LMFDB - Embedded newform 378.2.z.a.209.4

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			209.4
Character	$\chi$	$=$	378.209
Dual form			378.2.z.a.293.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342020 - 0.939693i) q^{2} +(-0.288948 + 1.70778i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(0.675752 + 3.83238i) q^{5} +(1.70361 - 0.312573i) q^{6} +(2.47966 - 0.922664i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.83302 - 0.986917i) q^{9} +O(q^{10})$	\(q+(-0.342020 - 0.939693i) q^{2} +(-0.288948 + 1.70778i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(0.675752 + 3.83238i) q^{5} +(1.70361 - 0.312573i) q^{6} +(2.47966 - 0.922664i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.83302 - 0.986917i) q^{9} +(3.37014 - 1.94575i) q^{10} +(-2.70819 - 0.477527i) q^{11} +(-0.876392 - 1.49397i) q^{12} +(-0.574003 + 1.57706i) q^{13} +(-1.71511 - 2.01454i) q^{14} +(-6.74011 + 0.0466780i) q^{15} +(0.173648 - 0.984808i) q^{16} +(2.48502 + 4.30419i) q^{17} +(0.0415504 + 2.99971i) q^{18} +(-6.24771 - 3.60712i) q^{19} +(-2.98106 - 2.50141i) q^{20} +(0.859215 + 4.50131i) q^{21} +(0.477527 + 2.70819i) q^{22} +(3.43594 + 4.09479i) q^{23} +(-1.10413 + 1.33451i) q^{24} +(-9.53201 + 3.46937i) q^{25} +1.67827 q^{26} +(2.50403 - 4.55300i) q^{27} +(-1.30645 + 2.30069i) q^{28} +(-0.869378 - 2.38860i) q^{29} +(2.34912 + 6.31767i) q^{30} +(5.22704 + 6.22935i) q^{31} +(-0.984808 + 0.173648i) q^{32} +(1.59804 - 4.48701i) q^{33} +(3.19468 - 3.80728i) q^{34} +(5.21163 + 8.87948i) q^{35} +(2.80460 - 1.06501i) q^{36} +(-0.177172 - 0.306871i) q^{37} +(-1.25274 + 7.10463i) q^{38} +(-2.52741 - 1.43596i) q^{39} +(-1.33097 + 3.65681i) q^{40} +(-3.97955 - 1.44844i) q^{41} +(3.93597 - 2.34694i) q^{42} +(1.65693 - 9.39692i) q^{43} +(2.38154 - 1.37498i) q^{44} +(1.86782 - 11.5241i) q^{45} +(2.67269 - 4.62923i) q^{46} +(5.79089 + 4.85913i) q^{47} +(1.63166 + 0.581111i) q^{48} +(5.29738 - 4.57578i) q^{49} +(6.52028 + 7.77057i) q^{50} +(-8.06864 + 3.00019i) q^{51} +(-0.574003 - 1.57706i) q^{52} +6.43428i q^{53} +(-5.13485 - 0.795801i) q^{54} -10.7015i q^{55} +(2.60878 + 0.440778i) q^{56} +(7.96542 - 9.62744i) q^{57} +(-1.94720 + 1.63390i) q^{58} +(0.927668 + 5.26107i) q^{59} +(5.13322 - 4.36822i) q^{60} +(-3.29907 + 3.93168i) q^{61} +(4.06592 - 7.04237i) q^{62} +(-7.93550 + 0.166708i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-6.43177 - 1.13409i) q^{65} +(-4.76297 + 0.0329855i) q^{66} +(-1.47671 - 0.537479i) q^{67} +(-4.67032 - 1.69986i) q^{68} +(-7.98581 + 4.68464i) q^{69} +(6.56150 - 7.93429i) q^{70} +(6.90603 - 3.98720i) q^{71} +(-1.96001 - 2.27120i) q^{72} +(1.45847 + 0.842046i) q^{73} +(-0.227768 + 0.271443i) q^{74} +(-3.17066 - 17.2810i) q^{75} +(7.10463 - 1.25274i) q^{76} +(-7.15598 + 1.31465i) q^{77} +(-0.484933 + 2.86612i) q^{78} +(15.6048 - 5.67967i) q^{79} +3.89150 q^{80} +(7.05199 + 5.59191i) q^{81} +4.23495i q^{82} +(-3.91696 + 1.42566i) q^{83} +(-3.55158 - 2.89591i) q^{84} +(-14.8160 + 12.4321i) q^{85} +(-9.39692 + 1.65693i) q^{86} +(4.33040 - 0.794527i) q^{87} +(-2.10660 - 1.76765i) q^{88} +(-2.32657 + 4.02974i) q^{89} +(-11.4680 + 2.18630i) q^{90} +(0.0317666 + 4.44018i) q^{91} +(-5.26416 - 0.928214i) q^{92} +(-12.1487 + 7.12668i) q^{93} +(2.58549 - 7.10357i) q^{94} +(9.60193 - 26.3811i) q^{95} +(-0.0119949 - 1.73201i) q^{96} +(8.44682 + 1.48940i) q^{97} +(-6.11164 - 3.41290i) q^{98} +(7.20107 + 4.02560i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	−0.342020	−	0.939693i	−0.241845	−	0.664463i
$2$	−0.342020	−	0.939693i	−0.241845	−	0.664463i
$3$	−0.288948	+	1.70778i	−0.166824	+	0.985987i
$3$	−0.288948	+	1.70778i	−0.166824	+	0.985987i
$4$	−0.766044	+	0.642788i	−0.383022	+	0.321394i
$5$	0.675752	+	3.83238i	0.302205	+	1.71389i	0.636376	+	0.771379i	$0.280433\pi$
$5$	0.675752	+	3.83238i	0.302205	+	1.71389i	−0.334171	+	0.942512i	$0.608456\pi$
$6$	1.70361	−	0.312573i	0.695497	−	0.127607i
$7$	2.47966	−	0.922664i	0.937222	−	0.348734i
$7$	2.47966	−	0.922664i	0.937222	−	0.348734i
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−2.83302	−	0.986917i	−0.944340	−	0.328972i
$10$	3.37014	−	1.94575i	1.06573	−	0.615300i
$11$	−2.70819	−	0.477527i	−0.816550	−	0.143980i	−0.250253	−	0.968181i	$-0.580514\pi$
$11$	−2.70819	−	0.477527i	−0.816550	−	0.143980i	−0.566298	+	0.824201i	$0.691625\pi$
$12$	−0.876392	−	1.49397i	−0.252993	−	0.431271i
$13$	−0.574003	+	1.57706i	−0.159200	+	0.437398i	−0.993489	−	0.113930i	$-0.963656\pi$
$13$	−0.574003	+	1.57706i	−0.159200	+	0.437398i	0.834289	+	0.551327i	$0.185878\pi$
$14$	−1.71511	−	2.01454i	−0.458383	−	0.538410i
$15$	−6.74011	+	0.0466780i	−1.74029	+	0.0120522i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	2.48502	+	4.30419i	0.602707	+	1.04392i	0.992409	+	0.122978i	$0.0392444\pi$
$17$	2.48502	+	4.30419i	0.602707	+	1.04392i	−0.389703	+	0.920941i	$0.627422\pi$
$18$	0.0415504	+	2.99971i	0.00979353	+	0.707039i
$19$	−6.24771	−	3.60712i	−1.43332	−	0.827529i	−0.435950	−	0.899971i	$-0.643588\pi$
$19$	−6.24771	−	3.60712i	−1.43332	−	0.827529i	−0.997373	+	0.0724417i	$0.976921\pi$
$20$	−2.98106	−	2.50141i	−0.666585	−	0.559332i
$21$	0.859215	+	4.50131i	0.187496	+	0.982265i
$22$	0.477527	+	2.70819i	0.101809	+	0.577388i
$23$	3.43594	+	4.09479i	0.716443	+	0.853823i	0.994280	−	0.106805i	$-0.0340620\pi$
$23$	3.43594	+	4.09479i	0.716443	+	0.853823i	−0.277837	+	0.960628i	$0.589618\pi$
$24$	−1.10413	+	1.33451i	−0.225379	+	0.272405i
$25$	−9.53201	+	3.46937i	−1.90640	+	0.693874i
$26$	1.67827			0.329136
$27$	2.50403	−	4.55300i	0.481901	−	0.876226i
$28$	−1.30645	+	2.30069i	−0.246896	+	0.434790i
$29$	−0.869378	−	2.38860i	−0.161439	−	0.443551i	0.832427	−	0.554134i	$-0.186951\pi$
$29$	−0.869378	−	2.38860i	−0.161439	−	0.443551i	−0.993867	+	0.110583i	$0.964728\pi$
$30$	2.34912	+	6.31767i	0.428888	+	1.15344i
$31$	5.22704	+	6.22935i	0.938804	+	1.11882i	0.992740	+	0.120279i	$0.0383789\pi$
$31$	5.22704	+	6.22935i	0.938804	+	1.11882i	−0.0539358	+	0.998544i	$0.517177\pi$
$32$	−0.984808	+	0.173648i	−0.174091	+	0.0306970i
$33$	1.59804	−	4.48701i	0.278182	−	0.781088i
$34$	3.19468	−	3.80728i	0.547884	−	0.652942i
$35$	5.21163	+	8.87948i	0.880926	+	1.50091i
$36$	2.80460	−	1.06501i	0.467433	−	0.177501i
$37$	−0.177172	−	0.306871i	−0.0291269	−	0.0504492i	0.851095	−	0.525012i	$-0.175939\pi$
$37$	−0.177172	−	0.306871i	−0.0291269	−	0.0504492i	−0.880221	+	0.474563i	$0.842606\pi$
$38$	−1.25274	+	7.10463i	−0.203221	+	1.15252i
$39$	−2.52741	−	1.43596i	−0.404710	−	0.229937i
$40$	−1.33097	+	3.65681i	−0.210445	+	0.578193i
$41$	−3.97955	−	1.44844i	−0.621502	−	0.226208i	0.0120264	−	0.999928i	$-0.496172\pi$
$41$	−3.97955	−	1.44844i	−0.621502	−	0.226208i	−0.633528	+	0.773719i	$0.718394\pi$
$42$	3.93597	−	2.34694i	0.607334	−	0.362140i
$43$	1.65693	−	9.39692i	0.252680	−	1.43302i	−0.549280	−	0.835638i	$-0.685098\pi$
$43$	1.65693	−	9.39692i	0.252680	−	1.43302i	0.801959	−	0.597379i	$-0.203791\pi$
$44$	2.38154	−	1.37498i	0.359031	−	0.207287i
$45$	1.86782	−	11.5241i	0.278439	−	1.71791i
$46$	2.67269	−	4.62923i	0.394066	−	0.682543i
$47$	5.79089	+	4.85913i	0.844687	+	0.708777i	0.958613	−	0.284712i	$-0.0918981\pi$
$47$	5.79089	+	4.85913i	0.844687	+	0.708777i	−0.113926	+	0.993489i	$0.536343\pi$
$48$	1.63166	+	0.581111i	0.235510	+	0.0838761i
$49$	5.29738	−	4.57578i	0.756769	−	0.653682i
$50$	6.52028	+	7.77057i	0.922107	+	1.09892i
$51$	−8.06864	+	3.00019i	−1.12984	+	0.420110i
$52$	−0.574003	−	1.57706i	−0.0795998	−	0.218699i
$53$			6.43428i			0.883817i	0.897060	+	0.441908i	$0.145698\pi$
$53$			6.43428i			0.883817i	−0.897060	+	0.441908i	$0.854302\pi$
$54$	−5.13485	−	0.795801i	−0.698765	−	0.108295i
$55$		−	10.7015i		−	1.44299i
$56$	2.60878	+	0.440778i	0.348612	+	0.0589014i
$57$	7.96542	−	9.62744i	1.05505	−	1.27519i
$58$	−1.94720	+	1.63390i	−0.255680	+	0.214541i
$59$	0.927668	+	5.26107i	0.120772	+	0.684932i	0.983730	+	0.179656i	$0.0574984\pi$
$59$	0.927668	+	5.26107i	0.120772	+	0.684932i	−0.862957	+	0.505277i	$0.831390\pi$
$60$	5.13322	−	4.36822i	0.662696	−	0.563934i
$61$	−3.29907	+	3.93168i	−0.422402	+	0.503400i	−0.934714	−	0.355400i	$-0.884345\pi$
$61$	−3.29907	+	3.93168i	−0.422402	+	0.503400i	0.512312	+	0.858799i	$0.328789\pi$
$62$	4.06592	−	7.04237i	0.516372	−	0.894382i
$63$	−7.93550	+	0.166708i	−0.999779	+	0.0210033i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−6.43177	−	1.13409i	−0.797763	−	0.140667i
$66$	−4.76297	+	0.0329855i	−0.586281	+	0.00406023i
$67$	−1.47671	−	0.537479i	−0.180409	−	0.0656635i	0.250236	−	0.968185i	$-0.419492\pi$
$67$	−1.47671	−	0.537479i	−0.180409	−	0.0656635i	−0.430645	+	0.902521i	$0.641714\pi$
$68$	−4.67032	−	1.69986i	−0.566359	−	0.206138i
$69$	−7.98581	+	4.68464i	−0.961378	+	0.563965i
$70$	6.56150	−	7.93429i	0.784250	−	0.948329i
$71$	6.90603	−	3.98720i	0.819595	−	0.473194i	−0.0306816	−	0.999529i	$-0.509768\pi$
$71$	6.90603	−	3.98720i	0.819595	−	0.473194i	0.850277	+	0.526336i	$0.176434\pi$
$72$	−1.96001	−	2.27120i	−0.230989	−	0.267664i
$73$	1.45847	+	0.842046i	0.170701	+	0.0985541i	0.582916	−	0.812532i	$-0.301912\pi$
$73$	1.45847	+	0.842046i	0.170701	+	0.0985541i	−0.412216	+	0.911086i	$0.635245\pi$
$74$	−0.227768	+	0.271443i	−0.0264775	+	0.0315546i
$75$	−3.17066	−	17.2810i	−0.366117	−	1.99544i
