LMFDB - Embedded newform 378.2.z.a.41.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.7
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(0.0283469 + 1.73182i) q^{3} +(0.939693 - 0.342020i) q^{4} +(2.71537 + 2.27847i) q^{5} +(-0.328643 - 1.70059i) q^{6} +(-1.56393 + 2.13404i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.99839 + 0.0981834i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(0.0283469 + 1.73182i) q^{3} +(0.939693 - 0.342020i) q^{4} +(2.71537 + 2.27847i) q^{5} +(-0.328643 - 1.70059i) q^{6} +(-1.56393 + 2.13404i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.99839 + 0.0981834i) q^{9} +(-3.06977 - 1.77233i) q^{10} +(1.42913 + 1.70317i) q^{11} +(0.618954 + 1.61768i) q^{12} +(0.837731 + 0.147715i) q^{13} +(1.16960 - 2.37319i) q^{14} +(-3.86892 + 4.76712i) q^{15} +(0.766044 - 0.642788i) q^{16} +(3.72130 - 6.44549i) q^{17} +(2.93579 - 0.617357i) q^{18} +(-3.28549 + 1.89688i) q^{19} +(3.33089 + 1.21235i) q^{20} +(-3.74010 - 2.64795i) q^{21} +(-1.70317 - 1.42913i) q^{22} +(-1.39191 - 3.82423i) q^{23} +(-0.890459 - 1.48563i) q^{24} +(1.31359 + 7.44972i) q^{25} -0.850655 q^{26} +(-0.255031 - 5.18989i) q^{27} +(-0.739727 + 2.54024i) q^{28} +(0.660968 - 0.116547i) q^{29} +(2.98234 - 5.36652i) q^{30} +(0.511255 + 1.40466i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-2.90907 + 2.52328i) q^{33} +(-2.54552 + 6.99376i) q^{34} +(-9.10898 + 2.23135i) q^{35} +(-2.78399 + 1.11777i) q^{36} +(-0.928886 + 1.60888i) q^{37} +(2.90618 - 2.43858i) q^{38} +(-0.232068 + 1.45499i) q^{39} +(-3.49081 - 0.615524i) q^{40} +(-1.60199 + 9.08534i) q^{41} +(4.14309 + 1.95826i) q^{42} +(-7.43999 + 6.24290i) q^{43} +(1.92546 + 1.11167i) q^{44} +(-8.36545 - 6.56513i) q^{45} +(2.03483 + 3.52443i) q^{46} +(11.7218 + 4.26638i) q^{47} +(1.13491 + 1.30843i) q^{48} +(-2.10826 - 6.67497i) q^{49} +(-2.58726 - 7.10844i) q^{50} +(11.2679 + 6.26191i) q^{51} +(0.837731 - 0.147715i) q^{52} -13.4606i q^{53} +(1.15237 + 5.06676i) q^{54} +7.88097i q^{55} +(0.287381 - 2.63010i) q^{56} +(-3.37818 - 5.63610i) q^{57} +(-0.630689 + 0.229552i) q^{58} +(-2.15673 - 1.80971i) q^{59} +(-2.00514 + 5.80287i) q^{60} +(-0.533089 + 1.46465i) q^{61} +(-0.747405 - 1.29454i) q^{62} +(4.47974 - 6.55224i) q^{63} +(0.500000 - 0.866025i) q^{64} +(1.93819 + 2.30984i) q^{65} +(2.42672 - 2.99010i) q^{66} +(1.46505 - 8.30872i) q^{67} +(1.29240 - 7.32954i) q^{68} +(6.58342 - 2.51893i) q^{69} +(8.58313 - 3.77921i) q^{70} +(11.5884 + 6.69059i) q^{71} +(2.54759 - 1.58423i) q^{72} +(5.45139 - 3.14736i) q^{73} +(0.635395 - 1.74573i) q^{74} +(-12.8643 + 2.48607i) q^{75} +(-2.43858 + 2.90618i) q^{76} +(-5.86970 + 0.386185i) q^{77} +(-0.0241134 - 1.47318i) q^{78} +(-0.102413 - 0.580815i) q^{79} +3.54466 q^{80} +(8.98072 - 0.588785i) q^{81} -9.22550i q^{82} +(-1.26685 - 7.18468i) q^{83} +(-4.42020 - 1.20907i) q^{84} +(24.7905 - 9.02302i) q^{85} +(6.24290 - 7.43999i) q^{86} +(0.220574 + 1.14137i) q^{87} +(-2.08925 - 0.760425i) q^{88} +(8.62919 + 14.9462i) q^{89} +(9.37839 + 5.01275i) q^{90} +(-1.62538 + 1.55674i) q^{91} +(-2.61593 - 3.11754i) q^{92} +(-2.41813 + 0.925219i) q^{93} +(-12.2846 - 2.16610i) q^{94} +(-13.2433 - 2.33515i) q^{95} +(-1.34487 - 1.09148i) q^{96} +(3.69346 + 4.40170i) q^{97} +(3.23533 + 6.20747i) q^{98} +(-4.45232 - 4.96646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	0.0283469	+	1.73182i	0.0163661	+	0.999866i
$3$	0.0283469	+	1.73182i	0.0163661	+	0.999866i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	2.71537	+	2.27847i	1.21435	+	1.01896i	0.999101	+	0.0424018i	$0.0135010\pi$
$5$	2.71537	+	2.27847i	1.21435	+	1.01896i	0.215250	+	0.976559i	$0.430943\pi$
$6$	−0.328643	−	1.70059i	−0.134168	−	0.694261i
$7$	−1.56393	+	2.13404i	−0.591109	+	0.806591i
$7$	−1.56393	+	2.13404i	−0.591109	+	0.806591i
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−2.99839	+	0.0981834i	−0.999464	+	0.0327278i
$10$	−3.06977	−	1.77233i	−0.970746	−	0.560461i
$11$	1.42913	+	1.70317i	0.430899	+	0.513526i	0.937182	−	0.348842i	$-0.113425\pi$
$11$	1.42913	+	1.70317i	0.430899	+	0.513526i	−0.506282	+	0.862368i	$0.668981\pi$
$12$	0.618954	+	1.61768i	0.178677	+	0.466985i
$13$	0.837731	+	0.147715i	0.232345	+	0.0409687i	0.288608	−	0.957447i	$-0.406808\pi$
$13$	0.837731	+	0.147715i	0.232345	+	0.0409687i	−0.0562633	+	0.998416i	$0.517919\pi$
$14$	1.16960	−	2.37319i	0.312588	−	0.634262i
$15$	−3.86892	+	4.76712i	−0.998950	+	1.23086i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	3.72130	−	6.44549i	0.902549	−	1.56326i	0.0783742	−	0.996924i	$-0.475027\pi$
$17$	3.72130	−	6.44549i	0.902549	−	1.56326i	0.824174	−	0.566336i	$-0.191640\pi$
$18$	2.93579	−	0.617357i	0.691973	−	0.145512i
$19$	−3.28549	+	1.89688i	−0.753742	+	0.435173i	−0.827045	−	0.562136i	$-0.809980\pi$
$19$	−3.28549	+	1.89688i	−0.753742	+	0.435173i	0.0733021	+	0.997310i	$0.476646\pi$
$20$	3.33089	+	1.21235i	0.744811	+	0.271089i
$21$	−3.74010	−	2.64795i	−0.816158	−	0.577829i
$22$	−1.70317	−	1.42913i	−0.363118	−	0.304692i
$23$	−1.39191	−	3.82423i	−0.290232	−	0.797407i	−0.996032	−	0.0889955i	$-0.971634\pi$
$23$	−1.39191	−	3.82423i	−0.290232	−	0.797407i	0.705800	−	0.708412i	$-0.250588\pi$
$24$	−0.890459	−	1.48563i	−0.181764	−	0.303252i
$25$	1.31359	+	7.44972i	0.262717	+	1.48994i
$26$	−0.850655			−0.166827
$27$	−0.255031	−	5.18989i	−0.0490807	−	0.998795i
$28$	−0.739727	+	2.54024i	−0.139795	+	0.480060i
$29$	0.660968	−	0.116547i	0.122739	−	0.0216421i	−0.111941	−	0.993715i	$-0.535707\pi$
$29$	0.660968	−	0.116547i	0.122739	−	0.0216421i	0.234680	+	0.972073i	$0.424596\pi$
$30$	2.98234	−	5.36652i	0.544498	−	0.979789i
$31$	0.511255	+	1.40466i	0.0918241	+	0.252285i	0.977100	−	0.212782i	$-0.0682525\pi$
$31$	0.511255	+	1.40466i	0.0918241	+	0.252285i	−0.885276	+	0.465067i	$0.846030\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	−2.90907	+	2.52328i	−0.506405	+	0.439246i
$34$	−2.54552	+	6.99376i	−0.436553	+	1.19942i
$35$	−9.10898	+	2.23135i	−1.53970	+	0.377167i
$36$	−2.78399	+	1.11777i	−0.463998	+	0.186296i
$37$	−0.928886	+	1.60888i	−0.152708	+	0.264498i	−0.932222	−	0.361887i	$-0.882133\pi$
$37$	−0.928886	+	1.60888i	−0.152708	+	0.264498i	0.779514	+	0.626385i	$0.215466\pi$
$38$	2.90618	−	2.43858i	0.471445	−	0.395590i
$39$	−0.232068	+	1.45499i	−0.0371606	+	0.232984i
$40$	−3.49081	−	0.615524i	−0.551946	−	0.0973229i
$41$	−1.60199	+	9.08534i	−0.250189	+	1.41889i	0.557938	+	0.829883i	$0.311593\pi$
$41$	−1.60199	+	9.08534i	−0.250189	+	1.41889i	−0.808127	+	0.589009i	$0.799518\pi$
$42$	4.14309	+	1.95826i	0.639293	+	0.302165i
$43$	−7.43999	+	6.24290i	−1.13459	+	0.952033i	−0.999248	−	0.0387666i	$-0.987657\pi$
$43$	−7.43999	+	6.24290i	−1.13459	+	0.952033i	−0.135340	+	0.990799i	$0.543213\pi$
$44$	1.92546	+	1.11167i	0.290274	+	0.167590i
$45$	−8.36545	−	6.56513i	−1.24705	−	0.978672i
$46$	2.03483	+	3.52443i	0.300019	+	0.519649i
$47$	11.7218	+	4.26638i	1.70980	+	0.622316i	0.996880	−	0.0789301i	$-0.0251504\pi$
$47$	11.7218	+	4.26638i	1.70980	+	0.622316i	0.712919	+	0.701246i	$0.247373\pi$
$48$	1.13491	+	1.30843i	0.163810	+	0.188855i
$49$	−2.10826	−	6.67497i	−0.301180	−	0.953567i
$50$	−2.58726	−	7.10844i	−0.365894	−	1.00528i
$51$	11.2679	+	6.26191i	1.57782	+	0.876843i
$52$	0.837731	−	0.147715i	0.116172	−	0.0204843i
$53$		−	13.4606i		−	1.84896i	−0.381229	−	0.924480i	$-0.624499\pi$
$53$		−	13.4606i		−	1.84896i	0.381229	−	0.924480i	$-0.375501\pi$
$54$	1.15237	+	5.06676i	0.156818	+	0.689498i
$55$			7.88097i			1.06267i
$56$	0.287381	−	2.63010i	0.0384029	−	0.351462i
$57$	−3.37818	−	5.63610i	−0.447451	−	0.746519i
$58$	−0.630689	+	0.229552i	−0.0828135	+	0.0301416i
$59$	−2.15673	−	1.80971i	−0.280782	−	0.235604i	0.491510	−	0.870872i	$-0.336445\pi$
$59$	−2.15673	−	1.80971i	−0.280782	−	0.235604i	−0.772292	+	0.635268i	$0.780890\pi$
$60$	−2.00514	+	5.80287i	−0.258863	+	0.749147i
$61$	−0.533089	+	1.46465i	−0.0682550	+	0.187529i	−0.969130	−	0.246549i	$-0.920703\pi$
$61$	−0.533089	+	1.46465i	−0.0682550	+	0.187529i	0.900875	+	0.434078i	$0.142926\pi$
$62$	−0.747405	−	1.29454i	−0.0949205	−	0.164407i
$63$	4.47974	−	6.55224i	0.564395	−	0.825505i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	1.93819	+	2.30984i	0.240403	+	0.286501i
$66$	2.42672	−	2.99010i	0.298708	−	0.368055i
$67$	1.46505	−	8.30872i	0.178985	−	1.01507i	−0.754459	−	0.656347i	$-0.772101\pi$
$67$	1.46505	−	8.30872i	0.178985	−	1.01507i	0.933443	−	0.358725i	$-0.116788\pi$
$68$	1.29240	−	7.32954i	0.156726	−	0.888837i
$69$	6.58342	−	2.51893i	0.792550	−	0.303244i
$70$	8.58313	−	3.77921i	1.02588	−	0.451702i
$71$	11.5884	+	6.69059i	1.37530	+	0.794027i	0.991589	−	0.129428i	$-0.0413142\pi$
$71$	11.5884	+	6.69059i	1.37530	+	0.794027i	0.383706	+	0.923455i	$0.374648\pi$
$72$	2.54759	−	1.58423i	0.300237	−	0.186703i
$73$	5.45139	−	3.14736i	0.638037	−	0.368371i	−0.145821	−	0.989311i	$-0.546582\pi$
$73$	5.45139	−	3.14736i	0.638037	−	0.368371i	0.783858	+	0.620940i	$0.213249\pi$
$74$	0.635395	−	1.74573i	0.0738632	−	0.202937i
$75$	−12.8643	+	2.48607i	−1.48544	+	0.287067i
$76$	−2.43858	+	2.90618i	−0.279724	+	0.333362i
$77$	−5.86970	+	0.386185i	−0.668914	+	0.0440098i
$78$	−0.0241134	−	1.47318i	−0.00273031	−	0.166805i
$79$	−0.102413	−	0.580815i	−0.0115224	−	0.0653468i	0.978504	−	0.206226i	$-0.0661182\pi$
