LMFDB - Embedded newform 363.2.f.b.215.2

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			215.2
Root			$0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	363.215
Dual form			363.2.f.b.233.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 1.80902i) q^{2} +(-1.67229 - 0.451057i) q^{3} +(-1.30902 + 0.951057i) q^{4} +(2.48990 + 0.809017i) q^{5} +(-0.166977 - 3.29032i) q^{6} +(-0.427051 - 0.587785i) q^{7} +(0.587785 + 0.427051i) q^{8} +(2.59310 + 1.50859i) q^{9} +O(q^{10})$	\(q+(0.587785 + 1.80902i) q^{2} +(-1.67229 - 0.451057i) q^{3} +(-1.30902 + 0.951057i) q^{4} +(2.48990 + 0.809017i) q^{5} +(-0.166977 - 3.29032i) q^{6} +(-0.427051 - 0.587785i) q^{7} +(0.587785 + 0.427051i) q^{8} +(2.59310 + 1.50859i) q^{9} +4.97980i q^{10} +(2.61803 - 1.00000i) q^{12} +(2.92705 - 0.951057i) q^{13} +(0.812299 - 1.11803i) q^{14} +(-3.79892 - 2.47599i) q^{15} +(-1.42705 + 4.39201i) q^{16} +(-0.812299 + 2.50000i) q^{17} +(-1.20489 + 5.57768i) q^{18} +(-2.50000 + 3.44095i) q^{19} +(-4.02874 + 1.30902i) q^{20} +(0.449028 + 1.17557i) q^{21} +1.76393i q^{23} +(-0.790322 - 0.979277i) q^{24} +(1.50000 + 1.08981i) q^{25} +(3.44095 + 4.73607i) q^{26} +(-3.65594 - 3.69244i) q^{27} +(1.11803 + 0.363271i) q^{28} +(3.07768 - 2.23607i) q^{29} +(2.24617 - 8.32766i) q^{30} +(-0.263932 - 0.812299i) q^{31} -7.33094 q^{32} -5.00000 q^{34} +(-0.587785 - 1.80902i) q^{35} +(-4.82916 + 0.491407i) q^{36} +(-2.42705 + 1.76336i) q^{37} +(-7.69421 - 2.50000i) q^{38} +(-5.32385 + 0.270175i) q^{39} +(1.11803 + 1.53884i) q^{40} +(2.48990 + 1.80902i) q^{41} +(-1.86269 + 1.50328i) q^{42} -1.62460i q^{43} +(5.23607 + 5.85410i) q^{45} +(-3.19098 + 1.03681i) q^{46} +(4.30625 - 5.92705i) q^{47} +(4.36749 - 6.70103i) q^{48} +(2.00000 - 6.15537i) q^{49} +(-1.08981 + 3.35410i) q^{50} +(2.48604 - 3.81433i) q^{51} +(-2.92705 + 4.02874i) q^{52} +(4.61653 - 1.50000i) q^{53} +(4.53077 - 8.78402i) q^{54} -0.527864i q^{56} +(5.73279 - 4.62663i) q^{57} +(5.85410 + 4.25325i) q^{58} +(-1.53884 - 2.11803i) q^{59} +(7.32766 - 0.371864i) q^{60} +(4.04508 + 1.31433i) q^{61} +(1.31433 - 0.954915i) q^{62} +(-0.220655 - 2.16843i) q^{63} +(-1.45492 - 4.47777i) q^{64} +8.05748 q^{65} -8.32624 q^{67} +(-1.31433 - 4.04508i) q^{68} +(0.795633 - 2.94980i) q^{69} +(2.92705 - 2.12663i) q^{70} +(9.82084 + 3.19098i) q^{71} +(0.879937 + 1.99411i) q^{72} +(-8.94427 - 12.3107i) q^{73} +(-4.61653 - 3.35410i) q^{74} +(-2.01686 - 2.49907i) q^{75} -6.88191i q^{76} +(-3.61803 - 9.47214i) q^{78} +(-10.1631 + 3.30220i) q^{79} +(-7.10642 + 9.78115i) q^{80} +(4.44829 + 7.82385i) q^{81} +(-1.80902 + 5.56758i) q^{82} +(4.47777 - 13.7812i) q^{83} +(-1.70582 - 1.11179i) q^{84} +(-4.04508 + 5.56758i) q^{85} +(2.93893 - 0.954915i) q^{86} +(-6.15537 + 2.35114i) q^{87} -9.47214i q^{89} +(-7.51249 + 12.9131i) q^{90} +(-1.80902 - 1.31433i) q^{91} +(-1.67760 - 2.30902i) q^{92} +(0.0749776 + 1.47745i) q^{93} +(13.2533 + 4.30625i) q^{94} +(-9.00854 + 6.54508i) q^{95} +(12.2594 + 3.30667i) 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	$0.134779\pi$
$2$	0.587785	+	1.80902i	0.415627	+	1.27917i	−0.496062	+	0.868287i	$0.665221\pi$
$3$	−1.67229	−	0.451057i	−0.965496	−	0.260418i
$3$	−1.67229	−	0.451057i	−0.965496	−	0.260418i
$4$	−1.30902	+	0.951057i	−0.654508	+	0.475528i
$5$	2.48990	+	0.809017i	1.11352	+	0.361803i	0.807290	−	0.590155i	$-0.200933\pi$
$5$	2.48990	+	0.809017i	1.11352	+	0.361803i	0.306227	+	0.951959i	$0.400933\pi$
$6$	−0.166977	−	3.29032i	−0.0681683	−	1.34327i
$7$	−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
$9$	2.59310	+	1.50859i	0.864365	+	0.502864i
$10$			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
$15$	−3.79892	−	2.47599i	−0.980876	−	0.639299i
$16$	−1.42705	+	4.39201i	−0.356763	+	1.09800i
$17$	−0.812299	+	2.50000i	−0.197012	+	0.606339i	0.802936	+	0.596066i	$0.203270\pi$
$17$	−0.812299	+	2.50000i	−0.197012	+	0.606339i	−0.999947	+	0.0102734i	$0.996730\pi$
$18$	−1.20489	+	5.57768i	−0.283995	+	1.31467i
$19$	−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	$0.0588731\pi$
$23$			1.76393i			0.367805i	−0.982944	+	0.183903i	$0.941127\pi$
$24$	−0.790322	−	0.979277i	−0.161324	−	0.199894i
$25$	1.50000	+	1.08981i	0.300000	+	0.217963i
$26$	3.44095	+	4.73607i	0.674827	+	0.928819i
$27$	−3.65594	−	3.69244i	−0.703587	−	0.710610i
$28$	1.11803	+	0.363271i	0.211289	+	0.0686518i
$29$	3.07768	−	2.23607i	0.571511	−	0.415227i	−0.264142	−	0.964484i	$-0.585089\pi$
$29$	3.07768	−	2.23607i	0.571511	−	0.415227i	0.835654	+	0.549256i	$0.185089\pi$
$30$	2.24617	−	8.32766i	0.410093	−	1.52041i
$31$	−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
$36$	−4.82916	+	0.491407i	−0.804861	+	0.0819012i
$37$	−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
$39$	−5.32385	+	0.270175i	−0.852499	+	0.0432627i
$40$	1.11803	+	1.53884i	0.176777	+	0.243312i
$41$	2.48990	+	1.80902i	0.388857	+	0.282521i	0.764987	−	0.644046i	$-0.222745\pi$
$41$	2.48990	+	1.80902i	0.388857	+	0.282521i	−0.376130	+	0.926567i	$0.622745\pi$
$42$	−1.86269	+	1.50328i	−0.287420	+	0.231961i
$43$		−	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	−0.369781	−	0.929119i	$-0.620567\pi$
$47$	4.30625	−	5.92705i	0.628132	−	0.864549i	0.997913	+	0.0645695i	$0.0205674\pi$
$48$	4.36749	−	6.70103i	0.630392	−	0.967210i
$49$	2.00000	−	6.15537i	0.285714	−	0.879338i
$50$	−1.08981	+	3.35410i	−0.154123	+	0.474342i
$51$	2.48604	−	3.81433i	0.348115	−	0.534113i
$52$	−2.92705	+	4.02874i	−0.405909	+	0.558686i
$53$	4.61653	−	1.50000i	0.634129	−	0.206041i	0.0257255	−	0.999669i	$-0.491810\pi$
$53$	4.61653	−	1.50000i	0.634129	−	0.206041i	0.608403	+	0.793628i	$0.291810\pi$
$54$	4.53077	−	8.78402i	0.616560	−	1.19535i
$55$		0			0
$56$		−	0.527864i		−	0.0705388i
$57$	5.73279	−	4.62663i	0.759326	−	0.612812i
$58$	5.85410	+	4.25325i	0.768681	+	0.558480i
$59$	−1.53884	−	2.11803i	−0.200340	−	0.275745i	0.697012	−	0.717059i	$-0.254512\pi$
$59$	−1.53884	−	2.11803i	−0.200340	−	0.275745i	−0.897352	+	0.441315i	$0.854512\pi$
$60$	7.32766	−	0.371864i	0.945996	−	0.0480075i
