LMFDB - Embedded newform 363.3.h.m.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.m.245.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.465695 - 0.640974i) q^{2} +(-2.79015 - 1.10230i) q^{3} +(1.04209 + 3.20723i) q^{4} +(-1.48377 - 2.04223i) q^{5} +(-2.00590 + 1.27508i) q^{6} +(-1.46615 - 4.51235i) q^{7} +(5.55509 + 1.80496i) q^{8} +(6.56989 + 6.15114i) q^{9} +O(q^{10})$	\(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	−0.676565	−	0.736383i	$-0.736532\pi$
$2$	0.465695	−	0.640974i	0.232847	−	0.320487i	0.909412	+	0.415896i	$0.136532\pi$
$3$	−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	$-0.989946\pi$
$7$	−1.46615	−	4.51235i	−0.209450	−	0.644621i	0.790051	−	0.613041i	$-0.210054\pi$
$8$	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	0.922219	−	0.386669i	$-0.126374\pi$
$13$	10.9129	+	7.92871i	0.839456	+	0.609901i	−0.0827624	+	0.996569i	$0.526374\pi$
$14$	−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	$-0.967752\pi$
$17$	−13.3216	−	18.3357i	−0.783626	−	1.07857i	0.211246	−	0.977433i	$-0.432248\pi$
$18$	7.00228	−	1.34657i	0.389016	−	0.0748097i
$19$	2.54435	−	7.83070i	0.133913	−	0.412142i	−0.861506	−	0.507747i	$-0.830478\pi$
$19$	2.54435	−	7.83070i	0.133913	−	0.412142i	0.995419	+	0.0956047i	$0.0304785\pi$
$20$	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	0.762484	−	0.647007i	$-0.223979\pi$
$29$	51.0298	−	16.5806i	1.75965	−	0.571744i	0.997164	+	0.0752622i	$0.0239794\pi$
$30$	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	0.644441	−	0.764654i	$-0.277090\pi$
$41$	29.3705	+	9.54305i	0.716353	+	0.232757i	0.0719120	+	0.997411i	$0.477090\pi$
$42$	8.69456	+	7.18186i	0.207013	+	0.170997i
$43$	35.4891			0.825328			0.412664	−	0.910883i	$-0.364598\pi$
$43$	35.4891			0.825328			0.412664	+	0.910883i	$0.364598\pi$
$44$		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	−0.874120	−	0.485709i	$-0.838561\pi$
$61$	−41.6204	+	30.2390i	−0.682301	+	0.495721i	0.191819	+	0.981430i	$0.438561\pi$
$62$	−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	$-0.893437\pi$
$73$	−27.2657	−	83.9152i	−0.373503	−	1.14952i	0.570980	−	0.820964i	$-0.306563\pi$
$74$	−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	0.952998	−	0.302976i	$-0.0979801\pi$
$79$	75.7882	+	55.0633i	0.959344	+	0.697004i	0.00634552	+	0.999980i	$0.497980\pi$
$80$	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	0.912661	−	0.408718i	$-0.134024\pi$
$83$	20.0793	+	27.6368i	0.241919	+	0.332973i	−0.670742	+	0.741691i	$0.734024\pi$
$84$	−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	−0.988585	−	0.150663i	$-0.951859\pi$
$101$	−54.5204	+	75.0409i	−0.539806	+	0.742979i	0.448779	+	0.893643i	$0.351859\pi$
$102$	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	−0.0912630	−	0.995827i	$-0.529090\pi$
$107$	−80.2959	−	26.0897i	−0.750429	−	0.243829i	−0.659166	+	0.751998i	$0.729090\pi$
$108$	66.2343	−	62.4773i	0.613280	−	0.578494i
$109$	167.723			1.53874			0.769371	−	0.638803i	$-0.220570\pi$
$109$	167.723			1.53874			0.769371	+	0.638803i	$0.220570\pi$
$110$		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	−0.0961504	−	0.995367i	$-0.530653\pi$
$127$	104.240	−	75.7348i	0.820788	−	0.596337i	0.916938	+	0.399030i	$0.130653\pi$
$128$	−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	$-0.840308\pi$
$131$		−	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
$135$	−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	$-0.943897\pi$
