LMFDB - Embedded newform 378.2.z.a.41.9

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			41.9
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(0.826027 + 1.52239i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.99843 - 1.67688i) q^{5} +(-1.07784 - 1.35583i) q^{6} +(1.84005 - 1.90111i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.63536 + 2.51507i) q^{9} +O(q^{10})$	\(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} +(1.84005 - 1.90111i) 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} +(-1.48197 + 2.19175i) 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} +(4.41416 + 1.23092i) 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} +(-6.86515 + 0.713683i) 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} +(-4.56085 - 0.445703i) 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} +(-0.228422 - 6.99627i) 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} +(-0.642977 + 2.56643i) 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} +(1.77228 + 7.73686i) 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} +(6.63693 - 1.89496i) 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} +(4.51855 + 0.321120i) 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} +(4.56896 - 0.353051i) 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} +(14.2460 - 10.3256i) 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} +(1.43984 + 6.85032i) 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	0.0752280	−	0.997166i	$-0.476032\pi$
$5$	−1.99843	−	1.67688i	−0.893726	−	0.749925i	−0.968954	+	0.247241i	$0.920476\pi$
$6$	−1.07784	−	1.35583i	−0.440026	−	0.553514i
$7$	1.84005	−	1.90111i	0.695474	−	0.718551i
$7$	1.84005	−	1.90111i	0.695474	−	0.718551i
$8$	−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	0.975342	−	0.220697i	$-0.0708333\pi$
$13$	6.54906	+	1.15478i	1.81638	+	0.320277i	0.841039	+	0.540974i	$0.181944\pi$
$14$	−1.48197	+	2.19175i	−0.396074	+	0.585769i
$15$	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	$-0.551499\pi$
$17$	3.19200	−	5.52870i	0.774173	−	1.34091i	0.935258	−	0.353967i	$-0.115167\pi$
$18$	1.17378	−	2.76084i	0.276662	−	0.650737i
$19$	−1.36673	+	0.789081i	−0.313549	+	0.181028i	−0.648513	−	0.761203i	$-0.724609\pi$
$19$	−1.36673	+	0.789081i	−0.313549	+	0.181028i	0.334965	+	0.942231i	$0.391276\pi$
$20$	−2.45144	−	0.892251i	−0.548159	−	0.199513i
$21$	4.41416	+	1.23092i	0.963250	+	0.268608i
$22$	−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	0.963841	−	0.266479i	$-0.0858603\pi$
$31$	0.301809	+	0.829214i	0.0542065	+	0.148931i	−0.909634	+	0.415410i	$0.863638\pi$
$32$	−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
$35$	−6.86515	+	0.713683i	−1.16042	+	0.120634i
$36$	−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	−0.993901	−	0.110273i	$-0.964827\pi$
$41$	−0.142302	+	0.807035i	−0.0222239	+	0.126038i	0.971677	+	0.236311i	$0.0759385\pi$
$42$	−4.56085	−	0.445703i	−0.703754	−	0.0687735i
$43$	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	−0.188292	−	0.982113i	$-0.560295\pi$
$47$	−6.60763	−	2.40498i	−0.963823	−	0.350803i	−0.775530	+	0.631310i	$0.782517\pi$
$48$	1.61135	+	0.635261i	0.232578	+	0.0916920i
$49$	−0.228422	−	6.99627i	−0.0326318	−	0.999467i
$50$	−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
$56$	−0.642977	+	2.56643i	−0.0859214	+	0.342954i
$57$	−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	0.686629	−	0.727008i	$-0.259090\pi$
$59$	0.690522	+	0.579417i	0.0898983	+	0.0754336i	−0.596731	+	0.802441i	$0.703534\pi$
$60$	−0.666598	−	4.46908i	−0.0860574	−	0.576955i
$61$	−1.46604	+	4.02791i	−0.187707	+	0.515722i	−0.997474	−	0.0710302i	$-0.977371\pi$
$61$	−1.46604	+	4.02791i	−0.187707	+	0.515722i	0.809767	+	0.586752i	$0.199594\pi$
$62$	−0.441216	−	0.764208i	−0.0560344	−	0.0970545i
$63$	1.77228	+	7.73686i	0.223286	+	0.974753i
$64$	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
