LMFDB - Embedded newform 900.3.u.d.149.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(149,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("900.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.u (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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.15
Character	$\chi$	$=$	900.149
Dual form			900.3.u.d.749.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.70777 - 1.29149i) q^{3} +(-3.00081 + 1.73252i) q^{7} +(5.66408 - 6.99415i) q^{9} +O(q^{10})$	\(q+(2.70777 - 1.29149i) q^{3} +(-3.00081 + 1.73252i) q^{7} +(5.66408 - 6.99415i) q^{9} +(-12.3770 + 7.14587i) q^{11} +(-5.28062 - 3.04877i) q^{13} -11.7361 q^{17} -23.4795 q^{19} +(-5.88797 + 8.56679i) q^{21} +(-14.3544 + 24.8625i) q^{23} +(6.30414 - 26.2537i) q^{27} +(13.3136 - 7.68660i) q^{29} +(-18.4920 + 32.0291i) q^{31} +(-24.2853 + 35.3342i) q^{33} -46.7299i q^{37} +(-18.2362 - 1.43548i) q^{39} +(-17.1469 - 9.89974i) q^{41} +(-4.76655 + 2.75197i) q^{43} +(5.15814 + 8.93416i) q^{47} +(-18.4968 + 32.0374i) q^{49} +(-31.7788 + 15.1571i) q^{51} +41.5607 q^{53} +(-63.5772 + 30.3237i) q^{57} +(-58.5202 - 33.7866i) q^{59} +(-26.5253 - 45.9431i) q^{61} +(-4.87932 + 30.8012i) q^{63} +(27.5426 + 15.9017i) q^{67} +(-6.75860 + 85.8606i) q^{69} -2.28568i q^{71} +86.2854i q^{73} +(24.7607 - 42.8867i) q^{77} +(-58.4264 - 101.198i) q^{79} +(-16.8364 - 79.2309i) q^{81} +(65.2494 + 113.015i) q^{83} +(26.1230 - 38.0080i) q^{87} -75.3347i q^{89} +21.1282 q^{91} +(-8.70677 + 110.610i) q^{93} +(24.4829 - 14.1352i) q^{97} +(-20.1251 + 127.041i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 28 q^{9}+O(q^{10}) $ 32 * q - 28 * q^9	$ 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) $ 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	2.70777	−	1.29149i	0.902591	−	0.430498i
$3$	2.70777	−	1.29149i	0.902591	−	0.430498i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.00081	+	1.73252i	−0.428686	+	0.247502i	−0.698787	−	0.715330i	$-0.746276\pi$
$7$	−3.00081	+	1.73252i	−0.428686	+	0.247502i	0.270100	+	0.962832i	$0.412943\pi$
$8$		0			0
$9$	5.66408	−	6.99415i	0.629342	−	0.777128i
$10$		0			0
$11$	−12.3770	+	7.14587i	−1.12518	+	0.649624i	−0.942719	−	0.333588i	$-0.891741\pi$
$11$	−12.3770	+	7.14587i	−1.12518	+	0.649624i	−0.182464	+	0.983213i	$0.558407\pi$
$12$		0			0
$13$	−5.28062	−	3.04877i	−0.406202	−	0.234521i	0.282955	−	0.959133i	$-0.408685\pi$
$13$	−5.28062	−	3.04877i	−0.406202	−	0.234521i	−0.689156	+	0.724613i	$0.742019\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−11.7361			−0.690360			−0.345180	−	0.938536i	$-0.612182\pi$
$17$	−11.7361			−0.690360			−0.345180	+	0.938536i	$0.612182\pi$
$18$		0			0
$19$	−23.4795			−1.23576			−0.617882	−	0.786271i	$-0.712009\pi$
$19$	−23.4795			−1.23576			−0.617882	+	0.786271i	$0.712009\pi$
$20$		0			0
$21$	−5.88797	+	8.56679i	−0.280379	+	0.407942i
$22$		0			0
$23$	−14.3544	+	24.8625i	−0.624103	+	1.08098i	0.364611	+	0.931160i	$0.381202\pi$
$23$	−14.3544	+	24.8625i	−0.624103	+	1.08098i	−0.988714	+	0.149818i	$0.952131\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	6.30414	−	26.2537i	0.233487	−	0.972360i
$28$		0			0
$29$	13.3136	−	7.68660i	0.459089	−	0.265055i	−0.252572	−	0.967578i	$-0.581277\pi$
$29$	13.3136	−	7.68660i	0.459089	−	0.265055i	0.711661	+	0.702523i	$0.247943\pi$
$30$		0			0
$31$	−18.4920	+	32.0291i	−0.596517	+	1.03320i	0.396814	+	0.917899i	$0.370116\pi$
$31$	−18.4920	+	32.0291i	−0.596517	+	1.03320i	−0.993331	+	0.115298i	$0.963218\pi$
$32$		0			0
$33$	−24.2853	+	35.3342i	−0.735918	+	1.07073i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	46.7299i		−	1.26297i	−0.775388	−	0.631485i	$-0.782446\pi$
$37$		−	46.7299i		−	1.26297i	0.775388	−	0.631485i	$-0.217554\pi$
$38$		0			0
$39$	−18.2362	−	1.43548i	−0.467595	−	0.0368072i
$40$		0			0
$41$	−17.1469	−	9.89974i	−0.418216	−	0.241457i	0.276098	−	0.961130i	$-0.410959\pi$
$41$	−17.1469	−	9.89974i	−0.418216	−	0.241457i	−0.694314	+	0.719672i	$0.744292\pi$
$42$		0			0
$43$	−4.76655	+	2.75197i	−0.110850	+	0.0639992i	−0.554400	−	0.832250i	$-0.687052\pi$
$43$	−4.76655	+	2.75197i	−0.110850	+	0.0639992i	0.443550	+	0.896250i	$0.353719\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.15814	+	8.93416i	0.109748	+	0.190089i	0.915668	−	0.401935i	$-0.131662\pi$
$47$	5.15814	+	8.93416i	0.109748	+	0.190089i	−0.805920	+	0.592024i	$0.798329\pi$
$48$		0			0
$49$	−18.4968	+	32.0374i	−0.377485	+	0.653824i
$50$		0			0
$51$	−31.7788	+	15.1571i	−0.623113	+	0.297199i
$52$		0			0
$53$	41.5607			0.784164			0.392082	−	0.919930i	$-0.371755\pi$
$53$	41.5607			0.784164			0.392082	+	0.919930i	$0.371755\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−63.5772	+	30.3237i	−1.11539	+	0.531994i
$58$		0			0
$59$	−58.5202	−	33.7866i	−0.991867	−	0.572655i	−0.0860352	−	0.996292i	$-0.527420\pi$
$59$	−58.5202	−	33.7866i	−0.991867	−	0.572655i	−0.905832	+	0.423637i	$0.860753\pi$
$60$		0			0
$61$	−26.5253	−	45.9431i	−0.434841	−	0.753166i	0.562442	−	0.826837i	$-0.309862\pi$
$61$	−26.5253	−	45.9431i	−0.434841	−	0.753166i	−0.997283	+	0.0736707i	$0.976529\pi$
$62$		0			0
$63$	−4.87932	+	30.8012i	−0.0774496	+	0.488908i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	27.5426	+	15.9017i	0.411084	+	0.237339i	0.691255	−	0.722611i	$-0.257058\pi$
$67$	27.5426	+	15.9017i	0.411084	+	0.237339i	−0.280172	+	0.959950i	$0.590391\pi$
$68$		0			0
$69$	−6.75860	+	85.8606i	−0.0979507	+	1.24436i
$70$		0			0
$71$		−	2.28568i		−	0.0321927i	−0.999870	−	0.0160964i	$-0.994876\pi$
$71$		−	2.28568i		−	0.0321927i	0.999870	−	0.0160964i	$-0.00512385\pi$
$72$		0			0
$73$			86.2854i			1.18199i	0.806675	+	0.590996i	$0.201265\pi$
$73$			86.2854i			1.18199i	−0.806675	+	0.590996i	$0.798735\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	24.7607	−	42.8867i	0.321567	−	0.556970i
$78$		0			0
$79$	−58.4264	−	101.198i	−0.739575	−	1.28098i	−0.952687	−	0.303953i	$-0.901693\pi$
$79$	−58.4264	−	101.198i	−0.739575	−	1.28098i	0.213112	−	0.977028i	$-0.431640\pi$
$80$		0			0
$81$	−16.8364	−	79.2309i	−0.207856	−	0.978159i
$82$		0			0
$83$	65.2494	+	113.015i	0.786137	+	1.36163i	0.928317	+	0.371789i	$0.121256\pi$
