LMFDB - Embedded newform 585.4.c.e.469.13

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			469.13
Character	$\chi$	$=$	585.469
Dual form			585.4.c.e.469.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.29959i q^{2} +6.31107 q^{4} +(-8.47931 - 7.28706i) q^{5} -34.4577i q^{7} +18.5985i q^{8} +(9.47018 - 11.0196i) q^{10} -7.37405 q^{11} -13.0000i q^{13} +44.7808 q^{14} +26.3181 q^{16} +67.1647i q^{17} +63.6576 q^{19} +(-53.5135 - 45.9891i) q^{20} -9.58323i q^{22} -165.181i q^{23} +(18.7975 + 123.579i) q^{25} +16.8947 q^{26} -217.465i q^{28} -212.104 q^{29} -230.655 q^{31} +182.991i q^{32} -87.2865 q^{34} +(-251.095 + 292.177i) q^{35} -316.168i q^{37} +82.7287i q^{38} +(135.528 - 157.703i) q^{40} -76.4857 q^{41} +267.960i q^{43} -46.5381 q^{44} +214.667 q^{46} -47.5459i q^{47} -844.331 q^{49} +(-160.601 + 24.4290i) q^{50} -82.0439i q^{52} -426.730i q^{53} +(62.5268 + 53.7351i) q^{55} +640.861 q^{56} -275.647i q^{58} -818.534 q^{59} +127.566 q^{61} -299.756i q^{62} -27.2677 q^{64} +(-94.7318 + 110.231i) q^{65} +538.837i q^{67} +423.881i q^{68} +(-379.711 - 326.320i) q^{70} +221.935 q^{71} -145.837i q^{73} +410.888 q^{74} +401.747 q^{76} +254.092i q^{77} -1274.18 q^{79} +(-223.160 - 191.782i) q^{80} -99.3999i q^{82} -1010.87i q^{83} +(489.433 - 569.510i) q^{85} -348.238 q^{86} -137.146i q^{88} +1441.62 q^{89} -447.950 q^{91} -1042.47i q^{92} +61.7901 q^{94} +(-539.772 - 463.876i) q^{95} -1000.71i q^{97} -1097.28i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			1.29959i			0.459474i	0.973253	+	0.229737i	$0.0737866\pi$
$2$			1.29959i			0.459474i	−0.973253	+	0.229737i	$0.926213\pi$
$3$		0			0
$3$		0			0
$4$	6.31107			0.788884
$5$	−8.47931	−	7.28706i	−0.758413	−	0.651774i
$5$	−8.47931	−	7.28706i	−0.758413	−	0.651774i
$6$		0			0
$7$		−	34.4577i		−	1.86054i	−0.366876	−	0.930270i	$-0.619573\pi$
$7$		−	34.4577i		−	1.86054i	0.366876	−	0.930270i	$-0.380427\pi$
$8$			18.5985i			0.821946i
$9$		0			0
$10$	9.47018	−	11.0196i	0.299473	−	0.348471i
$11$	−7.37405			−0.202123			−0.101062	−	0.994880i	$-0.532224\pi$
$11$	−7.37405			−0.202123			−0.101062	+	0.994880i	$0.532224\pi$
$12$		0			0
$13$		−	13.0000i		−	0.277350i
$13$		−	13.0000i		−	0.277350i
$14$	44.7808			0.854870
$15$		0			0
$16$	26.3181			0.411221
$17$			67.1647i			0.958225i	0.877754	+	0.479112i	$0.159041\pi$
$17$			67.1647i			0.958225i	−0.877754	+	0.479112i	$0.840959\pi$
$18$		0			0
$19$	63.6576			0.768634			0.384317	−	0.923201i	$-0.374437\pi$
$19$	63.6576			0.768634			0.384317	+	0.923201i	$0.374437\pi$
$20$	−53.5135	−	45.9891i	−0.598299	−	0.514174i
$21$		0			0
$22$		−	9.58323i		−	0.0928705i
$23$		−	165.181i		−	1.49750i	−0.662850	−	0.748752i	$-0.730653\pi$
$23$		−	165.181i		−	1.49750i	0.662850	−	0.748752i	$-0.269347\pi$
$24$		0			0
$25$	18.7975	+	123.579i	0.150380	+	0.988628i
$26$	16.8947			0.127435
$27$		0			0
$28$		−	217.465i		−	1.46775i
$29$	−212.104			−1.35816			−0.679080	−	0.734064i	$-0.737621\pi$
$29$	−212.104			−1.35816			−0.679080	+	0.734064i	$0.737621\pi$
$30$		0			0
$31$	−230.655			−1.33635			−0.668174	−	0.744005i	$-0.732924\pi$
$31$	−230.655			−1.33635			−0.668174	+	0.744005i	$0.732924\pi$
$32$			182.991i			1.01089i
$33$		0			0
$34$	−87.2865			−0.440280
$35$	−251.095	+	292.177i	−1.21265	+	1.41106i
$36$		0			0
$37$		−	316.168i		−	1.40480i	−0.711781	−	0.702401i	$-0.752111\pi$
$37$		−	316.168i		−	1.40480i	0.711781	−	0.702401i	$-0.247889\pi$
$38$			82.7287i			0.353167i
$39$		0			0
$40$	135.528	−	157.703i	0.535723	−	0.623374i
$41$	−76.4857			−0.291343			−0.145671	−	0.989333i	$-0.546534\pi$
$41$	−76.4857			−0.291343			−0.145671	+	0.989333i	$0.546534\pi$
$42$		0			0
$43$			267.960i			0.950314i	0.879901	+	0.475157i	$0.157609\pi$
$43$			267.960i			0.950314i	−0.879901	+	0.475157i	$0.842391\pi$
$44$	−46.5381			−0.159452
$45$		0			0
$46$	214.667			0.688064
$47$		−	47.5459i		−	0.147559i	−0.997275	−	0.0737796i	$-0.976494\pi$
$47$		−	47.5459i		−	0.147559i	0.997275	−	0.0737796i	$-0.0235061\pi$
$48$		0			0
$49$	−844.331			−2.46161
$50$	−160.601	+	24.4290i	−0.454249	+	0.0690958i
$51$		0			0
$52$		−	82.0439i		−	0.218797i
$53$		−	426.730i		−	1.10596i	−0.833194	−	0.552980i	$-0.813490\pi$
$53$		−	426.730i		−	1.10596i	0.833194	−	0.552980i	$-0.186510\pi$
$54$		0			0
$55$	62.5268	+	53.7351i	0.153293	+	0.131739i
$56$	640.861			1.52926
$57$		0			0
$58$		−	275.647i		−	0.624039i
$59$	−818.534			−1.80617			−0.903085	−	0.429462i	$-0.858703\pi$
$59$	−818.534			−1.80617			−0.903085	+	0.429462i	$0.858703\pi$
$60$		0			0
$61$	127.566			0.267756			0.133878	−	0.990998i	$-0.457257\pi$
$61$	127.566			0.267756			0.133878	+	0.990998i	$0.457257\pi$
$62$		−	299.756i		−	0.614017i
$63$		0			0
$64$	−27.2677			−0.0532573
$65$	−94.7318	+	110.231i	−0.180770	+	0.210346i
$66$		0			0
$67$			538.837i			0.982528i	0.871011	+	0.491264i	$0.163465\pi$
$67$			538.837i			0.982528i	−0.871011	+	0.491264i	$0.836535\pi$
$68$			423.881i			0.755928i
$69$		0			0
$70$	−379.711	−	326.320i	−0.648344	−	0.557182i
$71$	221.935			0.370969			0.185485	−	0.982647i	$-0.440615\pi$
$71$	221.935			0.370969			0.185485	+	0.982647i	$0.440615\pi$
$72$		0			0
$73$		−	145.837i		−	0.233820i	−0.993142	−	0.116910i	$-0.962701\pi$
$73$		−	145.837i		−	0.233820i	0.993142	−	0.116910i	$-0.0372989\pi$
$74$	410.888			0.645470
$75$		0			0
$76$	401.747			0.606363
$77$			254.092i			0.376059i
$78$		0			0
$79$	−1274.18			−1.81464			−0.907319	−	0.420443i	$-0.861875\pi$
$79$	−1274.18			−1.81464			−0.907319	+	0.420443i	$0.861875\pi$
$80$	−223.160	−	191.782i	−0.311875	−	0.268023i
$81$		0			0
$82$		−	99.3999i		−	0.133864i
$83$		−	1010.87i		−	1.33684i	−0.743786	−	0.668418i	$-0.766972\pi$
$83$		−	1010.87i		−	1.33684i	0.743786	−	0.668418i	$-0.233028\pi$
$84$		0			0
$85$	489.433	−	569.510i	0.624547	−	0.726730i
$86$	−348.238			−0.436645
$87$		0			0
$88$		−	137.146i		−	0.166135i
