LMFDB - Embedded newform 363.2.f.b.215.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(161,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("363.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.f (of order $10$, degree $4$, not 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			215.1
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	363.215
Dual form			363.2.f.b.233.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 1.80902i) q^{2} +(-0.945746 - 1.45106i) q^{3} +(-1.30902 + 0.951057i) q^{4} +(-2.48990 - 0.809017i) q^{5} +(-2.06909 + 2.56378i) q^{6} +(-0.427051 - 0.587785i) q^{7} +(-0.587785 - 0.427051i) q^{8} +(-1.21113 + 2.74466i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 1.80902i) q^{2} +(-0.945746 - 1.45106i) q^{3} +(-1.30902 + 0.951057i) q^{4} +(-2.48990 - 0.809017i) q^{5} +(-2.06909 + 2.56378i) q^{6} +(-0.427051 - 0.587785i) q^{7} +(-0.587785 - 0.427051i) q^{8} +(-1.21113 + 2.74466i) q^{9} +4.97980i q^{10} +(2.61803 + 1.00000i) q^{12} +(2.92705 - 0.951057i) q^{13} +(-0.812299 + 1.11803i) q^{14} +(1.18088 + 4.37811i) q^{15} +(-1.42705 + 4.39201i) q^{16} +(0.812299 - 2.50000i) q^{17} +(5.67702 + 0.577684i) q^{18} +(-2.50000 + 3.44095i) q^{19} +(4.02874 - 1.30902i) q^{20} +(-0.449028 + 1.17557i) q^{21} -1.76393i q^{23} +(-0.0637797 + 1.25679i) q^{24} +(1.50000 + 1.08981i) q^{25} +(-3.44095 - 4.73607i) q^{26} +(5.12808 - 0.838333i) q^{27} +(1.11803 + 0.363271i) q^{28} +(-3.07768 + 2.23607i) q^{29} +(7.22597 - 4.70962i) q^{30} +(-0.263932 - 0.812299i) q^{31} +7.33094 q^{32} -5.00000 q^{34} +(0.587785 + 1.80902i) q^{35} +(-1.02494 - 4.74466i) q^{36} +(-2.42705 + 1.76336i) q^{37} +(7.69421 + 2.50000i) q^{38} +(-4.14828 - 3.34786i) q^{39} +(1.11803 + 1.53884i) q^{40} +(-2.48990 - 1.80902i) q^{41} +(2.39056 + 0.121316i) q^{42} -1.62460i q^{43} +(5.23607 - 5.85410i) q^{45} +(-3.19098 + 1.03681i) q^{46} +(-4.30625 + 5.92705i) q^{47} +(7.72268 - 2.08299i) q^{48} +(2.00000 - 6.15537i) q^{49} +(1.08981 - 3.35410i) q^{50} +(-4.39587 + 1.18567i) q^{51} +(-2.92705 + 4.02874i) q^{52} +(-4.61653 + 1.50000i) q^{53} +(-4.53077 - 8.78402i) q^{54} +0.527864i q^{56} +(7.35738 + 0.373373i) q^{57} +(5.85410 + 4.25325i) q^{58} +(1.53884 + 2.11803i) q^{59} +(-5.70962 - 4.60793i) q^{60} +(4.04508 + 1.31433i) q^{61} +(-1.31433 + 0.954915i) q^{62} +(2.13049 - 0.460226i) q^{63} +(-1.45492 - 4.47777i) q^{64} -8.05748 q^{65} -8.32624 q^{67} +(1.31433 + 4.04508i) q^{68} +(-2.55957 + 1.66823i) q^{69} +(2.92705 - 2.12663i) q^{70} +(-9.82084 - 3.19098i) q^{71} +(1.88399 - 1.09606i) q^{72} +(-8.94427 - 12.3107i) q^{73} +(4.61653 + 3.35410i) q^{74} +(0.162763 - 3.20727i) q^{75} -6.88191i q^{76} +(-3.61803 + 9.47214i) q^{78} +(-10.1631 + 3.30220i) q^{79} +(7.10642 - 9.78115i) q^{80} +(-6.06633 - 6.64828i) q^{81} +(-1.80902 + 5.56758i) q^{82} +(-4.47777 + 13.7812i) q^{83} +(-0.530249 - 1.96589i) q^{84} +(-4.04508 + 5.56758i) q^{85} +(-2.93893 + 0.954915i) q^{86} +(6.15537 + 2.35114i) q^{87} +9.47214i q^{89} +(-13.6679 - 6.03118i) q^{90} +(-1.80902 - 1.31433i) q^{91} +(1.67760 + 2.30902i) q^{92} +(-0.929080 + 1.15121i) q^{93} +(13.2533 + 4.30625i) q^{94} +(9.00854 - 6.54508i) q^{95} +(-6.93320 - 10.6376i) q^{96} +(-2.04508 - 6.29412i) q^{97} -12.3107 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9}+O(q^{10}) $ 8 * q - 6 * q^3 - 6 * q^4 + 10 * q^7 + 10 * q^9	$ 8 q - 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9} + 12 q^{12} + 10 q^{13} - 6 q^{15} + 2 q^{16} - 20 q^{19} + 10 q^{24} + 12 q^{25} - 12 q^{27} + 20 q^{30} - 20 q^{31} - 40 q^{34} - 10 q^{36} - 6 q^{37} - 20 q^{39} + 20 q^{42} + 24 q^{45} - 30 q^{46} + 26 q^{48} + 16 q^{49} - 30 q^{51} - 10 q^{52} + 30 q^{57} + 20 q^{58} + 2 q^{60} + 10 q^{61} + 30 q^{63} - 34 q^{64} - 4 q^{67} - 16 q^{69} + 10 q^{70} + 20 q^{72} + 6 q^{75} - 20 q^{78} - 50 q^{79} - 2 q^{81} - 10 q^{82} - 10 q^{85} - 40 q^{90} - 10 q^{91} + 10 q^{93} + 30 q^{94} - 10 q^{96} + 6 q^{97}+O(q^{100}) $ 8 * q - 6 * q^3 - 6 * q^4 + 10 * q^7 + 10 * q^9 + 12 * q^12 + 10 * q^13 - 6 * q^15 + 2 * q^16 - 20 * q^19 + 10 * q^24 + 12 * q^25 - 12 * q^27 + 20 * q^30 - 20 * q^31 - 40 * q^34 - 10 * q^36 - 6 * q^37 - 20 * q^39 + 20 * q^42 + 24 * q^45 - 30 * q^46 + 26 * q^48 + 16 * q^49 - 30 * q^51 - 10 * q^52 + 30 * q^57 + 20 * q^58 + 2 * q^60 + 10 * q^61 + 30 * q^63 - 34 * q^64 - 4 * q^67 - 16 * q^69 + 10 * q^70 + 20 * q^72 + 6 * q^75 - 20 * q^78 - 50 * q^79 - 2 * q^81 - 10 * q^82 - 10 * q^85 - 40 * q^90 - 10 * q^91 + 10 * q^93 + 30 * q^94 - 10 * q^96 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.587785	−	1.80902i	−0.415627	−	1.27917i	−0.911689	−	0.410881i	$-0.865221\pi$
$2$	−0.587785	−	1.80902i	−0.415627	−	1.27917i	0.496062	−	0.868287i	$-0.334779\pi$
$3$	−0.945746	−	1.45106i	−0.546027	−	0.837768i
$3$	−0.945746	−	1.45106i	−0.546027	−	0.837768i
$4$	−1.30902	+	0.951057i	−0.654508	+	0.475528i
$5$	−2.48990	−	0.809017i	−1.11352	−	0.361803i	−0.306227	−	0.951959i	$-0.599067\pi$
$5$	−2.48990	−	0.809017i	−1.11352	−	0.361803i	−0.807290	+	0.590155i	$0.799067\pi$
$6$	−2.06909	+	2.56378i	−0.844703	+	1.04666i
$7$	−0.427051	−	0.587785i	−0.161410	−	0.222162i	0.720650	−	0.693299i	$-0.243844\pi$
$7$	−0.427051	−	0.587785i	−0.161410	−	0.222162i	−0.882060	+	0.471137i	$0.843844\pi$
$8$	−0.587785	−	0.427051i	−0.207813	−	0.150985i
$9$	−1.21113	+	2.74466i	−0.403710	+	0.914887i
$10$			4.97980i			1.57475i
$11$		0			0
$11$		0			0
$12$	2.61803	+	1.00000i	0.755761	+	0.288675i
$13$	2.92705	−	0.951057i	0.811818	−	0.263776i	0.126450	−	0.991973i	$-0.459642\pi$
$13$	2.92705	−	0.951057i	0.811818	−	0.263776i	0.685368	+	0.728197i	$0.259642\pi$
$14$	−0.812299	+	1.11803i	−0.217096	+	0.298807i
$15$	1.18088	+	4.37811i	0.304902	+	1.13042i
$16$	−1.42705	+	4.39201i	−0.356763	+	1.09800i
$17$	0.812299	−	2.50000i	0.197012	−	0.606339i	−0.802936	−	0.596066i	$-0.796730\pi$
$17$	0.812299	−	2.50000i	0.197012	−	0.606339i	0.999947	−	0.0102734i	$-0.00327020\pi$
$18$	5.67702	+	0.577684i	1.33809	+	0.136161i
$19$	−2.50000	+	3.44095i	−0.573539	+	0.789409i	−0.992968	−	0.118379i	$-0.962230\pi$
$19$	−2.50000	+	3.44095i	−0.573539	+	0.789409i	0.419429	+	0.907788i	$0.362230\pi$
$20$	4.02874	−	1.30902i	0.900854	−	0.292705i
$21$	−0.449028	+	1.17557i	−0.0979859	+	0.256531i
$22$		0			0
$23$		−	1.76393i		−	0.367805i	−0.982944	−	0.183903i	$-0.941127\pi$
$23$		−	1.76393i		−	0.367805i	0.982944	−	0.183903i	$-0.0588731\pi$
$24$	−0.0637797	+	1.25679i	−0.0130190	+	0.256541i
$25$	1.50000	+	1.08981i	0.300000	+	0.217963i
$26$	−3.44095	−	4.73607i	−0.674827	−	0.928819i
$27$	5.12808	−	0.838333i	0.986899	−	0.161337i
$28$	1.11803	+	0.363271i	0.211289	+	0.0686518i
$29$	−3.07768	+	2.23607i	−0.571511	+	0.415227i	−0.835654	−	0.549256i	$-0.814911\pi$
$29$	−3.07768	+	2.23607i	−0.571511	+	0.415227i	0.264142	+	0.964484i	$0.414911\pi$
$30$	7.22597	−	4.70962i	1.31927	−	0.859855i
$31$	−0.263932	−	0.812299i	−0.0474036	−	0.145893i	0.924553	−	0.381053i	$-0.124439\pi$
$31$	−0.263932	−	0.812299i	−0.0474036	−	0.145893i	−0.971957	+	0.235160i	$0.924439\pi$
$32$	7.33094			1.29594
$33$		0			0
$34$	−5.00000			−0.857493
$35$	0.587785	+	1.80902i	0.0993538	+	0.305780i
$36$	−1.02494	−	4.74466i	−0.170823	−	0.790777i
$37$	−2.42705	+	1.76336i	−0.399005	+	0.289894i	−0.769135	−	0.639086i	$-0.779313\pi$
$37$	−2.42705	+	1.76336i	−0.399005	+	0.289894i	0.370131	+	0.928980i	$0.379313\pi$
$38$	7.69421	+	2.50000i	1.24817	+	0.405554i
$39$	−4.14828	−	3.34786i	−0.664257	−	0.536086i
$40$	1.11803	+	1.53884i	0.176777	+	0.243312i
$41$	−2.48990	−	1.80902i	−0.388857	−	0.282521i	0.376130	−	0.926567i	$-0.377255\pi$
$41$	−2.48990	−	1.80902i	−0.388857	−	0.282521i	−0.764987	+	0.644046i	$0.777255\pi$
$42$	2.39056	+	0.121316i	0.368871	+	0.0187195i
$43$		−	1.62460i		−	0.247749i	−0.992298	−	0.123874i	$-0.960468\pi$
$43$		−	1.62460i		−	0.247749i	0.992298	−	0.123874i	$-0.0395320\pi$
$44$		0			0
$45$	5.23607	−	5.85410i	0.780547	−	0.872678i
$46$	−3.19098	+	1.03681i	−0.470485	+	0.152870i
$47$	−4.30625	+	5.92705i	−0.628132	+	0.864549i	−0.997913	−	0.0645695i	$-0.979433\pi$
$47$	−4.30625	+	5.92705i	−0.628132	+	0.864549i	0.369781	+	0.929119i	$0.379433\pi$
$48$	7.72268	−	2.08299i	1.11467	−	0.300654i
$49$	2.00000	−	6.15537i	0.285714	−	0.879338i
$50$	1.08981	−	3.35410i	0.154123	−	0.474342i
$51$	−4.39587	+	1.18567i	−0.615545	+	0.166027i
$52$	−2.92705	+	4.02874i	−0.405909	+	0.558686i
$53$	−4.61653	+	1.50000i	−0.634129	+	0.206041i	−0.608403	−	0.793628i	$-0.708190\pi$
$53$	−4.61653	+	1.50000i	−0.634129	+	0.206041i	−0.0257255	+	0.999669i	$0.508190\pi$
$54$	−4.53077	−	8.78402i	−0.616560	−	1.19535i
$55$		0			0
$56$			0.527864i			0.0705388i
$57$	7.35738	+	0.373373i	0.974509	+	0.0494545i
$58$	5.85410	+	4.25325i	0.768681	+	0.558480i
$59$	1.53884	+	2.11803i	0.200340	+	0.275745i	0.897352	−	0.441315i	$-0.145488\pi$
$59$	1.53884	+	2.11803i	0.200340	+	0.275745i	−0.697012	+	0.717059i	$0.745488\pi$
$60$	−5.70962	−	4.60793i	−0.737109	−	0.594881i
$61$	4.04508	+	1.31433i	0.517920	+	0.168282i	0.556301	−	0.830981i	$-0.312220\pi$
$61$	4.04508	+	1.31433i	0.517920	+	0.168282i	−0.0383811	+	0.999263i	$0.512220\pi$
$62$	−1.31433	+	0.954915i	−0.166920	+	0.121274i
$63$	2.13049	−	0.460226i	0.268416	−	0.0579830i
$64$	−1.45492	−	4.47777i	−0.181864	−	0.559721i
$65$	−8.05748			−0.999407