$79$	−0.102413	−	0.580815i	−0.0115224	−	0.0653468i	−0.990027	+	0.140879i	$0.955007\pi$
$80$	3.54466			0.396305
$81$	8.98072	−	0.588785i	0.997858	−	0.0654205i
$82$		−	9.22550i		−	1.01879i
$83$	−1.26685	−	7.18468i	−0.139055	−	0.788621i	−0.971950	−	0.235189i	$-0.924429\pi$
$83$	−1.26685	−	7.18468i	−0.139055	−	0.788621i	0.832894	−	0.553432i	$-0.186682\pi$
$84$	−4.42020	−	1.20907i	−0.482283	−	0.131920i
$85$	24.7905	−	9.02302i	2.68891	−	0.978684i
$86$	6.24290	−	7.43999i	0.673189	−	0.802275i
$87$	0.220574	+	1.14137i	0.0236480	+	0.122368i
$88$	−2.08925	−	0.760425i	−0.222715	−	0.0810615i
$89$	8.62919	+	14.9462i	0.914692	+	1.58429i	0.807352	+	0.590071i	$0.200900\pi$
$89$	8.62919	+	14.9462i	0.914692	+	1.58429i	0.107340	+	0.994222i	$0.465767\pi$
$90$	9.37839	+	5.01275i	0.988569	+	0.528390i
$91$	−1.62538	+	1.55674i	−0.170386	+	0.163190i
$92$	−2.61593	−	3.11754i	−0.272729	−	0.325026i
$93$	−2.41813	+	0.925219i	−0.250748	+	0.0959407i
$94$	−12.2846	−	2.16610i	−1.26706	−	0.223416i
$95$	−13.2433	−	2.33515i	−1.35873	−	0.239581i
$96$	−1.34487	−	1.09148i	−0.137260	−	0.111398i
$97$	3.69346	+	4.40170i	0.375014	+	0.446925i	0.920234	−	0.391369i	$-0.127998\pi$
$97$	3.69346	+	4.40170i	0.375014	+	0.446925i	−0.545220	+	0.838293i	$0.683554\pi$
$98$	3.23533	+	6.20747i	0.326817	+	0.627049i
$99$	−4.45232	−	4.96646i	−0.447475	−	0.499148i
$100$	3.78232	+	6.55117i	0.378232	+	0.655117i
$101$	−7.18729	−	2.61596i	−0.715162	−	0.260298i	−0.0412915	−	0.999147i	$-0.513147\pi$
$101$	−7.18729	−	2.61596i	−0.715162	−	0.260298i	−0.673871	+	0.738849i	$0.735369\pi$
$102$	−12.1841	−	4.21013i	−1.20640	−	0.416865i
$103$	−1.62331	+	1.93458i	−0.159949	+	0.190620i	−0.840067	−	0.542483i	$-0.817484\pi$
$103$	−1.62331	+	1.93458i	−0.159949	+	0.190620i	0.680117	+	0.733103i	$0.261929\pi$
$104$	−0.799354	+	0.290941i	−0.0783831	+	0.0285291i
$105$	−4.12251	−	15.7119i	−0.402316	−	1.53332i
$106$	2.33742	+	13.2561i	0.227030	+	1.28755i
$107$			8.15918i			0.788778i	0.918944	+	0.394389i	$0.129044\pi$
$107$			8.15918i			0.788778i	−0.918944	+	0.394389i	$0.870956\pi$
$108$	−2.01470	−	4.78968i	−0.193864	−	0.460887i
$109$	9.75382			0.934247			0.467123	−	0.884192i	$-0.345290\pi$
$109$	9.75382			0.934247			0.467123	+	0.884192i	$0.345290\pi$
$110$	−1.36852	−	7.76124i	−0.130483	−	0.740005i
$111$	−2.81262	−	1.56306i	−0.266962	−	0.148359i
$112$	0.173696	+	2.64004i	0.0164128	+	0.249461i
$113$	7.27389	−	8.66869i	0.684270	−	0.815482i	−0.306380	−	0.951909i	$-0.599118\pi$
$113$	7.27389	−	8.66869i	0.684270	−	0.815482i	0.990650	+	0.136428i	$0.0435621\pi$
$114$	4.30556	+	4.96386i	0.403252	+	0.464908i
$115$	4.93384	−	13.5556i	0.460083	−	1.26407i
$116$	0.581246	−	0.335582i	0.0539673	−	0.0311580i
$117$	−2.52635	−	0.360655i	−0.233561	−	0.0333426i
$118$	2.43821	+	1.40770i	0.224456	+	0.129590i
$119$	7.93508	+	18.0217i	0.727407	+	1.65205i
$120$	0.967023	−	6.06290i	0.0882767	−	0.553465i
$121$	1.05175	−	5.96477i	0.0956137	−	0.542252i
$122$	0.270656	−	1.53497i	0.0245041	−	0.138970i
$123$	−15.7796	−	2.51682i	−1.42280	−	0.226934i
$124$	0.960845	+	1.14509i	0.0862865	+	0.102832i
$125$	−4.54539	+	7.87285i	−0.406552	+	0.704169i
$126$	−3.27390	+	7.23060i	−0.291662	+	0.644153i
$127$	−5.18385	−	8.97869i	−0.459992	−	0.796730i	0.538968	−	0.842326i	$-0.318814\pi$
$127$	−5.18385	−	8.97869i	−0.459992	−	0.796730i	−0.998960	+	0.0455966i	$0.985481\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	−11.0225	−	12.7078i	−0.970474	−	1.11886i
$130$	−2.30984	−	1.93819i	−0.202587	−	0.169990i
$131$	6.60246	−	2.40310i	0.576859	−	0.209960i	−0.0370807	−	0.999312i	$-0.511806\pi$
$131$	6.60246	−	2.40310i	0.576859	−	0.209960i	0.613940	+	0.789353i	$0.289584\pi$
$132$	−1.87062	+	3.36607i	−0.162817	+	0.292978i
$133$	1.09025	−	9.97794i	0.0945370	−	0.865197i
$134$			8.43690i			0.728837i
$135$	11.1325	−	14.6736i	0.958132	−	1.26290i
$136$			7.44261i			0.638198i
$137$	17.6831	−	3.11801i	1.51077	−	0.266390i	0.643972	−	0.765049i	$-0.277285\pi$
$137$	17.6831	−	3.11801i	1.51077	−	0.266390i	0.866798	+	0.498659i	$0.166174\pi$
$138$	−6.04599	+	3.62386i	−0.514669	+	0.308484i
$139$	3.42654	+	9.41434i	0.290635	+	0.798514i	0.995974	+	0.0896434i	$0.0285727\pi$
$139$	3.42654	+	9.41434i	0.290635	+	0.798514i	−0.705339	+	0.708871i	$0.749205\pi$
$140$	−7.79648	+	5.21224i	−0.658922	+	0.440515i
$141$	−7.05633	+	20.4210i	−0.594250	+	1.71976i
$142$	−12.5742	−	4.57663i	−1.05520	−	0.384063i
$143$	0.945644	+	1.63790i	0.0790788	+	0.136968i
$144$	−2.23379	+	2.00254i	−0.186149	+	0.166879i
$145$	2.06032	+	1.18953i	0.171100	+	0.0987848i
$146$	−4.82204	+	4.04617i	−0.399075	+	0.334864i
$147$	11.5001	−	3.84033i	0.948511	−	0.316745i
$148$	−0.322599	+	1.82955i	−0.0265174	+	0.150388i
$149$	−15.6709	−	2.76320i	−1.28381	−	0.226371i	−0.510214	−	0.860048i	$-0.670434\pi$
$149$	−15.6709	−	2.76320i	−1.28381	−	0.226371i	−0.773598	+	0.633677i	$0.781545\pi$
$150$	12.2372	−	4.68217i	0.999162	−	0.382297i
$151$	−6.19444	+	5.19775i	−0.504096	+	0.422987i	−0.859046	−	0.511898i	$-0.828942\pi$
$151$	−6.19444	+	5.19775i	−0.504096	+	0.422987i	0.354950	+	0.934885i	$0.384498\pi$
$152$	1.89688	−	3.28549i	0.153857	−	0.266488i
$153$	−10.5251	+	19.6915i	−0.850903	+	1.59196i
$154$	5.71346	−	1.39958i	0.460404	−	0.112781i
$155$	−1.81223	+	4.97905i	−0.145562	+	0.399927i
$156$	0.279562	+	1.44661i	0.0223829	+	0.115822i
$157$	5.95086	−	7.09196i	0.474930	−	0.566000i	−0.474388	−	0.880316i	$-0.657331\pi$
$157$	5.95086	−	7.09196i	0.474930	−	0.566000i	0.949318	+	0.314316i	$0.101775\pi$
$158$	0.201715	+	0.554207i	0.0160476	+	0.0440903i
$159$	23.3114	−	0.381567i	1.84871	−	0.0302603i
$160$	−3.49081	+	0.615524i	−0.275973	+	0.0486615i
$161$	10.3379	+	3.01044i	0.814741	+	0.237256i
$162$	−8.74204	+	2.13933i	−0.686840	+	0.168081i
$163$	−7.87094			−0.616500			−0.308250	−	0.951305i	$-0.599743\pi$
$163$	−7.87094			−0.616500			−0.308250	+	0.951305i	$0.599743\pi$
$164$	1.60199	+	9.08534i	0.125094	+	0.709446i
$165$	−13.6484	+	0.223401i	−1.06253	+	0.0173917i
$166$	2.49521	+	6.85554i	0.193666	+	0.532093i
$167$	1.44072	+	1.20891i	0.111487	+	0.0935484i	0.696827	−	0.717239i	$-0.254595\pi$
$167$	1.44072	+	1.20891i	0.111487	+	0.0935484i	−0.585340	+	0.810788i	$0.699039\pi$
$168$	4.56300	+	0.423137i	0.352043	+	0.0326457i
$169$	−11.5360	−	4.19877i	−0.887387	−	0.322982i
$170$	−22.8471	+	13.1908i	−1.75229	+	1.01169i
$171$	9.66494	−	6.01016i	0.739096	−	0.459609i
$172$	−4.85611	+	8.41103i	−0.370275	+	0.641335i
$173$	−9.94119	+	8.34165i	−0.755814	+	0.634204i	−0.937034	−	0.349239i	$-0.886440\pi$
$173$	−9.94119	+	8.34165i	−0.755814	+	0.634204i	0.181219	+	0.983443i	$0.441996\pi$
$174$	−0.415420	−	1.08573i	−0.0314929	−	0.0823091i
$175$	−17.9523	−	8.84757i	−1.35707	−	0.668814i
$176$	2.18956	+	0.386078i	0.165044	+	0.0291017i
$177$	3.07295	−	3.78636i	0.230977	−	0.284600i
$178$	−11.0935	−	13.2207i	−0.831491	−	0.990932i
$179$	−5.10296	−	2.94620i	−0.381413	−	0.220209i	0.297020	−	0.954871i	$-0.404007\pi$
$179$	−5.10296	−	2.94620i	−0.381413	−	0.220209i	−0.678433	+	0.734662i	$0.737341\pi$
$180$	−10.1064	−	3.30805i	−0.753284	−	0.246568i
$181$	13.9907	−	8.07755i	1.03992	−	0.600399i	0.120111	−	0.992760i	$-0.461675\pi$
$181$	13.9907	−	8.07755i	1.03992	−	0.600399i	0.919811	+	0.392361i	$0.128342\pi$
$182$	1.33036	−	1.81533i	0.0986131	−	0.134561i
$183$	−2.55162	−	0.881695i	−0.188621	−	0.0651768i
$184$	3.11754	+	2.61593i	0.229828	+	0.192849i
$185$	−6.18804	+	2.25226i	−0.454954	+	0.165590i
$186$	2.22073	−	1.33107i	0.162832	−	0.0975985i
$187$	16.2960	−	2.87342i	1.19168	−	0.210126i
$188$	12.4741			0.909765
$189$	11.4743	+	7.57237i	0.834631	+	0.550809i
$190$	13.4476			0.975590
$191$	−1.24585	+	0.219677i	−0.0901464	+	0.0158952i	−0.218539	−	0.975828i	$-0.570129\pi$
$191$	−1.24585	+	0.219677i	−0.0901464	+	0.0158952i	0.128393	+	0.991723i	$0.459018\pi$
$192$	1.51397	+	0.841360i	0.109262	+	0.0607199i
$193$	−5.56550	+	2.02567i	−0.400613	+	0.145811i	−0.534466	−	0.845190i	$-0.679487\pi$
$193$	−5.56550	+	2.02567i	−0.400613	+	0.145811i	0.133853	+	0.991001i	$0.457265\pi$
$194$	−4.40170	−	3.69346i	−0.316023	−	0.265175i
$195$	−3.94529	+	3.42207i	−0.282528	+	0.245059i
$196$	−4.26409	−	5.55136i	−0.304578	−	0.396525i
$197$	−0.223688	+	0.129147i	−0.0159371	+	0.00920131i	−0.507947	−	0.861388i	$-0.669596\pi$
$197$	−0.223688	+	0.129147i	−0.0159371	+	0.00920131i	0.492010	+	0.870589i	$0.336262\pi$
$198$	5.24710	+	4.11787i	0.372895	+	0.292644i
$199$	5.77698	+	3.33534i	0.409520	+	0.236436i	0.690583	−	0.723253i	$-0.257354\pi$
$199$	5.77698	+	3.33534i	0.409520	+	0.236436i	−0.281064	+	0.959689i	$0.590687\pi$
$200$	−4.86246	−	5.79485i	−0.343828	−	0.409758i
$201$	14.4307	+	2.30168i	1.01787	+	0.162348i
$202$	7.53235	+	1.32816i	0.529975	+	0.0934488i
$203$	−0.784992	+	1.59280i	−0.0550956	+	0.111793i
$204$	12.7301	+	2.03042i	0.891283	+	0.142158i
$205$	−25.0506	+	21.0200i	−1.74961	+	1.46810i
$206$	1.26271	−	2.18708i	0.0879772	−	0.152381i
$207$	4.54896	+	11.3299i	0.316174	+	0.787481i
$208$	0.736689	−	0.425327i	0.0510802	−	0.0294911i
$209$	−7.92610	−	2.88486i	−0.548260	−	0.199550i
$210$	6.78821	+	14.7573i	0.468431	+	1.01835i
$211$	8.16898	+	6.85459i	0.562376	+	0.471889i	0.879106	−	0.476627i	$-0.158141\pi$
$211$	8.16898	+	6.85459i	0.562376	+	0.471889i	−0.316730	+	0.948516i	$0.602585\pi$
