LMFDB - Embedded newform 363.3.h.l.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(245,363)]

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, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("363.245");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.343361479062744140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + \cdots + 6561 $ x^16 - x^15 + 3x^14 - 8x^13 + 8x^12 + 7x^11 + 6x^10 + 56x^9 - 137x^8 + 168x^7 + 54x^6 + 189x^5 + 648x^4 - 1944x^3 + 2187x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			323.2
Root			$1.59696 - 0.670602i$ of defining polynomial
Character	$\chi$	$=$	363.323
Dual form			363.3.h.l.245.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.465695 + 0.640974i) q^{2} +(-2.79015 - 1.10230i) q^{3} +(1.04209 + 3.20723i) q^{4} +(-1.48377 - 2.04223i) q^{5} +(2.00590 - 1.27508i) q^{6} +(1.46615 + 4.51235i) q^{7} +(-5.55509 - 1.80496i) q^{8} +(6.56989 + 6.15114i) q^{9} +O(q^{10})$	\(q+(-0.465695 + 0.640974i) q^{2} +(-2.79015 - 1.10230i) q^{3} +(1.04209 + 3.20723i) q^{4} +(-1.48377 - 2.04223i) q^{5} +(2.00590 - 1.27508i) q^{6} +(1.46615 + 4.51235i) q^{7} +(-5.55509 - 1.80496i) q^{8} +(6.56989 + 6.15114i) q^{9} +2.00000 q^{10} +(0.627719 - 10.0974i) q^{12} +(-10.9129 - 7.92871i) q^{13} +(-3.57507 - 1.16161i) q^{14} +(1.88880 + 7.33369i) q^{15} +(-7.16903 + 5.20860i) q^{16} +(13.3216 + 18.3357i) q^{17} +(-7.00228 + 1.34657i) q^{18} +(-2.54435 + 7.83070i) q^{19} +(5.00368 - 6.88698i) q^{20} +(0.883156 - 14.2063i) q^{21} -30.2372i q^{23} +(13.5099 + 11.1594i) q^{24} +(5.75628 - 17.7160i) q^{25} +(10.1642 - 3.30254i) q^{26} +(-11.5506 - 24.4046i) q^{27} +(-12.9443 + 9.40456i) q^{28} +(-51.0298 + 16.5806i) q^{29} +(-5.58030 - 2.20459i) q^{30} +(-20.9223 - 15.2010i) q^{31} -30.3846i q^{32} -17.9565 q^{34} +(7.03983 - 9.68950i) q^{35} +(-12.8817 + 27.4812i) q^{36} +(-13.1660 - 40.5207i) q^{37} +(-3.83438 - 5.27758i) q^{38} +(21.7090 + 34.1516i) q^{39} +(4.55632 + 14.0229i) q^{40} +(-29.3705 - 9.54305i) q^{41} +(8.69456 + 7.18186i) q^{42} -35.4891 q^{43} +(2.81386 - 22.5441i) q^{45} +(19.3812 + 14.0813i) q^{46} +(-29.7554 - 9.66813i) q^{47} +(25.7441 - 6.63041i) q^{48} +(21.4302 - 15.5699i) q^{49} +(8.67483 + 11.9399i) q^{50} +(-16.9581 - 65.8437i) q^{51} +(14.0569 - 43.2627i) q^{52} +(5.82625 - 8.01914i) q^{53} +(21.0217 + 3.96143i) q^{54} -27.7128i q^{56} +(15.7309 - 19.0442i) q^{57} +(13.1366 - 40.4302i) q^{58} +(-58.5127 + 19.0119i) q^{59} +(-21.5525 + 13.7002i) q^{60} +(41.6204 - 30.2390i) q^{61} +(19.4868 - 6.33165i) q^{62} +(-18.1236 + 38.6641i) q^{63} +(-9.20037 - 6.68446i) q^{64} +34.0511i q^{65} +34.3288 q^{67} +(-44.9243 + 61.8330i) q^{68} +(-33.3303 + 84.3662i) q^{69} +(2.93230 + 9.02469i) q^{70} +(-8.52360 - 11.7317i) q^{71} +(-25.3938 - 46.0285i) q^{72} +(27.2657 + 83.9152i) q^{73} +(32.1040 + 10.4312i) q^{74} +(-35.5892 + 43.0852i) q^{75} -27.7663 q^{76} +(-32.0000 - 1.98933i) q^{78} +(-75.7882 - 55.0633i) q^{79} +(21.2744 + 6.91246i) q^{80} +(5.32694 + 80.8246i) q^{81} +(19.7945 - 14.3816i) q^{82} +(-20.0793 - 27.6368i) q^{83} +(46.4831 - 11.9718i) q^{84} +(17.6795 - 54.4118i) q^{85} +(16.5271 - 22.7476i) q^{86} +(160.658 + 9.98755i) q^{87} +143.482i q^{89} +(13.1398 + 12.3023i) q^{90} +(19.7771 - 60.8676i) q^{91} +(96.9775 - 31.5099i) q^{92} +(41.6205 + 65.4755i) q^{93} +(20.0540 - 14.5701i) q^{94} +(19.7673 - 6.42280i) q^{95} +(-33.4928 + 84.7777i) q^{96} +(32.5915 + 23.6791i) q^{97} +20.9870i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 7 q^{9}+O(q^{10}) $ 16 * q + 5 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 7 * q^9	$ 16 q + 5 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 7 q^{9} + 32 q^{10} + 56 q^{12} - 8 q^{13} - 13 q^{15} + 22 q^{16} + 38 q^{18} - 36 q^{19} + 152 q^{21} + 24 q^{24} - 86 q^{25} + 20 q^{27} - 64 q^{28} + 10 q^{30} - 46 q^{31} + 448 q^{34} + 86 q^{36} + 90 q^{37} - 56 q^{39} - 36 q^{40} + 68 q^{42} - 384 q^{43} + 68 q^{45} - 88 q^{46} - 110 q^{48} + 60 q^{49} + 214 q^{51} - 136 q^{52} + 704 q^{54} + 144 q^{57} - 216 q^{58} - 56 q^{60} - 24 q^{61} + 158 q^{63} - 34 q^{64} - 232 q^{67} + 253 q^{69} + 8 q^{70} + 72 q^{72} - 284 q^{73} + 124 q^{75} - 720 q^{76} - 512 q^{78} - 76 q^{79} - 113 q^{81} - 40 q^{82} + 80 q^{84} - 68 q^{85} + 1008 q^{87} + 14 q^{90} - 256 q^{91} - 25 q^{93} + 260 q^{94} + 272 q^{96} - 218 q^{97}+O(q^{100}) $ 16 * q + 5 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 7 * q^9 + 32 * q^10 + 56 * q^12 - 8 * q^13 - 13 * q^15 + 22 * q^16 + 38 * q^18 - 36 * q^19 + 152 * q^21 + 24 * q^24 - 86 * q^25 + 20 * q^27 - 64 * q^28 + 10 * q^30 - 46 * q^31 + 448 * q^34 + 86 * q^36 + 90 * q^37 - 56 * q^39 - 36 * q^40 + 68 * q^42 - 384 * q^43 + 68 * q^45 - 88 * q^46 - 110 * q^48 + 60 * q^49 + 214 * q^51 - 136 * q^52 + 704 * q^54 + 144 * q^57 - 216 * q^58 - 56 * q^60 - 24 * q^61 + 158 * q^63 - 34 * q^64 - 232 * q^67 + 253 * q^69 + 8 * q^70 + 72 * q^72 - 284 * q^73 + 124 * q^75 - 720 * q^76 - 512 * q^78 - 76 * q^79 - 113 * q^81 - 40 * q^82 + 80 * q^84 - 68 * q^85 + 1008 * q^87 + 14 * q^90 - 256 * q^91 - 25 * q^93 + 260 * q^94 + 272 * q^96 - 218 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.465695	+	0.640974i	−0.232847	+	0.320487i	−0.909412	−	0.415896i	$-0.863468\pi$
$2$	−0.465695	+	0.640974i	−0.232847	+	0.320487i	0.676565	+	0.736383i	$0.263468\pi$
$3$	−2.79015	−	1.10230i	−0.930051	−	0.367432i
$3$	−2.79015	−	1.10230i	−0.930051	−	0.367432i
$4$	1.04209	+	3.20723i	0.260523	+	0.801808i
$5$	−1.48377	−	2.04223i	−0.296754	−	0.408446i	0.634439	−	0.772973i	$-0.281231\pi$
$5$	−1.48377	−	2.04223i	−0.296754	−	0.408446i	−0.931193	+	0.364526i	$0.881231\pi$
$6$	2.00590	−	1.27508i	0.334317	−	0.212513i
$7$	1.46615	+	4.51235i	0.209450	+	0.644621i	0.999501	+	0.0315801i	$0.0100539\pi$
$7$	1.46615	+	4.51235i	0.209450	+	0.644621i	−0.790051	+	0.613041i	$0.789946\pi$
$8$	−5.55509	−	1.80496i	−0.694386	−	0.225620i
$9$	6.56989	+	6.15114i	0.729988	+	0.683460i
$10$	2.00000			0.200000
$11$		0			0
$11$		0			0
$12$	0.627719	−	10.0974i	0.0523099	−	0.841446i
$13$	−10.9129	−	7.92871i	−0.839456	−	0.609901i	0.0827624	−	0.996569i	$-0.473626\pi$
$13$	−10.9129	−	7.92871i	−0.839456	−	0.609901i	−0.922219	+	0.386669i	$0.873626\pi$
$14$	−3.57507	−	1.16161i	−0.255362	−	0.0829723i
$15$	1.88880	+	7.33369i	0.125920	+	0.488913i
$16$	−7.16903	+	5.20860i	−0.448064	+	0.325538i
$17$	13.3216	+	18.3357i	0.783626	+	1.07857i	0.994873	+	0.101136i	$0.0322478\pi$
$17$	13.3216	+	18.3357i	0.783626	+	1.07857i	−0.211246	+	0.977433i	$0.567752\pi$
$18$	−7.00228	+	1.34657i	−0.389016	+	0.0748097i
$19$	−2.54435	+	7.83070i	−0.133913	+	0.412142i	−0.995419	−	0.0956047i	$-0.969522\pi$
$19$	−2.54435	+	7.83070i	−0.133913	+	0.412142i	0.861506	+	0.507747i	$0.169522\pi$
$20$	5.00368	−	6.88698i	0.250184	−	0.344349i
$21$	0.883156	−	14.2063i	0.0420550	−	0.676489i
$22$		0			0
$23$		−	30.2372i		−	1.31466i	−0.753603	−	0.657329i	$-0.771686\pi$
$23$		−	30.2372i		−	1.31466i	0.753603	−	0.657329i	$-0.228314\pi$
$24$	13.5099	+	11.1594i	0.562914	+	0.464977i
$25$	5.75628	−	17.7160i	0.230251	−	0.708641i
$26$	10.1642	−	3.30254i	0.390930	−	0.127021i
$27$	−11.5506	−	24.4046i	−0.427801	−	0.903873i
$28$	−12.9443	+	9.40456i	−0.462295	+	0.335877i
$29$	−51.0298	+	16.5806i	−1.75965	+	0.571744i	−0.997164	−	0.0752622i	$-0.976021\pi$
$29$	−51.0298	+	16.5806i	−1.75965	+	0.571744i	−0.762484	+	0.647007i	$0.776021\pi$
$30$	−5.58030	−	2.20459i	−0.186010	−	0.0734863i
$31$	−20.9223	−	15.2010i	−0.674913	−	0.490353i	0.196753	−	0.980453i	$-0.436960\pi$
$31$	−20.9223	−	15.2010i	−0.674913	−	0.490353i	−0.871666	+	0.490100i	$0.836960\pi$
$32$		−	30.3846i		−	0.949520i
$33$		0			0
$34$	−17.9565			−0.528132
$35$	7.03983	−	9.68950i	0.201138	−	0.276843i
$36$	−12.8817	+	27.4812i	−0.357825	+	0.763367i
$37$	−13.1660	−	40.5207i	−0.355837	−	1.09515i	−0.955523	−	0.294918i	$-0.904708\pi$
$37$	−13.1660	−	40.5207i	−0.355837	−	1.09515i	0.599686	−	0.800236i	$-0.295292\pi$
$38$	−3.83438	−	5.27758i	−0.100905	−	0.138884i
$39$	21.7090	+	34.1516i	0.556640	+	0.875681i
$40$	4.55632	+	14.0229i	0.113908	+	0.350573i
$41$	−29.3705	−	9.54305i	−0.716353	−	0.232757i	−0.0719120	−	0.997411i	$-0.522910\pi$
$41$	−29.3705	−	9.54305i	−0.716353	−	0.232757i	−0.644441	+	0.764654i	$0.722910\pi$
$42$	8.69456	+	7.18186i	0.207013	+	0.170997i
$43$	−35.4891			−0.825328			−0.412664	−	0.910883i	$-0.635402\pi$
$43$	−35.4891			−0.825328			−0.412664	+	0.910883i	$0.635402\pi$
$44$		0			0
$45$	2.81386	−	22.5441i	0.0625302	−	0.500980i
$46$	19.3812	+	14.0813i	0.421331	+	0.306115i
$47$	−29.7554	−	9.66813i	−0.633094	−	0.205705i	−0.0251491	−	0.999684i	$-0.508006\pi$
$47$	−29.7554	−	9.66813i	−0.633094	−	0.205705i	−0.607945	+	0.793979i	$0.708006\pi$
$48$	25.7441	−	6.63041i	0.536335	−	0.138134i
$49$	21.4302	−	15.5699i	0.437350	−	0.317753i
$50$	8.67483	+	11.9399i	0.173497	+	0.238798i
$51$	−16.9581	−	65.8437i	−0.332512	−	1.29105i
$52$	14.0569	−	43.2627i	0.270325	−	0.831976i
$53$	5.82625	−	8.01914i	0.109929	−	0.151305i	−0.750507	−	0.660862i	$-0.770191\pi$
$53$	5.82625	−	8.01914i	0.109929	−	0.151305i	0.860437	+	0.509557i	$0.170191\pi$
$54$	21.0217	+	3.96143i	0.389292	+	0.0733599i
$55$		0			0
