LMFDB - Embedded newform 357.2.i.f.256.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("357.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.5743021975227.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 2x^{8} + 10x^{7} - 8x^{6} - 12x^{5} - 24x^{4} + 90x^{3} + 54x^{2} - 324x + 243 $ x^10 - 4x^9 + 2x^8 + 10x^7 - 8x^6 - 12x^5 - 24x^4 + 90x^3 + 54x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			256.1
Root			$-1.68232 + 0.412079i$ of defining polynomial
Character	$\chi$	$=$	357.256
Dual form			357.2.i.f.205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19803 - 2.07505i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.87055 + 3.23989i) q^{4} +(-2.18232 - 3.77988i) q^{5} -2.39606 q^{6} +(-2.64467 - 0.0756600i) q^{7} +4.17178 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.19803 - 2.07505i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.87055 + 3.23989i) q^{4} +(-2.18232 - 3.77988i) q^{5} -2.39606 q^{6} +(-2.64467 - 0.0756600i) q^{7} +4.17178 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-5.22896 + 9.05683i) q^{10} +(1.09643 - 1.89907i) q^{11} +(1.87055 + 3.23989i) q^{12} +4.97572 q^{13} +(3.01139 + 5.57846i) q^{14} -4.36463 q^{15} +(-1.25681 - 2.17686i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-1.19803 + 2.07505i) q^{18} +(-1.28983 - 2.23406i) q^{19} +16.3285 q^{20} +(-1.38786 + 2.25252i) q^{21} -5.25422 q^{22} +(2.98429 + 5.16894i) q^{23} +(2.08589 - 3.61286i) q^{24} +(-7.02502 + 12.1677i) q^{25} +(-5.96106 - 10.3249i) q^{26} -1.00000 q^{27} +(5.19211 - 8.42690i) q^{28} -8.59607 q^{29} +(5.22896 + 9.05683i) q^{30} +(1.62736 - 2.81867i) q^{31} +(1.16038 - 2.00984i) q^{32} +(-1.09643 - 1.89907i) q^{33} +2.39606 q^{34} +(5.48552 + 10.1617i) q^{35} +3.74110 q^{36} +(-3.41799 - 5.92014i) q^{37} +(-3.09051 + 5.35293i) q^{38} +(2.48786 - 4.30910i) q^{39} +(-9.10414 - 15.7688i) q^{40} -2.32076 q^{41} +(6.33678 + 0.181286i) q^{42} +3.15824 q^{43} +(4.10185 + 7.10461i) q^{44} +(-2.18232 + 3.77988i) q^{45} +(7.15053 - 12.3851i) q^{46} +(-0.0918028 - 0.159007i) q^{47} -2.51362 q^{48} +(6.98855 + 0.400192i) q^{49} +33.6647 q^{50} +(0.500000 + 0.866025i) q^{51} +(-9.30734 + 16.1208i) q^{52} +(1.42933 - 2.47567i) q^{53} +(1.19803 + 2.07505i) q^{54} -9.57103 q^{55} +(-11.0330 - 0.315637i) q^{56} -2.57966 q^{57} +(10.2983 + 17.8372i) q^{58} +(3.78034 - 6.54775i) q^{59} +(8.16426 - 14.1409i) q^{60} +(-2.96235 - 5.13094i) q^{61} -7.79850 q^{62} +(1.25681 + 2.32818i) q^{63} -10.5879 q^{64} +(-10.8586 - 18.8077i) q^{65} +(-2.62711 + 4.55029i) q^{66} +(-0.801720 + 1.38862i) q^{67} +(-1.87055 - 3.23989i) q^{68} +5.96858 q^{69} +(14.5141 - 23.5567i) q^{70} -10.8783 q^{71} +(-2.08589 - 3.61286i) q^{72} +(-4.18694 + 7.25200i) q^{73} +(-8.18972 + 14.1850i) q^{74} +(7.02502 + 12.1677i) q^{75} +9.65078 q^{76} +(-3.04338 + 4.93946i) q^{77} -11.9221 q^{78} +(-3.55446 - 6.15651i) q^{79} +(-5.48552 + 9.50120i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.78034 + 4.81570i) q^{82} -0.625125 q^{83} +(-4.70185 - 8.70995i) q^{84} +4.36463 q^{85} +(-3.78367 - 6.55350i) q^{86} +(-4.29803 + 7.44441i) q^{87} +(4.57406 - 7.92250i) q^{88} +(-0.479661 - 0.830797i) q^{89} +10.4579 q^{90} +(-13.1591 - 0.376463i) q^{91} -22.3290 q^{92} +(-1.62736 - 2.81867i) q^{93} +(-0.219965 + 0.380990i) q^{94} +(-5.62965 + 9.75083i) q^{95} +(-1.16038 - 2.00984i) q^{96} -6.43415 q^{97} +(-7.54207 - 14.9810i) q^{98} -2.19286 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 5 q^{3} - 8 q^{4} - q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 - q^5 + 4 * q^6 - 5 * q^7 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 8 q^{4} - q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{9} - 13 q^{10} + 11 q^{11} + 8 q^{12} + 14 q^{13} + 3 q^{14} - 2 q^{15} + 2 q^{16} - 5 q^{17} + 2 q^{18} - 9 q^{19} + 24 q^{20} - 7 q^{21} + 10 q^{22} + 23 q^{23} - 14 q^{25} - 18 q^{26} - 10 q^{27} + 7 q^{28} - 36 q^{29} + 13 q^{30} - 9 q^{31} - 3 q^{32} - 11 q^{33} - 4 q^{34} - 5 q^{35} + 16 q^{36} + 7 q^{39} - 31 q^{40} + 6 q^{41} - 3 q^{42} + 24 q^{43} + 33 q^{44} - q^{45} - 13 q^{46} - 11 q^{47} + 4 q^{48} + 3 q^{49} + 48 q^{50} + 5 q^{51} - 5 q^{52} + 3 q^{53} - 2 q^{54} - 20 q^{55} - 27 q^{56} - 18 q^{57} + 34 q^{58} + 14 q^{59} + 12 q^{60} - 29 q^{61} - 10 q^{62} - 2 q^{63} + 8 q^{65} + 5 q^{66} - 16 q^{67} - 8 q^{68} + 46 q^{69} + 18 q^{70} - 38 q^{71} - 11 q^{73} - 45 q^{74} + 14 q^{75} + 18 q^{76} + 21 q^{77} - 36 q^{78} - q^{79} + 5 q^{80} - 5 q^{81} + 4 q^{82} + 10 q^{83} - 28 q^{84} + 2 q^{85} + 3 q^{86} - 18 q^{87} - 37 q^{88} - 8 q^{89} + 26 q^{90} - 33 q^{91} - 96 q^{92} + 9 q^{93} + 18 q^{94} + 21 q^{95} + 3 q^{96} + 38 q^{97} - 17 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 - q^5 + 4 * q^6 - 5 * q^7 - 5 * q^9 - 13 * q^10 + 11 * q^11 + 8 * q^12 + 14 * q^13 + 3 * q^14 - 2 * q^15 + 2 * q^16 - 5 * q^17 + 2 * q^18 - 9 * q^19 + 24 * q^20 - 7 * q^21 + 10 * q^22 + 23 * q^23 - 14 * q^25 - 18 * q^26 - 10 * q^27 + 7 * q^28 - 36 * q^29 + 13 * q^30 - 9 * q^31 - 3 * q^32 - 11 * q^33 - 4 * q^34 - 5 * q^35 + 16 * q^36 + 7 * q^39 - 31 * q^40 + 6 * q^41 - 3 * q^42 + 24 * q^43 + 33 * q^44 - q^45 - 13 * q^46 - 11 * q^47 + 4 * q^48 + 3 * q^49 + 48 * q^50 + 5 * q^51 - 5 * q^52 + 3 * q^53 - 2 * q^54 - 20 * q^55 - 27 * q^56 - 18 * q^57 + 34 * q^58 + 14 * q^59 + 12 * q^60 - 29 * q^61 - 10 * q^62 - 2 * q^63 + 8 * q^65 + 5 * q^66 - 16 * q^67 - 8 * q^68 + 46 * q^69 + 18 * q^70 - 38 * q^71 - 11 * q^73 - 45 * q^74 + 14 * q^75 + 18 * q^76 + 21 * q^77 - 36 * q^78 - q^79 + 5 * q^80 - 5 * q^81 + 4 * q^82 + 10 * q^83 - 28 * q^84 + 2 * q^85 + 3 * q^86 - 18 * q^87 - 37 * q^88 - 8 * q^89 + 26 * q^90 - 33 * q^91 - 96 * q^92 + 9 * q^93 + 18 * q^94 + 21 * q^95 + 3 * q^96 + 38 * q^97 - 17 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.19803	−	2.07505i	−0.847135	−	1.46728i	−0.883754	−	0.467951i	$-0.844992\pi$
$2$	−1.19803	−	2.07505i	−0.847135	−	1.46728i	0.0366195	−	0.999329i	$-0.488341\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.87055	+	3.23989i	−0.935275	+	1.61994i
$5$	−2.18232	−	3.77988i	−0.975962	−	1.69042i	−0.676724	−	0.736237i	$-0.736601\pi$
$5$	−2.18232	−	3.77988i	−0.975962	−	1.69042i	−0.299238	−	0.954178i	$-0.596733\pi$
$6$	−2.39606			−0.978187
$7$	−2.64467	−	0.0756600i	−0.999591	−	0.0285968i
$7$	−2.64467	−	0.0756600i	−0.999591	−	0.0285968i
$8$	4.17178			1.47495
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−5.22896	+	9.05683i	−1.65354	+	2.86402i
$11$	1.09643	−	1.89907i	0.330586	−	0.572592i	−0.652041	−	0.758184i	$-0.726087\pi$
$11$	1.09643	−	1.89907i	0.330586	−	0.572592i	0.982627	+	0.185592i	$0.0594203\pi$
$12$	1.87055	+	3.23989i	0.539981	+	0.935275i
$13$	4.97572			1.38002			0.690009	−	0.723801i	$-0.257607\pi$
$13$	4.97572			1.38002			0.690009	+	0.723801i	$0.257607\pi$
$14$	3.01139	+	5.57846i	0.804829	+	1.49091i
$15$	−4.36463			−1.12694
$16$	−1.25681	−	2.17686i	−0.314203	−	0.544215i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$18$	−1.19803	+	2.07505i	−0.282378	+	0.489093i
$19$	−1.28983	−	2.23406i	−0.295908	−	0.512527i	0.679288	−	0.733872i	$-0.262289\pi$
$19$	−1.28983	−	2.23406i	−0.295908	−	0.512527i	−0.975196	+	0.221345i	$0.928955\pi$
$20$	16.3285			3.65117
$21$	−1.38786	+	2.25252i	−0.302855	+	0.491540i
$22$	−5.25422			−1.12020
$23$	2.98429	+	5.16894i	0.622267	+	1.07780i	0.989063	+	0.147496i	$0.0471215\pi$
$23$	2.98429	+	5.16894i	0.622267	+	1.07780i	−0.366796	+	0.930302i	$0.619545\pi$
$24$	2.08589	−	3.61286i	0.425780	−	0.737473i
$25$	−7.02502	+	12.1677i	−1.40500	+	2.43354i
$26$	−5.96106	−	10.3249i	−1.16906	−	2.02487i
$27$	−1.00000			−0.192450
$28$	5.19211	−	8.42690i	0.981217	−	1.59253i
$29$	−8.59607			−1.59625			−0.798125	−	0.602492i	$-0.794174\pi$
$29$	−8.59607			−1.59625			−0.798125	+	0.602492i	$0.794174\pi$
$30$	5.22896	+	9.05683i	0.954673	+	1.65354i
$31$	1.62736	−	2.81867i	0.292283	−	0.506248i	−0.682067	−	0.731290i	$-0.738919\pi$
$31$	1.62736	−	2.81867i	0.292283	−	0.506248i	0.974349	+	0.225042i	$0.0722519\pi$
$32$	1.16038	−	2.00984i	0.205128	−	0.355293i
$33$	−1.09643	−	1.89907i	−0.190864	−	0.330586i
$34$	2.39606			0.410921
$35$	5.48552	+	10.1617i	0.927222	+	1.71763i
$36$	3.74110			0.623516
$37$	−3.41799	−	5.92014i	−0.561915	−	0.973265i	−0.997329	−	0.0730350i	$-0.976732\pi$
$37$	−3.41799	−	5.92014i	−0.561915	−	0.973265i	0.435415	−	0.900230i	$-0.356602\pi$
$38$	−3.09051	+	5.35293i	−0.501348	+	0.868360i
$39$	2.48786	−	4.30910i	0.398377	−	0.690009i
$40$	−9.10414	−	15.7688i	−1.43949	−	2.49327i
$41$	−2.32076			−0.362442			−0.181221	−	0.983442i	$-0.558005\pi$
$41$	−2.32076			−0.362442			−0.181221	+	0.983442i	$0.558005\pi$
$42$	6.33678	+	0.181286i	0.977787	+	0.0279730i
$43$	3.15824			0.481627			0.240814	−	0.970571i	$-0.422586\pi$
$43$	3.15824			0.481627			0.240814	+	0.970571i	$0.422586\pi$
$44$	4.10185	+	7.10461i	0.618377	+	1.07106i
$45$	−2.18232	+	3.77988i	−0.325321	+	0.563472i
$46$	7.15053	−	12.3851i	1.05429	−	1.82608i
$47$	−0.0918028	−	0.159007i	−0.0133908	−	0.0231936i	0.859252	−	0.511552i	$-0.170929\pi$
