LMFDB - Embedded newform 507.2.j.h.361.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(316,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.j (of order $6$, degree $2$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.6
Root			$1.56052 - 0.900969i$ of defining polynomial
Character	$\chi$	$=$	507.361
Dual form			507.2.j.h.316.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56052 - 0.900969i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.623490 - 1.07992i) q^{4} +1.44504i q^{5} +(-1.56052 - 0.900969i) q^{6} +(2.98349 + 1.72252i) q^{7} +1.35690i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.56052 - 0.900969i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.623490 - 1.07992i) q^{4} +1.44504i q^{5} +(-1.56052 - 0.900969i) q^{6} +(2.98349 + 1.72252i) q^{7} +1.35690i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.30194 + 2.25502i) q^{10} +(4.49119 - 2.59299i) q^{11} -1.24698 q^{12} +6.20775 q^{14} +(1.25144 - 0.722521i) q^{15} +(2.46950 + 4.27730i) q^{16} +(-0.376510 + 0.652135i) q^{17} +1.80194i q^{18} +(-6.89423 - 3.98039i) q^{19} +(1.56052 + 0.900969i) q^{20} -3.44504i q^{21} +(4.67241 - 8.09285i) q^{22} +(-1.41454 - 2.45006i) q^{23} +(1.17511 - 0.678448i) q^{24} +2.91185 q^{25} +1.00000 q^{27} +(3.72036 - 2.14795i) q^{28} +(1.95593 + 3.38776i) q^{29} +(1.30194 - 2.25502i) q^{30} -4.89977i q^{31} +(5.35722 + 3.09299i) q^{32} +(-4.49119 - 2.59299i) q^{33} +1.35690i q^{34} +(-2.48911 + 4.31127i) q^{35} +(0.623490 + 1.07992i) q^{36} +(-5.41004 + 3.12349i) q^{37} -14.3448 q^{38} -1.96077 q^{40} +(1.56052 - 0.900969i) q^{41} +(-3.10388 - 5.37607i) q^{42} +(-3.54892 + 6.14691i) q^{43} -6.46681i q^{44} +(-1.25144 - 0.722521i) q^{45} +(-4.41485 - 2.54892i) q^{46} -10.5526i q^{47} +(2.46950 - 4.27730i) q^{48} +(2.43416 + 4.21608i) q^{49} +(4.54402 - 2.62349i) q^{50} +0.753020 q^{51} -3.08815 q^{53} +(1.56052 - 0.900969i) q^{54} +(3.74698 + 6.48996i) q^{55} +(-2.33728 + 4.04829i) q^{56} +7.96077i q^{57} +(6.10454 + 3.52446i) q^{58} +(1.62640 + 0.939001i) q^{59} -1.80194i q^{60} +(-1.67241 + 2.89669i) q^{61} +(-4.41454 - 7.64621i) q^{62} +(-2.98349 + 1.72252i) q^{63} +1.26875 q^{64} -9.34481 q^{66} +(-3.93425 + 2.27144i) q^{67} +(0.469501 + 0.813199i) q^{68} +(-1.41454 + 2.45006i) q^{69} +8.97046i q^{70} +(7.89781 + 4.55980i) q^{71} +(-1.17511 - 0.678448i) q^{72} -2.95108i q^{73} +(-5.62833 + 9.74856i) q^{74} +(-1.45593 - 2.52174i) q^{75} +(-8.59696 + 4.96346i) q^{76} +17.8659 q^{77} -9.43296 q^{79} +(-6.18088 + 3.56853i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.62349 - 2.81197i) q^{82} -6.46681i q^{83} +(-3.72036 - 2.14795i) q^{84} +(-0.942362 - 0.544073i) q^{85} +12.7899i q^{86} +(1.95593 - 3.38776i) q^{87} +(3.51842 + 6.09408i) q^{88} +(-1.00358 + 0.579417i) q^{89} -2.60388 q^{90} -3.52781 q^{92} +(-4.24333 + 2.44989i) q^{93} +(-9.50753 - 16.4675i) q^{94} +(5.75182 - 9.96245i) q^{95} -6.18598i q^{96} +(-7.49819 - 4.32908i) q^{97} +(7.59712 + 4.38620i) q^{98} +5.18598i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 2 q^{4} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 2 * q^4 - 6 * q^9	$ 12 q - 6 q^{3} - 2 q^{4} - 6 q^{9} - 2 q^{10} + 4 q^{12} + 4 q^{14} + 10 q^{16} - 14 q^{17} + 10 q^{22} + 4 q^{23} + 20 q^{25} + 12 q^{27} + 16 q^{29} - 2 q^{30} - 36 q^{35} - 2 q^{36} - 80 q^{38} + 28 q^{40} - 2 q^{42} - 6 q^{43} + 10 q^{48} + 34 q^{49} + 28 q^{51} - 52 q^{53} + 26 q^{55} + 14 q^{56} + 26 q^{61} - 32 q^{62} - 16 q^{64} - 20 q^{66} - 14 q^{68} + 4 q^{69} - 14 q^{74} - 10 q^{75} + 60 q^{77} - 36 q^{79} - 6 q^{81} + 10 q^{82} + 16 q^{87} - 14 q^{88} + 4 q^{90} - 68 q^{92} - 64 q^{94} + 6 q^{95}+O(q^{100}) $ 12 * q - 6 * q^3 - 2 * q^4 - 6 * q^9 - 2 * q^10 + 4 * q^12 + 4 * q^14 + 10 * q^16 - 14 * q^17 + 10 * q^22 + 4 * q^23 + 20 * q^25 + 12 * q^27 + 16 * q^29 - 2 * q^30 - 36 * q^35 - 2 * q^36 - 80 * q^38 + 28 * q^40 - 2 * q^42 - 6 * q^43 + 10 * q^48 + 34 * q^49 + 28 * q^51 - 52 * q^53 + 26 * q^55 + 14 * q^56 + 26 * q^61 - 32 * q^62 - 16 * q^64 - 20 * q^66 - 14 * q^68 + 4 * q^69 - 14 * q^74 - 10 * q^75 + 60 * q^77 - 36 * q^79 - 6 * q^81 + 10 * q^82 + 16 * q^87 - 14 * q^88 + 4 * q^90 - 68 * q^92 - 64 * q^94 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.56052	−	0.900969i	1.10346	−	0.637081i	0.166330	−	0.986070i	$-0.446808\pi$
$2$	1.56052	−	0.900969i	1.10346	−	0.637081i	0.937127	+	0.348989i	$0.113475\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.623490	−	1.07992i	0.311745	−	0.539958i
$5$			1.44504i			0.646242i	0.946358	+	0.323121i	$0.104732\pi$
$5$			1.44504i			0.646242i	−0.946358	+	0.323121i	$0.895268\pi$
$6$	−1.56052	−	0.900969i	−0.637081	−	0.367819i
$7$	2.98349	+	1.72252i	1.12765	+	0.651052i	0.943344	−	0.331816i	$-0.107661\pi$
$7$	2.98349	+	1.72252i	1.12765	+	0.651052i	0.184311	+	0.982868i	$0.440995\pi$
$8$			1.35690i			0.479735i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.30194	+	2.25502i	0.411709	+	0.713101i
$11$	4.49119	−	2.59299i	1.35415	−	0.781816i	0.365318	−	0.930883i	$-0.380960\pi$
$11$	4.49119	−	2.59299i	1.35415	−	0.781816i	0.988827	+	0.149067i	$0.0476269\pi$
$12$	−1.24698			−0.359972
$13$		0			0
$13$		0			0
$14$	6.20775			1.65909
$15$	1.25144	−	0.722521i	0.323121	−	0.186554i
$16$	2.46950	+	4.27730i	0.617375	+	1.06933i
$17$	−0.376510	+	0.652135i	−0.0913171	+	0.158166i	−0.908066	−	0.418828i	$-0.862441\pi$
$17$	−0.376510	+	0.652135i	−0.0913171	+	0.158166i	0.816748	+	0.576994i	$0.195774\pi$
$18$			1.80194i			0.424721i
$19$	−6.89423	−	3.98039i	−1.58164	−	0.913163i	−0.994620	−	0.103594i	$-0.966966\pi$
$19$	−6.89423	−	3.98039i	−1.58164	−	0.913163i	−0.587025	−	0.809569i	$-0.699701\pi$
$20$	1.56052	+	0.900969i	0.348944	+	0.201463i
$21$		−	3.44504i		−	0.751770i
$22$	4.67241	−	8.09285i	0.996161	−	1.72540i
$23$	−1.41454	−	2.45006i	−0.294952	−	0.510873i	0.680021	−	0.733192i	$-0.261970\pi$
$23$	−1.41454	−	2.45006i	−0.294952	−	0.510873i	−0.974974	+	0.222320i	$0.928637\pi$
$24$	1.17511	−	0.678448i	0.239868	−	0.138488i
$25$	2.91185			0.582371
$26$		0			0
$27$	1.00000			0.192450
$28$	3.72036	−	2.14795i	0.703081	−	0.405924i
$29$	1.95593	+	3.38776i	0.363207	+	0.629092i	0.988487	−	0.151308i	$-0.0483486\pi$
$29$	1.95593	+	3.38776i	0.363207	+	0.629092i	−0.625280	+	0.780400i	$0.715015\pi$
$30$	1.30194	−	2.25502i	0.237700	−	0.411709i
$31$		−	4.89977i		−	0.880025i	−0.897992	−	0.440013i	$-0.854974\pi$
$31$		−	4.89977i		−	0.880025i	0.897992	−	0.440013i	$-0.145026\pi$
$32$	5.35722	+	3.09299i	0.947031	+	0.546769i
$33$	−4.49119	−	2.59299i	−0.781816	−	0.451382i
$34$			1.35690i			0.232706i
$35$	−2.48911	+	4.31127i	−0.420737	+	0.728738i
$36$	0.623490	+	1.07992i	0.103915	+	0.179986i
$37$	−5.41004	+	3.12349i	−0.889406	+	0.513499i	−0.873748	−	0.486379i	$-0.838317\pi$
$37$	−5.41004	+	3.12349i	−0.889406	+	0.513499i	−0.0156576	+	0.999877i	$0.504984\pi$
$38$	−14.3448			−2.32704
$39$		0			0
$40$	−1.96077			−0.310025
$41$	1.56052	−	0.900969i	0.243713	−	0.140708i	−0.373169	−	0.927763i	$-0.621729\pi$
$41$	1.56052	−	0.900969i	0.243713	−	0.140708i	0.616882	+	0.787056i	$0.288396\pi$
$42$	−3.10388	−	5.37607i	−0.478938	−	0.829546i
$43$	−3.54892	+	6.14691i	−0.541205	+	0.937394i	0.457630	+	0.889143i	$0.348698\pi$
$43$	−3.54892	+	6.14691i	−0.541205	+	0.937394i	−0.998835	+	0.0482517i	$0.984635\pi$
$44$		−	6.46681i		−	0.974909i
$45$	−1.25144	−	0.722521i	−0.186554	−	0.107707i
$46$	−4.41485	−	2.54892i	−0.650935	−	0.375817i
$47$		−	10.5526i		−	1.53925i	−0.638496	−	0.769625i	$-0.720443\pi$
$47$		−	10.5526i		−	1.53925i	0.638496	−	0.769625i	$-0.279557\pi$
$48$	2.46950	−	4.27730i	0.356442	−	0.617375i
$49$	2.43416	+	4.21608i	0.347737	+	0.602298i
$50$	4.54402	−	2.62349i	0.642621	−	0.371017i
$51$	0.753020			0.105444
$52$		0			0
$53$	−3.08815			−0.424189			−0.212095	−	0.977249i	$-0.568029\pi$
$53$	−3.08815			−0.424189			−0.212095	+	0.977249i	$0.568029\pi$
$54$	1.56052	−	0.900969i	0.212360	−	0.122606i
$55$	3.74698	+	6.48996i	0.505243	+	0.875106i
$56$	−2.33728	+	4.04829i	−0.312332	+	0.540976i
$57$			7.96077i			1.05443i
$58$	6.10454	+	3.52446i	0.801566	+	0.462784i
$59$	1.62640	+	0.939001i	0.211739	+	0.122248i	0.602119	−	0.798406i	$-0.294323\pi$
$59$	1.62640	+	0.939001i	0.211739	+	0.122248i	−0.390380	+	0.920654i	$0.627656\pi$
$60$		−	1.80194i		−	0.232629i
$61$	−1.67241	+	2.89669i	−0.214130	+	0.370884i	−0.953003	−	0.302961i	$-0.902025\pi$
$61$	−1.67241	+	2.89669i	−0.214130	+	0.370884i	0.738873	+	0.673844i	$0.235358\pi$
$62$	−4.41454	−	7.64621i	−0.560647	−	0.971070i
