LMFDB - Embedded newform 378.2.z.a.41.8

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			41.8
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(0.754516 - 1.55907i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-0.486827 - 0.408497i) q^{5} +(-0.472323 + 1.66641i) q^{6} +(-2.18779 + 1.48781i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.86141 - 2.35269i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(0.754516 - 1.55907i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-0.486827 - 0.408497i) q^{5} +(-0.472323 + 1.66641i) q^{6} +(-2.18779 + 1.48781i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.86141 - 2.35269i) q^{9} +(0.550366 + 0.317754i) q^{10} +(-3.72295 - 4.43684i) q^{11} +(0.175779 - 1.72311i) q^{12} +(0.505415 + 0.0891184i) q^{13} +(1.89620 - 1.84511i) q^{14} +(-1.00419 + 0.450782i) q^{15} +(0.766044 - 0.642788i) q^{16} +(1.66709 - 2.88748i) q^{17} +(2.24167 + 1.99372i) q^{18} +(-3.56339 + 2.05732i) q^{19} +(-0.597182 - 0.217357i) q^{20} +(0.668877 + 4.53350i) q^{21} +(4.43684 + 3.72295i) q^{22} +(-0.488119 - 1.34109i) q^{23} +(0.126106 + 1.72745i) q^{24} +(-0.798110 - 4.52630i) q^{25} -0.513212 q^{26} +(-5.07248 + 1.12694i) q^{27} +(-1.54699 + 2.14635i) q^{28} +(-3.07257 + 0.541776i) q^{29} +(0.910661 - 0.618310i) q^{30} +(2.46439 + 6.77086i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-9.72638 + 2.45669i) q^{33} +(-1.14036 + 3.13310i) q^{34} +(1.67284 + 0.169400i) q^{35} +(-2.55382 - 1.57416i) q^{36} +(-0.189555 + 0.328318i) q^{37} +(3.15200 - 2.64485i) q^{38} +(0.520286 - 0.720738i) q^{39} +(0.625853 + 0.110355i) q^{40} +(0.877198 - 4.97484i) q^{41} +(-1.44595 - 4.34847i) q^{42} +(7.02881 - 5.89787i) q^{43} +(-5.01592 - 2.89594i) q^{44} +(-0.0548789 + 1.90573i) q^{45} +(0.713582 + 1.23596i) q^{46} +(-5.23895 - 1.90682i) q^{47} +(-0.424160 - 1.67931i) q^{48} +(2.57286 - 6.51002i) q^{49} +(1.57197 + 4.31895i) q^{50} +(-3.24395 - 4.77776i) q^{51} +(0.505415 - 0.0891184i) q^{52} -3.85391i q^{53} +(4.79972 - 1.99064i) q^{54} +3.68079i q^{55} +(1.15078 - 2.38237i) q^{56} +(0.518884 + 7.10787i) q^{57} +(2.93181 - 1.06709i) q^{58} +(2.85807 + 2.39820i) q^{59} +(-0.789458 + 0.767051i) q^{60} +(-0.871745 + 2.39510i) q^{61} +(-3.60270 - 6.24006i) q^{62} +(7.57273 + 2.37777i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.209646 - 0.249846i) q^{65} +(9.15202 - 4.10833i) q^{66} +(-1.36783 + 7.75736i) q^{67} +(0.578974 - 3.28353i) q^{68} +(-2.45916 - 0.250865i) q^{69} +(-1.67684 + 0.123659i) q^{70} +(-2.67680 - 1.54545i) q^{71} +(2.78837 + 1.10678i) q^{72} +(11.5451 - 6.66557i) q^{73} +(0.129663 - 0.356246i) q^{74} +(-7.65902 - 2.17086i) q^{75} +(-2.64485 + 3.15200i) q^{76} +(14.7462 + 4.16785i) q^{77} +(-0.387227 + 0.800135i) q^{78} +(-0.238325 - 1.35161i) q^{79} -0.635508 q^{80} +(-2.07029 + 8.75865i) q^{81} +5.05158i q^{82} +(1.33547 + 7.57382i) q^{83} +(2.17909 + 4.03133i) q^{84} +(-1.99111 + 0.724706i) q^{85} +(-5.89787 + 7.02881i) q^{86} +(-1.47363 + 5.19913i) q^{87} +(5.44259 + 1.98094i) q^{88} +(2.08703 + 3.61484i) q^{89} +(-0.276882 - 1.88631i) q^{90} +(-1.23833 + 0.556988i) q^{91} +(-0.917363 - 1.09327i) q^{92} +(12.4157 + 1.26655i) q^{93} +(5.49047 + 0.968119i) q^{94} +(2.57517 + 0.454071i) q^{95} +(0.709325 + 1.58014i) q^{96} +(-11.4055 - 13.5925i) q^{97} +(-1.40332 + 6.85789i) q^{98} +(-3.50856 + 17.0177i) 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
$3$	0.754516	−	1.55907i	0.435620	−	0.900131i
$3$	0.754516	−	1.55907i	0.435620	−	0.900131i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	−0.486827	−	0.408497i	−0.217716	−	0.182685i	0.527407	−	0.849613i	$-0.323164\pi$
$5$	−0.486827	−	0.408497i	−0.217716	−	0.182685i	−0.745122	+	0.666928i	$0.767609\pi$
$6$	−0.472323	+	1.66641i	−0.192825	+	0.680308i
$7$	−2.18779	+	1.48781i	−0.826907	+	0.562338i
$7$	−2.18779	+	1.48781i	−0.826907	+	0.562338i
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−1.86141	−	2.35269i	−0.620471	−	0.784230i
$10$	0.550366	+	0.317754i	0.174041	+	0.100483i
$11$	−3.72295	−	4.43684i	−1.12251	−	1.33776i	−0.934653	−	0.355562i	$-0.884289\pi$
$11$	−3.72295	−	4.43684i	−1.12251	−	1.33776i	−0.187859	−	0.982196i	$-0.560155\pi$
$12$	0.175779	−	1.72311i	0.0507429	−	0.497418i
$13$	0.505415	+	0.0891184i	0.140177	+	0.0247170i	0.243296	−	0.969952i	$-0.421771\pi$
$13$	0.505415	+	0.0891184i	0.140177	+	0.0247170i	−0.103119	+	0.994669i	$0.532882\pi$
$14$	1.89620	−	1.84511i	0.506780	−	0.493126i
$15$	−1.00419	+	0.450782i	−0.259282	+	0.116391i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	1.66709	−	2.88748i	0.404329	−	0.700318i	−0.589914	−	0.807466i	$-0.700839\pi$
$17$	1.66709	−	2.88748i	0.404329	−	0.700318i	0.994243	+	0.107148i	$0.0341719\pi$
$18$	2.24167	+	1.99372i	0.528368	+	0.469923i
$19$	−3.56339	+	2.05732i	−0.817498	+	0.471983i	−0.849553	−	0.527503i	$-0.823128\pi$
$19$	−3.56339	+	2.05732i	−0.817498	+	0.471983i	0.0320550	+	0.999486i	$0.489795\pi$
$20$	−0.597182	−	0.217357i	−0.133534	−	0.0486024i
$21$	0.668877	+	4.53350i	0.145961	+	0.989290i
$22$	4.43684	+	3.72295i	0.945938	+	0.793736i
$23$	−0.488119	−	1.34109i	−0.101780	−	0.279638i	0.878343	−	0.478032i	$-0.158650\pi$
$23$	−0.488119	−	1.34109i	−0.101780	−	0.279638i	−0.980122	+	0.198394i	$0.936427\pi$
$24$	0.126106	+	1.72745i	0.0257414	+	0.352615i
$25$	−0.798110	−	4.52630i	−0.159622	−	0.905261i
$26$	−0.513212			−0.100649
$27$	−5.07248	+	1.12694i	−0.976198	+	0.216879i
$28$	−1.54699	+	2.14635i	−0.292354	+	0.405622i
$29$	−3.07257	+	0.541776i	−0.570561	+	0.100605i	−0.451483	−	0.892280i	$-0.649105\pi$
$29$	−3.07257	+	0.541776i	−0.570561	+	0.100605i	−0.119078	+	0.992885i	$0.537994\pi$
$30$	0.910661	−	0.618310i	0.166263	−	0.112887i
$31$	2.46439	+	6.77086i	0.442618	+	1.21608i	0.937764	+	0.347273i	$0.112892\pi$
$31$	2.46439	+	6.77086i	0.442618	+	1.21608i	−0.495147	+	0.868809i	$0.664886\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	−9.72638	+	2.45669i	−1.69315	+	0.427654i
$34$	−1.14036	+	3.13310i	−0.195570	+	0.537323i
$35$	1.67284	+	0.169400i	0.282762	+	0.0286338i
$36$	−2.55382	−	1.57416i	−0.425637	−	0.262361i
$37$	−0.189555	+	0.328318i	−0.0311626	+	0.0539752i	−0.881186	−	0.472770i	$-0.843254\pi$
$37$	−0.189555	+	0.328318i	−0.0311626	+	0.0539752i	0.850023	+	0.526745i	$0.176588\pi$
$38$	3.15200	−	2.64485i	0.511323	−	0.429051i
$39$	0.520286	−	0.720738i	0.0833124	−	0.115410i
$40$	0.625853	+	0.110355i	0.0989561	+	0.0174486i
$41$	0.877198	−	4.97484i	0.136995	−	0.776939i	−0.836454	−	0.548037i	$-0.815375\pi$
$41$	0.877198	−	4.97484i	0.136995	−	0.776939i	0.973449	−	0.228902i	$-0.0735135\pi$
$42$	−1.44595	−	4.34847i	−0.223115	−	0.670984i
$43$	7.02881	−	5.89787i	1.07188	−	0.899417i	0.0766617	−	0.997057i	$-0.475574\pi$
$43$	7.02881	−	5.89787i	1.07188	−	0.899417i	0.995222	+	0.0976401i	$0.0311294\pi$
$44$	−5.01592	−	2.89594i	−0.756178	−	0.436580i
$45$	−0.0548789	+	1.90573i	−0.00818086	+	0.284090i
$46$	0.713582	+	1.23596i	0.105212	+	0.182232i
$47$	−5.23895	−	1.90682i	−0.764179	−	0.278139i	−0.0696196	−	0.997574i	$-0.522179\pi$
$47$	−5.23895	−	1.90682i	−0.764179	−	0.278139i	−0.694560	+	0.719435i	$0.744401\pi$
$48$	−0.424160	−	1.67931i	−0.0612222	−	0.242388i
$49$	2.57286	−	6.51002i	0.367551	−	0.930003i
$50$	1.57197	+	4.31895i	0.222310	+	0.610792i
$51$	−3.24395	−	4.77776i	−0.454244	−	0.669021i
$52$	0.505415	−	0.0891184i	0.0700885	−	0.0123585i
$53$		−	3.85391i		−	0.529376i	−0.964334	−	0.264688i	$-0.914731\pi$
$53$		−	3.85391i		−	0.529376i	0.964334	−	0.264688i	$-0.0852689\pi$
$54$	4.79972	−	1.99064i	0.653160	−	0.270892i
$55$			3.68079i			0.496318i
$56$	1.15078	−	2.38237i	0.153779	−	0.318358i
$57$	0.518884	+	7.10787i	0.0687278	+	0.941460i
$58$	2.93181	−	1.06709i	0.384965	−	0.140116i
$59$	2.85807	+	2.39820i	0.372089	+	0.312220i	0.809587	−	0.587000i	$-0.199691\pi$
$59$	2.85807	+	2.39820i	0.372089	+	0.312220i	−0.437498	+	0.899219i	$0.644135\pi$
$60$	−0.789458	+	0.767051i	−0.101919	+	0.0990259i
$61$	−0.871745	+	2.39510i	−0.111616	+	0.306661i	−0.982906	−	0.184106i	$-0.941061\pi$
$61$	−0.871745	+	2.39510i	−0.111616	+	0.306661i	0.871291	+	0.490767i	$0.163283\pi$
$62$	−3.60270	−	6.24006i	−0.457543	−	0.792488i
$63$	7.57273	+	2.37777i	0.954074	+	0.299571i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−0.209646	−	0.249846i	−0.0260033	−	0.0309896i
$66$	9.15202	−	4.10833i	1.12654	−	0.505701i
$67$	−1.36783	+	7.75736i	−0.167107	+	0.947712i	0.779758	+	0.626081i	$0.215342\pi$
$67$	−1.36783	+	7.75736i	−0.167107	+	0.947712i	−0.946865	+	0.321631i	$0.895769\pi$
$68$	0.578974	−	3.28353i	0.0702109	−	0.398186i
$69$	−2.45916	−	0.250865i	−0.296048	−	0.0302006i
$70$	−1.67684	+	0.123659i	−0.200421	+	0.0147801i
$71$	−2.67680	−	1.54545i	−0.317678	−	0.183412i	0.332679	−	0.943040i	$-0.392047\pi$
$71$	−2.67680	−	1.54545i	−0.317678	−	0.183412i	−0.650357	+	0.759629i	$0.725381\pi$
$72$	2.78837	+	1.10678i	0.328613	+	0.130435i
$73$	11.5451	−	6.66557i	1.35125	−	0.780146i	0.362827	−	0.931856i	$-0.381811\pi$
$73$	11.5451	−	6.66557i	1.35125	−	0.780146i	0.988425	+	0.151710i	$0.0484781\pi$
$74$	0.129663	−	0.356246i	0.0150730	−	0.0414128i
$75$	−7.65902	−	2.17086i	−0.884388	−	0.250669i
$76$	−2.64485	+	3.15200i	−0.303385	+	0.361560i
$77$	14.7462	+	4.16785i	1.68049	+	0.474970i
$78$	−0.387227	+	0.800135i	−0.0438448	+	0.0905975i
