LMFDB - Embedded newform 1350.3.k.b.449.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,3,Mod(449,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1350.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1350.k (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:	$36.7848356886$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.14
Character	$\chi$	$=$	1350.449
Dual form			1350.3.k.b.899.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-5.74345 + 3.31598i) q^{7} -2.82843 q^{8} +(18.2172 - 10.5177i) q^{11} +(-8.47187 - 4.89124i) q^{13} +(-8.12247 - 4.68951i) q^{14} +(-2.00000 - 3.46410i) q^{16} +12.9017 q^{17} -16.1821 q^{19} +(25.7630 + 14.8743i) q^{22} +(-8.46823 + 14.6674i) q^{23} -13.8345i q^{26} -13.2639i q^{28} +(43.3525 - 25.0296i) q^{29} +(5.03212 - 8.71588i) q^{31} +(2.82843 - 4.89898i) q^{32} +(9.12285 + 15.8012i) q^{34} +2.54425i q^{37} +(-11.4425 - 19.8190i) q^{38} +(46.5617 + 26.8824i) q^{41} +(64.8089 - 37.4175i) q^{43} +42.0709i q^{44} -23.9518 q^{46} +(-23.6001 - 40.8766i) q^{47} +(-2.50850 + 4.34485i) q^{49} +(16.9437 - 9.78248i) q^{52} -1.08813 q^{53} +(16.2449 - 9.37902i) q^{56} +(61.3097 + 35.3972i) q^{58} +(8.34807 + 4.81976i) q^{59} +(22.4573 + 38.8971i) q^{61} +14.2330 q^{62} +8.00000 q^{64} +(2.89369 + 1.67067i) q^{67} +(-12.9017 + 22.3463i) q^{68} -38.4670i q^{71} +88.9201i q^{73} +(-3.11606 + 1.79906i) q^{74} +(16.1821 - 28.0283i) q^{76} +(-69.7532 + 120.816i) q^{77} +(58.8235 + 101.885i) q^{79} +76.0349i q^{82} +(73.5614 + 127.412i) q^{83} +(91.6537 + 52.9163i) q^{86} +(-51.5261 + 29.7486i) q^{88} -145.331i q^{89} +64.8771 q^{91} +(-16.9365 - 29.3348i) q^{92} +(33.3756 - 57.8083i) q^{94} +(-40.7494 + 23.5267i) q^{97} -7.09511 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 72 q^{14} - 64 q^{16} - 160 q^{19} - 144 q^{29} - 32 q^{31} + 96 q^{34} - 216 q^{41} + 48 q^{46} + 168 q^{49} + 144 q^{56} + 288 q^{59} - 152 q^{61} + 256 q^{64} - 576 q^{74} + 160 q^{76}+ \cdots + 168 q^{94}+O(q^{100}) $ 32 * q - 32 * q^4 - 72 * q^14 - 64 * q^16 - 160 * q^19 - 144 * q^29 - 32 * q^31 + 96 * q^34 - 216 * q^41 + 48 * q^46 + 168 * q^49 + 144 * q^56 + 288 * q^59 - 152 * q^61 + 256 * q^64 - 576 * q^74 + 160 * q^76 - 160 * q^79 + 432 * q^86 - 1312 * q^91 + 168 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−5.74345	+	3.31598i	−0.820493	+	0.473712i	−0.850587	−	0.525835i	$-0.823753\pi$
$7$	−5.74345	+	3.31598i	−0.820493	+	0.473712i	0.0300933	+	0.999547i	$0.490420\pi$
$8$	−2.82843			−0.353553
$9$		0			0
$10$		0			0
$11$	18.2172	−	10.5177i	1.65611	−	0.956156i	0.681627	−	0.731699i	$-0.261273\pi$
$11$	18.2172	−	10.5177i	1.65611	−	0.956156i	0.974484	−	0.224457i	$-0.0720608\pi$
$12$		0			0
$13$	−8.47187	−	4.89124i	−0.651683	−	0.376249i	0.137418	−	0.990513i	$-0.456120\pi$
$13$	−8.47187	−	4.89124i	−0.651683	−	0.376249i	−0.789101	+	0.614264i	$0.789453\pi$
$14$	−8.12247	−	4.68951i	−0.580176	−	0.334965i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	12.9017			0.758921			0.379460	−	0.925208i	$-0.376110\pi$
$17$	12.9017			0.758921			0.379460	+	0.925208i	$0.376110\pi$
$18$		0			0
$19$	−16.1821			−0.851691			−0.425845	−	0.904796i	$-0.640023\pi$
$19$	−16.1821			−0.851691			−0.425845	+	0.904796i	$0.640023\pi$
$20$		0			0
$21$		0			0
$22$	25.7630	+	14.8743i	1.17105	+	0.676105i
$23$	−8.46823	+	14.6674i	−0.368184	+	0.637713i	−0.989282	−	0.146020i	$-0.953354\pi$
$23$	−8.46823	+	14.6674i	−0.368184	+	0.637713i	0.621098	+	0.783733i	$0.286687\pi$
$24$		0			0
$25$		0			0
$26$		−	13.8345i		−	0.532097i
$27$		0			0
$28$		−	13.2639i		−	0.473712i
$29$	43.3525	−	25.0296i	1.49491	−	0.863089i	0.494930	−	0.868933i	$-0.335194\pi$
$29$	43.3525	−	25.0296i	1.49491	−	0.863089i	0.999983	+	0.00584415i	$0.00186026\pi$
$30$		0			0
$31$	5.03212	−	8.71588i	0.162326	−	0.281158i	−0.773376	−	0.633947i	$-0.781434\pi$
$31$	5.03212	−	8.71588i	0.162326	−	0.281158i	0.935703	+	0.352790i	$0.114767\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$		0			0
$34$	9.12285	+	15.8012i	0.268319	+	0.464742i
$35$		0			0
$36$		0			0
$37$			2.54425i			0.0687635i	0.999409	+	0.0343817i	$0.0109462\pi$
$37$			2.54425i			0.0687635i	−0.999409	+	0.0343817i	$0.989054\pi$
$38$	−11.4425	−	19.8190i	−0.301118	−	0.521552i
$39$		0			0
$40$		0			0
$41$	46.5617	+	26.8824i	1.13565	+	0.655669i	0.945350	−	0.326057i	$-0.105720\pi$
$41$	46.5617	+	26.8824i	1.13565	+	0.655669i	0.190301	+	0.981726i	$0.439054\pi$
$42$		0			0
$43$	64.8089	−	37.4175i	1.50718	−	0.870173i	0.507219	−	0.861817i	$-0.330673\pi$
$43$	64.8089	−	37.4175i	1.50718	−	0.870173i	0.999965	−	0.00835640i	$-0.00265996\pi$
$44$			42.0709i			0.956156i
$45$		0			0
$46$	−23.9518			−0.520690
$47$	−23.6001	−	40.8766i	−0.502131	−	0.869716i	−0.999997	−	0.00246200i	$-0.999216\pi$
$47$	−23.6001	−	40.8766i	−0.502131	−	0.869716i	0.497866	−	0.867254i	$-0.334117\pi$
$48$		0			0
$49$	−2.50850	+	4.34485i	−0.0511939	+	0.0886704i
$50$		0			0
$51$		0			0
$52$	16.9437	−	9.78248i	0.325841	−	0.188125i
$53$	−1.08813			−0.0205307			−0.0102654	−	0.999947i	$-0.503268\pi$
$53$	−1.08813			−0.0205307			−0.0102654	+	0.999947i	$0.503268\pi$
$54$		0			0
$55$		0			0
$56$	16.2449	−	9.37902i	0.290088	−	0.167482i
$57$		0			0
$58$	61.3097	+	35.3972i	1.05706	+	0.610296i
$59$	8.34807	+	4.81976i	0.141493	+	0.0816908i	0.569075	−	0.822285i	$-0.307301\pi$
$59$	8.34807	+	4.81976i	0.141493	+	0.0816908i	−0.427583	+	0.903976i	$0.640635\pi$
$60$		0			0
$61$	22.4573	+	38.8971i	0.368152	+	0.637657i	0.989277	−	0.146054i	$-0.0466574\pi$
$61$	22.4573	+	38.8971i	0.368152	+	0.637657i	−0.621125	+	0.783712i	$0.713324\pi$
$62$	14.2330			0.229564
$63$		0			0
$64$	8.00000			0.125000
$65$		0			0
$66$		0			0
$67$	2.89369	+	1.67067i	0.0431894	+	0.0249354i	0.521439	−	0.853288i	$-0.325395\pi$
$67$	2.89369	+	1.67067i	0.0431894	+	0.0249354i	−0.478250	+	0.878224i	$0.658729\pi$
$68$	−12.9017	+	22.3463i	−0.189730	+	0.328622i
$69$		0			0
$70$		0			0
$71$		−	38.4670i		−	0.541788i	−0.962609	−	0.270894i	$-0.912681\pi$
$71$		−	38.4670i		−	0.541788i	0.962609	−	0.270894i	$-0.0873193\pi$
$72$		0			0
$73$			88.9201i			1.21808i	0.793138	+	0.609042i	$0.208446\pi$
$73$			88.9201i			1.21808i	−0.793138	+	0.609042i	$0.791554\pi$
$74$	−3.11606	+	1.79906i	−0.0421089	+	0.0243116i
$75$		0			0
$76$	16.1821	−	28.0283i	0.212923	−	0.368793i
$77$	−69.7532	+	120.816i	−0.905885	+	1.56904i
$78$		0			0
$79$	58.8235	+	101.885i	0.744602	+	1.28969i	0.950381	+	0.311090i	$0.100694\pi$
$79$	58.8235	+	101.885i	0.744602	+	1.28969i	−0.205779	+	0.978599i	$0.565973\pi$
$80$		0			0
$81$		0			0
$82$			76.0349i			0.927255i
$83$	73.5614	+	127.412i	0.886282	+	1.53509i	0.844237	+	0.535970i	$0.180054\pi$
