LMFDB - Embedded newform 378.2.z.a.41.4

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			41.4
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(-0.826027 - 1.52239i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.99843 + 1.67688i) q^{5} +(1.07784 + 1.35583i) q^{6} +(0.187552 + 2.63910i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.63536 + 2.51507i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.826027 - 1.52239i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.99843 + 1.67688i) q^{5} +(1.07784 + 1.35583i) q^{6} +(0.187552 + 2.63910i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.63536 + 2.51507i) q^{9} +(-2.25926 - 1.30438i) q^{10} +(1.10056 + 1.31159i) q^{11} +(-1.29690 - 1.14806i) q^{12} +(-6.54906 - 1.15478i) q^{13} +(-0.642977 - 2.56643i) q^{14} +(0.902117 - 4.42755i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-3.19200 + 5.52870i) q^{17} +(1.17378 - 2.76084i) q^{18} +(1.36673 - 0.789081i) q^{19} +(2.45144 + 0.892251i) q^{20} +(3.86282 - 2.46549i) q^{21} +(-1.31159 - 1.10056i) q^{22} +(2.89352 + 7.94988i) q^{23} +(1.47656 + 0.905418i) q^{24} +(0.313551 + 1.77824i) q^{25} +6.65009 q^{26} +(5.17978 + 0.412142i) q^{27} +(1.07887 + 2.41579i) q^{28} +(3.93278 - 0.693456i) q^{29} +(-0.119576 + 4.51694i) q^{30} +(-0.301809 - 0.829214i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(1.08767 - 2.75889i) q^{33} +(2.18346 - 5.99900i) q^{34} +(-4.05064 + 5.58856i) q^{35} +(-0.676530 + 2.92272i) q^{36} +(-2.57189 + 4.45464i) q^{37} +(-1.20894 + 1.01442i) q^{38} +(3.65167 + 10.9241i) q^{39} +(-2.56913 - 0.453008i) q^{40} +(0.142302 - 0.807035i) q^{41} +(-3.37600 + 3.09881i) q^{42} +(6.82048 - 5.72306i) q^{43} +(1.48277 + 0.856080i) q^{44} +(-7.48564 + 2.28390i) q^{45} +(-4.23005 - 7.32665i) q^{46} +(6.60763 + 2.40498i) q^{47} +(-1.61135 - 0.635261i) q^{48} +(-6.92965 + 0.989938i) q^{49} +(-0.617575 - 1.69677i) q^{50} +(11.0535 + 0.292619i) q^{51} +(-6.54906 + 1.15478i) q^{52} -6.75035i q^{53} +(-5.17266 + 0.493579i) q^{54} +4.46663i q^{55} +(-1.48197 - 2.19175i) q^{56} +(-2.33024 - 1.42890i) q^{57} +(-3.75262 + 1.36584i) q^{58} +(-0.690522 - 0.579417i) q^{59} +(-0.666598 - 4.46908i) q^{60} +(1.46604 - 4.02791i) q^{61} +(0.441216 + 0.764208i) q^{62} +(-6.94424 - 3.84416i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-11.1514 - 13.2897i) q^{65} +(-0.592069 + 2.90584i) q^{66} +(-2.06631 + 11.7186i) q^{67} +(-1.10857 + 6.28701i) q^{68} +(9.71272 - 10.9719i) q^{69} +(3.01866 - 6.20704i) q^{70} +(2.69703 + 1.55713i) q^{71} +(0.158726 - 2.99580i) q^{72} +(-1.04793 + 0.605023i) q^{73} +(1.75928 - 4.83357i) q^{74} +(2.44817 - 1.94622i) q^{75} +(1.01442 - 1.20894i) q^{76} +(-3.25500 + 3.15046i) q^{77} +(-5.49315 - 10.1240i) q^{78} +(-1.88666 - 10.6998i) q^{79} +2.60877 q^{80} +(-3.65120 - 8.22610i) q^{81} +0.819485i q^{82} +(-0.170323 - 0.965952i) q^{83} +(2.78661 - 3.63797i) q^{84} +(-15.6500 + 5.69613i) q^{85} +(-5.72306 + 6.82048i) q^{86} +(-4.30430 - 5.41443i) q^{87} +(-1.60890 - 0.585593i) q^{88} +(1.37986 + 2.38999i) q^{89} +(6.97532 - 3.54907i) q^{90} +(1.81927 - 17.5002i) q^{91} +(5.43804 + 6.48081i) q^{92} +(-1.01309 + 1.14443i) q^{93} +(-6.92487 - 1.22104i) q^{94} +(4.05451 + 0.714919i) q^{95} +(1.69718 + 0.345802i) q^{96} +(11.7988 + 14.0613i) q^{97} +(6.65247 - 2.17822i) q^{98} +(-5.09855 + 0.623055i) 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
$3$	−0.826027	−	1.52239i	−0.476907	−	0.878954i
$3$	−0.826027	−	1.52239i	−0.476907	−	0.878954i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	1.99843	+	1.67688i	0.893726	+	0.749925i	0.968954	−	0.247241i	$-0.0795240\pi$
$5$	1.99843	+	1.67688i	0.893726	+	0.749925i	−0.0752280	+	0.997166i	$0.523968\pi$
$6$	1.07784	+	1.35583i	0.440026	+	0.553514i
$7$	0.187552	+	2.63910i	0.0708882	+	0.997484i
$7$	0.187552	+	2.63910i	0.0708882	+	0.997484i
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−1.63536	+	2.51507i	−0.545120	+	0.838358i
$10$	−2.25926	−	1.30438i	−0.714440	−	0.412482i
$11$	1.10056	+	1.31159i	0.331830	+	0.395459i	0.906001	−	0.423276i	$-0.139120\pi$
$11$	1.10056	+	1.31159i	0.331830	+	0.395459i	−0.574171	+	0.818735i	$0.694676\pi$
$12$	−1.29690	−	1.14806i	−0.374383	−	0.331417i
$13$	−6.54906	−	1.15478i	−1.81638	−	0.320277i	−0.841039	−	0.540974i	$-0.818056\pi$
$13$	−6.54906	−	1.15478i	−1.81638	−	0.320277i	−0.975342	+	0.220697i	$0.929167\pi$
$14$	−0.642977	−	2.56643i	−0.171843	−	0.685908i
$15$	0.902117	−	4.42755i	0.232926	−	1.14319i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−3.19200	+	5.52870i	−0.774173	+	1.34091i	0.161085	+	0.986941i	$0.448501\pi$
$17$	−3.19200	+	5.52870i	−0.774173	+	1.34091i	−0.935258	+	0.353967i	$0.884833\pi$
$18$	1.17378	−	2.76084i	0.276662	−	0.650737i
$19$	1.36673	−	0.789081i	0.313549	−	0.181028i	−0.334965	−	0.942231i	$-0.608724\pi$
$19$	1.36673	−	0.789081i	0.313549	−	0.181028i	0.648513	+	0.761203i	$0.275391\pi$
$20$	2.45144	+	0.892251i	0.548159	+	0.199513i
$21$	3.86282	−	2.46549i	0.842936	−	0.538014i
$22$	−1.31159	−	1.10056i	−0.279632	−	0.234639i
$23$	2.89352	+	7.94988i	0.603341	+	1.65767i	0.744455	+	0.667672i	$0.232709\pi$
$23$	2.89352	+	7.94988i	0.603341	+	1.65767i	−0.141114	+	0.989993i	$0.545069\pi$
$24$	1.47656	+	0.905418i	0.301401	+	0.184818i
$25$	0.313551	+	1.77824i	0.0627102	+	0.355647i
$26$	6.65009			1.30419
$27$	5.17978	+	0.412142i	0.996849	+	0.0793167i
$28$	1.07887	+	2.41579i	0.203886	+	0.456542i
$29$	3.93278	−	0.693456i	0.730300	−	0.128772i	0.203879	−	0.978996i	$-0.434645\pi$
$29$	3.93278	−	0.693456i	0.730300	−	0.128772i	0.526420	+	0.850224i	$0.323534\pi$
$30$	−0.119576	+	4.51694i	−0.0218316	+	0.824676i
$31$	−0.301809	−	0.829214i	−0.0542065	−	0.148931i	0.909634	−	0.415410i	$-0.136362\pi$
$31$	−0.301809	−	0.829214i	−0.0542065	−	0.148931i	−0.963841	+	0.266479i	$0.914140\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	1.08767	−	2.75889i	0.189339	−	0.480260i
$34$	2.18346	−	5.99900i	0.374460	−	1.02882i
$35$	−4.05064	+	5.58856i	−0.684684	+	0.944638i
$36$	−0.676530	+	2.92272i	−0.112755	+	0.487120i
$37$	−2.57189	+	4.45464i	−0.422816	+	0.732339i	−0.996214	−	0.0869382i	$-0.972292\pi$
$37$	−2.57189	+	4.45464i	−0.422816	+	0.732339i	0.573398	+	0.819277i	$0.305625\pi$
$38$	−1.20894	+	1.01442i	−0.196116	+	0.164561i
$39$	3.65167	+	10.9241i	0.584736	+	1.74926i
$40$	−2.56913	−	0.453008i	−0.406216	−	0.0716268i
$41$	0.142302	−	0.807035i	0.0222239	−	0.126038i	−0.971677	−	0.236311i	$-0.924062\pi$
$41$	0.142302	−	0.807035i	0.0222239	−	0.126038i	0.993901	+	0.110273i	$0.0351726\pi$
$42$	−3.37600	+	3.09881i	−0.520929	+	0.478156i
$43$	6.82048	−	5.72306i	1.04011	−	0.872758i	0.0480935	−	0.998843i	$-0.484685\pi$
$43$	6.82048	−	5.72306i	1.04011	−	0.872758i	0.992020	+	0.126084i	$0.0402410\pi$
$44$	1.48277	+	0.856080i	0.223537	+	0.129059i
$45$	−7.48564	+	2.28390i	−1.11589	+	0.340463i
$46$	−4.23005	−	7.32665i	−0.623686	−	1.08026i
$47$	6.60763	+	2.40498i	0.963823	+	0.350803i	0.775530	−	0.631310i	$-0.217483\pi$
$47$	6.60763	+	2.40498i	0.963823	+	0.350803i	0.188292	+	0.982113i	$0.439705\pi$
$48$	−1.61135	−	0.635261i	−0.232578	−	0.0916920i
$49$	−6.92965	+	0.989938i	−0.989950	+	0.141420i
$50$	−0.617575	−	1.69677i	−0.0873383	−	0.239960i
$51$	11.0535	+	0.292619i	1.54780	+	0.0409749i
$52$	−6.54906	+	1.15478i	−0.908191	+	0.160139i
$53$		−	6.75035i		−	0.927232i	−0.886036	−	0.463616i	$-0.846552\pi$
$53$		−	6.75035i		−	0.927232i	0.886036	−	0.463616i	$-0.153448\pi$
$54$	−5.17266	+	0.493579i	−0.703909	+	0.0671676i
$55$			4.46663i			0.602280i
$56$	−1.48197	−	2.19175i	−0.198037	−	0.292885i
$57$	−2.33024	−	1.42890i	−0.308648	−	0.189262i
$58$	−3.75262	+	1.36584i	−0.492743	+	0.179344i
$59$	−0.690522	−	0.579417i	−0.0898983	−	0.0754336i	0.596731	−	0.802441i	$-0.296466\pi$
$59$	−0.690522	−	0.579417i	−0.0898983	−	0.0754336i	−0.686629	+	0.727008i	$0.740910\pi$
$60$	−0.666598	−	4.46908i	−0.0860574	−	0.576955i
$61$	1.46604	−	4.02791i	0.187707	−	0.515722i	−0.809767	−	0.586752i	$-0.800406\pi$
$61$	1.46604	−	4.02791i	0.187707	−	0.515722i	0.997474	+	0.0710302i	$0.0226287\pi$
$62$	0.441216	+	0.764208i	0.0560344	+	0.0970545i
$63$	−6.94424	−	3.84416i	−0.874892	−	0.484319i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−11.1514	−	13.2897i	−1.38316	−	1.64839i
$66$	−0.592069	+	2.90584i	−0.0728786	+	0.357685i
$67$	−2.06631	+	11.7186i	−0.252440	+	1.43166i	0.550120	+	0.835086i	$0.314582\pi$
$67$	−2.06631	+	11.7186i	−0.252440	+	1.43166i	−0.802560	+	0.596572i	$0.796529\pi$
$68$	−1.10857	+	6.28701i	−0.134434	+	0.762412i
$69$	9.71272	−	10.9719i	1.16927	−	1.32086i
$70$	3.01866	−	6.20704i	0.360799	−	0.741883i
$71$	2.69703	+	1.55713i	0.320079	+	0.184798i	0.651428	−	0.758711i	$-0.274170\pi$
$71$	2.69703	+	1.55713i	0.320079	+	0.184798i	−0.331349	+	0.943508i	$0.607504\pi$
$72$	0.158726	−	2.99580i	0.0187061	−	0.353058i
$73$	−1.04793	+	0.605023i	−0.122651	+	0.0708126i	−0.560070	−	0.828445i	$-0.689226\pi$
$73$	−1.04793	+	0.605023i	−0.122651	+	0.0708126i	0.437419	+	0.899258i	$0.355893\pi$
$74$	1.75928	−	4.83357i	0.204512	−	0.561891i
$75$	2.44817	−	1.94622i	0.282691	−	0.224730i
$76$	1.01442	−	1.20894i	0.116362	−	0.138675i
$77$	−3.25500	+	3.15046i	−0.370942	+	0.359028i
$78$	−5.49315	−	10.1240i	−0.621977	−	1.14632i