$56$		−	27.7128i		−	0.494872i
$57$	15.7309	−	19.0442i	0.275980	−	0.334109i
$58$	13.1366	−	40.4302i	0.226493	−	0.697073i
$59$	−58.5127	+	19.0119i	−0.991740	+	0.322236i	−0.759560	−	0.650437i	$-0.774586\pi$
$59$	−58.5127	+	19.0119i	−0.991740	+	0.322236i	−0.232180	+	0.972673i	$0.574586\pi$
$60$	−21.5525	+	13.7002i	−0.359209	+	0.228336i
$61$	41.6204	−	30.2390i	0.682301	−	0.495721i	−0.191819	−	0.981430i	$-0.561439\pi$
$61$	41.6204	−	30.2390i	0.682301	−	0.495721i	0.874120	+	0.485709i	$0.161439\pi$
$62$	19.4868	−	6.33165i	0.314304	−	0.102123i
$63$	−18.1236	+	38.6641i	−0.287677	+	0.613716i
$64$	−9.20037	−	6.68446i	−0.143756	−	0.104445i
$65$			34.0511i			0.523863i
$66$		0			0
$67$	34.3288			0.512370			0.256185	−	0.966628i	$-0.417534\pi$
$67$	34.3288			0.512370			0.256185	+	0.966628i	$0.417534\pi$
$68$	−44.9243	+	61.8330i	−0.660652	+	0.909309i
$69$	−33.3303	+	84.3662i	−0.483047	+	1.22270i
$70$	2.93230	+	9.02469i	0.0418900	+	0.128924i
$71$	−8.52360	−	11.7317i	−0.120051	−	0.165236i	0.744762	−	0.667330i	$-0.232563\pi$
$71$	−8.52360	−	11.7317i	−0.120051	−	0.165236i	−0.864813	+	0.502094i	$0.832563\pi$
$72$	−25.3938	−	46.0285i	−0.352691	−	0.639284i
$73$	27.2657	+	83.9152i	0.373503	+	1.14952i	0.944483	+	0.328560i	$0.106563\pi$
$73$	27.2657	+	83.9152i	0.373503	+	1.14952i	−0.570980	+	0.820964i	$0.693437\pi$
$74$	32.1040	+	10.4312i	0.433838	+	0.140963i
$75$	−35.5892	+	43.0852i	−0.474522	+	0.574470i
$76$	−27.7663			−0.365346
$77$		0			0
$78$	−32.0000	−	1.98933i	−0.410256	−	0.0255043i
$79$	−75.7882	−	55.0633i	−0.959344	−	0.697004i	−0.00634552	−	0.999980i	$-0.502020\pi$
$79$	−75.7882	−	55.0633i	−0.959344	−	0.697004i	−0.952998	+	0.302976i	$0.902020\pi$
$80$	21.2744	+	6.91246i	0.265929	+	0.0864057i
$81$	5.32694	+	80.8246i	0.0657647	+	0.997835i
$82$	19.7945	−	14.3816i	0.241397	−	0.175385i
$83$	−20.0793	−	27.6368i	−0.241919	−	0.332973i	0.670742	−	0.741691i	$-0.265976\pi$
$83$	−20.0793	−	27.6368i	−0.241919	−	0.332973i	−0.912661	+	0.408718i	$0.865976\pi$
$84$	46.4831	−	11.9718i	0.553370	−	0.142521i
$85$	17.6795	−	54.4118i	0.207994	−	0.640139i
$86$	16.5271	−	22.7476i	0.192176	−	0.264507i
$87$	160.658	+	9.98755i	1.84664	+	0.114799i
$88$		0			0
$89$			143.482i			1.61216i	0.591805	+	0.806081i	$0.298416\pi$
$89$			143.482i			1.61216i	−0.591805	+	0.806081i	$0.701584\pi$
$90$	13.1398	+	12.3023i	0.145998	+	0.136692i
$91$	19.7771	−	60.8676i	0.217331	−	0.668875i
$92$	96.9775	−	31.5099i	1.05410	−	0.342499i
$93$	41.6205	+	65.4755i	0.447532	+	0.704038i
$94$	20.0540	−	14.5701i	0.213340	−	0.155001i
$95$	19.7673	−	6.42280i	0.208077	−	0.0676084i
$96$	−33.4928	+	84.7777i	−0.348884	+	0.883101i
$97$	32.5915	+	23.6791i	0.335995	+	0.244114i	0.742970	−	0.669325i	$-0.233417\pi$
$97$	32.5915	+	23.6791i	0.335995	+	0.244114i	−0.406975	+	0.913439i	$0.633417\pi$
$98$			20.9870i			0.214153i
$99$		0			0
$100$	62.8179			0.628179
$101$	54.5204	−	75.0409i	0.539806	−	0.742979i	−0.448779	−	0.893643i	$-0.648141\pi$
$101$	54.5204	−	75.0409i	0.539806	−	0.742979i	0.988585	+	0.150663i	$0.0481409\pi$
$102$	50.1014	+	19.7934i	0.491190	+	0.194053i
$103$	−6.04935	−	18.6180i	−0.0587316	−	0.180757i	0.917387	−	0.397997i	$-0.130295\pi$
$103$	−6.04935	−	18.6180i	−0.0587316	−	0.180757i	−0.976118	+	0.217240i	$0.930295\pi$
$104$	46.3113	+	63.7420i	0.445301	+	0.612904i
$105$	−30.3229	+	19.2752i	−0.288789	+	0.183573i
$106$	2.42681	+	7.46894i	0.0228944	+	0.0704617i
$107$	80.2959	+	26.0897i	0.750429	+	0.243829i	0.659166	−	0.751998i	$-0.270910\pi$
$107$	80.2959	+	26.0897i	0.750429	+	0.243829i	0.0912630	+	0.995827i	$0.470910\pi$
$108$	66.2343	−	62.4773i	0.613280	−	0.578494i
$109$	−167.723			−1.53874			−0.769371	−	0.638803i	$-0.779430\pi$
$109$	−167.723			−1.53874			−0.769371	+	0.638803i	$0.779430\pi$
$110$		0			0
$111$	−7.93070	+	127.572i	−0.0714478	+	1.14929i
$112$	−34.0139	−	24.7125i	−0.303696	−	0.220648i
$113$	117.463	+	38.1659i	1.03949	+	0.337751i	0.778536	−	0.627600i	$-0.215963\pi$
$113$	117.463	+	38.1659i	1.03949	+	0.337751i	0.260955	+	0.965351i	$0.415963\pi$
$114$	4.88107	+	18.9519i	0.0428164	+	0.166244i
$115$	−61.7513	+	44.8649i	−0.536968	+	0.390130i
$116$	−106.356	−	146.386i	−0.916858	−	1.26195i
$117$	−22.9262	−	119.218i	−0.195950	−	1.01895i
$118$	15.0629	−	46.3588i	0.127652	−	0.392871i
$119$	−63.2054	+	86.9947i	−0.531138	+	0.731048i
$120$	2.74456	−	44.1485i	0.0228714	−	0.367904i
$121$		0			0
$122$			40.7597i			0.334096i
$123$	71.4289	+	59.0015i	0.580722	+	0.479687i
$124$	26.9500	−	82.9435i	0.217338	−	0.668899i
$125$	−104.741	+	34.0324i	−0.837927	+	0.272259i
$126$	−16.3426	−	29.6224i	−0.129703	−	0.235099i
$127$	−104.240	+	75.7348i	−0.820788	+	0.596337i	−0.916938	−	0.399030i	$-0.869347\pi$
$127$	−104.240	+	75.7348i	−0.820788	+	0.596337i	0.0961504	+	0.995367i	$0.469347\pi$
$128$	124.159	−	40.3417i	0.969993	−	0.315170i
$129$	99.0200	+	39.1195i	0.767597	+	0.303252i
$130$	−21.8259	−	15.8574i	−0.167891	−	0.121980i
$131$			125.997i			0.961811i	0.876772	+	0.480906i	$0.159692\pi$
$131$			125.997i			0.961811i	−0.876772	+	0.480906i	$0.840308\pi$
$132$		0			0
$133$	−39.0652			−0.293724
$134$	−15.9867	+	22.0038i	−0.119304	+	0.164208i
$135$	−32.7014	+	59.7998i	−0.242232	+	0.442961i
$136$	−40.9078	−	125.901i	−0.300793	−	0.925744i
$137$	34.8644	+	47.9868i	0.254485	+	0.350268i	0.917076	−	0.398713i	$-0.130543\pi$
$137$	34.8644	+	47.9868i	0.254485	+	0.350268i	−0.662591	+	0.748982i	$0.730543\pi$
$138$	−38.5548	−	60.6527i	−0.279383	−	0.439512i
$139$	40.4611	+	124.526i	0.291087	+	0.895873i	0.984508	+	0.175340i	$0.0561026\pi$
$139$	40.4611	+	124.526i	0.291087	+	0.895873i	−0.693421	+	0.720533i	$0.743897\pi$
$140$	38.4126	+	12.4810i	0.274376	+	0.0891501i
$141$	72.3651	+	59.7748i	0.513227	+	0.423935i
$142$	11.4891			0.0809093
$143$		0			0
$144$	−79.1386	−	9.87774i	−0.549574	−	0.0685954i
$145$	109.578	+	79.6129i	0.755709	+	0.549055i
$146$	−66.4849	−	21.6023i	−0.455376	−	0.147961i
$147$	−76.9560	+	19.8201i	−0.523510	+	0.134830i
$148$	116.239	−	84.4526i	0.785399	−	0.570626i
$149$	43.6905	+	60.1348i	0.293225	+	0.403589i	0.930058	−	0.367412i	$-0.119756\pi$
$149$	43.6905	+	60.1348i	0.293225	+	0.403589i	−0.636833	+	0.771001i	$0.719756\pi$
$150$	−11.0428	−	42.8763i	−0.0736188	−	0.285842i
$151$	1.92632	−	5.92859i	0.0127571	−	0.0392622i	−0.944475	−	0.328582i	$-0.893429\pi$
$151$	1.92632	−	5.92859i	0.0127571	−	0.0392622i	0.957232	+	0.289320i	$0.0934292\pi$
$152$	28.2682	−	38.9078i	0.185975	−	0.255972i
$153$	−25.2635	+	202.407i	−0.165121	+	1.32292i
$154$		0			0
$155$			65.2829i			0.421180i
$156$	−86.9092	+	105.215i	−0.557110	+	0.674453i
$157$	30.5297	−	93.9607i	0.194457	−	0.598476i	−0.805526	−	0.592561i	$-0.798117\pi$
$157$	30.5297	−	93.9607i	0.194457	−	0.598476i	0.999983	−	0.00591538i	$-0.00188293\pi$
$158$	70.5883	−	22.9355i	0.446761	−	0.145162i
$159$	−25.0956	+	15.9524i	−0.157834	+	0.100329i
$160$	−62.0525	+	45.0838i	−0.387828	+	0.281773i
$161$	136.441	−	44.3322i	0.847457	−	0.275355i
$162$	−54.2872	−	34.2252i	−0.335106	−	0.211267i
$163$	−168.170	−	122.183i	−1.03172	−	0.749587i	−0.0630658	−	0.998009i	$-0.520088\pi$
$163$	−168.170	−	122.183i	−1.03172	−	0.749587i	−0.968652	+	0.248423i	$0.920088\pi$
$164$		−	104.143i		−	0.635016i
$165$		0			0
$166$	27.0652			0.163044
$167$	37.1265	−	51.1002i	0.222314	−	0.305989i	−0.683262	−	0.730174i	$-0.739439\pi$
$167$	37.1265	−	51.1002i	0.222314	−	0.305989i	0.905576	+	0.424184i	$0.139439\pi$
$168$	−30.5477	+	77.3229i	−0.181832	+	0.460256i
$169$	4.00378	+	12.3224i	0.0236910	+	0.0729134i
$170$	26.6433	+	36.6713i	0.156725	+	0.215714i
$171$	−64.8839	+	35.7962i	−0.379438	+	0.209335i
$172$	−36.9829	−	113.822i	−0.215017	−	0.661755i
$173$	−183.895	−	59.7512i	−1.06298	−	0.345383i	−0.275229	−	0.961379i	$-0.588754\pi$
$173$	−183.895	−	59.7512i	−1.06298	−	0.345383i	−0.787749	+	0.615996i	$0.788754\pi$
$174$	−81.2191	+	98.3261i	−0.466777	+	0.565093i
$175$	88.3804			0.505031
$176$		0			0
$177$	184.216	+	11.4521i	1.04077	+	0.0647011i
$178$	−91.9685	−	66.8190i	−0.516677	−	0.375388i
$179$	−29.4944	−	9.58330i	−0.164773	−	0.0535380i	0.225469	−	0.974250i	$-0.427609\pi$
$179$	−29.4944	−	9.58330i	−0.164773	−	0.0535380i	−0.390242	+	0.920712i	$0.627609\pi$
$180$	75.2365	−	14.4683i	0.417980	−	0.0803797i
$181$	−82.6319	+	60.0356i	−0.456530	+	0.331688i	−0.792168	−	0.610303i	$-0.791048\pi$
$181$	−82.6319	+	60.0356i	−0.456530	+	0.331688i	0.335639	+	0.941991i	$0.391048\pi$
$182$	29.8045	+	41.0223i	0.163761	+	0.225397i
$183$	−149.459	+	38.4934i	−0.816718	+	0.210346i
$184$	−54.5767	+	167.970i	−0.296613	+	0.912880i
$185$	−63.2174	+	87.0113i	−0.341716	+	0.470331i
$186$	−61.3505	−	3.81396i	−0.329842	−	0.0205052i
$187$		0			0
$188$		−	105.508i		−	0.561211i
$189$	93.1870	−	87.9012i	0.493053	−	0.465086i
$190$	−5.08870	+	15.6614i	−0.0267826	+	0.0824284i
$191$	−66.0867	+	21.4729i	−0.346003	+	0.112423i	−0.476863	−	0.878978i	$-0.658226\pi$
$191$	−66.0867	+	21.4729i	−0.346003	+	0.112423i	0.130860	+	0.991401i	$0.458226\pi$
$192$	18.3022	+	28.7922i	0.0953238	+	0.149959i
$193$	219.652	−	159.587i	1.13810	−	0.826875i	0.151243	−	0.988497i	$-0.451673\pi$
$193$	219.652	−	159.587i	1.13810	−	0.826875i	0.986853	+	0.161622i	$0.0516725\pi$
$194$	−30.3554	+	9.86305i	−0.156471	+	0.0508405i