$83$	73.5614	+	127.412i	0.886282	+	1.53509i	0.0420449	+	0.999116i	$0.486613\pi$
$84$		0			0
$85$		0			0
$86$	91.6537	+	52.9163i	1.06574	+	0.615305i
$87$		0			0
$88$	−51.5261	+	29.7486i	−0.585524	+	0.338052i
$89$		−	145.331i		−	1.63293i	−0.577396	−	0.816464i	$-0.695931\pi$
$89$		−	145.331i		−	1.63293i	0.577396	−	0.816464i	$-0.304069\pi$
$90$		0			0
$91$	64.8771			0.712935
$92$	−16.9365	−	29.3348i	−0.184092	−	0.318856i
$93$		0			0
$94$	33.3756	−	57.8083i	0.355060	−	0.614982i
$95$		0			0
$96$		0			0
$97$	−40.7494	+	23.5267i	−0.420097	+	0.242543i	−0.695119	−	0.718895i	$-0.744648\pi$
$97$	−40.7494	+	23.5267i	−0.420097	+	0.242543i	0.275022	+	0.961438i	$0.411315\pi$
$98$	−7.09511			−0.0723991
$99$		0			0
$100$		0			0
$101$	19.3600	−	11.1775i	0.191683	−	0.110668i	−0.401087	−	0.916040i	$-0.631368\pi$
$101$	19.3600	−	11.1775i	0.191683	−	0.110668i	0.592770	+	0.805372i	$0.298034\pi$
$102$		0			0
$103$	107.300	+	61.9495i	1.04174	+	0.601452i	0.920327	−	0.391150i	$-0.127923\pi$
$103$	107.300	+	61.9495i	1.04174	+	0.601452i	0.121418	+	0.992601i	$0.461256\pi$
$104$	23.9621	+	13.8345i	0.230405	+	0.133024i
$105$		0			0
$106$	−0.769422	−	1.33268i	−0.00725870	−	0.0125724i
$107$	47.3690			0.442701			0.221351	−	0.975194i	$-0.428954\pi$
$107$	47.3690			0.442701			0.221351	+	0.975194i	$0.428954\pi$
$108$		0			0
$109$	26.8745			0.246555			0.123278	−	0.992372i	$-0.460659\pi$
$109$	26.8745			0.246555			0.123278	+	0.992372i	$0.460659\pi$
$110$		0			0
$111$		0			0
$112$	22.9738	+	13.2639i	0.205123	+	0.118428i
$113$	9.40495	−	16.2899i	0.0832297	−	0.144158i	−0.821406	−	0.570344i	$-0.806810\pi$
$113$	9.40495	−	16.2899i	0.0832297	−	0.144158i	0.904635	+	0.426186i	$0.140143\pi$
$114$		0			0
$115$		0			0
$116$			100.118i			0.863089i
$117$		0			0
$118$			13.6323i			0.115528i
$119$	−74.1001	+	42.7817i	−0.622690	+	0.359510i
$120$		0			0
$121$	160.745	−	278.418i	1.32847	−	2.30098i
$122$	−31.7593	+	55.0088i	−0.260323	+	0.450892i
$123$		0			0
$124$	10.0642	+	17.4318i	0.0811632	+	0.140579i
$125$		0			0
$126$		0			0
$127$		−	128.820i		−	1.01433i	−0.861849	−	0.507166i	$-0.830693\pi$
$127$		−	128.820i		−	1.01433i	0.861849	−	0.507166i	$-0.169307\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	26.6836	+	15.4058i	0.203692	+	0.117601i	0.598376	−	0.801215i	$-0.295813\pi$
$131$	26.6836	+	15.4058i	0.203692	+	0.117601i	−0.394685	+	0.918817i	$0.629146\pi$
$132$		0			0
$133$	92.9413	−	53.6597i	0.698806	−	0.403456i
$134$			4.72538i			0.0352640i
$135$		0			0
$136$	−36.4914			−0.268319
$137$	53.2723	+	92.2703i	0.388849	+	0.673506i	0.992295	−	0.123898i	$-0.0395395\pi$
$137$	53.2723	+	92.2703i	0.388849	+	0.673506i	−0.603446	+	0.797404i	$0.706206\pi$
$138$		0			0
$139$	57.1183	−	98.9317i	0.410923	−	0.711739i	−0.584068	−	0.811705i	$-0.698540\pi$
$139$	57.1183	−	98.9317i	0.410923	−	0.711739i	0.994991	+	0.0999656i	$0.0318733\pi$
$140$		0			0
$141$		0			0
$142$	47.1122	−	27.2002i	0.331776	−	0.191551i
$143$	−205.779			−1.43901
$144$		0			0
$145$		0			0
$146$	−108.904	+	62.8760i	−0.745921	+	0.430658i
$147$		0			0
$148$	−4.40677	−	2.54425i	−0.0297755	−	0.0171909i
$149$	104.689	+	60.4419i	0.702607	+	0.405651i	0.808318	−	0.588746i	$-0.200378\pi$
$149$	104.689	+	60.4419i	0.702607	+	0.405651i	−0.105710	+	0.994397i	$0.533712\pi$
$150$		0			0
$151$	−63.4938	−	109.975i	−0.420489	−	0.728308i	0.575498	−	0.817803i	$-0.304808\pi$
$151$	−63.4938	−	109.975i	−0.420489	−	0.728308i	−0.995987	+	0.0894947i	$0.971475\pi$
$152$	45.7700			0.301118
$153$		0			0
$154$	−197.292			−1.28112
$155$		0			0
$156$		0			0
$157$	−90.2510	−	52.1064i	−0.574847	−	0.331888i	0.184236	−	0.982882i	$-0.441019\pi$
$157$	−90.2510	−	52.1064i	−0.574847	−	0.331888i	−0.759083	+	0.650994i	$0.774352\pi$
$158$	−83.1891	+	144.088i	−0.526513	+	0.911947i
$159$		0			0
$160$		0			0
$161$		−	112.322i		−	0.697652i
$162$		0			0
$163$			188.533i			1.15664i	0.815809	+	0.578321i	$0.196292\pi$
$163$			188.533i			1.15664i	−0.815809	+	0.578321i	$0.803708\pi$
$164$	−93.1234	+	53.7648i	−0.567826	+	0.327834i
$165$		0			0
$166$	−104.032	+	180.188i	−0.626696	+	1.08547i
$167$	−33.9581	+	58.8172i	−0.203342	+	0.352199i	−0.949603	−	0.313454i	$-0.898514\pi$
$167$	−33.9581	+	58.8172i	−0.203342	+	0.352199i	0.746261	+	0.665653i	$0.231847\pi$
$168$		0			0
$169$	−36.6516	−	63.4824i	−0.216873	−	0.375635i
$170$		0			0
$171$		0			0
$172$			149.670i			0.870173i
$173$	61.1963	+	105.995i	0.353736	+	0.612689i	0.986901	−	0.161328i	$-0.0515778\pi$
$173$	61.1963	+	105.995i	0.353736	+	0.612689i	−0.633165	+	0.774017i	$0.718244\pi$
$174$		0			0
$175$		0			0
$176$	−72.8689	−	42.0709i	−0.414028	−	0.239039i
$177$		0			0
$178$	177.993	−	102.764i	0.999961	−	0.577328i
$179$			78.4259i			0.438134i	0.975710	+	0.219067i	$0.0703013\pi$
$179$			78.4259i			0.438134i	−0.975710	+	0.219067i	$0.929699\pi$
$180$		0			0
$181$	219.562			1.21305			0.606525	−	0.795064i	$-0.292563\pi$
$181$	219.562			1.21305			0.606525	+	0.795064i	$0.292563\pi$
$182$	45.8750	+	79.4579i	0.252061	+	0.436582i
$183$		0			0
$184$	23.9518	−	41.4857i	0.130173	−	0.225466i
$185$		0			0
$186$		0			0
$187$	235.032	−	135.696i	1.25686	−	0.725647i
$188$	94.4006			0.502131
$189$		0			0
$190$		0			0
$191$	279.710	−	161.491i	1.46445	−	0.845501i	0.465239	−	0.885185i	$-0.345968\pi$
$191$	279.710	−	161.491i	1.46445	−	0.845501i	0.999212	+	0.0396836i	$0.0126350\pi$
$192$		0			0
$193$	−149.635	−	86.3918i	−0.775311	−	0.447626i	0.0594550	−	0.998231i	$-0.481064\pi$
$193$	−149.635	−	86.3918i	−0.775311	−	0.447626i	−0.834766	+	0.550605i	$0.814397\pi$
$194$	−57.6284	−	33.2718i	−0.297054	−	0.171504i
$195$		0			0
$196$	−5.01700	−	8.68970i	−0.0255970	−	0.0443352i
$197$	−71.7321			−0.364123			−0.182061	−	0.983287i	$-0.558277\pi$
$197$	−71.7321			−0.364123			−0.182061	+	0.983287i	$0.558277\pi$
$198$		0			0
$199$	−133.225			−0.669472			−0.334736	−	0.942312i	$-0.608647\pi$
$199$	−133.225			−0.669472			−0.334736	+	0.942312i	$0.608647\pi$
$200$		0			0
$201$		0			0
$202$	27.3792	+	15.8074i	0.135541	+	0.0782544i
$203$	−165.995	+	287.512i	−0.817711	+	1.41632i
$204$		0			0
$205$		0			0
$206$			175.220i			0.850581i
$207$		0			0
$208$			39.1299i			0.188125i
$209$	−294.793	+	170.199i	−1.41049	+	0.814349i
$210$		0			0
$211$	188.164	−	325.909i	0.891771	−	1.54459i	0.0540209	−	0.998540i	$-0.482796\pi$
$211$	188.164	−	325.909i	0.891771	−	1.54459i	0.837750	−	0.546053i	$-0.183870\pi$
$212$	1.08813	−	1.88469i	0.00513268	−	0.00889006i
$213$		0			0
$214$	33.4949	+	58.0150i	0.156518	+	0.271098i
$215$		0			0
$216$		0			0
$217$			66.7457i			0.307584i
$218$	19.0032	+	32.9144i	0.0871705	+	0.150984i
$219$		0			0