$79$	−0.238325	−	1.35161i	−0.0268136	−	0.152068i	0.968461	−	0.249164i	$-0.0801557\pi$
$79$	−0.238325	−	1.35161i	−0.0268136	−	0.152068i	−0.995275	+	0.0970961i	$0.969045\pi$
$80$	−0.635508			−0.0710520
$81$	−2.07029	+	8.75865i	−0.230032	+	0.973183i
$82$			5.05158i			0.557854i
$83$	1.33547	+	7.57382i	0.146587	+	0.831334i	0.966079	+	0.258245i	$0.0831442\pi$
$83$	1.33547	+	7.57382i	0.146587	+	0.831334i	−0.819493	+	0.573090i	$0.805745\pi$
$84$	2.17909	+	4.03133i	0.237758	+	0.439854i
$85$	−1.99111	+	0.724706i	−0.215966	+	0.0786054i
$86$	−5.89787	+	7.02881i	−0.635984	+	0.757936i
$87$	−1.47363	+	5.19913i	−0.157990	+	0.557405i
$88$	5.44259	+	1.98094i	0.580182	+	0.211169i
$89$	2.08703	+	3.61484i	0.221225	+	0.383172i	0.955180	−	0.296025i	$-0.0956613\pi$
$89$	2.08703	+	3.61484i	0.221225	+	0.383172i	−0.733955	+	0.679198i	$0.762328\pi$
$90$	−0.276882	−	1.88631i	−0.0291859	−	0.198835i
$91$	−1.23833	+	0.556988i	−0.129813	+	0.0583882i
$92$	−0.917363	−	1.09327i	−0.0956417	−	0.113981i
$93$	12.4157	+	1.26655i	1.28745	+	0.131336i
$94$	5.49047	+	0.968119i	0.566299	+	0.0998538i
$95$	2.57517	+	0.454071i	0.264207	+	0.0465867i
$96$	0.709325	+	1.58014i	0.0723952	+	0.161273i
$97$	−11.4055	−	13.5925i	−1.15805	−	1.38011i	−0.911662	−	0.410941i	$-0.865200\pi$
$97$	−11.4055	−	13.5925i	−1.15805	−	1.38011i	−0.246389	−	0.969171i	$-0.579244\pi$
$98$	−1.40332	+	6.85789i	−0.141757	+	0.692752i
$99$	−3.50856	+	17.0177i	−0.352623	+	1.71035i
$100$	−2.29806	−	3.98036i	−0.229806	−	0.398036i
$101$	17.2906	+	6.29325i	1.72048	+	0.626202i	0.997881	−	0.0650697i	$-0.0207270\pi$
$101$	17.2906	+	6.29325i	1.72048	+	0.626202i	0.722595	+	0.691272i	$0.242949\pi$
$102$	4.02432	+	4.14187i	0.398467	+	0.410107i
$103$	9.45121	−	11.2635i	0.931255	−	1.10983i	−0.0624778	−	0.998046i	$-0.519900\pi$
$103$	9.45121	−	11.2635i	0.931255	−	1.10983i	0.993733	−	0.111780i	$-0.0356553\pi$
$104$	−0.482262	+	0.175529i	−0.0472897	+	0.0172120i
$105$	1.52629	−	2.48027i	0.148951	−	0.242049i
$106$	0.669225	+	3.79536i	0.0650009	+	0.368638i
$107$			1.98291i			0.191695i	0.995396	+	0.0958475i	$0.0305561\pi$
$107$			1.98291i			0.191695i	−0.995396	+	0.0958475i	$0.969444\pi$
$108$	−4.38113	+	2.79386i	−0.421575	+	0.268840i
$109$	9.10407			0.872012			0.436006	−	0.899944i	$-0.356393\pi$
$109$	9.10407			0.872012			0.436006	+	0.899944i	$0.356393\pi$
$110$	−0.639162	−	3.62487i	−0.0609417	−	0.345618i
$111$	0.368850	+	0.543251i	0.0350097	+	0.0515631i
$112$	−0.719601	+	2.54601i	−0.0679959	+	0.240575i
$113$	12.8426	−	15.3052i	1.20813	−	1.43979i	0.342204	−	0.939626i	$-0.388827\pi$
$113$	12.8426	−	15.3052i	1.20813	−	1.43979i	0.865928	−	0.500169i	$-0.166729\pi$
$114$	−1.74527	−	6.90978i	−0.163459	−	0.647160i
$115$	−0.310203	+	0.852277i	−0.0289266	+	0.0794752i
$116$	−2.70197	+	1.55998i	−0.250872	+	0.144841i
$117$	−0.731119	−	1.35497i	−0.0675920	−	0.125267i
$118$	−3.23109	−	1.86547i	−0.297446	−	0.171731i
$119$	0.648776	+	8.79752i	0.0594732	+	0.806467i
$120$	0.644267	−	0.892486i	0.0588133	−	0.0814725i
$121$	−3.91506	+	22.2034i	−0.355914	+	2.01849i
$122$	0.442597	−	2.51009i	0.0400708	−	0.227253i
$123$	−7.09427	−	5.12121i	−0.639669	−	0.461764i
$124$	4.63154	+	5.51965i	0.415925	+	0.495680i
$125$	−3.04921	+	5.28138i	−0.272730	+	0.472381i
$126$	−7.87058	−	1.02665i	−0.701167	−	0.0914616i
$127$	−7.02060	−	12.1600i	−0.622978	−	1.07903i	−0.988928	−	0.148395i	$-0.952589\pi$
$127$	−7.02060	−	12.1600i	−0.622978	−	1.07903i	0.365951	−	0.930634i	$-0.380744\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	−3.89186	−	15.4085i	−0.342659	−	1.35664i
$130$	0.249846	+	0.209646i	0.0219129	+	0.0183871i
$131$	2.64877	−	0.964074i	0.231424	−	0.0842315i	−0.223705	−	0.974657i	$-0.571815\pi$
$131$	2.64877	−	0.964074i	0.231424	−	0.0842315i	0.455129	+	0.890425i	$0.349593\pi$
$132$	−8.29957	+	5.63515i	−0.722385	+	0.490477i
$133$	4.73505	−	9.80263i	0.410581	−	0.849996i
$134$		−	7.87703i		−	0.680472i
$135$	2.92977	+	1.52347i	0.252154	+	0.131119i
$136$			3.33418i			0.285904i
$137$	−16.1337	+	2.84480i	−1.37839	+	0.243048i	−0.813235	−	0.581935i	$-0.802296\pi$
$137$	−16.1337	+	2.84480i	−1.37839	+	0.243048i	−0.565157	+	0.824983i	$0.691185\pi$
$138$	2.46536	−	0.179975i	0.209865	−	0.0153205i
$139$	4.76880	+	13.1022i	0.404484	+	1.11131i	0.960047	+	0.279837i	$0.0902805\pi$
$139$	4.76880	+	13.1022i	0.404484	+	1.11131i	−0.555563	+	0.831474i	$0.687497\pi$
$140$	1.62989	−	0.412961i	0.137751	−	0.0349016i
$141$	−6.92574	+	6.72917i	−0.583253	+	0.566699i
$142$	2.90450	+	1.05715i	0.243740	+	0.0887143i
$143$	−1.48623	−	2.57423i	−0.124285	−	0.215268i
$144$	−2.93820	−	0.605771i	−0.244850	−	0.0504809i
$145$	1.71712	+	0.991381i	0.142599	+	0.0823297i
$146$	−10.2122	+	8.56909i	−0.845171	+	0.709183i
$147$	−8.20833	−	8.92319i	−0.677012	−	0.735972i
$148$	−0.0658317	+	0.373350i	−0.00541133	+	0.0306892i
$149$	21.7811	+	3.84060i	1.78438	+	0.314634i	0.965708	−	0.259629i	$-0.0836004\pi$
$149$	21.7811	+	3.84060i	1.78438	+	0.314634i	0.818671	+	0.574263i	$0.194711\pi$
$150$	7.91963	+	0.807901i	0.646635	+	0.0659649i
$151$	8.15215	−	6.84046i	0.663412	−	0.556669i	−0.247695	−	0.968838i	$-0.579673\pi$
$151$	8.15215	−	6.84046i	0.663412	−	0.556669i	0.911107	+	0.412169i	$0.135229\pi$
$152$	2.05732	−	3.56339i	0.166871	−	0.289029i
$153$	−9.89649	+	1.45266i	−0.800084	+	0.117440i
$154$	−15.2459	−	1.54388i	−1.22855	−	0.124409i
$155$	1.56614	−	4.30294i	0.125795	−	0.345620i
$156$	0.242402	−	0.855220i	0.0194077	−	0.0684724i
$157$	6.16172	−	7.34326i	0.491759	−	0.586056i	−0.461905	−	0.886929i	$-0.652834\pi$
$157$	6.16172	−	7.34326i	0.491759	−	0.586056i	0.953664	+	0.300874i	$0.0972783\pi$
$158$	0.469408	+	1.28969i	0.0373441	+	0.102602i
$159$	−6.00853	−	2.90784i	−0.476507	−	0.230607i
$160$	0.625853	−	0.110355i	0.0494780	−	0.00872431i
$161$	3.06319	+	2.20781i	0.241413	+	0.174000i
$162$	0.517911	−	8.98509i	0.0406910	−	0.705935i
$163$	−11.0908			−0.868699			−0.434350	−	0.900744i	$-0.643022\pi$
$163$	−11.0908			−0.868699			−0.434350	+	0.900744i	$0.643022\pi$
$164$	−0.877198	−	4.97484i	−0.0684976	−	0.388469i
$165$	5.73862	+	2.77721i	0.446751	+	0.216206i
$166$	−2.63036	−	7.22685i	−0.204155	−	0.560913i
$167$	−16.7437	−	14.0496i	−1.29567	−	1.08719i	−0.990876	−	0.134775i	$-0.956969\pi$
$167$	−16.7437	−	14.0496i	−1.29567	−	1.08719i	−0.304791	−	0.952419i	$-0.598587\pi$
$168$	−2.84601	−	3.59169i	−0.219575	−	0.277105i
$169$	−11.9685	−	4.35618i	−0.920654	−	0.335091i
$170$	1.83502	−	1.05945i	0.140740	−	0.0812560i
$171$	11.4732	+	4.55402i	0.877376	+	0.348255i
$172$	4.58773	−	7.94618i	0.349811	−	0.605891i
$173$	−15.6285	+	13.1139i	−1.18821	+	0.997030i	−0.188325	+	0.982107i	$0.560306\pi$
$173$	−15.6285	+	13.1139i	−1.18821	+	0.997030i	−0.999889	+	0.0149227i	$0.995250\pi$
$174$	0.548423	−	5.37604i	0.0415758	−	0.407556i
$175$	8.48036	+	8.71517i	0.641055	+	0.658805i
$176$	−5.70389	−	1.00575i	−0.429947	−	0.0758113i
$177$	5.89543	−	2.64645i	0.443128	−	0.198920i
$178$	−2.68303	−	3.19751i	−0.201102	−	0.239664i
$179$	−13.4545	−	7.76794i	−1.00563	−	0.580603i	−0.0957240	−	0.995408i	$-0.530517\pi$
$179$	−13.4545	−	7.76794i	−1.00563	−	0.580603i	−0.909911	+	0.414805i	$0.863850\pi$
$180$	0.600230	+	1.80957i	0.0447385	+	0.134878i
$181$	−5.90948	+	3.41184i	−0.439248	+	0.253600i	−0.703279	−	0.710914i	$-0.748281\pi$
$181$	−5.90948	+	3.41184i	−0.439248	+	0.253600i	0.264030	+	0.964514i	$0.414948\pi$
$182$	1.12280	−	0.763561i	0.0832276	−	0.0565989i
$183$	3.07639	+	3.16625i	0.227413	+	0.234056i
$184$	1.09327	+	0.917363i	0.0805970	+	0.0676289i
$185$	0.226397	−	0.0824019i	0.0166451	−	0.00605831i
$186$	−12.4470	+	0.908647i	−0.912658	+	0.0666252i
$187$	−19.0178	+	3.35335i	−1.39072	+	0.245221i
$188$	−5.57517			−0.406611
$189$	9.42085	−	10.0124i	0.685266	−	0.728293i
$190$	−2.61489			−0.189704
$191$	−15.6102	+	2.75250i	−1.12951	+	0.199164i	−0.707015	−	0.707199i	$-0.749959\pi$
$191$	−15.6102	+	2.75250i	−1.12951	+	0.199164i	−0.422500	+	0.906363i	$0.638847\pi$
$192$	−0.972938	−	1.43297i	−0.0702158	−	0.103415i
$193$	10.2343	−	3.72497i	0.736679	−	0.268129i	0.0536896	−	0.998558i	$-0.482902\pi$
$193$	10.2343	−	3.72497i	0.736679	−	0.268129i	0.682989	+	0.730429i	$0.260680\pi$
$194$	13.5925	+	11.4055i	0.975886	+	0.818866i
$195$	−0.547708	+	0.138340i	−0.0392222	+	0.00990673i
$196$	0.191138	−	6.99739i	0.0136527	−	0.499814i
$197$	19.7320	−	11.3923i	1.40585	−	0.811667i	0.410864	−	0.911697i	$-0.365227\pi$
$197$	19.7320	−	11.3923i	1.40585	−	0.811667i	0.994984	+	0.100030i	$0.0318938\pi$
$198$	0.500154	−	17.3685i	0.0355444	−	1.23432i
$199$	−9.06480	−	5.23356i	−0.642586	−	0.370997i	0.143024	−	0.989719i	$-0.454317\pi$
$199$	−9.06480	−	5.23356i	−0.642586	−	0.370997i	−0.785610	+	0.618722i	$0.787651\pi$
$200$	2.95434	+	3.52084i	0.208903	+	0.248961i
$201$	11.0622	+	7.98560i	0.780270	+	0.563261i
$202$	−18.1207	−	3.19517i	−1.27497	−	0.224811i
$203$	5.91607	−	5.75668i	0.415227	−	0.404040i
$204$	−4.68241	−	3.38013i	−0.327834	−	0.236657i
$205$	−2.45925	+	2.06355i	−0.171761	+	0.144125i
$206$	−7.35173	+	12.7336i	−0.512220	+	0.887190i
$207$	−2.24659	+	3.64472i	−0.156149	+	0.253326i
$208$	0.444455	−	0.256606i	0.0308174	−	0.0177924i
$209$	22.3944	+	8.15088i	1.54905	+	0.563808i
$210$	−1.07241	+	2.70762i	−0.0740033	+	0.186844i
$211$	−7.28487	−	6.11273i	−0.501511	−	0.420818i	0.356619	−	0.934250i	$-0.383929\pi$
