LMFDB - Embedded newform 585.4.c.e.469.6

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)

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")

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);

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			469.6
Character	$\chi$	$=$	585.469
Dual form			585.4.c.e.469.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.05864i q^{2} -1.35528 q^{4} +(8.72741 - 6.98802i) q^{5} +23.3910i q^{7} -20.3238i q^{8} +(-21.3738 - 26.6940i) q^{10} -52.9131 q^{11} -13.0000i q^{13} +71.5447 q^{14} -73.0055 q^{16} +49.4789i q^{17} -70.9199 q^{19} +(-11.8281 + 9.47071i) q^{20} +161.842i q^{22} -38.3284i q^{23} +(27.3353 - 121.975i) q^{25} -39.7623 q^{26} -31.7014i q^{28} -104.897 q^{29} -280.737 q^{31} +60.7069i q^{32} +151.338 q^{34} +(163.457 + 204.143i) q^{35} +1.68968i q^{37} +216.918i q^{38} +(-142.023 - 177.374i) q^{40} -455.197 q^{41} -454.499i q^{43} +71.7120 q^{44} -117.233 q^{46} -565.411i q^{47} -204.140 q^{49} +(-373.076 - 83.6087i) q^{50} +17.6186i q^{52} -385.295i q^{53} +(-461.794 + 369.758i) q^{55} +475.395 q^{56} +320.841i q^{58} +270.279 q^{59} +563.622 q^{61} +858.674i q^{62} -398.363 q^{64} +(-90.8442 - 113.456i) q^{65} +620.293i q^{67} -67.0577i q^{68} +(624.400 - 499.956i) q^{70} -816.400 q^{71} +581.269i q^{73} +5.16813 q^{74} +96.1162 q^{76} -1237.69i q^{77} -493.473 q^{79} +(-637.148 + 510.163i) q^{80} +1392.28i q^{82} +495.056i q^{83} +(345.759 + 431.823i) q^{85} -1390.15 q^{86} +1075.40i q^{88} +901.129 q^{89} +304.083 q^{91} +51.9456i q^{92} -1729.39 q^{94} +(-618.946 + 495.589i) q^{95} +3.53365i q^{97} +624.390i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	3.05864i		−	1.08139i	−0.841218	−	0.540696i	$-0.818161\pi$
$2$		−	3.05864i		−	1.08139i	0.841218	−	0.540696i	$-0.181839\pi$
$3$		0			0
$3$		0			0
$4$	−1.35528			−0.169410
$5$	8.72741	−	6.98802i	0.780603	−	0.625027i
$5$	8.72741	−	6.98802i	0.780603	−	0.625027i
$6$		0			0
$7$			23.3910i			1.26300i	0.775377	+	0.631498i	$0.217560\pi$
$7$			23.3910i			1.26300i	−0.775377	+	0.631498i	$0.782440\pi$
$8$		−	20.3238i		−	0.898194i
$9$		0			0
$10$	−21.3738	−	26.6940i	−0.675900	−	0.844138i
$11$	−52.9131			−1.45035			−0.725177	−	0.688562i	$-0.758242\pi$
$11$	−52.9131			−1.45035			−0.725177	+	0.688562i	$0.758242\pi$
$12$		0			0
$13$		−	13.0000i		−	0.277350i
$13$		−	13.0000i		−	0.277350i
$14$	71.5447			1.36579
$15$		0			0
$16$	−73.0055			−1.14071
$17$			49.4789i			0.705906i	0.935641	+	0.352953i	$0.114822\pi$
$17$			49.4789i			0.705906i	−0.935641	+	0.352953i	$0.885178\pi$
$18$		0			0
$19$	−70.9199			−0.856323			−0.428161	−	0.903702i	$-0.640839\pi$
$19$	−70.9199			−0.856323			−0.428161	+	0.903702i	$0.640839\pi$
$20$	−11.8281	+	9.47071i	−0.132242	+	0.105886i
$21$		0			0
$22$			161.842i			1.56840i
$23$		−	38.3284i		−	0.347479i	−0.984792	−	0.173739i	$-0.944415\pi$
$23$		−	38.3284i		−	0.347479i	0.984792	−	0.173739i	$-0.0555851\pi$
$24$		0			0
$25$	27.3353	−	121.975i	0.218682	−	0.975796i
$26$	−39.7623			−0.299924
$27$		0			0
$28$		−	31.7014i		−	0.213964i
$29$	−104.897			−0.671683			−0.335842	−	0.941918i	$-0.609021\pi$
$29$	−104.897			−0.671683			−0.335842	+	0.941918i	$0.609021\pi$
$30$		0			0
$31$	−280.737			−1.62651			−0.813256	−	0.581906i	$-0.802307\pi$
$31$	−280.737			−1.62651			−0.813256	+	0.581906i	$0.802307\pi$
$32$			60.7069i			0.335362i
$33$		0			0
$34$	151.338			0.763361
$35$	163.457	+	204.143i	0.789407	+	0.985899i
$36$		0			0
$37$			1.68968i			0.00750762i	0.999993	+	0.00375381i	$0.00119488\pi$
$37$			1.68968i			0.00750762i	−0.999993	+	0.00375381i	$0.998805\pi$
$38$			216.918i			0.926021i
$39$		0			0
$40$	−142.023	−	177.374i	−0.561396	−	0.701133i
$41$	−455.197			−1.73390			−0.866950	−	0.498395i	$-0.833923\pi$
$41$	−455.197			−1.73390			−0.866950	+	0.498395i	$0.833923\pi$
$42$		0			0
$43$		−	454.499i		−	1.61187i	−0.592003	−	0.805936i	$-0.701662\pi$
$43$		−	454.499i		−	1.61187i	0.592003	−	0.805936i	$-0.298338\pi$
$44$	71.7120			0.245704
$45$		0			0
$46$	−117.233			−0.375761
$47$		−	565.411i		−	1.75476i	−0.479798	−	0.877379i	$-0.659290\pi$
$47$		−	565.411i		−	1.75476i	0.479798	−	0.877379i	$-0.340710\pi$
$48$		0			0
$49$	−204.140			−0.595160
$50$	−373.076	−	83.6087i	−1.05522	−	0.236481i
$51$		0			0
$52$			17.6186i			0.0469858i
$53$		−	385.295i		−	0.998573i	−0.866437	−	0.499286i	$-0.833596\pi$
$53$		−	385.295i		−	0.998573i	0.866437	−	0.499286i	$-0.166404\pi$
$54$		0			0
$55$	−461.794	+	369.758i	−1.13215	+	0.906511i
$56$	475.395			1.13442
$57$		0			0
$58$			320.841i			0.726353i
$59$	270.279			0.596395			0.298197	−	0.954504i	$-0.403615\pi$
$59$	270.279			0.596395			0.298197	+	0.954504i	$0.403615\pi$
$60$		0			0
$61$	563.622			1.18302			0.591511	−	0.806297i	$-0.298532\pi$
$61$	563.622			1.18302			0.591511	+	0.806297i	$0.298532\pi$
$62$			858.674i			1.75890i
$63$		0			0
$64$	−398.363			−0.778053
$65$	−90.8442	−	113.456i	−0.173351	−	0.216500i
$66$		0			0
$67$			620.293i			1.13106i	0.824729	+	0.565529i	$0.191328\pi$
$67$			620.293i			1.13106i	−0.824729	+	0.565529i	$0.808672\pi$
$68$		−	67.0577i		−	0.119587i
$69$		0			0
$70$	624.400	−	499.956i	1.06614	−	0.853659i
$71$	−816.400			−1.36463			−0.682316	−	0.731058i	$-0.739027\pi$
$71$	−816.400			−1.36463			−0.682316	+	0.731058i	$0.739027\pi$
$72$		0			0
$73$			581.269i			0.931951i	0.884798	+	0.465976i	$0.154297\pi$
$73$			581.269i			0.931951i	−0.884798	+	0.465976i	$0.845703\pi$
$74$	5.16813			0.00811868
$75$		0			0
$76$	96.1162			0.145070
$77$		−	1237.69i		−	1.83179i
$78$		0			0
$79$	−493.473			−0.702786			−0.351393	−	0.936228i	$-0.614292\pi$
$79$	−493.473			−0.702786			−0.351393	+	0.936228i	$0.614292\pi$
$80$	−637.148	+	510.163i	−0.890442	+	0.712975i
$81$		0			0
$82$			1392.28i			1.87503i
$83$			495.056i			0.654693i	0.944904	+	0.327346i	$0.106154\pi$
$83$			495.056i			0.654693i	−0.944904	+	0.327346i	$0.893846\pi$