$212$	−4.60381	−	12.6489i	−0.316191	−	0.868727i
$213$	−11.2584	+	20.2587i	−0.771412	+	1.38811i
$214$	−1.41683	−	8.03523i	−0.0968523	−	0.549277i
$215$	−34.4266			−2.34787
$216$	2.81581	+	4.36706i	0.191591	+	0.297141i
$217$	−3.79717	−	1.10575i	−0.257769	−	0.0750633i
$218$	−9.60564	+	1.69373i	−0.650576	+	0.114714i
$219$	5.60519	+	9.35161i	0.378764	+	0.631923i
$220$	2.69545	+	7.40569i	0.181727	+	0.499291i
$221$	4.06955	−	4.84989i	0.273747	−	0.326239i
$222$	3.04131	+	1.05090i	0.204119	+	0.0705320i
$223$	−4.46007	+	12.2539i	−0.298668	+	0.820584i	0.696055	+	0.717988i	$0.254937\pi$
$223$	−4.46007	+	12.2539i	−0.298668	+	0.820584i	−0.994723	+	0.102596i	$0.967285\pi$
$224$	−0.629496	−	2.56977i	−0.0420600	−	0.171700i
$225$	−4.67009	−	22.2082i	−0.311339	−	1.48055i
$226$	−5.65809	+	9.80009i	−0.376370	+	0.651892i
$227$	−2.03352	+	1.70632i	−0.134969	+	0.113253i	−0.707773	−	0.706440i	$-0.750300\pi$
$227$	−2.03352	+	1.70632i	−0.134969	+	0.113253i	0.572804	+	0.819692i	$0.305856\pi$
$228$	−5.10211	−	4.14079i	−0.337895	−	0.274231i
$229$	−14.7504	−	2.60089i	−0.974733	−	0.171872i	−0.336474	−	0.941693i	$-0.609234\pi$
$229$	−14.7504	−	2.60089i	−0.974733	−	0.171872i	−0.638260	+	0.769821i	$0.720345\pi$
$230$	−2.50497	+	14.2064i	−0.165173	+	0.936744i
$231$	−0.835190	−	10.1543i	−0.0549515	−	0.668104i
$232$	−0.514142	+	0.431416i	−0.0337551	+	0.0283239i
$233$	−1.33037	−	0.768087i	−0.0871551	−	0.0503190i	0.455789	−	0.890088i	$-0.349357\pi$
$233$	−1.33037	−	0.768087i	−0.0871551	−	0.0503190i	−0.542944	+	0.839769i	$0.682690\pi$
$234$	2.55060	−	0.0835202i	0.166738	−	0.00545989i
$235$	22.1082	+	38.2925i	1.44218	+	2.49793i
$236$	−2.64562	−	0.962926i	−0.172215	−	0.0626811i
$237$	1.00296	−	0.193826i	0.0651494	−	0.0125903i
$238$	−10.9440	−	16.3700i	−0.709392	−	1.06111i
$239$	−6.01966	−	16.5389i	−0.389379	−	1.06981i	−0.967282	−	0.253705i	$-0.918351\pi$
$239$	−6.01966	−	16.5389i	−0.389379	−	1.06981i	0.577902	−	0.816106i	$-0.303871\pi$
$240$	0.100480	+	6.13872i	0.00648597	+	0.396252i
$241$	−7.03748	+	1.24090i	−0.453324	+	0.0799333i	−0.395648	−	0.918402i	$-0.629480\pi$
$241$	−7.03748	+	1.24090i	−0.453324	+	0.0799333i	−0.0576758	+	0.998335i	$0.518369\pi$
$242$			6.05679i			0.389345i
$243$	1.27424	+	15.5363i	0.0817428	+	0.996653i
$244$			1.55865i			0.0997822i
$245$	9.48400	−	22.9286i	0.605910	−	1.46486i
$246$	15.9769	−	0.261514i	1.01865	−	0.0166735i
$247$	−3.03255	+	1.10376i	−0.192957	+	0.0702305i
$248$	−1.14509	−	0.960845i	−0.0727133	−	0.0610137i
$249$	12.4067	−	2.39762i	0.786240	−	0.151943i
$250$	3.10923	−	8.54254i	0.196645	−	0.540278i
$251$	−0.569382	−	0.986198i	−0.0359390	−	0.0622483i	0.847496	−	0.530801i	$-0.178109\pi$
$251$	−0.569382	−	0.986198i	−0.0359390	−	0.0622483i	−0.883435	+	0.468553i	$0.844776\pi$
$252$	1.96858	−	7.68926i	0.124009	−	0.484378i
$253$	4.52411	−	7.83598i	0.284428	−	0.492644i
$254$	6.66423	+	7.94212i	0.418151	+	0.498333i
$255$	16.3290	+	42.6769i	1.02256	+	2.67253i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−0.320962	+	1.82027i	−0.0200211	+	0.113545i	−0.993181	−	0.116587i	$-0.962805\pi$
$257$	−0.320962	+	1.82027i	−0.0200211	+	0.113545i	0.973159	+	0.230132i	$0.0739158\pi$
$258$	13.0617	+	10.6007i	0.813185	+	0.659968i
$259$	−1.98070	−	4.49845i	−0.123075	−	0.279520i
$260$	2.61131	+	1.50764i	0.161947	+	0.0935000i
$261$	−1.97040	+	0.414348i	−0.121965	+	0.0256475i
$262$	−6.08486	+	3.51309i	−0.375924	+	0.217040i
$263$	7.97143	−	21.9013i	0.491540	−	1.35049i	−0.407731	−	0.913102i	$-0.633680\pi$
$263$	7.97143	−	21.9013i	0.491540	−	1.35049i	0.899271	−	0.437392i	$-0.144098\pi$
$264$	1.25769	−	3.63976i	0.0774057	−	0.224012i
$265$	30.6696	−	36.5506i	1.88402	−	2.24529i
$266$	0.658961	+	10.0157i	0.0404035	+	0.614100i
$267$	−25.6395	+	15.3679i	−1.56911	+	0.940498i
$268$	−1.46505	−	8.30872i	−0.0894923	−	0.507536i
$269$	−7.90680			−0.482086			−0.241043	−	0.970514i	$-0.577490\pi$
$269$	−7.90680			−0.482086			−0.241043	+	0.970514i	$0.577490\pi$
$270$	−8.41532	+	16.3838i	−0.512140	+	0.997084i
$271$		−	23.5951i		−	1.43330i	−0.697434	−	0.716649i	$-0.745675\pi$
$271$		−	23.5951i		−	1.43330i	0.697434	−	0.716649i	$-0.254325\pi$
$272$	−1.29240	−	7.32954i	−0.0783630	−	0.444418i
$273$	−2.74206	−	2.77074i	−0.165957	−	0.167693i
$274$	−16.8730	+	6.14128i	−1.01934	+	0.371008i
$275$	−10.8109	+	12.8839i	−0.651919	+	0.776927i
$276$	5.32486	−	4.61868i	0.320519	−	0.278012i
$277$	20.8479	+	7.58803i	1.25263	+	0.455920i	0.881290	−	0.472576i	$-0.156676\pi$
$277$	20.8479	+	7.58803i	1.25263	+	0.455920i	0.371341	+	0.928497i	$0.378898\pi$
$278$	−5.00927	−	8.67630i	−0.300436	−	0.520370i
$279$	−1.67086	−	4.16153i	−0.100032	−	0.249144i
$280$	6.77293	−	6.48690i	0.404760	−	0.387666i
$281$	13.3516	+	15.9119i	0.796492	+	0.949222i	0.999552	−	0.0299445i	$-0.00953306\pi$
$281$	13.3516	+	15.9119i	0.796492	+	0.949222i	−0.203060	+	0.979166i	$0.565089\pi$
$282$	3.40306	−	21.3360i	0.202649	−	1.27054i
$283$	−4.92624	−	0.868629i	−0.292835	−	0.0516347i	0.0253009	−	0.999680i	$-0.491946\pi$
$283$	−4.92624	−	0.868629i	−0.292835	−	0.0516347i	−0.318136	+	0.948045i	$0.603057\pi$
$284$	13.1779	+	2.32362i	0.781964	+	0.137881i
$285$	3.66865	−	23.0012i	0.217312	−	1.36247i
$286$	−1.21570	−	1.44881i	−0.0718857	−	0.0856700i
$287$	−16.8831	−	17.6275i	−0.996577	−	1.04052i
$288$	1.85212	−	2.36001i	0.109137	−	0.139065i
$289$	−19.1962	−	33.2488i	−1.12919	−	1.95581i
$290$	−2.23558	−	0.813684i	−0.131278	−	0.0477812i
$291$	−7.51824	+	6.52118i	−0.440727	+	0.382278i
$292$	4.04617	−	4.82204i	0.236784	−	0.282189i
$293$	−1.47042	+	0.535190i	−0.0859030	+	0.0312661i	−0.384614	−	0.923077i	$-0.625666\pi$
$293$	−1.47042	+	0.535190i	−0.0859030	+	0.0312661i	0.298711	+	0.954344i	$0.403443\pi$
$294$	−10.6585	+	5.77896i	−0.621616	+	0.337036i
$295$	−1.73295	−	9.82806i	−0.100896	−	0.572211i
$296$		−	1.85777i		−	0.107981i
$297$	8.47480	−	7.85139i	0.491758	−	0.455584i
$298$	15.9127			0.921796
$299$	−0.601148	−	3.40928i	−0.0347653	−	0.197164i
$300$	−11.2382	+	6.73600i	−0.648839	+	0.388903i
$301$	−1.68698	−	25.6407i	−0.0972357	−	1.47790i
$302$	5.19775	−	6.19444i	0.299097	−	0.356450i
$303$	4.32663	−	12.5212i	0.248558	−	0.719326i
$304$	−1.29754	+	3.56496i	−0.0744190	+	0.204465i
$305$	−4.78469	+	2.76244i	−0.273970	+	0.158177i
$306$	6.94580	−	21.2200i	0.397065	−	1.21307i
$307$	−27.5520	−	15.9071i	−1.57247	−	0.907868i	−0.995865	−	0.0908486i	$-0.971042\pi$
$307$	−27.5520	−	15.9071i	−1.57247	−	0.907868i	−0.576610	−	0.817020i	$-0.695625\pi$
$308$	−5.38363	+	2.37045i	−0.306761	+	0.135069i
$309$	−3.39636	−	2.75644i	−0.193212	−	0.156808i
$310$	0.920092	−	5.21810i	0.0522577	−	0.296368i
$311$	1.94921	−	11.0545i	0.110529	−	0.626843i	−0.878338	−	0.478041i	$-0.841347\pi$
$311$	1.94921	−	11.0545i	0.110529	−	0.626843i	0.988867	−	0.148802i	$-0.0475418\pi$
$312$	−0.526516	−	1.37609i	−0.0298081	−	0.0779057i
$313$	12.7798	+	15.2303i	0.722355	+	0.860869i	0.994857	−	0.101286i	$-0.0322957\pi$
$313$	12.7798	+	15.2303i	0.722355	+	0.860869i	−0.272502	+	0.962155i	$0.587851\pi$
$314$	−4.62895	+	8.01757i	−0.261227	+	0.452458i
$315$	27.0932	−	7.58482i	1.52653	−	0.427356i
$316$	−0.294887	−	0.510760i	−0.0165887	−	0.0287325i
$317$	1.13113	−	3.10777i	0.0635308	−	0.174549i	−0.903866	−	0.427817i	$-0.859283\pi$
$317$	1.13113	−	3.10777i	0.0635308	−	0.174549i	0.967396	+	0.253267i	$0.0815051\pi$
$318$	−22.8910	+	4.42375i	−1.28366	+	0.248072i
$319$	1.14311	+	0.959182i	0.0640018	+	0.0537039i
$320$	3.33089	−	1.21235i	0.186203	−	0.0677722i
$321$	−14.1302	+	0.231288i	−0.788672	+	0.0129092i
$322$	−10.7036	−	1.16954i	−0.596488	−	0.0651761i
$323$			28.2354i			1.57106i
$324$	8.23774	−	3.62486i	0.457652	−	0.201381i
$325$			6.43490i			0.356944i
$326$	7.75136	−	1.36677i	0.429308	−	0.0756986i
$327$	0.276491	+	16.8919i	0.0152900	+	0.934122i
$328$	−3.15531	−	8.66913i	−0.174223	−	0.478673i
$329$	−27.4367	+	18.3425i	−1.51263	+	1.01125i
$330$	13.4023	−	2.59003i	0.737770	−	0.142576i
$331$	14.6458	+	5.33064i	0.805006	+	0.292998i	0.711559	−	0.702626i	$-0.247989\pi$
$331$	14.6458	+	5.33064i	0.805006	+	0.292998i	0.0934468	+	0.995624i	$0.470211\pi$
$332$	−3.64776	−	6.31810i	−0.200197	−	0.346751i
$333$	2.62720	−	4.91525i	0.143970	−	0.269354i
$334$	−1.62876	−	0.940366i	−0.0891219	−	0.0514545i
$335$	22.9093	−	19.2232i	1.25167	−	1.05027i
$336$	−4.56715	+	0.375648i	−0.249159	+	0.0204933i
$337$	2.11766	−	12.0099i	0.115356	−	0.654218i	−0.871217	−	0.490898i	$-0.836669\pi$
$337$	2.11766	−	12.0099i	0.115356	−	0.654218i	0.986573	−	0.163320i	$-0.0522203\pi$
$338$	12.0899	+	2.13177i	0.657603	+	0.115953i
$339$	15.2188	+	12.3513i	0.826571	+	0.670833i
$340$	20.2094	−	16.9577i	1.09601	−	0.919662i
$341$	−1.66173	+	2.87820i	−0.0899877	+	0.155863i
$342$	−8.47445	+	7.59715i	−0.458246	+	0.410807i
$343$	17.5418	+	5.94007i	0.947169	+	0.320734i
$344$	3.32178	−	9.12650i	0.179098	−	0.492068i
$345$	23.6157	+	8.16025i	1.27143	+	0.439333i
$346$	8.34165	−	9.94119i	0.448450	−	0.534442i
$347$	−0.780871	−	2.14542i	−0.0419193	−	0.115172i	0.916967	−	0.398964i	$-0.130630\pi$
$347$	−0.780871	−	2.14542i	−0.0419193	−	0.115172i	−0.958886	+	0.283791i	$0.908408\pi$
$348$	0.597644	+	0.997100i	0.0320371	+	0.0534502i
$349$	−28.0714	+	4.94974i	−1.50263	+	0.264954i	−0.863579	−	0.504214i	$-0.831782\pi$
