LMFDB - Embedded newform 91.4.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,4,Mod(1,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	91.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$5.36917381052$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.5364412.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 27x^{2} - 24x + 76 $ x^4 - 27x^2 - 24x + 76
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.32361$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.323612 q^{2} +1.75980 q^{3} -7.89528 q^{4} -5.91876 q^{5} +0.569491 q^{6} +7.00000 q^{7} -5.14391 q^{8} -23.9031 q^{9} +O(q^{10})$	\(q+0.323612 q^{2} +1.75980 q^{3} -7.89528 q^{4} -5.91876 q^{5} +0.569491 q^{6} +7.00000 q^{7} -5.14391 q^{8} -23.9031 q^{9} -1.91538 q^{10} -60.8448 q^{11} -13.8941 q^{12} -13.0000 q^{13} +2.26529 q^{14} -10.4158 q^{15} +61.4976 q^{16} -1.36094 q^{17} -7.73534 q^{18} -4.20658 q^{19} +46.7303 q^{20} +12.3186 q^{21} -19.6901 q^{22} -10.6695 q^{23} -9.05222 q^{24} -89.9682 q^{25} -4.20696 q^{26} -89.5791 q^{27} -55.2669 q^{28} +124.031 q^{29} -3.37068 q^{30} +90.9367 q^{31} +61.0526 q^{32} -107.074 q^{33} -0.440417 q^{34} -41.4313 q^{35} +188.722 q^{36} +101.085 q^{37} -1.36130 q^{38} -22.8773 q^{39} +30.4456 q^{40} +235.305 q^{41} +3.98644 q^{42} +6.98363 q^{43} +480.386 q^{44} +141.477 q^{45} -3.45278 q^{46} -243.878 q^{47} +108.223 q^{48} +49.0000 q^{49} -29.1148 q^{50} -2.39498 q^{51} +102.639 q^{52} -282.024 q^{53} -28.9889 q^{54} +360.126 q^{55} -36.0073 q^{56} -7.40271 q^{57} +40.1380 q^{58} -675.683 q^{59} +82.2357 q^{60} +87.6018 q^{61} +29.4282 q^{62} -167.322 q^{63} -472.223 q^{64} +76.9439 q^{65} -34.6506 q^{66} +122.719 q^{67} +10.7450 q^{68} -18.7761 q^{69} -13.4077 q^{70} +35.3966 q^{71} +122.955 q^{72} -1073.70 q^{73} +32.7124 q^{74} -158.326 q^{75} +33.2121 q^{76} -425.914 q^{77} -7.40339 q^{78} +811.612 q^{79} -363.990 q^{80} +487.743 q^{81} +76.1477 q^{82} -1102.66 q^{83} -97.2585 q^{84} +8.05509 q^{85} +2.25999 q^{86} +218.269 q^{87} +312.980 q^{88} -1093.27 q^{89} +45.7837 q^{90} -91.0000 q^{91} +84.2387 q^{92} +160.030 q^{93} -78.9220 q^{94} +24.8977 q^{95} +107.440 q^{96} +911.865 q^{97} +15.8570 q^{98} +1454.38 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 5 q^{3} + 26 q^{4} - 36 q^{5} - 45 q^{6} + 28 q^{7} - 30 q^{8} + 21 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 5 * q^3 + 26 * q^4 - 36 * q^5 - 45 * q^6 + 28 * q^7 - 30 * q^8 + 21 * q^9	\( 4 q - 4 q^{2} - 5 q^{3} + 26 q^{4} - 36 q^{5} - 45 q^{6} + 28 q^{7} - 30 q^{8} + 21 q^{9} - 44 q^{10} - 95 q^{11} - 17 q^{12} - 52 q^{13} - 28 q^{14} - 16 q^{15} + 58 q^{16} - 146 q^{17} + 65 q^{18} - 48 q^{19} - 474 q^{20} - 35 q^{21} - 143 q^{22} - 121 q^{23} - 469 q^{24} + 506 q^{25} + 52 q^{26} - 83 q^{27} + 182 q^{28} - 440 q^{29} + 1548 q^{30} - 283 q^{31} - 114 q^{32} + 227 q^{33} + 1234 q^{34} - 252 q^{35} + 755 q^{36} - 209 q^{37} + 440 q^{38} + 65 q^{39} + 754 q^{40} - 93 q^{41} - 315 q^{42} + 526 q^{43} + 217 q^{44} - 768 q^{45} - 841 q^{46} - 783 q^{47} + 1407 q^{48} + 196 q^{49} + 446 q^{50} - 672 q^{51} - 338 q^{52} - 340 q^{53} - 199 q^{54} + 756 q^{55} - 210 q^{56} - 1014 q^{57} + 1916 q^{58} - 922 q^{59} - 396 q^{60} - 141 q^{61} + 1745 q^{62} + 147 q^{63} - 1510 q^{64} + 468 q^{65} + 503 q^{66} - 523 q^{67} - 1710 q^{68} + 1595 q^{69} - 308 q^{70} + 1468 q^{71} - 9 q^{72} - 47 q^{73} - 2249 q^{74} - 1547 q^{75} - 1382 q^{76} - 665 q^{77} + 585 q^{78} + 1025 q^{79} - 2538 q^{80} - 1772 q^{81} - 1561 q^{82} - 1190 q^{83} - 119 q^{84} - 568 q^{85} + 738 q^{86} + 720 q^{87} - 555 q^{88} - 2962 q^{89} - 1960 q^{90} - 364 q^{91} - 599 q^{92} - 763 q^{93} + 317 q^{94} + 2082 q^{95} - 45 q^{96} + 2715 q^{97} - 196 q^{98} + 586 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 5 * q^3 + 26 * q^4 - 36 * q^5 - 45 * q^6 + 28 * q^7 - 30 * q^8 + 21 * q^9 - 44 * q^10 - 95 * q^11 - 17 * q^12 - 52 * q^13 - 28 * q^14 - 16 * q^15 + 58 * q^16 - 146 * q^17 + 65 * q^18 - 48 * q^19 - 474 * q^20 - 35 * q^21 - 143 * q^22 - 121 * q^23 - 469 * q^24 + 506 * q^25 + 52 * q^26 - 83 * q^27 + 182 * q^28 - 440 * q^29 + 1548 * q^30 - 283 * q^31 - 114 * q^32 + 227 * q^33 + 1234 * q^34 - 252 * q^35 + 755 * q^36 - 209 * q^37 + 440 * q^38 + 65 * q^39 + 754 * q^40 - 93 * q^41 - 315 * q^42 + 526 * q^43 + 217 * q^44 - 768 * q^45 - 841 * q^46 - 783 * q^47 + 1407 * q^48 + 196 * q^49 + 446 * q^50 - 672 * q^51 - 338 * q^52 - 340 * q^53 - 199 * q^54 + 756 * q^55 - 210 * q^56 - 1014 * q^57 + 1916 * q^58 - 922 * q^59 - 396 * q^60 - 141 * q^61 + 1745 * q^62 + 147 * q^63 - 1510 * q^64 + 468 * q^65 + 503 * q^66 - 523 * q^67 - 1710 * q^68 + 1595 * q^69 - 308 * q^70 + 1468 * q^71 - 9 * q^72 - 47 * q^73 - 2249 * q^74 - 1547 * q^75 - 1382 * q^76 - 665 * q^77 + 585 * q^78 + 1025 * q^79 - 2538 * q^80 - 1772 * q^81 - 1561 * q^82 - 1190 * q^83 - 119 * q^84 - 568 * q^85 + 738 * q^86 + 720 * q^87 - 555 * q^88 - 2962 * q^89 - 1960 * q^90 - 364 * q^91 - 599 * q^92 - 763 * q^93 + 317 * q^94 + 2082 * q^95 - 45 * q^96 + 2715 * q^97 - 196 * q^98 + 586 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.323612	0.114414	0.0572071	−	0.998362i	$-0.481780\pi$
$2$	0.323612	0.114414	0.0572071	+	0.998362i	$0.481780\pi$
$3$	1.75980	0.338673	0.169336	−	0.985558i	$-0.445838\pi$
$3$	1.75980	0.338673	0.169336	+	0.985558i	$0.445838\pi$
$4$	−7.89528	−0.986909
$5$	−5.91876	−0.529390	−0.264695	−	0.964332i	$-0.585271\pi$
$5$	−5.91876	−0.529390	−0.264695	+	0.964332i	$0.585271\pi$
$6$	0.569491	0.0387490
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−5.14391	−0.227331
$9$	−23.9031	−0.885301
$10$	−1.91538	−0.0605698
$11$	−60.8448	−1.66776	−0.833882	−	0.551943i	$-0.813886\pi$
$11$	−60.8448	−1.66776	−0.833882	+	0.551943i	$0.813886\pi$
$12$	−13.8941	−0.334239
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	2.26529	0.0432445
$15$	−10.4158	−0.179290
$16$	61.4976	0.960900
$17$	−1.36094	−0.0194163	−0.00970813	−	0.999953i	$-0.503090\pi$
$17$	−1.36094	−0.0194163	−0.00970813	+	0.999953i	$0.503090\pi$
$18$	−7.73534	−0.101291
$19$	−4.20658	−0.0507923	−0.0253962	−	0.999677i	$-0.508085\pi$
$19$	−4.20658	−0.0507923	−0.0253962	+	0.999677i	$0.508085\pi$
$20$	46.7303	0.522460
$21$	12.3186	0.128006
$22$	−19.6901	−0.190816
$23$	−10.6695	−0.0967281	−0.0483640	−	0.998830i	$-0.515401\pi$
$23$	−10.6695	−0.0967281	−0.0483640	+	0.998830i	$0.515401\pi$
$24$	−9.05222	−0.0769907