$83$	65.2494	+	113.015i	0.786137	+	1.36163i	−0.142180	+	0.989841i	$0.545411\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	26.1230	−	38.0080i	0.300264	−	0.436873i
$88$		0			0
$89$		−	75.3347i		−	0.846457i	−0.906023	−	0.423229i	$-0.860897\pi$
$89$		−	75.3347i		−	0.846457i	0.906023	−	0.423229i	$-0.139103\pi$
$90$		0			0
$91$	21.1282			0.232178
$92$		0			0
$93$	−8.70677	+	110.610i	−0.0936212	+	1.18935i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	24.4829	−	14.1352i	0.252401	−	0.145724i	−0.368462	−	0.929643i	$-0.620116\pi$
$97$	24.4829	−	14.1352i	0.252401	−	0.145724i	0.620863	+	0.783919i	$0.286782\pi$
$98$		0			0
$99$	−20.1251	+	127.041i	−0.203284	+	1.28325i
$100$		0			0
$101$	−110.083	+	63.5564i	−1.08993	+	0.629272i	−0.933558	−	0.358426i	$-0.883313\pi$
$101$	−110.083	+	63.5564i	−1.08993	+	0.629272i	−0.156373	+	0.987698i	$0.549980\pi$
$102$		0			0
$103$	43.5261	+	25.1298i	0.422583	+	0.243978i	0.696182	−	0.717865i	$-0.254881\pi$
$103$	43.5261	+	25.1298i	0.422583	+	0.243978i	−0.273599	+	0.961844i	$0.588214\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	151.704			1.41779			0.708897	−	0.705312i	$-0.249193\pi$
$107$	151.704			1.41779			0.708897	+	0.705312i	$0.249193\pi$
$108$		0			0
$109$	−131.449			−1.20595			−0.602976	−	0.797759i	$-0.706018\pi$
$109$	−131.449			−1.20595			−0.602976	+	0.797759i	$0.706018\pi$
$110$		0			0
$111$	−60.3515	−	126.534i	−0.543707	−	1.13995i
$112$		0			0
$113$	−45.7257	+	79.1993i	−0.404652	+	0.700878i	−0.994281	−	0.106796i	$-0.965941\pi$
$113$	−45.7257	+	79.1993i	−0.404652	+	0.700878i	0.589629	+	0.807674i	$0.299274\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−51.2335	+	19.6650i	−0.437893	+	0.168077i
$118$		0			0
$119$	35.2178	−	20.3330i	0.295948	−	0.170866i
$120$		0			0
$121$	41.6269	−	72.0999i	0.344024	−	0.595867i
$122$		0			0
$123$	−59.2153	−	4.66119i	−0.481425	−	0.0378958i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	152.636i		−	1.20186i	−0.799301	−	0.600931i	$-0.794797\pi$
$127$		−	152.636i		−	1.20186i	0.799301	−	0.600931i	$-0.205203\pi$
$128$		0			0
$129$	−9.35258	+	13.6077i	−0.0725006	+	0.105486i
$130$		0			0
$131$	69.2312	+	39.9706i	0.528482	+	0.305119i	0.740398	−	0.672169i	$-0.234637\pi$
$131$	69.2312	+	39.9706i	0.528482	+	0.305119i	−0.211916	+	0.977288i	$0.567970\pi$
$132$		0			0
$133$	70.4574	−	40.6786i	0.529755	−	0.305854i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	54.9029	+	95.0945i	0.400751	+	0.694121i	0.993817	−	0.111033i	$-0.0354160\pi$
$137$	54.9029	+	95.0945i	0.400751	+	0.694121i	−0.593066	+	0.805154i	$0.702083\pi$
$138$		0			0
$139$	−96.4057	+	166.980i	−0.693566	+	1.20129i	0.277096	+	0.960842i	$0.410628\pi$
$139$	−96.4057	+	166.980i	−0.693566	+	1.20129i	−0.970662	+	0.240449i	$0.922705\pi$
$140$		0			0
$141$	25.5055	+	17.5300i	0.180890	+	0.124326i
$142$		0			0
$143$	87.1444			0.609402
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−8.70901	+	110.638i	−0.0592450	+	0.752642i
$148$		0			0
$149$	153.314	+	88.5160i	1.02895	+	0.594067i	0.916685	−	0.399610i	$-0.130855\pi$
$149$	153.314	+	88.5160i	1.02895	+	0.594067i	0.112270	+	0.993678i	$0.464188\pi$
$150$		0			0
$151$	61.7618	+	106.975i	0.409018	+	0.708441i	0.994780	−	0.102043i	$-0.0325379\pi$
$151$	61.7618	+	106.975i	0.409018	+	0.708441i	−0.585762	+	0.810483i	$0.699205\pi$
$152$		0			0
$153$	−66.4744	+	82.0843i	−0.434473	+	0.536499i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−204.764	−	118.221i	−1.30423	−	0.752997i	−0.323103	−	0.946364i	$-0.604726\pi$
$157$	−204.764	−	118.221i	−1.30423	−	0.752997i	−0.981127	+	0.193366i	$0.938059\pi$
$158$		0			0
$159$	112.537	−	53.6754i	0.707779	−	0.337581i
$160$		0			0
$161$		−	99.4766i		−	0.617867i
$162$		0			0
$163$		−	286.295i		−	1.75641i	−0.478284	−	0.878205i	$-0.658741\pi$
$163$		−	286.295i		−	1.75641i	0.478284	−	0.878205i	$-0.341259\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−17.9445	+	31.0808i	−0.107452	+	0.186113i	−0.914737	−	0.404049i	$-0.867603\pi$
$167$	−17.9445	+	31.0808i	−0.107452	+	0.186113i	0.807285	+	0.590161i	$0.200936\pi$
$168$		0			0
$169$	−65.9100	−	114.159i	−0.390000	−	0.675500i
$170$		0			0
$171$	−132.990	+	164.219i	−0.777719	+	0.960347i
$172$		0			0
$173$	49.1670	+	85.1597i	0.284202	+	0.492253i	0.972415	−	0.233256i	$-0.0749379\pi$
$173$	49.1670	+	85.1597i	0.284202	+	0.492253i	−0.688213	+	0.725509i	$0.741605\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−202.095	−	15.9081i	−1.14178	−	0.0898761i
$178$		0			0
$179$		−	312.477i		−	1.74568i	−0.488004	−	0.872841i	$-0.662275\pi$
$179$		−	312.477i		−	1.74568i	0.488004	−	0.872841i	$-0.337725\pi$
$180$		0			0
$181$	14.5133			0.0801838			0.0400919	−	0.999196i	$-0.487235\pi$
$181$	14.5133			0.0801838			0.0400919	+	0.999196i	$0.487235\pi$
$182$		0			0
$183$	−131.160	−	90.1463i	−0.716720	−	0.492603i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	145.258	−	83.8648i	0.776782	−	0.448475i
$188$		0			0
$189$	26.5675	+	89.7043i	0.140569	+	0.474626i
$190$		0			0
$191$	−224.881	+	129.835i	−1.17739	+	0.679766i	−0.955409	−	0.295285i	$-0.904585\pi$
$191$	−224.881	+	129.835i	−1.17739	+	0.679766i	−0.221980	+	0.975051i	$0.571252\pi$
$192$		0			0
$193$	−205.486	−	118.638i	−1.06470	−	0.614703i	−0.137969	−	0.990437i	$-0.544057\pi$
$193$	−205.486	−	118.638i	−1.06470	−	0.614703i	−0.926728	+	0.375734i	$0.877391\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−152.304			−0.773117			−0.386558	−	0.922265i	$-0.626336\pi$
$197$	−152.304			−0.773117			−0.386558	+	0.922265i	$0.626336\pi$
$198$		0			0
$199$	−382.914			−1.92419			−0.962096	−	0.272711i	$-0.912080\pi$
$199$	−382.914			−1.92419			−0.962096	+	0.272711i	$0.912080\pi$
$200$		0			0
$201$	95.1162	+	7.48716i	0.473215	+	0.0372495i
$202$		0			0
$203$	−26.6343	+	46.1320i	−0.131203	+	0.227251i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	92.5878	+	241.220i	0.447284	+	1.16531i
$208$		0			0
$209$	290.606	−	167.782i	1.39046	−	0.802782i
$210$		0			0
$211$	31.8015	−	55.0818i	0.150718	−	0.261051i	−0.780774	−	0.624814i	$-0.785175\pi$
$211$	31.8015	−	55.0818i	0.150718	−	0.261051i	0.931492	+	0.363763i	$0.118508\pi$
$212$		0			0
$213$	−2.95195	−	6.18912i	−0.0138589	−	0.0290569i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	128.151i		−	0.590557i
