LMFDB - Embedded newform 465.2.be.a.98.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [465,2,Mod(98,465)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(465, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("465.98");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.be (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:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			98.8
Character	$\chi$	$=$	465.98
Dual form			465.2.be.a.242.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46359 - 1.46359i) q^{2} +(-1.13704 - 1.30657i) q^{3} +2.28419i q^{4} +(2.22776 - 0.192591i) q^{5} +(-0.248128 + 3.57645i) q^{6} +(0.281899 + 1.05206i) q^{7} +(0.415932 - 0.415932i) q^{8} +(-0.414276 + 2.97126i) q^{9} +O(q^{10})$	\(q+(-1.46359 - 1.46359i) q^{2} +(-1.13704 - 1.30657i) q^{3} +2.28419i q^{4} +(2.22776 - 0.192591i) q^{5} +(-0.248128 + 3.57645i) q^{6} +(0.281899 + 1.05206i) q^{7} +(0.415932 - 0.415932i) q^{8} +(-0.414276 + 2.97126i) q^{9} +(-3.54240 - 2.97865i) q^{10} +(4.53767 - 2.61983i) q^{11} +(2.98446 - 2.59721i) q^{12} +(0.0954847 - 0.356354i) q^{13} +(1.12720 - 1.95237i) q^{14} +(-2.78469 - 2.69175i) q^{15} +3.35087 q^{16} +(0.773693 - 0.207310i) q^{17} +(4.95503 - 3.74237i) q^{18} +(5.38952 + 3.11164i) q^{19} +(0.439913 + 5.08862i) q^{20} +(1.05406 - 1.56456i) q^{21} +(-10.4756 - 2.80694i) q^{22} +(3.90927 - 3.90927i) q^{23} +(-1.01638 - 0.0705146i) q^{24} +(4.92582 - 0.858091i) q^{25} +(-0.661306 + 0.381805i) q^{26} +(4.35322 - 2.83716i) q^{27} +(-2.40310 + 0.643909i) q^{28} -8.73564 q^{29} +(0.136021 + 8.01525i) q^{30} +(-1.50212 + 5.36131i) q^{31} +(-5.73615 - 5.73615i) q^{32} +(-8.58251 - 2.94996i) q^{33} +(-1.43579 - 0.828952i) q^{34} +(0.830619 + 2.28944i) q^{35} +(-6.78691 - 0.946284i) q^{36} +(-1.12772 - 4.20871i) q^{37} +(-3.33388 - 12.4422i) q^{38} +(-0.574173 + 0.280431i) q^{39} +(0.846492 - 1.00670i) q^{40} +(3.18486 - 1.83878i) q^{41} +(-3.83259 + 0.747150i) q^{42} +(-7.84045 + 2.10084i) q^{43} +(5.98417 + 10.3649i) q^{44} +(-0.350670 + 6.69903i) q^{45} -11.4431 q^{46} +(3.64923 + 3.64923i) q^{47} +(-3.81007 - 4.37816i) q^{48} +(5.03481 - 2.90685i) q^{49} +(-8.46527 - 5.95348i) q^{50} +(-1.15059 - 0.775168i) q^{51} +(0.813979 + 0.218105i) q^{52} +(-11.0959 - 2.97314i) q^{53} +(-10.5238 - 2.21889i) q^{54} +(9.60428 - 6.71025i) q^{55} +(0.554836 + 0.320335i) q^{56} +(-2.06251 - 10.5799i) q^{57} +(12.7854 + 12.7854i) q^{58} +(2.58021 - 4.46906i) q^{59} +(6.14846 - 6.36074i) q^{60} -0.589128 q^{61} +(10.0452 - 5.64827i) q^{62} +(-3.24272 + 0.401750i) q^{63} +10.0890i q^{64} +(0.144087 - 0.812260i) q^{65} +(8.24375 + 16.8788i) q^{66} +(11.8119 + 3.16499i) q^{67} +(0.473536 + 1.76726i) q^{68} +(-9.55275 - 0.662754i) q^{69} +(2.13512 - 4.56649i) q^{70} +(-5.16123 + 2.97984i) q^{71} +(1.06353 + 1.40815i) q^{72} +(0.0752409 - 0.280803i) q^{73} +(-4.50930 + 7.81034i) q^{74} +(-6.72202 - 5.46027i) q^{75} +(-7.10757 + 12.3107i) q^{76} +(4.03538 + 4.03538i) q^{77} +(1.25079 + 0.429918i) q^{78} +(-2.59130 - 1.49609i) q^{79} +(7.46492 - 0.645345i) q^{80} +(-8.65675 - 2.46184i) q^{81} +(-7.35255 - 1.97011i) q^{82} +(3.40553 + 0.912510i) q^{83} +(3.57374 + 2.40768i) q^{84} +(1.68368 - 0.610844i) q^{85} +(14.5500 + 8.40043i) q^{86} +(9.93278 + 11.4138i) q^{87} +(0.797693 - 2.97703i) q^{88} -0.601121 q^{89} +(10.3179 - 9.29139i) q^{90} +0.401823 q^{91} +(8.92949 + 8.92949i) q^{92} +(8.71292 - 4.13339i) q^{93} -10.6819i q^{94} +(12.6058 + 5.89401i) q^{95} +(-0.972473 + 14.0170i) q^{96} +(3.18173 - 3.18173i) q^{97} +(-11.6233 - 3.11446i) q^{98} +(5.90433 + 14.5679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{6}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^6	$ 240 q - 6 q^{3} - 4 q^{6} + 4 q^{10} + 24 q^{12} - 4 q^{13} - 24 q^{15} - 216 q^{16} - 6 q^{18} - 4 q^{21} + 8 q^{22} + 48 q^{27} + 16 q^{28} + 60 q^{30} - 24 q^{31} - 4 q^{33} + 12 q^{36} + 12 q^{40} + 70 q^{42} - 4 q^{43} + 38 q^{45} - 96 q^{46} + 48 q^{48} + 4 q^{51} + 20 q^{52} - 52 q^{55} - 34 q^{57} - 104 q^{58} - 96 q^{60} + 16 q^{61} - 64 q^{63} - 208 q^{66} + 8 q^{67} + 96 q^{70} + 64 q^{72} + 12 q^{73} - 12 q^{75} - 12 q^{76} + 76 q^{78} + 12 q^{81} + 52 q^{82} - 56 q^{85} + 22 q^{87} + 48 q^{88} - 80 q^{91} + 6 q^{93} - 68 q^{96} - 144 q^{97}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^6 + 4 * q^10 + 24 * q^12 - 4 * q^13 - 24 * q^15 - 216 * q^16 - 6 * q^18 - 4 * q^21 + 8 * q^22 + 48 * q^27 + 16 * q^28 + 60 * q^30 - 24 * q^31 - 4 * q^33 + 12 * q^36 + 12 * q^40 + 70 * q^42 - 4 * q^43 + 38 * q^45 - 96 * q^46 + 48 * q^48 + 4 * q^51 + 20 * q^52 - 52 * q^55 - 34 * q^57 - 104 * q^58 - 96 * q^60 + 16 * q^61 - 64 * q^63 - 208 * q^66 + 8 * q^67 + 96 * q^70 + 64 * q^72 + 12 * q^73 - 12 * q^75 - 12 * q^76 + 76 * q^78 + 12 * q^81 + 52 * q^82 - 56 * q^85 + 22 * q^87 + 48 * q^88 - 80 * q^91 + 6 * q^93 - 68 * q^96 - 144 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.46359	−	1.46359i	−1.03491	−	1.03491i	−0.999368	−	0.0355458i	$-0.988683\pi$
$2$	−1.46359	−	1.46359i	−1.03491	−	1.03491i	−0.0355458	−	0.999368i	$-0.511317\pi$
$3$	−1.13704	−	1.30657i	−0.656471	−	0.754351i
$3$	−1.13704	−	1.30657i	−0.656471	−	0.754351i
$4$			2.28419i			1.14209i
$5$	2.22776	−	0.192591i	0.996284	−	0.0861292i
$5$	2.22776	−	0.192591i	0.996284	−	0.0861292i
$6$	−0.248128	+	3.57645i	−0.101298	+	1.46008i
$7$	0.281899	+	1.05206i	0.106548	+	0.397641i	0.998516	−	0.0544563i	$-0.0173426\pi$
$7$	0.281899	+	1.05206i	0.106548	+	0.397641i	−0.891969	+	0.452098i	$0.850676\pi$
$8$	0.415932	−	0.415932i	0.147054	−	0.147054i
$9$	−0.414276	+	2.97126i	−0.138092	+	0.990419i
$10$	−3.54240	−	2.97865i	−1.12020	−	0.941932i
$11$	4.53767	−	2.61983i	1.36816	−	0.789907i	0.377466	−	0.926023i	$-0.376795\pi$
$11$	4.53767	−	2.61983i	1.36816	−	0.789907i	0.990693	+	0.136116i	$0.0434621\pi$
$12$	2.98446	−	2.59721i	0.861540	−	0.749751i
$13$	0.0954847	−	0.356354i	0.0264827	−	0.0988348i	−0.951420	−	0.307898i	$-0.900375\pi$
$13$	0.0954847	−	0.356354i	0.0264827	−	0.0988348i	0.977902	+	0.209063i	$0.0670413\pi$
$14$	1.12720	−	1.95237i	0.301257	−	0.521792i
$15$	−2.78469	−	2.69175i	−0.719003	−	0.695007i
$16$	3.35087			0.837716
$17$	0.773693	−	0.207310i	0.187648	−	0.0502802i	−0.163771	−	0.986498i	$-0.552366\pi$
$17$	0.773693	−	0.207310i	0.187648	−	0.0502802i	0.351419	+	0.936218i	$0.385699\pi$
$18$	4.95503	−	3.74237i	1.16791	−	0.882085i
$19$	5.38952	+	3.11164i	1.23644	+	0.713859i	0.968365	−	0.249538i	$-0.0802789\pi$
$19$	5.38952	+	3.11164i	1.23644	+	0.713859i	0.268076	+	0.963398i	$0.413612\pi$
$20$	0.439913	+	5.08862i	0.0983675	+	1.13785i
$21$	1.05406	−	1.56456i	0.230016	−	0.341414i
$22$	−10.4756	−	2.80694i	−2.23341	−	0.598441i
$23$	3.90927	−	3.90927i	0.815139	−	0.815139i	−0.170261	−	0.985399i	$-0.554461\pi$
$23$	3.90927	−	3.90927i	0.815139	−	0.815139i	0.985399	+	0.170261i	$0.0544609\pi$
$24$	−1.01638	−	0.0705146i	−0.207467	−	0.0143937i
$25$	4.92582	−	0.858091i	0.985164	−	0.171618i
$26$	−0.661306	+	0.381805i	−0.129693	+	0.0748782i
$27$	4.35322	−	2.83716i	0.837778	−	0.546012i
$28$	−2.40310	+	0.643909i	−0.454143	+	0.121687i
$29$	−8.73564			−1.62217			−0.811084	−	0.584929i	$-0.801122\pi$
$29$	−8.73564			−1.62217			−0.811084	+	0.584929i	$0.801122\pi$
$30$	0.136021	+	8.01525i	0.0248340	+	1.46338i
$31$	−1.50212	+	5.36131i	−0.269789	+	0.962919i
$31$	−1.50212	+	5.36131i	−0.269789	+	0.962919i
$32$	−5.73615	−	5.73615i	−1.01402	−	1.01402i
$33$	−8.58251	−	2.94996i	−1.49402	−	0.513522i
$34$	−1.43579	−	0.828952i	−0.246235	−	0.142164i
$35$	0.830619	+	2.28944i	0.140400	+	0.386987i
$36$	−6.78691	−	0.946284i	−1.13115	−	0.157714i
$37$	−1.12772	−	4.20871i	−0.185396	−	0.691907i	−0.994545	−	0.104304i	$-0.966738\pi$
$37$	−1.12772	−	4.20871i	−0.185396	−	0.691907i	0.809149	−	0.587603i	$-0.199928\pi$
$38$	−3.33388	−	12.4422i	−0.540827	−	2.01839i
$39$	−0.574173	+	0.280431i	−0.0919413	+	0.0449049i
$40$	0.846492	−	1.00670i	0.133842	−	0.159173i
$41$	3.18486	−	1.83878i	0.497392	−	0.287169i	−0.230244	−	0.973133i	$-0.573952\pi$
$41$	3.18486	−	1.83878i	0.497392	−	0.287169i	0.727636	+	0.685964i	$0.240619\pi$
$42$	−3.83259	+	0.747150i	−0.591381	+	0.115288i
$43$	−7.84045	+	2.10084i	−1.19566	+	0.320376i	−0.801120	−	0.598504i	$-0.795762\pi$
$43$	−7.84045	+	2.10084i	−1.19566	+	0.320376i	−0.394538	+	0.918880i	$0.629095\pi$
$44$	5.98417	+	10.3649i	0.902147	+	1.56257i
$45$	−0.350670	+	6.69903i	−0.0522749	+	0.998633i
$46$	−11.4431			−1.68720
$47$	3.64923	+	3.64923i	0.532294	+	0.532294i	0.921255	−	0.388960i	$-0.127166\pi$
$47$	3.64923	+	3.64923i	0.532294	+	0.532294i	−0.388960	+	0.921255i	$0.627166\pi$
$48$	−3.81007	−	4.37816i	−0.549936	−	0.631932i
$49$	5.03481	−	2.90685i	0.719259	−	0.415265i
$50$	−8.46527	−	5.95348i	−1.19717	−	0.841949i
$51$	−1.15059	−	0.775168i	−0.161114	−	0.108545i
$52$	0.813979	+	0.218105i	0.112879	+	0.0302457i
$53$	−11.0959	−	2.97314i	−1.52414	−	0.408392i	−0.603038	−	0.797712i	$-0.706043\pi$
$53$	−11.0959	−	2.97314i	−1.52414	−	0.408392i	−0.921102	+	0.389320i	$0.872710\pi$
$54$	−10.5238	−	2.21889i	−1.43210	−	0.301953i
$55$	9.60428	−	6.71025i	1.29504	−	0.904810i
$56$	0.554836	+	0.320335i	0.0741431	+	0.0428065i
$57$	−2.06251	−	10.5799i	−0.273186	−	1.40134i
$58$	12.7854	+	12.7854i	1.67880	+	1.67880i
$59$	2.58021	−	4.46906i	0.335915	−	0.581822i	−0.647745	−	0.761857i	$-0.724288\pi$
$59$	2.58021	−	4.46906i	0.335915	−	0.581822i	0.983660	+	0.180035i	$0.0576212\pi$
$60$	6.14846	−	6.36074i	0.793763	−	0.821168i
$61$	−0.589128			−0.0754301			−0.0377150	−	0.999289i	$-0.512008\pi$