$25$	−89.9682	−0.719746
$26$	−4.20696	−0.0317328
$27$	−89.5791	−0.638500
$28$	−55.2669	−0.373017
$29$	124.031	0.794207	0.397103	−	0.917774i	$-0.370015\pi$
$29$	124.031	0.794207	0.397103	+	0.917774i	$0.370015\pi$
$30$	−3.37068	−0.0205133
$31$	90.9367	0.526862	0.263431	−	0.964678i	$-0.415146\pi$
$31$	90.9367	0.526862	0.263431	+	0.964678i	$0.415146\pi$
$32$	61.0526	0.337271
$33$	−107.074	−0.564826
$34$	−0.440417	−0.00222150
$35$	−41.4313	−0.200091
$36$	188.722	0.873712
$37$	101.085	0.449143	0.224572	−	0.974458i	$-0.427902\pi$
$37$	101.085	0.449143	0.224572	+	0.974458i	$0.427902\pi$
$38$	−1.36130	−0.00581137
$39$	−22.8773	−0.0939309
$40$	30.4456	0.120347
$41$	235.305	0.896306	0.448153	−	0.893957i	$-0.352082\pi$
$41$	235.305	0.896306	0.448153	+	0.893957i	$0.352082\pi$
$42$	3.98644	0.0146457
$43$	6.98363	0.0247673	0.0123836	−	0.999923i	$-0.496058\pi$
$43$	6.98363	0.0247673	0.0123836	+	0.999923i	$0.496058\pi$
$44$	480.386	1.64593
$45$	141.477	0.468670
$46$	−3.45278	−0.0110671
$47$	−243.878	−0.756879	−0.378440	−	0.925626i	$-0.623539\pi$
$47$	−243.878	−0.756879	−0.378440	+	0.925626i	$0.623539\pi$
$48$	108.223	0.325430
$49$	49.0000	0.142857
$50$	−29.1148	−0.0823491
$51$	−2.39498	−0.00657576
$52$	102.639	0.273719
$53$	−282.024	−0.730924	−0.365462	−	0.930826i	$-0.619089\pi$
$53$	−282.024	−0.730924	−0.365462	+	0.930826i	$0.619089\pi$
$54$	−28.9889	−0.0730535
$55$	360.126	0.882898
$56$	−36.0073	−0.0859229
$57$	−7.40271	−0.0172020
$58$	40.1380	0.0908685
$59$	−675.683	−1.49096	−0.745479	−	0.666529i	$-0.767779\pi$
$59$	−675.683	−1.49096	−0.745479	+	0.666529i	$0.767779\pi$
$60$	82.2357	0.176943
$61$	87.6018	0.183873	0.0919365	−	0.995765i	$-0.470694\pi$
$61$	87.6018	0.183873	0.0919365	+	0.995765i	$0.470694\pi$
$62$	29.4282	0.0602805
$63$	−167.322	−0.334612
$64$	−472.223	−0.922311
$65$	76.9439	0.146826
$66$	−34.6506	−0.0646241
$67$	122.719	0.223768	0.111884	−	0.993721i	$-0.464311\pi$
$67$	122.719	0.223768	0.111884	+	0.993721i	$0.464311\pi$
$68$	10.7450	0.0191621
$69$	−18.7761	−0.0327592
$70$	−13.4077	−0.0228932
$71$	35.3966	0.0591663	0.0295831	−	0.999562i	$-0.490582\pi$
$71$	35.3966	0.0591663	0.0295831	+	0.999562i	$0.490582\pi$
$72$	122.955	0.201256
$73$	−1073.70	−1.72147	−0.860733	−	0.509057i	$-0.829994\pi$
$73$	−1073.70	−1.72147	−0.860733	+	0.509057i	$0.829994\pi$
$74$	32.7124	0.0513884
$75$	−158.326	−0.243758
$76$	33.2121	0.0501274
$77$	−425.914	−0.630355
$78$	−7.40339	−0.0107470
$79$	811.612	1.15587	0.577934	−	0.816084i	$-0.303859\pi$
$79$	811.612	1.15587	0.577934	+	0.816084i	$0.303859\pi$
$80$	−363.990	−0.508691
$81$	487.743	0.669058
$82$	76.1477	0.102550
$83$	−1102.66	−1.45823	−0.729116	−	0.684391i	$-0.760068\pi$
$83$	−1102.66	−1.45823	−0.729116	+	0.684391i	$0.760068\pi$
$84$	−97.2585	−0.126331
$85$	8.05509	0.0102788
$86$	2.25999	0.00283373
$87$	218.269	0.268976
$88$	312.980	0.379134
$89$	−1093.27	−1.30209	−0.651044	−	0.759040i	$-0.725669\pi$
$89$	−1093.27	−1.30209	−0.651044	+	0.759040i	$0.725669\pi$
$90$	45.7837	0.0536225
$91$	−91.0000	−0.104828
$92$	84.2387	0.0954618
$93$	160.030	0.178434
$94$	−78.9220	−0.0865977
$95$	24.8977	0.0268890
$96$	107.440	0.114225
$97$	911.865	0.954494	0.477247	−	0.878769i	$-0.341635\pi$
$97$	911.865	0.954494	0.477247	+	0.878769i	$0.341635\pi$
$98$	15.8570	0.0163449
$99$	1454.38	1.47647
$100$	710.324	0.710324
$101$	−1708.38	−1.68307	−0.841535	−	0.540202i	$-0.818348\pi$
$101$	−1708.38	−1.68307	−0.841535	+	0.540202i	$0.818348\pi$
$102$	−0.775044	−0.000752360 0
$103$	−833.431	−0.797285	−0.398643	−	0.917106i	$-0.630519\pi$
$103$	−833.431	−0.797285	−0.398643	+	0.917106i	$0.630519\pi$
$104$	66.8708	0.0630502
$105$	−72.9107	−0.0677653
$106$	−91.2664	−0.0836281
$107$	296.677	0.268045	0.134022	−	0.990978i	$-0.457211\pi$
$107$	296.677	0.268045	0.134022	+	0.990978i	$0.457211\pi$
$108$	707.251	0.630142
$109$	−2012.35	−1.76833	−0.884166	−	0.467173i	$-0.845272\pi$
$109$	−2012.35	−1.76833	−0.884166	+	0.467173i	$0.845272\pi$
$110$	116.541	0.101016
$111$	177.889	0.152113
$112$	430.483	0.363186
$113$	−459.400	−0.382448	−0.191224	−	0.981546i	$-0.561246\pi$
$113$	−459.400	−0.382448	−0.191224	+	0.981546i	$0.561246\pi$
$114$	−2.39561	−0.00196815
$115$	63.1503	0.0512069
$116$	−979.259	−0.783810
$117$	310.741	0.245538
$118$	−218.659	−0.170587
$119$	−9.52658	−0.00733866
$120$	53.5780	0.0407581
$121$	2371.09	1.78143
$122$	28.3490	0.0210377
$123$	414.089	0.303554
$124$	−717.971	−0.519965
$125$	1272.35	0.910417
$126$	−54.1474	−0.0382844
$127$	2573.78	1.79832	0.899158	−	0.437624i	$-0.144180\pi$
$127$	2573.78	1.79832	0.899158	+	0.437624i	$0.144180\pi$
$128$	−641.238	−0.442797
$129$	12.2898	0.00838801
$130$	24.9000	0.0167990
$131$	599.610	0.399910	0.199955	−	0.979805i	$-0.435920\pi$
$131$	599.610	0.399910	0.199955	+	0.979805i	$0.435920\pi$
$132$	845.382	0.557432
$133$	−29.4460	−0.0191977
$134$	39.7133	0.0256023
$135$	530.197	0.338016
$136$	7.00055	0.00441391
$137$	−1501.25	−0.936207	−0.468104	−	0.883674i	$-0.655063\pi$
$137$	−1501.25	−0.936207	−0.468104	+	0.883674i	$0.655063\pi$
$138$	−6.07619	−0.00374811
$139$	2652.59	1.61863	0.809316	−	0.587374i	$-0.199838\pi$
$139$	2652.59	1.61863	0.809316	+	0.587374i	$0.199838\pi$
$140$	327.112	0.197471
$141$	−429.176	−0.256334
$142$	11.4548	0.00676946
$143$	790.982	0.462554
$144$	−1469.98	−0.850685
$145$	−734.111	−0.420445
$146$	−347.462	−0.196960
$147$	86.2300	0.0483818
$148$	−798.095	−0.443264
$149$	1316.52	0.723852	0.361926	−	0.932207i	$-0.382119\pi$
$149$	1316.52	0.723852	0.361926	+	0.932207i	$0.382119\pi$
$150$	−51.2361	−0.0278894
$151$	2051.26	1.10549	0.552744	−	0.833351i	$-0.313581\pi$
$151$	2051.26	1.10549	0.552744	+	0.833351i	$0.313581\pi$
$152$	21.6382	0.0115467
$153$	32.5307	0.0171892
$154$	−137.831	−0.0721216
$155$	−538.233	−0.278916
$156$	180.623	0.0927013
$157$	1313.72	0.667809	0.333904	−	0.942607i	$-0.391634\pi$
$157$	1313.72	0.667809	0.333904	+	0.942607i	$0.391634\pi$
$158$	262.648	0.132248
$159$	−496.305	−0.247544
$160$	−361.356	−0.178548
$161$	−74.6865	−0.0365598
$162$	157.840	0.0765498
$163$	−1850.44	−0.889190	−0.444595	−	0.895732i	$-0.646652\pi$
$163$	−1850.44	−0.889190	−0.444595	+	0.895732i	$0.646652\pi$
$164$	−1857.80	−0.884572
$165$	633.748	0.299013
$166$	−356.836	−0.166842
$167$	−1090.13	−0.505130	−0.252565	−	0.967580i	$-0.581274\pi$
$167$	−1090.13	−0.505130	−0.252565	+	0.967580i	$0.581274\pi$
$168$	−63.3655	−0.0290997
