LMFDB - Embedded newform 336.2.bs.a.19.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(19,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 0, 10]))

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

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

chi := DirichletCharacter("336.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bs (of order $12$, degree $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.9
Character	$\chi$	$=$	336.19
Dual form			336.2.bs.a.283.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02338 - 0.976055i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.0946319 + 1.99776i) q^{4} +(0.892283 - 0.239086i) q^{5} +(1.20767 - 0.735892i) q^{6} +(-1.55431 + 2.14106i) q^{7} +(1.85308 - 2.13684i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-1.02338 - 0.976055i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.0946319 + 1.99776i) q^{4} +(0.892283 - 0.239086i) q^{5} +(1.20767 - 0.735892i) q^{6} +(-1.55431 + 2.14106i) q^{7} +(1.85308 - 2.13684i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.14651 - 0.626240i) q^{10} +(-0.473979 + 1.76891i) q^{11} +(-1.95418 - 0.425651i) q^{12} +(-1.38078 + 1.38078i) q^{13} +(3.68045 - 0.674031i) q^{14} +0.923759i q^{15} +(-3.98209 + 0.378104i) q^{16} +(1.07254 - 0.619232i) q^{17} +(0.398249 + 1.35698i) q^{18} +(-4.11837 + 1.10351i) q^{19} +(0.562076 + 1.75994i) q^{20} +(-1.66582 - 2.05549i) q^{21} +(2.21162 - 1.34765i) q^{22} +(-2.51976 + 4.36436i) q^{23} +(1.58442 + 2.34299i) q^{24} +(-3.59112 + 2.07333i) q^{25} +(2.76079 - 0.0653513i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-4.42440 - 2.90253i) q^{28} +(2.73590 + 2.73590i) q^{29} +(0.901640 - 0.945361i) q^{30} +(4.65901 + 8.06964i) q^{31} +(4.44426 + 3.49979i) q^{32} +(-1.58596 - 0.915657i) q^{33} +(-1.70203 - 0.413147i) q^{34} +(-0.874987 + 2.28204i) q^{35} +(0.916926 - 1.77743i) q^{36} +(-0.381781 - 1.42483i) q^{37} +(5.29176 + 2.89044i) q^{38} +(-0.976359 - 1.69110i) q^{39} +(1.14258 - 2.34971i) q^{40} +4.96698 q^{41} +(-0.301506 + 3.72949i) q^{42} +(1.82451 + 1.82451i) q^{43} +(-3.57872 - 0.779500i) q^{44} +(-0.892283 - 0.239086i) q^{45} +(6.83854 - 2.00699i) q^{46} +(3.34606 - 5.79555i) q^{47} +(0.665420 - 3.94426i) q^{48} +(-2.16824 - 6.65573i) q^{49} +(5.69879 + 1.38331i) q^{50} +(0.320538 + 1.19626i) q^{51} +(-2.88913 - 2.62780i) q^{52} +(-5.15482 - 1.38123i) q^{53} +(-1.41382 + 0.0334668i) q^{54} +1.69169i q^{55} +(1.69484 + 7.28886i) q^{56} -4.26365i q^{57} +(-0.129488 - 5.47027i) q^{58} +(0.411834 + 0.110351i) q^{59} +(-1.84545 + 0.0874171i) q^{60} +(1.25535 + 4.68504i) q^{61} +(3.10846 - 12.8058i) q^{62} +(2.41660 - 1.07705i) q^{63} +(-1.13219 - 7.91948i) q^{64} +(-0.901921 + 1.56217i) q^{65} +(0.729320 + 2.48506i) q^{66} +(-11.5544 - 3.09601i) q^{67} +(1.33857 + 2.08408i) q^{68} +(-3.56348 - 3.56348i) q^{69} +(3.12285 - 1.48137i) q^{70} -0.751677 q^{71} +(-2.67324 + 0.924020i) q^{72} +(0.776623 + 1.34515i) q^{73} +(-1.00000 + 1.83079i) q^{74} +(-1.07324 - 4.00537i) q^{75} +(-2.59428 - 8.12308i) q^{76} +(-3.05063 - 3.76426i) q^{77} +(-0.651420 + 2.68363i) q^{78} +(13.7705 + 7.95042i) q^{79} +(-3.46275 + 1.28944i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-5.08313 - 4.84804i) q^{82} +(-7.48522 - 7.48522i) q^{83} +(3.94874 - 3.52242i) q^{84} +(0.808960 - 0.808960i) q^{85} +(-0.0863526 - 3.64800i) q^{86} +(-3.35078 + 1.93457i) q^{87} +(2.90157 + 4.29076i) q^{88} +(6.65111 - 11.5201i) q^{89} +(0.679787 + 1.11559i) q^{90} +(-0.810167 - 5.10249i) q^{91} +(-8.95739 - 4.62087i) q^{92} +(-9.00051 + 2.41168i) q^{93} +(-9.08108 + 2.66513i) q^{94} +(-3.41091 + 1.96929i) q^{95} +(-4.53080 + 3.38701i) q^{96} -9.09284i q^{97} +(-4.27742 + 8.92769i) q^{98} +(1.29493 - 1.29493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 24 q^{8}+O(q^{10}) $ 128 * q + 4 * q^4 - 24 * q^8	$ 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44} - 20 q^{46} - 32 q^{50} - 144 q^{52} - 16 q^{53} - 56 q^{56} - 40 q^{58} - 96 q^{59} - 24 q^{60} - 32 q^{64} - 72 q^{66} + 16 q^{67} - 60 q^{68} + 28 q^{70} + 128 q^{71} - 4 q^{72} - 72 q^{74} + 72 q^{78} - 36 q^{80} + 64 q^{81} - 60 q^{82} + 24 q^{84} - 44 q^{86} - 48 q^{88} - 8 q^{91} + 56 q^{92} + 36 q^{94} + 60 q^{96} + 148 q^{98} - 16 q^{99}+O(q^{100}) $ 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.02338	−	0.976055i	−0.723642	−	0.690175i
$2$	−1.02338	−	0.976055i	−0.723642	−	0.690175i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	0.0946319	+	1.99776i	0.0473160	+	0.998880i
$5$	0.892283	−	0.239086i	0.399041	−	0.106923i	−0.0537169	−	0.998556i	$-0.517107\pi$
$5$	0.892283	−	0.239086i	0.399041	−	0.106923i	0.452758	+	0.891633i	$0.350440\pi$
$6$	1.20767	−	0.735892i	0.493029	−	0.300427i
$7$	−1.55431	+	2.14106i	−0.587474	+	0.809243i
$7$	−1.55431	+	2.14106i	−0.587474	+	0.809243i
$8$	1.85308	−	2.13684i	0.655163	−	0.755488i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−1.14651	−	0.626240i	−0.362558	−	0.198034i
$11$	−0.473979	+	1.76891i	−0.142910	+	0.533348i	0.856929	+	0.515434i	$0.172369\pi$
$11$	−0.473979	+	1.76891i	−0.142910	+	0.533348i	−0.999840	+	0.0179139i	$0.994298\pi$
$12$	−1.95418	−	0.425651i	−0.564123	−	0.122875i
$13$	−1.38078	+	1.38078i	−0.382960	+	0.382960i	−0.872167	−	0.489208i	$-0.837286\pi$
$13$	−1.38078	+	1.38078i	−0.382960	+	0.382960i	0.489208	+	0.872167i	$0.337286\pi$
$14$	3.68045	−	0.674031i	0.983641	−	0.180142i
$15$			0.923759i			0.238514i
$16$	−3.98209	+	0.378104i	−0.995522	+	0.0945259i
$17$	1.07254	−	0.619232i	0.260130	−	0.150186i	−0.364264	−	0.931296i	$-0.618679\pi$
$17$	1.07254	−	0.619232i	0.260130	−	0.150186i	0.624394	+	0.781110i	$0.285346\pi$
$18$	0.398249	+	1.35698i	0.0938683	+	0.319843i
$19$	−4.11837	+	1.10351i	−0.944818	+	0.253163i	−0.698162	−	0.715940i	$-0.745999\pi$
$19$	−4.11837	+	1.10351i	−0.944818	+	0.253163i	−0.246656	+	0.969103i	$0.579332\pi$
$20$	0.562076	+	1.75994i	0.125684	+	0.393535i
$21$	−1.66582	−	2.05549i	−0.363511	−	0.448546i
$22$	2.21162	−	1.34765i	0.471519	−	0.287320i
$23$	−2.51976	+	4.36436i	−0.525407	+	0.910031i	0.474155	+	0.880441i	$0.342754\pi$
$23$	−2.51976	+	4.36436i	−0.525407	+	0.910031i	−0.999562	+	0.0295902i	$0.990580\pi$
$24$	1.58442	+	2.34299i	0.323418	+	0.478261i
$25$	−3.59112	+	2.07333i	−0.718224	+	0.414667i
$26$	2.76079	−	0.0653513i	0.541435	−	0.0128164i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−4.42440	−	2.90253i	−0.836134	−	0.548526i
$29$	2.73590	+	2.73590i	0.508044	+	0.508044i	0.913926	−	0.405882i	$-0.133036\pi$
$29$	2.73590	+	2.73590i	0.508044	+	0.508044i	−0.405882	+	0.913926i	$0.633036\pi$
$30$	0.901640	−	0.945361i	0.164616	−	0.172598i
$31$	4.65901	+	8.06964i	0.836782	+	1.44935i	0.892571	+	0.450907i	$0.148899\pi$
$31$	4.65901	+	8.06964i	0.836782	+	1.44935i	−0.0557885	+	0.998443i	$0.517767\pi$
$32$	4.44426	+	3.49979i	0.785641	+	0.618682i
$33$	−1.58596	−	0.915657i	−0.276081	−	0.159395i
$34$	−1.70203	−	0.413147i	−0.291895	−	0.0708542i
$35$	−0.874987	+	2.28204i	−0.147900	+	0.385735i
$36$	0.916926	−	1.77743i	0.152821	−	0.296238i
$37$	−0.381781	−	1.42483i	−0.0627644	−	0.234240i	0.927417	−	0.374029i	$-0.122024\pi$
$37$	−0.381781	−	1.42483i	−0.0627644	−	0.234240i	−0.990181	+	0.139789i	$0.955357\pi$
$38$	5.29176	+	2.89044i	0.858438	+	0.468891i
$39$	−0.976359	−	1.69110i	−0.156343	−	0.270793i
$40$	1.14258	−	2.34971i	0.180658	−	0.371522i
$41$	4.96698			0.775711			0.387856	−	0.921720i	$-0.373216\pi$
$41$	4.96698			0.775711			0.387856	+	0.921720i	$0.373216\pi$
$42$	−0.301506	+	3.72949i	−0.0465234	+	0.575473i
$43$	1.82451	+	1.82451i	0.278235	+	0.278235i	0.832404	−	0.554169i	$-0.186964\pi$
$43$	1.82451	+	1.82451i	0.278235	+	0.278235i	−0.554169	+	0.832404i	$0.686964\pi$
$44$	−3.57872	−	0.779500i	−0.539512	−	0.117514i
$45$	−0.892283	−	0.239086i	−0.133014	−	0.0356409i
$46$	6.83854	−	2.00699i	1.00829	−	0.295914i
$47$	3.34606	−	5.79555i	0.488073	−	0.845367i	−0.511833	−	0.859085i	$-0.671033\pi$
$47$	3.34606	−	5.79555i	0.488073	−	0.845367i	0.999906	+	0.0137178i	$0.00436665\pi$
$48$	0.665420	−	3.94426i	0.0960452	−	0.569305i
$49$	−2.16824	−	6.65573i	−0.309749	−	0.950819i
$50$	5.69879	+	1.38331i	0.805930	+	0.195630i
$51$	0.320538	+	1.19626i	0.0448843	+	0.167511i
$52$	−2.88913	−	2.62780i	−0.400651	−	0.364411i
$53$	−5.15482	−	1.38123i	−0.708069	−	0.189727i	−0.113227	−	0.993569i	$-0.536119\pi$
$53$	−5.15482	−	1.38123i	−0.708069	−	0.189727i	−0.594842	+	0.803843i	$0.702785\pi$
$54$	−1.41382	+	0.0334668i	−0.192396	+	0.00455426i
$55$			1.69169i			0.228108i
$56$	1.69484	+	7.28886i	0.226482	+	0.974015i
$57$		−	4.26365i		−	0.564734i
$58$	−0.129488	−	5.47027i	−0.0170026	−	0.718281i
$59$	0.411834	+	0.110351i	0.0536162	+	0.0143664i	0.285527	−	0.958371i	$-0.407831\pi$
$59$	0.411834	+	0.110351i	0.0536162	+	0.0143664i	−0.231911	+	0.972737i	$0.574498\pi$
$60$	−1.84545	+	0.0874171i	−0.238246	+	0.0112855i
$61$	1.25535	+	4.68504i	0.160731	+	0.599858i	0.998546	+	0.0539031i	$0.0171662\pi$
$61$	1.25535	+	4.68504i	0.160731	+	0.599858i	−0.837815	+	0.545955i	$0.816167\pi$
$62$	3.10846	−	12.8058i	0.394774	−	1.62634i
$63$	2.41660	−	1.07705i	0.304463	−	0.135696i
$64$	−1.13219	−	7.91948i	−0.141524	−	0.989935i
$65$	−0.901921	+	1.56217i	−0.111870	+	0.193764i
$66$	0.729320	+	2.48506i	0.0897730	+	0.305890i
$67$	−11.5544	−	3.09601i	−1.41160	−	0.378237i	−0.529104	−	0.848557i	$-0.677472\pi$
$67$	−11.5544	−	3.09601i	−1.41160	−	0.378237i	−0.882496	+	0.470320i	$0.844139\pi$
