LMFDB - Embedded newform 405.3.l.o.217.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(28,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("405.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.l (of order $12$, 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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			217.2
Character	$\chi$	$=$	405.217
Dual form			405.3.l.o.28.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.53204 + 0.678458i) q^{2} +(2.48682 - 1.43577i) q^{4} +(-1.78324 - 4.67119i) q^{5} +(-2.47213 + 0.662404i) q^{7} +(2.09171 - 2.09171i) q^{8} +O(q^{10})$	\(q+(-2.53204 + 0.678458i) q^{2} +(2.48682 - 1.43577i) q^{4} +(-1.78324 - 4.67119i) q^{5} +(-2.47213 + 0.662404i) q^{7} +(2.09171 - 2.09171i) q^{8} +(7.68445 + 10.6178i) q^{10} +(1.02939 - 1.78296i) q^{11} +(22.3537 + 5.98966i) q^{13} +(5.81011 - 3.35447i) q^{14} +(-9.62022 + 16.6627i) q^{16} +(-14.0526 - 14.0526i) q^{17} -7.13001i q^{19} +(-11.1413 - 9.05609i) q^{20} +(-1.39680 + 5.21291i) q^{22} +(-17.1676 - 4.60004i) q^{23} +(-18.6401 + 16.6597i) q^{25} -60.6642 q^{26} +(-5.19667 + 5.19667i) q^{28} +(31.6437 + 18.2695i) q^{29} +(11.0528 + 19.1440i) q^{31} +(9.99135 - 37.2882i) q^{32} +(45.1160 + 26.0477i) q^{34} +(7.50262 + 10.3666i) q^{35} +(-39.3412 - 39.3412i) q^{37} +(4.83742 + 18.0535i) q^{38} +(-13.5008 - 6.04075i) q^{40} +(-7.34318 - 12.7188i) q^{41} +(-17.1995 - 64.1894i) q^{43} -5.91185i q^{44} +46.5899 q^{46} +(-76.8895 + 20.6025i) q^{47} +(-36.7626 + 21.2249i) q^{49} +(35.8945 - 54.8297i) q^{50} +(64.1894 - 17.1995i) q^{52} +(21.4083 - 21.4083i) q^{53} +(-10.1642 - 1.62904i) q^{55} +(-3.78541 + 6.55652i) q^{56} +(-92.5183 - 24.7902i) q^{58} +(-31.9959 + 18.4728i) q^{59} +(23.1679 - 40.1281i) q^{61} +(-40.9745 - 40.9745i) q^{62} +24.2323i q^{64} +(-11.8832 - 115.100i) q^{65} +(28.1742 - 105.148i) q^{67} +(-55.1227 - 14.7701i) q^{68} +(-26.0302 - 21.1583i) q^{70} -102.118 q^{71} +(-10.4292 + 10.4292i) q^{73} +(126.305 + 72.9220i) q^{74} +(-10.2370 - 17.7311i) q^{76} +(-1.36374 + 5.08956i) q^{77} +(-63.6806 - 36.7660i) q^{79} +(94.9899 + 15.2242i) q^{80} +(27.2224 + 27.2224i) q^{82} +(-20.7497 - 77.4390i) q^{83} +(-40.5833 + 90.7019i) q^{85} +(87.0996 + 150.861i) q^{86} +(-1.57624 - 5.88261i) q^{88} +73.0044i q^{89} -59.2288 q^{91} +(-49.2973 + 13.2092i) q^{92} +(180.709 - 104.333i) q^{94} +(-33.3057 + 12.7145i) q^{95} +(-107.093 + 28.6955i) q^{97} +(78.6842 - 78.6842i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{7}+O(q^{10}) $ 32 * q + 8 * q^7	$ 32 q + 8 q^{7} - 64 q^{10} - 28 q^{13} + 20 q^{16} - 176 q^{22} - 64 q^{25} + 160 q^{28} + 208 q^{31} - 352 q^{37} + 252 q^{40} + 188 q^{43} + 376 q^{46} + 188 q^{52} - 272 q^{55} - 504 q^{58} - 296 q^{61} - 304 q^{67} - 684 q^{70} - 112 q^{73} + 732 q^{76} - 152 q^{82} + 788 q^{85} + 1128 q^{88} + 400 q^{91} + 284 q^{97}+O(q^{100}) $ 32 * q + 8 * q^7 - 64 * q^10 - 28 * q^13 + 20 * q^16 - 176 * q^22 - 64 * q^25 + 160 * q^28 + 208 * q^31 - 352 * q^37 + 252 * q^40 + 188 * q^43 + 376 * q^46 + 188 * q^52 - 272 * q^55 - 504 * q^58 - 296 * q^61 - 304 * q^67 - 684 * q^70 - 112 * q^73 + 732 * q^76 - 152 * q^82 + 788 * q^85 + 1128 * q^88 + 400 * q^91 + 284 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.53204	+	0.678458i	−1.26602	+	0.339229i	−0.828505	−	0.559982i	$-0.810808\pi$
$2$	−2.53204	+	0.678458i	−1.26602	+	0.339229i	−0.437515	+	0.899211i	$0.644141\pi$
$3$		0			0
$3$		0			0
$4$	2.48682	−	1.43577i	0.621705	−	0.358941i
$5$	−1.78324	−	4.67119i	−0.356649	−	0.934239i
$5$	−1.78324	−	4.67119i	−0.356649	−	0.934239i
$6$		0			0
$7$	−2.47213	+	0.662404i	−0.353161	+	0.0946292i	−0.431038	−	0.902334i	$-0.641852\pi$
$7$	−2.47213	+	0.662404i	−0.353161	+	0.0946292i	0.0778771	+	0.996963i	$0.475186\pi$
$8$	2.09171	−	2.09171i	0.261464	−	0.261464i
$9$		0			0
$10$	7.68445	+	10.6178i	0.768445	+	1.06178i
$11$	1.02939	−	1.78296i	0.0935809	−	0.162087i	−0.815435	−	0.578849i	$-0.803502\pi$
$11$	1.02939	−	1.78296i	0.0935809	−	0.162087i	0.909015	+	0.416762i	$0.136835\pi$
$12$		0			0
$13$	22.3537	+	5.98966i	1.71952	+	0.460743i	0.977725	−	0.209888i	$-0.0673100\pi$
$13$	22.3537	+	5.98966i	1.71952	+	0.460743i	0.741791	+	0.670631i	$0.233977\pi$
$14$	5.81011	−	3.35447i	0.415008	−	0.239605i
$15$		0			0
$16$	−9.62022	+	16.6627i	−0.601264	+	1.04142i
$17$	−14.0526	−	14.0526i	−0.826626	−	0.826626i	0.160422	−	0.987048i	$-0.448714\pi$
$17$	−14.0526	−	14.0526i	−0.826626	−	0.826626i	−0.987048	+	0.160422i	$0.948714\pi$
$18$		0			0
$19$		−	7.13001i		−	0.375264i	−0.982239	−	0.187632i	$-0.939919\pi$
$19$		−	7.13001i		−	0.375264i	0.982239	−	0.187632i	$-0.0600812\pi$
$20$	−11.1413	−	9.05609i	−0.557067	−	0.452805i
$21$		0			0
$22$	−1.39680	+	5.21291i	−0.0634907	+	0.236951i
$23$	−17.1676	−	4.60004i	−0.746417	−	0.200002i	−0.134489	−	0.990915i	$-0.542939\pi$
$23$	−17.1676	−	4.60004i	−0.746417	−	0.200002i	−0.611928	+	0.790913i	$0.709606\pi$
$24$		0			0
$25$	−18.6401	+	16.6597i	−0.745604	+	0.666390i
$26$	−60.6642			−2.33324
$27$		0			0
$28$	−5.19667	+	5.19667i	−0.185595	+	0.185595i
$29$	31.6437	+	18.2695i	1.09116	+	0.629983i	0.933886	−	0.357571i	$-0.116395\pi$
$29$	31.6437	+	18.2695i	1.09116	+	0.629983i	0.157277	+	0.987554i	$0.449728\pi$
$30$		0			0
$31$	11.0528	+	19.1440i	0.356541	+	0.617548i	0.987381	−	0.158366i	$-0.0506225\pi$
$31$	11.0528	+	19.1440i	0.356541	+	0.617548i	−0.630839	+	0.775914i	$0.717289\pi$
$32$	9.99135	−	37.2882i	0.312230	−	1.16526i
$33$		0			0
$34$	45.1160	+	26.0477i	1.32694	+	0.766110i
$35$	7.50262	+	10.3666i	0.214361	+	0.296187i
$36$		0			0
$37$	−39.3412	−	39.3412i	−1.06327	−	1.06327i	−0.997858	−	0.0654164i	$-0.979162\pi$
$37$	−39.3412	−	39.3412i	−1.06327	−	1.06327i	−0.0654164	−	0.997858i	$-0.520838\pi$
$38$	4.83742	+	18.0535i	0.127300	+	0.475092i
$39$		0			0
$40$	−13.5008	−	6.04075i	−0.337520	−	0.151019i
$41$	−7.34318	−	12.7188i	−0.179102	−	0.310214i	0.762471	−	0.647022i	$-0.223986\pi$
$41$	−7.34318	−	12.7188i	−0.179102	−	0.310214i	−0.941573	+	0.336808i	$0.890653\pi$
$42$		0			0
$43$	−17.1995	−	64.1894i	−0.399988	−	1.49278i	−0.813115	−	0.582103i	$-0.802230\pi$
$43$	−17.1995	−	64.1894i	−0.399988	−	1.49278i	0.413127	−	0.910673i	$-0.364437\pi$
$44$		−	5.91185i		−	0.134360i
$45$		0			0
$46$	46.5899			1.01282
$47$	−76.8895	+	20.6025i	−1.63595	+	0.438351i	−0.955630	−	0.294568i	$-0.904824\pi$
$47$	−76.8895	+	20.6025i	−1.63595	+	0.438351i	−0.680316	+	0.732919i	$0.738158\pi$
$48$		0			0
$49$	−36.7626	+	21.2249i	−0.750257	+	0.433161i
$50$	35.8945	−	54.8297i	0.717890	−	1.09659i
$51$		0			0
$52$	64.1894	−	17.1995i	1.23441	−	0.330759i
$53$	21.4083	−	21.4083i	0.403930	−	0.403930i	−0.475685	−	0.879615i	$-0.657800\pi$
$53$	21.4083	−	21.4083i	0.403930	−	0.403930i	0.879615	+	0.475685i	$0.157800\pi$
$54$		0			0
$55$	−10.1642	−	1.62904i	−0.184803	−	0.0296188i
$56$	−3.78541	+	6.55652i	−0.0675966	+	0.117081i
$57$		0			0
$58$	−92.5183	−	24.7902i	−1.59514	−	0.427417i
$59$	−31.9959	+	18.4728i	−0.542303	+	0.313099i	−0.746012	−	0.665933i	$-0.768034\pi$
$59$	−31.9959	+	18.4728i	−0.542303	+	0.313099i	0.203709	+	0.979032i	$0.434700\pi$
$60$		0			0
$61$	23.1679	−	40.1281i	0.379802	−	0.657837i	−0.611231	−	0.791452i	$-0.709325\pi$
$61$	23.1679	−	40.1281i	0.379802	−	0.657837i	0.991033	+	0.133615i	$0.0426586\pi$
$62$	−40.9745	−	40.9745i	−0.660879	−	0.660879i
$63$		0			0
$64$			24.2323i			0.378629i
$65$	−11.8832	−	115.100i	−0.182819	−	1.77076i
$66$		0			0
$67$	28.1742	−	105.148i	0.420511	−	1.56937i	−0.353025	−	0.935614i	$-0.614847\pi$
$67$	28.1742	−	105.148i	0.420511	−	1.56937i	0.773535	−	0.633753i	$-0.218487\pi$
$68$	−55.1227	−	14.7701i	−0.810628	−	0.217207i
$69$		0			0
$70$	−26.0302	−	21.1583i	−0.371860	−	0.302262i
