LMFDB - Embedded newform 61.2.e.a.20.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(9,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("61.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.e (of order $5$, degree $4$, 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:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
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} - 3 x^{11} + 9 x^{10} - 15 x^{9} + 29 x^{8} - 26 x^{7} + 43 x^{6} + 24 x^{5} + 16 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 9x^10 - 15x^9 + 29x^8 - 26x^7 + 43x^6 + 24x^5 + 16x^4 - 17x^3 + 14x^2 - 5*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			20.3
Root			$-0.689843 + 0.501200i$ of defining polynomial
Character	$\chi$	$=$	61.20
Dual form			61.2.e.a.58.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.263496 + 0.810959i) q^{2} +(-0.862402 - 2.65420i) q^{3} +(1.02981 - 0.748201i) q^{4} +(-0.339968 + 0.247001i) q^{5} +(1.92521 - 1.39874i) q^{6} +(-1.05338 + 3.24198i) q^{7} +(2.25780 + 1.64039i) q^{8} +(-3.87399 + 2.81462i) q^{9} +O(q^{10})$	\(q+(0.263496 + 0.810959i) q^{2} +(-0.862402 - 2.65420i) q^{3} +(1.02981 - 0.748201i) q^{4} +(-0.339968 + 0.247001i) q^{5} +(1.92521 - 1.39874i) q^{6} +(-1.05338 + 3.24198i) q^{7} +(2.25780 + 1.64039i) q^{8} +(-3.87399 + 2.81462i) q^{9} +(-0.289888 - 0.210616i) q^{10} -2.79991 q^{11} +(-2.87399 - 2.08807i) q^{12} +5.47505 q^{13} -2.90668 q^{14} +(0.948780 + 0.689329i) q^{15} +(0.0513422 - 0.158015i) q^{16} +(-3.09147 + 2.24609i) q^{17} +(-3.30332 - 2.40000i) q^{18} +(-1.75583 - 5.40389i) q^{19} +(-0.165296 + 0.508729i) q^{20} +9.51331 q^{21} +(-0.737766 - 2.27061i) q^{22} +(-2.46850 + 1.79347i) q^{23} +(2.40678 - 7.40731i) q^{24} +(-1.49052 + 4.58734i) q^{25} +(1.44266 + 4.44004i) q^{26} +(4.03809 + 2.93384i) q^{27} +(1.34087 + 4.12677i) q^{28} -1.66543 q^{29} +(-0.309017 + 0.951057i) q^{30} +(1.66567 - 5.12640i) q^{31} +5.72325 q^{32} +(2.41465 + 7.43152i) q^{33} +(-2.63608 - 1.91522i) q^{34} +(-0.442657 - 1.36236i) q^{35} +(-1.88357 + 5.79704i) q^{36} +(-0.278406 + 0.856845i) q^{37} +(3.91967 - 2.84781i) q^{38} +(-4.72170 - 14.5319i) q^{39} -1.17276 q^{40} +(3.41477 - 10.5096i) q^{41} +(2.50672 + 7.71490i) q^{42} +(-1.80465 - 1.31116i) q^{43} +(-2.88338 + 2.09490i) q^{44} +(0.621818 - 1.91376i) q^{45} +(-2.10487 - 1.52928i) q^{46} -0.616624 q^{47} -0.463681 q^{48} +(-3.73772 - 2.71562i) q^{49} -4.11289 q^{50} +(8.62766 + 6.26836i) q^{51} +(5.63827 - 4.09644i) q^{52} +(-1.81522 - 1.31884i) q^{53} +(-1.31520 + 4.04778i) q^{54} +(0.951880 - 0.691581i) q^{55} +(-7.69643 + 5.59178i) q^{56} +(-12.8288 + 9.32064i) q^{57} +(-0.438834 - 1.35059i) q^{58} +(4.61443 + 14.2018i) q^{59} +1.49282 q^{60} +(-7.73228 - 1.10083i) q^{61} +4.59619 q^{62} +(-5.04414 - 15.5243i) q^{63} +(1.40537 + 4.32529i) q^{64} +(-1.86134 + 1.35235i) q^{65} +(-5.39040 + 3.91635i) q^{66} +(3.77676 - 2.74397i) q^{67} +(-1.50311 + 4.62609i) q^{68} +(6.88906 + 5.00520i) q^{69} +(0.988178 - 0.717953i) q^{70} +(-1.07558 - 0.781456i) q^{71} -13.3637 q^{72} +(5.96471 + 4.33361i) q^{73} -0.768224 q^{74} +13.4611 q^{75} +(-5.85137 - 4.25127i) q^{76} +(2.94938 - 9.07726i) q^{77} +(10.5406 - 7.65820i) q^{78} +(2.18446 + 1.58710i) q^{79} +(0.0215752 + 0.0664016i) q^{80} +(-0.134641 + 0.414383i) q^{81} +9.42261 q^{82} +(-3.14899 - 9.69159i) q^{83} +(9.79691 - 7.11787i) q^{84} +(0.496216 - 1.52720i) q^{85} +(0.587775 - 1.80899i) q^{86} +(1.43627 + 4.42037i) q^{87} +(-6.32162 - 4.59293i) q^{88} +(-3.84087 - 11.8210i) q^{89} +1.71583 q^{90} +(-5.76734 + 17.7500i) q^{91} +(-1.20021 + 3.69387i) q^{92} -15.0430 q^{93} +(-0.162478 - 0.500057i) q^{94} +(1.93169 + 1.40346i) q^{95} +(-4.93574 - 15.1907i) q^{96} +(-3.68827 + 11.3513i) q^{97} +(1.21737 - 3.74669i) q^{98} +(10.8468 - 7.88067i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - q^{3} + 2 q^{4} - 5 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} - 6 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - q^3 + 2 * q^4 - 5 * q^5 - q^6 - 10 * q^7 + 4 * q^8 - 6 * q^9	\( 12 q - 2 q^{2} - q^{3} + 2 q^{4} - 5 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} + 6 q^{12} + 2 q^{13} - 2 q^{14} - 5 q^{15} + 10 q^{16} + 6 q^{17} - 15 q^{18} - q^{19} + 13 q^{20} + 32 q^{21} - 25 q^{22} - 7 q^{23} - 12 q^{25} + 2 q^{26} + 8 q^{27} - 13 q^{28} - 8 q^{29} + 3 q^{30} + 19 q^{31} + 26 q^{32} - q^{33} - 30 q^{34} + 10 q^{35} + 8 q^{36} + 31 q^{37} + 27 q^{38} - 23 q^{39} + 4 q^{41} + 11 q^{42} + q^{43} - 20 q^{44} - 18 q^{45} + 23 q^{46} - 22 q^{47} - 8 q^{48} + 3 q^{49} + 74 q^{50} + 9 q^{52} - 35 q^{53} - 26 q^{54} - 18 q^{56} - 31 q^{57} - 16 q^{58} - 13 q^{59} + 2 q^{60} - 6 q^{61} - 52 q^{62} + 7 q^{63} + 16 q^{64} + 4 q^{65} - 19 q^{66} - 9 q^{67} - 33 q^{68} + 35 q^{69} - 5 q^{70} - 24 q^{71} - 30 q^{72} + 51 q^{73} - 20 q^{74} + 40 q^{75} - 31 q^{76} + q^{77} + 22 q^{78} - 26 q^{79} - 23 q^{80} - 2 q^{81} + 78 q^{82} + 3 q^{83} + 17 q^{84} + 18 q^{85} + 55 q^{86} + 49 q^{87} - q^{88} - 17 q^{89} + 54 q^{90} - 27 q^{91} + 37 q^{92} + 10 q^{93} + 13 q^{94} + 4 q^{95} - 17 q^{96} + 17 q^{97} + 29 q^{98} + 19 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - q^3 + 2 * q^4 - 5 * q^5 - q^6 - 10 * q^7 + 4 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 + 6 * q^12 + 2 * q^13 - 2 * q^14 - 5 * q^15 + 10 * q^16 + 6 * q^17 - 15 * q^18 - q^19 + 13 * q^20 + 32 * q^21 - 25 * q^22 - 7 * q^23 - 12 * q^25 + 2 * q^26 + 8 * q^27 - 13 * q^28 - 8 * q^29 + 3 * q^30 + 19 * q^31 + 26 * q^32 - q^33 - 30 * q^34 + 10 * q^35 + 8 * q^36 + 31 * q^37 + 27 * q^38 - 23 * q^39 + 4 * q^41 + 11 * q^42 + q^43 - 20 * q^44 - 18 * q^45 + 23 * q^46 - 22 * q^47 - 8 * q^48 + 3 * q^49 + 74 * q^50 + 9 * q^52 - 35 * q^53 - 26 * q^54 - 18 * q^56 - 31 * q^57 - 16 * q^58 - 13 * q^59 + 2 * q^60 - 6 * q^61 - 52 * q^62 + 7 * q^63 + 16 * q^64 + 4 * q^65 - 19 * q^66 - 9 * q^67 - 33 * q^68 + 35 * q^69 - 5 * q^70 - 24 * q^71 - 30 * q^72 + 51 * q^73 - 20 * q^74 + 40 * q^75 - 31 * q^76 + q^77 + 22 * q^78 - 26 * q^79 - 23 * q^80 - 2 * q^81 + 78 * q^82 + 3 * q^83 + 17 * q^84 + 18 * q^85 + 55 * q^86 + 49 * q^87 - q^88 - 17 * q^89 + 54 * q^90 - 27 * q^91 + 37 * q^92 + 10 * q^93 + 13 * q^94 + 4 * q^95 - 17 * q^96 + 17 * q^97 + 29 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.263496	+	0.810959i	0.186320	+	0.573434i	0.999969	−	0.00792283i	$-0.00252194\pi$
$2$	0.263496	+	0.810959i	0.186320	+	0.573434i	−0.813649	+	0.581357i	$0.802522\pi$
$3$	−0.862402	−	2.65420i	−0.497908	−	1.53240i	−0.812376	−	0.583134i	$-0.801826\pi$
$3$	−0.862402	−	2.65420i	−0.497908	−	1.53240i	0.314468	−	0.949268i	$-0.398174\pi$
$4$	1.02981	−	0.748201i	0.514905	−	0.374101i
$5$	−0.339968	+	0.247001i	−0.152038	+	0.110462i	−0.661204	−	0.750206i	$-0.729954\pi$
$5$	−0.339968	+	0.247001i	−0.152038	+	0.110462i	0.509165	+	0.860669i	$0.329954\pi$
$6$	1.92521	−	1.39874i	0.785962	−	0.571035i
$7$	−1.05338	+	3.24198i	−0.398142	+	1.22535i	0.528346	+	0.849029i	$0.322813\pi$
$7$	−1.05338	+	3.24198i	−0.398142	+	1.22535i	−0.926488	+	0.376325i	$0.877187\pi$
$8$	2.25780	+	1.64039i	0.798252	+	0.579964i
$9$	−3.87399	+	2.81462i	−1.29133	+	0.938205i
$10$	−0.289888	−	0.210616i	−0.0916707	−	0.0666027i
$11$	−2.79991			−0.844204			−0.422102	−	0.906548i	$-0.638708\pi$
$11$	−2.79991			−0.844204			−0.422102	+	0.906548i	$0.638708\pi$
$12$	−2.87399	−	2.08807i	−0.829648	−	0.602775i
$13$	5.47505			1.51851			0.759253	−	0.650795i	$-0.225564\pi$
$13$	5.47505			1.51851			0.759253	+	0.650795i	$0.225564\pi$
$14$	−2.90668			−0.776842
$15$	0.948780	+	0.689329i	0.244974	+	0.177984i
$16$	0.0513422	−	0.158015i	0.0128355	−	0.0395038i
$17$	−3.09147	+	2.24609i	−0.749793	+	0.544756i	−0.895763	−	0.444533i	$-0.853370\pi$
$17$	−3.09147	+	2.24609i	−0.749793	+	0.544756i	0.145970	+	0.989289i	$0.453370\pi$
$18$	−3.30332	−	2.40000i	−0.778599	−	0.565686i
$19$	−1.75583	−	5.40389i	−0.402815	−	1.23974i	−0.922706	−	0.385504i	$-0.874027\pi$
$19$	−1.75583	−	5.40389i	−0.402815	−	1.23974i	0.519891	−	0.854233i	$-0.325973\pi$
$20$	−0.165296	+	0.508729i	−0.0369613	+	0.113755i
$21$	9.51331			2.07597
$22$	−0.737766	−	2.27061i	−0.157292	−	0.484096i
$23$	−2.46850	+	1.79347i	−0.514718	+	0.373964i	−0.814610	−	0.580009i	$-0.803049\pi$
$23$	−2.46850	+	1.79347i	−0.514718	+	0.373964i	0.299893	+	0.953973i	$0.403049\pi$
$24$	2.40678	−	7.40731i	0.491282	−	1.51201i
$25$	−1.49052	+	4.58734i	−0.298103	+	0.917467i
$26$	1.44266	+	4.44004i	0.282928	+	0.870764i
$27$	4.03809	+	2.93384i	0.777131	+	0.564619i
$28$	1.34087	+	4.12677i	0.253401	+	0.779887i
$29$	−1.66543			−0.309262			−0.154631	−	0.987972i	$-0.549419\pi$
$29$	−1.66543			−0.309262			−0.154631	+	0.987972i	$0.549419\pi$
$30$	−0.309017	+	0.951057i	−0.0564185	+	0.173638i
$31$	1.66567	−	5.12640i	0.299163	−	0.920728i	−0.682629	−	0.730765i	$-0.739163\pi$
$31$	1.66567	−	5.12640i	0.299163	−	0.920728i	0.981791	−	0.189963i	$-0.0608367\pi$
$32$	5.72325			1.01174
$33$	2.41465	+	7.43152i	0.420336	+	1.29366i
$34$	−2.63608	−	1.91522i	−0.452083	−	0.328458i
$35$	−0.442657	−	1.36236i	−0.0748227	−	0.230281i
$36$	−1.88357	+	5.79704i	−0.313929	+	0.966173i
$37$	−0.278406	+	0.856845i	−0.0457696	+	0.140864i	−0.971330	−	0.237736i	$-0.923595\pi$
$37$	−0.278406	+	0.856845i	−0.0457696	+	0.140864i	0.925560	+	0.378601i	$0.123595\pi$
$38$	3.91967	−	2.84781i	0.635855	−	0.461976i
$39$	−4.72170	−	14.5319i	−0.756076	−	2.32696i
$40$	−1.17276			−0.185429
$41$	3.41477	−	10.5096i	0.533297	−	1.64132i	−0.214003	−	0.976833i	$-0.568650\pi$
