	−30.4417	−	21.2454i	−1.13371	−	0.791218i
$722$	1.54309	+	2.67271i	0.0574278	+	0.0994679i
$723$	32.1698	−	19.8864i	1.19641	−	0.739582i
$724$	9.53436	+	16.5140i	0.354342	+	0.613738i
$725$	0.227646	+	0.394295i	0.00845457	+	0.0146437i
$726$	−0.803823	−	26.7206i	−0.0298327	−	0.991696i
$727$	0.0908081	+	0.157284i	0.00336789	+	0.00583335i	0.867704	−	0.497080i	$-0.165595\pi$
$727$	0.0908081	+	0.157284i	0.00336789	+	0.00583335i	−0.864337	+	0.502914i	$0.832261\pi$
$728$	−7.78102	+	3.64302i	−0.288384	+	0.135019i
$729$	−26.5616	+	4.84550i	−0.983765	+	0.179463i
$730$	6.94143	+	12.0229i	0.256914	+	0.444988i
$731$	20.9156			0.773593
$732$	8.83329	−	5.46047i	0.326488	−	0.201825i
$733$	46.1227			1.70358			0.851790	−	0.523883i	$-0.175517\pi$
$733$	46.1227			1.70358			0.851790	+	0.523883i	$0.175517\pi$
$734$	17.2794	−	29.9288i	0.637794	−	1.10469i
$735$	−9.54114	−	7.48109i	−0.351930	−	0.275944i
$736$	−1.33463	−	2.31164i	−0.0491950	−	0.0852082i
$737$	30.2761	+	52.4398i	1.11524	+	1.93165i
$738$	22.2260	−	1.33844i	0.818152	−	0.0492686i
$739$	−8.94515	+	15.4935i	−0.329053	+	0.569936i	−0.982324	−	0.187188i	$-0.940063\pi$
$739$	−8.94515	+	15.4935i	−0.329053	+	0.569936i	0.653271	+	0.757124i	$0.273396\pi$
$740$	−2.00070	+	3.46531i	−0.0735472	+	0.127387i
$741$	−22.4839	+	13.8989i	−0.825967	+	0.510587i
$742$	−0.738468	+	8.59390i	−0.0271100	+	0.315492i
$743$	−8.34901	+	14.4609i	−0.306295	+	0.530519i	−0.977549	−	0.210709i	$-0.932423\pi$
$743$	−8.34901	+	14.4609i	−0.306295	+	0.530519i	0.671253	+	0.741228i	$0.265756\pi$
$744$	10.8932	+	5.85975i	0.399366	+	0.214829i
$745$	12.3598			0.452827
$746$	4.48949	−	7.77603i	0.164372	−	0.284701i
$747$	36.7309	−	2.21192i	1.34391	−	0.0809298i
$748$	29.7888			1.08919
$749$	−3.30870	+	38.5048i	−0.120897	+	1.40694i
$750$	0.0520808	+	1.73127i	0.00190172	+	0.0632170i
$751$	31.2552			1.14052			0.570260	−	0.821464i	$-0.306843\pi$
$751$	31.2552			1.14052			0.570260	+	0.821464i	$0.306843\pi$
$752$	1.57921	+	2.73527i	0.0575879	+	0.0997452i
$753$	−8.33620	+	5.15318i	−0.303788	+	0.187792i
$754$	0.739241	−	1.28040i	0.0269216	−	0.0466295i
$755$	−19.4157			−0.706608
$756$	−13.7476	+	0.0618842i	−0.499995	+	0.00225071i
$757$	23.1959			0.843069			0.421534	−	0.906812i	$-0.361492\pi$
$757$	23.1959			0.843069			0.421534	+	0.906812i	$0.361492\pi$
$758$	−10.6144	+	18.3847i	−0.385532	+	0.667761i
$759$	−20.2189	+	12.4987i	−0.733901	+	0.453675i
$760$	−2.34980	−	4.06997i	−0.0852361	−	0.147633i
$761$	26.4849			0.960077			0.480039	−	0.877247i	$-0.340623\pi$
$761$	26.4849			0.960077			0.480039	+	0.877247i	$0.340623\pi$
$762$	0.120765	+	4.01446i	0.00437485	+	0.145428i
$763$	7.68638	−	3.59871i	0.278266	−	0.130282i
$764$	26.2989			0.951462