$61$	−0.589128			−0.0754301			−0.0377150	+	0.999289i	$0.512008\pi$
$62$	10.0452	−	5.64827i	1.27575	−	0.717330i
$63$	−3.24272	+	0.401750i	−0.408545	+	0.0506158i
$64$			10.0890i			1.26113i
$65$	0.144087	−	0.812260i	0.0178717	−	0.100748i
$66$	8.24375	+	16.8788i	1.01474	+	2.07764i
$67$	11.8119	+	3.16499i	1.44305	+	0.386665i	0.893602	−	0.448861i	$-0.148170\pi$
$67$	11.8119	+	3.16499i	1.44305	+	0.386665i	0.549451	+	0.835526i	$0.314837\pi$
$68$	0.473536	+	1.76726i	0.0574246	+	0.214312i
$69$	−9.55275	−	0.662754i	−1.15002	−	0.0797862i
$70$	2.13512	−	4.56649i	0.255196	−	0.545800i
$71$	−5.16123	+	2.97984i	−0.612525	+	0.353641i	−0.773953	−	0.633243i	$-0.781723\pi$
$71$	−5.16123	+	2.97984i	−0.612525	+	0.353641i	0.161428	+	0.986884i	$0.448390\pi$
$72$	1.06353	+	1.40815i	0.125338	+	0.165952i
$73$	0.0752409	−	0.280803i	0.00880628	−	0.0328655i	−0.961383	−	0.275214i	$-0.911251\pi$
$73$	0.0752409	−	0.280803i	0.00880628	−	0.0328655i	0.970189	+	0.242349i	$0.0779178\pi$
$74$	−4.50930	+	7.81034i	−0.524195	+	0.907933i
$75$	−6.72202	−	5.46027i	−0.776192	−	0.630497i
$76$	−7.10757	+	12.3107i	−0.815294	+	1.41213i
$77$	4.03538	+	4.03538i	0.459874	+	0.459874i
$78$	1.25079	+	0.429918i	0.141624	+	0.0486786i
$79$	−2.59130	−	1.49609i	−0.291544	−	0.168323i	0.347094	−	0.937830i	$-0.387168\pi$
$79$	−2.59130	−	1.49609i	−0.291544	−	0.168323i	−0.638638	+	0.769508i	$0.720502\pi$
$80$	7.46492	−	0.645345i	0.834603	−	0.0721518i
$81$	−8.65675	−	2.46184i	−0.961861	−	0.273538i
$82$	−7.35255	−	1.97011i	−0.811953	−	0.217562i
$83$	3.40553	+	0.912510i	0.373806	+	0.100161i	0.440831	−	0.897590i	$-0.354684\pi$
$83$	3.40553	+	0.912510i	0.373806	+	0.100161i	−0.0670246	+	0.997751i	$0.521351\pi$
$84$	3.57374	+	2.40768i	0.389927	+	0.262699i
$85$	1.68368	−	0.610844i	0.182620	−	0.0662553i
$86$	14.5500	+	8.40043i	1.56896	+	0.905842i
$87$	9.93278	+	11.4138i	1.06491	+	1.22369i
$88$	0.797693	−	2.97703i	0.0850344	−	0.317353i
$89$	−0.601121			−0.0637187			−0.0318593	−	0.999492i	$-0.510143\pi$
$89$	−0.601121			−0.0637187			−0.0318593	+	0.999492i	$0.510143\pi$
$90$	10.3179	−	9.29139i	1.08760	−	0.979399i
$91$	0.401823			0.0421225
$92$	8.92949	+	8.92949i	0.930964	+	0.930964i
$93$	8.71292	−	4.13339i	0.903488	−	0.428613i
$94$		−	10.6819i		−	1.10176i
$95$	12.6058	+	5.89401i	1.29333	+	0.604713i
$96$	−0.972473	+	14.0170i	−0.0992526	+	1.43060i
$97$	3.18173	−	3.18173i	0.323055	−	0.323055i	−0.526883	−	0.849938i	$-0.676639\pi$
$97$	3.18173	−	3.18173i	0.323055	−	0.323055i	0.849938	+	0.526883i	$0.176639\pi$
$98$	−11.6233	−	3.11446i	−1.17413	−	0.314608i
$99$	5.90433	+	14.5679i	0.593407	+	1.46413i
$100$	1.96004	+	11.2515i	0.196004	+	1.12515i
$101$		−	13.7579i		−	1.36896i	−0.729033	−	0.684479i	$-0.760030\pi$
$101$		−	13.7579i		−	1.36896i	0.729033	−	0.684479i	$-0.239970\pi$
$102$	0.549460	+	2.81851i	0.0544047	+	0.279074i
$103$	−1.93353	+	7.21605i	−0.190517	+	0.711019i	0.802865	+	0.596161i	$0.203308\pi$
$103$	−1.93353	+	7.21605i	−0.190517	+	0.711019i	−0.993382	+	0.114858i	$0.963359\pi$
$104$	−0.108504	−	0.187934i	−0.0106397	−	0.0184285i
$105$	2.04688	−	3.68846i	0.199755	−	0.359957i
$106$	11.8884	+	20.5913i	1.15470	+	2.00000i
$107$	−0.546288	+	0.146377i	−0.0528116	+	0.0141508i	−0.285128	−	0.958489i	$-0.592036\pi$
$107$	−0.546288	+	0.146377i	−0.0528116	+	0.0141508i	0.232316	+	0.972640i	$0.425369\pi$
$108$	6.48060	+	9.94357i	0.623596	+	0.956820i
$109$		−	17.3791i		−	1.66462i	−0.554314	−	0.832308i	$-0.687019\pi$
$109$		−	17.3791i		−	1.66462i	0.554314	−	0.832308i	$-0.312981\pi$
$110$	−23.8778	−	4.23567i	−2.27666	−	0.403855i
$111$	−4.21673	+	6.25892i	−0.400234	+	0.594071i
$112$	0.944604	+	3.52531i	0.0892567	+	0.333111i
$113$	17.6297	+	4.72387i	1.65846	+	0.444384i	0.961965	−	0.273174i	$-0.0880735\pi$
$113$	17.6297	+	4.72387i	1.65846	+	0.444384i	0.696499	+	0.717558i	$0.254740\pi$
$114$	−12.4659	+	18.5033i	−1.16754	+	1.73299i
$115$	7.95602	−	9.46179i	0.741902	−	0.882317i
$116$		−	19.9538i		−	1.85267i
$117$	1.01926	+	0.431339i	0.0942308	+	0.0398773i
$118$	−10.3172	+	2.76450i	−0.949779	+	0.254492i
$119$	0.436206	+	0.755531i	0.0399869	+	0.0692594i
$120$	−2.27783	+	0.0386554i	−0.207936	+	0.00352874i
$121$	8.22697	−	14.2495i	0.747906	−	1.29541i
$122$	0.862241	+	0.862241i	0.0780636	+	0.0780636i
$123$	−6.02382	−	2.07049i	−0.543150	−	0.186690i
$124$	−12.2462	−	3.43112i	−1.09974	−	0.308124i
$125$	10.8083	−	2.86029i	0.966721	−	0.255832i
$126$	5.33401	+	4.15802i	0.475192	+	0.370426i
$127$	0.529995	+	1.97797i	0.0470294	+	0.175516i	0.985446	−	0.169990i	$-0.0543737\pi$
$127$	0.529995	+	1.97797i	0.0470294	+	0.175516i	−0.938416	+	0.345507i	$0.887707\pi$
$128$	3.29387	−	3.29387i	0.291139	−	0.291139i
$129$	11.6598	+	7.85540i	1.02659	+	0.691629i
$130$	−1.39970	+	0.977931i	−0.122762	+	0.0857703i
$131$	−6.30740	−	3.64158i	−0.551080	−	0.318166i	0.198478	−	0.980105i	$-0.436400\pi$
$131$	−6.30740	−	3.64158i	−0.551080	−	0.318166i	−0.749557	+	0.661939i	$0.769734\pi$
$132$	6.73825	−	19.6041i	0.586490	−	1.70631i
$133$	−1.75433	+	6.54726i	−0.152120	+	0.567720i
$134$	−12.6555	−	21.9200i	−1.09327	−	1.89360i
$135$	9.15151	−	7.15890i	0.787637	−	0.616140i
$136$	0.235577	−	0.408031i	0.0202005	−	0.0349884i
$137$	−1.33875	+	4.99628i	−0.114377	+	0.426861i	−0.999240	−	0.0389913i	$-0.987586\pi$
$137$	−1.33875	+	4.99628i	−0.114377	+	0.426861i	0.884862	+	0.465852i	$0.154252\pi$
$138$	13.0113	+	14.9513i	1.10760	+	1.27274i
$139$		−	5.00658i		−	0.424652i	−0.977199	−	0.212326i	$-0.931896\pi$
$139$		−	5.00658i		−	0.424652i	0.977199	−	0.212326i	$-0.0681039\pi$
$140$	−5.22952	+	1.89729i	−0.441975	+	0.160350i
$141$	0.618668	−	8.91731i	0.0521012	−	0.750973i
$142$	11.9152	+	3.19266i	0.999899	+	0.267922i
$143$	−0.500307	−	1.86717i	−0.0418377	−	0.156141i
$144$	−1.38818	+	9.95629i	−0.115682	+	0.829691i
$145$	−19.4609	+	1.68240i	−1.61614	+	0.139716i
$146$	−0.521102	+	0.300858i	−0.0431267	+	0.0248992i
$147$	−9.52281	−	3.27315i	−0.785428	−	0.269965i
$148$	9.61347	−	2.57592i	0.790223	−	0.211739i
$149$	−11.2467	+	19.4799i	−0.921367	+	1.59585i	−0.124064	+	0.992274i	$0.539593\pi$
$149$	−11.2467	+	19.4799i	−0.921367	+	1.59585i	−0.797302	+	0.603580i	$0.793740\pi$
$150$	1.84669	+	17.8299i	0.150781	+	1.45580i
$151$	16.6634			1.35605			0.678026	−	0.735038i	$-0.262836\pi$
$151$	16.6634			1.35605			0.678026	+	0.735038i	$0.262836\pi$
$152$	3.53591	−	0.947443i	0.286800	−	0.0768478i
$153$	0.295450	+	2.38473i	0.0238857	+	0.192794i
$154$		−	11.8123i		−	0.951859i
$155$	−2.31383	+	12.2330i	−0.185851	+	0.982578i
$156$	−0.640557	−	1.31152i	−0.0512856	−	0.105006i
$157$	−4.16240	+	4.16240i	−0.332195	+	0.332195i	−0.853420	−	0.521224i	$-0.825475\pi$
$157$	−4.16240	+	4.16240i	−0.332195	+	0.332195i	0.521224	+	0.853420i	$0.325475\pi$
$158$	1.60294	+	5.98225i	0.127523	+	0.475922i
$159$	8.73187	+	17.8782i	0.692483	+	1.41784i
$160$	−13.8835	−	11.6740i	−1.09759	−	0.922914i
$161$	5.21480	+	3.01077i	0.410984	+	0.237282i
$162$	9.06680	+	16.2731i	0.712355	+	1.27853i
$163$	−7.78723	−	7.78723i	−0.609943	−	0.609943i	0.332988	−	0.942931i	$-0.391943\pi$
$163$	−7.78723	−	7.78723i	−0.609943	−	0.609943i	−0.942931	+	0.332988i	$0.891943\pi$
$164$	4.20012	+	7.27482i	0.327974	+	0.568068i
$165$	−19.6879	−	4.91888i	−1.53270	−	0.382934i
$166$	−3.64876	−	6.31984i	−0.283199	−	0.490515i
$167$	11.0648	−	2.96481i	0.856221	−	0.229424i	0.196101	−	0.980584i	$-0.437172\pi$
$167$	11.0648	−	2.96481i	0.856221	−	0.229424i	0.660120	+	0.751160i	$0.270505\pi$
$168$	−0.212330	−	1.08917i	−0.0163816	−	0.0840312i
$169$	11.1405	+	6.43195i	0.856958	+	0.494765i
$170$	−3.35823	−	1.57018i	−0.257565	−	0.120428i
$171$	−11.4782	+	14.7246i	−0.877763	+	1.12602i
$172$	−4.79872	−	17.9091i	−0.365899	−	1.36555i
$173$	−19.0125	−	5.09440i	−1.44550	−	0.387320i	−0.551042	−	0.834478i	$-0.685770\pi$
$173$	−19.0125	−	5.09440i	−1.44550	−	0.387320i	−0.894455	+	0.447158i	$0.852436\pi$
$174$	2.16756	−	31.2426i	0.164322	−	2.36849i
$175$	2.29134	+	4.94036i	0.173209	+	0.373456i
$176$	15.2051	−	8.77868i	1.14613	−	0.661718i
$177$	−8.77297	+	1.71026i	−0.659417	+	0.128551i
$178$	0.879794	+	0.879794i	0.0659433	+	0.0659433i
$179$	−5.90689	+	10.2310i	−0.441502	+	0.764704i	−0.997801	−	0.0662782i	$-0.978888\pi$
$179$	−5.90689	+	10.2310i	−0.441502	+	0.764704i	0.556299	+	0.830982i	$0.312221\pi$
$180$	−15.3018	−	0.800996i	−1.14053	−	0.0597028i
$181$	−7.36942	−	12.7642i	−0.547765	−	0.948756i	−0.998427	−	0.0560620i	$-0.982146\pi$
$181$	−7.36942	−	12.7642i	−0.547765	−	0.948756i	0.450663	−	0.892694i	$-0.351188\pi$
$182$	−0.588103	−	0.588103i	−0.0435931	−	0.0435931i
$183$	0.669862	+	0.769740i	0.0495177	+	0.0569008i
$184$		−	3.25198i		−	0.239739i
$185$	−3.32285	−	9.15880i	−0.244300	−	0.673368i
$186$	−18.8017	−	6.70255i	−1.37861	−	0.491455i
$187$	2.96765	−	2.96765i	0.217016	−	0.217016i
$188$	−8.33551	+	8.33551i	−0.607930	+	0.607930i
$189$	4.21203	+	3.78006i	0.306380	+	0.274959i
$190$	−9.82333	−	27.0762i	−0.712659	−	1.96431i
$191$	−8.87989	+	5.12681i	−0.642526	+	0.370963i	−0.785587	−	0.618751i	$-0.787639\pi$
$191$	−8.87989	+	5.12681i	−0.642526	+	0.370963i	0.143061	+	0.989714i	$0.454306\pi$
$192$	13.1821	−	11.4716i	0.951333	−	0.827893i
$193$	−6.27678	+	1.68186i	−0.451813	+	0.121063i	−0.477547	−	0.878606i	$-0.658474\pi$
$193$	−6.27678	+	1.68186i	−0.451813	+	0.121063i	0.0257347	+	0.999669i	$0.491807\pi$
$194$	−9.31348			−0.668669
$195$	−1.22511	+	0.735313i	−0.0877320	+	0.0526569i
$196$	6.63979	+	11.5005i	0.474271	+	0.821461i
$197$	−2.97624	+	11.1075i	−0.212048	+	0.791376i	0.775136	+	0.631794i	$0.217681\pi$
$197$	−2.97624	+	11.1075i	−0.212048	+	0.791376i	−0.987185	+	0.159582i	$0.948986\pi$