$89$	1441.62			1.71698			0.858492	−	0.512827i	$-0.171402\pi$
$89$	1441.62			1.71698			0.858492	+	0.512827i	$0.171402\pi$
$90$		0			0
$91$	−447.950			−0.516021
$92$		−	1042.47i		−	1.18136i
$93$		0			0
$94$	61.7901			0.0677996
$95$	−539.772	−	463.876i	−0.582942	−	0.500976i
$96$		0			0
$97$		−	1000.71i		−	1.04749i	−0.851875	−	0.523745i	$-0.824534\pi$
$97$		−	1000.71i		−	1.04749i	0.851875	−	0.523745i	$-0.175466\pi$
$98$		−	1097.28i		−	1.13104i
$99$		0			0
$100$	118.632	+	779.913i	0.118632	+	0.779913i
$101$	326.447			0.321611			0.160805	−	0.986986i	$-0.448591\pi$
$101$	326.447			0.321611			0.160805	+	0.986986i	$0.448591\pi$
$102$		0			0
$103$			1530.87i			1.46447i	0.681051	+	0.732236i	$0.261523\pi$
$103$			1530.87i			1.46447i	−0.681051	+	0.732236i	$0.738477\pi$
$104$	241.781			0.227967
$105$		0			0
$106$	554.574			0.508160
$107$			655.262i			0.592024i	0.955184	+	0.296012i	$0.0956568\pi$
$107$			655.262i			0.592024i	−0.955184	+	0.296012i	$0.904343\pi$
$108$		0			0
$109$	433.242			0.380707			0.190353	−	0.981716i	$-0.439037\pi$
$109$	433.242			0.380707			0.190353	+	0.981716i	$0.439037\pi$
$110$	−69.8336	+	81.2592i	−0.0605306	+	0.0704342i
$111$		0			0
$112$		−	906.862i		−	0.765093i
$113$		−	134.873i		−	0.112281i	−0.998423	−	0.0561407i	$-0.982120\pi$
$113$		−	134.873i		−	0.112281i	0.998423	−	0.0561407i	$-0.0178796\pi$
$114$		0			0
$115$	−1203.68	+	1400.62i	−0.976035	+	1.13573i
$116$	−1338.60			−1.07143
$117$		0			0
$118$		−	1063.76i		−	0.829888i
$119$	2314.34			1.78282
$120$		0			0
$121$	−1276.62			−0.959146
$122$			165.783i			0.123027i
$123$		0			0
$124$	−1455.68			−1.05422
$125$	741.134	−	1184.84i	0.530312	−	0.847802i
$126$		0			0
$127$		−	1784.09i		−	1.24655i	−0.782001	−	0.623277i	$-0.785801\pi$
$127$		−	1784.09i		−	1.24655i	0.782001	−	0.623277i	$-0.214199\pi$
$128$			1428.49i			0.986421i
$129$		0			0
$130$	−143.255	−	123.112i	−0.0966485	−	0.0830590i
$131$	−711.220			−0.474348			−0.237174	−	0.971467i	$-0.576221\pi$
$131$	−711.220			−0.474348			−0.237174	+	0.971467i	$0.576221\pi$
$132$		0			0
$133$		−	2193.49i		−	1.43007i
$134$	−700.266			−0.451446
$135$		0			0
$136$	−1249.16			−0.787609
$137$		−	906.564i		−	0.565350i	−0.959216	−	0.282675i	$-0.908778\pi$
$137$		−	906.564i		−	0.565350i	0.959216	−	0.282675i	$-0.0912218\pi$
$138$		0			0
$139$	−1341.99			−0.818893			−0.409446	−	0.912334i	$-0.634278\pi$
$139$	−1341.99			−0.818893			−0.409446	+	0.912334i	$0.634278\pi$
$140$	−1584.68	+	1843.95i	−0.956641	+	1.11316i
$141$		0			0
$142$			288.424i			0.170451i
$143$			95.8626i			0.0560590i
$144$		0			0
$145$	1798.49	+	1545.61i	1.03005	+	0.885214i
$146$	189.528			0.107434
$147$		0			0
$148$		−	1995.36i		−	1.10823i
$149$	−41.8158			−0.0229912			−0.0114956	−	0.999934i	$-0.503659\pi$
$149$	−41.8158			−0.0229912			−0.0114956	+	0.999934i	$0.503659\pi$
$150$		0			0
$151$	−659.349			−0.355345			−0.177673	−	0.984090i	$-0.556857\pi$
$151$	−659.349			−0.355345			−0.177673	+	0.984090i	$0.556857\pi$
$152$			1183.94i			0.631775i
$153$		0			0
$154$	−330.216			−0.172789
$155$	1955.79	+	1680.79i	1.01350	+	0.870998i
$156$		0			0
$157$		−	105.446i		−	0.0536021i	−0.999641	−	0.0268010i	$-0.991468\pi$
$157$		−	105.446i		−	0.0536021i	0.999641	−	0.0268010i	$-0.00853206\pi$
$158$		−	1655.91i		−	0.833779i
$159$		0			0
$160$	1333.47	−	1551.64i	0.658873	−	0.766673i
$161$	−5691.75			−2.78617
$162$		0			0
$163$		−	1082.39i		−	0.520119i	−0.965593	−	0.260060i	$-0.916258\pi$
$163$		−	1082.39i		−	0.520119i	0.965593	−	0.260060i	$-0.0837422\pi$
$164$	−482.706			−0.229836
$165$		0			0
$166$	1313.71			0.614241
$167$		−	3290.24i		−	1.52459i	−0.647231	−	0.762294i	$-0.724073\pi$
$167$		−	3290.24i		−	1.52459i	0.647231	−	0.762294i	$-0.275927\pi$
$168$		0			0
$169$	−169.000			−0.0769231
$170$	740.129	+	636.062i	0.333914	+	0.286963i
$171$		0			0
$172$			1691.11i			0.749687i
$173$		−	980.954i		−	0.431101i	−0.976493	−	0.215551i	$-0.930845\pi$
$173$		−	980.954i		−	0.431101i	0.976493	−	0.215551i	$-0.0691547\pi$
$174$		0			0
$175$	4258.23	−	647.719i	1.83938	−	0.279788i
$176$	−194.071			−0.0831174
$177$		0			0
$178$			1873.52i			0.788910i
$179$	2488.93			1.03928			0.519642	−	0.854384i	$-0.326065\pi$
$179$	2488.93			1.03928			0.519642	+	0.854384i	$0.326065\pi$
$180$		0			0
$181$	3993.42			1.63994			0.819969	−	0.572407i	$-0.193990\pi$
$181$	3993.42			1.63994			0.819969	+	0.572407i	$0.193990\pi$
$182$		−	582.151i		−	0.237098i
$183$		0			0
$184$	3072.12			1.23087
$185$	−2303.94	+	2680.89i	−0.915615	+	1.06542i
$186$		0			0
$187$		−	495.275i		−	0.193680i
$188$		−	300.065i		−	0.116407i
$189$		0			0
$190$	602.849	−	701.482i	0.230185	−	0.267847i
$191$	975.573			0.369581			0.184791	−	0.982778i	$-0.440839\pi$
$191$	975.573			0.369581			0.184791	+	0.982778i	$0.440839\pi$
$192$		0			0
$193$		−	677.513i		−	0.252686i	−0.991987	−	0.126343i	$-0.959676\pi$
$193$		−	677.513i		−	0.252686i	0.991987	−	0.126343i	$-0.0403240\pi$
$194$	1300.51			0.481294
$195$		0			0
$196$	−5328.63			−1.94192
$197$			61.4612i			0.0222280i	0.999938	+	0.0111140i	$0.00353778\pi$
$197$			61.4612i			0.0222280i	−0.999938	+	0.0111140i	$0.996462\pi$
$198$		0			0
$199$	3554.74			1.26628			0.633138	−	0.774039i	$-0.281767\pi$
$199$	3554.74			1.26628			0.633138	+	0.774039i	$0.281767\pi$
$200$	−2298.38	+	349.606i	−0.812599	+	0.123604i
$201$		0			0
$202$			424.247i			0.147772i
$203$			7308.59i			2.52691i
$204$		0			0
$205$	648.546	+	557.356i	0.220958	+	0.189890i
$206$	−1989.50			−0.672887
$207$		0			0
$208$		−	342.136i		−	0.114052i
$209$	−469.414			−0.155359
$210$		0			0
$211$	−3462.80			−1.12980			−0.564902	−	0.825158i	$-0.691086\pi$
$211$	−3462.80			−1.12980			−0.564902	+	0.825158i	$0.691086\pi$
$212$		−	2693.12i		−	0.872474i
$213$		0			0
$214$	−851.571			−0.272020
$215$	1952.64	−	2272.12i	0.619391	−	0.720730i
$216$		0			0
$217$			7947.82i			2.48633i
