LMFDB - Embedded newform 363.3.h.l.323.3

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			323.3
Root			$1.13127 - 1.31158i$ of defining polynomial
Character	$\chi$	$=$	363.323
Dual form			363.3.h.l.245.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.465695 - 0.640974i) q^{2} +(2.90519 + 0.748234i) q^{3} +(1.04209 + 3.20723i) q^{4} +(1.48377 + 2.04223i) q^{5} +(1.83253 - 1.51370i) q^{6} +(1.46615 + 4.51235i) q^{7} +(5.55509 + 1.80496i) q^{8} +(7.88029 + 4.34753i) q^{9} +O(q^{10})$	\(q+(0.465695 - 0.640974i) q^{2} +(2.90519 + 0.748234i) q^{3} +(1.04209 + 3.20723i) q^{4} +(1.48377 + 2.04223i) q^{5} +(1.83253 - 1.51370i) q^{6} +(1.46615 + 4.51235i) q^{7} +(5.55509 + 1.80496i) q^{8} +(7.88029 + 4.34753i) q^{9} +2.00000 q^{10} +(0.627719 + 10.0974i) q^{12} +(-10.9129 - 7.92871i) q^{13} +(3.57507 + 1.16161i) q^{14} +(2.78257 + 7.04328i) q^{15} +(-7.16903 + 5.20860i) q^{16} +(-13.3216 - 18.3357i) q^{17} +(6.45646 - 3.02644i) q^{18} +(-2.54435 + 7.83070i) q^{19} +(-5.00368 + 6.88698i) q^{20} +(0.883156 + 14.2063i) q^{21} +30.2372i q^{23} +(14.7881 + 9.40025i) q^{24} +(5.75628 - 17.7160i) q^{25} +(-10.1642 + 3.30254i) q^{26} +(19.6408 + 18.5267i) q^{27} +(-12.9443 + 9.40456i) q^{28} +(51.0298 - 16.5806i) q^{29} +(5.81039 + 1.49647i) q^{30} +(-20.9223 - 15.2010i) q^{31} +30.3846i q^{32} -17.9565 q^{34} +(-7.03983 + 9.68950i) q^{35} +(-5.73154 + 29.8044i) q^{36} +(-13.1660 - 40.5207i) q^{37} +(3.83438 + 5.27758i) q^{38} +(-25.7716 - 31.1999i) q^{39} +(4.55632 + 14.0229i) q^{40} +(29.3705 + 9.54305i) q^{41} +(9.51712 + 6.04970i) q^{42} -35.4891 q^{43} +(2.81386 + 22.5441i) q^{45} +(19.3812 + 14.0813i) q^{46} +(29.7554 + 9.66813i) q^{47} +(-24.7247 + 9.76788i) q^{48} +(21.4302 - 15.5699i) q^{49} +(-8.67483 - 11.9399i) q^{50} +(-24.9826 - 63.2364i) q^{51} +(14.0569 - 43.2627i) q^{52} +(-5.82625 + 8.01914i) q^{53} +(21.0217 - 3.96143i) q^{54} +27.7128i q^{56} +(-13.2510 + 20.8459i) q^{57} +(13.1366 - 40.4302i) q^{58} +(58.5127 - 19.0119i) q^{59} +(-19.6897 + 16.2641i) q^{60} +(41.6204 - 30.2390i) q^{61} +(-19.4868 + 6.33165i) q^{62} +(-8.06388 + 41.9327i) q^{63} +(-9.20037 - 6.68446i) q^{64} -34.0511i q^{65} +34.3288 q^{67} +(44.9243 - 61.8330i) q^{68} +(-22.6245 + 87.8448i) q^{69} +(2.93230 + 9.02469i) q^{70} +(8.52360 + 11.7317i) q^{71} +(35.9286 + 38.3745i) q^{72} +(27.2657 + 83.9152i) q^{73} +(-32.1040 - 10.4312i) q^{74} +(29.9788 - 47.1614i) q^{75} -27.7663 q^{76} +(-32.0000 + 1.98933i) q^{78} +(-75.7882 - 55.0633i) q^{79} +(-21.2744 - 6.91246i) q^{80} +(43.1980 + 68.5196i) q^{81} +(19.7945 - 14.3816i) q^{82} +(20.0793 + 27.6368i) q^{83} +(-44.6424 + 17.6367i) q^{84} +(17.6795 - 54.4118i) q^{85} +(-16.5271 + 22.7476i) q^{86} +(160.658 - 9.98755i) q^{87} -143.482i q^{89} +(15.7606 + 8.69506i) q^{90} +(19.7771 - 60.8676i) q^{91} +(-96.9775 + 31.5099i) q^{92} +(-49.4095 - 59.8165i) q^{93} +(20.0540 - 14.5701i) q^{94} +(-19.7673 + 6.42280i) q^{95} +(-22.7348 + 88.2732i) 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	−0.676565	−	0.736383i	$-0.736532\pi$
$2$	0.465695	−	0.640974i	0.232847	−	0.320487i	0.909412	+	0.415896i	$0.136532\pi$
$3$	2.90519	+	0.748234i	0.968398	+	0.249411i
$3$	2.90519	+	0.748234i	0.968398	+	0.249411i
$4$	1.04209	+	3.20723i	0.260523	+	0.801808i
$5$	1.48377	+	2.04223i	0.296754	+	0.408446i	0.931193	−	0.364526i	$-0.118769\pi$
$5$	1.48377	+	2.04223i	0.296754	+	0.408446i	−0.634439	+	0.772973i	$0.718769\pi$
$6$	1.83253	−	1.51370i	0.305422	−	0.252284i
$7$	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
$9$	7.88029	+	4.34753i	0.875588	+	0.483059i
$10$	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
$15$	2.78257	+	7.04328i	0.185504	+	0.469552i
$16$	−7.16903	+	5.20860i	−0.448064	+	0.325538i
$17$	−13.3216	−	18.3357i	−0.783626	−	1.07857i	−0.994873	−	0.101136i	$-0.967752\pi$
$17$	−13.3216	−	18.3357i	−0.783626	−	1.07857i	0.211246	−	0.977433i	$-0.432248\pi$
$18$	6.45646	−	3.02644i	0.358692	−	0.168135i
$19$	−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	$0.228314\pi$
$23$			30.2372i			1.31466i	−0.753603	+	0.657329i	$0.771686\pi$
$24$	14.7881	+	9.40025i	0.616169	+	0.391677i
$25$	5.75628	−	17.7160i	0.230251	−	0.708641i
$26$	−10.1642	+	3.30254i	−0.390930	+	0.127021i
$27$	19.6408	+	18.5267i	0.727437	+	0.686175i
$28$	−12.9443	+	9.40456i	−0.462295	+	0.335877i
$29$	51.0298	−	16.5806i	1.75965	−	0.571744i	0.762484	−	0.647007i	$-0.223979\pi$
$29$	51.0298	−	16.5806i	1.75965	−	0.571744i	0.997164	+	0.0752622i	$0.0239794\pi$
$30$	5.81039	+	1.49647i	0.193680	+	0.0498823i
$31$	−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
$36$	−5.73154	+	29.8044i	−0.159210	+	0.827901i
$37$	−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
$39$	−25.7716	−	31.1999i	−0.660811	−	0.799996i
$40$	4.55632	+	14.0229i	0.113908	+	0.350573i
$41$	29.3705	+	9.54305i	0.716353	+	0.232757i	0.644441	−	0.764654i	$-0.277090\pi$
$41$	29.3705	+	9.54305i	0.716353	+	0.232757i	0.0719120	+	0.997411i	$0.477090\pi$
$42$	9.51712	+	6.04970i	0.226598	+	0.144040i
$43$	−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	0.607945	−	0.793979i	$-0.291994\pi$
$47$	29.7554	+	9.66813i	0.633094	+	0.205705i	0.0251491	+	0.999684i	$0.491994\pi$
$48$	−24.7247	+	9.76788i	−0.515097	+	0.203498i
$49$	21.4302	−	15.5699i	0.437350	−	0.317753i
$50$	−8.67483	−	11.9399i	−0.173497	−	0.238798i
$51$	−24.9826	−	63.2364i	−0.489854	−	1.23993i
$52$	14.0569	−	43.2627i	0.270325	−	0.831976i
$53$	−5.82625	+	8.01914i	−0.109929	+	0.151305i	−0.860437	−	0.509557i	$-0.829809\pi$
$53$	−5.82625	+	8.01914i	−0.109929	+	0.151305i	0.750507	+	0.660862i	$0.229809\pi$
$54$	21.0217	−	3.96143i	0.389292	−	0.0733599i
$55$		0			0
$56$			27.7128i			0.494872i
$57$	−13.2510	+	20.8459i	−0.232474	+	0.365718i
$58$	13.1366	−	40.4302i	0.226493	−	0.697073i
$59$	58.5127	−	19.0119i	0.991740	−	0.322236i	0.232180	−	0.972673i	$-0.425414\pi$
$59$	58.5127	−	19.0119i	0.991740	−	0.322236i	0.759560	+	0.650437i	$0.225414\pi$
$60$	−19.6897	+	16.2641i	−0.328162	+	0.271068i