$47$	−0.0918028	−	0.159007i	−0.0133908	−	0.0231936i	−0.872643	+	0.488358i	$0.837596\pi$
$48$	−2.51362			−0.362810
$49$	6.98855	+	0.400192i	0.998364	+	0.0571702i
$50$	33.6647			4.76091
$51$	0.500000	+	0.866025i	0.0700140	+	0.121268i
$52$	−9.30734	+	16.1208i	−1.29070	+	2.23555i
$53$	1.42933	−	2.47567i	0.196334	−	0.340060i	−0.751003	−	0.660299i	$-0.770430\pi$
$53$	1.42933	−	2.47567i	0.196334	−	0.340060i	0.947337	+	0.320239i	$0.103763\pi$
$54$	1.19803	+	2.07505i	0.163031	+	0.282378i
$55$	−9.57103			−1.29056
$56$	−11.0330	−	0.315637i	−1.47434	−	0.0421787i
$57$	−2.57966			−0.341685
$58$	10.2983	+	17.8372i	1.35224	+	2.34215i
$59$	3.78034	−	6.54775i	0.492159	−	0.852444i	−0.507800	−	0.861475i	$-0.669541\pi$
$59$	3.78034	−	6.54775i	0.492159	−	0.852444i	0.999959	+	0.00903077i	$0.00287462\pi$
$60$	8.16426	−	14.1409i	1.05400	−	1.82558i
$61$	−2.96235	−	5.13094i	−0.379290	−	0.656950i	0.611669	−	0.791114i	$-0.290499\pi$
$61$	−2.96235	−	5.13094i	−0.379290	−	0.656950i	−0.990959	+	0.134164i	$0.957165\pi$
$62$	−7.79850			−0.990411
$63$	1.25681	+	2.32818i	0.158343	+	0.293323i
$64$	−10.5879			−1.32349
$65$	−10.8586	−	18.8077i	−1.34684	−	2.33280i
$66$	−2.62711	+	4.55029i	−0.323375	+	0.560102i
$67$	−0.801720	+	1.38862i	−0.0979456	+	0.169647i	−0.910834	−	0.412772i	$-0.864560\pi$
$67$	−0.801720	+	1.38862i	−0.0979456	+	0.169647i	0.812889	+	0.582419i	$0.197894\pi$
$68$	−1.87055	−	3.23989i	−0.226837	−	0.392894i
$69$	5.96858			0.718532
$70$	14.5141	−	23.5567i	1.73477	−	2.81556i
$71$	−10.8783			−1.29101			−0.645506	−	0.763755i	$-0.723353\pi$
$71$	−10.8783			−1.29101			−0.645506	+	0.763755i	$0.723353\pi$
$72$	−2.08589	−	3.61286i	−0.245824	−	0.425780i
$73$	−4.18694	+	7.25200i	−0.490045	+	0.848782i	−0.999934	−	0.0114575i	$-0.996353\pi$
$73$	−4.18694	+	7.25200i	−0.490045	+	0.848782i	0.509890	+	0.860240i	$0.329686\pi$
$74$	−8.18972	+	14.1850i	−0.952035	+	1.64897i
$75$	7.02502	+	12.1677i	0.811179	+	1.40500i
$76$	9.65078			1.10702
$77$	−3.04338	+	4.93946i	−0.346825	+	0.562904i
$78$	−11.9221			−1.34992
$79$	−3.55446	−	6.15651i	−0.399908	−	0.692662i	0.593806	−	0.804608i	$-0.297625\pi$
$79$	−3.55446	−	6.15651i	−0.399908	−	0.692662i	−0.993714	+	0.111947i	$0.964291\pi$
$80$	−5.48552	+	9.50120i	−0.613300	+	1.06227i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.78034	+	4.81570i	0.307038	+	0.531805i
$83$	−0.625125			−0.0686164			−0.0343082	−	0.999411i	$-0.510923\pi$
$83$	−0.625125			−0.0686164			−0.0343082	+	0.999411i	$0.510923\pi$
$84$	−4.70185	−	8.70995i	−0.513014	−	0.950334i
$85$	4.36463			0.473411
$86$	−3.78367	−	6.55350i	−0.408003	−	0.706682i
$87$	−4.29803	+	7.44441i	−0.460798	+	0.798125i
$88$	4.57406	−	7.92250i	0.487596	−	0.844541i
$89$	−0.479661	−	0.830797i	−0.0508440	−	0.0880643i	0.839483	−	0.543385i	$-0.182858\pi$
$89$	−0.479661	−	0.830797i	−0.0508440	−	0.0880643i	−0.890327	+	0.455321i	$0.849524\pi$
$90$	10.4579			1.10236
$91$	−13.1591	−	0.376463i	−1.37945	−	0.0394641i
$92$	−22.3290			−2.32796
$93$	−1.62736	−	2.81867i	−0.168749	−	0.292283i
$94$	−0.219965	+	0.380990i	−0.0226877	+	0.0392962i
$95$	−5.62965	+	9.75083i	−0.577590	+	1.00041i
$96$	−1.16038	−	2.00984i	−0.118431	−	0.205128i
$97$	−6.43415			−0.653289			−0.326644	−	0.945147i	$-0.605918\pi$
$97$	−6.43415			−0.653289			−0.326644	+	0.945147i	$0.605918\pi$
$98$	−7.54207	−	14.9810i	−0.761865	−	1.51331i
$99$	−2.19286			−0.220391
$100$	−26.2813	−	45.5205i	−2.62813	−	4.55205i
$101$	5.25964	−	9.10997i	0.523354	−	0.906475i	−0.476277	−	0.879295i	$-0.658014\pi$
$101$	5.25964	−	9.10997i	0.523354	−	0.906475i	0.999631	−	0.0271800i	$-0.00865272\pi$
$102$	1.19803	−	2.07505i	0.118623	−	0.205460i
$103$	1.08614	+	1.88125i	0.107020	+	0.185365i	0.914562	−	0.404446i	$-0.132536\pi$
$103$	1.08614	+	1.88125i	0.107020	+	0.185365i	−0.807541	+	0.589811i	$0.799202\pi$
$104$	20.7576			2.03545
$105$	11.5430	+	0.330228i	1.12648	+	0.0322270i
$106$	−6.84952			−0.665284
$107$	−1.59803	−	2.76786i	−0.154487	−	0.267579i	0.778385	−	0.627787i	$-0.216039\pi$
$107$	−1.59803	−	2.76786i	−0.154487	−	0.267579i	−0.932872	+	0.360208i	$0.882706\pi$
$108$	1.87055	−	3.23989i	0.179994	−	0.311758i
$109$	5.59519	−	9.69116i	0.535922	−	0.928244i	−0.463196	−	0.886256i	$-0.653297\pi$
$109$	5.59519	−	9.69116i	0.535922	−	0.928244i	0.999118	−	0.0419885i	$-0.0133693\pi$
$110$	11.4664	+	19.8603i	1.09328	+	1.89361i
$111$	−6.83599			−0.648843
$112$	3.15915	+	5.85217i	0.298511	+	0.552978i
$113$	−13.7644			−1.29484			−0.647422	−	0.762131i	$-0.724153\pi$
$113$	−13.7644			−1.29484			−0.647422	+	0.762131i	$0.724153\pi$
$114$	3.09051	+	5.35293i	0.289453	+	0.501348i
$115$	13.0253	−	22.5605i	1.21462	−	2.10378i
$116$	16.0794	−	27.8503i	1.49293	−	2.58583i
$117$	−2.48786	−	4.30910i	−0.230003	−	0.398377i
$118$	−18.1158			−1.66770
$119$	1.38786	−	2.25252i	0.127225	−	0.206488i
$120$	−18.2083			−1.66218
$121$	3.09568	+	5.36188i	0.281426	+	0.487444i
$122$	−7.09797	+	12.2940i	−0.642620	+	1.11305i
$123$	−1.16038	+	2.00984i	−0.104628	+	0.181221i
$124$	6.08812	+	10.5449i	0.546729	+	0.946962i
$125$	39.5001			3.53299
$126$	3.32539	−	5.39717i	0.296249	−	0.480818i
$127$	4.37337			0.388074			0.194037	−	0.980994i	$-0.437842\pi$
$127$	4.37337			0.388074			0.194037	+	0.980994i	$0.437842\pi$
$128$	10.3639	+	17.9508i	0.916047	+	1.58664i
$129$	1.57912	−	2.73512i	0.139034	−	0.240814i
$130$	−26.0179	+	45.0643i	−2.28192	+	3.95240i
$131$	3.57782	+	6.19696i	0.312595	+	0.541431i	0.978923	−	0.204228i	$-0.0654683\pi$
$131$	3.57782	+	6.19696i	0.312595	+	0.541431i	−0.666328	+	0.745659i	$0.732135\pi$
$132$	8.20370			0.714041
$133$	3.24215	+	6.00593i	0.281130	+	0.520780i
$134$	3.84194			0.331893
$135$	2.18232	+	3.77988i	0.187824	+	0.325321i
$136$	−2.08589	+	3.61286i	−0.178863	+	0.309800i
$137$	−9.04381	+	15.6643i	−0.772665	+	1.33829i	0.163433	+	0.986554i	$0.447743\pi$
$137$	−9.04381	+	15.6643i	−0.772665	+	1.33829i	−0.936098	+	0.351740i	$0.885590\pi$
$138$	−7.15053	−	12.3851i	−0.608693	−	1.05429i
$139$	17.3458			1.47125			0.735624	−	0.677390i	$-0.236889\pi$
$139$	17.3458			1.47125			0.735624	+	0.677390i	$0.236889\pi$
$140$	−43.1836	−	1.23542i	−3.64968	−	0.104412i
$141$	−0.183606			−0.0154624
$142$	13.0325	+	22.5729i	1.09366	+	1.89428i
$143$	5.45553	−	9.44926i	0.456214	−	0.790186i
$144$	−1.25681	+	2.17686i	−0.104734	+	0.181405i
$145$	18.7593	+	32.4921i	1.55788	+	2.69832i
$146$	20.0643			1.66054
$147$	3.84085	−	5.85217i	0.316788	−	0.482679i
$148$	25.5741			2.10218
$149$	−6.42817	−	11.1339i	−0.526616	−	0.912126i	−0.999519	−	0.0310117i	$-0.990127\pi$
$149$	−6.42817	−	11.1339i	−0.526616	−	0.912126i	0.472903	−	0.881115i	$-0.343206\pi$
$150$	16.8324	−	29.1545i	1.37436	−	2.38045i
$151$	3.40505	−	5.89773i	0.277099	−	0.479950i	−0.693563	−	0.720396i	$-0.743960\pi$
$151$	3.40505	−	5.89773i	0.277099	−	0.479950i	0.970663	+	0.240445i	$0.0772935\pi$
$152$	−5.38089	−	9.31998i	−0.436448	−	0.755950i
$153$	1.00000			0.0808452
$154$	13.8957	+	0.397534i	1.11975	+	0.0320342i
$155$	−14.2057			−1.14103
$156$	9.30734	+	16.1208i	0.745183	+	1.29070i
$157$	−3.63055	+	6.28830i	−0.289750	+	0.501861i	−0.973750	−	0.227621i	$-0.926905\pi$
$157$	−3.63055	+	6.28830i	−0.289750	+	0.501861i	0.684000	+	0.729482i	$0.260239\pi$
$158$	−8.51670	+	14.7514i	−0.677552	+	1.17356i
$159$	−1.42933	−	2.47567i	−0.113353	−	0.196334i
$160$	−10.1293			−0.800790
$161$	−7.50137	−	13.8959i	−0.591191	−	1.09515i
$162$	2.39606			0.188252
$163$	1.56698	+	2.71409i	0.122736	+	0.212584i	0.920846	−	0.389928i	$-0.127500\pi$
$163$	1.56698	+	2.71409i	0.122736	+	0.212584i	−0.798110	+	0.602512i	$0.794167\pi$
$164$	4.34110	−	7.51901i	0.338983	−	0.587136i
$165$	−4.78551	+	8.28875i	−0.372552	+	0.645279i
$166$	0.748918	+	1.29716i	0.0581273	+	0.100679i
$167$	21.3606			1.65293			0.826465	−	0.562988i	$-0.190348\pi$
$167$	21.3606			1.65293			0.826465	+	0.562988i	$0.190348\pi$
$168$	−5.78983	+	9.39701i	−0.446695	+	0.724995i
$169$	11.7578			0.904448
$170$	−5.22896	−	9.05683i	−0.401043	−	0.694627i
$171$	−1.28983	+	2.23406i	−0.0986359	+	0.170842i
$172$	−5.90765	+	10.2323i	−0.450454	+	0.780209i
$173$	−4.07001	−	7.04947i	−0.309437	−	0.535961i	0.668802	−	0.743441i	$-0.266807\pi$
$173$	−4.07001	−	7.04947i	−0.309437	−	0.535961i	−0.978239	+	0.207479i	$0.933474\pi$
$174$	20.5967			1.56143
$175$	19.4995	−	31.6480i	1.47402	−	2.39236i
$176$	−5.51202			−0.415484
$177$	−3.78034	−	6.54775i	−0.284148	−	0.492159i
$178$	−1.14930	+	1.99064i	−0.0861434	+	0.149205i
$179$	7.36309	−	12.7532i	0.550343	−	0.953222i	−0.447907	−	0.894080i	$-0.647830\pi$
$179$	7.36309	−	12.7532i	0.550343	−	0.953222i	0.998250	−	0.0591417i	$-0.0188364\pi$
$180$	−8.16426	−	14.1409i	−0.608528	−	1.05400i
$181$	−20.6446			−1.53450			−0.767251	−	0.641347i	$-0.778376\pi$
$181$	−20.6446			−1.53450			−0.767251	+	0.641347i	$0.778376\pi$
$182$	14.9839	+	27.7569i	1.11068	+	2.05748i
$183$	−5.92470			−0.437967
$184$	12.4498	+	21.5636i	0.917810	+	1.58969i
$185$	−14.9183	+	25.8392i	−1.09681	+	1.89974i
$186$	−3.89925	+	6.75370i	−0.285907	+	0.495205i
$187$	1.09643	+	1.89907i	0.0801789	+	0.138874i
$188$	0.686887			0.0500964