$218$		0			0
$219$	111.437	+	233.641i	0.508846	+	1.06686i
$220$		0			0
$221$	61.9741	+	35.7807i	0.280426	+	0.161904i
$222$		0			0
$223$	−1.39692	+	0.806511i	−0.00626421	+	0.00361664i	−0.503129	−	0.864211i	$-0.667818\pi$
$223$	−1.39692	+	0.806511i	−0.00626421	+	0.00361664i	0.496865	+	0.867828i	$0.334485\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	194.272	+	336.488i	0.855822	+	1.48233i	0.875880	+	0.482529i	$0.160282\pi$
$227$	194.272	+	336.488i	0.855822	+	1.48233i	−0.0200581	+	0.999799i	$0.506385\pi$
$228$		0			0
$229$	136.247	−	235.987i	0.594965	−	1.03051i	−0.398586	−	0.917131i	$-0.630499\pi$
$229$	136.247	−	235.987i	0.594965	−	1.03051i	0.993552	−	0.113380i	$-0.0361676\pi$
$230$		0			0
$231$	11.6583	−	148.106i	0.0504688	−	0.641151i
$232$		0			0
$233$	264.865			1.13676			0.568380	−	0.822766i	$-0.307570\pi$
$233$	264.865			1.13676			0.568380	+	0.822766i	$0.307570\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−288.902	−	198.563i	−1.21899	−	0.837817i
$238$		0			0
$239$	155.390	+	89.7143i	0.650166	+	0.375374i	0.788520	−	0.615009i	$-0.210848\pi$
$239$	155.390	+	89.7143i	0.650166	+	0.375374i	−0.138354	+	0.990383i	$0.544181\pi$
$240$		0			0
$241$	141.807	+	245.617i	0.588412	+	1.01916i	0.994441	+	0.105299i	$0.0335800\pi$
$241$	141.807	+	245.617i	0.588412	+	1.01916i	−0.406029	+	0.913860i	$0.633087\pi$
$242$		0			0
$243$	−147.915	−	192.795i	−0.608705	−	0.793396i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	123.986	+	71.5836i	0.501970	+	0.289812i
$248$		0			0
$249$	322.639	+	221.751i	1.29574	+	0.890565i
$250$		0			0
$251$			429.903i			1.71276i	0.516345	+	0.856381i	$0.327292\pi$
$251$			429.903i			1.71276i	−0.516345	+	0.856381i	$0.672708\pi$
$252$		0			0
$253$		−	410.298i		−	1.62173i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	95.1538	−	164.811i	0.370248	−	0.641289i	−0.619355	−	0.785111i	$-0.712606\pi$
$257$	95.1538	−	164.811i	0.370248	−	0.641289i	0.989604	+	0.143822i	$0.0459393\pi$
$258$		0			0
$259$	80.9603	+	140.227i	0.312588	+	0.541418i
$260$		0			0
$261$	21.6479	−	136.655i	0.0829423	−	0.523581i
$262$		0			0
$263$	−199.902	−	346.240i	−0.760083	−	1.31650i	−0.942807	−	0.333338i	$-0.891825\pi$
$263$	−199.902	−	346.240i	−0.760083	−	1.31650i	0.182725	−	0.983164i	$-0.441508\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−97.2944	−	203.989i	−0.364399	−	0.764005i
$268$		0			0
$269$		−	488.409i		−	1.81565i	−0.419353	−	0.907823i	$-0.637743\pi$
$269$		−	488.409i		−	1.81565i	0.419353	−	0.907823i	$-0.362257\pi$
$270$		0			0
$271$	302.576			1.11652			0.558258	−	0.829667i	$-0.311470\pi$
$271$	302.576			1.11652			0.558258	+	0.829667i	$0.311470\pi$
$272$		0			0
$273$	57.2103	−	27.2869i	0.209562	−	0.0999521i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	22.0638	−	12.7386i	0.0796528	−	0.0459876i	−0.459645	−	0.888103i	$-0.652023\pi$
$277$	22.0638	−	12.7386i	0.0796528	−	0.0459876i	0.539297	+	0.842115i	$0.318690\pi$
$278$		0			0
$279$	119.276	+	310.752i	0.427514	+	1.11381i
$280$		0			0
$281$	284.675	−	164.357i	1.01308	−	0.584901i	0.100986	−	0.994888i	$-0.467800\pi$
$281$	284.675	−	164.357i	1.01308	−	0.584901i	0.912091	+	0.409987i	$0.134467\pi$
$282$		0			0
$283$	70.8265	+	40.8917i	0.250270	+	0.144494i	0.619888	−	0.784690i	$-0.287178\pi$
$283$	70.8265	+	40.8917i	0.250270	+	0.144494i	−0.369618	+	0.929184i	$0.620511\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	68.6058			0.239045
$288$		0			0
$289$	−151.263			−0.523403
$290$		0			0
$291$	48.0386	−	69.8945i	0.165081	−	0.240187i
$292$		0			0
$293$	236.472	−	409.582i	0.807072	−	1.39789i	−0.107811	−	0.994171i	$-0.534384\pi$
$293$	236.472	−	409.582i	0.807072	−	1.39789i	0.914883	−	0.403719i	$-0.132283\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	109.579	+	369.991i	0.368954	+	1.24576i
$298$		0			0
$299$	151.600	−	87.5263i	0.507023	−	0.292730i
$300$		0			0
$301$	9.53565	−	16.5162i	0.0316799	−	0.0548712i
$302$		0			0
$303$	−215.997	+	314.268i	−0.712862	+	1.03719i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			447.529i			1.45775i	0.684647	+	0.728875i	$0.259957\pi$
$307$			447.529i			1.45775i	−0.684647	+	0.728875i	$0.740043\pi$
$308$		0			0
$309$	150.314	+	11.8321i	0.486452	+	0.0382915i
$310$		0			0
$311$	78.3670	+	45.2452i	0.251984	+	0.145483i	0.620672	−	0.784070i	$-0.286860\pi$
$311$	78.3670	+	45.2452i	0.251984	+	0.145483i	−0.368688	+	0.929553i	$0.620193\pi$
$312$		0			0
$313$	311.354	−	179.760i	0.994742	−	0.574314i	0.0880535	−	0.996116i	$-0.471935\pi$
$313$	311.354	−	179.760i	0.994742	−	0.574314i	0.906688	+	0.421801i	$0.138602\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	209.399	+	362.689i	0.660563	+	1.14413i	0.980468	+	0.196679i	$0.0630158\pi$
$317$	209.399	+	362.689i	0.660563	+	1.14413i	−0.319905	+	0.947450i	$0.603651\pi$
$318$		0			0
$319$	−109.855	+	190.274i	−0.344373	+	0.596471i
$320$		0			0
$321$	410.780	−	195.925i	1.27969	−	0.610358i
$322$		0			0
$323$	275.559			0.853122
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−355.933	+	169.765i	−1.08848	+	0.519160i
$328$		0			0
$329$	−30.9572	−	17.8731i	−0.0940947	−	0.0543256i
$330$		0			0
$331$	−135.615	−	234.891i	−0.409712	−	0.709641i	0.585146	−	0.810928i	$-0.301037\pi$
$331$	−135.615	−	234.891i	−0.409712	−	0.709641i	−0.994857	+	0.101287i	$0.967704\pi$
$332$		0			0
$333$	−326.836	−	264.682i	−0.981490	−	0.794841i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−246.800	−	142.490i	−0.732345	−	0.422819i	0.0869346	−	0.996214i	$-0.472293\pi$
$337$	−246.800	−	142.490i	−0.732345	−	0.422819i	−0.819279	+	0.573395i	$0.805626\pi$
$338$		0			0
$339$	−21.5295	+	273.508i	−0.0635087	+	0.806809i
$340$		0			0
$341$		−	528.566i		−	1.55005i
$342$		0			0
$343$		−	297.970i		−	0.868718i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	25.2479	−	43.7306i	0.0727604	−	0.126025i	−0.827350	−	0.561687i	$-0.810152\pi$
$347$	25.2479	−	43.7306i	0.0727604	−	0.126025i	0.900110	+	0.435662i	$0.143486\pi$
$348$		0			0
$349$	−122.113	−	211.507i	−0.349895	−	0.606036i	0.636335	−	0.771413i	$-0.280449\pi$
$349$	−122.113	−	211.507i	−0.349895	−	0.606036i	−0.986231	+	0.165376i	$0.947116\pi$
$350$		0			0
