LMFDB - Embedded newform 378.2.z.a.41.6

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			41.6
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(-0.0283469 - 1.73182i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.71537 - 2.27847i) q^{5} +(0.328643 + 1.70059i) q^{6} +(0.173696 - 2.64004i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.99839 + 0.0981834i) q^{9} +O(q^{10})$	\(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} +(0.173696 - 2.64004i) 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} +(0.287381 + 2.63010i) 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} +(-4.57700 - 0.225973i) 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} +(-6.48690 + 6.77293i) 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} +(4.54671 - 0.572247i) 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} +(-6.93966 - 0.917132i) 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} +(1.16960 + 2.37319i) 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} +(-0.261601 + 7.93294i) 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} +(5.21224 - 7.79648i) 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} +(4.74468 - 3.47713i) 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} +(-4.37826 + 1.35308i) 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} +(-0.535484 + 2.18599i) 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} +(6.99349 - 0.301861i) 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	$-0.986499\pi$
$5$	−2.71537	−	2.27847i	−1.21435	−	1.01896i	−0.215250	−	0.976559i	$-0.569057\pi$
$6$	0.328643	+	1.70059i	0.134168	+	0.694261i
$7$	0.173696	−	2.64004i	0.0656510	−	0.997843i
$7$	0.173696	−	2.64004i	0.0656510	−	0.997843i
$8$	−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	0.0562633	−	0.998416i	$-0.482081\pi$
$13$	−0.837731	−	0.147715i	−0.232345	−	0.0409687i	−0.288608	+	0.957447i	$0.593192\pi$
$14$	0.287381	+	2.63010i	0.0768059	+	0.702923i
$15$	−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	$0.524973\pi$
$17$	−3.72130	+	6.44549i	−0.902549	+	1.56326i	−0.824174	+	0.566336i	$0.808360\pi$
$18$	2.93579	−	0.617357i	0.691973	−	0.145512i
$19$	3.28549	−	1.89688i	0.753742	−	0.435173i	−0.0733021	−	0.997310i	$-0.523354\pi$
$19$	3.28549	−	1.89688i	0.753742	−	0.435173i	0.827045	+	0.562136i	$0.190020\pi$
$20$	−3.33089	−	1.21235i	−0.744811	−	0.271089i
$21$	−4.57700	−	0.225973i	−0.998783	−	0.0493115i
$22$	−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	0.885276	−	0.465067i	$-0.153970\pi$
$31$	−0.511255	−	1.40466i	−0.0918241	−	0.252285i	−0.977100	+	0.212782i	$0.931748\pi$
$32$	−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
$35$	−6.48690	+	6.77293i	−1.09649	+	1.14483i
$36$	−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	$-0.688407\pi$
$41$	1.60199	−	9.08534i	0.250189	−	1.41889i	0.808127	−	0.589009i	$-0.200482\pi$
$42$	4.54671	−	0.572247i	0.701572	−	0.0882997i
$43$	−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	−0.712919	−	0.701246i	$-0.752627\pi$
$47$	−11.7218	−	4.26638i	−1.70980	−	0.622316i	−0.996880	+	0.0789301i	$0.974850\pi$
$48$	−1.13491	−	1.30843i	−0.163810	−	0.188855i
$49$	−6.93966	−	0.917132i	−0.991380	−	0.131019i
$50$	−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
$56$	1.16960	+	2.37319i	0.156294	+	0.317131i
$57$	−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	0.772292	−	0.635268i	$-0.219110\pi$
$59$	2.15673	+	1.80971i	0.280782	+	0.235604i	−0.491510	+	0.870872i	$0.663555\pi$
$60$	−2.00514	+	5.80287i	−0.258863	+	0.749147i
$61$	0.533089	−	1.46465i	0.0682550	−	0.187529i	−0.900875	−	0.434078i	$-0.857074\pi$
$61$	0.533089	−	1.46465i	0.0682550	−	0.187529i	0.969130	+	0.246549i	$0.0792965\pi$
$62$	0.747405	+	1.29454i	0.0949205	+	0.164407i
$63$	−0.261601	+	7.93294i	−0.0329587	+	0.999457i
$64$	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