$195$	37.5344	−	95.0078i	0.192484	−	0.487219i
$196$	72.2685	+	52.5061i	0.368717	+	0.267888i
$197$		−	106.612i		−	0.541178i	−0.962695	−	0.270589i	$-0.912782\pi$
$197$		−	106.612i		−	0.541178i	0.962695	−	0.270589i	$-0.0872185\pi$
$198$		0			0
$199$	−289.272			−1.45363			−0.726813	−	0.686835i	$-0.758999\pi$
$199$	−289.272			−1.45363			−0.726813	+	0.686835i	$0.758999\pi$
$200$	−63.9533	+	88.0241i	−0.319766	+	0.440121i
$201$	−95.7825	−	37.8404i	−0.476530	−	0.188261i
$202$	22.7094	+	69.8923i	0.112423	+	0.346002i
$203$	−149.635	−	205.955i	−0.737117	−	1.01455i
$204$	193.504	−	123.004i	0.948549	−	0.602959i
$205$	24.0899	+	74.1410i	0.117512	+	0.361664i
$206$	14.7508	+	4.79283i	0.0716058	+	0.0232661i
$207$	185.993	−	198.655i	0.898517	−	0.959685i
$208$	119.533			0.574676
$209$		0			0
$210$	1.76631	−	28.4125i	0.00841101	−	0.135298i
$211$	−151.458	−	110.040i	−0.717809	−	0.521519i	0.167875	−	0.985808i	$-0.446310\pi$
$211$	−151.458	−	110.040i	−0.717809	−	0.521519i	−0.885683	+	0.464290i	$0.846310\pi$
$212$	31.7907	+	10.3294i	0.149956	+	0.0487237i
$213$	10.8503	+	42.1288i	0.0509404	+	0.197788i
$214$	−54.1162	+	39.3177i	−0.252879	+	0.183728i
$215$	52.6576	+	72.4770i	0.244919	+	0.337102i
$216$	20.1155	+	156.418i	0.0931272	+	0.724157i
$217$	37.9167	−	116.696i	0.174731	−	0.537768i
$218$	78.1076	−	107.506i	0.358292	−	0.493146i
$219$	16.4239	−	264.191i	0.0749949	−	1.20635i
$220$		0			0
$221$		−	305.719i		−	1.38335i
$222$	−78.0768	−	64.4928i	−0.351697	−	0.290508i
$223$	−70.3727	+	216.585i	−0.315573	+	0.971233i	0.659945	+	0.751314i	$0.270579\pi$
$223$	−70.3727	+	216.585i	−0.315573	+	0.971233i	−0.975518	+	0.219919i	$0.929421\pi$
$224$	137.106	−	44.5484i	0.612080	−	0.198877i
$225$	146.792	−	80.9846i	0.652408	−	0.359931i
$226$	−79.1650	+	57.5167i	−0.350288	+	0.254499i
$227$	−405.472	+	131.746i	−1.78622	+	0.580378i	−0.999326	−	0.0367091i	$-0.988312\pi$
$227$	−405.472	+	131.746i	−1.78622	+	0.580378i	−0.786895	+	0.617087i	$0.788312\pi$
$228$	77.4722	+	30.6067i	0.339790	+	0.134240i
$229$	82.1834	+	59.7097i	0.358879	+	0.260741i	0.752585	−	0.658496i	$-0.228807\pi$
$229$	82.1834	+	59.7097i	0.358879	+	0.260741i	−0.393705	+	0.919237i	$0.628807\pi$
$230$		−	60.4743i		−	0.262932i
$231$		0			0
$232$	313.402			1.35087
$233$	101.807	−	140.126i	0.436942	−	0.601399i	−0.532587	−	0.846375i	$-0.678780\pi$
$233$	101.807	−	140.126i	0.436942	−	0.601399i	0.969529	+	0.244976i	$0.0787802\pi$
$234$	87.0920	+	40.8240i	0.372188	+	0.174461i
$235$	24.4056	+	75.1128i	0.103854	+	0.319629i
$236$	−121.951	−	167.851i	−0.516742	−	0.711235i
$237$	150.764	+	237.176i	0.636137	+	1.00074i
$238$	−26.3269	−	81.0260i	−0.110617	−	0.340445i
$239$	153.403	+	49.8436i	0.641852	+	0.208550i	0.611818	−	0.790998i	$-0.290438\pi$
$239$	153.403	+	49.8436i	0.641852	+	0.208550i	0.0300341	+	0.999549i	$0.490438\pi$
$240$	−51.7391	−	42.7374i	−0.215580	−	0.178073i
$241$	56.7011			0.235274			0.117637	−	0.993057i	$-0.462468\pi$
$241$	56.7011			0.235274			0.117637	+	0.993057i	$0.462468\pi$
$242$		0			0
$243$	74.2296	−	231.385i	0.305472	−	0.952201i
$244$	140.356	+	101.974i	0.575228	+	0.417928i
$245$	−63.5948	−	20.6632i	−0.259570	−	0.0843396i
$246$	−71.0824	+	18.3073i	−0.288953	+	0.0744201i
$247$	89.8537	−	65.2825i	0.363780	−	0.264302i
$248$	88.7882	+	122.206i	0.358017	+	0.492768i
$249$	25.5604	+	99.2440i	0.102652	+	0.398570i
$250$	26.9634	−	82.9849i	0.107854	−	0.331939i
$251$	−39.6707	+	54.6021i	−0.158051	+	0.217538i	−0.880697	−	0.473680i	$-0.842925\pi$
$251$	−39.6707	+	54.6021i	−0.158051	+	0.217538i	0.722647	+	0.691218i	$0.242925\pi$
$252$	−142.891	−	17.8351i	−0.567029	−	0.0707741i
$253$		0			0
$254$		−	102.084i		−	0.401907i
$255$	−109.306	+	132.329i	−0.428652	+	0.518938i
$256$	−17.9053	+	55.1069i	−0.0699427	+	0.215261i
$257$	139.493	−	45.3242i	0.542776	−	0.176359i	−0.0247807	−	0.999693i	$-0.507889\pi$
$257$	139.493	−	45.3242i	0.542776	−	0.176359i	0.567557	+	0.823334i	$0.307889\pi$
$258$	−71.1877	+	45.2515i	−0.275921	+	0.175393i
$259$	163.540	−	118.819i	0.631429	−	0.458760i
$260$	−109.210	+	35.4844i	−0.420037	+	0.136478i
$261$	−437.250	−	204.959i	−1.67529	−	0.785283i
$262$	−80.7609	−	58.6763i	−0.308248	−	0.223955i
$263$		−	146.192i		−	0.555863i	−0.960601	−	0.277932i	$-0.910351\pi$
$263$		−	146.192i		−	0.555863i	0.960601	−	0.277932i	$-0.0896488\pi$
$264$		0			0
$265$	−25.0217			−0.0944217
$266$	18.1925	−	25.0398i	0.0683928	−	0.0941346i
$267$	158.160	−	400.338i	0.592360	−	1.49939i
$268$	35.7738	+	110.100i	0.133484	+	0.410822i
$269$	33.5098	+	46.1222i	0.124572	+	0.171458i	0.866748	−	0.498747i	$-0.166206\pi$
$269$	33.5098	+	46.1222i	0.124572	+	0.171458i	−0.742176	+	0.670205i	$0.766206\pi$
$270$	−23.1012	−	48.8091i	−0.0855601	−	0.180775i
$271$	−39.6717	−	122.097i	−0.146390	−	0.450542i	0.850797	−	0.525494i	$-0.176120\pi$
$271$	−39.6717	−	122.097i	−0.146390	−	0.450542i	−0.997187	+	0.0749520i	$0.976120\pi$
$272$	−191.007	−	62.0618i	−0.702230	−	0.228168i
$273$	−122.275	+	148.030i	−0.447894	+	0.542233i
$274$	−46.9944			−0.171513
$275$		0			0
$276$	−305.315	−	18.9804i	−1.10621	−	0.0687697i
$277$	191.152	+	138.880i	0.690080	+	0.501373i	0.876687	−	0.481062i	$-0.159749\pi$
$277$	191.152	+	138.880i	0.690080	+	0.501373i	−0.186606	+	0.982435i	$0.559749\pi$
$278$	−98.6606	−	32.0568i	−0.354894	−	0.115312i
$279$	−43.9541	−	228.565i	−0.157542	−	0.819228i
$280$	−56.5960	+	41.1194i	−0.202129	+	0.146855i
$281$	119.895	+	165.021i	0.426672	+	0.587264i	0.967185	−	0.254072i	$-0.0817700\pi$
$281$	119.895	+	165.021i	0.426672	+	0.587264i	−0.540513	+	0.841335i	$0.681770\pi$
$282$	−72.0141	+	18.5473i	−0.255369	+	0.0657705i
$283$	−148.085	+	455.758i	−0.523267	+	1.61045i	0.244450	+	0.969662i	$0.421393\pi$
$283$	−148.085	+	455.758i	−0.523267	+	1.61045i	−0.767717	+	0.640789i	$0.778607\pi$
$284$	28.7440	−	39.5627i	0.101211	−	0.139305i
$285$	−62.2337	−	3.86886i	−0.218364	−	0.0135750i
$286$		0			0
$287$		−	146.521i		−	0.510528i
$288$	186.900	−	199.624i	0.648959	−	0.693138i
$289$	−69.4247	+	213.667i	−0.240224	+	0.739333i
$290$	−102.060	+	33.1612i	−0.351930	+	0.114349i
$291$	−64.8338	−	101.994i	−0.222797	−	0.350494i
$292$	−240.722	+	174.895i	−0.824391	+	0.598955i
$293$	−8.89881	+	2.89140i	−0.0303714	+	0.00986825i	−0.324163	−	0.946001i	$-0.605083\pi$
$293$	−8.89881	+	2.89140i	−0.0303714	+	0.00986825i	0.293792	+	0.955869i	$0.405083\pi$
$294$	23.1339	−	58.5569i	0.0786866	−	0.199173i
$295$	125.646	+	91.2872i	0.425919	+	0.309448i
$296$			248.860i			0.840743i
$297$		0			0
$298$	−58.8913			−0.197622
$299$	−239.742	+	329.976i	−0.801811	+	1.10360i
$300$	−175.271	−	69.2439i	−0.584238	−	0.230813i
$301$	−52.0324	−	160.139i	−0.172865	−	0.532024i
$302$	2.90299	+	3.99563i	0.00961257	+	0.0132306i
$303$	−234.837	+	149.278i	−0.775041	+	0.492667i
$304$	−22.5465	−	69.3910i	−0.0741662	−	0.228260i
$305$	−123.510	−	40.1308i	−0.404951	−	0.131577i
$306$	−117.972	−	110.453i	−0.385530	−	0.360957i
$307$	−72.5271			−0.236245			−0.118122	−	0.992999i	$-0.537687\pi$
$307$	−72.5271			−0.236245			−0.118122	+	0.992999i	$0.537687\pi$
$308$		0			0
$309$	−3.64391	+	58.6152i	−0.0117926	+	0.189693i
$310$	−41.8446	−	30.4019i	−0.134983	−	0.0980707i
$311$	−362.016	−	117.626i	−1.16404	−	0.378219i	−0.337624	−	0.941281i	$-0.609623\pi$
$311$	−362.016	−	117.626i	−1.16404	−	0.378219i	−0.826415	+	0.563062i	$0.809623\pi$
$312$	−58.9530	−	228.899i	−0.188952	−	0.733649i
$313$	−42.9593	+	31.2118i	−0.137250	+	0.0997181i	−0.654292	−	0.756242i	$-0.727033\pi$
$313$	−42.9593	+	31.2118i	−0.137250	+	0.0997181i	0.517042	+	0.855960i	$0.327033\pi$
$314$	46.0088	+	63.3257i	0.146525	+	0.201674i
$315$	105.852	−	20.3560i	0.336039	−	0.0646221i
$316$	97.6225	−	300.451i	0.308932	−	0.950795i
$317$	43.0533	−	59.2578i	0.135815	−	0.186933i	−0.735692	−	0.677316i	$-0.763143\pi$
$317$	43.0533	−	59.2578i	0.135815	−	0.186933i	0.871507	+	0.490383i	$0.163143\pi$
$318$	1.46182	−	23.5145i	0.00459692	−	0.0739451i
$319$		0			0
$320$			28.7075i			0.0897109i
$321$	−195.279	−	161.304i	−0.608346	−	0.502505i
$322$	−35.1238	+	108.100i	−0.109080	+	0.335714i
$323$	−177.476	+	57.6655i	−0.549462	+	0.178531i
$324$	−253.672	+	101.311i	−0.782939	+	0.312690i
$325$	−203.283	+	147.694i	−0.625486	+	0.454442i
$326$	156.632	−	50.8927i	0.480465	−	0.156113i
$327$	467.972	+	184.880i	1.43111	+	0.565382i
$328$	145.931	+	106.025i	0.444911	+	0.323247i
$329$		−	148.442i		−	0.451191i
$330$		0			0
$331$	−167.351			−0.505591			−0.252795	−	0.967520i	$-0.581350\pi$
$331$	−167.351			−0.505591			−0.252795	+	0.967520i	$0.581350\pi$
$332$	67.7130	−	93.1989i	0.203955	−	0.280720i
$333$	162.749	−	347.202i	0.488737	−	1.04265i
$334$	15.4643	+	47.5942i	0.0463003	+	0.142498i
$335$	−50.9360	−	70.1073i	−0.152048	−	0.209276i
$336$	67.6634	+	106.445i	0.201379	+	0.316801i
$337$	−132.652	−	408.262i	−0.393627	−	1.21146i	−0.930026	−	0.367494i	$-0.880216\pi$
$337$	−132.652	−	408.262i	−0.393627	−	1.21146i	0.536399	−	0.843965i	$-0.319784\pi$
$338$	−9.76285	−	3.17214i	−0.0288842	−	0.00938504i
$339$	−285.668	−	235.967i	−0.842679	−	0.696068i
$340$	192.935			0.567455
$341$		0			0
$342$	7.27163	−	58.2589i	0.0212621	−	0.170348i
$343$	289.760	+	210.523i	0.844781	+	0.613769i