$220$		0			0
$221$	−109.301	−	63.1051i	−0.494576	−	0.285543i
$222$		0			0
$223$	−51.2488	+	29.5885i	−0.229815	+	0.132684i	−0.610487	−	0.792026i	$-0.709026\pi$
$223$	−51.2488	+	29.5885i	−0.229815	+	0.132684i	0.380672	+	0.924710i	$0.375693\pi$
$224$			37.5161i			0.167482i
$225$		0			0
$226$	26.6012			0.117705
$227$	−74.9193	−	129.764i	−0.330041	−	0.571647i	0.652479	−	0.757807i	$-0.273729\pi$
$227$	−74.9193	−	129.764i	−0.330041	−	0.571647i	−0.982520	+	0.186160i	$0.940396\pi$
$228$		0			0
$229$	−85.4319	+	147.972i	−0.373065	+	0.646167i	−0.990035	−	0.140819i	$-0.955026\pi$
$229$	−85.4319	+	147.972i	−0.373065	+	0.646167i	0.616970	+	0.786986i	$0.288360\pi$
$230$		0			0
$231$		0			0
$232$	−122.619	+	70.7943i	−0.528532	+	0.305148i
$233$	448.983			1.92697			0.963483	−	0.267770i	$-0.0862867\pi$
$233$	448.983			1.92697			0.963483	+	0.267770i	$0.0862867\pi$
$234$		0			0
$235$		0			0
$236$	−16.6961	+	9.63952i	−0.0707463	+	0.0408454i
$237$		0			0
$238$	−104.793	−	60.5024i	−0.440308	−	0.254212i
$239$	−200.845	−	115.958i	−0.840356	−	0.485180i	0.0170289	−	0.999855i	$-0.494579\pi$
$239$	−200.845	−	115.958i	−0.840356	−	0.485180i	−0.857385	+	0.514675i	$0.827913\pi$
$240$		0			0
$241$	198.671	+	344.108i	0.824359	+	1.42783i	0.902408	+	0.430882i	$0.141798\pi$
$241$	198.671	+	344.108i	0.824359	+	1.42783i	−0.0780488	+	0.996950i	$0.524869\pi$
$242$	454.655			1.87874
$243$		0			0
$244$	−89.8290			−0.368152
$245$		0			0
$246$		0			0
$247$	137.093	+	79.1506i	0.555032	+	0.320448i
$248$	−14.2330	+	24.6522i	−0.0573910	+	0.0994042i
$249$		0			0
$250$		0			0
$251$			193.179i			0.769636i	0.922992	+	0.384818i	$0.125736\pi$
$251$			193.179i			0.769636i	−0.922992	+	0.384818i	$0.874264\pi$
$252$		0			0
$253$			356.266i			1.40816i
$254$	157.772	−	91.0895i	0.621148	−	0.358620i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	60.4331	−	104.673i	0.235148	−	0.407289i	−0.724167	−	0.689624i	$-0.757776\pi$
$257$	60.4331	−	104.673i	0.235148	−	0.407289i	0.959316	+	0.282335i	$0.0911091\pi$
$258$		0			0
$259$	−8.43669	−	14.6128i	−0.0325741	−	0.0564200i
$260$		0			0
$261$		0			0
$262$			43.5741i			0.166313i
$263$	−150.518	−	260.705i	−0.572312	−	0.991273i	−0.996328	−	0.0856183i	$-0.972713\pi$
$263$	−150.518	−	260.705i	−0.572312	−	0.991273i	0.424016	−	0.905655i	$-0.360620\pi$
$264$		0			0
$265$		0			0
$266$	131.439	+	75.8862i	0.494131	+	0.285287i
$267$		0			0
$268$	−5.78738	+	3.34135i	−0.0215947	+	0.0124677i
$269$		−	128.065i		−	0.476077i	−0.971256	−	0.238038i	$-0.923496\pi$
$269$		−	128.065i		−	0.476077i	0.971256	−	0.238038i	$-0.0765044\pi$
$270$		0			0
$271$	−512.831			−1.89236			−0.946182	−	0.323635i	$-0.895095\pi$
$271$	−512.831			−1.89236			−0.946182	+	0.323635i	$0.895095\pi$
$272$	−25.8033	−	44.6927i	−0.0948651	−	0.164311i
$273$		0			0
$274$	−75.3384	+	130.490i	−0.274958	+	0.476240i
$275$		0			0
$276$		0			0
$277$	−240.341	+	138.761i	−0.867658	+	0.500942i	−0.866569	−	0.499057i	$-0.833680\pi$
$277$	−240.341	+	138.761i	−0.867658	+	0.500942i	−0.00108844	+	0.999999i	$0.500346\pi$
$278$	161.555			0.581133
$279$		0			0
$280$		0			0
$281$	89.3698	−	51.5977i	0.318042	−	0.183622i	−0.332478	−	0.943111i	$-0.607885\pi$
$281$	89.3698	−	51.5977i	0.318042	−	0.183622i	0.650519	+	0.759490i	$0.274551\pi$
$282$		0			0
$283$	−142.087	−	82.0340i	−0.502075	−	0.289873i	0.227495	−	0.973779i	$-0.426946\pi$
$283$	−142.087	−	82.0340i	−0.502075	−	0.289873i	−0.729570	+	0.683906i	$0.760280\pi$
$284$	66.6267	+	38.4670i	0.234601	+	0.135447i
$285$		0			0
$286$	−145.508	−	252.026i	−0.508768	−	0.881211i
$287$	−356.567			−1.24239
$288$		0			0
$289$	−122.547			−0.424039
$290$		0			0
$291$		0			0
$292$	−154.014	−	88.9201i	−0.527446	−	0.304521i
$293$	146.494	−	253.735i	0.499979	−	0.865988i	−0.500021	−	0.866013i	$-0.666675\pi$
$293$	146.494	−	253.735i	0.499979	−	0.865988i	1.00000		2.47977e-5i	$7.89334e-6\pi$
$294$		0			0
$295$		0			0
$296$		−	7.19622i		−	0.0243116i
$297$		0			0
$298$			170.956i			0.573677i
$299$	143.484	−	82.8402i	0.479878	−	0.277058i
$300$		0			0
$301$	−248.151	+	429.811i	−0.824423	+	1.42794i
$302$	89.7938	−	155.527i	0.297331	−	0.514992i
$303$		0			0
$304$	32.3642	+	56.0565i	0.106461	+	0.184396i
$305$		0			0
$306$		0			0
$307$		−	467.606i		−	1.52315i	−0.648079	−	0.761573i	$-0.724427\pi$
$307$		−	467.606i		−	1.52315i	0.648079	−	0.761573i	$-0.275573\pi$
$308$	−139.506	−	241.632i	−0.452943	−	0.784520i
$309$		0			0
$310$		0			0
$311$	−465.753	−	268.902i	−1.49760	−	0.864638i	−0.497601	−	0.867406i	$-0.665786\pi$
$311$	−465.753	−	268.902i	−1.49760	−	0.864638i	−0.999996	+	0.00276786i	$0.999119\pi$
$312$		0			0
$313$	230.586	−	133.129i	0.736697	−	0.425332i	−0.0841703	−	0.996451i	$-0.526824\pi$
$313$	230.586	−	133.129i	0.736697	−	0.425332i	0.820867	+	0.571119i	$0.193491\pi$
$314$		−	147.379i		−	0.469361i
$315$		0			0
$316$	−235.294			−0.744602
$317$	−238.437	−	412.986i	−0.752168	−	1.30279i	−0.946770	−	0.321911i	$-0.895675\pi$
$317$	−238.437	−	412.986i	−0.752168	−	1.30279i	0.194602	−	0.980882i	$-0.437659\pi$
$318$		0			0
$319$	526.508	−	911.939i	1.65050	−	2.85874i
$320$		0			0
$321$		0			0
$322$	137.566	−	79.4237i	0.427223	−	0.246657i
$323$	−208.776			−0.646366
$324$		0			0
$325$		0			0
$326$	−230.904	+	133.313i	−0.708296	+	0.408935i
$327$		0			0
$328$	−131.696	−	76.0349i	−0.401513	−	0.231814i
$329$	271.093	+	156.515i	0.823990	+	0.475731i
$330$		0			0
$331$	−17.6720	−	30.6088i	−0.0533898	−	0.0924738i	0.838095	−	0.545524i	$-0.183669\pi$
$331$	−17.6720	−	30.6088i	−0.0533898	−	0.0924738i	−0.891485	+	0.453050i	$0.850336\pi$
$332$	−294.246			−0.886282
$333$		0			0
$334$	−96.0482			−0.287569
$335$		0			0
$336$		0			0
$337$	215.201	+	124.246i	0.638579	+	0.368684i	0.784067	−	0.620676i	$-0.213142\pi$
$337$	215.201	+	124.246i	0.638579	+	0.368684i	−0.145488	+	0.989360i	$0.546475\pi$
$338$	51.8331	−	89.7776i	0.153352	−	0.265614i
$339$		0			0
$340$		0			0
$341$		−	211.706i		−	0.620838i
$342$		0			0
$343$		−	358.239i		−	1.04443i
$344$	−183.307	+	105.833i	−0.532870	+	0.307653i
$345$		0			0
$346$	−86.5447	+	149.900i	−0.250129	+	0.433237i
$347$	−1.34645	+	2.33212i	−0.00388026	+	0.00672082i	−0.867959	−	0.496636i	$-0.834568\pi$
$347$	−1.34645	+	2.33212i	−0.00388026	+	0.00672082i	0.864079	+	0.503357i	$0.167902\pi$
$348$		0			0
$349$	196.192	+	339.815i	0.562156	+	0.973682i	0.997308	+	0.0733253i	$0.0233611\pi$
$349$	196.192	+	339.815i	0.562156	+	0.973682i	−0.435152	+	0.900357i	$0.643306\pi$
$350$		0			0
$351$		0			0
$352$		−	118.994i		−	0.338052i
$353$	9.89124	+	17.1321i	0.0280205	+	0.0485329i	0.879696	−	0.475537i	$-0.157746\pi$
$353$	9.89124	+	17.1321i	0.0280205	+	0.0485329i	−0.851675	+	0.524070i	$0.824413\pi$