$211$	−7.28487	−	6.11273i	−0.501511	−	0.420818i	−0.858130	+	0.513432i	$0.828374\pi$
$212$	−1.31812	−	3.62149i	−0.0905286	−	0.248725i
$213$	−4.42916	+	3.00726i	−0.303481	+	0.206054i
$214$	−0.344329	−	1.95278i	−0.0235378	−	0.133490i
$215$	−5.83108			−0.397676
$216$	3.82942	−	3.51219i	0.260559	−	0.238975i
$217$	−15.4653	−	11.1467i	−1.04985	−	0.756686i
$218$	−8.96576	+	1.58091i	−0.607238	+	0.107072i
$219$	−1.68114	−	23.0289i	−0.113601	−	1.55615i
$220$	1.25890	+	3.45881i	0.0848753	+	0.233193i
$221$	1.09990	−	1.31081i	0.0739873	−	0.0881747i
$222$	−0.457581	−	0.470948i	−0.0307108	−	0.0316079i
$223$	8.69071	−	23.8775i	0.581973	−	1.59896i	−0.202830	−	0.979214i	$-0.565014\pi$
$223$	8.69071	−	23.8775i	0.581973	−	1.59896i	0.784804	−	0.619745i	$-0.212764\pi$
$224$	0.266558	−	2.63229i	0.0178102	−	0.175877i
$225$	−9.16337	+	10.3030i	−0.610892	+	0.686868i
$226$	−9.98978	+	17.3028i	−0.664510	+	1.15097i
$227$	−8.24824	+	6.92110i	−0.547455	+	0.459369i	−0.874078	−	0.485785i	$-0.838534\pi$
$227$	−8.24824	+	6.92110i	−0.547455	+	0.459369i	0.326623	+	0.945155i	$0.394089\pi$
$228$	2.91862	+	6.50174i	0.193291	+	0.430588i
$229$	−11.3312	−	1.99800i	−0.748788	−	0.132032i	−0.213784	−	0.976881i	$-0.568579\pi$
$229$	−11.3312	−	1.99800i	−0.748788	−	0.132032i	−0.535004	+	0.844849i	$0.679690\pi$
$230$	0.157494	−	0.893195i	0.0103849	−	0.0588955i
$231$	17.6242	−	19.8457i	1.15959	−	1.30575i
$232$	2.39003	−	2.00547i	0.156913	−	0.131666i
$233$	10.9246	+	6.30731i	0.715694	+	0.413206i	0.813166	−	0.582032i	$-0.197742\pi$
$233$	10.9246	+	6.30731i	0.715694	+	0.413206i	−0.0974721	+	0.995238i	$0.531076\pi$
$234$	0.955300	+	1.20743i	0.0624499	+	0.0789321i
$235$	1.77153	+	3.06839i	0.115562	+	0.200159i
$236$	3.50594	+	1.27606i	0.228217	+	0.0830643i
$237$	−2.28707	−	0.648242i	−0.148561	−	0.0421079i
$238$	−2.16659	−	8.55121i	−0.140439	−	0.554292i
$239$	5.39158	+	14.8133i	0.348753	+	0.958190i	0.982764	+	0.184866i	$0.0591851\pi$
$239$	5.39158	+	14.8133i	0.348753	+	0.958190i	−0.634011	+	0.773324i	$0.718593\pi$
$240$	−0.479501	+	0.990803i	−0.0309516	+	0.0639561i
$241$	−10.2809	+	1.81281i	−0.662254	+	0.116773i	−0.494665	−	0.869084i	$-0.664709\pi$
$241$	−10.2809	+	1.81281i	−0.662254	+	0.116773i	−0.167589	+	0.985857i	$0.553598\pi$
$242$		−	22.5459i		−	1.44931i
$243$	12.0933	+	9.83626i	0.775786	+	0.630997i
$244$			2.54881i			0.163171i
$245$	−3.91186	+	2.11825i	−0.249920	+	0.135330i
$246$	7.87578	+	3.81150i	0.502141	+	0.243012i
$247$	−1.98434	+	0.722240i	−0.126260	+	0.0459550i
$248$	−5.51965	−	4.63154i	−0.350498	−	0.294103i
$249$	12.8158	+	3.63247i	0.812166	+	0.230199i
$250$	2.08578	−	5.73064i	0.131916	−	0.362437i
$251$	2.66950	+	4.62370i	0.168497	+	0.291846i	0.937892	−	0.346928i	$-0.112775\pi$
$251$	2.66950	+	4.62370i	0.168497	+	0.291846i	−0.769395	+	0.638774i	$0.779442\pi$
$252$	7.92928	−	0.355655i	0.499498	−	0.0224041i
$253$	−4.13298	+	7.15854i	−0.259838	+	0.450053i
$254$	9.02551	+	10.7562i	0.566311	+	0.674903i
$255$	−0.372457	+	3.65109i	−0.0233242	+	0.228640i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−3.11009	+	17.6382i	−0.194002	+	1.10024i	0.719831	+	0.694149i	$0.244219\pi$
$257$	−3.11009	+	17.6382i	−0.194002	+	1.10024i	−0.913833	+	0.406090i	$0.866892\pi$
$258$	6.50839	+	14.4986i	0.405194	+	0.902641i
$259$	−0.0737684	−	1.00031i	−0.00458374	−	0.0621564i
$260$	−0.282455	−	0.163075i	−0.0175171	−	0.0101135i
$261$	6.99394	+	6.22032i	0.432914	+	0.385028i
$262$	−2.44112	+	1.40938i	−0.150813	+	0.0870719i
$263$	1.75653	−	4.82602i	0.108312	−	0.297585i	−0.873682	−	0.486498i	$-0.838274\pi$
$263$	1.75653	−	4.82602i	0.108312	−	0.297585i	0.981994	+	0.188913i	$0.0604964\pi$
$264$	7.19495	−	6.99074i	0.442819	−	0.430250i
$265$	−1.57431	+	1.87619i	−0.0967092	+	0.115253i
$266$	−2.96091	+	10.4759i	−0.181545	+	0.642321i
$267$	7.21049	−	0.526376i	0.441275	−	0.0322137i
$268$	1.36783	+	7.75736i	0.0835536	+	0.473856i
$269$	−18.0618			−1.10125			−0.550624	−	0.834754i	$-0.685610\pi$
$269$	−18.0618			−1.10125			−0.550624	+	0.834754i	$0.685610\pi$
$270$	−3.14981	−	0.991572i	−0.191691	−	0.0603452i
$271$			9.13586i			0.554964i	0.960731	+	0.277482i	$0.0894999\pi$
$271$			9.13586i			0.554964i	−0.960731	+	0.277482i	$0.910500\pi$
$272$	−0.578974	−	3.28353i	−0.0351055	−	0.199093i
$273$	−0.0659574	+	2.35091i	−0.00399193	+	0.142283i
$274$	15.3946	−	5.60316i	0.930020	−	0.338500i
$275$	−17.1112	+	20.3923i	−1.03184	+	1.22970i
$276$	−2.39665	+	0.605345i	−0.144262	+	0.0364375i
$277$	26.8186	+	9.76116i	1.61137	+	0.586492i	0.981711	−	0.190378i	$-0.0609714\pi$
$277$	26.8186	+	9.76116i	1.61137	+	0.586492i	0.629661	+	0.776870i	$0.283194\pi$
$278$	−6.97152	−	12.0750i	−0.418124	−	0.724212i
$279$	11.3425	−	18.4013i	0.679056	−	1.10166i
$280$	−1.53342	+	0.689716i	−0.0916395	+	0.0412184i
$281$	3.73499	+	4.45119i	0.222811	+	0.265536i	0.865857	−	0.500292i	$-0.166774\pi$
$281$	3.73499	+	4.45119i	0.222811	+	0.265536i	−0.643046	+	0.765828i	$0.722330\pi$
$282$	5.65202	−	7.82959i	0.336573	−	0.466245i
$283$	−22.8862	−	4.03545i	−1.36044	−	0.239883i	−0.554652	−	0.832083i	$-0.687149\pi$
$283$	−22.8862	−	4.03545i	−1.36044	−	0.239883i	−0.805791	+	0.592200i	$0.798260\pi$
$284$	−3.04395	−	0.536730i	−0.180625	−	0.0318491i
$285$	2.65093	−	3.67227i	0.157028	−	0.217526i
$286$	1.91066	+	2.27704i	0.112980	+	0.134644i
$287$	5.48247	+	12.1890i	0.323620	+	0.719494i
$288$	2.99876	+	0.0863543i	0.176703	+	0.00508848i
$289$	2.94162	+	5.09504i	0.173037	+	0.299708i
$290$	−1.86319	−	0.678145i	−0.109410	−	0.0398220i
$291$	−29.7973	+	7.52620i	−1.74675	+	0.441194i
$292$	8.56909	−	10.2122i	0.501468	−	0.597626i
$293$	−15.6864	+	5.70937i	−0.916407	+	0.333545i	−0.756808	−	0.653637i	$-0.773242\pi$
$293$	−15.6864	+	5.70937i	−0.916407	+	0.333545i	−0.159599	+	0.987182i	$0.551020\pi$
$294$	9.63313	+	7.36226i	0.561815	+	0.429376i
$295$	−0.411727	−	2.33502i	−0.0239717	−	0.135950i
$296$		−	0.379109i		−	0.0220353i
$297$	23.8846	+	18.3102i	1.38593	+	1.06247i
$298$	−22.1171			−1.28121
$299$	−0.127186	−	0.721310i	−0.00735538	−	0.0417145i
$300$	−7.93960	+	0.579602i	−0.458393	+	0.0334633i
$301$	−6.60267	+	23.3608i	−0.380572	+	1.34650i
$302$	−6.84046	+	8.15215i	−0.393624	+	0.469103i
$303$	22.8576	−	22.2089i	1.31314	−	1.27587i
$304$	−1.40729	+	3.86651i	−0.0807138	+	0.221759i
$305$	1.40278	−	0.809895i	0.0803229	−	0.0463745i
$306$	9.49389	−	3.14909i	0.542730	−	0.180022i
$307$	3.43942	+	1.98575i	0.196298	+	0.113333i	0.594928	−	0.803779i	$-0.297181\pi$
$307$	3.43942	+	1.98575i	0.196298	+	0.113333i	−0.398630	+	0.917112i	$0.630514\pi$
$308$	15.2824	−	1.12700i	0.870795	−	0.0642170i
$309$	−10.4295	−	23.2336i	−0.593316	−	1.32171i
$310$	−0.795150	+	4.50952i	−0.0451615	+	0.256124i
$311$	−0.777795	+	4.41110i	−0.0441047	+	0.250130i	−0.998887	−	0.0471771i	$-0.984977\pi$
$311$	−0.777795	+	4.41110i	−0.0441047	+	0.250130i	0.954782	+	0.297307i	$0.0960886\pi$
$312$	−0.0902117	+	0.884320i	−0.00510723	+	0.0500648i
$313$	−13.5703	−	16.1725i	−0.767039	−	0.914122i	0.231232	−	0.972899i	$-0.425724\pi$
$313$	−13.5703	−	16.1725i	−0.767039	−	0.914122i	−0.998271	+	0.0587768i	$0.981280\pi$
$314$	−4.79297	+	8.30167i	−0.270483	+	0.468490i
$315$	−2.71530	−	4.25100i	−0.152990	−	0.239517i
$316$	−0.686228	−	1.18858i	−0.0386034	−	0.0668630i
$317$	−4.74188	+	13.0282i	−0.266331	+	0.731737i	0.732376	+	0.680900i	$0.238411\pi$
$317$	−4.74188	+	13.0282i	−0.266331	+	0.731737i	−0.998707	+	0.0508372i	$0.983811\pi$
$318$	6.42219	+	1.82029i	0.360138	+	0.102077i
$319$	13.8428	+	11.6155i	0.775047	+	0.650342i
$320$	−0.597182	+	0.217357i	−0.0333835	+	0.0121506i
$321$	3.09150	+	1.49614i	0.172551	+	0.0835061i
$322$	−3.40004	−	1.64235i	−0.189477	−	0.0915246i
$323$			13.7190i			0.763344i
$324$	1.05020	+	8.93852i	0.0583445	+	0.496584i
$325$		−	2.35879i		−	0.130842i
$326$	10.9223	−	1.92590i	0.604931	−	0.106666i
$327$	6.86916	−	14.1939i	0.379866	−	0.784925i
$328$	1.72774	+	4.74693i	0.0953986	+	0.262106i
$329$	14.2987	−	3.62282i	0.788313	−	0.199733i
$330$	−6.13369	−	1.73852i	−0.337649	−	0.0957024i
$331$	−0.858086	−	0.312318i	−0.0471647	−	0.0171665i	0.318330	−	0.947980i	$-0.396878\pi$
$331$	−0.858086	−	0.312318i	−0.0471647	−	0.0171665i	−0.365495	+	0.930813i	$0.619100\pi$
$332$	3.84533	+	6.66030i	0.211040	+	0.365532i
$333$	1.12527	−	0.165173i	0.0616644	−	0.00905141i
$334$	18.9290	+	10.9287i	1.03575	+	0.597991i
$335$	3.83475	−	3.21774i	0.209515	−	0.175804i
$336$	3.42647	+	3.04292i	0.186929	+	0.166005i
$337$	−1.72863	+	9.80357i	−0.0941647	+	0.534035i	0.900835	+	0.434161i	$0.142955\pi$
$337$	−1.72863	+	9.80357i	−0.0941647	+	0.534035i	−0.995000	+	0.0998738i	$0.968156\pi$
$338$	12.5431	+	2.21169i	0.682256	+	0.120300i
$339$	−14.1720	−	31.5706i	−0.769718	−	1.71468i
$340$	−1.62317	+	1.36200i	−0.0880287	+	0.0738649i
$341$	20.8664	−	36.1417i	1.12998	−	1.95718i
$342$	−12.0897	−	2.49254i	−0.653735	−	0.134781i
$343$	4.05678	+	18.0705i	0.219046	+	0.975715i
$344$	−3.13819	+	8.62211i	−0.169200	+	0.464873i
$345$	1.09471	+	1.12669i	0.0589371	+	0.0606587i
$346$	13.1139	−	15.6285i	0.705006	−	0.840194i
$347$	−4.67022	−	12.8313i	−0.250710	−	0.688821i	−0.999657	−	0.0261909i	$-0.991662\pi$
$347$	−4.67022	−	12.8313i	−0.250710	−	0.688821i	0.748946	−	0.662631i	$-0.230560\pi$
$348$	0.393448	+	5.38960i	0.0210910	+	0.288913i