$351$	−113.331	+	119.416i	−0.322881	+	0.340217i
$352$		0			0
$353$	219.922	+	380.917i	0.623009	+	1.07908i	0.988922	+	0.148435i	$0.0474234\pi$
$353$	219.922	+	380.917i	0.623009	+	1.07908i	−0.365913	+	0.930649i	$0.619243\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	69.1019	−	100.541i	0.193563	−	0.281627i
$358$		0			0
$359$			33.2266i			0.0925532i	0.998929	+	0.0462766i	$0.0147356\pi$
$359$			33.2266i			0.0925532i	−0.998929	+	0.0462766i	$0.985264\pi$
$360$		0			0
$361$	190.288			0.527112
$362$		0			0
$363$	19.5996	−	248.991i	0.0539933	−	0.685926i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	439.356	−	253.662i	1.19715	−	0.691178i	0.237235	−	0.971452i	$-0.423759\pi$
$367$	439.356	−	253.662i	1.19715	−	0.691178i	0.959920	+	0.280275i	$0.0904255\pi$
$368$		0			0
$369$	−166.362	+	63.8548i	−0.450844	+	0.173048i
$370$		0			0
$371$	−124.715	+	72.0045i	−0.336160	+	0.194082i
$372$		0			0
$373$	−229.322	−	132.399i	−0.614804	−	0.354957i	0.160039	−	0.987111i	$-0.448838\pi$
$373$	−229.322	−	132.399i	−0.614804	−	0.354957i	−0.774843	+	0.632153i	$0.782171\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−93.7387			−0.248644
$378$		0			0
$379$	88.5410			0.233617			0.116809	−	0.993154i	$-0.462734\pi$
$379$	88.5410			0.233617			0.116809	+	0.993154i	$0.462734\pi$
$380$		0			0
$381$	−197.129	−	413.305i	−0.517399	−	1.08479i
$382$		0			0
$383$	−279.465	+	484.048i	−0.729674	+	1.26383i	0.227347	+	0.973814i	$0.426995\pi$
$383$	−279.465	+	484.048i	−0.729674	+	1.26383i	−0.957021	+	0.290018i	$0.906339\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−7.75043	+	48.9253i	−0.0200269	+	0.126422i
$388$		0			0
$389$	97.7241	−	56.4211i	0.251219	−	0.145041i	−0.369103	−	0.929388i	$-0.620335\pi$
$389$	97.7241	−	56.4211i	0.251219	−	0.145041i	0.620322	+	0.784347i	$0.287002\pi$
$390$		0			0
$391$	168.465	−	291.789i	0.430856	−	0.746264i
$392$		0			0
$393$	239.084	+	18.8197i	0.608357	+	0.0478874i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	687.758i		−	1.73239i	−0.499707	−	0.866195i	$-0.666559\pi$
$397$		−	687.758i		−	1.73239i	0.499707	−	0.866195i	$-0.333441\pi$
$398$		0			0
$399$	138.247	−	201.144i	0.346483	−	0.504120i
$400$		0			0
$401$	155.762	+	89.9295i	0.388435	+	0.224263i	0.681482	−	0.731835i	$-0.261336\pi$
$401$	155.762	+	89.9295i	0.388435	+	0.224263i	−0.293047	+	0.956098i	$0.594669\pi$
$402$		0			0
$403$	195.299	−	112.756i	0.484613	−	0.279791i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	333.926	+	578.377i	0.820457	+	1.42107i
$408$		0			0
$409$	−112.950	+	195.635i	−0.276162	+	0.478326i	−0.970428	−	0.241393i	$-0.922396\pi$
$409$	−112.950	+	195.635i	−0.276162	+	0.478326i	0.694266	+	0.719719i	$0.255729\pi$
$410$		0			0
$411$	271.479	+	186.588i	0.660532	+	0.453985i
$412$		0			0
$413$	234.143			0.566933
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−45.3916	+	576.650i	−0.108853	+	1.38285i
$418$		0			0
$419$	509.790	+	294.327i	1.21668	+	0.702452i	0.964207	−	0.265152i	$-0.0854221\pi$
$419$	509.790	+	294.327i	1.21668	+	0.702452i	0.252475	+	0.967603i	$0.418755\pi$
$420$		0			0
$421$	154.778	+	268.083i	0.367643	+	0.636776i	0.989197	−	0.146595i	$-0.0468316\pi$
$421$	154.778	+	268.083i	0.367643	+	0.636776i	−0.621554	+	0.783372i	$0.713498\pi$
$422$		0			0
$423$	91.7030	+	14.5270i	0.216792	+	0.0343428i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	159.194	+	91.9109i	0.372821	+	0.215248i
$428$		0			0
$429$	235.967	−	112.547i	0.550041	−	0.262346i
$430$		0			0
$431$			73.7566i			0.171129i	0.996333	+	0.0855645i	$0.0272694\pi$
$431$			73.7566i			0.171129i	−0.996333	+	0.0855645i	$0.972731\pi$
$432$		0			0
$433$			153.697i			0.354958i	0.984125	+	0.177479i	$0.0567941\pi$
$433$			153.697i			0.354958i	−0.984125	+	0.177479i	$0.943206\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	337.033	−	583.759i	0.771244	−	1.33583i
$438$		0			0
$439$	−117.866	−	204.149i	−0.268487	−	0.465033i	0.699985	−	0.714158i	$-0.253190\pi$
$439$	−117.866	−	204.149i	−0.268487	−	0.465033i	−0.968471	+	0.249125i	$0.919857\pi$
$440$		0			0
$441$	119.307	+	310.832i	0.270537	+	0.704833i
$442$		0			0
$443$	−121.716	−	210.818i	−0.274753	−	0.475887i	0.695319	−	0.718701i	$-0.255263\pi$
$443$	−121.716	−	210.818i	−0.274753	−	0.475887i	−0.970073	+	0.242814i	$0.921930\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	529.458	+	41.6768i	1.18447	+	0.0932367i
$448$		0			0
$449$		−	286.103i		−	0.637201i	−0.947889	−	0.318600i	$-0.896787\pi$
$449$		−	286.103i		−	0.637201i	0.947889	−	0.318600i	$-0.103213\pi$
$450$		0			0
$451$	282.969			0.627426
$452$		0			0
$453$	305.394	+	209.898i	0.674159	+	0.463351i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−619.606	+	357.730i	−1.35581	+	0.782778i	−0.989056	−	0.147539i	$-0.952865\pi$
$457$	−619.606	+	357.730i	−1.35581	+	0.782778i	−0.366755	+	0.930317i	$0.619531\pi$
$458$		0			0
$459$	−73.9862	+	308.117i	−0.161190	+	0.671279i
$460$		0			0
$461$	−643.206	+	371.355i	−1.39524	+	0.805543i	−0.993889	−	0.110381i	$-0.964793\pi$
$461$	−643.206	+	371.355i	−1.39524	+	0.805543i	−0.401352	+	0.915924i	$0.631460\pi$
$462$		0			0
$463$	−174.430	−	100.707i	−0.376738	−	0.217510i	0.299660	−	0.954046i	$-0.403127\pi$
$463$	−174.430	−	100.707i	−0.376738	−	0.217510i	−0.676398	+	0.736536i	$0.736460\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−870.009			−1.86298			−0.931488	−	0.363773i	$-0.881488\pi$
$467$	−870.009			−1.86298			−0.931488	+	0.363773i	$0.881488\pi$
$468$		0			0
$469$	−110.200			−0.234968
$470$		0			0
$471$	−707.136	−	55.6629i	−1.50135	−	0.118180i
$472$		0			0
$473$	39.3304	−	68.1222i	0.0831509	−	0.144022i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	235.403	−	290.682i	0.493507	−	0.609396i
$478$		0			0
$479$	−372.537	+	215.085i	−0.777740	+	0.449028i	−0.835629	−	0.549295i	$-0.814896\pi$
$479$	−372.537	+	215.085i	−0.777740	+	0.449028i	0.0578889	+	0.998323i	$0.481563\pi$
$480$		0			0
$481$	−142.469	+	246.763i	−0.296193	+	0.513021i
$482$		0			0
$483$	−128.474	−	269.360i	−0.265991	−	0.557682i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	128.924i		−	0.264732i	−0.991201	−	0.132366i	$-0.957743\pi$
$487$		−	128.924i		−	0.264732i	0.991201	−	0.132366i	$-0.0422574\pi$
$488$		0			0