$765$	−9.57997	−	14.5033i	−0.346364	−	0.524370i
$766$	0.108153	−	0.187326i	0.00390771	−	0.00676835i
$767$	36.1529			1.30540
$768$	−1.52536	−	0.820531i	−0.0550418	−	0.0296083i
$769$	20.5798	−	35.6452i	0.742126	−	1.28540i	−0.209399	−	0.977830i	$-0.567151\pi$
$769$	20.5798	−	35.6452i	0.742126	−	1.28540i	0.951525	−	0.307570i	$-0.0995159\pi$
$770$	−12.3195	+	5.76791i	−0.443964	+	0.207861i
$771$	11.4367	−	7.06985i	0.411884	−	0.254614i
$772$	−2.34431	+	4.06047i	−0.0843736	+	0.146139i
$773$	−13.2736	+	22.9905i	−0.477418	+	0.826912i	−0.999665	−	0.0258823i	$-0.991761\pi$
$773$	−13.2736	+	22.9905i	−0.477418	+	0.826912i	0.522247	+	0.852794i	$0.325094\pi$
$774$	−4.84136	+	9.68745i	−0.174019	+	0.348208i
$775$	−3.57071	−	6.18465i	−0.128264	−	0.222159i
$776$	−3.91728	−	6.78493i	−0.140622	−	0.243565i
$777$	8.27097	+	16.3654i	0.296719	+	0.587105i
$778$	−5.81312	+	10.0686i	−0.208410	+	0.360977i
$779$	34.8809			1.24974
$780$	4.78422	−	2.95746i	0.171303	−	0.105894i
$781$	−22.5496			−0.806889
$782$	−7.73269	−	13.3934i	−0.276520	−	0.478947i
$783$	1.93391	−	1.36267i	0.0691122	−	0.0486978i
$784$	−6.89738	−	1.19419i	−0.246335	−	0.0426497i
$785$	−1.23050	−	2.13128i	−0.0439183	−	0.0760687i
$786$	0.977145	+	32.4822i	0.0348536	+	1.15860i
$787$	−12.1086	−	20.9727i	−0.431624	−	0.747595i	0.565389	−	0.824824i	$-0.308726\pi$
$787$	−12.1086	−	20.9727i	−0.431624	−	0.747595i	−0.997013	+	0.0772296i	$0.975393\pi$
$788$	−5.22882	−	9.05658i	−0.186269	−	0.322627i
$789$	13.5286	−	8.36298i	0.481632	−	0.297730i
$790$	−1.47595	−	2.55642i	−0.0525119	−	0.0909533i
$791$	5.50959	−	2.57955i	0.195898	−	0.0917183i
$792$	−6.89523	+	13.7972i	−0.245011	+	0.490263i
$793$	9.73492	+	16.8614i	0.345697	+	0.598765i
$794$	−28.3334			−1.00552
$795$	−0.169792	−	5.64421i	−0.00602189	−	0.200179i
$796$	16.3211			0.578485
$797$	3.05746	−	5.29567i	0.108301	−	0.187582i	−0.806781	−	0.590850i	$-0.798792\pi$
$797$	3.05746	−	5.29567i	0.108301	−	0.187582i	0.915082	+	0.403268i	$0.132126\pi$
$798$	−21.5029	−	1.19777i	−0.761195	−	0.0424007i
$799$	9.14978	+	15.8479i	0.323696	+	0.560658i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−28.9404	+	1.74277i	−1.02256	+	0.0615779i
$802$	−3.41125	+	5.90845i	−0.120455	+	0.208635i
$803$	35.6888	−	61.8148i	1.25943	−	2.18140i
$804$	−0.613374	−	20.3898i	−0.0216320	−	0.719091i
$805$	5.79126	+	4.04174i	0.204115	+	0.142453i
$806$	−11.5952	+	20.0836i	−0.408425	+	0.707413i
$807$	−0.940592	−	31.2671i	−0.0331104	−	1.10065i
$808$	5.72942			0.201560
$809$	10.3380	−	17.9059i	0.363464	−	0.629538i	−0.625065	−	0.780573i	$-0.714927\pi$
$809$	10.3380	−	17.9059i	0.363464	−	0.629538i	0.988528	+	0.151035i	$0.0482607\pi$
$810$	8.93496	−	1.08003i	0.313943	−	0.0379485i