$71$	−102.118			−1.43828			−0.719140	−	0.694865i	$-0.755464\pi$
$71$	−102.118			−1.43828			−0.719140	+	0.694865i	$0.755464\pi$
$72$		0			0
$73$	−10.4292	+	10.4292i	−0.142865	+	0.142865i	−0.774922	−	0.632057i	$-0.782211\pi$
$73$	−10.4292	+	10.4292i	−0.142865	+	0.142865i	0.632057	+	0.774922i	$0.282211\pi$
$74$	126.305	+	72.9220i	1.70682	+	0.985433i
$75$		0			0
$76$	−10.2370	−	17.7311i	−0.134698	−	0.233303i
$77$	−1.36374	+	5.08956i	−0.0177110	+	0.0660982i
$78$		0			0
$79$	−63.6806	−	36.7660i	−0.806084	−	0.465393i	0.0395101	−	0.999219i	$-0.487420\pi$
$79$	−63.6806	−	36.7660i	−0.806084	−	0.465393i	−0.845594	+	0.533826i	$0.820754\pi$
$80$	94.9899	+	15.2242i	1.18737	+	0.190303i
$81$		0			0
$82$	27.2224	+	27.2224i	0.331980	+	0.331980i
$83$	−20.7497	−	77.4390i	−0.249996	−	0.933000i	−0.970806	−	0.239866i	$-0.922896\pi$
$83$	−20.7497	−	77.4390i	−0.249996	−	0.933000i	0.720809	−	0.693133i	$-0.243770\pi$
$84$		0			0
$85$	−40.5833	+	90.7019i	−0.477451	+	1.06708i
$86$	87.0996	+	150.861i	1.01279	+	1.75420i
$87$		0			0
$88$	−1.57624	−	5.88261i	−0.0179118	−	0.0668478i
$89$			73.0044i			0.820274i	0.912024	+	0.410137i	$0.134519\pi$
$89$			73.0044i			0.820274i	−0.912024	+	0.410137i	$0.865481\pi$
$90$		0			0
$91$	−59.2288			−0.650866
$92$	−49.2973	+	13.2092i	−0.535840	+	0.143578i
$93$		0			0
$94$	180.709	−	104.333i	1.92244	−	1.10992i
$95$	−33.3057	+	12.7145i	−0.350586	+	0.133837i
$96$		0			0
$97$	−107.093	+	28.6955i	−1.10405	+	0.295830i	−0.764413	−	0.644727i	$-0.776971\pi$
$97$	−107.093	+	28.6955i	−1.10405	+	0.295830i	−0.339638	+	0.940556i	$0.610305\pi$
$98$	78.6842	−	78.6842i	0.802900	−	0.802900i
$99$		0			0
$100$	−22.4350	+	68.1926i	−0.224350	+	0.681926i
$101$	−30.1560	+	52.2317i	−0.298574	+	0.517146i	−0.975810	−	0.218620i	$-0.929844\pi$
$101$	−30.1560	+	52.2317i	−0.298574	+	0.517146i	0.677236	+	0.735766i	$0.263178\pi$
$102$		0			0
$103$	−91.4015	−	24.4910i	−0.887393	−	0.237776i	−0.213799	−	0.976878i	$-0.568584\pi$
$103$	−91.4015	−	24.4910i	−0.887393	−	0.237776i	−0.673594	+	0.739101i	$0.735250\pi$
$104$	59.2861	−	34.2288i	0.570058	−	0.329123i
$105$		0			0
$106$	−39.6820	+	68.7313i	−0.374359	+	0.648408i
$107$	49.2226	+	49.2226i	0.460024	+	0.460024i	0.898663	−	0.438639i	$-0.144539\pi$
$107$	49.2226	+	49.2226i	0.460024	+	0.460024i	−0.438639	+	0.898663i	$0.644539\pi$
$108$		0			0
$109$		−	33.0939i		−	0.303614i	−0.988410	−	0.151807i	$-0.951491\pi$
$109$		−	33.0939i		−	0.303614i	0.988410	−	0.151807i	$-0.0485092\pi$
$110$	26.8413	−	2.77119i	0.244012	−	0.0251926i
$111$		0			0
$112$	12.7449	−	47.5648i	0.113794	−	0.424685i
$113$	9.28610	+	2.48820i	0.0821779	+	0.0220195i	0.299674	−	0.954042i	$-0.403122\pi$
$113$	9.28610	+	2.48820i	0.0821779	+	0.0220195i	−0.217496	+	0.976061i	$0.569789\pi$
$114$		0			0
$115$	9.12629	+	88.3961i	0.0793591	+	0.768662i
$116$	104.923			0.904509
$117$		0			0
$118$	68.4818	−	68.4818i	0.580354	−	0.580354i
$119$	44.0484	+	25.4314i	0.370155	+	0.213709i
$120$		0			0
$121$	58.3807	+	101.118i	0.482485	+	0.835689i
$122$	−31.4370	+	117.324i	−0.257680	+	0.961675i
$123$		0			0
$124$	54.9726	+	31.7384i	0.443327	+	0.255955i
$125$	111.061	+	57.3631i	0.888485	+	0.458905i
$126$		0			0
$127$	111.358	+	111.358i	0.876835	+	0.876835i	0.993206	−	0.116371i	$-0.0371260\pi$
$127$	111.358	+	111.358i	0.876835	+	0.876835i	−0.116371	+	0.993206i	$0.537126\pi$
$128$	23.5248	+	87.7958i	0.183788	+	0.685905i
$129$		0			0
$130$	108.179	+	283.374i	0.832146	+	2.17980i
$131$	−26.5948	−	46.0636i	−0.203014	−	0.351630i	0.746484	−	0.665403i	$-0.231740\pi$
$131$	−26.5948	−	46.0636i	−0.203014	−	0.351630i	−0.949498	+	0.313773i	$0.898407\pi$
$132$		0			0
$133$	4.72295	+	17.6263i	0.0355109	+	0.132529i
$134$			285.353i			2.12950i
$135$		0			0
$136$	−58.7881			−0.432265
$137$	−27.3871	+	7.33836i	−0.199906	+	0.0535647i	−0.357383	−	0.933958i	$-0.616331\pi$
$137$	−27.3871	+	7.33836i	−0.199906	+	0.0535647i	0.157477	+	0.987523i	$0.449664\pi$
$138$		0			0
$139$	113.006	−	65.2439i	0.812991	−	0.469381i	−0.0350022	−	0.999387i	$-0.511144\pi$
$139$	113.006	−	65.2439i	0.812991	−	0.469381i	0.847994	+	0.530006i	$0.177810\pi$
$140$	33.5416	+	15.0077i	0.239583	+	0.107198i
$141$		0			0
$142$	258.567	−	69.2827i	1.82089	−	0.487906i
$143$	33.6900	−	33.6900i	0.235594	−	0.235594i
$144$		0			0
$145$	28.9120	−	180.393i	0.199393	−	1.24409i
$146$	19.3313	−	33.4828i	0.132406	−	0.229334i
$147$		0			0
$148$	−154.319	−	41.3497i	−1.04270	−	0.279390i
$149$	−143.708	+	82.9697i	−0.964482	+	0.556844i	−0.897549	−	0.440914i	$-0.854654\pi$
$149$	−143.708	+	82.9697i	−0.964482	+	0.556844i	−0.0669323	+	0.997758i	$0.521321\pi$
$150$		0			0
$151$	−44.7735	+	77.5500i	−0.296513	+	0.513576i	−0.975336	−	0.220726i	$-0.929157\pi$
$151$	−44.7735	+	77.5500i	−0.296513	+	0.513576i	0.678822	+	0.734302i	$0.262491\pi$
$152$	−14.9139	−	14.9139i	−0.0981179	−	0.0981179i
$153$		0			0
$154$		−	13.8122i		−	0.0896897i
$155$	69.7154	−	85.7681i	0.449777	−	0.553342i
$156$		0			0
$157$	−21.4143	+	79.9192i	−0.136397	+	0.509040i	0.863591	+	0.504192i	$0.168210\pi$
$157$	−21.4143	+	79.9192i	−0.136397	+	0.509040i	−0.999988	+	0.00484755i	$0.998457\pi$
$158$	186.186	+	49.8884i	1.17839	+	0.315750i
$159$		0			0
$160$	−191.998	+	19.8224i	−1.19998	+	0.123890i
$161$	45.4875			0.282531
$162$		0			0
$163$	−32.4956	+	32.4956i	−0.199360	+	0.199360i	−0.799725	−	0.600366i	$-0.795022\pi$
$163$	−32.4956	+	32.4956i	−0.199360	+	0.199360i	0.600366	+	0.799725i	$0.295022\pi$
$164$	−36.5223	−	21.0862i	−0.222697	−	0.128574i
$165$		0			0
$166$	105.078	+	182.001i	0.633001	+	1.09639i
$167$	−28.7775	+	107.399i	−0.172320	+	0.643108i	0.824672	+	0.565611i	$0.191360\pi$
$167$	−28.7775	+	107.399i	−0.172320	+	0.643108i	−0.996993	+	0.0774974i	$0.975307\pi$
$168$		0			0
$169$	317.454	+	183.282i	1.87843	+	1.08451i
$170$	41.2212	−	257.195i	0.242478	−	1.51291i
$171$		0			0
$172$	−134.933	−	134.933i	−0.784494	−	0.784494i
$173$	−72.4603	−	270.425i	−0.418846	−	1.56315i	−0.777006	−	0.629493i	$-0.783263\pi$
$173$	−72.4603	−	270.425i	−0.418846	−	1.56315i	0.358161	−	0.933660i	$-0.383404\pi$
$174$		0			0
$175$	35.0452	−	53.5323i	0.200258	−	0.305899i
$176$	19.8059	+	34.3048i	0.112534	+	0.194914i
$177$		0			0
$178$	−49.5304	−	184.850i	−0.278261	−	1.03848i
$179$		−	264.555i		−	1.47796i	−0.673727	−	0.738981i	$-0.735308\pi$
$179$		−	264.555i		−	1.47796i	0.673727	−	0.738981i	$-0.264692\pi$
$180$		0			0
$181$	114.827			0.634403			0.317201	−	0.948358i	$-0.397257\pi$
$181$	114.827			0.634403			0.317201	+	0.948358i	$0.397257\pi$
$182$	149.970	−	40.1842i	0.824009	−	0.220792i
$183$		0			0
$184$	−45.5315	+	26.2876i	−0.247454	+	0.142868i
$185$	−113.615	+	253.925i	−0.614137	+	1.37257i
$186$		0			0
$187$	−39.5209	+	10.5896i	−0.211342	+	0.0566288i
$188$	−161.630	+	161.630i	−0.859734	+	0.859734i
$189$		0			0
$190$	75.7050	−	54.7902i	0.398447	−	0.288370i
$191$	−97.3180	+	168.560i	−0.509518	+	0.882511i	0.490421	+	0.871486i	$0.336843\pi$
$191$	−97.3180	+	168.560i	−0.509518	+	0.882511i	−0.999939	+	0.0110258i	$0.996490\pi$
$192$		0			0
$193$	−193.768	−	51.9201i	−1.00398	−	0.269016i	−0.280869	−	0.959746i	$-0.590623\pi$
$193$	−193.768	−	51.9201i	−1.00398	−	0.269016i	−0.723113	+	0.690730i	$0.757289\pi$
$194$	251.695	−	145.316i	1.29740	−	0.749052i
$195$		0			0
$196$	−60.9480	+	105.565i	−0.310959	+	0.538597i
$197$	66.5728	+	66.5728i	0.337933	+	0.337933i	0.855589	−	0.517656i	$-0.173195\pi$
$197$	66.5728	+	66.5728i	0.337933	+	0.337933i	−0.517656	+	0.855589i	$0.673195\pi$
$198$		0			0
$199$		−	50.9462i		−	0.256011i	−0.991773	−	0.128006i	$-0.959142\pi$
$199$		−	50.9462i		−	0.256011i	0.991773	−	0.128006i	$-0.0408575\pi$
$200$	−4.14231	+	73.8370i	−0.0207115	+	0.369185i
$201$		0			0
$202$	40.9192	−	152.712i	0.202570	−	0.756002i