$169$	169.000	0.0769231
$170$	2.60672	0.00117604
$171$	100.550	0.0449665
$172$	−55.1377	−0.0244431
$173$	2306.38	1.01359	0.506795	−	0.862066i	$-0.330830\pi$
$173$	2306.38	1.01359	0.506795	+	0.862066i	$0.330830\pi$
$174$	70.6346	0.0307747
$175$	−629.778	−0.272038
$176$	−3741.81	−1.60255
$177$	−1189.06	−0.504947
$178$	−353.794	−0.148977
$179$	−363.408	−0.151745	−0.0758726	−	0.997118i	$-0.524174\pi$
$179$	−363.408	−0.151745	−0.0758726	+	0.997118i	$0.524174\pi$
$180$	−1117.00	−0.462535
$181$	−3863.47	−1.58657	−0.793287	−	0.608848i	$-0.791632\pi$
$181$	−3863.47	−1.58657	−0.793287	+	0.608848i	$0.791632\pi$
$182$	−29.4487	−0.0119939
$183$	154.161	0.0622728
$184$	54.8829	0.0219893
$185$	−598.299	−0.237772
$186$	51.7877	0.0204154
$187$	82.8061	0.0323817
$188$	1925.49	0.746971
$189$	−627.053	−0.241330
$190$	8.05721	0.00307648
$191$	−1304.09	−0.494035	−0.247017	−	0.969011i	$-0.579450\pi$
$191$	−1304.09	−0.494035	−0.247017	+	0.969011i	$0.579450\pi$
$192$	−831.016	−0.312362
$193$	−96.9311	−0.0361516	−0.0180758	−	0.999837i	$-0.505754\pi$
$193$	−96.9311	−0.0361516	−0.0180758	+	0.999837i	$0.505754\pi$
$194$	295.091	0.109208
$195$	135.406	0.0497261
$196$	−386.868	−0.140987
$197$	−3135.09	−1.13384	−0.566919	−	0.823774i	$-0.691865\pi$
$197$	−3135.09	−1.13384	−0.566919	+	0.823774i	$0.691865\pi$
$198$	470.655	0.168929
$199$	3431.34	1.22232	0.611159	−	0.791508i	$-0.290704\pi$
$199$	3431.34	1.22232	0.611159	+	0.791508i	$0.290704\pi$
$200$	462.788	0.163620
$201$	215.960	0.0757842
$202$	−552.853	−0.192567
$203$	868.217	0.300182
$204$	18.9090	0.00648968
$205$	−1392.72	−0.474496
$206$	−269.708	−0.0912207
$207$	255.034	0.0856334
$208$	−799.468	−0.266506
$209$	255.948	0.0847096
$210$	−23.5948	−0.00775331
$211$	4599.00	1.50051	0.750256	−	0.661147i	$-0.229930\pi$
$211$	4599.00	1.50051	0.750256	+	0.661147i	$0.229930\pi$
$212$	2226.66	0.721356
$213$	62.2908	0.0200380
$214$	96.0082	0.0306681
$215$	−41.3345	−0.0131116
$216$	460.786	0.145151
$217$	636.557	0.199135
$218$	−651.221	−0.202322
$219$	−1889.49	−0.583014
$220$	−2843.29	−0.871340
$221$	17.6922	0.00538510
$222$	57.5671	0.0174038
$223$	−4769.56	−1.43226	−0.716129	−	0.697968i	$-0.754088\pi$
$223$	−4769.56	−1.43226	−0.716129	+	0.697968i	$0.754088\pi$
$224$	427.368	0.127477
$225$	2150.52	0.637192
$226$	−148.667	−0.0437575
$227$	5426.06	1.58652	0.793260	−	0.608883i	$-0.208382\pi$
$227$	5426.06	1.58652	0.793260	+	0.608883i	$0.208382\pi$
$228$	58.4464	0.0169768
$229$	−3946.45	−1.13881	−0.569407	−	0.822056i	$-0.692827\pi$
$229$	−3946.45	−1.13881	−0.569407	+	0.822056i	$0.692827\pi$
$230$	20.4362	0.00585880
$231$	−749.521	−0.213484
$232$	−638.004	−0.180547
$233$	−4611.04	−1.29648	−0.648238	−	0.761437i	$-0.724494\pi$
$233$	−4611.04	−1.29648	−0.648238	+	0.761437i	$0.724494\pi$
$234$	100.559	0.0280931
$235$	1443.46	0.400685
$236$	5334.71	1.47144
$237$	1428.27	0.391461
$238$	−3.08292	−0.000839647 0
$239$	−1663.03	−0.450094	−0.225047	−	0.974348i	$-0.572253\pi$
$239$	−1663.03	−0.450094	−0.225047	+	0.974348i	$0.572253\pi$
$240$	−640.547	−0.172280
$241$	2964.29	0.792311	0.396156	−	0.918183i	$-0.370344\pi$
$241$	2964.29	0.792311	0.396156	+	0.918183i	$0.370344\pi$
$242$	767.313	0.203821
$243$	3276.96	0.865092
$244$	−691.640	−0.181466
$245$	−290.019	−0.0756272
$246$	134.004	0.0347309
$247$	54.6855	0.0140873
$248$	−467.770	−0.119772
$249$	−1940.46	−0.493863
$250$	411.747	0.104165
$251$	−3483.07	−0.875893	−0.437947	−	0.899001i	$-0.644294\pi$
$251$	−3483.07	−0.875893	−0.437947	+	0.899001i	$0.644294\pi$
$252$	1321.05	0.330232
$253$	649.184	0.161320
$254$	832.907	0.205753
$255$	14.1753	0.00348114
$256$	3570.27	0.871649
$257$	4983.36	1.20955	0.604774	−	0.796397i	$-0.293264\pi$
$257$	4983.36	1.20955	0.604774	+	0.796397i	$0.293264\pi$
$258$	3.97712	0.000959707 0
$259$	707.596	0.169760
$260$	−607.494	−0.144904
$261$	−2964.73	−0.703112
$262$	194.041	0.0457553
$263$	7413.00	1.73804	0.869021	−	0.494776i	$-0.164750\pi$
$263$	7413.00	1.73804	0.869021	+	0.494776i	$0.164750\pi$
$264$	550.780	0.128402
$265$	1669.23	0.386944
$266$	−9.52909	−0.00219649
$267$	−1923.92	−0.440982
$268$	−968.898	−0.220839
$269$	−7815.61	−1.77147	−0.885736	−	0.464189i	$-0.846346\pi$
$269$	−7815.61	−1.77147	−0.885736	+	0.464189i	$0.846346\pi$
$270$	171.578	0.0386738
$271$	−940.210	−0.210752	−0.105376	−	0.994432i	$-0.533605\pi$
$271$	−940.210	−0.210752	−0.105376	+	0.994432i	$0.533605\pi$
$272$	−83.6945	−0.0186571
$273$	−160.141	−0.0355025
$274$	−485.823	−0.107115
$275$	5474.10	1.20037
$276$	148.243	0.0323303
$277$	1086.00	0.235565	0.117783	−	0.993039i	$-0.462421\pi$
$277$	1086.00	0.235565	0.117783	+	0.993039i	$0.462421\pi$
$278$	858.411	0.185194
$279$	−2173.67	−0.466431
$280$	213.119	0.0454868
$281$	81.9702	0.0174019	0.00870095	−	0.999962i	$-0.497230\pi$
$281$	81.9702	0.0174019	0.00870095	+	0.999962i	$0.497230\pi$
$282$	−138.887	−0.0293283
$283$	8459.84	1.77698	0.888490	−	0.458896i	$-0.151755\pi$
$283$	8459.84	1.77698	0.888490	+	0.458896i	$0.151755\pi$
$284$	−279.466	−0.0583918
$285$	43.8149	0.00910656
$286$	255.972	0.0529228
$287$	1647.14	0.338772
$288$	−1459.35	−0.298586
$289$	−4911.15	−0.999623
$290$	−237.567	−0.0481049
$291$	1604.70	0.323261
$292$	8477.15	1.69893
$293$	−3439.10	−0.685714	−0.342857	−	0.939388i	$-0.611395\pi$
$293$	−3439.10	−0.685714	−0.342857	+	0.939388i	$0.611395\pi$
$294$	27.9051	0.00553557
$295$	3999.21	0.789298
$296$	−519.973	−0.102104
$297$	5450.42	1.06487
$298$	426.043	0.0828189
$299$	138.704	0.0268275
$300$	1250.02	0.240567
$301$	48.8854	0.00936116
$302$	663.811	0.126484
$303$	−3006.40	−0.570010
$304$	−258.694	−0.0488063
$305$	−518.494	−0.0973406
$306$	10.5273	0.00196669
$307$	−1076.49	−0.200126	−0.100063	−	0.994981i	$-0.531904\pi$
$307$	−1076.49	−0.200126	−0.100063	+	0.994981i	$0.531904\pi$
$308$	3362.70	0.622104
$309$	−1466.67	−0.270019
$310$	−174.179	−0.0319119
$311$	−7001.34	−1.27656	−0.638279	−	0.769805i	$-0.720353\pi$
$311$	−7001.34	−1.27656	−0.638279	+	0.769805i	$0.720353\pi$
$312$	117.679	0.0213534
$313$	−7431.60	−1.34204	−0.671020	−	0.741439i	$-0.734144\pi$
$313$	−7431.60	−1.34204	−0.671020	+	0.741439i	$0.734144\pi$
$314$	425.135	0.0764068
$315$	990.339	0.177140
$316$	−6407.90	−1.14074
$317$	−7181.40	−1.27239	−0.636195	−	0.771528i	$-0.719493\pi$
$317$	−7181.40	−1.27239	−0.636195	+	0.771528i	$0.719493\pi$
$318$	−160.610	−0.0283226
$319$	−7546.64	−1.32455
$320$	2794.98	0.488263