$79$	−1.88666	−	10.6998i	−0.212266	−	1.20382i	−0.885588	−	0.464471i	$-0.846245\pi$
$79$	−1.88666	−	10.6998i	−0.212266	−	1.20382i	0.673323	−	0.739349i	$-0.264867\pi$
$80$	2.60877			0.291669
$81$	−3.65120	−	8.22610i	−0.405688	−	0.914011i
$82$			0.819485i			0.0904970i
$83$	−0.170323	−	0.965952i	−0.0186954	−	0.106027i	0.974032	−	0.226410i	$-0.0726989\pi$
$83$	−0.170323	−	0.965952i	−0.0186954	−	0.106027i	−0.992728	+	0.120383i	$0.961588\pi$
$84$	2.78661	−	3.63797i	0.304044	−	0.396935i
$85$	−15.6500	+	5.69613i	−1.69748	+	0.617832i
$86$	−5.72306	+	6.82048i	−0.617133	+	0.735471i
$87$	−4.30430	−	5.41443i	−0.461469	−	0.580488i
$88$	−1.60890	−	0.585593i	−0.171510	−	0.0624244i
$89$	1.37986	+	2.38999i	0.146265	+	0.253339i	0.929844	−	0.367953i	$-0.119941\pi$
$89$	1.37986	+	2.38999i	0.146265	+	0.253339i	−0.783579	+	0.621292i	$0.786608\pi$
$90$	6.97532	−	3.54907i	0.735264	−	0.374105i
$91$	1.81927	−	17.5002i	0.190711	−	1.83452i
$92$	5.43804	+	6.48081i	0.566955	+	0.675671i
$93$	−1.01309	+	1.14443i	−0.105052	+	0.118671i
$94$	−6.92487	−	1.22104i	−0.714246	−	0.125941i
$95$	4.05451	+	0.714919i	0.415984	+	0.0733492i
$96$	1.69718	+	0.345802i	0.173218	+	0.0352933i
$97$	11.7988	+	14.0613i	1.19799	+	1.42770i	0.876912	+	0.480650i	$0.159599\pi$
$97$	11.7988	+	14.0613i	1.19799	+	1.42770i	0.321074	+	0.947054i	$0.395956\pi$
$98$	6.65247	−	2.17822i	0.672001	−	0.220033i
$99$	−5.09855	+	0.623055i	−0.512424	+	0.0626194i
$100$	0.902835	+	1.56376i	0.0902835	+	0.156376i
$101$	1.77454	+	0.645878i	0.176573	+	0.0642673i	0.428794	−	0.903402i	$-0.358939\pi$
$101$	1.77454	+	0.645878i	0.176573	+	0.0642673i	−0.252221	+	0.967670i	$0.581161\pi$
$102$	−10.9364	+	1.63125i	−1.08287	+	0.161518i
$103$	11.5732	−	13.7924i	1.14034	−	1.35900i	0.216475	−	0.976288i	$-0.430544\pi$
$103$	11.5732	−	13.7924i	1.14034	−	1.35900i	0.923866	−	0.382717i	$-0.125011\pi$
$104$	6.24904	−	2.27446i	0.612768	−	0.223029i
$105$	11.8539	+	1.55038i	1.15682	+	0.151301i
$106$	1.17219	+	6.64779i	0.113853	+	0.645691i
$107$		−	12.3862i		−	1.19742i	−0.800967	−	0.598708i	$-0.795681\pi$
$107$		−	12.3862i		−	1.19742i	0.800967	−	0.598708i	$-0.204319\pi$
$108$	5.00836	−	1.38430i	0.481930	−	0.133205i
$109$	−5.18562			−0.496692			−0.248346	−	0.968671i	$-0.579887\pi$
$109$	−5.18562			−0.496692			−0.248346	+	0.968671i	$0.579887\pi$
$110$	−0.775622	−	4.39877i	−0.0739526	−	0.419406i
$111$	8.90617	+	0.235772i	0.845336	+	0.0223785i
$112$	1.84005	+	1.90111i	0.173869	+	0.179638i
$113$	−11.9051	+	14.1880i	−1.11994	+	1.33469i	−0.183843	+	0.982956i	$0.558854\pi$
$113$	−11.9051	+	14.1880i	−1.11994	+	1.33469i	−0.936098	+	0.351739i	$0.885591\pi$
$114$	2.54297	+	1.00254i	0.238171	+	0.0938969i
$115$	−7.54853	+	20.7394i	−0.703904	+	1.93396i
$116$	3.45843	−	1.99673i	0.321107	−	0.185391i
$117$	13.6144	−	14.5829i	1.25865	−	1.34819i
$118$	0.780646	+	0.450706i	0.0718643	+	0.0414909i
$119$	−15.1894	−	7.38707i	−1.39241	−	0.677171i
$120$	1.43252	+	4.28543i	0.130770	+	0.391204i
$121$	1.40108	−	7.94593i	0.127371	−	0.722357i
$122$	−0.744328	+	4.22130i	−0.0673883	+	0.382178i
$123$	−1.34617	+	0.449993i	−0.121380	+	0.0405745i
$124$	−0.567216	−	0.675982i	−0.0509375	−	0.0607049i
$125$	4.16663	−	7.21682i	0.372675	−	0.645492i
$126$	7.50627	+	2.57991i	0.668712	+	0.229836i
$127$	1.15030	+	1.99238i	0.102073	+	0.176796i	0.912539	−	0.408991i	$-0.134119\pi$
$127$	1.15030	+	1.99238i	0.102073	+	0.176796i	−0.810466	+	0.585786i	$0.800786\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	−14.3466	−	5.65605i	−1.26315	−	0.497987i
$130$	13.2897	+	11.1514i	1.16559	+	0.978044i
$131$	−13.0034	+	4.73283i	−1.13611	+	0.413510i	−0.840506	−	0.541802i	$-0.817742\pi$
$131$	−13.0034	+	4.73283i	−1.13611	+	0.413510i	−0.295602	+	0.955311i	$0.595520\pi$
$132$	0.0784792	−	2.96451i	0.00683073	−	0.258027i
$133$	2.33879	+	3.45893i	0.202799	+	0.299927i
$134$		−	11.8994i		−	1.02795i
$135$	9.66033	+	9.50953i	0.831429	+	0.818450i
$136$		−	6.38400i		−	0.547423i
$137$	−9.76310	+	1.72150i	−0.834118	+	0.147078i	−0.574367	−	0.818598i	$-0.694752\pi$
$137$	−9.76310	+	1.72150i	−0.834118	+	0.147078i	−0.259751	+	0.965676i	$0.583641\pi$
$138$	−7.65991	+	12.4918i	−0.652055	+	1.06337i
$139$	2.00774	+	5.51622i	0.170294	+	0.467879i	0.995254	−	0.0973121i	$-0.0310245\pi$
$139$	2.00774	+	5.51622i	0.170294	+	0.467879i	−0.824960	+	0.565191i	$0.808802\pi$
$140$	−1.89496	+	6.63693i	−0.160154	+	0.560923i
$141$	−1.79675	−	12.0460i	−0.151314	−	1.01446i
$142$	−2.92645	−	1.06514i	−0.245582	−	0.0893846i
$143$	−5.69301	−	9.86057i	−0.476073	−	0.824583i
$144$	0.363900	+	2.97785i	0.0303250	+	0.248154i
$145$	9.02225	+	5.20900i	0.749257	+	0.432584i
$146$	0.926949	−	0.777803i	0.0767148	−	0.0643714i
$147$	7.23115	+	9.73193i	0.596415	+	0.802676i
$148$	−0.893208	+	5.06563i	−0.0734212	+	0.416393i
$149$	2.92838	+	0.516353i	0.239903	+	0.0423013i	0.292307	−	0.956325i	$-0.405577\pi$
$149$	2.92838	+	0.516353i	0.239903	+	0.0423013i	−0.0524040	+	0.998626i	$0.516688\pi$
$150$	−2.07302	+	2.34177i	−0.169262	+	0.191205i
$151$	−1.27898	+	1.07319i	−0.104082	+	0.0873353i	−0.693344	−	0.720607i	$-0.743863\pi$
$151$	−1.27898	+	1.07319i	−0.104082	+	0.0873353i	0.589262	+	0.807942i	$0.299419\pi$
$152$	−0.789081	+	1.36673i	−0.0640029	+	0.110856i
$153$	−8.68503	−	17.0695i	−0.702143	−	1.37999i
$154$	2.65848	−	3.66782i	0.214226	−	0.295562i
$155$	0.787350	−	2.16323i	0.0632415	−	0.173755i
$156$	7.16772	+	9.01636i	0.573877	+	0.721887i
$157$	4.83620	−	5.76356i	0.385971	−	0.459983i	−0.537718	−	0.843125i	$-0.680714\pi$
$157$	4.83620	−	5.76356i	0.385971	−	0.459983i	0.923689	+	0.383142i	$0.125158\pi$
$158$	3.71600	+	10.2096i	0.295629	+	0.812233i
$159$	−10.2767	+	5.57597i	−0.814994	+	0.442203i
$160$	−2.56913	+	0.453008i	−0.203108	+	0.0358134i
$161$	−20.4378	+	9.12730i	−1.61073	+	0.719332i
$162$	5.02417	+	7.46711i	0.394736	+	0.586671i
$163$	−7.10349			−0.556388			−0.278194	−	0.960525i	$-0.589736\pi$
$163$	−7.10349			−0.556388			−0.278194	+	0.960525i	$0.589736\pi$
$164$	−0.142302	−	0.807035i	−0.0111119	−	0.0630189i
$165$	6.79996	−	3.68955i	0.529376	−	0.287231i
$166$	0.335471	+	0.921700i	0.0260376	+	0.0715378i
$167$	−9.09652	−	7.63288i	−0.703910	−	0.590650i	0.218973	−	0.975731i	$-0.429729\pi$
$167$	−9.09652	−	7.63288i	−0.703910	−	0.590650i	−0.922883	+	0.385080i	$0.874174\pi$
$168$	−2.11255	+	4.06659i	−0.162987	+	0.313744i
$169$	29.3406	+	10.6791i	2.25697	+	0.821470i
$170$	14.4231	−	8.32718i	1.10620	−	0.638666i
$171$	−0.250495	+	4.72785i	−0.0191559	+	0.361548i
$172$	4.45175	−	7.71066i	0.339443	−	0.587932i
$173$	−4.23871	+	3.55670i	−0.322263	+	0.270411i	−0.789539	−	0.613701i	$-0.789680\pi$
$173$	−4.23871	+	3.55670i	−0.322263	+	0.270411i	0.467275	+	0.884112i	$0.345236\pi$
$174$	5.17911	+	4.58474i	0.392627	+	0.347568i
$175$	−4.63413	+	1.16100i	−0.350307	+	0.0877637i
$176$	1.68615	+	0.297313i	0.127098	+	0.0224108i
$177$	−0.311710	+	1.52986i	−0.0234296	+	0.114991i
$178$	−1.77392	−	2.11407i	−0.132961	−	0.158457i
$179$	16.3924	+	9.46415i	1.22522	+	0.707384i	0.966027	−	0.258441i	$-0.0832087\pi$
$179$	16.3924	+	9.46415i	1.22522	+	0.707384i	0.259197	+	0.965824i	$0.416542\pi$
$180$	−6.25306	+	4.70640i	−0.466076	+	0.350794i
$181$	11.2216	−	6.47882i	0.834099	−	0.481567i	−0.0211554	−	0.999776i	$-0.506734\pi$
$181$	11.2216	−	6.47882i	0.834099	−	0.481567i	0.855254	+	0.518209i	$0.173401\pi$
$182$	1.24724	+	17.5502i	0.0924516	+	1.30091i
$183$	−7.34306	+	1.09527i	−0.542814	+	0.0809650i
$184$	−6.48081	−	5.43804i	−0.477771	−	0.400898i
$185$	−12.6097	+	4.58954i	−0.927081	+	0.337430i
$186$	0.798969	−	1.30296i	0.0585832	−	0.0955376i
$187$	−10.7644	+	1.89805i	−0.787168	+	0.138799i
$188$	7.03170			0.512839
$189$	−0.116201	+	13.7472i	−0.00845237	+	0.999964i
$190$	−4.11706			−0.298683
$191$	1.21312	−	0.213906i	0.0877784	−	0.0154777i	−0.129586	−	0.991568i	$-0.541365\pi$
$191$	1.21312	−	0.213906i	0.0877784	−	0.0154777i	0.217365	+	0.976090i	$0.430254\pi$
$192$	−1.73144	−	0.0458363i	−0.124956	−	0.00330795i
$193$	−24.6718	+	8.97980i	−1.77591	+	0.646380i	−0.776037	+	0.630687i	$0.782773\pi$
$193$	−24.6718	+	8.97980i	−1.77591	+	0.646380i	−0.999877	+	0.0156930i	$0.995005\pi$
$194$	−14.0613	−	11.7988i	−1.00954	−	0.847104i
$195$	−11.0208	+	27.9545i	−0.789219	+	2.00187i
$196$	−6.17316	+	3.30032i	−0.440940	+	0.235737i
$197$	9.13794	−	5.27579i	0.651051	−	0.375884i	−0.137808	−	0.990459i	$-0.544006\pi$
$197$	9.13794	−	5.27579i	0.651051	−	0.375884i	0.788859	+	0.614575i	$0.210672\pi$
$198$	4.91290	−	1.49894i	0.349145	−	0.106525i
$199$	5.90158	+	3.40728i	0.418352	+	0.241536i	0.694372	−	0.719616i	$-0.255682\pi$
$199$	5.90158	+	3.40728i	0.418352	+	0.241536i	−0.276020	+	0.961152i	$0.589016\pi$
$200$	−1.16066	−	1.38322i	−0.0820712	−	0.0978086i
$201$	19.5472	−	6.53416i	1.37875	−	0.460884i
$202$	−1.85973	−	0.327921i	−0.130850	−	0.0230724i
$203$	2.56770	+	10.2489i	0.180217	+	0.719334i
$204$	10.4870	−	3.50556i	0.734237	−	0.245438i
$205$	1.63769	−	1.37418i	0.114381	−	0.0959770i
$206$	−9.00235	+	15.5925i	−0.627223	+	1.08638i
$207$	−24.7265	−	5.72350i	−1.71861	−	0.397811i
$208$	−5.75914	+	3.32504i	−0.399325	+	0.230550i
$209$	2.53911	+	0.924161i	0.175634	+	0.0639255i
$210$	−11.9431	+	0.531589i	−0.824149	+	0.0366831i
$211$	0.224300	+	0.188210i	0.0154414	+	0.0129569i	0.650476	−	0.759527i	$-0.274570\pi$