$84$		0			0
$85$	345.759	+	431.823i	0.441210	+	0.551032i
$86$	−1390.15			−1.74307
$87$		0			0
$88$			1075.40i			1.30270i
$89$	901.129			1.07325			0.536626	−	0.843820i	$-0.319699\pi$
$89$	901.129			1.07325			0.536626	+	0.843820i	$0.319699\pi$
$90$		0			0
$91$	304.083			0.350292
$92$			51.9456i			0.0588664i
$93$		0			0
$94$	−1729.39			−1.89758
$95$	−618.946	+	495.589i	−0.668448	+	0.535225i
$96$		0			0
$97$			3.53365i			0.00369884i	0.999998	+	0.00184942i	$0.000588689\pi$
$97$			3.53365i			0.00369884i	−0.999998	+	0.00184942i	$0.999411\pi$
$98$			624.390i			0.643601i
$99$		0			0
$100$	−37.0469	+	165.310i	−0.0370469	+	0.165310i
$101$	911.133			0.897635			0.448818	−	0.893623i	$-0.351845\pi$
$101$	911.133			0.897635			0.448818	+	0.893623i	$0.351845\pi$
$102$		0			0
$103$			2012.57i			1.92528i	0.270776	+	0.962642i	$0.412720\pi$
$103$			2012.57i			1.92528i	−0.270776	+	0.962642i	$0.587280\pi$
$104$	−264.210			−0.249114
$105$		0			0
$106$	−1178.48			−1.07985
$107$		−	1513.18i		−	1.36715i	−0.729882	−	0.683573i	$-0.760425\pi$
$107$		−	1513.18i		−	1.36715i	0.729882	−	0.683573i	$-0.239575\pi$
$108$		0			0
$109$	1401.01			1.23112			0.615562	−	0.788089i	$-0.288929\pi$
$109$	1401.01			1.23112			0.615562	+	0.788089i	$0.288929\pi$
$110$	1130.96	+	1412.46i	0.980294	+	1.22430i
$111$		0			0
$112$		−	1707.67i		−	1.44071i
$113$			762.555i			0.634825i	0.948288	+	0.317412i	$0.102814\pi$
$113$			762.555i			0.634825i	−0.948288	+	0.317412i	$0.897186\pi$
$114$		0			0
$115$	−267.839	−	334.507i	−0.217184	−	0.271243i
$116$	142.164			0.113790
$117$		0			0
$118$		−	826.685i		−	0.644937i
$119$	−1157.36			−0.891557
$120$		0			0
$121$	1468.80			1.10353
$122$		−	1723.92i		−	1.27931i
$123$		0			0
$124$	380.477			0.275547
$125$	−613.794	−	1255.54i	−0.439195	−	0.898392i
$126$		0			0
$127$		−	1284.03i		−	0.897156i	−0.893744	−	0.448578i	$-0.851931\pi$
$127$		−	1284.03i		−	0.897156i	0.893744	−	0.448578i	$-0.148069\pi$
$128$			1704.10i			1.17674i
$129$		0			0
$130$	−347.022	+	277.860i	−0.234122	+	0.187461i
$131$	−198.399			−0.132322			−0.0661612	−	0.997809i	$-0.521075\pi$
$131$	−198.399			−0.132322			−0.0661612	+	0.997809i	$0.521075\pi$
$132$		0			0
$133$		−	1658.89i		−	1.08153i
$134$	1897.25			1.22312
$135$		0			0
$136$	1005.60			0.634040
$137$			1685.72i			1.05125i	0.850717	+	0.525624i	$0.176168\pi$
$137$			1685.72i			1.05125i	−0.850717	+	0.525624i	$0.823832\pi$
$138$		0			0
$139$	−2226.02			−1.35834			−0.679169	−	0.733982i	$-0.737660\pi$
$139$	−2226.02			−1.35834			−0.679169	+	0.733982i	$0.737660\pi$
$140$	−221.530	−	276.671i	−0.133733	−	0.167021i
$141$		0			0
$142$			2497.07i			1.47570i
$143$			687.870i			0.402256i
$144$		0			0
$145$	−915.476	+	733.019i	−0.524318	+	0.419820i
$146$	1777.89			1.00781
$147$		0			0
$148$		−	2.28999i		−	0.00127186i
$149$	539.815			0.296801			0.148401	−	0.988927i	$-0.452587\pi$
$149$	539.815			0.296801			0.148401	+	0.988927i	$0.452587\pi$
$150$		0			0
$151$	2266.17			1.22131			0.610657	−	0.791896i	$-0.290906\pi$
$151$	2266.17			1.22131			0.610657	+	0.791896i	$0.290906\pi$
$152$			1441.36i			0.769144i
$153$		0			0
$154$	−3785.65			−1.98089
$155$	−2450.11	+	1961.80i	−1.26966	+	1.01661i
$156$		0			0
$157$		−	279.967i		−	0.142317i	−0.997465	−	0.0711585i	$-0.977330\pi$
$157$		−	279.967i		−	0.142317i	0.997465	−	0.0711585i	$-0.0226696\pi$
$158$			1509.36i			0.759987i
$159$		0			0
$160$	424.221	+	529.814i	0.209610	+	0.261784i
$161$	896.539			0.438865
$162$		0			0
$163$			719.186i			0.345589i	0.984958	+	0.172795i	$0.0552797\pi$
$163$			719.186i			0.345589i	−0.984958	+	0.172795i	$0.944720\pi$
$164$	616.919			0.293740
$165$		0			0
$166$	1514.20			0.707980
$167$			658.201i			0.304989i	0.988304	+	0.152494i	$0.0487306\pi$
$167$			658.201i			0.304989i	−0.988304	+	0.152494i	$0.951269\pi$
$168$		0			0
$169$	−169.000			−0.0769231
$170$	1320.79	−	1057.55i	0.595882	−	0.477122i
$171$		0			0
$172$			615.973i			0.273067i
$173$		−	1009.51i		−	0.443652i	−0.975086	−	0.221826i	$-0.928798\pi$
$173$		−	1009.51i		−	0.443652i	0.975086	−	0.221826i	$-0.0712018\pi$
$174$		0			0
$175$	2853.11	+	639.400i	1.23243	+	0.276195i
$176$	3862.94			1.65443
$177$		0			0
$178$		−	2756.23i		−	1.16061i
$179$	1299.47			0.542608			0.271304	−	0.962494i	$-0.412545\pi$
$179$	1299.47			0.542608			0.271304	+	0.962494i	$0.412545\pi$
$180$		0			0
$181$	417.244			0.171345			0.0856727	−	0.996323i	$-0.472696\pi$
$181$	417.244			0.171345			0.0856727	+	0.996323i	$0.472696\pi$
$182$		−	930.081i		−	0.378803i
$183$		0			0
$184$	−778.978			−0.312103
$185$	11.8075	+	14.7465i	0.00469247	+	0.00586047i
$186$		0			0
$187$		−	2618.08i		−	1.02381i
$188$			766.289i			0.297273i
$189$		0			0
$190$	1515.83	+	1893.13i	0.578788	+	0.722855i
$191$	−1231.11			−0.466389			−0.233195	−	0.972430i	$-0.574918\pi$
$191$	−1231.11			−0.466389			−0.233195	+	0.972430i	$0.574918\pi$
$192$		0			0
$193$		−	1290.49i		−	0.481302i	−0.970612	−	0.240651i	$-0.922639\pi$
$193$		−	1290.49i		−	0.481302i	0.970612	−	0.240651i	$-0.0773609\pi$
$194$	10.8082			0.00399990
$195$		0			0
$196$	276.666			0.100826
$197$			2815.55i			1.01827i	0.860686	+	0.509136i	$0.170035\pi$
$197$			2815.55i			1.01827i	−0.860686	+	0.509136i	$0.829965\pi$
$198$		0			0
$199$	−1894.42			−0.674833			−0.337417	−	0.941355i	$-0.609553\pi$
$199$	−1894.42			−0.674833			−0.337417	+	0.941355i	$0.609553\pi$
$200$	−2478.99	−	555.557i	−0.876454	−	0.196419i
$201$		0			0
$202$		−	2786.83i		−	0.970696i
$203$		−	2453.64i		−	0.848333i
$204$		0			0
$205$	−3972.69	+	3180.93i	−1.35349	+	1.08373i
$206$	6155.73			2.08199
$207$		0			0
$208$			949.071i			0.316376i
$209$	3752.59			1.24197
$210$		0			0
$211$	4940.22			1.61184			0.805921	−	0.592023i	$-0.201671\pi$
$211$	4940.22			1.61184			0.805921	+	0.592023i	$0.201671\pi$
$212$			522.183i			0.169168i
$213$		0			0
$214$	−4628.27			−1.47842
