LMFDB - Embedded newform 252.2.ba.a.155.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(155,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("252.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.ba (of order $6$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.4
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27695 - 0.607789i) q^{2} +(-1.63407 - 0.574282i) q^{3} +(1.26118 + 1.55223i) q^{4} +(-3.32396 + 1.91909i) q^{5} +(1.73758 + 1.72650i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.667037 - 2.74865i) q^{8} +(2.34040 + 1.87684i) q^{9} +O(q^{10})$	\(q+(-1.27695 - 0.607789i) q^{2} +(-1.63407 - 0.574282i) q^{3} +(1.26118 + 1.55223i) q^{4} +(-3.32396 + 1.91909i) q^{5} +(1.73758 + 1.72650i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.667037 - 2.74865i) q^{8} +(2.34040 + 1.87684i) q^{9} +(5.41092 - 0.430306i) q^{10} +(2.92354 - 5.06371i) q^{11} +(-1.16945 - 3.26073i) q^{12} +(-0.515084 - 0.892151i) q^{13} +(-0.801973 - 1.16483i) q^{14} +(6.53369 - 1.22704i) q^{15} +(-0.818829 + 3.91529i) q^{16} +0.189865i q^{17} +(-1.84784 - 3.81909i) q^{18} -4.14257i q^{19} +(-7.17099 - 2.73922i) q^{20} +(-1.12801 - 1.31438i) q^{21} +(-6.81087 + 4.68920i) q^{22} +(0.717351 + 1.24249i) q^{23} +(-0.488512 + 4.87456i) q^{24} +(4.86580 - 8.42781i) q^{25} +(0.115494 + 1.45229i) q^{26} +(-2.74655 - 4.41095i) q^{27} +(0.316103 + 1.97486i) q^{28} +(3.21880 + 1.85838i) q^{29} +(-9.08896 - 2.40424i) q^{30} +(6.05438 - 3.49550i) q^{31} +(3.42527 - 4.50194i) q^{32} +(-7.68528 + 6.59555i) q^{33} +(0.115398 - 0.242447i) q^{34} -3.83818 q^{35} +(0.0383905 + 5.99988i) q^{36} +4.78395 q^{37} +(-2.51781 + 5.28984i) q^{38} +(0.329339 + 1.75365i) q^{39} +(7.49210 + 7.85629i) q^{40} +(8.15688 - 4.70938i) q^{41} +(0.641541 + 2.36399i) q^{42} +(-5.25147 - 3.03194i) q^{43} +(11.5472 - 1.84828i) q^{44} +(-11.3812 - 1.74710i) q^{45} +(-0.160848 - 2.02259i) q^{46} +(-1.78283 + 3.08795i) q^{47} +(3.58651 - 5.92764i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-11.3357 + 7.80449i) q^{50} +(0.109036 - 0.310253i) q^{51} +(0.735207 - 1.92469i) q^{52} -4.68954i q^{53} +(0.826274 + 7.30187i) q^{54} +22.4421i q^{55} +(0.796653 - 2.71392i) q^{56} +(-2.37901 + 6.76927i) q^{57} +(-2.98074 - 4.32940i) q^{58} +(4.24070 + 7.34512i) q^{59} +(10.1448 + 8.59426i) q^{60} +(-0.477327 + 0.826755i) q^{61} +(-9.85564 + 0.783775i) q^{62} +(1.08843 + 2.79559i) q^{63} +(-7.11012 + 3.66690i) q^{64} +(3.42423 + 1.97698i) q^{65} +(13.8224 - 3.75114i) q^{66} +(0.704892 - 0.406970i) q^{67} +(-0.294713 + 0.239454i) q^{68} +(-0.458666 - 2.44228i) q^{69} +(4.90115 + 2.33280i) q^{70} -5.09132 q^{71} +(3.59764 - 7.68485i) q^{72} -8.12043 q^{73} +(-6.10885 - 2.90763i) q^{74} +(-12.7910 + 10.9773i) q^{75} +(6.43022 - 5.22455i) q^{76} +(5.06371 - 2.92354i) q^{77} +(0.645299 - 2.43948i) q^{78} +(-6.10558 - 3.52506i) q^{79} +(-4.79204 - 14.5857i) q^{80} +(1.95494 + 8.78511i) q^{81} +(-13.2782 + 1.05596i) q^{82} +(7.57956 - 13.1282i) q^{83} +(0.617592 - 3.40860i) q^{84} +(-0.364367 - 0.631102i) q^{85} +(4.86307 + 7.06341i) q^{86} +(-4.19253 - 4.88523i) q^{87} +(-15.8685 - 4.65809i) q^{88} +2.51704i q^{89} +(13.4713 + 9.14834i) q^{90} -1.03017i q^{91} +(-1.02391 + 2.68050i) q^{92} +(-11.9007 + 2.23498i) q^{93} +(4.15339 - 2.85956i) q^{94} +(7.94997 + 13.7697i) q^{95} +(-8.18254 + 5.38944i) q^{96} +(1.26529 - 2.19154i) q^{97} +(-0.112112 - 1.40976i) q^{98} +(16.3460 - 6.36410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 72 * q + 6 * q^6 + 4 * q^9	$ 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) $ 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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 $

$2$	−1.27695	−	0.607789i	−0.902937	−	0.429772i
$2$	−1.27695	−	0.607789i	−0.902937	−	0.429772i
$3$	−1.63407	−	0.574282i	−0.943433	−	0.331562i
$3$	−1.63407	−	0.574282i	−0.943433	−	0.331562i
$4$	1.26118	+	1.55223i	0.630592	+	0.776114i
$5$	−3.32396	+	1.91909i	−1.48652	+	0.858242i	−0.999882	−	0.0153615i	$-0.995110\pi$
$5$	−3.32396	+	1.91909i	−1.48652	+	0.858242i	−0.486638	+	0.873604i	$0.661777\pi$
$6$	1.73758	+	1.72650i	0.709365	+	0.704841i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$	−0.667037	−	2.74865i	−0.235833	−	0.971794i
$9$	2.34040	+	1.87684i	0.780133	+	0.625613i
$10$	5.41092	−	0.430306i	1.71108	−	0.136075i
$11$	2.92354	−	5.06371i	0.881479	−	1.52677i	0.0317829	−	0.999495i	$-0.489881\pi$
$11$	2.92354	−	5.06371i	0.881479	−	1.52677i	0.849696	−	0.527272i	$-0.176785\pi$
$12$	−1.16945	−	3.26073i	−0.337592	−	0.941293i
$13$	−0.515084	−	0.892151i	−0.142859	−	0.247438i	0.785713	−	0.618591i	$-0.212296\pi$
$13$	−0.515084	−	0.892151i	−0.142859	−	0.247438i	−0.928572	+	0.371152i	$0.878963\pi$
$14$	−0.801973	−	1.16483i	−0.214336	−	0.311315i
$15$	6.53369	−	1.22704i	1.68699	−	0.316821i
$16$	−0.818829	+	3.91529i	−0.204707	+	0.978823i
$17$			0.189865i			0.0460489i	0.999735	+	0.0230245i	$0.00732956\pi$
$17$			0.189865i			0.0460489i	−0.999735	+	0.0230245i	$0.992670\pi$
$18$	−1.84784	−	3.81909i	−0.435541	−	0.900169i
$19$		−	4.14257i		−	0.950372i	−0.879885	−	0.475186i	$-0.842381\pi$
$19$		−	4.14257i		−	0.950372i	0.879885	−	0.475186i	$-0.157619\pi$
$20$	−7.17099	−	2.73922i	−1.60348	−	0.612508i
$21$	−1.12801	−	1.31438i	−0.246152	−	0.286821i
$22$	−6.81087	+	4.68920i	−1.45208	+	0.999740i
$23$	0.717351	+	1.24249i	0.149578	+	0.259077i	0.931072	−	0.364837i	$-0.118875\pi$
$23$	0.717351	+	1.24249i	0.149578	+	0.259077i	−0.781493	+	0.623913i	$0.785542\pi$
$24$	−0.488512	+	4.87456i	−0.0997170	+	0.995016i
$25$	4.86580	−	8.42781i	0.973160	−	1.68556i
$26$	0.115494	+	1.45229i	0.0226503	+	0.284818i
$27$	−2.74655	−	4.41095i	−0.528574	−	0.848887i
$28$	0.316103	+	1.97486i	0.0597379	+	0.373214i
$29$	3.21880	+	1.85838i	0.597717	+	0.345092i	0.768143	−	0.640278i	$-0.221181\pi$
$29$	3.21880	+	1.85838i	0.597717	+	0.345092i	−0.170426	+	0.985370i	$0.554514\pi$
$30$	−9.08896	−	2.40424i	−1.65941	−	0.438952i
$31$	6.05438	−	3.49550i	1.08740	−	0.627810i	0.154515	−	0.987990i	$-0.450618\pi$
$31$	6.05438	−	3.49550i	1.08740	−	0.627810i	0.932883	+	0.360181i	$0.117285\pi$
$32$	3.42527	−	4.50194i	0.605509	−	0.795839i
$33$	−7.68528	+	6.59555i	−1.33783	+	1.14814i
$34$	0.115398	−	0.242447i	0.0197905	−	0.0415793i
$35$	−3.83818			−0.648770
$36$	0.0383905	+	5.99988i	0.00639842	+	0.999980i
$37$	4.78395			0.786476			0.393238	−	0.919437i	$-0.371355\pi$
$37$	4.78395			0.786476			0.393238	+	0.919437i	$0.371355\pi$
$38$	−2.51781	+	5.28984i	−0.408443	+	0.858126i
$39$	0.329339	+	1.75365i	0.0527364	+	0.280808i
$40$	7.49210	+	7.85629i	1.18460	+	1.24219i
$41$	8.15688	−	4.70938i	1.27389	−	0.735481i	0.298172	−	0.954512i	$-0.403623\pi$
$41$	8.15688	−	4.70938i	1.27389	−	0.735481i	0.975718	+	0.219031i	$0.0702896\pi$
$42$	0.641541	+	2.36399i	0.0989919	+	0.364771i
$43$	−5.25147	−	3.03194i	−0.800842	−	0.462366i	0.0429236	−	0.999078i	$-0.486333\pi$
$43$	−5.25147	−	3.03194i	−0.800842	−	0.462366i	−0.843765	+	0.536712i	$0.819666\pi$
$44$	11.5472	−	1.84828i	1.74080	−	0.278638i
$45$	−11.3812	−	1.74710i	−1.69661	−	0.260443i
$46$	−0.160848	−	2.02259i	−0.0237157	−	0.298215i
$47$	−1.78283	+	3.08795i	−0.260052	+	0.450423i	−0.966255	−	0.257586i	$-0.917073\pi$
$47$	−1.78283	+	3.08795i	−0.260052	+	0.450423i	0.706204	+	0.708009i	$0.250406\pi$
$48$	3.58651	−	5.92764i	0.517668	−	0.855581i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−11.3357	+	7.80449i	−1.60311	+	1.10372i
$51$	0.109036	−	0.310253i	0.0152681	−	0.0434441i
$52$	0.735207	−	1.92469i	0.101955	−	0.266907i
$53$		−	4.68954i		−	0.644158i	−0.946713	−	0.322079i	$-0.895618\pi$
$53$		−	4.68954i		−	0.644158i	0.946713	−	0.322079i	$-0.104382\pi$
$54$	0.826274	+	7.30187i	0.112442	+	0.993658i
$55$			22.4421i			3.02609i
$56$	0.796653	−	2.71392i	0.106457	−	0.362662i
$57$	−2.37901	+	6.76927i	−0.315107	+	0.896612i
$58$	−2.98074	−	4.32940i	−0.391390	−	0.568478i
$59$	4.24070	+	7.34512i	0.552093	+	0.956253i	0.998123	+	0.0612350i	$0.0195039\pi$
$59$	4.24070	+	7.34512i	0.552093	+	0.956253i	−0.446031	+	0.895018i	$0.647163\pi$
$60$	10.1448	+	8.59426i	1.30969	+	1.10951i
$61$	−0.477327	+	0.826755i	−0.0611155	+	0.105855i	−0.894964	−	0.446138i	$-0.852799\pi$
$61$	−0.477327	+	0.826755i	−0.0611155	+	0.105855i	0.833849	+	0.551993i	$0.186132\pi$
$62$	−9.85564	+	0.783775i	−1.25167	+	0.0995396i
$63$	1.08843	+	2.79559i	0.137129	+	0.352211i
$64$	−7.11012	+	3.66690i	−0.888766	+	0.458362i
$65$	3.42423	+	1.97698i	0.424724	+	0.245214i
$66$	13.8224	−	3.75114i	1.70142	−	0.461733i
$67$	0.704892	−	0.406970i	0.0861163	−	0.0497192i	−0.456323	−	0.889814i	$-0.650834\pi$
$67$	0.704892	−	0.406970i	0.0861163	−	0.0497192i	0.542440	+	0.840095i	$0.317501\pi$
$68$	−0.294713	+	0.239454i	−0.0357392	+	0.0290381i
$69$	−0.458666	−	2.44228i	−0.0552169	−	0.294016i
$70$	4.90115	+	2.33280i	0.585799	+	0.278823i
$71$	−5.09132			−0.604229			−0.302114	−	0.953272i	$-0.597692\pi$
$71$	−5.09132			−0.604229			−0.302114	+	0.953272i	$0.597692\pi$
$72$	3.59764	−	7.68485i	0.423986	−	0.905669i
$73$	−8.12043			−0.950424			−0.475212	−	0.879871i	$-0.657629\pi$