$61$	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
$63$	−0.220655	−	2.16843i	−0.0278000	−	0.273196i
$64$	−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
$69$	0.795633	−	2.94980i	0.0957830	−	0.355115i
$70$	2.92705	−	2.12663i	0.349850	−	0.254181i
$71$	9.82084	+	3.19098i	1.16552	+	0.378700i	0.826968	−	0.562248i	$-0.190063\pi$
$71$	9.82084	+	3.19098i	1.16552	+	0.378700i	0.338550	+	0.940948i	$0.390063\pi$
$72$	0.879937	+	1.99411i	0.103702	+	0.235008i
$73$	−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
$75$	−2.01686	−	2.49907i	−0.232887	−	0.288567i
$76$		−	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
$81$	4.44829	+	7.82385i	0.494255	+	0.869317i
$82$	−1.80902	+	5.56758i	−0.199773	+	0.614837i
$83$	4.47777	−	13.7812i	0.491499	−	1.51268i	−0.330844	−	0.943686i	$-0.607333\pi$
$83$	4.47777	−	13.7812i	0.491499	−	1.51268i	0.822343	−	0.568993i	$-0.192667\pi$
$84$	−1.70582	−	1.11179i	−0.186120	−	0.121306i
$85$	−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	$-0.832590\pi$
$89$		−	9.47214i		−	1.00404i	0.864855	−	0.502022i	$-0.167410\pi$
$90$	−7.51249	+	12.9131i	−0.791886	+	1.36116i
$91$	−1.80902	−	1.31433i	−0.189637	−	0.137779i
$92$	−1.67760	−	2.30902i	−0.174902	−	0.240732i
$93$	0.0749776	+	1.47745i	0.00777481	+	0.153204i
$94$	13.2533	+	4.30625i	1.36697	+	0.444156i
$95$	−9.00854	+	6.54508i	−0.924256	+	0.671512i
$96$	12.2594	+	3.30667i	1.25122	+	0.337485i
$97$	−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	$0.113279\pi$
$101$	3.85723	+	11.8713i	0.383808	+	1.18124i	−0.553533	+	0.832827i	$0.686721\pi$
$102$	8.36144	+	2.25528i	0.827906	+	0.223306i
$103$	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
$105$	0.166977	+	3.29032i	0.0162953	+	0.321103i
$106$	5.42705	+	7.46969i	0.527122	+	0.725521i
$107$	0.138757	+	0.100813i	0.0134142	+	0.00974597i	0.594472	−	0.804116i	$-0.297361\pi$
$107$	0.138757	+	0.100813i	0.0134142	+	0.00974597i	−0.581058	+	0.813862i	$0.697361\pi$
$108$	8.29741	+	1.35645i	0.798418	+	0.130525i
$109$		−	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	$0.587416\pi$
$113$	−11.7229	+	16.1353i	−1.10280	+	1.51788i	−0.831617	+	0.555350i	$0.812584\pi$
$114$	11.7393	+	7.65124i	1.09949	+	0.716605i
$115$	−1.42705	+	4.39201i	−0.133073	+	0.409557i
$116$	−1.90211	+	5.85410i	−0.176607	+	0.543540i
$117$	9.02488	+	1.94955i	0.834351	+	0.180236i
$118$	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
$123$	−3.34786	−	4.14828i	−0.301866	−	0.374038i
$124$	1.11803	+	0.812299i	0.100402	+	0.0729466i
$125$	−4.84104	−	6.66312i	−0.432996	−	0.595967i
$126$	3.79303	−	1.67374i	0.337910	−	0.149109i
$127$	−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
$129$	−0.732786	+	2.71680i	−0.0645182	+	0.239201i
$130$	4.73607	+	14.5761i	0.415381	+	1.27841i
$131$	−4.08174			−0.356623			−0.178312	−	0.983974i	$-0.557064\pi$
$131$	−4.08174			−0.356623			−0.178312	+	0.983974i	$0.557064\pi$
$132$		0			0
$133$	3.09017			0.267952
$134$	−4.89404	−	15.0623i	−0.422781	−	1.30119i
$135$	−6.11568	−	12.1515i	−0.526354	−	1.04584i
$136$	−1.54508	+	1.12257i	−0.132490	+	0.0962596i
$137$	−8.28199	−	2.69098i	−0.707579	−	0.229906i	−0.0669491	−	0.997756i	$-0.521327\pi$
$137$	−8.28199	−	2.69098i	−0.707579	−	0.229906i	−0.640629	+	0.767850i	$0.721327\pi$
$138$	5.80390	−	0.294537i	0.494061	−	0.0250726i
$139$	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
$141$	−9.87473	+	7.96937i	−0.831603	+	0.671142i
$142$			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
$147$	−6.12099	+	9.39144i	−0.504851	+	0.774593i
$148$	1.50000	−	4.61653i	0.123299	−	0.379476i
$149$	0.0530006	−	0.163119i	0.00434198	−	0.0133632i	−0.948862	−	0.315691i	$-0.897764\pi$
$149$	0.0530006	−	0.163119i	0.00434198	−	0.0133632i	0.953204	+	0.302328i	$0.0977637\pi$
$150$	3.33537	−	5.11746i	0.272332	−	0.417839i
$151$	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
$156$	6.71206	−	5.41695i	0.537395	−	0.433703i
$157$	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
$159$	−8.39675	+	0.426119i	−0.665905	+	0.0337934i
$160$	−18.2533	−	5.93085i	−1.44305	−	0.468875i
$161$	1.03681	−	0.753289i	0.0817123	−	0.0593675i
$162$	−11.5388	+	12.6458i	−0.906577	+	0.993547i
$163$	−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	0.952316	−	0.305114i	$-0.0986945\pi$
$167$	0.0327561	+	0.100813i	0.00253475	+	0.00780115i	−0.949781	+	0.312915i	$0.898695\pi$
$168$	−0.238097	+	0.882741i	−0.0183695	+	0.0681049i
$169$	−2.85410	+	2.07363i	−0.219546	+	0.159510i
$170$	−12.4495	−	4.04508i	−0.954832	−	0.310244i
$171$	−11.6737	+	5.15124i	−0.892713	+	0.393925i
$172$	1.54508	+	2.12663i	0.117812	+	0.162154i
$173$	−17.9313	−	13.0279i	−1.36329	−	0.990490i	−0.998228	−	0.0595081i	$-0.981047\pi$
$173$	−17.9313	−	13.0279i	−1.36329	−	0.990490i	−0.365065	−	0.930982i	$-0.618953\pi$
$174$	−7.87129	−	9.75320i	−0.596721	−	0.739388i
$175$		−	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	−0.886822	−	0.462112i	$-0.847092\pi$
$179$	−2.31838	+	3.19098i	−0.173284	+	0.238505i	0.713537	+	0.700617i	$0.247092\pi$
$180$	−12.4217	−	2.68332i	−0.925858	−	0.200003i
$181$	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
$183$	−6.17171	−	4.02250i	−0.456226	−	0.297352i
$184$	−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
$189$	−0.609085	+	3.72577i	−0.0443044	+	0.271010i
$190$	−17.1353	−	12.4495i	−1.24312	−	0.903181i
$191$	11.6169	+	15.9894i	0.840573	+	1.15695i	0.985862	+	0.167560i	$0.0535888\pi$
$191$	11.6169	+	15.9894i	0.840573	+	1.15695i	−0.145289	+	0.989389i	$0.546411\pi$
$192$	0.413311	+	8.14437i	0.0298281	+	0.587769i
$193$	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
$195$	−13.4744	−	3.63438i	−0.964924	−	0.260263i
$196$	3.23607	+	9.95959i	0.231148	+	0.711400i
$197$	−15.8374			−1.12837			−0.564186	−	0.825648i	$-0.690810\pi$
$197$	−15.8374			−1.12837			−0.564186	+	0.825648i	$0.690810\pi$
$198$		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
$201$	13.9239	+	3.75560i	0.982114	+	0.264900i
$202$	−19.2082	+	13.9556i	−1.35148	+	0.981911i