$70$	5.21224	−	7.79648i	0.622982	−	0.931857i
$71$	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	−0.783858	−	0.620940i	$-0.786751\pi$
$73$	−5.45139	+	3.14736i	−0.638037	+	0.368371i	0.145821	+	0.989311i	$0.453418\pi$
$74$	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
$77$	4.74468	−	3.47713i	0.540707	−	0.396256i
$78$	−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	$0.0755710\pi$
$83$	1.26685	+	7.18468i	0.139055	+	0.788621i	−0.832894	+	0.553432i	$0.813318\pi$
$84$	−4.37826	+	1.35308i	−0.477707	+	0.147633i
$85$	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	$-0.799100\pi$
$89$	−8.62919	−	14.9462i	−0.914692	−	1.58429i	−0.107340	−	0.994222i	$-0.534233\pi$
$90$	−9.37839	−	5.01275i	−0.988569	−	0.528390i
$91$	−0.535484	+	2.18599i	−0.0561340	+	0.229154i
$92$	−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	0.545220	−	0.838293i	$-0.316446\pi$
$97$	−3.69346	−	4.40170i	−0.375014	−	0.446925i	−0.920234	+	0.391369i	$0.872002\pi$
$98$	6.99349	−	0.301861i	0.706449	−	0.0304925i
$99$	−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	0.673871	−	0.738849i	$-0.264631\pi$
$101$	7.18729	+	2.61596i	0.715162	+	0.260298i	0.0412915	+	0.999147i	$0.486853\pi$
$102$	−12.1841	−	4.21013i	−1.20640	−	0.416865i
$103$	1.62331	−	1.93458i	0.159949	−	0.190620i	−0.680117	−	0.733103i	$-0.738071\pi$
$103$	1.62331	−	1.93458i	0.159949	−	0.190620i	0.840067	+	0.542483i	$0.182516\pi$
$104$	0.799354	−	0.290941i	0.0783831	−	0.0285291i
$105$	11.9134	+	11.0421i	1.16263	+	1.07760i
$106$	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
$112$	−1.56393	−	2.13404i	−0.147777	−	0.201648i
$113$	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
$119$	16.3700	+	10.9440i	1.50063	+	1.00323i
$120$	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
$126$	−1.11991	−	7.85785i	−0.0997699	−	0.700033i
$127$	−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	−0.613940	−	0.789353i	$-0.710416\pi$
$131$	−6.60246	+	2.40310i	−0.576859	+	0.209960i	0.0370807	+	0.999312i	$0.488194\pi$
$132$	1.87062	−	3.36607i	0.162817	−	0.292978i
$133$	−4.43716	−	9.00331i	−0.384751	−	0.780686i
$134$			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	$-0.971427\pi$
$139$	−3.42654	−	9.41434i	−0.290635	−	0.798514i	0.705339	−	0.708871i	$-0.250795\pi$
$140$	−3.77921	+	8.58313i	−0.319402	+	0.725406i
$141$	−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
$147$	−1.39159	+	12.0442i	−0.114776	+	0.993391i
$148$	−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
$154$	−4.06880	+	4.24821i	−0.327873	+	0.342331i
$155$	−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	−0.949318	−	0.314316i	$-0.898225\pi$
$157$	−5.95086	+	7.09196i	−0.474930	+	0.566000i	0.474388	+	0.880316i	$0.342669\pi$
$158$	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	0.585340	−	0.810788i	$-0.300961\pi$
$167$	−1.44072	−	1.20891i	−0.111487	−	0.0935484i	−0.696827	+	0.717239i	$0.745405\pi$
$168$	4.07679	−	2.09280i	0.314531	−	0.161463i
$169$	−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	−0.181219	−	0.983443i	$-0.558004\pi$
$173$	9.94119	−	8.34165i	0.755814	−	0.634204i	0.937034	+	0.349239i	$0.113560\pi$
$174$	0.415420	+	1.08573i	0.0314929	+	0.0823091i
$175$	19.8957	−	2.17394i	1.50398	−	0.164334i
$176$	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	−0.919811	−	0.392361i	$-0.871658\pi$
$181$	−13.9907	+	8.07755i	−1.03992	+	0.600399i	−0.120111	+	0.992760i	$0.538325\pi$
$182$	0.147756	−	2.24577i	0.0109524	−	0.166467i
$183$	−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
$189$	13.7458	+	0.228172i	0.999862	+	0.0165971i
$190$	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
$196$	−6.83482	+	1.51168i	−0.488202	+	0.107977i
$197$	−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	0.281064	−	0.959689i	$-0.409313\pi$
$199$	−5.77698	−	3.33534i	−0.409520	−	0.236436i	−0.690583	+	0.723253i	$0.742646\pi$