$198$	12.6799	−	29.9630i	0.901124	−	2.12938i
$199$	−8.42042	+	4.86153i	−0.596908	+	0.344625i	−0.767824	−	0.640661i	$-0.778661\pi$
$199$	−8.42042	+	4.86153i	−0.596908	+	0.344625i	0.170916	+	0.985286i	$0.445327\pi$
$200$	1.69190	−	2.40571i	0.119635	−	0.170110i
$201$	−9.29531	−	19.0318i	−0.655641	−	1.34240i
$202$	−20.1358	+	20.1358i	−1.41675	+	1.41675i
$203$	−2.46257	−	9.19042i	−0.172838	−	0.645041i
$204$	1.77063	−	2.62816i	0.123969	−	0.184008i
$205$	6.74097	−	4.70974i	0.470810	−	0.328942i
$206$	13.3912	−	7.73143i	0.933011	−	0.538674i
$207$	9.99593	+	13.2350i	0.694765	+	0.919893i
$208$	0.319957	−	1.19409i	0.0221850	−	0.0827955i
$209$	32.6078			2.25553
$210$	−8.39418	+	2.40259i	−0.579254	+	0.165795i
$211$	4.23930	−	7.34267i	0.291845	−	0.505491i	−0.682401	−	0.730978i	$-0.739064\pi$
$211$	4.23930	−	7.34267i	0.291845	−	0.505491i	0.974246	+	0.225488i	$0.0723975\pi$
$212$	6.79121	−	25.3451i	0.466422	−	1.74071i
$213$	9.76191	+	3.35533i	0.668875	+	0.229904i
$214$	1.01378	+	0.585305i	0.0693004	+	0.0400106i
$215$	−17.0620	+	6.19017i	−1.16362	+	0.422166i
$216$	0.630578	−	2.99071i	0.0429054	−	0.203492i
$217$	−6.06386	−	0.0689758i	−0.411642	−	0.00468238i
$218$	−25.4359	+	25.4359i	−1.72273	+	1.72273i
$219$	−0.452442	+	0.220976i	−0.0305732	+	0.0149322i
$220$	15.3275	+	21.9380i	1.03338	+	1.47906i
$221$		−	0.295504i		−	0.0198777i
$222$	15.3320	−	2.98893i	1.02902	−	0.200604i
$223$	7.70702	−	2.06509i	0.516100	−	0.138289i	0.00863792	−	0.999963i	$-0.497250\pi$
$223$	7.70702	−	2.06509i	0.516100	−	0.138289i	0.507462	+	0.861674i	$0.330584\pi$
$224$	4.41776	−	7.65179i	0.295174	−	0.511257i
$225$	0.508962	+	14.9914i	0.0339308	+	0.999424i
$226$	−18.8888	−	32.7164i	−1.25647	−	2.17627i
$227$	−7.63815	+	28.5060i	−0.506962	+	1.89201i	−0.0583165	+	0.998298i	$0.518573\pi$
$227$	−7.63815	+	28.5060i	−0.506962	+	1.89201i	−0.448645	+	0.893710i	$0.648093\pi$
$228$	24.1664	−	4.71116i	1.60046	−	0.312004i
$229$	0.877933	+	0.506875i	0.0580155	+	0.0334952i	0.528727	−	0.848792i	$-0.322669\pi$
$229$	0.877933	+	0.506875i	0.0580155	+	0.0334952i	−0.470712	+	0.882287i	$0.656003\pi$
$230$	−25.4925	+	2.20384i	−1.68093	+	0.145317i
$231$	0.684133	−	9.86091i	0.0450127	−	0.648800i
$232$	−3.63343	+	3.63343i	−0.238547	+	0.238547i
$233$	−6.63986	+	6.63986i	−0.434992	+	0.434992i	−0.890322	−	0.455331i	$-0.849521\pi$
$233$	−6.63986	+	6.63986i	−0.434992	+	0.434992i	0.455331	+	0.890322i	$0.349521\pi$
$234$	−0.860479	−	2.12308i	−0.0562513	−	0.138790i
$235$	8.83240	+	7.42679i	0.576162	+	0.484470i
$236$	10.2082	+	5.89369i	0.664495	+	0.383646i
$237$	0.991662	+	5.08683i	0.0644154	+	0.330425i
$238$	0.467360	−	1.74421i	0.0302945	−	0.113061i
$239$	−5.71340	−	9.89589i	−0.369569	−	0.640112i	0.619929	−	0.784658i	$-0.287161\pi$
$239$	−5.71340	−	9.89589i	−0.369569	−	0.640112i	−0.989498	+	0.144546i	$0.953828\pi$
$240$	−9.33111	−	9.01969i	−0.602321	−	0.582219i
$241$	−12.9228	+	22.3830i	−0.832432	+	1.44181i	0.0636729	+	0.997971i	$0.479719\pi$
$241$	−12.9228	+	22.3830i	−0.832432	+	1.44181i	−0.896105	+	0.443843i	$0.853615\pi$
$242$	−32.8964	+	8.81455i	−2.11466	+	0.566621i
$243$	6.62650	+	14.1099i	0.425090	+	0.905151i
$244$		−	1.34568i		−	0.0861482i
$245$	10.6565	−	7.44542i	0.680820	−	0.475671i
$246$	5.78605	+	11.8468i	0.368905	+	0.755321i
$247$	1.62346	−	1.62346i	0.103298	−	0.103298i
$248$	1.60516	+	2.85472i	0.101928	+	0.181275i
$249$	−2.67997	−	5.48715i	−0.169836	−	0.347734i
$250$	−20.0052	−	11.6326i	−1.26524	−	0.735709i
$251$	8.66335	+	5.00178i	0.546825	+	0.315710i	0.747841	−	0.663878i	$-0.231091\pi$
$251$	8.66335	+	5.00178i	0.546825	+	0.315710i	−0.201015	+	0.979588i	$0.564424\pi$
$252$	−0.917673	−	7.40699i	−0.0578079	−	0.466596i
$253$	7.49737	−	27.9806i	0.471356	−	1.75912i
$254$	2.11924	−	3.67063i	0.132973	−	0.230316i
$255$	−2.71252	−	1.50529i	−0.169865	−	0.0942652i
$256$	10.5363			0.658519
$257$	2.75266	−	10.2731i	0.171706	−	0.640817i	−0.825383	−	0.564573i	$-0.809041\pi$
$257$	2.75266	−	10.2731i	0.171706	−	0.640817i	0.997089	−	0.0762434i	$-0.0242926\pi$
$258$	−5.56812	−	28.5623i	−0.346656	−	1.77821i
$259$	4.10991	−	2.37286i	0.255377	−	0.147442i
$260$	1.85535	+	0.329120i	0.115064	+	0.0204112i
$261$	3.61897	−	25.9559i	0.224008	−	1.60663i
$262$	3.90166	+	14.5612i	0.241046	+	0.899595i
$263$	16.5688	−	16.5688i	1.02168	−	1.02168i	0.0219158	−	0.999760i	$-0.493023\pi$
$263$	16.5688	−	16.5688i	1.02168	−	1.02168i	0.999760	−	0.0219158i	$-0.00697656\pi$
$264$	−4.79673	+	2.34276i	−0.295218	+	0.144187i
$265$	−25.2916	−	4.48647i	−1.55365	−	0.275602i
$266$	12.1501	−	7.01488i	0.744972	−	0.430110i
$267$	0.683499	+	0.785409i	0.0418294	+	0.0480663i
$268$	−7.22942	+	26.9806i	−0.441607	+	1.64810i
$269$	−10.9538	−	18.9725i	−0.667865	−	1.15678i	−0.978500	−	0.206247i	$-0.933875\pi$
$269$	−10.9538	−	18.9725i	−0.667865	−	1.15678i	0.310635	−	0.950529i	$-0.399458\pi$
$270$	−23.8717	−	2.91637i	−1.45279	−	0.177485i
$271$	8.64660			0.525243			0.262622	−	0.964899i	$-0.415413\pi$
$271$	8.64660			0.525243			0.262622	+	0.964899i	$0.415413\pi$
$272$	2.59254	−	0.694669i	0.157196	−	0.0421205i
$273$	−0.456889	−	0.525011i	−0.0276522	−	0.0317751i
$274$	9.27188	−	5.35312i	0.560135	−	0.323394i
$275$	20.1037	−	16.7985i	1.21230	−	1.01299i
$276$	1.51385	−	21.8203i	0.0911232	−	1.31342i
$277$	−9.06090	+	9.06090i	−0.544417	+	0.544417i	−0.924820	−	0.380404i	$-0.875785\pi$
$277$	−9.06090	+	9.06090i	−0.544417	+	0.544417i	0.380404	+	0.924820i	$0.375785\pi$
$278$	−7.32757	+	7.32757i	−0.439479	+	0.439479i
$279$	−15.3075	−	6.68425i	−0.916438	−	0.400176i
$280$	1.29773	+	0.606772i	0.0775545	+	0.0362616i
$281$			29.1859i			1.74109i	0.492092	+	0.870543i	$0.336232\pi$
$281$			29.1859i			1.74109i	−0.492092	+	0.870543i	$0.663768\pi$
$282$	−13.9567	+	12.1458i	−0.831112	+	0.723272i
$283$	7.51106	+	7.51106i	0.446486	+	0.446486i	0.894185	−	0.447698i	$-0.147756\pi$
$283$	7.51106	+	7.51106i	0.446486	+	0.446486i	−0.447698	+	0.894185i	$0.647756\pi$
$284$	−6.80650	−	11.7892i	−0.403892	−	0.699561i
$285$	−6.63237	−	23.1722i	−0.392867	−	1.37260i
$286$	−2.00053	+	3.46501i	−0.118294	+	0.204891i
$287$	2.83232	+	2.83232i	0.167186	+	0.167186i
$288$	19.4199	−	14.6672i	1.14433	−	0.864276i
$289$	−14.1668	+	8.17921i	−0.833342	+	0.481130i
$290$	30.9451	+	26.0204i	1.81716	+	1.52797i
$291$	−7.77492	−	0.539411i	−0.455774	−	0.0316208i
$292$	0.641406	+	0.171864i	0.0375354	+	0.0100576i
$293$	4.01677	+	14.9908i	0.234662	+	0.875772i	0.978301	+	0.207190i	$0.0664318\pi$
$293$	4.01677	+	14.9908i	0.234662	+	0.875772i	−0.743638	+	0.668582i	$0.766902\pi$
$294$	9.14693	+	18.7280i	0.533460	+	1.09224i
$295$	4.88739	−	10.4529i	0.284555	−	0.608592i
$296$	−2.21959	−	1.28148i	−0.129011	−	0.0744846i
$297$	12.3206	−	24.2788i	0.714915	−	1.40880i
$298$	44.9711	−	12.0500i	2.60511	−	0.698036i
$299$	−1.01981	−	1.76636i	−0.0589770	−	0.102151i
$300$	12.4723	−	15.3543i	0.720086	−	0.886483i
$301$	−4.42043	−	7.65640i	−0.254789	−	0.441308i
$302$	−24.3884	−	24.3884i	−1.40340	−	1.40340i
$303$	−17.9757	+	15.6432i	−1.03268	+	0.898681i
$304$	18.0596	+	10.4267i	1.03579	+	0.598012i
$305$	−1.31243	+	0.113461i	−0.0751498	+	0.00649673i
$306$	3.05784	−	3.92268i	0.174805	−	0.224245i
$307$	0.133078	+	0.496654i	0.00759517	+	0.0283456i	0.969619	−	0.244618i	$-0.0786627\pi$
$307$	0.133078	+	0.496654i	0.00759517	+	0.0283456i	−0.962024	+	0.272964i	$0.911996\pi$
$308$	−9.21755	+	9.21755i	−0.525219	+	0.525219i
$309$	11.6268	−	5.67864i	0.661427	−	0.323046i
$310$	21.2906	−	14.5176i	1.20922	−	0.824544i
$311$		−	12.6847i		−	0.719286i	−0.933090	−	0.359643i	$-0.882899\pi$
$311$		−	12.6847i		−	0.719286i	0.933090	−	0.359643i	$-0.117101\pi$
$312$	−0.122177	+	0.355457i	−0.00691690	+	0.0201238i
$313$	−30.4778	+	8.16651i	−1.72271	+	0.461598i	−0.978483	−	0.206329i	$-0.933848\pi$
$313$	−30.4778	+	8.16651i	−1.72271	+	0.461598i	−0.744226	+	0.667927i	$0.767182\pi$
$314$	12.1841			0.687587
$315$	−7.14664	+	1.51952i	−0.402667	+	0.0856153i
$316$	3.41734	−	5.91900i	0.192240	−	0.332970i
$317$	4.54615	−	1.21814i	0.255337	−	0.0684173i	−0.128880	−	0.991660i	$-0.541138\pi$
$317$	4.54615	−	1.21814i	0.255337	−	0.0684173i	0.384217	+	0.923243i	$0.374471\pi$
$318$	13.3865	−	38.9462i	0.750677	−	2.18400i
$319$	−39.6395	+	22.8859i	−2.21938	+	1.28136i
$320$	1.94305	+	22.4759i	0.108620	+	1.25644i
$321$	0.812405	+	0.547329i	0.0453440	+	0.0305489i
$322$	−3.22580	−	12.0388i	−0.179767	−	0.670899i
$323$	4.81491	+	1.29015i	0.267909	+	0.0717859i
$324$	5.62331	−	19.7736i	0.312406	−	1.09854i
$325$	0.164556	−	1.83727i	0.00912794	−	0.101913i
$326$			22.7946i			1.26248i
$327$	−22.7071	+	19.7607i	−1.25570	+	1.09277i
$328$	0.559878	−	2.08949i	0.0309141	−	0.115373i
$329$	−2.81049	+	4.86792i	−0.154947	+	0.268377i
$330$	21.6158	+	36.0142i	1.18991	+	1.98252i
$331$	2.00721	+	3.47659i	0.110326	+	0.191091i	0.915902	−	0.401402i	$-0.131477\pi$
$331$	2.00721	+	3.47659i	0.110326	+	0.191091i	−0.805576	+	0.592493i	$0.798144\pi$
$332$	−2.08434	+	7.77888i	−0.114393	+	0.426921i
$333$	12.9723	−	1.60718i	0.710880	−	0.0880729i
$334$	−20.5336	−	11.8551i	−1.12355	−	0.648681i
$335$	26.9236	+	4.77597i	1.47099	+	0.260939i
$336$	3.53203	−	5.24262i	0.192688	−	0.286008i
$337$	−14.0095	+	14.0095i	−0.763148	+	0.763148i	−0.976890	−	0.213742i	$-0.931435\pi$
$337$	−14.0095	+	14.0095i	−0.763148	+	0.763148i	0.213742	+	0.976890i	$0.431435\pi$
$338$	−6.89133	−	25.7188i	−0.374839	−	1.39892i
$339$	−13.8736	−	28.4058i	−0.753511	−	1.54279i
$340$	1.39528	+	3.84583i	0.0756697	+	0.208569i
$341$	7.22956	+	28.2631i	0.391503	+	1.53054i
$342$	38.3502	−	4.75131i	2.07374	−	0.256921i