$66$		0			0
$67$	−8.32624			−1.01721			−0.508606	−	0.860999i	$-0.669839\pi$
$67$	−8.32624			−1.01721			−0.508606	+	0.860999i	$0.669839\pi$
$68$	1.31433	+	4.04508i	0.159386	+	0.490539i
$69$	−2.55957	+	1.66823i	−0.308135	+	0.200831i
$70$	2.92705	−	2.12663i	0.349850	−	0.254181i
$71$	−9.82084	−	3.19098i	−1.16552	−	0.378700i	−0.338550	−	0.940948i	$-0.609937\pi$
$71$	−9.82084	−	3.19098i	−1.16552	−	0.378700i	−0.826968	+	0.562248i	$0.809937\pi$
$72$	1.88399	−	1.09606i	0.222031	−	0.129172i
$73$	−8.94427	−	12.3107i	−1.04685	−	1.44086i	−0.891510	−	0.453001i	$-0.850353\pi$
$73$	−8.94427	−	12.3107i	−1.04685	−	1.44086i	−0.155338	−	0.987861i	$-0.549647\pi$
$74$	4.61653	+	3.35410i	0.536660	+	0.389906i
$75$	0.162763	−	3.20727i	0.0187942	−	0.370344i
$76$		−	6.88191i		−	0.789409i
$77$		0			0
$78$	−3.61803	+	9.47214i	−0.409662	+	1.07251i
$79$	−10.1631	+	3.30220i	−1.14344	+	0.371526i	−0.818669	−	0.574266i	$-0.805287\pi$
$79$	−10.1631	+	3.30220i	−1.14344	+	0.371526i	−0.324772	+	0.945792i	$0.605287\pi$
$80$	7.10642	−	9.78115i	0.794522	−	1.09357i
$81$	−6.06633	−	6.64828i	−0.674036	−	0.738698i
$82$	−1.80902	+	5.56758i	−0.199773	+	0.614837i
$83$	−4.47777	+	13.7812i	−0.491499	+	1.51268i	0.330844	+	0.943686i	$0.392667\pi$
$83$	−4.47777	+	13.7812i	−0.491499	+	1.51268i	−0.822343	+	0.568993i	$0.807333\pi$
$84$	−0.530249	−	1.96589i	−0.0578549	−	0.214496i
$85$	−4.04508	+	5.56758i	−0.438751	+	0.603889i
$86$	−2.93893	+	0.954915i	−0.316913	+	0.102971i
$87$	6.15537	+	2.35114i	0.659925	+	0.252069i
$88$		0			0
$89$			9.47214i			1.00404i	0.864855	+	0.502022i	$0.167410\pi$
$89$			9.47214i			1.00404i	−0.864855	+	0.502022i	$0.832590\pi$
$90$	−13.6679	−	6.03118i	−1.44072	−	0.635742i
$91$	−1.80902	−	1.31433i	−0.189637	−	0.137779i
$92$	1.67760	+	2.30902i	0.174902	+	0.240732i
$93$	−0.929080	+	1.15121i	−0.0963411	+	0.119375i
$94$	13.2533	+	4.30625i	1.36697	+	0.444156i
$95$	9.00854	−	6.54508i	0.924256	−	0.671512i
$96$	−6.93320	−	10.6376i	−0.707617	−	1.08570i
$97$	−2.04508	−	6.29412i	−0.207647	−	0.639072i	−0.999594	−	0.0284822i	$-0.990933\pi$
$97$	−2.04508	−	6.29412i	−0.207647	−	0.639072i	0.791947	−	0.610589i	$-0.209067\pi$
$98$	−12.3107			−1.24357
$99$		0			0
$100$	−3.00000			−0.300000
$101$	−3.85723	−	11.8713i	−0.383808	−	1.18124i	−0.937341	−	0.348413i	$-0.886721\pi$
$101$	−3.85723	−	11.8713i	−0.383808	−	1.18124i	0.553533	−	0.832827i	$-0.313279\pi$
$102$	4.72873	+	7.25528i	0.468214	+	0.718380i
$103$	5.47214	−	3.97574i	0.539186	−	0.391741i	−0.284597	−	0.958647i	$-0.591860\pi$
$103$	5.47214	−	3.97574i	0.539186	−	0.391741i	0.823782	+	0.566906i	$0.191860\pi$
$104$	−2.12663	−	0.690983i	−0.208533	−	0.0677565i
$105$	2.06909	−	2.56378i	0.201923	−	0.250199i
$106$	5.42705	+	7.46969i	0.527122	+	0.725521i
$107$	−0.138757	−	0.100813i	−0.0134142	−	0.00974597i	0.581058	−	0.813862i	$-0.302639\pi$
$107$	−0.138757	−	0.100813i	−0.0134142	−	0.00974597i	−0.594472	+	0.804116i	$0.702639\pi$
$108$	−5.91544	+	5.97449i	−0.569214	+	0.574895i
$109$		−	7.60845i		−	0.728758i	−0.931251	−	0.364379i	$-0.881281\pi$
$109$		−	7.60845i		−	0.728758i	0.931251	−	0.364379i	$-0.118719\pi$
$110$		0			0
$111$	4.85410	+	1.85410i	0.460731	+	0.175984i
$112$	3.19098	−	1.03681i	0.301520	−	0.0979696i
$113$	11.7229	−	16.1353i	1.10280	−	1.51788i	0.271186	−	0.962527i	$-0.412584\pi$
$113$	11.7229	−	16.1353i	1.10280	−	1.51788i	0.831617	−	0.555350i	$-0.187416\pi$
$114$	−3.64912	−	13.5291i	−0.341772	−	1.26712i
$115$	−1.42705	+	4.39201i	−0.133073	+	0.409557i
$116$	1.90211	−	5.85410i	0.176607	−	0.543540i
$117$	−0.934712	+	9.18562i	−0.0864141	+	0.849210i
$118$	2.92705	−	4.02874i	0.269457	−	0.370876i
$119$	−1.81636	+	0.590170i	−0.166505	+	0.0541008i
$120$	1.17557	−	3.07768i	0.107314	−	0.280953i
$121$		0			0
$122$		−	8.09017i		−	0.732450i
$123$	−0.270175	+	5.32385i	−0.0243609	+	0.480036i
$124$	1.11803	+	0.812299i	0.100402	+	0.0729466i
$125$	4.84104	+	6.66312i	0.432996	+	0.595967i
$126$	−2.08482	−	3.58357i	−0.185731	−	0.319250i
$127$	−12.5623	−	4.08174i	−1.11472	−	0.362196i	−0.306972	−	0.951718i	$-0.599316\pi$
$127$	−12.5623	−	4.08174i	−1.11472	−	0.362196i	−0.807752	+	0.589522i	$0.799316\pi$
$128$	4.61653	−	3.35410i	0.408047	−	0.296464i
$129$	−2.35738	+	1.53646i	−0.207556	+	0.135278i
$130$	4.73607	+	14.5761i	0.415381	+	1.27841i
$131$	4.08174			0.356623			0.178312	−	0.983974i	$-0.442936\pi$
$131$	4.08174			0.356623			0.178312	+	0.983974i	$0.442936\pi$
$132$		0			0
$133$	3.09017			0.267952
$134$	4.89404	+	15.0623i	0.422781	+	1.30119i
$135$	−13.4466	−	2.06134i	−1.15730	−	0.177412i
$136$	−1.54508	+	1.12257i	−0.132490	+	0.0962596i
$137$	8.28199	+	2.69098i	0.707579	+	0.229906i	0.640629	−	0.767850i	$-0.278673\pi$
$137$	8.28199	+	2.69098i	0.707579	+	0.229906i	0.0669491	+	0.997756i	$0.478673\pi$
$138$	4.52233	+	3.64973i	0.384967	+	0.310686i
$139$	1.01722	+	1.40008i	0.0862796	+	0.118754i	0.849975	−	0.526823i	$-0.176617\pi$
$139$	1.01722	+	1.40008i	0.0862796	+	0.118754i	−0.763695	+	0.645577i	$0.776617\pi$
$140$	−2.48990	−	1.80902i	−0.210435	−	0.152890i
$141$	12.6731	+	0.643136i	1.06727	+	0.0541618i
$142$			19.6417i			1.64829i
$143$		0			0
$144$	−10.3262	−	9.23607i	−0.860520	−	0.769672i
$145$	9.47214	−	3.07768i	0.786618	−	0.255588i
$146$	−17.0130	+	23.4164i	−1.40801	+	1.93796i
$147$	−10.8233	+	2.91930i	−0.892689	+	0.240780i
$148$	1.50000	−	4.61653i	0.123299	−	0.379476i
$149$	−0.0530006	+	0.163119i	−0.00434198	+	0.0133632i	−0.953204	−	0.302328i	$-0.902236\pi$
$149$	−0.0530006	+	0.163119i	−0.00434198	+	0.0133632i	0.948862	+	0.315691i	$0.102236\pi$
$150$	−5.89768	+	1.59075i	−0.481543	+	0.129884i
$151$	10.3262	−	14.2128i	0.840337	−	1.15663i	−0.145573	−	0.989348i	$-0.546502\pi$
$151$	10.3262	−	14.2128i	0.840337	−	1.15663i	0.985910	−	0.167278i	$-0.0534976\pi$
$152$	2.93893	−	0.954915i	0.238378	−	0.0774538i
$153$	5.87785	+	5.25731i	0.475196	+	0.425028i
$154$		0			0
$155$			2.23607i			0.179605i
$156$	8.61418	+	0.437153i	0.689686	+	0.0350002i
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	0.701028	−	0.713134i	$-0.252725\pi$
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	−0.461601	+	0.887087i	$0.652725\pi$
$158$	11.9475	+	16.4443i	0.950489	+	1.30824i
$159$	6.54264	+	5.28022i	0.518865	+	0.418749i
$160$	−18.2533	−	5.93085i	−1.44305	−	0.468875i
$161$	−1.03681	+	0.753289i	−0.0817123	+	0.0593675i
$162$	−8.46116	+	14.8819i	−0.664771	+	1.16923i
$163$	−3.82624	−	11.7759i	−0.299694	−	0.922364i	−0.981604	−	0.190928i	$-0.938850\pi$
$163$	−3.82624	−	11.7759i	−0.299694	−	0.922364i	0.681910	−	0.731436i	$-0.261150\pi$
$164$	4.97980			0.388857
$165$		0			0
$166$	27.5623			2.13925
$167$	−0.0327561	−	0.100813i	−0.00253475	−	0.00780115i	0.949781	−	0.312915i	$-0.101305\pi$
$167$	−0.0327561	−	0.100813i	−0.00253475	−	0.00780115i	−0.952316	+	0.305114i	$0.901305\pi$
$168$	0.765961	−	0.499225i	0.0590951	−	0.0385161i
$169$	−2.85410	+	2.07363i	−0.219546	+	0.159510i
$170$	12.4495	+	4.04508i	0.954832	+	0.310244i
$171$	−6.41643	−	11.0291i	−0.490677	−	0.843416i
$172$	1.54508	+	2.12663i	0.117812	+	0.162154i
$173$	17.9313	+	13.0279i	1.36329	+	0.990490i	0.998228	+	0.0595081i	$0.0189532\pi$
$173$	17.9313	+	13.0279i	1.36329	+	0.990490i	0.365065	+	0.930982i	$0.381047\pi$
$174$	0.635220	−	12.5171i	0.0481559	−	0.948921i
$175$		−	1.34708i		−	0.101830i
$176$		0			0
$177$	1.61803	−	4.23607i	0.121619	−	0.318402i
$178$	17.1353	−	5.56758i	1.28434	−	0.417308i
$179$	2.31838	−	3.19098i	0.173284	−	0.238505i	−0.713537	−	0.700617i	$-0.752908\pi$
$179$	2.31838	−	3.19098i	0.173284	−	0.238505i	0.886822	+	0.462112i	$0.152908\pi$
$180$	−1.28652	+	12.6429i	−0.0958915	+	0.942347i
$181$	3.78115	−	11.6372i	0.281051	−	0.864986i	−0.706504	−	0.707709i	$-0.749729\pi$
$181$	3.78115	−	11.6372i	0.281051	−	0.864986i	0.987555	−	0.157276i	$-0.0502713\pi$
$182$	−1.31433	+	4.04508i	−0.0974245	+	0.299842i
$183$	−1.91846	−	7.11267i	−0.141816	−	0.525783i
$184$	−0.753289	+	1.03681i	−0.0555332	+	0.0764349i
$185$	7.46969	−	2.42705i	0.549183	−	0.178440i
$186$	2.62866	+	1.00406i	0.192742	+	0.0736210i
$187$		0			0
$188$		−	11.8541i		−	0.864549i
$189$	−2.68271	−	2.65620i	−0.195139	−	0.193210i
$190$	−17.1353	−	12.4495i	−1.24312	−	0.903181i
$191$	−11.6169	−	15.9894i	−0.840573	−	1.15695i	−0.985862	−	0.167560i	$-0.946411\pi$
$191$	−11.6169	−	15.9894i	−0.840573	−	1.15695i	0.145289	−	0.989389i	$-0.453589\pi$
$192$	−5.12151	+	6.34599i	−0.369613	+	0.457983i
$193$	19.2082	+	6.24112i	1.38264	+	0.449246i	0.903535	−	0.428514i	$-0.140963\pi$
$193$	19.2082	+	6.24112i	1.38264	+	0.449246i	0.479101	+	0.877760i	$0.340963\pi$
$194$	−10.1841	+	7.39919i	−0.731176	+	0.531231i
$195$	7.62033	+	11.6919i	0.545703	+	0.837271i
$196$	3.23607	+	9.95959i	0.231148	+	0.711400i
$197$	15.8374			1.12837			0.564186	−	0.825648i	$-0.309190\pi$
$197$	15.8374			1.12837			0.564186	+	0.825648i	$0.309190\pi$
$198$		0			0
$199$	−2.23607			−0.158511			−0.0792553	−	0.996854i	$-0.525254\pi$
$199$	−2.23607			−0.158511			−0.0792553	+	0.996854i	$0.525254\pi$
$200$	−0.416272	−	1.28115i	−0.0294349	−	0.0905912i
$201$	7.87450	+	12.0818i	0.555425	+	0.852187i
$202$	−19.2082	+	13.9556i	−1.35148	+	0.981911i
$203$	2.62866	+	0.854102i	0.184495	+	0.0599462i
$204$	4.62663	−	5.73279i	0.323929	−	0.401375i
$205$	4.73607	+	6.51864i	0.330781	+	0.455281i
