LMFDB - Embedded newform 1911.2.a.x.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,2,Mod(1,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1911.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1911.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:	$15.2594118263$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 10x^{8} + 52x^{7} + 16x^{6} - 212x^{5} + 64x^{4} + 300x^{3} - 159x^{2} - 80x + 46 $ x^10 - 4x^9 - 10x^8 + 52x^7 + 16x^6 - 212x^5 + 64x^4 + 300x^3 - 159x^2 - 80*x + 46
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.58460$ of defining polynomial
Character	$\chi$	$=$	1911.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58460 q^{2} -1.00000 q^{3} +4.68016 q^{4} +3.63737 q^{5} +2.58460 q^{6} -6.92714 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.58460 q^{2} -1.00000 q^{3} +4.68016 q^{4} +3.63737 q^{5} +2.58460 q^{6} -6.92714 q^{8} +1.00000 q^{9} -9.40115 q^{10} +1.98745 q^{11} -4.68016 q^{12} +1.00000 q^{13} -3.63737 q^{15} +8.54357 q^{16} +0.153618 q^{17} -2.58460 q^{18} -7.49381 q^{19} +17.0235 q^{20} -5.13675 q^{22} -5.05612 q^{23} +6.92714 q^{24} +8.23047 q^{25} -2.58460 q^{26} -1.00000 q^{27} +6.44813 q^{29} +9.40115 q^{30} +8.55159 q^{31} -8.22744 q^{32} -1.98745 q^{33} -0.397040 q^{34} +4.68016 q^{36} -6.58538 q^{37} +19.3685 q^{38} -1.00000 q^{39} -25.1966 q^{40} +11.6259 q^{41} -0.332035 q^{43} +9.30156 q^{44} +3.63737 q^{45} +13.0681 q^{46} +8.65999 q^{47} -8.54357 q^{48} -21.2725 q^{50} -0.153618 q^{51} +4.68016 q^{52} +10.7719 q^{53} +2.58460 q^{54} +7.22908 q^{55} +7.49381 q^{57} -16.6659 q^{58} -9.83780 q^{59} -17.0235 q^{60} -7.09311 q^{61} -22.1024 q^{62} +4.17750 q^{64} +3.63737 q^{65} +5.13675 q^{66} -2.34780 q^{67} +0.718955 q^{68} +5.05612 q^{69} +12.4750 q^{71} -6.92714 q^{72} -0.865288 q^{73} +17.0206 q^{74} -8.23047 q^{75} -35.0722 q^{76} +2.58460 q^{78} +13.6398 q^{79} +31.0761 q^{80} +1.00000 q^{81} -30.0482 q^{82} -7.50617 q^{83} +0.558764 q^{85} +0.858178 q^{86} -6.44813 q^{87} -13.7673 q^{88} +6.23704 q^{89} -9.40115 q^{90} -23.6635 q^{92} -8.55159 q^{93} -22.3826 q^{94} -27.2578 q^{95} +8.22744 q^{96} -8.19000 q^{97} +1.98745 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 10 q^{3} + 16 q^{4} + 6 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - 10 * q^3 + 16 * q^4 + 6 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9	$ 10 q + 4 q^{2} - 10 q^{3} + 16 q^{4} + 6 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 12 q^{11} - 16 q^{12} + 10 q^{13} - 6 q^{15} + 24 q^{16} + 4 q^{18} - 10 q^{19} + 16 q^{20} + 8 q^{22} + 14 q^{23} - 12 q^{24} + 32 q^{25} + 4 q^{26} - 10 q^{27} + 18 q^{29} + 8 q^{30} - 14 q^{31} + 28 q^{32} - 12 q^{33} - 4 q^{34} + 16 q^{36} + 24 q^{37} + 4 q^{38} - 10 q^{39} - 16 q^{40} + 24 q^{41} + 2 q^{43} + 48 q^{44} + 6 q^{45} + 20 q^{46} + 18 q^{47} - 24 q^{48} - 28 q^{50} + 16 q^{52} + 10 q^{53} - 4 q^{54} - 12 q^{55} + 10 q^{57} + 12 q^{58} + 12 q^{59} - 16 q^{60} + 4 q^{61} - 4 q^{62} + 32 q^{64} + 6 q^{65} - 8 q^{66} - 12 q^{67} + 40 q^{68} - 14 q^{69} + 32 q^{71} + 12 q^{72} + 18 q^{73} + 24 q^{74} - 32 q^{75} - 32 q^{76} - 4 q^{78} + 34 q^{79} + 32 q^{80} + 10 q^{81} - 48 q^{82} + 30 q^{83} + 40 q^{86} - 18 q^{87} + 32 q^{88} + 10 q^{89} - 8 q^{90} - 40 q^{92} + 14 q^{93} + 24 q^{94} - 30 q^{95} - 28 q^{96} + 2 q^{97} + 12 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 - 10 * q^3 + 16 * q^4 + 6 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9 - 8 * q^10 + 12 * q^11 - 16 * q^12 + 10 * q^13 - 6 * q^15 + 24 * q^16 + 4 * q^18 - 10 * q^19 + 16 * q^20 + 8 * q^22 + 14 * q^23 - 12 * q^24 + 32 * q^25 + 4 * q^26 - 10 * q^27 + 18 * q^29 + 8 * q^30 - 14 * q^31 + 28 * q^32 - 12 * q^33 - 4 * q^34 + 16 * q^36 + 24 * q^37 + 4 * q^38 - 10 * q^39 - 16 * q^40 + 24 * q^41 + 2 * q^43 + 48 * q^44 + 6 * q^45 + 20 * q^46 + 18 * q^47 - 24 * q^48 - 28 * q^50 + 16 * q^52 + 10 * q^53 - 4 * q^54 - 12 * q^55 + 10 * q^57 + 12 * q^58 + 12 * q^59 - 16 * q^60 + 4 * q^61 - 4 * q^62 + 32 * q^64 + 6 * q^65 - 8 * q^66 - 12 * q^67 + 40 * q^68 - 14 * q^69 + 32 * q^71 + 12 * q^72 + 18 * q^73 + 24 * q^74 - 32 * q^75 - 32 * q^76 - 4 * q^78 + 34 * q^79 + 32 * q^80 + 10 * q^81 - 48 * q^82 + 30 * q^83 + 40 * q^86 - 18 * q^87 + 32 * q^88 + 10 * q^89 - 8 * q^90 - 40 * q^92 + 14 * q^93 + 24 * q^94 - 30 * q^95 - 28 * q^96 + 2 * q^97 + 12 * 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 $

$2$	−2.58460	−1.82759	−0.913794	−	0.406177i	$-0.866861\pi$
$2$	−2.58460	−1.82759	−0.913794	+	0.406177i	$0.866861\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.68016	2.34008
$5$	3.63737	1.62668	0.813341	−	0.581787i	$-0.197646\pi$
$5$	3.63737	1.62668	0.813341	+	0.581787i	$0.197646\pi$
$6$	2.58460	1.05516
$7$	0	0
$7$	0	0
$8$	−6.92714	−2.44911
$9$	1.00000	0.333333
$10$	−9.40115	−2.97291
$11$	1.98745	0.599238	0.299619	−	0.954059i	$-0.403141\pi$
$11$	1.98745	0.599238	0.299619	+	0.954059i	$0.403141\pi$
$12$	−4.68016	−1.35105
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−3.63737	−0.939165
$16$	8.54357	2.13589
$17$	0.153618	0.0372577	0.0186289	−	0.999826i	$-0.494070\pi$
$17$	0.153618	0.0372577	0.0186289	+	0.999826i	$0.494070\pi$
$18$	−2.58460	−0.609196
$19$	−7.49381	−1.71920	−0.859599	−	0.510969i	$-0.829287\pi$
$19$	−7.49381	−1.71920	−0.859599	+	0.510969i	$0.829287\pi$
$20$	17.0235	3.80657
$21$	0	0
$22$	−5.13675	−1.09516
$23$	−5.05612	−1.05427	−0.527137	−	0.849780i	$-0.676735\pi$
$23$	−5.05612	−1.05427	−0.527137	+	0.849780i	$0.676735\pi$
$24$	6.92714	1.41400
$25$	8.23047	1.64609
$26$	−2.58460	−0.506882
$27$	−1.00000	−0.192450
$28$	0	0
$29$	6.44813	1.19739	0.598694	−	0.800978i	$-0.295686\pi$
$29$	6.44813	1.19739	0.598694	+	0.800978i	$0.295686\pi$
$30$	9.40115	1.71641
$31$	8.55159	1.53591	0.767955	−	0.640503i	$-0.221274\pi$
$31$	8.55159	1.53591	0.767955	+	0.640503i	$0.221274\pi$