$321$	522.090	0.0907795
$322$	−24.1695	−0.00418296
$323$	5.72490	0.000986198 0
$324$	−3850.87	−0.660300
$325$	1169.59	0.199622
$326$	−598.826	−0.101736
$327$	−3541.32	−0.598886
$328$	−1210.39	−0.203758
$329$	−1707.15	−0.286073
$330$	205.089	0.0342114
$331$	−3742.93	−0.621540	−0.310770	−	0.950485i	$-0.600587\pi$
$331$	−3742.93	−0.621540	−0.310770	+	0.950485i	$0.600587\pi$
$332$	8705.84	1.43914
$333$	−2416.25	−0.397627
$334$	−352.779	−0.0577940
$335$	−726.343	−0.118461
$336$	757.562	0.123001
$337$	10859.5	1.75535	0.877674	−	0.479258i	$-0.159094\pi$
$337$	10859.5	1.75535	0.877674	+	0.479258i	$0.159094\pi$
$338$	54.6905	0.00880109
$339$	−808.449	−0.129525
$340$	−63.5971	−0.0101442
$341$	−5533.03	−0.878681
$342$	32.5393	0.00514481
$343$	343.000	0.0539949
$344$	−35.9231	−0.00563037
$345$	111.132	0.0173424
$346$	746.374	0.115969
$347$	267.989	0.0414594	0.0207297	−	0.999785i	$-0.493401\pi$
$347$	267.989	0.0414594	0.0207297	+	0.999785i	$0.493401\pi$
$348$	−1723.30	−0.265455
$349$	−5082.15	−0.779488	−0.389744	−	0.920923i	$-0.627437\pi$
$349$	−5082.15	−0.779488	−0.389744	+	0.920923i	$0.627437\pi$
$350$	−203.804	−0.0311251
$351$	1164.53	0.177088
$352$	−3714.73	−0.562489
$353$	9356.72	1.41079	0.705394	−	0.708815i	$-0.250770\pi$
$353$	9356.72	1.41079	0.705394	+	0.708815i	$0.250770\pi$
$354$	−384.796	−0.0577731
$355$	−209.504	−0.0313221
$356$	8631.63	1.28504
$357$	−16.7648	−0.00248540
$358$	−117.603	−0.0173618
$359$	−499.977	−0.0735036	−0.0367518	−	0.999324i	$-0.511701\pi$
$359$	−499.977	−0.0735036	−0.0367518	+	0.999324i	$0.511701\pi$
$360$	−727.744	−0.106543
$361$	−6841.30	−0.997420
$362$	−1250.27	−0.181527
$363$	4172.63	0.603323
$364$	718.470	0.103456
$365$	6354.97	0.911327
$366$	49.8884	0.00712489
$367$	−2754.73	−0.391814	−0.195907	−	0.980622i	$-0.562765\pi$
$367$	−2754.73	−0.391814	−0.195907	+	0.980622i	$0.562765\pi$
$368$	−656.149	−0.0929460
$369$	−5624.53	−0.793500
$370$	−193.617	−0.0272045
$371$	−1974.17	−0.276263
$372$	−1263.48	−0.176098
$373$	−9414.45	−1.30687	−0.653434	−	0.756984i	$-0.726672\pi$
$373$	−9414.45	−1.30687	−0.653434	+	0.756984i	$0.726672\pi$
$374$	26.7971	0.00370493
$375$	2239.07	0.308333
$376$	1254.49	0.172062
$377$	−1612.40	−0.220273
$378$	−202.922	−0.0276116
$379$	−11295.5	−1.53090	−0.765451	−	0.643494i	$-0.777484\pi$
$379$	−11295.5	−1.53090	−0.765451	+	0.643494i	$0.777484\pi$
$380$	−196.574	−0.0265370
$381$	4529.33	0.609041
$382$	−422.019	−0.0565246
$383$	265.629	0.0354386	0.0177193	−	0.999843i	$-0.494359\pi$
$383$	265.629	0.0354386	0.0177193	+	0.999843i	$0.494359\pi$
$384$	−1128.45	−0.149963
$385$	2520.88	0.333704
$386$	−31.3681	−0.00413625
$387$	−166.931	−0.0219265
$388$	−7199.43	−0.941999
$389$	11601.0	1.51207	0.756037	−	0.654529i	$-0.227133\pi$
$389$	11601.0	1.51207	0.756037	+	0.654529i	$0.227133\pi$
$390$	43.8189	0.00568937
$391$	14.5206	0.00187810
$392$	−252.051	−0.0324758
$393$	1055.19	0.135438
$394$	−1014.55	−0.129727
$395$	−4803.74	−0.611905
$396$	−11482.7	−1.45714
$397$	6664.32	0.842501	0.421250	−	0.906944i	$-0.361591\pi$
$397$	6664.32	0.842501	0.421250	+	0.906944i	$0.361591\pi$
$398$	1110.42	0.139851
$399$	−51.8190	−0.00650174
$400$	−5532.83	−0.691603
$401$	7874.09	0.980582	0.490291	−	0.871559i	$-0.336891\pi$
$401$	7874.09	0.980582	0.490291	+	0.871559i	$0.336891\pi$
$402$	69.8872	0.00867079
$403$	−1182.18	−0.146125
$404$	13488.1	1.66104
$405$	−2886.84	−0.354193
$406$	280.966	0.0343451
$407$	−6150.51	−0.749065
$408$	12.3195	0.00149487
$409$	−2311.74	−0.279483	−0.139741	−	0.990188i	$-0.544627\pi$
$409$	−2311.74	−0.279483	−0.139741	+	0.990188i	$0.544627\pi$
$410$	−450.700	−0.0542890
$411$	−2641.89	−0.317068
$412$	6580.16	0.786848
$413$	−4729.78	−0.563529
$414$	82.5323	0.00979768
$415$	6526.41	0.771973
$416$	−793.684	−0.0935422
$417$	4668.02	0.548186
$418$	82.8280	0.00969198
$419$	−3945.48	−0.460023	−0.230011	−	0.973188i	$-0.573876\pi$
$419$	−3945.48	−0.460023	−0.230011	+	0.973188i	$0.573876\pi$
$420$	575.650	0.0668782
$421$	−699.284	−0.0809526	−0.0404763	−	0.999180i	$-0.512888\pi$
$421$	−699.284	−0.0809526	−0.0404763	+	0.999180i	$0.512888\pi$
$422$	1488.29	0.171680
$423$	5829.46	0.670066
$424$	1450.70	0.166161
$425$	122.441	0.0139748
$426$	20.1581	0.00229263
$427$	613.212	0.0694975
$428$	−2342.34	−0.264536
$429$	1391.97	0.156655
$430$	−13.3763	−0.00150015
$431$	14778.0	1.65158	0.825789	−	0.563980i	$-0.190730\pi$
$431$	14778.0	1.65158	0.825789	+	0.563980i	$0.190730\pi$
$432$	−5508.89	−0.613534
$433$	4217.17	0.468046	0.234023	−	0.972231i	$-0.424811\pi$
$433$	4217.17	0.468046	0.234023	+	0.972231i	$0.424811\pi$
$434$	205.998	0.0227839
$435$	−1291.88	−0.142393
$436$	15888.1	1.74518
$437$	44.8821	0.00491305
$438$	−611.462	−0.0667050
$439$	6372.34	0.692791	0.346395	−	0.938089i	$-0.387406\pi$
$439$	6372.34	0.692791	0.346395	+	0.938089i	$0.387406\pi$
$440$	−1852.45	−0.200710
$441$	−1171.25	−0.126472
$442$	5.72542	0.000616132 0
$443$	7824.17	0.839137	0.419568	−	0.907724i	$-0.362181\pi$
$443$	7824.17	0.839137	0.419568	+	0.907724i	$0.362181\pi$
$444$	−1404.48	−0.150121
$445$	6470.78	0.689313
$446$	−1543.49	−0.163871
$447$	2316.81	0.245149
$448$	−3305.56	−0.348601
$449$	3132.31	0.329226	0.164613	−	0.986358i	$-0.447362\pi$
$449$	3132.31	0.329226	0.164613	+	0.986358i	$0.447362\pi$
$450$	695.935	0.0729038
$451$	−14317.1	−1.49483
$452$	3627.09	0.377442
$453$	3609.79	0.374399
$454$	1755.94	0.181520
$455$	538.608	0.0554952
$456$	38.0788	0.00391054
$457$	2253.14	0.230629	0.115314	−	0.993329i	$-0.463212\pi$
$457$	2253.14	0.230629	0.115314	+	0.993329i	$0.463212\pi$
$458$	−1277.12	−0.130297
$459$	121.912	0.0123973
$460$	−498.589	−0.0505366
$461$	−9164.98	−0.925934	−0.462967	−	0.886375i	$-0.653215\pi$
$461$	−9164.98	−0.925934	−0.462967	+	0.886375i	$0.653215\pi$
$462$	−242.554	−0.0244256
$463$	7086.00	0.711263	0.355631	−	0.934626i	$-0.384266\pi$
$463$	7086.00	0.711263	0.355631	+	0.934626i	$0.384266\pi$
$464$	7627.61	0.763153
$465$	−947.180	−0.0944611
$466$	−1492.19	−0.148335
$467$	11174.0	1.10721	0.553607	−	0.832778i	$-0.313251\pi$
$467$	11174.0	1.10721	0.553607	+	0.832778i	$0.313251\pi$
$468$	−2453.38	−0.242324
$469$	859.031	0.0845764
$470$	467.121	0.0458440
$471$	2311.87	0.226169
$472$	3475.65	0.338940
$473$	−424.918	−0.0413060
$474$	462.206	0.0447887
$475$	378.458	0.0365576
$476$	75.2150	0.00724259
$477$	6741.25	0.647088
$478$	−538.176	−0.0514971
$479$	8240.34	0.786035	0.393018	−	0.919531i	$-0.371431\pi$