$211$	0.224300	+	0.188210i	0.0154414	+	0.0129569i	−0.635034	+	0.772484i	$0.719014\pi$
$212$	−2.30875	−	6.34325i	−0.158566	−	0.435656i
$213$	0.142746	−	5.39217i	0.00978083	−	0.369466i
$214$	2.15084	+	12.1980i	0.147028	+	0.833838i
$215$	23.2272			1.58408
$216$	−4.69189	+	2.23297i	−0.319243	+	0.151934i
$217$	2.13177	−	0.952025i	0.144714	−	0.0646276i
$218$	5.10683	−	0.900473i	0.345878	−	0.0609877i
$219$	1.78670	+	1.09560i	0.120734	+	0.0740336i
$220$	1.52768	+	4.19726i	0.102996	+	0.282979i
$221$	27.2890	−	32.5218i	1.83566	−	2.18765i
$222$	−8.81180	+	1.31435i	−0.591410	+	0.0882134i
$223$	5.80906	−	15.9603i	0.389003	−	1.06878i	−0.578448	−	0.815719i	$-0.696341\pi$
$223$	5.80906	−	15.9603i	0.389003	−	1.06878i	0.967451	−	0.253058i	$-0.0814364\pi$
$224$	−2.14222	−	1.55270i	−0.143133	−	0.103744i
$225$	−4.98517	−	2.11945i	−0.332345	−	0.141297i
$226$	9.26056	−	16.0398i	0.616003	−	1.06695i
$227$	20.3610	−	17.0849i	1.35141	−	1.13397i	0.372874	−	0.927882i	$-0.378372\pi$
$227$	20.3610	−	17.0849i	1.35141	−	1.13397i	0.978534	−	0.206085i	$-0.0660722\pi$
$228$	−2.67842	−	0.545732i	−0.177383	−	0.0361420i
$229$	−0.678629	−	0.119661i	−0.0448451	−	0.00790739i	0.151181	−	0.988506i	$-0.451692\pi$
$229$	−0.678629	−	0.119661i	−0.0448451	−	0.00790739i	−0.196026	+	0.980599i	$0.562804\pi$
$230$	3.83249	−	21.7351i	0.252707	−	1.43317i
$231$	7.48496	+	2.35302i	0.492474	+	0.154818i
$232$	−3.05916	+	2.56694i	−0.200844	+	0.168528i
$233$	−4.56619	−	2.63629i	−0.299141	−	0.172709i	0.342916	−	0.939366i	$-0.388585\pi$
$233$	−4.56619	−	2.63629i	−0.299141	−	0.172709i	−0.642057	+	0.766657i	$0.721919\pi$
$234$	−10.8753	+	16.7255i	−0.710940	+	1.09338i
$235$	9.17203	+	15.8864i	0.598318	+	1.03632i
$236$	−0.847050	−	0.308301i	−0.0551383	−	0.0200687i
$237$	−14.7308	+	11.7105i	−0.956871	+	0.760682i
$238$	16.2414	+	4.63722i	1.05278	+	0.300586i
$239$	7.71216	+	21.1890i	0.498858	+	1.37060i	0.892380	+	0.451285i	$0.149034\pi$
$239$	7.71216	+	21.1890i	0.498858	+	1.37060i	−0.393522	+	0.919315i	$0.628743\pi$
$240$	−2.15491	−	3.97157i	−0.139099	−	0.256364i
$241$	23.0229	−	4.05955i	1.48303	−	0.261499i	0.627244	−	0.778823i	$-0.284183\pi$
$241$	23.0229	−	4.05955i	1.48303	−	0.261499i	0.855790	+	0.517324i	$0.173072\pi$
$242$			8.06851i			0.518663i
$243$	−9.50737	+	12.3535i	−0.609898	+	0.792480i
$244$		−	4.28642i		−	0.274410i
$245$	−15.5084	−	9.64189i	−0.990798	−	0.615998i
$246$	1.24758	−	0.676917i	0.0795427	−	0.0431586i
$247$	−9.86199	+	3.58947i	−0.627503	+	0.228393i
$248$	0.675982	+	0.567216i	0.0429249	+	0.0360182i
$249$	−1.32987	+	1.05720i	−0.0842768	+	0.0669974i
$250$	−2.85014	+	7.83071i	−0.180259	+	0.495258i
$251$	9.14058	+	15.8320i	0.576949	+	0.999304i	0.995827	+	0.0912619i	$0.0290900\pi$
$251$	9.14058	+	15.8320i	0.576949	+	0.999304i	−0.418878	+	0.908042i	$0.637577\pi$
$252$	−7.84023	−	1.23726i	−0.493888	−	0.0779402i
$253$	−7.24251	+	12.5444i	−0.455333	+	0.788660i
$254$	−1.47880	−	1.76237i	−0.0927883	−	0.110581i
$255$	21.5991	+	19.1203i	1.35259	+	1.19736i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−0.169038	+	0.958665i	−0.0105443	+	0.0597999i	−0.989626	−	0.143668i	$-0.954110\pi$
$257$	−0.169038	+	0.958665i	−0.0105443	+	0.0597999i	0.979082	+	0.203468i	$0.0652213\pi$
$258$	15.1108	+	3.07885i	0.940760	+	0.191681i
$259$	−12.2386	−	5.95198i	−0.760469	−	0.369838i
$260$	−15.0243	−	8.67427i	−0.931766	−	0.537955i
$261$	−4.68742	+	11.0253i	−0.290144	+	0.682449i
$262$	11.9840	−	6.91894i	0.740371	−	0.427454i
$263$	7.50286	−	20.6139i	0.462646	−	1.27111i	−0.460842	−	0.887482i	$-0.652452\pi$
$263$	7.50286	−	20.6139i	0.462646	−	1.27111i	0.923488	−	0.383628i	$-0.125325\pi$
$264$	0.437495	+	2.93310i	0.0269259	+	0.180520i
$265$	11.3195	−	13.4901i	0.695354	−	0.828691i
$266$	−2.90390	−	3.00026i	−0.178049	−	0.183957i
$267$	2.49871	−	4.07489i	0.152918	−	0.249379i
$268$	2.06631	+	11.7186i	0.126220	+	0.715829i
$269$	−11.0618			−0.674447			−0.337224	−	0.941425i	$-0.609488\pi$
$269$	−11.0618			−0.674447			−0.337224	+	0.941425i	$0.609488\pi$
$270$	−11.1649	−	7.68756i	−0.679473	−	0.467850i
$271$			5.87429i			0.356838i	0.983955	+	0.178419i	$0.0570982\pi$
$271$			5.87429i			0.356838i	−0.983955	+	0.178419i	$0.942902\pi$
$272$	1.10857	+	6.28701i	0.0672169	+	0.381206i
$273$	−28.1449	+	11.6860i	−1.70341	+	0.707266i
$274$	9.31584	−	3.39069i	0.562791	−	0.204839i
$275$	−1.98724	+	2.36830i	−0.119835	+	0.142814i
$276$	5.37436	−	13.6322i	0.323499	−	0.820559i
$277$	9.97230	+	3.62962i	0.599177	+	0.218083i	0.623761	−	0.781615i	$-0.285604\pi$
$277$	9.97230	+	3.62962i	0.599177	+	0.218083i	−0.0245838	+	0.999698i	$0.507826\pi$
$278$	−2.93512	−	5.08377i	−0.176037	−	0.304904i
$279$	2.57910	+	0.596991i	0.154407	+	0.0357409i
$280$	0.713683	−	6.86515i	0.0426507	−	0.410271i
$281$	−0.941246	−	1.12173i	−0.0561500	−	0.0669170i	0.737238	−	0.675633i	$-0.236129\pi$
$281$	−0.941246	−	1.12173i	−0.0561500	−	0.0669170i	−0.793388	+	0.608716i	$0.791685\pi$
$282$	3.86122	+	11.5510i	0.229932	+	0.687851i
$283$	−5.63290	−	0.993233i	−0.334841	−	0.0590416i	0.00369981	−	0.999993i	$-0.498822\pi$
$283$	−5.63290	−	0.993233i	−0.334841	−	0.0590416i	−0.338541	+	0.940952i	$0.609933\pi$
$284$	3.06695	+	0.540786i	0.181990	+	0.0320898i
$285$	−2.26074	−	6.76310i	−0.133915	−	0.400611i
$286$	7.31879	+	8.72219i	0.432769	+	0.515754i
$287$	2.15653	+	0.224187i	0.127296	+	0.0132334i
$288$	−0.875469	−	2.86942i	−0.0515875	−	0.169082i
$289$	−11.8777	−	20.5728i	−0.698689	−	1.21016i
$290$	−9.78971	−	3.56316i	−0.574872	−	0.209236i
$291$	11.6606	−	29.5774i	0.683559	−	1.73386i
$292$	−0.777803	+	0.926949i	−0.0455175	+	0.0542456i
$293$	19.9297	−	7.25381i	1.16430	−	0.423772i	0.313671	−	0.949532i	$-0.398441\pi$
$293$	19.9297	−	7.25381i	1.16430	−	0.423772i	0.850633	+	0.525760i	$0.176219\pi$
$294$	−8.81122	−	8.32841i	−0.513881	−	0.485723i
$295$	−0.408347	−	2.31585i	−0.0237749	−	0.134834i
$296$		−	5.14378i		−	0.298976i
$297$	5.16007	+	7.24734i	0.299418	+	0.420533i
$298$	−2.97356			−0.172254
$299$	−9.76950	−	55.4056i	−0.564985	−	3.20419i
$300$	1.63488	−	2.66617i	0.0943901	−	0.153932i
$301$	16.3829	+	16.9265i	0.944295	+	0.975628i
$302$	1.07319	−	1.27898i	0.0617554	−	0.0735972i
$303$	−0.482534	−	3.23505i	−0.0277208	−	0.185849i
$304$	0.539763	−	1.48299i	0.0309575	−	0.0850551i
$305$	9.68413	−	5.59113i	0.554511	−	0.320147i
$306$	11.5172	+	15.3021i	0.658393	+	0.874761i
$307$	−9.39899	−	5.42651i	−0.536429	−	0.309707i	0.207202	−	0.978298i	$-0.433564\pi$
$307$	−9.39899	−	5.42651i	−0.536429	−	0.309707i	−0.743630	+	0.668591i	$0.766898\pi$
$308$	−1.98118	+	4.07374i	−0.112888	+	0.232123i
$309$	−30.5572	−	6.22606i	−1.73834	−	0.354188i
$310$	−0.399748	+	2.26709i	−0.0227042	+	0.128762i
$311$	1.03703	−	5.88131i	0.0588048	−	0.333499i	−0.941186	−	0.337890i	$-0.890287\pi$
$311$	1.03703	−	5.88131i	0.0588048	−	0.333499i	0.999990	+	0.00439151i	$0.00139786\pi$
$312$	−8.62450	−	7.63472i	−0.488266	−	0.432231i
$313$	−2.45451	−	2.92517i	−0.138737	−	0.165340i	0.692202	−	0.721704i	$-0.256641\pi$
$313$	−2.45451	−	2.92517i	−0.138737	−	0.165340i	−0.830939	+	0.556363i	$0.812196\pi$
$314$	−3.76190	+	6.51580i	−0.212296	+	0.367708i
$315$	−7.43137	−	19.3270i	−0.418710	−	1.08895i
$316$	−5.43242	−	9.40923i	−0.305598	−	0.529311i
$317$	−6.10186	+	16.7647i	−0.342715	+	0.941601i	0.641889	+	0.766798i	$0.278151\pi$
$317$	−6.10186	+	16.7647i	−0.342715	+	0.941601i	−0.984603	+	0.174803i	$0.944071\pi$
$318$	9.15230	−	7.27578i	0.513235	−	0.408006i
$319$	5.23778	+	4.39502i	0.293259	+	0.246074i
$320$	2.45144	−	0.892251i	0.137040	−	0.0498784i
$321$	−18.8566	+	10.2313i	−1.05247	+	0.571056i
$322$	18.5424	−	12.5376i	1.03333	−	0.698694i
$323$			10.0750i			0.560587i
$324$	−6.24449	−	6.48123i	−0.346916	−	0.360068i
$325$		−	12.0079i		−	0.666076i
$326$	6.99557	−	1.23351i	0.387449	−	0.0683177i
$327$	4.28346	+	7.89454i	0.236876	+	0.436569i
$328$	0.280280	+	0.770064i	0.0154759	+	0.0425197i
$329$	−5.10770	+	17.8892i	−0.281597	+	0.986266i
$330$	−6.05597	+	4.81430i	−0.333370	+	0.265019i
$331$	19.6490	+	7.15164i	1.08000	+	0.393090i	0.819909	−	0.572493i	$-0.194024\pi$
$331$	19.6490	+	7.15164i	1.08000	+	0.393090i	0.260095	+	0.965583i	$0.416246\pi$
$332$	−0.490426	−	0.849443i	−0.0269156	−	0.0466193i
$333$	−6.99779	−	13.7534i	−0.383477	−	0.753684i
$334$	10.2838	+	5.93733i	0.562702	+	0.324876i
$335$	−23.7801	+	19.9539i	−1.29925	+	1.09020i
$336$	1.37430	−	4.37165i	0.0749743	−	0.238493i
$337$	4.43907	−	25.1752i	0.241812	−	1.37138i	−0.585970	−	0.810333i	$-0.699286\pi$
$337$	4.43907	−	25.1752i	0.241812	−	1.37138i	0.827782	−	0.561050i	$-0.189602\pi$
$338$	−30.7493	−	5.42193i	−1.67254	−	0.294914i
$339$	31.4337	+	6.40464i	1.70724	+	0.347852i
$340$	−12.7580	+	10.7052i	−0.691899	+	0.580572i
$341$	0.755432	−	1.30845i	0.0409089	−	0.0708563i
$342$	−0.574293	−	4.69952i	−0.0310542	−	0.254121i
$343$	−3.91221	−	18.1023i	−0.211240	−	0.977434i
$344$	−3.04518	+	8.36655i	−0.164185	+	0.451094i
$345$	37.8088	−	5.63948i	2.03556	−	0.303619i
$346$	3.55670	−	4.23871i	0.191210	−	0.227875i
$347$	1.84812	+	5.07767i	0.0992124	+	0.272584i	0.979362	−	0.202112i	$-0.0647804\pi$
$347$	1.84812	+	5.07767i	0.0992124	+	0.272584i	−0.880150	+	0.474695i	$0.842558\pi$
$348$	−5.89656	−	3.61574i	−0.316089	−	0.193824i
$349$	13.2466	−	2.33574i	0.709076	−	0.125029i	0.192533	−	0.981291i	$-0.438330\pi$
