LMFDB - Embedded newform 280.2.w.a.43.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(43,280)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("280.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.w (of order $4$, degree $2$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.18
Character	$\chi$	$=$	280.43
Dual form			280.2.w.a.267.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.102291 + 1.41051i) q^{2} +(-0.977895 - 0.977895i) q^{3} +(-1.97907 - 0.288564i) q^{4} +(2.23508 + 0.0665977i) q^{5} +(1.47936 - 1.27930i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.609464 - 2.76198i) q^{8} -1.08744i q^{9} +O(q^{10})$	\(q+(-0.102291 + 1.41051i) q^{2} +(-0.977895 - 0.977895i) q^{3} +(-1.97907 - 0.288564i) q^{4} +(2.23508 + 0.0665977i) q^{5} +(1.47936 - 1.27930i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.609464 - 2.76198i) q^{8} -1.08744i q^{9} +(-0.322565 + 3.14578i) q^{10} -0.190002 q^{11} +(1.65314 + 2.21751i) q^{12} +(3.83102 - 3.83102i) q^{13} +(1.06971 - 0.925050i) q^{14} +(-2.12054 - 2.25080i) q^{15} +(3.83346 + 1.14218i) q^{16} +(1.66411 - 1.66411i) q^{17} +(1.53385 + 0.111235i) q^{18} +7.16664i q^{19} +(-4.40416 - 0.776765i) q^{20} +1.38295i q^{21} +(0.0194354 - 0.267999i) q^{22} +(5.10656 - 5.10656i) q^{23} +(-3.29692 + 2.10494i) q^{24} +(4.99113 + 0.297702i) q^{25} +(5.01181 + 5.79557i) q^{26} +(-3.99709 + 3.99709i) q^{27} +(1.19537 + 1.60346i) q^{28} +0.389233 q^{29} +(3.39168 - 2.76081i) q^{30} -5.59194i q^{31} +(-2.00318 + 5.29030i) q^{32} +(0.185802 + 0.185802i) q^{33} +(2.17702 + 2.51747i) q^{34} +(-1.53335 - 1.62753i) q^{35} +(-0.313797 + 2.15213i) q^{36} +(0.807349 + 0.807349i) q^{37} +(-10.1086 - 0.733082i) q^{38} -7.49267 q^{39} +(1.54614 - 6.13265i) q^{40} -9.77556 q^{41} +(-1.95067 - 0.141463i) q^{42} +(-2.07740 - 2.07740i) q^{43} +(0.376027 + 0.0548277i) q^{44} +(0.0724212 - 2.43052i) q^{45} +(6.68050 + 7.72521i) q^{46} +(-2.90099 - 2.90099i) q^{47} +(-2.63179 - 4.86566i) q^{48} +1.00000i q^{49} +(-0.930458 + 7.00958i) q^{50} -3.25466 q^{51} +(-8.68736 + 6.47637i) q^{52} +(-3.87887 + 3.87887i) q^{53} +(-5.22907 - 6.04680i) q^{54} +(-0.424668 - 0.0126537i) q^{55} +(-2.38397 + 1.52206i) q^{56} +(7.00822 - 7.00822i) q^{57} +(-0.0398150 + 0.549017i) q^{58} +3.53327i q^{59} +(3.54721 + 5.06640i) q^{60} +10.7990i q^{61} +(7.88749 + 0.572005i) q^{62} +(-0.768938 + 0.768938i) q^{63} +(-7.25711 - 3.36666i) q^{64} +(8.81776 - 8.30748i) q^{65} +(-0.281081 + 0.243069i) q^{66} +(7.88947 - 7.88947i) q^{67} +(-3.77361 + 2.81320i) q^{68} -9.98737 q^{69} +(2.45249 - 1.99632i) q^{70} +1.44759i q^{71} +(-3.00350 - 0.662757i) q^{72} +(-6.73133 - 6.73133i) q^{73} +(-1.22136 + 1.05619i) q^{74} +(-4.58968 - 5.17192i) q^{75} +(2.06804 - 14.1833i) q^{76} +(0.134351 + 0.134351i) q^{77} +(0.766432 - 10.5685i) q^{78} +9.81369 q^{79} +(8.49201 + 2.80816i) q^{80} +4.55514 q^{81} +(0.999951 - 13.7885i) q^{82} +(-0.608923 - 0.608923i) q^{83} +(0.399071 - 2.73696i) q^{84} +(3.83025 - 3.60860i) q^{85} +(3.14270 - 2.71770i) q^{86} +(-0.380629 - 0.380629i) q^{87} +(-0.115799 + 0.524781i) q^{88} +16.1054i q^{89} +(3.42086 + 0.350770i) q^{90} -5.41788 q^{91} +(-11.5798 + 8.63269i) q^{92} +(-5.46833 + 5.46833i) q^{93} +(4.38861 - 3.79512i) q^{94} +(-0.477282 + 16.0180i) q^{95} +(7.13226 - 3.21445i) q^{96} +(0.0632673 - 0.0632673i) q^{97} +(-1.41051 - 0.102291i) q^{98} +0.206616i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{6}+O(q^{10}) $ 72 * q + 8 * q^6	$ 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) $ 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.102291	+	1.41051i	−0.0723306	+	0.997381i
$2$	−0.102291	+	1.41051i	−0.0723306	+	0.997381i
$3$	−0.977895	−	0.977895i	−0.564588	−	0.564588i	0.366019	−	0.930607i	$-0.380720\pi$
$3$	−0.977895	−	0.977895i	−0.564588	−	0.564588i	−0.930607	+	0.366019i	$0.880720\pi$
$4$	−1.97907	−	0.288564i	−0.989537	−	0.144282i
$5$	2.23508	+	0.0665977i	0.999556	+	0.0297834i
$5$	2.23508	+	0.0665977i	0.999556	+	0.0297834i
$6$	1.47936	−	1.27930i	0.603946	−	0.522272i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	0.609464	−	2.76198i	0.215478	−	0.976509i
$9$		−	1.08744i		−	0.362481i
$10$	−0.322565	+	3.14578i	−0.102004	+	0.994784i
$11$	−0.190002			−0.0572876			−0.0286438	−	0.999590i	$-0.509119\pi$
$11$	−0.190002			−0.0572876			−0.0286438	+	0.999590i	$0.509119\pi$
$12$	1.65314	+	2.21751i	0.477220	+	0.640140i
$13$	3.83102	−	3.83102i	1.06253	−	1.06253i	0.0646238	−	0.997910i	$-0.479415\pi$
$13$	3.83102	−	3.83102i	1.06253	−	1.06253i	0.997910	−	0.0646238i	$-0.0205847\pi$
$14$	1.06971	−	0.925050i	0.285892	−	0.247230i
$15$	−2.12054	−	2.25080i	−0.547522	−	0.581153i
$16$	3.83346	+	1.14218i	0.958365	+	0.285545i
$17$	1.66411	−	1.66411i	0.403607	−	0.403607i	−0.475895	−	0.879502i	$-0.657876\pi$
$17$	1.66411	−	1.66411i	0.403607	−	0.403607i	0.879502	+	0.475895i	$0.157876\pi$
$18$	1.53385	+	0.111235i	0.361531	+	0.0262184i
$19$			7.16664i			1.64414i	0.569386	+	0.822070i	$0.307181\pi$
$19$			7.16664i			1.64414i	−0.569386	+	0.822070i	$0.692819\pi$
$20$	−4.40416	−	0.776765i	−0.984800	−	0.173690i
$21$			1.38295i			0.301785i
$22$	0.0194354	−	0.267999i	0.00414365	−	0.0571376i
$23$	5.10656	−	5.10656i	1.06479	−	1.06479i	0.0670422	−	0.997750i	$-0.478644\pi$
$23$	5.10656	−	5.10656i	1.06479	−	1.06479i	0.997750	−	0.0670422i	$-0.0213562\pi$
$24$	−3.29692	+	2.10494i	−0.672981	+	0.429669i
$25$	4.99113	+	0.297702i	0.998226	+	0.0595404i
$26$	5.01181	+	5.79557i	0.982897	+	1.13660i
$27$	−3.99709	+	3.99709i	−0.769240	+	0.769240i
$28$	1.19537	+	1.60346i	0.225904	+	0.303026i
$29$	0.389233			0.0722788			0.0361394	−	0.999347i	$-0.488494\pi$
$29$	0.389233			0.0722788			0.0361394	+	0.999347i	$0.488494\pi$
$30$	3.39168	−	2.76081i	0.619233	−	0.504053i
$31$		−	5.59194i		−	1.00434i	−0.864768	−	0.502171i	$-0.832535\pi$
$31$		−	5.59194i		−	1.00434i	0.864768	−	0.502171i	$-0.167465\pi$
$32$	−2.00318	+	5.29030i	−0.354116	+	0.935201i
$33$	0.185802	+	0.185802i	0.0323439	+	0.0323439i
$34$	2.17702	+	2.51747i	0.373357	+	0.431743i
$35$	−1.53335	−	1.62753i	−0.259183	−	0.275103i
$36$	−0.313797	+	2.15213i	−0.0522995	+	0.358688i
$37$	0.807349	+	0.807349i	0.132727	+	0.132727i	0.770349	−	0.637622i	$-0.220082\pi$
$37$	0.807349	+	0.807349i	0.132727	+	0.132727i	−0.637622	+	0.770349i	$0.720082\pi$
$38$	−10.1086	−	0.733082i	−1.63983	−	0.118922i
$39$	−7.49267			−1.19979
$40$	1.54614	−	6.13265i	0.244466	−	0.969658i
$41$	−9.77556			−1.52669			−0.763343	−	0.645993i	$-0.776443\pi$
$41$	−9.77556			−1.52669			−0.763343	+	0.645993i	$0.776443\pi$
$42$	−1.95067	−	0.141463i	−0.300995	−	0.0218283i
$43$	−2.07740	−	2.07740i	−0.316801	−	0.316801i	0.530736	−	0.847537i	$-0.321916\pi$
$43$	−2.07740	−	2.07740i	−0.316801	−	0.316801i	−0.847537	+	0.530736i	$0.821916\pi$
$44$	0.376027	+	0.0548277i	0.0566882	+	0.00826558i
$45$	0.0724212	−	2.43052i	0.0107959	−	0.362320i
$46$	6.68050	+	7.72521i	0.984986	+	1.13902i
$47$	−2.90099	−	2.90099i	−0.423152	−	0.423152i	0.463135	−	0.886288i	$-0.346724\pi$
$47$	−2.90099	−	2.90099i	−0.423152	−	0.423152i	−0.886288	+	0.463135i	$0.846724\pi$
$48$	−2.63179	−	4.86566i	−0.379866	−	0.702297i
$49$			1.00000i			0.142857i
$50$	−0.930458	+	7.00958i	−0.131587	+	0.991305i
$51$	−3.25466			−0.455743
$52$	−8.68736	+	6.47637i	−1.20472	+	0.898111i
$53$	−3.87887	+	3.87887i	−0.532804	+	0.532804i	−0.921406	−	0.388602i	$-0.872958\pi$
$53$	−3.87887	+	3.87887i	−0.532804	+	0.532804i	0.388602	+	0.921406i	$0.372958\pi$
$54$	−5.22907	−	6.04680i	−0.711586	−	0.822865i
$55$	−0.424668	−	0.0126537i	−0.0572622	−	0.00170622i
$56$	−2.38397	+	1.52206i	−0.318572	+	0.203394i
$57$	7.00822	−	7.00822i	0.928262	−	0.928262i
$58$	−0.0398150	+	0.549017i	−0.00522796	+	0.0720894i
$59$			3.53327i			0.459993i	0.973191	+	0.229997i	$0.0738715\pi$
$59$			3.53327i			0.459993i	−0.973191	+	0.229997i	$0.926129\pi$
$60$	3.54721	+	5.06640i	0.457943	+	0.654070i
$61$			10.7990i			1.38267i	0.722537	+	0.691333i	$0.242976\pi$
$61$			10.7990i			1.38267i	−0.722537	+	0.691333i	$0.757024\pi$
$62$	7.88749	+	0.572005i	1.00171	+	0.0726447i
$63$	−0.768938	+	0.768938i	−0.0968771	+	0.0968771i
$64$	−7.25711	−	3.36666i	−0.907138	−	0.420832i
$65$	8.81776	−	8.30748i	1.09371	−	1.03042i
$66$	−0.281081	+	0.243069i	−0.0345986	+	0.0299197i
$67$	7.88947	−	7.88947i	0.963852	−	0.963852i	−0.0355169	−	0.999369i	$-0.511308\pi$
$67$	7.88947	−	7.88947i	0.963852	−	0.963852i	0.999369	+	0.0355169i	$0.0113078\pi$
$68$	−3.77361	+	2.81320i	−0.457617	+	0.341151i
$69$	−9.98737			−1.20234
$70$	2.45249	−	1.99632i	0.293129	−	0.238606i
$71$			1.44759i			0.171797i	0.996304	+	0.0858985i	$0.0273761\pi$
$71$			1.44759i			0.171797i	−0.996304	+	0.0858985i	$0.972624\pi$
$72$	−3.00350	−	0.662757i	−0.353966	−	0.0781067i
$73$	−6.73133	−	6.73133i	−0.787843	−	0.787843i	0.193298	−	0.981140i	$-0.438082\pi$