$139$	−40.4611	−	124.526i	−0.291087	−	0.895873i	0.693421	−	0.720533i	$-0.256103\pi$
$140$	−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	0.636833	−	0.771001i	$-0.280244\pi$
$149$	−43.6905	−	60.1348i	−0.293225	−	0.403589i	−0.930058	+	0.367412i	$0.880244\pi$
$150$	11.0428	+	42.8763i	0.0736188	+	0.285842i
$151$	−1.92632	+	5.92859i	−0.0127571	+	0.0392622i	−0.957232	−	0.289320i	$-0.906571\pi$
$151$	−1.92632	+	5.92859i	−0.0127571	+	0.0392622i	0.944475	+	0.328582i	$0.106571\pi$
$152$	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	−0.905576	−	0.424184i	$-0.860561\pi$
$167$	−37.1265	+	51.1002i	−0.222314	+	0.305989i	0.683262	+	0.730174i	$0.260561\pi$
$168$	−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	0.787749	−	0.615996i	$-0.211246\pi$
$173$	183.895	+	59.7512i	1.06298	+	0.345383i	0.275229	+	0.961379i	$0.411246\pi$
$174$	−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	−0.986853	−	0.161622i	$-0.948327\pi$
$193$	−219.652	+	159.587i	−1.13810	+	0.826875i	−0.151243	+	0.988497i	$0.548327\pi$
$194$	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	$0.0872185\pi$
$197$			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
$201$	−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	0.885683	−	0.464290i	$-0.153690\pi$
$211$	151.458	+	110.040i	0.717809	+	0.521519i	−0.167875	+	0.985808i	$0.553690\pi$
$212$	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	0.786895	−	0.617087i	$-0.211688\pi$
$227$	405.472	−	131.746i	1.78622	−	0.580378i	0.999326	+	0.0367091i	$0.0116875\pi$
$228$	−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	−0.969529	−	0.244976i	$-0.921220\pi$
$233$	−101.807	+	140.126i	−0.436942	+	0.601399i	0.532587	+	0.846375i	$0.321220\pi$
$234$	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	−0.0300341	−	0.999549i	$-0.509562\pi$
$239$	−153.403	−	49.8436i	−0.641852	−	0.208550i	−0.611818	+	0.790998i	$0.709562\pi$
$240$	−51.7391	−	42.7374i	−0.215580	−	0.178073i
$241$	−56.7011			−0.235274			−0.117637	−	0.993057i	$-0.537532\pi$
$241$	−56.7011			−0.235274			−0.117637	+	0.993057i	$0.537532\pi$
$242$		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	$0.0896488\pi$
$263$			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
$267$	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	0.997187	−	0.0749520i	$-0.0238804\pi$
$271$	39.6717	+	122.097i	0.146390	+	0.450542i	−0.850797	+	0.525494i	$0.823880\pi$
$272$	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	0.186606	−	0.982435i	$-0.440251\pi$
$277$	−191.152	−	138.880i	−0.690080	−	0.501373i	−0.876687	+	0.481062i	$0.840251\pi$
$278$	−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	0.540513	−	0.841335i	$-0.318230\pi$
$281$	−119.895	−	165.021i	−0.426672	−	0.587264i	−0.967185	+	0.254072i	$0.918230\pi$
$282$	72.0141	−	18.5473i	0.255369	−	0.0657705i
$283$	148.085	−	455.758i	0.523267	−	1.61045i	−0.244450	−	0.969662i	$-0.578607\pi$
$283$	148.085	−	455.758i	0.523267	−	1.61045i	0.767717	−	0.640789i	$-0.221393\pi$
$284$	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	−0.293792	−	0.955869i	$-0.594917\pi$
$293$	8.89881	−	2.89140i	0.0303714	−	0.00986825i	0.324163	+	0.946001i	$0.394917\pi$
$294$	−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	$-0.462313\pi$
$307$	72.5271			0.236245			0.118122	+	0.992999i	$0.462313\pi$
$308$		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	$0.119784\pi$