$349$	13.2466	−	2.33574i	0.709076	−	0.125029i	0.516543	+	0.856261i	$0.327219\pi$
$350$	4.36212	−	1.94807i	0.233165	−	0.104129i
$351$	−33.4468	−	8.68062i	−1.78526	−	0.463337i
$352$	−1.71216			−0.0912584
$353$	1.52656	+	8.65757i	0.0812507	+	0.460796i	0.998103	+	0.0615688i	$0.0196103\pi$
$353$	1.52656	+	8.65757i	0.0812507	+	0.460796i	−0.916852	+	0.399227i	$0.869279\pi$
$354$	0.0413174	−	1.56074i	0.00219600	−	0.0829527i
$355$	2.77871	+	7.63443i	0.147478	+	0.405193i
$356$	2.11407	+	1.77392i	0.112046	+	0.0940175i
$357$	1.30087	+	29.2262i	0.0688492	+	1.54682i
$358$	−17.7868	−	6.47386i	−0.940060	−	0.342154i
$359$	−23.4946	+	13.5646i	−1.24000	+	0.715914i	−0.969094	−	0.246692i	$-0.920656\pi$
$359$	−23.4946	+	13.5646i	−1.24000	+	0.715914i	−0.270905	+	0.962606i	$0.587323\pi$
$360$	5.34081	−	5.72073i	0.281485	−	0.301509i
$361$	−8.25470	+	14.2976i	−0.434458	+	0.752503i
$362$	−9.92613	+	8.32901i	−0.521706	+	0.437763i
$363$	−13.2542	+	4.43055i	−0.695663	+	0.232544i
$364$	−4.27585	−	17.0670i	−0.224116	−	0.894554i
$365$	−3.10877	−	0.548160i	−0.162721	−	0.0286920i
$366$	7.04131	−	2.35374i	0.368055	−	0.123032i
$367$	−14.0714	−	16.7696i	−0.734521	−	0.875368i	0.261434	−	0.965221i	$-0.415805\pi$
$367$	−14.0714	−	16.7696i	−0.734521	−	0.875368i	−0.995955	+	0.0898533i	$0.971360\pi$
$368$	7.32665	+	4.23005i	0.381928	+	0.220506i
$369$	1.79704	+	1.67769i	0.0935501	+	0.0873373i
$370$	11.6211	−	6.70946i	0.604154	−	0.348808i
$371$	17.8148	−	1.26604i	0.924899	−	0.0657297i
$372$	−0.560574	+	1.42190i	−0.0290644	+	0.0737223i
$373$	3.63872	+	3.05325i	0.188406	+	0.158091i	0.732112	−	0.681185i	$-0.238535\pi$
$373$	3.63872	+	3.05325i	0.188406	+	0.158091i	−0.543706	+	0.839276i	$0.682979\pi$
$374$	10.2712	−	3.73843i	0.531113	−	0.193309i
$375$	−14.4286	−	0.381966i	−0.745089	−	0.0197247i
$376$	−6.92487	+	1.22104i	−0.357123	+	0.0629704i
$377$	−26.5568			−1.36775
$378$	−2.27275	−	13.5586i	−0.116897	−	0.697377i
$379$	25.0501			1.28674			0.643368	−	0.765557i	$-0.277537\pi$
$379$	25.0501			1.28674			0.643368	+	0.765557i	$0.277537\pi$
$380$	4.05451	−	0.714919i	0.207992	−	0.0366746i
$381$	2.08301	−	3.39698i	0.106716	−	0.174032i
$382$	−1.15755	+	0.421312i	−0.0592252	+	0.0215562i
$383$	8.07952	+	6.77952i	0.412844	+	0.346417i	0.825433	−	0.564500i	$-0.190931\pi$
$383$	8.07952	+	6.77952i	0.412844	+	0.346417i	−0.412589	+	0.910917i	$0.635375\pi$
$384$	1.71310	−	0.255522i	0.0874212	−	0.0130396i
$385$	−11.7879	+	0.837727i	−0.600765	+	0.0426945i
$386$	22.7376	−	13.1276i	1.15732	−	0.668176i
$387$	3.23999	+	26.5133i	0.164698	+	1.34775i
$388$	15.8965	+	9.17783i	0.807021	+	0.465934i
$389$	−14.6938	−	17.5114i	−0.745007	−	0.887865i	0.251795	−	0.967781i	$-0.418979\pi$
$389$	−14.6938	−	17.5114i	−0.745007	−	0.887865i	−0.996802	+	0.0799161i	$0.974535\pi$
$390$	5.99916	−	29.4436i	0.303779	−	1.49093i
$391$	−53.1887	−	9.37860i	−2.68987	−	0.474296i
$392$	5.50628	−	4.32214i	0.278109	−	0.218301i
$393$	17.9464	+	15.8868i	0.905274	+	0.801381i
$394$	−8.08298	+	6.78242i	−0.407215	+	0.341694i
$395$	14.1719	−	24.5465i	0.713067	−	1.23507i
$396$	−4.57797	+	2.32929i	−0.230052	+	0.117051i
$397$	−14.8355	+	8.56528i	−0.744572	+	0.429879i	−0.823729	−	0.566983i	$-0.808110\pi$
$397$	−14.8355	+	8.56528i	−0.744572	+	0.429879i	0.0791571	+	0.996862i	$0.474777\pi$
$398$	−6.40359	−	2.33072i	−0.320983	−	0.116828i
$399$	3.33395	−	6.41773i	0.166906	−	0.321288i
$400$	1.38322	+	1.16066i	0.0691612	+	0.0580331i
$401$	−7.32564	−	20.1270i	−0.365825	−	1.00510i	−0.976932	−	0.213549i	$-0.931498\pi$
$401$	−7.32564	−	20.1270i	−0.365825	−	1.00510i	0.611107	−	0.791548i	$-0.290724\pi$
$402$	−18.1156	+	9.82922i	−0.903522	+	0.490237i
$403$	1.01901	+	5.77909i	0.0507605	+	0.287877i
$404$	1.88842			0.0939525
$405$	6.49755	−	22.5619i	0.322866	−	1.12111i
$406$	−4.30840	−	9.64735i	−0.213822	−	0.478790i
$407$	−8.67318	+	1.52932i	−0.429913	+	0.0758053i
$408$	−9.71895	+	5.27335i	−0.481160	+	0.261070i
$409$	4.78260	+	13.1401i	0.236484	+	0.649735i	0.999992	+	0.00393670i	$0.00125309\pi$
$409$	4.78260	+	13.1401i	0.236484	+	0.649735i	−0.763508	+	0.645798i	$0.776525\pi$
$410$	−1.37418	+	1.63769i	−0.0678660	+	0.0808795i
$411$	10.6854	+	13.4413i	0.527071	+	0.663009i
$412$	6.15797	−	16.9189i	0.303381	−	0.833533i
$413$	1.39963	−	1.93102i	0.0688711	−	0.0950195i
$414$	25.3447	+	1.34284i	1.24563	+	0.0659969i
$415$	1.27941	−	2.21600i	0.0628037	−	0.108779i
$416$	5.09426	−	4.27459i	0.249767	−	0.209579i
$417$	6.73940	−	7.61311i	0.330030	−	0.372816i
$418$	−2.66101	−	0.469209i	−0.130154	−	0.0229497i
$419$	−0.291638	+	1.65396i	−0.0142475	+	0.0808014i	−0.991102	−	0.133101i	$-0.957506\pi$
$419$	−0.291638	+	1.65396i	−0.0142475	+	0.0808014i	0.976855	+	0.213903i	$0.0686175\pi$
$420$	11.6693	−	2.59740i	0.569404	−	0.126740i
$421$	22.7105	−	19.0564i	1.10684	−	0.928752i	0.108977	−	0.994044i	$-0.465242\pi$
$421$	22.7105	−	19.0564i	1.10684	−	0.928752i	0.997866	+	0.0652923i	$0.0207980\pi$
$422$	−0.253575	−	0.146401i	−0.0123438	−	0.00712671i
$423$	−16.8546	+	12.6857i	−0.819497	+	0.616799i
$424$	3.37517	+	5.84597i	0.163913	+	0.283906i
$425$	−10.8322	−	3.94260i	−0.525439	−	0.191244i
$426$	0.795763	+	5.33504i	0.0385549	+	0.258484i
$427$	10.9050	+	3.11358i	0.527730	+	0.150677i
$428$	−4.23632	−	11.6392i	−0.204770	−	0.562602i
$429$	−10.3091	+	16.8121i	−0.497728	+	0.811695i
$430$	−22.8743	+	4.03336i	−1.10310	+	0.194506i
$431$			4.02188i			0.193727i	0.995298	+	0.0968635i	$0.0308810\pi$
$431$			4.02188i			0.193727i	−0.995298	+	0.0968635i	$0.969119\pi$
$432$	4.23286	−	3.01378i	0.203654	−	0.145001i
$433$			13.4318i			0.645489i	0.946486	+	0.322744i	$0.104605\pi$
$433$			13.4318i			0.645489i	−0.946486	+	0.322744i	$0.895395\pi$
$434$	−1.93407	+	1.30774i	−0.0928382	+	0.0627735i
$435$	0.477523	−	18.0382i	0.0228955	−	0.864864i
$436$	−4.87288	+	1.77358i	−0.233369	+	0.0849393i
$437$	10.2278	+	8.58211i	0.489260	+	0.410538i
$438$	−1.94981	−	0.768695i	−0.0931653	−	0.0367297i
$439$	0.194851	−	0.535350i	0.00929975	−	0.0255509i	−0.934956	−	0.354764i	$-0.884561\pi$
$439$	0.194851	−	0.535350i	0.00929975	−	0.0255509i	0.944256	+	0.329213i	$0.106783\pi$
$440$	−2.23331	−	3.86821i	−0.106469	−	0.184410i
$441$	8.84270	−	19.0475i	0.421081	−	0.907023i
$442$	−21.2271	+	36.7664i	−1.00967	+	1.74880i
$443$	20.8026	+	24.7916i	0.988360	+	1.17788i	0.984050	+	0.177891i	$0.0569276\pi$
$443$	20.8026	+	24.7916i	0.988360	+	1.17788i	0.00431031	+	0.999991i	$0.498628\pi$
$444$	8.44970	−	2.82454i	0.401005	−	0.134047i
$445$	−1.25018	+	7.09011i	−0.0592641	+	0.336103i
$446$	−2.94934	+	16.7265i	−0.139655	+	0.792023i
$447$	−1.63283	−	4.88467i	−0.0772303	−	0.231037i
$448$	2.37930	+	1.15712i	0.112411	+	0.0546689i
$449$	6.83982	+	3.94897i	0.322791	+	0.186364i	0.652636	−	0.757672i	$-0.273663\pi$
$449$	6.83982	+	3.94897i	0.322791	+	0.186364i	−0.329845	+	0.944035i	$0.606996\pi$
$450$	5.27747	+	1.22159i	0.248782	+	0.0575863i
$451$	1.21511	−	0.701545i	0.0572174	−	0.0330345i
$452$	−6.33459	+	17.4042i	−0.297954	+	0.818622i
$453$	2.69030	+	1.06063i	0.126401	+	0.0498326i
$454$	−17.0849	+	20.3610i	−0.801835	+	0.955590i
$455$	32.9814	−	31.9222i	1.54619	−	1.49654i
$456$	2.73250	+	0.0723372i	0.127961	+	0.00338750i
$457$	−4.40132	−	24.9611i	−0.205885	−	1.16763i	−0.896041	−	0.443971i	$-0.853569\pi$
$457$	−4.40132	−	24.9611i	−0.205885	−	1.16763i	0.690156	−	0.723660i	$-0.257542\pi$
$458$	0.689098			0.0321994
$459$	−18.8125	+	27.3219i	−0.878091	+	1.27528i
$460$			22.0704i			1.02904i
$461$	6.86447	+	38.9304i	0.319710	+	1.81317i	0.544500	+	0.838761i	$0.316719\pi$
$461$	6.86447	+	38.9304i	0.319710	+	1.81317i	−0.224790	+	0.974407i	$0.572170\pi$
$462$	−7.77984	−	1.01753i	−0.361951	−	0.0473396i
$463$	9.30119	−	3.38536i	0.432263	−	0.157331i	−0.116719	−	0.993165i	$-0.537238\pi$
$463$	9.30119	−	3.38536i	0.432263	−	0.157331i	0.548982	+	0.835834i	$0.315016\pi$
$464$	2.56694	−	3.05916i	0.119167	−	0.142018i
$465$	−3.94365	+	0.588227i	−0.182883	+	0.0272784i
$466$	4.95461	+	1.80333i	0.229518	+	0.0835376i
$467$	12.3433	+	21.3792i	0.571180	+	0.989313i	0.996445	+	0.0842444i	$0.0268477\pi$
$467$	12.3433	+	21.3792i	0.571180	+	0.989313i	−0.425265	+	0.905069i	$0.639819\pi$
$468$	7.80572	−	18.3598i	0.360819	−	0.848684i
$469$	−31.3141	−	3.25533i	−1.44595	−	0.150317i
$470$	−11.7913	−	14.0524i	−0.543894	−	0.648188i
$471$	−12.7692	−	2.60175i	−0.588376	−	0.119882i
$472$	0.887718	+	0.156529i	0.0408605	+	0.00720481i
$473$	15.0126	+	2.64713i	0.690281	+	0.121715i
$474$	12.4735	−	14.0906i	0.572928	−	0.647204i
$475$	1.83171	+	2.18295i	0.0840447	+	0.100161i
$476$	−16.7999	−	1.74648i	−0.770024	−	0.0800496i
$477$	16.9776	+	11.0392i	0.777352	+	0.505452i
$478$	−11.2744	−	19.5279i	−0.515680	−	0.893184i
$479$	3.12136	+	1.13608i	0.142619	+	0.0519090i	0.412343	−	0.911029i	$-0.364710\pi$
$479$	3.12136	+	1.13608i	0.142619	+	0.0519090i	−0.269725	+	0.962938i	$0.586933\pi$
$480$	2.81183	+	3.53704i	0.128342	+	0.161443i
$481$	21.9876	−	26.2038i	1.00255	−	1.19479i
$482$	−21.9682	+	7.99576i	−1.00062	+	0.364197i
$483$	30.7775	+	23.5750i	1.40043	+	1.07270i
$484$	−1.40108	−	7.94593i	−0.0636855	−	0.361179i
$485$			47.8857i			2.17438i
$486$	7.21777	−	13.8168i	0.327405	−	0.626743i
$487$	−27.7371			−1.25689			−0.628445	−	0.777854i	$-0.716308\pi$
$487$	−27.7371			−1.25689			−0.628445	+	0.777854i	$0.716308\pi$