$343$	9.86862	+	9.86862i	0.532855	+	0.532855i
$344$	−2.38729	+	4.13490i	−0.128714	+	0.222939i
$345$	−21.4089	+	0.363314i	−1.15261	+	0.0195602i
$346$	20.3704	+	35.2827i	1.09512	+	1.89681i
$347$	−2.84243	+	0.761628i	−0.152590	+	0.0408863i	−0.334305	−	0.942465i	$-0.608502\pi$
$347$	−2.84243	+	0.761628i	−0.152590	+	0.0408863i	0.181715	+	0.983351i	$0.441835\pi$
$348$	−26.0712	+	22.6883i	−1.39756	+	1.21622i
$349$			19.2377i			1.02977i	0.857259	+	0.514886i	$0.172166\pi$
$349$			19.2377i			1.02977i	−0.857259	+	0.514886i	$0.827834\pi$
$350$	3.87707	−	10.5842i	0.207238	−	0.565752i
$351$	−0.595367	−	1.82219i	−0.0317783	−	0.0972614i
$352$	−41.0565	−	11.0011i	−2.18832	−	0.586358i
$353$	1.99828	+	7.45768i	0.106358	+	0.396932i	0.998496	−	0.0548307i	$-0.0174619\pi$
$353$	1.99828	+	7.45768i	0.106358	+	0.396932i	−0.892138	+	0.451763i	$0.850795\pi$
$354$	15.3431	+	10.3369i	0.815479	+	0.549400i
$355$	−10.9241	+	7.63236i	−0.579790	+	0.405084i
$356$		−	1.37307i		−	0.0727727i
$357$	0.491174	−	1.42901i	0.0259957	−	0.0756310i
$358$	23.6193	−	6.32877i	1.24832	−	0.334486i
$359$	−6.86628	−	11.8927i	−0.362388	−	0.627675i	0.625965	−	0.779851i	$-0.284705\pi$
$359$	−6.86628	−	11.8927i	−0.362388	−	0.627675i	−0.988353	+	0.152176i	$0.951372\pi$
$360$	2.64049	+	2.93220i	0.139166	+	0.154540i
$361$	9.86462	+	17.0860i	0.519190	+	0.899264i
$362$	−7.89576	+	29.4674i	−0.414992	+	1.54877i
$363$	−27.9725	+	5.45315i	−1.46817	+	0.286216i
$364$			0.917838i			0.0481078i
$365$	0.113539	−	0.640052i	0.00594288	−	0.0335018i
$366$	0.146179	−	2.10699i	0.00764091	−	0.110134i
$367$	2.39441	+	0.641581i	0.124987	+	0.0334902i	0.320770	−	0.947157i	$-0.396058\pi$
$367$	2.39441	+	0.641581i	0.124987	+	0.0334902i	−0.195783	+	0.980647i	$0.562725\pi$
$368$	13.0994	−	13.0994i	0.682855	−	0.682855i
$369$	4.14408	+	10.2248i	0.215732	+	0.532282i
$370$	−8.54143	+	18.2680i	−0.444048	+	0.949708i
$371$		−	12.5117i		−	0.649574i
$372$	9.44144	+	19.9019i	0.489516	+	1.03187i
$373$	14.2368	+	14.2368i	0.737155	+	0.737155i	0.972027	−	0.234871i	$-0.0754668\pi$
$373$	14.2368	+	14.2368i	0.737155	+	0.737155i	−0.234871	+	0.972027i	$0.575467\pi$
$374$	−8.68683			−0.449185
$375$	−16.0266	−	10.8696i	−0.827611	−	0.561301i
$376$	3.03566			0.156552
$377$	−0.834121	+	3.11298i	−0.0429594	+	0.160327i
$378$	−0.632228	−	11.6971i	−0.0325183	−	0.601635i
$379$	24.1349	+	13.9343i	1.23973	+	0.715756i	0.969038	−	0.246912i	$-0.0794158\pi$
$379$	24.1349	+	13.9343i	1.23973	+	0.715756i	0.270687	+	0.962667i	$0.412749\pi$
$380$	−13.4630	+	28.7940i	−0.690639	+	1.47710i
$381$	1.98174	−	2.94151i	0.101527	−	0.150698i
$382$	20.5001	+	5.49297i	1.04887	+	0.281045i
$383$	1.09657	+	0.293826i	0.0560323	+	0.0150138i	0.286726	−	0.958013i	$-0.407433\pi$
$383$	1.09657	+	0.293826i	0.0560323	+	0.0150138i	−0.230694	+	0.973026i	$0.574100\pi$
$384$	−8.04894	−	0.558422i	−0.410746	−	0.0284969i
$385$	9.76702	+	8.21267i	0.497773	+	0.418556i
$386$	11.6482	+	6.72508i	0.592877	+	0.342298i
$387$	−2.99404	−	24.1663i	−0.152195	−	1.22844i
$388$	7.26766	+	7.26766i	0.368959	+	0.368959i
$389$	3.39998	−	5.88895i	0.172386	−	0.298581i	−0.766868	−	0.641805i	$-0.778186\pi$
$389$	3.39998	−	5.88895i	0.172386	−	0.298581i	0.939254	+	0.343224i	$0.111519\pi$
$390$	2.86926	+	0.716863i	0.145290	+	0.0362998i
$391$	2.21414	−	3.83500i	0.111974	−	0.193945i
$392$	0.885088	−	3.30319i	0.0447037	−	0.166836i
$393$	2.41377	+	12.3817i	0.121759	+	0.624575i
$394$	20.6128	−	11.9008i	1.03846	−	0.599554i
$395$	−6.06091	−	2.83386i	−0.304958	−	0.142587i
$396$	−33.2758	+	13.4866i	−1.67217	+	0.677727i
$397$	1.43981	+	5.37343i	0.0722618	+	0.269685i	0.992598	−	0.121442i	$-0.0387520\pi$
$397$	1.43981	+	5.37343i	0.0722618	+	0.269685i	−0.920337	+	0.391127i	$0.872085\pi$
$398$	19.4393	+	5.20875i	0.974405	+	0.261091i
$399$	10.5492	−	5.15234i	0.528123	−	0.257940i
$400$	16.5058	−	2.87535i	0.825288	−	0.143767i
$401$			23.8035i			1.18869i	0.804210	+	0.594345i	$0.202589\pi$
$401$			23.8035i			1.18869i	−0.804210	+	0.594345i	$0.797411\pi$
$402$	−14.2503	+	41.4593i	−0.710740	+	2.06780i
$403$	1.76709	+	1.04721i	0.0880252	+	0.0521652i
$404$	31.4255			1.56348
$405$	−19.7593	−	3.81718i	−0.981847	−	0.189677i
$406$	−9.84681	+	17.0552i	−0.488689	+	0.846435i
$407$	−16.1433	−	16.1433i	−0.800194	−	0.800194i
$408$	−0.800983	+	0.156149i	−0.0396546	+	0.00773053i
$409$	−7.10368	−	4.10131i	−0.351254	−	0.202797i	0.313983	−	0.949429i	$-0.398336\pi$
$409$	−7.10368	−	4.10131i	−0.351254	−	0.202797i	−0.665238	+	0.746632i	$0.731670\pi$
$410$	−16.7591	−	2.97290i	−0.827674	−	0.146821i
$411$	8.05023	−	3.93180i	0.397088	−	0.193941i
$412$	−16.4828	−	4.41655i	−0.812049	−	0.217588i
$413$	5.42907	+	1.45472i	0.267147	+	0.0715819i
$414$	4.74061	−	34.0005i	0.232988	−	1.67103i
$415$	7.76245	+	1.37698i	0.381044	+	0.0675932i
$416$	−2.59182	+	1.49639i	−0.127074	+	0.0733664i
$417$	−6.54147	+	5.69268i	−0.320337	+	0.278772i
$418$	−47.7245	−	47.7245i	−2.33428	−	2.33428i
$419$	−28.1274			−1.37411			−0.687056	−	0.726604i	$-0.741098\pi$
$419$	−28.1274			−1.37411			−0.687056	+	0.726604i	$0.741098\pi$
$420$	8.42512	+	4.67546i	0.411104	+	0.228139i
$421$	−9.53832	−	16.5209i	−0.464869	−	0.805177i	0.534326	−	0.845278i	$-0.320565\pi$
$421$	−9.53832	−	16.5209i	−0.464869	−	0.805177i	−0.999196	+	0.0401011i	$0.987232\pi$
$422$	−16.9512	+	4.54207i	−0.825174	+	0.221105i
$423$	−12.3546	+	9.33101i	−0.600700	+	0.453689i
$424$	−5.85177	+	3.37852i	−0.284187	+	0.164075i
$425$	3.63318	−	1.68507i	0.176235	−	0.0817380i
$426$	−9.37659	−	19.1983i	−0.454297	−	0.930158i
$427$	−0.166074	−	0.619798i	−0.00803690	−	0.0299941i
$428$	−0.334353	−	1.24782i	−0.0161616	−	0.0603158i
$429$	−1.87073	+	2.77674i	−0.0903196	+	0.134062i
$430$	34.0317	+	15.9119i	1.64115	+	0.767342i
$431$	−20.9050	−	12.0695i	−1.00696	−	0.581368i	−0.0966595	−	0.995318i	$-0.530816\pi$
$431$	−20.9050	−	12.0695i	−1.00696	−	0.581368i	−0.910300	+	0.413949i	$0.864149\pi$
$432$	14.5871	−	9.50694i	0.701820	−	0.457403i
$433$	−2.74815	−	2.74815i	−0.132068	−	0.132068i	0.637983	−	0.770051i	$-0.279769\pi$
$433$	−2.74815	−	2.74815i	−0.132068	−	0.132068i	−0.770051	+	0.637983i	$0.779769\pi$
$434$	8.77405	+	8.97596i	0.421168	+	0.430860i
$435$	24.3260	+	23.5142i	1.16634	+	1.12742i
$436$	39.6971			1.90115
$437$	33.2333	−	8.90484i	1.58976	−	0.425976i
$438$	0.985608	+	0.338770i	0.0470942	+	0.0161871i
$439$	11.0040	−	6.35313i	0.525190	−	0.303219i	−0.213866	−	0.976863i	$-0.568605\pi$
$439$	11.0040	−	6.35313i	0.525190	−	0.303219i	0.739055	+	0.673645i	$0.235272\pi$
$440$	1.20372	−	6.78574i	0.0573851	−	0.323497i
$441$	6.55120	+	16.1640i	0.311962	+	0.769713i
$442$	−0.432496	+	0.432496i	−0.0205717	+	0.0205717i
$443$	29.6052	+	7.93269i	1.40659	+	0.376894i	0.880705	−	0.473664i	$-0.157069\pi$
$443$	29.6052	+	7.93269i	1.40659	+	0.376894i	0.525881	+	0.850558i	$0.323736\pi$
$444$	−14.2965	−	9.63179i	−0.678484	−	0.457105i
$445$	−1.33915	+	0.115770i	−0.0634819	+	0.00548804i
$446$	−14.3023	−	8.25746i	−0.677236	−	0.391002i
$447$	38.2399	−	7.45475i	1.80869	−	0.352597i
$448$	−10.6142	+	2.84408i	−0.501476	+	0.134370i
$449$	2.70591			0.127700			0.0638498	−	0.997960i	$-0.479662\pi$
$449$	2.70591			0.127700			0.0638498	+	0.997960i	$0.479662\pi$
$450$	21.1963	−	22.6861i	0.999202	−	1.06943i
$451$	9.63457	−	16.6876i	0.453674	−	0.785787i
$452$	−10.7902	+	40.2695i	−0.507528	+	1.89412i
$453$	−18.9470	−	21.7720i	−0.890208	−	1.02294i
$454$	52.9002	−	30.5419i	2.48273	−	1.43340i
$455$	0.895164	−	0.0773873i	0.0419659	−	0.00362797i
$456$	−5.25837	−	3.54264i	−0.246246	−	0.165900i
$457$	−1.34004	+	1.34004i	−0.0626843	+	0.0626843i	−0.737754	−	0.675070i	$-0.764114\pi$
$457$	−1.34004	+	1.34004i	−0.0626843	+	0.0626843i	0.675070	+	0.737754i	$0.264114\pi$
$458$	−0.543077	−	2.02679i	−0.0253763	−	0.0947057i
$459$	2.77988	−	3.09756i	0.129754	−	0.144582i
$460$	21.6125	+	18.1730i	1.00769	+	0.847322i
$461$		−	24.7389i		−	1.15221i	−0.817377	−	0.576103i	$-0.804573\pi$
$461$		−	24.7389i		−	1.15221i	0.817377	−	0.576103i	$-0.195427\pi$
$462$	−15.4336	+	13.4310i	−0.718036	+	0.624868i
$463$	6.15764	+	6.15764i	0.286170	+	0.286170i	0.835564	−	0.549394i	$-0.185141\pi$
$463$	6.15764	+	6.15764i	0.286170	+	0.286170i	−0.549394	+	0.835564i	$0.685141\pi$
$464$	−29.2720			−1.35892
$465$	18.6142	−	10.8862i	0.863215	−	0.504837i
$466$	19.4360			0.900357
$467$	6.97415	+	6.97415i	0.322725	+	0.322725i	0.849812	−	0.527086i	$-0.176716\pi$
$467$	6.97415	+	6.97415i	0.322725	+	0.322725i	−0.527086	+	0.849812i	$0.676716\pi$
$468$	−0.985258	+	2.32819i	−0.0455436	+	0.107620i
$469$			13.3190i			0.615015i
$470$	−2.05724	−	23.7968i	−0.0948935	−	1.09766i
$471$	10.1713	+	0.705668i	0.468669	+	0.0325155i
$472$	−0.785632	−	2.93202i	−0.0361616	−	0.134957i
$473$	−30.0736	+	30.0736i	−1.38278	+	1.38278i
$474$	5.99365	−	8.89642i	0.275297	−	0.408626i
$475$	29.2179	+	10.7027i	1.34061	+	0.491072i
$476$	−1.72577	+	0.996376i	−0.0791007	+	0.0456688i
$477$	13.4307	−	31.7371i	0.614951	−	1.45314i
$478$	−6.12146	+	22.8456i	−0.279989	+	1.04493i
$479$	−1.48057	+	2.56443i	−0.0676491	+	0.117172i	−0.897866	−	0.440269i	$-0.854883\pi$
$479$	−1.48057	+	2.56443i	−0.0676491	+	0.117172i	0.830217	+	0.557440i	$0.188216\pi$
$480$	0.533099	+	31.4137i	0.0243325	+	1.43383i
$481$	−1.60747			−0.0732943
$482$	51.6732	−	13.8458i	2.35365	−	0.630658i
$483$	−1.99565	−	10.2369i	−0.0908052	−	0.465795i
$484$	32.5486	+	18.7919i	1.47948	+	0.854179i
$485$	6.47535	−	7.70089i	0.294030	−	0.349679i
$486$	10.9526	−	30.3496i	0.496822	−	1.37668i
$487$	−25.0298	−	6.70672i	−1.13421	−	0.303911i	−0.357589	−	0.933879i	$-0.616401\pi$