$344$	197.145	+	64.0563i	0.573096	+	0.186210i
$345$	221.750	−	57.1118i	0.642753	−	0.165542i
$346$	123.938	−	90.0462i	0.358202	−	0.260249i
$347$	−302.906	−	416.915i	−0.872929	−	1.20148i	−0.978329	−	0.207054i	$-0.933612\pi$
$347$	−302.906	−	416.915i	−0.872929	−	1.20148i	0.105400	−	0.994430i	$-0.466388\pi$
$348$	135.388	+	525.674i	0.389045	+	1.51056i
$349$	−86.5298	+	266.311i	−0.247936	+	0.763069i	0.747203	+	0.664595i	$0.231396\pi$
$349$	−86.5298	+	266.311i	−0.247936	+	0.763069i	−0.995140	+	0.0984739i	$0.968604\pi$
$350$	−41.1583	+	56.6495i	−0.117595	+	0.161856i
$351$	−67.4456	+	357.907i	−0.192153	+	1.01968i
$352$		0			0
$353$			373.911i			1.05924i	0.848236	+	0.529619i	$0.177665\pi$
$353$			373.911i			1.05924i	−0.848236	+	0.529619i	$0.822335\pi$
$354$	−93.1289	+	112.744i	−0.263076	+	0.318487i
$355$	−11.3119	+	34.8143i	−0.0318644	+	0.0980686i
$356$	−460.181	+	149.522i	−1.29264	+	0.420006i
$357$	272.246	−	173.058i	0.762595	−	0.484755i
$358$	19.8780	−	14.4422i	0.0555252	−	0.0403414i
$359$	103.534	−	33.6402i	0.288395	−	0.0937052i	−0.161247	−	0.986914i	$-0.551552\pi$
$359$	103.534	−	33.6402i	0.288395	−	0.0937052i	0.449642	+	0.893209i	$0.351552\pi$
$360$	−56.3224	+	120.156i	−0.156451	+	0.333765i
$361$	237.209	+	172.342i	0.657088	+	0.477403i
$362$		−	80.9231i		−	0.223544i
$363$		0			0
$364$	215.826			0.592929
$365$	130.918	−	180.194i	0.358680	−	0.493681i
$366$	44.9292	−	113.726i	0.122757	−	0.310726i
$367$	147.699	+	454.571i	0.402450	+	1.23861i	0.923006	+	0.384786i	$0.125725\pi$
$367$	147.699	+	454.571i	0.402450	+	1.23861i	−0.520556	+	0.853828i	$0.674275\pi$
$368$	157.493	+	216.771i	0.427971	+	0.589052i
$369$	−134.260	−	243.359i	−0.363849	−	0.659509i
$370$	−26.3319	−	81.0414i	−0.0711674	−	0.219031i
$371$	44.7273	+	14.5328i	0.120559	+	0.0391719i
$372$	−166.623	+	201.718i	−0.447910	+	0.542253i
$373$	207.081			0.555178			0.277589	−	0.960700i	$-0.410465\pi$
$373$	207.081			0.555178			0.277589	+	0.960700i	$0.410465\pi$
$374$		0			0
$375$	329.757	+	20.4999i	0.879351	+	0.0546663i
$376$	147.843	+	107.415i	0.393201	+	0.285677i
$377$	688.347	+	223.658i	1.82585	+	0.593256i
$378$	12.9457	+	100.665i	0.0342478	+	0.266311i
$379$	−251.286	+	182.570i	−0.663022	+	0.481714i	−0.867682	−	0.497119i	$-0.834391\pi$
$379$	−251.286	+	182.570i	−0.663022	+	0.481714i	0.204660	+	0.978833i	$0.434391\pi$
$380$	41.1988	+	56.7053i	0.108418	+	0.149224i
$381$	374.328	−	96.4083i	0.982487	−	0.253040i
$382$	17.0127	−	52.3596i	0.0445358	−	0.137067i
$383$	211.526	−	291.140i	0.552287	−	0.760158i	−0.438033	−	0.898959i	$-0.644325\pi$
$383$	211.526	−	291.140i	0.552287	−	0.760158i	0.990320	+	0.138801i	$0.0443248\pi$
$384$	−390.891	−	24.3004i	−1.01795	−	0.0632823i
$385$		0			0
$386$			215.110i			0.557280i
$387$	−233.160	−	218.299i	−0.602480	−	0.564079i
$388$	−41.9810	+	129.204i	−0.108198	+	0.333000i
$389$	593.973	−	192.994i	1.52692	−	0.496128i	0.579191	−	0.815192i	$-0.303369\pi$
$389$	593.973	−	192.994i	1.52692	−	0.496128i	0.947733	+	0.319064i	$0.103369\pi$
$390$	43.4179	+	68.3031i	0.111328	+	0.175136i
$391$	554.418	−	402.809i	1.41795	−	1.03020i
$392$	−147.149	+	47.8117i	−0.375381	+	0.121969i
$393$	138.886	−	351.552i	0.353400	−	0.894533i
$394$	68.3355	+	49.6487i	0.173440	+	0.126012i
$395$			236.478i			0.598679i
$396$		0			0
$397$	−78.7284			−0.198308			−0.0991541	−	0.995072i	$-0.531614\pi$
$397$	−78.7284			−0.198308			−0.0991541	+	0.995072i	$0.531614\pi$
$398$	134.712	−	185.415i	0.338473	−	0.465868i
$399$	108.998	+	43.0614i	0.273178	+	0.107923i
$400$	51.0088	+	156.989i	0.127522	+	0.392472i
$401$	464.411	+	639.207i	1.15813	+	1.59403i	0.717894	+	0.696153i	$0.245106\pi$
$401$	464.411	+	639.207i	1.15813	+	1.59403i	0.440239	+	0.897881i	$0.354894\pi$
$402$	68.8601	−	43.7720i	0.171294	−	0.108885i
$403$	107.800	+	331.774i	0.267494	+	0.823260i
$404$	297.489	+	96.6600i	0.736359	+	0.239257i
$405$	157.159	−	130.804i	0.388046	−	0.322973i
$406$	201.696			0.496787
$407$		0			0
$408$	−24.6414	+	396.376i	−0.0603955	+	0.971510i
$409$	−410.734	−	298.416i	−1.00424	−	0.729623i	−0.0412471	−	0.999149i	$-0.513133\pi$
$409$	−410.734	−	298.416i	−1.00424	−	0.729623i	−0.962993	+	0.269526i	$0.913133\pi$
$410$	−58.7410	−	19.0861i	−0.143271	−	0.0465515i
$411$	−44.3815	−	172.321i	−0.107984	−	0.419273i
$412$	53.4082	−	38.8033i	0.129632	−	0.0941829i
$413$	−171.577	−	236.155i	−0.415440	−	0.571804i
$414$	40.7166	+	211.729i	0.0983492	+	0.511423i
$415$	−26.6477	+	82.0131i	−0.0642113	+	0.197622i
$416$	−240.911	+	331.585i	−0.579113	+	0.797080i
$417$	24.3723	−	392.047i	0.0584467	−	0.940162i
$418$		0			0
$419$			334.392i			0.798073i	0.916935	+	0.399036i	$0.130655\pi$
$419$			334.392i			0.798073i	−0.916935	+	0.399036i	$0.869345\pi$
$420$	−93.4192	−	77.1659i	−0.222427	−	0.183728i
$421$	−136.992	+	421.618i	−0.325396	+	1.00147i	0.645865	+	0.763452i	$0.276497\pi$
$421$	−136.992	+	421.618i	−0.325396	+	1.00147i	−0.971261	+	0.238016i	$0.923503\pi$
$422$	141.066	−	45.8351i	0.334280	−	0.108614i
$423$	−136.020	−	246.548i	−0.321560	−	0.582857i
$424$	−46.8395	+	34.0309i	−0.110471	+	0.0802615i
$425$	401.518	−	130.461i	0.944749	−	0.306967i
$426$	−32.0564	−	12.6644i	−0.0752498	−	0.0297287i
$427$	197.471	+	143.471i	0.462460	+	0.335997i
$428$			284.715i			0.665222i
$429$		0			0
$430$	−70.9783			−0.165066
$431$	−467.467	+	643.414i	−1.08461	+	1.49284i	−0.230270	+	0.973127i	$0.573961\pi$
$431$	−467.467	+	643.414i	−1.08461	+	1.49284i	−0.854341	+	0.519712i	$0.826039\pi$
$432$	209.920	+	114.794i	0.485927	+	0.265728i
$433$	−5.75456	−	17.7107i	−0.0132900	−	0.0409024i	0.944192	−	0.329397i	$-0.106845\pi$
$433$	−5.75456	−	17.7107i	−0.0132900	−	0.0409024i	−0.957482	+	0.288494i	$0.906845\pi$
$434$	57.1412	+	78.6481i	0.131662	+	0.181217i
$435$	−217.982	−	342.919i	−0.501107	−	0.788320i
$436$	−174.783	−	537.926i	−0.400878	−	1.23377i
$437$	236.778	+	76.9339i	0.541826	+	0.176050i
$438$	161.691	+	133.560i	0.369158	+	0.304931i
$439$	254.891			0.580618			0.290309	−	0.956933i	$-0.406242\pi$
$439$	254.891			0.580618			0.290309	+	0.956933i	$0.406242\pi$
$440$		0			0
$441$	236.567	+	29.5272i	0.536432	+	0.0669551i
$442$	195.958	+	142.372i	0.443344	+	0.322108i
$443$	−58.5394	−	19.0206i	−0.132143	−	0.0429359i	0.242199	−	0.970227i	$-0.422131\pi$
$443$	−58.5394	−	19.0206i	−0.132143	−	0.0429359i	−0.374342	+	0.927291i	$0.622131\pi$
$444$	−417.416	+	107.506i	−0.940126	+	0.242130i
$445$	293.025	−	212.895i	0.658482	−	0.478415i
$446$	−106.053	−	145.970i	−0.237787	−	0.327286i
$447$	−55.6168	−	215.945i	−0.124422	−	0.483099i
$448$	16.6735	−	51.3157i	0.0372176	−	0.114544i
$449$	80.7809	−	111.185i	0.179913	−	0.247629i	−0.709530	−	0.704675i	$-0.751093\pi$
$449$	80.7809	−	111.185i	0.179913	−	0.247629i	0.889443	+	0.457046i	$0.151093\pi$
$450$	−16.4512	+	131.804i	−0.0365582	+	0.292897i
$451$		0			0
$452$			416.502i			0.921464i
$453$	−11.9098	+	14.4183i	−0.0262909	+	0.0318285i
$454$	104.381	−	321.250i	0.229913	−	0.707600i
$455$	−153.650	+	49.9240i	−0.337693	+	0.109723i
$456$	−121.760	+	77.3988i	−0.267018	+	0.169734i
$457$	−248.847	+	180.798i	−0.544524	+	0.395620i	−0.825762	−	0.564018i	$-0.809255\pi$
$457$	−248.847	+	180.798i	−0.544524	+	0.395620i	0.281239	+	0.959638i	$0.409255\pi$
$458$	−76.5447	+	24.8709i	−0.167128	+	0.0543032i
$459$	293.601	−	536.897i	0.639654	−	1.16971i
$460$	−208.243	−	151.297i	−0.452702	−	0.328907i
$461$			528.162i			1.14569i	0.819664	+	0.572844i	$0.194160\pi$
$461$			528.162i			1.14569i	−0.819664	+	0.572844i	$0.805840\pi$
$462$		0			0
$463$	−45.9484			−0.0992406			−0.0496203	−	0.998768i	$-0.515801\pi$
$463$	−45.9484			−0.0992406			−0.0496203	+	0.998768i	$0.515801\pi$
$464$	279.472	−	384.661i	0.602311	−	0.829010i
$465$	71.9610	−	182.149i	0.154755	−	0.391719i
$466$	42.4058	+	130.512i	0.0909996	+	0.280068i
$467$	−211.054	−	290.491i	−0.451936	−	0.622036i	0.520876	−	0.853632i	$-0.325605\pi$
$467$	−211.054	−	290.491i	−0.451936	−	0.622036i	−0.972812	+	0.231596i	$0.925605\pi$
$468$	358.468	−	197.765i	0.765956	−	0.422576i
$469$	50.3312	+	154.903i	0.107316	+	0.330284i
$470$	−59.5109	−	19.3363i	−0.126619	−	0.0411410i
$471$	−188.755	+	228.512i	−0.400754	+	0.485163i
$472$	359.359			0.761353
$473$		0			0
$474$	−222.234	−	13.8155i	−0.468847	−	0.0291467i
$475$	124.083	+	90.1515i	0.261227	+	0.189793i
$476$	−344.878	−	112.058i	−0.724534	−	0.235415i
$477$	87.6047	−	16.8468i	0.183658	−	0.0353183i
$478$	−103.387	+	75.1152i	−0.216291	+	0.157145i
$479$	−339.387	−	467.127i	−0.708533	−	0.975213i	−0.999827	−	0.0185790i	$-0.994086\pi$
$479$	−339.387	−	467.127i	−0.708533	−	0.975213i	0.291294	−	0.956634i	$-0.405914\pi$
$480$	222.831	−	57.3904i	0.464232	−	0.119563i
$481$	−177.597	+	546.589i	−0.369225	+	1.13636i
$482$	−26.4054	+	36.3439i	−0.0547829	+	0.0754023i
$483$	−429.557	−	26.7041i	−0.889352	−	0.0552880i
$484$		0			0
$485$		−	101.694i		−	0.209678i
$486$	113.743	+	155.334i	0.234040	+	0.319617i
$487$	−187.542	+	577.196i	−0.385097	+	1.18521i	0.551313	+	0.834299i	$0.314127\pi$
$487$	−187.542	+	577.196i	−0.385097	+	1.18521i	−0.936410	+	0.350908i	$0.885873\pi$
$488$	−285.785	+	92.8571i	−0.585625	+	0.190281i
$489$	334.538	+	526.281i	0.684128	+	1.07624i
$490$	42.8603	−	31.1398i	0.0874700	−	0.0635507i