$61$	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
$63$	−8.06388	+	41.9327i	−0.127998	+	0.665599i
$64$	−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
$69$	−22.6245	+	87.8448i	−0.327891	+	1.27311i
$70$	2.93230	+	9.02469i	0.0418900	+	0.128924i
$71$	8.52360	+	11.7317i	0.120051	+	0.165236i	0.864813	−	0.502094i	$-0.167437\pi$
$71$	8.52360	+	11.7317i	0.120051	+	0.165236i	−0.744762	+	0.667330i	$0.767437\pi$
$72$	35.9286	+	38.3745i	0.499008	+	0.532979i
$73$	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
$75$	29.9788	−	47.1614i	0.399718	−	0.628818i
$76$	−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
$81$	43.1980	+	68.5196i	0.533308	+	0.845921i
$82$	19.7945	−	14.3816i	0.241397	−	0.175385i
$83$	20.0793	+	27.6368i	0.241919	+	0.332973i	0.912661	−	0.408718i	$-0.134024\pi$
$83$	20.0793	+	27.6368i	0.241919	+	0.332973i	−0.670742	+	0.741691i	$0.734024\pi$
$84$	−44.6424	+	17.6367i	−0.531457	+	0.209961i
$85$	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	$-0.701584\pi$
$89$		−	143.482i		−	1.61216i	0.591805	−	0.806081i	$-0.298416\pi$
$90$	15.7606	+	8.69506i	0.175118	+	0.0966118i
$91$	19.7771	−	60.8676i	0.217331	−	0.668875i
$92$	−96.9775	+	31.5099i	−1.05410	+	0.342499i
$93$	−49.4095	−	59.8165i	−0.531285	−	0.643188i
$94$	20.0540	−	14.5701i	0.213340	−	0.155001i
$95$	−19.7673	+	6.42280i	−0.208077	+	0.0676084i
$96$	−22.7348	+	88.2732i	−0.236821	+	0.919513i
$97$	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	−0.988585	−	0.150663i	$-0.951859\pi$
$101$	−54.5204	+	75.0409i	−0.539806	+	0.742979i	0.448779	+	0.893643i	$0.351859\pi$
$102$	−52.1671	−	13.4357i	−0.511442	−	0.131722i
$103$	−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
$105$	−27.7021	+	22.8824i	−0.263829	+	0.217928i
$106$	2.42681	+	7.46894i	0.0228944	+	0.0704617i
$107$	−80.2959	−	26.0897i	−0.750429	−	0.243829i	−0.0912630	−	0.995827i	$-0.529090\pi$
$107$	−80.2959	−	26.0897i	−0.750429	−	0.243829i	−0.659166	+	0.751998i	$0.729090\pi$
$108$	−38.9519	+	82.2991i	−0.360666	+	0.762029i
$109$	−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	−0.260955	−	0.965351i	$-0.584037\pi$
$113$	−117.463	−	38.1659i	−1.03949	−	0.337751i	−0.778536	+	0.627600i	$0.784037\pi$
$114$	7.19076	+	18.2014i	0.0630768	+	0.159661i
$115$	−61.7513	+	44.8649i	−0.536968	+	0.390130i
$116$	106.356	+	146.386i	0.916858	+	1.26195i
$117$	−51.5268	−	109.925i	−0.440400	−	0.939529i
$118$	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
$123$	78.1865	+	49.7004i	0.635663	+	0.404068i
$124$	26.9500	−	82.9435i	0.217338	−	0.668899i
$125$	104.741	−	34.0324i	0.837927	−	0.272259i
$126$	23.1225	+	24.6966i	0.183512	+	0.196005i
$127$	−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
$129$	−103.103	−	26.5542i	−0.799246	−	0.205846i
$130$	−21.8259	−	15.8574i	−0.167891	−	0.121980i
$131$		−	125.997i		−	0.961811i	−0.876772	−	0.480906i	$-0.840308\pi$
$131$		−	125.997i		−	0.961811i	0.876772	−	0.480906i	$-0.159692\pi$
$132$		0			0
$133$	−39.0652			−0.293724
$134$	15.9867	−	22.0038i	0.119304	−	0.164208i
$135$	−8.69348	+	67.6004i	−0.0643961	+	0.500744i
$136$	−40.9078	−	125.901i	−0.300793	−	0.925744i
$137$	−34.8644	−	47.9868i	−0.254485	−	0.350268i	0.662591	−	0.748982i	$-0.269457\pi$
$137$	−34.8644	−	47.9868i	−0.254485	−	0.350268i	−0.917076	+	0.398713i	$0.869457\pi$
$138$	45.7701	+	55.4105i	0.331667	+	0.401526i
$139$	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
$141$	79.2113	+	50.3518i	0.561782	+	0.357105i
$142$	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
$147$	73.9087	−	29.1988i	0.502780	−	0.198632i
$148$	116.239	−	84.4526i	0.785399	−	0.570626i
$149$	−43.6905	−	60.1348i	−0.293225	−	0.403589i	0.636833	−	0.771001i	$-0.280244\pi$
$149$	−43.6905	−	60.1348i	−0.293225	−	0.403589i	−0.930058	+	0.367412i	$0.880244\pi$
$150$	−16.2682	−	41.1784i	−0.108455	−	0.274523i
$151$	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
$156$	73.2087	−	115.169i	0.469287	−	0.738261i
$157$	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
$159$	−22.9266	+	18.9378i	−0.144192	+	0.119105i
$160$	−62.0525	+	45.0838i	−0.387828	+	0.281773i
$161$	−136.441	+	44.3322i	−0.847457	+	0.275355i
$162$	64.0363	+	4.22047i	0.395286	+	0.0260523i
$163$	−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	−0.905576	−	0.424184i	$-0.860561\pi$
$167$	−37.1265	+	51.1002i	−0.222314	+	0.305989i	0.683262	+	0.730174i	$0.260561\pi$
$168$	−20.7357	+	80.5111i	−0.123427	+	0.479233i
$169$	4.00378	+	12.3224i	0.0236910	+	0.0729134i
$170$	−26.6433	−	36.6713i	−0.156725	−	0.215714i
$171$	−54.0944	+	50.6466i	−0.316342	+	0.296179i
$172$	−36.9829	−	113.822i	−0.215017	−	0.661755i
$173$	183.895	+	59.7512i	1.06298	+	0.345383i	0.787749	−	0.615996i	$-0.211246\pi$
$173$	183.895	+	59.7512i	1.06298	+	0.345383i	0.275229	+	0.961379i	$0.411246\pi$
$174$	68.4156	−	107.628i	0.393193	−	0.618554i
$175$	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	0.390242	−	0.920712i	$-0.372391\pi$
$179$	29.4944	+	9.58330i	0.164773	+	0.0535380i	−0.225469	+	0.974250i	$0.572391\pi$
$180$	−69.3719	+	32.5177i	−0.385399	+	0.180654i
$181$	−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
$183$	143.541	−	56.7083i	0.784378	−	0.309881i
$184$	−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
$189$	−54.8026	+	115.789i	−0.289961	+	0.612640i
$190$	−5.08870	+	15.6614i	−0.0267826	+	0.0824284i
$191$	66.0867	−	21.4729i	0.346003	−	0.112423i	−0.130860	−	0.991401i	$-0.541774\pi$
$191$	66.0867	−	21.4729i	0.346003	−	0.112423i	0.476863	+	0.878978i	$0.341774\pi$
$192$	−21.7273	−	26.3037i	−0.113163	−	0.136998i
$193$	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
$195$	25.4782	−	98.9250i	0.130658	−	0.507308i
$196$	72.2685	+	52.5061i	0.368717	+	0.267888i
$197$			106.612i			0.541178i	0.962695	+	0.270589i	$0.0872185\pi$
$197$			106.612i			0.541178i	−0.962695	+	0.270589i	$0.912782\pi$
$198$		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
$201$	99.7317	+	25.6860i	0.496178	+	0.127791i
$202$	22.7094	+	69.8923i	0.112423	+	0.346002i