$349$	−28.0714	+	4.94974i	−1.50263	+	0.264954i	−0.639047	+	0.769167i	$0.720671\pi$
$350$	19.2160	+	5.59577i	1.02714	+	0.299106i
$351$	0.552975	−	4.38541i	0.0295156	−	0.234076i
$352$	−2.22333			−0.118504
$353$	2.20743	+	12.5189i	0.117490	+	0.666316i	0.985487	+	0.169748i	$0.0542955\pi$
$353$	2.20743	+	12.5189i	0.117490	+	0.666316i	−0.867998	+	0.496568i	$0.834593\pi$
$354$	−2.36877	+	4.26245i	−0.125899	+	0.226547i
$355$	16.2226	+	44.5713i	0.861008	+	2.36560i
$356$	13.2207	+	11.0935i	0.700695	+	0.587953i
$357$	−30.9854	+	14.2530i	−1.63992	+	0.754347i
$358$	5.53704	+	2.01532i	0.292641	+	0.106513i
$359$	17.3017	−	9.98915i	0.913149	−	0.527207i	0.0317063	−	0.999497i	$-0.489906\pi$
$359$	17.3017	−	9.98915i	0.913149	−	0.527207i	0.881443	+	0.472290i	$0.156573\pi$
$360$	10.5273	+	1.50284i	0.554835	+	0.0792068i
$361$	−2.30372	+	3.99016i	−0.121248	+	0.210008i
$362$	−12.3755	+	10.3843i	−0.650443	+	0.545786i
$363$	10.3597	+	1.65236i	0.543744	+	0.0867263i
$364$	−0.994923	+	2.01877i	−0.0521481	+	0.105812i
$365$	21.9737	+	3.87456i	1.15016	+	0.202804i
$366$	2.66596	+	0.425216i	0.139352	+	0.0222264i
$367$	16.8766	+	20.1128i	0.880952	+	1.04988i	0.998386	+	0.0567969i	$0.0180887\pi$
$367$	16.8766	+	20.1128i	0.880952	+	1.04988i	−0.117434	+	0.993081i	$0.537467\pi$
$368$	−3.52443	−	2.03483i	−0.183724	−	0.106073i
$369$	3.91137	−	27.3987i	0.203618	−	1.42632i
$370$	5.70293	−	3.29259i	0.296481	−	0.171173i
$371$	28.7255	+	21.0515i	1.49136	+	1.09294i
$372$	−1.95585	+	1.69647i	−0.101406	+	0.0879579i
$373$	−14.0512	−	11.7903i	−0.727542	−	0.610480i	0.201919	−	0.979402i	$-0.435282\pi$
$373$	−14.0512	−	11.7903i	−0.727542	−	0.610480i	−0.929460	+	0.368922i	$0.879727\pi$
$374$	−15.5495	+	5.65954i	−0.804044	+	0.292648i
$375$	−13.7632	−	7.64863i	−0.710729	−	0.394973i
$376$	−12.2846	+	2.16610i	−0.633528	+	0.111708i
$377$	0.570929			0.0294044
$378$	−12.6149	−	5.46484i	−0.648840	−	0.281081i
$379$	3.31264			0.170159			0.0850795	−	0.996374i	$-0.472886\pi$
$379$	3.31264			0.170159			0.0850795	+	0.996374i	$0.472886\pi$
$380$	−13.2433	+	2.33515i	−0.679366	+	0.119791i
$381$	15.4025	−	9.23200i	0.789095	−	0.472970i
$382$	1.18877	−	0.432679i	0.0608230	−	0.0221378i
$383$	−21.3595	−	17.9228i	−1.09142	−	0.915810i	−0.0946018	−	0.995515i	$-0.530158\pi$
$383$	−21.3595	−	17.9228i	−1.09142	−	0.915810i	−0.996819	+	0.0797048i	$0.974602\pi$
$384$	−1.63707	−	0.565680i	−0.0835415	−	0.0288672i
$385$	−16.8183	−	12.3253i	−0.857140	−	0.628154i
$386$	5.12919	−	2.96134i	0.261069	−	0.150728i
$387$	21.6951	−	19.4491i	1.10282	−	0.988655i
$388$	4.97619	+	2.87300i	0.252628	+	0.145855i
$389$	−9.58597	−	11.4241i	−0.486028	−	0.579225i	0.466175	−	0.884693i	$-0.345632\pi$
$389$	−9.58597	−	11.4241i	−0.486028	−	0.579225i	−0.952203	+	0.305467i	$0.901187\pi$
$390$	3.29111	−	4.05517i	0.166652	−	0.205341i
$391$	−29.8287	−	5.25961i	−1.50850	−	0.265990i
$392$	5.16329	+	4.72657i	0.260786	+	0.238728i
$393$	4.34889	+	11.3661i	0.219372	+	0.573346i
$394$	0.197864	−	0.166028i	0.00996825	−	0.00836435i
$395$	1.04528	−	1.81047i	0.0525936	−	0.0910947i
$396$	−5.88244	−	3.14416i	−0.295604	−	0.158000i
$397$	−28.4273	+	16.4125i	−1.42673	+	0.823721i	−0.996861	−	0.0791725i	$-0.974772\pi$
$397$	−28.4273	+	16.4125i	−1.42673	+	0.823721i	−0.429865	+	0.902893i	$0.641439\pi$
$398$	−6.26840	−	2.28151i	−0.314206	−	0.114362i
$399$	17.3109	+	1.60528i	0.866629	+	0.0803644i
$400$	5.79485	+	4.86246i	0.289743	+	0.243123i
$401$	13.3069	+	36.5603i	0.664513	+	1.82573i	0.555183	+	0.831728i	$0.312648\pi$
$401$	13.3069	+	36.5603i	0.664513	+	1.82573i	0.109330	+	0.994005i	$0.465129\pi$
$402$	−14.6112	+	0.239160i	−0.728739	+	0.0119282i
$403$	0.220805	+	1.25225i	0.0109991	+	0.0623790i
$404$	−7.64855			−0.380530
$405$	25.7275	+	18.8635i	1.27841	+	0.937335i
$406$	0.496479	−	1.70492i	0.0246398	−	0.0846136i
$407$	−4.06769	+	0.717244i	−0.201628	+	0.0355525i
$408$	−12.8892	+	0.210975i	−0.638113	+	0.0104448i
$409$	6.09161	+	16.7366i	0.301211	+	0.827570i	0.994290	+	0.106709i	$0.0340313\pi$
$409$	6.09161	+	16.7366i	0.301211	+	0.827570i	−0.693079	+	0.720861i	$0.743746\pi$
$410$	21.0200	−	25.0506i	1.03810	−	1.23716i
$411$	5.90109	+	30.5356i	0.291079	+	1.50621i
$412$	−0.863744	+	2.37312i	−0.0425536	+	0.116915i
$413$	7.23496	−	1.77229i	0.356009	−	0.0872086i
$414$	−6.44726	−	10.3678i	−0.316866	−	0.509551i
$415$	12.9301	−	22.3955i	0.634712	−	1.09935i
$416$	−0.651639	+	0.546790i	−0.0319492	+	0.0268086i
$417$	−16.2068	+	6.20101i	−0.793650	+	0.303665i
$418$	8.30663	+	1.46468i	0.406291	+	0.0716400i
$419$	−1.35458	+	7.68222i	−0.0661757	+	0.375301i	0.933677	+	0.358117i	$0.116581\pi$
$419$	−1.35458	+	7.68222i	−0.0661757	+	0.375301i	−0.999852	+	0.0171838i	$0.994530\pi$
$420$	−9.24766	−	13.3543i	−0.451240	−	0.651625i
$421$	−4.41555	+	3.70509i	−0.215201	+	0.180575i	−0.744015	−	0.668162i	$-0.767081\pi$
$421$	−4.41555	+	3.70509i	−0.215201	+	0.180575i	0.528815	+	0.848737i	$0.322637\pi$
$422$	−9.23516	−	5.33192i	−0.449560	−	0.259554i
$423$	−35.5654	−	11.6414i	−1.72925	−	0.566025i
$424$	6.73032	+	11.6573i	0.326853	+	0.566126i
$425$	52.9053	+	19.2560i	2.56628	+	0.934051i
$426$	7.56946	−	21.9060i	0.366742	−	1.06135i
$427$	−2.29191	−	3.42824i	−0.110913	−	0.165904i
$428$	2.79060	+	7.66712i	0.134889	+	0.370604i
$429$	−2.80975	+	1.68411i	−0.135656	+	0.0813098i
$430$	33.9035	−	5.97811i	1.63497	−	0.288290i
$431$		−	29.1465i		−	1.40394i	−0.712209	−	0.701968i	$-0.752305\pi$
$431$		−	29.1465i		−	1.40394i	0.712209	−	0.701968i	$-0.247695\pi$
$432$	−3.53136	−	3.81176i	−0.169903	−	0.183393i
$433$		−	16.0344i		−	0.770562i	−0.922799	−	0.385281i	$-0.874104\pi$
$433$		−	16.0344i		−	0.770562i	0.922799	−	0.385281i	$-0.125896\pi$
$434$	3.93150	+	0.429580i	0.188718	+	0.0206205i
$435$	−2.00164	+	3.60182i	−0.0959713	+	0.172694i
$436$	9.16560	−	3.33600i	0.438952	−	0.159766i
$437$	11.8272	+	9.92418i	0.565771	+	0.474738i
$438$	−7.14393	−	8.23620i	−0.341350	−	0.393541i
$439$	−0.574218	+	1.57765i	−0.0274059	+	0.0752971i	−0.952641	−	0.304097i	$-0.901645\pi$
$439$	−0.574218	+	1.57765i	−0.0274059	+	0.0752971i	0.925235	+	0.379394i	$0.123868\pi$
$440$	−3.94048	−	6.82512i	−0.187855	−	0.325375i
$441$	6.97676	+	19.8072i	0.332226	+	0.943200i
$442$	−3.16554	+	5.48288i	−0.150570	+	0.260794i
$443$	−6.79389	−	8.09664i	−0.322787	−	0.384683i	0.580111	−	0.814538i	$-0.303009\pi$
$443$	−6.79389	−	8.09664i	−0.322787	−	0.384683i	−0.902898	+	0.429855i	$0.858565\pi$
$444$	−3.17759	−	0.506820i	−0.150802	−	0.0240526i
$445$	−10.6229	+	60.2457i	−0.503576	+	2.85592i
$446$	2.26444	−	12.8423i	0.107224	−	0.608098i
$447$	4.34115	−	27.2175i	0.205329	−	1.28734i
$448$	1.06617	+	2.42142i	0.0503718	+	0.114401i
$449$	−30.6194	−	17.6781i	−1.44502	−	0.834282i	−0.446840	−	0.894614i	$-0.647451\pi$
$449$	−30.6194	−	17.6781i	−1.44502	−	0.834282i	−0.998178	+	0.0603326i	$0.980784\pi$
$450$	8.45555	+	21.0599i	0.398598	+	0.992771i
$451$	−17.7634	+	10.2557i	−0.836444	+	0.482921i
$452$	3.87036	−	10.6337i	0.182046	−	0.500168i
$453$	−9.17715	−	10.5803i	−0.431180	−	0.497106i
$454$	1.70632	−	2.03352i	0.0800818	−	0.0954377i
$455$	−7.96048	+	0.523744i	−0.373193	+	0.0245535i
$456$	5.74364	+	3.19191i	0.268971	+	0.149475i
$457$	−1.06288	−	6.02787i	−0.0497193	−	0.281972i	0.949804	−	0.312846i	$-0.101282\pi$
$457$	−1.06288	−	6.02787i	−0.0497193	−	0.281972i	−0.999523	+	0.0308735i	$0.990171\pi$
$458$	14.9779			0.699873
$459$	−34.4004	−	17.6694i	−1.60567	−	0.824735i
$460$		−	14.4256i		−	0.672596i
$461$	−3.82751	−	21.7069i	−0.178265	−	1.01099i	−0.934307	−	0.356468i	$-0.883981\pi$
$461$	−3.82751	−	21.7069i	−0.178265	−	1.01099i	0.756042	−	0.654523i	$-0.227130\pi$
$462$	2.58578	+	9.85501i	0.120301	+	0.458496i
$463$	11.4892	−	4.18174i	0.533950	−	0.194342i	−0.0609512	−	0.998141i	$-0.519413\pi$
$463$	11.4892	−	4.18174i	0.533950	−	0.194342i	0.594901	+	0.803799i	$0.297191\pi$
$464$	0.431416	−	0.514142i	0.0200280	−	0.0238684i
$465$	−8.67419	−	2.99731i	−0.402256	−	0.138997i
$466$	1.44353	+	0.525402i	0.0668703	+	0.0243388i
$467$	−14.1323	−	24.4779i	−0.653965	−	1.13270i	−0.982152	−	0.188088i	$-0.939771\pi$
$467$	−14.1323	−	24.4779i	−0.653965	−	1.13270i	0.328187	−	0.944613i	$-0.393562\pi$
$468$	−2.49734	+	0.525158i	−0.115440	+	0.0242754i
$469$	15.4399	+	16.1207i	0.712949	+	0.744386i
$470$	−28.4217	−	33.8717i	−1.31100	−	1.56239i
$471$	12.4507	+	10.1048i	0.573697	+	0.465604i
$472$	2.77263	+	0.488890i	0.127621	+	0.0225030i
$473$	−21.2654	−	3.74967i	−0.977786	−	0.172410i
$474$	−0.954068	+	0.365044i	−0.0438218	+	0.0167670i
$475$	−18.4470	−	21.9842i	−0.846405	−	1.00871i
$476$	13.6203	+	14.2209i	0.624286	+	0.651814i
$477$	1.32161	+	40.3603i	0.0605124	+	1.84797i
$478$	8.80015	+	15.2423i	0.402510	+	0.697167i
$479$	−35.2144	−	12.8170i	−1.60899	−	0.585624i	−0.627749	−	0.778416i	$-0.716024\pi$
$479$	−35.2144	−	12.8170i	−1.60899	−	0.585624i	−0.981240	+	0.192792i	$0.938246\pi$
$480$	−1.16493	−	6.02801i	−0.0531716	−	0.275140i
$481$	−1.01581	+	1.21060i	−0.0463170	+	0.0551985i
$482$	6.71509	−	2.44409i	0.305864	−	0.111325i
$483$	−4.92048	+	17.9887i	−0.223890	+	0.818515i
$484$	−1.05175	−	5.96477i	−0.0478068	−	0.271126i
$485$			20.3677i			0.924848i
$486$	−3.95273	−	15.0790i	−0.179300	−	0.683997i
$487$	−30.5776			−1.38560			−0.692802	−	0.721128i	$-0.743624\pi$