$349$	11.1326	−	1.96297i	0.595912	−	0.105075i	0.132446	−	0.991190i	$-0.457717\pi$
$349$	11.1326	−	1.96297i	0.595912	−	0.105075i	0.463466	+	0.886115i	$0.346606\pi$
$350$	−9.86490	−	7.11017i	−0.527301	−	0.380055i
$351$	−2.66414	+	0.117520i	−0.142201	+	0.00627277i
$352$	5.79188			0.308708
$353$	−3.50744	−	19.8917i	−0.186682	−	1.05873i	−0.923775	−	0.382935i	$-0.874913\pi$
$353$	−3.50744	−	19.8917i	−0.186682	−	1.05873i	0.737093	−	0.675791i	$-0.236198\pi$
$354$	−5.34631	+	3.62998i	−0.284153	+	0.192931i
$355$	0.671829	+	1.84583i	0.0356570	+	0.0979667i
$356$	3.19751	+	2.68303i	0.169468	+	0.142200i
$357$	14.2055	+	5.62638i	0.751834	+	0.297779i
$358$	14.5990	+	5.31359i	0.771579	+	0.280832i
$359$	0.0633911	−	0.0365989i	0.00334566	−	0.00193162i	−0.498326	−	0.866990i	$-0.666052\pi$
$359$	0.0633911	−	0.0365989i	0.00334566	−	0.00193162i	0.501672	+	0.865058i	$0.332718\pi$
$360$	−0.905341	−	1.67785i	−0.0477156	−	0.0884307i
$361$	−1.03483	+	1.79238i	−0.0544648	+	0.0943359i
$362$	5.22724	−	4.38618i	0.274738	−	0.230532i
$363$	31.6627	+	22.8567i	1.66186	+	1.19966i
$364$	−0.973152	+	0.946933i	−0.0510070	+	0.0496328i
$365$	−8.34334	−	1.47116i	−0.436710	−	0.0770038i
$366$	−3.57947	−	2.58394i	−0.187102	−	0.135065i
$367$	19.7388	+	23.5238i	1.03036	+	1.22793i	0.973295	+	0.229559i	$0.0737285\pi$
$367$	19.7388	+	23.5238i	1.03036	+	1.22793i	0.0570611	+	0.998371i	$0.481827\pi$
$368$	−1.23596	−	0.713582i	−0.0644289	−	0.0371980i
$369$	−13.3371	+	7.19645i	−0.694300	+	0.374632i
$370$	−0.208649	+	0.120464i	−0.0108471	+	0.00626260i
$371$	5.73388	+	8.43156i	0.297688	+	0.437745i
$372$	12.1001	−	3.05624i	0.627361	−	0.158459i
$373$	−23.4944	−	19.7142i	−1.21650	−	1.02076i	−0.999000	−	0.0446993i	$-0.985767\pi$
$373$	−23.4944	−	19.7142i	−1.21650	−	1.02076i	−0.217495	−	0.976061i	$-0.569789\pi$
$374$	18.1466	−	6.60481i	0.938337	−	0.341527i
$375$	5.93338	+	8.73882i	0.306399	+	0.451271i
$376$	5.49047	−	0.968119i	0.283150	−	0.0499269i
$377$	−1.60120			−0.0824662
$378$	−7.53910	+	11.4962i	−0.387769	+	0.591299i
$379$	10.9028			0.560038			0.280019	−	0.959995i	$-0.409659\pi$
$379$	10.9028			0.560038			0.280019	+	0.959995i	$0.409659\pi$
$380$	2.57517	−	0.454071i	0.132103	−	0.0232934i
$381$	−24.2555	+	1.77069i	−1.24265	+	0.0907150i
$382$	14.8951	−	5.42137i	0.762099	−	0.277381i
$383$	−4.68369	−	3.93008i	−0.239325	−	0.200818i	0.515234	−	0.857049i	$-0.327705\pi$
$383$	−4.68369	−	3.93008i	−0.239325	−	0.200818i	−0.754559	+	0.656232i	$0.772149\pi$
$384$	1.20699	+	1.24225i	0.0615939	+	0.0633931i
$385$	−5.47631	−	8.05280i	−0.279098	−	0.410409i
$386$	−9.43195	+	5.44554i	−0.480074	+	0.277171i
$387$	−26.9594	−	5.55823i	−1.37042	−	0.282541i
$388$	−15.3666	−	8.87189i	−0.780119	−	0.450402i
$389$	−11.8344	−	14.1037i	−0.600027	−	0.715084i	0.377473	−	0.926021i	$-0.376793\pi$
$389$	−11.8344	−	14.1037i	−0.600027	−	0.715084i	−0.977500	+	0.210937i	$0.932349\pi$
$390$	0.515365	−	0.231347i	0.0260965	−	0.0117147i
$391$	−4.68613	−	0.826291i	−0.236988	−	0.0417873i
$392$	1.02685	+	6.92427i	0.0518638	+	0.349729i
$393$	0.495478	−	4.85703i	0.0249936	−	0.245005i
$394$	−17.4540	+	14.6456i	−0.879320	+	0.737837i
$395$	−0.436104	+	0.755353i	−0.0219428	+	0.0380060i
$396$	2.52344	+	17.1914i	0.126808	+	0.863902i
$397$	24.3764	−	14.0737i	1.22342	−	0.706340i	0.257772	−	0.966206i	$-0.417012\pi$
$397$	24.3764	−	14.0737i	1.22342	−	0.706340i	0.965645	+	0.259866i	$0.0836784\pi$
$398$	9.83588	+	3.57997i	0.493028	+	0.179448i
$399$	−11.7103	−	14.7785i	−0.586251	−	0.739852i
$400$	−3.52084	−	2.95434i	−0.176042	−	0.147717i
$401$	−10.3696	−	28.4901i	−0.517831	−	1.42273i	−0.872905	−	0.487891i	$-0.837766\pi$
$401$	−10.3696	−	28.4901i	−0.517831	−	1.42273i	0.355074	−	0.934838i	$-0.384456\pi$
$402$	−12.2809	−	5.94334i	−0.612513	−	0.296427i
$403$	0.642133	+	3.64172i	0.0319869	+	0.181407i
$404$	18.4002			0.915446
$405$	4.58575	−	3.41824i	0.227868	−	0.169854i
$406$	−4.82656	+	6.69654i	−0.239538	+	0.332344i
$407$	2.16240	−	0.381289i	0.107186	−	0.0188998i
$408$	5.19823	+	2.51569i	0.257351	+	0.124545i
$409$	−3.44095	−	9.45394i	−0.170144	−	0.467467i	0.825088	−	0.565005i	$-0.191126\pi$
$409$	−3.44095	−	9.45394i	−0.170144	−	0.467467i	−0.995232	+	0.0975374i	$0.968903\pi$
$410$	2.06355	−	2.45925i	0.101912	−	0.121454i
$411$	−7.73785	+	27.3000i	−0.381680	+	1.34661i
$412$	5.02888	−	13.8167i	0.247755	−	0.680702i
$413$	−9.82092	−	0.994514i	−0.483256	−	0.0489369i
$414$	1.57956	−	3.97947i	0.0776311	−	0.195580i
$415$	2.44374	−	4.23268i	0.119958	−	0.207774i
$416$	−0.393143	+	0.329886i	−0.0192754	+	0.0161740i
$417$	24.0254	+	2.45089i	1.17653	+	0.120021i
$418$	−23.4695	−	4.13831i	−1.14793	−	0.202411i
$419$	4.20764	−	23.8627i	0.205556	−	1.16577i	−0.691005	−	0.722850i	$-0.742832\pi$
$419$	4.20764	−	23.8627i	0.205556	−	1.16577i	0.896562	−	0.442919i	$-0.146057\pi$
$420$	0.585944	−	2.85271i	0.0285912	−	0.139198i
$421$	0.481683	−	0.404180i	0.0234758	−	0.0196985i	−0.630974	−	0.775804i	$-0.717345\pi$
$421$	0.481683	−	0.404180i	0.0234758	−	0.0196985i	0.654450	+	0.756105i	$0.272900\pi$
$422$	8.23566	+	4.75486i	0.400905	+	0.231463i
$423$	5.26569	+	15.8750i	0.256027	+	0.771869i
$424$	1.92696	+	3.33759i	0.0935813	+	0.162088i
$425$	−14.4002	−	5.24123i	−0.698510	−	0.254237i
$426$	3.83967	−	3.73069i	0.186033	−	0.180753i
$427$	−1.65625	−	6.53697i	−0.0801516	−	0.316346i
$428$	0.678195	+	1.86332i	0.0327818	+	0.0900672i
$429$	−5.13480	+	0.374847i	−0.247910	+	0.0180978i
$430$	5.74249	−	1.01256i	0.276928	−	0.0488298i
$431$			2.89765i			0.139575i	0.997562	+	0.0697875i	$0.0222321\pi$
$431$			2.89765i			0.139575i	−0.997562	+	0.0697875i	$0.977768\pi$
$432$	−3.16136	+	4.12381i	−0.152101	+	0.198407i
$433$			5.77940i			0.277740i	0.990311	+	0.138870i	$0.0443471\pi$
$433$			5.77940i			0.277740i	−0.990311	+	0.138870i	$0.955653\pi$
$434$	17.1660	+	8.29182i	0.823992	+	0.398020i
$435$	2.84123	−	1.92911i	0.136227	−	0.0924936i
$436$	8.55503	−	3.11378i	0.409712	−	0.149123i
$437$	4.49842	+	3.77463i	0.215189	+	0.180565i
$438$	5.65453	+	22.3871i	0.270184	+	1.06970i
$439$	−12.9832	+	35.6709i	−0.619652	+	1.70248i	0.0881850	+	0.996104i	$0.471893\pi$
$439$	−12.9832	+	35.6709i	−0.619652	+	1.70248i	−0.707837	+	0.706376i	$0.750329\pi$
$440$	−1.84039	−	3.18766i	−0.0877374	−	0.151966i
$441$	−20.1052	+	6.06470i	−0.957391	+	0.288795i
$442$	−0.855571	+	1.48189i	−0.0406954	+	0.0704864i
$443$	1.51019	+	1.79977i	0.0717512	+	0.0855097i	0.800726	−	0.599031i	$-0.204447\pi$
$443$	1.51019	+	1.79977i	0.0717512	+	0.0855097i	−0.728975	+	0.684541i	$0.760003\pi$
$444$	0.532408	+	0.384335i	0.0252670	+	0.0182397i
$445$	0.460627	−	2.61235i	0.0218358	−	0.123837i
$446$	−4.41239	+	25.0239i	−0.208933	+	1.18492i
$447$	22.4220	−	31.0605i	1.06052	−	1.46911i
$448$	0.194583	+	2.63859i	0.00919320	+	0.124661i
$449$	7.90828	+	4.56585i	0.373215	+	0.215476i	0.674862	−	0.737944i	$-0.264203\pi$
$449$	7.90828	+	4.56585i	0.373215	+	0.215476i	−0.301647	+	0.953420i	$0.597536\pi$
$450$	7.23506	−	11.7377i	0.341064	−	0.553320i
$451$	−25.3383	+	14.6291i	−1.19314	+	0.688857i
$452$	6.83341	−	18.7746i	0.321417	−	0.883085i
$453$	−4.51386	−	17.8710i	−0.212079	−	0.839654i
$454$	6.92110	−	8.24824i	0.324823	−	0.387109i
$455$	0.830383	+	0.234698i	0.0389290	+	0.0110028i
$456$	−4.00330	−	5.89615i	−0.187472	−	0.276113i
$457$	−4.03573	−	22.8878i	−0.188783	−	1.07064i	−0.920997	−	0.389569i	$-0.872624\pi$
$457$	−4.03573	−	22.8878i	−0.188783	−	1.07064i	0.732214	−	0.681075i	$-0.238487\pi$
$458$	11.5060			0.537641
$459$	−5.20226	+	16.5254i	−0.242821	+	0.771340i
$460$			0.906974i			0.0422879i
$461$	4.45849	+	25.2853i	0.207652	+	1.17766i	0.893211	+	0.449638i	$0.148447\pi$
$461$	4.45849	+	25.2853i	0.207652	+	1.17766i	−0.685559	+	0.728017i	$0.740442\pi$
$462$	−13.9103	+	22.6046i	−0.647165	+	1.05166i
$463$	24.6191	−	8.96061i	1.14415	−	0.416435i	0.300737	−	0.953707i	$-0.402767\pi$
$463$	24.6191	−	8.96061i	1.14415	−	0.416435i	0.843409	+	0.537272i	$0.180545\pi$
$464$	−2.00547	+	2.39003i	−0.0931018	+	0.110954i
$465$	−5.52691	−	5.68836i	−0.256304	−	0.263791i
$466$	−11.8539	−	4.31446i	−0.549120	−	0.199863i
$467$	3.89959	+	6.75429i	0.180452	+	0.312551i	0.942034	−	0.335516i	$-0.108911\pi$
$467$	3.89959	+	6.75429i	0.180452	+	0.312551i	−0.761583	+	0.648068i	$0.775577\pi$
$468$	−1.15045	−	1.02320i	−0.0531798	−	0.0472974i
$469$	−8.54893	−	19.0066i	−0.394753	−	0.877641i
$470$	−2.27744	−	2.71415i	−0.105050	−	0.125194i
$471$	−6.79955	−	15.1472i	−0.313307	−	0.697945i
$472$	−3.67426	−	0.647871i	−0.169122	−	0.0298207i
$473$	−52.3358	−	9.22822i	−2.40640	−	0.424314i
$474$	2.36489	+	0.241248i	0.108623	+	0.0110809i
$475$	12.1561	+	14.4870i	0.557758	+	0.664710i
$476$	3.61858	+	8.04507i	0.165857	+	0.368745i
$477$	−9.06706	+	7.17372i	−0.415152	+	0.328462i
$478$	−7.88197	−	13.6520i	−0.360513	−	0.624426i
$479$	−37.5764	−	13.6767i	−1.71691	−	0.624903i	−0.719344	−	0.694655i	$-0.755557\pi$
$479$	−37.5764	−	13.6767i	−1.71691	−	0.624903i	−0.997564	+	0.0697511i	$0.977779\pi$
$480$	0.300165	−	1.05901i	0.0137006	−	0.0483372i
$481$	−0.125063	+	0.149044i	−0.00570239	+	0.00679584i
$482$	9.80996	−	3.57053i	0.446831	−	0.162633i
$483$	5.75336	−	3.10991i	0.261787	−	0.141506i
$484$	3.91506	+	22.2034i	0.177957	+	1.00925i
$485$			11.2763i			0.512031i
$486$	−13.6176	−	7.58685i	−0.617708	−	0.344146i
$487$	33.9761			1.53961			0.769803	−	0.638282i	$-0.220355\pi$