$76$	7.10463	−	1.25274i	0.814957	−	0.143699i
$77$	−7.15598	+	1.31465i	−0.815499	+	0.149818i
$78$	−0.484933	+	2.86612i	−0.0549078	+	0.324524i
$79$	15.6048	−	5.67967i	1.75567	−	0.639013i	0.755798	−	0.654805i	$-0.227249\pi$
$79$	15.6048	−	5.67967i	1.75567	−	0.639013i	0.999875	+	0.0157919i	$0.00502692\pi$
$80$	3.89150			0.435083
$81$	7.05199	+	5.59191i	0.783554	+	0.621323i
$82$			4.23495i			0.467672i
$83$	−3.91696	+	1.42566i	−0.429943	+	0.156486i	−0.547921	−	0.836530i	$-0.684581\pi$
$83$	−3.91696	+	1.42566i	−0.429943	+	0.156486i	0.117979	+	0.993016i	$0.462359\pi$
$84$	−3.55158	−	2.89591i	−0.387509	−	0.315969i
$85$	−14.8160	+	12.4321i	−1.60702	+	1.34845i
$86$	−9.39692	+	1.65693i	−1.01330	+	0.178671i
$87$	4.33040	−	0.794527i	0.464268	−	0.0851822i
$88$	−2.10660	−	1.76765i	−0.224564	−	0.188432i
$89$	−2.32657	+	4.02974i	−0.246616	+	0.427152i	−0.962585	−	0.270981i	$-0.912652\pi$
$89$	−2.32657	+	4.02974i	−0.246616	+	0.427152i	0.715969	+	0.698133i	$0.245985\pi$
$90$	−11.4680	+	2.18630i	−1.20883	+	0.230456i
$91$	0.0317666	+	4.44018i	0.00333004	+	0.465457i
$92$	−5.26416	−	0.928214i	−0.548827	−	0.0967730i
$93$	−12.1487	+	7.12668i	−1.25976	+	0.739002i
$94$	2.58549	−	7.10357i	0.266673	−	0.732678i
$95$	9.60193	−	26.3811i	0.985137	−	2.70664i
$96$	−0.0119949	−	1.73201i	−0.00122422	−	0.176772i
$97$	8.44682	+	1.48940i	0.857645	+	0.151226i	0.585144	−	0.810929i	$-0.301038\pi$
$97$	8.44682	+	1.48940i	0.857645	+	0.151226i	0.272501	+	0.962155i	$0.412149\pi$
$98$	−6.11164	−	3.41290i	−0.617368	−	0.344755i
$99$	7.20107	+	4.02560i	0.723735	+	0.404588i
$100$	5.07188	−	8.78475i	0.507188	−	0.878475i
$101$	−1.34123	−	1.12543i	−0.133457	−	0.111984i	0.573616	−	0.819125i	$-0.305540\pi$
$101$	−1.34123	−	1.12543i	−0.133457	−	0.111984i	−0.707073	+	0.707141i	$0.749985\pi$
$102$	5.57889	+	6.55592i	0.552392	+	0.649133i
$103$	2.90951	−	0.513024i	0.286682	−	0.0505498i	−0.0284578	−	0.999595i	$-0.509060\pi$
$103$	2.90951	−	0.513024i	0.286682	−	0.0505498i	0.315140	+	0.949045i	$0.397949\pi$
$104$	−1.28563	+	1.07877i	−0.126066	+	0.105782i
$105$	−16.6701	+	6.33460i	−1.62683	+	0.618194i
$106$	6.04625	−	2.20065i	0.587264	−	0.213746i
$107$		−	6.80171i		−	0.657546i	−0.944409	−	0.328773i	$-0.893365\pi$
$107$		−	6.80171i		−	0.657546i	0.944409	−	0.328773i	$-0.106635\pi$
$108$	1.00841	+	5.09736i	0.0970347	+	0.490494i
$109$	14.3654			1.37596			0.687979	−	0.725731i	$-0.258498\pi$
$109$	14.3654			1.37596			0.687979	+	0.725731i	$0.258498\pi$
$110$	−10.0561	+	3.66013i	−0.958813	+	0.348980i
$111$	0.575261	−	0.213901i	0.0546013	−	0.0203026i
$112$	−0.478059	−	2.60220i	−0.0451723	−	0.245885i
$113$	3.25368	−	0.573711i	0.306080	−	0.0539702i	−0.0184986	−	0.999829i	$-0.505889\pi$
$113$	3.25368	−	0.573711i	0.306080	−	0.0539702i	0.324579	+	0.945859i	$0.394778\pi$
$114$	−11.7712	−	4.19227i	−1.10247	−	0.392642i
$115$	−13.3710	+	15.9349i	−1.24685	+	1.48594i
$116$	2.20134	+	1.27095i	0.204390	+	0.118004i
$117$	3.18259	−	3.90134i	0.294230	−	0.360679i
$118$	4.62650	−	2.67111i	0.425904	−	0.245896i
$119$	10.1333	+	8.38006i	0.928920	+	0.768199i
$120$	−5.86045	−	3.32963i	−0.534983	−	0.303952i
$121$	−3.23035	−	1.17575i	−0.293669	−	0.106887i
$122$	4.82291	+	1.75540i	0.436646	+	0.158926i
$123$	3.62350	−	6.37768i	0.326720	−	0.575056i
$124$	−8.00829	−	1.41208i	−0.719166	−	0.126808i
$125$	−10.0085	−	17.3352i	−0.895184	−	1.55050i
$126$	2.87076	+	7.39992i	0.255747	+	0.659237i
$127$	6.06645	−	10.5074i	0.538310	−	0.932381i	−0.460685	−	0.887564i	$-0.652396\pi$
$127$	6.06645	−	10.5074i	0.538310	−	0.932381i	0.998995	−	0.0448173i	$-0.0142706\pi$
$128$	0.642788	−	0.766044i	0.0568149	−	0.0677094i
$129$	15.5691	+	5.54489i	1.37078	+	0.488200i
$130$	1.13409	+	6.43177i	0.0994667	+	0.564103i
$131$	17.1170	−	14.3629i	1.49552	−	1.25489i	0.608157	−	0.793817i	$-0.291909\pi$
$131$	17.1170	−	14.3629i	1.49552	−	1.25489i	0.887362	−	0.461073i	$-0.152535\pi$
$132$	1.66003	+	4.46445i	0.144487	+	0.388580i
$133$	−18.8203	−	3.17987i	−1.63193	−	0.275730i
$134$			1.57148i			0.135755i
$135$	19.1409	+	6.51969i	1.64739	+	0.561126i
$136$			4.97005i			0.426178i
$137$	−4.31074	−	11.8437i	−0.368292	−	1.01187i	−0.976011	−	0.217721i	$-0.930138\pi$
$137$	−4.31074	−	11.8437i	−0.368292	−	1.01187i	0.607719	−	0.794152i	$-0.292085\pi$
$138$	7.13343	+	5.90196i	0.607238	+	0.502408i
$139$	−8.45500	−	10.0763i	−0.717144	−	0.854659i	0.277206	−	0.960810i	$-0.410591\pi$
$139$	−8.45500	−	10.0763i	−0.717144	−	0.854659i	−0.994350	+	0.106152i	$0.966147\pi$
$140$	−9.69996	−	3.45211i	−0.819796	−	0.291757i
$141$	−9.97158	+	8.48552i	−0.839759	+	0.714610i
$142$	−6.10875	−	5.12585i	−0.512634	−	0.430151i
$143$	2.30760	−	3.99688i	0.192971	−	0.334236i
$144$	−1.46387	+	2.61860i	−0.121989	+	0.218217i
$145$	8.56652	−	4.94588i	0.711411	−	0.410733i
$146$	0.292440	−	1.65851i	0.0242025	−	0.137259i
$147$	6.28375	+	10.3689i	0.518275	+	0.855214i
$148$	0.332974	+	0.121193i	0.0273703	+	0.00996198i
$149$	−0.202016	+	0.555033i	−0.0165498	+	0.0454701i	−0.947692	−	0.319185i	$-0.896591\pi$
$149$	−0.202016	+	0.555033i	−0.0165498	+	0.0454701i	0.931143	+	0.364655i	$0.118813\pi$
$150$	−15.1544	+	8.88991i	−1.23735	+	0.725858i
$151$	−3.14466	+	17.8343i	−0.255909	+	1.45133i	0.537820	+	0.843060i	$0.319248\pi$
$151$	−3.14466	+	17.8343i	−0.255909	+	1.45133i	−0.793729	+	0.608272i	$0.791863\pi$
$152$	−3.60712	−	6.24771i	−0.292576	−	0.506756i
$153$	−2.79224	−	14.6464i	−0.225739	−	1.18409i
$154$	3.68285	+	6.27478i	0.296773	+	0.505636i
$155$	−20.3410	+	24.2415i	−1.63383	+	1.94712i
$156$	2.85913	−	0.524582i	0.228913	−	0.0420002i
$157$	−2.28213	+	0.402401i	−0.182134	+	0.0321151i	−0.263971	−	0.964531i	$-0.585032\pi$
$157$	−2.28213	+	0.402401i	−0.182134	+	0.0321151i	0.0818374	+	0.996646i	$0.473921\pi$
$158$	−10.6743	−	12.7211i	−0.849201	−	1.01204i
$159$	−10.9883	−	1.85917i	−0.871432	−	0.147442i
$160$	−1.33097	−	3.65681i	−0.105222	−	0.289096i
$161$	12.2981	+	6.98346i	0.969223	+	0.550374i
$162$	2.84276	−	8.53925i	0.223348	−	0.670907i
$163$	16.8886			1.32281			0.661407	−	0.750027i	$-0.269960\pi$
$163$	16.8886			1.32281			0.661407	+	0.750027i	$0.269960\pi$
$164$	3.97955	−	1.44844i	0.310751	−	0.113104i
$165$	18.2758	+	3.09217i	1.42277	+	0.240725i
$166$	2.67936	+	3.19314i	0.207959	+	0.247836i
$167$	−0.610365	−	3.46155i	−0.0472315	−	0.267863i	0.952042	−	0.305966i	$-0.0989795\pi$
$167$	−0.610365	−	3.46155i	−0.0472315	−	0.267863i	−0.999274	+	0.0381034i	$0.987868\pi$
$168$	−1.50655	+	4.32785i	−0.116233	+	0.333901i
$169$	7.80094	+	6.54577i	0.600072	+	0.503521i
$170$	16.7497	+	9.67046i	1.28465	+	0.741690i
$171$	14.1399	+	16.3850i	1.08131	+	1.25299i
$172$	4.77094	+	8.26351i	0.363781	+	0.630087i
$173$	−2.05049	+	11.6289i	−0.155896	+	0.884130i	0.802066	+	0.597235i	$0.203734\pi$
$173$	−2.05049	+	11.6289i	−0.155896	+	0.884130i	−0.957962	+	0.286895i	$0.907377\pi$
$174$	−2.22770	−	3.79750i	−0.168881	−	0.287888i
$175$	−20.4350	+	17.3977i	−1.54474	+	1.31514i
$176$	−0.940545	+	2.58413i	−0.0708962	+	0.194786i
$177$	−9.25279	+	0.0640792i	−0.695482	+	0.00481649i
$178$	4.58245	+	0.808010i	0.343469	+	0.0605629i
$179$	−9.62789	+	5.55866i	−0.719622	+	0.415474i	−0.814614	−	0.580004i	$-0.803051\pi$
$179$	−9.62789	+	5.55866i	−0.719622	+	0.415474i	0.0949914	+	0.995478i	$0.469718\pi$
$180$	5.97672	+	10.0286i	0.445478	+	0.747487i
$181$	3.23752	+	1.86918i	0.240643	+	0.138935i	0.615472	−	0.788159i	$-0.288965\pi$
$181$	3.23752	+	1.86918i	0.240643	+	0.138935i	−0.374829	+	0.927094i	$0.622299\pi$
$182$	4.16154	−	1.54848i	0.308473	−	0.114781i
$183$	−5.76118	−	6.77013i	−0.425878	−	0.500462i
$184$	0.928214	+	5.26416i	0.0684289	+	0.388079i
$185$	1.05632	−	0.886357i	0.0776622	−	0.0651663i
$186$	10.8520	+	8.97856i	0.795706	+	0.658340i
$187$	−4.67455	−	12.8432i	−0.341837	−	0.939189i
$188$	−7.55946			−0.551331
$189$	2.00824	−	13.6003i	0.146078	−	0.989273i
$190$	−28.0742			−2.03671
$191$	4.67506	+	12.8446i	0.338275	+	0.929404i	0.985884	+	0.167431i	$0.0535471\pi$
$191$	4.67506	+	12.8446i	0.338275	+	0.929404i	−0.647608	+	0.761973i	$0.724231\pi$
$192$	−1.62345	+	0.603654i	−0.117163	+	0.0435649i
$193$	−6.13489	+	5.14778i	−0.441599	+	0.370545i	−0.836307	−	0.548261i	$-0.815290\pi$
$193$	−6.13489	+	5.14778i	−0.441599	+	0.370545i	0.394709	+	0.918806i	$0.370846\pi$
$194$	−1.48940	−	8.44682i	−0.106933	−	0.606447i
$195$	3.79523	−	10.6563i	0.271782	−	0.763117i
$196$	−1.11678	+	6.91034i	−0.0797699	+	0.493596i
$197$	10.5622	+	6.09810i	0.752527	+	0.434472i	0.826606	−	0.562781i	$-0.190268\pi$
$197$	10.5622	+	6.09810i	0.752527	+	0.434472i	−0.0740793	+	0.997252i	$0.523602\pi$
$198$	1.31992	−	8.14363i	0.0938024	−	0.578743i
$199$	−5.96407	+	3.44336i	−0.422781	+	0.244093i	−0.696267	−	0.717783i	$-0.745157\pi$
$199$	−5.96407	+	3.44336i	−0.422781	+	0.244093i	0.273485	+	0.961876i	$0.411824\pi$
$200$	−9.98965	−	1.76144i	−0.706375	−	0.124553i
$201$	1.34459	−	2.36659i	0.0948398	−	0.166926i
$202$	−0.598826	+	1.64526i	−0.0421333	+	0.115760i
$203$	−4.35963	−	5.12075i	−0.305986	−	0.359406i
$204$	4.25245	−	7.48470i	0.297731	−	0.524034i
$205$	2.86178	−	16.2299i	0.199875	−	1.13355i
$206$	−1.47720	−	2.55858i	−0.102921	−	0.178265i
$207$	−5.69286	−	14.9916i	−0.395681	−	1.04199i
$208$	1.45343	+	0.839136i	0.100777	+	0.0581836i
$209$	15.1975	+	12.7522i	1.05123	+	0.882089i
