LMFDB - Embedded newform 810.3.j.g.539.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(269,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("810.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			539.11
Character	$\chi$	$=$	810.539
Dual form			810.3.j.g.269.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.24727 - 4.84193i) q^{5} +(0.315907 - 0.182389i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.24727 - 4.84193i) q^{5} +(0.315907 - 0.182389i) q^{7} -2.82843 q^{8} +(6.81209 - 1.89618i) q^{10} +(-8.32536 + 4.80665i) q^{11} +(-6.62954 - 3.82757i) q^{13} +(0.446760 + 0.257937i) q^{14} +(-2.00000 - 3.46410i) q^{16} -12.3400 q^{17} +5.36509 q^{19} +(7.13920 + 7.00227i) q^{20} +(-11.7738 - 6.79763i) q^{22} +(6.03305 - 10.4495i) q^{23} +(-21.8886 - 12.0784i) q^{25} -10.8260i q^{26} +0.729555i q^{28} +(-27.1888 + 15.6975i) q^{29} +(-2.45982 + 4.26054i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-8.72566 - 15.1133i) q^{34} +(-0.489094 - 1.75709i) q^{35} +40.2567i q^{37} +(3.79369 + 6.57087i) q^{38} +(-3.52781 + 13.6951i) q^{40} +(-54.8152 - 31.6476i) q^{41} +(-46.6042 + 26.9070i) q^{43} -19.2266i q^{44} +17.0640 q^{46} +(-14.1167 - 24.4509i) q^{47} +(-24.4335 + 42.3200i) q^{49} +(-0.684649 - 35.3487i) q^{50} +(13.2591 - 7.65513i) q^{52} +41.6903 q^{53} +(12.8895 + 46.3060i) q^{55} +(-0.893519 + 0.515874i) q^{56} +(-38.4508 - 22.1996i) q^{58} +(-97.2149 - 56.1271i) q^{59} +(-22.9787 - 39.8003i) q^{61} -6.95743 q^{62} +8.00000 q^{64} +(-26.8016 + 27.3258i) q^{65} +(39.9594 + 23.0706i) q^{67} +(12.3400 - 21.3734i) q^{68} +(1.80614 - 1.84146i) q^{70} -125.617i q^{71} +59.0826i q^{73} +(-49.3042 + 28.4658i) q^{74} +(-5.36509 + 9.29261i) q^{76} +(-1.75336 + 3.03691i) q^{77} +(-25.3435 - 43.8963i) q^{79} +(-19.2675 + 5.36320i) q^{80} -89.5128i q^{82} +(-29.5183 - 51.1271i) q^{83} +(-15.3913 + 59.7492i) q^{85} +(-65.9083 - 38.0522i) q^{86} +(23.5477 - 13.5953i) q^{88} +8.93057i q^{89} -2.79242 q^{91} +(12.0661 + 20.8991i) q^{92} +(19.9641 - 34.5788i) q^{94} +(6.69172 - 25.9774i) q^{95} +(113.714 - 65.6530i) q^{97} -69.1083 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) $ 24 * q - 24 * q^4 - 24 * q^7	$ 24 q - 24 q^{4} - 24 q^{7} - 12 q^{10} - 48 q^{13} - 48 q^{16} + 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{43} - 36 q^{49} + 96 q^{52} + 216 q^{55} - 396 q^{58} - 60 q^{61} + 192 q^{64} + 1032 q^{67} - 480 q^{70} - 240 q^{79} - 396 q^{85} - 240 q^{88} + 48 q^{91} - 48 q^{94} + 1440 q^{97}+O(q^{100}) $ 24 * q - 24 * q^4 - 24 * q^7 - 12 * q^10 - 48 * q^13 - 48 * q^16 + 120 * q^22 + 24 * q^25 + 60 * q^34 + 24 * q^43 - 36 * q^49 + 96 * q^52 + 216 * q^55 - 396 * q^58 - 60 * q^61 + 192 * q^64 + 1032 * q^67 - 480 * q^70 - 240 * q^79 - 396 * q^85 - 240 * q^88 + 48 * q^91 - 48 * q^94 + 1440 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	1.24727	−	4.84193i	0.249454	−	0.968387i
$5$	1.24727	−	4.84193i	0.249454	−	0.968387i
$6$		0			0
$7$	0.315907	−	0.182389i	0.0451295	−	0.0260556i	−0.477265	−	0.878759i	$-0.658372\pi$
$7$	0.315907	−	0.182389i	0.0451295	−	0.0260556i	0.522395	+	0.852704i	$0.325039\pi$
$8$	−2.82843			−0.353553
$9$		0			0
$10$	6.81209	−	1.89618i	0.681209	−	0.189618i
$11$	−8.32536	+	4.80665i	−0.756851	+	0.436968i	−0.828164	−	0.560486i	$-0.810614\pi$
$11$	−8.32536	+	4.80665i	−0.756851	+	0.436968i	0.0713128	+	0.997454i	$0.477281\pi$
$12$		0			0
$13$	−6.62954	−	3.82757i	−0.509965	−	0.294428i	0.222854	−	0.974852i	$-0.428463\pi$
$13$	−6.62954	−	3.82757i	−0.509965	−	0.294428i	−0.732819	+	0.680424i	$0.761796\pi$
$14$	0.446760	+	0.257937i	0.0319114	+	0.0184241i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−12.3400			−0.725879			−0.362940	−	0.931813i	$-0.618227\pi$
$17$	−12.3400			−0.725879			−0.362940	+	0.931813i	$0.618227\pi$
$18$		0			0
$19$	5.36509			0.282373			0.141187	−	0.989983i	$-0.454908\pi$
$19$	5.36509			0.282373			0.141187	+	0.989983i	$0.454908\pi$
$20$	7.13920	+	7.00227i	0.356960	+	0.350113i
$21$		0			0
$22$	−11.7738	−	6.79763i	−0.535175	−	0.308983i
$23$	6.03305	−	10.4495i	0.262307	−	0.454328i	−0.704548	−	0.709656i	$-0.748850\pi$
$23$	6.03305	−	10.4495i	0.262307	−	0.454328i	0.966854	+	0.255328i	$0.0821835\pi$
$24$		0			0
$25$	−21.8886	−	12.0784i	−0.875545	−	0.483136i
$26$		−	10.8260i		−	0.416384i
$27$		0			0
$28$			0.729555i			0.0260556i
$29$	−27.1888	+	15.6975i	−0.937545	+	0.541292i	−0.889190	−	0.457539i	$-0.848731\pi$
$29$	−27.1888	+	15.6975i	−0.937545	+	0.541292i	−0.0483548	+	0.998830i	$0.515398\pi$
$30$		0			0
$31$	−2.45982	+	4.26054i	−0.0793491	+	0.137437i	−0.902969	−	0.429705i	$-0.858618\pi$
$31$	−2.45982	+	4.26054i	−0.0793491	+	0.137437i	0.823620	+	0.567142i	$0.191951\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$		0			0
$34$	−8.72566	−	15.1133i	−0.256637	−	0.444509i
$35$	−0.489094	−	1.75709i	−0.0139741	−	0.0502025i
$36$		0			0
$37$			40.2567i			1.08802i	0.839079	+	0.544010i	$0.183095\pi$
$37$			40.2567i			1.08802i	−0.839079	+	0.544010i	$0.816905\pi$
$38$	3.79369	+	6.57087i	0.0998340	+	0.172918i
$39$		0			0
$40$	−3.52781	+	13.6951i	−0.0881953	+	0.342376i
$41$	−54.8152	−	31.6476i	−1.33696	−	0.771892i	−0.350601	−	0.936525i	$-0.614023\pi$
$41$	−54.8152	−	31.6476i	−1.33696	−	0.771892i	−0.986355	+	0.164633i	$0.947356\pi$
$42$		0			0
$43$	−46.6042	+	26.9070i	−1.08382	+	0.625743i	−0.931924	−	0.362653i	$-0.881871\pi$
$43$	−46.6042	+	26.9070i	−1.08382	+	0.625743i	−0.151895	+	0.988397i	$0.548538\pi$
$44$		−	19.2266i		−	0.436968i
$45$		0			0
$46$	17.0640			0.370957
$47$	−14.1167	−	24.4509i	−0.300356	−	0.520232i	0.675860	−	0.737030i	$-0.263772\pi$
$47$	−14.1167	−	24.4509i	−0.300356	−	0.520232i	−0.976217	+	0.216797i	$0.930439\pi$
$48$		0			0
$49$	−24.4335	+	42.3200i	−0.498642	+	0.863674i
$50$	−0.684649	−	35.3487i	−0.0136930	−	0.706974i
$51$		0			0
$52$	13.2591	−	7.65513i	0.254982	−	0.147214i
$53$	41.6903			0.786610			0.393305	−	0.919408i	$-0.371332\pi$
$53$	41.6903			0.786610			0.393305	+	0.919408i	$0.371332\pi$
$54$		0			0
$55$	12.8895	+	46.3060i	0.234355	+	0.841928i
$56$	−0.893519	+	0.515874i	−0.0159557	+	0.00921203i
$57$		0			0
$58$	−38.4508	−	22.1996i	−0.662944	−	0.382751i
$59$	−97.2149	−	56.1271i	−1.64771	−	0.951306i	−0.977979	−	0.208702i	$-0.933076\pi$
$59$	−97.2149	−	56.1271i	−1.64771	−	0.951306i	−0.669731	−	0.742604i	$-0.733591\pi$
$60$		0			0
$61$	−22.9787	−	39.8003i	−0.376701	−	0.652465i	0.613879	−	0.789400i	$-0.289608\pi$
$61$	−22.9787	−	39.8003i	−0.376701	−	0.652465i	−0.990580	+	0.136935i	$0.956275\pi$
$62$	−6.95743			−0.112217
$63$		0			0
$64$	8.00000			0.125000
$65$	−26.8016	+	27.3258i	−0.412333	+	0.420397i
$66$		0			0
$67$	39.9594	+	23.0706i	0.596409	+	0.344337i	0.767628	−	0.640896i	$-0.221437\pi$
$67$	39.9594	+	23.0706i	0.596409	+	0.344337i	−0.171218	+	0.985233i	$0.554770\pi$
$68$	12.3400	−	21.3734i	0.181470	−	0.314315i
$69$		0			0
$70$	1.80614	−	1.84146i	0.0258020	−	0.0263066i
$71$		−	125.617i		−	1.76926i	−0.466295	−	0.884629i	$-0.654412\pi$
$71$		−	125.617i		−	1.76926i	0.466295	−	0.884629i	$-0.345588\pi$
$72$		0			0
$73$			59.0826i			0.809351i	0.914460	+	0.404676i	$0.132616\pi$
$73$			59.0826i			0.809351i	−0.914460	+	0.404676i	$0.867384\pi$
$74$	−49.3042	+	28.4658i	−0.666273	+	0.384673i
$75$		0			0
$76$	−5.36509	+	9.29261i	−0.0705933	+	0.122271i