$32$	−8.22744	−1.45442
$33$	−1.98745	−0.345970
$34$	−0.397040	−0.0680918
$35$	0	0
$36$	4.68016	0.780027
$37$	−6.58538	−1.08263	−0.541315	−	0.840820i	$-0.682073\pi$
$37$	−6.58538	−1.08263	−0.541315	+	0.840820i	$0.682073\pi$
$38$	19.3685	3.14199
$39$	−1.00000	−0.160128
$40$	−25.1966	−3.98393
$41$	11.6259	1.81565	0.907827	−	0.419345i	$-0.137740\pi$
$41$	11.6259	1.81565	0.907827	+	0.419345i	$0.137740\pi$
$42$	0	0
$43$	−0.332035	−0.0506349	−0.0253174	−	0.999679i	$-0.508060\pi$
$43$	−0.332035	−0.0506349	−0.0253174	+	0.999679i	$0.508060\pi$
$44$	9.30156	1.40226
$45$	3.63737	0.542227
$46$	13.0681	1.92678
$47$	8.65999	1.26319	0.631594	−	0.775299i	$-0.282401\pi$
$47$	8.65999	1.26319	0.631594	+	0.775299i	$0.282401\pi$
$48$	−8.54357	−1.23316
$49$	0	0
$50$	−21.2725	−3.00838
$51$	−0.153618	−0.0215108
$52$	4.68016	0.649021
$53$	10.7719	1.47964	0.739818	−	0.672808i	$-0.234912\pi$
$53$	10.7719	1.47964	0.739818	+	0.672808i	$0.234912\pi$
$54$	2.58460	0.351720
$55$	7.22908	0.974769
$56$	0	0
$57$	7.49381	0.992579
$58$	−16.6659	−2.18833
$59$	−9.83780	−1.28077	−0.640386	−	0.768053i	$-0.721226\pi$
$59$	−9.83780	−1.28077	−0.640386	+	0.768053i	$0.721226\pi$
$60$	−17.0235	−2.19772
$61$	−7.09311	−0.908179	−0.454090	−	0.890956i	$-0.650035\pi$
$61$	−7.09311	−0.908179	−0.454090	+	0.890956i	$0.650035\pi$
$62$	−22.1024	−2.80701
$63$	0	0
$64$	4.17750	0.522187
$65$	3.63737	0.451160
$66$	5.13675	0.632291
$67$	−2.34780	−0.286830	−0.143415	−	0.989663i	$-0.545808\pi$
$67$	−2.34780	−0.286830	−0.143415	+	0.989663i	$0.545808\pi$
$68$	0.718955	0.0871861
$69$	5.05612	0.608685
$70$	0	0
$71$	12.4750	1.48051	0.740254	−	0.672327i	$-0.234705\pi$
$71$	12.4750	1.48051	0.740254	+	0.672327i	$0.234705\pi$
$72$	−6.92714	−0.816371
$73$	−0.865288	−0.101274	−0.0506372	−	0.998717i	$-0.516125\pi$
$73$	−0.865288	−0.101274	−0.0506372	+	0.998717i	$0.516125\pi$
$74$	17.0206	1.97860
$75$	−8.23047	−0.950373
$76$	−35.0722	−4.02306
$77$	0	0
$78$	2.58460	0.292648
$79$	13.6398	1.53460	0.767300	−	0.641289i	$-0.221600\pi$
$79$	13.6398	1.53460	0.767300	+	0.641289i	$0.221600\pi$
$80$	31.0761	3.47442
$81$	1.00000	0.111111
$82$	−30.0482	−3.31827
$83$	−7.50617	−0.823909	−0.411954	−	0.911204i	$-0.635154\pi$
$83$	−7.50617	−0.823909	−0.411954	+	0.911204i	$0.635154\pi$
$84$	0	0
$85$	0.558764	0.0606065
$86$	0.858178	0.0925397
$87$	−6.44813	−0.691313
$88$	−13.7673	−1.46760
$89$	6.23704	0.661124	0.330562	−	0.943784i	$-0.392762\pi$
$89$	6.23704	0.661124	0.330562	+	0.943784i	$0.392762\pi$
$90$	−9.40115	−0.990968
$91$	0	0
$92$	−23.6635	−2.46709
$93$	−8.55159	−0.886759
$94$	−22.3826	−2.30859
$95$	−27.2578	−2.79659
$96$	8.22744	0.839710
$97$	−8.19000	−0.831568	−0.415784	−	0.909463i	$-0.636493\pi$
$97$	−8.19000	−0.831568	−0.415784	+	0.909463i	$0.636493\pi$
$98$	0	0
$99$	1.98745	0.199746
$100$	38.5199	3.85199
$101$	4.91193	0.488755	0.244378	−	0.969680i	$-0.421416\pi$
$101$	4.91193	0.488755	0.244378	+	0.969680i	$0.421416\pi$
$102$	0.397040	0.0393128
$103$	4.61507	0.454736	0.227368	−	0.973809i	$-0.426988\pi$
$103$	4.61507	0.454736	0.227368	+	0.973809i	$0.426988\pi$
$104$	−6.92714	−0.679262
$105$	0	0
$106$	−27.8411	−2.70416
$107$	−10.7824	−1.04237	−0.521186	−	0.853443i	$-0.674510\pi$
$107$	−10.7824	−1.04237	−0.521186	+	0.853443i	$0.674510\pi$
$108$	−4.68016	−0.450349
$109$	−1.32351	−0.126769	−0.0633845	−	0.997989i	$-0.520189\pi$
$109$	−1.32351	−0.126769	−0.0633845	+	0.997989i	$0.520189\pi$
$110$	−18.6843	−1.78148
$111$	6.58538	0.625057
$112$	0	0
$113$	7.31323	0.687971	0.343986	−	0.938975i	$-0.388223\pi$
$113$	7.31323	0.687971	0.343986	+	0.938975i	$0.388223\pi$
$114$	−19.3685	−1.81403
$115$	−18.3910	−1.71497
$116$	30.1783	2.80198
$117$	1.00000	0.0924500
$118$	25.4268	2.34072
$119$	0	0
$120$	25.1966	2.30012
$121$	−7.05006	−0.640914
$122$	18.3328	1.65978
$123$	−11.6259	−1.04827
$124$	40.0228	3.59415
$125$	11.7504	1.05099
$126$	0	0
$127$	−0.461478	−0.0409495	−0.0204748	−	0.999790i	$-0.506518\pi$
$127$	−0.461478	−0.0409495	−0.0204748	+	0.999790i	$0.506518\pi$
$128$	5.65772	0.500076
$129$	0.332035	0.0292341
$130$	−9.40115	−0.824536
$131$	−4.13651	−0.361409	−0.180704	−	0.983537i	$-0.557838\pi$
$131$	−4.13651	−0.361409	−0.180704	+	0.983537i	$0.557838\pi$
$132$	−9.30156	−0.809597
$133$	0	0
$134$	6.06814	0.524207
$135$	−3.63737	−0.313055
$136$	−1.06413	−0.0912485
$137$	17.2668	1.47520	0.737600	−	0.675238i	$-0.235959\pi$
$137$	17.2668	1.47520	0.737600	+	0.675238i	$0.235959\pi$
$138$	−13.0681	−1.11243
$139$	−17.2932	−1.46679	−0.733393	−	0.679805i	$-0.762064\pi$
$139$	−17.2932	−1.46679	−0.733393	+	0.679805i	$0.762064\pi$
$140$	0	0
$141$	−8.65999	−0.729302
$142$	−32.2428	−2.70576
$143$	1.98745	0.166199
$144$	8.54357	0.711964
$145$	23.4543	1.94777
$146$	2.23642	0.185088
$147$	0	0
$148$	−30.8206	−2.53344
$149$	11.0179	0.902619	0.451310	−	0.892367i	$-0.350957\pi$
$149$	11.0179	0.902619	0.451310	+	0.892367i	$0.350957\pi$
$150$	21.2725	1.73689
$151$	3.47140	0.282498	0.141249	−	0.989974i	$-0.454888\pi$
$151$	3.47140	0.282498	0.141249	+	0.989974i	$0.454888\pi$
$152$	51.9107	4.21051
$153$	0.153618	0.0124192
$154$	0	0
$155$	31.1053	2.49844
$156$	−4.68016	−0.374713
$157$	4.23125	0.337691	0.168845	−	0.985643i	$-0.445996\pi$
$157$	4.23125	0.337691	0.168845	+	0.985643i	$0.445996\pi$
$158$	−35.2535	−2.80462
$159$	−10.7719	−0.854268
$160$	−29.9263	−2.36588
$161$	0	0
$162$	−2.58460	−0.203065
$163$	15.9537	1.24959	0.624796	−	0.780788i	$-0.285182\pi$
$163$	15.9537	1.24959	0.624796	+	0.780788i	$0.285182\pi$
$164$	54.4109	4.24877
$165$	−7.22908	−0.562783
$166$	19.4004	1.50577
$167$	−10.2209	−0.790920	−0.395460	−	0.918483i	$-0.629415\pi$
$167$	−10.2209	−0.790920	−0.395460	+	0.918483i	$0.629415\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−1.44418	−0.110764
$171$	−7.49381	−0.573066
$172$	−1.55398	−0.118490
$173$	−8.90199	−0.676806	−0.338403	−	0.941001i	$-0.609887\pi$