$189$	2.64467	+	0.0756600i	0.192371	+	0.00550346i
$190$	26.9779			1.95718
$191$	−8.66754	−	15.0126i	−0.627162	−	1.08628i	−0.988119	−	0.153693i	$-0.950883\pi$
$191$	−8.66754	−	15.0126i	−0.627162	−	1.08628i	0.360957	−	0.932582i	$-0.382450\pi$
$192$	−5.29397	+	9.16942i	−0.382059	+	0.661746i
$193$	0.280724	−	0.486229i	0.0202070	−	0.0349995i	−0.855745	−	0.517398i	$-0.826901\pi$
$193$	0.280724	−	0.486229i	0.0202070	−	0.0349995i	0.875952	+	0.482398i	$0.160234\pi$
$194$	7.70830	+	13.3512i	0.553423	+	0.958558i
$195$	−21.7172			−1.55520
$196$	−14.3690	+	21.8935i	−1.02636	+	1.56382i
$197$	−1.87318			−0.133459			−0.0667294	−	0.997771i	$-0.521256\pi$
$197$	−1.87318			−0.133459			−0.0667294	+	0.997771i	$0.521256\pi$
$198$	2.62711	+	4.55029i	0.186701	+	0.323375i
$199$	3.40899	−	5.90455i	0.241657	−	0.418562i	−0.719529	−	0.694462i	$-0.755642\pi$
$199$	3.40899	−	5.90455i	0.241657	−	0.418562i	0.961186	+	0.275900i	$0.0889758\pi$
$200$	−29.3068	+	50.7608i	−2.07230	+	3.58933i
$201$	0.801720	+	1.38862i	0.0565489	+	0.0979456i
$202$	−25.2048			−1.77340
$203$	22.7338	+	0.650379i	1.59560	+	0.0456476i
$204$	−3.74110			−0.261929
$205$	5.06464	+	8.77222i	0.353730	+	0.612678i
$206$	2.60245	−	4.50758i	0.181321	−	0.314058i
$207$	2.98429	−	5.16894i	0.207422	−	0.359266i
$208$	−6.25354	−	10.8315i	−0.433605	−	0.751026i
$209$	−5.65684			−0.391292
$210$	−13.1436	−	24.3479i	−0.906997	−	1.68017i
$211$	2.55589			0.175955			0.0879774	−	0.996122i	$-0.471960\pi$
$211$	2.55589			0.175955			0.0879774	+	0.996122i	$0.471960\pi$
$212$	5.34727	+	9.26174i	0.367252	+	0.636099i
$213$	−5.43913	+	9.42085i	−0.372683	+	0.645506i
$214$	−3.82896	+	6.63196i	−0.261743	+	0.453351i
$215$	−6.89228	−	11.9378i	−0.470050	−	0.814150i
$216$	−4.17178			−0.283853
$217$	−4.51709	+	7.33133i	−0.306640	+	0.497683i
$218$	−26.8128			−1.81599
$219$	4.18694	+	7.25200i	0.282927	+	0.490045i
$220$	17.9031	−	31.0090i	1.20703	−	2.09063i
$221$	−2.48786	+	4.30910i	−0.167352	+	0.289862i
$222$	8.18972	+	14.1850i	0.549658	+	0.952035i
$223$	19.1692			1.28366			0.641832	−	0.766845i	$-0.278175\pi$
$223$	19.1692			1.28366			0.641832	+	0.766845i	$0.278175\pi$
$224$	−3.22089	+	5.22757i	−0.215205	+	0.349282i
$225$	14.0500			0.936669
$226$	16.4901	+	28.5618i	1.09691	+	1.89990i
$227$	0.938026	−	1.62471i	0.0622589	−	0.107836i	−0.833216	−	0.552948i	$-0.813503\pi$
$227$	0.938026	−	1.62471i	0.0622589	−	0.107836i	0.895475	+	0.445112i	$0.146836\pi$
$228$	4.82539	−	8.35782i	0.319569	−	0.553510i
$229$	−2.89889	−	5.02103i	−0.191564	−	0.331799i	0.754205	−	0.656640i	$-0.228023\pi$
$229$	−2.89889	−	5.02103i	−0.191564	−	0.331799i	−0.945769	+	0.324840i	$0.894689\pi$
$230$	−62.4189			−4.11578
$231$	2.75601	+	5.10537i	0.181332	+	0.335909i
$232$	−35.8609			−2.35438
$233$	1.15626	+	2.00271i	0.0757493	+	0.131202i	0.901412	−	0.432963i	$-0.142532\pi$
$233$	1.15626	+	2.00271i	0.0757493	+	0.131202i	−0.825663	+	0.564164i	$0.809198\pi$
$234$	−5.96106	+	10.3249i	−0.389687	+	0.674958i
$235$	−0.400686	+	0.694008i	−0.0261379	+	0.0452721i
$236$	14.1426	+	24.4958i	0.920607	+	1.59454i
$237$	−7.10893			−0.461774
$238$	−6.33678	−	0.181286i	−0.410753	−	0.0117510i
$239$	−19.1330			−1.23761			−0.618805	−	0.785545i	$-0.712383\pi$
$239$	−19.1330			−1.23761			−0.618805	+	0.785545i	$0.712383\pi$
$240$	5.48552	+	9.50120i	0.354089	+	0.613300i
$241$	6.40283	−	11.0900i	0.412442	−	0.714371i	−0.582714	−	0.812677i	$-0.698009\pi$
$241$	6.40283	−	11.0900i	0.412442	−	0.714371i	0.995156	+	0.0983064i	$0.0313425\pi$
$242$	7.41744	−	12.8474i	0.476811	−	0.825861i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	22.1649			1.41896
$245$	−13.7386	−	27.2893i	−0.877724	−	1.74345i
$246$	5.56069			0.354536
$247$	−6.41785	−	11.1160i	−0.408358	−	0.707297i
$248$	6.78898	−	11.7589i	0.431101	−	0.746689i
$249$	−0.312562	+	0.541374i	−0.0198078	+	0.0343082i
$250$	−47.3223	−	81.9646i	−2.99292	−	5.18389i
$251$	21.7013			1.36977			0.684887	−	0.728649i	$-0.259852\pi$
$251$	21.7013			1.36977			0.684887	+	0.728649i	$0.259852\pi$
$252$	−9.89397	−	0.283052i	−0.623261	−	0.0178306i
$253$	13.0882			0.822851
$254$	−5.23943	−	9.07496i	−0.328751	−	0.569413i
$255$	2.18232	−	3.77988i	0.136662	−	0.236706i
$256$	14.2446	−	24.6723i	0.890285	−	1.54202i
$257$	8.34036	+	14.4459i	0.520257	+	0.901112i	0.999723	+	0.0235512i	$0.00749726\pi$
$257$	8.34036	+	14.4459i	0.520257	+	0.901112i	−0.479465	+	0.877561i	$0.659169\pi$
$258$	−7.56733			−0.471122
$259$	8.59155	+	15.9154i	0.533853	+	0.988936i
$260$	81.2462			5.03868
$261$	4.29803	+	7.44441i	0.266042	+	0.460798i
$262$	8.57266	−	14.8483i	0.529621	−	0.917330i
$263$	4.82913	−	8.36429i	0.297777	−	0.515764i	−0.677850	−	0.735200i	$-0.737088\pi$
$263$	4.82913	−	8.36429i	0.297777	−	0.515764i	0.975627	+	0.219436i	$0.0704216\pi$
$264$	−4.57406	−	7.92250i	−0.281514	−	0.487596i
$265$	−12.4770			−0.766457
$266$	8.57839	−	13.9229i	0.525975	−	0.853667i
$267$	−0.959322			−0.0587095
$268$	−2.99931	−	5.19496i	−0.183212	−	0.317333i
$269$	0.722251	−	1.25097i	0.0440364	−	0.0762733i	−0.843167	−	0.537652i	$-0.819312\pi$
$269$	0.722251	−	1.25097i	0.0440364	−	0.0762733i	0.887203	+	0.461378i	$0.152645\pi$
$270$	5.22896	−	9.05683i	0.318224	−	0.551181i
$271$	1.38122	+	2.39235i	0.0839032	+	0.145325i	0.904923	−	0.425575i	$-0.139928\pi$
$271$	1.38122	+	2.39235i	0.0839032	+	0.145325i	−0.821020	+	0.570899i	$0.806595\pi$
$272$	2.51362			0.152411
$273$	−6.90560	+	11.2079i	−0.417946	+	0.678334i
$274$	43.3390			2.61820
$275$	15.4049	+	26.6820i	0.928949	+	1.60899i
$276$	−11.1645	+	19.3375i	−0.672025	+	1.16398i
$277$	5.17139	−	8.95712i	0.310719	−	0.538181i	−0.667799	−	0.744341i	$-0.732764\pi$
$277$	5.17139	−	8.95712i	0.310719	−	0.538181i	0.978518	+	0.206160i	$0.0660969\pi$
$278$	−20.7807	−	35.9933i	−1.24635	−	2.15873i
$279$	−3.25472			−0.194855
$280$	22.8844	+	42.3922i	1.36760	+	2.53342i
$281$	1.78040			0.106210			0.0531048	−	0.998589i	$-0.483088\pi$
$281$	1.78040			0.106210			0.0531048	+	0.998589i	$0.483088\pi$
$282$	0.219965	+	0.380990i	0.0130987	+	0.0226877i
$283$	6.43481	−	11.1454i	0.382510	−	0.662526i	−0.608911	−	0.793239i	$-0.708393\pi$
$283$	6.43481	−	11.1454i	0.382510	−	0.662526i	0.991420	+	0.130713i	$0.0417265\pi$
$284$	20.3483	−	35.2443i	1.20745	−	2.09137i
$285$	5.62965	+	9.75083i	0.333471	+	0.577590i
$286$	−26.1435			−1.54590
$287$	6.13765	+	0.175589i	0.362294	+	0.0103647i
$288$	−2.32076			−0.136752
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	44.9485	−	77.8531i	2.63947	−	4.57169i
$291$	−3.21707	+	5.57213i	−0.188588	+	0.326644i
$292$	−15.6638	−	27.1304i	−0.916653	−	1.58769i
$293$	−21.5809			−1.26077			−0.630384	−	0.776283i	$-0.717103\pi$
$293$	−21.5809			−1.26077			−0.630384	+	0.776283i	$0.717103\pi$
$294$	−16.7450	−	0.958882i	−0.976587	−	0.0559232i
$295$	−32.9996			−1.92131
$296$	−14.2591	−	24.6975i	−0.828794	−	1.43551i
$297$	−1.09643	+	1.89907i	−0.0636213	+	0.110195i
$298$	−15.4023	+	26.6775i	−0.892230	+	1.54539i
$299$	14.8490	+	25.7192i	0.858739	+	1.48738i
$300$	−52.5626			−3.03470
$301$	−8.35250	−	0.238953i	−0.481430	−	0.0137730i
$302$	−16.3174			−0.938962
$303$	−5.25964	−	9.10997i	−0.302158	−	0.523354i
$304$	−3.24215	+	5.61557i	−0.185950	+	0.322075i
$305$	−12.9296	+	22.3947i	−0.740346	+	1.28232i
$306$	−1.19803	−	2.07505i	−0.0684868	−	0.118623i
$307$	−24.3141			−1.38768			−0.693840	−	0.720129i	$-0.744083\pi$
$307$	−24.3141			−1.38768			−0.693840	+	0.720129i	$0.744083\pi$
$308$	−10.3105	−	19.0997i	−0.587495	−	1.08831i
$309$	2.17228			0.123577
$310$	17.0188	+	29.4774i	0.966603	+	1.67421i
$311$	7.40974	−	12.8340i	0.420168	−	0.727752i	−0.575788	−	0.817599i	$-0.695305\pi$
$311$	7.40974	−	12.8340i	0.420168	−	0.727752i	0.995956	+	0.0898473i	$0.0286379\pi$
$312$	10.3788	−	17.9766i	0.587584	−	1.01773i
$313$	4.81325	+	8.33680i	0.272061	+	0.471224i	0.969389	−	0.245528i	$-0.0789614\pi$
$313$	4.81325	+	8.33680i	0.272061	+	0.471224i	−0.697328	+	0.716752i	$0.745628\pi$
$314$	17.3980			0.981828
$315$	6.05749	−	9.83143i	0.341301	−	0.553938i
$316$	26.5952			1.49610
$317$	11.4779	+	19.8803i	0.644663	+	1.11659i	0.984379	+	0.176061i	$0.0563358\pi$
$317$	11.4779	+	19.8803i	0.644663	+	1.11659i	−0.339716	+	0.940528i	$0.610331\pi$
$318$	−3.42476	+	5.93186i	−0.192051	+	0.332642i
$319$	−9.42498	+	16.3245i	−0.527698	+	0.913999i
$320$	23.1062	+	40.0211i	1.29168	+	2.23725i
$321$	−3.19605			−0.178386
$322$	−19.8478	+	32.2134i	−1.10608	+	1.79518i
$323$	2.57966			0.143536
$324$	−1.87055	−	3.23989i	−0.103919	−	0.179994i
$325$	−34.9545	+	60.5430i	−1.93893	+	3.35832i
$326$	3.75458	−	6.50313i	0.207947	−	0.360175i
$327$	−5.59519	−	9.69116i	−0.309415	−	0.535922i
$328$	−9.68170			−0.534583
$329$	0.230758	+	0.427467i	0.0127221	+	0.0235670i
$330$	22.9327			1.26241
$331$	−6.92669	−	11.9974i	−0.380725	−	0.659435i	0.610441	−	0.792062i	$-0.290992\pi$
$331$	−6.92669	−	11.9974i	−0.380725	−	0.659435i	−0.991166	+	0.132626i	$0.957659\pi$
$332$	1.16933	−	2.02533i	0.0641752	−	0.111155i
$333$	−3.41799	+	5.92014i	−0.187305	+	0.324422i
$334$	−25.5906	−	44.3242i	−1.40025	−	2.42531i
$335$	6.99843			0.382365
$336$	6.64770	+	0.190181i	0.362662	+	0.0103752i