$73$	−6.73133	−	6.73133i	−0.787843	−	0.787843i	−0.981140	+	0.193298i	$0.938082\pi$
$74$	−1.22136	+	1.05619i	−0.141980	+	0.122779i
$75$	−4.58968	−	5.17192i	−0.529971	−	0.597202i
$76$	2.06804	−	14.1833i	0.237220	−	1.62694i
$77$	0.134351	+	0.134351i	0.0153108	+	0.0153108i
$78$	0.766432	−	10.5685i	0.0867813	−	1.19664i
$79$	9.81369			1.10413			0.552063	−	0.833802i	$-0.313841\pi$
$79$	9.81369			1.10413			0.552063	+	0.833802i	$0.313841\pi$
$80$	8.49201	+	2.80816i	0.949436	+	0.313962i
$81$	4.55514			0.506127
$82$	0.999951	−	13.7885i	0.110426	−	1.52269i
$83$	−0.608923	−	0.608923i	−0.0668380	−	0.0668380i	0.672898	−	0.739736i	$-0.265049\pi$
$83$	−0.608923	−	0.608923i	−0.0668380	−	0.0668380i	−0.739736	+	0.672898i	$0.765049\pi$
$84$	0.399071	−	2.73696i	0.0435422	−	0.298627i
$85$	3.83025	−	3.60860i	0.415449	−	0.391407i
$86$	3.14270	−	2.71770i	0.338886	−	0.293057i
$87$	−0.380629	−	0.380629i	−0.0408077	−	0.0408077i
$88$	−0.115799	+	0.524781i	−0.0123442	+	0.0559419i
$89$			16.1054i			1.70717i	0.520956	+	0.853584i	$0.325576\pi$
$89$			16.1054i			1.70717i	−0.520956	+	0.853584i	$0.674424\pi$
$90$	3.42086	+	0.350770i	0.360590	+	0.0369744i
$91$	−5.41788			−0.567948
$92$	−11.5798	+	8.63269i	−1.20728	+	0.900020i
$93$	−5.46833	+	5.46833i	−0.567040	+	0.567040i
$94$	4.38861	−	3.79512i	0.452651	−	0.391437i
$95$	−0.477282	+	16.0180i	−0.0489681	+	1.64341i
$96$	7.13226	−	3.21445i	0.727933	−	0.328074i
$97$	0.0632673	−	0.0632673i	0.00642382	−	0.00642382i	−0.703888	−	0.710311i	$-0.748554\pi$
$97$	0.0632673	−	0.0632673i	0.00642382	−	0.00642382i	0.710311	+	0.703888i	$0.248554\pi$
$98$	−1.41051	−	0.102291i	−0.142483	−	0.0103329i
$99$			0.206616i			0.0207657i
$100$	−9.79190	−	2.02944i	−0.979190	−	0.202944i
$101$			8.26466i			0.822364i	0.911553	+	0.411182i	$0.134884\pi$
$101$			8.26466i			0.822364i	−0.911553	+	0.411182i	$0.865116\pi$
$102$	0.332922	−	4.59073i	0.0329642	−	0.454550i
$103$	−4.02301	+	4.02301i	−0.396399	+	0.396399i	−0.876961	−	0.480562i	$-0.840433\pi$
$103$	−4.02301	+	4.02301i	−0.396399	+	0.396399i	0.480562	+	0.876961i	$0.340433\pi$
$104$	−8.24634	−	12.9161i	−0.808621	−	1.26653i
$105$	−0.0921015	+	3.09100i	−0.00898819	+	0.301651i
$106$	−5.07441	−	5.86796i	−0.492870	−	0.569946i
$107$	−11.7697	+	11.7697i	−1.13782	+	1.13782i	−0.148974	+	0.988841i	$0.547597\pi$
$107$	−11.7697	+	11.7697i	−1.13782	+	1.13782i	−0.988841	+	0.148974i	$0.952403\pi$
$108$	9.06395	−	6.75712i	0.872179	−	0.650204i
$109$	16.7835			1.60756			0.803782	−	0.594924i	$-0.202818\pi$
$109$	16.7835			1.60756			0.803782	+	0.594924i	$0.202818\pi$
$110$	0.0612878	−	0.597704i	0.00584356	−	0.0569888i
$111$		−	1.57900i		−	0.149872i
$112$	−1.90302	−	3.51831i	−0.179819	−	0.332449i
$113$	12.0340	+	12.0340i	1.13206	+	1.13206i	0.989834	+	0.142227i	$0.0454263\pi$
$113$	12.0340	+	12.0340i	1.13206	+	1.13206i	0.142227	+	0.989834i	$0.454574\pi$
$114$	9.16829	+	10.6020i	0.858689	+	0.992972i
$115$	11.7536	−	11.0735i	1.09603	−	1.03261i
$116$	−0.770321	−	0.112319i	−0.0715225	−	0.0104285i
$117$	−4.16601	−	4.16601i	−0.385148	−	0.385148i
$118$	−4.98372	−	0.361422i	−0.458788	−	0.0332716i
$119$	−2.35341			−0.215737
$120$	−7.50906	+	4.48513i	−0.685480	+	0.409434i
$121$	−10.9639			−0.996718
$122$	−15.2320	−	1.10463i	−1.37904	−	0.100009i
$123$	9.55947	+	9.55947i	0.861949	+	0.861949i
$124$	−1.61364	+	11.0669i	−0.144909	+	0.993834i
$125$	11.1357	+	0.997785i	0.996010	+	0.0892446i
$126$	−1.00594	−	1.16325i	−0.0896161	−	0.103630i
$127$	1.04181	+	1.04181i	0.0924458	+	0.0924458i	0.751817	−	0.659371i	$-0.229178\pi$
$127$	1.04181	+	1.04181i	0.0924458	+	0.0924458i	−0.659371	+	0.751817i	$0.729178\pi$
$128$	5.49104	−	9.89184i	0.485344	−	0.874323i
$129$			4.06297i			0.357724i
$130$	10.8158	+	13.2873i	0.948609	+	1.16537i
$131$	−4.45039			−0.388832			−0.194416	−	0.980919i	$-0.562281\pi$
$131$	−4.45039			−0.388832			−0.194416	+	0.980919i	$0.562281\pi$
$132$	−0.314099	−	0.421331i	−0.0273388	−	0.0366721i
$133$	5.06758	−	5.06758i	0.439415	−	0.439415i
$134$	10.3212	+	11.9352i	0.891612	+	1.03104i
$135$	−9.20000	+	8.66760i	−0.791810	+	0.745988i
$136$	−3.58204	−	5.61047i	−0.307157	−	0.481094i
$137$	−0.571011	+	0.571011i	−0.0487848	+	0.0487848i	−0.731078	−	0.682294i	$-0.760983\pi$
$137$	−0.571011	+	0.571011i	−0.0487848	+	0.0487848i	0.682294	+	0.731078i	$0.260983\pi$
$138$	1.02162	−	14.0873i	0.0869658	−	1.19919i
$139$			6.22561i			0.528050i	0.964516	+	0.264025i	$0.0850501\pi$
$139$			6.22561i			0.528050i	−0.964516	+	0.264025i	$0.914950\pi$
$140$	2.56496	+	3.66347i	0.216778	+	0.309620i
$141$			5.67372i			0.477813i
$142$	−2.04184	−	0.148075i	−0.171347	−	0.0124262i
$143$	−0.727899	+	0.727899i	−0.0608700	+	0.0608700i
$144$	1.24206	−	4.16867i	0.103505	−	0.347389i
$145$	0.869965	+	0.0259220i	0.0722467	+	0.00215271i
$146$	10.1832	−	8.80605i	0.842764	−	0.728794i
$147$	0.977895	−	0.977895i	0.0806554	−	0.0806554i
$148$	−1.36483	−	1.83077i	−0.112188	−	0.150489i
$149$	−13.1449			−1.07687			−0.538436	−	0.842666i	$-0.680985\pi$
$149$	−13.1449			−1.07687			−0.538436	+	0.842666i	$0.680985\pi$
$150$	7.76453	−	5.94475i	0.633971	−	0.485386i
$151$		−	6.94946i		−	0.565539i	−0.959188	−	0.282769i	$-0.908747\pi$
$151$		−	6.94946i		−	0.565539i	0.959188	−	0.282769i	$-0.0912531\pi$
$152$	19.7941	+	4.36781i	1.60552	+	0.354276i
$153$	−1.80963	−	1.80963i	−0.146300	−	0.146300i
$154$	−0.203247	+	0.175761i	−0.0163781	+	0.0141632i
$155$	0.372411	−	12.4984i	0.0299128	−	1.00390i
$156$	14.8285	+	2.16212i	1.18723	+	0.173108i
$157$	1.29124	+	1.29124i	0.103052	+	0.103052i	0.756753	−	0.653701i	$-0.226785\pi$
$157$	1.29124	+	1.29124i	0.103052	+	0.103052i	−0.653701	+	0.756753i	$0.726785\pi$
$158$	−1.00385	+	13.8423i	−0.0798621	+	1.10123i
$159$	7.58626			0.601629
$160$	−4.82959	+	11.6908i	−0.381813	+	0.924240i
$161$	−7.22177			−0.569155
$162$	−0.465949	+	6.42507i	−0.0366084	+	0.504801i
$163$	13.5507	+	13.5507i	1.06138	+	1.06138i	0.997989	+	0.0633870i	$0.0201902\pi$
$163$	13.5507	+	13.5507i	1.06138	+	1.06138i	0.0633870	+	0.997989i	$0.479810\pi$
$164$	19.3465	+	2.82088i	1.51071	+	0.220274i
$165$	0.402907	+	0.427655i	0.0313662	+	0.0332929i
$166$	0.921179	−	0.796605i	0.0714974	−	0.0618285i
$167$	14.0581	+	14.0581i	1.08785	+	1.08785i	0.995750	+	0.0920998i	$0.0293579\pi$
$167$	14.0581	+	14.0581i	1.08785	+	1.08785i	0.0920998	+	0.995750i	$0.470642\pi$
$168$	3.81969	+	0.842860i	0.294696	+	0.0650280i
$169$		−	16.3534i		−	1.25795i
$170$	4.69816	+	5.77173i	0.360332	+	0.442671i
$171$	7.79331			0.595969
$172$	3.51187	+	4.71080i	0.267778	+	0.359195i
$173$	−3.44989	+	3.44989i	−0.262290	+	0.262290i	−0.825984	−	0.563694i	$-0.809380\pi$
$173$	−3.44989	+	3.44989i	−0.262290	+	0.262290i	0.563694	+	0.825984i	$0.309380\pi$
$174$	0.575816	−	0.497946i	0.0436525	−	0.0377492i
$175$	−3.31875	−	3.73977i	−0.250874	−	0.282700i
$176$	−0.728363	−	0.217016i	−0.0549025	−	0.0163582i
$177$	3.45517	−	3.45517i	0.259707	−	0.259707i
$178$	−22.7168	−	1.64743i	−1.70270	−	0.123480i
$179$		−	15.4934i		−	1.15803i	−0.815317	−	0.579015i	$-0.803437\pi$
$179$		−	15.4934i		−	1.15803i	0.815317	−	0.579015i	$-0.196563\pi$
$180$	−0.844687	+	4.78927i	−0.0629593	+	0.356971i
$181$		−	7.22988i		−	0.537392i	−0.963225	−	0.268696i	$-0.913407\pi$
$181$		−	7.22988i		−	0.537392i	0.963225	−	0.268696i	$-0.0865928\pi$
$182$	0.554200	−	7.64197i	0.0410800	−	0.566460i
$183$	10.5603	−	10.5603i	0.780636	−	0.780636i
$184$	−10.9920	−	17.2165i	−0.810340	−	1.26922i
$185$	1.75072	+	1.85825i	0.128715	+	0.136622i
$186$	−7.15378	−	8.27250i	−0.524540	−	0.606569i
$187$	−0.316184	+	0.316184i	−0.0231217	+	0.0231217i
$188$	4.90414	+	6.57839i	0.357671	+	0.479778i
$189$	5.65274			0.411176
$190$	−22.5447	−	2.31170i	−1.63556	−	0.167709i
$191$		−	5.11923i		−	0.370414i	−0.982700	−	0.185207i	$-0.940704\pi$
$191$		−	5.11923i		−	0.370414i	0.982700	−	0.185207i	$-0.0592956\pi$
$192$	3.80445	+	10.3889i	0.274563	+	0.749756i
$193$	4.25152	+	4.25152i	0.306031	+	0.306031i	0.843368	−	0.537337i	$-0.180570\pi$
$193$	4.25152	+	4.25152i	0.306031	+	0.306031i	−0.537337	+	0.843368i	$0.680570\pi$
$194$	0.0827674	+	0.0957108i	0.00594236	+	0.00687163i
$195$	−16.7467	−	0.498995i	−1.19926	−	0.0357338i
$196$	0.288564	−	1.97907i	0.0206117	−	0.141362i
$197$	−13.6475	−	13.6475i	−0.972343	−	0.972343i	0.0272843	−	0.999628i	$-0.491314\pi$
$197$	−13.6475	−	13.6475i	−0.972343	−	0.972343i	−0.999628	+	0.0272843i	$0.991314\pi$
$198$	−0.291433	−	0.0211349i	−0.0207113	−	0.00150199i
$199$	−5.43938			−0.385587			−0.192794	−	0.981239i	$-0.561755\pi$
$199$	−5.43938			−0.385587			−0.192794	+	0.981239i	$0.561755\pi$
$200$	3.86416	−	13.6040i	0.273237	−	0.961947i
$201$	−15.4301			−1.08836
$202$	−11.6574	−	0.845399i	−0.820210	−	0.0594821i
$203$	−0.275229	−	0.275229i	−0.0193173	−	0.0193173i
$204$	6.44121	+	0.939179i	0.450975	+	0.0657557i
$205$	−21.8491	−	0.651030i	−1.52601	−	0.0454699i
$206$	−5.26298	−	6.08601i	−0.366689	−	0.424032i
$207$	−5.55309	−	5.55309i	−0.385967	−	0.385967i