$215$	−3176.05	−	3966.60i	−1.00746	−	1.25823i
$216$		0			0
$217$		−	6566.73i		−	2.05428i
$218$		−	4285.19i		−	1.33133i
$219$		0			0
$220$	625.860	−	501.125i	0.191798	−	0.153572i
$221$	643.226			0.195783
$222$		0			0
$223$		−	1893.57i		−	0.568622i	−0.958732	−	0.284311i	$-0.908235\pi$
$223$		−	1893.57i		−	0.568622i	0.958732	−	0.284311i	$-0.0917647\pi$
$224$	−1420.00			−0.423560
$225$		0			0
$226$	2332.38			0.686495
$227$		−	1405.63i		−	0.410990i	−0.978658	−	0.205495i	$-0.934120\pi$
$227$		−	1405.63i		−	0.410990i	0.978658	−	0.205495i	$-0.0658804\pi$
$228$		0			0
$229$	2033.07			0.586676			0.293338	−	0.956009i	$-0.405234\pi$
$229$	2033.07			0.586676			0.293338	+	0.956009i	$0.405234\pi$
$230$	−1023.14	+	819.224i	−0.293320	+	0.234861i
$231$		0			0
$232$			2131.90i			0.603302i
$233$		−	5297.72i		−	1.48955i	−0.667315	−	0.744775i	$-0.732557\pi$
$233$		−	5297.72i		−	1.48955i	0.667315	−	0.744775i	$-0.267443\pi$
$234$		0			0
$235$	−3951.10	−	4934.57i	−1.09677	−	1.36977i
$236$	−366.303			−0.101035
$237$		0			0
$238$			3539.96i			0.964123i
$239$	−2335.56			−0.632113			−0.316057	−	0.948740i	$-0.602359\pi$
$239$	−2335.56			−0.632113			−0.316057	+	0.948740i	$0.602359\pi$
$240$		0			0
$241$	4733.71			1.26525			0.632625	−	0.774458i	$-0.281978\pi$
$241$	4733.71			1.26525			0.632625	+	0.774458i	$0.281978\pi$
$242$		−	4492.52i		−	1.19335i
$243$		0			0
$244$	−763.865			−0.200416
$245$	−1781.61	+	1426.53i	−0.464584	+	0.371991i
$246$		0			0
$247$			921.958i			0.237501i
$248$			5705.65i			1.46092i
$249$		0			0
$250$	−3840.25	+	1877.37i	−0.971514	+	0.474942i
$251$	−6940.51			−1.74534			−0.872671	−	0.488308i	$-0.837614\pi$
$251$	−6940.51			−1.74534			−0.872671	+	0.488308i	$0.837614\pi$
$252$		0			0
$253$			2028.07i			0.503968i
$254$	−3927.37			−0.970178
$255$		0			0
$256$	2025.34			0.494467
$257$			1177.03i			0.285686i	0.989745	+	0.142843i	$0.0456244\pi$
$257$			1177.03i			0.285686i	−0.989745	+	0.142843i	$0.954376\pi$
$258$		0			0
$259$	−39.5234			−0.00948209
$260$	123.119	+	153.765i	0.0293674	+	0.0366773i
$261$		0			0
$262$			606.832i			0.143092i
$263$		−	7802.79i		−	1.82943i	−0.404097	−	0.914716i	$-0.632414\pi$
$263$		−	7802.79i		−	1.82943i	0.404097	−	0.914716i	$-0.367586\pi$
$264$		0			0
$265$	−2692.45	−	3362.63i	−0.624135	−	0.779489i
$266$	−5073.94			−1.16956
$267$		0			0
$268$		−	840.670i		−	0.191612i
$269$	−5042.71			−1.14297			−0.571486	−	0.820612i	$-0.693633\pi$
$269$	−5042.71			−1.14297			−0.571486	+	0.820612i	$0.693633\pi$
$270$		0			0
$271$	−8864.90			−1.98710			−0.993551	−	0.113390i	$-0.963829\pi$
$271$	−8864.90			−1.98710			−0.993551	+	0.113390i	$0.963829\pi$
$272$		−	3612.23i		−	0.805234i
$273$		0			0
$274$	5156.01			1.13681
$275$	−1446.39	+	6454.05i	−0.317167	+	1.41525i
$276$		0			0
$277$		−	6320.33i		−	1.37095i	−0.728098	−	0.685473i	$-0.759596\pi$
$277$		−	6320.33i		−	1.37095i	0.728098	−	0.685473i	$-0.240404\pi$
$278$			6808.61i			1.46890i
$279$		0			0
$280$	4148.96	−	3322.07i	0.885528	−	0.709041i
$281$	−1980.02			−0.420348			−0.210174	−	0.977664i	$-0.567403\pi$
$281$	−1980.02			−0.420348			−0.210174	+	0.977664i	$0.567403\pi$
$282$		0			0
$283$			0.330895i			6.95042e-5i	1.00000		3.47521e-5i	$1.10619e-5\pi$
$283$			0.330895i			6.95042e-5i	−1.00000		3.47521e-5i	$0.999989\pi$
$284$	1106.45			0.231182
$285$		0			0
$286$	2103.95			0.434997
$287$		−	10647.5i		−	2.18991i
$288$		0			0
$289$	2464.84			0.501697
$290$	2242.04	+	2800.11i	0.453991	+	0.566994i
$291$		0			0
$292$		−	787.782i		−	0.157882i
$293$			486.067i			0.0969159i	0.998825	+	0.0484580i	$0.0154307\pi$
$293$			486.067i			0.0969159i	−0.998825	+	0.0484580i	$0.984569\pi$
$294$		0			0
$295$	2358.83	−	1888.71i	0.465548	−	0.372763i
$296$	34.3408			0.00674330
$297$		0			0
$298$		−	1651.10i		−	0.320959i
$299$	−498.269			−0.0963733
$300$		0			0
$301$	10631.2			2.03579
$302$		−	6931.40i		−	1.32072i
$303$		0			0
$304$	5177.54			0.976816
$305$	4918.96	−	3938.60i	0.923471	−	0.739421i
$306$		0			0
$307$		−	2414.57i		−	0.448882i	−0.974488	−	0.224441i	$-0.927944\pi$
$307$		−	2414.57i		−	0.448882i	0.974488	−	0.224441i	$-0.0720556\pi$
$308$			1677.42i			0.310324i
$309$		0			0
$310$	6000.43	+	7494.00i	1.09936	+	1.37300i
$311$	−1563.08			−0.284996			−0.142498	−	0.989795i	$-0.545514\pi$
$311$	−1563.08			−0.284996			−0.142498	+	0.989795i	$0.545514\pi$
$312$		0			0
$313$		−	4198.11i		−	0.758119i	−0.925372	−	0.379060i	$-0.876248\pi$
$313$		−	4198.11i		−	0.758119i	0.925372	−	0.379060i	$-0.123752\pi$
$314$	−856.317			−0.153901
$315$		0			0
$316$	668.794			0.119059
$317$			1790.36i			0.317213i	0.987342	+	0.158607i	$0.0507001\pi$
$317$			1790.36i			0.317213i	−0.987342	+	0.158607i	$0.949300\pi$
$318$		0			0
$319$	5550.41			0.974179
$320$	−3476.68	+	2783.77i	−0.607350	+	0.486304i
$321$		0			0
$322$		−	2742.19i		−	0.474585i
$323$		−	3509.04i		−	0.604483i
$324$		0			0
$325$	−1585.67	−	355.358i	−0.270637	−	0.0606515i
$326$	2199.73			0.373718
$327$		0			0
$328$			9251.35i			1.55738i
$329$	13225.5			2.21625
$330$		0			0
$331$	−1077.36			−0.178904			−0.0894521	−	0.995991i	$-0.528512\pi$
$331$	−1077.36			−0.178904			−0.0894521	+	0.995991i	$0.528512\pi$
$332$		−	670.939i		−	0.110911i
$333$		0			0
$334$	2013.20			0.329812
$335$	4334.62	+	5413.55i	0.706942	+	0.882907i
$336$		0			0
$337$		−	2564.26i		−	0.414493i	−0.978289	−	0.207246i	$-0.933550\pi$
$337$		−	2564.26i		−	0.414493i	0.978289	−	0.207246i	$-0.0664502\pi$
$338$			516.910i			0.0831840i
$339$		0			0
$340$	−468.601	−	585.240i	−0.0747454	−	0.0933503i
$341$	14854.7			2.35902
$342$		0			0
$343$			3248.08i			0.511312i
$344$	−9237.16			−1.44777
$345$		0			0
$346$	−3087.74			−0.479763
$347$		−	5426.27i		−	0.839473i	−0.907646	−	0.419737i	$-0.862122\pi$
$347$		−	5426.27i		−	0.839473i	0.907646	−	0.419737i	$-0.137878\pi$
$348$		0			0
$349$	−1044.75			−0.160241			−0.0801203	−	0.996785i	$-0.525530\pi$