$70$	6.63693	−	1.89496i	0.793265	−	0.226491i
$71$	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	−0.437419	−	0.899258i	$-0.644107\pi$
$73$	1.04793	−	0.605023i	0.122651	−	0.0708126i	0.560070	+	0.828445i	$0.310774\pi$
$74$	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
$77$	4.51855	+	0.321120i	0.514937	+	0.0365950i
$78$	−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	0.992728	−	0.120383i	$-0.0384122\pi$
$83$	0.170323	+	0.965952i	0.0186954	+	0.106027i	−0.974032	+	0.226410i	$0.927301\pi$
$84$	4.56896	−	0.353051i	0.498514	−	0.0385211i
$85$	−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	0.783579	−	0.621292i	$-0.213392\pi$
$89$	−1.37986	−	2.38999i	−0.146265	−	0.253339i	−0.929844	+	0.367953i	$0.880059\pi$
$90$	−6.97532	+	3.54907i	−0.735264	+	0.374105i
$91$	14.2460	−	10.3256i	1.49338	−	1.08242i
$92$	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	$-0.840401\pi$
$97$	−11.7988	−	14.0613i	−1.19799	−	1.42770i	−0.321074	−	0.947054i	$-0.604044\pi$
$98$	1.43984	+	6.85032i	0.145446	+	0.691987i
$99$	−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	0.252221	−	0.967670i	$-0.418839\pi$
$101$	−1.77454	−	0.645878i	−0.176573	−	0.0642673i	−0.428794	+	0.903402i	$0.641061\pi$
$102$	−10.9364	+	1.63125i	−1.08287	+	0.161518i
$103$	−11.5732	+	13.7924i	−1.14034	+	1.35900i	−0.216475	+	0.976288i	$0.569456\pi$
$103$	−11.5732	+	13.7924i	−1.14034	+	1.35900i	−0.923866	+	0.382717i	$0.874989\pi$
$104$	−6.24904	+	2.27446i	−0.612768	+	0.223029i
$105$	−6.75731	−	9.86194i	−0.659446	−	0.962427i
$106$	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
$112$	0.187552	−	2.63910i	0.0177220	−	0.249371i
$113$	−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
$119$	−4.63722	−	16.2414i	−0.425093	−	1.48885i
$120$	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
$126$	−3.08885	−	7.31157i	−0.275176	−	0.651366i
$127$	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	0.295602	−	0.955311i	$-0.404480\pi$
$131$	13.0034	−	4.73283i	1.13611	−	0.413510i	0.840506	+	0.541802i	$0.182258\pi$
$132$	−0.0784792	+	2.96451i	−0.00683073	+	0.258027i
$133$	−1.01472	+	4.05025i	−0.0879875	+	0.351201i
$134$		−	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	0.824960	−	0.565191i	$-0.191198\pi$
$139$	−2.00774	−	5.51622i	−0.170294	−	0.467879i	−0.995254	+	0.0973121i	$0.968976\pi$
$140$	−6.20704	+	3.01866i	−0.524591	+	0.255124i
$141$	−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
$147$	10.4624	−	6.12686i	0.862924	−	0.505335i
$148$	−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
$154$	−4.50567	+	0.468397i	−0.363077	+	0.0377445i
$155$	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	−0.923689	−	0.383142i	$-0.874842\pi$
$157$	−4.83620	+	5.76356i	−0.385971	+	0.459983i	0.537718	+	0.843125i	$0.319286\pi$
$158$	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	0.922883	−	0.385080i	$-0.125826\pi$
$167$	9.09652	+	7.63288i	0.703910	+	0.590650i	−0.218973	+	0.975731i	$0.570271\pi$
$168$	−4.43824	+	1.14108i	−0.342417	+	0.0880361i
$169$	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	−0.467275	−	0.884112i	$-0.654764\pi$
$173$	4.23871	−	3.55670i	0.322263	−	0.270411i	0.789539	+	0.613701i	$0.210320\pi$
$174$	−5.17911	−	4.58474i	−0.392627	−	0.347568i
$175$	3.95757	+	2.67595i	0.299164	+	0.202283i
$176$	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	−0.855254	−	0.518209i	$-0.826599\pi$
$181$	−11.2216	+	6.47882i	−0.834099	+	0.481567i	0.0211554	+	0.999776i	$0.493266\pi$
$182$	−12.2365	+	12.6425i	−0.907030	+	0.937127i
$183$	−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
$189$	−10.3146	+	9.08896i	−0.750276	+	0.661125i
$190$	−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
$196$	−2.60751	−	6.49622i	−0.186251	−	0.464016i
$197$	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	0.276020	−	0.961152i	$-0.410984\pi$
