LMFDB - Embedded newform 585.4.c.e.469.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,4,Mod(469,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.469"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	585.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,0,0,-110,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$34.5161173534$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.19
Character	$\chi$	$=$	585.469
Dual form			585.4.c.e.469.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.60776i q^{2} -13.2315 q^{4} +(3.07988 + 10.7478i) q^{5} -15.5130i q^{7} -24.1055i q^{8} +(-49.5231 + 14.1914i) q^{10} -7.26574 q^{11} -13.0000i q^{13} +71.4805 q^{14} +5.22048 q^{16} -27.0519i q^{17} -73.2802 q^{19} +(-40.7515 - 142.209i) q^{20} -33.4788i q^{22} -198.479i q^{23} +(-106.029 + 66.2037i) q^{25} +59.9009 q^{26} +205.261i q^{28} +210.483 q^{29} -4.60080 q^{31} -168.789i q^{32} +124.649 q^{34} +(166.730 - 47.7784i) q^{35} -311.656i q^{37} -337.658i q^{38} +(259.080 - 74.2421i) q^{40} -266.261 q^{41} -350.071i q^{43} +96.1366 q^{44} +914.545 q^{46} +89.0893i q^{47} +102.345 q^{49} +(-305.051 - 488.555i) q^{50} +172.009i q^{52} +409.598i q^{53} +(-22.3776 - 78.0904i) q^{55} -373.950 q^{56} +969.854i q^{58} -69.1227 q^{59} -705.722 q^{61} -21.1994i q^{62} +819.505 q^{64} +(139.721 - 40.0385i) q^{65} -285.963i q^{67} +357.936i q^{68} +(220.151 + 768.255i) q^{70} +728.849 q^{71} -42.7017i q^{73} +1436.04 q^{74} +969.606 q^{76} +112.714i q^{77} +486.631 q^{79} +(16.0785 + 56.1084i) q^{80} -1226.87i q^{82} +259.760i q^{83} +(290.747 - 83.3166i) q^{85} +1613.04 q^{86} +175.144i q^{88} -71.9228 q^{89} -201.670 q^{91} +2626.17i q^{92} -410.502 q^{94} +(-225.694 - 787.597i) q^{95} -953.857i q^{97} +471.584i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 110 q^{4} - 8 q^{5} - 58 q^{10} - 200 q^{11} + 300 q^{14} + 1022 q^{16} - 88 q^{19} + 296 q^{20} - 346 q^{25} - 78 q^{26} + 560 q^{29} + 512 q^{31} - 156 q^{34} - 36 q^{35} + 10 q^{40} - 1400 q^{41}+ \cdots - 2376 q^{95}+O(q^{100}) $ 22 * q - 110 * q^4 - 8 * q^5 - 58 * q^10 - 200 * q^11 + 300 * q^14 + 1022 * q^16 - 88 * q^19 + 296 * q^20 - 346 * q^25 - 78 * q^26 + 560 * q^29 + 512 * q^31 - 156 * q^34 - 36 * q^35 + 10 * q^40 - 1400 * q^41 + 3348 * q^44 + 1240 * q^46 - 3986 * q^49 - 2240 * q^50 + 2592 * q^55 - 2628 * q^56 + 3764 * q^59 + 2624 * q^61 - 9190 * q^64 - 390 * q^65 + 2776 * q^70 - 1580 * q^71 - 684 * q^74 - 1216 * q^76 - 3532 * q^79 - 7416 * q^80 + 620 * q^85 + 2664 * q^86 + 7288 * q^89 - 520 * q^91 - 13432 * q^94 - 2376 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			4.60776i			1.62909i	0.580100	+	0.814545i	$0.303014\pi$
$2$			4.60776i			1.62909i	−0.580100	+	0.814545i	$0.696986\pi$
$3$		0			0
$3$		0			0
$4$	−13.2315			−1.65394
$5$	3.07988	+	10.7478i	0.275473	+	0.961309i
$5$	3.07988	+	10.7478i	0.275473	+	0.961309i
$6$		0			0
$7$		−	15.5130i		−	0.837626i	−0.908073	−	0.418813i	$-0.862446\pi$
$7$		−	15.5130i		−	0.837626i	0.908073	−	0.418813i	$-0.137554\pi$
$8$		−	24.1055i		−	1.06532i
$9$		0			0
$10$	−49.5231	+	14.1914i	−1.56606	+	0.448771i
$11$	−7.26574			−0.199155			−0.0995774	−	0.995030i	$-0.531749\pi$
$11$	−7.26574			−0.199155			−0.0995774	+	0.995030i	$0.531749\pi$
$12$		0			0
$13$		−	13.0000i		−	0.277350i
$13$		−	13.0000i		−	0.277350i
$14$	71.4805			1.36457
$15$		0			0
$16$	5.22048			0.0815699
$17$		−	27.0519i		−	0.385943i	−0.981204	−	0.192972i	$-0.938187\pi$
$17$		−	27.0519i		−	0.385943i	0.981204	−	0.192972i	$-0.0618126\pi$
$18$		0			0
$19$	−73.2802			−0.884822			−0.442411	−	0.896812i	$-0.645877\pi$
$19$	−73.2802			−0.884822			−0.442411	+	0.896812i	$0.645877\pi$
$20$	−40.7515	−	142.209i	−0.455615	−	1.58994i
$21$		0			0
$22$		−	33.4788i		−	0.324441i
$23$		−	198.479i		−	1.79938i	−0.436529	−	0.899690i	$-0.643792\pi$
$23$		−	198.479i		−	1.79938i	0.436529	−	0.899690i	$-0.356208\pi$
$24$		0			0
$25$	−106.029	+	66.2037i	−0.848229	+	0.529630i
$26$	59.9009			0.451828
$27$		0			0
$28$			205.261i			1.38538i
$29$	210.483			1.34778			0.673890	−	0.738832i	$-0.264622\pi$
$29$	210.483			1.34778			0.673890	+	0.738832i	$0.264622\pi$
$30$		0			0
$31$	−4.60080			−0.0266558			−0.0133279	−	0.999911i	$-0.504243\pi$
$31$	−4.60080			−0.0266558			−0.0133279	+	0.999911i	$0.504243\pi$
$32$		−	168.789i		−	0.932437i
$33$		0			0
$34$	124.649			0.628737
$35$	166.730	−	47.7784i	0.805217	−	0.230743i
$36$		0			0
$37$		−	311.656i		−	1.38476i	−0.721535	−	0.692378i	$-0.756563\pi$
$37$		−	311.656i		−	1.38476i	0.721535	−	0.692378i	$-0.243437\pi$
$38$		−	337.658i		−	1.44146i
$39$		0			0
$40$	259.080	−	74.2421i	1.02410	−	0.293468i
$41$	−266.261			−1.01422			−0.507109	−	0.861882i	$-0.669286\pi$
$41$	−266.261			−1.01422			−0.507109	+	0.861882i	$0.669286\pi$
$42$		0			0
$43$		−	350.071i		−	1.24152i	−0.784002	−	0.620759i	$-0.786825\pi$
$43$		−	350.071i		−	1.24152i	0.784002	−	0.620759i	$-0.213175\pi$
$44$	96.1366			0.329390
$45$		0			0
$46$	914.545			2.93135
$47$			89.0893i			0.276490i	0.990398	+	0.138245i	$0.0441461\pi$
$47$			89.0893i			0.276490i	−0.990398	+	0.138245i	$0.955854\pi$
$48$		0			0
$49$	102.345			0.298383
$50$	−305.051	−	488.555i	−0.862815	−	1.38184i
$51$		0			0
$52$			172.009i			0.458720i
$53$			409.598i			1.06156i	0.847510	+	0.530780i	$0.178101\pi$
$53$			409.598i			1.06156i	−0.847510	+	0.530780i	$0.821899\pi$
$54$		0			0
$55$	−22.3776	−	78.0904i	−0.0548618	−	0.191449i
$56$	−373.950			−0.892341
$57$		0			0
$58$			969.854i			2.19566i
$59$	−69.1227			−0.152525			−0.0762627	−	0.997088i	$-0.524299\pi$
$59$	−69.1227			−0.152525			−0.0762627	+	0.997088i	$0.524299\pi$
$60$		0			0
$61$	−705.722			−1.48129			−0.740643	−	0.671899i	$-0.765479\pi$
$61$	−705.722			−1.48129			−0.740643	+	0.671899i	$0.765479\pi$
$62$		−	21.1994i		−	0.0434247i
$63$		0			0
$64$	819.505			1.60060
$65$	139.721	−	40.0385i	0.266619	−	0.0764025i
$66$		0			0
$67$		−	285.963i		−	0.521431i	−0.965416	−	0.260716i	$-0.916042\pi$
$67$		−	285.963i		−	0.521431i	0.965416	−	0.260716i	$-0.0839585\pi$
$68$			357.936i			0.638326i