$487$	−30.5776			−1.38560			−0.692802	+	0.721128i	$0.743624\pi$
$488$	−0.270656	−	1.53497i	−0.0122520	−	0.0694848i
$489$	−0.223117	−	13.6310i	−0.0100897	−	0.616417i
$490$	−5.35840	+	24.2272i	−0.242068	+	1.09447i
$491$	−0.00662625	+	0.00789685i	−0.000299038	+	0.000356380i	−0.766194	−	0.642609i	$-0.777852\pi$
$491$	−0.00662625	+	0.00789685i	−0.000299038	+	0.000356380i	0.765895	+	0.642966i	$0.222296\pi$
$492$	−15.6888	+	3.03190i	−0.707303	+	0.136689i
$493$	1.70846	−	4.69397i	0.0769454	−	0.211406i
$494$	2.79481	−	1.61359i	0.125745	−	0.0725987i
$495$	−0.773780	−	23.6302i	−0.0347788	−	1.06210i
$496$	1.29454	+	0.747405i	0.0581267	+	0.0335595i
$497$	−32.4015	+	14.2666i	−1.45341	+	0.639945i
$498$	−11.8018	+	4.51559i	−0.528852	+	0.202348i
$499$	−4.62591	+	26.2349i	−0.207084	+	1.17443i	0.687042	+	0.726618i	$0.258909\pi$
$499$	−4.62591	+	26.2349i	−0.207084	+	1.17443i	−0.894126	+	0.447816i	$0.852202\pi$
$500$	−1.57860	+	8.95268i	−0.0705971	+	0.400376i
$501$	−2.05278	+	2.52934i	−0.0917112	+	0.113003i
$502$	0.731983	+	0.872343i	0.0326700	+	0.0389346i
$503$	13.9825	−	24.2184i	0.623449	−	1.07984i	−0.365390	−	0.930855i	$-0.619064\pi$
$503$	13.9825	−	24.2184i	0.623449	−	1.07984i	0.988839	−	0.148990i	$-0.0476024\pi$
$504$	−0.603450	+	7.91428i	−0.0268798	+	0.352530i
$505$	−13.5558	−	23.4793i	−0.603224	−	1.04481i
$506$	−3.09467	+	8.50254i	−0.137575	+	0.377984i
$507$	6.94450	−	20.0973i	0.308416	−	0.892554i
$508$	−7.94212	−	6.66423i	−0.352374	−	0.295677i
$509$	10.8413	−	3.94589i	0.480530	−	0.174899i	−0.0903863	−	0.995907i	$-0.528810\pi$
$509$	10.8413	−	3.94589i	0.480530	−	0.174899i	0.570917	+	0.821008i	$0.306588\pi$
$510$	−23.4917	−	39.1931i	−1.04023	−	1.73550i
$511$	−1.80899	+	16.5557i	−0.0800249	+	0.732383i
$512$			1.00000i			0.0441942i
$513$	10.6825	+	16.5676i	0.471643	+	0.731475i
$514$		−	1.84835i		−	0.0815271i
$515$	−8.81577	+	1.55446i	−0.388469	+	0.0684976i
$516$	−14.7040	−	8.17148i	−0.647309	−	0.359729i
$517$	9.48559	+	26.0615i	0.417176	+	1.14618i
$518$	2.73175	+	4.08616i	0.120026	+	0.179536i
$519$	−14.7280	−	16.9799i	−0.646488	−	0.745334i
$520$	−2.83344	−	1.03129i	−0.124255	−	0.0452250i
$521$	17.6953	+	30.6492i	0.775247	+	1.34277i	0.934656	+	0.355554i	$0.115708\pi$
$521$	17.6953	+	30.6492i	0.775247	+	1.34277i	−0.159409	+	0.987213i	$0.550959\pi$
$522$	1.86851	−	0.750210i	0.0817826	−	0.0328358i
$523$	−1.31727	−	0.760529i	−0.0576004	−	0.0332556i	0.470923	−	0.882174i	$-0.343921\pi$
$523$	−1.31727	−	0.760529i	−0.0576004	−	0.0332556i	−0.528524	+	0.848919i	$0.677254\pi$
$524$	5.38237	−	4.51635i	0.235130	−	0.197298i
$525$	14.8135	−	31.3410i	0.646514	−	1.36783i
$526$	−4.04720	+	22.9528i	−0.176466	+	1.00079i
$527$	10.9563	+	1.93189i	0.477262	+	0.0841542i
$528$	−0.606550	+	3.80286i	−0.0263967	+	0.165498i
$529$	4.93169	−	4.13818i	0.214421	−	0.179921i
$530$	−23.8567	+	41.3210i	−1.03627	+	1.79487i
$531$	6.64440	+	5.21446i	0.288342	+	0.226288i
$532$	−2.38815	−	9.74909i	−0.103540	−	0.422676i
$533$	−2.68408	+	7.37444i	−0.116260	+	0.319422i
$534$	22.5814	−	19.5866i	0.977191	−	0.847597i
$535$	−18.5904	+	22.1552i	−0.803734	+	0.957853i
$536$	2.88559	+	7.92809i	0.124638	+	0.342441i
$537$	4.95762	−	8.92092i	0.213937	−	0.384966i
$538$	7.78668	−	1.37300i	0.335708	−	0.0591943i
$539$	8.35565	−	13.1301i	0.359903	−	0.565555i
$540$	5.44246	−	17.5962i	0.234206	−	0.757218i
$541$	31.7769			1.36620			0.683098	−	0.730327i	$-0.260632\pi$
$541$	31.7769			1.36620			0.683098	+	0.730327i	$0.260632\pi$
$542$	4.09724	+	23.2366i	0.175992	+	0.998098i
$543$	14.3854	+	24.0004i	0.617338	+	1.02996i
$544$	2.54552	+	6.99376i	0.109138	+	0.299855i
$545$	26.4852	+	22.2238i	1.13450	+	0.951961i
$546$	3.18154	+	2.25249i	0.136157	+	0.0963976i
$547$	−4.25116	−	1.54730i	−0.181767	−	0.0661576i	0.249533	−	0.968366i	$-0.419723\pi$
$547$	−4.25116	−	1.54730i	−0.181767	−	0.0661576i	−0.431300	+	0.902209i	$0.641945\pi$
$548$	15.5503	−	8.97795i	0.664275	−	0.383519i
$549$	1.45461	−	4.44394i	0.0620811	−	0.189663i
$550$	8.40936	−	14.5654i	0.358576	−	0.621072i
$551$	−1.95053	+	1.63669i	−0.0830953	+	0.0697252i
$552$	−4.44194	+	5.47317i	−0.189061	+	0.232954i
$553$	1.39965	+	0.689798i	0.0595191	+	0.0293332i
$554$	−21.8488	−	3.85254i	−0.928269	−	0.163679i
$555$	−4.07592	−	10.6527i	−0.173013	−	0.452183i
$556$	6.43979	+	7.67464i	0.273108	+	0.325477i
$557$	−24.4707	−	14.1282i	−1.03686	−	0.598629i	−0.117915	−	0.993024i	$-0.537621\pi$
$557$	−24.4707	−	14.1282i	−1.03686	−	0.598629i	−0.918941	+	0.394395i	$0.870954\pi$
$558$	2.36812	+	3.80817i	0.100250	+	0.161213i
$559$	−7.15488	+	4.13087i	−0.302619	+	0.174717i
$560$	−5.54360	+	7.56446i	−0.234260	+	0.319657i
$561$	5.43819	+	28.1403i	0.229601	+	1.18808i
$562$	−15.9119	−	13.3516i	−0.671201	−	0.563205i
$563$	35.4365	−	12.8978i	1.49347	−	0.543578i	0.539108	−	0.842236i	$-0.318761\pi$
$563$	35.4365	−	12.8978i	1.49347	−	0.543578i	0.954360	+	0.298658i	$0.0965391\pi$
$564$	0.353601	+	21.6028i	0.0148893	+	0.909643i
$565$	39.5026	−	6.96538i	1.66189	−	0.293036i
$566$	5.00224			0.210260
$567$	−12.7887	+	20.0860i	−0.537075	+	0.843534i
$568$	−13.3812			−0.561462
$569$	4.79790	−	0.846000i	0.201139	−	0.0354662i	−0.0721710	−	0.997392i	$-0.522993\pi$
$569$	4.79790	−	0.846000i	0.201139	−	0.0354662i	0.273310	+	0.961926i	$0.411882\pi$
$570$	0.381197	+	23.2888i	0.0159666	+	0.975459i
$571$	20.8731	−	7.59719i	0.873512	−	0.317933i	0.133924	−	0.990992i	$-0.457242\pi$
$571$	20.8731	−	7.59719i	0.873512	−	0.317933i	0.739589	+	0.673059i	$0.235020\pi$
$572$	1.44881	+	1.21570i	0.0605778	+	0.0508308i
$573$	−0.415756	−	2.15136i	−0.0173685	−	0.0898742i
$574$	19.6876	+	14.4280i	0.821744	+	0.602214i
$575$	26.6610	−	15.3928i	1.11184	−	0.641922i
$576$	−1.41417	+	2.64578i	−0.0589236	+	0.110241i
$577$	−8.83941	−	5.10344i	−0.367989	−	0.212459i	0.304590	−	0.952483i	$-0.401480\pi$
$577$	−8.83941	−	5.10344i	−0.367989	−	0.212459i	−0.672580	+	0.740025i	$0.734814\pi$
$578$	24.6782	+	29.4103i	1.02648	+	1.22331i
$579$	−3.66587	−	9.58101i	−0.152348	−	0.398173i
$580$	2.34291	+	0.413118i	0.0972841	+	0.0171538i
$581$	17.3137	+	8.53281i	0.718292	+	0.354000i
$582$	6.27163	−	7.72764i	0.259968	−	0.320321i
$583$	22.9258	−	19.2370i	0.949489	−	0.796716i
$584$	−3.14736	+	5.45139i	−0.130239	+	0.225580i
$585$	−6.03824	−	6.73552i	−0.249650	−	0.278479i
$586$	1.35515	−	0.782396i	0.0559807	−	0.0323205i
$587$	−40.3204	−	14.6754i	−1.66420	−	0.605720i	−0.673188	−	0.739472i	$-0.735075\pi$
$587$	−40.3204	−	14.6754i	−1.66420	−	0.605720i	−0.991015	+	0.133751i	$0.957298\pi$
$588$	9.49307	−	7.54199i	0.391488	−	0.311027i
$589$	−4.34419	−	3.64521i	−0.178999	−	0.150198i
$590$	3.41325	+	9.37782i	0.140521	+	0.386079i
$591$	−0.229999	−	0.383727i	−0.00946091	−	0.0157844i
$592$	0.322599	+	1.82955i	0.0132587	+	0.0751940i
$593$	−18.6478			−0.765772			−0.382886	−	0.923796i	$-0.625070\pi$
$593$	−18.6478			−0.765772			−0.382886	+	0.923796i	$0.625070\pi$
$594$	−6.98267	+	9.20375i	−0.286502	+	0.377634i
$595$	−19.5151	+	67.0154i	−0.800042	+	2.74736i
$596$	−15.6709	+	2.76320i	−0.641906	+	0.113185i
$597$	−5.61245	+	10.0992i	−0.229702	+	0.413334i
$598$	1.18403	+	3.25310i	0.0484186	+	0.133029i
$599$	10.2866	−	12.2591i	0.420299	−	0.500893i	−0.513799	−	0.857911i	$-0.671762\pi$
$599$	10.2866	−	12.2591i	0.420299	−	0.500893i	0.934097	+	0.357018i	$0.116207\pi$
$600$	9.89780	−	8.58516i	0.404076	−	0.350488i
$601$	−5.04304	+	13.8556i	−0.205710	+	0.565183i	−0.999049	−	0.0435963i	$-0.986118\pi$
$601$	−5.04304	+	13.8556i	−0.205710	+	0.565183i	0.793339	+	0.608780i	$0.208341\pi$
$602$	6.11381	+	24.9582i	0.249180	+	1.01722i
$603$	−3.57702	+	25.0567i	−0.145668	+	1.02039i
$604$	−4.04313	+	7.00291i	−0.164513	+	0.284944i
$605$	16.4464	−	13.8002i	0.668642	−	0.561057i
$606$	−2.08661	+	13.0823i	−0.0847627	+	0.531433i
$607$	−20.6494	−	3.64104i	−0.838133	−	0.147785i	−0.261924	−	0.965088i	$-0.584357\pi$
$607$	−20.6494	−	3.64104i	−0.838133	−	0.147785i	−0.576208	+	0.817303i	$0.695468\pi$
$608$	0.658778	−	3.73612i	0.0267170	−	0.151520i
$609$	−2.78070	−	1.31431i	−0.112680	−	0.0532586i
$610$	4.23231	−	3.55133i	0.171361	−	0.143789i
$611$	9.18951	+	5.30556i	0.371768	+	0.214640i
$612$	−3.15547	+	22.1037i	−0.127552	+	0.893490i
$613$	−14.9370	−	25.8716i	−0.603298	−	1.04494i	−0.992318	−	0.123714i	$-0.960519\pi$
$613$	−14.9370	−	25.8716i	−0.603298	−	1.04494i	0.389019	−	0.921230i	$-0.372814\pi$
$614$	29.8956	+	10.8811i	1.20649	+	0.439126i
$615$	−37.1129	−	42.7873i	−1.49654	−	1.72535i
$616$	4.89021	−	3.26929i	0.197032	−	0.131724i
$617$	8.58366	+	23.5834i	0.345565	+	0.949433i	0.983749	+	0.179549i	$0.0574637\pi$
$617$	8.58366	+	23.5834i	0.345565	+	0.949433i	−0.638184	+	0.769884i	$0.720314\pi$
$618$	3.82342	+	2.12479i	0.153800	+	0.0854715i
$619$	−15.5389	+	2.73993i	−0.624562	+	0.110127i	−0.476968	−	0.878921i	$-0.658264\pi$
$619$	−15.5389	+	2.73993i	−0.624562	+	0.110127i	−0.147594	+	0.989048i	$0.547153\pi$
$620$			5.29860i			0.212797i
$621$	−19.4924	+	8.19914i	−0.782201	+	0.329020i
$622$			11.2250i			0.450083i
$623$	−45.3912	−	4.95973i	−1.81856	−	0.198708i
$624$	0.757473	+	1.26375i	0.0303232	+	0.0505907i
$625$	5.26174	−	1.91512i	0.210470	−	0.0766046i
$626$	−15.2303	−	12.7798i	−0.608726	−	0.510782i
$627$	4.77138	−	13.8083i	0.190551	−	0.551452i
