LMFDB - Embedded newform 312.2.ba.a.251.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,2,Mod(179,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))

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

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

chi := DirichletCharacter("312.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.ba (of order $6$, 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:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$52$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.34
Character	$\chi$	$=$	312.251
Dual form			312.2.ba.a.179.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.563917 + 1.29692i) q^{2} +(-1.23972 + 1.20959i) q^{3} +(-1.36400 + 1.46271i) q^{4} -3.72006i q^{5} +(-2.26783 - 0.925705i) q^{6} +(-1.77405 - 3.07274i) q^{7} +(-2.66619 - 0.944145i) q^{8} +(0.0737946 - 2.99909i) q^{9} +O(q^{10})$	\(q+(0.563917 + 1.29692i) q^{2} +(-1.23972 + 1.20959i) q^{3} +(-1.36400 + 1.46271i) q^{4} -3.72006i q^{5} +(-2.26783 - 0.925705i) q^{6} +(-1.77405 - 3.07274i) q^{7} +(-2.66619 - 0.944145i) q^{8} +(0.0737946 - 2.99909i) q^{9} +(4.82462 - 2.09781i) q^{10} +(-0.294499 + 0.510088i) q^{11} +(-0.0783063 - 3.46322i) q^{12} +(-3.60542 + 0.0310714i) q^{13} +(2.98468 - 4.03356i) q^{14} +(4.49974 + 4.61183i) q^{15} +(-0.279032 - 3.99026i) q^{16} +(1.74784 - 1.00911i) q^{17} +(3.93119 - 1.59553i) q^{18} +(-5.27545 + 3.04578i) q^{19} +(5.44137 + 5.07415i) q^{20} +(5.91606 + 1.66346i) q^{21} +(-0.827615 - 0.0942945i) q^{22} +(-1.45159 + 2.51423i) q^{23} +(4.44735 - 2.05452i) q^{24} -8.83888 q^{25} +(-2.07345 - 4.65841i) q^{26} +(3.53618 + 3.80729i) q^{27} +(6.91432 + 1.59629i) q^{28} +(1.71397 - 2.96869i) q^{29} +(-3.44368 + 8.43649i) q^{30} +5.99017 q^{31} +(5.01769 - 2.61205i) q^{32} +(-0.251900 - 0.988587i) q^{33} +(2.29437 + 1.69774i) q^{34} +(-11.4308 + 6.59957i) q^{35} +(4.28614 + 4.19869i) q^{36} +(-1.19644 + 2.07229i) q^{37} +(-6.92504 - 5.12426i) q^{38} +(4.43211 - 4.39959i) q^{39} +(-3.51228 + 9.91841i) q^{40} +(4.93476 - 8.54726i) q^{41} +(1.17880 + 8.61071i) q^{42} +(-2.65252 - 4.59430i) q^{43} +(-0.344414 - 1.12652i) q^{44} +(-11.1568 - 0.274521i) q^{45} +(-4.07933 - 0.464779i) q^{46} -7.27332i q^{47} +(5.17249 + 4.60927i) q^{48} +(-2.79449 + 4.84019i) q^{49} +(-4.98439 - 11.4633i) q^{50} +(-0.946209 + 3.36517i) q^{51} +(4.87233 - 5.31606i) q^{52} -6.78400 q^{53} +(-2.94363 + 6.73313i) q^{54} +(1.89756 + 1.09556i) q^{55} +(1.82884 + 9.86748i) q^{56} +(2.85592 - 10.1570i) q^{57} +(4.81668 + 0.548790i) q^{58} +(-0.596307 - 1.03283i) q^{59} +(-12.8834 + 0.291305i) q^{60} +(-3.72531 + 2.15081i) q^{61} +(3.37795 + 7.76876i) q^{62} +(-9.34635 + 5.09378i) q^{63} +(6.21718 + 5.03455i) q^{64} +(0.115587 + 13.4124i) q^{65} +(1.14007 - 0.884175i) q^{66} +(-0.440139 - 0.254114i) q^{67} +(-0.908001 + 3.93300i) q^{68} +(-1.24162 - 4.87276i) q^{69} +(-15.0051 - 11.1032i) q^{70} +(-0.151877 + 0.0876865i) q^{71} +(-3.02833 + 7.92649i) q^{72} +9.04801i q^{73} +(-3.36228 - 0.383082i) q^{74} +(10.9577 - 10.6914i) q^{75} +(2.74060 - 11.8709i) q^{76} +2.08982 q^{77} +(8.20525 + 3.26709i) q^{78} +1.99512i q^{79} +(-14.8440 + 1.03802i) q^{80} +(-8.98911 - 0.442633i) q^{81} +(13.8679 + 1.58004i) q^{82} +16.5592 q^{83} +(-10.5026 + 6.38452i) q^{84} +(-3.75397 - 6.50206i) q^{85} +(4.46263 - 6.03090i) q^{86} +(1.46605 + 5.75353i) q^{87} +(1.26679 - 1.08194i) q^{88} +(3.71133 - 6.42821i) q^{89} +(-5.93549 - 14.6243i) q^{90} +(6.49166 + 11.0234i) q^{91} +(-1.69762 - 5.55265i) q^{92} +(-7.42611 + 7.24563i) q^{93} +(9.43290 - 4.10155i) q^{94} +(11.3305 + 19.6250i) q^{95} +(-3.06100 + 9.30754i) q^{96} +(11.0238 - 6.36461i) q^{97} +(-7.85320 - 0.894756i) q^{98} +(1.50807 + 0.920872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 2 q^{3} - 2 q^{4} - 12 q^{6} - 2 q^{9}+O(q^{10}) $ 104 * q - 2 * q^3 - 2 * q^4 - 12 * q^6 - 2 * q^9	$ 104 q - 2 q^{3} - 2 q^{4} - 12 q^{6} - 2 q^{9} + 6 q^{10} + 8 q^{12} - 6 q^{16} - 12 q^{19} + 8 q^{22} - 36 q^{24} - 88 q^{25} + 16 q^{27} + 12 q^{28} + 14 q^{30} - 6 q^{33} + 22 q^{36} + 4 q^{40} + 26 q^{42} - 20 q^{43} - 36 q^{46} + 14 q^{48} - 24 q^{49} - 20 q^{51} - 16 q^{52} - 36 q^{54} - 66 q^{58} + 28 q^{64} + 32 q^{66} - 12 q^{67} - 66 q^{72} + 2 q^{75} - 60 q^{76} - 14 q^{78} - 2 q^{81} + 50 q^{82} - 90 q^{84} + 24 q^{88} + 8 q^{90} + 44 q^{91} + 72 q^{94} + 12 q^{97}+O(q^{100}) $ 104 * q - 2 * q^3 - 2 * q^4 - 12 * q^6 - 2 * q^9 + 6 * q^10 + 8 * q^12 - 6 * q^16 - 12 * q^19 + 8 * q^22 - 36 * q^24 - 88 * q^25 + 16 * q^27 + 12 * q^28 + 14 * q^30 - 6 * q^33 + 22 * q^36 + 4 * q^40 + 26 * q^42 - 20 * q^43 - 36 * q^46 + 14 * q^48 - 24 * q^49 - 20 * q^51 - 16 * q^52 - 36 * q^54 - 66 * q^58 + 28 * q^64 + 32 * q^66 - 12 * q^67 - 66 * q^72 + 2 * q^75 - 60 * q^76 - 14 * q^78 - 2 * q^81 + 50 * q^82 - 90 * q^84 + 24 * q^88 + 8 * q^90 + 44 * q^91 + 72 * q^94 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	0.563917	+	1.29692i	0.398749	+	0.917060i
$2$	0.563917	+	1.29692i	0.398749	+	0.917060i
$3$	−1.23972	+	1.20959i	−0.715751	+	0.698356i
$3$	−1.23972	+	1.20959i	−0.715751	+	0.698356i
$4$	−1.36400	+	1.46271i	−0.681998	+	0.731354i
$5$		−	3.72006i		−	1.66366i	−0.555028	−	0.831832i	$-0.687292\pi$
$5$		−	3.72006i		−	1.66366i	0.555028	−	0.831832i	$-0.312708\pi$
$6$	−2.26783	−	0.925705i	−0.925839	−	0.377917i
$7$	−1.77405	−	3.07274i	−0.670527	−	1.16139i	−0.977755	−	0.209751i	$-0.932735\pi$
$7$	−1.77405	−	3.07274i	−0.670527	−	1.16139i	0.307228	−	0.951636i	$-0.400599\pi$
$8$	−2.66619	−	0.944145i	−0.942642	−	0.333806i
$9$	0.0737946	−	2.99909i	0.0245982	−	0.999697i
$10$	4.82462	−	2.09781i	1.52568	−	0.663385i
$11$	−0.294499	+	0.510088i	−0.0887948	+	0.153797i	−0.907002	−	0.421126i	$-0.861635\pi$
$11$	−0.294499	+	0.510088i	−0.0887948	+	0.153797i	0.818207	+	0.574924i	$0.194968\pi$
$12$	−0.0783063	−	3.46322i	−0.0226051	−	0.999744i
$13$	−3.60542	+	0.0310714i	−0.999963	+	0.00861765i
$13$	−3.60542	+	0.0310714i	−0.999963	+	0.00861765i
$14$	2.98468	−	4.03356i	0.797689	−	1.07802i
$15$	4.49974	+	4.61183i	1.16183	+	1.19077i
$16$	−0.279032	−	3.99026i	−0.0697580	−	0.997564i
$17$	1.74784	−	1.00911i	0.423912	−	0.244746i	−0.272837	−	0.962060i	$-0.587962\pi$
$17$	1.74784	−	1.00911i	0.423912	−	0.244746i	0.696750	+	0.717314i	$0.254629\pi$
$18$	3.93119	−	1.59553i	0.926591	−	0.376071i
$19$	−5.27545	+	3.04578i	−1.21027	+	0.698750i	−0.962818	−	0.270150i	$-0.912927\pi$
$19$	−5.27545	+	3.04578i	−1.21027	+	0.698750i	−0.247452	+	0.968900i	$0.579593\pi$
$20$	5.44137	+	5.07415i	1.21673	+	1.13461i
$21$	5.91606	+	1.66346i	1.29099	+	0.362997i
$22$	−0.827615	−	0.0942945i	−0.176448	−	0.0201037i
$23$	−1.45159	+	2.51423i	−0.302678	+	0.524253i	−0.976742	−	0.214420i	$-0.931214\pi$
$23$	−1.45159	+	2.51423i	−0.302678	+	0.524253i	0.674064	+	0.738673i	$0.264547\pi$
$24$	4.44735	−	2.05452i	0.907812	−	0.419378i
$25$	−8.83888			−1.76778
$26$	−2.07345	−	4.65841i	−0.406638	−	0.913590i
$27$	3.53618	+	3.80729i	0.680538	+	0.732712i
$28$	6.91432	+	1.59629i	1.30668	+	0.301670i
$29$	1.71397	−	2.96869i	0.318277	−	0.551271i	−0.661852	−	0.749635i	$-0.730229\pi$
$29$	1.71397	−	2.96869i	0.318277	−	0.551271i	0.980129	+	0.198363i	$0.0635626\pi$
$30$	−3.44368	+	8.43649i	−0.628727	+	1.54029i
$31$	5.99017			1.07587			0.537933	−	0.842988i	$-0.319205\pi$
$31$	5.99017			1.07587			0.537933	+	0.842988i	$0.319205\pi$
$32$	5.01769	−	2.61205i	0.887010	−	0.461750i
$33$	−0.251900	−	0.988587i	−0.0438502	−	0.172091i
$34$	2.29437	+	1.69774i	0.393481	+	0.291161i
$35$	−11.4308	+	6.59957i	−1.93216	+	1.11553i
$36$	4.28614	+	4.19869i	0.714357	+	0.699781i
$37$	−1.19644	+	2.07229i	−0.196693	+	0.340682i	−0.947454	−	0.319891i	$-0.896354\pi$
$37$	−1.19644	+	2.07229i	−0.196693	+	0.340682i	0.750761	+	0.660574i	$0.229687\pi$
$38$	−6.92504	−	5.12426i	−1.12339	−	0.831264i
$39$	4.43211	−	4.39959i	0.709706	−	0.704498i
$40$	−3.51228	+	9.91841i	−0.555340	+	1.56824i
$41$	4.93476	−	8.54726i	0.770681	−	1.33486i	−0.166510	−	0.986040i	$-0.553250\pi$
$41$	4.93476	−	8.54726i	0.770681	−	1.33486i	0.937190	−	0.348818i	$-0.113417\pi$
$42$	1.17880	+	8.61071i	0.181892	+	1.32866i
$43$	−2.65252	−	4.59430i	−0.404505	−	0.700624i	0.589758	−	0.807580i	$-0.299223\pi$
$43$	−2.65252	−	4.59430i	−0.404505	−	0.700624i	−0.994264	+	0.106956i	$0.965890\pi$
$44$	−0.344414	−	1.12652i	−0.0519223	−	0.169830i
$45$	−11.1568	−	0.274521i	−1.66316	−	0.0409231i
$46$	−4.07933	−	0.464779i	−0.601464	−	0.0685279i
$47$		−	7.27332i		−	1.06092i	−0.847709	−	0.530461i	$-0.822019\pi$
$47$		−	7.27332i		−	1.06092i	0.847709	−	0.530461i	$-0.177981\pi$
$48$	5.17249	+	4.60927i	0.746584	+	0.665291i
$49$	−2.79449	+	4.84019i	−0.399213	+	0.691456i
$50$	−4.98439	−	11.4633i	−0.704900	−	1.62116i
$51$	−0.946209	+	3.36517i	−0.132496	+	0.471219i
$52$	4.87233	−	5.31606i	0.675670	−	0.737204i
$53$	−6.78400			−0.931853			−0.465927	−	0.884823i	$-0.654279\pi$
$53$	−6.78400			−0.931853			−0.465927	+	0.884823i	$0.654279\pi$
$54$	−2.94363	+	6.73313i	−0.400577	+	0.916263i
$55$	1.89756	+	1.09556i	0.255867	+	0.147725i
$56$	1.82884	+	9.86748i	0.244389	+	1.31860i
$57$	2.85592	−	10.1570i	0.378276	−	1.34533i
$58$	4.81668	+	0.548790i	0.632461	+	0.0720596i
$59$	−0.596307	−	1.03283i	−0.0776325	−	0.134463i	0.824596	−	0.565723i	$-0.191403\pi$
$59$	−0.596307	−	1.03283i	−0.0776325	−	0.134463i	−0.902228	+	0.431259i	$0.858069\pi$
$60$	−12.8834	+	0.291305i	−1.66324	+	0.0376073i