$203$	−2.62866	−	0.854102i	−0.184495	−	0.0599462i
$204$	0.373373	+	7.35738i	0.0261413	+	0.515120i
$205$	4.73607	+	6.51864i	0.330781	+	0.455281i
$206$	10.4086	+	7.56231i	0.725203	+	0.526891i
$207$	−2.66106	+	4.57405i	−0.184956	+	0.317918i
$208$			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
$213$	−14.9840	−	9.76600i	−1.02668	−	0.669155i
$214$	−0.100813	+	0.310271i	−0.00689144	+	0.0212097i
$215$	1.31433	−	4.04508i	0.0896364	−	0.275873i
$216$	−0.572051	−	3.73163i	−0.0389232	−	0.253905i
$217$	−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
$222$	6.20727	+	7.69134i	0.416605	+	0.516209i
$223$	−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
$225$	2.24556	+	5.08888i	0.149704	+	0.339259i
$226$	−36.0795	−	11.7229i	−2.39997	−	0.779799i
$227$	5.11855	−	3.71885i	0.339730	−	0.246829i	−0.404818	−	0.914397i	$-0.632665\pi$
$227$	5.11855	−	3.71885i	0.339730	−	0.246829i	0.744548	+	0.667569i	$0.232665\pi$
$228$	−3.10413	+	11.5085i	−0.205576	+	0.762171i
$229$	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	0.997003	−	0.0773625i	$-0.0246499\pi$
$233$	2.21238	+	6.80902i	0.144938	+	0.446074i	−0.852065	+	0.523436i	$0.824650\pi$
$234$	1.77793	+	17.4721i	0.116227	+	1.14219i
$235$	15.5172	−	11.2739i	1.01223	−	0.735430i
$236$	4.02874	+	1.30902i	0.262249	+	0.0852097i
$237$	18.4851	−	0.938085i	1.20074	−	0.0609352i
$238$	2.13525	+	2.93893i	0.138408	+	0.190502i
$239$	20.8702	+	15.1631i	1.34998	+	0.980821i	0.999012	+	0.0444345i	$0.0141486\pi$
$239$	20.8702	+	15.1631i	1.34998	+	0.980821i	0.350971	+	0.936386i	$0.385851\pi$
$240$	16.2958	−	13.1515i	1.05189	−	0.848926i
$241$		−	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
$246$	5.53649	−	8.49463i	0.352994	−	0.541598i
$247$	−4.04508	+	12.4495i	−0.257383	+	0.792142i
$248$	0.191758	−	0.590170i	0.0121766	−	0.0374758i
$249$	−13.7042	+	21.0263i	−0.868468	+	1.33249i
$250$	9.20820	−	12.6740i	0.582378	−	0.801574i
$251$	−4.44501	+	1.44427i	−0.280567	+	0.0911616i	−0.445920	−	0.895073i	$-0.647123\pi$
$251$	−4.44501	+	1.44427i	−0.280567	+	0.0911616i	0.165354	+	0.986234i	$0.447123\pi$
$252$	2.35114	+	2.62866i	0.148108	+	0.165590i
$253$		0			0
$254$		−	25.1246i		−	1.57646i
$255$	9.27584	−	7.48604i	0.580876	−	0.468794i
$256$	−16.3992	−	11.9147i	−1.02495	−	0.744669i
$257$	6.62464	+	9.11803i	0.413234	+	0.568767i	0.964003	−	0.265890i	$-0.0856658\pi$
$257$	6.62464	+	9.11803i	0.413234	+	0.568767i	−0.550770	+	0.834657i	$0.685666\pi$
$258$	−5.34545	+	0.271271i	−0.332793	+	0.0168886i
$259$	2.07295	+	0.673542i	0.128807	+	0.0418519i
$260$	−10.5474	+	7.66312i	−0.654121	+	0.475246i
$261$	11.3540	−	1.15537i	0.702798	−	0.0715154i
$262$	−2.39919	−	7.38394i	−0.148222	−	0.456181i
$263$	23.2744			1.43516			0.717580	−	0.696476i	$-0.245250\pi$
$263$	23.2744			1.43516			0.717580	+	0.696476i	$0.245250\pi$
$264$		0			0
$265$	12.7082			0.780659
$266$	1.81636	+	5.59017i	0.111368	+	0.342755i
$267$	−4.27247	+	15.8401i	−0.261471	+	0.969401i
$268$	10.8992	−	7.91872i	0.665774	−	0.483713i
$269$	22.0988	+	7.18034i	1.34739	+	0.437793i	0.891813	−	0.452404i	$-0.149434\pi$
$269$	22.0988	+	7.18034i	1.34739	+	0.437793i	0.455575	+	0.890197i	$0.349434\pi$
$270$	18.3876	−	18.2059i	1.11903	−	1.10797i
$271$	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
$273$	2.43236	+	3.01390i	0.147213	+	0.182410i
$274$		−	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
$279$	0.541028	−	2.50454i	0.0323905	−	0.149943i
$280$	0.427051	−	1.31433i	0.0255212	−	0.0785461i
$281$	−5.08580	+	15.6525i	−0.303393	+	0.933748i	0.676879	+	0.736095i	$0.263332\pi$
$281$	−5.08580	+	15.6525i	−0.303393	+	0.933748i	−0.980272	+	0.197654i	$0.936668\pi$
$282$	−20.2210	−	13.1793i	−1.20414	−	0.784815i
$283$	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
$288$	−19.0098	−	11.0594i	−1.12016	−	0.651681i
$289$	8.16312	+	5.93085i	0.480183	+	0.348874i
$290$	11.1352	+	15.3262i	0.653879	+	0.899988i
$291$	0.580966	+	11.4480i	0.0340568	+	0.671096i
$292$	23.4164	+	7.60845i	1.37034	+	0.445251i
$293$	−7.91872	+	5.75329i	−0.462617	+	0.336111i	−0.794557	−	0.607190i	$-0.792297\pi$
$293$	−7.91872	+	5.75329i	−0.462617	+	0.336111i	0.331940	+	0.943300i	$0.392297\pi$
$294$	−20.5871	−	5.55284i	−1.20066	−	0.323848i
$295$	−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
$300$	5.01686	+	1.35317i	0.289649	+	0.0781253i
$301$	−0.954915	+	0.693786i	−0.0550404	+	0.0399892i
$302$	31.7809	+	10.3262i	1.82878	+	0.594208i
$303$	−1.09576	−	21.5921i	−0.0629496	−	1.24043i
$304$	−11.5451	−	15.8904i	−0.662156	−	0.911380i
$305$	9.00854	+	6.54508i	0.515827	+	0.374770i
$306$	−12.9655	−	7.54297i	−0.741187	−	0.431203i
$307$			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	−0.884172	−	0.467161i	$-0.845277\pi$
$311$	−2.93893	+	4.04508i	−0.166651	+	0.229376i	0.717521	+	0.696537i	$0.245277\pi$
$312$	−3.24466	−	2.11475i	−0.183693	−	0.119724i
$313$	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
$315$	1.20489	−	5.57768i	0.0678877	−	0.314267i
$316$	10.1631	−	13.9883i	0.571720	−	0.786905i
$317$	−0.224514	+	0.0729490i	−0.0126100	+	0.00409722i	−0.315315	−	0.948987i	$-0.602110\pi$
$317$	−0.224514	+	0.0729490i	−0.0126100	+	0.00409722i	0.302705	+	0.953084i	$0.402110\pi$
$318$	−5.70634	−	14.9394i	−0.319996	−	0.837759i
$319$		0			0
$320$		−	12.3262i		−	0.689058i
$321$	−0.186570	−	0.231176i	−0.0104133	−	0.0129030i
$322$	1.97214	+	1.43284i	0.109903	+	0.0798491i
$323$	−6.57164	−	9.04508i	−0.365656	−	0.503282i
$324$	−13.2638	−	6.01098i	−0.736879	−	0.333943i
$325$	5.42705	+	1.76336i	0.301039	+	0.0978134i
$326$	19.0539	−	13.8435i	1.05530	−	0.766718i
$327$	−3.43184	+	12.7235i	−0.189781	+	0.703613i
$328$	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
$333$	−8.95376	+	0.911119i	−0.490663	+	0.0499290i
$334$	−0.163119	+	0.118513i	−0.00892547	+	0.00648474i
$335$	−20.7315	−	6.73607i	−1.13268	−	0.368031i
$336$	−5.80390	+	0.294537i	−0.316629	+	0.0160683i
$337$	−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
$339$	26.8821	−	21.6951i	1.46003	−	1.17832i