$173$	−8.90199	−0.676806	−0.338403	+	0.941001i	$0.609887\pi$
$174$	16.6659	1.26343
$175$	0	0
$176$	16.9799	1.27991
$177$	9.83780	0.739454
$178$	−16.1202	−1.20826
$179$	3.99314	0.298462	0.149231	−	0.988802i	$-0.452320\pi$
$179$	3.99314	0.298462	0.149231	+	0.988802i	$0.452320\pi$
$180$	17.0235	1.26886
$181$	20.6480	1.53475	0.767377	−	0.641197i	$-0.221562\pi$
$181$	20.6480	1.53475	0.767377	+	0.641197i	$0.221562\pi$
$182$	0	0
$183$	7.09311	0.524337
$184$	35.0245	2.58204
$185$	−23.9535	−1.76110
$186$	22.1024	1.62063
$187$	0.305307	0.0223262
$188$	40.5301	2.95596
$189$	0	0
$190$	70.4504	5.11101
$191$	17.6359	1.27609	0.638045	−	0.769999i	$-0.279743\pi$
$191$	17.6359	1.27609	0.638045	+	0.769999i	$0.279743\pi$
$192$	−4.17750	−0.301485
$193$	21.9176	1.57766	0.788832	−	0.614609i	$-0.210686\pi$
$193$	21.9176	1.57766	0.788832	+	0.614609i	$0.210686\pi$
$194$	21.1679	1.51976
$195$	−3.63737	−0.260478
$196$	0	0
$197$	−2.40028	−0.171013	−0.0855064	−	0.996338i	$-0.527251\pi$
$197$	−2.40028	−0.171013	−0.0855064	+	0.996338i	$0.527251\pi$
$198$	−5.13675	−0.365053
$199$	−7.77606	−0.551230	−0.275615	−	0.961268i	$-0.588882\pi$
$199$	−7.77606	−0.551230	−0.275615	+	0.961268i	$0.588882\pi$
$200$	−57.0136	−4.03147
$201$	2.34780	0.165601
$202$	−12.6954	−0.893244
$203$	0	0
$204$	−0.718955	−0.0503369
$205$	42.2876	2.95349
$206$	−11.9281	−0.831071
$207$	−5.05612	−0.351425
$208$	8.54357	0.592390
$209$	−14.8935	−1.03021
$210$	0	0
$211$	10.9087	0.750982	0.375491	−	0.926826i	$-0.377474\pi$
$211$	10.9087	0.750982	0.375491	+	0.926826i	$0.377474\pi$
$212$	50.4142	3.46246
$213$	−12.4750	−0.854772
$214$	27.8681	1.90503
$215$	−1.20774	−0.0823669
$216$	6.92714	0.471332
$217$	0	0
$218$	3.42074	0.231682
$219$	0.865288	0.0584708
$220$	33.8332	2.28104
$221$	0.153618	0.0103334
$222$	−17.0206	−1.14235
$223$	15.7560	1.05510	0.527550	−	0.849524i	$-0.323111\pi$
$223$	15.7560	1.05510	0.527550	+	0.849524i	$0.323111\pi$
$224$	0	0
$225$	8.23047	0.548698
$226$	−18.9018	−1.25733
$227$	−5.74979	−0.381627	−0.190813	−	0.981626i	$-0.561113\pi$
$227$	−5.74979	−0.381627	−0.190813	+	0.981626i	$0.561113\pi$
$228$	35.0722	2.32271
$229$	−3.61863	−0.239126	−0.119563	−	0.992827i	$-0.538149\pi$
$229$	−3.61863	−0.239126	−0.119563	+	0.992827i	$0.538149\pi$
$230$	47.5334	3.13426
$231$	0	0
$232$	−44.6671	−2.93254
$233$	−22.6643	−1.48479	−0.742394	−	0.669964i	$-0.766310\pi$
$233$	−22.6643	−1.48479	−0.742394	+	0.669964i	$0.766310\pi$
$234$	−2.58460	−0.168961
$235$	31.4996	2.05481
$236$	−46.0425	−2.99711
$237$	−13.6398	−0.886002
$238$	0	0
$239$	26.3984	1.70757	0.853785	−	0.520625i	$-0.174301\pi$
$239$	26.3984	1.70757	0.853785	+	0.520625i	$0.174301\pi$
$240$	−31.0761	−2.00596
$241$	18.4736	1.18999	0.594995	−	0.803729i	$-0.297154\pi$
$241$	18.4736	1.18999	0.594995	+	0.803729i	$0.297154\pi$
$242$	18.2216	1.17133
$243$	−1.00000	−0.0641500
$244$	−33.1969	−2.12521
$245$	0	0
$246$	30.0482	1.91580
$247$	−7.49381	−0.476820
$248$	−59.2381	−3.76162
$249$	7.50617	0.475684
$250$	−30.3702	−1.92078
$251$	−0.420884	−0.0265660	−0.0132830	−	0.999912i	$-0.504228\pi$
$251$	−0.420884	−0.0265660	−0.0132830	+	0.999912i	$0.504228\pi$
$252$	0	0
$253$	−10.0488	−0.631761
$254$	1.19274	0.0748389
$255$	−0.558764	−0.0349912
$256$	−22.9779	−1.43612
$257$	−17.2906	−1.07856	−0.539280	−	0.842126i	$-0.681304\pi$
$257$	−17.2906	−1.07856	−0.539280	+	0.842126i	$0.681304\pi$
$258$	−0.858178	−0.0534278
$259$	0	0
$260$	17.0235	1.05575
$261$	6.44813	0.399129
$262$	10.6912	0.660506
$263$	−8.56523	−0.528154	−0.264077	−	0.964502i	$-0.585067\pi$
$263$	−8.56523	−0.528154	−0.264077	+	0.964502i	$0.585067\pi$
$264$	13.7673	0.847320
$265$	39.1814	2.40690
$266$	0	0
$267$	−6.23704	−0.381700
$268$	−10.9881	−0.671205
$269$	−10.2462	−0.624722	−0.312361	−	0.949964i	$-0.601120\pi$
$269$	−10.2462	−0.624722	−0.312361	+	0.949964i	$0.601120\pi$
$270$	9.40115	0.572136
$271$	−3.08506	−0.187404	−0.0937020	−	0.995600i	$-0.529870\pi$
$271$	−3.08506	−0.187404	−0.0937020	+	0.995600i	$0.529870\pi$
$272$	1.31244	0.0795786
$273$	0	0
$274$	−44.6277	−2.69606
$275$	16.3576	0.986402
$276$	23.6635	1.42437
$277$	5.11252	0.307181	0.153591	−	0.988135i	$-0.450916\pi$
$277$	5.11252	0.307181	0.153591	+	0.988135i	$0.450916\pi$
$278$	44.6959	2.68068
$279$	8.55159	0.511970
$280$	0	0
$281$	−15.4838	−0.923688	−0.461844	−	0.886961i	$-0.652812\pi$
$281$	−15.4838	−0.923688	−0.461844	+	0.886961i	$0.652812\pi$
$282$	22.3826	1.33286
$283$	−11.0143	−0.654731	−0.327365	−	0.944898i	$-0.606161\pi$
$283$	−11.0143	−0.654731	−0.327365	+	0.944898i	$0.606161\pi$
$284$	58.3849	3.46451
$285$	27.2578	1.61461
$286$	−5.13675	−0.303743
$287$	0	0
$288$	−8.22744	−0.484807
$289$	−16.9764	−0.998612
$290$	−60.6199	−3.55972
$291$	8.19000	0.480106
$292$	−4.04969	−0.236990
$293$	23.2005	1.35539	0.677695	−	0.735343i	$-0.262979\pi$
$293$	23.2005	1.35539	0.677695	+	0.735343i	$0.262979\pi$
$294$	0	0
$295$	−35.7837	−2.08341
$296$	45.6179	2.65148
$297$	−1.98745	−0.115323
$298$	−28.4768	−1.64962
$299$	−5.05612	−0.292403
$300$	−38.5199	−2.22395
$301$	0	0
$302$	−8.97218	−0.516291
$303$	−4.91193	−0.282183
$304$	−64.0239	−3.67202
$305$	−25.8003	−1.47732
$306$	−0.397040	−0.0226973
$307$	−30.0350	−1.71419	−0.857093	−	0.515162i	$-0.827732\pi$
$307$	−30.0350	−1.71419	−0.857093	+	0.515162i	$0.827732\pi$
$308$	0	0
$309$	−4.61507	−0.262542
$310$	−80.3948	−4.56612
$311$	−22.6288	−1.28316	−0.641580	−	0.767056i	$-0.721721\pi$
$311$	−22.6288	−1.28316	−0.641580	+	0.767056i	$0.721721\pi$
$312$	6.92714	0.392172
$313$	−17.2097	−0.972752	−0.486376	−	0.873750i	$-0.661681\pi$
$313$	−17.2097	−0.972752	−0.486376	+	0.873750i	$0.661681\pi$
$314$	−10.9361	−0.617160
$315$	0	0
$316$	63.8365	3.59109
$317$	21.6413	1.21549	0.607747	−	0.794130i	$-0.292073\pi$
$317$	21.6413	1.21549	0.607747	+	0.794130i	$0.292073\pi$
$318$	27.8411	1.56125