$491$	731.236	−	237.593i	1.48928	−	0.483896i	0.552409	−	0.833573i	$-0.313709\pi$
$491$	731.236	−	237.593i	1.48928	−	0.483896i	0.936870	+	0.349677i	$0.113709\pi$
$492$	−114.796	+	290.574i	−0.233325	+	0.590597i
$493$	−983.817	−	714.785i	−1.99557	−	1.44987i
$494$			87.9956i			0.178129i
$495$		0			0
$496$	229.168			0.462033
$497$	40.4408	−	55.6619i	0.0813697	−	0.111996i
$498$	−75.5161	−	29.8339i	−0.151639	−	0.0599074i
$499$	−153.900	−	473.657i	−0.308418	−	0.949212i	−0.978380	−	0.206817i	$-0.933690\pi$
$499$	−153.900	−	473.657i	−0.308418	−	0.949212i	0.669962	−	0.742395i	$-0.266310\pi$
$500$	−218.299	−	300.463i	−0.436599	−	0.600927i
$501$	−159.916	+	101.653i	−0.319194	+	0.202900i
$502$	−16.5240	−	50.8558i	−0.0329164	−	0.101306i
$503$	162.170	+	52.6924i	0.322406	+	0.104756i	0.465749	−	0.884917i	$-0.345785\pi$
$503$	162.170	+	52.6924i	0.322406	+	0.104756i	−0.143342	+	0.989673i	$0.545785\pi$
$504$	170.465	−	182.070i	0.338225	−	0.361250i
$505$	−234.147			−0.463657
$506$		0			0
$507$	2.41173	−	38.7946i	0.00475687	−	0.0765180i
$508$	−351.527	−	255.399i	−0.691982	−	0.502754i
$509$	392.594	+	127.561i	0.771304	+	0.250612i	0.668123	−	0.744051i	$-0.267098\pi$
$509$	392.594	+	127.561i	0.771304	+	0.250612i	0.103181	+	0.994663i	$0.467098\pi$
$510$	−33.9162	−	131.687i	−0.0665023	−	0.258211i
$511$	−338.679	+	246.065i	−0.662777	+	0.481536i
$512$	279.955	+	385.324i	0.546786	+	0.752587i
$513$	220.494	−	28.3557i	0.429812	−	0.0552743i
$514$	−35.9097	+	110.519i	−0.0698633	+	0.215017i
$515$	−29.0464	+	39.9790i	−0.0564008	+	0.0776291i
$516$	−22.2772	+	358.346i	−0.0431728	+	0.694469i
$517$		0			0
$518$			160.158i			0.309186i
$519$	447.232	+	369.422i	0.861719	+	0.711795i
$520$	61.4608	−	189.157i	0.118194	−	0.363763i
$521$	−105.824	+	34.3843i	−0.203117	+	0.0659968i	−0.408809	−	0.912620i	$-0.634056\pi$
$521$	−105.824	+	34.3843i	−0.203117	+	0.0659968i	0.205691	+	0.978617i	$0.434056\pi$
$522$	334.998	−	184.817i	0.641759	−	0.354056i
$523$	−247.432	+	179.770i	−0.473100	+	0.343728i	−0.798648	−	0.601798i	$-0.794451\pi$
$523$	−247.432	+	179.770i	−0.473100	+	0.343728i	0.325548	+	0.945526i	$0.394451\pi$
$524$	−404.102	+	131.301i	−0.771188	+	0.250574i
$525$	−246.595	−	97.4213i	−0.469704	−	0.185564i
$526$	93.7052	+	68.0808i	0.178147	+	0.129431i
$527$		−	586.126i		−	1.11219i
$528$		0			0
$529$	−385.285			−0.728328
$530$	11.6525	−	16.0383i	0.0219858	−	0.0302609i
$531$	−501.367	−	235.013i	−0.944194	−	0.442587i
$532$	−40.7096	−	125.291i	−0.0765218	−	0.235510i
$533$	244.854	+	337.013i	0.459389	+	0.632294i
$534$	182.952	+	287.812i	0.342606	+	0.538973i
$535$	−65.8592	−	202.694i	−0.123101	−	0.378867i
$536$	−190.699	−	61.9620i	−0.355782	−	0.115601i
$537$	71.7301	+	59.2503i	0.133576	+	0.110336i
$538$	−45.1684			−0.0839562
$539$		0			0
$540$	−225.870	−	42.5639i	−0.418277	−	0.0788220i
$541$	252.246	+	183.268i	0.466259	+	0.338757i	0.795982	−	0.605321i	$-0.206955\pi$
$541$	252.246	+	183.268i	0.466259	+	0.338757i	−0.329722	+	0.944078i	$0.606955\pi$
$542$	96.7359	+	31.4314i	0.178479	+	0.0579915i
$543$	296.732	−	76.4236i	0.546468	−	0.140743i
$544$	557.123	−	404.773i	1.02412	−	0.744068i
$545$	248.862	+	342.529i	0.456627	+	0.628493i
$546$	−37.9403	−	147.312i	−0.0694876	−	0.269802i
$547$	272.857	−	839.767i	0.498824	−	1.53522i	−0.312087	−	0.950054i	$-0.601028\pi$
$547$	272.857	−	839.767i	0.498824	−	1.53522i	0.810911	−	0.585170i	$-0.198972\pi$
$548$	−117.573	+	161.825i	−0.214549	+	0.295301i
$549$	459.446	+	57.3460i	0.836877	+	0.104455i
$550$		0			0
$551$		−	441.786i		−	0.801789i
$552$	337.430	−	408.502i	0.611286	−	0.740040i
$553$	137.348	−	422.714i	0.248369	−	0.764401i
$554$	−178.037	+	57.8478i	−0.321367	+	0.104418i
$555$	272.298	−	173.090i	0.490627	−	0.311875i
$556$	−357.220	+	259.536i	−0.642483	+	0.466791i
$557$	−308.044	+	100.090i	−0.553041	+	0.179694i	−0.572188	−	0.820123i	$-0.693905\pi$
$557$	−308.044	+	100.090i	−0.553041	+	0.179694i	0.0191464	+	0.999817i	$0.493905\pi$
$558$	166.973	+	78.2679i	0.299235	+	0.140265i
$559$	387.290	+	281.383i	0.692827	+	0.503368i
$560$			106.132i			0.189521i
$561$		0			0
$562$	−161.609			−0.287560
$563$	−291.084	+	400.643i	−0.517024	+	0.711622i	−0.985084	−	0.172074i	$-0.944953\pi$
$563$	−291.084	+	400.643i	−0.517024	+	0.711622i	0.468060	+	0.883697i	$0.344953\pi$
$564$	−116.301	+	294.382i	−0.206207	+	0.521954i
$565$	−96.3436	−	296.515i	−0.170520	−	0.524805i
$566$	−223.166	−	307.162i	−0.394287	−	0.542689i
$567$	−356.899	+	142.538i	−0.629451	+	0.251390i
$568$	26.1741	+	80.5555i	0.0460811	+	0.141823i
$569$	−517.800	−	168.244i	−0.910018	−	0.295683i	−0.183652	−	0.982991i	$-0.558792\pi$
$569$	−517.800	−	168.244i	−0.910018	−	0.295683i	−0.726366	+	0.687308i	$0.758792\pi$
$570$	31.4617	−	38.0884i	0.0551960	−	0.0668218i
$571$	−779.886			−1.36582			−0.682912	−	0.730500i	$-0.739287\pi$
$571$	−779.886			−1.36582			−0.682912	+	0.730500i	$0.739287\pi$
$572$		0			0
$573$	208.061	+	12.9345i	0.363109	+	0.0225732i
$574$	93.9164	+	68.2342i	0.163617	+	0.118875i
$575$	−535.682	−	174.054i	−0.931620	−	0.302702i
$576$	−19.3284	−	100.509i	−0.0335562	−	0.174495i
$577$	−918.474	+	667.310i	−1.59181	+	1.15652i	−0.690507	+	0.723326i	$0.742612\pi$
$577$	−918.474	+	667.310i	−1.59181	+	1.15652i	−0.901302	+	0.433191i	$0.857388\pi$
$578$	−104.624	−	144.003i	−0.181011	−	0.249140i
$579$	−788.775	+	203.150i	−1.36231	+	0.350863i
$580$	−141.147	+	434.405i	−0.243357	+	0.748975i
$581$	95.2674	−	131.124i	0.163971	−	0.225687i
$582$	95.5680	+	5.94115i	0.164206	+	0.0102082i
$583$		0			0
$584$		−	515.370i		−	0.882482i
$585$	−209.453	+	223.712i	−0.358040	+	0.382414i
$586$	2.29082	−	7.05041i	0.00390924	−	0.0120314i
$587$	596.792	−	193.909i	1.01668	−	0.330340i	0.247169	−	0.968972i	$-0.420500\pi$
$587$	596.792	−	193.909i	1.01668	−	0.330340i	0.769512	+	0.638633i	$0.220500\pi$
$588$	−143.763	−	226.161i	−0.244495	−	0.384628i
$589$	172.268	−	125.160i	0.292475	−	0.212496i
$590$	−117.025	+	38.0238i	−0.198348	+	0.0644472i
$591$	−117.518	+	297.464i	−0.198846	+	0.503323i
$592$	305.443	+	221.918i	0.515952	+	0.374861i
$593$		−	961.677i		−	1.62171i	−0.585244	−	0.810857i	$-0.699001\pi$
$593$		−	961.677i		−	1.62171i	0.585244	−	0.810857i	$-0.300999\pi$
$594$		0			0
$595$	271.446			0.456211
$596$	−147.337	+	202.791i	−0.247209	+	0.340254i
$597$	807.112	+	318.863i	1.35195	+	0.534108i
$598$	−99.8595	−	307.336i	−0.166989	−	0.513940i
$599$	−577.456	−	794.800i	−0.964034	−	1.32688i	−0.945004	−	0.327060i	$-0.893942\pi$
$599$	−577.456	−	794.800i	−0.964034	−	1.32688i	−0.0190299	−	0.999819i	$-0.506058\pi$
$600$	275.468	−	175.105i	0.459113	−	0.291842i
$601$	99.2684	+	305.517i	0.165172	+	0.508347i	0.999049	−	0.0436032i	$-0.0138837\pi$
$601$	99.2684	+	305.517i	0.165172	+	0.508347i	−0.833877	+	0.551950i	$0.813884\pi$
$602$	126.876	+	41.2246i	0.210758	+	0.0684794i
$603$	225.536	+	211.161i	0.374024	+	0.350184i
$604$	21.0217			0.0348042
$605$		0			0
$606$	13.6793	−	220.043i	0.0225731	−	0.363107i
$607$	−405.771	−	294.810i	−0.668485	−	0.485683i	0.201033	−	0.979585i	$-0.435570\pi$
$607$	−405.771	−	294.810i	−0.668485	−	0.485683i	−0.869518	+	0.493902i	$0.835570\pi$
$608$	237.933	+	77.3091i	0.391337	+	0.127153i
$609$	190.481	+	739.586i	0.312777	+	1.21443i
$610$	83.2408	−	60.4780i	0.136460	−	0.0991442i
$611$	248.063	+	341.430i	0.405996	+	0.558805i
$612$	−675.492	+	129.900i	−1.10374	+	0.212256i
$613$	114.259	−	351.653i	0.186393	−	0.573659i	−0.813576	−	0.581458i	$-0.802482\pi$
$613$	114.259	−	351.653i	0.186393	−	0.573659i	0.999970	+	0.00779866i	$0.00248241\pi$
$614$	33.7755	−	46.4879i	0.0550089	−	0.0757133i
$615$	14.5109	−	233.419i	0.0235949	−	0.379543i
$616$		0			0
$617$		−	560.582i		−	0.908560i	−0.890859	−	0.454280i	$-0.849897\pi$
$617$		−	560.582i		−	0.908560i	0.890859	−	0.454280i	$-0.150103\pi$
$618$	−35.8739	−	29.6324i	−0.0580483	−	0.0479489i
$619$	127.751	−	393.176i	0.206383	−	0.635180i	−0.793271	−	0.608868i	$-0.791624\pi$
$619$	127.751	−	393.176i	0.206383	−	0.635180i	0.999654	−	0.0263117i	$-0.00837625\pi$
$620$	−209.377	+	68.0308i	−0.337705	+	0.109727i
$621$	−737.925	+	349.258i	−1.18828	+	0.562412i
$622$	243.984	−	177.265i	0.392258	−	0.284992i
$623$	−647.443	+	210.367i	−1.03923	+	0.337668i
$624$	−333.514	−	131.760i	−0.534478	−	0.211154i
$625$	−151.840	−	110.318i	−0.242944	−	0.176509i
$626$		−	42.0710i		−	0.0672060i
$627$		0			0
$628$	333.168			0.530523
$629$	567.582	−	781.209i	0.902356	−	1.24199i
$630$	−36.2473	+	77.3283i	−0.0575353	+	0.122743i
$631$	338.529	+	1041.88i	0.536496	+	1.65116i	0.740395	+	0.672172i	$0.234639\pi$
$631$	338.529	+	1041.88i	0.536496	+	1.65116i	−0.203899	+	0.978992i	$0.565361\pi$
$632$	321.623	+	442.676i	0.508897	+	0.700436i
$633$	301.293	+	473.980i	0.475976	+	0.748784i
$634$	17.9330	+	55.1921i	0.0282855	+	0.0870538i
$635$	309.336	+	100.509i	0.487144	+	0.158283i
$636$	−77.3148	−	63.8634i	−0.121564	−	0.100414i
$637$	−357.315			−0.560934
$638$		0			0
$639$	16.1644	−	129.506i	0.0252964	−	0.202670i
$640$	−266.611	−	193.704i	−0.416579	−	0.302662i
$641$	−939.589	−	305.291i	−1.46582	−	0.476273i	−0.535975	−	0.844234i	$-0.680056\pi$
$641$	−939.589	−	305.291i	−1.46582	−	0.476273i	−0.929841	+	0.367961i	$0.880056\pi$
$642$	194.332	−	50.0503i	0.302698	−	0.0779600i