$69$		0			0
$70$	220.151	+	768.255i	0.375902	+	1.31177i
$71$	728.849			1.21829			0.609144	−	0.793060i	$-0.291513\pi$
$71$	728.849			1.21829			0.609144	+	0.793060i	$0.291513\pi$
$72$		0			0
$73$		−	42.7017i		−	0.0684638i	−0.999414	−	0.0342319i	$-0.989102\pi$
$73$		−	42.7017i		−	0.0684638i	0.999414	−	0.0342319i	$-0.0108985\pi$
$74$	1436.04			2.25589
$75$		0			0
$76$	969.606			1.46344
$77$			112.714i			0.166817i
$78$		0			0
$79$	486.631			0.693042			0.346521	−	0.938042i	$-0.387363\pi$
$79$	486.631			0.693042			0.346521	+	0.938042i	$0.387363\pi$
$80$	16.0785	+	56.1084i	0.0224703	+	0.0784139i
$81$		0			0
$82$		−	1226.87i		−	1.65225i
$83$			259.760i			0.343522i	0.985139	+	0.171761i	$0.0549457\pi$
$83$			259.760i			0.343522i	−0.985139	+	0.171761i	$0.945054\pi$
$84$		0			0
$85$	290.747	−	83.3166i	0.371011	−	0.106317i
$86$	1613.04			2.02254
$87$		0			0
$88$			175.144i			0.212164i
$89$	−71.9228			−0.0856607			−0.0428304	−	0.999082i	$-0.513637\pi$
$89$	−71.9228			−0.0856607			−0.0428304	+	0.999082i	$0.513637\pi$
$90$		0			0
$91$	−201.670			−0.232316
$92$			2626.17i			2.97606i
$93$		0			0
$94$	−410.502			−0.450427
$95$	−225.694	−	787.597i	−0.243745	−	0.850587i
$96$		0			0
$97$		−	953.857i		−	0.998448i	−0.866473	−	0.499224i	$-0.833618\pi$
$97$		−	953.857i		−	0.998448i	0.866473	−	0.499224i	$-0.166382\pi$
$98$			471.584i			0.486093i
$99$		0			0
$100$	1402.92	−	875.974i	1.40292	−	0.875974i
$101$	531.923			0.524043			0.262021	−	0.965062i	$-0.415611\pi$
$101$	531.923			0.524043			0.262021	+	0.965062i	$0.415611\pi$
$102$		0			0
$103$			1417.30i			1.35584i	0.735137	+	0.677918i	$0.237118\pi$
$103$			1417.30i			1.35584i	−0.735137	+	0.677918i	$0.762882\pi$
$104$	−313.371			−0.295467
$105$		0			0
$106$	−1887.33			−1.72938
$107$			126.610i			0.114391i	0.998363	+	0.0571955i	$0.0182158\pi$
$107$			126.610i			0.114391i	−0.998363	+	0.0571955i	$0.981784\pi$
$108$		0			0
$109$	−421.390			−0.370292			−0.185146	−	0.982711i	$-0.559276\pi$
$109$	−421.390			−0.370292			−0.185146	+	0.982711i	$0.559276\pi$
$110$	359.822	−	103.111i	0.311888	−	0.0893749i
$111$		0			0
$112$		−	80.9855i		−	0.0683251i
$113$			1781.99i			1.48350i	0.670674	+	0.741752i	$0.266005\pi$
$113$			1781.99i			1.48350i	−0.670674	+	0.741752i	$0.733995\pi$
$114$		0			0
$115$	2133.20	−	611.292i	1.72976	−	0.495681i
$116$	−2785.00			−2.22914
$117$		0			0
$118$		−	318.501i		−	0.248478i
$119$	−419.657			−0.323276
$120$		0			0
$121$	−1278.21			−0.960337
$122$		−	3251.80i		−	2.41315i
$123$		0			0
$124$	60.8755			0.0440869
$125$	−1038.10	−	935.670i	−0.742802	−	0.669511i
$126$		0			0
$127$		−	2328.29i		−	1.62679i	−0.581712	−	0.813395i	$-0.697617\pi$
$127$		−	2328.29i		−	1.62679i	0.581712	−	0.813395i	$-0.302383\pi$
$128$			2425.77i			1.67508i
$129$		0			0
$130$	184.488	+	643.801i	0.124467	+	0.434347i
$131$	−2036.06			−1.35795			−0.678974	−	0.734162i	$-0.737575\pi$
$131$	−2036.06			−1.35795			−0.678974	+	0.734162i	$0.737575\pi$
$132$		0			0
$133$			1136.80i			0.741150i
$134$	1317.65			0.849459
$135$		0			0
$136$	−652.098			−0.411154
$137$		−	2176.47i		−	1.35729i	−0.734467	−	0.678645i	$-0.762568\pi$
$137$		−	2176.47i		−	1.35729i	0.734467	−	0.678645i	$-0.237432\pi$
$138$		0			0
$139$	−469.168			−0.286290			−0.143145	−	0.989702i	$-0.545722\pi$
$139$	−469.168			−0.286290			−0.143145	+	0.989702i	$0.545722\pi$
$140$	−2206.09	+	632.179i	−1.33178	+	0.381635i
$141$		0			0
$142$			3358.36i			1.98470i
$143$			94.4546i			0.0552356i
$144$		0			0
$145$	648.262	+	2262.22i	0.371277	+	1.29563i
$146$	196.760			0.111534
$147$		0			0
$148$			4123.68i			2.29030i
$149$	1451.75			0.798201			0.399101	−	0.916907i	$-0.369322\pi$
$149$	1451.75			0.798201			0.399101	+	0.916907i	$0.369322\pi$
$150$		0			0
$151$	1055.40			0.568789			0.284395	−	0.958707i	$-0.408207\pi$
$151$	1055.40			0.568789			0.284395	+	0.958707i	$0.408207\pi$
$152$			1766.45i			0.942621i
$153$		0			0
$154$	−519.358			−0.271760
$155$	−14.1699	−	49.4483i	−0.00734295	−	0.0256244i
$156$		0			0
$157$			435.872i			0.221569i	0.993844	+	0.110785i	$0.0353364\pi$
$157$			435.872i			0.221569i	−0.993844	+	0.110785i	$0.964664\pi$
$158$			2242.28i			1.12903i
$159$		0			0
$160$	1814.11	−	519.851i	0.896360	−	0.256862i
$161$	−3079.01			−1.50721
$162$		0			0
$163$		−	3289.27i		−	1.58059i	−0.612729	−	0.790293i	$-0.709928\pi$
$163$		−	3289.27i		−	1.58059i	0.612729	−	0.790293i	$-0.290072\pi$
$164$	3523.03			1.67745
$165$		0			0
$166$	−1196.91			−0.559629
$167$			1417.63i			0.656882i	0.944525	+	0.328441i	$0.106523\pi$
$167$			1417.63i			0.656882i	−0.944525	+	0.328441i	$0.893477\pi$
$168$		0			0
$169$	−169.000			−0.0769231
$170$	383.903	+	1339.69i	0.173200	+	0.604410i
$171$		0			0
$172$			4631.96i			2.05339i
$173$			3327.52i			1.46235i	0.682191	+	0.731174i	$0.261027\pi$
$173$			3327.52i			1.46235i	−0.682191	+	0.731174i	$0.738973\pi$
$174$		0			0
$175$	1027.02	+	1644.83i	0.443631	+	0.710498i
$176$	−37.9306			−0.0162450
$177$		0			0
$178$		−	331.403i		−	0.139549i
$179$	−3853.95			−1.60926			−0.804630	−	0.593777i	$-0.797636\pi$
$179$	−3853.95			−1.60926			−0.804630	+	0.593777i	$0.797636\pi$
$180$		0			0
$181$	−1552.03			−0.637355			−0.318678	−	0.947863i	$-0.603239\pi$
$181$	−1552.03			−0.637355			−0.318678	+	0.947863i	$0.603239\pi$
$182$		−	929.246i		−	0.378463i
$183$		0			0
$184$	−4784.44			−1.91692
$185$	3349.61	−	959.866i	1.33118	−	0.381463i
$186$		0			0
$187$			196.552i			0.0768625i
$188$		−	1178.78i		−	0.457296i
$189$		0			0
$190$	3629.06	−	1039.95i	1.38568	−	0.397082i
$191$	2054.01			0.778129			0.389065	−	0.921210i	$-0.372798\pi$
$191$	2054.01			0.778129			0.389065	+	0.921210i	$0.372798\pi$
$192$		0			0
$193$		−	2971.10i		−	1.10810i	−0.832482	−	0.554052i	$-0.813081\pi$
$193$		−	2971.10i		−	1.10810i	0.832482	−	0.554052i	$-0.186919\pi$
$194$	4395.15			1.62656
$195$		0			0
$196$	−1354.18			−0.493507
$197$		−	4538.98i		−	1.64157i	−0.571239	−	0.820784i	$-0.693537\pi$
$197$		−	4538.98i		−	1.64157i	0.571239	−	0.820784i	$-0.306463\pi$
$198$		0			0
