LMFDB - Embedded newform 1127.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1127,2,Mod(1,1127)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1127, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1127.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1127 = 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1127.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:	$8.99914030780$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.2147108.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 9x^{3} + 17x^{2} + 16x - 27 $ x^5 - 2x^4 - 9x^3 + 17x^2 + 16x - 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 161)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.50216$ of defining polynomial
Character	$\chi$	$=$	1127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.50216 q^{2} +3.04067 q^{3} +0.256481 q^{4} +3.82405 q^{5} -4.56757 q^{6} +2.61904 q^{8} +6.24568 q^{9} +O(q^{10})$	\(q-1.50216 q^{2} +3.04067 q^{3} +0.256481 q^{4} +3.82405 q^{5} -4.56757 q^{6} +2.61904 q^{8} +6.24568 q^{9} -5.74433 q^{10} -0.542019 q^{11} +0.779873 q^{12} +1.21662 q^{13} +11.6277 q^{15} -4.44718 q^{16} +3.66299 q^{17} -9.38200 q^{18} -5.00432 q^{19} +0.980794 q^{20} +0.814198 q^{22} -1.00000 q^{23} +7.96365 q^{24} +9.62336 q^{25} -1.82756 q^{26} +9.86904 q^{27} +3.72840 q^{29} -17.4666 q^{30} -9.04067 q^{31} +1.44228 q^{32} -1.64810 q^{33} -5.50239 q^{34} +1.60189 q^{36} -9.08566 q^{37} +7.51728 q^{38} +3.69934 q^{39} +10.0154 q^{40} +4.86472 q^{41} +3.64810 q^{43} -0.139017 q^{44} +23.8838 q^{45} +1.50216 q^{46} -10.6393 q^{47} -13.5224 q^{48} -14.4558 q^{50} +11.1379 q^{51} +0.312039 q^{52} +7.48704 q^{53} -14.8249 q^{54} -2.07271 q^{55} -15.2165 q^{57} -5.60065 q^{58} -5.18027 q^{59} +2.98227 q^{60} -3.26161 q^{61} +13.5805 q^{62} +6.72782 q^{64} +4.65242 q^{65} +2.47571 q^{66} -12.0377 q^{67} +0.939485 q^{68} -3.04067 q^{69} -5.29796 q^{71} +16.3577 q^{72} -8.19070 q^{73} +13.6481 q^{74} +29.2615 q^{75} -1.28351 q^{76} -5.55700 q^{78} +10.0291 q^{79} -17.0062 q^{80} +11.2715 q^{81} -7.30758 q^{82} -7.64810 q^{83} +14.0075 q^{85} -5.48003 q^{86} +11.3368 q^{87} -1.41957 q^{88} +4.74703 q^{89} -35.8772 q^{90} -0.256481 q^{92} -27.4897 q^{93} +15.9819 q^{94} -19.1368 q^{95} +4.38551 q^{96} +10.9894 q^{97} -3.38527 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} + 12 q^{4} + 4 q^{5} + 3 q^{6} + 3 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 + 12 * q^4 + 4 * q^5 + 3 * q^6 + 3 * q^8 + 11 * q^9	$ 5 q + 2 q^{2} + 12 q^{4} + 4 q^{5} + 3 q^{6} + 3 q^{8} + 11 q^{9} + 8 q^{10} - 4 q^{11} - 3 q^{12} + 6 q^{13} + 10 q^{15} + 10 q^{16} + 12 q^{17} - 19 q^{18} - 6 q^{19} + 14 q^{22} - 5 q^{23} + 36 q^{24} + 19 q^{25} - q^{26} - 4 q^{29} - 48 q^{30} - 30 q^{31} + 8 q^{32} + 22 q^{33} - 6 q^{34} - q^{36} + 4 q^{37} + 40 q^{38} + 16 q^{39} + 50 q^{40} - 6 q^{41} - 12 q^{43} - 26 q^{44} + 12 q^{45} - 2 q^{46} - 10 q^{47} - 25 q^{48} - 2 q^{50} - 4 q^{51} + 21 q^{52} + 16 q^{53} - 33 q^{54} - 18 q^{55} + 6 q^{57} + 13 q^{58} - 22 q^{59} + 30 q^{60} + 18 q^{61} - 15 q^{62} + 25 q^{64} - 26 q^{65} - 4 q^{66} - 2 q^{67} - 12 q^{68} + 4 q^{71} - 41 q^{72} + 