$811$	15.2973			0.537160			0.268580	−	0.963257i	$-0.413446\pi$
$811$	15.2973			0.537160			0.268580	+	0.963257i	$0.413446\pi$
$812$	1.09094	−	0.510771i	0.0382845	−	0.0179246i
$813$	−37.3605	−	20.0971i	−1.31029	−	0.704837i
$814$	20.5729			0.721078
$815$	−4.96118	−	8.59301i	−0.173782	−	0.301000i
$816$	−8.83779	−	4.75407i	−0.309384	−	0.166426i
$817$	−8.48264	+	14.6924i	−0.296770	+	0.514021i
$818$	−11.1738			−0.390684
$819$	0.659041	−	25.7664i	0.0230288	−	0.900351i
$820$	−7.42210			−0.259191
$821$	−3.37590	+	5.84724i	−0.117820	+	0.204070i	−0.918903	−	0.394482i	$-0.870924\pi$
$821$	−3.37590	+	5.84724i	−0.117820	+	0.204070i	0.801084	+	0.598552i	$0.204257\pi$
$822$	0.333208	+	11.0765i	0.0116220	+	0.386337i
$823$	−11.3370	−	19.6362i	−0.395183	−	0.684476i	0.597942	−	0.801540i	$-0.295985\pi$
$823$	−11.3370	−	19.6362i	−0.395183	−	0.684476i	−0.993124	+	0.117063i	$0.962652\pi$
$824$	14.0309			0.488789
$825$	7.57475	−	4.68248i	0.263719	−	0.163023i
$826$	24.1546	+	16.8576i	0.840448	+	0.586551i
$827$	−26.0867			−0.907122			−0.453561	−	0.891225i	$-0.649847\pi$
$827$	−26.0867			−0.907122			−0.453561	+	0.891225i	$0.649847\pi$
$828$	7.99328	−	0.481351i	0.277786	−	0.0167281i
$829$	−1.68725	+	2.92240i	−0.0586005	+	0.101499i	−0.893837	−	0.448391i	$-0.851997\pi$
$829$	−1.68725	+	2.92240i	−0.0586005	+	0.101499i	0.835237	+	0.549890i	$0.185330\pi$
$830$	−12.2658			−0.425753
$831$	−19.3245	+	11.9458i	−0.670361	+	0.414397i
$832$	1.62366	−	2.81226i	0.0562903	−	0.0974977i
$833$	−39.9627	−	6.91903i	−1.38463	−	0.239730i
$834$	−31.9546	−	17.1892i	−1.10650	−	0.595212i
$835$	3.26841	−	5.66106i	0.113108	−	0.195909i
$836$	−12.0813	+	20.9254i	−0.417840	+	0.723720i
$837$	−30.3340	+	21.3739i	−1.04850	+	0.738790i
$838$	2.78160	+	4.81787i	0.0960887	+	0.166430i
$839$	−11.2557	−	19.4955i	−0.388590	−	0.673058i	0.603670	−	0.797234i	$-0.293704\pi$
$839$	−11.2557	−	19.4955i	−0.388590	−	0.673058i	−0.992260	+	0.124176i	$0.960371\pi$
$840$	4.57548	+	0.254868i	0.157869	+	0.00879377i
$841$	14.3964	−	24.9352i	0.496426	−	0.859835i
$842$	−34.5798			−1.19170
$843$	3.23551	+	1.74046i	0.111437	+	0.0599447i
$844$	4.34991			0.149730
$845$	−1.22744	−	2.12600i	−0.0422254	−	0.0731365i
$846$	−9.45813	+	0.569563i	−0.325177	+	0.0195820i
$847$	33.4862	+	23.3701i	1.15060	+	0.803008i
$848$	−1.63008	−	2.82338i	−0.0559771	−	0.0969553i
$849$	17.1658	+	9.23392i	0.589129	+	0.316907i
$850$	2.89695	+	5.01766i	0.0993645	+	0.172104i
$851$	−5.34037	−	9.24980i	−0.183066	−	0.317079i
$852$	6.69006	+	3.59875i	0.229198	+	0.123291i
$853$	12.9138	+	22.3673i	0.442159	+	0.765842i	0.997849	−	0.0655473i	$-0.0208793\pi$
$853$	12.9138	+	22.3673i	0.442159	+	0.765842i	−0.555690	+	0.831389i	$0.687546\pi$
$854$	−1.35809	+	15.8048i	−0.0464730	+	0.540828i