$203$	149.635	+	205.955i	0.737117	+	1.01455i
$204$	176.779	−	146.023i	0.866566	−	0.715799i
$205$	24.0899	+	74.1410i	0.117512	+	0.361664i
$206$	−14.7508	−	4.79283i	−0.0716058	−	0.0232661i
$207$	−131.457	+	238.278i	−0.635058	+	1.15110i
$208$	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
$213$	15.9846	+	40.4606i	0.0750452	+	0.189956i
$214$	−54.1162	+	39.3177i	−0.252879	+	0.183728i
$215$	−52.6576	−	72.4770i	−0.244919	−	0.337102i
$216$	75.6663	+	138.368i	0.350307	+	0.640594i
$217$	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
$222$	−85.4633	−	54.3260i	−0.384970	−	0.244712i
$223$	−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
$225$	122.382	−	114.582i	0.543920	−	0.509252i
$226$	−79.1650	+	57.5167i	−0.350288	+	0.254499i
$227$	405.472	−	131.746i	1.78622	−	0.580378i	0.786895	−	0.617087i	$-0.211688\pi$
$227$	405.472	−	131.746i	1.78622	−	0.580378i	0.999326	+	0.0367091i	$0.0116875\pi$
$228$	−80.6665	−	20.7757i	−0.353800	−	0.0911215i
$229$	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	−0.969529	−	0.244976i	$-0.921220\pi$
$233$	−101.807	+	140.126i	−0.436942	+	0.601399i	0.532587	+	0.846375i	$0.321220\pi$
$234$	−94.4547	−	18.1641i	−0.403652	−	0.0776244i
$235$	24.4056	+	75.1128i	0.103854	+	0.319629i
$236$	121.951	+	167.851i	0.516742	+	0.711235i
$237$	−178.979	−	216.677i	−0.755185	−	0.914248i
$238$	−26.3269	−	81.0260i	−0.110617	−	0.340445i
$239$	−153.403	−	49.8436i	−0.641852	−	0.208550i	−0.0300341	−	0.999549i	$-0.509562\pi$
$239$	−153.403	−	49.8436i	−0.641852	−	0.208550i	−0.611818	+	0.790998i	$0.709562\pi$
$240$	−56.6340	−	36.0002i	−0.235975	−	0.150001i
$241$	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
$246$	68.2677	−	26.9703i	0.277511	−	0.109635i
$247$	89.8537	−	65.2825i	0.363780	−	0.264302i
$248$	−88.7882	−	122.206i	−0.358017	−	0.492768i
$249$	37.6554	+	95.3141i	0.151227	+	0.382788i
$250$	26.9634	−	82.9849i	0.107854	−	0.331939i
$251$	39.6707	−	54.6021i	0.158051	−	0.217538i	−0.722647	−	0.691218i	$-0.757075\pi$
$251$	39.6707	−	54.6021i	0.158051	−	0.217538i	0.880697	+	0.473680i	$0.157075\pi$
$252$	−142.891	+	17.8351i	−0.567029	+	0.0707741i
$253$		0			0
$254$			102.084i			0.401907i
$255$	92.0750	−	144.848i	0.361079	−	0.568033i
$256$	−17.9053	+	55.1069i	−0.0699427	+	0.215261i
$257$	−139.493	+	45.3242i	−0.542776	+	0.176359i	−0.567557	−	0.823334i	$-0.692111\pi$
$257$	−139.493	+	45.3242i	−0.542776	+	0.176359i	0.0247807	+	0.999693i	$0.492111\pi$
$258$	−65.0349	+	53.7200i	−0.252073	+	0.208217i
$259$	163.540	−	118.819i	0.631429	−	0.458760i
$260$	109.210	−	35.4844i	0.420037	−	0.136478i
$261$	474.214	+	91.1938i	1.81691	+	0.349401i
$262$	−80.7609	−	58.6763i	−0.308248	−	0.223955i
$263$			146.192i			0.555863i	0.960601	+	0.277932i	$0.0896488\pi$
$263$			146.192i			0.555863i	−0.960601	+	0.277932i	$0.910351\pi$
$264$		0			0
$265$	−25.0217			−0.0944217
$266$	−18.1925	+	25.0398i	−0.0683928	+	0.0941346i
$267$	107.359	−	416.844i	0.402092	−	1.56121i
$268$	35.7738	+	110.100i	0.133484	+	0.410822i
$269$	−33.5098	−	46.1222i	−0.124572	−	0.171458i	0.742176	−	0.670205i	$-0.233794\pi$
$269$	−33.5098	−	46.1222i	−0.124572	−	0.171458i	−0.866748	+	0.498747i	$0.833794\pi$
$270$	39.2816	+	37.0534i	0.145487	+	0.137235i
$271$	−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
$273$	103.000	−	162.034i	0.377288	−	0.593532i
$274$	−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
$279$	−98.7873	−	210.748i	−0.354076	−	0.755370i
$280$	−56.5960	+	41.1194i	−0.202129	+	0.146855i
$281$	−119.895	−	165.021i	−0.426672	−	0.587264i	0.540513	−	0.841335i	$-0.318230\pi$
$281$	−119.895	−	165.021i	−0.426672	−	0.587264i	−0.967185	+	0.254072i	$0.918230\pi$
$282$	69.1624	−	27.3238i	0.245257	−	0.0968928i
$283$	−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
$288$	−132.098	+	239.440i	−0.458674	+	0.831388i
$289$	−69.4247	+	213.667i	−0.240224	+	0.739333i
$290$	102.060	−	33.1612i	0.351930	−	0.114349i
$291$	76.9670	+	93.1784i	0.264491	+	0.320201i
$292$	−240.722	+	174.895i	−0.824391	+	0.598955i
$293$	8.89881	−	2.89140i	0.0303714	−	0.00986825i	−0.293792	−	0.955869i	$-0.594917\pi$
$293$	8.89881	−	2.89140i	0.0303714	−	0.00986825i	0.324163	+	0.946001i	$0.394917\pi$
$294$	15.7032	−	60.9713i	0.0534122	−	0.207385i
$295$	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
$300$	182.498	+	47.0025i	0.608327	+	0.156675i
$301$	−52.0324	−	160.139i	−0.172865	−	0.532024i
$302$	−2.90299	−	3.99563i	−0.00961257	−	0.0132306i
$303$	−214.541	+	177.214i	−0.708055	+	0.584866i
$304$	−22.5465	−	69.3910i	−0.0741662	−	0.228260i
$305$	123.510	+	40.1308i	0.404951	+	0.131577i
$306$	−141.502	−	78.0664i	−0.462426	−	0.255119i
$307$	−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	0.826415	−	0.563062i	$-0.190377\pi$
$311$	362.016	+	117.626i	1.16404	+	0.378219i	0.337624	+	0.941281i	$0.390377\pi$
$312$	−86.8493	−	219.835i	−0.278363	−	0.704598i
$313$	−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
$315$	−97.6013	+	45.7502i	−0.309845	+	0.145239i
$316$	97.6225	−	300.451i	0.308932	−	0.950795i
$317$	−43.0533	+	59.2578i	−0.135815	+	0.186933i	−0.871507	−	0.490383i	$-0.836857\pi$
$317$	−43.0533	+	59.2578i	−0.135815	+	0.186933i	0.735692	+	0.677316i	$0.236857\pi$
$318$	1.46182	+	23.5145i	0.00459692	+	0.0739451i
$319$		0			0
$320$		−	28.7075i		−	0.0897109i
$321$	−213.754	−	135.876i	−0.665899	−	0.423289i
$322$	−35.1238	+	108.100i	−0.109080	+	0.335714i
$323$	177.476	−	57.6655i	0.549462	−	0.178531i
$324$	−174.742	+	209.950i	−0.539327	+	0.647992i
$325$	−203.283	+	147.694i	−0.625486	+	0.454442i
$326$	−156.632	+	50.8927i	−0.480465	+	0.156113i
$327$	−487.267	−	125.496i	−1.49011	−	0.383780i
$328$	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
$333$	72.4133	−	376.554i	0.217457	−	1.13079i
$334$	15.4643	+	47.5942i	0.0463003	+	0.142498i
$335$	50.9360	+	70.1073i	0.152048	+	0.209276i
$336$	−80.3262	−	97.2451i	−0.239066	−	0.289420i
$337$	−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
$339$	−312.694	−	198.769i	−0.922402	−	0.586339i