$63$	−2.98349	+	1.72252i	−0.375885	+	0.217017i
$64$	1.26875			0.158594
$65$		0			0
$66$	−9.34481			−1.15027
$67$	−3.93425	+	2.27144i	−0.480645	+	0.277500i	−0.720685	−	0.693263i	$-0.756173\pi$
$67$	−3.93425	+	2.27144i	−0.480645	+	0.277500i	0.240040	+	0.970763i	$0.422839\pi$
$68$	0.469501	+	0.813199i	0.0569353	+	0.0986148i
$69$	−1.41454	+	2.45006i	−0.170291	+	0.294952i
$70$			8.97046i			1.07218i
$71$	7.89781	+	4.55980i	0.937298	+	0.541149i	0.889112	−	0.457689i	$-0.151323\pi$
$71$	7.89781	+	4.55980i	0.937298	+	0.541149i	0.0481854	+	0.998838i	$0.484656\pi$
$72$	−1.17511	−	0.678448i	−0.138488	−	0.0799559i
$73$		−	2.95108i		−	0.345398i	−0.984975	−	0.172699i	$-0.944751\pi$
$73$		−	2.95108i		−	0.345398i	0.984975	−	0.172699i	$-0.0552488\pi$
$74$	−5.62833	+	9.74856i	−0.654281	+	1.13325i
$75$	−1.45593	−	2.52174i	−0.168116	−	0.291185i
$76$	−8.59696	+	4.96346i	−0.986139	+	0.569348i
$77$	17.8659			2.03601
$78$		0			0
$79$	−9.43296			−1.06129			−0.530645	−	0.847594i	$-0.678050\pi$
$79$	−9.43296			−1.06129			−0.530645	+	0.847594i	$0.678050\pi$
$80$	−6.18088	+	3.56853i	−0.691043	+	0.398974i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.62349	−	2.81197i	0.179284	−	0.310530i
$83$		−	6.46681i		−	0.709825i	−0.934900	−	0.354912i	$-0.884511\pi$
$83$		−	6.46681i		−	0.709825i	0.934900	−	0.354912i	$-0.115489\pi$
$84$	−3.72036	−	2.14795i	−0.405924	−	0.234360i
$85$	−0.942362	−	0.544073i	−0.102214	−	0.0590130i
$86$			12.7899i			1.37917i
$87$	1.95593	−	3.38776i	0.209697	−	0.363207i
$88$	3.51842	+	6.09408i	0.375065	+	0.649631i
$89$	−1.00358	+	0.579417i	−0.106379	+	0.0614181i	−0.552246	−	0.833681i	$-0.686229\pi$
$89$	−1.00358	+	0.579417i	−0.106379	+	0.0614181i	0.445866	+	0.895099i	$0.352896\pi$
$90$	−2.60388			−0.274473
$91$		0			0
$92$	−3.52781			−0.367800
$93$	−4.24333	+	2.44989i	−0.440013	+	0.254041i
$94$	−9.50753	−	16.4675i	−0.980627	−	1.69850i
$95$	5.75182	−	9.96245i	0.590125	−	1.02213i
$96$		−	6.18598i		−	0.631354i
$97$	−7.49819	−	4.32908i	−0.761326	−	0.439552i	0.0684454	−	0.997655i	$-0.478196\pi$
$97$	−7.49819	−	4.32908i	−0.761326	−	0.439552i	−0.829772	+	0.558103i	$0.811529\pi$
$98$	7.59712	+	4.38620i	0.767425	+	0.443073i
$99$			5.18598i			0.521211i
$100$	1.81551	−	3.14456i	0.181551	−	0.314456i
$101$	−4.23825	−	7.34087i	−0.421722	−	0.730443i	0.574386	−	0.818584i	$-0.305241\pi$
$101$	−4.23825	−	7.34087i	−0.421722	−	0.730443i	−0.996108	+	0.0881410i	$0.971907\pi$
$102$	1.17511	−	0.678448i	0.116353	−	0.0671764i
$103$	−5.64742			−0.556456			−0.278228	−	0.960515i	$-0.589747\pi$
$103$	−5.64742			−0.556456			−0.278228	+	0.960515i	$0.589747\pi$
$104$		0			0
$105$	4.97823			0.485825
$106$	−4.81913	+	2.78232i	−0.468075	+	0.270243i
$107$	3.36778	+	5.83317i	0.325576	+	0.563914i	0.981629	−	0.190801i	$-0.0611086\pi$
$107$	3.36778	+	5.83317i	0.325576	+	0.563914i	−0.656053	+	0.754715i	$0.727775\pi$
$108$	0.623490	−	1.07992i	0.0599953	−	0.103915i
$109$		−	2.07606i		−	0.198851i	−0.995045	−	0.0994255i	$-0.968300\pi$
$109$		−	2.07606i		−	0.198851i	0.995045	−	0.0994255i	$-0.0317005\pi$
$110$	11.6945	+	6.75182i	1.11503	+	0.643761i
$111$	5.41004	+	3.12349i	0.513499	+	0.296469i
$112$			17.0151i			1.60777i
$113$	−3.08426	+	5.34210i	−0.290143	+	0.502542i	−0.973843	−	0.227221i	$-0.927036\pi$
$113$	−3.08426	+	5.34210i	−0.290143	+	0.502542i	0.683700	+	0.729763i	$0.260370\pi$
$114$	7.17241	+	12.4230i	0.671757	+	1.16352i
$115$	3.54044	−	2.04407i	0.330148	−	0.190611i
$116$	4.87800			0.452911
$117$		0			0
$118$	3.38404			0.311526
$119$	−2.24663	+	1.29709i	−0.205948	+	0.118904i
$120$	0.980386	+	1.69808i	0.0894966	+	0.155013i
$121$	7.94720	−	13.7650i	0.722473	−	1.25136i
$122$			6.02715i			0.545672i
$123$	−1.56052	−	0.900969i	−0.140708	−	0.0812376i
$124$	−5.29134	−	3.05496i	−0.475177	−	0.274343i
$125$			11.4330i			1.02260i
$126$	−3.10388	+	5.37607i	−0.276515	+	0.478938i
$127$	−7.13102	−	12.3513i	−0.632776	−	1.09600i	−0.986982	−	0.160833i	$-0.948582\pi$
$127$	−7.13102	−	12.3513i	−0.632776	−	1.09600i	0.354206	−	0.935168i	$-0.384751\pi$
$128$	−8.73452	+	5.04288i	−0.772030	+	0.445732i
$129$	7.09783			0.624929
$130$		0			0
$131$	22.6015			1.97470			0.987350	−	0.158554i	$-0.0506831\pi$
$131$	22.6015			1.97470			0.987350	+	0.158554i	$0.0506831\pi$
$132$	−5.60042	+	3.23341i	−0.487454	+	0.281432i
$133$	−13.7126	−	23.7509i	−1.18903	−	2.05947i
$134$	−4.09299	+	7.08927i	−0.353581	+	0.612419i
$135$			1.44504i			0.124369i
$136$	−0.884879	−	0.510885i	−0.0758777	−	0.0438080i
$137$	−11.8085	−	6.81767i	−1.00887	−	0.582473i	−0.0980109	−	0.995185i	$-0.531248\pi$
$137$	−11.8085	−	6.81767i	−1.00887	−	0.582473i	−0.910861	+	0.412713i	$0.864581\pi$
$138$			5.09783i			0.433957i
$139$	−8.80074	+	15.2433i	−0.746469	+	1.29292i	0.203036	+	0.979171i	$0.434919\pi$
$139$	−8.80074	+	15.2433i	−0.746469	+	1.29292i	−0.949505	+	0.313751i	$0.898414\pi$
$140$	3.10388	+	5.37607i	0.262325	+	0.454361i
$141$	−9.13879	+	5.27628i	−0.769625	+	0.444343i
$142$	16.4330			1.37902
$143$		0			0
$144$	−4.93900			−0.411583
$145$	−4.89546	+	2.82640i	−0.406546	+	0.234719i
$146$	−2.65883	−	4.60523i	−0.220047	−	0.381132i
$147$	2.43416	−	4.21608i	0.200766	−	0.347737i
$148$			7.78986i			0.640322i
$149$	−11.0319	−	6.36927i	−0.903769	−	0.521791i	−0.0253478	−	0.999679i	$-0.508069\pi$
$149$	−11.0319	−	6.36927i	−0.903769	−	0.521791i	−0.878421	+	0.477888i	$0.841403\pi$
$150$	−4.54402	−	2.62349i	−0.371017	−	0.214207i
$151$		−	15.6407i		−	1.27282i	−0.771350	−	0.636412i	$-0.780418\pi$
$151$		−	15.6407i		−	1.27282i	0.771350	−	0.636412i	$-0.219582\pi$
$152$	5.40097	−	9.35475i	0.438076	−	0.758771i
$153$	−0.376510	−	0.652135i	−0.0304390	−	0.0527220i
$154$	27.8802	−	16.0966i	2.24665	−	1.29710i
$155$	7.08038			0.568710
$156$		0			0
$157$	−0.823708			−0.0657391			−0.0328695	−	0.999460i	$-0.510465\pi$
$157$	−0.823708			−0.0657391			−0.0328695	+	0.999460i	$0.510465\pi$
$158$	−14.7204	+	8.49880i	−1.17109	+	0.676129i
$159$	1.54407	+	2.67441i	0.122453	+	0.212095i
$160$	−4.46950	+	7.74140i	−0.353345	+	0.612012i
$161$		−	9.74632i		−	0.768117i
$162$	−1.56052	−	0.900969i	−0.122606	−	0.0707868i
$163$	5.42890	+	3.13437i	0.425224	+	0.245503i	0.697310	−	0.716770i	$-0.254380\pi$
$163$	5.42890	+	3.13437i	0.425224	+	0.245503i	−0.272086	+	0.962273i	$0.587713\pi$
$164$		−	2.24698i		−	0.175460i
$165$	3.74698	−	6.48996i	0.291702	−	0.505243i
$166$	−5.82640	−	10.0916i	−0.452216	−	0.783261i
$167$	6.45225	−	3.72521i	0.499290	−	0.288265i	−0.229130	−	0.973396i	$-0.573588\pi$
$167$	6.45225	−	3.72521i	0.499290	−	0.288265i	0.728420	+	0.685130i	$0.240255\pi$
$168$	4.67456			0.360650
$169$		0			0
$170$	−1.96077			−0.150384
$171$	6.89423	−	3.98039i	0.527215	−	0.304388i
$172$	4.42543	+	7.66507i	0.337436	+	0.584456i
$173$	−1.00484	+	1.74044i	−0.0763969	+	0.132323i	−0.901693	−	0.432377i	$-0.857675\pi$
$173$	−1.00484	+	1.74044i	−0.0763969	+	0.132323i	0.825296	+	0.564700i	$0.191008\pi$
$174$		−	7.04892i		−	0.534377i
$175$	8.68750	+	5.01573i	0.656713	+	0.379154i
$176$	22.1820	+	12.8068i	1.67203	+	0.965348i
$177$		−	1.87800i		−	0.141159i
$178$	−1.04407	+	1.80839i	−0.0782566	+	0.135544i
$179$	10.0184	+	17.3524i	0.748812	+	1.29698i	0.948393	+	0.317099i	$0.102709\pi$
$179$	10.0184	+	17.3524i	0.748812	+	1.29698i	−0.199581	+	0.979881i	$0.563958\pi$
$180$	−1.56052	+	0.900969i	−0.116315	+	0.0671543i
$181$	−24.1226			−1.79302			−0.896509	−	0.443026i	$-0.853905\pi$
$181$	−24.1226			−1.79302			−0.896509	+	0.443026i	$0.853905\pi$
$182$		0			0
$183$	3.34481			0.247256
$184$	3.32448	−	1.91939i	0.245084	−	0.141499i
$185$	−4.51357	−	7.81774i	−0.331845	−	0.574772i
$186$	−4.41454	+	7.64621i	−0.323690	+	0.560647i
$187$			3.90515i			0.285573i
$188$	−11.3959	−	6.57942i	−0.831130	−	0.479853i
$189$	2.98349	+	1.72252i	0.217017	+	0.125295i
$190$		−	20.7289i		−	1.50383i
$191$	3.54019	−	6.13179i	0.256159	−	0.443680i	−0.709051	−	0.705158i	$-0.750876\pi$
$191$	3.54019	−	6.13179i	0.256159	−	0.443680i	0.965210	+	0.261477i	$0.0842096\pi$
$192$	−0.634375	−	1.09877i	−0.0457821	−	0.0792969i
$193$	−8.45941	+	4.88404i	−0.608922	+	0.351561i	−0.772543	−	0.634962i	$-0.781016\pi$
$193$	−8.45941	+	4.88404i	−0.608922	+	0.351561i	0.163622	+	0.986523i	$0.447682\pi$
$194$	−15.6015			−1.12012
$195$		0			0
$196$	6.07069			0.433621
$197$	20.2747	−	11.7056i	1.44451	−	0.833989i	0.446365	−	0.894851i	$-0.352718\pi$
$197$	20.2747	−	11.7056i	1.44451	−	0.833989i	0.998146	+	0.0608617i	$0.0193849\pi$
$198$	4.67241	+	8.09285i	0.332054	+	0.575134i
$199$	2.01238	−	3.48554i	0.142654	−	0.247083i	−0.785841	−	0.618428i	$-0.787770\pi$