$479$	8240.34	0.786035	0.393018	+	0.919531i	$0.371431\pi$
$480$	−635.913	−0.0604694
$481$	−1314.11	−0.124570
$482$	959.282	0.0906517
$483$	−131.433	−0.0123818
$484$	−18720.4	−1.75811
$485$	−5397.12	−0.505300
$486$	1060.47	0.0989788
$487$	−9967.60	−0.927464	−0.463732	−	0.885975i	$-0.653490\pi$
$487$	−9967.60	−0.927464	−0.463732	+	0.885975i	$0.653490\pi$
$488$	−450.615	−0.0418000
$489$	−3256.40	−0.301144
$490$	−93.8538	−0.00865283
$491$	11339.8	1.04228	0.521138	−	0.853473i	$-0.325508\pi$
$491$	11339.8	1.04228	0.521138	+	0.853473i	$0.325508\pi$
$492$	−3269.35	−0.299581
$493$	−168.799	−0.0154205
$494$	17.6969	0.00161178
$495$	−8608.14	−0.781630
$496$	5592.39	0.506261
$497$	247.776	0.0223628
$498$	−627.958	−0.0565050
$499$	8011.01	0.718682	0.359341	−	0.933206i	$-0.383002\pi$
$499$	8011.01	0.718682	0.359341	+	0.933206i	$0.383002\pi$
$500$	−10045.5	−0.898499
$501$	−1918.40	−0.171074
$502$	−1127.16	−0.100215
$503$	−17925.8	−1.58901	−0.794503	−	0.607260i	$-0.792269\pi$
$503$	−17925.8	−1.58901	−0.794503	+	0.607260i	$0.792269\pi$
$504$	860.688	0.0760676
$505$	10111.5	0.891001
$506$	210.084	0.0184572
$507$	297.405	0.0260517
$508$	−20320.7	−1.77477
$509$	−13744.2	−1.19686	−0.598429	−	0.801176i	$-0.704208\pi$
$509$	−13744.2	−1.19686	−0.598429	+	0.801176i	$0.704208\pi$
$510$	4.58730	0.000398292 0
$511$	−7515.90	−0.650653
$512$	6285.29	0.542526
$513$	376.821	0.0324309
$514$	1612.68	0.138389
$515$	4932.88	0.422075
$516$	−97.0310	−0.00827820
$517$	14838.7	1.26230
$518$	228.987	0.0194230
$519$	4058.77	0.343276
$520$	−395.792	−0.0333782
$521$	2637.79	0.221811	0.110906	−	0.993831i	$-0.464625\pi$
$521$	2637.79	0.221811	0.110906	+	0.993831i	$0.464625\pi$
$522$	−959.423	−0.0804460
$523$	−16059.6	−1.34271	−0.671353	−	0.741138i	$-0.734287\pi$
$523$	−16059.6	−1.34271	−0.671353	+	0.741138i	$0.734287\pi$
$524$	−4734.08	−0.394674
$525$	−1108.28	−0.0921320
$526$	2398.94	0.198857
$527$	−123.759	−0.0102297
$528$	−6584.81	−0.542741
$529$	−12053.2	−0.990644
$530$	540.184	0.0442719
$531$	16150.9	1.31995
$532$	232.484	0.0189464
$533$	−3058.97	−0.248590
$534$	−622.605	−0.0504546
$535$	−1755.96	−0.141900
$536$	−631.253	−0.0508694
$537$	−639.524	−0.0513920
$538$	−2529.23	−0.202682
$539$	−2981.39	−0.238252
$540$	−4186.05	−0.333591
$541$	10315.9	0.819804	0.409902	−	0.912130i	$-0.365563\pi$
$541$	10315.9	0.819804	0.409902	+	0.912130i	$0.365563\pi$
$542$	−304.263	−0.0241130
$543$	−6798.92	−0.537329
$544$	−83.0890	−0.00654855
$545$	11910.6	0.936138
$546$	−51.8237	−0.00406200
$547$	−5327.06	−0.416396	−0.208198	−	0.978087i	$-0.566760\pi$
$547$	−5327.06	−0.416396	−0.208198	+	0.978087i	$0.566760\pi$
$548$	11852.8	0.923952
$549$	−2093.96	−0.162783
$550$	1771.49	0.137339
$551$	−521.746	−0.0403396
$552$	96.5827	0.00744716
$553$	5681.29	0.436877
$554$	351.444	0.0269520
$555$	−1052.88	−0.0805270
$556$	−20942.9	−1.59744
$557$	11816.4	0.898884	0.449442	−	0.893310i	$-0.351623\pi$
$557$	11816.4	0.898884	0.449442	+	0.893310i	$0.351623\pi$
$558$	−703.427	−0.0533664
$559$	−90.7872	−0.00686921
$560$	−2547.93	−0.192267
$561$	145.722	0.0109668
$562$	26.5266	0.00199102
$563$	−20627.2	−1.54411	−0.772054	−	0.635557i	$-0.780770\pi$
$563$	−20627.2	−1.54411	−0.772054	+	0.635557i	$0.780770\pi$
$564$	3388.46	0.252979
$565$	2719.08	0.202465
$566$	2737.71	0.203312
$567$	3414.20	0.252880
$568$	−182.077	−0.0134503
$569$	−13529.3	−0.996798	−0.498399	−	0.866948i	$-0.666078\pi$
$569$	−13529.3	−0.996798	−0.498399	+	0.866948i	$0.666078\pi$
$570$	14.1790	0.00104192
$571$	−13230.8	−0.969690	−0.484845	−	0.874600i	$-0.661124\pi$
$571$	−13230.8	−0.969690	−0.484845	+	0.874600i	$0.661124\pi$
$572$	−6245.02	−0.456499
$573$	−2294.93	−0.167316
$574$	533.034	0.0387603
$575$	959.917	0.0696196
$576$	11287.6	0.816523
$577$	21279.3	1.53530	0.767650	−	0.640870i	$-0.221426\pi$
$577$	21279.3	1.53530	0.767650	+	0.640870i	$0.221426\pi$
$578$	−1589.31	−0.114371
$579$	−170.579	−0.0122435
$580$	5796.00	0.414941
$581$	−7718.65	−0.551160
$582$	519.299	0.0369857
$583$	17159.7	1.21901
$584$	5523.01	0.391342
$585$	−1839.20	−0.129986
$586$	−1112.93	−0.0784555
$587$	−13737.6	−0.965945	−0.482972	−	0.875636i	$-0.660443\pi$
$587$	−13737.6	−0.965945	−0.482972	+	0.875636i	$0.660443\pi$
$588$	−680.809	−0.0477485
$589$	−382.532	−0.0267606
$590$	1294.19	0.0903070
$591$	−5517.12	−0.384000
$592$	6216.49	0.431582
$593$	−22012.2	−1.52434	−0.762169	−	0.647379i	$-0.775865\pi$
$593$	−22012.2	−1.52434	−0.762169	+	0.647379i	$0.775865\pi$
$594$	1763.82	0.121836
$595$	56.3856	0.00388502
$596$	−10394.3	−0.714376
$597$	6038.46	0.413966
$598$	44.8862	0.00306945
$599$	3333.73	0.227400	0.113700	−	0.993515i	$-0.463730\pi$
$599$	3333.73	0.227400	0.113700	+	0.993515i	$0.463730\pi$
$600$	814.412	0.0554137
$601$	17140.5	1.16336	0.581678	−	0.813419i	$-0.302396\pi$
$601$	17140.5	1.16336	0.581678	+	0.813419i	$0.302396\pi$
$602$	15.8199	0.00107105
$603$	−2933.36	−0.198102
$604$	−16195.2	−1.09102
$605$	−14033.9	−0.943074
$606$	−972.907	−0.0652173
$607$	−2365.32	−0.158164	−0.0790818	−	0.996868i	$-0.525199\pi$
$607$	−2365.32	−0.158164	−0.0790818	+	0.996868i	$0.525199\pi$
$608$	−256.822	−0.0171308
$609$	1527.88	0.101663
$610$	−167.791	−0.0111372
$611$	3170.42	0.209921
$612$	−256.839	−0.0169642
$613$	−165.695	−0.0109174	−0.00545869	−	0.999985i	$-0.501738\pi$
$613$	−165.695	−0.0109174	−0.00545869	+	0.999985i	$0.501738\pi$
$614$	−348.367	−0.0228973
$615$	−2450.90	−0.160699
$616$	2190.86	0.143299
$617$	5993.71	0.391082	0.195541	−	0.980696i	$-0.437354\pi$
$617$	5993.71	0.391082	0.195541	+	0.980696i	$0.437354\pi$
$618$	−474.632	−0.0308940
$619$	−7157.52	−0.464758	−0.232379	−	0.972625i	$-0.574651\pi$
$619$	−7157.52	−0.464758	−0.232379	+	0.972625i	$0.574651\pi$
$620$	4249.50	0.275264
$621$	955.764	0.0617609
$622$	−2265.72	−0.146056
$623$	−7652.86	−0.492143
$624$	−1406.90	−0.0902582
$625$	3715.31	0.237780
$626$	−2404.96	−0.153549
$627$	450.416	0.0286888
$628$	−10372.2	−0.659067
$629$	−137.571	−0.00872069
$630$	320.486	0.0202674
$631$	25765.6	1.62554	0.812769	−	0.582586i	$-0.197959\pi$
$631$	25765.6	1.62554	0.812769	+	0.582586i	$0.197959\pi$
$632$	−4174.86	−0.262764
$633$	8093.30	0.508183
$634$	−2323.99	−0.145580
$635$	−15233.6	−0.952011
$636$	3918.46	0.244304
$637$	−637.000	−0.0396214
$638$	−2442.19	−0.151547
$639$	−846.090	−0.0523800
$640$	3795.34	0.234412
$641$	−20628.0	−1.27107	−0.635536	−	0.772072i	$-0.719221\pi$