$337$	132.652	+	408.262i	0.393627	+	1.21146i	−0.536399	+	0.843965i	$0.680216\pi$
$338$	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	$0.0663876\pi$
$347$	302.906	+	416.915i	0.872929	+	1.20148i	−0.105400	+	0.994430i	$0.533612\pi$
$348$	−135.388	−	525.674i	−0.389045	−	1.51056i
$349$	86.5298	−	266.311i	0.247936	−	0.763069i	−0.747203	−	0.664595i	$-0.768604\pi$
$349$	86.5298	−	266.311i	0.247936	−	0.763069i	0.995140	−	0.0984739i	$-0.0313961\pi$
$350$	−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	−0.449642	−	0.893209i	$-0.648448\pi$
$359$	−103.534	+	33.6402i	−0.288395	+	0.0937052i	0.161247	+	0.986914i	$0.448448\pi$
$360$	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	$-0.589535\pi$
$373$	−207.081			−0.555178			−0.277589	+	0.960700i	$0.589535\pi$
$374$		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	0.962993	−	0.269526i	$-0.0868669\pi$
$409$	410.734	+	298.416i	1.00424	+	0.729623i	0.0412471	+	0.999149i	$0.486867\pi$
$410$	−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	$-0.426039\pi$
$431$	467.467	−	643.414i	1.08461	−	1.49284i	0.854341	−	0.519712i	$-0.173961\pi$
$432$	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	$-0.593758\pi$
$439$	−254.891			−0.580618			−0.290309	+	0.956933i	$0.593758\pi$
$440$		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	−0.281239	−	0.959638i	$-0.590745\pi$
$457$	248.847	−	180.798i	0.544524	−	0.395620i	0.825762	+	0.564018i	$0.190745\pi$
$458$	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	$-0.805840\pi$
$461$		−	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
$465$	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	$0.00591421\pi$
$479$	339.387	+	467.127i	0.708533	+	0.975213i	−0.291294	+	0.956634i	$0.594086\pi$
$480$	−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	−0.936870	−	0.349677i	$-0.886291\pi$
$491$	−731.236	+	237.593i	−1.48928	+	0.483896i	−0.552409	+	0.833573i	$0.686291\pi$
$492$	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	0.143342	−	0.989673i	$-0.454215\pi$
$503$	−162.170	−	52.6924i	−0.322406	−	0.104756i	−0.465749	+	0.884917i	$0.654215\pi$
$504$	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	−0.325548	−	0.945526i	$-0.605549\pi$
$523$	247.432	−	179.770i	0.473100	−	0.343728i	0.798648	+	0.601798i	$0.205549\pi$
$524$	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	0.329722	−	0.944078i	$-0.393045\pi$
$541$	−252.246	−	183.268i	−0.466259	−	0.338757i	−0.795982	+	0.605321i	$0.793045\pi$
$542$	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	$0.398972\pi$
$547$	−272.857	+	839.767i	−0.498824	+	1.53522i	−0.810911	+	0.585170i	$0.801028\pi$
$548$	−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	−0.0191464	−	0.999817i	$-0.506095\pi$
$557$	308.044	−	100.090i	0.553041	−	0.179694i	0.572188	+	0.820123i	$0.306095\pi$
$558$	−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	−0.468060	−	0.883697i	$-0.655047\pi$
$563$	291.084	−	400.643i	0.517024	−	0.711622i	0.985084	+	0.172074i	$0.0550470\pi$
$564$	−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	0.726366	−	0.687308i	$-0.241208\pi$
$569$	517.800	+	168.244i	0.910018	+	0.295683i	0.183652	+	0.982991i	$0.441208\pi$
$570$	31.4617	−	38.0884i	0.0551960	−	0.0668218i
$571$	779.886			1.36582			0.682912	−	0.730500i	$-0.260713\pi$
$571$	779.886			1.36582			0.682912	+	0.730500i	$0.260713\pi$
$572$		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	$0.300999\pi$