$61$	−3.72531	+	2.15081i	−0.476978	+	0.275383i	−0.719156	−	0.694849i	$-0.755471\pi$
$61$	−3.72531	+	2.15081i	−0.476978	+	0.275383i	0.242179	+	0.970232i	$0.422138\pi$
$62$	3.37795	+	7.76876i	0.429001	+	0.986633i
$63$	−9.34635	+	5.09378i	−1.17753	+	0.641756i
$64$	6.21718	+	5.03455i	0.777147	+	0.629319i
$65$	0.115587	+	13.4124i	0.0143369	+	1.66360i
$66$	1.14007	−	0.884175i	0.140332	−	0.108834i
$67$	−0.440139	−	0.254114i	−0.0537715	−	0.0310450i	0.472873	−	0.881130i	$-0.343217\pi$
$67$	−0.440139	−	0.254114i	−0.0537715	−	0.0310450i	−0.526645	+	0.850085i	$0.676550\pi$
$68$	−0.908001	+	3.93300i	−0.110111	+	0.476946i
$69$	−1.24162	−	4.87276i	−0.149473	−	0.586611i
$70$	−15.0051	−	11.1032i	−1.79346	−	1.32709i
$71$	−0.151877	+	0.0876865i	−0.0180245	+	0.0104065i	−0.508985	−	0.860775i	$-0.669979\pi$
$71$	−0.151877	+	0.0876865i	−0.0180245	+	0.0104065i	0.490961	+	0.871182i	$0.336646\pi$
$72$	−3.02833	+	7.92649i	−0.356892	+	0.934146i
$73$			9.04801i			1.05899i	0.848313	+	0.529495i	$0.177618\pi$
$73$			9.04801i			1.05899i	−0.848313	+	0.529495i	$0.822382\pi$
$74$	−3.36228	−	0.383082i	−0.390857	−	0.0445324i
$75$	10.9577	−	10.6914i	1.26529	−	1.23454i
$76$	2.74060	−	11.8709i	0.314368	−	1.36168i
$77$	2.08982			0.238157
$78$	8.20525	+	3.26709i	0.929062	+	0.369925i
$79$			1.99512i			0.224469i	0.993682	+	0.112234i	$0.0358007\pi$
$79$			1.99512i			0.224469i	−0.993682	+	0.112234i	$0.964199\pi$
$80$	−14.8440	+	1.03802i	−1.65961	+	0.116054i
$81$	−8.98911	−	0.442633i	−0.998790	−	0.0491815i
$82$	13.8679	+	1.58004i	1.53145	+	0.174486i
$83$	16.5592			1.81761			0.908803	−	0.417225i	$-0.136997\pi$
$83$	16.5592			1.81761			0.908803	+	0.417225i	$0.136997\pi$
$84$	−10.5026	+	6.38452i	−1.14593	+	0.696609i
$85$	−3.75397	−	6.50206i	−0.407175	−	0.705247i
$86$	4.46263	−	6.03090i	0.481218	−	0.650329i
$87$	1.46605	+	5.75353i	0.157177	+	0.616843i
$88$	1.26679	−	1.08194i	0.135040	−	0.115335i
$89$	3.71133	−	6.42821i	0.393400	−	0.681389i	−0.599495	−	0.800378i	$-0.704632\pi$
$89$	3.71133	−	6.42821i	0.393400	−	0.681389i	0.992896	+	0.118989i	$0.0379654\pi$
$90$	−5.93549	−	14.6243i	−0.625655	−	1.54154i
$91$	6.49166	+	11.0234i	0.680510	+	1.15557i
$92$	−1.69762	−	5.55265i	−0.176989	−	0.578904i
$93$	−7.42611	+	7.24563i	−0.770051	+	0.751337i
$94$	9.43290	−	4.10155i	0.972930	−	0.423042i
$95$	11.3305	+	19.6250i	1.16248	+	2.01348i
$96$	−3.06100	+	9.30754i	−0.312412	+	0.949947i
$97$	11.0238	−	6.36461i	1.11930	−	0.646228i	0.178078	−	0.984016i	$-0.443012\pi$
$97$	11.0238	−	6.36461i	1.11930	−	0.646228i	0.941222	+	0.337788i	$0.109679\pi$
$98$	−7.85320	−	0.894756i	−0.793293	−	0.0903840i
$99$	1.50807	+	0.920872i	0.151566	+	0.0925511i
$100$	12.0562	−	12.9287i	1.20562	−	1.29287i
$101$	1.66350	−	2.88126i	0.165524	−	0.286696i	−0.771317	−	0.636451i	$-0.780402\pi$
$101$	1.66350	−	2.88126i	0.165524	−	0.286696i	0.936841	+	0.349755i	$0.113735\pi$
$102$	−4.89794	+	0.670522i	−0.484968	+	0.0663916i
$103$		−	5.49562i		−	0.541500i	−0.962650	−	0.270750i	$-0.912728\pi$
$103$		−	5.49562i		−	0.541500i	0.962650	−	0.270750i	$-0.0872716\pi$
$104$	9.64208	+	3.32120i	0.945483	+	0.325670i
$105$	6.18818	−	22.0081i	0.603905	−	2.14777i
$106$	−3.82561	−	8.79829i	−0.371576	−	0.854565i
$107$	−16.5374	−	9.54789i	−1.59873	−	0.923029i	−0.991732	−	0.128328i	$-0.959039\pi$
$107$	−16.5374	−	9.54789i	−1.59873	−	0.923029i	−0.607002	−	0.794701i	$-0.707628\pi$
$108$	−10.3923	−	0.0207187i	−0.999998	−	0.00199366i
$109$	9.44857			0.905009			0.452504	−	0.891762i	$-0.350531\pi$
$109$	9.44857			0.905009			0.452504	+	0.891762i	$0.350531\pi$
$110$	−0.350782	+	3.07878i	−0.0334457	+	0.293550i
$111$	−1.02337	−	4.01625i	−0.0971343	−	0.381205i
$112$	−11.7660	+	7.93630i	−1.11178	+	0.749909i
$113$	−12.5797	+	7.26287i	−1.18339	+	0.683233i	−0.956797	−	0.290755i	$-0.906093\pi$
$113$	−12.5797	+	7.26287i	−1.18339	+	0.683233i	−0.226597	+	0.973989i	$0.572760\pi$
$114$	14.7833	−	2.02382i	1.38459	−	0.189548i
$115$	9.35310	+	5.40001i	0.872181	+	0.503554i
$116$	2.00447	+	6.55631i	0.186111	+	0.608739i
$117$	−0.172874	+	10.8153i	−0.0159822	+	0.999872i
$118$	1.00323	−	1.35579i	0.0923552	−	0.124811i
$119$	−6.20149	−	3.58043i	−0.568489	−	0.328217i
$120$	−7.64296	−	16.5444i	−0.697703	−	1.51029i
$121$	5.32654	+	9.22584i	0.484231	+	0.838713i
$122$	−4.89019	−	3.61855i	−0.442737	−	0.327608i
$123$	4.22096	+	16.5652i	0.380591	+	1.49364i
$124$	−8.17056	+	8.76186i	−0.733738	+	0.786839i
$125$			14.2809i			1.27732i
$126$	−11.8768	−	9.24898i	−1.05807	−	0.823965i
$127$	−13.7409	−	7.93329i	−1.21930	−	0.703965i	−0.254535	−	0.967064i	$-0.581922\pi$
$127$	−13.7409	−	7.93329i	−1.21930	−	0.703965i	−0.964769	+	0.263098i	$0.915256\pi$
$128$	−3.02343	+	10.9022i	−0.267236	+	0.963631i
$129$	8.84558	+	2.48717i	0.778810	+	0.218983i
$130$	−17.3296	+	7.71338i	−1.51991	+	0.676508i
$131$		−	1.28751i		−	0.112491i	−0.998417	−	0.0562453i	$-0.982087\pi$
$131$		−	1.28751i		−	0.112491i	0.998417	−	0.0562453i	$-0.0179129\pi$
$132$	1.78960	+	0.979971i	0.155765	+	0.0852956i
$133$	18.7178	+	10.8067i	1.62304	+	0.937061i
$134$	0.0813639	−	0.714124i	0.00702877	−	0.0616909i
$135$	14.1633	−	13.1548i	1.21899	−	1.13219i
$136$	−5.61282	+	1.04028i	−0.481295	+	0.0892033i
$137$	3.42870	+	5.93869i	0.292934	+	0.507377i	0.974502	−	0.224378i	$-0.0720350\pi$
$137$	3.42870	+	5.93869i	0.292934	+	0.507377i	−0.681568	+	0.731755i	$0.738702\pi$
$138$	5.61940	−	4.35811i	0.478355	−	0.370987i
$139$	3.07665	+	5.32891i	0.260958	+	0.451992i	0.966497	−	0.256679i	$-0.0826283\pi$
$139$	3.07665	+	5.32891i	0.260958	+	0.451992i	−0.705539	+	0.708671i	$0.749295\pi$
$140$	5.93830	−	25.7217i	0.501878	−	2.17388i
$141$	8.79772	+	9.01686i	0.740902	+	0.759356i
$142$	−0.199369	−	0.147525i	−0.0167306	−	0.0123800i
$143$	1.04594	−	1.84823i	0.0874662	−	0.154557i
$144$	−11.9877	+	0.542383i	−0.998978	+	0.0451986i
$145$	−11.0437	−	6.37608i	−0.917130	−	0.529505i
$146$	−11.7345	+	5.10232i	−0.971156	+	0.422271i
$147$	−2.39027	−	9.38065i	−0.197146	−	0.773703i
$148$	−1.39922	−	4.57663i	−0.115015	−	0.376197i
$149$	16.0495	−	9.26620i	1.31483	−	0.759117i	0.331938	−	0.943301i	$-0.392298\pi$
$149$	16.0495	−	9.26620i	1.31483	−	0.759117i	0.982892	+	0.184184i	$0.0589643\pi$
$150$	20.0451	+	8.18219i	1.63668	+	0.668073i
$151$	−21.3837			−1.74018			−0.870090	−	0.492892i	$-0.835940\pi$
$151$	−21.3837			−1.74018			−0.870090	+	0.492892i	$0.835940\pi$
$152$	16.9410	−	3.13985i	1.37410	−	0.254676i
$153$	−2.89744	−	5.31639i	−0.234244	−	0.429804i
$154$	1.17849	+	2.71033i	0.0949651	+	0.218405i
$155$		−	22.2838i		−	1.78988i
$156$	0.389934	+	12.4839i	0.0312197	+	0.999513i
$157$		−	14.9143i		−	1.19029i	−0.803618	−	0.595146i	$-0.797094\pi$
$157$		−	14.9143i		−	1.19029i	0.803618	−	0.595146i	$-0.202906\pi$
$158$	−2.58751	+	1.12508i	−0.205851	+	0.0895068i
$159$	8.41023	−	8.20584i	0.666975	−	0.650765i
$160$	−9.71701	−	18.6661i	−0.768197	−	1.47569i
$161$	10.3008			0.811814
$162$	−4.49505	−	11.9078i	−0.353165	−	0.935561i
$163$	−6.18058	+	3.56836i	−0.484100	+	0.279496i	−0.722124	−	0.691764i	$-0.756834\pi$
$163$	−6.18058	+	3.56836i	−0.484100	+	0.279496i	0.238023	+	0.971259i	$0.423501\pi$
$164$	5.77116	+	18.8765i	0.450652	+	1.47401i
$165$	−3.67761	+	0.937085i	−0.286301	+	0.0729520i
$166$	9.33800	+	21.4759i	0.724770	+	1.66685i
$167$	−6.05123	−	3.49368i	−0.468259	−	0.270349i	0.247252	−	0.968951i	$-0.420472\pi$
$167$	−6.05123	−	3.49368i	−0.468259	−	0.270349i	−0.715510	+	0.698602i	$0.753806\pi$
$168$	−14.2028	−	10.0207i	−1.09577	−	0.773116i
$169$	12.9981	−	0.224050i	0.999851	−	0.0172347i
$170$	6.31572	−	8.53521i	0.484393	−	0.654621i
$171$	8.74528	+	16.0463i	0.668768	+	1.22709i
$172$	10.3381	+	2.38674i	0.788276	+	0.181987i
$173$	−11.3654	−	19.6855i	−0.864096	−	1.49666i	−0.867942	−	0.496666i	$-0.834557\pi$
$173$	−11.3654	−	19.6855i	−0.864096	−	1.49666i	0.00384554	−	0.999993i	$-0.498776\pi$
$174$	−6.63513	+	5.14586i	−0.503008	+	0.390106i
$175$	15.6806	+	27.1596i	1.18534	+	2.05307i
$176$	2.11755	+	1.03280i	0.159617	+	0.0778500i
$177$	1.98855	+	0.559136i	0.149469	+	0.0420272i
$178$	10.4297	+	1.18832i	0.781743	+	0.0890680i
$179$	10.2338	+	5.90847i	0.764908	+	0.441620i	0.831055	−	0.556190i	$-0.187737\pi$
$179$	10.2338	+	5.90847i	0.764908	+	0.441620i	−0.0661471	+	0.997810i	$0.521071\pi$
$180$	15.6194	−	15.9447i	1.16420	−	1.18845i
$181$			11.6344i			0.864777i	0.901687	+	0.432389i	$0.142329\pi$
$181$			11.6344i			0.864777i	−0.901687	+	0.432389i	$0.857671\pi$
$182$	−10.6357	+	14.6354i	−0.788369	+	1.08485i
$183$	2.01674	−	7.17249i	0.149082	−	0.530206i
$184$	6.24402	−	5.33291i	0.460315	−	0.393147i
$185$	7.70905	+	4.45082i	0.566781	+	0.327231i
$186$	−13.5847	−	5.54512i	−0.996079	−	0.406588i
$187$			1.18873i			0.0869287i
$188$	10.6387	+	9.92078i	0.775910	+	0.723547i
$189$	5.42545	−	17.6201i	0.394643	−	1.28167i
$190$	−19.0626	+	25.7616i	−1.38294	+	1.86894i
$191$	−2.47953	−	4.29467i	−0.179412	−	0.310751i	0.762267	−	0.647263i	$-0.224086\pi$
$191$	−2.47953	−	4.29467i	−0.179412	−	0.310751i	−0.941679	+	0.336511i	$0.890753\pi$
$192$	−13.7973	+	1.27881i	−0.995732	+	0.0922902i
$193$	−11.7522	−	6.78516i	−0.845945	−	0.488407i	0.0133354	−	0.999911i	$-0.495755\pi$
$193$	−11.7522	−	6.78516i	−0.845945	−	0.488407i	−0.859281	+	0.511504i	$0.829088\pi$
$194$	14.4709	+	10.7079i	1.03895	+	0.768782i
$195$	−16.3668	−	16.4877i	−1.17205	−	1.18071i
$196$	−3.26812	−	10.6895i	−0.233437	−	0.763537i
$197$	10.3600	+	5.98134i	0.738118	+	0.426153i	0.821385	−	0.570375i	$-0.193202\pi$