$340$		−	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
$345$	4.36749	−	6.70103i	0.235138	−	0.360771i
$346$	13.0279	−	40.0956i	0.700382	−	2.15556i
$347$	−9.51057	+	29.2705i	−0.510554	+	1.57132i	0.280675	+	0.959803i	$0.409442\pi$
$347$	−9.51057	+	29.2705i	−0.510554	+	1.57132i	−0.791229	+	0.611520i	$0.790558\pi$
$348$	5.82141	−	8.93179i	0.312060	−	0.478794i
$349$	−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	$0.136241\pi$
$353$			15.5967i			0.830131i	−0.909792	+	0.415066i	$0.863759\pi$
$354$	−6.71206	+	5.41695i	−0.356742	+	0.287908i
$355$	21.8713	+	15.8904i	1.16081	+	0.843377i
$356$	9.00854	+	12.3992i	0.477451	+	0.657156i
$357$	−3.30367	+	0.167655i	−0.174849	+	0.00887324i
$358$	−7.13525	−	2.31838i	−0.377110	−	0.122530i
$359$	20.1967	−	14.6738i	1.06594	−	0.774452i	0.0907628	−	0.995873i	$-0.471069\pi$
$359$	20.1967	−	14.6738i	1.06594	−	0.774452i	0.975178	+	0.221421i	$0.0710695\pi$
$360$	0.577684	+	5.67702i	0.0304466	+	0.299205i
$361$	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
$366$	3.64912	−	13.5291i	0.190743	−	0.707177i
$367$	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
$369$	3.72747	+	8.44720i	0.194045	+	0.439744i
$370$	−8.78115	−	12.0862i	−0.456510	−	0.628333i
$371$	−2.85317	−	2.07295i	−0.148129	−	0.107622i
$372$	−1.50328	−	1.86269i	−0.0779416	−	0.0965762i
$373$		−	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
$378$	−7.09799	+	1.08811i	−0.365081	+	0.0559662i
$379$	−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
$381$	19.1667	+	12.4922i	0.981940	+	0.639993i
$382$	−22.0967	+	30.4136i	−1.13057	+	1.55609i
$383$	13.7108	−	4.45492i	0.700590	−	0.227636i	0.0630025	−	0.998013i	$-0.479932\pi$
$383$	13.7108	−	4.45492i	0.700590	−	0.227636i	0.637588	+	0.770378i	$0.279932\pi$
$384$	9.23305	−	3.52671i	0.471172	−	0.179972i
$385$		0			0
$386$			38.4164i			1.95534i
$387$	2.45086	−	4.21274i	0.124584	−	0.214146i
$388$	8.66312	+	6.29412i	0.439803	+	0.319536i
$389$	−5.65334	−	7.78115i	−0.286636	−	0.394520i	0.641282	−	0.767305i	$-0.278403\pi$
$389$	−5.65334	−	7.78115i	−0.286636	−	0.394520i	−0.927918	+	0.372785i	$0.878403\pi$
$390$	−1.34542	−	26.5117i	−0.0681279	−	1.34247i
$391$	−4.40983	−	1.43284i	−0.223015	−	0.0724619i
$392$	3.80423	−	2.76393i	0.192142	−	0.139600i
$393$	6.82585	+	1.84110i	0.344318	+	0.0928710i
$394$	−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
$399$	−5.16765	−	1.39384i	−0.258706	−	0.0697793i
$400$	−6.92705	+	5.03280i	−0.346353	+	0.251640i
$401$	−20.1109	−	6.53444i	−1.00429	−	0.326314i	−0.239713	−	0.970844i	$-0.577053\pi$
$401$	−20.1109	−	6.53444i	−1.00429	−	0.326314i	−0.764580	+	0.644529i	$0.777053\pi$
$402$	1.39029	+	27.3960i	0.0693416	+	1.36639i
$403$	−1.54508	−	2.12663i	−0.0769662	−	0.105935i
$404$	−16.3395	−	11.8713i	−0.812919	−	0.590620i
$405$	4.74617	+	23.0793i	0.235839	+	1.14682i
$406$		−	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
$411$	12.6361	+	8.23575i	0.623293	+	0.406239i
$412$	−3.38197	+	10.4086i	−0.166618	+	0.512796i
$413$	−0.587785	+	1.80902i	−0.0289230	+	0.0890159i
$414$	−9.83865	−	2.12534i	−0.483543	−	0.104455i
$415$	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	$-0.954326\pi$
$419$		−	5.85410i		−	0.285992i	0.989723	−	0.142996i	$-0.0456735\pi$
$420$	−3.34786	−	4.14828i	−0.163359	−	0.202415i
$421$	−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
$423$	20.1080	−	8.87303i	0.977686	−	0.431421i
$424$	3.35410	+	1.08981i	0.162890	+	0.0529260i
$425$	−3.94298	+	2.86475i	−0.191263	+	0.138961i
$426$	8.85950	−	32.8465i	0.429244	−	1.59142i
$427$	−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	$-0.917271\pi$
$431$	−6.96767	−	21.4443i	−0.335621	−	1.03293i	0.630795	−	0.775950i	$-0.282729\pi$
$432$	21.4344	−	10.7877i	1.03126	−	0.519021i
$433$	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
$435$	−17.2284	+	0.874305i	−0.826036	+	0.0419197i
$436$	7.23607	+	9.95959i	0.346545	+	0.476978i
$437$	−6.06961	−	4.40983i	−0.290349	−	0.210951i
$438$	−39.0128	+	31.4852i	−1.86410	+	1.50442i
$439$			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	−0.637358	−	0.770568i	$-0.719973\pi$
$443$	6.15537	−	8.47214i	0.292450	−	0.402523i	0.929808	+	0.368045i	$0.119973\pi$
$444$	−4.59075	+	7.04358i	−0.217867	+	0.334273i
$445$	7.66312	−	23.5847i	0.363267	−	1.11802i
$446$	3.66547	−	11.2812i	0.173565	−	0.534178i
$447$	−0.162208	+	0.248876i	−0.00767218	+	0.0117714i
$448$	−2.01064	+	2.76741i	−0.0949940	+	0.130748i
$449$	−7.50245	+	2.43769i	−0.354063	+	0.115042i	−0.480648	−	0.876914i	$-0.659598\pi$
$449$	−7.50245	+	2.43769i	−0.354063	+	0.115042i	0.126585	+	0.991956i	$0.459598\pi$
$450$	−7.88597	+	7.05342i	−0.371748	+	0.332502i
$451$		0			0
$452$		−	32.2705i		−	1.51788i
$453$	−23.6792	+	19.1103i	−1.11255	+	0.897878i
$454$	9.73607	+	7.07367i	0.456936	+	0.331984i
$455$	−3.44095	−	4.73607i	−0.161314	−	0.222030i
$456$	5.34545	−	0.271271i	0.250324	−	0.0127034i
$457$	−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
$459$	12.2008	−	6.14050i	0.569485	−	0.286614i
$460$	−2.30902	−	7.10642i	−0.107658	−	0.331339i
$461$	26.8666			1.25130			0.625651	−	0.780103i	$-0.284833\pi$
$461$	26.8666			1.25130			0.625651	+	0.780103i	$0.284833\pi$
$462$		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
$465$	−1.00859	+	3.73935i	−0.0467724	+	0.173408i
$466$	−11.0172	+	8.00448i	−0.510363	+	0.370800i
$467$	−22.4948	−	7.30902i	−1.04094	−	0.338221i	−0.261831	−	0.965114i	$-0.584326\pi$
$467$	−22.4948	−	7.30902i	−1.04094	−	0.338221i	−0.779106	+	0.626893i	$0.784326\pi$
$468$	−13.6679	+	6.03118i	−0.631797	+	0.278791i
$469$	3.55573	+	4.89404i	0.164188	+	0.225986i
$470$	29.5155	+	21.4443i	1.36145	+	0.989151i
$471$	−4.03373	−	4.99814i	−0.185864	−	0.230302i
$472$		−	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
$477$	14.2340	+	3.07481i	0.651729	+	0.140786i
$478$	−15.1631	+	46.6673i	−0.693545	+	2.13451i
$479$	7.07367	−	21.7705i	0.323204	−	0.994720i	−0.649041	−	0.760754i	$-0.724829\pi$
$479$	7.07367	−	21.7705i	0.323204	−	0.994720i	0.972245	−	0.233966i	$-0.0751705\pi$