$319$	12.8153	0.717520
$320$	15.1951	0.849433
$321$	10.7824	0.601814
$322$	0	0
$323$	−1.15118	−0.0640534
$324$	4.68016	0.260009
$325$	8.23047	0.456544
$326$	−41.2340	−2.28374
$327$	1.32351	0.0731901
$328$	−80.5340	−4.44674
$329$	0	0
$330$	18.6843	1.02854
$331$	5.55131	0.305128	0.152564	−	0.988294i	$-0.451247\pi$
$331$	5.55131	0.305128	0.152564	+	0.988294i	$0.451247\pi$
$332$	−35.1301	−1.92801
$333$	−6.58538	−0.360877
$334$	26.4171	1.44548
$335$	−8.53984	−0.466581
$336$	0	0
$337$	12.9963	0.707954	0.353977	−	0.935254i	$-0.384829\pi$
$337$	12.9963	0.707954	0.353977	+	0.935254i	$0.384829\pi$
$338$	−2.58460	−0.140584
$339$	−7.31323	−0.397200
$340$	2.61511	0.141824
$341$	16.9958	0.920375
$342$	19.3685	1.04733
$343$	0	0
$344$	2.30005	0.124011
$345$	18.3910	0.990138
$346$	23.0081	1.23692
$347$	7.60830	0.408435	0.204217	−	0.978926i	$-0.434535\pi$
$347$	7.60830	0.408435	0.204217	+	0.978926i	$0.434535\pi$
$348$	−30.1783	−1.61773
$349$	−18.4439	−0.987278	−0.493639	−	0.869667i	$-0.664334\pi$
$349$	−18.4439	−0.987278	−0.493639	+	0.869667i	$0.664334\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	−16.3516	−0.871543
$353$	−25.8576	−1.37626	−0.688132	−	0.725586i	$-0.741569\pi$
$353$	−25.8576	−1.37626	−0.688132	+	0.725586i	$0.741569\pi$
$354$	−25.4268	−1.35142
$355$	45.3761	2.40832
$356$	29.1903	1.54708
$357$	0	0
$358$	−10.3207	−0.545465
$359$	−2.66416	−0.140609	−0.0703046	−	0.997526i	$-0.522397\pi$
$359$	−2.66416	−0.140609	−0.0703046	+	0.997526i	$0.522397\pi$
$360$	−25.1966	−1.32798
$361$	37.1572	1.95564
$362$	−53.3668	−2.80490
$363$	7.05006	0.370032
$364$	0	0
$365$	−3.14737	−0.164741
$366$	−18.3328	−0.958273
$367$	16.2009	0.845682	0.422841	−	0.906204i	$-0.361033\pi$
$367$	16.2009	0.845682	0.422841	+	0.906204i	$0.361033\pi$
$368$	−43.1973	−2.25182
$369$	11.6259	0.605218
$370$	61.9102	3.21856
$371$	0	0
$372$	−40.0228	−2.07509
$373$	−25.6198	−1.32654	−0.663271	−	0.748379i	$-0.730832\pi$
$373$	−25.6198	−1.32654	−0.663271	+	0.748379i	$0.730832\pi$
$374$	−0.789096	−0.0408032
$375$	−11.7504	−0.606790
$376$	−59.9889	−3.09369
$377$	6.44813	0.332096
$378$	0	0
$379$	20.5759	1.05691	0.528457	−	0.848960i	$-0.322771\pi$
$379$	20.5759	1.05691	0.528457	+	0.848960i	$0.322771\pi$
$380$	−127.571	−6.54424
$381$	0.461478	0.0236422
$382$	−45.5818	−2.33217
$383$	−3.56048	−0.181932	−0.0909659	−	0.995854i	$-0.528995\pi$
$383$	−3.56048	−0.181932	−0.0909659	+	0.995854i	$0.528995\pi$
$384$	−5.65772	−0.288719
$385$	0	0
$386$	−56.6483	−2.88332
$387$	−0.332035	−0.0168783
$388$	−38.3305	−1.94594
$389$	−11.3718	−0.576575	−0.288288	−	0.957544i	$-0.593086\pi$
$389$	−11.3718	−0.576575	−0.288288	+	0.957544i	$0.593086\pi$
$390$	9.40115	0.476046
$391$	−0.776709	−0.0392799
$392$	0	0
$393$	4.13651	0.208659
$394$	6.20376	0.312541
$395$	49.6131	2.49631
$396$	9.30156	0.467421
$397$	26.3262	1.32128	0.660638	−	0.750705i	$-0.270286\pi$
$397$	26.3262	1.32128	0.660638	+	0.750705i	$0.270286\pi$
$398$	20.0980	1.00742
$399$	0	0
$400$	70.3176	3.51588
$401$	34.1195	1.70385	0.851923	−	0.523666i	$-0.175436\pi$
$401$	34.1195	1.70385	0.851923	+	0.523666i	$0.175436\pi$
$402$	−6.06814	−0.302651
$403$	8.55159	0.425985
$404$	22.9886	1.14373
$405$	3.63737	0.180742
$406$	0	0
$407$	−13.0881	−0.648753
$408$	1.06413	0.0526823
$409$	2.46837	0.122053	0.0610264	−	0.998136i	$-0.480563\pi$
$409$	2.46837	0.122053	0.0610264	+	0.998136i	$0.480563\pi$
$410$	−109.296	−5.39777
$411$	−17.2668	−0.851707
$412$	21.5993	1.06412
$413$	0	0
$414$	13.0681	0.642260
$415$	−27.3027	−1.34024
$416$	−8.22744	−0.403383
$417$	17.2932	0.846849
$418$	38.4939	1.88280
$419$	6.92473	0.338295	0.169148	−	0.985591i	$-0.445899\pi$
$419$	6.92473	0.338295	0.169148	+	0.985591i	$0.445899\pi$
$420$	0	0
$421$	−15.3301	−0.747143	−0.373572	−	0.927601i	$-0.621867\pi$
$421$	−15.3301	−0.747143	−0.373572	+	0.927601i	$0.621867\pi$
$422$	−28.1945	−1.37249
$423$	8.65999	0.421063
$424$	−74.6185	−3.62380
$425$	1.26435	0.0613298
$426$	32.2428	1.56217
$427$	0	0
$428$	−50.4632	−2.43923
$429$	−1.98745	−0.0959548
$430$	3.12151	0.150533
$431$	−0.953618	−0.0459342	−0.0229671	−	0.999736i	$-0.507311\pi$
$431$	−0.953618	−0.0459342	−0.0229671	+	0.999736i	$0.507311\pi$
$432$	−8.54357	−0.411053
$433$	−17.7964	−0.855241	−0.427621	−	0.903958i	$-0.640648\pi$
$433$	−17.7964	−0.855241	−0.427621	+	0.903958i	$0.640648\pi$
$434$	0	0
$435$	−23.4543	−1.12455
$436$	−6.19422	−0.296650
$437$	37.8896	1.81251
$438$	−2.23642	−0.106860
$439$	38.1402	1.82033	0.910167	−	0.414242i	$-0.135953\pi$
$439$	38.1402	1.82033	0.910167	+	0.414242i	$0.135953\pi$
$440$	−50.0769	−2.38732
$441$	0	0
$442$	−0.397040	−0.0188853
$443$	−12.2641	−0.582686	−0.291343	−	0.956619i	$-0.594102\pi$
$443$	−12.2641	−0.582686	−0.291343	+	0.956619i	$0.594102\pi$
$444$	30.8206	1.46268
$445$	22.6864	1.07544
$446$	−40.7229	−1.92829
$447$	−11.0179	−0.521127
$448$	0	0
$449$	22.9767	1.08434	0.542168	−	0.840270i	$-0.317604\pi$
$449$	22.9767	1.08434	0.542168	+	0.840270i	$0.317604\pi$
$450$	−21.2725	−1.00279
$451$	23.1058	1.08801
$452$	34.2271	1.60991
$453$	−3.47140	−0.163101
$454$	14.8609	0.697457
$455$	0	0
$456$	−51.9107	−2.43094
$457$	−21.8893	−1.02394	−0.511968	−	0.859005i	$-0.671083\pi$
$457$	−21.8893	−1.02394	−0.511968	+	0.859005i	$0.671083\pi$
$458$	9.35272	0.437024
$459$	−0.153618	−0.00717026
$460$	−86.0728	−4.01316
$461$	−2.39917	−0.111741	−0.0558703	−	0.998438i	$-0.517793\pi$
$461$	−2.39917	−0.111741	−0.0558703	+	0.998438i	$0.517793\pi$
$462$	0	0
$463$	6.72484	0.312530	0.156265	−	0.987715i	$-0.450055\pi$
$463$	6.72484	0.312530	0.156265	+	0.987715i	$0.450055\pi$
$464$	55.0901	2.55749
$465$	−31.1053	−1.44247
$466$	58.5781	2.71358
$467$	9.16836	0.424261	0.212131	−	0.977241i	$-0.431960\pi$
$467$	9.16836	0.424261	0.212131	+	0.977241i	$0.431960\pi$
$468$	4.68016	0.216340
$469$	0	0
$470$	−81.4138	−3.75534
$471$	−4.23125	−0.194966