$203$	−90.3291	−	24.2036i	−0.444971	−	0.119230i
$204$		0			0
$205$	−46.3171	+	56.9821i	−0.225937	+	0.277961i
$206$	248.048			1.20412
$207$		0			0
$208$	−314.851	+	314.851i	−1.51371	+	1.51371i
$209$	−12.7125	−	7.33956i	−0.0608254	−	0.0351175i
$210$		0			0
$211$	−91.3558	−	158.233i	−0.432966	−	0.749919i	0.564161	−	0.825665i	$-0.309200\pi$
$211$	−91.3558	−	158.233i	−0.432966	−	0.749919i	−0.997127	+	0.0757458i	$0.975866\pi$
$212$	22.5013	−	83.9759i	0.106138	−	0.396113i
$213$		0			0
$214$	−158.029	−	91.2381i	−0.738453	−	0.426346i
$215$	−269.170	+	194.807i	−1.25195	+	0.906081i
$216$		0			0
$217$	−40.0049	−	40.0049i	−0.184355	−	0.184355i
$218$	22.4528	+	83.7951i	0.102995	+	0.384381i
$219$		0			0
$220$	−27.6154	+	10.5423i	−0.125525	+	0.0479194i
$221$	−229.958	−	398.299i	−1.04054	−	1.80226i
$222$		0			0
$223$	−99.2520	−	370.413i	−0.445076	−	1.66105i	−0.715736	−	0.698371i	$-0.753908\pi$
$223$	−99.2520	−	370.413i	−0.445076	−	1.66105i	0.270660	−	0.962675i	$-0.412758\pi$
$224$			98.7995i			0.441069i
$225$		0			0
$226$	−25.2009			−0.111508
$227$	−162.180	+	43.4559i	−0.714447	+	0.191436i	−0.597693	−	0.801725i	$-0.703916\pi$
$227$	−162.180	+	43.4559i	−0.714447	+	0.191436i	−0.116755	+	0.993161i	$0.537249\pi$
$228$		0			0
$229$	83.2488	−	48.0637i	0.363532	−	0.209885i	−0.307097	−	0.951678i	$-0.599358\pi$
$229$	83.2488	−	48.0637i	0.363532	−	0.209885i	0.670629	+	0.741793i	$0.266024\pi$
$230$	−83.0812	−	217.631i	−0.361222	−	0.946220i
$231$		0			0
$232$	104.404	−	27.9750i	0.450017	−	0.120582i
$233$	−20.3322	+	20.3322i	−0.0872627	+	0.0872627i	−0.749391	−	0.662128i	$-0.769653\pi$
$233$	−20.3322	+	20.3322i	−0.0872627	+	0.0872627i	0.662128	+	0.749391i	$0.269653\pi$
$234$		0			0
$235$	233.351	+	322.426i	0.992982	+	1.37203i
$236$	−53.0453	+	91.8772i	−0.224768	+	0.389310i
$237$		0			0
$238$	−128.787	−	34.5082i	−0.541120	−	0.144993i
$239$	76.7115	−	44.2894i	0.320968	−	0.185311i	−0.330856	−	0.943681i	$-0.607337\pi$
$239$	76.7115	−	44.2894i	0.320968	−	0.185311i	0.651824	+	0.758370i	$0.274004\pi$
$240$		0			0
$241$	70.5190	−	122.142i	0.292610	−	0.506815i	−0.681816	−	0.731524i	$-0.738810\pi$
$241$	70.5190	−	122.142i	0.292610	−	0.506815i	0.974426	+	0.224708i	$0.0721429\pi$
$242$	−216.427	−	216.427i	−0.894326	−	0.894326i
$243$		0			0
$244$		−	133.055i		−	0.545307i
$245$	164.702	+	133.876i	0.672254	+	0.546433i
$246$		0			0
$247$	42.7064	−	159.382i	0.172900	−	0.645272i
$248$	63.1628	+	16.9244i	0.254689	+	0.0682437i
$249$		0			0
$250$	−320.129	−	69.8956i	−1.28051	−	0.279582i
$251$	−77.6528			−0.309374			−0.154687	−	0.987964i	$-0.549437\pi$
$251$	−77.6528			−0.309374			−0.154687	+	0.987964i	$0.549437\pi$
$252$		0			0
$253$	−25.8738	+	25.8738i	−0.102268	+	0.102268i
$254$	−357.515	−	206.411i	−1.40754	−	0.812643i
$255$		0			0
$256$	−167.596	−	290.285i	−0.654672	−	1.13393i
$257$	36.0405	−	134.505i	0.140236	−	0.523366i	−0.859686	−	0.510823i	$-0.829341\pi$
$257$	36.0405	−	134.505i	0.140236	−	0.523366i	0.999921	−	0.0125431i	$-0.00399269\pi$
$258$		0			0
$259$	123.316	+	71.1965i	0.476124	+	0.274890i
$260$	−194.807	−	269.170i	−0.749259	−	1.03527i
$261$		0			0
$262$	98.5914	+	98.5914i	0.376303	+	0.376303i
$263$	46.1508	+	172.237i	0.175478	+	0.654895i	0.996470	+	0.0839537i	$0.0267548\pi$
$263$	46.1508	+	172.237i	0.175478	+	0.654895i	−0.820991	+	0.570941i	$0.806579\pi$
$264$		0			0
$265$	−138.178	−	61.8261i	−0.521428	−	0.233306i
$266$	−23.9174	−	41.4262i	−0.0899150	−	0.155737i
$267$		0			0
$268$	−80.9031	−	301.935i	−0.301877	−	1.12662i
$269$		−	175.683i		−	0.653096i	−0.945181	−	0.326548i	$-0.894115\pi$
$269$		−	175.683i		−	0.653096i	0.945181	−	0.326548i	$-0.105885\pi$
$270$		0			0
$271$	79.8046			0.294482			0.147241	−	0.989101i	$-0.452961\pi$
$271$	79.8046			0.294482			0.147241	+	0.989101i	$0.452961\pi$
$272$	369.345	−	98.9656i	1.35788	−	0.363844i
$273$		0			0
$274$	64.3666	−	37.1621i	0.234915	−	0.135628i
$275$	10.5157	+	50.3838i	0.0382388	+	0.183214i
$276$		0			0
$277$	279.010	−	74.7606i	1.00726	−	0.269894i	0.282775	−	0.959186i	$-0.408745\pi$
$277$	279.010	−	74.7606i	1.00726	−	0.269894i	0.724483	+	0.689292i	$0.242078\pi$
$278$	−241.870	+	241.870i	−0.870036	+	0.870036i
$279$		0			0
$280$	37.3771	+	5.99051i	0.133490	+	0.0213947i
$281$	145.967	−	252.823i	0.519457	−	0.899726i	−0.480287	−	0.877111i	$-0.659468\pi$
$281$	145.967	−	252.823i	0.519457	−	0.899726i	0.999744	−	0.0226148i	$-0.00719912\pi$
$282$		0			0
$283$	134.470	+	36.0311i	0.475159	+	0.127319i	0.488448	−	0.872593i	$-0.337563\pi$
$283$	134.470	+	36.0311i	0.475159	+	0.127319i	−0.0132884	+	0.999912i	$0.504230\pi$
$284$	−253.949	+	146.617i	−0.894186	+	0.516258i
$285$		0			0
$286$	−62.4471	+	108.162i	−0.218347	+	0.378187i
$287$	26.5782	+	26.5782i	0.0926071	+	0.0926071i
$288$		0			0
$289$			105.954i			0.366622i
$290$	49.1828	+	476.378i	0.169596	+	1.64268i
$291$		0			0
$292$	−10.9616	+	40.9093i	−0.0375398	+	0.140100i
$293$	346.421	+	92.8233i	1.18233	+	0.316803i	0.795848	−	0.605496i	$-0.207025\pi$
$293$	346.421	+	92.8233i	1.18233	+	0.316803i	0.386477	+	0.922299i	$0.373692\pi$
$294$		0			0
$295$	143.347	+	116.517i	0.485920	+	0.394974i
$296$	−164.580			−0.556015
$297$		0			0
$298$	307.582	−	307.582i	1.03216	−	1.03216i
$299$	−356.207	−	205.656i	−1.19133	−	0.687812i
$300$		0			0
$301$	85.0386	+	147.291i	0.282520	+	0.489340i
$302$	60.7539	−	226.737i	0.201172	−	0.750784i
$303$		0			0
$304$	118.805	+	68.5923i	0.390807	+	0.225633i
$305$	−228.760	−	36.6639i	−0.750033	−	0.120209i
$306$		0			0
$307$	−135.946	−	135.946i	−0.442822	−	0.442822i	0.450137	−	0.892959i	$-0.351375\pi$
$307$	−135.946	−	135.946i	−0.442822	−	0.442822i	−0.892959	+	0.450137i	$0.851375\pi$
$308$	3.91603	+	14.6148i	0.0127144	+	0.0474508i
$309$		0			0
$310$	−118.332	+	264.467i	−0.381717	+	0.853120i
$311$	−52.0392	−	90.1345i	−0.167329	−	0.289822i	0.770151	−	0.637861i	$-0.220181\pi$
$311$	−52.0392	−	90.1345i	−0.167329	−	0.289822i	−0.937480	+	0.348040i	$0.886847\pi$
$312$		0			0
$313$	14.9909	+	55.9469i	0.0478943	+	0.178744i	0.985730	−	0.168337i	$-0.0538396\pi$
$313$	14.9909	+	55.9469i	0.0478943	+	0.178744i	−0.937835	+	0.347081i	$0.887173\pi$
$314$		−	216.887i		−	0.690724i
$315$		0			0
$316$	−211.150			−0.668195
$317$	474.566	−	127.160i	1.49705	−	0.401134i	0.584942	−	0.811075i	$-0.301117\pi$
$317$	474.566	−	127.160i	1.49705	−	0.401134i	0.912112	+	0.409941i	$0.134451\pi$
$318$		0			0
$319$	65.1475	−	37.6129i	0.204224	−	0.117909i
$320$	113.194	−	43.2120i	0.353730	−	0.135038i
$321$		0			0
$322$	−115.176	+	30.8614i	−0.357690	+	0.0958428i
$323$	−100.196	+	100.196i	−0.310203	+	0.310203i
$324$		0			0
$325$	−516.461	+	260.759i	−1.58911	+	0.802336i
$326$	60.2333	−	104.327i	0.184765	−	0.320022i
$327$		0			0
$328$	−41.9638	−	11.2442i	−0.127938	−	0.0342810i
$329$	176.433	−	101.864i	0.536272	−	0.309617i
$330$		0			0
$331$	−12.5491	+	21.7357i	−0.0379128	+	0.0656669i	−0.884359	−	0.466807i	$-0.845404\pi$
$331$	−12.5491	+	21.7357i	−0.0379128	+	0.0656669i	0.846446	+	0.532474i	$0.178738\pi$
$332$	−162.785	−	162.785i	−0.490316	−	0.490316i
$333$		0			0
$334$		−	291.463i		−	0.872644i
$335$	−541.406	+	55.8965i	−1.61614	+	0.166855i
$336$		0			0
$337$	−26.8402	+	100.169i	−0.0796444	+	0.297237i	−0.994246	−	0.107119i	$-0.965838\pi$
$337$	−26.8402	+	100.169i	−0.0796444	+	0.297237i	0.914602	+	0.404356i	$0.132504\pi$
$338$	−928.156	−	248.699i	−2.74602	−	0.735795i
$339$		0			0
$340$	29.3033	+	283.827i	0.0861860	+	0.834786i
$341$	45.5105			0.133462
$342$		0			0
$343$	165.499	−	165.499i	0.482504	−	0.482504i
$344$	−170.242	−	98.2892i	−0.494889	−	0.285724i
$345$		0			0
$346$	366.945	+	635.567i	1.06053	+	1.83690i
$347$	9.22343	−	34.4223i	0.0265805	−	0.0991997i	−0.951361	−	0.308077i	$-0.900314\pi$