$488$	0.744328	+	4.22130i	0.0336942	+	0.191089i
$489$	5.86767	+	10.8143i	0.265345	+	0.489040i
$490$	16.9471	+	6.80240i	0.765593	+	0.307301i
$491$	6.47307	−	7.71430i	0.292125	−	0.348142i	−0.599942	−	0.800043i	$-0.704810\pi$
$491$	6.47307	−	7.71430i	0.292125	−	0.348142i	0.892068	+	0.451902i	$0.149254\pi$
$492$	−1.11108	+	0.883273i	−0.0500913	+	0.0398210i
$493$	−8.71953	+	23.9567i	−0.392708	+	1.07896i
$494$	9.08886	−	5.24745i	0.408927	−	0.236094i
$495$	−11.2339	−	7.30454i	−0.504926	−	0.328315i
$496$	−0.764208	−	0.441216i	−0.0343140	−	0.0198112i
$497$	−3.60358	+	7.40977i	−0.161643	+	0.332373i
$498$	1.12608	−	1.27207i	0.0504609	−	0.0570027i
$499$	2.56761	−	14.5616i	0.114942	−	0.651868i	−0.871837	−	0.489796i	$-0.837071\pi$
$499$	2.56761	−	14.5616i	0.114942	−	0.651868i	0.986779	−	0.162072i	$-0.0518176\pi$
$500$	1.44706	−	8.20667i	0.0647143	−	0.367013i
$501$	−4.10628	+	20.1534i	−0.183455	+	0.900389i
$502$	−11.7509	−	14.0042i	−0.524469	−	0.625037i
$503$	4.12896	−	7.15158i	0.184101	−	0.318873i	−0.759172	−	0.650890i	$-0.774396\pi$
$503$	4.12896	−	7.15158i	0.184101	−	0.318873i	0.943273	+	0.332017i	$0.107729\pi$
$504$	7.93597	−	0.142976i	0.353496	−	0.00636865i
$505$	2.46323	+	4.26643i	0.109612	+	0.189854i
$506$	4.95417	−	13.6115i	0.220240	−	0.605104i
$507$	−7.97833	−	53.4892i	−0.354330	−	2.37554i
$508$	1.76237	+	1.47880i	0.0781924	+	0.0656112i
$509$	−22.9263	+	8.34449i	−1.01619	+	0.369863i	−0.795807	−	0.605551i	$-0.792953\pi$
$509$	−22.9263	+	8.34449i	−1.01619	+	0.369863i	−0.220383	+	0.975413i	$0.570731\pi$
$510$	−24.5911	−	15.0792i	−1.08891	−	0.667716i
$511$	−1.79326	−	2.65212i	−0.0793289	−	0.117323i
$512$			1.00000i			0.0441942i
$513$	7.40457	−	3.52398i	0.326920	−	0.155588i
$514$		−	0.973454i		−	0.0429372i
$515$	46.2565	−	8.15626i	2.03830	−	0.359408i
$516$	−15.4159	−	0.408104i	−0.678648	−	0.0179658i
$517$	4.11771	+	11.3133i	0.181097	+	0.497560i
$518$	13.0862	+	3.73635i	0.574975	+	0.164166i
$519$	8.91599	+	3.51506i	0.391368	+	0.154294i
$520$	16.3023	+	5.93355i	0.714903	+	0.260203i
$521$	14.6429	+	25.3623i	0.641518	+	1.11114i	0.985094	+	0.172017i	$0.0550285\pi$
$521$	14.6429	+	25.3623i	0.641518	+	1.11114i	−0.343575	+	0.939125i	$0.611638\pi$
$522$	2.70169	−	11.6718i	0.118250	−	0.510859i
$523$	24.7419	+	14.2847i	1.08189	+	0.624628i	0.931405	−	0.363985i	$-0.118584\pi$
$523$	24.7419	+	14.2847i	1.08189	+	0.624628i	0.150482	+	0.988613i	$0.451917\pi$
$524$	−10.6004	+	8.89482i	−0.463082	+	0.388572i
$525$	5.59542	+	6.09595i	0.244204	+	0.266049i
$526$	−3.80930	+	21.6036i	−0.166093	+	0.941963i
$527$	5.54785	+	0.978236i	0.241668	+	0.0426126i
$528$	−0.940176	−	2.81257i	−0.0409159	−	0.122401i
$529$	−37.2092	+	31.2222i	−1.61779	+	1.35749i
$530$	−8.80504	+	15.2508i	−0.382467	+	0.662452i
$531$	2.58653	−	0.789159i	0.112246	−	0.0342466i
$532$	3.38077	+	2.45042i	0.146575	+	0.106239i
$533$	−1.86389	+	5.12099i	−0.0807340	+	0.221815i
$534$	−1.75315	+	4.44688i	−0.0758661	+	0.192435i
$535$	20.7702	−	24.7529i	0.897973	−	1.07016i
$536$	−4.06984	−	11.1818i	−0.175790	−	0.482979i
$537$	0.867604	−	32.7733i	0.0374399	−	1.41427i
$538$	10.8937	−	1.92085i	0.469661	−	0.0828139i
$539$	−8.92485	−	7.99938i	−0.384421	−	0.344558i
$540$	12.3302	+	5.63201i	0.530607	+	0.242363i
$541$	26.0907			1.12173			0.560864	−	0.827908i	$-0.310469\pi$
$541$	26.0907			1.12173			0.560864	+	0.827908i	$0.310469\pi$
$542$	−1.02006	−	5.78505i	−0.0438154	−	0.248489i
$543$	−19.1327	−	11.7321i	−0.821062	−	0.503472i
$544$	−2.18346	−	5.99900i	−0.0936149	−	0.257205i
$545$	−10.3631	−	8.69567i	−0.443906	−	0.372482i
$546$	25.6881	−	16.3957i	1.09935	−	0.701673i
$547$	−40.8376	−	14.8637i	−1.74609	−	0.635525i	−0.746536	−	0.665345i	$-0.768284\pi$
$547$	−40.8376	−	14.8637i	−1.74609	−	0.635525i	−0.999555	+	0.0298202i	$0.990507\pi$
$548$	−8.58553	+	4.95686i	−0.366756	+	0.211746i
$549$	7.73300	+	10.2743i	0.330036	+	0.438496i
$550$	1.54580	−	2.67740i	0.0659130	−	0.114165i
$551$	4.82785	−	4.05105i	0.205673	−	0.172581i
$552$	−2.92552	+	14.3583i	−0.124518	+	0.611130i
$553$	27.8839	−	6.98585i	1.18574	−	0.297068i
$554$	−10.4511	−	1.84281i	−0.444024	−	0.0782933i
$555$	17.4030	+	15.4058i	0.738717	+	0.653939i
$556$	3.77331	+	4.49686i	0.160024	+	0.190709i
$557$	−2.66929	−	1.54111i	−0.113101	−	0.0652990i	0.442382	−	0.896827i	$-0.354133\pi$
$557$	−2.66929	−	1.54111i	−0.113101	−	0.0652990i	−0.555483	+	0.831528i	$0.687467\pi$
$558$	−2.64359	−	0.140065i	−0.111912	−	0.00592942i
$559$	−51.2765	+	29.6045i	−2.16877	+	1.25214i
$560$	0.489281	+	6.88479i	0.0206759	+	0.290935i
$561$	11.7812	+	14.8198i	0.497404	+	0.625691i
$562$	1.12173	+	0.941246i	0.0473175	+	0.0397041i
$563$	7.80618	−	2.84122i	0.328991	−	0.119743i	−0.172243	−	0.985054i	$-0.555102\pi$
$563$	7.80618	−	2.84122i	0.328991	−	0.119743i	0.501235	+	0.865311i	$0.332879\pi$
$564$	−5.80837	−	10.7050i	−0.244577	−	0.450762i
$565$	−47.5832	+	8.39021i	−2.00184	+	0.352979i
$566$	5.71980			0.240421
$567$	21.0247	−	11.1787i	0.882954	−	0.469460i
$568$	−3.11426			−0.130672
$569$	−14.6123	+	2.57654i	−0.612579	+	0.108014i	−0.471326	−	0.881959i	$-0.656224\pi$
$569$	−14.6123	+	2.57654i	−0.612579	+	0.108014i	−0.141253	+	0.989973i	$0.545113\pi$
$570$	3.40080	+	6.26778i	0.142444	+	0.262528i
$571$	18.9116	−	6.88326i	0.791425	−	0.288055i	0.0854969	−	0.996338i	$-0.472752\pi$
$571$	18.9116	−	6.88326i	0.791425	−	0.288055i	0.705928	+	0.708283i	$0.250530\pi$
$572$	−8.72219	−	7.31879i	−0.364693	−	0.306014i
$573$	−1.32772	−	1.67015i	−0.0554663	−	0.0697717i
$574$	−2.16270	+	0.153696i	−0.0902693	+	0.00641517i
$575$	−13.2295	+	7.63806i	−0.551709	+	0.318529i
$576$	1.36044	+	2.67380i	0.0566849	+	0.111408i
$577$	−13.3663	−	7.71706i	−0.556448	−	0.321265i	0.195271	−	0.980749i	$-0.437442\pi$
$577$	−13.3663	−	7.71706i	−0.556448	−	0.321265i	−0.751719	+	0.659484i	$0.770775\pi$
$578$	15.2697	+	18.1977i	0.635135	+	0.756925i
$579$	34.0503	+	30.1426i	1.41508	+	1.25268i
$580$	10.2597	+	1.80907i	0.426012	+	0.0751174i
$581$	2.51729	−	0.630666i	0.104435	−	0.0261644i
$582$	−6.34743	+	31.1529i	−0.263109	+	1.29133i
$583$	8.85369	−	7.42913i	0.366682	−	0.307683i
$584$	0.605023	−	1.04793i	0.0250360	−	0.0433637i
$585$	51.6613	−	6.31313i	2.13593	−	0.261016i
$586$	−18.3673	+	10.6044i	−0.758745	+	0.438062i
$587$	21.2817	+	7.74592i	0.878391	+	0.319708i	0.741560	−	0.670886i	$-0.234086\pi$
$587$	21.2817	+	7.74592i	0.878391	+	0.319708i	0.136831	+	0.990594i	$0.456308\pi$
$588$	10.1236	+	6.67183i	0.417489	+	0.275141i
$589$	−1.06681	−	0.895158i	−0.0439571	−	0.0368844i
$590$	0.804286	+	2.20976i	0.0331119	+	0.0909743i
$591$	−15.5800	−	9.55359i	−0.640876	−	0.392982i
$592$	0.893208	+	5.06563i	0.0367106	+	0.208196i
$593$	3.92178			0.161048			0.0805242	−	0.996753i	$-0.474341\pi$
$593$	3.92178			0.161048			0.0805242	+	0.996753i	$0.474341\pi$
$594$	−6.34017	−	6.24120i	−0.260140	−	0.256079i
$595$	−17.9678	−	40.2335i	−0.736609	−	1.64941i
$596$	2.92838	−	0.516353i	0.119951	−	0.0211506i
$597$	0.312355	−	11.7990i	0.0127838	−	0.482902i
$598$	19.2422	+	52.8674i	0.786871	+	2.16191i
$599$	−6.18718	+	7.37360i	−0.252802	+	0.301277i	−0.877488	−	0.479599i	$-0.840782\pi$
$599$	−6.18718	+	7.37360i	−0.252802	+	0.301277i	0.624687	+	0.780876i	$0.285227\pi$
$600$	−1.14707	+	2.90956i	−0.0468290	+	0.118782i
$601$	2.98399	−	8.19846i	0.121720	−	0.334422i	−0.863836	−	0.503773i	$-0.831945\pi$
$601$	2.98399	−	8.19846i	0.121720	−	0.334422i	0.985556	+	0.169351i	$0.0541671\pi$
$602$	−19.0733	−	13.8245i	−0.777368	−	0.563445i
$603$	−26.0940	−	24.3611i	−1.06263	−	0.992060i
$604$	−0.834797	+	1.44591i	−0.0339674	+	0.0588333i
$605$	16.1244	−	13.5299i	0.655549	−	0.550071i
$606$	1.03696	+	3.10211i	0.0421238	+	0.126015i
$607$	−20.4674	−	3.60895i	−0.830745	−	0.146483i	−0.257926	−	0.966165i	$-0.583039\pi$
$607$	−20.4674	−	3.60895i	−0.830745	−	0.146483i	−0.572819	+	0.819682i	$0.694150\pi$
$608$	−0.274045	+	1.55419i	−0.0111140	+	0.0630305i
$609$	13.4819	−	12.3749i	0.546315	−	0.501458i
$610$	−8.56611	+	7.18782i	−0.346832	+	0.291026i
$611$	−40.4966	−	23.3807i	−1.63832	−	0.945882i
$612$	−13.9994	−	13.0697i	−0.565892	−	0.528310i
$613$	14.4313	+	24.9958i	0.582875	+	1.00957i	0.995137	+	0.0985035i	$0.0314056\pi$
$613$	14.4313	+	24.9958i	0.582875	+	1.00957i	−0.412262	+	0.911065i	$0.635261\pi$
$614$	10.1985	+	3.71195i	0.411578	+	0.149802i
$615$	−3.44482	−	1.35809i	−0.138908	−	0.0547635i
$616$	1.24368	−	4.35588i	0.0501094	−	0.175503i
$617$	−5.76580	−	15.8414i	−0.232122	−	0.637751i	0.767874	−	0.640601i	$-0.221315\pi$
$617$	−5.76580	−	15.8414i	−0.232122	−	0.637751i	−0.999996	+	0.00285055i	$0.999093\pi$
$618$	31.1741	+	0.825269i	1.25401	+	0.0331972i
$619$	−11.3516	+	2.00160i	−0.456261	+	0.0804511i	−0.397055	−	0.917795i	$-0.629968\pi$
$619$	−11.3516	+	2.00160i	−0.456261	+	0.0804511i	−0.0592057	+	0.998246i	$0.518857\pi$
$620$		−	2.30206i		−	0.0924529i
$621$	11.7113	+	42.3712i	0.469959	+	1.70030i
$622$			5.97204i			0.239457i
$623$	−6.04862	+	4.08984i	−0.242333	+	0.163856i
$624$	9.81923	+	6.02110i	0.393084	+	0.241037i
$625$	28.9124	−	10.5232i	1.15649	−	0.420930i
$626$	2.92517	+	2.45451i	0.116913	+	0.0981019i
$627$	−0.690437	−	4.62890i	−0.0275734	−	0.184861i
$628$	2.57329	−	7.07006i	0.102685	−	0.282126i
$629$	−16.4189	−	28.4384i	−0.654666	−	1.13391i
$630$	10.6746	+	17.7429i	0.425285	+	0.706894i