$77$	−1.75336	+	3.03691i	−0.0227709	+	0.0394404i
$78$		0			0
$79$	−25.3435	−	43.8963i	−0.320804	−	0.555649i	0.659850	−	0.751397i	$-0.270620\pi$
$79$	−25.3435	−	43.8963i	−0.320804	−	0.555649i	−0.980654	+	0.195748i	$0.937287\pi$
$80$	−19.2675	+	5.36320i	−0.240844	+	0.0670400i
$81$		0			0
$82$		−	89.5128i		−	1.09162i
$83$	−29.5183	−	51.1271i	−0.355642	−	0.615990i	0.631586	−	0.775306i	$-0.282404\pi$
$83$	−29.5183	−	51.1271i	−0.355642	−	0.615990i	−0.987228	+	0.159316i	$0.949071\pi$
$84$		0			0
$85$	−15.3913	+	59.7492i	−0.181074	+	0.702932i
$86$	−65.9083	−	38.0522i	−0.766376	−	0.442467i
$87$		0			0
$88$	23.5477	−	13.5953i	0.267587	−	0.154492i
$89$			8.93057i			0.100344i	0.998741	+	0.0501718i	$0.0159769\pi$
$89$			8.93057i			0.100344i	−0.998741	+	0.0501718i	$0.984023\pi$
$90$		0			0
$91$	−2.79242			−0.0306860
$92$	12.0661	+	20.8991i	0.131153	+	0.227164i
$93$		0			0
$94$	19.9641	−	34.5788i	0.212384	−	0.367860i
$95$	6.69172	−	25.9774i	0.0704391	−	0.273447i
$96$		0			0
$97$	113.714	−	65.6530i	1.17231	−	0.676835i	0.218089	−	0.975929i	$-0.430018\pi$
$97$	113.714	−	65.6530i	1.17231	−	0.676835i	0.954224	+	0.299093i	$0.0966842\pi$
$98$	−69.1083			−0.705187
$99$		0			0
$100$	42.8090	−	25.8338i	0.428090	−	0.258338i
$101$	9.48116	−	5.47395i	0.0938729	−	0.0541975i	−0.452329	−	0.891851i	$-0.649407\pi$
$101$	9.48116	−	5.47395i	0.0938729	−	0.0541975i	0.546202	+	0.837654i	$0.316073\pi$
$102$		0			0
$103$	−45.4294	−	26.2287i	−0.441063	−	0.254648i	0.262986	−	0.964800i	$-0.415293\pi$
$103$	−45.4294	−	26.2287i	−0.441063	−	0.254648i	−0.704048	+	0.710152i	$0.748626\pi$
$104$	18.7512	+	10.8260i	0.180300	+	0.104096i
$105$		0			0
$106$	29.4795	+	51.0600i	0.278109	+	0.481698i
$107$	189.947			1.77521			0.887603	−	0.460608i	$-0.152369\pi$
$107$	189.947			1.77521			0.887603	+	0.460608i	$0.152369\pi$
$108$		0			0
$109$	142.655			1.30876			0.654382	−	0.756164i	$-0.272929\pi$
$109$	142.655			1.30876			0.654382	+	0.756164i	$0.272929\pi$
$110$	−47.5988	+	48.5297i	−0.432717	+	0.441179i
$111$		0			0
$112$	−1.26363	−	0.729555i	−0.0112824	−	0.00651389i
$113$	−40.8390	+	70.7352i	−0.361407	+	0.625975i	−0.988193	−	0.153216i	$-0.951037\pi$
$113$	−40.8390	+	70.7352i	−0.361407	+	0.625975i	0.626786	+	0.779192i	$0.284370\pi$
$114$		0			0
$115$	−43.0712	−	42.2450i	−0.374532	−	0.367348i
$116$		−	62.7898i		−	0.541292i
$117$		0			0
$118$		−	158.751i		−	1.34535i
$119$	−3.89827	+	2.25067i	−0.0327586	+	0.0189132i
$120$		0			0
$121$	−14.2922	+	24.7548i	−0.118117	+	0.204585i
$122$	32.4968	−	56.2862i	0.266368	−	0.461362i
$123$		0			0
$124$	−4.91964	−	8.52107i	−0.0396745	−	0.0687183i
$125$	−85.7838	+	90.9183i	−0.686271	+	0.727346i
$126$		0			0
$127$		−	83.4011i		−	0.656701i	−0.944556	−	0.328351i	$-0.893507\pi$
$127$		−	83.4011i		−	0.656701i	0.944556	−	0.328351i	$-0.106493\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−52.4187	−	13.5029i	−0.403221	−	0.103869i
$131$	−98.6364	−	56.9478i	−0.752950	−	0.434716i	0.0738090	−	0.997272i	$-0.476484\pi$
$131$	−98.6364	−	56.9478i	−0.752950	−	0.434716i	−0.826759	+	0.562557i	$0.809818\pi$
$132$		0			0
$133$	1.69487	−	0.978533i	0.0127434	−	0.00735739i
$134$			65.2535i			0.486966i
$135$		0			0
$136$	34.9027			0.256637
$137$	−76.3672	−	132.272i	−0.557425	−	0.965488i	−0.997710	−	0.0676304i	$-0.978456\pi$
$137$	−76.3672	−	132.272i	−0.557425	−	0.965488i	0.440286	−	0.897858i	$-0.354877\pi$
$138$		0			0
$139$	−50.2751	+	87.0790i	−0.361691	+	0.626467i	−0.988239	−	0.152915i	$-0.951134\pi$
$139$	−50.2751	+	87.0790i	−0.361691	+	0.626467i	0.626548	+	0.779383i	$0.284467\pi$
$140$	3.53246	+	0.909953i	0.0252318	+	0.00649966i
$141$		0			0
$142$	153.849	−	88.8249i	1.08345	−	0.625527i
$143$	73.5911			0.514623
$144$		0			0
$145$	42.0943	+	151.225i	0.290305	+	1.04293i
$146$	−72.3612	+	41.7777i	−0.495624	+	0.286149i
$147$		0			0
$148$	−69.7267	−	40.2567i	−0.471126	−	0.272005i
$149$	22.4980	+	12.9892i	0.150993	+	0.0871761i	0.573593	−	0.819140i	$-0.305549\pi$
$149$	22.4980	+	12.9892i	0.150993	+	0.0871761i	−0.422600	+	0.906316i	$0.638882\pi$
$150$		0			0
$151$	77.9769	+	135.060i	0.516403	+	0.894437i	0.999819	+	0.0190456i	$0.00606276\pi$
$151$	77.9769	+	135.060i	0.516403	+	0.894437i	−0.483415	+	0.875391i	$0.660604\pi$
$152$	−15.1748			−0.0998340
$153$		0			0
$154$	−4.95925			−0.0322029
$155$	17.5612	+	17.2243i	0.113298	+	0.111125i
$156$		0			0
$157$	218.848	+	126.352i	1.39394	+	0.804790i	0.993748	−	0.111643i	$-0.0356114\pi$
$157$	218.848	+	126.352i	1.39394	+	0.804790i	0.400188	+	0.916433i	$0.368945\pi$
$158$	35.8412	−	62.0787i	0.226843	−	0.392903i
$159$		0			0
$160$	−20.1927	−	19.8054i	−0.126204	−	0.123784i
$161$		−	4.40144i		−	0.0273382i
$162$		0			0
$163$			156.387i			0.959430i	0.877424	+	0.479715i	$0.159260\pi$
$163$			156.387i			0.959430i	−0.877424	+	0.479715i	$0.840740\pi$
$164$	109.630	−	63.2951i	0.668478	−	0.385946i
$165$		0			0
$166$	41.7451	−	72.3047i	0.251477	−	0.435570i
$167$	−160.031	+	277.182i	−0.958268	+	1.65977i	−0.231564	+	0.972820i	$0.574384\pi$
$167$	−160.031	+	277.182i	−0.958268	+	1.65977i	−0.726705	+	0.686950i	$0.758949\pi$
$168$		0			0
$169$	−55.1995	−	95.6083i	−0.326624	−	0.565729i
$170$	−84.0608	+	23.3987i	−0.494475	+	0.137640i
$171$		0			0
$172$		−	107.628i		−	0.625743i
$173$	−19.8360	−	34.3570i	−0.114659	−	0.198595i	0.802984	−	0.596000i	$-0.203244\pi$
$173$	−19.8360	−	34.3570i	−0.114659	−	0.198595i	−0.917643	+	0.397405i	$0.869911\pi$
$174$		0			0
$175$	−9.11773	+	0.176596i	−0.0521013	+	0.00100912i
$176$	33.3015	+	19.2266i	0.189213	+	0.109242i
$177$		0			0
$178$	−10.9377	+	6.31487i	−0.0614476	+	0.0354768i
$179$			51.3204i			0.286706i	0.989672	+	0.143353i	$0.0457884\pi$
$179$			51.3204i			0.286706i	−0.989672	+	0.143353i	$0.954212\pi$
$180$		0			0
$181$	−298.058			−1.64673			−0.823363	−	0.567515i	$-0.807905\pi$
$181$	−298.058			−1.64673			−0.823363	+	0.567515i	$0.807905\pi$
$182$	−1.97454	−	3.42000i	−0.0108491	−	0.0187912i
$183$		0			0
$184$	−17.0640	+	29.5558i	−0.0927394	+	0.160629i
$185$	194.920	+	50.2110i	1.05362	+	0.271411i
$186$		0			0
$187$	102.735	−	59.3138i	0.549383	−	0.317186i
$188$	56.4670			0.300356
$189$		0			0
$190$	36.5475	−	10.1732i	0.192355	−	0.0535430i
$191$	186.106	−	107.448i	0.974377	−	0.562557i	0.0738091	−	0.997272i	$-0.476484\pi$
$191$	186.106	−	107.448i	0.974377	−	0.562557i	0.900568	+	0.434716i	$0.143151\pi$
$192$		0			0
$193$	152.179	+	87.8608i	0.788494	+	0.455237i	0.839432	−	0.543464i	$-0.182888\pi$
$193$	152.179	+	87.8608i	0.788494	+	0.455237i	−0.0509379	+	0.998702i	$0.516221\pi$
$194$	160.816	+	92.8474i	0.828951	+	0.478595i
$195$		0			0
$196$	−48.8669	−	84.6400i	−0.249321	−	0.431837i
$197$	147.580			0.749136			0.374568	−	0.927200i	$-0.377791\pi$
$197$	147.580			0.749136			0.374568	+	0.927200i	$0.377791\pi$
$198$		0			0
$199$	−192.973			−0.969716			−0.484858	−	0.874593i	$-0.661129\pi$
$199$	−192.973			−0.969716			−0.484858	+	0.874593i	$0.661129\pi$
$200$	61.9104	+	34.1629i	0.309552	+	0.170814i
$201$		0			0
$202$	13.4084	+	7.74134i	0.0663781	+	0.0383234i
$203$	−5.72608	+	9.91787i	−0.0282073	+	0.0488565i
$204$		0			0
$205$	−221.605	+	225.938i	−1.08100	+	1.10214i
$206$		−	74.1860i		−	0.360126i
$207$		0			0
$208$			30.6205i			0.147214i
$209$	−44.6663	+	25.7881i	−0.213715	+	0.123388i
$210$		0			0
$211$	191.949	−	332.466i	0.909712	−	1.57567i	0.0952487	−	0.995454i	$-0.469635\pi$