$337$	24.5717			1.33850			0.669252	−	0.743035i	$-0.266615\pi$
$337$	24.5717			1.33850			0.669252	+	0.743035i	$0.266615\pi$
$338$	−14.0862	−	24.3981i	−0.766189	−	1.32708i
$339$	−6.88219	+	11.9203i	−0.373789	+	0.647422i
$340$	−8.16426	+	14.1409i	−0.442769	+	0.766899i
$341$	−3.56857	−	6.18095i	−0.193249	−	0.334717i
$342$	6.18103			0.334232
$343$	−18.4521	−	1.58713i	−0.996321	−	0.0856969i
$344$	13.1755			0.710374
$345$	−13.0253	−	22.5605i	−0.701260	−	1.21462i
$346$	−9.75199	+	16.8909i	−0.524270	+	0.908063i
$347$	11.5530	−	20.0104i	0.620197	−	1.07421i	−0.369251	−	0.929330i	$-0.620386\pi$
$347$	11.5530	−	20.0104i	0.620197	−	1.07421i	0.989449	−	0.144884i	$-0.0462808\pi$
$348$	−16.0794	−	27.8503i	−0.861945	−	1.49293i
$349$	20.4788			1.09621			0.548104	−	0.836410i	$-0.315350\pi$
$349$	20.4788			1.09621			0.548104	+	0.836410i	$0.315350\pi$
$350$	−89.0320	−	2.54707i	−4.75896	−	0.136147i
$351$	−4.97572			−0.265584
$352$	−2.54455	−	4.40730i	−0.135625	−	0.234910i
$353$	1.03754	−	1.79706i	0.0552224	−	0.0956481i	−0.837093	−	0.547061i	$-0.815747\pi$
$353$	1.03754	−	1.79706i	0.0552224	−	0.0956481i	0.892315	+	0.451413i	$0.149080\pi$
$354$	−9.05792	+	15.6888i	−0.481423	+	0.833850i
$355$	23.7398	+	41.1185i	1.25998	+	2.18235i
$356$	3.58892			0.190212
$357$	−1.25681	−	2.32818i	−0.0665175	−	0.123220i
$358$	−35.2848			−1.86486
$359$	−4.22642	−	7.32038i	−0.223062	−	0.386355i	0.732674	−	0.680580i	$-0.238272\pi$
$359$	−4.22642	−	7.32038i	−0.223062	−	0.386355i	−0.955736	+	0.294225i	$0.904939\pi$
$360$	−9.10414	+	15.7688i	−0.479830	+	0.831090i
$361$	6.17267	−	10.6914i	0.324877	−	0.562704i
$362$	24.7329	+	42.8386i	1.29993	+	2.25154i
$363$	6.19137			0.324963
$364$	25.8345	−	41.9299i	1.35410	−	2.19773i
$365$	36.5490			1.91306
$366$	7.09797	+	12.2940i	0.371017	+	0.642620i
$367$	12.8169	−	22.1995i	0.669035	−	1.15880i	−0.309139	−	0.951017i	$-0.600041\pi$
$367$	12.8169	−	22.1995i	0.669035	−	1.15880i	0.978174	−	0.207787i	$-0.0666259\pi$
$368$	7.50137	−	12.9928i	0.391036	−	0.677294i
$369$	1.16038	+	2.00984i	0.0604071	+	0.104628i
$370$	71.4902			3.71660
$371$	−3.96742	+	6.43920i	−0.205978	+	0.334306i
$372$	12.1762			0.631308
$373$	−3.38282	−	5.85921i	−0.175156	−	0.303379i	0.765059	−	0.643960i	$-0.222710\pi$
$373$	−3.38282	−	5.85921i	−0.175156	−	0.303379i	−0.940215	+	0.340581i	$0.889376\pi$
$374$	2.62711	−	4.55029i	0.135845	−	0.235290i
$375$	19.7500	−	34.2081i	1.01989	−	1.76650i
$376$	−0.382981	−	0.663342i	−0.0197507	−	0.0342093i
$377$	−42.7717			−2.20285
$378$	−3.01139	−	5.57846i	−0.154889	−	0.286925i
$379$	−20.6501			−1.06072			−0.530361	−	0.847772i	$-0.677944\pi$
$379$	−20.6501			−1.06072			−0.530361	+	0.847772i	$0.677944\pi$
$380$	−21.0611	−	36.4788i	−1.08041	−	1.87132i
$381$	2.18669	−	3.78745i	0.112027	−	0.194037i
$382$	−20.7679	+	35.9711i	−1.06258	+	1.84044i
$383$	−8.24800	−	14.2859i	−0.421453	−	0.729978i	0.574629	−	0.818414i	$-0.305146\pi$
$383$	−8.24800	−	14.2859i	−0.421453	−	0.729978i	−0.996082	+	0.0884362i	$0.971813\pi$
$384$	20.7278			1.05776
$385$	25.3122	+	0.724144i	1.29003	+	0.0369058i
$386$	−1.34526			−0.0684722
$387$	−1.57912	−	2.73512i	−0.0802712	−	0.139034i
$388$	12.0354	−	20.8459i	0.611004	−	1.05829i
$389$	−15.1210	+	26.1903i	−0.766665	+	1.32790i	0.172696	+	0.984975i	$0.444752\pi$
$389$	−15.1210	+	26.1903i	−0.766665	+	1.32790i	−0.939362	+	0.342928i	$0.888581\pi$
$390$	26.0179	+	45.0643i	1.31747	+	2.28192i
$391$	−5.96858			−0.301844
$392$	29.1547	+	1.66951i	1.47253	+	0.0843229i
$393$	7.15563			0.360954
$394$	2.24413	+	3.88695i	0.113058	+	0.195821i
$395$	−15.5139	+	26.8709i	−0.780591	+	1.35202i
$396$	4.10185	−	7.10461i	0.206126	−	0.357020i
$397$	−7.73265	−	13.3933i	−0.388090	−	0.672192i	0.604102	−	0.796907i	$-0.293532\pi$
$397$	−7.73265	−	13.3933i	−0.388090	−	0.672192i	−0.992193	+	0.124714i	$0.960199\pi$
$398$	−16.3363			−0.818864
$399$	6.82236	+	0.195177i	0.341545	+	0.00977110i
$400$	35.3165			1.76582
$401$	9.61275	+	16.6498i	0.480038	+	0.831450i	0.999738	−	0.0228989i	$-0.00728958\pi$
$401$	9.61275	+	16.6498i	0.480038	+	0.831450i	−0.519700	+	0.854349i	$0.673956\pi$
$402$	1.92097	−	3.32721i	0.0958092	−	0.165946i
$403$	8.09730	−	14.0249i	0.403355	−	0.698631i
$404$	19.6768	+	34.0813i	0.978959	+	1.69561i
$405$	4.36463			0.216880
$406$	−25.8861	−	47.9528i	−1.28471	−	2.37986i
$407$	−14.9904			−0.743045
$408$	2.08589	+	3.61286i	0.103267	+	0.178863i
$409$	14.3357	−	24.8302i	0.708857	−	1.22778i	−0.256424	−	0.966564i	$-0.582544\pi$
$409$	14.3357	−	24.8302i	0.708857	−	1.22778i	0.965281	−	0.261212i	$-0.0841222\pi$
$410$	12.1352	−	21.0187i	0.599314	−	1.03804i
$411$	9.04381	+	15.6643i	0.446098	+	0.772665i
$412$	−8.12670			−0.400374
$413$	−10.4932	+	17.0306i	−0.516335	+	0.838021i
$414$	−14.3011			−0.702859
$415$	1.36422	+	2.36290i	0.0669670	+	0.115990i
$416$	5.77374	−	10.0004i	0.283081	−	0.490310i
$417$	8.67288	−	15.0219i	0.424713	−	0.735624i
$418$	6.77706	+	11.7382i	0.331477	+	0.574135i
$419$	20.2899			0.991228			0.495614	−	0.868543i	$-0.334943\pi$
$419$	20.2899			0.991228			0.495614	+	0.868543i	$0.334943\pi$
$420$	−22.6617	+	36.7803i	−1.10578	+	1.79470i
$421$	−38.1649			−1.86004			−0.930022	−	0.367505i	$-0.880212\pi$
$421$	−38.1649			−1.86004			−0.930022	+	0.367505i	$0.880212\pi$
$422$	−3.06203	−	5.30359i	−0.149057	−	0.258175i
$423$	−0.0918028	+	0.159007i	−0.00446361	+	0.00773119i
$424$	5.96285	−	10.3280i	0.289581	−	0.501570i
$425$	−7.02502	−	12.1677i	−0.340763	−	0.590219i
$426$	26.0649			1.26285
$427$	7.44623	+	13.7938i	0.360349	+	0.667528i
$428$	11.9567			0.577951
$429$	−5.45553	−	9.44926i	−0.263395	−	0.456214i
$430$	−16.5143	+	28.6036i	−0.796391	+	1.37939i
$431$	−16.3906	+	28.3894i	−0.789509	+	1.36747i	0.136760	+	0.990604i	$0.456331\pi$
$431$	−16.3906	+	28.3894i	−0.789509	+	1.36747i	−0.926268	+	0.376865i	$0.877002\pi$
$432$	1.25681	+	2.17686i	0.0604684	+	0.104734i
$433$	4.92769			0.236809			0.118405	−	0.992965i	$-0.462222\pi$
$433$	4.92769			0.236809			0.118405	+	0.992965i	$0.462222\pi$
$434$	20.6245	+	0.590035i	0.990006	+	0.0283226i
$435$	37.5187			1.79888
$436$	20.9322	+	36.2556i	1.00247	+	1.73633i
$437$	7.69846	−	13.3341i	0.368267	−	0.637858i
$438$	10.0322	−	17.3762i	0.479355	−	0.830268i
$439$	−20.3065	−	35.1719i	−0.969177	−	1.67866i	−0.697947	−	0.716149i	$-0.745903\pi$
$439$	−20.3065	−	35.1719i	−0.969177	−	1.67866i	−0.271229	−	0.962515i	$-0.587430\pi$
$440$	−39.9282			−1.90350
$441$	−3.14770	−	6.25236i	−0.149890	−	0.297731i
$442$	11.9221			0.567078
$443$	16.5925	+	28.7390i	0.788333	+	1.36543i	0.926988	+	0.375092i	$0.122389\pi$
$443$	16.5925	+	28.7390i	0.788333	+	1.36543i	−0.138655	+	0.990341i	$0.544278\pi$
$444$	12.7871	−	22.1478i	0.606847	−	1.05109i
$445$	−2.09354	+	3.62613i	−0.0992435	+	0.171895i
$446$	−22.9652	−	39.7770i	−1.08744	−	1.88349i
$447$	−12.8563			−0.608084
$448$	28.0016	+	0.801083i	1.32295	+	0.0378476i
$449$	−1.65248			−0.0779855			−0.0389928	−	0.999239i	$-0.512415\pi$
$449$	−1.65248			−0.0779855			−0.0389928	+	0.999239i	$0.512415\pi$
$450$	−16.8324	−	29.1545i	−0.793485	−	1.37436i
$451$	−2.54455	+	4.40730i	−0.119818	+	0.207531i
$452$	25.7470	−	44.5951i	1.21104	−	2.09757i
$453$	−3.40505	−	5.89773i	−0.159983	−	0.277099i
$454$	−4.49513			−0.210967
$455$	27.2944	+	50.5616i	1.27958	+	2.37036i
$456$	−10.7618			−0.503967
$457$	−16.8113	−	29.1180i	−0.786400	−	1.36208i	−0.928159	−	0.372183i	$-0.878609\pi$
$457$	−16.8113	−	29.1180i	−0.786400	−	1.36208i	0.141759	−	0.989901i	$-0.454724\pi$
$458$	−6.94592	+	12.0307i	−0.324562	+	0.562157i
$459$	0.500000	−	0.866025i	0.0233380	−	0.0404226i
$460$	48.7290	+	84.4011i	2.27200	+	3.93522i
$461$	2.06554			0.0962018			0.0481009	−	0.998842i	$-0.484683\pi$
$461$	2.06554			0.0962018			0.0481009	+	0.998842i	$0.484683\pi$
$462$	7.29211	−	11.8352i	0.339260	−	0.550625i
$463$	20.3132			0.944034			0.472017	−	0.881590i	$-0.343526\pi$
$463$	20.3132			0.944034			0.472017	+	0.881590i	$0.343526\pi$
$464$	10.8036	+	18.7124i	0.501546	+	0.868703i
$465$	−7.10283	+	12.3025i	−0.329386	+	0.570513i
$466$	2.77048	−	4.79860i	0.128340	−	0.222291i
$467$	−6.02188	−	10.4302i	−0.278659	−	0.482652i	0.692392	−	0.721521i	$-0.256557\pi$
$467$	−6.02188	−	10.4302i	−0.278659	−	0.482652i	−0.971052	+	0.238869i	$0.923223\pi$
$468$	18.6147			0.860464
$469$	2.22535	−	3.61178i	0.102757	−	0.166777i
$470$	1.92013			0.0885691
$471$	3.63055	+	6.28830i	0.167287	+	0.289750i
$472$	15.7707	−	27.3157i	0.725907	−	1.25731i
$473$	3.46279	−	5.99773i	0.159219	−	0.275776i
$474$	8.51670	+	14.7514i	0.391185	+	0.677552i
$475$	36.2444			1.66301
$476$	4.70185	+	8.70995i	0.215509	+	0.399220i
$477$	−2.85866			−0.130889
$478$	22.9219	+	39.7019i	1.04842	+	1.81592i
$479$	−0.106277	+	0.184077i	−0.00485591	+	0.00841069i	−0.868443	−	0.495789i	$-0.834879\pi$
$479$	−0.106277	+	0.184077i	−0.00485591	+	0.00841069i	0.863587	+	0.504199i	$0.168212\pi$
$480$	−5.06464	+	8.77222i	−0.231168	+	0.400395i
$481$	−17.0070	−	29.4570i	−0.775452	−	1.34312i
$482$	−30.6831			−1.39758
$483$	−15.7849	−	0.451583i	−0.718238	−	0.0205477i
$484$	−23.1625			−1.05284