$197$	10.3600	+	5.98134i	0.738118	+	0.426153i	−0.0832666	+	0.996527i	$0.526535\pi$
$198$	−0.343871	+	2.47514i	−0.0244379	+	0.175900i
$199$	1.00483	−	0.580141i	0.0712307	−	0.0411251i	−0.463962	−	0.885855i	$-0.653572\pi$
$199$	1.00483	−	0.580141i	0.0712307	−	0.0411251i	0.535192	+	0.844730i	$0.320239\pi$
$200$	23.5662	+	8.34519i	1.66638	+	0.590094i
$201$	0.853021	−	0.217357i	0.0601675	−	0.0153312i
$202$	4.67484	+	0.532629i	0.328920	+	0.0374756i
$203$	−12.1627			−0.853652
$204$	−3.63164	−	5.97411i	−0.254266	−	0.418272i
$205$	−31.7964	−	18.3576i	−2.22075	−	1.28215i
$206$	7.12738	−	3.09907i	0.496588	−	0.215923i
$207$	7.43329	+	4.53899i	0.516649	+	0.315482i
$208$	1.13001	+	14.3779i	0.0783521	+	0.996926i
$209$		−	3.58792i		−	0.248182i
$210$	32.0324	−	4.38519i	2.21044	−	0.302607i
$211$	8.60377	−	14.9022i	0.592308	−	1.02591i	−0.401613	−	0.915809i	$-0.631550\pi$
$211$	8.60377	−	14.9022i	0.592308	−	1.02591i	0.993921	−	0.110098i	$-0.0351163\pi$
$212$	9.25334	−	9.92301i	0.635522	−	0.681515i
$213$	0.0822205	−	0.292416i	0.00563366	−	0.0200360i
$214$	3.05710	−	26.8319i	0.208979	−	1.83419i
$215$	−17.0911	+	9.86754i	−1.16560	+	0.672961i
$216$	−5.83351	−	13.4896i	−0.396920	−	0.917853i
$217$	−10.6268	−	18.4062i	−0.721397	−	1.24950i
$218$	5.32821	+	12.2540i	0.360872	+	0.829947i
$219$	−10.9444	−	11.2170i	−0.739551	−	0.757972i
$220$	−4.19074	+	1.28124i	−0.282540	+	0.0863813i
$221$	−6.27032	+	3.69258i	−0.421787	+	0.248390i
$222$	4.63165	−	3.59206i	0.310856	−	0.241083i
$223$	1.36308	−	2.36092i	0.0912786	−	0.158099i	−0.816771	−	0.576962i	$-0.804238\pi$
$223$	1.36308	−	2.36092i	0.0912786	−	0.158099i	0.908049	+	0.418863i	$0.137571\pi$
$224$	−16.9278	−	10.7841i	−1.13103	−	0.720545i
$225$	−0.652261	+	26.5086i	−0.0434841	+	1.76724i
$226$	−16.5132	−	12.2191i	−1.09844	−	0.812805i
$227$	−6.52437	−	11.3005i	−0.433037	−	0.750043i	0.564096	−	0.825709i	$-0.309225\pi$
$227$	−6.52437	−	11.3005i	−0.433037	−	0.750043i	−0.997133	+	0.0756665i	$0.975892\pi$
$228$	10.9613	+	18.0315i	0.725929	+	1.19417i
$229$	13.8413			0.914661			0.457331	−	0.889297i	$-0.348806\pi$
$229$	13.8413			0.914661			0.457331	+	0.889297i	$0.348806\pi$
$230$	−1.72901	+	15.1754i	−0.114007	+	1.00063i
$231$	−2.59079	+	2.52782i	−0.170461	+	0.166319i
$232$	−7.37265	+	6.29685i	−0.484038	+	0.413409i
$233$			17.8660i			1.17044i	0.810874	+	0.585221i	$0.198992\pi$
$233$			17.8660i			1.17044i	−0.810874	+	0.585221i	$0.801008\pi$
$234$	−14.1240	+	5.87471i	−0.923316	+	0.384042i
$235$	−27.0572			−1.76502
$236$	2.32409	+	0.536558i	0.151286	+	0.0349269i
$237$	−2.41328	−	2.47339i	−0.156759	−	0.160664i
$238$	1.14640	−	10.0619i	0.0743103	−	0.652215i
$239$		−	2.56145i		−	0.165686i	−0.996563	−	0.0828431i	$-0.973600\pi$
$239$		−	2.56145i		−	0.165686i	0.996563	−	0.0828431i	$-0.0264000\pi$
$240$	17.1468	−	19.2420i	1.10682	−	1.24206i
$241$	15.3529	−	8.86401i	0.988968	−	0.570981i	0.0840022	−	0.996466i	$-0.473230\pi$
$241$	15.3529	−	8.86401i	0.988968	−	0.570981i	0.904966	+	0.425485i	$0.139896\pi$
$242$	−8.96144	+	12.1107i	−0.576063	+	0.778505i
$243$	11.6794	−	10.3244i	0.749231	−	0.662309i
$244$	1.93530	−	8.38274i	0.123895	−	0.536650i
$245$	18.0058	+	10.3957i	1.15035	+	0.664155i
$246$	−19.1035	+	14.8156i	−1.21799	+	0.944611i
$247$	18.9255	−	11.1452i	1.20420	−	0.709154i
$248$	−15.9709	−	5.65559i	−1.01416	−	0.359130i
$249$	−20.5287	+	20.0298i	−1.30095	+	1.26934i
$250$	−18.5211	+	8.05323i	−1.17138	+	0.509331i
$251$	12.0260	−	6.94319i	0.759071	−	0.438250i	−0.0698909	−	0.997555i	$-0.522265\pi$
$251$	12.0260	−	6.94319i	0.759071	−	0.438250i	0.828962	+	0.559305i	$0.188932\pi$
$252$	5.29766	−	20.6189i	0.333721	−	1.29887i
$253$	−0.854985	−	1.48088i	−0.0537524	−	0.0931019i
$254$	2.54013	−	22.2945i	0.159382	−	1.39888i
$255$	12.5187	+	3.51996i	0.783949	+	0.220428i
$256$	−15.8443	+	2.22682i	−0.990268	+	0.139176i
$257$	0.832307	+	0.480533i	0.0519179	+	0.0299748i	0.525734	−	0.850649i	$-0.323791\pi$
$257$	0.832307	+	0.480533i	0.0519179	+	0.0299748i	−0.473816	+	0.880624i	$0.657124\pi$
$258$	1.76251	+	12.8746i	0.109729	+	0.801535i
$259$	8.49014			0.527552
$260$	−19.7761	−	18.1254i	−1.22646	−	1.12409i
$261$	−8.77688	−	5.35943i	−0.543275	−	0.331740i
$262$	1.66980	−	0.726050i	0.103161	−	0.0448555i
$263$	−9.97984	+	17.2856i	−0.615384	+	1.06588i	0.374934	+	0.927052i	$0.377666\pi$
$263$	−9.97984	+	17.2856i	−0.615384	+	1.06588i	−0.990317	+	0.138824i	$0.955668\pi$
$264$	−0.261755	+	2.87359i	−0.0161099	+	0.176857i
$265$			25.2369i			1.55029i
$266$	−3.46016	+	30.3695i	−0.212156	+	1.86207i
$267$	3.17449	+	12.4583i	0.194276	+	0.762438i
$268$	0.972043	−	0.297184i	0.0593770	−	0.0181534i
$269$	12.5727	+	21.7766i	0.766572	+	1.32774i	0.939412	+	0.342791i	$0.111372\pi$
$269$	12.5727	+	21.7766i	0.766572	+	1.32774i	−0.172840	+	0.984950i	$0.555294\pi$
$270$	25.0477	+	10.9505i	1.52435	+	0.666425i
$271$	−6.18983	+	10.7211i	−0.376005	+	0.651260i	−0.990477	−	0.137679i	$-0.956036\pi$
$271$	−6.18983	+	10.7211i	−0.376005	+	0.651260i	0.614472	+	0.788939i	$0.289369\pi$
$272$	−4.51432	−	6.69274i	−0.273721	−	0.405807i
$273$	−21.3816	−	5.81365i	−1.29407	−	0.351858i
$274$	−5.76849	+	7.79568i	−0.348487	+	0.470954i
$275$	2.60304	−	4.50860i	0.156969	−	0.271879i
$276$	8.82099	+	4.83029i	0.530961	+	0.290750i
$277$	−6.79972	+	3.92582i	−0.408555	+	0.235880i	−0.690169	−	0.723648i	$-0.742464\pi$
$277$	−6.79972	+	3.92582i	−0.408555	+	0.235880i	0.281613	+	0.959528i	$0.409130\pi$
$278$	−5.17619	+	6.99522i	−0.310447	+	0.419546i
$279$	0.442042	−	17.9651i	0.0264643	−	1.07554i
$280$	36.7077	−	6.80341i	2.19370	−	0.406581i
$281$	−1.44768			−0.0863613			−0.0431806	−	0.999067i	$-0.513749\pi$
$281$	−1.44768			−0.0863613			−0.0431806	+	0.999067i	$0.513749\pi$
$282$	−6.73295	+	16.4947i	−0.400941	+	0.982244i
$283$	6.23292	−	10.7957i	0.370508	−	0.641739i	−0.619135	−	0.785284i	$-0.712517\pi$
$283$	6.23292	−	10.7957i	0.370508	−	0.641739i	0.989644	+	0.143545i	$0.0458501\pi$
$284$	0.0789004	−	0.341756i	0.00468188	−	0.0202795i
$285$	−37.7848	−	10.6242i	−2.23818	−	0.629323i
$286$	2.98683	+	0.314256i	0.176615	+	0.0185823i
$287$	−35.0180			−2.06705
$288$	−7.46351	−	15.2413i	−0.439792	−	0.898100i
$289$	−6.46338	+	11.1949i	−0.380199	+	0.658524i
$290$	2.04153	−	17.9184i	0.119883	−	1.05220i
$291$	−5.96787	+	21.2246i	−0.349843	+	1.24421i
$292$	−13.2346	−	12.3414i	−0.774496	−	0.722228i
$293$	−8.41966	+	4.86109i	−0.491882	+	0.283988i	−0.725355	−	0.688375i	$-0.758324\pi$
$293$	−8.41966	+	4.86109i	−0.491882	+	0.283988i	0.233473	+	0.972363i	$0.424991\pi$
$294$	10.8180	−	8.38989i	0.630920	−	0.489308i
$295$	−3.84221	+	2.21830i	−0.223702	+	0.129154i
$296$	5.14648	−	4.39552i	0.299133	−	0.255484i
$297$	−2.98345	+	0.682520i	−0.173117	+	0.0396038i
$298$	21.0681	+	15.5896i	1.22044	+	0.903080i
$299$	5.15547	−	9.10995i	0.298149	−	0.526842i
$300$	0.692140	+	30.6110i	0.0399607	+	1.76732i
$301$	−9.41139	+	16.3010i	−0.542463	+	0.939574i
$302$	−12.0586	−	27.7329i	−0.693896	−	1.59585i
$303$	1.42287	+	5.58410i	0.0817420	+	0.320798i
$304$	13.6255	+	20.2005i	0.781474	+	1.15858i
$305$	8.00115	+	13.8584i	0.458145	+	0.793530i
$306$	5.26100	−	6.75575i	0.300752	−	0.386200i
$307$		−	10.3616i		−	0.591365i	−0.955286	−	0.295683i	$-0.904453\pi$
$307$		−	10.3616i		−	0.591365i	0.955286	−	0.295683i	$-0.0955471\pi$
$308$	−2.85051	+	3.05680i	−0.162423	+	0.174177i
$309$	6.64744	+	6.81302i	0.378160	+	0.387579i
$310$	28.9003	−	12.5662i	1.64143	−	0.713713i
$311$	10.3353			0.586061			0.293030	−	0.956103i	$-0.405336\pi$
$311$	10.3353			0.586061			0.293030	+	0.956103i	$0.405336\pi$
$312$	−15.9707	+	7.54560i	−0.904164	+	0.427185i
$313$	−6.10939			−0.345323			−0.172662	−	0.984981i	$-0.555237\pi$
$313$	−6.10939			−0.345323			−0.172662	+	0.984981i	$0.555237\pi$
$314$	19.3426	−	8.41043i	1.09157	−	0.474628i
$315$	18.9492	+	34.7690i	1.06767	+	1.95901i
$316$	−2.91828	−	2.72134i	−0.164166	−	0.153087i
$317$		−	13.9709i		−	0.784682i	−0.919820	−	0.392341i	$-0.871665\pi$
$317$		−	13.9709i		−	0.784682i	0.919820	−	0.392341i	$-0.128335\pi$
$318$	15.3850	+	6.27998i	0.862747	+	0.352164i
$319$	1.00953	+	1.74855i	0.0565226	+	0.0979001i
$320$	18.7288	−	23.1283i	1.04697	−	1.29291i
$321$	32.0507	−	8.16679i	1.78890	−	0.455826i
$322$	5.80877	+	13.3593i	0.323710	+	0.744482i
$323$	−6.14707	+	10.6470i	−0.342032	+	0.592417i
$324$	12.9085	−	12.5447i	0.717142	−	0.696928i
$325$	31.8679	−	0.274636i	1.76771	−	0.0152341i
$326$	−8.11321	−	6.00345i	−0.449349	−	0.332500i
$327$	−11.7135	+	11.4289i	−0.647761	+	0.632018i
$328$	−21.2269	+	18.1295i	−1.17206	+	1.00104i
$329$	−22.3490	+	12.9032i	−1.23214	+	0.711377i
$330$	−3.28919	−	4.24112i	−0.181064	−	0.233466i
$331$	−4.53078	+	2.61584i	−0.249034	+	0.143780i	−0.619322	−	0.785137i	$-0.712592\pi$
$331$	−4.53078	+	2.61584i	−0.249034	+	0.143780i	0.370288	+	0.928917i	$0.379259\pi$
$332$	−22.5867	+	24.2213i	−1.23960	+	1.32931i
$333$	6.12670	+	3.74115i	0.335741	+	0.205014i
$334$	1.11863	−	9.81810i	0.0612086	−	0.537223i
$335$	−0.945322	+	1.63735i	−0.0516485	+	0.0894578i
$336$	4.98686	−	24.0708i	0.272056	−	1.31317i
$337$	10.2205			0.556748			0.278374	−	0.960473i	$-0.410205\pi$
$337$	10.2205			0.556748			0.278374	+	0.960473i	$0.410205\pi$
$338$	7.62041	+	16.7311i	0.414495	+	0.910051i
$339$	6.81013	−	24.2201i	0.369876	−	1.31546i
$340$	14.6310	+	3.37782i	0.793478	+	0.183188i
$341$	−1.76410	+	3.05551i	−0.0955313	+	0.165465i
$342$	−15.8791	+	20.3907i	−0.858646	+	1.10260i
$343$	−5.00645			−0.270323