$347$	9.22343	−	34.4223i	0.0265805	−	0.0991997i	0.977942	+	0.208878i	$0.0669811\pi$
$348$		0			0
$349$	97.4468	+	56.2609i	0.279217	+	0.161206i	0.633069	−	0.774095i	$-0.281795\pi$
$349$	97.4468	+	56.2609i	0.279217	+	0.161206i	−0.353852	+	0.935301i	$0.615128\pi$
$350$	−52.4164	+	159.322i	−0.149761	+	0.455207i
$351$		0			0
$352$	−56.1983	−	56.1983i	−0.159654	−	0.159654i
$353$	2.22178	+	8.29180i	0.00629400	+	0.0234895i	0.969001	−	0.247055i	$-0.0794629\pi$
$353$	2.22178	+	8.29180i	0.00629400	+	0.0234895i	−0.962707	+	0.270545i	$0.912796\pi$
$354$		0			0
$355$	182.101	+	477.012i	0.512961	+	1.34370i
$356$	104.817	+	181.549i	0.294430	+	0.509968i
$357$		0			0
$358$	179.489	+	669.864i	0.501367	+	1.87113i
$359$		−	576.227i		−	1.60509i	−0.596592	−	0.802544i	$-0.703479\pi$
$359$		−	576.227i		−	1.60509i	0.596592	−	0.802544i	$-0.296521\pi$
$360$		0			0
$361$	310.163			0.859177
$362$	−290.746	+	77.9052i	−0.803166	+	0.215208i
$363$		0			0
$364$	−147.291	+	85.0386i	−0.404646	+	0.233623i
$365$	67.3144	+	30.1189i	0.184423	+	0.0825176i
$366$		0			0
$367$	−151.249	+	40.5271i	−0.412123	+	0.110428i	−0.458923	−	0.888476i	$-0.651764\pi$
$367$	−151.249	+	40.5271i	−0.412123	+	0.110428i	0.0467996	+	0.998904i	$0.485098\pi$
$368$	241.805	−	241.805i	0.657079	−	0.657079i
$369$		0			0
$370$	115.401	−	720.031i	0.311895	−	1.94603i
$371$	−38.7431	+	67.1049i	−0.104429	+	0.180876i
$372$		0			0
$373$	95.8703	+	25.6884i	0.257025	+	0.0688696i	0.385031	−	0.922904i	$-0.374191\pi$
$373$	95.8703	+	25.6884i	0.257025	+	0.0688696i	−0.128006	+	0.991773i	$0.540858\pi$
$374$	92.8839	−	53.6265i	0.248353	−	0.143386i
$375$		0			0
$376$	−117.736	+	203.925i	−0.313128	+	0.542353i
$377$	597.927	+	597.927i	1.58601	+	1.58601i
$378$		0			0
$379$			648.160i			1.71018i	0.518476	+	0.855092i	$0.326500\pi$
$379$			648.160i			1.71018i	−0.518476	+	0.855092i	$0.673500\pi$
$380$	−64.5701	+	79.4379i	−0.169921	+	0.209047i
$381$		0			0
$382$	132.052	−	492.826i	0.345687	−	1.29012i
$383$	516.208	+	138.318i	1.34780	+	0.361142i	0.859323	−	0.511433i	$-0.170885\pi$
$383$	516.208	+	138.318i	1.34780	+	0.361142i	0.488479	+	0.872576i	$0.337552\pi$
$384$		0			0
$385$	26.2062	−	2.70561i	0.0680681	−	0.00702757i
$386$	525.855			1.36232
$387$		0			0
$388$	−225.121	+	225.121i	−0.580208	+	0.580208i
$389$	120.396	+	69.5109i	0.309502	+	0.178691i	0.646704	−	0.762741i	$-0.276147\pi$
$389$	120.396	+	69.5109i	0.309502	+	0.178691i	−0.337202	+	0.941432i	$0.609480\pi$
$390$		0			0
$391$	176.607	+	305.893i	0.451681	+	0.782334i
$392$	−32.5004	+	121.293i	−0.0829091	+	0.309421i
$393$		0			0
$394$	−213.732	−	123.398i	−0.542466	−	0.313193i
$395$	−58.1832	+	363.027i	−0.147299	+	0.919057i
$396$		0			0
$397$	−291.864	−	291.864i	−0.735175	−	0.735175i	0.236465	−	0.971640i	$-0.424011\pi$
$397$	−291.864	−	291.864i	−0.735175	−	0.735175i	−0.971640	+	0.236465i	$0.924011\pi$
$398$	34.5649	+	128.998i	0.0868464	+	0.324115i
$399$		0			0
$400$	−98.2747	−	470.865i	−0.245687	−	1.17716i
$401$	−115.801	−	200.573i	−0.288781	−	0.500183i	0.684738	−	0.728789i	$-0.259917\pi$
$401$	−115.801	−	200.573i	−0.288781	−	0.500183i	−0.973519	+	0.228606i	$0.926583\pi$
$402$		0			0
$403$	132.405	+	494.142i	0.328548	+	1.22616i
$404$			173.188i			0.428683i
$405$		0			0
$406$	245.138			0.603788
$407$	−110.641	+	29.6461i	−0.271845	+	0.0728406i
$408$		0			0
$409$	−4.81530	+	2.78012i	−0.0117734	+	0.00679735i	−0.505875	−	0.862607i	$-0.668830\pi$
$409$	−4.81530	+	2.78012i	−0.0117734	+	0.00679735i	0.494102	+	0.869404i	$0.335497\pi$
$410$	78.6169	−	175.705i	0.191749	−	0.428549i
$411$		0			0
$412$	−262.462	+	70.3265i	−0.637044	+	0.170695i
$413$	66.8614	−	66.8614i	0.161892	−	0.161892i
$414$		0			0
$415$	−324.731	+	235.018i	−0.782483	+	0.566309i
$416$	446.688	−	773.686i	1.07377	−	1.85982i
$417$		0			0
$418$	37.1681	+	9.95917i	0.0889190	+	0.0238258i
$419$	−481.905	+	278.228i	−1.15013	+	0.664028i	−0.948919	−	0.315519i	$-0.897821\pi$
$419$	−481.905	+	278.228i	−1.15013	+	0.664028i	−0.201212	+	0.979548i	$0.564488\pi$
$420$		0			0
$421$	296.998	−	514.416i	0.705459	−	1.22189i	−0.261066	−	0.965321i	$-0.584074\pi$
$421$	296.998	−	514.416i	0.705459	−	1.22189i	0.966526	−	0.256570i	$-0.0825925\pi$
$422$	338.671	+	338.671i	0.802537	+	0.802537i
$423$		0			0
$424$		−	89.5598i		−	0.211226i
$425$	496.056	+	27.8291i	1.16719	+	0.0654802i
$426$		0			0
$427$	−30.6931	+	114.548i	−0.0718808	+	0.268263i
$428$	193.080	+	51.7356i	0.451121	+	0.120877i
$429$		0			0
$430$	549.381	−	675.881i	1.27763	−	1.57182i
$431$	−566.825			−1.31514			−0.657569	−	0.753394i	$-0.728415\pi$
$431$	−566.825			−1.31514			−0.657569	+	0.753394i	$0.728415\pi$
$432$		0			0
$433$	347.506	−	347.506i	0.802555	−	0.802555i	−0.180940	−	0.983494i	$-0.557914\pi$
$433$	347.506	−	347.506i	0.802555	−	0.802555i	0.983494	+	0.180940i	$0.0579138\pi$
$434$	128.436	+	74.1524i	0.295935	+	0.170858i
$435$		0			0
$436$	−47.5151	−	82.2986i	−0.108980	−	0.188758i
$437$	−32.7983	+	122.405i	−0.0750534	+	0.280103i
$438$		0			0
$439$	−697.518	−	402.712i	−1.58888	−	0.917340i	−0.993492	−	0.113900i	$-0.963666\pi$
$439$	−697.518	−	402.712i	−1.58888	−	0.917340i	−0.595387	−	0.803439i	$-0.703001\pi$
$440$	−24.6680	+	17.8530i	−0.0560636	+	0.0405751i
$441$		0			0
$442$	852.493	+	852.493i	1.92872	+	1.92872i
$443$	191.992	+	716.524i	0.433391	+	1.61744i	0.744888	+	0.667189i	$0.232503\pi$
$443$	191.992	+	716.524i	0.433391	+	1.61744i	−0.311497	+	0.950247i	$0.600831\pi$
$444$		0			0
$445$	341.018	−	130.185i	0.766332	−	0.292550i
$446$	502.620	+	870.563i	1.12695	+	1.95194i
$447$		0			0
$448$	−16.0516	−	59.9052i	−0.0358294	−	0.133717i
$449$		−	345.404i		−	0.769273i	−0.923068	−	0.384637i	$-0.874327\pi$
$449$		−	345.404i		−	0.769273i	0.923068	−	0.384637i	$-0.125673\pi$
$450$		0			0
$451$	−30.2360			−0.0670421
$452$	26.6653	−	7.14495i	0.0589941	−	0.0158074i
$453$		0			0
$454$	381.162	−	220.064i	0.839564	−	0.484723i
$455$	105.619	+	276.669i	0.232130	+	0.608064i
$456$		0			0
$457$	−452.454	+	121.235i	−0.990053	+	0.265284i	−0.717273	−	0.696793i	$-0.754610\pi$
$457$	−452.454	+	121.235i	−0.990053	+	0.265284i	−0.272780	+	0.962076i	$0.587943\pi$
$458$	−178.180	+	178.180i	−0.389040	+	0.389040i
$459$		0			0
$460$	149.612	+	206.722i	0.325242	+	0.449395i
$461$	−34.6834	+	60.0734i	−0.0752351	+	0.130311i	−0.901188	−	0.433427i	$-0.857304\pi$
$461$	−34.6834	+	60.0734i	−0.0752351	+	0.130311i	0.825953	+	0.563738i	$0.190637\pi$
$462$		0			0
$463$	−221.742	−	59.4157i	−0.478925	−	0.128328i	0.0112769	−	0.999936i	$-0.496410\pi$
$463$	−221.742	−	59.4157i	−0.478925	−	0.128328i	−0.490202	+	0.871609i	$0.663077\pi$
$464$	−608.839	+	351.513i	−1.31215	+	0.757572i
$465$		0			0
$466$	37.6874	−	65.2765i	0.0808743	−	0.140078i
$467$	−104.749	−	104.749i	−0.224303	−	0.224303i	0.586005	−	0.810308i	$-0.300700\pi$
$467$	−104.749	−	104.749i	−0.224303	−	0.224303i	−0.810308	+	0.586005i	$0.800700\pi$
$468$		0			0
$469$			278.601i			0.594032i
$470$	−809.606	−	658.078i	−1.72257	−	1.40017i
$471$		0			0
$472$	−28.2863	+	105.566i	−0.0599286	+	0.223656i
$473$	−132.152	−	35.4100i	−0.279391	−	0.0748625i
$474$		0			0
$475$	118.784	+	132.904i	0.250072	+	0.279798i
$476$	146.054			0.306836
$477$		0			0
$478$	−164.188	+	164.188i	−0.343489	+	0.343489i
$479$	436.864	+	252.223i	0.912033	+	0.526563i	0.881085	−	0.472958i	$-0.156814\pi$
$479$	436.864	+	252.223i	0.912033	+	0.526563i	0.0309484	+	0.999521i	$0.490147\pi$
$480$		0			0
$481$	−643.781	−	1115.06i	−1.33842	−	2.31821i
$482$	−95.6884	+	357.114i	−0.198524	+	0.740900i
$483$		0			0
$484$	290.365	+	167.642i	0.599927	+	0.346368i
$485$	325.015	+	449.081i	0.670134	+	0.925940i
$486$		0			0
$487$	−435.576	−	435.576i	−0.894407	−	0.894407i	0.100527	−	0.994934i	$-0.467947\pi$
