LMFDB - Embedded newform 312.2.ba.a.179.19

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			179.19
Character	$\chi$	$=$	312.179
Dual form			312.2.ba.a.251.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.563917 + 1.29692i) q^{2} +(-0.427675 - 1.67842i) q^{3} +(-1.36400 - 1.46271i) q^{4} -3.72006i q^{5} +(2.41795 + 0.391829i) q^{6} +(-1.77405 + 3.07274i) q^{7} +(2.66619 - 0.944145i) q^{8} +(-2.63419 + 1.43564i) q^{9} +O(q^{10})$	\(q+(-0.563917 + 1.29692i) q^{2} +(-0.427675 - 1.67842i) q^{3} +(-1.36400 - 1.46271i) q^{4} -3.72006i q^{5} +(2.41795 + 0.391829i) q^{6} +(-1.77405 + 3.07274i) q^{7} +(2.66619 - 0.944145i) q^{8} +(-2.63419 + 1.43564i) q^{9} +(4.82462 + 2.09781i) q^{10} +(0.294499 + 0.510088i) q^{11} +(-1.87169 + 2.91492i) q^{12} +(-3.60542 - 0.0310714i) q^{13} +(-2.98468 - 4.03356i) q^{14} +(-6.24383 + 1.59098i) q^{15} +(-0.279032 + 3.99026i) q^{16} +(-1.74784 - 1.00911i) q^{17} +(-0.376443 - 4.22591i) 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} +(-2.72494 - 4.07121i) 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} +(1.45763 - 8.99492i) q^{30} +5.99017 q^{31} +(-5.01769 - 2.61205i) q^{32} +(0.730191 - 0.712445i) q^{33} +(2.29437 - 1.69774i) q^{34} +(11.4308 + 6.59957i) q^{35} +(5.69294 + 1.89484i) q^{36} +(-1.19644 - 2.07229i) q^{37} +(6.92504 - 5.12426i) q^{38} +(1.48980 + 6.06469i) q^{39} +(-3.51228 - 9.91841i) q^{40} +(-4.93476 - 8.54726i) q^{41} +(-5.49354 + 6.73460i) q^{42} +(-2.65252 + 4.59430i) q^{43} +(0.344414 - 1.12652i) q^{44} +(5.34067 + 9.79935i) q^{45} +(-4.07933 + 0.464779i) q^{46} -7.27332i q^{47} +(6.81666 - 1.23820i) 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} +(-6.93185 + 2.43915i) 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} +(10.8437 + 6.96281i) q^{60} +(-3.72531 - 2.15081i) q^{61} +(-3.37795 + 7.76876i) q^{62} +(0.261830 - 10.6411i) q^{63} +(6.21718 - 5.03455i) q^{64} +(-0.115587 + 13.4124i) q^{65} +(0.512216 + 1.34876i) q^{66} +(-0.440139 + 0.254114i) q^{67} +(0.908001 + 3.93300i) q^{68} +(3.59912 - 3.51165i) q^{69} +(-15.0051 + 11.1032i) q^{70} +(0.151877 + 0.0876865i) q^{71} +(-5.66780 + 6.31475i) q^{72} -9.04801i q^{73} +(3.36228 - 0.383082i) q^{74} +(3.78017 + 14.8354i) q^{75} +(2.74060 + 11.8709i) q^{76} -2.08982 q^{77} +(-8.70554 - 1.48784i) q^{78} -1.99512i q^{79} +(14.8440 + 1.03802i) q^{80} +(4.87789 - 7.56348i) q^{81} +(13.8679 - 1.58004i) q^{82} -16.5592 q^{83} +(-5.63633 - 10.9224i) q^{84} +(-3.75397 + 6.50206i) q^{85} +(-4.46263 - 6.03090i) q^{86} +(-4.24968 + 4.14640i) q^{87} +(1.26679 + 1.08194i) q^{88} +(-3.71133 - 6.42821i) q^{89} +(-15.7206 + 1.40039i) q^{90} +(6.49166 - 11.0234i) q^{91} +(1.69762 - 5.55265i) q^{92} +(-2.56185 - 10.0540i) q^{93} +(9.43290 + 4.10155i) q^{94} +(-11.3305 + 19.6250i) q^{95} +(-2.23818 + 9.53890i) 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 $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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
$3$	−0.427675	−	1.67842i	−0.246919	−	0.969036i
$3$	−0.427675	−	1.67842i	−0.246919	−	0.969036i
$4$	−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	$-0.312708\pi$
$6$	2.41795	+	0.391829i	0.987123	+	0.159964i
$7$	−1.77405	+	3.07274i	−0.670527	+	1.16139i	0.307228	+	0.951636i	$0.400599\pi$
$7$	−1.77405	+	3.07274i	−0.670527	+	1.16139i	−0.977755	+	0.209751i	$0.932735\pi$
$8$	2.66619	−	0.944145i	0.942642	−	0.333806i
$9$	−2.63419	+	1.43564i	−0.878062	+	0.478546i
$10$	4.82462	+	2.09781i	1.52568	+	0.663385i
$11$	0.294499	+	0.510088i	0.0887948	+	0.153797i	0.907002	−	0.421126i	$-0.138365\pi$
$11$	0.294499	+	0.510088i	0.0887948	+	0.153797i	−0.818207	+	0.574924i	$0.805032\pi$
$12$	−1.87169	+	2.91492i	−0.540311	+	0.841466i
$13$	−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
$15$	−6.24383	+	1.59098i	−1.61215	+	0.410789i
$16$	−0.279032	+	3.99026i	−0.0697580	+	0.997564i
$17$	−1.74784	−	1.00911i	−0.423912	−	0.244746i	0.272837	−	0.962060i	$-0.412038\pi$
$17$	−1.74784	−	1.00911i	−0.423912	−	0.244746i	−0.696750	+	0.717314i	$0.745371\pi$
$18$	−0.376443	−	4.22591i	−0.0887285	−	0.996056i
$19$	−5.27545	−	3.04578i	−1.21027	−	0.698750i	−0.247452	−	0.968900i	$-0.579593\pi$
$19$	−5.27545	−	3.04578i	−1.21027	−	0.698750i	−0.962818	+	0.270150i	$0.912927\pi$
$20$	−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	$-0.0687861\pi$
$23$	1.45159	+	2.51423i	0.302678	+	0.524253i	−0.674064	+	0.738673i	$0.735453\pi$
$24$	−2.72494	−	4.07121i	−0.556226	−	0.831031i
$25$	−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	$-0.269771\pi$
$29$	−1.71397	−	2.96869i	−0.318277	−	0.551271i	−0.980129	+	0.198363i	$0.936437\pi$
$30$	1.45763	−	8.99492i	0.266125	−	1.64224i
$31$	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
$33$	0.730191	−	0.712445i	0.127110	−	0.124021i
$34$	2.29437	−	1.69774i	0.393481	−	0.291161i
$35$	11.4308	+	6.59957i	1.93216	+	1.11553i
$36$	5.69294	+	1.89484i	0.948823	+	0.315807i
$37$	−1.19644	−	2.07229i	−0.196693	−	0.340682i	0.750761	−	0.660574i	$-0.229687\pi$
$37$	−1.19644	−	2.07229i	−0.196693	−	0.340682i	−0.947454	+	0.319891i	$0.896354\pi$
$38$	6.92504	−	5.12426i	1.12339	−	0.831264i
$39$	1.48980	+	6.06469i	0.238559	+	0.971128i
$40$	−3.51228	−	9.91841i	−0.555340	−	1.56824i
$41$	−4.93476	−	8.54726i	−0.770681	−	1.33486i	−0.937190	−	0.348818i	$-0.886583\pi$
$41$	−4.93476	−	8.54726i	−0.770681	−	1.33486i	0.166510	−	0.986040i	$-0.446750\pi$
$42$	−5.49354	+	6.73460i	−0.847672	+	1.03917i
$43$	−2.65252	+	4.59430i	−0.404505	+	0.700624i	−0.994264	−	0.106956i	$-0.965890\pi$
$43$	−2.65252	+	4.59430i	−0.404505	+	0.700624i	0.589758	+	0.807580i	$0.299223\pi$
$44$	0.344414	−	1.12652i	0.0519223	−	0.169830i
$45$	5.34067	+	9.79935i	0.796140	+	1.46080i
$46$	−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	$-0.177981\pi$
$48$	6.81666	−	1.23820i	0.983900	−	0.178719i
$49$	−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	$-0.345721\pi$
$53$	6.78400			0.931853			0.465927	+	0.884823i	$0.345721\pi$
$54$	−6.93185	+	2.43915i	−0.943305	+	0.331926i
$55$	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	$-0.808597\pi$
$59$	0.596307	−	1.03283i	0.0776325	−	0.134463i	0.902228	+	0.431259i	$0.141931\pi$
$60$	10.8437	+	6.96281i	1.39992	+	0.898895i
$61$	−3.72531	−	2.15081i	−0.476978	−	0.275383i	0.242179	−	0.970232i	$-0.422138\pi$
$61$	−3.72531	−	2.15081i	−0.476978	−	0.275383i	−0.719156	+	0.694849i	$0.755471\pi$
$62$	−3.37795	+	7.76876i	−0.429001	+	0.986633i
$63$	0.261830	−	10.6411i	0.0329875	−	1.34065i
$64$	6.21718	−	5.03455i	0.777147	−	0.629319i
$65$	−0.115587	+	13.4124i	−0.0143369	+	1.66360i
$66$	0.512216	+	1.34876i	0.0630495	+	0.166021i
$67$	−0.440139	+	0.254114i	−0.0537715	+	0.0310450i	−0.526645	−	0.850085i	$-0.676550\pi$
$67$	−0.440139	+	0.254114i	−0.0537715	+	0.0310450i	0.472873	+	0.881130i	$0.343217\pi$
$68$	0.908001	+	3.93300i	0.110111	+	0.476946i
$69$	3.59912	−	3.51165i	0.433283	−	0.422753i
$70$	−15.0051	+	11.1032i	−1.79346	+	1.32709i
$71$	0.151877	+	0.0876865i	0.0180245	+	0.0104065i	0.508985	−	0.860775i	$-0.330021\pi$
$71$	0.151877	+	0.0876865i	0.0180245	+	0.0104065i	−0.490961	+	0.871182i	$0.663354\pi$
$72$	−5.66780	+	6.31475i	−0.667957	+	0.744200i
$73$		−	9.04801i		−	1.05899i	−0.848313	−	0.529495i	$-0.822382\pi$
$73$		−	9.04801i		−	1.05899i	0.848313	−	0.529495i	$-0.177618\pi$
$74$	3.36228	−	0.383082i	0.390857	−	0.0445324i
$75$	3.78017	+	14.8354i	0.436497	+	1.71304i
$76$	2.74060	+	11.8709i	0.314368	+	1.36168i