$206$	−10.4086	−	7.56231i	−0.725203	−	0.526891i
$207$	4.84140	+	2.13635i	0.336500	+	0.148487i
$208$			14.2128i			0.985484i
$209$		0			0
$210$	−5.85410	−	2.23607i	−0.403971	−	0.154303i
$211$	−6.44427	+	2.09387i	−0.443642	+	0.144148i	−0.522315	−	0.852752i	$-0.674932\pi$
$211$	−6.44427	+	2.09387i	−0.443642	+	0.144148i	0.0786733	+	0.996900i	$0.474932\pi$
$212$	4.61653	−	6.35410i	0.317064	−	0.436402i
$213$	4.65772	+	17.2684i	0.319142	+	1.18321i
$214$	−0.100813	+	0.310271i	−0.00689144	+	0.0212097i
$215$	−1.31433	+	4.04508i	−0.0896364	+	0.275873i
$216$	−3.37222	−	1.69719i	−0.229451	−	0.115479i
$217$	−0.364745	+	0.502029i	−0.0247605	+	0.0340799i
$218$	−13.7638	+	4.47214i	−0.932203	+	0.302891i
$219$	−9.40456	+	24.6215i	−0.635502	+	1.66376i
$220$		0			0
$221$		−	8.09017i		−	0.544204i
$222$	0.500932	−	9.87097i	0.0336204	−	0.662496i
$223$	−5.04508	−	3.66547i	−0.337844	−	0.245458i	0.405908	−	0.913914i	$-0.366955\pi$
$223$	−5.04508	−	3.66547i	−0.337844	−	0.245458i	−0.743752	+	0.668456i	$0.766955\pi$
$224$	−3.13068	−	4.30902i	−0.209178	−	0.287908i
$225$	−4.80786	+	2.79709i	−0.320524	+	0.186472i
$226$	−36.0795	−	11.7229i	−2.39997	−	0.779799i
$227$	−5.11855	+	3.71885i	−0.339730	+	0.246829i	−0.744548	−	0.667569i	$-0.767335\pi$
$227$	−5.11855	+	3.71885i	−0.339730	+	0.246829i	0.404818	+	0.914397i	$0.367335\pi$
$228$	−9.98604	+	6.50854i	−0.661342	+	0.431038i
$229$	7.76393	+	23.8949i	0.513055	+	1.57902i	0.786793	+	0.617217i	$0.211740\pi$
$229$	7.76393	+	23.8949i	0.513055	+	1.57902i	−0.273738	+	0.961804i	$0.588260\pi$
$230$	8.78402			0.579201
$231$		0			0
$232$	2.76393			0.181461
$233$	−2.21238	−	6.80902i	−0.144938	−	0.446074i	0.852065	−	0.523436i	$-0.175350\pi$
$233$	−2.21238	−	6.80902i	−0.144938	−	0.446074i	−0.997003	+	0.0773625i	$0.975350\pi$
$234$	17.1663	−	3.70826i	1.12220	−	0.242417i
$235$	15.5172	−	11.2739i	1.01223	−	0.735430i
$236$	−4.02874	−	1.30902i	−0.262249	−	0.0852097i
$237$	14.4034	+	11.6242i	0.935601	+	0.755074i
$238$	2.13525	+	2.93893i	0.138408	+	0.190502i
$239$	−20.8702	−	15.1631i	−1.34998	−	0.980821i	−0.999012	−	0.0444345i	$-0.985851\pi$
$239$	−20.8702	−	15.1631i	−1.34998	−	0.980821i	−0.350971	−	0.936386i	$-0.614149\pi$
$240$	−20.9139	−	1.06134i	−1.34998	−	0.0685091i
$241$		−	19.5762i		−	1.26101i	−0.776185	−	0.630506i	$-0.782848\pi$
$241$		−	19.5762i		−	1.26101i	0.776185	−	0.630506i	$-0.217152\pi$
$242$		0			0
$243$	−3.90983	+	15.0902i	−0.250816	+	0.968035i
$244$	−6.54508	+	2.12663i	−0.419006	+	0.136143i
$245$	−9.95959	+	13.7082i	−0.636295	+	0.875785i
$246$	9.78975	−	2.64053i	0.624171	−	0.168354i
$247$	−4.04508	+	12.4495i	−0.257383	+	0.792142i
$248$	−0.191758	+	0.590170i	−0.0121766	+	0.0374758i
$249$	24.2321	−	6.53597i	1.53564	−	0.414200i
$250$	9.20820	−	12.6740i	0.582378	−	0.801574i
$251$	4.44501	−	1.44427i	0.280567	−	0.0911616i	−0.165354	−	0.986234i	$-0.552877\pi$
$251$	4.44501	−	1.44427i	0.280567	−	0.0911616i	0.445920	+	0.895073i	$0.352877\pi$
$252$	−2.35114	+	2.62866i	−0.148108	+	0.165590i
$253$		0			0
$254$			25.1246i			1.57646i
$255$	11.9045	+	0.604130i	0.745489	+	0.0378321i
$256$	−16.3992	−	11.9147i	−1.02495	−	0.744669i
$257$	−6.62464	−	9.11803i	−0.413234	−	0.568767i	0.550770	−	0.834657i	$-0.314334\pi$
$257$	−6.62464	−	9.11803i	−0.413234	−	0.568767i	−0.964003	+	0.265890i	$0.914334\pi$
$258$	4.16511	+	3.36144i	0.259309	+	0.209274i
$259$	2.07295	+	0.673542i	0.128807	+	0.0418519i
$260$	10.5474	−	7.66312i	0.654121	−	0.475246i
$261$	−2.40977	−	11.1554i	−0.149161	−	0.690500i
$262$	−2.39919	−	7.38394i	−0.148222	−	0.456181i
$263$	−23.2744			−1.43516			−0.717580	−	0.696476i	$-0.754750\pi$
$263$	−23.2744			−1.43516			−0.717580	+	0.696476i	$0.754750\pi$
$264$		0			0
$265$	12.7082			0.780659
$266$	−1.81636	−	5.59017i	−0.111368	−	0.342755i
$267$	13.7446	−	8.95823i	0.841156	−	0.548235i
$268$	10.8992	−	7.91872i	0.665774	−	0.483713i
$269$	−22.0988	−	7.18034i	−1.34739	−	0.437793i	−0.455575	−	0.890197i	$-0.650566\pi$
$269$	−22.0988	−	7.18034i	−1.34739	−	0.437793i	−0.891813	+	0.452404i	$0.850566\pi$
$270$	4.17473	+	25.5368i	0.254066	+	1.55412i
$271$	13.8820	+	19.1069i	0.843269	+	1.16066i	0.985306	+	0.170799i	$0.0546350\pi$
$271$	13.8820	+	19.1069i	0.843269	+	1.16066i	−0.142036	+	0.989861i	$0.545365\pi$
$272$	9.82084	+	7.13525i	0.595476	+	0.432638i
$273$	−0.196294	+	3.86801i	−0.0118802	+	0.234102i
$274$		−	16.5640i		−	1.00067i
$275$		0			0
$276$	1.76393	−	4.61803i	0.106176	−	0.277973i
$277$	−19.5344	+	6.34712i	−1.17371	+	0.381362i	−0.830027	−	0.557724i	$-0.811675\pi$
$277$	−19.5344	+	6.34712i	−1.17371	+	0.381362i	−0.343684	+	0.939085i	$0.611675\pi$
$278$	1.93487	−	2.66312i	0.116046	−	0.159723i
$279$	2.54914	+	0.259396i	0.152613	+	0.0155296i
$280$	0.427051	−	1.31433i	0.0255212	−	0.0785461i
$281$	5.08580	−	15.6525i	0.303393	−	0.933748i	−0.676879	−	0.736095i	$-0.736668\pi$
$281$	5.08580	−	15.6525i	0.303393	−	0.933748i	0.980272	−	0.197654i	$-0.0633322\pi$
$282$	−6.28562	−	23.3039i	−0.374303	−	1.38773i
$283$	4.67376	−	6.43288i	0.277826	−	0.382395i	−0.647186	−	0.762332i	$-0.724054\pi$
$283$	4.67376	−	6.43288i	0.277826	−	0.382395i	0.925012	+	0.379937i	$0.124054\pi$
$284$	15.8904	−	5.16312i	0.942925	−	0.306375i
$285$	−18.0171	−	6.88191i	−1.06724	−	0.407649i
$286$		0			0
$287$			2.23607i			0.131991i
$288$	−8.87872	+	20.1209i	−0.523184	+	1.18564i
$289$	8.16312	+	5.93085i	0.480183	+	0.348874i
$290$	−11.1352	−	15.3262i	−0.653879	−	0.899988i
$291$	−7.19900	+	8.92018i	−0.422013	+	0.522910i
$292$	23.4164	+	7.60845i	1.37034	+	0.445251i
$293$	7.91872	−	5.75329i	0.462617	−	0.336111i	−0.331940	−	0.943300i	$-0.607703\pi$
$293$	7.91872	−	5.75329i	0.462617	−	0.336111i	0.794557	+	0.607190i	$0.207703\pi$
$294$	11.6428	+	17.8636i	0.679023	+	1.04182i
$295$	−2.11803	−	6.51864i	−0.123317	−	0.379530i
$296$	2.17963			0.126688
$297$		0			0
$298$	0.326238			0.0188985
$299$	−1.67760	−	5.16312i	−0.0970181	−	0.298591i
$300$	2.83724	+	4.35317i	0.163808	+	0.251330i
$301$	−0.954915	+	0.693786i	−0.0550404	+	0.0399892i
$302$	−31.7809	−	10.3262i	−1.82878	−	0.594208i
$303$	−13.5780	+	16.8243i	−0.780036	+	0.966531i
$304$	−11.5451	−	15.8904i	−0.662156	−	0.911380i
$305$	−9.00854	−	6.54508i	−0.515827	−	0.374770i
$306$	6.05565	−	13.7233i	0.346178	−	0.784509i
$307$			5.87785i			0.335467i	0.985832	+	0.167733i	$0.0536448\pi$
$307$			5.87785i			0.335467i	−0.985832	+	0.167733i	$0.946355\pi$
$308$		0			0
$309$	−10.9443	−	4.18034i	−0.622598	−	0.237811i
$310$	4.04508	−	1.31433i	0.229745	−	0.0746488i
$311$	2.93893	−	4.04508i	0.166651	−	0.229376i	−0.717521	−	0.696537i	$-0.754723\pi$
$311$	2.93893	−	4.04508i	0.166651	−	0.229376i	0.884172	+	0.467161i	$0.154723\pi$
$312$	1.00859	+	3.73935i	0.0571003	+	0.211699i
$313$	3.39919	−	10.4616i	0.192133	−	0.591326i	−0.807865	−	0.589368i	$-0.799377\pi$
$313$	3.39919	−	10.4616i	0.192133	−	0.591326i	0.999998	−	0.00195780i	$-0.000623187\pi$
$314$	2.17963	−	6.70820i	0.123004	−	0.378566i
$315$	−5.67702	−	0.577684i	−0.319864	−	0.0325488i
$316$	10.1631	−	13.9883i	0.571720	−	0.786905i
$317$	0.224514	−	0.0729490i	0.0126100	−	0.00409722i	−0.302705	−	0.953084i	$-0.597890\pi$
$317$	0.224514	−	0.0729490i	0.0126100	−	0.00409722i	0.315315	+	0.948987i	$0.397890\pi$
$318$	5.70634	−	14.9394i	0.319996	−	0.837759i
$319$		0			0
$320$			12.3262i			0.689058i
$321$	−0.0150563	+	0.296688i	−0.000840363	+	0.0165595i
$322$	1.97214	+	1.43284i	0.109903	+	0.0798491i
$323$	6.57164	+	9.04508i	0.365656	+	0.503282i
$324$	14.2638	+	2.93329i	0.792434	+	0.162961i
$325$	5.42705	+	1.76336i	0.301039	+	0.0978134i
$326$	−19.0539	+	13.8435i	−1.05530	+	0.766718i
$327$	−11.0403	+	7.19566i	−0.610530	+	0.397921i
$328$	0.690983	+	2.12663i	0.0381532	+	0.117423i
$329$	5.32282			0.293457
$330$		0			0
$331$	−22.8885			−1.25807			−0.629034	−	0.777378i	$-0.716549\pi$
$331$	−22.8885			−1.25807			−0.629034	+	0.777378i	$0.716549\pi$
$332$	−7.24518	−	22.2984i	−0.397631	−	1.22378i
$333$	−1.90034	−	8.79709i	−0.104138	−	0.482077i
$334$	−0.163119	+	0.118513i	−0.00892547	+	0.00648474i
$335$	20.7315	+	6.73607i	1.13268	+	0.368031i
$336$	−4.52233	−	3.64973i	−0.246713	−	0.199109i
$337$	−6.05573	−	8.33499i	−0.329877	−	0.454036i	0.611574	−	0.791187i	$-0.290537\pi$
$337$	−6.05573	−	8.33499i	−0.329877	−	0.454036i	−0.941451	+	0.337151i	$0.890537\pi$
$338$	5.42882	+	3.94427i	0.295289	+	0.214540i
$339$	−34.5001	−	1.75081i	−1.87379	−	0.0950911i
$340$		−	11.1352i		−	0.603889i
$341$		0			0
$342$	−16.1803	+	18.0902i	−0.874933	+	0.978204i
$343$	−9.30902	+	3.02468i	−0.502640	+	0.163318i
$344$	−0.693786	+	0.954915i	−0.0374065	+	0.0514856i
$345$	7.72268	−	2.08299i	0.415775	−	0.112145i
$346$	13.0279	−	40.0956i	0.700382	−	2.15556i
$347$	9.51057	−	29.2705i	0.510554	−	1.57132i	−0.280675	−	0.959803i	$-0.590558\pi$
$347$	9.51057	−	29.2705i	0.510554	−	1.57132i	0.791229	−	0.611520i	$-0.209442\pi$
$348$	−10.2935	+	2.77642i	−0.551792	+	0.148832i
$349$	−9.57295	+	13.1760i	−0.512428	+	0.705297i	−0.984326	−	0.176356i	$-0.943569\pi$
$349$	−9.57295	+	13.1760i	−0.512428	+	0.705297i	0.471898	+	0.881653i	$0.343569\pi$
$350$	−2.43690	+	0.791796i	−0.130258	+	0.0423233i
$351$	14.2128	−	7.33094i	0.758626	−	0.391297i
$352$		0			0
$353$		−	15.5967i		−	0.830131i	−0.909792	−	0.415066i	$-0.863759\pi$
$353$		−	15.5967i		−	0.830131i	0.909792	−	0.415066i	$-0.136241\pi$