$344$	2.73444	+	14.7537i	0.147431	+	0.795464i
$345$	−18.1270	+	4.61891i	−0.975924	+	0.248674i
$346$	19.1213	−	25.8410i	1.02797	−	1.38922i
$347$	3.53236	−	2.03941i	0.189627	−	0.109481i	−0.402181	−	0.915560i	$-0.631748\pi$
$347$	3.53236	−	2.03941i	0.189627	−	0.109481i	0.591808	+	0.806079i	$0.298414\pi$
$348$	−10.4154	−	5.70339i	−0.558325	−	0.305734i
$349$	0.702729	−	1.21716i	0.0376162	−	0.0651532i	−0.846604	−	0.532223i	$-0.821357\pi$
$349$	0.702729	−	1.21716i	0.0376162	−	0.0651532i	0.884221	+	0.467070i	$0.154690\pi$
$350$	−26.3812	+	35.6522i	−1.41014	+	1.90569i
$351$	−12.8677	−	13.6170i	−0.686827	−	0.726821i
$352$	−0.145328	+	3.32871i	−0.00774602	+	0.177421i
$353$	−8.62123	+	14.9324i	−0.458862	+	0.794772i	−0.998901	−	0.0468677i	$-0.985076\pi$
$353$	−8.62123	+	14.9324i	−0.458862	+	0.794772i	0.540039	+	0.841640i	$0.318409\pi$
$354$	0.396226	+	2.89430i	0.0210592	+	0.153830i
$355$	0.326199	+	0.564994i	0.0173129	+	0.0299868i
$356$	4.34036	+	14.1966i	0.230039	+	0.752421i
$357$	12.0189	−	3.06252i	0.636109	−	0.162086i
$358$	−1.89181	+	16.6043i	−0.0999852	+	0.877562i
$359$		−	26.1725i		−	1.38133i	−0.723175	−	0.690665i	$-0.757318\pi$
$359$		−	26.1725i		−	1.38133i	0.723175	−	0.690665i	$-0.242682\pi$
$360$	29.4870	+	11.2656i	1.55410	+	0.593748i
$361$	9.05355	−	15.6812i	0.476503	−	0.825327i
$362$	−15.0889	+	6.56083i	−0.793053	+	0.344830i
$363$	−17.7629	−	4.99451i	−0.932309	−	0.262144i
$364$	−24.9786	−	5.54045i	−1.30923	−	0.290399i
$365$	33.6592			1.76180
$366$	10.4394	−	1.42914i	0.545677	−	0.0747024i
$367$	2.47051	+	1.42635i	0.128959	+	0.0744547i	0.563092	−	0.826394i	$-0.309612\pi$
$367$	2.47051	+	1.42635i	0.128959	+	0.0744547i	−0.434133	+	0.900849i	$0.642945\pi$
$368$	10.4375	+	5.09067i	0.544090	+	0.265369i
$369$	−25.2699	−	15.4306i	−1.31550	−	0.803283i
$370$	−1.42509	+	12.5079i	−0.0740870	+	0.650255i
$371$	12.0351	+	20.8455i	0.624833	+	1.08224i
$372$	−0.469068	−	20.7452i	−0.0243200	−	1.07559i
$373$	−9.40704	+	5.43116i	−0.487078	+	0.281215i	−0.723361	−	0.690470i	$-0.757404\pi$
$373$	−9.40704	+	5.43116i	−0.487078	+	0.281215i	0.236283	+	0.971684i	$0.424071\pi$
$374$	−1.54169	+	0.670346i	−0.0797188	+	0.0346628i
$375$	−17.2740	−	17.7043i	−0.892025	−	0.914244i
$376$	−6.86707	+	19.3921i	−0.354142	+	1.00007i
$377$	−6.08734	+	10.7566i	−0.313514	+	0.553993i
$378$	25.9113	−	2.89989i	1.33273	−	0.149154i
$379$	−31.6202	−	18.2560i	−1.62422	−	0.937745i	−0.985773	−	0.168081i	$-0.946243\pi$
$379$	−31.6202	−	18.2560i	−1.62422	−	0.937745i	−0.638449	−	0.769664i	$-0.720424\pi$
$380$	−44.1604	−	10.1952i	−2.26538	−	0.523003i
$381$	26.6308	−	6.78574i	1.36434	−	0.347644i
$382$	4.17159	−	5.63758i	0.213437	−	0.288444i
$383$	9.35500	−	5.40111i	0.478018	−	0.275984i	−0.241572	−	0.970383i	$-0.577663\pi$
$383$	9.35500	−	5.40111i	0.478018	−	0.275984i	0.719590	+	0.694399i	$0.244330\pi$
$384$	−9.43903	−	17.1728i	−0.481683	−	0.876345i
$385$		−	7.77427i		−	0.396214i
$386$	2.17251	−	19.0680i	0.110578	−	0.970534i
$387$	−13.9745	+	7.61611i	−0.710362	+	0.387149i
$388$	−5.72688	+	24.8059i	−0.290738	+	1.25933i
$389$	5.71199			0.289609			0.144805	−	0.989460i	$-0.453745\pi$
$389$	5.71199			0.289609			0.144805	+	0.989460i	$0.453745\pi$
$390$	12.1538	−	30.5241i	0.615430	−	1.54565i
$391$			5.85928i			0.296316i
$392$	12.0205	−	10.2665i	0.607127	−	0.518536i
$393$	1.55736	+	1.59615i	0.0785584	+	0.0805152i
$394$	−1.91514	+	16.8090i	−0.0964834	+	0.846827i
$395$	7.42198			0.373440
$396$	−3.40396	+	0.949797i	−0.171056	+	0.0477291i
$397$	−4.12607	−	7.14657i	−0.207082	−	0.358676i	0.743712	−	0.668500i	$-0.233063\pi$
$397$	−4.12607	−	7.14657i	−0.207082	−	0.358676i	−0.950794	+	0.309824i	$0.899730\pi$
$398$	1.31904	+	0.976035i	0.0661174	+	0.0489242i
$399$	−36.2764	+	9.24353i	−1.81609	+	0.462755i
$400$	2.46633	+	35.2694i	0.123317	+	1.76347i
$401$	18.1067	−	31.3618i	0.904207	−	1.56613i	0.0822297	−	0.996613i	$-0.473796\pi$
$401$	18.1067	−	31.3618i	0.904207	−	1.56613i	0.821978	−	0.569520i	$-0.192871\pi$
$402$	0.762927	+	0.983728i	0.0380514	+	0.0490639i
$403$	−21.5970	+	0.186123i	−1.07583	+	0.00927143i
$404$	1.94544	+	6.36324i	0.0967895	+	0.316583i
$405$	−1.64662	+	33.4401i	−0.0818214	+	1.66165i
$406$	−6.85873	−	15.7740i	−0.340393	−	0.782850i
$407$	−0.704700	−	1.22058i	−0.0349307	−	0.0605017i
$408$	5.69999	−	8.07885i	0.282192	−	0.399963i
$409$	−7.70920	+	4.45091i	−0.381195	+	0.220083i	−0.678338	−	0.734750i	$-0.737300\pi$
$409$	−7.70920	+	4.45091i	−0.381195	+	0.220083i	0.297143	+	0.954833i	$0.403966\pi$
$410$	5.87786	−	51.5895i	0.290287	−	2.54782i
$411$	−11.4340	−	3.21497i	−0.563997	−	0.158583i
$412$	8.03849	+	7.49601i	0.396028	+	0.369302i
$413$	−2.11575	+	3.66459i	−0.104109	+	0.180323i
$414$	−1.69495	+	12.2000i	−0.0833021	+	0.599596i
$415$		−	61.6012i		−	3.02389i
$416$	−18.0097	+	9.57345i	−0.882998	+	0.469377i
$417$	−10.2600	−	2.88486i	−0.502432	−	0.141272i
$418$	4.65324	−	2.02329i	0.227597	−	0.0989622i
$419$	−3.55319	−	2.05143i	−0.173585	−	0.100219i	0.410690	−	0.911775i	$-0.365288\pi$
$419$	−3.55319	−	2.05143i	−0.173585	−	0.100219i	−0.584275	+	0.811556i	$0.698621\pi$
$420$	23.7508	+	39.0705i	1.15892	+	1.90645i
$421$	27.3251			1.33174			0.665872	−	0.746066i	$-0.268060\pi$
$421$	27.3251			1.33174			0.665872	+	0.746066i	$0.268060\pi$
$422$	24.1787	+	2.75481i	1.17700	+	0.134102i
$423$	−21.8134	−	0.536732i	−1.06060	−	0.0260968i
$424$	18.0874	+	6.40508i	0.878404	+	0.311058i
$425$	−15.4489	+	8.91943i	−0.749382	+	0.432656i
$426$	0.425605	−	0.0582648i	0.0206206	−	0.00282294i
$427$	13.2178	+	7.63128i	0.639652	+	0.369304i
$428$	36.5228	−	11.1662i	1.76539	−	0.539737i
$429$	0.938922	+	3.55644i	0.0453316	+	0.171707i
$430$	−22.4353	−	16.6013i	−1.08193	−	0.800584i
$431$	12.1679	+	7.02516i	0.586109	+	0.338390i	0.763557	−	0.645740i	$-0.223451\pi$
$431$	12.1679	+	7.02516i	0.586109	+	0.338390i	−0.177448	+	0.984130i	$0.556784\pi$
$432$	14.2053	−	15.1726i	0.683455	−	0.729993i
$433$	−7.05544	−	12.2204i	−0.339063	−	0.587274i	0.645194	−	0.764019i	$-0.276777\pi$
$433$	−7.05544	−	12.2204i	−0.339063	−	0.587274i	−0.984257	+	0.176745i	$0.943443\pi$
$434$	17.8787	−	24.1617i	0.858206	−	1.15980i
$435$	21.4035	−	5.45379i	1.02622	−	0.261489i
$436$	−12.8878	+	13.8205i	−0.617214	+	0.661882i
$437$		−	17.6849i		−	0.845984i
$438$	8.37578	−	20.5194i	0.400210	−	0.980454i
$439$	−3.70296	−	2.13791i	−0.176733	−	0.102037i	0.409024	−	0.912524i	$-0.365869\pi$
$439$	−3.70296	−	2.13791i	−0.176733	−	0.102037i	−0.585757	+	0.810487i	$0.699203\pi$
$440$	−4.02490	−	4.71254i	−0.191879	−	0.224661i
$441$	14.3100	+	8.73811i	0.681427	+	0.416100i
$442$	−8.32492	−	6.04979i	−0.395976	−	0.287759i
$443$		−	1.56101i		−	0.0741659i	−0.999312	−	0.0370830i	$-0.988193\pi$
$443$		−	1.56101i		−	0.0741659i	0.999312	−	0.0370830i	$-0.0118066\pi$
$444$	7.27048	+	3.98125i	0.345042	+	0.188942i
$445$	−23.9134	−	13.8064i	−1.13360	−	0.654485i
$446$	3.83059	+	0.436439i	0.181384	+	0.0206660i
$447$	−8.68859	+	30.9008i	−0.410956	+	1.46156i
$448$	4.44029	−	28.0353i	0.209784	−	1.32454i
$449$	−18.5111	−	32.0622i	−0.873594	−	1.51311i	−0.858253	−	0.513227i	$-0.828450\pi$
$449$	−18.5111	−	32.0622i	−0.873594	−	1.51311i	−0.0153408	−	0.999882i	$-0.504883\pi$
$450$	−34.7473	+	14.1027i	−1.63801	+	0.664809i
$451$	2.90657	+	5.03432i	0.136865	+	0.237057i
$452$	6.53514	−	28.3069i	0.307387	−	1.33144i
$453$	26.5097	−	25.8655i	1.24554	−	1.21527i
$454$	10.9767	−	14.8341i	0.515161	−	0.696200i
$455$	41.0077	−	24.1494i	1.92247	−	1.13214i
$456$	−17.2041	+	24.3842i	−0.805657	+	1.14189i
$457$	29.1804	+	16.8473i	1.36500	+	0.788084i	0.990285	−	0.139056i	$-0.0444067\pi$
$457$	29.1804	+	16.8473i	1.36500	+	0.788084i	0.374716	+	0.927139i	$0.377740\pi$
$458$	7.80536	+	17.9511i	0.364721	+	0.838799i
$459$	10.0226	+	3.08610i	0.467817	+	0.144047i
$460$	−20.6562	+	6.31526i	−0.963101	+	0.294450i
$461$	−30.8903	+	17.8345i	−1.43871	+	0.830637i	−0.997760	−	0.0668967i	$-0.978690\pi$
$461$	−30.8903	+	17.8345i	−1.43871	+	0.830637i	−0.440946	+	0.897534i	$0.645357\pi$
$462$	−4.73937	−	1.93456i	−0.220495	−	0.0900038i
$463$	27.8126			1.29256			0.646281	−	0.763099i	$-0.276323\pi$
$463$	27.8126			1.29256			0.646281	+	0.763099i	$0.276323\pi$
$464$	−12.3241	−	6.01083i	−0.572131	−	0.279046i
$465$	26.9542	+	27.6256i	1.24997	+	1.28111i
$466$	−23.1708	+	10.0750i	−1.07337	+	0.466713i
$467$			0.0179632i			0.000831239i	1.00000		0.000415620i	$0.000132296\pi$
$467$			0.0179632i			0.000831239i	−1.00000		0.000415620i	$0.999868\pi$
$468$	−15.5838	−	15.0048i	−0.720361	−	0.693599i
$469$			1.80324i			0.0832661i
$470$	−15.2580	−	35.0910i	−0.703800	−	1.61863i
$471$	18.0402	+	18.4895i	0.831247	+	0.851952i
$472$	0.614724	+	3.31674i	0.0282950	+	0.152665i
$473$	3.12466			0.143672
$474$	1.84689	−	4.52461i	0.0848306	−	0.207822i
$475$	46.6290	−	26.9213i	2.13949	−	1.23523i
$476$	13.6959	−	4.18728i	0.627752	−	0.191923i
$477$	−0.500622	+	20.3458i	−0.0229219	+	0.931571i
$478$	3.32199	−	1.44444i	0.151944	−	0.0660672i
$479$	−7.63328	−	4.40707i	−0.348773	−	0.201364i	0.315372	−	0.948968i	$-0.397871\pi$
$479$	−7.63328	−	4.40707i	−0.348773	−	0.201364i	−0.664145	+	0.747604i	$0.731204\pi$
$480$	34.6246	+	11.3871i	1.58039	+	0.519748i
$481$	4.24927	−	7.50864i	0.193750	−	0.342365i
$482$	20.1537	+	14.9129i	0.917974	+	0.679264i
$483$	−12.7700	+	12.4597i	−0.581056	+	0.566935i
$484$	−20.7601	−	4.79283i	−0.943640	−	0.217856i
$485$	−23.6768	−	41.0093i	−1.07511	−	1.86214i
$486$	19.9761	+	9.32508i	0.906132	+	0.422994i