$199$	2.01238	−	3.48554i	0.142654	−	0.247083i	0.928495	+	0.371345i	$0.121103\pi$
$200$			3.95108i			0.279384i
$201$	3.93425	+	2.27144i	0.277500	+	0.160215i
$202$	−13.2278	−	7.63706i	−0.930703	−	0.537342i
$203$			13.4765i			0.945865i
$204$	0.469501	−	0.813199i	0.0328716	−	0.0569353i
$205$	1.30194	+	2.25502i	0.0909313	+	0.157498i
$206$	−8.81293	+	5.08815i	−0.614026	+	0.354508i
$207$	2.82908			0.196635
$208$		0			0
$209$	−41.2844			−2.85570
$210$	7.76865	−	4.48523i	0.536088	−	0.309510i
$211$	1.95593	+	3.38776i	0.134652	+	0.233223i	0.925464	−	0.378835i	$-0.123675\pi$
$211$	1.95593	+	3.38776i	0.134652	+	0.233223i	−0.790813	+	0.612058i	$0.790342\pi$
$212$	−1.92543	+	3.33494i	−0.132239	+	0.229045i
$213$		−	9.11960i		−	0.624865i
$214$	10.5110	+	6.06853i	0.718518	+	0.414836i
$215$	−8.88254	−	5.12833i	−0.605784	−	0.349749i
$216$			1.35690i			0.0923251i
$217$	8.43996	−	14.6184i	0.572942	−	0.992364i
$218$	−1.87047	−	3.23975i	−0.126684	−	0.219423i
$219$	−2.55571	+	1.47554i	−0.172699	+	0.0997078i
$220$	9.34481			0.630027
$221$		0			0
$222$	11.2567			0.755498
$223$	6.45133	−	3.72468i	0.432013	−	0.249423i	−0.268191	−	0.963366i	$-0.586426\pi$
$223$	6.45133	−	3.72468i	0.432013	−	0.249423i	0.700204	+	0.713943i	$0.253092\pi$
$224$	10.6555	+	18.4558i	0.711949	+	1.23313i
$225$	−1.45593	+	2.52174i	−0.0970618	+	0.168116i
$226$			11.1153i			0.739378i
$227$	18.4030	+	10.6250i	1.22145	+	0.705205i	0.965227	−	0.261413i	$-0.0841884\pi$
$227$	18.4030	+	10.6250i	1.22145	+	0.705205i	0.256223	+	0.966618i	$0.417522\pi$
$228$	8.59696	+	4.96346i	0.569348	+	0.328713i
$229$		−	9.29590i		−	0.614290i	−0.951663	−	0.307145i	$-0.900626\pi$
$229$		−	9.29590i		−	0.614290i	0.951663	−	0.307145i	$-0.0993737\pi$
$230$	3.68329	−	6.37965i	0.242869	−	0.420662i
$231$	−8.93296	−	15.4723i	−0.587746	−	1.01801i
$232$	−4.59684	+	2.65399i	−0.301798	+	0.174243i
$233$	−16.2107			−1.06200			−0.531000	−	0.847372i	$-0.678184\pi$
$233$	−16.2107			−1.06200			−0.531000	+	0.847372i	$0.678184\pi$
$234$		0			0
$235$	15.2489			0.994728
$236$	2.02808	−	1.17092i	0.132017	−	0.0762201i
$237$	4.71648	+	8.16918i	0.306368	+	0.530645i
$238$	−2.33728	+	4.04829i	−0.151503	+	0.262412i
$239$		−	13.5090i		−	0.873826i	−0.899504	−	0.436913i	$-0.856072\pi$
$239$		−	13.5090i		−	0.873826i	0.899504	−	0.436913i	$-0.143928\pi$
$240$	6.18088	+	3.56853i	0.398974	+	0.230348i
$241$	5.42890	+	3.13437i	0.349706	+	0.201903i	0.664556	−	0.747239i	$-0.268621\pi$
$241$	5.42890	+	3.13437i	0.349706	+	0.201903i	−0.314850	+	0.949142i	$0.601954\pi$
$242$		−	28.6407i		−	1.84109i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.08546	+	3.61212i	0.133508	+	0.231242i
$245$	−6.09242	+	3.51746i	−0.389230	+	0.224722i
$246$	−3.24698			−0.207020
$247$		0			0
$248$	6.64848			0.422179
$249$	−5.60042	+	3.23341i	−0.354912	+	0.204909i
$250$	10.3007	+	17.8414i	0.651476	+	1.12839i
$251$	−0.376510	+	0.652135i	−0.0237651	+	0.0411624i	−0.877663	−	0.479278i	$-0.840899\pi$
$251$	−0.376510	+	0.652135i	−0.0237651	+	0.0411624i	0.853898	+	0.520440i	$0.174232\pi$
$252$			4.29590i			0.270616i
$253$	−12.7060	−	7.33579i	−0.798817	−	0.461197i
$254$	−22.2563	−	12.8497i	−1.39648	−	0.806259i
$255$			1.08815i			0.0681423i
$256$	−10.3557	+	17.9366i	−0.647231	+	1.12104i
$257$	9.86323	+	17.0836i	0.615252	+	1.06565i	0.990340	+	0.138658i	$0.0442789\pi$
$257$	9.86323	+	17.0836i	0.615252	+	1.06565i	−0.375089	+	0.926989i	$0.622388\pi$
$258$	11.0763	−	6.39493i	0.689583	−	0.398131i
$259$	−21.5211			−1.33726
$260$		0			0
$261$	−3.91185			−0.242138
$262$	35.2702	−	20.3632i	2.17900	−	1.25804i
$263$	8.80463	+	15.2501i	0.542917	+	0.940359i	0.998735	+	0.0502861i	$0.0160133\pi$
$263$	8.80463	+	15.2501i	0.542917	+	0.940359i	−0.455818	+	0.890073i	$0.650653\pi$
$264$	3.51842	−	6.09408i	0.216544	−	0.375065i
$265$		−	4.46250i		−	0.274129i
$266$	−42.7977	−	24.7092i	−2.62409	−	1.51502i
$267$	1.00358	+	0.579417i	0.0614181	+	0.0354597i
$268$			5.66487i			0.346037i
$269$	8.19351	−	14.1916i	0.499567	−	0.865276i	−0.500433	−	0.865776i	$-0.666826\pi$
$269$	8.19351	−	14.1916i	0.499567	−	0.865276i	1.00000		0.000499532i	$0.000159006\pi$
$270$	1.30194	+	2.25502i	0.0792334	+	0.137236i
$271$	0.688692	−	0.397616i	0.0418351	−	0.0241535i	−0.478937	−	0.877849i	$-0.658978\pi$
$271$	0.688692	−	0.397616i	0.0418351	−	0.0241535i	0.520772	+	0.853696i	$0.325644\pi$
$272$	−3.71917			−0.225508
$273$		0			0
$274$	−24.5700			−1.48433
$275$	13.0777	−	7.55041i	0.788615	−	0.455307i
$276$	1.76391	+	3.05517i	0.106175	+	0.183900i
$277$	−2.41670	+	4.18584i	−0.145205	+	0.251503i	−0.929450	−	0.368949i	$-0.879718\pi$
$277$	−2.41670	+	4.18584i	−0.145205	+	0.251503i	0.784244	+	0.620452i	$0.213051\pi$
$278$			31.7168i			1.90225i
$279$	4.24333	+	2.44989i	0.254041	+	0.146671i
$280$	−5.84995	−	3.37747i	−0.349601	−	0.201842i
$281$		−	18.7748i		−	1.12001i	−0.828489	−	0.560005i	$-0.810799\pi$
$281$		−	18.7748i		−	1.12001i	0.828489	−	0.560005i	$-0.189201\pi$
$282$	−9.50753	+	16.4675i	−0.566165	+	0.980627i
$283$	−3.95862	−	6.85652i	−0.235315	−	0.407578i	0.724049	−	0.689749i	$-0.242279\pi$
$283$	−3.95862	−	6.85652i	−0.235315	−	0.407578i	−0.959364	+	0.282171i	$0.908946\pi$
$284$	9.84841	−	5.68598i	0.584395	−	0.337401i
$285$	−11.5036			−0.681417
$286$		0			0
$287$	6.20775			0.366432
$288$	−5.35722	+	3.09299i	−0.315677	+	0.182256i
$289$	8.21648	+	14.2314i	0.483322	+	0.837139i
$290$	−5.09299	+	8.82132i	−0.299071	+	0.518006i
$291$			8.65817i			0.507551i
$292$	−3.18692	−	1.83997i	−0.186500	−	0.107676i
$293$	5.69769	+	3.28956i	0.332862	+	0.192178i	0.657111	−	0.753794i	$-0.271778\pi$
$293$	5.69769	+	3.28956i	0.332862	+	0.192178i	−0.324249	+	0.945972i	$0.605112\pi$
$294$		−	8.77240i		−	0.511617i
$295$	−1.35690	+	2.35021i	−0.0790015	+	0.136835i
$296$	−4.23825	−	7.34087i	−0.246343	−	0.426679i
$297$	4.49119	−	2.59299i	0.260605	−	0.150461i
$298$	−22.9541			−1.32969
$299$		0			0
$300$	−3.63102			−0.209637
$301$	−21.1763	+	12.2262i	−1.22058	+	0.704705i
$302$	−14.0918	−	24.4077i	−0.810892	−	1.40451i
$303$	−4.23825	+	7.34087i	−0.243481	+	0.421722i
$304$		−	39.3183i		−	2.25506i
$305$	−4.18584	−	2.41670i	−0.239681	−	0.138380i
$306$	−1.17511	−	0.678448i	−0.0671764	−	0.0387843i
$307$			24.8649i			1.41911i	0.704649	+	0.709556i	$0.251105\pi$
$307$			24.8649i			1.41911i	−0.704649	+	0.709556i	$0.748895\pi$
$308$	11.1392	−	19.2937i	0.634716	−	1.09936i
$309$	2.82371	+	4.89081i	0.160635	+	0.278228i
$310$	11.0491	−	6.37920i	0.627546	−	0.362314i
$311$	17.0804			0.968539			0.484270	−	0.874919i	$-0.339085\pi$
$311$	17.0804			0.968539			0.484270	+	0.874919i	$0.339085\pi$
$312$		0			0
$313$	15.6974			0.887269			0.443635	−	0.896208i	$-0.353689\pi$
$313$	15.6974			0.887269			0.443635	+	0.896208i	$0.353689\pi$
$314$	−1.28542	+	0.742135i	−0.0725402	+	0.0418811i
$315$	−2.48911	−	4.31127i	−0.140246	−	0.242913i
$316$	−5.88135	+	10.1868i	−0.330852	+	0.573053i
$317$			32.7821i			1.84123i	0.390477	+	0.920613i	$0.372310\pi$
$317$			32.7821i			1.84123i	−0.390477	+	0.920613i	$0.627690\pi$
$318$	4.81913	+	2.78232i	0.270243	+	0.156025i
$319$	17.5689	+	10.1434i	0.983669	+	0.567921i
$320$			1.83340i			0.102490i
$321$	3.36778	−	5.83317i	0.187971	−	0.325576i
$322$	−8.78113	−	15.2094i	−0.489353	−	0.847584i
$323$	5.19150	−	2.99731i	0.288863	−	0.166775i
$324$	−1.24698			−0.0692766
$325$		0			0
$326$	11.2959			0.625622
$327$	−1.79792	+	1.03803i	−0.0994255	+	0.0574033i
$328$	1.22252	+	2.11747i	0.0675024	+	0.116918i
$329$	18.1770	−	31.4835i	1.00213	−	1.73574i
$330$		−	13.5036i		−	0.743351i
$331$	25.2549	+	14.5809i	1.38813	+	0.801439i	0.993105	−	0.117230i	$-0.0374013\pi$
$331$	25.2549	+	14.5809i	1.38813	+	0.801439i	0.395029	+	0.918669i	$0.370735\pi$
$332$	−6.98361	−	4.03199i	−0.383276	−	0.221284i
$333$		−	6.24698i		−	0.342332i
$334$	6.71260	−	11.6266i	0.367297	−	0.636177i
$335$	−3.28232	−	5.68515i	−0.179332	−	0.310613i
$336$	14.7355	−	8.50753i	0.803886	−	0.464124i
$337$	33.2911			1.81348			0.906741	−	0.421688i	$-0.138562\pi$
$337$	33.2911			1.81348			0.906741	+	0.421688i	$0.138562\pi$
$338$		0			0
$339$	6.16852			0.335028
$340$	−1.17511	+	0.678448i	−0.0637291	+	0.0367940i
$341$	−12.7051	−	22.0058i	−0.688018	−	1.19168i
$342$	7.17241	−	12.4230i	0.387839	−	0.671757i
$343$		−	7.34375i		−	0.396525i
$344$	−8.34071	−	4.81551i	−0.449701	−	0.259635i
$345$	−3.54044	−	2.04407i	−0.190611	−	0.110049i
$346$			3.62133i			0.194684i
$347$	0.436845	−	0.756638i	0.0234511	−	0.0406185i	−0.854062	−	0.520172i	$-0.825868\pi$