$199$	−2664.57			−0.949177			−0.474588	−	0.880208i	$-0.657403\pi$
$199$	−2664.57			−0.949177			−0.474588	+	0.880208i	$0.657403\pi$
$200$	1595.87	+	2555.87i	0.564226	+	0.903637i
$201$		0			0
$202$			2450.98i			0.853713i
$203$		−	3265.23i		−	1.12894i
$204$		0			0
$205$	−820.053	−	2861.71i	−0.279390	−	0.974978i
$206$	−6530.60			−2.20878
$207$		0			0
$208$		−	67.8662i		−	0.0226234i
$209$	532.435			0.176217
$210$		0			0
$211$	3958.31			1.29148			0.645738	−	0.763559i	$-0.276550\pi$
$211$	3958.31			1.29148			0.645738	+	0.763559i	$0.276550\pi$
$212$		−	5419.60i		−	1.75575i
$213$		0			0
$214$	−583.388			−0.186353
$215$	3762.47	−	1078.18i	1.19348	−	0.342005i
$216$		0			0
$217$			71.3725i			0.0223275i
$218$		−	1941.67i		−	0.603239i
$219$		0			0
$220$	296.090	+	1033.25i	0.0907380	+	0.316645i
$221$	−351.674			−0.107041
$222$		0			0
$223$		−	5306.39i		−	1.59346i	−0.604334	−	0.796731i	$-0.706561\pi$
$223$		−	5306.39i		−	1.59346i	0.604334	−	0.796731i	$-0.293439\pi$
$224$	−2618.43			−0.781034
$225$		0			0
$226$	−8211.01			−2.41676
$227$		−	4651.05i		−	1.35992i	−0.733251	−	0.679958i	$-0.761998\pi$
$227$		−	4651.05i		−	1.35992i	0.733251	−	0.679958i	$-0.238002\pi$
$228$		0			0
$229$	−211.979			−0.0611702			−0.0305851	−	0.999532i	$-0.509737\pi$
$229$	−211.979			−0.0611702			−0.0305851	+	0.999532i	$0.509737\pi$
$230$	2816.69	+	9829.31i	0.807509	+	2.81794i
$231$		0			0
$232$		−	5073.79i		−	1.43582i
$233$		−	2907.23i		−	0.817420i	−0.912664	−	0.408710i	$-0.865979\pi$
$233$		−	2907.23i		−	0.817420i	0.912664	−	0.408710i	$-0.134021\pi$
$234$		0			0
$235$	−957.510	+	274.385i	−0.265792	+	0.0761655i
$236$	914.596			0.252267
$237$		0			0
$238$		−	1933.68i		−	0.526646i
$239$	1656.44			0.448310			0.224155	−	0.974554i	$-0.428038\pi$
$239$	1656.44			0.448310			0.224155	+	0.974554i	$0.428038\pi$
$240$		0			0
$241$	−731.123			−0.195418			−0.0977091	−	0.995215i	$-0.531151\pi$
$241$	−731.123			−0.195418			−0.0977091	+	0.995215i	$0.531151\pi$
$242$		−	5889.69i		−	1.56448i
$243$		0			0
$244$	9337.75			2.44995
$245$	315.212	+	1099.98i	0.0821966	+	0.286838i
$246$		0			0
$247$			952.642i			0.245406i
$248$			110.905i			0.0283970i
$249$		0			0
$250$	4311.35	−	4783.31i	1.09069	−	1.21009i
$251$	−3711.12			−0.933242			−0.466621	−	0.884457i	$-0.654529\pi$
$251$	−3711.12			−0.933242			−0.466621	+	0.884457i	$0.654529\pi$
$252$		0			0
$253$			1442.10i			0.358355i
$254$	10728.2			2.65019
$255$		0			0
$256$	−4621.34			−1.12826
$257$		−	4243.03i		−	1.02986i	−0.857233	−	0.514928i	$-0.827818\pi$
$257$		−	4243.03i		−	1.02986i	0.857233	−	0.514928i	$-0.172182\pi$
$258$		0			0
$259$	−4834.74			−1.15991
$260$	−1848.72	+	529.769i	−0.440971	+	0.126365i
$261$		0			0
$262$		−	9381.68i		−	2.21222i
$263$		−	4234.49i		−	0.992813i	−0.868090	−	0.496407i	$-0.834652\pi$
$263$		−	4234.49i		−	0.992813i	0.868090	−	0.496407i	$-0.165348\pi$
$264$		0			0
$265$	−4402.26	+	1261.52i	−1.02049	+	0.292431i
$266$	−5238.10			−1.20740
$267$		0			0
$268$			3783.71i			0.862414i
$269$	−2511.08			−0.569156			−0.284578	−	0.958653i	$-0.591854\pi$
$269$	−2511.08			−0.569156			−0.284578	+	0.958653i	$0.591854\pi$
$270$		0			0
$271$	16.4711			0.00369207			0.00184604	−	0.999998i	$-0.499412\pi$
$271$	16.4711			0.00369207			0.00184604	+	0.999998i	$0.499412\pi$
$272$		−	141.224i		−	0.0314814i
$273$		0			0
$274$	10028.7			2.21115
$275$	770.377	−	481.019i	0.168929	−	0.105478i
$276$		0			0
$277$			5246.31i			1.13798i	0.822345	+	0.568990i	$0.192666\pi$
$277$			5246.31i			1.13798i	−0.822345	+	0.568990i	$0.807334\pi$
$278$		−	2161.81i		−	0.466392i
$279$		0			0
$280$	−1151.72	−	4019.12i	−0.245816	−	0.857815i
$281$	−2303.88			−0.489104			−0.244552	−	0.969636i	$-0.578641\pi$
$281$	−2303.88			−0.489104			−0.244552	+	0.969636i	$0.578641\pi$
$282$		0			0
$283$		−	7433.79i		−	1.56146i	−0.624869	−	0.780730i	$-0.714847\pi$
$283$		−	7433.79i		−	1.56146i	0.624869	−	0.780730i	$-0.285153\pi$
$284$	−9643.76			−2.01497
$285$		0			0
$286$	−435.225			−0.0899838
$287$			4130.52i			0.849536i
$288$		0			0
$289$	4181.20			0.851048
$290$	−10423.8	+	2987.04i	−2.11070	+	0.604844i
$291$		0			0
$292$			565.008i			0.113235i
$293$			2524.65i			0.503384i	0.967807	+	0.251692i	$0.0809870\pi$
$293$			2524.65i			0.503384i	−0.967807	+	0.251692i	$0.919013\pi$
$294$		0			0
$295$	−212.890	−	742.914i	−0.0420167	−	0.146624i
$296$	−7512.63			−1.47521
$297$		0			0
$298$			6689.32i			1.30034i
$299$	−2580.23			−0.499058
$300$		0			0
$301$	−5430.66			−1.03993
$302$			4863.03i			0.926609i
$303$		0			0
$304$	−382.557			−0.0721749
$305$	−2173.54	−	7584.93i	−0.408054	−	1.42397i
$306$		0			0
$307$		−	5733.57i		−	1.06590i	−0.846146	−	0.532951i	$-0.821083\pi$
$307$		−	5733.57i		−	1.06590i	0.846146	−	0.532951i	$-0.178917\pi$
$308$		−	1491.37i		−	0.275905i
$309$		0			0
$310$	227.846	−	65.2917i	0.0417445	−	0.0119623i
$311$	3971.45			0.724117			0.362058	−	0.932155i	$-0.382074\pi$
$311$	3971.45			0.724117			0.362058	+	0.932155i	$0.382074\pi$
$312$		0			0
$313$			1184.44i			0.213893i	0.994265	+	0.106947i	$0.0341074\pi$
$313$			1184.44i			0.213893i	−0.994265	+	0.106947i	$0.965893\pi$
$314$	−2008.40			−0.360956
$315$		0			0
$316$	−6438.86			−1.14625
$317$			7759.96i			1.37490i	0.726232	+	0.687449i	$0.241270\pi$
$317$			7759.96i			1.37490i	−0.726232	+	0.687449i	$0.758730\pi$
$318$		0			0
$319$	−1529.31			−0.268417
$320$	2523.98	+	8807.84i	0.440921	+	1.53867i
$321$		0			0
$322$		−	14187.4i		−	2.45538i
$323$			1982.36i			0.341491i
$324$		0			0
$325$	860.648	+	1378.37i	0.146893	+	0.235256i
$326$	15156.2			2.57492
$327$		0			0
$328$			6418.35i			1.08047i
$329$	1382.05			0.231595
$330$		0			0
$331$	−2742.15			−0.455353			−0.227677	−	0.973737i	$-0.573113\pi$
$331$	−2742.15			−0.455353			−0.227677	+	0.973737i	$0.573113\pi$
$332$		−	3437.01i		−	0.568164i
$333$		0			0
$334$	−6532.09			−1.07012
$335$	3073.46	−	880.731i	0.501256	−	0.143640i
$336$		0			0
$337$			8277.10i			1.33793i	0.743294	+	0.668965i	$0.233263\pi$
$337$			8277.10i			1.33793i	−0.743294	+	0.668965i	$0.766737\pi$
$338$		−	778.712i		−	0.125315i
$339$		0			0