$211$	191.949	−	332.466i	0.909712	−	1.57567i	0.814464	−	0.580215i	$-0.197031\pi$
$212$	−41.6903	+	72.2097i	−0.196652	+	0.340612i
$213$		0			0
$214$	134.313	+	232.637i	0.627630	+	1.08709i
$215$	72.1537	+	259.215i	0.335598	+	1.20565i
$216$		0			0
$217$			1.79458i			0.00826994i
$218$	100.872	+	174.716i	0.462718	+	0.801451i
$219$		0			0
$220$	−93.0939	−	23.9808i	−0.423154	−	0.109003i
$221$	81.8082	+	47.2320i	0.370173	+	0.213719i
$222$		0			0
$223$	−299.254	+	172.774i	−1.34195	+	0.774773i	−0.987093	−	0.160149i	$-0.948803\pi$
$223$	−299.254	+	172.774i	−1.34195	+	0.774773i	−0.354853	+	0.934922i	$0.615469\pi$
$224$		−	2.06349i		−	0.00921203i
$225$		0			0
$226$	−115.510			−0.511107
$227$	−136.398	−	236.248i	−0.600872	−	1.04074i	−0.992689	−	0.120697i	$-0.961487\pi$
$227$	−136.398	−	236.248i	−0.600872	−	1.04074i	0.391818	−	0.920043i	$-0.371846\pi$
$228$		0			0
$229$	−0.0521213	+	0.0902767i	−0.000227604	+	0.000394221i	−0.866139	−	0.499803i	$-0.833406\pi$
$229$	−0.0521213	+	0.0902767i	−0.000227604	+	0.000394221i	0.865912	+	0.500197i	$0.166739\pi$
$230$	21.2835	−	82.6230i	0.0925368	−	0.359230i
$231$		0			0
$232$	76.9015	−	44.3991i	0.331472	−	0.191375i
$233$	−317.302			−1.36181			−0.680905	−	0.732372i	$-0.738413\pi$
$233$	−317.302			−1.36181			−0.680905	+	0.732372i	$0.738413\pi$
$234$		0			0
$235$	−135.997	+	37.8554i	−0.578711	+	0.161087i
$236$	194.430	−	112.254i	0.823855	−	0.475653i
$237$		0			0
$238$	−5.51299	−	3.18293i	−0.0231638	−	0.0133736i
$239$	167.164	+	96.5123i	0.699432	+	0.403817i	0.807136	−	0.590366i	$-0.201017\pi$
$239$	167.164	+	96.5123i	0.699432	+	0.403817i	−0.107704	+	0.994183i	$0.534350\pi$
$240$		0			0
$241$	157.363	+	272.561i	0.652959	+	1.13096i	0.982401	+	0.186783i	$0.0598061\pi$
$241$	157.363	+	272.561i	0.652959	+	1.13096i	−0.329442	+	0.944176i	$0.606861\pi$
$242$	−40.4245			−0.167043
$243$		0			0
$244$	91.9149			0.376701
$245$	174.436	+	171.090i	0.711982	+	0.698325i
$246$		0			0
$247$	−35.5681	−	20.5352i	−0.144000	−	0.0831387i
$248$	6.95743	−	12.0506i	0.0280541	−	0.0485912i
$249$		0			0
$250$	−172.010	−	40.7744i	−0.688040	−	0.163097i
$251$		−	57.1694i		−	0.227767i	−0.993494	−	0.113883i	$-0.963671\pi$
$251$		−	57.1694i		−	0.227767i	0.993494	−	0.113883i	$-0.0363290\pi$
$252$		0			0
$253$			115.995i			0.458479i
$254$	102.145	−	58.9735i	0.402146	−	0.232179i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−35.8560	+	62.1044i	−0.139517	+	0.241651i	−0.927314	−	0.374284i	$-0.877888\pi$
$257$	−35.8560	+	62.1044i	−0.139517	+	0.241651i	0.787797	+	0.615935i	$0.211222\pi$
$258$		0			0
$259$	7.34238	+	12.7174i	0.0283490	+	0.0491018i
$260$	−20.5280	−	73.7476i	−0.0789538	−	0.283645i
$261$		0			0
$262$		−	161.073i		−	0.614781i
$263$	114.235	+	197.861i	0.434353	+	0.752322i	0.997243	−	0.0742102i	$-0.0236436\pi$
$263$	114.235	+	197.861i	0.434353	+	0.752322i	−0.562889	+	0.826532i	$0.690310\pi$
$264$		0			0
$265$	51.9991	−	201.862i	0.196223	−	0.761742i
$266$	2.39691	+	1.38385i	0.00901093	+	0.00520246i
$267$		0			0
$268$	−79.9188	+	46.1412i	−0.298205	+	0.172169i
$269$			8.79629i			0.0326999i	0.999866	+	0.0163500i	$0.00520459\pi$
$269$			8.79629i			0.0326999i	−0.999866	+	0.0163500i	$0.994795\pi$
$270$		0			0
$271$	0.783006			0.00288932			0.00144466	−	0.999999i	$-0.499540\pi$
$271$	0.783006			0.00288932			0.00144466	+	0.999999i	$0.499540\pi$
$272$	24.6799	+	42.7468i	0.0907349	+	0.157158i
$273$		0			0
$274$	108.000	−	187.061i	0.394159	−	0.682703i
$275$	240.287	−	4.65399i	0.873773	−	0.0169236i
$276$		0			0
$277$	408.921	−	236.091i	1.47625	−	0.852313i	0.476609	−	0.879115i	$-0.341866\pi$
$277$	408.921	−	236.091i	1.47625	−	0.852313i	0.999641	+	0.0268020i	$0.00853238\pi$
$278$	−142.199			−0.511509
$279$		0			0
$280$	1.38337	+	4.96979i	0.00494059	+	0.0177493i
$281$	205.633	−	118.722i	0.731790	−	0.422499i	−0.0872870	−	0.996183i	$-0.527820\pi$
$281$	205.633	−	118.722i	0.731790	−	0.422499i	0.819076	+	0.573684i	$0.194486\pi$
$282$		0			0
$283$	−230.663	−	133.173i	−0.815064	−	0.470577i	0.0336474	−	0.999434i	$-0.489288\pi$
$283$	−230.663	−	133.173i	−0.815064	−	0.470577i	−0.848711	+	0.528856i	$0.822621\pi$
$284$	217.576	+	125.617i	0.766111	+	0.442315i
$285$		0			0
$286$	52.0368	+	90.1303i	0.181947	+	0.315141i
$287$	−23.0886			−0.0804482
$288$		0			0
$289$	−136.726			−0.473099
$290$	−155.447	+	158.487i	−0.536025	+	0.546507i
$291$		0			0
$292$	−102.334	−	59.0826i	−0.350459	−	0.202338i
$293$	165.793	−	287.162i	0.565847	−	0.980075i	−0.431124	−	0.902293i	$-0.641883\pi$
$293$	165.793	−	287.162i	0.565847	−	0.980075i	0.996970	−	0.0777821i	$-0.0247839\pi$
$294$		0			0
$295$	−393.017	+	400.703i	−1.33226	+	1.35831i
$296$		−	113.863i		−	0.384673i
$297$		0			0
$298$			36.7391i			0.123286i
$299$	−79.9927	+	46.1838i	−0.267534	+	0.154461i
$300$		0			0
$301$	−9.81506	+	17.0002i	−0.0326082	+	0.0564790i
$302$	−110.276	+	191.004i	−0.365152	+	0.632462i
$303$		0			0
$304$	−10.7302	−	18.5852i	−0.0352967	−	0.0611356i
$305$	−221.371	+	61.6197i	−0.725807	+	0.202032i
$306$		0			0
$307$		−	414.087i		−	1.34882i	−0.738358	−	0.674409i	$-0.764399\pi$
$307$		−	414.087i		−	1.34882i	0.738358	−	0.674409i	$-0.235601\pi$
$308$	−3.50672	−	6.07381i	−0.0113855	−	0.0197202i
$309$		0			0
$310$	−8.67779	+	33.6874i	−0.0279929	+	0.108669i
$311$	427.244	+	246.669i	1.37377	+	0.793149i	0.991401	−	0.130858i	$-0.0417734\pi$
$311$	427.244	+	246.669i	1.37377	+	0.793149i	0.382374	+	0.924008i	$0.375107\pi$
$312$		0			0
$313$	−95.3452	+	55.0476i	−0.304617	+	0.175871i	−0.644515	−	0.764591i	$-0.722941\pi$
$313$	−95.3452	+	55.0476i	−0.304617	+	0.175871i	0.339898	+	0.940462i	$0.389607\pi$
$314$			357.377i			1.13814i
$315$		0			0
$316$	101.374			0.320804
$317$	49.7880	+	86.2353i	0.157060	+	0.272036i	0.933807	−	0.357777i	$-0.116465\pi$
$317$	49.7880	+	86.2353i	0.157060	+	0.272036i	−0.776747	+	0.629812i	$0.783132\pi$
$318$		0			0
$319$	150.904	−	261.374i	0.473055	−	0.819355i
$320$	9.97816	−	38.7355i	0.0311817	−	0.121048i
$321$		0			0
$322$	5.39065	−	3.11229i	0.0167411	−	0.00966550i
$323$	−66.2050			−0.204969
$324$		0			0
$325$	98.8807	+	163.854i	0.304248	+	0.504167i
$326$	−191.534	+	110.582i	−0.587528	+	0.339210i
$327$		0			0
$328$	155.041	+	89.5128i	0.472685	+	0.272905i
$329$	−8.91915	−	5.14948i	−0.0271099	−	0.0156519i
$330$		0			0
$331$	−99.4038	−	172.172i	−0.300314	−	0.520158i	0.675893	−	0.736999i	$-0.263758\pi$
$331$	−99.4038	−	172.172i	−0.300314	−	0.520158i	−0.976207	+	0.216841i	$0.930425\pi$
$332$	118.073			0.355642
$333$		0			0
$334$	−452.636			−1.35520
$335$	161.546	−	164.706i	0.482228	−	0.491658i
$336$		0			0
$337$	281.276	+	162.395i	0.834648	+	0.481884i	0.855441	−	0.517900i	$-0.173286\pi$
$337$	281.276	+	162.395i	0.834648	+	0.481884i	−0.0207935	+	0.999784i	$0.506619\pi$
$338$	78.0638	−	135.211i	0.230958	−	0.400031i
$339$		0			0
$340$	−88.0974	−	86.4076i	−0.259110	−	0.254140i
$341$		−	47.2940i		−	0.138692i
$342$		0			0
$343$			35.6997i			0.104081i
$344$	131.817	−	76.1044i	0.383188	−	0.221234i
$345$		0			0
$346$	28.0523	−	48.5881i	0.0810761	−	0.140428i
$347$	−220.679	+	382.228i	−0.635963	+	1.10152i	0.350347	+	0.936620i	$0.386064\pi$
$347$	−220.679	+	382.228i	−0.635963	+	1.10152i	−0.986310	+	0.164901i	$0.947270\pi$
$348$		0			0
$349$	0.0673877	+	0.116719i	0.000193088	+	0.000334438i	0.866122	−	0.499833i	$-0.166605\pi$