$210$	11.6541	+	13.4982i	0.804208	+	0.931464i
$211$	2.81430	+	15.9607i	0.193745	+	1.09878i	0.914195	+	0.405274i	$0.132824\pi$
$211$	2.81430	+	15.9607i	0.193745	+	1.09878i	−0.720451	+	0.693506i	$0.756065\pi$
$212$	−4.13588	−	4.92895i	−0.284053	−	0.338521i
$213$	4.81377	+	12.9461i	0.329834	+	0.887050i
$214$	−6.39152	+	2.32632i	−0.436915	+	0.159024i
$215$	37.1322			2.53240
$216$	4.44506	−	2.69100i	0.302448	−	0.183099i
$217$	18.7089	+	10.6238i	1.27004	+	0.721192i
$218$	−4.91326	−	13.4991i	−0.332768	−	0.914273i
$219$	−1.85945	+	2.24743i	−0.125650	+	0.151867i
$220$	6.87879	+	8.19782i	0.463768	+	0.552697i
$221$	−8.21437	+	1.44841i	−0.552558	+	0.0974309i
$222$	−0.397752	−	0.467410i	−0.0266953	−	0.0313705i
$223$	−10.8119	+	12.8851i	−0.724016	+	0.862849i	−0.995014	−	0.0997312i	$-0.968202\pi$
$223$	−10.8119	+	12.8851i	−0.724016	+	0.862849i	0.270999	+	0.962580i	$0.412646\pi$
$224$	−2.28177	+	1.33923i	−0.152457	+	0.0894813i
$225$	30.4283	−	0.421477i	2.02856	−	0.0280985i
$226$	−1.65193	−	2.86123i	−0.109885	−	0.190326i
$227$	3.32251	−	18.8429i	0.220523	−	1.25065i	−0.650539	−	0.759473i	$-0.725457\pi$
$227$	3.32251	−	18.8429i	0.220523	−	1.25065i	0.871062	−	0.491173i	$-0.163432\pi$
$228$	0.0865337	+	12.4951i	0.00573083	+	0.827509i
$229$	2.45664	−	6.74955i	0.162339	−	0.446023i	−0.831677	−	0.555260i	$-0.812619\pi$
$229$	2.45664	−	6.74955i	0.162339	−	0.446023i	0.994016	+	0.109237i	$0.0348409\pi$
$230$	19.5470	+	7.11453i	1.28889	+	0.469118i
$231$	−0.177423	−	12.6007i	−0.0116736	−	0.829065i
$232$	0.441395	−	2.50327i	0.0289790	−	0.164348i
$233$	−12.2778	+	7.08860i	−0.804346	+	0.464389i	−0.844989	−	0.534784i	$-0.820393\pi$
$233$	−12.2778	+	7.08860i	−0.804346	+	0.464389i	0.0406425	+	0.999174i	$0.487060\pi$
$234$	−4.75457	−	1.65632i	−0.310816	−	0.108277i
$235$	−14.7088	+	25.4764i	−0.959498	+	1.66190i
$236$	−4.09238	−	3.43392i	−0.266391	−	0.223529i
$237$	5.19066	+	28.2906i	0.337170	+	1.83767i
$238$	4.40888	−	12.3884i	0.285785	−	0.803018i
$239$	−3.51743	−	4.19191i	−0.227523	−	0.271152i	0.640190	−	0.768217i	$-0.278856\pi$
$239$	−3.51743	−	4.19191i	−0.227523	−	0.271152i	−0.867713	+	0.497065i	$0.834411\pi$
$240$	−1.12444	+	6.64582i	−0.0725822	+	0.428986i
$241$	0.722609	+	1.98535i	0.0465474	+	0.127888i	0.960788	−	0.277283i	$-0.0894341\pi$
$241$	0.722609	+	1.98535i	0.0465474	+	0.127888i	−0.914241	+	0.405171i	$0.867212\pi$
$242$			3.43767i			0.220982i
$243$	−11.5874	+	10.4275i	−0.743332	+	0.668922i
$244$		−	5.13244i		−	0.328571i
$245$	21.1158	+	17.2095i	1.34904	+	1.09947i
$246$	−7.23237	−	1.22368i	−0.461119	−	0.0780190i
$247$	9.27484	−	7.78251i	0.590144	−	0.495189i
$248$	1.41208	+	8.00829i	0.0896670	+	0.508527i
$249$	−1.30291	−	7.10125i	−0.0825687	−	0.450023i
$250$	−12.8666	+	15.3338i	−0.813757	+	0.969797i
$251$	−0.00894719	+	0.0154970i	−0.000564742	+	0.000978161i	−0.866308	−	0.499511i	$-0.833513\pi$
$251$	−0.00894719	+	0.0154970i	−0.000564742	+	0.000978161i	0.865743	+	0.500489i	$0.166846\pi$
$252$	5.97179	−	5.22855i	0.376187	−	0.329368i
$253$	−7.34980	−	12.7302i	−0.462078	−	0.800343i
$254$	−11.9486	−	2.10686i	−0.749720	−	0.132196i
$255$	−16.9502	−	28.8947i	−1.06147	−	1.80946i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−18.6003	−	6.76995i	−1.16025	−	0.422298i	−0.311066	−	0.950388i	$-0.600686\pi$
$257$	−18.6003	−	6.76995i	−1.16025	−	0.422298i	−0.849188	+	0.528090i	$0.822908\pi$
$258$	−0.114454	−	16.5266i	−0.00712557	−	1.02890i
$259$	−0.722463	−	0.597463i	−0.0448917	−	0.0371246i
$260$	5.65600	−	3.26549i	0.350770	−	0.202517i
$261$	0.105617	+	7.62494i	0.00653751	+	0.471972i
$262$	−19.3510	−	11.1723i	−1.19551	−	0.690229i
$263$	6.42905	−	7.66185i	0.396432	−	0.472450i	−0.530496	−	0.847687i	$-0.677994\pi$
$263$	6.42905	−	7.66185i	0.396432	−	0.472450i	0.926929	+	0.375237i	$0.122439\pi$
$264$	3.62745	−	3.08685i	0.223254	−	0.189982i
$265$	−24.6586	+	4.34798i	−1.51477	+	0.267094i
$266$	3.44883	+	18.7729i	0.211461	+	1.15104i
$267$	−6.20965	−	5.13766i	−0.380024	−	0.314419i
$268$	1.47671	−	0.537479i	0.0902044	−	0.0328317i
$269$	−26.7576			−1.63144			−0.815720	−	0.578447i	$-0.803659\pi$
$269$	−26.7576			−1.63144			−0.815720	+	0.578447i	$0.803659\pi$
$270$	−0.420075	−	20.2165i	−0.0255649	−	1.23033i
$271$		−	26.6221i		−	1.61718i	−0.588373	−	0.808590i	$-0.700231\pi$
$271$		−	26.6221i		−	1.61718i	0.588373	−	0.808590i	$-0.299769\pi$
$272$	4.67032	−	1.69986i	0.283179	−	0.103069i
$273$	−7.59202	−	1.22873i	−0.459490	−	0.0743660i
$274$	−9.65505	+	8.10155i	−0.583283	+	0.489433i
$275$	27.4712	−	4.84392i	1.65658	−	0.292099i
$276$	3.10625	−	8.72182i	0.186974	−	0.524992i
$277$	−11.8133	−	9.91258i	−0.709795	−	0.595589i	0.214746	−	0.976670i	$-0.431108\pi$
$277$	−11.8133	−	9.91258i	−0.709795	−	0.595589i	−0.924542	+	0.381081i	$0.875552\pi$
$278$	−6.57682	+	11.3914i	−0.394452	+	0.683210i
$279$	−8.66046	−	22.8065i	−0.518488	−	1.36539i
$280$	0.0736588	+	10.2957i	0.00440196	+	0.615284i
$281$	−24.7789	−	4.36919i	−1.47819	−	0.260644i	−0.624334	−	0.781158i	$-0.714629\pi$
$281$	−24.7789	−	4.36919i	−1.47819	−	0.260644i	−0.853853	+	0.520514i	$0.825740\pi$
$282$	11.3843	+	6.46800i	0.677923	+	0.385164i
$283$	4.29784	−	11.8082i	0.255480	−	0.701926i	−0.743952	−	0.668233i	$-0.767051\pi$
$283$	4.29784	−	11.8082i	0.255480	−	0.701926i	0.999432	−	0.0336931i	$-0.0107269\pi$
$284$	−2.72741	+	7.49349i	−0.161842	+	0.444657i
$285$	42.2786	+	24.0207i	2.50437	+	1.42287i
$286$	−4.54508	−	0.801420i	−0.268756	−	0.0473890i
$287$	−11.2043	+	0.0801598i	−0.661372	+	0.00473168i
$288$	2.96136	+	0.479975i	0.174500	+	0.0282828i
$289$	−3.85068	+	6.66957i	−0.226510	+	0.392327i
$290$	−7.57753	−	6.35831i	−0.444968	−	0.373373i
$291$	−4.98426	+	13.9949i	−0.292183	+	0.820398i
$292$	−1.65851	+	0.292440i	−0.0970568	+	0.0171137i
$293$	−10.1575	+	8.52312i	−0.593405	+	0.497926i	−0.889318	−	0.457289i	$-0.848821\pi$
$293$	−10.1575	+	8.52312i	−0.593405	+	0.497926i	0.295913	+	0.955215i	$0.404376\pi$
$294$	7.59443	−	9.45117i	0.442916	−	0.551204i
$295$	−19.5355	+	7.11035i	−1.13740	+	0.413980i
$296$		−	0.354344i		−	0.0205958i
$297$	−8.95558	+	11.1347i	−0.519655	+	0.646098i
$298$	0.590654			0.0342157
$299$	−8.42997	+	3.06826i	−0.487518	+	0.177442i
$300$	13.5369	+	11.2000i	0.781554	+	0.646631i
$301$	−4.56158	−	24.8299i	−0.262925	−	1.43117i
$302$	17.8343	−	3.14466i	1.02625	−	0.180955i
$303$	2.30952	−	1.96533i	0.132679	−	0.112906i
$304$	−4.63722	+	5.52642i	−0.265963	+	0.316962i
$305$	−17.2970	−	9.98644i	−0.990424	−	0.571822i
$306$	−12.8081	+	7.63319i	−0.732188	+	0.436361i
$307$	−15.3747	+	8.87658i	−0.877480	+	0.506613i	−0.869827	−	0.493357i	$-0.835769\pi$
$307$	−15.3747	+	8.87658i	−0.877480	+	0.506613i	−0.00765328	+	0.999971i	$0.502436\pi$
$308$	4.63676	−	5.60685i	0.264204	−	0.319480i
$309$	0.0354375	+	5.11703i	0.00201597	+	0.291098i
$310$	29.7366	+	10.8232i	1.68892	+	0.614718i
$311$	−26.0813	−	9.49283i	−1.47894	−	0.538289i	−0.528425	−	0.848980i	$-0.677217\pi$
$311$	−26.0813	−	9.49283i	−1.47894	−	0.538289i	−0.950511	+	0.310691i	$0.899440\pi$
$312$	−1.47082	−	2.50728i	−0.0832690	−	0.141947i
$313$	27.7620	+	4.89518i	1.56920	+	0.276692i	0.889547	−	0.456843i	$-0.151020\pi$
$313$	27.7620	+	4.89518i	1.56920	+	0.276692i	0.679652	+	0.733535i	$0.262131\pi$
$314$	1.15867	+	2.00687i	0.0653873	+	0.113254i
$315$	−6.00132	−	30.2992i	−0.338136	−	1.70717i
$316$	−8.30312	+	14.3814i	−0.467087	+	0.809019i
$317$	6.01723	−	7.17106i	0.337962	−	0.402767i	−0.570119	−	0.821562i	$-0.693103\pi$
$317$	6.01723	−	7.17106i	0.337962	−	0.402767i	0.908081	+	0.418795i	$0.137547\pi$
$318$	2.01118	+	10.9615i	0.112782	+	0.614692i
$319$	1.21382	+	6.88393i	0.0679610	+	0.385426i
$320$	−2.98106	+	2.50141i	−0.166646	+	0.139833i
$321$	11.6158	+	1.96534i	0.648332	+	0.109695i
$322$	2.35612	−	13.9449i	0.131301	−	0.777118i
$323$		−	35.8551i		−	1.99503i
$324$	−8.99655	+	0.249279i	−0.499808	+	0.0138488i
$325$		−	17.0240i		−	0.944320i
$326$	−5.77623	−	15.8701i	−0.319916	−	0.878961i
$327$	−4.15085	+	24.5330i	−0.229543	+	1.35668i
$328$	−2.72218	−	3.24416i	−0.150307	−	0.179129i
$329$	18.8427	+	6.70593i	1.03883	+	0.369710i
$330$	−3.34500	−	18.2312i	−0.184136	−	1.00360i
$331$	15.4208	+	12.9396i	0.847601	+	0.711222i	0.959260	−	0.282525i	$-0.0911719\pi$
$331$	15.4208	+	12.9396i	0.847601	+	0.711222i	−0.111659	+	0.993747i	$0.535616\pi$
$332$	2.08417	−	3.60989i	0.114384	−	0.198119i
$333$	0.199075	+	1.04422i	0.0109092	+	0.0572231i
$334$	−3.04404	+	1.75748i	−0.166562	+	0.0961648i
$335$	1.06193	−	6.02251i	0.0580195	−	0.329045i
$336$	4.58212	−	0.0645183i	0.249975	−	0.00351976i
$337$	20.6806	+	7.52714i	1.12655	+	0.410029i	0.837037	−	0.547146i	$-0.184286\pi$
$337$	20.6806	+	7.52714i	1.12655	+	0.410029i	0.289509	+	0.957175i	$0.406508\pi$
$338$	3.48293	−	9.56927i	0.189446	−	0.520500i
$339$	0.0396294	+	5.72233i	0.00215238	+	0.310794i
$340$	3.35852	−	19.0471i	0.182141	−	1.03297i
$341$	−11.1811	−	19.3663i	−0.605493	−	1.04874i
$342$	10.5607	−	18.8912i	0.571058	−	1.02152i
$343$	8.91378	−	16.2341i	0.481299	−	0.876556i
$344$	6.13340	−	7.30951i	0.330691	−	0.394102i
$345$	−23.3497	−	27.4390i	−1.25711	−	1.47726i
$346$	11.6289	−	2.05049i	0.625174	−	0.110235i
$347$	−15.6453	−	18.6454i	−0.839884	−	1.00094i	−0.999904	−	0.0138213i	$-0.995600\pi$
$347$	−15.6453	−	18.6454i	−0.839884	−	1.00094i	0.160020	−	0.987114i	$-0.448844\pi$