$349$	−1044.75			−0.160241			−0.0801203	+	0.996785i	$0.525530\pi$
$350$	1955.69	−	8726.63i	0.298675	−	1.33274i
$351$		0			0
$352$		−	3212.19i		−	0.486393i
$353$			2608.59i			0.393318i	0.980472	+	0.196659i	$0.0630093\pi$
$353$			2608.59i			0.393318i	−0.980472	+	0.196659i	$0.936991\pi$
$354$		0			0
$355$	−7125.05	+	5705.01i	−1.06524	+	0.852932i
$356$	−1221.28			−0.181820
$357$		0			0
$358$		−	3974.61i		−	0.586773i
$359$	3550.24			0.521935			0.260967	−	0.965348i	$-0.415959\pi$
$359$	3550.24			0.521935			0.260967	+	0.965348i	$0.415959\pi$
$360$		0			0
$361$	−1829.37			−0.266711
$362$		−	1276.20i		−	0.185292i
$363$		0			0
$364$	−412.118			−0.0593430
$365$	4061.92	+	5072.97i	0.582495	+	0.727484i
$366$		0			0
$367$		−	3013.25i		−	0.428585i	−0.976770	−	0.214292i	$-0.931256\pi$
$367$		−	3013.25i		−	0.428585i	0.976770	−	0.214292i	$-0.0687445\pi$
$368$			2798.18i			0.396373i
$369$		0			0
$370$	45.1043	−	36.1150i	0.00633747	−	0.00507440i
$371$	9012.45			1.26119
$372$		0			0
$373$			1861.68i			0.258430i	0.991617	+	0.129215i	$0.0412457\pi$
$373$			1861.68i			0.258430i	−0.991617	+	0.129215i	$0.958754\pi$
$374$	−8007.77			−1.10714
$375$		0			0
$376$	−11491.3			−1.57611
$377$			1363.66i			0.186291i
$378$		0			0
$379$	2021.24			0.273943			0.136971	−	0.990575i	$-0.456263\pi$
$379$	2021.24			0.273943			0.136971	+	0.990575i	$0.456263\pi$
$380$	838.845	−	671.662i	0.113242	−	0.0906724i
$381$		0			0
$382$			3765.54i			0.504350i
$383$			5533.46i			0.738242i	0.929381	+	0.369121i	$0.120341\pi$
$383$			5533.46i			0.738242i	−0.929381	+	0.369121i	$0.879659\pi$
$384$		0			0
$385$	−8649.01	−	10801.8i	−1.14492	−	1.42990i
$386$	−3947.13			−0.520476
$387$		0			0
$388$		−	4.78908i		−	0.000626620i
$389$	7493.91			0.976752			0.488376	−	0.872633i	$-0.337590\pi$
$389$	7493.91			0.976752			0.488376	+	0.872633i	$0.337590\pi$
$390$		0			0
$391$	1896.45			0.245287
$392$			4148.90i			0.534569i
$393$		0			0
$394$	8611.75			1.10115
$395$	−4306.74	+	3448.40i	−0.548597	+	0.439260i
$396$		0			0
$397$			8446.68i			1.06782i	0.845540	+	0.533912i	$0.179279\pi$
$397$			8446.68i			1.06782i	−0.845540	+	0.533912i	$0.820721\pi$
$398$			5794.35i			0.729760i
$399$		0			0
$400$	−1995.62	+	8904.80i	−0.249453	+	1.11310i
$401$	−7883.98			−0.981814			−0.490907	−	0.871212i	$-0.663334\pi$
$401$	−7883.98			−0.981814			−0.490907	+	0.871212i	$0.663334\pi$
$402$		0			0
$403$			3649.58i			0.451113i
$404$	−1234.84			−0.152068
$405$		0			0
$406$	−7504.80			−0.917382
$407$		−	89.4063i		−	0.0108887i
$408$		0			0
$409$	−2089.46			−0.252609			−0.126305	−	0.991992i	$-0.540312\pi$
$409$	−2089.46			−0.252609			−0.126305	+	0.991992i	$0.540312\pi$
$410$	9729.31	+	12151.0i	1.17194	+	1.46365i
$411$		0			0
$412$		−	2727.59i		−	0.326162i
$413$			6322.10i			0.753245i
$414$		0			0
$415$	3459.46	+	4320.56i	0.409201	+	0.511055i
$416$	789.190			0.0930125
$417$		0			0
$418$		−	11477.8i		−	1.34306i
$419$	8066.10			0.940465			0.470232	−	0.882543i	$-0.344170\pi$
$419$	8066.10			0.940465			0.470232	+	0.882543i	$0.344170\pi$
$420$		0			0
$421$	−13021.8			−1.50747			−0.753736	−	0.657177i	$-0.771750\pi$
$421$	−13021.8			−1.50747			−0.753736	+	0.657177i	$0.771750\pi$
$422$		−	15110.3i		−	1.74303i
$423$		0			0
$424$	−7830.67			−0.896912
$425$	6035.17	+	1352.52i	0.688820	+	0.154369i
$426$		0			0
$427$			13183.7i			1.49415i
$428$			2050.78i			0.231608i
$429$		0			0
$430$	−12132.4	+	9714.39i	−1.36064	+	1.08946i
$431$	7530.49			0.841603			0.420802	−	0.907153i	$-0.361749\pi$
$431$	7530.49			0.841603			0.420802	+	0.907153i	$0.361749\pi$
$432$		0			0
$433$		−	790.361i		−	0.0877190i	−0.999038	−	0.0438595i	$-0.986035\pi$
$433$		−	790.361i		−	0.0877190i	0.999038	−	0.0438595i	$-0.0139654\pi$
$434$	−20085.3			−2.22148
$435$		0			0
$436$	−1898.76			−0.208564
$437$			2718.24i			0.297554i
$438$		0			0
$439$	9607.62			1.04453			0.522263	−	0.852785i	$-0.325088\pi$
$439$	9607.62			1.04453			0.522263	+	0.852785i	$0.325088\pi$
$440$	7514.88	+	9385.42i	0.814223	+	1.01689i
$441$		0			0
$442$		−	1967.40i		−	0.211718i
$443$		−	6282.26i		−	0.673767i	−0.941546	−	0.336884i	$-0.890627\pi$
$443$		−	6282.26i		−	0.673767i	0.941546	−	0.336884i	$-0.109373\pi$
$444$		0			0
$445$	7864.52	−	6297.10i	0.837784	−	0.670812i
$446$	−5791.74			−0.614903
$447$		0			0
$448$		−	9318.12i		−	0.982678i
$449$	8666.17			0.910873			0.455437	−	0.890268i	$-0.349483\pi$
$449$	8666.17			0.910873			0.455437	+	0.890268i	$0.349483\pi$
$450$		0			0
$451$	24085.9			2.51477
$452$		−	1033.48i		−	0.107546i
$453$		0			0
$454$	−4299.30			−0.444441
$455$	2653.86	−	2124.94i	0.273439	−	0.218942i
$456$		0			0
$457$		−	11944.5i		−	1.22263i	−0.791387	−	0.611315i	$-0.790641\pi$
$457$		−	11944.5i		−	1.22263i	0.791387	−	0.611315i	$-0.209359\pi$
$458$		−	6218.42i		−	0.634427i
$459$		0			0
$460$	362.997	+	453.351i	0.0367931	+	0.0459513i
$461$	−4144.88			−0.418755			−0.209378	−	0.977835i	$-0.567144\pi$
$461$	−4144.88			−0.418755			−0.209378	+	0.977835i	$0.567144\pi$
$462$		0			0
$463$			8572.00i			0.860421i	0.902729	+	0.430210i	$0.141561\pi$
$463$			8572.00i			0.860421i	−0.902729	+	0.430210i	$0.858439\pi$
$464$	7658.03			0.766196
$465$		0			0
$466$	−16203.8			−1.61079
$467$			8107.44i			0.803357i	0.915781	+	0.401678i	$0.131573\pi$
$467$			8107.44i			0.803357i	−0.915781	+	0.401678i	$0.868427\pi$
$468$		0			0
$469$	−14509.3			−1.42852
$470$	−15093.1	+	12085.0i	−1.48126	+	1.18604i
$471$		0			0
$472$		−	5493.09i		−	0.535678i
$473$			24049.0i			2.33779i
$474$		0			0
$475$	−1938.61	+	8650.42i	−0.187262	+	0.835596i
$476$	1568.55			0.151039
$477$		0			0
$478$			7143.65i			0.683562i
$479$	−20524.1			−1.95777			−0.978884	−	0.204414i	$-0.934471\pi$
$479$	−20524.1			−1.95777			−0.978884	+	0.204414i	$0.934471\pi$
$480$		0			0
$481$	21.9659			0.00208224
$482$		−	14478.7i		−	1.36823i
$483$		0			0
$484$	−1990.63			−0.186949