$199$	−5.90158	−	3.40728i	−0.418352	−	0.241536i	−0.694372	+	0.719616i	$0.744318\pi$
$200$	−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
$203$	5.91819	−	8.75264i	0.415376	−	0.614315i
$204$	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
$210$	8.36716	+	8.53872i	0.577389	+	0.589228i
$211$	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	$0.303659\pi$
$223$	−5.80906	+	15.9603i	−0.389003	+	1.06878i	−0.967451	+	0.253058i	$0.918564\pi$
$224$	0.273571	+	2.63157i	0.0182787	+	0.175829i
$225$	−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	$0.621628\pi$
$227$	−20.3610	+	17.0849i	−1.35141	+	1.13397i	−0.978534	+	0.206085i	$0.933928\pi$
$228$	−2.67842	−	0.545732i	−0.177383	−	0.0361420i
$229$	0.678629	+	0.119661i	0.0448451	+	0.00790739i	0.196026	−	0.980599i	$-0.437196\pi$
$229$	0.678629	+	0.119661i	0.0448451	+	0.00790739i	−0.151181	+	0.988506i	$0.548308\pi$
$230$	−3.83249	+	21.7351i	−0.252707	+	1.43317i
$231$	3.24358	+	7.14427i	0.213412	+	0.470058i
$232$	−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
$238$	7.38707	+	15.1894i	0.478832	+	0.984585i
$239$	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	−0.855790	−	0.517324i	$-0.826928\pi$
$241$	−23.0229	+	4.05955i	−1.48303	+	0.261499i	−0.627244	+	0.778823i	$0.715817\pi$
$242$			8.06851i			0.518663i
$243$	9.50737	−	12.3535i	0.609898	−	0.792480i
$244$			4.28642i			0.274410i
$245$	−11.2754	+	14.3646i	−0.720362	+	0.917721i
$246$	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	$-0.970910\pi$
$251$	−9.14058	−	15.8320i	−0.576949	−	0.999304i	0.418878	−	0.908042i	$-0.362423\pi$
$252$	4.31156	+	6.66412i	0.271603	+	0.419800i
$253$	−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	−0.979082	−	0.203468i	$-0.934779\pi$
$257$	0.169038	−	0.958665i	0.0105443	−	0.0597999i	0.989626	+	0.143668i	$0.0458898\pi$
$258$	−15.1108	−	3.07885i	−0.940760	−	0.191681i
$259$	3.73635	+	13.0862i	0.232165	+	0.813138i
$260$	−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
$266$	0.295988	−	4.16492i	0.0181482	−	0.255368i
$267$	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	$-0.390512\pi$
$269$	11.0618			0.674447			0.337224	+	0.941425i	$0.390512\pi$
$270$	−11.1649	−	7.68756i	−0.679473	−	0.467850i
$271$		−	5.87429i		−	0.356838i	−0.983955	−	0.178419i	$-0.942902\pi$
$271$		−	5.87429i		−	0.356838i	0.983955	−	0.178419i	$-0.0570982\pi$
$272$	−1.10857	−	6.28701i	−0.0672169	−	0.381206i
$273$	27.4872	+	13.1587i	1.66360	+	0.796401i
$274$	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
$280$	5.58856	−	4.05064i	0.333980	−	0.242072i
$281$	−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	0.338541	−	0.940952i	$-0.390067\pi$
$283$	5.63290	+	0.993233i	0.334841	+	0.0590416i	−0.00369981	+	0.999993i	$0.501178\pi$
$284$	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
$287$	1.27242	+	1.75552i	0.0751085	+	0.103625i
$288$	−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	−0.850633	−	0.525760i	$-0.823781\pi$
$293$	−19.9297	+	7.25381i	−1.16430	+	0.423772i	−0.313671	+	0.949532i	$0.601559\pi$
$294$	−9.23953	+	7.85055i	−0.538860	+	0.457853i
$295$	−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
$301$	1.66987	−	23.4972i	0.0962499	−	1.35436i
$302$	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	0.743630	−	0.668591i	$-0.233102\pi$
$307$	9.39899	+	5.42651i	0.536429	+	0.309707i	−0.207202	+	0.978298i	$0.566436\pi$
$308$	4.35588	−	1.24368i	0.248199	−	0.0708654i
$309$	−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	−0.999990	−	0.00439151i	$-0.998602\pi$
$311$	−1.03703	+	5.88131i	−0.0588048	+	0.333499i	0.941186	+	0.337890i	$0.109713\pi$
$312$	−8.62450	−	7.63472i	−0.488266	−	0.432231i
$313$	2.45451	+	2.92517i	0.138737	+	0.165340i	0.830939	−	0.556363i	$-0.187804\pi$
$313$	2.45451	+	2.92517i	0.138737	+	0.165340i	−0.692202	+	0.721704i	$0.743359\pi$
$314$	3.76190	−	6.51580i	0.212296	−	0.367708i
$315$	9.43203	−	18.4335i	0.531435	−	1.03861i