$68$	1.33857	+	2.08408i	0.162326	+	0.252732i
$69$	−3.56348	−	3.56348i	−0.428993	−	0.428993i
$70$	3.12285	−	1.48137i	0.373252	−	0.177058i
$71$	−0.751677			−0.0892076			−0.0446038	−	0.999005i	$-0.514203\pi$
$71$	−0.751677			−0.0892076			−0.0446038	+	0.999005i	$0.514203\pi$
$72$	−2.67324	+	0.924020i	−0.315044	+	0.108897i
$73$	0.776623	+	1.34515i	0.0908969	+	0.157438i	0.907889	−	0.419211i	$-0.137693\pi$
$73$	0.776623	+	1.34515i	0.0908969	+	0.157438i	−0.816992	+	0.576649i	$0.804360\pi$
$74$	−1.00000	+	1.83079i	−0.116248	+	0.212824i
$75$	−1.07324	−	4.00537i	−0.123927	−	0.462501i
$76$	−2.59428	−	8.12308i	−0.297585	−	0.931782i
$77$	−3.05063	−	3.76426i	−0.347652	−	0.428977i
$78$	−0.651420	+	2.68363i	−0.0737588	+	0.303861i
$79$	13.7705	+	7.95042i	1.54931	+	0.894493i	0.998195	+	0.0600611i	$0.0191295\pi$
$79$	13.7705	+	7.95042i	1.54931	+	0.894493i	0.551112	+	0.834431i	$0.314204\pi$
$80$	−3.46275	+	1.28944i	−0.387147	+	0.144164i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−5.08313	−	4.84804i	−0.561337	−	0.535377i
$83$	−7.48522	−	7.48522i	−0.821610	−	0.821610i	0.164729	−	0.986339i	$-0.447325\pi$
$83$	−7.48522	−	7.48522i	−0.821610	−	0.821610i	−0.986339	+	0.164729i	$0.947325\pi$
$84$	3.94874	−	3.52242i	0.430843	−	0.384327i
$85$	0.808960	−	0.808960i	0.0877441	−	0.0877441i
$86$	−0.0863526	−	3.64800i	−0.00931164	−	0.393374i
$87$	−3.35078	+	1.93457i	−0.359241	+	0.207408i
$88$	2.90157	+	4.29076i	0.309308	+	0.457396i
$89$	6.65111	−	11.5201i	0.705017	−	1.22112i	−0.261669	−	0.965158i	$-0.584273\pi$
$89$	6.65111	−	11.5201i	0.705017	−	1.22112i	0.966686	−	0.255967i	$-0.0823938\pi$
$90$	0.679787	+	1.11559i	0.0716558	+	0.117594i
$91$	−0.810167	−	5.10249i	−0.0849286	−	0.534886i
$92$	−8.95739	−	4.62087i	−0.933872	−	0.481759i
$93$	−9.00051	+	2.41168i	−0.933310	+	0.250080i
$94$	−9.08108	+	2.66513i	−0.936642	+	0.274887i
$95$	−3.41091	+	1.96929i	−0.349952	+	0.202045i
$96$	−4.53080	+	3.38701i	−0.462423	+	0.345685i
$97$		−	9.09284i		−	0.923239i	−0.887078	−	0.461619i	$-0.847269\pi$
$97$		−	9.09284i		−	0.923239i	0.887078	−	0.461619i	$-0.152731\pi$
$98$	−4.27742	+	8.92769i	−0.432084	+	0.901833i
$99$	1.29493	−	1.29493i	0.130146	−	0.130146i
$100$	−4.48186	−	6.97799i	−0.448186	−	0.697799i
$101$	3.67474	−	13.7143i	0.365650	−	1.36463i	−0.500887	−	0.865513i	$-0.666993\pi$
$101$	3.67474	−	13.7143i	0.365650	−	1.36463i	0.866537	−	0.499113i	$-0.166341\pi$
$102$	0.839587	−	1.53710i	0.0831315	−	0.152196i
$103$	15.7176	+	9.07457i	1.54870	+	0.894144i	0.998241	+	0.0592832i	$0.0188815\pi$
$103$	15.7176	+	9.07457i	1.54870	+	0.894144i	0.550461	+	0.834861i	$0.314452\pi$
$104$	0.391815	+	5.50921i	0.0384206	+	0.540222i
$105$	−1.97782	−	1.43581i	−0.193015	−	0.140121i
$106$	3.92721	+	6.44492i	0.381444	+	0.625986i
$107$	−11.7066	+	3.13678i	−1.13172	+	0.303244i	−0.775618	−	0.631203i	$-0.782562\pi$
$107$	−11.7066	+	3.13678i	−1.13172	+	0.303244i	−0.356103	+	0.934447i	$0.615895\pi$
$108$	1.47954	+	1.34571i	0.142369	+	0.129491i
$109$	−1.44460	+	5.39133i	−0.138368	+	0.516396i	0.861593	+	0.507599i	$0.169467\pi$
$109$	−1.44460	+	5.39133i	−0.138368	+	0.516396i	−0.999961	+	0.00879707i	$0.997200\pi$
$110$	1.65119	−	1.73125i	0.157434	−	0.165068i
$111$	1.47509			0.140009
$112$	5.37986	−	9.11357i	0.508349	−	0.861151i
$113$	6.33333			0.595790			0.297895	−	0.954599i	$-0.403715\pi$
$113$	6.33333			0.595790			0.297895	+	0.954599i	$0.403715\pi$
$114$	−4.16156	+	4.36335i	−0.389766	+	0.408665i
$115$	−1.20488	+	4.49668i	−0.112356	+	0.419318i
$116$	−5.20677	+	5.72457i	−0.483436	+	0.531513i
$117$	1.88618	−	0.505401i	0.174378	−	0.0467243i
$118$	−0.313756	−	0.514904i	−0.0288836	−	0.0474008i
$119$	−0.341252	+	3.25885i	−0.0312825	+	0.298738i
$120$	1.97393	+	1.71180i	0.180194	+	0.156265i
$121$	6.62188	+	3.82314i	0.601989	+	0.347559i
$122$	3.28815	−	6.01989i	0.297695	−	0.545015i
$123$	−1.28555	+	4.79773i	−0.115914	+	0.432597i
$124$	−15.6803	+	10.0712i	−1.40813	+	0.904423i
$125$	−5.97457	+	5.97457i	−0.534382	+	0.534382i
$126$	−3.52438	−	1.25650i	−0.313976	−	0.111937i
$127$		−	7.22412i		−	0.641037i	−0.947242	−	0.320518i	$-0.896143\pi$
$127$		−	7.22412i		−	0.641037i	0.947242	−	0.320518i	$-0.103857\pi$
$128$	−6.57118	+	9.20976i	−0.580816	+	0.814035i
$129$	−2.23456	+	1.29012i	−0.196742	+	0.113589i
$130$	2.44778	−	0.718379i	0.214684	−	0.0630060i
$131$	14.6670	−	3.93000i	1.28146	−	0.343366i	0.447049	−	0.894509i	$-0.352475\pi$
$131$	14.6670	−	3.93000i	1.28146	−	0.343366i	0.834411	+	0.551143i	$0.185808\pi$
$132$	1.67918	−	3.25503i	0.146154	−	0.283314i
$133$	4.03854	−	10.5329i	0.350186	−	0.913315i
$134$	8.80277	+	14.4462i	0.760444	+	1.24796i
$135$	0.461880	−	0.799999i	0.0397523	−	0.0688529i
$136$	0.664303	−	3.43934i	0.0569635	−	0.294921i
$137$	13.8508	−	7.99679i	1.18336	−	0.683212i	0.226569	−	0.973995i	$-0.427249\pi$
$137$	13.8508	−	7.99679i	1.18336	−	0.683212i	0.956789	+	0.290783i	$0.0939159\pi$
$138$	0.168657	+	7.12497i	0.0143570	+	0.606518i
$139$	16.5134	−	16.5134i	1.40065	−	1.40065i	0.602616	−	0.798032i	$-0.294125\pi$
$139$	16.5134	−	16.5134i	1.40065	−	1.40065i	0.798032	−	0.602616i	$-0.205875\pi$
$140$	−4.64177	−	1.53206i	−0.392301	−	0.129483i
$141$	4.73204	+	4.73204i	0.398510	+	0.398510i
$142$	0.769254	+	0.733678i	0.0645544	+	0.0615689i
$143$	−1.78802	−	3.09694i	−0.149522	−	0.258979i
$144$	3.63764	+	1.66360i	0.303137	+	0.138633i
$145$	3.09531	+	1.78708i	0.257052	+	0.148409i
$146$	0.518158	−	2.13463i	0.0428830	−	0.176664i
$147$	6.99012	−	0.371729i	0.576536	−	0.0306597i
$148$	2.81033	−	0.897541i	0.231008	−	0.0737774i
$149$	5.48517	+	20.4709i	0.449362	+	1.67704i	0.704154	+	0.710047i	$0.251327\pi$
$149$	5.48517	+	20.4709i	0.449362	+	1.67704i	−0.254791	+	0.966996i	$0.582007\pi$
$150$	−2.81113	+	5.14658i	−0.229528	+	0.420216i
$151$	8.23943	+	14.2711i	0.670515	+	1.16137i	0.977758	+	0.209735i	$0.0672602\pi$
$151$	8.23943	+	14.2711i	0.670515	+	1.16137i	−0.307243	+	0.951631i	$0.599406\pi$
$152$	−5.27363	+	10.8452i	−0.427748	+	0.879662i
$153$	−1.23846			−0.100124
$154$	−0.552152	+	6.82987i	−0.0444937	+	0.550366i
$155$	6.08649	+	6.08649i	0.488879	+	0.488879i
$156$	3.28603	−	2.11056i	0.263093	−	0.168980i
$157$	−9.49026	−	2.54291i	−0.757405	−	0.202946i	−0.140605	−	0.990066i	$-0.544905\pi$
$157$	−9.49026	−	2.54291i	−0.757405	−	0.202946i	−0.616800	+	0.787120i	$0.711571\pi$
$158$	−6.33250	−	21.5771i	−0.503787	−	1.71659i
$159$	2.66833	−	4.62169i	0.211613	−	0.366524i
$160$	4.80229	+	2.06024i	0.379654	+	0.162877i
$161$	−5.42784	−	12.1785i	−0.427774	−	0.959802i
$162$	0.333596	−	1.37430i	0.0262098	−	0.107976i
$163$	1.47209	+	5.49390i	0.115303	+	0.430315i	0.999309	−	0.0371588i	$-0.0118307\pi$
$163$	1.47209	+	5.49390i	0.115303	+	0.430315i	−0.884007	+	0.467474i	$0.845164\pi$
$164$	0.470034	+	9.92282i	0.0367035	+	0.774842i
$165$	−1.63405	−	0.437842i	−0.127211	−	0.0340860i
$166$	0.354270	+	14.9663i	0.0274967	+	1.16161i
$167$			3.95453i			0.306011i	0.988225	+	0.153005i	$0.0488952\pi$
$167$			3.95453i			0.306011i	−0.988225	+	0.153005i	$0.951105\pi$
$168$	−7.47916	−	0.249407i	−0.577030	−	0.0192422i
$169$			9.18689i			0.706684i
$170$	−1.61747	+	0.0382875i	−0.124054	+	0.00293651i
$171$	4.11837	+	1.10351i	0.314939	+	0.0843878i
$172$	−3.47228	+	3.81759i	−0.264759	+	0.291089i
$173$	1.85214	+	6.91229i	0.140816	+	0.525531i	0.999906	+	0.0137074i	$0.00436334\pi$
$173$	1.85214	+	6.91229i	0.140816	+	0.525531i	−0.859090	+	0.511824i	$0.828970\pi$
$174$	5.31739	+	1.29073i	0.403110	+	0.0978502i
$175$	1.14259	−	10.9114i	0.0863717	−	0.824824i
$176$	1.21859	−	7.22319i	0.0918550	−	0.544468i
$177$	−0.213181	+	0.369240i	−0.0160237	+	0.0277538i
$178$	−18.0509	+	5.29760i	−1.35297	+	0.397072i
$179$	−25.0367	−	6.70856i	−1.87133	−	0.501421i	−0.999941	−	0.0108285i	$-0.996553\pi$
$179$	−25.0367	−	6.70856i	−1.87133	−	0.501421i	−0.871389	−	0.490593i	$-0.836780\pi$
$180$	0.393199	−	1.80519i	0.0293073	−	0.134551i
$181$	10.5885	+	10.5885i	0.787040	+	0.787040i	0.981008	−	0.193968i	$-0.0621357\pi$
$181$	10.5885	+	10.5885i	0.787040	+	0.787040i	−0.193968	+	0.981008i	$0.562136\pi$
$182$	−4.15120	+	6.01258i	−0.307707	+	0.445682i
$183$	−4.85031			−0.358545
$184$	4.65662	+	13.4718i	0.343291	+	0.993157i
$185$	−0.681314	−	1.18007i	−0.0500912	−	0.0867604i
$186$	11.5649	+	6.31692i	0.847981	+	0.463179i
$187$	0.587006	+	2.19074i	0.0429261	+	0.160202i
$188$	11.8948	+	6.13618i	0.867514	+	0.447527i
$189$	0.414892	+	2.61302i	0.0301789	+	0.190069i
$190$	5.41282	+	1.31390i	0.392687	+	0.0953202i
$191$	−9.11996	−	5.26541i	−0.659897	−	0.380992i	0.132341	−	0.991204i	$-0.457751\pi$
$191$	−9.11996	−	5.26541i	−0.659897	−	0.380992i	−0.792238	+	0.610212i	$0.791084\pi$
$192$	7.94266	+	0.956097i	0.573212	+	0.0690004i
$193$	3.17335	+	5.49641i	0.228423	+	0.395640i	0.957341	−	0.288961i	$-0.0933098\pi$
$193$	3.17335	+	5.49641i	0.228423	+	0.395640i	−0.728918	+	0.684601i	$0.759976\pi$
$194$	−8.87512	+	9.30548i	−0.637196	+	0.668094i
$195$	−1.27551	−	1.27551i	−0.0913411	−	0.0913411i
$196$	13.0914	−	4.96147i	0.935098	−	0.354391i
$197$	−14.3477	+	14.3477i	−1.02223	+	1.02223i	−0.0224814	+	0.999747i	$0.507157\pi$
$197$	−14.3477	+	14.3477i	−1.02223	+	1.02223i	−0.999747	+	0.0224814i	$0.992843\pi$
$198$	−2.58914	+	0.0612882i	−0.184002	+	0.00435557i
$199$	−7.00334	+	4.04338i	−0.496454	+	0.286628i	−0.727248	−	0.686375i	$-0.759201\pi$
$199$	−7.00334	+	4.04338i	−0.496454	+	0.286628i	0.230794	+	0.973003i	$0.425868\pi$
$200$	−2.22424	+	11.5157i	−0.157278	+	0.814284i