$218$			563.036i			0.174925i
$219$		0			0
$220$	394.611	+	339.126i	0.120930	+	0.103927i
$221$	873.141			0.265764
$222$		0			0
$223$			5484.63i			1.64699i	0.567326	+	0.823494i	$0.307978\pi$
$223$			5484.63i			1.64699i	−0.567326	+	0.823494i	$0.692022\pi$
$224$	6305.44			1.88080
$225$		0			0
$226$	175.280			0.0515904
$227$		−	426.505i		−	0.124706i	−0.998054	−	0.0623528i	$-0.980140\pi$
$227$		−	426.505i		−	0.124706i	0.998054	−	0.0623528i	$-0.0198604\pi$
$228$		0			0
$229$	4057.32			1.17081			0.585405	−	0.810741i	$-0.300935\pi$
$229$	4057.32			1.17081			0.585405	+	0.810741i	$0.300935\pi$
$230$	−1820.23	−	1564.29i	−0.521837	−	0.448463i
$231$		0			0
$232$		−	3944.81i		−	1.11633i
$233$			4462.65i			1.25476i	0.778715	+	0.627378i	$0.215872\pi$
$233$			4462.65i			1.25476i	−0.778715	+	0.627378i	$0.784128\pi$
$234$		0			0
$235$	−346.470	+	403.156i	−0.0961753	+	0.111911i
$236$	−5165.82			−1.42486
$237$		0			0
$238$			3007.69i			0.819157i
$239$	1052.41			0.284832			0.142416	−	0.989807i	$-0.454513\pi$
$239$	1052.41			0.284832			0.142416	+	0.989807i	$0.454513\pi$
$240$		0			0
$241$	4364.55			1.16658			0.583289	−	0.812264i	$-0.301765\pi$
$241$	4364.55			1.16658			0.583289	+	0.812264i	$0.301765\pi$
$242$		−	1659.09i		−	0.440703i
$243$		0			0
$244$	805.075			0.211228
$245$	7159.35	+	6152.69i	1.86691	+	1.60441i
$246$		0			0
$247$		−	827.548i		−	0.213181i
$248$		−	4289.83i		−	1.09841i
$249$		0			0
$250$	1539.80	+	963.170i	0.389543	+	0.243665i
$251$	4805.44			1.20843			0.604216	−	0.796821i	$-0.293486\pi$
$251$	4805.44			1.20843			0.604216	+	0.796821i	$0.293486\pi$
$252$		0			0
$253$			1218.05i			0.302681i
$254$	2318.58			0.572759
$255$		0			0
$256$	−2074.59			−0.506492
$257$		−	2347.80i		−	0.569851i	−0.958550	−	0.284925i	$-0.908031\pi$
$257$		−	2347.80i		−	0.569851i	0.958550	−	0.284925i	$-0.0919688\pi$
$258$		0			0
$259$	−10894.4			−2.61369
$260$	−597.859	+	695.676i	−0.142606	+	0.165938i
$261$		0			0
$262$		−	924.294i		−	0.217951i
$263$			4806.77i			1.12699i	0.826120	+	0.563494i	$0.190543\pi$
$263$			4806.77i			1.12699i	−0.826120	+	0.563494i	$0.809457\pi$
$264$		0			0
$265$	−3109.61	+	3618.38i	−0.720837	+	0.838775i
$266$	2850.64			0.657082
$267$		0			0
$268$			3400.64i			0.775100i
$269$	−8182.98			−1.85474			−0.927370	−	0.374146i	$-0.877936\pi$
$269$	−8182.98			−1.85474			−0.927370	+	0.374146i	$0.877936\pi$
$270$		0			0
$271$	−1339.97			−0.300358			−0.150179	−	0.988659i	$-0.547985\pi$
$271$	−1339.97			−0.300358			−0.150179	+	0.988659i	$0.547985\pi$
$272$			1767.65i			0.394042i
$273$		0			0
$274$	1178.16			0.259764
$275$	−138.614	−	911.274i	−0.0303953	−	0.199825i
$276$		0			0
$277$			5200.44i			1.12803i	0.825765	+	0.564015i	$0.190744\pi$
$277$			5200.44i			1.12803i	−0.825765	+	0.564015i	$0.809256\pi$
$278$		−	1744.03i		−	0.376260i
$279$		0			0
$280$	−5434.06	−	4669.99i	−1.15981	−	0.996734i
$281$	319.973			0.0679288			0.0339644	−	0.999423i	$-0.489187\pi$
$281$	319.973			0.0679288			0.0339644	+	0.999423i	$0.489187\pi$
$282$		0			0
$283$			1977.17i			0.415301i	0.978203	+	0.207651i	$0.0665817\pi$
$283$			1977.17i			0.415301i	−0.978203	+	0.207651i	$0.933418\pi$
$284$	1400.65			0.292651
$285$		0			0
$286$	−124.582			−0.0257576
$287$			2635.52i			0.542055i
$288$		0			0
$289$	401.908			0.0818049
$290$	−2008.66	+	2337.30i	−0.406733	+	0.473279i
$291$		0			0
$292$		−	920.384i		−	0.184457i
$293$		−	1406.36i		−	0.280412i	−0.990122	−	0.140206i	$-0.955224\pi$
$293$		−	1406.36i		−	0.280412i	0.990122	−	0.140206i	$-0.0447764\pi$
$294$		0			0
$295$	6940.60	+	5964.71i	1.36982	+	1.17722i
$296$	5880.25			1.15467
$297$		0			0
$298$		−	54.3434i		−	0.0105639i
$299$	−2147.35			−0.415333
$300$		0			0
$301$	9233.28			1.76810
$302$		−	856.883i		−	0.163272i
$303$		0			0
$304$	1675.35			0.316078
$305$	−1081.67	−	929.578i	−0.203069	−	0.174516i
$306$		0			0
$307$		−	2911.87i		−	0.541332i	−0.962673	−	0.270666i	$-0.912756\pi$
$307$		−	2911.87i		−	0.541332i	0.962673	−	0.270666i	$-0.0872439\pi$
$308$			1603.59i			0.296667i
$309$		0			0
$310$	−2184.34	+	2541.73i	−0.400201	+	0.465679i
$311$	−503.366			−0.0917789			−0.0458895	−	0.998947i	$-0.514612\pi$
$311$	−503.366			−0.0917789			−0.0458895	+	0.998947i	$0.514612\pi$
$312$		0			0
$313$		−	2245.38i		−	0.405483i	−0.979232	−	0.202741i	$-0.935015\pi$
$313$		−	2245.38i		−	0.405483i	0.979232	−	0.202741i	$-0.0649851\pi$
$314$	137.037			0.0246288
$315$		0			0
$316$	−8041.43			−1.43154
$317$		−	5949.98i		−	1.05421i	−0.849801	−	0.527104i	$-0.823278\pi$
$317$		−	5949.98i		−	1.05421i	0.849801	−	0.527104i	$-0.176722\pi$
$318$		0			0
$319$	1564.06			0.274516
$320$	231.212	+	198.701i	0.0403910	+	0.0347117i
$321$		0			0
$322$		−	7396.93i		−	1.28017i
$323$			4275.54i			0.736524i
$324$		0			0
$325$	1606.52	−	244.368i	0.274196	−	0.0417079i
$326$	1406.66			0.238981
$327$		0			0
$328$		−	1422.52i		−	0.239468i
$329$	−1638.32			−0.274540
$330$		0			0
$331$	3442.15			0.571594			0.285797	−	0.958290i	$-0.407742\pi$
$331$	3442.15			0.571594			0.285797	+	0.958290i	$0.407742\pi$
$332$		−	6379.67i		−	1.05461i
$333$		0			0
$334$	4275.96			0.700509
$335$	3926.54	−	4568.97i	0.640387	−	0.745162i
$336$		0			0
$337$		−	7274.80i		−	1.17592i	−0.808892	−	0.587958i	$-0.799932\pi$
$337$		−	7274.80i		−	1.17592i	0.808892	−	0.587958i	$-0.200068\pi$
$338$		−	219.631i		−	0.0353442i
$339$		0			0
$340$	3088.85	−	3594.22i	0.492695	−	0.573305i
$341$	1700.86			0.270107
$342$		0			0
$343$			17274.7i			2.71938i
$344$	−4983.65			−0.781107
$345$		0			0
$346$	1274.84			0.198080
$347$		−	5232.06i		−	0.809429i	−0.914443	−	0.404714i	$-0.867371\pi$
$347$		−	5232.06i		−	0.809429i	0.914443	−	0.404714i	$-0.132629\pi$
$348$		0			0
$349$	−887.135			−0.136067			−0.0680333	−	0.997683i	$-0.521672\pi$
$349$	−887.135			−0.136067			−0.0680333	+	0.997683i	$0.521672\pi$
$350$	841.768	+	5533.95i	0.128555	+	0.845148i