$643$	829.799	−	602.884i	1.29051	−	0.937611i	0.290695	−	0.956816i	$-0.406113\pi$
$643$	829.799	−	602.884i	1.29051	−	0.937611i	0.999816	+	0.0192046i	$0.00611338\pi$
$644$	284.367	+	391.398i	0.441564	+	0.607761i
$645$	−67.0317	−	260.266i	−0.103925	−	0.403513i
$646$	45.6876	−	140.612i	0.0707239	−	0.217666i
$647$	282.730	−	389.145i	0.436987	−	0.601460i	−0.532553	−	0.846397i	$-0.678767\pi$
$647$	282.730	−	389.145i	0.436987	−	0.601460i	0.969539	+	0.244936i	$0.0787671\pi$
$648$	116.293	−	458.603i	0.179465	−	0.707720i
$649$		0			0
$650$		−	199.079i		−	0.306276i
$651$	−234.426	+	283.803i	−0.360102	+	0.435950i
$652$	216.619	−	666.685i	0.332238	−	1.02252i
$653$	738.203	−	239.857i	1.13048	−	0.367315i	0.316721	−	0.948519i	$-0.397418\pi$
$653$	738.203	−	239.857i	1.13048	−	0.367315i	0.813758	+	0.581204i	$0.197418\pi$
$654$	−336.435	+	213.860i	−0.514427	+	0.327003i
$655$	257.316	−	186.951i	0.392848	−	0.285421i
$656$	260.264	−	84.5649i	0.396744	−	0.128910i
$657$	−337.042	+	719.029i	−0.513001	+	1.09441i
$658$	95.1473	+	69.1285i	0.144601	+	0.105059i
$659$		−	52.5987i		−	0.0798160i	−0.999203	−	0.0399080i	$-0.987294\pi$
$659$		−	52.5987i		−	0.0798160i	0.999203	−	0.0399080i	$-0.0127065\pi$
$660$		0			0
$661$	−233.530			−0.353297			−0.176649	−	0.984274i	$-0.556526\pi$
$661$	−233.530			−0.353297			−0.176649	+	0.984274i	$0.556526\pi$
$662$	77.9342	−	107.267i	0.117725	−	0.162035i
$663$	−336.993	+	853.003i	−0.508285	+	1.28658i
$664$	61.6590	+	189.767i	0.0928599	+	0.285793i
$665$	57.9638	+	79.7803i	0.0871636	+	0.119970i
$666$	146.756	+	266.008i	0.220354	+	0.399412i
$667$	501.350	+	1543.00i	0.751649	+	2.31334i
$668$	202.579	+	65.8220i	0.303263	+	0.0985360i
$669$	435.091	−	526.733i	0.650360	−	0.787344i
$670$	68.6576			0.102474
$671$		0			0
$672$	−431.652	−	26.8344i	−0.642339	−	0.0399321i
$673$	191.341	+	139.018i	0.284311	+	0.206564i	0.720796	−	0.693148i	$-0.243777\pi$
$673$	191.341	+	139.018i	0.284311	+	0.206564i	−0.436485	+	0.899712i	$0.643777\pi$
$674$	323.460	+	105.099i	0.479911	+	0.155933i
$675$	−498.840	+	64.1513i	−0.739023	+	0.0950390i
$676$	−35.3484	+	25.6821i	−0.0522905	+	0.0379912i
$677$	173.786	+	239.196i	0.256701	+	0.353318i	0.917844	−	0.396942i	$-0.129928\pi$
$677$	173.786	+	239.196i	0.256701	+	0.353318i	−0.661143	+	0.750260i	$0.729928\pi$
$678$	284.283	−	73.2172i	0.419296	−	0.107990i
$679$	−59.0643	+	181.781i	−0.0869872	+	0.267719i
$680$	−196.422	+	270.351i	−0.288856	+	0.397576i
$681$	1276.55	+	79.3589i	1.87452	+	0.116533i
$682$		0			0
$683$		−	905.661i		−	1.32600i	−0.748617	−	0.663002i	$-0.769282\pi$
$683$		−	905.661i		−	1.32600i	0.748617	−	0.663002i	$-0.230718\pi$
$684$	−182.422	−	170.794i	−0.266698	−	0.249700i
$685$	46.2694	−	142.403i	0.0675466	−	0.207887i
$686$	−269.879	+	87.6891i	−0.393410	+	0.127827i
$687$	−163.486	−	257.189i	−0.237971	−	0.374366i
$688$	254.423	−	184.849i	0.369800	−	0.268676i
$689$	−127.163	+	41.3177i	−0.184561	+	0.0599677i
$690$	−66.6605	+	168.732i	−0.0966095	+	0.244540i
$691$	284.794	+	206.915i	0.412147	+	0.299442i	0.774470	−	0.632610i	$-0.218016\pi$
$691$	284.794	+	206.915i	0.412147	+	0.299442i	−0.362323	+	0.932052i	$0.618016\pi$
$692$		−	652.061i		−	0.942284i
$693$		0			0
$694$	408.293			0.588319
$695$	194.277	−	267.399i	0.279535	−	0.384747i
$696$	−874.439	−	345.462i	−1.25638	−	0.496353i
$697$	−216.285	−	665.657i	−0.310308	−	0.955031i
$698$	−130.402	−	179.483i	−0.186822	−	0.257139i
$699$	−438.518	+	278.751i	−0.627351	+	0.398785i
$700$	92.1005	+	283.456i	0.131572	+	0.404937i
$701$	−1189.16	−	386.381i	−1.69637	−	0.551186i	−0.708401	−	0.705810i	$-0.750583\pi$
$701$	−1189.16	−	386.381i	−1.69637	−	0.551186i	−0.987973	+	0.154624i	$0.950583\pi$
$702$	−198.000	−	209.906i	−0.282051	−	0.299012i
$703$	350.804			0.499010
$704$		0			0
$705$	14.7011	−	236.478i	0.0208526	−	0.335430i
$706$	−239.667	−	174.128i	−0.339472	−	0.246641i
$707$	418.546	+	135.994i	0.592003	+	0.192353i
$708$	155.241	+	602.757i	0.219266	+	0.851352i
$709$	109.162	−	79.3109i	0.153966	−	0.111863i	−0.508135	−	0.861277i	$-0.669665\pi$
$709$	109.162	−	79.3109i	0.153966	−	0.111863i	0.662101	+	0.749414i	$0.269665\pi$
$710$	−17.0472	−	23.4635i	−0.0240101	−	0.0330471i
$711$	−159.218	−	827.944i	−0.223935	−	1.16448i
$712$	258.980	−	797.058i	0.363736	−	1.11946i
$713$	−459.634	+	632.631i	−0.644647	+	0.887281i
$714$	−15.8584	+	255.095i	−0.0222106	+	0.357276i
$715$		0			0
$716$		−	104.582i		−	0.146064i
$717$	−373.074	−	308.166i	−0.520327	−	0.429799i
$718$	−26.6527	+	82.0285i	−0.0371207	+	0.114246i
$719$	−106.782	+	34.6957i	−0.148515	+	0.0482554i	−0.382331	−	0.924025i	$-0.624879\pi$
$719$	−106.782	+	34.6957i	−0.148515	+	0.0482554i	0.233816	+	0.972281i	$0.424879\pi$
$720$	97.2507	+	176.276i	0.135070	+	0.244827i
$721$	75.1416	−	54.5936i	0.104219	−	0.0757192i
$722$	−220.934	+	71.7858i	−0.306003	+	0.0994263i
$723$	−158.205	−	62.5013i	−0.218817	−	0.0864472i
$724$	−278.658	−	202.457i	−0.384887	−	0.279636i
$725$			999.487i			1.37860i
$726$		0			0
$727$	160.372			0.220595			0.110297	−	0.993899i	$-0.464820\pi$
$727$	160.372			0.220595			0.110297	+	0.993899i	$0.464820\pi$
$728$	−219.727	+	302.428i	−0.301823	+	0.415423i
$729$	−462.166	+	563.776i	−0.633973	+	0.773355i
$730$	54.5314	+	167.830i	0.0747006	+	0.229905i
$731$	−472.774	−	650.717i	−0.646749	−	0.890174i
$732$	−279.208	−	439.237i	−0.381431	−	0.600051i
$733$	−151.721	−	466.948i	−0.206986	−	0.637037i	−0.999626	−	0.0273472i	$-0.991294\pi$
$733$	−151.721	−	466.948i	−0.206986	−	0.637037i	0.792640	−	0.609690i	$-0.208706\pi$
$734$	−360.151	−	117.020i	−0.490669	−	0.159428i
$735$	154.662	+	127.754i	0.210425	+	0.173814i
$736$	−918.745			−1.24829
$737$		0			0
$738$	218.511	+	27.2736i	0.296085	+	0.0369561i
$739$	−192.027	−	139.516i	−0.259847	−	0.188790i	0.450232	−	0.892911i	$-0.351341\pi$
$739$	−192.027	−	139.516i	−0.259847	−	0.188790i	−0.710080	+	0.704121i	$0.751341\pi$
$740$	−344.944	−	112.079i	−0.466140	−	0.151458i
$741$	−322.666	+	83.1028i	−0.435447	+	0.112150i
$742$	−30.1444	+	21.9012i	−0.0406259	+	0.0295164i
$743$	144.127	+	198.374i	0.193980	+	0.266991i	0.894917	−	0.446232i	$-0.147235\pi$
$743$	144.127	+	198.374i	0.193980	+	0.266991i	−0.700937	+	0.713223i	$0.747235\pi$
$744$	−113.025	−	438.845i	−0.151915	−	0.589846i
$745$	57.9827	−	178.452i	0.0778291	−	0.239533i
$746$	−96.4367	+	132.734i	−0.129272	+	0.177927i
$747$	38.0789	−	305.081i	0.0509758	−	0.408408i
$748$		0			0
$749$			400.574i			0.534812i
$750$	−166.706	+	201.819i	−0.222274	+	0.269092i
$751$	228.868	−	704.384i	0.304751	−	0.937928i	−0.675019	−	0.737801i	$-0.735864\pi$
$751$	228.868	−	704.384i	0.304751	−	0.937928i	0.979770	−	0.200127i	$-0.0641356\pi$
$752$	263.675	−	85.6732i	0.350632	−	0.113927i
$753$	170.875	−	108.619i	0.226926	−	0.144249i
$754$	−463.918	+	337.056i	−0.615276	+	0.447024i
$755$	−14.9658	+	4.86267i	−0.0198222	+	0.00644062i
$756$	379.029	+	207.271i	0.501361	+	0.274168i
$757$	−262.702	−	190.864i	−0.347030	−	0.252132i	0.400592	−	0.916257i	$-0.368805\pi$
$757$	−262.702	−	190.864i	−0.347030	−	0.252132i	−0.747622	+	0.664124i	$0.768805\pi$
$758$		−	246.089i		−	0.324656i
$759$		0			0
$760$	−121.402			−0.159740
$761$	−398.255	+	548.151i	−0.523331	+	0.720303i	−0.986096	−	0.166178i	$-0.946857\pi$
$761$	−398.255	+	548.151i	−0.523331	+	0.720303i	0.462765	+	0.886481i	$0.346857\pi$
$762$	−112.527	+	284.831i	−0.147673	+	0.373794i
$763$	−245.907	−	756.824i	−0.322289	−	0.991905i
$764$	−137.737	−	189.578i	−0.180284	−	0.248139i
$765$	450.847	−	248.731i	0.589342	−	0.325138i
$766$	88.1069	+	271.165i	0.115022	+	0.354001i
$767$	789.285	+	256.454i	1.02905	+	0.334360i
$768$	110.703	−	134.020i	0.144144	−	0.174505i
$769$	−632.440			−0.822419			−0.411209	−	0.911541i	$-0.634894\pi$
$769$	−632.440			−0.822419			−0.411209	+	0.911541i	$0.634894\pi$
$770$		0			0
$771$	−439.168	−	27.3016i	−0.569609	−	0.0354107i
$772$	740.730	+	538.172i	0.959494	+	0.697114i
$773$	−176.035	−	57.1971i	−0.227729	−	0.0739937i	0.192930	−	0.981213i	$-0.438201\pi$
$773$	−176.035	−	57.1971i	−0.227729	−	0.0739937i	−0.420659	+	0.907219i	$0.638201\pi$
$774$	248.505	−	47.7887i	0.321066	−	0.0617426i
$775$	−389.735	+	283.159i	−0.502884	+	0.365367i
$776$	−138.309	−	190.366i	−0.178233	−	0.245317i
$777$	−587.275	+	151.253i	−0.755824	+	0.194663i
$778$	−152.906	+	470.597i	−0.196538	+	0.604881i
$779$	149.458	−	205.711i	0.191858	−	0.264070i
$780$	343.826	+	21.3745i	0.440803	+	0.0274032i
$781$		0			0
$782$			542.953i			0.694314i
$783$	994.068	+	1053.84i	1.26956	+	1.34591i
$784$	−72.5358	+	223.242i	−0.0925202	+	0.284748i
$785$	−237.189	+	77.0673i	−0.302151	+	0.0981748i
$786$	160.657	+	252.738i	0.204398	+	0.321550i
$787$	752.162	−	546.477i	0.955733	−	0.694380i	0.00357686	−	0.999994i	$-0.498861\pi$
$787$	752.162	−	546.477i	0.955733	−	0.694380i	0.952156	+	0.305613i	$0.0988614\pi$
$788$	341.930	−	111.100i	0.433921	−	0.140989i
$789$	−161.147	+	407.898i	−0.204242	+	0.516981i
$790$	−151.576	−	110.127i	−0.191869	−	0.139401i
$791$			585.989i			0.740820i
$792$		0			0
$793$	−693.957			−0.875103
$794$	36.6634	−	50.4628i	0.0461755	−	0.0635552i
$795$	69.8145	+	27.5814i	0.0878169	+	0.0346935i
$796$	−301.448	−	927.761i	−0.378703	−	1.16553i