$208$	19.0618	−	10.3103i	1.32170	−	0.714894i
$209$		−	1.36167i		−	0.0941889i
$210$	−4.35047	−	0.446092i	−0.300211	−	0.0307832i
$211$	19.3842			1.33447			0.667233	−	0.744849i	$-0.267479\pi$
$211$	19.3842			1.33447			0.667233	+	0.744849i	$0.267479\pi$
$212$	8.79587	−	6.55727i	0.604103	−	0.450355i
$213$	1.41559	−	1.41559i	0.0969946	−	0.0969946i
$214$	−15.3973	−	17.8051i	−1.05254	−	1.21713i
$215$	−4.50481	−	4.78151i	−0.307225	−	0.326096i
$216$	8.60381	+	13.4760i	0.585415	+	0.916924i
$217$	−3.95410	+	3.95410i	−0.268422	+	0.268422i
$218$	−1.71679	+	23.6732i	−0.116276	+	1.60335i
$219$			13.1651i			0.889613i
$220$	0.836797	+	0.147587i	0.0564169	+	0.00995029i
$221$		−	12.7505i		−	0.857692i
$222$	2.22720	+	0.161518i	0.149480	+	0.0108404i
$223$	−3.41717	+	3.41717i	−0.228831	+	0.228831i	−0.812204	−	0.583373i	$-0.801732\pi$
$223$	−3.41717	+	3.41717i	−0.228831	+	0.228831i	0.583373	+	0.812204i	$0.301732\pi$
$224$	5.15727	−	2.32434i	0.344585	−	0.155302i
$225$	0.323734	−	5.42757i	0.0215823	−	0.361838i
$226$	−18.2050	+	15.7431i	−1.21098	+	1.04721i
$227$	−1.43025	+	1.43025i	−0.0949289	+	0.0949289i	−0.752976	−	0.658048i	$-0.771383\pi$
$227$	−1.43025	+	1.43025i	−0.0949289	+	0.0949289i	0.658048	+	0.752976i	$0.271383\pi$
$228$	−15.8921	+	11.8475i	−1.05248	+	0.784617i
$229$	24.9137			1.64634			0.823170	−	0.567794i	$-0.192203\pi$
$229$	24.9137			1.64634			0.823170	+	0.567794i	$0.192203\pi$
$230$	14.4169	+	17.7113i	0.950625	+	1.16785i
$231$		−	0.262763i		−	0.0172885i
$232$	0.237223	−	1.07506i	0.0155745	−	0.0705808i
$233$	−10.6761	−	10.6761i	−0.699413	−	0.699413i	0.264871	−	0.964284i	$-0.414671\pi$
$233$	−10.6761	−	10.6761i	−0.699413	−	0.699413i	−0.964284	+	0.264871i	$0.914671\pi$
$234$	6.30234	−	5.45005i	0.411997	−	0.356281i
$235$	−6.29073	−	6.67712i	−0.410362	−	0.435568i
$236$	1.01958	−	6.99261i	0.0663688	−	0.455180i
$237$	−9.59676	−	9.59676i	−0.623376	−	0.623376i
$238$	0.240733	−	3.31951i	0.0156044	−	0.215172i
$239$	−11.2248			−0.726072			−0.363036	−	0.931775i	$-0.618260\pi$
$239$	−11.2248			−0.726072			−0.363036	+	0.931775i	$0.618260\pi$
$240$	−5.55821	−	11.0504i	−0.358781	−	0.713299i
$241$	0.513121			0.0330530			0.0165265	−	0.999863i	$-0.494739\pi$
$241$	0.513121			0.0330530			0.0165265	+	0.999863i	$0.494739\pi$
$242$	1.12151	−	15.4647i	0.0720932	−	0.994107i
$243$	7.53682	+	7.53682i	0.483487	+	0.483487i
$244$	3.11620	−	21.3719i	0.199494	−	1.36820i
$245$	−0.0665977	+	2.23508i	−0.00425477	+	0.142794i
$246$	−14.4616	+	12.5059i	−0.922036	+	0.797346i
$247$	27.4555	+	27.4555i	1.74695	+	1.74695i
$248$	−15.4449	−	3.40809i	−0.980750	−	0.216414i
$249$			1.19093i			0.0754719i
$250$	−2.54647	+	15.6050i	−0.161053	+	0.986946i
$251$	3.98170			0.251323			0.125661	−	0.992073i	$-0.459895\pi$
$251$	3.98170			0.251323			0.125661	+	0.992073i	$0.459895\pi$
$252$	1.74367	−	1.29990i	0.109841	−	0.0818858i
$253$	−0.970255	+	0.970255i	−0.0609994	+	0.0609994i
$254$	−1.57605	+	1.36292i	−0.0988904	+	0.0855170i
$255$	−7.27441	−	0.216753i	−0.455541	−	0.0135736i
$256$	13.3908	+	8.75701i	0.836928	+	0.547313i
$257$	−6.51642	+	6.51642i	−0.406483	+	0.406483i	−0.880510	−	0.474027i	$-0.842800\pi$
$257$	−6.51642	+	6.51642i	−0.406483	+	0.406483i	0.474027	+	0.880510i	$0.342800\pi$
$258$	−5.73085	−	0.415604i	−0.356787	−	0.0258744i
$259$		−	1.14176i		−	0.0709457i
$260$	−19.8482	+	13.8966i	−1.23093	+	0.861832i
$261$		−	0.423268i		−	0.0261997i
$262$	0.455234	−	6.27731i	0.0281244	−	0.387814i
$263$	4.84321	−	4.84321i	0.298645	−	0.298645i	−0.541838	−	0.840483i	$-0.682271\pi$
$263$	4.84321	−	4.84321i	0.298645	−	0.298645i	0.840483	+	0.541838i	$0.182271\pi$
$264$	0.626420	−	0.399942i	0.0385535	−	0.0246147i
$265$	−8.92790	+	8.41125i	−0.548436	+	0.516699i
$266$	6.62950	+	7.66624i	0.406481	+	0.470047i
$267$	15.7494	−	15.7494i	0.963846	−	0.963846i
$268$	−17.8905	+	13.3372i	−1.09283	+	0.814700i
$269$	−5.88042			−0.358535			−0.179268	−	0.983800i	$-0.557373\pi$
$269$	−5.88042			−0.358535			−0.179268	+	0.983800i	$0.557373\pi$
$270$	−11.2847	−	13.8633i	−0.686762	−	0.843693i
$271$			12.0871i			0.734239i	0.930174	+	0.367119i	$0.119656\pi$
$271$			12.0871i			0.734239i	−0.930174	+	0.367119i	$0.880344\pi$
$272$	8.28003	−	4.47860i	0.502051	−	0.271555i
$273$	5.29812	+	5.29812i	0.320657	+	0.320657i
$274$	−0.747007	−	0.863826i	−0.0451284	−	0.0521856i
$275$	−0.948322	−	0.0565638i	−0.0571860	−	0.00341093i
$276$	19.7657	+	2.88200i	1.18976	+	0.173476i
$277$	0.956631	+	0.956631i	0.0574784	+	0.0574784i	0.735262	−	0.677783i	$-0.237059\pi$
$277$	0.956631	+	0.956631i	0.0574784	+	0.0574784i	−0.677783	+	0.735262i	$0.737059\pi$
$278$	−8.78128	−	0.636823i	−0.526666	−	0.0381941i
$279$	−6.08092			−0.364055
$280$	−5.42973	+	3.24316i	−0.324488	+	0.193816i
$281$	−16.9850			−1.01324			−0.506621	−	0.862169i	$-0.669106\pi$
$281$	−16.9850			−1.01324			−0.506621	+	0.862169i	$0.669106\pi$
$282$	−8.00284	−	0.580370i	−0.476562	−	0.0345605i
$283$	−7.53917	−	7.53917i	−0.448157	−	0.448157i	0.446584	−	0.894742i	$-0.352640\pi$
$283$	−7.53917	−	7.53917i	−0.448157	−	0.448157i	−0.894742	+	0.446584i	$0.852640\pi$
$284$	0.417722	−	2.86488i	0.0247873	−	0.170000i
$285$	16.1306	−	15.1972i	0.955497	−	0.900203i
$286$	−0.952251	−	1.10117i	−0.0563078	−	0.0651133i
$287$	6.91237	+	6.91237i	0.408024	+	0.408024i
$288$	5.75289	+	2.17835i	0.338993	+	0.128360i
$289$			11.4614i			0.674203i
$290$	−0.125553	+	1.22444i	−0.00737271	+	0.0719018i
$291$	−0.123738			−0.00725362
$292$	11.3794	+	15.2642i	0.665927	+	0.893271i
$293$	−21.2315	+	21.2315i	−1.24036	+	1.24036i	−0.280505	+	0.959853i	$0.590502\pi$
$293$	−21.2315	+	21.2315i	−1.24036	+	1.24036i	−0.959853	+	0.280505i	$0.909498\pi$
$294$	1.27930	+	1.47936i	0.0746103	+	0.0862780i
$295$	−0.235308	+	7.89714i	−0.0137002	+	0.459789i
$296$	2.72193	−	1.73783i	0.158209	−	0.101010i
$297$	0.759453	−	0.759453i	0.0440679	−	0.0440679i
$298$	1.34460	−	18.5410i	0.0778908	−	1.07405i
$299$		−	39.1267i		−	2.26275i
$300$	7.59088	+	11.5600i	0.438260	+	0.667419i
$301$			2.93789i			0.169337i
$302$	9.80227	+	0.710866i	0.564058	+	0.0409057i
$303$	8.08197	−	8.08197i	0.464297	−	0.464297i
$304$	−8.18559	+	27.4730i	−0.469476	+	1.57569i
$305$	−0.719186	+	24.1365i	−0.0411805	+	1.38205i
$306$	2.73761	−	2.36739i	0.156499	−	0.135335i
$307$	−8.98616	+	8.98616i	−0.512867	+	0.512867i	−0.915404	−	0.402537i	$-0.868129\pi$
$307$	−8.98616	+	8.98616i	−0.512867	+	0.512867i	0.402537	+	0.915404i	$0.368129\pi$
$308$	−0.227122	−	0.304660i	−0.0129415	−	0.0173596i
$309$	7.86816			0.447604
$310$	17.5910	+	1.80376i	0.999104	+	0.102447i
$311$		−	18.6142i		−	1.05551i	−0.849395	−	0.527757i	$-0.823033\pi$
$311$		−	18.6142i		−	1.05551i	0.849395	−	0.527757i	$-0.176967\pi$
$312$	−4.56651	+	20.6946i	−0.258528	+	1.17160i
$313$	−14.0127	−	14.0127i	−0.792045	−	0.792045i	0.189782	−	0.981826i	$-0.439222\pi$
$313$	−14.0127	−	14.0127i	−0.792045	−	0.792045i	−0.981826	+	0.189782i	$0.939222\pi$
$314$	−1.95339	+	1.68922i	−0.110236	+	0.0953284i
$315$	−1.76984	+	1.66743i	−0.0997194	+	0.0939488i
$316$	−19.4220	−	2.83188i	−1.09257	−	0.159306i
$317$	−19.3688	−	19.3688i	−1.08786	−	1.08786i	−0.995749	−	0.0921118i	$-0.970638\pi$
$317$	−19.3688	−	19.3688i	−1.08786	−	1.08786i	−0.0921118	−	0.995749i	$-0.529362\pi$
$318$	−0.776005	+	10.7005i	−0.0435162	+	0.600054i
$319$	−0.0739549			−0.00414068
$320$	−15.9960	−	8.00805i	−0.894202	−	0.447663i
$321$	23.0190			1.28479
$322$	0.738721	−	10.1864i	0.0411673	−	0.567665i
$323$	11.9261	+	11.9261i	0.663586	+	0.663586i
$324$	−9.01496	−	1.31445i	−0.500831	−	0.0730251i
$325$	20.2616	−	17.9806i	1.12391	−	0.997385i
$326$	−20.4996	+	17.7273i	−1.13537	+	0.981826i
$327$	−16.4125	−	16.4125i	−0.907611	−	0.907611i
$328$	−5.95785	+	26.9999i	−0.328967	+	1.49082i
$329$			4.10261i			0.226184i
$330$	−0.644424	+	0.524558i	−0.0354744	+	0.0288760i
$331$	−8.50554			−0.467507			−0.233753	−	0.972296i	$-0.575101\pi$
$331$	−8.50554			−0.467507			−0.233753	+	0.972296i	$0.575101\pi$
$332$	1.02939	+	1.38082i	0.0564951	+	0.0757822i
$333$	0.877945	−	0.877945i	0.0481111	−	0.0481111i
$334$	−21.2671	+	18.3911i	−1.16368	+	1.00632i
$335$	18.1590	−	17.1081i	0.992131	−	0.934718i
$336$	−1.57958	+	5.30149i	−0.0861732	+	0.289220i
$337$	23.2419	−	23.2419i	1.26607	−	1.26607i	0.317962	−	0.948104i	$-0.397002\pi$
$337$	23.2419	−	23.2419i	1.26607	−	1.26607i	0.948104	−	0.317962i	$-0.102998\pi$
$338$	23.0666	+	1.67280i	1.25466	+	0.0909886i
$339$		−	23.5359i		−	1.27830i
$340$	−8.62165	+	6.03640i	−0.467575	+	0.327370i
$341$			1.06248i			0.0575364i
$342$	−0.797184	+	10.9925i	−0.0431068	+	0.594408i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−7.00386	+	4.47165i	−0.377623	+	0.241095i
$345$	−22.3225	−	0.665136i	−1.20180	−	0.0358097i
$346$	−4.51320	−	5.21899i	−0.242631	−	0.280575i
$347$	−10.5611	+	10.5611i	−0.566950	+	0.566950i	−0.931273	−	0.364323i	$-0.881301\pi$