$77$	−2.08982			−0.238157
$78$	−8.70554	−	1.48784i	−0.985708	−	0.168464i
$79$		−	1.99512i		−	0.224469i	−0.993682	−	0.112234i	$-0.964199\pi$
$79$		−	1.99512i		−	0.224469i	0.993682	−	0.112234i	$-0.0358007\pi$
$80$	14.8440	+	1.03802i	1.65961	+	0.116054i
$81$	4.87789	−	7.56348i	0.541987	−	0.840387i
$82$	13.8679	−	1.58004i	1.53145	−	0.174486i
$83$	−16.5592			−1.81761			−0.908803	−	0.417225i	$-0.863003\pi$
$83$	−16.5592			−1.81761			−0.908803	+	0.417225i	$0.863003\pi$
$84$	−5.63633	−	10.9224i	−0.614974	−	1.19173i
$85$	−3.75397	+	6.50206i	−0.407175	+	0.705247i
$86$	−4.46263	−	6.03090i	−0.481218	−	0.650329i
$87$	−4.24968	+	4.14640i	−0.455613	+	0.444541i
$88$	1.26679	+	1.08194i	0.135040	+	0.115335i
$89$	−3.71133	−	6.42821i	−0.393400	−	0.681389i	0.599495	−	0.800378i	$-0.295368\pi$
$89$	−3.71133	−	6.42821i	−0.393400	−	0.681389i	−0.992896	+	0.118989i	$0.962035\pi$
$90$	−15.7206	+	1.40039i	−1.65710	+	0.147614i
$91$	6.49166	−	11.0234i	0.680510	−	1.15557i
$92$	1.69762	−	5.55265i	0.176989	−	0.578904i
$93$	−2.56185	−	10.0540i	−0.265651	−	1.04255i
$94$	9.43290	+	4.10155i	0.972930	+	0.423042i
$95$	−11.3305	+	19.6250i	−1.16248	+	2.01348i
$96$	−2.23818	+	9.53890i	−0.228434	+	0.973560i
$97$	11.0238	+	6.36461i	1.11930	+	0.646228i	0.941222	−	0.337788i	$-0.109679\pi$
$97$	11.0238	+	6.36461i	1.11930	+	0.646228i	0.178078	+	0.984016i	$0.443012\pi$
$98$	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	$-0.219598\pi$
$101$	−1.66350	−	2.88126i	−0.165524	−	0.286696i	−0.936841	+	0.349755i	$0.886265\pi$
$102$	−3.83077	−	3.12484i	−0.379303	−	0.309405i
$103$			5.49562i			0.541500i	0.962650	+	0.270750i	$0.0872716\pi$
$103$			5.49562i			0.541500i	−0.962650	+	0.270750i	$0.912728\pi$
$104$	−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	0.607002	−	0.794701i	$-0.292372\pi$
$107$	16.5374	−	9.54789i	1.59873	−	0.923029i	0.991732	−	0.128328i	$-0.0409612\pi$
$108$	0.745613	−	10.3655i	0.0717467	−	0.997423i
$109$	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
$111$	−2.96649	+	2.89439i	−0.281566	+	0.274723i
$112$	−11.7660	−	7.93630i	−1.11178	−	0.749909i
$113$	12.5797	+	7.26287i	1.18339	+	0.683233i	0.956797	−	0.290755i	$-0.0939065\pi$
$113$	12.5797	+	7.26287i	1.18339	+	0.683233i	0.226597	+	0.973989i	$0.427240\pi$
$114$	−11.5623	−	9.43161i	−1.08291	−	0.883351i
$115$	9.35310	−	5.40001i	0.872181	−	0.503554i
$116$	−2.00447	+	6.55631i	−0.186111	+	0.608739i
$117$	9.54195	−	5.09423i	0.882154	−	0.470961i
$118$	1.00323	+	1.35579i	0.0923552	+	0.124811i
$119$	6.20149	−	3.58043i	0.568489	−	0.328217i
$120$	−15.1451	+	10.1369i	−1.38256	+	0.925372i
$121$	5.32654	−	9.22584i	0.484231	−	0.838713i
$122$	4.89019	−	3.61855i	0.442737	−	0.327608i
$123$	−12.2354	+	11.9381i	−1.10323	+	1.07642i
$124$	−8.17056	−	8.76186i	−0.733738	−	0.786839i
$125$			14.2809i			1.27732i
$126$	13.6529	+	6.34025i	1.21630	+	0.564834i
$127$	−13.7409	+	7.93329i	−1.21930	+	0.703965i	−0.964769	−	0.263098i	$-0.915256\pi$
$127$	−13.7409	+	7.93329i	−1.21930	+	0.703965i	−0.254535	+	0.967064i	$0.581922\pi$
$128$	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	$-0.0179129\pi$
$132$	−2.03808	−	0.0962844i	−0.177392	−	0.00838048i
$133$	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	$-0.927965\pi$
$137$	−3.42870	+	5.93869i	−0.292934	+	0.507377i	0.681568	+	0.731755i	$0.261298\pi$
$138$	2.52472	+	6.64805i	0.214919	+	0.565920i
$139$	3.07665	−	5.32891i	0.260958	−	0.451992i	−0.705539	−	0.708671i	$-0.749295\pi$
$139$	3.07665	−	5.32891i	0.260958	−	0.451992i	0.966497	+	0.256679i	$0.0826283\pi$
$140$	−5.93830	−	25.7217i	−0.501878	−	2.17388i
$141$	−12.2077	+	3.11062i	−1.02807	+	0.261962i
$142$	−0.199369	+	0.147525i	−0.0167306	+	0.0123800i
$143$	−1.04594	−	1.84823i	−0.0874662	−	0.154557i
$144$	−4.99354	−	10.9117i	−0.416128	−	0.909306i
$145$	−11.0437	+	6.37608i	−0.917130	+	0.529505i
$146$	11.7345	+	5.10232i	0.971156	+	0.422271i
$147$	−6.92875	+	6.76036i	−0.571473	+	0.557585i
$148$	−1.39922	+	4.57663i	−0.115015	+	0.376197i
$149$	−16.0495	−	9.26620i	−1.31483	−	0.759117i	−0.331938	−	0.943301i	$-0.607702\pi$
$149$	−16.0495	−	9.26620i	−1.31483	−	0.759117i	−0.982892	+	0.184184i	$0.941036\pi$
$150$	−21.3719	−	3.46333i	−1.74501	−	0.282780i
$151$	−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
$153$	6.05285	+	0.148934i	0.489344	+	0.0120406i
$154$	1.17849	−	2.71033i	0.0949651	−	0.218405i
$155$		−	22.2838i		−	1.78988i
$156$	6.83880	−	10.4514i	0.547542	−	0.836778i
$157$			14.9143i			1.19029i	0.803618	+	0.595146i	$0.202906\pi$
$157$			14.9143i			1.19029i	−0.803618	+	0.595146i	$0.797094\pi$
$158$	2.58751	+	1.12508i	0.205851	+	0.0895068i
$159$	−2.90135	−	11.3864i	−0.230092	−	0.903000i
$160$	−9.71701	+	18.6661i	−0.768197	+	1.47569i
$161$	−10.3008			−0.811814
$162$	7.05850	+	10.5914i	0.554568	+	0.832139i
$163$	−6.18058	−	3.56836i	−0.484100	−	0.279496i	0.238023	−	0.971259i	$-0.423501\pi$
$163$	−6.18058	−	3.56836i	−0.484100	−	0.279496i	−0.722124	+	0.691764i	$0.756834\pi$
$164$	−5.77116	+	18.8765i	−0.450652	+	1.47401i
$165$	−2.65034	−	2.71636i	−0.206329	−	0.211468i
$166$	9.33800	−	21.4759i	0.724770	−	1.66685i
$167$	6.05123	−	3.49368i	0.468259	−	0.270349i	−0.247252	−	0.968951i	$-0.579528\pi$
$167$	6.05123	−	3.49368i	0.468259	−	0.270349i	0.715510	+	0.698602i	$0.246194\pi$
$168$	17.3439	−	1.15052i	1.33811	−	0.0887642i
$169$	12.9981	+	0.224050i	0.999851	+	0.0172347i
$170$	−6.31572	−	8.53521i	−0.484393	−	0.654621i
$171$	18.2691	+	0.449524i	1.39708	+	0.0343760i
$172$	10.3381	−	2.38674i	0.788276	−	0.181987i
$173$	11.3654	−	19.6855i	0.864096	−	1.49666i	−0.00384554	−	0.999993i	$-0.501224\pi$
$173$	11.3654	−	19.6855i	0.864096	−	1.49666i	0.867942	−	0.496666i	$-0.165443\pi$
$174$	−2.98108	−	7.84971i	−0.225995	−	0.595085i
$175$	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	$-0.812263\pi$
$179$	−10.2338	+	5.90847i	−0.764908	+	0.441620i	0.0661471	+	0.997810i	$0.478929\pi$
$180$	7.04894	−	21.1781i	0.525397	−	1.57852i
$181$		−	11.6344i		−	0.864777i	−0.901687	−	0.432389i	$-0.857671\pi$
$181$		−	11.6344i		−	0.864777i	0.901687	−	0.432389i	$-0.142329\pi$
$182$	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
$186$	14.4839	+	2.34712i	1.06201	+	0.172099i
$187$		−	1.18873i		−	0.0869287i
$188$	−10.6387	+	9.92078i	−0.775910	+	0.723547i
$189$	−17.9722	+	4.11146i	−1.30728	+	0.299065i
$190$	−19.0626	−	25.7616i	−1.38294	−	1.86894i
$191$	2.47953	−	4.29467i	0.179412	−	0.310751i	−0.762267	−	0.647263i	$-0.775914\pi$
$191$	2.47953	−	4.29467i	0.179412	−	0.310751i	0.941679	+	0.336511i	$0.109247\pi$
$192$	−11.1090	−	8.28188i	−0.801725	−	0.597694i
$193$	−11.7522	+	6.78516i	−0.845945	+	0.488407i	−0.859281	−	0.511504i	$-0.829088\pi$
$193$	−11.7522	+	6.78516i	−0.845945	+	0.488407i	0.0133354	+	0.999911i	$0.495755\pi$
$194$	−14.4709	+	10.7079i	−1.03895	+	0.768782i
$195$	22.5611	−	5.54214i	1.61563	−	0.396881i
$196$	−3.26812	+	10.6895i	−0.233437	+	0.763537i
$197$	−10.3600	+	5.98134i	−0.738118	+	0.426153i	−0.821385	−	0.570375i	$-0.806798\pi$
$197$	−10.3600	+	5.98134i	−0.738118	+	0.426153i	0.0832666	+	0.996527i	$0.473465\pi$
$198$	2.04472	−	1.43655i	0.145312	−	0.102091i
$199$	1.00483	+	0.580141i	0.0712307	+	0.0411251i	0.535192	−	0.844730i	$-0.320239\pi$
$199$	1.00483	+	0.580141i	0.0712307	+	0.0411251i	−0.463962	+	0.885855i	$0.653572\pi$
$200$	−23.5662	+	8.34519i	−1.66638	+	0.590094i
$201$	0.614747	+	0.630060i	0.0433609	+	0.0444410i
$202$	4.67484	−	0.532629i	0.328920	−	0.0374756i
$203$	12.1627			0.853652