$485$	24.6932	+	30.8396i	0.00231188	+	0.00288733i
$486$		0			0
$487$		−	11390.8i		−	1.05989i	−0.848033	−	0.529943i	$-0.822213\pi$
$487$		−	11390.8i		−	1.05989i	0.848033	−	0.529943i	$-0.177787\pi$
$488$		−	11454.9i		−	1.06258i
$489$		0			0
$490$	4363.25	+	5449.31i	0.402268	+	0.502397i
$491$	−12827.9			−1.17905			−0.589525	−	0.807750i	$-0.700685\pi$
$491$	−12827.9			−1.17905			−0.589525	+	0.807750i	$0.700685\pi$
$492$		0			0
$493$		−	5190.17i		−	0.474145i
$494$	2819.94			0.256832
$495$		0			0
$496$	20495.3			1.85538
$497$		−	19096.4i		−	1.72352i
$498$		0			0
$499$	20141.2			1.80691			0.903453	−	0.428688i	$-0.141024\pi$
$499$	20141.2			1.80691			0.903453	+	0.428688i	$0.141024\pi$
$500$	831.862	+	1701.61i	0.0744040	+	0.152196i
$501$		0			0
$502$			21228.5i			1.88740i
$503$			18757.4i			1.66273i	0.555728	+	0.831364i	$0.312440\pi$
$503$			18757.4i			1.66273i	−0.555728	+	0.831364i	$0.687560\pi$
$504$		0			0
$505$	7951.83	−	6367.01i	0.700697	−	0.561046i
$506$	6203.14			0.544987
$507$		0			0
$508$			1740.21i			0.151987i
$509$	−21180.7			−1.84444			−0.922219	−	0.386668i	$-0.873626\pi$
$509$	−21180.7			−1.84444			−0.922219	+	0.386668i	$0.873626\pi$
$510$		0			0
$511$	−13596.5			−1.17705
$512$			7438.06i			0.642029i
$513$		0			0
$514$	3600.12			0.308939
$515$	14063.9	+	17564.5i	1.20336	+	1.50288i
$516$		0			0
$517$			29917.6i			2.54502i
$518$			120.888i			0.0102539i
$519$		0			0
$520$	−2305.86	+	1846.30i	−0.194459	+	0.155703i
$521$	−6568.62			−0.552354			−0.276177	−	0.961107i	$-0.589068\pi$
$521$	−6568.62			−0.552354			−0.276177	+	0.961107i	$0.589068\pi$
$522$		0			0
$523$		−	5901.75i		−	0.493433i	−0.969088	−	0.246717i	$-0.920648\pi$
$523$		−	5901.75i		−	0.493433i	0.969088	−	0.246717i	$-0.0793517\pi$
$524$	268.887			0.0224167
$525$		0			0
$526$	−23865.9			−1.97833
$527$		−	13890.6i		−	1.14816i
$528$		0			0
$529$	10697.9			0.879258
$530$	−10285.1	+	8235.23i	−0.842934	+	0.674935i
$531$		0			0
$532$			2248.26i			0.183222i
$533$			5917.57i			0.480897i
$534$		0			0
$535$	−10574.1	−	13206.1i	−0.854504	−	1.06720i
$536$	12606.7			1.01591
$537$		0			0
$538$			15423.8i			1.23600i
$539$	10801.7			0.863193
$540$		0			0
$541$	−11634.0			−0.924555			−0.462278	−	0.886735i	$-0.652968\pi$
$541$	−11634.0			−0.924555			−0.462278	+	0.886735i	$0.652968\pi$
$542$			27114.5i			2.14884i
$543$		0			0
$544$	−3003.71			−0.236734
$545$	12227.2	−	9790.28i	0.961019	−	0.769486i
$546$		0			0
$547$			146.415i			0.0114447i	0.999984	+	0.00572235i	$0.00182149\pi$
$547$			146.415i			0.0114447i	−0.999984	+	0.00572235i	$0.998179\pi$
$548$		−	2284.62i		−	0.178092i
$549$		0			0
$550$	19740.6	+	4424.00i	1.53044	+	0.342982i
$551$	7439.25			0.575178
$552$		0			0
$553$		−	11542.8i		−	0.887616i
$554$	−19331.6			−1.48253
$555$		0			0
$556$	3016.88			0.230116
$557$		−	24443.9i		−	1.85946i	−0.368242	−	0.929730i	$-0.620040\pi$
$557$		−	24443.9i		−	1.85946i	0.368242	−	0.929730i	$-0.379960\pi$
$558$		0			0
$559$	−5908.49			−0.447053
$560$	−11933.2	−	14903.5i	−0.900485	−	1.12462i
$561$		0			0
$562$			6056.16i			0.454561i
$563$			3271.79i			0.244920i	0.992473	+	0.122460i	$0.0390782\pi$
$563$			3271.79i			0.244920i	−0.992473	+	0.122460i	$0.960922\pi$
$564$		0			0
$565$	5328.75	+	6655.13i	0.396783	+	0.495546i
$566$	1.01209			7.51613e−5
$567$		0			0
$568$			16592.4i			1.22570i
$569$	17910.6			1.31960			0.659801	−	0.751441i	$-0.270641\pi$
$569$	17910.6			1.31960			0.659801	+	0.751441i	$0.270641\pi$
$570$		0			0
$571$	21000.7			1.53915			0.769573	−	0.638559i	$-0.220469\pi$
$571$	21000.7			1.53915			0.769573	+	0.638559i	$0.220469\pi$
$572$		−	932.256i		−	0.0681461i
$573$		0			0
$574$	−32567.0			−2.36815
$575$	−4675.08	−	1047.72i	−0.339069	−	0.0759874i
$576$		0			0
$577$		−	11643.7i		−	0.840096i	−0.907502	−	0.420048i	$-0.862013\pi$
$577$		−	11643.7i		−	0.840096i	0.907502	−	0.420048i	$-0.137987\pi$
$578$		−	7539.05i		−	0.542531i
$579$		0			0
$580$	1240.72	−	993.446i	0.0888246	−	0.0711217i
$581$	−11579.9			−0.826874
$582$		0			0
$583$			20387.2i			1.44828i
$584$	11813.6			0.837073
$585$		0			0
$586$	1486.71			0.104804
$587$		−	27008.3i		−	1.89907i	−0.313666	−	0.949533i	$-0.601557\pi$
$587$		−	27008.3i		−	1.89907i	0.313666	−	0.949533i	$-0.398443\pi$
$588$		0			0
$589$	19909.8			1.39282
$590$	−5776.89	−	7214.82i	−0.403103	−	0.503440i
$591$		0			0
$592$		−	123.356i		−	0.00856402i
$593$		−	13608.0i		−	0.942347i	−0.882041	−	0.471173i	$-0.843831\pi$
$593$		−	13608.0i		−	0.942347i	0.882041	−	0.471173i	$-0.156169\pi$
$594$		0			0
$595$	−10100.8	+	8087.67i	−0.695952	+	0.557247i
$596$	−731.600			−0.0502811
$597$		0			0
$598$			1524.02i			0.104217i
$599$	−24055.7			−1.64088			−0.820440	−	0.571732i	$-0.806272\pi$
$599$	−24055.7			−1.64088			−0.820440	+	0.571732i	$0.806272\pi$
$600$		0			0
$601$	−6660.65			−0.452069			−0.226035	−	0.974119i	$-0.572576\pi$
$601$	−6660.65			−0.452069			−0.226035	+	0.974119i	$0.572576\pi$
$602$		−	32517.0i		−	2.20149i
$603$		0			0
$604$	−3071.29			−0.206903
$605$	12818.8	−	10264.0i	0.861417	−	0.689735i
$606$		0			0
$607$		−	19022.2i		−	1.27197i	−0.771700	−	0.635986i	$-0.780593\pi$
$607$		−	19022.2i		−	1.27197i	0.771700	−	0.635986i	$-0.219407\pi$
$608$		−	4305.33i		−	0.287178i
$609$		0			0
$610$	−12046.8	−	15045.3i	−0.799605	−	0.998635i
$611$	−7350.34			−0.486682
$612$		0			0
$613$			9274.89i			0.611108i	0.952175	+	0.305554i	$0.0988417\pi$
$613$			9274.89i			0.611108i	−0.952175	+	0.305554i	$0.901158\pi$
$614$	−7385.30			−0.485417
$615$		0			0
$616$	−25154.6			−1.64530
$617$			19322.8i			1.26079i	0.776276	+	0.630393i	$0.217106\pi$
$617$			19322.8i			1.26079i	−0.776276	+	0.630393i	$0.782894\pi$
$618$		0			0
$619$	8665.16			0.562653			0.281327	−	0.959612i	$-0.409226\pi$
$619$	8665.16			0.562653			0.281327	+	0.959612i	$0.409226\pi$
$620$	3320.58	−	2658.78i	0.215093	−	0.172225i
$621$		0			0