$485$	14.0413	+	24.3203i	0.637585	+	1.10433i
$486$	1.19803	−	2.07505i	0.0543437	−	0.0941261i
$487$	17.3209	−	30.0006i	0.784883	−	1.35946i	−0.144186	−	0.989551i	$-0.546056\pi$
$487$	17.3209	−	30.0006i	0.784883	−	1.35946i	0.929069	−	0.369906i	$-0.120610\pi$
$488$	−12.3583	−	21.4051i	−0.559432	−	0.968965i
$489$	3.13396			0.141723
$490$	−40.1673	+	61.2015i	−1.81457	+	2.76480i
$491$	−26.4747			−1.19479			−0.597394	−	0.801948i	$-0.703797\pi$
$491$	−26.4747			−1.19479			−0.597394	+	0.801948i	$0.703797\pi$
$492$	−4.34110	−	7.51901i	−0.195712	−	0.338983i
$493$	4.29803	−	7.44441i	0.193574	−	0.335279i
$494$	−15.3775	+	26.6347i	−0.691868	+	1.19835i
$495$	4.78551	+	8.28875i	0.215093	+	0.372552i
$496$	−8.18114			−0.367344
$497$	28.7694	+	0.823049i	1.29048	+	0.0369188i
$498$	1.49784			0.0671196
$499$	14.7664	+	25.5762i	0.661036	+	1.14495i	0.980344	+	0.197296i	$0.0632161\pi$
$499$	14.7664	+	25.5762i	0.661036	+	1.14495i	−0.319308	+	0.947651i	$0.603451\pi$
$500$	−73.8868	+	127.976i	−3.30432	+	5.72325i
$501$	10.6803	−	18.4988i	0.477160	−	0.826465i
$502$	−25.9988	−	45.0312i	−1.16038	−	2.00984i
$503$	36.7527			1.63872			0.819361	−	0.573277i	$-0.194328\pi$
$503$	36.7527			1.63872			0.819361	+	0.573277i	$0.194328\pi$
$504$	5.24313	+	9.71265i	0.233548	+	0.432636i
$505$	−45.9128			−2.04309
$506$	−15.6801	−	27.1587i	−0.697066	−	1.20735i
$507$	5.87891	−	10.1826i	0.261092	−	0.452224i
$508$	−8.18061	+	14.1692i	−0.362956	+	0.628658i
$509$	−0.494132	−	0.855862i	−0.0219020	−	0.0379354i	0.854867	−	0.518848i	$-0.173639\pi$
$509$	−0.494132	−	0.855862i	−0.0219020	−	0.0379354i	−0.876769	+	0.480912i	$0.840306\pi$
$510$	−10.4579			−0.463085
$511$	11.6218	−	18.8624i	0.514117	−	0.834421i
$512$	−26.8061			−1.18467
$513$	1.28983	+	2.23406i	0.0569475	+	0.0986359i
$514$	19.9840	−	34.6133i	0.881456	−	1.52673i
$515$	4.74060	−	8.21096i	0.208896	−	0.361818i
$516$	5.90765	+	10.2323i	0.260070	+	0.450454i
$517$	−0.402621			−0.0177073
$518$	22.7323	−	36.8950i	0.998801	−	1.62107i
$519$	−8.14003			−0.357307
$520$	−45.2997	−	78.4613i	−1.98652	−	3.44076i
$521$	−15.8889	+	27.5204i	−0.696107	+	1.20569i	0.273700	+	0.961815i	$0.411753\pi$
$521$	−15.8889	+	27.5204i	−0.696107	+	1.20569i	−0.969806	+	0.243877i	$0.921581\pi$
$522$	10.2983	−	17.8372i	0.450746	−	0.780715i
$523$	−18.2958	−	31.6892i	−0.800018	−	1.38567i	−0.919604	−	0.392847i	$-0.871490\pi$
$523$	−18.2958	−	31.6892i	−0.800018	−	1.38567i	0.119586	−	0.992824i	$-0.461843\pi$
$524$	−26.7699			−1.16945
$525$	−17.6582	−	32.7110i	−0.770669	−	1.42763i
$526$	−23.1417			−1.00903
$527$	1.62736	+	2.81867i	0.0708889	+	0.122783i
$528$	−2.75601	+	4.77355i	−0.119940	+	0.207742i
$529$	−6.31194	+	10.9326i	−0.274432	+	0.475331i
$530$	14.9478	+	25.8904i	0.649292	+	1.12461i
$531$	−7.56069			−0.328106
$532$	−25.5231	−	0.730178i	−1.10657	−	0.0316572i
$533$	−11.5475			−0.500177
$534$	1.14930	+	1.99064i	0.0497349	+	0.0861434i
$535$	−6.97480	+	12.0807i	−0.301547	+	0.522294i
$536$	−3.34459	+	5.79301i	−0.144464	+	0.250220i
$537$	−7.36309	−	12.7532i	−0.317741	−	0.550343i
$538$	−3.46111			−0.149219
$539$	8.42245	−	12.8330i	0.362780	−	0.552755i
$540$	−16.3285			−0.702668
$541$	11.1998	+	19.3987i	0.481518	+	0.834014i	0.999775	−	0.0212110i	$-0.00675217\pi$
$541$	11.1998	+	19.3987i	0.481518	+	0.834014i	−0.518257	+	0.855225i	$0.673419\pi$
$542$	3.30949	−	5.73220i	0.142155	−	0.246219i
$543$	−10.3223	+	17.8788i	−0.442972	+	0.767251i
$544$	1.16038	+	2.00984i	0.0497510	+	0.0861712i
$545$	−48.8419			−2.09216
$546$	31.5301	+	0.902028i	1.34936	+	0.0386033i
$547$	−7.71216			−0.329748			−0.164874	−	0.986315i	$-0.552722\pi$
$547$	−7.71216			−0.329748			−0.164874	+	0.986315i	$0.552722\pi$
$548$	−33.8338	−	58.6018i	−1.44531	−	2.50335i
$549$	−2.96235	+	5.13094i	−0.126430	+	0.218983i
$550$	36.9110	−	63.9317i	1.57389	−	2.72606i
$551$	11.0875	+	19.2041i	0.472343	+	0.818122i
$552$	24.8996			1.05980
$553$	8.93458	+	16.5509i	0.379937	+	0.703814i
$554$	−24.7819			−1.05288
$555$	14.9183	+	25.8392i	0.633246	+	1.09681i
$556$	−32.4461	+	56.1983i	−1.37602	+	2.38334i
$557$	16.6240	−	28.7937i	0.704383	−	1.22003i	−0.262531	−	0.964924i	$-0.584557\pi$
$557$	16.6240	−	28.7937i	0.704383	−	1.22003i	0.966914	−	0.255104i	$-0.0821096\pi$
$558$	3.89925	+	6.75370i	0.165068	+	0.285907i
$559$	15.7145			0.664654
$560$	15.2262	−	24.7125i	0.643426	−	1.04429i
$561$	2.19286			0.0925826
$562$	−2.13297	−	3.69441i	−0.0899739	−	0.155839i
$563$	−10.6025	+	18.3640i	−0.446841	+	0.773952i	−0.998178	−	0.0603305i	$-0.980785\pi$
$563$	−10.6025	+	18.3640i	−0.446841	+	0.773952i	0.551337	+	0.834283i	$0.314118\pi$
$564$	0.343443	−	0.594861i	0.0144616	−	0.0250482i
$565$	30.0383	+	52.0278i	1.26372	+	2.18883i
$566$	−30.8364			−1.29615
$567$	1.38786	−	2.25252i	0.0582846	−	0.0945970i
$568$	−45.3816			−1.90417
$569$	10.7030	+	18.5381i	0.448691	+	0.777156i	0.998301	−	0.0582653i	$-0.0185569\pi$
$569$	10.7030	+	18.5381i	0.448691	+	0.777156i	−0.549610	+	0.835421i	$0.685224\pi$
$570$	13.4890	−	23.3636i	0.564991	−	0.978592i
$571$	−1.25694	+	2.17709i	−0.0526014	+	0.0911083i	−0.891127	−	0.453754i	$-0.850085\pi$
$571$	−1.25694	+	2.17709i	−0.0526014	+	0.0911083i	0.838526	+	0.544862i	$0.183418\pi$
$572$	20.4097	+	35.3506i	0.853371	+	1.47808i
$573$	−17.3351			−0.724184
$574$	−6.98873	−	12.9463i	−0.291704	−	0.540367i
$575$	−83.8587			−3.49715
$576$	5.29397	+	9.16942i	0.220582	+	0.382059i
$577$	−12.7436	+	22.0726i	−0.530523	+	0.918893i	0.468843	+	0.883282i	$0.344671\pi$
$577$	−12.7436	+	22.0726i	−0.530523	+	0.918893i	−0.999366	+	0.0356110i	$0.988662\pi$
$578$	−1.19803	+	2.07505i	−0.0498315	+	0.0863106i
$579$	−0.280724	−	0.486229i	−0.0116665	−	0.0202070i
$580$	−140.361			−5.82818
$581$	1.65325	+	0.0472970i	0.0685883	+	0.00196221i
$582$	15.4166			0.639038
$583$	−3.13432	−	5.42880i	−0.129810	−	0.224838i
$584$	−17.4670	+	30.2537i	−0.722789	+	1.25191i
$585$	−10.8586	+	18.8077i	−0.448948	+	0.777601i
$586$	25.8545	+	44.7814i	1.06804	+	1.84990i
$587$	−6.39447			−0.263928			−0.131964	−	0.991255i	$-0.542128\pi$
$587$	−6.39447			−0.263928			−0.131964	+	0.991255i	$0.542128\pi$
$588$	11.7759	+	23.3907i	0.485628	+	0.964616i
$589$	−8.39609			−0.345955
$590$	39.5345	+	68.4758i	1.62761	+	2.81910i
$591$	−0.936592	+	1.62222i	−0.0385262	+	0.0667294i
$592$	−8.59155	+	14.8810i	−0.353110	+	0.611605i
$593$	5.98440	+	10.3653i	0.245750	+	0.425651i	0.962342	−	0.271841i	$-0.0876325\pi$
$593$	5.98440	+	10.3653i	0.245750	+	0.425651i	−0.716592	+	0.697492i	$0.754299\pi$
$594$	5.25422			0.215583
$595$	−11.5430	−	0.330228i	−0.473217	−	0.0135380i
$596$	48.0969			1.97012
$597$	−3.40899	−	5.90455i	−0.139521	−	0.241657i
$598$	35.5791	−	61.6247i	1.45494	−	2.52002i
$599$	1.76721	−	3.06089i	0.0722061	−	0.125065i	−0.827662	−	0.561227i	$-0.810329\pi$
$599$	1.76721	−	3.06089i	0.0722061	−	0.125065i	0.899868	+	0.436163i	$0.143663\pi$
$600$	29.3068	+	50.7608i	1.19644	+	2.07230i
$601$	−42.9126			−1.75044			−0.875222	−	0.483722i	$-0.839284\pi$
$601$	−42.9126			−1.75044			−0.875222	+	0.483722i	$0.839284\pi$
$602$	9.51071	+	17.6181i	0.387628	+	0.718061i
$603$	1.60344			0.0652971
$604$	12.7386	+	22.0640i	0.518328	+	0.897771i
$605$	13.5115	−	23.4027i	0.549322	−	0.951453i
$606$	−12.6024	+	21.8280i	−0.511938	+	0.886702i
$607$	13.4819	+	23.3513i	0.547213	+	0.947801i	0.998464	+	0.0554040i	$0.0176447\pi$
$607$	13.4819	+	23.3513i	0.547213	+	0.947801i	−0.451251	+	0.892397i	$0.649022\pi$
$608$	−5.98679			−0.242796
$609$	11.9301	−	19.3628i	0.483433	−	0.784621i
$610$	61.9601			2.50869
$611$	−0.456785	−	0.791175i	−0.0184796	−	0.0320075i
$612$	−1.87055	+	3.23989i	−0.0756125	+	0.130965i
$613$	−5.29975	+	9.17944i	−0.214055	+	0.370754i	−0.952980	−	0.303034i	$-0.902000\pi$
$613$	−5.29975	+	9.17944i	−0.214055	+	0.370754i	0.738925	+	0.673788i	$0.235334\pi$
$614$	29.1290	+	50.4530i	1.17555	+	2.03612i
$615$	10.1293			0.408452
$616$	−12.6963	+	20.6063i	−0.511548	+	0.830252i
$617$	23.5671			0.948775			0.474388	−	0.880316i	$-0.342670\pi$
$617$	23.5671			0.948775			0.474388	+	0.880316i	$0.342670\pi$
$618$	−2.60245	−	4.50758i	−0.104686	−	0.181321i
$619$	4.84300	−	8.38832i	0.194657	−	0.337155i	−0.752131	−	0.659013i	$-0.770974\pi$
$619$	4.84300	−	8.38832i	0.194657	−	0.337155i	0.946788	+	0.321858i	$0.104307\pi$
$620$	26.5724	−	46.0247i	1.06717	−	1.84840i
$621$	−2.98429	−	5.16894i	−0.119755	−	0.207422i
$622$	−35.5083			−1.42375
$623$	1.20569	+	2.23347i	0.0483048	+	0.0894823i
$624$	−12.5071			−0.500684
$625$	−51.0766	−	88.4673i	−2.04306	−	3.53869i
$626$	11.5328	−	19.9755i	0.460945	−	0.798380i
$627$	−2.82842	+	4.89897i	−0.112956	+	0.195646i
$628$	−13.5823	−	23.5252i	−0.541991	−	0.938756i
$629$	6.83599			0.272569
$630$	−27.6577	−	0.791247i	−1.10191	−	0.0315240i
$631$	43.5486			1.73364			0.866822	−	0.498618i	$-0.166159\pi$
$631$	43.5486			1.73364			0.866822	+	0.498618i	$0.166159\pi$
$632$	−14.8284	−	25.6836i	−0.589843	−	1.02164i
$633$	1.27794	−	2.21347i	0.0507938	−	0.0879774i
$634$	27.5017	−	47.6344i	1.09223	−	1.89180i
$635$	−9.54408	−	16.5308i	−0.378745	−	0.656006i
$636$	10.6945			0.424066
$637$	34.7731	+	1.99124i	1.37776	+	0.0788959i