$200$	−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
$203$	−0.192880	−	1.76523i	−0.0135375	−	0.123895i
$204$	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
$210$	−13.6498	−	8.80565i	−0.941928	−	0.607648i
$211$	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	$-0.745063\pi$
$223$	4.46007	−	12.2539i	0.298668	−	0.820584i	0.994723	−	0.102596i	$-0.0327147\pi$
$224$	1.91074	+	1.83005i	0.127667	+	0.122275i
$225$	−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	−0.572804	−	0.819692i	$-0.694144\pi$
$227$	2.03352	−	1.70632i	0.134969	−	0.113253i	0.707773	+	0.706440i	$0.249700\pi$
$228$	−5.10211	−	4.14079i	−0.337895	−	0.274231i
$229$	14.7504	+	2.60089i	0.974733	+	0.171872i	0.638260	−	0.769821i	$-0.279655\pi$
$229$	14.7504	+	2.60089i	0.974733	+	0.171872i	0.336474	+	0.941693i	$0.390766\pi$
$230$	2.50497	−	14.2064i	0.165173	−	0.936744i
$231$	−6.15626	−	8.11837i	−0.405052	−	0.534149i
$232$	−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
$238$	−18.0217	−	7.93508i	−1.16817	−	0.514355i
$239$	−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	0.0576758	−	0.998335i	$-0.481631\pi$
$241$	7.03748	−	1.24090i	0.453324	−	0.0799333i	0.395648	+	0.918402i	$0.370520\pi$
$242$			6.05679i			0.389345i
$243$	−1.27424	−	15.5363i	−0.0817428	−	0.996653i
$244$		−	1.55865i		−	0.0997822i
$245$	16.7541	+	18.3021i	1.07038	+	1.16928i
$246$	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	0.883435	−	0.468553i	$-0.155224\pi$
$251$	0.569382	+	0.986198i	0.0359390	+	0.0622483i	−0.847496	+	0.530801i	$0.821891\pi$
$252$	2.46740	+	7.54400i	0.155432	+	0.475227i
$253$	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	−0.973159	−	0.230132i	$-0.926084\pi$
$257$	0.320962	−	1.82027i	0.0200211	−	0.113545i	0.993181	+	0.116587i	$0.0371953\pi$
$258$	−13.0617	−	10.6007i	−0.813185	−	0.659968i
$259$	4.08616	+	2.73175i	0.253902	+	0.169743i
$260$	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
$266$	5.93316	+	8.09602i	0.363785	+	0.496399i
$267$	−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	$-0.422510\pi$
$269$	7.90680			0.482086			0.241043	+	0.970514i	$0.422510\pi$
$270$	−8.41532	+	16.3838i	−0.512140	+	0.997084i
$271$			23.5951i			1.43330i	0.697434	+	0.716649i	$0.254325\pi$
$271$			23.5951i			1.43330i	−0.697434	+	0.716649i	$0.745675\pi$
$272$	1.29240	+	7.32954i	0.0783630	+	0.444418i
$273$	3.80092	+	0.865395i	0.230042	+	0.0523761i
$274$	−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
$280$	2.23135	−	9.10898i	0.133349	−	0.544366i
$281$	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	0.318136	−	0.948045i	$-0.396943\pi$
$283$	4.92624	+	0.868629i	0.292835	+	0.0516347i	−0.0253009	+	0.999680i	$0.508054\pi$
$284$	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
$287$	−23.7074	−	5.80741i	−1.39941	−	0.342801i
$288$	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	−0.298711	−	0.954344i	$-0.596557\pi$
$293$	1.47042	−	0.535190i	0.0859030	−	0.0312661i	0.384614	+	0.923077i	$0.374334\pi$
$294$	−0.721012	−	12.1029i	−0.0420503	−	0.705855i
$295$	−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
$301$	15.1892	+	20.7263i	0.875492	+	1.19464i
$302$	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	$0.0289580\pi$
$307$	27.5520	+	15.9071i	1.57247	+	0.907868i	0.576610	+	0.817020i	$0.304375\pi$
$308$	3.26929	−	4.89021i	0.186285	−	0.278646i
$309$	−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	$0.158653\pi$
$311$	−1.94921	+	11.0545i	−0.110529	+	0.626843i	−0.988867	+	0.148802i	$0.952458\pi$
$312$	−0.526516	−	1.37609i	−0.0298081	−	0.0779057i
$313$	−12.7798	−	15.2303i	−0.722355	−	0.860869i	0.272502	−	0.962155i	$-0.412149\pi$
$313$	−12.7798	−	15.2303i	−0.722355	−	0.860869i	−0.994857	+	0.101286i	$0.967704\pi$
$314$	4.62895	−	8.01757i	0.261227	−	0.452458i
$315$	18.7853	−	20.9448i	1.05843	−	1.18011i