$349$	0.0673877	+	0.116719i	0.000193088	+	0.000334438i	−0.865929	+	0.500167i	$0.833272\pi$
$350$	−6.66350	−	11.0420i	−0.0190386	−	0.0315486i
$351$		0			0
$352$			54.3811i			0.154492i
$353$	261.124	+	452.281i	0.739729	+	1.28125i	0.952617	+	0.304172i	$0.0983797\pi$
$353$	261.124	+	452.281i	0.739729	+	1.28125i	−0.212888	+	0.977077i	$0.568287\pi$
$354$		0			0
$355$	−608.231	−	156.679i	−1.71333	−	0.441349i
$356$	−15.4682	−	8.93057i	−0.0434500	−	0.0250859i
$357$		0			0
$358$	−62.8544	+	36.2890i	−0.175571	+	0.101366i
$359$			146.484i			0.408034i	0.978967	+	0.204017i	$0.0653998\pi$
$359$			146.484i			0.408034i	−0.978967	+	0.204017i	$0.934600\pi$
$360$		0			0
$361$	−332.216			−0.920265
$362$	−210.758	−	365.044i	−0.582206	−	1.00841i
$363$		0			0
$364$	2.79242	−	4.83662i	0.00767149	−	0.0132874i
$365$	286.074	+	73.6920i	0.783765	+	0.201896i
$366$		0			0
$367$	294.167	−	169.838i	0.801546	−	0.462773i	−0.0424654	−	0.999098i	$-0.513521\pi$
$367$	294.167	−	169.838i	0.801546	−	0.462773i	0.844012	+	0.536325i	$0.180188\pi$
$368$	−48.2644			−0.131153
$369$		0			0
$370$	76.3339	+	274.232i	0.206308	+	0.741168i
$371$	13.1703	−	7.60385i	0.0354993	−	0.0204955i
$372$		0			0
$373$	378.262	+	218.390i	1.01411	+	0.585496i	0.912392	−	0.409318i	$-0.134233\pi$
$373$	378.262	+	218.390i	1.01411	+	0.585496i	0.101716	+	0.994813i	$0.467567\pi$
$374$	145.289	+	83.8824i	0.388472	+	0.224285i
$375$		0			0
$376$	39.9282	+	69.1577i	0.106192	+	0.183930i
$377$	240.332			0.637486
$378$		0			0
$379$	677.751			1.78826			0.894130	−	0.447807i	$-0.147795\pi$
$379$	677.751			1.78826			0.894130	+	0.447807i	$0.147795\pi$
$380$	38.3025	+	37.5678i	0.100796	+	0.0988627i
$381$		0			0
$382$	263.194	+	151.955i	0.688989	+	0.397788i
$383$	−72.5570	+	125.672i	−0.189444	+	0.328127i	−0.945065	−	0.326882i	$-0.894002\pi$
$383$	−72.5570	+	125.672i	−0.189444	+	0.328127i	0.755621	+	0.655009i	$0.227335\pi$
$384$		0			0
$385$	12.5176	+	12.2775i	0.0325132	+	0.0318896i
$386$			248.508i			0.643803i
$387$		0			0
$388$			262.612i			0.676835i
$389$	−27.6862	+	15.9846i	−0.0711728	+	0.0410916i	−0.535164	−	0.844748i	$-0.679750\pi$
$389$	−27.6862	+	15.9846i	−0.0711728	+	0.0410916i	0.463991	+	0.885840i	$0.346417\pi$
$390$		0			0
$391$	−74.4475	+	128.947i	−0.190403	+	0.329788i
$392$	69.1083	−	119.699i	0.176297	−	0.305355i
$393$		0			0
$394$	104.355	+	180.748i	0.264859	+	0.458750i
$395$	−244.153	+	67.9612i	−0.618109	+	0.172054i
$396$		0			0
$397$		−	399.771i		−	1.00698i	−0.864001	−	0.503490i	$-0.832049\pi$
$397$		−	399.771i		−	1.00698i	0.864001	−	0.503490i	$-0.167951\pi$
$398$	−136.453	−	236.343i	−0.342846	−	0.593827i
$399$		0			0
$400$	1.93648	+	99.9812i	0.00484120	+	0.249953i
$401$	−68.8518	−	39.7516i	−0.171700	−	0.0991311i	0.411687	−	0.911325i	$-0.364940\pi$
$401$	−68.8518	−	39.7516i	−0.171700	−	0.0991311i	−0.583387	+	0.812194i	$0.698273\pi$
$402$		0			0
$403$	32.6150	−	18.8303i	0.0809305	−	0.0467252i
$404$			21.8958i			0.0541975i
$405$		0			0
$406$	−16.1958			−0.0398912
$407$	−193.500	−	335.152i	−0.475430	−	0.823469i
$408$		0			0
$409$	−229.459	+	397.434i	−0.561024	+	0.971721i	0.436384	+	0.899761i	$0.356259\pi$
$409$	−229.459	+	397.434i	−0.561024	+	0.971721i	−0.997407	+	0.0719608i	$0.977074\pi$
$410$	−433.415	−	111.647i	−1.05711	−	0.272309i
$411$		0			0
$412$	90.8589	−	52.4574i	0.220531	−	0.127324i
$413$	−40.9478			−0.0991472
$414$		0			0
$415$	−284.371	+	79.1561i	−0.685232	+	0.190738i
$416$	−37.5023	+	21.6520i	−0.0901499	+	0.0520480i
$417$		0			0
$418$	−63.1678	−	36.4699i	−0.151119	−	0.0872486i
$419$	−639.066	−	368.965i	−1.52522	−	0.880585i	−0.999553	−	0.0298924i	$-0.990484\pi$
$419$	−639.066	−	368.965i	−1.52522	−	0.880585i	−0.525664	−	0.850692i	$-0.676183\pi$
$420$		0			0
$421$	51.2781	+	88.8163i	0.121801	+	0.210965i	0.920478	−	0.390795i	$-0.127800\pi$
$421$	51.2781	+	88.8163i	0.121801	+	0.210965i	−0.798677	+	0.601760i	$0.794466\pi$
$422$	542.915			1.28653
$423$		0			0
$424$	−117.918			−0.278109
$425$	270.105	+	149.047i	0.635540	+	0.350698i
$426$		0			0
$427$	−14.5183	−	8.38213i	−0.0340006	−	0.0196303i
$428$	−189.947	+	328.998i	−0.443802	+	0.768687i
$429$		0			0
$430$	−266.452	+	271.662i	−0.619655	+	0.631773i
$431$			251.755i			0.584118i	0.956400	+	0.292059i	$0.0943403\pi$
$431$			251.755i			0.584118i	−0.956400	+	0.292059i	$0.905660\pi$
$432$		0			0
$433$			153.868i			0.355353i	0.984089	+	0.177676i	$0.0568581\pi$
$433$			153.868i			0.355353i	−0.984089	+	0.177676i	$0.943142\pi$
$434$	−2.19790	+	1.26896i	−0.00506428	+	0.00292386i
$435$		0			0
$436$	−142.655	+	247.086i	−0.327191	+	0.566711i
$437$	32.3679	−	56.0628i	0.0740683	−	0.128290i
$438$		0			0
$439$	−246.438	−	426.843i	−0.561362	−	0.972308i	−0.997378	−	0.0723691i	$-0.976944\pi$
$439$	−246.438	−	426.843i	−0.561362	−	0.972308i	0.436016	−	0.899939i	$-0.356389\pi$
$440$	−36.4570	−	130.973i	−0.0828569	−	0.297667i
$441$		0			0
$442$			133.592i			0.302245i
$443$	−258.290	−	447.372i	−0.583048	−	1.00987i	−0.995116	−	0.0987152i	$-0.968527\pi$
$443$	−258.290	−	447.372i	−0.583048	−	1.00987i	0.412068	−	0.911153i	$-0.364807\pi$
$444$		0			0
$445$	43.2412	+	11.1388i	0.0971713	+	0.0250311i
$446$	−423.209	−	244.340i	−0.948899	−	0.547847i
$447$		0			0
$448$	2.52725	−	1.45911i	0.00564119	−	0.00325694i
$449$		−	612.611i		−	1.36439i	−0.731170	−	0.682195i	$-0.761026\pi$
$449$		−	612.611i		−	1.36439i	0.731170	−	0.682195i	$-0.238974\pi$
$450$		0			0
$451$	608.475			1.34917
$452$	−81.6780	−	141.470i	−0.180703	−	0.312988i
$453$		0			0
$454$	192.896	−	334.105i	0.424880	−	0.735914i
$455$	−3.48290	+	13.5207i	−0.00765473	+	0.0297159i
$456$		0			0
$457$	764.584	−	441.433i	1.67305	−	0.965936i	0.707135	−	0.707079i	$-0.249987\pi$
$457$	764.584	−	441.433i	1.67305	−	0.965936i	0.965916	−	0.258857i	$-0.0833460\pi$
$458$	−0.147421			−0.000321880
$459$		0			0
$460$	116.242	−	32.3564i	0.252699	−	0.0703401i
$461$	−297.353	+	171.677i	−0.645017	+	0.372401i	−0.786545	−	0.617534i	$-0.788132\pi$
$461$	−297.353	+	171.677i	−0.645017	+	0.372401i	0.141527	+	0.989934i	$0.454799\pi$
$462$		0			0
$463$	−566.909	−	327.305i	−1.22442	−	0.706922i	−0.258566	−	0.965993i	$-0.583250\pi$
$463$	−566.909	−	327.305i	−1.22442	−	0.706922i	−0.965858	+	0.259072i	$0.916583\pi$
$464$	108.755	+	62.7898i	0.234386	+	0.135323i
$465$		0			0
$466$	−224.366	−	388.614i	−0.481473	−	0.833935i
$467$	861.410			1.84456			0.922280	−	0.386522i	$-0.126324\pi$
$467$	861.410			1.84456			0.922280	+	0.386522i	$0.126324\pi$
$468$		0			0
$469$	16.8313			0.0358876
$470$	−142.528	−	139.794i	−0.303251	−	0.297434i
$471$		0			0
$472$	274.965	+	158.751i	0.582554	+	0.336337i
$473$	258.665	−	448.020i	0.546860	−	0.947189i
$474$		0			0
$475$	−117.435	−	64.8017i	−0.247231	−	0.136425i
$476$		−	9.00268i		−	0.0189132i
$477$		0			0
$478$			272.978i			0.571084i
$479$	−311.459	+	179.821i	−0.650227	+	0.375409i	−0.788543	−	0.614979i	$-0.789164\pi$
$479$	−311.459	+	179.821i	−0.650227	+	0.375409i	0.138316	+	0.990388i	$0.455831\pi$
$480$		0			0
$481$	154.085	−	266.884i	0.320344	−	0.554852i
$482$	−222.545	+	385.460i	−0.461712	+	0.799709i
$483$		0			0
$484$	−28.5844	−	49.5097i	−0.0590587	−	0.102293i
$485$	−176.055	−	632.485i	−0.363000	−	1.30409i
$486$		0			0
$487$		−	771.071i		−	1.58331i	−0.610970	−	0.791654i	$-0.709220\pi$
$487$		−	771.071i		−	1.58331i	0.610970	−	0.791654i	$-0.290780\pi$