$41$	3.41477	−	10.5096i	0.533297	−	1.64132i	0.747300	−	0.664487i	$-0.231350\pi$
$42$	2.50672	+	7.71490i	0.386796	+	1.19044i
$43$	−1.80465	−	1.31116i	−0.275207	−	0.199950i	0.441617	−	0.897204i	$-0.354405\pi$
$43$	−1.80465	−	1.31116i	−0.275207	−	0.199950i	−0.716824	+	0.697254i	$0.754405\pi$
$44$	−2.88338	+	2.09490i	−0.434685	+	0.315817i
$45$	0.621818	−	1.91376i	0.0926951	−	0.285286i
$46$	−2.10487	−	1.52928i	−0.310346	−	0.225480i
$47$	−0.616624			−0.0899439			−0.0449719	−	0.998988i	$-0.514320\pi$
$47$	−0.616624			−0.0899439			−0.0449719	+	0.998988i	$0.514320\pi$
$48$	−0.463681			−0.0669266
$49$	−3.73772	−	2.71562i	−0.533961	−	0.387945i
$50$	−4.11289			−0.581650
$51$	8.62766	+	6.26836i	1.20811	+	0.877746i
$52$	5.63827	−	4.09644i	0.781887	−	0.568074i
$53$	−1.81522	−	1.31884i	−0.249340	−	0.181156i	0.456094	−	0.889932i	$-0.349248\pi$
$53$	−1.81522	−	1.31884i	−0.249340	−	0.181156i	−0.705434	+	0.708775i	$0.749248\pi$
$54$	−1.31520	+	4.04778i	−0.178977	+	0.550833i
$55$	0.951880	−	0.691581i	0.128351	−	0.0932528i
$56$	−7.69643	+	5.59178i	−1.02848	+	0.747234i
$57$	−12.8288	+	9.32064i	−1.69921	+	1.23455i
$58$	−0.438834	−	1.35059i	−0.0576217	−	0.177341i
$59$	4.61443	+	14.2018i	0.600748	+	1.84891i	0.523732	+	0.851883i	$0.324539\pi$
$59$	4.61443	+	14.2018i	0.600748	+	1.84891i	0.0770157	+	0.997030i	$0.475461\pi$
$60$	1.49282			0.192722
$61$	−7.73228	−	1.10083i	−0.990017	−	0.140947i
$61$	−7.73228	−	1.10083i	−0.990017	−	0.140947i
$62$	4.59619			0.583717
$63$	−5.04414	−	15.5243i	−0.635502	−	1.95587i
$64$	1.40537	+	4.32529i	0.175671	+	0.540661i
$65$	−1.86134	+	1.35235i	−0.230871	+	0.167738i
$66$	−5.39040	+	3.91635i	−0.663512	+	0.482070i
$67$	3.77676	−	2.74397i	0.461404	−	0.335230i	−0.332678	−	0.943041i	$-0.607952\pi$
$67$	3.77676	−	2.74397i	0.461404	−	0.335230i	0.794082	+	0.607811i	$0.207952\pi$
$68$	−1.50311	+	4.62609i	−0.182279	+	0.560996i
$69$	6.88906	+	5.00520i	0.829346	+	0.602555i
$70$	0.988178	−	0.717953i	0.118110	−	0.0858118i
$71$	−1.07558	−	0.781456i	−0.127648	−	0.0927418i	0.522129	−	0.852866i	$-0.325138\pi$
$71$	−1.07558	−	0.781456i	−0.127648	−	0.0927418i	−0.649777	+	0.760125i	$0.725138\pi$
$72$	−13.3637			−1.57493
$73$	5.96471	+	4.33361i	0.698116	+	0.507211i	0.879318	−	0.476235i	$-0.157999\pi$
$73$	5.96471	+	4.33361i	0.698116	+	0.507211i	−0.181202	+	0.983446i	$0.557999\pi$
$74$	−0.768224			−0.0893043
$75$	13.4611			1.55436
$76$	−5.85137	−	4.25127i	−0.671198	−	0.487654i
$77$	2.94938	−	9.07726i	0.336113	−	1.03445i
$78$	10.5406	−	7.65820i	1.19349	−	0.867120i
$79$	2.18446	+	1.58710i	0.245771	+	0.178563i	0.703851	−	0.710348i	$-0.251462\pi$
$79$	2.18446	+	1.58710i	0.245771	+	0.178563i	−0.458079	+	0.888911i	$0.651462\pi$
$80$	0.0215752	+	0.0664016i	0.00241218	+	0.00742393i
$81$	−0.134641	+	0.414383i	−0.0149601	+	0.0460426i
$82$	9.42261			1.04055
$83$	−3.14899	−	9.69159i	−0.345647	−	1.06379i	−0.961237	−	0.275724i	$-0.911082\pi$
$83$	−3.14899	−	9.69159i	−0.345647	−	1.06379i	0.615590	−	0.788066i	$-0.288918\pi$
$84$	9.79691	−	7.11787i	1.06893	−	0.776623i
$85$	0.496216	−	1.52720i	0.0538222	−	0.165648i
$86$	0.587775	−	1.80899i	0.0633814	−	0.195068i
$87$	1.43627	+	4.42037i	0.153984	+	0.473913i
$88$	−6.32162	−	4.59293i	−0.673887	−	0.489608i
$89$	−3.84087	−	11.8210i	−0.407131	−	1.25302i	−0.919102	−	0.394019i	$-0.871084\pi$
$89$	−3.84087	−	11.8210i	−0.407131	−	1.25302i	0.511971	−	0.859003i	$-0.328916\pi$
$90$	1.71583			0.180864
$91$	−5.76734	+	17.7500i	−0.604581	+	1.86071i
$92$	−1.20021	+	3.69387i	−0.125131	+	0.385112i
$93$	−15.0430			−1.55988
$94$	−0.162478	−	0.500057i	−0.0167584	−	0.0515769i
$95$	1.93169	+	1.40346i	0.198188	+	0.143992i
$96$	−4.93574	−	15.1907i	−0.503752	−	1.55039i
$97$	−3.68827	+	11.3513i	−0.374487	+	1.15255i	0.569338	+	0.822104i	$0.307200\pi$
$97$	−3.68827	+	11.3513i	−0.374487	+	1.15255i	−0.943824	+	0.330448i	$0.892800\pi$
$98$	1.21737	−	3.74669i	0.122973	−	0.378473i
$99$	10.8468	−	7.88067i	1.09014	−	0.792037i
$100$	1.89730	+	5.83929i	0.189730	+	0.583929i
$101$	15.9052			1.58263			0.791313	−	0.611411i	$-0.209398\pi$
$101$	15.9052			1.58263			0.791313	+	0.611411i	$0.209398\pi$
$102$	−2.81002	+	8.64836i	−0.278234	+	0.856315i
$103$	0.854384	+	2.62952i	0.0841849	+	0.259095i	0.984285	−	0.176589i	$-0.0565065\pi$
$103$	0.854384	+	2.62952i	0.0841849	+	0.259095i	−0.900100	+	0.435684i	$0.856507\pi$
$104$	12.3616	+	8.98120i	1.21215	+	0.880679i
$105$	−3.23422	+	2.34980i	−0.315628	+	0.229317i
$106$	0.591218	−	1.81958i	0.0574241	−	0.176733i
$107$	6.51519	+	4.73356i	0.629847	+	0.457611i	0.856347	−	0.516400i	$-0.172728\pi$
$107$	6.51519	+	4.73356i	0.629847	+	0.457611i	−0.226500	+	0.974011i	$0.572728\pi$
$108$	6.35357			0.611373
$109$	7.13460			0.683371			0.341685	−	0.939814i	$-0.389002\pi$
$109$	7.13460			0.683371			0.341685	+	0.939814i	$0.389002\pi$
$110$	0.811660	+	0.589706i	0.0773888	+	0.0562262i
$111$	2.51433			0.238650
$112$	0.458199	+	0.332901i	0.0432957	+	0.0314562i
$113$	4.67007	−	3.39300i	0.439323	−	0.319187i	−0.346043	−	0.938219i	$-0.612475\pi$
$113$	4.67007	−	3.39300i	0.439323	−	0.319187i	0.785366	+	0.619032i	$0.212475\pi$
$114$	−10.9390	−	7.94764i	−1.02453	−	0.744365i
$115$	0.396222	−	1.21944i	0.0369479	−	0.113714i
$116$	−1.71507	+	1.24607i	−0.159241	+	0.115695i
$117$	−21.2103	+	15.4102i	−1.96089	+	1.42467i
$118$	−10.3012	+	7.48423i	−0.948298	+	0.688979i
$119$	−4.02527	−	12.3885i	−0.368996	−	1.13565i
$120$	1.01139	+	3.11273i	0.0923265	+	0.284152i
$121$	−3.16051			−0.287319
$122$	−1.14470	−	6.56062i	−0.103636	−	0.593971i
$123$	−30.8394			−2.78070
$124$	−2.12025	−	6.52547i	−0.190404	−	0.586005i
$125$	−1.27563	−	3.92599i	−0.114096	−	0.351151i
$126$	11.2604	−	8.18118i	1.00316	−	0.728837i
$127$	−1.68098	+	1.22130i	−0.149162	+	0.108373i	−0.659864	−	0.751385i	$-0.729386\pi$
$127$	−1.68098	+	1.22130i	−0.149162	+	0.108373i	0.510701	+	0.859758i	$0.329386\pi$
$128$	6.12310	−	4.44869i	0.541210	−	0.393212i
$129$	−1.92374	+	5.92066i	−0.169376	+	0.521285i
$130$	−1.58715	−	1.15313i	−0.139203	−	0.101137i
$131$	−0.847635	+	0.615843i	−0.0740583	+	0.0538065i	−0.624198	−	0.781266i	$-0.714574\pi$
$131$	−0.847635	+	0.615843i	−0.0740583	+	0.0538065i	0.550140	+	0.835072i	$0.314574\pi$
$132$	8.04690	+	5.84641i	0.700392	+	0.508865i
$133$	19.3689			1.67950
$134$	3.22041	+	2.33977i	0.278201	+	0.202125i
$135$	−2.09748			−0.180523
$136$	−10.6644			−0.914462
$137$	−2.77896	−	2.01903i	−0.237422	−	0.172497i	0.462712	−	0.886509i	$-0.346876\pi$
$137$	−2.77896	−	2.01903i	−0.237422	−	0.172497i	−0.700134	+	0.714011i	$0.746876\pi$
$138$	−2.24376	+	6.90560i	−0.191002	+	0.587843i
$139$	−2.58705	+	1.87960i	−0.219431	+	0.159426i	−0.692070	−	0.721830i	$-0.743301\pi$
$139$	−2.58705	+	1.87960i	−0.219431	+	0.159426i	0.472640	+	0.881256i	$0.343301\pi$
$140$	−1.47517	−	1.07177i	−0.124675	−	0.0905815i
$141$	0.531778	+	1.63664i	0.0447838	+	0.137830i
$142$	0.350316	−	1.07816i	0.0293979	−	0.0904775i
$143$	−15.3297			−1.28193
$144$	0.245853	+	0.756656i	0.0204877	+	0.0630547i
$145$	0.566192	−	0.411362i	0.0470196	−	0.0341618i
$146$	−1.94270	+	5.97902i	−0.160779	+	0.494827i
$147$	−3.98437	+	12.2626i	−0.328625	+	1.01140i
$148$	0.354387	+	1.09069i	0.0291304	+	0.0896543i
$149$	14.7251	+	10.6984i	1.20633	+	0.876451i	0.994892	−	0.100941i	$-0.0321853\pi$
$149$	14.7251	+	10.6984i	1.20633	+	0.876451i	0.211438	+	0.977391i	$0.432185\pi$
$150$	3.54696	+	10.9164i	0.289608	+	0.891322i
$151$	−6.46079			−0.525772			−0.262886	−	0.964827i	$-0.584674\pi$
$151$	−6.46079			−0.525772			−0.262886	+	0.964827i	$0.584674\pi$
$152$	4.90015	−	15.0811i	0.397455	−	1.22324i
$153$	5.65445	−	17.4026i	0.457135	−	1.40692i
$154$	8.13843			0.655814
$155$	0.699953	+	2.15423i	0.0562216	+	0.173032i
$156$	−15.7352	−	11.4323i	−1.25983	−	0.915317i
$157$	−0.0511166	−	0.157321i	−0.00407955	−	0.0125556i	0.948996	−	0.315288i	$-0.102101\pi$
$157$	−0.0511166	−	0.157321i	−0.00407955	−	0.0125556i	−0.953076	+	0.302732i	$0.902101\pi$
$158$	−0.711478	+	2.18970i	−0.0566021	+	0.174203i
$159$	−1.93501	+	5.95534i	−0.153456	+	0.472289i
$160$	−1.94572	+	1.41365i	−0.153823	+	0.111759i
$161$	−3.21412	−	9.89205i	−0.253308	−	0.779603i
$162$	−0.371525			−0.0291898
$163$	−4.31080	+	13.2673i	−0.337648	+	1.03917i	0.627755	+	0.778411i	$0.283974\pi$
$163$	−4.31080	+	13.2673i	−0.337648	+	1.03917i	−0.965403	+	0.260762i	$0.916026\pi$
$164$	−4.34671	−	13.3778i	−0.339421	−	1.04463i
$165$	−2.65650	−	1.93006i	−0.206808	−	0.150255i
$166$	7.02973	−	5.10740i	0.545613	−	0.396411i
$167$	0.367472	−	1.13096i	0.0284358	−	0.0875164i	−0.935831	−	0.352448i	$-0.885349\pi$
$167$	0.367472	−	1.13096i	0.0284358	−	0.0875164i	0.964267	+	0.264932i	$0.0853494\pi$
$168$	21.4791	+	15.6055i	1.65715	+	1.20399i
$169$	16.9762			1.30586
$170$	1.36924			0.105016
$171$	22.0119	+	15.9926i	1.68329	+	1.22298i
$172$	−2.83946			−0.216507
$173$	−15.2107	−	11.0513i	−1.15645	−	0.840211i	−0.167127	−	0.985935i	$-0.553449\pi$
$173$	−15.2107	−	11.0513i	−1.15645	−	0.840211i	−0.989325	+	0.145724i	$0.953449\pi$
$174$	−3.20629	+	2.32950i	−0.243068	+	0.176599i
$175$	−13.3020	−	9.66446i	−1.00554	−	0.730565i
$176$	−0.143753	+	0.442428i	−0.0108358	+	0.0333492i
$177$	33.7148	−	24.4953i	2.53416	−	1.84118i
$178$	8.57427	−	6.22957i	0.642669	−	0.466926i
$179$	3.09816	−	2.25095i	0.231568	−	0.168244i	−0.465951	−	0.884811i	$-0.654288\pi$
$179$	3.09816	−	2.25095i	0.231568	−	0.168244i	0.697518	+	0.716567i	$0.254288\pi$
$180$	−0.791522	−	2.43605i	−0.0589966	−	0.181573i
$181$	−2.87168	−	8.83813i	−0.213450	−	0.656933i	−0.999260	−	0.0384644i	$-0.987753\pi$
$181$	−2.87168	−	8.83813i	−0.213450	−	0.656933i	0.785809	−	0.618469i	$-0.212247\pi$