$487$	−435.576	−	435.576i	−0.894407	−	0.894407i	−0.994934	+	0.100527i	$0.967947\pi$
$488$	−35.4756	−	132.397i	−0.0726959	−	0.271305i
$489$		0			0
$490$	−507.862	−	227.236i	−1.03645	−	0.463747i
$491$	244.367	+	423.256i	0.497693	+	0.862030i	0.999996	−	0.00266188i	$-0.000847305\pi$
$491$	244.367	+	423.256i	0.497693	+	0.862030i	−0.502303	+	0.864691i	$0.667514\pi$
$492$		0			0
$493$	−187.943	−	701.413i	−0.381223	−	1.42275i
$494$			432.537i			0.875580i
$495$		0			0
$496$	−425.321			−0.857501
$497$	252.448	−	67.6433i	0.507944	−	0.136103i
$498$		0			0
$499$	−451.561	+	260.709i	−0.904932	+	0.522463i	−0.878797	−	0.477196i	$-0.841653\pi$
$499$	−451.561	+	260.709i	−0.904932	+	0.522463i	−0.0261349	+	0.999658i	$0.508320\pi$
$500$	358.548	−	16.8055i	0.717096	−	0.0336110i
$501$		0			0
$502$	196.620	−	52.6842i	0.391673	−	0.104949i
$503$	638.392	−	638.392i	1.26917	−	1.26917i	0.322650	−	0.946518i	$-0.395426\pi$
$503$	638.392	−	638.392i	1.26917	−	1.26917i	0.946518	−	0.322650i	$-0.104574\pi$
$504$		0			0
$505$	297.760	+	47.7226i	0.589624	+	0.0945003i
$506$	47.9592	−	83.0678i	0.0947810	−	0.164166i
$507$		0			0
$508$	436.812	+	117.043i	0.859865	+	0.230400i
$509$	746.883	−	431.213i	1.46735	−	0.847177i	0.468021	−	0.883717i	$-0.344967\pi$
$509$	746.883	−	431.213i	1.46735	−	0.847177i	0.999332	+	0.0365406i	$0.0116338\pi$
$510$		0			0
$511$	18.8739	−	32.6905i	0.0369352	−	0.0639736i
$512$	364.222	+	364.222i	0.711372	+	0.711372i
$513$		0			0
$514$			365.024i			0.710164i
$515$	48.5891	+	470.627i	0.0943477	+	0.913839i
$516$		0			0
$517$	−42.4160	+	158.299i	−0.0820425	+	0.306187i
$518$	−360.545	−	96.6077i	−0.696033	−	0.186501i
$519$		0			0
$520$	−265.611	−	215.898i	−0.510790	−	0.415189i
$521$	810.812			1.55626			0.778130	−	0.628103i	$-0.216168\pi$
$521$	810.812			1.55626			0.778130	+	0.628103i	$0.216168\pi$
$522$		0			0
$523$	81.0491	−	81.0491i	0.154970	−	0.154970i	−0.625364	−	0.780333i	$-0.715049\pi$
$523$	81.0491	−	81.0491i	0.154970	−	0.154970i	0.780333	+	0.625364i	$0.215049\pi$
$524$	−132.273	−	76.3679i	−0.252429	−	0.145740i
$525$		0			0
$526$	−233.712	−	404.800i	−0.444319	−	0.769582i
$527$	113.703	−	424.345i	0.215755	−	0.805208i
$528$		0			0
$529$	−184.562	−	106.557i	−0.348888	−	0.201431i
$530$	391.820	+	62.7978i	0.739283	+	0.118486i
$531$		0			0
$532$	37.0524	+	37.0524i	0.0696473	+	0.0696473i
$533$	−87.9663	−	328.295i	−0.165040	−	0.615938i
$534$		0			0
$535$	142.152	−	317.704i	0.265705	−	0.593839i
$536$	−161.006	−	278.870i	−0.300384	−	0.520281i
$537$		0			0
$538$	119.193	+	444.836i	0.221549	+	0.826832i
$539$			87.3948i			0.162143i
$540$		0			0
$541$	−473.428			−0.875098			−0.437549	−	0.899195i	$-0.644153\pi$
$541$	−473.428			−0.875098			−0.437549	+	0.899195i	$0.644153\pi$
$542$	−202.069	+	54.1441i	−0.372820	+	0.0998969i
$543$		0			0
$544$	−664.403	+	383.593i	−1.22133	+	0.705135i
$545$	−154.588	+	59.0145i	−0.283648	+	0.108283i
$546$		0			0
$547$	−61.3233	+	16.4315i	−0.112108	+	0.0300394i	−0.314437	−	0.949278i	$-0.601816\pi$
$547$	−61.3233	+	16.4315i	−0.112108	+	0.0300394i	0.202329	+	0.979318i	$0.435149\pi$
$548$	−57.5707	+	57.5707i	−0.105056	+	0.105056i
$549$		0			0
$550$	−60.8094	−	120.439i	−0.110563	−	0.218981i
$551$	130.262	−	225.620i	0.236410	−	0.409474i
$552$		0			0
$553$	181.781	+	48.7080i	0.328717	+	0.0880795i
$554$	−655.744	+	378.594i	−1.18365	+	0.683382i
$555$		0			0
$556$	187.350	−	324.500i	0.336960	−	0.583633i
$557$	−245.069	−	245.069i	−0.439981	−	0.439981i	0.452025	−	0.892005i	$-0.350702\pi$
$557$	−245.069	−	245.069i	−0.439981	−	0.439981i	−0.892005	+	0.452025i	$0.850702\pi$
$558$		0			0
$559$		−	1537.89i		−	2.75114i
$560$	−244.912	+	25.2855i	−0.437342	+	0.0451526i
$561$		0			0
$562$	−198.066	+	739.191i	−0.352430	+	1.31529i
$563$	125.838	+	33.7181i	0.223513	+	0.0598901i	0.368837	−	0.929494i	$-0.379756\pi$
$563$	125.838	+	33.7181i	0.223513	+	0.0598901i	−0.145324	+	0.989384i	$0.546423\pi$
$564$		0			0
$565$	−4.93649	−	47.8142i	−0.00873716	−	0.0846270i
$566$	−364.929			−0.644751
$567$		0			0
$568$	−213.601	+	213.601i	−0.376058	+	0.376058i
$569$	−45.7087	−	26.3899i	−0.0803316	−	0.0463794i	0.459296	−	0.888283i	$-0.348102\pi$
$569$	−45.7087	−	26.3899i	−0.0803316	−	0.0463794i	−0.539628	+	0.841904i	$0.681435\pi$
$570$		0			0
$571$	−93.9063	−	162.650i	−0.164459	−	0.284852i	0.772004	−	0.635618i	$-0.219255\pi$
$571$	−93.9063	−	162.650i	−0.164459	−	0.284852i	−0.936463	+	0.350766i	$0.885921\pi$
$572$	35.4100	−	132.152i	0.0619055	−	0.231035i
$573$		0			0
$574$	−85.3294	−	49.2649i	−0.148657	−	0.0858274i
$575$	396.641	−	200.262i	0.689810	−	0.348282i
$576$		0			0
$577$	115.526	+	115.526i	0.200218	+	0.200218i	0.800093	−	0.599875i	$-0.204783\pi$
$577$	115.526	+	115.526i	0.200218	+	0.200218i	−0.599875	+	0.800093i	$0.704783\pi$
$578$	−71.8852	−	268.279i	−0.124369	−	0.464151i
$579$		0			0
$580$	−187.103	−	490.116i	−0.322592	−	0.845027i
$581$	102.592	+	177.694i	0.176578	+	0.305842i
$582$		0			0
$583$	−16.1326	−	60.2075i	−0.0276716	−	0.103272i
$584$			43.6296i			0.0747081i
$585$		0			0
$586$	−940.129			−1.60432
$587$	−782.587	+	209.694i	−1.33320	+	0.357229i	−0.853906	−	0.520427i	$-0.825773\pi$
$587$	−782.587	+	209.694i	−1.33320	+	0.357229i	−0.479291	+	0.877656i	$0.659106\pi$
$588$		0			0
$589$	136.497	−	78.8065i	0.231743	−	0.133797i
$590$	−442.011	−	197.772i	−0.749172	−	0.335207i
$591$		0			0
$592$	1034.00	−	277.060i	1.74662	−	0.468006i
$593$	374.017	−	374.017i	0.630721	−	0.630721i	−0.317528	−	0.948249i	$-0.602853\pi$
$593$	374.017	−	374.017i	0.630721	−	0.630721i	0.948249	+	0.317528i	$0.102853\pi$
$594$		0			0
$595$	40.2458	−	251.109i	0.0676400	−	0.422032i
$596$	−238.250	+	412.661i	−0.399749	+	0.692385i
$597$		0			0
$598$	1041.46	+	279.058i	1.74157	+	0.466652i
$599$	468.661	−	270.581i	0.782405	−	0.451722i	−0.0548770	−	0.998493i	$-0.517477\pi$
$599$	468.661	−	270.581i	0.782405	−	0.451722i	0.837282	+	0.546771i	$0.184143\pi$
$600$		0			0
$601$	−457.889	+	793.087i	−0.761878	+	1.31961i	0.180003	+	0.983666i	$0.442389\pi$
$601$	−457.889	+	793.087i	−0.761878	+	1.31961i	−0.941881	+	0.335946i	$0.890944\pi$
$602$	−315.252	−	315.252i	−0.523675	−	0.523675i
$603$		0			0
$604$			257.137i			0.425724i
$605$	368.236	−	453.026i	0.608655	−	0.748804i
$606$		0			0
$607$	−289.094	+	1078.91i	−0.476266	+	1.77745i	0.140258	+	0.990115i	$0.455207\pi$
$607$	−289.094	+	1078.91i	−0.476266	+	1.77745i	−0.616524	+	0.787336i	$0.711460\pi$
$608$	−265.866	−	71.2385i	−0.437279	−	0.117169i
$609$		0			0
$610$	604.104	−	62.3697i	0.990335	−	0.102245i
$611$	−1842.17			−3.01500
$612$		0			0
$613$	54.2959	−	54.2959i	0.0885741	−	0.0885741i	−0.661432	−	0.750006i	$-0.730051\pi$
$613$	54.2959	−	54.2959i	0.0885741	−	0.0885741i	0.750006	+	0.661432i	$0.230051\pi$
$614$	436.456	+	251.988i	0.710840	+	0.410404i
$615$		0			0
$616$	7.79333	+	13.4984i	0.0126515	+	0.0219131i
$617$	−200.040	+	746.561i	−0.324214	+	1.20998i	0.590885	+	0.806756i	$0.298779\pi$
$617$	−200.040	+	746.561i	−0.324214	+	1.20998i	−0.915099	+	0.403229i	$0.867888\pi$
$618$		0			0
$619$	667.402	+	385.325i	1.07819	+	0.622495i	0.930409	−	0.366524i	$-0.119452\pi$
$619$	667.402	+	385.325i	1.07819	+	0.622495i	0.147785	+	0.989019i	$0.452786\pi$
$620$	50.2269	−	313.385i	0.0810111	−	0.505459i
$621$		0			0
$622$	192.918	+	192.918i	0.310157	+	0.310157i
$623$	−48.3584	−	180.476i	−0.0776218	−	0.289689i
$624$		0			0
$625$	69.9059	−	621.078i	0.111849	−	0.993725i
$626$	−75.9152	−	131.489i	−0.121270	−	0.210046i
$627$		0			0
$628$	61.4918	+	229.491i	0.0979169	+	0.365431i
$629$			1105.69i			1.75786i
$630$		0			0
$631$	1187.77			1.88236			0.941181	−	0.337903i	$-0.109718\pi$
$631$	1187.77			1.88236			0.941181	+	0.337903i	$0.109718\pi$