$487$	7.09936	+	12.2965i	0.321703	+	0.557206i	0.980839	−	0.194818i	$-0.0624115\pi$
$487$	7.09936	+	12.2965i	0.321703	+	0.557206i	−0.659137	+	0.752023i	$0.729078\pi$
$488$	11.9631	−	2.21724i	0.541543	−	0.100370i
$489$	3.34592	−	11.8997i	0.151308	−	0.538124i
$490$	−3.32855	+	29.2144i	−0.150369	+	1.31977i
$491$	−15.2530	−	8.80634i	−0.688360	−	0.397425i	0.114638	−	0.993407i	$-0.463429\pi$
$491$	−15.2530	−	8.80634i	−0.688360	−	0.397425i	−0.802997	+	0.595983i	$0.796763\pi$
$492$	−29.9874	−	16.4209i	−1.35194	−	0.740309i
$493$		−	6.91837i		−	0.311587i
$494$	25.1269	+	18.2599i	1.13051	+	0.821552i
$495$	3.42570	−	5.61011i	0.153974	−	0.252156i
$496$	−1.67145	−	23.9023i	−0.0750502	−	1.07324i
$497$	0.538876	+	0.311120i	0.0241719	+	0.0139556i
$498$	−37.5535	−	15.3289i	−1.68281	−	0.686905i
$499$		−	25.9485i		−	1.16161i	−0.814041	−	0.580807i	$-0.802737\pi$
$499$		−	25.9485i		−	1.16161i	0.814041	−	0.580807i	$-0.197263\pi$
$500$	−20.8888	−	19.4791i	−0.934174	−	0.871130i
$501$	11.7277	−	2.98832i	0.523956	−	0.133508i
$502$	15.7864	+	11.6813i	0.704581	+	0.521362i
$503$	7.23565	+	12.5325i	0.322622	+	0.558797i	0.981028	−	0.193866i	$-0.0621026\pi$
$503$	7.23565	+	12.5325i	0.322622	+	0.558797i	−0.658407	+	0.752662i	$0.728769\pi$
$504$	29.7284	−	4.75670i	1.32421	−	0.211880i
$505$	−10.7185	−	6.18832i	−0.476966	−	0.275377i
$506$	1.43844	−	1.94394i	0.0639463	−	0.0864185i
$507$	−15.8429	+	16.0001i	−0.703608	+	0.710588i
$508$	30.3466	−	9.27790i	1.34641	−	0.411640i
$509$	0.522951	+	0.301926i	0.0231794	+	0.0133826i	0.511545	−	0.859257i	$-0.329073\pi$
$509$	0.522951	+	0.301926i	0.0231794	+	0.0133826i	−0.488366	+	0.872639i	$0.662407\pi$
$510$	2.49439	+	18.2207i	0.110453	+	0.806824i
$511$	27.8022	−	16.0516i	1.22990	−	0.710081i
$512$	−11.8229	−	19.2930i	−0.522501	−	0.852638i
$513$	−30.2511	−	9.31470i	−1.33562	−	0.411254i
$514$	−0.153860	+	1.35041i	−0.00678647	+	0.0595643i
$515$	−20.4441			−0.900874
$516$	−15.7033	+	9.54601i	−0.691301	+	0.420240i
$517$	3.71003	+	2.14199i	0.163167	+	0.0942045i
$518$	4.78774	+	11.0110i	0.210361	+	0.483797i
$519$	37.9012	+	10.6569i	1.66368	+	0.467788i
$520$	12.3551	−	35.8692i	0.541805	−	1.57297i
$521$			6.34128i			0.277817i	0.990305	+	0.138908i	$0.0443593\pi$
$521$			6.34128i			0.277817i	−0.990305	+	0.138908i	$0.955641\pi$
$522$	2.00132	−	14.4052i	0.0875952	−	0.630497i
$523$	0.335974	−	0.581925i	0.0146911	−	0.0254458i	−0.858586	−	0.512669i	$-0.828657\pi$
$523$	0.335974	−	0.581925i	0.0146911	−	0.0254458i	0.873278	+	0.487223i	$0.161990\pi$
$524$	1.88326	+	1.75616i	0.0822704	+	0.0767183i
$525$	−52.2914	−	14.7031i	−2.28218	−	0.641697i
$526$	−28.0458	−	3.19541i	−1.22286	−	0.139326i
$527$	10.4698	−	6.04475i	0.456073	−	0.263314i
$528$	−3.87443	+	1.28099i	−0.168613	+	0.0557481i
$529$	7.28577	+	12.6193i	0.316772	+	0.548666i
$530$	−32.7302	+	14.2315i	−1.42171	+	0.618177i
$531$	−3.14157	+	1.71216i	−0.136332	+	0.0743015i
$532$	−41.3380	+	12.6383i	−1.79223	+	0.547942i
$533$	−17.5263	+	30.9698i	−0.759149	+	1.34145i
$534$	−14.3673	+	11.1425i	−0.621734	+	0.482184i
$535$	−35.5188	+	61.5203i	−1.53561	+	2.65975i
$536$	0.933575	+	1.09307i	0.0403243	+	0.0472136i
$537$	−19.8338	+	5.05382i	−0.855891	+	0.218088i
$538$	−21.1525	+	28.5860i	−0.911948	+	1.23243i
$539$	−1.64595	−	2.85087i	−0.0708960	−	0.122796i
$540$	−0.0770748	+	38.6600i	−0.00331677	+	1.66366i
$541$	−31.1873			−1.34085			−0.670424	−	0.741978i	$-0.733888\pi$
$541$	−31.1873			−1.34085			−0.670424	+	0.741978i	$0.733888\pi$
$542$	−17.3949	−	1.98190i	−0.747176	−	0.0851297i
$543$	−14.0728	−	14.4233i	−0.603922	−	0.618965i
$544$	6.13423	−	9.62885i	0.263003	−	0.412834i
$545$		−	35.1493i		−	1.50563i
$546$	−4.51760	−	31.0086i	−0.193335	−	1.32704i
$547$	24.7721			1.05918			0.529589	−	0.848254i	$-0.322346\pi$
$547$	24.7721			1.05918			0.529589	+	0.848254i	$0.322346\pi$
$548$	−13.3633	−	3.08515i	−0.570852	−	0.131791i
$549$	6.17557	+	11.3313i	0.263567	+	0.483607i
$550$	7.31519	+	0.833458i	0.311921	+	0.0355388i
$551$			20.8815i			0.889583i
$552$	−1.29019	+	14.1640i	−0.0549143	+	0.602859i
$553$	6.13049	−	3.53944i	0.260695	−	0.150512i
$554$	−8.92594	−	6.60484i	−0.379227	−	0.280613i
$555$	−14.9407	+	3.80702i	−0.634197	+	0.161599i
$556$	−11.9912	−	2.76837i	−0.508539	−	0.117405i
$557$	−18.6831	−	10.7867i	−0.791627	−	0.457046i	0.0489082	−	0.998803i	$-0.484426\pi$
$557$	−18.6831	−	10.7867i	−0.791627	−	0.457046i	−0.840535	+	0.541757i	$0.817759\pi$
$558$	23.5485	−	9.55751i	0.996887	−	0.404602i
$559$	9.70619	+	16.4819i	0.410528	+	0.697112i
$560$	29.5235	+	43.7703i	1.24760	+	1.84963i
$561$	−1.43788	−	1.47369i	−0.0607072	−	0.0622193i
$562$	−0.816370	−	1.87752i	−0.0344365	−	0.0791985i
$563$	26.6787	−	15.4029i	1.12437	−	0.649156i	0.181858	−	0.983325i	$-0.441789\pi$
$563$	26.6787	−	15.4029i	1.12437	−	0.649156i	0.942513	+	0.334169i	$0.108456\pi$
$564$	−25.1891	+	0.569547i	−1.06065	+	0.0239823i
$565$	27.0183	+	46.7971i	1.13667	+	1.96877i
$566$	17.5160	+	1.99569i	0.736254	+	0.0838852i
$567$	14.5870	+	28.4064i	0.612597	+	1.19296i
$568$	0.487724	−	0.0903948i	0.0204644	−	0.00379288i
$569$	−0.994883	−	0.574396i	−0.0417077	−	0.0240799i	0.479001	−	0.877814i	$-0.340999\pi$
$569$	−0.994883	−	0.574396i	−0.0417077	−	0.0240799i	−0.520709	+	0.853734i	$0.674332\pi$
$570$	−7.52874	−	54.9949i	−0.315344	−	2.30348i
$571$	37.7248			1.57873			0.789366	−	0.613923i	$-0.210409\pi$
$571$	37.7248			1.57873			0.789366	+	0.613923i	$0.210409\pi$
$572$	1.27676	+	4.05089i	0.0533839	+	0.169376i
$573$	8.26869	+	2.32496i	0.345429	+	0.0971267i
$574$	−19.7473	−	45.4155i	−0.824234	−	1.89561i
$575$	12.8304	−	22.2230i	0.535066	−	0.926762i
$576$	15.5579	−	18.2744i	0.648245	−	0.761432i
$577$			1.02376i			0.0426199i	0.999773	+	0.0213099i	$0.00678368\pi$
$577$			1.02376i			0.0426199i	−0.999773	+	0.0213099i	$0.993216\pi$
$578$	−18.1637	−	2.06948i	−0.755510	−	0.0860792i
$579$	22.7767	−	5.80370i	0.946568	−	0.241193i
$580$	24.3899	−	7.45677i	1.01274	−	0.309625i
$581$	−29.3768	−	50.8821i	−1.21875	−	2.11094i
$582$	−30.8920	+	4.22907i	−1.28051	+	0.175301i
$583$	1.99788	−	3.46043i	0.0827438	−	0.143316i
$584$	8.54263	−	24.1237i	0.353497	−	0.998247i
$585$	40.2335	+	0.643104i	1.66345	+	0.0265891i
$586$	−11.0524	−	8.17836i	−0.456572	−	0.337845i
$587$	−4.61426	+	7.99213i	−0.190451	+	0.329871i	−0.945400	−	0.325913i	$-0.894328\pi$
$587$	−4.61426	+	7.99213i	−0.190451	+	0.329871i	0.754949	+	0.655784i	$0.227662\pi$
$588$	16.9815	+	9.29890i	0.700304	+	0.383480i
$589$	−31.6008	+	18.2447i	−1.30209	+	0.751761i
$590$	−5.04364	−	3.73209i	−0.207643	−	0.153648i
$591$	−20.0784	+	5.11614i	−0.825915	+	0.210450i
$592$	8.60281	+	4.19585i	0.353573	+	0.172449i
$593$	38.1844			1.56804			0.784022	−	0.620733i	$-0.213165\pi$
$593$	38.1844			1.56804			0.784022	+	0.620733i	$0.213165\pi$
$594$	−2.56759	−	3.48441i	−0.105350	−	0.142967i
$595$	−13.3194	+	23.0699i	−0.546043	+	0.945775i
$596$	−8.33774	+	36.1149i	−0.341527	+	1.47932i
$597$	−0.543977	+	1.93464i	−0.0222635	+	0.0791797i
$598$	14.7221	+	1.54897i	0.602032	+	0.0633422i
$599$	4.09541			0.167334			0.0836670	−	0.996494i	$-0.473337\pi$
$599$	4.09541			0.167334			0.0836670	+	0.996494i	$0.473337\pi$
$600$	−39.3096	+	18.1597i	−1.60481	+	0.741366i
$601$	1.94649	−	3.37142i	0.0793991	−	0.137523i	−0.823592	−	0.567183i	$-0.808033\pi$
$601$	1.94649	−	3.37142i	0.0793991	−	0.137523i	0.902991	+	0.429660i	$0.141367\pi$
$602$	−26.4483	−	3.01339i	−1.07795	−	0.122817i
$603$	−0.794592	+	1.30127i	−0.0323583	+	0.0529916i
$604$	29.1673	−	31.2781i	1.18680	−	1.27269i
$605$	34.3207	−	19.8151i	1.39534	−	0.805597i
$606$	−6.43974	+	4.99432i	−0.261596	+	0.202880i
$607$	9.29224	−	5.36488i	0.377160	−	0.217754i	−0.299422	−	0.954121i	$-0.596794\pi$
$607$	9.29224	−	5.36488i	0.377160	−	0.217754i	0.676582	+	0.736367i	$0.263460\pi$
$608$	−18.5148	+	29.0625i	−0.750874	+	1.17864i
$609$	15.0783	−	14.7118i	0.611002	−	0.596153i
$610$	−13.4612	+	18.1918i	−0.545030	+	0.736566i
$611$	0.225992	+	26.2234i	0.00914266	+	1.06088i
$612$	11.7284	+	3.01341i	0.474093	+	0.121810i
$613$	14.4049	−	24.9501i	0.581809	−	1.00772i	−0.413456	−	0.910524i	$-0.635678\pi$
$613$	14.4049	−	24.9501i	0.581809	−	1.00772i	0.995265	−	0.0971992i	$-0.0309884\pi$
$614$	13.4381	−	5.84306i	0.542317	−	0.235807i
$615$	61.6237	−	15.7022i	2.48491	−	0.633175i
$616$	−5.57187	−	1.97310i	−0.224497	−	0.0794983i
$617$	2.91655	+	5.05161i	0.117416	+	0.203370i	0.918743	−	0.394856i	$-0.129206\pi$
$617$	2.91655	+	5.05161i	0.117416	+	0.203370i	−0.801327	+	0.598226i	$0.795872\pi$
$618$	−5.08732	+	12.4632i	−0.204642	+	0.501342i
$619$			45.7442i			1.83861i	0.393542	+	0.919306i	$0.371249\pi$
$619$			45.7442i			1.83861i	−0.393542	+	0.919306i	$0.628751\pi$
$620$	32.5947	+	30.3950i	1.30903	+	1.22069i
$621$	−14.7055	+	3.36415i	−0.590110	+	0.134999i
$622$	5.82825	+	13.4040i	0.233691	+	0.537453i
$623$	−26.3363			−1.05514
$624$	−18.7922	−	16.4576i	−0.752289	−	0.658833i
$625$	8.93141			0.357256
$626$	−3.44519	−	7.92339i	−0.137697	−	0.316682i
$627$	4.33990	+	4.44800i	0.173319	+	0.177636i
$628$	21.8153	+	20.3431i	0.870525	+	0.811776i
$629$			4.82936i			0.192559i
$630$	−34.4068	+	44.1824i	−1.37080	+	1.76027i
$631$	4.98809	+	8.63962i	0.198573	+	0.343938i	0.948066	−	0.318074i	$-0.103036\pi$
$631$	4.98809	+	8.63962i	0.198573	+	0.343938i	−0.749493	+	0.662012i	$0.769703\pi$
$632$	1.88369	−	5.31938i	0.0749290	−	0.211594i
$633$	7.35924	+	28.8815i	0.292504	+	1.14794i