$488$	64.9937	+	112.572i	0.133184	+	0.230681i
$489$		0			0
$490$	−86.1967	+	334.618i	−0.175912	+	0.682893i
$491$	−137.273	−	79.2546i	−0.279578	−	0.161415i	0.353654	−	0.935376i	$-0.384939\pi$
$491$	−137.273	−	79.2546i	−0.279578	−	0.161415i	−0.633233	+	0.773962i	$0.718272\pi$
$492$		0			0
$493$	335.508	−	193.706i	0.680544	−	0.392912i
$494$		−	58.0825i		−	0.117576i
$495$		0			0
$496$	19.6786			0.0396745
$497$	−22.9112	−	39.6834i	−0.0460990	−	0.0798458i
$498$		0			0
$499$	−317.053	+	549.152i	−0.635377	+	1.10050i	0.351058	+	0.936354i	$0.385822\pi$
$499$	−317.053	+	549.152i	−0.635377	+	1.10050i	−0.986435	+	0.164151i	$0.947511\pi$
$500$	−71.6913	−	239.500i	−0.143383	−	0.479000i
$501$		0			0
$502$	70.0180	−	40.4249i	0.139478	−	0.0805277i
$503$	−212.791			−0.423043			−0.211522	−	0.977373i	$-0.567842\pi$
$503$	−212.791			−0.423043			−0.211522	+	0.977373i	$0.567842\pi$
$504$		0			0
$505$	−14.6789	−	52.7346i	−0.0290672	−	0.104425i
$506$	−142.064	+	82.0209i	−0.280760	+	0.162097i
$507$		0			0
$508$	144.455	+	83.4011i	0.284360	+	0.164175i
$509$	−850.733	−	491.171i	−1.67138	−	0.964973i	−0.966866	−	0.255284i	$-0.917831\pi$
$509$	−850.733	−	491.171i	−1.67138	−	0.964973i	−0.704516	−	0.709688i	$-0.748836\pi$
$510$		0			0
$511$	10.7760	+	18.6646i	0.0210881	+	0.0365256i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	−101.416			−0.197307
$515$	−183.660	+	187.252i	−0.356622	+	0.363596i
$516$		0			0
$517$	235.054	+	135.709i	0.454650	+	0.262492i
$518$	−10.3837	+	17.9851i	−0.0200457	+	0.0347202i
$519$		0			0
$520$	75.8065	−	77.2890i	0.145782	−	0.148633i
$521$			148.759i			0.285525i	0.989757	+	0.142763i	$0.0455986\pi$
$521$			148.759i			0.285525i	−0.989757	+	0.142763i	$0.954401\pi$
$522$		0			0
$523$		−	896.212i		−	1.71360i	−0.515650	−	0.856799i	$-0.672450\pi$
$523$		−	896.212i		−	1.71360i	0.515650	−	0.856799i	$-0.327550\pi$
$524$	197.273	−	113.896i	0.376475	−	0.217358i
$525$		0			0
$526$	−161.553	+	279.817i	−0.307134	+	0.531972i
$527$	30.3541	−	52.5748i	0.0575979	−	0.0997625i
$528$		0			0
$529$	191.705	+	332.042i	0.362391	+	0.627679i
$530$	283.998	−	79.0522i	0.535845	−	0.149155i
$531$		0			0
$532$			3.91413i			0.00735739i
$533$	242.266	+	419.617i	0.454533	+	0.787275i
$534$		0			0
$535$	236.915	−	919.711i	0.442832	−	1.71909i
$536$	−113.022	−	65.2535i	−0.210863	−	0.121742i
$537$		0			0
$538$	−10.7732	+	6.21991i	−0.0200245	+	0.0115612i
$539$		−	469.773i		−	0.871563i
$540$		0			0
$541$	513.074			0.948381			0.474190	−	0.880422i	$-0.342741\pi$
$541$	513.074			0.948381			0.474190	+	0.880422i	$0.342741\pi$
$542$	0.553669	+	0.958983i	0.00102153	+	0.00176934i
$543$		0			0
$544$	−34.9027	+	60.4532i	−0.0641593	+	0.111127i
$545$	177.930	−	690.727i	0.326476	−	1.26739i
$546$		0			0
$547$	489.598	−	282.669i	0.895060	−	0.516763i	0.0194656	−	0.999811i	$-0.493804\pi$
$547$	489.598	−	282.669i	0.895060	−	0.516763i	0.875594	+	0.483048i	$0.160470\pi$
$548$	305.469			0.557425
$549$		0			0
$550$	175.609	+	291.000i	0.319289	+	0.529091i
$551$	−145.870	+	84.2183i	−0.264738	+	0.152846i
$552$		0			0
$553$	−16.0124	−	9.24476i	−0.0289555	−	0.0167175i
$554$	578.302	+	333.883i	1.04387	+	0.602676i
$555$		0			0
$556$	−100.550	−	174.158i	−0.180846	−	0.313234i
$557$	−487.883			−0.875913			−0.437956	−	0.898996i	$-0.644298\pi$
$557$	−487.883			−0.875913			−0.437956	+	0.898996i	$0.644298\pi$
$558$		0			0
$559$	411.953			0.736946
$560$	−5.10854	+	5.20845i	−0.00912240	+	0.00930080i
$561$		0			0
$562$	290.809	+	167.899i	0.517453	+	0.298752i
$563$	145.172	−	251.445i	0.257854	−	0.446616i	−0.707813	−	0.706400i	$-0.750318\pi$
$563$	145.172	−	251.445i	0.257854	−	0.446616i	0.965667	+	0.259784i	$0.0836514\pi$
$564$		0			0
$565$	291.558	+	285.966i	0.516032	+	0.506134i
$566$		−	376.671i		−	0.665497i
$567$		0			0
$568$			355.300i			0.625527i
$569$	−506.632	+	292.504i	−0.890390	+	0.514067i	−0.874070	−	0.485800i	$-0.838528\pi$
$569$	−506.632	+	292.504i	−0.890390	+	0.514067i	−0.0163200	+	0.999867i	$0.505195\pi$
$570$		0			0
$571$	−324.738	+	562.462i	−0.568717	+	0.985048i	0.427976	+	0.903790i	$0.359227\pi$
$571$	−324.738	+	562.462i	−0.568717	+	0.985048i	−0.996693	+	0.0812573i	$0.974106\pi$
$572$	−73.5911	+	127.464i	−0.128656	+	0.222838i
$573$		0			0
$574$	−16.3261	−	28.2777i	−0.0284428	−	0.0492643i
$575$	−258.269	+	155.857i	−0.449164	+	0.271055i
$576$		0			0
$577$		−	362.217i		−	0.627760i	−0.949463	−	0.313880i	$-0.898371\pi$
$577$		−	362.217i		−	0.627760i	0.949463	−	0.313880i	$-0.101629\pi$
$578$	−96.6796	−	167.454i	−0.167266	−	0.289713i
$579$		0			0
$580$	−304.024	−	78.3159i	−0.524180	−	0.135027i
$581$	−18.6500	−	10.7676i	−0.0320999	−	0.0185329i
$582$		0			0
$583$	−347.087	+	200.391i	−0.595347	+	0.343723i
$584$		−	167.111i		−	0.286149i
$585$		0			0
$586$	468.933			0.800228
$587$	−129.737	−	224.711i	−0.221017	−	0.382812i	0.734100	−	0.679041i	$-0.237604\pi$
$587$	−129.737	−	224.711i	−0.221017	−	0.382812i	−0.955117	+	0.296229i	$0.904271\pi$
$588$		0			0
$589$	−13.1972	+	22.8582i	−0.0224061	+	0.0388084i
$590$	−768.663	−	198.006i	−1.30282	−	0.335603i
$591$		0			0
$592$	139.453	−	80.5135i	0.235563	−	0.136002i
$593$	−207.377			−0.349709			−0.174854	−	0.984594i	$-0.555945\pi$
$593$	−207.377			−0.349709			−0.174854	+	0.984594i	$0.555945\pi$
$594$		0			0
$595$	6.03539	+	21.6824i	0.0101435	+	0.0364410i
$596$	−44.9961	+	25.9785i	−0.0754967	+	0.0435881i
$597$		0			0
$598$	−113.127	−	65.3138i	−0.189175	−	0.109220i
$599$	−666.866	−	385.015i	−1.11330	−	0.642764i	−0.173617	−	0.984813i	$-0.555546\pi$
$599$	−666.866	−	385.015i	−1.11330	−	0.642764i	−0.939682	+	0.342050i	$0.888879\pi$
$600$		0			0
$601$	−349.168	−	604.777i	−0.580979	−	1.00628i	−0.995364	−	0.0961831i	$-0.969337\pi$
$601$	−349.168	−	604.777i	−0.580979	−	1.00628i	0.414385	−	0.910102i	$-0.363997\pi$
$602$	−27.7612			−0.0461149
$603$		0			0
$604$	−311.908			−0.516403
$605$	102.035	+	100.078i	0.168653	+	0.165418i
$606$		0			0
$607$	−835.380	−	482.307i	−1.37624	−	0.794575i	−0.384539	−	0.923109i	$-0.625639\pi$
$607$	−835.380	−	482.307i	−1.37624	−	0.794575i	−0.991705	+	0.128534i	$0.958973\pi$
$608$	15.1748	−	26.2835i	0.0249585	−	0.0432294i
$609$		0			0
$610$	−232.002	−	227.552i	−0.380330	−	0.373035i
$611$			216.131i			0.353734i
$612$		0			0
$613$			123.585i			0.201607i	0.994906	+	0.100803i	$0.0321413\pi$
$613$			123.585i			0.201607i	−0.994906	+	0.100803i	$0.967859\pi$
$614$	507.151	−	292.804i	0.825979	−	0.476879i
$615$		0			0
$616$	4.95925	−	8.58967i	0.00805073	−	0.0139443i
$617$	62.6768	−	108.559i	0.101583	−	0.175947i	−0.810754	−	0.585387i	$-0.800943\pi$
$617$	62.6768	−	108.559i	0.101583	−	0.175947i	0.912337	+	0.409440i	$0.134276\pi$
$618$		0			0
$619$	−88.0358	−	152.482i	−0.142223	−	0.246337i	0.786111	−	0.618086i	$-0.212092\pi$
$619$	−88.0358	−	152.482i	−0.142223	−	0.246337i	−0.928333	+	0.371749i	$0.878758\pi$
$620$	−47.3946	+	13.1925i	−0.0764429	+	0.0212782i
$621$		0			0
$622$			697.686i			1.12168i
$623$	1.62884	+	2.82123i	0.00261451	+	0.00452846i
$624$		0			0
$625$	333.225	+	528.759i	0.533160	+	0.846015i
$626$	−134.838	−	77.8490i	−0.215397	−	0.124359i
$627$		0			0
$628$	−437.696	+	252.704i	−0.696968	+	0.402395i
$629$		−	496.766i		−	0.789771i
$630$		0			0
$631$	−154.760			−0.245262			−0.122631	−	0.992452i	$-0.539133\pi$