$201$	5.98102	−	10.3594i	0.421869	−	0.730698i
$202$	−17.1466	+	10.4483i	−1.20643	+	0.735138i
$203$	−10.1101	+	1.60528i	−0.709593	+	0.112668i
$204$	−2.35952	+	0.753563i	−0.165199	+	0.0527600i
$205$	4.43195	−	1.18754i	0.309541	−	0.0829412i
$206$	−7.22788	−	24.6280i	−0.503590	−	1.71592i
$207$	4.36436	−	2.51976i	0.303344	−	0.175136i
$208$	4.97631	−	6.02047i	0.345045	−	0.417445i
$209$		−	7.80808i		−	0.540096i
$210$	0.622642	+	3.39985i	0.0429664	+	0.234612i
$211$	3.83387	−	3.83387i	0.263935	−	0.263935i	−0.562716	−	0.826650i	$-0.690243\pi$
$211$	3.83387	−	3.83387i	0.263935	−	0.263935i	0.826650	+	0.562716i	$0.190243\pi$
$212$	2.27156	−	10.4288i	0.156011	−	0.716253i
$213$	0.194548	−	0.726064i	0.0133302	−	0.0497491i
$214$	15.0420	+	8.21617i	1.02825	+	0.561646i
$215$	2.06419	+	1.19176i	0.140777	+	0.0812776i
$216$	−0.200651	−	2.82130i	−0.0136526	−	0.191965i
$217$	−24.5191	−	2.56752i	−1.66446	−	0.174295i
$218$	6.74063	−	4.10740i	0.456533	−	0.278188i
$219$	−1.50032	+	0.402010i	−0.101382	+	0.0271653i
$220$	−3.37960	+	0.160088i	−0.227852	+	0.0107931i
$221$	−0.625921	+	2.33597i	−0.0421040	+	0.157134i
$222$	−1.50958	−	1.43977i	−0.101317	−	0.0966309i
$223$	−18.5363			−1.24128			−0.620642	−	0.784094i	$-0.713128\pi$
$223$	−18.5363			−1.24128			−0.620642	+	0.784094i	$0.713128\pi$
$224$	−14.4010	+	4.07564i	−0.962208	+	0.272315i
$225$	4.14667			0.276445
$226$	−6.48144	−	6.18168i	−0.431139	−	0.411199i
$227$	2.06123	−	7.69261i	0.136808	−	0.510576i	−0.863175	−	0.504904i	$-0.831528\pi$
$227$	2.06123	−	7.69261i	0.136808	−	0.510576i	0.999984	−	0.00567210i	$-0.00180550\pi$
$228$	8.51775	−	0.403477i	0.564102	−	0.0267209i
$229$	−1.49525	+	0.400652i	−0.0988092	+	0.0264758i	−0.307885	−	0.951424i	$-0.599621\pi$
$229$	−1.49525	+	0.400652i	−0.0988092	+	0.0264758i	0.209076	+	0.977899i	$0.432954\pi$
$230$	5.62207	−	3.42580i	0.370708	−	0.225891i
$231$	4.42555	−	1.97242i	0.291180	−	0.129776i
$232$	10.9160	−	0.776348i	0.716672	−	0.0509697i
$233$	23.1824	+	13.3844i	1.51873	+	0.876839i	0.999757	+	0.0220484i	$0.00701878\pi$
$233$	23.1824	+	13.3844i	1.51873	+	0.876839i	0.518973	+	0.854791i	$0.326315\pi$
$234$	−2.42359	−	1.32380i	−0.158435	−	0.0865394i
$235$	1.60000	−	5.97126i	0.104372	−	0.389522i
$236$	−0.181481	+	0.833189i	−0.0118134	+	0.0542360i
$237$	−11.2436	+	11.2436i	−0.730350	+	0.730350i
$238$	3.53005	−	3.00198i	0.228819	−	0.194589i
$239$		−	7.18814i		−	0.464962i	−0.972601	−	0.232481i	$-0.925316\pi$
$239$		−	7.18814i		−	0.464962i	0.972601	−	0.232481i	$-0.0746844\pi$
$240$	−0.349277	−	3.67849i	−0.0225457	−	0.237446i
$241$	0.547044	−	0.315836i	0.0352382	−	0.0203448i	−0.482277	−	0.876019i	$-0.660190\pi$
$241$	0.547044	−	0.315836i	0.0352382	−	0.0203448i	0.517516	+	0.855674i	$0.326857\pi$
$242$	−3.04513	−	10.3759i	−0.195748	−	0.666986i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−9.24079	+	2.95125i	−0.591581	+	0.188934i
$245$	−3.52598	−	5.42040i	−0.225266	−	0.346296i
$246$	5.99846	−	3.65516i	0.382448	−	0.233044i
$247$	4.16285	−	7.21027i	0.264876	−	0.458779i
$248$	25.8771	+	4.99811i	1.64319	+	0.317381i
$249$	9.16749	−	5.29285i	0.580966	−	0.335421i
$250$	11.9458	−	0.282772i	0.755518	−	0.0178841i
$251$	0.622699	−	0.622699i	0.0393044	−	0.0393044i	−0.687181	−	0.726486i	$-0.741152\pi$
$251$	0.622699	−	0.622699i	0.0393044	−	0.0393044i	0.726486	+	0.687181i	$0.241152\pi$
$252$	2.38038	+	4.72586i	0.149950	+	0.297701i
$253$	−6.52586	−	6.52586i	−0.410277	−	0.410277i
$254$	−7.05114	+	7.39305i	−0.442428	+	0.463881i
$255$	0.572021	+	0.990770i	0.0358214	+	0.0620444i
$256$	15.7141	−	3.01129i	0.982130	−	0.188205i
$257$	−5.07261	−	2.92867i	−0.316421	−	0.182686i	0.333375	−	0.942794i	$-0.391812\pi$
$257$	−5.07261	−	2.92867i	−0.316421	−	0.182686i	−0.649796	+	0.760109i	$0.725146\pi$
$258$	3.54605	+	0.860761i	0.220767	+	0.0535886i
$259$	3.64404	+	1.39721i	0.226430	+	0.0868183i
$260$	−3.20620	−	1.65399i	−0.198840	−	0.102576i
$261$	−1.00141	−	3.73731i	−0.0619856	−	0.231334i
$262$	−18.8459	−	10.2939i	−1.16430	−	0.635958i
$263$	−13.1372	−	22.7543i	−0.810076	−	1.40309i	−0.912810	−	0.408383i	$-0.866093\pi$
$263$	−13.1372	−	22.7543i	−0.810076	−	1.40309i	0.102735	−	0.994709i	$-0.467241\pi$
$264$	−4.89553	+	1.69217i	−0.301299	+	0.104146i
$265$	−4.92979			−0.302835
$266$	−14.4136	+	6.83733i	−0.883756	+	0.419224i
$267$	9.40610	+	9.40610i	0.575644	+	0.575644i
$268$	5.09166	−	23.3760i	0.311022	−	1.42792i
$269$	2.87336	+	0.769914i	0.175192	+	0.0469425i	0.345348	−	0.938475i	$-0.387761\pi$
$269$	2.87336	+	0.769914i	0.175192	+	0.0469425i	−0.170157	+	0.985417i	$0.554427\pi$
$270$	−1.25352	+	0.367886i	−0.0762870	+	0.0223889i
$271$	−0.0735018	+	0.127309i	−0.00446492	+	0.00773346i	−0.868249	−	0.496128i	$-0.834755\pi$
$271$	−0.0735018	+	0.127309i	−0.00446492	+	0.00773346i	0.863784	+	0.503862i	$0.168088\pi$
$272$	−4.03682	+	2.87137i	−0.244768	+	0.174102i
$273$	5.13831	+	0.538060i	0.310985	+	0.0325649i
$274$	−21.9801	−	5.33540i	−1.32786	−	0.322323i
$275$	−1.96543	−	7.33510i	−0.118520	−	0.442323i
$276$	6.78176	−	7.45620i	0.408214	−	0.448811i
$277$	12.2971	+	3.29499i	0.738860	+	0.197977i	0.608571	−	0.793499i	$-0.291743\pi$
$277$	12.2971	+	3.29499i	0.738860	+	0.197977i	0.130289	+	0.991476i	$0.458410\pi$
$278$	−33.0175	+	0.781566i	−1.98026	+	0.0468752i
$279$		−	9.31801i		−	0.557855i
$280$	3.25494	+	6.09851i	0.194520	+	0.364456i
$281$			10.0323i			0.598474i	0.954179	+	0.299237i	$0.0967321\pi$
$281$			10.0323i			0.598474i	−0.954179	+	0.299237i	$0.903268\pi$
$282$	−0.223964	−	9.46144i	−0.0133369	−	0.563420i
$283$	−11.3217	−	3.03365i	−0.673007	−	0.180332i	−0.0938982	−	0.995582i	$-0.529933\pi$
$283$	−11.3217	−	3.03365i	−0.673007	−	0.180332i	−0.579109	+	0.815250i	$0.696599\pi$
$284$	−0.0711326	−	1.50167i	−0.00422094	−	0.0891077i
$285$	−1.01938	−	3.80438i	−0.0603829	−	0.225352i
$286$	−1.19295	+	4.91457i	−0.0705409	+	0.290605i
$287$	−7.72022	+	10.6346i	−0.455710	+	0.627739i
$288$	−2.09894	−	5.25304i	−0.123681	−	0.309538i
$289$	−7.73310	+	13.3941i	−0.454888	+	0.787890i
$290$	−1.42341	−	4.85007i	−0.0835853	−	0.284806i
$291$	8.78301	+	2.35340i	0.514869	+	0.137959i
$292$	−2.61380	+	1.67880i	−0.152961	+	0.0982444i
$293$	14.5304	+	14.5304i	0.848874	+	0.848874i	0.989993	−	0.141119i	$-0.0450700\pi$
$293$	14.5304	+	14.5304i	0.848874	+	0.848874i	−0.141119	+	0.989993i	$0.545070\pi$
$294$	−7.51641	−	6.44232i	−0.438366	−	0.375724i
$295$	0.393856			0.0229312
$296$	−3.75210	−	1.82451i	−0.218086	−	0.106048i
$297$	0.915657	+	1.58596i	0.0531318	+	0.0920270i
$298$	14.3673	−	26.3035i	0.832277	−	1.52372i
$299$	−2.54698	−	9.50546i	−0.147296	−	0.549715i
$300$	7.90021	−	2.52311i	0.456119	−	0.145672i
$301$	−6.74223	+	1.07052i	−0.388616	+	0.0617039i
$302$	5.49729	−	22.6470i	0.316333	−	1.30319i
$303$	12.2959	+	7.09905i	0.706382	+	0.407830i
$304$	15.9825	−	5.95146i	0.916657	−	0.341340i
$305$	2.24026	+	3.88024i	0.128277	+	0.222182i
$306$	1.26743	+	1.20881i	0.0724539	+	0.0691030i
$307$	−12.7707	−	12.7707i	−0.728865	−	0.728865i	0.241529	−	0.970394i	$-0.422351\pi$
$307$	−12.7707	−	12.7707i	−0.728865	−	0.728865i	−0.970394	+	0.241529i	$0.922351\pi$
$308$	7.23139	−	6.45065i	0.412047	−	0.367560i
$309$	−12.8334	+	12.8334i	−0.730065	+	0.730065i
$310$	−0.288069	−	12.1696i	−0.0163612	−	0.691186i
$311$	−7.68399	+	4.43635i	−0.435719	+	0.251562i	−0.701780	−	0.712394i	$-0.747611\pi$
$311$	−7.68399	+	4.43635i	−0.435719	+	0.251562i	0.266061	+	0.963956i	$0.414278\pi$
$312$	−5.42290	−	1.04742i	−0.307011	−	0.0592987i
$313$	−6.93655	+	12.0145i	−0.392077	+	0.679097i	−0.992723	−	0.120418i	$-0.961577\pi$
$313$	−6.93655	+	12.0145i	−0.392077	+	0.679097i	0.600646	+	0.799515i	$0.294910\pi$
$314$	7.23017	+	11.8654i	0.408022	+	0.669603i
$315$	1.89878	−	1.53881i	0.106984	−	0.0867023i
$316$	−14.5799	+	28.2626i	−0.820184	+	1.58989i
$317$	26.0305	−	6.97486i	1.46202	−	0.391747i	0.561834	−	0.827250i	$-0.310096\pi$
$317$	26.0305	−	6.97486i	1.46202	−	0.391747i	0.900187	+	0.435503i	$0.143429\pi$
$318$	−7.24175	+	2.12532i	−0.406097	+	0.119182i
$319$	−6.13633	+	3.54281i	−0.343568	+	0.198359i
$320$	−2.90368	−	6.79572i	−0.162320	−	0.379892i
$321$		−	12.1196i		−	0.676449i
$322$	−6.33214	+	17.7612i	−0.352876	+	0.989792i
$323$	−3.73379	+	3.73379i	−0.207754	+	0.207754i
$324$	−1.68279	+	1.08083i	−0.0934886	+	0.0600463i
$325$	2.09573	−	7.82137i	0.116250	−	0.433852i
$326$	3.85584	−	7.05921i	0.213555	−	0.390973i
$327$	−4.83374	−	2.79076i	−0.267306	−	0.154329i
$328$	9.20420	−	10.6136i	0.508217	−	0.586041i
$329$	7.20777	+	16.1722i	0.397377	+	0.891601i
$330$	1.24490	+	2.04300i	0.0685297	+	0.112464i
$331$	9.60775	−	2.57439i	0.528090	−	0.141501i	0.0150838	−	0.999886i	$-0.495198\pi$
$331$	9.60775	−	2.57439i	0.528090	−	0.141501i	0.513006	+	0.858385i	$0.328532\pi$
$332$	14.2453	−	15.6620i	0.781815	−	0.859565i
$333$	−0.381781	+	1.42483i	−0.0209215	+	0.0780800i
$334$	3.85984	−	4.04700i	0.211201	−	0.221442i
$335$	−11.0500			−0.603729
$336$	7.41062	+	7.55531i	0.404282	+	0.412176i
$337$	−20.1065			−1.09527			−0.547635	−	0.836717i	$-0.684472\pi$
$337$	−20.1065			−1.09527			−0.547635	+	0.836717i	$0.684472\pi$
$338$	8.96691	−	9.40172i	0.487736	−	0.511386i
$339$	−1.63919	+	6.11753i	−0.0890284	+	0.332259i
$340$	1.69266	+	1.53956i	0.0917975	+	0.0834941i
$341$	−16.4828	+	4.41654i	−0.892592	+	0.239169i
$342$	−3.13758	−	5.14907i	−0.169661	−	0.278430i
$343$	17.6204	+	5.70274i	0.951412	+	0.307919i
$344$	7.27965	−	0.517729i	0.392493	−	0.0279141i