$348$	−2.80657	+	3.39217i	−0.150448	+	0.181839i
$349$	−6.00922	−	16.5102i	−0.321666	−	0.883770i	−0.990146	−	0.140040i	$-0.955277\pi$
$349$	−6.00922	−	16.5102i	−0.321666	−	0.883770i	0.668480	−	0.743730i	$-0.266945\pi$
$350$	23.3377	+	13.2523i	1.24745	+	0.708365i
$351$	5.74303	+	6.56244i	0.306540	+	0.350277i
$352$	2.74997			0.146574
$353$	11.2811	−	4.10598i	0.600432	−	0.218539i	−0.0238797	−	0.999715i	$-0.507602\pi$
$353$	11.2811	−	4.10598i	0.600432	−	0.218539i	0.624311	+	0.781176i	$0.285380\pi$
$354$	3.22485	+	8.67286i	0.171399	+	0.460957i
$355$	19.9472	+	23.7722i	1.05869	+	1.26170i
$356$	−0.808010	−	4.58245i	−0.0428245	−	0.242870i
$357$	−17.2393	+	14.8841i	−0.912400	+	0.787748i
$358$	8.51637	+	7.14608i	0.450104	+	0.377682i
$359$	−13.3990	−	7.73591i	−0.707172	−	0.408286i	0.102841	−	0.994698i	$-0.467207\pi$
$359$	−13.3990	−	7.73591i	−0.707172	−	0.408286i	−0.810013	+	0.586412i	$0.800540\pi$
$360$	7.37964	−	9.04626i	0.388941	−	0.476780i
$361$	16.5226	+	28.6179i	0.869609	+	1.50621i
$362$	0.649161	−	3.68157i	0.0341191	−	0.193499i
$363$	2.94133	−	5.17700i	0.154380	−	0.271722i
$364$	−2.87842	−	3.38095i	−0.150870	−	0.177210i
$365$	−2.24148	+	6.15841i	−0.117324	+	0.322346i
$366$	−4.39140	+	7.72926i	−0.229542	+	0.404015i
$367$	−13.6855	−	2.41312i	−0.714377	−	0.125964i	−0.195365	−	0.980731i	$-0.562589\pi$
$367$	−13.6855	−	2.41312i	−0.714377	−	0.125964i	−0.519012	+	0.854767i	$0.673700\pi$
$368$	4.62923	−	2.67269i	0.241315	−	0.139323i
$369$	9.84466	+	8.03095i	0.512493	+	0.418074i
$370$	−1.19419	−	0.689464i	−0.0620828	−	0.0358435i
$371$	5.93668	+	15.9548i	0.308217	+	0.828332i
$372$	4.72549	−	13.2684i	0.245005	−	0.687933i
$373$	−5.89351	−	33.4238i	−0.305154	−	1.73062i	−0.622777	−	0.782399i	$-0.713996\pi$
$373$	−5.89351	−	33.4238i	−0.305154	−	1.73062i	0.317623	−	0.948217i	$-0.397115\pi$
$374$	−10.4699	+	8.78528i	−0.541385	+	0.454276i
$375$	32.4965	−	12.0833i	1.67811	−	0.623978i
$376$	2.58549	+	7.10357i	0.133336	+	0.366339i
$377$	4.26598			0.219709
$378$	−13.4669	+	2.76443i	−0.692664	+	0.142187i
$379$	5.88433			0.302258			0.151129	−	0.988514i	$-0.451709\pi$
$379$	5.88433			0.302258			0.151129	+	0.988514i	$0.451709\pi$
$380$	9.60193	+	26.3811i	0.492569	+	1.35332i
$381$	16.1914	+	13.3962i	0.829512	+	0.686311i
$382$	10.4710	−	8.78624i	0.535744	−	0.449543i
$383$	−3.97094	−	22.5203i	−0.202906	−	1.15074i	−0.900701	−	0.434439i	$-0.856947\pi$
$383$	−3.97094	−	22.5203i	−0.202906	−	1.15074i	0.697796	−	0.716297i	$-0.254164\pi$
$384$	1.12250	+	1.31909i	0.0572825	+	0.0673143i
$385$	−9.87388	−	26.5360i	−0.503220	−	1.35240i
$386$	6.93559	+	4.00426i	0.353012	+	0.203812i
$387$	−13.9681	+	24.9864i	−0.710038	+	1.27013i
$388$	−7.42801	+	4.28856i	−0.377100	+	0.217719i
$389$	34.5428	+	6.09083i	1.75139	+	0.308818i	0.955141	−	0.296150i	$-0.0957029\pi$
$389$	34.5428	+	6.09083i	1.75139	+	0.308818i	0.796250	+	0.604968i	$0.206814\pi$
$390$	−11.3117	+	0.0783383i	−0.572792	+	0.00396681i
$391$	−9.08636	+	24.9646i	−0.459517	+	1.26251i
$392$	6.87556	−	1.31405i	0.347268	−	0.0663694i
$393$	19.5827	+	33.3822i	0.987816	+	1.68391i
$394$	2.11785	−	12.0109i	0.106696	−	0.605101i
$395$	32.3116	+	55.9653i	1.62577	+	2.81592i
$396$	−8.10395	+	1.54497i	−0.407239	+	0.0776377i
$397$	9.45939	+	5.46138i	0.474753	+	0.274099i	0.718227	−	0.695809i	$-0.244954\pi$
$397$	9.45939	+	5.46138i	0.474753	+	0.274099i	−0.243474	+	0.969907i	$0.578287\pi$
$398$	5.27553	+	4.42669i	0.264438	+	0.221890i
$399$	10.8686	−	31.2221i	0.544111	−	1.56306i
$400$	1.76144	+	9.98965i	0.0880722	+	0.499482i
$401$	−3.54267	−	4.22199i	−0.176912	−	0.210836i	0.670300	−	0.742090i	$-0.266165\pi$
$401$	−3.54267	−	4.22199i	−0.176912	−	0.210836i	−0.847212	+	0.531254i	$0.821721\pi$
$402$	−2.68374	−	0.454076i	−0.133853	−	0.0226473i
$403$	−12.8244	+	4.66769i	−0.638828	+	0.232514i
$404$	1.75085			0.0871081
$405$	−16.6649	+	30.8046i	−0.828086	+	1.53069i
$406$	−3.32085	+	5.84811i	−0.164811	+	0.290237i
$407$	0.333276	+	0.915668i	0.0165199	+	0.0453880i
$408$	−8.48774	−	1.43608i	−0.420206	−	0.0710967i
$409$	9.82756	+	11.7120i	0.485942	+	0.579123i	0.952180	−	0.305536i	$-0.0988357\pi$
$409$	9.82756	+	11.7120i	0.485942	+	0.579123i	−0.466239	+	0.884659i	$0.654391\pi$
$410$	−16.2299	+	2.86178i	−0.801540	+	0.141333i
$411$	21.4720	−	3.93960i	1.05913	−	0.194326i
$412$	−1.89905	+	2.26319i	−0.0935593	+	0.111500i
$413$	7.15449	+	12.1897i	0.352050	+	0.599816i
$414$	−12.1404	+	10.4770i	−0.596670	+	0.514915i
$415$	−8.11055	−	14.0479i	−0.398131	−	0.689584i
$416$	0.291429	−	1.65277i	0.0142885	−	0.0810339i
$417$	19.6511	−	11.5278i	0.962319	−	0.564517i
$418$	6.78531	−	18.6425i	0.331880	−	0.911834i
$419$	7.80252	+	2.83989i	0.381178	+	0.138738i	0.525501	−	0.850793i	$-0.323878\pi$
$419$	7.80252	+	2.83989i	0.381178	+	0.138738i	−0.144322	+	0.989531i	$0.546100\pi$
$420$	8.69822	−	15.5679i	0.424430	−	0.759636i
$421$	3.40910	−	19.3340i	0.166149	−	0.942280i	−0.781722	−	0.623627i	$-0.785658\pi$
$421$	3.40910	−	19.3340i	0.166149	−	0.942280i	0.947871	−	0.318653i	$-0.103230\pi$
$422$	14.0356	−	8.10346i	0.683242	−	0.394470i
$423$	−11.6101	−	19.4811i	−0.564504	−	0.947205i
$424$	−3.21714	+	5.57225i	−0.156238	+	0.270613i
$425$	−38.6201	−	32.4061i	−1.87335	−	1.57193i
$426$	10.5189	−	8.95129i	0.509643	−	0.433691i
$427$	−4.55294	+	12.7931i	−0.220332	+	0.619103i
$428$	4.37206	+	5.21041i	0.211331	+	0.251855i
$429$	6.15901	+	5.09575i	0.297360	+	0.246025i
$430$	−12.7000	−	34.8929i	−0.612447	−	1.68268i
$431$		−	15.3638i		−	0.740050i	−0.929022	−	0.370025i	$-0.879349\pi$
$431$		−	15.3638i		−	0.740050i	0.929022	−	0.370025i	$-0.120651\pi$
$432$	−4.04901	−	3.25661i	−0.194808	−	0.156684i
$433$			10.6521i			0.511908i	0.966689	+	0.255954i	$0.0823895\pi$
$433$			10.6521i			0.511908i	−0.966689	+	0.255954i	$0.917610\pi$
$434$	3.58433	−	21.2141i	0.172053	−	1.01831i
$435$	5.97120	+	16.0588i	0.286297	+	0.769962i
$436$	−11.0045	+	9.23391i	−0.527022	+	0.442224i
$437$	−6.69635	−	37.9769i	−0.320330	−	1.81668i
$438$	2.74786	+	0.978644i	0.131298	+	0.0467614i
$439$	−12.7922	+	15.2452i	−0.610540	+	0.727613i	−0.979413	−	0.201867i	$-0.935299\pi$
$439$	−12.7922	+	15.2452i	−0.610540	+	0.727613i	0.368873	+	0.929480i	$0.379744\pi$
$440$	5.35075	−	9.26777i	0.255087	−	0.441824i
$441$	−19.5235	+	7.73518i	−0.929690	+	0.368342i
$442$	4.17054	+	7.22359i	0.198372	+	0.343591i
$443$	−17.4953	−	3.08489i	−0.831225	−	0.146567i	−0.258186	−	0.966095i	$-0.583125\pi$
$443$	−17.4953	−	3.08489i	−0.831225	−	0.146567i	−0.573039	+	0.819528i	$0.694236\pi$
$444$	−0.303182	+	0.533628i	−0.0143884	+	0.0253249i
$445$	−17.0157	−	6.19320i	−0.806620	−	0.293586i
$446$	15.8059	+	5.75287i	0.748430	+	0.272406i
$447$	−0.889502	−	0.505373i	−0.0420720	−	0.0239033i
$448$	2.03888	+	1.68611i	0.0963279	+	0.0796613i
$449$	−8.15435	+	4.70791i	−0.384827	+	0.222180i	−0.679917	−	0.733290i	$-0.737984\pi$
$449$	−8.15435	+	4.70791i	−0.384827	+	0.222180i	0.295089	+	0.955470i	$0.404651\pi$
$450$	−10.8032	−	28.4491i	−0.509266	−	1.34111i
$451$	10.0857	+	5.82300i	0.474918	+	0.274194i
$452$	−2.12369	+	2.53091i	−0.0998898	+	0.119044i
$453$	−29.5483	−	10.5236i	−1.38830	−	0.494440i
$454$	−18.8429	+	3.32251i	−0.884340	+	0.155933i
$455$	−16.9950	+	3.12220i	−0.796736	+	0.146371i
$456$	11.7120	−	4.35490i	0.548463	−	0.203937i
$457$	−24.5535	+	8.93673i	−1.14856	+	0.418043i	−0.844999	−	0.534768i	$-0.820399\pi$
$457$	−24.5535	+	8.93673i	−1.14856	+	0.418043i	−0.303564	+	0.952811i	$0.598177\pi$
$458$	−7.18272			−0.335627
$459$	25.8195	−	0.536501i	1.20515	−	0.0250417i
$460$		−	20.8015i		−	0.969875i
$461$	1.47622	−	0.537300i	0.0687543	−	0.0250245i	−0.307414	−	0.951576i	$-0.599464\pi$
$461$	1.47622	−	0.537300i	0.0687543	−	0.0250245i	0.376168	+	0.926551i	$0.377241\pi$
$462$	−11.7801	+	4.47641i	−0.548060	+	0.208262i
$463$	2.89321	−	2.42769i	0.134459	−	0.112824i	−0.573078	−	0.819501i	$-0.694251\pi$
$463$	2.89321	−	2.42769i	0.134459	−	0.112824i	0.707537	+	0.706677i	$0.249806\pi$
$464$	−2.50327	+	0.441395i	−0.116212	+	0.0204912i
$465$	−35.5216	−	41.7425i	−1.64728	−	1.93576i
$466$	10.8604	+	9.11292i	0.503096	+	0.422148i
$467$	−15.5675	+	26.9637i	−0.720377	+	1.24773i	0.240472	+	0.970656i	$0.422698\pi$
$467$	−15.5675	+	26.9637i	−0.720377	+	1.24773i	−0.960849	+	0.277074i	$0.910635\pi$
$468$	0.0697329	+	5.03433i	0.00322340	+	0.232712i
$469$	−4.15764	+	0.0297452i	−0.191982	+	0.00137351i
$470$	28.9707	+	5.10832i	1.33632	+	0.235629i
$471$	−0.0277961	−	4.01364i	−0.00128078	−	0.184939i
$472$	−1.82715	+	5.02005i	−0.0841014	+	0.231067i
$473$	−8.97457	+	24.6574i	−0.412651	+	1.13375i
$474$	24.8092	−	14.5536i	1.13952	−	0.668468i
$475$	72.0676	+	12.7075i	3.30669	+	0.583059i
$476$	−13.1492	+	0.0940737i	−0.602691	+	0.00431186i
$477$	6.35011	−	18.2284i	0.290751	−	0.834623i
$478$	−2.73607	+	4.73902i	−0.125145	+	0.216758i
$479$	6.19661	+	5.19957i	0.283130	+	0.237574i	0.773281	−	0.634063i	$-0.218614\pi$
$479$	6.19661	+	5.19957i	0.283130	+	0.237574i	−0.490151	+	0.871637i	$0.663058\pi$
$480$	6.62961	−	1.21638i	0.302599	−	0.0555197i
$481$	0.585650	−	0.103266i	0.0267033	−	0.00470852i
$482$	1.61847	−	1.35806i	0.0737195	−	0.0618580i
$483$	−15.4797	+	18.9845i	−0.704351	+	0.863826i
$484$	3.23035	−	1.17575i	0.146834	−	0.0534433i
$485$			33.3779i			1.51561i