$73$	−8.12043			−0.950424			−0.475212	+	0.879871i	$0.657629\pi$
$74$	−6.10885	−	2.90763i	−0.710139	−	0.338005i
$75$	−12.7910	+	10.9773i	−1.47698	+	1.26755i
$76$	6.43022	−	5.22455i	0.737597	−	0.599297i
$77$	5.06371	−	2.92354i	0.577064	−	0.333168i
$78$	0.645299	−	2.43948i	0.0730657	−	0.276217i
$79$	−6.10558	−	3.52506i	−0.686931	−	0.396600i	0.115530	−	0.993304i	$-0.463143\pi$
$79$	−6.10558	−	3.52506i	−0.686931	−	0.396600i	−0.802461	+	0.596704i	$0.796477\pi$
$80$	−4.79204	−	14.5857i	−0.535766	−	1.63073i
$81$	1.95494	+	8.78511i	0.217216	+	0.976124i
$82$	−13.2782	+	1.05596i	−1.46633	+	0.116611i
$83$	7.57956	−	13.1282i	0.831965	−	1.44101i	−0.0645125	−	0.997917i	$-0.520549\pi$
$83$	7.57956	−	13.1282i	0.831965	−	1.44101i	0.896478	−	0.443089i	$-0.146117\pi$
$84$	0.617592	−	3.40860i	0.0673848	−	0.371909i
$85$	−0.364367	−	0.631102i	−0.0395211	−	0.0684526i
$86$	4.86307	+	7.06341i	0.524398	+	0.761667i
$87$	−4.19253	−	4.88523i	−0.449487	−	0.523751i
$88$	−15.8685	−	4.65809i	−1.69158	−	0.496554i
$89$			2.51704i			0.266806i	0.991062	+	0.133403i	$0.0425905\pi$
$89$			2.51704i			0.266806i	−0.991062	+	0.133403i	$0.957410\pi$
$90$	13.4713	+	9.14834i	1.42000	+	0.964320i
$91$		−	1.03017i		−	0.107991i
$92$	−1.02391	+	2.68050i	−0.106751	+	0.279462i
$93$	−11.9007	+	2.23498i	−1.23405	+	0.231757i
$94$	4.15339	−	2.85956i	0.428390	−	0.294941i
$95$	7.94997	+	13.7697i	0.815649	+	1.41275i
$96$	−8.18254	+	5.38944i	−0.835127	+	0.550057i
$97$	1.26529	−	2.19154i	0.128471	−	0.222517i	−0.794614	−	0.607115i	$-0.792327\pi$
$97$	1.26529	−	2.19154i	0.128471	−	0.222517i	0.923084	+	0.384598i	$0.125660\pi$
$98$	−0.112112	−	1.40976i	−0.0113250	−	0.142408i
$99$	16.3460	−	6.36410i	1.64284	−	0.639617i
$100$	19.2186	−	3.07619i	1.92186	−	0.307619i
$101$	−2.49788	−	1.44215i	−0.248549	−	0.143500i	0.370551	−	0.928812i	$-0.379169\pi$
$101$	−2.49788	−	1.44215i	−0.248549	−	0.143500i	−0.619099	+	0.785313i	$0.712502\pi$
$102$	−0.327801	+	0.329905i	−0.0324572	+	0.0326655i
$103$	9.45187	−	5.45704i	0.931321	−	0.537698i	0.0440916	−	0.999027i	$-0.485961\pi$
$103$	9.45187	−	5.45704i	0.931321	−	0.537698i	0.887229	+	0.461329i	$0.152627\pi$
$104$	−2.10863	+	2.01088i	−0.206768	+	0.197183i
$105$	6.27187	+	2.20420i	0.612072	+	0.215108i
$106$	−2.85025	+	5.98829i	−0.276841	+	0.581634i
$107$	−13.4510			−1.30036			−0.650179	−	0.759781i	$-0.725306\pi$
$107$	−13.4510			−1.30036			−0.650179	+	0.759781i	$0.725306\pi$
$108$	3.38289	−	9.82629i	0.325519	−	0.945536i
$109$	5.00998			0.479869			0.239934	−	0.970789i	$-0.422874\pi$
$109$	5.00998			0.479869			0.239934	+	0.970789i	$0.422874\pi$
$110$	13.6401	−	28.6574i	1.30053	−	2.73237i
$111$	−7.81733	−	2.74734i	−0.741988	−	0.260766i
$112$	−2.66677	+	2.98133i	−0.251986	+	0.281709i
$113$	3.70388	−	2.13843i	0.348431	−	0.201167i	−0.315563	−	0.948905i	$-0.602193\pi$
$113$	3.70388	−	2.13843i	0.348431	−	0.201167i	0.663994	+	0.747738i	$0.268860\pi$
$114$	7.15216	−	7.19807i	0.669861	−	0.674161i
$115$	−4.76889	−	2.75332i	−0.444702	−	0.256749i
$116$	1.17488	+	7.34008i	0.109085	+	0.681509i
$117$	0.468923	−	3.05472i	0.0433519	−	0.282409i
$118$	−0.950869	−	11.9568i	−0.0875346	−	1.10071i
$119$	−0.0949323	+	0.164427i	−0.00870243	+	0.0150730i
$120$	−7.73092	−	17.1403i	−0.705734	−	1.56469i
$121$	−11.5941	−	20.0816i	−1.05401	−	1.82560i
$122$	1.11201	−	0.765608i	0.100677	−	0.0693149i
$123$	−16.0335	+	3.01112i	−1.44569	+	0.271504i
$124$	13.0615	+	4.98931i	1.17296	+	0.448054i
$125$			18.1607i			1.62434i
$126$	0.309269	−	4.23135i	0.0275519	−	0.376959i
$127$		−	5.78278i		−	0.513139i	−0.966526	−	0.256569i	$-0.917408\pi$
$127$		−	5.78278i		−	0.513139i	0.966526	−	0.256569i	$-0.0825922\pi$
$128$	11.3079	−	0.360972i	0.999491	−	0.0319058i
$129$	6.84011	+	7.97024i	0.602238	+	0.701740i
$130$	−3.17097	−	4.60571i	−0.278113	−	0.403948i
$131$	−4.22134	−	7.31158i	−0.368820	−	0.638815i	0.620561	−	0.784158i	$-0.286905\pi$
$131$	−4.22134	−	7.31158i	−0.368820	−	0.638815i	−0.989381	+	0.145343i	$0.953572\pi$
$132$	−19.9304	−	3.61110i	−1.73471	−	0.314306i
$133$	2.07129	−	3.58757i	0.179603	−	0.311082i
$134$	−1.14746	+	0.0912525i	−0.0991255	+	0.00788302i
$135$	17.5944	+	9.39093i	1.51429	+	0.808242i
$136$	0.521871	−	0.126647i	0.0447500	−	0.0108599i
$137$	17.5423	+	10.1280i	1.49874	+	0.865297i	0.999999	−	0.00145585i	$-0.000463412\pi$
$137$	17.5423	+	10.1280i	1.49874	+	0.865297i	0.498739	+	0.866752i	$0.333797\pi$
$138$	−0.898700	+	3.39744i	−0.0765025	+	0.289209i
$139$	−1.85791	+	1.07266i	−0.157586	+	0.0909822i	−0.576719	−	0.816942i	$-0.695667\pi$
$139$	−1.85791	+	1.07266i	−0.157586	+	0.0909822i	0.419133	+	0.907925i	$0.362334\pi$
$140$	−4.84065	−	5.95773i	−0.409109	−	0.503520i
$141$	4.68662	−	4.02209i	0.394685	−	0.338721i
$142$	6.50134	+	3.09445i	0.545581	+	0.259681i
$143$	−6.02346			−0.503707
$144$	−9.26476	+	7.62654i	−0.772064	+	0.635545i
$145$	−14.2656			−1.18469
$146$	10.3693	+	4.93551i	0.858173	+	0.408466i
$147$	−0.319694	−	1.70229i	−0.0263679	−	0.140403i
$148$	6.03344	+	7.42578i	0.495946	+	0.610396i
$149$	−10.2202	+	5.90065i	−0.837274	+	0.483400i	−0.856337	−	0.516418i	$-0.827265\pi$
$149$	−10.2202	+	5.90065i	−0.837274	+	0.483400i	0.0190630	+	0.999818i	$0.493932\pi$
$150$	23.0054	−	6.24322i	1.87838	−	0.509757i
$151$	−11.5465	−	6.66639i	−0.939643	−	0.542503i	−0.0497946	−	0.998759i	$-0.515857\pi$
$151$	−11.5465	−	6.66639i	−0.939643	−	0.542503i	−0.889848	+	0.456256i	$0.849190\pi$
$152$	−11.3865	+	2.76325i	−0.923565	+	0.224129i
$153$	−0.356345	+	0.444359i	−0.0288088	+	0.0359243i
$154$	−8.24298	+	0.655528i	−0.664239	+	0.0528240i
$155$	−13.4163	+	23.2378i	−1.07763	+	1.86650i
$156$	−2.30670	+	2.72288i	−0.184684	+	0.218005i
$157$	−0.586019	−	1.01501i	−0.0467694	−	0.0810069i	0.841693	−	0.539956i	$-0.181559\pi$
$157$	−0.586019	−	1.01501i	−0.0467694	−	0.0810069i	−0.888462	+	0.458949i	$0.848226\pi$
$158$	5.65400	+	8.21221i	0.449808	+	0.653328i
$159$	−2.69312	+	7.66306i	−0.213578	+	0.607720i
$160$	−2.74584	+	21.5377i	−0.217078	+	1.70270i
$161$			1.43470i			0.113070i
$162$	2.84314	−	12.4063i	0.223378	−	0.974732i
$163$			15.6643i			1.22693i	0.789723	+	0.613463i	$0.210224\pi$
$163$			15.6643i			1.22693i	−0.789723	+	0.613463i	$0.789776\pi$
$164$	17.5974	+	6.72195i	1.37412	+	0.524896i
$165$	12.8881	−	36.6721i	1.00334	−	2.85492i
$166$	−17.6579	+	12.1572i	−1.37052	+	0.943583i
$167$	−7.87953	−	13.6477i	−0.609736	−	1.05609i	−0.991284	−	0.131745i	$-0.957942\pi$
$167$	−7.87953	−	13.6477i	−0.609736	−	1.05609i	0.381548	−	0.924349i	$-0.375391\pi$
$168$	−2.86034	+	3.97724i	−0.220680	+	0.306851i
$169$	5.96938	−	10.3393i	0.459183	−	0.795328i
$170$	0.0816999	+	1.02734i	0.00626610	+	0.0787935i
$171$	7.77495	−	9.69528i	0.594565	−	0.741417i
$172$	−1.91681	−	11.9753i	−0.146155	−	0.913109i
$173$	10.7242	+	6.19161i	0.815344	+	0.470739i	0.848808	−	0.528701i	$-0.177321\pi$
$173$	10.7242	+	6.19161i	0.815344	+	0.470739i	−0.0334641	+	0.999440i	$0.510654\pi$
$174$	2.38445	+	8.78635i	0.180765	+	0.666092i
$175$	8.42781	−	4.86580i	0.637083	−	0.367820i
$176$	17.4320	+	15.5928i	1.31399	+	1.17535i
$177$	−2.71146	−	14.4378i	−0.203806	−	1.08521i
$178$	1.52983	−	3.21413i	0.114666	−	0.240909i
$179$	14.6038			1.09154			0.545769	−	0.837936i	$-0.316238\pi$
$179$	14.6038			1.09154			0.545769	+	0.837936i	$0.316238\pi$
$180$	−11.6419	−	19.8697i	−0.867736	−	1.48100i
$181$	−6.78702			−0.504476			−0.252238	−	0.967665i	$-0.581167\pi$
$181$	−6.78702			−0.504476			−0.252238	+	0.967665i	$0.581167\pi$
$182$	−0.626125	+	1.31547i	−0.0464115	+	0.0975090i
$183$	1.25478	−	1.07686i	0.0927560	−	0.0796037i
$184$	2.93666	−	2.80053i	0.216494	−	0.206458i
$185$	−15.9016	+	9.18082i	−1.16911	+	0.674987i
$186$	16.5550	+	4.37917i	1.21387	+	0.321096i
$187$	0.961419	+	0.555076i	0.0703059	+	0.0405912i
$188$	−7.04167	+	1.12711i	−0.513567	+	0.0822032i
$189$	−0.173111	−	5.19327i	−0.0125920	−	0.377755i
$190$	−1.78258	−	22.4151i	−0.129322	−	1.62616i
$191$	11.0178	−	19.0834i	0.797219	−	1.38082i	−0.124202	−	0.992257i	$-0.539637\pi$
$191$	11.0178	−	19.0834i	0.797219	−	1.38082i	0.921421	−	0.388567i	$-0.127030\pi$
$192$	13.7243	−	1.90876i	0.990467	−	0.137753i
$193$	2.98789	+	5.17517i	0.215073	+	0.372517i	0.953295	−	0.302041i	$-0.0976678\pi$
$193$	2.98789	+	5.17517i	0.215073	+	0.372517i	−0.738222	+	0.674557i	$0.764334\pi$
$194$	−2.94770	+	2.02945i	−0.211633	+	0.145706i
$195$	−4.46011	−	5.19701i	−0.319395	−	0.372166i
$196$	−0.713677	+	1.86833i	−0.0509770	+	0.133452i
$197$			1.32760i			0.0945878i	0.998881	+	0.0472939i	$0.0150597\pi$
$197$			1.32760i			0.0945878i	−0.998881	+	0.0472939i	$0.984940\pi$
$198$	−24.7410	−	1.80832i	−1.75827	−	0.128512i
$199$			4.06971i			0.288494i	0.989542	+	0.144247i	$0.0460760\pi$
$199$			4.06971i			0.288494i	−0.989542	+	0.144247i	$0.953924\pi$
$200$	−26.4108	−	7.75271i	−1.86752	−	0.548199i
$201$	−1.38556	+	0.260212i	−0.0977300	+	0.0183539i
$202$	2.31314	+	3.35974i	0.162752	+	0.236390i
$203$	1.85838	+	3.21880i	0.130433	+	0.225916i
$204$	0.619098	−	0.222037i	0.0433455	−	0.0155457i
$205$	−18.0754	+	31.3075i	−1.26244	+	2.18661i
$206$	−15.3863	+	1.22360i	−1.07201	+	0.0852524i
$207$	−0.653064	+	4.25427i	−0.0453911	+	0.295693i