$480$	27.8496	+	18.1514i	1.27116	+	0.828492i
$481$	−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
$486$	25.0002	−	15.9427i	1.13403	−	0.723177i
$487$	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
$489$	1.08695	+	21.4186i	0.0491538	+	0.968584i
$490$	30.6525	+	9.95959i	1.38474	+	0.449929i
$491$	−21.5968	+	15.6910i	−0.974649	+	0.708124i	−0.956506	−	0.291711i	$-0.905775\pi$
$491$	−21.5968	+	15.6910i	−0.974649	+	0.708124i	−0.0181429	+	0.999835i	$0.505775\pi$
$492$	8.32766	+	2.24617i	0.375440	+	0.101265i
$493$	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
$498$	−46.0921	−	12.4322i	−2.06544	−	0.557098i
$499$	−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
$501$	−0.00930534	−	0.183363i	−0.000415732	−	0.00819207i
$502$	−5.22542	−	7.19218i	−0.233222	−	0.321003i
$503$	−4.25325	−	3.09017i	−0.189643	−	0.137784i	0.488912	−	0.872333i	$-0.337394\pi$
$503$	−4.25325	−	3.09017i	−0.189643	−	0.137784i	−0.678556	+	0.734549i	$0.737394\pi$
$504$	0.796332	−	1.36880i	0.0354714	−	0.0609713i
$505$			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	−0.812526	−	0.582925i	$-0.801908\pi$
$509$	−0.159002	+	0.218847i	−0.00704763	+	0.00970022i	0.805479	+	0.592625i	$0.201908\pi$
$510$	18.9946	+	12.3800i	0.841094	+	0.548194i
$511$	−3.41641	+	10.5146i	−0.151133	+	0.465140i
$512$	8.38800	−	25.8156i	0.370701	−	1.14090i
$513$	21.8454	−	3.34885i	0.964496	−	0.147855i
$514$	−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
$519$	24.1100	+	29.8744i	1.05831	+	1.31134i
$520$	4.73607	+	3.44095i	0.207690	+	0.150896i
$521$	−11.9272	−	16.4164i	−0.522541	−	0.719216i	0.463430	−	0.886134i	$-0.346619\pi$
$521$	−11.9272	−	16.4164i	−0.522541	−	0.719216i	−0.985971	+	0.166918i	$0.946619\pi$
$522$	8.76382	+	19.8606i	0.383582	+	0.869273i
$523$	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
$525$	−0.607611	+	2.25271i	−0.0265183	+	0.0983164i
$526$	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
$531$	−0.795113	−	7.81375i	−0.0345050	−	0.339088i
$532$	−4.04508	+	2.93893i	−0.175377	+	0.127419i
$533$	9.00854	+	2.92705i	0.390203	+	0.126785i
$534$	−31.1664	+	1.58163i	−1.34870	+	0.0684440i
$535$	0.263932	+	0.363271i	0.0114108	+	0.0157056i
$536$	−4.89404	−	3.55573i	−0.211390	−	0.153584i
$537$	5.31632	−	4.29052i	0.229416	−	0.185150i
$538$			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
$543$	−11.5722	+	17.7552i	−0.496611	+	0.761950i
$544$	5.95492	−	18.3273i	0.255315	−	0.785778i
$545$	6.15537	−	18.9443i	0.263667	−	0.811483i
$546$	−4.02250	+	6.17171i	−0.172147	+	0.264125i
$547$	−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
$552$	1.72738	−	1.39407i	0.0735221	−	0.0593358i
$553$	6.28115	+	4.56352i	0.267102	+	0.194061i
$554$	−22.9641	−	31.6074i	−0.975652	−	1.34287i
$555$	13.5862	−	0.689474i	0.576703	−	0.0292666i
$556$	−2.66312	−	0.865300i	−0.112941	−	0.0366969i
$557$	6.51864	−	4.73607i	0.276204	−	0.200674i	−0.441056	−	0.897479i	$-0.645396\pi$
$557$	6.51864	−	4.73607i	0.276204	−	0.200674i	0.717260	+	0.696806i	$0.245396\pi$
$558$	4.84876	−	0.493401i	0.205264	−	0.0208873i
$559$	−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	$0.0610353\pi$
$563$	7.10642	+	21.8713i	0.299500	+	0.921766i	−0.682173	+	0.731191i	$0.738965\pi$
$564$	5.34687	−	19.8235i	0.225144	−	0.834719i
$565$	−42.2426	+	30.6911i	−1.77716	+	1.29118i
$566$	14.3844	+	4.67376i	0.604620	+	0.196453i
$567$	2.69910	−	5.95583i	0.113351	−	0.250121i
$568$	4.40983	+	6.06961i	0.185032	+	0.254675i
$569$	−6.60440	−	4.79837i	−0.276871	−	0.201158i	0.440681	−	0.897664i	$-0.354737\pi$
$569$	−6.60440	−	4.79837i	−0.276871	−	0.201158i	−0.717551	+	0.696506i	$0.754737\pi$
$570$	23.0397	+	28.5481i	0.965025	+	1.19575i
$571$		−	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
$576$	2.98240	−	13.8062i	0.124266	−	0.575257i
$577$	−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
$579$	−29.3066	−	19.1009i	−1.21794	−	0.793808i
$580$	−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
$585$	20.8938	+	12.1555i	0.863853	+	0.502566i
$586$	−15.0623	−	10.9434i	−0.622218	−	0.452068i
$587$	−3.49396	−	4.80902i	−0.144211	−	0.198489i	0.730801	−	0.682590i	$-0.239147\pi$
$587$	−3.49396	−	4.80902i	−0.144211	−	0.198489i	−0.875012	+	0.484101i	$0.839147\pi$
$588$	−0.919299	−	18.1150i	−0.0379113	−	0.747048i
$589$	3.45492	+	1.12257i	0.142357	+	0.0462547i
$590$	10.5474	−	7.66312i	0.434229	−	0.315486i
$591$	26.4848	+	7.14358i	1.08944	+	0.293848i
$592$	−4.28115	−	13.1760i	−0.175954	−	0.541532i
$593$	3.35520			0.137781			0.0688907	−	0.997624i	$-0.478054\pi$
$593$	3.35520			0.137781			0.0688907	+	0.997624i	$0.478054\pi$
$594$		0			0
$595$	5.00000			0.204980
$596$	0.0857567	+	0.263932i	0.00351273	+	0.0108111i
$597$	3.73935	+	1.00859i	0.153041	+	0.0412790i
$598$	−8.35410	+	6.06961i	−0.341625	+	0.248205i
$599$	7.88597	+	2.56231i	0.322212	+	0.104693i	0.465657	−	0.884965i	$-0.345818\pi$
$599$	7.88597	+	2.56231i	0.322212	+	0.104693i	−0.143445	+	0.989658i	$0.545818\pi$
$600$	−0.118254	−	2.33022i	−0.00482770	−	0.0951308i
$601$	−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
$603$	−21.5907	−	12.5609i	−0.879243	−	0.511520i
$604$			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
$609$	4.01062	+	2.61398i	0.162519	+	0.105924i
$610$	−6.54508	+	20.1437i	−0.265003	+	0.815595i
$611$	6.96767	−	21.4443i	0.281882	−	0.867542i
$612$	2.69421	−	12.4721i	0.108907	−	0.504154i
$613$	−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	$0.133542\pi$
$617$			20.2361i			0.814673i	−0.913278	+	0.407337i	$0.866458\pi$
$618$	−13.9952	−	17.3412i	−0.562969	−	0.697567i
$619$	−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
$621$	6.51320	−	6.44884i	0.261366	−	0.258783i
$622$	−9.04508	−	2.93893i	−0.362675	−	0.117840i
$623$	−5.56758	+	4.04508i	−0.223060	+	0.162063i
$624$	6.41080	−	23.7680i	0.256637	−	0.951481i
$625$	−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
$630$	10.7983	−	1.09882i	0.430216	−	0.0437780i
$631$	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
$633$	11.7211	−	0.594825i	0.465873	−	0.0236422i