$347$	0.436845	−	0.756638i	0.0234511	−	0.0406185i	0.877513	+	0.479553i	$0.159201\pi$
$348$	−2.43900	−	4.22447i	−0.130744	−	0.226456i
$349$	2.79892	−	1.61596i	0.149823	−	0.0865002i	−0.423215	−	0.906029i	$-0.639098\pi$
$349$	2.79892	−	1.61596i	0.149823	−	0.0865002i	0.573037	+	0.819529i	$0.305765\pi$
$350$	18.0761			0.966206
$351$		0			0
$352$	32.0804			1.70989
$353$	7.05529	−	4.07338i	0.375515	−	0.216804i	−0.300350	−	0.953829i	$-0.597103\pi$
$353$	7.05529	−	4.07338i	0.375515	−	0.216804i	0.675865	+	0.737025i	$0.263770\pi$
$354$	−1.69202	−	2.93067i	−0.0899299	−	0.155763i
$355$	−6.58911	+	11.4127i	−0.349713	+	0.605721i
$356$			1.44504i			0.0765871i
$357$	2.24663	+	1.29709i	0.118904	+	0.0686495i
$358$	31.2680	+	18.0526i	1.65256	+	0.954108i
$359$		−	2.64071i		−	0.139371i	−0.997569	−	0.0696857i	$-0.977800\pi$
$359$		−	2.64071i		−	0.139371i	0.997569	−	0.0696857i	$-0.0221996\pi$
$360$	0.980386	−	1.69808i	0.0516709	−	0.0894966i
$361$	22.1869	+	38.4289i	1.16773	+	2.02257i
$362$	−37.6439	+	21.7337i	−1.97852	+	1.14230i
$363$	−15.8944			−0.834239
$364$		0			0
$365$	4.26444			0.223211
$366$	5.21966	−	3.01357i	0.272836	−	0.157522i
$367$	1.45204	+	2.51501i	0.0757960	+	0.131282i	0.901432	−	0.432920i	$-0.142517\pi$
$367$	1.45204	+	2.51501i	0.0757960	+	0.131282i	−0.825636	+	0.564203i	$0.809184\pi$
$368$	6.98643	−	12.1008i	0.364193	−	0.630800i
$369$			1.80194i			0.0938051i
$370$	−14.0871	−	8.13318i	−0.732352	−	0.422824i
$371$	−9.21346	−	5.31940i	−0.478339	−	0.276169i
$372$			6.10992i			0.316784i
$373$	4.19926	−	7.27333i	0.217429	−	0.376599i	−0.736592	−	0.676337i	$-0.763566\pi$
$373$	4.19926	−	7.27333i	0.217429	−	0.376599i	0.954021	+	0.299739i	$0.0968995\pi$
$374$	3.51842	+	6.09408i	0.181933	+	0.315117i
$375$	9.90123	−	5.71648i	0.511298	−	0.295198i
$376$	14.3187			0.738432
$377$		0			0
$378$	6.20775			0.319292
$379$	13.6384	−	7.87412i	0.700556	−	0.404466i	−0.106998	−	0.994259i	$-0.534124\pi$
$379$	13.6384	−	7.87412i	0.700556	−	0.404466i	0.807555	+	0.589793i	$0.200791\pi$
$380$	−7.17241	−	12.4230i	−0.367937	−	0.637285i
$381$	−7.13102	+	12.3513i	−0.365333	+	0.632776i
$382$		−	12.7584i		−	0.652776i
$383$	−11.0319	−	6.36927i	−0.563704	−	0.325455i	0.190927	−	0.981604i	$-0.438851\pi$
$383$	−11.0319	−	6.36927i	−0.563704	−	0.325455i	−0.754631	+	0.656150i	$0.772184\pi$
$384$	8.73452	+	5.04288i	0.445732	+	0.257343i
$385$			25.8170i			1.31576i
$386$	−8.80074	+	15.2433i	−0.447946	+	0.775865i
$387$	−3.54892	−	6.14691i	−0.180402	−	0.312465i
$388$	−9.35010	+	5.39828i	−0.474679	+	0.274056i
$389$	0.310371			0.0157365			0.00786823	−	0.999969i	$-0.497495\pi$
$389$	0.310371			0.0157365			0.00786823	+	0.999969i	$0.497495\pi$
$390$		0			0
$391$	2.13036			0.107737
$392$	−5.72079	+	3.30290i	−0.288943	+	0.166822i
$393$	−11.3007	−	19.5735i	−0.570047	−	0.987350i
$394$	21.0928	−	36.5337i	1.06264	−	1.84054i
$395$		−	13.6310i		−	0.685851i
$396$	5.60042	+	3.23341i	0.281432	+	0.162485i
$397$	1.29122	+	0.745488i	0.0648046	+	0.0374150i	0.532052	−	0.846712i	$-0.321421\pi$
$397$	1.29122	+	0.745488i	0.0648046	+	0.0374150i	−0.467248	+	0.884127i	$0.654754\pi$
$398$		−	7.25236i		−	0.363528i
$399$	−13.7126	+	23.7509i	−0.686488	+	1.18903i
$400$	7.19083	+	12.4549i	0.359541	+	0.622744i
$401$	20.6403	−	11.9167i	1.03073	−	0.595092i	0.113535	−	0.993534i	$-0.463782\pi$
$401$	20.6403	−	11.9167i	1.03073	−	0.595092i	0.917193	+	0.398442i	$0.130449\pi$
$402$	8.18598			0.408280
$403$		0			0
$404$	−10.5700			−0.525878
$405$	1.25144	−	0.722521i	0.0621847	−	0.0359024i
$406$	12.1419	+	21.0304i	0.602593	+	1.04372i
$407$	−16.1984	+	28.0564i	−0.802923	+	1.39070i
$408$			1.02177i			0.0505852i
$409$	−3.69570	−	2.13371i	−0.182740	−	0.105505i	0.405839	−	0.913945i	$-0.366979\pi$
$409$	−3.69570	−	2.13371i	−0.182740	−	0.105505i	−0.588580	+	0.808439i	$0.700313\pi$
$410$	4.06341	+	2.34601i	0.200678	+	0.115861i
$411$			13.6353i			0.672581i
$412$	−3.52111	+	6.09873i	−0.173472	+	0.300463i
$413$	3.23490	+	5.60301i	0.159179	+	0.275706i
$414$	4.41485	−	2.54892i	0.216978	−	0.125272i
$415$	9.34481			0.458719
$416$		0			0
$417$	17.6015			0.861948
$418$	−64.4253	+	37.1960i	−3.15114	+	1.81931i
$419$	−14.8448	−	25.7120i	−0.725217	−	1.25611i	−0.958885	−	0.283796i	$-0.908406\pi$
$419$	−14.8448	−	25.7120i	−0.725217	−	1.25611i	0.233668	−	0.972316i	$-0.424927\pi$
$420$	3.10388	−	5.37607i	0.151454	−	0.262325i
$421$			29.3991i			1.43282i	0.697677	+	0.716412i	$0.254217\pi$
$421$			29.3991i			1.43282i	−0.697677	+	0.716412i	$0.745783\pi$
$422$	6.10454	+	3.52446i	0.297164	+	0.171568i
$423$	9.13879	+	5.27628i	0.444343	+	0.256542i
$424$		−	4.19029i		−	0.203499i
$425$	−1.09634	+	1.89892i	−0.0531804	+	0.0921112i
$426$	−8.21648	−	14.2314i	−0.398090	−	0.689512i
$427$	−9.97923	+	5.76151i	−0.482929	+	0.278819i
$428$	8.39911			0.405986
$429$		0			0
$430$	−18.4819			−0.891275
$431$	−28.6275	+	16.5281i	−1.37894	+	0.796131i	−0.992032	−	0.125988i	$-0.959790\pi$
$431$	−28.6275	+	16.5281i	−1.37894	+	0.796131i	−0.386907	+	0.922119i	$0.626457\pi$
$432$	2.46950	+	4.27730i	0.118814	+	0.205792i
$433$	−14.6332	+	25.3454i	−0.703226	+	1.21802i	0.264102	+	0.964495i	$0.414924\pi$
$433$	−14.6332	+	25.3454i	−0.703226	+	1.21802i	−0.967328	+	0.253528i	$0.918409\pi$
$434$		−	30.4166i		−	1.46004i
$435$	4.89546	+	2.82640i	0.234719	+	0.135515i
$436$	−2.24198	−	1.29440i	−0.107371	−	0.0619908i
$437$			22.5217i			1.07736i
$438$	−2.65883	+	4.60523i	−0.127044	+	0.220047i
$439$	−1.06584	−	1.84609i	−0.0508699	−	0.0881093i	0.839469	−	0.543407i	$-0.182866\pi$
$439$	−1.06584	−	1.84609i	−0.0508699	−	0.0881093i	−0.890339	+	0.455298i	$0.849533\pi$
$440$	−8.80620	+	5.08426i	−0.419819	+	0.242383i
$441$	−4.86831			−0.231824
$442$		0			0
$443$	−22.9922			−1.09239			−0.546197	−	0.837657i	$-0.683925\pi$
$443$	−22.9922			−1.09239			−0.546197	+	0.837657i	$0.683925\pi$
$444$	6.74621	−	3.89493i	0.320161	−	0.184845i
$445$	−0.837282	−	1.45021i	−0.0396910	−	0.0687467i
$446$	6.71164	−	11.6249i	0.317805	−	0.550455i
$447$			12.7385i			0.602513i
$448$	3.78531	+	2.18545i	0.178839	+	0.103253i
$449$	−11.2046	−	6.46897i	−0.528777	−	0.305289i	0.211741	−	0.977326i	$-0.432087\pi$
$449$	−11.2046	−	6.46897i	−0.528777	−	0.305289i	−0.740518	+	0.672036i	$0.765420\pi$
$450$			5.24698i			0.247345i
$451$	4.67241	−	8.09285i	0.220015	−	0.381077i
$452$	3.84601	+	6.66149i	0.180901	+	0.313330i
$453$	−13.5453	+	7.82036i	−0.636412	+	0.367432i
$454$	38.2911			1.79709
$455$		0			0
$456$	−10.8019			−0.505847
$457$	−4.20304	+	2.42662i	−0.196610	+	0.113513i	−0.595073	−	0.803672i	$-0.702877\pi$
$457$	−4.20304	+	2.42662i	−0.196610	+	0.113513i	0.398463	+	0.917184i	$0.369544\pi$
$458$	−8.37531	−	14.5065i	−0.391353	−	0.677843i
$459$	−0.376510	+	0.652135i	−0.0175740	+	0.0304390i
$460$		−	5.09783i		−	0.237688i
$461$	−16.3111	−	9.41723i	−0.759685	−	0.438604i	0.0694978	−	0.997582i	$-0.477860\pi$
$461$	−16.3111	−	9.41723i	−0.759685	−	0.438604i	−0.829183	+	0.558978i	$0.811194\pi$
$462$	−27.8802	−	16.0966i	−1.29710	−	0.748883i
$463$			22.8767i			1.06317i	0.847005	+	0.531585i	$0.178403\pi$
$463$			22.8767i			1.06317i	−0.847005	+	0.531585i	$0.821597\pi$
$464$	−9.66033	+	16.7322i	−0.448469	+	0.776772i
$465$	−3.54019	−	6.13179i	−0.164172	−	0.284355i
$466$	−25.2972	+	14.6054i	−1.17187	+	0.676581i
$467$	−13.0000			−0.601568			−0.300784	−	0.953692i	$-0.597248\pi$
$467$	−13.0000			−0.601568			−0.300784	+	0.953692i	$0.597248\pi$
$468$		0			0
$469$	−15.6504			−0.722668
$470$	23.7963	−	13.7388i	1.09764	−	0.633723i
$471$	0.411854	+	0.713352i	0.0189772	+	0.0328695i
$472$	−1.27413	+	2.20685i	−0.0586464	+	0.101579i
$473$			36.8092i			1.69249i
$474$	14.7204	+	8.49880i	0.676129	+	0.390363i
$475$	−20.0750	−	11.5903i	−0.921104	−	0.531800i
$476$			3.23490i			0.148271i
$477$	1.54407	−	2.67441i	0.0706982	−	0.122453i
$478$	−12.1712	−	21.0812i	−0.556698	−	0.964230i
$479$	32.9870	−	19.0450i	1.50721	−	0.870190i	0.507248	−	0.861800i	$-0.330663\pi$
$479$	32.9870	−	19.0450i	1.50721	−	0.870190i	0.999965	−	0.00838964i	$-0.00267054\pi$
$480$	8.93900			0.408008
$481$		0			0
$482$	11.2959			0.514514
$483$	−8.44056	+	4.87316i	−0.384059	+	0.221736i
$484$	−9.90999	−	17.1646i	−0.450454	−	0.780210i
$485$	6.25571	−	10.8352i	0.284057	−	0.492001i
$486$			1.80194i			0.0817376i
$487$	18.4030	+	10.6250i	0.833920	+	0.481464i	0.855193	−	0.518310i	$-0.173439\pi$
$487$	18.4030	+	10.6250i	0.833920	+	0.481464i	−0.0212730	+	0.999774i	$0.506772\pi$
$488$	−3.93051	−	2.26928i	−0.177926	−	0.102726i
$489$		−	6.26875i		−	0.283483i
$490$	−6.33824	+	10.9782i	−0.286333	+	0.495943i