$208$	3.91480	−	1.28618i	0.271442	−	0.0891809i
$209$	−20.9768	−	12.1110i	−1.45100	−	0.837733i
$210$	−6.66915	−	6.62662i	−0.460215	−	0.457280i
$211$	−5.65597	+	3.26548i	−0.389373	+	0.224805i	−0.681889	−	0.731456i	$-0.738841\pi$
$211$	−5.65597	+	3.26548i	−0.389373	+	0.224805i	0.292515	+	0.956261i	$0.405508\pi$
$212$	7.27924	−	5.91437i	0.499940	−	0.406201i
$213$	8.31960	+	2.92385i	0.570049	+	0.200339i
$214$	17.1762	+	8.17538i	1.17414	+	0.558857i
$215$	23.2742			1.58729
$216$	−10.2921	+	10.4916i	−0.700288	+	0.713861i
$217$	6.99099			0.474579
$218$	−6.39747	−	3.04501i	−0.433291	−	0.206234i
$219$	13.2694	+	4.66342i	0.896662	+	0.315124i
$220$	−34.8353	+	28.3036i	−2.34859	+	1.90823i
$221$	0.169388	−	0.0977961i	0.0113943	−	0.00657848i
$222$	8.31251	+	8.25949i	0.557899	+	0.554341i
$223$	21.6090	+	12.4760i	1.44705	+	0.835452i	0.998304	−	0.0582095i	$-0.0185391\pi$
$223$	21.6090	+	12.4760i	1.44705	+	0.835452i	0.448741	+	0.893662i	$0.351872\pi$
$224$	5.21735	−	2.18616i	0.348599	−	0.146069i
$225$	27.2056	−	10.5921i	1.81371	−	0.706142i
$226$	−6.02937	+	0.479489i	−0.401068	+	0.0318951i
$227$	−5.18442	+	8.97967i	−0.344102	+	0.596002i	−0.985190	−	0.171465i	$-0.945150\pi$
$227$	−5.18442	+	8.97967i	−0.344102	+	0.596002i	0.641088	+	0.767467i	$0.278483\pi$
$228$	−13.5078	+	4.84454i	−0.894578	+	0.320838i
$229$	11.0340	+	19.1115i	0.729150	+	1.26293i	0.957243	+	0.289286i	$0.0934179\pi$
$229$	11.0340	+	19.1115i	0.729150	+	1.26293i	−0.228092	+	0.973640i	$0.573249\pi$
$230$	4.41618	+	6.41433i	0.291194	+	0.422948i
$231$	−9.95342	+	1.86928i	−0.654887	+	0.122989i
$232$	2.96096	−	10.0870i	0.194397	−	0.662241i
$233$		−	22.9418i		−	1.50297i	−0.659751	−	0.751485i	$-0.729338\pi$
$233$		−	22.9418i		−	1.50297i	0.659751	−	0.751485i	$-0.270662\pi$
$234$	−2.45542	+	3.61571i	−0.160516	+	0.236366i
$235$		−	13.6856i		−	0.892750i
$236$	−6.05299	+	15.8461i	−0.394016	+	1.03149i
$237$	7.95259	+	9.26653i	0.516576	+	0.601926i
$238$	0.221161	−	0.152266i	0.0143357	−	0.00986996i
$239$	7.15276	+	12.3890i	0.462674	+	0.801375i	0.999093	−	0.0425770i	$-0.0135568\pi$
$239$	7.15276	+	12.3890i	0.462674	+	0.801375i	−0.536419	+	0.843952i	$0.680223\pi$
$240$	−0.545741	+	26.5861i	−0.0352275	+	1.71612i
$241$	−4.03440	+	6.98778i	−0.259878	+	0.450123i	−0.966209	−	0.257759i	$-0.917016\pi$
$241$	−4.03440	+	6.98778i	−0.259878	+	0.450123i	0.706331	+	0.707882i	$0.250349\pi$
$242$	2.59969	+	32.6899i	0.167114	+	2.10139i
$243$	1.85061	−	15.4782i	0.118717	−	0.992928i
$244$	−1.88531	+	0.301769i	−0.120695	+	0.0193188i
$245$	−3.32396	−	1.91909i	−0.212360	−	0.122606i
$246$	22.3040	+	5.89992i	1.42205	+	0.376165i
$247$	−3.69580	+	2.13377i	−0.235158	+	0.135769i
$248$	−13.6464	−	14.3097i	−0.866546	−	0.908668i
$249$	−19.9249	+	17.0996i	−1.26269	+	1.08365i
$250$	11.0379	−	23.1903i	0.698098	−	1.46668i
$251$	−6.31087			−0.398338			−0.199169	−	0.979965i	$-0.563824\pi$
$251$	−6.31087			−0.398338			−0.199169	+	0.979965i	$0.563824\pi$
$252$	−2.96669	+	5.21524i	−0.186884	+	0.328529i
$253$	8.38881			0.527400
$254$	−3.51471	+	7.38430i	−0.220533	+	0.463332i
$255$	0.232972	+	1.24052i	0.0145893	+	0.0776842i
$256$	−14.6590	−	6.41191i	−0.916190	−	0.400744i
$257$	−12.4534	+	7.18998i	−0.776822	+	0.448499i	−0.835303	−	0.549790i	$-0.814708\pi$
$257$	−12.4534	+	7.18998i	−0.776822	+	0.448499i	0.0584805	+	0.998289i	$0.481374\pi$
$258$	−3.89022	−	14.3349i	−0.242195	−	0.892453i
$259$	4.14302	+	2.39197i	0.257435	+	0.148630i
$260$	1.24986	+	7.80853i	0.0775131	+	0.484265i
$261$	4.04541	+	10.3905i	0.250405	+	0.643157i
$262$	0.946528	+	11.9022i	0.0584767	+	0.735319i
$263$	−3.95944	+	6.85794i	−0.244149	+	0.422879i	−0.961892	−	0.273429i	$-0.911842\pi$
$263$	−3.95944	+	6.85794i	−0.244149	+	0.422879i	0.717743	+	0.696308i	$0.245175\pi$
$264$	23.2552	+	16.7246i	1.43126	+	1.02933i
$265$	8.99964	+	15.5878i	0.552843	+	0.957553i
$266$	−4.82541	+	3.32223i	−0.295865	+	0.203699i
$267$	1.44549	−	4.11304i	0.0884628	−	0.251714i
$268$	1.52071	+	0.580890i	0.0928921	+	0.0354835i
$269$			8.59237i			0.523886i	0.965083	+	0.261943i	$0.0843632\pi$
$269$			8.59237i			0.523886i	−0.965083	+	0.261943i	$0.915637\pi$
$270$	−16.7594	−	22.6854i	−1.01995	−	1.38059i
$271$		−	2.69257i		−	0.163562i	−0.996650	−	0.0817811i	$-0.973939\pi$
$271$		−	2.69257i		−	0.163562i	0.996650	−	0.0817811i	$-0.0260608\pi$
$272$	−0.743375	−	0.155466i	−0.0450737	−	0.00942654i
$273$	−0.591607	+	1.68337i	−0.0358057	+	0.101882i
$274$	−16.2448	−	23.5950i	−0.981386	−	1.42542i
$275$	−28.4507	−	49.2780i	−1.71564	−	2.97158i
$276$	3.21252	−	3.79212i	0.193371	−	0.228259i
$277$	−10.2042	+	17.6742i	−0.613112	+	1.06194i	0.377601	+	0.925969i	$0.376749\pi$
$277$	−10.2042	+	17.6742i	−0.613112	+	1.06194i	−0.990713	+	0.135973i	$0.956584\pi$
$278$	3.02440	−	0.240517i	0.181392	−	0.0144253i
$279$	20.7301	+	3.18224i	1.24108	+	0.190516i
$280$	2.56020	+	10.5498i	0.153001	+	0.630471i
$281$	−23.5939	−	13.6219i	−1.40749	−	0.812616i	−0.412347	−	0.911027i	$-0.635291\pi$
$281$	−23.5939	−	13.6219i	−1.40749	−	0.812616i	−0.995146	+	0.0984104i	$0.968624\pi$
$282$	−8.42915	+	2.28751i	−0.501949	+	0.136219i
$283$	−6.95732	+	4.01681i	−0.413570	+	0.238775i	−0.692322	−	0.721588i	$-0.743412\pi$
$283$	−6.95732	+	4.01681i	−0.413570	+	0.238775i	0.278753	+	0.960363i	$0.410079\pi$
$284$	−6.42109	−	7.90289i	−0.381022	−	0.468951i
$285$	−5.08312	−	27.0663i	−0.301098	−	1.60327i
$286$	7.69164	+	3.66100i	0.454816	+	0.216479i
$287$	9.41875			0.555971
$288$	16.4659	−	4.10766i	0.970265	−	0.242046i
$289$	16.9640			0.997879
$290$	18.2164	+	8.67046i	1.06970	+	0.509147i
$291$	−3.32614	+	2.85451i	−0.194982	+	0.167334i
$292$	−10.2414	−	12.6048i	−0.599330	−	0.737638i
$293$	25.8214	−	14.9080i	1.50850	−	0.870933i	0.508549	−	0.861033i	$-0.330182\pi$
$293$	25.8214	−	14.9080i	1.50850	−	0.870933i	0.999951	−	0.00989946i	$-0.00315115\pi$
$294$	−0.626402	+	2.36804i	−0.0365325	+	0.138107i
$295$	−28.1919	−	16.2766i	−1.64139	−	0.947659i
$296$	−3.19107	−	13.1494i	−0.185477	−	0.764293i
$297$	−30.3654	+	1.01219i	−1.76198	+	0.0587334i
$298$	16.6370	−	1.32307i	0.963757	−	0.0766434i
$299$	0.738992	−	1.27997i	0.0427370	−	0.0740227i
$300$	−33.1712	−	6.01016i	−1.91514	−	0.346997i
$301$	−3.03194	−	5.25147i	−0.174758	−	0.302690i
$302$	10.6925	+	15.5305i	0.615286	+	0.893679i
$303$	3.25352	+	3.79108i	0.186910	+	0.217792i
$304$	16.2194	+	3.39206i	0.930246	+	0.194548i
$305$		−	3.66413i		−	0.209808i
$306$	0.725110	−	0.350840i	0.0414518	−	0.0200562i
$307$		−	19.7274i		−	1.12590i	−0.826490	−	0.562951i	$-0.809666\pi$
$307$		−	19.7274i		−	1.12590i	0.826490	−	0.562951i	$-0.190334\pi$
$308$	10.9243	+	4.17292i	0.622468	+	0.237774i
$309$	−18.5789	+	3.48917i	−1.05692	+	0.198492i
$310$	31.2556	−	21.5191i	1.77520	−	1.22220i
$311$	7.44017	+	12.8868i	0.421893	+	0.730741i	0.996125	−	0.0879525i	$-0.0280324\pi$
$311$	7.44017	+	12.8868i	0.421893	+	0.730741i	−0.574231	+	0.818693i	$0.694699\pi$
$312$	4.60047	−	2.07498i	0.260450	−	0.117473i
$313$	12.3404	−	21.3741i	0.697518	−	1.20814i	−0.271807	−	0.962352i	$-0.587621\pi$
$313$	12.3404	−	21.3741i	0.697518	−	1.20814i	0.969324	−	0.245785i	$-0.0790456\pi$
$314$	0.131400	+	1.65229i	0.00741531	+	0.0932444i
$315$	−8.98287	−	7.20364i	−0.506127	−	0.405879i
$316$	−2.22856	−	13.9230i	−0.125366	−	0.783230i
$317$	16.1561	+	9.32772i	0.907416	+	0.523897i	0.879599	−	0.475716i	$-0.157811\pi$
$317$	16.1561	+	9.32772i	0.907416	+	0.523897i	0.0278171	+	0.999613i	$0.491144\pi$
$318$	8.09649	−	8.14846i	0.454029	−	0.456943i
$319$	18.8206	−	10.8661i	1.05375	−	0.608383i
$320$	16.5967	−	25.8336i	0.927782	−	1.44414i
$321$	21.9800	+	7.72468i	1.22680	+	0.431149i
$322$	0.871997	−	1.83204i	0.0485945	−	0.102096i
$323$	0.786528			0.0437636
$324$	−11.1710	+	14.1142i	−0.620609	+	0.784120i
$325$	−10.0252			−0.556097
$326$	9.52062	−	20.0025i	0.527299	−	1.10784i
$327$	−8.18668	−	2.87714i	−0.452724	−	0.159106i
$328$	−18.3853	−	19.2791i	−1.01516	−	1.06451i
$329$	−3.08795	+	1.78283i	−0.170244	+	0.0982904i
$330$	−38.7463	+	38.9950i	−2.13291	+	2.14660i
$331$	14.3672	+	8.29491i	0.789693	+	0.455930i	0.839855	−	0.542811i	$-0.182640\pi$
$331$	14.3672	+	8.29491i	0.789693	+	0.455930i	−0.0501612	+	0.998741i	$0.515973\pi$
$332$	29.9372	−	4.79185i	1.64302	−	0.262987i
$333$	11.1964	+	8.97870i	0.613556	+	0.492030i
$334$	1.76678	+	22.2165i	0.0966740	+	1.21563i
$335$	−1.56202	+	2.70550i	−0.0853423	+	0.147817i
$336$	6.06983	−	3.34023i	0.331136	−	0.182225i
$337$	2.97884	+	5.15950i	0.162268	+	0.281056i	0.935682	−	0.352846i	$-0.114786\pi$
$337$	2.97884	+	5.15950i	0.162268	+	0.281056i	−0.773414	+	0.633901i	$0.781453\pi$
$338$	−13.9067	+	9.57456i	−0.756423	+	0.520788i
$339$	−7.28047	+	1.36729i	−0.395421	+	0.0742610i
$340$	0.520081	−	1.36152i	0.0282053	−	0.0738386i
$341$		−	40.8768i		−	2.21360i
$342$	−15.8209	+	7.65482i	−0.855495	+	0.413925i
$343$			1.00000i			0.0539949i
$344$	−4.83081	+	16.4569i	−0.260460	+	0.887294i
$345$	6.21154	+	7.23782i	0.334418	+	0.389671i
$346$	−9.93101	−	14.4244i	−0.533894	−	0.775460i
$347$	6.43730	+	11.1497i	0.345572	+	0.598549i	0.985458	−	0.169922i	$-0.0543515\pi$
$347$	6.43730	+	11.1497i	0.345572	+	0.598549i	−0.639885	+	0.768470i	$0.721018\pi$