$641$	−20628.0	−1.27107	−0.635536	+	0.772072i	$0.719221\pi$
$642$	168.955	0.0103865
$643$	25301.9	1.55180	0.775901	−	0.630854i	$-0.217296\pi$
$643$	25301.9	1.55180	0.775901	+	0.630854i	$0.217296\pi$
$644$	589.671	0.0360812
$645$	−72.7402	−0.00444053
$646$	1.85265	0.000112835 0
$647$	−14852.8	−0.902508	−0.451254	−	0.892396i	$-0.649023\pi$
$647$	−14852.8	−0.902508	−0.451254	+	0.892396i	$0.649023\pi$
$648$	−2508.91	−0.152097
$649$	41111.8	2.48656
$650$	378.493	0.0228395
$651$	1120.21	0.0674416
$652$	14609.8	0.877550
$653$	25682.0	1.53907	0.769537	−	0.638602i	$-0.220487\pi$
$653$	25682.0	1.53907	0.769537	+	0.638602i	$0.220487\pi$
$654$	−1146.02	−0.0685210
$655$	−3548.95	−0.211708
$656$	14470.7	0.861260
$657$	25664.8	1.52402
$658$	−552.454	−0.0327309
$659$	−7290.57	−0.430956	−0.215478	−	0.976509i	$-0.569131\pi$
$659$	−7290.57	−0.430956	−0.215478	+	0.976509i	$0.569131\pi$
$660$	−5003.61	−0.295099
$661$	16930.0	0.996222	0.498111	−	0.867113i	$-0.334027\pi$
$661$	16930.0	0.996222	0.498111	+	0.867113i	$0.334027\pi$
$662$	−1211.26	−0.0711131
$663$	31.1347	0.00182379
$664$	5672.00	0.331501
$665$	174.284	0.0101631
$666$	−781.929	−0.0454942
$667$	−1323.35	−0.0768221
$668$	8606.87	0.498517
$669$	−8393.45	−0.485067
$670$	−235.053	−0.0135536
$671$	−5330.11	−0.306657
$672$	752.081	0.0431728
$673$	16730.2	0.958249	0.479125	−	0.877747i	$-0.340954\pi$
$673$	16730.2	0.958249	0.479125	+	0.877747i	$0.340954\pi$
$674$	3514.25	0.200837
$675$	8059.27	0.459558
$676$	−1334.30	−0.0759161
$677$	−5093.48	−0.289156	−0.144578	−	0.989493i	$-0.546182\pi$
$677$	−5093.48	−0.289156	−0.144578	+	0.989493i	$0.546182\pi$
$678$	−261.624	−0.0148195
$679$	6383.06	0.360765
$680$	−41.4346	−0.00233668
$681$	9548.75	0.537311
$682$	−1790.56	−0.100534
$683$	25619.5	1.43529	0.717645	−	0.696409i	$-0.245220\pi$
$683$	25619.5	1.43529	0.717645	+	0.696409i	$0.245220\pi$
$684$	−793.872	−0.0443779
$685$	8885.54	0.495619
$686$	110.999	0.00617779
$687$	−6944.94	−0.385685
$688$	429.476	0.0237989
$689$	3666.31	0.202722
$690$	35.9635	0.00198422
$691$	−31693.2	−1.74482	−0.872408	−	0.488778i	$-0.837443\pi$
$691$	−31693.2	−1.74482	−0.872408	+	0.488778i	$0.837443\pi$
$692$	−18209.5	−1.00032
$693$	10180.7	0.558054
$694$	86.7245	0.00474354
$695$	−15700.1	−0.856888
$696$	−1122.76	−0.0611465
$697$	−320.237	−0.0174029
$698$	−1644.65	−0.0891845
$699$	−8114.48	−0.439081
$700$	4972.27	0.268477
$701$	2661.14	0.143381	0.0716905	−	0.997427i	$-0.477161\pi$
$701$	2661.14	0.143381	0.0716905	+	0.997427i	$0.477161\pi$
$702$	376.855	0.0202614
$703$	−425.223	−0.0228130
$704$	28732.3	1.53820
$705$	2540.19	0.135701
$706$	3027.95	0.161414
$707$	−11958.7	−0.636141
$708$	9387.99	0.498337
$709$	−16745.3	−0.887000	−0.443500	−	0.896274i	$-0.646263\pi$
$709$	−16745.3	−0.887000	−0.443500	+	0.896274i	$0.646263\pi$
$710$	−67.7981	−0.00358369
$711$	−19400.1	−1.02329
$712$	5623.65	0.296005
$713$	−970.250	−0.0509623
$714$	−5.42531	−0.000284365 0
$715$	−4681.64	−0.244872
$716$	2869.21	0.149759
$717$	−2926.59	−0.152434
$718$	−161.799	−0.00840986
$719$	7621.40	0.395313	0.197657	−	0.980271i	$-0.436667\pi$
$719$	7621.40	0.395313	0.197657	+	0.980271i	$0.436667\pi$
$720$	8700.49	0.450344
$721$	−5834.02	−0.301345
$722$	−2213.93	−0.114119
$723$	5216.55	0.268334
$724$	30503.2	1.56580
$725$	−11158.9	−0.571627
$726$	1350.31	0.0690287
$727$	−33363.8	−1.70206	−0.851028	−	0.525120i	$-0.824021\pi$
$727$	−33363.8	−1.70206	−0.851028	+	0.525120i	$0.824021\pi$
$728$	468.095	0.0238307
$729$	−7402.29	−0.376075
$730$	2056.55	0.104269
$731$	−9.50431	−0.000480888 0
$732$	−1217.14	−0.0614576
$733$	−10628.8	−0.535583	−0.267791	−	0.963477i	$-0.586294\pi$
$733$	−10628.8	−0.535583	−0.267791	+	0.963477i	$0.586294\pi$
$734$	−891.465	−0.0448291
$735$	−510.375	−0.0256129
$736$	−651.401	−0.0326236
$737$	−7466.79	−0.373192
$738$	−1820.17	−0.0907877
$739$	13321.7	0.663120	0.331560	−	0.943434i	$-0.392425\pi$
$739$	13321.7	0.663120	0.331560	+	0.943434i	$0.392425\pi$
$740$	4723.74	0.234660
$741$	96.2352	0.00477097
$742$	−638.865	−0.0316085
$743$	−1456.36	−0.0719092	−0.0359546	−	0.999353i	$-0.511447\pi$
$743$	−1456.36	−0.0719092	−0.0359546	+	0.999353i	$0.511447\pi$
$744$	−823.179	−0.0405635
$745$	−7792.20	−0.383200
$746$	−3046.63	−0.149524
$747$	26357.1	1.29097
$748$	−653.777	−0.0319578
$749$	2076.74	0.101311
$750$	724.590	0.0352777
$751$	−3929.23	−0.190918	−0.0954591	−	0.995433i	$-0.530432\pi$
$751$	−3929.23	−0.190918	−0.0954591	+	0.995433i	$0.530432\pi$
$752$	−14997.9	−0.727285
$753$	−6129.48	−0.296641
$754$	−521.794	−0.0252024
$755$	−12140.9	−0.585235
$756$	4950.76	0.238171
$757$	−27434.8	−1.31722	−0.658610	−	0.752484i	$-0.728855\pi$
$757$	−27434.8	−1.31722	−0.658610	+	0.752484i	$0.728855\pi$
$758$	−3655.37	−0.175157
$759$	1142.43	0.0546345
$760$	−128.072	−0.00611269
$761$	−19994.8	−0.952445	−0.476222	−	0.879325i	$-0.657994\pi$
$761$	−19994.8	−0.952445	−0.476222	+	0.879325i	$0.657994\pi$
$762$	1465.75	0.0696829
$763$	−14086.4	−0.668367
$764$	10296.1	0.487567
$765$	−192.542	−0.00909982
$766$	85.9607	0.00405468
$767$	8783.88	0.413517
$768$	6282.95	0.295204
$769$	−7948.30	−0.372722	−0.186361	−	0.982481i	$-0.559669\pi$
$769$	−7948.30	−0.372722	−0.186361	+	0.982481i	$0.559669\pi$
$770$	815.788	0.0381805
$771$	8769.70	0.409641
$772$	765.297	0.0356783
$773$	−21350.2	−0.993418	−0.496709	−	0.867917i	$-0.665458\pi$
$773$	−21350.2	−0.993418	−0.496709	+	0.867917i	$0.665458\pi$
$774$	−54.0208	−0.00250870
$775$	−8181.42	−0.379207
$776$	−4690.55	−0.216986
$777$	1245.22	0.0574932
$778$	3754.24	0.173003
$779$	−989.830	−0.0455255
$780$	−1069.06	−0.0490752
$781$	−2153.70	−0.0986754
$782$	4.69903	0.000214881 0
$783$	−11110.6	−0.507101
$784$	3013.38	0.137271
$785$	−7775.58	−0.353532
$786$	341.473	0.0154961
$787$	−20880.3	−0.945744	−0.472872	−	0.881131i	$-0.656783\pi$
$787$	−20880.3	−0.945744	−0.472872	+	0.881131i	$0.656783\pi$
$788$	24752.4	1.11900
$789$	13045.4	0.588627
$790$	−1554.55	−0.0700106
$791$	−3215.80	−0.144552
$792$	−7481.20	−0.335647
$793$	−1138.82	−0.0509972
$794$	2156.66	0.0963941
$795$	2937.51	0.131047
$796$	−27091.4	−1.20632
$797$	−40432.4	−1.79697	−0.898487	−	0.439001i	$-0.855332\pi$
$797$	−40432.4	−1.79697	−0.898487	+	0.439001i	$0.855332\pi$
$798$	−16.7693	−0.000743891 0
$799$	331.904	0.0146958
$800$	−5492.80	−0.242750
$801$	26132.4	1.15274
$802$	2548.15	0.112192
$803$	65329.0	2.87100
$804$	−1705.06	−0.0747921