$354$		0			0
$355$		0			0
$356$	251.720	+	145.331i	0.707079	+	0.408232i
$357$		0			0
$358$	−96.0517	+	55.4555i	−0.268301	+	0.154904i
$359$		−	415.325i		−	1.15689i	−0.815720	−	0.578447i	$-0.803659\pi$
$359$		−	415.325i		−	1.15689i	0.815720	−	0.578447i	$-0.196341\pi$
$360$		0			0
$361$	−99.1389			−0.274623
$362$	155.254	+	268.908i	0.428878	+	0.742839i
$363$		0			0
$364$	−64.8771	+	112.370i	−0.178234	+	0.308710i
$365$		0			0
$366$		0			0
$367$	−461.927	+	266.694i	−1.25866	+	0.726685i	−0.972813	−	0.231591i	$-0.925607\pi$
$367$	−461.927	+	266.694i	−1.25866	+	0.726685i	−0.285843	+	0.958276i	$0.592274\pi$
$368$	67.7458			0.184092
$369$		0			0
$370$		0			0
$371$	6.24961	−	3.60821i	0.0168453	−	0.00972564i
$372$		0			0
$373$	−186.697	−	107.790i	−0.500529	−	0.288981i	0.228403	−	0.973567i	$-0.426650\pi$
$373$	−186.697	−	107.790i	−0.500529	−	0.288981i	−0.728932	+	0.684586i	$0.759983\pi$
$374$	332.386	+	191.903i	0.888733	+	0.513110i
$375$		0			0
$376$	66.7513	+	115.617i	0.177530	+	0.307491i
$377$	−489.702			−1.29895
$378$		0			0
$379$	−176.846			−0.466612			−0.233306	−	0.972403i	$-0.574954\pi$
$379$	−176.846			−0.466612			−0.233306	+	0.972403i	$0.574954\pi$
$380$		0			0
$381$		0			0
$382$	395.570	+	228.382i	1.03552	+	0.597860i
$383$	−8.60134	+	14.8980i	−0.0224578	+	0.0388980i	−0.877036	−	0.480425i	$-0.840482\pi$
$383$	−8.60134	+	14.8980i	−0.0224578	+	0.0388980i	0.854578	+	0.519323i	$0.173816\pi$
$384$		0			0
$385$		0			0
$386$		−	244.353i		−	0.633039i
$387$		0			0
$388$		−	94.1068i		−	0.242543i
$389$	298.375	−	172.267i	0.767030	−	0.442845i	−0.0647844	−	0.997899i	$-0.520636\pi$
$389$	298.375	−	172.267i	0.767030	−	0.442845i	0.831814	+	0.555055i	$0.187303\pi$
$390$		0			0
$391$	−109.254	+	189.234i	−0.279422	+	0.483974i
$392$	7.09511	−	12.2891i	0.0180998	−	0.0313497i
$393$		0			0
$394$	−50.7223	−	87.8536i	−0.128737	−	0.222979i
$395$		0			0
$396$		0			0
$397$			68.9955i			0.173792i	0.996217	+	0.0868960i	$0.0276948\pi$
$397$			68.9955i			0.173792i	−0.996217	+	0.0868960i	$0.972305\pi$
$398$	−94.2042	−	163.167i	−0.236694	−	0.409966i
$399$		0			0
$400$		0			0
$401$	154.315	+	89.0938i	0.384825	+	0.222179i	0.679916	−	0.733290i	$-0.262016\pi$
$401$	154.315	+	89.0938i	0.384825	+	0.222179i	−0.295090	+	0.955469i	$0.595350\pi$
$402$		0			0
$403$	−85.2629	+	49.2266i	−0.211571	+	0.122150i
$404$			44.7100i			0.110668i
$405$		0			0
$406$	−469.506			−1.15642
$407$	26.7597	+	46.3492i	0.0657487	+	0.113880i
$408$		0			0
$409$	5.64530	−	9.77795i	0.0138027	−	0.0239070i	−0.859042	−	0.511906i	$-0.828940\pi$
$409$	5.64530	−	9.77795i	0.0138027	−	0.0239070i	0.872844	+	0.487999i	$0.162273\pi$
$410$		0			0
$411$		0			0
$412$	−214.599	+	123.899i	−0.520872	+	0.300726i
$413$	−63.9290			−0.154792
$414$		0			0
$415$		0			0
$416$	−47.9242	+	27.6690i	−0.115202	+	0.0665121i
$417$		0			0
$418$	−416.901	−	240.698i	−0.997370	−	0.575832i
$419$	−56.3602	−	32.5396i	−0.134511	−	0.0776601i	0.431234	−	0.902240i	$-0.358078\pi$
$419$	−56.3602	−	32.5396i	−0.134511	−	0.0776601i	−0.565746	+	0.824580i	$0.691412\pi$
$420$		0			0
$421$	115.044	+	199.262i	0.273263	+	0.473306i	0.969696	−	0.244317i	$-0.0785636\pi$
$421$	115.044	+	199.262i	0.273263	+	0.473306i	−0.696432	+	0.717623i	$0.745230\pi$
$422$	532.207			1.26116
$423$		0			0
$424$	3.07769			0.00725870
$425$		0			0
$426$		0			0
$427$	−257.964	−	148.936i	−0.604132	−	0.348796i
$428$	−47.3690	+	82.0455i	−0.110675	+	0.191695i
$429$		0			0
$430$		0			0
$431$			67.4877i			0.156584i	0.996930	+	0.0782920i	$0.0249467\pi$
$431$			67.4877i			0.156584i	−0.996930	+	0.0782920i	$0.975053\pi$
$432$		0			0
$433$		−	132.060i		−	0.304989i	−0.988304	−	0.152495i	$-0.951269\pi$
$433$		−	132.060i		−	0.304989i	0.988304	−	0.152495i	$-0.0487307\pi$
$434$	−81.7464	+	47.1963i	−0.188356	+	0.108747i
$435$		0			0
$436$	−26.8745	+	46.5480i	−0.0616388	+	0.106762i
$437$	137.034	−	237.350i	0.313579	−	0.543134i
$438$		0			0
$439$	344.511	+	596.711i	0.784764	+	1.35925i	0.929140	+	0.369728i	$0.120549\pi$
$439$	344.511	+	596.711i	0.784764	+	1.35925i	−0.144376	+	0.989523i	$0.546118\pi$
$440$		0			0
$441$		0			0
$442$		−	178.488i		−	0.403819i
$443$	34.0413	+	58.9612i	0.0768426	+	0.133095i	0.901886	−	0.431974i	$-0.142183\pi$
$443$	34.0413	+	58.9612i	0.0768426	+	0.133095i	−0.825043	+	0.565069i	$0.808849\pi$
$444$		0			0
$445$		0			0
$446$	−72.4767	−	41.8444i	−0.162504	−	0.0938216i
$447$		0			0
$448$	−45.9476	+	26.5279i	−0.102562	+	0.0592140i
$449$			685.554i			1.52685i	0.645898	+	0.763423i	$0.276483\pi$
$449$			685.554i			1.52685i	−0.645898	+	0.763423i	$0.723517\pi$
$450$		0			0
$451$	1130.97			2.50769
$452$	18.8099	+	32.5797i	0.0416148	+	0.0720790i
$453$		0			0
$454$	105.952	−	183.514i	0.233374	−	0.404216i
$455$		0			0
$456$		0			0
$457$	449.810	−	259.698i	0.984266	−	0.568266i	0.0807109	−	0.996738i	$-0.474281\pi$
$457$	449.810	−	259.698i	0.984266	−	0.568266i	0.903555	+	0.428471i	$0.140948\pi$
$458$	−241.638			−0.527593
$459$		0			0
$460$		0			0
$461$	−77.5379	+	44.7665i	−0.168195	+	0.0971074i	−0.581734	−	0.813379i	$-0.697626\pi$
$461$	−77.5379	+	44.7665i	−0.168195	+	0.0971074i	0.413539	+	0.910486i	$0.364292\pi$
$462$		0			0
$463$	−441.640	−	254.981i	−0.953865	−	0.550714i	−0.0595857	−	0.998223i	$-0.518978\pi$
$463$	−441.640	−	254.981i	−0.953865	−	0.550714i	−0.894279	+	0.447509i	$0.852311\pi$
$464$	−173.410	−	100.118i	−0.373728	−	0.215772i
$465$		0			0
$466$	317.479	+	549.890i	0.681285	+	1.18002i
$467$	539.803			1.15590			0.577948	−	0.816074i	$-0.303854\pi$
$467$	539.803			1.15590			0.577948	+	0.816074i	$0.303854\pi$
$468$		0			0
$469$	−22.1597			−0.0472488
$470$		0			0
$471$		0			0
$472$	−23.6119	−	13.6323i	−0.0500252	−	0.0288821i
$473$	787.093	−	1363.28i	1.66404	−	2.88221i
$474$		0			0
$475$		0			0
$476$		−	171.127i		−	0.359510i
$477$		0			0
$478$		−	327.979i		−	0.686148i
$479$	94.2261	−	54.4015i	0.196714	−	0.113573i	−0.398408	−	0.917208i	$-0.630437\pi$
$479$	94.2261	−	54.4015i	0.196714	−	0.113573i	0.595122	+	0.803635i	$0.297104\pi$
$480$		0			0
$481$	12.4445	−	21.5546i	0.0258722	−	0.0448120i
$482$	−280.963	+	486.642i	−0.582910	+	1.00963i
$483$		0			0
$484$	321.490	+	556.837i	0.664235	+	1.15049i
$485$		0			0
$486$		0			0
$487$			342.524i			0.703334i	0.936125	+	0.351667i	$0.114385\pi$
$487$			342.524i			0.703334i	−0.936125	+	0.351667i	$0.885615\pi$
$488$	−63.5187	−	110.018i	−0.130161	−	0.225446i
$489$		0			0
$490$		0			0
$491$	−430.657	−	248.640i	−0.877102	−	0.506395i	−0.00740027	−	0.999973i	$-0.502356\pi$
$491$	−430.657	−	248.640i	−0.877102	−	0.506395i	−0.869702	+	0.493577i	$0.835689\pi$
$492$		0			0
