LMFDB - Embedded newform 135.3.g.b.82.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(28,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("135.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.g (of order $4$, degree $2$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 286x^{12} + 16269x^{8} + 85684x^{4} + 62500 $ x^16 + 286x^12 + 16269x^8 + 85684*x^4 + 62500
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			82.5
Root			$0.683187 + 0.683187i$ of defining polynomial
Character	$\chi$	$=$	135.82
Dual form			135.3.g.b.28.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.683187 + 0.683187i) q^{2} -3.06651i q^{4} +(2.52793 + 4.31388i) q^{5} +(1.91393 + 1.91393i) q^{7} +(4.82775 - 4.82775i) q^{8} +(-1.22013 + 4.67423i) q^{10} +16.0422 q^{11} +(0.607722 - 0.607722i) q^{13} +2.61514i q^{14} -5.66955 q^{16} +(7.56049 + 7.56049i) q^{17} -21.0707i q^{19} +(13.2286 - 7.75194i) q^{20} +(10.9598 + 10.9598i) q^{22} +(-25.2822 + 25.2822i) q^{23} +(-12.2191 + 21.8104i) q^{25} +0.830376 q^{26} +(5.86908 - 5.86908i) q^{28} -13.4595i q^{29} -39.2058 q^{31} +(-23.1843 - 23.1843i) q^{32} +10.3305i q^{34} +(-3.41817 + 13.0947i) q^{35} +(5.47784 + 5.47784i) q^{37} +(14.3952 - 14.3952i) q^{38} +(33.0305 + 8.62209i) q^{40} -69.4260 q^{41} +(55.6177 - 55.6177i) q^{43} -49.1937i q^{44} -34.5449 q^{46} +(-13.7120 - 13.7120i) q^{47} -41.6738i q^{49} +(-23.2485 + 6.55265i) q^{50} +(-1.86359 - 1.86359i) q^{52} +(-34.8894 + 34.8894i) q^{53} +(40.5537 + 69.2043i) q^{55} +18.4799 q^{56} +(9.19538 - 9.19538i) q^{58} +62.0004i q^{59} -67.2121 q^{61} +(-26.7849 - 26.7849i) q^{62} -9.00028i q^{64} +(4.15792 + 1.08536i) q^{65} +(29.2919 + 29.2919i) q^{67} +(23.1843 - 23.1843i) q^{68} +(-11.2814 + 6.61090i) q^{70} +71.3882 q^{71} +(-23.5751 + 23.5751i) q^{73} +7.48478i q^{74} -64.6135 q^{76} +(30.7037 + 30.7037i) q^{77} -5.61768i q^{79} +(-14.3322 - 24.4577i) q^{80} +(-47.4309 - 47.4309i) q^{82} +(26.0960 - 26.0960i) q^{83} +(-13.5026 + 51.7275i) q^{85} +75.9945 q^{86} +(77.4479 - 77.4479i) q^{88} +23.2369i q^{89} +2.32627 q^{91} +(77.5282 + 77.5282i) q^{92} -18.7357i q^{94} +(90.8964 - 53.2653i) q^{95} +(97.3193 + 97.3193i) q^{97} +(28.4710 - 28.4710i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{7} + 40 q^{10} + 40 q^{13} - 152 q^{16} - 136 q^{22} - 32 q^{25} - 112 q^{28} + 200 q^{31} + 16 q^{37} - 48 q^{40} + 136 q^{43} + 152 q^{46} + 640 q^{52} + 248 q^{55} + 48 q^{58} - 280 q^{61}+ \cdots + 448 q^{97}+O(q^{100}) $ 16 * q + 16 * q^7 + 40 * q^10 + 40 * q^13 - 152 * q^16 - 136 * q^22 - 32 * q^25 - 112 * q^28 + 200 * q^31 + 16 * q^37 - 48 * q^40 + 136 * q^43 + 152 * q^46 + 640 * q^52 + 248 * q^55 + 48 * q^58 - 280 * q^61 - 344 * q^67 - 696 * q^70 - 776 * q^73 + 144 * q^76 - 880 * q^82 - 176 * q^85 + 1200 * q^88 + 152 * q^91 + 448 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.683187	+	0.683187i	0.341593	+	0.341593i	0.856966	−	0.515373i	$-0.172347\pi$
$2$	0.683187	+	0.683187i	0.341593	+	0.341593i	−0.515373	+	0.856966i	$0.672347\pi$
$3$		0			0
$3$		0			0
$4$		−	3.06651i		−	0.766628i
$5$	2.52793	+	4.31388i	0.505587	+	0.862776i
$5$	2.52793	+	4.31388i	0.505587	+	0.862776i
$6$		0			0
$7$	1.91393	+	1.91393i	0.273418	+	0.273418i	0.830475	−	0.557056i	$-0.188069\pi$
$7$	1.91393	+	1.91393i	0.273418	+	0.273418i	−0.557056	+	0.830475i	$0.688069\pi$
$8$	4.82775	−	4.82775i	0.603468	−	0.603468i
$9$		0			0
$10$	−1.22013	+	4.67423i	−0.122013	+	0.467423i
$11$	16.0422			1.45839			0.729193	−	0.684308i	$-0.239896\pi$
$11$	16.0422			1.45839			0.729193	+	0.684308i	$0.239896\pi$
$12$		0			0
$13$	0.607722	−	0.607722i	0.0467479	−	0.0467479i	−0.683346	−	0.730094i	$-0.739476\pi$
$13$	0.607722	−	0.607722i	0.0467479	−	0.0467479i	0.730094	+	0.683346i	$0.239476\pi$
$14$			2.61514i			0.186796i
$15$		0			0
$16$	−5.66955			−0.354347
$17$	7.56049	+	7.56049i	0.444735	+	0.444735i	0.893600	−	0.448865i	$-0.148172\pi$
$17$	7.56049	+	7.56049i	0.444735	+	0.444735i	−0.448865	+	0.893600i	$0.648172\pi$
$18$		0			0
$19$		−	21.0707i		−	1.10898i	−0.832189	−	0.554492i	$-0.812913\pi$
$19$		−	21.0707i		−	1.10898i	0.832189	−	0.554492i	$-0.187087\pi$
$20$	13.2286	−	7.75194i	0.661428	−	0.387597i
$21$		0			0
$22$	10.9598	+	10.9598i	0.498175	+	0.498175i
$23$	−25.2822	+	25.2822i	−1.09923	+	1.09923i	−0.104725	+	0.994501i	$0.533396\pi$
$23$	−25.2822	+	25.2822i	−1.09923	+	1.09923i	−0.994501	+	0.104725i	$0.966604\pi$
$24$		0			0
$25$	−12.2191	+	21.8104i	−0.488764	+	0.872416i
$26$	0.830376			0.0319375
$27$		0			0
$28$	5.86908	−	5.86908i	0.209610	−	0.209610i
$29$		−	13.4595i		−	0.464122i	−0.972701	−	0.232061i	$-0.925453\pi$
$29$		−	13.4595i		−	0.464122i	0.972701	−	0.232061i	$-0.0745469\pi$
$30$		0			0
$31$	−39.2058			−1.26470			−0.632352	−	0.774681i	$-0.717910\pi$
$31$	−39.2058			−1.26470			−0.632352	+	0.774681i	$0.717910\pi$
$32$	−23.1843	−	23.1843i	−0.724511	−	0.724511i
$33$		0			0
$34$			10.3305i			0.303837i
$35$	−3.41817	+	13.0947i	−0.0976620	+	0.374135i
$36$		0			0
$37$	5.47784	+	5.47784i	0.148050	+	0.148050i	0.777246	−	0.629196i	$-0.216616\pi$
$37$	5.47784	+	5.47784i	0.148050	+	0.148050i	−0.629196	+	0.777246i	$0.716616\pi$
$38$	14.3952	−	14.3952i	0.378821	−	0.378821i
$39$		0			0
$40$	33.0305	+	8.62209i	0.825763	+	0.215552i
$41$	−69.4260			−1.69332			−0.846658	−	0.532137i	$-0.821389\pi$
$41$	−69.4260			−1.69332			−0.846658	+	0.532137i	$0.821389\pi$
$42$		0			0
$43$	55.6177	−	55.6177i	1.29343	−	1.29343i	0.360785	−	0.932649i	$-0.382509\pi$
$43$	55.6177	−	55.6177i	1.29343	−	1.29343i	0.932649	−	0.360785i	$-0.117491\pi$
$44$		−	49.1937i		−	1.11804i
$45$		0			0
$46$	−34.5449			−0.750976
$47$	−13.7120	−	13.7120i	−0.291745	−	0.291745i	0.546024	−	0.837769i	$-0.316141\pi$
$47$	−13.7120	−	13.7120i	−0.291745	−	0.291745i	−0.837769	+	0.546024i	$0.816141\pi$
$48$		0			0
$49$		−	41.6738i		−	0.850485i
$50$	−23.2485	+	6.55265i	−0.464970	+	0.131053i
$51$		0			0
$52$	−1.86359	−	1.86359i	−0.0358382	−	0.0358382i
$53$	−34.8894	+	34.8894i	−0.658290	+	0.658290i	−0.954975	−	0.296685i	$-0.904119\pi$
$53$	−34.8894	+	34.8894i	−0.658290	+	0.658290i	0.296685	+	0.954975i	$0.404119\pi$
$54$		0			0
$55$	40.5537	+	69.2043i	0.737341	+	1.25826i
$56$	18.4799			0.329998
$57$		0			0
$58$	9.19538	−	9.19538i	0.158541	−	0.158541i
$59$			62.0004i			1.05085i	0.850839	+	0.525427i	$0.176094\pi$
$59$			62.0004i			1.05085i	−0.850839	+	0.525427i	$0.823906\pi$
$60$		0			0
$61$	−67.2121			−1.10184			−0.550919	−	0.834559i	$-0.685723\pi$
$61$	−67.2121			−1.10184			−0.550919	+	0.834559i	$0.685723\pi$
$62$	−26.7849	−	26.7849i	−0.432014	−	0.432014i
$63$		0			0
$64$		−	9.00028i		−	0.140629i
$65$	4.15792	+	1.08536i	0.0639680	+	0.0166978i
$66$		0			0
$67$	29.2919	+	29.2919i	0.437192	+	0.437192i	0.891066	−	0.453874i	$-0.149958\pi$
$67$	29.2919	+	29.2919i	0.437192	+	0.437192i	−0.453874	+	0.891066i	$0.649958\pi$
$68$	23.1843	−	23.1843i	0.340946	−	0.340946i
$69$		0			0
$70$	−11.2814	+	6.61090i	−0.161163	+	0.0944414i
$71$	71.3882			1.00547			0.502734	−	0.864441i	$-0.332328\pi$