$340$	−3847.01	+	1102.40i	−0.613628	+	0.175842i
$341$	33.4282			0.00530862
$342$		0			0
$343$		−	6908.66i		−	1.08756i
$344$	−8438.62			−1.32262
$345$		0			0
$346$	−15332.4			−2.38230
$347$		−	6827.30i		−	1.05622i	−0.849176	−	0.528110i	$-0.822901\pi$
$347$		−	6827.30i		−	1.05622i	0.849176	−	0.528110i	$-0.177099\pi$
$348$		0			0
$349$	−11728.9			−1.79895			−0.899474	−	0.436975i	$-0.856050\pi$
$349$	−11728.9			−1.79895			−0.899474	+	0.436975i	$0.856050\pi$
$350$	−7578.97	+	4732.27i	−1.15747	+	0.722716i
$351$		0			0
$352$			1226.38i			0.185699i
$353$		−	2260.06i		−	0.340767i	−0.985378	−	0.170384i	$-0.945499\pi$
$353$		−	2260.06i		−	0.340767i	0.985378	−	0.170384i	$-0.0545007\pi$
$354$		0			0
$355$	2244.77	+	7833.49i	0.335606	+	1.17115i
$356$	951.646			0.141677
$357$		0			0
$358$		−	17758.1i		−	2.62163i
$359$	5043.28			0.741432			0.370716	−	0.928746i	$-0.379112\pi$
$359$	5043.28			0.741432			0.370716	+	0.928746i	$0.379112\pi$
$360$		0			0
$361$	−1489.02			−0.217090
$362$		−	7151.38i		−	1.03831i
$363$		0			0
$364$	2668.39			0.384235
$365$	458.948	−	131.516i	0.0658149	−	0.0188600i
$366$		0			0
$367$		−	8537.90i		−	1.21437i	−0.794559	−	0.607186i	$-0.792298\pi$
$367$		−	8537.90i		−	1.21437i	0.794559	−	0.607186i	$-0.207702\pi$
$368$		−	1036.16i		−	0.146775i
$369$		0			0
$370$	4422.83	+	15434.2i	0.621438	+	2.16861i
$371$	6354.12			0.889190
$372$		0			0
$373$			12709.6i			1.76429i	0.470981	+	0.882143i	$0.343900\pi$
$373$			12709.6i			1.76429i	−0.470981	+	0.882143i	$0.656100\pi$
$374$	−905.664			−0.125216
$375$		0			0
$376$	2147.54			0.294550
$377$		−	2736.27i		−	0.373807i
$378$		0			0
$379$	−235.876			−0.0319687			−0.0159844	−	0.999872i	$-0.505088\pi$
$379$	−235.876			−0.0319687			−0.0159844	+	0.999872i	$0.505088\pi$
$380$	2986.27	+	10421.1i	0.403138	+	1.40682i
$381$		0			0
$382$			9464.38i			1.26764i
$383$			8586.76i			1.14560i	0.819697	+	0.572798i	$0.194142\pi$
$383$			8586.76i			1.14560i	−0.819697	+	0.572798i	$0.805858\pi$
$384$		0			0
$385$	−1211.42	+	347.145i	−0.160363	+	0.0459537i
$386$	13690.1			1.80520
$387$		0			0
$388$			12621.0i			1.65137i
$389$	−3296.96			−0.429723			−0.214862	−	0.976645i	$-0.568930\pi$
$389$	−3296.96			−0.429723			−0.214862	+	0.976645i	$0.568930\pi$
$390$		0			0
$391$	−5369.23			−0.694459
$392$		−	2467.09i		−	0.317874i
$393$		0			0
$394$	20914.5			2.67426
$395$	1498.77	+	5230.20i	0.190914	+	0.666227i
$396$		0			0
$397$			4730.33i			0.598006i	0.954252	+	0.299003i	$0.0966541\pi$
$397$			4730.33i			0.598006i	−0.954252	+	0.299003i	$0.903346\pi$
$398$		−	12277.7i		−	1.54630i
$399$		0			0
$400$	−553.520	+	345.615i	−0.0691900	+	0.0432018i
$401$	−12626.0			−1.57235			−0.786177	−	0.618002i	$-0.787943\pi$
$401$	−12626.0			−1.57235			−0.786177	+	0.618002i	$0.787943\pi$
$402$		0			0
$403$			59.8104i			0.00739298i
$404$	−7038.14			−0.866734
$405$		0			0
$406$	15045.4			1.83914
$407$			2264.42i			0.275781i
$408$		0			0
$409$	−7326.05			−0.885697			−0.442848	−	0.896597i	$-0.646032\pi$
$409$	−7326.05			−0.885697			−0.442848	+	0.896597i	$0.646032\pi$
$410$	13186.1	−	3778.61i	1.58833	−	0.455152i
$411$		0			0
$412$		−	18753.1i		−	2.24247i
$413$			1072.30i			0.127759i
$414$		0			0
$415$	−2791.83	+	800.030i	−0.330231	+	0.0946311i
$416$	−2194.26			−0.258612
$417$		0			0
$418$			2453.33i			0.287073i
$419$	10595.9			1.23542			0.617712	−	0.786404i	$-0.288060\pi$
$419$	10595.9			1.23542			0.617712	+	0.786404i	$0.288060\pi$
$420$		0			0
$421$	13411.1			1.55253			0.776266	−	0.630406i	$-0.217112\pi$
$421$	13411.1			1.55253			0.776266	+	0.630406i	$0.217112\pi$
$422$			18239.0i			2.10393i
$423$		0			0
$424$	9873.57			1.13090
$425$	1790.93	+	2868.27i	0.204407	+	0.327368i
$426$		0			0
$427$			10947.9i			1.24076i
$428$		−	1675.24i		−	0.189195i
$429$		0			0
$430$	4967.98	+	17336.6i	0.557157	+	1.94429i
$431$	−3483.79			−0.389347			−0.194673	−	0.980868i	$-0.562365\pi$
$431$	−3483.79			−0.389347			−0.194673	+	0.980868i	$0.562365\pi$
$432$		0			0
$433$		−	7229.81i		−	0.802407i	−0.915989	−	0.401204i	$-0.868592\pi$
$433$		−	7229.81i		−	0.802407i	0.915989	−	0.401204i	$-0.131408\pi$
$434$	−328.867			−0.0363736
$435$		0			0
$436$	5575.62			0.612439
$437$			14544.6i			1.59213i
$438$		0			0
$439$	2991.18			0.325196			0.162598	−	0.986692i	$-0.448013\pi$
$439$	2991.18			0.325196			0.162598	+	0.986692i	$0.448013\pi$
$440$	−1882.41	+	539.424i	−0.203955	+	0.0584455i
$441$		0			0
$442$		−	1620.43i		−	0.174380i
$443$			9683.42i			1.03854i	0.854610	+	0.519270i	$0.173796\pi$
$443$			9683.42i			1.03854i	−0.854610	+	0.519270i	$0.826204\pi$
$444$		0			0
$445$	−221.514	−	773.009i	−0.0235972	−	0.0823464i
$446$	24450.6			2.59589
$447$		0			0
$448$		−	12713.0i		−	1.34070i
$449$	−13916.7			−1.46273			−0.731367	−	0.681984i	$-0.761117\pi$
$449$	−13916.7			−1.46273			−0.731367	+	0.681984i	$0.761117\pi$
$450$		0			0
$451$	1934.58			0.201987
$452$		−	23578.5i		−	2.45362i
$453$		0			0
$454$	21430.9			2.21543
$455$	−621.119	−	2167.50i	−0.0639967	−	0.223327i
$456$		0			0
$457$			11538.4i			1.18106i	0.807016	+	0.590529i	$0.201081\pi$
$457$			11538.4i			1.18106i	−0.807016	+	0.590529i	$0.798919\pi$
$458$		−	976.750i		−	0.0996518i
$459$		0			0
$460$	−28225.5	+	8088.31i	−2.86091	+	0.819825i
$461$	−5478.18			−0.553458			−0.276729	−	0.960948i	$-0.589250\pi$
$461$	−5478.18			−0.553458			−0.276729	+	0.960948i	$0.589250\pi$
$462$		0			0
$463$			14242.4i			1.42959i	0.699333	+	0.714796i	$0.253480\pi$
$463$			14242.4i			1.42959i	−0.699333	+	0.714796i	$0.746520\pi$
$464$	1098.82			0.109938
$465$		0			0
$466$	13395.8			1.33165
$467$			17956.2i			1.77926i	0.456685	+	0.889629i	$0.349037\pi$
$467$			17956.2i			1.77926i	−0.456685	+	0.889629i	$0.650963\pi$
$468$		0			0
$469$	−4436.15			−0.436764
$470$	−1264.30	−	4411.98i	−0.124080	−	0.432999i
$471$		0			0
$472$			1666.24i			0.162489i
$473$			2543.52i			0.247254i
$474$		0			0
$475$	7769.80	−	4851.42i	0.750532	−	0.468628i
$476$	5552.68			0.534678
$477$		0			0
$478$			7632.47i			0.730337i
$479$	−19663.3			−1.87566			−0.937830	−	0.347096i	$-0.887168\pi$