$638$	45.1656			1.78812
$639$	5.43913	+	9.42085i	0.215169	+	0.372683i
$640$	45.2346	−	78.3486i	1.78805	−	3.09700i
$641$	−2.92920	+	5.07352i	−0.115696	+	0.200392i	−0.918058	−	0.396446i	$-0.870243\pi$
$641$	−2.92920	+	5.07352i	−0.115696	+	0.200392i	0.802361	+	0.596838i	$0.203577\pi$
$642$	3.82896	+	6.63196i	0.151117	+	0.261743i
$643$	23.5636			0.929257			0.464629	−	0.885506i	$-0.346188\pi$
$643$	23.5636			0.929257			0.464629	+	0.885506i	$0.346188\pi$
$644$	59.0529	+	1.68941i	2.32701	+	0.0665723i
$645$	−13.7846			−0.542767
$646$	−3.09051	−	5.35293i	−0.121595	−	0.210608i
$647$	6.14288	−	10.6398i	0.241502	−	0.418293i	−0.719641	−	0.694347i	$-0.755693\pi$
$647$	6.14288	−	10.6398i	0.241502	−	0.418293i	0.961142	+	0.276054i	$0.0890268\pi$
$648$	−2.08589	+	3.61286i	−0.0819414	+	0.141927i
$649$	−8.28976	−	14.3583i	−0.325401	−	0.563612i
$650$	167.506			6.57014
$651$	4.09057	+	7.57758i	0.160322	+	0.296989i
$652$	−11.7245			−0.459166
$653$	9.69477	+	16.7918i	0.379386	+	0.657116i	0.990973	−	0.134061i	$-0.0428020\pi$
$653$	9.69477	+	16.7918i	0.379386	+	0.657116i	−0.611587	+	0.791177i	$0.709469\pi$
$654$	−13.4064	+	23.2206i	−0.524232	+	0.907997i
$655$	15.6159	−	27.0475i	0.610162	−	1.05683i
$656$	2.91676	+	5.05198i	0.113880	+	0.197247i
$657$	8.37389			0.326696
$658$	0.610560	−	0.990951i	0.0238021	−	0.0386313i
$659$	3.43238			0.133707			0.0668533	−	0.997763i	$-0.478704\pi$
$659$	3.43238			0.133707			0.0668533	+	0.997763i	$0.478704\pi$
$660$	−17.9031	−	31.0090i	−0.696876	−	1.20703i
$661$	−6.29680	+	10.9064i	−0.244917	+	0.424209i	−0.962108	−	0.272668i	$-0.912094\pi$
$661$	−6.29680	+	10.9064i	−0.244917	+	0.424209i	0.717191	+	0.696876i	$0.245427\pi$
$662$	−16.5968	+	28.7464i	−0.645051	+	1.11726i
$663$	2.48786	+	4.30910i	0.0966205	+	0.167352i
$664$	−2.60788			−0.101205
$665$	15.6263	−	25.3618i	0.605962	−	0.983488i
$666$	16.3794			0.634690
$667$	−25.6531	−	44.4325i	−0.993293	−	1.72043i
$668$	−39.9560	+	69.2058i	−1.54594	+	2.67765i
$669$	9.58459	−	16.6010i	0.370562	−	0.641832i
$670$	−8.38432	−	14.5221i	−0.323915	−	0.561037i
$671$	−12.9920			−0.501552
$672$	2.91676	+	5.40316i	0.112517	+	0.208431i
$673$	26.6163			1.02598			0.512992	−	0.858393i	$-0.328537\pi$
$673$	26.6163			1.02598			0.512992	+	0.858393i	$0.328537\pi$
$674$	−29.4376	−	50.9874i	−1.13389	−	1.96396i
$675$	7.02502	−	12.1677i	0.270393	−	0.468334i
$676$	−21.9936	+	38.0940i	−0.845907	+	1.46515i
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	0.802600	−	0.596518i	$-0.203449\pi$
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	−0.917899	+	0.396813i	$0.870116\pi$
$678$	32.9803			1.26660
$679$	17.0162	+	0.486808i	0.653021	+	0.0186820i
$680$	18.2083			0.698255
$681$	−0.938026	−	1.62471i	−0.0359452	−	0.0622589i
$682$	−8.55051	+	14.8099i	−0.327416	+	0.567101i
$683$	−18.7560	+	32.4863i	−0.717678	+	1.24305i	0.244240	+	0.969715i	$0.421462\pi$
$683$	−18.7560	+	32.4863i	−0.717678	+	1.24305i	−0.961918	+	0.273340i	$0.911872\pi$
$684$	−4.82539	−	8.35782i	−0.184503	−	0.319569i
$685$	78.9458			3.01637
$686$	18.8128	+	40.1905i	0.718277	+	1.53448i
$687$	−5.79779			−0.221199
$688$	−3.96931	−	6.87505i	−0.151329	−	0.262109i
$689$	7.11196	−	12.3183i	0.270944	−	0.469289i
$690$	−31.2094	+	54.0563i	−1.18812	+	2.05789i
$691$	12.5446	+	21.7279i	0.477219	+	0.826567i	0.999659	−	0.0261090i	$-0.00831169\pi$
$691$	12.5446	+	21.7279i	0.477219	+	0.826567i	−0.522441	+	0.852676i	$0.674978\pi$
$692$	30.4526			1.15764
$693$	5.79939	+	0.165912i	0.220300	+	0.00630247i
$694$	−55.3633			−2.10156
$695$	−37.8539	−	65.5649i	−1.43588	−	2.48702i
$696$	−17.9304	+	31.0564i	−0.679651	+	1.17719i
$697$	1.16038	−	2.00984i	0.0439526	−	0.0761281i
$698$	−24.5343	−	42.4946i	−0.928635	−	1.60844i
$699$	2.31253			0.0874678
$700$	66.0612	+	122.375i	2.49688	+	4.62535i
$701$	−8.29504			−0.313300			−0.156650	−	0.987654i	$-0.550069\pi$
$701$	−8.29504			−0.313300			−0.156650	+	0.987654i	$0.550069\pi$
$702$	5.96106	+	10.3249i	0.224986	+	0.389687i
$703$	−8.81728	+	15.2720i	−0.332550	+	0.575993i
$704$	−11.6089	+	20.1072i	−0.437528	+	0.757820i
$705$	0.400686	+	0.694008i	0.0150907	+	0.0261379i
$706$	−4.97199			−0.187123
$707$	−14.5993	+	23.6949i	−0.549062	+	0.891138i
$708$	28.2853			1.06303
$709$	9.63068	+	16.6808i	0.361688	+	0.626462i	0.988239	−	0.152919i	$-0.0488673\pi$
$709$	9.63068	+	16.6808i	0.361688	+	0.626462i	−0.626551	+	0.779381i	$0.715534\pi$
$710$	56.8820	−	98.5225i	2.13474	−	3.69748i
$711$	−3.55446	+	6.15651i	−0.133303	+	0.230887i
$712$	−2.00104	−	3.46590i	−0.0749921	−	0.129890i
$713$	19.4260			0.727511
$714$	−3.32539	+	5.39717i	−0.124450	+	0.201984i
$715$	−47.6228			−1.78099
$716$	27.5460	+	47.7111i	1.02944	+	1.78305i
$717$	−9.56650	+	16.5697i	−0.357267	+	0.618805i
$718$	−10.1268	+	17.5401i	−0.377927	+	0.654589i
$719$	−21.7489	−	37.6702i	−0.811098	−	1.40486i	−0.912096	−	0.409976i	$-0.865537\pi$
$719$	−21.7489	−	37.6702i	−0.811098	−	1.40486i	0.100998	−	0.994887i	$-0.467796\pi$
$720$	10.9710			0.408867
$721$	−2.73014	−	5.05745i	−0.101676	−	0.188349i
$722$	−29.5801			−1.10086
$723$	−6.40283	−	11.0900i	−0.238124	−	0.412442i
$724$	38.6168	−	66.8862i	1.43518	−	2.48581i
$725$	60.3875	−	104.594i	2.24274	−	3.88453i
$726$	−7.41744	−	12.8474i	−0.275287	−	0.476811i
$727$	9.10836			0.337810			0.168905	−	0.985632i	$-0.445977\pi$
$727$	9.10836			0.337810			0.168905	+	0.985632i	$0.445977\pi$
$728$	−54.8970	−	1.57052i	−2.03462	−	0.0582074i
$729$	1.00000			0.0370370
$730$	−43.7867	−	75.8408i	−1.62062	−	2.80700i
$731$	−1.57912	+	2.73512i	−0.0584059	+	0.101162i
$732$	11.0825	−	19.1954i	0.409619	−	0.709481i
$733$	−15.9462	−	27.6197i	−0.588987	−	1.02016i	−0.994365	−	0.106007i	$-0.966194\pi$
$733$	−15.9462	−	27.6197i	−0.588987	−	1.02016i	0.405378	−	0.914149i	$-0.367140\pi$
$734$	−61.4200			−2.26705
$735$	−30.5025	−	1.74669i	−1.12510	−	0.0644276i
$736$	13.8517			0.510579
$737$	1.75806	+	3.04505i	0.0647589	+	0.112166i
$738$	2.78034	−	4.81570i	0.102346	−	0.177268i
$739$	−23.8982	+	41.3928i	−0.879108	+	1.52266i	−0.0267867	+	0.999641i	$0.508527\pi$
$739$	−23.8982	+	41.3928i	−0.879108	+	1.52266i	−0.852321	+	0.523019i	$0.824806\pi$
$740$	−55.8108	−	96.6672i	−2.05165	−	3.55356i
$741$	−12.8357			−0.471531
$742$	18.1147	+	0.518235i	0.665012	+	0.0190250i
$743$	9.63256			0.353385			0.176692	−	0.984266i	$-0.443460\pi$
$743$	9.63256			0.353385			0.176692	+	0.984266i	$0.443460\pi$
$744$	−6.78898	−	11.7589i	−0.248896	−	0.431101i
$745$	−28.0566	+	48.5955i	−1.02792	+	1.78040i
$746$	−8.10543	+	14.0390i	−0.296761	+	0.514005i
$747$	0.312562	+	0.541374i	0.0114361	+	0.0198078i
$748$	−8.20370			−0.299957
$749$	4.01683	+	7.44099i	0.146772	+	0.271888i
$750$	−94.6445			−3.45593
$751$	−6.83617	−	11.8406i	−0.249455	−	0.432069i	0.713919	−	0.700228i	$-0.246918\pi$
$751$	−6.83617	−	11.8406i	−0.249455	−	0.432069i	−0.963375	+	0.268159i	$0.913585\pi$
$752$	−0.230758	+	0.399684i	−0.00841486	+	0.0145750i
$753$	10.8506	−	18.7939i	0.395420	−	0.684887i
$754$	51.2417	+	88.7532i	1.86611	+	3.23220i
$755$	−29.7236			−1.08175
$756$	−5.19211	+	8.42690i	−0.188835	+	0.306483i
$757$	−6.75888			−0.245656			−0.122828	−	0.992428i	$-0.539196\pi$
$757$	−6.75888			−0.245656			−0.122828	+	0.992428i	$0.539196\pi$
$758$	24.7394	+	42.8499i	0.898575	+	1.55638i
$759$	6.54412	−	11.3348i	0.237537	−	0.411425i
$760$	−23.4856	+	40.6783i	−0.851913	+	1.47556i
$761$	−24.3809	−	42.2289i	−0.883805	−	1.53080i	−0.847077	−	0.531470i	$-0.821640\pi$
$761$	−24.3809	−	42.2289i	−0.883805	−	1.53080i	−0.0367281	−	0.999325i	$-0.511694\pi$
$762$	−10.4789			−0.379609
$763$	−15.5307	+	25.2066i	−0.562248	+	0.912539i
$764$	64.8523			2.34627
$765$	−2.18232	−	3.77988i	−0.0789018	−	0.136662i
$766$	−19.7627	+	34.2300i	−0.714055	+	1.23678i
$767$	18.8099	−	32.5798i	0.679188	−	1.17639i
$768$	−14.2446	−	24.6723i	−0.514006	−	0.890285i
$769$	−5.85163			−0.211015			−0.105508	−	0.994419i	$-0.533647\pi$
$769$	−5.85163			−0.211015			−0.105508	+	0.994419i	$0.533647\pi$
$770$	−28.8221	−	53.3916i	−1.03868	−	1.92410i
$771$	16.6807			0.600741
$772$	1.05022	+	1.81903i	0.0377982	+	0.0654683i
$773$	−4.54763	+	7.87672i	−0.163567	+	0.283306i	−0.936145	−	0.351613i	$-0.885633\pi$
$773$	−4.54763	+	7.87672i	−0.163567	+	0.283306i	0.772579	+	0.634919i	$0.218967\pi$
$774$	−3.78367	+	6.55350i	−0.136001	+	0.235561i
$775$	22.8645	+	39.6024i	0.821316	+	1.42256i
$776$	−26.8418			−0.963565
$777$	18.0789	+	0.517211i	0.648578	+	0.0185548i
$778$	72.4616			2.59788
$779$	2.99340	+	5.18471i	0.107250	+	0.185762i
$780$	40.6231	−	70.3613i	1.45454	−	2.51934i
$781$	−11.9272	+	20.6586i	−0.426790	+	0.739222i
$782$	7.15053	+	12.3851i	0.255702	+	0.442890i
$783$	8.59607			0.307198
$784$	−7.91213	−	15.7161i	−0.282576	−	0.561288i
$785$	31.6921			1.13114
$786$	−8.57266	−	14.8483i	−0.305777	−	0.529621i
$787$	−3.76255	+	6.51693i	−0.134120	+	0.232303i	−0.925261	−	0.379331i	$-0.876154\pi$
$787$	−3.76255	+	6.51693i	−0.134120	+	0.232303i	0.791141	+	0.611634i	$0.209488\pi$
$788$	3.50388	−	6.06890i	0.124821	−	0.216196i
$789$	−4.82913	−	8.36429i	−0.171921	−	0.297777i
$790$	74.3446			2.64506