$491$	−3.17510	−	5.49943i	−0.143290	−	0.248186i	0.785444	−	0.618933i	$-0.212435\pi$
$491$	−3.17510	−	5.49943i	−0.143290	−	0.248186i	−0.928734	+	0.370748i	$0.879102\pi$
$492$	−1.94594	+	1.12349i	−0.0877298	+	0.0506508i
$493$	−2.94571			−0.132668
$494$		0			0
$495$	−7.49396			−0.336828
$496$	20.9578	−	12.1000i	0.941033	−	0.543306i
$497$	15.7087	+	27.2083i	0.704632	+	1.22046i
$498$	−5.82640	+	10.0916i	−0.261087	+	0.452216i
$499$		−	4.65087i		−	0.208202i	−0.994567	−	0.104101i	$-0.966804\pi$
$499$		−	4.65087i		−	0.208202i	0.994567	−	0.104101i	$-0.0331965\pi$
$500$	12.3466	+	7.12833i	0.552158	+	0.318789i
$501$	−6.45225	−	3.72521i	−0.288265	−	0.166430i
$502$			1.35690i			0.0605612i
$503$	−7.73759	+	13.4019i	−0.345002	+	0.597561i	−0.985354	−	0.170521i	$-0.945455\pi$
$503$	−7.73759	+	13.4019i	−0.345002	+	0.597561i	0.640352	+	0.768081i	$0.278788\pi$
$504$	−2.33728	−	4.04829i	−0.104111	−	0.180325i
$505$	10.6079	−	6.12445i	0.472043	−	0.272534i
$506$	−26.4373			−1.17528
$507$		0			0
$508$	−17.7845			−0.789059
$509$	−17.7576	+	10.2524i	−0.787092	+	0.454428i	−0.838938	−	0.544227i	$-0.816823\pi$
$509$	−17.7576	+	10.2524i	−0.787092	+	0.454428i	0.0518459	+	0.998655i	$0.483490\pi$
$510$	0.980386	+	1.69808i	0.0434122	+	0.0751921i
$511$	5.08330	−	8.80454i	0.224872	−	0.389490i
$512$			17.1491i			0.757892i
$513$	−6.89423	−	3.98039i	−0.304388	−	0.175738i
$514$	30.7836	+	17.7729i	1.35781	+	0.783930i
$515$		−	8.16075i		−	0.359606i
$516$	4.42543	−	7.66507i	0.194819	−	0.337436i
$517$	−27.3627	−	47.3936i	−1.20341	−	2.08437i
$518$	−33.5842	+	19.3898i	−1.47561	+	0.851941i
$519$	2.00969			0.0882155
$520$		0			0
$521$	−42.0267			−1.84122			−0.920611	−	0.390481i	$-0.872309\pi$
$521$	−42.0267			−1.84122			−0.920611	+	0.390481i	$0.872309\pi$
$522$	−6.10454	+	3.52446i	−0.267189	+	0.154261i
$523$	14.9943	+	25.9708i	0.655653	+	1.13562i	0.981730	+	0.190281i	$0.0609399\pi$
$523$	14.9943	+	25.9708i	0.655653	+	1.13562i	−0.326077	+	0.945343i	$0.605727\pi$
$524$	14.0918	−	24.4077i	0.615603	−	1.06626i
$525$		−	10.0315i		−	0.437809i
$526$	27.4797	+	15.8654i	1.19817	+	0.691764i
$527$	3.19531	+	1.84481i	0.139190	+	0.0803614i
$528$		−	25.6136i		−	1.11469i
$529$	7.49814	−	12.9872i	0.326006	−	0.564659i
$530$	−4.02057	−	6.96384i	−0.174643	−	0.302490i
$531$	−1.62640	+	0.939001i	−0.0705796	+	0.0407492i
$532$	−34.1987			−1.48270
$533$		0			0
$534$	2.08815			0.0903629
$535$	−8.42917	+	4.86658i	−0.364425	+	0.210401i
$536$	−3.08211	−	5.33836i	−0.133127	−	0.230582i
$537$	10.0184	−	17.3524i	0.432327	−	0.748812i
$538$		−	29.5284i		−	1.27306i
$539$	21.8645	+	12.6235i	0.941772	+	0.543732i
$540$	1.56052	+	0.900969i	0.0671543	+	0.0387715i
$541$		−	36.3803i		−	1.56411i	−0.623208	−	0.782056i	$-0.714171\pi$
$541$		−	36.3803i		−	1.56411i	0.623208	−	0.782056i	$-0.285829\pi$
$542$	0.716480	−	1.24098i	0.0307755	−	0.0533047i
$543$	12.0613	+	20.8908i	0.517600	+	0.896509i
$544$	−4.03409	+	2.32908i	−0.172960	+	0.0998587i
$545$	3.00000			0.128506
$546$		0			0
$547$	−25.8159			−1.10381			−0.551905	−	0.833907i	$-0.686099\pi$
$547$	−25.8159			−1.10381			−0.551905	+	0.833907i	$0.686099\pi$
$548$	−14.7250	+	8.50149i	−0.629022	+	0.363166i
$549$	−1.67241	−	2.89669i	−0.0713766	−	0.123628i
$550$	13.6054	−	23.5652i	0.580135	−	1.00482i
$551$		−	31.1414i		−	1.32667i
$552$	−3.32448	−	1.91939i	−0.141499	−	0.0816945i
$553$	−28.1432	−	16.2485i	−1.19677	−	0.690955i
$554$			8.70948i			0.370030i
$555$	−4.51357	+	7.81774i	−0.191591	+	0.331845i
$556$	10.9743	+	19.0081i	0.465416	+	0.806124i
$557$	−15.5801	+	8.99516i	−0.660149	+	0.381137i	−0.792334	−	0.610088i	$-0.791134\pi$
$557$	−15.5801	+	8.99516i	−0.660149	+	0.381137i	0.132185	+	0.991225i	$0.457801\pi$
$558$	8.82908			0.373765
$559$		0			0
$560$	−24.5875			−1.03901
$561$	3.38196	−	1.95257i	0.142786	−	0.0824378i
$562$	−16.9155	−	29.2985i	−0.713537	−	1.23588i
$563$	−19.5661	+	33.8895i	−0.824614	+	1.42827i	0.0775992	+	0.996985i	$0.475275\pi$
$563$	−19.5661	+	33.8895i	−0.824614	+	1.42827i	−0.902214	+	0.431289i	$0.858059\pi$
$564$			13.1588i			0.554087i
$565$	−7.71955	−	4.45689i	−0.324764	−	0.187503i
$566$	−12.3550	−	7.13318i	−0.519321	−	0.299830i
$567$		−	3.44504i		−	0.144678i
$568$	−6.18718	+	10.7165i	−0.259608	+	0.449655i
$569$	15.3001	+	26.5005i	0.641413	+	1.11096i	0.985118	+	0.171882i	$0.0549846\pi$
$569$	15.3001	+	26.5005i	0.641413	+	1.11096i	−0.343705	+	0.939078i	$0.611682\pi$
$570$	−17.9517	+	10.3644i	−0.751915	+	0.434118i
$571$	2.96184			0.123949			0.0619745	−	0.998078i	$-0.480260\pi$
$571$	2.96184			0.123949			0.0619745	+	0.998078i	$0.480260\pi$
$572$		0			0
$573$	−7.08038			−0.295787
$574$	9.68734	−	5.59299i	0.404342	−	0.233447i
$575$	−4.11894	−	7.13422i	−0.171772	−	0.297517i
$576$	−0.634375	+	1.09877i	−0.0264323	+	0.0457821i
$577$		−	0.819396i		−	0.0341119i	−0.999855	−	0.0170560i	$-0.994571\pi$
$577$		−	0.819396i		−	0.0341119i	0.999855	−	0.0170560i	$-0.00542934\pi$
$578$	25.6440	+	14.8056i	1.06665	+	0.615831i
$579$	8.45941	+	4.88404i	0.351561	+	0.202974i
$580$			7.04892i			0.292690i
$581$	11.1392	−	19.2937i	0.462133	−	0.800437i
$582$	7.80074	+	13.5113i	0.323351	+	0.560061i
$583$	−13.8695	+	8.00753i	−0.574414	+	0.331638i
$584$	4.00431			0.165700
$585$		0			0
$586$	11.8552			0.489732
$587$	−27.5392	+	15.8998i	−1.13666	+	0.656254i	−0.945603	−	0.325324i	$-0.894527\pi$
$587$	−27.5392	+	15.8998i	−1.13666	+	0.656254i	−0.191062	+	0.981578i	$0.561193\pi$
$588$	−3.03534	−	5.25737i	−0.125175	−	0.216810i
$589$	−19.5030	+	33.7802i	−0.803606	+	1.39189i
$590$			4.89008i			0.201322i
$591$	−20.2747	−	11.7056i	−0.833989	−	0.481504i
$592$	−26.7202	−	15.4269i	−1.09819	−	0.634042i
$593$			4.26337i			0.175076i	0.996161	+	0.0875379i	$0.0278999\pi$
$593$			4.26337i			0.175076i	−0.996161	+	0.0875379i	$0.972100\pi$
$594$	4.67241	−	8.09285i	0.191711	−	0.332054i
$595$	−1.87435	−	3.24648i	−0.0768410	−	0.133093i
$596$	−13.7566	+	7.94235i	−0.563491	+	0.325331i
$597$	−4.02475			−0.164722
$598$		0			0
$599$	24.7278			1.01035			0.505175	−	0.863017i	$-0.331428\pi$
$599$	24.7278			1.01035			0.505175	+	0.863017i	$0.331428\pi$
$600$	3.42174	−	1.97554i	0.139692	−	0.0806511i
$601$	−3.41185	−	5.90950i	−0.139172	−	0.241054i	0.788011	−	0.615661i	$-0.211111\pi$
$601$	−3.41185	−	5.90950i	−0.139172	−	0.241054i	−0.927184	+	0.374607i	$0.877778\pi$
$602$	−22.0308	+	38.1585i	−0.897908	+	1.55522i
$603$		−	4.54288i		−	0.185000i
$604$	−16.8907	−	9.75182i	−0.687271	−	0.396796i
$605$	19.8909	+	11.4840i	0.808681	+	0.466892i
$606$			15.2741i			0.620469i
$607$	−15.9981	+	27.7096i	−0.649344	+	1.12470i	0.333935	+	0.942596i	$0.391623\pi$
$607$	−15.9981	+	27.7096i	−0.649344	+	1.12470i	−0.983280	+	0.182102i	$0.941710\pi$
$608$	−24.6226	−	42.6476i	−0.998578	−	1.72959i
$609$	11.6710	−	6.73825i	0.472932	−	0.273048i
$610$	−8.70948			−0.352637
$611$		0			0
$612$	−0.939001			−0.0379569
$613$	29.0876	−	16.7937i	1.17484	−	0.678293i	0.220023	−	0.975495i	$-0.429387\pi$
$613$	29.0876	−	16.7937i	1.17484	−	0.678293i	0.954815	+	0.297202i	$0.0960534\pi$
$614$	22.4025	+	38.8022i	0.904090	+	1.56593i
$615$	1.30194	−	2.25502i	0.0524992	−	0.0909313i
$616$			24.2422i			0.976746i
$617$	23.0250	+	13.2935i	0.926953	+	0.535176i	0.885846	−	0.463978i	$-0.153579\pi$
$617$	23.0250	+	13.2935i	0.926953	+	0.535176i	0.0411061	+	0.999155i	$0.486912\pi$
$618$	8.81293	+	5.08815i	0.354508	+	0.204675i
$619$			9.17928i			0.368946i	0.982838	+	0.184473i	$0.0590579\pi$
$619$			9.17928i			0.368946i	−0.982838	+	0.184473i	$0.940942\pi$
$620$	4.41454	−	7.64621i	0.177292	−	0.307079i
$621$	−1.41454	−	2.45006i	−0.0567636	−	0.0983175i
$622$	26.6543	−	15.3889i	1.06874	−	0.617038i
$623$	−3.99223			−0.159945
$624$		0			0
$625$	−1.96184			−0.0784735
$626$	24.4962	−	14.1429i	0.979064	−	0.565263i
$627$	20.6422	+	35.7533i	0.824370	+	1.42785i
$628$	−0.513574	+	0.889535i	−0.0204938	+	0.0354963i
$629$		−	4.70410i		−	0.187565i
$630$	−7.76865	−	4.48523i	−0.309510	−	0.178696i
$631$	14.7262	+	8.50216i	0.586239	+	0.338465i	0.763609	−	0.645679i	$-0.223425\pi$
$631$	14.7262	+	8.50216i	0.586239	+	0.338465i	−0.177370	+	0.984144i	$0.556759\pi$
$632$		−	12.7995i		−	0.509139i
$633$	1.95593	−	3.38776i	0.0777411	−	0.134652i
$634$	29.5356	+	51.1572i	1.17301	+	2.03171i
$635$	17.8481	−	10.3046i	0.708282	−	0.408927i
$636$	3.85086			0.152696
$637$		0			0
$638$	36.5555			1.44725
$639$	−7.89781	+	4.55980i	−0.312433	+	0.180383i
$640$	−7.28717	−	12.6217i	−0.288051	−	0.498918i
$641$	−10.8324	+	18.7623i	−0.427856	+	0.741068i	−0.996682	−	0.0813898i	$-0.974064\pi$