$340$	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
$345$	−212.969	+	84.1368i	−0.617301	+	0.243875i
$346$	123.938	−	90.0462i	0.358202	−	0.260249i
$347$	302.906	+	416.915i	0.872929	+	1.20148i	0.978329	+	0.207054i	$0.0663876\pi$
$347$	302.906	+	416.915i	0.872929	+	1.20148i	−0.105400	+	0.994430i	$0.533612\pi$
$348$	199.452	+	504.858i	0.573139	+	1.45074i
$349$	−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	$-0.822335\pi$
$353$		−	373.911i		−	1.05924i	0.848236	−	0.529619i	$-0.177665\pi$
$354$	78.4479	−	123.411i	0.221604	−	0.348618i
$355$	−11.3119	+	34.8143i	−0.0318644	+	0.0980686i
$356$	460.181	−	149.522i	1.29264	−	0.420006i
$357$	248.716	−	205.444i	0.696684	−	0.575474i
$358$	19.8780	−	14.4422i	0.0555252	−	0.0403414i
$359$	−103.534	+	33.6402i	−0.288395	+	0.0937052i	−0.449642	−	0.893209i	$-0.648448\pi$
$359$	−103.534	+	33.6402i	−0.288395	+	0.0937052i	0.161247	+	0.986914i	$0.448448\pi$
$360$	−25.0599	+	130.313i	−0.0696109	+	0.361982i
$361$	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
$366$	30.4978	−	118.415i	0.0833274	−	0.323538i
$367$	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
$369$	189.959	+	202.891i	0.514795	+	0.549840i
$370$	−26.3319	−	81.0414i	−0.0711674	−	0.219031i
$371$	−44.7273	−	14.5328i	−0.120559	−	0.0391719i
$372$	140.356	−	220.802i	0.377301	−	0.593554i
$373$	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
$378$	48.6964	+	89.0494i	0.128827	+	0.235580i
$379$	−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
$381$	−359.505	+	142.028i	−0.943582	+	0.372778i
$382$	17.0127	−	52.3596i	0.0445358	−	0.137067i
$383$	−211.526	+	291.140i	−0.552287	+	0.760158i	−0.990320	−	0.138801i	$-0.955675\pi$
$383$	−211.526	+	291.140i	−0.552287	+	0.760158i	0.438033	+	0.898959i	$0.355675\pi$
$384$	−390.891	+	24.3004i	−1.01795	+	0.0632823i
$385$		0			0
$386$		−	215.110i		−	0.557280i
$387$	−279.665	−	154.290i	−0.722648	−	0.398682i
$388$	−41.9810	+	129.204i	−0.108198	+	0.333000i
$389$	−593.973	+	192.994i	−1.52692	+	0.496128i	−0.947733	−	0.319064i	$-0.896631\pi$
$389$	−593.973	+	192.994i	−1.52692	+	0.496128i	−0.579191	+	0.815192i	$0.696631\pi$
$390$	−51.5433	−	62.3997i	−0.132162	−	0.159999i
$391$	554.418	−	402.809i	1.41795	−	1.03020i
$392$	147.149	−	47.8117i	0.375381	−	0.121969i
$393$	94.2755	−	366.046i	0.239887	−	0.931416i
$394$	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
$399$	−113.492	−	29.2300i	−0.284441	−	0.0732581i
$400$	51.0088	+	156.989i	0.127522	+	0.392472i
$401$	−464.411	−	639.207i	−1.15813	−	1.59403i	−0.717894	−	0.696153i	$-0.754894\pi$
$401$	−464.411	−	639.207i	−1.15813	−	1.59403i	−0.440239	−	0.897881i	$-0.645106\pi$
$402$	62.9086	−	51.9636i	0.156489	−	0.129263i
$403$	107.800	+	331.774i	0.267494	+	0.823260i
$404$	−297.489	−	96.6600i	−0.736359	−	0.239257i
$405$	−75.8372	+	189.887i	−0.187252	+	0.468858i
$406$	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
$411$	−65.3826	−	165.498i	−0.159082	−	0.402671i
$412$	53.4082	−	38.8033i	0.129632	−	0.0941829i
$413$	171.577	+	236.155i	0.415440	+	0.571804i
$414$	91.5108	+	195.225i	0.221041	+	0.471558i
$415$	−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	$-0.869345\pi$
$419$		−	334.392i		−	0.798073i	0.916935	−	0.399036i	$-0.130655\pi$
$420$	−102.257	−	65.0014i	−0.243470	−	0.154765i
$421$	−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
$423$	192.449	+	205.550i	0.454962	+	0.485935i
$424$	−46.8395	+	34.0309i	−0.110471	+	0.0802615i
$425$	−401.518	+	130.461i	−0.944749	+	0.306967i
$426$	33.3781	+	8.59656i	0.0783524	+	0.0201797i
$427$	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	$-0.426039\pi$
$431$	467.467	−	643.414i	1.08461	−	1.49284i	0.854341	−	0.519712i	$-0.173961\pi$
$432$	−237.304	−	30.5175i	−0.549314	−	0.0706423i
$433$	−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
$435$	258.776	+	313.281i	0.594886	+	0.720186i
$436$	−174.783	−	537.926i	−0.400878	−	1.23377i
$437$	−236.778	−	76.9339i	−0.541826	−	0.176050i
$438$	176.988	+	112.505i	0.404082	+	0.256861i
$439$	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	0.374342	−	0.927291i	$-0.377869\pi$
$443$	58.5394	+	19.0206i	0.132143	+	0.0429359i	−0.242199	+	0.970227i	$0.577869\pi$
$444$	400.887	−	158.377i	0.902899	−	0.356705i
$445$	293.025	−	212.895i	0.658482	−	0.478415i
$446$	106.053	+	145.970i	0.237787	+	0.327286i
$447$	−81.9344	−	207.394i	−0.183298	−	0.463969i
$448$	16.6735	−	51.3157i	0.0372176	−	0.114544i
$449$	−80.7809	+	111.185i	−0.179913	+	0.247629i	−0.889443	−	0.457046i	$-0.848907\pi$
$449$	−80.7809	+	111.185i	−0.179913	+	0.247629i	0.709530	+	0.704675i	$0.248907\pi$
$450$	−16.4512	−	131.804i	−0.0365582	−	0.292897i
$451$		0			0
$452$		−	416.502i		−	0.921464i
$453$	10.0323	−	15.7824i	0.0221463	−	0.0348396i
$454$	104.381	−	321.250i	0.229913	−	0.707600i
$455$	153.650	−	49.9240i	0.337693	−	0.109723i
$456$	−111.237	+	91.8834i	−0.243940	+	0.201499i
$457$	−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
$459$	78.0522	−	606.933i	0.170048	−	1.32230i
$460$	−208.243	−	151.297i	−0.452702	−	0.328907i
$461$		−	528.162i		−	1.14569i	−0.819664	−	0.572844i	$-0.805840\pi$
$461$		−	528.162i		−	1.14569i	0.819664	−	0.572844i	$-0.194160\pi$
$462$		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
$465$	48.8469	−	189.659i	0.105047	−	0.407870i
$466$	42.4058	+	130.512i	0.0909996	+	0.280068i
$467$	211.054	+	290.491i	0.451936	+	0.622036i	0.972812	−	0.231596i	$-0.0743948\pi$
$467$	211.054	+	290.491i	0.451936	+	0.622036i	−0.520876	+	0.853632i	$0.674395\pi$
$468$	298.859	−	279.810i	0.638587	−	0.597885i
$469$	50.3312	+	154.903i	0.107316	+	0.330284i
$470$	59.5109	+	19.3363i	0.126619	+	0.0411410i
$471$	158.999	−	250.131i	0.337578	−	0.531063i
$472$	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
$477$	−80.7760	+	37.8634i	−0.169342	+	0.0793781i
$478$	−103.387	+	75.1152i	−0.216291	+	0.157145i
$479$	339.387	+	467.127i	0.708533	+	0.975213i	0.999827	+	0.0185790i	$0.00591421\pi$
$479$	339.387	+	467.127i	0.708533	+	0.975213i	−0.291294	+	0.956634i	$0.594086\pi$