$855$	14.0733	−	0.847485i	0.481296	−	0.0289834i
$856$	−7.30355	−	12.6501i	−0.249630	−	0.432372i
$857$	24.4314			0.834562			0.417281	−	0.908777i	$-0.362983\pi$
$857$	24.4314			0.834562			0.417281	+	0.908777i	$0.362983\pi$
$858$	−25.4672	−	13.6994i	−0.869436	−	0.467691i
$859$	18.9041			0.644999			0.322500	−	0.946570i	$-0.395477\pi$
$859$	18.9041			0.644999			0.322500	+	0.946570i	$0.395477\pi$
$860$	1.80497	−	3.12631i	0.0615491	−	0.106606i
$861$	−18.6181	+	28.4641i	−0.634502	+	0.970055i
$862$	−19.2277	−	33.3034i	−0.654899	−	1.13432i
$863$	1.64446	+	2.84828i	0.0559779	+	0.0969566i	0.892656	−	0.450738i	$-0.148839\pi$
$863$	1.64446	+	2.84828i	0.0559779	+	0.0969566i	−0.836679	+	0.547694i	$0.815506\pi$
$864$	4.24762	−	2.99295i	0.144507	−	0.101822i
$865$	6.36448	−	11.0236i	0.216399	−	0.374814i
$866$	15.4775	−	26.8078i	0.525946	−	0.910965i
$867$	−25.2740	−	13.5955i	−0.858351	−	0.461729i
$868$	−17.1118	+	8.01162i	−0.580811	+	0.271932i
$869$	−7.58846	+	13.1436i	−0.257421	+	0.445866i
$870$	−0.670774	+	0.414652i	−0.0227414	+	0.0140580i
$871$	38.2449			1.29588
$872$	−1.60392	+	2.77806i	−0.0543154	+	0.0940771i
$873$	23.4612	−	1.41282i	0.794041	−	0.0478167i
$874$	12.5444			0.424321
$875$	−2.16962	−	1.51418i	−0.0733465	−	0.0511888i
$876$	−20.4534	+	12.6436i	−0.691055	+	0.427189i
$877$	−26.7992			−0.904946			−0.452473	−	0.891778i	$-0.649458\pi$
$877$	−26.7992			−0.904946			−0.452473	+	0.891778i	$0.649458\pi$
$878$	13.4194	+	23.2431i	0.452883	+	0.784417i
$879$	−0.500949	−	16.6525i	−0.0168966	−	0.561676i
$880$	2.57071	−	4.45260i	0.0866585	−	0.150097i
$881$	20.9761			0.706703			0.353352	−	0.935491i	$-0.385042\pi$
$881$	20.9761			0.706703			0.353352	+	0.935491i	$0.385042\pi$
$882$	12.4549	−	16.9079i	0.419377	−	0.569318i
$883$	−24.9042			−0.838093			−0.419047	−	0.907965i	$-0.637636\pi$
$883$	−24.9042			−0.838093			−0.419047	+	0.907965i	$0.637636\pi$
$884$	9.40732	−	16.2940i	0.316403	−	0.548025i
$885$	−16.9821	−	9.13507i	−0.570846	−	0.307072i
$886$	−16.1258	−	27.9308i	−0.541758	−	0.938353i
$887$	22.1820			0.744798			0.372399	−	0.928073i	$-0.378535\pi$
$887$	22.1820			0.744798			0.372399	+	0.928073i	$0.378535\pi$
$888$	−6.10358	−	3.28327i	−0.204823	−	0.110179i
$889$	−5.03091	−	3.51109i	−0.168731	−	0.117758i
$890$	9.66427			0.323947
$891$	−27.7781	−	37.0073i	−0.930602	−	1.23979i
$892$	1.72717	−	2.99154i	0.0578298	−	0.100164i
$893$	−14.8433			−0.496712
$894$	0.643707	+	21.3981i	0.0215288	+	0.715659i
$895$	−11.6182	+	20.1233i	−0.388354	+	0.672649i
$896$	2.39613	−	1.12185i	0.0800491	−	0.0374785i
$897$	0.451433	+	15.0065i	0.0150729	+	0.501053i
$898$	−4.72515	+	8.18419i	−0.157680	+	0.273110i
$899$	1.62572	−	2.81582i	0.0542207	−	0.0939130i