$489$	−369.748	−	775.222i	−0.756132	−	1.58532i
$490$		0			0
$491$	412.034	+	237.888i	0.839173	+	0.484497i	0.856983	−	0.515344i	$-0.172336\pi$
$491$	412.034	+	237.888i	0.839173	+	0.484497i	−0.0178098	+	0.999841i	$0.505669\pi$
$492$		0			0
$493$	−156.250	+	90.2109i	−0.316937	+	0.182984i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.95998	+	6.85889i	0.00796777	+	0.0138006i
$498$		0			0
$499$	−191.161	+	331.101i	−0.383088	+	0.663528i	−0.991502	−	0.130092i	$-0.958473\pi$
$499$	−191.161	+	331.101i	−0.383088	+	0.663528i	0.608414	+	0.793620i	$0.291806\pi$
$500$		0			0
$501$	−8.44898	+	107.335i	−0.0168642	+	0.214242i
$502$		0			0
$503$	−787.756			−1.56612			−0.783058	−	0.621949i	$-0.786341\pi$
$503$	−787.756			−1.56612			−0.783058	+	0.621949i	$0.786341\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−325.906	−	223.996i	−0.642812	−	0.441806i
$508$		0			0
$509$	416.243	+	240.318i	0.817766	+	0.472137i	0.849645	−	0.527354i	$-0.176816\pi$
$509$	416.243	+	240.318i	0.817766	+	0.472137i	−0.0318795	+	0.999492i	$0.510149\pi$
$510$		0			0
$511$	−149.491	−	258.926i	−0.292546	−	0.506704i
$512$		0			0
$513$	−148.018	+	616.425i	−0.288534	+	1.20161i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−127.685	−	73.7188i	−0.246972	−	0.142590i
$518$		0			0
$519$	243.117	+	167.094i	0.468433	+	0.321955i
$520$		0			0
$521$		−	241.071i		−	0.462709i	−0.972870	−	0.231354i	$-0.925684\pi$
$521$		−	241.071i		−	0.462709i	0.972870	−	0.231354i	$-0.0743157\pi$
$522$		0			0
$523$			779.301i			1.49006i	0.667032	+	0.745029i	$0.267565\pi$
$523$			779.301i			1.49006i	−0.667032	+	0.745029i	$0.732435\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	217.025	−	375.898i	0.411812	−	0.713279i
$528$		0			0
$529$	−147.596	−	255.643i	−0.279009	−	0.483257i
$530$		0			0
$531$	−567.772	+	217.929i	−1.06925	+	0.410412i
$532$		0			0
$533$	60.3641	+	104.554i	0.113253	+	0.196161i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−403.563	−	846.117i	−0.751513	−	1.57564i
$538$		0			0
$539$		−	528.702i		−	0.980895i
$540$		0			0
$541$	−811.510			−1.50002			−0.750009	−	0.661428i	$-0.769951\pi$
$541$	−811.510			−1.50002			−0.750009	+	0.661428i	$0.769951\pi$
$542$		0			0
$543$	39.2986	−	18.7438i	0.0723732	−	0.0345190i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−354.493	+	204.667i	−0.648069	+	0.374163i	−0.787716	−	0.616039i	$-0.788736\pi$
$547$	−354.493	+	204.667i	−0.648069	+	0.374163i	0.139647	+	0.990201i	$0.455403\pi$
$548$		0			0
$549$	−471.575	−	74.7038i	−0.858970	−	0.136072i
$550$		0			0
$551$	−312.596	+	180.478i	−0.567326	+	0.327546i
$552$		0			0
$553$	350.653	+	202.449i	0.634091	+	0.366093i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−72.8356			−0.130764			−0.0653820	−	0.997860i	$-0.520827\pi$
$557$	−72.8356			−0.130764			−0.0653820	+	0.997860i	$0.520827\pi$
$558$		0			0
$559$	33.5605			0.0600366
$560$		0			0
$561$	285.015	−	414.687i	0.508049	−	0.739193i
$562$		0			0
$563$	−40.9255	+	70.8850i	−0.0726918	+	0.125906i	−0.900080	−	0.435724i	$-0.856492\pi$
$563$	−40.9255	+	70.8850i	−0.0726918	+	0.125906i	0.827388	+	0.561630i	$0.189826\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	187.791	+	208.587i	0.331202	+	0.367879i
$568$		0			0
$569$	−880.986	+	508.637i	−1.54831	+	0.893914i	−0.550034	+	0.835142i	$0.685385\pi$
$569$	−880.986	+	508.637i	−1.54831	+	0.893914i	−0.998271	+	0.0587719i	$0.981282\pi$
$570$		0			0
$571$	−243.972	+	422.572i	−0.427271	+	0.740056i	−0.996630	−	0.0820339i	$-0.973858\pi$
$571$	−243.972	+	422.572i	−0.427271	+	0.740056i	0.569358	+	0.822090i	$0.307192\pi$
$572$		0			0
$573$	−441.246	+	641.998i	−0.770063	+	1.12042i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	328.037i		−	0.568522i	−0.958747	−	0.284261i	$-0.908252\pi$
$577$		−	328.037i		−	0.568522i	0.958747	−	0.284261i	$-0.0917482\pi$
$578$		0			0
$579$	−709.631	−	55.8592i	−1.22561	−	0.0964754i
$580$		0			0
$581$	−391.601	−	226.091i	−0.674013	−	0.389142i
$582$		0			0
$583$	−514.397	+	296.987i	−0.882327	+	0.509412i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	46.5708	+	80.6629i	0.0793369	+	0.137416i	0.902964	−	0.429716i	$-0.141386\pi$
$587$	46.5708	+	80.6629i	0.0793369	+	0.137416i	−0.823627	+	0.567132i	$0.808053\pi$
$588$		0			0
$589$	434.184	−	752.028i	0.737154	−	1.27679i
$590$		0			0
$591$	−412.405	+	196.700i	−0.697808	+	0.332825i
$592$		0			0
$593$	61.3791			0.103506			0.0517530	−	0.998660i	$-0.483519\pi$
$593$	61.3791			0.103506			0.0517530	+	0.998660i	$0.483519\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1036.85	+	494.532i	−1.73676	+	0.828362i
$598$		0			0
$599$	−720.881	−	416.201i	−1.20347	−	0.694826i	−0.242148	−	0.970239i	$-0.577852\pi$
$599$	−720.881	−	416.201i	−1.20347	−	0.694826i	−0.961326	+	0.275413i	$0.911185\pi$
$600$		0			0
$601$	−192.246	−	332.980i	−0.319877	−	0.554043i	0.660585	−	0.750751i	$-0.270308\pi$
$601$	−192.246	−	332.980i	−0.319877	−	0.554043i	−0.980462	+	0.196708i	$0.936975\pi$
$602$		0			0
$603$	267.223	−	102.569i	0.443155	−	0.170097i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	628.428	+	362.823i	1.03530	+	0.597732i	0.918499	−	0.395423i	$-0.129402\pi$
$607$	628.428	+	362.823i	1.03530	+	0.597732i	0.116803	+	0.993155i	$0.462735\pi$
$608$		0			0
$609$	−12.5405	+	159.313i	−0.0205919	+	0.261598i
$610$		0			0
$611$		−	62.9039i		−	0.102952i
$612$		0			0
$613$			3.61994i			0.00590529i	0.999996	+	0.00295265i	$0.000939858\pi$
$613$			3.61994i			0.00590529i	−0.999996	+	0.00295265i	$0.999060\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	239.072	−	414.084i	0.387474	−	0.671125i	−0.604635	−	0.796503i	$-0.706681\pi$
$617$	239.072	−	414.084i	0.387474	−	0.671125i	0.992109	+	0.125378i	$0.0400143\pi$
$618$		0			0
$619$	160.807	+	278.525i	0.259784	+	0.449960i	0.966184	−	0.257853i	$-0.0830151\pi$
$619$	160.807	+	278.525i	0.259784	+	0.449960i	−0.706400	+	0.707813i	$0.749682\pi$
$620$		0			0
$621$	562.241	+	533.592i	0.905380	+	0.859246i
$622$		0			0
$623$	130.519	+	226.065i	0.209500	+	0.362865i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	570.207	−	829.631i	0.909421	−	1.32318i
$628$		0			0
$629$			548.428i			0.871905i
$630$		0			0
$631$	−457.380			−0.724850			−0.362425	−	0.932013i	$-0.618051\pi$