$805$	442.052	0.0193544
$806$	−382.567	−0.0167188
$807$	−13753.9	−0.599950
$808$	8787.74	0.382614
$809$	19268.3	0.837376	0.418688	−	0.908130i	$-0.362490\pi$
$809$	19268.3	0.837376	0.418688	+	0.908130i	$0.362490\pi$
$810$	−934.216	−0.0405247
$811$	−37223.2	−1.61169	−0.805846	−	0.592125i	$-0.798289\pi$
$811$	−37223.2	−1.61169	−0.805846	+	0.592125i	$0.798289\pi$
$812$	−6854.82	−0.296252
$813$	−1654.58	−0.0713758
$814$	−1990.38	−0.0857037
$815$	10952.3	0.470729
$816$	−147.285	−0.00631864
$817$	−29.3772	−0.00125799
$818$	−748.109	−0.0319768
$819$	2175.18	0.0928047
$820$	10995.9	0.468284
$821$	−883.967	−0.0375769	−0.0187885	−	0.999823i	$-0.505981\pi$
$821$	−883.967	−0.0375769	−0.0187885	+	0.999823i	$0.505981\pi$
$822$	−854.949	−0.0362771
$823$	41410.5	1.75392	0.876961	−	0.480561i	$-0.159567\pi$
$823$	41410.5	1.75392	0.876961	+	0.480561i	$0.159567\pi$
$824$	4287.09	0.181247
$825$	9633.29	0.406531
$826$	−1530.62	−0.0644757
$827$	−37881.9	−1.59285	−0.796423	−	0.604739i	$-0.793277\pi$
$827$	−37881.9	−1.59285	−0.796423	+	0.604739i	$0.793277\pi$
$828$	−2013.57	−0.0845124
$829$	−4896.97	−0.205161	−0.102581	−	0.994725i	$-0.532710\pi$
$829$	−4896.97	−0.205161	−0.102581	+	0.994725i	$0.532710\pi$
$830$	2112.03	0.0883247
$831$	1911.14	0.0797795
$832$	6138.90	0.255803
$833$	−66.6861	−0.00277375
$834$	1510.63	0.0627203
$835$	6452.21	0.267411
$836$	−2020.78	−0.0836007
$837$	−8146.03	−0.336401
$838$	−1276.81	−0.0526331
$839$	93.0019	0.00382692	0.00191346	−	0.999998i	$-0.499391\pi$
$839$	93.0019	0.00382692	0.00191346	+	0.999998i	$0.499391\pi$
$840$	375.046	0.0154051
$841$	−9005.30	−0.369236
$842$	−226.297	−0.00926212
$843$	144.251	0.00589355
$844$	−36310.4	−1.48087
$845$	−1000.27	−0.0407223
$846$	1886.48	0.0766650
$847$	16597.6	0.673319
$848$	−17343.8	−0.702345
$849$	14887.6	0.601815
$850$	39.6235	0.00159891
$851$	−1078.53	−0.0434448
$852$	−491.803	−0.0197757
$853$	−8325.23	−0.334174	−0.167087	−	0.985942i	$-0.553436\pi$
$853$	−8325.23	−0.334174	−0.167087	+	0.985942i	$0.553436\pi$
$854$	198.443	0.00795150
$855$	−595.133	−0.0238048
$856$	−1526.08	−0.0609348
$857$	−3891.72	−0.155121	−0.0775606	−	0.996988i	$-0.524713\pi$
$857$	−3891.72	−0.155121	−0.0775606	+	0.996988i	$0.524713\pi$
$858$	450.458	0.0179235
$859$	35346.9	1.40398	0.701991	−	0.712186i	$-0.252295\pi$
$859$	35346.9	1.40398	0.701991	+	0.712186i	$0.252295\pi$
$860$	326.347	0.0129399
$861$	2898.63	0.114733
$862$	4782.33	0.188964
$863$	−21075.1	−0.831290	−0.415645	−	0.909527i	$-0.636444\pi$
$863$	−21075.1	−0.831290	−0.415645	+	0.909527i	$0.636444\pi$
$864$	−5469.04	−0.215348
$865$	−13650.9	−0.536585
$866$	1364.73	0.0535512
$867$	−8642.61	−0.338545
$868$	−5025.79	−0.196528
$869$	−49382.4	−1.92771
$870$	−418.070	−0.0162918
$871$	−1595.34	−0.0620621
$872$	10351.3	0.401996
$873$	−21796.4	−0.845014
$874$	14.5244	0.000562122 0
$875$	8906.42	0.344105
$876$	14918.1	0.575382
$877$	−47944.7	−1.84604	−0.923021	−	0.384751i	$-0.874287\pi$
$877$	−47944.7	−1.84604	−0.923021	+	0.384751i	$0.874287\pi$
$878$	2062.17	0.0792651
$879$	−6052.11	−0.232233
$880$	22146.9	0.848376
$881$	37133.6	1.42005	0.710024	−	0.704178i	$-0.248684\pi$
$881$	37133.6	1.42005	0.710024	+	0.704178i	$0.248684\pi$
$882$	−379.032	−0.0144701
$883$	1686.40	0.0642715	0.0321358	−	0.999484i	$-0.489769\pi$
$883$	1686.40	0.0642715	0.0321358	+	0.999484i	$0.489769\pi$
$884$	−139.685	−0.00531461
$885$	7037.79	0.267314
$886$	2532.00	0.0960092
$887$	11389.6	0.431146	0.215573	−	0.976488i	$-0.430838\pi$
$887$	11389.6	0.431146	0.215573	+	0.976488i	$0.430838\pi$
$888$	−915.046	−0.0345799
$889$	18016.5	0.679700
$890$	2094.02	0.0788672
$891$	−29676.7	−1.11583
$892$	37657.0	1.41351
$893$	1025.89	0.0384437
$894$	749.749	0.0280485
$895$	2150.93	0.0803325
$896$	−4488.67	−0.167361
$897$	244.090	0.00908576
$898$	1013.65	0.0376682
$899$	11279.0	0.418437
$900$	−16979.0	−0.628850
$901$	383.818	0.0141918
$902$	−4633.19	−0.171029
$903$	86.0283	0.00317037
$904$	2363.11	0.0869423
$905$	22867.0	0.839917
$906$	1168.17	0.0428366
$907$	−29663.9	−1.08597	−0.542985	−	0.839743i	$-0.682706\pi$
$907$	−29663.9	−1.08597	−0.542985	+	0.839743i	$0.682706\pi$
$908$	−42840.2	−1.56575
$909$	40835.6	1.49002
$910$	174.300	0.00634944
$911$	16210.3	0.589541	0.294770	−	0.955568i	$-0.404757\pi$
$911$	16210.3	0.589541	0.294770	+	0.955568i	$0.404757\pi$
$912$	−455.249	−0.0165294
$913$	67091.4	2.43198
$914$	729.143	0.0263872
$915$	−912.444	−0.0329666
$916$	31158.3	1.12391
$917$	4197.27	0.151152
$918$	39.4521	0.00141843
$919$	−13025.5	−0.467542	−0.233771	−	0.972292i	$-0.575107\pi$
$919$	−13025.5	−0.467542	−0.233771	+	0.972292i	$0.575107\pi$
$920$	−324.839	−0.0116409
$921$	−1894.41	−0.0677773
$922$	−2965.90	−0.105940
$923$	−460.156	−0.0164098
$924$	5917.67	0.210690
$925$	−9094.46	−0.323269
$926$	2293.12	0.0813785
$927$	19921.6	0.705837
$928$	7572.42	0.267863
$929$	46834.2	1.65401	0.827007	−	0.562192i	$-0.190042\pi$
$929$	46834.2	1.65401	0.827007	+	0.562192i	$0.190042\pi$
$930$	−306.519	−0.0108077
$931$	−206.122	−0.00725605
$932$	36405.4	1.27951
$933$	−12320.9	−0.432335
$934$	3616.03	0.126681
$935$	−490.110	−0.0171426
$936$	−1598.42	−0.0558184
$937$	24171.1	0.842727	0.421363	−	0.906892i	$-0.361552\pi$
$937$	24171.1	0.842727	0.421363	+	0.906892i	$0.361552\pi$
$938$	277.993	0.00967675
$939$	−13078.1	−0.454513
$940$	−11396.5	−0.395439
$941$	−32410.4	−1.12279	−0.561397	−	0.827547i	$-0.689736\pi$
$941$	−32410.4	−1.12279	−0.561397	+	0.827547i	$0.689736\pi$
$942$	748.150	0.0258769
$943$	−2510.59	−0.0866979
$944$	−41552.9	−1.43266
$945$	3711.38	0.127758
$946$	−137.509	−0.00472599
$947$	−36285.0	−1.24509	−0.622547	−	0.782582i	$-0.713902\pi$
$947$	−36285.0	−1.24509	−0.622547	+	0.782582i	$0.713902\pi$
$948$	−11276.6	−0.386336
$949$	13958.1	0.477449
$950$	122.474	0.00418271
$951$	−12637.8	−0.430924
$952$	49.0038	0.00166830
$953$	31851.1	1.08264	0.541321	−	0.840816i	$-0.317924\pi$
$953$	31851.1	1.08264	0.541321	+	0.840816i	$0.317924\pi$
$954$	2181.55	0.0740360
$955$	7718.60	0.261537
$956$	13130.1	0.444202
$957$	−13280.5	−0.448588
$958$	2666.68	0.0899336
$959$	−10508.7	−0.353853
$960$	4918.59	0.165361
$961$	−21521.5	−0.722416
$962$	−425.261	−0.0142526
$963$	−7091.50	−0.237300
$964$	−23403.9	−0.781939
$965$	573.712	0.0191383
$966$	−42.5333	−0.00141665
$967$	455.696	0.0151543	0.00757714	−	0.999971i	$-0.497588\pi$
$967$	455.696	0.0151543	0.00757714	+	0.999971i	$0.497588\pi$