$472$	68.1478	3.13676
$473$	−0.659902	−0.0303423
$474$	35.2535	1.61925
$475$	−61.6776	−2.82996
$476$	0	0
$477$	10.7719	0.493212
$478$	−68.2293	−3.12074
$479$	19.0189	0.868995	0.434498	−	0.900673i	$-0.356926\pi$
$479$	19.0189	0.868995	0.434498	+	0.900673i	$0.356926\pi$
$480$	29.9263	1.36594
$481$	−6.58538	−0.300268
$482$	−47.7469	−2.17481
$483$	0	0
$484$	−32.9954	−1.49979
$485$	−29.7901	−1.35270
$486$	2.58460	0.117240
$487$	0.222118	0.0100651	0.00503256	−	0.999987i	$-0.498398\pi$
$487$	0.222118	0.0100651	0.00503256	+	0.999987i	$0.498398\pi$
$488$	49.1349	2.22423
$489$	−15.9537	−0.721452
$490$	0	0
$491$	−28.6415	−1.29257	−0.646287	−	0.763095i	$-0.723679\pi$
$491$	−28.6415	−1.29257	−0.646287	+	0.763095i	$0.723679\pi$
$492$	−54.4109	−2.45303
$493$	0.990547	0.0446120
$494$	19.3685	0.871430
$495$	7.22908	0.324923
$496$	73.0611	3.28054
$497$	0	0
$498$	−19.4004	−0.869355
$499$	25.0497	1.12138	0.560688	−	0.828027i	$-0.310537\pi$
$499$	25.0497	1.12138	0.560688	+	0.828027i	$0.310537\pi$
$500$	54.9939	2.45940
$501$	10.2209	0.456638
$502$	1.08782	0.0485517
$503$	4.83818	0.215724	0.107862	−	0.994166i	$-0.465600\pi$
$503$	4.83818	0.215724	0.107862	+	0.994166i	$0.465600\pi$
$504$	0	0
$505$	17.8665	0.795050
$506$	25.9720	1.15460
$507$	−1.00000	−0.0444116
$508$	−2.15979	−0.0958251
$509$	22.6569	1.00425	0.502124	−	0.864795i	$-0.332552\pi$
$509$	22.6569	1.00425	0.502124	+	0.864795i	$0.332552\pi$
$510$	1.44418	0.0639495
$511$	0	0
$512$	48.0733	2.12456
$513$	7.49381	0.330860
$514$	44.6894	1.97116
$515$	16.7867	0.739712
$516$	1.55398	0.0684100
$517$	17.2113	0.756950
$518$	0	0
$519$	8.90199	0.390754
$520$	−25.1966	−1.10494
$521$	13.8168	0.605325	0.302662	−	0.953098i	$-0.402125\pi$
$521$	13.8168	0.605325	0.302662	+	0.953098i	$0.402125\pi$
$522$	−16.6659	−0.729444
$523$	−12.9345	−0.565584	−0.282792	−	0.959181i	$-0.591261\pi$
$523$	−12.9345	−0.565584	−0.282792	+	0.959181i	$0.591261\pi$
$524$	−19.3595	−0.845725
$525$	0	0
$526$	22.1377	0.965249
$527$	1.31367	0.0572246
$528$	−16.9799	−0.738955
$529$	2.56436	0.111494
$530$	−101.268	−4.39882
$531$	−9.83780	−0.426924
$532$	0	0
$533$	11.6259	0.503572
$534$	16.1202	0.697591
$535$	−39.2195	−1.69561
$536$	16.2636	0.702479
$537$	−3.99314	−0.172317
$538$	26.4823	1.14173
$539$	0	0
$540$	−17.0235	−0.732574
$541$	16.7522	0.720234	0.360117	−	0.932907i	$-0.382737\pi$
$541$	16.7522	0.720234	0.360117	+	0.932907i	$0.382737\pi$
$542$	7.97364	0.342497
$543$	−20.6480	−0.886090
$544$	−1.26388	−0.0541884
$545$	−4.81409	−0.206213
$546$	0	0
$547$	16.8961	0.722425	0.361212	−	0.932484i	$-0.382363\pi$
$547$	16.8961	0.722425	0.361212	+	0.932484i	$0.382363\pi$
$548$	80.8112	3.45208
$549$	−7.09311	−0.302726
$550$	−42.2779	−1.80274
$551$	−48.3211	−2.05855
$552$	−35.0245	−1.49074
$553$	0	0
$554$	−13.2138	−0.561401
$555$	23.9535	1.01677
$556$	−80.9347	−3.43240
$557$	−18.7023	−0.792440	−0.396220	−	0.918156i	$-0.629678\pi$
$557$	−18.7023	−0.792440	−0.396220	+	0.918156i	$0.629678\pi$
$558$	−22.1024	−0.935671
$559$	−0.332035	−0.0140436
$560$	0	0
$561$	−0.305307	−0.0128901
$562$	40.0195	1.68812
$563$	13.9098	0.586229	0.293114	−	0.956077i	$-0.405308\pi$
$563$	13.9098	0.586229	0.293114	+	0.956077i	$0.405308\pi$
$564$	−40.5301	−1.70663
$565$	26.6009	1.11911
$566$	28.4675	1.19658
$567$	0	0
$568$	−86.4159	−3.62593
$569$	−40.1529	−1.68330	−0.841648	−	0.540027i	$-0.818414\pi$
$569$	−40.1529	−1.68330	−0.841648	+	0.540027i	$0.818414\pi$
$570$	−70.4504	−2.95084
$571$	−34.7569	−1.45453	−0.727265	−	0.686356i	$-0.759209\pi$
$571$	−34.7569	−1.45453	−0.727265	+	0.686356i	$0.759209\pi$
$572$	9.30156	0.388918
$573$	−17.6359	−0.736751
$574$	0	0
$575$	−41.6143	−1.73543
$576$	4.17750	0.174062
$577$	17.5908	0.732314	0.366157	−	0.930553i	$-0.380673\pi$
$577$	17.5908	0.732314	0.366157	+	0.930553i	$0.380673\pi$
$578$	43.8772	1.82505
$579$	−21.9176	−0.910865
$580$	109.770	4.55794
$581$	0	0
$582$	−21.1679	−0.877436
$583$	21.4086	0.886653
$584$	5.99397	0.248032
$585$	3.63737	0.150387
$586$	−59.9641	−2.47709
$587$	35.4587	1.46354	0.731769	−	0.681553i	$-0.238695\pi$
$587$	35.4587	1.46354	0.731769	+	0.681553i	$0.238695\pi$
$588$	0	0
$589$	−64.0840	−2.64053
$590$	92.4866	3.80761
$591$	2.40028	0.0987342
$592$	−56.2627	−2.31238
$593$	−2.72267	−0.111807	−0.0559034	−	0.998436i	$-0.517804\pi$
$593$	−2.72267	−0.111807	−0.0559034	+	0.998436i	$0.517804\pi$
$594$	5.13675	0.210764
$595$	0	0
$596$	51.5654	2.11220
$597$	7.77606	0.318253
$598$	13.0681	0.534392
$599$	−36.5301	−1.49258	−0.746289	−	0.665622i	$-0.768166\pi$
$599$	−36.5301	−1.49258	−0.746289	+	0.665622i	$0.768166\pi$
$600$	57.0136	2.32757
$601$	−25.0561	−1.02206	−0.511030	−	0.859563i	$-0.670736\pi$
$601$	−25.0561	−1.02206	−0.511030	+	0.859563i	$0.670736\pi$
$602$	0	0
$603$	−2.34780	−0.0956100
$604$	16.2467	0.661069
$605$	−25.6437	−1.04256
$606$	12.6954	0.515714
$607$	10.6430	0.431986	0.215993	−	0.976395i	$-0.430701\pi$
$607$	10.6430	0.431986	0.215993	+	0.976395i	$0.430701\pi$
$608$	61.6549	2.50043
$609$	0	0
$610$	66.6834	2.69993
$611$	8.65999	0.350345
$612$	0.718955	0.0290620
$613$	5.31284	0.214583	0.107292	−	0.994228i	$-0.465782\pi$
$613$	5.31284	0.214583	0.107292	+	0.994228i	$0.465782\pi$
$614$	77.6284	3.13283
$615$	−42.2876	−1.70520
$616$	0	0
$617$	19.9494	0.803131	0.401566	−	0.915830i	$-0.368466\pi$
$617$	19.9494	0.803131	0.401566	+	0.915830i	$0.368466\pi$
$618$	11.9281	0.479819
$619$	−27.5833	−1.10867	−0.554333	−	0.832295i	$-0.687027\pi$
$619$	−27.5833	−1.10867	−0.554333	+	0.832295i	$0.687027\pi$
$620$	145.578	5.84655
$621$	5.05612	0.202895
$622$	58.4864	2.34509
$623$	0	0
$624$	−8.54357	−0.342017
$625$	1.58832	0.0635327
$626$	44.4803	1.77779
$627$	14.8935	0.594791
$628$	19.8029	0.790223
$629$	−1.01163	−0.0403364
$630$	0	0
$631$	18.4763	0.735531	0.367765	−	0.929919i	$-0.380123\pi$
$631$	18.4763	0.735531	0.367765	+	0.929919i	$0.380123\pi$