$71$	71.3882			1.00547			0.502734	+	0.864441i	$0.332328\pi$
$72$		0			0
$73$	−23.5751	+	23.5751i	−0.322947	+	0.322947i	−0.849896	−	0.526950i	$-0.823336\pi$
$73$	−23.5751	+	23.5751i	−0.322947	+	0.322947i	0.526950	+	0.849896i	$0.323336\pi$
$74$			7.48478i			0.101146i
$75$		0			0
$76$	−64.6135			−0.850178
$77$	30.7037	+	30.7037i	0.398749	+	0.398749i
$78$		0			0
$79$		−	5.61768i		−	0.0711099i	−0.999368	−	0.0355550i	$-0.988680\pi$
$79$		−	5.61768i		−	0.0711099i	0.999368	−	0.0355550i	$-0.0113199\pi$
$80$	−14.3322	−	24.4577i	−0.179153	−	0.305722i
$81$		0			0
$82$	−47.4309	−	47.4309i	−0.578425	−	0.578425i
$83$	26.0960	−	26.0960i	0.314410	−	0.314410i	−0.532206	−	0.846615i	$-0.678637\pi$
$83$	26.0960	−	26.0960i	0.314410	−	0.314410i	0.846615	+	0.532206i	$0.178637\pi$
$84$		0			0
$85$	−13.5026	+	51.7275i	−0.158854	+	0.608559i
$86$	75.9945			0.883657
$87$		0			0
$88$	77.4479	−	77.4479i	0.880089	−	0.880089i
$89$			23.2369i			0.261089i	0.991442	+	0.130545i	$0.0416726\pi$
$89$			23.2369i			0.261089i	−0.991442	+	0.130545i	$0.958327\pi$
$90$		0			0
$91$	2.32627			0.0255634
$92$	77.5282	+	77.5282i	0.842698	+	0.842698i
$93$		0			0
$94$		−	18.7357i		−	0.199316i
$95$	90.8964	−	53.2653i	0.956804	−	0.560688i
$96$		0			0
$97$	97.3193	+	97.3193i	1.00329	+	1.00329i	0.999995	+	0.00329707i	$0.00104949\pi$
$97$	97.3193	+	97.3193i	1.00329	+	1.00329i	0.00329707	+	0.999995i	$0.498951\pi$
$98$	28.4710	−	28.4710i	0.290520	−	0.290520i
$99$		0			0
$100$	66.8819	+	37.4700i	0.668819	+	0.374700i
$101$	−122.375			−1.21163			−0.605815	−	0.795606i	$-0.707153\pi$
$101$	−122.375			−1.21163			−0.605815	+	0.795606i	$0.707153\pi$
$102$		0			0
$103$	−14.4661	+	14.4661i	−0.140447	+	0.140447i	−0.773835	−	0.633387i	$-0.781664\pi$
$103$	−14.4661	+	14.4661i	−0.140447	+	0.140447i	0.633387	+	0.773835i	$0.281664\pi$
$104$		−	5.86786i		−	0.0564217i
$105$		0			0
$106$	−47.6719			−0.449735
$107$	133.967	+	133.967i	1.25203	+	1.25203i	0.954809	+	0.297221i	$0.0960599\pi$
$107$	133.967	+	133.967i	1.25203	+	1.25203i	0.297221	+	0.954809i	$0.403940\pi$
$108$		0			0
$109$		−	162.075i		−	1.48692i	−0.668778	−	0.743462i	$-0.733183\pi$
$109$		−	162.075i		−	1.48692i	0.668778	−	0.743462i	$-0.266817\pi$
$110$	−19.5737	+	74.9852i	−0.177942	+	0.681684i
$111$		0			0
$112$	−10.8511	−	10.8511i	−0.0968848	−	0.0968848i
$113$	93.7017	−	93.7017i	0.829219	−	0.829219i	−0.158190	−	0.987409i	$-0.550566\pi$
$113$	93.7017	−	93.7017i	0.829219	−	0.829219i	0.987409	+	0.158190i	$0.0505658\pi$
$114$		0			0
$115$	−172.976	−	45.1526i	−1.50414	−	0.392631i
$116$	−41.2738			−0.355809
$117$		0			0
$118$	−42.3578	+	42.3578i	−0.358965	+	0.358965i
$119$			28.9405i			0.243197i
$120$		0			0
$121$	136.353			1.12689
$122$	−45.9184	−	45.9184i	−0.376380	−	0.376380i
$123$		0			0
$124$			120.225i			0.969558i
$125$	−124.977	+	2.42357i	−0.999812	+	0.0193885i
$126$		0			0
$127$	24.9948	+	24.9948i	0.196810	+	0.196810i	0.798631	−	0.601821i	$-0.205558\pi$
$127$	24.9948	+	24.9948i	0.196810	+	0.196810i	−0.601821	+	0.798631i	$0.705558\pi$
$128$	−86.5885	+	86.5885i	−0.676473	+	0.676473i
$129$		0			0
$130$	2.09913	+	3.58214i	0.0161472	+	0.0275549i
$131$	80.1902			0.612139			0.306069	−	0.952009i	$-0.400986\pi$
$131$	80.1902			0.612139			0.306069	+	0.952009i	$0.400986\pi$
$132$		0			0
$133$	40.3278	−	40.3278i	0.303216	−	0.303216i
$134$			40.0237i			0.298684i
$135$		0			0
$136$	73.0003			0.536767
$137$	−156.457	−	156.457i	−1.14202	−	1.14202i	−0.988080	−	0.153940i	$-0.950804\pi$
$137$	−156.457	−	156.457i	−1.14202	−	1.14202i	−0.153940	−	0.988080i	$-0.549196\pi$
$138$		0			0
$139$		−	63.5449i		−	0.457158i	−0.973525	−	0.228579i	$-0.926592\pi$
$139$		−	63.5449i		−	0.457158i	0.973525	−	0.228579i	$-0.0734079\pi$
$140$	40.1552	+	10.4819i	0.286823	+	0.0748704i
$141$		0			0
$142$	48.7715	+	48.7715i	0.343461	+	0.343461i
$143$	9.74923	−	9.74923i	0.0681764	−	0.0681764i
$144$		0			0
$145$	58.0628	−	34.0248i	0.400433	−	0.234654i
$146$	−32.2124			−0.220633
$147$		0			0
$148$	16.7979	−	16.7979i	0.113499	−	0.113499i
$149$		−	148.160i		−	0.994360i	−0.867647	−	0.497180i	$-0.834369\pi$
$149$		−	148.160i		−	0.994360i	0.867647	−	0.497180i	$-0.165631\pi$
$150$		0			0
$151$	−37.1721			−0.246173			−0.123086	−	0.992396i	$-0.539279\pi$
$151$	−37.1721			−0.246173			−0.123086	+	0.992396i	$0.539279\pi$
$152$	−101.724	−	101.724i	−0.669237	−	0.669237i
$153$		0			0
$154$			41.9527i			0.272420i
$155$	−99.1097	−	169.129i	−0.639418	−	1.09116i
$156$		0			0
$157$	−135.379	−	135.379i	−0.862285	−	0.862285i	0.129318	−	0.991603i	$-0.458721\pi$
$157$	−135.379	−	135.379i	−0.862285	−	0.862285i	−0.991603	+	0.129318i	$0.958721\pi$
$158$	3.83793	−	3.83793i	0.0242907	−	0.0242907i
$159$		0			0
$160$	41.4059	−	158.623i	0.258787	−	0.991393i
$161$	−96.7766			−0.601097
$162$		0			0
$163$	−202.426	+	202.426i	−1.24188	+	1.24188i	−0.282654	+	0.959222i	$0.591215\pi$
$163$	−202.426	+	202.426i	−1.24188	+	1.24188i	−0.959222	+	0.282654i	$0.908785\pi$
$164$			212.896i			1.29814i
$165$		0			0
$166$	35.6569			0.214800
$167$	15.4478	+	15.4478i	0.0925018	+	0.0925018i	0.751843	−	0.659342i	$-0.229165\pi$
$167$	15.4478	+	15.4478i	0.0925018	+	0.0925018i	−0.659342	+	0.751843i	$0.729165\pi$
$168$		0			0
$169$			168.261i			0.995629i
$170$	−44.5643	+	26.1147i	−0.262143	+	0.153616i
$171$		0			0
$172$	−170.552	−	170.552i	−0.991583	−	0.991583i
$173$	−102.849	+	102.849i	−0.594501	+	0.594501i	−0.938844	−	0.344343i	$-0.888102\pi$
$173$	−102.849	+	102.849i	−0.594501	+	0.594501i	0.344343	+	0.938844i	$0.388102\pi$
$174$		0			0
$175$	−65.1300	+	18.3571i	−0.372171	+	0.104898i
$176$	−90.9522			−0.516774
$177$		0			0
$178$	−15.8752	+	15.8752i	−0.0891863	+	0.0891863i
$179$		−	159.775i		−	0.892599i	−0.894884	−	0.446299i	$-0.852742\pi$
$179$		−	159.775i		−	0.892599i	0.894884	−	0.446299i	$-0.147258\pi$
$180$		0			0
$181$	204.918			1.13214			0.566070	−	0.824357i	$-0.308463\pi$
$181$	204.918			1.13214			0.566070	+	0.824357i	$0.308463\pi$
$182$	1.58928	+	1.58928i	0.00873230	+	0.00873230i
$183$		0			0
$184$			244.112i			1.32670i
$185$	−9.78312	+	37.4784i	−0.0528817	+	0.202586i
$186$		0			0
$187$	121.287	+	121.287i	0.648595	+	0.648595i
$188$	−42.0481	+	42.0481i	−0.223660	+	0.223660i
$189$		0			0
$190$	98.4894	+	25.7091i	0.518365	+	0.135311i
$191$	57.2319			0.299644			0.149822	−	0.988713i	$-0.452130\pi$
$191$	57.2319			0.299644			0.149822	+	0.988713i	$0.452130\pi$
$192$		0			0
$193$	−94.2729	+	94.2729i	−0.488461	+	0.488461i	−0.907820	−	0.419359i	$-0.862255\pi$
$193$	−94.2729	+	94.2729i	−0.488461	+	0.488461i	0.419359	+	0.907820i	$0.362255\pi$
$194$			132.974i			0.685435i
$195$		0			0
$196$	−127.793			−0.652006
$197$	−45.0889	−	45.0889i	−0.228878	−	0.228878i	0.583346	−	0.812224i	$-0.301743\pi$
$197$	−45.0889	−	45.0889i	−0.228878	−	0.228878i	−0.812224	+	0.583346i	$0.801743\pi$
$198$		0			0
$199$		−	158.275i		−	0.795352i	−0.917526	−	0.397676i	$-0.869817\pi$
$199$		−	158.275i		−	0.795352i	0.917526	−	0.397676i	$-0.130183\pi$
$200$	46.3044	+	164.286i	0.231522	+	0.821429i
$201$		0			0
$202$	−83.6047	−	83.6047i	−0.413885	−	0.413885i