$634$	−0.263932	−	0.363271i	−0.0104821	−	0.0144273i
$635$	−27.9767	−	20.3262i	−1.11022	−	0.806622i
$636$	10.5862	−	8.54358i	0.419771	−	0.338775i
$637$		−	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	−0.964310	−	0.264778i	$-0.914701\pi$
$641$	−10.4944	+	14.4443i	−0.414503	+	0.570514i	0.549806	+	0.835292i	$0.314701\pi$
$642$	0.308538	−	0.473390i	0.0121770	−	0.0186832i
$643$	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
$645$	−4.02250	+	6.17171i	−0.158386	+	0.243011i
$646$	12.5000	−	17.2048i	0.491806	−	0.676913i
$647$	−41.9978	+	13.6459i	−1.65110	+	0.536476i	−0.978979	−	0.203963i	$-0.934618\pi$
$647$	−41.9978	+	13.6459i	−1.65110	+	0.536476i	−0.672124	+	0.740439i	$0.734618\pi$
$648$	−0.726543	+	6.49839i	−0.0285413	+	0.255281i
$649$		0			0
$650$			10.8541i			0.425733i
$651$	0.836402	−	0.675016i	0.0327812	−	0.0264560i
$652$	16.2082	+	11.7759i	0.634762	+	0.461182i
$653$	20.6582	+	28.4336i	0.808419	+	1.11269i	0.991565	+	0.129608i	$0.0413719\pi$
$653$	20.6582	+	28.4336i	0.808419	+	1.11269i	−0.183146	+	0.983086i	$0.558628\pi$
$654$	−25.0343	+	1.27044i	−0.978917	+	0.0496781i
$655$	−10.1631	−	3.30220i	−0.397106	−	0.129028i
$656$	−11.4984	+	8.35410i	−0.448938	+	0.326173i
$657$	−4.62147	−	45.4162i	−0.180301	−	1.77185i
$658$	−3.12868	−	9.62908i	−0.121969	−	0.375381i
$659$	−39.8384			−1.55188			−0.775941	−	0.630805i	$-0.782725\pi$
$659$	−39.8384			−1.55188			−0.775941	+	0.630805i	$0.782725\pi$
$660$		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
$663$	3.64912	−	13.5291i	0.141720	−	0.525427i
$664$	8.51722	−	6.18812i	0.330532	−	0.240146i
$665$	7.69421	+	2.50000i	0.298369	+	0.0969458i
$666$	−6.91112	−	15.6620i	−0.267800	−	0.606889i
$667$	3.94427	+	5.42882i	0.152723	+	0.210205i
$668$	−0.138757	−	0.100813i	−0.00536868	−	0.00390057i
$669$	6.78350	+	8.40534i	0.262265	+	0.324969i
$670$		−	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
$675$	−1.45985	−	9.52295i	−0.0561896	−	0.366539i
$676$	1.76393	−	5.42882i	0.0678435	−	0.208801i
$677$	−12.2047	+	37.5623i	−0.469066	+	1.44364i	0.384730	+	0.923029i	$0.374295\pi$
$677$	−12.2047	+	37.5623i	−0.469066	+	1.44364i	−0.853796	+	0.520608i	$0.825705\pi$
$678$	55.0477	+	35.8781i	2.11409	+	1.37789i
$679$	−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	$0.0550836\pi$
$683$			9.00000i			0.344375i	−0.985064	+	0.172188i	$0.944916\pi$
$684$	10.3820	−	17.8455i	0.396966	−	0.682338i
$685$	−18.4443	−	13.4005i	−0.704719	−	0.512009i
$686$	−10.9434	−	15.0623i	−0.417821	−	0.575082i
$687$	−2.20557	−	43.4612i	−0.0841478	−	1.65815i
$688$	7.13525	+	2.31838i	0.272029	+	0.0883876i
$689$	12.0862	−	8.78115i	0.460448	−	0.334535i
$690$	14.6894	+	3.96209i	0.559217	+	0.150834i
$691$	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
$696$	−4.62209	−	1.24669i	−0.175200	−	0.0472556i
$697$	−6.54508	+	4.75528i	−0.247913	+	0.180119i
$698$	−29.4625	−	9.57295i	−1.11517	−	0.362341i
$699$	−0.628492	−	12.3845i	−0.0237717	−	0.468427i
$700$	1.28115	+	1.76336i	0.0484230	+	0.0666486i
$701$	14.1271	+	10.2639i	0.533573	+	0.387663i	0.821693	−	0.569931i	$-0.193030\pi$
$701$	14.1271	+	10.2639i	0.533573	+	0.387663i	−0.288120	+	0.957594i	$0.593030\pi$
$702$	4.90769	−	30.0203i	0.185229	−	1.13304i
$703$		−	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
$708$	−6.14677	−	4.00624i	−0.231010	−	0.150564i
$709$	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
$711$	−31.3356	−	6.76910i	−1.17518	−	0.253861i
$712$	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
$717$	−28.0616	−	34.7708i	−1.04798	−	1.29854i
$718$	38.4164	+	27.9112i	1.43369	+	1.04164i
$719$	5.95110	+	8.19098i	0.221938	+	0.305472i	0.905438	−	0.424479i	$-0.139543\pi$
$719$	5.95110	+	8.19098i	0.221938	+	0.305472i	−0.683499	+	0.729951i	$0.739543\pi$
$720$	−33.1834	+	14.6428i	−1.23667	+	0.545704i
$721$	−4.67376	−	1.51860i	−0.174060	−	0.0565555i
$722$	−1.40008	+	1.01722i	−0.0521057	+	0.0378570i
$723$	−8.82995	+	32.7370i	−0.328390	+	1.21750i
$724$	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
$729$	−0.268157	+	26.9987i	−0.00993173	+	0.999951i
$730$	61.3050	−	44.5407i	2.26900	−	1.64852i
$731$	4.06150	+	1.31966i	0.150220	+	0.0488094i
$732$	11.9045	−	0.604130i	0.440003	−	0.0223293i
$733$	−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
$735$	−22.8385	+	18.4317i	−0.842410	+	0.679865i
$736$		−	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
$741$	12.3800	−	18.9946i	0.454790	−	0.697783i
$742$	2.07295	−	6.37988i	0.0761004	−	0.234213i
$743$	−12.9188	+	39.7599i	−0.473943	+	1.45865i	0.373434	+	0.927657i	$0.378180\pi$
$743$	−12.9188	+	39.7599i	−0.473943	+	1.45865i	−0.847377	+	0.530991i	$0.821820\pi$
$744$	−0.586874	+	0.900441i	−0.0215159	+	0.0330118i
$745$	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
$750$	−21.1155	+	17.0412i	−0.771028	+	0.622256i
$751$	−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
$753$	8.08479	−	0.410287i	0.294626	−	0.0149517i
$754$	21.1803	+	6.88191i	0.771342	+	0.250624i
$755$	37.2097	−	27.0344i	1.35420	−	0.983884i
$756$	−2.74611	−	5.45637i	−0.0998752	−	0.198446i
$757$	−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	$0.195352\pi$
$761$	13.6453	+	41.9959i	0.494642	+	1.52235i	−0.322872	+	0.946443i	$0.604648\pi$
$762$	−11.3326	+	42.0156i	−0.410538	+	1.52206i
$763$	−4.47214	+	3.24920i	−0.161902	+	0.117629i
$764$	−30.4136	−	9.88197i	−1.10032	−	0.357517i
$765$	−18.8885	+	8.33489i	−0.682915	+	0.301348i
$766$	16.1180	+	22.1846i	0.582368	+	0.801561i
$767$	−6.51864	−	4.73607i	−0.235374	−	0.171010i
$768$	22.0500	+	27.3218i	0.795659	+	0.985890i
$769$			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	−0.718153	−	0.695885i	$-0.755012\pi$
$773$	4.60401	−	6.33688i	0.165595	−	0.227922i	0.883748	+	0.467964i	$0.155012\pi$
$774$	9.06150	+	1.95746i	0.325709	+	0.0703593i
$775$	0.489357	−	1.50609i	0.0175782	−	0.0541002i
$776$	1.48584	−	4.57295i	0.0533386	−	0.164159i
$777$	−3.16276	−	2.06137i	−0.113463	−	0.0739514i
$778$	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