$632$	−94.4850	−3.75841
$633$	−10.9087	−0.433580
$634$	−55.9340	−2.22142
$635$	−1.67857	−0.0666118
$636$	−50.4142	−1.99905
$637$	0	0
$638$	−33.1225	−1.31133
$639$	12.4750	0.493503
$640$	20.5792	0.813465
$641$	0.454568	0.0179544	0.00897718	−	0.999960i	$-0.497142\pi$
$641$	0.454568	0.0179544	0.00897718	+	0.999960i	$0.497142\pi$
$642$	−27.8681	−1.09987
$643$	12.4903	0.492571	0.246285	−	0.969197i	$-0.420790\pi$
$643$	12.4903	0.492571	0.246285	+	0.969197i	$0.420790\pi$
$644$	0	0
$645$	1.20774	0.0475545
$646$	2.97534	0.117063
$647$	−20.9746	−0.824597	−0.412299	−	0.911049i	$-0.635274\pi$
$647$	−20.9746	−0.824597	−0.412299	+	0.911049i	$0.635274\pi$
$648$	−6.92714	−0.272124
$649$	−19.5521	−0.767487
$650$	−21.2725	−0.834375
$651$	0	0
$652$	74.6659	2.92414
$653$	12.1626	0.475960	0.237980	−	0.971270i	$-0.423515\pi$
$653$	12.1626	0.475960	0.237980	+	0.971270i	$0.423515\pi$
$654$	−3.42074	−0.133761
$655$	−15.0460	−0.587897
$656$	99.3264	3.87804
$657$	−0.865288	−0.0337581
$658$	0	0
$659$	8.65324	0.337082	0.168541	−	0.985695i	$-0.446094\pi$
$659$	8.65324	0.337082	0.168541	+	0.985695i	$0.446094\pi$
$660$	−33.8332	−1.31696
$661$	−5.06831	−0.197134	−0.0985672	−	0.995130i	$-0.531426\pi$
$661$	−5.06831	−0.197134	−0.0985672	+	0.995130i	$0.531426\pi$
$662$	−14.3479	−0.557648
$663$	−0.153618	−0.00596601
$664$	51.9963	2.01785
$665$	0	0
$666$	17.0206	0.659534
$667$	−32.6025	−1.26238
$668$	−47.8356	−1.85082
$669$	−15.7560	−0.609162
$670$	22.0721	0.852718
$671$	−14.0972	−0.544215
$672$	0	0
$673$	8.04418	0.310080	0.155040	−	0.987908i	$-0.450449\pi$
$673$	8.04418	0.310080	0.155040	+	0.987908i	$0.450449\pi$
$674$	−33.5903	−1.29385
$675$	−8.23047	−0.316791
$676$	4.68016	0.180006
$677$	−19.5484	−0.751307	−0.375654	−	0.926760i	$-0.622582\pi$
$677$	−19.5484	−0.751307	−0.375654	+	0.926760i	$0.622582\pi$
$678$	18.9018	0.725919
$679$	0	0
$680$	−3.87064	−0.148432
$681$	5.74979	0.220332
$682$	−43.9274	−1.68207
$683$	−33.0966	−1.26641	−0.633203	−	0.773986i	$-0.718260\pi$
$683$	−33.0966	−1.26641	−0.633203	+	0.773986i	$0.718260\pi$
$684$	−35.0722	−1.34102
$685$	62.8057	2.39968
$686$	0	0
$687$	3.61863	0.138059
$688$	−2.83677	−0.108151
$689$	10.7719	0.410377
$690$	−47.5334	−1.80956
$691$	−25.6309	−0.975046	−0.487523	−	0.873110i	$-0.662100\pi$
$691$	−25.6309	−0.975046	−0.487523	+	0.873110i	$0.662100\pi$
$692$	−41.6627	−1.58378
$693$	0	0
$694$	−19.6644	−0.746451
$695$	−62.9016	−2.38599
$696$	44.6671	1.69310
$697$	1.78594	0.0676472
$698$	47.6700	1.80434
$699$	22.6643	0.857242
$700$	0	0
$701$	40.6042	1.53360	0.766800	−	0.641886i	$-0.221848\pi$
$701$	40.6042	1.53360	0.766800	+	0.641886i	$0.221848\pi$
$702$	2.58460	0.0975495
$703$	49.3496	1.86126
$704$	8.30255	0.312914
$705$	−31.4996	−1.18634
$706$	66.8317	2.51524
$707$	0	0
$708$	46.0425	1.73038
$709$	19.0199	0.714309	0.357154	−	0.934045i	$-0.383747\pi$
$709$	19.0199	0.714309	0.357154	+	0.934045i	$0.383747\pi$
$710$	−117.279	−4.40141
$711$	13.6398	0.511533
$712$	−43.2048	−1.61917
$713$	−43.2379	−1.61927
$714$	0	0
$715$	7.22908	0.270352
$716$	18.6885	0.698424
$717$	−26.3984	−0.985867
$718$	6.88580	0.256976
$719$	12.8714	0.480022	0.240011	−	0.970770i	$-0.422849\pi$
$719$	12.8714	0.480022	0.240011	+	0.970770i	$0.422849\pi$
$720$	31.0761	1.15814
$721$	0	0
$722$	−96.0365	−3.57411
$723$	−18.4736	−0.687042
$724$	96.6359	3.59144
$725$	53.0712	1.97101
$726$	−18.2216	−0.676266
$727$	−24.7107	−0.916471	−0.458235	−	0.888831i	$-0.651518\pi$
$727$	−24.7107	−0.916471	−0.458235	+	0.888831i	$0.651518\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	8.13471	0.301079
$731$	−0.0510064	−0.00188654
$732$	33.1969	1.22699
$733$	39.8899	1.47337	0.736683	−	0.676239i	$-0.236391\pi$
$733$	39.8899	1.47337	0.736683	+	0.676239i	$0.236391\pi$
$734$	−41.8730	−1.54556
$735$	0	0
$736$	41.5989	1.53336
$737$	−4.66613	−0.171879
$738$	−30.0482	−1.10609
$739$	−48.5451	−1.78576	−0.892880	−	0.450295i	$-0.851319\pi$
$739$	−48.5451	−1.78576	−0.892880	+	0.450295i	$0.851319\pi$
$740$	−112.106	−4.12110
$741$	7.49381	0.275292
$742$	0	0
$743$	−0.683870	−0.0250888	−0.0125444	−	0.999921i	$-0.503993\pi$
$743$	−0.683870	−0.0250888	−0.0125444	+	0.999921i	$0.503993\pi$
$744$	59.2381	2.17177
$745$	40.0761	1.46827
$746$	66.2169	2.42437
$747$	−7.50617	−0.274636
$748$	1.42888	0.0522452
$749$	0	0
$750$	30.3702	1.10896
$751$	0.229499	0.00837452	0.00418726	−	0.999991i	$-0.498667\pi$
$751$	0.229499	0.00837452	0.00418726	+	0.999991i	$0.498667\pi$
$752$	73.9872	2.69804
$753$	0.420884	0.0153379
$754$	−16.6659	−0.606934
$755$	12.6268	0.459535
$756$	0	0
$757$	0.705771	0.0256517	0.0128258	−	0.999918i	$-0.495917\pi$
$757$	0.705771	0.0256517	0.0128258	+	0.999918i	$0.495917\pi$
$758$	−53.1805	−1.93160
$759$	10.0488	0.364747
$760$	188.818	6.84916
$761$	12.0017	0.435062	0.217531	−	0.976053i	$-0.430200\pi$
$761$	12.0017	0.435062	0.217531	+	0.976053i	$0.430200\pi$
$762$	−1.19274	−0.0432082
$763$	0	0
$764$	82.5389	2.98615
$765$	0.558764	0.0202022
$766$	9.20241	0.332497
$767$	−9.83780	−0.355222
$768$	22.9779	0.829145
$769$	23.0117	0.829822	0.414911	−	0.909862i	$-0.363813\pi$
$769$	23.0117	0.829822	0.414911	+	0.909862i	$0.363813\pi$
$770$	0	0
$771$	17.2906	0.622707
$772$	102.578	3.69186
$773$	−1.32886	−0.0477957	−0.0238979	−	0.999714i	$-0.507608\pi$
$773$	−1.32886	−0.0477957	−0.0238979	+	0.999714i	$0.507608\pi$
$774$	0.858178	0.0308466
$775$	70.3836	2.52825
$776$	56.7333	2.03661
$777$	0	0
$778$	29.3917	1.05374
$779$	−87.1220	−3.12147
$780$	−17.0235	−0.609538
$781$	24.7934	0.887176
$782$	2.00748	0.0717874
$783$	−6.44813	−0.230438
$784$	0	0
$785$	15.3906	0.549315
$786$	−10.6912	−0.381343
$787$	−35.3032	−1.25842	−0.629212	−	0.777234i	$-0.716622\pi$
$787$	−35.3032	−1.25842	−0.629212	+	0.777234i	$0.716622\pi$
$788$	−11.2337	−0.400183
$789$	8.56523	0.304930
$790$	−128.230	−4.56222
$791$	0	0
$792$	−13.7673	−0.489200