$486$	13.7617	+	7.32219i	0.624245	+	0.332141i
$487$	−18.0725			−0.818945			−0.409472	−	0.912323i	$-0.634287\pi$
$487$	−18.0725			−0.818945			−0.409472	+	0.912323i	$0.634287\pi$
$488$	−4.82291	+	1.75540i	−0.218323	+	0.0794631i
$489$	−4.87991	+	28.8419i	−0.220677	+	1.30428i
$490$	8.94959	−	25.7284i	0.404301	−	1.16229i
$491$	9.13275	−	1.61035i	0.412155	−	0.0726741i	0.0362739	−	0.999342i	$-0.488451\pi$
$491$	9.13275	−	1.61035i	0.412155	−	0.0726741i	0.375881	+	0.926668i	$0.377340\pi$
$492$	1.32373	+	7.21472i	0.0596784	+	0.325265i
$493$	8.12054	−	9.67768i	0.365731	−	0.435861i
$494$	−10.4854	−	6.05372i	−0.471758	−	0.272370i
$495$	−10.5615	+	30.3175i	−0.474704	+	1.36267i
$496$	7.04237	−	4.06592i	0.316212	−	0.182565i
$497$	13.4457	−	16.2588i	0.603124	−	0.729308i
$498$	−6.22737	+	3.65311i	−0.279055	+	0.163700i
$499$	−24.0969	−	8.77057i	−1.07873	−	0.392625i	−0.259293	−	0.965799i	$-0.583490\pi$
$499$	−24.0969	−	8.77057i	−1.07873	−	0.392625i	−0.819434	+	0.573174i	$0.805712\pi$
$500$	18.8097	+	6.84619i	0.841197	+	0.306171i
$501$	6.08793	−	0.0421613i	0.271989	−	0.00188363i
$502$	0.0176225	+	0.00310733i	0.000786532	+	0.000138687i
$503$	−5.40271	−	9.35777i	−0.240895	−	0.417242i	0.720075	−	0.693897i	$-0.244108\pi$
$503$	−5.40271	−	9.35777i	−0.240895	−	0.417242i	−0.960969	+	0.276655i	$0.910774\pi$
$504$	−6.95570	−	3.82338i	−0.309832	−	0.170307i
$505$	3.40672	−	5.90061i	0.151597	−	0.262573i
$506$	−9.44873	+	11.2606i	−0.420047	+	0.500593i
$507$	−13.4328	+	11.4309i	−0.596571	+	0.507664i
$508$	2.10686	+	11.9486i	0.0934766	+	0.530132i
$509$	10.9511	−	9.18908i	0.485400	−	0.407299i	−0.366974	−	0.930231i	$-0.619606\pi$
$509$	10.9511	−	9.18908i	0.485400	−	0.407299i	0.852374	+	0.522932i	$0.175162\pi$
$510$	−21.3548	+	25.8106i	−0.945607	+	1.14291i
$511$	4.39342	+	0.742310i	0.194354	+	0.0328379i
$512$			1.00000i			0.0441942i
$513$	−32.0677	+	19.4135i	−1.41582	+	0.857127i
$514$			19.7940i			0.873076i
$515$	3.93221	+	10.8036i	0.173274	+	0.476066i
$516$	−15.4908	+	5.75999i	−0.681945	+	0.253569i
$517$	−13.3625	−	15.9248i	−0.587680	−	0.700370i
$518$	−0.314335	+	0.883238i	−0.0138111	+	0.0388073i
$519$	−19.2671	−	6.86193i	−0.845733	−	0.301206i
$520$	−5.00303	−	4.19804i	−0.219397	−	0.184096i
$521$	3.15077	−	5.45729i	0.138038	−	0.239088i	−0.788716	−	0.614758i	$-0.789254\pi$
$521$	3.15077	−	5.45729i	0.138038	−	0.239088i	0.926754	+	0.375669i	$0.122587\pi$
$522$	7.12898	−	2.70713i	0.312027	−	0.118488i
$523$	7.93681	−	4.58232i	0.347052	−	0.200371i	−0.316334	−	0.948648i	$-0.602452\pi$
$523$	7.93681	−	4.58232i	0.347052	−	0.200371i	0.663386	+	0.748277i	$0.269119\pi$
$524$	−3.88011	+	22.0052i	−0.169503	+	0.961301i
$525$	−23.8067	−	39.9256i	−1.03901	−	1.74249i
$526$	−9.39865	−	3.42083i	−0.409801	−	0.149155i
$527$	−13.8229	+	37.9782i	−0.602137	+	1.65436i
$528$	−4.14135	−	2.35292i	−0.180229	−	0.102398i
$529$	−0.967743	+	5.48834i	−0.0420758	+	0.238624i
$530$	12.5195	+	21.6844i	0.543812	+	0.941911i
$531$	2.56414	−	15.8202i	0.111274	−	0.686539i
$532$	16.4612	−	9.66155i	0.713683	−	0.418881i
$533$	4.56855	−	5.44459i	0.197886	−	0.235831i
$534$	−2.70399	+	7.59235i	−0.117013	+	0.328553i
$535$	26.0667	−	4.59627i	1.12696	−	0.198714i
$536$	−1.01013	−	1.20383i	−0.0436309	−	0.0519973i
$537$	−6.71101	−	18.0485i	−0.289602	−	0.778849i
$538$	9.15164	+	25.1439i	0.394555	+	1.08403i
$539$	−16.5314	+	9.86243i	−0.712057	+	0.424805i
$540$	−18.8536	+	7.30917i	−0.811329	+	0.314537i
$541$	2.09293			0.0899820			0.0449910	−	0.998987i	$-0.485674\pi$
$541$	2.09293			0.0899820			0.0449910	+	0.998987i	$0.485674\pi$
$542$	−25.0166	+	9.10531i	−1.07456	+	0.391106i
$543$	−4.12763	+	4.98888i	−0.177134	+	0.214093i
$544$	−3.19468	−	3.80728i	−0.136971	−	0.163236i
$545$	9.70745	+	55.0537i	0.415822	+	2.35824i
$546$	1.44200	+	7.55441i	0.0617117	+	0.323299i
$547$	−6.22461	−	5.22307i	−0.266145	−	0.223322i	0.499942	−	0.866059i	$-0.333355\pi$
$547$	−6.22461	−	5.22307i	−0.266145	−	0.223322i	−0.766087	+	0.642736i	$0.777799\pi$
$548$	10.9152	+	6.30189i	0.466274	+	0.269203i
$549$	13.2266	−	7.88260i	0.564496	−	0.336421i
$550$	−13.9475	−	24.1578i	−0.594724	−	1.03009i
$551$	−3.18433	+	18.0592i	−0.135657	+	0.769348i
$552$	−9.25824	+	0.0641170i	−0.394057	+	0.00272900i
$553$	33.4540	−	28.4816i	1.42261	−	1.21116i
$554$	−5.27437	+	14.4912i	−0.224087	+	0.615673i
$555$	1.20848	+	2.06007i	0.0512972	+	0.0874452i
$556$	12.9538	+	2.28411i	0.549364	+	0.0968677i
$557$	−2.48334	+	1.43375i	−0.105222	+	0.0607501i	−0.551688	−	0.834051i	$-0.686016\pi$
$557$	−2.48334	+	1.43375i	−0.105222	+	0.0607501i	0.446465	+	0.894801i	$0.352683\pi$
$558$	−18.4691	+	15.9385i	−0.781858	+	0.674728i
$559$	13.8684	+	8.00693i	0.586572	+	0.338657i
$560$	9.64957	−	3.59054i	0.407769	−	0.151728i
$561$	23.2841	−	4.27208i	0.983055	−	0.180367i
$562$	4.36919	+	24.7789i	0.184303	+	1.04524i
$563$	14.5659	−	12.2222i	0.613878	−	0.515105i	−0.281994	−	0.959416i	$-0.590996\pi$
$563$	14.5659	−	12.2222i	0.613878	−	0.515105i	0.895873	+	0.444311i	$0.146551\pi$
$564$	2.18429	−	12.9099i	0.0919752	−	0.543605i
$565$	4.39735	+	12.0816i	0.184998	+	0.508278i
$566$	−12.5661			−0.528191
$567$	22.6460	+	7.35940i	0.951041	+	0.309066i
$568$	7.97440			0.334598
$569$	−2.25815	−	6.20422i	−0.0946667	−	0.260095i	0.883317	−	0.468776i	$-0.155305\pi$
$569$	−2.25815	−	6.20422i	−0.0946667	−	0.260095i	−0.977984	+	0.208682i	$0.933083\pi$
$570$	8.11196	−	47.9445i	0.339773	−	2.00817i
$571$	−2.31409	+	1.94175i	−0.0968415	+	0.0812597i	−0.689923	−	0.723883i	$-0.742356\pi$
$571$	−2.31409	+	1.94175i	−0.0968415	+	0.0812597i	0.593081	+	0.805142i	$0.297911\pi$
$572$	0.801420	+	4.54508i	0.0335091	+	0.190039i
$573$	−23.2866	+	4.27255i	−0.972812	+	0.178488i
$574$	3.90744	+	10.5012i	0.163093	+	0.438313i
$575$	−46.9578	−	27.1111i	−1.95827	−	1.13061i
$576$	−0.561814	−	2.94692i	−0.0234089	−	0.122789i
$577$	23.9090	−	13.8039i	0.995344	−	0.574662i	0.0884765	−	0.996078i	$-0.471800\pi$
$577$	23.9090	−	13.8039i	0.995344	−	0.574662i	0.906867	+	0.421416i	$0.138467\pi$
$578$	7.58435	+	1.33733i	0.315467	+	0.0556254i
$579$	−7.01861	−	11.9645i	−0.291683	−	0.497226i
$580$	−3.38318	+	9.29522i	−0.140479	+	0.385963i
$581$	−8.39732	+	7.14918i	−0.348379	+	0.296598i
$582$	14.8557	−	0.102881i	0.615787	−	0.00426457i
$583$	3.07254	−	17.4253i	0.127252	−	0.721681i
$584$	0.842046	+	1.45847i	0.0348441	+	0.0603518i
$585$	17.1021	+	9.56054i	0.707083	+	0.395279i
$586$	11.4832	+	6.62981i	0.474366	+	0.273875i
$587$	2.43294	+	2.04148i	0.100418	+	0.0842609i	0.691615	−	0.722267i	$-0.256900\pi$
$587$	2.43294	+	2.04148i	0.100418	+	0.0842609i	−0.591196	+	0.806528i	$0.701344\pi$
$588$	−11.4786	−	3.90394i	−0.473371	−	0.160996i
$589$	−10.1871	−	57.7737i	−0.419750	−	2.38052i
$590$	13.3631	+	15.9255i	0.550149	+	0.655642i
$591$	−13.4661	+	16.2759i	−0.553923	+	0.669501i
$592$	−0.332974	+	0.121193i	−0.0136852	+	0.00498099i
$593$	18.0122			0.739672			0.369836	−	0.929097i	$-0.379414\pi$
$593$	18.0122			0.739672			0.369836	+	0.929097i	$0.379414\pi$
$594$	13.5261	+	4.60721i	0.554984	+	0.189036i
$595$	−25.2679	+	44.4975i	−1.03588	+	1.82422i
$596$	−0.202016	−	0.555033i	−0.00827488	−	0.0227350i
$597$	−4.15719	−	11.1803i	−0.170142	−	0.457577i
$598$	5.76644	+	6.87217i	0.235807	+	0.281024i
$599$	25.1383	−	4.43257i	1.02712	−	0.181110i	0.365395	−	0.930853i	$-0.380934\pi$
$599$	25.1383	−	4.43257i	1.02712	−	0.181110i	0.661729	+	0.749743i	$0.269823\pi$
$600$	5.89464	−	16.5511i	0.240648	−	0.675698i
$601$	−11.3131	+	13.4824i	−0.461469	+	0.549958i	−0.945725	−	0.324969i	$-0.894646\pi$
$601$	−11.3131	+	13.4824i	−0.461469	+	0.549958i	0.484255	+	0.874927i	$0.339091\pi$
$602$	−21.7723	+	12.7788i	−0.887374	+	0.520826i
$603$	3.65310	+	2.98008i	0.148766	+	0.121358i
$604$	−9.05469	−	15.6832i	−0.368430	−	0.638140i
$605$	2.32301	−	13.1745i	0.0944438	−	0.535618i
$606$	−2.63671	−	1.49806i	−0.107109	−	0.0608544i
$607$	2.13495	−	5.86573i	0.0866550	−	0.238083i	−0.888795	−	0.458306i	$-0.848456\pi$
$607$	2.13495	−	5.86573i	0.0866550	−	0.238083i	0.975449	+	0.220223i	$0.0706786\pi$
$608$	6.77916	+	2.46741i	0.274931	+	0.100067i
$609$	10.0048	−	5.96566i	0.405416	−	0.241741i
$610$	−3.46825	+	19.6694i	−0.140425	+	0.796392i
$611$	−10.9871	+	6.34342i	−0.444491	+	0.256627i
$612$	11.5535	+	9.42494i	0.467021	+	0.380981i
$613$	−0.906241	+	1.56966i	−0.0366027	+	0.0633978i	−0.883746	−	0.467966i	$-0.844987\pi$
$613$	−0.906241	+	1.56966i	−0.0366027	+	0.0633978i	0.847144	+	0.531364i	$0.178320\pi$
$614$	13.5997	+	11.4115i	0.548840	+	0.460531i
$615$	26.8902	+	9.57688i	1.08432	+	0.386177i
$616$	−6.85458	−	2.43947i	−0.276179	−	0.0982891i
$617$	−24.8564	−	29.6227i	−1.00068	−	1.19256i	−0.981247	−	0.192753i	$-0.938258\pi$
$617$	−24.8564	−	29.6227i	−1.00068	−	1.19256i	−0.0194332	−	0.999811i	$-0.506186\pi$
$618$	4.79632	−	1.78343i	0.192936	−	0.0717400i
$619$	−4.30111	−	11.8172i	−0.172876	−	0.474973i	0.822750	−	0.568404i	$-0.192439\pi$
$619$	−4.30111	−	11.8172i	−0.172876	−	0.474973i	−0.995626	+	0.0934307i	$0.970217\pi$
$620$		−	31.6450i		−	1.27089i
$621$	27.2473	−	5.39035i	1.09340	−	0.216307i
$622$			27.7552i			1.11288i
$623$	−2.05100	+	12.1390i	−0.0821717	+	0.486339i
$624$	−1.85302	+	2.23966i	−0.0741803	+	0.0896583i
$625$	20.8188	−	17.4690i	0.832751	−	0.698761i
$626$	−4.89518	−	27.7620i	−0.195651	−	1.10959i