$479$	−19663.3			−1.87566			−0.937830	+	0.347096i	$0.887168\pi$
$480$		0			0
$481$	−4051.53			−0.384062
$482$		−	3368.84i		−	0.318354i
$483$		0			0
$484$	16912.6			1.58834
$485$	10251.8	−	2937.77i	0.959817	−	0.275046i
$486$		0			0
$487$		−	14318.4i		−	1.33229i	−0.745821	−	0.666147i	$-0.767942\pi$
$487$		−	14318.4i		−	1.33229i	0.745821	−	0.666147i	$-0.232058\pi$
$488$			17011.8i			1.57805i
$489$		0			0
$490$	−5068.47	+	1452.42i	−0.467286	+	0.133906i
$491$	−16948.2			−1.55776			−0.778880	−	0.627172i	$-0.784212\pi$
$491$	−16948.2			−1.55776			−0.778880	+	0.627172i	$0.784212\pi$
$492$		0			0
$493$		−	5693.94i		−	0.520167i
$494$	−4389.55			−0.399788
$495$		0			0
$496$	−24.0184			−0.00217431
$497$		−	11306.7i		−	1.02047i
$498$		0			0
$499$	−7039.18			−0.631497			−0.315749	−	0.948843i	$-0.602256\pi$
$499$	−7039.18			−0.631497			−0.315749	+	0.948843i	$0.602256\pi$
$500$	13735.6	+	12380.3i	1.22855	+	1.10733i
$501$		0			0
$502$		−	17100.0i		−	1.52034i
$503$		−	18039.0i		−	1.59905i	−0.600636	−	0.799523i	$-0.705086\pi$
$503$		−	18039.0i		−	1.59905i	0.600636	−	0.799523i	$-0.294914\pi$
$504$		0			0
$505$	1638.26	+	5716.98i	0.144360	+	0.503767i
$506$	−6644.85			−0.583793
$507$		0			0
$508$			30806.7i			2.69061i
$509$	15072.8			1.31256			0.656278	−	0.754519i	$-0.272130\pi$
$509$	15072.8			1.31256			0.656278	+	0.754519i	$0.272130\pi$
$510$		0			0
$511$	−662.434			−0.0573471
$512$		−	1887.90i		−	0.162957i
$513$		0			0
$514$	19550.9			1.67773
$515$	−15232.8	+	4365.13i	−1.30338	+	0.373497i
$516$		0			0
$517$		−	647.300i		−	0.0550642i
$518$		−	22277.3i		−	1.88960i
$519$		0			0
$520$	−965.147	−	3368.04i	−0.0813933	−	0.284035i
$521$	15226.2			1.28037			0.640183	−	0.768223i	$-0.278859\pi$
$521$	15226.2			1.28037			0.640183	+	0.768223i	$0.278859\pi$
$522$		0			0
$523$			11261.4i			0.941545i	0.882255	+	0.470773i	$0.156025\pi$
$523$			11261.4i			0.941545i	−0.882255	+	0.470773i	$0.843975\pi$
$524$	26940.1			2.24596
$525$		0			0
$526$	19511.5			1.61738
$527$			124.460i			0.0102876i
$528$		0			0
$529$	−27226.9			−2.23777
$530$	−5812.77	−	20284.6i	−0.476397	−	1.66247i
$531$		0			0
$532$		−	15041.5i		−	1.22581i
$533$			3461.39i			0.281294i
$534$		0			0
$535$	−1360.77	+	389.943i	−0.109965	+	0.0315116i
$536$	−6893.27			−0.555492
$537$		0			0
$538$		−	11570.5i		−	0.927208i
$539$	−743.616			−0.0594245
$540$		0			0
$541$	340.898			0.0270912			0.0135456	−	0.999908i	$-0.495688\pi$
$541$	340.898			0.0270912			0.0135456	+	0.999908i	$0.495688\pi$
$542$			75.8952i			0.00601472i
$543$		0			0
$544$	−4566.06			−0.359868
$545$	−1297.83	−	4529.00i	−0.102006	−	0.355965i
$546$		0			0
$547$			9854.49i			0.770288i	0.922856	+	0.385144i	$0.125848\pi$
$547$			9854.49i			0.770288i	−0.922856	+	0.385144i	$0.874152\pi$
$548$			28798.0i			2.24487i
$549$		0			0
$550$	2216.42	+	3549.71i	0.171834	+	0.275201i
$551$	−15424.2			−1.19255
$552$		0			0
$553$		−	7549.14i		−	0.580510i
$554$	−24173.8			−1.85387
$555$		0			0
$556$	6207.79			0.473505
$557$		−	24514.0i		−	1.86479i	−0.361436	−	0.932397i	$-0.617713\pi$
$557$		−	24514.0i		−	1.86479i	0.361436	−	0.932397i	$-0.382287\pi$
$558$		0			0
$559$	−4550.92			−0.344335
$560$	870.412	−	249.426i	0.0656815	−	0.0188217i
$561$		0			0
$562$		−	10615.7i		−	0.796794i
$563$			25586.8i			1.91537i	0.287815	+	0.957686i	$0.407071\pi$
$563$			25586.8i			1.91537i	−0.287815	+	0.957686i	$0.592929\pi$
$564$		0			0
$565$	−19152.5	+	5488.34i	−1.42611	+	0.408666i
$566$	34253.2			2.54376
$567$		0			0
$568$		−	17569.3i		−	1.29787i
$569$	−19238.6			−1.41744			−0.708720	−	0.705490i	$-0.750727\pi$
$569$	−19238.6			−1.41744			−0.708720	+	0.705490i	$0.750727\pi$
$570$		0			0
$571$	15889.4			1.16453			0.582267	−	0.812998i	$-0.302166\pi$
$571$	15889.4			1.16453			0.582267	+	0.812998i	$0.302166\pi$
$572$		−	1249.78i		−	0.0913562i
$573$		0			0
$574$	−19032.5			−1.38397
$575$	13140.0	+	21044.5i	0.953005	+	1.52629i
$576$		0			0
$577$		−	25125.7i		−	1.81282i	−0.422401	−	0.906409i	$-0.638813\pi$
$577$		−	25125.7i		−	1.81282i	0.422401	−	0.906409i	$-0.361187\pi$
$578$			19266.0i			1.38643i
$579$		0			0
$580$	−8577.47	−	29932.5i	−0.614069	−	2.14290i
$581$	4029.66			0.287743
$582$		0			0
$583$		−	2976.04i		−	0.211415i
$584$	−1029.35			−0.0729361
$585$		0			0
$586$	−11633.0			−0.820058
$587$			12738.4i			0.895691i	0.894111	+	0.447846i	$0.147809\pi$
$587$			12738.4i			0.895691i	−0.894111	+	0.447846i	$0.852191\pi$
$588$		0			0
$589$	337.148			0.0235856
$590$	3423.17	−	980.946i	0.238864	−	0.0684490i
$591$		0			0
$592$		−	1626.99i		−	0.112955i
$593$			6645.07i			0.460169i	0.973171	+	0.230085i	$0.0739003\pi$
$593$			6645.07i			0.460169i	−0.973171	+	0.230085i	$0.926100\pi$
$594$		0			0
$595$	−1292.49	−	4510.37i	−0.0890539	−	0.310768i
$596$	−19208.8			−1.32017
$597$		0			0
$598$		−	11889.1i		−	0.813011i
$599$	593.901			0.0405111			0.0202555	−	0.999795i	$-0.493552\pi$
$599$	593.901			0.0405111			0.0202555	+	0.999795i	$0.493552\pi$
$600$		0			0
$601$	25783.8			1.74999			0.874995	−	0.484131i	$-0.160864\pi$
$601$	25783.8			1.74999			0.874995	+	0.484131i	$0.160864\pi$
$602$		−	25023.2i		−	1.69414i
$603$		0			0
$604$	−13964.5			−0.940741
$605$	−3936.74	−	13737.9i	−0.264547	−	0.923181i
$606$		0			0
$607$			13616.8i			0.910524i	0.890357	+	0.455262i	$0.150454\pi$
$607$			13616.8i			0.910524i	−0.890357	+	0.455262i	$0.849546\pi$
$608$			12368.9i			0.825041i
$609$		0			0
$610$	34949.6	−	10015.2i	2.31978	−	0.664758i
$611$	1158.16			0.0766844
$612$		0			0
$613$		−	8294.23i		−	0.546494i	−0.961944	−	0.273247i	$-0.911902\pi$
$613$		−	8294.23i		−	0.546494i	0.961944	−	0.273247i	$-0.0880976\pi$
$614$	26418.9			1.73645
$615$		0			0
$616$	2717.02			0.177714
$617$		−	24173.6i		−	1.57730i	−0.614845	−	0.788648i	$-0.710781\pi$
$617$		−	24173.6i		−	1.57730i	0.614845	−	0.788648i	$-0.289219\pi$
$618$		0			0
$619$	19579.7			1.27137			0.635684	−	0.771950i	$-0.280718\pi$
$619$	19579.7			1.27137			0.635684	+	0.771950i	$0.280718\pi$
$620$	187.489	+	654.275i	0.0121448	+	0.0423812i
$621$		0			0