2 q^{73} + 38 q^{74} + 30 q^{75} - 10 q^{76} + 41 q^{78} + 30 q^{79} + 10 q^{80} - 3 q^{81} + 7 q^{82} - 8 q^{83} - 12 q^{85} + 8 q^{86} + 12 q^{87} + 4 q^{88} + 20 q^{89} - 34 q^{90} - 12 q^{92} - 26 q^{93} + 25 q^{94} + 8 q^{95} + q^{96} + 12 q^{97} - 8 q^{99}+O(q^{100}) $ 5 * q + 2 * q^2 + 12 * q^4 + 4 * q^5 + 3 * q^6 + 3 * q^8 + 11 * q^9 + 8 * q^10 - 4 * q^11 - 3 * q^12 + 6 * q^13 + 10 * q^15 + 10 * q^16 + 12 * q^17 - 19 * q^18 - 6 * q^19 + 14 * q^22 - 5 * q^23 + 36 * q^24 + 19 * q^25 - q^26 - 4 * q^29 - 48 * q^30 - 30 * q^31 + 8 * q^32 + 22 * q^33 - 6 * q^34 - q^36 + 4 * q^37 + 40 * q^38 + 16 * q^39 + 50 * q^40 - 6 * q^41 - 12 * q^43 - 26 * q^44 + 12 * q^45 - 2 * q^46 - 10 * q^47 - 25 * q^48 - 2 * q^50 - 4 * q^51 + 21 * q^52 + 16 * q^53 - 33 * q^54 - 18 * q^55 + 6 * q^57 + 13 * q^58 - 22 * q^59 + 30 * q^60 + 18 * q^61 - 15 * q^62 + 25 * q^64 - 26 * q^65 - 4 * q^66 - 2 * q^67 - 12 * q^68 + 4 * q^71 - 41 * q^72 + 2 * q^73 + 38 * q^74 + 30 * q^75 - 10 * q^76 + 41 * q^78 + 30 * q^79 + 10 * q^80 - 3 * q^81 + 7 * q^82 - 8 * q^83 - 12 * q^85 + 8 * q^86 + 12 * q^87 + 4 * q^88 + 20 * q^89 - 34 * q^90 - 12 * q^92 - 26 * q^93 + 25 * q^94 + 8 * q^95 + q^96 + 12 * q^97 - 8 * 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 $

$2$	−1.50216	−1.06219	−0.531093	−	0.847313i	$-0.678219\pi$
$2$	−1.50216	−1.06219	−0.531093	+	0.847313i	$0.678219\pi$
$3$	3.04067	1.75553	0.877766	−	0.479090i	$-0.159033\pi$
$3$	3.04067	1.75553	0.877766	+	0.479090i	$0.159033\pi$
$4$	0.256481	0.128240
$5$	3.82405	1.71017	0.855084	−	0.518490i	$-0.173506\pi$
$5$	3.82405	1.71017	0.855084	+	0.518490i	$0.173506\pi$
$6$	−4.56757	−1.86470
$7$	0	0
$7$	0	0
$8$	2.61904	0.925971
$9$	6.24568	2.08189
$10$	−5.74433	−1.81652
$11$	−0.542019	−0.163425	−0.0817124	−	0.996656i	$-0.526039\pi$
$11$	−0.542019	−0.163425	−0.0817124	+	0.996656i	$0.526039\pi$
$12$	0.779873	0.225130
$13$	1.21662	0.337430	0.168715	−	0.985665i	$-0.446038\pi$
$13$	1.21662	0.337430	0.168715	+	0.985665i	$0.446038\pi$
$14$	0	0
$15$	11.6277	3.00225
$16$	−4.44718	−1.11179
$17$	3.66299	0.888405	0.444203	−	0.895926i	$-0.353487\pi$
$17$	3.66299	0.888405	0.444203	+	0.895926i	$0.353487\pi$
$18$	−9.38200	−2.21136
$19$	−5.00432	−1.14807	−0.574035	−	0.818831i	$-0.694622\pi$
$19$	−5.00432	−1.14807	−0.574035	+	0.818831i	$0.694622\pi$
$20$	0.980794	0.219312
$21$	0	0
$22$	0.814198	0.173588
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	7.96365	1.62557
$25$	9.62336	1.92467
$26$	−1.82756	−0.358413
$27$	9.86904	1.89930
$28$	0	0
$29$	3.72840	0.692346	0.346173	−	0.938171i	$-0.387481\pi$
$29$	3.72840	0.692346	0.346173	+	0.938171i	$0.387481\pi$
$30$	−17.4666	−3.18895
$31$	−9.04067	−1.62375	−0.811876	−	0.583830i	$-0.801554\pi$
$31$	−9.04067	−1.62375	−0.811876	+	0.583830i	$0.801554\pi$
$32$	1.44228	0.254962
$33$	−1.64810	−0.286897
$34$	−5.50239	−0.943652
$35$	0	0
$36$	1.60189	0.266982
$37$	−9.08566	−1.49367	−0.746837	−	0.665008i	$-0.768428\pi$
$37$	−9.08566	−1.49367	−0.746837	+	0.665008i	$0.768428\pi$
$38$	7.51728	1.21946
$39$	3.69934	0.592369
$40$	10.0154	1.58357
$41$	4.86472	0.759742	0.379871	−	0.925040i	$-0.375968\pi$
$41$	4.86472	0.759742	0.379871	+	0.925040i	$0.375968\pi$