$487$	−25.0298	−	6.70672i	−1.13421	−	0.303911i	−0.776621	+	0.629968i	$0.783068\pi$
$488$	−0.245037	+	0.245037i	−0.0110923	+	0.0110923i
$489$	−1.32020	+	19.0290i	−0.0597015	+	0.860521i
$490$	−26.4938	−	4.69973i	−1.19687	−	0.212312i
$491$	−27.7147	+	16.0011i	−1.25075	+	0.722120i	−0.971258	−	0.238028i	$-0.923499\pi$
$491$	−27.7147	+	16.0011i	−1.25075	+	0.722120i	−0.279491	+	0.960148i	$0.590166\pi$
$492$	4.72939	−	13.7595i	0.213217	−	0.620328i
$493$	−6.75871	+	1.81099i	−0.304397	+	0.0815629i
$494$	−4.75216			−0.213810
$495$	15.9591	+	31.3167i	0.717307	+	1.40758i
$496$	−5.03341	+	17.9650i	−0.226007	+	0.806653i
$497$	−4.58991	−	4.58991i	−0.205886	−	0.205886i
$498$	−4.10856	+	11.9533i	−0.184109	+	0.535640i
$499$	−0.0332566	−	0.0192007i	−0.00148877	−	0.000859542i	0.499255	−	0.866455i	$-0.333607\pi$
$499$	−0.0332566	−	0.0192007i	−0.00148877	−	0.000859542i	−0.500744	+	0.865595i	$0.666940\pi$
$500$	6.53343	+	24.6881i	0.292184	+	1.10409i
$501$	−16.4549	−	11.0859i	−0.735151	−	0.495282i
$502$	−5.35902	−	20.0001i	−0.239185	−	0.892650i
$503$	−2.65176	−	9.89650i	−0.118236	−	0.441263i	0.881272	−	0.472609i	$-0.156688\pi$
$503$	−2.65176	−	9.89650i	−0.118236	−	0.441263i	−0.999509	+	0.0313452i	$0.990021\pi$
$504$	−1.18165	+	1.51585i	−0.0526350	+	0.0675215i
$505$	−2.64963	−	30.6492i	−0.117907	−	1.36387i
$506$	−51.9251	+	29.9790i	−2.30835	+	1.33273i
$507$	−4.26334	−	21.8692i	−0.189341	−	0.971247i
$508$	−4.51805	+	1.21061i	−0.200456	+	0.0537120i
$509$	1.00953	+	1.74855i	0.0447465	+	0.0775032i	0.887531	−	0.460748i	$-0.152419\pi$
$509$	1.00953	+	1.74855i	0.0447465	+	0.0775032i	−0.842785	+	0.538251i	$0.819085\pi$
$510$	1.76688	+	6.17315i	0.0782390	+	0.273352i
$511$	0.316632			0.0140070
$512$	−22.0085	−	22.0085i	−0.972649	−	0.972649i
$513$	32.2900	−	1.74527i	1.42564	−	0.0770555i
$514$	−19.0643	+	11.0068i	−0.840891	+	0.485489i
$515$	−2.91770	+	16.4480i	−0.128569	+	0.724785i
$516$	−17.9432	+	26.6332i	−0.789905	+	1.17246i
$517$	26.1193	+	6.99865i	1.14873	+	0.307800i
$518$	−9.48811	−	2.54233i	−0.416883	−	0.111704i
$519$	14.9618	+	30.6338i	0.656751	+	1.34468i
$520$	−0.277915	−	0.397775i	−0.0121874	−	0.0174436i
$521$	−34.7176	−	20.0442i	−1.52100	−	0.878152i	−0.999693	−	0.0247854i	$-0.992110\pi$
$521$	−34.7176	−	20.0442i	−1.52100	−	0.878152i	−0.521311	−	0.853367i	$-0.674557\pi$
$522$	−43.2854	+	32.6920i	−1.89455	+	1.43089i
$523$	−32.0949	−	32.0949i	−1.40341	−	1.40341i	−0.788933	−	0.614479i	$-0.789366\pi$
$523$	−32.0949	−	32.0949i	−1.40341	−	1.40341i	−0.614479	−	0.788933i	$-0.710634\pi$
$524$	8.31804	−	14.4073i	0.363375	−	0.629385i
$525$	3.84960	−	8.61120i	0.168010	−	0.375824i
$526$	−48.4998			−2.11469
$527$	−0.0507254	+	4.45941i	−0.00220963	+	0.194255i
$528$	−28.7589	−	9.88491i	−1.25157	−	0.430186i
$529$		−	7.56474i		−	0.328902i
$530$	30.4502	+	43.5829i	1.32267	+	1.89312i
$531$	12.2098	+	9.51790i	0.529861	+	0.413042i
$532$	−14.9552	−	4.00723i	−0.648389	−	0.173735i
$533$	−0.351151	−	1.31051i	−0.0152100	−	0.0567646i
$534$	0.149155	−	2.14988i	0.00645457	−	0.0930343i
$535$	−1.18881	+	0.431303i	−0.0513966	+	0.0186469i
$536$	6.22937	−	3.59653i	0.269068	−	0.155346i
$537$	20.0840	−	3.91531i	0.866689	−	0.168958i
$538$	−11.7361	+	43.7999i	−0.505981	+	1.88835i
$539$	15.2309	−	26.3807i	0.656041	−	1.13630i
$540$	16.3523	+	20.9038i	0.703689	+	0.899555i
$541$	−3.30487	+	5.72420i	−0.142087	+	0.246103i	−0.928283	−	0.371876i	$-0.878715\pi$
$541$	−3.30487	+	5.72420i	−0.142087	+	0.246103i	0.786195	+	0.617978i	$0.212048\pi$
$542$	−12.6551	−	12.6551i	−0.543582	−	0.543582i
$543$	−8.29807	+	24.1421i	−0.356104	+	1.03604i
$544$	−5.62719	−	3.24886i	−0.241264	−	0.139294i
$545$	−3.34705	−	38.7164i	−0.143372	−	1.65843i
$546$	−0.0997035	+	1.43710i	−0.00426692	+	0.0615021i
$547$	−8.45925	−	2.26665i	−0.361691	−	0.0969149i	0.0733967	−	0.997303i	$-0.476616\pi$
$547$	−8.45925	−	2.26665i	−0.361691	−	0.0969149i	−0.435088	+	0.900388i	$0.643283\pi$
$548$	−11.4124	−	3.05795i	−0.487515	−	0.130629i
$549$	0.244062	−	1.75045i	0.0104163	−	0.0747074i
$550$	−54.0097	−	4.83741i	−2.30298	−	0.206268i
$551$	−47.0809	−	27.1822i	−2.00572	−	1.15800i
$552$	−4.24895	+	3.69763i	−0.180848	+	0.157382i
$553$	0.843489	−	3.14794i	0.0358688	−	0.133864i
$554$	26.5229			1.12685
$555$	−8.18844	+	14.7555i	−0.347580	+	0.626335i
$556$	11.4360			0.484993
$557$	−28.0900	−	28.0900i	−1.19021	−	1.19021i	−0.977008	−	0.213202i	$-0.931611\pi$
$557$	−28.0900	−	28.0900i	−1.19021	−	1.19021i	−0.213202	−	0.977008i	$-0.568389\pi$
$558$	12.6210	+	32.1869i	0.534288	+	1.36258i
$559$			2.99457i			0.126657i
$560$	2.78329	+	7.67162i	0.117616	+	0.324185i
$561$	−7.25179	−	0.503117i	−0.306171	−	0.0212416i
$562$	42.7162	−	42.7162i	1.80187	−	1.80187i
$563$	−4.58833	−	1.22944i	−0.193375	−	0.0518147i	0.160832	−	0.986982i	$-0.448582\pi$
$563$	−4.58833	−	1.22944i	−0.193375	−	0.0518147i	−0.354207	+	0.935167i	$0.615249\pi$
$564$	20.3688	+	1.41315i	0.857681	+	0.0595045i
$565$	40.1845	+	7.12832i	1.69057	+	0.299891i
$566$		−	21.9862i		−	0.924150i
$567$	0.149679	−	9.80141i	0.00628594	−	0.411620i
$568$	−0.907311	+	3.38613i	−0.0380699	+	0.142079i
$569$	−2.44435	−	4.23373i	−0.102472	−	0.177487i	0.810230	−	0.586112i	$-0.199342\pi$
$569$	−2.44435	−	4.23373i	−0.102472	−	0.177487i	−0.912703	+	0.408624i	$0.866009\pi$
$570$	−24.2075	+	43.6216i	−1.01394	+	1.82711i
$571$	9.36241	+	16.2162i	0.391805	+	0.678625i	0.992688	−	0.120712i	$-0.0385176\pi$
$571$	9.36241	+	16.2162i	0.391805	+	0.678625i	−0.600883	+	0.799337i	$0.705184\pi$
$572$	4.26496	−	1.14279i	0.178327	−	0.0477826i
$573$	16.7954	+	5.77285i	0.701636	+	0.241164i
$574$		−	8.29069i		−	0.346047i
$575$	15.9018	−	22.6108i	0.663152	−	0.942937i
$576$	−29.9771	−	4.17964i	−1.24904	−	0.174152i
$577$	−4.18230	−	15.6086i	−0.174111	−	0.649793i	−0.996701	−	0.0811576i	$-0.974138\pi$
$577$	−4.18230	−	15.6086i	−0.174111	−	0.649793i	0.822590	−	0.568635i	$-0.192528\pi$
$578$	32.7054	+	8.76338i	1.36036	+	0.364509i
$579$	9.33443	+	6.28875i	0.387926	+	0.261351i
$580$	−3.84292	−	44.4523i	−0.159569	−	1.84578i
$581$			3.84006i			0.159313i
$582$	10.5898	+	12.1688i	0.438962	+	0.504411i
$583$	−58.1387	+	15.5782i	−2.40786	+	0.645184i
$584$	−0.0854998	−	0.148090i	−0.00353801	−	0.00612801i
$585$	2.35374	+	0.764618i	0.0973153	+	0.0316131i
$586$	16.0615	−	27.8193i	0.663493	−	1.14920i
$587$	8.74190	+	8.74190i	0.360817	+	0.360817i	0.864114	−	0.503297i	$-0.167880\pi$
$587$	8.74190	+	8.74190i	0.360817	+	0.360817i	−0.503297	+	0.864114i	$0.667880\pi$
$588$	7.47649	−	21.7519i	0.308325	−	0.897032i
$589$	−24.7782	+	24.2208i	−1.02097	+	0.998001i
$590$	−22.4519	+	8.14563i	−0.924330	+	0.335350i
$591$	17.8969	−	8.74098i	0.736179	−	0.359556i
$592$	−3.77884	−	14.1028i	−0.155309	−	0.579622i
$593$	−11.0391	+	11.0391i	−0.453322	+	0.453322i	−0.896456	−	0.443134i	$-0.853867\pi$
$593$	−11.0391	+	11.0391i	−0.453322	+	0.453322i	0.443134	+	0.896456i	$0.353867\pi$
$594$	−53.5665	+	17.5018i	−2.19786	+	0.718109i
$595$	1.11727	+	1.59913i	0.0458036	+	0.0655580i
$596$	−44.4957	−	25.6896i	−1.82261	−	1.05229i
$597$	15.9263	+	5.47415i	0.651821	+	0.224042i
$598$	−1.09264	+	4.07780i	−0.0446815	+	0.166754i
$599$	8.91034	+	15.4332i	0.364067	+	0.630582i	0.988626	−	0.150396i	$-0.0480547\pi$
$599$	8.91034	+	15.4332i	0.364067	+	0.630582i	−0.624559	+	0.780977i	$0.714721\pi$
$600$	−5.06700	+	0.524803i	−0.206859	+	0.0214250i
$601$	−8.64173	+	14.9679i	−0.352504	+	0.610554i	−0.986687	−	0.162628i	$-0.948003\pi$
$601$	−8.64173	+	14.9679i	−0.352504	+	0.610554i	0.634184	+	0.773182i	$0.281336\pi$
$602$	−4.73614	+	17.6755i	−0.193031	+	0.720400i
$603$	−14.2974	+	33.7850i	−0.582234	+	1.37583i
$604$			38.0624i			1.54874i
$605$	15.5834	−	33.3289i	0.633554	−	1.35501i
$606$	49.2043	+	3.41371i	1.99879	+	0.138673i
$607$	−31.0177	−	8.31116i	−1.25897	−	0.337339i	−0.433173	−	0.901311i	$-0.642606\pi$
$607$	−31.0177	−	8.31116i	−1.25897	−	0.337339i	−0.825794	+	0.563971i	$0.809273\pi$
$608$	−13.0663	−	48.7640i	−0.529907	−	1.97764i
$609$	−9.20793	+	13.6674i	−0.373124	+	0.553831i
$610$	2.08692	+	1.75481i	0.0844971	+	0.0710500i
$611$	1.64886	−	0.951971i	0.0667058	−	0.0385126i
$612$	−5.44716	+	0.674864i	−0.220188	+	0.0272797i
$613$	23.9772	−	6.42468i	0.968432	−	0.259490i	0.260266	−	0.965537i	$-0.416190\pi$
$613$	23.9772	−	6.42468i	0.968432	−	0.259490i	0.708166	+	0.706046i	$0.249523\pi$
$614$	0.532126	−	0.921670i	0.0214749	−	0.0371956i
$615$	−13.8184	−	3.45242i	−0.557211	−	0.139215i
$616$	3.35688			0.135253
$617$	−5.37312	+	1.43972i	−0.216314	+	0.0579611i	−0.365348	−	0.930871i	$-0.619050\pi$
$617$	−5.37312	+	1.43972i	−0.216314	+	0.0579611i	0.149035	+	0.988832i	$0.452383\pi$
$618$	−25.3281	−	8.70569i	−1.01884	−	0.350194i
$619$		−	27.4752i		−	1.10432i	−0.833737	−	0.552161i	$-0.813803\pi$
$619$		−	27.4752i		−	1.10432i	0.833737	−	0.552161i	$-0.186197\pi$
$620$	−27.9424	−	5.28521i	−1.12220	−	0.212259i
$621$	5.92669	−	28.1091i	0.237830	−	1.12798i
$622$	−18.5652	+	18.5652i	−0.744399	+	0.744399i
$623$	−0.169455	−	0.632415i	−0.00678907	−	0.0253372i
$624$	−1.92398	+	0.939687i	−0.0770207	+	0.0376176i
$625$	23.5274	−	8.45360i	0.941094	−	0.338144i
$626$	56.5594	+	32.6546i	2.26057	+	1.30514i
$627$	−37.0764	−	42.6046i	−1.48069	−	1.70146i
$628$	−9.50769	−	9.50769i	−0.379398	−	0.379398i
$629$	−1.74502	−	3.02246i	−0.0695784	−	0.120513i
$630$	12.6837	+	8.23578i	0.505330	+	0.328121i
$631$	13.9380	+	24.1413i	0.554863	+	0.961051i	0.997914	+	0.0645548i	$0.0205627\pi$
$631$	13.9380	+	24.1413i	0.554863	+	0.961051i	−0.443051	+	0.896496i	$0.646104\pi$
$632$	−1.70007	+	0.455533i	−0.0676253	+	0.0181201i
$633$	−14.4140	+	2.80996i	−0.572905	+	0.111686i