$622$			18299.5i			1.17965i
$623$			1115.74i			0.0717516i
$624$		0			0
$625$	6859.14	−	14039.0i	0.438985	−	0.898494i
$626$	−5457.62			−0.348451
$627$		0			0
$628$		−	5767.24i		−	0.366462i
$629$	−8430.88			−0.534438
$630$		0			0
$631$	23156.0			1.46090			0.730449	−	0.682967i	$-0.239311\pi$
$631$	23156.0			1.46090			0.730449	+	0.682967i	$0.239311\pi$
$632$		−	11730.5i		−	0.738313i
$633$		0			0
$634$	−35756.1			−2.23983
$635$	25023.9	−	7170.86i	1.56385	−	0.448137i
$636$		0			0
$637$		−	1330.49i		−	0.0827566i
$638$		−	7046.71i		−	0.437276i
$639$		0			0
$640$	−26071.6	+	7471.09i	−1.61027	+	0.461439i
$641$	17175.7			1.05835			0.529173	−	0.848514i	$-0.322502\pi$
$641$	17175.7			1.05835			0.529173	+	0.848514i	$0.322502\pi$
$642$		0			0
$643$			22948.5i			1.40747i	0.710464	+	0.703734i	$0.248485\pi$
$643$			22948.5i			1.40747i	−0.710464	+	0.703734i	$0.751515\pi$
$644$	40740.0			2.49282
$645$		0			0
$646$	−9134.27			−0.556320
$647$		−	2612.89i		−	0.158768i	−0.996844	−	0.0793842i	$-0.974705\pi$
$647$		−	2612.89i		−	0.158768i	0.996844	−	0.0793842i	$-0.0252954\pi$
$648$		0			0
$649$	502.227			0.0303762
$650$	−6351.21	+	3965.66i	−0.383254	+	0.239302i
$651$		0			0
$652$			43522.0i			2.61419i
$653$			18404.3i			1.10294i	0.834196	+	0.551468i	$0.185932\pi$
$653$			18404.3i			1.10294i	−0.834196	+	0.551468i	$0.814068\pi$
$654$		0			0
$655$	−6270.82	−	21883.1i	−0.374078	−	1.30541i
$656$	−1390.01			−0.0827298
$657$		0			0
$658$			6368.14i			0.377289i
$659$	−2276.60			−0.134573			−0.0672867	−	0.997734i	$-0.521434\pi$
$659$	−2276.60			−0.134573			−0.0672867	+	0.997734i	$0.521434\pi$
$660$		0			0
$661$	−12436.5			−0.731807			−0.365903	−	0.930653i	$-0.619240\pi$
$661$	−12436.5			−0.731807			−0.365903	+	0.930653i	$0.619240\pi$
$662$		−	12635.2i		−	0.741812i
$663$		0			0
$664$	6261.63			0.365962
$665$	−12218.0	+	3501.21i	−0.712474	+	0.204167i
$666$		0			0
$667$		−	41776.4i		−	2.42517i
$668$		−	18757.3i		−	1.08644i
$669$		0			0
$670$	4058.20	+	14161.8i	0.234003	+	0.816592i
$671$	5127.59			0.295005
$672$		0			0
$673$			27945.7i			1.60064i	0.599575	+	0.800319i	$0.295336\pi$
$673$			27945.7i			1.60064i	−0.599575	+	0.800319i	$0.704664\pi$
$674$	−38138.9			−2.17961
$675$		0			0
$676$	2236.12			0.127226
$677$		−	5001.39i		−	0.283928i	−0.989872	−	0.141964i	$-0.954658\pi$
$677$		−	5001.39i		−	0.283928i	0.989872	−	0.141964i	$-0.0453417\pi$
$678$		0			0
$679$	−14797.2			−0.836326
$680$	−2008.39	−	7008.59i	−0.113262	−	0.395246i
$681$		0			0
$682$			154.029i			0.00864823i
$683$			19835.3i			1.11124i	0.831437	+	0.555619i	$0.187519\pi$
$683$			19835.3i			1.11124i	−0.831437	+	0.555619i	$0.812481\pi$
$684$		0			0
$685$	23392.2	−	6703.29i	1.30477	−	0.373897i
$686$	31833.5			1.77173
$687$		0			0
$688$		−	1827.53i		−	0.101270i
$689$	5324.78			0.294424
$690$		0			0
$691$	18355.0			1.01050			0.505250	−	0.862973i	$-0.331400\pi$
$691$	18355.0			1.01050			0.505250	+	0.862973i	$0.331400\pi$
$692$		−	44028.0i		−	2.41863i
$693$		0			0
$694$	31458.6			1.72068
$695$	−1444.98	−	5042.50i	−0.0788652	−	0.275213i
$696$		0			0
$697$			7202.85i			0.391431i
$698$		−	54043.9i		−	2.93065i
$699$		0			0
$700$	−13589.0	−	21763.5i	−0.733738	−	1.17512i
$701$	4531.23			0.244140			0.122070	−	0.992521i	$-0.461047\pi$
$701$	4531.23			0.244140			0.122070	+	0.992521i	$0.461047\pi$
$702$		0			0
$703$			22838.2i			1.22526i
$704$	−5954.31			−0.318766
$705$		0			0
$706$	10413.8			0.555141
$707$		−	8251.75i		−	0.438952i
$708$		0			0
$709$	−11693.2			−0.619392			−0.309696	−	0.950836i	$-0.600227\pi$
$709$	−11693.2			−0.619392			−0.309696	+	0.950836i	$0.600227\pi$
$710$	−36094.9	+	10343.4i	−1.90791	+	0.546732i
$711$		0			0
$712$			1733.74i			0.0912563i
$713$			913.163i			0.0479638i
$714$		0			0
$715$	−1015.18	+	290.909i	−0.0530985	+	0.0152159i
$716$	50993.5			2.66161
$717$		0			0
$718$			23238.2i			1.20786i
$719$	−17181.6			−0.891190			−0.445595	−	0.895235i	$-0.647008\pi$
$719$	−17181.6			−0.891190			−0.445595	+	0.895235i	$0.647008\pi$
$720$		0			0
$721$	21986.7			1.13568
$722$		−	6861.04i		−	0.353659i
$723$		0			0
$724$	20535.6			1.05414
$725$	−22317.2	+	13934.7i	−1.14323	+	0.713824i
$726$		0			0
$727$		−	7061.52i		−	0.360244i	−0.983644	−	0.180122i	$-0.942351\pi$
$727$		−	7061.52i		−	0.360244i	0.983644	−	0.180122i	$-0.0576493\pi$
$728$			4861.34i			0.247491i
$729$		0			0
$730$	605.997	+	2114.72i	0.0307246	+	0.107218i
$731$	−9470.06			−0.479156
$732$		0			0
$733$		−	33615.1i		−	1.69386i	−0.531703	−	0.846931i	$-0.678448\pi$
$733$		−	33615.1i		−	1.69386i	0.531703	−	0.846931i	$-0.321552\pi$
$734$	39340.6			1.97832
$735$		0			0
$736$	−33501.1			−1.67781
$737$			2077.73i			0.103846i
$738$		0			0
$739$	20338.2			1.01238			0.506192	−	0.862421i	$-0.331053\pi$
$739$	20338.2			1.01238			0.506192	+	0.862421i	$0.331053\pi$
$740$	−44320.3	+	12700.5i	−2.20169	+	0.630916i
$741$		0			0
$742$			29278.3i			1.44857i
$743$			3421.96i			0.168963i	0.996425	+	0.0844815i	$0.0269234\pi$
$743$			3421.96i			0.168963i	−0.996425	+	0.0844815i	$0.973077\pi$
$744$		0			0
$745$	4471.22	+	15603.1i	0.219883	+	0.767318i
$746$	−58562.9			−2.87418
$747$		0			0
$748$		−	2600.67i		−	0.127126i
$749$	1964.10			0.0958168
$750$		0			0
$751$	9652.18			0.468992			0.234496	−	0.972117i	$-0.424656\pi$
$751$	9652.18			0.468992			0.234496	+	0.972117i	$0.424656\pi$
$752$			465.088i			0.0225532i
$753$		0			0
$754$	12608.1			0.608966
$755$	3250.51	+	11343.2i	0.156686	+	0.546782i
$756$		0			0
$757$		−	9943.18i		−	0.477399i	−0.971093	−	0.238700i	$-0.923279\pi$
$757$		−	9943.18i		−	0.477399i	0.971093	−	0.238700i	$-0.0767211\pi$
$758$		−	1086.86i		−	0.0520799i
$759$		0			0
$760$	−18985.4	+	5440.47i	−0.906150	+	0.259667i
$761$	19328.5			0.920704			0.460352	−	0.887736i	$-0.347723\pi$
$761$	19328.5			0.920704			0.460352	+	0.887736i	$0.347723\pi$
$762$		0			0
$763$			6537.04i			0.310166i
$764$	−27177.6			−1.28698
$765$		0			0
$766$	−39565.8			−1.86628
$767$			898.595i			0.0423030i
$768$		0			0
$769$	−29180.1			−1.36835			−0.684174	−	0.729319i	$-0.739837\pi$