$345$	−4.03162	−	2.32765i	−0.217055	−	0.125317i
$346$	4.85132	−	8.88172i	0.260809	−	0.477484i
$347$	−5.11175	+	19.0773i	−0.274413	+	1.02412i	0.681821	+	0.731519i	$0.261188\pi$
$347$	−5.11175	+	19.0773i	−0.274413	+	1.02412i	−0.956234	+	0.292604i	$0.905478\pi$
$348$	−4.18190	−	6.51098i	−0.224174	−	0.349025i
$349$	18.4750	−	18.4750i	0.988943	−	0.988943i	−0.0109965	−	0.999940i	$-0.503500\pi$
$349$	18.4750	−	18.4750i	0.988943	−	0.988943i	0.999940	+	0.0109965i	$0.00350038\pi$
$350$	−11.8194	+	10.0513i	−0.631775	+	0.537266i
$351$			1.95272i			0.104228i
$352$	−8.29732	+	6.20268i	−0.442249	+	0.330604i
$353$	−3.13068	+	1.80750i	−0.166629	+	0.0962035i	−0.580995	−	0.813907i	$-0.697337\pi$
$353$	−3.13068	+	1.80750i	−0.166629	+	0.0962035i	0.414366	+	0.910110i	$0.364003\pi$
$354$	0.578565	−	0.169798i	0.0307504	−	0.00902469i
$355$	−0.670708	+	0.179716i	−0.0355975	+	0.00953832i
$356$	23.6437	+	12.1972i	1.25312	+	0.646448i
$357$	−3.05948	−	1.17308i	−0.161925	−	0.0620858i
$358$	19.0742	+	31.3026i	1.00810	+	1.65440i
$359$	16.1239	−	27.9275i	0.850989	−	1.47396i	−0.0293272	−	0.999570i	$-0.509336\pi$
$359$	16.1239	−	27.9275i	0.850989	−	1.47396i	0.880316	−	0.474387i	$-0.157330\pi$
$360$	−2.16436	+	1.46362i	−0.114072	+	0.0771396i
$361$	−0.711267	+	0.410650i	−0.0374351	+	0.0216132i
$362$	−0.501147	−	21.1712i	−0.0263397	−	1.11273i
$363$	−5.40674	+	5.40674i	−0.283780	+	0.283780i
$364$	10.1169	−	2.10138i	0.530269	−	0.110142i
$365$	1.01457	+	1.01457i	0.0531053	+	0.0531053i
$366$	4.96373	+	4.73417i	0.259458	+	0.247459i
$367$	10.8305	+	18.7590i	0.565349	+	0.979213i	0.997017	+	0.0771806i	$0.0245918\pi$
$367$	10.8305	+	18.7590i	0.565349	+	0.979213i	−0.431668	+	0.902032i	$0.642075\pi$
$368$	8.38374	−	18.3320i	0.437033	−	0.955621i
$369$	−4.30153	−	2.48349i	−0.223929	−	0.129285i
$370$	−0.454568	+	1.87266i	−0.0236318	+	0.0973552i
$371$	10.9695	−	8.88990i	0.569507	−	0.461541i
$372$	−5.66969	−	17.7526i	−0.293960	−	0.920431i
$373$	1.01566	+	3.79050i	0.0525890	+	0.196265i	0.987223	−	0.159347i	$-0.0509390\pi$
$373$	1.01566	+	3.79050i	0.0525890	+	0.196265i	−0.934634	+	0.355612i	$0.884272\pi$
$374$	1.53755	−	2.81492i	0.0795047	−	0.145556i
$375$	−4.22466	−	7.31733i	−0.218160	−	0.377865i
$376$	−6.18365	−	17.8896i	−0.318898	−	0.922586i
$377$	−7.55535			−0.389121
$378$	2.12586	−	3.07908i	0.109342	−	0.158371i
$379$	−14.4121	−	14.4121i	−0.740300	−	0.740300i	0.232336	−	0.972636i	$-0.425363\pi$
$379$	−14.4121	−	14.4121i	−0.740300	−	0.740300i	−0.972636	+	0.232336i	$0.925363\pi$
$380$	−4.25695	−	6.62783i	−0.218377	−	0.340000i
$381$	6.97796	+	1.86974i	0.357492	+	0.0957896i
$382$	4.19389	+	14.2901i	0.214578	+	0.731147i
$383$	7.05586	−	12.2211i	0.360537	−	0.624469i	−0.627512	−	0.778607i	$-0.715927\pi$
$383$	7.05586	−	12.2211i	0.360537	−	0.624469i	0.988049	+	0.154138i	$0.0492600\pi$
$384$	−7.19519	−	8.73093i	−0.367178	−	0.445549i
$385$	−3.62201	−	2.62942i	−0.184595	−	0.134007i
$386$	2.11724	−	8.72231i	0.107765	−	0.443954i
$387$	−0.667817	−	2.49233i	−0.0339470	−	0.126692i
$388$	18.1653	−	0.860473i	0.922204	−	0.0436839i
$389$	−7.39543	−	1.98160i	−0.374963	−	0.100471i	0.0664155	−	0.997792i	$-0.478844\pi$
$389$	−7.39543	−	1.98160i	−0.374963	−	0.100471i	−0.441378	+	0.897321i	$0.645510\pi$
$390$	0.0603688	+	2.55030i	0.00305689	+	0.129140i
$391$			6.24127i			0.315635i
$392$	−18.2402	−	7.70041i	−0.921268	−	0.388929i
$393$			15.1844i			0.765950i
$394$	28.6873	−	0.679064i	1.44524	−	0.0342107i
$395$	14.1881	+	3.80168i	0.713878	+	0.191283i
$396$	2.70951	+	2.46443i	0.136158	+	0.123842i
$397$	−5.24283	−	19.5665i	−0.263130	−	0.982014i	−0.963385	−	0.268122i	$-0.913597\pi$
$397$	−5.24283	−	19.5665i	−0.263130	−	0.982014i	0.700255	−	0.713893i	$-0.253070\pi$
$398$	11.1137	+	2.69771i	0.557078	+	0.135224i
$399$	9.12871	+	6.62703i	0.457007	+	0.331767i
$400$	13.5162	−	9.61402i	0.675811	−	0.480701i
$401$	−17.4967	+	30.3051i	−0.873742	+	1.51337i	−0.0156450	+	0.999878i	$0.504980\pi$
$401$	−17.4967	+	30.3051i	−0.873742	+	1.51337i	−0.858097	+	0.513488i	$0.828353\pi$
$402$	−16.2323	+	4.76388i	−0.809592	+	0.237601i
$403$	−17.5755	−	4.70933i	−0.875496	−	0.234589i
$404$	27.7457	+	6.04344i	1.38040	+	0.300672i
$405$	0.653196	+	0.653196i	0.0324576	+	0.0324576i
$406$	11.9134	+	8.22525i	0.591253	+	0.408212i
$407$	2.70135			0.133901
$408$	3.15021	+	1.53183i	0.155959	+	0.0758371i
$409$	4.89773	+	8.48311i	0.242177	+	0.419463i	0.961334	−	0.275385i	$-0.0888052\pi$
$409$	4.89773	+	8.48311i	0.242177	+	0.419463i	−0.719157	+	0.694848i	$0.755472\pi$
$410$	−5.69469	−	3.11052i	−0.281241	−	0.153618i
$411$	4.13944	+	15.4486i	0.204184	+	0.762024i
$412$	−16.6414	+	32.2588i	−0.819864	+	1.58928i
$413$	−0.876385	+	0.710241i	−0.0431241	+	0.0349487i
$414$	−6.92584	−	1.68117i	−0.340387	−	0.0826249i
$415$	−8.46855	−	4.88932i	−0.415705	−	0.240007i
$416$	−10.9690	+	1.30410i	−0.537799	+	0.0639387i
$417$	11.6767	+	20.2247i	0.571812	+	0.990407i
$418$	−7.62112	+	7.99067i	−0.372761	+	0.390836i
$419$	16.3771	+	16.3771i	0.800071	+	0.800071i	0.983106	−	0.183035i	$-0.0585922\pi$
$419$	16.3771	+	16.3771i	0.800071	+	0.800071i	−0.183035	+	0.983106i	$0.558592\pi$
$420$	2.68124	−	4.08708i	0.130831	−	0.199429i
$421$	−19.2256	+	19.2256i	−0.937000	+	0.937000i	−0.998130	−	0.0611298i	$-0.980530\pi$
$421$	−19.2256	+	19.2256i	−0.937000	+	0.937000i	0.0611298	+	0.998130i	$0.480530\pi$
$422$	−7.66560	+	0.181454i	−0.373156	+	0.00883305i
$423$	−5.79555	+	3.34606i	−0.281789	+	0.162691i
$424$	−12.5038	+	8.45552i	−0.607237	+	0.410636i
$425$	−2.56775	+	4.44747i	−0.124554	+	0.215734i
$426$	−0.907776	+	0.553153i	−0.0439819	+	0.0268003i
$427$	−11.9821	−	4.59422i	−0.579856	−	0.222330i
$428$	−7.37435	−	23.0902i	−0.356453	−	1.11611i
$429$	3.45419	−	0.925548i	0.166770	−	0.0446859i
$430$	−0.949238	−	3.23440i	−0.0457763	−	0.155977i
$431$	−11.8680	+	6.85198i	−0.571660	+	0.330048i	−0.757812	−	0.652473i	$-0.773732\pi$
$431$	−11.8680	+	6.85198i	−0.571660	+	0.330048i	0.186152	+	0.982521i	$0.440398\pi$
$432$	−2.54840	+	3.08312i	−0.122610	+	0.148337i
$433$			14.1708i			0.681006i	0.940243	+	0.340503i	$0.110597\pi$
$433$			14.1708i			0.681006i	−0.940243	+	0.340503i	$0.889403\pi$
$434$	22.5864	+	26.5596i	1.08418	+	1.27490i
$435$	−2.52731	+	2.52731i	−0.121175	+	0.121175i
$436$	−10.9073	−	2.37578i	−0.522365	−	0.113779i
$437$	5.56118	−	20.7546i	0.266028	−	0.992828i
$438$	1.92779	+	1.05299i	0.0921133	+	0.0503136i
$439$	12.4152	+	7.16792i	0.592546	+	0.342106i	0.766103	−	0.642717i	$-0.222193\pi$
$439$	12.4152	+	7.16792i	0.592546	+	0.342106i	−0.173558	+	0.984824i	$0.555526\pi$
$440$	3.61488	+	3.13484i	0.172333	+	0.149448i
$441$	−1.45011	+	6.84815i	−0.0690530	+	0.326102i
$442$	2.92059	−	1.77966i	0.138918	−	0.0846498i
$443$	−27.2167	+	7.29270i	−1.29311	+	0.346487i	−0.838840	−	0.544379i	$-0.816765\pi$
$443$	−27.2167	+	7.29270i	−1.29311	+	0.346487i	−0.454267	+	0.890866i	$0.650099\pi$
$444$	0.139591	+	2.94687i	0.00662467	+	0.139852i
$445$	3.18038	−	11.8693i	0.150765	−	0.562661i
$446$	18.9698	+	18.0925i	0.898245	+	0.856703i
$447$	−21.1931			−1.00240
$448$	18.7158	+	9.88524i	0.884240	+	0.467034i
$449$	6.95416			0.328187			0.164094	−	0.986445i	$-0.447530\pi$
$449$	6.95416			0.328187			0.164094	+	0.986445i	$0.447530\pi$
$450$	−4.24364	−	4.04738i	−0.200047	−	0.190795i
$451$	−2.35424	+	8.78615i	−0.110857	+	0.413724i
$452$	0.599335	+	12.6525i	0.0281904	+	0.595123i
$453$	−15.9174	+	4.26504i	−0.747863	+	0.200389i
$454$	−9.61784	+	5.86062i	−0.451388	+	0.275053i
$455$	−1.94283	−	4.35916i	−0.0910815	−	0.204361i
$456$	−9.11075	−	7.90088i	−0.426650	−	0.369993i
$457$	−13.9033	−	8.02709i	−0.650370	−	0.375491i	0.138228	−	0.990400i	$-0.455859\pi$
$457$	−13.9033	−	8.02709i	−0.650370	−	0.375491i	−0.788598	+	0.614909i	$0.789193\pi$
$458$	1.92128	+	1.04943i	0.0897755	+	0.0490366i
$459$	0.320538	−	1.19626i	0.0149614	−	0.0558369i
$460$	−9.09731	−	1.98154i	−0.424164	−	0.0923896i
$461$	−7.74855	+	7.74855i	−0.360886	+	0.360886i	−0.864139	−	0.503253i	$-0.832136\pi$
$461$	−7.74855	+	7.74855i	−0.360886	+	0.360886i	0.503253	+	0.864139i	$0.332136\pi$
$462$	−6.45424	−	2.30104i	−0.300278	−	0.107054i
$463$		−	41.7766i		−	1.94152i	−0.240047	−	0.970761i	$-0.577163\pi$
$463$		−	41.7766i		−	1.94152i	0.240047	−	0.970761i	$-0.422837\pi$
$464$	−11.9291	−	9.86014i	−0.553792	−	0.457746i
$465$	−7.45440	+	4.30380i	−0.345690	+	0.199584i
$466$	−10.6606	−	36.3247i	−0.493844	−	1.68271i
$467$	21.0392	−	5.63744i	0.973579	−	0.260870i	0.263241	−	0.964730i	$-0.415209\pi$
$467$	21.0392	−	5.63744i	0.973579	−	0.260870i	0.710338	+	0.703860i	$0.248542\pi$
$468$	1.18816	+	3.72031i	0.0549228	+	0.171971i
$469$	24.5879	−	19.9266i	1.13536	−	0.920123i
$470$	−7.46569	+	4.54921i	−0.344367	+	0.209840i
$471$	4.91252	−	8.50874i	0.226357	−	0.392062i
$472$	0.998964	−	0.675536i	0.0459810	−	0.0310941i
$473$	−4.09218	+	2.36262i	−0.188159	+	0.108633i
$474$	22.4809	−	0.532151i	1.03258	−	0.0244425i
$475$	12.5016	−	12.5016i	0.573613	−	0.573613i
$476$	−6.54269	−	0.373348i	−0.299884	−	0.0171124i
$477$	3.77359	+	3.77359i	0.172781	+	0.172781i
$478$	−7.01603	+	7.35624i	−0.320906	+	0.336466i
$479$	15.6984	+	27.1904i	0.717278	+	1.24236i	0.962074	+	0.272788i	$0.0879457\pi$
$479$	15.6984	+	27.1904i	0.717278	+	1.24236i	−0.244796	+	0.969575i	$0.578721\pi$
$480$	−3.23297	+	4.10543i	−0.147564	+	0.187386i
$481$	2.49453	+	1.44022i	0.113741	+	0.0656683i
$482$	−0.868109	−	0.210723i	−0.0395413	−	0.00959819i
$483$	13.1684	−	2.09086i	0.599182	−	0.0951373i