$204$	6.21290	−	3.20606i	0.434990	−	0.224469i
$205$	−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
$210$	25.0532	+	20.4363i	1.72883	+	1.41024i
$211$	8.60377	+	14.9022i	0.592308	+	1.02591i	0.993921	+	0.110098i	$0.0351163\pi$
$211$	8.60377	+	14.9022i	0.592308	+	1.02591i	−0.401613	+	0.915809i	$0.631550\pi$
$212$	−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
$216$	13.0228	+	6.81229i	0.886088	+	0.463518i
$217$	−10.6268	+	18.4062i	−0.721397	+	1.24950i
$218$	−5.32821	+	12.2540i	−0.360872	+	0.829947i
$219$	−15.1864	+	3.86961i	−1.02620	+	0.261484i
$220$	−4.19074	−	1.28124i	−0.282540	−	0.0863813i
$221$	6.27032	+	3.69258i	0.421787	+	0.248390i
$222$	−2.08094	−	5.47949i	−0.139663	−	0.367759i
$223$	1.36308	+	2.36092i	0.0912786	+	0.158099i	0.908049	−	0.418863i	$-0.137571\pi$
$223$	1.36308	+	2.36092i	0.0912786	+	0.158099i	−0.816771	+	0.576962i	$0.804238\pi$
$224$	16.9278	−	10.7841i	1.13103	−	0.720545i
$225$	23.2833	−	12.6894i	1.55222	−	0.845962i
$226$	−16.5132	+	12.2191i	−1.09844	+	0.812805i
$227$	6.52437	−	11.3005i	0.433037	−	0.750043i	−0.564096	−	0.825709i	$-0.690775\pi$
$227$	6.52437	−	11.3005i	0.433037	−	0.750043i	0.997133	+	0.0756665i	$0.0241084\pi$
$228$	18.7522	−	9.67675i	1.24190	−	0.640858i
$229$	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
$231$	0.893766	+	3.50760i	0.0588055	+	0.230783i
$232$	−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	$0.801008\pi$
$234$	1.22593	+	15.2479i	0.0801416	+	0.996783i
$235$	−27.0572			−1.76502
$236$	−2.32409	+	0.536558i	−0.151286	+	0.0349269i
$237$	−3.34865	+	0.853265i	−0.217518	+	0.0554255i
$238$	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	$-0.0264000\pi$
$240$	−4.60619	−	25.3584i	−0.297328	−	1.63688i
$241$	15.3529	+	8.86401i	0.988968	+	0.570981i	0.904966	−	0.425485i	$-0.139896\pi$
$241$	15.3529	+	8.86401i	0.988968	+	0.570981i	0.0840022	+	0.996466i	$0.473230\pi$
$242$	8.96144	+	12.1107i	0.576063	+	0.778505i
$243$	−14.7808	−	4.95243i	−0.948192	−	0.317698i
$244$	1.93530	+	8.38274i	0.123895	+	0.536650i
$245$	−18.0058	+	10.3957i	−1.15035	+	0.664155i
$246$	−8.58294	−	22.6004i	−0.547228	−	1.44095i
$247$	18.9255	+	11.1452i	1.20420	+	0.709154i
$248$	15.9709	−	5.65559i	1.01416	−	0.359130i
$249$	7.08196	+	27.7933i	0.448801	+	1.76133i
$250$	−18.5211	−	8.05323i	−1.17138	−	0.509331i
$251$	−12.0260	−	6.94319i	−0.759071	−	0.438250i	0.0698909	−	0.997555i	$-0.477735\pi$
$251$	−12.0260	−	6.94319i	−0.759071	−	0.438250i	−0.828962	+	0.559305i	$0.811068\pi$
$252$	−15.9219	+	14.1314i	−1.00299	+	0.890193i
$253$	−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	$-0.676209\pi$
$257$	−0.832307	+	0.480533i	−0.0519179	+	0.0299748i	0.473816	+	0.880624i	$0.342876\pi$
$258$	−8.21383	+	10.0694i	−0.511371	+	0.626896i
$259$	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	0.990317	+	0.138824i	$0.0443322\pi$
$263$	9.97984	+	17.2856i	0.615384	+	1.06588i	−0.374934	+	0.927052i	$0.622334\pi$
$264$	1.27418	−	2.58892i	0.0784203	−	0.159337i
$265$		−	25.2369i		−	1.55029i
$266$	3.46016	+	30.3695i	0.212156	+	1.86207i
$267$	−9.20199	+	8.97836i	−0.563153	+	0.549466i
$268$	0.972043	+	0.297184i	0.0593770	+	0.0181534i
$269$	−12.5727	+	21.7766i	−0.766572	+	1.32774i	0.172840	+	0.984950i	$0.444706\pi$
$269$	−12.5727	+	21.7766i	−0.766572	+	1.32774i	−0.939412	+	0.342791i	$0.888628\pi$
$270$	9.07378	+	25.7869i	0.552213	+	1.56934i
$271$	−6.18983	−	10.7211i	−0.376005	−	0.651260i	0.614472	−	0.788939i	$-0.289369\pi$
$271$	−6.18983	−	10.7211i	−0.376005	−	0.651260i	−0.990477	+	0.137679i	$0.956036\pi$
$272$	4.51432	−	6.69274i	0.273721	−	0.405807i
$273$	−21.2782	−	6.18129i	−1.28782	−	0.374109i
$274$	−5.76849	−	7.79568i	−0.348487	−	0.470954i
$275$	−2.60304	−	4.50860i	−0.156969	−	0.271879i
$276$	−10.0457	−	0.474587i	−0.604681	−	0.0285668i
$277$	−6.79972	−	3.92582i	−0.408555	−	0.235880i	0.281613	−	0.959528i	$-0.409130\pi$
$277$	−6.79972	−	3.92582i	−0.408555	−	0.235880i	−0.690169	+	0.723648i	$0.742464\pi$
$278$	5.17619	+	6.99522i	0.310447	+	0.419546i
$279$	−15.7792	+	8.59971i	−0.944677	+	0.514851i
$280$	36.7077	+	6.80341i	2.19370	+	0.406581i
$281$	1.44768			0.0863613			0.0431806	−	0.999067i	$-0.486251\pi$
$281$	1.44768			0.0863613			0.0431806	+	0.999067i	$0.486251\pi$
$282$	2.84990	−	17.5865i	0.169709	−	1.04726i
$283$	6.23292	+	10.7957i	0.370508	+	0.641739i	0.989644	−	0.143545i	$-0.0458501\pi$
$283$	6.23292	+	10.7957i	0.370508	+	0.641739i	−0.619135	+	0.785284i	$0.712517\pi$
$284$	−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
$288$	16.9675	−	0.322941i	0.999819	−	0.0190295i
$289$	−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	$-0.241676\pi$
$293$	8.41966	+	4.86109i	0.491882	+	0.283988i	−0.233473	+	0.972363i	$0.575009\pi$
$294$	−4.86040	−	12.7983i	−0.283464	−	0.746412i
$295$	−3.84221	−	2.21830i	−0.223702	−	0.129154i
$296$	−5.14648	−	4.39552i	−0.299133	−	0.255484i
$297$	−0.900646	+	2.92500i	−0.0522608	+	0.169726i
$298$	21.0681	−	15.5896i	1.22044	−	0.903080i
$299$	−5.15547	−	9.10995i	−0.298149	−	0.526842i
$300$	16.5437	−	25.7646i	0.955149	−	1.48752i
$301$	−9.41139	−	16.3010i	−0.542463	−	0.939574i
$302$	12.0586	−	27.7329i	0.693896	−	1.59585i
$303$	−4.12453	+	4.02429i	−0.236948	+	0.231190i
$304$	13.6255	−	20.2005i	0.781474	−	1.15858i
$305$	−8.00115	+	13.8584i	−0.458145	+	0.793530i
$306$	−3.60646	+	7.76606i	−0.206167	+	0.443956i
$307$			10.3616i			0.591365i	0.955286	+	0.295683i	$0.0955471\pi$
$307$			10.3616i			0.591365i	−0.955286	+	0.295683i	$0.904453\pi$
$308$	2.85051	+	3.05680i	0.162423	+	0.174177i
$309$	9.22396	−	2.35034i	0.524733	−	0.133706i
$310$	28.9003	+	12.5662i	1.64143	+	0.713713i
$311$	−10.3353			−0.586061			−0.293030	−	0.956103i	$-0.594664\pi$
$311$	−10.3353			−0.586061			−0.293030	+	0.956103i	$0.594664\pi$
$312$	9.69804	+	14.7631i	0.549043	+	0.835794i
$313$	−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
$315$	−39.5854	−	0.974025i	−2.23039	−	0.0548801i
$316$	−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	$-0.128335\pi$
$318$	16.4033	+	2.65817i	0.919854	+	0.149063i
$319$	1.00953	−	1.74855i	0.0565226	−	0.0979001i
$320$	−18.7288	−	23.1283i	−1.04697	−	1.29291i
$321$	−23.0980	−	23.6733i	−1.28921	−	1.32132i
$322$	5.80877	−	13.3593i	0.323710	−	0.744482i
$323$	6.14707	+	10.6470i	0.342032	+	0.592417i
$324$	−17.7166	+	3.18163i	−0.984255	+	0.176757i
$325$	31.8679	+	0.274636i	1.76771	+	0.0152341i
$326$	8.11321	−	6.00345i	0.449349	−	0.332500i
$327$	−4.04092	−	15.8587i	−0.223463	−	0.876986i
$328$	−21.2269	−	18.1295i	−1.17206	−	1.00104i
$329$	22.3490	+	12.9032i	1.23214	+	0.711377i
$330$	5.01747	−	1.90548i	0.276203	−	0.104893i
$331$	−4.53078	−	2.61584i	−0.249034	−	0.143780i	0.370288	−	0.928917i	$-0.379259\pi$
$331$	−4.53078	−	2.61584i	−0.249034	−	0.143780i	−0.619322	+	0.785137i	$0.712592\pi$
$332$	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
$336$	−8.28841	+	23.1425i	−0.452170	+	1.26252i
$337$	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
$342$	−10.8853	+	23.4401i	−0.588608	+	1.26750i
$343$	−5.00645			−0.270323
$344$	−2.73444	+	14.7537i	−0.147431	+	0.795464i
$345$	−13.0636	−	13.3890i	−0.703319	−	0.720838i
$346$	19.1213	+	25.8410i	1.02797	+	1.38922i
$347$	−3.53236	−	2.03941i	−0.189627	−	0.109481i	0.402181	−	0.915560i	$-0.368252\pi$
$347$	−3.53236	−	2.03941i	−0.189627	−	0.109481i	−0.591808	+	0.806079i	$0.701586\pi$
$348$	11.8615	+	0.560371i	0.635844	+	0.0300390i
$349$	0.702729	+	1.21716i	0.0376162	+	0.0651532i	0.884221	−	0.467070i	$-0.154690\pi$