$631$	−154.760			−0.245262			−0.122631	+	0.992452i	$0.539133\pi$
$632$	71.6824	+	124.157i	0.113421	+	0.196452i
$633$		0			0
$634$	−70.4108	+	121.955i	−0.111058	+	0.192358i
$635$	−403.823	−	104.024i	−0.635941	−	0.163817i
$636$		0			0
$637$	323.965	−	187.041i	0.508580	−	0.293629i
$638$	426.822			0.669000
$639$		0			0
$640$	54.4967	−	15.1694i	0.0851511	−	0.0237022i
$641$	−796.683	+	459.965i	−1.24288	+	0.717574i	−0.969679	−	0.244384i	$-0.921414\pi$
$641$	−796.683	+	459.965i	−1.24288	+	0.717574i	−0.273196	+	0.961958i	$0.588081\pi$
$642$		0			0
$643$	−544.318	−	314.262i	−0.846528	−	0.488743i	0.0129497	−	0.999916i	$-0.495878\pi$
$643$	−544.318	−	314.262i	−0.846528	−	0.488743i	−0.859478	+	0.511173i	$0.829211\pi$
$644$	7.62353	+	4.40144i	0.0118378	+	0.00683454i
$645$		0			0
$646$	−46.8140	−	81.0842i	−0.0724675	−	0.125517i
$647$	−423.162			−0.654037			−0.327019	−	0.945018i	$-0.606044\pi$
$647$	−423.162			−0.654037			−0.327019	+	0.945018i	$0.606044\pi$
$648$		0			0
$649$	1079.13			1.66276
$650$	−130.761	+	236.966i	−0.201170	+	0.364563i
$651$		0			0
$652$	−270.870	−	156.387i	−0.415445	−	0.239857i
$653$	105.321	−	182.421i	0.161288	−	0.279358i	−0.774043	−	0.633133i	$-0.781769\pi$
$653$	105.321	−	182.421i	0.161288	−	0.279358i	0.935331	+	0.353775i	$0.115102\pi$
$654$		0			0
$655$	−398.763	+	406.562i	−0.608799	+	0.620705i
$656$			253.180i			0.385946i
$657$		0			0
$658$		−	14.5649i		−	0.0221351i
$659$	−336.939	+	194.532i	−0.511288	+	0.295192i	−0.733363	−	0.679837i	$-0.762050\pi$
$659$	−336.939	+	194.532i	−0.511288	+	0.295192i	0.222075	+	0.975030i	$0.428717\pi$
$660$		0			0
$661$	−263.498	+	456.392i	−0.398636	+	0.690457i	−0.993558	−	0.113326i	$-0.963849\pi$
$661$	−263.498	+	456.392i	−0.398636	+	0.690457i	0.594922	+	0.803783i	$0.297183\pi$
$662$	140.578	−	243.489i	0.212354	−	0.367808i
$663$		0			0
$664$	83.4903	+	144.609i	0.125738	+	0.217785i
$665$	−2.62403	−	9.42694i	−0.00394591	−	0.0141758i
$666$		0			0
$667$			378.814i			0.567937i
$668$	−320.062	−	554.363i	−0.479134	−	0.829885i
$669$		0			0
$670$	315.953	+	81.3887i	0.471571	+	0.121476i
$671$	382.613	+	220.902i	0.570213	+	0.329212i
$672$		0			0
$673$	−326.464	+	188.484i	−0.485087	+	0.280065i	−0.722534	−	0.691335i	$-0.757023\pi$
$673$	−326.464	+	188.484i	−0.485087	+	0.280065i	0.237447	+	0.971401i	$0.423689\pi$
$674$			459.322i			0.681487i
$675$		0			0
$676$	220.798			0.326624
$677$	−151.338	−	262.125i	−0.223542	−	0.387185i	0.732339	−	0.680940i	$-0.238429\pi$
$677$	−151.338	−	262.125i	−0.223542	−	0.387185i	−0.955881	+	0.293754i	$0.905095\pi$
$678$		0			0
$679$	23.9488	−	41.4805i	0.0352706	−	0.0610905i
$680$	43.5330	−	168.996i	0.0640192	−	0.248524i
$681$		0			0
$682$	57.9231	−	33.4419i	0.0849313	−	0.0490351i
$683$	665.773			0.974777			0.487389	−	0.873185i	$-0.337950\pi$
$683$	665.773			0.974777			0.487389	+	0.873185i	$0.337950\pi$
$684$		0			0
$685$	−735.702	+	204.786i	−1.07402	+	0.298958i
$686$	−43.7230	+	25.2435i	−0.0637362	+	0.0367981i
$687$		0			0
$688$	186.417	+	107.628i	0.270955	+	0.156436i
$689$	−276.388	−	159.572i	−0.401143	−	0.231600i
$690$		0			0
$691$	−355.665	−	616.031i	−0.514711	−	0.891506i	−0.999854	−	0.0170712i	$-0.994566\pi$
$691$	−355.665	−	616.031i	−0.514711	−	0.891506i	0.485143	−	0.874435i	$-0.338768\pi$
$692$	79.3440			0.114659
$693$		0			0
$694$	−624.175			−0.899388
$695$	358.924	+	352.040i	0.516437	+	0.506532i
$696$		0			0
$697$	676.417	+	390.529i	0.970469	+	0.560300i
$698$	−0.0953007	+	0.165066i	−0.000136534	+	0.000236484i
$699$		0			0
$700$	8.81186	−	15.9690i	0.0125884	−	0.0228128i
$701$			792.935i			1.13115i	0.824698	+	0.565574i	$0.191345\pi$
$701$			792.935i			1.13115i	−0.824698	+	0.565574i	$0.808655\pi$
$702$		0			0
$703$			215.981i			0.307228i
$704$	−66.6029	+	38.4532i	−0.0946064	+	0.0546210i
$705$		0			0
$706$	−369.286	+	639.621i	−0.523067	+	0.905979i
$707$	1.99678	−	3.45852i	0.00282429	−	0.00489182i
$708$		0			0
$709$	−605.619	−	1048.96i	−0.854188	−	1.47950i	−0.877396	−	0.479766i	$-0.840721\pi$
$709$	−605.619	−	1048.96i	−0.854188	−	1.47950i	0.0232083	−	0.999731i	$-0.492612\pi$
$710$	−238.193	−	855.716i	−0.335483	−	1.20523i
$711$		0			0
$712$		−	25.2595i		−	0.0354768i
$713$	29.6805	+	51.4081i	0.0416276	+	0.0721011i
$714$		0			0
$715$	91.7880	−	356.323i	0.128375	−	0.498354i
$716$	−88.8895	−	51.3204i	−0.124147	−	0.0716765i
$717$		0			0
$718$	−179.406	+	103.580i	−0.249869	+	0.144262i
$719$		−	239.649i		−	0.333309i	−0.986015	−	0.166654i	$-0.946704\pi$
$719$		−	239.649i		−	0.333309i	0.986015	−	0.166654i	$-0.0532964\pi$
$720$		0			0
$721$	−19.1353			−0.0265399
$722$	−234.912	−	406.880i	−0.325363	−	0.563545i
$723$		0			0
$724$	298.058	−	516.251i	0.411682	−	0.713054i
$725$	784.726	−	15.1989i	1.08238	−	0.0209640i
$726$		0			0
$727$	−958.582	+	553.438i	−1.31855	+	0.761262i	−0.983495	−	0.180938i	$-0.942087\pi$
$727$	−958.582	+	553.438i	−1.31855	+	0.761262i	−0.335051	+	0.942200i	$0.608753\pi$
$728$	7.89816			0.0108491
$729$		0			0
$730$	112.031	+	402.476i	0.153467	+	0.551337i
$731$	575.094	−	332.031i	0.786722	−	0.454214i
$732$		0			0
$733$	−245.992	−	142.023i	−0.335596	−	0.193756i	0.322727	−	0.946492i	$-0.395400\pi$
$733$	−245.992	−	142.023i	−0.335596	−	0.193756i	−0.658323	+	0.752736i	$0.728734\pi$
$734$	416.016	+	240.187i	0.566779	+	0.327230i
$735$		0			0
$736$	−34.1281	−	59.1116i	−0.0463697	−	0.0803146i
$737$	−443.569			−0.601857
$738$		0			0
$739$	−851.158			−1.15177			−0.575885	−	0.817531i	$-0.695342\pi$
$739$	−851.158			−1.15177			−0.575885	+	0.817531i	$0.695342\pi$
$740$	−281.888	+	287.401i	−0.380930	+	0.388380i
$741$		0			0
$742$	18.6256	+	10.7535i	0.0251018	+	0.0144925i
$743$	−469.349	+	812.936i	−0.631695	+	1.09413i	0.355511	+	0.934672i	$0.384307\pi$
$743$	−469.349	+	812.936i	−0.631695	+	1.09413i	−0.987205	+	0.159455i	$0.949026\pi$
$744$		0			0
$745$	90.9542	−	92.7329i	0.122086	−	0.124474i
$746$			617.700i			0.828016i
$747$		0			0
$748$			237.255i			0.317186i
$749$	60.0056	−	34.6442i	0.0801143	−	0.0462540i
$750$		0			0
$751$	353.207	−	611.773i	0.470316	−	0.814611i	−0.529108	−	0.848555i	$-0.677473\pi$
$751$	353.207	−	611.773i	0.470316	−	0.814611i	0.999424	+	0.0339437i	$0.0108067\pi$
$752$	−56.4670	+	97.8037i	−0.0750891	+	0.130058i
$753$		0			0
$754$	169.941	+	294.346i	0.225385	+	0.390379i
$755$	751.209	−	209.103i	0.994979	−	0.276957i
$756$		0			0
$757$			624.266i			0.824658i	0.911035	+	0.412329i	$0.135284\pi$
$757$			624.266i			0.824658i	−0.911035	+	0.412329i	$0.864716\pi$
$758$	479.242	+	830.072i	0.632246	+	1.09508i
$759$		0			0
$760$	−18.9270	+	73.4752i	−0.0249040	+	0.0966779i
$761$	679.179	+	392.124i	0.892482	+	0.515275i	0.874753	−	0.484568i	$-0.161023\pi$
$761$	679.179	+	392.124i	0.892482	+	0.515275i	0.0177283	+	0.999843i	$0.494357\pi$
$762$		0			0
$763$	45.0658	−	26.0187i	0.0590639	−	0.0341006i
$764$			429.793i			0.562557i
$765$		0			0
$766$	−205.222			−0.267914
$767$	429.660	+	744.193i	0.560183	+	0.970265i
$768$		0			0
$769$	−338.456	+	586.223i	−0.440125	+	0.762319i	−0.997698	−	0.0678090i	$-0.978399\pi$
$769$	−338.456	+	586.223i	−0.440125	+	0.762319i	0.557573	+	0.830128i	$0.311732\pi$
$770$	−6.18552	+	24.0124i	−0.00803315	+	0.0311849i
$771$		0			0
$772$	−304.359	+	175.722i	−0.394247	+	0.227619i
$773$	−1033.43			−1.33691			−0.668453	−	0.743754i	$-0.733043\pi$
$773$	−1033.43			−1.33691			−0.668453	+	0.743754i	$0.733043\pi$