$487$	33.9761			1.53961			0.769803	+	0.638282i	$0.220355\pi$
$488$	−0.442597	−	2.51009i	−0.0200354	−	0.113626i
$489$	−8.36819	+	17.2914i	−0.378422	+	0.781943i
$490$	3.48460	−	2.76536i	0.157418	−	0.124926i
$491$	10.8839	−	12.9710i	0.491185	−	0.585371i	−0.462334	−	0.886706i	$-0.652988\pi$
$491$	10.8839	−	12.9710i	0.491185	−	0.585371i	0.953518	+	0.301335i	$0.0974322\pi$
$492$	−8.41799	−	2.38598i	−0.379512	−	0.107568i
$493$	−3.55787	+	9.77517i	−0.160239	+	0.440252i
$494$	1.82878	−	1.05584i	0.0822805	−	0.0475047i
$495$	8.65975	−	6.85147i	0.389227	−	0.307951i
$496$	6.24006	+	3.60270i	0.280187	+	0.161766i
$497$	8.15562	−	0.601439i	0.365830	−	0.0269782i
$498$	−13.2518	−	1.35185i	−0.593829	−	0.0605780i
$499$	2.91424	−	16.5275i	0.130459	−	0.739872i	−0.847455	−	0.530867i	$-0.821866\pi$
$499$	2.91424	−	16.5275i	0.130459	−	0.739872i	0.977915	−	0.209005i	$-0.0670225\pi$
$500$	−1.05898	+	6.00577i	−0.0473590	+	0.268586i
$501$	−34.5378	+	15.5040i	−1.54304	+	0.692667i
$502$	−3.43184	−	4.08991i	−0.153170	−	0.182541i
$503$	16.1195	−	27.9198i	0.718734	−	1.24488i	−0.242768	−	0.970084i	$-0.578055\pi$
$503$	16.1195	−	27.9198i	0.718734	−	1.24488i	0.961502	−	0.274799i	$-0.0886113\pi$
$504$	−7.74706	+	1.72716i	−0.345081	+	0.0769337i
$505$	−5.84675	−	10.1269i	−0.260177	−	0.450640i
$506$	2.82713	−	7.76747i	0.125681	−	0.345306i
$507$	−15.8220	+	15.3730i	−0.702680	+	0.682737i
$508$	−10.7562	−	9.02551i	−0.477229	−	0.400442i
$509$	−27.2666	+	9.92421i	−1.20857	+	0.439883i	−0.866207	−	0.499685i	$-0.833449\pi$
$509$	−27.2666	+	9.92421i	−1.20857	+	0.439883i	−0.342362	+	0.939568i	$0.611227\pi$
$510$	−0.267207	−	3.66030i	−0.0118321	−	0.162081i
$511$	−15.3412	+	31.7598i	−0.678655	+	1.40497i
$512$			1.00000i			0.0441942i
$513$	15.7567	−	14.4514i	0.695677	−	0.638047i
$514$		−	17.9103i		−	0.789989i
$515$	−9.20221	+	1.62260i	−0.405498	+	0.0715002i
$516$	−8.92716	−	13.1481i	−0.392996	−	0.578814i
$517$	11.0441	+	30.3434i	0.485719	+	1.33450i
$518$	0.246350	+	0.972306i	0.0108240	+	0.0427207i
$519$	8.65353	+	34.2606i	0.379848	+	1.50387i
$520$	0.306481	+	0.111550i	0.0134401	+	0.00489179i
$521$	10.9353	+	18.9406i	0.479086	+	0.829801i	0.999712	−	0.0239834i	$-0.00763490\pi$
$521$	10.9353	+	18.9406i	0.479086	+	0.829801i	−0.520626	+	0.853785i	$0.674302\pi$
$522$	−7.96784	−	4.91133i	−0.348743	−	0.214963i
$523$	34.5237	+	19.9323i	1.50961	+	0.871576i	0.999937	+	0.0112110i	$0.00356864\pi$
$523$	34.5237	+	19.9323i	1.50961	+	0.871576i	0.509678	+	0.860365i	$0.329765\pi$
$524$	2.15930	−	1.81187i	0.0943294	−	0.0791517i
$525$	19.9862	−	6.64577i	0.872267	−	0.290045i
$526$	−0.891812	+	5.05772i	−0.0388849	+	0.220527i
$527$	23.6591	+	4.17174i	1.03061	+	0.181724i
$528$	−5.87171	+	8.13393i	−0.255534	+	0.353984i
$529$	16.0587	−	13.4749i	0.698206	−	0.585865i
$530$	1.22460	−	2.12106i	0.0531931	−	0.0921331i
$531$	0.322183	−	11.1882i	0.0139816	−	0.485526i
$532$	1.09679	−	10.8309i	0.0475521	−	0.469581i
$533$	0.886699	−	2.43618i	0.0384072	−	0.105523i
$534$	−7.00955	+	1.77047i	−0.303333	+	0.0766156i
$535$	0.810012	−	0.965334i	0.0350199	−	0.0417350i
$536$	−2.69410	−	7.40199i	−0.116368	−	0.319717i
$537$	−22.2624	+	15.1155i	−0.960693	+	0.652280i
$538$	17.7874	−	3.13640i	0.766869	−	0.135220i
$539$	−38.4626	+	12.8211i	−1.65670	+	0.552245i
$540$	3.27414	+	0.429550i	0.140897	+	0.0184849i
$541$	−12.4848			−0.536763			−0.268382	−	0.963313i	$-0.586489\pi$
$541$	−12.4848			−0.536763			−0.268382	+	0.963313i	$0.586489\pi$
$542$	−1.58643	−	8.99706i	−0.0681428	−	0.386457i
$543$	0.860510	+	11.7876i	0.0369280	+	0.505854i
$544$	1.14036	+	3.13310i	0.0488924	+	0.134331i
$545$	−4.43211	−	3.71898i	−0.189851	−	0.159304i
$546$	−0.343276	−	2.32665i	−0.0146908	−	0.0995713i
$547$	−8.02394	−	2.92048i	−0.343079	−	0.124871i	0.164734	−	0.986338i	$-0.447324\pi$
$547$	−8.02394	−	2.92048i	−0.343079	−	0.124871i	−0.507813	+	0.861468i	$0.669546\pi$
$548$	−14.1877	+	8.19128i	−0.606069	+	0.349914i
$549$	7.25760	−	2.40732i	0.309747	−	0.102742i
$550$	13.3101	−	23.0538i	0.567546	−	0.983018i
$551$	9.83414	−	8.25182i	0.418949	−	0.351540i
$552$	2.25512	−	1.01232i	0.0959845	−	0.0430873i
$553$	2.53233	+	2.60245i	0.107686	+	0.110667i
$554$	−28.1062	−	4.95587i	−1.19412	−	0.210555i
$555$	0.0423498	−	0.415143i	0.00179765	−	0.0176219i
$556$	8.96241	+	10.6810i	0.380091	+	0.452975i
$557$	−12.2712	−	7.08480i	−0.519949	−	0.300193i	0.216965	−	0.976179i	$-0.430384\pi$
$557$	−12.2712	−	7.08480i	−0.519949	−	0.300193i	−0.736914	+	0.675987i	$0.763718\pi$
$558$	−7.97480	+	20.0913i	−0.337600	+	0.850535i
$559$	4.07808	−	2.35448i	0.172484	−	0.0995839i
$560$	1.39036	−	0.945514i	0.0587534	−	0.0399552i
$561$	−9.12111	+	32.1803i	−0.385094	+	1.35865i
$562$	−4.45119	−	3.73499i	−0.187762	−	0.157551i
$563$	−4.30657	+	1.56746i	−0.181500	+	0.0660607i	−0.431172	−	0.902270i	$-0.641900\pi$
$563$	−4.30657	+	1.56746i	−0.181500	+	0.0660607i	0.249671	+	0.968331i	$0.419677\pi$
$564$	−4.20656	+	8.69210i	−0.177128	+	0.366003i
$565$	−12.5043	+	2.20484i	−0.526059	+	0.0927583i
$566$	23.2392			0.976819
$567$	−8.50182	−	22.2423i	−0.357043	−	0.934088i
$568$	3.09091			0.129692
$569$	34.0499	−	6.00391i	1.42744	−	0.251697i	0.594073	−	0.804411i	$-0.297519\pi$
$569$	34.0499	−	6.00391i	1.42744	−	0.251697i	0.833371	+	0.552714i	$0.186408\pi$
$570$	−1.97298	+	4.07681i	−0.0826389	+	0.170759i
$571$	18.2532	−	6.64362i	0.763872	−	0.278027i	0.0694413	−	0.997586i	$-0.477878\pi$
$571$	18.2532	−	6.64362i	0.763872	−	0.278027i	0.694431	+	0.719559i	$0.255656\pi$
$572$	−2.27704	−	1.91066i	−0.0952079	−	0.0798889i
$573$	−7.48680	+	26.4142i	−0.312765	+	1.10347i
$574$	−7.51578	−	11.0518i	−0.313703	−	0.461293i
$575$	−5.68063	+	3.27971i	−0.236899	+	0.136774i
$576$	−2.96819	+	0.435686i	−0.123675	+	0.0181536i
$577$	13.5159	+	7.80342i	0.562675	+	0.324860i	0.754218	−	0.656624i	$-0.228016\pi$
$577$	13.5159	+	7.80342i	0.562675	+	0.324860i	−0.191544	+	0.981484i	$0.561349\pi$
$578$	−3.78168	−	4.50683i	−0.157297	−	0.187459i
$579$	1.91442	−	18.7665i	0.0795605	−	0.779910i
$580$	1.95264	+	0.344303i	0.0810790	+	0.0142964i
$581$	−14.1901	−	14.5830i	−0.588705	−	0.605005i
$582$	28.0377	−	12.5861i	1.16220	−	0.521711i
$583$	−17.0992	+	14.3479i	−0.708177	+	0.594231i
$584$	−6.66557	+	11.5451i	−0.275823	+	0.477740i
$585$	−0.197573	+	0.958297i	−0.00816862	+	0.0396207i
$586$	14.4566	−	8.34654i	0.597198	−	0.344792i
$587$	20.1730	+	7.34238i	0.832630	+	0.303053i	0.722938	−	0.690913i	$-0.242791\pi$
$587$	20.1730	+	7.34238i	0.832630	+	0.303053i	0.109692	+	0.993966i	$0.465013\pi$
$588$	−10.7652	−	5.57764i	−0.443950	−	0.230018i
$589$	−22.7114	−	19.0572i	−0.935809	−	0.785237i
$590$	0.810945	+	2.22805i	0.0333861	+	0.0917275i
$591$	−2.87328	−	39.3593i	−0.118191	−	1.61903i
$592$	0.0658317	+	0.373350i	0.00270566	+	0.0153446i
$593$	48.5176			1.99238			0.996189	−	0.0872183i	$-0.0277978\pi$
$593$	48.5176			1.99238			0.996189	+	0.0872183i	$0.0277978\pi$
$594$	−26.7013	−	13.8845i	−1.09557	−	0.569690i
$595$	3.27792	−	4.54790i	0.134381	−	0.186446i
$596$	21.7811	−	3.84060i	0.892189	−	0.157317i
$597$	−14.9990	+	10.1839i	−0.613870	+	0.416798i
$598$	0.250508	+	0.688266i	0.0102441	+	0.0281453i
$599$	14.5703	−	17.3642i	0.595327	−	0.709483i	−0.381293	−	0.924454i	$-0.624521\pi$
$599$	14.5703	−	17.3642i	0.595327	−	0.709483i	0.976620	+	0.214971i	$0.0689657\pi$
$600$	7.71833	−	1.94949i	0.315100	−	0.0795877i
$601$	6.19093	−	17.0094i	0.252533	−	0.693829i	−0.747045	−	0.664774i	$-0.768528\pi$
$601$	6.19093	−	17.0094i	0.252533	−	0.693829i	0.999578	−	0.0290552i	$-0.00924987\pi$
$602$	2.44580	−	24.1525i	0.0996832	−	0.984381i
$603$	20.7967	−	11.2216i	0.846909	−	0.456977i
$604$	5.32094	−	9.21613i	0.216506	−	0.374999i
$605$	10.9760	−	9.20994i	0.446237	−	0.374437i
$606$	−18.6538	+	25.8407i	−0.757761	+	1.04971i
$607$	−20.1947	−	3.56086i	−0.819676	−	0.144531i	−0.251941	−	0.967743i	$-0.581069\pi$
$607$	−20.1947	−	3.56086i	−0.819676	−	0.144531i	−0.567735	+	0.823211i	$0.692180\pi$
$608$	0.714501	−	4.05214i	0.0289769	−	0.164336i
$609$	−4.51131	−	13.5671i	−0.182807	−	0.549766i
$610$	−1.24083	+	1.04118i	−0.0502398	+	0.0421562i
$611$	−2.47791	−	1.43062i	−0.100246	−	0.0578768i
$612$	−8.80282	+	4.74985i	−0.355833	+	0.192001i
$613$	20.5244	+	35.5492i	0.828971	+	1.43582i	0.898846	+	0.438265i	$0.144407\pi$
$613$	20.5244	+	35.5492i	0.828971	+	1.43582i	−0.0698747	+	0.997556i	$0.522260\pi$
$614$	−3.73199	−	1.35833i	−0.150611	−	0.0548178i
$615$	1.36169	+	5.39113i	0.0549086	+	0.217391i
$616$	−14.8545	+	3.76364i	−0.598505	+	0.151641i
$617$	−9.04615	−	24.8541i	−0.364184	−	1.00059i	−0.977534	−	0.210777i	$-0.932401\pi$
$617$	−9.04615	−	24.8541i	−0.364184	−	1.00059i	0.613350	−	0.789811i	$-0.289822\pi$
$618$	14.3056	+	21.0696i	0.575454	+	0.847542i
$619$	22.7108	−	4.00453i	0.912824	−	0.160956i	0.302539	−	0.953137i	$-0.402166\pi$
$619$	22.7108	−	4.00453i	0.912824	−	0.160956i	0.610286	+	0.792182i	$0.291055\pi$
$620$		−	4.57909i		−	0.183901i
$621$	3.98730	+	6.25259i	0.160005	+	0.250908i
$622$		−	4.47914i		−	0.179597i
$623$	−9.94417	−	4.80342i	−0.398405	−	0.192445i
$624$	−0.0647194	−	0.886551i	−0.00259085	−	0.0354904i
$625$	−17.9529	+	6.53431i	−0.718115	+	0.261373i
$626$	16.1725	+	13.5703i	0.646382	+	0.542379i
$627$	29.6047	−	28.7644i	1.18230	−	1.14874i
$628$	3.27858	−	9.00784i	0.130830	−	0.359452i