$351$		0			0
$352$		−	1349.38i		−	0.204325i
$353$		−	458.015i		−	0.0690586i	−0.999404	−	0.0345293i	$-0.989007\pi$
$353$		−	458.015i		−	0.0690586i	0.999404	−	0.0345293i	$-0.0109932\pi$
$354$		0			0
$355$	−1881.85	−	1617.25i	−0.281348	−	0.241788i
$356$	9098.17			1.35450
$357$		0			0
$358$			3234.59i			0.477524i
$359$	−7501.93			−1.10289			−0.551444	−	0.834212i	$-0.685923\pi$
$359$	−7501.93			−1.10289			−0.551444	+	0.834212i	$0.685923\pi$
$360$		0			0
$361$	−2806.71			−0.409202
$362$			5189.81i			0.753509i
$363$		0			0
$364$	−2827.04			−0.407080
$365$	−1062.72	+	1236.59i	−0.152398	+	0.177332i
$366$		0			0
$367$		−	690.319i		−	0.0981862i	−0.998794	−	0.0490931i	$-0.984367\pi$
$367$		−	690.319i		−	0.0981862i	0.998794	−	0.0490931i	$-0.0156331\pi$
$368$		−	4347.25i		−	0.615805i
$369$		0			0
$370$	−3484.05	−	2994.17i	−0.489533	−	0.420701i
$371$	−14704.1			−2.05768
$372$		0			0
$373$		−	7288.68i		−	1.01178i	−0.862598	−	0.505889i	$-0.831164\pi$
$373$		−	7288.68i		−	1.01178i	0.862598	−	0.505889i	$-0.168836\pi$
$374$	643.654			0.0889908
$375$		0			0
$376$	884.282			0.121286
$377$			2757.35i			0.376686i
$378$		0			0
$379$	−2989.30			−0.405146			−0.202573	−	0.979267i	$-0.564930\pi$
$379$	−2989.30			−0.405146			−0.202573	+	0.979267i	$0.564930\pi$
$380$	−3406.54	−	2927.56i	−0.459873	−	0.395212i
$381$		0			0
$382$			1267.84i			0.169813i
$383$		−	3767.68i		−	0.502661i	−0.967901	−	0.251331i	$-0.919132\pi$
$383$		−	3767.68i		−	0.502661i	0.967901	−	0.251331i	$-0.0808681\pi$
$384$		0			0
$385$	1851.59	−	2154.53i	0.245105	−	0.285208i
$386$	880.488			0.116103
$387$		0			0
$388$		−	6315.54i		−	0.826348i
$389$	−1109.98			−0.144675			−0.0723373	−	0.997380i	$-0.523046\pi$
$389$	−1109.98			−0.144675			−0.0723373	+	0.997380i	$0.523046\pi$
$390$		0			0
$391$	11094.3			1.43495
$392$		−	15703.3i		−	2.02331i
$393$		0			0
$394$	−79.8742			−0.0102132
$395$	10804.2	+	9285.02i	1.37624	+	1.18273i
$396$		0			0
$397$		−	3401.28i		−	0.429988i	−0.976615	−	0.214994i	$-0.931027\pi$
$397$		−	3401.28i		−	0.429988i	0.976615	−	0.214994i	$-0.0689732\pi$
$398$			4619.70i			0.581821i
$399$		0			0
$400$	494.716	+	3252.36i	0.0618394	+	0.406545i
$401$	2705.68			0.336945			0.168473	−	0.985706i	$-0.446117\pi$
$401$	2705.68			0.336945			0.168473	+	0.985706i	$0.446117\pi$
$402$		0			0
$403$			2998.51i			0.370636i
$404$	2060.23			0.253713
$405$		0			0
$406$	−9498.17			−1.16105
$407$			2331.44i			0.283944i
$408$		0			0
$409$	6105.65			0.738153			0.369077	−	0.929399i	$-0.379674\pi$
$409$	6105.65			0.738153			0.369077	+	0.929399i	$0.379674\pi$
$410$	−724.333	+	842.843i	−0.0872495	+	0.101525i
$411$		0			0
$412$			9661.40i			1.15530i
$413$			28204.8i			3.36045i
$414$		0			0
$415$	−7366.26	+	8571.48i	−0.871315	+	1.01387i
$416$	2378.88			0.280371
$417$		0			0
$418$		−	610.045i		−	0.0713834i
$419$	−1808.37			−0.210846			−0.105423	−	0.994427i	$-0.533620\pi$
$419$	−1808.37			−0.210846			−0.105423	+	0.994427i	$0.533620\pi$
$420$		0			0
$421$	7391.07			0.855627			0.427813	−	0.903867i	$-0.359284\pi$
$421$	7391.07			0.855627			0.427813	+	0.903867i	$0.359284\pi$
$422$		−	4500.21i		−	0.519116i
$423$		0			0
$424$	7936.55			0.909040
$425$	−8300.11	+	1262.53i	−0.947328	+	0.144098i
$426$		0			0
$427$		−	4395.61i		−	0.498170i
$428$			4135.40i			0.467038i
$429$		0			0
$430$	2952.82	+	2537.63i	0.331157	+	0.284594i
$431$	3726.18			0.416436			0.208218	−	0.978082i	$-0.433234\pi$
$431$	3726.18			0.416436			0.208218	+	0.978082i	$0.433234\pi$
$432$		0			0
$433$		−	6064.24i		−	0.673046i	−0.941675	−	0.336523i	$-0.890749\pi$
$433$		−	6064.24i		−	0.673046i	0.941675	−	0.336523i	$-0.109251\pi$
$434$	−10328.9			−1.14240
$435$		0			0
$436$	2734.22			0.300333
$437$		−	10515.0i		−	1.15103i
$438$		0			0
$439$	2083.49			0.226514			0.113257	−	0.993566i	$-0.463872\pi$
$439$	2083.49			0.226514			0.113257	+	0.993566i	$0.463872\pi$
$440$	−999.393	+	1162.91i	−0.108282	+	0.125999i
$441$		0			0
$442$			1134.72i			0.122112i
$443$		−	4087.56i		−	0.438388i	−0.975681	−	0.219194i	$-0.929657\pi$
$443$		−	4087.56i		−	0.438388i	0.975681	−	0.219194i	$-0.0703428\pi$
$444$		0			0
$445$	−12224.0	−	10505.2i	−1.30218	−	1.11909i
$446$	−7127.77			−0.756748
$447$		0			0
$448$			939.582i			0.0990872i
$449$	−5467.89			−0.574712			−0.287356	−	0.957824i	$-0.592776\pi$
$449$	−5467.89			−0.574712			−0.287356	+	0.957824i	$0.592776\pi$
$450$		0			0
$451$	564.009			0.0588872
$452$		−	851.194i		−	0.0885770i
$453$		0			0
$454$	554.282			0.0572989
$455$	3798.31	+	3264.24i	0.391357	+	0.336329i
$456$		0			0
$457$		−	5504.65i		−	0.563450i	−0.959495	−	0.281725i	$-0.909093\pi$
$457$		−	5504.65i		−	0.563450i	0.959495	−	0.281725i	$-0.0909066\pi$
$458$			5272.85i			0.537957i
$459$		0			0
$460$	−7596.53	+	8839.41i	−0.769978	+	0.895956i
$461$	10313.0			1.04192			0.520961	−	0.853580i	$-0.325574\pi$
$461$	10313.0			1.04192			0.520961	+	0.853580i	$0.325574\pi$
$462$		0			0
$463$		−	6518.86i		−	0.654335i	−0.944966	−	0.327168i	$-0.893906\pi$
$463$		−	6518.86i		−	0.654335i	0.944966	−	0.327168i	$-0.106094\pi$
$464$	−5582.17			−0.558504
$465$		0			0
$466$	−5799.62			−0.576528
$467$		−	6516.94i		−	0.645756i	−0.946441	−	0.322878i	$-0.895350\pi$
$467$		−	6516.94i		−	0.645756i	0.946441	−	0.322878i	$-0.104650\pi$
$468$		0			0
$469$	18567.1			1.82803
$470$	−523.937	−	450.268i	−0.0514201	−	0.0441900i
$471$		0			0
$472$		−	15223.5i		−	1.48457i
$473$		−	1975.95i		−	0.192081i
$474$		0			0
$475$	1196.60	+	7866.71i	0.115587	+	0.759893i
$476$	14605.9			1.40643
$477$		0			0
$478$			1367.70i			0.130873i
$479$	8778.84			0.837401			0.418701	−	0.908124i	$-0.362486\pi$
$479$	8778.84			0.837401			0.418701	+	0.908124i	$0.362486\pi$
$480$		0			0
$481$	−4110.18			−0.389622
$482$			5672.12i			0.536013i
$483$		0			0
$484$	−8056.86			−0.756655
$485$	−7292.22	+	8485.32i	−0.682727	+	0.794430i
$486$		0			0