$774$		0			0
$775$	105.303	−	63.5466i	0.135874	−	0.0819956i
$776$	−321.633	+	185.695i	−0.414475	+	0.239297i
$777$		0			0
$778$	−39.1542	−	22.6057i	−0.0503268	−	0.0290562i
$779$	−294.088	−	169.792i	−0.377520	−	0.217962i
$780$		0			0
$781$	603.799	+	1045.81i	0.773110	+	1.33907i
$782$	−210.569			−0.269270
$783$		0			0
$784$	195.468			0.249321
$785$	884.750	−	902.053i	1.12707	−	1.14911i
$786$		0			0
$787$	−349.242	−	201.635i	−0.443763	−	0.256207i	0.261429	−	0.965223i	$-0.415806\pi$
$787$	−349.242	−	201.635i	−0.443763	−	0.256207i	−0.705193	+	0.709016i	$0.749140\pi$
$788$	−147.580	+	255.616i	−0.187284	+	0.324385i
$789$		0			0
$790$	−255.878	−	250.970i	−0.323896	−	0.317683i
$791$			29.7943i			0.0376666i
$792$		0			0
$793$			351.811i			0.443645i
$794$	489.618	−	282.681i	0.616647	−	0.356021i
$795$		0			0
$796$	192.973	−	334.240i	0.242429	−	0.419899i
$797$	7.31120	−	12.6634i	0.00917340	−	0.0158888i	−0.861402	−	0.507923i	$-0.830413\pi$
$797$	7.31120	−	12.6634i	0.00917340	−	0.0158888i	0.870576	+	0.492035i	$0.163747\pi$
$798$		0			0
$799$	174.200	+	301.723i	0.218022	+	0.377626i
$800$	−121.082	+	73.0691i	−0.151353	+	0.0913364i
$801$		0			0
$802$		−	112.434i		−	0.140193i
$803$	−283.990	−	491.884i	−0.353661	−	0.612558i
$804$		0			0
$805$	−21.3115	−	5.48979i	−0.0264739	−	0.00681961i
$806$	46.1245	+	26.6300i	0.0572265	+	0.0330397i
$807$		0			0
$808$	−26.8168	+	15.4827i	−0.0331891	+	0.0191617i
$809$		−	225.767i		−	0.279069i	−0.990217	−	0.139535i	$-0.955439\pi$
$809$		−	225.767i		−	0.279069i	0.990217	−	0.139535i	$-0.0445607\pi$
$810$		0			0
$811$	198.448			0.244696			0.122348	−	0.992487i	$-0.460958\pi$
$811$	198.448			0.244696			0.122348	+	0.992487i	$0.460958\pi$
$812$	−11.4522	−	19.8357i	−0.0141037	−	0.0244282i
$813$		0			0
$814$	273.650	−	473.976i	0.336180	−	0.582281i
$815$	757.216	+	195.057i	0.929099	+	0.239334i
$816$		0			0
$817$	−250.036	+	144.358i	−0.306042	+	0.176693i
$818$	−649.007			−0.793407
$819$		0			0
$820$	−169.732	−	609.769i	−0.206990	−	0.743621i
$821$	−105.099	+	60.6790i	−0.128013	+	0.0739086i	−0.562639	−	0.826703i	$-0.690214\pi$
$821$	−105.099	+	60.6790i	−0.128013	+	0.0739086i	0.434626	+	0.900611i	$0.356881\pi$
$822$		0			0
$823$	−214.396	−	123.782i	−0.260506	−	0.150403i	0.364059	−	0.931376i	$-0.381390\pi$
$823$	−214.396	−	123.782i	−0.260506	−	0.150403i	−0.624565	+	0.780973i	$0.714724\pi$
$824$	128.494	+	74.1860i	0.155939	+	0.0900315i
$825$		0			0
$826$	−28.9545	−	50.1506i	−0.0350538	−	0.0607150i
$827$	457.912			0.553703			0.276851	−	0.960913i	$-0.410709\pi$
$827$	457.912			0.553703			0.276851	+	0.960913i	$0.410709\pi$
$828$		0			0
$829$	−116.297			−0.140286			−0.0701429	−	0.997537i	$-0.522346\pi$
$829$	−116.297			−0.140286			−0.0701429	+	0.997537i	$0.522346\pi$
$830$	−298.027	−	292.311i	−0.359069	−	0.352182i
$831$		0			0
$832$	−53.0363	−	30.6205i	−0.0637456	−	0.0368035i
$833$	301.508	−	522.227i	0.361954	−	0.626923i
$834$		0			0
$835$	1142.49	+	1120.58i	1.36825	+	1.34201i
$836$		−	103.153i		−	0.123388i
$837$		0			0
$838$		−	1043.59i		−	1.24533i
$839$	478.220	−	276.100i	0.569988	−	0.329083i	−0.187156	−	0.982330i	$-0.559927\pi$
$839$	478.220	−	276.100i	0.569988	−	0.329083i	0.757145	+	0.653247i	$0.226594\pi$
$840$		0			0
$841$	72.3203	−	125.262i	0.0859932	−	0.148945i
$842$	−72.5182	+	125.605i	−0.0861261	+	0.149175i
$843$		0			0
$844$	383.899	+	664.932i	0.454856	+	0.787834i
$845$	−531.778	+	148.023i	−0.629323	+	0.175175i
$846$		0			0
$847$			10.4270i			0.0123105i
$848$	−83.3806	−	144.419i	−0.0983262	−	0.170306i
$849$		0			0
$850$	8.44854	+	436.201i	0.00993945	+	0.513178i
$851$	420.665	+	242.871i	0.494318	+	0.285395i
$852$		0			0
$853$	238.466	−	137.678i	0.279561	−	0.161405i	−0.353664	−	0.935373i	$-0.615064\pi$
$853$	238.466	−	137.678i	0.279561	−	0.161405i	0.633225	+	0.773968i	$0.281731\pi$
$854$		−	23.7082i		−	0.0277614i
$855$		0			0
$856$	−537.252			−0.627630
$857$	811.725	+	1405.95i	0.947170	+	1.64055i	0.751346	+	0.659908i	$0.229405\pi$
$857$	811.725	+	1405.95i	0.947170	+	1.64055i	0.195824	+	0.980639i	$0.437262\pi$
$858$		0			0
$859$	511.175	−	885.381i	0.595082	−	1.03071i	−0.398454	−	0.917188i	$-0.630453\pi$
$859$	511.175	−	885.381i	0.595082	−	1.03071i	0.993535	−	0.113523i	$-0.0362136\pi$
$860$	−521.127	−	134.241i	−0.605961	−	0.156094i
$861$		0			0
$862$	−308.335	+	178.018i	−0.357698	+	0.206517i
$863$	588.647			0.682094			0.341047	−	0.940046i	$-0.389218\pi$
$863$	588.647			0.682094			0.341047	+	0.940046i	$0.389218\pi$
$864$		0			0
$865$	−191.095	+	53.1922i	−0.220919	+	0.0614938i
$866$	−188.449	+	108.801i	−0.217608	+	0.125636i
$867$		0			0
$868$	−3.10830	−	1.79458i	−0.00358099	−	0.00206748i
$869$	421.988	+	243.635i	0.485602	+	0.280363i
$870$		0			0
$871$	−176.608	−	305.895i	−0.202765	−	0.351199i
$872$	−403.490			−0.462718
$873$		0			0
$874$	91.5502			0.104748
$875$	−10.5172	+	44.3677i	−0.0120197	+	0.0507060i
$876$		0			0
$877$	528.533	+	305.149i	0.602661	+	0.347946i	0.770088	−	0.637938i	$-0.220213\pi$
$877$	528.533	+	305.149i	0.602661	+	0.347946i	−0.167427	+	0.985884i	$0.553546\pi$
$878$	348.516	−	603.648i	0.396943	−	0.687526i
$879$		0			0
$880$	134.630	−	137.263i	0.152988	−	0.155980i
$881$			677.101i			0.768559i	0.923217	+	0.384280i	$0.125550\pi$
$881$			677.101i			0.768559i	−0.923217	+	0.384280i	$0.874450\pi$
$882$		0			0
$883$		−	760.076i		−	0.860788i	−0.902641	−	0.430394i	$-0.858375\pi$
$883$		−	760.076i		−	0.860788i	0.902641	−	0.430394i	$-0.141625\pi$
$884$	−163.616	+	94.4640i	−0.185086	+	0.106860i
$885$		0			0
$886$	365.277	−	632.679i	0.412277	−	0.714085i
$887$	320.061	−	554.363i	0.360836	−	0.624986i	−0.627263	−	0.778808i	$-0.715825\pi$
$887$	320.061	−	554.363i	0.360836	−	0.624986i	0.988099	+	0.153822i	$0.0491581\pi$
$888$		0			0
$889$	−15.2114	−	26.3470i	−0.0171107	−	0.0296366i
$890$	16.9339	+	60.8358i	0.0190269	+	0.0683549i
$891$		0			0
$892$		−	691.098i		−	0.774773i
$893$	−75.7377	−	131.181i	−0.0848126	−	0.146900i
$894$		0			0
$895$	248.490	+	64.0103i	0.277642	+	0.0715199i
$896$	3.57408	+	2.06349i	0.00398893	+	0.00230301i
$897$		0			0
$898$	750.292	−	433.181i	0.835515	−	0.482385i
$899$		−	154.452i		−	0.171804i
$900$		0			0
$901$	−514.456			−0.570984
$902$	430.257	+	745.227i	0.477003	+	0.826194i
$903$		0			0
$904$	115.510	−	200.069i	0.127777	−	0.221316i
$905$	−371.758	+	1443.17i	−0.410783	+	1.59467i
$906$		0			0
$907$	−152.547	+	88.0733i	−0.168189	+	0.0971040i	−0.581732	−	0.813381i	$-0.697625\pi$
$907$	−152.547	+	88.0733i	−0.168189	+	0.0971040i	0.413543	+	0.910485i	$0.364291\pi$
$908$	545.591			0.600872
$909$		0			0
$910$	−19.0222	+	5.29492i	−0.0209035	+	0.00581860i
$911$	1244.54	−	718.538i	1.36613	−	0.788735i	0.375698	−	0.926742i	$-0.377403\pi$
$911$	1244.54	−	718.538i	1.36613	−	0.788735i	0.990431	+	0.138007i	$0.0440697\pi$
$912$		0			0
$913$	491.501	+	283.768i	0.538336	+	0.310808i
$914$	1081.29	+	624.280i	1.18303	+	0.683020i
$915$		0			0
$916$	−0.104243	−	0.180553i	−0.000113802	−	0.000197111i
$917$	−41.5465			−0.0453070
$918$		0			0
$919$	217.751			0.236944			0.118472	−	0.992957i	$-0.462200\pi$
$919$	217.751			0.236944			0.118472	+	0.992957i	$0.462200\pi$
$920$	121.824	+	119.487i	0.132417	+	0.129877i
$921$		0			0
$922$	−420.520	−	242.788i	−0.456096	−	0.263327i
$923$	−480.809	+	832.785i	−0.520920	+	0.902259i
$924$		0			0