$347$	−10.5611	+	10.5611i	−0.566950	+	0.566950i	0.364323	+	0.931273i	$0.381301\pi$
$348$	0.643457	+	0.863129i	0.0344929	+	0.0462686i
$349$	−11.9701			−0.640747			−0.320374	−	0.947291i	$-0.603808\pi$
$349$	−11.9701			−0.640747			−0.320374	+	0.947291i	$0.603808\pi$
$350$	5.61446	−	4.29859i	0.300105	−	0.229769i
$351$			30.6259i			1.63469i
$352$	0.380608	−	1.00516i	0.0202865	−	0.0535755i
$353$	13.8829	+	13.8829i	0.738912	+	0.738912i	0.972368	−	0.233455i	$-0.0750033\pi$
$353$	13.8829	+	13.8829i	0.738912	+	0.738912i	−0.233455	+	0.972368i	$0.575003\pi$
$354$	4.52012	+	5.22698i	0.240242	+	0.277811i
$355$	−0.0964061	+	3.23547i	−0.00511670	+	0.171721i
$356$	4.64744	−	31.8737i	0.246314	−	1.68930i
$357$	2.30139	+	2.30139i	0.121803	+	0.121803i
$358$	21.8536	+	1.58483i	1.15500	+	0.0837609i
$359$	23.4677			1.23858			0.619290	−	0.785162i	$-0.287421\pi$
$359$	23.4677			1.23858			0.619290	+	0.785162i	$0.287421\pi$
$360$	−6.66891	−	1.68134i	−0.351482	−	0.0886143i
$361$	−32.3607			−1.70320
$362$	10.1978	+	0.739550i	0.535985	+	0.0388699i
$363$	10.7215	+	10.7215i	0.562735	+	0.562735i
$364$	10.7224	+	1.56341i	0.562005	+	0.0819448i
$365$	−14.5967	−	15.4933i	−0.764028	−	0.810958i
$366$	13.8151	+	15.9755i	0.722128	+	0.835055i
$367$	7.44229	+	7.44229i	0.388484	+	0.388484i	0.874147	−	0.485662i	$-0.161422\pi$
$367$	7.44229	+	7.44229i	0.388484	+	0.388484i	−0.485662	+	0.874147i	$0.661422\pi$
$368$	25.4084	−	13.7432i	1.32451	−	0.716414i
$369$			10.6304i			0.553394i
$370$	−2.80017	+	2.27932i	−0.145574	+	0.118496i
$371$	5.48555			0.284796
$372$	12.4002	−	9.24427i	0.642921	−	0.479293i
$373$	15.4169	−	15.4169i	0.798258	−	0.798258i	−0.184563	−	0.982821i	$-0.559087\pi$
$373$	15.4169	−	15.4169i	0.798258	−	0.798258i	0.982821	+	0.184563i	$0.0590869\pi$
$374$	−0.413638	−	0.478324i	−0.0213887	−	0.0247335i
$375$	−9.91384	−	11.8653i	−0.511949	−	0.612722i
$376$	−9.78052	+	6.24443i	−0.504392	+	0.322032i
$377$	1.49116	−	1.49116i	0.0767986	−	0.0767986i
$378$	−0.578224	+	7.97324i	−0.0297406	+	0.410099i
$379$			13.4167i			0.689172i	0.938755	+	0.344586i	$0.111981\pi$
$379$			13.4167i			0.689172i	−0.938755	+	0.344586i	$0.888019\pi$
$380$	5.56680	−	31.5630i	0.285571	−	1.61915i
$381$		−	2.03757i		−	0.104388i
$382$	7.22072	+	0.523650i	0.369444	+	0.0267923i
$383$	−8.01467	+	8.01467i	−0.409531	+	0.409531i	−0.881575	−	0.472044i	$-0.843516\pi$
$383$	−8.01467	+	8.01467i	−0.409531	+	0.409531i	0.472044	+	0.881575i	$0.343516\pi$
$384$	−15.0428	+	4.30352i	−0.767652	+	0.219613i
$385$	0.291338	+	0.309233i	0.0148480	+	0.0157600i
$386$	−6.43170	+	5.56192i	−0.327365	+	0.283094i
$387$	−2.25906	+	2.25906i	−0.114834	+	0.114834i
$388$	−0.143467	+	0.106954i	−0.00728345	+	0.00542976i
$389$	−2.27653			−0.115425			−0.0577124	−	0.998333i	$-0.518381\pi$
$389$	−2.27653			−0.115425			−0.0577124	+	0.998333i	$0.518381\pi$
$390$	2.41687	−	23.5703i	0.122383	−	1.19353i
$391$		−	16.9958i		−	0.859515i
$392$	2.76198	+	0.609464i	0.139501	+	0.0307826i
$393$	4.35201	+	4.35201i	0.219530	+	0.219530i
$394$	20.6459	−	17.8539i	1.04013	−	0.899466i
$395$	21.9343	+	0.653570i	1.10364	+	0.0328847i
$396$	0.0596219	−	0.408908i	0.00299612	−	0.0205484i
$397$	−16.0025	−	16.0025i	−0.803141	−	0.803141i	0.180444	−	0.983585i	$-0.442246\pi$
$397$	−16.0025	−	16.0025i	−0.803141	−	0.803141i	−0.983585	+	0.180444i	$0.942246\pi$
$398$	0.556399	−	7.67230i	0.0278898	−	0.384577i
$399$	−9.91112			−0.496177
$400$	18.7933	+	6.84200i	0.939664	+	0.342100i
$401$	25.0082			1.24885			0.624424	−	0.781085i	$-0.285334\pi$
$401$	25.0082			1.24885			0.624424	+	0.781085i	$0.285334\pi$
$402$	1.57836	−	21.7644i	0.0787216	−	1.08551i
$403$	−21.4228	−	21.4228i	−1.06715	−	1.06715i
$404$	2.38489	−	16.3564i	0.118653	−	0.813759i
$405$	10.1811	+	0.303362i	0.505902	+	0.0150742i
$406$	0.416367	−	0.360060i	0.0206639	−	0.0178695i
$407$	−0.153397	−	0.153397i	−0.00760363	−	0.00760363i
$408$	−1.98360	+	8.98931i	−0.0982027	+	0.445037i
$409$			33.9619i			1.67931i	0.543122	+	0.839654i	$0.317242\pi$
$409$			33.9619i			1.67931i	−0.543122	+	0.839654i	$0.682758\pi$
$410$	3.15325	−	30.7518i	0.155728	−	1.51872i
$411$	1.11678			0.0550866
$412$	9.12273	−	6.80093i	0.449445	−	0.335058i
$413$	2.49840	−	2.49840i	0.122938	−	0.122938i
$414$	8.40072	−	7.26466i	0.412873	−	0.357039i
$415$	−1.32044	−	1.40154i	−0.0648177	−	0.0687990i
$416$	12.5930	+	27.9415i	0.617422	+	1.36994i
$417$	6.08800	−	6.08800i	0.298130	−	0.298130i
$418$	1.92065	+	0.139287i	0.0939422	+	0.00681273i
$419$		−	19.1122i		−	0.933690i	−0.884339	−	0.466845i	$-0.845391\pi$
$419$		−	19.1122i		−	0.933690i	0.884339	−	0.466845i	$-0.154609\pi$
$420$	1.07423	−	6.09075i	0.0524170	−	0.297198i
$421$			3.35409i			0.163468i	0.996654	+	0.0817341i	$0.0260458\pi$
$421$			3.35409i			0.163468i	−0.996654	+	0.0817341i	$0.973954\pi$
$422$	−1.98283	+	27.3417i	−0.0965227	+	1.33097i
$423$	−3.15466	+	3.15466i	−0.153385	+	0.153385i
$424$	8.34935	+	13.0774i	0.405480	+	0.635095i
$425$	8.80122	−	7.81040i	0.426922	−	0.378860i
$426$	1.85190	+	2.14150i	0.0897248	+	0.103756i
$427$	7.63602	−	7.63602i	0.369533	−	0.369533i
$428$	26.6893	−	19.8967i	1.29008	−	0.961743i
$429$	1.42362			0.0687330
$430$	7.20516	−	5.86497i	0.347464	−	0.282834i
$431$		−	30.2273i		−	1.45600i	−0.685579	−	0.727998i	$-0.740451\pi$
$431$		−	30.2273i		−	1.45600i	0.685579	−	0.727998i	$-0.259549\pi$
$432$	−19.8881	+	10.7573i	−0.956866	+	0.517560i
$433$	−9.18648	−	9.18648i	−0.441474	−	0.441474i	0.451033	−	0.892507i	$-0.351056\pi$
$433$	−9.18648	−	9.18648i	−0.441474	−	0.441474i	−0.892507	+	0.451033i	$0.851056\pi$
$434$	−5.17283	−	5.98177i	−0.248304	−	0.287134i
$435$	−0.825386	−	0.876084i	−0.0395742	−	0.0420050i
$436$	−33.2157	−	4.84311i	−1.59074	−	0.231943i
$437$	36.5969	+	36.5969i	1.75067	+	1.75067i
$438$	−18.5695	−	1.34667i	−0.887283	−	0.0643462i
$439$	−3.23073			−0.154194			−0.0770971	−	0.997024i	$-0.524565\pi$
$439$	−3.23073			−0.154194			−0.0770971	+	0.997024i	$0.524565\pi$
$440$	−0.293769	+	1.16521i	−0.0140049	+	0.0555494i
$441$	1.08744			0.0517830
$442$	17.9847	+	1.30426i	0.855445	+	0.0620373i
$443$	−0.267232	−	0.267232i	−0.0126966	−	0.0126966i	0.700730	−	0.713427i	$-0.252858\pi$
$443$	−0.267232	−	0.267232i	−0.0126966	−	0.0126966i	−0.713427	+	0.700730i	$0.752858\pi$
$444$	−0.455645	+	3.12497i	−0.0216239	+	0.148304i
$445$	−1.07258	+	35.9968i	−0.0508453	+	1.70641i
$446$	−4.47040	−	5.16949i	−0.211680	−	0.244783i
$447$	12.8543	+	12.8543i	0.607989	+	0.607989i
$448$	2.75096	+	7.51214i	0.129971	+	0.354915i
$449$		−	5.60587i		−	0.264558i	−0.991213	−	0.132279i	$-0.957771\pi$
$449$		−	5.60587i		−	0.264558i	0.991213	−	0.132279i	$-0.0422294\pi$
$450$	7.62252	+	1.01182i	0.359329	+	0.0476976i
$451$	1.85737			0.0874602
$452$	−20.3435	−	27.2887i	−0.956880	−	1.28355i
$453$	−6.79584	+	6.79584i	−0.319296	+	0.319296i
$454$	−1.87108	−	2.16368i	−0.0878139	−	0.101546i
$455$	−12.1094	−	0.360819i	−0.567696	−	0.0169154i
$456$	−15.0853	−	23.6279i	−0.706436	−	1.10648i
$457$	22.0740	−	22.0740i	1.03258	−	1.03258i	0.0331292	−	0.999451i	$-0.489453\pi$
$457$	22.0740	−	22.0740i	1.03258	−	1.03258i	0.999451	−	0.0331292i	$-0.0105473\pi$
$458$	−2.54844	+	35.1409i	−0.119081	+	1.64203i
$459$			13.3032i			0.620941i
$460$	−26.4567	+	18.5235i	−1.23355	+	0.863664i
$461$			23.0782i			1.07486i	0.843309	+	0.537429i	$0.180604\pi$
$461$			23.0782i			1.07486i	−0.843309	+	0.537429i	$0.819396\pi$
$462$	0.370630	+	0.0268783i	0.0172433	+	0.00125049i
$463$	11.6894	−	11.6894i	0.543253	−	0.543253i	−0.381228	−	0.924481i	$-0.624499\pi$
$463$	11.6894	−	11.6894i	0.543253	−	0.543253i	0.924481	+	0.381228i	$0.124499\pi$
$464$	1.49211	+	0.444574i	0.0692695	+	0.0206388i
$465$	−12.5863	+	11.8580i	−0.583677	+	0.549900i
$466$	16.1508	−	13.9666i	0.748170	−	0.646992i
$467$	−6.35715	+	6.35715i	−0.294174	+	0.294174i	−0.838727	−	0.544553i	$-0.816699\pi$
$467$	−6.35715	+	6.35715i	−0.294174	+	0.294174i	0.544553	+	0.838727i	$0.316699\pi$
$468$	7.04268	+	9.44701i	0.325548	+	0.436688i
$469$	−11.1574			−0.515201
$470$	10.0616	−	8.19012i	0.464108	−	0.377782i
$471$		−	2.52539i		−	0.116364i
$472$	9.75885	+	2.15340i	0.449187	+	0.0991184i
$473$	0.394710	+	0.394710i	0.0181488	+	0.0181488i
$474$	14.5180	−	12.5547i	0.666833	−	0.576654i
$475$	−2.13352	+	35.7696i	−0.0978928	+	1.64122i
$476$	4.65758	+	0.679111i	0.213480	+	0.0311270i
$477$	4.21805	+	4.21805i	0.193131	+	0.193131i
$478$	1.14819	−	15.8327i	0.0525172	−	0.724170i
$479$	−24.5578			−1.12208			−0.561038	−	0.827790i	$-0.689598\pi$
$479$	−24.5578			−1.12208			−0.561038	+	0.827790i	$0.689598\pi$
$480$	16.1552	−	6.70955i	0.737381	−	0.306248i
$481$	6.18594			0.282054
$482$	−0.0524875	+	0.723761i	−0.00239074	+	0.0329664i
$483$	7.06214	+	7.06214i	0.321338	+	0.321338i
$484$	21.6984	+	3.16379i	0.986289	+	0.143809i
$485$	0.145621	−	0.137194i	0.00661229	−	0.00622965i
$486$	−11.4017	+	9.85981i	−0.517192	+	0.447250i
$487$	25.1500	+	25.1500i	1.13966	+	1.13966i	0.988512	+	0.151144i	$0.0482957\pi$