$182$	−15.9142			−1.17964
$183$	3.74651	+	21.4724i	0.276950	+	1.58728i
$184$	−8.51535			−0.627760
$185$	−0.116993	−	0.360066i	−0.00860147	−	0.0264726i
$186$	−3.96376	−	12.1992i	−0.290637	−	0.894490i
$187$	8.65585	−	6.28884i	0.632978	−	0.459886i
$188$	−0.635006	+	0.461359i	−0.0463126	+	0.0336481i
$189$	−13.7651	+	10.0010i	−1.00127	+	0.727463i
$190$	−0.629151	+	1.93633i	−0.0456434	+	0.140476i
$191$	7.86759	+	5.71614i	0.569279	+	0.413605i	0.834843	−	0.550488i	$-0.185558\pi$
$191$	7.86759	+	5.71614i	0.569279	+	0.413605i	−0.265564	+	0.964093i	$0.585558\pi$
$192$	10.2682	−	7.46027i	0.741042	−	0.538399i
$193$	−4.16615	−	3.02688i	−0.299886	−	0.217880i	0.427659	−	0.903940i	$-0.359339\pi$
$193$	−4.16615	−	3.02688i	−0.299886	−	0.217880i	−0.727544	+	0.686060i	$0.759339\pi$
$194$	−10.1773			−0.730687
$195$	5.19462	+	3.77411i	0.371994	+	0.270270i
$196$	−5.88098			−0.420070
$197$	11.0144			0.784740			0.392370	−	0.919807i	$-0.371655\pi$
$197$	11.0144			0.784740			0.392370	+	0.919807i	$0.371655\pi$
$198$	9.24899	+	6.71978i	0.657297	+	0.477554i
$199$	−2.17191	+	6.68445i	−0.153963	+	0.473848i	−0.998054	−	0.0623508i	$-0.980140\pi$
$199$	−2.17191	+	6.68445i	−0.153963	+	0.473848i	0.844092	+	0.536199i	$0.180140\pi$
$200$	−10.8903	+	7.91225i	−0.770059	+	0.559481i
$201$	−10.5401	−	7.65786i	−0.743444	−	0.540144i
$202$	4.19096	+	12.8985i	0.294875	+	0.907532i
$203$	1.75433	−	5.39928i	0.123130	−	0.378955i
$204$	13.5748			0.950429
$205$	1.43497	+	4.41637i	0.100222	+	0.308453i
$206$	−1.90731	+	1.38574i	−0.132888	+	0.0965490i
$207$	4.51500	−	13.8957i	0.313814	−	0.965821i
$208$	0.281101	−	0.865141i	0.0194909	−	0.0599867i
$209$	4.91616	+	15.1304i	0.340058	+	1.04659i
$210$	−2.75780	−	2.00366i	−0.190306	−	0.138265i
$211$	−4.17044	−	12.8353i	−0.287105	−	0.883619i	−0.985760	−	0.168160i	$-0.946218\pi$
$211$	−4.17044	−	12.8353i	−0.287105	−	0.883619i	0.698655	−	0.715459i	$-0.253782\pi$
$212$	−2.85609			−0.196157
$213$	−1.14656	+	3.52874i	−0.0785607	+	0.241785i
$214$	−2.12199	+	6.53083i	−0.145057	+	0.446438i
$215$	0.937383			0.0639290
$216$	4.30455	+	13.2480i	0.292888	+	0.901415i
$217$	14.8651	+	10.8001i	1.00911	+	0.733161i
$218$	1.87994	+	5.78587i	0.127326	+	0.391868i
$219$	6.35830	−	19.5688i	0.429654	−	1.32234i
$220$	0.462814	−	1.42439i	0.0312029	−	0.0960327i
$221$	−16.9260	+	12.2975i	−1.13857	+	0.827216i
$222$	0.662518	+	2.03902i	0.0444653	+	0.136850i
$223$	−6.18406			−0.414116			−0.207058	−	0.978329i	$-0.566389\pi$
$223$	−6.18406			−0.414116			−0.207058	+	0.978329i	$0.566389\pi$
$224$	−6.02879	+	18.5547i	−0.402815	+	1.23974i
$225$	−7.13735	−	21.9665i	−0.475823	−	1.46443i
$226$	3.98213	+	2.89319i	0.264887	+	0.192452i
$227$	3.28070	−	2.38357i	0.217748	−	0.158203i	−0.473565	−	0.880759i	$-0.657033\pi$
$227$	3.28070	−	2.38357i	0.217748	−	0.158203i	0.691312	+	0.722556i	$0.257033\pi$
$228$	−6.23748	+	19.1970i	−0.413087	+	1.27135i
$229$	−21.4216	−	15.5637i	−1.41558	−	1.02848i	−0.992482	−	0.122391i	$-0.960944\pi$
$229$	−21.4216	−	15.5637i	−1.41558	−	1.02848i	−0.423095	−	0.906085i	$-0.639056\pi$
$230$	1.09332			0.0720915
$231$	−26.6364			−1.75255
$232$	−3.76019	−	2.73194i	−0.246869	−	0.179361i
$233$	−11.8475			−0.776153			−0.388077	−	0.921627i	$-0.626860\pi$
$233$	−11.8475			−0.776153			−0.388077	+	0.921627i	$0.626860\pi$
$234$	−18.0858	−	13.1401i	−1.18231	−	0.858997i
$235$	0.209633	−	0.152307i	0.0136749	−	0.00993541i
$236$	15.3778	+	11.1726i	1.00101	+	0.727275i
$237$	2.32861	−	7.16672i	0.151259	−	0.465528i
$238$	8.98592	−	6.52865i	0.582471	−	0.423190i
$239$	21.7482	−	15.8010i	1.40677	−	1.02208i	0.412990	−	0.910735i	$-0.364484\pi$
$239$	21.7482	−	15.8010i	1.40677	−	1.02208i	0.993782	−	0.111345i	$-0.0355157\pi$
$240$	0.157637	−	0.114530i	0.0101754	−	0.00739286i
$241$	4.25781	+	13.1042i	0.274270	+	0.844115i	0.989412	+	0.145136i	$0.0463620\pi$
$241$	4.25781	+	13.1042i	0.274270	+	0.844115i	−0.715142	+	0.698979i	$0.753638\pi$
$242$	−0.832783	−	2.56304i	−0.0535333	−	0.164759i
$243$	16.1900			1.03859
$244$	−8.78643	+	4.65166i	−0.562493	+	0.297792i
$245$	1.94147			0.124036
$246$	−8.12607	−	25.0095i	−0.518099	−	1.59455i
$247$	−9.61326	−	29.5866i	−0.611677	−	1.88255i
$248$	12.1700	−	8.84203i	0.772796	−	0.561469i
$249$	−23.0077	+	16.7161i	−1.45806	+	1.05934i
$250$	2.84769	−	2.06897i	0.180104	−	0.130853i
$251$	−6.52978	+	20.0966i	−0.412156	+	1.26848i	0.502615	+	0.864511i	$0.332372\pi$
$251$	−6.52978	+	20.0966i	−0.412156	+	1.26848i	−0.914770	+	0.403974i	$0.867628\pi$
$252$	−16.8098	−	12.2130i	−1.05892	−	0.769348i
$253$	6.91157	−	5.02155i	0.434527	−	0.315702i
$254$	−1.43336	−	1.04139i	−0.0899367	−	0.0653428i
$255$	−4.48142			−0.280637
$256$	12.5797	+	9.13972i	0.786234	+	0.571232i
$257$	−11.8528			−0.739359			−0.369680	−	0.929159i	$-0.620533\pi$
$257$	−11.8528			−0.739359			−0.369680	+	0.929159i	$0.620533\pi$
$258$	−5.30831			−0.330481
$259$	−2.48461	−	1.80517i	−0.154386	−	0.112168i
$260$	−0.905005	+	2.78532i	−0.0561260	+	0.172738i
$261$	6.45183	−	4.68753i	0.399358	−	0.290151i
$262$	−0.722772	−	0.525125i	−0.0446530	−	0.0324423i
$263$	8.16021	+	25.1145i	0.503180	+	1.54863i	0.803809	+	0.594887i	$0.202803\pi$
$263$	8.16021	+	25.1145i	0.503180	+	1.54863i	−0.300629	+	0.953741i	$0.597197\pi$
$264$	−6.73877	+	20.7398i	−0.414743	+	1.27645i
$265$	0.942873			0.0579202
$266$	5.10363	+	15.7074i	0.312924	+	0.963080i
$267$	−28.0629	+	20.3889i	−1.71742	+	1.24778i
$268$	1.83630	−	5.65155i	0.112170	−	0.345223i
$269$	−0.861641	+	2.65186i	−0.0525352	+	0.161687i	−0.973882	−	0.227055i	$-0.927090\pi$
$269$	−0.861641	+	2.65186i	−0.0525352	+	0.161687i	0.921347	+	0.388742i	$0.127090\pi$
$270$	−0.552680	−	1.70097i	−0.0336350	−	0.103518i
$271$	13.9365	+	10.1255i	0.846584	+	0.615079i	0.924202	−	0.381904i	$-0.124732\pi$
$271$	13.9365	+	10.1255i	0.846584	+	0.615079i	−0.0776183	+	0.996983i	$0.524732\pi$
$272$	0.196192	+	0.603818i	0.0118959	+	0.0366119i
$273$	52.0859			3.15238
$274$	0.905104	−	2.78562i	0.0546794	−	0.168286i
$275$	4.17331	−	12.8441i	0.251660	−	0.774530i
$276$	10.8393			0.652451
$277$	−7.88308	−	24.2616i	−0.473648	−	1.45774i	−0.847772	−	0.530361i	$-0.822056\pi$
$277$	−7.88308	−	24.2616i	−0.473648	−	1.45774i	0.374124	−	0.927379i	$-0.377944\pi$
$278$	−2.20596	−	1.60272i	−0.132304	−	0.0961248i
$279$	7.97606	+	24.5478i	0.477514	+	1.46964i
$280$	1.23536	−	3.80206i	0.0738271	−	0.227216i
$281$	3.65191	−	11.2394i	0.217855	−	0.670487i	−0.781084	−	0.624426i	$-0.785333\pi$
$281$	3.65191	−	11.2394i	0.217855	−	0.670487i	0.998939	−	0.0460615i	$-0.0146670\pi$
$282$	−1.18713	+	0.862499i	−0.0706925	+	0.0513611i
$283$	3.88223	+	11.9483i	0.230774	+	0.710250i	0.997654	+	0.0684594i	$0.0218083\pi$
$283$	3.88223	+	11.9483i	0.230774	+	0.710250i	−0.766880	+	0.641791i	$0.778192\pi$
$284$	−1.69233			−0.100421
$285$	2.05916	−	6.33744i	0.121974	−	0.375398i
$286$	−4.03931	−	12.4317i	−0.238849	−	0.735103i
$287$	30.4748	+	22.1412i	1.79887	+	1.30696i
$288$	−22.1718	+	16.1088i	−1.30649	+	0.949217i
$289$	−0.740985	+	2.28052i	−0.0435874	+	0.134148i
$290$	0.482787	+	0.350765i	0.0283502	+	0.0205977i
$291$	33.3094			1.95263
$292$	9.38493			0.549212
$293$	−21.0222	−	15.2736i	−1.22813	−	0.892290i	−0.231384	−	0.972863i	$-0.574325\pi$
$293$	−21.0222	−	15.2736i	−1.22813	−	0.892290i	−0.996749	+	0.0805723i	$0.974325\pi$
$294$	−10.9943			−0.641203
$295$	−5.07662	−	3.68838i	−0.295572	−	0.214746i
$296$	−2.03414	+	1.47789i	−0.118232	+	0.0859005i
$297$	−11.3063	−	8.21450i	−0.656057	−	0.476653i
$298$	−4.79597	+	14.7605i	−0.277823	+	0.855052i
$299$	−13.5152	+	9.81934i	−0.781602	+	0.567867i
$300$	13.8624	−	10.0716i	0.800347	−	0.581486i
$301$	6.15175	−	4.46951i	0.354581	−	0.257618i
$302$	−1.70240	−	5.23944i	−0.0979619	−	0.301496i
$303$	−13.7167	−	42.2156i	−0.788002	−	2.42522i
$304$	−0.944043			−0.0541446
$305$	2.90064	−	1.53564i	0.166090	−	0.0879303i
$306$	15.6027			0.891949
$307$	4.51013	+	13.8808i	0.257407	+	0.792217i	0.993346	+	0.115169i	$0.0367410\pi$
$307$	4.51013	+	13.8808i	0.257407	+	0.792217i	−0.735939	+	0.677048i	$0.763259\pi$
$308$	−3.75431	−	11.5546i	−0.213922	−	0.658384i
$309$	6.24245	−	4.53541i	0.355121	−	0.258010i
$310$	−1.56256	+	1.13527i	−0.0887474	+	0.0644788i
$311$	−21.7227	+	15.7824i	−1.23178	+	0.894940i	−0.997022	−	0.0771142i	$-0.975429\pi$
$311$	−21.7227	+	15.7824i	−1.23178	+	0.894940i	−0.234757	+	0.972054i	$0.575429\pi$
$312$	13.1773	−	40.5554i	0.746015	−	2.29600i
$313$	0.891732	+	0.647881i	0.0504037	+	0.0366204i	0.612702	−	0.790314i	$-0.290083\pi$
$313$	0.891732	+	0.647881i	0.0504037	+	0.0366204i	−0.562298	+	0.826935i	$0.690083\pi$
$314$	0.114112	−	0.0829069i	0.00643969	−	0.00467871i
$315$	5.54936	+	4.03185i	0.312671	+	0.227169i
$316$	3.43705			0.193349
$317$	6.90694	+	5.01818i	0.387932	+	0.281849i	0.764608	−	0.644496i	$-0.222933\pi$
$317$	6.90694	+	5.01818i	0.387932	+	0.281849i	−0.376675	+	0.926345i	$0.622933\pi$
$318$	−5.33940			−0.299419
$319$	4.66304			0.261080
$320$	−1.54613	−	1.12333i	−0.0864315	−	0.0627962i
$321$	6.94511	−	21.3748i	0.387638	−	1.19303i
$322$	7.17513	−	5.21304i	0.399854	−	0.290511i
$323$	17.5657	+	12.7622i	0.977382	+	0.710110i
$324$	0.171387	+	0.527475i	0.00952150	+	0.0293042i
$325$	−8.16066	+	25.1159i	−0.452672	+	1.39318i
$326$	−11.8951			−0.658808
$327$	−6.15289	−	18.9367i	−0.340256	−	1.04720i
$328$	24.9496	−	18.1269i	1.37761	−	1.00089i
$329$	0.649542	−	1.99909i	0.0358104	−	0.110213i
$330$	0.865219	−	2.66287i	0.0476288	−	0.146586i
$331$	−2.49005	−	7.66360i	−0.136866	−	0.421229i	0.859010	−	0.511959i	$-0.171080\pi$