$925$	486.237	−	881.165i	0.525661	−	0.952611i
$926$		−	925.758i		−	0.999738i
$927$		0			0
$928$			177.596i			0.191375i
$929$	−254.358	+	146.854i	−0.273798	+	0.158077i	−0.630612	−	0.776098i	$-0.717196\pi$
$929$	−254.358	+	146.854i	−0.273798	+	0.158077i	0.356814	+	0.934175i	$0.383863\pi$
$930$		0			0
$931$	−131.088	+	227.051i	−0.140803	+	0.243878i
$932$	317.302	−	549.583i	0.340453	−	0.589681i
$933$		0			0
$934$	609.109	+	1055.01i	0.652150	+	1.12956i
$935$	−159.056	−	571.414i	−0.170113	−	0.611138i
$936$		0			0
$937$			375.806i			0.401074i	0.979686	+	0.200537i	$0.0642686\pi$
$937$			375.806i			0.401074i	−0.979686	+	0.200537i	$0.935731\pi$
$938$	11.9015	+	20.6140i	0.0126882	+	0.0219766i
$939$		0			0
$940$	70.4296	−	273.409i	0.0749251	−	0.290861i
$941$	962.551	+	555.729i	1.02290	+	0.590573i	0.914943	−	0.403583i	$-0.132235\pi$
$941$	962.551	+	555.729i	1.02290	+	0.590573i	0.107959	+	0.994155i	$0.465569\pi$
$942$		0			0
$943$	−661.405	+	381.863i	−0.701384	+	0.404944i
$944$			449.016i			0.475653i
$945$		0			0
$946$	731.614			0.773377
$947$	−908.613	−	1573.76i	−0.959465	−	1.66184i	−0.723803	−	0.690007i	$-0.757607\pi$
$947$	−908.613	−	1573.76i	−0.959465	−	1.66184i	−0.235662	−	0.971835i	$-0.575726\pi$
$948$		0			0
$949$	226.143	−	391.691i	0.238296	−	0.412740i
$950$	−3.67321	−	189.649i	−0.00386653	−	0.199631i
$951$		0			0
$952$	11.0260	−	6.36586i	0.0115819	−	0.00668682i
$953$	817.241			0.857545			0.428773	−	0.903412i	$-0.358946\pi$
$953$	817.241			0.857545			0.428773	+	0.903412i	$0.358946\pi$
$954$		0			0
$955$	−288.133	−	1035.13i	−0.301710	−	1.08391i
$956$	−334.328	+	193.025i	−0.349716	+	0.201909i
$957$		0			0
$958$	−440.469	−	254.305i	−0.459780	−	0.265454i
$959$	−48.2498	−	27.8571i	−0.0503127	−	0.0290480i
$960$		0			0
$961$	468.399	+	811.290i	0.487407	+	0.844214i
$962$	435.819			0.453034
$963$		0			0
$964$	−629.453			−0.652959
$965$	615.225	−	627.256i	0.637539	−	0.650007i
$966$		0			0
$967$	−42.1958	−	24.3618i	−0.0436358	−	0.0251931i	0.478023	−	0.878347i	$-0.341353\pi$
$967$	−42.1958	−	24.3618i	−0.0436358	−	0.0251931i	−0.521659	+	0.853154i	$0.674687\pi$
$968$	40.4245	−	70.0172i	0.0417608	−	0.0723319i
$969$		0			0
$970$	650.142	−	662.857i	0.670250	−	0.683357i
$971$			260.809i			0.268598i	0.990941	+	0.134299i	$0.0428783\pi$
$971$			260.809i			0.268598i	−0.990941	+	0.134299i	$0.957122\pi$
$972$		0			0
$973$			36.6785i			0.0376963i
$974$	944.365	−	545.229i	0.969574	−	0.559784i
$975$		0			0
$976$	−91.9149	+	159.201i	−0.0941751	+	0.163116i
$977$	124.626	−	215.859i	0.127560	−	0.220941i	−0.795171	−	0.606386i	$-0.792619\pi$
$977$	124.626	−	215.859i	0.127560	−	0.220941i	0.922731	+	0.385445i	$0.125952\pi$
$978$		0			0
$979$	−42.9261	−	74.3503i	−0.0438469	−	0.0759451i
$980$	−470.772	+	131.041i	−0.480379	+	0.133716i
$981$		0			0
$982$		−	224.166i		−	0.228275i
$983$	294.126	+	509.440i	0.299212	+	0.518251i	0.975956	−	0.217968i	$-0.0699428\pi$
$983$	294.126	+	509.440i	0.299212	+	0.518251i	−0.676744	+	0.736219i	$0.736610\pi$
$984$		0			0
$985$	184.072	−	714.571i	0.186875	−	0.725453i
$986$	474.480	+	273.941i	0.481218	+	0.277831i
$987$		0			0
$988$	71.1362	−	41.0705i	0.0720002	−	0.0415693i
$989$			649.324i			0.656546i
$990$		0			0
$991$	−598.851			−0.604289			−0.302145	−	0.953262i	$-0.597703\pi$
$991$	−598.851			−0.604289			−0.302145	+	0.953262i	$0.597703\pi$
$992$	13.9149	+	24.1012i	0.0140271	+	0.0242956i
$993$		0			0
$994$	32.4013	−	56.1208i	0.0325969	−	0.0564595i
$995$	−240.690	+	934.365i	−0.241900	+	0.939060i
$996$		0			0
$997$	−797.523	+	460.450i	−0.799922	+	0.461835i	−0.843444	−	0.537217i	$-0.819476\pi$
$997$	−797.523	+	460.450i	−0.799922	+	0.461835i	0.0435217	+	0.999052i	$0.486142\pi$
$998$	−896.761			−0.898559
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.g.539.11		24
3.2	odd	2	inner	810.3.j.g.539.3		24
5.4	even	2		810.3.j.h.539.3		24
9.2	odd	6		810.3.j.h.269.3		24
9.4	even	3		810.3.b.c.809.2	yes	24
9.5	odd	6		810.3.b.c.809.23	yes	24
9.7	even	3		810.3.j.h.269.11		24
15.14	odd	2		810.3.j.h.539.11		24
45.4	even	6		810.3.b.c.809.24	yes	24
45.14	odd	6		810.3.b.c.809.1	✓	24
45.29	odd	6	inner	810.3.j.g.269.11		24
45.34	even	6	inner	810.3.j.g.269.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.3.b.c.809.1	✓	24	45.14	odd	6
810.3.b.c.809.2	yes	24	9.4	even	3
810.3.b.c.809.23	yes	24	9.5	odd	6
810.3.b.c.809.24	yes	24	45.4	even	6
810.3.j.g.269.3		24	45.34	even	6	inner
810.3.j.g.269.11		24	45.29	odd	6	inner
810.3.j.g.539.3		24	3.2	odd	2	inner
810.3.j.g.539.11		24	1.1	even	1	trivial
810.3.j.h.269.3		24	9.2	odd	6
810.3.j.h.269.11		24	9.7	even	3
810.3.j.h.539.3		24	5.4	even	2
810.3.j.h.539.11		24	15.14	odd	2

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.24727 - 4.84193i) q^{5} +(0.315907 - 0.182389i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.24727 - 4.84193i) q^{5} +(0.315907 - 0.182389i) q^{7} -2.82843 q^{8} +(6.81209 - 1.89618i) q^{10} +(-8.32536 + 4.80665i) q^{11} +(-6.62954 - 3.82757i) q^{13} +(0.446760 + 0.257937i) q^{14} +(-2.00000 - 3.46410i) q^{16} -12.3400 q^{17} +5.36509 q^{19} +(7.13920 + 7.00227i) q^{20} +(-11.7738 - 6.79763i) q^{22} +(6.03305 - 10.4495i) q^{23} +(-21.8886 - 12.0784i) q^{25} -10.8260i q^{26} +0.729555i q^{28} +(-27.1888 + 15.6975i) q^{29} +(-2.45982 + 4.26054i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-8.72566 - 15.1133i) q^{34} +(-0.489094 - 1.75709i) q^{35} +40.2567i q^{37} +(3.79369 + 6.57087i) q^{38} +(-3.52781 + 13.6951i) q^{40} +(-54.8152 - 31.6476i) q^{41} +(-46.6042 + 26.9070i) q^{43} -19.2266i q^{44} +17.0640 q^{46} +(-14.1167 - 24.4509i) q^{47} +(-24.4335 + 42.3200i) q^{49} +(-0.684649 - 35.3487i) q^{50} +(13.2591 - 7.65513i) q^{52} +41.6903 q^{53} +(12.8895 + 46.3060i) q^{55} +(-0.893519 + 0.515874i) q^{56} +(-38.4508 - 22.1996i) q^{58} +(-97.2149 - 56.1271i) q^{59} +(-22.9787 - 39.8003i) q^{61} -6.95743 q^{62} +8.00000 q^{64} +(-26.8016 + 27.3258i) q^{65} +(39.9594 + 23.0706i) q^{67} +(12.3400 - 21.3734i) q^{68} +(1.80614 - 1.84146i) q^{70} -125.617i q^{71} +59.0826i q^{73} +(-49.3042 + 28.4658i) q^{74} +(-5.36509 + 9.29261i) q^{76} +(-1.75336 + 3.03691i) q^{77} +(-25.3435 - 43.8963i) q^{79} +(-19.2675 + 5.36320i) q^{80} -89.5128i q^{82} +(-29.5183 - 51.1271i) q^{83} +(-15.3913 + 59.7492i) q^{85} +(-65.9083 - 38.0522i) q^{86} +(23.5477 - 13.5953i) q^{88} +8.93057i q^{89} -2.79242 q^{91} +(12.0661 + 20.8991i) q^{92} +(19.9641 - 34.5788i) q^{94} +(6.69172 - 25.9774i) q^{95} +(113.714 - 65.6530i) q^{97} -69.1083 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) \) 24 * q - 24 * q^4 - 24 * q^7	\( 24 q - 24 q^{4} - 24 q^{7} - 12 q^{10} - 48 q^{13} - 48 q^{16} + 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{43} - 36 q^{49} + 96 q^{52} + 216 q^{55} - 396 q^{58} - 60 q^{61} + 192 q^{64} + 1032 q^{67} - 480 q^{70} - 240 q^{79} - 396 q^{85} - 240 q^{88} + 48 q^{91} - 48 q^{94} + 1440 q^{97}+O(q^{100}) \) 24 * q - 24 * q^4 - 24 * q^7 - 12 * q^10 - 48 * q^13 - 48 * q^16 + 120 * q^22 + 24 * q^25 + 60 * q^34 + 24 * q^43 - 36 * q^49 + 96 * q^52 + 216 * q^55 - 396 * q^58 - 60 * q^61 + 192 * q^64 + 1032 * q^67 - 480 * q^70 - 240 * q^79 - 396 * q^85 - 240 * q^88 + 48 * q^91 - 48 * q^94 + 1440 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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