$622$			4780.89i			0.308193i
$623$			21078.3i			1.35551i
$624$		0			0
$625$	−14130.6	−	6668.41i	−0.904356	−	0.426778i
$626$	−12840.5			−0.819824
$627$		0			0
$628$			379.433i			0.0241099i
$629$	−83.6036			−0.00529967
$630$		0			0
$631$	6938.93			0.437773			0.218886	−	0.975750i	$-0.429758\pi$
$631$	6938.93			0.437773			0.218886	+	0.975750i	$0.429758\pi$
$632$			10029.3i			0.631238i
$633$		0			0
$634$	5476.06			0.343032
$635$	−8972.79	−	11206.2i	−0.560747	−	0.700323i
$636$		0			0
$637$			2653.82i			0.165068i
$638$		−	16976.7i		−	1.05347i
$639$		0			0
$640$	11908.3	+	14872.4i	0.735496	+	0.918568i
$641$	718.616			0.0442803			0.0221401	−	0.999755i	$-0.492952\pi$
$641$	718.616			0.0442803			0.0221401	+	0.999755i	$0.492952\pi$
$642$		0			0
$643$			19271.5i			1.18195i	0.806690	+	0.590975i	$0.201257\pi$
$643$			19271.5i			1.18195i	−0.806690	+	0.590975i	$0.798743\pi$
$644$	−1215.06			−0.0743480
$645$		0			0
$646$	−10732.9			−0.653684
$647$			19909.3i			1.20976i	0.796317	+	0.604880i	$0.206779\pi$
$647$			19909.3i			1.20976i	−0.796317	+	0.604880i	$0.793221\pi$
$648$		0			0
$649$	−14301.3			−0.864984
$650$	−1086.91	+	4849.99i	−0.0655881	+	0.292665i
$651$		0			0
$652$		−	974.698i		−	0.0585462i
$653$			3104.48i			0.186045i	0.995664	+	0.0930227i	$0.0296529\pi$
$653$			3104.48i			0.186045i	−0.995664	+	0.0930227i	$0.970347\pi$
$654$		0			0
$655$	−1731.51	+	1386.42i	−0.103291	+	0.0827051i
$656$	33231.9			1.97788
$657$		0			0
$658$		−	40452.1i		−	2.39664i
$659$	−22088.3			−1.30567			−0.652837	−	0.757498i	$-0.726421\pi$
$659$	−22088.3			−1.30567			−0.652837	+	0.757498i	$0.726421\pi$
$660$		0			0
$661$	15905.4			0.935930			0.467965	−	0.883747i	$-0.344987\pi$
$661$	15905.4			0.935930			0.467965	+	0.883747i	$0.344987\pi$
$662$			3295.27i			0.193466i
$663$		0			0
$664$	10061.4			0.588041
$665$	−11592.3	−	14477.8i	−0.675987	−	0.844248i
$666$		0			0
$667$			4020.52i			0.233396i
$668$		−	892.046i		−	0.0516681i
$669$		0			0
$670$	16558.1	−	13258.0i	0.954769	−	0.764481i
$671$	−29823.0			−1.71580
$672$		0			0
$673$		−	6334.82i		−	0.362837i	−0.983406	−	0.181419i	$-0.941931\pi$
$673$		−	6334.82i		−	0.362837i	0.983406	−	0.181419i	$-0.0580689\pi$
$674$	−7843.14			−0.448229
$675$		0			0
$676$	229.042			0.0130315
$677$			18414.8i			1.04540i	0.852516	+	0.522701i	$0.175076\pi$
$677$			18414.8i			1.04540i	−0.852516	+	0.522701i	$0.824924\pi$
$678$		0			0
$679$	−82.6556			−0.00467162
$680$	8776.28	−	7027.15i	0.494934	−	0.396293i
$681$		0			0
$682$		−	45435.1i		−	2.55103i
$683$		−	17256.2i		−	0.966749i	−0.875414	−	0.483374i	$-0.839411\pi$
$683$		−	17256.2i		−	0.966749i	0.875414	−	0.483374i	$-0.160589\pi$
$684$		0			0
$685$	11779.8	+	14712.0i	0.657058	+	0.820607i
$686$	9934.71			0.552929
$687$		0			0
$688$			33180.9i			1.83868i
$689$	−5008.84			−0.276954
$690$		0			0
$691$	−32243.8			−1.77513			−0.887564	−	0.460684i	$-0.847604\pi$
$691$	−32243.8			−1.77513			−0.887564	+	0.460684i	$0.847604\pi$
$692$			1368.17i			0.0751591i
$693$		0			0
$694$	−16597.0			−0.907800
$695$	−19427.4	+	15555.5i	−1.06032	+	0.848998i
$696$		0			0
$697$		−	22522.7i		−	1.22397i
$698$			3195.50i			0.173283i
$699$		0			0
$700$	−3866.76	−	866.565i	−0.208785	−	0.0467901i
$701$	−20420.4			−1.10024			−0.550120	−	0.835085i	$-0.685418\pi$
$701$	−20420.4			−1.10024			−0.550120	+	0.835085i	$0.685418\pi$
$702$		0			0
$703$		−	119.832i		−	0.00642894i
$704$	21078.6			1.12845
$705$		0			0
$706$	7978.75			0.425332
$707$			21312.3i			1.13371i
$708$		0			0
$709$	13991.6			0.741137			0.370568	−	0.928805i	$-0.379163\pi$
$709$	13991.6			0.741137			0.370568	+	0.928805i	$0.379163\pi$
$710$	17449.6	+	21793.0i	0.922354	+	1.15194i
$711$		0			0
$712$		−	18314.4i		−	0.963989i
$713$			10760.2i			0.565179i
$714$		0			0
$715$	4806.85	+	6003.32i	0.251421	+	0.314002i
$716$	−1761.14			−0.0919232
$717$		0			0
$718$		−	10858.9i		−	0.564416i
$719$	19706.6			1.02216			0.511080	−	0.859533i	$-0.329246\pi$
$719$	19706.6			1.02216			0.511080	+	0.859533i	$0.329246\pi$
$720$		0			0
$721$	−47076.1			−2.43163
$722$			5595.39i			0.288420i
$723$		0			0
$724$	−565.482			−0.0290276
$725$	−2867.38	+	12794.7i	−0.146885	+	0.655426i
$726$		0			0
$727$		−	10826.8i		−	0.552329i	−0.961110	−	0.276165i	$-0.910937\pi$
$727$		−	10826.8i		−	0.552329i	0.961110	−	0.276165i	$-0.0890635\pi$
$728$		−	6180.13i		−	0.314630i
$729$		0			0
$730$	15516.4	−	12424.0i	0.786696	−	0.629906i
$731$	22488.1			1.13783
$732$		0			0
$733$		−	11970.1i		−	0.603171i	−0.953439	−	0.301586i	$-0.902484\pi$
$733$		−	11970.1i		−	0.603171i	0.953439	−	0.301586i	$-0.0975159\pi$
$734$	−9216.46			−0.463468
$735$		0			0
$736$	2326.80			0.116531
$737$		−	32821.6i		−	1.64043i
$738$		0			0
$739$	11147.2			0.554881			0.277440	−	0.960743i	$-0.410514\pi$
$739$	11147.2			0.554881			0.277440	+	0.960743i	$0.410514\pi$
$740$	−16.0025	−	19.9857i	−0.000794950	−	0.000992821i
$741$		0			0
$742$		−	27565.8i		−	1.36385i
$743$			18552.2i			0.916033i	0.888944	+	0.458017i	$0.151440\pi$
$743$			18552.2i			0.916033i	−0.888944	+	0.458017i	$0.848560\pi$
$744$		0			0
$745$	4711.19	−	3772.24i	0.231684	−	0.185509i
$746$	5694.22			0.279464
$747$		0			0
$748$			3548.23i			0.173444i
$749$	35394.8			1.72670
$750$		0			0
$751$	1479.95			0.0719096			0.0359548	−	0.999353i	$-0.488553\pi$
$751$	1479.95			0.0719096			0.0359548	+	0.999353i	$0.488553\pi$
$752$			41278.1i			2.00167i
$753$		0			0
$754$	4170.93			0.201454
$755$	19777.8	−	15836.0i	0.953361	−	0.763354i
$756$		0			0
$757$		−	11865.0i		−	0.569669i	−0.958577	−	0.284834i	$-0.908061\pi$
$757$		−	11865.0i		−	0.569669i	0.958577	−	0.284834i	$-0.0919386\pi$
$758$		−	6182.25i		−	0.296239i
$759$		0			0
$760$	10072.3	+	12579.4i	0.480736	+	0.600396i
$761$	−8558.59			−0.407686			−0.203843	−	0.979004i	$-0.565343\pi$
$761$	−8558.59			−0.407686			−0.203843	+	0.979004i	$0.565343\pi$
$762$		0			0