$631$	−457.380			−0.724850			−0.362425	+	0.932013i	$0.618051\pi$
$632$		0			0
$633$	14.9734	−	190.221i	0.0236547	−	0.300507i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	195.349	−	112.785i	0.306670	−	0.177056i
$638$		0			0
$639$	−15.9864	−	12.9463i	−0.0250179	−	0.0202603i
$640$		0			0
$641$	8.11287	−	4.68397i	0.0126566	−	0.00730728i	−0.493658	−	0.869656i	$-0.664341\pi$
$641$	8.11287	−	4.68397i	0.0126566	−	0.00730728i	0.506315	+	0.862349i	$0.331007\pi$
$642$		0			0
$643$	461.736	+	266.583i	0.718096	+	0.414593i	0.814051	−	0.580793i	$-0.197257\pi$
$643$	461.736	+	266.583i	0.718096	+	0.414593i	−0.0959557	+	0.995386i	$0.530591\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−792.544			−1.22495			−0.612476	−	0.790489i	$-0.709826\pi$
$647$	−792.544			−1.22495			−0.612476	+	0.790489i	$0.709826\pi$
$648$		0			0
$649$	965.739			1.48804
$650$		0			0
$651$	−165.506	−	347.004i	−0.254234	−	0.533032i
$652$		0			0
$653$	−367.827	+	637.096i	−0.563288	+	0.975644i	0.433918	+	0.900952i	$0.357131\pi$
$653$	−367.827	+	637.096i	−0.563288	+	0.975644i	−0.997207	+	0.0746918i	$0.976203\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	603.493	+	488.728i	0.918559	+	0.743878i
$658$		0			0
$659$	−859.395	+	496.172i	−1.30409	+	0.752917i	−0.981103	−	0.193487i	$-0.938020\pi$
$659$	−859.395	+	496.172i	−1.30409	+	0.752917i	−0.322987	+	0.946403i	$0.604687\pi$
$660$		0			0
$661$	−336.164	+	582.252i	−0.508568	+	0.880866i	0.491383	+	0.870944i	$0.336492\pi$
$661$	−336.164	+	582.252i	−0.508568	+	0.880866i	−0.999951	+	0.00992217i	$0.996842\pi$
$662$		0			0
$663$	214.022	+	16.8470i	0.322809	+	0.0254102i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			441.345i			0.661687i
$668$		0			0
$669$	−2.74093	+	3.98796i	−0.00409706	+	0.00596108i
$670$		0			0
$671$	656.607	+	379.092i	0.978550	+	0.564966i
$672$		0			0
$673$	−642.106	+	370.720i	−0.954095	+	0.550847i	−0.894351	−	0.447366i	$-0.852362\pi$
$673$	−642.106	+	370.720i	−0.954095	+	0.550847i	−0.0597446	+	0.998214i	$0.519029\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−330.560	−	572.547i	−0.488272	−	0.845711i	0.511637	−	0.859202i	$-0.329039\pi$
$677$	−330.560	−	572.547i	−0.488272	−	0.845711i	−0.999909	+	0.0134901i	$0.995706\pi$
$678$		0			0
$679$	−48.9789	+	84.8340i	−0.0721339	+	0.124940i
$680$		0			0
$681$	960.617	+	660.234i	1.41060	+	0.969506i
$682$		0			0
$683$	1179.82			1.72741			0.863704	−	0.503999i	$-0.168138\pi$
$683$	1179.82			1.72741			0.863704	+	0.503999i	$0.168138\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	64.1505	−	814.962i	0.0933777	−	1.18626i
$688$		0			0
$689$	−219.466	−	126.709i	−0.318529	−	0.183903i
$690$		0			0
$691$	−23.3297	−	40.4083i	−0.0337623	−	0.0584780i	0.848651	−	0.528954i	$-0.177416\pi$
$691$	−23.3297	−	40.4083i	−0.0337623	−	0.0584780i	−0.882413	+	0.470476i	$0.844082\pi$
$692$		0			0
$693$	−159.710	−	416.094i	−0.230462	−	0.600424i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	201.238	+	116.185i	0.288720	+	0.166692i
$698$		0			0
$699$	717.194	−	342.072i	1.02603	−	0.489373i
$700$		0			0
$701$		−	1384.15i		−	1.97453i	−0.159078	−	0.987266i	$-0.550852\pi$
$701$		−	1384.15i		−	1.97453i	0.159078	−	0.987266i	$-0.449148\pi$
$702$		0			0
$703$			1097.20i			1.56073i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	220.225	−	381.441i	0.311492	−	0.539521i
$708$		0			0
$709$	563.387	+	975.815i	0.794622	+	1.37633i	0.923079	+	0.384610i	$0.125664\pi$
$709$	563.387	+	975.815i	0.794622	+	1.37633i	−0.128457	+	0.991715i	$0.541002\pi$
$710$		0			0
$711$	−1038.72	−	164.548i	−1.46093	−	0.231431i
$712$		0			0
$713$	−530.882	−	919.515i	−0.744576	−	1.28964i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	536.626	+	42.2410i	0.748432	+	0.0589135i
$718$		0			0
$719$		−	205.596i		−	0.285947i	−0.989726	−	0.142974i	$-0.954334\pi$
$719$		−	205.596i		−	0.285947i	0.989726	−	0.142974i	$-0.0456664\pi$
$720$		0			0
$721$	−174.151			−0.241541
$722$		0			0
$723$	701.196	+	481.933i	0.969842	+	0.666574i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	157.186	−	90.7513i	0.216212	−	0.124830i	−0.387983	−	0.921666i	$-0.626828\pi$
$727$	157.186	−	90.7513i	0.216212	−	0.124830i	0.604195	+	0.796837i	$0.293495\pi$
$728$		0			0
$729$	−649.516	−	331.014i	−0.890968	−	0.454066i
$730$		0			0
$731$	55.9408	−	32.2974i	0.0765264	−	0.0441825i
$732$		0			0
$733$	424.253	+	244.943i	0.578790	+	0.334165i	0.760652	−	0.649159i	$-0.224879\pi$
$733$	424.253	+	244.943i	0.578790	+	0.334165i	−0.181862	+	0.983324i	$0.558213\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−454.527			−0.616726
$738$		0			0
$739$	−312.730			−0.423180			−0.211590	−	0.977359i	$-0.567864\pi$
$739$	−312.730			−0.423180			−0.211590	+	0.977359i	$0.567864\pi$
$740$		0			0
$741$	428.177	+	33.7044i	0.577837	+	0.0454850i
$742$		0			0
$743$	−660.954	+	1144.81i	−0.889574	+	1.54079i	−0.0491945	+	0.998789i	$0.515665\pi$
$743$	−660.954	+	1144.81i	−0.889574	+	1.54079i	−0.840380	+	0.541998i	$0.817668\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1160.02	+	183.763i	1.55291	+	0.246002i
$748$		0			0
$749$	−455.234	+	262.829i	−0.607789	+	0.350907i
$750$		0			0
$751$	637.535	−	1104.24i	0.848914	−	1.47036i	−0.0332638	−	0.999447i	$-0.510590\pi$
$751$	637.535	−	1104.24i	0.848914	−	1.47036i	0.882178	−	0.470916i	$-0.156077\pi$
$752$		0			0
$753$	555.218	+	1164.08i	0.737341	+	1.54592i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			1371.91i			1.81230i	0.422959	+	0.906149i	$0.360991\pi$
$757$			1371.91i			1.81230i	−0.422959	+	0.906149i	$0.639009\pi$
$758$		0			0
$759$	−529.897	−	1110.99i	−0.698152	−	1.46376i
$760$		0			0
$761$	−733.212	−	423.320i	−0.963485	−	0.556269i	−0.0662413	−	0.997804i	$-0.521101\pi$
$761$	−733.212	−	423.320i	−0.963485	−	0.556269i	−0.897244	+	0.441535i	$0.854434\pi$
$762$		0			0
$763$	394.452	−	227.737i	0.516975	−	0.298476i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	206.015	+	356.829i	0.268599	+	0.465227i
$768$		0			0
$769$	−155.867	+	269.969i	−0.202688	+	0.351066i	−0.949394	−	0.314089i	$-0.898301\pi$
$769$	−155.867	+	269.969i	−0.202688	+	0.351066i	0.746706	+	0.665154i	$0.231634\pi$
$770$		0			0
$771$	44.8021	−	569.162i	0.0581091	−	0.738213i