$487$	25.1500	+	25.1500i	1.13966	+	1.13966i	0.151144	+	0.988512i	$0.451704\pi$
$488$	29.8266	+	6.58158i	1.35018	+	0.297934i
$489$		−	26.5024i		−	1.19848i
$490$	−3.14578	−	0.322565i	−0.142112	−	0.0145720i
$491$	−14.6432			−0.660838			−0.330419	−	0.943834i	$-0.607190\pi$
$491$	−14.6432			−0.660838			−0.330419	+	0.943834i	$0.607190\pi$
$492$	−16.1604	−	21.6774i	−0.728566	−	0.977294i
$493$	0.647728	−	0.647728i	0.0291722	−	0.0291722i
$494$	−41.5347	+	35.9178i	−1.86874	+	1.61602i
$495$	−0.0137601	+	0.461802i	−0.000618472	+	0.0207564i
$496$	6.38701	−	21.4365i	0.286785	−	0.962527i
$497$	1.02360	−	1.02360i	0.0459147	−	0.0459147i
$498$	−1.67981	−	0.121821i	−0.0752742	−	0.00545892i
$499$			27.9633i			1.25181i	0.779899	+	0.625905i	$0.215270\pi$
$499$			27.9633i			1.25181i	−0.779899	+	0.625905i	$0.784730\pi$
$500$	−21.7505	−	5.18806i	−0.972712	−	0.232017i
$501$		−	27.4947i		−	1.22837i
$502$	−0.407292	+	5.61623i	−0.0181783	+	0.250665i
$503$	−1.54942	+	1.54942i	−0.0690854	+	0.0690854i	−0.740805	−	0.671720i	$-0.765556\pi$
$503$	−1.54942	+	1.54942i	−0.0690854	+	0.0690854i	0.671720	+	0.740805i	$0.265556\pi$
$504$	1.65515	+	2.59243i	0.0737264	+	0.115476i
$505$	−0.550407	+	18.4721i	−0.0244928	+	0.821999i
$506$	−1.26931	−	1.46780i	−0.0564275	−	0.0652518i
$507$	−15.9919	+	15.9919i	−0.710226	+	0.710226i
$508$	−1.76119	−	2.36245i	−0.0781403	−	0.104817i
$509$	7.36059			0.326253			0.163126	−	0.986605i	$-0.447842\pi$
$509$	7.36059			0.326253			0.163126	+	0.986605i	$0.447842\pi$
$510$	1.04984	−	10.2384i	0.0464876	−	0.453366i
$511$			9.51954i			0.421120i
$512$	−13.7216	+	17.9922i	−0.606415	+	0.795148i
$513$	−28.6457	−	28.6457i	−1.26474	−	1.26474i
$514$	−8.52491	−	9.85805i	−0.376018	−	0.434820i
$515$	−9.25966	+	8.72381i	−0.408029	+	0.384417i
$516$	1.17243	−	8.04091i	0.0516133	−	0.353981i
$517$	0.551192	+	0.551192i	0.0242414	+	0.0242414i
$518$	1.61047	+	0.116792i	0.0707599	+	0.00513154i
$519$	6.74725			0.296172
$520$	−17.5710	−	29.4176i	−0.770540	−	1.29005i
$521$	22.1558			0.970664			0.485332	−	0.874330i	$-0.338699\pi$
$521$	22.1558			0.970664			0.485332	+	0.874330i	$0.338699\pi$
$522$	0.597024	+	0.0432965i	0.0261310	+	0.00189504i
$523$	−4.03905	−	4.03905i	−0.176616	−	0.176616i	0.613263	−	0.789879i	$-0.289857\pi$
$523$	−4.03905	−	4.03905i	−0.176616	−	0.176616i	−0.789879	+	0.613263i	$0.789857\pi$
$524$	8.80764	+	1.28422i	0.384763	+	0.0561015i
$525$	−0.411708	+	6.90250i	−0.0179684	+	0.301250i
$526$	6.33597	+	7.32680i	0.276262	+	0.319464i
$527$	−9.30563	−	9.30563i	−0.405360	−	0.405360i
$528$	0.500044	+	0.924482i	0.0217616	+	0.0402329i
$529$		−	29.1540i		−	1.26757i
$530$	−10.9509	−	13.4533i	−0.475677	−	0.584373i
$531$	3.84223			0.166739
$532$	−11.4914	+	8.56679i	−0.498217	+	0.371417i
$533$	−37.4504	+	37.4504i	−1.62216	+	1.62216i
$534$	20.6036	+	23.8257i	0.891606	+	1.03104i
$535$	−27.0899	+	25.5222i	−1.17120	+	1.10342i
$536$	−16.9822	−	26.5989i	−0.733521	−	1.14890i
$537$	−15.1509	+	15.1509i	−0.653810	+	0.653810i
$538$	0.601513	−	8.29438i	0.0259331	−	0.357596i
$539$		−	0.190002i		−	0.00818394i
$540$	20.7086	−	14.4990i	0.891157	−	0.623939i
$541$			15.3515i			0.660013i	0.943979	+	0.330007i	$0.107051\pi$
$541$			15.3515i			0.660013i	−0.943979	+	0.330007i	$0.892949\pi$
$542$	−17.0490	−	1.23640i	−0.732316	−	0.0531079i
$543$	−7.07006	+	7.07006i	−0.303405	+	0.303405i
$544$	5.47013	+	12.1372i	0.234530	+	0.520378i
$545$	37.5123	+	1.11774i	1.60685	+	0.0478787i
$546$	−8.01499	+	6.93109i	−0.343010	+	0.296623i
$547$	−30.8931	+	30.8931i	−1.32090	+	1.32090i	−0.407844	+	0.913052i	$0.633719\pi$
$547$	−30.8931	+	30.8931i	−1.32090	+	1.32090i	−0.913052	+	0.407844i	$0.866281\pi$
$548$	1.29485	−	0.965299i	0.0553131	−	0.0412355i
$549$	11.7432			0.501190
$550$	0.176789	−	1.33183i	0.00753829	−	0.0567895i
$551$			2.78949i			0.118836i
$552$	−6.08694	+	27.5849i	−0.259077	+	1.17409i
$553$	−6.93933	−	6.93933i	−0.295090	−	0.295090i
$554$	−1.44719	+	1.25148i	−0.0614853	+	0.0531704i
$555$	0.105158	−	3.52920i	0.00446371	−	0.149806i
$556$	1.79649	−	12.3209i	0.0761882	−	0.522524i
$557$	2.52914	+	2.52914i	0.107163	+	0.107163i	0.758655	−	0.651492i	$-0.225857\pi$
$557$	2.52914	+	2.52914i	0.107163	+	0.107163i	−0.651492	+	0.758655i	$0.725857\pi$
$558$	0.622022	−	8.57719i	0.0263323	−	0.363101i
$559$	−15.9172			−0.673224
$560$	−4.01909	−	7.99043i	−0.169838	−	0.337657i
$561$	0.618390			0.0261084
$562$	1.73741	−	23.9576i	0.0732884	−	1.01059i
$563$	−8.99685	−	8.99685i	−0.379172	−	0.379172i	0.491631	−	0.870803i	$-0.336401\pi$
$563$	−8.99685	−	8.99685i	−0.379172	−	0.379172i	−0.870803	+	0.491631i	$0.836401\pi$
$564$	1.63723	−	11.2287i	0.0689400	−	0.472814i
$565$	26.0954	+	27.6983i	1.09784	+	1.16528i
$566$	11.4053	−	9.86288i	0.479399	−	0.414568i
$567$	−3.22097	−	3.22097i	−0.135268	−	0.135268i
$568$	3.99821	+	0.882253i	0.167761	+	0.0370185i
$569$		−	22.7081i		−	0.951974i	−0.879452	−	0.475987i	$-0.842091\pi$
$569$		−	22.7081i		−	0.951974i	0.879452	−	0.475987i	$-0.157909\pi$
$570$	19.7857	+	24.3070i	0.828734	+	1.01811i
$571$	33.3350			1.39503			0.697514	−	0.716571i	$-0.254290\pi$
$571$	33.3350			1.39503			0.697514	+	0.716571i	$0.254290\pi$
$572$	1.65061	−	1.23052i	0.0690156	−	0.0514506i
$573$	−5.00607	+	5.00607i	−0.209131	+	0.209131i
$574$	−10.4570	+	9.04288i	−0.436468	+	0.377443i
$575$	27.0078	−	23.9673i	1.12630	−	0.999505i
$576$	−3.66105	+	7.89169i	−0.152544	+	0.328820i
$577$	24.8923	−	24.8923i	1.03628	−	1.03628i	0.0369654	−	0.999317i	$-0.488231\pi$
$577$	24.8923	−	24.8923i	1.03628	−	1.03628i	0.999317	−	0.0369654i	$-0.0117691\pi$
$578$	−16.1665	−	1.17240i	−0.672437	−	0.0487655i
$579$		−	8.31508i		−	0.345563i
$580$	−1.71425	−	0.302343i	−0.0711801	−	0.0125541i
$581$			0.861147i			0.0357264i
$582$	0.0126572	−	0.174533i	0.000524659	−	0.00723462i
$583$	0.736991	−	0.736991i	0.0305231	−	0.0305231i
$584$	−22.6943	+	14.4893i	−0.939098	+	0.599572i
$585$	−9.03391	−	9.58880i	−0.373506	−	0.396448i
$586$	−27.7754	−	32.1190i	−1.14739	−	1.32682i
$587$	15.8631	−	15.8631i	0.654739	−	0.654739i	−0.299391	−	0.954130i	$-0.596784\pi$
$587$	15.8631	−	15.8631i	0.654739	−	0.654739i	0.954130	+	0.299391i	$0.0967836\pi$
$588$	−2.21751	+	1.65314i	−0.0914486	+	0.0681744i
$589$	40.0755			1.65128
$590$	−11.1149	−	1.13971i	−0.457594	−	0.0469211i
$591$			26.6916i			1.09795i
$592$	2.17280	+	4.01708i	0.0893016	+	0.165101i
$593$	23.5609	+	23.5609i	0.967529	+	0.967529i	0.999489	−	0.0319602i	$-0.0101750\pi$
$593$	23.5609	+	23.5609i	0.967529	+	0.967529i	−0.0319602	+	0.999489i	$0.510175\pi$
$594$	0.993531	+	1.14890i	0.0407651	+	0.0471400i
$595$	−5.26006	−	0.156732i	−0.215641	−	0.00642538i
$596$	26.0147	+	3.79315i	1.06561	+	0.155374i
$597$	5.31914	+	5.31914i	0.217698	+	0.217698i
$598$	55.1886	+	4.00230i	2.25683	+	0.163666i
$599$	−41.1389			−1.68089			−0.840444	−	0.541898i	$-0.817706\pi$
$599$	−41.1389			−1.68089			−0.840444	+	0.541898i	$0.817706\pi$
$600$	−17.0820	+	9.52452i	−0.697370	+	0.388837i
$601$	27.8723			1.13694			0.568468	−	0.822705i	$-0.307536\pi$
$601$	27.8723			1.13694			0.568468	+	0.822705i	$0.307536\pi$
$602$	−4.14393	−	0.300520i	−0.168894	−	0.0122483i
$603$	−8.57934	−	8.57934i	−0.349378	−	0.349378i
$604$	−2.00537	+	13.7535i	−0.0815972	+	0.559621i
$605$	−24.5051	−	0.730171i	−0.996276	−	0.0296857i
$606$	10.5730	+	12.2264i	0.429498	+	0.496664i
$607$	−26.2644	−	26.2644i	−1.06604	−	1.06604i	−0.997659	−	0.0683798i	$-0.978217\pi$
$607$	−26.2644	−	26.2644i	−1.06604	−	1.06604i	−0.0683798	−	0.997659i	$-0.521783\pi$
$608$	−37.9137	−	14.3561i	−1.53760	−	0.582217i
$609$			0.538291i			0.0218126i
$610$	−33.9712	−	3.48336i	−1.37545	−	0.141037i
$611$	−22.2275			−0.899227
$612$	3.05919	+	4.10358i	0.123661	+	0.165877i
$613$	−1.36058	+	1.36058i	−0.0549533	+	0.0549533i	−0.734049	−	0.679096i	$-0.762372\pi$
$613$	−1.36058	+	1.36058i	−0.0549533	+	0.0549533i	0.679096	+	0.734049i	$0.262372\pi$
$614$	−11.7559	−	13.5943i	−0.474428	−	0.548620i
$615$	20.7295	+	22.0028i	0.835894	+	0.887238i
$616$	0.452959	−	0.289194i	0.0182502	−	0.0116520i
$617$	−31.0294	+	31.0294i	−1.24919	+	1.24919i	−0.293119	+	0.956076i	$0.594693\pi$
$617$	−31.0294	+	31.0294i	−1.24919	+	1.24919i	−0.956076	+	0.293119i	$0.905307\pi$
$618$	−0.804841	+	11.0981i	−0.0323755	+	0.446432i
$619$		−	35.2030i		−	1.41493i	−0.706750	−	0.707463i	$-0.749839\pi$
$619$		−	35.2030i		−	1.41493i	0.706750	−	0.707463i	$-0.250161\pi$
$620$	−4.34363	+	24.6278i	−0.174444	+	0.989077i
$621$			40.8228i			1.63816i
$622$	26.2555	+	1.90406i	1.05275	+	0.0763459i
$623$	11.3882	−	11.3882i	0.456260	−	0.456260i
$624$	−28.7229	−	8.55798i	−1.14983	−	0.342593i
$625$	24.8227	+	2.97174i	0.992910	+	0.118870i
$626$	21.1984	−	18.3317i	0.847259	−	0.732681i
$627$	−1.33157	+	1.33157i	−0.0531779	+	0.0531779i
$628$	−2.18285	−	2.92806i	−0.0871052	−	0.116842i
$629$	2.68704			0.107139
$630$	−2.17088	−	2.66694i	−0.0864899	−	0.106254i