$763$			32771.1i			1.55490i
$764$	1668.50			0.0790109
$765$		0			0
$766$	16924.9			0.798329
$767$		−	3513.62i		−	0.165410i
$768$		0			0
$769$	−20203.5			−0.947409			−0.473704	−	0.880684i	$-0.657084\pi$
$769$	−20203.5			−0.947409			−0.473704	+	0.880684i	$0.657084\pi$
$770$	−33038.9	+	26454.2i	−1.54629	+	1.23811i
$771$		0			0
$772$			1748.97i			0.0815373i
$773$		−	22049.9i		−	1.02597i	−0.858396	−	0.512987i	$-0.828539\pi$
$773$		−	22049.9i		−	1.02597i	0.858396	−	0.512987i	$-0.171461\pi$
$774$		0			0
$775$	−7674.03	+	34242.8i	−0.355689	+	1.58714i
$776$	71.8172			0.00332228
$777$		0			0
$778$		−	22921.2i		−	1.05625i
$779$	32282.5			1.48478
$780$		0			0
$781$	43198.2			1.97920
$782$		−	5800.54i		−	0.265252i
$783$		0			0
$784$	14903.3			0.678905
$785$	−1956.41	−	2443.38i	−0.0889520	−	0.111093i
$786$		0			0
$787$		−	1316.61i		−	0.0596342i	−0.999555	−	0.0298171i	$-0.990508\pi$
$787$		−	1316.61i		−	0.0596342i	0.999555	−	0.0298171i	$-0.00949248\pi$
$788$		−	3815.86i		−	0.172505i
$789$		0			0
$790$	10547.4	+	13172.8i	0.475013	+	0.593248i
$791$	−17836.9			−0.801781
$792$		0			0
$793$		−	7327.08i		−	0.328111i
$794$	25835.3			1.15474
$795$		0			0
$796$	2567.47			0.114323
$797$			1967.65i			0.0874502i	0.999044	+	0.0437251i	$0.0139226\pi$
$797$			1967.65i			0.0874502i	−0.999044	+	0.0437251i	$0.986077\pi$
$798$		0			0
$799$	27975.9			1.23869
$800$	7404.70	+	1659.44i	0.327244	+	0.0733376i
$801$		0			0
$802$			24114.3i			1.06173i
$803$		−	30756.8i		−	1.35166i
$804$		0			0
$805$	7824.46	−	6265.03i	0.342579	−	0.274302i
$806$	11162.8			0.487831
$807$		0			0
$808$		−	18517.7i		−	0.806250i
$809$	29356.4			1.27579			0.637897	−	0.770122i	$-0.279805\pi$
$809$	29356.4			1.27579			0.637897	+	0.770122i	$0.279805\pi$
$810$		0			0
$811$	−16910.3			−0.732183			−0.366092	−	0.930579i	$-0.619304\pi$
$811$	−16910.3			−0.732183			−0.366092	+	0.930579i	$0.619304\pi$
$812$			3325.37i			0.143716i
$813$		0			0
$814$	−273.462			−0.0117750
$815$	5025.69	+	6276.63i	0.216003	+	0.269768i
$816$		0			0
$817$			32233.0i			1.38028i
$818$			6390.91i			0.273170i
$819$		0			0
$820$	5384.11	−	4311.04i	0.229294	−	0.183595i
$821$	−32568.4			−1.38446			−0.692231	−	0.721676i	$-0.743372\pi$
$821$	−32568.4			−1.38446			−0.692231	+	0.721676i	$0.743372\pi$
$822$		0			0
$823$		−	12859.0i		−	0.544635i	−0.962207	−	0.272318i	$-0.912210\pi$
$823$		−	12859.0i		−	0.544635i	0.962207	−	0.272318i	$-0.0877902\pi$
$824$	40903.1			1.72928
$825$		0			0
$826$	19337.0			0.814553
$827$		−	24021.4i		−	1.01004i	−0.863107	−	0.505022i	$-0.831484\pi$
$827$		−	24021.4i		−	1.01004i	0.863107	−	0.505022i	$-0.168516\pi$
$828$		0			0
$829$	−44341.2			−1.85770			−0.928850	−	0.370456i	$-0.879202\pi$
$829$	−44341.2			−1.85770			−0.928850	+	0.370456i	$0.879202\pi$
$830$	13215.0	−	10581.2i	0.552651	−	0.442507i
$831$		0			0
$832$			5178.72i			0.215793i
$833$		−	10100.6i		−	0.420127i
$834$		0			0
$835$	4599.52	+	5744.39i	0.190626	+	0.238075i
$836$	−5085.81			−0.210402
$837$		0			0
$838$		−	24671.3i		−	1.01701i
$839$	−1668.57			−0.0686594			−0.0343297	−	0.999411i	$-0.510930\pi$
$839$	−1668.57			−0.0686594			−0.0343297	+	0.999411i	$0.510930\pi$
$840$		0			0
$841$	−13385.7			−0.548842
$842$			39829.1i			1.63017i
$843$		0			0
$844$	−6695.37			−0.273062
$845$	−1474.93	+	1180.97i	−0.0600464	+	0.0480790i
$846$		0			0
$847$			34356.6i			1.39375i
$848$			28128.7i			1.13908i
$849$		0			0
$850$	4136.87	−	18459.4i	0.166933	−	0.744885i
$851$	64.7627			0.00260874
$852$		0			0
$853$			5729.70i			0.229990i	0.993366	+	0.114995i	$0.0366852\pi$
$853$			5729.70i			0.229990i	−0.993366	+	0.114995i	$0.963315\pi$
$854$	40324.2			1.61577
$855$		0			0
$856$	−30753.6			−1.22796
$857$		−	1248.23i		−	0.0497534i	−0.999691	−	0.0248767i	$-0.992081\pi$
$857$		−	1248.23i		−	0.0497534i	0.999691	−	0.0248767i	$-0.00791931\pi$
$858$		0			0
$859$	−33870.7			−1.34535			−0.672674	−	0.739939i	$-0.734854\pi$
$859$	−33870.7			−1.34535			−0.672674	+	0.739939i	$0.734854\pi$
$860$	4304.43	+	5375.85i	0.170674	+	0.213157i
$861$		0			0
$862$		−	23033.1i		−	0.910104i
$863$			12216.6i			0.481875i	0.970541	+	0.240938i	$0.0774549\pi$
$863$			12216.6i			0.481875i	−0.970541	+	0.240938i	$0.922545\pi$
$864$		0			0
$865$	−7054.50	−	8810.43i	−0.277295	−	0.346316i
$866$	−2417.43			−0.0948587
$867$		0			0
$868$			8899.75i			0.348015i
$869$	26111.2			1.01929
$870$		0			0
$871$	8063.81			0.313699
$872$		−	28473.9i		−	1.10579i
$873$		0			0
$874$	8314.12			0.321773
$875$	29368.4	−	14357.3i	1.13467	−	0.554702i
$876$		0			0
$877$		−	18452.1i		−	0.710470i	−0.934777	−	0.355235i	$-0.884401\pi$
$877$		−	18452.1i		−	0.710470i	0.934777	−	0.355235i	$-0.115599\pi$
$878$		−	29386.3i		−	1.12954i
$879$		0			0
$880$	33713.5	−	26994.3i	1.29146	−	1.03407i
$881$	10016.3			0.383041			0.191521	−	0.981489i	$-0.438658\pi$
$881$	10016.3			0.383041			0.191521	+	0.981489i	$0.438658\pi$
$882$		0			0
$883$		−	4225.09i		−	0.161025i	−0.996754	−	0.0805127i	$-0.974344\pi$
$883$		−	4225.09i		−	0.161025i	0.996754	−	0.0805127i	$-0.0256558\pi$
$884$	−871.751			−0.0331676
$885$		0			0
$886$	−19215.2			−0.728607
$887$		−	37432.5i		−	1.41698i	−0.705721	−	0.708490i	$-0.749377\pi$
$887$		−	37432.5i		−	1.41698i	0.705721	−	0.708490i	$-0.250623\pi$
$888$		0			0
$889$	30034.7			1.13310
$890$	−19260.6	−	24054.7i	−0.725411	−	0.905973i
$891$		0			0
$892$			2566.31i			0.0963301i
$893$			40098.8i			1.50264i
$894$		0			0
$895$	11341.0	−	9080.71i	0.423562	−	0.339145i
$896$	−39860.7			−1.48622
$897$		0			0
$898$		−	26506.7i		−	0.985012i
$899$	29448.4			1.09250
$900$		0			0
$901$	19064.0			0.704899
$902$		−	73670.1i		−	2.71945i
$903$		0			0
$904$	15498.0			0.570196
$905$	3641.46	−	2915.71i	0.133753	−	0.107095i
$906$		0			0
$907$		−	12442.0i		−	0.455490i	−0.973721	−	0.227745i	$-0.926865\pi$
$907$		−	12442.0i		−	0.455490i	0.973721	−	0.227745i	$-0.0731353\pi$