$348$	2.29544	−	12.6689i	0.123048	−	0.679127i
$349$	8.33062	−	14.4291i	0.445928	−	0.772370i	−0.552188	−	0.833719i	$-0.686207\pi$
$349$	8.33062	−	14.4291i	0.445928	−	0.772370i	0.998116	+	0.0613493i	$0.0195404\pi$
$350$	−13.7192	+	1.09103i	−0.733325	+	0.0583181i
$351$	−2.52053	+	4.72235i	−0.134536	+	0.252060i
$352$	−12.7826	−	30.5062i	−0.681317	−	1.62599i
$353$	−25.3982	−	14.6636i	−1.35181	−	0.780467i	−0.363306	−	0.931670i	$-0.618352\pi$
$353$	−25.3982	−	14.6636i	−1.35181	−	0.780467i	−0.988503	+	0.151203i	$0.951685\pi$
$354$	−5.31277	+	20.0843i	−0.282371	+	1.06747i
$355$	16.9233	−	9.77069i	0.898198	−	0.518575i
$356$	−3.90703	+	3.17446i	−0.207072	+	0.168246i
$357$	0.249554	−	0.214169i	0.0132078	−	0.0113350i
$358$	−18.6482	−	8.87602i	−0.985590	−	0.469112i
$359$	2.39895			0.126612			0.0633060	−	0.997994i	$-0.479836\pi$
$359$	2.39895			0.126612			0.0633060	+	0.997994i	$0.479836\pi$
$360$	2.78951	+	32.4483i	0.147020	+	1.71018i
$361$	1.83908			0.0967938
$362$	8.66667	+	4.12508i	0.455510	+	0.216809i
$363$	7.41315	+	39.4732i	0.389090	+	2.07180i
$364$	1.59906	−	1.29923i	0.0838133	−	0.0680982i
$365$	26.9920	−	15.5838i	1.41282	−	0.815694i
$366$	−2.25679	+	0.612450i	−0.117964	+	0.0320133i
$367$	−17.1124	−	9.87986i	−0.893261	−	0.515724i	−0.0182530	−	0.999833i	$-0.505810\pi$
$367$	−17.1124	−	9.87986i	−0.893261	−	0.515724i	−0.875008	+	0.484109i	$0.839144\pi$
$368$	−5.45210	+	1.79126i	−0.284210	+	0.0933756i
$369$	27.9291	+	4.28733i	1.45393	+	0.223190i
$370$	25.8856	−	2.05856i	1.34573	−	0.107020i
$371$	2.34477	−	4.06126i	0.121734	−	0.210850i
$372$	−18.4782	−	15.6539i	−0.958049	−	0.811616i
$373$	8.62492	+	14.9388i	0.446582	+	0.773502i	0.998161	−	0.0606204i	$-0.0193079\pi$
$373$	8.62492	+	14.9388i	0.446582	+	0.773502i	−0.551579	+	0.834122i	$0.685975\pi$
$374$	−0.890312	−	1.29314i	−0.0460369	−	0.0668668i
$375$	10.4294	−	29.6760i	0.538571	−	1.53246i
$376$	9.67688	+	2.84059i	0.499047	+	0.146492i
$377$		−	3.82888i		−	0.197197i
$378$	−2.93536	+	6.73674i	−0.150979	+	0.346501i
$379$			26.3144i			1.35168i	0.737049	+	0.675840i	$0.236219\pi$
$379$			26.3144i			1.35168i	−0.737049	+	0.675840i	$0.763781\pi$
$380$	−11.3474	+	29.7063i	−0.582110	+	1.52390i
$381$	−3.32095	+	9.44949i	−0.170137	+	0.484112i
$382$	−25.6678	+	17.6719i	−1.31328	+	0.904175i
$383$	9.11566	+	15.7888i	0.465788	+	0.806769i	0.999237	−	0.0390634i	$-0.0124374\pi$
$383$	9.11566	+	15.7888i	0.465788	+	0.806769i	−0.533448	+	0.845833i	$0.679104\pi$
$384$	−18.6853	−	5.90410i	−0.953532	−	0.301292i
$385$	−11.2210	+	19.4354i	−0.571878	+	0.990521i
$386$	−0.669957	−	8.42442i	−0.0340999	−	0.428792i
$387$	−6.60008	−	16.9521i	−0.335501	−	0.861725i
$388$	4.99754	−	0.799923i	0.253711	−	0.0406099i
$389$	−28.6977	−	16.5687i	−1.45503	−	0.840064i	−0.456273	−	0.889840i	$-0.650816\pi$
$389$	−28.6977	−	16.5687i	−1.45503	−	0.840064i	−0.998760	+	0.0497759i	$0.984149\pi$
$390$	2.53663	+	9.34711i	0.128447	+	0.473310i
$391$	−0.235905	+	0.136200i	−0.0119302	+	0.00688791i
$392$	2.04688	−	1.95199i	0.103383	−	0.0985906i
$393$	2.69908	+	14.3719i	0.136150	+	0.724967i
$394$	0.806903	−	1.69528i	0.0406512	−	0.0854068i
$395$	27.0596			1.36151
$396$	30.4939	+	17.3465i	1.53238	+	0.871692i
$397$	−7.24602			−0.363667			−0.181834	−	0.983329i	$-0.558203\pi$
$397$	−7.24602			−0.363667			−0.181834	+	0.983329i	$0.558203\pi$
$398$	2.47353	−	5.19680i	0.123987	−	0.260492i
$399$	−5.44492	+	4.67286i	−0.272587	+	0.233936i
$400$	29.0131	+	25.9520i	1.45066	+	1.29760i
$401$	−18.5998	+	10.7386i	−0.928831	+	0.536261i	−0.886442	−	0.462841i	$-0.846830\pi$
$401$	−18.5998	+	10.7386i	−0.928831	+	0.536261i	−0.0423890	+	0.999101i	$0.513497\pi$
$402$	1.92744	+	0.509853i	0.0961321	+	0.0254292i
$403$	−6.23702	−	3.60095i	−0.310688	−	0.179376i
$404$	−0.911738	−	5.69611i	−0.0453607	−	0.283392i
$405$	−23.3576	−	25.4496i	−1.16065	−	1.26460i
$406$	−0.416693	−	5.23974i	−0.0206802	−	0.260044i
$407$	13.9860	−	24.2245i	0.693263	−	1.20077i
$408$	−0.925506	−	0.0927510i	−0.0458194	−	0.00459186i
$409$	2.23549	+	3.87198i	0.110538	+	0.191457i	0.915987	−	0.401207i	$-0.131409\pi$
$409$	2.23549	+	3.87198i	0.110538	+	0.191457i	−0.805449	+	0.592664i	$0.798076\pi$
$410$	42.1097	−	28.9920i	2.07965	−	1.43181i
$411$	−22.8490	−	26.6242i	−1.12706	−	1.31327i
$412$	20.3911	+	7.78913i	1.00460	+	0.383743i
$413$			8.48141i			0.417343i
$414$	3.41963	−	5.03556i	0.168066	−	0.247484i
$415$			58.1834i			2.85611i
$416$	−5.78072	−	0.736984i	−0.283423	−	0.0361336i
$417$	3.65197	−	0.685849i	0.178838	−	0.0335862i
$418$	19.4253	+	28.2145i	0.950125	+	1.38002i
$419$	−7.21795	−	12.5019i	−0.352620	−	0.610756i	0.634088	−	0.773261i	$-0.281376\pi$
$419$	−7.21795	−	12.5019i	−0.352620	−	0.610756i	−0.986708	+	0.162505i	$0.948043\pi$
$420$	4.48856	+	12.5153i	0.219019	+	0.610683i
$421$	−6.17131	+	10.6890i	−0.300771	+	0.520951i	−0.976311	−	0.216372i	$-0.930577\pi$
$421$	−6.17131	+	10.6890i	−0.300771	+	0.520951i	0.675539	+	0.737324i	$0.263911\pi$
$422$	9.20710	−	0.732200i	0.448195	−	0.0356429i
$423$	−9.96811	+	3.88095i	−0.484666	+	0.188698i
$424$	−12.8899	+	3.12809i	−0.625988	+	0.151914i
$425$	1.60014	+	0.923843i	0.0776183	+	0.0448130i
$426$	−8.84659	−	8.79017i	−0.428619	−	0.425885i
$427$	−0.826755	+	0.477327i	−0.0400095	+	0.0230995i
$428$	−16.9642	−	20.8790i	−0.819996	−	1.00923i
$429$	9.84279	+	3.45917i	0.475214	+	0.167010i
$430$	−29.7199	−	14.1458i	−1.43322	−	0.682172i
$431$	−33.1403			−1.59631			−0.798155	−	0.602452i	$-0.794190\pi$
$431$	−33.1403			−1.59631			−0.798155	+	0.602452i	$0.794190\pi$
$432$	19.5191	−	7.14175i	0.939113	−	0.343608i
$433$	−2.62906			−0.126345			−0.0631723	−	0.998003i	$-0.520122\pi$
$433$	−2.62906			−0.126345			−0.0631723	+	0.998003i	$0.520122\pi$
$434$	−8.92712	−	4.24905i	−0.428516	−	0.203961i
$435$	23.3110	+	8.19246i	1.11768	+	0.392798i
$436$	6.31850	+	7.77663i	0.302601	+	0.372433i
$437$	5.14710	−	2.97168i	0.246219	−	0.142155i
$438$	−14.1099	−	14.0199i	−0.674198	−	0.669898i
$439$	21.0031	+	12.1261i	1.00242	+	0.578749i	0.908964	−	0.416874i	$-0.136874\pi$
$439$	21.0031	+	12.1261i	1.00242	+	0.578749i	0.0934587	+	0.995623i	$0.470208\pi$
$440$	61.6854	−	14.9697i	2.94074	−	0.713652i
$441$	−0.455191	+	2.96527i	−0.0216758	+	0.141203i
$442$	−0.275739	+	0.0219283i	−0.0131155	+	0.00104302i
$443$	2.13519	−	3.69826i	0.101446	−	0.175710i	−0.810835	−	0.585275i	$-0.800986\pi$
$443$	2.13519	−	3.69826i	0.101446	−	0.175710i	0.912281	+	0.409566i	$0.134320\pi$
$444$	−5.59460	−	15.5992i	−0.265508	−	0.740304i
$445$	−4.83043	−	8.36655i	−0.228984	−	0.396613i
$446$	−20.0108	−	29.0649i	−0.947538	−	1.37626i
$447$	20.0893	−	3.77281i	0.950189	−	0.178448i
$448$	−7.99100	−	0.379437i	−0.377539	−	0.0179267i
$449$			32.8830i			1.55184i	0.630829	+	0.775922i	$0.282715\pi$
$449$			32.8830i			1.55184i	−0.630829	+	0.775922i	$0.717285\pi$
$450$	−41.1778	−	3.00968i	−1.94114	−	0.141878i
$451$		−	55.0721i		−	2.59324i
$452$	7.99061	+	3.05230i	0.375847	+	0.143568i
$453$	15.0395	+	17.5243i	0.706617	+	0.823365i
$454$	12.0780	−	8.31553i	0.566847	−	0.390267i
$455$	1.97698	+	3.42423i	0.0926824	+	0.160531i
$456$	20.1932	+	2.02370i	0.945635	+	0.0947682i
$457$	7.47452	−	12.9463i	0.349643	−	0.605600i	−0.636543	−	0.771241i	$-0.719636\pi$
$457$	7.47452	−	12.9463i	0.349643	−	0.605600i	0.986186	+	0.165641i	$0.0529694\pi$
$458$	−2.47410	−	31.1108i	−0.115607	−	1.45371i
$459$	0.837482	−	0.521473i	0.0390903	−	0.0243403i
$460$	−1.74067	−	10.8749i	−0.0811590	−	0.507043i
$461$	2.46420	+	1.42270i	0.114769	+	0.0662620i	0.556286	−	0.830991i	$-0.312226\pi$
$461$	2.46420	+	1.42270i	0.114769	+	0.0662620i	−0.441517	+	0.897253i	$0.645559\pi$
$462$	13.8461	+	3.66262i	0.644179	+	0.170400i
$463$	−21.5768	+	12.4574i	−1.00276	+	0.578943i	−0.909063	−	0.416658i	$-0.863201\pi$
$463$	−21.5768	+	12.4574i	−1.00276	+	0.578943i	−0.0936949	+	0.995601i	$0.529868\pi$
$464$	−9.91174	+	11.0809i	−0.460141	+	0.514416i
$465$	35.2683	−	30.2675i	1.63553	−	1.40362i
$466$	−13.9438	+	29.2955i	−0.645934	+	1.35709i
$467$	−6.16661			−0.285356			−0.142678	−	0.989769i	$-0.545571\pi$
$467$	−6.16661			−0.285356			−0.142678	+	0.989769i	$0.545571\pi$
$468$	5.33302	−	3.12469i	0.246519	−	0.144439i
$469$	0.813939			0.0375842
$470$	−8.31797	+	17.4758i	−0.383679	+	0.806098i
$471$	0.374694	+	1.99515i	0.0172650	+	0.0919316i
$472$	17.3604	−	16.5557i	0.799078	−	0.762036i
$473$	−30.7057	+	17.7280i	−1.41185	+	0.815133i
$474$	−4.52293	−	16.6664i	−0.207745	−	0.765511i
$475$	−34.9128	−	20.1569i	−1.60191	−	0.924864i
$476$	−0.374956	+	0.0600168i	−0.0171861	+	0.00275086i
$477$	8.80151	−	10.9754i	0.402994	−	0.502529i
$478$	−1.60382	−	20.1674i	−0.0733572	−	0.922435i
$479$	−15.1497	+	26.2401i	−0.692209	+	1.19894i	0.278904	+	0.960319i	$0.410029\pi$
$479$	−15.1497	+	26.2401i	−0.692209	+	1.19894i	−0.971113	+	0.238622i	$0.923304\pi$
$480$	16.8556	−	33.6173i	0.769350	−	1.53441i
$481$	−2.46413	−	4.26801i	−0.112355	−	0.194604i
$482$	9.39881	−	6.47096i	0.428104	−	0.294744i
$483$	0.823924	−	2.34441i	0.0374898	−	0.106674i
$484$	16.5489	−	43.3234i	0.752224	−	1.96924i
$485$			9.71280i			0.441035i
$486$	−11.7706	+	18.6401i	−0.533926	+	0.845531i