$349$	0.702729	+	1.21716i	0.0376162	+	0.0651532i	−0.846604	+	0.532223i	$0.821357\pi$
$350$	26.3812	+	35.6522i	1.41014	+	1.90569i
$351$	−12.6311	−	13.8367i	−0.674199	−	0.738550i
$352$	−0.145328	−	3.32871i	−0.00774602	−	0.177421i
$353$	8.62123	+	14.9324i	0.458862	+	0.794772i	0.998901	−	0.0468677i	$-0.0149239\pi$
$353$	8.62123	+	14.9324i	0.458862	+	0.794772i	−0.540039	+	0.841640i	$0.681591\pi$
$354$	1.84653	−	2.26369i	0.0981421	−	0.120314i
$355$	0.326199	−	0.564994i	0.0173129	−	0.0299868i
$356$	−4.34036	+	14.1966i	−0.230039	+	0.752421i
$357$	−8.66169	−	8.87743i	−0.458425	−	0.469844i
$358$	−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	$-0.242682\pi$
$360$	23.4913	+	21.0846i	1.23810	+	1.11126i
$361$	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
$366$	−8.16486	−	6.66023i	−0.426784	−	0.348136i
$367$	2.47051	−	1.42635i	0.128959	−	0.0744547i	−0.434133	−	0.900849i	$-0.642945\pi$
$367$	2.47051	−	1.42635i	0.128959	−	0.0744547i	0.563092	+	0.826394i	$0.309612\pi$
$368$	−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
$372$	−11.2117	+	17.4609i	−0.581302	+	0.905304i
$373$	−9.40704	−	5.43116i	−0.487078	−	0.281215i	0.236283	−	0.971684i	$-0.424071\pi$
$373$	−9.40704	−	5.43116i	−0.487078	−	0.281215i	−0.723361	+	0.690470i	$0.757404\pi$
$374$	1.54169	+	0.670346i	0.0797188	+	0.0346628i
$375$	23.9693	−	6.10758i	1.23777	−	0.315394i
$376$	−6.86707	−	19.3921i	−0.354142	−	1.00007i
$377$	6.08734	+	10.7566i	0.313514	+	0.553993i
$378$	4.80257	−	25.6269i	0.247017	−	1.31811i
$379$	−31.6202	+	18.2560i	−1.62422	+	0.937745i	−0.638449	+	0.769664i	$0.720424\pi$
$379$	−31.6202	+	18.2560i	−1.62422	+	0.937745i	−0.985773	+	0.168081i	$0.946243\pi$
$380$	44.1604	−	10.1952i	2.26538	−	0.523003i
$381$	19.1920	+	19.6701i	0.983237	+	1.00773i
$382$	4.17159	+	5.63758i	0.213437	+	0.288444i
$383$	−9.35500	−	5.40111i	−0.478018	−	0.275984i	0.241572	−	0.970383i	$-0.422337\pi$
$383$	−9.35500	−	5.40111i	−0.478018	−	0.275984i	−0.719590	+	0.694399i	$0.755670\pi$
$384$	17.0055	−	9.73720i	0.867808	−	0.496900i
$385$			7.77427i			0.396214i
$386$	−2.17251	−	19.0680i	−0.110578	−	0.970534i
$387$	0.391483	−	15.9103i	0.0199002	−	0.808766i
$388$	−5.72688	−	24.8059i	−0.290738	−	1.25933i
$389$	−5.71199			−0.289609			−0.144805	−	0.989460i	$-0.546255\pi$
$389$	−5.71199			−0.289609			−0.144805	+	0.989460i	$0.546255\pi$
$390$	−5.53485	+	32.3852i	−0.280268	+	1.63989i
$391$		−	5.85928i		−	0.296316i
$392$	−12.0205	−	10.2665i	−0.607127	−	0.518536i
$393$	−2.16099	+	0.550638i	−0.109007	+	0.0277760i
$394$	−1.91514	−	16.8090i	−0.0964834	−	0.846827i
$395$	−7.42198			−0.373440
$396$	0.710030	+	3.46193i	0.0356803	+	0.173968i
$397$	−4.12607	+	7.14657i	−0.207082	+	0.358676i	−0.950794	−	0.309824i	$-0.899730\pi$
$397$	−4.12607	+	7.14657i	−0.207082	+	0.358676i	0.743712	+	0.668500i	$0.233063\pi$
$398$	−1.31904	+	0.976035i	−0.0661174	+	0.0489242i
$399$	−26.1433	−	26.7945i	−1.30880	−	1.34140i
$400$	2.46633	−	35.2694i	0.123317	−	1.76347i
$401$	−18.1067	−	31.3618i	−0.904207	−	1.56613i	−0.821978	−	0.569520i	$-0.807129\pi$
$401$	−18.1067	−	31.3618i	−0.904207	−	1.56613i	−0.0822297	−	0.996613i	$-0.526204\pi$
$402$	−1.16380	+	0.441976i	−0.0580452	+	0.0220438i
$403$	−21.5970	−	0.186123i	−1.07583	−	0.00927143i
$404$	−1.94544	+	6.36324i	−0.0967895	+	0.316583i
$405$	−28.1366	−	18.1461i	−1.39812	−	0.901685i
$406$	−6.85873	+	15.7740i	−0.340393	+	0.782850i
$407$	0.704700	−	1.22058i	0.0349307	−	0.0605017i
$408$	0.654436	+	9.86557i	0.0323994	+	0.488418i
$409$	−7.70920	−	4.45091i	−0.381195	−	0.220083i	0.297143	−	0.954833i	$-0.403966\pi$
$409$	−7.70920	−	4.45091i	−0.381195	−	0.220083i	−0.678338	+	0.734750i	$0.737300\pi$
$410$	−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
$414$	10.0785	−	7.08075i	0.495329	−	0.348000i
$415$			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	$-0.634712\pi$
$419$	3.55319	−	2.05143i	0.173585	−	0.100219i	0.584275	+	0.811556i	$0.301379\pi$
$420$	−40.6322	+	20.9675i	−1.98265	+	1.02311i
$421$	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
$423$	10.4419	+	19.1593i	0.507700	+	0.931557i
$424$	18.0874	−	6.40508i	0.878404	−	0.311058i
$425$	15.4489	+	8.91943i	0.749382	+	0.432656i
$426$	0.332874	+	0.271531i	0.0161278	+	0.0131557i
$427$	13.2178	−	7.63128i	0.639652	−	0.369304i
$428$	−36.5228	−	11.1662i	−1.76539	−	0.539737i
$429$	−2.65478	+	2.54597i	−0.128174	+	0.122921i
$430$	−22.4353	+	16.6013i	−1.08193	+	0.800584i
$431$	−12.1679	+	7.02516i	−0.586109	+	0.338390i	−0.763557	−	0.645740i	$-0.776549\pi$
$431$	−12.1679	+	7.02516i	−0.586109	+	0.338390i	0.177448	+	0.984130i	$0.443216\pi$
$432$	−16.1788	+	13.0479i	−0.778401	+	0.627768i
$433$	−7.05544	+	12.2204i	−0.339063	+	0.587274i	−0.984257	−	0.176745i	$-0.943443\pi$
$433$	−7.05544	+	12.2204i	−0.339063	+	0.587274i	0.645194	+	0.764019i	$0.276777\pi$
$434$	−17.8787	−	24.1617i	−0.858206	−	1.15980i
$435$	15.4249	+	15.8091i	0.739566	+	0.757987i
$436$	−12.8878	−	13.8205i	−0.617214	−	0.661882i
$437$		−	17.6849i		−	0.845984i
$438$	3.54527	−	21.8776i	0.169400	−	1.04535i
$439$	−3.70296	+	2.13791i	−0.176733	+	0.102037i	−0.585757	−	0.810487i	$-0.699203\pi$
$439$	−3.70296	+	2.13791i	−0.176733	+	0.102037i	0.409024	+	0.912524i	$0.365869\pi$
$440$	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	$-0.0118066\pi$
$444$	8.27992	+	0.391167i	0.392948	+	0.0185639i
$445$	−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	0.0153408	−	0.999882i	$-0.495117\pi$
$449$	18.5111	−	32.0622i	0.873594	−	1.51311i	0.858253	−	0.513227i	$-0.171550\pi$
$450$	3.32734	+	37.3523i	0.156852	+	1.76080i
$451$	2.90657	−	5.03432i	0.136865	−	0.237057i
$452$	−6.53514	−	28.3069i	−0.307387	−	1.33144i
$453$	9.14528	+	35.8908i	0.429683	+	1.68630i
$454$	10.9767	+	14.8341i	0.515161	+	0.696200i
$455$	−41.0077	−	24.1494i	−1.92247	−	1.13214i
$456$	1.97527	+	29.7770i	0.0925004	+	1.39443i
$457$	29.1804	−	16.8473i	1.36500	−	0.788084i	0.374716	−	0.927139i	$-0.377740\pi$
$457$	29.1804	−	16.8473i	1.36500	−	0.788084i	0.990285	+	0.139056i	$0.0444067\pi$
$458$	−7.80536	+	17.9511i	−0.364721	+	0.838799i
$459$	−2.33868	−	10.2229i	−0.109160	−	0.477165i
$460$	−20.6562	−	6.31526i	−0.963101	−	0.294450i
$461$	30.8903	+	17.8345i	1.43871	+	0.830637i	0.997760	−	0.0668967i	$-0.0213098\pi$
$461$	30.8903	+	17.8345i	1.43871	+	0.830637i	0.440946	+	0.897534i	$0.354643\pi$
$462$	−5.05308	−	0.818853i	−0.235091	−	0.0380965i
$463$	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
$465$	−37.4016	+	9.53024i	−1.73446	+	0.441954i
$466$	−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	$0.999868\pi$
$468$	−20.4665	−	7.00859i	−0.946067	−	0.323972i
$469$		−	1.80324i		−	0.0832661i
$470$	15.2580	−	35.0910i	0.703800	−	1.61863i
$471$	25.0325	−	6.37848i	1.15344	−	0.293905i
$472$	0.614724	−	3.31674i	0.0282950	−	0.152665i
$473$	−3.12466			−0.143672
$474$	0.781747	−	4.82410i	0.0359068	−	0.221578i
$475$	46.6290	+	26.9213i	2.13949	+	1.23523i
$476$	−13.6959	−	4.18728i	−0.627752	−	0.191923i
$477$	−17.8703	+	9.73936i	−0.818226	+	0.445935i
$478$	3.32199	+	1.44444i	0.151944	+	0.0660672i
$479$	7.63328	−	4.40707i	0.348773	−	0.201364i	−0.315372	−	0.948968i	$-0.602129\pi$
$479$	7.63328	−	4.40707i	0.348773	−	0.201364i	0.664145	+	0.747604i	$0.268796\pi$
$480$	35.4853	+	8.32618i	1.61968	+	0.380037i
$481$	4.24927	+	7.50864i	0.193750	+	0.342365i
$482$	−20.1537	+	14.9129i	−0.917974	+	0.679264i
$483$	4.40538	+	17.2890i	0.200452	+	0.786677i