$783$	−19.5084	−	3.18921i	−0.697172	−	0.113973i
$784$	24.1803	+	17.5680i	0.863584	+	0.627430i
$785$	5.70634	+	7.85410i	0.203668	+	0.280325i
$786$	0.681559	+	13.4302i	0.0243104	+	0.479041i
$787$	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
$789$	−38.9215	−	10.4981i	−1.38564	−	0.373741i
$790$	−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
$795$	−21.2518	−	5.73212i	−0.753723	−	0.203297i
$796$	2.92705	−	2.12663i	0.103747	−	0.0753763i
$797$	−20.9888	−	6.81966i	−0.743460	−	0.241565i	−0.0872952	−	0.996182i	$-0.527822\pi$
$797$	−20.9888	−	6.81966i	−0.743460	−	0.241565i	−0.656165	+	0.754618i	$0.727822\pi$
$798$	−0.515989	−	10.1677i	−0.0182658	−	0.359931i
$799$	11.3197	+	15.5802i	0.400461	+	0.551187i
$800$	−10.9964	−	7.98936i	−0.388782	−	0.282466i
$801$	14.2896	−	24.5622i	0.504898	−	0.867861i
$802$		−	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
$807$	−33.7168	−	21.9754i	−1.18689	−	0.773571i
$808$	−2.80244	+	8.62502i	−0.0985895	+	0.303427i
$809$	8.09024	−	24.8992i	0.284438	−	0.875409i	−0.702129	−	0.712050i	$-0.747767\pi$
$809$	8.09024	−	24.8992i	0.284438	−	0.875409i	0.986567	−	0.163359i	$-0.0522329\pi$
$810$	−38.9612	+	22.1516i	−1.36896	+	0.778328i
$811$	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
$816$	13.2049	+	16.3620i	0.462263	+	0.572783i
$817$	5.59017	+	4.06150i	0.195575	+	0.142094i
$818$	38.2793	+	52.6869i	1.33840	+	1.84215i
$819$	−2.70817	−	6.13725i	−0.0946311	−	0.214453i
$820$	−12.3992	−	4.02874i	−0.432998	−	0.140690i
$821$	−29.9115	+	21.7320i	−1.04392	+	0.758452i	−0.971047	−	0.238889i	$-0.923217\pi$
$821$	−29.9115	+	21.7320i	−1.04392	+	0.758452i	−0.0728729	+	0.997341i	$0.523217\pi$
$822$	−7.47129	+	27.6998i	−0.260591	+	0.966140i
$823$	−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	0.952883	−	0.303339i	$-0.0981016\pi$
$827$	0.106001	+	0.326238i	0.00368602	+	0.0113444i	−0.949197	+	0.314684i	$0.898102\pi$
$828$	−0.866808	−	8.51832i	−0.0301237	−	0.296032i
$829$	−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
$831$	35.5301	−	1.80309i	1.23253	−	0.0625483i
$832$	−8.51722	−	11.7229i	−0.295282	−	0.406420i
$833$	13.7638	+	10.0000i	0.476888	+	0.346479i
$834$	4.43688	−	3.58077i	0.153636	−	0.123992i
$835$			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	−0.995865	−	0.0908462i	$-0.971043\pi$
$839$	−17.4293	+	23.9894i	−0.601726	+	0.828205i	0.394139	+	0.919051i	$0.371043\pi$
$840$	−1.30699	+	2.00531i	−0.0450954	+	0.0691898i
$841$	−4.48936	+	13.8168i	−0.154805	+	0.476442i
$842$	15.1967	−	46.7705i	0.523711	−	1.61182i
$843$	15.5651	−	23.8815i	0.536090	−	0.822521i
$844$	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
$849$	−10.7175	+	8.64950i	−0.367823	+	0.296850i
$850$	−7.50000	−	5.44907i	−0.257248	−	0.186902i
$851$	−3.11044	−	4.28115i	−0.106624	−	0.146756i
$852$	28.9023	−	1.46673i	0.990175	−	0.0502495i
$853$	−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
$855$	−33.2339	+	3.38182i	−1.13657	+	0.115656i
$856$	0.0385072	+	0.118513i	0.00131615	+	0.00405069i
$857$	−24.2380			−0.827953			−0.413976	−	0.910288i	$-0.635860\pi$
$857$	−24.2380			−0.827953			−0.413976	+	0.910288i	$0.635860\pi$
$858$		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
$861$	−1.00859	+	3.73935i	−0.0343728	+	0.127437i
$862$	34.6976	−	25.2093i	1.18180	−	0.858631i
$863$	37.2097	+	12.0902i	1.26663	+	0.411554i	0.863854	−	0.503743i	$-0.168044\pi$
$863$	37.2097	+	12.0902i	1.26663	+	0.411554i	0.402780	+	0.915297i	$0.368044\pi$
$864$	26.8015	+	27.0690i	0.911805	+	0.920907i
$865$	−34.1074	−	46.9448i	−1.15969	−	1.59617i
$866$	9.23305	+	6.70820i	0.313752	+	0.227954i
$867$	−10.9759	−	13.6001i	−0.372762	−	0.461884i
$868$		−	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
$873$	4.19217	−	19.4065i	0.141883	−	0.656809i
$874$	4.40983	−	13.5721i	0.149165	−	0.459082i
$875$	−1.84911	+	5.69098i	−0.0625114	+	0.192390i
$876$	−35.7271	−	23.2856i	−1.20711	−	0.786749i
$877$	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	$-0.799800\pi$
$881$		−	34.9230i		−	1.17659i	0.808648	−	0.588293i	$-0.200200\pi$
$882$	31.9229	+	18.5719i	1.07490	+	0.625348i
$883$	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
$885$	0.601689	+	11.8564i	0.0202256	+	0.398548i
$886$	18.9443	+	6.15537i	0.636445	+	0.206794i
$887$	7.91872	−	5.75329i	0.265885	−	0.193177i	−0.446853	−	0.894608i	$-0.647455\pi$
$887$	7.91872	−	5.75329i	0.265885	−	0.193177i	0.712737	+	0.701431i	$0.247455\pi$
$888$	3.64497	+	0.983135i	0.122317	+	0.0329919i
$889$	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
$894$	−0.545564	−	0.147152i	−0.0182464	−	0.00492149i
$895$	−8.35410	+	6.06961i	−0.279247	+	0.202885i
$896$	3.94298	+	1.28115i	0.131726	+	0.0428003i
$897$	−0.476571	−	9.39092i	−0.0159122	−	0.313554i
$898$	−8.81966	−	12.1392i	−0.294316	−	0.405091i
$899$	−2.62866	−	1.90983i	−0.0876706	−	0.0636964i
$900$	−7.77929	−	4.52578i	−0.259310	−	0.150859i
$901$			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
$906$	−48.4891	−	31.6034i	−1.61094	−	1.04995i
$907$	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
$909$	−7.90684	+	36.6025i	−0.262253	+	1.21403i
$910$	6.54508	−	9.00854i	0.216967	−	0.298630i
$911$	54.8963	−	17.8369i	1.81879	−	0.590962i	0.818941	−	0.573878i	$-0.194562\pi$
$911$	54.8963	−	17.8369i	1.81879	−	0.590962i	0.999854	−	0.0170841i	$-0.00543829\pi$
$912$	12.1392	+	31.7809i	0.401970	+	1.05237i
$913$		0			0
$914$		−	20.5279i		−	0.679001i
$915$	−12.1127	−	15.0086i	−0.400432	−	0.496170i
$916$	−32.8885	−	23.8949i	−1.08667	−	0.789511i
$917$	1.74311	+	2.39919i	0.0575626	+	0.0792281i
$918$	18.2797	+	18.4622i	0.603321	+	0.609343i
$919$	−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
$921$	2.65124	−	9.82946i	0.0873614	−	0.323892i
$922$	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
$927$	20.1875	−	2.05425i	0.663046	−	0.0674704i
$928$	−22.5623	+	16.3925i	−0.740644	+	0.538109i
$929$	28.8217	+	9.36475i	0.945610	+	0.307247i	0.740930	−	0.671582i	$-0.234385\pi$
$929$	28.8217	+	9.36475i	0.945610	+	0.307247i	0.204680	+	0.978829i	$0.434385\pi$