$632$	−210.105	+	56.2975i	−0.332445	+	0.0890784i
$633$		0			0
$634$	−1115.35	+	643.946i	−1.75922	+	1.01569i
$635$	321.597	−	718.754i	0.506451	−	1.13190i
$636$		0			0
$637$	−948.911	+	254.260i	−1.48966	+	0.399152i
$638$	−139.437	+	139.437i	−0.218554	+	0.218554i
$639$		0			0
$640$	368.161	−	266.450i	0.575251	−	0.416329i
$641$	−342.087	+	592.513i	−0.533678	+	0.924357i	0.465548	+	0.885022i	$0.345857\pi$
$641$	−342.087	+	592.513i	−0.533678	+	0.924357i	−0.999226	+	0.0393345i	$0.987476\pi$
$642$		0			0
$643$	−8.17432	−	2.19030i	−0.0127128	−	0.00340638i	0.252457	−	0.967608i	$-0.418761\pi$
$643$	−8.17432	−	2.19030i	−0.0127128	−	0.00340638i	−0.265170	+	0.964202i	$0.585428\pi$
$644$	113.119	−	65.3094i	0.175651	−	0.101412i
$645$		0			0
$646$	185.721	−	321.678i	0.287493	−	0.497953i
$647$	−425.885	−	425.885i	−0.658246	−	0.658246i	0.296719	−	0.954965i	$-0.404107\pi$
$647$	−425.885	−	425.885i	−0.658246	−	0.658246i	−0.954965	+	0.296719i	$0.904107\pi$
$648$		0			0
$649$			76.0630i			0.117200i
$650$	1130.79	−	1010.65i	1.73967	−	1.55485i
$651$		0			0
$652$	−34.1546	+	127.467i	−0.0523844	+	0.195501i
$653$	390.454	+	104.622i	0.597939	+	0.160217i	0.545079	−	0.838385i	$-0.316500\pi$
$653$	390.454	+	104.622i	0.597939	+	0.160217i	0.0528597	+	0.998602i	$0.483166\pi$
$654$		0			0
$655$	−167.747	+	206.372i	−0.256102	+	0.315072i
$656$	282.572			0.430750
$657$		0			0
$658$	−377.626	+	377.626i	−0.573900	+	0.573900i
$659$	838.533	+	484.127i	1.27243	+	0.734639i	0.975445	−	0.220243i	$-0.0706850\pi$
$659$	838.533	+	484.127i	1.27243	+	0.734639i	0.296987	+	0.954882i	$0.404018\pi$
$660$		0			0
$661$	276.023	+	478.085i	0.417583	+	0.723275i	0.995696	−	0.0926817i	$-0.0295439\pi$
$661$	276.023	+	478.085i	0.417583	+	0.723275i	−0.578113	+	0.815957i	$0.696211\pi$
$662$	17.0281	−	63.5498i	0.0257222	−	0.0959967i
$663$		0			0
$664$	−205.382	−	118.577i	−0.309310	−	0.178580i
$665$	73.9137	−	53.4938i	0.111148	−	0.0804418i
$666$		0			0
$667$	−459.206	−	459.206i	−0.688465	−	0.688465i
$668$	82.6355	+	308.400i	0.123706	+	0.461677i
$669$		0			0
$670$	1332.94	−	508.854i	1.98946	−	0.759483i
$671$	−47.6977	−	82.6148i	−0.0710845	−	0.123122i
$672$		0			0
$673$	175.926	+	656.564i	0.261405	+	0.975577i	0.964414	+	0.264396i	$0.0851727\pi$
$673$	175.926	+	656.564i	0.261405	+	0.975577i	−0.703009	+	0.711181i	$0.748161\pi$
$674$		−	271.841i		−	0.403326i
$675$		0			0
$676$	1052.60			1.55710
$677$	655.719	−	175.699i	0.968566	−	0.259527i	0.260344	−	0.965516i	$-0.416164\pi$
$677$	655.719	−	175.699i	0.968566	−	0.259527i	0.708222	+	0.705989i	$0.249497\pi$
$678$		0			0
$679$	245.739	−	141.878i	0.361914	−	0.208951i
$680$	104.833	+	274.611i	0.154167	+	0.403839i
$681$		0			0
$682$	−115.234	+	30.8770i	−0.168965	+	0.0452741i
$683$	−641.686	+	641.686i	−0.939511	+	0.939511i	−0.998272	−	0.0587612i	$-0.981285\pi$
$683$	−641.686	+	641.686i	−0.939511	+	0.939511i	0.0587612	+	0.998272i	$0.481285\pi$
$684$		0			0
$685$	83.1169	+	114.845i	0.121338	+	0.167656i
$686$	−306.765	+	531.333i	−0.447180	+	0.774538i
$687$		0			0
$688$	1235.03	+	330.926i	1.79510	+	0.480997i
$689$	606.783	−	350.326i	0.880672	−	0.508456i
$690$		0			0
$691$	424.566	−	735.370i	0.614423	−	1.06421i	−0.376063	−	0.926594i	$-0.622722\pi$
$691$	424.566	−	735.370i	0.614423	−	1.06421i	0.990486	−	0.137617i	$-0.0439443\pi$
$692$	−568.463	−	568.463i	−0.821479	−	0.821479i
$693$		0			0
$694$			93.4164i			0.134606i
$695$	−506.284	−	411.526i	−0.728466	−	0.592124i
$696$		0			0
$697$	−75.5412	+	281.923i	−0.108380	+	0.404481i
$698$	−284.910	−	76.3414i	−0.408180	−	0.109372i
$699$		0			0
$700$	10.2912	−	183.442i	0.0147017	−	0.262060i
$701$	295.917			0.422136			0.211068	−	0.977471i	$-0.432306\pi$
$701$	295.917			0.422136			0.211068	+	0.977471i	$0.432306\pi$
$702$		0			0
$703$	−280.503	+	280.503i	−0.399009	+	0.399009i
$704$	43.2051	+	24.9445i	0.0613708	+	0.0354325i
$705$		0			0
$706$	−11.2513	−	19.4878i	−0.0159367	−	0.0276031i
$707$	39.9509	−	149.099i	0.0565077	−	0.210889i
$708$		0			0
$709$	−549.552	−	317.284i	−0.775108	−	0.447509i	0.0595858	−	0.998223i	$-0.481022\pi$
$709$	−549.552	−	317.284i	−0.775108	−	0.447509i	−0.834694	+	0.550714i	$0.814355\pi$
$710$	−784.720	−	1084.27i	−1.10524	−	1.52714i
$711$		0			0
$712$	152.704	+	152.704i	0.214472	+	0.214472i
$713$	−101.686	−	379.499i	−0.142618	−	0.532257i
$714$		0			0
$715$	−217.450	−	97.2950i	−0.304126	−	0.136077i
$716$	−379.839	−	657.901i	−0.530501	−	0.918856i
$717$		0			0
$718$	390.946	+	1459.03i	0.544493	+	2.03207i
$719$			200.698i			0.279135i	0.990213	+	0.139568i	$0.0445712\pi$
$719$			200.698i			0.279135i	−0.990213	+	0.139568i	$0.955429\pi$
$720$		0			0
$721$	242.179			0.335893
$722$	−785.345	+	210.433i	−1.08774	+	0.291458i
$723$		0			0
$724$	285.554	−	164.864i	0.394411	−	0.227713i
$725$	−894.208	+	186.631i	−1.23339	+	0.257422i
$726$		0			0
$727$	−773.536	+	207.268i	−1.06401	+	0.285101i	−0.748030	−	0.663665i	$-0.769000\pi$
$727$	−773.536	+	207.268i	−1.06401	+	0.285101i	−0.315981	+	0.948766i	$0.602334\pi$
$728$	−123.889	+	123.889i	−0.170178	+	0.170178i
$729$		0			0
$730$	−190.877	−	30.5923i	−0.261476	−	0.0419073i
$731$	−660.332	+	1143.73i	−0.903327	+	1.56461i
$732$		0			0
$733$	618.020	+	165.598i	0.843137	+	0.225918i	0.654437	−	0.756117i	$-0.272906\pi$
$733$	618.020	+	165.598i	0.843137	+	0.225918i	0.188701	+	0.982035i	$0.439572\pi$
$734$	355.473	−	205.232i	0.484296	−	0.279608i
$735$		0			0
$736$	−343.055	+	594.188i	−0.466107	+	0.807321i
$737$	−158.471	−	158.471i	−0.215022	−	0.215022i
$738$		0			0
$739$			831.653i			1.12538i	0.826669	+	0.562688i	$0.190233\pi$
$739$			831.653i			1.12538i	−0.826669	+	0.562688i	$0.809767\pi$
$740$	82.0361	+	794.590i	0.110860	+	1.07377i
$741$		0			0
$742$	52.5711	−	196.198i	0.0708505	−	0.264418i
$743$	−429.421	−	115.063i	−0.577956	−	0.154863i	−0.0420131	−	0.999117i	$-0.513377\pi$
$743$	−429.421	−	115.063i	−0.577956	−	0.154863i	−0.535943	+	0.844254i	$0.680044\pi$
$744$		0			0
$745$	643.833	+	523.332i	0.864206	+	0.702459i
$746$	−260.176			−0.348761
$747$		0			0
$748$	−83.0771	+	83.0771i	−0.111066	+	0.111066i
$749$	−154.290	−	89.0792i	−0.205994	−	0.118931i
$750$		0			0
$751$	−113.684	−	196.907i	−0.151377	−	0.262192i	0.780357	−	0.625334i	$-0.215037\pi$
$751$	−113.684	−	196.907i	−0.151377	−	0.262192i	−0.931734	+	0.363142i	$0.881704\pi$
$752$	396.401	−	1479.39i	0.527128	−	1.96727i
$753$		0			0
$754$	−1919.64	−	1108.31i	−2.54595	−	1.46990i
$755$	442.093	+	70.8552i	0.585554	+	0.0938480i
$756$		0			0
$757$	453.799	+	453.799i	0.599470	+	0.599470i	0.940171	−	0.340702i	$-0.110665\pi$
$757$	453.799	+	453.799i	0.599470	+	0.599470i	−0.340702	+	0.940171i	$0.610665\pi$
$758$	−439.749	−	1641.17i	−0.580144	−	2.16513i
$759$		0			0
$760$	−43.0706	+	96.2609i	−0.0566719	+	0.126659i
$761$	−409.633	−	709.506i	−0.538283	−	0.932333i	−0.998997	−	0.0447846i	$-0.985740\pi$
$761$	−409.633	−	709.506i	−0.538283	−	0.932333i	0.460714	−	0.887549i	$-0.347593\pi$
$762$		0			0
$763$	21.9215	+	81.8123i	0.0287307	+	0.107225i
$764$			558.903i			0.731549i
$765$		0			0
$766$	−1400.90			−1.82885
$767$	−825.872	+	221.292i	−1.07676	+	0.288516i
$768$		0			0
$769$	−168.643	+	97.3659i	−0.219301	+	0.126614i	−0.605627	−	0.795749i	$-0.707077\pi$
$769$	−168.643	+	97.3659i	−0.219301	+	0.126614i	0.386325	+	0.922363i	$0.373744\pi$
$770$	−64.5195	+	24.6305i	−0.0837916	+	0.0319877i
$771$		0			0
$772$	−556.412	+	149.090i	−0.720741	+	0.193122i
$773$	−57.3776	+	57.3776i	−0.0742271	+	0.0742271i	−0.743246	−	0.669019i	$-0.766715\pi$
$773$	−57.3776	+	57.3776i	−0.0742271	+	0.0742271i	0.669019	+	0.743246i	$0.266715\pi$
$774$		0			0
$775$	−524.959	−	172.709i	−0.677366	−	0.222850i
$776$	−163.985	+	284.030i	−0.211321	+	0.366018i
$777$		0			0