$480$	−214.008	+	84.5472i	−0.445849	+	0.176140i
$481$	−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
$486$	182.880	+	60.1754i	0.376296	+	0.123818i
$487$	−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
$489$	−397.145	−	480.795i	−0.812157	−	0.983220i
$490$	42.8603	−	31.1398i	0.0874700	−	0.0635507i
$491$	−731.236	+	237.593i	−1.48928	+	0.483896i	−0.936870	−	0.349677i	$-0.886291\pi$
$491$	−731.236	+	237.593i	−1.48928	+	0.483896i	−0.552409	+	0.833573i	$0.686291\pi$
$492$	−77.9231	+	302.555i	−0.158380	+	0.614948i
$493$	−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
$498$	78.6298	+	20.2512i	0.157891	+	0.0406650i
$499$	−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
$501$	−146.095	+	120.677i	−0.291606	+	0.240872i
$502$	−16.5240	−	50.8558i	−0.0329164	−	0.101306i
$503$	−162.170	−	52.6924i	−0.322406	−	0.104756i	0.143342	−	0.989673i	$-0.454215\pi$
$503$	−162.170	−	52.6924i	−0.322406	−	0.104756i	−0.465749	+	0.884917i	$0.654215\pi$
$504$	−120.482	+	218.385i	−0.239052	+	0.433304i
$505$	−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	−0.103181	−	0.994663i	$-0.532902\pi$
$509$	−392.594	−	127.561i	−0.771304	−	0.250612i	−0.668123	+	0.744051i	$0.732902\pi$
$510$	−49.9651	−	126.473i	−0.0979708	−	0.247986i
$511$	−338.679	+	246.065i	−0.662777	+	0.481536i
$512$	−279.955	−	385.324i	−0.546786	−	0.752587i
$513$	−195.050	+	106.663i	−0.380215	+	0.207920i
$514$	−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
$519$	489.543	+	311.185i	0.943243	+	0.599587i
$520$	61.4608	−	189.157i	0.118194	−	0.363763i
$521$	105.824	−	34.3843i	0.203117	−	0.0659968i	−0.205691	−	0.978617i	$-0.565944\pi$
$521$	105.824	−	34.3843i	0.203117	−	0.0659968i	0.408809	+	0.912620i	$0.365944\pi$
$522$	279.292	−	261.490i	0.535042	−	0.500939i
$523$	−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
$525$	256.762	+	66.1292i	0.489071	+	0.125960i
$526$	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
$531$	543.752	+	104.566i	1.02401	+	0.196923i
$532$	−40.7096	−	125.291i	−0.0765218	−	0.235510i
$533$	−244.854	−	337.013i	−0.459389	−	0.632294i
$534$	−217.190	−	262.936i	−0.406723	−	0.492390i
$535$	−65.8592	−	202.694i	−0.123101	−	0.378867i
$536$	190.699	+	61.9620i	0.355782	+	0.115601i
$537$	78.5162	+	49.9100i	0.146213	+	0.0929423i
$538$	−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
$543$	−284.982	+	112.587i	−0.524829	+	0.207342i
$544$	557.123	−	404.773i	1.02412	−	0.744068i
$545$	−248.862	−	342.529i	−0.456627	−	0.628493i
$546$	−55.8934	−	141.478i	−0.102369	−	0.259118i
$547$	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
$552$	−284.237	+	447.149i	−0.514922	+	0.810052i
$553$	137.348	−	422.714i	0.248369	−	0.764401i
$554$	178.037	−	57.8478i	0.321367	−	0.104418i
$555$	248.764	−	205.483i	0.448223	−	0.370240i
$556$	−357.220	+	259.536i	−0.642483	+	0.466791i
$557$	308.044	−	100.090i	0.553041	−	0.179694i	−0.0191464	−	0.999817i	$-0.506095\pi$
$557$	308.044	−	100.090i	0.553041	−	0.179694i	0.572188	+	0.820123i	$0.306095\pi$
$558$	−181.089	−	34.8243i	−0.324532	−	0.0624091i
$559$	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	−0.468060	−	0.883697i	$-0.655047\pi$
$563$	291.084	−	400.643i	0.517024	−	0.711622i	0.985084	+	0.172074i	$0.0550470\pi$
$564$	−78.9444	+	306.520i	−0.139972	+	0.543475i
$565$	−96.3436	−	296.515i	−0.170520	−	0.524805i
$566$	223.166	+	307.162i	0.394287	+	0.542689i
$567$	−245.850	+	295.384i	−0.433597	+	0.520960i
$568$	26.1741	+	80.5555i	0.0460811	+	0.141823i
$569$	517.800	+	168.244i	0.910018	+	0.295683i	0.726366	−	0.687308i	$-0.241208\pi$
$569$	517.800	+	168.244i	0.910018	+	0.295683i	0.183652	+	0.982991i	$0.441208\pi$
$570$	−26.5021	+	41.6919i	−0.0464948	+	0.0731436i
$571$	−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
$576$	−43.4407	−	92.6744i	−0.0754179	−	0.160893i
$577$	−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
$579$	757.541	−	299.279i	1.30836	−	0.516889i
$580$	−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
$585$	148.038	−	268.333i	0.253057	−	0.458688i
$586$	2.29082	−	7.05041i	0.00390924	−	0.0120314i
$587$	−596.792	+	193.909i	−1.01668	+	0.330340i	−0.769512	−	0.638633i	$-0.779500\pi$
$587$	−596.792	+	193.909i	−1.01668	+	0.330340i	−0.247169	+	0.968972i	$0.579500\pi$
$588$	170.667	+	206.614i	0.290250	+	0.351385i
$589$	172.268	−	125.160i	0.292475	−	0.212496i
$590$	117.025	−	38.0238i	0.198348	−	0.0644472i
$591$	−79.7708	+	309.729i	−0.134976	+	0.524076i
$592$	305.443	+	221.918i	0.515952	+	0.374861i
$593$			961.677i			1.62171i	0.585244	+	0.810857i	$0.300999\pi$
$593$			961.677i			1.62171i	−0.585244	+	0.810857i	$0.699001\pi$
$594$		0			0
$595$	271.446			0.456211
$596$	147.337	−	202.791i	0.247209	−	0.340254i
$597$	−840.390	−	216.443i	−1.40769	−	0.362551i
$598$	−99.8595	−	307.336i	−0.166989	−	0.513940i
$599$	577.456	+	794.800i	0.964034	+	1.32688i	0.945004	+	0.327060i	$0.106058\pi$
$599$	577.456	+	794.800i	0.964034	+	1.32688i	0.0190299	+	0.999819i	$0.493942\pi$
$600$	251.659	−	207.875i	0.419432	−	0.346458i
$601$	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
$603$	270.521	+	149.245i	0.448625	+	0.247505i
$604$	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
$609$	280.615	+	710.299i	0.460781	+	1.16634i
$610$	83.2408	−	60.4780i	0.136460	−	0.0991442i
$611$	−248.063	−	341.430i	−0.405996	−	0.558805i
$612$	622.838	−	291.952i	1.01771	−	0.477046i
$613$	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	$0.150103\pi$
$617$			560.582i			0.908560i	−0.890859	+	0.454280i	$0.849897\pi$
$618$	−39.2678	−	24.9611i	−0.0635401	−	0.0403902i
$619$	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
$621$	−560.195	+	593.882i	−0.902086	+	0.956331i
$622$	243.984	−	177.265i	0.392258	−	0.284992i
$623$	647.443	−	210.367i	1.03923	−	0.337668i
$624$	347.265	+	89.4384i	0.556515	+	0.143331i
$625$	−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
$630$	−16.1278	+	83.8655i	−0.0255996	+	0.133120i
$631$	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