$797$	530.616	+	730.331i	0.665767	+	0.916350i	0.999655	−	0.0262628i	$-0.00836067\pi$
$797$	530.616	+	730.331i	0.665767	+	0.916350i	−0.333888	+	0.942613i	$0.608361\pi$
$798$	−78.3610	+	49.8113i	−0.0981967	+	0.0624202i
$799$	−219.120	−	674.381i	−0.274243	−	0.844032i
$800$	−538.294	−	174.902i	−0.672868	−	0.218628i
$801$	−882.581	+	942.664i	−1.10185	+	1.17686i
$802$	−625.989			−0.780535
$803$		0			0
$804$	21.5488	−	346.630i	0.0268020	−	0.431132i
$805$	−292.983	−	212.864i	−0.363954	−	0.264428i
$806$	−262.860	−	85.4084i	−0.326129	−	0.105966i
$807$	−42.6570	−	165.626i	−0.0528587	−	0.205236i
$808$	−438.311	+	318.452i	−0.542464	+	0.394123i
$809$	180.254	+	248.099i	0.222811	+	0.306673i	0.905758	−	0.423794i	$-0.139302\pi$
$809$	180.254	+	248.099i	0.222811	+	0.306673i	−0.682947	+	0.730468i	$0.739302\pi$
$810$	10.6539	+	161.649i	0.0131529	+	0.199567i
$811$	402.918	−	1240.05i	0.496816	−	1.52904i	−0.317291	−	0.948328i	$-0.602773\pi$
$811$	402.918	−	1240.05i	0.496816	−	1.52904i	0.814107	−	0.580714i	$-0.197227\pi$
$812$	504.610	−	694.537i	0.621441	−	0.855341i
$813$	−23.8968	+	384.399i	−0.0293934	+	0.472816i
$814$		0			0
$815$			524.733i			0.643844i
$816$	464.527	+	383.707i	0.569273	+	0.470230i
$817$	90.2967	−	277.905i	0.110522	−	0.340153i
$818$	382.553	−	124.299i	0.467669	−	0.151955i
$819$	504.339	−	278.242i	0.615798	−	0.339734i
$820$	−212.683	+	154.524i	−0.259370	+	0.188443i
$821$	1296.33	−	421.204i	1.57897	−	0.513038i	0.617178	−	0.786824i	$-0.288276\pi$
$821$	1296.33	−	421.204i	1.57897	−	0.513038i	0.961791	+	0.273786i	$0.0882759\pi$
$822$	131.122	+	51.8017i	0.159515	+	0.0630192i
$823$	−217.060	−	157.704i	−0.263743	−	0.191620i	0.448053	−	0.894007i	$-0.352118\pi$
$823$	−217.060	−	157.704i	−0.263743	−	0.191620i	−0.711796	+	0.702387i	$0.752118\pi$
$824$			114.343i			0.138766i
$825$		0			0
$826$	231.272			0.279990
$827$	374.434	−	515.364i	0.452761	−	0.623172i	−0.520227	−	0.854028i	$-0.674153\pi$
$827$	374.434	−	515.364i	0.452761	−	0.623172i	0.972988	+	0.230856i	$0.0741526\pi$
$828$	830.953	+	389.506i	1.00357	+	0.470417i
$829$	8.40302	+	25.8618i	0.0101363	+	0.0311964i	0.955997	−	0.293377i	$-0.0947792\pi$
$829$	8.40302	+	25.8618i	0.0101363	+	0.0311964i	−0.945860	+	0.324574i	$0.894779\pi$
$830$	−40.1586	−	55.2735i	−0.0483838	−	0.0665946i
$831$	−380.257	−	598.203i	−0.457589	−	0.719859i
$832$	47.4039	+	145.894i	0.0569758	+	0.175353i
$833$	570.970	+	185.519i	0.685438	+	0.222712i
$834$	239.942	+	198.196i	0.287700	+	0.237646i
$835$	−159.446			−0.190953
$836$		0			0
$837$	−129.307	+	686.181i	−0.154489	+	0.819810i
$838$	−214.337	−	155.725i	−0.255772	−	0.185829i
$839$	964.295	+	313.318i	1.14934	+	0.373443i	0.820894	−	0.571081i	$-0.193476\pi$
$839$	964.295	+	313.318i	1.14934	+	0.373443i	0.328444	+	0.944523i	$0.393476\pi$
$840$	203.237	−	52.3439i	0.241949	−	0.0623141i
$841$	1648.74	−	1197.88i	1.96045	−	1.42435i
$842$	−206.449	−	284.153i	−0.245189	−	0.337474i
$843$	−152.623	−	592.593i	−0.181047	−	0.702958i
$844$	195.092	−	600.432i	0.231152	−	0.711412i
$845$	19.2244	−	26.4602i	0.0227508	−	0.0313138i
$846$	221.375	+	27.6311i	0.261672	+	0.0326608i
$847$		0			0
$848$			87.8361i			0.103580i
$849$	915.558	−	1108.40i	1.07840	−	1.30554i
$850$	−103.363	+	318.118i	−0.121603	+	0.374256i
$851$	−1225.23	+	398.101i	−1.43975	+	0.467804i
$852$	−123.810	+	78.7016i	−0.145317	+	0.0923727i
$853$	−1043.92	+	758.451i	−1.22382	+	0.889157i	−0.996411	−	0.0846431i	$-0.973025\pi$
$853$	−1043.92	+	758.451i	−1.22382	+	0.889157i	−0.227408	+	0.973800i	$0.573025\pi$
$854$	−183.922	+	59.7599i	−0.215365	+	0.0699764i
$855$	169.377	+	79.3946i	0.198102	+	0.0928592i
$856$	−398.960	−	289.861i	−0.466074	−	0.338623i
$857$		−	618.449i		−	0.721644i	−0.932635	−	0.360822i	$-0.882496\pi$
$857$		−	618.449i		−	0.721644i	0.932635	−	0.360822i	$-0.117504\pi$
$858$		0			0
$859$	1207.23			1.40538			0.702692	−	0.711494i	$-0.251981\pi$
$859$	1207.23			1.40538			0.702692	+	0.711494i	$0.251981\pi$
$860$	−177.576	+	244.413i	−0.206484	+	0.284201i
$861$	−161.510	+	408.817i	−0.187584	+	0.474816i
$862$	−194.714	−	599.269i	−0.225887	−	0.695207i
$863$	649.669	+	894.193i	0.752803	+	1.03614i	0.997779	+	0.0666155i	$0.0212201\pi$
$863$	649.669	+	894.193i	0.752803	+	1.03614i	−0.244975	+	0.969529i	$0.578780\pi$
$864$	−741.524	+	350.961i	−0.858245	+	0.406205i
$865$	150.832	+	464.214i	0.174372	+	0.536663i
$866$	14.0320	+	4.55927i	0.0162032	+	0.00526474i
$867$	429.230	−	519.638i	0.495075	−	0.599351i
$868$	413.783			0.476708
$869$		0			0
$870$	321.315	+	19.9751i	0.369328	+	0.0229599i
$871$	−374.628	−	272.183i	−0.430112	−	0.312495i
$872$	931.715	+	302.732i	1.06848	+	0.347170i
$873$	68.4690	+	356.044i	0.0784296	+	0.407839i
$874$	−159.579	+	115.941i	−0.182585	+	0.132655i
$875$	−307.132	−	422.731i	−0.351008	−	0.483121i
$876$	864.437	−	222.636i	0.986800	−	0.254151i
$877$	−411.721	+	1267.15i	−0.469466	+	1.44487i	0.383813	+	0.923411i	$0.374611\pi$
$877$	−411.721	+	1267.15i	−0.469466	+	1.44487i	−0.853278	+	0.521456i	$0.825389\pi$
$878$	−118.701	+	163.379i	−0.135195	+	0.186080i
$879$	28.0162	+	1.74167i	0.0318728	+	0.00198143i
$880$		0			0
$881$			1171.98i			1.33029i	0.746715	+	0.665145i	$0.231630\pi$
$881$			1171.98i			1.33029i	−0.746715	+	0.665145i	$0.768370\pi$
$882$	−129.094	+	137.882i	−0.146365	+	0.156329i
$883$	225.025	−	692.555i	0.254841	−	0.784320i	−0.739020	−	0.673684i	$-0.764711\pi$
$883$	225.025	−	692.555i	0.254841	−	0.784320i	0.993861	−	0.110637i	$-0.0352890\pi$
$884$	980.512	−	318.588i	1.10918	−	0.360393i
$885$	−249.946	−	393.204i	−0.282425	−	0.444298i
$886$	39.4532	−	28.6644i	0.0445295	−	0.0323526i
$887$	−931.819	+	302.766i	−1.05053	+	0.341337i	−0.782876	−	0.622178i	$-0.786248\pi$
$887$	−931.819	+	302.766i	−1.05053	+	0.341337i	−0.267653	+	0.963515i	$0.586248\pi$
$888$	274.317	−	694.357i	0.308916	−	0.781933i
$889$	−494.573	−	359.329i	−0.556325	−	0.404194i
$890$			286.965i			0.322433i
$891$		0			0
$892$	−767.973			−0.860956
$893$	151.416	−	208.407i	0.169559	−	0.233378i
$894$	164.316	+	64.9155i	0.183798	+	0.0726125i
$895$	24.1915	+	74.4537i	0.0270296	+	0.0831885i
$896$	364.072	+	501.102i	0.406330	+	0.559266i
$897$	1032.65	−	656.417i	1.15122	−	0.731792i
$898$	33.6477	+	103.557i	0.0374696	+	0.115319i
$899$	1319.70	+	428.797i	1.46797	+	0.476971i
$900$	412.707	+	386.402i	0.458563	+	0.429335i
$901$	224.652			0.249336
$902$		0			0
$903$	−31.3424	+	504.168i	−0.0347092	+	0.558325i
$904$	−583.627	−	424.030i	−0.645605	−	0.469059i
$905$	245.213	+	79.6746i	0.270954	+	0.0880382i
$906$	−3.69543	−	14.3484i	−0.00407884	−	0.0158371i
$907$	−892.108	+	648.154i	−0.983581	+	0.714613i	−0.958506	−	0.285072i	$-0.907982\pi$
$907$	−892.108	+	648.154i	−0.983581	+	0.714613i	−0.0250750	+	0.999686i	$0.507982\pi$
$908$	−845.079	−	1163.15i	−0.930703	−	1.28100i
$909$	819.781	−	157.648i	0.901849	−	0.173430i
$910$	39.5542	−	121.735i	0.0434661	−	0.133775i
$911$	−272.307	+	374.799i	−0.298910	+	0.411415i	−0.931883	−	0.362760i	$-0.881835\pi$
$911$	−272.307	+	374.799i	−0.298910	+	0.411415i	0.632973	+	0.774174i	$0.281835\pi$
$912$	−13.5812	+	218.464i	−0.0148917	+	0.239544i
$913$		0			0
$914$		−	243.701i		−	0.266632i
$915$	300.376	+	248.116i	0.328279	+	0.271165i
$916$	−105.860	+	325.804i	−0.115568	+	0.355681i
$917$	−568.543	+	184.731i	−0.620004	+	0.201451i
$918$	207.409	+	438.221i	0.225935	+	0.477365i
$919$	158.510	−	115.164i	0.172481	−	0.125315i	−0.498196	−	0.867065i	$-0.666004\pi$
$919$	158.510	−	115.164i	0.172481	−	0.125315i	0.670677	+	0.741750i	$0.266004\pi$
$920$	424.013	−	137.770i	0.460884	−	0.149750i
$921$	202.362	+	79.9462i	0.219719	+	0.0868037i
$922$	−338.538	−	245.962i	−0.367178	−	0.266771i
$923$			195.609i			0.211927i
$924$		0			0
$925$	−793.652			−0.858002
$926$	21.3979	−	29.4517i	0.0231079	−	0.0318053i
$927$	74.7783	−	159.529i	0.0806670	−	0.172091i
$928$	503.795	+	1550.52i	0.542882	+	1.67082i
$929$	−71.4310	−	98.3163i	−0.0768902	−	0.105830i	0.768840	−	0.639442i	$-0.220834\pi$
$929$	−71.4310	−	98.3163i	−0.0768902	−	0.105830i	−0.845730	+	0.533611i	$0.820834\pi$
$930$	83.2410	+	130.951i	0.0895065	+	0.140808i
$931$	67.3976	+	207.428i	0.0723927	+	0.222802i
$932$	555.509	+	180.496i	0.596039	+	0.193665i
$933$	880.421	+	727.244i	0.943646	+	0.779468i
$934$	284.484			0.304586
$935$		0			0
$936$	−87.8260	+	703.645i	−0.0938312	+	0.751758i
$937$	267.314	+	194.215i	0.285288	+	0.207274i	0.721220	−	0.692706i	$-0.243581\pi$
$937$	267.314	+	194.215i	0.285288	+	0.207274i	−0.435933	+	0.899979i	$0.643581\pi$
$938$	−122.728	−	39.8767i	−0.130840	−	0.0425125i
$939$	154.268	−	39.7317i	0.164289	−	0.0423128i
$940$	−215.471	+	156.549i	−0.229225	+	0.166541i
$941$	−526.117	−	724.138i	−0.559104	−	0.769541i	0.432108	−	0.901822i	$-0.357770\pi$
$941$	−526.117	−	724.138i	−0.559104	−	0.769541i	−0.991212	+	0.132281i	$0.957770\pi$
$942$	−58.5680	−	227.404i	−0.0621741	−	0.241405i
$943$	−288.555	+	888.080i	−0.305996	+	0.941760i
$944$	320.453	−	441.066i	0.339463	−	0.467231i
$945$	−317.783	−	59.8844i	−0.336278	−	0.0633697i
$946$		0			0
$947$			1308.11i			1.38132i	0.723181	+	0.690659i	$0.242679\pi$
$947$			1308.11i			1.38132i	−0.723181	+	0.690659i	$0.757321\pi$
$948$	−603.567	+	730.695i	−0.636674	+	0.770776i