$641$	−10.8324	+	18.7623i	−0.427856	+	0.741068i	0.568827	+	0.822457i	$0.307397\pi$
$642$		−	12.1371i		−	0.479012i
$643$	−8.10216	−	4.67778i	−0.319518	−	0.184474i	0.331660	−	0.943399i	$-0.392391\pi$
$643$	−8.10216	−	4.67778i	−0.319518	−	0.184474i	−0.651178	+	0.758925i	$0.725725\pi$
$644$	−10.5252	−	6.07673i	−0.414751	−	0.239457i
$645$			10.2567i			0.403856i
$646$	5.40097	−	9.35475i	0.212498	−	0.368058i
$647$	−0.351388	−	0.608621i	−0.0138145	−	0.0239274i	0.859036	−	0.511916i	$-0.171064\pi$
$647$	−0.351388	−	0.608621i	−0.0138145	−	0.0239274i	−0.872850	+	0.487989i	$0.837731\pi$
$648$	1.17511	−	0.678448i	0.0461625	−	0.0266520i
$649$	9.73928			0.382300
$650$		0			0
$651$	−16.8799			−0.661576
$652$	6.76972	−	3.90850i	0.265123	−	0.153069i
$653$	18.6705	+	32.3383i	0.730635	+	1.26550i	0.956612	+	0.291364i	$0.0941092\pi$
$653$	18.6705	+	32.3383i	0.730635	+	1.26550i	−0.225977	+	0.974133i	$0.572557\pi$
$654$	−1.87047	+	3.23975i	−0.0731411	+	0.126684i
$655$			32.6601i			1.27614i
$656$	7.70743	+	4.44989i	0.300925	+	0.173739i
$657$	2.55571	+	1.47554i	0.0997078	+	0.0575664i
$658$		−	65.5077i		−	2.55376i
$659$	0.367781	−	0.637015i	0.0143267	−	0.0248146i	−0.858773	−	0.512356i	$-0.828773\pi$
$659$	0.367781	−	0.637015i	0.0143267	−	0.0248146i	0.873100	+	0.487541i	$0.162106\pi$
$660$	−4.67241	−	8.09285i	−0.181873	−	0.315014i
$661$	−11.9931	+	6.92423i	−0.466478	+	0.269321i	−0.714764	−	0.699365i	$-0.753466\pi$
$661$	−11.9931	+	6.92423i	−0.466478	+	0.269321i	0.248286	+	0.968687i	$0.420133\pi$
$662$	52.5478			2.04233
$663$		0			0
$664$	8.77479			0.340528
$665$	34.3211	−	19.8153i	1.33091	−	0.768403i
$666$	−5.62833	−	9.74856i	−0.218094	−	0.377749i
$667$	5.53348	−	9.58427i	0.214257	−	0.371105i
$668$		−	9.29052i		−	0.359461i
$669$	−6.45133	−	3.72468i	−0.249423	−	0.144004i
$670$	−10.2443	−	5.91454i	−0.395771	−	0.228499i
$671$			17.3461i			0.669640i
$672$	10.6555	−	18.4558i	0.411044	−	0.711949i
$673$	−3.17510	−	5.49943i	−0.122391	−	0.211987i	0.798319	−	0.602235i	$-0.205723\pi$
$673$	−3.17510	−	5.49943i	−0.122391	−	0.211987i	−0.920710	+	0.390247i	$0.872390\pi$
$674$	51.9516	−	29.9943i	2.00110	−	1.15534i
$675$	2.91185			0.112077
$676$		0			0
$677$	33.7241			1.29612			0.648061	−	0.761589i	$-0.275580\pi$
$677$	33.7241			1.29612			0.648061	+	0.761589i	$0.275580\pi$
$678$	9.62613	−	5.55765i	0.369689	−	0.213440i
$679$	−14.9139	−	25.8316i	−0.572342	−	0.991326i
$680$	0.738250	−	1.27869i	0.0283106	−	0.0490354i
$681$		−	21.2500i		−	0.814300i
$682$	−39.6531	−	22.8937i	−1.51840	−	0.876646i
$683$	16.6872	+	9.63437i	0.638519	+	0.368649i	0.784044	−	0.620705i	$-0.213154\pi$
$683$	16.6872	+	9.63437i	0.638519	+	0.368649i	−0.145525	+	0.989355i	$0.546487\pi$
$684$		−	9.92692i		−	0.379565i
$685$	9.85181	−	17.0638i	0.376418	−	0.651976i
$686$	−6.61649	−	11.4601i	−0.252619	−	0.437548i
$687$	−8.05048	+	4.64795i	−0.307145	+	0.177330i
$688$	−35.0562			−1.33651
$689$		0			0
$690$	−7.36658			−0.280441
$691$	−34.1223	+	19.7005i	−1.29807	+	0.749443i	−0.980071	−	0.198647i	$-0.936345\pi$
$691$	−34.1223	+	19.7005i	−1.29807	+	0.749443i	−0.318002	+	0.948090i	$0.603012\pi$
$692$	1.25302	+	2.17029i	0.0476327	+	0.0825022i
$693$	−8.93296	+	15.4723i	−0.339335	+	0.587746i
$694$		−	1.57434i		−	0.0597610i
$695$	−22.0273	−	12.7174i	−0.835541	−	0.482400i
$696$	4.59684	+	2.65399i	0.174243	+	0.100599i
$697$			1.35690i			0.0513961i
$698$	2.91185	−	5.04348i	0.110215	−	0.190898i
$699$	8.10537	+	14.0389i	0.306573	+	0.531000i
$700$	10.8331	−	6.25451i	0.409454	−	0.236398i
$701$	−18.3985			−0.694902			−0.347451	−	0.937698i	$-0.612953\pi$
$701$	−18.3985			−0.694902			−0.347451	+	0.937698i	$0.612953\pi$
$702$		0			0
$703$	49.7308			1.87563
$704$	5.69820	−	3.28986i	0.214759	−	0.123991i
$705$	−7.62445	−	13.2059i	−0.287153	−	0.497364i
$706$	7.33997	−	12.7132i	0.276243	−	0.478468i
$707$		−	29.2019i		−	1.09825i
$708$	−2.02808	−	1.17092i	−0.0762201	−	0.0440057i
$709$	−33.3033	−	19.2277i	−1.25073	−	0.722110i	−0.279476	−	0.960153i	$-0.590161\pi$
$709$	−33.3033	−	19.2277i	−1.25073	−	0.722110i	−0.971255	+	0.238043i	$0.923494\pi$
$710$			23.7463i			0.891183i
$711$	4.71648	−	8.16918i	0.176882	−	0.306368i
$712$	−0.786208	−	1.36175i	−0.0294644	−	0.0510338i
$713$	−12.0047	+	6.93094i	−0.449581	+	0.259566i
$714$	4.67456			0.174941
$715$		0			0
$716$	24.9855			0.933753
$717$	−11.6992	+	6.75451i	−0.436913	+	0.252252i
$718$	−2.37920	−	4.12089i	−0.0887909	−	0.153790i
$719$	24.2500	−	42.0022i	0.904371	−	1.56642i	0.0826117	−	0.996582i	$-0.473674\pi$
$719$	24.2500	−	42.0022i	0.904371	−	1.56642i	0.821759	−	0.569835i	$-0.192993\pi$
$720$		−	7.13706i		−	0.265983i
$721$	−16.8490	−	9.72779i	−0.627491	−	0.362282i
$722$	69.2465	+	39.9795i	2.57709	+	1.48788i
$723$		−	6.26875i		−	0.233137i
$724$	−15.0402	+	26.0504i	−0.558964	+	0.968154i
$725$	5.69537	+	9.86468i	0.211521	+	0.366365i
$726$	−24.8036	+	14.3204i	−0.920547	+	0.531478i
$727$	−19.0344			−0.705948			−0.352974	−	0.935633i	$-0.614830\pi$
$727$	−19.0344			−0.705948			−0.352974	+	0.935633i	$0.614830\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	6.65476	−	3.84213i	0.246304	−	0.142203i
$731$	−2.67241	−	4.62874i	−0.0988425	−	0.171200i
$732$	2.08546	−	3.61212i	0.0770807	−	0.133508i
$733$			24.6213i			0.909410i	0.890642	+	0.454705i	$0.150255\pi$
$733$			24.6213i			0.909410i	−0.890642	+	0.454705i	$0.849745\pi$
$734$	4.53189	+	2.61649i	0.167275	+	0.0965764i
$735$	6.09242	+	3.51746i	0.224722	+	0.129743i
$736$		−	17.5007i		−	0.645083i
$737$	−11.7796	+	20.4029i	−0.433908	+	0.751551i
$738$	1.62349	+	2.81197i	0.0597615	+	0.103510i
$739$	38.5481	−	22.2558i	1.41802	−	0.818692i	0.421891	−	0.906647i	$-0.361366\pi$
$739$	38.5481	−	22.2558i	1.41802	−	0.818692i	0.996124	+	0.0879549i	$0.0280331\pi$
$740$	−11.2567			−0.413803
$741$		0			0
$742$	−19.1704			−0.703769
$743$	9.01636	−	5.20560i	0.330778	−	0.190975i	−0.325408	−	0.945574i	$-0.605502\pi$
$743$	9.01636	−	5.20560i	0.330778	−	0.190975i	0.656186	+	0.754599i	$0.272168\pi$
$744$	−3.32424	−	5.75775i	−0.121873	−	0.211089i
$745$	9.20387	−	15.9416i	0.337204	−	0.584054i
$746$		−	15.1336i		−	0.554081i
$747$	5.60042	+	3.23341i	0.204909	+	0.118304i
$748$	4.21723	+	2.43482i	0.154197	+	0.0890259i
$749$			23.2043i			0.847866i
$750$	10.3007	−	17.8414i	0.376130	−	0.651476i
$751$	0.849896	+	1.47206i	0.0310131	+	0.0537163i	0.881115	−	0.472901i	$-0.156793\pi$
$751$	0.849896	+	1.47206i	0.0310131	+	0.0537163i	−0.850102	+	0.526618i	$0.823460\pi$
$752$	45.1365	−	26.0596i	1.64596	−	0.950295i
$753$	0.753020			0.0274416
$754$		0			0
$755$	22.6015			0.822552
$756$	3.72036	−	2.14795i	0.135308	−	0.0781201i
$757$	−13.7126	−	23.7509i	−0.498393	−	0.863242i	0.501606	−	0.865096i	$-0.332743\pi$
$757$	−13.7126	−	23.7509i	−0.498393	−	0.863242i	−0.999998	+	0.00185490i	$0.999410\pi$
$758$	14.1887	−	24.5755i	0.515356	−	0.892622i
$759$			14.6716i			0.532545i
$760$	13.5180	+	7.80463i	0.490350	+	0.283104i
$761$	−4.35271	−	2.51304i	−0.157786	−	0.0910977i	0.419028	−	0.907973i	$-0.362371\pi$
$761$	−4.35271	−	2.51304i	−0.157786	−	0.0910977i	−0.576814	+	0.816876i	$0.695704\pi$
$762$			25.6993i			0.930988i
$763$	3.57606	−	6.19393i	0.129462	−	0.224235i
$764$	−4.41454	−	7.64621i	−0.159713	−	0.276630i
$765$	0.942362	−	0.544073i	0.0340712	−	0.0196710i
$766$	−22.9541			−0.829364
$767$		0			0
$768$	20.7114			0.747358
$769$	36.7590	−	21.2228i	1.32556	−	0.765314i	0.340953	−	0.940080i	$-0.389250\pi$
$769$	36.7590	−	21.2228i	1.32556	−	0.765314i	0.984610	+	0.174766i	$0.0559169\pi$
$770$	23.2603	+	40.2880i	0.838244	+	1.45188i
$771$	9.86323	−	17.0836i	0.355216	−	0.615252i
$772$			12.1806i			0.438390i
$773$	−22.8278	−	13.1796i	−0.821059	−	0.474039i	0.0297223	−	0.999558i	$-0.490538\pi$
$773$	−22.8278	−	13.1796i	−0.821059	−	0.474039i	−0.850782	+	0.525519i	$0.823871\pi$
$774$	−11.0763	−	6.39493i	−0.398131	−	0.229861i
$775$		−	14.2674i		−	0.512501i
$776$	5.87412	−	10.1743i	0.210869	−	0.365235i
$777$	10.7606	+	18.6378i	0.386033	+	0.668628i
$778$	0.484342	−	0.279635i	0.0173645	−	0.0100254i
$779$	−14.3448			−0.513956
$780$		0			0
$781$	47.2941			1.69232
$782$	3.32448	−	1.91939i	0.118883	−	0.0686371i
$783$	1.95593	+	3.38776i	0.0698991	+	0.121069i
$784$	−12.0223	+	20.8232i	−0.429368	+	0.743687i
$785$		−	1.19029i		−	0.0424834i
$786$	−35.2702	−	20.3632i	−1.25804	−	0.726332i
$787$	14.8458	+	8.57122i	0.529195	+	0.305531i	0.740689	−	0.671848i	$-0.234499\pi$
$787$	14.8458	+	8.57122i	0.529195	+	0.305531i	−0.211493	+	0.977379i	$0.567833\pi$
$788$		−	29.1933i		−	1.03997i