$316$	−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
$322$	−21.7123	−	5.43965i	−1.20998	−	0.303140i
$323$			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
$329$	−16.7305	+	8.13654i	−0.922383	+	0.448582i
$330$	−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
$336$	4.17266	−	1.89443i	0.227637	−	0.103350i
$337$	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
$343$	−13.7210	−	12.4392i	−0.740863	−	0.671656i
$344$	−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	−0.516543	−	0.856261i	$-0.672781\pi$
$349$	−13.2466	+	2.33574i	−0.709076	+	0.125029i	−0.192533	+	0.981291i	$0.561670\pi$
$350$	−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	$-0.980390\pi$
$353$	−1.52656	−	8.65757i	−0.0812507	−	0.460796i	0.916852	−	0.399227i	$-0.130721\pi$
$354$	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
$357$	20.8954	−	20.4755i	1.10590	−	1.08368i
$358$	−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
$364$	9.85525	−	14.5753i	0.516555	−	0.763954i
$365$	−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	0.995955	−	0.0898533i	$-0.0286398\pi$
$367$	14.0714	+	16.7696i	0.734521	+	0.875368i	−0.261434	+	0.965221i	$0.584195\pi$
$368$	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
$371$	−12.8331	−	12.4210i	−0.666263	−	0.644865i
$372$	−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
$378$	8.57961	−	10.7420i	0.441287	−	0.552508i
$379$	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	0.412589	−	0.910917i	$-0.364625\pi$
$383$	−8.07952	−	6.77952i	−0.412844	−	0.346417i	−0.825433	+	0.564500i	$0.809069\pi$
$384$	−1.71310	+	0.255522i	−0.0874212	+	0.0130396i
$385$	−8.49154	−	8.21882i	−0.432769	−	0.418870i
$386$	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
$392$	3.69596	+	5.94474i	0.186674	+	0.300255i
$393$	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	−0.0791571	−	0.996862i	$-0.525223\pi$
$397$	14.8355	−	8.56528i	0.744572	−	0.429879i	0.823729	+	0.566983i	$0.191890\pi$
$398$	6.40359	+	2.33072i	0.320983	+	0.116828i
$399$	−7.00425	+	1.80081i	−0.350651	+	0.0901531i
$400$	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	$-0.998747\pi$
$409$	−4.78260	−	13.1401i	−0.236484	−	0.649735i	0.763508	−	0.645798i	$-0.223475\pi$
$410$	−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
$413$	2.37213	−	0.246600i	0.116725	−	0.0121344i
$414$	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	−0.976855	−	0.213903i	$-0.931382\pi$
$419$	0.291638	−	1.65396i	0.0142475	−	0.0808014i	0.991102	+	0.133101i	$0.0424936\pi$
$420$	−9.72277	−	6.95606i	−0.474423	−	0.339421i
$421$	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
$427$	4.95991	+	10.1987i	0.240027	+	0.493548i
$428$	−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	$-0.895395\pi$
$433$		−	13.4318i		−	0.645489i	0.946486	−	0.322744i	$-0.104605\pi$
$434$	−2.26470	−	0.567383i	−0.108709	−	0.0272353i
$435$	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	−0.944256	−	0.329213i	$-0.893217\pi$
$439$	−0.194851	+	0.535350i	−0.00929975	+	0.0255509i	0.934956	+	0.354764i	$0.115439\pi$
$440$	2.23331	+	3.86821i	0.106469	+	0.184410i
$441$	17.9697	+	10.8669i	0.855700	+	0.517473i
$442$	−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
$448$	−0.726382	−	2.54409i	−0.0343183	−	0.120197i
$449$	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
$455$	−45.7844	−	3.25376i	−2.14641	−	0.152539i
$456$	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	$-0.683281\pi$
$461$	−6.86447	−	38.9304i	−0.319710	−	1.81317i	0.224790	−	0.974407i	$-0.427830\pi$
$462$	−4.43489	−	6.47249i	−0.206330	−	0.301127i
$463$	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	$-0.973152\pi$
$467$	−12.3433	−	21.3792i	−0.571180	−	0.989313i	0.425265	−	0.905069i	$-0.360181\pi$
$468$	−7.80572	+	18.3598i	−0.360819	+	0.848684i
$469$	18.4763	+	25.4911i	0.853154	+	1.17707i
$470$	−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