$772$		0			0
$773$	−140.050			−0.181178			−0.0905889	−	0.995888i	$-0.528875\pi$
$773$	−140.050			−0.181178			−0.0905889	+	0.995888i	$0.528875\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	400.325	+	275.144i	0.515219	+	0.354111i
$778$		0			0
$779$	402.600	+	232.441i	0.516816	+	0.298384i
$780$		0			0
$781$	16.3332	+	28.2899i	0.0209132	+	0.0362227i
$782$		0			0
$783$	−117.871	−	397.988i	−0.150538	−	0.508287i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−321.229	−	185.462i	−0.408169	−	0.235657i	0.281833	−	0.959463i	$-0.409057\pi$
$787$	−321.229	−	185.462i	−0.408169	−	0.235657i	−0.690003	+	0.723807i	$0.742391\pi$
$788$		0			0
$789$	−988.456	−	679.368i	−1.25280	−	0.861049i
$790$		0			0
$791$		−	316.882i		−	0.400609i
$792$		0			0
$793$			323.478i			0.407917i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.56272	+	13.0990i	−0.00948898	+	0.0164354i	−0.870731	−	0.491760i	$-0.836354\pi$
$797$	−7.56272	+	13.0990i	−0.00948898	+	0.0164354i	0.861242	+	0.508195i	$0.169687\pi$
$798$		0			0
$799$	−60.5366	−	104.852i	−0.0757655	−	0.131230i
$800$		0			0
$801$	−526.903	−	426.702i	−0.657806	−	0.532712i
$802$		0			0
$803$	−616.584	−	1067.96i	−0.767851	−	1.32996i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−630.778	−	1322.50i	−0.781633	−	1.63879i
$808$		0			0
$809$			1123.71i			1.38901i	0.719488	+	0.694505i	$0.244377\pi$
$809$			1123.71i			1.38901i	−0.719488	+	0.694505i	$0.755623\pi$
$810$		0			0
$811$	181.717			0.224065			0.112033	−	0.993705i	$-0.464264\pi$
$811$	181.717			0.224065			0.112033	+	0.993705i	$0.464264\pi$
$812$		0			0
$813$	819.307	−	390.775i	1.00776	−	0.480658i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	111.916	−	64.6148i	0.136984	−	0.0790879i
$818$		0			0
$819$	119.672	−	147.774i	0.146119	−	0.180432i
$820$		0			0
$821$	−532.274	+	307.308i	−0.648323	+	0.374310i	−0.787814	−	0.615914i	$-0.788787\pi$
$821$	−532.274	+	307.308i	−0.648323	+	0.374310i	0.139490	+	0.990223i	$0.455454\pi$
$822$		0			0
$823$	382.649	+	220.922i	0.464944	+	0.268436i	0.714121	−	0.700022i	$-0.246827\pi$
$823$	382.649	+	220.922i	0.464944	+	0.268436i	−0.249177	+	0.968458i	$0.580160\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1400.26			−1.69318			−0.846589	−	0.532247i	$-0.821348\pi$
$827$	−1400.26			−1.69318			−0.846589	+	0.532247i	$0.821348\pi$
$828$		0			0
$829$	166.752			0.201149			0.100574	−	0.994930i	$-0.467932\pi$
$829$	166.752			0.201149			0.100574	+	0.994930i	$0.467932\pi$
$830$		0			0
$831$	43.2921	−	62.9885i	0.0520964	−	0.0757984i
$832$		0			0
$833$	217.081	−	375.995i	0.260601	−	0.451374i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	724.307	+	687.400i	0.865361	+	0.821267i
$838$		0			0
$839$	−682.428	+	394.000i	−0.813382	+	0.469607i	−0.848129	−	0.529790i	$-0.822271\pi$
$839$	−682.428	+	394.000i	−0.813382	+	0.469607i	0.0347467	+	0.999396i	$0.488938\pi$
$840$		0			0
$841$	−302.332	+	523.655i	−0.359492	+	0.622658i
$842$		0			0
$843$	558.569	−	812.698i	0.662596	−	0.964055i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			288.477i			0.340587i
$848$		0			0
$849$	244.593	+	19.2534i	0.288096	+	0.0226777i
$850$		0			0
$851$	1161.82	+	670.778i	1.36524	+	0.788224i
$852$		0			0
$853$	−385.927	+	222.815i	−0.452435	+	0.261213i	−0.708858	−	0.705351i	$-0.750789\pi$
$853$	−385.927	+	222.815i	−0.452435	+	0.261213i	0.256423	+	0.966565i	$0.417456\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	451.485	+	781.995i	0.526820	+	0.912479i	0.999512	+	0.0312512i	$0.00994918\pi$
$857$	451.485	+	781.995i	0.526820	+	0.912479i	−0.472691	+	0.881228i	$0.656717\pi$
$858$		0			0
$859$	376.214	−	651.622i	0.437967	−	0.758582i	−0.559565	−	0.828786i	$-0.689032\pi$
$859$	376.214	−	651.622i	0.437967	−	0.758582i	0.997533	+	0.0702046i	$0.0223652\pi$
$860$		0			0
$861$	185.769	−	88.6041i	0.215760	−	0.102908i
$862$		0			0
$863$	−900.969			−1.04400			−0.521998	−	0.852946i	$-0.674813\pi$
$863$	−900.969			−1.04400			−0.521998	+	0.852946i	$0.674813\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−409.587	+	195.356i	−0.472419	+	0.225324i
$868$		0			0
$869$	1446.29	+	835.015i	1.66431	+	0.960892i
$870$		0			0
$871$	−96.9614	−	167.942i	−0.111322	−	0.192815i
$872$		0			0
$873$	39.8093	−	251.300i	0.0456006	−	0.287858i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−719.863	−	415.613i	−0.820824	−	0.473903i	0.0298765	−	0.999554i	$-0.490489\pi$
$877$	−719.863	−	415.613i	−0.820824	−	0.473903i	−0.850701	+	0.525651i	$0.823822\pi$
$878$		0			0
$879$	111.340	−	1414.46i	0.126667	−	1.60917i
$880$		0			0
$881$		−	1140.44i		−	1.29448i	−0.762286	−	0.647240i	$-0.775923\pi$
$881$		−	1140.44i		−	1.29448i	0.762286	−	0.647240i	$-0.224077\pi$
$882$		0			0
$883$		−	137.466i		−	0.155680i	−0.996966	−	0.0778401i	$-0.975198\pi$
$883$		−	137.466i		−	0.155680i	0.996966	−	0.0778401i	$-0.0248024\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	168.286	−	291.479i	0.189724	−	0.328612i	−0.755434	−	0.655225i	$-0.772574\pi$
$887$	168.286	−	291.479i	0.189724	−	0.328612i	0.945158	+	0.326613i	$0.105907\pi$
$888$		0			0
$889$	264.445	+	458.032i	0.297463	+	0.515222i
$890$		0			0
$891$	774.558	+	860.331i	0.869313	+	0.965579i
$892$		0			0
$893$	−121.111	−	209.770i	−0.135622	−	0.234905i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	297.459	−	432.792i	0.331615	−	0.482488i
$898$		0			0
$899$			568.563i			0.632439i
$900$		0			0
$901$	−487.761			−0.541355
$902$		0			0
$903$	4.48976	−	57.0375i	0.00497205	−	0.0631644i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−343.242	+	198.171i	−0.378437	+	0.218490i	−0.677138	−	0.735856i	$-0.736780\pi$
$907$	−343.242	+	198.171i	−0.378437	+	0.218490i	0.298701	+	0.954347i	$0.403447\pi$
$908$		0			0
$909$	−178.996	+	1129.93i	−0.196915	+	1.24304i
$910$		0			0
$911$	738.564	−	426.410i	0.810718	−	0.468068i	−0.0364874	−	0.999334i	$-0.511617\pi$
$911$	738.564	−	426.410i	0.810718	−	0.468068i	0.847205	+	0.531266i	$0.178284\pi$
$912$		0			0
$913$	−1615.18	−	932.527i	−1.76910	−	1.02139i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−276.999			−0.302071
$918$		0			0
$919$	1499.67			1.63185			0.815924	−	0.578160i	$-0.196229\pi$
$919$	1499.67			1.63185			0.815924	+	0.578160i	$0.196229\pi$