$354$	−8.61418	−	0.437153i	−0.457838	−	0.0232344i
$355$	21.8713	+	15.8904i	1.16081	+	0.843377i
$356$	−9.00854	−	12.3992i	−0.477451	−	0.657156i
$357$	2.57418	+	2.07748i	0.136240	+	0.109952i
$358$	−7.13525	−	2.31838i	−0.377110	−	0.122530i
$359$	−20.1967	+	14.6738i	−1.06594	+	0.774452i	−0.975178	−	0.221421i	$-0.928931\pi$
$359$	−20.1967	+	14.6738i	−1.06594	+	0.774452i	−0.0907628	+	0.995873i	$0.528931\pi$
$360$	−5.57768	+	1.20489i	−0.293970	+	0.0635031i
$361$	0.281153	+	0.865300i	0.0147975	+	0.0455421i
$362$	−23.2744			−1.22327
$363$		0			0
$364$	3.61803			0.189637
$365$	12.3107	+	37.8885i	0.644373	+	1.98318i
$366$	−11.7393	+	7.65124i	−0.613623	+	0.399937i
$367$	18.5902	−	13.5065i	0.970399	−	0.705036i	0.0148565	−	0.999890i	$-0.495271\pi$
$367$	18.5902	−	13.5065i	0.970399	−	0.705036i	0.955542	+	0.294854i	$0.0952709\pi$
$368$	7.74721	+	2.51722i	0.403851	+	0.131219i
$369$	7.98073	−	4.64297i	0.415460	−	0.241703i
$370$	−8.78115	−	12.0862i	−0.456510	−	0.628333i
$371$	2.85317	+	2.07295i	0.148129	+	0.107622i
$372$	0.121316	−	2.39056i	0.00628995	−	0.123945i
$373$		−	19.5357i		−	1.01152i	−0.862675	−	0.505759i	$-0.831212\pi$
$373$		−	19.5357i		−	1.01152i	0.862675	−	0.505759i	$-0.168788\pi$
$374$		0			0
$375$	5.09017	−	13.3262i	0.262855	−	0.688164i
$376$	5.06231	−	1.64484i	0.261068	−	0.0848263i
$377$	−6.88191	+	9.47214i	−0.354436	+	0.487840i
$378$	−3.22825	+	6.41434i	−0.166043	+	0.329918i
$379$	−10.1631	+	31.2789i	−0.522044	+	1.60669i	0.248043	+	0.968749i	$0.420213\pi$
$379$	−10.1631	+	31.2789i	−0.522044	+	1.60669i	−0.770087	+	0.637938i	$0.779787\pi$
$380$	−5.56758	+	17.1353i	−0.285611	+	0.879020i
$381$	5.95791	+	22.0889i	0.305233	+	1.13165i
$382$	−22.0967	+	30.4136i	−1.13057	+	1.55609i
$383$	−13.7108	+	4.45492i	−0.700590	+	0.227636i	−0.637588	−	0.770378i	$-0.720068\pi$
$383$	−13.7108	+	4.45492i	−0.700590	+	0.227636i	−0.0630025	+	0.998013i	$0.520068\pi$
$384$	−9.23305	−	3.52671i	−0.471172	−	0.179972i
$385$		0			0
$386$		−	38.4164i		−	1.95534i
$387$	4.45897	+	1.96760i	0.226662	+	0.100019i
$388$	8.66312	+	6.29412i	0.439803	+	0.319536i
$389$	5.65334	+	7.78115i	0.286636	+	0.394520i	0.927918	−	0.372785i	$-0.121597\pi$
$389$	5.65334	+	7.78115i	0.286636	+	0.394520i	−0.641282	+	0.767305i	$0.721597\pi$
$390$	16.6717	−	20.6576i	0.844202	−	1.04604i
$391$	−4.40983	−	1.43284i	−0.223015	−	0.0724619i
$392$	−3.80423	+	2.76393i	−0.192142	+	0.139600i
$393$	−3.86029	−	5.92284i	−0.194726	−	0.298768i
$394$	−9.30902	−	28.6502i	−0.468982	−	1.44338i
$395$	27.9767			1.40766
$396$		0			0
$397$	−23.0000			−1.15434			−0.577168	−	0.816625i	$-0.695842\pi$
$397$	−23.0000			−1.15434			−0.577168	+	0.816625i	$0.695842\pi$
$398$	1.31433	+	4.04508i	0.0658813	+	0.202762i
$399$	−2.92252	−	4.48401i	−0.146309	−	0.224481i
$400$	−6.92705	+	5.03280i	−0.346353	+	0.251640i
$401$	20.1109	+	6.53444i	1.00429	+	0.326314i	0.764580	−	0.644529i	$-0.222947\pi$
$401$	20.1109	+	6.53444i	1.00429	+	0.326314i	0.239713	+	0.970844i	$0.422947\pi$
$402$	17.2277	−	21.3466i	0.859242	−	1.06467i
$403$	−1.54508	−	2.12663i	−0.0769662	−	0.105935i
$404$	16.3395	+	11.8713i	0.812919	+	0.590620i
$405$	9.72597	+	21.4613i	0.483287	+	1.06642i
$406$		−	5.25731i		−	0.260916i
$407$		0			0
$408$	3.09017	+	1.18034i	0.152986	+	0.0584355i
$409$	32.5623	−	10.5801i	1.61010	−	0.523154i	0.640525	−	0.767938i	$-0.278717\pi$
$409$	32.5623	−	10.5801i	1.61010	−	0.523154i	0.969578	+	0.244784i	$0.0787169\pi$
$410$	9.00854	−	12.3992i	0.444900	−	0.612352i
$411$	−3.92789	−	14.5626i	−0.193749	−	0.718321i
$412$	−3.38197	+	10.4086i	−0.166618	+	0.512796i
$413$	0.587785	−	1.80902i	0.0289230	−	0.0890159i
$414$	1.01899	−	10.0139i	0.0500808	−	0.492155i
$415$	22.2984	−	30.6911i	1.09458	−	1.50657i
$416$	21.4580	−	6.97214i	1.05207	−	0.341837i
$417$	1.06957	−	2.80017i	0.0523770	−	0.137125i
$418$		0			0
$419$			5.85410i			0.285992i	0.989723	+	0.142996i	$0.0456735\pi$
$419$			5.85410i			0.285992i	−0.989723	+	0.142996i	$0.954326\pi$
$420$	−0.270175	+	5.32385i	−0.0131832	+	0.259777i
$421$	−20.9164	−	15.1967i	−1.01940	−	0.740640i	−0.0532429	−	0.998582i	$-0.516956\pi$
$421$	−20.9164	−	15.1967i	−1.01940	−	0.740640i	−0.966160	+	0.257942i	$0.916956\pi$
$422$	7.57570	+	10.4271i	0.368779	+	0.507581i
$423$	−11.0523	−	18.9976i	−0.537382	−	0.923697i
$424$	3.35410	+	1.08981i	0.162890	+	0.0529260i
$425$	3.94298	−	2.86475i	0.191263	−	0.138961i
$426$	28.5012	−	18.5760i	1.38089	−	0.900011i
$427$	−0.954915	−	2.93893i	−0.0462116	−	0.142225i
$428$	0.277515			0.0134142
$429$		0			0
$430$	8.09017			0.390143
$431$	6.96767	+	21.4443i	0.335621	+	1.03293i	0.966416	+	0.256985i	$0.0827290\pi$
$431$	6.96767	+	21.4443i	0.335621	+	1.03293i	−0.630795	+	0.775950i	$0.717271\pi$
$432$	−3.63606	+	23.7189i	−0.174940	+	1.14118i
$433$	4.85410	−	3.52671i	0.233273	−	0.169483i	−0.465008	−	0.885307i	$-0.653949\pi$
$433$	4.85410	−	3.52671i	0.233273	−	0.169483i	0.698281	+	0.715824i	$0.253949\pi$
$434$	1.12257	+	0.364745i	0.0538851	+	0.0175083i
$435$	−13.4241	−	10.8339i	−0.643638	−	0.519446i
$436$	7.23607	+	9.95959i	0.346545	+	0.476978i
$437$	6.06961	+	4.40983i	0.290349	+	0.210951i
$438$	50.0685	+	2.54088i	2.39237	+	0.121408i
$439$			25.3480i			1.20979i	0.796304	+	0.604897i	$0.206786\pi$
$439$			25.3480i			1.20979i	−0.796304	+	0.604897i	$0.793214\pi$
$440$		0			0
$441$	14.4721	+	12.9443i	0.689149	+	0.616394i
$442$	−14.6353	+	4.75528i	−0.696128	+	0.226186i
$443$	−6.15537	+	8.47214i	−0.292450	+	0.402523i	−0.929808	−	0.368045i	$-0.880027\pi$
$443$	−6.15537	+	8.47214i	−0.292450	+	0.402523i	0.637358	+	0.770568i	$0.280027\pi$
$444$	−8.11746	+	2.18947i	−0.385237	+	0.103908i
$445$	7.66312	−	23.5847i	0.363267	−	1.11802i
$446$	−3.66547	+	11.2812i	−0.173565	+	0.534178i
$447$	0.286820	−	0.0773622i	0.0135661	−	0.00365911i
$448$	−2.01064	+	2.76741i	−0.0949940	+	0.130748i
$449$	7.50245	−	2.43769i	0.354063	−	0.115042i	−0.126585	−	0.991956i	$-0.540402\pi$
$449$	7.50245	−	2.43769i	0.354063	−	0.115042i	0.480648	+	0.876914i	$0.340402\pi$
$450$	7.88597	+	7.05342i	0.371748	+	0.332502i
$451$		0			0
$452$			32.2705i			1.51788i
$453$	−30.3896	−	1.54222i	−1.42783	−	0.0724596i
$454$	9.73607	+	7.07367i	0.456936	+	0.331984i
$455$	3.44095	+	4.73607i	0.161314	+	0.222030i
$456$	−4.16511	−	3.36144i	−0.195049	−	0.157414i
$457$	−10.2639	−	3.33495i	−0.480126	−	0.156003i	0.0589473	−	0.998261i	$-0.481226\pi$
$457$	−10.2639	−	3.33495i	−0.480126	−	0.156003i	−0.539074	+	0.842259i	$0.681226\pi$
$458$	38.6628	−	28.0902i	1.80659	−	1.31257i
$459$	2.06970	−	13.5012i	0.0966054	−	0.630181i
$460$	−2.30902	−	7.10642i	−0.107658	−	0.331339i
$461$	−26.8666			−1.25130			−0.625651	−	0.780103i	$-0.715167\pi$
$461$	−26.8666			−1.25130			−0.625651	+	0.780103i	$0.715167\pi$
$462$		0			0
$463$	−0.270510			−0.0125717			−0.00628583	−	0.999980i	$-0.502001\pi$
$463$	−0.270510			−0.0125717			−0.00628583	+	0.999980i	$0.502001\pi$
$464$	−5.42882	−	16.7082i	−0.252027	−	0.775659i
$465$	3.24466	−	2.11475i	0.150468	−	0.0980693i
$466$	−11.0172	+	8.00448i	−0.510363	+	0.370800i
$467$	22.4948	+	7.30902i	1.04094	+	0.338221i	0.779106	−	0.626893i	$-0.215674\pi$
$467$	22.4948	+	7.30902i	1.04094	+	0.338221i	0.261831	+	0.965114i	$0.415674\pi$
$468$	−7.51249	−	12.9131i	−0.347265	−	0.596908i
$469$	3.55573	+	4.89404i	0.164188	+	0.225986i
$470$	−29.5155	−	21.4443i	−1.36145	−	0.989151i
$471$	0.325526	−	6.41454i	0.0149994	−	0.295567i
$472$		−	1.90211i		−	0.0875518i
$473$		0			0
$474$	12.5623	−	32.8885i	0.577006	−	1.51062i
$475$	−7.50000	+	2.43690i	−0.344124	+	0.111813i
$476$	1.81636	−	2.50000i	0.0832526	−	0.114587i
$477$	1.47422	−	14.4875i	0.0674999	−	0.663337i
$478$	−15.1631	+	46.6673i	−0.693545	+	2.13451i
$479$	−7.07367	+	21.7705i	−0.323204	+	0.994720i	0.649041	+	0.760754i	$0.275171\pi$
$479$	−7.07367	+	21.7705i	−0.323204	+	0.994720i	−0.972245	+	0.233966i	$0.924829\pi$
$480$	8.65697	+	32.0956i	0.395135	+	1.46496i
$481$	−5.42705	+	7.46969i	−0.247452	+	0.340589i
$482$	−35.4136	+	11.5066i	−1.61305	+	0.524110i
$483$	2.07363	+	0.792055i	0.0943533	+	0.0360397i
$484$		0			0
$485$			17.3262i			0.786744i
$486$	29.5965	−	1.79683i	1.34253	−	0.0815059i
$487$	6.04508	+	4.39201i	0.273929	+	0.199021i	0.716265	−	0.697828i	$-0.245850\pi$
$487$	6.04508	+	4.39201i	0.273929	+	0.199021i	−0.442336	+	0.896849i	$0.645850\pi$
$488$	−1.81636	−	2.50000i	−0.0822226	−	0.113170i
$489$	−13.4689	+	16.6891i	−0.609086	+	0.754709i
$490$	30.6525	+	9.95959i	1.38474	+	0.449929i
$491$	21.5968	−	15.6910i	0.974649	−	0.708124i	0.0181429	−	0.999835i	$-0.494225\pi$
$491$	21.5968	−	15.6910i	0.974649	−	0.708124i	0.956506	+	0.291711i	$0.0942246\pi$
$492$	−4.70962	−	7.22597i	−0.212326	−	0.325772i
$493$	3.09017	+	9.51057i	0.139174	+	0.428334i
$494$	24.8990			1.12026
$495$		0			0
$496$	3.94427			0.177103
$497$	2.31838	+	7.13525i	0.103994	+	0.320060i
$498$	−26.0669	−	39.9945i	−1.16809	−	1.79219i
$499$	−8.88197	+	6.45313i	−0.397611	+	0.288882i	−0.768567	−	0.639769i	$-0.779030\pi$
$499$	−8.88197	+	6.45313i	−0.397611	+	0.288882i	0.370956	+	0.928650i	$0.379030\pi$
$500$	−12.6740	−	4.11803i	−0.566799	−	0.184164i
$501$	−0.115306	+	0.142875i	−0.00515151	+	0.00638316i
$502$	−5.22542	−	7.19218i	−0.233222	−	0.321003i
$503$	4.25325	+	3.09017i	0.189643	+	0.137784i	0.678556	−	0.734549i	$-0.262606\pi$
$503$	4.25325	+	3.09017i	0.189643	+	0.137784i	−0.488912	+	0.872333i	$0.662606\pi$