$789$	8.80463	−	15.2501i	0.313453	−	0.542917i
$790$	−12.2811	−	21.2715i	−0.436943	−	0.756807i
$791$	−18.4037	+	10.6254i	−0.654362	+	0.377796i
$792$	−7.03684			−0.250043
$793$		0			0
$794$	2.68664			0.0953455
$795$	−3.86464	+	2.23125i	−0.137065	+	0.0791343i
$796$	−2.50939	−	4.34640i	−0.0889431	−	0.154054i
$797$	15.0814	−	26.1218i	0.534212	−	0.925282i	−0.464989	−	0.885316i	$-0.653942\pi$
$797$	15.0814	−	26.1218i	0.534212	−	0.925282i	0.999201	−	0.0399660i	$-0.0127249\pi$
$798$			49.4185i			1.74940i
$799$	6.88169	+	3.97315i	0.243457	+	0.140560i
$800$	15.5994	+	9.00634i	0.551523	+	0.318422i
$801$		−	1.15883i		−	0.0409454i
$802$	21.4731	−	37.1926i	0.758243	−	1.31332i
$803$	−7.65213	−	13.2539i	−0.270038	−	0.467719i
$804$	4.90593	−	2.83244i	0.173019	−	0.0998924i
$805$	14.0838			0.496390
$806$		0			0
$807$	−16.3870			−0.576851
$808$	9.96079	−	5.75086i	0.350419	−	0.202315i
$809$	14.9252	+	25.8512i	0.524742	+	0.908879i	0.999585	+	0.0288090i	$0.00917144\pi$
$809$	14.9252	+	25.8512i	0.524742	+	0.908879i	−0.474843	+	0.880070i	$0.657495\pi$
$810$	1.30194	−	2.25502i	0.0457454	−	0.0792334i
$811$			47.7362i			1.67624i	0.545484	+	0.838122i	$0.316346\pi$
$811$			47.7362i			1.67624i	−0.545484	+	0.838122i	$0.683654\pi$
$812$	14.5535	+	8.40246i	0.510727	+	0.294869i
$813$	−0.688692	−	0.397616i	−0.0241535	−	0.0139450i
$814$			58.3769i			2.04611i
$815$	−4.52930	+	7.84498i	−0.158655	+	0.274798i
$816$	1.85958	+	3.22089i	0.0650985	+	0.112754i
$817$	48.9341	−	28.2521i	1.71199	−	0.988417i
$818$	−7.68963			−0.268862
$819$		0			0
$820$	3.24698			0.113389
$821$	−15.5278	+	8.96495i	−0.541922	+	0.312879i	−0.745858	−	0.666105i	$-0.767960\pi$
$821$	−15.5278	+	8.96495i	−0.541922	+	0.312879i	0.203935	+	0.978984i	$0.434627\pi$
$822$	12.2850	+	21.2783i	0.428489	+	0.742165i
$823$	27.1598	−	47.0421i	0.946731	−	1.63979i	0.194483	−	0.980906i	$-0.437697\pi$
$823$	27.1598	−	47.0421i	0.946731	−	1.63979i	0.752248	−	0.658880i	$-0.228970\pi$
$824$		−	7.66296i		−	0.266952i
$825$	−13.0777	−	7.55041i	−0.455307	−	0.262872i
$826$	10.0963	+	5.82908i	0.351294	+	0.202820i
$827$		−	49.1041i		−	1.70752i	−0.520670	−	0.853758i	$-0.674318\pi$
$827$		−	49.1041i		−	1.70752i	0.520670	−	0.853758i	$-0.325682\pi$
$828$	1.76391	−	3.05517i	0.0613000	−	0.106175i
$829$	−3.67898	−	6.37218i	−0.127776	−	0.221315i	0.795038	−	0.606559i	$-0.207451\pi$
$829$	−3.67898	−	6.37218i	−0.127776	−	0.221315i	−0.922815	+	0.385244i	$0.874117\pi$
$830$	14.5828	−	8.41939i	0.506177	−	0.292241i
$831$	4.83340			0.167669
$832$		0			0
$833$	−3.66594			−0.127017
$834$	27.4675	−	15.8584i	0.951123	−	0.549131i
$835$	5.38308	+	9.32377i	0.186289	+	0.322663i
$836$	−25.7404	+	44.5837i	−0.890251	+	1.54196i
$837$		−	4.89977i		−	0.169361i
$838$	−46.3314	−	26.7494i	−1.60049	−	0.924044i
$839$	−31.6110	−	18.2506i	−1.09133	−	0.630082i	−0.157402	−	0.987535i	$-0.550312\pi$
$839$	−31.6110	−	18.2506i	−1.09133	−	0.630082i	−0.933931	+	0.357453i	$0.883645\pi$
$840$			6.75494i			0.233068i
$841$	6.84870	−	11.8623i	0.236162	−	0.409045i
$842$	26.4877	+	45.8780i	0.912826	+	1.58106i
$843$	−16.2594	+	9.38740i	−0.560005	+	0.323319i
$844$	4.87800			0.167908
$845$		0			0
$846$	19.0151			0.653751
$847$	47.4208	−	27.3784i	1.62940	−	0.940734i
$848$	−7.62618	−	13.2089i	−0.261884	−	0.453596i
$849$	−3.95862	+	6.85652i	−0.135859	+	0.235315i
$850$			3.95108i			0.135521i
$851$	15.3055	+	8.83662i	0.524665	+	0.302915i
$852$	−9.84841	−	5.68598i	−0.337401	−	0.194798i
$853$			9.73855i			0.333441i	0.986004	+	0.166721i	$0.0533178\pi$
$853$			9.73855i			0.333441i	−0.986004	+	0.166721i	$0.946682\pi$
$854$	−10.3819	+	17.9820i	−0.355261	+	0.615330i
$855$	5.75182	+	9.96245i	0.196708	+	0.340709i
$856$	−7.91500	+	4.56973i	−0.270529	+	0.156190i
$857$	15.2030			0.519323			0.259662	−	0.965700i	$-0.416389\pi$
$857$	15.2030			0.519323			0.259662	+	0.965700i	$0.416389\pi$
$858$		0			0
$859$	−31.9885			−1.09143			−0.545717	−	0.837970i	$-0.683743\pi$
$859$	−31.9885			−1.09143			−0.545717	+	0.837970i	$0.683743\pi$
$860$	−11.0763	+	6.39493i	−0.377700	+	0.218065i
$861$	−3.10388	−	5.37607i	−0.105780	−	0.183216i
$862$	−29.7826	+	51.5850i	−1.01440	+	1.75699i
$863$		−	35.2905i		−	1.20130i	−0.799511	−	0.600652i	$-0.794908\pi$
$863$		−	35.2905i		−	1.20130i	0.799511	−	0.600652i	$-0.205092\pi$
$864$	5.35722	+	3.09299i	0.182256	+	0.105226i
$865$	−2.51501	−	1.45204i	−0.0855129	−	0.0493709i
$866$			52.7362i			1.79205i
$867$	8.21648	−	14.2314i	0.279046	−	0.483322i
$868$	−10.5245	−	18.2289i	−0.357223	−	0.618729i
$869$	−42.3652	+	24.4596i	−1.43714	+	0.829734i
$870$	10.1860			0.345337
$871$		0			0
$872$	2.81700			0.0953958
$873$	7.49819	−	4.32908i	0.253775	−	0.146517i
$874$	20.2913	+	35.1456i	0.686365	+	1.18882i
$875$	−19.6935	+	34.1102i	−0.665762	+	1.15313i
$876$			3.67994i			0.124334i
$877$	13.2730	+	7.66315i	0.448196	+	0.258766i	0.707068	−	0.707146i	$-0.250017\pi$
$877$	13.2730	+	7.66315i	0.448196	+	0.258766i	−0.258872	+	0.965912i	$0.583351\pi$
$878$	−3.32655	−	1.92058i	−0.112266	−	0.0648165i
$879$		−	6.57912i		−	0.221908i
$880$	−18.5063	+	32.0539i	−0.623848	+	1.08054i
$881$	−18.2153	−	31.5498i	−0.613689	−	1.06294i	−0.990613	−	0.136696i	$-0.956352\pi$
$881$	−18.2153	−	31.5498i	−0.613689	−	1.06294i	0.376925	−	0.926244i	$-0.376982\pi$
$882$	−7.59712	+	4.38620i	−0.255808	+	0.147691i
$883$	37.6819			1.26810			0.634048	−	0.773294i	$-0.281392\pi$
$883$	37.6819			1.26810			0.634048	+	0.773294i	$0.281392\pi$
$884$		0			0
$885$	2.71379			0.0912231
$886$	−35.8799	+	20.7153i	−1.20541	+	0.695944i
$887$	−2.12445	−	3.67965i	−0.0713320	−	0.123551i	0.828153	−	0.560502i	$-0.189392\pi$
$887$	−2.12445	−	3.67965i	−0.0713320	−	0.123551i	−0.899485	+	0.436951i	$0.856058\pi$
$888$	−4.23825	+	7.34087i	−0.142226	+	0.246343i
$889$		−	49.1333i		−	1.64788i
$890$	−2.61320	−	1.50873i	−0.0875945	−	0.0505727i
$891$	−4.49119	−	2.59299i	−0.150461	−	0.0868684i
$892$		−	9.28919i		−	0.311025i
$893$	−42.0033	+	72.7518i	−1.40559	+	2.43455i
$894$	11.4770	+	19.8788i	0.383849	+	0.664847i
$895$	−25.0750	+	14.4770i	−0.838163	+	0.483914i
$896$	−34.7458			−1.16078
$897$		0			0
$898$	−23.3134			−0.777977
$899$	16.5993	−	9.58360i	0.553617	−	0.319631i
$900$	1.81551	+	3.14456i	0.0605170	+	0.104819i
$901$	1.16272	−	2.01389i	0.0387358	−	0.0670923i
$902$		−	16.8388i		−	0.560670i
$903$	21.1763	+	12.2262i	0.704705	+	0.406861i
$904$	−7.24867	−	4.18502i	−0.241087	−	0.139192i
$905$		−	34.8582i		−	1.15872i
$906$	−14.0918	+	24.4077i	−0.468168	+	0.810892i
$907$	−6.30917	−	10.9278i	−0.209493	−	0.362852i	0.742062	−	0.670331i	$-0.233848\pi$
$907$	−6.30917	−	10.9278i	−0.209493	−	0.362852i	−0.951555	+	0.307479i	$0.900515\pi$
$908$	22.9482	−	13.2491i	0.761562	−	0.439688i
$909$	8.47650			0.281148
$910$		0			0
$911$	6.77777			0.224558			0.112279	−	0.993677i	$-0.464185\pi$
$911$	6.77777			0.224558			0.112279	+	0.993677i	$0.464185\pi$
$912$	−34.0506	+	19.6591i	−1.12753	+	0.650979i
$913$	−16.7684	−	29.0437i	−0.554952	−	0.961206i
$914$	−4.37263	+	7.57361i	−0.144634	+	0.250513i
$915$			4.83340i			0.159787i
$916$	−10.0388	−	5.79590i	−0.331691	−	0.191502i
$917$	67.4314	+	38.9315i	2.22678	+	1.28563i
$918$			1.35690i			0.0447842i
$919$	10.2337	−	17.7253i	0.337579	−	0.584703i	−0.646398	−	0.763000i	$-0.723725\pi$
$919$	10.2337	−	17.7253i	0.337579	−	0.584703i	0.983977	+	0.178297i	$0.0570588\pi$
$920$	2.77359	+	4.80401i	0.0914427	+	0.158383i
$921$	21.5336	−	12.4324i	0.709556	−	0.409662i
$922$	−33.9385			−1.11771
$923$		0			0
$924$	−22.2784			−0.732907
$925$	−15.7533	+	9.09515i	−0.517964	+	0.299047i
$926$	20.6112	+	35.6996i	0.677325	+	1.17316i
$927$	2.82371	−	4.89081i	0.0927427	−	0.160635i
$928$			24.1987i			0.794360i
$929$	4.02892	+	2.32610i	0.132185	+	0.0763169i	0.564634	−	0.825341i	$-0.309017\pi$
$929$	4.02892	+	2.32610i	0.132185	+	0.0763169i	−0.432449	+	0.901658i	$0.642351\pi$
$930$	−11.0491	−	6.37920i	−0.362314	−	0.209182i
$931$		−	38.7555i		−	1.27016i
$932$	−10.1072	+	17.5062i	−0.331073	+	0.573436i
$933$	−8.54019	−	14.7920i	−0.279593	−	0.484270i
$934$	−20.2868	+	11.7126i	−0.663805	+	0.383248i
$935$	−5.64310			−0.184549
$936$		0			0
$937$	−41.8544			−1.36732			−0.683662	−	0.729798i	$-0.739614\pi$
$937$	−41.8544			−1.36732			−0.683662	+	0.729798i	$0.739614\pi$
$938$	−24.4228	+	14.1005i	−0.797433	+	0.460398i
$939$	−7.84870	−	13.5943i	−0.256133	−	0.443635i
$940$	9.50753	−	16.4675i	0.310102	−	0.537112i
$941$			30.3454i			0.989232i	0.869112	+	0.494616i	$0.164691\pi$
$941$			30.3454i			0.989232i	−0.869112	+	0.494616i	$0.835309\pi$