$484$	−20.7601	+	4.79283i	−0.943640	+	0.217856i
$485$	23.6768	−	41.0093i	1.07511	−	1.86214i
$486$	14.7581	−	16.3768i	0.669439	−	0.742867i
$487$	7.09936	−	12.2965i	0.321703	−	0.557206i	−0.659137	−	0.752023i	$-0.729078\pi$
$487$	7.09936	−	12.2965i	0.321703	−	0.557206i	0.980839	+	0.194818i	$0.0624115\pi$
$488$	−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	$-0.536571\pi$
$491$	15.2530	−	8.80634i	0.688360	−	0.397425i	0.802997	+	0.595983i	$0.203237\pi$
$492$	34.1510	+	1.61339i	1.53964	+	0.0727371i
$493$			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
$498$	−40.0392	−	6.48837i	−1.79420	−	0.290751i
$499$			25.9485i			1.16161i	0.814041	+	0.580807i	$0.197263\pi$
$499$			25.9485i			1.16161i	−0.814041	+	0.580807i	$0.802737\pi$
$500$	20.8888	−	19.4791i	0.934174	−	0.871130i
$501$	−8.45183	−	8.66235i	−0.377600	−	0.387005i
$502$	15.7864	−	11.6813i	0.704581	−	0.521362i
$503$	−7.23565	+	12.5325i	−0.322622	+	0.558797i	−0.981028	−	0.193866i	$-0.937897\pi$
$503$	−7.23565	+	12.5325i	−0.322622	+	0.558797i	0.658407	+	0.752662i	$0.271231\pi$
$504$	−9.34862	−	28.6183i	−0.416421	−	1.27476i
$505$	−10.7185	+	6.18832i	−0.476966	+	0.275377i
$506$	−1.43844	−	1.94394i	−0.0639463	−	0.0864185i
$507$	−5.18290	−	21.9120i	−0.230181	−	0.973148i
$508$	30.3466	+	9.27790i	1.34641	+	0.411640i
$509$	−0.522951	+	0.301926i	−0.0231794	+	0.0133826i	−0.511545	−	0.859257i	$-0.670927\pi$
$509$	−0.522951	+	0.301926i	−0.0231794	+	0.0133826i	0.488366	+	0.872639i	$0.337593\pi$
$510$	−11.6246	+	14.2507i	−0.514745	+	0.631033i
$511$	27.8022	+	16.0516i	1.22990	+	0.710081i
$512$	11.8229	−	19.2930i	0.522501	−	0.852638i
$513$	−7.05878	−	30.8556i	−0.311653	−	1.36231i
$514$	−0.153860	−	1.35041i	−0.00678647	−	0.0595643i
$515$	20.4441			0.900874
$516$	−8.42732	−	16.3310i	−0.370992	−	0.718932i
$517$	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	$0.955641\pi$
$522$	−11.9002	+	8.36063i	−0.520857	+	0.365935i
$523$	0.335974	+	0.581925i	0.0146911	+	0.0254458i	0.873278	−	0.487223i	$-0.161990\pi$
$523$	0.335974	+	0.581925i	0.0146911	+	0.0254458i	−0.858586	+	0.512669i	$0.828657\pi$
$524$	−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
$528$	2.63909	+	3.11244i	0.114852	+	0.135452i
$529$	7.28577	−	12.6193i	0.316772	−	0.548666i
$530$	32.7302	+	14.2315i	1.42171	+	0.618177i
$531$	−0.0880084	+	3.57676i	−0.00381924	+	0.155218i
$532$	−41.3380	−	12.6383i	−1.79223	−	0.547942i
$533$	17.5263	+	30.9698i	0.759149	+	1.34145i
$534$	−6.45504	−	16.9973i	−0.279337	−	0.735544i
$535$	−35.5188	−	61.5203i	−1.53561	−	2.65975i
$536$	−0.933575	+	1.09307i	−0.0403243	+	0.0472136i
$537$	14.2936	+	14.6497i	0.616816	+	0.632180i
$538$	−21.1525	−	28.5860i	−0.911948	−	1.23243i
$539$	1.64595	−	2.85087i	0.0708960	−	0.122796i
$540$	−38.5604	−	2.77373i	−1.65938	−	0.119362i
$541$	−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
$543$	−19.5274	+	4.97574i	−0.838001	+	0.213530i
$544$	6.13423	+	9.62885i	0.263003	+	0.412834i
$545$		−	35.1493i		−	1.50563i
$546$	20.0158	−	24.1104i	0.856596	−	1.03183i
$547$	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
$549$	12.9010	+	0.317436i	0.550600	+	0.0135479i
$550$	7.31519	−	0.833458i	0.311921	−	0.0355388i
$551$			20.8815i			0.889583i
$552$	6.28045	−	12.7608i	0.267314	−	0.543138i
$553$	6.13049	+	3.53944i	0.260695	+	0.150512i
$554$	8.92594	−	6.60484i	0.379227	−	0.280613i
$555$	10.7673	+	11.0355i	0.457047	+	0.468432i
$556$	−11.9912	+	2.76837i	−0.508539	+	0.117405i
$557$	18.6831	−	10.7867i	0.791627	−	0.457046i	−0.0489082	−	0.998803i	$-0.515574\pi$
$557$	18.6831	−	10.7867i	0.791627	−	0.457046i	0.840535	+	0.541757i	$0.182241\pi$
$558$	−2.25496	−	25.3139i	−0.0954599	−	1.07162i
$559$	9.70619	−	16.4819i	0.410528	−	0.697112i
$560$	−29.5235	+	43.7703i	−1.24760	+	1.84963i
$561$	−1.99519	+	0.508392i	−0.0842371	+	0.0214643i
$562$	−0.816370	+	1.87752i	−0.0344365	+	0.0791985i
$563$	−26.6787	−	15.4029i	−1.12437	−	0.649156i	−0.181858	−	0.983325i	$-0.558211\pi$
$563$	−26.6787	−	15.4029i	−1.12437	−	0.649156i	−0.942513	+	0.334169i	$0.891544\pi$
$564$	21.2012	+	13.6134i	0.892730	+	0.573228i
$565$	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	$-0.659001\pi$
$569$	0.994883	−	0.574396i	0.0417077	−	0.0240799i	0.520709	+	0.853734i	$0.325668\pi$
$570$	−35.0862	+	43.0126i	−1.46960	+	1.80160i
$571$	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
$576$	−9.14942	+	22.1876i	−0.381226	+	0.924482i
$577$		−	1.02376i		−	0.0426199i	−0.999773	−	0.0213099i	$-0.993216\pi$
$577$		−	1.02376i		−	0.0426199i	0.999773	−	0.0213099i	$-0.00678368\pi$
$578$	18.1637	−	2.06948i	0.755510	−	0.0860792i
$579$	16.4145	+	16.8234i	0.682163	+	0.699155i
$580$	24.3899	+	7.45677i	1.01274	+	0.309625i
$581$	29.3768	−	50.8821i	1.21875	−	2.11094i
$582$	24.1612	+	19.7087i	1.00151	+	0.816954i
$583$	1.99788	+	3.46043i	0.0827438	+	0.143316i
$584$	−8.54263	−	24.1237i	−0.353497	−	0.998247i
$585$	−18.9509	−	35.4967i	−0.783521	−	1.46761i
$586$	−11.0524	+	8.17836i	−0.456572	+	0.337845i
$587$	4.61426	+	7.99213i	0.190451	+	0.329871i	0.945400	−	0.325913i	$-0.105672\pi$
$587$	4.61426	+	7.99213i	0.190451	+	0.329871i	−0.754949	+	0.655784i	$0.772338\pi$
$588$	19.3392	+	0.913638i	0.797536	+	0.0376778i
$589$	−31.6008	−	18.2447i	−1.30209	−	0.751761i
$590$	5.04364	−	3.73209i	0.207643	−	0.153648i
$591$	14.4699	+	14.8303i	0.595212	+	0.610038i
$592$	8.60281	−	4.19585i	0.353573	−	0.172449i
$593$	−38.1844			−1.56804			−0.784022	−	0.620733i	$-0.786835\pi$
$593$	−38.1844			−1.56804			−0.784022	+	0.620733i	$0.786835\pi$
$594$	−3.28560	−	2.81752i	−0.134810	−	0.115604i
$595$	−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	$-0.526663\pi$
$599$	−4.09541			−0.167334			−0.0836670	+	0.996494i	$0.526663\pi$
$600$	24.0854	+	35.9849i	0.983282	+	1.46908i
$601$	1.94649	+	3.37142i	0.0793991	+	0.137523i	0.902991	−	0.429660i	$-0.141367\pi$
$601$	1.94649	+	3.37142i	0.0793991	+	0.137523i	−0.823592	+	0.567183i	$0.808033\pi$
$602$	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
$606$	−2.89329	−	7.61855i	−0.117532	−	0.309482i
$607$	9.29224	+	5.36488i	0.377160	+	0.217754i	0.676582	−	0.736367i	$-0.263460\pi$
$607$	9.29224	+	5.36488i	0.377160	+	0.217754i	−0.299422	+	0.954121i	$0.596794\pi$
$608$	18.5148	+	29.0625i	0.750874	+	1.17864i
$609$	−5.20167	−	20.4141i	−0.210782	−	0.827220i
$610$	−13.4612	−	18.1918i	−0.545030	−	0.736566i
$611$	−0.225992	+	26.2234i	−0.00914266	+	1.06088i
$612$	−8.03821	−	9.05670i	−0.324925	−	0.366095i
$613$	14.4049	+	24.9501i	0.581809	+	1.00772i	0.995265	+	0.0971992i	$0.0309884\pi$
$613$	14.4049	+	24.9501i	0.581809	+	1.00772i	−0.413456	+	0.910524i	$0.635678\pi$
$614$	−13.4381	−	5.84306i	−0.542317	−	0.235807i
$615$	44.4104	+	45.5165i	1.79080	+	1.83540i
$616$	−5.57187	+	1.97310i	−0.224497	+	0.0794983i
$617$	−2.91655	+	5.05161i	−0.117416	+	0.203370i	−0.918743	−	0.394856i	$-0.870794\pi$
$617$	−2.91655	+	5.05161i	−0.117416	+	0.203370i	0.801327	+	0.598226i	$0.204128\pi$
$618$	−2.15334	+	13.2881i	−0.0866202	+	0.534527i
$619$		−	45.7442i		−	1.83861i	−0.393542	−	0.919306i	$-0.628751\pi$
$619$		−	45.7442i		−	1.83861i	0.393542	−	0.919306i	$-0.371249\pi$
$620$	−32.5947	+	30.3950i	−1.30903	+	1.22069i
$621$	−4.43930	+	14.4174i	−0.178143	+	0.578550i
$622$	5.82825	−	13.4040i	0.233691	−	0.537453i
$623$	26.3363			1.05514
$624$	−24.6154	+	4.25243i	−0.985404	+	0.170233i
$625$	8.93141			0.357256
$626$	3.44519	−	7.92339i	0.137697	−	0.316682i
$627$	−6.02203	+	1.53446i	−0.240497	+	0.0612806i