$487$			17.9066i			0.811425i	0.914001	+	0.405713i	$0.132977\pi$
$487$			17.9066i			0.811425i	−0.914001	+	0.405713i	$0.867023\pi$
$488$	2.59085	+	0.760529i	0.117282	+	0.0344275i
$489$	8.99576	−	25.5967i	0.406802	−	1.15752i
$490$	3.07812	+	4.47084i	0.139055	+	0.201972i
$491$	−3.95405	−	6.84862i	−0.178444	−	0.309074i	0.762904	−	0.646512i	$-0.223773\pi$
$491$	−3.95405	−	6.84862i	−0.178444	−	0.309074i	−0.941348	+	0.337438i	$0.890440\pi$
$492$	−24.8951	−	21.0900i	−1.12236	−	0.950811i
$493$	−0.352840	+	0.611137i	−0.0158911	+	0.0275242i
$494$	6.01623	−	0.478444i	0.270683	−	0.0215262i
$495$	−42.1202	+	52.5235i	−1.89316	+	2.36076i
$496$	8.72839	+	26.5669i	0.391916	+	1.19289i
$497$	−4.40921	−	2.54566i	−0.197780	−	0.114188i
$498$	35.8359	−	9.72520i	1.60585	−	0.435797i
$499$	−28.2925	+	16.3347i	−1.26654	+	0.731240i	−0.974333	−	0.225113i	$-0.927725\pi$
$499$	−28.2925	+	16.3347i	−1.26654	+	0.731240i	−0.292212	+	0.956353i	$0.594391\pi$
$500$	−28.1896	+	22.9040i	−1.26068	+	1.02430i
$501$	5.03808	+	26.8265i	0.225085	+	1.19852i
$502$	8.05864	+	3.83568i	0.359675	+	0.171195i
$503$	−37.5962			−1.67633			−0.838166	−	0.545415i	$-0.816372\pi$
$503$	−37.5962			−1.67633			−0.838166	+	0.545415i	$0.816372\pi$
$504$	6.95807	−	4.85646i	0.309937	−	0.216324i
$505$	11.0705			0.492630
$506$	−10.7121	−	5.09863i	−0.476209	−	0.226662i
$507$	−15.6921	+	13.4670i	−0.696909	+	0.598092i
$508$	8.97620	−	7.29315i	0.398254	−	0.323581i
$509$	−8.47297	+	4.89187i	−0.375558	+	0.216828i	−0.675884	−	0.737008i	$-0.736238\pi$
$509$	−8.47297	+	4.89187i	−0.375558	+	0.216828i	0.300326	+	0.953837i	$0.402905\pi$
$510$	0.456480	−	1.72567i	0.0202133	−	0.0764140i
$511$	−7.03250	−	4.06021i	−0.311099	−	0.179613i
$512$	14.8217	+	17.0973i	0.655034	+	0.755600i
$513$	−18.2727	+	11.3778i	−0.806758	+	0.502342i
$514$	20.2723	−	1.61217i	0.894174	−	0.0711097i
$515$	−20.9451	+	36.2780i	−0.922951	+	1.59860i
$516$	−3.74500	+	20.6694i	−0.164864	+	0.909918i
$517$	10.4243	+	18.0554i	0.458461	+	0.794077i
$518$	−3.83660	−	5.57251i	−0.168570	−	0.244842i
$519$	−13.9684	−	16.2763i	−0.613144	−	0.714448i
$520$	3.14994	−	10.7307i	0.138134	−	0.470574i
$521$		−	28.3001i		−	1.23985i	−0.784662	−	0.619924i	$-0.787163\pi$
$521$		−	28.3001i		−	1.23985i	0.784662	−	0.619924i	$-0.212837\pi$
$522$	1.14948	−	15.7269i	0.0503112	−	0.688348i
$523$			20.8387i			0.911213i	0.890181	+	0.455607i	$0.150578\pi$
$523$			20.8387i			0.911213i	−0.890181	+	0.455607i	$0.849422\pi$
$524$	6.02535	−	15.7737i	0.263219	−	0.689079i
$525$	−16.5660	+	3.11114i	−0.723000	+	0.135781i
$526$	9.22417	−	6.35072i	0.402193	−	0.276905i
$527$	0.663671	+	1.14951i	0.0289099	+	0.0500735i
$528$	−19.5306	−	35.4907i	−0.849960	−	1.54454i
$529$	10.4708	−	18.1360i	0.455253	−	0.788521i
$530$	−2.01794	−	25.3747i	−0.0876536	−	1.10221i
$531$	−3.86066	+	25.1496i	−0.167538	+	1.09140i
$532$	8.18101	−	1.30948i	0.354692	−	0.0567732i
$533$	−8.40295	−	4.85145i	−0.363972	−	0.210139i
$534$	−4.34568	+	4.37357i	−0.188056	+	0.189263i
$535$	44.7106	−	25.8137i	1.93301	−	1.11602i
$536$	−1.58880	−	1.66604i	−0.0686259	−	0.0719618i
$537$	−23.8637	−	8.38669i	−1.02979	−	0.361912i
$538$	5.22235	−	10.9720i	0.225151	−	0.473036i
$539$	5.84707			0.251851
$540$	7.61294	+	39.1543i	0.327609	+	1.68493i
$541$	−20.0201			−0.860732			−0.430366	−	0.902655i	$-0.641615\pi$
$541$	−20.0201			−0.860732			−0.430366	+	0.902655i	$0.641615\pi$
$542$	−1.63652	+	3.43827i	−0.0702945	+	0.147686i
$543$	11.0905	+	3.89767i	0.475939	+	0.167265i
$544$	0.854759	+	0.650338i	0.0366475	+	0.0278830i
$545$	−16.6530	+	9.61459i	−0.713334	+	0.411844i
$546$	1.77858	−	1.79000i	0.0761164	−	0.0766050i
$547$	29.8020	+	17.2062i	1.27424	+	0.735684i	0.975783	−	0.218739i	$-0.0701943\pi$
$547$	29.8020	+	17.2062i	1.27424	+	0.735684i	0.298458	+	0.954423i	$0.403528\pi$
$548$	6.40301	+	40.0029i	0.273523	+	1.70884i
$549$	−2.66882	+	1.03907i	−0.113903	+	0.0443465i
$550$	6.37934	+	80.2174i	0.272016	+	3.42048i
$551$	7.69846	−	13.3341i	0.327966	−	0.568053i
$552$	−6.40702	+	2.88980i	−0.272701	+	0.122998i
$553$	−3.52506	−	6.10558i	−0.149901	−	0.259635i
$554$	23.7724	−	16.3670i	1.00999	−	0.695368i
$555$	31.2569	−	5.87011i	1.32678	−	0.249172i
$556$	−4.00819	−	1.53107i	−0.169985	−	0.0649319i
$557$		−	9.89200i		−	0.419137i	−0.977794	−	0.209569i	$-0.932794\pi$
$557$		−	9.89200i		−	0.419137i	0.977794	−	0.209569i	$-0.0672060\pi$
$558$	−24.5372	−	16.6631i	−1.03874	−	0.705406i
$559$			6.24681i			0.264212i
$560$	3.14281	−	15.0276i	0.132808	−	0.635031i
$561$	−1.25226	−	1.45916i	−0.0528705	−	0.0616058i
$562$	21.8489	+	31.7346i	0.921638	+	1.33864i
$563$	18.6487	+	32.3004i	0.785947	+	1.36130i	0.928432	+	0.371503i	$0.121158\pi$
$563$	18.6487	+	32.3004i	0.785947	+	1.36130i	−0.142485	+	0.989797i	$0.545509\pi$
$564$	12.1539	+	2.20212i	0.511771	+	0.0927259i
$565$	−8.20769	+	14.2161i	−0.345300	+	0.598077i
$566$	11.3255	−	0.900667i	0.476046	−	0.0378579i
$567$	−2.69953	+	8.58560i	−0.113369	+	0.360561i
$568$	3.39610	+	13.9942i	0.142497	+	0.587185i
$569$	−9.96571	−	5.75371i	−0.417784	−	0.241208i	0.276345	−	0.961059i	$-0.410877\pi$
$569$	−9.96571	−	5.75371i	−0.417784	−	0.241208i	−0.694129	+	0.719851i	$0.744210\pi$
$570$	−9.95975	+	37.6517i	−0.417168	+	1.57706i
$571$	−6.13735	+	3.54340i	−0.256840	+	0.148287i	−0.622892	−	0.782308i	$-0.714042\pi$
$571$	−6.13735	+	3.54340i	−0.256840	+	0.148287i	0.366052	+	0.930594i	$0.380709\pi$
$572$	−7.59670	−	9.34979i	−0.317634	−	0.390935i
$573$	−28.9631	+	24.8563i	−1.20995	+	1.03839i
$574$	−12.0272	−	5.72462i	−0.502007	−	0.238941i
$575$	13.9620			0.582254
$576$	−23.5227	−	4.76256i	−0.980113	−	0.198440i
$577$	35.9128			1.49507			0.747534	−	0.664223i	$-0.231238\pi$
$577$	35.9128			1.49507			0.747534	+	0.664223i	$0.231238\pi$
$578$	−21.6621	−	10.3105i	−0.901023	−	0.428861i
$579$	−1.91042	−	10.1725i	−0.0793944	−	0.422755i
$580$	−17.9915	−	22.1434i	−0.747056	−	0.919455i
$581$	13.1282	−	7.57956i	0.544649	−	0.314453i
$582$	5.98224	−	1.62347i	0.247972	−	0.0672949i
$583$	−23.7465	−	13.7100i	−0.983479	−	0.567812i
$584$	5.41662	+	22.3202i	0.224141	+	0.923616i
$585$	4.30360	+	11.0537i	0.177932	+	0.457013i
$586$	−42.0334	+	3.34273i	−1.73638	+	0.138087i
$587$	−0.675757	+	1.17045i	−0.0278915	+	0.0483095i	−0.879634	−	0.475651i	$-0.842213\pi$
$587$	−0.675757	+	1.17045i	−0.0278915	+	0.0483095i	0.851743	+	0.523960i	$0.175546\pi$
$588$	2.23915	−	2.64314i	0.0923411	−	0.109001i
$589$	−14.4803	−	25.0807i	−0.596652	−	1.03343i
$590$	26.1068	+	37.9190i	1.07480	+	1.56110i
$591$	0.762418	−	2.16940i	0.0313617	−	0.0892372i
$592$	−3.91723	+	18.7306i	−0.160997	+	0.769821i
$593$			14.2740i			0.586162i	0.956088	+	0.293081i	$0.0946805\pi$
$593$			14.2740i			0.586162i	−0.956088	+	0.293081i	$0.905319\pi$
$594$	39.3902	+	17.1633i	1.61620	+	0.704217i
$595$		−	0.728734i		−	0.0298752i
$596$	−22.0487	−	8.42232i	−0.903152	−	0.344992i
$597$	2.33716	−	6.65021i	0.0956537	−	0.272175i
$598$	−1.72161	+	1.18530i	−0.0704017	+	0.0484707i
$599$	−22.8918	−	39.6498i	−0.935335	−	1.62005i	−0.774035	−	0.633143i	$-0.781764\pi$
$599$	−22.8918	−	39.6498i	−0.935335	−	1.62005i	−0.161301	−	0.986905i	$-0.551569\pi$
$600$	38.7049	+	27.8357i	1.58012	+	1.13639i
$601$	9.37297	−	16.2345i	0.382331	−	0.662218i	−0.609064	−	0.793121i	$-0.708455\pi$
$601$	9.37297	−	16.2345i	0.382331	−	0.662218i	0.991395	+	0.130904i	$0.0417879\pi$
$602$	0.679834	+	8.54863i	0.0277080	+	0.348416i
$603$	2.41355	+	0.370498i	0.0982872	+	0.0150878i
$604$	−4.21453	−	26.3304i	−0.171487	−	1.07137i
$605$	77.0768	+	44.5003i	3.13362	+	1.80920i
$606$	−1.85040	−	6.81846i	−0.0751674	−	0.276981i
$607$	−8.08350	+	4.66701i	−0.328099	+	0.189428i	−0.654997	−	0.755632i	$-0.727330\pi$
$607$	−8.08350	+	4.66701i	−0.328099	+	0.189428i	0.326898	+	0.945060i	$0.393997\pi$
$608$	−18.6496	−	14.1894i	−0.756343	−	0.575458i
$609$	−1.18823	−	6.32700i	−0.0481493	−	0.256383i
$610$	−2.22702	+	4.67890i	−0.0901695	+	0.189443i
$611$	3.67322			0.148603
$612$	−1.13916	+	0.00728899i	−0.0460480	+	0.000294640i
$613$	−5.11320			−0.206520			−0.103260	−	0.994654i	$-0.532927\pi$
$613$	−5.11320			−0.206520			−0.103260	+	0.994654i	$0.532927\pi$
$614$	−11.9901	+	25.1908i	−0.483881	+	1.01662i
$615$	47.5159	−	40.7785i	1.91603	−	1.64435i
$616$	−11.4135	−	11.9683i	−0.459861	−	0.482215i
$617$	−4.20354	+	2.42691i	−0.169228	+	0.0977038i	−0.582222	−	0.813030i	$-0.697816\pi$
$617$	−4.20354	+	2.42691i	−0.169228	+	0.0977038i	0.412994	+	0.910734i	$0.364483\pi$
$618$	25.8450	+	6.83660i	1.03964	+	0.275008i
$619$	18.5748	+	10.7241i	0.746582	+	0.431040i	0.824458	−	0.565924i	$-0.191480\pi$
$619$	18.5748	+	10.7241i	0.746582	+	0.431040i	−0.0778753	+	0.996963i	$0.524814\pi$
$620$	−52.9908	+	8.48189i	−2.12816	+	0.340641i
$621$	3.51031	−	6.57676i	0.140864	−	0.263916i
$622$	−1.66827	−	20.9777i	−0.0668914	−	0.841131i
$623$	−1.25852	+	2.17982i	−0.0504216	+	0.0873328i
$624$	−7.13571	−	0.146477i	−0.285657	−	0.00586378i
$625$	−10.5230	−	18.2264i	−0.420921	−	0.729057i
$626$	−28.7489	+	19.7933i	−1.14904	+	0.791098i
$627$	27.3226	+	31.8368i	1.09116	+	1.27144i
$628$	0.836456	−	2.18975i	0.0333782	−	0.0873807i
$629$			0.908302i			0.0362164i