$633$	−357.678	−	433.014i	−0.565052	−	0.684067i
$634$	17.9330	+	55.1921i	0.0282855	+	0.0870538i
$635$	−309.336	−	100.509i	−0.487144	−	0.158283i
$636$	−84.6293	−	53.7959i	−0.133065	−	0.0845847i
$637$	−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	0.929841	−	0.367961i	$-0.119944\pi$
$641$	939.589	+	305.291i	1.46582	+	0.476273i	0.535975	+	0.844234i	$0.319944\pi$
$642$	−186.637	+	73.7339i	−0.290711	+	0.114850i
$643$	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
$645$	−98.7508	−	249.960i	−0.153102	−	0.387535i
$646$	45.6876	−	140.612i	0.0707239	−	0.217666i
$647$	−282.730	+	389.145i	−0.436987	+	0.601460i	−0.969539	−	0.244936i	$-0.921233\pi$
$647$	−282.730	+	389.145i	−0.436987	+	0.601460i	0.532553	+	0.846397i	$0.321233\pi$
$648$	116.293	+	458.603i	0.179465	+	0.707720i
$649$		0			0
$650$			199.079i			0.306276i
$651$	197.471	−	310.653i	0.303335	−	0.477193i
$652$	216.619	−	666.685i	0.332238	−	1.02252i
$653$	−738.203	+	239.857i	−1.13048	+	0.367315i	−0.813758	−	0.581204i	$-0.802582\pi$
$653$	−738.203	+	239.857i	−1.13048	+	0.367315i	−0.316721	+	0.948519i	$0.602582\pi$
$654$	−307.357	+	253.883i	−0.469965	+	0.388200i
$655$	257.316	−	186.951i	0.392848	−	0.285421i
$656$	−260.264	+	84.5649i	−0.396744	+	0.128910i
$657$	−149.962	+	779.815i	−0.228253	+	1.18693i
$658$	95.1473	+	69.1285i	0.144601	+	0.105059i
$659$			52.5987i			0.0798160i	0.999203	+	0.0399080i	$0.0127065\pi$
$659$			52.5987i			0.0798160i	−0.999203	+	0.0399080i	$0.987294\pi$
$660$		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
$663$	−228.750	+	888.174i	−0.345022	+	1.33963i
$664$	61.6590	+	189.767i	0.0928599	+	0.285793i
$665$	−57.9638	−	79.7803i	−0.0871636	−	0.119970i
$666$	−207.639	−	221.774i	−0.311770	−	0.332994i
$667$	501.350	+	1543.00i	0.751649	+	2.31334i
$668$	−202.579	−	65.8220i	−0.303263	−	0.0985360i
$669$	−366.503	+	576.566i	−0.547837	+	0.861832i
$670$	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
$675$	441.278	−	241.311i	0.653745	−	0.357498i
$676$	−35.3484	+	25.6821i	−0.0522905	+	0.0379912i
$677$	−173.786	−	239.196i	−0.256701	−	0.353318i	0.661143	−	0.750260i	$-0.270072\pi$
$677$	−173.786	−	239.196i	−0.256701	−	0.353318i	−0.917844	+	0.396942i	$0.870072\pi$
$678$	−273.026	+	107.863i	−0.402693	+	0.159090i
$679$	−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	$0.230718\pi$
$683$			905.661i			1.32600i	−0.748617	+	0.663002i	$0.769282\pi$
$684$	−218.807	−	120.715i	−0.319893	−	0.176484i
$685$	46.2694	−	142.403i	0.0675466	−	0.207887i
$686$	269.879	−	87.6891i	0.393410	−	0.127827i
$687$	194.082	+	234.961i	0.282506	+	0.342010i
$688$	254.423	−	184.849i	0.369800	−	0.268676i
$689$	127.163	−	41.3177i	0.184561	−	0.0599677i
$690$	−45.2490	+	175.690i	−0.0655782	+	0.254622i
$691$	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
$696$	910.494	+	234.498i	1.30818	+	0.336923i
$697$	−216.285	−	665.657i	−0.310308	−	0.955031i
$698$	130.402	+	179.483i	0.186822	+	0.257139i
$699$	−400.617	+	330.917i	−0.573129	+	0.473415i
$700$	92.1005	+	283.456i	0.131572	+	0.404937i
$701$	1189.16	+	386.381i	1.69637	+	0.551186i	0.987973	−	0.154624i	$-0.0494166\pi$
$701$	1189.16	+	386.381i	1.69637	+	0.551186i	0.708401	+	0.705810i	$0.249417\pi$
$702$	−260.818	−	123.444i	−0.371536	−	0.175847i
$703$	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
$708$	228.700	+	578.889i	0.323022	+	0.817640i
$709$	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
$711$	−357.843	−	763.406i	−0.503296	−	1.07371i
$712$	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
$717$	−408.370	−	259.586i	−0.569553	−	0.362045i
$718$	−26.6527	+	82.0285i	−0.0371207	+	0.114246i
$719$	106.782	−	34.6957i	0.148515	−	0.0482554i	−0.233816	−	0.972281i	$-0.575121\pi$
$719$	106.782	−	34.6957i	0.148515	−	0.0482554i	0.382331	+	0.924025i	$0.375121\pi$
$720$	−137.596	−	146.963i	−0.191106	−	0.204115i
$721$	75.1416	−	54.5936i	0.104219	−	0.0757192i
$722$	220.934	−	71.7858i	0.306003	−	0.0994263i
$723$	164.728	+	42.4257i	0.227839	+	0.0586801i
$724$	−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
$729$	42.5213	+	727.759i	0.0583282	+	0.998297i
$730$	54.5314	+	167.830i	0.0747006	+	0.229905i
$731$	472.774	+	650.717i	0.646749	+	0.890174i
$732$	331.459	+	401.274i	0.452814	+	0.548189i
$733$	−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
$735$	169.294	+	107.614i	0.230332	+	0.146414i
$736$	−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
$741$	309.889	−	122.427i	0.418204	−	0.165218i
$742$	−30.1444	+	21.9012i	−0.0406259	+	0.0295164i
$743$	−144.127	−	198.374i	−0.193980	−	0.266991i	0.700937	−	0.713223i	$-0.252765\pi$
$743$	−144.127	−	198.374i	−0.193980	−	0.266991i	−0.894917	+	0.446232i	$0.852765\pi$
$744$	−166.508	−	421.468i	−0.223801	−	0.566489i
$745$	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
$750$	140.426	−	220.912i	0.187235	−	0.294549i
$751$	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
$753$	156.106	−	128.947i	0.207312	−	0.171244i
$754$	−463.918	+	337.056i	−0.615276	+	0.447024i
$755$	14.9658	−	4.86267i	0.0198222	−	0.00644062i
$756$	−428.471	−	55.1018i	−0.566761	−	0.0728860i
$757$	−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	−0.462765	−	0.886481i	$-0.653143\pi$
$761$	398.255	−	548.151i	0.523331	−	0.720303i	0.986096	+	0.166178i	$0.0531426\pi$
$762$	−76.3831	+	296.575i	−0.100240	+	0.389206i
$763$	−245.907	−	756.824i	−0.322289	−	0.991905i
$764$	137.737	+	189.578i	0.180284	+	0.248139i
$765$	375.876	−	351.919i	0.491341	−	0.460024i
$766$	88.1069	+	271.165i	0.115022	+	0.354001i
$767$	−789.285	−	256.454i	−1.02905	−	0.334360i
$768$	−93.2513	+	146.699i	−0.121421	+	0.191014i
$769$	−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	0.420659	−	0.907219i	$-0.361799\pi$
$773$	176.035	+	57.1971i	0.227729	+	0.0739937i	−0.192930	+	0.981213i	$0.561799\pi$
$774$	−229.134	+	107.406i	−0.296039	+	0.138767i
$775$	−389.735	+	283.159i	−0.502884	+	0.365367i
$776$	138.309	+	190.366i	0.178233	+	0.245317i
$777$	564.020	−	222.825i	0.725894	−	0.286776i
$778$	−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