$628$	21.8153	−	20.3431i	0.870525	−	0.811776i
$629$			4.82936i			0.192559i
$630$	23.5861	−	50.7898i	0.939694	−	2.02352i
$631$	4.98809	−	8.63962i	0.198573	−	0.343938i	−0.749493	−	0.662012i	$-0.769703\pi$
$631$	4.98809	−	8.63962i	0.198573	−	0.343938i	0.948066	+	0.318074i	$0.103036\pi$
$632$	−1.88369	−	5.31938i	−0.0749290	−	0.211594i
$633$	21.3325	−	20.8140i	0.847889	−	0.827283i
$634$	18.1191	+	7.87841i	0.719601	+	0.312892i
$635$	29.5123	+	51.1169i	1.17116	+	2.02851i
$636$	−12.6975	+	19.7748i	−0.503491	+	0.784123i
$637$	9.92490	+	17.5377i	0.393239	+	0.694871i
$638$	1.69844	+	2.29531i	0.0672419	+	0.0908722i
$639$	−0.525960	−	0.0129416i	−0.0208066	−	0.000511961i
$640$	40.5570	−	11.2473i	1.60316	−	0.444590i
$641$	2.47142	+	1.42687i	0.0976152	+	0.0563581i	0.548013	−	0.836470i	$-0.315384\pi$
$641$	2.47142	+	1.42687i	0.0976152	+	0.0563581i	−0.450398	+	0.892828i	$0.648718\pi$
$642$	43.7278	−	16.6064i	1.72580	−	0.655404i
$643$	−11.4570	−	6.61468i	−0.451819	−	0.260858i	0.256779	−	0.966470i	$-0.417339\pi$
$643$	−11.4570	−	6.61468i	−0.451819	−	0.260858i	−0.708598	+	0.705612i	$0.750672\pi$
$644$	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	$-0.0761027\pi$
$647$	7.13974	+	12.3664i	0.280692	+	0.486173i	−0.690863	+	0.722985i	$0.742769\pi$
$648$	5.86437	−	24.7711i	0.230374	−	0.973102i
$649$	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	0.999784	+	0.0207979i	$0.00662066\pi$
$653$	13.2344	+	22.9227i	0.517903	+	0.897035i	−0.481880	+	0.876237i	$0.660046\pi$
$654$	22.8461	+	3.70222i	0.893355	+	0.144768i
$655$	−4.78963			−0.187146
$656$	35.4827	−	17.3060i	1.38537	−	0.675686i
$657$	12.9897	+	23.8341i	0.506775	+	0.929859i
$658$	−29.3374	+	21.7085i	−1.14369	+	0.846286i
$659$	−12.9512	−	7.47737i	−0.504507	−	0.291277i	0.226066	−	0.974112i	$-0.427414\pi$
$659$	−12.9512	−	7.47737i	−0.504507	−	0.291277i	−0.730573	+	0.682835i	$0.760747\pi$
$660$	−0.358184	+	7.58178i	−0.0139423	+	0.295120i
$661$	−8.28018	−	14.3417i	−0.322062	−	0.557827i	0.658851	−	0.752273i	$-0.271043\pi$
$661$	−8.28018	−	14.3417i	−0.322062	−	0.557827i	−0.980913	+	0.194446i	$0.937709\pi$
$662$	5.94752	−	4.40093i	0.231157	−	0.171047i
$663$	3.51604	−	12.1035i	0.136552	−	0.470059i
$664$	−44.1500	+	15.6343i	−1.71335	+	0.606728i
$665$	−40.2017	−	69.6313i	−1.55895	−	2.70019i
$666$	−8.30691	+	5.83613i	−0.321886	+	0.226146i
$667$	4.97597	−	8.61863i	0.192670	−	0.333715i
$668$	−13.3641	−	4.08582i	−0.517072	−	0.158085i
$669$	3.37967	−	3.29753i	0.130665	−	0.127490i
$670$	−2.65659	+	0.302679i	−0.102633	+	0.0116935i
$671$		−	2.53365i		−	0.0978104i
$672$	−25.3399	−	23.7998i	−0.977508	−	0.918097i
$673$	5.34089	+	9.25069i	0.205876	+	0.356588i	0.950412	−	0.310995i	$-0.100662\pi$
$673$	5.34089	+	9.25069i	0.205876	+	0.356588i	−0.744535	+	0.667583i	$0.767329\pi$
$674$	−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	$-0.697566\pi$
$677$	−30.2646			−1.16316			−0.581581	+	0.813489i	$0.697566\pi$
$678$	27.5712	+	22.4903i	1.05886	+	0.863735i
$679$	−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	$-0.777496\pi$
$683$	4.56099	−	7.89986i	0.174521	−	0.302280i	0.939996	+	0.341187i	$0.110829\pi$
$684$	−24.2615	−	27.3356i	−0.927662	−	1.04520i
$685$	22.0923	+	12.7550i	0.844104	+	0.487344i
$686$	2.82322	−	6.49296i	0.107791	−	0.247902i
$687$	−5.91960	−	23.2316i	−0.225847	−	0.886340i
$688$	−17.5923	−	11.8662i	−0.670700	−	0.452394i
$689$	−24.4591	−	0.210788i	−0.931819	−	0.00803038i
$690$	24.7312	−	9.39213i	0.941500	−	0.357552i
$691$	20.8998	−	12.0665i	0.795065	−	0.459031i	−0.0466775	−	0.998910i	$-0.514863\pi$
$691$	20.8998	−	12.0665i	0.795065	−	0.459031i	0.841743	+	0.539879i	$0.181530\pi$
$692$	−44.2965	+	10.2266i	−1.68390	+	0.388757i
$693$	5.50498	−	3.00023i	0.209117	−	0.113969i
$694$	4.63690	−	3.43112i	0.176014	−	0.130244i
$695$	−19.8239	−	11.4453i	−0.751963	−	0.434146i
$696$	−7.41566	+	15.0674i	−0.281090	+	0.571129i
$697$			19.9189i			0.754484i
$698$	−1.97484	+	0.225004i	−0.0747489	+	0.00851653i
$699$	29.9867	−	7.64086i	1.13420	−	0.289004i
$700$	−61.1148	+	14.1094i	−2.30992	+	0.533286i
$701$	52.5345			1.98420			0.992100	−	0.125450i	$-0.0400376\pi$
$701$	52.5345			1.98420			0.992100	+	0.125450i	$0.0400376\pi$
$702$	25.0680	−	8.57876i	0.946131	−	0.323784i
$703$			14.5763i			0.549757i
$704$	4.39902	+	1.68864i	0.165794	+	0.0636428i
$705$	11.5717	+	45.4134i	0.435816	+	1.71037i
$706$	−24.2278	+	2.76040i	−0.911825	+	0.103889i
$707$	11.8045			0.443954
$708$	1.89453	+	3.67133i	0.0712007	+	0.137977i
$709$	9.54850	−	16.5385i	0.358601	−	0.621116i	−0.629126	−	0.777303i	$-0.716587\pi$
$709$	9.54850	−	16.5385i	0.358601	−	0.621116i	0.987727	+	0.156188i	$0.0499204\pi$
$710$	0.548802	+	0.741664i	0.0205962	+	0.0278341i
$711$	2.86427	+	5.25552i	0.107419	+	0.197098i
$712$	−15.9643	−	13.6348i	−0.598287	−	0.510987i
$713$	8.69527	+	15.0606i	0.325640	+	0.564026i
$714$	16.3978	−	6.22737i	0.613672	−	0.233053i
$715$	−6.87553	+	3.89098i	−0.257130	+	0.145514i
$716$	22.6012	+	6.90990i	0.844646	+	0.258235i
$717$	−4.29918	+	1.09547i	−0.160556	+	0.0409110i
$718$	33.9436	+	14.7591i	1.26676	+	0.550804i
$719$	−17.5778	+	30.4456i	−0.655541	+	1.13543i	0.326217	+	0.945295i	$0.394226\pi$
$719$	−17.5778	+	30.4456i	−0.655541	+	1.13543i	−0.981758	+	0.190135i	$0.939107\pi$
$720$	−40.5921	+	18.5763i	−1.51278	+	0.692298i
$721$	−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
$726$	16.4942	−	20.2205i	0.612159	−	0.750453i
$727$		−	37.8297i		−	1.40303i	−0.712656	−	0.701514i	$-0.752508\pi$
$727$		−	37.8297i		−	1.40303i	0.712656	−	0.701514i	$-0.247492\pi$
$728$	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
$732$	13.2421	−	6.83334i	0.489441	−	0.252568i
$733$	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
$735$	25.1490	+	25.7754i	0.927633	+	0.950739i
$736$	−0.716325	−	16.4072i	−0.0264041	−	0.604779i
$737$	−0.259241	−	0.149673i	−0.00954927	−	0.00551327i
$738$	−34.2623	+	24.0714i	−1.26121	+	0.886081i
$739$	1.91745	−	1.10704i	0.0705347	−	0.0407232i	−0.464318	−	0.885669i	$-0.653700\pi$
$739$	1.91745	−	1.10704i	0.0705347	−	0.0407232i	0.534853	+	0.844945i	$0.320367\pi$
$740$	17.0254	+	5.20519i	0.625865	+	0.191347i
$741$	10.6124	−	36.5316i	0.389855	−	1.34202i
$742$	−20.2480	−	27.3637i	−0.743329	−	1.00455i
$743$	23.9890	−	13.8501i	0.880071	−	0.508109i	0.00938946	−	0.999956i	$-0.497011\pi$
$743$	23.9890	−	13.8501i	0.880071	−	0.508109i	0.870682	+	0.491846i	$0.163678\pi$
$744$	−16.3228	−	24.3872i	−0.598424	−	0.894078i
$745$	−34.4709	+	59.7053i	−1.26292	+	2.18743i
$746$	12.3486	−	9.13744i	0.452113	−	0.334546i
$747$	43.6200	−	23.7730i	1.59597	−	0.869808i
$748$	−1.73877	+	1.62143i	−0.0635757	+	0.0592852i
$749$			67.7536i			2.47566i
$750$	−5.59567	+	34.5304i	−0.204325	+	1.26087i
$751$	−11.0887	+	6.40206i	−0.404632	+	0.233614i	−0.688481	−	0.725255i	$-0.741722\pi$
$751$	−11.0887	+	6.40206i	−0.404632	+	0.233614i	0.283849	+	0.958869i	$0.408389\pi$
$752$	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
$756$	30.5278	+	20.6800i	1.11029	+	0.752124i
$757$	−0.297231	+	0.171606i	−0.0108030	+	0.00623713i	−0.505392	−	0.862890i	$-0.668652\pi$
$757$	−0.297231	+	0.171606i	−0.0108030	+	0.00623713i	0.494589	+	0.869127i	$0.335319\pi$
$758$	−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	0.0979349	−	0.995193i	$-0.468776\pi$
$761$	25.1264	−	43.5201i	0.910830	−	1.57760i	0.812895	−	0.582411i	$-0.197890\pi$
$762$	−36.3332	+	13.7982i	−1.31621	+	0.499856i
$763$	−16.7622	+	29.0330i	−0.606833	+	1.05106i