$628$	3.16639	−	8.69958i	0.126353	−	0.347151i
$629$	6.91333	+	11.9742i	0.275653	+	0.477444i
$630$	−25.3645	+	12.1743i	−1.01055	+	0.485035i
$631$	−15.2442	+	26.4038i	−0.606863	+	1.05112i	0.384891	+	0.922962i	$0.374239\pi$
$631$	−15.2442	+	26.4038i	−0.606863	+	1.05112i	−0.991754	+	0.128156i	$0.959094\pi$
$632$	0.379100	+	0.451794i	0.0150798	+	0.0179714i
$633$	−11.6393	+	14.3415i	−0.462622	+	0.570023i
$634$	−0.574292	+	3.25697i	−0.0228080	+	0.129351i
$635$	6.38157	−	36.1917i	0.253245	−	1.43622i
$636$	21.7750	−	8.33152i	0.863436	−	0.330366i
$637$	−0.780162	−	5.90325i	−0.0309112	−	0.233895i
$638$	−1.29230	−	0.746111i	−0.0511628	−	0.0295388i
$639$	−35.4036	−	18.9232i	−1.40055	−	0.748591i
$640$	−3.06977	+	1.77233i	−0.121343	+	0.0700576i
$641$	3.13118	−	8.60285i	0.123674	−	0.339792i	−0.862369	−	0.506280i	$-0.831020\pi$
$641$	3.13118	−	8.60285i	0.123674	−	0.339792i	0.986044	+	0.166488i	$0.0532425\pi$
$642$	13.8754	−	2.68146i	0.547618	−	0.105829i
$643$	28.2540	−	33.6718i	1.11423	−	1.32789i	0.175011	−	0.984566i	$-0.444004\pi$
$643$	28.2540	−	33.6718i	1.11423	−	1.32789i	0.939218	−	0.343320i	$-0.111552\pi$
$644$	10.7441	−	0.706885i	0.423376	−	0.0278552i
$645$	−0.975886	−	59.6206i	−0.0384255	−	2.34756i
$646$	−4.90303	−	27.8065i	−0.192907	−	1.09403i
$647$	26.2447			1.03178			0.515892	−	0.856653i	$-0.327460\pi$
$647$	26.2447			1.03178			0.515892	+	0.856653i	$0.327460\pi$
$648$	−7.48314	+	5.00026i	−0.293965	+	0.196429i
$649$		−	6.25959i		−	0.245710i
$650$	−1.11741	−	6.33714i	−0.0438283	−	0.248563i
$651$	1.80732	−	6.60736i	0.0708346	−	0.258963i
$652$	−7.39627	+	2.69202i	−0.289660	+	0.105428i
$653$	−21.0314	+	25.0643i	−0.823024	+	0.980841i	−0.999994	−	0.00337486i	$-0.998926\pi$
$653$	−21.0314	+	25.0643i	−0.823024	+	0.980841i	0.176971	+	0.984216i	$0.443370\pi$
$654$	−3.20553	−	16.5872i	−0.125346	−	0.648612i
$655$	23.4035	+	8.51817i	0.914450	+	0.332833i
$656$	4.61275	+	7.98951i	0.180098	+	0.311938i
$657$	−16.0364	+	9.97227i	−0.625640	+	0.389055i
$658$	23.8347	−	22.8281i	0.929174	−	0.889933i
$659$	13.6491	+	16.2664i	0.531693	+	0.633647i	0.963304	−	0.268413i	$-0.0864990\pi$
$659$	13.6491	+	16.2664i	0.531693	+	0.633647i	−0.431611	+	0.902060i	$0.642055\pi$
$660$	−12.7489	+	4.87796i	−0.496250	+	0.189874i
$661$	−8.02105	−	1.41433i	−0.311983	−	0.0550110i	0.0154646	−	0.999880i	$-0.495077\pi$
$661$	−8.02105	−	1.41433i	−0.311983	−	0.0550110i	−0.327447	+	0.944869i	$0.606188\pi$
$662$	−15.3490	−	2.70644i	−0.596554	−	0.105189i
$663$	8.51450	+	6.91024i	0.330676	+	0.268371i
$664$	4.68947	+	5.58869i	0.181987	+	0.216883i
$665$	25.6948	−	24.6097i	0.996403	−	0.954323i
$666$	−1.73376	+	5.29678i	−0.0671819	+	0.205246i
$667$	−1.36571	−	2.36547i	−0.0528804	−	0.0915915i
$668$	1.76731	+	0.643248i	0.0683793	+	0.0248880i
$669$	−21.3480	−	7.37667i	−0.825362	−	0.285198i
$670$	−19.2232	+	22.9093i	−0.742656	+	0.885063i
$671$	−3.25640	+	1.18523i	−0.125712	+	0.0457555i
$672$	4.43254	−	1.16302i	0.170989	−	0.0448644i
$673$	6.30308	+	35.7465i	0.242966	+	1.37793i	0.825170	+	0.564885i	$0.191079\pi$
$673$	6.30308	+	35.7465i	0.242966	+	1.37793i	−0.582204	+	0.813043i	$0.697810\pi$
$674$			12.1951i			0.469739i
$675$	38.3282	−	8.71728i	1.47525	−	0.335528i
$676$	−12.2764			−0.472169
$677$	0.989246	+	5.61030i	0.0380198	+	0.215621i	0.997899	−	0.0647939i	$-0.0206390\pi$
$677$	0.989246	+	5.61030i	0.0380198	+	0.215621i	−0.959879	+	0.280415i	$0.909528\pi$
$678$	−17.1324	−	9.52098i	−0.657965	−	0.365651i
$679$	−15.1697	+	0.998060i	−0.582160	+	0.0383020i
$680$	−16.9577	+	20.2094i	−0.650299	+	0.774996i
$681$	−3.01269	−	3.47332i	−0.115446	−	0.133098i
$682$	1.13669	−	3.12303i	0.0435261	−	0.119587i
$683$	39.3275	−	22.7057i	1.50482	−	0.868811i	0.504840	−	0.863213i	$-0.331551\pi$
$683$	39.3275	−	22.7057i	1.50482	−	0.868811i	0.999984	−	0.00559823i	$-0.00178198\pi$
$684$	7.02648	−	8.95331i	0.268664	−	0.342338i
$685$	55.1205	+	31.8238i	2.10604	+	1.21593i
$686$	−18.3068	−	2.80372i	−0.698957	−	0.107047i
$687$	4.08615	−	25.6187i	0.155896	−	0.977416i
$688$	−1.68651	+	9.56467i	−0.0642976	+	0.364650i
$689$	1.98833	−	11.2764i	0.0757495	−	0.429597i
$690$	−24.6740	−	3.93545i	−0.939321	−	0.149820i
$691$	−20.8491	−	24.8470i	−0.793136	−	0.945223i	0.206310	−	0.978487i	$-0.433854\pi$
$691$	−20.8491	−	24.8470i	−0.793136	−	0.945223i	−0.999447	+	0.0332634i	$0.989410\pi$
$692$	−6.48865	+	11.2387i	−0.246661	+	0.427230i
$693$	17.5617	−	1.73424i	0.667115	−	0.0658784i
$694$	1.14156	+	1.97723i	0.0433329	+	0.0750548i
$695$	−12.1459	+	33.3707i	−0.460721	+	1.26582i
$696$	−0.761709	−	0.878172i	−0.0288725	−	0.0332870i
$697$	52.5979	+	44.1349i	1.99229	+	1.67173i
$698$	26.7854	−	9.74908i	1.01384	−	0.369008i
$699$	1.29248	−	2.32572i	0.0488859	−	0.0879670i
$700$	−19.8957	−	2.17394i	−0.751988	−	0.0821670i
$701$		−	38.8359i		−	1.46681i	−0.679790	−	0.733407i	$-0.737929\pi$
$701$		−	38.8359i		−	1.46681i	0.679790	−	0.733407i	$-0.262071\pi$
$702$	0.216943	+	4.41480i	0.00818800	+	0.166626i
$703$		−	7.04793i		−	0.265818i
$704$	2.18956	−	0.386078i	0.0825220	−	0.0145509i
$705$	−65.6890	+	39.3729i	−2.47399	+	1.48287i
$706$	−4.34779	−	11.9454i	−0.163631	−	0.449573i
$707$	16.8230	−	11.2468i	0.632693	−	0.422979i
$708$	1.59262	−	4.60902i	0.0598542	−	0.173218i
$709$	−10.1591	−	3.69761i	−0.381533	−	0.138867i	0.144132	−	0.989559i	$-0.453961\pi$
$709$	−10.1591	−	3.69761i	−0.381533	−	0.138867i	−0.525665	+	0.850692i	$0.676183\pi$
$710$	−23.7159	−	41.0771i	−0.890042	−	1.54160i
$711$	0.364102	+	1.73146i	0.0136549	+	0.0649347i
$712$	−14.9462	−	8.62919i	−0.560132	−	0.323392i
$713$	4.66013	−	3.91031i	0.174523	−	0.146442i
$714$	28.0396	−	19.4170i	1.04936	−	0.726663i
$715$	−1.16413	+	6.60213i	−0.0435362	+	0.246906i
$716$	−5.80287	−	1.02320i	−0.216864	−	0.0382389i
$717$	28.4717	−	10.8938i	1.06330	−	0.406836i
$718$	−15.3043	+	12.8418i	−0.571150	+	0.479252i
$719$	9.17385	−	15.8896i	0.342127	−	0.592581i	−0.642701	−	0.766117i	$-0.722186\pi$
$719$	9.17385	−	15.8896i	0.342127	−	0.592581i	0.984827	+	0.173537i	$0.0555195\pi$
$720$	−10.6283	+	0.348027i	−0.396093	+	0.0129702i
$721$	−1.58974	−	6.48976i	−0.0592051	−	0.241691i
$722$	1.57584	−	4.32957i	0.0586465	−	0.161130i
$723$	−2.34850	−	12.1525i	−0.0873417	−	0.451955i
$724$	10.3843	−	12.3755i	0.385929	−	0.459933i
$725$	1.73648	+	4.77093i	0.0644911	+	0.177188i
$726$	−10.4893	+	0.171691i	−0.389293	+	0.00637206i
$727$	−41.7009	+	7.35299i	−1.54660	+	0.272707i	−0.880823	−	0.473445i	$-0.843010\pi$
$727$	−41.7009	+	7.35299i	−1.54660	+	0.272707i	−0.665776	+	0.746152i	$0.731899\pi$
$728$	0.629252	−	2.16086i	0.0233216	−	0.0800870i
$729$	−26.8699	+	2.64717i	−0.995182	+	0.0980432i
$730$	−22.3127			−0.825830
$731$	12.5520	+	71.1861i	0.464253	+	2.63291i
$732$	−2.69930	+	0.0441828i	−0.0997688	+	0.00163305i
$733$	6.61059	+	18.1624i	0.244168	+	0.670845i	0.999873	+	0.0159333i	$0.00507194\pi$
$733$	6.61059	+	18.1624i	0.244168	+	0.670845i	−0.755705	+	0.654912i	$0.772706\pi$
$734$	−20.1128	−	16.8766i	−0.742376	−	0.622927i
$735$	39.9770	+	15.7746i	1.47458	+	0.581855i
$736$	3.82423	+	1.39191i	0.140963	+	0.0513063i
$737$	16.2449	−	9.37902i	0.598390	−	0.345481i
$738$	0.905791	+	27.6617i	0.0333426	+	1.01824i
$739$	18.1967	−	31.5176i	0.669377	−	1.15940i	−0.308702	−	0.951159i	$-0.599894\pi$
$739$	18.1967	−	31.5176i	0.669377	−	1.15940i	0.978079	−	0.208236i	$-0.0667722\pi$
$740$	−5.04454	+	4.23287i	−0.185441	+	0.155603i
$741$	−1.99747	−	5.22054i	−0.0733790	−	0.191781i
$742$	−31.9447	−	15.7435i	−1.17273	−	0.577963i
$743$	−17.7368	−	3.12748i	−0.650700	−	0.114736i	−0.161452	−	0.986881i	$-0.551618\pi$
$743$	−17.7368	−	3.12748i	−0.650700	−	0.114736i	−0.489248	+	0.872145i	$0.662729\pi$
$744$	1.63155	−	2.01033i	0.0598155	−	0.0737022i
$745$	−36.2565	−	43.2088i	−1.32833	−	1.58305i
$746$	15.8851	+	9.17125i	0.581594	+	0.335783i
$747$	4.50394	+	21.4181i	0.164791	+	0.783648i
$748$	14.3305	−	8.27370i	0.523974	−	0.302516i
$749$	−17.4120	−	12.7604i	−0.636222	−	0.466254i
$750$	14.8823	+	5.14247i	0.543424	+	0.187776i
$751$	−35.5528	−	29.8323i	−1.29734	−	1.08860i	−0.990598	−	0.136804i	$-0.956317\pi$
$751$	−35.5528	−	29.8323i	−1.29734	−	1.08860i	−0.306741	−	0.951793i	$-0.599238\pi$
$752$	11.7218	−	4.26638i	0.427450	−	0.155579i
$753$	1.69178	−	1.01402i	0.0616517	−	0.0369530i
$754$	−0.562256	+	0.0991409i	−0.0204761	+	0.00361050i
$755$	−28.6631			−1.04316
$756$	13.3722	+	3.19126i	0.486342	+	0.116065i
$757$	34.0275			1.23675			0.618376	−	0.785883i	$-0.287791\pi$
$757$	34.0275			1.23675			0.618376	+	0.785883i	$0.287791\pi$
$758$	−3.26231	+	0.575234i	−0.118493	+	0.0208934i
$759$	13.6987	+	7.61280i	0.497233	+	0.276327i
$760$	12.6366	−	4.59934i	0.458377	−	0.166836i
$761$	36.9654	+	31.0176i	1.33999	+	1.12439i	0.981627	+	0.190808i	$0.0611107\pi$
$761$	36.9654	+	31.0176i	1.33999	+	1.12439i	0.358367	+	0.933581i	$0.383334\pi$
$762$	−13.5654	+	11.7664i	−0.491422	+	0.426251i
$763$	−15.2543	+	20.8151i	−0.552242	+	0.753556i
$764$	−1.09558	+	0.632534i	−0.0396367	+	0.0228843i
$765$	−73.4459	+	29.4886i	−2.65544	+	1.06616i
$766$	24.1473	+	13.9414i	0.872476	+	0.503725i
$767$	−1.53944	−	1.83463i	−0.0555858	−	0.0662446i
$768$	1.71043	+	0.272811i	0.0617199	+	0.00984422i
$769$	1.83279	+	0.323170i	0.0660921	+	0.0116538i	0.206596	−	0.978426i	$-0.433761\pi$