$631$	11.5880	−	20.0711i	0.461313	−	0.799017i	−0.537714	−	0.843127i	$-0.680712\pi$
$631$	11.5880	−	20.0711i	0.461313	−	0.799017i	0.999027	+	0.0441100i	$0.0140452\pi$
$632$	6.98379	+	8.32295i	0.277800	+	0.331069i
$633$	0.101252	−	0.496939i	0.00402440	−	0.0197516i
$634$	3.09800	−	17.5696i	0.123037	−	0.697779i
$635$	−1.04219	+	5.91057i	−0.0413582	+	0.234554i
$636$	−7.74983	+	8.75453i	−0.307301	+	0.347140i
$637$	46.5258	+	1.51903i	1.84342	+	0.0601861i
$638$	−5.92139	−	3.41872i	−0.234430	−	0.135348i
$639$	−8.32692	+	4.23676i	−0.329408	+	0.167604i
$640$	−2.25926	+	1.30438i	−0.0893051	+	0.0515603i
$641$	−5.63020	+	15.4689i	−0.222380	+	0.610983i	−0.999839	−	0.0179503i	$-0.994286\pi$
$641$	−5.63020	+	15.4689i	−0.222380	+	0.610983i	0.777459	+	0.628933i	$0.216508\pi$
$642$	16.7935	−	13.3503i	0.662786	−	0.526894i
$643$	−20.4845	+	24.4125i	−0.807832	+	0.962736i	−0.999826	−	0.0186599i	$-0.994060\pi$
$643$	−20.4845	+	24.4125i	−0.807832	+	0.962736i	0.191994	+	0.981396i	$0.438504\pi$
$644$	−16.0835	+	15.5670i	−0.633780	+	0.613426i
$645$	−19.1863	−	35.3609i	−0.755458	−	1.39233i
$646$	−1.74950	−	9.92192i	−0.0688332	−	0.390373i
$647$	−18.2647			−0.718060			−0.359030	−	0.933326i	$-0.616892\pi$
$647$	−18.2647			−0.718060			−0.359030	+	0.933326i	$0.616892\pi$
$648$	7.27508	+	5.29842i	0.285792	+	0.208141i
$649$		−	1.54336i		−	0.0605823i
$650$	2.08514	+	11.8254i	0.0817860	+	0.463832i
$651$	−3.21025	−	2.45899i	−0.125820	−	0.0963756i
$652$	−6.67510	+	2.42954i	−0.261417	+	0.0951480i
$653$	8.08178	−	9.63149i	0.316264	−	0.376909i	−0.584370	−	0.811488i	$-0.698658\pi$
$653$	8.08178	−	9.63149i	0.316264	−	0.376909i	0.900634	+	0.434578i	$0.143103\pi$
$654$	−5.58925	−	7.03079i	−0.218557	−	0.274926i
$655$	−33.9227	−	12.3469i	−1.32547	−	0.482432i
$656$	−0.409743	−	0.709695i	−0.0159978	−	0.0277089i
$657$	0.192066	−	3.62505i	0.00749321	−	0.141427i
$658$	1.92367	−	18.5044i	0.0749924	−	0.721377i
$659$	11.1909	+	13.3368i	0.435935	+	0.519527i	0.938625	−	0.344940i	$-0.112101\pi$
$659$	11.1909	+	13.3368i	0.435935	+	0.519527i	−0.502690	+	0.864467i	$0.667656\pi$
$660$	5.12797	−	5.79277i	0.199606	−	0.225483i
$661$	−17.2877	−	3.04829i	−0.672413	−	0.118565i	−0.172991	−	0.984923i	$-0.555343\pi$
$661$	−17.2877	−	3.04829i	−0.672413	−	0.118565i	−0.499422	+	0.866359i	$0.666454\pi$
$662$	−20.5923	−	3.63098i	−0.800343	−	0.141122i
$663$	−72.0523	−	14.6807i	−2.79828	−	0.570152i
$664$	0.630480	+	0.751377i	0.0244674	+	0.0291591i
$665$	−1.12631	+	10.8343i	−0.0436763	+	0.420137i
$666$	9.27974	+	12.3293i	0.359583	+	0.477752i
$667$	16.8925	+	29.2587i	0.654080	+	1.13290i
$668$	−11.1585	−	4.06137i	−0.431737	−	0.157139i
$669$	−29.0962	+	4.33993i	−1.12492	+	0.167791i
$670$	19.9539	−	23.7801i	0.770887	−	0.918707i
$671$	6.89643	−	2.51010i	0.266234	−	0.0969012i
$672$	−0.594294	+	4.54388i	−0.0229254	+	0.175284i
$673$	5.35143	+	30.3495i	0.206283	+	1.16989i	0.895409	+	0.445245i	$0.146883\pi$
$673$	5.35143	+	30.3495i	0.206283	+	1.16989i	−0.689126	+	0.724641i	$0.742005\pi$
$674$			25.5636i			0.984673i
$675$	0.891241	+	9.34011i	0.0343039	+	0.359501i
$676$	31.2236			1.20091
$677$	−3.20150	−	18.1566i	−0.123044	−	0.697814i	−0.982451	−	0.186523i	$-0.940278\pi$
$677$	−3.20150	−	18.1566i	−0.123044	−	0.697814i	0.859407	−	0.511292i	$-0.170833\pi$
$678$	−32.0683	−	0.848940i	−1.23157	−	0.0326033i
$679$	−34.8961	+	33.7754i	−1.33919	+	1.29618i
$680$	10.7052	−	12.7580i	0.410526	−	0.489246i
$681$	−42.8287	−	16.8849i	−1.64120	−	0.647030i
$682$	−0.516746	+	1.41975i	−0.0197872	+	0.0543649i
$683$	−3.63658	+	2.09958i	−0.139150	+	0.0803382i	−0.567959	−	0.823057i	$-0.692267\pi$
$683$	−3.63658	+	2.09958i	−0.139150	+	0.0803382i	0.428809	+	0.903395i	$0.358933\pi$
$684$	1.38163	+	4.52840i	0.0528280	+	0.173148i
$685$	−22.3976	−	12.9313i	−0.855770	−	0.494079i
$686$	6.99621	+	17.1480i	0.267117	+	0.654713i
$687$	0.378395	+	1.13198i	0.0144367	+	0.0431878i
$688$	1.54608	−	8.76824i	0.0589436	−	0.334286i
$689$	−7.79513	+	44.2084i	−0.296971	+	1.68421i
$690$	−36.2551	+	12.1192i	−1.38021	+	0.461371i
$691$	−7.54937	−	8.99699i	−0.287192	−	0.342262i	0.603089	−	0.797674i	$-0.293936\pi$
$691$	−7.54937	−	8.99699i	−0.287192	−	0.342262i	−0.890281	+	0.455412i	$0.849492\pi$
$692$	−2.76662	+	4.79193i	−0.105171	+	0.182162i
$693$	−2.60055	−	13.3387i	−0.0987867	−	0.506696i
$694$	−2.70177	−	4.67961i	−0.102558	−	0.177635i
$695$	−5.23772	+	14.3905i	−0.198678	+	0.545864i
$696$	6.43485	+	2.53688i	0.243912	+	0.0961604i
$697$	4.00763	+	3.36280i	0.151800	+	0.127375i
$698$	−12.6398	+	4.60051i	−0.478423	+	0.174132i
$699$	−0.241676	+	9.12918i	−0.00914102	+	0.345297i
$700$	−3.95757	+	2.67595i	−0.149582	+	0.101142i
$701$			18.0424i			0.681453i	0.940162	+	0.340726i	$0.110673\pi$
$701$			18.0424i			0.681453i	−0.940162	+	0.340726i	$0.889327\pi$
$702$	34.4460	+	2.74078i	1.30008	+	0.103444i
$703$			8.11772i			0.306165i
$704$	1.68615	−	0.297313i	0.0635491	−	0.0112054i
$705$	16.6090	−	27.0861i	0.625533	−	1.02012i
$706$	−3.00674	−	8.26095i	−0.113160	−	0.310905i
$707$	−1.37172	+	4.80431i	−0.0515887	+	0.180685i
$708$	0.230331	+	1.54421i	0.00865636	+	0.0580349i
$709$	−24.2443	−	8.82421i	−0.910514	−	0.331400i	−0.156056	−	0.987748i	$-0.549878\pi$
$709$	−24.2443	−	8.82421i	−0.910514	−	0.331400i	−0.754458	+	0.656348i	$0.772100\pi$
$710$	−4.06220	−	7.03593i	−0.152451	−	0.264054i
$711$	29.9961	+	12.7529i	1.12494	+	0.478271i
$712$	−2.38999	−	1.37986i	−0.0895688	−	0.0517126i
$713$	5.71887	−	4.79870i	0.214173	−	0.179713i
$714$	−6.35618	−	28.5563i	−0.237874	−	1.06869i
$715$	5.15795	−	29.2522i	0.192896	−	1.09397i
$716$	18.6407	+	3.28686i	0.696637	+	0.122836i
$717$	25.8875	−	29.2436i	0.966786	−	1.09212i
$718$	20.7822	−	17.4383i	0.775585	−	0.650793i
$719$	17.8367	−	30.8941i	0.665198	−	1.15216i	−0.314034	−	0.949412i	$-0.601681\pi$
$719$	17.8367	−	30.8941i	0.665198	−	1.15216i	0.979232	−	0.202744i	$-0.0649860\pi$
$720$	−4.26627	+	6.56124i	−0.158995	+	0.244523i
$721$	38.5700	+	27.9560i	1.43642	+	1.04113i
$722$	5.64655	−	15.5138i	0.210143	−	0.577363i
$723$	−25.1977	−	31.6966i	−0.937114	−	1.17881i
$724$	8.32901	−	9.92613i	0.309545	−	0.368902i
$725$	2.46626	+	6.77599i	0.0915945	+	0.251654i
$726$	12.2834	−	6.66480i	0.455881	−	0.247354i
$727$	17.0647	−	3.00897i	0.632895	−	0.111596i	0.152008	−	0.988379i	$-0.451426\pi$
$727$	17.0647	−	3.00897i	0.632895	−	0.111596i	0.480886	+	0.876783i	$0.340315\pi$
$728$	7.17455	+	16.0652i	0.265906	+	0.595417i
$729$	26.6603	+	4.26961i	0.987418	+	0.158134i
$730$	3.15673			0.116836
$731$	9.87015	+	55.9764i	0.365061	+	2.07036i
$732$	−6.52561	+	3.54069i	−0.241194	+	0.130868i
$733$	1.69293	+	4.65129i	0.0625298	+	0.171799i	0.967023	−	0.254689i	$-0.0819729\pi$
$733$	1.69293	+	4.65129i	0.0625298	+	0.171799i	−0.904493	+	0.426488i	$0.859751\pi$
$734$	16.7696	+	14.0714i	0.618979	+	0.519385i
$735$	−1.86836	+	31.5744i	−0.0689154	+	1.16464i
$736$	−7.94988	−	2.89352i	−0.293037	−	0.106657i
$737$	−17.6441	+	10.1868i	−0.649930	+	0.375237i
$738$	−2.06107	−	1.34015i	−0.0758689	−	0.0493317i
$739$	10.0817	−	17.4621i	0.370863	−	0.642353i	−0.618836	−	0.785520i	$-0.712395\pi$
$739$	10.0817	−	17.4621i	0.370863	−	0.642353i	0.989699	+	0.143167i	$0.0457287\pi$
$740$	−10.2795	+	8.62552i	−0.377882	+	0.317080i
$741$	13.6108	+	12.0488i	0.500007	+	0.442625i
$742$	−17.3243	+	4.34032i	−0.635996	+	0.159338i
$743$	11.0456	+	1.94764i	0.405224	+	0.0714519i	0.372545	−	0.928014i	$-0.378485\pi$
$743$	11.0456	+	1.94764i	0.405224	+	0.0714519i	0.0326787	+	0.999466i	$0.489596\pi$
$744$	0.305147	−	1.49765i	0.0111872	−	0.0549063i
$745$	4.98631	+	5.94246i	0.182684	+	0.217715i
$746$	−4.11363	−	2.37500i	−0.150611	−	0.0869551i
$747$	2.70798	+	1.15130i	0.0990798	+	0.0421240i
$748$	−9.46603	+	5.46521i	−0.346112	+	0.199828i
$749$	32.6883	−	2.32306i	1.19440	−	0.0848827i
$750$	14.2757	−	2.12933i	0.521275	−	0.0777523i
$751$	−1.24071	−	1.04108i	−0.0452740	−	0.0379894i	0.619870	−	0.784705i	$-0.287185\pi$
$751$	−1.24071	−	1.04108i	−0.0452740	−	0.0379894i	−0.665144	+	0.746715i	$0.731630\pi$
$752$	6.60763	−	2.40498i	0.240956	−	0.0877007i
$753$	16.5521	−	26.9932i	0.603192	−	0.983686i
$754$	26.1534	−	4.61154i	0.952449	−	0.167942i
$755$	−4.35558			−0.158516
$756$	4.59264	+	12.9579i	0.167033	+	0.471275i
$757$	25.8070			0.937972			0.468986	−	0.883206i	$-0.344619\pi$
$757$	25.8070			0.937972			0.468986	+	0.883206i	$0.344619\pi$
$758$	−24.6695	+	4.34990i	−0.896036	+	0.157995i
$759$	25.0800	+	0.663941i	0.910347	+	0.0240995i
$760$	−3.86877	+	1.40812i	−0.140335	+	0.0510777i
$761$	28.5821	+	23.9832i	1.03610	+	0.869391i	0.991564	−	0.129617i	$-0.0413747\pi$
$761$	28.5821	+	23.9832i	1.03610	+	0.869391i	0.0445359	+	0.999008i	$0.485819\pi$
$762$	−1.46149	+	3.70708i	−0.0529441	+	0.134293i
$763$	−0.972575	−	13.6853i	−0.0352096	−	0.495442i
$764$	1.06680	−	0.615918i	0.0385955	−	0.0222831i
$765$	11.2672	−	48.6761i	0.407365	−	1.75989i
$766$	−9.13403	−	5.27353i	−0.330026	−	0.190540i
$767$	3.85317	+	4.59203i	0.139130	+	0.165809i
$768$	−1.64270	+	0.549117i	−0.0592759	+	0.0198145i
$769$	−24.6590	−	4.34804i	−0.889226	−	0.156795i	−0.289669	−	0.957127i	$-0.593545\pi$
$769$	−24.6590	−	4.34804i	−0.889226	−	0.156795i	−0.599557	+	0.800332i	$0.704656\pi$
$770$	11.4633	−	2.87194i	0.413109	−	0.103498i
$771$	1.59909	−	0.534540i	0.0575900	−	0.0192510i