$900$	−2.99458	+	0.180332i	−0.0998192	+	0.00601105i
$901$	−9.44451	−	16.3584i	−0.314642	−	0.544976i
$902$	19.0801	+	33.0476i	0.635296	+	1.10037i
$903$	−7.46183	−	14.7644i	−0.248314	−	0.491328i
$904$	−1.14968	+	1.99131i	−0.0382379	+	0.0662300i
$905$	19.0687			0.633866
$906$	−1.01118	−	33.6137i	−0.0335943	−	1.11674i
$907$	56.6729			1.88179			0.940897	−	0.338694i	$-0.109985\pi$
$907$	56.6729			1.88179			0.940897	+	0.338694i	$0.109985\pi$
$908$	9.60477	+	16.6359i	0.318745	+	0.552083i
$909$	−7.68382	+	15.3751i	−0.254856	+	0.509962i
$910$	−0.735561	+	8.56007i	−0.0243836	+	0.283763i
$911$	22.6917	+	39.3032i	0.751809	+	1.30217i	0.946945	+	0.321396i	$0.104152\pi$
$911$	22.6917	+	39.3032i	0.751809	+	1.30217i	−0.195136	+	0.980776i	$0.562515\pi$
$912$	6.92382	−	4.28009i	0.229271	−	0.141728i
$913$	31.5318	+	54.6148i	1.04355	+	1.80748i
$914$	12.6657	+	21.9376i	0.418943	+	0.725630i
$915$	−0.312259	−	10.3801i	−0.0103230	−	0.343155i
$916$	10.8311	+	18.7600i	0.357870	+	0.619848i
$917$	−40.7066	−	28.4093i	−1.34425	−	0.938157i
$918$	24.6102	−	17.3408i	0.812259	−	0.572333i
$919$	−5.64196	−	9.77216i	−0.186111	−	0.322354i	0.757839	−	0.652441i	$-0.226255\pi$
$919$	−5.64196	−	9.77216i	−0.186111	−	0.322354i	−0.943950	+	0.330087i	$0.892922\pi$
$920$	−2.66925			−0.0880027
$921$	−13.4589	+	8.31990i	−0.443487	+	0.274150i
$922$	0.137691			0.00453460
$923$	−7.12119	+	12.3343i	−0.234397	+	0.405987i
$924$	−10.6274	−	21.0280i	−0.349616	−	0.691769i
$925$	2.00070	+	3.46531i	0.0657826	+	0.113939i
$926$	8.01422	+	13.8810i	0.263364	+	0.456159i
$927$	−18.8170	+	37.6525i	−0.618033	+	1.23667i
$928$	−0.227646	+	0.394295i	−0.00747285	+	0.0129434i
$929$	4.35489	−	7.54290i	0.142879	−	0.247474i	−0.785700	−	0.618607i	$-0.787697\pi$
$929$	4.35489	−	7.54290i	0.142879	−	0.247474i	0.928580	+	0.371133i	$0.121031\pi$
$930$	10.5213	−	6.50395i	0.345007	−	0.213273i
$931$	21.0678	−	25.2660i	0.690468	−	0.828060i
$932$	−1.36959	+	2.37220i	−0.0448624	+	0.0777040i
$933$	−31.4145	−	16.8986i	−1.02846	−	0.553236i
$934$	21.8064			0.713527
$935$	14.8944	−	25.7979i	0.487099	−	0.843680i
$936$	5.36932	+	8.12874i	0.175502	+	0.265696i
$937$	−12.4809			−0.407735			−0.203867	−	0.978999i	$-0.565351\pi$
$937$	−12.4809			−0.407735			−0.203867	+	0.978999i	$0.565351\pi$
$938$	25.5524	+	17.8331i	0.834315	+	0.582271i
$939$	−0.0286889	−	0.953675i	−0.000936227	−	0.0311220i
$940$	3.15842			0.103016
$941$	−11.7985	−	20.4356i	−0.384620	−	0.666182i	0.607096	−	0.794629i	$-0.292334\pi$
$941$	−11.7985	−	20.4356i	−0.384620	−	0.666182i	−0.991716	+	0.128446i	$0.959001\pi$
$942$	3.62573	−	2.24132i	0.118133	−	0.0730261i
$943$	9.90574	−	17.1572i	0.322575	−	0.558717i
$944$	−11.1331			−0.362353
$945$	−6.82020	+	11.9367i	−0.221861	+	0.388301i