$331$	−2.49005	−	7.66360i	−0.136866	−	0.421229i	−0.995876	+	0.0907297i	$0.971080\pi$
$332$	−10.4941	−	7.62443i	−0.575940	−	0.418445i
$333$	−1.33315	−	4.10301i	−0.0730561	−	0.224843i
$334$	1.01399			0.0554831
$335$	−0.606212	+	1.86573i	−0.0331209	+	0.101936i
$336$	0.488434	−	1.50325i	0.0266463	−	0.0820088i
$337$	0.000980689	0		5.34215e−5	0		2.67108e−5	−	1.00000i	$-0.499991\pi$
$337$	0.000980689	0		5.34215e−5	0		2.67108e−5		1.00000i	$0.499991\pi$
$338$	4.47317	+	13.7670i	0.243309	+	0.748827i
$339$	−13.0332	−	9.46916i	−0.707865	−	0.514294i
$340$	−0.631641	−	1.94399i	−0.0342556	−	0.105428i
$341$	−4.66372	+	14.3534i	−0.252554	+	0.777283i
$342$	−7.16927	+	22.0647i	−0.387670	+	1.19312i
$343$	−6.56333	+	4.76854i	−0.354387	+	0.257477i
$344$	−1.92374	−	5.92066i	−0.103721	−	0.319220i
$345$	−3.57835			−0.192652
$346$	4.95413	−	15.2473i	0.266336	−	0.819697i
$347$	3.88085	+	11.9440i	0.208335	+	0.641189i	0.999560	+	0.0296637i	$0.00944362\pi$
$347$	3.88085	+	11.9440i	0.208335	+	0.641189i	−0.791225	+	0.611525i	$0.790556\pi$
$348$	4.78641	+	3.47753i	0.256578	+	0.186415i
$349$	−2.52552	+	1.83490i	−0.135188	+	0.0982200i	−0.653324	−	0.757078i	$-0.726626\pi$
$349$	−2.52552	+	1.83490i	−0.135188	+	0.0982200i	0.518136	+	0.855298i	$0.326626\pi$
$350$	4.33245	−	13.3339i	0.231579	−	0.712728i
$351$	22.1088	+	16.0630i	1.18008	+	0.857377i
$352$	−16.0246			−0.854113
$353$	−20.6386			−1.09848			−0.549241	−	0.835664i	$-0.685083\pi$
$353$	−20.6386			−1.09848			−0.549241	+	0.835664i	$0.685083\pi$
$354$	28.7484	+	20.8869i	1.52796	+	1.11013i
$355$	0.558684			0.0296519
$356$	−12.7998	−	9.29963i	−0.678390	−	0.492879i
$357$	−29.4102	+	21.3677i	−1.55655	+	1.13090i
$358$	2.64178	+	1.91937i	0.139622	+	0.101442i
$359$	4.17457	−	12.8480i	0.220325	−	0.678091i	−0.778407	−	0.627759i	$-0.783972\pi$
$359$	4.17457	−	12.8480i	0.220325	−	0.678091i	0.998733	−	0.0503317i	$-0.0160279\pi$
$360$	4.54324	−	3.30086i	0.239450	−	0.173970i
$361$	−10.7477	+	7.80869i	−0.565670	+	0.410984i
$362$	6.41068	−	4.65763i	0.336938	−	0.244800i
$363$	2.72563	+	8.38863i	0.143058	+	0.440289i
$364$	7.34134	+	22.5943i	0.384791	+	1.18426i
$365$	−3.09822			−0.162168
$366$	−16.4260	+	8.69616i	−0.858601	+	0.454556i
$367$	−24.8273			−1.29597			−0.647987	−	0.761652i	$-0.724389\pi$
$367$	−24.8273			−1.29597			−0.647987	+	0.761652i	$0.724389\pi$
$368$	0.156657	+	0.482141i	0.00816631	+	0.0251333i
$369$	16.3516	+	50.3252i	0.851233	+	2.61982i
$370$	0.261172	−	0.189752i	0.0135777	−	0.00986476i
$371$	6.18778	−	4.49569i	0.321254	−	0.233404i
$372$	−15.4914	+	11.2552i	−0.803191	+	0.583553i
$373$	2.24380	−	6.90572i	0.116180	−	0.357564i	−0.876012	−	0.482290i	$-0.839805\pi$
$373$	2.24380	−	6.90572i	0.116180	−	0.357564i	0.992191	+	0.124726i	$0.0398051\pi$
$374$	7.38077	+	5.36245i	0.381651	+	0.277285i
$375$	−9.32025	+	6.77156i	−0.481296	+	0.349682i
$376$	−1.39221	−	1.01150i	−0.0717979	−	0.0521642i
$377$	−9.11829			−0.469616
$378$	−11.7374	−	8.52774i	−0.603708	−	0.438620i
$379$	−19.1437			−0.983347			−0.491673	−	0.870780i	$-0.663615\pi$
$379$	−19.1437			−0.983347			−0.491673	+	0.870780i	$0.663615\pi$
$380$	3.03935			0.155915
$381$	4.69125	+	3.40839i	0.240340	+	0.174617i
$382$	−2.56247	+	7.88648i	−0.131107	+	0.403507i
$383$	−7.65978	+	5.56516i	−0.391397	+	0.284366i	−0.766028	−	0.642808i	$-0.777769\pi$
$383$	−7.65978	+	5.56516i	−0.391397	+	0.284366i	0.374631	+	0.927174i	$0.377769\pi$
$384$	−17.0883	−	12.4154i	−0.872032	−	0.633569i
$385$	1.23940	+	3.81448i	0.0631657	+	0.194404i
$386$	1.35691	−	4.17614i	0.0690650	−	0.212560i
$387$	10.6816			0.542977
$388$	4.69485	+	14.4493i	0.238345	+	0.733551i
$389$	14.7170	−	10.6925i	0.746183	−	0.542134i	−0.148458	−	0.988919i	$-0.547431\pi$
$389$	14.7170	−	10.6925i	0.746183	−	0.542134i	0.894641	+	0.446785i	$0.147431\pi$
$390$	−1.69188	+	5.20709i	−0.0856719	+	0.263671i
$391$	3.60301	−	11.0889i	0.182212	−	0.560791i
$392$	−3.98437	−	12.2626i	−0.201241	−	0.619356i
$393$	2.36557	+	1.71869i	0.119327	+	0.0866964i
$394$	2.90224	+	8.93219i	0.146213	+	0.449997i
$395$	−1.13466			−0.0570911
$396$	5.27383	−	16.2312i	0.265020	−	0.815648i
$397$	6.37747	−	19.6278i	0.320076	−	0.985093i	−0.653538	−	0.756893i	$-0.726716\pi$
$397$	6.37747	−	19.6278i	0.320076	−	0.985093i	0.973614	−	0.228199i	$-0.0732838\pi$
$398$	−5.99310			−0.300407
$399$	−16.7038	−	51.4089i	−0.836234	−	2.57366i
$400$	0.648342	+	0.471048i	0.0324171	+	0.0235524i
$401$	2.45515	+	7.55618i	0.122604	+	0.377338i	0.993457	−	0.114207i	$-0.0364326\pi$
$401$	2.45515	+	7.55618i	0.122604	+	0.377338i	−0.870853	+	0.491544i	$0.836433\pi$
$402$	3.43292	−	10.5654i	0.171218	−	0.526956i
$403$	9.11962	−	28.0673i	0.454281	−	1.39813i
$404$	16.3793	−	11.9003i	0.814903	−	0.592062i
$405$	−0.0565794	−	0.174134i	−0.00281145	−	0.00865277i
$406$	4.84086			0.240248
$407$	0.779511	−	2.39909i	0.0386389	−	0.118918i
$408$	9.19697	+	28.3054i	0.455318	+	1.40132i
$409$	−13.9203	−	10.1137i	−0.688313	−	0.500089i	0.187792	−	0.982209i	$-0.439867\pi$
$409$	−13.9203	−	10.1137i	−0.688313	−	0.500089i	−0.876105	+	0.482120i	$0.839867\pi$
$410$	−3.20339	+	2.32740i	−0.158204	+	0.114942i
$411$	−2.96233	+	9.11712i	−0.146121	+	0.449714i
$412$	2.84727	+	2.06866i	0.140275	+	0.101916i
$413$	−50.9027			−2.50476
$414$	12.4586			0.612305
$415$	3.46439	+	2.51703i	0.170060	+	0.123556i
$416$	31.3351			1.53633
$417$	7.21991	+	5.24557i	0.353561	+	0.256877i
$418$	−10.9747	+	7.97361i	−0.536792	+	0.390002i
$419$	−20.5814	−	14.9532i	−1.00547	−	0.730514i	−0.0422127	−	0.999109i	$-0.513441\pi$
$419$	−20.5814	−	14.9532i	−1.00547	−	0.730514i	−0.963253	+	0.268595i	$0.913441\pi$
$420$	−1.57251	+	4.83970i	−0.0767308	+	0.236153i
$421$	−9.59294	+	6.96968i	−0.467531	+	0.339681i	−0.796478	−	0.604667i	$-0.793306\pi$
$421$	−9.59294	+	6.96968i	−0.467531	+	0.339681i	0.328947	+	0.944348i	$0.393306\pi$
$422$	9.31001	−	6.76411i	0.453204	−	0.329272i
$423$	2.38879	−	1.73556i	0.116147	−	0.0843858i
$424$	−1.93501	−	5.95534i	−0.0939722	−	0.289217i
$425$	−5.69567	−	17.5295i	−0.276281	−	0.850304i
$426$	−3.16377			−0.153285
$427$	11.7139	−	23.9083i	0.566877	−	1.15701i
$428$	10.2511			0.495504
$429$	13.2203	+	40.6880i	0.638283	+	1.96443i
$430$	0.246997	+	0.760179i	0.0119113	+	0.0366591i
$431$	−4.67058	+	3.39337i	−0.224974	+	0.163453i	−0.694563	−	0.719432i	$-0.744402\pi$
$431$	−4.67058	+	3.39337i	−0.224974	+	0.163453i	0.469589	+	0.882885i	$0.344402\pi$
$432$	0.670916	−	0.487449i	0.0322794	−	0.0234524i
$433$	17.8027	−	12.9344i	0.855543	−	0.621589i	−0.0711256	−	0.997467i	$-0.522659\pi$
$433$	17.8027	−	12.9344i	0.855543	−	0.621589i	0.926669	+	0.375879i	$0.122659\pi$
$434$	−4.84156	+	14.9008i	−0.232402	+	0.715261i
$435$	−1.58012	−	1.14803i	−0.0757610	−	0.0550436i
$436$	7.34729	−	5.33812i	0.351871	−	0.255649i
$437$	14.0260	+	10.1905i	0.670953	+	0.487476i
$438$	17.5449			0.838328
$439$	23.9382	+	17.3921i	1.14251	+	0.830080i	0.987467	−	0.157829i	$-0.0504493\pi$
$439$	23.9382	+	17.3921i	1.14251	+	0.830080i	0.155040	+	0.987908i	$0.450449\pi$
$440$	3.28361			0.156540
$441$	22.1233			1.05349
$442$	−14.4327	−	10.4859i	−0.686492	−	0.498765i
$443$	−7.39236	+	22.7514i	−0.351222	+	1.08095i	0.606946	+	0.794743i	$0.292394\pi$
$443$	−7.39236	+	22.7514i	−0.351222	+	1.08095i	−0.958168	+	0.286207i	$0.907606\pi$
$444$	2.58929	−	1.88123i	0.122882	−	0.0892791i
$445$	4.22557	+	3.07006i	0.200311	+	0.145535i
$446$	−1.62948	−	5.01502i	−0.0771580	−	0.237468i
$447$	15.6968	−	48.3098i	0.742434	−	2.28498i
$448$	−15.5029			−0.732444
$449$	0.163674	+	0.503736i	0.00772424	+	0.0237728i	0.954844	−	0.297106i	$-0.0960216\pi$
$449$	0.163674	+	0.503736i	0.00772424	+	0.0237728i	−0.947120	+	0.320879i	$0.896022\pi$
$450$	15.9333	−	11.5762i	0.751101	−	0.545707i
$451$	−9.56104	+	29.4258i	−0.450212	+	1.38561i
$452$	2.27064	−	6.98830i	0.106802	−	0.328702i
$453$	5.57180	+	17.1482i	0.261786	+	0.805694i
$454$	2.79743	+	2.03245i	0.131290	+	0.0953876i
$455$	−2.42357	−	7.45899i	−0.113619	−	0.349683i
$456$	−44.2542			−2.07239
$457$	−4.09305	+	12.5971i	−0.191465	+	0.589268i	0.808535	+	0.588448i	$0.200261\pi$
$457$	−4.09305	+	12.5971i	−0.191465	+	0.589268i	−1.00000		0.000819653i	$0.999739\pi$
$458$	6.97699	−	21.4730i	0.326013	−	1.00337i
$459$	−19.0733			−0.890266
$460$	−0.504357	−	1.55225i	−0.0235158	−	0.0723741i
$461$	7.57740	+	5.50531i	0.352915	+	0.256408i	0.750091	−	0.661335i	$-0.230010\pi$
$461$	7.57740	+	5.50531i	0.352915	+	0.256408i	−0.397176	+	0.917742i	$0.630010\pi$
$462$	−7.01860	−	21.6010i	−0.326535	−	1.00497i
$463$	2.97643	−	9.16052i	0.138327	−	0.425725i	−0.857766	−	0.514040i	$-0.828148\pi$
$463$	2.97643	−	9.16052i	0.138327	−	0.425725i	0.996093	+	0.0883148i	$0.0281482\pi$
$464$	−0.0855066	+	0.263162i	−0.00396954	+	0.0122170i
$465$	5.11412	−	3.71563i	0.237162	−	0.172308i
$466$	−3.12176	−	9.60780i	−0.144613	−	0.445073i
$467$	17.0209			0.787633			0.393817	−	0.919189i	$-0.371155\pi$
$467$	17.0209			0.787633			0.393817	+	0.919189i	$0.371155\pi$
$468$	−10.3127	+	31.7391i	−0.476703	+	1.46714i
$469$	4.91755	+	15.1346i	0.227071	+	0.698853i
$470$	0.178752	+	0.129871i	0.00824522	+	0.00599050i
$471$	−0.373477	+	0.271347i	−0.0172089	+	0.0125030i
$472$	−12.8779	+	39.6342i	−0.592754	+	1.82431i
$473$	5.05287	+	3.67112i	0.232331	+	0.168798i
$474$	6.42549			0.295133
$475$	27.4065			1.25750
$476$	−13.4144	−	9.74610i	−0.614846	−	0.446712i
$477$	10.7442			0.491942
$478$	18.5445	+	13.4734i	0.848206	+	0.616257i
$479$	26.9710	−	19.5956i	1.23234	−	0.895346i	0.235275	−	0.971929i	$-0.424401\pi$
$479$	26.9710	−	19.5956i	1.23234	−	0.895346i	0.997063	+	0.0765826i	$0.0244009\pi$