$487$		−	15756.7i		−	1.46613i	−0.680161	−	0.733063i	$-0.738090\pi$
$487$		−	15756.7i		−	1.46613i	0.680161	−	0.733063i	$-0.261910\pi$
$488$			2372.53i			0.220081i
$489$		0			0
$490$	−7995.97	+	9304.21i	−0.737186	+	0.857799i
$491$	4658.98			0.428222			0.214111	−	0.976809i	$-0.431315\pi$
$491$	4658.98			0.428222			0.214111	+	0.976809i	$0.431315\pi$
$492$		0			0
$493$		−	14245.9i		−	1.30142i
$494$	1075.47			0.0979510
$495$		0			0
$496$	−6070.40			−0.549534
$497$		−	7647.35i		−	0.690203i
$498$		0			0
$499$	20634.7			1.85117			0.925586	−	0.378538i	$-0.123573\pi$
$499$	20634.7			1.85117			0.925586	+	0.378538i	$0.123573\pi$
$500$	4677.35	−	7477.60i	0.418355	−	0.668817i
$501$		0			0
$502$			6245.09i			0.555243i
$503$		−	17508.7i		−	1.55204i	−0.630709	−	0.776020i	$-0.717236\pi$
$503$		−	17508.7i		−	1.55204i	0.630709	−	0.776020i	$-0.282764\pi$
$504$		0			0
$505$	−2768.05	−	2378.84i	−0.243914	−	0.209618i
$506$	−1582.97			−0.139074
$507$		0			0
$508$		−	11259.5i		−	0.983386i
$509$	−4358.36			−0.379530			−0.189765	−	0.981830i	$-0.560773\pi$
$509$	−4358.36			−0.379530			−0.189765	+	0.981830i	$0.560773\pi$
$510$		0			0
$511$	−5025.19			−0.435032
$512$			8731.80i			0.753701i
$513$		0			0
$514$	3051.17			0.261832
$515$	11155.5	−	12980.7i	0.954506	−	1.11067i
$516$		0			0
$517$			350.605i			0.0298252i
$518$		−	14158.3i		−	1.20092i
$519$		0			0
$520$	−2050.13	−	1761.87i	−0.172893	−	0.148583i
$521$	11846.0			0.996128			0.498064	−	0.867140i	$-0.334045\pi$
$521$	11846.0			0.996128			0.498064	+	0.867140i	$0.334045\pi$
$522$		0			0
$523$		−	9865.36i		−	0.824822i	−0.910998	−	0.412411i	$-0.864687\pi$
$523$		−	9865.36i		−	0.824822i	0.910998	−	0.412411i	$-0.135313\pi$
$524$	−4488.56			−0.374205
$525$		0			0
$526$	−6246.82			−0.517822
$527$		−	15491.8i		−	1.28052i
$528$		0			0
$529$	−15117.7			−1.24252
$530$	−4702.41	−	4041.21i	−0.385395	−	0.331206i
$531$		0			0
$532$		−	13843.3i		−	1.12816i
$533$			994.314i			0.0808040i
$534$		0			0
$535$	4774.93	−	5556.17i	0.385866	−	0.448998i
$536$	−10021.6			−0.807585
$537$		0			0
$538$		−	10634.5i		−	0.852205i
$539$	6226.14			0.497549
$540$		0			0
$541$	−6987.96			−0.555334			−0.277667	−	0.960677i	$-0.589561\pi$
$541$	−6987.96			−0.555334			−0.277667	+	0.960677i	$0.589561\pi$
$542$		−	1741.40i		−	0.138007i
$543$		0			0
$544$	−12290.5			−0.968661
$545$	−3673.59	−	3157.06i	−0.288733	−	0.248135i
$546$		0			0
$547$		−	4266.50i		−	0.333496i	−0.986000	−	0.166748i	$-0.946673\pi$
$547$		−	4266.50i		−	0.333496i	0.986000	−	0.166748i	$-0.0533266\pi$
$548$		−	5721.39i		−	0.445995i
$549$		0			0
$550$	1184.28	−	180.141i	0.0918144	−	0.0139659i
$551$	−13502.0			−1.04393
$552$		0			0
$553$			43905.3i			3.37621i
$554$	−6758.44			−0.518300
$555$		0			0
$556$	−8469.39			−0.646011
$557$			4717.62i			0.358873i	0.983770	+	0.179436i	$0.0574274\pi$
$557$			4717.62i			0.358873i	−0.983770	+	0.179436i	$0.942573\pi$
$558$		0			0
$559$	3483.48			0.263570
$560$	−6608.36	+	7689.57i	−0.498668	+	0.580256i
$561$		0			0
$562$			415.834i			0.0312115i
$563$		−	7201.26i		−	0.539071i	−0.962990	−	0.269536i	$-0.913130\pi$
$563$		−	7201.26i		−	0.539071i	0.962990	−	0.269536i	$-0.0868702\pi$
$564$		0			0
$565$	−982.830	+	1143.63i	−0.0731822	+	0.0851557i
$566$	−2569.50			−0.190820
$567$		0			0
$568$			4127.65i			0.304916i
$569$	3826.65			0.281936			0.140968	−	0.990014i	$-0.454979\pi$
$569$	3826.65			0.281936			0.140968	+	0.990014i	$0.454979\pi$
$570$		0			0
$571$	−25460.9			−1.86604			−0.933018	−	0.359830i	$-0.882835\pi$
$571$	−25460.9			−1.86604			−0.933018	+	0.359830i	$0.882835\pi$
$572$			604.995i			0.0442240i
$573$		0			0
$574$	−3425.09			−0.249060
$575$	20412.8	−	3104.99i	1.48047	−	0.225195i
$576$		0			0
$577$			15564.3i			1.12296i	0.827489	+	0.561481i	$0.189768\pi$
$577$			15564.3i			1.12296i	−0.827489	+	0.561481i	$0.810232\pi$
$578$			522.315i			0.0375872i
$579$		0			0
$580$	11350.4	+	9754.46i	0.812586	+	0.698331i
$581$	−34832.2			−2.48723
$582$		0			0
$583$			3146.73i			0.223541i
$584$	2712.34			0.192188
$585$		0			0
$586$	1827.69			0.128842
$587$		−	17777.5i		−	1.25001i	−0.780622	−	0.625004i	$-0.785097\pi$
$587$		−	17777.5i		−	1.25001i	0.780622	−	0.625004i	$-0.214903\pi$
$588$		0			0
$589$	−14682.9			−1.02716
$590$	−7751.66	+	9019.93i	−0.540900	+	0.629398i
$591$		0			0
$592$		−	8320.95i		−	0.577684i
$593$			23341.0i			1.61636i	0.588937	+	0.808179i	$0.299547\pi$
$593$			23341.0i			1.61636i	−0.588937	+	0.808179i	$0.700453\pi$
$594$		0			0
$595$	−19624.0	−	16864.7i	−1.35211	−	1.16199i
$596$	−263.903			−0.0181374
$597$		0			0
$598$		−	2790.67i		−	0.190835i
$599$	−10743.4			−0.732824			−0.366412	−	0.930453i	$-0.619414\pi$
$599$	−10743.4			−0.732824			−0.366412	+	0.930453i	$0.619414\pi$
$600$		0			0
$601$	19744.4			1.34009			0.670043	−	0.742323i	$-0.266276\pi$
$601$	19744.4			1.34009			0.670043	+	0.742323i	$0.266276\pi$
$602$			11999.5i			0.812395i
$603$		0			0
$604$	−4161.20			−0.280326
$605$	10824.9	+	9302.83i	0.727429	+	0.625147i
$606$		0			0
$607$		−	8231.01i		−	0.550389i	−0.961389	−	0.275195i	$-0.911258\pi$
$607$		−	8231.01i		−	0.550389i	0.961389	−	0.275195i	$-0.0887423\pi$
$608$			11648.7i			0.777005i
$609$		0			0
$610$	1208.07	−	1405.72i	0.0801858	−	0.0933051i
$611$	−618.096			−0.0409255
$612$		0			0
$613$		−	1430.13i		−	0.0942292i	−0.998889	−	0.0471146i	$-0.984997\pi$
$613$		−	1430.13i		−	0.0942292i	0.998889	−	0.0471146i	$-0.0150026\pi$
$614$	3784.23			0.248728
$615$		0			0
$616$	−4725.74			−0.309100
$617$			10008.4i			0.653037i	0.945191	+	0.326519i	$0.105876\pi$
$617$			10008.4i			0.653037i	−0.945191	+	0.326519i	$0.894124\pi$
$618$		0			0
$619$	−14399.2			−0.934979			−0.467490	−	0.883999i	$-0.654841\pi$
$619$	−14399.2			−0.934979			−0.467490	+	0.883999i	$0.654841\pi$
$620$	12343.1	+	10607.6i	0.799536	+	0.687116i
$621$		0			0
$622$		−	654.169i		−	0.0421700i