$946$	−18.5602			−0.603445
$947$	7.86869	−	13.6290i	0.255698	−	0.442882i	−0.709387	−	0.704819i	$-0.751028\pi$
$947$	7.86869	−	13.6290i	0.255698	−	0.442882i	0.965085	+	0.261937i	$0.0843614\pi$
$948$	4.34897	−	2.68840i	0.141248	−	0.0873152i
$949$	−22.5411	−	39.0423i	−0.731714	−	1.26737i
$950$	−4.69959			−0.152475
$951$	−1.40485	−	46.6999i	−0.0455554	−	1.51435i
$952$	13.8829	−	6.49989i	0.449948	−	0.210663i
$953$	−3.60070			−0.116638			−0.0583191	−	0.998298i	$-0.518574\pi$
$953$	−3.60070			−0.116638			−0.0583191	+	0.998298i	$0.518574\pi$
$954$	9.76279	−	0.587910i	0.316082	−	0.0190343i
$955$	13.1495	−	22.7755i	0.425507	−	0.736999i
$956$	−22.4363			−0.725641
$957$	3.57064	+	1.92074i	0.115422	+	0.0620886i
$958$	−8.13300	+	14.0868i	−0.262765	+	0.455123i
$959$	−13.8810	−	9.68761i	−0.448242	−	0.312829i
$960$	−1.47328	+	0.910737i	−0.0475500	+	0.0293939i
$961$	−9.99990	+	17.3203i	−0.322578	+	0.558721i
$962$	6.49692	−	11.2530i	0.209469	−	0.362811i
$963$	43.7420	−	2.63412i	1.40957	−	0.0848834i
$964$	−10.9177	−	18.9101i	−0.351636	−	0.609052i
$965$	2.34431	+	4.06047i	0.0754660	+	0.130711i
$966$	−6.69572	+	10.2367i	−0.215431	+	0.329361i
$967$	17.9234	−	31.0443i	0.576379	−	0.998317i	−0.419511	−	0.907750i	$-0.637799\pi$
$967$	17.9234	−	31.0443i	0.576379	−	0.998317i	0.995890	−	0.0905674i	$-0.0288681\pi$
$968$	−15.4341			−0.496072
$969$	40.1159	−	24.7984i	1.28871	−	0.796640i
$970$	−7.83456			−0.251553
$971$	−4.25320	−	7.36675i	−0.136492	−	0.236410i	0.789675	−	0.613526i	$-0.210249\pi$
$971$	−4.25320	−	7.36675i	−0.136492	−	0.236410i	−0.926166	+	0.377115i	$0.876916\pi$
$972$	2.33517	+	15.4126i	0.0749005	+	0.494358i
$973$	50.1962	−	23.5015i	1.60922	−	0.753424i
$974$	17.0685	+	29.5636i	0.546911	+	0.947278i
$975$	−0.169123	−	5.62199i	−0.00541628	−	0.180048i
$976$	−2.99783	−	5.19239i	−0.0959581	−	0.166204i
$977$	−17.7804	−	30.7965i	−0.568845	−	0.985269i	−0.996681	−	0.0814119i	$-0.974057\pi$
$977$	−17.7804	−	30.7965i	−0.568845	−	0.985269i	0.427835	−	0.903857i	$-0.359276\pi$
$978$	14.6184	−	9.03666i	0.467446	−	0.288960i
$979$	−24.8440	−	43.0311i	−0.794018	−	1.37528i
$980$	−4.48289	+	5.37621i	−0.143201	+	0.171737i
$981$	−5.30402	−	8.02988i	−0.169344	−	0.256374i
$982$	−21.6539	−	37.5057i	−0.691004	−	1.19685i
$983$	−61.4109			−1.95870			−0.979351	−	0.202167i	$-0.935202\pi$
$983$	−61.4109			−1.95870			−0.979351	+	0.202167i	$0.935202\pi$
$984$	−0.386549	−	12.8496i	−0.0123227	−	0.409632i
$985$	−10.4576			−0.333208
$986$	−1.31896	+	2.28450i	−0.0420042	+	0.0727534i
$987$	7.92279	−	12.1127i	0.252185	−	0.385552i
$988$	7.63055	+	13.2165i	0.242760	+	0.420473i
$989$	4.81793	+	8.34490i	0.153201	+	0.265352i
$990$	8.50112	+	12.8701i	0.270183	+	0.409037i