$793$	−7.09311	−0.251884
$794$	−68.0428	−2.41475
$795$	−39.1814	−1.38962
$796$	−36.3932	−1.28992
$797$	19.2272	0.681061	0.340531	−	0.940233i	$-0.389393\pi$
$797$	19.2272	0.681061	0.340531	+	0.940233i	$0.389393\pi$
$798$	0	0
$799$	1.33033	0.0470636
$800$	−67.7157	−2.39411
$801$	6.23704	0.220375
$802$	−88.1853	−3.11393
$803$	−1.71971	−0.0606874
$804$	10.9881	0.387520
$805$	0	0
$806$	−22.1024	−0.778525
$807$	10.2462	0.360683
$808$	−34.0256	−1.19702
$809$	−25.6601	−0.902163	−0.451081	−	0.892483i	$-0.648962\pi$
$809$	−25.6601	−0.902163	−0.451081	+	0.892483i	$0.648962\pi$
$810$	−9.40115	−0.330323
$811$	−51.2939	−1.80117	−0.900586	−	0.434677i	$-0.856862\pi$
$811$	−51.2939	−1.80117	−0.900586	+	0.434677i	$0.856862\pi$
$812$	0	0
$813$	3.08506	0.108198
$814$	33.8275	1.18565
$815$	58.0296	2.03269
$816$	−1.31244	−0.0459447
$817$	2.48821	0.0870514
$818$	−6.37974	−0.223062
$819$	0	0
$820$	197.913	6.91141
$821$	44.0012	1.53565	0.767827	−	0.640657i	$-0.221338\pi$
$821$	44.0012	1.53565	0.767827	+	0.640657i	$0.221338\pi$
$822$	44.6277	1.55657
$823$	−31.6523	−1.10333	−0.551665	−	0.834066i	$-0.686007\pi$
$823$	−31.6523	−1.10333	−0.551665	+	0.834066i	$0.686007\pi$
$824$	−31.9692	−1.11370
$825$	−16.3576	−0.569499
$826$	0	0
$827$	−36.3403	−1.26368	−0.631838	−	0.775100i	$-0.717699\pi$
$827$	−36.3403	−1.26368	−0.631838	+	0.775100i	$0.717699\pi$
$828$	−23.6635	−0.822362
$829$	−24.2792	−0.843251	−0.421625	−	0.906770i	$-0.638540\pi$
$829$	−24.2792	−0.843251	−0.421625	+	0.906770i	$0.638540\pi$
$830$	70.5666	2.44940
$831$	−5.11252	−0.177351
$832$	4.17750	0.144829
$833$	0	0
$834$	−44.6959	−1.54769
$835$	−37.1774	−1.28658
$836$	−69.7041	−2.41077
$837$	−8.55159	−0.295586
$838$	−17.8977	−0.618264
$839$	−48.8312	−1.68584	−0.842919	−	0.538040i	$-0.819165\pi$
$839$	−48.8312	−1.68584	−0.842919	+	0.538040i	$0.819165\pi$
$840$	0	0
$841$	12.5784	0.433739
$842$	39.6222	1.36547
$843$	15.4838	0.533292
$844$	51.0542	1.75736
$845$	3.63737	0.125129
$846$	−22.3826	−0.769530
$847$	0	0
$848$	92.0306	3.16034
$849$	11.0143	0.378009
$850$	−3.26783	−0.112086
$851$	33.2965	1.14139
$852$	−58.3849	−2.00023
$853$	3.63003	0.124290	0.0621449	−	0.998067i	$-0.480206\pi$
$853$	3.63003	0.124290	0.0621449	+	0.998067i	$0.480206\pi$
$854$	0	0
$855$	−27.2578	−0.932196
$856$	74.6911	2.55289
$857$	−13.7965	−0.471281	−0.235640	−	0.971840i	$-0.575719\pi$
$857$	−13.7965	−0.471281	−0.235640	+	0.971840i	$0.575719\pi$
$858$	5.13675	0.175366
$859$	13.0742	0.446087	0.223044	−	0.974808i	$-0.428401\pi$
$859$	13.0742	0.446087	0.223044	+	0.974808i	$0.428401\pi$
$860$	−5.65239	−0.192745
$861$	0	0
$862$	2.46472	0.0839488
$863$	23.2766	0.792346	0.396173	−	0.918176i	$-0.370338\pi$
$863$	23.2766	0.792346	0.396173	+	0.918176i	$0.370338\pi$
$864$	8.22744	0.279903
$865$	−32.3798	−1.10095
$866$	45.9966	1.56303
$867$	16.9764	0.576549
$868$	0	0
$869$	27.1084	0.919590
$870$	60.6199	2.05521
$871$	−2.34780	−0.0795523
$872$	9.16812	0.310472
$873$	−8.19000	−0.277189
$874$	−97.9295	−3.31251
$875$	0	0
$876$	4.04969	0.136826
$877$	−48.8340	−1.64901	−0.824504	−	0.565856i	$-0.808546\pi$
$877$	−48.8340	−1.64901	−0.824504	+	0.565856i	$0.808546\pi$
$878$	−98.5772	−3.32682
$879$	−23.2005	−0.782535
$880$	61.7622	2.08200
$881$	−23.0372	−0.776144	−0.388072	−	0.921629i	$-0.626859\pi$
$881$	−23.0372	−0.776144	−0.388072	+	0.921629i	$0.626859\pi$
$882$	0	0
$883$	−2.92284	−0.0983613	−0.0491806	−	0.998790i	$-0.515661\pi$
$883$	−2.92284	−0.0983613	−0.0491806	+	0.998790i	$0.515661\pi$
$884$	0.718955	0.0241811
$885$	35.7837	1.20286
$886$	31.6978	1.06491
$887$	3.98674	0.133862	0.0669308	−	0.997758i	$-0.478679\pi$
$887$	3.98674	0.133862	0.0669308	+	0.997758i	$0.478679\pi$
$888$	−45.6179	−1.53084
$889$	0	0
$890$	−58.6353	−1.96546
$891$	1.98745	0.0665819
$892$	73.7406	2.46902
$893$	−64.8963	−2.17167
$894$	28.4768	0.952406
$895$	14.5245	0.485502
$896$	0	0
$897$	5.05612	0.168819
$898$	−59.3855	−1.98172
$899$	55.1418	1.83908
$900$	38.5199	1.28400
$901$	1.65475	0.0551279
$902$	−59.7192	−1.98843
$903$	0	0
$904$	−50.6598	−1.68492
$905$	75.1044	2.49656
$906$	8.97218	0.298081
$907$	1.77883	0.0590650	0.0295325	−	0.999564i	$-0.490598\pi$
$907$	1.77883	0.0590650	0.0295325	+	0.999564i	$0.490598\pi$
$908$	−26.9099	−0.893037
$909$	4.91193	0.162918
$910$	0	0
$911$	41.3761	1.37085	0.685425	−	0.728143i	$-0.259616\pi$
$911$	41.3761	1.37085	0.685425	+	0.728143i	$0.259616\pi$
$912$	64.0239	2.12004
$913$	−14.9181	−0.493717
$914$	56.5750	1.87133
$915$	25.8003	0.852930
$916$	−16.9358	−0.559574
$917$	0	0
$918$	0.397040	0.0131043
$919$	1.50506	0.0496474	0.0248237	−	0.999692i	$-0.492098\pi$
$919$	1.50506	0.0496474	0.0248237	+	0.999692i	$0.492098\pi$
$920$	127.397	4.20015
$921$	30.0350	0.989686
$922$	6.20091	0.204216
$923$	12.4750	0.410619
$924$	0	0
$925$	−54.2008	−1.78211
$926$	−17.3810	−0.571176
$927$	4.61507	0.151579
$928$	−53.0516	−1.74151
$929$	−21.6670	−0.710870	−0.355435	−	0.934701i	$-0.615667\pi$
$929$	−21.6670	−0.710870	−0.355435	+	0.934701i	$0.615667\pi$
$930$	80.3948	2.63625
$931$	0	0
$932$	−106.073	−3.47452
$933$	22.6288	0.740833
$934$	−23.6966	−0.775375
$935$	1.11051	0.0363177
$936$	−6.92714	−0.226421
$937$	13.0062	0.424895	0.212447	−	0.977173i	$-0.431857\pi$
$937$	13.0062	0.424895	0.212447	+	0.977173i	$0.431857\pi$
$938$	0	0
$939$	17.2097	0.561619
$940$	147.423	4.80841
$941$	−40.1945	−1.31030	−0.655152	−	0.755497i	$-0.727395\pi$
$941$	−40.1945	−1.31030	−0.655152	+	0.755497i	$0.727395\pi$
$942$	10.9361	0.356317
$943$	−58.7817	−1.91420
$944$	−84.0499	−2.73559
$945$	0	0
$946$	1.70558	0.0554533
$947$	30.0700	0.977144	0.488572	−	0.872524i	$-0.337518\pi$
$947$	30.0700	0.977144	0.488572	+	0.872524i	$0.337518\pi$
$948$	−63.8365	−2.07331
$949$	−0.865288	−0.0280884
$950$	159.412	5.17201
$951$	−21.6413	−0.701766
$952$	0	0
$953$	27.0100	0.874939	0.437469	−	0.899233i	$-0.355875\pi$