$769$	−29180.1			−1.36835			−0.684174	+	0.729319i	$0.739837\pi$
$770$	−1599.56	−	5581.94i	−0.0748627	−	0.261246i
$771$		0			0
$772$			39312.0i			1.83273i
$773$		−	13489.9i		−	0.627684i	−0.949475	−	0.313842i	$-0.898384\pi$
$773$		−	13489.9i		−	0.627684i	0.949475	−	0.313842i	$-0.101616\pi$
$774$		0			0
$775$	487.817	−	304.590i	0.0226102	−	0.0141177i
$776$	−22993.2			−1.06367
$777$		0			0
$778$		−	15191.6i		−	0.700058i
$779$	19511.6			0.897403
$780$		0			0
$781$	−5295.63			−0.242628
$782$		−	24740.1i		−	1.13134i
$783$		0			0
$784$	534.292			0.0243391
$785$	−4684.65	+	1342.44i	−0.212996	+	0.0610364i
$786$		0			0
$787$			20683.4i			0.936829i	0.883509	+	0.468414i	$0.155175\pi$
$787$			20683.4i			0.936829i	−0.883509	+	0.468414i	$0.844825\pi$
$788$			60057.4i			2.71505i
$789$		0			0
$790$	−24099.5	+	6905.97i	−1.08534	+	0.311017i
$791$	27644.2			1.24262
$792$		0			0
$793$			9174.38i			0.410835i
$794$	−21796.2			−0.974206
$795$		0			0
$796$	35256.2			1.56988
$797$		−	708.657i		−	0.0314955i	−0.999876	−	0.0157478i	$-0.994987\pi$
$797$		−	708.657i		−	0.0314955i	0.999876	−	0.0157478i	$-0.00501288\pi$
$798$		0			0
$799$	2410.03			0.106709
$800$	11174.5	+	17896.5i	0.493846	+	0.790921i
$801$		0			0
$802$		−	58177.8i		−	2.56151i
$803$			310.260i			0.0136349i
$804$		0			0
$805$	−9483.01	−	33092.5i	−0.415195	−	1.44889i
$806$	−275.592			−0.0120438
$807$		0			0
$808$		−	12822.3i		−	0.558275i
$809$	30881.0			1.34205			0.671025	−	0.741435i	$-0.265854\pi$
$809$	30881.0			1.34205			0.671025	+	0.741435i	$0.265854\pi$
$810$		0			0
$811$	−5265.77			−0.227998			−0.113999	−	0.993481i	$-0.536366\pi$
$811$	−5265.77			−0.227998			−0.113999	+	0.993481i	$0.536366\pi$
$812$			43203.8i			1.86719i
$813$		0			0
$814$	−10433.9			−0.449272
$815$	35352.3	−	10130.6i	1.51943	−	0.435409i
$816$		0			0
$817$			25653.2i			1.09852i
$818$		−	33756.7i		−	1.44288i
$819$		0			0
$820$	10850.5	+	37864.7i	0.462094	+	1.61255i
$821$	2427.29			0.103183			0.0515915	−	0.998668i	$-0.483571\pi$
$821$	2427.29			0.103183			0.0515915	+	0.998668i	$0.483571\pi$
$822$		0			0
$823$		−	33181.6i		−	1.40539i	−0.711491	−	0.702696i	$-0.751980\pi$
$823$		−	33181.6i		−	1.40539i	0.711491	−	0.702696i	$-0.248020\pi$
$824$	34164.8			1.44440
$825$		0			0
$826$	−4940.92			−0.208131
$827$		−	18438.8i		−	0.775310i	−0.921805	−	0.387655i	$-0.873285\pi$
$827$		−	18438.8i		−	0.775310i	0.921805	−	0.387655i	$-0.126715\pi$
$828$		0			0
$829$	−19682.4			−0.824604			−0.412302	−	0.911047i	$-0.635275\pi$
$829$	−19682.4			−0.824604			−0.412302	+	0.911047i	$0.635275\pi$
$830$	−3686.35	−	12864.1i	−0.154163	−	0.537976i
$831$		0			0
$832$		−	10653.6i		−	0.443925i
$833$		−	2768.63i		−	0.115159i
$834$		0			0
$835$	−15236.3	+	4366.13i	−0.631466	+	0.180953i
$836$	−7044.91			−0.291451
$837$		0			0
$838$			48823.4i			2.01262i
$839$	29228.3			1.20271			0.601355	−	0.798982i	$-0.294628\pi$
$839$	29228.3			1.20271			0.601355	+	0.798982i	$0.294628\pi$
$840$		0			0
$841$	19913.9			0.816512
$842$			61795.1i			2.52921i
$843$		0			0
$844$	−52374.4			−2.13602
$845$	−520.500	−	1816.37i	−0.0211902	−	0.0739468i
$846$		0			0
$847$			19828.9i			0.804403i
$848$			2138.30i			0.0865914i
$849$		0			0
$850$	−13216.3	+	8252.20i	−0.533313	+	0.332998i
$851$	−61857.3			−2.49170
$852$		0			0
$853$			6132.64i			0.246163i	0.992397	+	0.123082i	$0.0392777\pi$
$853$			6132.64i			0.246163i	−0.992397	+	0.123082i	$0.960722\pi$
$854$	−50445.3			−2.02131
$855$		0			0
$856$	3051.99			0.121863
$857$			21620.7i			0.861784i	0.902404	+	0.430892i	$0.141801\pi$
$857$			21620.7i			0.861784i	−0.902404	+	0.430892i	$0.858199\pi$
$858$		0			0
$859$	−10726.9			−0.426073			−0.213037	−	0.977044i	$-0.568335\pi$
$859$	−10726.9			−0.426073			−0.213037	+	0.977044i	$0.568335\pi$
$860$	−49783.1	+	14265.9i	−1.97394	+	0.565654i
$861$		0			0
$862$		−	16052.5i		−	0.634281i
$863$			7036.86i			0.277564i	0.990323	+	0.138782i	$0.0443187\pi$
$863$			7036.86i			0.277564i	−0.990323	+	0.138782i	$0.955681\pi$
$864$		0			0
$865$	−35763.3	+	10248.4i	−1.40577	+	0.402838i
$866$	33313.3			1.30719
$867$		0			0
$868$		−	944.364i		−	0.0369284i
$869$	−3535.74			−0.138023
$870$		0			0
$871$	−3717.51			−0.144619
$872$			10157.8i			0.394480i
$873$		0			0
$874$	−67018.0			−2.59373
$875$	−14515.1	+	16104.0i	−0.560800	+	0.622190i
$876$		0			0
$877$			4785.61i			0.184263i	0.995747	+	0.0921315i	$0.0293680\pi$
$877$			4785.61i			0.184263i	−0.995747	+	0.0921315i	$0.970632\pi$
$878$			13782.6i			0.529774i
$879$		0			0
$880$	−116.822	−	407.669i	−0.00447507	−	0.0156165i
$881$	−32703.8			−1.25065			−0.625324	−	0.780365i	$-0.715033\pi$
$881$	−32703.8			−1.25065			−0.625324	+	0.780365i	$0.715033\pi$
$882$		0			0
$883$		−	14021.1i		−	0.534368i	−0.963645	−	0.267184i	$-0.913907\pi$
$883$		−	14021.1i		−	0.534368i	0.963645	−	0.267184i	$-0.0860932\pi$
$884$	4653.17			0.177040
$885$		0			0
$886$	−44618.9			−1.69188
$887$			22537.4i			0.853136i	0.904455	+	0.426568i	$0.140278\pi$
$887$			22537.4i			0.853136i	−0.904455	+	0.426568i	$0.859722\pi$
$888$		0			0
$889$	−36118.8			−1.36264
$890$	3561.84	−	1020.68i	0.134150	−	0.0384420i
$891$		0			0
$892$			70211.4i			2.63548i
$893$		−	6528.48i		−	0.244644i
$894$		0			0
$895$	−11869.7	−	41421.3i	−0.443308	−	1.54700i
$896$	37631.1			1.40309
$897$		0			0
$898$		−	64124.7i		−	2.38293i
$899$	−968.389			−0.0359261
$900$		0			0
$901$	11080.4			0.409702
$902$			8914.10i			0.329055i
$903$		0			0
$904$	42955.9			1.58041
$905$	−4780.06	−	16680.8i	−0.175574	−	0.612695i
$906$		0			0
$907$		−	23079.9i		−	0.844935i	−0.906378	−	0.422467i	$-0.861164\pi$
$907$		−	23079.9i		−	0.844935i	0.906378	−	0.422467i	$-0.138836\pi$
$908$			61540.3i			2.24921i
$909$		0			0
$910$	9987.31	−	2861.97i	0.363820	−	0.104256i
$911$	7039.90			0.256029			0.128014	−	0.991772i	$-0.459140\pi$
$911$	7039.90			0.256029			0.128014	+	0.991772i	$0.459140\pi$
$912$		0			0
$913$		−	1887.35i		−	0.0684141i
$914$	−53166.2			−1.92405
$915$		0			0
$916$	2804.80			0.101172
$917$			31585.5i			1.13745i
$918$		0			0