$480$	5.43010	+	3.94520i	0.247849	+	0.180073i
$481$	−1.52429	+	4.69127i	−0.0695015	+	0.213904i
$482$	−9.50504	+	6.90581i	−0.432943	+	0.314551i
$483$	−23.4836	+	17.0618i	−1.06854	+	0.776340i
$484$	−3.25473	+	2.36470i	−0.147942	+	0.107486i
$485$	−1.54990	−	4.77009i	−0.0703772	−	0.216599i
$486$	4.26601	+	13.1294i	0.193510	+	0.595564i
$487$	5.23231			0.237099			0.118549	−	0.992948i	$-0.462176\pi$
$487$	5.23231			0.237099			0.118549	+	0.992948i	$0.462176\pi$
$488$	−15.6521	−	15.1694i	−0.708539	−	0.686685i
$489$	38.9316			1.76055
$490$	0.511570	+	1.57445i	0.0231104	+	0.0711264i
$491$	−4.73034	−	14.5585i	−0.213477	−	0.657015i	−0.999258	−	0.0385106i	$-0.987739\pi$
$491$	−4.73034	−	14.5585i	−0.213477	−	0.657015i	0.785781	−	0.618505i	$-0.212261\pi$
$492$	−31.7587	+	23.0741i	−1.43179	+	1.04026i
$493$	5.14862	−	3.74069i	0.231882	−	0.168472i
$494$	21.4604	−	15.5919i	0.965550	−	0.701513i
$495$	−1.74103	+	5.35835i	−0.0782536	+	0.240840i
$496$	−0.724529	−	0.526401i	−0.0325323	−	0.0236361i
$497$	3.66647	−	2.66385i	0.164464	−	0.119490i
$498$	−19.6185	−	14.2537i	−0.879126	−	0.638723i
$499$	8.39563			0.375840			0.187920	−	0.982184i	$-0.439825\pi$
$499$	8.39563			0.375840			0.187920	+	0.982184i	$0.439825\pi$
$500$	−4.25109	−	3.08860i	−0.190115	−	0.138126i
$501$	−3.31870			−0.148269
$502$	−18.0181			−0.804186
$503$	0.775593	+	0.563502i	0.0345820	+	0.0251253i	0.604942	−	0.796270i	$-0.293196\pi$
$503$	0.775593	+	0.563502i	0.0345820	+	0.0251253i	−0.570360	+	0.821395i	$0.693196\pi$
$504$	14.0771	−	43.3250i	0.627046	−	1.92985i
$505$	−5.40726	+	3.92861i	−0.240620	+	0.174821i
$506$	5.89344	+	4.28184i	0.261996	+	0.190351i
$507$	−14.6403	−	45.0583i	−0.650199	−	2.00111i
$508$	−0.817308	+	2.51542i	−0.0362622	+	0.111604i
$509$	1.62117			0.0718571			0.0359286	−	0.999354i	$-0.488561\pi$
$509$	1.62117			0.0718571			0.0359286	+	0.999354i	$0.488561\pi$
$510$	−1.18084	−	3.63425i	−0.0522884	−	0.160927i
$511$	−20.3326	+	14.7725i	−0.899463	+	0.653498i
$512$	0.580415	−	1.78633i	0.0256510	−	0.0789455i
$513$	8.76397	−	26.9727i	0.386939	−	1.19087i
$514$	−3.12318	−	9.61215i	−0.137757	−	0.423974i
$515$	−0.939959	−	0.682920i	−0.0414195	−	0.0300930i
$516$	2.44876	+	7.53650i	0.107801	+	0.331776i
$517$	1.72649			0.0759310
$518$	0.809236	−	2.49057i	0.0355558	−	0.109429i
$519$	−16.2145	+	49.9030i	−0.711736	+	2.19050i
$520$	−6.42090			−0.281575
$521$	6.04916	+	18.6174i	0.265019	+	0.815643i	0.991689	+	0.128657i	$0.0410667\pi$
$521$	6.04916	+	18.6174i	0.265019	+	0.815643i	−0.726671	+	0.686986i	$0.758933\pi$
$522$	5.50143	+	3.99702i	0.240791	+	0.174945i
$523$	−11.9768	−	36.8608i	−0.523709	−	1.61181i	−0.766855	−	0.641820i	$-0.778180\pi$
$523$	−11.9768	−	36.8608i	−0.523709	−	1.61181i	0.243147	−	0.969989i	$-0.421820\pi$
$524$	−0.412129	+	1.26840i	−0.0180040	+	0.0554105i
$525$	−14.1797	+	43.6408i	−0.618855	+	1.90464i
$526$	−18.2167	+	13.2352i	−0.794284	+	0.577081i
$527$	6.36497	+	19.5894i	0.277262	+	0.853326i
$528$	1.29826			0.0564997
$529$	−4.23044	+	13.0199i	−0.183932	+	0.566085i
$530$	0.248444	+	0.764631i	0.0107917	+	0.0332134i
$531$	−57.8488	−	42.0296i	−2.51042	−	1.82393i
$532$	19.9463	−	14.4918i	0.864781	−	0.628300i
$533$	18.6960	−	57.5405i	0.809815	−	2.49236i
$534$	−23.9290	−	17.3854i	−1.03551	−	0.752341i
$535$	−3.38415			−0.146310
$536$	13.0283			0.562738
$537$	−8.64632	−	6.28192i	−0.373116	−	0.271085i
$538$	−2.37759			−0.102505
$539$	10.4653	+	7.60348i	0.450772	+	0.327505i
$540$	−2.16001	+	1.56934i	−0.0929521	+	0.0675337i
$541$	25.4005	+	18.4546i	1.09205	+	0.793424i	0.979745	−	0.200249i	$-0.0641751\pi$
$541$	25.4005	+	18.4546i	1.09205	+	0.793424i	0.112310	+	0.993673i	$0.464175\pi$
$542$	−4.53912	+	13.9700i	−0.194972	+	0.600062i
$543$	−20.9816	+	15.2440i	−0.900407	+	0.654184i
$544$	−17.6933	+	12.8549i	−0.758593	+	0.551150i
$545$	−2.42554	+	1.76226i	−0.103899	+	0.0754867i
$546$	13.7244	+	42.2395i	0.587352	+	1.80768i
$547$	10.8166	+	33.2901i	0.462485	+	1.42338i	0.862118	+	0.506708i	$0.169138\pi$
$547$	10.8166	+	33.2901i	0.462485	+	1.42338i	−0.399633	+	0.916675i	$0.630862\pi$
$548$	−4.37244			−0.186781
$549$	33.0532	−	17.4988i	1.41067	−	0.746831i
$550$	11.5157			0.491031
$551$	2.92420	+	8.99977i	0.124575	+	0.383403i
$552$	7.34365	+	22.6014i	0.312567	+	0.961981i
$553$	−7.44644	+	5.41016i	−0.316655	+	0.230063i
$554$	17.5980	−	12.7857i	0.747668	−	0.543212i
$555$	−0.854793	+	0.621044i	−0.0362840	+	0.0263618i
$556$	−1.25785	+	3.87127i	−0.0533447	+	0.164178i
$557$	7.67983	+	5.57972i	0.325405	+	0.236420i	0.738478	−	0.674277i	$-0.235545\pi$
$557$	7.67983	+	5.57972i	0.325405	+	0.236420i	−0.413073	+	0.910698i	$0.635545\pi$
$558$	−17.8056	+	12.9365i	−0.753771	+	0.547646i
$559$	−9.88058	−	7.17866i	−0.417904	−	0.303625i
$560$	−0.238000			−0.0100573
$561$	−24.1566	−	17.5508i	−1.01989	−	0.740997i
$562$	10.0770			0.425071
$563$	−34.2346			−1.44282			−0.721408	−	0.692511i	$-0.756505\pi$
$563$	−34.2346			−1.44282			−0.721408	+	0.692511i	$0.756505\pi$
$564$	1.77217	+	1.28756i	0.0746218	+	0.0542159i
$565$	−0.749598	+	2.30703i	−0.0315358	+	0.0970573i
$566$	−8.66659	+	6.29665i	−0.364284	+	0.264668i
$567$	−1.20159	−	0.873009i	−0.0504622	−	0.0366629i
$568$	−1.14656	−	3.52874i	−0.0481084	−	0.148063i
$569$	−11.2715	+	34.6901i	−0.472526	+	1.45428i	0.376740	+	0.926319i	$0.377045\pi$
$569$	−11.2715	+	34.6901i	−0.472526	+	1.45428i	−0.849266	+	0.527965i	$0.822955\pi$
$570$	5.68198			0.237992
$571$	−13.9010	−	42.7830i	−0.581741	−	1.79041i	−0.611982	−	0.790871i	$-0.709628\pi$
$571$	−13.9010	−	42.7830i	−0.581741	−	1.79041i	0.0302415	−	0.999543i	$-0.490372\pi$
$572$	−15.7866	+	11.4697i	−0.660073	+	0.479571i
$573$	8.38675	−	25.8118i	0.350362	−	1.07830i
$574$	−9.92563	+	30.5479i	−0.414288	+	1.27505i
$575$	−4.54791	−	13.9970i	−0.189661	−	0.583717i
$576$	−17.6184	−	12.8005i	−0.734101	−	0.533355i
$577$	−11.6367	−	35.8141i	−0.484442	−	1.49096i	−0.832787	−	0.553593i	$-0.813256\pi$
$577$	−11.6367	−	35.8141i	−0.484442	−	1.49096i	0.348345	−	0.937366i	$-0.386744\pi$
$578$	−2.04465			−0.0850463
$579$	−4.44106	+	13.6682i	−0.184564	+	0.568030i
$580$	0.275288	−	0.847250i	0.0114307	−	0.0351802i
$581$	34.7371			1.44114
$582$	8.77691	+	27.0126i	0.363815	+	1.11971i
$583$	5.08246	+	3.69263i	0.210494	+	0.152933i
$584$	6.35830	+	19.5688i	0.263108	+	0.809764i
$585$	3.40449	−	10.4779i	0.140758	−	0.433209i
$586$	6.84693	−	21.0727i	0.282844	−	0.870505i
$587$	24.2977	−	17.6533i	1.00287	−	0.728630i	0.0401710	−	0.999193i	$-0.487210\pi$
$587$	24.2977	−	17.6533i	1.00287	−	0.728630i	0.962702	+	0.270563i	$0.0872097\pi$
$588$	5.07176	+	15.6093i	0.209156	+	0.643716i
$589$	−30.6271			−1.26197
$590$	1.65345	−	5.08880i	0.0680715	−	0.209503i
$591$	−9.49880	−	29.2343i	−0.390728	−	1.20254i
$592$	0.121100	+	0.0879846i	0.00497719	+	0.00361614i
$593$	4.86953	−	3.53792i	0.199968	−	0.145285i	−0.483295	−	0.875457i	$-0.660560\pi$
$593$	4.86953	−	3.53792i	0.199968	−	0.145285i	0.683263	+	0.730172i	$0.260560\pi$
$594$	3.68245	−	11.3334i	0.151093	−	0.465016i
$595$	4.42844	+	3.21745i	0.181548	+	0.131903i
$596$	23.1687			0.949027
$597$	19.6149			0.802785
$598$	−11.5243	−	8.37288i	−0.471263	−	0.342392i
$599$	20.3589			0.831842			0.415921	−	0.909401i	$-0.363459\pi$
$599$	20.3589			0.831842			0.415921	+	0.909401i	$0.363459\pi$
$600$	30.3925	+	22.0814i	1.24077	+	0.901471i
$601$	6.94878	−	5.04858i	0.283447	−	0.205936i	−0.436973	−	0.899475i	$-0.643949\pi$
$601$	6.94878	−	5.04858i	0.283447	−	0.205936i	0.720419	+	0.693539i	$0.243949\pi$
$602$	5.24555	+	3.81111i	0.213793	+	0.155329i
$603$	−6.90787	+	21.2602i	−0.281310	+	0.865784i
$604$	−6.65339	+	4.83397i	−0.270723	+	0.196692i
$605$	1.07447	−	0.780650i	0.0436835	−	0.0317379i
$606$	30.6208	−	22.2473i	1.24388	−	0.903735i
$607$	3.87056	+	11.9124i	0.157101	+	0.483507i	0.998368	−	0.0571130i	$-0.0181895\pi$
$607$	3.87056	+	11.9124i	0.157101	+	0.483507i	−0.841267	+	0.540620i	$0.818190\pi$
$608$	−10.0491	−	30.9278i	−0.407543	−	1.25429i
$609$	−15.8437			−0.642020
$610$	2.00964	+	1.94766i	0.0813681	+	0.0788584i
$611$	−3.37605			−0.136580
$612$	−7.19764	−	22.1521i	−0.290948	−	0.895444i
$613$	10.4001	+	32.0083i	0.420057	+	1.29280i	0.907649	+	0.419730i	$0.137875\pi$
$613$	10.4001	+	32.0083i	0.420057	+	1.29280i	−0.487592	+	0.873071i	$0.662125\pi$
$614$	−10.0683	+	7.31506i	−0.406324	+	0.295212i
$615$	10.4844	−	7.61737i	0.422772	−	0.307162i
$616$	21.5493	−	15.6565i	0.868246	−	0.630818i
$617$	−7.47306	+	22.9997i	−0.300854	+	0.925934i	0.680338	+	0.732899i	$0.261833\pi$
$617$	−7.47306	+	22.9997i	−0.300854	+	0.925934i	−0.981192	+	0.193035i	$0.938167\pi$
$618$	5.32289	+	3.86731i	0.214118	+	0.155566i
$619$	24.9595	−	18.1341i	1.00321	−	0.728872i	0.0404329	−	0.999182i	$-0.487126\pi$
$619$	24.9595	−	18.1341i	1.00321	−	0.728872i	0.962773	+	0.270310i	$0.0871263\pi$
$620$	2.33262	+	1.69475i	0.0936802	+	0.0680627i
$621$	−15.2298			−0.611150
$622$	−18.5227	−	13.4576i	−0.742694	−	0.539599i
$623$	42.3694			1.69749
$624$	−2.53868			−0.101628
$625$	−18.1077	−	13.1560i	−0.724309	−	0.526241i
$626$	−0.290437	+	0.893872i	−0.0116082	+	0.0357263i
$627$	35.9194	−	26.0969i	1.43448	−	1.04221i
$628$	−0.170348	−	0.123765i	−0.00679762	−	0.00493876i
$629$	−1.06386	−	3.27424i	−0.0424190	−	0.130552i
$630$	−1.80742	+	5.56268i	−0.0720095	+	0.221622i
$631$	−7.90779			−0.314804			−0.157402	−	0.987535i	$-0.550312\pi$
$631$	−7.90779			−0.314804			−0.157402	+	0.987535i	$0.550312\pi$
$632$	2.32861	+	7.16672i	0.0926270	+	0.285077i
$633$	−30.4709	+	22.1384i	−1.21111	+	0.879922i
$634$	−2.24959	+	6.92351i	−0.0893425	+	0.274968i