$593$			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
$597$	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	0.833877	−	0.551950i	$-0.186116\pi$
$601$	−99.2684	−	305.517i	−0.165172	−	0.508347i	−0.999049	+	0.0436032i	$0.986116\pi$
$602$	−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	0.869518	−	0.493902i	$-0.164430\pi$
$607$	405.771	+	294.810i	0.668485	+	0.485683i	−0.201033	+	0.979585i	$0.564430\pi$
$608$	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	−0.999970	−	0.00779866i	$-0.997518\pi$
$613$	−114.259	+	351.653i	−0.186393	+	0.573659i	0.813576	+	0.581458i	$0.197518\pi$
$614$	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	$0.0127065\pi$
$659$			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
$663$	−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	0.436485	−	0.899712i	$-0.356223\pi$
$673$	−191.341	−	139.018i	−0.284311	−	0.206564i	−0.720796	+	0.693148i	$0.756223\pi$
$674$	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	0.661143	−	0.750260i	$-0.270072\pi$
$677$	−173.786	−	239.196i	−0.256701	−	0.353318i	−0.917844	+	0.396942i	$0.870072\pi$
$678$	−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	0.987973	−	0.154624i	$-0.0494166\pi$
$701$	1189.16	+	386.381i	1.69637	+	0.551186i	0.708401	+	0.705810i	$0.249417\pi$
$702$	−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	$0.00870596\pi$
$733$	151.721	+	466.948i	0.206986	+	0.637037i	−0.792640	+	0.609690i	$0.791294\pi$
$734$	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	0.710080	−	0.704121i	$-0.248659\pi$
$739$	192.027	+	139.516i	0.259847	+	0.188790i	−0.450232	+	0.892911i	$0.648659\pi$
$740$	−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	0.700937	−	0.713223i	$-0.252765\pi$
$743$	−144.127	−	198.374i	−0.193980	−	0.266991i	−0.894917	+	0.446232i	$0.852765\pi$
$744$	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	−0.462765	−	0.886481i	$-0.653143\pi$
$761$	398.255	−	548.151i	0.523331	−	0.720303i	0.986096	+	0.166178i	$0.0531426\pi$
$762$	−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	$-0.365106\pi$
$769$	632.440			0.822419			0.411209	+	0.911541i	$0.365106\pi$
$770$		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	−0.952156	−	0.305613i	$-0.901139\pi$
$787$	−752.162	+	546.477i	−0.955733	+	0.694380i	−0.00357686	+	0.999994i	$0.501139\pi$
$788$	−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	0.682947	−	0.730468i	$-0.260698\pi$
$809$	−180.254	−	248.099i	−0.222811	−	0.306673i	−0.905758	+	0.423794i	$0.860698\pi$
$810$	−10.6539	−	161.649i	−0.0131529	−	0.199567i
$811$	−402.918	+	1240.05i	−0.496816	+	1.52904i	0.317291	+	0.948328i	$0.397227\pi$
$811$	−402.918	+	1240.05i	−0.496816	+	1.52904i	−0.814107	+	0.580714i	$0.802773\pi$
$812$	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	−0.961791	−	0.273786i	$-0.911724\pi$
$821$	−1296.33	+	421.204i	−1.57897	+	0.513038i	−0.617178	+	0.786824i	$0.711724\pi$
$822$	−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	−0.972988	−	0.230856i	$-0.925847\pi$
$827$	−374.434	+	515.364i	−0.452761	+	0.623172i	0.520227	+	0.854028i	$0.325847\pi$
$828$	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	0.227408	−	0.973800i	$-0.426975\pi$
$853$	1043.92	−	758.451i	1.22382	−	0.889157i	0.996411	+	0.0846431i	$0.0269750\pi$
$854$	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	$0.117504\pi$
$857$			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