$634$	18.1191	−	7.87841i	0.719601	−	0.312892i
$635$	−29.5123	+	51.1169i	−1.17116	+	2.02851i
$636$	0.531230	+	23.4944i	0.0210646	+	0.931615i
$637$	9.92490	−	17.5377i	0.393239	−	0.694871i
$638$	−1.69844	+	2.29531i	−0.0672419	+	0.0908722i
$639$	0.251772	+	0.461965i	0.00995995	+	0.0182751i
$640$	40.5570	+	11.2473i	1.60316	+	0.444590i
$641$	−2.47142	+	1.42687i	−0.0976152	+	0.0563581i	−0.548013	−	0.836470i	$-0.684616\pi$
$641$	−2.47142	+	1.42687i	−0.0976152	+	0.0563581i	0.450398	+	0.892828i	$0.351282\pi$
$642$	28.6656	+	36.9618i	1.13134	+	1.45877i
$643$	−11.4570	+	6.61468i	−0.451819	+	0.260858i	−0.708598	−	0.705612i	$-0.750672\pi$
$643$	−11.4570	+	6.61468i	−0.451819	+	0.260858i	0.256779	+	0.966470i	$0.417339\pi$
$644$	−14.0502	+	15.0670i	−0.553655	+	0.593724i
$645$	9.25244	−	32.9061i	0.364315	−	1.29568i
$646$	−17.2748	−	1.96821i	−0.679667	−	0.0774381i
$647$	−7.13974	+	12.3664i	−0.280692	+	0.486173i	−0.971555	−	0.236813i	$-0.923897\pi$
$647$	−7.13974	+	12.3664i	−0.280692	+	0.486173i	0.690863	+	0.722985i	$0.257231\pi$
$648$	23.5488	+	9.66717i	0.925084	+	0.379762i
$649$	0.702447			0.0275735
$650$	18.3270	+	41.1751i	0.718844	+	1.61502i
$651$	35.4382	+	9.96441i	1.38893	+	0.390536i
$652$	3.21081	−	13.9076i	0.125745	−	0.544664i
$653$	−13.2344	+	22.9227i	−0.517903	+	0.897035i	0.481880	+	0.876237i	$0.339954\pi$
$653$	−13.2344	+	22.9227i	−0.517903	+	0.897035i	−0.999784	+	0.0207979i	$0.993379\pi$
$654$	−21.4278	−	8.74658i	−0.837893	−	0.342018i
$655$	−4.78963			−0.187146
$656$	−35.4827	−	17.3060i	−1.38537	−	0.675686i
$657$	27.1358	+	0.667694i	1.05867	+	0.0260492i
$658$	−29.3374	−	21.7085i	−1.14369	−	0.846286i
$659$	12.9512	−	7.47737i	0.504507	−	0.291277i	−0.226066	−	0.974112i	$-0.572586\pi$
$659$	12.9512	−	7.47737i	0.504507	−	0.291277i	0.730573	+	0.682835i	$0.239253\pi$
$660$	3.64556	−	6.65745i	0.141903	−	0.259141i
$661$	−8.28018	+	14.3417i	−0.322062	+	0.557827i	−0.980913	−	0.194446i	$-0.937709\pi$
$661$	−8.28018	+	14.3417i	−0.322062	+	0.557827i	0.658851	+	0.752273i	$0.271043\pi$
$662$	−5.94752	−	4.40093i	−0.231157	−	0.171047i
$663$	3.30692	−	12.1623i	0.128430	−	0.472343i
$664$	−44.1500	−	15.6343i	−1.71335	−	0.606728i
$665$	40.2017	−	69.6313i	1.55895	−	2.70019i
$666$	−1.39702	+	10.0555i	−0.0541333	+	0.389644i
$667$	4.97597	+	8.61863i	0.192670	+	0.333715i
$668$	13.3641	−	4.08582i	0.517072	−	0.158085i
$669$	1.16591	+	4.57564i	0.0450768	+	0.176905i
$670$	−2.65659	−	0.302679i	−0.102633	−	0.0116935i
$671$		−	2.53365i		−	0.0978104i
$672$	34.0300	−	7.10636i	1.31274	−	0.274134i
$673$	5.34089	−	9.25069i	0.205876	−	0.356588i	−0.744535	−	0.667583i	$-0.767329\pi$
$673$	5.34089	−	9.25069i	0.205876	−	0.356588i	0.950412	+	0.310995i	$0.100662\pi$
$674$	5.76353	+	13.2552i	0.222003	+	0.510571i
$675$	−31.2559	−	33.6521i	−1.20304	−	1.29527i
$676$	−17.4016	+	19.3180i	−0.669292	+	0.743000i
$677$	30.2646			1.16316			0.581581	−	0.813489i	$-0.302434\pi$
$677$	30.2646			1.16316			0.581581	+	0.813489i	$0.302434\pi$
$678$	35.2518	−	4.82593i	1.35384	−	0.185339i
$679$	−39.1136	−	22.5822i	−1.50104	−	0.866627i
$680$	3.86991	+	20.8800i	0.148404	+	0.800713i
$681$	21.7574	+	6.11767i	0.833744	+	0.234429i
$682$	−4.95755	−	0.564840i	−0.189834	−	0.0216288i
$683$	−4.56099	−	7.89986i	−0.174521	−	0.302280i	0.765474	−	0.643467i	$-0.222504\pi$
$683$	−4.56099	−	7.89986i	−0.174521	−	0.302280i	−0.939996	+	0.341187i	$0.889171\pi$
$684$	−35.3996	−	9.09531i	−1.35354	−	0.347768i
$685$	22.0923	−	12.7550i	0.844104	−	0.487344i
$686$	−2.82322	−	6.49296i	−0.107791	−	0.247902i
$687$	−17.1593	+	16.7423i	−0.654669	+	0.638759i
$688$	−17.5923	+	11.8662i	−0.670700	+	0.452394i
$689$	24.4591	−	0.210788i	0.931819	−	0.00803038i
$690$	−16.2125	−	20.9045i	−0.617198	−	0.795822i
$691$	20.8998	+	12.0665i	0.795065	+	0.459031i	0.841743	−	0.539879i	$-0.181530\pi$
$691$	20.8998	+	12.0665i	0.795065	+	0.459031i	−0.0466775	+	0.998910i	$0.514863\pi$
$692$	44.2965	+	10.2266i	1.68390	+	0.388757i
$693$	0.154218	−	6.26757i	0.00585824	−	0.238085i
$694$	4.63690	+	3.43112i	0.176014	+	0.130244i
$695$	19.8239	−	11.4453i	0.751963	−	0.434146i
$696$	1.52340	−	16.7242i	0.0577444	−	0.633929i
$697$		−	19.9189i		−	0.754484i
$698$	1.97484	+	0.225004i	0.0747489	+	0.00851653i
$699$	−21.6105	−	22.1488i	−0.817385	−	0.837745i
$700$	−61.1148	−	14.1094i	−2.30992	−	0.533286i
$701$	−52.5345			−1.98420			−0.992100	−	0.125450i	$-0.959962\pi$
$701$	−52.5345			−1.98420			−0.992100	+	0.125450i	$0.959962\pi$
$702$	10.4038	−	24.3672i	0.392666	−	0.919681i
$703$		−	14.5763i		−	0.549757i
$704$	−4.39902	+	1.68864i	−0.165794	+	0.0636428i
$705$	33.5433	−	32.7281i	1.26331	−	1.23261i
$706$	−24.2278	−	2.76040i	−0.911825	−	0.103889i
$707$	−11.8045			−0.443954
$708$	−3.53023	+	2.14602i	−0.132674	+	0.0806523i
$709$	9.54850	+	16.5385i	0.358601	+	0.621116i	0.987727	−	0.156188i	$-0.0499204\pi$
$709$	9.54850	+	16.5385i	0.358601	+	0.621116i	−0.629126	+	0.777303i	$0.716587\pi$
$710$	−0.548802	+	0.741664i	−0.0205962	+	0.0278341i
$711$	5.98355	+	0.147229i	0.224401	+	0.00552152i
$712$	−15.9643	+	13.6348i	−0.598287	+	0.510987i
$713$	−8.69527	+	15.0606i	−0.325640	+	0.564026i
$714$	10.7495	+	13.8606i	0.402291	+	0.518718i
$715$	−6.87553	−	3.89098i	−0.257130	−	0.145514i
$716$	−22.6012	+	6.90990i	−0.844646	+	0.258235i
$717$	3.09829	+	3.17547i	0.115708	+	0.118590i
$718$	33.9436	−	14.7591i	1.26676	−	0.550804i
$719$	17.5778	+	30.4456i	0.655541	+	1.13543i	0.981758	+	0.190135i	$0.0608927\pi$
$719$	17.5778	+	30.4456i	0.655541	+	1.13543i	−0.326217	+	0.945295i	$0.605774\pi$
$720$	2.01770	+	44.5952i	0.0751953	+	1.66196i
$721$	−16.8866	+	9.74950i	−0.628891	+	0.363090i
$722$	25.4427	+	2.89882i	0.946879	+	0.107883i
$723$	−8.31146	+	29.5595i	−0.309107	+	1.09933i
$724$	−17.0177	−	15.8693i	−0.632459	−	0.589776i
$725$	−15.1496	+	26.2399i	−0.562642	+	0.974524i
$726$	−3.53931	−	25.8535i	−0.131356	−	0.959512i
$727$			37.8297i			1.40303i	0.712656	+	0.701514i	$0.247492\pi$
$727$			37.8297i			1.40303i	−0.712656	+	0.701514i	$0.752508\pi$
$728$	−6.90033	−	35.5196i	−0.255743	−	1.31644i
$729$	−1.99085	+	26.9265i	−0.0737350	+	0.997278i
$730$	18.9810	+	43.6532i	0.702517	+	1.61568i
$731$	−9.27233	−	5.35338i	−0.342950	−	0.198002i
$732$	7.74044	+	12.7331i	0.286095	+	0.470631i
$733$	14.8301			0.547762			0.273881	−	0.961764i	$-0.411693\pi$
$733$	14.8301			0.547762			0.273881	+	0.961764i	$0.411693\pi$
$734$	−0.456696	+	4.00839i	−0.0168570	+	0.147952i
$735$	−34.8966	+	8.89195i	−1.28718	+	0.327985i
$736$	−0.716325	+	16.4072i	−0.0264041	+	0.604779i
$737$	0.259241	−	0.149673i	0.00954927	−	0.00551327i
$738$	5.76207	−	41.4745i	0.212105	−	1.52670i
$739$	1.91745	+	1.10704i	0.0705347	+	0.0407232i	0.534853	−	0.844945i	$-0.320367\pi$
$739$	1.91745	+	1.10704i	0.0705347	+	0.0407232i	−0.464318	+	0.885669i	$0.653700\pi$
$740$	−17.0254	+	5.20519i	−0.625865	+	0.191347i
$741$	−9.98119	+	36.7090i	−0.366668	+	1.34854i
$742$	−20.2480	+	27.3637i	−0.743329	+	1.00455i
$743$	−23.9890	−	13.8501i	−0.880071	−	0.508109i	−0.00938946	−	0.999956i	$-0.502989\pi$
$743$	−23.9890	−	13.8501i	−0.880071	−	0.508109i	−0.870682	+	0.491846i	$0.836322\pi$
$744$	26.6404	−	12.3069i	0.976683	−	0.451194i
$745$	−34.4709	−	59.7053i	−1.26292	−	2.18743i
$746$	−12.3486	−	9.13744i	−0.452113	−	0.334546i
$747$	1.22198	−	49.6625i	0.0447098	−	1.81706i
$748$	−1.73877	−	1.62143i	−0.0635757	−	0.0592852i
$749$			67.7536i			2.47566i
$750$	13.2199	−	32.3867i	0.482722	−	1.18259i
$751$	−11.0887	−	6.40206i	−0.404632	−	0.233614i	0.283849	−	0.958869i	$-0.408389\pi$
$751$	−11.0887	−	6.40206i	−0.404632	−	0.233614i	−0.688481	+	0.725255i	$0.741722\pi$
$752$	−29.0224	+	2.02949i	−1.05834	+	0.0740078i
$753$	−6.51038	+	23.1540i	−0.237251	+	0.843780i
$754$	−17.3832	−	1.82895i	−0.633059	−	0.0666066i
$755$			79.5487i			2.89508i
$756$	18.3727	+	31.9695i	0.668210	+	1.16272i
$757$	−0.297231	−	0.171606i	−0.0108030	−	0.00623713i	0.494589	−	0.869127i	$-0.335319\pi$
$757$	−0.297231	−	0.171606i	−0.0108030	−	0.00623713i	−0.505392	+	0.862890i	$0.668652\pi$
$758$	5.84530	−	51.3037i	0.212311	−	1.86343i
$759$	2.85119	+	0.801689i	0.103492	+	0.0290995i
$760$	−11.6805	−	63.0217i	−0.423695	−	2.28604i
$761$	−25.1264	−	43.5201i	−0.910830	−	1.57760i	−0.812895	−	0.582411i	$-0.802110\pi$
$761$	−25.1264	−	43.5201i	−0.910830	−	1.57760i	−0.0979349	−	0.995193i	$-0.531224\pi$
$762$	23.8181	+	30.7113i	0.862839	+	1.11255i
$763$	−16.7622	−	29.0330i	−0.606833	−	1.05106i
$764$	9.66391	+	2.23108i	0.349628	+	0.0807177i
$765$	−19.7773	+	10.7787i	−0.715050	+	0.389704i
$766$	12.2802	+	9.08690i	0.443703	+	0.328323i
$767$	2.18203	+	3.70527i	0.0787884	+	0.133789i
$768$	16.9489	−	21.9257i	0.611590	−	0.791175i
$769$	−17.8409	−	10.3005i	−0.643361	−	0.371444i	0.142547	−	0.989788i	$-0.454471\pi$
$769$	−17.8409	−	10.3005i	−0.643361	−	0.371444i	−0.785908	+	0.618344i	$0.787804\pi$
$770$	10.0826	−	4.38404i	0.363352	−	0.157990i
$771$	−1.61307	+	0.411024i	−0.0580933	+	0.0148027i
$772$	25.9547	−	7.93518i	0.934131	−	0.285593i
$773$	10.0645	−	5.81076i	0.361996	−	0.208999i	−0.307960	−	0.951399i	$-0.599646\pi$
$773$	10.0645	−	5.81076i	0.361996	−	0.208999i	0.669956	+	0.742401i	$0.266313\pi$
$774$	−17.7579	−	13.8289i	−0.638295	−	0.497069i
$775$	−52.9464			−1.90189
$776$	−35.4008	+	6.56119i	−1.27081	+	0.235533i
$777$	−10.5254	+	10.2696i	−0.377596	+	0.368419i
$778$	3.22109	+	7.40799i	0.115482	+	0.265589i
$779$			60.1208i			2.15405i
$780$	46.4409	−	1.45058i	1.66285	−	0.0519391i