$629$	0.632009	+	1.09467i	0.0251999	+	0.0436475i
$630$	3.41223	+	3.71491i	0.135946	+	0.148005i
$631$	−8.92423	+	15.4572i	−0.355268	+	0.615343i	−0.987164	−	0.159711i	$-0.948944\pi$
$631$	−8.92423	+	15.4572i	−0.355268	+	0.615343i	0.631896	+	0.775053i	$0.282277\pi$
$632$	0.882198	+	1.05136i	0.0350920	+	0.0418210i
$633$	−15.0267	+	6.74548i	−0.597259	+	0.268109i
$634$	2.40752	−	13.6537i	0.0956147	−	0.542258i
$635$	−1.54951	+	8.78773i	−0.0614906	+	0.348731i
$636$	−6.64071	−	0.677436i	−0.263321	−	0.0268621i
$637$	1.88053	−	3.06098i	0.0745091	−	0.121280i
$638$	−15.6495	−	9.03524i	−0.619569	−	0.357709i
$639$	1.34667	+	9.17441i	0.0532733	+	0.362934i
$640$	0.550366	−	0.317754i	0.0217551	−	0.0125603i
$641$	−2.07231	+	5.69363i	−0.0818514	+	0.224885i	−0.973867	−	0.227120i	$-0.927069\pi$
$641$	−2.07231	+	5.69363i	−0.0818514	+	0.224885i	0.892015	+	0.452005i	$0.149291\pi$
$642$	−3.30433	−	0.936573i	−0.130412	−	0.0369636i
$643$	−2.10930	+	2.51377i	−0.0831827	+	0.0991333i	−0.806031	−	0.591874i	$-0.798388\pi$
$643$	−2.10930	+	2.51377i	−0.0831827	+	0.0991333i	0.722848	+	0.691007i	$0.242833\pi$
$644$	3.63357	+	1.02699i	0.143183	+	0.0404690i
$645$	−4.39964	+	9.09107i	−0.173236	+	0.357961i
$646$	−2.38228	−	13.5106i	−0.0937294	−	0.531566i
$647$	4.11102			0.161621			0.0808105	−	0.996729i	$-0.474249\pi$
$647$	4.11102			0.161621			0.0808105	+	0.996729i	$0.474249\pi$
$648$	−2.58640	−	8.62035i	−0.101604	−	0.338640i
$649$		−	21.6092i		−	0.848235i
$650$	0.409600	+	2.32295i	0.0160658	+	0.0911138i
$651$	−29.0473	+	15.7012i	−1.13845	+	0.615378i
$652$	−10.4219	+	3.79328i	−0.408155	+	0.148556i
$653$	−7.45623	+	8.88599i	−0.291785	+	0.347736i	−0.891945	−	0.452144i	$-0.850659\pi$
$653$	−7.45623	+	8.88599i	−0.291785	+	0.347736i	0.600160	+	0.799880i	$0.295104\pi$
$654$	−4.30006	+	15.1711i	−0.168146	+	0.593236i
$655$	−1.68332	−	0.612677i	−0.0657726	−	0.0239393i
$656$	−2.52579	−	4.37480i	−0.0986156	−	0.170807i
$657$	−37.1722	−	14.7547i	−1.45023	−	0.575634i
$658$	−13.4524	+	6.05073i	−0.524429	+	0.235882i
$659$	−1.35660	−	1.61674i	−0.0528458	−	0.0629791i	0.738974	−	0.673734i	$-0.235311\pi$
$659$	−1.35660	−	1.61674i	−0.0528458	−	0.0629791i	−0.791820	+	0.610755i	$0.790866\pi$
$660$	6.34240	+	0.647004i	0.246878	+	0.0251846i
$661$	−9.69896	−	1.71019i	−0.377246	−	0.0665186i	−0.0181896	−	0.999835i	$-0.505790\pi$
$661$	−9.69896	−	1.71019i	−0.377246	−	0.0665186i	−0.359056	+	0.933316i	$0.616901\pi$
$662$	0.899283	+	0.158568i	0.0349516	+	0.00616291i
$663$	−1.21376	−	2.70385i	−0.0471384	−	0.105009i
$664$	−4.94346	−	5.89138i	−0.191843	−	0.228630i
$665$	−6.30950	+	2.83794i	−0.244672	+	0.110051i
$666$	−1.07949	+	0.358065i	−0.0418295	+	0.0138747i
$667$	2.22635	+	3.85615i	0.0862046	+	0.149311i
$668$	−20.5392	−	7.47566i	−0.794686	−	0.289242i
$669$	−30.6695	−	31.5654i	−1.18575	−	1.22039i
$670$	−3.21774	+	3.83475i	−0.124312	+	0.148149i
$671$	13.8721	−	5.04905i	0.535528	−	0.194916i
$672$	−3.90281	−	2.40169i	−0.150554	−	0.0926471i
$673$	−3.66938	−	20.8101i	−0.141444	−	0.802169i	−0.970154	−	0.242490i	$-0.922036\pi$
$673$	−3.66938	−	20.8101i	−0.141444	−	0.802169i	0.828710	−	0.559679i	$-0.189075\pi$
$674$		−	9.95481i		−	0.383445i
$675$	9.14925	+	22.0602i	0.352155	+	0.849096i
$676$	−12.7366			−0.489870
$677$	−3.60031	−	20.4184i	−0.138371	−	0.784743i	−0.972453	−	0.233101i	$-0.925113\pi$
$677$	−3.60031	−	20.4184i	−0.138371	−	0.784743i	0.834081	−	0.551642i	$-0.185998\pi$
$678$	19.4389	+	28.6300i	0.746546	+	1.09953i
$679$	45.1759	+	12.7684i	1.73369	+	0.490008i
$680$	1.36200	−	1.62317i	0.0522304	−	0.0622457i
$681$	4.56706	+	18.0817i	0.175010	+	0.692892i
$682$	−14.2735	+	39.2160i	−0.546559	+	1.50166i
$683$	−20.8519	+	12.0389i	−0.797877	+	0.460654i	−0.842728	−	0.538339i	$-0.819052\pi$
$683$	−20.8519	+	12.0389i	−0.797877	+	0.460654i	0.0448513	+	0.998994i	$0.485719\pi$
$684$	12.3388	+	0.355318i	0.471787	+	0.0135859i
$685$	9.01640	+	5.20562i	0.344499	+	0.198897i
$686$	−7.13306	−	17.0915i	−0.272341	−	0.652557i
$687$	−11.6646	+	16.1587i	−0.445032	+	0.616492i
$688$	1.59330	−	9.03606i	0.0607441	−	0.344497i
$689$	0.343455	−	1.94783i	0.0130846	−	0.0742063i
$690$	−1.27372	−	0.919475i	−0.0484898	−	0.0350038i
$691$	8.80297	+	10.4910i	0.334881	+	0.399095i	0.907038	−	0.421049i	$-0.138338\pi$
$691$	8.80297	+	10.4910i	0.334881	+	0.399095i	−0.572157	+	0.820144i	$0.693893\pi$
$692$	−10.2008	+	17.6683i	−0.387776	+	0.671647i
$693$	−17.6431	−	42.4513i	−0.670207	−	1.61259i
$694$	6.82740	+	11.8254i	0.259165	+	0.448886i
$695$	3.03061	−	8.32654i	0.114958	−	0.315843i
$696$	−1.32336	−	5.23939i	−0.0501620	−	0.198599i
$697$	−12.9024	−	10.8264i	−0.488713	−	0.410079i
$698$	−10.6226	+	3.86630i	−0.402070	+	0.146342i
$699$	18.0763	−	12.2733i	0.683710	−	0.464217i
$700$	10.9497	+	5.28913i	0.413860	+	0.199910i
$701$			3.27800i			0.123808i	0.998082	+	0.0619042i	$0.0197173\pi$
$701$			3.27800i			0.123808i	−0.998082	+	0.0619042i	$0.980283\pi$
$702$	2.60326	−	0.578358i	0.0982536	−	0.0218287i
$703$		−	1.55990i		−	0.0588328i
$704$	−5.70389	+	1.00575i	−0.214974	+	0.0379056i
$705$	6.12049	−	0.446804i	0.230511	−	0.0168276i
$706$	6.90830	+	18.9804i	0.259997	+	0.714337i
$707$	−47.1913	+	11.9567i	−1.77481	+	0.449678i
$708$	4.63475	−	4.50321i	0.174185	−	0.169241i
$709$	3.87481	+	1.41031i	0.145521	+	0.0529655i	0.413754	−	0.910389i	$-0.364217\pi$
$709$	3.87481	+	1.41031i	0.145521	+	0.0529655i	−0.268233	+	0.963354i	$0.586440\pi$
$710$	−0.982148	−	1.70113i	−0.0368594	−	0.0638423i
$711$	−2.73629	+	3.07660i	−0.102619	+	0.115381i
$712$	−3.61484	−	2.08703i	−0.135472	−	0.0782147i
$713$	7.87745	−	6.60996i	0.295013	−	0.247545i
$714$	−14.9667	−	3.07414i	−0.560114	−	0.115047i
$715$	−0.328026	+	1.86033i	−0.0122675	+	0.0695723i
$716$	−15.2999	−	2.69778i	−0.571783	−	0.100821i
$717$	27.1630	+	2.77096i	1.01442	+	0.103483i
$718$	−0.0560727	+	0.0470506i	−0.00209262	+	0.00175591i
$719$	8.74299	−	15.1433i	0.326059	−	0.564750i	−0.655668	−	0.755050i	$-0.727613\pi$
$719$	8.74299	−	15.1433i	0.326059	−	0.564750i	0.981726	+	0.190300i	$0.0609460\pi$
$720$	1.18294	+	1.49515i	0.0440857	+	0.0557210i
$721$	−3.91933	+	38.7038i	−0.145964	+	1.44140i
$722$	0.707867	−	1.94485i	0.0263441	−	0.0723797i
$723$	−4.93083	+	17.3965i	−0.183380	+	0.646984i
$724$	−4.38618	+	5.22724i	−0.163011	+	0.194269i
$725$	4.90449	+	13.4750i	0.182148	+	0.500448i
$726$	−35.1507	−	17.0113i	−1.30457	−	0.631347i
$727$	36.7468	−	6.47944i	1.36286	−	0.240309i	0.556065	−	0.831139i	$-0.312310\pi$
$727$	36.7468	−	6.47944i	1.36286	−	0.240309i	0.806797	+	0.590829i	$0.201199\pi$
$728$	0.793935	−	1.10153i	0.0294252	−	0.0408255i
$729$	24.4600	−	11.4327i	0.905927	−	0.423434i
$730$	8.47205			0.313565
$731$	−5.31235	−	30.1279i	−0.196485	−	1.11432i
$732$	3.97378	+	1.92312i	0.146875	+	0.0710805i
$733$	3.33963	+	9.17556i	0.123352	+	0.338907i	0.985964	−	0.166960i	$-0.0533950\pi$
$733$	3.33963	+	9.17556i	0.123352	+	0.338907i	−0.862612	+	0.505867i	$0.831173\pi$
$734$	−23.5238	−	19.7388i	−0.868278	−	0.728572i
$735$	0.350949	+	7.69713i	0.0129450	+	0.283913i
$736$	1.34109	+	0.488119i	0.0494334	+	0.0179923i
$737$	39.5105	−	22.8114i	1.45539	−	0.840270i
$738$	11.8848	−	9.40308i	0.437485	−	0.346132i
$739$	13.3646	−	23.1482i	0.491624	−	0.851518i	−0.508329	−	0.861163i	$-0.669737\pi$
$739$	13.3646	−	23.1482i	0.491624	−	0.851518i	0.999953	+	0.00964443i	$0.00306997\pi$
$740$	0.184561	−	0.154865i	0.00678459	−	0.00569295i
$741$	−0.371190	+	3.63867i	−0.0136360	+	0.133670i
$742$	−7.11090	−	7.30779i	−0.261049	−	0.268277i
$743$	11.1754	+	1.97053i	0.409986	+	0.0722916i	0.374838	−	0.927090i	$-0.377698\pi$
$743$	11.1754	+	1.97053i	0.409986	+	0.0722916i	0.0351486	+	0.999382i	$0.488810\pi$
$744$	−11.3856	+	5.11097i	−0.417415	+	0.187377i
$745$	−9.03477	−	10.7672i	−0.331009	−	0.394481i
$746$	26.5608	+	15.3349i	0.972461	+	0.561450i
$747$	15.3330	−	17.2399i	0.561004	−	0.630776i
$748$	−16.7240	+	9.65559i	−0.611489	+	0.353043i
$749$	−2.95019	−	4.33819i	−0.107797	−	0.158514i
$750$	−7.36072	−	7.57574i	−0.268776	−	0.276627i
$751$	12.2746	+	10.2996i	0.447906	+	0.375837i	0.838658	−	0.544658i	$-0.183341\pi$
$751$	12.2746	+	10.2996i	0.447906	+	0.375837i	−0.390752	+	0.920496i	$0.627785\pi$
$752$	−5.23895	+	1.90682i	−0.191045	+	0.0695346i
$753$	9.22287	−	0.673282i	0.336100	−	0.0245358i
$754$	1.57688	−	0.278046i	0.0574265	−	0.0101258i
$755$	−6.76300			−0.246131
$756$	5.42827	−	12.6307i	0.197424	−	0.459373i
$757$	42.1339			1.53138			0.765691	−	0.643209i	$-0.222397\pi$
$757$	42.1339			1.53138			0.765691	+	0.643209i	$0.222397\pi$
$758$	−10.7371	+	1.89325i	−0.389990	+	0.0687658i
$759$	8.04228	+	11.8448i	0.291916	+	0.429941i
$760$	−2.45720	+	0.894346i	−0.0891318	+	0.0324413i
$761$	31.5496	+	26.4733i	1.14367	+	0.959656i	0.999553	−	0.0299041i	$-0.00952018\pi$
$761$	31.5496	+	26.4733i	1.14367	+	0.959656i	0.144121	+	0.989560i	$0.453965\pi$
$762$	23.5796	−	5.95571i	0.854197	−	0.215753i
$763$	−19.9178	+	13.5451i	−0.721073	+	0.490366i
$764$	−13.7274	+	7.92551i	−0.496639	+	0.286735i
$765$	5.41129	+	3.33549i	0.195646	+	0.120595i
$766$	5.29498	+	3.05706i	0.191315	+	0.110456i
$767$	1.23079	+	1.46680i	0.0444412	+	0.0529629i
$768$	−1.40437	−	1.01378i	−0.0506757	−	0.0365817i
$769$	−33.0863	−	5.83400i	−1.19312	−	0.210380i	−0.458399	−	0.888747i	$-0.651577\pi$