$627$	−26.1692	+	22.2692i	−1.04510	+	0.889348i
$628$	1.48955	−	1.77518i	0.0594396	−	0.0708374i
$629$	0.880552	−	1.52516i	0.0351099	−	0.0608121i
$630$	−26.4194	+	16.0023i	−1.05257	+	0.637548i
$631$	4.91349	+	8.51042i	0.195603	+	0.338795i	0.947098	−	0.320944i	$-0.104000\pi$
$631$	4.91349	+	8.51042i	0.195603	+	0.338795i	−0.751495	+	0.659739i	$0.770667\pi$
$632$	16.3540	+	2.88364i	0.650526	+	0.114705i
$633$	−28.0705	+	0.194400i	−1.11570	+	0.00772669i
$634$	−8.79661	−	3.20170i	−0.349358	−	0.127156i
$635$	44.3677	+	16.1485i	1.76068	+	0.640835i
$636$	9.61260	−	5.63896i	0.381165	−	0.223599i
$637$	4.17556	+	10.9808i	0.165442	+	0.435075i
$638$	6.05362	−	3.49506i	0.239665	−	0.138371i
$639$	−23.5000	+	4.48013i	−0.929644	+	0.177231i
$640$	3.37014	+	1.94575i	0.133216	+	0.0769125i
$641$	−16.5805	+	19.7598i	−0.654890	+	0.780467i	−0.986643	−	0.162899i	$-0.947915\pi$
$641$	−16.5805	+	19.7598i	−0.654890	+	0.780467i	0.331753	+	0.943366i	$0.392360\pi$
$642$	−2.12603	−	11.5875i	−0.0839078	−	0.457322i
$643$	10.6331	−	1.87490i	0.419327	−	0.0739388i	0.0399966	−	0.999200i	$-0.487265\pi$
$643$	10.6331	−	1.87490i	0.419327	−	0.0739388i	0.379331	+	0.925261i	$0.376154\pi$
$644$	−13.9097	+	2.55540i	−0.548121	+	0.100697i
$645$	−10.7293	+	63.4136i	−0.422464	+	2.49691i
$646$	−33.6927	+	12.2632i	−1.32562	+	0.482487i
$647$	−39.5343			−1.55425			−0.777126	−	0.629345i	$-0.783323\pi$
$647$	−39.5343			−1.55425			−0.777126	+	0.629345i	$0.783323\pi$
$648$	3.31125	+	8.36873i	0.130078	+	0.328755i
$649$		−	14.6910i		−	0.576671i
$650$	−15.9973	+	5.82254i	−0.627466	+	0.228379i
$651$	−23.5490	+	28.8809i	−0.922959	+	1.13193i
$652$	−12.9374	+	10.8558i	−0.506667	+	0.425144i
$653$	15.9540	−	2.81312i	0.624328	−	0.110086i	0.147471	−	0.989066i	$-0.452887\pi$
$653$	15.9540	−	2.81312i	0.624328	−	0.110086i	0.476858	+	0.878981i	$0.341776\pi$
$654$	24.4731	−	4.49024i	0.956974	−	0.175582i
$655$	66.6108	+	55.8931i	2.60270	+	2.18392i
$656$	−2.11748	+	3.66758i	−0.0826736	+	0.143195i
$657$	−3.30083	−	3.82492i	−0.128778	−	0.149224i
$658$	−0.143087	−	19.9999i	−0.00557810	−	0.779679i
$659$	36.4944	+	6.43494i	1.42162	+	0.250670i	0.830996	−	0.556278i	$-0.187771\pi$
$659$	36.4944	+	6.43494i	1.42162	+	0.250670i	0.590622	+	0.806948i	$0.298882\pi$
$660$	−15.9877	+	9.37871i	−0.622320	+	0.365066i
$661$	11.2106	−	30.8008i	0.436040	−	1.19801i	−0.506007	−	0.862530i	$-0.668879\pi$
$661$	11.2106	−	30.8008i	0.436040	−	1.19801i	0.942047	−	0.335481i	$-0.108899\pi$
$662$	6.88499	−	18.9164i	0.267593	−	0.735205i
$663$	−0.100050	−	14.4468i	−0.00388563	−	0.561069i
$664$	−4.10502	−	0.723826i	−0.159306	−	0.0280899i
$665$	−0.531392	−	74.2754i	−0.0206065	−	2.88028i
$666$	0.913162	−	0.544215i	0.0353843	−	0.0210879i
$667$	6.79368	−	11.7670i	0.263052	−	0.455620i
$668$	2.69261	+	2.25937i	0.104180	+	0.0874175i
$669$	−18.8808	−	22.1874i	−0.729974	−	0.857814i
$670$	−6.02251	+	1.06193i	−0.232670	+	0.0410260i
$671$	10.8120	−	9.07233i	0.417392	−	0.350234i
$672$	−1.62781	−	4.28372i	−0.0627940	−	0.165248i
$673$	22.8679	−	8.32324i	0.881493	−	0.320837i	0.138681	−	0.990337i	$-0.455714\pi$
$673$	22.8679	−	8.32324i	0.881493	−	0.320837i	0.742812	+	0.669500i	$0.233491\pi$
$674$		−	22.0079i		−	0.847712i
$675$	−8.07241	+	52.0867i	−0.310707	+	2.00482i
$676$	−10.1834			−0.391669
$677$	−34.4338	+	12.5329i	−1.32340	+	0.481678i	−0.904546	−	0.426376i	$-0.859790\pi$
$677$	−34.4338	+	12.5329i	−1.32340	+	0.481678i	−0.418854	+	0.908054i	$0.637568\pi$
$678$	5.36368	−	1.99439i	0.205991	−	0.0765942i
$679$	22.3194	−	4.10037i	0.856541	−	0.157358i
$680$	−19.0471	+	3.35852i	−0.730423	+	0.128793i
$681$	31.2195	+	11.1187i	1.19633	+	0.426070i
$682$	−14.3742	+	17.1305i	−0.550417	+	0.655961i
$683$	15.9286	+	9.19636i	0.609490	+	0.351889i	0.772766	−	0.634691i	$-0.218873\pi$
$683$	15.9286	+	9.19636i	0.609490	+	0.351889i	−0.163276	+	0.986580i	$0.552206\pi$
$684$	−21.3639	−	3.46265i	−0.816869	−	0.132398i
$685$	42.4764	−	24.5238i	1.62294	−	0.937005i
$686$	−18.3037	−	2.82384i	−0.698839	−	0.107815i
$687$	10.8169	+	6.14566i	0.412691	+	0.234471i
$688$	−8.96644	−	3.26352i	−0.341842	−	0.124420i
$689$	−10.1472	−	3.69330i	−0.386579	−	0.140703i
$690$	−17.7981	+	31.3263i	−0.677563	+	1.19257i
$691$	−14.3552	−	2.53121i	−0.546098	−	0.0962918i	−0.106209	−	0.994344i	$-0.533871\pi$
$691$	−14.3552	−	2.53121i	−0.546098	−	0.0962918i	−0.439889	+	0.898052i	$0.644982\pi$
$692$	−5.90416	−	10.2263i	−0.224442	−	0.388746i
$693$	21.5705	+	3.33794i	0.819394	+	0.126798i
$694$	−12.1699	+	21.0789i	−0.461963	+	0.800143i
$695$	32.9026	−	39.2118i	1.24807	−	1.48739i
$696$	4.14750	+	1.47712i	0.157211	+	0.0559901i
$697$	−3.65493	−	20.7281i	−0.138440	−	0.785135i
$698$	−13.4592	+	11.2936i	−0.509439	+	0.427470i
$699$	−8.55811	−	23.0160i	−0.323698	−	0.870546i
$700$	4.47114	−	26.4628i	0.168993	−	1.00020i
$701$			27.2657i			1.02981i	0.857246	+	0.514906i	$0.172173\pi$
$701$			27.2657i			1.02981i	−0.857246	+	0.514906i	$0.827827\pi$
$702$	4.20244	−	7.64117i	0.158611	−	0.288398i
$703$			2.55632i			0.0964133i
$704$	−0.940545	−	2.58413i	−0.0354481	−	0.0973929i
$705$	−39.2580	−	32.4808i	−1.47854	−	1.22330i
$706$	−7.71672	−	9.19643i	−0.290423	−	0.346112i
$707$	−4.36418	−	1.55316i	−0.164132	−	0.0584127i
$708$	7.04686	−	5.99666i	0.264837	−	0.225368i
$709$	32.5801	+	27.3380i	1.22357	+	1.02670i	0.998630	+	0.0523278i	$0.0166641\pi$
$709$	32.5801	+	27.3380i	1.22357	+	1.02670i	0.224943	+	0.974372i	$0.427780\pi$
$710$	15.5162	−	26.8748i	0.582312	−	1.00859i
$711$	−49.8140	+	0.689996i	−1.86817	+	0.0258769i
$712$	−4.02974	+	2.32657i	−0.151021	+	0.0871920i
$713$	−7.54808	+	42.8073i	−0.282678	+	1.60315i
$714$	19.8826	+	11.1090i	0.744089	+	0.415743i
$715$	16.8769	+	6.14269i	0.631160	+	0.229724i
$716$	3.80235	−	10.4469i	0.142100	−	0.390418i
$717$	8.17520	−	4.79575i	0.305308	−	0.179100i
$718$	−2.68665	+	15.2368i	−0.100265	+	0.568631i
$719$	2.10155	+	3.63999i	0.0783746	+	0.135749i	0.902549	−	0.430588i	$-0.141694\pi$
$719$	2.10155	+	3.63999i	0.0783746	+	0.135749i	−0.824174	+	0.566336i	$0.808360\pi$
$720$	−11.0247	−	3.84059i	−0.410866	−	0.143130i
$721$	6.74122	−	3.95662i	0.251056	−	0.147352i
$722$	21.2410	−	25.3141i	0.790509	−	0.942091i
$723$	−3.59934	+	0.660394i	−0.133861	+	0.0245603i
$724$	−3.68157	+	0.649161i	−0.136825	+	0.0241259i
$725$	16.5738	+	19.7519i	0.615537	+	0.733569i
$726$	−5.87078	−	0.993307i	−0.217885	−	0.0368651i
$727$	−5.68368	−	15.6158i	−0.210796	−	0.579157i	0.788563	−	0.614954i	$-0.210825\pi$
$727$	−5.68368	−	15.6158i	−0.210796	−	0.579157i	−0.999359	+	0.0357966i	$0.988603\pi$
$728$	−2.19258	+	3.86119i	−0.0812623	+	0.143105i
$729$	−14.4597	−	22.8017i	−0.535543	−	0.844508i
$730$	6.55364			0.242561
$731$	44.5636	−	16.2198i	1.64824	−	0.599912i
$732$	8.76507	+	1.48301i	0.323966	+	0.0548135i
$733$	34.3190	+	40.8998i	1.26760	+	1.51067i	0.761449	+	0.648224i	$0.224488\pi$
$733$	34.3190	+	40.8998i	1.26760	+	1.51067i	0.506152	+	0.862444i	$0.331067\pi$
$734$	2.41312	+	13.6855i	0.0890700	+	0.505141i
$735$	−35.4914	+	31.0885i	−1.30912	+	1.14672i
$736$	−4.09479	−	3.43594i	−0.150936	−	0.126650i
$737$	3.74255	+	2.16076i	0.137859	+	0.0795927i
$738$	4.17955	−	11.9977i	0.153851	−	0.441642i
$739$	−10.2380	−	17.7327i	−0.376609	−	0.652307i	0.613957	−	0.789339i	$-0.289577\pi$
$739$	−10.2380	−	17.7327i	−0.376609	−	0.652307i	−0.990567	+	0.137033i	$0.956243\pi$
$740$	−0.239448	+	1.35798i	−0.00880229	+	0.0499203i
$741$	10.6109	+	18.0881i	0.389800	+	0.664483i
$742$	12.9621	−	11.0355i	0.475855	−	0.405127i
$743$	−3.65287	+	10.0362i	−0.134011	+	0.368192i	−0.988488	−	0.151296i	$-0.951655\pi$
$743$	−3.65287	+	10.0362i	−0.134011	+	0.368192i	0.854478	+	0.519488i	$0.173877\pi$
$744$	−14.0844	+	0.0975402i	−0.516359	+	0.00357600i
$745$	−2.26361	−	0.399135i	−0.0829322	−	0.0146232i
$746$	−29.3924	+	16.9697i	−1.07613	+	0.621304i
$747$	12.5038	−	0.173196i	0.457491	−	0.00633693i
$748$	11.8364	+	6.83374i	0.432781	+	0.249866i
$749$	−6.27569	−	16.8659i	−0.229309	−	0.616267i
$750$	−22.4690	−	26.4040i	−0.820453	−	0.964139i
$751$	−0.707778	−	4.01401i	−0.0258272	−	0.146473i	0.969167	−	0.246404i	$-0.0792490\pi$
$751$	−0.707778	−	4.01401i	−0.0258272	−	0.146473i	−0.994994	+	0.0999307i	$0.968138\pi$
$752$	5.79089	−	4.85913i	0.211172	−	0.177194i
$753$	−0.0238802	−	0.0197576i	−0.000870242	−	0.000720009i
$754$	−1.45905	−	4.00871i	−0.0531356	−	0.145989i
$755$	−70.4726			−2.56476
$756$	7.20367	+	11.7093i	0.261995	+	0.425862i
$757$	−29.7948			−1.08291			−0.541456	−	0.840729i	$-0.682127\pi$
$757$	−29.7948			−1.08291			−0.541456	+	0.840729i	$0.682127\pi$
$758$	−2.01256	−	5.52946i	−0.0730994	−	0.200839i
$759$	23.8641	−	8.87347i	0.866213	−	0.322087i
$760$	21.5061	−	18.0457i	0.780107	−	0.654587i
$761$	1.45761	+	8.26651i	0.0528383	+	0.299661i	0.999762	−	0.0217963i	$-0.00693852\pi$
$761$	1.45761	+	8.26651i	0.0528383	+	0.299661i	−0.946924	+	0.321457i	$0.895827\pi$
$762$	7.05056	−	19.7968i	0.255415	−	0.717161i
$763$	35.6213	−	13.2544i	1.28958	−	0.479843i
$764$	−11.8377	−	6.83448i	−0.428272	−	0.247263i
$765$	54.2435	−	20.5982i	1.96118	−	0.744730i
$766$	−19.8041	+	11.4339i	−0.715549	+	0.413123i
$767$	−8.82950	−	1.55688i	−0.318815	−	0.0562156i
$768$	0.855617	−	1.50596i	0.0308744	−	0.0543417i
$769$	2.77761	−	7.63141i	0.100163	−	0.275196i	−0.879482	−	0.475932i	$-0.842111\pi$