$942$	1.28542	+	0.742135i	0.0418811	+	0.0241801i
$943$	−4.41485	−	2.54892i	−0.143767	−	0.0830042i
$944$			9.27545i			0.301890i
$945$	−2.48911	+	4.31127i	−0.0809709	+	0.140246i
$946$	33.1640	+	57.4417i	1.07825	+	1.86759i
$947$	−10.4205	+	6.01626i	−0.338620	+	0.195502i	−0.659662	−	0.751563i	$-0.729300\pi$
$947$	−10.4205	+	6.01626i	−0.338620	+	0.195502i	0.321042	+	0.947065i	$0.395967\pi$
$948$	11.7627			0.382035
$949$		0			0
$950$	−41.7700			−1.35520
$951$	28.3901	−	16.3910i	0.920613	−	0.531516i
$952$	−1.76002	−	3.04845i	−0.0570426	−	0.0988007i
$953$	11.4913	−	19.9035i	0.372239	−	0.644736i	−0.617671	−	0.786437i	$-0.711924\pi$
$953$	11.4913	−	19.9035i	0.372239	−	0.644736i	0.989910	+	0.141700i	$0.0452569\pi$
$954$		−	5.56465i		−	0.180162i
$955$	8.86069	+	5.11572i	0.286725	+	0.165541i
$956$	−14.5886	−	8.42274i	−0.471829	−	0.272411i
$957$		−	20.2868i		−	0.655779i
$958$	34.3180	−	59.4405i	1.10876	−	1.92043i
$959$	−23.4871	−	40.6809i	−0.758440	−	1.31366i
$960$	1.58777	−	0.916698i	0.0512450	−	0.0295863i
$961$	6.99223			0.225556
$962$		0			0
$963$	−6.73556			−0.217050
$964$	6.76972	−	3.90850i	0.218038	−	0.125884i
$965$	−7.05765	−	12.2242i	−0.227194	−	0.393511i
$966$	−8.78113	+	15.2094i	−0.282528	+	0.489353i
$967$		−	38.8883i		−	1.25056i	−0.780399	−	0.625281i	$-0.784984\pi$
$967$		−	38.8883i		−	1.25056i	0.780399	−	0.625281i	$-0.215016\pi$
$968$	18.6776	+	10.7835i	0.600321	+	0.346595i
$969$	−5.19150	−	2.99731i	−0.166775	−	0.0962875i
$970$		−	22.5448i		−	0.723870i
$971$	28.7567	−	49.8080i	0.922845	−	1.59842i	0.127855	−	0.991793i	$-0.459191\pi$
$971$	28.7567	−	49.8080i	0.922845	−	1.59842i	0.794990	−	0.606622i	$-0.207476\pi$
$972$	0.623490	+	1.07992i	0.0199984	+	0.0346383i
$973$	−52.5139	+	30.3189i	−1.68352	+	0.971980i
$974$	38.2911			1.22693
$975$		0			0
$976$	−16.5200			−0.528794
$977$	14.1760	−	8.18449i	0.453529	−	0.261845i	−0.255791	−	0.966732i	$-0.582336\pi$
$977$	14.1760	−	8.18449i	0.453529	−	0.261845i	0.709319	+	0.704887i	$0.249002\pi$
$978$	−5.64795	−	9.78253i	−0.180601	−	0.312811i
$979$	−3.00484	+	5.20454i	−0.0960352	+	0.166338i
$980$			8.77240i			0.280224i
$981$	1.79792	+	1.03803i	0.0574033	+	0.0331418i
$982$	−9.90962	−	5.72132i	−0.316229	−	0.182575i
$983$			15.6963i			0.500635i	0.968164	+	0.250318i	$0.0805351\pi$
$983$			15.6963i			0.500635i	−0.968164	+	0.250318i	$0.919465\pi$
$984$	1.22252	−	2.11747i	0.0389725	−	0.0675024i
$985$	16.9151	+	29.2978i	0.538959	+	0.933505i
$986$	−4.59684	+	2.65399i	−0.146393	+	0.0845202i
$987$	−36.3540			−1.15716
$988$		0			0
$989$	20.0804			0.638519
$990$	−11.6945	+	6.75182i	−0.371676	+	0.214587i
$991$	5.63222	+	9.75529i	0.178913	+	0.309887i	0.941509	−	0.336989i	$-0.109408\pi$
$991$	5.63222	+	9.75529i	0.178913	+	0.309887i	−0.762595	+	0.646876i	$0.776075\pi$
$992$	15.1549	−	26.2491i	0.481170	−	0.833411i
$993$		−	29.1618i		−	0.925422i
$994$	49.0276	+	28.3061i	1.55506	+	0.897816i
$995$	5.03675	+	2.90797i	0.159676	+	0.0921888i
$996$			8.06398i			0.255517i
$997$	3.85056	−	6.66936i	0.121948	−	0.211221i	−0.798588	−	0.601879i	$-0.794419\pi$
$997$	3.85056	−	6.66936i	0.121948	−	0.211221i	0.920536	+	0.390658i	$0.127752\pi$
$998$	−4.19029	−	7.25780i	−0.132641	−	0.229742i
$999$	−5.41004	+	3.12349i	−0.171166	+	0.0988228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.j.h.361.6		12
13.2	odd	12		507.2.a.k.1.3	yes	3
13.3	even	3		507.2.b.g.337.6		6
13.4	even	6	inner	507.2.j.h.316.6		12
13.5	odd	4		507.2.e.j.484.1		6
13.6	odd	12		507.2.e.j.22.1		6
13.7	odd	12		507.2.e.k.22.3		6
13.8	odd	4		507.2.e.k.484.3		6
13.9	even	3	inner	507.2.j.h.316.1		12
13.10	even	6		507.2.b.g.337.1		6
13.11	odd	12		507.2.a.j.1.1	✓	3
13.12	even	2	inner	507.2.j.h.361.1		12
39.2	even	12		1521.2.a.p.1.1		3
39.11	even	12		1521.2.a.q.1.3		3
39.23	odd	6		1521.2.b.m.1351.6		6
39.29	odd	6		1521.2.b.m.1351.1		6
52.11	even	12		8112.2.a.by.1.2		3
52.15	even	12		8112.2.a.cf.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.j.1.1	✓	3	13.11	odd	12
507.2.a.k.1.3	yes	3	13.2	odd	12
507.2.b.g.337.1		6	13.10	even	6
507.2.b.g.337.6		6	13.3	even	3
507.2.e.j.22.1		6	13.6	odd	12
507.2.e.j.484.1		6	13.5	odd	4
507.2.e.k.22.3		6	13.7	odd	12
507.2.e.k.484.3		6	13.8	odd	4
507.2.j.h.316.1		12	13.9	even	3	inner
507.2.j.h.316.6		12	13.4	even	6	inner
507.2.j.h.361.1		12	13.12	even	2	inner
507.2.j.h.361.6		12	1.1	even	1	trivial
1521.2.a.p.1.1		3	39.2	even	12
1521.2.a.q.1.3		3	39.11	even	12
1521.2.b.m.1351.1		6	39.29	odd	6
1521.2.b.m.1351.6		6	39.23	odd	6
8112.2.a.by.1.2		3	52.11	even	12
8112.2.a.cf.1.2		3	52.15	even	12

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.56052 - 0.900969i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.623490 - 1.07992i) q^{4} +1.44504i q^{5} +(-1.56052 - 0.900969i) q^{6} +(2.98349 + 1.72252i) q^{7} +1.35690i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.56052 - 0.900969i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.623490 - 1.07992i) q^{4} +1.44504i q^{5} +(-1.56052 - 0.900969i) q^{6} +(2.98349 + 1.72252i) q^{7} +1.35690i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.30194 + 2.25502i) q^{10} +(4.49119 - 2.59299i) q^{11} -1.24698 q^{12} +6.20775 q^{14} +(1.25144 - 0.722521i) q^{15} +(2.46950 + 4.27730i) q^{16} +(-0.376510 + 0.652135i) q^{17} +1.80194i q^{18} +(-6.89423 - 3.98039i) q^{19} +(1.56052 + 0.900969i) q^{20} -3.44504i q^{21} +(4.67241 - 8.09285i) q^{22} +(-1.41454 - 2.45006i) q^{23} +(1.17511 - 0.678448i) q^{24} +2.91185 q^{25} +1.00000 q^{27} +(3.72036 - 2.14795i) q^{28} +(1.95593 + 3.38776i) q^{29} +(1.30194 - 2.25502i) q^{30} -4.89977i q^{31} +(5.35722 + 3.09299i) q^{32} +(-4.49119 - 2.59299i) q^{33} +1.35690i q^{34} +(-2.48911 + 4.31127i) q^{35} +(0.623490 + 1.07992i) q^{36} +(-5.41004 + 3.12349i) q^{37} -14.3448 q^{38} -1.96077 q^{40} +(1.56052 - 0.900969i) q^{41} +(-3.10388 - 5.37607i) q^{42} +(-3.54892 + 6.14691i) q^{43} -6.46681i q^{44} +(-1.25144 - 0.722521i) q^{45} +(-4.41485 - 2.54892i) q^{46} -10.5526i q^{47} +(2.46950 - 4.27730i) q^{48} +(2.43416 + 4.21608i) q^{49} +(4.54402 - 2.62349i) q^{50} +0.753020 q^{51} -3.08815 q^{53} +(1.56052 - 0.900969i) q^{54} +(3.74698 + 6.48996i) q^{55} +(-2.33728 + 4.04829i) q^{56} +7.96077i q^{57} +(6.10454 + 3.52446i) q^{58} +(1.62640 + 0.939001i) q^{59} -1.80194i q^{60} +(-1.67241 + 2.89669i) q^{61} +(-4.41454 - 7.64621i) q^{62} +(-2.98349 + 1.72252i) q^{63} +1.26875 q^{64} -9.34481 q^{66} +(-3.93425 + 2.27144i) q^{67} +(0.469501 + 0.813199i) q^{68} +(-1.41454 + 2.45006i) q^{69} +8.97046i q^{70} +(7.89781 + 4.55980i) q^{71} +(-1.17511 - 0.678448i) q^{72} -2.95108i q^{73} +(-5.62833 + 9.74856i) q^{74} +(-1.45593 - 2.52174i) q^{75} +(-8.59696 + 4.96346i) q^{76} +17.8659 q^{77} -9.43296 q^{79} +(-6.18088 + 3.56853i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.62349 - 2.81197i) q^{82} -6.46681i q^{83} +(-3.72036 - 2.14795i) q^{84} +(-0.942362 - 0.544073i) q^{85} +12.7899i q^{86} +(1.95593 - 3.38776i) q^{87} +(3.51842 + 6.09408i) q^{88} +(-1.00358 + 0.579417i) q^{89} -2.60388 q^{90} -3.52781 q^{92} +(-4.24333 + 2.44989i) q^{93} +(-9.50753 - 16.4675i) q^{94} +(5.75182 - 9.96245i) q^{95} -6.18598i q^{96} +(-7.49819 - 4.32908i) q^{97} +(7.59712 + 4.38620i) q^{98} +5.18598i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 2 q^{4} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 2 * q^4 - 6 * q^9	\( 12 q - 6 q^{3} - 2 q^{4} - 6 q^{9} - 2 q^{10} + 4 q^{12} + 4 q^{14} + 10 q^{16} - 14 q^{17} + 10 q^{22} + 4 q^{23} + 20 q^{25} + 12 q^{27} + 16 q^{29} - 2 q^{30} - 36 q^{35} - 2 q^{36} - 80 q^{38} + 28 q^{40} - 2 q^{42} - 6 q^{43} + 10 q^{48} + 34 q^{49} + 28 q^{51} - 52 q^{53} + 26 q^{55} + 14 q^{56} + 26 q^{61} - 32 q^{62} - 16 q^{64} - 20 q^{66} - 14 q^{68} + 4 q^{69} - 14 q^{74} - 10 q^{75} + 60 q^{77} - 36 q^{79} - 6 q^{81} + 10 q^{82} + 16 q^{87} - 14 q^{88} + 4 q^{90} - 68 q^{92} - 64 q^{94} + 6 q^{95}+O(q^{100}) \) 12 * q - 6 * q^3 - 2 * q^4 - 6 * q^9 - 2 * q^10 + 4 * q^12 + 4 * q^14 + 10 * q^16 - 14 * q^17 + 10 * q^22 + 4 * q^23 + 20 * q^25 + 12 * q^27 + 16 * q^29 - 2 * q^30 - 36 * q^35 - 2 * q^36 - 80 * q^38 + 28 * q^40 - 2 * q^42 - 6 * q^43 + 10 * q^48 + 34 * q^49 + 28 * q^51 - 52 * q^53 + 26 * q^55 + 14 * q^56 + 26 * q^61 - 32 * q^62 - 16 * q^64 - 20 * q^66 - 14 * q^68 + 4 * q^69 - 14 * q^74 - 10 * q^75 + 60 * q^77 - 36 * q^79 - 6 * q^81 + 10 * q^82 + 16 * q^87 - 14 * q^88 + 4 * q^90 - 68 * q^92 - 64 * q^94 + 6 * q^95

Introduction

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