$623$		−	49674.9i		−	3.19452i
$624$		0			0
$625$	−14918.3	+	4645.94i	−0.954772	+	0.297340i
$626$	2918.07			0.186309
$627$		0			0
$628$		−	665.479i		−	0.0422858i
$629$	21235.3			1.34612
$630$		0			0
$631$	−22166.7			−1.39848			−0.699241	−	0.714886i	$-0.746479\pi$
$631$	−22166.7			−1.39848			−0.699241	+	0.714886i	$0.746479\pi$
$632$		−	23697.8i		−	1.49153i
$633$		0			0
$634$	7732.53			0.484382
$635$	−13000.8	+	15127.9i	−0.812472	+	0.945403i
$636$		0			0
$637$			10976.3i			0.682727i
$638$			2032.64i			0.126133i
$639$		0			0
$640$	10409.5	−	12112.6i	0.642924	−	0.748114i
$641$	−10016.5			−0.617202			−0.308601	−	0.951192i	$-0.599861\pi$
$641$	−10016.5			−0.617202			−0.308601	+	0.951192i	$0.599861\pi$
$642$		0			0
$643$			5085.35i			0.311892i	0.987766	+	0.155946i	$0.0498426\pi$
$643$			5085.35i			0.311892i	−0.987766	+	0.155946i	$0.950157\pi$
$644$	−35921.0			−2.19796
$645$		0			0
$646$	−5556.44			−0.338414
$647$			16584.2i			1.00772i	0.863787	+	0.503858i	$0.168086\pi$
$647$			16584.2i			1.00772i	−0.863787	+	0.503858i	$0.831914\pi$
$648$		0			0
$649$	6035.91			0.365069
$650$	317.577	+	2087.82i	0.0191637	+	0.125986i
$651$		0			0
$652$		−	6831.04i		−	0.410313i
$653$		−	811.964i		−	0.0486594i	−0.999704	−	0.0243297i	$-0.992255\pi$
$653$		−	811.964i		−	0.0486594i	0.999704	−	0.0243297i	$-0.00774515\pi$
$654$		0			0
$655$	6030.66	+	5182.70i	0.359752	+	0.309168i
$656$	−2012.96			−0.119806
$657$		0			0
$658$		−	2129.14i		−	0.126144i
$659$	16570.7			0.979516			0.489758	−	0.871858i	$-0.337085\pi$
$659$	16570.7			0.979516			0.489758	+	0.871858i	$0.337085\pi$
$660$		0			0
$661$	23023.9			1.35480			0.677402	−	0.735613i	$-0.263106\pi$
$661$	23023.9			1.35480			0.677402	+	0.735613i	$0.263106\pi$
$662$			4473.38i			0.262633i
$663$		0			0
$664$	18800.7			1.09881
$665$	−15984.1	+	18599.3i	−0.932086	+	1.08459i
$666$		0			0
$667$			35035.4i			2.03385i
$668$		−	20764.9i		−	1.20272i
$669$		0			0
$670$	5937.78	+	5102.88i	0.342383	+	0.294241i
$671$	−940.675			−0.0541197
$672$		0			0
$673$			19697.5i			1.12821i	0.825704	+	0.564104i	$0.190778\pi$
$673$			19697.5i			1.12821i	−0.825704	+	0.564104i	$0.809222\pi$
$674$	9454.25			0.540303
$675$		0			0
$676$	−1066.57			−0.0606834
$677$		−	32440.9i		−	1.84166i	−0.389963	−	0.920831i	$-0.627512\pi$
$677$		−	32440.9i		−	1.84166i	0.389963	−	0.920831i	$-0.372488\pi$
$678$		0			0
$679$	−34482.1			−1.94890
$680$	10592.0	+	9102.72i	0.597333	+	0.513343i
$681$		0			0
$682$			2210.42i			0.124107i
$683$			33834.7i			1.89553i	0.318963	+	0.947767i	$0.396665\pi$
$683$			33834.7i			1.89553i	−0.318963	+	0.947767i	$0.603335\pi$
$684$		0			0
$685$	−6606.18	+	7687.04i	−0.368481	+	0.428769i
$686$	−22450.0			−1.24948
$687$		0			0
$688$			7052.21i			0.390789i
$689$	−5547.49			−0.306738
$690$		0			0
$691$	24823.5			1.36661			0.683306	−	0.730132i	$-0.260541\pi$
$691$	24823.5			1.36661			0.683306	+	0.730132i	$0.260541\pi$
$692$		−	6190.87i		−	0.340089i
$693$		0			0
$694$	6799.53			0.371911
$695$	11379.2	+	9779.16i	0.621059	+	0.533733i
$696$		0			0
$697$		−	5137.14i		−	0.279172i
$698$		−	1152.91i		−	0.0625191i
$699$		0			0
$700$	26874.0	−	4087.80i	1.45106	−	0.220720i
$701$	17310.4			0.932675			0.466338	−	0.884607i	$-0.345573\pi$
$701$	17310.4			0.932675			0.466338	+	0.884607i	$0.345573\pi$
$702$		0			0
$703$		−	20126.5i		−	1.07978i
$704$	201.073			0.0107645
$705$		0			0
$706$	595.231			0.0317306
$707$		−	11248.6i		−	0.598369i
$708$		0			0
$709$	−29550.3			−1.56528			−0.782642	−	0.622472i	$-0.786128\pi$
$709$	−29550.3			−1.56528			−0.782642	+	0.622472i	$0.786128\pi$
$710$	2101.76	−	2445.64i	0.111095	−	0.129272i
$711$		0			0
$712$			26812.0i			1.41127i
$713$			38099.7i			2.00119i
$714$		0			0
$715$	698.556	−	812.849i	0.0365378	−	0.0425158i
$716$	15707.8			0.819873
$717$		0			0
$718$		−	9749.42i		−	0.506748i
$719$	30745.3			1.59473			0.797363	−	0.603500i	$-0.206228\pi$
$719$	30745.3			1.59473			0.797363	+	0.603500i	$0.206228\pi$
$720$		0			0
$721$	52750.1			2.72471
$722$		−	3647.57i		−	0.188018i
$723$		0			0
$724$	25202.8			1.29372
$725$	−3987.02	−	26211.4i	−0.204240	−	1.34272i
$726$		0			0
$727$		−	13223.2i		−	0.674581i	−0.941401	−	0.337290i	$-0.890490\pi$
$727$		−	13223.2i		−	0.674581i	0.941401	−	0.337290i	$-0.109510\pi$
$728$		−	8331.20i		−	0.424141i
$729$		0			0
$730$	−1607.06	−	1381.10i	−0.0814796	−	0.0700230i
$731$	−17997.4			−0.910615
$732$		0			0
$733$		−	15543.6i		−	0.783241i	−0.920127	−	0.391621i	$-0.871915\pi$
$733$		−	15543.6i		−	0.783241i	0.920127	−	0.391621i	$-0.128085\pi$
$734$	897.131			0.0451140
$735$		0			0
$736$	30226.6			1.51381
$737$		−	3973.41i		−	0.198592i
$738$		0			0
$739$	34338.2			1.70927			0.854635	−	0.519230i	$-0.173781\pi$
$739$	34338.2			1.70927			0.854635	+	0.519230i	$0.173781\pi$
$740$	−14540.3	+	16919.3i	−0.722313	+	0.840493i
$741$		0			0
$742$		−	19109.3i		−	0.945452i
$743$			31456.9i			1.55322i	0.629982	+	0.776610i	$0.283062\pi$
$743$			31456.9i			1.55322i	−0.629982	+	0.776610i	$0.716938\pi$
$744$		0			0
$745$	354.570	+	304.715i	0.0174368	+	0.0149851i
$746$	9472.29			0.464886
$747$		0			0
$748$		−	3125.72i		−	0.152791i
$749$	22578.8			1.10148
$750$		0			0
$751$	−2665.04			−0.129492			−0.0647461	−	0.997902i	$-0.520624\pi$
$751$	−2665.04			−0.129492			−0.0647461	+	0.997902i	$0.520624\pi$
$752$		−	1251.32i		−	0.0606794i
$753$		0			0
$754$	−3583.42			−0.173077
$755$	5590.83	+	4804.72i	0.269498	+	0.231605i
$756$		0			0
$757$		−	5447.26i		−	0.261538i	−0.991413	−	0.130769i	$-0.958255\pi$
$757$		−	5447.26i		−	0.261538i	0.991413	−	0.130769i	$-0.0417446\pi$
$758$		−	3884.87i		−	0.186154i
$759$		0			0
$760$	8627.41	−	10039.0i	0.411775	−	0.479147i
$761$	32255.4			1.53648			0.768238	−	0.640164i	$-0.221134\pi$
$761$	32255.4			1.53648			0.768238	+	0.640164i	$0.221134\pi$
$762$		0			0
$763$		−	14928.5i		−	0.708320i
$764$	6156.91			0.291557