$484$	−7.01108	+	13.5907i	−0.318686	+	0.617760i
$485$	−2.17398	−	8.11339i	−0.0987152	−	0.368410i
$486$	1.24114	+	0.677926i	0.0562990	+	0.0307513i
$487$	−13.6892	−	23.7104i	−0.620318	−	1.07442i	−0.989426	−	0.145036i	$-0.953670\pi$
$487$	−13.6892	−	23.7104i	−0.620318	−	1.07442i	0.369108	−	0.929386i	$-0.379663\pi$
$488$	12.3375	+	5.99926i	0.558490	+	0.271574i
$489$	−5.68770			−0.257207
$490$	−1.68218	+	8.98870i	−0.0759929	+	0.406068i
$491$	22.5984	+	22.5984i	1.01985	+	1.01985i	0.999799	+	0.0200513i	$0.00638297\pi$
$491$	22.5984	+	22.5984i	1.01985	+	1.01985i	0.0200513	+	0.999799i	$0.493617\pi$
$492$	−9.70637	−	2.11420i	−0.437597	−	0.0953154i
$493$	4.62852	+	1.24021i	0.208458	+	0.0558562i
$494$	−11.2978	+	3.31571i	−0.508313	+	0.149181i
$495$	0.845847	−	1.46505i	0.0380180	−	0.0658491i
$496$	−21.6037	−	30.3724i	−0.970037	−	1.36376i
$497$	1.16834	−	1.60938i	0.0524071	−	0.0721906i
$498$	−14.5480	−	3.53135i	−0.651911	−	0.158244i
$499$	−0.518930	−	1.93667i	−0.0232305	−	0.0866974i	0.953337	−	0.301907i	$-0.0976232\pi$
$499$	−0.518930	−	1.93667i	−0.0232305	−	0.0866974i	−0.976568	+	0.215210i	$0.930957\pi$
$500$	−12.5011	−	11.3704i	−0.559068	−	0.508499i
$501$	−3.81978	−	1.02351i	−0.170655	−	0.0457269i
$502$	−1.24505	+	0.0294718i	−0.0555692	+	0.00131539i
$503$			37.0922i			1.65386i	0.562305	+	0.826930i	$0.309915\pi$
$503$			37.0922i			1.65386i	−0.562305	+	0.826930i	$0.690085\pi$
$504$	2.17666	−	7.15976i	0.0969560	−	0.318921i
$505$		−	13.1156i		−	0.583638i
$506$	0.308864	+	13.0481i	0.0137307	+	0.580057i
$507$	−8.87385	−	2.37774i	−0.394102	−	0.105599i
$508$	14.4320	−	0.683632i	0.640319	−	0.0303313i
$509$	−0.218605	−	0.815844i	−0.00968949	−	0.0361617i	0.960912	−	0.276855i	$-0.0892920\pi$
$509$	−0.218605	−	0.815844i	−0.00968949	−	0.0361617i	−0.970601	+	0.240693i	$0.922625\pi$
$510$	0.381649	−	1.57226i	0.0168997	−	0.0696210i
$511$	−4.08716	−	0.427988i	−0.180805	−	0.0189331i
$512$	−19.0207	−	12.2561i	−0.840605	−	0.541648i
$513$	−2.13182	+	3.69243i	−0.0941223	+	0.163025i
$514$	2.33268	+	7.94831i	0.102890	+	0.350585i
$515$	16.1942	+	4.33921i	0.713600	+	0.191209i
$516$	−2.78882	−	4.34203i	−0.122771	−	0.191147i
$517$	8.66586	+	8.66586i	0.381124	+	0.381124i
$518$	−2.36550	−	4.98667i	−0.103934	−	0.219102i
$519$	−7.15613			−0.314119
$520$	1.66679	+	4.82209i	0.0730934	+	0.211463i
$521$	−19.9978	−	34.6372i	−0.876120	−	1.51748i	−0.855565	−	0.517696i	$-0.826790\pi$
$521$	−19.9978	−	34.6372i	−0.876120	−	1.51748i	−0.0205558	−	0.999789i	$-0.506544\pi$
$522$	−2.62299	+	4.80213i	−0.114805	+	0.210184i
$523$	−5.88405	−	21.9596i	−0.257292	−	0.960226i	−0.966801	−	0.255530i	$-0.917750\pi$
$523$	−5.88405	−	21.9596i	−0.257292	−	0.960226i	0.709509	−	0.704696i	$-0.248917\pi$
$524$	9.23917	+	28.9292i	0.403615	+	1.26378i
$525$	10.2439	+	3.92773i	0.447079	+	0.171420i
$526$	−8.76506	+	36.1091i	−0.382175	+	1.57443i
$527$	9.99396	+	5.77001i	0.435344	+	0.251346i
$528$	6.66167	+	3.04657i	0.289912	+	0.132585i
$529$	−1.19841	−	2.07571i	−0.0521049	−	0.0902483i
$530$	5.04507	+	4.81175i	0.219144	+	0.209009i
$531$	−0.301484	−	0.301484i	−0.0130833	−	0.0130833i
$532$	21.4243	+	7.07128i	0.928861	+	0.306579i
$533$	−6.85830	+	6.85830i	−0.297066	+	0.297066i
$534$	−0.445183	−	18.8069i	−0.0192650	−	0.813855i
$535$	−9.69565	+	5.59779i	−0.419179	+	0.242013i
$536$	−28.0270	+	18.9529i	−1.21058	+	0.818640i
$537$	12.9599	−	22.4473i	0.559263	−	0.968672i
$538$	−2.18907	−	3.59248i	−0.0943776	−	0.154883i
$539$	12.8011	−	0.680753i	0.551383	−	0.0293221i
$540$	1.64191	+	0.847019i	0.0706567	+	0.0364499i
$541$	2.41537	−	0.647198i	0.103845	−	0.0278252i	−0.206522	−	0.978442i	$-0.566215\pi$
$541$	2.41537	−	0.647198i	0.103845	−	0.0278252i	0.310367	+	0.950617i	$0.399548\pi$
$542$	0.199481	−	0.0585441i	0.00856845	−	0.00251468i
$543$	−12.9683	+	7.48723i	−0.556521	+	0.321308i
$544$	6.93384	+	1.00165i	0.297286	+	0.0429452i
$545$			5.15598i			0.220858i
$546$	−4.73329	−	5.56592i	−0.202566	−	0.238199i
$547$	16.0246	−	16.0246i	0.685161	−	0.685161i	−0.275998	−	0.961158i	$-0.589008\pi$
$547$	16.0246	−	16.0246i	0.685161	−	0.685161i	0.961158	+	0.275998i	$0.0890082\pi$
$548$	17.2864	+	26.9139i	0.738438	+	1.14971i
$549$	1.25535	−	4.68504i	0.0535771	−	0.199953i
$550$	−5.14807	+	9.42500i	−0.219514	+	0.401883i
$551$	−14.2865	−	8.24834i	−0.608627	−	0.351391i
$552$	−14.2180	+	1.01119i	−0.605159	+	0.0430389i
$553$	−38.4260	+	17.1261i	−1.63404	+	0.728274i
$554$	−9.36855	−	15.3747i	−0.398032	−	0.653208i
$555$	1.31620	−	0.352674i	0.0558694	−	0.0149702i
$556$	34.5525	+	31.4271i	1.46535	+	1.33281i
$557$	3.80483	−	14.1998i	0.161216	−	0.601665i	−0.837277	−	0.546779i	$-0.815854\pi$
$557$	3.80483	−	14.1998i	0.161216	−	0.601665i	0.998493	−	0.0548861i	$-0.0174796\pi$
$558$	−9.09490	+	9.53591i	−0.385018	+	0.403687i
$559$	−5.03850			−0.213106
$560$	2.62143	−	9.41813i	0.110776	−	0.397989i
$561$	−2.26802			−0.0957558
$562$	9.79203	−	10.2668i	0.413052	−	0.433081i
$563$	−10.1723	+	37.9634i	−0.428710	+	1.59997i	0.326976	+	0.945033i	$0.393970\pi$
$563$	−10.1723	+	37.9634i	−0.428710	+	1.59997i	−0.755686	+	0.654934i	$0.772696\pi$
$564$	−9.00568	+	9.90129i	−0.379208	+	0.416919i
$565$	5.65112	−	1.51421i	0.237745	−	0.0637035i
$566$	8.62548	+	14.1552i	0.362556	+	0.594989i
$567$	−2.63136	−	0.275544i	−0.110507	−	0.0115718i
$568$	−1.39292	+	1.60621i	−0.0584455	+	0.0673953i
$569$	0.120537	+	0.0695923i	0.00505319	+	0.00291746i	0.502524	−	0.864563i	$-0.332405\pi$
$569$	0.120537	+	0.0695923i	0.00505319	+	0.00291746i	−0.497471	+	0.867480i	$0.665738\pi$
$570$	−2.67007	+	4.88832i	−0.111837	+	0.204749i
$571$	−8.67918	+	32.3911i	−0.363212	+	1.35553i	0.506616	+	0.862172i	$0.330896\pi$
$571$	−8.67918	+	32.3911i	−0.363212	+	1.35553i	−0.869828	+	0.493355i	$0.835770\pi$
$572$	6.01774	−	3.86511i	0.251615	−	0.161608i
$573$	7.44642	−	7.44642i	0.311079	−	0.311079i
$574$	18.2807	−	3.34789i	0.763021	−	0.139738i
$575$		−	20.8972i		−	0.871475i
$576$	−2.97923	+	7.42457i	−0.124135	+	0.309357i
$577$	29.6633	−	17.1261i	1.23490	−	0.712969i	0.266852	−	0.963738i	$-0.414017\pi$
$577$	29.6633	−	17.1261i	1.23490	−	0.712969i	0.968047	+	0.250769i	$0.0806833\pi$
$578$	20.9873	−	6.15941i	0.872959	−	0.256198i
$579$	−6.13045	+	1.64265i	−0.254773	+	0.0682661i
$580$	−3.27724	+	6.35281i	−0.136080	+	0.263786i
$581$	27.6606	−	4.39192i	1.14756	−	0.182208i
$582$	−6.69135	−	10.9811i	−0.277365	−	0.455183i
$583$	4.88656	−	8.46376i	0.202380	−	0.350533i
$584$	4.31352	+	0.833150i	0.178495	+	0.0344760i
$585$	1.56217	−	0.901921i	0.0645879	−	0.0372898i
$586$	−0.687711	−	29.0526i	−0.0284091	−	1.20015i
$587$	9.72679	−	9.72679i	0.401467	−	0.401467i	−0.477282	−	0.878750i	$-0.658378\pi$
$587$	9.72679	−	9.72679i	0.401467	−	0.401467i	0.878750	+	0.477282i	$0.158378\pi$
$588$	1.40411	+	13.9294i	0.0579047	+	0.574439i
$589$	−28.0925	−	28.0925i	−1.15753	−	1.15753i
$590$	−0.403066	−	0.384425i	−0.0165940	−	0.0158265i
$591$	−10.1453	−	17.5722i	−0.417323	−	0.722825i
$592$	2.05902	+	5.52943i	0.0846252	+	0.227258i
$593$	39.4370	+	22.7689i	1.61948	+	0.935008i	0.987054	+	0.160389i	$0.0512747\pi$
$593$	39.4370	+	22.7689i	1.61948	+	0.935008i	0.632428	+	0.774620i	$0.282059\pi$
$594$	0.610920	−	2.51678i	0.0250663	−	0.103265i
$595$	0.474654	+	2.98940i	0.0194589	+	0.122554i
$596$	−40.3769	+	12.8953i	−1.65390	+	0.528210i
$597$	−2.09301	−	7.81121i	−0.0856611	−	0.319692i
$598$	−6.67132	+	12.2137i	−0.272810	+	0.499457i
$599$	−7.49716	−	12.9855i	−0.306326	−	0.530572i	0.671230	−	0.741249i	$-0.265766\pi$
$599$	−7.49716	−	12.9855i	−0.306326	−	0.530572i	−0.977556	+	0.210677i	$0.932433\pi$
$600$	−10.5476	−	5.12894i	−0.430606	−	0.209388i
$601$	−7.67438			−0.313045			−0.156522	−	0.987674i	$-0.550028\pi$
$601$	−7.67438			−0.313045			−0.156522	+	0.987674i	$0.550028\pi$
$602$	7.94479	+	5.48523i	0.323805	+	0.223561i
$603$	8.45844	+	8.45844i	0.344454	+	0.344454i
$604$	−27.7305	+	17.8109i	−1.12834	+	0.724715i
$605$	6.82265	+	1.82812i	0.277380	+	0.0743238i
$606$	−5.65439	−	19.2666i	−0.229694	−	0.782651i
$607$	−18.0418	+	31.2493i	−0.732295	+	1.26837i	0.223606	+	0.974680i	$0.428217\pi$
$607$	−18.0418	+	31.2493i	−0.732295	+	1.26837i	−0.955900	+	0.293692i	$0.905116\pi$
$608$	−22.1652	−	9.50914i	−0.898916	−	0.385647i
$609$	1.06612	−	10.1811i	0.0432014	−	0.412560i
$610$	1.49468	−	6.15760i	0.0605180	−	0.249314i
$611$	3.38220	+	12.6226i	0.136829	+	0.510654i
$612$	−0.117198	−	2.47415i	−0.00473746	−	0.100012i
$613$	30.2336	+	8.10107i	1.22112	+	0.327199i	0.811117	−	0.584883i	$-0.198860\pi$
$613$	30.2336	+	8.10107i	1.22112	+	0.327199i	0.410007	+	0.912083i	$0.365526\pi$
$614$	0.604429	+	25.5343i	0.0243928	+	1.03048i
$615$			4.58829i			0.185018i
$616$	−13.6967	−	0.456743i	−0.551855	−	0.0184027i
$617$		−	39.8109i		−	1.60272i	−0.598179	−	0.801362i	$-0.704109\pi$
$617$		−	39.8109i		−	1.60272i	0.598179	−	0.801362i	$-0.295891\pi$
$618$	25.6596	−	0.607394i	1.03218	−	0.0244330i
$619$	−5.64007	−	1.51125i	−0.226693	−	0.0607423i	0.143684	−	0.989624i	$-0.454105\pi$
$619$	−5.64007	−	1.51125i	−0.226693	−	0.0607423i	−0.370378	+	0.928881i	$0.620772\pi$
$620$	−11.5834	+	12.7353i	−0.465200	+	0.511463i
$621$	1.30433	+	4.86781i	0.0523408	+	0.195338i
$622$	12.1938	+	2.95990i	0.488927	+	0.118681i
$623$	14.3272	+	32.1462i	0.574008	+	1.28791i
$624$	4.52736	+	6.36496i	0.181240	+	0.254802i
$625$	6.46410	−	11.1962i	0.258564	−	0.447846i
$626$	18.8255	−	5.52495i	0.752419	−	0.220821i
$627$	7.54203	+	2.02088i	0.301199	+	0.0807062i