$504$	−1.44881	−	0.639312i	−0.0645350	−	0.0284772i
$505$			32.6789i			1.45419i
$506$		0			0
$507$	5.70820	+	2.18034i	0.253510	+	0.0968323i
$508$	20.3262	−	6.60440i	0.901831	−	0.293023i
$509$	0.159002	−	0.218847i	0.00704763	−	0.00970022i	−0.805479	−	0.592625i	$-0.798092\pi$
$509$	0.159002	−	0.218847i	0.00704763	−	0.00970022i	0.812526	+	0.582925i	$0.198092\pi$
$510$	−5.90441	−	21.8905i	−0.261452	−	0.969329i
$511$	−3.41641	+	10.5146i	−0.151133	+	0.465140i
$512$	−8.38800	+	25.8156i	−0.370701	+	1.14090i
$513$	−9.93553	+	19.7413i	−0.438664	+	0.871601i
$514$	−12.6008	+	17.3435i	−0.555798	+	0.764990i
$515$	−16.8415	+	5.47214i	−0.742125	+	0.241131i
$516$	1.62460	−	4.25325i	0.0715190	−	0.187239i
$517$		0			0
$518$		−	4.14590i		−	0.182160i
$519$	1.94570	−	38.3404i	0.0854068	−	1.68296i
$520$	4.73607	+	3.44095i	0.207690	+	0.150896i
$521$	11.9272	+	16.4164i	0.522541	+	0.719216i	0.985971	−	0.166918i	$-0.0533814\pi$
$521$	11.9272	+	16.4164i	0.522541	+	0.719216i	−0.463430	+	0.886134i	$0.653381\pi$
$522$	−18.7638	+	10.9163i	−0.821270	+	0.477793i
$523$	3.02786	+	0.983813i	0.132399	+	0.0430191i	0.374467	−	0.927240i	$-0.377826\pi$
$523$	3.02786	+	0.983813i	0.132399	+	0.0430191i	−0.242068	+	0.970259i	$0.577826\pi$
$524$	−5.34307	+	3.88197i	−0.233413	+	0.169584i
$525$	−1.95469	+	1.27400i	−0.0853099	+	0.0556019i
$526$	13.6803	+	42.1038i	0.596491	+	1.83581i
$527$	−2.24514			−0.0977998
$528$		0			0
$529$	19.8885			0.864719
$530$	−7.46969	−	22.9894i	−0.324463	−	0.998594i
$531$	−7.67702	+	1.65838i	−0.333154	+	0.0719678i
$532$	−4.04508	+	2.93893i	−0.175377	+	0.127419i
$533$	−9.00854	−	2.92705i	−0.390203	−	0.126785i
$534$	−24.2845	−	19.5987i	−1.05089	−	0.848119i
$535$	0.263932	+	0.363271i	0.0114108	+	0.0157056i
$536$	4.89404	+	3.55573i	0.211390	+	0.153584i
$537$	−6.82290	−	0.346249i	−0.294430	−	0.0149417i
$538$			44.1976i			1.90550i
$539$		0			0
$540$	19.5623	−	10.0902i	0.841828	−	0.434212i
$541$	−23.5172	+	7.64121i	−1.01108	+	0.328521i	−0.767286	−	0.641305i	$-0.778393\pi$
$541$	−23.5172	+	7.64121i	−1.01108	+	0.328521i	−0.243798	+	0.969826i	$0.578393\pi$
$542$	26.4051	−	36.3435i	1.13419	−	1.56109i
$543$	−20.4622	+	5.51916i	−0.878118	+	0.236850i
$544$	5.95492	−	18.3273i	0.255315	−	0.785778i
$545$	−6.15537	+	18.9443i	−0.263667	+	0.811483i
$546$	7.11267	−	1.91846i	0.304394	−	0.0821024i
$547$	−18.0517	+	24.8460i	−0.771833	+	1.06234i	0.224303	+	0.974519i	$0.427989\pi$
$547$	−18.0517	+	24.8460i	−0.771833	+	1.06234i	−0.996137	+	0.0878181i	$0.972011\pi$
$548$	−13.4005	+	4.35410i	−0.572443	+	0.185998i
$549$	−8.50651	+	9.51057i	−0.363049	+	0.405901i
$550$		0			0
$551$		−	16.1803i		−	0.689306i
$552$	2.21689	+	0.112503i	0.0943573	+	0.00478845i
$553$	6.28115	+	4.56352i	0.267102	+	0.194061i
$554$	22.9641	+	31.6074i	0.975652	+	1.34287i
$555$	−10.5862	−	8.54358i	−0.449360	−	0.362655i
$556$	−2.66312	−	0.865300i	−0.112941	−	0.0366969i
$557$	−6.51864	+	4.73607i	−0.276204	+	0.200674i	−0.717260	−	0.696806i	$-0.754604\pi$
$557$	−6.51864	+	4.73607i	−0.276204	+	0.200674i	0.441056	+	0.897479i	$0.354604\pi$
$558$	−1.02910	−	4.76391i	−0.0435651	−	0.201672i
$559$	−1.54508	−	4.75528i	−0.0653501	−	0.201127i
$560$	−8.78402			−0.371193
$561$		0			0
$562$	−31.3050			−1.32052
$563$	−7.10642	−	21.8713i	−0.299500	−	0.921766i	−0.981673	−	0.190575i	$-0.938965\pi$
$563$	−7.10642	−	21.8713i	−0.299500	−	0.921766i	0.682173	−	0.731191i	$-0.261035\pi$
$564$	−17.2010	+	11.2110i	−0.724292	+	0.472067i
$565$	−42.2426	+	30.6911i	−1.77716	+	1.29118i
$566$	−14.3844	−	4.67376i	−0.604620	−	0.196453i
$567$	−1.31713	+	6.40485i	−0.0553143	+	0.268979i
$568$	4.40983	+	6.06961i	0.185032	+	0.254675i
$569$	6.60440	+	4.79837i	0.276871	+	0.201158i	0.717551	−	0.696506i	$-0.245263\pi$
$569$	6.60440	+	4.79837i	0.276871	+	0.201158i	−0.440681	+	0.897664i	$0.645263\pi$
$570$	−1.85932	+	36.6383i	−0.0778784	+	1.53461i
$571$		−	6.04937i		−	0.253158i	−0.991957	−	0.126579i	$-0.959600\pi$
$571$		−	6.04937i		−	0.253158i	0.991957	−	0.126579i	$-0.0403997\pi$
$572$		0			0
$573$	−12.2148	+	31.9787i	−0.510280	+	1.33593i
$574$	4.04508	−	1.31433i	0.168839	−	0.0548590i
$575$	1.92236	−	2.64590i	0.0801678	−	0.110342i
$576$	14.0520	+	1.42991i	0.585502	+	0.0595796i
$577$	−2.47214	+	7.60845i	−0.102916	+	0.316744i	−0.989236	−	0.146330i	$-0.953254\pi$
$577$	−2.47214	+	7.60845i	−0.102916	+	0.316744i	0.886319	+	0.463074i	$0.153254\pi$
$578$	5.93085	−	18.2533i	0.246691	−	0.759237i
$579$	−9.10985	−	33.7747i	−0.378593	−	1.40363i
$580$	−9.47214	+	13.0373i	−0.393309	+	0.541343i
$581$	10.0126	−	3.25329i	0.415392	−	0.134969i
$582$	20.3682	+	7.77997i	0.844290	+	0.322490i
$583$		0			0
$584$			11.0557i			0.457489i
$585$	9.75866	−	22.1151i	0.403471	−	0.914345i
$586$	−15.0623	−	10.9434i	−0.622218	−	0.452068i
$587$	3.49396	+	4.80902i	0.144211	+	0.198489i	0.875012	−	0.484101i	$-0.160853\pi$
$587$	3.49396	+	4.80902i	0.144211	+	0.198489i	−0.730801	+	0.682590i	$0.760853\pi$
$588$	11.3914	−	14.1150i	0.469775	−	0.582091i
$589$	3.45492	+	1.12257i	0.142357	+	0.0462547i
$590$	−10.5474	+	7.66312i	−0.434229	+	0.315486i
$591$	−14.9782	−	22.9810i	−0.616121	−	0.945313i
$592$	−4.28115	−	13.1760i	−0.175954	−	0.541532i
$593$	−3.35520			−0.137781			−0.0688907	−	0.997624i	$-0.521946\pi$
$593$	−3.35520			−0.137781			−0.0688907	+	0.997624i	$0.521946\pi$
$594$		0			0
$595$	5.00000			0.204980
$596$	−0.0857567	−	0.263932i	−0.00351273	−	0.0108111i
$597$	2.11475	+	3.24466i	0.0865510	+	0.132795i
$598$	−8.35410	+	6.06961i	−0.341625	+	0.248205i
$599$	−7.88597	−	2.56231i	−0.322212	−	0.104693i	0.143445	−	0.989658i	$-0.454182\pi$
$599$	−7.88597	−	2.56231i	−0.322212	−	0.104693i	−0.465657	+	0.884965i	$0.654182\pi$
$600$	−1.46534	+	1.81568i	−0.0598222	+	0.0741248i
$601$	−10.2254	−	14.0741i	−0.417104	−	0.574094i	0.547829	−	0.836590i	$-0.315454\pi$
$601$	−10.2254	−	14.0741i	−0.417104	−	0.574094i	−0.964933	+	0.262496i	$0.915454\pi$
$602$	1.81636	+	1.31966i	0.0740292	+	0.0537853i
$603$	10.0842	−	22.8527i	0.410659	−	0.930634i
$604$			28.4257i			1.15663i
$605$		0			0
$606$	38.4164	+	14.6738i	1.56056	+	0.596081i
$607$	11.7705	−	3.82447i	0.477750	−	0.155230i	−0.0602359	−	0.998184i	$-0.519185\pi$
$607$	11.7705	−	3.82447i	0.477750	−	0.155230i	0.537986	+	0.842954i	$0.319185\pi$
$608$	−18.3273	+	25.2254i	−0.743272	+	1.02303i
$609$	−1.24669	−	4.62209i	−0.0505184	−	0.187297i
$610$	−6.54508	+	20.1437i	−0.265003	+	0.815595i
$611$	−6.96767	+	21.4443i	−0.281882	+	0.867542i
$612$	−12.6942	−	1.29174i	−0.513133	−	0.0522155i
$613$	−13.8197	+	19.0211i	−0.558171	+	0.768256i	−0.991092	−	0.133175i	$-0.957483\pi$
$613$	−13.8197	+	19.0211i	−0.558171	+	0.768256i	0.432922	+	0.901432i	$0.357483\pi$
$614$	10.6331	−	3.45492i	0.429118	−	0.139429i
$615$	4.97980	−	13.0373i	0.200805	−	0.525714i
$616$		0			0
$617$		−	20.2361i		−	0.814673i	−0.913278	−	0.407337i	$-0.866458\pi$
$617$		−	20.2361i		−	0.814673i	0.913278	−	0.407337i	$-0.133542\pi$
$618$	−1.12942	+	22.2555i	−0.0454321	+	0.895248i
$619$	−10.0451	−	7.29818i	−0.403746	−	0.293339i	0.367319	−	0.930095i	$-0.380276\pi$
$619$	−10.0451	−	7.29818i	−0.403746	−	0.293339i	−0.771065	+	0.636756i	$0.780276\pi$
$620$	−2.12663	−	2.92705i	−0.0854074	−	0.117553i
$621$	−1.47876	−	9.04558i	−0.0593407	−	0.362987i
$622$	−9.04508	−	2.93893i	−0.362675	−	0.117840i
$623$	5.56758	−	4.04508i	0.223060	−	0.162063i
$624$	20.6236	−	13.4417i	0.825607	−	0.538100i
$625$	−9.52786	−	29.3238i	−0.381115	−	1.17295i
$626$	−20.9232			−0.836261
$627$		0			0
$628$	−6.00000			−0.239426
$629$	2.43690	+	7.50000i	0.0971655	+	0.299045i
$630$	2.29183	+	10.6094i	0.0913087	+	0.422688i
$631$	10.0729	−	7.31843i	0.400998	−	0.291342i	−0.368950	−	0.929449i	$-0.620282\pi$
$631$	10.0729	−	7.31843i	0.400998	−	0.291342i	0.769947	+	0.638108i	$0.220282\pi$
$632$	7.38394	+	2.39919i	0.293717	+	0.0954345i
$633$	9.13297	+	7.37073i	0.363003	+	0.292960i
$634$	−0.263932	−	0.363271i	−0.0104821	−	0.0144273i
$635$	27.9767	+	20.3262i	1.11022	+	0.806622i
$636$	−13.5862	−	0.689474i	−0.538729	−	0.0273394i
$637$		−	19.9192i		−	0.789227i
$638$		0			0
$639$	20.6525	−	23.0902i	0.816999	−	0.913433i
$640$	−14.2082	+	4.61653i	−0.561629	+	0.182484i
$641$	10.4944	−	14.4443i	0.414503	−	0.570514i	−0.549806	−	0.835292i	$-0.685299\pi$
$641$	10.4944	−	14.4443i	0.414503	−	0.570514i	0.964310	+	0.264778i	$0.0852985\pi$
$642$	0.545564	−	0.147152i	0.0215317	−	0.00580762i
$643$	2.44427	−	7.52270i	0.0963927	−	0.296666i	−0.891221	−	0.453568i	$-0.850151\pi$
$643$	2.44427	−	7.52270i	0.0963927	−	0.296666i	0.987614	+	0.156902i	$0.0501508\pi$
$644$	0.640786	−	1.97214i	0.0252505	−	0.0777130i
$645$	7.11267	−	1.91846i	0.280061	−	0.0755392i
$646$	12.5000	−	17.2048i	0.491806	−	0.676913i
$647$	41.9978	−	13.6459i	1.65110	−	0.536476i	0.672124	−	0.740439i	$-0.265382\pi$
$647$	41.9978	−	13.6459i	1.65110	−	0.536476i	0.978979	+	0.203963i	$0.0653823\pi$
$648$	0.726543	+	6.49839i	0.0285413	+	0.255281i
$649$		0			0
$650$		−	10.8541i		−	0.425733i
$651$	1.07343	+	0.0544744i	0.0420710	+	0.00213502i
$652$	16.2082	+	11.7759i	0.634762	+	0.461182i
$653$	−20.6582	−	28.4336i	−0.808419	−	1.11269i	−0.991565	−	0.129608i	$-0.958628\pi$
$653$	−20.6582	−	28.4336i	−0.808419	−	1.11269i	0.183146	−	0.983086i	$-0.441372\pi$
$654$	19.5064	+	15.7426i	0.762760	+	0.615583i