$630$	7.09234	+	14.6584i	0.282566	+	0.584003i
$631$		−	19.1254i		−	0.761369i	−0.924705	−	0.380684i	$-0.875688\pi$
$631$		−	19.1254i		−	0.761369i	0.924705	−	0.380684i	$-0.124312\pi$
$632$	−5.61649	+	19.1334i	−0.223412	+	0.761086i
$633$	11.1176	−	2.08791i	0.441885	−	0.0829870i
$634$	−14.9612	−	21.7305i	−0.594184	−	0.863028i
$635$	11.0977	+	19.2217i	0.440397	+	0.762791i
$636$	−15.2913	+	5.48419i	−0.606341	+	0.217462i
$637$	0.515084	−	0.892151i	0.0204084	−	0.0353483i
$638$	−30.6371	+	2.43644i	−1.21294	+	0.0964595i
$639$	−11.9157	−	9.55559i	−0.471379	−	0.378013i
$640$	−36.8944	+	22.9008i	−1.45838	+	0.905234i
$641$	12.4751	+	7.20251i	0.492737	+	0.284482i	0.725709	−	0.688001i	$-0.241512\pi$
$641$	12.4751	+	7.20251i	0.492737	+	0.284482i	−0.232972	+	0.972483i	$0.574845\pi$
$642$	−23.3722	−	23.2232i	−0.922429	−	0.916546i
$643$	−7.01273	+	4.04880i	−0.276555	+	0.159669i	−0.631863	−	0.775080i	$-0.717709\pi$
$643$	−7.01273	+	4.04880i	−0.276555	+	0.159669i	0.355308	+	0.934749i	$0.384376\pi$
$644$	−2.22699	+	1.80942i	−0.0877556	+	0.0713013i
$645$	−38.0318	−	13.3660i	−1.49750	−	0.526285i
$646$	−1.00435	−	0.478043i	−0.0395158	−	0.0188084i
$647$	16.2684			0.639576			0.319788	−	0.947489i	$-0.396388\pi$
$647$	16.2684			0.639576			0.319788	+	0.947489i	$0.396388\pi$
$648$	22.8432	−	11.2334i	0.897364	−	0.441291i
$649$	49.5914			1.94663
$650$	12.8016	+	6.09320i	0.502121	+	0.238995i
$651$	−11.4238	−	4.01480i	−0.447734	−	0.157352i
$652$	−24.3147	+	19.7556i	−0.952235	+	0.773690i
$653$	26.4229	−	15.2553i	1.03401	−	0.596985i	0.115878	−	0.993263i	$-0.463032\pi$
$653$	26.4229	−	15.2553i	1.03401	−	0.596985i	0.918131	+	0.396278i	$0.129698\pi$
$654$	8.70525	+	8.64973i	0.340402	+	0.338231i
$655$	28.0631	+	16.2023i	1.09652	+	0.633074i
$656$	11.7595	+	35.7927i	0.459131	+	1.39747i
$657$	−19.0050	−	15.2407i	−0.741457	−	0.594598i
$658$	5.02672	−	0.399753i	0.195962	−	0.0155840i
$659$	16.4657	−	28.5194i	0.641413	−	1.11096i	−0.343705	−	0.939078i	$-0.611682\pi$
$659$	16.4657	−	28.5194i	0.641413	−	1.11096i	0.985118	−	0.171882i	$-0.0549847\pi$
$660$	73.1777	−	26.2450i	2.84844	−	1.02158i
$661$	14.0288	+	24.2985i	0.545655	+	0.945103i	0.998565	+	0.0535464i	$0.0170525\pi$
$661$	14.0288	+	24.2985i	0.545655	+	0.945103i	−0.452910	+	0.891556i	$0.649614\pi$
$662$	−13.3046	−	19.3244i	−0.517098	−	0.751064i
$663$	−0.332955	+	0.0625297i	−0.0129309	+	0.00242845i
$664$	−41.1406	−	12.0766i	−1.59657	−	0.468662i
$665$			15.8999i			0.616573i
$666$	−8.83998	−	18.2703i	−0.342542	−	0.707962i
$667$			5.33244i			0.206473i
$668$	11.2469	−	29.4431i	0.435155	−	1.13919i
$669$	−28.1460	−	32.7963i	−1.08819	−	1.26798i
$670$	3.63899	−	2.50540i	0.140587	−	0.0967920i
$671$	2.79097	+	4.83410i	0.107744	+	0.186618i
$672$	−9.78101	+	0.576122i	−0.377311	+	0.0222244i
$673$	−19.1422	+	33.1553i	−0.737877	+	1.27804i	0.215572	+	0.976488i	$0.430838\pi$
$673$	−19.1422	+	33.1553i	−0.737877	+	1.27804i	−0.953449	+	0.301553i	$0.902495\pi$
$674$	−0.667928	−	8.39891i	−0.0257276	−	0.323514i
$675$	−50.5388	+	1.68465i	−1.94524	+	0.0648421i
$676$	23.5774	−	3.77388i	0.906823	−	0.145149i
$677$	20.7627	+	11.9873i	0.797973	+	0.460710i	0.842762	−	0.538286i	$-0.180928\pi$
$677$	20.7627	+	11.9873i	0.797973	+	0.460710i	−0.0447886	+	0.998996i	$0.514261\pi$
$678$	10.1278	+	2.67904i	0.388956	+	0.102888i
$679$	2.19154	−	1.26529i	0.0841037	−	0.0485573i
$680$	−1.49163	+	1.42248i	−0.0572014	+	0.0545498i
$681$	13.6286	−	11.6961i	0.522249	−	0.448197i
$682$	−24.8445	+	52.1975i	−0.951345	+	1.99875i
$683$	29.2758			1.12021			0.560104	−	0.828422i	$-0.310761\pi$
$683$	29.2758			1.12021			0.560104	+	0.828422i	$0.310761\pi$
$684$	24.8549	−	0.159036i	0.950352	−	0.00608087i
$685$	−77.7464			−2.97054
$686$	0.607789	−	1.27695i	0.0232055	−	0.0487540i
$687$	−7.05505	−	37.5663i	−0.269167	−	1.43324i
$688$	16.1710	−	18.0784i	0.616513	−	0.689233i
$689$	−4.18378	+	2.41550i	−0.159389	+	0.0920234i
$690$	−3.53274	−	13.0176i	−0.134489	−	0.495572i
$691$	−12.8452	−	7.41617i	−0.488654	−	0.282125i	0.235362	−	0.971908i	$-0.424372\pi$
$691$	−12.8452	−	7.41617i	−0.488654	−	0.282125i	−0.724016	+	0.689783i	$0.757706\pi$
$692$	3.91437	+	24.4551i	0.148802	+	0.929645i
$693$	17.3381	+	2.66154i	0.658621	+	0.101103i
$694$	−1.44340	−	18.1501i	−0.0547907	−	0.688969i
$695$	4.11707	−	7.13098i	0.156170	−	0.270494i
$696$	−10.6312	+	14.7824i	−0.402975	+	0.560326i
$697$	0.894143	+	1.54870i	0.0338681	+	0.0586613i
$698$	−19.4076	+	13.3619i	−0.734588	+	0.505755i
$699$	−13.1751	+	37.4887i	−0.498328	+	1.41795i
$700$	18.1819	+	6.94522i	0.687210	+	0.262505i
$701$		−	2.86753i		−	0.108305i	−0.998533	−	0.0541525i	$-0.982754\pi$
$701$		−	2.86753i		−	0.108305i	0.998533	−	0.0541525i	$-0.0172457\pi$
$702$	6.08877	−	4.49823i	0.229806	−	0.169775i
$703$		−	19.8179i		−	0.747445i
$704$	−2.21859	+	46.7239i	−0.0836164	+	1.76097i
$705$	−7.85940	+	22.3633i	−0.296002	+	0.842251i
$706$	23.5197	+	34.1614i	0.885176	+	1.28568i
$707$	−1.44215	−	2.49788i	−0.0542378	−	0.0939425i
$708$	18.9912	−	22.4176i	0.713732	−	0.842504i
$709$	6.21193	−	10.7594i	0.233294	−	0.404077i	−0.725482	−	0.688241i	$-0.758383\pi$
$709$	6.21193	−	10.7594i	0.233294	−	0.404077i	0.958775	+	0.284165i	$0.0917163\pi$
$710$	−27.5487	+	2.19083i	−1.03389	+	0.0822203i
$711$	−7.67352	−	19.7092i	−0.287780	−	0.739154i
$712$	6.91847	−	1.67896i	0.259281	−	0.0629217i
$713$	8.68623	+	5.01500i	0.325302	+	0.187813i
$714$	−0.448837	+	0.121806i	−0.0167973	+	0.00455847i
$715$	20.0217	−	11.5596i	0.748771	−	0.432303i
$716$	18.4180	+	22.6684i	0.688315	+	0.847158i
$717$	−4.57340	−	24.3522i	−0.170797	−	0.909449i
$718$	−3.06334	−	1.45806i	−0.114323	−	0.0544143i
$719$	−37.0087			−1.38019			−0.690095	−	0.723719i	$-0.742431\pi$
$719$	−37.0087			−1.38019			−0.690095	+	0.723719i	$0.742431\pi$
$720$	16.1597	−	43.1302i	0.602236	−	1.60737i
$721$	10.9141			0.406462
$722$	−2.34841	−	1.11777i	−0.0873988	−	0.0415993i
$723$	10.6055	−	9.10168i	0.394422	−	0.338495i
$724$	−8.55969	−	10.5350i	−0.318118	−	0.391531i
$725$	31.3241	−	18.0850i	1.16335	−	0.671660i
$726$	14.5252	−	54.9108i	0.539080	−	2.03793i
$727$	−3.21382	−	1.85550i	−0.119194	−	0.0688167i	0.439218	−	0.898381i	$-0.355256\pi$
$727$	−3.21382	−	1.85550i	−0.119194	−	0.0688167i	−0.558412	+	0.829564i	$0.688589\pi$
$728$	−2.83157	+	0.687159i	−0.104945	+	0.0254678i
$729$	−11.9129	+	24.2298i	−0.441218	+	0.897400i
$730$	−43.9390	+	3.49427i	−1.62625	+	0.129329i
$731$	0.575657	−	0.997068i	0.0212915	−	0.0368779i
$732$	3.25404	+	0.589587i	0.120273	+	0.0217918i
$733$	−21.5278	−	37.2872i	−0.795147	−	1.37723i	−0.922746	−	0.385409i	$-0.874060\pi$
$733$	−21.5278	−	37.2872i	−0.795147	−	1.37723i	0.127599	−	0.991826i	$-0.459273\pi$
$734$	15.8468	+	23.0168i	0.584915	+	0.849565i
$735$	4.32950	+	5.04482i	0.159696	+	0.186081i
$736$	8.05074	+	1.02639i	0.296754	+	0.0378332i
$737$		−	4.75916i		−	0.175306i
$738$	−33.0582	−	22.4497i	−1.21689	−	0.826385i
$739$		−	23.8378i		−	0.876886i	−0.898759	−	0.438443i	$-0.855530\pi$
$739$		−	23.8378i		−	0.876886i	0.898759	−	0.438443i	$-0.144470\pi$
$740$	−34.3056	−	13.1043i	−1.26110	−	0.481723i
$741$	7.26460	−	1.36431i	0.266872	−	0.0501192i
$742$	−5.46253	+	3.76088i	−0.200536	+	0.138066i
$743$	−4.54659	−	7.87492i	−0.166798	−	0.288903i	0.770494	−	0.637447i	$-0.220009\pi$
$743$	−4.54659	−	7.87492i	−0.166798	−	0.288903i	−0.937292	+	0.348544i	$0.886676\pi$
$744$	14.0814	+	31.2200i	0.516248	+	1.14458i
$745$	22.6477	−	39.2270i	0.829749	−	1.43717i
$746$	−1.93392	−	24.3182i	−0.0708058	−	0.890352i
$747$	42.3787	−	16.4996i	1.55056	−	0.603688i
$748$	0.350922	+	2.19240i	0.0128310	+	0.0801619i
$749$	−11.6489	−	6.72550i	−0.425642	−	0.245745i
$750$	−31.3545	+	31.5558i	−1.14490	+	1.15225i
$751$	−39.4261	+	22.7626i	−1.43868	+	0.830621i	−0.997758	−	0.0669258i	$-0.978681\pi$
$751$	−39.4261	+	22.7626i	−1.43868	+	0.830621i	−0.440920	+	0.897547i	$0.645348\pi$
$752$	−10.6304	−	9.50879i	−0.387650	−	0.346750i
$753$	10.3124	+	3.62422i	0.375806	+	0.132074i
$754$	−2.32715	+	4.88927i	−0.0847499	+	0.178057i
$755$	51.1736			1.86240
$756$	7.84282	−	6.81838i	0.285240	−	0.247982i
$757$	−45.3678			−1.64892			−0.824461	−	0.565919i	$-0.808521\pi$
$757$	−45.3678			−1.64892			−0.824461	+	0.565919i	$0.808521\pi$
$758$	15.9936	−	33.6021i	0.580914	−	1.22048i
$759$	−13.7079	−	4.81754i	−0.497567	−	0.174866i
$760$	32.5453	−	31.0366i	1.18054	−	1.12581i
$761$	36.3207	−	20.9698i	1.31662	−	0.760153i	0.333440	−	0.942771i	$-0.391791\pi$
$761$	36.3207	−	20.9698i	1.31662	−	0.760153i	0.983184	+	0.182618i	$0.0584573\pi$
$762$	9.98397	−	10.0481i	0.361681	−	0.364003i
$763$	4.33877	+	2.50499i	0.157074	+	0.0906867i
$764$	43.5172	−	6.96551i	1.57440	−	0.252003i
$765$	0.331713	−	2.16089i	0.0119931	−	0.0781271i
$766$	−2.04395	−	25.7018i	−0.0738510	−	0.928645i
$767$	4.36864	−	7.56670i	0.157742	−	0.273218i
$768$	20.2717	+	18.8960i	0.731493	+	0.681849i
$769$	4.76432	+	8.25204i	0.171806	+	0.297576i	0.939051	−	0.343777i	$-0.111707\pi$
$769$	4.76432	+	8.25204i	0.171806	+	0.297576i	−0.767246	+	0.641353i	$0.778373\pi$
$770$	26.1413	−	17.9980i	0.942068	−	0.648602i
$771$	24.4789	−	4.59719i	0.881585	−	0.165564i