$920$		0			0
$921$	577.982	+	1211.81i	0.627559	+	1.31575i
$922$		0			0
$923$	−6.96852	+	12.0698i	−0.00754986	+	0.0130767i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	422.297	−	162.091i	0.455552	−	0.174855i
$928$		0			0
$929$	−949.861	+	548.402i	−1.02246	+	0.590315i	−0.914814	−	0.403875i	$-0.867663\pi$
$929$	−949.861	+	548.402i	−1.02246	+	0.590315i	−0.107641	+	0.994190i	$0.534330\pi$
$930$		0			0
$931$	434.295	−	752.222i	0.466483	−	0.807972i
$932$		0			0
$933$	270.634	+	21.3032i	0.290069	+	0.0228330i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			950.251i			1.01414i	0.861904	+	0.507071i	$0.169272\pi$
$937$			950.251i			1.01414i	−0.861904	+	0.507071i	$0.830728\pi$
$938$		0			0
$939$	610.917	−	888.863i	0.650604	−	0.946606i
$940$		0			0
$941$	1163.08	+	671.503i	1.23600	+	0.713606i	0.968274	−	0.249889i	$-0.0803941\pi$
$941$	1163.08	+	671.503i	1.23600	+	0.713606i	0.267727	+	0.963495i	$0.413727\pi$
$942$		0			0
$943$	492.264	−	284.209i	0.522020	−	0.301388i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−294.370	−	509.863i	−0.310844	−	0.538398i	0.667701	−	0.744430i	$-0.267278\pi$
$947$	−294.370	−	509.863i	−0.310844	−	0.538398i	−0.978545	+	0.206031i	$0.933945\pi$
$948$		0			0
$949$	263.064	−	455.641i	0.277202	−	0.480127i
$950$		0			0
$951$	1035.42	+	711.643i	1.08876	+	0.748310i
$952$		0			0
$953$	80.5286			0.0845001			0.0422501	−	0.999107i	$-0.486547\pi$
$953$	80.5286			0.0845001			0.0422501	+	0.999107i	$0.486547\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−51.7240	+	657.097i	−0.0540480	+	0.686621i
$958$		0			0
$959$	−329.506	−	190.240i	−0.343593	−	0.198373i
$960$		0			0
$961$	−203.410	−	352.316i	−0.211665	−	0.366614i
$962$		0			0
$963$	859.263	−	1061.04i	0.892277	−	1.10181i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	249.502	+	144.050i	0.258017	+	0.148966i	0.623429	−	0.781880i	$-0.285739\pi$
$967$	249.502	+	144.050i	0.258017	+	0.148966i	−0.365413	+	0.930846i	$0.619072\pi$
$968$		0			0
$969$	746.150	−	355.882i	0.770021	−	0.367268i
$970$		0			0
$971$			1036.38i			1.06733i	0.845696	+	0.533665i	$0.179186\pi$
$971$			1036.38i			1.06733i	−0.845696	+	0.533665i	$0.820814\pi$
$972$		0			0
$973$		−	668.097i		−	0.686636i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	793.878	−	1375.04i	0.812567	−	1.40741i	−0.0984946	−	0.995138i	$-0.531403\pi$
$977$	793.878	−	1375.04i	0.812567	−	1.40741i	0.911062	−	0.412270i	$-0.135264\pi$
$978$		0			0
$979$	538.332	+	932.418i	0.549879	+	0.952419i
$980$		0			0
$981$	−744.536	+	919.373i	−0.758956	+	0.937179i
$982$		0			0
$983$	−602.511	−	1043.58i	−0.612931	−	1.06163i	−0.990744	−	0.135745i	$-0.956657\pi$
$983$	−602.511	−	1043.58i	−0.612931	−	1.06163i	0.377813	−	0.925882i	$-0.376676\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−106.908	−	8.41537i	−0.108316	−	0.00852621i
$988$		0			0
$989$		−	158.011i		−	0.159768i
$990$		0			0
$991$	−326.691			−0.329658			−0.164829	−	0.986322i	$-0.552707\pi$
$991$	−326.691			−0.329658			−0.164829	+	0.986322i	$0.552707\pi$
$992$		0			0
$993$	−670.574	−	460.887i	−0.675301	−	0.464136i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	239.663	−	138.370i	0.240384	−	0.138786i	−0.374969	−	0.927037i	$-0.622347\pi$
$997$	239.663	−	138.370i	0.240384	−	0.138786i	0.615353	+	0.788251i	$0.289013\pi$
$998$		0			0
$999$	−1226.83	−	294.592i	−1.22806	−	0.294887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.d.149.15		32
3.2	odd	2		2700.3.u.d.449.7		32
5.2	odd	4		900.3.p.e.401.3	yes	16
5.3	odd	4		900.3.p.d.401.6	yes	16
5.4	even	2	inner	900.3.u.d.149.2		32
9.2	odd	6	inner	900.3.u.d.749.2		32
9.7	even	3		2700.3.u.d.2249.10		32
15.2	even	4		2700.3.p.d.2501.4		16
15.8	even	4		2700.3.p.e.2501.5		16
15.14	odd	2		2700.3.u.d.449.10		32
45.2	even	12		900.3.p.e.101.3	yes	16
45.7	odd	12		2700.3.p.d.1601.4		16
45.29	odd	6	inner	900.3.u.d.749.15		32
45.34	even	6		2700.3.u.d.2249.7		32
45.38	even	12		900.3.p.d.101.6	✓	16
45.43	odd	12		2700.3.p.e.1601.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.6	✓	16	45.38	even	12
900.3.p.d.401.6	yes	16	5.3	odd	4
900.3.p.e.101.3	yes	16	45.2	even	12
900.3.p.e.401.3	yes	16	5.2	odd	4
900.3.u.d.149.2		32	5.4	even	2	inner
900.3.u.d.149.15		32	1.1	even	1	trivial
900.3.u.d.749.2		32	9.2	odd	6	inner
900.3.u.d.749.15		32	45.29	odd	6	inner
2700.3.p.d.1601.4		16	45.7	odd	12
2700.3.p.d.2501.4		16	15.2	even	4
2700.3.p.e.1601.5		16	45.43	odd	12
2700.3.p.e.2501.5		16	15.8	even	4
2700.3.u.d.449.7		32	3.2	odd	2
2700.3.u.d.449.10		32	15.14	odd	2
2700.3.u.d.2249.7		32	45.34	even	6
2700.3.u.d.2249.10		32	9.7	even	3

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.70777 - 1.29149i) q^{3} +(-3.00081 + 1.73252i) q^{7} +(5.66408 - 6.99415i) q^{9} +O(q^{10})\)	\(q+(2.70777 - 1.29149i) q^{3} +(-3.00081 + 1.73252i) q^{7} +(5.66408 - 6.99415i) q^{9} +(-12.3770 + 7.14587i) q^{11} +(-5.28062 - 3.04877i) q^{13} -11.7361 q^{17} -23.4795 q^{19} +(-5.88797 + 8.56679i) q^{21} +(-14.3544 + 24.8625i) q^{23} +(6.30414 - 26.2537i) q^{27} +(13.3136 - 7.68660i) q^{29} +(-18.4920 + 32.0291i) q^{31} +(-24.2853 + 35.3342i) q^{33} -46.7299i q^{37} +(-18.2362 - 1.43548i) q^{39} +(-17.1469 - 9.89974i) q^{41} +(-4.76655 + 2.75197i) q^{43} +(5.15814 + 8.93416i) q^{47} +(-18.4968 + 32.0374i) q^{49} +(-31.7788 + 15.1571i) q^{51} +41.5607 q^{53} +(-63.5772 + 30.3237i) q^{57} +(-58.5202 - 33.7866i) q^{59} +(-26.5253 - 45.9431i) q^{61} +(-4.87932 + 30.8012i) q^{63} +(27.5426 + 15.9017i) q^{67} +(-6.75860 + 85.8606i) q^{69} -2.28568i q^{71} +86.2854i q^{73} +(24.7607 - 42.8867i) q^{77} +(-58.4264 - 101.198i) q^{79} +(-16.8364 - 79.2309i) q^{81} +(65.2494 + 113.015i) q^{83} +(26.1230 - 38.0080i) q^{87} -75.3347i q^{89} +21.1282 q^{91} +(-8.70677 + 110.610i) q^{93} +(24.4829 - 14.1352i) q^{97} +(-20.1251 + 127.041i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 28 q^{9}+O(q^{10}) \) 32 * q - 28 * q^9	\( 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) \) 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * q^99

Introduction

L-functions

Modular forms

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Database

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