$631$			12.2938i			0.489410i	0.969598	+	0.244705i	$0.0786912\pi$
$631$			12.2938i			0.489410i	−0.969598	+	0.244705i	$0.921309\pi$
$632$	5.98109	−	27.1052i	0.237915	−	1.07819i
$633$	−18.9558	−	18.9558i	−0.753424	−	0.753424i
$634$	29.3011	−	25.3386i	1.16370	−	1.00633i
$635$	2.25915	+	2.39791i	0.0896515	+	0.0951582i
$636$	−15.0138	−	2.18912i	−0.595334	−	0.0868044i
$637$	3.83102	+	3.83102i	0.151790	+	0.151790i
$638$	0.00756491	−	0.104314i	0.000299498	−	0.00412983i
$639$	1.57417			0.0622731
$640$	12.9317	−	21.7433i	0.511169	−	0.859480i
$641$	18.1021			0.714990			0.357495	−	0.933915i	$-0.383631\pi$
$641$	18.1021			0.714990			0.357495	+	0.933915i	$0.383631\pi$
$642$	−2.35463	+	32.4685i	−0.0929299	+	1.28143i
$643$	−5.87658	−	5.87658i	−0.231750	−	0.231750i	0.581673	−	0.813423i	$-0.302398\pi$
$643$	−5.87658	−	5.87658i	−0.231750	−	0.231750i	−0.813423	+	0.581673i	$0.802398\pi$
$644$	14.2924	+	2.08395i	0.563200	+	0.0821190i
$645$	−0.270584	+	9.08104i	−0.0106543	+	0.357566i
$646$	−18.0418	+	15.6020i	−0.709846	+	0.613851i
$647$	−28.7326	−	28.7326i	−1.12959	−	1.12959i	−0.990243	−	0.139351i	$-0.955499\pi$
$647$	−28.7326	−	28.7326i	−1.12959	−	1.12959i	−0.139351	−	0.990243i	$-0.544501\pi$
$648$	2.77619	−	12.5812i	0.109059	−	0.494237i
$649$		−	0.671327i		−	0.0263519i
$650$	23.2892	+	30.4184i	0.913479	+	1.19311i
$651$	7.73339			0.303096
$652$	−22.9076	−	30.7282i	−0.897133	−	1.20341i
$653$	14.0740	−	14.0740i	0.550759	−	0.550759i	−0.375901	−	0.926660i	$-0.622667\pi$
$653$	14.0740	−	14.0740i	0.550759	−	0.550759i	0.926660	+	0.375901i	$0.122667\pi$
$654$	24.8288	−	21.4711i	0.970882	−	0.839586i
$655$	−9.94695	−	0.296386i	−0.388660	−	0.0115807i
$656$	−37.4742	−	11.1655i	−1.46312	−	0.435938i
$657$	−7.31993	+	7.31993i	−0.285578	+	0.285578i
$658$	−5.78678	−	0.419660i	−0.225592	−	0.0163600i
$659$			30.7363i			1.19732i	0.801005	+	0.598658i	$0.204299\pi$
$659$			30.7363i			1.19732i	−0.801005	+	0.598658i	$0.795701\pi$
$660$	−0.673976	−	0.962624i	−0.0262345	−	0.0374701i
$661$		−	15.9721i		−	0.621245i	−0.950533	−	0.310622i	$-0.899463\pi$
$661$		−	15.9721i		−	0.621245i	0.950533	−	0.310622i	$-0.100537\pi$
$662$	0.870039	−	11.9971i	0.0338150	−	0.466282i
$663$	−12.4687	+	12.4687i	−0.484242	+	0.484242i
$664$	−2.05295	+	1.31072i	−0.0796700	+	0.0508658i
$665$	11.6639	−	10.9889i	0.452307	−	0.426133i
$666$	1.14854	+	1.32816i	0.0445052	+	0.0514650i
$667$	1.98764	−	1.98764i	0.0769619	−	0.0769619i
$668$	−23.7654	−	31.8787i	−0.919510	−	1.23342i
$669$	6.68327			0.258390
$670$	22.2737	+	27.3634i	0.860508	+	1.05714i
$671$		−	2.05182i		−	0.0792096i
$672$	−7.31623	−	2.77031i	−0.282230	−	0.106867i
$673$	−10.2352	−	10.2352i	−0.394537	−	0.394537i	0.481764	−	0.876301i	$-0.339996\pi$
$673$	−10.2352	−	10.2352i	−0.394537	−	0.394537i	−0.876301	+	0.481764i	$0.839996\pi$
$674$	30.4054	+	35.1603i	1.17117	+	1.35432i
$675$	−21.1399	+	18.7601i	−0.813676	+	0.722075i
$676$	−4.71901	+	32.3646i	−0.181501	+	1.24479i
$677$	−19.7505	−	19.7505i	−0.759073	−	0.759073i	0.217081	−	0.976154i	$-0.430346\pi$
$677$	−19.7505	−	19.7505i	−0.759073	−	0.759073i	−0.976154	+	0.217081i	$0.930346\pi$
$678$	33.1976	+	2.40751i	1.27495	+	0.0924599i
$679$	−0.0894735			−0.00343368
$680$	−7.63248	−	12.7784i	−0.292692	−	0.490029i
$681$	2.79726			0.107191
$682$	−1.49864	−	0.108682i	−0.0573857	−	0.00416164i
$683$	−25.8382	−	25.8382i	−0.988672	−	0.988672i	0.0112646	−	0.999937i	$-0.496414\pi$
$683$	−25.8382	−	25.8382i	−0.988672	−	0.988672i	−0.999937	+	0.0112646i	$0.996414\pi$
$684$	−15.4235	−	2.24887i	−0.589733	−	0.0859878i
$685$	−1.31428	+	1.23823i	−0.0502161	+	0.0473101i
$686$	0.925050	+	1.06971i	0.0353186	+	0.0408418i
$687$	−24.3629	−	24.3629i	−0.929504	−	0.929504i
$688$	−5.59088	−	10.3364i	−0.213150	−	0.394072i
$689$			29.7201i			1.13224i
$690$	3.22157	−	31.4181i	0.122643	−	1.19607i
$691$	−2.86884			−0.109136			−0.0545680	−	0.998510i	$-0.517378\pi$
$691$	−2.86884			−0.109136			−0.0545680	+	0.998510i	$0.517378\pi$
$692$	7.82309	−	5.83206i	0.297389	−	0.221702i
$693$	0.146099	−	0.146099i	0.00554986	−	0.00554986i
$694$	−13.8162	−	15.9769i	−0.524457	−	0.606473i
$695$	−0.414612	+	13.9147i	−0.0157271	+	0.527815i
$696$	−1.28327	+	0.819312i	−0.0486423	+	0.0310559i
$697$	−16.2676	+	16.2676i	−0.616181	+	0.616181i
$698$	1.22444	−	16.8840i	0.0463456	−	0.639069i
$699$			20.8802i			0.789761i
$700$	5.48889	+	8.35895i	0.207461	+	0.315939i
$701$			12.7081i			0.479978i	0.970776	+	0.239989i	$0.0771438\pi$
$701$			12.7081i			0.479978i	−0.970776	+	0.239989i	$0.922856\pi$
$702$	−43.1981	−	3.13275i	−1.63041	−	0.118238i
$703$	−5.78598	+	5.78598i	−0.218222	+	0.218222i
$704$	1.37886	+	0.639670i	0.0519678	+	0.0241085i
$705$	−0.377857	+	12.6812i	−0.0142309	+	0.477602i
$706$	−21.0021	+	18.1619i	−0.790423	+	0.683531i
$707$	5.84399	−	5.84399i	0.219786	−	0.219786i
$708$	−7.83508	+	5.84100i	−0.294460	+	0.219518i
$709$	−37.1155			−1.39390			−0.696951	−	0.717118i	$-0.745461\pi$
$709$	−37.1155			−1.39390			−0.696951	+	0.717118i	$0.745461\pi$
$710$	−4.55380	−	0.466941i	−0.170901	−	0.0175240i
$711$		−	10.6718i		−	0.400225i
$712$	44.4828	+	9.81565i	1.66706	+	0.367857i
$713$	−28.5556	−	28.5556i	−1.06942	−	1.06942i
$714$	−3.48154	+	3.01072i	−0.130294	+	0.112673i
$715$	−1.67539	+	1.57843i	−0.0626559	+	0.0590301i
$716$	−4.47084	+	30.6625i	−0.167083	+	1.14591i
$717$	10.9767	+	10.9767i	0.409931	+	0.409931i
$718$	−2.40054	+	33.1015i	−0.0895872	+	1.23534i
$719$	46.7100			1.74199			0.870995	−	0.491292i	$-0.163475\pi$
$719$	46.7100			1.74199			0.870995	+	0.491292i	$0.163475\pi$
$720$	3.05371	−	9.23457i	0.113805	−	0.344152i
$721$	5.68939			0.211884
$722$	3.31021	−	45.6451i	0.123193	−	1.69874i
$723$	−0.501778	−	0.501778i	−0.0186613	−	0.0186613i
$724$	−2.08628	+	14.3085i	−0.0775362	+	0.531769i
$725$	1.94271	+	0.115875i	0.0721505	+	0.00430351i
$726$	−16.2196	+	14.0261i	−0.601964	+	0.520558i
$727$	−6.77143	−	6.77143i	−0.251138	−	0.251138i	0.570299	−	0.821437i	$-0.306827\pi$
$727$	−6.77143	−	6.77143i	−0.251138	−	0.251138i	−0.821437	+	0.570299i	$0.806827\pi$
$728$	−3.30200	+	14.9641i	−0.122380	+	0.554606i
$729$		−	28.4059i		−	1.05207i
$730$	23.3466	−	19.0040i	0.864096	−	0.703370i
$731$	−6.91408			−0.255726
$732$	−23.9468	+	17.8522i	−0.885100	+	0.659836i
$733$	23.0830	−	23.0830i	0.852590	−	0.852590i	−0.137862	−	0.990451i	$-0.544023\pi$
$733$	23.0830	−	23.0830i	0.852590	−	0.852590i	0.990451	+	0.137862i	$0.0440229\pi$
$734$	−11.2587	+	9.73614i	−0.415566	+	0.359367i
$735$	2.25080	−	2.12054i	0.0830218	−	0.0782175i
$736$	16.7859	+	37.2446i	0.618735	+	1.37286i
$737$	−1.49901	+	1.49901i	−0.0552168	+	0.0552168i
$738$	−14.9942	−	1.08739i	−0.551945	−	0.0400273i
$739$			25.7840i			0.948479i	0.880396	+	0.474240i	$0.157277\pi$
$739$			25.7840i			0.948479i	−0.880396	+	0.474240i	$0.842723\pi$
$740$	−2.92857	−	4.18281i	−0.107657	−	0.153763i
$741$		−	53.6973i		−	1.97262i
$742$	−0.561122	+	7.73742i	−0.0205994	+	0.284050i
$743$	5.02261	−	5.02261i	0.184262	−	0.184262i	−0.608948	−	0.793210i	$-0.708408\pi$
$743$	5.02261	−	5.02261i	0.184262	−	0.184262i	0.793210	+	0.608948i	$0.208408\pi$
$744$	11.7707	+	18.4362i	0.431535	+	0.675904i
$745$	−29.3799	−	0.875421i	−1.07640	−	0.0320730i
$746$	20.1687	+	23.3227i	0.738429	+	0.853905i
$747$	−0.662169	+	0.662169i	−0.0242275	+	0.0242275i
$748$	0.716991	−	0.534512i	0.0262158	−	0.0195437i
$749$	16.6448			0.608188
$750$	17.7502	−	12.7699i	0.648146	−	0.466289i
$751$		−	21.8883i		−	0.798714i	−0.916795	−	0.399357i	$-0.869233\pi$
$751$		−	21.8883i		−	0.798714i	0.916795	−	0.399357i	$-0.130767\pi$
$752$	−7.80737	−	14.4343i	−0.284705	−	0.526364i
$753$	−3.89369	−	3.89369i	−0.141894	−	0.141894i
$754$	1.95076	+	2.25583i	0.0710426	+	0.0821523i
$755$	0.462818	−	15.5326i	0.0168437	−	0.565288i
$756$	−11.1872	−	1.63118i	−0.406874	−	0.0593254i
$757$	−25.7512	−	25.7512i	−0.935944	−	0.935944i	0.0621241	−	0.998068i	$-0.480213\pi$
$757$	−25.7512	−	25.7512i	−0.935944	−	0.935944i	−0.998068	+	0.0621241i	$0.980213\pi$
$758$	−18.9244	−	1.37241i	−0.687367	−	0.0498482i
$759$	1.89762			0.0688791
$760$	43.9505	+	11.0806i	1.59425	+	0.401937i
$761$	41.0284			1.48728			0.743639	−	0.668581i	$-0.233098\pi$
$761$	41.0284			1.48728			0.743639	+	0.668581i	$0.233098\pi$
$762$	2.87400	+	0.208424i	0.104114	+	0.00755042i
$763$	−11.8677	−	11.8677i	−0.429639	−	0.429639i
$764$	−1.47723	+	10.1313i	−0.0534442	+	0.366538i
$765$	−3.92414	−	4.16517i	−0.141878	−	0.150592i
$766$	−10.4849	−	12.1246i	−0.378836	−	0.438079i
$767$	13.5360	+	13.5360i	0.488758	+	0.488758i
$768$	−4.53141	−	21.6583i	−0.163513	−	0.781526i
$769$			2.58142i			0.0930883i	0.998916	+	0.0465441i	$0.0148208\pi$
$769$			2.58142i			0.0930883i	−0.998916	+	0.0465441i	$0.985179\pi$
$770$	−0.465977	+	0.379303i	−0.0167927	+	0.0136691i
$771$	12.7448			0.458991
$772$	−7.18723	−	9.64090i	−0.258674	−	0.346984i
$773$	18.9207	−	18.9207i	0.680532	−	0.680532i	−0.279588	−	0.960120i	$-0.590198\pi$