$772$	−4.26477	+	11.1647i	−0.153493	+	0.401827i
$773$		−	4.15447i		−	0.149426i	−0.997205	−	0.0747129i	$-0.976196\pi$
$773$		−	4.15447i		−	0.149426i	0.997205	−	0.0747129i	$-0.0238041\pi$
$774$	−1.87537	+	25.6584i	−0.0674087	+	0.922272i
$775$		−	68.0335i		−	2.44384i
$776$	−6.86777	−	2.01599i	−0.246539	−	0.0723699i
$777$	−5.39634	−	6.28793i	−0.193593	−	0.225578i
$778$	26.5752	+	38.5995i	0.952768	+	1.38386i
$779$	−19.5089	−	33.7905i	−0.698980	−	1.21067i
$780$	2.44194	−	13.4775i	0.0874353	−	0.482572i
$781$	−14.8847	+	25.7810i	−0.532615	+	0.922516i
$782$	0.384018	−	0.0305393i	0.0137325	−	0.00109208i
$783$	−0.643411	−	19.3021i	−0.0229936	−	0.689801i
$784$	−3.80016	+	1.24852i	−0.135720	+	0.0445900i
$785$	3.89580	+	2.24924i	0.139047	+	0.0802789i
$786$	5.28851	−	19.9926i	0.188635	−	0.713113i
$787$	5.57632	−	3.21949i	0.198774	−	0.114762i	−0.397309	−	0.917685i	$-0.630056\pi$
$787$	5.57632	−	3.21949i	0.198774	−	0.114762i	0.596084	+	0.802922i	$0.296723\pi$
$788$	−2.06074	+	1.67435i	−0.0734109	+	0.0596463i
$789$	10.4084	−	8.93256i	0.370549	−	0.318008i
$790$	−34.5536	−	16.4465i	−1.22936	−	0.585141i
$791$	4.27687			0.152068
$792$	−28.3961	−	40.6844i	−1.00901	−	1.44566i
$793$	0.983454			0.0349235
$794$	9.25278	+	4.40405i	0.328369	+	0.156294i
$795$	−5.75427	−	30.6400i	−0.204083	−	1.08669i
$796$	−6.31712	+	5.13266i	−0.223905	+	0.181922i
$797$	−0.509800	+	0.294333i	−0.0180580	+	0.0104258i	−0.509002	−	0.860765i	$-0.669985\pi$
$797$	−0.509800	+	0.294333i	−0.0180580	+	0.0104258i	0.490944	+	0.871191i	$0.336652\pi$
$798$	9.79298	−	2.65763i	0.346668	−	0.0940791i
$799$	−0.586291	−	0.338495i	−0.0207415	−	0.0119751i
$800$	−21.2748	−	50.7731i	−0.752180	−	1.79510i
$801$	−4.72409	+	5.89089i	−0.166917	+	0.208144i
$802$	30.2778	−	2.40786i	1.06915	−	0.0850244i
$803$	−23.7404	+	41.1195i	−0.837779	+	1.45108i
$804$	−2.15136	−	1.82253i	−0.0758725	−	0.0642758i
$805$	−2.75332	−	4.76889i	−0.0970418	−	0.168081i
$806$	5.77572	+	8.38901i	0.203441	+	0.295490i
$807$	4.93444	−	14.0406i	0.173701	−	0.494252i
$808$	−2.29779	+	7.82777i	−0.0808360	+	0.275380i
$809$			39.3028i			1.38181i	0.722944	+	0.690907i	$0.242789\pi$
$809$			39.3028i			1.38181i	−0.722944	+	0.690907i	$0.757211\pi$
$810$	14.3583	+	46.6943i	0.504500	+	1.64067i
$811$		−	8.97336i		−	0.315097i	−0.987511	−	0.157549i	$-0.949641\pi$
$811$		−	8.97336i		−	0.315097i	0.987511	−	0.157549i	$-0.0503591\pi$
$812$	−2.65256	+	6.94413i	−0.0930867	+	0.243691i
$813$	−1.54630	+	4.39987i	−0.0542310	+	0.154310i
$814$	−32.5828	+	22.4329i	−1.14203	+	0.786272i
$815$	−30.0613	−	52.0677i	−1.05300	−	1.82385i
$816$	1.12545	+	0.680951i	0.0393986	+	0.0238381i
$817$	−12.5600	+	21.7546i	−0.439420	+	0.761097i
$818$	−0.501251	−	6.30302i	−0.0175258	−	0.220380i
$819$	1.93346	−	2.41100i	0.0675605	−	0.0842473i
$820$	−71.3929	+	11.4274i	−2.49315	+	0.399062i
$821$	20.5858	+	11.8852i	0.718449	+	0.414797i	0.814182	−	0.580610i	$-0.197186\pi$
$821$	20.5858	+	11.8852i	0.718449	+	0.414797i	−0.0957326	+	0.995407i	$0.530519\pi$
$822$	12.9951	+	47.8851i	0.453256	+	1.67018i
$823$	29.7775	−	17.1921i	1.03798	−	0.599278i	0.118719	−	0.992928i	$-0.462121\pi$
$823$	29.7775	−	17.1921i	1.03798	−	0.599278i	0.919260	+	0.393650i	$0.128788\pi$
$824$	−21.3042	−	22.3398i	−0.742168	−	0.778244i
$825$	18.1911	+	96.8627i	0.633331	+	3.37233i
$826$	5.15491	−	10.8303i	0.179362	−	0.376835i
$827$	−19.5161			−0.678640			−0.339320	−	0.940671i	$-0.610197\pi$
$827$	−19.5161			−0.678640			−0.339320	+	0.940671i	$0.610197\pi$
$828$	−7.42724	+	4.35172i	−0.258114	+	0.151233i
$829$	27.1294			0.942244			0.471122	−	0.882068i	$-0.343849\pi$
$829$	27.1294			0.942244			0.471122	+	0.882068i	$0.343849\pi$
$830$	35.3633	−	74.2971i	1.22748	−	2.57889i
$831$	26.8244	−	23.0209i	0.930530	−	0.798586i
$832$	6.93374	+	4.45455i	0.240384	+	0.154434i
$833$	−0.164427	+	0.0949323i	−0.00569707	+	0.00328921i
$834$	−5.08023	−	1.34384i	−0.175914	−	0.0465333i
$835$	52.3824	+	30.2430i	1.81277	+	1.04660i
$836$	−7.65663	−	47.8350i	−0.264810	−	1.65441i
$837$	−32.0471	−	17.1050i	−1.10771	−	0.591234i
$838$	1.61844	+	20.3512i	0.0559081	+	0.703021i
$839$	−3.29790	+	5.71213i	−0.113856	+	0.197205i	−0.917322	−	0.398146i	$-0.869654\pi$
$839$	−3.29790	+	5.71213i	−0.113856	+	0.197205i	0.803466	+	0.595351i	$0.202987\pi$
$840$	1.87499	−	18.7094i	0.0646934	−	0.645537i
$841$	−7.59287	−	13.1512i	−0.261823	−	0.453491i
$842$	14.3771	−	9.89846i	0.495468	−	0.341123i
$843$	30.7313	+	35.8088i	1.05844	+	1.23332i
$844$	−12.2020	−	4.66100i	−0.420010	−	0.160438i
$845$			45.8231i			1.57636i
$846$	15.0875	+	1.10275i	0.518720	+	0.0379132i
$847$		−	23.1883i		−	0.796758i
$848$	18.3609	+	3.83993i	0.630516	+	0.131864i
$849$	13.6756	−	2.56830i	0.469344	−	0.0881439i
$850$	−1.48179	−	2.15225i	−0.0508251	−	0.0738215i
$851$	3.43177	+	5.94400i	0.117640	+	0.203758i
$852$	5.95405	+	16.6014i	0.203983	+	0.568756i
$853$	26.3454	−	45.6316i	0.902051	−	1.56240i	0.0772227	−	0.997014i	$-0.475395\pi$
$853$	26.3454	−	45.6316i	0.902051	−	1.56240i	0.824828	−	0.565384i	$-0.191272\pi$
$854$	1.34584	−	0.107028i	0.0460536	−	0.00366244i
$855$	−7.23751	+	47.1475i	−0.247518	+	1.61241i
$856$	8.97232	+	36.9721i	0.306667	+	1.26368i
$857$	22.9985	+	13.2782i	0.785615	+	0.453575i	0.838417	−	0.545030i	$-0.183482\pi$
$857$	22.9985	+	13.2782i	0.785615	+	0.453575i	−0.0528014	+	0.998605i	$0.516815\pi$
$858$	−10.4663	−	10.3995i	−0.357313	−	0.355034i
$859$	1.60435	−	0.926272i	0.0547398	−	0.0316040i	−0.472380	−	0.881395i	$-0.656605\pi$
$859$	1.60435	−	0.926272i	0.0547398	−	0.0316040i	0.527120	+	0.849791i	$0.323272\pi$
$860$	29.3531	+	36.1269i	1.00093	+	1.23192i
$861$	−15.3909	−	5.40902i	−0.524522	−	0.184339i
$862$	42.3183	+	20.1423i	1.44137	+	0.686049i
$863$	14.3763			0.489376			0.244688	−	0.969602i	$-0.421315\pi$
$863$	14.3763			0.489376			0.244688	+	0.969602i	$0.421315\pi$
$864$	−29.2655	−	2.74387i	−0.995633	−	0.0933485i
$865$	−47.5290			−1.61603
$866$	3.35717	+	1.59791i	0.114081	+	0.0542994i
$867$	−27.7204	−	9.74210i	−0.941433	−	0.330859i
$868$	8.81693	+	10.8516i	0.299266	+	0.368328i
$869$	−35.6997	+	20.6113i	−1.21103	+	0.699189i
$870$	−24.7876	−	24.6295i	−0.840378	−	0.835018i
$871$	−0.726157	−	0.419247i	−0.0246049	−	0.0142056i
$872$	−3.34184	−	13.7707i	−0.113169	−	0.466333i
$873$	7.07445	−	2.75434i	0.239434	−	0.0932204i
$874$	−8.37873	+	0.666323i	−0.283415	+	0.0225387i
$875$	−9.08036	+	15.7276i	−0.306972	+	0.531692i
$876$	9.49645	+	26.4785i	0.320855	+	0.894627i
$877$	−12.7181	−	22.0285i	−0.429461	−	0.743849i	0.567364	−	0.823467i	$-0.307963\pi$
$877$	−12.7181	−	22.0285i	−0.429461	−	0.743849i	−0.996825	+	0.0796183i	$0.974630\pi$
$878$	−19.4497	−	28.2499i	−0.656395	−	0.953388i
$879$	−50.7554	+	9.53199i	−1.71194	+	0.321506i
$880$	−87.8674	−	18.3762i	−2.96201	−	0.619463i
$881$			48.0956i			1.62038i	0.586166	+	0.810191i	$0.300637\pi$
$881$			48.0956i			1.62038i	−0.586166	+	0.810191i	$0.699363\pi$
$882$	2.38351	−	3.50983i	0.0802570	−	0.118182i
$883$			12.3742i			0.416423i	0.978084	+	0.208212i	$0.0667643\pi$
$883$			12.3742i			0.416423i	−0.978084	+	0.208212i	$0.933236\pi$
$884$	0.365431	+	0.139590i	0.0122908	+	0.00469491i
$885$	36.7202	+	42.7872i	1.23434	+	1.43828i
$886$	−4.97429	+	3.42474i	−0.167115	+	0.115056i
$887$	10.9124	+	18.9008i	0.366401	+	0.634625i	0.989000	−	0.147916i	$-0.0472565\pi$
$887$	10.9124	+	18.9008i	0.366401	+	0.634625i	−0.622599	+	0.782541i	$0.713923\pi$
$888$	−2.33701	+	23.3197i	−0.0784251	+	0.782556i
$889$	2.89139	−	5.00803i	0.0969741	−	0.167964i
$890$	1.08310	+	13.6195i	0.0363056	+	0.456527i
$891$	50.2006	+	15.7843i	1.68178	+	0.528795i
$892$	7.88738	+	49.2766i	0.264089	+	1.64990i
$893$	12.7920	+	7.38549i	0.428069	+	0.247146i
$894$	−27.9460	−	7.39236i	−0.934653	−	0.247237i
$895$	−48.5423	+	28.0259i	−1.62259	+	0.936804i
$896$	9.97346	+	5.34136i	0.333190	+	0.178442i
$897$	−1.94263	+	1.66718i	−0.0648626	+	0.0556655i
$898$	19.9859	−	41.9898i	0.666939	−	1.40122i
$899$	25.9838			0.866608
$900$	50.7527	+	28.8707i	1.69176	+	0.962355i
$901$	0.890377			0.0296628
$902$	−33.4722	+	70.3241i	−1.11450	+	2.34154i
$903$	1.93859	+	10.3225i	0.0645121	+	0.343511i
$904$	−8.34842	−	8.75423i	−0.277664	−	0.291161i
$905$	22.5598	−	13.0249i	0.749913	−	0.432962i
$906$	−8.55352	−	31.5185i	−0.284172	−	1.04713i
$907$	14.3578	+	8.28950i	0.476744	+	0.275248i	0.719059	−	0.694949i	$-0.244573\pi$
$907$	14.3578	+	8.28950i	0.476744	+	0.275248i	−0.242315	+	0.970198i	$0.577907\pi$
$908$	−20.4770	+	3.27762i	−0.679553	+	0.108772i
$909$	−3.13935	−	8.06334i	−0.104126	−	0.267444i
$910$	−0.443288	−	5.57415i	−0.0146948	−	0.184781i
$911$	−5.19404	+	8.99634i	−0.172086	+	0.298062i	−0.939149	−	0.343510i	$-0.888384\pi$
$911$	−5.19404	+	8.99634i	−0.172086	+	0.298062i	0.767063	+	0.641572i	$0.221717\pi$
$912$	−24.5557	−	14.8574i	−0.813120	−	0.491977i
$913$	−44.3183	−	76.7615i	−1.46672	−	2.54043i
$914$	−17.4132	+	11.9887i	−0.575976	+	0.396552i
$915$	−2.10425	+	5.98747i	−0.0695643	+	0.197940i
$916$	−15.7495	+	41.2305i	−0.520378	+	1.36229i
$917$		−	8.44268i		−	0.278802i
$918$	−1.38637	+	0.156880i	−0.0457569	+	0.00517782i