$316$	−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
$322$	9.65809	−	4.75986i	0.538224	−	0.265257i
$323$			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
$329$	−13.2995	+	30.2050i	−0.733224	+	1.66525i
$330$	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
$336$	−3.65144	+	2.76893i	−0.199202	+	0.151058i
$337$	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
$343$	−3.62666	+	18.1617i	−0.195821	+	0.980640i
$344$	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	0.639047	−	0.769167i	$-0.279329\pi$
$349$	28.0714	−	4.94974i	1.50263	−	0.264954i	0.863579	+	0.504214i	$0.168218\pi$
$350$	−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	$-0.945704\pi$
$353$	−2.20743	−	12.5189i	−0.117490	−	0.666316i	0.867998	−	0.496568i	$-0.165407\pi$
$354$	−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
$357$	18.4889	−	28.6601i	0.978537	−	1.51685i
$358$	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
$364$	0.244462	+	2.23730i	0.0128133	+	0.117267i
$365$	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	$-0.981911\pi$
$367$	−16.8766	−	20.1128i	−0.880952	−	1.04988i	0.117434	−	0.993081i	$-0.462533\pi$
$368$	−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
$371$	−35.5367	−	2.33806i	−1.84497	−	0.121386i
$372$	−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
$378$	−13.5766	+	2.16223i	−0.698306	+	0.111213i
$379$	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	0.996819	−	0.0797048i	$-0.0253978\pi$
$383$	21.3595	+	17.9228i	1.09142	+	0.915810i	0.0946018	+	0.995515i	$0.469842\pi$
$384$	1.63707	+	0.565680i	0.0835415	+	0.0288672i
$385$	−20.8061	−	1.36890i	−1.06038	−	0.0697654i
$386$	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
$392$	6.46849	−	2.67557i	0.326708	−	0.135137i
$393$	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	0.429865	−	0.902893i	$-0.358561\pi$
$397$	28.4273	−	16.4125i	1.42673	−	0.823721i	0.996861	+	0.0791725i	$0.0252278\pi$
$398$	6.26840	+	2.28151i	0.314206	+	0.114362i
$399$	−15.4663	+	7.93957i	−0.774284	+	0.397476i
$400$	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	$-0.965969\pi$
$409$	−6.09161	−	16.7366i	−0.301211	−	0.827570i	0.693079	−	0.720861i	$-0.256254\pi$
$410$	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
$413$	5.15232	−	5.37951i	0.253529	−	0.264708i
$414$	−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	$-0.883419\pi$
$419$	1.35458	−	7.68222i	0.0661757	−	0.375301i	0.999852	−	0.0171838i	$-0.00547003\pi$
$420$	14.9715	+	6.30160i	0.730537	+	0.307487i
$421$	−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
$427$	−3.77414	−	1.66178i	−0.182644	−	0.0804193i
$428$	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	$0.125896\pi$
$433$			16.0344i			0.770562i	−0.922799	+	0.385281i	$0.874104\pi$
$434$	3.54747	−	1.74832i	0.170284	−	0.0839223i
$435$	−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	−0.925235	−	0.379394i	$-0.876132\pi$
$439$	0.574218	−	1.57765i	0.0274059	−	0.0752971i	0.952641	+	0.304097i	$0.0983547\pi$
$440$	3.94048	+	6.82512i	0.187855	+	0.325375i
$441$	20.8979	+	2.06856i	0.995137	+	0.0985029i
$442$	−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
$448$	−2.19950	−	1.47045i	−0.103916	−	0.0694721i
$449$	−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
$455$	6.43474	−	4.71569i	0.301665	−	0.221075i
$456$	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	$0.116019\pi$
$461$	3.82751	+	21.7069i	0.178265	+	1.01099i	−0.756042	+	0.654523i	$0.772870\pi$
$462$	7.47247	+	6.92601i	0.347651	+	0.322227i
$463$	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	$0.0602289\pi$
$467$	14.1323	+	24.4779i	0.653965	+	1.13270i	−0.328187	+	0.944613i	$0.606438\pi$
$468$	2.49734	−	0.525158i	0.115440	−	0.0242754i
$469$	−21.6809	−	5.31099i	−1.00113	−	0.245239i
$470$	−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
$476$	19.1258	+	4.68509i	0.876630	+	0.214741i