$203$	25.7606	−	25.7606i	0.126899	−	0.126899i
$204$		0			0
$205$	−175.504	−	299.495i	−0.856118	−	1.46095i
$206$	−19.7661			−0.0959518
$207$		0			0
$208$	−3.44551	+	3.44551i	−0.0165650	+	0.0165650i
$209$		−	338.021i		−	1.61733i
$210$		0			0
$211$	261.703			1.24030			0.620150	−	0.784484i	$-0.287072\pi$
$211$	261.703			1.24030			0.620150	+	0.784484i	$0.287072\pi$
$212$	106.989	+	106.989i	0.504664	+	0.504664i
$213$		0			0
$214$			183.049i			0.855370i
$215$	380.526	+	99.3300i	1.76989	+	0.462000i
$216$		0			0
$217$	−75.0371	−	75.0371i	−0.345793	−	0.345793i
$218$	110.727	−	110.727i	0.507923	−	0.507923i
$219$		0			0
$220$	212.216	−	124.359i	0.964617	−	0.565266i
$221$	9.18936			0.0415808
$222$		0			0
$223$	180.063	−	180.063i	0.807458	−	0.807458i	−0.176790	−	0.984249i	$-0.556572\pi$
$223$	180.063	−	180.063i	0.807458	−	0.807458i	0.984249	+	0.176790i	$0.0565715\pi$
$224$		−	88.7463i		−	0.396189i
$225$		0			0
$226$	128.032			0.566511
$227$	187.888	+	187.888i	0.827699	+	0.827699i	0.987198	−	0.159499i	$-0.0509880\pi$
$227$	187.888	+	187.888i	0.827699	+	0.827699i	−0.159499	+	0.987198i	$0.550988\pi$
$228$		0			0
$229$			132.747i			0.579679i	0.957075	+	0.289840i	$0.0936020\pi$
$229$			132.747i			0.579679i	−0.957075	+	0.289840i	$0.906398\pi$
$230$	−87.3273	−	149.023i	−0.379684	−	0.647924i
$231$		0			0
$232$	−64.9792	−	64.9792i	−0.280083	−	0.280083i
$233$	−53.9875	+	53.9875i	−0.231706	+	0.231706i	−0.813404	−	0.581699i	$-0.802388\pi$
$233$	−53.9875	+	53.9875i	−0.231706	+	0.231706i	0.581699	+	0.813404i	$0.302388\pi$
$234$		0			0
$235$	24.4889	−	93.8151i	0.104208	−	0.399213i
$236$	190.125			0.805614
$237$		0			0
$238$	−19.7717	+	19.7717i	−0.0830745	+	0.0830745i
$239$			103.767i			0.434171i	0.976153	+	0.217085i	$0.0696550\pi$
$239$			103.767i			0.434171i	−0.976153	+	0.217085i	$0.930345\pi$
$240$		0			0
$241$	281.196			1.16679			0.583395	−	0.812188i	$-0.301724\pi$
$241$	281.196			1.16679			0.583395	+	0.812188i	$0.301724\pi$
$242$	93.1549	+	93.1549i	0.384938	+	0.384938i
$243$		0			0
$244$			206.107i			0.844699i
$245$	179.776	−	105.349i	0.733778	−	0.429994i
$246$		0			0
$247$	−12.8051	−	12.8051i	−0.0518426	−	0.0518426i
$248$	−189.276	+	189.276i	−0.763209	+	0.763209i
$249$		0			0
$250$	−87.0380	−	83.7265i	−0.348152	−	0.334906i
$251$	313.354			1.24842			0.624212	−	0.781255i	$-0.285420\pi$
$251$	313.354			1.24842			0.624212	+	0.781255i	$0.285420\pi$
$252$		0			0
$253$	−405.583	+	405.583i	−1.60310	+	1.60310i
$254$			34.1523i			0.134458i
$255$		0			0
$256$	−154.313			−0.602786
$257$	−141.763	−	141.763i	−0.551609	−	0.551609i	0.375296	−	0.926905i	$-0.377541\pi$
$257$	−141.763	−	141.763i	−0.551609	−	0.551609i	−0.926905	+	0.375296i	$0.877541\pi$
$258$		0			0
$259$			20.9684i			0.0809590i
$260$	3.32826	−	12.7503i	0.0128010	−	0.0490397i
$261$		0			0
$262$	54.7849	+	54.7849i	0.209103	+	0.209103i
$263$	170.260	−	170.260i	0.647375	−	0.647375i	−0.304983	−	0.952358i	$-0.598651\pi$
$263$	170.260	−	170.260i	0.647375	−	0.647375i	0.952358	+	0.304983i	$0.0986507\pi$
$264$		0			0
$265$	−238.707	−	62.3105i	−0.900780	−	0.235134i
$266$	55.1028			0.207153
$267$		0			0
$268$	89.8240	−	89.8240i	0.335164	−	0.335164i
$269$			476.960i			1.77309i	0.462646	+	0.886543i	$0.346900\pi$
$269$			476.960i			1.77309i	−0.462646	+	0.886543i	$0.653100\pi$
$270$		0			0
$271$	105.987			0.391095			0.195548	−	0.980694i	$-0.437352\pi$
$271$	105.987			0.391095			0.195548	+	0.980694i	$0.437352\pi$
$272$	−42.8646	−	42.8646i	−0.157590	−	0.157590i
$273$		0			0
$274$		−	213.778i		−	0.780213i
$275$	−196.022	+	349.888i	−0.712806	+	1.27232i
$276$		0			0
$277$	2.45621	+	2.45621i	0.00886718	+	0.00886718i	0.711526	−	0.702659i	$-0.248004\pi$
$277$	2.45621	+	2.45621i	0.00886718	+	0.00886718i	−0.702659	+	0.711526i	$0.748004\pi$
$278$	43.4130	−	43.4130i	0.156162	−	0.156162i
$279$		0			0
$280$	46.7160	+	79.7201i	0.166843	+	0.284715i
$281$	206.625			0.735321			0.367660	−	0.929960i	$-0.380159\pi$
$281$	206.625			0.735321			0.367660	+	0.929960i	$0.380159\pi$
$282$		0			0
$283$	−40.8251	+	40.8251i	−0.144258	+	0.144258i	−0.775547	−	0.631289i	$-0.782526\pi$
$283$	−40.8251	+	40.8251i	−0.144258	+	0.144258i	0.631289	+	0.775547i	$0.282526\pi$
$284$		−	218.913i		−	0.770820i
$285$		0			0
$286$	13.3211			0.0465772
$287$	−132.876	−	132.876i	−0.462984	−	0.462984i
$288$		0			0
$289$		−	174.678i		−	0.604422i
$290$	62.9130	+	16.4224i	0.216942	+	0.0566291i
$291$		0			0
$292$	72.2934	+	72.2934i	0.247580	+	0.247580i
$293$	−212.663	+	212.663i	−0.725811	+	0.725811i	−0.969782	−	0.243971i	$-0.921550\pi$
$293$	−212.663	+	212.663i	−0.725811	+	0.725811i	0.243971	+	0.969782i	$0.421550\pi$
$294$		0			0
$295$	−267.462	+	156.733i	−0.906651	+	0.531298i
$296$	52.8913			0.178687
$297$		0			0
$298$	101.221	−	101.221i	0.339667	−	0.339667i
$299$			30.7291i			0.102773i
$300$		0			0
$301$	212.896			0.707297
$302$	−25.3955	−	25.3955i	−0.0840910	−	0.0840910i
$303$		0			0
$304$			119.461i			0.392965i
$305$	−169.908	−	289.945i	−0.557074	−	0.950638i
$306$		0			0
$307$	6.45878	+	6.45878i	0.0210384	+	0.0210384i	0.717548	−	0.696509i	$-0.245265\pi$
$307$	6.45878	+	6.45878i	0.0210384	+	0.0210384i	−0.696509	+	0.717548i	$0.745265\pi$
$308$	94.1532	−	94.1532i	0.305692	−	0.305692i
$309$		0			0
$310$	47.8363	−	183.257i	0.154311	−	0.591152i
$311$	−429.168			−1.37996			−0.689980	−	0.723828i	$-0.742381\pi$
$311$	−429.168			−1.37996			−0.689980	+	0.723828i	$0.742381\pi$
$312$		0			0
$313$	−91.6067	+	91.6067i	−0.292673	+	0.292673i	−0.838135	−	0.545462i	$-0.816354\pi$
$313$	−91.6067	+	91.6067i	−0.292673	+	0.292673i	0.545462	+	0.838135i	$0.316354\pi$
$314$		−	184.978i		−	0.589102i
$315$		0			0
$316$	−17.2267			−0.0545148
$317$	−101.368	−	101.368i	−0.319771	−	0.319771i	0.528908	−	0.848679i	$-0.322602\pi$
$317$	−101.368	−	101.368i	−0.319771	−	0.319771i	−0.848679	+	0.528908i	$0.822602\pi$
$318$		0			0
$319$		−	215.921i		−	0.676869i
$320$	38.8261	−	22.7521i	0.121332	−	0.0711003i
$321$		0			0
$322$	−66.1165	−	66.1165i	−0.205331	−	0.205331i
$323$	159.305	−	159.305i	0.493204	−	0.493204i
$324$		0			0
$325$	5.82885	+	20.6805i	0.0179349	+	0.0636323i
$326$	−276.589			−0.848433
$327$		0			0
$328$	−335.171	+	335.171i	−1.02186	+	1.02186i
$329$		−	52.4877i		−	0.159537i
$330$		0			0
$331$	−40.7620			−0.123148			−0.0615741	−	0.998103i	$-0.519612\pi$
$331$	−40.7620			−0.123148			−0.0615741	+	0.998103i	$0.519612\pi$
$332$	−80.0237	−	80.0237i	−0.241035	−	0.241035i
$333$		0			0
$334$			21.1075i			0.0631960i
$335$	−52.3137	+	200.410i	−0.156160	+	0.598238i
$336$		0			0
$337$	251.752	+	251.752i	0.747038	+	0.747038i	0.973922	−	0.226884i	$-0.0728539\pi$
$337$	251.752	+	251.752i	0.747038	+	0.747038i	−0.226884	+	0.973922i	$0.572854\pi$
$338$	−114.954	+	114.954i	−0.340100	+	0.340100i
$339$		0			0
$340$	158.623	+	41.4059i	0.466538	+	0.121782i
$341$	−628.949			−1.84443
$342$		0			0
$343$	173.543	−	173.543i	0.505956	−	0.505956i
$344$		−	537.016i		−	1.56109i
$345$		0			0
$346$	−140.530			−0.406155
$347$	119.157	+	119.157i	0.343392	+	0.343392i	0.857641	−	0.514249i	$-0.171929\pi$