$493$	559.319	−	322.923i	1.13452	−	0.655016i
$494$			223.872i			0.453182i
$495$		0			0
$496$	−40.2569			−0.0811632
$497$	127.556	+	220.933i	0.256652	+	0.444533i
$498$		0			0
$499$	77.5164	−	134.262i	0.155343	−	0.269063i	−0.777841	−	0.628462i	$-0.783685\pi$
$499$	77.5164	−	134.262i	0.155343	−	0.269063i	0.933184	+	0.359399i	$0.117018\pi$
$500$		0			0
$501$		0			0
$502$	−236.595	+	136.598i	−0.471304	+	0.272107i
$503$	−580.438			−1.15395			−0.576976	−	0.816761i	$-0.695767\pi$
$503$	−580.438			−1.15395			−0.576976	+	0.816761i	$0.695767\pi$
$504$		0			0
$505$		0			0
$506$	−436.335	+	251.918i	−0.862321	+	0.497862i
$507$		0			0
$508$	223.123	+	128.820i	0.439218	+	0.253583i
$509$	158.209	+	91.3419i	0.310823	+	0.179454i	0.647295	−	0.762240i	$-0.275900\pi$
$509$	158.209	+	91.3419i	0.310823	+	0.179454i	−0.336472	+	0.941694i	$0.609234\pi$
$510$		0			0
$511$	−294.858	−	510.709i	−0.577021	−	0.999430i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	170.931			0.332550
$515$		0			0
$516$		0			0
$517$	−859.858	−	496.439i	−1.66317	−	0.960231i
$518$	11.9313	−	20.6656i	0.0230334	−	0.0398950i
$519$		0			0
$520$		0			0
$521$		−	47.7611i		−	0.0916720i	−0.998949	−	0.0458360i	$-0.985405\pi$
$521$		−	47.7611i		−	0.0916720i	0.998949	−	0.0458360i	$-0.0145952\pi$
$522$		0			0
$523$		−	266.851i		−	0.510230i	−0.966911	−	0.255115i	$-0.917887\pi$
$523$		−	266.851i		−	0.510230i	0.966911	−	0.255115i	$-0.0821134\pi$
$524$	−53.3672	+	30.8116i	−0.101846	+	0.0588007i
$525$		0			0
$526$	212.865	−	368.692i	0.404685	−	0.700936i
$527$	64.9227	−	112.449i	0.123193	−	0.213376i
$528$		0			0
$529$	121.078	+	209.714i	0.228881	+	0.396434i
$530$		0			0
$531$		0			0
$532$			214.639i			0.403456i
$533$	−262.977	−	455.489i	−0.493389	−	0.854576i
$534$		0			0
$535$		0			0
$536$	−8.18459	−	4.72538i	−0.0152698	−	0.00881600i
$537$		0			0
$538$	156.847	−	90.5554i	0.291536	−	0.168319i
$539$			105.535i			0.195798i
$540$		0			0
$541$	−707.266			−1.30733			−0.653666	−	0.756783i	$-0.726770\pi$
$541$	−707.266			−1.30733			−0.653666	+	0.756783i	$0.726770\pi$
$542$	−362.626	−	628.087i	−0.669052	−	1.15883i
$543$		0			0
$544$	36.4914	−	63.2050i	0.0670798	−	0.116186i
$545$		0			0
$546$		0			0
$547$	178.686	−	103.164i	0.326665	−	0.188600i	−0.327695	−	0.944784i	$-0.606272\pi$
$547$	178.686	−	103.164i	0.326665	−	0.188600i	0.654359	+	0.756184i	$0.272938\pi$
$548$	−213.089			−0.388849
$549$		0			0
$550$		0			0
$551$	−701.535	+	405.032i	−1.27320	+	0.735084i
$552$		0			0
$553$	−675.700	−	390.116i	−1.22188	−	0.705454i
$554$	−339.894	−	196.238i	−0.613527	−	0.354220i
$555$		0			0
$556$	114.237	+	197.863i	0.205461	+	0.355870i
$557$	643.753			1.15575			0.577876	−	0.816125i	$-0.303882\pi$
$557$	643.753			1.15575			0.577876	+	0.816125i	$0.303882\pi$
$558$		0			0
$559$	−732.071			−1.30961
$560$		0			0
$561$		0			0
$562$	126.388	+	72.9701i	0.224890	+	0.129840i
$563$	361.822	−	626.694i	0.642668	−	1.11313i	−0.342167	−	0.939639i	$-0.611161\pi$
$563$	361.822	−	626.694i	0.642668	−	1.11313i	0.984835	−	0.173494i	$-0.0555058\pi$
$564$		0			0
$565$		0			0
$566$		−	232.027i		−	0.409942i
$567$		0			0
$568$			108.801i			0.191551i
$569$	329.204	−	190.066i	0.578566	−	0.334035i	−0.181997	−	0.983299i	$-0.558256\pi$
$569$	329.204	−	190.066i	0.578566	−	0.334035i	0.760563	+	0.649264i	$0.224923\pi$
$570$		0			0
$571$	−20.7292	+	35.9040i	−0.0363033	+	0.0628791i	−0.883606	−	0.468231i	$-0.844892\pi$
$571$	−20.7292	+	35.9040i	−0.0363033	+	0.0628791i	0.847303	+	0.531110i	$0.178225\pi$
$572$	205.779	−	356.419i	0.359753	−	0.623110i
$573$		0			0
$574$	−252.131	−	436.703i	−0.439252	−	0.760807i
$575$		0			0
$576$		0			0
$577$		−	601.252i		−	1.04203i	−0.853547	−	0.521016i	$-0.825553\pi$
$577$		−	601.252i		−	1.04203i	0.853547	−	0.521016i	$-0.174447\pi$
$578$	−86.6540	−	150.089i	−0.149920	−	0.259670i
$579$		0			0
$580$		0			0
$581$	−844.993	−	487.857i	−1.45438	−	0.839685i
$582$		0			0
$583$	−19.8227	+	11.4446i	−0.0340011	+	0.0196306i
$584$		−	251.504i		−	0.430658i
$585$		0			0
$586$	414.347			0.707076
$587$	363.988	+	630.446i	0.620082	+	1.07401i	0.989470	+	0.144738i	$0.0462340\pi$
$587$	363.988	+	630.446i	0.620082	+	1.07401i	−0.369388	+	0.929275i	$0.620433\pi$
$588$		0			0
$589$	−81.4303	+	141.041i	−0.138252	+	0.239459i
$590$		0			0
$591$		0			0
$592$	8.81354	−	5.08850i	0.0148877	−	0.00859544i
$593$	−418.998			−0.706573			−0.353286	−	0.935515i	$-0.614936\pi$
$593$	−418.998			−0.706573			−0.353286	+	0.935515i	$0.614936\pi$
$594$		0			0
$595$		0			0
$596$	−209.377	+	120.884i	−0.351304	+	0.202825i
$597$		0			0
$598$	202.916	+	117.154i	0.339325	+	0.195909i
$599$	−760.433	−	439.036i	−1.26950	−	0.732948i	−0.294610	−	0.955618i	$-0.595190\pi$
$599$	−760.433	−	439.036i	−1.26950	−	0.732948i	−0.974894	+	0.222669i	$0.928523\pi$
$600$		0			0
$601$	266.229	+	461.122i	0.442977	+	0.767259i	0.997909	−	0.0646372i	$-0.0205890\pi$
$601$	266.229	+	461.122i	0.442977	+	0.767259i	−0.554932	+	0.831896i	$0.687256\pi$
$602$	−701.878			−1.16591
$603$		0			0
$604$	253.975			0.420489
$605$		0			0
$606$		0			0
$607$	−81.8641	−	47.2643i	−0.134867	−	0.0778653i	0.431049	−	0.902329i	$-0.358144\pi$
$607$	−81.8641	−	47.2643i	−0.134867	−	0.0778653i	−0.565915	+	0.824463i	$0.691477\pi$
$608$	−45.7700	+	79.2759i	−0.0752795	+	0.130388i
$609$		0			0
$610$		0			0
$611$			461.736i			0.755705i
$612$		0			0
$613$			816.657i			1.33223i	0.745849	+	0.666115i	$0.232044\pi$
$613$			816.657i			1.33223i	−0.745849	+	0.666115i	$0.767956\pi$
$614$	572.698	−	330.647i	0.932733	−	0.538513i
$615$		0			0
$616$	197.292	−	341.719i	0.320279	−	0.554739i
$617$	94.8195	−	164.232i	0.153678	−	0.266179i	−0.778899	−	0.627150i	$-0.784221\pi$
$617$	94.8195	−	164.232i	0.153678	−	0.266179i	0.932577	+	0.360971i	$0.117555\pi$
$618$		0			0
$619$	−47.7312	−	82.6728i	−0.0771101	−	0.133559i	0.824892	−	0.565291i	$-0.191236\pi$
$619$	−47.7312	−	82.6728i	−0.0771101	−	0.133559i	−0.902002	+	0.431732i	$0.857903\pi$
$620$		0			0
$621$		0			0
$622$		−	760.571i		−	1.22278i
$623$	481.914	+	834.700i	0.773538	+	1.33981i
$624$		0			0
$625$		0			0
$626$	326.098	+	188.273i	0.520923	+	0.300755i
$627$		0			0
$628$	180.502	−	104.213i	0.287423	−	0.165944i
$629$			32.8250i			0.0521861i
$630$		0			0
$631$	−192.912			−0.305724			−0.152862	−	0.988248i	$-0.548849\pi$
$631$	−192.912			−0.305724			−0.152862	+	0.988248i	$0.548849\pi$
$632$	−166.378	−	288.175i	−0.263257	−	0.455974i
$633$		0			0
$634$	337.201	−	584.050i	0.531863	−	0.921214i
$635$		0			0
$636$		0			0
$637$	42.5034	−	24.5394i	0.0667244	−	0.0385233i
$638$	1489.19			2.33415
$639$		0			0
$640$		0			0
$641$	277.039	−	159.949i	0.432198	−	0.249530i	−0.268084	−	0.963395i	$-0.586391\pi$