$953$	27.0100	0.874939	0.437469	+	0.899233i	$0.355875\pi$
$954$	−27.8411	−0.901388
$955$	64.1484	2.07579
$956$	123.549	3.99585
$957$	−12.8153	−0.414260
$958$	−49.1562	−1.58817
$959$	0	0
$960$	−15.1951	−0.490420
$961$	42.1297	1.35902
$962$	17.0206	0.548766
$963$	−10.7824	−0.347457
$964$	86.4595	2.78467
$965$	79.7225	2.56636
$966$	0	0
$967$	31.9526	1.02753	0.513763	−	0.857932i	$-0.328251\pi$
$967$	31.9526	1.02753	0.513763	+	0.857932i	$0.328251\pi$
$968$	48.8367	1.56967
$969$	1.15118	0.0369813
$970$	76.9954	2.47217
$971$	31.6859	1.01685	0.508424	−	0.861107i	$-0.330228\pi$
$971$	31.6859	1.01685	0.508424	+	0.861107i	$0.330228\pi$
$972$	−4.68016	−0.150116
$973$	0	0
$974$	−0.574086	−0.0183949
$975$	−8.23047	−0.263586
$976$	−60.6005	−1.93977
$977$	−25.7422	−0.823567	−0.411784	−	0.911282i	$-0.635094\pi$
$977$	−25.7422	−0.823567	−0.411784	+	0.911282i	$0.635094\pi$
$978$	41.2340	1.31852
$979$	12.3958	0.396171
$980$	0	0
$981$	−1.32351	−0.0422563
$982$	74.0269	2.36229
$983$	−1.09859	−0.0350397	−0.0175198	−	0.999847i	$-0.505577\pi$
$983$	−1.09859	−0.0350397	−0.0175198	+	0.999847i	$0.505577\pi$
$984$	80.5340	2.56733
$985$	−8.73070	−0.278183
$986$	−2.56017	−0.0815324
$987$	0	0
$988$	−35.0722	−1.11580
$989$	1.67881	0.0533830
$990$	−18.6843	−0.593825
$991$	20.3818	0.647449	0.323724	−	0.946151i	$-0.395065\pi$
$991$	20.3818	0.647449	0.323724	+	0.946151i	$0.395065\pi$
$992$	−70.3577	−2.23386
$993$	−5.55131	−0.176166
$994$	0	0
$995$	−28.2844	−0.896677
$996$	35.1301	1.11314
$997$	32.6872	1.03521	0.517607	−	0.855618i	$-0.326823\pi$
$997$	32.6872	1.03521	0.517607	+	0.855618i	$0.326823\pi$
$998$	−64.7434	−2.04942
$999$	6.58538	0.208352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.2.a.x.1.1	✓	10
3.2	odd	2		5733.2.a.bw.1.10		10
7.6	odd	2		1911.2.a.y.1.1	yes	10
21.20	even	2		5733.2.a.bx.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.2.a.x.1.1	✓	10	1.1	even	1	trivial
1911.2.a.y.1.1	yes	10	7.6	odd	2
5733.2.a.bw.1.10		10	3.2	odd	2
5733.2.a.bx.1.10		10	21.20	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:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58460 q^{2} -1.00000 q^{3} +4.68016 q^{4} +3.63737 q^{5} +2.58460 q^{6} -6.92714 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.58460 q^{2} -1.00000 q^{3} +4.68016 q^{4} +3.63737 q^{5} +2.58460 q^{6} -6.92714 q^{8} +1.00000 q^{9} -9.40115 q^{10} +1.98745 q^{11} -4.68016 q^{12} +1.00000 q^{13} -3.63737 q^{15} +8.54357 q^{16} +0.153618 q^{17} -2.58460 q^{18} -7.49381 q^{19} +17.0235 q^{20} -5.13675 q^{22} -5.05612 q^{23} +6.92714 q^{24} +8.23047 q^{25} -2.58460 q^{26} -1.00000 q^{27} +6.44813 q^{29} +9.40115 q^{30} +8.55159 q^{31} -8.22744 q^{32} -1.98745 q^{33} -0.397040 q^{34} +4.68016 q^{36} -6.58538 q^{37} +19.3685 q^{38} -1.00000 q^{39} -25.1966 q^{40} +11.6259 q^{41} -0.332035 q^{43} +9.30156 q^{44} +3.63737 q^{45} +13.0681 q^{46} +8.65999 q^{47} -8.54357 q^{48} -21.2725 q^{50} -0.153618 q^{51} +4.68016 q^{52} +10.7719 q^{53} +2.58460 q^{54} +7.22908 q^{55} +7.49381 q^{57} -16.6659 q^{58} -9.83780 q^{59} -17.0235 q^{60} -7.09311 q^{61} -22.1024 q^{62} +4.17750 q^{64} +3.63737 q^{65} +5.13675 q^{66} -2.34780 q^{67} +0.718955 q^{68} +5.05612 q^{69} +12.4750 q^{71} -6.92714 q^{72} -0.865288 q^{73} +17.0206 q^{74} -8.23047 q^{75} -35.0722 q^{76} +2.58460 q^{78} +13.6398 q^{79} +31.0761 q^{80} +1.00000 q^{81} -30.0482 q^{82} -7.50617 q^{83} +0.558764 q^{85} +0.858178 q^{86} -6.44813 q^{87} -13.7673 q^{88} +6.23704 q^{89} -9.40115 q^{90} -23.6635 q^{92} -8.55159 q^{93} -22.3826 q^{94} -27.2578 q^{95} +8.22744 q^{96} -8.19000 q^{97} +1.98745 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 10 q^{3} + 16 q^{4} + 6 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - 10 * q^3 + 16 * q^4 + 6 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} - 10 q^{3} + 16 q^{4} + 6 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 12 q^{11} - 16 q^{12} + 10 q^{13} - 6 q^{15} + 24 q^{16} + 4 q^{18} - 10 q^{19} + 16 q^{20} + 8 q^{22} + 14 q^{23} - 12 q^{24} + 32 q^{25} + 4 q^{26} - 10 q^{27} + 18 q^{29} + 8 q^{30} - 14 q^{31} + 28 q^{32} - 12 q^{33} - 4 q^{34} + 16 q^{36} + 24 q^{37} + 4 q^{38} - 10 q^{39} - 16 q^{40} + 24 q^{41} + 2 q^{43} + 48 q^{44} + 6 q^{45} + 20 q^{46} + 18 q^{47} - 24 q^{48} - 28 q^{50} + 16 q^{52} + 10 q^{53} - 4 q^{54} - 12 q^{55} + 10 q^{57} + 12 q^{58} + 12 q^{59} - 16 q^{60} + 4 q^{61} - 4 q^{62} + 32 q^{64} + 6 q^{65} - 8 q^{66} - 12 q^{67} + 40 q^{68} - 14 q^{69} + 32 q^{71} + 12 q^{72} + 18 q^{73} + 24 q^{74} - 32 q^{75} - 32 q^{76} - 4 q^{78} + 34 q^{79} + 32 q^{80} + 10 q^{81} - 48 q^{82} + 30 q^{83} + 40 q^{86} - 18 q^{87} + 32 q^{88} + 10 q^{89} - 8 q^{90} - 40 q^{92} + 14 q^{93} + 24 q^{94} - 30 q^{95} - 28 q^{96} + 2 q^{97} + 12 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 10 * q^3 + 16 * q^4 + 6 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9 - 8 * q^10 + 12 * q^11 - 16 * q^12 + 10 * q^13 - 6 * q^15 + 24 * q^16 + 4 * q^18 - 10 * q^19 + 16 * q^20 + 8 * q^22 + 14 * q^23 - 12 * q^24 + 32 * q^25 + 4 * q^26 - 10 * q^27 + 18 * q^29 + 8 * q^30 - 14 * q^31 + 28 * q^32 - 12 * q^33 - 4 * q^34 + 16 * q^36 + 24 * q^37 + 4 * q^38 - 10 * q^39 - 16 * q^40 + 24 * q^41 + 2 * q^43 + 48 * q^44 + 6 * q^45 + 20 * q^46 + 18 * q^47 - 24 * q^48 - 28 * q^50 + 16 * q^52 + 10 * q^53 - 4 * q^54 - 12 * q^55 + 10 * q^57 + 12 * q^58 + 12 * q^59 - 16 * q^60 + 4 * q^61 - 4 * q^62 + 32 * q^64 + 6 * q^65 - 8 * q^66 - 12 * q^67 + 40 * q^68 - 14 * q^69 + 32 * q^71 + 12 * q^72 + 18 * q^73 + 24 * q^74 - 32 * q^75 - 32 * q^76 - 4 * q^78 + 34 * q^79 + 32 * q^80 + 10 * q^81 - 48 * q^82 + 30 * q^83 + 40 * q^86 - 18 * q^87 + 32 * q^88 + 10 * q^89 - 8 * q^90 - 40 * q^92 + 14 * q^93 + 24 * q^94 - 30 * q^95 - 28 * q^96 + 2 * q^97 + 12 * q^99

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