$347$	119.157	+	119.157i	0.343392	+	0.343392i	−0.514249	+	0.857641i	$0.671929\pi$
$348$		0			0
$349$			16.0231i			0.0459116i	0.999736	+	0.0229558i	$0.00730770\pi$
$349$			16.0231i			0.0459116i	−0.999736	+	0.0229558i	$0.992692\pi$
$350$	−57.0372	−	31.9546i	−0.162964	−	0.0912990i
$351$		0			0
$352$	−371.929	−	371.929i	−1.05662	−	1.05662i
$353$	−147.916	+	147.916i	−0.419025	+	0.419025i	−0.884868	−	0.465842i	$-0.845751\pi$
$353$	−147.916	+	147.916i	−0.419025	+	0.419025i	0.465842	+	0.884868i	$0.345751\pi$
$354$		0			0
$355$	180.465	+	307.960i	0.508351	+	0.867493i
$356$	71.2563			0.200158
$357$		0			0
$358$	109.156	−	109.156i	0.304906	−	0.304906i
$359$			160.120i			0.446018i	0.974816	+	0.223009i	$0.0715879\pi$
$359$			160.120i			0.446018i	−0.974816	+	0.223009i	$0.928412\pi$
$360$		0			0
$361$	−82.9741			−0.229845
$362$	139.997	+	139.997i	0.386732	+	0.386732i
$363$		0			0
$364$		−	7.13355i		−	0.0195977i
$365$	−161.297	−	42.1038i	−0.441908	−	0.115353i
$366$		0			0
$367$	146.732	+	146.732i	0.399814	+	0.399814i	0.878168	−	0.478353i	$-0.158766\pi$
$367$	146.732	+	146.732i	0.399814	+	0.399814i	−0.478353	+	0.878168i	$0.658766\pi$
$368$	143.339	−	143.339i	0.389507	−	0.389507i
$369$		0			0
$370$	−32.2884	+	18.9210i	−0.0872660	+	0.0511379i
$371$	−133.552			−0.359977
$372$		0			0
$373$	275.593	−	275.593i	0.738854	−	0.738854i	−0.233502	−	0.972356i	$-0.575019\pi$
$373$	275.593	−	275.593i	0.738854	−	0.738854i	0.972356	+	0.233502i	$0.0750185\pi$
$374$			165.724i			0.443111i
$375$		0			0
$376$	−132.396			−0.352118
$377$	−8.17966	−	8.17966i	−0.0216967	−	0.0216967i
$378$		0			0
$379$		−	276.991i		−	0.730846i	−0.930842	−	0.365423i	$-0.880924\pi$
$379$		−	276.991i		−	0.730846i	0.930842	−	0.365423i	$-0.119076\pi$
$380$	−163.339	−	278.735i	−0.429839	−	0.733513i
$381$		0			0
$382$	39.1001	+	39.1001i	0.102356	+	0.102356i
$383$	−29.6395	+	29.6395i	−0.0773876	+	0.0773876i	−0.744741	−	0.667353i	$-0.767427\pi$
$383$	−29.6395	+	29.6395i	−0.0773876	+	0.0773876i	0.667353	+	0.744741i	$0.267427\pi$
$384$		0			0
$385$	−54.8351	+	210.069i	−0.142429	+	0.545634i
$386$	−128.812			−0.333710
$387$		0			0
$388$	298.431	−	298.431i	0.769152	−	0.769152i
$389$			609.728i			1.56742i	0.621124	+	0.783712i	$0.286676\pi$
$389$			609.728i			1.56742i	−0.621124	+	0.783712i	$0.713324\pi$
$390$		0			0
$391$	−382.292			−0.977728
$392$	−201.190	−	201.190i	−0.513241	−	0.513241i
$393$		0			0
$394$		−	61.6083i		−	0.156366i
$395$	24.2340	−	14.2011i	0.0613519	−	0.0359522i
$396$		0			0
$397$	353.820	+	353.820i	0.891235	+	0.891235i	0.994639	−	0.103404i	$-0.0329735\pi$
$397$	353.820	+	353.820i	0.891235	+	0.891235i	−0.103404	+	0.994639i	$0.532974\pi$
$398$	108.131	−	108.131i	0.271687	−	0.271687i
$399$		0			0
$400$	69.2767	−	123.655i	0.173192	−	0.309138i
$401$	510.979			1.27426			0.637131	−	0.770756i	$-0.280121\pi$
$401$	510.979			1.27426			0.637131	+	0.770756i	$0.280121\pi$
$402$		0			0
$403$	−23.8263	+	23.8263i	−0.0591222	+	0.0591222i
$404$			375.263i			0.928869i
$405$		0			0
$406$	35.1986			0.0866960
$407$	87.8769	+	87.8769i	0.215914	+	0.215914i
$408$		0			0
$409$		−	129.175i		−	0.315831i	−0.987453	−	0.157916i	$-0.949523\pi$
$409$		−	129.175i		−	0.315831i	0.987453	−	0.157916i	$-0.0504774\pi$
$410$	84.7089	−	324.513i	0.206607	−	0.791496i
$411$		0			0
$412$	44.3604	+	44.3604i	0.107671	+	0.107671i
$413$	−118.664	+	118.664i	−0.287323	+	0.287323i
$414$		0			0
$415$	178.544	+	46.6060i	0.430226	+	0.112304i
$416$	−28.1793			−0.0677387
$417$		0			0
$418$	230.931	−	230.931i	0.552468	−	0.552468i
$419$		−	359.249i		−	0.857396i	−0.903448	−	0.428698i	$-0.858972\pi$
$419$		−	359.249i		−	0.857396i	0.903448	−	0.428698i	$-0.141028\pi$
$420$		0			0
$421$	−105.532			−0.250669			−0.125335	−	0.992115i	$-0.540000\pi$
$421$	−105.532			−0.250669			−0.125335	+	0.992115i	$0.540000\pi$
$422$	178.792	+	178.792i	0.423678	+	0.423678i
$423$		0			0
$424$			336.874i			0.794515i
$425$	−257.280	+	72.5150i	−0.605364	+	0.170624i
$426$		0			0
$427$	−128.639	−	128.639i	−0.301262	−	0.301262i
$428$	410.812	−	410.812i	0.959841	−	0.959841i
$429$		0			0
$430$	192.109	+	327.831i	0.446765	+	0.762398i
$431$	402.361			0.933551			0.466776	−	0.884376i	$-0.345416\pi$
$431$	402.361			0.933551			0.466776	+	0.884376i	$0.345416\pi$
$432$		0			0
$433$	36.1598	−	36.1598i	0.0835098	−	0.0835098i	−0.664118	−	0.747628i	$-0.731193\pi$
$433$	36.1598	−	36.1598i	0.0835098	−	0.0835098i	0.747628	+	0.664118i	$0.231193\pi$
$434$		−	102.529i		−	0.236241i
$435$		0			0
$436$	−497.004			−1.13992
$437$	532.713	+	532.713i	1.21902	+	1.21902i
$438$		0			0
$439$		−	172.795i		−	0.393611i	−0.980443	−	0.196805i	$-0.936943\pi$
$439$		−	172.795i		−	0.393611i	0.980443	−	0.196805i	$-0.0630567\pi$
$440$	529.884	+	138.318i	1.20428	+	0.314358i
$441$		0			0
$442$	6.27805	+	6.27805i	0.0142037	+	0.0142037i
$443$	−238.409	+	238.409i	−0.538170	+	0.538170i	−0.922991	−	0.384821i	$-0.874263\pi$
$443$	−238.409	+	238.409i	−0.538170	+	0.538170i	0.384821	+	0.922991i	$0.374263\pi$
$444$		0			0
$445$	−100.241	+	58.7414i	−0.225261	+	0.132003i
$446$	246.033			0.551644
$447$		0			0
$448$	17.2259	−	17.2259i	0.0384506	−	0.0384506i
$449$		−	272.621i		−	0.607174i	−0.952804	−	0.303587i	$-0.901816\pi$
$449$		−	272.621i		−	0.607174i	0.952804	−	0.303587i	$-0.0981843\pi$
$450$		0			0
$451$	−1113.75			−2.46951
$452$	−287.338	−	287.338i	−0.635703	−	0.635703i
$453$		0			0
$454$			256.725i			0.565473i
$455$	5.88067	+	10.0353i	0.0129245	+	0.0220555i
$456$		0			0
$457$	−583.277	−	583.277i	−1.27632	−	1.27632i	−0.942713	−	0.333605i	$-0.891735\pi$
$457$	−583.277	−	583.277i	−1.27632	−	1.27632i	−0.333605	−	0.942713i	$-0.608265\pi$
$458$	−90.6907	+	90.6907i	−0.198015	+	0.198015i
$459$		0			0
$460$	−138.461	+	530.433i	−0.301002	+	1.15312i
$461$	506.067			1.09776			0.548879	−	0.835902i	$-0.315055\pi$
$461$	506.067			1.09776			0.548879	+	0.835902i	$0.315055\pi$
$462$		0			0
$463$	129.301	−	129.301i	0.279267	−	0.279267i	−0.553549	−	0.832816i	$-0.686727\pi$
$463$	129.301	−	129.301i	0.279267	−	0.279267i	0.832816	+	0.553549i	$0.186727\pi$
$464$			76.3095i			0.164460i
$465$		0			0
$466$	−73.7670			−0.158298
$467$	−160.498	−	160.498i	−0.343679	−	0.343679i	0.514070	−	0.857748i	$-0.328137\pi$
$467$	−160.498	−	160.498i	−0.343679	−	0.343679i	−0.857748	+	0.514070i	$0.828137\pi$
$468$		0			0
$469$			112.125i			0.239073i
$470$	80.8237	−	47.3627i	0.171965	−	0.100772i
$471$		0			0
$472$	299.322	+	299.322i	0.634157	+	0.634157i
$473$	892.232	−	892.232i	1.88633	−	1.88633i
$474$		0			0
$475$	459.560	+	257.465i	0.967495	+	0.542031i
$476$	88.7463			0.186442
$477$		0			0
$478$	−70.8921	+	70.8921i	−0.148310	+	0.148310i
$479$			779.221i			1.62677i	0.581729	+	0.813383i	$0.302376\pi$
$479$			779.221i			1.62677i	−0.581729	+	0.813383i	$0.697624\pi$
$480$		0			0
$481$	6.65801			0.0138420
$482$	192.110	+	192.110i	0.398568	+	0.398568i
$483$		0			0
$484$		−	418.130i		−	0.863904i
$485$	−173.807	+	665.840i	−0.358365	+	1.37287i
$486$		0			0
$487$	523.288	+	523.288i	1.07451	+	1.07451i	0.996991	+	0.0775227i	$0.0247010\pi$