$783$	1309.45	+	619.759i	1.67235	+	0.791518i
$784$	−72.5358	+	223.242i	−0.0925202	+	0.284748i
$785$	237.189	−	77.0673i	0.302151	−	0.0981748i
$786$	−190.722	−	230.894i	−0.242649	−	0.293758i
$787$	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
$789$	−109.386	+	424.716i	−0.138639	+	0.538296i
$790$	−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
$795$	−72.6930	−	18.7221i	−0.0914377	−	0.0235499i
$796$	−301.448	−	927.761i	−0.378703	−	1.16553i
$797$	−530.616	−	730.331i	−0.665767	−	0.916350i	0.333888	−	0.942613i	$-0.391639\pi$
$797$	−530.616	−	730.331i	−0.665767	−	0.916350i	−0.999655	+	0.0262628i	$0.991639\pi$
$798$	−71.5883	+	59.1332i	−0.0897096	+	0.0741017i
$799$	−219.120	−	674.381i	−0.274243	−	0.844032i
$800$	538.294	+	174.902i	0.672868	+	0.218628i
$801$	623.795	−	1130.68i	0.778770	−	1.41159i
$802$	−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
$807$	−62.8421	−	159.067i	−0.0778712	−	0.197109i
$808$	−438.311	+	318.452i	−0.542464	+	0.394123i
$809$	−180.254	−	248.099i	−0.222811	−	0.306673i	0.682947	−	0.730468i	$-0.260698\pi$
$809$	−180.254	−	248.099i	−0.222811	−	0.306673i	−0.905758	+	0.423794i	$0.860698\pi$
$810$	86.3959	+	137.039i	0.106662	+	0.169184i
$811$	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
$816$	508.474	+	323.219i	0.623130	+	0.396102i
$817$	90.2967	−	277.905i	0.110522	−	0.340153i
$818$	−382.553	+	124.299i	−0.467669	+	0.151955i
$819$	420.473	−	393.673i	0.513398	−	0.480675i
$820$	−212.683	+	154.524i	−0.259370	+	0.188443i
$821$	−1296.33	+	421.204i	−1.57897	+	0.513038i	−0.961791	−	0.273786i	$-0.911724\pi$
$821$	−1296.33	+	421.204i	−1.57897	+	0.513038i	−0.617178	+	0.786824i	$0.711724\pi$
$822$	−136.528	−	35.1629i	−0.166092	−	0.0427772i
$823$	−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	−0.972988	−	0.230856i	$-0.925847\pi$
$827$	−374.434	+	515.364i	−0.452761	+	0.623172i	0.520227	+	0.854028i	$0.325847\pi$
$828$	−901.201	−	173.306i	−1.08841	−	0.209306i
$829$	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
$831$	451.419	+	546.501i	0.543224	+	0.657642i
$832$	47.4039	+	145.894i	0.0569758	+	0.175353i
$833$	−570.970	−	185.519i	−0.685438	−	0.222712i
$834$	262.642	+	166.952i	0.314919	+	0.200183i
$835$	−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	−0.328444	−	0.944523i	$-0.606524\pi$
$839$	−964.295	−	313.318i	−1.14934	−	0.373443i	−0.820894	+	0.571081i	$0.806524\pi$
$840$	−195.189	+	77.1127i	−0.232368	+	0.0918008i
$841$	1648.74	−	1197.88i	1.96045	−	1.42435i
$842$	206.449	+	284.153i	0.245189	+	0.337474i
$843$	−224.843	−	569.127i	−0.266718	−	0.675121i
$844$	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
$849$	−771.228	+	1213.26i	−0.908396	+	1.42905i
$850$	−103.363	+	318.118i	−0.121603	+	0.374256i
$851$	1225.23	−	398.101i	1.43975	−	0.467804i
$852$	−113.109	+	93.4300i	−0.132757	+	0.109660i
$853$	−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
$855$	−183.696	−	35.3256i	−0.214849	−	0.0413165i
$856$	−398.960	−	289.861i	−0.466074	−	0.338623i
$857$			618.449i			0.721644i	0.932635	+	0.360822i	$0.117504\pi$
$857$			618.449i			0.721644i	−0.932635	+	0.360822i	$0.882496\pi$
$858$		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
$861$	−109.632	+	425.673i	−0.127331	+	0.494394i
$862$	−194.714	−	599.269i	−0.225887	−	0.695207i
$863$	−649.669	−	894.193i	−0.752803	−	1.03614i	−0.997779	−	0.0666155i	$-0.978780\pi$
$863$	−649.669	−	894.193i	−0.752803	−	1.03614i	0.244975	−	0.969529i	$-0.421220\pi$
$864$	−562.927	+	596.778i	−0.651536	+	0.690715i
$865$	150.832	+	464.214i	0.174372	+	0.536663i
$866$	−14.0320	−	4.55927i	−0.0162032	−	0.00526474i
$867$	−361.565	+	568.799i	−0.417031	+	0.656054i
$868$	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
$873$	153.885	+	328.291i	0.176271	+	0.376049i
$874$	−159.579	+	115.941i	−0.182585	+	0.132655i
$875$	307.132	+	422.731i	0.351008	+	0.483121i
$876$	−830.206	+	327.987i	−0.947724	+	0.374414i
$877$	−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	$-0.768370\pi$
$881$		−	1171.98i		−	1.33029i	0.746715	−	0.665145i	$-0.231630\pi$
$882$	91.2416	−	165.384i	0.103449	−	0.187510i
$883$	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
$885$	296.722	+	359.220i	0.335279	+	0.405898i
$886$	39.4532	−	28.6644i	0.0445295	−	0.0323526i
$887$	931.819	−	302.766i	1.05053	−	0.341337i	0.267653	−	0.963515i	$-0.413752\pi$
$887$	931.819	−	302.766i	1.05053	−	0.341337i	0.782876	+	0.622178i	$0.213752\pi$
$888$	186.206	−	722.986i	0.209691	−	0.814173i
$889$	−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
$894$	−171.090	−	44.0645i	−0.191376	−	0.0492891i
$895$	24.1915	+	74.4537i	0.0270296	+	0.0831885i
$896$	−364.072	−	501.102i	−0.406330	−	0.559266i
$897$	943.395	−	779.261i	1.05172	−	0.868741i
$898$	33.6477	+	103.557i	0.0374696	+	0.115319i
$899$	−1319.70	−	428.797i	−1.46797	−	0.476971i
$900$	495.023	+	273.103i	0.550026	+	0.303448i
$901$	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
$906$	−5.44409	−	13.7802i	−0.00600893	−	0.0152099i
$907$	−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
$909$	−755.880	+	354.315i	−0.831551	+	0.389786i
$910$	39.5542	−	121.735i	0.0434661	−	0.133775i
$911$	272.307	−	374.799i	0.298910	−	0.411415i	−0.632973	−	0.774174i	$-0.718165\pi$
$911$	272.307	−	374.799i	0.298910	−	0.411415i	0.931883	+	0.362760i	$0.118165\pi$
$912$	−13.5812	−	218.464i	−0.0148917	−	0.239544i
$913$		0			0
$914$			243.701i			0.266632i
$915$	328.793	+	209.002i	0.359337	+	0.228418i
$916$	−105.860	+	325.804i	−0.115568	+	0.355681i
$917$	568.543	−	184.731i	0.620004	−	0.201451i
$918$	−352.680	−	332.675i	−0.384183	−	0.362391i
$919$	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
$921$	−210.705	−	54.2673i	−0.228779	−	0.0589221i
$922$	−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
$927$	33.2717	−	173.015i	0.0358918	−	0.186640i
$928$	503.795	+	1550.52i	0.542882	+	1.67082i
$929$	71.4310	+	98.3163i	0.0768902	+	0.105830i	0.845730	−	0.533611i	$-0.179166\pi$