$628$	4.18204	−	19.1999i	0.166881	−	0.766160i
$629$	−1.29177	−	1.29177i	−0.0515064	−	0.0515064i
$630$	−3.44515	−	0.278519i	−0.137258	−	0.0110965i
$631$	−13.2551			−0.527679			−0.263839	−	0.964567i	$-0.584989\pi$
$631$	−13.2551			−0.527679			−0.263839	+	0.964567i	$0.584989\pi$
$632$	42.5067	−	14.6927i	1.69083	−	0.584444i
$633$	2.71096	+	4.69552i	0.107751	+	0.186630i
$634$	−33.4471	−	18.2693i	−1.32835	−	0.725566i
$635$	−1.72719	−	6.44595i	−0.0685414	−	0.255800i
$636$	9.48553	+	4.89333i	0.376126	+	0.194033i
$637$	12.1840	+	6.19624i	0.482746	+	0.245504i
$638$	9.73780	+	2.36374i	0.385523	+	0.0935813i
$639$	0.650971	+	0.375838i	0.0257520	+	0.0148679i
$640$	−3.66142	+	9.78879i	−0.144730	+	0.386936i
$641$	4.56443	+	7.90582i	0.180284	+	0.312261i	0.941977	−	0.335677i	$-0.108965\pi$
$641$	4.56443	+	7.90582i	0.180284	+	0.312261i	−0.761693	+	0.647938i	$0.775632\pi$
$642$	−11.8294	+	12.4030i	−0.466868	+	0.489507i
$643$	34.1665	+	34.1665i	1.34740	+	1.34740i	0.888478	+	0.458919i	$0.151763\pi$
$643$	34.1665	+	34.1665i	1.34740	+	1.34740i	0.458919	+	0.888478i	$0.348237\pi$
$644$	23.8161	−	11.9960i	0.938486	−	0.472709i
$645$	−1.68541	+	1.68541i	−0.0663629	+	0.0663629i
$646$	7.46549	−	0.176717i	0.293726	−	0.00695285i
$647$	12.3209	−	7.11347i	0.484385	−	0.279660i	−0.237857	−	0.971300i	$-0.576445\pi$
$647$	12.3209	−	7.11347i	0.484385	−	0.279660i	0.722242	+	0.691641i	$0.243112\pi$
$648$	2.77710	+	0.536393i	0.109095	+	0.0210715i
$649$	−0.390402	+	0.676195i	−0.0153246	+	0.0265430i
$650$	−9.77883	+	5.95872i	−0.383557	+	0.233720i
$651$	8.82604	−	23.0191i	0.345920	−	0.902189i
$652$	−10.8362	+	3.46077i	−0.424378	+	0.135534i
$653$	2.60466	−	0.697916i	0.101928	−	0.0273116i	−0.207494	−	0.978236i	$-0.566531\pi$
$653$	2.60466	−	0.697916i	0.101928	−	0.0273116i	0.309423	+	0.950925i	$0.399864\pi$
$654$	2.22284	+	7.57402i	0.0869198	+	0.296168i
$655$	12.1475	−	7.01335i	0.474641	−	0.274034i
$656$	−19.7789	+	1.87803i	−0.772238	+	0.0733248i
$657$		−	1.55325i		−	0.0605979i
$658$	8.40862	−	23.5855i	0.327802	−	0.919460i
$659$	9.67146	−	9.67146i	0.376747	−	0.376747i	−0.493180	−	0.869927i	$-0.664166\pi$
$659$	9.67146	−	9.67146i	0.376747	−	0.376747i	0.869927	+	0.493180i	$0.164166\pi$
$660$	0.720071	−	3.30587i	0.0280287	−	0.128681i
$661$	3.91296	−	14.6034i	0.152197	−	0.568006i	−0.847132	−	0.531382i	$-0.821673\pi$
$661$	3.91296	−	14.6034i	0.152197	−	0.568006i	0.999329	−	0.0366239i	$-0.0116604\pi$
$662$	−12.3452	−	6.74311i	−0.479809	−	0.262078i
$663$	−2.09437	−	1.20919i	−0.0813387	−	0.0469609i
$664$	−29.8655	+	2.12403i	−1.15900	+	0.0824284i
$665$	1.08525	−	10.3638i	0.0420843	−	0.401893i
$666$	1.78142	−	1.08551i	0.0690286	−	0.0420625i
$667$	−18.8343	+	5.04663i	−0.729266	+	0.195406i
$668$	−7.90020	+	0.374225i	−0.305668	+	0.0144792i
$669$	4.79755	−	17.9047i	0.185484	−	0.692236i
$670$	11.3084	+	10.7855i	0.436883	+	0.416679i
$671$	−8.88244			−0.342903
$672$	−0.209511	−	14.9652i	−0.00808206	−	0.577294i
$673$	30.1316			1.16149			0.580743	−	0.814087i	$-0.302762\pi$
$673$	30.1316			1.16149			0.580743	+	0.814087i	$0.302762\pi$
$674$	20.5767	+	19.6251i	0.792584	+	0.755929i
$675$	−1.07324	+	4.00537i	−0.0413089	+	0.154167i
$676$	−18.3532	+	0.869373i	−0.705892	+	0.0334374i
$677$	−5.19133	+	1.39101i	−0.199519	+	0.0534610i	−0.357195	−	0.934030i	$-0.616267\pi$
$677$	−5.19133	+	1.39101i	−0.199519	+	0.0534610i	0.157675	+	0.987491i	$0.449600\pi$
$678$	7.64857	−	4.66065i	0.293741	−	0.178991i
$679$	19.4683	+	14.1331i	0.747124	+	0.542379i
$680$	−0.229553	−	3.22769i	−0.00880296	−	0.123776i
$681$	6.89700	+	3.98199i	0.264294	+	0.152590i
$682$	21.1790	+	11.5683i	0.810986	+	0.442972i
$683$	8.97128	−	33.4813i	0.343276	−	1.28112i	−0.551337	−	0.834283i	$-0.685882\pi$
$683$	8.97128	−	33.4813i	0.343276	−	1.28112i	0.894613	−	0.446842i	$-0.147451\pi$
$684$	−1.81483	+	8.33194i	−0.0693916	+	0.318580i
$685$	10.4469	−	10.4469i	0.399157	−	0.399157i
$686$	−12.4663	−	23.0346i	−0.475964	−	0.879465i
$687$		−	1.54800i		−	0.0590599i
$688$	−7.95522	−	6.57551i	−0.303290	−	0.250689i
$689$	9.02486	−	5.21050i	0.343820	−	0.198504i
$690$	1.85397	+	6.31717i	0.0705796	+	0.240490i
$691$	−12.8562	+	3.44482i	−0.489074	+	0.131047i	−0.494925	−	0.868936i	$-0.664804\pi$
$691$	−12.8562	+	3.44482i	−0.489074	+	0.131047i	0.00585047	+	0.999983i	$0.498138\pi$
$692$	−13.6338	+	4.35426i	−0.518280	+	0.165524i
$693$	0.759797	+	4.78526i	0.0288623	+	0.181777i
$694$	23.8518	−	14.5341i	0.905401	−	0.551706i
$695$	10.7865	−	18.6827i	0.409155	−	0.708677i
$696$	−2.07538	+	10.7450i	−0.0786671	+	0.407288i
$697$	5.32729	−	3.07571i	0.201785	−	0.116501i
$698$	−36.9396	+	0.874406i	−1.39818	+	0.0330968i
$699$	−18.9284	+	18.9284i	−0.715936	+	0.715936i
$700$	21.9065	+	1.25006i	0.827987	+	0.0472476i
$701$	−7.91074	−	7.91074i	−0.298785	−	0.298785i	0.541753	−	0.840538i	$-0.317761\pi$
$701$	−7.91074	−	7.91074i	−0.298785	−	0.298785i	−0.840538	+	0.541753i	$0.817761\pi$
$702$	1.90596	−	1.99838i	0.0719359	−	0.0754241i
$703$	3.14463	+	5.44666i	0.118602	+	0.205425i
$704$	14.5455	+	1.75091i	0.548204	+	0.0659901i
$705$	5.35369	+	3.09095i	0.201632	+	0.116412i
$706$	4.96811	+	1.20595i	0.186977	+	0.0453865i
$707$	23.6514	+	29.1841i	0.889504	+	1.09758i
$708$	−0.757828	−	0.390943i	−0.0284809	−	0.0146925i
$709$	−7.67904	−	28.6586i	−0.288392	−	1.07630i	−0.946325	−	0.323218i	$-0.895235\pi$
$709$	−7.67904	−	28.6586i	−0.288392	−	1.07630i	0.657932	−	0.753077i	$-0.271431\pi$
$710$	0.861805	+	0.470730i	0.0323430	+	0.0176662i
$711$	−7.95042	−	13.7705i	−0.298164	−	0.516435i
$712$	−12.2915	−	35.5600i	−0.460645	−	1.33267i
$713$	−46.9584			−1.75861
$714$	1.98604	+	4.18673i	0.0743258	+	0.156685i
$715$	−2.33586	−	2.33586i	−0.0873561	−	0.0873561i
$716$	11.0328	−	50.6521i	0.412316	−	1.89296i
$717$	6.94321	+	1.86043i	0.259299	+	0.0694790i
$718$	−43.7598	+	12.8427i	−1.63310	+	0.479285i
$719$	19.5189	−	33.8078i	0.727934	−	1.26082i	−0.229821	−	0.973233i	$-0.573814\pi$
$719$	19.5189	−	33.8078i	0.727934	−	1.26082i	0.957755	−	0.287586i	$-0.0928526\pi$
$720$	3.64355	+	0.614688i	0.135787	+	0.0229081i
$721$	−43.8592	+	19.5476i	−1.63340	+	0.727991i
$722$	1.12872	+	0.273983i	0.0420065	+	0.0101966i
$723$	0.163489	+	0.610148i	0.00608021	+	0.0226916i
$724$	−20.1513	+	22.1554i	−0.748919	+	0.823398i
$725$	−15.4974	−	4.15251i	−0.575558	−	0.154220i
$726$	10.8105	−	0.255897i	0.401214	−	0.00949722i
$727$			20.7216i			0.768522i	0.923224	+	0.384261i	$0.125544\pi$
$727$			20.7216i			0.768522i	−0.923224	+	0.384261i	$0.874456\pi$
$728$	−12.4045	−	7.72412i	−0.459742	−	0.286275i
$729$		−	1.00000i		−	0.0370370i
$730$	−0.0480190	−	2.02858i	−0.00177726	−	0.0750812i
$731$	3.08666	+	0.827068i	0.114164	+	0.0305902i
$732$	−0.458994	−	9.68975i	−0.0169649	−	0.358144i
$733$	−0.0620914	−	0.231728i	−0.00229340	−	0.00855907i	0.964770	−	0.263096i	$-0.0847436\pi$
$733$	−0.0620914	−	0.231728i	−0.00229340	−	0.00855907i	−0.967063	+	0.254537i	$0.918077\pi$
$734$	7.22605	−	29.7689i	0.266718	−	1.09879i
$735$	6.14829	−	2.00293i	0.226783	−	0.0738792i
$736$	−26.4728	+	10.5777i	−0.975802	+	0.389899i
$737$	10.9531	−	18.9714i	0.403464	−	0.698820i
$738$	1.97809	+	6.74009i	0.0728147	+	0.248106i
$739$	−12.3184	−	3.30071i	−0.453140	−	0.121419i	0.0250282	−	0.999687i	$-0.492032\pi$
$739$	−12.3184	−	3.30071i	−0.453140	−	0.121419i	−0.478168	+	0.878268i	$0.658699\pi$
$740$	2.29302	−	1.47277i	0.0842932	−	0.0541402i
$741$	5.88716	+	5.88716i	0.216270	+	0.216270i
$742$	−19.9030	−	1.60904i	−0.730664	−	0.0590696i
$743$	−24.2704			−0.890394			−0.445197	−	0.895433i	$-0.646866\pi$
$743$	−24.2704			−0.890394			−0.445197	+	0.895433i	$0.646866\pi$
$744$	−11.5253	+	23.7017i	−0.422537	+	0.868947i
$745$	9.78864	+	16.9544i	0.358628	+	0.621162i
$746$	2.66033	−	4.87049i	0.0974015	−	0.178321i
$747$	2.73978	+	10.2250i	0.100243	+	0.374113i
$748$	−4.32102	+	1.38001i	−0.157992	+	0.0504582i
$749$	11.4797	−	29.9400i	0.419459	−	1.09399i
$750$	−2.81866	+	11.6119i	−0.102923	+	0.424008i
$751$	13.9676	+	8.06423i	0.509687	+	0.294268i	0.732705	−	0.680547i	$-0.238258\pi$
$751$	13.9676	+	8.06423i	0.509687	+	0.294268i	−0.223018	+	0.974814i	$0.571591\pi$
$752$	−11.1330	+	24.3435i	−0.405978	+	0.887718i
$753$	0.440315	+	0.762647i	0.0160460	+	0.0277924i
$754$	7.73203	+	7.37444i	0.281584	+	0.268561i
$755$	10.7639	+	10.7639i	0.391739	+	0.391739i
$756$	−5.18092	+	1.07613i	−0.188428	+	0.0391384i
$757$	−3.84167	+	3.84167i	−0.139628	+	0.139628i	−0.773466	−	0.633838i	$-0.781479\pi$
$757$	−3.84167	+	3.84167i	−0.139628	+	0.139628i	0.633838	+	0.773466i	$0.281479\pi$
$758$	0.682113	+	28.8161i	0.0247755	+	1.04665i
$759$	7.99251	−	4.61448i	0.290110	−	0.167495i
$760$	−2.11263	+	10.9378i	−0.0766330	+	0.396757i
$761$	−24.6888	+	42.7623i	−0.894969	+	1.55013i	−0.0611253	+	0.998130i	$0.519469\pi$
$761$	−24.6888	+	42.7623i	−0.894969	+	1.55013i	−0.833843	+	0.552001i	$0.813864\pi$
$762$	−5.31617	−	8.72434i	−0.192584	−	0.316049i
$763$	−9.29779	−	11.4728i	−0.336602	−	0.415343i
$764$	9.65599	−	18.7178i	0.349341	−	0.677185i
$765$	−1.10506	+	0.296100i	−0.0399535	+	0.0107055i
$766$	−19.1493	+	5.61998i	−0.691893	+	0.203058i
$767$	−0.721023	+	0.416283i	−0.0260346	+	0.0150311i
$768$	−1.15842	+	15.9580i	−0.0418010	+	0.575835i
$769$		−	28.8854i		−	1.04163i	−0.853669	−	0.520816i	$-0.825628\pi$
$769$		−	28.8854i		−	1.04163i	0.853669	−	0.520816i	$-0.174372\pi$
$770$	1.14025	+	6.22619i	0.0410919	+	0.224376i
$771$	4.14177	−	4.14177i	0.149162	−	0.149162i