$968$	−12196.7	−0.404975
$969$	10.0746	0.000333998 0
$970$	−1746.57	−0.0578135
$971$	10641.2	0.351690	0.175845	−	0.984418i	$-0.443734\pi$
$971$	10641.2	0.351690	0.175845	+	0.984418i	$0.443734\pi$
$972$	−25872.5	−0.853767
$973$	18568.1	0.611785
$974$	−3225.64	−0.106115
$975$	2058.23	0.0676064
$976$	5387.30	0.176684
$977$	19412.9	0.635694	0.317847	−	0.948142i	$-0.397040\pi$
$977$	19412.9	0.635694	0.317847	+	0.948142i	$0.397040\pi$
$978$	−1053.81	−0.0344552
$979$	66519.5	2.17158
$980$	2289.78	0.0746372
$981$	48101.4	1.56551
$982$	3669.69	0.119251
$983$	44913.0	1.45728	0.728639	−	0.684898i	$-0.240153\pi$
$983$	44913.0	1.45728	0.728639	+	0.684898i	$0.240153\pi$
$984$	−2130.04	−0.0690072
$985$	18555.9	0.600243
$986$	−54.6254	−0.00176433
$987$	−3004.23	−0.0968853
$988$	−431.757	−0.0139029
$989$	−74.5119	−0.00239569
$990$	−2785.70	−0.0894296
$991$	36377.2	1.16605	0.583027	−	0.812453i	$-0.301868\pi$
$991$	36377.2	1.16605	0.583027	+	0.812453i	$0.301868\pi$
$992$	5551.93	0.177695
$993$	−6586.79	−0.210499
$994$	80.1835	0.00255862
$995$	−20309.3	−0.647083
$996$	15320.5	0.487398
$997$	6366.39	0.202232	0.101116	−	0.994875i	$-0.467759\pi$
$997$	6366.39	0.202232	0.101116	+	0.994875i	$0.467759\pi$
$998$	2592.46	0.0822274
$999$	−9055.12	−0.286778

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.4.a.b.1.3	✓	4
3.2	odd	2		819.4.a.h.1.2		4
4.3	odd	2		1456.4.a.s.1.2		4
5.4	even	2		2275.4.a.h.1.2		4
7.6	odd	2		637.4.a.d.1.3		4
13.12	even	2		1183.4.a.e.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.4.a.b.1.3	✓	4	1.1	even	1	trivial
637.4.a.d.1.3		4	7.6	odd	2
819.4.a.h.1.2		4	3.2	odd	2
1183.4.a.e.1.2		4	13.12	even	2
1456.4.a.s.1.2		4	4.3	odd	2
2275.4.a.h.1.2		4	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q+0.323612 q^{2} +1.75980 q^{3} -7.89528 q^{4} -5.91876 q^{5} +0.569491 q^{6} +7.00000 q^{7} -5.14391 q^{8} -23.9031 q^{9} +O(q^{10})\)	\(q+0.323612 q^{2} +1.75980 q^{3} -7.89528 q^{4} -5.91876 q^{5} +0.569491 q^{6} +7.00000 q^{7} -5.14391 q^{8} -23.9031 q^{9} -1.91538 q^{10} -60.8448 q^{11} -13.8941 q^{12} -13.0000 q^{13} +2.26529 q^{14} -10.4158 q^{15} +61.4976 q^{16} -1.36094 q^{17} -7.73534 q^{18} -4.20658 q^{19} +46.7303 q^{20} +12.3186 q^{21} -19.6901 q^{22} -10.6695 q^{23} -9.05222 q^{24} -89.9682 q^{25} -4.20696 q^{26} -89.5791 q^{27} -55.2669 q^{28} +124.031 q^{29} -3.37068 q^{30} +90.9367 q^{31} +61.0526 q^{32} -107.074 q^{33} -0.440417 q^{34} -41.4313 q^{35} +188.722 q^{36} +101.085 q^{37} -1.36130 q^{38} -22.8773 q^{39} +30.4456 q^{40} +235.305 q^{41} +3.98644 q^{42} +6.98363 q^{43} +480.386 q^{44} +141.477 q^{45} -3.45278 q^{46} -243.878 q^{47} +108.223 q^{48} +49.0000 q^{49} -29.1148 q^{50} -2.39498 q^{51} +102.639 q^{52} -282.024 q^{53} -28.9889 q^{54} +360.126 q^{55} -36.0073 q^{56} -7.40271 q^{57} +40.1380 q^{58} -675.683 q^{59} +82.2357 q^{60} +87.6018 q^{61} +29.4282 q^{62} -167.322 q^{63} -472.223 q^{64} +76.9439 q^{65} -34.6506 q^{66} +122.719 q^{67} +10.7450 q^{68} -18.7761 q^{69} -13.4077 q^{70} +35.3966 q^{71} +122.955 q^{72} -1073.70 q^{73} +32.7124 q^{74} -158.326 q^{75} +33.2121 q^{76} -425.914 q^{77} -7.40339 q^{78} +811.612 q^{79} -363.990 q^{80} +487.743 q^{81} +76.1477 q^{82} -1102.66 q^{83} -97.2585 q^{84} +8.05509 q^{85} +2.25999 q^{86} +218.269 q^{87} +312.980 q^{88} -1093.27 q^{89} +45.7837 q^{90} -91.0000 q^{91} +84.2387 q^{92} +160.030 q^{93} -78.9220 q^{94} +24.8977 q^{95} +107.440 q^{96} +911.865 q^{97} +15.8570 q^{98} +1454.38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 5 q^{3} + 26 q^{4} - 36 q^{5} - 45 q^{6} + 28 q^{7} - 30 q^{8} + 21 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 5 * q^3 + 26 * q^4 - 36 * q^5 - 45 * q^6 + 28 * q^7 - 30 * q^8 + 21 * q^9	\( 4 q - 4 q^{2} - 5 q^{3} + 26 q^{4} - 36 q^{5} - 45 q^{6} + 28 q^{7} - 30 q^{8} + 21 q^{9} - 44 q^{10} - 95 q^{11} - 17 q^{12} - 52 q^{13} - 28 q^{14} - 16 q^{15} + 58 q^{16} - 146 q^{17} + 65 q^{18} - 48 q^{19} - 474 q^{20} - 35 q^{21} - 143 q^{22} - 121 q^{23} - 469 q^{24} + 506 q^{25} + 52 q^{26} - 83 q^{27} + 182 q^{28} - 440 q^{29} + 1548 q^{30} - 283 q^{31} - 114 q^{32} + 227 q^{33} + 1234 q^{34} - 252 q^{35} + 755 q^{36} - 209 q^{37} + 440 q^{38} + 65 q^{39} + 754 q^{40} - 93 q^{41} - 315 q^{42} + 526 q^{43} + 217 q^{44} - 768 q^{45} - 841 q^{46} - 783 q^{47} + 1407 q^{48} + 196 q^{49} + 446 q^{50} - 672 q^{51} - 338 q^{52} - 340 q^{53} - 199 q^{54} + 756 q^{55} - 210 q^{56} - 1014 q^{57} + 1916 q^{58} - 922 q^{59} - 396 q^{60} - 141 q^{61} + 1745 q^{62} + 147 q^{63} - 1510 q^{64} + 468 q^{65} + 503 q^{66} - 523 q^{67} - 1710 q^{68} + 1595 q^{69} - 308 q^{70} + 1468 q^{71} - 9 q^{72} - 47 q^{73} - 2249 q^{74} - 1547 q^{75} - 1382 q^{76} - 665 q^{77} + 585 q^{78} + 1025 q^{79} - 2538 q^{80} - 1772 q^{81} - 1561 q^{82} - 1190 q^{83} - 119 q^{84} - 568 q^{85} + 738 q^{86} + 720 q^{87} - 555 q^{88} - 2962 q^{89} - 1960 q^{90} - 364 q^{91} - 599 q^{92} - 763 q^{93} + 317 q^{94} + 2082 q^{95} - 45 q^{96} + 2715 q^{97} - 196 q^{98} + 586 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 5 * q^3 + 26 * q^4 - 36 * q^5 - 45 * q^6 + 28 * q^7 - 30 * q^8 + 21 * q^9 - 44 * q^10 - 95 * q^11 - 17 * q^12 - 52 * q^13 - 28 * q^14 - 16 * q^15 + 58 * q^16 - 146 * q^17 + 65 * q^18 - 48 * q^19 - 474 * q^20 - 35 * q^21 - 143 * q^22 - 121 * q^23 - 469 * q^24 + 506 * q^25 + 52 * q^26 - 83 * q^27 + 182 * q^28 - 440 * q^29 + 1548 * q^30 - 283 * q^31 - 114 * q^32 + 227 * q^33 + 1234 * q^34 - 252 * q^35 + 755 * q^36 - 209 * q^37 + 440 * q^38 + 65 * q^39 + 754 * q^40 - 93 * q^41 - 315 * q^42 + 526 * q^43 + 217 * q^44 - 768 * q^45 - 841 * q^46 - 783 * q^47 + 1407 * q^48 + 196 * q^49 + 446 * q^50 - 672 * q^51 - 338 * q^52 - 340 * q^53 - 199 * q^54 + 756 * q^55 - 210 * q^56 - 1014 * q^57 + 1916 * q^58 - 922 * q^59 - 396 * q^60 - 141 * q^61 + 1745 * q^62 + 147 * q^63 - 1510 * q^64 + 468 * q^65 + 503 * q^66 - 523 * q^67 - 1710 * q^68 + 1595 * q^69 - 308 * q^70 + 1468 * q^71 - 9 * q^72 - 47 * q^73 - 2249 * q^74 - 1547 * q^75 - 1382 * q^76 - 665 * q^77 + 585 * q^78 + 1025 * q^79 - 2538 * q^80 - 1772 * q^81 - 1561 * q^82 - 1190 * q^83 - 119 * q^84 - 568 * q^85 + 738 * q^86 + 720 * q^87 - 555 * q^88 - 2962 * q^89 - 1960 * q^90 - 364 * q^91 - 599 * q^92 - 763 * q^93 + 317 * q^94 + 2082 * q^95 - 45 * q^96 + 2715 * q^97 - 196 * q^98 + 586 * q^99

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