$635$	0.269815	−	0.830406i	0.0107073	−	0.0329537i
$636$	2.46310	+	7.58064i	0.0976683	+	0.300592i
$637$	−20.4642	−	14.8681i	−0.810823	−	0.589097i
$638$	1.22869	+	3.78153i	0.0486445	+	0.149712i
$639$	6.36629			0.251846
$640$	−0.982825	+	3.02483i	−0.0388496	+	0.119567i
$641$	−6.86951	+	21.1422i	−0.271329	+	0.835066i	0.718838	+	0.695178i	$0.244674\pi$
$641$	−6.86951	+	21.1422i	−0.271329	+	0.835066i	−0.990167	+	0.139888i	$0.955326\pi$
$642$	19.1641			0.756348
$643$	10.5416	+	32.4437i	0.415720	+	1.27945i	0.911606	+	0.411066i	$0.134843\pi$
$643$	10.5416	+	32.4437i	0.415720	+	1.27945i	−0.495886	+	0.868388i	$0.665157\pi$
$644$	−10.7112	−	7.78213i	−0.422080	−	0.306659i
$645$	−0.808400	−	2.48800i	−0.0318307	−	0.0979649i
$646$	−5.72114	+	17.6079i	−0.225095	+	0.692772i
$647$	−1.31128	+	4.03569i	−0.0515516	+	0.158660i	−0.973518	−	0.228610i	$-0.926582\pi$
$647$	−1.31128	+	4.03569i	−0.0515516	+	0.158660i	0.921966	+	0.387270i	$0.126582\pi$
$648$	−0.983740	+	0.714729i	−0.0386450	+	0.0280772i
$649$	−12.9200	−	39.7637i	−0.507154	−	1.56086i
$650$	−22.5183			−0.883239
$651$	15.8460	−	48.7690i	0.621054	−	1.91141i
$652$	5.48728	+	16.8881i	0.214899	+	0.661390i
$653$	−32.0533	−	23.2881i	−1.25434	−	0.911334i	−0.255877	−	0.966709i	$-0.582364\pi$
$653$	−32.0533	−	23.2881i	−1.25434	−	0.911334i	−0.998466	+	0.0553756i	$0.982364\pi$
$654$	13.7356	−	9.97948i	0.537103	−	0.390228i
$655$	0.136055	−	0.418734i	0.00531611	−	0.0163613i
$656$	−1.48535	−	1.07917i	−0.0579931	−	0.0421345i
$657$	−35.3046			−1.37737
$658$	1.79233			0.0698722
$659$	−18.0523	−	13.1158i	−0.703218	−	0.510918i	0.177761	−	0.984074i	$-0.443115\pi$
$659$	−18.0523	−	13.1158i	−0.703218	−	0.510918i	−0.880979	+	0.473156i	$0.843115\pi$
$660$	−4.17976			−0.162697
$661$	33.2774	+	24.1774i	1.29434	+	0.940393i	0.999883	−	0.0152723i	$-0.00486152\pi$
$661$	33.2774	+	24.1774i	1.29434	+	0.940393i	0.294456	+	0.955665i	$0.404862\pi$
$662$	5.55874	−	4.03866i	0.216047	−	0.156967i
$663$	47.2369	+	34.3196i	1.83453	+	1.33286i
$664$	8.78817	−	27.0472i	0.341047	−	1.04964i
$665$	−6.58480	+	4.78414i	−0.255348	+	0.185521i
$666$	2.97609	−	2.16226i	0.115321	−	0.0837857i
$667$	4.11110	−	2.98689i	0.159182	−	0.115653i
$668$	−0.467760	−	1.43962i	−0.0180982	−	0.0557005i
$669$	5.33315	+	16.4137i	0.206191	+	0.634592i
$670$	−1.67276			−0.0646245
$671$	21.6497	+	3.08222i	0.835777	+	0.118988i
$672$	54.4471			2.10034
$673$	14.4094	+	44.3476i	0.555442	+	1.70947i	0.694774	+	0.719228i	$0.255505\pi$
$673$	14.4094	+	44.3476i	0.555442	+	1.70947i	−0.139332	+	0.990246i	$0.544495\pi$
$674$	0.000258408	0	0.000795298i	9.95351e−6	0	3.06337e-5i
$675$	−19.4774	+	14.1511i	−0.749684	+	0.544678i
$676$	17.4823	−	12.7016i	0.672396	−	0.488524i
$677$	6.07691	−	4.41513i	0.233555	−	0.169687i	−0.464852	−	0.885388i	$-0.653893\pi$
$677$	6.07691	−	4.41513i	0.233555	−	0.169687i	0.698407	+	0.715701i	$0.253893\pi$
$678$	4.24490	−	13.0645i	0.163024	−	0.501738i
$679$	−32.9156	−	23.9146i	−1.26319	−	0.917758i
$680$	3.62555	−	2.63411i	0.139033	−	0.101014i
$681$	−9.15574	−	6.65204i	−0.350849	−	0.254907i
$682$	−12.8689			−0.492776
$683$	−22.1283	−	16.0771i	−0.846716	−	0.615175i	0.0775228	−	0.996991i	$-0.475299\pi$
$683$	−22.1283	−	16.0771i	−0.846716	−	0.615175i	−0.924239	+	0.381816i	$0.875299\pi$
$684$	34.6338			1.32426
$685$	1.44346			0.0551517
$686$	−5.59650	−	4.06610i	−0.213675	−	0.155244i
$687$	−22.8351	+	70.2792i	−0.871214	+	2.68132i
$688$	−0.299838	+	0.217845i	−0.0114312	+	0.00830525i
$689$	−9.93845	−	7.22071i	−0.378625	−	0.275087i
$690$	−0.942883	−	2.90189i	−0.0358949	−	0.110473i
$691$	14.8936	−	45.8378i	0.566579	−	1.74375i	−0.0966346	−	0.995320i	$-0.530808\pi$
$691$	14.8936	−	45.8378i	0.566579	−	1.74375i	0.663213	−	0.748430i	$-0.269192\pi$
$692$	−23.9328			−0.909787
$693$	14.1231	+	43.4665i	0.536494	+	1.65116i
$694$	−8.66352	+	6.29441i	−0.328863	+	0.238933i
$695$	0.415250	−	1.27801i	0.0157513	−	0.0484776i
$696$	−4.00832	+	12.3363i	−0.151935	+	0.467607i
$697$	13.0488	+	40.1599i	0.494257	+	1.52117i
$698$	−2.15349	−	1.56461i	−0.0815110	−	0.0592212i
$699$	10.2173	+	31.4455i	0.386453	+	1.18938i
$700$	−20.9295			−0.791060
$701$	7.09531	−	21.8371i	0.267986	−	0.824777i	−0.723004	−	0.690844i	$-0.757239\pi$
$701$	7.09531	−	21.8371i	0.267986	−	0.824777i	0.990990	−	0.133933i	$-0.0427608\pi$
$702$	−7.20081	+	22.1618i	−0.271777	+	0.836444i
$703$	5.11913			0.193071
$704$	−3.93491	−	12.1104i	−0.148303	−	0.456429i
$705$	−0.585041	−	0.425057i	−0.0220339	−	0.0160086i
$706$	−5.43820	−	16.7371i	−0.204669	−	0.629907i
$707$	−16.7543	+	51.5644i	−0.630110	+	1.93928i
$708$	16.3925	−	50.4509i	0.616068	−	1.89606i
$709$	31.7100	−	23.0387i	1.19089	−	0.865235i	0.197536	−	0.980296i	$-0.436706\pi$
$709$	31.7100	−	23.0387i	1.19089	−	0.865235i	0.993359	+	0.115060i	$0.0367061\pi$
$710$	0.147211	+	0.453070i	0.00552474	+	0.0170034i
$711$	−12.9297			−0.484900
$712$	10.7191	−	32.9899i	0.401714	−	1.23635i
$713$	5.08234	+	15.6418i	0.190335	+	0.585791i
$714$	−25.0778	−	18.2201i	−0.938514	−	0.681870i
$715$	5.21159	−	3.78644i	0.194903	−	0.141605i
$716$	1.50636	−	4.63610i	0.0562953	−	0.173259i
$717$	−60.6946	−	44.0972i	−2.26668	−	1.64684i
$718$	11.5192			0.429892
$719$	−24.2070			−0.902770			−0.451385	−	0.892329i	$-0.649070\pi$
$719$	−24.2070			−0.902770			−0.451385	+	0.892329i	$0.649070\pi$
$720$	−0.270477	−	0.196513i	−0.0100801	−	0.00732361i
$721$	−9.42487			−0.351000
$722$	−9.16451	−	6.65841i	−0.341068	−	0.247800i
$723$	31.1092	−	22.6021i	1.15696	−	0.840583i
$724$	−9.56999	−	6.95300i	−0.355666	−	0.258406i
$725$	2.48234	−	7.63987i	0.0921919	−	0.283738i
$726$	−6.08463	+	4.42075i	−0.225822	+	0.164069i
$727$	13.5431	−	9.83963i	0.502285	−	0.364932i	−0.307604	−	0.951514i	$-0.599527\pi$
$727$	13.5431	−	9.83963i	0.502285	−	0.364932i	0.809889	+	0.586583i	$0.199527\pi$
$728$	−42.1384	+	30.6153i	−1.56175	+	1.13468i
$729$	−13.5584	−	41.7284i	−0.502162	−	1.54550i
$730$	−0.816369	−	2.51253i	−0.0302152	−	0.0929928i
$731$	8.52402			0.315272
$732$	19.9239	+	19.3093i	0.736407	+	0.713693i
$733$	−5.57781			−0.206021			−0.103011	−	0.994680i	$-0.532848\pi$
$733$	−5.57781			−0.206021			−0.103011	+	0.994680i	$0.532848\pi$
$734$	−6.54190	−	20.1339i	−0.241466	−	0.743156i
$735$	−1.67432	−	5.15304i	−0.0617584	−	0.190073i
$736$	−14.1278	+	10.2645i	−0.520759	+	0.378354i
$737$	−10.5746	+	7.68288i	−0.389520	+	0.283002i
$738$	−36.5030	+	26.5210i	−1.34370	+	0.976252i
$739$	−0.316770	+	0.974918i	−0.0116526	+	0.0358630i	−0.956714	−	0.291031i	$-0.906002\pi$
$739$	−0.316770	+	0.974918i	−0.0116526	+	0.0358630i	0.945061	+	0.326894i	$0.106002\pi$
$740$	−0.389882	−	0.283266i	−0.0143324	−	0.0104131i
$741$	−70.2382	+	51.0310i	−2.58026	+	1.87467i
$742$	5.27627	+	3.83344i	0.193698	+	0.140730i
$743$	52.8258			1.93799			0.968995	−	0.247082i	$-0.0794717\pi$
$743$	52.8258			1.93799			0.968995	+	0.247082i	$0.0794717\pi$
$744$	−33.9639	−	24.6762i	−1.24518	−	0.904675i
$745$	−7.64861			−0.280223
$746$	6.19148			0.226686
$747$	39.4772	+	28.6819i	1.44440	+	1.04942i
$748$	4.20856	−	12.9526i	0.153880	−	0.473595i
$749$	−22.2091	+	16.1359i	−0.811504	+	0.589592i
$750$	−7.94731	−	5.77406i	−0.290195	−	0.210839i
$751$	2.04871	+	6.30527i	0.0747584	+	0.230083i	0.981452	−	0.191707i	$-0.0614022\pi$
$751$	2.04871	+	6.30527i	0.0747584	+	0.230083i	−0.906694	+	0.421789i	$0.861402\pi$
$752$	−0.0316588	+	0.0974359i	−0.00115448	+	0.00355312i
$753$	58.9716			2.14905
$754$	−2.40264	−	7.39456i	−0.0874989	−	0.269294i
$755$	2.19646	−	1.59582i	0.0799375	−	0.0580780i
$756$	−6.69276	+	20.5982i	−0.243413	+	0.749149i
$757$	9.38441	−	28.8822i	0.341082	−	1.04974i	−0.622566	−	0.782567i	$-0.713910\pi$
$757$	9.38441	−	28.8822i	0.341082	−	1.04974i	0.963648	−	0.267175i	$-0.0860903\pi$
$758$	−5.04430	−	15.5248i	−0.183217	−	0.563885i
$759$	−19.2887	−	14.0141i	−0.700137	−	0.508679i
$760$	2.05916	+	6.33744i	0.0746936	+	0.229883i
$761$	−20.2716			−0.734845			−0.367422	−	0.930054i	$-0.619760\pi$
$761$	−20.2716			−0.734845			−0.367422	+	0.930054i	$0.619760\pi$
$762$	−1.52794	+	4.70251i	−0.0553513	+	0.170354i
$763$	−7.51548	+	23.1303i	−0.272079	+	0.837372i
$764$	12.3790			0.447855
$765$	2.37614	+	7.31299i	0.0859094	+	0.264402i
$766$	−6.53144	−	4.74537i	−0.235990	−	0.171457i
$767$	25.2643	+	77.7555i	0.912240	+	2.80759i
$768$	13.4098	−	41.2712i	0.483886	−	1.48925i
$769$	−13.4719	+	41.4623i	−0.485810	+	1.49517i	0.344995	+	0.938605i	$0.387881\pi$
$769$	−13.4719	+	41.4623i	−0.485810	+	1.49517i	−0.830804	+	0.556564i	$0.812119\pi$
$770$	−2.76681	+	2.01020i	−0.0997088	+	0.0724427i
$771$	10.2219	+	31.4598i	0.368133	+	1.13300i
$772$	−6.55506			−0.235922
$773$	11.8190	−	36.3751i	0.425099	−	1.30832i	−0.477801	−	0.878468i	$-0.658566\pi$
$773$	11.8190	−	36.3751i	0.425099	−	1.30832i	0.902900	−	0.429852i	$-0.141434\pi$
$774$	2.81457	+	8.66234i	0.101167	+	0.311362i
$775$	21.0338	+	15.2820i	0.755557	+	0.548944i
$776$	−26.9479	+	19.5788i	−0.967373	+	0.702837i
$777$	−2.64856	+	8.15143i	−0.0950166	+	0.292431i
$778$	12.5491	+	9.11745i	0.449907	+	0.326877i
$779$	−62.7883			−2.24962
$780$	8.17327			0.292650
$781$	3.01153	+	2.18801i	0.107761	+	0.0782930i
$782$	9.94204			0.355527
$783$	−6.72514	−	4.88610i	−0.240337	−	0.174615i
$784$	−0.621011	+	0.451191i	−0.0221790	+	0.0161140i
$785$	0.0562364	+	0.0408582i	0.00200716	+	0.00145829i
$786$	−0.770466	+	2.37125i	−0.0274816	+	0.0845797i
$787$	−22.3776	+	16.2583i	−0.797675	+	0.579545i	−0.910231	−	0.414100i	$-0.864096\pi$
$787$	−22.3776	+	16.2583i	−0.797675	+	0.579545i	0.112556	+	0.993645i	$0.464096\pi$
$788$	11.3427	−	8.24095i	0.404067	−	0.293572i