$487$	523.288	+	523.288i	1.07451	+	1.07451i	0.0775227	+	0.996991i	$0.475299\pi$
$488$	−324.483	+	324.483i	−0.664924	+	0.664924i
$489$		0			0
$490$	194.793	+	50.8475i	0.397537	+	0.103770i
$491$	−160.638			−0.327166			−0.163583	−	0.986530i	$-0.552305\pi$
$491$	−160.638			−0.327166			−0.163583	+	0.986530i	$0.552305\pi$
$492$		0			0
$493$	101.761	−	101.761i	0.206411	−	0.206411i
$494$		−	17.4966i		−	0.0354182i
$495$		0			0
$496$	222.279			0.448144
$497$	136.632	+	136.632i	0.274913	+	0.274913i
$498$		0			0
$499$		−	192.018i		−	0.384806i	−0.981316	−	0.192403i	$-0.938372\pi$
$499$		−	192.018i		−	0.384806i	0.981316	−	0.192403i	$-0.0616280\pi$
$500$	7.43189	+	383.242i	0.0148638	+	0.766484i
$501$		0			0
$502$	214.079	+	214.079i	0.426453	+	0.426453i
$503$	179.873	−	179.873i	0.357600	−	0.357600i	−0.505328	−	0.862928i	$-0.668628\pi$
$503$	179.873	−	179.873i	0.357600	−	0.357600i	0.862928	+	0.505328i	$0.168628\pi$
$504$		0			0
$505$	−309.355	−	527.909i	−0.612584	−	1.04536i
$506$	−554.178			−1.09521
$507$		0			0
$508$	76.6470	−	76.6470i	0.150880	−	0.150880i
$509$		−	45.1629i		−	0.0887286i	−0.999015	−	0.0443643i	$-0.985874\pi$
$509$		−	45.1629i		−	0.0887286i	0.999015	−	0.0443643i	$-0.0141262\pi$
$510$		0			0
$511$	−90.2421			−0.176599
$512$	240.929	+	240.929i	0.470565	+	0.470565i
$513$		0			0
$514$		−	193.702i		−	0.376852i
$515$	−98.9742	−	25.8356i	−0.192183	−	0.0501662i
$516$		0			0
$517$	−219.972	−	219.972i	−0.425477	−	0.425477i
$518$	−14.3253	+	14.3253i	−0.0276551	+	0.0276551i
$519$		0			0
$520$	25.3132	−	14.8336i	0.0486793	−	0.0285261i
$521$	−284.623			−0.546301			−0.273150	−	0.961971i	$-0.588066\pi$
$521$	−284.623			−0.546301			−0.273150	+	0.961971i	$0.588066\pi$
$522$		0			0
$523$	451.674	−	451.674i	0.863621	−	0.863621i	−0.128135	−	0.991757i	$-0.540899\pi$
$523$	451.674	−	451.674i	0.863621	−	0.863621i	0.991757	+	0.128135i	$0.0408992\pi$
$524$		−	245.904i		−	0.469283i
$525$		0			0
$526$	232.638			0.442278
$527$	−296.415	−	296.415i	−0.562458	−	0.562458i
$528$		0			0
$529$		−	749.379i		−	1.41660i
$530$	−120.512	−	205.651i	−0.227380	−	0.388021i
$531$		0			0
$532$	−123.666	−	123.666i	−0.232454	−	0.232454i
$533$	−42.1917	+	42.1917i	−0.0791589	+	0.0791589i
$534$		0			0
$535$	−239.258	+	916.578i	−0.447211	+	1.71323i
$536$	282.828			0.527664
$537$		0			0
$538$	−325.853	+	325.853i	−0.605674	+	0.605674i
$539$		−	668.541i		−	1.24033i
$540$		0			0
$541$	88.5229			0.163628			0.0818142	−	0.996648i	$-0.473929\pi$
$541$	88.5229			0.163628			0.0818142	+	0.996648i	$0.473929\pi$
$542$	72.4088	+	72.4088i	0.133595	+	0.133595i
$543$		0			0
$544$		−	350.570i		−	0.644430i
$545$	699.170	−	409.714i	1.28288	−	0.751769i
$546$		0			0
$547$	183.312	+	183.312i	0.335123	+	0.335123i	0.854528	−	0.519405i	$-0.173846\pi$
$547$	183.312	+	183.312i	0.335123	+	0.335123i	−0.519405	+	0.854528i	$0.673846\pi$
$548$	−479.776	+	479.776i	−0.875505	+	0.875505i
$549$		0			0
$550$	−372.958	+	105.119i	−0.678105	+	0.191126i
$551$	−283.602			−0.514704
$552$		0			0
$553$	10.7518	−	10.7518i	0.0194427	−	0.0194427i
$554$			3.35610i			0.00605794i
$555$		0			0
$556$	−194.861			−0.350470
$557$	−372.533	−	372.533i	−0.668821	−	0.668821i	0.288622	−	0.957443i	$-0.406803\pi$
$557$	−372.533	−	372.533i	−0.668821	−	0.668821i	−0.957443	+	0.288622i	$0.906803\pi$
$558$		0			0
$559$		−	67.6002i		−	0.120931i
$560$	19.3795	−	74.2412i	0.0346062	−	0.132574i
$561$		0			0
$562$	141.163	+	141.163i	0.251181	+	0.251181i
$563$	−727.111	+	727.111i	−1.29149	+	1.29149i	−0.357630	+	0.933863i	$0.616415\pi$
$563$	−727.111	+	727.111i	−1.29149	+	1.29149i	−0.933863	+	0.357630i	$0.883585\pi$
$564$		0			0
$565$	641.090	+	167.346i	1.13467	+	0.296188i
$566$	−55.7823			−0.0985553
$567$		0			0
$568$	344.644	−	344.644i	0.606768	−	0.606768i
$569$		−	407.776i		−	0.716653i	−0.933596	−	0.358327i	$-0.883347\pi$
$569$		−	407.776i		−	0.716653i	0.933596	−	0.358327i	$-0.116653\pi$
$570$		0			0
$571$	−107.205			−0.187750			−0.0938748	−	0.995584i	$-0.529925\pi$
$571$	−107.205			−0.187750			−0.0938748	+	0.995584i	$0.529925\pi$
$572$	−29.8961	−	29.8961i	−0.0522660	−	0.0522660i
$573$		0			0
$574$		−	181.559i		−	0.316304i
$575$	−242.489	−	860.341i	−0.421721	−	1.49624i
$576$		0			0
$577$	539.921	+	539.921i	0.935738	+	0.935738i	0.998056	−	0.0623179i	$-0.0198493\pi$
$577$	539.921	+	539.921i	0.935738	+	0.935738i	−0.0623179	+	0.998056i	$0.519849\pi$
$578$	119.338	−	119.338i	0.206466	−	0.206466i
$579$		0			0
$580$	−104.338	−	178.050i	−0.179892	−	0.306983i
$581$	99.8917			0.171931
$582$		0			0
$583$	−559.704	+	559.704i	−0.960041	+	0.960041i
$584$			227.629i			0.389776i
$585$		0			0
$586$	−290.577			−0.495864
$587$	−523.572	−	523.572i	−0.891946	−	0.891946i	0.102760	−	0.994706i	$-0.467233\pi$
$587$	−523.572	−	523.572i	−0.891946	−	0.891946i	−0.994706	+	0.102760i	$0.967233\pi$
$588$		0			0
$589$			826.094i			1.40254i
$590$	−289.804	−	75.6487i	−0.491194	−	0.128218i
$591$		0			0
$592$	−31.0569	−	31.0569i	−0.0524609	−	0.0524609i
$593$	−43.9329	+	43.9329i	−0.0740858	+	0.0740858i	−0.743179	−	0.669093i	$-0.766683\pi$
$593$	−43.9329	+	43.9329i	−0.0740858	+	0.0740858i	0.669093	+	0.743179i	$0.266683\pi$
$594$		0			0
$595$	−124.846	+	73.1596i	−0.209825	+	0.122957i
$596$	−454.333			−0.762304
$597$		0			0
$598$	−20.9937	+	20.9937i	−0.0351066	+	0.0351066i
$599$		−	110.244i		−	0.184047i	−0.995757	−	0.0920237i	$-0.970666\pi$
$599$		−	110.244i		−	0.184047i	0.995757	−	0.0920237i	$-0.0293336\pi$
$600$		0			0
$601$	614.730			1.02284			0.511422	−	0.859329i	$-0.329119\pi$
$601$	614.730			1.02284			0.511422	+	0.859329i	$0.329119\pi$
$602$	145.448	+	145.448i	0.241608	+	0.241608i
$603$		0			0
$604$			113.989i			0.188723i
$605$	344.693	+	588.212i	0.569740	+	0.972252i
$606$		0			0
$607$	−643.427	−	643.427i	−1.06001	−	1.06001i	−0.998080	−	0.0619314i	$-0.980274\pi$
$607$	−643.427	−	643.427i	−1.06001	−	1.06001i	−0.0619314	−	0.998080i	$-0.519726\pi$
$608$	−488.510	+	488.510i	−0.803471	+	0.803471i
$609$		0			0
$610$	82.0077	−	314.165i	0.134439	−	0.515025i
$611$	−16.6662			−0.0272769
$612$		0			0
$613$	60.7205	−	60.7205i	0.0990546	−	0.0990546i	−0.655843	−	0.754897i	$-0.727687\pi$
$613$	60.7205	−	60.7205i	0.0990546	−	0.0990546i	0.754897	+	0.655843i	$0.227687\pi$
$614$			8.82511i			0.0143731i
$615$		0			0
$616$	296.459			0.481265
$617$	−627.123	−	627.123i	−1.01641	−	1.01641i	−0.999863	−	0.0165444i	$-0.994734\pi$
$617$	−627.123	−	627.123i	−1.01641	−	1.01641i	−0.0165444	−	0.999863i	$-0.505266\pi$
$618$		0			0
$619$		−	587.816i		−	0.949622i	−0.880088	−	0.474811i	$-0.842516\pi$
$619$		−	587.816i		−	0.949622i	0.880088	−	0.474811i	$-0.157484\pi$
$620$	−518.637	+	303.921i	−0.836511	+	0.490196i
$621$		0			0
$622$	−293.201	−	293.201i	−0.471385	−	0.471385i
$623$	−44.4738	+	44.4738i	−0.0713865	+	0.0713865i
$624$		0			0
$625$	−326.387	−	533.007i	−0.522220	−	0.852811i
$626$	−125.169			−0.199950
$627$		0			0
$628$	−415.141	+	415.141i	−0.661052	+	0.661052i
$629$			82.8304i			0.131686i
$630$		0			0
$631$	−347.806			−0.551197			−0.275599	−	0.961273i	$-0.588876\pi$