$861$	−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	$-0.625389\pi$
$877$	411.721	−	1267.15i	0.469466	−	1.44487i	0.853278	−	0.521456i	$-0.174611\pi$
$878$	−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	0.267653	−	0.963515i	$-0.413752\pi$
$887$	931.819	−	302.766i	1.05053	−	0.341337i	0.782876	+	0.622178i	$0.213752\pi$
$888$	−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	−0.670677	−	0.741750i	$-0.733996\pi$
$919$	−158.510	+	115.164i	−0.172481	+	0.125315i	0.498196	+	0.867065i	$0.333996\pi$
$920$	−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	0.435933	−	0.899979i	$-0.356419\pi$
$937$	−267.314	−	194.215i	−0.285288	−	0.207274i	−0.721220	+	0.692706i	$0.756419\pi$
$938$	−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	0.991212	−	0.132281i	$-0.0422301\pi$
$941$	526.117	+	724.138i	0.559104	+	0.769541i	−0.432108	+	0.901822i	$0.642230\pi$
$942$	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	−0.310030	−	0.950727i	$-0.600339\pi$
$953$	−1.93085	+	0.627370i	−0.00202607	+	0.000658311i	0.308004	+	0.951385i	$0.400339\pi$
$954$	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	$-0.586766\pi$
$967$	−520.674			−0.538442			−0.269221	+	0.963078i	$0.586766\pi$
$968$		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	0.897063	−	0.441903i	$-0.145697\pi$
$997$	−88.1554	−	271.314i	−0.0884206	−	0.272131i	−0.985483	+	0.169773i	$0.945697\pi$
$998$	−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.m.323.3		16
3.2	odd	2	inner	363.3.h.m.323.2		16
11.2	odd	10		363.3.h.l.269.3		16
11.3	even	5	inner	363.3.h.m.245.2		16
11.4	even	5	inner	363.3.h.m.251.3		16
11.5	even	5		33.3.b.b.23.3	yes	4
11.6	odd	10		363.3.b.h.122.2		4
11.7	odd	10		363.3.h.l.251.2		16
11.8	odd	10		363.3.h.l.245.3		16
11.9	even	5	inner	363.3.h.m.269.2		16
11.10	odd	2		363.3.h.l.323.2		16
33.2	even	10		363.3.h.l.269.2		16
33.5	odd	10		33.3.b.b.23.2	✓	4
33.8	even	10		363.3.h.l.245.2		16
33.14	odd	10	inner	363.3.h.m.245.3		16
33.17	even	10		363.3.b.h.122.3		4
33.20	odd	10	inner	363.3.h.m.269.3		16
33.26	odd	10	inner	363.3.h.m.251.2		16
33.29	even	10		363.3.h.l.251.3		16
33.32	even	2		363.3.h.l.323.3		16
44.27	odd	10		528.3.i.d.353.2		4
132.71	even	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	33.5	odd	10
33.3.b.b.23.3	yes	4	11.5	even	5
363.3.b.h.122.2		4	11.6	odd	10
363.3.b.h.122.3		4	33.17	even	10
363.3.h.l.245.2		16	33.8	even	10
363.3.h.l.245.3		16	11.8	odd	10
363.3.h.l.251.2		16	11.7	odd	10
363.3.h.l.251.3		16	33.29	even	10
363.3.h.l.269.2		16	33.2	even	10
363.3.h.l.269.3		16	11.2	odd	10
363.3.h.l.323.2		16	11.10	odd	2
363.3.h.l.323.3		16	33.32	even	2
363.3.h.m.245.2		16	11.3	even	5	inner
363.3.h.m.245.3		16	33.14	odd	10	inner
363.3.h.m.251.2		16	33.26	odd	10	inner
363.3.h.m.251.3		16	11.4	even	5	inner
363.3.h.m.269.2		16	11.9	even	5	inner
363.3.h.m.269.3		16	33.20	odd	10	inner
363.3.h.m.323.2		16	3.2	odd	2	inner
363.3.h.m.323.3		16	1.1	even	1	trivial
528.3.i.d.353.1		4	132.71	even	10
528.3.i.d.353.2		4	44.27	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)

\(f(q)\)	\(=\)	\(q+(0.465695 - 0.640974i) q^{2} +(-2.79015 - 1.10230i) q^{3} +(1.04209 + 3.20723i) q^{4} +(-1.48377 - 2.04223i) q^{5} +(-2.00590 + 1.27508i) q^{6} +(-1.46615 - 4.51235i) q^{7} +(5.55509 + 1.80496i) q^{8} +(6.56989 + 6.15114i) q^{9} +O(q^{10})\)	\(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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