$772$	−10.6802	+	6.85973i	−0.384389	+	0.246887i
$773$	10.4038	−	38.8274i	0.374197	−	1.39652i	−0.480317	−	0.877095i	$-0.659478\pi$
$773$	10.4038	−	38.8274i	0.374197	−	1.39652i	0.854514	−	0.519428i	$-0.173855\pi$
$774$	−1.74922	+	3.20244i	−0.0628743	+	0.115109i
$775$	−33.4621	−	19.3194i	−1.20199	−	0.693972i
$776$	−19.4300	−	16.8498i	−0.697496	−	0.604871i
$777$	−2.29275	+	3.15825i	−0.0822518	+	0.113302i
$778$	5.63421	+	9.24628i	0.201996	+	0.331495i
$779$	−20.4558	+	5.48112i	−0.732906	+	0.196382i
$780$	2.42746	−	2.66886i	0.0869169	−	0.0955607i
$781$	0.356279	−	1.32965i	0.0127487	−	0.0475786i
$782$	6.09183	−	6.38722i	0.217843	−	0.228407i
$783$	3.86915			0.138272
$784$	11.1507	+	25.6839i	0.398239	+	0.917282i
$785$	−9.07597			−0.323935
$786$	14.8208	−	15.5395i	0.528640	−	0.554274i
$787$	3.19017	−	11.9059i	0.113717	−	0.424399i	−0.885470	−	0.464696i	$-0.846164\pi$
$787$	3.19017	−	11.9059i	0.113717	−	0.424399i	0.999188	+	0.0402970i	$0.0128304\pi$
$788$	−30.0209	−	27.3054i	−1.06945	−	0.972716i
$789$	25.3792	−	6.80033i	0.903522	−	0.242098i
$790$	−10.8092	−	17.7389i	−0.384574	−	0.631122i
$791$	−9.84396	+	13.5600i	−0.350011	+	0.482139i
$792$	−0.367455	−	5.16669i	−0.0130569	−	0.183590i
$793$	−8.20238	−	4.73564i	−0.291275	−	0.168168i
$794$	−13.7326	+	25.1413i	−0.487350	+	0.892233i
$795$	1.27592	−	4.76181i	0.0452524	−	0.168884i
$796$	−8.74044	−	13.6084i	−0.309797	−	0.482335i
$797$	−14.3319	+	14.3319i	−0.507662	+	0.507662i	−0.913808	−	0.406146i	$-0.866872\pi$
$797$	−14.3319	+	14.3319i	−0.507662	+	0.507662i	0.406146	+	0.913808i	$0.366872\pi$
$798$	−2.87383	−	15.6921i	−0.101732	−	0.555495i
$799$		−	8.28795i		−	0.293207i
$800$	−23.2161	−	3.35375i	−0.820814	−	0.118573i
$801$	−11.5201	+	6.65111i	−0.407042	+	0.235006i
$802$	47.4853	−	13.9361i	1.67676	−	0.492100i
$803$	−2.74756	+	0.736206i	−0.0969592	+	0.0259802i
$804$	21.2617	+	10.9683i	0.749841	+	0.386823i
$805$	−7.75489	−	9.56896i	−0.273324	−	0.337262i
$806$	13.3899	+	21.9741i	0.471639	+	0.774004i
$807$	−1.48736	+	2.57618i	−0.0523575	+	0.0906859i
$808$	−22.4958	−	33.2661i	−0.791398	−	1.17030i
$809$	7.50666	−	4.33397i	0.263920	−	0.152374i	−0.362201	−	0.932100i	$-0.617975\pi$
$809$	7.50666	−	4.33397i	0.263920	−	0.152374i	0.626121	+	0.779726i	$0.284641\pi$
$810$	−0.0309153	−	1.30603i	−0.00108625	−	0.0458891i
$811$	27.6360	−	27.6360i	0.970433	−	0.970433i	−0.0291427	−	0.999575i	$-0.509278\pi$
$811$	27.6360	−	27.6360i	0.970433	−	0.970433i	0.999575	+	0.0291427i	$0.00927773\pi$
$812$	−4.16370	−	20.0457i	−0.146117	−	0.703468i
$813$	−0.103947	−	0.103947i	−0.00364559	−	0.00364559i
$814$	−2.76452	−	2.63667i	−0.0968964	−	0.0924152i
$815$	2.62703	+	4.55016i	0.0920210	+	0.159385i
$816$	−1.72872	−	4.64244i	−0.0605174	−	0.162518i
$817$	−9.52738	−	5.50063i	−0.333321	−	0.192443i
$818$	3.26773	−	13.4619i	0.114253	−	0.470686i
$819$	−1.84962	+	4.82397i	−0.0646309	+	0.168563i
$820$	2.79182	+	8.74159i	0.0974945	+	0.305269i
$821$	−12.1482	−	45.3377i	−0.423975	−	1.58230i	−0.766151	−	0.642660i	$-0.777831\pi$
$821$	−12.1482	−	45.3377i	−0.423975	−	1.58230i	0.342177	−	0.939636i	$-0.388836\pi$
$822$	10.8425	−	19.8502i	0.378174	−	0.692355i
$823$	8.72163	+	15.1063i	0.304017	+	0.526573i	0.977042	−	0.213047i	$-0.0683388\pi$
$823$	8.72163	+	15.1063i	0.304017	+	0.526573i	−0.673025	+	0.739620i	$0.735005\pi$
$824$	48.5169	−	16.7702i	1.69017	−	0.584217i
$825$	7.59385			0.264384
$826$	1.59011	+	0.128551i	0.0553271	+	0.00447285i
$827$	26.3933	+	26.3933i	0.917785	+	0.917785i	0.996868	−	0.0790826i	$-0.0251991\pi$
$827$	26.3933	+	26.3933i	0.917785	+	0.917785i	−0.0790826	+	0.996868i	$0.525199\pi$
$828$	5.44689	+	8.48049i	0.189292	+	0.294717i
$829$	4.87582	+	1.30647i	0.169344	+	0.0453757i	0.342495	−	0.939520i	$-0.388728\pi$
$829$	4.87582	+	1.30647i	0.169344	+	0.0453757i	−0.173151	+	0.984895i	$0.555395\pi$
$830$	3.89434	+	13.2694i	0.135174	+	0.460589i
$831$	−6.36544	+	11.0253i	−0.220815	+	0.382462i
$832$	12.4984	+	9.37175i	0.433303	+	0.324907i
$833$	−6.44697	−	5.79590i	−0.223374	−	0.200816i
$834$	7.79063	−	32.0948i	0.269767	−	1.11135i
$835$	0.945474	+	3.52856i	0.0327195	+	0.122111i
$836$	15.5987	−	0.738894i	0.539491	−	0.0255552i
$837$	9.00051	+	2.41168i	0.311103	+	0.0833598i
$838$	−0.775113	−	32.7449i	−0.0267758	−	1.13115i
$839$		−	39.5809i		−	1.36648i	−0.730192	−	0.683242i	$-0.760570\pi$
$839$		−	39.5809i		−	1.36648i	0.730192	−	0.683242i	$-0.239430\pi$
$840$	−6.73315	+	1.56562i	−0.232316	+	0.0540191i
$841$		−	14.0297i		−	0.483783i
$842$	38.4405	−	0.909934i	1.32475	−	0.0313584i
$843$	−9.69041	−	2.59654i	−0.333755	−	0.0894295i
$844$	8.02197	+	7.29635i	0.276127	+	0.251151i
$845$	2.19646	+	8.19730i	0.0755605	+	0.281996i
$846$	9.19701	+	2.23247i	0.316200	+	0.0767538i
$847$	−18.4780	+	8.23546i	−0.634912	+	0.282974i
$848$	21.0492	+	3.55113i	0.722833	+	0.121946i
$849$	5.86056	−	10.1508i	0.201134	−	0.348374i
$850$	6.96878	−	2.04521i	0.239027	−	0.0701501i
$851$	7.18045	+	1.92400i	0.246143	+	0.0659537i
$852$	1.46891	+	0.319952i	0.0503241	+	0.0109614i
$853$	19.3971	+	19.3971i	0.664143	+	0.664143i	0.956354	−	0.292211i	$-0.0943909\pi$
$853$	19.3971	+	19.3971i	0.664143	+	0.664143i	−0.292211	+	0.956354i	$0.594391\pi$
$854$	7.77812	+	16.3969i	0.266162	+	0.561090i
$855$	3.93858			0.134697
$856$	−14.9905	+	30.8279i	−0.512364	+	1.05368i
$857$	−16.3538	−	28.3256i	−0.558634	−	0.967582i	−0.997611	−	0.0690840i	$-0.977992\pi$
$857$	−16.3538	−	28.3256i	−0.558634	−	0.967582i	0.438977	−	0.898498i	$-0.355341\pi$
$858$	−4.43835	−	2.42429i	−0.151523	−	0.0827639i
$859$	12.4423	+	46.4352i	0.424525	+	1.58435i	0.764957	+	0.644081i	$0.222760\pi$
$859$	12.4423	+	46.4352i	0.424525	+	1.58435i	−0.340432	+	0.940269i	$0.610573\pi$
$860$	−2.18552	+	4.23654i	−0.0745256	+	0.144465i
$861$	−8.27407	−	10.2096i	−0.281979	−	0.347942i
$862$	18.8334	+	4.57159i	0.641469	+	0.155709i
$863$	−12.2908	−	7.09607i	−0.418382	−	0.241553i	0.276003	−	0.961157i	$-0.410990\pi$
$863$	−12.2908	−	7.09607i	−0.418382	−	0.241553i	−0.694385	+	0.719604i	$0.744323\pi$
$864$	5.61729	−	0.667837i	0.191104	−	0.0227203i
$865$	3.30527	+	5.72489i	0.112382	+	0.194652i
$866$	13.8315	−	14.5022i	0.470014	−	0.492805i
$867$	−10.9363	−	10.9363i	−0.371415	−	0.371415i
$868$	2.80901	−	49.2262i	0.0953440	−	1.67085i
$869$	−20.5906	+	20.5906i	−0.698487	+	0.698487i
$870$	5.05321	−	0.119616i	0.171320	−	0.00405535i
$871$	20.2291	−	11.6793i	0.685436	−	0.395736i
$872$	8.84347	+	13.0775i	0.299478	+	0.442859i
$873$	−4.54642	+	7.87463i	−0.153873	+	0.266516i
$874$	−25.9489	+	15.8119i	−0.877734	+	0.534847i
$875$	−3.50555	−	22.0782i	−0.118509	−	0.746380i
$876$	−0.945097	−	2.95924i	−0.0319319	−	0.0999834i
$877$	7.07559	−	1.89590i	0.238926	−	0.0640200i	−0.137369	−	0.990520i	$-0.543865\pi$
$877$	7.07559	−	1.89590i	0.238926	−	0.0640200i	0.376295	+	0.926500i	$0.377198\pi$
$878$	−5.70924	−	19.4535i	−0.192678	−	0.656523i
$879$	−17.7960	+	10.2745i	−0.600244	+	0.346551i
$880$	−0.639635	−	6.73647i	−0.0215621	−	0.227086i
$881$		−	17.2314i		−	0.580542i	−0.956945	−	0.290271i	$-0.906255\pi$
$881$		−	17.2314i		−	0.580542i	0.956945	−	0.290271i	$-0.0937454\pi$
$882$	8.16820	−	5.59290i	0.275038	−	0.188323i
$883$	−9.00522	+	9.00522i	−0.303050	+	0.303050i	−0.842206	−	0.539156i	$-0.818743\pi$
$883$	−9.00522	+	9.00522i	−0.303050	+	0.303050i	0.539156	+	0.842206i	$0.318743\pi$
$884$	−4.72594	−	1.02938i	−0.158950	−	0.0346219i
$885$	−0.101937	+	0.380436i	−0.00342659	+	0.0127882i
$886$	34.9713	+	19.1018i	1.17488	+	0.641738i
$887$	−7.60624	−	4.39147i	−0.255393	−	0.147451i	0.366838	−	0.930285i	$-0.380440\pi$
$887$	−7.60624	−	4.39147i	−0.255393	−	0.147451i	−0.622231	+	0.782834i	$0.713774\pi$
$888$	2.73346	−	3.15203i	0.0917288	−	0.105775i
$889$	15.4672	+	11.2285i	0.518754	+	0.376592i
$890$	−14.8399	+	9.04268i	−0.497434	+	0.303111i
$891$	−1.76891	+	0.473979i	−0.0592608	+	0.0158789i
$892$	−1.75413	−	37.0311i	−0.0587325	−	1.23989i
$893$	−7.38484	+	27.5606i	−0.247124	+	0.922281i
$894$	21.6887	+	20.6856i	0.725377	+	0.691830i
$895$	−23.9437			−0.800351
$896$	−9.50495	−	28.3841i	−0.317538	−	0.948246i
$897$	9.84078			0.328574
$898$	−7.11678	−	6.78765i	−0.237490	−	0.226507i
$899$	−9.33114	+	34.8243i	−0.311211	+	1.16146i
$900$	0.392407	+	8.28405i	0.0130802	+	0.276135i
$901$	−6.38406	+	1.71060i	−0.212684	+	0.0569885i
$902$	10.9851	−	6.69374i	0.365763	−	0.222877i
$903$	0.710972	−	6.78957i	0.0236597	−	0.225943i
$904$	11.7362	−	13.5333i	0.390339	−	0.450112i
$905$	11.9796	+	6.91640i	0.398214	+	0.229909i
$906$	20.4525	+	11.1714i	0.679488	+	0.371146i
$907$	−5.41145	+	20.1958i	−0.179684	+	0.670590i	0.816022	+	0.578021i	$0.196175\pi$
$907$	−5.41145	+	20.1958i	−0.179684	+	0.670590i	−0.995706	+	0.0925696i	$0.970492\pi$
$908$	15.5630	+	3.38987i	0.516478	+	0.112497i
$909$	−10.0396	+	10.0396i	−0.332992	+	0.332992i
$910$	−2.26652	+	6.35742i	−0.0751344	+	0.210746i
$911$			7.28220i			0.241270i	0.992697	+	0.120635i	$0.0384931\pi$
$911$			7.28220i			0.241270i	−0.992697	+	0.120635i	$0.961507\pi$
$912$	1.61210	+	16.9782i	0.0533820	+	0.562205i
$913$	16.7886	−	9.69288i	0.555620	−	0.320787i
$914$	6.39356	+	21.7852i	0.211480	+	0.720591i
$915$	−4.32785	+	1.15964i	−0.143074	+	0.0383366i
$916$	−0.941906	−	2.94924i	−0.0311214	−	0.0974458i
$917$	−14.3827	+	37.5113i	−0.474958	+	1.23873i
$918$	−1.49565	+	0.911376i	−0.0493639	+	0.0300799i
$919$	0.0785390	−	0.136034i	0.00259076	−	0.00448733i	−0.864727	−	0.502242i	$-0.832509\pi$
$919$	0.0785390	−	0.136034i	0.00259076	−	0.00448733i	0.867318	+	0.497755i	$0.165842\pi$