$476$	−9.91246	−	13.6759i	−0.454337	−	0.626835i
$477$	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	0.269725	−	0.962938i	$-0.413067\pi$
$479$	−3.12136	−	1.13608i	−0.142619	−	0.0519090i	−0.412343	+	0.911029i	$0.635290\pi$
$480$	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
$483$	2.98685	+	38.6538i	0.135906	+	1.75881i
$484$	−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
$490$	8.60976	−	16.1043i	0.388949	−	0.727520i
$491$	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
$497$	7.92295	−	2.26215i	0.355393	−	0.101471i
$498$	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	−0.943273	−	0.332017i	$-0.892271\pi$
$503$	−4.12896	+	7.15158i	−0.184101	+	0.318873i	0.759172	+	0.650890i	$0.225604\pi$
$504$	−5.40327	−	5.81418i	−0.240681	−	0.258984i
$505$	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	0.220383	−	0.975413i	$-0.429269\pi$
$509$	22.9263	−	8.34449i	1.01619	−	0.369863i	0.795807	+	0.605551i	$0.207047\pi$
$510$	24.5911	+	15.0792i	1.08891	+	0.667716i
$511$	0.778032	−	3.10550i	0.0344181	−	0.137379i
$512$			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
$518$	−5.95198	−	12.2386i	−0.261515	−	0.537733i
$519$	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	$-0.944971\pi$
$521$	−14.6429	−	25.3623i	−0.641518	−	1.11114i	0.343575	−	0.939125i	$-0.388362\pi$
$522$	2.70169	−	11.6718i	0.118250	−	0.510859i
$523$	−24.7419	−	14.2847i	−1.08189	−	0.624628i	−0.150482	−	0.988613i	$-0.548083\pi$
$523$	−24.7419	−	14.2847i	−1.08189	−	0.624628i	−0.931405	+	0.363985i	$0.881416\pi$
$524$	10.6004	−	8.89482i	0.463082	−	0.388572i
$525$	−0.804793	+	8.23539i	−0.0351240	+	0.359422i
$526$	−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
$532$	0.431739	+	4.15304i	0.0187183	+	0.180057i
$533$	−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
$546$	−29.3546	−	8.18569i	−1.25626	−	0.350315i
$547$	−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
$553$	−23.8130	−	16.1014i	−1.01263	−	0.684701i
$554$	−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
$560$	−4.80027	+	4.95955i	−0.202848	+	0.209579i
$561$	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	−0.501235	−	0.865311i	$-0.667121\pi$
$563$	−7.80618	+	2.84122i	−0.328991	+	0.119743i	0.172243	+	0.985054i	$0.444898\pi$
$564$	−5.80837	−	10.7050i	−0.244577	−	0.450762i
$565$	47.5832	−	8.39021i	2.00184	−	0.352979i
$566$	−5.71980			−0.240421
$567$	−22.3571	−	8.19513i	−0.938910	−	0.344163i
$568$	−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
$574$	−1.55793	−	1.50789i	−0.0650267	−	0.0629383i
$575$	−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	0.751719	−	0.659484i	$-0.229225\pi$
$577$	13.3663	+	7.71706i	0.556448	+	0.321265i	−0.195271	+	0.980749i	$0.562558\pi$
$578$	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
$581$	2.14978	+	1.45360i	0.0891880	+	0.0603054i
$582$	−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	−0.136831	−	0.990594i	$-0.543692\pi$
$587$	−21.2817	−	7.74592i	−0.878391	−	0.319708i	−0.741560	+	0.670886i	$0.765914\pi$
$588$	7.73592	−	9.33571i	0.319024	−	0.384998i
$589$	−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	$-0.525659\pi$
$593$	−3.92178			−0.161048			−0.0805242	+	0.996753i	$0.525659\pi$
$594$	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	−0.985556	−	0.169351i	$-0.945833\pi$
$601$	−2.98399	+	8.19846i	−0.121720	+	0.334422i	0.863836	+	0.503773i	$0.168055\pi$
$602$	2.43574	+	23.4302i	0.0992733	+	0.954943i
$603$	−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	0.572819	−	0.819682i	$-0.305850\pi$
$607$	20.4674	+	3.60895i	0.830745	+	0.146483i	0.257926	+	0.966165i	$0.416961\pi$
$608$	0.274045	−	1.55419i	0.0111140	−	0.0630305i
$609$	18.2135	+	1.77989i	0.738050	+	0.0721250i
$610$	−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
$616$	−4.07374	+	1.98118i	−0.164136	+	0.0798240i
$617$	−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	0.0592057	−	0.998246i	$-0.481143\pi$