$631$	−347.806			−0.551197			−0.275599	+	0.961273i	$0.588876\pi$
$632$	−27.1207	−	27.1207i	−0.0429126	−	0.0429126i
$633$		0			0
$634$		−	138.506i		−	0.218464i
$635$	−44.6394	+	171.010i	−0.0702982	+	0.269307i
$636$		0			0
$637$	−25.3261	−	25.3261i	−0.0397584	−	0.0397584i
$638$	147.514	−	147.514i	0.231214	−	0.231214i
$639$		0			0
$640$	−592.422	−	154.642i	−0.925660	−	0.241629i
$641$	532.992			0.831500			0.415750	−	0.909479i	$-0.363519\pi$
$641$	532.992			0.831500			0.415750	+	0.909479i	$0.363519\pi$
$642$		0			0
$643$	717.465	−	717.465i	1.11581	−	1.11581i	0.123460	−	0.992350i	$-0.460601\pi$
$643$	717.465	−	717.465i	1.11581	−	1.11581i	0.992350	−	0.123460i	$-0.0393990\pi$
$644$			296.767i			0.460818i
$645$		0			0
$646$	217.670			0.336950
$647$	−28.7251	−	28.7251i	−0.0443973	−	0.0443973i	0.684560	−	0.728957i	$-0.259995\pi$
$647$	−28.7251	−	28.7251i	−0.0443973	−	0.0443973i	−0.728957	+	0.684560i	$0.759995\pi$
$648$		0			0
$649$			994.625i			1.53255i
$650$	−10.1464	+	18.1108i	−0.0156099	+	0.0278628i
$651$		0			0
$652$	620.741	+	620.741i	0.952057	+	0.952057i
$653$	18.3291	−	18.3291i	0.0280690	−	0.0280690i	−0.692933	−	0.721002i	$-0.743682\pi$
$653$	18.3291	−	18.3291i	0.0280690	−	0.0280690i	0.721002	+	0.692933i	$0.243682\pi$
$654$		0			0
$655$	202.716	+	345.931i	0.309489	+	0.528139i
$656$	393.614			0.600021
$657$		0			0
$658$	35.8589	−	35.8589i	0.0544968	−	0.0544968i
$659$		−	698.827i		−	1.06043i	−0.847862	−	0.530217i	$-0.822110\pi$
$659$		−	698.827i		−	1.06043i	0.847862	−	0.530217i	$-0.177890\pi$
$660$		0			0
$661$	229.808			0.347667			0.173833	−	0.984775i	$-0.444385\pi$
$661$	229.808			0.347667			0.173833	+	0.984775i	$0.444385\pi$
$662$	−27.8481	−	27.8481i	−0.0420666	−	0.0420666i
$663$		0			0
$664$		−	251.970i		−	0.379472i
$665$	275.915	+	72.0232i	0.414910	+	0.108306i
$666$		0			0
$667$	340.287	+	340.287i	0.510175	+	0.510175i
$668$	47.3709	−	47.3709i	0.0709145	−	0.0709145i
$669$		0			0
$670$	−172.657	+	101.177i	−0.257697	+	0.151011i
$671$	−1078.23			−1.60690
$672$		0			0
$673$	−739.046	+	739.046i	−1.09814	+	1.09814i	−0.103509	+	0.994629i	$0.533007\pi$
$673$	−739.046	+	739.046i	−1.09814	+	1.09814i	−0.994629	+	0.103509i	$0.966993\pi$
$674$			343.987i			0.510366i
$675$		0			0
$676$	515.975			0.763277
$677$	671.650	+	671.650i	0.992098	+	0.992098i	0.999969	−	0.00787098i	$-0.00250544\pi$
$677$	671.650	+	671.650i	0.992098	+	0.992098i	−0.00787098	+	0.999969i	$0.502505\pi$
$678$		0			0
$679$			372.524i			0.548636i
$680$	184.540	+	314.914i	0.271382	+	0.463109i
$681$		0			0
$682$	−429.690	−	429.690i	−0.630044	−	0.630044i
$683$	293.612	−	293.612i	0.429885	−	0.429885i	−0.458704	−	0.888589i	$-0.651686\pi$
$683$	293.612	−	293.612i	0.429885	−	0.429885i	0.888589	+	0.458704i	$0.151686\pi$
$684$		0			0
$685$	279.423	−	1070.45i	0.407917	−	1.56270i
$686$	237.125			0.345663
$687$		0			0
$688$	−315.327	+	315.327i	−0.458324	+	0.458324i
$689$			42.4061i			0.0615474i
$690$		0			0
$691$	−566.147			−0.819316			−0.409658	−	0.912239i	$-0.634352\pi$
$691$	−566.147			−0.819316			−0.409658	+	0.912239i	$0.634352\pi$
$692$	315.387	+	315.387i	0.455761	+	0.455761i
$693$		0			0
$694$			162.813i			0.234601i
$695$	274.125	−	160.637i	0.394425	−	0.231133i
$696$		0			0
$697$	−524.895	−	524.895i	−0.753077	−	0.753077i
$698$	−10.9468	+	10.9468i	−0.0156831	+	0.0156831i
$699$		0			0
$700$	56.2922	+	199.722i	0.0804174	+	0.285317i
$701$	660.345			0.942004			0.471002	−	0.882132i	$-0.343892\pi$
$701$	660.345			0.942004			0.471002	+	0.882132i	$0.343892\pi$
$702$		0			0
$703$	115.422	−	115.422i	0.164185	−	0.164185i
$704$		−	144.385i		−	0.205092i
$705$		0			0
$706$	−202.108			−0.286272
$707$	−234.216	−	234.216i	−0.331282	−	0.331282i
$708$		0			0
$709$			1216.32i			1.71554i	0.514034	+	0.857770i	$0.328151\pi$
$709$			1216.32i			1.71554i	−0.514034	+	0.857770i	$0.671849\pi$
$710$	−87.1031	+	333.685i	−0.122680	+	0.469979i
$711$		0			0
$712$	112.182	+	112.182i	0.157559	+	0.157559i
$713$	991.209	−	991.209i	1.39020	−	1.39020i
$714$		0			0
$715$	66.7024	+	17.4116i	0.0932901	+	0.0243519i
$716$	−489.953			−0.684291
$717$		0			0
$718$	−109.392	+	109.392i	−0.152357	+	0.152357i
$719$		−	376.633i		−	0.523829i	−0.965091	−	0.261914i	$-0.915646\pi$
$719$		−	376.633i		−	0.523829i	0.965091	−	0.261914i	$-0.0843538\pi$
$720$		0			0
$721$	−55.3741			−0.0768018
$722$	−56.6868	−	56.6868i	−0.0785135	−	0.0785135i
$723$		0			0
$724$		−	628.382i		−	0.867931i
$725$	293.558	+	164.463i	0.404908	+	0.226846i
$726$		0			0
$727$	−562.754	−	562.754i	−0.774077	−	0.774077i	0.204740	−	0.978816i	$-0.434365\pi$
$727$	−562.754	−	562.754i	−0.774077	−	0.774077i	−0.978816	+	0.204740i	$0.934365\pi$
$728$	11.2307	−	11.2307i	0.0154267	−	0.0154267i
$729$		0			0
$730$	−81.4308	−	138.960i	−0.111549	−	0.190357i
$731$	840.994			1.15047
$732$		0			0
$733$	−316.775	+	316.775i	−0.432163	+	0.432163i	−0.889364	−	0.457201i	$-0.848852\pi$
$733$	−316.775	+	316.775i	−0.432163	+	0.432163i	0.457201	+	0.889364i	$0.348852\pi$
$734$			200.491i			0.273148i
$735$		0			0
$736$	1172.30			1.59280
$737$	469.908	+	469.908i	0.637595	+	0.637595i
$738$		0			0
$739$			322.406i			0.436273i	0.975918	+	0.218137i	$0.0699979\pi$
$739$			322.406i			0.436273i	−0.975918	+	0.218137i	$0.930002\pi$
$740$	114.928	+	30.0001i	0.155308	+	0.0405406i
$741$		0			0
$742$	−91.2406	−	91.2406i	−0.122966	−	0.122966i
$743$	33.6619	−	33.6619i	0.0453054	−	0.0453054i	−0.684091	−	0.729397i	$-0.739801\pi$
$743$	33.6619	−	33.6619i	0.0453054	−	0.0453054i	0.729397	+	0.684091i	$0.239801\pi$
$744$		0			0
$745$	639.143	−	374.538i	0.857910	−	0.502735i
$746$	376.562			0.504775
$747$		0			0
$748$	371.929	−	371.929i	0.497231	−	0.497231i
$749$			512.807i			0.684656i
$750$		0			0
$751$	1008.00			1.34221			0.671106	−	0.741362i	$-0.265820\pi$
$751$	1008.00			1.34221			0.671106	+	0.741362i	$0.265820\pi$
$752$	77.7410	+	77.7410i	0.103379	+	0.103379i
$753$		0			0
$754$		−	11.1765i		−	0.0148229i
$755$	−93.9686	−	160.356i	−0.124462	−	0.212392i
$756$		0			0
$757$	−839.534	−	839.534i	−1.10903	−	1.10903i	−0.993278	−	0.115750i	$-0.963073\pi$
$757$	−839.534	−	839.534i	−1.10903	−	1.10903i	−0.115750	−	0.993278i	$-0.536927\pi$
$758$	189.236	−	189.236i	0.249652	−	0.249652i
$759$		0			0
$760$	181.673	−	695.976i	0.239044	−	0.915758i
$761$	233.272			0.306534			0.153267	−	0.988185i	$-0.451021\pi$
$761$	233.272			0.306534			0.153267	+	0.988185i	$0.451021\pi$
$762$		0			0
$763$	310.199	−	310.199i	0.406552	−	0.406552i
$764$		−	175.502i		−	0.229715i
$765$		0			0
$766$	−40.4986			−0.0528702
$767$	37.6790	+	37.6790i	0.0491252	+	0.0491252i
$768$		0			0
$769$			1059.42i			1.37766i	0.724922	+	0.688831i	$0.241876\pi$
$769$			1059.42i			1.37766i	−0.724922	+	0.688831i	$0.758124\pi$
$770$	−180.979	+	106.054i	−0.235037	+	0.137732i
$771$		0			0
$772$	289.089	+	289.089i	0.374468	+	0.374468i
$773$	−672.938	+	672.938i	−0.870554	+	0.870554i	−0.992533	−	0.121979i	$-0.961076\pi$
$773$	−672.938	+	672.938i	−0.870554	+	0.870554i	0.121979	+	0.992533i	$0.461076\pi$
$774$		0			0
$775$	479.060	−	855.095i	0.618142	−	1.10335i