$919$	−19802.7			−0.710806			−0.355403	−	0.934713i	$-0.615656\pi$
$919$	−19802.7			−0.710806			−0.355403	+	0.934713i	$0.615656\pi$
$920$	−14735.5	−	51422.0i	−0.528060	−	1.84275i
$921$		0			0
$922$		−	25242.2i		−	0.901634i
$923$		−	9475.04i		−	0.337892i
$924$		0			0
$925$	20632.8	+	33044.5i	0.733408	+	1.17459i
$926$	−65625.7			−2.32893
$927$		0			0
$928$		−	35527.2i		−	1.25672i
$929$	33592.5			1.18636			0.593182	−	0.805068i	$-0.297871\pi$
$929$	33592.5			1.18636			0.593182	+	0.805068i	$0.297871\pi$
$930$		0			0
$931$	−7499.89			−0.264016
$932$			38467.0i			1.35196i
$933$		0			0
$934$	−82737.9			−2.89857
$935$	−2112.49	+	605.357i	−0.0738886	+	0.0211736i
$936$		0			0
$937$		−	47627.5i		−	1.66054i	−0.557365	−	0.830268i	$-0.688188\pi$
$937$		−	47627.5i		−	1.66054i	0.557365	−	0.830268i	$-0.311812\pi$
$938$		−	20440.7i		−	0.711528i
$939$		0			0
$940$	12669.3	−	3630.52i	0.439603	−	0.125973i
$941$	−12356.8			−0.428077			−0.214038	−	0.976825i	$-0.568662\pi$
$941$	−12356.8			−0.428077			−0.214038	+	0.976825i	$0.568662\pi$
$942$		0			0
$943$			52847.2i			1.82497i
$944$	−360.853			−0.0124415
$945$		0			0
$946$	−11719.9			−0.402800
$947$			17132.5i			0.587888i	0.955823	+	0.293944i	$0.0949680\pi$
$947$			17132.5i			0.587888i	−0.955823	+	0.293944i	$0.905032\pi$
$948$		0			0
$949$	−555.123			−0.0189885
$950$	22354.2	+	35801.4i	0.763438	+	1.22268i
$951$		0			0
$952$			10116.0i			0.344393i
$953$		−	18815.9i		−	0.639566i	−0.947491	−	0.319783i	$-0.896390\pi$
$953$		−	18815.9i		−	0.639566i	0.947491	−	0.319783i	$-0.103610\pi$
$954$		0			0
$955$	6326.10	+	22076.0i	0.214354	+	0.748022i
$956$	−21917.1			−0.741476
$957$		0			0
$958$		−	90604.0i		−	3.05562i
$959$	−33763.7			−1.13690
$960$		0			0
$961$	−29769.8			−0.999289
$962$		−	18668.5i		−	0.625673i
$963$		0			0
$964$	9673.85			0.323209
$965$	31932.6	−	9150.63i	1.06523	−	0.305253i
$966$		0			0
$967$		−	4660.19i		−	0.154976i	−0.996993	−	0.0774878i	$-0.975310\pi$
$967$		−	4660.19i		−	0.154976i	0.996993	−	0.0774878i	$-0.0246899\pi$
$968$			30811.9i			1.02307i
$969$		0			0
$970$	13536.5	+	47238.0i	0.448074	+	1.56363i
$971$	7114.83			0.235145			0.117572	−	0.993064i	$-0.462489\pi$
$971$	7114.83			0.235145			0.117572	+	0.993064i	$0.462489\pi$
$972$		0			0
$973$			7278.22i			0.239804i
$974$	65975.7			2.17043
$975$		0			0
$976$	−3684.20			−0.120828
$977$			6368.51i			0.208543i	0.994549	+	0.104272i	$0.0332511\pi$
$977$			6368.51i			0.208543i	−0.994549	+	0.104272i	$0.966749\pi$
$978$		0			0
$979$	522.573			0.0170597
$980$	−4170.73	−	14554.4i	−0.135948	−	0.474413i
$981$		0			0
$982$		−	78093.2i		−	2.53773i
$983$		−	19570.3i		−	0.634990i	−0.948260	−	0.317495i	$-0.897158\pi$
$983$		−	19570.3i		−	0.634990i	0.948260	−	0.317495i	$-0.102842\pi$
$984$		0			0
$985$	48783.8	−	13979.5i	1.57805	−	0.452208i
$986$	26236.3			0.847399
$987$		0			0
$988$		−	12604.9i		−	0.405885i
$989$	−69481.7			−2.23396
$990$		0			0
$991$	61858.8			1.98286			0.991428	−	0.130653i	$-0.0417072\pi$
$991$	61858.8			1.98286			0.991428	+	0.130653i	$0.0417072\pi$
$992$			776.566i			0.0248548i
$993$		0			0
$994$	52098.5			1.66244
$995$	−8206.56	−	28638.1i	−0.261473	−	0.912452i
$996$		0			0
$997$		−	14499.2i		−	0.460576i	−0.973123	−	0.230288i	$-0.926033\pi$
$997$		−	14499.2i		−	0.460576i	0.973123	−	0.230288i	$-0.0739668\pi$
$998$		−	32434.9i		−	1.02877i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.4.c.e.469.19		22
3.2	odd	2		195.4.c.c.79.4	✓	22
5.4	even	2	inner	585.4.c.e.469.4		22
15.2	even	4		975.4.a.bb.1.10		11
15.8	even	4		975.4.a.bc.1.2		11
15.14	odd	2		195.4.c.c.79.19	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.4.c.c.79.4	✓	22	3.2	odd	2
195.4.c.c.79.19	yes	22	15.14	odd	2
585.4.c.e.469.4		22	5.4	even	2	inner
585.4.c.e.469.19		22	1.1	even	1	trivial
975.4.a.bb.1.10		11	15.2	even	4
975.4.a.bc.1.2		11	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	585.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4.60776i q^{2} -13.2315 q^{4} +(3.07988 + 10.7478i) q^{5} -15.5130i q^{7} -24.1055i q^{8} +(-49.5231 + 14.1914i) q^{10} -7.26574 q^{11} -13.0000i q^{13} +71.4805 q^{14} +5.22048 q^{16} -27.0519i q^{17} -73.2802 q^{19} +(-40.7515 - 142.209i) q^{20} -33.4788i q^{22} -198.479i q^{23} +(-106.029 + 66.2037i) q^{25} +59.9009 q^{26} +205.261i q^{28} +210.483 q^{29} -4.60080 q^{31} -168.789i q^{32} +124.649 q^{34} +(166.730 - 47.7784i) q^{35} -311.656i q^{37} -337.658i q^{38} +(259.080 - 74.2421i) q^{40} -266.261 q^{41} -350.071i q^{43} +96.1366 q^{44} +914.545 q^{46} +89.0893i q^{47} +102.345 q^{49} +(-305.051 - 488.555i) q^{50} +172.009i q^{52} +409.598i q^{53} +(-22.3776 - 78.0904i) q^{55} -373.950 q^{56} +969.854i q^{58} -69.1227 q^{59} -705.722 q^{61} -21.1994i q^{62} +819.505 q^{64} +(139.721 - 40.0385i) q^{65} -285.963i q^{67} +357.936i q^{68} +(220.151 + 768.255i) q^{70} +728.849 q^{71} -42.7017i q^{73} +1436.04 q^{74} +969.606 q^{76} +112.714i q^{77} +486.631 q^{79} +(16.0785 + 56.1084i) q^{80} -1226.87i q^{82} +259.760i q^{83} +(290.747 - 83.3166i) q^{85} +1613.04 q^{86} +175.144i q^{88} -71.9228 q^{89} -201.670 q^{91} +2626.17i q^{92} -410.502 q^{94} +(-225.694 - 787.597i) q^{95} -953.857i q^{97} +471.584i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 110 q^{4} - 8 q^{5} - 58 q^{10} - 200 q^{11} + 300 q^{14} + 1022 q^{16} - 88 q^{19} + 296 q^{20} - 346 q^{25} - 78 q^{26} + 560 q^{29} + 512 q^{31} - 156 q^{34} - 36 q^{35} + 10 q^{40} - 1400 q^{41}+ \cdots - 2376 q^{95}+O(q^{100}) \) 22 * q - 110 * q^4 - 8 * q^5 - 58 * q^10 - 200 * q^11 + 300 * q^14 + 1022 * q^16 - 88 * q^19 + 296 * q^20 - 346 * q^25 - 78 * q^26 + 560 * q^29 + 512 * q^31 - 156 * q^34 - 36 * q^35 + 10 * q^40 - 1400 * q^41 + 3348 * q^44 + 1240 * q^46 - 3986 * q^49 - 2240 * q^50 + 2592 * q^55 - 2628 * q^56 + 3764 * q^59 + 2624 * q^61 - 9190 * q^64 - 390 * q^65 + 2776 * q^70 - 1580 * q^71 - 684 * q^74 - 1216 * q^76 - 3532 * q^79 - 7416 * q^80 + 620 * q^85 + 2664 * q^86 + 7288 * q^89 - 520 * q^91 - 13432 * q^94 - 2376 * q^95

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