$641$	277.039	−	159.949i	0.432198	−	0.249530i	0.700283	+	0.713866i	$0.253057\pi$
$642$		0			0
$643$	131.937	+	76.1741i	0.205190	+	0.118467i	0.599074	−	0.800693i	$-0.295535\pi$
$643$	131.937	+	76.1741i	0.205190	+	0.118467i	−0.393884	+	0.919160i	$0.628869\pi$
$644$	194.547	+	112.322i	0.302092	+	0.174413i
$645$		0			0
$646$	−147.627	−	255.698i	−0.228525	−	0.395817i
$647$	−632.862			−0.978148			−0.489074	−	0.872242i	$-0.662665\pi$
$647$	−632.862			−0.978148			−0.489074	+	0.872242i	$0.662665\pi$
$648$		0			0
$649$	202.772			0.312437
$650$		0			0
$651$		0			0
$652$	−326.548	−	188.533i	−0.500841	−	0.289160i
$653$	−408.937	+	708.299i	−0.626243	+	1.08468i	0.362056	+	0.932156i	$0.382075\pi$
$653$	−408.937	+	708.299i	−0.626243	+	1.08468i	−0.988299	+	0.152529i	$0.951258\pi$
$654$		0			0
$655$		0			0
$656$		−	215.059i		−	0.327834i
$657$		0			0
$658$			442.692i			0.672785i
$659$	368.474	−	212.738i	0.559141	−	0.322820i	−0.193660	−	0.981069i	$-0.562036\pi$
$659$	368.474	−	212.738i	0.559141	−	0.322820i	0.752800	+	0.658249i	$0.228703\pi$
$660$		0			0
$661$	−142.986	+	247.659i	−0.216318	+	0.374673i	−0.953679	−	0.300825i	$-0.902738\pi$
$661$	−142.986	+	247.659i	−0.216318	+	0.374673i	0.737362	+	0.675498i	$0.236071\pi$
$662$	24.9920	−	43.2874i	0.0377523	−	0.0653889i
$663$		0			0
$664$	−208.063	−	360.376i	−0.313348	−	0.542735i
$665$		0			0
$666$		0			0
$667$			847.824i			1.27110i
$668$	−67.9163	−	117.634i	−0.101671	−	0.176100i
$669$		0			0
$670$		0			0
$671$	818.218	+	472.398i	1.21940	+	0.704021i
$672$		0			0
$673$	−1036.99	+	598.709i	−1.54085	+	0.889612i	−0.542068	+	0.840335i	$0.682358\pi$
$673$	−1036.99	+	598.709i	−1.54085	+	0.889612i	−0.998785	+	0.0492769i	$0.984308\pi$
$674$			351.422i			0.521398i
$675$		0			0
$676$	146.606			0.216873
$677$	452.777	+	784.232i	0.668799	+	1.15839i	0.978240	+	0.207475i	$0.0665245\pi$
$677$	452.777	+	784.232i	0.668799	+	1.15839i	−0.309442	+	0.950918i	$0.600142\pi$
$678$		0			0
$679$	156.028	−	270.249i	0.229791	−	0.398010i
$680$		0			0
$681$		0			0
$682$	259.285	−	149.698i	0.380184	−	0.219499i
$683$	31.1970			0.0456764			0.0228382	−	0.999739i	$-0.492730\pi$
$683$	31.1970			0.0456764			0.0228382	+	0.999739i	$0.492730\pi$
$684$		0			0
$685$		0			0
$686$	438.751	−	253.313i	0.639579	−	0.369261i
$687$		0			0
$688$	−259.236	−	149.670i	−0.376796	−	0.217543i
$689$	9.21848	+	5.32229i	0.0133795	+	0.00772466i
$690$		0			0
$691$	101.532	+	175.858i	0.146935	+	0.254498i	0.930093	−	0.367324i	$-0.119726\pi$
$691$	101.532	+	175.858i	0.146935	+	0.254498i	−0.783158	+	0.621822i	$0.786393\pi$
$692$	−244.785			−0.353736
$693$		0			0
$694$	−3.80834			−0.00548752
$695$		0			0
$696$		0			0
$697$	600.723	+	346.828i	0.861870	+	0.497601i
$698$	−277.458	+	480.571i	−0.397504	+	0.688497i
$699$		0			0
$700$		0			0
$701$			633.699i			0.903993i	0.892020	+	0.451997i	$0.149288\pi$
$701$			633.699i			0.903993i	−0.892020	+	0.451997i	$0.850712\pi$
$702$		0			0
$703$		−	41.1714i		−	0.0585652i
$704$	145.738	−	84.1418i	0.207014	−	0.119520i
$705$		0			0
$706$	−13.9883	+	24.2285i	−0.0198135	+	0.0343180i
$707$	−74.1289	+	128.395i	−0.104850	+	0.181605i
$708$		0			0
$709$	−74.6901	−	129.367i	−0.105346	−	0.182464i	0.808534	−	0.588450i	$-0.200262\pi$
$709$	−74.6901	−	129.367i	−0.105346	−	0.182464i	−0.913879	+	0.405986i	$0.866928\pi$
$710$		0			0
$711$		0			0
$712$			411.057i			0.577328i
$713$	85.2262	+	147.616i	0.119532	+	0.207035i
$714$		0			0
$715$		0			0
$716$	−135.838	−	78.4259i	−0.189717	−	0.109533i
$717$		0			0
$718$	508.667	−	293.679i	0.708451	−	0.409024i
$719$			257.590i			0.358262i	0.983825	+	0.179131i	$0.0573285\pi$
$719$			257.590i			0.358262i	−0.983825	+	0.179131i	$0.942671\pi$
$720$		0			0
$721$	−821.694			−1.13966
$722$	−70.1018	−	121.420i	−0.0970939	−	0.168172i
$723$		0			0
$724$	−219.562	+	380.293i	−0.303263	+	0.525266i
$725$		0			0
$726$		0			0
$727$	526.008	−	303.691i	0.723532	−	0.417731i	−0.0925193	−	0.995711i	$-0.529492\pi$
$727$	526.008	−	303.691i	0.723532	−	0.417731i	0.816051	+	0.577980i	$0.196159\pi$
$728$	−183.500			−0.252061
$729$		0			0
$730$		0			0
$731$	836.143	−	482.747i	1.14383	−	0.660393i
$732$		0			0
$733$	768.411	+	443.643i	1.04831	+	0.605242i	0.922176	−	0.386771i	$-0.126410\pi$
$733$	768.411	+	443.643i	1.04831	+	0.605242i	0.126134	+	0.992013i	$0.459743\pi$
$734$	−653.263	−	377.162i	−0.890004	−	0.513844i
$735$		0			0
$736$	47.9035	+	82.9713i	0.0650863	+	0.112733i
$737$	70.2867			0.0953686
$738$		0			0
$739$	30.1955			0.0408599			0.0204300	−	0.999791i	$-0.493496\pi$
$739$	30.1955			0.0408599			0.0204300	+	0.999791i	$0.493496\pi$
$740$		0			0
$741$		0			0
$742$	8.83828	+	5.10278i	0.0119114	+	0.00687707i
$743$	−285.008	+	493.648i	−0.383591	+	0.664399i	−0.991573	−	0.129552i	$-0.958646\pi$
$743$	−285.008	+	493.648i	−0.383591	+	0.664399i	0.607982	+	0.793951i	$0.291979\pi$
$744$		0			0
$745$		0			0
$746$		−	304.876i		−	0.408680i
$747$		0			0
$748$			542.784i			0.725647i
$749$	−272.062	+	157.075i	−0.363233	+	0.209713i
$750$		0			0
$751$	−213.747	+	370.221i	−0.284617	+	0.492970i	−0.972516	−	0.232836i	$-0.925200\pi$
$751$	−213.747	+	370.221i	−0.284617	+	0.492970i	0.687900	+	0.725806i	$0.258533\pi$
$752$	−94.4006	+	163.507i	−0.125533	+	0.217429i
$753$		0			0
$754$	−346.272	−	599.760i	−0.459247	−	0.795438i
$755$		0			0
$756$		0			0
$757$		−	587.791i		−	0.776474i	−0.921560	−	0.388237i	$-0.873084\pi$
$757$		−	587.791i		−	0.776474i	0.921560	−	0.388237i	$-0.126916\pi$
$758$	−125.049	−	216.591i	−0.164972	−	0.285740i
$759$		0			0
$760$		0			0
$761$	1135.73	+	655.716i	1.49242	+	0.861651i	0.999962	−	0.00868376i	$-0.00276416\pi$
$761$	1135.73	+	655.716i	1.49242	+	0.861651i	0.492461	+	0.870335i	$0.336097\pi$
$762$		0			0
$763$	−154.353	+	89.1155i	−0.202297	+	0.116796i
$764$			645.963i			0.845501i
$765$		0			0
$766$	−24.3283			−0.0317601
$767$	−47.1492	−	81.6648i	−0.0614722	−	0.106473i
$768$		0			0
$769$	−595.762	+	1031.89i	−0.774724	+	1.34186i	0.160226	+	0.987080i	$0.448778\pi$
$769$	−595.762	+	1031.89i	−0.774724	+	1.34186i	−0.934950	+	0.354780i	$0.884556\pi$
$770$		0			0
$771$		0			0
$772$	299.270	−	172.784i	0.387655	−	0.223813i
$773$	−204.848			−0.265003			−0.132502	−	0.991183i	$-0.542301\pi$
$773$	−204.848			−0.265003			−0.132502	+	0.991183i	$0.542301\pi$
$774$		0			0
$775$		0			0
$776$	115.257	−	66.5435i	0.148527	−	0.0857520i
$777$		0			0
$778$	421.965	+	243.622i	0.542372	+	0.313139i
$779$	−753.467	−	435.014i	−0.967223	−	0.558427i
$780$		0			0
$781$	−404.585	−	700.761i	−0.518034	−	0.897261i
$782$	−309.017			−0.395163
$783$		0			0
$784$	20.0680			0.0255970
$785$		0			0