$778$	−352.009	−	94.3204i	−0.452453	−	0.121234i
$779$	−90.6850	+	52.3570i	−0.116412	+	0.0672105i
$780$		0			0
$781$	−105.119	+	182.072i	−0.134596	+	0.233126i
$782$	−654.712	−	654.712i	−0.837228	−	0.837228i
$783$		0			0
$784$		−	816.753i		−	1.04178i
$785$	411.505	−	42.4851i	0.524210	−	0.0541212i
$786$		0			0
$787$	238.115	−	888.656i	0.302560	−	1.12917i	−0.632466	−	0.774588i	$-0.717957\pi$
$787$	238.115	−	888.656i	0.302560	−	1.12917i	0.935026	−	0.354580i	$-0.115376\pi$
$788$	261.137	+	69.9715i	0.331393	+	0.0887964i
$789$		0			0
$790$	−98.9766	−	958.675i	−0.125287	−	1.21351i
$791$	−24.6046			−0.0311057
$792$		0			0
$793$	758.243	−	758.243i	0.956170	−	0.956170i
$794$	937.030	+	540.995i	1.18014	+	0.681354i
$795$		0			0
$796$	−73.1468	−	126.694i	−0.0918930	−	0.159163i
$797$	111.445	−	415.919i	0.139831	−	0.521856i	−0.860100	−	0.510125i	$-0.829599\pi$
$797$	111.445	−	415.919i	0.139831	−	0.521856i	0.999931	−	0.0117311i	$-0.00373422\pi$
$798$		0			0
$799$	1370.02	+	790.982i	1.71467	+	0.989964i
$800$	434.973	+	861.509i	0.543716	+	1.07689i
$801$		0			0
$802$	429.294	+	429.294i	0.535279	+	0.535279i
$803$	7.85906	+	29.3304i	0.00978712	+	0.0365260i
$804$		0			0
$805$	−81.1153	−	212.481i	−0.100764	−	0.263951i
$806$	−670.509	−	1161.35i	−0.831896	−	1.44089i
$807$		0			0
$808$	46.1760	+	172.331i	0.0571485	+	0.213281i
$809$			324.798i			0.401480i	0.979645	+	0.200740i	$0.0643347\pi$
$809$			324.798i			0.401480i	−0.979645	+	0.200740i	$0.935665\pi$
$810$		0			0
$811$	−341.672			−0.421297			−0.210649	−	0.977562i	$-0.567558\pi$
$811$	−341.672			−0.421297			−0.210649	+	0.977562i	$0.567558\pi$
$812$	−259.383	+	69.5014i	−0.319437	+	0.0855929i
$813$		0			0
$814$	260.034	−	150.130i	0.319452	−	0.184435i
$815$	209.741	+	93.8457i	0.257351	+	0.115148i
$816$		0			0
$817$	−457.671	+	122.633i	−0.560185	+	0.150101i
$818$	10.3063	−	10.3063i	0.0125994	−	0.0125994i
$819$		0			0
$820$	−33.3694	+	208.205i	−0.0406944	+	0.253908i
$821$	531.861	−	921.210i	0.647821	−	1.12206i	−0.335822	−	0.941926i	$-0.609014\pi$
$821$	531.861	−	921.210i	0.647821	−	1.12206i	0.983642	−	0.180133i	$-0.0576528\pi$
$822$		0			0
$823$	−525.820	−	140.893i	−0.638906	−	0.171194i	−0.0751984	−	0.997169i	$-0.523959\pi$
$823$	−525.820	−	140.893i	−0.638906	−	0.171194i	−0.563708	+	0.825974i	$0.690626\pi$
$824$	−242.413	+	139.957i	−0.294191	+	0.169851i
$825$		0			0
$826$	−123.933	+	214.658i	−0.150040	+	0.259877i
$827$	−464.647	−	464.647i	−0.561846	−	0.561846i	0.367985	−	0.929832i	$-0.380048\pi$
$827$	−464.647	−	464.647i	−0.561846	−	0.561846i	−0.929832	+	0.367985i	$0.880048\pi$
$828$		0			0
$829$			1169.96i			1.41130i	0.708563	+	0.705648i	$0.249344\pi$
$829$			1169.96i			1.41130i	−0.708563	+	0.705648i	$0.750656\pi$
$830$	662.781	−	815.392i	0.798531	−	0.982400i
$831$		0			0
$832$	−145.143	+	541.681i	−0.174451	+	0.651059i
$833$	814.878	+	218.346i	0.978245	+	0.262120i
$834$		0			0
$835$	552.999	−	57.0934i	0.662275	−	0.0683754i
$836$	−42.1516			−0.0504205
$837$		0			0
$838$	1031.44	−	1031.44i	1.23083	−	1.23083i
$839$	−886.076	−	511.576i	−1.05611	−	0.609745i	−0.131756	−	0.991282i	$-0.542062\pi$
$839$	−886.076	−	511.576i	−1.05611	−	0.609745i	−0.924354	+	0.381537i	$0.875395\pi$
$840$		0			0
$841$	247.051	+	427.904i	0.293758	+	0.508804i
$842$	−403.002	+	1504.02i	−0.478624	+	1.78625i
$843$		0			0
$844$	−454.371	−	262.331i	−0.538354	−	0.310819i
$845$	290.049	−	1809.73i	0.343253	−	2.14169i
$846$		0			0
$847$	−211.306	−	211.306i	−0.249475	−	0.249475i
$848$	150.768	+	562.672i	0.177792	+	0.663529i
$849$		0			0
$850$	−1274.91	+	266.089i	−1.49990	+	0.313046i
$851$	494.422	+	856.363i	0.580989	+	1.00630i
$852$		0			0
$853$	−393.113	−	1467.12i	−0.460860	−	1.71995i	−0.670264	−	0.742123i	$-0.733819\pi$
$853$	−393.113	−	1467.12i	−0.460860	−	1.71995i	0.209404	−	0.977829i	$-0.432848\pi$
$854$		−	310.864i		−	0.364010i
$855$		0			0
$856$	205.919			0.240559
$857$	1324.14	−	354.803i	1.54509	−	0.414006i	0.617185	−	0.786818i	$-0.288273\pi$
$857$	1324.14	−	354.803i	1.54509	−	0.414006i	0.927907	+	0.372812i	$0.121606\pi$
$858$		0			0
$859$	−533.146	+	307.812i	−0.620659	+	0.358338i	−0.777126	−	0.629346i	$-0.783323\pi$
$859$	−533.146	+	307.812i	−0.620659	+	0.358338i	0.156466	+	0.987683i	$0.449990\pi$
$860$	−389.680	+	870.916i	−0.453116	+	1.01269i
$861$		0			0
$862$	1435.22	−	384.567i	1.66499	−	0.446133i
$863$	691.930	−	691.930i	0.801773	−	0.801773i	−0.181600	−	0.983373i	$-0.558128\pi$
$863$	691.930	−	691.930i	0.801773	−	0.801773i	0.983373	+	0.181600i	$0.0581275\pi$
$864$		0			0
$865$	−1134.00	+	820.710i	−1.31098	+	0.948798i
$866$	−644.131	+	1115.67i	−0.743800	+	1.28830i
$867$		0			0
$868$	−156.923	−	42.0473i	−0.180787	−	0.0484416i
$869$	−131.104	+	75.6932i	−0.150868	+	0.0871038i
$870$		0			0
$871$	1259.60	−	2181.69i	1.44615	−	2.50481i
$872$	−69.2228	−	69.2228i	−0.0793840	−	0.0793840i
$873$		0			0
$874$		−	332.187i		−	0.380077i
$875$	−312.554	−	68.2417i	−0.357204	−	0.0779905i
$876$		0			0
$877$	121.564	−	453.685i	0.138614	−	0.517314i	−0.861343	−	0.508024i	$-0.830376\pi$
$877$	121.564	−	453.685i	0.138614	−	0.517314i	0.999957	−	0.00929031i	$-0.00295724\pi$
$878$	2039.37	+	546.447i	2.32274	+	0.622376i
$879$		0			0
$880$	124.926	−	153.691i	0.141961	−	0.174649i
$881$	239.224			0.271537			0.135768	−	0.990741i	$-0.456650\pi$
$881$	239.224			0.271537			0.135768	+	0.990741i	$0.456650\pi$
$882$		0			0
$883$	2.33713	−	2.33713i	0.00264681	−	0.00264681i	−0.705782	−	0.708429i	$-0.749404\pi$
$883$	2.33713	−	2.33713i	0.00264681	−	0.00264681i	0.708429	+	0.705782i	$0.249404\pi$
$884$	−1143.73	−	660.332i	−1.29381	−	0.746982i
$885$		0			0
$886$	−972.263	−	1684.01i	−1.09736	−	1.90069i
$887$	−359.037	+	1339.94i	−0.404776	+	1.51065i	0.399691	+	0.916650i	$0.369117\pi$
$887$	−359.037	+	1339.94i	−0.404776	+	1.51065i	−0.804468	+	0.593996i	$0.797549\pi$
$888$		0			0
$889$	−349.055	−	201.527i	−0.392638	−	0.226690i
$890$	−775.145	+	560.999i	−0.870950	+	0.630335i
$891$		0			0
$892$	−778.648	−	778.648i	−0.872924	−	0.872924i
$893$	146.896	+	548.223i	0.164497	+	0.613912i
$894$		0			0
$895$	−1235.79	+	471.766i	−1.38077	+	0.527113i
$896$	−116.313	−	201.459i	−0.129813	−	0.224843i
$897$		0			0
$898$	234.342	+	874.576i	0.260960	+	0.973915i
$899$			807.716i			0.898461i
$900$		0			0
$901$	−601.686			−0.667798
$902$	76.5587	−	20.5139i	0.0848767	−	0.0227426i
$903$		0			0
$904$	24.6284	−	14.2192i	0.0272438	−	0.0157292i
$905$	−204.764	−	536.378i	−0.226259	−	0.592683i
$906$		0			0
$907$	−228.699	+	61.2798i	−0.252149	+	0.0675631i	−0.382679	−	0.923881i	$-0.624999\pi$
$907$	−228.699	+	61.2798i	−0.252149	+	0.0675631i	0.130530	+	0.991444i	$0.458332\pi$
$908$	−340.919	+	340.919i	−0.375461	+	0.375461i
$909$		0			0
$910$	−455.141	−	628.879i	−0.500154	−	0.691075i
$911$	477.353	−	826.800i	0.523988	−	0.907574i	−0.475622	−	0.879650i	$-0.657777\pi$
$911$	477.353	−	826.800i	0.523988	−	0.907574i	0.999610	−	0.0279241i	$-0.00888967\pi$
$912$		0			0
$913$	−159.430	−	42.7191i	−0.174622	−	0.0467898i
$914$	1063.38	−	613.942i	1.16343	−	0.671709i
$915$		0			0
$916$	138.016	−	239.052i	0.150673	−	0.260973i
$917$	96.2585	+	96.2585i	0.104971	+	0.104971i
$918$		0			0
$919$			549.663i			0.598110i	0.954236	+	0.299055i	$0.0966714\pi$
$919$			549.663i			0.598110i	−0.954236	+	0.299055i	$0.903329\pi$
$920$	203.988	+	165.809i	0.221727	+	0.180228i
$921$		0			0
$922$	47.0624	−	175.639i	0.0510438	−	0.190498i
$923$	−2282.71	−	611.651i	−2.47315	−	0.662678i
$924$		0			0
$925$	1388.74	+	77.9091i	1.50134	+	0.0842260i
$926$	601.772			0.649861
$927$		0			0
$928$	997.402	−	997.402i	1.07479	−	1.07479i
$929$	293.189	+	169.273i	0.315597	+	0.182210i	0.649428	−	0.760423i	$-0.275008\pi$