$477$	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	0.981240	−	0.192792i	$-0.0617542\pi$
$479$	35.2144	+	12.8170i	1.60899	+	0.585624i	0.627749	+	0.778416i	$0.283976\pi$
$480$	−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
$483$	5.50658	+	17.8180i	0.250558	+	0.810749i
$484$	−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
$490$	−19.6777	−	15.1148i	−0.888947	−	0.682815i
$491$	−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
$497$	19.6763	−	29.4319i	0.882604	−	1.32020i
$498$	−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	$0.380936\pi$
$503$	−13.9825	+	24.2184i	−0.623449	+	1.07984i	−0.988839	+	0.148990i	$0.952398\pi$
$504$	−3.73992	−	7.00093i	−0.166589	−	0.311846i
$505$	−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	−0.570917	−	0.821008i	$-0.693412\pi$
$509$	−10.8413	+	3.94589i	−0.480530	+	0.174899i	0.0903863	+	0.995907i	$0.471190\pi$
$510$	23.4917	+	39.1931i	1.04023	+	1.73550i
$511$	7.36229	+	14.9386i	0.325689	+	0.660845i
$512$			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
$518$	−4.49845	−	1.98070i	−0.197650	−	0.0870269i
$519$	−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	$-0.884292\pi$
$521$	−17.6953	−	30.6492i	−0.775247	−	1.34277i	0.159409	−	0.987213i	$-0.449041\pi$
$522$	1.86851	−	0.750210i	0.0817826	−	0.0328358i
$523$	1.31727	+	0.760529i	0.0576004	+	0.0332556i	0.528524	−	0.848919i	$-0.322746\pi$
$523$	1.31727	+	0.760529i	0.0576004	+	0.0332556i	−0.470923	+	0.882174i	$0.656079\pi$
$524$	−5.38237	+	4.51635i	−0.235130	+	0.197298i
$525$	−4.32885	−	34.3942i	−0.188926	−	1.50109i
$526$	−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
$532$	−7.24888	−	6.94274i	−0.314279	−	0.301006i
$533$	−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
$546$	−3.89345	−	0.192225i	−0.166624	−	0.00822649i
$547$	−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
$553$	−1.55117	+	0.169490i	−0.0659623	+	0.00720746i
$554$	−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
$560$	−0.615695	+	9.35807i	−0.0260179	+	0.395450i
$561$	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	−0.954360	−	0.298658i	$-0.903461\pi$
$563$	−35.4365	+	12.8978i	−1.49347	+	0.543578i	−0.539108	+	0.842236i	$0.681239\pi$
$564$	0.353601	+	21.6028i	0.0148893	+	0.909643i
$565$	−39.5026	+	6.96538i	−1.66189	+	0.293036i
$566$	−5.00224			−0.210260
$567$	0.00550022	−	23.8118i	0.000230988	−	1.00000i
$568$	−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
$574$	24.3557	+	1.60243i	1.01659	+	0.0668843i
$575$	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	0.672580	−	0.740025i	$-0.265186\pi$
$577$	8.83941	+	5.10344i	0.367989	+	0.212459i	−0.304590	+	0.952483i	$0.598520\pi$
$578$	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
$581$	19.1879	−	2.09659i	0.796049	−	0.0869814i
$582$	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	0.991015	−	0.133751i	$-0.0427023\pi$
$587$	40.3204	+	14.6754i	1.66420	+	0.605720i	0.673188	+	0.739472i	$0.264925\pi$
$588$	2.81170	+	11.7938i	0.115953	+	0.486369i
$589$	−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	$-0.374930\pi$
$593$	18.6478			0.765772			0.382886	+	0.923796i	$0.374930\pi$
$594$	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	−0.793339	−	0.608780i	$-0.791659\pi$
$601$	5.04304	−	13.8556i	0.205710	−	0.565183i	0.999049	+	0.0435963i	$0.0138815\pi$
$602$	−18.5575	−	17.7738i	−0.756349	−	0.724407i
$603$	−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	0.576208	−	0.817303i	$-0.304532\pi$
$607$	20.6494	+	3.64104i	0.838133	+	0.147785i	0.261924	+	0.965088i	$0.415643\pi$
$608$	−0.658778	+	3.73612i	−0.0267170	+	0.151520i
$609$	−3.05159	+	0.384072i	−0.123657	+	0.0155634i
$610$	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
$616$	−2.37045	+	5.38363i	−0.0955081	+	0.216913i
$617$	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	0.147594	−	0.989048i	$-0.452847\pi$