$776$	939.666			1.21091
$777$		0			0
$778$	−416.558	+	416.558i	−0.535421	+	0.535421i
$779$			1462.85i			1.87786i
$780$		0			0
$781$	1145.23			1.46636
$782$	−261.177	−	261.177i	−0.333985	−	0.333985i
$783$		0			0
$784$			236.271i			0.301366i
$785$	241.779	−	926.236i	0.307999	−	1.17992i
$786$		0			0
$787$	441.897	+	441.897i	0.561496	+	0.561496i	0.929732	−	0.368236i	$-0.120038\pi$
$787$	441.897	+	441.897i	0.561496	+	0.561496i	−0.368236	+	0.929732i	$0.620038\pi$
$788$	−138.266	+	138.266i	−0.175464	+	0.175464i
$789$		0			0
$790$	26.2584	+	6.85432i	0.0332384	+	0.00867635i
$791$	358.677			0.453447
$792$		0			0
$793$	−40.8463	+	40.8463i	−0.0515086	+	0.0515086i
$794$			483.451i			0.608880i
$795$		0			0
$796$	−485.352			−0.609739
$797$	880.801	+	880.801i	1.10515	+	1.10515i	0.993779	+	0.111366i	$0.0355227\pi$
$797$	880.801	+	880.801i	1.10515	+	1.10515i	0.111366	+	0.993779i	$0.464477\pi$
$798$		0			0
$799$		−	207.339i		−	0.259499i
$800$	788.952	−	222.368i	0.986189	−	0.277960i
$801$		0			0
$802$	349.094	+	349.094i	0.435279	+	0.435279i
$803$	−378.198	+	378.198i	−0.470981	+	0.470981i
$804$		0			0
$805$	−244.645	−	417.483i	−0.303907	−	0.518612i
$806$	−32.5556			−0.0403915
$807$		0			0
$808$	−590.793	+	590.793i	−0.731180	+	0.731180i
$809$		−	1201.69i		−	1.48540i	−0.669623	−	0.742701i	$-0.733544\pi$
$809$		−	1201.69i		−	1.48540i	0.669623	−	0.742701i	$-0.266456\pi$
$810$		0			0
$811$	−214.518			−0.264511			−0.132255	−	0.991216i	$-0.542222\pi$
$811$	−214.518			−0.264511			−0.132255	+	0.991216i	$0.542222\pi$
$812$	−78.9952	−	78.9952i	−0.0972847	−	0.0972847i
$813$		0			0
$814$			120.073i			0.147509i
$815$	−1384.96	−	361.521i	−1.69934	−	0.443584i
$816$		0			0
$817$	−1171.90	−	1171.90i	−1.43440	−	1.43440i
$818$	88.2506	−	88.2506i	0.107886	−	0.107886i
$819$		0			0
$820$	−918.406	+	538.186i	−1.12001	+	0.656324i
$821$	−1242.79			−1.51375			−0.756877	−	0.653557i	$-0.773276\pi$
$821$	−1242.79			−1.51375			−0.756877	+	0.653557i	$0.773276\pi$
$822$		0			0
$823$	−76.3353	+	76.3353i	−0.0927525	+	0.0927525i	−0.751961	−	0.659208i	$-0.770892\pi$
$823$	−76.3353	+	76.3353i	−0.0927525	+	0.0927525i	0.659208	+	0.751961i	$0.270892\pi$
$824$			139.677i			0.169511i
$825$		0			0
$826$	−162.140			−0.196295
$827$	323.536	+	323.536i	0.391216	+	0.391216i	0.875121	−	0.483905i	$-0.160782\pi$
$827$	323.536	+	323.536i	0.391216	+	0.391216i	−0.483905	+	0.875121i	$0.660782\pi$
$828$		0			0
$829$			361.865i			0.436507i	0.975892	+	0.218254i	$0.0700360\pi$
$829$			361.865i			0.436507i	−0.975892	+	0.218254i	$0.929964\pi$
$830$	90.1382	+	153.819i	0.108600	+	0.185325i
$831$		0			0
$832$	−5.46967	−	5.46967i	−0.00657412	−	0.00657412i
$833$	315.074	−	315.074i	0.378240	−	0.378240i
$834$		0			0
$835$	−27.5889	+	105.691i	−0.0330406	+	0.126576i
$836$	−1036.55			−1.23989
$837$		0			0
$838$	245.434	−	245.434i	0.292881	−	0.292881i
$839$			35.4295i			0.0422283i	0.999777	+	0.0211141i	$0.00672134\pi$
$839$			35.4295i			0.0422283i	−0.999777	+	0.0211141i	$0.993279\pi$
$840$		0			0
$841$	659.841			0.784591
$842$	−72.0979	−	72.0979i	−0.0856270	−	0.0856270i
$843$		0			0
$844$		−	802.516i		−	0.950848i
$845$	−725.859	+	425.354i	−0.859005	+	0.503377i
$846$		0			0
$847$	260.971	+	260.971i	0.308112	+	0.308112i
$848$	197.807	−	197.807i	0.233263	−	0.233263i
$849$		0			0
$850$	−225.311	−	126.229i	−0.265072	−	0.148504i
$851$	−276.984			−0.325480
$852$		0			0
$853$	−996.367	+	996.367i	−1.16807	+	1.16807i	−0.185414	+	0.982661i	$0.559362\pi$
$853$	−996.367	+	996.367i	−1.16807	+	1.16807i	−0.982661	+	0.185414i	$0.940638\pi$
$854$		−	175.769i		−	0.205818i
$855$		0			0
$856$	1293.52			1.51112
$857$	613.451	+	613.451i	0.715812	+	0.715812i	0.967745	−	0.251932i	$-0.0810661\pi$
$857$	613.451	+	613.451i	0.715812	+	0.715812i	−0.251932	+	0.967745i	$0.581066\pi$
$858$		0			0
$859$			199.954i			0.232776i	0.993204	+	0.116388i	$0.0371316\pi$
$859$			199.954i			0.232776i	−0.993204	+	0.116388i	$0.962868\pi$
$860$	304.597	−	1166.89i	0.354182	−	1.35684i
$861$		0			0
$862$	274.887	+	274.887i	0.318895	+	0.318895i
$863$	290.842	−	290.842i	0.337013	−	0.337013i	−0.518229	−	0.855242i	$-0.673409\pi$
$863$	290.842	−	290.842i	0.337013	−	0.337013i	0.855242	+	0.518229i	$0.173409\pi$
$864$		0			0
$865$	−703.671	−	183.682i	−0.813493	−	0.212349i
$866$	49.4077			0.0570528
$867$		0			0
$868$	−230.102	+	230.102i	−0.265095	+	0.265095i
$869$		−	90.1202i		−	0.103706i
$870$		0			0
$871$	35.6027			0.0408756
$872$	−782.455	−	782.455i	−0.897311	−	0.897311i
$873$		0			0
$874$			727.885i			0.832821i
$875$	−243.835	−	234.557i	−0.278668	−	0.268066i
$876$		0			0
$877$	57.7576	+	57.7576i	0.0658582	+	0.0658582i	0.739269	−	0.673411i	$-0.235171\pi$
$877$	57.7576	+	57.7576i	0.0658582	+	0.0658582i	−0.673411	+	0.739269i	$0.735171\pi$
$878$	118.051	−	118.051i	0.134455	−	0.134455i
$879$		0			0
$880$	−229.921	−	392.357i	−0.261274	−	0.445860i
$881$	−673.852			−0.764872			−0.382436	−	0.923982i	$-0.624915\pi$
$881$	−673.852			−0.764872			−0.382436	+	0.923982i	$0.624915\pi$
$882$		0			0
$883$	−701.206	+	701.206i	−0.794118	+	0.794118i	−0.982161	−	0.188043i	$-0.939786\pi$
$883$	−701.206	+	701.206i	−0.794118	+	0.794118i	0.188043	+	0.982161i	$0.439786\pi$
$884$		−	28.1793i		−	0.0318770i
$885$		0			0
$886$	−325.756			−0.367671
$887$	−713.261	−	713.261i	−0.804128	−	0.804128i	0.179610	−	0.983738i	$-0.442516\pi$
$887$	−713.261	−	713.261i	−0.804128	−	0.804128i	−0.983738	+	0.179610i	$0.942516\pi$
$888$		0			0
$889$			95.6766i			0.107623i
$890$	−108.615	−	28.3522i	−0.122039	−	0.0318564i
$891$		0			0
$892$	−552.166	−	552.166i	−0.619020	−	0.619020i
$893$	−288.922	+	288.922i	−0.323541	+	0.323541i
$894$		0			0
$895$	689.251	−	403.901i	0.770113	−	0.451286i
$896$	−331.448			−0.369920
$897$		0			0
$898$	186.251	−	186.251i	0.207407	−	0.207407i
$899$			527.692i			0.586977i
$900$		0			0
$901$	−527.562			−0.585529
$902$	−760.898	−	760.898i	−0.843567	−	0.843567i
$903$		0			0
$904$		−	904.736i		−	1.00081i
$905$	518.018	+	883.989i	0.572396	+	0.976784i
$906$		0			0
$907$	10.7160	+	10.7160i	0.0118148	+	0.0118148i	0.712990	−	0.701175i	$-0.247341\pi$
$907$	10.7160	+	10.7160i	0.0118148	+	0.0118148i	−0.701175	+	0.712990i	$0.747341\pi$
$908$	576.160	−	576.160i	0.634537	−	0.634537i
$909$		0			0
$910$	−2.83836	+	10.8735i	−0.00311908	+	0.0119490i
$911$	−952.181			−1.04520			−0.522602	−	0.852577i	$-0.675039\pi$
$911$	−952.181			−1.04520			−0.522602	+	0.852577i	$0.675039\pi$
$912$		0			0
$913$	418.638	−	418.638i	0.458530	−	0.458530i
$914$		−	796.975i		−	0.871963i
$915$		0			0
$916$	407.069			0.444398
$917$	153.478	+	153.478i	0.167370	+	0.167370i
$918$		0			0
$919$			605.183i			0.658523i	0.944239	+	0.329262i	$0.106800\pi$
$919$			605.183i			0.658523i	−0.944239	+	0.329262i	$0.893200\pi$
$920$	−1053.07	+	617.099i	−1.14464	+	0.670760i
$921$		0			0
$922$	345.738	+	345.738i	0.374987	+	0.374987i
$923$	43.3842	−	43.3842i	0.0470035	−	0.0470035i
$924$		0			0
$925$	−186.408	+	52.5397i	−0.201522	+	0.0567996i
$926$	176.673			0.190791
$927$		0			0