$764$	−9.66391	+	2.23108i	−0.349628	+	0.0807177i
$765$	0.554045	−	22.5170i	0.0200315	−	0.814103i
$766$	12.2802	−	9.08690i	0.443703	−	0.328323i
$767$	−2.18203	+	3.70527i	−0.0787884	+	0.133789i
$768$	3.03868	+	27.5457i	0.109649	+	0.993970i
$769$	−17.8409	+	10.3005i	−0.643361	+	0.371444i	−0.785908	−	0.618344i	$-0.787804\pi$
$769$	−17.8409	+	10.3005i	−0.643361	+	0.371444i	0.142547	+	0.989788i	$0.454471\pi$
$770$	−10.0826	−	4.38404i	−0.363352	−	0.157990i
$771$	1.16249	+	1.19145i	0.0418662	+	0.0429090i
$772$	25.9547	+	7.93518i	0.934131	+	0.285593i
$773$	−10.0645	−	5.81076i	−0.361996	−	0.208999i	0.307960	−	0.951399i	$-0.400354\pi$
$773$	−10.0645	−	5.81076i	−0.361996	−	0.208999i	−0.669956	+	0.742401i	$0.733687\pi$
$774$	20.4136	+	9.47981i	0.733752	+	0.340745i
$775$	−52.9464			−1.90189
$776$	35.4008	+	6.56119i	1.27081	+	0.235533i
$777$	−3.63103	−	14.2500i	−0.130262	−	0.511217i
$778$	3.22109	−	7.40799i	0.115482	−	0.265589i
$779$			60.1208i			2.15405i
$780$	−38.8797	−	25.4408i	−1.39212	−	0.910926i
$781$			0.103294i			0.00369616i
$782$	7.59901	+	3.30415i	0.271740	+	0.118156i
$783$	5.24172	−	17.0234i	0.187324	−	0.608366i
$784$	20.0934	−	9.80015i	0.717620	−	0.350005i
$785$	55.4822			1.98024
$786$	0.504485	−	3.11314i	0.0179944	−	0.111042i
$787$	−39.3135	−	22.6977i	−1.40137	−	0.809084i	−0.406841	−	0.913499i	$-0.633370\pi$
$787$	−39.3135	−	22.6977i	−1.40137	−	0.809084i	−0.994534	+	0.104415i	$0.966703\pi$
$788$	22.8799	+	6.99511i	0.815063	+	0.249191i
$789$	24.7444	−	24.1430i	0.880922	−	0.859513i
$790$	4.18538	−	9.62571i	0.148909	−	0.342467i
$791$	−44.6338	+	25.7693i	−1.58700	+	0.916252i
$792$	−4.89024	−	1.03139i	−0.173767	−	0.0366488i
$793$	13.3645	+	7.87032i	0.474587	+	0.279483i
$794$	−6.94175	−	9.38125i	−0.246354	−	0.332928i
$795$	−42.3581	+	10.7932i	−1.50229	+	0.382796i
$796$	−0.522011	−	2.26109i	−0.0185022	−	0.0801421i
$797$	6.94433	−	12.0279i	0.245981	−	0.426051i	−0.716426	−	0.697663i	$-0.754223\pi$
$797$	6.94433	−	12.0279i	0.245981	−	0.426051i	0.962407	+	0.271612i	$0.0875566\pi$
$798$	49.4930	−	18.7959i	1.75203	−	0.665368i
$799$	−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
$804$	0.0830809	−	1.75859i	0.00293004	−	0.0620209i
$805$			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	$-0.467012\pi$
$809$	28.9138	−	16.6934i	1.01655	−	0.586908i	0.913104	+	0.407727i	$0.133678\pi$
$810$	39.4007	−	26.2581i	1.38440	−	0.922614i
$811$			16.8255i			0.590823i	0.955370	+	0.295411i	$0.0954567\pi$
$811$			16.8255i			0.590823i	−0.955370	+	0.295411i	$0.904543\pi$
$812$	−16.5898	−	17.7904i	−0.582189	−	0.624322i
$813$	−15.3473	+	14.9743i	−0.538252	+	0.525171i
$814$	1.18559	+	1.60224i	0.0415551	+	0.0561585i
$815$	−13.2745	+	22.9922i	−0.464987	+	0.805380i
$816$	−13.1639	−	4.71461i	−0.460828	−	0.165044i
$817$	27.9864	−	16.1580i	0.979121	−	0.565296i
$818$	10.1198	−	7.48826i	0.353831	−	0.261821i
$819$	−1.27464	+	38.3573i	−0.0445395	+	1.34031i
$820$	70.2220	+	21.4691i	2.45226	+	0.749733i
$821$	−25.4054	+	14.6678i	−0.886653	+	0.511909i	−0.872846	−	0.487995i	$-0.837728\pi$
$821$	−25.4054	+	14.6678i	−0.886653	+	0.511909i	−0.0138067	+	0.999905i	$0.504395\pi$
$822$	−10.6174	+	13.0160i	−0.370324	+	0.453984i
$823$	−16.5273	−	9.54205i	−0.576106	−	0.332615i	0.183478	−	0.983024i	$-0.441264\pi$
$823$	−16.5273	−	9.54205i	−0.576106	−	0.332615i	−0.759584	+	0.650409i	$0.774598\pi$
$824$	5.18867	+	14.6524i	0.180756	+	0.510440i
$825$	−6.45407	+	6.29722i	−0.224702	+	0.219241i
$826$	−5.94579	+	0.677434i	−0.206880	+	0.0235710i
$827$	−43.0109			−1.49564			−0.747818	−	0.663903i	$-0.768899\pi$
$827$	−43.0109			−1.49564			−0.747818	+	0.663903i	$0.768899\pi$
$828$	3.49975	+	17.0639i	0.121625	+	0.593011i
$829$	−13.0937	+	7.55968i	−0.454765	+	0.262558i	−0.709840	−	0.704363i	$-0.751233\pi$
$829$	−13.0937	+	7.55968i	−0.454765	+	0.262558i	0.255076	+	0.966921i	$0.417900\pi$
$830$	−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
$834$	9.52719	−	11.6795i	0.329900	−	0.404428i
$835$	−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	$-0.179907\pi$
$839$	23.2564	+	13.4271i	0.802901	+	0.463555i	−0.0415836	+	0.999135i	$0.513240\pi$
$840$	−4.27999	−	64.5205i	−0.147674	−	2.22617i
$841$	8.62460	−	14.9383i	0.297400	−	0.515112i
$842$	−15.4091	+	35.4385i	−0.531032	+	1.22129i
$843$	−0.619137	−	2.42981i	−0.0213242	−	0.0836872i
$844$	10.0620	−	32.9113i	0.346349	−	1.13285i
$845$	0.833482	−	48.3537i	0.0286727	−	1.66342i
$846$	−30.7364	+	2.73799i	−1.05674	+	0.0941341i
$847$	18.8991	+	32.7341i	0.649380	+	1.12476i
$848$	−1.89295	+	27.0699i	−0.0650042	+	0.929583i
$849$	15.4541	−	15.0785i	0.530383	−	0.517494i
$850$	−20.2797	+	15.0062i	−0.695587	+	0.514707i
$851$	3.47347	−	6.01623i	0.119069	−	0.206234i
$852$	−0.539867	+	0.278589i	−0.0184955	+	0.00954430i
$853$	−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
$855$	1.67226	−	67.9624i	0.0571900	−	2.32427i
$856$	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	$0.939546\pi$
$858$	−1.80485	−	4.87875i	−0.0616164	−	0.166558i
$859$	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
$861$	−14.9763	−	58.7749i	−0.510393	−	2.00304i
$862$	−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	$0.918443\pi$
$864$	−7.79861	−	28.3405i	−0.265314	−	0.964162i
$865$	−73.2312	−	42.2801i	−2.48994	−	1.43757i
$866$	−11.8702	−	16.0416i	−0.403364	−	0.545116i
$867$	−16.0255	+	15.6361i	−0.544255	+	0.531028i
$868$	41.4179	−	9.56204i	1.40581	−	0.324557i
$869$	1.01769	−	0.587562i	0.0345227	−	0.0199317i
$870$	−29.2014	+	11.0898i	−0.990021	+	0.375979i
$871$	1.59478	−	0.902513i	0.0540371	−	0.0305805i
$872$	25.1917	−	8.92082i	0.853099	−	0.302097i
$873$	−38.1761	−	0.939347i	−1.29207	−	0.0317921i
$874$	22.9359	+	9.97282i	0.775818	+	0.337336i
$875$	−43.8814	−	25.3350i	−1.48346	−	0.856478i
$876$	26.3742	+	16.9351i	0.891103	+	0.572183i
$877$	22.2886	−	38.6049i	0.752631	−	1.30360i	−0.193912	−	0.981019i	$-0.562118\pi$
$877$	22.2886	−	38.6049i	0.752631	−	1.30360i	0.946543	−	0.322577i	$-0.104549\pi$
$878$	−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	$-0.378201\pi$
$881$	40.4696	−	23.3651i	1.36345	−	0.787191i	0.990082	+	0.140490i	$0.0448679\pi$
$882$	−19.4022	+	13.6313i	−0.653308	+	0.458990i
$883$	−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	−0.877965	−	0.478725i	$-0.841099\pi$
$887$	−25.4215	−	44.0313i	−0.853571	−	1.47843i	0.0243939	−	0.999702i	$-0.492234\pi$
$888$	−5.17650	+	10.5178i	−0.173712	+	0.352954i
$889$		−	56.2961i		−	1.88811i
$890$	−4.42061	−	38.7993i	−0.148179	−	1.30056i
$891$	5.29457	+	0.260710i	0.177375	+	0.00873413i
$892$	1.59411	−	5.21408i	0.0533747	−	0.174580i
$893$	−22.1529	+	38.3700i	−0.741320	+	1.28400i
$894$	−35.1762	−	28.6939i	−1.17647	−	0.959667i
$895$	21.9799	+	38.0703i	0.734707	+	1.27255i
$896$	−38.8635	−	10.0509i	−1.29834	−	0.335776i
$897$	−13.0855	+	12.5491i	−0.436911	+	0.419004i
$898$	31.1433	+	42.0878i	1.03927	+	1.40449i
$899$	−10.2670	−	17.7829i	−0.342423	−	0.593093i
$900$	−50.3192	−	16.7483i	−1.67731	−	0.558277i
$901$	−11.8573	−	6.84582i	−0.395024	−	0.228067i
$902$	4.89005	+	6.60852i	0.162821	+	0.220040i
$903$	−23.3349	+	22.7678i	−0.776537	+	0.757665i
$904$	40.3970	+	7.48719i	1.34358	+	0.249020i
$905$	−43.2807			−1.43870
$906$	−51.7047	−	8.37875i	−1.71777	−	0.278365i
$907$	−9.09627	−	15.7552i	−0.302037	−	0.523143i	0.674560	−	0.738220i	$-0.264333\pi$
$907$	−9.09627	−	15.7552i	−0.302037	−	0.523143i	−0.976597	+	0.215077i	$0.931000\pi$