$919$		−	47.3884i		−	1.56320i	−0.623780	−	0.781600i	$-0.714404\pi$
$919$		−	47.3884i		−	1.56320i	0.623780	−	0.781600i	$-0.285596\pi$
$920$	−4.38688	+	14.9446i	−0.144631	+	0.492708i
$921$	−11.3291	+	32.2360i	−0.373306	+	1.06221i
$922$	−2.28194	−	3.31443i	−0.0751518	−	0.109155i
$923$	2.62246	+	4.54223i	0.0863192	+	0.149509i
$924$	−15.4546	−	13.0925i	−0.508420	−	0.430711i
$925$	23.2777	−	40.3182i	0.765367	−	1.32566i
$926$	35.1238	−	2.79324i	1.15424	−	0.0917917i
$927$	32.3632	+	4.96799i	1.06295	+	0.163170i
$928$	19.3916	−	8.12542i	0.636560	−	0.266730i
$929$	−37.3688	−	21.5749i	−1.22603	−	0.707849i	−0.259833	−	0.965654i	$-0.583668\pi$
$929$	−37.3688	−	21.5749i	−1.22603	−	0.707849i	−0.966197	+	0.257805i	$0.917001\pi$
$930$	−63.4320	+	17.2142i	−2.08002	+	0.564477i
$931$	3.58757	−	2.07129i	0.117578	−	0.0678837i
$932$	35.6110	−	28.9339i	1.16648	−	0.947761i
$933$	−4.75716	−	25.3307i	−0.155742	−	0.829289i
$934$	7.87442	+	3.74800i	0.257659	+	0.122638i
$935$	−4.26096			−0.139348
$936$	−8.70914	+	0.748706i	−0.284667	+	0.0244722i
$937$	−14.1414			−0.461978			−0.230989	−	0.972956i	$-0.574196\pi$
$937$	−14.1414			−0.461978			−0.230989	+	0.972956i	$0.574196\pi$
$938$	−1.03936	−	0.494704i	−0.0339362	−	0.0161526i
$939$	−32.4398	+	27.8401i	−1.05863	+	0.908526i
$940$	21.2432	−	17.2601i	0.692876	−	0.562961i
$941$	−7.29412	+	4.21126i	−0.237781	+	0.137283i	−0.614157	−	0.789184i	$-0.710504\pi$
$941$	−7.29412	+	4.21126i	−0.237781	+	0.137283i	0.376375	+	0.926467i	$0.377170\pi$
$942$	0.734166	−	2.77543i	0.0239204	−	0.0904285i
$943$	11.7027	+	6.75655i	0.381092	+	0.220024i
$944$	−32.2307	+	10.5892i	−1.04902	+	0.344649i
$945$	10.5418	+	16.9300i	0.342923	+	0.550733i
$946$	49.9844	−	3.97504i	1.62513	−	0.129240i
$947$	−23.2734	+	40.3107i	−0.756284	+	1.30992i	0.188450	+	0.982083i	$0.439654\pi$
$947$	−23.2734	+	40.3107i	−0.756284	+	1.30992i	−0.944733	+	0.327839i	$0.893680\pi$
$948$	−4.35409	+	24.0310i	−0.141414	+	0.780492i
$949$	4.18270	+	7.24465i	0.135776	+	0.235171i
$950$	32.3307	+	46.9590i	1.04894	+	1.52355i
$951$	−21.0435	−	24.5203i	−0.682382	−	0.795126i
$952$	0.515276	+	0.151256i	0.0167002	+	0.00490224i
$953$			21.4063i			0.693419i	0.937973	+	0.346710i	$0.112701\pi$
$953$			21.4063i			0.693419i	−0.937973	+	0.346710i	$0.887299\pi$
$954$	−17.9098	+	8.66553i	−0.579851	+	0.280557i
$955$			84.5764i			2.73683i
$956$	−10.2095	+	26.7275i	−0.330200	+	0.864428i
$957$	−36.9944	+	6.94764i	−1.19586	+	0.224585i
$958$	35.2938	−	24.2994i	1.14029	−	0.785077i
$959$	10.1280	+	17.5423i	0.327051	+	0.566470i
$960$	−41.9559	+	32.6828i	−1.35412	+	1.05483i
$961$	8.93698	−	15.4793i	0.288290	−	0.499332i
$962$	0.552519	+	6.94769i	0.0178139	+	0.224002i
$963$	−31.4807	−	25.2454i	−1.01445	−	0.813521i
$964$	−15.9348	+	2.55057i	−0.513224	+	0.0821484i
$965$	−19.8632	−	11.4680i	−0.639420	−	0.369169i
$966$	−2.47702	+	2.49292i	−0.0796967	+	0.0802082i
$967$	−7.92319	+	4.57446i	−0.254793	+	0.147105i	−0.621957	−	0.783052i	$-0.713662\pi$
$967$	−7.92319	+	4.57446i	−0.254793	+	0.147105i	0.367164	+	0.930156i	$0.380329\pi$
$968$	−47.4636	+	45.2633i	−1.52554	+	1.45482i
$969$	−1.28524	−	0.451689i	−0.0412880	−	0.0145103i
$970$	5.90333	−	12.4027i	0.189545	−	0.398227i
$971$	22.8058			0.731872			0.365936	−	0.930640i	$-0.380749\pi$
$971$	22.8058			0.731872			0.365936	+	0.930640i	$0.380749\pi$
$972$	26.3597	−	16.6483i	0.845488	−	0.533995i
$973$	−2.14533			−0.0687761
$974$	10.8834	−	22.8658i	0.348728	−	0.732666i
$975$	16.3819	+	5.75728i	0.524640	+	0.184381i
$976$	−2.84614	−	2.54585i	−0.0911027	−	0.0814906i
$977$	34.1902	−	19.7397i	1.09384	−	0.631529i	0.159244	−	0.987239i	$-0.449094\pi$
$977$	34.1902	−	19.7397i	1.09384	−	0.631529i	0.934596	+	0.355710i	$0.115761\pi$
$978$	−27.0445	+	27.2181i	−0.864788	+	0.870339i
$979$	12.7456	+	7.35867i	0.407351	+	0.235184i
$980$	−1.21326	−	7.57987i	−0.0387562	−	0.242130i
$981$	11.7254	+	9.40293i	0.374362	+	0.300212i
$982$	0.886595	+	11.1485i	0.0282924	+	0.355765i
$983$	9.06226	−	15.6963i	0.289041	−	0.500634i	−0.684540	−	0.728975i	$-0.739997\pi$
$983$	9.06226	−	15.6963i	0.289041	−	0.500634i	0.973581	+	0.228341i	$0.0733302\pi$
$984$	18.9714	+	42.0618i	0.604787	+	1.34088i
$985$	−2.54779	−	4.41290i	−0.0811792	−	0.140607i
$986$	0.822000	−	0.565936i	0.0261778	−	0.0180231i
$987$	6.06978	−	1.13992i	0.193203	−	0.0362840i
$988$	−7.97319	−	3.04565i	−0.253661	−	0.0968950i
$989$		−	8.69986i		−	0.276639i
$990$	85.7085	−	41.4695i	2.72399	−	1.31799i
$991$			2.44943i			0.0778088i	0.999243	+	0.0389044i	$0.0123868\pi$
$991$			2.44943i			0.0778088i	−0.999243	+	0.0389044i	$0.987613\pi$
$992$	5.00137	−	39.2295i	0.158794	−	1.24554i
$993$	−18.7135	−	21.8053i	−0.593854	−	0.691972i
$994$	4.08310	+	5.93054i	0.129508	+	0.188105i
$995$	−7.81014	−	13.5276i	−0.247598	−	0.428852i
$996$	−51.6715	−	9.36215i	−1.63727	−	0.296651i
$997$	−7.06115	+	12.2303i	−0.223629	+	0.387336i	−0.955907	−	0.293669i	$-0.905124\pi$
$997$	−7.06115	+	12.2303i	−0.223629	+	0.387336i	0.732278	+	0.681005i	$0.238457\pi$
$998$	46.0560	−	3.66263i	1.45788	−	0.115939i
$999$	−13.1394	−	21.1017i	−0.415711	−	0.667629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.ba.a.155.4	✓	72
3.2	odd	2		756.2.ba.a.575.33		72
4.3	odd	2	inner	252.2.ba.a.155.9	yes	72
9.4	even	3		756.2.ba.a.71.28		72
9.5	odd	6	inner	252.2.ba.a.239.9	yes	72
12.11	even	2		756.2.ba.a.575.28		72
36.23	even	6	inner	252.2.ba.a.239.4	yes	72
36.31	odd	6		756.2.ba.a.71.33		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.4	✓	72	1.1	even	1	trivial
252.2.ba.a.155.9	yes	72	4.3	odd	2	inner
252.2.ba.a.239.4	yes	72	36.23	even	6	inner
252.2.ba.a.239.9	yes	72	9.5	odd	6	inner
756.2.ba.a.71.28		72	9.4	even	3
756.2.ba.a.71.33		72	36.31	odd	6
756.2.ba.a.575.28		72	12.11	even	2
756.2.ba.a.575.33		72	3.2	odd	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27695 - 0.607789i) q^{2} +(-1.63407 - 0.574282i) q^{3} +(1.26118 + 1.55223i) q^{4} +(-3.32396 + 1.91909i) q^{5} +(1.73758 + 1.72650i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.667037 - 2.74865i) q^{8} +(2.34040 + 1.87684i) q^{9} +O(q^{10})\)	\(q+(-1.27695 - 0.607789i) q^{2} +(-1.63407 - 0.574282i) q^{3} +(1.26118 + 1.55223i) q^{4} +(-3.32396 + 1.91909i) q^{5} +(1.73758 + 1.72650i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.667037 - 2.74865i) q^{8} +(2.34040 + 1.87684i) q^{9} +(5.41092 - 0.430306i) q^{10} +(2.92354 - 5.06371i) q^{11} +(-1.16945 - 3.26073i) q^{12} +(-0.515084 - 0.892151i) q^{13} +(-0.801973 - 1.16483i) q^{14} +(6.53369 - 1.22704i) q^{15} +(-0.818829 + 3.91529i) q^{16} +0.189865i q^{17} +(-1.84784 - 3.81909i) q^{18} -4.14257i q^{19} +(-7.17099 - 2.73922i) q^{20} +(-1.12801 - 1.31438i) q^{21} +(-6.81087 + 4.68920i) q^{22} +(0.717351 + 1.24249i) q^{23} +(-0.488512 + 4.87456i) q^{24} +(4.86580 - 8.42781i) q^{25} +(0.115494 + 1.45229i) q^{26} +(-2.74655 - 4.41095i) q^{27} +(0.316103 + 1.97486i) q^{28} +(3.21880 + 1.85838i) q^{29} +(-9.08896 - 2.40424i) q^{30} +(6.05438 - 3.49550i) q^{31} +(3.42527 - 4.50194i) q^{32} +(-7.68528 + 6.59555i) q^{33} +(0.115398 - 0.242447i) q^{34} -3.83818 q^{35} +(0.0383905 + 5.99988i) q^{36} +4.78395 q^{37} +(-2.51781 + 5.28984i) q^{38} +(0.329339 + 1.75365i) q^{39} +(7.49210 + 7.85629i) q^{40} +(8.15688 - 4.70938i) q^{41} +(0.641541 + 2.36399i) q^{42} +(-5.25147 - 3.03194i) q^{43} +(11.5472 - 1.84828i) q^{44} +(-11.3812 - 1.74710i) q^{45} +(-0.160848 - 2.02259i) q^{46} +(-1.78283 + 3.08795i) q^{47} +(3.58651 - 5.92764i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-11.3357 + 7.80449i) q^{50} +(0.109036 - 0.310253i) q^{51} +(0.735207 - 1.92469i) q^{52} -4.68954i q^{53} +(0.826274 + 7.30187i) q^{54} +22.4421i q^{55} +(0.796653 - 2.71392i) q^{56} +(-2.37901 + 6.76927i) q^{57} +(-2.98074 - 4.32940i) q^{58} +(4.24070 + 7.34512i) q^{59} +(10.1448 + 8.59426i) q^{60} +(-0.477327 + 0.826755i) q^{61} +(-9.85564 + 0.783775i) q^{62} +(1.08843 + 2.79559i) q^{63} +(-7.11012 + 3.66690i) q^{64} +(3.42423 + 1.97698i) q^{65} +(13.8224 - 3.75114i) q^{66} +(0.704892 - 0.406970i) q^{67} +(-0.294713 + 0.239454i) q^{68} +(-0.458666 - 2.44228i) q^{69} +(4.90115 + 2.33280i) q^{70} -5.09132 q^{71} +(3.59764 - 7.68485i) q^{72} -8.12043 q^{73} +(-6.10885 - 2.90763i) q^{74} +(-12.7910 + 10.9773i) q^{75} +(6.43022 - 5.22455i) q^{76} +(5.06371 - 2.92354i) q^{77} +(0.645299 - 2.43948i) q^{78} +(-6.10558 - 3.52506i) q^{79} +(-4.79204 - 14.5857i) q^{80} +(1.95494 + 8.78511i) q^{81} +(-13.2782 + 1.05596i) q^{82} +(7.57956 - 13.1282i) q^{83} +(0.617592 - 3.40860i) q^{84} +(-0.364367 - 0.631102i) q^{85} +(4.86307 + 7.06341i) q^{86} +(-4.19253 - 4.88523i) q^{87} +(-15.8685 - 4.65809i) q^{88} +2.51704i q^{89} +(13.4713 + 9.14834i) q^{90} -1.03017i q^{91} +(-1.02391 + 2.68050i) q^{92} +(-11.9007 + 2.23498i) q^{93} +(4.15339 - 2.85956i) q^{94} +(7.94997 + 13.7697i) q^{95} +(-8.18254 + 5.38944i) q^{96} +(1.26529 - 2.19154i) q^{97} +(-0.112112 - 1.40976i) q^{98} +(16.3460 - 6.36410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 72 * q + 6 * q^6 + 4 * q^9	\( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

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