$949$	367.791	−	1131.94i	0.387556	−	1.19277i
$950$	−115.569	+	37.5508i	−0.121652	+	0.0395271i
$951$	−185.445	+	117.881i	−0.195000	+	0.123955i
$952$	508.133	−	369.180i	0.533753	−	0.387794i
$953$	1.93085	−	0.627370i	0.00202607	−	0.000658311i	−0.308004	−	0.951385i	$-0.599661\pi$
$953$	1.93085	−	0.627370i	0.00202607	−	0.000658311i	0.310030	+	0.950727i	$0.399661\pi$
$954$	−29.9987	+	63.9978i	−0.0314451	+	0.0670836i
$955$	141.910	+	103.104i	0.148597	+	0.107962i
$956$			543.939i			0.568974i
$957$		0			0
$958$	457.467			0.477523
$959$	−165.417	+	227.676i	−0.172489	+	0.237410i
$960$	31.6441	−	80.0982i	0.0329626	−	0.0834356i
$961$	−90.2909	−	277.887i	−0.0939552	−	0.289164i
$962$	−267.643	−	368.379i	−0.278215	−	0.382930i
$963$	367.054	+	665.318i	0.381156	+	0.690880i
$964$	59.0877	+	181.853i	0.0612943	+	0.188645i
$965$	−651.827	−	211.791i	−0.675468	−	0.219473i
$966$	217.159	−	262.899i	0.224802	−	0.272152i
$967$	520.674			0.538442			0.269221	−	0.963078i	$-0.413234\pi$
$967$	520.674			0.538442			0.269221	+	0.963078i	$0.413234\pi$
$968$		0			0
$969$	558.750	+	34.7356i	0.576625	+	0.0358469i
$970$	65.1830	+	47.3582i	0.0671989	+	0.0488229i
$971$	−1723.37	−	559.956i	−1.77484	−	0.576680i	−0.776281	−	0.630387i	$-0.782896\pi$
$971$	−1723.37	−	559.956i	−1.77484	−	0.576680i	−0.998557	+	0.0537073i	$0.982896\pi$
$972$	819.459	−	3.05285i	0.843064	−	0.00314079i
$973$	−502.584	+	365.149i	−0.516530	+	0.375281i
$974$	−282.630	−	389.006i	−0.290174	−	0.399391i
$975$	729.993	−	188.010i	0.748710	−	0.192831i
$976$	−140.875	+	433.568i	−0.144339	+	0.444230i
$977$	−251.212	+	345.764i	−0.257126	+	0.353904i	−0.917991	−	0.396601i	$-0.870190\pi$
$977$	−251.212	+	345.764i	−0.257126	+	0.353904i	0.660865	+	0.750505i	$0.270190\pi$
$978$	−493.125	−	30.6559i	−0.504218	−	0.0313455i
$979$		0			0
$980$		−	225.496i		−	0.230098i
$981$	−1101.92	−	1031.69i	−1.12326	−	1.05167i
$982$	−188.242	+	579.349i	−0.191692	+	0.589968i
$983$	−954.405	+	310.105i	−0.970910	+	0.315468i	−0.751183	−	0.660094i	$-0.770517\pi$
$983$	−954.405	+	310.105i	−0.970910	+	0.315468i	−0.219727	+	0.975561i	$0.570517\pi$
$984$	−290.298	−	456.684i	−0.295019	−	0.464110i
$985$	−217.727	+	158.188i	−0.221042	+	0.160597i
$986$	916.317	−	297.729i	0.929327	−	0.301957i
$987$	−163.627	+	414.175i	−0.165782	+	0.419630i
$988$	303.012	+	220.151i	0.306692	+	0.222825i
$989$			1073.09i			1.08503i
$990$		0			0
$991$	862.380			0.870212			0.435106	−	0.900379i	$-0.356711\pi$
$991$	862.380			0.870212			0.435106	+	0.900379i	$0.356711\pi$
$992$	−461.875	+	635.717i	−0.465600	+	0.640844i
$993$	466.933	+	184.470i	0.470225	+	0.185770i
$994$	16.8448	+	51.8429i	0.0169465	+	0.0521559i
$995$	429.212	+	590.760i	0.431369	+	0.593728i
$996$	−291.662	+	185.399i	−0.292834	+	0.186144i
$997$	88.1554	+	271.314i	0.0884206	+	0.272131i	0.985483	−	0.169773i	$-0.0543034\pi$
$997$	88.1554	+	271.314i	0.0884206	+	0.272131i	−0.897063	+	0.441903i	$0.854303\pi$
$998$	375.272	+	121.933i	0.376024	+	0.122178i
$999$	−836.815	+	789.349i	−0.837653	+	0.790139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.l.323.2		16
3.2	odd	2	inner	363.3.h.l.323.3		16
11.2	odd	10		363.3.h.m.269.2		16
11.3	even	5	inner	363.3.h.l.245.3		16
11.4	even	5	inner	363.3.h.l.251.2		16
11.5	even	5		363.3.b.h.122.2		4
11.6	odd	10		33.3.b.b.23.3	yes	4
11.7	odd	10		363.3.h.m.251.3		16
11.8	odd	10		363.3.h.m.245.2		16
11.9	even	5	inner	363.3.h.l.269.3		16
11.10	odd	2		363.3.h.m.323.3		16
33.2	even	10		363.3.h.m.269.3		16
33.5	odd	10		363.3.b.h.122.3		4
33.8	even	10		363.3.h.m.245.3		16
33.14	odd	10	inner	363.3.h.l.245.2		16
33.17	even	10		33.3.b.b.23.2	✓	4
33.20	odd	10	inner	363.3.h.l.269.2		16
33.26	odd	10	inner	363.3.h.l.251.3		16
33.29	even	10		363.3.h.m.251.2		16
33.32	even	2		363.3.h.m.323.2		16
44.39	even	10		528.3.i.d.353.2		4
132.83	odd	10		528.3.i.d.353.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.b.b.23.2	✓	4	33.17	even	10
33.3.b.b.23.3	yes	4	11.6	odd	10
363.3.b.h.122.2		4	11.5	even	5
363.3.b.h.122.3		4	33.5	odd	10
363.3.h.l.245.2		16	33.14	odd	10	inner
363.3.h.l.245.3		16	11.3	even	5	inner
363.3.h.l.251.2		16	11.4	even	5	inner
363.3.h.l.251.3		16	33.26	odd	10	inner
363.3.h.l.269.2		16	33.20	odd	10	inner
363.3.h.l.269.3		16	11.9	even	5	inner
363.3.h.l.323.2		16	1.1	even	1	trivial
363.3.h.l.323.3		16	3.2	odd	2	inner
363.3.h.m.245.2		16	11.8	odd	10
363.3.h.m.245.3		16	33.8	even	10
363.3.h.m.251.2		16	33.29	even	10
363.3.h.m.251.3		16	11.7	odd	10
363.3.h.m.269.2		16	11.2	odd	10
363.3.h.m.269.3		16	33.2	even	10
363.3.h.m.323.2		16	33.32	even	2
363.3.h.m.323.3		16	11.10	odd	2
528.3.i.d.353.1		4	132.83	odd	10
528.3.i.d.353.2		4	44.39	even	10

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.465695 + 0.640974i) q^{2} +(-2.79015 - 1.10230i) q^{3} +(1.04209 + 3.20723i) q^{4} +(-1.48377 - 2.04223i) q^{5} +(2.00590 - 1.27508i) q^{6} +(1.46615 + 4.51235i) q^{7} +(-5.55509 - 1.80496i) q^{8} +(6.56989 + 6.15114i) q^{9} +O(q^{10})\)	\(q+(-0.465695 + 0.640974i) q^{2} +(-2.79015 - 1.10230i) q^{3} +(1.04209 + 3.20723i) q^{4} +(-1.48377 - 2.04223i) q^{5} +(2.00590 - 1.27508i) q^{6} +(1.46615 + 4.51235i) q^{7} +(-5.55509 - 1.80496i) q^{8} +(6.56989 + 6.15114i) q^{9} +2.00000 q^{10} +(0.627719 - 10.0974i) q^{12} +(-10.9129 - 7.92871i) q^{13} +(-3.57507 - 1.16161i) q^{14} +(1.88880 + 7.33369i) q^{15} +(-7.16903 + 5.20860i) q^{16} +(13.3216 + 18.3357i) q^{17} +(-7.00228 + 1.34657i) q^{18} +(-2.54435 + 7.83070i) q^{19} +(5.00368 - 6.88698i) q^{20} +(0.883156 - 14.2063i) q^{21} -30.2372i q^{23} +(13.5099 + 11.1594i) q^{24} +(5.75628 - 17.7160i) q^{25} +(10.1642 - 3.30254i) q^{26} +(-11.5506 - 24.4046i) q^{27} +(-12.9443 + 9.40456i) q^{28} +(-51.0298 + 16.5806i) q^{29} +(-5.58030 - 2.20459i) q^{30} +(-20.9223 - 15.2010i) q^{31} -30.3846i q^{32} -17.9565 q^{34} +(7.03983 - 9.68950i) q^{35} +(-12.8817 + 27.4812i) q^{36} +(-13.1660 - 40.5207i) q^{37} +(-3.83438 - 5.27758i) q^{38} +(21.7090 + 34.1516i) q^{39} +(4.55632 + 14.0229i) q^{40} +(-29.3705 - 9.54305i) q^{41} +(8.69456 + 7.18186i) q^{42} -35.4891 q^{43} +(2.81386 - 22.5441i) q^{45} +(19.3812 + 14.0813i) q^{46} +(-29.7554 - 9.66813i) q^{47} +(25.7441 - 6.63041i) q^{48} +(21.4302 - 15.5699i) q^{49} +(8.67483 + 11.9399i) q^{50} +(-16.9581 - 65.8437i) q^{51} +(14.0569 - 43.2627i) q^{52} +(5.82625 - 8.01914i) q^{53} +(21.0217 + 3.96143i) q^{54} -27.7128i q^{56} +(15.7309 - 19.0442i) q^{57} +(13.1366 - 40.4302i) q^{58} +(-58.5127 + 19.0119i) q^{59} +(-21.5525 + 13.7002i) q^{60} +(41.6204 - 30.2390i) q^{61} +(19.4868 - 6.33165i) q^{62} +(-18.1236 + 38.6641i) q^{63} +(-9.20037 - 6.68446i) q^{64} +34.0511i q^{65} +34.3288 q^{67} +(-44.9243 + 61.8330i) q^{68} +(-33.3303 + 84.3662i) q^{69} +(2.93230 + 9.02469i) q^{70} +(-8.52360 - 11.7317i) q^{71} +(-25.3938 - 46.0285i) q^{72} +(27.2657 + 83.9152i) q^{73} +(32.1040 + 10.4312i) q^{74} +(-35.5892 + 43.0852i) q^{75} -27.7663 q^{76} +(-32.0000 - 1.98933i) q^{78} +(-75.7882 - 55.0633i) q^{79} +(21.2744 + 6.91246i) q^{80} +(5.32694 + 80.8246i) q^{81} +(19.7945 - 14.3816i) q^{82} +(-20.0793 - 27.6368i) q^{83} +(46.4831 - 11.9718i) q^{84} +(17.6795 - 54.4118i) q^{85} +(16.5271 - 22.7476i) q^{86} +(160.658 + 9.98755i) q^{87} +143.482i q^{89} +(13.1398 + 12.3023i) q^{90} +(19.7771 - 60.8676i) q^{91} +(96.9775 - 31.5099i) q^{92} +(41.6205 + 65.4755i) q^{93} +(20.0540 - 14.5701i) q^{94} +(19.7673 - 6.42280i) q^{95} +(-33.4928 + 84.7777i) q^{96} +(32.5915 + 23.6791i) q^{97} +20.9870i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 7 q^{9}+O(q^{10}) \) 16 * q + 5 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 7 * q^9	\( 16 q + 5 q^{3} - 2 q^{4} - 2 q^{6} + 4 q^{7} + 7 q^{9} + 32 q^{10} + 56 q^{12} - 8 q^{13} - 13 q^{15} + 22 q^{16} + 38 q^{18} - 36 q^{19} + 152 q^{21} + 24 q^{24} - 86 q^{25} + 20 q^{27} - 64 q^{28} + 10 q^{30} - 46 q^{31} + 448 q^{34} + 86 q^{36} + 90 q^{37} - 56 q^{39} - 36 q^{40} + 68 q^{42} - 384 q^{43} + 68 q^{45} - 88 q^{46} - 110 q^{48} + 60 q^{49} + 214 q^{51} - 136 q^{52} + 704 q^{54} + 144 q^{57} - 216 q^{58} - 56 q^{60} - 24 q^{61} + 158 q^{63} - 34 q^{64} - 232 q^{67} + 253 q^{69} + 8 q^{70} + 72 q^{72} - 284 q^{73} + 124 q^{75} - 720 q^{76} - 512 q^{78} - 76 q^{79} - 113 q^{81} - 40 q^{82} + 80 q^{84} - 68 q^{85} + 1008 q^{87} + 14 q^{90} - 256 q^{91} - 25 q^{93} + 260 q^{94} + 272 q^{96} - 218 q^{97}+O(q^{100}) \) 16 * q + 5 * q^3 - 2 * q^4 - 2 * q^6 + 4 * q^7 + 7 * q^9 + 32 * q^10 + 56 * q^12 - 8 * q^13 - 13 * q^15 + 22 * q^16 + 38 * q^18 - 36 * q^19 + 152 * q^21 + 24 * q^24 - 86 * q^25 + 20 * q^27 - 64 * q^28 + 10 * q^30 - 46 * q^31 + 448 * q^34 + 86 * q^36 + 90 * q^37 - 56 * q^39 - 36 * q^40 + 68 * q^42 - 384 * q^43 + 68 * q^45 - 88 * q^46 - 110 * q^48 + 60 * q^49 + 214 * q^51 - 136 * q^52 + 704 * q^54 + 144 * q^57 - 216 * q^58 - 56 * q^60 - 24 * q^61 + 158 * q^63 - 34 * q^64 - 232 * q^67 + 253 * q^69 + 8 * q^70 + 72 * q^72 - 284 * q^73 + 124 * q^75 - 720 * q^76 - 512 * q^78 - 76 * q^79 - 113 * q^81 - 40 * q^82 + 80 * q^84 - 68 * q^85 + 1008 * q^87 + 14 * q^90 - 256 * q^91 - 25 * q^93 + 260 * q^94 + 272 * q^96 - 218 * q^97

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