$908$	−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	$-0.458908\pi$
$911$	7.77122			0.257472			0.128736	+	0.991679i	$0.458908\pi$
$912$	−39.7322	−	14.2300i	−1.31566	−	0.471202i
$913$	−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
$918$	14.5771	+	2.73180i	0.481116	+	0.0901627i
$919$	20.7562	+	11.9836i	0.684685	+	0.395303i	0.801618	−	0.597837i	$-0.203973\pi$
$919$	20.7562	+	11.9836i	0.684685	+	0.395303i	−0.116933	+	0.993140i	$0.537306\pi$
$920$	19.8388	−	23.2282i	0.654065	−	0.765810i
$921$	17.3910	−	4.43138i	0.573054	−	0.146019i
$922$	−40.5495	+	30.0050i	−1.33543	+	0.988163i
$923$	−0.544857	−	0.320865i	−0.0179342	−	0.0105614i
$924$	3.91150	−	6.09167i	0.128679	−	0.200401i
$925$	10.5752	+	18.3167i	0.347709	+	0.602250i
$926$	−15.6840	+	36.0707i	−0.515408	+	1.18536i
$927$	−7.88973	−	14.4765i	−0.259133	−	0.475471i
$928$	0.845803	+	19.3729i	0.0277648	+	0.635947i
$929$	−18.8035	+	32.5687i	−0.616924	+	1.06854i	0.373120	+	0.927783i	$0.378288\pi$
$929$	−18.8035	+	32.5687i	−0.616924	+	1.06854i	−0.990044	+	0.140760i	$0.955045\pi$
$930$	8.73144	−	53.8811i	0.286315	−	1.76683i
$931$			34.0456i			1.11580i
$932$	26.1328	−	24.3692i	0.856008	−	0.798239i
$933$	4.42015	+	17.3470i	0.144709	+	0.567914i
$934$	−0.0232968	−	0.0101298i	−0.000762296	−	0.000331456i
$935$	−4.42216			−0.144620
$936$	20.6310	−	22.5912i	0.674345	−	0.738416i
$937$	−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
$939$	2.61284	+	10.2541i	0.0852667	+	0.334631i
$940$	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	$-0.338354\pi$
$942$	−5.84386	+	36.0620i	−0.190403	+	1.17496i
$943$	14.3265	−	24.8143i	0.466536	−	0.808063i
$944$	3.95488	+	2.66761i	0.128720	+	0.0868233i
$945$	15.2949	+	66.8576i	0.497543	+	2.17488i
$946$	1.76205	−	4.05243i	0.0572891	−	0.131756i
$947$	−20.8087	−	36.0417i	−0.676192	−	1.17120i	−0.976119	−	0.217237i	$-0.930296\pi$
$947$	−20.8087	−	36.0417i	−0.676192	−	1.17120i	0.299927	−	0.953962i	$-0.403038\pi$
$948$	5.81562	+	3.73425i	0.188883	+	0.121283i
$949$	−0.281134	+	32.6218i	−0.00912599	+	1.05895i
$950$	−61.2096	+	45.2927i	−1.98590	+	1.46949i
$951$	−23.4490	+	5.97500i	−0.760385	+	0.193753i
$952$	13.1539	−	15.4012i	0.426321	−	0.499156i
$953$	−6.26808	−	3.61887i	−0.203043	−	0.117227i	0.395031	−	0.918668i	$-0.370734\pi$
$953$	−6.26808	−	3.61887i	−0.203043	−	0.117227i	−0.598074	+	0.801441i	$0.704067\pi$
$954$	−2.55379	−	28.6685i	−0.0826820	−	0.928178i
$955$	−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
$960$	−30.8091	+	41.3263i	−0.994361	+	1.33380i
$961$	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
$966$	−24.9067	−	4.03614i	−0.801360	−	0.129861i
$967$	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
$969$	15.2413	−	14.8708i	0.489620	−	0.477721i
$970$	39.8341	+	53.8327i	1.27899	+	1.72846i
$971$	4.94162	+	2.85304i	0.158584	+	0.0915585i	0.577192	−	0.816609i	$-0.304148\pi$
$971$	4.94162	+	2.85304i	0.158584	+	0.0915585i	−0.418608	+	0.908167i	$0.637482\pi$
$972$	12.9171	+	28.3752i	0.414315	+	0.910134i
$973$	10.9162	+	18.9075i	0.349958	+	0.606146i
$974$	11.9441	+	16.1415i	0.382712	+	0.517206i
$975$	−13.1681	−	53.6051i	−0.421718	−	1.71674i
$976$	9.62177	−	14.2648i	0.307985	−	0.456605i
$977$	−8.40488	−	14.5577i	−0.268896	−	0.465741i	0.699681	−	0.714455i	$-0.253325\pi$
$977$	−8.40488	−	14.5577i	−0.268896	−	0.465741i	−0.968577	+	0.248714i	$0.919992\pi$
$978$	−13.5461	−	11.0498i	−0.433158	−	0.353335i
$979$	2.18597	−	3.78621i	0.0698638	−	0.121008i
$980$	39.7657	+	12.1576i	1.27027	+	0.388361i
$981$	−24.8893	+	13.5647i	−0.794654	+	0.433088i
$982$	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	$-0.154783\pi$
$984$	−21.3507	+	43.3812i	−0.680636	+	1.38294i
$985$	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
$990$	−5.34404	−	7.60649i	−0.169845	−	0.241750i
$991$	13.2251	−	7.63550i	0.420108	−	0.242550i	−0.275015	−	0.961440i	$-0.588683\pi$
$991$	13.2251	−	7.63550i	0.420108	−	0.242550i	0.695124	+	0.718890i	$0.255350\pi$
$992$	−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
$996$	30.9937	−	48.2687i	0.982073	−	1.52945i
$997$	−15.3673	−	8.87229i	−0.486686	−	0.280988i	0.236513	−	0.971628i	$-0.423996\pi$
$997$	−15.3673	−	8.87229i	−0.486686	−	0.280988i	−0.723199	+	0.690640i	$0.757329\pi$
$998$	−33.6531	−	14.6328i	−1.06527	−	0.463193i
$999$	3.65898	−	11.8832i	0.115765	−	0.375967i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.ba.a.179.1	✓	104	24.11	even	2	inner
312.2.ba.a.179.19	yes	104	1.1	even	1	trivial
312.2.ba.a.179.34	yes	104	3.2	odd	2	inner
312.2.ba.a.179.52	yes	104	8.3	odd	2	inner
312.2.ba.a.251.1	yes	104	13.4	even	6	inner
312.2.ba.a.251.19	yes	104	312.251	even	6	inner
312.2.ba.a.251.34	yes	104	104.43	odd	6	inner
312.2.ba.a.251.52	yes	104	39.17	odd	6	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)

\(f(q)\)	\(=\)	\(q+(-0.563917 + 1.29692i) q^{2} +(-0.427675 - 1.67842i) q^{3} +(-1.36400 - 1.46271i) q^{4} -3.72006i q^{5} +(2.41795 + 0.391829i) q^{6} +(-1.77405 + 3.07274i) q^{7} +(2.66619 - 0.944145i) q^{8} +(-2.63419 + 1.43564i) q^{9} +O(q^{10})\)	\(q+(-0.563917 + 1.29692i) q^{2} +(-0.427675 - 1.67842i) q^{3} +(-1.36400 - 1.46271i) q^{4} -3.72006i q^{5} +(2.41795 + 0.391829i) q^{6} +(-1.77405 + 3.07274i) q^{7} +(2.66619 - 0.944145i) q^{8} +(-2.63419 + 1.43564i) q^{9} +(4.82462 + 2.09781i) q^{10} +(0.294499 + 0.510088i) q^{11} +(-1.87169 + 2.91492i) q^{12} +(-3.60542 - 0.0310714i) q^{13} +(-2.98468 - 4.03356i) q^{14} +(-6.24383 + 1.59098i) q^{15} +(-0.279032 + 3.99026i) q^{16} +(-1.74784 - 1.00911i) q^{17} +(-0.376443 - 4.22591i) 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} +(-2.72494 - 4.07121i) 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} +(1.45763 - 8.99492i) q^{30} +5.99017 q^{31} +(-5.01769 - 2.61205i) q^{32} +(0.730191 - 0.712445i) q^{33} +(2.29437 - 1.69774i) q^{34} +(11.4308 + 6.59957i) q^{35} +(5.69294 + 1.89484i) q^{36} +(-1.19644 - 2.07229i) q^{37} +(6.92504 - 5.12426i) q^{38} +(1.48980 + 6.06469i) q^{39} +(-3.51228 - 9.91841i) q^{40} +(-4.93476 - 8.54726i) q^{41} +(-5.49354 + 6.73460i) q^{42} +(-2.65252 + 4.59430i) q^{43} +(0.344414 - 1.12652i) q^{44} +(5.34067 + 9.79935i) q^{45} +(-4.07933 + 0.464779i) q^{46} -7.27332i q^{47} +(6.81666 - 1.23820i) 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} +(-6.93185 + 2.43915i) 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} +(10.8437 + 6.96281i) q^{60} +(-3.72531 - 2.15081i) q^{61} +(-3.37795 + 7.76876i) q^{62} +(0.261830 - 10.6411i) q^{63} +(6.21718 - 5.03455i) q^{64} +(-0.115587 + 13.4124i) q^{65} +(0.512216 + 1.34876i) q^{66} +(-0.440139 + 0.254114i) q^{67} +(0.908001 + 3.93300i) q^{68} +(3.59912 - 3.51165i) q^{69} +(-15.0051 + 11.1032i) q^{70} +(0.151877 + 0.0876865i) q^{71} +(-5.66780 + 6.31475i) q^{72} -9.04801i q^{73} +(3.36228 - 0.383082i) q^{74} +(3.78017 + 14.8354i) q^{75} +(2.74060 + 11.8709i) q^{76} -2.08982 q^{77} +(-8.70554 - 1.48784i) q^{78} -1.99512i q^{79} +(14.8440 + 1.03802i) q^{80} +(4.87789 - 7.56348i) q^{81} +(13.8679 - 1.58004i) q^{82} -16.5592 q^{83} +(-5.63633 - 10.9224i) q^{84} +(-3.75397 + 6.50206i) q^{85} +(-4.46263 - 6.03090i) q^{86} +(-4.24968 + 4.14640i) q^{87} +(1.26679 + 1.08194i) q^{88} +(-3.71133 - 6.42821i) q^{89} +(-15.7206 + 1.40039i) q^{90} +(6.49166 - 11.0234i) q^{91} +(1.69762 - 5.55265i) q^{92} +(-2.56185 - 10.0540i) q^{93} +(9.43290 + 4.10155i) q^{94} +(-11.3305 + 19.6250i) q^{95} +(-2.23818 + 9.53890i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more