$765$		0			0
$766$	4896.43			0.230960
$767$			10640.9i			0.500941i
$768$		0			0
$769$	−2752.71			−0.129084			−0.0645418	−	0.997915i	$-0.520559\pi$
$769$	−2752.71			−0.129084			−0.0645418	+	0.997915i	$0.520559\pi$
$770$	2800.00	+	2406.30i	0.131046	+	0.112620i
$771$		0			0
$772$		−	4275.83i		−	0.199340i
$773$		−	10269.8i		−	0.477850i	−0.971038	−	0.238925i	$-0.923205\pi$
$773$		−	10269.8i		−	0.477850i	0.971038	−	0.238925i	$-0.0767951\pi$
$774$		0			0
$775$	−4335.73	−	28504.0i	−0.200960	−	1.32115i
$776$	18611.7			0.860980
$777$		0			0
$778$		−	1442.52i		−	0.0664742i
$779$	−4868.89			−0.223936
$780$		0			0
$781$	−1636.56			−0.0749815
$782$			14418.1i			0.659320i
$783$		0			0
$784$	−22221.2			−1.01226
$785$	−768.393	+	894.112i	−0.0349365	+	0.0406525i
$786$		0			0
$787$		−	17070.3i		−	0.773177i	−0.922252	−	0.386589i	$-0.873653\pi$
$787$		−	17070.3i		−	0.773177i	0.922252	−	0.386589i	$-0.126347\pi$
$788$			387.886i			0.0175353i
$789$		0			0
$790$	−12066.7	+	14041.0i	−0.543436	+	0.632349i
$791$	−4647.42			−0.208904
$792$		0			0
$793$		−	1658.35i		−	0.0742621i
$794$	4420.26			0.197568
$795$		0			0
$796$	22434.2			0.998944
$797$			8366.45i			0.371838i	0.982565	+	0.185919i	$0.0595262\pi$
$797$			8366.45i			0.371838i	−0.982565	+	0.185919i	$0.940474\pi$
$798$		0			0
$799$	3193.40			0.141395
$800$	−22613.7	+	3439.77i	−0.999395	+	0.152018i
$801$		0			0
$802$			3516.27i			0.154818i
$803$			1075.41i			0.0472606i
$804$		0			0
$805$	48262.1	+	41476.1i	2.11306	+	1.81595i
$806$	−3896.83			−0.170298
$807$		0			0
$808$			6071.42i			0.264346i
$809$	−35142.0			−1.52723			−0.763613	−	0.645674i	$-0.776576\pi$
$809$	−35142.0			−1.52723			−0.763613	+	0.645674i	$0.776576\pi$
$810$		0			0
$811$	7588.23			0.328556			0.164278	−	0.986414i	$-0.447471\pi$
$811$	7588.23			0.328556			0.164278	+	0.986414i	$0.447471\pi$
$812$			46125.0i			1.99344i
$813$		0			0
$814$	−3029.91			−0.130465
$815$	−7887.45	+	9177.93i	−0.339000	+	0.394465i
$816$		0			0
$817$			17057.7i			0.730444i
$818$			7934.83i			0.339162i
$819$		0			0
$820$	4093.02	+	3517.51i	0.174310	+	0.149801i
$821$	8416.56			0.357783			0.178892	−	0.983869i	$-0.442749\pi$
$821$	8416.56			0.357783			0.178892	+	0.983869i	$0.442749\pi$
$822$		0			0
$823$			29841.8i			1.26394i	0.774993	+	0.631969i	$0.217753\pi$
$823$			29841.8i			1.26394i	−0.774993	+	0.631969i	$0.782247\pi$
$824$	−28471.8			−1.20372
$825$		0			0
$826$	−36654.6			−1.54404
$827$		−	20935.7i		−	0.880298i	−0.897925	−	0.440149i	$-0.854926\pi$
$827$		−	20935.7i		−	0.880298i	0.897925	−	0.440149i	$-0.145074\pi$
$828$		0			0
$829$	−9906.70			−0.415047			−0.207524	−	0.978230i	$-0.566540\pi$
$829$	−9906.70			−0.415047			−0.207524	+	0.978230i	$0.566540\pi$
$830$	−11139.4	−	9573.12i	−0.465848	−	0.400347i
$831$		0			0
$832$			354.480i			0.0147709i
$833$		−	56709.2i		−	2.35877i
$834$		0			0
$835$	−23976.2	+	27899.0i	−0.993688	+	1.15627i
$836$	−2962.50			−0.122560
$837$		0			0
$838$		−	2350.13i		−	0.0968783i
$839$	5870.13			0.241549			0.120774	−	0.992680i	$-0.461462\pi$
$839$	5870.13			0.241549			0.120774	+	0.992680i	$0.461462\pi$
$840$		0			0
$841$	20598.9			0.844598
$842$			9605.36i			0.393138i
$843$		0			0
$844$	−21853.9			−0.891284
$845$	1433.00	+	1231.51i	0.0583394	+	0.0501365i
$846$		0			0
$847$			43989.5i			1.78453i
$848$		−	11230.7i		−	0.454794i
$849$		0			0
$850$	−1640.77	−	10786.7i	−0.0662093	−	0.435273i
$851$	−52224.9			−2.10370
$852$		0			0
$853$			9104.66i			0.365460i	0.983163	+	0.182730i	$0.0584935\pi$
$853$			9104.66i			0.365460i	−0.983163	+	0.182730i	$0.941507\pi$
$854$	5712.49			0.228896
$855$		0			0
$856$	−12186.9			−0.486611
$857$			32110.0i			1.27988i	0.768425	+	0.639940i	$0.221041\pi$
$857$			32110.0i			1.27988i	−0.768425	+	0.639940i	$0.778959\pi$
$858$		0			0
$859$	12871.9			0.511272			0.255636	−	0.966773i	$-0.417715\pi$
$859$	12871.9			0.511272			0.255636	+	0.966773i	$0.417715\pi$
$860$	12323.2	−	14339.5i	0.488627	−	0.568572i
$861$		0			0
$862$			4842.50i			0.191341i
$863$		−	4537.25i		−	0.178969i	−0.995988	−	0.0894843i	$-0.971478\pi$
$863$		−	4537.25i		−	0.178969i	0.995988	−	0.0894843i	$-0.0285219\pi$
$864$		0			0
$865$	−7148.27	+	8317.82i	−0.280981	+	0.326953i
$866$	7881.02			0.309247
$867$		0			0
$868$			50159.3i			1.96142i
$869$	9395.86			0.366781
$870$		0			0
$871$	7004.88			0.272504
$872$			8057.65i			0.312920i
$873$		0			0
$874$	13665.2			0.528870
$875$	−40826.8	−	25537.8i	−1.57737	−	0.986667i
$876$		0			0
$877$		−	17128.9i		−	0.659521i	−0.944065	−	0.329761i	$-0.893032\pi$
$877$		−	17128.9i		−	0.659521i	0.944065	−	0.329761i	$-0.106968\pi$
$878$			2707.68i			0.104077i
$879$		0			0
$880$	1645.59	+	1414.21i	0.0630373	+	0.0541738i
$881$	21401.5			0.818428			0.409214	−	0.912438i	$-0.365803\pi$
$881$	21401.5			0.818428			0.409214	+	0.912438i	$0.365803\pi$
$882$		0			0
$883$		−	4340.60i		−	0.165428i	−0.996573	−	0.0827139i	$-0.973641\pi$
$883$		−	4340.60i		−	0.165428i	0.996573	−	0.0827139i	$-0.0263588\pi$
$884$	5510.45			0.209657
$885$		0			0
$886$	5312.15			0.201428
$887$		−	26728.7i		−	1.01180i	−0.862593	−	0.505898i	$-0.831161\pi$
$887$		−	26728.7i		−	1.01180i	0.862593	−	0.505898i	$-0.168839\pi$
$888$		0			0
$889$	−61475.6			−2.31926
$890$	13652.4	−	15886.1i	0.514191	−	0.598319i
$891$		0			0
$892$			34613.9i			1.29928i
$893$		−	3026.65i		−	0.113419i
$894$		0			0
$895$	−21104.5	−	18137.0i	−0.788206	−	0.677378i
$896$	49222.4			1.83527
$897$		0			0
$898$		−	7106.01i		−	0.264065i
$899$	48922.7			1.81497
$900$		0			0
$901$	28661.2			1.05976
$902$			732.980i			0.0270572i
$903$		0			0
$904$	2508.44			0.0922893
$905$	−33861.5	−	29100.3i	−1.24375	−	1.06887i
$906$		0			0
$907$		−	38923.7i		−	1.42496i	−0.701692	−	0.712480i	$-0.747572\pi$
$907$		−	38923.7i		−	1.42496i	0.701692	−	0.712480i	$-0.252428\pi$
$908$		−	2691.70i		−	0.0983781i
$909$		0			0