$769$	−33.0863	−	5.83400i	−1.19312	−	0.210380i	−0.734723	+	0.678367i	$0.762688\pi$
$770$	6.79146	+	6.97951i	0.244747	+	0.251524i
$771$	25.1526	+	18.1571i	0.905849	+	0.653913i
$772$	8.34305	−	7.00065i	0.300273	−	0.251959i
$773$	5.04004	−	8.72960i	0.181277	−	0.313982i	−0.761038	−	0.648707i	$-0.775310\pi$
$773$	5.04004	−	8.72960i	0.181277	−	0.313982i	0.942316	+	0.334725i	$0.108643\pi$
$774$	27.5150	+	0.792341i	0.989005	+	0.0284801i
$775$	28.6801	−	16.5585i	1.03022	−	0.594798i
$776$	16.6737	+	6.06873i	0.598551	+	0.217855i
$777$	−1.61522	−	0.639741i	−0.0579457	−	0.0229506i
$778$	14.1037	+	11.8344i	0.505641	+	0.424283i
$779$	7.10905	+	19.5320i	0.254708	+	0.699805i
$780$	−0.467363	+	0.317324i	−0.0167343	+	0.0113620i
$781$	3.10868	+	17.6302i	0.111237	+	0.630858i
$782$	4.75842			0.170161
$783$	14.9750	−	6.21073i	0.535162	−	0.221953i
$784$	−2.21364	−	6.64077i	−0.0790585	−	0.237170i
$785$	−5.99939	+	1.05785i	−0.214127	+	0.0377564i
$786$	0.355464	+	4.86928i	0.0126790	+	0.173682i
$787$	3.38555	+	9.30172i	0.120682	+	0.331570i	0.985294	−	0.170870i	$-0.0546578\pi$
$787$	3.38555	+	9.30172i	0.120682	+	0.331570i	−0.864612	+	0.502440i	$0.832436\pi$
$788$	14.6456	−	17.4540i	0.521729	−	0.621773i
$789$	−6.19878	−	6.37986i	−0.220683	−	0.227129i
$790$	0.298312	−	0.819607i	0.0106135	−	0.0291603i
$791$	−5.32572	+	52.5920i	−0.189361	+	1.86996i
$792$	−5.47037	−	16.4921i	−0.194381	−	0.586020i
$793$	−0.654041	+	1.13283i	−0.0232257	+	0.0402280i
$794$	−21.5622	+	18.0928i	−0.765214	+	0.642090i
$795$	1.73727	+	3.87008i	0.0616148	+	0.137258i
$796$	−10.3081	−	1.81760i	−0.365361	−	0.0644230i
$797$	0.793459	−	4.49993i	0.0281058	−	0.159396i	−0.967525	−	0.252776i	$-0.918656\pi$
$797$	0.793459	−	4.49993i	0.0281058	−	0.159396i	0.995630	+	0.0933808i	$0.0297674\pi$
$798$	14.0987	+	12.5205i	0.499089	+	0.443222i
$799$	−14.2397	+	11.9485i	−0.503765	+	0.422709i
$800$	3.98036	+	2.29806i	0.140727	+	0.0812489i
$801$	4.61977	−	11.6388i	0.163232	−	0.411238i
$802$	15.1593	+	26.2566i	0.535293	+	0.927154i
$803$	−72.5559	−	26.4082i	−2.56044	−	0.931925i
$804$	13.1263	+	3.72050i	0.462930	+	0.131212i
$805$	−0.589363	−	2.32613i	−0.0207723	−	0.0819852i
$806$	−1.26476	−	3.47489i	−0.0445491	−	0.122398i
$807$	−13.6279	+	28.1596i	−0.479725	+	0.991266i
$808$	−18.1207	+	3.19517i	−0.637484	+	0.112406i
$809$			24.5688i			0.863791i	0.901924	+	0.431896i	$0.142155\pi$
$809$			24.5688i			0.863791i	−0.901924	+	0.431896i	$0.857845\pi$
$810$	−3.92251	+	4.16262i	−0.137823	+	0.146260i
$811$		−	19.8079i		−	0.695548i	−0.937578	−	0.347774i	$-0.886938\pi$
$811$		−	19.8079i		−	0.695548i	0.937578	−	0.347774i	$-0.113062\pi$
$812$	3.59039	−	7.43292i	0.125998	−	0.260845i
$813$	14.2435	+	6.89315i	0.499540	+	0.241753i
$814$	−2.06334	+	0.750994i	−0.0723200	+	0.0263223i
$815$	5.39931	+	4.53056i	0.189130	+	0.158699i
$816$	−5.55610	−	1.57481i	−0.194502	−	0.0551293i
$817$	−12.9126	+	35.4770i	−0.451753	+	1.24118i
$818$	5.03034	+	8.71280i	0.175882	+	0.304636i
$819$	3.61547	+	1.87663i	0.126335	+	0.0655748i
$820$	−1.60516	+	2.78022i	−0.0560546	+	0.0970895i
$821$	6.40767	+	7.63636i	0.223629	+	0.266511i	0.866180	−	0.499732i	$-0.166568\pi$
$821$	6.40767	+	7.63636i	0.223629	+	0.266511i	−0.642551	+	0.766243i	$0.722124\pi$
$822$	2.87970	−	28.2289i	0.100441	−	0.984597i
$823$	−2.85161	+	16.1723i	−0.0994010	+	0.563731i	0.893909	+	0.448249i	$0.147952\pi$
$823$	−2.85161	+	16.1723i	−0.0994010	+	0.563731i	−0.993310	+	0.115482i	$0.963159\pi$
$824$	−2.55323	+	14.4801i	−0.0889460	+	0.504438i
$825$	18.8824	+	42.0639i	0.657401	+	1.46448i
$826$	9.84441	−	0.725979i	0.342531	−	0.0252601i
$827$	−20.3061	−	11.7237i	−0.706112	−	0.407674i	0.103508	−	0.994629i	$-0.466993\pi$
$827$	−20.3061	−	11.7237i	−0.706112	−	0.407674i	−0.809620	+	0.586955i	$0.800327\pi$
$828$	−0.864534	+	4.19330i	−0.0300446	+	0.145727i
$829$	11.6276	−	6.71317i	0.403842	−	0.233158i	−0.284299	−	0.958736i	$-0.591761\pi$
$829$	11.6276	−	6.71317i	0.403842	−	0.233158i	0.688140	+	0.725578i	$0.258427\pi$
$830$	−1.67161	+	4.59272i	−0.0580226	+	0.159416i
$831$	35.4534	−	34.4472i	1.22986	−	1.19496i
$832$	0.329886	−	0.393143i	0.0114368	−	0.0136298i
$833$	−14.5084	−	18.2819i	−0.502686	−	0.633430i
$834$	−24.0860	+	1.75831i	−0.834029	+	0.0608852i
$835$	2.41207	+	13.6795i	0.0834730	+	0.473399i
$836$	23.8316			0.824232
$837$	−20.1309	−	31.5678i	−0.695825	−	1.09114i
$838$			24.2308i			0.837039i
$839$	1.69849	+	9.63259i	0.0586382	+	0.332554i	0.999988	−	0.00487812i	$-0.00155276\pi$
$839$	1.69849	+	9.63259i	0.0586382	+	0.332554i	−0.941350	+	0.337432i	$0.890442\pi$
$840$	−0.0816747	+	2.91112i	−0.00281805	+	0.100443i
$841$	−18.1039	+	6.58930i	−0.624274	+	0.227217i
$842$	−0.404180	+	0.481683i	−0.0139290	+	0.0165999i
$843$	9.75784	−	2.46463i	0.336078	−	0.0848864i
$844$	−8.93621	−	3.25251i	−0.307597	−	0.111956i
$845$	4.04711	+	7.00980i	0.139225	+	0.241144i
$846$	−7.94236	−	14.7194i	−0.273064	−	0.506065i
$847$	−24.4691	−	54.4013i	−0.840767	−	1.86925i
$848$	−2.47725	−	2.95227i	−0.0850690	−	0.101381i
$849$	−23.5596	+	32.6364i	−0.808562	+	1.12008i
$850$	15.0915	+	2.66104i	0.517634	+	0.0912729i
$851$	0.532831	+	0.0939525i	0.0182652	+	0.00322065i
$852$	−3.13351	+	4.34077i	−0.107352	+	0.148712i
$853$	−4.34115	−	5.17358i	−0.148638	−	0.177140i	0.686588	−	0.727047i	$-0.259108\pi$
$853$	−4.34115	−	5.17358i	−0.148638	−	0.177140i	−0.835226	+	0.549907i	$0.814663\pi$
$854$	2.76622	+	6.15005i	0.0946581	+	0.210450i
$855$	−3.72516	−	6.90378i	−0.127398	−	0.236104i
$856$	−0.991454	−	1.71725i	−0.0338872	−	0.0586944i
$857$	52.1248	+	18.9719i	1.78055	+	0.648067i	0.999728	+	0.0233112i	$0.00742085\pi$
$857$	52.1248	+	18.9719i	1.78055	+	0.648067i	0.780820	+	0.624756i	$0.214801\pi$
$858$	4.99170	−	1.26080i	0.170414	−	0.0430430i
$859$	16.4364	−	19.5882i	0.560804	−	0.668340i	−0.408912	−	0.912574i	$-0.634092\pi$
$859$	16.4364	−	19.5882i	0.560804	−	0.668340i	0.969716	+	0.244233i	$0.0785363\pi$
$860$	−5.47942	+	1.99435i	−0.186847	+	0.0680067i
$861$	23.1401	+	0.649223i	0.788614	+	0.0221255i
$862$	−0.503172	−	2.85363i	−0.0171381	−	0.0971950i
$863$			50.5355i			1.72025i	0.510086	+	0.860123i	$0.329614\pi$
$863$			50.5355i			1.72025i	−0.510086	+	0.860123i	$0.670386\pi$
$864$	2.39724	−	4.61012i	0.0815558	−	0.156840i
$865$	12.9654			0.440836
$866$	−1.00358	−	5.69160i	−0.0341031	−	0.193408i
$867$	10.1630	−	0.741916i	0.345155	−	0.0251968i
$868$	−18.3450	−	5.18501i	−0.622671	−	0.175991i
$869$	−5.10959	+	6.08937i	−0.173331	+	0.206568i
$870$	−2.46308	+	2.39317i	−0.0835063	+	0.0811362i
$871$	−1.38265	+	3.79879i	−0.0468492	+	0.128717i
$872$	−7.88436	+	4.55204i	−0.266998	+	0.154151i
$873$	−10.7487	+	52.1348i	−0.363787	+	1.76450i
$874$	−5.08554	−	2.93614i	−0.172021	−	0.0993164i
$875$	−1.18665	−	16.0912i	−0.0401161	−	0.543982i
$876$	−9.45612	−	21.0651i	−0.319493	−	0.711725i
$877$	0.912675	−	5.17604i	0.0308189	−	0.174782i	−0.965513	−	0.260354i	$-0.916161\pi$
$877$	0.912675	−	5.17604i	0.0308189	−	0.174782i	0.996332	+	0.0855719i	$0.0272717\pi$
$878$	6.59172	−	37.3835i	0.222460	−	1.26163i
$879$	−2.93429	+	28.7640i	−0.0989710	+	0.970185i
$880$	2.36597	+	2.81965i	0.0797567	+	0.0950503i
$881$	5.72759	−	9.92048i	0.192968	−	0.334230i	−0.753265	−	0.657717i	$-0.771522\pi$
$881$	5.72759	−	9.92048i	0.192968	−	0.334230i	0.946232	+	0.323488i	$0.104855\pi$
$882$	18.7466	−	9.46380i	0.631232	−	0.318663i
$883$	−13.5072	−	23.3952i	−0.454554	−	0.787310i	0.544109	−	0.839015i	$-0.316868\pi$
$883$	−13.5072	−	23.3952i	−0.454554	−	0.787310i	−0.998662	+	0.0517044i	$0.983535\pi$
$884$	0.585245	−	1.60795i	0.0196839	−	0.0540811i
$885$	−3.95112	−	1.11990i	−0.132816	−	0.0376450i
$886$	−1.79977	−	1.51019i	−0.0604645	−	0.0507357i
$887$	24.1190	−	8.77858i	0.809835	−	0.294756i	0.0962794	−	0.995354i	$-0.469306\pi$
$887$	24.1190	−	8.77858i	0.809835	−	0.294756i	0.713556	+	0.700598i	$0.247084\pi$
$888$	−0.591059	−	0.286044i	−0.0198346	−	0.00959901i
$889$	33.4514	+	16.1583i	1.12192	+	0.541933i
$890$			2.65265i			0.0889170i
$891$	46.5683	−	23.4225i	1.56010	−	0.784683i
$892$		−	25.4099i		−	0.850788i
$893$	22.5914	−	3.98347i	0.755992	−	0.133302i
$894$	−16.6877	+	34.4822i	−0.558121	+	1.15326i
$895$	3.37683	+	9.27776i	0.112875	+	0.310121i
$896$	−0.649813	−	2.56471i	−0.0217087	−	0.0856810i
$897$	−1.22054	−	0.345947i	−0.0407526	−	0.0115508i
$898$	−8.58099	−	3.12322i	−0.286351	−	0.104223i
$899$	−11.2403	−	19.4688i	−0.374885	−	0.649319i
$900$	−5.08691	+	12.8157i	−0.169564	+	0.427191i
$901$	−11.1281	−	6.42482i	−0.370731	−	0.214042i
$902$	22.4131	−	18.8068i	0.746273	−	0.626198i
$903$	31.4394	+	27.9201i	1.04624	+	0.929124i
$904$	−3.46941	+	19.6760i	−0.115391	+	0.654415i
$905$	4.27062	+	0.753026i	0.141960	+	0.0250314i
$906$	7.54855	+	16.8157i	0.250784	+	0.558664i
$907$	−38.9812	+	32.7091i	−1.29435	+	1.08609i	−0.303259	+	0.952908i	$0.598075\pi$
$907$	−38.9812	+	32.7091i	−1.29435	+	1.08609i	−0.991092	+	0.133181i	$0.957481\pi$
$908$	−5.38366	+	9.32477i	−0.178663	+	0.309453i
$909$	−17.3788	−	52.3937i	−0.576419	−	1.73779i
$910$	−0.858523	−	0.0869382i	−0.0284597	−	0.00288197i
$911$	16.7564	−	46.0378i	0.555164	−	1.52530i	−0.271406	−	0.962465i	$-0.587489\pi$
$911$	16.7564	−	46.0378i	0.555164	−	1.52530i	0.826570	−	0.562834i	$-0.190289\pi$
$912$	4.96634	+	5.11141i	0.164452	+	0.169256i
$913$	28.6319	−	34.1222i	0.947579	−	1.12928i