$789$	59.6216	−	43.3176i	2.12258	−	1.54215i
$790$	−0.298980	−	0.920165i	−0.0106372	−	0.0327380i
$791$	6.08069	+	18.7144i	0.216204	+	0.665409i
$792$	37.4172			1.32956
$793$	−42.3347	−	6.02709i	−1.50335	−	0.214028i
$794$	17.5978			0.624522
$795$	−0.813135	−	2.50257i	−0.0288389	−	0.0887571i
$796$	2.76466	+	8.50874i	0.0979907	+	0.301584i
$797$	−20.6651	+	15.0141i	−0.731995	+	0.531826i	−0.890194	−	0.455582i	$-0.849431\pi$
$797$	−20.6651	+	15.0141i	−0.731995	+	0.531826i	0.158199	+	0.987407i	$0.449431\pi$
$798$	37.2891	−	27.0921i	1.32002	−	0.959050i
$799$	1.90628	−	1.38499i	0.0674393	−	0.0489975i
$800$	−8.53060	+	26.2545i	−0.301602	+	0.928236i
$801$	48.1510	+	34.9837i	1.70133	+	1.23609i
$802$	−5.48083	+	3.98205i	−0.193535	+	0.140611i
$803$	−16.7006	−	12.1337i	−0.589353	−	0.428190i
$804$	−16.5840			−0.584871
$805$	3.53605	+	2.56909i	0.124629	+	0.0905485i
$806$	25.1644			0.886378
$807$	7.78164			0.273927
$808$	35.9107	+	26.0907i	1.26333	+	0.917866i
$809$	9.27843	−	28.5561i	0.326212	−	1.00398i	−0.644678	−	0.764454i	$-0.723009\pi$
$809$	9.27843	−	28.5561i	0.326212	−	1.00398i	0.970890	−	0.239524i	$-0.0769914\pi$
$810$	0.126307	−	0.0917671i	0.00443796	−	0.00322437i
$811$	−1.37118	−	0.996223i	−0.0481487	−	0.0349821i	0.563451	−	0.826150i	$-0.309474\pi$
$811$	−1.37118	−	0.996223i	−0.0481487	−	0.0349821i	−0.611599	+	0.791168i	$0.709474\pi$
$812$	−2.23312	−	6.87283i	−0.0783671	−	0.241189i
$813$	14.8562	−	45.7225i	0.521028	−	1.60356i
$814$	2.15096			0.0753910
$815$	−1.81150	−	5.57522i	−0.0634541	−	0.195292i
$816$	1.43346	−	1.04147i	0.0501810	−	0.0364587i
$817$	−3.91669	+	12.0543i	−0.137028	+	0.421727i
$818$	4.53382	−	13.9537i	0.158521	−	0.487879i
$819$	−27.6169	−	84.9962i	−0.965014	−	2.97001i
$820$	4.78208	+	3.47438i	0.166997	+	0.121331i
$821$	5.26429	+	16.2018i	0.183725	+	0.565448i	0.999924	−	0.0123233i	$-0.00392272\pi$
$821$	5.26429	+	16.2018i	0.183725	+	0.565448i	−0.816199	+	0.577771i	$0.803923\pi$
$822$	−8.17417			−0.285107
$823$	9.18319	−	28.2630i	0.320106	−	0.985185i	−0.653496	−	0.756930i	$-0.726698\pi$
$823$	9.18319	−	28.2630i	0.320106	−	0.985185i	0.973601	−	0.228255i	$-0.0733018\pi$
$824$	−2.38441	+	7.33845i	−0.0830647	+	0.255647i
$825$	−37.6899			−1.31220
$826$	−13.4127	−	41.2800i	−0.466687	−	1.43631i
$827$	1.08675	+	0.789567i	0.0377899	+	0.0274559i	0.606520	−	0.795068i	$-0.292565\pi$
$827$	1.08675	+	0.789567i	0.0377899	+	0.0274559i	−0.568730	+	0.822524i	$0.692565\pi$
$828$	−5.74722	−	17.6881i	−0.199730	−	0.614705i
$829$	3.20186	−	9.85432i	0.111205	−	0.342255i	−0.879931	−	0.475101i	$-0.842412\pi$
$829$	3.20186	−	9.85432i	0.111205	−	0.342255i	0.991137	+	0.132846i	$0.0424116\pi$
$830$	−1.12835	+	3.47271i	−0.0391656	+	0.120539i
$831$	−57.5968	+	41.8465i	−1.99801	+	1.45164i
$832$	7.69449	+	23.6812i	0.266758	+	0.820998i
$833$	17.6546			0.611695
$834$	−2.35152	+	7.23724i	−0.0814265	+	0.250605i
$835$	0.154420	+	0.475257i	0.00534393	+	0.0164469i
$836$	16.3833	+	11.9032i	0.566628	+	0.411679i
$837$	21.7662	−	15.8140i	0.752349	−	0.546613i
$838$	6.70334	−	20.6308i	0.231563	−	0.712678i
$839$	19.6000	+	14.2402i	0.676667	+	0.491627i	0.872250	−	0.489060i	$-0.162660\pi$
$839$	19.6000	+	14.2402i	0.676667	+	0.491627i	−0.195584	+	0.980687i	$0.562660\pi$
$840$	−11.1568			−0.384946
$841$	−26.2264			−0.904357
$842$	−8.17982	−	5.94299i	−0.281895	−	0.204809i
$843$	−32.9811			−1.13593
$844$	−13.8982	−	10.0976i	−0.478394	−	0.347574i
$845$	−5.77137	+	4.19315i	−0.198541	+	0.144249i
$846$	2.03691	+	1.47990i	0.0700303	+	0.0508800i
$847$	3.32923	−	10.2463i	0.114394	−	0.352068i
$848$	−0.301594	+	0.219121i	−0.0103568	+	0.00752464i
$849$	28.3650	−	20.6084i	0.973485	−	0.707278i
$850$	12.7149	−	9.23790i	0.436117	−	0.316857i
$851$	−0.849481	−	2.61443i	−0.0291198	−	0.0896216i
$852$	1.45947	+	4.49179i	0.0500006	+	0.153886i
$853$	11.6307			0.398228			0.199114	−	0.979976i	$-0.436194\pi$
$853$	11.6307			0.398228			0.199114	+	0.979976i	$0.436194\pi$
$854$	22.4753	+	3.19975i	0.769087	+	0.109493i
$855$	−11.4335			−0.391019
$856$	6.94511	+	21.3748i	0.237379	+	0.730577i
$857$	−11.5070	−	35.4150i	−0.393072	−	1.20975i	−0.930453	−	0.366412i	$-0.880586\pi$
$857$	−11.5070	−	35.4150i	−0.393072	−	1.20975i	0.537380	−	0.843340i	$-0.319414\pi$
$858$	−29.5127	+	21.4423i	−1.00755	+	0.732027i
$859$	17.4832	−	12.7023i	0.596519	−	0.433397i	−0.248122	−	0.968729i	$-0.579813\pi$
$859$	17.4832	−	12.7023i	0.596519	−	0.433397i	0.844642	+	0.535332i	$0.179813\pi$
$860$	0.965327	−	0.701351i	0.0329174	−	0.0239159i
$861$	32.4857	−	99.9809i	1.10711	−	3.40734i
$862$	−3.98256	−	2.89350i	−0.135647	−	0.0985531i
$863$	23.5493	−	17.1095i	0.801626	−	0.582416i	−0.109764	−	0.993958i	$-0.535010\pi$
$863$	23.5493	−	17.1095i	0.801626	−	0.582416i	0.911391	+	0.411542i	$0.135010\pi$
$864$	23.1110	+	16.7911i	0.786252	+	0.571246i
$865$	7.90084			0.268637
$866$	15.1802	+	11.0291i	0.515845	+	0.374783i
$867$	6.69197			0.227271
$868$	23.3889			0.793872
$869$	−6.11629	−	4.44375i	−0.207481	−	0.150744i
$870$	0.514645	−	1.58391i	0.0174481	−	0.0536997i
$871$	20.6780	−	15.0234i	0.700646	−	0.509049i
$872$	16.1085	+	11.7035i	0.545502	+	0.396330i
$873$	−17.6613	−	54.3559i	−0.597744	−	1.83967i
$874$	−4.56825	+	14.0596i	−0.154523	+	0.475574i
$875$	14.0717			0.475711
$876$	−8.09358	−	24.9095i	−0.273457	−	0.841613i
$877$	33.6087	−	24.4182i	1.13489	−	0.824543i	0.148488	−	0.988914i	$-0.452559\pi$
$877$	33.6087	−	24.4182i	1.13489	−	0.824543i	0.986399	+	0.164371i	$0.0525594\pi$
$878$	−7.79665	+	23.9956i	−0.263124	+	0.809813i
$879$	−22.4094	+	68.9691i	−0.755851	+	2.32627i
$880$	−0.0604086	−	0.185919i	−0.00203637	−	0.00626731i
$881$	11.9342	+	8.67073i	0.402074	+	0.292124i	0.770385	−	0.637578i	$-0.220064\pi$
$881$	11.9342	+	8.67073i	0.402074	+	0.292124i	−0.368311	+	0.929703i	$0.620064\pi$
$882$	5.82941	+	17.9411i	0.196286	+	0.604108i
$883$	−30.0584			−1.01155			−0.505773	−	0.862667i	$-0.668793\pi$
$883$	−30.0584			−1.01155			−0.505773	+	0.862667i	$0.668793\pi$
$884$	−8.22960	+	25.3281i	−0.276791	+	0.851876i
$885$	−5.41161	+	16.6552i	−0.181909	+	0.559859i
$886$	−20.3983			−0.685293
$887$	2.81802	+	8.67296i	0.0946197	+	0.291209i	0.987154	−	0.159769i	$-0.0510750\pi$
$887$	2.81802	+	8.67296i	0.0946197	+	0.291209i	−0.892535	+	0.450979i	$0.851075\pi$
$888$	5.67685	+	4.12448i	0.190503	+	0.138408i
$889$	−2.18872	−	6.73620i	−0.0734074	−	0.225925i
$890$	−1.37627	+	4.23571i	−0.0461325	+	0.141981i
$891$	0.376983	−	1.16023i	0.0126294	−	0.0388693i
$892$	−6.36841	+	4.62692i	−0.213230	+	0.154921i
$893$	1.08269	+	3.33217i	0.0362307	+	0.111507i
$894$	43.3133			1.44861
$895$	−0.497290	+	1.53050i	−0.0166226	+	0.0511590i
$896$	7.97261	+	24.5372i	0.266346	+	0.819729i
$897$	37.7180	+	27.4037i	1.25937	+	0.914984i
$898$	−0.365382	+	0.265465i	−0.0121929	+	0.00885869i
$899$	−2.77405	+	8.53763i	−0.0925196	+	0.284746i
$900$	−23.7855	−	17.2812i	−0.792850	−	0.576039i
$901$	8.57395			0.285640
$902$	−26.3824			−0.878439
$903$	−17.1682	−	12.4735i	−0.571323	−	0.415091i
$904$	16.1099			0.535807
$905$	3.15931	+	2.29537i	0.105019	+	0.0763008i
$906$	−12.4384	+	9.03700i	−0.413237	+	0.300234i
$907$	15.4999	+	11.2614i	0.514667	+	0.373928i	0.814591	−	0.580035i	$-0.196961\pi$
$907$	15.4999	+	11.2614i	0.514667	+	0.373928i	−0.299924	+	0.953963i	$0.596961\pi$
$908$	1.59511	−	4.90925i	0.0529356	−	0.162919i
$909$	−61.6165	+	44.7670i	−2.04369	+	1.48483i
$910$	5.41033	−	3.93083i	0.179351	−	0.130306i
$911$	−25.7647	+	18.7191i	−0.853622	+	0.620192i	−0.926142	−	0.377174i	$-0.876896\pi$
$911$	−25.7647	+	18.7191i	−0.853622	+	0.620192i	0.0725206	+	0.997367i	$0.476896\pi$
$912$	0.814145	+	2.50568i	0.0269590	+	0.0829713i
$913$	8.81688	+	27.1356i	0.291796	+	0.898057i
$914$	−11.2942			−0.373580
$915$	−6.57740	−	6.37453i	−0.217442	−	0.210735i
$916$	−33.7049			−1.11364
$917$	−1.10367	−	3.39674i	−0.0364463	−	0.112170i
$918$	−5.02575	−	15.4677i	−0.165875	−	0.510509i
$919$	47.3966	−	34.4356i	1.56347	−	1.13593i	0.630376	−	0.776290i	$-0.282901\pi$
$919$	47.3966	−	34.4356i	1.56347	−	1.13593i	0.933093	−	0.359636i	$-0.117099\pi$
$920$	2.89495	−	2.10330i	0.0954436	−	0.0693438i
$921$	32.9528	−	23.9416i	1.08583	−	0.788902i
$922$	−2.46796	+	7.59559i	−0.0812778	+	0.250147i
$923$	−5.88887	−	4.27851i	−0.193835	−	0.140829i
$924$	−27.4305	+	19.9294i	−0.902396	+	0.655629i
$925$	−3.51567	−	2.55428i	−0.115594	−	0.0839843i
$926$	8.21308			0.269899
$927$	−10.7110	−	7.78197i	−0.351794	−	0.255593i
$928$	−9.53165			−0.312892
$929$	−49.6851			−1.63012			−0.815058	−	0.579379i	$-0.803295\pi$
$929$	−49.6851			−1.63012			−0.815058	+	0.579379i	$0.803295\pi$
$930$	4.36077	+	3.16829i	0.142995	+	0.103892i
$931$	−8.11207	+	24.9664i	−0.265863	+	0.818241i
$932$	−12.2006	+	8.86429i	−0.399645	+	0.290359i
$933$	60.6234	+	44.0455i	1.98472	+	1.44198i
$934$	4.48494	+	13.8032i	0.146752	+	0.451656i
$935$	−1.38936	+	4.27601i	−0.0454369	+	0.139840i
$936$	−73.1671			−2.39154
$937$	6.97169	+	21.4567i	0.227755	+	0.700958i	0.998000	+	0.0632102i	$0.0201339\pi$
$937$	6.97169	+	21.4567i	0.227755	+	0.700958i	−0.770245	+	0.637748i	$0.779866\pi$
$938$	−10.9778	+	7.97585i	−0.358438	+	0.260421i
$939$	0.950575	−	2.92557i	0.0310208	−	0.0954723i
$940$	0.101926	−	0.313695i	0.00332445	−	0.0102316i
$941$	−7.20569	−	22.1768i	−0.234899	−	0.722944i	−0.997135	−	0.0756450i	$-0.975898\pi$
$941$	−7.20569	−	22.1768i	−0.234899	−	0.722944i	0.762236	−	0.647299i	$-0.224102\pi$
$942$	−0.318461	−	0.231376i	−0.0103760	−	0.00753863i
$943$	10.4192	+	32.0672i	0.339297	+	1.04425i
$944$	2.48101			0.0807499