$619$	11.3516	−	2.00160i	0.456261	−	0.0804511i	0.397055	+	0.917795i	$0.370032\pi$
$620$		−	2.30206i		−	0.0924529i
$621$	−11.7113	−	42.3712i	−0.469959	−	1.70030i
$622$		−	5.97204i		−	0.239457i
$623$	−7.08266	−	1.77444i	−0.283761	−	0.0710915i
$624$	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
$630$	−6.08779	+	19.7913i	−0.242544	+	0.788505i
$631$	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
$637$	6.58317	−	46.0828i	0.260835	−	1.82587i
$638$	−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	−0.191994	−	0.981396i	$-0.561496\pi$
$643$	20.4845	−	24.4125i	0.807832	−	0.962736i	0.999826	+	0.0186599i	$0.00593997\pi$
$644$	22.3270	+	1.58671i	0.879806	+	0.0625252i
$645$	−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	$-0.383108\pi$
$647$	18.2647			0.718060			0.359030	+	0.933326i	$0.383108\pi$
$648$	7.27508	+	5.29842i	0.285792	+	0.208141i
$649$			1.54336i			0.0605823i
$650$	−2.08514	−	11.8254i	−0.0817860	−	0.463832i
$651$	0.311544	+	4.03179i	0.0122104	+	0.158018i
$652$	−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
$658$	15.0634	−	10.9181i	0.587234	−	0.425634i
$659$	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	0.499422	−	0.866359i	$-0.333546\pi$
$661$	17.2877	+	3.04829i	0.672413	+	0.118565i	0.172991	+	0.984923i	$0.444657\pi$
$662$	−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
$665$	8.81964	−	6.39257i	0.342011	−	0.247893i
$666$	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
$672$	−3.78031	+	2.59023i	−0.145828	+	0.0999203i
$673$	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	$0.0597218\pi$
$677$	3.20150	+	18.1566i	0.123044	+	0.697814i	−0.859407	+	0.511292i	$0.829167\pi$
$678$	32.0683	+	0.848940i	1.23157	+	0.0326033i
$679$	−48.4424	−	3.44265i	−1.85905	−	0.132117i
$680$	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
$686$	15.6726	+	9.86764i	0.598382	+	0.376748i
$687$	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	0.890281	−	0.455412i	$-0.150508\pi$
$691$	7.54937	+	8.99699i	0.287192	+	0.342262i	−0.603089	+	0.797674i	$0.706064\pi$
$692$	2.76662	−	4.79193i	0.105171	−	0.182162i
$693$	−8.19710	+	10.8394i	−0.311382	+	0.411753i
$694$	−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
$700$	4.63413	+	1.16100i	0.175154	+	0.0438818i
$701$			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
$707$	−4.49312	+	2.18514i	−0.168981	+	0.0821805i
$708$	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
$714$	−17.0224	+	23.7929i	−0.637047	+	0.890427i
$715$	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	$0.398319\pi$
$719$	−17.8367	+	30.8941i	−0.665198	+	1.15216i	−0.979232	+	0.202744i	$0.935014\pi$
$720$	4.26627	−	6.56124i	0.158995	−	0.244523i
$721$	4.92556	+	47.3806i	0.183437	+	1.76455i
$722$	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	−0.480886	−	0.876783i	$-0.659685\pi$
$727$	−17.0647	+	3.00897i	−0.632895	+	0.111596i	−0.152008	+	0.988379i	$0.548574\pi$
$728$	−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	0.904493	−	0.426488i	$-0.140249\pi$
$733$	−1.69293	−	4.65129i	−0.0625298	−	0.171799i	−0.967023	+	0.254689i	$0.918027\pi$
$734$	−16.7696	−	14.0714i	−0.618979	−	0.519385i
$735$	−31.1824	−	5.30011i	−1.15018	−	0.195497i
$736$	−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
$742$	14.7951	+	10.0038i	0.543144	+	0.367252i
$743$	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
$749$	−23.5475	−	22.7912i	−0.860405	−	0.832772i
$750$	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
$756$	−6.58394	+	12.0686i	−0.239455	+	0.438932i
$757$	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	−0.0445359	−	0.999008i	$-0.514181\pi$
$761$	−28.5821	−	23.9832i	−1.03610	−	0.869391i	−0.991564	+	0.129617i	$0.958625\pi$
$762$	1.46149	−	3.70708i	0.0529441	−	0.134293i
$763$	−9.54180	+	9.85841i	−0.345436	+	0.356899i