$930$	−7.35738	+	0.373373i	−0.241258	+	0.0122434i
$931$	16.1803	+	22.2703i	0.530289	+	0.729880i
$932$	−9.37181	−	6.80902i	−0.306984	−	0.223037i
$933$	6.73929	−	5.43893i	0.220635	−	0.178062i
$934$		−	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
$939$	−10.4032	+	15.9616i	−0.339496	+	0.520888i
$940$	−9.59017	+	29.5155i	−0.312797	+	0.962690i
$941$	14.9596	−	46.0410i	0.487670	−	1.50089i	−0.340406	−	0.940279i	$-0.610564\pi$
$941$	14.9596	−	46.0410i	0.487670	−	1.50089i	0.828076	−	0.560616i	$-0.189436\pi$
$942$	6.67074	−	10.2349i	0.217345	−	0.333472i
$943$	−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	$0.126688\pi$
$947$			23.8541i			0.775154i	−0.921837	+	0.387577i	$0.873312\pi$
$948$	−23.3052	+	18.8084i	−0.756917	+	0.610868i
$949$	−37.8885	−	27.5276i	−1.22991	−	0.893585i
$950$	−8.81678	−	12.1353i	−0.286054	−	0.393720i
$951$	0.408356	−	0.0207233i	0.0132419	−	0.000671999i
$952$	1.31966	+	0.428784i	0.0427704	+	0.0138970i
$953$	36.0341	−	26.1803i	1.16726	−	0.848064i	0.176582	−	0.984286i	$-0.443496\pi$
$953$	36.0341	−	26.1803i	1.16726	−	0.848064i	0.990678	+	0.136222i	$0.0434959\pi$
$954$	2.80413	+	27.5568i	0.0907872	+	0.892186i
$955$	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
$960$	−5.55983	+	20.6130i	−0.179443	+	0.665282i
$961$	24.4894	−	17.7926i	0.789979	−	0.573954i
$962$	−16.7027	−	5.42705i	−0.538518	−	0.174975i
$963$	0.207725	+	0.470746i	0.00669385	+	0.0151696i
$964$	18.6180	+	25.6255i	0.599646	+	0.825343i
$965$	42.7773	+	31.0795i	1.37705	+	1.00049i
$966$	−2.65169	−	3.28567i	−0.0853167	−	0.105715i
$967$			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	−0.921538	−	0.388288i	$-0.873066\pi$
$971$	−8.33499	+	11.4721i	−0.267483	+	0.368158i	0.654055	+	0.756447i	$0.273066\pi$
$972$	19.4696	+	16.0348i	0.624489	+	0.514317i
$973$	0.388544	−	1.19581i	0.0124561	−	0.0383361i
$974$	−4.39201	+	13.5172i	−0.140729	+	0.433120i
$975$	−8.28022	−	5.39675i	−0.265179	−	0.172834i
$976$	−11.5451	+	15.8904i	−0.369549	+	0.508641i
$977$	49.4019	−	16.0517i	1.58051	−	0.513538i	0.618320	−	0.785926i	$-0.287813\pi$
$977$	49.4019	−	16.0517i	1.58051	−	0.513538i	0.962188	+	0.272388i	$0.0878134\pi$
$978$	−38.1078	+	14.5559i	−1.21855	+	0.465446i
$979$		0			0
$980$			27.4164i			0.875785i
$981$	11.4781	−	19.7294i	0.366466	−	0.629913i
$982$	−41.0795	−	29.8460i	−1.31090	−	0.952425i
$983$	3.11817	+	4.29180i	0.0994543	+	0.136887i	0.855844	−	0.517234i	$-0.173038\pi$
$983$	3.11817	+	4.29180i	0.0994543	+	0.136887i	−0.756389	+	0.654122i	$0.773038\pi$
$984$	−0.196294	−	3.86801i	−0.00625762	−	0.123308i
$985$	−39.4336	−	12.8128i	−1.25646	−	0.408249i
$986$	−15.3884	+	11.1803i	−0.490067	+	0.356055i
$987$	8.90130	+	2.40089i	0.283331	+	0.0764213i
$988$	−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
$993$	38.2762	+	10.3240i	1.21466	+	0.327623i
$994$	11.5451	−	8.38800i	0.366188	−	0.266051i
$995$	−5.56758	−	1.80902i	−0.176504	−	0.0573497i
$996$	−2.05820	−	40.5573i	−0.0652167	−	1.28511i
$997$	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
$999$	15.3842	+	2.51500i	0.486736	+	0.0795711i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.587785 + 1.80902i) q^{2} +(-1.67229 - 0.451057i) q^{3} +(-1.30902 + 0.951057i) q^{4} +(2.48990 + 0.809017i) q^{5} +(-0.166977 - 3.29032i) q^{6} +(-0.427051 - 0.587785i) q^{7} +(0.587785 + 0.427051i) q^{8} +(2.59310 + 1.50859i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 1.80902i) q^{2} +(-1.67229 - 0.451057i) q^{3} +(-1.30902 + 0.951057i) q^{4} +(2.48990 + 0.809017i) q^{5} +(-0.166977 - 3.29032i) q^{6} +(-0.427051 - 0.587785i) q^{7} +(0.587785 + 0.427051i) q^{8} +(2.59310 + 1.50859i) q^{9} +4.97980i q^{10} +(2.61803 - 1.00000i) q^{12} +(2.92705 - 0.951057i) q^{13} +(0.812299 - 1.11803i) q^{14} +(-3.79892 - 2.47599i) q^{15} +(-1.42705 + 4.39201i) q^{16} +(-0.812299 + 2.50000i) q^{17} +(-1.20489 + 5.57768i) q^{18} +(-2.50000 + 3.44095i) q^{19} +(-4.02874 + 1.30902i) q^{20} +(0.449028 + 1.17557i) q^{21} +1.76393i q^{23} +(-0.790322 - 0.979277i) q^{24} +(1.50000 + 1.08981i) q^{25} +(3.44095 + 4.73607i) q^{26} +(-3.65594 - 3.69244i) q^{27} +(1.11803 + 0.363271i) q^{28} +(3.07768 - 2.23607i) q^{29} +(2.24617 - 8.32766i) q^{30} +(-0.263932 - 0.812299i) q^{31} -7.33094 q^{32} -5.00000 q^{34} +(-0.587785 - 1.80902i) q^{35} +(-4.82916 + 0.491407i) q^{36} +(-2.42705 + 1.76336i) q^{37} +(-7.69421 - 2.50000i) q^{38} +(-5.32385 + 0.270175i) q^{39} +(1.11803 + 1.53884i) q^{40} +(2.48990 + 1.80902i) q^{41} +(-1.86269 + 1.50328i) q^{42} -1.62460i q^{43} +(5.23607 + 5.85410i) q^{45} +(-3.19098 + 1.03681i) q^{46} +(4.30625 - 5.92705i) q^{47} +(4.36749 - 6.70103i) q^{48} +(2.00000 - 6.15537i) q^{49} +(-1.08981 + 3.35410i) q^{50} +(2.48604 - 3.81433i) q^{51} +(-2.92705 + 4.02874i) q^{52} +(4.61653 - 1.50000i) q^{53} +(4.53077 - 8.78402i) q^{54} -0.527864i q^{56} +(5.73279 - 4.62663i) q^{57} +(5.85410 + 4.25325i) q^{58} +(-1.53884 - 2.11803i) q^{59} +(7.32766 - 0.371864i) q^{60} +(4.04508 + 1.31433i) q^{61} +(1.31433 - 0.954915i) q^{62} +(-0.220655 - 2.16843i) q^{63} +(-1.45492 - 4.47777i) q^{64} +8.05748 q^{65} -8.32624 q^{67} +(-1.31433 - 4.04508i) q^{68} +(0.795633 - 2.94980i) q^{69} +(2.92705 - 2.12663i) q^{70} +(9.82084 + 3.19098i) q^{71} +(0.879937 + 1.99411i) q^{72} +(-8.94427 - 12.3107i) q^{73} +(-4.61653 - 3.35410i) q^{74} +(-2.01686 - 2.49907i) q^{75} -6.88191i q^{76} +(-3.61803 - 9.47214i) q^{78} +(-10.1631 + 3.30220i) q^{79} +(-7.10642 + 9.78115i) q^{80} +(4.44829 + 7.82385i) q^{81} +(-1.80902 + 5.56758i) q^{82} +(4.47777 - 13.7812i) q^{83} +(-1.70582 - 1.11179i) q^{84} +(-4.04508 + 5.56758i) q^{85} +(2.93893 - 0.954915i) q^{86} +(-6.15537 + 2.35114i) q^{87} -9.47214i q^{89} +(-7.51249 + 12.9131i) q^{90} +(-1.80902 - 1.31433i) q^{91} +(-1.67760 - 2.30902i) q^{92} +(0.0749776 + 1.47745i) q^{93} +(13.2533 + 4.30625i) q^{94} +(-9.00854 + 6.54508i) q^{95} +(12.2594 + 3.30667i) 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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