$634$	−8.43654	−	4.87084i	−0.335058	−	0.193446i
$635$	1.56164	+	4.30436i	0.0619718	+	0.170813i
$636$	−40.8372	+	19.9452i	−1.61930	+	0.790880i
$637$	−0.555120	−	2.07174i	−0.0219947	−	0.0820852i
$638$	91.5114	+	24.5204i	3.62297	+	0.970772i
$639$	−6.71569	−	16.5698i	−0.265669	−	0.655492i
$640$	6.70357	−	7.97230i	0.264982	−	0.315133i
$641$	30.8942	−	17.8368i	1.22025	−	0.704510i	0.255276	−	0.966868i	$-0.417834\pi$
$641$	30.8942	−	17.8368i	1.22025	−	0.704510i	0.964970	+	0.262358i	$0.0845003\pi$
$642$	−0.387962	−	1.99009i	−0.0153116	−	0.0785426i
$643$	24.8716	+	24.8716i	0.980839	+	0.980839i	0.999820	−	0.0189813i	$-0.00604229\pi$
$643$	24.8716	+	24.8716i	0.980839	+	0.980839i	−0.0189813	+	0.999820i	$0.506042\pi$
$644$	−6.87715	+	11.9116i	−0.270998	+	0.469382i
$645$	27.4882	+	15.2544i	1.08234	+	0.600640i
$646$	−5.15880	−	8.93530i	−0.202970	−	0.351555i
$647$	4.61133	+	4.61133i	0.181290	+	0.181290i	0.791918	−	0.610628i	$-0.209083\pi$
$647$	4.61133	+	4.61133i	0.181290	+	0.181290i	−0.610628	+	0.791918i	$0.709083\pi$
$648$	−4.62458	+	2.57666i	−0.181671	+	0.101221i
$649$		−	27.0388i		−	1.06137i
$650$	−2.92985	+	2.44816i	−0.114918	+	0.0960249i
$651$	6.80474	+	8.00132i	0.266699	+	0.313596i
$652$	17.7875	−	17.7875i	0.696611	−	0.696611i
$653$	12.4508	−	12.4508i	0.487236	−	0.487236i	−0.420197	−	0.907433i	$-0.638039\pi$
$653$	12.4508	−	12.4508i	0.487236	−	0.487236i	0.907433	+	0.420197i	$0.138039\pi$
$654$	62.1554	+	4.31224i	2.43047	+	0.168622i
$655$	−14.7527	−	6.89781i	−0.576435	−	0.269520i
$656$	10.6720	−	6.16151i	0.416673	−	0.240566i
$657$	0.803167	+	0.339890i	0.0313345	+	0.0132604i
$658$	11.2380	−	3.01122i	0.438104	−	0.117390i
$659$	19.2235			0.748841			0.374420	−	0.927259i	$-0.377842\pi$
$659$	19.2235			0.748841			0.374420	+	0.927259i	$0.377842\pi$
$660$	11.2356	−	44.9708i	0.437347	−	1.75049i
$661$	−11.9319	−	20.6667i	−0.464099	−	0.803843i	0.535061	−	0.844813i	$-0.320288\pi$
$661$	−11.9319	−	20.6667i	−0.464099	−	0.803843i	−0.999160	+	0.0409703i	$0.986955\pi$
$662$	2.15057	−	8.02603i	0.0835842	−	0.311941i
$663$	−0.386098	+	0.336000i	−0.0149948	+	0.0130491i
$664$	1.79601	−	1.03693i	0.0696988	−	0.0402406i
$665$	−2.64729	+	14.9236i	−0.102658	+	0.578712i
$666$	−21.3384	−	16.6339i	−0.826847	−	0.644552i
$667$	−34.1500	+	34.1500i	−1.32229	+	1.32229i
$668$	6.77218	+	25.2741i	0.262023	+	0.977885i
$669$	−11.4614	−	7.72170i	−0.443123	−	0.298538i
$670$	−32.4150	−	46.3951i	−1.25230	−	1.79240i
$671$	−2.67327	+	1.54341i	−0.103200	+	0.0595828i
$672$	−15.0208	+	2.92826i	−0.579441	+	0.112960i
$673$	7.07964	−	26.4216i	0.272900	−	1.01848i	−0.684335	−	0.729168i	$-0.739907\pi$
$673$	7.07964	−	26.4216i	0.272900	−	1.01848i	0.957235	−	0.289310i	$-0.0934258\pi$
$674$	41.0084			1.57958
$675$	19.0086	−	17.7108i	0.731642	−	0.681689i
$676$	−14.6918	+	25.4469i	−0.565068	+	0.978726i
$677$	−12.1673	+	45.4091i	−0.467628	+	1.74521i	0.180398	+	0.983594i	$0.442261\pi$
$677$	−12.1673	+	45.4091i	−0.467628	+	1.74521i	−0.648026	+	0.761618i	$0.724405\pi$
$678$	−21.2691	+	61.8796i	−0.816835	+	2.37647i
$679$	4.24429	+	2.45044i	0.162881	+	0.0940394i
$680$	0.446225	−	0.954364i	0.0171120	−	0.0365982i
$681$	45.9301	−	22.4326i	1.76004	−	0.859621i
$682$	30.7845	−	51.9467i	1.17880	−	1.98914i
$683$	−18.1965	+	18.1965i	−0.696269	+	0.696269i	−0.963604	−	0.267335i	$-0.913857\pi$
$683$	−18.1965	+	18.1965i	−0.696269	+	0.696269i	0.267335	+	0.963604i	$0.413857\pi$
$684$	−33.6337	−	26.2184i	−1.28602	−	1.00249i
$685$	−2.02017	+	11.3883i	−0.0771869	+	0.435126i
$686$		−	28.8872i		−	1.10292i
$687$	−0.335976	−	1.72342i	−0.0128183	−	0.0657527i
$688$	−26.2723	+	7.03964i	−1.00162	+	0.268384i
$689$	−2.11898	+	3.67018i	−0.0807267	+	0.139823i
$690$	31.8655	+	30.8020i	1.21310	+	1.17261i
$691$	−8.44230	−	14.6225i	−0.321160	−	0.556266i	0.659568	−	0.751645i	$-0.270739\pi$
$691$	−8.44230	−	14.6225i	−0.321160	−	0.556266i	−0.980728	+	0.195380i	$0.937406\pi$
$692$	11.6365	−	43.4282i	0.442355	−	1.65089i
$693$	−13.6619	+	10.3184i	−0.518973	+	0.391963i
$694$	5.27487	+	3.04545i	0.200231	+	0.115604i
$695$	−0.964220	−	11.1534i	−0.0365750	−	0.423074i
$696$	8.87872	+	0.615991i	0.336547	+	0.0233491i
$697$	2.08291	−	2.08291i	0.0788957	−	0.0788957i
$698$	28.1561	−	28.1561i	1.06572	−	1.06572i
$699$	16.2253	+	1.12568i	0.613696	+	0.0425772i
$700$	−11.2847	+	5.23386i	−0.426522	+	0.197821i
$701$	−5.69056	−	3.28545i	−0.214929	−	0.124090i	0.388671	−	0.921377i	$-0.372934\pi$
$701$	−5.69056	−	3.28545i	−0.214929	−	0.124090i	−0.603600	+	0.797287i	$0.706268\pi$
$702$	−1.79557	+	3.53831i	−0.0677694	+	0.133545i
$703$	7.01812	−	26.1920i	0.264693	−	0.987849i
$704$	26.4315	+	45.7806i	0.996173	+	1.72542i
$705$	−0.339147	−	19.9848i	−0.0127730	−	0.752669i
$706$	7.99032	−	13.8396i	0.300720	−	0.520862i
$707$	14.4741	−	3.87832i	0.544354	−	0.145859i
$708$	−3.90656	−	20.0391i	−0.146817	−	0.753115i
$709$		−	6.48557i		−	0.243571i	−0.992556	−	0.121785i	$-0.961138\pi$
$709$		−	6.48557i		−	0.243571i	0.992556	−	0.121785i	$-0.0388619\pi$
$710$	27.1590	+	4.81773i	1.01926	+	0.180806i
$711$	5.51877	−	7.07962i	0.206970	−	0.265506i
$712$	−0.250025	+	0.250025i	−0.00937010	+	0.00937010i
$713$	15.0866	+	26.8310i	0.564997	+	1.00483i
$714$	−2.81035	+	1.37260i	−0.105175	+	0.0513683i
$715$	−1.47416	−	4.06325i	−0.0551305	−	0.151957i
$716$	−23.3696	−	13.4924i	−0.873363	−	0.504236i
$717$	−6.43336	+	18.7170i	−0.240258	+	0.699000i
$718$	−7.35668	+	27.4555i	−0.274549	+	1.02463i
$719$	−14.8228	+	25.6738i	−0.552797	+	0.957472i	0.445275	+	0.895394i	$0.353106\pi$
$719$	−14.8228	+	25.6738i	−0.552797	+	0.957472i	−0.998071	+	0.0620777i	$0.980227\pi$
$720$	−1.17505	+	22.4476i	−0.0437915	+	0.836571i
$721$	−8.13678			−0.303029
$722$	10.5692	−	39.4447i	0.393344	−	1.46798i
$723$	43.9388	−	8.56573i	1.63410	−	0.318563i
$724$	29.1558	−	16.8331i	1.08357	−	0.625598i
$725$	−43.0302	+	7.49598i	−1.59810	+	0.278394i
$726$	48.9214	+	32.9590i	1.81564	+	1.22323i
$727$	−12.5641	−	46.8897i	−0.465975	−	1.73904i	−0.653635	−	0.756810i	$-0.726757\pi$
$727$	−12.5641	−	46.8897i	−0.465975	−	1.73904i	0.187660	−	0.982234i	$-0.439910\pi$
$728$	0.167131	−	0.167131i	0.00619428	−	0.00619428i
$729$	10.9011	−	24.7016i	0.403743	−	0.914873i
$730$	−1.10295	+	0.770599i	−0.0408219	+	0.0285211i
$731$	−5.63058	+	3.25082i	−0.208254	+	0.120236i
$732$	−1.75823	+	1.53009i	−0.0649860	+	0.0565538i
$733$	4.23275	−	15.7968i	0.156340	−	0.583469i	−0.842647	−	0.538467i	$-0.819004\pi$
$733$	4.23275	−	15.7968i	0.156340	−	0.583469i	0.998987	−	0.0450023i	$-0.0143295\pi$
$734$	−2.56542	−	4.44345i	−0.0946915	−	0.164011i
$735$	−21.8449	−	5.45779i	−0.805761	−	0.201314i
$736$	−44.8483			−1.65313
$737$	61.8902	−	16.5834i	2.27976	−	0.610859i
$738$	8.89969	−	21.0302i	0.327602	−	0.774131i
$739$	35.8225	−	20.6821i	1.31775	−	0.760804i	0.334385	−	0.942437i	$-0.391472\pi$
$739$	35.8225	−	20.6821i	1.31775	−	0.760804i	0.983366	+	0.181633i	$0.0581382\pi$
$740$	20.9204	−	7.59000i	0.769049	−	0.279014i
$741$	−3.96712	−	0.275232i	−0.145736	−	0.0101109i
$742$	−18.3120	+	18.3120i	−0.672253	+	0.672253i
$743$	3.45238	−	3.45238i	0.126656	−	0.126656i	−0.640937	−	0.767593i	$-0.721454\pi$
$743$	3.45238	−	3.45238i	0.126656	−	0.126656i	0.767593	+	0.640937i	$0.221454\pi$
$744$	1.90477	−	5.34320i	0.0698324	−	0.195891i
$745$	−21.3033	+	45.5625i	−0.780493	+	1.66928i
$746$		−	41.6738i		−	1.52578i
$747$	−4.12214	+	9.74069i	−0.150821	+	0.356393i
$748$	6.77866	+	6.77866i	0.247852	+	0.247852i
$749$	−0.307995	−	0.533464i	−0.0112539	−	0.0194923i
$750$	7.54783	+	39.3650i	0.275608	+	1.43741i
$751$	−24.7337	+	42.8400i	−0.902544	+	1.56325i	−0.0783635	+	0.996925i	$0.524969\pi$
$751$	−24.7337	+	42.8400i	−0.902544	+	1.56325i	−0.824180	+	0.566327i	$0.808364\pi$
$752$	12.2281	+	12.2281i	0.445912	+	0.445912i
$753$	−3.31537	−	17.0065i	−0.120819	−	0.619753i
$754$	5.77694	−	3.33532i	0.210384	−	0.121465i
$755$	37.1221	−	3.20922i	1.35101	−	0.116796i
$756$	−8.63435	+	9.62106i	−0.314028	+	0.349914i
$757$	34.5201	+	9.24962i	1.25465	+	0.336183i	0.824132	−	0.566398i	$-0.191663\pi$
$757$	34.5201	+	9.24962i	1.25465	+	0.336183i	0.430521	+	0.902581i	$0.358330\pi$
$758$	−14.9295	−	55.7176i	−0.542263	−	2.02375i
$759$	−45.0835	+	22.0192i	−1.63643	+	0.799245i
$760$	7.69468	−	2.79166i	0.279115	−	0.101264i
$761$	24.5841	+	14.1936i	0.891172	+	0.514518i	0.874326	−	0.485340i	$-0.161304\pi$
$761$	24.5841	+	14.1936i	0.891172	+	0.514518i	0.0168464	+	0.999858i	$0.494637\pi$
$762$	−7.20561	+	1.40471i	−0.261032	+	0.0508873i
$763$	18.2838	−	4.89914i	0.661920	−	0.177361i
$764$	−11.7106	−	20.2833i	−0.423674	−	0.733825i
$765$	1.11747	+	5.25569i	0.0404021	+	0.190020i
$766$	−1.17489	−	2.03497i	−0.0424506	−	0.0735266i
$767$	−1.34620	−	1.34620i	−0.0486083	−	0.0486083i
$768$	−11.9802	−	13.7665i	−0.432298	−	0.496755i
$769$	−43.0636	−	24.8628i	−1.55291	−	0.896574i	−0.997903	−	0.0647306i	$-0.979381\pi$
$769$	−43.0636	−	24.8628i	−1.55291	−	0.896574i	−0.555010	−	0.831844i	$-0.687285\pi$
$770$	−2.27493	−	26.3149i	−0.0819829	−	0.948322i
$771$	−16.5524	+	8.08435i	−0.596121	+	0.291151i
$772$	−3.84168	−	14.3373i	−0.138265	−	0.516012i
$773$	20.9405	−	20.9405i	0.753178	−	0.753178i	−0.221893	−	0.975071i	$-0.571224\pi$
$773$	20.9405	−	20.9405i	0.753178	−	0.753178i	0.975071	+	0.221893i	$0.0712235\pi$
$774$	−30.9876	+	39.7516i	−1.11382	+	1.42884i
$775$	−2.79868	+	27.6978i	−0.100532	+	0.994934i
$776$		−	2.64676i		−	0.0950133i
$777$	−7.77345	−	2.67187i	−0.278871	−	0.0958527i
$778$	−13.5952	+	3.64282i	−0.487411	+	0.130601i
$779$	22.8865			0.819994
$780$	−1.67959	−	2.79838i	−0.0601390	−	0.100198i