$781$		−	0.103294i		−	0.00369616i
$782$	−7.59901	+	3.30415i	−0.271740	+	0.118156i
$783$	17.3635	−	3.97223i	0.620523	−	0.141956i
$784$	20.0934	+	9.80015i	0.717620	+	0.350005i
$785$	−55.4822			−1.98024
$786$	−1.19186	+	2.91986i	−0.0425121	+	0.104148i
$787$	−39.3135	+	22.6977i	−1.40137	+	0.809084i	−0.994534	−	0.104415i	$-0.966703\pi$
$787$	−39.3135	+	22.6977i	−1.40137	+	0.809084i	−0.406841	+	0.913499i	$0.633370\pi$
$788$	−22.8799	+	6.99511i	−0.815063	+	0.249191i
$789$	−8.53627	−	33.5007i	−0.303899	−	1.19266i
$790$	4.18538	+	9.62571i	0.148909	+	0.342467i
$791$	44.6338	+	25.7693i	1.58700	+	0.916252i
$792$	−3.15136	−	3.87906i	−0.111979	−	0.137836i
$793$	13.3645	−	7.87032i	0.474587	−	0.279483i
$794$	6.94175	−	9.38125i	0.246354	−	0.332928i
$795$	−30.5262	−	31.2866i	−1.08265	−	1.10962i
$796$	−0.522011	+	2.26109i	−0.0185022	+	0.0801421i
$797$	−6.94433	−	12.0279i	−0.245981	−	0.426051i	0.716426	−	0.697663i	$-0.245777\pi$
$797$	−6.94433	−	12.0279i	−0.245981	−	0.426051i	−0.962407	+	0.271612i	$0.912443\pi$
$798$	−32.4450	−	41.8350i	−1.14854	−	1.48094i
$799$	−7.33960	−	12.7126i	−0.259657	−	0.449738i
$800$	−44.3507	+	23.0876i	−1.56804	+	0.816271i
$801$	−19.0049	−	11.6050i	−0.671506	−	0.410042i
$802$	50.8844	+	5.79752i	1.79679	+	0.204718i
$803$	−4.61528	−	2.66463i	−0.162870	−	0.0940328i
$804$	−0.845588	+	1.54420i	−0.0298216	+	0.0544596i
$805$		−	38.3195i		−	1.35059i
$806$	−12.4203	−	27.9047i	−0.437487	−	0.982899i
$807$	−41.9273	−	11.7890i	−1.47591	−	0.414992i
$808$	−7.15554	+	6.11142i	−0.251731	+	0.214999i
$809$	−28.9138	−	16.6934i	−1.01655	−	0.586908i	−0.103450	−	0.994635i	$-0.532988\pi$
$809$	−28.9138	−	16.6934i	−1.01655	−	0.586908i	−0.913104	+	0.407727i	$0.866322\pi$
$810$	−44.2976	+	16.7219i	−1.55646	+	0.587547i
$811$		−	16.8255i		−	0.590823i	−0.955370	−	0.295411i	$-0.904543\pi$
$811$		−	16.8255i		−	0.590823i	0.955370	−	0.295411i	$-0.0954567\pi$
$812$	16.5898	−	17.7904i	0.582189	−	0.624322i
$813$	−5.29447	−	20.7783i	−0.185685	−	0.728725i
$814$	1.18559	−	1.60224i	0.0415551	−	0.0561585i
$815$	13.2745	+	22.9922i	0.464987	+	0.805380i
$816$	13.6919	+	2.83663i	0.479313	+	0.0993018i
$817$	27.9864	+	16.1580i	0.979121	+	0.565296i
$818$	−10.1198	−	7.48826i	−0.353831	−	0.261821i
$819$	33.5392	−	18.6556i	1.17195	−	0.651880i
$820$	70.2220	−	21.4691i	2.45226	−	0.749733i
$821$	25.4054	+	14.6678i	0.886653	+	0.511909i	0.872846	−	0.487995i	$-0.162272\pi$
$821$	25.4054	+	14.6678i	0.886653	+	0.511909i	0.0138067	+	0.999905i	$0.495605\pi$
$822$	−2.27826	−	16.6419i	−0.0794634	−	0.580454i
$823$	−16.5273	+	9.54205i	−0.576106	+	0.332615i	−0.759584	−	0.650409i	$-0.774598\pi$
$823$	−16.5273	+	9.54205i	−0.576106	+	0.332615i	0.183478	+	0.983024i	$0.441264\pi$
$824$	−5.18867	+	14.6524i	−0.180756	+	0.510440i
$825$	2.22652	+	8.73800i	0.0775173	+	0.304218i
$826$	−5.94579	−	0.677434i	−0.206880	−	0.0235710i
$827$	43.0109			1.49564			0.747818	−	0.663903i	$-0.231101\pi$
$827$	43.0109			1.49564			0.747818	+	0.663903i	$0.231101\pi$
$828$	−16.7782	+	4.68157i	−0.583082	+	0.162696i
$829$	−13.0937	−	7.55968i	−0.454765	−	0.262558i	0.255076	−	0.966921i	$-0.417900\pi$
$829$	−13.0937	−	7.55968i	−0.454765	−	0.262558i	−0.709840	+	0.704363i	$0.751233\pi$
$830$	79.8918	−	34.7380i	2.77308	−	1.20577i
$831$	3.68110	−	13.0918i	0.127696	−	0.454148i
$832$	−22.5720	−	17.9585i	−0.782542	−	0.622598i
$833$			11.2798i			0.390823i
$834$	−2.04433	−	14.9331i	−0.0707893	−	0.517093i
$835$	−12.9967	+	22.5110i	−0.449770	+	0.779025i
$836$	5.24808	+	4.89391i	0.181509	+	0.169259i
$837$	21.1823	+	22.8063i	0.732168	+	0.788300i
$838$	0.656841	−	5.76504i	0.0226902	−	0.199150i
$839$	−23.2564	+	13.4271i	−0.802901	+	0.463555i	−0.844485	−	0.535580i	$-0.820093\pi$
$839$	−23.2564	+	13.4271i	−0.802901	+	0.463555i	0.0415836	+	0.999135i	$0.486760\pi$
$840$	−37.2778	+	52.8354i	−1.28621	+	1.82300i
$841$	8.62460	+	14.9383i	0.297400	+	0.515112i
$842$	15.4091	+	35.4385i	0.531032	+	1.22129i
$843$	1.79471	−	1.75109i	0.0618131	−	0.0603109i
$844$	10.0620	+	32.9113i	0.346349	+	1.13285i
$845$	−0.833482	−	48.3537i	−0.0286727	−	1.66342i
$846$	−11.6048	−	28.5928i	−0.398982	−	0.983042i
$847$	18.8991	−	32.7341i	0.649380	−	1.12476i
$848$	1.89295	+	27.0699i	0.0650042	+	0.929583i
$849$	5.33133	+	20.9229i	0.182971	+	0.718072i
$850$	−20.2797	−	15.0062i	−0.695587	−	0.514707i
$851$	−3.47347	−	6.01623i	−0.119069	−	0.206234i
$852$	0.315570	+	0.519118i	0.0108113	+	0.0177847i
$853$	−33.0782			−1.13258			−0.566288	−	0.824208i	$-0.691621\pi$
$853$	−33.0782			−1.13258			−0.566288	+	0.824208i	$0.691621\pi$
$854$	−2.44343	+	21.4458i	−0.0836124	+	0.733859i
$855$	59.6933	−	32.5330i	2.04147	−	1.11260i
$856$	35.0774	+	41.0703i	1.19892	+	1.40375i
$857$			11.0531i			0.377566i	0.982019	+	0.188783i	$0.0604543\pi$
$857$			11.0531i			0.377566i	−0.982019	+	0.188783i	$0.939546\pi$
$858$	−4.08294	+	3.22324i	−0.139389	+	0.110040i
$859$	22.2355			0.758665			0.379333	−	0.925260i	$-0.376154\pi$
$859$	22.2355			0.758665			0.379333	+	0.925260i	$0.376154\pi$
$860$	8.87883	−	38.4586i	0.302765	−	1.31143i
$861$	43.4124	−	42.3574i	1.47949	−	1.44354i
$862$	−2.24936	+	19.7424i	−0.0766135	+	0.672430i
$863$			14.8896i			0.506849i	0.967355	+	0.253424i	$0.0815569\pi$
$863$			14.8896i			0.506849i	−0.967355	+	0.253424i	$0.918443\pi$
$864$	27.6883	+	9.86707i	0.941975	+	0.335684i
$865$	−73.2312	+	42.2801i	−2.48994	+	1.43757i
$866$	11.8702	−	16.0416i	0.403364	−	0.545116i
$867$	−5.52846	−	21.6965i	−0.187756	−	0.736853i
$868$	41.4179	+	9.56204i	1.40581	+	0.324557i
$869$	−1.01769	−	0.587562i	−0.0345227	−	0.0199317i
$870$	19.1429	+	24.6831i	0.649006	+	0.836836i
$871$	1.59478	+	0.902513i	0.0540371	+	0.0305805i
$872$	−25.1917	−	8.92082i	−0.853099	−	0.302097i
$873$	−18.2746	−	33.5311i	−0.618500	−	1.13486i
$874$	22.9359	−	9.97282i	0.775818	−	0.337336i
$875$	43.8814	−	25.3350i	1.48346	−	0.856478i
$876$	31.3352	−	0.708516i	1.05872	−	0.0239385i
$877$	22.2886	+	38.6049i	0.752631	+	1.30360i	0.946543	+	0.322577i	$0.104549\pi$
$877$	22.2886	+	38.6049i	0.752631	+	1.30360i	−0.193912	+	0.981019i	$0.562118\pi$
$878$	0.684528	−	6.00804i	0.0231017	−	0.202762i
$879$	4.55807	−	16.2107i	0.153740	−	0.546773i
$880$	3.84207	−	7.87744i	0.129516	−	0.265548i
$881$	−40.4696	−	23.3651i	−1.36345	−	0.787191i	−0.373373	−	0.927681i	$-0.621799\pi$
$881$	−40.4696	−	23.3651i	−1.36345	−	0.787191i	−0.990082	+	0.140490i	$0.955132\pi$
$882$	−3.26298	+	23.4864i	−0.109870	+	0.790829i
$883$	−23.3385			−0.785404			−0.392702	−	0.919666i	$-0.628460\pi$
$883$	−23.3385			−0.785404			−0.392702	+	0.919666i	$0.628460\pi$
$884$	3.15152	−	14.2083i	0.105997	−	0.477877i
$885$	2.08002	−	7.39755i	0.0699191	−	0.248666i
$886$	2.02451	−	0.880281i	0.0680146	−	0.0295736i
$887$	25.4215	−	44.0313i	0.853571	−	1.47843i	−0.0243939	−	0.999702i	$-0.507766\pi$
$887$	25.4215	−	44.0313i	0.853571	−	1.47843i	0.877965	−	0.478725i	$-0.158901\pi$
$888$	−1.06341	+	11.6743i	−0.0356857	+	0.391764i
$889$			56.2961i			1.88811i
$890$	4.42061	−	38.7993i	0.148179	−	1.30056i
$891$	2.87307	−	4.45488i	0.0962514	−	0.149244i
$892$	1.59411	+	5.21408i	0.0533747	+	0.174580i
$893$	22.1529	+	38.3700i	0.741320	+	1.28400i
$894$	−44.9755	+	6.15708i	−1.50420	+	0.205924i
$895$	21.9799	−	38.0703i	0.734707	−	1.27255i
$896$	38.8635	−	10.0509i	1.29834	−	0.335776i
$897$	4.62796	+	17.5298i	0.154523	+	0.585301i
$898$	31.1433	−	42.0878i	1.03927	−	1.40449i
$899$	10.2670	−	17.7829i	0.342423	−	0.593093i
$900$	−37.8847	−	37.1117i	−1.26282	−	1.23706i
$901$	−11.8573	+	6.84582i	−0.395024	+	0.228067i
$902$	−4.89005	+	6.60852i	−0.162821	+	0.220040i
$903$	−8.05004	−	31.5925i	−0.267889	−	1.05133i
$904$	40.3970	−	7.48719i	1.34358	−	0.249020i
$905$	43.2807			1.43870
$906$	48.4947	+	19.7950i	1.61113	+	0.657644i
$907$	−9.09627	+	15.7552i	−0.302037	+	0.523143i	−0.976597	−	0.215077i	$-0.931000\pi$
$907$	−9.09627	+	15.7552i	−0.302037	+	0.523143i	0.674560	+	0.738220i	$0.264333\pi$
$908$	25.4286	+	5.87063i	0.843878	+	0.194824i
$909$	−8.51842	−	5.20161i	−0.282538	−	0.172526i
$910$	54.4447	+	39.5654i	1.80482	+	1.31158i
$911$	−7.77122			−0.257472			−0.128736	−	0.991679i	$-0.541092\pi$
$911$	−7.77122			−0.257472			−0.128736	+	0.991679i	$0.541092\pi$
$912$	−41.3260	−	8.56171i	−1.36844	−	0.283507i
$913$	−4.87667	+	8.44663i	−0.161394	+	0.279543i
$914$	−5.39427	+	47.3451i	−0.178427	+	1.56604i
$915$	−26.6821	−	7.50240i	−0.882084	−	0.248022i
$916$	−18.8795	+	20.2458i	−0.623797	+	0.668941i
$917$	−3.95619	+	2.28411i	−0.130645	+	0.0754279i
$918$	1.64952	+	14.7389i	0.0544421	+	0.486455i
$919$	20.7562	−	11.9836i	0.684685	−	0.395303i	−0.116933	−	0.993140i	$-0.537306\pi$
$919$	20.7562	−	11.9836i	0.684685	−	0.395303i	0.801618	+	0.597837i	$0.203973\pi$
$920$	−19.8388	−	23.2282i	−0.654065	−	0.765810i
$921$	12.5332	+	12.8454i	0.412983	+	0.423270i
$922$	−40.5495	−	30.0050i	−1.33543	−	0.988163i
$923$	0.544857	−	0.320865i	0.0179342	−	0.0105614i
$924$	−0.163646	−	7.23751i	−0.00538357	−	0.238096i
$925$	10.5752	−	18.3167i	0.347709	−	0.602250i
$926$	15.6840	+	36.0707i	0.515408	+	1.18536i
$927$	−16.4819	−	0.405547i	−0.541336	−	0.0133199i
$928$	0.845803	−	19.3729i	0.0277648	−	0.635947i
$929$	18.8035	+	32.5687i	0.616924	+	1.06854i	0.990044	+	0.140760i	$0.0449547\pi$
$929$	18.8035	+	32.5687i	0.616924	+	1.06854i	−0.373120	+	0.927783i	$0.621712\pi$
$930$	−20.6282	+	50.5360i	−0.676426	+	1.65714i
$931$		−	34.0456i		−	1.11580i
$932$	−26.1328	−	24.3692i	−0.856008	−	0.798239i