$619$	15.5389	−	2.73993i	0.624562	−	0.110127i	0.476968	+	0.878921i	$0.341736\pi$
$620$			5.29860i			0.212797i
$621$	19.4924	−	8.19914i	0.782201	−	0.329020i
$622$		−	11.2250i		−	0.450083i
$623$	−40.9574	+	20.1853i	−1.64093	+	0.808708i
$624$	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
$630$	−14.8629	+	23.8887i	−0.592151	+	0.951747i
$631$	−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
$637$	5.67810	+	1.79340i	0.224974	+	0.0710571i
$638$	−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	$0.555996\pi$
$643$	−28.2540	+	33.6718i	−1.11423	+	1.32789i	−0.939218	+	0.343320i	$0.888448\pi$
$644$	−8.68482	+	6.36466i	−0.342230	+	0.250803i
$645$	−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	$-0.672540\pi$
$647$	−26.2447			−1.03178			−0.515892	+	0.856653i	$0.672540\pi$
$648$	−7.48314	+	5.00026i	−0.293965	+	0.196429i
$649$			6.25959i			0.245710i
$650$	1.11741	+	6.33714i	0.0438283	+	0.248563i
$651$	2.02260	+	6.54467i	0.0792719	+	0.256506i
$652$	−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
$658$	7.85238	−	32.0555i	0.306118	−	1.24965i
$659$	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	0.327447	−	0.944869i	$-0.393812\pi$
$661$	8.02105	+	1.41433i	0.311983	+	0.0550110i	−0.0154646	+	0.999880i	$0.504923\pi$
$662$	−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
$665$	−8.46520	+	34.5572i	−0.328266	+	1.34007i
$666$	−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
$672$	3.11515	−	3.36093i	0.120169	−	0.129651i
$673$	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	0.959879	−	0.280415i	$-0.0904721\pi$
$677$	−0.989246	−	5.61030i	−0.0380198	−	0.215621i	−0.997899	+	0.0647939i	$0.979361\pi$
$678$	17.1324	+	9.52098i	0.657965	+	0.365651i
$679$	−12.2622	+	8.98634i	−0.470580	+	0.344864i
$680$	−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
$686$	0.417817	−	18.5155i	0.0159523	−	0.706927i
$687$	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	0.999447	−	0.0332634i	$-0.0105900\pi$
$691$	20.8491	+	24.8470i	0.793136	+	0.945223i	−0.206310	+	0.978487i	$0.566146\pi$
$692$	6.48865	−	11.2387i	0.246661	−	0.427230i
$693$	−13.8850	+	10.8917i	−0.527449	+	0.413740i
$694$	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
$700$	17.9523	−	8.84757i	0.678535	−	0.334407i
$701$		−	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
$707$	8.15465	−	18.5204i	0.306687	−	0.696530i
$708$	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
$714$	−13.2313	+	31.4352i	−0.495167	+	1.17643i
$715$	−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	−0.984827	−	0.173537i	$-0.944481\pi$
$719$	−9.17385	+	15.8896i	−0.342127	+	0.592581i	0.642701	+	0.766117i	$0.277814\pi$
$720$	10.6283	−	0.348027i	0.396093	−	0.0129702i
$721$	−4.82542	−	4.62164i	−0.179708	−	0.172119i
$722$	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	0.665776	−	0.746152i	$-0.268101\pi$
$727$	41.7009	−	7.35299i	1.54660	−	0.272707i	0.880823	+	0.473445i	$0.156990\pi$
$728$	−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	$-0.994928\pi$
$733$	−6.61059	−	18.1624i	−0.244168	−	0.670845i	0.755705	−	0.654912i	$-0.227294\pi$
$734$	20.1128	+	16.8766i	0.742376	+	0.622927i
$735$	31.2210	−	29.5339i	1.15161	−	1.08937i
$736$	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
$742$	35.4028	−	3.86834i	1.29968	−	0.142011i
$743$	−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
$749$	21.5406	+	1.41722i	0.787076	+	0.0517841i
$750$	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
$756$	12.9949	−	4.48694i	0.472620	−	0.163188i
$757$	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	$-0.938889\pi$
$761$	−36.9654	−	31.0176i	−1.33999	−	1.12439i	−0.358367	−	0.933581i	$-0.616666\pi$
$762$	13.5654	−	11.7664i	0.491422	−	0.426251i
$763$	1.69420	−	25.7505i	0.0613343	−	0.932231i
$764$	−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	0.140504	−	0.990080i	$-0.455128\pi$