$929$	71.4310	+	98.3163i	0.0768902	+	0.105830i	−0.768840	+	0.639442i	$0.779166\pi$
$930$	−98.8190	−	119.633i	−0.106257	−	0.128638i
$931$	67.3976	+	207.428i	0.0723927	+	0.222802i
$932$	−555.509	−	180.496i	−0.596039	−	0.193665i
$933$	963.715	+	612.600i	1.03292	+	0.656592i
$934$	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
$939$	−148.159	+	58.5326i	−0.157784	+	0.0623350i
$940$	−215.471	+	156.549i	−0.229225	+	0.166541i
$941$	526.117	+	724.138i	0.559104	+	0.769541i	0.991212	−	0.132281i	$-0.0422301\pi$
$941$	526.117	+	724.138i	0.559104	+	0.769541i	−0.432108	+	0.901822i	$0.642230\pi$
$942$	−86.2820	−	218.399i	−0.0915945	−	0.231846i
$943$	−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	$-0.757321\pi$
$947$		−	1308.11i		−	1.38132i	0.723181	−	0.690659i	$-0.242679\pi$
$948$	508.420	−	799.824i	0.536308	−	0.843696i
$949$	367.791	−	1131.94i	0.387556	−	1.19277i
$950$	115.569	−	37.5508i	0.121652	−	0.0395271i
$951$	−169.417	+	139.941i	−0.178146	+	0.147152i
$952$	508.133	−	369.180i	0.533753	−	0.387794i
$953$	−1.93085	+	0.627370i	−0.00202607	+	0.000658311i	−0.310030	−	0.950727i	$-0.600339\pi$
$953$	−1.93085	+	0.627370i	−0.00202607	+	0.000658311i	0.308004	+	0.951385i	$0.400339\pi$
$954$	−13.3475	+	69.4080i	−0.0139911	+	0.0727548i
$955$	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
$960$	21.4799	−	83.4008i	0.0223749	−	0.0868758i
$961$	−90.2909	−	277.887i	−0.0939552	−	0.289164i
$962$	267.643	+	368.379i	0.278215	+	0.382930i
$963$	−519.329	−	554.683i	−0.539282	−	0.575995i
$964$	59.0877	+	181.853i	0.0612943	+	0.188645i
$965$	651.827	+	211.791i	0.675468	+	0.219473i
$966$	−182.926	+	287.771i	−0.189364	+	0.297899i
$967$	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	0.998557	−	0.0537073i	$-0.0171038\pi$
$971$	1723.37	+	559.956i	1.77484	+	0.576680i	0.776281	+	0.630387i	$0.217104\pi$
$972$	−664.750	+	479.196i	−0.683900	+	0.493000i
$973$	−502.584	+	365.149i	−0.516530	+	0.375281i
$974$	282.630	+	389.006i	0.290174	+	0.399391i
$975$	−701.086	+	276.975i	−0.719062	+	0.284077i
$976$	−140.875	+	433.568i	−0.144339	+	0.444230i
$977$	251.212	−	345.764i	0.257126	−	0.353904i	−0.660865	−	0.750505i	$-0.729810\pi$
$977$	251.212	−	345.764i	0.257126	−	0.353904i	0.917991	+	0.396601i	$0.129810\pi$
$978$	−493.125	+	30.6559i	−0.504218	+	0.0313455i
$979$		0			0
$980$			225.496i			0.230098i
$981$	−1321.70	−	729.180i	−1.34730	−	0.743303i
$982$	−188.242	+	579.349i	−0.191692	+	0.589968i
$983$	954.405	−	310.105i	0.970910	−	0.315468i	0.219727	−	0.975561i	$-0.429483\pi$
$983$	954.405	−	310.105i	0.970910	−	0.315468i	0.751183	+	0.660094i	$0.229483\pi$
$984$	344.626	+	417.213i	0.350229	+	0.423997i
$985$	−217.727	+	158.188i	−0.221042	+	0.160597i
$986$	−916.317	+	297.729i	−0.929327	+	0.301957i
$987$	−111.069	+	431.252i	−0.112532	+	0.436932i
$988$	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
$993$	−486.186	−	125.217i	−0.489613	−	0.126100i
$994$	16.8448	+	51.8429i	0.0169465	+	0.0521559i
$995$	−429.212	−	590.760i	−0.431369	−	0.593728i
$996$	−266.454	+	220.096i	−0.267524	+	0.220980i
$997$	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
$999$	492.125	−	1039.78i	0.492618	−	1.04082i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.465695 - 0.640974i) q^{2} +(2.90519 + 0.748234i) q^{3} +(1.04209 + 3.20723i) q^{4} +(1.48377 + 2.04223i) q^{5} +(1.83253 - 1.51370i) q^{6} +(1.46615 + 4.51235i) q^{7} +(5.55509 + 1.80496i) q^{8} +(7.88029 + 4.34753i) q^{9} +O(q^{10})\)	\(q+(0.465695 - 0.640974i) q^{2} +(2.90519 + 0.748234i) q^{3} +(1.04209 + 3.20723i) q^{4} +(1.48377 + 2.04223i) q^{5} +(1.83253 - 1.51370i) q^{6} +(1.46615 + 4.51235i) q^{7} +(5.55509 + 1.80496i) q^{8} +(7.88029 + 4.34753i) q^{9} +2.00000 q^{10} +(0.627719 + 10.0974i) q^{12} +(-10.9129 - 7.92871i) q^{13} +(3.57507 + 1.16161i) q^{14} +(2.78257 + 7.04328i) q^{15} +(-7.16903 + 5.20860i) q^{16} +(-13.3216 - 18.3357i) q^{17} +(6.45646 - 3.02644i) q^{18} +(-2.54435 + 7.83070i) q^{19} +(-5.00368 + 6.88698i) q^{20} +(0.883156 + 14.2063i) q^{21} +30.2372i q^{23} +(14.7881 + 9.40025i) q^{24} +(5.75628 - 17.7160i) q^{25} +(-10.1642 + 3.30254i) q^{26} +(19.6408 + 18.5267i) q^{27} +(-12.9443 + 9.40456i) q^{28} +(51.0298 - 16.5806i) q^{29} +(5.81039 + 1.49647i) q^{30} +(-20.9223 - 15.2010i) q^{31} +30.3846i q^{32} -17.9565 q^{34} +(-7.03983 + 9.68950i) q^{35} +(-5.73154 + 29.8044i) q^{36} +(-13.1660 - 40.5207i) q^{37} +(3.83438 + 5.27758i) q^{38} +(-25.7716 - 31.1999i) q^{39} +(4.55632 + 14.0229i) q^{40} +(29.3705 + 9.54305i) q^{41} +(9.51712 + 6.04970i) q^{42} -35.4891 q^{43} +(2.81386 + 22.5441i) q^{45} +(19.3812 + 14.0813i) q^{46} +(29.7554 + 9.66813i) q^{47} +(-24.7247 + 9.76788i) q^{48} +(21.4302 - 15.5699i) q^{49} +(-8.67483 - 11.9399i) q^{50} +(-24.9826 - 63.2364i) q^{51} +(14.0569 - 43.2627i) q^{52} +(-5.82625 + 8.01914i) q^{53} +(21.0217 - 3.96143i) q^{54} +27.7128i q^{56} +(-13.2510 + 20.8459i) q^{57} +(13.1366 - 40.4302i) q^{58} +(58.5127 - 19.0119i) q^{59} +(-19.6897 + 16.2641i) q^{60} +(41.6204 - 30.2390i) q^{61} +(-19.4868 + 6.33165i) q^{62} +(-8.06388 + 41.9327i) q^{63} +(-9.20037 - 6.68446i) q^{64} -34.0511i q^{65} +34.3288 q^{67} +(44.9243 - 61.8330i) q^{68} +(-22.6245 + 87.8448i) q^{69} +(2.93230 + 9.02469i) q^{70} +(8.52360 + 11.7317i) q^{71} +(35.9286 + 38.3745i) q^{72} +(27.2657 + 83.9152i) q^{73} +(-32.1040 - 10.4312i) q^{74} +(29.9788 - 47.1614i) q^{75} -27.7663 q^{76} +(-32.0000 + 1.98933i) q^{78} +(-75.7882 - 55.0633i) q^{79} +(-21.2744 - 6.91246i) q^{80} +(43.1980 + 68.5196i) q^{81} +(19.7945 - 14.3816i) q^{82} +(20.0793 + 27.6368i) q^{83} +(-44.6424 + 17.6367i) q^{84} +(17.6795 - 54.4118i) q^{85} +(-16.5271 + 22.7476i) q^{86} +(160.658 - 9.98755i) q^{87} -143.482i q^{89} +(15.7606 + 8.69506i) q^{90} +(19.7771 - 60.8676i) q^{91} +(-96.9775 + 31.5099i) q^{92} +(-49.4095 - 59.8165i) q^{93} +(20.0540 - 14.5701i) q^{94} +(-19.7673 + 6.42280i) q^{95} +(-22.7348 + 88.2732i) 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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