$791$	36.4023	+	1.04141i	1.29432	+	0.0370284i
$792$	−9.14811			−0.325064
$793$	−14.7398	−	25.5302i	−0.523427	−	0.906603i
$794$	−18.5279	+	32.0912i	−0.657530	+	1.13888i
$795$	−6.23851	+	10.8054i	−0.221257	+	0.383228i
$796$	12.7534	+	22.0895i	0.452031	+	0.782941i
$797$	26.6126			0.942666			0.471333	−	0.881955i	$-0.343773\pi$
$797$	26.6126			0.942666			0.471333	+	0.881955i	$0.343773\pi$
$798$	−7.76839	−	14.3906i	−0.274998	−	0.509420i
$799$	0.183606			0.00649550
$800$	16.3034	+	28.2383i	0.576412	+	0.998375i
$801$	−0.479661	+	0.830797i	−0.0169480	+	0.0293548i
$802$	23.0327	−	39.8938i	0.813314	−	1.40870i
$803$	9.18138	+	15.9026i	0.324004	+	0.561191i
$804$	−5.99862			−0.211555
$805$	−36.1546	+	58.6796i	−1.27428	+	2.06819i
$806$	−38.8032			−1.36678
$807$	−0.722251	−	1.25097i	−0.0254244	−	0.0440364i
$808$	21.9420	−	38.0047i	0.771918	−	1.33700i
$809$	3.17606	−	5.50109i	0.111664	−	0.193408i	−0.804777	−	0.593577i	$-0.797715\pi$
$809$	3.17606	−	5.50109i	0.111664	−	0.193408i	0.916441	+	0.400169i	$0.131049\pi$
$810$	−5.22896	−	9.05683i	−0.183727	−	0.318224i
$811$	7.80208			0.273968			0.136984	−	0.990573i	$-0.456259\pi$
$811$	7.80208			0.273968			0.136984	+	0.990573i	$0.456259\pi$
$812$	−44.6318	+	72.4382i	−1.56627	+	2.54208i
$813$	2.76244			0.0968831
$814$	17.9589	+	31.1057i	0.629459	+	1.09025i
$815$	6.83931	−	11.8460i	0.239570	−	0.414948i
$816$	1.25681	−	2.17686i	0.0439972	−	0.0762054i
$817$	−4.07360	−	7.05569i	−0.142517	−	0.246847i
$818$	−68.6986			−2.40199
$819$	6.25354	+	11.5844i	0.218517	+	0.404791i
$820$	−37.8946			−1.32334
$821$	−25.5601	−	44.2713i	−0.892053	−	1.54508i	−0.837411	−	0.546574i	$-0.815932\pi$
$821$	−25.5601	−	44.2713i	−0.892053	−	1.54508i	−0.0546419	−	0.998506i	$-0.517402\pi$
$822$	21.6695	−	37.5327i	0.755811	−	1.30910i
$823$	−26.6959	+	46.2386i	−0.930560	+	1.61178i	−0.148194	+	0.988958i	$0.547346\pi$
$823$	−26.6959	+	46.2386i	−0.930560	+	1.61178i	−0.782366	+	0.622819i	$0.785987\pi$
$824$	4.53113	+	7.84814i	0.157849	+	0.273403i
$825$	30.8097			1.07266
$826$	47.9104	+	1.37065i	1.66702	+	0.0476909i
$827$	31.7470			1.10395			0.551976	−	0.833860i	$-0.313874\pi$
$827$	31.7470			1.10395			0.551976	+	0.833860i	$0.313874\pi$
$828$	11.1645	+	19.3375i	0.387994	+	0.672025i
$829$	−12.4345	+	21.5372i	−0.431869	+	0.748018i	−0.997034	−	0.0769591i	$-0.975479\pi$
$829$	−12.4345	+	21.5372i	−0.431869	+	0.748018i	0.565166	+	0.824977i	$0.308812\pi$
$830$	3.26875	−	5.66165i	0.113460	−	0.196519i
$831$	−5.17139	−	8.95712i	−0.179394	−	0.310719i
$832$	−52.6826			−1.82644
$833$	−3.84085	+	5.85217i	−0.133078	+	0.202766i
$834$	−41.5615			−1.43916
$835$	−46.6155	−	80.7405i	−1.61320	−	2.79414i
$836$	10.5814	−	18.3275i	0.365965	−	0.633871i
$837$	−1.62736	+	2.81867i	−0.0562498	+	0.0974275i
$838$	−24.3079	−	42.1026i	−0.839704	−	1.45441i
$839$	−10.8963			−0.376184			−0.188092	−	0.982151i	$-0.560230\pi$
$839$	−10.8963			−0.376184			−0.188092	+	0.982151i	$0.560230\pi$
$840$	48.1549	+	1.37764i	1.66150	+	0.0475330i
$841$	44.8924			1.54801
$842$	45.7227	+	79.1940i	1.57571	+	2.72920i
$843$	0.890199	−	1.54187i	0.0306601	−	0.0531048i
$844$	−4.78092	+	8.28079i	−0.164566	+	0.285037i
$845$	−25.6593	−	44.4432i	−0.882707	−	1.52889i
$846$	0.439930			0.0151251
$847$	−7.78138	−	14.4146i	−0.267371	−	0.495292i
$848$	−7.18560			−0.246754
$849$	−6.43481	−	11.1454i	−0.220842	−	0.382510i
$850$	−16.8324	+	29.1545i	−0.577345	+	0.999991i
$851$	20.4006	−	35.3348i	0.699322	−	1.21126i
$852$	−20.3483	−	35.2443i	−0.697122	−	1.20745i
$853$	−12.7086			−0.435134			−0.217567	−	0.976045i	$-0.569812\pi$
$853$	−12.7086			−0.435134			−0.217567	+	0.976045i	$0.569812\pi$
$854$	19.7020	−	31.9767i	0.674187	−	1.09422i
$855$	11.2593			0.385060
$856$	−6.66660	−	11.5469i	−0.227860	−	0.394665i
$857$	9.21088	−	15.9537i	0.314638	−	0.544969i	−0.664723	−	0.747090i	$-0.731450\pi$
$857$	9.21088	−	15.9537i	0.314638	−	0.544969i	0.979360	+	0.202122i	$0.0647836\pi$
$858$	−13.0718	+	22.6410i	−0.446263	+	0.772950i
$859$	−15.3763	−	26.6325i	−0.524632	−	0.908689i	−0.999589	−	0.0286799i	$-0.990870\pi$
$859$	−15.3763	−	26.6325i	−0.524632	−	0.908689i	0.474957	−	0.880009i	$-0.342464\pi$
$860$	51.5694			1.75850
$861$	3.22089	−	5.22757i	0.109768	−	0.178155i
$862$	78.5458			2.67528
$863$	25.1654	+	43.5878i	0.856641	+	1.48375i	0.875114	+	0.483916i	$0.160786\pi$
$863$	25.1654	+	43.5878i	0.856641	+	1.48375i	−0.0184737	+	0.999829i	$0.505881\pi$
$864$	−1.16038	+	2.00984i	−0.0394770	+	0.0683761i
$865$	−17.7641	+	30.7684i	−0.603998	+	1.04616i
$866$	−5.90351	−	10.2252i	−0.200610	−	0.347466i
$867$	−1.00000			−0.0339618
$868$	−15.3032	−	28.3485i	−0.519425	−	0.962210i
$869$	−15.5889			−0.528816
$870$	−44.9485	−	77.8531i	−1.52390	−	2.63947i
$871$	−3.98914	+	6.90939i	−0.135167	+	0.234116i
$872$	23.3419	−	40.4293i	0.790456	−	1.36911i
$873$	3.21707	+	5.57213i	0.108881	+	0.188588i
$874$	−36.8919			−1.24789
$875$	−104.465	−	2.98858i	−3.53155	−	0.101032i
$876$	−31.3275			−1.05846
$877$	−27.0243	−	46.8075i	−0.912546	−	1.58058i	−0.810455	−	0.585801i	$-0.800780\pi$
$877$	−27.0243	−	46.8075i	−0.912546	−	1.58058i	−0.102091	−	0.994775i	$-0.532553\pi$
$878$	−48.6556	+	84.2740i	−1.64205	+	2.84411i
$879$	−10.7904	+	18.6896i	−0.363953	+	0.630384i
$880$	12.0290	+	20.8348i	0.405497	+	0.702341i
$881$	54.8806			1.84898			0.924488	−	0.381212i	$-0.124493\pi$
$881$	54.8806			1.84898			0.924488	+	0.381212i	$0.124493\pi$
$882$	−9.20291	+	14.0221i	−0.309878	+	0.472150i
$883$	2.87978			0.0969124			0.0484562	−	0.998825i	$-0.484570\pi$
$883$	2.87978			0.0969124			0.0484562	+	0.998825i	$0.484570\pi$
$884$	−9.30734	−	16.1208i	−0.313040	−	0.542201i
$885$	−16.4998	+	28.5785i	−0.554635	+	0.960656i
$886$	39.7566	−	68.8604i	1.33565	−	2.31341i
$887$	14.9536	+	25.9004i	0.502093	+	0.869650i	0.999997	+	0.00241828i	$0.000769762\pi$
$887$	14.9536	+	25.9004i	0.502093	+	0.869650i	−0.497904	+	0.867232i	$0.665897\pi$
$888$	−28.5182			−0.957008
$889$	−11.5661	−	0.330889i	−0.387915	−	0.0110977i
$890$	10.0325			0.336291
$891$	1.09643	+	1.89907i	0.0367318	+	0.0636213i
$892$	−35.8569	+	62.1060i	−1.20058	+	2.07946i
$893$	−0.236820	+	0.410185i	−0.00792489	+	0.0137263i
$894$	15.4023	+	26.6775i	0.515129	+	0.892230i
$895$	−64.2744			−2.14846
$896$	−26.0509	−	48.2580i	−0.870300	−	1.61219i
$897$	29.6980			0.991587
$898$	1.97972	+	3.42898i	0.0660642	+	0.114427i
$899$	−13.9889	+	24.2295i	−0.466556	+	0.808099i
$900$	−26.2813	+	45.5205i	−0.876043	+	1.51735i
$901$	1.42933	+	2.47567i	0.0476179	+	0.0824767i
$902$	12.1938			0.406009
$903$	−4.38319	+	7.11400i	−0.145863	+	0.236739i
$904$	−57.4219			−1.90983
$905$	45.0531	+	78.0342i	1.49762	+	2.59395i
$906$	−8.15871	+	14.1313i	−0.271055	+	0.469481i
$907$	13.5091	−	23.3984i	0.448561	−	0.776931i	−0.549731	−	0.835342i	$-0.685270\pi$
$907$	13.5091	−	23.3984i	0.448561	−	0.776931i	0.998293	+	0.0584105i	$0.0186032\pi$
$908$	3.50925	+	6.07819i	0.116458	+	0.201712i
$909$	−10.5193			−0.348903
$910$	72.2182	−	117.212i	2.39401	−	3.88553i
$911$	5.30202			0.175664			0.0878318	−	0.996135i	$-0.472006\pi$
$911$	5.30202			0.175664			0.0878318	+	0.996135i	$0.472006\pi$
$912$	3.24215	+	5.61557i	0.107358	+	0.185950i
$913$	−0.685405	+	1.18716i	−0.0226836	+	0.0392892i
$914$	−40.2809	+	69.7685i	−1.33237	+	2.30774i
$915$	12.9296	+	22.3947i	0.427439	+	0.740346i
$916$	21.6901			0.716661
$917$	−8.99328	−	16.6596i	−0.296984	−	0.550149i
$918$	−2.39606			−0.0790817
$919$	12.5494	+	21.7361i	0.413965	+	0.717009i	0.995319	−	0.0966420i	$-0.0308102\pi$
$919$	12.5494	+	21.7361i	0.413965	+	0.717009i	−0.581354	+	0.813651i	$0.697477\pi$
$920$	54.3387	−	94.1174i	1.79149	−	3.10296i
$921$	−12.1571	+	21.0566i	−0.400589	+	0.693840i
$922$	−2.47458	−	4.28610i	−0.0814959	−	0.141155i
$923$	−54.1272			−1.78162
$924$	−21.6961	−	0.620692i	−0.713749	−	0.0204193i
$925$	96.0459			3.15797
$926$	−24.3358	−	42.1508i	−0.799724	−	1.38516i
$927$	1.08614	−	1.88125i	0.0356735	−	0.0617883i
$928$	−9.97472	+	17.2767i	−0.327436	+	0.567136i
$929$	−8.14447	−	14.1066i	−0.267212	−	0.462824i	0.700929	−	0.713231i	$-0.252769\pi$
$929$	−8.14447	−	14.1066i	−0.267212	−	0.462824i	−0.968141	+	0.250407i	$0.919436\pi$
$930$	34.0376			1.11614
$931$	−8.12001	−	16.1290i	−0.266123	−	0.528606i
$932$	−8.65139			−0.283386
$933$	−7.40974	−	12.8340i	−0.242584	−	0.420168i
$934$	−14.4288	+	24.9914i	−0.472124	+	0.817743i
$935$	4.78551	−	8.28875i	0.156503	−	0.271071i
$936$	−10.3788	−	17.9766i	−0.339242	−	0.587584i
$937$	9.08956			0.296943			0.148471	−	0.988917i	$-0.452565\pi$
$937$	9.08956			0.296943			0.148471	+	0.988917i	$0.452565\pi$
$938$	−10.1606	−	0.290681i	−0.331757	−	0.00949107i
$939$	9.62650			0.314149
$940$	−1.49900	−	2.59635i	−0.0488921	−	0.0846837i
$941$	27.8005	−	48.1519i	0.906271	−	1.56971i	0.0870689	−	0.996202i	$-0.472250\pi$
$941$	27.8005	−	48.1519i	0.906271	−	1.56971i	0.819202	−	0.573505i	$-0.194417\pi$
$942$	8.69902	−	15.0671i	0.283429	−	0.490914i
$943$	−6.92583	−	11.9959i	−0.225536	−	0.390640i
$944$	−19.0047			−0.618551
$945$	−5.48552	−	10.1617i	−0.178444	−	0.330559i
$946$	−16.5941			−0.539520