$945$	2.20946	−	6.80001i	0.0718737	−	0.221204i
$946$	−1.64572	+	5.06499i	−0.0535069	+	0.164677i
$947$	−21.3146			−0.692631			−0.346316	−	0.938118i	$-0.612567\pi$
$947$	−21.3146			−0.692631			−0.346316	+	0.938118i	$0.612567\pi$
$948$	−2.96412	−	9.12263i	−0.0962702	−	0.296289i
$949$	32.6571	+	23.7268i	1.06009	+	0.770204i
$950$	7.22153	+	22.2256i	0.234297	+	0.721093i
$951$	7.36270	−	22.6601i	0.238752	−	0.734803i
$952$	11.2337	−	34.5737i	0.364086	−	1.12054i
$953$	−29.9994	+	21.7958i	−0.971776	+	0.706037i	−0.955856	−	0.293836i	$-0.905068\pi$
$953$	−29.9994	+	21.7958i	−0.971776	+	0.706037i	−0.0159206	+	0.999873i	$0.505068\pi$
$954$	2.83105	+	8.71308i	0.0916587	+	0.282096i
$955$	−4.08663			−0.132240
$956$	10.5742	−	32.5440i	0.341994	−	1.05255i
$957$	−4.02141	−	12.3766i	−0.129994	−	0.400080i
$958$	22.9980	+	16.7090i	0.743032	+	0.539844i
$959$	9.47297	−	6.88252i	0.305898	−	0.222248i
$960$	−1.64816	+	5.07251i	−0.0531941	+	0.163715i
$961$	1.57402	+	1.14359i	0.0507749	+	0.0368901i
$962$	−4.20607			−0.135609
$963$	−38.5629			−1.24267
$964$	14.1893	+	10.3091i	0.457007	+	0.332035i
$965$	2.16400			0.0696617
$966$	−20.0243	−	14.5485i	−0.644271	−	0.468090i
$967$	−37.0591	+	26.9250i	−1.19174	+	0.865851i	−0.993447	−	0.114292i	$-0.963540\pi$
$967$	−37.0591	+	26.9250i	−1.19174	+	0.865851i	−0.198294	+	0.980143i	$0.563540\pi$
$968$	−7.13579	−	5.18446i	−0.229353	−	0.166635i
$969$	18.7248	−	57.6290i	0.601528	−	1.85131i
$970$	3.45995	−	2.51380i	0.111092	−	0.0807134i
$971$	14.6449	−	10.6401i	0.469976	−	0.341457i	−0.327456	−	0.944866i	$-0.606191\pi$
$971$	14.6449	−	10.6401i	0.469976	−	0.341457i	0.797432	+	0.603409i	$0.206191\pi$
$972$	16.6727	−	12.1134i	0.534776	−	0.388537i
$973$	−3.36848	−	10.3671i	−0.107989	−	0.332354i
$974$	1.37870	+	4.24319i	0.0441763	+	0.135961i
$975$	73.7004			2.36030
$976$	−0.570940	+	1.16530i	−0.0182753	+	0.0373003i
$977$	−1.81750			−0.0581469			−0.0290734	−	0.999577i	$-0.509256\pi$
$977$	−1.81750			−0.0581469			−0.0290734	+	0.999577i	$0.509256\pi$
$978$	10.2583	+	31.5719i	0.328026	+	1.00956i
$979$	10.7541	+	33.0977i	0.343702	+	1.05781i
$980$	1.99934	−	1.45261i	0.0638667	−	0.0464019i
$981$	−27.6393	+	20.0812i	−0.882456	+	0.641142i
$982$	10.5599	−	7.67222i	0.336980	−	0.244830i
$983$	13.2524	−	40.7866i	0.422685	−	1.30089i	−0.482509	−	0.875891i	$-0.660274\pi$
$983$	13.2524	−	40.7866i	0.422685	−	1.30089i	0.905194	−	0.424999i	$-0.139726\pi$
$984$	−69.6291	−	50.5885i	−2.21969	−	1.61270i
$985$	−3.74453	+	2.72056i	−0.119311	+	0.0866842i
$986$	4.39019	+	3.18966i	0.139812	+	0.101579i
$987$	−5.86614			−0.186721
$988$	−32.0366	−	23.2759i	−1.01922	−	0.740506i
$989$	6.80631			0.216428
$990$	−4.80416			−0.152686
$991$	−41.6494	−	30.2601i	−1.32304	−	0.961243i	−0.999889	−	0.0148944i	$-0.995259\pi$
$991$	−41.6494	−	30.2601i	−1.32304	−	0.961243i	−0.323148	−	0.946348i	$-0.604741\pi$
$992$	9.53304	−	29.3397i	0.302674	−	0.931535i
$993$	−18.1933	+	13.2182i	−0.577346	+	0.419467i
$994$	3.12637	+	2.27144i	0.0991624	+	0.0720457i
$995$	−0.912687	−	2.80896i	−0.0289341	−	0.0890501i
$996$	−11.1866	+	34.4288i	−0.354461	+	1.09092i
$997$	−58.1323			−1.84107			−0.920534	−	0.390663i	$-0.872246\pi$
$997$	−58.1323			−1.84107			−0.920534	+	0.390663i	$0.872246\pi$
$998$	2.21222	+	6.80851i	0.0700266	+	0.215520i
$999$	−3.63808	+	2.64322i	−0.115104	+	0.0836277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.e.a.20.3	✓	12
3.2	odd	2		549.2.k.a.325.1		12
4.3	odd	2		976.2.v.a.81.3		12
61.27	even	10		3721.2.a.h.1.2		6
61.34	even	5		3721.2.a.g.1.5		6
61.58	even	5	inner	61.2.e.a.58.3	yes	12
183.119	odd	10		549.2.k.a.424.1		12
244.119	odd	10		976.2.v.a.241.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.e.a.20.3	✓	12	1.1	even	1	trivial
61.2.e.a.58.3	yes	12	61.58	even	5	inner
549.2.k.a.325.1		12	3.2	odd	2
549.2.k.a.424.1		12	183.119	odd	10
976.2.v.a.81.3		12	4.3	odd	2
976.2.v.a.241.3		12	244.119	odd	10
3721.2.a.g.1.5		6	61.34	even	5
3721.2.a.h.1.2		6	61.27	even	10

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.263496 + 0.810959i) q^{2} +(-0.862402 - 2.65420i) q^{3} +(1.02981 - 0.748201i) q^{4} +(-0.339968 + 0.247001i) q^{5} +(1.92521 - 1.39874i) q^{6} +(-1.05338 + 3.24198i) q^{7} +(2.25780 + 1.64039i) q^{8} +(-3.87399 + 2.81462i) q^{9} +O(q^{10})\)	\(q+(0.263496 + 0.810959i) q^{2} +(-0.862402 - 2.65420i) q^{3} +(1.02981 - 0.748201i) q^{4} +(-0.339968 + 0.247001i) q^{5} +(1.92521 - 1.39874i) q^{6} +(-1.05338 + 3.24198i) q^{7} +(2.25780 + 1.64039i) q^{8} +(-3.87399 + 2.81462i) q^{9} +(-0.289888 - 0.210616i) q^{10} -2.79991 q^{11} +(-2.87399 - 2.08807i) q^{12} +5.47505 q^{13} -2.90668 q^{14} +(0.948780 + 0.689329i) q^{15} +(0.0513422 - 0.158015i) q^{16} +(-3.09147 + 2.24609i) q^{17} +(-3.30332 - 2.40000i) q^{18} +(-1.75583 - 5.40389i) q^{19} +(-0.165296 + 0.508729i) q^{20} +9.51331 q^{21} +(-0.737766 - 2.27061i) q^{22} +(-2.46850 + 1.79347i) q^{23} +(2.40678 - 7.40731i) q^{24} +(-1.49052 + 4.58734i) q^{25} +(1.44266 + 4.44004i) q^{26} +(4.03809 + 2.93384i) q^{27} +(1.34087 + 4.12677i) q^{28} -1.66543 q^{29} +(-0.309017 + 0.951057i) q^{30} +(1.66567 - 5.12640i) q^{31} +5.72325 q^{32} +(2.41465 + 7.43152i) q^{33} +(-2.63608 - 1.91522i) q^{34} +(-0.442657 - 1.36236i) q^{35} +(-1.88357 + 5.79704i) q^{36} +(-0.278406 + 0.856845i) q^{37} +(3.91967 - 2.84781i) q^{38} +(-4.72170 - 14.5319i) q^{39} -1.17276 q^{40} +(3.41477 - 10.5096i) q^{41} +(2.50672 + 7.71490i) q^{42} +(-1.80465 - 1.31116i) q^{43} +(-2.88338 + 2.09490i) q^{44} +(0.621818 - 1.91376i) q^{45} +(-2.10487 - 1.52928i) q^{46} -0.616624 q^{47} -0.463681 q^{48} +(-3.73772 - 2.71562i) q^{49} -4.11289 q^{50} +(8.62766 + 6.26836i) q^{51} +(5.63827 - 4.09644i) q^{52} +(-1.81522 - 1.31884i) q^{53} +(-1.31520 + 4.04778i) q^{54} +(0.951880 - 0.691581i) q^{55} +(-7.69643 + 5.59178i) q^{56} +(-12.8288 + 9.32064i) q^{57} +(-0.438834 - 1.35059i) q^{58} +(4.61443 + 14.2018i) q^{59} +1.49282 q^{60} +(-7.73228 - 1.10083i) q^{61} +4.59619 q^{62} +(-5.04414 - 15.5243i) q^{63} +(1.40537 + 4.32529i) q^{64} +(-1.86134 + 1.35235i) q^{65} +(-5.39040 + 3.91635i) q^{66} +(3.77676 - 2.74397i) q^{67} +(-1.50311 + 4.62609i) q^{68} +(6.88906 + 5.00520i) q^{69} +(0.988178 - 0.717953i) q^{70} +(-1.07558 - 0.781456i) q^{71} -13.3637 q^{72} +(5.96471 + 4.33361i) q^{73} -0.768224 q^{74} +13.4611 q^{75} +(-5.85137 - 4.25127i) q^{76} +(2.94938 - 9.07726i) q^{77} +(10.5406 - 7.65820i) q^{78} +(2.18446 + 1.58710i) q^{79} +(0.0215752 + 0.0664016i) q^{80} +(-0.134641 + 0.414383i) q^{81} +9.42261 q^{82} +(-3.14899 - 9.69159i) q^{83} +(9.79691 - 7.11787i) q^{84} +(0.496216 - 1.52720i) q^{85} +(0.587775 - 1.80899i) q^{86} +(1.43627 + 4.42037i) q^{87} +(-6.32162 - 4.59293i) q^{88} +(-3.84087 - 11.8210i) q^{89} +1.71583 q^{90} +(-5.76734 + 17.7500i) q^{91} +(-1.20021 + 3.69387i) q^{92} -15.0430 q^{93} +(-0.162478 - 0.500057i) q^{94} +(1.93169 + 1.40346i) q^{95} +(-4.93574 - 15.1907i) q^{96} +(-3.68827 + 11.3513i) q^{97} +(1.21737 - 3.74669i) q^{98} +(10.8468 - 7.88067i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - q^{3} + 2 q^{4} - 5 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} - 6 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - q^3 + 2 * q^4 - 5 * q^5 - q^6 - 10 * q^7 + 4 * q^8 - 6 * q^9	\( 12 q - 2 q^{2} - q^{3} + 2 q^{4} - 5 q^{5} - q^{6} - 10 q^{7} + 4 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} + 6 q^{12} + 2 q^{13} - 2 q^{14} - 5 q^{15} + 10 q^{16} + 6 q^{17} - 15 q^{18} - q^{19} + 13 q^{20} + 32 q^{21} - 25 q^{22} - 7 q^{23} - 12 q^{25} + 2 q^{26} + 8 q^{27} - 13 q^{28} - 8 q^{29} + 3 q^{30} + 19 q^{31} + 26 q^{32} - q^{33} - 30 q^{34} + 10 q^{35} + 8 q^{36} + 31 q^{37} + 27 q^{38} - 23 q^{39} + 4 q^{41} + 11 q^{42} + q^{43} - 20 q^{44} - 18 q^{45} + 23 q^{46} - 22 q^{47} - 8 q^{48} + 3 q^{49} + 74 q^{50} + 9 q^{52} - 35 q^{53} - 26 q^{54} - 18 q^{56} - 31 q^{57} - 16 q^{58} - 13 q^{59} + 2 q^{60} - 6 q^{61} - 52 q^{62} + 7 q^{63} + 16 q^{64} + 4 q^{65} - 19 q^{66} - 9 q^{67} - 33 q^{68} + 35 q^{69} - 5 q^{70} - 24 q^{71} - 30 q^{72} + 51 q^{73} - 20 q^{74} + 40 q^{75} - 31 q^{76} + q^{77} + 22 q^{78} - 26 q^{79} - 23 q^{80} - 2 q^{81} + 78 q^{82} + 3 q^{83} + 17 q^{84} + 18 q^{85} + 55 q^{86} + 49 q^{87} - q^{88} - 17 q^{89} + 54 q^{90} - 27 q^{91} + 37 q^{92} + 10 q^{93} + 13 q^{94} + 4 q^{95} - 17 q^{96} + 17 q^{97} + 29 q^{98} + 19 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - q^3 + 2 * q^4 - 5 * q^5 - q^6 - 10 * q^7 + 4 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 + 6 * q^12 + 2 * q^13 - 2 * q^14 - 5 * q^15 + 10 * q^16 + 6 * q^17 - 15 * q^18 - q^19 + 13 * q^20 + 32 * q^21 - 25 * q^22 - 7 * q^23 - 12 * q^25 + 2 * q^26 + 8 * q^27 - 13 * q^28 - 8 * q^29 + 3 * q^30 + 19 * q^31 + 26 * q^32 - q^33 - 30 * q^34 + 10 * q^35 + 8 * q^36 + 31 * q^37 + 27 * q^38 - 23 * q^39 + 4 * q^41 + 11 * q^42 + q^43 - 20 * q^44 - 18 * q^45 + 23 * q^46 - 22 * q^47 - 8 * q^48 + 3 * q^49 + 74 * q^50 + 9 * q^52 - 35 * q^53 - 26 * q^54 - 18 * q^56 - 31 * q^57 - 16 * q^58 - 13 * q^59 + 2 * q^60 - 6 * q^61 - 52 * q^62 + 7 * q^63 + 16 * q^64 + 4 * q^65 - 19 * q^66 - 9 * q^67 - 33 * q^68 + 35 * q^69 - 5 * q^70 - 24 * q^71 - 30 * q^72 + 51 * q^73 - 20 * q^74 + 40 * q^75 - 31 * q^76 + q^77 + 22 * q^78 - 26 * q^79 - 23 * q^80 - 2 * q^81 + 78 * q^82 + 3 * q^83 + 17 * q^84 + 18 * q^85 + 55 * q^86 + 49 * q^87 - q^88 - 17 * q^89 + 54 * q^90 - 27 * q^91 + 37 * q^92 + 10 * q^93 + 13 * q^94 + 4 * q^95 - 17 * q^96 + 17 * q^97 + 29 * q^98 + 19 * q^99

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