$781$	−15.6133	+	27.0430i	−0.558688	+	0.967676i
$782$	−8.85346	+	2.37228i	−0.316599	+	0.0848325i
$783$	−38.0282	+	24.7844i	−1.35902	+	0.885723i
$784$	16.8710	−	9.74047i	0.602535	−	0.347874i
$785$	−8.47117	+	10.0745i	−0.302349	+	0.359573i
$786$	14.5890	−	21.6545i	0.520371	−	0.772391i
$787$	9.97286	+	37.2192i	0.355494	+	1.32672i	0.879862	+	0.475230i	$0.157635\pi$
$787$	9.97286	+	37.2192i	0.355494	+	1.32672i	−0.524367	+	0.851492i	$0.675698\pi$
$788$	−25.3716	−	6.79829i	−0.903825	−	0.242179i
$789$	−40.4878	−	2.80897i	−1.44140	−	0.100002i
$790$	4.72308	+	13.0183i	0.168040	+	0.463170i
$791$			19.8792i			0.706821i
$792$	8.51507	+	3.60347i	0.302570	+	0.128044i
$793$	−0.0562527	+	0.209938i	−0.00199759	+	0.00745512i
$794$	5.75721	−	9.97178i	0.204316	−	0.353885i
$795$	22.8957	+	38.1467i	0.812026	+	1.35292i
$796$	−11.1046	−	19.2338i	−0.393594	−	0.681724i
$797$	12.5508	−	46.8401i	0.444571	−	1.65916i	−0.272495	−	0.962157i	$-0.587849\pi$
$797$	12.5508	−	46.8401i	0.444571	−	1.65916i	0.717066	−	0.697005i	$-0.245484\pi$
$798$	−22.9807	−	7.89885i	−0.813507	−	0.279616i
$799$	3.57990	+	2.06686i	0.126648	+	0.0731202i
$800$	−33.1774	−	23.3331i	−1.17300	−	0.824950i
$801$	0.249030	−	1.78608i	0.00879904	−	0.0631082i
$802$	34.8385	−	34.8385i	1.23019	−	1.23019i
$803$	−0.394236	−	1.47131i	−0.0139123	−	0.0519214i
$804$	43.4723	−	21.2322i	1.53315	−	0.748803i
$805$	12.1972	+	5.70294i	0.429893	+	0.201002i
$806$	−1.05361	−	4.11898i	−0.0371120	−	0.145085i
$807$	−12.3341	+	35.8845i	−0.434182	+	1.26320i
$808$	−5.72233	−	5.72233i	−0.201311	−	0.201311i
$809$	3.88186	−	6.72359i	0.136479	−	0.236389i	−0.789682	−	0.613516i	$-0.789755\pi$
$809$	3.88186	−	6.72359i	0.136479	−	0.236389i	0.926162	+	0.377127i	$0.123088\pi$
$810$	23.3327	+	34.5063i	0.819827	+	1.21243i
$811$	−14.5961	−	25.2813i	−0.512540	−	0.887745i	−0.999894	−	0.0145407i	$-0.995371\pi$
$811$	−14.5961	−	25.2813i	−0.512540	−	0.887745i	0.487355	−	0.873204i	$-0.337962\pi$
$812$	20.9926	−	5.62496i	0.736697	−	0.197397i
$813$	−9.83153	−	11.2974i	−0.344807	−	0.396218i
$814$			47.2543i			1.65626i
$815$	−18.8478	−	15.8483i	−0.660210	−	0.555142i
$816$	−3.85546	−	2.59748i	−0.134968	−	0.0909301i
$817$	−48.7934	−	13.0741i	−1.70706	−	0.457406i
$818$	4.39423	+	16.3995i	0.153641	+	0.573395i
$819$	−0.166465	+	1.19392i	−0.00581677	+	0.0417189i
$820$	10.7579	+	15.3976i	0.375683	+	0.537709i
$821$			42.1769i			1.47198i	0.676990	+	0.735992i	$0.263284\pi$
$821$			42.1769i			1.47198i	−0.676990	+	0.735992i	$0.736716\pi$
$822$	−17.5368	−	6.02769i	−0.611665	−	0.210240i
$823$	−8.50968	+	2.28016i	−0.296629	+	0.0794814i	−0.404064	−	0.914731i	$-0.632403\pi$
$823$	−8.50968	+	2.28016i	−0.296629	+	0.0794814i	0.107435	+	0.994212i	$0.465736\pi$
$824$	2.19717	+	3.80561i	0.0765420	+	0.132575i
$825$	−44.8072	−	7.16638i	−1.55999	−	0.249501i
$826$	−5.81683	−	10.0750i	−0.202393	−	0.350556i
$827$	−7.60076	+	28.3664i	−0.264304	+	0.986397i	0.698371	+	0.715736i	$0.253909\pi$
$827$	−7.60076	+	28.3664i	−0.264304	+	0.986397i	−0.962675	+	0.270660i	$0.912758\pi$
$828$	−30.2311	+	22.8326i	−1.05060	+	0.793486i
$829$		−	2.36533i		−	0.0821513i	−0.999156	−	0.0410757i	$-0.986922\pi$
$829$		−	2.36533i		−	0.0821513i	0.999156	−	0.0410757i	$-0.0130785\pi$
$830$	−9.34571	−	13.3764i	−0.324394	−	0.464301i
$831$	22.1414	+	1.53613i	0.768075	+	0.0532878i
$832$	3.59526	+	0.963347i	0.124643	+	0.0333981i
$833$	3.29278	−	3.29278i	0.114088	−	0.114088i
$834$	17.9058	+	1.24227i	0.620026	+	0.0430164i
$835$	24.0787	−	8.73586i	0.833279	−	0.302317i
$836$			74.4823i			2.57603i
$837$	8.67182	+	27.6007i	0.299742	+	0.954020i
$838$	41.1669	+	41.1669i	1.42209	+	1.42209i
$839$	28.4695			0.982878			0.491439	−	0.870912i	$-0.336471\pi$
$839$	28.4695			0.982878			0.491439	+	0.870912i	$0.336471\pi$
$840$	−0.682784	−	2.38551i	−0.0235583	−	0.0823080i
$841$	47.3115			1.63143
$842$	−10.2196	+	38.1399i	−0.352189	+	1.31439i
$843$	38.1336	−	33.1856i	1.31339	−	1.14297i
$844$	16.7720	+	9.68334i	0.577317	+	0.333314i
$845$	26.0570	+	12.1833i	0.896388	+	0.419118i
$846$	31.7388	+	4.42527i	1.09120	+	0.152144i
$847$	17.3105	+	4.63834i	0.594797	+	0.159375i
$848$	−37.1809	−	9.96259i	−1.27680	−	0.342117i
$849$	1.27338	−	18.3542i	0.0437023	−	0.629913i
$850$	−7.78374	−	2.85123i	−0.266980	−	0.0977963i
$851$	−20.8615	−	12.0444i	−0.715124	−	0.412877i
$852$	−7.66421	+	22.2980i	−0.262572	+	0.763917i
$853$	19.6468	+	19.6468i	0.672694	+	0.672694i	0.958336	−	0.285643i	$-0.0922070\pi$
$853$	19.6468	+	19.6468i	0.672694	+	0.672694i	−0.285643	+	0.958336i	$0.592207\pi$
$854$	−0.664065	+	1.15019i	−0.0227238	+	0.0393588i
$855$	−22.7349	+	35.0134i	−0.777518	+	1.19743i
$856$	−0.166336	+	0.288102i	−0.00568523	+	0.00984711i
$857$	−7.58274	+	28.2992i	−0.259021	+	0.966681i	0.706788	+	0.707426i	$0.250144\pi$
$857$	−7.58274	+	28.2992i	−0.259021	+	0.966681i	−0.965809	+	0.259255i	$0.916523\pi$
$858$	6.80198	−	1.32602i	0.232216	−	0.0452697i
$859$	33.3554	−	19.2577i	1.13807	−	0.657066i	0.192119	−	0.981372i	$-0.438464\pi$
$859$	33.3554	−	19.2577i	1.13807	−	0.657066i	0.945952	+	0.324306i	$0.105131\pi$
$860$	−14.1395	−	38.9729i	−0.482153	−	1.32896i
$861$	0.480174	−	6.92109i	0.0163643	−	0.235870i
$862$	12.9315	+	48.2612i	0.440450	+	1.64378i
$863$	50.3393	+	13.4884i	1.71357	+	0.459149i	0.976295	−	0.216445i	$-0.0694461\pi$
$863$	50.3393	+	13.4884i	1.71357	+	0.459149i	0.737274	+	0.675594i	$0.236113\pi$
$864$	−41.2451	−	8.69636i	−1.40319	−	0.295856i
$865$	−43.3365	−	7.68744i	−1.47348	−	0.261381i
$866$			8.04432i			0.273357i
$867$	26.7950	+	9.20990i	0.910006	+	0.312785i
$868$	0.157554	−	13.8510i	0.00534772	−	0.470133i
$869$	−15.6779			−0.531837
$870$	−1.18823	−	70.0184i	−0.0402849	−	2.37385i
$871$	2.25571	−	3.90701i	0.0764319	−	0.132384i
$872$	−7.22852	−	7.22852i	−0.244789	−	0.244789i
$873$	8.13562	+	10.7718i	0.275349	+	0.364572i
$874$	−61.6729	−	35.6069i	−2.08612	−	1.20442i
$875$	6.05603	+	10.5646i	0.204731	+	0.357150i
$876$	−0.504751	−	1.03346i	−0.0170540	−	0.0349174i
$877$	−5.48542	−	1.46981i	−0.185229	−	0.0496321i	0.165012	−	0.986292i	$-0.447234\pi$
$877$	−5.48542	−	1.46981i	−0.185229	−	0.0496321i	−0.350241	+	0.936660i	$0.613900\pi$
$878$	−25.4036	−	6.80688i	−0.857331	−	0.229721i
$879$	15.0194	−	22.2934i	0.506591	−	0.751937i
$880$	32.1827	−	22.4851i	1.08488	−	0.757974i
$881$	−44.4747	+	25.6775i	−1.49839	+	0.865097i	−0.999998	−	0.00185450i	$-0.999410\pi$
$881$	−44.4747	+	25.6775i	−1.49839	+	0.865097i	−0.498393	+	0.866951i	$0.666076\pi$
$882$	14.0691	−	33.2457i	0.473733	−	1.11944i
$883$	−23.2658	−	23.2658i	−0.782955	−	0.782955i	0.197373	−	0.980328i	$-0.436759\pi$
$883$	−23.2658	−	23.2658i	−0.782955	−	0.782955i	−0.980328	+	0.197373i	$0.936759\pi$
$884$	0.674985			0.0227022
$885$	−19.2147	+	5.49964i	−0.645894	+	0.184868i
$886$	−31.7197	−	54.9401i	−1.06564	−	1.84575i
$887$	−50.3408	+	13.4888i	−1.69028	+	0.452909i	−0.970462	−	0.241254i	$-0.922441\pi$
$887$	−50.3408	+	13.4888i	−1.69028	+	0.452909i	−0.719818	+	0.694163i	$0.755775\pi$
$888$	0.849414	+	4.35716i	0.0285045	+	0.146217i
$889$	−1.93154	+	1.11517i	−0.0647816	+	0.0374017i
$890$	2.12941	+	1.79053i	0.0713779	+	0.0600186i
$891$	−45.7311	+	11.5081i	−1.53205	+	0.385537i
$892$	4.71705	+	17.6043i	0.157938	+	0.589434i
$893$	8.31250	+	31.0227i	0.278167	+	1.03813i
$894$	−66.8782	−	45.0568i	−2.23674	−	1.50693i
$895$	−11.1887	+	23.9299i	−0.373998	+	0.799888i
$896$	4.39388	+	2.53681i	0.146789	+	0.0847488i
$897$	−1.14832	+	3.34088i	−0.0383412	+	0.111549i
$898$	−3.96033	−	3.96033i	−0.132158	−	0.132158i
$899$	13.1220	−	46.8345i	0.437643	−	1.56202i
$900$	−34.2431	+	1.16256i	−1.14144	+	0.0387521i
$901$	−9.20119			−0.306536
$902$	−38.5248	+	10.3227i	−1.28274	+	0.343708i
$903$	−4.97746	+	14.4813i	−0.165639	+	0.481906i
$904$	9.29757	−	5.36795i	0.309233	−	0.178535i
$905$	−18.8756	−	27.0163i	−0.627445	−	0.898052i
$906$	−4.13467	+	59.5960i	−0.137365	+	1.97994i
$907$	−7.90940	+	7.90940i	−0.262627	+	0.262627i	−0.826121	−	0.563493i	$-0.809457\pi$
$907$	−7.90940	+	7.90940i	−0.262627	+	0.262627i	0.563493	+	0.826121i	$0.309457\pi$
$908$	−65.1130	−	17.4470i	−2.16085	−	0.578998i
$909$	40.8781	+	5.69955i	1.35584	+	0.189042i
$910$	−1.42342	−	1.19689i	−0.0471858	−	0.0396765i
$911$	34.6918	+	20.0293i	1.14939	+	0.663602i	0.948739	−	0.316061i	$-0.102360\pi$
$911$	34.6918	+	20.0293i	1.14939	+	0.663602i	0.200653	+	0.979662i	$0.435694\pi$
$912$	−6.91120	−	35.4517i	−0.228853	−	1.17392i
$913$	17.8438	−	4.78124i	0.590544	−	0.158236i
$914$	3.92253			0.129746
$915$	1.64054	+	1.58579i	0.0542345	+	0.0524244i
$916$	−1.15780	+	2.00536i	−0.0382547	+	0.0662591i
$917$	2.05311	−	7.66231i	0.0677997	−	0.253032i
$918$	−8.60216	+	0.464946i	−0.283914	+	0.0153455i
$919$	−9.20524	+	5.31465i	−0.303653	+	0.175314i	−0.644083	−	0.764956i	$-0.722761\pi$
$919$	−9.20524	+	5.31465i	−0.303653	+	0.175314i	0.340430	+	0.940270i	$0.389427\pi$
$920$	−0.626301	−	7.24463i	−0.0206485	−	0.238848i
$921$	0.497601	−	0.738593i	0.0163965	−	0.0243375i
$922$	−36.2076	+	36.2076i	−1.19243	+	1.19243i
$923$	0.569058	+	2.12375i	0.0187308	+	0.0699042i
$924$	22.5241	+	1.56269i	0.740990	+	0.0514087i
$925$	−9.16640	−	19.7636i	−0.301389	−	0.649824i
$926$		−	18.0245i		−	0.592322i
$927$	−20.6397	−	8.73447i	−0.677898	−	0.286878i
$928$	50.1090	+	50.1090i	1.64491	+	1.64491i
$929$	−46.5452			−1.52710			−0.763549	−	0.645750i	$-0.776545\pi$
$929$	−46.5452			−1.52710			−0.763549	+	0.645750i	$0.776545\pi$
$930$	−43.1766	−	11.3106i	−1.41582	−	0.370890i
$931$	36.1803			1.18576
$932$	−15.1667	−	15.1667i	−0.496801	−	0.496801i
$933$	−16.5736	+	14.4231i	−0.542594	+	0.472190i
$934$		−	20.4146i		−	0.667986i