$908$			1905.01i			0.0696257i
$909$		0			0
$910$	−6499.42	−	8117.20i	−0.236762	−	0.295695i
$911$	−22262.1			−0.809635			−0.404818	−	0.914397i	$-0.632665\pi$
$911$	−22262.1			−0.809635			−0.404818	+	0.914397i	$0.632665\pi$
$912$		0			0
$913$		−	26195.0i		−	0.949536i
$914$	−36534.0			−1.32214
$915$		0			0
$916$	−2755.37			−0.0993888
$917$		−	4640.76i		−	0.167123i
$918$		0			0
$919$	42011.8			1.50799			0.753994	−	0.656882i	$-0.228125\pi$
$919$	42011.8			1.50799			0.753994	+	0.656882i	$0.228125\pi$
$920$	−6798.46	+	5443.51i	−0.243629	+	0.195073i
$921$		0			0
$922$			12677.7i			0.452839i
$923$			10613.2i			0.378481i
$924$		0			0
$925$	206.098	+	46.1879i	0.00732590	+	0.00164178i
$926$	26218.7			0.930453
$927$		0			0
$928$		−	6367.95i		−	0.225257i
$929$	−44065.6			−1.55624			−0.778119	−	0.628117i	$-0.783826\pi$
$929$	−44065.6			−1.55624			−0.778119	+	0.628117i	$0.783826\pi$
$930$		0			0
$931$	14477.6			0.509649
$932$			7179.89i			0.252345i
$933$		0			0
$934$	24797.7			0.868744
$935$	−18295.2	−	22849.1i	−0.639911	−	0.799192i
$936$		0			0
$937$		−	41905.4i		−	1.46104i	−0.682894	−	0.730518i	$-0.739279\pi$
$937$		−	41905.4i		−	1.46104i	0.682894	−	0.730518i	$-0.260721\pi$
$938$			44378.7i			1.54479i
$939$		0			0
$940$	5354.84	+	6687.72i	0.185804	+	0.232052i
$941$	27117.1			0.939418			0.469709	−	0.882821i	$-0.344359\pi$
$941$	27117.1			0.939418			0.469709	+	0.882821i	$0.344359\pi$
$942$		0			0
$943$			17447.0i			0.602494i
$944$	−19731.8			−0.680314
$945$		0			0
$946$	73557.1			2.52806
$947$			44607.8i			1.53069i	0.643622	+	0.765343i	$0.277431\pi$
$947$			44607.8i			1.53069i	−0.643622	+	0.765343i	$0.722569\pi$
$948$		0			0
$949$	7556.50			0.258477
$950$	26458.5	+	5929.52i	0.903608	+	0.202504i
$951$		0			0
$952$			23522.0i			0.800791i
$953$			30550.0i			1.03842i	0.854647	+	0.519209i	$0.173773\pi$
$953$			30550.0i			1.03842i	−0.854647	+	0.519209i	$0.826227\pi$
$954$		0			0
$955$	−10744.4	+	8603.05i	−0.364065	+	0.291506i
$956$	3165.34			0.107086
$957$		0			0
$958$			62775.9i			2.11712i
$959$	−39430.7			−1.32772
$960$		0			0
$961$	49022.4			1.64554
$962$		−	67.1856i		−	0.00225172i
$963$		0			0
$964$	−6415.50			−0.214346
$965$	−9017.94	−	11262.6i	−0.300827	−	0.375706i
$966$		0			0
$967$			40412.4i			1.34393i	0.740585	+	0.671963i	$0.234549\pi$
$967$			40412.4i			1.34393i	−0.740585	+	0.671963i	$0.765451\pi$
$968$		−	29851.5i		−	0.991182i
$969$		0			0
$970$	94.3271	−	75.5275i	0.00312233	−	0.00250004i
$971$	46775.8			1.54594			0.772970	−	0.634443i	$-0.218770\pi$
$971$	46775.8			1.54594			0.772970	+	0.634443i	$0.218770\pi$
$972$		0			0
$973$		−	52069.0i		−	1.71558i
$974$	−34840.2			−1.14615
$975$		0			0
$976$	−41147.5			−1.34949
$977$		−	7003.40i		−	0.229333i	−0.993404	−	0.114667i	$-0.963420\pi$
$977$		−	7003.40i		−	0.229333i	0.993404	−	0.114667i	$-0.0365800\pi$
$978$		0			0
$979$	−47681.5			−1.55660
$980$	2414.58	−	1933.35i	0.0787050	−	0.0630190i
$981$		0			0
$982$			39235.9i			1.27502i
$983$		−	19541.2i		−	0.634048i	−0.948418	−	0.317024i	$-0.897316\pi$
$983$		−	19541.2i		−	0.634048i	0.948418	−	0.317024i	$-0.102684\pi$
$984$		0			0
$985$	19675.1	+	24572.4i	0.636448	+	0.794866i
$986$	−15874.9			−0.512737
$987$		0			0
$988$		−	1249.51i		−	0.0402350i
$989$	−17420.2			−0.560092
$990$		0			0
$991$	−31571.3			−1.01200			−0.506002	−	0.862532i	$-0.668877\pi$
$991$	−31571.3			−1.01200			−0.506002	+	0.862532i	$0.668877\pi$
$992$		−	17042.7i		−	0.545470i
$993$		0			0
$994$	−58409.1			−1.86381
$995$	−16533.4	+	13238.2i	−0.526777	+	0.421789i
$996$		0			0
$997$			27558.5i			0.875413i	0.899118	+	0.437706i	$0.144209\pi$
$997$			27558.5i			0.875413i	−0.899118	+	0.437706i	$0.855791\pi$
$998$		−	61604.8i		−	1.95397i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.4.c.e.469.6		22
3.2	odd	2		195.4.c.c.79.17	yes	22
5.4	even	2	inner	585.4.c.e.469.17		22
15.2	even	4		975.4.a.bb.1.4		11
15.8	even	4		975.4.a.bc.1.8		11
15.14	odd	2		195.4.c.c.79.6	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.4.c.c.79.6	✓	22	15.14	odd	2
195.4.c.c.79.17	yes	22	3.2	odd	2
585.4.c.e.469.6		22	1.1	even	1	trivial
585.4.c.e.469.17		22	5.4	even	2	inner
975.4.a.bb.1.4		11	15.2	even	4
975.4.a.bc.1.8		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)

\(f(q)\)	\(=\)	\(q-3.05864i q^{2} -1.35528 q^{4} +(8.72741 - 6.98802i) q^{5} +23.3910i q^{7} -20.3238i q^{8} +(-21.3738 - 26.6940i) q^{10} -52.9131 q^{11} -13.0000i q^{13} +71.5447 q^{14} -73.0055 q^{16} +49.4789i q^{17} -70.9199 q^{19} +(-11.8281 + 9.47071i) q^{20} +161.842i q^{22} -38.3284i q^{23} +(27.3353 - 121.975i) q^{25} -39.7623 q^{26} -31.7014i q^{28} -104.897 q^{29} -280.737 q^{31} +60.7069i q^{32} +151.338 q^{34} +(163.457 + 204.143i) q^{35} +1.68968i q^{37} +216.918i q^{38} +(-142.023 - 177.374i) q^{40} -455.197 q^{41} -454.499i q^{43} +71.7120 q^{44} -117.233 q^{46} -565.411i q^{47} -204.140 q^{49} +(-373.076 - 83.6087i) q^{50} +17.6186i q^{52} -385.295i q^{53} +(-461.794 + 369.758i) q^{55} +475.395 q^{56} +320.841i q^{58} +270.279 q^{59} +563.622 q^{61} +858.674i q^{62} -398.363 q^{64} +(-90.8442 - 113.456i) q^{65} +620.293i q^{67} -67.0577i q^{68} +(624.400 - 499.956i) q^{70} -816.400 q^{71} +581.269i q^{73} +5.16813 q^{74} +96.1162 q^{76} -1237.69i q^{77} -493.473 q^{79} +(-637.148 + 510.163i) q^{80} +1392.28i q^{82} +495.056i q^{83} +(345.759 + 431.823i) q^{85} -1390.15 q^{86} +1075.40i q^{88} +901.129 q^{89} +304.083 q^{91} +51.9456i q^{92} -1729.39 q^{94} +(-618.946 + 495.589i) q^{95} +3.53365i q^{97} +624.390i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 110 q^{4} - 8 q^{5} - 58 q^{10} - 200 q^{11} + 300 q^{14} + 1022 q^{16} - 88 q^{19} + 296 q^{20} - 346 q^{25} - 78 q^{26} + 560 q^{29} + 512 q^{31} - 156 q^{34} - 36 q^{35} + 10 q^{40} - 1400 q^{41}+ \cdots - 2376 q^{95}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more