$910$	−4242.17	+	4936.24i	−0.154535	+	0.179818i
$911$	6424.23			0.233638			0.116819	−	0.993153i	$-0.462730\pi$
$911$	6424.23			0.233638			0.116819	+	0.993153i	$0.462730\pi$
$912$		0			0
$913$			7454.20i			0.270206i
$914$	7153.78			0.258891
$915$		0			0
$916$	25606.1			0.923633
$917$			24507.0i			0.882543i
$918$		0			0
$919$	−46325.0			−1.66281			−0.831404	−	0.555669i	$-0.812462\pi$
$919$	−46325.0			−1.66281			−0.831404	+	0.555669i	$0.812462\pi$
$920$	−26049.4	−	22386.7i	−0.933505	−	0.802248i
$921$		0			0
$922$			13402.7i			0.478736i
$923$		−	2885.15i		−	0.102888i
$924$		0			0
$925$	39071.6	−	5943.17i	1.38883	−	0.211254i
$926$	8471.84			0.300650
$927$		0			0
$928$		−	38813.0i		−	1.37295i
$929$	23921.0			0.844803			0.422401	−	0.906409i	$-0.361187\pi$
$929$	23921.0			0.844803			0.422401	+	0.906409i	$0.361187\pi$
$930$		0			0
$931$	−53748.1			−1.89208
$932$			28164.1i			0.989856i
$933$		0			0
$934$	8469.35			0.296708
$935$	−3609.10	+	4199.59i	−0.126236	+	0.146889i
$936$		0			0
$937$		−	45609.5i		−	1.59018i	−0.606492	−	0.795090i	$-0.707424\pi$
$937$		−	45609.5i		−	1.59018i	0.606492	−	0.795090i	$-0.292576\pi$
$938$			24129.5i			0.839934i
$939$		0			0
$940$	−2186.59	+	2544.35i	−0.0758711	+	0.0882845i
$941$	30390.8			1.05283			0.526414	−	0.850228i	$-0.323536\pi$
$941$	30390.8			1.05283			0.526414	+	0.850228i	$0.323536\pi$
$942$		0			0
$943$			12634.0i			0.436287i
$944$	−21542.3			−0.742735
$945$		0			0
$946$	2567.92			0.0882561
$947$		−	40335.6i		−	1.38409i	−0.721855	−	0.692044i	$-0.756710\pi$
$947$		−	40335.6i		−	1.38409i	0.721855	−	0.692044i	$-0.243290\pi$
$948$		0			0
$949$	−1895.88			−0.0648501
$950$	−10223.5	+	1555.09i	−0.349151	+	0.0531093i
$951$		0			0
$952$			43043.2i			1.46538i
$953$			37307.9i			1.26812i	0.773282	+	0.634062i	$0.218614\pi$
$953$			37307.9i			1.26812i	−0.773282	+	0.634062i	$0.781386\pi$
$954$		0			0
$955$	−8272.19	−	7109.06i	−0.280295	−	0.240884i
$956$	6641.83			0.224699
$957$		0			0
$958$			11408.9i			0.384764i
$959$	−31238.1			−1.05186
$960$		0			0
$961$	23410.6			0.785827
$962$		−	5341.55i		−	0.179021i
$963$		0			0
$964$	27545.0			0.920295
$965$	−4937.08	+	5744.84i	−0.164694	+	0.191640i
$966$		0			0
$967$		−	16551.2i		−	0.550415i	−0.961385	−	0.275208i	$-0.911253\pi$
$967$		−	16551.2i		−	0.550415i	0.961385	−	0.275208i	$-0.0887466\pi$
$968$		−	23743.3i		−	0.788366i
$969$		0			0
$970$	−11027.4	−	9476.89i	−0.365020	−	0.313695i
$971$	−11812.2			−0.390394			−0.195197	−	0.980764i	$-0.562535\pi$
$971$	−11812.2			−0.390394			−0.195197	+	0.980764i	$0.562535\pi$
$972$		0			0
$973$			46241.8i			1.52358i
$974$	20477.2			0.673647
$975$		0			0
$976$	3357.29			0.110107
$977$			4881.53i			0.159851i	0.996801	+	0.0799253i	$0.0254682\pi$
$977$			4881.53i			0.159851i	−0.996801	+	0.0799253i	$0.974532\pi$
$978$		0			0
$979$	−10630.6			−0.347043
$980$	45183.1	+	38830.1i	1.47278	+	1.26569i
$981$		0			0
$982$			6054.76i			0.196757i
$983$			49666.3i			1.61150i	0.592253	+	0.805752i	$0.298239\pi$
$983$			49666.3i			1.61150i	−0.592253	+	0.805752i	$0.701761\pi$
$984$		0			0
$985$	447.871	−	521.148i	0.0144877	−	0.0168580i
$986$	18513.8			0.597970
$987$		0			0
$988$		−	5222.71i		−	0.168175i
$989$	44261.9			1.42310
$990$		0			0
$991$	39146.6			1.25483			0.627413	−	0.778686i	$-0.284114\pi$
$991$	39146.6			1.25483			0.627413	+	0.778686i	$0.284114\pi$
$992$		−	42207.7i		−	1.35090i
$993$		0			0
$994$	9938.41			0.317130
$995$	−30141.8	−	25903.6i	−0.960360	−	0.825326i
$996$		0			0
$997$			19628.2i			0.623503i	0.950164	+	0.311751i	$0.100916\pi$
$997$			19628.2i			0.623503i	−0.950164	+	0.311751i	$0.899084\pi$
$998$			26816.6i			0.850565i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.4.c.e.469.13		22
3.2	odd	2		195.4.c.c.79.10	✓	22
5.4	even	2	inner	585.4.c.e.469.10		22
15.2	even	4		975.4.a.bb.1.7		11
15.8	even	4		975.4.a.bc.1.5		11
15.14	odd	2		195.4.c.c.79.13	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.4.c.c.79.10	✓	22	3.2	odd	2
195.4.c.c.79.13	yes	22	15.14	odd	2
585.4.c.e.469.10		22	5.4	even	2	inner
585.4.c.e.469.13		22	1.1	even	1	trivial
975.4.a.bb.1.7		11	15.2	even	4
975.4.a.bc.1.5		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)

\(f(q)\)	\(=\)	\(q+1.29959i q^{2} +6.31107 q^{4} +(-8.47931 - 7.28706i) q^{5} -34.4577i q^{7} +18.5985i q^{8} +(9.47018 - 11.0196i) q^{10} -7.37405 q^{11} -13.0000i q^{13} +44.7808 q^{14} +26.3181 q^{16} +67.1647i q^{17} +63.6576 q^{19} +(-53.5135 - 45.9891i) q^{20} -9.58323i q^{22} -165.181i q^{23} +(18.7975 + 123.579i) q^{25} +16.8947 q^{26} -217.465i q^{28} -212.104 q^{29} -230.655 q^{31} +182.991i q^{32} -87.2865 q^{34} +(-251.095 + 292.177i) q^{35} -316.168i q^{37} +82.7287i q^{38} +(135.528 - 157.703i) q^{40} -76.4857 q^{41} +267.960i q^{43} -46.5381 q^{44} +214.667 q^{46} -47.5459i q^{47} -844.331 q^{49} +(-160.601 + 24.4290i) q^{50} -82.0439i q^{52} -426.730i q^{53} +(62.5268 + 53.7351i) q^{55} +640.861 q^{56} -275.647i q^{58} -818.534 q^{59} +127.566 q^{61} -299.756i q^{62} -27.2677 q^{64} +(-94.7318 + 110.231i) q^{65} +538.837i q^{67} +423.881i q^{68} +(-379.711 - 326.320i) q^{70} +221.935 q^{71} -145.837i q^{73} +410.888 q^{74} +401.747 q^{76} +254.092i q^{77} -1274.18 q^{79} +(-223.160 - 191.782i) q^{80} -99.3999i q^{82} -1010.87i q^{83} +(489.433 - 569.510i) q^{85} -348.238 q^{86} -137.146i q^{88} +1441.62 q^{89} -447.950 q^{91} -1042.47i q^{92} +61.7901 q^{94} +(-539.772 - 463.876i) q^{95} -1000.71i q^{97} -1097.28i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 110 q^{4} - 8 q^{5} - 58 q^{10} - 200 q^{11} + 300 q^{14} + 1022 q^{16} - 88 q^{19} + 296 q^{20} - 346 q^{25} - 78 q^{26} + 560 q^{29} + 512 q^{31} - 156 q^{34} - 36 q^{35} + 10 q^{40} - 1400 q^{41}+ \cdots - 2376 q^{95}+O(q^{100}) \) 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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