$655$	−10.1631	−	3.30220i	−0.397106	−	0.129028i
$656$	11.4984	−	8.35410i	0.448938	−	0.326173i
$657$	44.6215	−	9.63909i	1.74085	−	0.376057i
$658$	−3.12868	−	9.62908i	−0.121969	−	0.375381i
$659$	39.8384			1.55188			0.775941	−	0.630805i	$-0.217275\pi$
$659$	39.8384			1.55188			0.775941	+	0.630805i	$0.217275\pi$
$660$		0			0
$661$	32.4508			1.26219			0.631096	−	0.775705i	$-0.282605\pi$
$661$	32.4508			1.26219			0.631096	+	0.775705i	$0.282605\pi$
$662$	13.4535	+	41.4058i	0.522887	+	1.60928i
$663$	−11.7393	+	7.65124i	−0.455916	+	0.297150i
$664$	8.51722	−	6.18812i	0.330532	−	0.240146i
$665$	−7.69421	−	2.50000i	−0.298369	−	0.0969458i
$666$	−14.7971	+	8.60854i	−0.573375	+	0.333574i
$667$	3.94427	+	5.42882i	0.152723	+	0.210205i
$668$	0.138757	+	0.100813i	0.00536868	+	0.00390057i
$669$	−0.547435	+	10.7873i	−0.0211651	+	0.417061i
$670$		−	41.4630i		−	1.60185i
$671$		0			0
$672$	−3.29180	+	8.61803i	−0.126984	+	0.332448i
$673$	28.5795	−	9.28605i	1.10166	−	0.357951i	0.298919	−	0.954279i	$-0.403374\pi$
$673$	28.5795	−	9.28605i	1.10166	−	0.357951i	0.802741	+	0.596328i	$0.203374\pi$
$674$	−11.5187	+	15.8541i	−0.443683	+	0.610677i
$675$	8.60575	+	4.33115i	0.331235	+	0.166706i
$676$	1.76393	−	5.42882i	0.0678435	−	0.208801i
$677$	12.2047	−	37.5623i	0.469066	−	1.44364i	−0.384730	−	0.923029i	$-0.625705\pi$
$677$	12.2047	−	37.5623i	0.469066	−	1.44364i	0.853796	−	0.520608i	$-0.174295\pi$
$678$	17.1114	+	63.4404i	0.657159	+	2.43641i
$679$	−2.82624	+	3.88998i	−0.108461	+	0.149284i
$680$	4.75528	−	1.54508i	0.182357	−	0.0592513i
$681$	10.2371	+	3.91023i	0.392287	+	0.149840i
$682$		0			0
$683$		−	9.00000i		−	0.344375i	−0.985064	−	0.172188i	$-0.944916\pi$
$683$		−	9.00000i		−	0.344375i	0.985064	−	0.172188i	$-0.0550836\pi$
$684$	18.8885	+	8.33489i	0.722220	+	0.318692i
$685$	−18.4443	−	13.4005i	−0.704719	−	0.512009i
$686$	10.9434	+	15.0623i	0.417821	+	0.575082i
$687$	27.3302	−	33.8644i	1.04271	−	1.29201i
$688$	7.13525	+	2.31838i	0.272029	+	0.0883876i
$689$	−12.0862	+	8.78115i	−0.460448	+	0.334535i
$690$	−8.30745	−	12.7461i	−0.316259	−	0.485236i
$691$	10.6180	+	32.6789i	0.403929	+	1.24317i	0.921786	+	0.387699i	$0.126730\pi$
$691$	10.6180	+	32.6789i	0.403929	+	1.24317i	−0.517857	+	0.855467i	$0.673270\pi$
$692$	−35.8626			−1.36329
$693$		0			0
$694$	−58.5410			−2.22219
$695$	−1.40008	−	4.30902i	−0.0531082	−	0.163450i
$696$	−2.61398	−	4.01062i	−0.0990825	−	0.152022i
$697$	−6.54508	+	4.75528i	−0.247913	+	0.180119i
$698$	29.4625	+	9.57295i	1.11517	+	0.362341i
$699$	−7.78792	+	9.64989i	−0.294566	+	0.364992i
$700$	1.28115	+	1.76336i	0.0484230	+	0.0666486i
$701$	−14.1271	−	10.2639i	−0.533573	−	0.387663i	0.288120	−	0.957594i	$-0.406970\pi$
$701$	−14.1271	−	10.2639i	−0.533573	−	0.387663i	−0.821693	+	0.569931i	$0.806970\pi$
$702$	−21.6159	−	21.4023i	−0.815839	−	0.807776i
$703$		−	12.7598i		−	0.481244i
$704$		0			0
$705$	−31.0344	−	11.8541i	−1.16882	−	0.446451i
$706$	−28.2148	+	9.16754i	−1.06188	+	0.345025i
$707$	−5.33056	+	7.33688i	−0.200476	+	0.275932i
$708$	1.91071	+	7.08393i	0.0718087	+	0.266230i
$709$	5.40983	−	16.6497i	0.203170	−	0.625294i	−0.796613	−	0.604489i	$-0.793377\pi$
$709$	5.40983	−	16.6497i	0.203170	−	0.625294i	0.999784	−	0.0208048i	$-0.00662286\pi$
$710$	15.8904	−	48.9058i	0.596358	−	1.83540i
$711$	3.24545	−	31.8937i	0.121714	−	1.19611i
$712$	4.04508	−	5.56758i	0.151596	−	0.208654i
$713$	−1.43284	+	0.465558i	−0.0536603	+	0.0174353i
$714$	2.24514	−	5.87785i	0.0840222	−	0.219973i
$715$		0			0
$716$			6.38197i			0.238505i
$717$	−2.26460	+	44.6244i	−0.0845730	+	1.66653i
$718$	38.4164	+	27.9112i	1.43369	+	1.04164i
$719$	−5.95110	−	8.19098i	−0.221938	−	0.305472i	0.683499	−	0.729951i	$-0.260457\pi$
$719$	−5.95110	−	8.19098i	−0.221938	−	0.305472i	−0.905438	+	0.424479i	$0.860457\pi$
$720$	18.2391	+	31.3510i	0.679733	+	1.16838i
$721$	−4.67376	−	1.51860i	−0.174060	−	0.0565555i
$722$	1.40008	−	1.01722i	0.0521057	−	0.0378570i
$723$	−28.4061	+	18.5141i	−1.05643	+	0.688546i
$724$	6.11803	+	18.8294i	0.227375	+	0.699788i
$725$	−7.05342			−0.261958
$726$		0			0
$727$	−21.1459			−0.784258			−0.392129	−	0.919910i	$-0.628261\pi$
$727$	−21.1459			−0.784258			−0.392129	+	0.919910i	$0.628261\pi$
$728$	0.502029	+	1.54508i	0.0186064	+	0.0572647i
$729$	25.5944	−	8.59808i	0.947941	−	0.318447i
$730$	61.3050	−	44.5407i	2.26900	−	1.64852i
$731$	−4.06150	−	1.31966i	−0.150220	−	0.0488094i
$732$	9.27584	+	7.48604i	0.342845	+	0.276692i
$733$	−20.2016	−	27.8052i	−0.746164	−	1.02701i	−0.998240	−	0.0592994i	$-0.981113\pi$
$733$	−20.2016	−	27.8052i	−0.746164	−	1.02701i	0.252076	−	0.967707i	$-0.418887\pi$
$734$	−35.3606	−	25.6910i	−1.30518	−	0.948271i
$735$	29.3106	+	1.48746i	1.08114	+	0.0548657i
$736$		−	12.9313i		−	0.476653i
$737$		0			0
$738$	−13.0902	−	11.7082i	−0.481856	−	0.430985i
$739$	15.4894	−	5.03280i	0.569785	−	0.185134i	−0.00993415	−	0.999951i	$-0.503162\pi$
$739$	15.4894	−	5.03280i	0.569785	−	0.185134i	0.579719	+	0.814816i	$0.303162\pi$
$740$	−7.46969	+	10.2812i	−0.274591	+	0.377943i
$741$	21.8905	−	5.90441i	0.804169	−	0.216904i
$742$	2.07295	−	6.37988i	0.0761004	−	0.234213i
$743$	12.9188	−	39.7599i	0.473943	−	1.45865i	−0.373434	−	0.927657i	$-0.621820\pi$
$743$	12.9188	−	39.7599i	0.473943	−	1.45865i	0.847377	−	0.530991i	$-0.178180\pi$
$744$	1.03772	−	0.279899i	0.0380448	−	0.0102616i
$745$	0.263932	−	0.363271i	0.00966972	−	0.0133092i
$746$	−35.3404	+	11.4828i	−1.29390	+	0.420414i
$747$	−32.4014	−	28.9807i	−1.18551	−	1.06035i
$748$		0			0
$749$			0.124612i			0.00455322i
$750$	−27.0993	−	1.37524i	−0.989527	−	0.0502166i
$751$	−4.50000	−	3.26944i	−0.164207	−	0.119304i	0.502647	−	0.864492i	$-0.332360\pi$
$751$	−4.50000	−	3.26944i	−0.164207	−	0.119304i	−0.666854	+	0.745188i	$0.732360\pi$
$752$	−19.8864	−	27.3713i	−0.725183	−	0.998129i
$753$	−6.29957	−	5.08405i	−0.229569	−	0.185273i
$754$	21.1803	+	6.88191i	0.771342	+	0.250624i
$755$	−37.2097	+	27.0344i	−1.35420	+	0.983884i
$756$	6.03791	+	0.925599i	0.219597	+	0.0336637i
$757$	−7.69098	−	23.6704i	−0.279534	−	0.860316i	−0.987984	−	0.154555i	$-0.950606\pi$
$757$	−7.69098	−	23.6704i	−0.279534	−	0.860316i	0.708451	−	0.705760i	$-0.249394\pi$
$758$	62.5577			2.27220
$759$		0			0
$760$	−8.09017			−0.293461
$761$	−13.6453	−	41.9959i	−0.494642	−	1.52235i	−0.817514	−	0.575909i	$-0.804648\pi$
$761$	−13.6453	−	41.9959i	−0.494642	−	1.52235i	0.322872	−	0.946443i	$-0.395352\pi$
$762$	36.4572	−	23.7615i	1.32071	−	0.860788i
$763$	−4.47214	+	3.24920i	−0.161902	+	0.117629i
$764$	30.4136	+	9.88197i	1.10032	+	0.357517i
$765$	−10.3820	−	17.8455i	−0.375362	−	0.645204i
$766$	16.1180	+	22.1846i	0.582368	+	0.801561i
$767$	6.51864	+	4.73607i	0.235374	+	0.171010i
$768$	−1.77945	+	35.0644i	−0.0642104	+	1.26528i
$769$			26.8666i			0.968835i	0.874837	+	0.484417i	$0.160968\pi$
$769$			26.8666i			0.968835i	−0.874837	+	0.484417i	$0.839032\pi$
$770$		0			0
$771$	−6.96556	+	18.2361i	−0.250858	+	0.656756i
$772$	−31.0795	+	10.0984i	−1.11858	+	0.363448i
$773$	−4.60401	+	6.33688i	−0.165595	+	0.227922i	−0.883748	−	0.467964i	$-0.844988\pi$
$773$	−4.60401	+	6.33688i	−0.165595	+	0.227922i	0.718153	+	0.695885i	$0.244988\pi$
$774$	0.938504	−	9.22288i	0.0337338	−	0.331510i
$775$	0.489357	−	1.50609i	0.0175782	−	0.0541002i
$776$	−1.48584	+	4.57295i	−0.0533386	+	0.164159i
$777$	−0.983135	−	3.64497i	−0.0352698	−	0.130762i
$778$	10.7533	−	14.8006i	0.385524	−	0.530628i
$779$	12.4495	−	4.04508i	0.446049	−	0.144930i
$780$	−21.0948	−	8.05748i	−0.755313	−	0.288504i
$781$		0			0
$782$			8.81966i			0.315390i
$783$	−13.9080	+	14.0469i	−0.497033	+	0.501994i
$784$	24.1803	+	17.5680i	0.863584	+	0.627430i
$785$	−5.70634	−	7.85410i	−0.203668	−	0.280325i
$786$	−8.44549	+	10.4647i	−0.301241	+	0.373263i
$787$	51.8328	+	16.8415i	1.84764	+	0.600335i	0.997244	+	0.0741922i	$0.0236378\pi$
$787$	51.8328	+	16.8415i	1.84764	+	0.600335i	0.850396	+	0.526143i	$0.176362\pi$
$788$	−20.7315	+	15.0623i	−0.738529	+	0.536572i
$789$	22.0116	+	33.7724i	0.783635	+	1.20233i
$790$	−16.4443	−	50.6103i	−0.585061	−	1.80063i
$791$	−14.4904			−0.515218
$792$		0			0
$793$	13.0902			0.464846
$794$	13.5191	+	41.6074i	0.479774	+	1.47659i
$795$	−12.0187	−	18.4403i	−0.426260	−	0.654011i
$796$	2.92705	−	2.12663i	0.103747	−	0.0753763i
$797$	20.9888	+	6.81966i	0.743460	+	0.241565i	0.656165	−	0.754618i	$-0.272178\pi$
$797$	20.9888	+	6.81966i	0.743460	+	0.241565i	0.0872952	+	0.996182i	$0.472178\pi$
$798$	−6.39384	+	7.92252i	−0.226340	+	0.280454i
$799$	11.3197	+	15.5802i	0.400461	+	0.551187i
$800$	10.9964	+	7.98936i	0.388782	+	0.282466i
$801$	−25.9978	−	11.4720i	−0.918587	−	0.405343i
$802$		−	40.2219i		−	1.42028i
$803$		0			0
$804$	−21.7984	−	8.32624i	−0.768769	−	0.293644i
$805$	3.19098	−	1.03681i	0.112467	−	0.0365429i
$806$	−2.93893	+	4.04508i	−0.103519	+	0.142482i
$807$	10.4808	+	38.8574i	0.368941	+	1.36785i
$808$	−2.80244	+	8.62502i	−0.0985895	+	0.303427i
$809$	−8.09024	+	24.8992i	−0.284438	+	0.875409i	0.702129	+	0.712050i	$0.252233\pi$
$809$	−8.09024	+	24.8992i	−0.284438	+	0.875409i	−0.986567	+	0.163359i	$0.947767\pi$
$810$	33.1071	−	30.2091i	1.16326	−	1.06144i
$811$	7.60081	−	10.4616i	0.266901	−	0.367357i	−0.654440	−	0.756114i	$-0.727095\pi$
$811$	7.60081	−	10.4616i	0.266901	−	0.367357i	0.921340	+	0.388757i	$0.127095\pi$