$769$	1.83279	+	0.323170i	0.0660921	+	0.0116538i	−0.140504	+	0.990080i	$0.544872\pi$
$770$	18.7031	+	9.21755i	0.674011	+	0.332177i
$771$	−3.16147	−	0.504249i	−0.113858	−	0.0181601i
$772$	−4.53703	+	3.80702i	−0.163291	+	0.137018i
$773$	−5.15925	+	8.93608i	−0.185565	+	0.321409i	−0.943767	−	0.330612i	$-0.892745\pi$
$773$	−5.15925	+	8.93608i	−0.185565	+	0.321409i	0.758202	+	0.652020i	$0.226078\pi$
$774$	−17.9882	+	22.9210i	−0.646571	+	0.823877i
$775$	−9.79275	+	5.65385i	−0.351766	+	0.203092i
$776$	−5.39948	−	1.96525i	−0.193830	−	0.0705484i
$777$	7.73435	−	3.55773i	0.277468	−	0.127633i
$778$	11.4241	+	9.58597i	0.409574	+	0.343674i
$779$	−11.9705	−	32.8885i	−0.428886	−	1.17835i
$780$	−2.53694	+	4.56506i	−0.0908371	+	0.163455i
$781$	5.16618	+	29.2988i	0.184860	+	1.04839i
$782$	30.2889			1.08313
$783$	−0.773431	−	3.40063i	−0.0276402	−	0.121529i
$784$	−5.90561	−	3.75816i	−0.210915	−	0.134220i
$785$	32.3176	−	5.69846i	1.15346	−	0.203387i
$786$	−6.25653	−	10.4383i	−0.223163	−	0.372321i
$787$	4.58113	+	12.5866i	0.163300	+	0.448663i	0.994173	−	0.107800i	$-0.0343806\pi$
$787$	4.58113	+	12.5866i	0.163300	+	0.448663i	−0.830873	+	0.556462i	$0.812158\pi$
$788$	−0.166028	+	0.197864i	−0.00591449	+	0.00704861i
$789$	38.1551	+	13.1842i	1.35836	+	0.469372i
$790$	−0.715011	+	1.96448i	−0.0254390	+	0.0698930i
$791$	7.12349	+	29.0800i	0.253282	+	1.03397i
$792$	6.33905	+	2.07492i	0.225248	+	0.0737292i
$793$	−0.662936	+	1.14824i	−0.0235415	+	0.0407751i
$794$	25.1454	−	21.0995i	0.892378	−	0.748794i
$795$	64.1684	+	52.0781i	2.27582	+	1.84702i
$796$	6.56934	+	1.15835i	0.232844	+	0.0410567i
$797$	1.67296	−	9.48782i	0.0592592	−	0.336076i	−0.940736	−	0.339140i	$-0.889864\pi$
$797$	1.67296	−	9.48782i	0.0592592	−	0.336076i	0.999995	+	0.00306373i	$0.000975217\pi$
$798$	−17.3267	+	1.42511i	−0.613357	+	0.0504485i
$799$	71.1193	−	59.6762i	2.51602	−	2.11119i
$800$	−6.55117	−	3.78232i	−0.231619	−	0.133725i
$801$	−27.3412	−	43.9673i	−0.966052	−	1.55351i
$802$	−19.4533	−	33.6941i	−0.686921	−	1.18978i
$803$	13.1513	+	4.78667i	0.464098	+	0.168918i
$804$	14.3477	−	2.77273i	0.506003	−	0.0977867i
$805$	21.2120	+	31.7290i	0.747626	+	1.11830i
$806$	−0.434902	−	1.19488i	−0.0153188	−	0.0420879i
$807$	−0.224133	−	13.6931i	−0.00788987	−	0.482022i
$808$	7.53235	−	1.32816i	0.264987	−	0.0467244i
$809$			8.72744i			0.306841i	0.988161	+	0.153420i	$0.0490288\pi$
$809$			8.72744i			0.306841i	−0.988161	+	0.153420i	$0.950971\pi$
$810$	−28.6123	−	14.1094i	−1.00533	−	0.495753i
$811$		−	1.24370i		−	0.0436723i	−0.999762	−	0.0218362i	$-0.993049\pi$
$811$		−	1.24370i		−	0.0436723i	0.999762	−	0.0218362i	$-0.00695122\pi$
$812$	−0.192880	+	1.76523i	−0.00676877	+	0.0619474i
$813$	40.8624	−	0.668847i	1.43311	−	0.0234575i
$814$	3.88135	−	1.41270i	0.136041	−	0.0495150i
$815$	−21.3725	−	17.9337i	−0.748647	−	0.628189i
$816$	12.6568	−	2.44596i	0.443076	−	0.0856259i
$817$	12.6020	−	34.6237i	0.440888	−	1.21133i
$818$	−8.90534	−	15.4245i	−0.311368	−	0.539305i
$819$	4.72068	−	4.82730i	0.164954	−	0.168679i
$820$	−16.3506	+	28.3201i	−0.570989	+	0.988982i
$821$	−20.1412	−	24.0033i	−0.702933	−	0.837723i	0.289922	−	0.957050i	$-0.406371\pi$
$821$	−20.1412	−	24.0033i	−0.702933	−	0.837723i	−0.992855	+	0.119328i	$0.961926\pi$
$822$	−11.1139	−	29.0469i	−0.387641	−	1.01313i
$823$	5.15273	−	29.2226i	0.179613	−	1.01864i	−0.753071	−	0.657940i	$-0.771428\pi$
$823$	5.15273	−	29.2226i	0.179613	−	1.01864i	0.932684	−	0.360696i	$-0.117461\pi$
$824$	0.438535	−	2.48705i	0.0152771	−	0.0866406i
$825$	−22.6190	−	18.3572i	−0.787493	−	0.639117i
$826$	−6.81729	+	3.00170i	−0.237204	+	0.104442i
$827$	9.91384	+	5.72376i	0.344738	+	0.199035i	0.662365	−	0.749181i	$-0.269553\pi$
$827$	9.91384	+	5.72376i	0.344738	+	0.199035i	−0.317627	+	0.948216i	$0.602886\pi$
$828$	8.14967	+	9.09077i	0.283221	+	0.315926i
$829$	−19.7903	+	11.4260i	−0.687347	+	0.396840i	−0.802617	−	0.596494i	$-0.796560\pi$
$829$	−19.7903	+	11.4260i	−0.687347	+	0.396840i	0.115270	+	0.993334i	$0.463227\pi$
$830$	−8.84469	+	24.3006i	−0.307004	+	0.843486i
$831$	−12.5501	+	36.3199i	−0.435359	+	1.25992i
$832$	0.546790	−	0.651639i	0.0189565	−	0.0225915i
$833$	−50.8689	−	11.2508i	−1.76250	−	0.389819i
$834$	14.8838	−	8.92109i	0.515383	−	0.308912i
$835$	1.15764	+	6.56528i	0.0400617	+	0.227201i
$836$	−8.43478			−0.291723
$837$	7.15966	−	3.01159i	0.247474	−	0.104096i
$838$		−	7.80073i		−	0.269472i
$839$	−5.51605	−	31.2831i	−0.190435	−	1.08001i	−0.918771	−	0.394791i	$-0.870817\pi$
$839$	−5.51605	−	31.2831i	−0.190435	−	1.08001i	0.728335	−	0.685221i	$-0.240294\pi$
$840$	11.4261	+	11.5456i	0.394239	+	0.398361i
$841$	−26.8278	+	9.76452i	−0.925096	+	0.336707i
$842$	3.70509	−	4.41555i	0.127686	−	0.152170i
$843$	−27.1780	+	23.5737i	−0.936059	+	0.811920i
$844$	10.0207	+	3.64725i	0.344928	+	0.125543i
$845$	−21.7578	−	37.6857i	−0.748492	−	1.29643i
$846$	37.0466	+	5.28868i	1.27369	+	0.181829i
$847$	11.0842	+	11.5730i	0.380858	+	0.397651i
$848$	−8.65233	−	10.3114i	−0.297122	−	0.354097i
$849$	1.36466	−	8.55598i	0.0468352	−	0.293641i
$850$	−55.4453	−	9.77650i	−1.90176	−	0.335331i
$851$	7.44564	+	1.31287i	0.255233	+	0.0450045i
$852$	−3.65053	+	22.8876i	−0.125065	+	0.784116i
$853$	19.7478	+	23.5346i	0.676153	+	0.805808i	0.989607	−	0.143796i	$-0.0459308\pi$
$853$	19.7478	+	23.5346i	0.676153	+	0.805808i	−0.313454	+	0.949603i	$0.601486\pi$
$854$	2.85240	+	2.97817i	0.0976070	+	0.101911i
$855$	39.9378	+	5.70142i	1.36585	+	0.194984i
$856$	−4.07959	−	7.06606i	−0.139438	−	0.241513i
$857$	−11.5975	−	4.22114i	−0.396163	−	0.144191i	0.136254	−	0.990674i	$-0.456494\pi$
$857$	−11.5975	−	4.22114i	−0.396163	−	0.144191i	−0.532417	+	0.846482i	$0.678716\pi$
$858$	2.47462	−	2.14644i	0.0844820	−	0.0732781i
$859$	24.4310	−	29.1157i	0.833574	−	0.993415i	−0.166399	−	0.986059i	$-0.553214\pi$
$859$	24.4310	−	29.1157i	0.833574	−	0.993415i	0.999973	−	0.00735665i	$-0.00234172\pi$
$860$	−32.3504	+	11.7746i	−1.10314	+	0.401510i
$861$	30.0491	−	29.7381i	1.02407	−	1.01347i
$862$	5.06123	+	28.7037i	0.172386	+	0.977651i
$863$		−	23.5019i		−	0.800014i	−0.916512	−	0.400007i	$-0.869008\pi$
$863$		−	23.5019i		−	0.800014i	0.916512	−	0.400007i	$-0.130992\pi$
$864$	4.13962	+	3.14063i	0.140833	+	0.106846i
$865$	−46.0002			−1.56405
$866$	2.78434	+	15.7908i	0.0946156	+	0.536592i
$867$	57.0367	−	34.1868i	1.93707	−	1.16105i
$868$	−3.94636	+	0.259643i	−0.133948	+	0.00881286i
$869$	0.842866	−	1.00449i	0.0285923	−	0.0340749i
$870$	1.34578	−	3.89468i	0.0456263	−	0.132042i
$871$	2.45464	−	6.74407i	0.0831723	−	0.228514i
$872$	−8.44706	+	4.87691i	−0.286054	+	0.165153i
$873$	−11.5066	−	12.8354i	−0.389440	−	0.434412i
$874$	−13.3708	−	7.71964i	−0.452275	−	0.261121i
$875$	−9.69231	−	22.0126i	−0.327660	−	0.744163i
$876$	8.46560	+	6.87055i	0.286026	+	0.232134i
$877$	2.40276	−	13.6267i	0.0811354	−	0.460142i	−0.916988	−	0.398914i	$-0.869387\pi$
$877$	2.40276	−	13.6267i	0.0811354	−	0.460142i	0.998124	−	0.0612280i	$-0.0195017\pi$
$878$	0.291538	−	1.65339i	0.00983893	−	0.0557993i
$879$	−0.968534	−	2.53134i	−0.0326679	−	0.0853798i
$880$	5.06579	+	6.03717i	0.170768	+	0.203513i
$881$	11.2449	−	19.4768i	0.378851	−	0.656189i	−0.612045	−	0.790823i	$-0.709653\pi$
$881$	11.2449	−	19.4768i	0.378851	−	0.656189i	0.990895	+	0.134634i	$0.0429860\pi$
$882$	−10.3102	−	18.2948i	−0.347164	−	0.616017i
$883$	−4.54260	−	7.86802i	−0.152871	−	0.264780i	0.779411	−	0.626513i	$-0.215518\pi$
$883$	−4.54260	−	7.86802i	−0.152871	−	0.264780i	−0.932282	+	0.361733i	$0.882185\pi$
$884$	2.16536	−	5.94928i	0.0728289	−	0.200096i
$885$	16.9713	−	3.27975i	0.570484	−	0.110248i
$886$	8.09664	+	6.79389i	0.272012	+	0.228245i
$887$	−7.27019	+	2.64613i	−0.244109	+	0.0888484i	−0.461177	−	0.887308i	$-0.652573\pi$
$887$	−7.27019	+	2.64613i	−0.244109	+	0.0888484i	0.217068	+	0.976156i	$0.430351\pi$
$888$	3.21732	−	0.0526621i	0.107966	−	0.00176722i
$889$	27.2681	+	2.97948i	0.914541	+	0.0999286i
$890$		−	61.1751i		−	2.05059i
$891$	13.8374	+	14.4543i	0.463571	+	0.484236i
$892$			13.0404i			0.436624i
$893$	−46.6046	+	8.21765i	−1.55956	+	0.274993i
$894$	0.451075	+	27.5578i	0.0150862	+	0.921672i
$895$	−7.14362	−	19.6269i	−0.238785	−	0.656056i
$896$	−1.47045	−	2.19950i	−0.0491242	−	0.0734800i
$897$	5.88722	−	1.13772i	0.196568	−	0.0379875i
$898$	33.2240	+	12.0925i	1.10870	+	0.403533i
$899$	0.501632	+	0.868852i	0.0167304	+	0.0289778i
$900$	−11.9841	−	19.2716i	−0.399470	−	0.642387i
$901$	−86.7604	−	50.0911i	−2.89041	−	1.66878i
$902$	15.7126	−	13.1844i	0.523173	−	0.438994i
$903$	44.3572	−	3.64837i	1.47612	−	0.121410i
$904$	−1.96503	+	11.1443i	−0.0653560	+	0.370652i
$905$	56.3944	+	9.94386i	1.87461	+	0.330545i
$906$	10.8750	+	8.82597i	0.361297	+	0.293223i
$907$	−10.3786	+	8.70869i	−0.344616	+	0.289167i	−0.798624	−	0.601830i	$-0.794438\pi$
$907$	−10.3786	+	8.70869i	−0.344616	+	0.289167i	0.454008	+	0.890998i	$0.349994\pi$
$908$	−1.32728	+	2.29892i	−0.0440475	+	0.0762925i
$909$	21.8072	+	7.13800i	0.723298	+	0.236753i
$910$	7.74860	−	1.89811i	0.256864	−	0.0629217i
$911$	8.53906	−	23.4609i	0.282912	−	0.777293i	−0.714100	−	0.700044i	$-0.753164\pi$
$911$	8.53906	−	23.4609i	0.282912	−	0.777293i	0.997012	−	0.0772497i	$-0.0246139\pi$
$912$	−6.21065	−	2.14605i	−0.205655	−	0.0710628i
$913$	10.4262	−	12.4255i	0.345058	−	0.411225i