$786$		0			0
$787$	−115.378	−	66.6137i	−0.146605	−	0.0846426i	0.424903	−	0.905239i	$-0.360308\pi$
$787$	−115.378	−	66.6137i	−0.146605	−	0.0846426i	−0.571508	+	0.820596i	$0.693642\pi$
$788$	71.7321	−	124.244i	0.0910306	−	0.157670i
$789$		0			0
$790$		0			0
$791$			124.747i			0.157708i
$792$		0			0
$793$		−	439.375i		−	0.554067i
$794$	−84.5018	+	48.7872i	−0.106425	+	0.0614448i
$795$		0			0
$796$	133.225	−	230.752i	0.167368	−	0.289890i
$797$	304.460	−	527.341i	0.382008	−	0.661657i	−0.609341	−	0.792908i	$-0.708566\pi$
$797$	304.460	−	527.341i	0.382008	−	0.661657i	0.991349	+	0.131251i	$0.0418993\pi$
$798$		0			0
$799$	−304.481	−	527.376i	−0.381077	−	0.660046i
$800$		0			0
$801$		0			0
$802$			251.995i			0.314208i
$803$	935.237	+	1619.88i	1.16468	+	2.01728i
$804$		0			0
$805$		0			0
$806$	−120.580	−	69.6169i	−0.149603	−	0.0863733i
$807$		0			0
$808$	−54.7584	+	31.6148i	−0.0677703	+	0.0391272i
$809$		−	164.342i		−	0.203142i	−0.994828	−	0.101571i	$-0.967613\pi$
$809$		−	164.342i		−	0.203142i	0.994828	−	0.101571i	$-0.0323869\pi$
$810$		0			0
$811$	−1026.77			−1.26606			−0.633028	−	0.774129i	$-0.718188\pi$
$811$	−1026.77			−1.26606			−0.633028	+	0.774129i	$0.718188\pi$
$812$	−331.991	−	575.025i	−0.408855	−	0.708158i
$813$		0			0
$814$	−37.8439	+	65.5476i	−0.0464913	+	0.0805253i
$815$		0			0
$816$		0			0
$817$	−1048.75	+	605.494i	−1.28365	+	0.741118i
$818$	15.9673			0.0195200
$819$		0			0
$820$		0			0
$821$	−262.140	+	151.347i	−0.319293	+	0.184344i	−0.651078	−	0.759011i	$-0.725683\pi$
$821$	−262.140	+	151.347i	−0.319293	+	0.184344i	0.331784	+	0.943355i	$0.392349\pi$
$822$		0			0
$823$	−603.723	−	348.559i	−0.733563	−	0.423523i	0.0861609	−	0.996281i	$-0.472540\pi$
$823$	−603.723	−	348.559i	−0.733563	−	0.423523i	−0.819724	+	0.572758i	$0.805873\pi$
$824$	−303.489	−	175.220i	−0.368312	−	0.212645i
$825$		0			0
$826$	−45.2046	−	78.2967i	−0.0547271	−	0.0947902i
$827$	−454.516			−0.549596			−0.274798	−	0.961502i	$-0.588611\pi$
$827$	−454.516			−0.549596			−0.274798	+	0.961502i	$0.588611\pi$
$828$		0			0
$829$	−591.488			−0.713496			−0.356748	−	0.934201i	$-0.616115\pi$
$829$	−591.488			−0.713496			−0.356748	+	0.934201i	$0.616115\pi$
$830$		0			0
$831$		0			0
$832$	−67.7750	−	39.1299i	−0.0814603	−	0.0470311i
$833$	−32.3638	+	56.0558i	−0.0388521	+	0.0672939i
$834$		0			0
$835$		0			0
$836$		−	680.796i		−	0.814349i
$837$		0			0
$838$		−	92.0359i		−	0.109828i
$839$	−1342.11	+	774.866i	−1.59965	+	0.923559i	−0.608097	+	0.793863i	$0.708067\pi$
$839$	−1342.11	+	774.866i	−1.59965	+	0.923559i	−0.991554	+	0.129696i	$0.958600\pi$
$840$		0			0
$841$	832.459	−	1441.86i	0.989844	−	1.71446i
$842$	−162.697	+	281.799i	−0.193226	+	0.334678i
$843$		0			0
$844$	376.327	+	651.818i	0.445886	+	0.772297i
$845$		0			0
$846$		0			0
$847$			2132.11i			2.51725i
$848$	2.17626	+	3.76938i	0.00256634	+	0.00444503i
$849$		0			0
$850$		0			0
$851$	−37.3175	−	21.5453i	−0.0438514	−	0.0253176i
$852$		0			0
$853$	1421.62	−	820.773i	1.66661	−	0.962219i	0.697169	−	0.716907i	$-0.254443\pi$
$853$	1421.62	−	820.773i	1.66661	−	0.962219i	0.969444	−	0.245312i	$-0.0788905\pi$
$854$		−	421.254i		−	0.493272i
$855$		0			0
$856$	−133.980			−0.156518
$857$	−159.321	−	275.953i	−0.185906	−	0.321998i	0.757976	−	0.652283i	$-0.226189\pi$
$857$	−159.321	−	275.953i	−0.185906	−	0.321998i	−0.943881	+	0.330285i	$0.892855\pi$
$858$		0			0
$859$	−314.166	+	544.152i	−0.365735	+	0.633471i	−0.988894	−	0.148624i	$-0.952516\pi$
$859$	−314.166	+	544.152i	−0.365735	+	0.633471i	0.623159	+	0.782095i	$0.285849\pi$
$860$		0			0
$861$		0			0
$862$	−82.6552	+	47.7210i	−0.0958878	+	0.0553608i
$863$	−183.620			−0.212770			−0.106385	−	0.994325i	$-0.533928\pi$
$863$	−183.620			−0.212770			−0.106385	+	0.994325i	$0.533928\pi$
$864$		0			0
$865$		0			0
$866$	161.740	−	93.3807i	0.186767	−	0.107830i
$867$		0			0
$868$	−115.607	−	66.7457i	−0.133188	−	0.0768960i
$869$	2143.20	+	1237.38i	2.46629	+	1.42391i
$870$		0			0
$871$	−16.3433	−	28.3075i	−0.0187639	−	0.0325000i
$872$	−76.0126			−0.0871705
$873$		0			0
$874$	387.590			0.443467
$875$		0			0
$876$		0			0
$877$	1251.66	+	722.647i	1.42721	+	0.823999i	0.996900	−	0.0786834i	$-0.0250716\pi$
$877$	1251.66	+	722.647i	1.42721	+	0.823999i	0.430308	+	0.902682i	$0.358405\pi$
$878$	−487.213	+	843.877i	−0.554912	+	0.961136i
$879$		0			0
$880$		0			0
$881$			608.977i			0.691234i	0.938376	+	0.345617i	$0.112330\pi$
$881$			608.977i			0.691234i	−0.938376	+	0.345617i	$0.887670\pi$
$882$		0			0
$883$			120.519i			0.136488i	0.997669	+	0.0682440i	$0.0217396\pi$
$883$			120.519i			0.136488i	−0.997669	+	0.0682440i	$0.978260\pi$
$884$	218.602	−	126.210i	0.247288	−	0.142772i
$885$		0			0
$886$	−48.1416	+	83.3837i	−0.0543359	+	0.0941126i
$887$	803.710	−	1392.07i	0.906100	−	1.56941i	0.0866653	−	0.996237i	$-0.472379\pi$
$887$	803.710	−	1392.07i	0.906100	−	1.56941i	0.819434	−	0.573173i	$-0.194288\pi$
$888$		0			0
$889$	427.165	+	739.872i	0.480501	+	0.832252i
$890$		0			0
$891$		0			0
$892$		−	118.354i		−	0.132684i
$893$	381.900	+	661.471i	0.427660	+	0.740729i
$894$		0			0
$895$		0			0
$896$	−64.9797	−	37.5161i	−0.0725220	−	0.0418706i
$897$		0			0
$898$	−839.629	+	484.760i	−0.934999	+	0.539822i
$899$		−	503.807i		−	0.560408i
$900$		0			0
$901$	−14.0386			−0.0155812
$902$	799.714	+	1385.15i	0.886601	+	1.53564i
$903$		0			0
$904$	−26.6012	+	46.0747i	−0.0294261	+	0.0509676i
$905$		0			0
$906$		0			0
$907$	561.175	−	323.994i	0.618715	−	0.357215i	−0.157653	−	0.987495i	$-0.550393\pi$
$907$	561.175	−	323.994i	0.618715	−	0.357215i	0.776369	+	0.630279i	$0.217060\pi$
$908$	299.677			0.330041
$909$		0			0
$910$		0			0
$911$	173.671	−	100.269i	0.190638	−	0.110065i	−0.401643	−	0.915796i	$-0.631561\pi$
$911$	173.671	−	100.269i	0.190638	−	0.110065i	0.592281	+	0.805731i	$0.298227\pi$
$912$		0			0
$913$	2680.17	+	1547.40i	2.93556	+	1.69485i
$914$	636.127	+	367.268i	0.695981	+	0.401825i
$915$		0			0
$916$	−170.864	−	295.945i	−0.186532	−	0.323084i
$917$	−204.341			−0.222837
$918$		0			0
$919$	619.581			0.674191			0.337095	−	0.941471i	$-0.390556\pi$
$919$	619.581			0.674191			0.337095	+	0.941471i	$0.390556\pi$
$920$		0			0
$921$		0			0
$922$	−109.655	−	63.3094i	−0.118932	−	0.0686653i
$923$	−188.151	+	325.887i	−0.203847	+	0.353074i
$924$		0			0
$925$		0			0
$926$		−	721.194i		−	0.778828i
$927$		0			0
$928$		−	283.177i		−	0.305148i
$929$	−615.591	+	355.411i	−0.662638	+	0.382574i	−0.793281	−	0.608855i	$-0.791629\pi$
$929$	−615.591	+	355.411i	−0.662638	+	0.382574i	0.130643	+	0.991429i	$0.458296\pi$
$930$		0			0
$931$	40.5929	−	70.3089i	0.0436014	−	0.0755198i
$932$	−448.983	+	777.661i	−0.481741	+	0.834401i