$812$	−4.25325	+	1.38197i	−0.149260	+	0.0484975i
$813$	14.5964	−	38.2138i	0.511917	−	1.34022i
$814$		0			0
$815$			32.4164i			1.13550i
$816$	1.06564	−	20.9987i	0.0373050	−	0.735102i
$817$	5.59017	+	4.06150i	0.195575	+	0.142094i
$818$	−38.2793	−	52.6869i	−1.33840	−	1.84215i
$819$	5.79834	−	3.37332i	0.202610	−	0.117873i
$820$	−12.3992	−	4.02874i	−0.432998	−	0.140690i
$821$	29.9115	−	21.7320i	1.04392	−	0.758452i	0.0728729	−	0.997341i	$-0.476783\pi$
$821$	29.9115	−	21.7320i	1.04392	−	0.758452i	0.971047	+	0.238889i	$0.0767832\pi$
$822$	−24.0353	+	15.6653i	−0.838327	+	0.546391i
$823$	−4.36475	−	13.4333i	−0.152145	−	0.468256i	0.845715	−	0.533635i	$-0.179174\pi$
$823$	−4.36475	−	13.4333i	−0.152145	−	0.468256i	−0.997860	+	0.0653792i	$0.979174\pi$
$824$	−4.91428			−0.171197
$825$		0			0
$826$	−3.61803			−0.125888
$827$	−0.106001	−	0.326238i	−0.00368602	−	0.0113444i	0.949197	−	0.314684i	$-0.101898\pi$
$827$	−0.106001	−	0.326238i	−0.00368602	−	0.0113444i	−0.952883	+	0.303339i	$0.901898\pi$
$828$	−8.36926	+	1.80792i	−0.290852	+	0.0628296i
$829$	−22.8713	+	16.6170i	−0.794354	+	0.577132i	−0.909252	−	0.416245i	$-0.863346\pi$
$829$	−22.8713	+	16.6170i	−0.794354	+	0.577132i	0.114898	+	0.993377i	$0.463346\pi$
$830$	−68.6273	−	22.2984i	−2.38209	−	0.773988i
$831$	27.6847	+	22.3428i	0.960370	+	0.775064i
$832$	−8.51722	−	11.7229i	−0.295282	−	0.406420i
$833$	−13.7638	−	10.0000i	−0.476888	−	0.346479i
$834$	−5.69423	−	0.288971i	−0.197175	−	0.0100063i
$835$			0.277515i			0.00960379i
$836$		0			0
$837$	−2.03444	−	3.94427i	−0.0703206	−	0.136334i
$838$	10.5902	−	3.44095i	0.365831	−	0.118866i
$839$	17.4293	−	23.9894i	0.601726	−	0.828205i	−0.394139	−	0.919051i	$-0.628957\pi$
$839$	17.4293	−	23.9894i	0.601726	−	0.828205i	0.995865	+	0.0908462i	$0.0289572\pi$
$840$	−2.31105	+	0.623345i	−0.0797386	+	0.0215074i
$841$	−4.48936	+	13.8168i	−0.154805	+	0.476442i
$842$	−15.1967	+	46.7705i	−0.523711	+	1.61182i
$843$	−27.5225	+	7.42348i	−0.947925	+	0.255678i
$844$	6.44427	−	8.86978i	0.221821	−	0.305310i
$845$	8.78402	−	2.85410i	0.302180	−	0.0981841i
$846$	−27.8707	+	31.1604i	−0.958213	+	1.07131i
$847$		0			0
$848$		−	22.4164i		−	0.769783i
$849$	−13.7547	−	0.698023i	−0.472059	−	0.0239561i
$850$	−7.50000	−	5.44907i	−0.257248	−	0.186902i
$851$	3.11044	+	4.28115i	0.106624	+	0.146756i
$852$	−22.5203	−	18.1749i	−0.771533	−	0.622663i
$853$	−43.0517	−	13.9883i	−1.47406	−	0.478951i	−0.541728	−	0.840554i	$-0.682230\pi$
$853$	−43.0517	−	13.9883i	−1.47406	−	0.478951i	−0.932332	+	0.361602i	$0.882230\pi$
$854$	−4.75528	+	3.45492i	−0.162722	+	0.118225i
$855$	7.05353	+	32.6523i	0.241226	+	1.11669i
$856$	0.0385072	+	0.118513i	0.00131615	+	0.00405069i
$857$	24.2380			0.827953			0.413976	−	0.910288i	$-0.364140\pi$
$857$	24.2380			0.827953			0.413976	+	0.910288i	$0.364140\pi$
$858$		0			0
$859$	34.5279			1.17808			0.589038	−	0.808106i	$-0.299507\pi$
$859$	34.5279			1.17808			0.589038	+	0.808106i	$0.299507\pi$
$860$	−2.12663	−	6.54508i	−0.0725174	−	0.223186i
$861$	3.24466	−	2.11475i	0.110578	−	0.0720705i
$862$	34.6976	−	25.2093i	1.18180	−	0.858631i
$863$	−37.2097	−	12.0902i	−1.26663	−	0.411554i	−0.402780	−	0.915297i	$-0.631956\pi$
$863$	−37.2097	−	12.0902i	−1.26663	−	0.411554i	−0.863854	+	0.503743i	$0.831956\pi$
$864$	37.5936	−	6.14577i	1.27896	−	0.209083i
$865$	−34.1074	−	46.9448i	−1.15969	−	1.59617i
$866$	−9.23305	−	6.70820i	−0.313752	−	0.227954i
$867$	0.885768	−	17.4542i	0.0300823	−	0.592777i
$868$		−	1.00406i		−	0.0340799i
$869$		0			0
$870$	−11.7082	+	30.6525i	−0.396945	+	1.03922i
$871$	−24.3713	+	7.91872i	−0.825791	+	0.268316i
$872$	−3.24920	+	4.47214i	−0.110032	+	0.151446i
$873$	19.7521	+	2.00994i	0.668507	+	0.0680261i
$874$	4.40983	−	13.5721i	0.149165	−	0.459082i
$875$	1.84911	−	5.69098i	0.0625114	−	0.192390i
$876$	−11.1057	−	41.1742i	−0.375226	−	1.39115i
$877$	4.77458	−	6.57164i	0.161226	−	0.221908i	−0.720759	−	0.693185i	$-0.756207\pi$
$877$	4.77458	−	6.57164i	0.161226	−	0.221908i	0.881985	+	0.471277i	$0.156207\pi$
$878$	45.8550	−	14.8992i	1.54753	−	0.502823i
$879$	−15.8374	−	6.04937i	−0.534184	−	0.204040i
$880$		0			0
$881$			34.9230i			1.17659i	0.808648	+	0.588293i	$0.200200\pi$
$881$			34.9230i			1.17659i	−0.808648	+	0.588293i	$0.799800\pi$
$882$	14.9099	−	33.7888i	0.502042	−	1.13773i
$883$	14.4164	+	10.4741i	0.485151	+	0.352483i	0.803316	−	0.595552i	$-0.203067\pi$
$883$	14.4164	+	10.4741i	0.485151	+	0.352483i	−0.318166	+	0.948035i	$0.603067\pi$
$884$	7.69421	+	10.5902i	0.258784	+	0.356186i
$885$	−7.45579	+	9.23836i	−0.250624	+	0.310544i
$886$	18.9443	+	6.15537i	0.636445	+	0.206794i
$887$	−7.91872	+	5.75329i	−0.265885	+	0.193177i	−0.712737	−	0.701431i	$-0.752545\pi$
$887$	−7.91872	+	5.75329i	−0.265885	+	0.193177i	0.446853	+	0.894608i	$0.352545\pi$
$888$	−2.06137	−	3.16276i	−0.0691752	−	0.106135i
$889$	2.96556	+	9.12705i	0.0994616	+	0.306111i
$890$	−47.1693			−1.58112
$891$		0			0
$892$	10.0902			0.337844
$893$	−9.62908	−	29.6353i	−0.322225	−	0.991706i
$894$	−0.308538	−	0.473390i	−0.0103191	−	0.0158325i
$895$	−8.35410	+	6.06961i	−0.279247	+	0.202885i
$896$	−3.94298	−	1.28115i	−0.131726	−	0.0428003i
$897$	−5.90540	+	7.31729i	−0.197175	+	0.244317i
$898$	−8.81966	−	12.1392i	−0.294316	−	0.405091i
$899$	2.62866	+	1.90983i	0.0876706	+	0.0636964i
$900$	3.63339	−	8.23398i	0.121113	−	0.274466i
$901$			12.7598i			0.425089i
$902$		0			0
$903$	1.90983	+	0.729490i	0.0635552	+	0.0242759i
$904$	−13.7812	+	4.47777i	−0.458354	+	0.148928i
$905$	−18.8294	+	25.9164i	−0.625910	+	0.861491i
$906$	15.0727	+	55.8819i	0.500757	+	1.85655i
$907$	13.1008	−	40.3202i	0.435005	−	1.33881i	−0.458076	−	0.888913i	$-0.651461\pi$
$907$	13.1008	−	40.3202i	0.435005	−	1.33881i	0.893081	−	0.449896i	$-0.148539\pi$
$908$	3.16344	−	9.73607i	0.104982	−	0.323103i
$909$	37.2544	+	3.79094i	1.23565	+	0.125737i
$910$	6.54508	−	9.00854i	0.216967	−	0.298630i
$911$	−54.8963	+	17.8369i	−1.81879	+	0.590962i	−0.818941	+	0.573878i	$0.805438\pi$
$911$	−54.8963	+	17.8369i	−1.81879	+	0.590962i	−0.999854	+	0.0170841i	$0.994562\pi$
$912$	−12.1392	+	31.7809i	−0.401970	+	1.05237i
$913$		0			0
$914$			20.5279i			0.679001i
$915$	−0.977503	+	19.2619i	−0.0323153	+	0.636778i
$916$	−32.8885	−	23.8949i	−1.08667	−	0.789511i
$917$	−1.74311	−	2.39919i	−0.0575626	−	0.0792281i
$918$	−25.6404	+	4.19167i	−0.846259	+	0.138346i
$919$	−29.7599	−	9.66957i	−0.981687	−	0.318970i	−0.226163	−	0.974090i	$-0.572618\pi$
$919$	−29.7599	−	9.66957i	−0.981687	−	0.318970i	−0.755525	+	0.655120i	$0.772618\pi$
$920$	2.71441	−	1.97214i	0.0894915	−	0.0650194i
$921$	8.52910	−	5.55895i	0.281043	−	0.183174i
$922$	15.7918	+	48.6022i	0.520075	+	1.60063i
$923$	−31.7809			−1.04608
$924$		0			0
$925$	−5.56231			−0.182887
$926$	0.159002	+	0.489357i	0.00522512	+	0.0160813i
$927$	4.28459	+	19.8343i	0.140724	+	0.651444i
$928$	−22.5623	+	16.3925i	−0.740644	+	0.538109i
$929$	−28.8217	−	9.36475i	−0.945610	−	0.307247i	−0.204680	−	0.978829i	$-0.565615\pi$
$929$	−28.8217	−	9.36475i	−0.945610	−	0.307247i	−0.740930	+	0.671582i	$0.765615\pi$
$930$	−5.73279	−	4.62663i	−0.187985	−	0.151713i
$931$	16.1803	+	22.2703i	0.530289	+	0.729880i
$932$	9.37181	+	6.80902i	0.306984	+	0.223037i
$933$	−8.64912	−	0.438926i	−0.283160	−	0.0143698i
$934$		−	44.9897i		−	1.47211i
$935$		0			0
$936$	4.47214	−	5.00000i	0.146176	−	0.163430i
$937$	36.0172	−	11.7027i	1.17663	−	0.382311i	0.345517	−	0.938412i	$-0.387704\pi$
$937$	36.0172	−	11.7027i	1.17663	−	0.382311i	0.831114	+	0.556102i	$0.187704\pi$
$938$	6.76340	−	9.30902i	0.220833	−	0.303950i
$939$	−18.3952	+	4.96162i	−0.600304	+	0.161916i
$940$	−9.59017	+	29.5155i	−0.312797	+	0.962690i
$941$	−14.9596	+	46.0410i	−0.487670	+	1.50089i	0.340406	+	0.940279i	$0.389436\pi$
$941$	−14.9596	+	46.0410i	−0.487670	+	1.50089i	−0.828076	+	0.560616i	$0.810564\pi$
$942$	−11.7954	+	3.18149i	−0.384313	+	0.103659i
$943$	−3.19098	+	4.39201i	−0.103913	+	0.143024i
$944$	−11.4984	+	3.73607i	−0.374242	+	0.121599i
$945$	4.53077	+	8.78402i	0.147386	+	0.285744i
$946$		0			0
$947$		−	23.8541i		−	0.775154i	−0.921837	−	0.387577i	$-0.873312\pi$
$947$		−	23.8541i		−	0.775154i	0.921837	−	0.387577i	$-0.126688\pi$
$948$	−29.9096	−	1.51785i	−0.971418	−	0.0492976i
$949$	−37.8885	−	27.5276i	−1.22991	−	0.893585i
$950$	8.81678	+	12.1353i	0.286054	+	0.393720i
$951$	−0.318186	−	0.256791i	−0.0103179	−	0.00832703i
$952$	1.31966	+	0.428784i	0.0427704	+	0.0138970i
$953$	−36.0341	+	26.1803i	−1.16726	+	0.848064i	−0.990678	−	0.136222i	$-0.956504\pi$
$953$	−36.0341	+	26.1803i	−1.16726	+	0.848064i	−0.176582	+	0.984286i	$0.556504\pi$
$954$	−27.0746	+	5.84864i	−0.876574	+	0.189357i
$955$	15.9894	+	49.2102i	0.517403	+	1.59240i
$956$	41.7405			1.34998
$957$		0			0
$958$	43.5410			1.40675
$959$	−1.95511	−	6.01722i	−0.0631339	−	0.194306i
$960$	17.8861	−	11.6575i	0.577270	−	0.376244i
$961$	24.4894	−	17.7926i	0.789979	−	0.573954i
$962$	16.7027	+	5.42705i	0.538518	+	0.174975i
$963$	0.444751	−	0.258744i	0.0143319	−	0.00833791i
$964$	18.6180	+	25.6255i	0.599646	+	0.825343i
$965$	−42.7773	−	31.0795i	−1.37705	−	1.00049i
$966$	0.213994	−	4.21678i	0.00688513	−	0.135673i
$967$			20.9232i			0.672846i	0.941711	+	0.336423i	$0.109217\pi$
$967$			20.9232i			0.672846i	−0.941711	+	0.336423i	$0.890783\pi$
$968$		0			0
$969$	6.90983	−	18.0902i	0.221976	−	0.581140i