$947$	−2.65557	−	4.59959i	−0.0862946	−	0.149467i	0.819648	−	0.572868i	$-0.194169\pi$
$947$	−2.65557	−	4.59959i	−0.0862946	−	0.149467i	−0.905942	+	0.423402i	$0.860836\pi$
$948$	13.2976	−	23.0321i	0.431886	−	0.748048i
$949$	−20.8331	+	36.0839i	−0.676270	+	1.17133i
$950$	−43.4218	−	75.2088i	−1.40879	−	2.44010i
$951$	22.9558			0.744393
$952$	5.78983	−	9.39701i	0.187650	−	0.304559i
$953$	40.9327			1.32594			0.662971	−	0.748645i	$-0.269295\pi$
$953$	40.9327			1.32594			0.662971	+	0.748645i	$0.269295\pi$
$954$	3.42476	+	5.93186i	0.110881	+	0.192051i
$955$	−37.8307	+	65.5246i	−1.22417	+	2.12033i
$956$	35.7892	−	61.9887i	1.15751	−	2.00486i
$957$	9.42498	+	16.3245i	0.304666	+	0.527698i
$958$	0.509291			0.0164545
$959$	25.1030	−	40.7427i	0.810620	−	1.31565i
$960$	46.2124			1.49150
$961$	10.2034	+	17.6728i	0.329142	+	0.570090i
$962$	−40.7498	+	70.5807i	−1.31383	+	2.27561i
$963$	−1.59803	+	2.76786i	−0.0514957	+	0.0891931i
$964$	23.9536	+	41.4889i	0.771494	+	1.33627i
$965$	−2.45052			−0.0788850
$966$	17.9737	+	33.2954i	0.578295	+	1.07126i
$967$	52.0112			1.67257			0.836284	−	0.548296i	$-0.184723\pi$
$967$	52.0112			1.67257			0.836284	+	0.548296i	$0.184723\pi$
$968$	12.9145	+	22.3686i	0.415088	+	0.718953i
$969$	1.28983	−	2.23406i	0.0414354	−	0.0717682i
$970$	33.6439	−	58.2729i	1.08024	−	1.87103i
$971$	−9.32140	−	16.1451i	−0.299138	−	0.518122i	0.676801	−	0.736166i	$-0.263366\pi$
$971$	−9.32140	−	16.1451i	−0.299138	−	0.518122i	−0.975939	+	0.218044i	$0.930032\pi$
$972$	−3.74110			−0.119996
$973$	−45.8738	−	1.31238i	−1.47065	−	0.0420730i
$974$	−83.0036			−2.65961
$975$	34.9545	+	60.5430i	1.11944	+	1.93893i
$976$	−7.44623	+	12.8973i	−0.238348	+	0.412831i
$977$	−9.24492	+	16.0127i	−0.295771	+	0.512291i	−0.975164	−	0.221484i	$-0.928910\pi$
$977$	−9.24492	+	16.0127i	−0.295771	+	0.512291i	0.679393	+	0.733775i	$0.262243\pi$
$978$	−3.75458	−	6.50313i	−0.120058	−	0.207947i
$979$	−2.10366			−0.0672332
$980$	114.113	+	6.53454i	3.64520	+	0.208738i
$981$	−11.1904			−0.357281
$982$	31.7175	+	54.9363i	1.01215	+	1.75309i
$983$	−12.4403	+	21.5472i	−0.396784	+	0.687249i	−0.993327	−	0.115331i	$-0.963207\pi$
$983$	−12.4403	+	21.5472i	−0.396784	+	0.687249i	0.596544	+	0.802581i	$0.296540\pi$
$984$	−4.84085	+	8.38460i	−0.154321	+	0.267291i
$985$	4.08788	+	7.08042i	0.130251	+	0.225601i
$986$	−20.5967			−0.655932
$987$	0.485576	+	0.0138916i	0.0154561	+	0.000442175i
$988$	48.0196			1.52771
$989$	9.42510	+	16.3248i	0.299701	+	0.519097i
$990$	11.4664	−	19.8603i	0.364425	−	0.631203i
$991$	8.08189	−	13.9982i	0.256730	−	0.444669i	−0.708634	−	0.705576i	$-0.750688\pi$
$991$	8.08189	−	13.9982i	0.256730	−	0.444669i	0.965364	+	0.260907i	$0.0840216\pi$
$992$	−3.77672	−	6.54147i	−0.119911	−	0.207692i
$993$	−13.8534			−0.439624
$994$	−32.7587	−	60.6839i	−1.03904	−	1.92478i
$995$	−29.7580			−0.943392
$996$	−1.16933	−	2.02533i	−0.0370515	−	0.0641752i
$997$	−9.16220	+	15.8694i	−0.290170	+	0.502589i	−0.973850	−	0.227193i	$-0.927045\pi$
$997$	−9.16220	+	15.8694i	−0.290170	+	0.502589i	0.683680	+	0.729782i	$0.260378\pi$
$998$	35.3812	−	61.2820i	1.11997	−	1.93985i
$999$	3.41799	+	5.92014i	0.108141	+	0.187305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.i.f.256.1	yes	10
3.2	odd	2		1071.2.i.g.613.5		10
7.2	even	3	inner	357.2.i.f.205.1	✓	10
7.3	odd	6		2499.2.a.bb.1.5		5
7.4	even	3		2499.2.a.ba.1.5		5
21.2	odd	6		1071.2.i.g.919.5		10
21.11	odd	6		7497.2.a.bv.1.1		5
21.17	even	6		7497.2.a.bw.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.i.f.205.1	✓	10	7.2	even	3	inner
357.2.i.f.256.1	yes	10	1.1	even	1	trivial
1071.2.i.g.613.5		10	3.2	odd	2
1071.2.i.g.919.5		10	21.2	odd	6
2499.2.a.ba.1.5		5	7.4	even	3
2499.2.a.bb.1.5		5	7.3	odd	6
7497.2.a.bv.1.1		5	21.11	odd	6
7497.2.a.bw.1.1		5	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19803 - 2.07505i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.87055 + 3.23989i) q^{4} +(-2.18232 - 3.77988i) q^{5} -2.39606 q^{6} +(-2.64467 - 0.0756600i) q^{7} +4.17178 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.19803 - 2.07505i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.87055 + 3.23989i) q^{4} +(-2.18232 - 3.77988i) q^{5} -2.39606 q^{6} +(-2.64467 - 0.0756600i) q^{7} +4.17178 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-5.22896 + 9.05683i) q^{10} +(1.09643 - 1.89907i) q^{11} +(1.87055 + 3.23989i) q^{12} +4.97572 q^{13} +(3.01139 + 5.57846i) q^{14} -4.36463 q^{15} +(-1.25681 - 2.17686i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-1.19803 + 2.07505i) q^{18} +(-1.28983 - 2.23406i) q^{19} +16.3285 q^{20} +(-1.38786 + 2.25252i) q^{21} -5.25422 q^{22} +(2.98429 + 5.16894i) q^{23} +(2.08589 - 3.61286i) q^{24} +(-7.02502 + 12.1677i) q^{25} +(-5.96106 - 10.3249i) q^{26} -1.00000 q^{27} +(5.19211 - 8.42690i) q^{28} -8.59607 q^{29} +(5.22896 + 9.05683i) q^{30} +(1.62736 - 2.81867i) q^{31} +(1.16038 - 2.00984i) q^{32} +(-1.09643 - 1.89907i) q^{33} +2.39606 q^{34} +(5.48552 + 10.1617i) q^{35} +3.74110 q^{36} +(-3.41799 - 5.92014i) q^{37} +(-3.09051 + 5.35293i) q^{38} +(2.48786 - 4.30910i) q^{39} +(-9.10414 - 15.7688i) q^{40} -2.32076 q^{41} +(6.33678 + 0.181286i) q^{42} +3.15824 q^{43} +(4.10185 + 7.10461i) q^{44} +(-2.18232 + 3.77988i) q^{45} +(7.15053 - 12.3851i) q^{46} +(-0.0918028 - 0.159007i) q^{47} -2.51362 q^{48} +(6.98855 + 0.400192i) q^{49} +33.6647 q^{50} +(0.500000 + 0.866025i) q^{51} +(-9.30734 + 16.1208i) q^{52} +(1.42933 - 2.47567i) q^{53} +(1.19803 + 2.07505i) q^{54} -9.57103 q^{55} +(-11.0330 - 0.315637i) q^{56} -2.57966 q^{57} +(10.2983 + 17.8372i) q^{58} +(3.78034 - 6.54775i) q^{59} +(8.16426 - 14.1409i) q^{60} +(-2.96235 - 5.13094i) q^{61} -7.79850 q^{62} +(1.25681 + 2.32818i) q^{63} -10.5879 q^{64} +(-10.8586 - 18.8077i) q^{65} +(-2.62711 + 4.55029i) q^{66} +(-0.801720 + 1.38862i) q^{67} +(-1.87055 - 3.23989i) q^{68} +5.96858 q^{69} +(14.5141 - 23.5567i) q^{70} -10.8783 q^{71} +(-2.08589 - 3.61286i) q^{72} +(-4.18694 + 7.25200i) q^{73} +(-8.18972 + 14.1850i) q^{74} +(7.02502 + 12.1677i) q^{75} +9.65078 q^{76} +(-3.04338 + 4.93946i) q^{77} -11.9221 q^{78} +(-3.55446 - 6.15651i) q^{79} +(-5.48552 + 9.50120i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.78034 + 4.81570i) q^{82} -0.625125 q^{83} +(-4.70185 - 8.70995i) q^{84} +4.36463 q^{85} +(-3.78367 - 6.55350i) q^{86} +(-4.29803 + 7.44441i) q^{87} +(4.57406 - 7.92250i) q^{88} +(-0.479661 - 0.830797i) q^{89} +10.4579 q^{90} +(-13.1591 - 0.376463i) q^{91} -22.3290 q^{92} +(-1.62736 - 2.81867i) q^{93} +(-0.219965 + 0.380990i) q^{94} +(-5.62965 + 9.75083i) q^{95} +(-1.16038 - 2.00984i) q^{96} -6.43415 q^{97} +(-7.54207 - 14.9810i) q^{98} -2.19286 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 5 q^{3} - 8 q^{4} - q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 - q^5 + 4 * q^6 - 5 * q^7 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 8 q^{4} - q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{9} - 13 q^{10} + 11 q^{11} + 8 q^{12} + 14 q^{13} + 3 q^{14} - 2 q^{15} + 2 q^{16} - 5 q^{17} + 2 q^{18} - 9 q^{19} + 24 q^{20} - 7 q^{21} + 10 q^{22} + 23 q^{23} - 14 q^{25} - 18 q^{26} - 10 q^{27} + 7 q^{28} - 36 q^{29} + 13 q^{30} - 9 q^{31} - 3 q^{32} - 11 q^{33} - 4 q^{34} - 5 q^{35} + 16 q^{36} + 7 q^{39} - 31 q^{40} + 6 q^{41} - 3 q^{42} + 24 q^{43} + 33 q^{44} - q^{45} - 13 q^{46} - 11 q^{47} + 4 q^{48} + 3 q^{49} + 48 q^{50} + 5 q^{51} - 5 q^{52} + 3 q^{53} - 2 q^{54} - 20 q^{55} - 27 q^{56} - 18 q^{57} + 34 q^{58} + 14 q^{59} + 12 q^{60} - 29 q^{61} - 10 q^{62} - 2 q^{63} + 8 q^{65} + 5 q^{66} - 16 q^{67} - 8 q^{68} + 46 q^{69} + 18 q^{70} - 38 q^{71} - 11 q^{73} - 45 q^{74} + 14 q^{75} + 18 q^{76} + 21 q^{77} - 36 q^{78} - q^{79} + 5 q^{80} - 5 q^{81} + 4 q^{82} + 10 q^{83} - 28 q^{84} + 2 q^{85} + 3 q^{86} - 18 q^{87} - 37 q^{88} - 8 q^{89} + 26 q^{90} - 33 q^{91} - 96 q^{92} + 9 q^{93} + 18 q^{94} + 21 q^{95} + 3 q^{96} + 38 q^{97} - 17 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 - q^5 + 4 * q^6 - 5 * q^7 - 5 * q^9 - 13 * q^10 + 11 * q^11 + 8 * q^12 + 14 * q^13 + 3 * q^14 - 2 * q^15 + 2 * q^16 - 5 * q^17 + 2 * q^18 - 9 * q^19 + 24 * q^20 - 7 * q^21 + 10 * q^22 + 23 * q^23 - 14 * q^25 - 18 * q^26 - 10 * q^27 + 7 * q^28 - 36 * q^29 + 13 * q^30 - 9 * q^31 - 3 * q^32 - 11 * q^33 - 4 * q^34 - 5 * q^35 + 16 * q^36 + 7 * q^39 - 31 * q^40 + 6 * q^41 - 3 * q^42 + 24 * q^43 + 33 * q^44 - q^45 - 13 * q^46 - 11 * q^47 + 4 * q^48 + 3 * q^49 + 48 * q^50 + 5 * q^51 - 5 * q^52 + 3 * q^53 - 2 * q^54 - 20 * q^55 - 27 * q^56 - 18 * q^57 + 34 * q^58 + 14 * q^59 + 12 * q^60 - 29 * q^61 - 10 * q^62 - 2 * q^63 + 8 * q^65 + 5 * q^66 - 16 * q^67 - 8 * q^68 + 46 * q^69 + 18 * q^70 - 38 * q^71 - 11 * q^73 - 45 * q^74 + 14 * q^75 + 18 * q^76 + 21 * q^77 - 36 * q^78 - q^79 + 5 * q^80 - 5 * q^81 + 4 * q^82 + 10 * q^83 - 28 * q^84 + 2 * q^85 + 3 * q^86 - 18 * q^87 - 37 * q^88 - 8 * q^89 + 26 * q^90 - 33 * q^91 - 96 * q^92 + 9 * q^93 + 18 * q^94 + 21 * q^95 + 3 * q^96 + 38 * q^97 - 17 * q^98 - 22 * q^99

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