$772$	−20.1126	+	16.8765i	−0.723869	+	0.607398i
$773$	11.4775	−	19.8797i	0.412818	−	0.715022i	−0.582378	−	0.812918i	$-0.697878\pi$
$773$	11.4775	−	19.8797i	0.412818	−	0.715022i	0.995197	+	0.0978955i	$0.0312111\pi$
$774$	−7.79474	−	25.5479i	−0.280176	−	0.918299i
$775$	1.37991	−	0.796690i	0.0495677	−	0.0286179i
$776$	−17.2487	−	6.27801i	−0.619192	−	0.225367i
$777$	1.04815	+	23.5484i	0.0376021	+	0.844796i
$778$	17.5114	+	14.6938i	0.627815	+	0.526799i
$779$	−0.442328	−	1.21529i	−0.0158480	−	0.0435421i
$780$	−0.795193	+	30.0380i	−0.0284725	+	1.07553i
$781$	0.925912	+	5.25111i	0.0331318	+	0.187899i
$782$	54.0092			1.93136
$783$	20.6568	−	1.97109i	0.738213	−	0.0704408i
$784$	−4.67210	+	5.21263i	−0.166861	+	0.186165i
$785$	19.3297	−	3.40834i	0.689905	−	0.121649i
$786$	−20.4324	−	12.5291i	−0.728800	−	0.446897i
$787$	−15.2313	−	41.8475i	−0.542936	−	1.49170i	−0.843069	−	0.537806i	$-0.819253\pi$
$787$	−15.2313	−	41.8475i	−0.542936	−	1.49170i	0.300133	−	0.953897i	$-0.402969\pi$
$788$	6.78242	−	8.08298i	0.241614	−	0.287944i
$789$	−37.5801	+	5.60536i	−1.33789	+	0.199556i
$790$	−9.69417	+	26.6345i	−0.344903	+	0.947613i
$791$	−39.6763	−	28.7578i	−1.41073	−	1.02251i
$792$	4.10395	−	3.08886i	0.145827	−	0.109758i
$793$	−14.2525	+	24.6861i	−0.506122	+	0.876629i
$794$	13.1228	−	11.0113i	0.465710	−	0.390777i
$795$	−29.8875	−	6.08961i	−1.06000	−	0.215976i
$796$	6.71103	+	1.18334i	0.237866	+	0.0419423i
$797$	9.17058	−	52.0089i	0.324839	−	1.84225i	−0.185968	−	0.982556i	$-0.559542\pi$
$797$	9.17058	−	52.0089i	0.324839	−	1.84225i	0.510807	−	0.859696i	$-0.329347\pi$
$798$	−2.16887	+	6.89916i	−0.0767772	+	0.244228i
$799$	−34.3880	+	28.8550i	−1.21656	+	1.02081i
$800$	−1.56376	−	0.902835i	−0.0552871	−	0.0319200i
$801$	−8.26758	−	0.438041i	−0.292121	−	0.0154774i
$802$	10.7094	+	18.5492i	0.378161	+	0.654994i
$803$	−1.94685	−	0.708595i	−0.0687028	−	0.0250058i
$804$	16.1335	−	12.8256i	0.568985	−	0.452325i
$805$	−56.1490	−	16.0316i	−1.97899	−	0.565038i
$806$	−2.00706	−	5.51435i	−0.0706956	−	0.194235i
$807$	9.13730	+	16.8403i	0.321648	+	0.592808i
$808$	−1.85973	+	0.327921i	−0.0654252	+	0.0115362i
$809$		−	37.0491i		−	1.30258i	−0.758831	−	0.651288i	$-0.774229\pi$
$809$		−	37.0491i		−	1.30258i	0.758831	−	0.651288i	$-0.225771\pi$
$810$	−2.48100	+	23.3475i	−0.0871734	+	0.820346i
$811$		−	31.7238i		−	1.11397i	−0.830522	−	0.556986i	$-0.811958\pi$
$811$		−	31.7238i		−	1.11397i	0.830522	−	0.556986i	$-0.188042\pi$
$812$	5.91819	+	8.75264i	0.207688	+	0.307158i
$813$	8.94298	−	4.85232i	0.313644	−	0.170178i
$814$	8.27585	−	3.01216i	0.290068	−	0.105576i
$815$	−14.1958	−	11.9117i	−0.497259	−	0.417249i
$816$	8.65559	−	6.88092i	0.303006	−	0.240880i
$817$	4.80578	−	13.2038i	0.168133	−	0.461942i
$818$	−6.99169	−	12.1100i	−0.244459	−	0.423415i
$819$	41.0390	+	33.1947i	1.43402	+	1.15992i
$820$	1.06892	−	1.85143i	0.0373284	−	0.0646547i
$821$	−5.14728	−	6.13429i	−0.179641	−	0.214088i	0.668708	−	0.743525i	$-0.266848\pi$
$821$	−5.14728	−	6.13429i	−0.179641	−	0.214088i	−0.848349	+	0.529437i	$0.822403\pi$
$822$	−12.8571	−	11.3816i	−0.448443	−	0.396978i
$823$	3.04272	−	17.2561i	0.106063	−	0.601511i	−0.884728	−	0.466108i	$-0.845656\pi$
$823$	3.04272	−	17.2561i	0.106063	−	0.601511i	0.990791	−	0.135403i	$-0.0432329\pi$
$824$	−3.12648	+	17.7312i	−0.108916	+	0.617694i
$825$	5.24699	+	1.06908i	0.182677	+	0.0372206i
$826$	−1.04304	+	2.14473i	−0.0362922	+	0.0746247i
$827$	−2.60090	−	1.50163i	−0.0904421	−	0.0522168i	0.454097	−	0.890952i	$-0.349962\pi$
$827$	−2.60090	−	1.50163i	−0.0904421	−	0.0522168i	−0.544539	+	0.838736i	$0.683295\pi$
$828$	−25.1929	+	3.07863i	−0.875512	+	0.106990i
$829$	−12.4560	+	7.19145i	−0.432613	+	0.249769i	−0.700459	−	0.713692i	$-0.747021\pi$
$829$	−12.4560	+	7.19145i	−0.432613	+	0.249769i	0.267846	+	0.963462i	$0.413688\pi$
$830$	−0.875167	+	2.40450i	−0.0303775	+	0.0834615i
$831$	−2.71168	−	18.1799i	−0.0940670	−	0.630654i
$832$	−4.27459	+	5.09426i	−0.148195	+	0.176612i
$833$	16.6464	−	41.4719i	0.576762	−	1.43691i
$834$	−5.31501	+	8.66773i	−0.184044	+	0.300139i
$835$	−5.37931	−	30.5076i	−0.186159	−	1.05576i
$836$	2.70206			0.0934529
$837$	−1.22155	−	4.41954i	−0.0422230	−	0.152762i
$838$		−	1.67948i		−	0.0580166i
$839$	7.03061	+	39.8726i	0.242724	+	1.37655i	0.825720	+	0.564080i	$0.190769\pi$
$839$	7.03061	+	39.8726i	0.242724	+	1.37655i	−0.582997	+	0.812474i	$0.698120\pi$
$840$	−11.0410	+	4.58429i	−0.380950	+	0.158173i
$841$	−12.2652	+	4.46416i	−0.422937	+	0.153937i
$842$	−19.0564	+	22.7105i	−0.656727	+	0.782656i
$843$	−0.930225	+	2.35953i	−0.0320386	+	0.0812665i
$844$	0.275145	+	0.100144i	0.00947087	+	0.00344711i
$845$	40.7276	+	70.5423i	1.40107	+	2.42673i
$846$	14.3957	−	15.4197i	0.494933	−	0.530141i
$847$	21.2328	+	2.20731i	0.729569	+	0.0758441i
$848$	−4.33904	−	5.17107i	−0.149003	−	0.177575i
$849$	3.14084	+	9.39593i	0.107793	+	0.322467i
$850$	11.3523	+	2.00171i	0.389379	+	0.0686581i
$851$	−42.8557	−	7.55662i	−1.46908	−	0.259038i
$852$	−1.71009	−	5.11581i	−0.0585869	−	0.175265i
$853$	10.7909	+	12.8601i	0.369473	+	0.440321i	0.918462	−	0.395508i	$-0.129432\pi$
$853$	10.7909	+	12.8601i	0.369473	+	0.440321i	−0.548989	+	0.835830i	$0.684987\pi$
$854$	−11.2800	−	1.17264i	−0.385994	−	0.0401269i
$855$	−8.42866	+	9.02824i	−0.288254	+	0.308759i
$856$	6.19309	+	10.7267i	0.211675	+	0.366632i
$857$	−37.4450	−	13.6289i	−1.27910	−	0.465554i	−0.388964	−	0.921253i	$-0.627167\pi$
$857$	−37.4450	−	13.6289i	−1.27910	−	0.465554i	−0.890134	+	0.455699i	$0.849389\pi$
$858$	7.23309	−	18.3468i	0.246934	−	0.626350i
$859$	11.7894	−	14.0501i	0.402251	−	0.479384i	−0.526454	−	0.850204i	$-0.676479\pi$
$859$	11.7894	−	14.0501i	0.402251	−	0.479384i	0.928705	+	0.370820i	$0.120923\pi$
$860$	21.8264	−	7.94416i	0.744274	−	0.270894i
$861$	−1.44005	−	3.46827i	−0.0490768	−	0.118198i
$862$	−0.698392	−	3.96078i	−0.0237873	−	0.134905i
$863$		−	47.2485i		−	1.60836i	−0.594388	−	0.804179i	$-0.702606\pi$
$863$		−	47.2485i		−	1.60836i	0.594388	−	0.804179i	$-0.297394\pi$
$864$	−3.64522	+	3.70302i	−0.124013	+	0.125979i
$865$	−14.4350			−0.490803
$866$	−2.33240	−	13.2277i	−0.0792582	−	0.449495i
$867$	−21.5086	+	35.0762i	−0.730469	+	1.19125i
$868$	1.67760	−	1.62372i	0.0569414	−	0.0551126i
$869$	11.9574	−	14.2502i	0.405626	−	0.483406i
$870$	2.66203	+	17.8471i	0.0902512	+	0.605072i
$871$	27.0648	−	74.3598i	0.917054	−	2.51959i
$872$	4.49087	−	2.59281i	0.152080	−	0.0878035i
$873$	−54.6604	+	6.67963i	−1.84997	+	0.226071i
$874$	−11.5626	−	6.67569i	−0.391112	−	0.225809i
$875$	19.8273	+	9.64261i	0.670286	+	0.325980i
$876$	2.05367	+	0.418436i	0.0693869	+	0.0141377i
$877$	4.68898	−	26.5925i	0.158336	−	0.897967i	−0.797337	−	0.603535i	$-0.793758\pi$
$877$	4.68898	−	26.5925i	0.158336	−	0.897967i	0.955672	−	0.294432i	$-0.0951304\pi$
$878$	−0.0989287	+	0.561053i	−0.00333868	+	0.0189346i
$879$	−27.5056	−	24.3489i	−0.927740	−	0.821270i
$880$	2.87109	+	3.42164i	0.0967845	+	0.115343i
$881$	1.97656	−	3.42350i	0.0665919	−	0.115341i	−0.830807	−	0.556560i	$-0.812121\pi$
$881$	1.97656	−	3.42350i	0.0665919	−	0.115341i	0.897399	+	0.441220i	$0.145454\pi$
$882$	−5.40080	+	20.2936i	−0.181854	+	0.683322i
$883$	−19.1656	−	33.1958i	−0.644974	−	1.11713i	−0.984308	−	0.176461i	$-0.943535\pi$
$883$	−19.1656	−	33.1958i	−0.644974	−	1.11713i	0.339334	−	0.940666i	$-0.389798\pi$
$884$	14.5202	−	39.8938i	0.488366	−	1.34177i
$885$	−3.18833	+	2.53462i	−0.107174	+	0.0852002i
$886$	−24.7916	−	20.8026i	−0.832888	−	0.698876i
$887$	−1.93287	+	0.703507i	−0.0648994	+	0.0236215i	−0.374266	−	0.927321i	$-0.622105\pi$
$887$	−1.93287	+	0.703507i	−0.0648994	+	0.0236215i	0.309366	+	0.950943i	$0.399883\pi$
$888$	−7.83085	+	4.24890i	−0.262786	+	0.142584i
$889$	−5.04235	+	3.40944i	−0.169115	+	0.114349i
$890$		−	7.19949i		−	0.241327i
$891$	6.77094	−	13.8422i	0.226835	−	0.463730i
$892$		−	16.9845i		−	0.568685i
$893$	10.9286	−	1.92700i	0.365710	−	0.0644846i
$894$	2.45624	+	4.52693i	0.0821489	+	0.151403i
$895$	16.8888	+	46.4016i	0.564530	+	1.55103i
$896$	−2.54409	−	0.726382i	−0.0849919	−	0.0242667i
$897$	−76.2792	+	60.6395i	−2.54689	+	2.02470i
$898$	−7.42164	−	2.70126i	−0.247663	−	0.0901421i
$899$	−1.76197	−	3.05183i	−0.0587651	−	0.101784i
$900$	−5.40942	−	0.286607i	−0.180314	−	0.00955357i
$901$	37.3207	+	21.5471i	1.24333	+	0.717838i
$902$	−1.07483	+	0.901889i	−0.0357879	+	0.0300296i
$903$	12.2361	−	38.9230i	0.407192	−	1.29528i
$904$	3.21616	−	18.2397i	0.106968	−	0.606645i
$905$	33.2899	+	5.86991i	1.10659	+	0.195123i
$906$	−2.83360	−	0.577349i	−0.0941401	−	0.0191811i
$907$	30.4959	−	25.5891i	1.01260	−	0.849673i	0.0239210	−	0.999714i	$-0.492385\pi$
$907$	30.4959	−	25.5891i	1.01260	−	0.849673i	0.988680	+	0.150041i	$0.0479406\pi$
$908$	13.2897	−	23.0185i	0.441035	−	0.763894i
$909$	−4.52644	+	3.40685i	−0.150132	+	0.112998i
$910$	−26.9371	+	37.1644i	−0.892957	+	1.23199i
$911$	1.01769	−	2.79608i	0.0337175	−	0.0926382i	−0.921692	−	0.387923i	$-0.873192\pi$
$911$	1.01769	−	2.79608i	0.0337175	−	0.0926382i	0.955409	+	0.295285i	$0.0954147\pi$
$912$	−2.70355	+	0.403255i	−0.0895234	+	0.0133531i
$913$	1.07948	−	1.28648i	0.0357257	−	0.0425762i
$914$	8.66890	+	23.8176i	0.286742	+	0.787817i
$915$	−16.5112	−	10.1246i	−0.545845	−	0.334710i
$916$	−0.678629	+	0.119661i	−0.0224225	+	0.00395370i