$933$		0			0
$934$	381.699	+	661.122i	0.408671	+	0.707839i
$935$		0			0
$936$		0			0
$937$			435.674i			0.464967i	0.972600	+	0.232483i	$0.0746851\pi$
$937$			435.674i			0.464967i	−0.972600	+	0.232483i	$0.925315\pi$
$938$	−15.6693	−	27.1400i	−0.0167050	−	0.0289339i
$939$		0			0
$940$		0			0
$941$	−109.205	−	63.0496i	−0.116052	−	0.0670027i	0.440850	−	0.897581i	$-0.354677\pi$
$941$	−109.205	−	63.0496i	−0.116052	−	0.0670027i	−0.556902	+	0.830578i	$0.688010\pi$
$942$		0			0
$943$	−788.590	+	455.293i	−0.836257	+	0.482813i
$944$		−	38.5581i		−	0.0408454i
$945$		0			0
$946$	2226.23			2.35331
$947$	283.686	+	491.359i	0.299563	+	0.518858i	0.976036	−	0.217609i	$-0.0698258\pi$
$947$	283.686	+	491.359i	0.299563	+	0.518858i	−0.676473	+	0.736467i	$0.736493\pi$
$948$		0			0
$949$	434.930	−	753.320i	0.458303	−	0.793804i
$950$		0			0
$951$		0			0
$952$	209.587	−	121.005i	0.220154	−	0.127106i
$953$	−873.128			−0.916189			−0.458095	−	0.888903i	$-0.651468\pi$
$953$	−873.128			−0.916189			−0.458095	+	0.888903i	$0.651468\pi$
$954$		0			0
$955$		0			0
$956$	401.690	−	231.916i	0.420178	−	0.242590i
$957$		0			0
$958$	133.256	+	76.9353i	0.139098	+	0.0803082i
$959$	−611.934	−	353.300i	−0.638095	−	0.368405i
$960$		0			0
$961$	429.856	+	744.532i	0.447300	+	0.774747i
$962$	35.1985			0.0365888
$963$		0			0
$964$	−794.682			−0.824359
$965$		0			0
$966$		0			0
$967$	728.109	+	420.374i	0.752957	+	0.434720i	0.826761	−	0.562553i	$-0.190181\pi$
$967$	728.109	+	420.374i	0.752957	+	0.434720i	−0.0738046	+	0.997273i	$0.523514\pi$
$968$	−454.655	+	787.486i	−0.469685	+	0.813518i
$969$		0			0
$970$		0			0
$971$		−	258.099i		−	0.265807i	−0.991129	−	0.132903i	$-0.957570\pi$
$971$		−	258.099i		−	0.265807i	0.991129	−	0.132903i	$-0.0424300\pi$
$972$		0			0
$973$			757.613i			0.778636i
$974$	−419.504	+	242.201i	−0.430703	+	0.248666i
$975$		0			0
$976$	89.8290	−	155.588i	0.0920379	−	0.159414i
$977$	−575.995	+	997.653i	−0.589555	+	1.02114i	0.404736	+	0.914434i	$0.367364\pi$
$977$	−575.995	+	997.653i	−0.589555	+	1.02114i	−0.994291	+	0.106706i	$0.965970\pi$
$978$		0			0
$979$	−1528.55	−	2647.52i	−1.56134	−	2.70431i
$980$		0			0
$981$		0			0
$982$		−	703.260i		−	0.716151i
$983$	−319.689	−	553.718i	−0.325218	−	0.563294i	0.656338	−	0.754467i	$-0.272104\pi$
$983$	−319.689	−	553.718i	−0.325218	−	0.563294i	−0.981556	+	0.191172i	$0.938771\pi$
$984$		0			0
$985$		0			0
$986$	790.996	+	456.682i	0.802228	+	0.463166i
$987$		0			0
$988$	−274.186	+	158.301i	−0.277516	+	0.160224i
$989$			1267.44i			1.28153i
$990$		0			0
$991$	1875.09			1.89212			0.946060	−	0.323992i	$-0.105025\pi$
$991$	1875.09			1.89212			0.946060	+	0.323992i	$0.105025\pi$
$992$	−28.4660	−	49.3045i	−0.0286955	−	0.0497021i
$993$		0			0
$994$	−180.391	+	312.447i	−0.181480	+	0.314333i
$995$		0			0
$996$		0			0
$997$	−818.736	+	472.697i	−0.821199	+	0.474120i	−0.850830	−	0.525441i	$-0.823900\pi$
$997$	−818.736	+	472.697i	−0.821199	+	0.474120i	0.0296306	+	0.999561i	$0.490567\pi$
$998$	219.249			0.219689
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.3.k.b.449.14		32
3.2	odd	2		450.3.k.c.149.3		32
5.2	odd	4		1350.3.i.g.1151.2		16
5.3	odd	4		270.3.h.a.71.6		16
5.4	even	2	inner	1350.3.k.b.449.3		32
9.2	odd	6	inner	1350.3.k.b.899.3		32
9.7	even	3		450.3.k.c.299.14		32
15.2	even	4		450.3.i.g.401.6		16
15.8	even	4		90.3.h.a.41.3	yes	16
15.14	odd	2		450.3.k.c.149.14		32
20.3	even	4		2160.3.bs.d.881.1		16
45.2	even	12		1350.3.i.g.251.2		16
45.7	odd	12		450.3.i.g.101.6		16
45.13	odd	12		810.3.d.c.161.13		16
45.23	even	12		810.3.d.c.161.1		16
45.29	odd	6	inner	1350.3.k.b.899.14		32
45.34	even	6		450.3.k.c.299.3		32
45.38	even	12		270.3.h.a.251.6		16
45.43	odd	12		90.3.h.a.11.3	✓	16
60.23	odd	4		720.3.bs.d.401.5		16
180.43	even	12		720.3.bs.d.641.5		16
180.83	odd	12		2160.3.bs.d.1601.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.h.a.11.3	✓	16	45.43	odd	12
90.3.h.a.41.3	yes	16	15.8	even	4
270.3.h.a.71.6		16	5.3	odd	4
270.3.h.a.251.6		16	45.38	even	12
450.3.i.g.101.6		16	45.7	odd	12
450.3.i.g.401.6		16	15.2	even	4
450.3.k.c.149.3		32	3.2	odd	2
450.3.k.c.149.14		32	15.14	odd	2
450.3.k.c.299.3		32	45.34	even	6
450.3.k.c.299.14		32	9.7	even	3
720.3.bs.d.401.5		16	60.23	odd	4
720.3.bs.d.641.5		16	180.43	even	12
810.3.d.c.161.1		16	45.23	even	12
810.3.d.c.161.13		16	45.13	odd	12
1350.3.i.g.251.2		16	45.2	even	12
1350.3.i.g.1151.2		16	5.2	odd	4
1350.3.k.b.449.3		32	5.4	even	2	inner
1350.3.k.b.449.14		32	1.1	even	1	trivial
1350.3.k.b.899.3		32	9.2	odd	6	inner
1350.3.k.b.899.14		32	45.29	odd	6	inner
2160.3.bs.d.881.1		16	20.3	even	4
2160.3.bs.d.1601.1		16	180.83	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1350.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-5.74345 + 3.31598i) q^{7} -2.82843 q^{8} +(18.2172 - 10.5177i) q^{11} +(-8.47187 - 4.89124i) q^{13} +(-8.12247 - 4.68951i) q^{14} +(-2.00000 - 3.46410i) q^{16} +12.9017 q^{17} -16.1821 q^{19} +(25.7630 + 14.8743i) q^{22} +(-8.46823 + 14.6674i) q^{23} -13.8345i q^{26} -13.2639i q^{28} +(43.3525 - 25.0296i) q^{29} +(5.03212 - 8.71588i) q^{31} +(2.82843 - 4.89898i) q^{32} +(9.12285 + 15.8012i) q^{34} +2.54425i q^{37} +(-11.4425 - 19.8190i) q^{38} +(46.5617 + 26.8824i) q^{41} +(64.8089 - 37.4175i) q^{43} +42.0709i q^{44} -23.9518 q^{46} +(-23.6001 - 40.8766i) q^{47} +(-2.50850 + 4.34485i) q^{49} +(16.9437 - 9.78248i) q^{52} -1.08813 q^{53} +(16.2449 - 9.37902i) q^{56} +(61.3097 + 35.3972i) q^{58} +(8.34807 + 4.81976i) q^{59} +(22.4573 + 38.8971i) q^{61} +14.2330 q^{62} +8.00000 q^{64} +(2.89369 + 1.67067i) q^{67} +(-12.9017 + 22.3463i) q^{68} -38.4670i q^{71} +88.9201i q^{73} +(-3.11606 + 1.79906i) q^{74} +(16.1821 - 28.0283i) q^{76} +(-69.7532 + 120.816i) q^{77} +(58.8235 + 101.885i) q^{79} +76.0349i q^{82} +(73.5614 + 127.412i) q^{83} +(91.6537 + 52.9163i) q^{86} +(-51.5261 + 29.7486i) q^{88} -145.331i q^{89} +64.8771 q^{91} +(-16.9365 - 29.3348i) q^{92} +(33.3756 - 57.8083i) q^{94} +(-40.7494 + 23.5267i) q^{97} -7.09511 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 72 q^{14} - 64 q^{16} - 160 q^{19} - 144 q^{29} - 32 q^{31} + 96 q^{34} - 216 q^{41} + 48 q^{46} + 168 q^{49} + 144 q^{56} + 288 q^{59} - 152 q^{61} + 256 q^{64} - 576 q^{74} + 160 q^{76}+ \cdots + 168 q^{94}+O(q^{100}) \) 32 * q - 32 * q^4 - 72 * q^14 - 64 * q^16 - 160 * q^19 - 144 * q^29 - 32 * q^31 + 96 * q^34 - 216 * q^41 + 48 * q^46 + 168 * q^49 + 144 * q^56 + 288 * q^59 - 152 * q^61 + 256 * q^64 - 576 * q^74 + 160 * q^76 - 160 * q^79 + 432 * q^86 - 1312 * q^91 + 168 * q^94

Introduction

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