$991$	−12.6801	+	21.9626i	−0.402796	+	0.697664i	−0.994062	−	0.108813i	$-0.965295\pi$
$991$	−12.6801	+	21.9626i	−0.402796	+	0.697664i	0.591266	+	0.806477i	$0.298628\pi$
$992$	3.57071	−	6.18465i	0.113370	−	0.196363i
$993$	−0.879524	−	29.2371i	−0.0279108	−	0.927811i
$994$	−10.5091	+	4.92031i	−0.333330	+	0.156063i
$995$	8.16053	−	14.1345i	0.258706	−	0.448093i
$996$	−0.638814	−	21.2354i	−0.0202416	−	0.672870i
$997$	−1.33138			−0.0421652			−0.0210826	−	0.999778i	$-0.506711\pi$
$997$	−1.33138			−0.0421652			−0.0210826	+	0.999778i	$0.506711\pi$
$998$	3.32314	−	5.75585i	0.105192	−	0.182198i
$999$	16.9964	−	11.9760i	0.537743	−	0.378903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.l.i.571.7	yes	16
3.2	odd	2		1890.2.l.i.361.7		16
7.2	even	3		630.2.i.i.121.4	✓	16
9.2	odd	6		1890.2.i.i.991.4		16
9.7	even	3		630.2.i.i.151.4	yes	16
21.2	odd	6		1890.2.i.i.1171.4		16
63.2	odd	6		1890.2.l.i.1801.7		16
63.16	even	3	inner	630.2.l.i.331.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.i.121.4	✓	16	7.2	even	3
630.2.i.i.151.4	yes	16	9.7	even	3
630.2.l.i.331.7	yes	16	63.16	even	3	inner
630.2.l.i.571.7	yes	16	1.1	even	1	trivial
1890.2.i.i.991.4		16	9.2	odd	6
1890.2.i.i.1171.4		16	21.2	odd	6
1890.2.l.i.361.7		16	3.2	odd	2
1890.2.l.i.1801.7		16	63.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.47328 - 0.910737i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.0520808 - 1.73127i) q^{6} +(2.16962 + 1.51418i) q^{7} -1.00000 q^{8} +(1.34112 - 2.68354i) q^{9} +(-0.500000 + 0.866025i) q^{10} +5.14142 q^{11} +(-1.52536 - 0.820531i) q^{12} +(1.62366 - 2.81226i) q^{13} +(2.39613 - 1.12185i) q^{14} +(-1.47328 + 0.910737i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.89695 + 5.01766i) q^{17} +(-1.65346 - 2.50321i) q^{18} +(-2.34980 - 4.06997i) q^{19} +(0.500000 + 0.866025i) q^{20} +(4.57548 + 0.254868i) q^{21} +(2.57071 - 4.45260i) q^{22} -2.66925 q^{23} +(-1.47328 + 0.910737i) q^{24} +1.00000 q^{25} +(-1.62366 - 2.81226i) q^{26} +(-0.468162 - 5.17502i) q^{27} +(0.226513 - 2.63604i) q^{28} +(0.227646 + 0.394295i) q^{29} +(0.0520808 + 1.73127i) q^{30} +(-3.57071 - 6.18465i) q^{31} +(0.500000 + 0.866025i) q^{32} +(7.57475 - 4.68248i) q^{33} +(2.89695 + 5.01766i) q^{34} +(-2.16962 - 1.51418i) q^{35} +(-2.99458 + 0.180332i) q^{36} +(2.00070 + 3.46531i) q^{37} -4.69959 q^{38} +(-0.169123 - 5.62199i) q^{39} +1.00000 q^{40} +(-3.71105 + 6.42773i) q^{41} +(2.50846 - 3.83505i) q^{42} +(-1.80497 - 3.12631i) q^{43} +(-2.57071 - 4.45260i) q^{44} +(-1.34112 + 2.68354i) q^{45} +(-1.33463 + 2.31164i) q^{46} +(1.57921 - 2.73527i) q^{47} +(0.0520808 + 1.73127i) q^{48} +(2.41449 + 6.57041i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.301751 + 10.0308i) q^{51} -3.24732 