$773$	18.9207	−	18.9207i	0.680532	−	0.680532i	0.960120	+	0.279588i	$0.0901979\pi$
$774$	−2.95534	−	3.41750i	−0.106228	−	0.122840i
$775$	1.66473	−	27.9101i	0.0597990	−	1.00256i
$776$	−0.136184	−	0.213302i	−0.00488872	−	0.00765711i
$777$	−1.11652	+	1.11652i	−0.0400551	+	0.0400551i
$778$	0.232869	−	3.21107i	0.00834874	−	0.115123i
$779$		−	70.0579i		−	2.51009i
$780$	32.9989	+	5.82005i	1.18155	+	0.208391i
$781$		−	0.275044i		−	0.00984185i
$782$	23.9728	+	1.73852i	0.857264	+	0.0621692i
$783$	−1.55580	+	1.55580i	−0.0555997	+	0.0555997i
$784$	−1.14218	+	3.83346i	−0.0407922	+	0.136909i
$785$	2.80002	+	2.97201i	0.0999371	+	0.106076i
$786$	−6.58372	+	5.69338i	−0.234834	+	0.203076i
$787$	−4.86216	+	4.86216i	−0.173317	+	0.173317i	−0.788435	−	0.615118i	$-0.789108\pi$
$787$	−4.86216	+	4.86216i	−0.173317	+	0.173317i	0.615118	+	0.788435i	$0.289108\pi$
$788$	23.0712	+	30.9476i	0.821878	+	1.10246i
$789$	−9.47230			−0.337223
$790$	−3.16555	+	30.8717i	−0.112625	+	1.09837i
$791$		−	17.0186i		−	0.605112i
$792$	0.570669	+	0.125925i	0.0202778	+	0.00447454i
$793$	41.3710	+	41.3710i	1.46913	+	1.46913i
$794$	24.2085	−	20.9347i	0.859129	−	0.742946i
$795$	16.9559	+	0.505228i	0.601363	+	0.0179186i
$796$	10.7649	+	1.56961i	0.381553	+	0.0556334i
$797$	−5.82096	−	5.82096i	−0.206189	−	0.206189i	0.596457	−	0.802645i	$-0.296575\pi$
$797$	−5.82096	−	5.82096i	−0.206189	−	0.206189i	−0.802645	+	0.596457i	$0.796575\pi$
$798$	1.01382	−	13.9797i	0.0358887	−	0.494877i
$799$	−9.65514			−0.341574
$800$	−11.5731	+	25.8082i	−0.409170	+	0.912458i
$801$	17.5137			0.618815
$802$	−2.55811	+	35.2743i	−0.0903299	+	1.24558i
$803$	1.27896	+	1.27896i	0.0451336	+	0.0451336i
$804$	30.5374	+	4.45259i	1.07697	+	0.157031i
$805$	−16.1412	−	0.480954i	−0.568903	−	0.0169514i
$806$	32.4085	−	28.0258i	1.14154	−	0.987165i
$807$	5.75043	+	5.75043i	0.202425	+	0.202425i
$808$	22.8268	+	5.03701i	0.803046	+	0.177201i
$809$		−	0.720009i		−	0.0253142i	−0.999920	−	0.0126571i	$-0.995971\pi$
$809$		−	0.720009i		−	0.0253142i	0.999920	−	0.0126571i	$-0.00402898\pi$
$810$	−1.46933	+	14.3295i	−0.0516269	+	0.503487i
$811$	46.2131			1.62276			0.811381	−	0.584517i	$-0.198716\pi$
$811$	46.2131			1.62276			0.811381	+	0.584517i	$0.198716\pi$
$812$	0.465278	+	0.624120i	0.0163280	+	0.0219023i
$813$	11.8199	−	11.8199i	0.414542	−	0.414542i
$814$	0.232060	−	0.200677i	0.00813369	−	0.00703374i
$815$	29.3845	+	31.1894i	1.02929	+	1.09252i
$816$	−12.4766	−	3.71741i	−0.436769	−	0.130135i
$817$	14.8880	−	14.8880i	0.520866	−	0.520866i
$818$	−47.9036	−	3.47399i	−1.67491	−	0.121465i
$819$			5.89163i			0.205870i
$820$	43.0531	+	7.59332i	1.50348	+	0.265170i
$821$			4.68294i			0.163436i	0.996655	+	0.0817179i	$0.0260407\pi$
$821$			4.68294i			0.163436i	−0.996655	+	0.0817179i	$0.973959\pi$
$822$	−0.114236	+	1.57523i	−0.00398444	+	0.0549423i
$823$	27.5402	−	27.5402i	0.959990	−	0.959990i	−0.0392395	−	0.999230i	$-0.512494\pi$
$823$	27.5402	−	27.5402i	0.959990	−	0.959990i	0.999230	+	0.0392395i	$0.0124935\pi$
$824$	8.65961	+	13.5634i	0.301672	+	0.472502i
$825$	0.872046	+	0.982673i	0.0303607	+	0.0342123i
$826$	3.26846	+	3.77958i	0.113724	+	0.131509i
$827$	−29.9928	+	29.9928i	−1.04295	+	1.04295i	−0.0439155	+	0.999035i	$0.513983\pi$
$827$	−29.9928	+	29.9928i	−1.04295	+	1.04295i	−0.999035	+	0.0439155i	$0.986017\pi$
$828$	9.38755	+	12.5924i	0.326240	+	0.437616i
$829$	−38.3026			−1.33030			−0.665152	−	0.746708i	$-0.731633\pi$
$829$	−38.3026			−1.33030			−0.665152	+	0.746708i	$0.731633\pi$
$830$	2.11196	−	1.71912i	0.0733071	−	0.0596716i
$831$		−	1.87097i		−	0.0649032i
$832$	−40.6999	+	14.9044i	−1.41101	+	0.516716i
$833$	1.66411	+	1.66411i	0.0576581	+	0.0576581i
$834$	7.96443	+	9.20992i	0.275786	+	0.318913i
$835$	30.4847	+	32.3572i	1.05497	+	1.11977i
$836$	−0.392930	+	2.69485i	−0.0135898	+	0.0932033i
$837$	22.3515	+	22.3515i	0.772581	+	0.772581i
$838$	26.9579	+	1.95500i	0.931244	+	0.0675343i
$839$	27.0712			0.934603			0.467301	−	0.884098i	$-0.345226\pi$
$839$	27.0712			0.934603			0.467301	+	0.884098i	$0.345226\pi$
$840$	8.48117	+	2.13824i	0.292628	+	0.0737762i
$841$	−28.8485			−0.994776
$842$	−4.73097	−	0.343093i	−0.163040	−	0.0118238i
$843$	16.6096	+	16.6096i	0.572064	+	0.572064i
$844$	−38.3628	−	5.59360i	−1.32050	−	0.192540i
$845$	1.08910	−	36.5511i	0.0374662	−	1.25740i
$846$	−4.12698	−	4.77236i	−0.141888	−	0.164077i
$847$	7.75265	+	7.75265i	0.266384	+	0.266384i
$848$	−19.2999	+	10.4391i	−0.662760	+	0.358481i
$849$			14.7450i			0.506048i
$850$	10.1164	+	13.2131i	0.346988	+	0.453207i
$851$	8.24556			0.282654
$852$	−3.21004	+	2.39307i	−0.109974	+	0.0819851i
$853$	5.58882	−	5.58882i	0.191357	−	0.191357i	−0.604925	−	0.796282i	$-0.706797\pi$
$853$	5.58882	−	5.58882i	0.191357	−	0.191357i	0.796282	+	0.604925i	$0.206797\pi$
$854$	9.98958	+	11.5518i	0.341836	+	0.395293i
$855$	17.4186	+	0.519017i	0.595705	+	0.0177500i
$856$	25.3344	+	39.6808i	0.865912	+	1.35626i
$857$	−33.5432	+	33.5432i	−1.14581	+	1.14581i	−0.158446	+	0.987368i	$0.550648\pi$
$857$	−33.5432	+	33.5432i	−1.14581	+	1.14581i	−0.987368	+	0.158446i	$0.949352\pi$
$858$	−0.145623	+	2.00803i	−0.00497149	+	0.0685529i
$859$			27.1224i			0.925406i	0.886513	+	0.462703i	$0.153120\pi$
$859$			27.1224i			0.925406i	−0.886513	+	0.462703i	$0.846880\pi$
$860$	7.53557	+	10.7629i	0.256961	+	0.367011i
$861$		−	13.5191i		−	0.460731i
$862$	42.6358	+	3.09197i	1.45218	+	0.105313i
$863$	−3.11723	+	3.11723i	−0.106112	+	0.106112i	−0.758169	−	0.652058i	$-0.773906\pi$
$863$	−3.11723	+	3.11723i	−0.106112	+	0.106112i	0.652058	+	0.758169i	$0.273906\pi$
$864$	−13.1389	−	29.1527i	−0.446994	−	0.991795i
$865$	−7.94051	+	7.48100i	−0.269986	+	0.254362i
$866$	13.8973	−	12.0179i	0.472250	−	0.408386i
$867$	11.2081	−	11.2081i	0.380647	−	0.380647i
$868$	8.96647	−	6.68444i	0.304342	−	0.226885i
$869$	−1.86462			−0.0632528
$870$	1.32015	−	1.07460i	0.0447574	−	0.0364323i
$871$		−	60.4494i		−	2.04825i
$872$	10.2289	−	46.3556i	0.346395	−	1.56980i
$873$	−0.0687995	−	0.0687995i	−0.00232851	−	0.00232851i
$874$	−55.3638	+	47.8768i	−1.87271	+	1.61946i
$875$	−7.16861	−	8.57969i	−0.242343	−	0.290046i
$876$	3.79897	−	26.0546i	0.128355	−	0.880305i
$877$	9.88679	+	9.88679i	0.333853	+	0.333853i	0.854048	−	0.520195i	$-0.174141\pi$
$877$	9.88679	+	9.88679i	0.333853	+	0.333853i	−0.520195	+	0.854048i	$0.674141\pi$
$878$	0.330474	−	4.55697i	0.0111529	−	0.153790i
$879$	41.5244			1.40058
$880$	−1.61349	−	0.533555i	−0.0543909	−	0.0179861i
$881$	−43.8445			−1.47716			−0.738579	−	0.674167i	$-0.764503\pi$
$881$	−43.8445			−1.47716			−0.738579	+	0.674167i	$0.764503\pi$
$882$	−0.111235	+	1.53385i	−0.00374549	+	0.0516473i
$883$	−41.4767	−	41.4767i	−1.39580	−	1.39580i	−0.811626	−	0.584177i	$-0.801417\pi$
$883$	−41.4767	−	41.4767i	−1.39580	−	1.39580i	−0.584177	−	0.811626i	$-0.698583\pi$
$884$	−3.67934	+	25.2342i	−0.123750	+	0.848717i
$885$	7.95268	−	7.49246i	0.267326	−	0.251856i
$886$	0.404269	−	0.349598i	0.0135817	−	0.0117450i
$887$	5.54879	+	5.54879i	0.186310	+	0.186310i	0.794099	−	0.607789i	$-0.207943\pi$
$887$	5.54879	+	5.54879i	0.186310	+	0.186310i	−0.607789	+	0.794099i	$0.707943\pi$
$888$	−4.36119	−	0.962346i	−0.146352	−	0.0322942i
$889$		−	1.47334i		−	0.0494144i
$890$	−50.6640	−	5.19503i	−1.69826	−	0.174138i
$891$	−0.865484			−0.0289948
$892$	7.74890	−	5.77675i	0.259452	−	0.193420i
$893$	20.7903	−	20.7903i	0.695722	−	0.695722i
$894$	−19.4460	+	16.8163i	−0.650373	+	0.562421i
$895$	1.03182	−	34.6289i	0.0344901	−	1.15752i
$896$	−10.8773	+	3.11184i	−0.363386	+	0.103959i
$897$	−38.2618	+	38.2618i	−1.27752	+	1.27752i
$898$	7.90714	+	0.573430i	0.263865	+	0.0191356i
$899$		−	2.17657i		−	0.0725927i
$900$	−2.20690	+	10.6481i	−0.0735632	+	0.354938i
$901$			12.9098i			0.430087i
$902$	−0.189992	+	2.61984i	−0.00632605	+	0.0872311i
$903$	2.87295	−	2.87295i	0.0956059	−	0.0956059i
$904$	40.5719	−	25.9034i	1.34940	−	0.861533i
$905$	0.481493	−	16.1593i	0.0160054	−	0.537154i
$906$	−8.89044	−	10.2807i	−0.295365	−	0.341555i
$907$	25.6230	−	25.6230i	0.850799	−	0.850799i	−0.139433	−	0.990232i	$-0.544528\pi$
$907$	25.6230	−	25.6230i	0.850799	−	0.850799i	0.990232	+	0.139433i	$0.0445279\pi$
$908$	3.24328	−	2.41785i	0.107632	−	0.0802390i
$909$	8.98734			0.298091
$910$	1.74762	−	17.0435i	0.0579329	−	0.564986i
$911$			11.3318i			0.375440i	0.982223	+	0.187720i	$0.0601098\pi$
$911$			11.3318i			0.375440i	−0.982223	+	0.187720i	$0.939890\pi$
$912$	34.8704	−	18.8611i	1.15467	−	0.624553i
$913$	0.115696	+	0.115696i	0.00382899	+	0.00382899i
$914$	28.8777	+	33.3936i	0.955189	+	1.10456i
$915$	24.3063	−	22.8997i	0.803540	−	0.757040i
$916$	−49.3060	−	7.18920i	−1.62911	−	0.237538i
$917$	3.14690	+	3.14690i	0.103920	+	0.103920i
$918$	−18.7643	−	1.36080i	−0.619315	−	0.0449130i
$919$	8.51161			0.280772			0.140386	−	0.990097i	$-0.455166\pi$
$919$	8.51161			0.280772			0.140386	+	0.990097i	$0.455166\pi$