$920$	7.37596	+	10.9074i	0.243178	+	0.359605i
$921$	15.6409	−	9.03028i	0.515385	−	0.297558i
$922$	15.4928	−	0.366733i	0.510227	−	0.0120777i
$923$	1.03790	−	1.03790i	0.0341629	−	0.0341629i
$924$	4.35923	+	8.65454i	0.143408	+	0.284713i
$925$	4.32516	+	4.32516i	0.142211	+	0.142211i
$926$	−40.7763	+	42.7535i	−1.33999	+	1.40497i
$927$	−9.07457	−	15.7176i	−0.298048	−	0.516234i
$928$	2.58396	+	21.7341i	0.0848227	+	0.713458i
$929$	−43.1398	−	24.9068i	−1.41537	−	0.817164i	−0.419482	−	0.907763i	$-0.637788\pi$
$929$	−43.1398	−	24.9068i	−1.41537	−	0.817164i	−0.995887	+	0.0905992i	$0.971122\pi$
$930$	11.8295	+	2.87147i	0.387904	+	0.0941591i
$931$	16.2743	+	25.0181i	0.533369	+	0.819934i
$932$	−24.5450	+	47.5795i	−0.803997	+	1.55852i
$933$	−2.29642	−	8.57037i	−0.0751816	−	0.280581i
$934$	−27.0337	−	14.7662i	−0.884569	−	0.483164i
$935$	1.04755	+	1.81441i	0.0342586	+	0.0593376i
$936$	2.41528	−	4.96702i	0.0789460	−	0.162352i
$937$	10.9499			0.357718			0.178859	−	0.983875i	$-0.442759\pi$
$937$	10.9499			0.357718			0.178859	+	0.983875i	$0.442759\pi$
$938$	−44.6123	−	3.60663i	−1.45664	−	0.117761i
$939$	−9.80976	−	9.80976i	−0.320129	−	0.320129i
$940$	12.0806	+	2.63133i	0.394024	+	0.0858247i
$941$	−45.7502	−	12.2587i	−1.49141	−	0.399623i	−0.581200	−	0.813760i	$-0.697417\pi$
$941$	−45.7502	−	12.2587i	−1.49141	−	0.399623i	−0.910215	+	0.414137i	$0.864083\pi$
$942$	−13.3324	+	3.91282i	−0.434393	+	0.127486i
$943$	−12.5156	+	21.6777i	−0.407564	+	0.705922i
$944$	−1.68168	−	0.283710i	−0.0547342	−	0.00923398i
$945$	0.994938	+	2.23236i	0.0323653	+	0.0726186i
$946$	6.49392	+	1.57632i	0.211136	+	0.0512507i
$947$	−11.9163	−	44.4724i	−0.387229	−	1.44516i	−0.834623	−	0.550822i	$-0.814314\pi$
$947$	−11.9163	−	44.4724i	−0.387229	−	1.44516i	0.447394	−	0.894337i	$-0.352352\pi$
$948$	−23.5260	−	21.3980i	−0.764089	−	0.694975i
$949$	−2.92971	−	0.785012i	−0.0951023	−	0.0254826i
$950$	−24.9962	+	0.591691i	−0.810984	+	0.0191970i
$951$			26.9488i			0.873875i
$952$	6.33128	+	6.76811i	0.205198	+	0.219356i
$953$			19.8032i			0.641488i	0.947166	+	0.320744i	$0.103933\pi$
$953$			19.8032i			0.641488i	−0.947166	+	0.320744i	$0.896067\pi$
$954$	−0.178601	−	7.54507i	−0.00578243	−	0.244281i
$955$	−9.39647	−	2.51778i	−0.304063	−	0.0814734i
$956$	14.3602	−	0.680228i	0.464442	−	0.0220001i
$957$	−1.83389	−	6.84418i	−0.0592814	−	0.221241i
$958$	10.4739	−	43.1488i	0.338395	−	1.39407i
$959$	−4.40694	+	42.0849i	−0.142307	+	1.35899i
$960$	7.31569	−	1.04587i	0.236113	−	0.0337554i
$961$	−27.9127	+	48.3462i	−0.900410	+	1.55956i
$962$	−1.14713	−	3.90869i	−0.0369850	−	0.126021i
$963$	11.7066	+	3.13678i	0.377240	+	0.101081i
$964$	0.682732	+	1.06297i	0.0219893	+	0.0342361i
$965$	4.14564	+	4.14564i	0.133453	+	0.133453i
$966$	−15.5171	−	10.7133i	−0.499255	−	0.344695i
$967$	7.75390			0.249349			0.124674	−	0.992198i	$-0.460211\pi$
$967$	7.75390			0.249349			0.124674	+	0.992198i	$0.460211\pi$
$968$	20.4403	−	7.06533i	0.656977	−	0.227088i
$969$	−2.64019	−	4.57294i	−0.0848151	−	0.146904i
$970$	−5.69430	+	10.4250i	−0.182833	+	0.334728i
$971$	2.60940	+	9.73841i	0.0837396	+	0.312521i	0.995073	−	0.0991496i	$-0.0316122\pi$
$971$	2.60940	+	9.73841i	0.0837396	+	0.312521i	−0.911333	+	0.411670i	$0.864946\pi$
$972$	−0.608466	−	1.90520i	−0.0195165	−	0.0611092i
$973$	9.68916	+	61.0230i	0.310620	+	1.95631i
$974$	−9.13335	+	37.6263i	−0.292652	+	1.20563i
$975$	7.01245	+	4.04864i	0.224578	+	0.129660i
$976$	−6.77036	−	18.1816i	−0.216714	−	0.581978i
$977$	19.6009	+	33.9498i	0.627090	+	1.08615i	0.988133	+	0.153602i	$0.0490875\pi$
$977$	19.6009	+	33.9498i	0.627090	+	1.08615i	−0.361043	+	0.932549i	$0.617579\pi$
$978$	5.82071	+	5.55151i	0.186126	+	0.177518i
$979$	17.2255	+	17.2255i	0.550530	+	0.550530i
$980$	10.4950	−	7.55700i	0.335250	−	0.241400i
$981$	3.94673	−	3.94673i	0.126009	−	0.126009i
$982$	−1.06956	−	45.1841i	−0.0341311	−	1.44188i
$983$	−9.78392	+	5.64875i	−0.312059	+	0.180167i	−0.647847	−	0.761770i	$-0.724331\pi$
$983$	−9.78392	+	5.64875i	−0.312059	+	0.180167i	0.335789	+	0.941937i	$0.390997\pi$
$984$	7.86977	+	11.6376i	0.250879	+	0.370993i
$985$	−9.37184	+	16.2325i	−0.298612	+	0.517211i
$986$	−3.52625	−	5.78690i	−0.112299	−	0.184293i
$987$	−17.4866	+	2.77651i	−0.556606	+	0.0883772i
$988$	14.7983	+	7.63406i	0.470798	+	0.242872i
$989$	−12.5601	+	3.36548i	−0.399389	+	0.107016i
$990$	−2.29560	+	0.673716i	−0.0729588	+	0.0214121i
$991$	13.6213	−	7.86425i	0.432694	−	0.249816i	−0.267800	−	0.963475i	$-0.586297\pi$
$991$	13.6213	−	7.86425i	0.432694	−	0.249816i	0.700494	+	0.713659i	$0.252963\pi$
$992$	−7.53624	+	52.1691i	−0.239276	+	1.65637i
$993$			9.94668i			0.315648i
$994$	−2.76650	+	0.506653i	−0.0877482	+	0.0160701i
$995$	−5.28224	+	5.28224i	−0.167458	+	0.167458i
$996$	11.4414	+	17.8136i	0.362534	+	0.564445i
$997$	−11.7711	+	43.9305i	−0.372796	+	1.39129i	0.483744	+	0.875210i	$0.339277\pi$
$997$	−11.7711	+	43.9305i	−0.372796	+	1.39129i	−0.856539	+	0.516082i	$0.827390\pi$
$998$	−1.35924	+	2.48847i	−0.0430258	+	0.0787710i
$999$	−1.27746	−	0.737545i	−0.0404172	−	0.0233349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bs.a.19.9	✓	128
7.3	odd	6	inner	336.2.bs.a.115.29	yes	128
16.11	odd	4	inner	336.2.bs.a.187.29	yes	128
112.59	even	12	inner	336.2.bs.a.283.9	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bs.a.19.9	✓	128	1.1	even	1	trivial
336.2.bs.a.115.29	yes	128	7.3	odd	6	inner
336.2.bs.a.187.29	yes	128	16.11	odd	4	inner
336.2.bs.a.283.9	yes	128	112.59	even	12	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02338 - 0.976055i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.0946319 + 1.99776i) q^{4} +(0.892283 - 0.239086i) q^{5} +(1.20767 - 0.735892i) q^{6} +(-1.55431 + 2.14106i) q^{7} +(1.85308 - 2.13684i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-1.02338 - 0.976055i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.0946319 + 1.99776i) q^{4} +(0.892283 - 0.239086i) q^{5} +(1.20767 - 0.735892i) q^{6} +(-1.55431 + 2.14106i) q^{7} +(1.85308 - 2.13684i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.14651 - 0.626240i) q^{10} +(-0.473979 + 1.76891i) q^{11} +(-1.95418 - 0.425651i) q^{12} +(-1.38078 + 1.38078i) q^{13} +(3.68045 - 0.674031i) q^{14} +0.923759i q^{15} +(-3.98209 + 0.378104i) q^{16} +(1.07254 - 0.619232i) q^{17} +(0.398249 + 1.35698i) q^{18} +(-4.11837 + 1.10351i) q^{19} +(0.562076 + 1.75994i) q^{20} +(-1.66582 - 2.05549i) q^{21} +(2.21162 - 1.34765i) q^{22} +(-2.51976 + 4.36436i) q^{23} +(1.58442 + 2.34299i) q^{24} +(-3.59112 + 2.07333i) q^{25} +(2.76079 - 0.0653513i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-4.42440 - 2.90253i) q^{28} +(2.73590 + 2.73590i) q^{29} +(0.901640 - 0.945361i) q^{30} +(4.65901 + 8.06964i) q^{31} +(4.44426 + 3.49979i) q^{32} +(-1.58596 - 0.915657i) q^{33} +(-1.70203 - 0.413147i) q^{34} +(-0.874987 + 2.28204i) q^{35} +(0.916926 - 1.77743i) q^{36} +(-0.381781 - 1.42483i) q^{37} +(5.29176 + 2.89044i) q^{38} +(-0.976359 - 1.69110i) q^{39} +(1.14258 - 2.34971i) q^{40} +4.96698 q^{41} +(-0.301506 + 3.72949i) q^{42} +(1.82451 + 1.82451i) q^{43} +(-3.57872 - 0.779500i) q^{44} +(-0.892283 - 0.239086i) q^{45} +(6.83854 - 2.00699i) q^{46} +(3.34606 - 5.79555i) q^{47} +(0.665420 - 3.94426i) q^{48} +(-2.16824 - 6.65573i) q^{49} +(5.69879 + 1.38331i) q^{50} +(0.320538 + 1.19626i) q^{51} +(-2.88913 - 2.62780i) q^{52} +(-5.15482 - 1.38123i) q^{53} +(-1.41382 + 0.0334668i) q^{54} +1.69169i q^{55} +(1.69484 + 7.28886i) q^{56} -4.26365i q^{57} +(-0.129488 - 5.47027i) q^{58} +(0.411834 + 0.110351i) q^{59} +(-1.84545 + 0.0874171i) q^{60} +(1.25535 + 4.68504i) q^{61} +(3.10846 - 12.8058i) q^{62} +(2.41660 - 1.07705i) q^{63} +(-1.13219 - 7.91948i) q^{64} +(-0.901921 + 1.56217i) q^{65} +(0.729320 + 2.48506i) q^{66} +(-11.5544 - 3.09601i) q^{67} +(1.33857 + 2.08408i) q^{68} +(-3.56348 - 3.56348i) q^{69} +(3.12285 - 1.48137i) q^{70} -0.751677 q^{71} +(-2.67324 + 0.924020i) q^{72} +(0.776623 + 1.34515i) q^{73} +(-1.00000 + 1.83079i) q^{74} +(-1.07324 - 4.00537i) q^{75} +(-2.59428 - 8.12308i) q^{76} +(-3.05063 - 3.76426i) q^{77} +(-0.651420 + 2.68363i) q^{78} +(13.7705 + 7.95042i) q^{79} +(-3.46275 + 1.28944i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-5.08313 - 4.84804i) q^{82} +(-7.48522 - 7.48522i) q^{83} +(3.94874 - 3.52242i) q^{84} +(0.808960 - 0.808960i) q^{85} +(-0.0863526 - 3.64800i) q^{86} +(-3.35078 + 1.93457i) q^{87} +(2.90157 + 4.29076i) q^{88} +(6.65111 - 11.5201i) q^{89} +(0.679787 + 1.11559i) q^{90} +(-0.810167 - 5.10249i) q^{91} +(-8.95739 - 4.62087i) q^{92} +(-9.00051 + 2.41168i) q^{93} +(-9.08108 + 2.66513i) q^{94} +(-3.41091 + 1.96929i) q^{95} +(-4.53080 + 3.38701i) q^{96} -9.09284i q^{97} +(-4.27742 + 8.92769i) q^{98} +(1.29493 - 1.29493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 24 q^{8}+O(q^{10}) \) 128 * q + 4 * q^4 - 24 * q^8	\( 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44} - 20 q^{46} - 32 q^{50} - 144 q^{52} - 16 q^{53} - 56 q^{56} - 40 q^{58} - 96 q^{59} - 24 q^{60} - 32 q^{64} - 72 q^{66} + 16 q^{67} - 60 q^{68} + 28 q^{70} + 128 q^{71} - 4 q^{72} - 72 q^{74} + 72 q^{78} - 36 q^{80} + 64 q^{81} - 60 q^{82} + 24 q^{84} - 44 q^{86} - 48 q^{88} - 8 q^{91} + 56 q^{92} + 36 q^{94} + 60 q^{96} + 148 q^{98} - 16 q^{99}+O(q^{100}) \) 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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