$769$	−1.83279	−	0.323170i	−0.0660921	−	0.0116538i	−0.206596	+	0.978426i	$0.566239\pi$
$770$	20.7277	−	2.26484i	0.746975	−	0.0816193i
$771$	−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	−0.758202	−	0.652020i	$-0.773922\pi$
$773$	5.15925	−	8.93608i	0.185565	−	0.321409i	0.943767	+	0.330612i	$0.107255\pi$
$774$	−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
$777$	4.61507	−	7.15393i	0.165565	−	0.256646i
$778$	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	0.830873	−	0.556462i	$-0.187842\pi$
$787$	−4.58113	−	12.5866i	−0.163300	−	0.448663i	−0.994173	+	0.107800i	$0.965619\pi$
$788$	−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
$791$	−21.6223	−	20.7091i	−0.768799	−	0.736331i
$792$	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	−0.999995	−	0.00306373i	$-0.999025\pi$
$797$	−1.67296	+	9.48782i	−0.0592592	+	0.336076i	0.940736	+	0.339140i	$0.110136\pi$
$798$	13.8527	−	10.5047i	0.490379	−	0.371861i
$799$	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
$805$	34.9304	+	15.3801i	1.23113	+	0.542077i
$806$	−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	$0.00695122\pi$
$811$			1.24370i			0.0436723i	−0.999762	+	0.0218362i	$0.993049\pi$
$812$	−0.784992	−	1.59280i	−0.0275478	−	0.0558964i
$813$	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
$819$	1.39096	−	6.60703i	0.0486042	−	0.230868i
$820$	−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
$826$	−4.13991	+	6.19248i	−0.144046	+	0.215464i
$827$	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	−0.115270	−	0.993334i	$-0.536773\pi$
$829$	19.7903	−	11.4260i	0.687347	−	0.396840i	0.802617	+	0.596494i	$0.203440\pi$
$830$	−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
$833$	31.7359	−	41.3166i	1.09959	−	1.43153i
$834$	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	$0.129183\pi$
$839$	5.51605	+	31.2831i	0.190435	+	1.08001i	−0.728335	+	0.685221i	$0.759706\pi$
$840$	−15.8384	−	3.60609i	−0.546475	−	0.124422i
$841$	−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
$847$	−15.5646	−	3.81273i	−0.534805	−	0.131007i
$848$	−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	0.313454	−	0.949603i	$-0.398514\pi$
$853$	−19.7478	−	23.5346i	−0.676153	−	0.805808i	−0.989607	+	0.143796i	$0.954069\pi$
$854$	4.00537	+	0.981163i	0.137061	+	0.0335747i
$855$	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	0.532417	−	0.846482i	$-0.321284\pi$
$857$	11.5975	+	4.22114i	0.396163	+	0.144191i	−0.136254	+	0.990674i	$0.543506\pi$
$858$	2.47462	−	2.14644i	0.0844820	−	0.0732781i
$859$	−24.4310	+	29.1157i	−0.833574	+	0.993415i	0.166399	+	0.986059i	$0.446786\pi$
$859$	−24.4310	+	29.1157i	−0.833574	+	0.993415i	−0.999973	+	0.00735665i	$0.997658\pi$
$860$	32.3504	−	11.7746i	1.10314	−	0.401510i
$861$	−9.38536	+	41.2216i	−0.319852	+	1.40483i
$862$	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
$868$	−3.18999	+	2.33778i	−0.108275	+	0.0793493i
$869$	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
$875$	−19.9952	−	13.3675i	−0.675959	−	0.451905i
$876$	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	−0.990895	−	0.134634i	$-0.957014\pi$
$881$	−11.2449	+	19.4768i	−0.378851	+	0.656189i	0.612045	+	0.790823i	$0.290347\pi$
$882$	−20.9396	+	1.59174i	−0.705073	+	0.0535967i
$883$	−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	−0.217068	−	0.976156i	$-0.569649\pi$
$887$	7.27019	−	2.64613i	0.244109	−	0.0888484i	0.461177	+	0.887308i	$0.347427\pi$
$888$	−3.21732	+	0.0526621i	−0.107966	+	0.00176722i
$889$	−24.6045	+	12.1260i	−0.825210	+	0.406694i
$890$		−	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
$896$	2.42142	+	1.06617i	0.0808940	+	0.0356182i
$897$	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
$903$	35.4636	−	26.8925i	1.18015	−	0.894926i
$904$	−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