$929$	293.189	+	169.273i	0.315597	+	0.182210i	−0.333832	+	0.942633i	$0.608342\pi$
$930$		0			0
$931$	151.334	+	262.118i	0.162550	+	0.281545i
$932$	−21.3702	+	79.7548i	−0.0229294	+	0.0855738i
$933$		0			0
$934$	336.297	+	194.161i	0.360062	+	0.207882i
$935$	119.941	+	165.726i	0.128280	+	0.177247i
$936$		0			0
$937$	721.149	+	721.149i	0.769636	+	0.769636i	0.978042	−	0.208406i	$-0.0668277\pi$
$937$	721.149	+	721.149i	0.769636	+	0.769636i	−0.208406	+	0.978042i	$0.566828\pi$
$938$	−189.019	−	705.428i	−0.201513	−	0.752056i
$939$		0			0
$940$	1043.23	+	466.779i	1.10982	+	0.496574i
$941$	9.03984	+	15.6575i	0.00960663	+	0.0166392i	0.870789	−	0.491657i	$-0.163609\pi$
$941$	9.03984	+	15.6575i	0.00960663	+	0.0166392i	−0.861182	+	0.508297i	$0.830275\pi$
$942$		0			0
$943$	67.5579	+	252.129i	0.0716414	+	0.267369i
$944$		−	710.850i		−	0.753019i
$945$		0			0
$946$	358.638			0.379110
$947$	−172.765	+	46.2923i	−0.182434	+	0.0488831i	−0.348879	−	0.937168i	$-0.613438\pi$
$947$	−172.765	+	46.2923i	−0.182434	+	0.0488831i	0.166445	+	0.986051i	$0.446771\pi$
$948$		0			0
$949$	−295.598	+	170.663i	−0.311483	+	0.179835i
$950$	−390.936	−	255.928i	−0.411512	−	0.269398i
$951$		0			0
$952$	145.332	−	38.9415i	0.152659	−	0.0409049i
$953$	−1120.28	+	1120.28i	−1.17553	+	1.17553i	−0.194656	+	0.980872i	$0.562359\pi$
$953$	−1120.28	+	1120.28i	−1.17553	+	1.17553i	−0.980872	+	0.194656i	$0.937641\pi$
$954$		0			0
$955$	960.916	+	154.008i	1.00620	+	0.161265i
$956$	127.178	−	220.279i	0.133032	−	0.230418i
$957$		0			0
$958$	−1277.28	−	342.246i	−1.33328	−	0.357251i
$959$	62.8435	−	36.2827i	0.0655303	−	0.0378339i
$960$		0			0
$961$	236.172	−	409.062i	0.245756	−	0.425663i
$962$	2386.60	+	2386.60i	2.48087	+	2.48087i
$963$		0			0
$964$		−	404.995i		−	0.420119i
$965$	103.007	+	997.716i	0.106743	+	1.03390i
$966$		0			0
$967$	97.2056	−	362.776i	0.100523	−	0.375157i	−0.897276	−	0.441470i	$-0.854457\pi$
$967$	97.2056	−	362.776i	0.100523	−	0.375157i	0.997799	+	0.0663136i	$0.0211238\pi$
$968$	333.626	+	89.3947i	0.344655	+	0.0923499i
$969$		0			0
$970$	−1127.63	−	916.582i	−1.16251	−	0.944930i
$971$	416.272			0.428704			0.214352	−	0.976756i	$-0.431236\pi$
$971$	416.272			0.428704			0.214352	+	0.976756i	$0.431236\pi$
$972$		0			0
$973$	−236.147	+	236.147i	−0.242700	+	0.242700i
$974$	1398.42	+	807.376i	1.43575	+	0.828929i
$975$		0			0
$976$	445.761	+	772.081i	0.456723	+	0.791067i
$977$	163.289	−	609.405i	0.167134	−	0.623751i	−0.830625	−	0.556832i	$-0.812017\pi$
$977$	163.289	−	609.405i	0.167134	−	0.623751i	0.997758	−	0.0669185i	$-0.0213167\pi$
$978$		0			0
$979$	130.164	+	75.1500i	0.132956	+	0.0767620i
$980$	601.800	+	96.4518i	0.614081	+	0.0984202i
$981$		0			0
$982$	−905.909	−	905.909i	−0.922515	−	0.922515i
$983$	286.624	+	1069.70i	0.291581	+	1.08820i	0.943895	+	0.330247i	$0.107132\pi$
$983$	286.624	+	1069.70i	0.291581	+	1.08820i	−0.652313	+	0.757949i	$0.726201\pi$
$984$		0			0
$985$	192.259	−	429.690i	0.195187	−	0.436233i
$986$	951.759	+	1648.50i	0.965273	+	1.67190i
$987$		0			0
$988$	−122.633	−	457.671i	−0.124122	−	0.463230i
$989$			1181.09i			1.19423i
$990$		0			0
$991$	416.020			0.419798			0.209899	−	0.977723i	$-0.432686\pi$
$991$	416.020			0.419798			0.209899	+	0.977723i	$0.432686\pi$
$992$	824.278	−	220.865i	0.830925	−	0.222646i
$993$		0			0
$994$	−593.316	+	342.551i	−0.596897	+	0.344619i
$995$	−237.980	+	90.8494i	−0.239175	+	0.0913060i
$996$		0			0
$997$	367.205	−	98.3922i	0.368310	−	0.0986883i	−0.0699169	−	0.997553i	$-0.522273\pi$
$997$	367.205	−	98.3922i	0.368310	−	0.0986883i	0.438227	+	0.898865i	$0.355607\pi$
$998$	966.491	−	966.491i	0.968427	−	0.968427i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.o.217.2		32
3.2	odd	2	inner	405.3.l.o.217.7		32
5.3	odd	4	inner	405.3.l.o.298.7		32
9.2	odd	6		135.3.g.a.82.2	yes	16
9.4	even	3	inner	405.3.l.o.352.7		32
9.5	odd	6	inner	405.3.l.o.352.2		32
9.7	even	3		135.3.g.a.82.7	yes	16
15.8	even	4	inner	405.3.l.o.298.2		32
45.2	even	12		675.3.g.k.568.7		16
45.7	odd	12		675.3.g.k.568.2		16
45.13	odd	12	inner	405.3.l.o.28.2		32
45.23	even	12	inner	405.3.l.o.28.7		32
45.29	odd	6		675.3.g.k.82.7		16
45.34	even	6		675.3.g.k.82.2		16
45.38	even	12		135.3.g.a.28.2	✓	16
45.43	odd	12		135.3.g.a.28.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.a.28.2	✓	16	45.38	even	12
135.3.g.a.28.7	yes	16	45.43	odd	12
135.3.g.a.82.2	yes	16	9.2	odd	6
135.3.g.a.82.7	yes	16	9.7	even	3
405.3.l.o.28.2		32	45.13	odd	12	inner
405.3.l.o.28.7		32	45.23	even	12	inner
405.3.l.o.217.2		32	1.1	even	1	trivial
405.3.l.o.217.7		32	3.2	odd	2	inner
405.3.l.o.298.2		32	15.8	even	4	inner
405.3.l.o.298.7		32	5.3	odd	4	inner
405.3.l.o.352.2		32	9.5	odd	6	inner
405.3.l.o.352.7		32	9.4	even	3	inner
675.3.g.k.82.2		16	45.34	even	6
675.3.g.k.82.7		16	45.29	odd	6
675.3.g.k.568.2		16	45.7	odd	12
675.3.g.k.568.7		16	45.2	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.53204 + 0.678458i) q^{2} +(2.48682 - 1.43577i) q^{4} +(-1.78324 - 4.67119i) q^{5} +(-2.47213 + 0.662404i) q^{7} +(2.09171 - 2.09171i) q^{8} +O(q^{10})\)	\(q+(-2.53204 + 0.678458i) q^{2} +(2.48682 - 1.43577i) q^{4} +(-1.78324 - 4.67119i) q^{5} +(-2.47213 + 0.662404i) q^{7} +(2.09171 - 2.09171i) q^{8} +(7.68445 + 10.6178i) q^{10} +(1.02939 - 1.78296i) q^{11} +(22.3537 + 5.98966i) q^{13} +(5.81011 - 3.35447i) q^{14} +(-9.62022 + 16.6627i) q^{16} +(-14.0526 - 14.0526i) q^{17} -7.13001i q^{19} +(-11.1413 - 9.05609i) q^{20} +(-1.39680 + 5.21291i) q^{22} +(-17.1676 - 4.60004i) q^{23} +(-18.6401 + 16.6597i) q^{25} -60.6642 q^{26} +(-5.19667 + 5.19667i) q^{28} +(31.6437 + 18.2695i) q^{29} +(11.0528 + 19.1440i) q^{31} +(9.99135 - 37.2882i) q^{32} +(45.1160 + 26.0477i) q^{34} +(7.50262 + 10.3666i) q^{35} +(-39.3412 - 39.3412i) q^{37} +(4.83742 + 18.0535i) q^{38} +(-13.5008 - 6.04075i) q^{40} +(-7.34318 - 12.7188i) q^{41} +(-17.1995 - 64.1894i) q^{43} -5.91185i q^{44} +46.5899 q^{46} +(-76.8895 + 20.6025i) q^{47} +(-36.7626 + 21.2249i) q^{49} +(35.8945 - 54.8297i) q^{50} +(64.1894 - 17.1995i) q^{52} +(21.4083 - 21.4083i) q^{53} +(-10.1642 - 1.62904i) q^{55} +(-3.78541 + 6.55652i) q^{56} +(-92.5183 - 24.7902i) q^{58} +(-31.9959 + 18.4728i) q^{59} +(23.1679 - 40.1281i) q^{61} +(-40.9745 - 40.9745i) q^{62} +24.2323i q^{64} +(-11.8832 - 115.100i) q^{65} +(28.1742 - 105.148i) q^{67} +(-55.1227 - 14.7701i) q^{68} +(-26.0302 - 21.1583i) q^{70} -102.118 q^{71} +(-10.4292 + 10.4292i) q^{73} +(126.305 + 72.9220i) q^{74} +(-10.2370 - 17.7311i) q^{76} +(-1.36374 + 5.08956i) q^{77} +(-63.6806 - 36.7660i) q^{79} +(94.9899 + 15.2242i) q^{80} +(27.2224 + 27.2224i) q^{82} +(-20.7497 - 77.4390i) q^{83} +(-40.5833 + 90.7019i) q^{85} +(87.0996 + 150.861i) q^{86} +(-1.57624 - 5.88261i) q^{88} +73.0044i q^{89} -59.2288 q^{91} +(-49.2973 + 13.2092i) q^{92} +(180.709 - 104.333i) q^{94} +(-33.3057 + 12.7145i) q^{95} +(-107.093 + 28.6955i) q^{97} +(78.6842 - 78.6842i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7}+O(q^{10}) \) 32 * q + 8 * q^7	\( 32 q + 8 q^{7} - 64 q^{10} - 28 q^{13} + 20 q^{16} - 176 q^{22} - 64 q^{25} + 160 q^{28} + 208 q^{31} - 352 q^{37} + 252 q^{40} + 188 q^{43} + 376 q^{46} + 188 q^{52} - 272 q^{55} - 504 q^{58} - 296 q^{61} - 304 q^{67} - 684 q^{70} - 112 q^{73} + 732 q^{76} - 152 q^{82} + 788 q^{85} + 1128 q^{88} + 400 q^{91} + 284 q^{97}+O(q^{100}) \) 32 * q + 8 * q^7 - 64 * q^10 - 28 * q^13 + 20 * q^16 - 176 * q^22 - 64 * q^25 + 160 * q^28 + 208 * q^31 - 352 * q^37 + 252 * q^40 + 188 * q^43 + 376 * q^46 + 188 * q^52 - 272 * q^55 - 504 * q^58 - 296 * q^61 - 304 * q^67 - 684 * q^70 - 112 * q^73 + 732 * q^76 - 152 * q^82 + 788 * q^85 + 1128 * q^88 + 400 * q^91 + 284 * q^97

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