$769$	2.77761	−	7.63141i	0.100163	−	0.275196i	0.979645	+	0.200736i	$0.0643332\pi$
$770$	−21.5586	+	18.3543i	−0.776920	+	0.661442i
$771$	16.9361	−	29.8090i	0.609938	−	1.07355i
$772$	1.39067	−	7.88686i	0.0500512	−	0.283854i
$773$	26.0125	+	45.0550i	0.935604	+	1.62051i	0.773553	+	0.633732i	$0.218478\pi$
$773$	26.0125	+	45.0550i	0.935604	+	1.62051i	0.162052	+	0.986782i	$0.448189\pi$
$774$	28.2569	+	4.57987i	1.01567	+	0.164620i
$775$	−71.4361	−	41.2437i	−2.56606	−	1.48152i
$776$	6.57046	+	5.51327i	0.235866	+	0.197915i
$777$	1.22909	−	1.06117i	0.0440933	−	0.0380693i
$778$	−6.09083	−	34.5428i	−0.218367	−	1.23842i
$779$	19.6384	+	23.4041i	0.703619	+	0.838540i
$780$	3.94245	+	10.6028i	0.141163	+	0.379640i
$781$	−20.6069	+	7.50028i	−0.737371	+	0.268381i
$782$	26.5667			0.950025
$783$	−13.0522	−	2.02284i	−0.466449	−	0.0722904i
$784$	−3.58638	−	6.01148i	−0.128085	−	0.214696i
$785$	−3.08430	−	8.47405i	−0.110083	−	0.302452i
$786$	24.6713	−	29.8191i	0.879996	−	1.06361i
$787$	−32.1979	−	38.3719i	−1.14773	−	1.36781i	−0.918969	−	0.394329i	$-0.870977\pi$
$787$	−32.1979	−	38.3719i	−1.14773	−	1.36781i	−0.228761	−	0.973483i	$-0.573467\pi$
$788$	−12.0109	+	2.11785i	−0.427871	+	0.0754452i
$789$	11.2271	+	13.1933i	0.399695	+	0.469693i
$790$	41.5390	−	49.5042i	1.47789	−	1.76128i
$791$	7.53865	−	4.42465i	0.268044	−	0.157323i
$792$	4.22351	+	7.08681i	0.150076	+	0.251819i
$793$	−4.30681	−	7.45962i	−0.152939	−	0.264899i
$794$	1.89672	−	10.7568i	0.0673120	−	0.381745i
$795$	−0.300339	−	43.3678i	−0.0106519	−	1.53810i
$796$	2.35539	−	6.47139i	0.0834847	−	0.229372i
$797$	12.2234	+	4.44894i	0.432974	+	0.157589i	0.549307	−	0.835621i	$-0.314892\pi$
$797$	12.2234	+	4.44894i	0.432974	+	0.157589i	−0.116333	+	0.993210i	$0.537114\pi$
$798$	−33.0565	+	0.465450i	−1.17019	+	0.0164768i
$799$	−6.52411	+	37.0001i	−0.230807	+	1.30897i
$800$	8.78475	−	5.07188i	0.310588	−	0.179318i
$801$	10.5682	−	9.12020i	0.373411	−	0.322246i
$802$	−2.75571	+	4.77302i	−0.0973073	+	0.168541i
$803$	−3.54771	−	2.97688i	−0.125196	−	0.105052i
$804$	0.491203	+	2.67720i	0.0173234	+	0.0944175i
$805$	−18.4528	+	51.8499i	−0.650376	+	1.82747i
$806$	8.77239	+	10.4545i	0.308994	+	0.368245i
$807$	7.73155	−	45.6961i	0.272163	−	1.60858i
$808$	−0.598826	−	1.64526i	−0.0210666	−	0.0578801i
$809$		−	51.6997i		−	1.81767i	−0.417160	−	0.908833i	$-0.636974\pi$
$809$		−	51.6997i		−	1.81767i	0.417160	−	0.908833i	$-0.363026\pi$
$810$	34.6466	+	5.12410i	1.21736	+	0.180043i
$811$			26.0086i			0.913284i	0.889650	+	0.456642i	$0.150948\pi$
$811$			26.0086i			0.913284i	−0.889650	+	0.456642i	$0.849052\pi$
$812$	6.63123	+	1.12041i	0.232710	+	0.0393186i
$813$	45.4647	+	7.69240i	1.59452	+	0.269784i
$814$	0.746460	−	0.626354i	0.0261634	−	0.0219537i
$815$	11.4125	+	64.7233i	0.399761	+	2.26716i
$816$	1.55350	+	8.46704i	0.0543834	+	0.296406i
$817$	−44.2478	+	52.7325i	−1.54803	+	1.84488i
$818$	7.64449	−	13.2406i	0.267283	−	0.462948i
$819$	4.29209	−	12.6104i	0.149978	−	0.440645i
$820$	8.24016	+	14.2724i	0.287759	+	0.498413i
$821$	35.9281	+	6.33509i	1.25390	+	0.221096i	0.760863	−	0.648913i	$-0.224776\pi$
$821$	35.9281	+	6.33509i	1.25390	+	0.221096i	0.493036	+	0.870009i	$0.335887\pi$
$822$	−11.0459	−	18.8296i	−0.385268	−	0.656758i
$823$	−31.1346	−	11.3321i	−1.08529	−	0.395011i	−0.263413	−	0.964683i	$-0.584848\pi$
$823$	−31.1346	−	11.3321i	−1.08529	−	0.395011i	−0.821872	+	0.569672i	$0.807070\pi$
$824$	2.77622	+	1.01046i	0.0967142	+	0.0352011i
$825$	0.334597	+	48.3144i	0.0116492	+	1.68209i
$826$	9.00760	−	10.8921i	0.313414	−	0.378986i
$827$	−34.8967	+	20.1476i	−1.21348	+	0.700601i	−0.963515	−	0.267654i	$-0.913752\pi$
$827$	−34.8967	+	20.1476i	−1.21348	+	0.700601i	−0.249962	+	0.968256i	$0.580418\pi$
$828$	13.9974	+	7.82494i	0.486443	+	0.271936i
$829$	−8.06805	−	4.65809i	−0.280215	−	0.161782i	0.353306	−	0.935508i	$-0.385058\pi$
$829$	−8.06805	−	4.65809i	−0.280215	−	0.161782i	−0.633521	+	0.773726i	$0.718391\pi$
$830$	−10.4267	+	12.4261i	−0.361917	+	0.431316i
$831$	20.3419	−	17.3104i	0.705654	−	0.600490i
$832$	−1.65277	+	0.291429i	−0.0572997	+	0.0101035i
$833$	32.8591	+	11.4300i	1.13850	+	0.396026i
$834$	−17.5536	−	14.5233i	−0.607832	−	0.502900i
$835$	12.8535	−	4.67830i	0.444814	−	0.161899i
$836$	−19.8389			−0.686143
$837$	41.4509	−	8.20026i	1.43275	−	0.283442i
$838$		−	8.30327i		−	0.286832i
$839$	46.5072	−	16.9273i	1.60561	−	0.584394i	0.625044	−	0.780590i	$-0.285081\pi$
$839$	46.5072	−	16.9273i	1.60561	−	0.584394i	0.980565	+	0.196196i	$0.0628589\pi$
$840$	−17.6040	−	2.84912i	−0.607396	−	0.0983039i
$841$	17.2657	−	14.4877i	0.595369	−	0.499574i
$842$	−19.3340	+	3.40910i	−0.666293	+	0.117485i
$843$	14.6214	−	41.0545i	0.503589	−	1.41399i
$844$	−12.4152	−	10.4176i	−0.427349	−	0.358589i
$845$	−19.8143	+	34.3195i	−0.681634	+	1.18063i
$846$	−14.3354	+	17.5729i	−0.492860	+	0.604168i
$847$	−9.09499	+	0.0650687i	−0.312508	+	0.00223579i
$848$	6.33653	+	1.11730i	0.217597	+	0.0383683i
$849$	18.9240	+	10.7517i	0.649470	+	0.368998i
$850$	−17.2429	+	47.3745i	−0.591427	+	1.62493i
$851$	0.647820	−	1.77987i	0.0222070	−	0.0610132i
$852$	−12.0091	−	6.82303i	−0.411426	−	0.233753i
$853$	37.4492	+	6.60330i	1.28224	+	0.226093i	0.772929	−	0.634492i	$-0.218791\pi$
$853$	37.4492	+	6.60330i	1.28224	+	0.226093i	0.509307	+	0.860585i	$0.329902\pi$
$854$	13.5788	−	0.0971475i	0.464657	−	0.00332432i
$855$	−53.2384	+	65.2618i	−1.82072	+	2.23191i
$856$	3.40086	−	5.89046i	0.116239	−	0.201332i
$857$	−26.4169	−	22.1664i	−0.902383	−	0.757189i	0.0682716	−	0.997667i	$-0.478252\pi$
$857$	−26.4169	−	22.1664i	−0.902383	−	0.757189i	−0.970655	+	0.240477i	$0.922696\pi$
$858$	2.68194	−	7.53042i	0.0915599	−	0.257084i
$859$	−8.59516	+	1.51556i	−0.293263	+	0.0517102i	−0.318344	−	0.947975i	$-0.603127\pi$
$859$	−8.59516	+	1.51556i	−0.293263	+	0.0517102i	0.0250811	+	0.999685i	$0.492016\pi$
$860$	−28.4449	+	23.8681i	−0.969964	+	0.813896i
$861$	3.10057	−	19.1577i	0.105667	−	0.652893i
$862$	−14.4373	+	5.25474i	−0.491736	+	0.178977i
$863$			19.9087i			0.677701i	0.940840	+	0.338850i	$0.110038\pi$
$863$			19.9087i			0.677701i	−0.940840	+	0.338850i	$0.889962\pi$
$864$	−1.67537	+	4.91865i	−0.0569972	+	0.167336i
$865$	−45.9520			−1.56242
$866$	10.0097	−	3.64324i	0.340144	−	0.123802i
$867$	−10.2775	−	8.50326i	−0.349042	−	0.288786i
$868$	−21.1607	+	3.88749i	−0.718240	+	0.131950i
$869$	−44.9729	+	7.92993i	−1.52560	+	0.269005i
$870$	13.0481	−	11.1035i	0.442372	−	0.376445i
$871$	1.69527	−	2.02035i	0.0574421	−	0.0684568i
$872$	12.4408	+	7.18271i	0.421299	+	0.243237i
$873$	−22.4601	−	12.5558i	−0.760159	−	0.424950i
$874$	−33.3963	+	19.2814i	−1.12965	+	0.652202i
$875$	−40.8120	−	33.7508i	−1.37970	−	1.14098i
$876$	−0.0202005	−	2.91686i	−0.000682510	−	0.0985517i
$877$	27.9768	+	10.1827i	0.944711	+	0.343847i	0.768024	−	0.640421i	$-0.221240\pi$
$877$	27.9768	+	10.1827i	0.944711	+	0.343847i	0.176686	+	0.984267i	$0.443462\pi$
$878$	18.7010	+	6.80660i	0.631127	+	0.229712i
$879$	−11.6206	−	19.8094i	−0.391954	−	0.668156i
$880$	−10.5389	−	1.85830i	−0.355267	−	0.0626431i
$881$	−4.75324	−	8.23286i	−0.160141	−	0.277372i	0.774778	−	0.632233i	$-0.217862\pi$
$881$	−4.75324	−	8.23286i	−0.160141	−	0.277372i	−0.934919	+	0.354861i	$0.884528\pi$
$882$	13.9461	+	15.7005i	0.469590	+	0.528663i
$883$	24.7631	−	42.8910i	0.833345	−	1.44340i	−0.0620253	−	0.998075i	$-0.519756\pi$
$883$	24.7631	−	42.8910i	0.833345	−	1.44340i	0.895371	−	0.445322i	$-0.146911\pi$
$884$	5.36155	−	6.38964i	0.180328	−	0.214907i
$885$	−6.49816	−	35.4169i	−0.218433	−	1.19052i
$886$	3.08489	+	17.4953i	0.103639	+	0.587765i
$887$	28.7681	−	24.1393i	0.965938	−	0.810518i	−0.0159708	−	0.999872i	$-0.505084\pi$
$887$	28.7681	−	24.1393i	0.965938	−	0.810518i	0.981909	+	0.189354i	$0.0606394\pi$
$888$	0.605141	+	0.102387i	0.0203072	+	0.00343587i
$889$	5.34791	−	31.6520i	0.179363	−	1.06158i
$890$			18.1077i			0.606972i
$891$	−16.4278	−	18.5115i	−0.550353	−	0.620158i
$892$		−	16.8203i		−	0.563184i
$893$	−18.6523	−	51.2468i	−0.624176	−	1.71491i
$894$	−0.170668	+	1.00871i	−0.00570799	+	0.0337362i
$895$	−27.8090	−	33.1414i	−0.929551	−	1.10780i
$896$	0.887090	−	2.49260i	0.0296356	−	0.0832720i
$897$	−2.80409	−	15.2831i	−0.0936257	−	0.510288i
$898$	7.21294	+	6.05238i	0.240699	+	0.201970i
$899$	10.3351	−	17.9010i	0.344696	−	0.597030i
$900$	−23.0385	+	19.8818i	−0.767952	+	0.662728i
$901$	−27.6943	+	15.9893i	−0.922633	+	0.532682i
$902$	2.02231	−	11.4691i	0.0673354	−	0.381878i
$903$	43.7221	−	0.615626i	1.45498	−	0.0204868i
$904$	3.10462	+	1.12999i	0.103258	+	0.0375829i
$905$	−4.97566	+	13.6705i	−0.165397	+	0.454423i
$906$	0.217220	+	31.3656i	0.00721664	+	1.04205i
$907$	−0.149258	+	0.846482i	−0.00495602	+	0.0281070i	−0.987185	−	0.159577i	$-0.948987\pi$
$907$	−0.149258	+	0.846482i	−0.00495602	+	0.0281070i	0.982229	+	0.187684i	$0.0600981\pi$
$908$	9.56678	+	16.5702i	0.317485	+	0.549900i
$909$	2.68903	+	4.51203i	0.0891894	+	0.149655i
$910$	8.74652	+	14.9022i	0.289944	+	0.494003i
$911$	8.53917	−	10.1766i	0.282915	−	0.337165i	−0.605807	−	0.795612i	$-0.707150\pi$
$911$	8.53917	−	10.1766i	0.282915	−	0.337165i	0.888722	+	0.458447i	$0.151594\pi$
$912$	−8.09800	−	9.51619i	−0.268151	−	0.315113i
$913$	11.2887	−	1.99050i	0.373601	−	0.0658759i
$914$	16.7956	+	20.0162i	0.555548	+	0.662076i