$910$	−5.51811	+	5.76143i	−0.182924	+	0.190989i
$911$	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
$924$	−8.56164	−	5.52320i	−0.281657	−	0.181700i
$925$	−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	−0.646110	−	0.763245i	$-0.723605\pi$
$929$	−0.202876	+	0.170233i	−0.00665613	+	0.00558516i	0.639453	+	0.768830i	$0.279161\pi$
$930$	−9.06289	−	1.44552i	−0.297184	−	0.0474003i
$931$	−24.5398	+	10.1505i	−0.804261	+	0.332668i
$932$	−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	−0.371963	−	0.928248i	$-0.621315\pi$
$937$	7.52839	−	4.34652i	0.245942	−	0.141995i	0.617905	+	0.786253i	$0.287982\pi$
$938$	22.2738	+	1.46546i	0.727265	+	0.0478489i
$939$	−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	−0.555971	−	0.831201i	$-0.687654\pi$
$941$	−13.7300	+	4.99730i	−0.447584	+	0.162907i	0.108387	+	0.994109i	$0.465431\pi$
$942$	−14.0162	−	7.78922i	−0.456672	−	0.253787i
$943$	−36.9742	+	6.51956i	−1.20405	+	0.212306i
$944$	2.81541			0.0916337
$945$	−36.8051	−	31.9390i	−1.19727	−	1.03898i
$946$	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
$952$	−19.6488	−	1.29275i	−0.636821	−	0.0418984i
$953$	−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
$959$	−5.16019	−	47.2258i	−0.166631	−	1.52500i
$960$	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
$966$	−8.51699	−	16.5911i	−0.274030	−	0.533811i
$967$	−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	$-0.386998\pi$
$971$	21.6628			0.695193			0.347597	+	0.937644i	$0.386998\pi$
$972$	−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
$980$	22.0034	+	11.4681i	0.702872	+	0.366336i
$981$	−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	−0.965711	−	0.259619i	$-0.916403\pi$
$983$	−27.5193	+	23.0915i	−0.877731	+	0.736504i	0.0879804	+	0.996122i	$0.471959\pi$
$984$	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
$987$	52.6866	+	22.1761i	1.67703	+	0.705872i
$988$	−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
$994$	−14.2666	+	32.4015i	−0.452509	+	1.02771i
$995$	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	−0.490497	−	0.871443i	$-0.663185\pi$
$997$	−20.6301	+	3.63765i	−0.653363	+	0.115206i	−0.162866	+	0.986648i	$0.552074\pi$
$998$		−	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.41.6	✓	144
7.6	odd	2	inner	378.2.z.a.41.7	yes	144
27.2	odd	18	inner	378.2.z.a.83.7	yes	144
189.83	even	18	inner	378.2.z.a.83.6	yes	144

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

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.0283469 - 1.73182i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.71537 - 2.27847i) q^{5} +(0.328643 + 1.70059i) q^{6} +(0.173696 - 2.64004i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.99839 + 0.0981834i) q^{9} +O(q^{10})\)	\(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} +(0.173696 - 2.64004i) 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} +(0.287381 + 2.63010i) 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} +(-4.57700 - 0.225973i) 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} +(-6.48690 + 6.77293i) 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} +(4.54671 - 0.572247i) 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} +(-6.93966 - 0.917132i) 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} +(1.16960 + 2.37319i) 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} +(-0.261601 + 7.93294i) 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} +(5.21224 - 7.79648i) 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} +(4.74468 - 3.47713i) 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} +(-4.37826 + 1.35308i) 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} +(-0.535484 + 2.18599i) 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} +(6.99349 - 0.301861i) 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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