$920$	−23.4213	−	39.2123i	−0.772178	−	1.29279i
$921$	17.5750			0.579117
$922$	−32.5520	−	2.36069i	−1.07204	−	0.0777451i
$923$	5.54574	+	5.54574i	0.182540	+	0.182540i
$924$	−0.0758241	+	0.520027i	−0.00249443	+	0.0171076i
$925$	3.78923	+	4.26993i	0.124589	+	0.140394i
$926$	15.2923	+	17.6837i	0.502536	+	0.581124i
$927$	4.37479	+	4.37479i	0.143687	+	0.143687i
$928$	−0.779705	+	2.05916i	−0.0255951	+	0.0675952i
$929$		−	38.7826i		−	1.27241i	−0.771518	−	0.636207i	$-0.780502\pi$
$929$		−	38.7826i		−	1.27241i	0.771518	−	0.636207i	$-0.219498\pi$
$930$	−15.4383	−	18.9661i	−0.506242	−	0.621923i
$931$	−7.16664			−0.234877
$932$	18.0480	+	24.2095i	0.591182	+	0.793008i
$933$	−18.2027	+	18.2027i	−0.595930	+	0.595930i
$934$	−8.31654	−	9.61709i	−0.272125	−	0.314681i
$935$	−0.727753	+	0.685639i	−0.0238001	+	0.0224228i
$936$	−14.0455	+	8.96742i	−0.459091	+	0.293109i
$937$	−20.7441	+	20.7441i	−0.677681	+	0.677681i	−0.959475	−	0.281794i	$-0.909071\pi$
$937$	−20.7441	+	20.7441i	−0.677681	+	0.677681i	0.281794	+	0.959475i	$0.409071\pi$
$938$	1.14130	−	15.7376i	0.0372648	−	0.513851i
$939$			27.4059i			0.894358i
$940$	10.5230	+	15.0298i	0.343223	+	0.490218i
$941$		−	2.61287i		−	0.0851773i	−0.999093	−	0.0425886i	$-0.986440\pi$
$941$		−	2.61287i		−	0.0851773i	0.999093	−	0.0425886i	$-0.0135605\pi$
$942$	3.56209	+	0.258325i	0.116059	+	0.00841667i
$943$	−49.9195	+	49.9195i	−1.62560	+	1.62560i
$944$	−4.03564	+	13.5447i	−0.131349	+	0.440841i
$945$	12.6343	+	0.376460i	0.410994	+	0.0122462i
$946$	−0.597117	+	0.516367i	−0.0194140	+	0.0167885i
$947$	5.45319	−	5.45319i	0.177205	−	0.177205i	−0.612931	−	0.790136i	$-0.710010\pi$
$947$	5.45319	−	5.45319i	0.177205	−	0.177205i	0.790136	+	0.612931i	$0.210010\pi$
$948$	16.2234	+	21.7620i	0.526912	+	0.706796i
$949$	−51.5757			−1.67422
$950$	−50.2352	−	6.66826i	−1.62984	−	0.216347i
$951$			37.8813i			1.22839i
$952$	−1.43432	+	6.50009i	−0.0464866	+	0.210669i
$953$	20.7601	+	20.7601i	0.672486	+	0.672486i	0.958289	−	0.285802i	$-0.0922601\pi$
$953$	20.7601	+	20.7601i	0.672486	+	0.672486i	−0.285802	+	0.958289i	$0.592260\pi$
$954$	−6.38107	+	5.51813i	−0.206595	+	0.178656i
$955$	0.340929	−	11.4419i	0.0110322	−	0.370250i
$956$	22.2147	+	3.23908i	0.718474	+	0.104759i
$957$	0.0723201	+	0.0723201i	0.00233778	+	0.00233778i
$958$	2.51204	−	34.6391i	0.0811604	−	1.11914i
$959$	0.807532			0.0260766
$960$	7.81136	+	23.4734i	0.252110	+	0.757601i
$961$	−0.269842			−0.00870458
$962$	−0.632765	+	8.72532i	−0.0204012	+	0.281316i
$963$	12.7988	+	12.7988i	0.412436	+	0.412436i
$964$	−1.01550	−	0.148068i	−0.0327072	−	0.00476896i
$965$	9.21933	+	9.78561i	0.296781	+	0.315010i
$966$	−10.6836	+	9.23882i	−0.343739	+	0.297254i
$967$	4.00389	+	4.00389i	0.128756	+	0.128756i	0.768548	−	0.639792i	$-0.220979\pi$
$967$	4.00389	+	4.00389i	0.128756	+	0.128756i	−0.639792	+	0.768548i	$0.720979\pi$
$968$	−6.68210	+	30.2821i	−0.214771	+	0.973304i
$969$		−	23.3250i		−	0.749306i
$970$	0.178617	+	0.219433i	0.00573506	+	0.00704557i
$971$	11.6636			0.374304			0.187152	−	0.982331i	$-0.440074\pi$
$971$	11.6636			0.374304			0.187152	+	0.982331i	$0.440074\pi$
$972$	−12.7411	−	17.0908i	−0.408670	−	0.548187i
$973$	4.40217	−	4.40217i	0.141127	−	0.141127i
$974$	−38.0469	+	32.9017i	−1.21910	+	1.05424i
$975$	−37.3969	−	2.23058i	−1.19766	−	0.0714358i
$976$	−12.3344	+	41.3974i	−0.394813	+	1.32510i
$977$	−11.3339	+	11.3339i	−0.362605	+	0.362605i	−0.864771	−	0.502166i	$-0.832537\pi$
$977$	−11.3339	+	11.3339i	−0.362605	+	0.362605i	0.502166	+	0.864771i	$0.332537\pi$
$978$	37.3819	+	2.71095i	1.19534	+	0.0866868i
$979$		−	3.06005i		−	0.0977995i
$980$	0.776765	−	4.40416i	0.0248129	−	0.140686i
$981$		−	18.2510i		−	0.582711i
$982$	1.49787	−	20.6544i	0.0477988	−	0.659107i
$983$	23.8269	−	23.8269i	0.759959	−	0.759959i	−0.216356	−	0.976315i	$-0.569417\pi$
$983$	23.8269	−	23.8269i	0.759959	−	0.759959i	0.976315	+	0.216356i	$0.0694172\pi$
$984$	32.2293	−	20.5770i	1.02743	−	0.655969i
$985$	−29.5943	−	31.4121i	−0.942952	−	1.00087i
$986$	0.847370	+	0.979883i	0.0269858	+	0.0312058i
$987$	4.01193	−	4.01193i	0.127701	−	0.127701i
$988$	−46.4138	−	62.2592i	−1.47662	−	1.98073i
$989$	−21.2168			−0.674655
$990$	−0.649968	−	0.0666469i	−0.0206573	−	0.00211818i
$991$			32.7816i			1.04134i	0.853757	+	0.520671i	$0.174318\pi$
$991$			32.7816i			1.04134i	−0.853757	+	0.520671i	$0.825682\pi$
$992$	29.5831	+	11.2017i	0.939263	+	0.355654i
$993$	8.31752	+	8.31752i	0.263949	+	0.263949i
$994$	1.33909	+	1.54850i	0.0424734	+	0.0491155i
$995$	−12.1574	−	0.362250i	−0.385416	−	0.0114841i
$996$	0.343659	−	2.35693i	0.0108892	−	0.0746822i
$997$	24.7684	+	24.7684i	0.784424	+	0.784424i	0.980574	−	0.196150i	$-0.0628439\pi$
$997$	24.7684	+	24.7684i	0.784424	+	0.784424i	−0.196150	+	0.980574i	$0.562844\pi$
$998$	−39.4425	−	2.86039i	−1.24853	−	0.0905442i
$999$	−6.45409			−0.204198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.w.a.43.18	yes	72
4.3	odd	2		1120.2.bi.a.463.26		72
5.2	odd	4	inner	280.2.w.a.267.1	yes	72
8.3	odd	2	inner	280.2.w.a.43.1	✓	72
8.5	even	2		1120.2.bi.a.463.25		72
20.7	even	4		1120.2.bi.a.687.25		72
40.27	even	4	inner	280.2.w.a.267.18	yes	72
40.37	odd	4		1120.2.bi.a.687.26		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.w.a.43.1	✓	72	8.3	odd	2	inner
280.2.w.a.43.18	yes	72	1.1	even	1	trivial
280.2.w.a.267.1	yes	72	5.2	odd	4	inner
280.2.w.a.267.18	yes	72	40.27	even	4	inner
1120.2.bi.a.463.25		72	8.5	even	2
1120.2.bi.a.463.26		72	4.3	odd	2
1120.2.bi.a.687.25		72	20.7	even	4
1120.2.bi.a.687.26		72	40.37	odd	4

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.102291 + 1.41051i) q^{2} +(-0.977895 - 0.977895i) q^{3} +(-1.97907 - 0.288564i) q^{4} +(2.23508 + 0.0665977i) q^{5} +(1.47936 - 1.27930i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.609464 - 2.76198i) q^{8} -1.08744i q^{9} +O(q^{10})\)	\(q+(-0.102291 + 1.41051i) q^{2} +(-0.977895 - 0.977895i) q^{3} +(-1.97907 - 0.288564i) q^{4} +(2.23508 + 0.0665977i) q^{5} +(1.47936 - 1.27930i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.609464 - 2.76198i) q^{8} -1.08744i q^{9} +(-0.322565 + 3.14578i) q^{10} -0.190002 q^{11} +(1.65314 + 2.21751i) q^{12} +(3.83102 - 3.83102i) q^{13} +(1.06971 - 0.925050i) q^{14} +(-2.12054 - 2.25080i) q^{15} +(3.83346 + 1.14218i) q^{16} +(1.66411 - 1.66411i) q^{17} +(1.53385 + 0.111235i) q^{18} +7.16664i q^{19} +(-4.40416 - 0.776765i) q^{20} +1.38295i q^{21} +(0.0194354 - 0.267999i) q^{22} +(5.10656 - 5.10656i) q^{23} +(-3.29692 + 2.10494i) q^{24} +(4.99113 + 0.297702i) q^{25} +(5.01181 + 5.79557i) q^{26} +(-3.99709 + 3.99709i) q^{27} +(1.19537 + 1.60346i) q^{28} +0.389233 q^{29} +(3.39168 - 2.76081i) q^{30} -5.59194i q^{31} +(-2.00318 + 5.29030i) q^{32} +(0.185802 + 0.185802i) q^{33} +(2.17702 + 2.51747i) q^{34} +(-1.53335 - 1.62753i) q^{35} +(-0.313797 + 2.15213i) q^{36} +(0.807349 + 0.807349i) q^{37} +(-10.1086 - 0.733082i) q^{38} -7.49267 q^{39} +(1.54614 - 6.13265i) q^{40} -9.77556 q^{41} +(-1.95067 - 0.141463i) q^{42} +(-2.07740 - 2.07740i) q^{43} +(0.376027 + 0.0548277i) q^{44} +(0.0724212 - 2.43052i) q^{45} +(6.68050 + 7.72521i) q^{46} +(-2.90099 - 2.90099i) q^{47} +(-2.63179 - 4.86566i) q^{48} +1.00000i q^{49} +(-0.930458 + 7.00958i) q^{50} -3.25466 q^{51} +(-8.68736 + 6.47637i) q^{52} +(-3.87887 + 3.87887i) q^{53} +(-5.22907 - 6.04680i) q^{54} +(-0.424668 - 0.0126537i) q^{55} +(-2.38397 + 1.52206i) q^{56} +(7.00822 - 7.00822i) q^{57} +(-0.0398150 + 0.549017i) q^{58} +3.53327i q^{59} +(3.54721 + 5.06640i) q^{60} +10.7990i q^{61} +(7.88749 + 0.572005i) q^{62} +(-0.768938 + 0.768938i) q^{63} +(-7.25711 - 3.36666i) q^{64} +(8.81776 - 8.30748i) q^{65} +(-0.281081 + 0.243069i) q^{66} +(7.88947 - 7.88947i) q^{67} +(-3.77361 + 2.81320i) q^{68} -9.98737 q^{69} +(2.45249 - 1.99632i) q^{70} +1.44759i q^{71} +(-3.00350 - 0.662757i) q^{72} +(-6.73133 - 6.73133i) q^{73} +(-1.22136 + 1.05619i) q^{74} +(-4.58968 - 5.17192i) q^{75} +(2.06804 - 14.1833i) q^{76} +(0.134351 + 0.134351i) q^{77} +(0.766432 - 10.5685i) q^{78} +9.81369 q^{79} +(8.49201 + 2.80816i) q^{80} +4.55514 q^{81} +(0.999951 - 13.7885i) q^{82} +(-0.608923 - 0.608923i) q^{83} +(0.399071 - 2.73696i) q^{84} +(3.83025 - 3.60860i) q^{85} +(3.14270 - 2.71770i) q^{86} +(-0.380629 - 0.380629i) q^{87} +(-0.115799 + 0.524781i) q^{88} +16.1054i q^{89} +(3.42086 + 0.350770i) q^{90} -5.41788 q^{91} +(-11.5798 + 8.63269i) q^{92} +(-5.46833 + 5.46833i) q^{93} +(4.38861 - 3.79512i) q^{94} +(-0.477282 + 16.0180i) q^{95} +(7.13226 - 3.21445i) q^{96} +(0.0632673 - 0.0632673i) q^{97} +(-1.41051 - 0.102291i) q^{98} +0.206616i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{6}+O(q^{10}) \) 72 * q + 8 * q^6	\( 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) \) 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

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