$914$	7.94883	+	21.8392i	0.262924	+	0.722378i
$915$	−0.204266	−	2.79811i	−0.00675283	−	0.0925028i
$916$	−11.3312	+	1.99800i	−0.374394	+	0.0660158i
$917$	−4.36060	+	6.05005i	−0.144000	+	0.199790i
$918$	2.25362	−	17.1777i	0.0743806	−	0.566949i
$919$	20.0385			0.661008			0.330504	−	0.943805i	$-0.392781\pi$
$919$	20.0385			0.661008			0.330504	+	0.943805i	$0.392781\pi$
$920$	−0.157494	−	0.893195i	−0.00519244	−	0.0294478i
$921$	5.69102	−	3.86402i	0.187526	−	0.127324i
$922$	−8.78150	−	24.1270i	−0.289203	−	0.794580i
$923$	−1.21517	−	1.01965i	−0.0399978	−	0.0335621i
$924$	9.77372	−	24.6767i	0.321532	−	0.811803i
$925$	1.63735	+	0.595948i	0.0538359	+	0.0195947i
$926$	−22.6891	+	13.0995i	−0.745609	+	0.430478i
$927$	−44.0921	−	1.26971i	−1.44818	−	0.0417027i
$928$	1.55998	−	2.70197i	0.0512089	−	0.0886965i
$929$	−35.3221	+	29.6387i	−1.15888	+	0.972416i	−0.999890	−	0.0148643i	$-0.995268\pi$
$929$	−35.3221	+	29.6387i	−1.15888	+	0.972416i	−0.158991	+	0.987280i	$0.550824\pi$
$930$	6.43072	+	4.64220i	0.210871	+	0.152224i
$931$	4.22513	+	28.4910i	0.138473	+	0.933753i
$932$	12.4230	+	2.19051i	0.406928	+	0.0717524i
$933$	6.29036	+	4.54088i	0.205937	+	0.148662i
$934$	−5.01322	−	5.97452i	−0.164038	−	0.195492i
$935$	10.6282	+	6.13621i	0.347580	+	0.200675i
$936$	1.31065	+	0.807880i	0.0428400	+	0.0264064i
$937$	−11.5715	+	6.68078i	−0.378023	+	0.218252i	−0.676958	−	0.736022i	$-0.736702\pi$
$937$	−11.5715	+	6.68078i	−0.378023	+	0.218252i	0.298935	+	0.954274i	$0.403369\pi$
$938$	11.7195	+	17.2333i	0.382655	+	0.562687i
$939$	−35.4531	+	8.95472i	−1.15697	+	0.292226i
$940$	2.71415	+	2.27744i	0.0885257	+	0.0742819i
$941$	−36.2054	+	13.1777i	−1.18026	+	0.429580i	−0.856294	−	0.516488i	$-0.827239\pi$
$941$	−36.2054	+	13.1777i	−1.18026	+	0.429580i	−0.323967	+	0.946068i	$0.605017\pi$
$942$	9.32653	+	13.7363i	0.303875	+	0.447554i
$943$	−7.09990	+	1.25190i	−0.231205	+	0.0407676i
$944$	3.73094			0.121432
$945$	−8.67635	+	1.02591i	−0.282242	+	0.0333728i
$946$	53.1432			1.72783
$947$	47.4571	−	8.36796i	1.54215	−	0.271922i	0.663054	−	0.748572i	$-0.269260\pi$
$947$	47.4571	−	8.36796i	1.54215	−	0.271922i	0.879093	+	0.476650i	$0.158149\pi$
$948$	−2.37086	+	0.173076i	−0.0770018	+	0.00562124i
$949$	6.42910	−	2.34000i	0.208697	−	0.0759596i
$950$	−14.4870	−	12.1561i	−0.470021	−	0.394394i
$951$	16.7341	+	17.2229i	0.542640	+	0.558492i
$952$	−4.96062	−	7.29449i	−0.160774	−	0.236416i
$953$	−7.60492	+	4.39070i	−0.246348	+	0.142229i	−0.618091	−	0.786107i	$-0.712094\pi$
$953$	−7.60492	+	4.39070i	−0.246348	+	0.142229i	0.371743	+	0.928336i	$0.378760\pi$
$954$	7.68361	−	8.63922i	0.248766	−	0.279705i
$955$	8.72386	+	5.03673i	0.282298	+	0.162985i
$956$	10.1329	+	12.0759i	0.327720	+	0.390562i
$957$	28.5540	−	12.8178i	0.923019	−	0.414342i
$958$	39.3804	+	6.94383i	1.27232	+	0.224345i
$959$	31.0646	−	30.2276i	1.00313	−	0.976101i
$960$	−0.111709	+	1.09505i	−0.00360538	+	0.0353426i
$961$	−16.0239	+	13.4457i	−0.516901	+	0.433731i
$962$	0.0972818	−	0.168497i	0.00313649	−	0.00543256i
$963$	4.66517	−	3.69101i	0.150333	−	0.118941i
$964$	−9.04091	+	5.21977i	−0.291188	+	0.168117i
$965$	−6.50396	−	2.36725i	−0.209370	−	0.0762044i
$966$	−5.12592	+	4.06173i	−0.164924	+	0.130684i
$967$	2.92554	+	2.45482i	0.0940791	+	0.0789417i	0.688614	−	0.725128i	$-0.258219\pi$
$967$	2.92554	+	2.45482i	0.0940791	+	0.0789417i	−0.594535	+	0.804070i	$0.702664\pi$
$968$	−7.71116	−	21.1862i	−0.247846	−	0.680952i
$969$	21.3889	+	10.3512i	0.687110	+	0.332528i
$970$	−1.95811	−	11.1050i	−0.0628712	−	0.356560i
$971$	34.9807			1.12258			0.561291	−	0.827618i	$-0.310305\pi$
$971$	34.9807			1.12258			0.561291	+	0.827618i	$0.310305\pi$
$972$	14.7282	+	5.10691i	0.472407	+	0.163804i
$973$	−29.9266	−	21.5698i	−0.959404	−	0.691495i
$974$	−33.4600	+	5.89989i	−1.07213	+	0.189045i
$975$	−3.67752	−	1.77974i	−0.117775	−	0.0569974i
$976$	0.871745	+	2.39510i	0.0279039	+	0.0766653i
$977$	2.25071	−	2.68229i	0.0720065	−	0.0858141i	−0.728839	−	0.684686i	$-0.759940\pi$
$977$	2.25071	−	2.68229i	0.0720065	−	0.0858141i	0.800845	+	0.598871i	$0.204384\pi$
$978$	5.23844	−	18.4818i	0.167507	−	0.590983i
$979$	8.26856	−	22.7177i	0.264264	−	0.726061i
$980$	−2.95146	+	3.32844i	−0.0942810	+	0.106323i
$981$	−16.9464	−	21.4190i	−0.541058	−	0.683857i
$982$	−8.46619	+	14.6639i	−0.270167	+	0.467943i
$983$	5.06013	−	4.24596i	0.161393	−	0.135425i	−0.558515	−	0.829495i	$-0.688629\pi$
$983$	5.06013	−	4.24596i	0.161393	−	0.135425i	0.719908	+	0.694070i	$0.244184\pi$
$984$	8.70442	+	0.887960i	0.277487	+	0.0283071i
$985$	−14.2598	−	2.51439i	−0.454355	−	0.0801151i
$986$	1.80638	−	10.2445i	0.0575268	−	0.326251i
$987$	5.14036	−	25.0262i	0.163620	−	0.796593i
$988$	−1.61765	+	1.35737i	−0.0514642	+	0.0431836i
$989$	−11.3405	−	6.54744i	−0.360607	−	0.208197i
$990$	−7.33845	+	8.25113i	−0.233231	+	0.262238i
$991$	−24.9020	−	43.1315i	−0.791038	−	1.37012i	−0.925325	−	0.379175i	$-0.876208\pi$
$991$	−24.9020	−	43.1315i	−0.791038	−	1.37012i	0.134288	−	0.990942i	$-0.457125\pi$
$992$	−6.77086	−	2.46439i	−0.214975	−	0.0782445i
$993$	−1.13436	+	1.10217i	−0.0359980	+	0.0349763i
$994$	−7.92728	+	2.00851i	−0.251438	+	0.0637061i
$995$	2.27510	+	6.25078i	0.0721255	+	0.198163i
$996$	13.2853	−	0.969841i	0.420959	−	0.0307306i
$997$	−31.5063	+	5.55541i	−0.997815	+	0.175942i	−0.648623	−	0.761110i	$-0.724655\pi$
$997$	−31.5063	+	5.55541i	−0.997815	+	0.175942i	−0.349192	+	0.937051i	$0.613544\pi$
$998$			16.7824i			0.531239i
$999$	0.591518	−	1.87900i	0.0187148	−	0.0594490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.41.8	yes	144
7.6	odd	2	inner	378.2.z.a.41.5	✓	144
27.2	odd	18	inner	378.2.z.a.83.5	yes	144
189.83	even	18	inner	378.2.z.a.83.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.5	✓	144	7.6	odd	2	inner
378.2.z.a.41.8	yes	144	1.1	even	1	trivial
378.2.z.a.83.5	yes	144	27.2	odd	18	inner
378.2.z.a.83.8	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)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.754516 - 1.55907i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-0.486827 - 0.408497i) q^{5} +(-0.472323 + 1.66641i) q^{6} +(-2.18779 + 1.48781i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.86141 - 2.35269i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.754516 - 1.55907i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-0.486827 - 0.408497i) q^{5} +(-0.472323 + 1.66641i) q^{6} +(-2.18779 + 1.48781i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.86141 - 2.35269i) q^{9} +(0.550366 + 0.317754i) q^{10} +(-3.72295 - 4.43684i) q^{11} +(0.175779 - 1.72311i) q^{12} +(0.505415 + 0.0891184i) q^{13} +(1.89620 - 1.84511i) q^{14} +(-1.00419 + 0.450782i) q^{15} +(0.766044 - 0.642788i) q^{16} +(1.66709 - 2.88748i) q^{17} +(2.24167 + 1.99372i) q^{18} +(-3.56339 + 2.05732i) q^{19} +(-0.597182 - 0.217357i) q^{20} +(0.668877 + 4.53350i) q^{21} +(4.43684 + 3.72295i) q^{22} +(-0.488119 - 1.34109i) q^{23} +(0.126106 + 1.72745i) q^{24} +(-0.798110 - 4.52630i) q^{25} -0.513212 q^{26} +(-5.07248 + 1.12694i) q^{27} +(-1.54699 + 2.14635i) q^{28} +(-3.07257 + 0.541776i) q^{29} +(0.910661 - 0.618310i) q^{30} +(2.46439 + 6.77086i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-9.72638 + 2.45669i) q^{33} +(-1.14036 + 3.13310i) q^{34} +(1.67284 + 0.169400i) q^{35} +(-2.55382 - 1.57416i) q^{36} +(-0.189555 + 0.328318i) q^{37} +(3.15200 - 2.64485i) q^{38} +(0.520286 - 0.720738i) q^{39} +(0.625853 + 0.110355i) q^{40} +(0.877198 - 4.97484i) q^{41} +(-1.44595 - 4.34847i) q^{42} +(7.02881 - 5.89787i) q^{43} +(-5.01592 - 2.89594i) q^{44} +(-0.0548789 + 1.90573i) q^{45} +(0.713582 + 1.23596i) q^{46} +(-5.23895 - 1.90682i) q^{47} +(-0.424160 - 1.67931i) q^{48} +(2.57286 - 6.51002i) q^{49} +(1.57197 + 4.31895i) q^{50} +(-3.24395 - 4.77776i) q^{51} +(0.505415 - 0.0891184i) q^{52} -3.85391i q^{53} +(4.79972 - 1.99064i) q^{54} +3.68079i q^{55} +(1.15078 - 2.38237i) q^{56} +(0.518884 + 7.10787i) q^{57} +(2.93181 - 1.06709i) q^{58} +(2.85807 + 2.39820i) q^{59} +(-0.789458 + 0.767051i) q^{60} +(-0.871745 + 2.39510i) q^{61} +(-3.60270 - 6.24006i) q^{62} +(7.57273 + 2.37777i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-0.209646 - 0.249846i) q^{65} +(9.15202 - 4.10833i) q^{66} +(-1.36783 + 7.75736i) q^{67} +(0.578974 - 3.28353i) q^{68} +(-2.45916 - 0.250865i) q^{69} +(-1.67684 + 0.123659i) q^{70} +(-2.67680 - 1.54545i) q^{71} +(2.78837 + 1.10678i) q^{72} +(11.5451 - 6.66557i) q^{73} +(0.129663 - 0.356246i) q^{74} +(-7.65902 - 2.17086i) q^{75} +(-2.64485 + 3.15200i) q^{76} +(14.7462 + 4.16785i) q^{77} +(-0.387227 + 0.800135i) q^{78} +(-0.238325 - 1.35161i) q^{79} -0.635508 q^{80} +(-2.07029 + 8.75865i) q^{81} +5.05158i q^{82} +(1.33547 + 7.57382i) q^{83} +(2.17909 + 4.03133i) q^{84} +(-1.99111 + 0.724706i) q^{85} +(-5.89787 + 7.02881i) q^{86} +(-1.47363 + 5.19913i) q^{87} +(5.44259 + 1.98094i) q^{88} +(2.08703 + 3.61484i) q^{89} +(-0.276882 - 1.88631i) q^{90} +(-1.23833 + 0.556988i) q^{91} +(-0.917363 - 1.09327i) q^{92} +(12.4157 + 1.26655i) q^{93} +(5.49047 + 0.968119i) q^{94} +(2.57517 + 0.454071i) q^{95} +(0.709325 + 1.58014i) q^{96} +(-11.4055 - 13.5925i) q^{97} +(-1.40332 + 6.85789i) q^{98} +(-3.50856 + 17.0177i) 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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