$917$	−14.9292	−	33.4294i	−0.493006	−	1.10394i
$918$	13.7823	−	30.1736i	0.454882	−	0.995877i
$919$	15.1817			0.500798			0.250399	−	0.968143i	$-0.419438\pi$
$919$	15.1817			0.500798			0.250399	+	0.968143i	$0.419438\pi$
$920$	−3.83249	−	21.7351i	−0.126353	−	0.716585i
$921$	−0.497463	+	18.7914i	−0.0163920	+	0.619198i
$922$	−13.5204	−	37.1469i	−0.445270	−	1.22337i
$923$	−15.8649	−	13.3122i	−0.522199	−	0.438177i
$924$	7.83834	−	0.348887i	0.257863	−	0.0114775i
$925$	−8.72783	−	3.17667i	−0.286969	−	0.104448i
$926$	−8.57202	+	4.94906i	−0.281694	+	0.162636i
$927$	15.7626	+	51.6630i	0.517710	+	1.69683i
$928$	−1.99673	+	3.45843i	−0.0655458	+	0.113529i
$929$	−5.71285	+	4.79365i	−0.187432	+	0.157274i	−0.731676	−	0.681653i	$-0.761261\pi$
$929$	−5.71285	+	4.79365i	−0.187432	+	0.157274i	0.544243	+	0.838928i	$0.316817\pi$
$930$	3.78160	−	1.26410i	0.124003	−	0.0414514i
$931$	−8.68980	+	6.82103i	−0.284797	+	0.223550i
$932$	−5.19248	−	0.915574i	−0.170085	−	0.0299906i
$933$	−9.81029	+	3.27935i	−0.321174	+	0.107361i
$934$	−15.8683	−	18.9111i	−0.519225	−	0.618789i
$935$	−24.6947	−	14.2575i	−0.807602	−	0.466269i
$936$	−4.49898	+	19.4364i	−0.147054	+	0.635297i
$937$	17.4418	−	10.0701i	0.569800	−	0.328974i	−0.187269	−	0.982309i	$-0.559964\pi$
$937$	17.4418	−	10.0701i	0.569800	−	0.328974i	0.757070	+	0.653334i	$0.226630\pi$
$938$	31.4037	−	2.23176i	1.02537	−	0.0728696i
$939$	−2.42577	+	6.15299i	−0.0791619	+	0.200795i
$940$	14.0524	+	11.7913i	0.458338	+	0.384591i
$941$	−42.0905	+	15.3197i	−1.37211	+	0.499408i	−0.919777	−	0.392441i	$-0.871631\pi$
$941$	−42.0905	+	15.3197i	−1.37211	+	0.499408i	−0.452334	+	0.891849i	$0.649408\pi$
$942$	13.0270	+	0.344863i	0.424444	+	0.0112363i
$943$	6.82759	−	1.20389i	0.222337	−	0.0392040i
$944$	−0.901412			−0.0293385
$945$	−23.2847	+	27.2781i	−0.757452	+	0.887355i
$946$	−15.2442			−0.495632
$947$	4.85809	−	0.856612i	0.157867	−	0.0278361i	−0.0941562	−	0.995557i	$-0.530015\pi$
$947$	4.85809	−	0.856612i	0.157867	−	0.0278361i	0.252023	+	0.967721i	$0.418904\pi$
$948$	−9.83722	+	16.0426i	−0.319498	+	0.521038i
$949$	7.56162	−	2.75221i	0.245461	−	0.0893404i
$950$	−2.18295	−	1.83171i	−0.0708242	−	0.0594286i
$951$	30.5628	−	4.55868i	0.991067	−	0.147825i
$952$	16.8480	−	1.19733i	0.546046	−	0.0388058i
$953$	−49.2238	+	28.4194i	−1.59451	+	0.920593i	−0.601996	+	0.798499i	$0.705628\pi$
$953$	−49.2238	+	28.4194i	−1.59451	+	0.920593i	−0.992518	+	0.122095i	$0.961039\pi$
$954$	−18.6366	−	7.92340i	−0.603384	−	0.256530i
$955$	2.78304	+	1.60679i	0.0900569	+	0.0519944i
$956$	14.4941	+	17.2734i	0.468773	+	0.558662i
$957$	2.36440	−	11.6044i	0.0764301	−	0.375115i
$958$	−3.27122	−	0.576805i	−0.105688	−	0.0186357i
$959$	−6.37429	−	25.4429i	−0.205837	−	0.821594i
$960$	−3.38331	−	2.99503i	−0.109196	−	0.0966642i
$961$	23.1509	−	19.4259i	0.746802	−	0.626642i
$962$	−17.1033	+	29.6238i	−0.551432	+	0.955109i
$963$	31.1521	+	20.2558i	1.00386	+	0.652736i
$964$	20.2460	−	11.6890i	0.652079	−	0.376478i
$965$	−64.3630	−	23.4262i	−2.07192	−	0.754116i
$966$	−34.4037	−	17.8724i	−1.10692	−	0.575034i
$967$	30.5452	+	25.6305i	0.982267	+	0.824220i	0.984430	−	0.175778i	$-0.0562440\pi$
$967$	30.5452	+	25.6305i	0.982267	+	0.824220i	−0.00216292	+	0.999998i	$0.500688\pi$
$968$	2.75959	+	7.58192i	0.0886967	+	0.243692i
$969$	15.3381	−	8.32220i	0.492730	−	0.267348i
$970$	−8.31526	−	47.1582i	−0.266987	−	1.51416i
$971$	−34.0504			−1.09273			−0.546365	−	0.837547i	$-0.683989\pi$
$971$	−34.0504			−1.09273			−0.546365	+	0.837547i	$0.683989\pi$
$972$	−4.70885	+	14.8602i	−0.151037	+	0.476642i
$973$	−14.1813	+	6.33319i	−0.454630	+	0.203033i
$974$	27.3158	−	4.81650i	0.875253	−	0.154331i
$975$	−18.2807	+	9.91881i	−0.585450	+	0.317656i
$976$	−1.46604	−	4.02791i	−0.0469268	−	0.128930i
$977$	21.2958	−	25.3793i	0.681312	−	0.811956i	−0.308964	−	0.951074i	$-0.599982\pi$
$977$	21.2958	−	25.3793i	0.681312	−	0.811956i	0.990276	+	0.139117i	$0.0444266\pi$
$978$	−7.65641	−	9.63110i	−0.244825	−	0.307968i
$979$	−1.61608	+	4.44014i	−0.0516501	+	0.141907i
$980$	−17.8709	−	3.75621i	−0.570865	−	0.119988i
$981$	8.48035	−	13.0422i	0.270757	−	0.416406i
$982$	−5.03515	+	8.72114i	−0.160678	+	0.278303i
$983$	32.0118	−	26.8611i	1.02102	−	0.856735i	0.0312625	−	0.999511i	$-0.490047\pi$
$983$	32.0118	−	26.8611i	1.02102	−	0.856735i	0.989755	+	0.142776i	$0.0456028\pi$
$984$	0.940821	−	1.06279i	0.0299923	−	0.0338805i
$985$	27.1084	+	4.77995i	0.863746	+	0.152302i
$986$	4.42702	−	25.1069i	0.140985	−	0.799566i
$987$	31.4535	−	7.00106i	1.00118	−	0.222846i
$988$	−8.03957	+	6.74600i	−0.255773	+	0.214619i
$989$	65.2329	+	37.6622i	2.07428	+	1.19759i
$990$	12.3317	+	5.24283i	0.391926	+	0.166628i
$991$	7.10137	+	12.2999i	0.225583	+	0.390721i	0.956494	−	0.291752i	$-0.0942381\pi$
$991$	7.10137	+	12.2999i	0.225583	+	0.390721i	−0.730911	+	0.682472i	$0.760905\pi$
$992$	0.829214	+	0.301809i	0.0263276	+	0.00958245i
$993$	−5.34297	−	35.8209i	−0.169554	−	1.13674i
$994$	2.26215	−	7.92295i	0.0717509	−	0.251301i
$995$	6.08030	+	16.7055i	0.192759	+	0.529600i
$996$	−0.888081	+	1.44828i	−0.0281399	+	0.0458907i
$997$	−38.8181	+	6.84468i	−1.22938	+	0.216773i	−0.750360	−	0.661030i	$-0.770120\pi$
$997$	−38.8181	+	6.84468i	−1.22938	+	0.216773i	−0.479022	+	0.877803i	$0.659009\pi$
$998$			14.7863i			0.468051i
$999$	−15.1578	+	22.0141i	−0.479571	+	0.696495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.41.4	✓	144
7.6	odd	2	inner	378.2.z.a.41.9	yes	144
27.2	odd	18	inner	378.2.z.a.83.9	yes	144
189.83	even	18	inner	378.2.z.a.83.4	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.4	✓	144	1.1	even	1	trivial
378.2.z.a.41.9	yes	144	7.6	odd	2	inner
378.2.z.a.83.4	yes	144	189.83	even	18	inner
378.2.z.a.83.9	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)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.826027 - 1.52239i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.99843 + 1.67688i) q^{5} +(1.07784 + 1.35583i) q^{6} +(0.187552 + 2.63910i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.63536 + 2.51507i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.826027 - 1.52239i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.99843 + 1.67688i) q^{5} +(1.07784 + 1.35583i) q^{6} +(0.187552 + 2.63910i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.63536 + 2.51507i) q^{9} +(-2.25926 - 1.30438i) q^{10} +(1.10056 + 1.31159i) q^{11} +(-1.29690 - 1.14806i) q^{12} +(-6.54906 - 1.15478i) q^{13} +(-0.642977 - 2.56643i) q^{14} +(0.902117 - 4.42755i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-3.19200 + 5.52870i) q^{17} +(1.17378 - 2.76084i) q^{18} +(1.36673 - 0.789081i) q^{19} +(2.45144 + 0.892251i) q^{20} +(3.86282 - 2.46549i) q^{21} +(-1.31159 - 1.10056i) q^{22} +(2.89352 + 7.94988i) q^{23} +(1.47656 + 0.905418i) q^{24} +(0.313551 + 1.77824i) q^{25} +6.65009 q^{26} +(5.17978 + 0.412142i) q^{27} +(1.07887 + 2.41579i) q^{28} +(3.93278 - 0.693456i) q^{29} +(-0.119576 + 4.51694i) q^{30} +(-0.301809 - 0.829214i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(1.08767 - 2.75889i) q^{33} +(2.18346 - 5.99900i) q^{34} +(-4.05064 + 5.58856i) q^{35} +(-0.676530 + 2.92272i) q^{36} +(-2.57189 + 4.45464i) q^{37} +(-1.20894 + 1.01442i) q^{38} +(3.65167 + 10.9241i) q^{39} +(-2.56913 - 0.453008i) q^{40} +(0.142302 - 0.807035i) q^{41} +(-3.37600 + 3.09881i) q^{42} +(6.82048 - 5.72306i) q^{43} +(1.48277 + 0.856080i) q^{44} +(-7.48564 + 2.28390i) q^{45} +(-4.23005 - 7.32665i) q^{46} +(6.60763 + 2.40498i) q^{47} +(-1.61135 - 0.635261i) q^{48} +(-6.92965 + 0.989938i) q^{49} +(-0.617575 - 1.69677i) q^{50} +(11.0535 + 0.292619i) q^{51} +(-6.54906 + 1.15478i) q^{52} -6.75035i q^{53} +(-5.17266 + 0.493579i) q^{54} +4.46663i q^{55} +(-1.48197 - 2.19175i) q^{56} +(-2.33024 - 1.42890i) q^{57} +(-3.75262 + 1.36584i) q^{58} +(-0.690522 - 0.579417i) q^{59} +(-0.666598 - 4.46908i) q^{60} +(1.46604 - 4.02791i) q^{61} +(0.441216 + 0.764208i) q^{62} +(-6.94424 - 3.84416i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-11.1514 - 13.2897i) q^{65} +(-0.592069 + 2.90584i) q^{66} +(-2.06631 + 11.7186i) q^{67} +(-1.10857 + 6.28701i) q^{68} +(9.71272 - 10.9719i) q^{69} +(3.01866 - 6.20704i) q^{70} +(2.69703 + 1.55713i) q^{71} +(0.158726 - 2.99580i) q^{72} +(-1.04793 + 0.605023i) q^{73} +(1.75928 - 4.83357i) q^{74} +(2.44817 - 1.94622i) q^{75} +(1.01442 - 1.20894i) q^{76} +(-3.25500 + 3.15046i) q^{77} +(-5.49315 - 10.1240i) q^{78} +(-1.88666 - 10.6998i) q^{79} +2.60877 q^{80} +(-3.65120 - 8.22610i) q^{81} +0.819485i q^{82} +(-0.170323 - 0.965952i) q^{83} +(2.78661 - 3.63797i) q^{84} +(-15.6500 + 5.69613i) q^{85} +(-5.72306 + 6.82048i) q^{86} +(-4.30430 - 5.41443i) q^{87} +(-1.60890 - 0.585593i) q^{88} +(1.37986 + 2.38999i) q^{89} +(6.97532 - 3.54907i) q^{90} +(1.81927 - 17.5002i) q^{91} +(5.43804 + 6.48081i) q^{92} +(-1.01309 + 1.14443i) q^{93} +(-6.92487 - 1.22104i) q^{94} +(4.05451 + 0.714919i) q^{95} +(1.69718 + 0.345802i) q^{96} +(11.7988 + 14.0613i) q^{97} +(6.65247 - 2.17822i) q^{98} +(-5.09855 + 0.623055i) 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

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Representations

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Database

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