$915$	22.0526	−	26.6539i	0.729035	−	0.881152i
$916$	2.45664	+	6.74955i	0.0811695	+	0.223011i
$917$	29.1922	−	51.4082i	0.964010	−	1.69765i
$918$	−9.33495	−	24.0789i	−0.308099	−	0.794723i
$919$	−41.8388			−1.38013			−0.690067	−	0.723746i	$-0.742419\pi$
$919$	−41.8388			−1.38013			−0.690067	+	0.723746i	$0.742419\pi$
$920$	−19.5470	+	7.11453i	−0.644446	+	0.234559i
$921$	−10.7168	−	28.8214i	−0.353129	−	0.949699i
$922$	−1.00979	−	1.20342i	−0.0332558	−	0.0396327i
$923$	2.32397	+	13.1799i	0.0764944	+	0.433821i
$924$	8.23548	+	9.53864i	0.270927	+	0.313798i
$925$	2.75345	+	2.31042i	0.0905329	+	0.0759661i
$926$	−3.27082	−	1.88841i	−0.107486	−	0.0620569i
$927$	−8.74900	−	1.41803i	−0.287355	−	0.0465744i
$928$	1.27095	+	2.20134i	0.0417208	+	0.0722626i
$929$	2.46186	−	13.9619i	0.0807709	−	0.458075i	−0.917418	−	0.397924i	$-0.869731\pi$
$929$	2.46186	−	13.9619i	0.0807709	−	0.458075i	0.998189	−	0.0601508i	$-0.0191581\pi$
$930$	−27.0760	+	47.6562i	−0.887857	+	1.56271i
$931$	−49.6019	+	9.47984i	−1.62564	+	0.310689i
$932$	4.84889	−	13.3222i	0.158831	−	0.436383i
$933$	23.7478	−	41.7982i	0.777468	−	1.36841i
$934$	30.6620	+	5.40653i	1.00329	+	0.176907i
$935$	46.0612	−	26.5935i	1.50636	−	0.869699i
$936$	4.70687	−	1.78737i	0.153849	−	0.0584220i
$937$	1.73753	+	1.00316i	0.0567625	+	0.0327719i	0.528113	−	0.849174i	$-0.322900\pi$
$937$	1.73753	+	1.00316i	0.0567625	+	0.0327719i	−0.471350	+	0.881946i	$0.656233\pi$
$938$	1.44995	+	3.89673i	0.0473425	+	0.127233i
$939$	−16.3816	+	45.9968i	−0.534595	+	1.50105i
$940$	−5.10832	−	28.9707i	−0.166615	−	0.944921i
$941$	−13.0465	+	10.9473i	−0.425305	+	0.356873i	−0.830177	−	0.557500i	$-0.811761\pi$
$941$	−13.0465	+	10.9473i	−0.425305	+	0.356873i	0.404872	+	0.914373i	$0.367316\pi$
$942$	−3.76208	+	1.39887i	−0.122575	+	0.0455775i
$943$	−7.74245	−	21.2722i	−0.252129	−	0.692718i
$944$	5.34223			0.173875
$945$	53.4784	−	1.49404i	1.73965	−	0.0486013i
$946$	26.2399			0.853132
$947$	18.0611	+	49.6224i	0.586906	+	1.61251i	0.776127	+	0.630577i	$0.217182\pi$
$947$	18.0611	+	49.6224i	0.586906	+	1.61251i	−0.189221	+	0.981935i	$0.560596\pi$
$948$	−22.1611	−	18.3354i	−0.719760	−	0.595505i
$949$	−2.16512	+	1.81675i	−0.0702828	+	0.0589743i
$950$	−12.7075	−	72.0676i	−0.412285	−	2.33818i
$951$	10.5079	+	12.3482i	0.340743	+	0.400417i
$952$	4.58568	+	12.3240i	0.148623	+	0.399423i
$953$	27.3754	+	15.8052i	0.886777	+	0.511981i	0.872887	−	0.487922i	$-0.162245\pi$
$953$	27.3754	+	15.8052i	0.886777	+	0.511981i	0.0138903	+	0.999904i	$0.495578\pi$
$954$	−19.3010	+	0.267347i	−0.624893	+	0.00865568i
$955$	−46.0662	+	26.5964i	−1.49067	+	0.860638i
$956$	5.38901	+	0.950228i	0.174293	+	0.0307326i
$957$	−12.1070	+	0.0838455i	−0.391362	+	0.00271034i
$958$	2.76663	−	7.60127i	0.0893859	−	0.245586i
$959$	−21.6169	−	25.3909i	−0.698046	−	0.819914i
$960$	−3.41048	−	5.81377i	−0.110073	−	0.187639i
$961$	−6.09969	+	34.5930i	−0.196764	+	1.11590i
$962$	−0.297342	−	0.515012i	−0.00958670	−	0.0166047i
$963$	−6.71273	+	19.2694i	−0.216315	+	0.620947i
$964$	−1.82971	−	1.05638i	−0.0589310	−	0.0340238i
$965$	−23.8739	−	20.0326i	−0.768528	−	0.644871i
$966$	23.1340	+	8.05307i	0.744324	+	0.259103i
$967$	−3.82228	−	21.6772i	−0.122916	−	0.697093i	−0.982524	−	0.186138i	$-0.940403\pi$
$967$	−3.82228	−	21.6772i	−0.122916	−	0.697093i	0.859607	−	0.510955i	$-0.170708\pi$
$968$	−2.20969	−	2.63341i	−0.0710222	−	0.0846410i
$969$	61.2325	+	10.3602i	1.96707	+	0.332819i
$970$	31.3649	−	11.4159i	1.00707	−	0.366543i
$971$	23.3166			0.748265			0.374133	−	0.927375i	$-0.377940\pi$
$971$	23.3166			0.748265			0.374133	+	0.927375i	$0.377940\pi$
$972$	2.17382	−	15.4361i	0.0697253	−	0.495115i
$973$	−30.2625	−	17.1846i	−0.970171	−	0.550912i
$974$	6.18117	+	16.9826i	0.198057	+	0.544158i
$975$	29.0732	+	4.91904i	0.931087	+	0.157535i
$976$	3.29907	+	3.93168i	0.105601	+	0.125850i
$977$	−24.2880	+	4.28263i	−0.777041	+	0.137013i	−0.548084	−	0.836423i	$-0.684643\pi$
$977$	−24.2880	+	4.28263i	−0.777041	+	0.137013i	−0.228957	+	0.973437i	$0.573532\pi$
$978$	28.7716	−	5.27890i	0.920013	−	0.168801i
$979$	8.22511	−	9.80231i	0.262876	−	0.313283i
$980$	−27.2377	+	0.389756i	−0.870076	+	0.0124503i
$981$	−40.6975	−	14.1775i	−1.29937	−	0.452652i
$982$	−4.63682	−	8.03121i	−0.147967	−	0.256286i
$983$	−1.76507	+	10.0102i	−0.0562969	+	0.319276i	−0.999931	−	0.0117137i	$-0.996271\pi$
$983$	−1.76507	+	10.0102i	−0.0562969	+	0.319276i	0.943634	+	0.330989i	$0.107382\pi$
$984$	6.32688	−	3.71148i	0.201694	−	0.118318i
$985$	−16.2328	+	44.5992i	−0.517220	+	1.42105i
$986$	−11.8714	−	4.32085i	−0.378064	−	0.137604i
$987$	−16.8968	+	30.2416i	−0.537831	+	0.962600i
$988$	−2.10243	+	11.9235i	−0.0668874	+	0.379337i
$989$	44.1716	−	25.5025i	1.40457	−	0.810931i
$990$	32.1014	−	0.444652i	1.02025	−	0.0141320i
$991$	6.38576	−	11.0605i	0.202850	−	0.351347i	−0.746595	−	0.665279i	$-0.768313\pi$
$991$	6.38576	−	11.0605i	0.202850	−	0.351347i	0.949446	+	0.313931i	$0.101646\pi$
$992$	−6.22935	−	5.22704i	−0.197782	−	0.165959i
$993$	−26.5537	+	22.5964i	−0.842656	+	0.717075i
$994$	−19.8770	−	7.07401i	−0.630461	−	0.224374i
$995$	−17.2265	−	20.5297i	−0.546116	−	0.650835i
$996$	5.56268	+	4.60238i	0.176260	+	0.145832i
$997$	4.57970	+	12.5826i	0.145041	+	0.398496i	0.990846	−	0.134995i	$-0.0431020\pi$
$997$	4.57970	+	12.5826i	0.145041	+	0.398496i	−0.845806	+	0.533491i	$0.820880\pi$
$998$			25.6434i			0.811728i
$999$	−1.84083	+	0.0382503i	−0.0582412	+	0.00121018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.209.4	✓	144
7.6	odd	2	inner	378.2.z.a.209.9	yes	144
27.23	odd	18	inner	378.2.z.a.293.9	yes	144
189.104	even	18	inner	378.2.z.a.293.4	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.209.4	✓	144	1.1	even	1	trivial
378.2.z.a.209.9	yes	144	7.6	odd	2	inner
378.2.z.a.293.4	yes	144	189.104	even	18	inner
378.2.z.a.293.9	yes	144	27.23	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)

\(f(q)\)	\(=\)	\(q+(-0.342020 - 0.939693i) q^{2} +(-0.288948 + 1.70778i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(0.675752 + 3.83238i) q^{5} +(1.70361 - 0.312573i) q^{6} +(2.47966 - 0.922664i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.83302 - 0.986917i) q^{9} +O(q^{10})\)	\(q+(-0.342020 - 0.939693i) q^{2} +(-0.288948 + 1.70778i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(0.675752 + 3.83238i) q^{5} +(1.70361 - 0.312573i) q^{6} +(2.47966 - 0.922664i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.83302 - 0.986917i) q^{9} +(3.37014 - 1.94575i) q^{10} +(-2.70819 - 0.477527i) q^{11} +(-0.876392 - 1.49397i) q^{12} +(-0.574003 + 1.57706i) q^{13} +(-1.71511 - 2.01454i) q^{14} +(-6.74011 + 0.0466780i) q^{15} +(0.173648 - 0.984808i) q^{16} +(2.48502 + 4.30419i) q^{17} +(0.0415504 + 2.99971i) q^{18} +(-6.24771 - 3.60712i) q^{19} +(-2.98106 - 2.50141i) q^{20} +(0.859215 + 4.50131i) q^{21} +(0.477527 + 2.70819i) q^{22} +(3.43594 + 4.09479i) q^{23} +(-1.10413 + 1.33451i) q^{24} +(-9.53201 + 3.46937i) q^{25} +1.67827 q^{26} +(2.50403 - 4.55300i) q^{27} +(-1.30645 + 2.30069i) q^{28} +(-0.869378 - 2.38860i) q^{29} +(2.34912 + 6.31767i) q^{30} +(5.22704 + 6.22935i) q^{31} +(-0.984808 + 0.173648i) q^{32} +(1.59804 - 4.48701i) q^{33} +(3.19468 - 3.80728i) q^{34} +(5.21163 + 8.87948i) q^{35} +(2.80460 - 1.06501i) q^{36} +(-0.177172 - 0.306871i) q^{37} +(-1.25274 + 7.10463i) q^{38} +(-2.52741 - 1.43596i) q^{39} +(-1.33097 + 3.65681i) q^{40} +(-3.97955 - 1.44844i) q^{41} +(3.93597 - 2.34694i) q^{42} +(1.65693 - 9.39692i) q^{43} +(2.38154 - 1.37498i) q^{44} +(1.86782 - 11.5241i) q^{45} +(2.67269 - 4.62923i) q^{46} +(5.79089 + 4.85913i) q^{47} +(1.63166 + 0.581111i) q^{48} +(5.29738 - 4.57578i) q^{49} +(6.52028 + 7.77057i) q^{50} +(-8.06864 + 3.00019i) q^{51} +(-0.574003 - 1.57706i) q^{52} +6.43428i q^{53} +(-5.13485 - 0.795801i) q^{54} -10.7015i q^{55} +(2.60878 + 0.440778i) q^{56} +(7.96542 - 9.62744i) q^{57} +(-1.94720 + 1.63390i) q^{58} +(0.927668 + 5.26107i) q^{59} +(5.13322 - 4.36822i) q^{60} +(-3.29907 + 3.93168i) q^{61} +(4.06592 - 7.04237i) q^{62} +(-7.93550 + 0.166708i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-6.43177 - 1.13409i) q^{65} +(-4.76297 + 0.0329855i) q^{66} +(-1.47671 - 0.537479i) q^{67} +(-4.67032 - 1.69986i) q^{68} +(-7.98581 + 4.68464i) q^{69} +(6.56150 - 7.93429i) q^{70} +(6.90603 - 3.98720i) q^{71} +(-1.96001 - 2.27120i) q^{72} +(1.45847 + 0.842046i) q^{73} +(-0.227768 + 0.271443i) q^{74} +(-3.17066 - 17.2810i) q^{75} +(7.10463 - 1.25274i) q^{76} +(-7.15598 + 1.31465i) q^{77} +(-0.484933 + 2.86612i) q^{78} +(15.6048 - 5.67967i) q^{79} +3.89150 q^{80} +(7.05199 + 5.59191i) q^{81} +4.23495i q^{82} +(-3.91696 + 1.42566i) q^{83} +(-3.55158 - 2.89591i) q^{84} +(-14.8160 + 12.4321i) q^{85} +(-9.39692 + 1.65693i) q^{86} +(4.33040 - 0.794527i) q^{87} +(-2.10660 - 1.76765i) q^{88} +(-2.32657 + 4.02974i) q^{89} +(-11.4680 + 2.18630i) q^{90} +(0.0317666 + 4.44018i) q^{91} +(-5.26416 - 0.928214i) q^{92} +(-12.1487 + 7.12668i) q^{93} +(2.58549 - 7.10357i) q^{94} +(9.60193 - 26.3811i) q^{95} +(-0.0119949 - 1.73201i) q^{96} +(8.44682 + 1.48940i) q^{97} +(-6.11164 - 3.41290i) q^{98} +(7.20107 + 4.02560i) 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

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