$933$	−12.8128	+	12.5014i	−0.419473	+	0.409279i
$934$	−0.0232968	+	0.0101298i	−0.000762296	+	0.000331456i
$935$	4.42216			0.144620
$936$	10.6721	−	28.6724i	0.348829	−	0.937187i
$937$	−26.6551			−0.870785			−0.435392	−	0.900241i	$-0.643390\pi$
$937$	−26.6551			−0.870785			−0.435392	+	0.900241i	$0.643390\pi$
$938$	−2.33866	+	1.01688i	−0.0763600	+	0.0332023i
$939$	7.57392	−	7.38985i	0.247165	−	0.241159i
$940$	36.9059	−	39.5768i	1.20374	−	1.29085i
$941$		−	53.6092i		−	1.74761i	−0.486278	−	0.873804i	$-0.661646\pi$
$941$		−	53.6092i		−	1.74761i	0.486278	−	0.873804i	$-0.338354\pi$
$942$	−13.8062	+	33.8232i	−0.449832	+	1.10202i
$943$	14.3265	+	24.8143i	0.466536	+	0.808063i
$944$	−3.95488	+	2.66761i	−0.128720	+	0.0868233i
$945$	−65.5478	−	20.1830i	−2.13227	−	0.656553i
$946$	1.76205	+	4.05243i	0.0572891	+	0.131756i
$947$	20.8087	−	36.0417i	0.676192	−	1.17120i	−0.299927	−	0.953962i	$-0.596962\pi$
$947$	20.8087	−	36.0417i	0.676192	−	1.17120i	0.976119	−	0.217237i	$-0.0697044\pi$
$948$	6.90954	−	0.156231i	0.224411	−	0.00507414i
$949$	−0.281134	−	32.6218i	−0.00912599	−	1.05895i
$950$	61.2096	+	45.2927i	1.98590	+	1.46949i
$951$	16.8990	+	17.3199i	0.547987	+	0.561637i
$952$	13.1539	+	15.4012i	0.426321	+	0.499156i
$953$	6.26808	−	3.61887i	0.203043	−	0.117227i	−0.395031	−	0.918668i	$-0.629266\pi$
$953$	6.26808	−	3.61887i	0.203043	−	0.117227i	0.598074	+	0.801441i	$0.295933\pi$
$954$	−26.6692	+	10.8241i	−0.863447	+	0.350443i
$955$	−15.9764	+	9.22400i	−0.516985	+	0.298482i
$956$	3.74665	+	3.49380i	0.121175	+	0.112998i
$957$	−3.36655	−	0.946597i	−0.108825	−	0.0305991i
$958$	1.41108	−	12.3850i	0.0455900	−	0.400140i
$959$	12.1654	−	21.0710i	0.392840	−	0.680419i
$960$	4.75726	+	51.3267i	0.153540	+	1.65656i
$961$	4.88208			0.157486
$962$	12.1343	+	1.27670i	0.391227	+	0.0411625i
$963$	−29.8554	+	48.8927i	−0.962076	+	1.57554i
$964$	−7.97584	+	34.5473i	−0.256885	+	1.11269i
$965$	−25.2412	+	43.7191i	−0.812544	+	1.40737i
$966$	−23.3604	−	9.53546i	−0.751609	−	0.306799i
$967$	14.9589			0.481045			0.240523	−	0.970644i	$-0.422681\pi$
$967$	14.9589			0.481045			0.240523	+	0.970644i	$0.422681\pi$
$968$	−5.49106	−	29.6269i	−0.176489	−	0.952245i
$969$	−5.25790	−	20.6347i	−0.168908	−	0.662883i
$970$	39.8341	−	53.8327i	1.27899	−	1.72846i
$971$	−4.94162	+	2.85304i	−0.158584	+	0.0915585i	−0.577192	−	0.816609i	$-0.695852\pi$
$971$	−4.94162	+	2.85304i	−0.158584	+	0.0915585i	0.418608	+	0.908167i	$0.362518\pi$
$972$	−0.829031	+	31.1659i	−0.0265912	+	0.999646i
$973$	10.9162	−	18.9075i	0.349958	−	0.606146i
$974$	−11.9441	+	16.1415i	−0.382712	+	0.517206i
$975$	−39.1749	+	38.8874i	−1.25460	+	1.24539i
$976$	9.62177	+	14.2648i	0.307985	+	0.456605i
$977$	8.40488	−	14.5577i	0.268896	−	0.465741i	−0.699681	−	0.714455i	$-0.746675\pi$
$977$	8.40488	−	14.5577i	0.268896	−	0.465741i	0.968577	+	0.248714i	$0.0800079\pi$
$978$	17.3198	−	2.37106i	0.553825	−	0.0758180i
$979$	2.18597	+	3.78621i	0.0698638	+	0.121008i
$980$	−39.7657	+	12.1576i	−1.27027	+	0.388361i
$981$	0.697253	−	28.3371i	0.0222616	−	0.904735i
$982$	2.81967	−	24.7480i	0.0899792	−	0.789740i
$983$		−	29.3040i		−	0.934653i	−0.884085	−	0.467327i	$-0.845217\pi$
$983$		−	29.3040i		−	0.934653i	0.884085	−	0.467327i	$-0.154783\pi$
$984$	4.38608	−	48.1513i	0.139823	−	1.53501i
$985$	22.2510	−	38.5398i	0.708975	−	1.22798i
$986$	8.97256	−	3.90138i	0.285744	−	0.124245i
$987$	12.0989	−	43.0294i	0.385112	−	1.36964i
$988$	−9.51215	+	42.8846i	−0.302622	+	1.36434i
$989$	15.4015			0.489739
$990$	9.20766	+	1.27922i	0.292639	+	0.0406564i
$991$	13.2251	+	7.63550i	0.420108	+	0.242550i	0.695124	−	0.718890i	$-0.255350\pi$
$991$	13.2251	+	7.63550i	0.420108	+	0.242550i	−0.275015	+	0.961440i	$0.588683\pi$
$992$	30.0568	−	15.6466i	0.954303	−	0.496781i
$993$	2.45278	−	8.72328i	0.0778368	−	0.276825i
$994$	−0.0996163	+	0.874324i	−0.00315964	+	0.0277319i
$995$	−2.15816	−	3.73804i	−0.0684183	−	0.118504i
$996$	−1.29669	−	57.3480i	−0.0410872	−	1.81714i
$997$	−15.3673	+	8.87229i	−0.486686	+	0.280988i	−0.723199	−	0.690640i	$-0.757329\pi$
$997$	−15.3673	+	8.87229i	−0.486686	+	0.280988i	0.236513	+	0.971628i	$0.423996\pi$
$998$	33.6531	−	14.6328i	1.06527	−	0.463193i
$999$	−12.1206	+	2.77281i	−0.383479	+	0.0877280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.ba.a.251.34	yes	104
3.2	odd	2	inner	312.2.ba.a.251.19	yes	104
8.3	odd	2	inner	312.2.ba.a.251.1	yes	104
13.10	even	6	inner	312.2.ba.a.179.52	yes	104
24.11	even	2	inner	312.2.ba.a.251.52	yes	104
39.23	odd	6	inner	312.2.ba.a.179.1	✓	104
104.75	odd	6	inner	312.2.ba.a.179.19	yes	104
312.179	even	6	inner	312.2.ba.a.179.34	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.ba.a.179.1	✓	104	39.23	odd	6	inner
312.2.ba.a.179.19	yes	104	104.75	odd	6	inner
312.2.ba.a.179.34	yes	104	312.179	even	6	inner
312.2.ba.a.179.52	yes	104	13.10	even	6	inner
312.2.ba.a.251.1	yes	104	8.3	odd	2	inner
312.2.ba.a.251.19	yes	104	3.2	odd	2	inner
312.2.ba.a.251.34	yes	104	1.1	even	1	trivial
312.2.ba.a.251.52	yes	104	24.11	even	2	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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.563917 + 1.29692i) q^{2} +(-1.23972 + 1.20959i) q^{3} +(-1.36400 + 1.46271i) q^{4} -3.72006i q^{5} +(-2.26783 - 0.925705i) q^{6} +(-1.77405 - 3.07274i) q^{7} +(-2.66619 - 0.944145i) q^{8} +(0.0737946 - 2.99909i) q^{9} +O(q^{10})\)	\(q+(0.563917 + 1.29692i) q^{2} +(-1.23972 + 1.20959i) q^{3} +(-1.36400 + 1.46271i) q^{4} -3.72006i q^{5} +(-2.26783 - 0.925705i) q^{6} +(-1.77405 - 3.07274i) q^{7} +(-2.66619 - 0.944145i) q^{8} +(0.0737946 - 2.99909i) q^{9} +(4.82462 - 2.09781i) q^{10} +(-0.294499 + 0.510088i) q^{11} +(-0.0783063 - 3.46322i) q^{12} +(-3.60542 + 0.0310714i) q^{13} +(2.98468 - 4.03356i) q^{14} +(4.49974 + 4.61183i) q^{15} +(-0.279032 - 3.99026i) q^{16} +(1.74784 - 1.00911i) q^{17} +(3.93119 - 1.59553i) q^{18} +(-5.27545 + 3.04578i) q^{19} +(5.44137 + 5.07415i) q^{20} +(5.91606 + 1.66346i) q^{21} +(-0.827615 - 0.0942945i) q^{22} +(-1.45159 + 2.51423i) q^{23} +(4.44735 - 2.05452i) q^{24} -8.83888 q^{25} +(-2.07345 - 4.65841i) q^{26} +(3.53618 + 3.80729i) q^{27} +(6.91432 + 1.59629i) q^{28} +(1.71397 - 2.96869i) q^{29} +(-3.44368 + 8.43649i) q^{30} +5.99017 q^{31} +(5.01769 - 2.61205i) q^{32} +(-0.251900 - 0.988587i) q^{33} +(2.29437 + 1.69774i) q^{34} +(-11.4308 + 6.59957i) q^{35} +(4.28614 + 4.19869i) q^{36} +(-1.19644 + 2.07229i) q^{37} +(-6.92504 - 5.12426i) q^{38} +(4.43211 - 4.39959i) q^{39} +(-3.51228 + 9.91841i) q^{40} +(4.93476 - 8.54726i) q^{41} +(1.17880 + 8.61071i) q^{42} +(-2.65252 - 4.59430i) q^{43} +(-0.344414 - 1.12652i) q^{44} +(-11.1568 - 0.274521i) q^{45} +(-4.07933 - 0.464779i) q^{46} -7.27332i q^{47} +(5.17249 + 4.60927i) q^{48} +(-2.79449 + 4.84019i) q^{49} +(-4.98439 - 11.4633i) q^{50} +(-0.946209 + 3.36517i) q^{51} +(4.87233 - 5.31606i) q^{52} -6.78400 q^{53} +(-2.94363 + 6.73313i) q^{54} +(1.89756 + 1.09556i) q^{55} +(1.82884 + 9.86748i) q^{56} +(2.85592 - 10.1570i) q^{57} +(4.81668 + 0.548790i) q^{58} +(-0.596307 - 1.03283i) q^{59} +(-12.8834 + 0.291305i) q^{60} +(-3.72531 + 2.15081i) q^{61} +(3.37795 + 7.76876i) q^{62} +(-9.34635 + 5.09378i) q^{63} +(6.21718 + 5.03455i) q^{64} +(0.115587 + 13.4124i) q^{65} +(1.14007 - 0.884175i) q^{66} +(-0.440139 - 0.254114i) q^{67} +(-0.908001 + 3.93300i) q^{68} +(-1.24162 - 4.87276i) q^{69} +(-15.0051 - 11.1032i) q^{70} +(-0.151877 + 0.0876865i) q^{71} +(-3.02833 + 7.92649i) q^{72} +9.04801i q^{73} +(-3.36228 - 0.383082i) q^{74} +(10.9577 - 10.6914i) q^{75} +(2.74060 - 11.8709i) q^{76} +2.08982 q^{77} +(8.20525 + 3.26709i) q^{78} +1.99512i q^{79} +(-14.8440 + 1.03802i) q^{80} +(-8.98911 - 0.442633i) q^{81} +(13.8679 + 1.58004i) q^{82} +16.5592 q^{83} +(-10.5026 + 6.38452i) q^{84} +(-3.75397 - 6.50206i) q^{85} +(4.46263 - 6.03090i) q^{86} +(1.46605 + 5.75353i) q^{87} +(1.26679 - 1.08194i) q^{88} +(3.71133 - 6.42821i) q^{89} +(-5.93549 - 14.6243i) q^{90} +(6.49166 + 11.0234i) q^{91} +(-1.69762 - 5.55265i) q^{92} +(-7.42611 + 7.24563i) q^{93} +(9.43290 - 4.10155i) q^{94} +(11.3305 + 19.6250i) q^{95} +(-3.06100 + 9.30754i) q^{96} +(11.0238 - 6.36461i) q^{97} +(-7.85320 - 0.894756i) q^{98} +(1.50807 + 0.920872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 2 q^{3} - 2 q^{4} - 12 q^{6} - 2 q^{9}+O(q^{10}) \) 104 * q - 2 * q^3 - 2 * q^4 - 12 * q^6 - 2 * q^9	\( 104 q - 2 q^{3} - 2 q^{4} - 12 q^{6} - 2 q^{9} + 6 q^{10} + 8 q^{12} - 6 q^{16} - 12 q^{19} + 8 q^{22} - 36 q^{24} - 88 q^{25} + 16 q^{27} + 12 q^{28} + 14 q^{30} - 6 q^{33} + 22 q^{36} + 4 q^{40} + 26 q^{42} - 20 q^{43} - 36 q^{46} + 14 q^{48} - 24 q^{49} - 20 q^{51} - 16 q^{52} - 36 q^{54} - 66 q^{58} + 28 q^{64} + 32 q^{66} - 12 q^{67} - 66 q^{72} + 2 q^{75} - 60 q^{76} - 14 q^{78} - 2 q^{81} + 50 q^{82} - 90 q^{84} + 24 q^{88} + 8 q^{90} + 44 q^{91} + 72 q^{94} + 12 q^{97}+O(q^{100}) \) 104 * q - 2 * q^3 - 2 * q^4 - 12 * q^6 - 2 * q^9 + 6 * q^10 + 8 * q^12 - 6 * q^16 - 12 * q^19 + 8 * q^22 - 36 * q^24 - 88 * q^25 + 16 * q^27 + 12 * q^28 + 14 * q^30 - 6 * q^33 + 22 * q^36 + 4 * q^40 + 26 * q^42 - 20 * q^43 - 36 * q^46 + 14 * q^48 - 24 * q^49 - 20 * q^51 - 16 * q^52 - 36 * q^54 - 66 * q^58 + 28 * q^64 + 32 * q^66 - 12 * q^67 - 66 * q^72 + 2 * q^75 - 60 * q^76 - 14 * q^78 - 2 * q^81 + 50 * q^82 - 90 * q^84 + 24 * q^88 + 8 * q^90 + 44 * q^91 + 72 * q^94 + 12 * q^97

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