$914$	2.09346	+	5.75173i	0.0692454	+	0.190250i
$915$	−4.91968	−	8.20791i	−0.162640	−	0.271345i
$916$	−14.7504	+	2.60089i	−0.487367	+	0.0859359i
$917$	−5.19746	+	17.8482i	−0.171635	+	0.589399i
$918$	36.9460	+	11.4273i	1.21940	+	0.377159i
$919$	−31.0298			−1.02358			−0.511789	−	0.859111i	$-0.671017\pi$
$919$	−31.0298			−1.02358			−0.511789	+	0.859111i	$0.671017\pi$
$920$	2.50497	+	14.2064i	0.0825866	+	0.468372i
$921$	26.7673	−	48.1659i	0.882012	−	1.58712i
$922$	7.53872	+	20.7125i	0.248275	+	0.682129i
$923$	8.71970	+	7.31670i	0.287013	+	0.240832i
$924$	−4.25780	−	9.25627i	−0.140071	−	0.304509i
$925$	−13.2059	−	4.80654i	−0.434206	−	0.158038i
$926$	−10.5885	+	6.11329i	−0.347961	+	0.200895i
$927$	4.67737	−	5.96002i	0.153625	−	0.195753i
$928$	−0.335582	+	0.581246i	−0.0110160	+	0.0190803i
$929$	0.202876	−	0.170233i	0.00665613	−	0.00558516i	−0.639453	−	0.768830i	$-0.720839\pi$
$929$	0.202876	−	0.170233i	0.00665613	−	0.00558516i	0.646110	+	0.763245i	$0.276395\pi$
$930$	9.06289	+	1.44552i	0.297184	+	0.0474003i
$931$	19.5883	+	17.9314i	0.641979	+	0.587679i
$932$	−1.51284	−	0.266754i	−0.0495546	−	0.00873781i
$933$	19.1996	+	3.06231i	0.628568	+	0.100256i
$934$	18.1681	+	21.6519i	0.594479	+	0.708473i
$935$	50.7967	+	29.3275i	1.66123	+	0.959111i
$936$	2.36821	−	0.950839i	0.0774074	−	0.0310791i
$937$	−7.52839	+	4.34652i	−0.245942	+	0.141995i	−0.617905	−	0.786253i	$-0.712018\pi$
$937$	−7.52839	+	4.34652i	−0.245942	+	0.141995i	0.371963	+	0.928248i	$0.378685\pi$
$938$	−18.0047	−	13.1947i	−0.587874	−	0.430822i
$939$	−26.0139	+	22.5640i	−0.848932	+	0.736347i
$940$	33.8717	+	28.4217i	1.10477	+	0.927015i
$941$	13.7300	−	4.99730i	0.447584	−	0.162907i	−0.108387	−	0.994109i	$-0.534569\pi$
$941$	13.7300	−	4.99730i	0.447584	−	0.162907i	0.555971	+	0.831201i	$0.312346\pi$
$942$	−14.0162	−	7.78922i	−0.456672	−	0.253787i
$943$	36.9742	−	6.51956i	1.20405	−	0.212306i
$944$	−2.81541			−0.0916337
$945$	13.9035	+	46.7055i	0.452282	+	1.51933i
$946$	21.5935			0.702065
$947$	−16.9102	+	2.98172i	−0.549508	+	0.0968930i	−0.441507	−	0.897258i	$-0.645556\pi$
$947$	−16.9102	+	2.98172i	−0.549508	+	0.0968930i	−0.108001	+	0.994151i	$0.534445\pi$
$948$	0.876185	−	0.525170i	0.0284572	−	0.0170567i
$949$	5.03171	−	1.83139i	0.163336	−	0.0594496i
$950$	21.9842	+	18.4470i	0.713263	+	0.598498i
$951$	5.41415	+	1.87082i	0.175566	+	0.0606656i
$952$	−15.8828	−	11.6397i	−0.514765	−	0.377245i
$953$	−24.0959	+	13.9118i	−0.780543	+	0.450646i	−0.836623	−	0.547780i	$-0.815473\pi$
$953$	−24.0959	+	13.9118i	−0.780543	+	0.450646i	0.0560800	+	0.998426i	$0.482140\pi$
$954$	−8.31002	−	39.5176i	−0.269047	−	1.27943i
$955$	−3.88346	−	2.24212i	−0.125666	−	0.0725533i
$956$	−11.3133	−	13.4826i	−0.365897	−	0.436059i
$957$	−1.62873	+	2.00685i	−0.0526493	+	0.0648722i
$958$	36.9051	+	6.50736i	1.19235	+	0.210243i
$959$	−21.0012	+	42.6128i	−0.678163	+	1.37604i
$960$	2.19398	+	5.73414i	0.0708106	+	0.185069i
$961$	22.0357	−	18.4901i	0.710829	−	0.596456i
$962$	0.790161	−	1.36860i	0.0254758	−	0.0441254i
$963$	−0.801096	−	24.4644i	−0.0258150	−	0.788355i
$964$	−6.18866	+	3.57302i	−0.199323	+	0.115079i
$965$	−19.7278	−	7.18034i	−0.635061	−	0.231143i
$966$	1.72202	−	18.5699i	0.0554052	−	0.597475i
$967$	−26.1602	−	21.9510i	−0.841255	−	0.705897i	0.116590	−	0.993180i	$-0.462804\pi$
$967$	−26.1602	−	21.9510i	−0.841255	−	0.705897i	−0.957846	+	0.287283i	$0.907248\pi$
$968$	2.07154	+	5.69152i	0.0665819	+	0.182932i
$969$	−48.8986	+	0.800387i	−1.57085	+	0.0257121i
$970$	−3.53681	−	20.0582i	−0.113560	−	0.644031i
$971$	−21.6628			−0.695193			−0.347597	−	0.937644i	$-0.613002\pi$
$971$	−21.6628			−0.695193			−0.347597	+	0.937644i	$0.613002\pi$
$972$	6.51112	+	14.1635i	0.208844	+	0.454295i
$973$	−25.4494	−	7.41098i	−0.815872	−	0.237585i
$974$	30.1131	−	5.30975i	0.964885	−	0.170135i
$975$	−11.1441	+	0.182409i	−0.356896	+	0.00584178i
$976$	0.533089	+	1.46465i	0.0170638	+	0.0468823i
$977$	6.23944	−	7.43587i	0.199617	−	0.237895i	−0.656945	−	0.753939i	$-0.728152\pi$
$977$	6.23944	−	7.43587i	0.199617	−	0.237895i	0.856562	+	0.516044i	$0.172596\pi$
$978$	2.58673	+	13.3852i	0.0827146	+	0.428012i
$979$	−13.1237	+	36.0571i	−0.419435	+	1.15239i
$980$	1.07000	−	24.7896i	0.0341797	−	0.791874i
$981$	−29.2458	+	0.957664i	−0.933747	+	0.0305759i
$982$	0.00515430	−	0.00892752i	0.000164480	−	0.000284889i
$983$	27.5193	−	23.0915i	0.877731	−	0.736504i	−0.0879804	−	0.996122i	$-0.528041\pi$
$983$	27.5193	−	23.0915i	0.877731	−	0.736504i	0.965711	+	0.259619i	$0.0835968\pi$
$984$	14.9239	−	5.71016i	0.475757	−	0.182033i
$985$	−0.901653	−	0.158986i	−0.0287290	−	0.00506571i
$986$	−0.867410	+	4.91933i	−0.0276240	+	0.156663i
$987$	−32.5436	−	46.9954i	−1.03587	−	1.49588i
$988$	−2.47216	+	2.07439i	−0.0786499	+	0.0659951i
$989$	34.2300	+	19.7627i	1.08845	+	0.628418i
$990$	4.86537	+	23.1369i	0.154632	+	0.735338i
$991$	13.2282	+	22.9119i	0.420208	+	0.727821i	0.995959	−	0.0898036i	$-0.0286239\pi$
$991$	13.2282	+	22.9119i	0.420208	+	0.727821i	−0.575752	+	0.817624i	$0.695291\pi$
$992$	−1.40466	−	0.511255i	−0.0445981	−	0.0162324i
$993$	−8.81653	+	25.5150i	−0.279784	+	0.809694i
$994$	29.4319	−	19.6763i	0.933522	−	0.624095i
$995$	8.08718	+	22.2194i	0.256381	+	0.704401i
$996$	10.8384	−	6.49635i	0.343428	−	0.205845i
$997$	20.6301	−	3.63765i	0.653363	−	0.115206i	0.162866	−	0.986648i	$-0.447926\pi$
$997$	20.6301	−	3.63765i	0.653363	−	0.115206i	0.490497	+	0.871443i	$0.336815\pi$
$998$		−	26.6396i		−	0.843261i
$999$	8.58679	+	4.41050i	0.271674	+	0.139542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.41.7	yes	144
7.6	odd	2	inner	378.2.z.a.41.6	✓	144
27.2	odd	18	inner	378.2.z.a.83.6	yes	144
189.83	even	18	inner	378.2.z.a.83.7	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.6	✓	144	7.6	odd	2	inner
378.2.z.a.41.7	yes	144	1.1	even	1	trivial
378.2.z.a.83.6	yes	144	27.2	odd	18	inner
378.2.z.a.83.7	yes	144	189.83	even	18	inner

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.0283469 + 1.73182i) q^{3} +(0.939693 - 0.342020i) q^{4} +(2.71537 + 2.27847i) q^{5} +(-0.328643 - 1.70059i) q^{6} +(-1.56393 + 2.13404i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.99839 + 0.0981834i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.0283469 + 1.73182i) q^{3} +(0.939693 - 0.342020i) q^{4} +(2.71537 + 2.27847i) q^{5} +(-0.328643 - 1.70059i) q^{6} +(-1.56393 + 2.13404i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.99839 + 0.0981834i) q^{9} +(-3.06977 - 1.77233i) q^{10} +(1.42913 + 1.70317i) q^{11} +(0.618954 + 1.61768i) q^{12} +(0.837731 + 0.147715i) q^{13} +(1.16960 - 2.37319i) q^{14} +(-3.86892 + 4.76712i) q^{15} +(0.766044 - 0.642788i) q^{16} +(3.72130 - 6.44549i) q^{17} +(2.93579 - 0.617357i) q^{18} +(-3.28549 + 1.89688i) q^{19} +(3.33089 + 1.21235i) q^{20} +(-3.74010 - 2.64795i) q^{21} +(-1.70317 - 1.42913i) q^{22} +(-1.39191 - 3.82423i) q^{23} +(-0.890459 - 1.48563i) q^{24} +(1.31359 + 7.44972i) q^{25} -0.850655 q^{26} +(-0.255031 - 5.18989i) q^{27} +(-0.739727 + 2.54024i) q^{28} +(0.660968 - 0.116547i) q^{29} +(2.98234 - 5.36652i) q^{30} +(0.511255 + 1.40466i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-2.90907 + 2.52328i) q^{33} +(-2.54552 + 6.99376i) q^{34} +(-9.10898 + 2.23135i) q^{35} +(-2.78399 + 1.11777i) q^{36} +(-0.928886 + 1.60888i) q^{37} +(2.90618 - 2.43858i) q^{38} +(-0.232068 + 1.45499i) q^{39} +(-3.49081 - 0.615524i) q^{40} +(-1.60199 + 9.08534i) q^{41} +(4.14309 + 1.95826i) q^{42} +(-7.43999 + 6.24290i) q^{43} +(1.92546 + 1.11167i) q^{44} +(-8.36545 - 6.56513i) q^{45} +(2.03483 + 3.52443i) q^{46} +(11.7218 + 4.26638i) q^{47} +(1.13491 + 1.30843i) q^{48} +(-2.10826 - 6.67497i) q^{49} +(-2.58726 - 7.10844i) q^{50} +(11.2679 + 6.26191i) q^{51} +(0.837731 - 0.147715i) q^{52} -13.4606i q^{53} +(1.15237 + 5.06676i) q^{54} +7.88097i q^{55} +(0.287381 - 2.63010i) q^{56} +(-3.37818 - 5.63610i) q^{57} +(-0.630689 + 0.229552i) q^{58} +(-2.15673 - 1.80971i) q^{59} +(-2.00514 + 5.80287i) q^{60} +(-0.533089 + 1.46465i) q^{61} +(-0.747405 - 1.29454i) q^{62} +(4.47974 - 6.55224i) q^{63} +(0.500000 - 0.866025i) q^{64} +(1.93819 + 2.30984i) q^{65} +(2.42672 - 2.99010i) q^{66} +(1.46505 - 8.30872i) q^{67} +(1.29240 - 7.32954i) q^{68} +(6.58342 - 2.51893i) q^{69} +(8.58313 - 3.77921i) q^{70} +(11.5884 + 6.69059i) q^{71} +(2.54759 - 1.58423i) q^{72} +(5.45139 - 3.14736i) q^{73} +(0.635395 - 1.74573i) q^{74} +(-12.8643 + 2.48607i) q^{75} +(-2.43858 + 2.90618i) q^{76} +(-5.86970 + 0.386185i) q^{77} +(-0.0241134 - 1.47318i) q^{78} +(-0.102413 - 0.580815i) q^{79} +3.54466 q^{80} +(8.98072 - 0.588785i) q^{81} -9.22550i q^{82} +(-1.26685 - 7.18468i) q^{83} +(-4.42020 - 1.20907i) q^{84} +(24.7905 - 9.02302i) q^{85} +(6.24290 - 7.43999i) q^{86} +(0.220574 + 1.14137i) q^{87} +(-2.08925 - 0.760425i) q^{88} +(8.62919 + 14.9462i) q^{89} +(9.37839 + 5.01275i) q^{90} +(-1.62538 + 1.55674i) q^{91} +(-2.61593 - 3.11754i) q^{92} +(-2.41813 + 0.925219i) q^{93} +(-12.2846 - 2.16610i) q^{94} +(-13.2433 - 2.33515i) q^{95} +(-1.34487 - 1.09148i) q^{96} +(3.69346 + 4.40170i) q^{97} +(3.23533 + 6.20747i) q^{98} +(-4.45232 - 4.96646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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