$970$	31.3435	−	10.1841i	1.00638	−	0.326992i
$971$	8.33499	−	11.4721i	0.267483	−	0.368158i	−0.654055	−	0.756447i	$-0.726934\pi$
$971$	8.33499	−	11.4721i	0.267483	−	0.368158i	0.921538	+	0.388288i	$0.126934\pi$
$972$	−9.23357	−	23.4718i	−0.296167	−	0.752857i
$973$	0.388544	−	1.19581i	0.0124561	−	0.0383361i
$974$	4.39201	−	13.5172i	0.140729	−	0.433120i
$975$	−2.57388	−	9.54264i	−0.0824302	−	0.305609i
$976$	−11.5451	+	15.8904i	−0.369549	+	0.508641i
$977$	−49.4019	+	16.0517i	−1.58051	+	0.513538i	−0.962188	−	0.272388i	$-0.912187\pi$
$977$	−49.4019	+	16.0517i	−1.58051	+	0.513538i	−0.618320	+	0.785926i	$0.712187\pi$
$978$	38.1078	+	14.5559i	1.21855	+	0.465446i
$979$		0			0
$980$		−	27.4164i		−	0.875785i
$981$	20.8826	+	9.21482i	0.666731	+	0.294207i
$982$	−41.0795	−	29.8460i	−1.31090	−	0.952425i
$983$	−3.11817	−	4.29180i	−0.0994543	−	0.136887i	0.756389	−	0.654122i	$-0.226962\pi$
$983$	−3.11817	−	4.29180i	−0.0994543	−	0.136887i	−0.855844	+	0.517234i	$0.826962\pi$
$984$	2.43236	−	3.01390i	0.0775409	−	0.0960797i
$985$	−39.4336	−	12.8128i	−1.25646	−	0.408249i
$986$	15.3884	−	11.1803i	0.490067	−	0.356055i
$987$	−5.03404	−	7.72372i	−0.160235	−	0.245849i
$988$	−6.54508	−	20.1437i	−0.208227	−	0.640856i
$989$	−2.86568			−0.0911234
$990$		0			0
$991$	7.56231			0.240225			0.120112	−	0.992760i	$-0.461675\pi$
$991$	7.56231			0.240225			0.120112	+	0.992760i	$0.461675\pi$
$992$	−1.93487	−	5.95492i	−0.0614322	−	0.189069i
$993$	21.6467	+	33.2126i	0.686939	+	1.05397i
$994$	11.5451	−	8.38800i	0.366188	−	0.266051i
$995$	5.56758	+	1.80902i	0.176504	+	0.0573497i
$996$	−25.5041	+	31.6018i	−0.808128	+	1.00134i
$997$	24.0066	+	33.0422i	0.760296	+	1.04646i	0.997189	+	0.0749220i	$0.0238708\pi$
$997$	24.0066	+	33.0422i	0.760296	+	1.04646i	−0.236893	+	0.971536i	$0.576129\pi$
$998$	16.8945	+	12.2746i	0.534786	+	0.388545i
$999$	−10.9678	+	11.0773i	−0.347007	+	0.350470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.f.b.215.1		8
3.2	odd	2	inner	363.2.f.b.215.2		8
11.2	odd	10	inner	363.2.f.b.233.2		8
11.3	even	5		363.2.d.f.362.2		8
11.4	even	5		363.2.f.d.239.2		8
11.5	even	5		363.2.f.e.161.2		8
11.6	odd	10		363.2.f.d.161.1		8
11.7	odd	10		363.2.f.e.239.1		8
11.8	odd	10		363.2.d.f.362.8		8
11.9	even	5		33.2.f.a.2.1	✓	8
11.10	odd	2		33.2.f.a.17.2	yes	8
33.2	even	10	inner	363.2.f.b.233.1		8
33.5	odd	10		363.2.f.e.161.1		8
33.8	even	10		363.2.d.f.362.1		8
33.14	odd	10		363.2.d.f.362.7		8
33.17	even	10		363.2.f.d.161.2		8
33.20	odd	10		33.2.f.a.2.2	yes	8
33.26	odd	10		363.2.f.d.239.1		8
33.29	even	10		363.2.f.e.239.2		8
33.32	even	2		33.2.f.a.17.1	yes	8
44.31	odd	10		528.2.bn.c.497.2		8
44.43	even	2		528.2.bn.c.17.1		8
55.9	even	10		825.2.bi.b.101.2		8
55.32	even	4		825.2.bs.a.149.1		8
55.42	odd	20		825.2.bs.a.299.2		8
55.43	even	4		825.2.bs.d.149.2		8
55.53	odd	20		825.2.bs.d.299.1		8
55.54	odd	2		825.2.bi.b.776.1		8
99.20	odd	30		891.2.u.a.134.1		16
99.31	even	15		891.2.u.a.431.1		16
99.32	even	6		891.2.u.a.512.2		16
99.43	odd	6		891.2.u.a.215.2		16
99.65	even	6		891.2.u.a.215.1		16
99.76	odd	6		891.2.u.a.512.1		16
99.86	odd	30		891.2.u.a.431.2		16
99.97	even	15		891.2.u.a.134.2		16
132.119	even	10		528.2.bn.c.497.1		8
132.131	odd	2		528.2.bn.c.17.2		8
165.32	odd	4		825.2.bs.d.149.1		8
165.53	even	20		825.2.bs.a.299.1		8
165.98	odd	4		825.2.bs.a.149.2		8
165.119	odd	10		825.2.bi.b.101.1		8
165.152	even	20		825.2.bs.d.299.2		8
165.164	even	2		825.2.bi.b.776.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.f.a.2.1	✓	8	11.9	even	5
33.2.f.a.2.2	yes	8	33.20	odd	10
33.2.f.a.17.1	yes	8	33.32	even	2
33.2.f.a.17.2	yes	8	11.10	odd	2
363.2.d.f.362.1		8	33.8	even	10
363.2.d.f.362.2		8	11.3	even	5
363.2.d.f.362.7		8	33.14	odd	10
363.2.d.f.362.8		8	11.8	odd	10
363.2.f.b.215.1		8	1.1	even	1	trivial
363.2.f.b.215.2		8	3.2	odd	2	inner
363.2.f.b.233.1		8	33.2	even	10	inner
363.2.f.b.233.2		8	11.2	odd	10	inner
363.2.f.d.161.1		8	11.6	odd	10
363.2.f.d.161.2		8	33.17	even	10
363.2.f.d.239.1		8	33.26	odd	10
363.2.f.d.239.2		8	11.4	even	5
363.2.f.e.161.1		8	33.5	odd	10
363.2.f.e.161.2		8	11.5	even	5
363.2.f.e.239.1		8	11.7	odd	10
363.2.f.e.239.2		8	33.29	even	10
528.2.bn.c.17.1		8	44.43	even	2
528.2.bn.c.17.2		8	132.131	odd	2
528.2.bn.c.497.1		8	132.119	even	10
528.2.bn.c.497.2		8	44.31	odd	10
825.2.bi.b.101.1		8	165.119	odd	10
825.2.bi.b.101.2		8	55.9	even	10
825.2.bi.b.776.1		8	55.54	odd	2
825.2.bi.b.776.2		8	165.164	even	2
825.2.bs.a.149.1		8	55.32	even	4
825.2.bs.a.149.2		8	165.98	odd	4
825.2.bs.a.299.1		8	165.53	even	20
825.2.bs.a.299.2		8	55.42	odd	20
825.2.bs.d.149.1		8	165.32	odd	4
825.2.bs.d.149.2		8	55.43	even	4
825.2.bs.d.299.1		8	55.53	odd	20
825.2.bs.d.299.2		8	165.152	even	20
891.2.u.a.134.1		16	99.20	odd	30
891.2.u.a.134.2		16	99.97	even	15
891.2.u.a.215.1		16	99.65	even	6
891.2.u.a.215.2		16	99.43	odd	6
891.2.u.a.431.1		16	99.31	even	15
891.2.u.a.431.2		16	99.86	odd	30
891.2.u.a.512.1		16	99.76	odd	6
891.2.u.a.512.2		16	99.32	even	6

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.f (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 1.80902i) q^{2} +(-0.945746 - 1.45106i) q^{3} +(-1.30902 + 0.951057i) q^{4} +(-2.48990 - 0.809017i) q^{5} +(-2.06909 + 2.56378i) q^{6} +(-0.427051 - 0.587785i) q^{7} +(-0.587785 - 0.427051i) q^{8} +(-1.21113 + 2.74466i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 1.80902i) q^{2} +(-0.945746 - 1.45106i) q^{3} +(-1.30902 + 0.951057i) q^{4} +(-2.48990 - 0.809017i) q^{5} +(-2.06909 + 2.56378i) q^{6} +(-0.427051 - 0.587785i) q^{7} +(-0.587785 - 0.427051i) q^{8} +(-1.21113 + 2.74466i) q^{9} +4.97980i q^{10} +(2.61803 + 1.00000i) q^{12} +(2.92705 - 0.951057i) q^{13} +(-0.812299 + 1.11803i) q^{14} +(1.18088 + 4.37811i) q^{15} +(-1.42705 + 4.39201i) q^{16} +(0.812299 - 2.50000i) q^{17} +(5.67702 + 0.577684i) q^{18} +(-2.50000 + 3.44095i) q^{19} +(4.02874 - 1.30902i) q^{20} +(-0.449028 + 1.17557i) q^{21} -1.76393i q^{23} +(-0.0637797 + 1.25679i) q^{24} +(1.50000 + 1.08981i) q^{25} +(-3.44095 - 4.73607i) q^{26} +(5.12808 - 0.838333i) q^{27} +(1.11803 + 0.363271i) q^{28} +(-3.07768 + 2.23607i) q^{29} +(7.22597 - 4.70962i) q^{30} +(-0.263932 - 0.812299i) q^{31} +7.33094 q^{32} -5.00000 q^{34} +(0.587785 + 1.80902i) q^{35} +(-1.02494 - 4.74466i) q^{36} +(-2.42705 + 1.76336i) q^{37} +(7.69421 + 2.50000i) q^{38} +(-4.14828 - 3.34786i) q^{39} +(1.11803 + 1.53884i) q^{40} +(-2.48990 - 1.80902i) q^{41} +(2.39056 + 0.121316i) q^{42} -1.62460i q^{43} +(5.23607 - 5.85410i) q^{45} +(-3.19098 + 1.03681i) q^{46} +(-4.30625 + 5.92705i) q^{47} +(7.72268 - 2.08299i) q^{48} +(2.00000 - 6.15537i) q^{49} +(1.08981 - 3.35410i) q^{50} +(-4.39587 + 1.18567i) q^{51} +(-2.92705 + 4.02874i) q^{52} +(-4.61653 + 1.50000i) q^{53} +(-4.53077 - 8.78402i) q^{54} +0.527864i q^{56} +(7.35738 + 0.373373i) q^{57} +(5.85410 + 4.25325i) q^{58} +(1.53884 + 2.11803i) q^{59} +(-5.70962 - 4.60793i) q^{60} +(4.04508 + 1.31433i) q^{61} +(-1.31433 + 0.954915i) q^{62} +(2.13049 - 0.460226i) q^{63} +(-1.45492 - 4.47777i) q^{64} -8.05748 q^{65} -8.32624 q^{67} +(1.31433 + 4.04508i) q^{68} +(-2.55957 + 1.66823i) q^{69} +(2.92705 - 2.12663i) q^{70} +(-9.82084 - 3.19098i) q^{71} +(1.88399 - 1.09606i) q^{72} +(-8.94427 - 12.3107i) q^{73} +(4.61653 + 3.35410i) q^{74} +(0.162763 - 3.20727i) q^{75} -6.88191i q^{76} +(-3.61803 + 9.47214i) q^{78} +(-10.1631 + 3.30220i) q^{79} +(7.10642 - 9.78115i) q^{80} +(-6.06633 - 6.64828i) q^{81} +(-1.80902 + 5.56758i) q^{82} +(-4.47777 + 13.7812i) q^{83} +(-0.530249 - 1.96589i) q^{84} +(-4.04508 + 5.56758i) q^{85} +(-2.93893 + 0.954915i) q^{86} +(6.15537 + 2.35114i) q^{87} +9.47214i q^{89} +(-13.6679 - 6.03118i) q^{90} +(-1.80902 - 1.31433i) q^{91} +(1.67760 + 2.30902i) q^{92} +(-0.929080 + 1.15121i) q^{93} +(13.2533 + 4.30625i) q^{94} +(9.00854 - 6.54508i) q^{95} +(-6.93320 - 10.6376i) q^{96} +(-2.04508 - 6.29412i) q^{97} -12.3107 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9}+O(q^{10}) \) 8 * q - 6 * q^3 - 6 * q^4 + 10 * q^7 + 10 * q^9	\( 8 q - 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9} + 12 q^{12} + 10 q^{13} - 6 q^{15} + 2 q^{16} - 20 q^{19} + 10 q^{24} + 12 q^{25} - 12 q^{27} + 20 q^{30} - 20 q^{31} - 40 q^{34} - 10 q^{36} - 6 q^{37} - 20 q^{39} + 20 q^{42} + 24 q^{45} - 30 q^{46} + 26 q^{48} + 16 q^{49} - 30 q^{51} - 10 q^{52} + 30 q^{57} + 20 q^{58} + 2 q^{60} + 10 q^{61} + 30 q^{63} - 34 q^{64} - 4 q^{67} - 16 q^{69} + 10 q^{70} + 20 q^{72} + 6 q^{75} - 20 q^{78} - 50 q^{79} - 2 q^{81} - 10 q^{82} - 10 q^{85} - 40 q^{90} - 10 q^{91} + 10 q^{93} + 30 q^{94} - 10 q^{96} + 6 q^{97}+O(q^{100}) \) 8 * q - 6 * q^3 - 6 * q^4 + 10 * q^7 + 10 * q^9 + 12 * q^12 + 10 * q^13 - 6 * q^15 + 2 * q^16 - 20 * q^19 + 10 * q^24 + 12 * q^25 - 12 * q^27 + 20 * q^30 - 20 * q^31 - 40 * q^34 - 10 * q^36 - 6 * q^37 - 20 * q^39 + 20 * q^42 + 24 * q^45 - 30 * q^46 + 26 * q^48 + 16 * q^49 - 30 * q^51 - 10 * q^52 + 30 * q^57 + 20 * q^58 + 2 * q^60 + 10 * q^61 + 30 * q^63 - 34 * q^64 - 4 * q^67 - 16 * q^69 + 10 * q^70 + 20 * q^72 + 6 * q^75 - 20 * q^78 - 50 * q^79 - 2 * q^81 - 10 * q^82 - 10 * q^85 - 40 * q^90 - 10 * q^91 + 10 * q^93 + 30 * q^94 - 10 * q^96 + 6 * q^97

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