q^{52} +(-1.63008 + 2.82338i) q^{53} +(-4.71578 - 2.18207i) q^{54} -5.14142 q^{55} +(-2.16962 - 1.51418i) q^{56} +(-7.16858 - 3.85616i) q^{57} +0.455293 q^{58} +(5.56657 + 9.64157i) q^{59} +(1.52536 + 0.820531i) q^{60} +(-2.99783 + 5.19239i) q^{61} -7.14142 q^{62} +(6.97309 - 3.79157i) q^{63} +1.00000 q^{64} +(-1.62366 + 2.81226i) q^{65} +(-0.267769 - 8.90117i) q^{66} +(5.88868 + 10.1995i) q^{67} +5.79389 q^{68} +(-3.93256 + 2.43099i) q^{69} +(-2.39613 + 1.12185i) q^{70} -4.38588 q^{71} +(-1.34112 + 2.68354i) q^{72} +(6.94143 - 12.0229i) q^{73} +4.00140 q^{74} +(1.47328 - 0.910737i) q^{75} +(-2.34980 + 4.06997i) q^{76} +(11.1549 + 7.78505i) q^{77} +(-4.95334 - 2.66453i) q^{78} +(-1.47595 + 2.55642i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-5.40282 - 7.19789i) q^{81} +(3.71105 + 6.42773i) q^{82} +(6.13291 + 10.6225i) q^{83} +(-2.06702 - 4.08992i) q^{84} +(2.89695 - 5.01766i) q^{85} -3.60995 q^{86} +(0.694486 + 0.373581i) q^{87} -5.14142 q^{88} +(-4.83214 - 8.36951i) q^{89} +(1.65346 + 2.50321i) q^{90} +(7.78102 - 3.64302i) q^{91} +(1.33463 + 2.31164i) q^{92} +(-10.8932 - 5.85975i) q^{93} +(-1.57921 - 2.73527i) q^{94} +(2.34980 + 4.06997i) q^{95} +(1.52536 + 0.820531i) q^{96} +(3.91728 + 6.78493i) q^{97} +(6.89738 + 1.19419i) q^{98} +(6.89523 - 13.7972i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - q^{3} - 8 q^{4} - 16 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} + 9 q^{9} - 8 q^{10} - 2 q^{11} - q^{12} + 2 q^{13} + 8 q^{14} + q^{15} - 8 q^{16} + 11 q^{17} + 3 q^{18} - 2 q^{19} + 8 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - q^3 - 8 * q^4 - 16 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 + 9 * q^9 - 8 * q^10 - 2 * q^11 - q^12 + 2 * q^13 + 8 * q^14 + q^15 - 8 * q^16 + 11 * q^17 + 3 * q^18 - 2 * q^19 + 8 * q^20 - q^22 - 22 * q^23 + q^24 + 16 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 + 2 * q^30 - 15 * q^31 + 8 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 - 4 * q^38 + 33 * q^39 + 16 * q^40 + 7 * q^41 - 9 * q^42 - 13 * q^43 + q^44 - 9 * q^45 - 11 * q^46 - 5 * q^47 + 2 * q^48 + 10 * q^49 + 8 * q^50 + 30 * q^51 - 4 * q^52 + 18 * q^53 + q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 + 34 * q^58 + q^59 + q^60 - 27 * q^61 - 30 * q^62 + 14 * q^63 + 16 * q^64 - 2 * q^65 + 10 * q^66 - 10 * q^67 - 22 * q^68 - 14 * q^69 - 8 * q^70 - 38 * q^71 - 9 * q^72 - 8 * q^73 - 4 * q^74 - q^75 - 2 * q^76 - 19 * q^77 - 25 * q^79 + 8 * q^80 + 9 * q^81 - 7 * q^82 + 2 * q^83 - 9 * q^84 - 11 * q^85 - 26 * q^86 + 58 * q^87 + 2 * q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 + 3 * q^93 + 5 * q^94 + 2 * q^95 + q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more