$764$	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	0.599557	−	0.800332i	$-0.295344\pi$
$769$	24.6590	+	4.34804i	0.889226	+	0.156795i	0.289669	+	0.957127i	$0.406455\pi$
$770$	9.78972	+	6.61942i	0.352797	+	0.238547i
$771$	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	−0.995197	−	0.0978955i	$-0.968789\pi$
$773$	−11.4775	+	19.8797i	−0.412818	+	0.715022i	0.582378	+	0.812918i	$0.302122\pi$
$774$	−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
$777$	−16.8360	+	16.4978i	−0.603989	+	0.591854i
$778$	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	$0.180747\pi$
$787$	15.2313	+	41.8475i	0.542936	+	1.49170i	−0.300133	+	0.953897i	$0.597031\pi$
$788$	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
$791$	5.06684	+	48.7396i	0.180156	+	1.73298i
$792$	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	$0.440458\pi$
$797$	−9.17058	+	52.0089i	−0.324839	+	1.84225i	−0.510807	+	0.859696i	$0.670653\pi$
$798$	6.58514	−	2.98972i	0.233111	−	0.105835i
$799$	−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
$805$	−25.5382	−	52.5121i	−0.900102	−	1.85081i
$806$	−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	$0.188042\pi$
$811$			31.7238i			1.11397i	−0.830522	+	0.556986i	$0.811958\pi$
$812$	2.56770	−	10.2489i	0.0901086	−	0.359667i
$813$	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
$819$	2.67243	+	52.7157i	0.0933824	+	1.84204i
$820$	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
$826$	−2.29327	+	0.654770i	−0.0797930	+	0.0227824i
$827$	−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	−0.267846	−	0.963462i	$-0.586312\pi$
$829$	12.4560	−	7.19145i	0.432613	−	0.249769i	0.700459	+	0.713692i	$0.252979\pi$
$830$	−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
$833$	−39.4094	−	21.0692i	−1.36546	−	0.730005i
$834$	−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	$-0.809231\pi$
$839$	−7.03061	−	39.8726i	−0.242724	−	1.37655i	0.582997	−	0.812474i	$-0.301880\pi$
$840$	10.7830	+	5.16204i	0.372048	+	0.178107i
$841$	−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
$847$	−12.5280	−	17.2845i	−0.430467	−	0.593903i
$848$	−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	0.548989	−	0.835830i	$-0.315013\pi$
$853$	−10.7909	−	12.8601i	−0.369473	−	0.440321i	−0.918462	+	0.395508i	$0.870568\pi$
$854$	−6.65554	−	9.18245i	−0.227748	−	0.314217i
$855$	−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	0.890134	−	0.455699i	$-0.150611\pi$
$857$	37.4450	+	13.6289i	1.27910	+	0.465554i	0.388964	+	0.921253i	$0.372833\pi$
$858$	7.23309	−	18.3468i	0.246934	−	0.626350i
$859$	−11.7894	+	14.0501i	−0.402251	+	0.479384i	−0.928705	−	0.370820i	$-0.879077\pi$
$859$	−11.7894	+	14.0501i	−0.402251	+	0.479384i	0.526454	+	0.850204i	$0.323521\pi$
$860$	−21.8264	+	7.94416i	−0.744274	+	0.270894i
$861$	−1.62154	+	3.38723i	−0.0552618	+	0.115436i
$862$	−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
$868$	2.32882	+	0.165502i	0.0790453	+	0.00561751i
$869$	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
$875$	6.05314	+	21.2005i	0.204633	+	0.716709i
$876$	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	−0.897399	−	0.441220i	$-0.854546\pi$
$881$	−1.97656	+	3.42350i	−0.0665919	+	0.115341i	0.830807	+	0.556560i	$0.187879\pi$
$882$	−19.5837	−	7.58143i	−0.659418	−	0.255280i
$883$	−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	−0.309366	−	0.950943i	$-0.600117\pi$
$887$	1.93287	−	0.703507i	0.0648994	−	0.0236215i	0.374266	+	0.927321i	$0.377895\pi$
$888$	7.83085	−	4.24890i	0.262786	−	0.142584i
$889$	5.90436	+	1.47924i	0.198026	+	0.0496121i
$890$		−	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
$896$	1.15712	+	2.37930i	0.0386567	+	0.0794868i
$897$	−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
$903$	37.1513	−	16.8671i	1.23632	−	0.561302i
$904$	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
$910$	45.6539	−	4.74605i	1.51341	−	0.157330i
$911$	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