$928$	−312.051	+	312.051i	−0.336261	+	0.336261i
$929$		−	278.073i		−	0.299325i	−0.988737	−	0.149663i	$-0.952181\pi$
$929$		−	278.073i		−	0.299325i	0.988737	−	0.149663i	$-0.0478188\pi$
$930$		0			0
$931$	−878.095			−0.943174
$932$	165.553	+	165.553i	0.177632	+	0.177632i
$933$		0			0
$934$		−	219.300i		−	0.234797i
$935$	−216.612	+	829.825i	−0.231671	+	0.887513i
$936$		0			0
$937$	896.938	+	896.938i	0.957244	+	0.957244i	0.999123	−	0.0418787i	$-0.0133343\pi$
$937$	896.938	+	896.938i	0.957244	+	0.957244i	−0.0418787	+	0.999123i	$0.513334\pi$
$938$	−76.6024	+	76.6024i	−0.0816657	+	0.0816657i
$939$		0			0
$940$	−287.685	−	75.0956i	−0.306048	−	0.0798889i
$941$	360.668			0.383282			0.191641	−	0.981465i	$-0.438619\pi$
$941$	360.668			0.383282			0.191641	+	0.981465i	$0.438619\pi$
$942$		0			0
$943$	1755.24	−	1755.24i	1.86134	−	1.86134i
$944$		−	351.514i		−	0.372366i
$945$		0			0
$946$	1219.12			1.28871
$947$	−934.038	−	934.038i	−0.986313	−	0.986313i	0.0135946	−	0.999908i	$-0.495673\pi$
$947$	−934.038	−	934.038i	−0.986313	−	0.986313i	−0.999908	+	0.0135946i	$0.995673\pi$
$948$		0			0
$949$			28.6542i			0.0301941i
$950$	138.069	+	489.862i	0.145336	+	0.515644i
$951$		0			0
$952$	139.717	+	139.717i	0.146762	+	0.146762i
$953$	−546.187	+	546.187i	−0.573124	+	0.573124i	−0.933000	−	0.359876i	$-0.882819\pi$
$953$	−546.187	+	546.187i	−0.573124	+	0.573124i	0.359876	+	0.933000i	$0.382819\pi$
$954$		0			0
$955$	144.679	+	246.892i	0.151496	+	0.258525i
$956$	318.202			0.332847
$957$		0			0
$958$	−532.353	+	532.353i	−0.555692	+	0.555692i
$959$		−	598.894i		−	0.624498i
$960$		0			0
$961$	576.097			0.599476
$962$	4.54867	+	4.54867i	0.00472834	+	0.00472834i
$963$		0			0
$964$		−	862.292i		−	0.894494i
$965$	−644.998	−	168.366i	−0.668391	−	0.174473i
$966$		0			0
$967$	−760.948	−	760.948i	−0.786916	−	0.786916i	0.194072	−	0.980987i	$-0.437831\pi$
$967$	−760.948	−	760.948i	−0.786916	−	0.786916i	−0.980987	+	0.194072i	$0.937831\pi$
$968$	658.280	−	658.280i	0.680041	−	0.680041i
$969$		0			0
$970$	−573.636	+	336.151i	−0.591377	+	0.346547i
$971$	−892.281			−0.918930			−0.459465	−	0.888196i	$-0.651959\pi$
$971$	−892.281			−0.918930			−0.459465	+	0.888196i	$0.651959\pi$
$972$		0			0
$973$	121.620	−	121.620i	0.124995	−	0.124995i
$974$			715.007i			0.734093i
$975$		0			0
$976$	381.062			0.390432
$977$	−263.487	−	263.487i	−0.269690	−	0.269690i	0.559285	−	0.828975i	$-0.311076\pi$
$977$	−263.487	−	263.487i	−0.269690	−	0.269690i	−0.828975	+	0.559285i	$0.811076\pi$
$978$		0			0
$979$			372.773i			0.380769i
$980$	−323.053	−	551.284i	−0.329645	−	0.562535i
$981$		0			0
$982$	−109.746	−	109.746i	−0.111758	−	0.111758i
$983$	−917.630	+	917.630i	−0.933499	+	0.933499i	−0.997923	−	0.0644232i	$-0.979479\pi$
$983$	−917.630	+	917.630i	−0.933499	+	0.933499i	0.0644232	+	0.997923i	$0.479479\pi$
$984$		0			0
$985$	80.5263	−	308.490i	0.0817525	−	0.313188i
$986$	139.043			0.141017
$987$		0			0
$988$	−39.2671	+	39.2671i	−0.0397440	+	0.0397440i
$989$			2812.27i			2.84355i
$990$		0			0
$991$	−1393.97			−1.40663			−0.703315	−	0.710878i	$-0.748298\pi$
$991$	−1393.97			−1.40663			−0.703315	+	0.710878i	$0.748298\pi$
$992$	908.961	+	908.961i	0.916292	+	0.916292i
$993$		0			0
$994$			186.690i			0.187817i
$995$	682.779	−	400.109i	0.686210	−	0.402119i
$996$		0			0
$997$	−243.100	−	243.100i	−0.243831	−	0.243831i	0.574602	−	0.818433i	$-0.305157\pi$
$997$	−243.100	−	243.100i	−0.243831	−	0.243831i	−0.818433	+	0.574602i	$0.805157\pi$
$998$	131.184	−	131.184i	0.131447	−	0.131447i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.g.b.82.5	yes	16
3.2	odd	2	inner	135.3.g.b.82.4	yes	16
5.2	odd	4		675.3.g.j.568.4		16
5.3	odd	4	inner	135.3.g.b.28.5	yes	16
5.4	even	2		675.3.g.j.82.4		16
9.2	odd	6		405.3.l.n.352.4		32
9.4	even	3		405.3.l.n.217.4		32
9.5	odd	6		405.3.l.n.217.5		32
9.7	even	3		405.3.l.n.352.5		32
15.2	even	4		675.3.g.j.568.5		16
15.8	even	4	inner	135.3.g.b.28.4	✓	16
15.14	odd	2		675.3.g.j.82.5		16
45.13	odd	12		405.3.l.n.298.5		32
45.23	even	12		405.3.l.n.298.4		32
45.38	even	12		405.3.l.n.28.5		32
45.43	odd	12		405.3.l.n.28.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.b.28.4	✓	16	15.8	even	4	inner
135.3.g.b.28.5	yes	16	5.3	odd	4	inner
135.3.g.b.82.4	yes	16	3.2	odd	2	inner
135.3.g.b.82.5	yes	16	1.1	even	1	trivial
405.3.l.n.28.4		32	45.43	odd	12
405.3.l.n.28.5		32	45.38	even	12
405.3.l.n.217.4		32	9.4	even	3
405.3.l.n.217.5		32	9.5	odd	6
405.3.l.n.298.4		32	45.23	even	12
405.3.l.n.298.5		32	45.13	odd	12
405.3.l.n.352.4		32	9.2	odd	6
405.3.l.n.352.5		32	9.7	even	3
675.3.g.j.82.4		16	5.4	even	2
675.3.g.j.82.5		16	15.14	odd	2
675.3.g.j.568.4		16	5.2	odd	4
675.3.g.j.568.5		16	15.2	even	4

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.683187 + 0.683187i) q^{2} -3.06651i q^{4} +(2.52793 + 4.31388i) q^{5} +(1.91393 + 1.91393i) q^{7} +(4.82775 - 4.82775i) q^{8} +(-1.22013 + 4.67423i) q^{10} +16.0422 q^{11} +(0.607722 - 0.607722i) q^{13} +2.61514i q^{14} -5.66955 q^{16} +(7.56049 + 7.56049i) q^{17} -21.0707i q^{19} +(13.2286 - 7.75194i) q^{20} +(10.9598 + 10.9598i) q^{22} +(-25.2822 + 25.2822i) q^{23} +(-12.2191 + 21.8104i) q^{25} +0.830376 q^{26} +(5.86908 - 5.86908i) q^{28} -13.4595i q^{29} -39.2058 q^{31} +(-23.1843 - 23.1843i) q^{32} +10.3305i q^{34} +(-3.41817 + 13.0947i) q^{35} +(5.47784 + 5.47784i) q^{37} +(14.3952 - 14.3952i) q^{38} +(33.0305 + 8.62209i) q^{40} -69.4260 q^{41} +(55.6177 - 55.6177i) q^{43} -49.1937i q^{44} -34.5449 q^{46} +(-13.7120 - 13.7120i) q^{47} -41.6738i q^{49} +(-23.2485 + 6.55265i) q^{50} +(-1.86359 - 1.86359i) q^{52} +(-34.8894 + 34.8894i) q^{53} +(40.5537 + 69.2043i) q^{55} +18.4799 q^{56} +(9.19538 - 9.19538i) q^{58} +62.0004i q^{59} -67.2121 q^{61} +(-26.7849 - 26.7849i) q^{62} -9.00028i q^{64} +(4.15792 + 1.08536i) q^{65} +(29.2919 + 29.2919i) q^{67} +(23.1843 - 23.1843i) q^{68} +(-11.2814 + 6.61090i) q^{70} +71.3882 q^{71} +(-23.5751 + 23.5751i) q^{73} +7.48478i q^{74} -64.6135 q^{76} +(30.7037 + 30.7037i) q^{77} -5.61768i q^{79} +(-14.3322 - 24.4577i) q^{80} +(-47.4309 - 47.4309i) q^{82} +(26.0960 - 26.0960i) q^{83} +(-13.5026 + 51.7275i) q^{85} +75.9945 q^{86} +(77.4479 - 77.4479i) q^{88} +23.2369i q^{89} +2.32627 q^{91} +(77.5282 + 77.5282i) q^{92} -18.7357i q^{94} +(90.8964 - 53.2653i) q^{95} +(97.3193 + 97.3193i) q^{97} +(28.4710 - 28.4710i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{7} + 40 q^{10} + 40 q^{13} - 152 q^{16} - 136 q^{22} - 32 q^{25} - 112 q^{28} + 200 q^{31} + 16 q^{37} - 48 q^{40} + 136 q^{43} + 152 q^{46} + 640 q^{52} + 248 q^{55} + 48 q^{58} - 280 q^{61}+ \cdots + 448 q^{97}+O(q^{100}) \) 16 * q + 16 * q^7 + 40 * q^10 + 40 * q^13 - 152 * q^16 - 136 * q^22 - 32 * q^25 - 112 * q^28 + 200 * q^31 + 16 * q^37 - 48 * q^40 + 136 * q^43 + 152 * q^46 + 640 * q^52 + 248 * q^55 + 48 * q^58 - 280 * q^61 - 344 * q^67 - 696 * q^70 - 776 * q^73 + 144 * q^76 - 880 * q^82 - 176 * q^85 + 1200 * q^88 + 152 * q^91 + 448 * q^97

Introduction

L-functions

Modular forms

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