$935$	6.03966	−	7.18274i	0.197518	−	0.234901i
$936$	0.603352	−	0.244536i	0.0197212	−	0.00799292i
$937$	−2.29325	−	8.55854i	−0.0749173	−	0.279595i	0.918297	−	0.395892i	$-0.129564\pi$
$937$	−2.29325	−	8.55854i	−0.0749173	−	0.279595i	−0.993215	+	0.116296i	$0.962898\pi$
$938$	19.4936	−	19.4936i	0.636488	−	0.636488i
$939$	45.3247	+	30.5359i	1.47912	+	0.996502i
$940$	−16.9642	+	20.1749i	−0.553310	+	0.658031i
$941$	−23.5009	+	13.5682i	−0.766106	+	0.442311i	−0.831484	−	0.555549i	$-0.812508\pi$
$941$	−23.5009	+	13.5682i	−0.766106	+	0.442311i	0.0653778	+	0.997861i	$0.479175\pi$
$942$	−13.8538	−	15.9194i	−0.451381	−	0.518682i
$943$	5.26219	−	19.6388i	0.171361	−	0.639526i
$944$	8.64594	−	14.9752i	0.281402	−	0.487402i
$945$	10.1114	+	7.60986i	0.328923	+	0.247549i
$946$	88.0307			2.86212
$947$	−41.5348	+	11.1292i	−1.34970	+	0.361651i	−0.860024	−	0.510254i	$-0.829552\pi$
$947$	−41.5348	+	11.1292i	−1.34970	+	0.361651i	−0.489676	+	0.871905i	$0.662885\pi$
$948$	−11.6193	+	2.26514i	−0.377376	+	0.0735683i
$949$	−0.0928808	−	0.0536248i	−0.00301504	−	0.00174073i
$950$	−27.0986	−	58.4273i	−0.879196	−	1.89563i
$951$	−6.76074	−	4.55481i	−0.219232	−	0.147700i
$952$	0.495682	+	0.132817i	0.0160651	+	0.00430464i
$953$	1.23383	−	1.23383i	0.0399677	−	0.0399677i	−0.686841	−	0.726808i	$-0.741003\pi$
$953$	1.23383	−	1.23383i	0.0399677	−	0.0399677i	0.726808	+	0.686841i	$0.241003\pi$
$954$	−66.1072	+	26.7930i	−2.14030	+	0.867456i
$955$	−18.7949	+	13.1315i	−0.608188	+	0.424924i
$956$	22.6041	−	13.0505i	0.731068	−	0.422082i
$957$	74.9738	+	25.7698i	2.42356	+	0.833019i
$958$	5.92022	−	1.58632i	0.191273	−	0.0512516i
$959$	−5.63378			−0.181924
$960$	27.1571	−	28.0947i	0.876492	−	0.906754i
$961$	−26.4873	−	16.1067i	−0.854428	−	0.519570i
$962$	2.35267	+	2.35267i	0.0758533	+	0.0758533i
$963$	−0.208611	−	1.68380i	−0.00672240	−	0.0542598i
$964$	−51.1269	−	29.5181i	−1.64669	−	0.950715i
$965$	−13.6592	+	4.95563i	−0.439707	+	0.159527i
$966$	−12.0618	+	17.9034i	−0.388082	+	0.576033i
$967$	−6.48764	−	24.2122i	−0.208629	−	0.778612i	−0.988313	−	0.152439i	$-0.951287\pi$
$967$	−6.48764	−	24.2122i	−0.208629	−	0.778612i	0.779684	−	0.626173i	$-0.215380\pi$
$968$	−2.50498	−	9.34870i	−0.0805130	−	0.300478i
$969$	−3.78907	−	7.75800i	−0.121722	−	0.249223i
$970$	−20.7482	+	1.79369i	−0.666184	+	0.0575919i
$971$	24.3842	−	14.0782i	0.782526	−	0.451792i	−0.0547986	−	0.998497i	$-0.517452\pi$
$971$	24.3842	−	14.0782i	0.782526	−	0.451792i	0.837325	+	0.546706i	$0.184118\pi$
$972$	−32.2297	+	15.1362i	−1.03377	+	0.485492i
$973$	5.26722	−	1.41135i	0.168859	−	0.0452457i
$974$	26.8175	+	46.4493i	0.859288	+	1.48833i
$975$	−2.58764	+	1.87404i	−0.0828707	+	0.0600175i
$976$	−1.97409			−0.0631890
$977$	10.0735	+	10.0735i	0.322279	+	0.322279i	0.849641	−	0.527362i	$-0.176819\pi$
$977$	10.0735	+	10.0735i	0.322279	+	0.322279i	−0.527362	+	0.849641i	$0.676819\pi$
$978$	29.7829	−	25.9184i	0.952351	−	0.828779i
$979$	−2.72769	+	1.57483i	−0.0871773	+	0.0503318i
$980$	17.0067	+	24.3415i	0.543260	+	0.777560i
$981$	51.6378	+	7.19974i	1.64867	+	0.229870i
$982$	63.9821	+	17.1439i	2.04175	+	0.547085i
$983$	13.7907	+	3.69521i	0.439855	+	0.117859i	0.471949	−	0.881626i	$-0.343551\pi$
$983$	13.7907	+	3.69521i	0.439855	+	0.117859i	−0.0320935	+	0.999485i	$0.510217\pi$
$984$	−3.36669	+	1.64432i	−0.107326	+	0.0524189i
$985$	−4.49115	+	25.3180i	−0.143100	+	0.806698i
$986$	12.5425	+	7.24143i	0.399435	+	0.230614i
$987$	9.55594	−	1.86290i	0.304169	−	0.0592968i
$988$	3.70829	+	3.70829i	0.117976	+	0.117976i
$989$	−22.4377	+	38.8632i	−0.713476	+	1.23578i
$990$	22.4773	−	69.1923i	0.714374	−	2.19908i
$991$	39.1284			1.24296			0.621478	−	0.783432i	$-0.286533\pi$
$991$	39.1284			1.24296			0.621478	+	0.783432i	$0.286533\pi$
$992$	39.3697	−	22.1369i	1.24999	−	0.702847i
$993$	2.26015	−	6.57560i	0.0717236	−	0.208670i
$994$			13.4355i			0.426148i
$995$	−17.8224	+	12.4520i	−0.565007	+	0.394755i
$996$	12.5337	−	6.12155i	0.397144	−	0.193969i
$997$	33.5451	+	8.98838i	1.06238	+	0.284665i	0.747360	−	0.664419i	$-0.231321\pi$
$997$	33.5451	+	8.98838i	1.06238	+	0.284665i	0.315023	+	0.949084i	$0.397988\pi$
$998$	0.0205721	+	0.0767760i	0.000651197	+	0.00243030i
$999$	−16.8500	−	15.1219i	−0.533110	−	0.478436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.be.a.98.8	✓	240
3.2	odd	2	inner	465.2.be.a.98.53	yes	240
5.2	odd	4	inner	465.2.be.a.377.53	yes	240
15.2	even	4	inner	465.2.be.a.377.8	yes	240
31.25	even	3	inner	465.2.be.a.428.8	yes	240
93.56	odd	6	inner	465.2.be.a.428.53	yes	240
155.87	odd	12	inner	465.2.be.a.242.53	yes	240
465.242	even	12	inner	465.2.be.a.242.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.be.a.98.8	✓	240	1.1	even	1	trivial
465.2.be.a.98.53	yes	240	3.2	odd	2	inner
465.2.be.a.242.8	yes	240	465.242	even	12	inner
465.2.be.a.242.53	yes	240	155.87	odd	12	inner
465.2.be.a.377.8	yes	240	15.2	even	4	inner
465.2.be.a.377.53	yes	240	5.2	odd	4	inner
465.2.be.a.428.8	yes	240	31.25	even	3	inner
465.2.be.a.428.53	yes	240	93.56	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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46359 - 1.46359i) q^{2} +(-1.13704 - 1.30657i) q^{3} +2.28419i q^{4} +(2.22776 - 0.192591i) q^{5} +(-0.248128 + 3.57645i) q^{6} +(0.281899 + 1.05206i) q^{7} +(0.415932 - 0.415932i) q^{8} +(-0.414276 + 2.97126i) q^{9} +O(q^{10})\)	\(q+(-1.46359 - 1.46359i) q^{2} +(-1.13704 - 1.30657i) q^{3} +2.28419i q^{4} +(2.22776 - 0.192591i) q^{5} +(-0.248128 + 3.57645i) q^{6} +(0.281899 + 1.05206i) q^{7} +(0.415932 - 0.415932i) q^{8} +(-0.414276 + 2.97126i) q^{9} +(-3.54240 - 2.97865i) q^{10} +(4.53767 - 2.61983i) q^{11} +(2.98446 - 2.59721i) q^{12} +(0.0954847 - 0.356354i) q^{13} +(1.12720 - 1.95237i) q^{14} +(-2.78469 - 2.69175i) q^{15} +3.35087 q^{16} +(0.773693 - 0.207310i) q^{17} +(4.95503 - 3.74237i) q^{18} +(5.38952 + 3.11164i) q^{19} +(0.439913 + 5.08862i) q^{20} +(1.05406 - 1.56456i) q^{21} +(-10.4756 - 2.80694i) q^{22} +(3.90927 - 3.90927i) q^{23} +(-1.01638 - 0.0705146i) q^{24} +(4.92582 - 0.858091i) q^{25} +(-0.661306 + 0.381805i) q^{26} +(4.35322 - 2.83716i) q^{27} +(-2.40310 + 0.643909i) q^{28} -8.73564 q^{29} +(0.136021 + 8.01525i) q^{30} +(-1.50212 + 5.36131i) q^{31} +(-5.73615 - 5.73615i) q^{32} +(-8.58251 - 2.94996i) q^{33} +(-1.43579 - 0.828952i) q^{34} +(0.830619 + 2.28944i) q^{35} +(-6.78691 - 0.946284i) q^{36} +(-1.12772 - 4.20871i) q^{37} +(-3.33388 - 12.4422i) q^{38} +(-0.574173 + 0.280431i) q^{39} +(0.846492 - 1.00670i) q^{40} +(3.18486 - 1.83878i) q^{41} +(-3.83259 + 0.747150i) q^{42} +(-7.84045 + 2.10084i) q^{43} +(5.98417 + 10.3649i) q^{44} +(-0.350670 + 6.69903i) q^{45} -11.4431 q^{46} +(3.64923 + 3.64923i) q^{47} +(-3.81007 - 4.37816i) q^{48} +(5.03481 - 2.90685i) q^{49} +(-8.46527 - 5.95348i) q^{50} +(-1.15059 - 0.775168i) q^{51} +(0.813979 + 0.218105i) q^{52} +(-11.0959 - 2.97314i) q^{53} +(-10.5238 - 2.21889i) q^{54} +(9.60428 - 6.71025i) q^{55} +(0.554836 + 0.320335i) q^{56} +(-2.06251 - 10.5799i) q^{57} +(12.7854 + 12.7854i) q^{58} +(2.58021 - 4.46906i) q^{59} +(6.14846 - 6.36074i) q^{60} -0.589128 q^{61} +(10.0452 - 5.64827i) q^{62} +(-3.24272 + 0.401750i) q^{63} +10.0890i q^{64} +(0.144087 - 0.812260i) q^{65} +(8.24375 + 16.8788i) q^{66} +(11.8119 + 3.16499i) q^{67} +(0.473536 + 1.76726i) q^{68} +(-9.55275 - 0.662754i) q^{69} +(2.13512 - 4.56649i) q^{70} +(-5.16123 + 2.97984i) q^{71} +(1.06353 + 1.40815i) q^{72} +(0.0752409 - 0.280803i) q^{73} +(-4.50930 + 7.81034i) q^{74} +(-6.72202 - 5.46027i) q^{75} +(-7.10757 + 12.3107i) q^{76} +(4.03538 + 4.03538i) q^{77} +(1.25079 + 0.429918i) q^{78} +(-2.59130 - 1.49609i) q^{79} +(7.46492 - 0.645345i) q^{80} +(-8.65675 - 2.46184i) q^{81} +(-7.35255 - 1.97011i) q^{82} +(3.40553 + 0.912510i) q^{83} +(3.57374 + 2.40768i) q^{84} +(1.68368 - 0.610844i) q^{85} +(14.5500 + 8.40043i) q^{86} +(9.93278 + 11.4138i) q^{87} +(0.797693 - 2.97703i) q^{88} -0.601121 q^{89} +(10.3179 - 9.29139i) q^{90} +0.401823 q^{91} +(8.92949 + 8.92949i) q^{92} +(8.71292 - 4.13339i) q^{93} -10.6819i q^{94} +(12.6058 + 5.89401i) q^{95} +(-0.972473 + 14.0170i) q^{96} +(3.18173 - 3.18173i) q^{97} +(-11.6233 - 3.11446i) q^{98} +(5.90433 + 14.5679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{6}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^6	\( 240 q - 6 q^{3} - 4 q^{6} + 4 q^{10} + 24 q^{12} - 4 q^{13} - 24 q^{15} - 216 q^{16} - 6 q^{18} - 4 q^{21} + 8 q^{22} + 48 q^{27} + 16 q^{28} + 60 q^{30} - 24 q^{31} - 4 q^{33} + 12 q^{36} + 12 q^{40} + 70 q^{42} - 4 q^{43} + 38 q^{45} - 96 q^{46} + 48 q^{48} + 4 q^{51} + 20 q^{52} - 52 q^{55} - 34 q^{57} - 104 q^{58} - 96 q^{60} + 16 q^{61} - 64 q^{63} - 208 q^{66} + 8 q^{67} + 96 q^{70} + 64 q^{72} + 12 q^{73} - 12 q^{75} - 12 q^{76} + 76 q^{78} + 12 q^{81} + 52 q^{82} - 56 q^{85} + 22 q^{87} + 48 q^{88} - 80 q^{91} + 6 q^{93} - 68 q^{96} - 144 q^{97}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^6 + 4 * q^10 + 24 * q^12 - 4 * q^13 - 24 * q^15 - 216 * q^16 - 6 * q^18 - 4 * q^21 + 8 * q^22 + 48 * q^27 + 16 * q^28 + 60 * q^30 - 24 * q^31 - 4 * q^33 + 12 * q^36 + 12 * q^40 + 70 * q^42 - 4 * q^43 + 38 * q^45 - 96 * q^46 + 48 * q^48 + 4 * q^51 + 20 * q^52 - 52 * q^55 - 34 * q^57 - 104 * q^58 - 96 * q^60 + 16 * q^61 - 64 * q^63 - 208 * q^66 + 8 * q^67 + 96 * q^70 + 64 * q^72 + 12 * q^73 - 12 * q^75 - 12 * q^76 + 76 * q^78 + 12 * q^81 + 52 * q^82 - 56 * q^85 + 22 * q^87 + 48 * q^88 - 80 * q^91 + 6 * q^93 - 68 * q^96 - 144 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more