$924$	5.49145	+	5.60405i	0.180655	+	0.184360i
$925$	−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	−0.544243	−	0.838928i	$-0.683183\pi$
$929$	5.71285	−	4.79365i	0.187432	−	0.157274i	0.731676	+	0.681653i	$0.238739\pi$
$930$	−3.78160	+	1.26410i	−0.124003	+	0.0414514i
$931$	5.83281	+	9.38176i	0.191163	+	0.307475i
$932$	−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	−0.757070	−	0.653334i	$-0.773370\pi$
$937$	−17.4418	+	10.0701i	−0.569800	+	0.328974i	0.187269	+	0.982309i	$0.440036\pi$
$938$	−22.6220	−	21.8955i	−0.738636	−	0.714914i
$939$	−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	0.452334	−	0.891849i	$-0.350592\pi$
$941$	42.0905	−	15.3197i	1.37211	−	0.499408i	0.919777	+	0.392441i	$0.128369\pi$
$942$	13.0270	+	0.344863i	0.424444	+	0.0112363i
$943$	−6.82759	+	1.20389i	−0.222337	+	0.0392040i
$944$	0.901412			0.0293385
$945$	35.8541	−	0.867305i	1.16634	−	0.0282134i
$946$	−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
$952$	12.1367	+	11.7469i	0.393352	+	0.380719i
$953$	−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
$959$	−14.6919	+	21.7284i	−0.474425	+	0.701645i
$960$	−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
$966$	−9.65363	−	37.5479i	−0.310600	−	1.20808i
$967$	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	$-0.316011\pi$
$971$	34.0504			1.09273			0.546365	+	0.837547i	$0.316011\pi$
$972$	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
$980$	−5.68247	+	17.3548i	−0.181520	+	0.554377i
$981$	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	−0.989755	−	0.142776i	$-0.954397\pi$
$983$	−32.0118	+	26.8611i	−1.02102	+	0.856735i	−0.0312625	+	0.999511i	$0.509953\pi$
$984$	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
$987$	−26.2069	−	18.7494i	−0.834173	−	0.596801i
$988$	−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
$994$	−7.40977	+	3.60358i	−0.235024	+	0.114299i
$995$	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	0.479022	−	0.877803i	$-0.340991\pi$
$997$	38.8181	−	6.84468i	1.22938	−	0.216773i	0.750360	+	0.661030i	$0.229880\pi$
$998$			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.41.9	yes	144
7.6	odd	2	inner	378.2.z.a.41.4	✓	144
27.2	odd	18	inner	378.2.z.a.83.4	yes	144
189.83	even	18	inner	378.2.z.a.83.9	yes	144

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

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.826027 + 1.52239i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.99843 - 1.67688i) q^{5} +(-1.07784 - 1.35583i) q^{6} +(1.84005 - 1.90111i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-1.63536 + 2.51507i) q^{9} +O(q^{10})\)	\(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} +(1.84005 - 1.90111i) 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} +(-1.48197 + 2.19175i) 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} +(4.41416 + 1.23092i) 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} +(-6.86515 + 0.713683i) 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} +(-4.56085 - 0.445703i) 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} +(-0.228422 - 6.99627i) 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} +(-0.642977 + 2.56643i) 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} +(1.77228 + 7.73686i) 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} +(6.63693 - 1.89496i) 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} +(4.51855 + 0.321120i) 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} +(4.56896 - 0.353051i) 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} +(14.2460 - 10.3256i) 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} +(1.43984 + 6.85032i) 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

Varieties

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Representations

Groups

Database

Properties

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