$42$	0	0
$43$	3.64810	0.556330	0.278165	−	0.960533i	$-0.410274\pi$
$43$	3.64810	0.556330	0.278165	+	0.960533i	$0.410274\pi$
$44$	−0.139017	−0.0209576
$45$	23.8838	3.56038
$46$	1.50216	0.221481
$47$	−10.6393	−1.55190	−0.775950	−	0.630794i	$-0.782729\pi$
$47$	−10.6393	−1.55190	−0.775950	+	0.630794i	$0.782729\pi$
$48$	−13.5224	−1.95179
$49$	0	0
$50$	−14.4558	−2.04436
$51$	11.1379	1.55962
$52$	0.312039	0.0432721
$53$	7.48704	1.02842	0.514212	−	0.857663i	$-0.328084\pi$
$53$	7.48704	1.02842	0.514212	+	0.857663i	$0.328084\pi$
$54$	−14.8249	−2.01741
$55$	−2.07271	−0.279484
$56$	0	0
$57$	−15.2165	−2.01547
$58$	−5.60065	−0.735401
$59$	−5.18027	−0.674413	−0.337207	−	0.941431i	$-0.609482\pi$
$59$	−5.18027	−0.674413	−0.337207	+	0.941431i	$0.609482\pi$
$60$	2.98227	0.385010
$61$	−3.26161	−0.417606	−0.208803	−	0.977958i	$-0.566957\pi$
$61$	−3.26161	−0.417606	−0.208803	+	0.977958i	$0.566957\pi$
$62$	13.5805	1.72473
$63$	0	0
$64$	6.72782	0.840978
$65$	4.65242	0.577061
$66$	2.47571	0.304739
$67$	−12.0377	−1.47064	−0.735319	−	0.677721i	$-0.762968\pi$
$67$	−12.0377	−1.47064	−0.735319	+	0.677721i	$0.762968\pi$
$68$	0.939485	0.113929
$69$	−3.04067	−0.366054
$70$	0	0
$71$	−5.29796	−0.628752	−0.314376	−	0.949298i	$-0.601795\pi$
$71$	−5.29796	−0.628752	−0.314376	+	0.949298i	$0.601795\pi$
$72$	16.3577	1.92777
$73$	−8.19070	−0.958649	−0.479324	−	0.877638i	$-0.659118\pi$
$73$	−8.19070	−0.958649	−0.479324	+	0.877638i	$0.659118\pi$
$74$	13.6481	1.58656
$75$	29.2615	3.37882
$76$	−1.28351	−0.147229
$77$	0	0
$78$	−5.55700	−0.629206
$79$	10.0291	1.12836	0.564179	−	0.825653i	$-0.309193\pi$
$79$	10.0291	1.12836	0.564179	+	0.825653i	$0.309193\pi$
$80$	−17.0062	−1.90135
$81$	11.2715	1.25238
$82$	−7.30758	−0.806987
$83$	−7.64810	−0.839488	−0.419744	−	0.907643i	$-0.637880\pi$
$83$	−7.64810	−0.839488	−0.419744	+	0.907643i	$0.637880\pi$
$84$	0	0
$85$	14.0075	1.51932
$86$	−5.48003	−0.590926
$87$	11.3368	1.21544
$88$	−1.41957	−0.151327
$89$	4.74703	0.503184	0.251592	−	0.967833i	$-0.419046\pi$
$89$	4.74703	0.503184	0.251592	+	0.967833i	$0.419046\pi$
$90$	−35.8772	−3.78179
$91$	0	0
$92$	−0.256481	−0.0267399
$93$	−27.4897	−2.85055
$94$	15.9819	1.64841
$95$	−19.1368	−1.96339
$96$	4.38551	0.447594
$97$	10.9894	1.11581	0.557904	−	0.829906i	$-0.311606\pi$
$97$	10.9894	1.11581	0.557904	+	0.829906i	$0.311606\pi$
$98$	0	0
$99$	−3.38527	−0.340233
$100$	2.46820	0.246820
$101$	−3.59862	−0.358076	−0.179038	−	0.983842i	$-0.557299\pi$
$101$	−3.59862	−0.358076	−0.179038	+	0.983842i	$0.557299\pi$
$102$	−16.7310	−1.65661
$103$	−9.48704	−0.934786	−0.467393	−	0.884050i	$-0.654807\pi$
$103$	−9.48704	−0.934786	−0.467393	+	0.884050i	$0.654807\pi$
$104$	3.18638	0.312450
$105$	0	0
$106$	−11.2467	−1.09238
$107$	6.60294	0.638330	0.319165	−	0.947699i	$-0.396598\pi$
$107$	6.60294	0.638330	0.319165	+	0.947699i	$0.396598\pi$
$108$	2.53122	0.243566
$109$	1.10726	0.106057	0.0530283	−	0.998593i	$-0.483113\pi$
$109$	1.10726	0.106057	0.0530283	+	0.998593i	$0.483113\pi$
$110$	3.11353	0.296864
$111$	−27.6265	−2.62219
$112$	0	0
$113$	0.433241	0.0407559	0.0203779	−	0.999792i	$-0.493513\pi$
$113$	0.433241	0.0407559	0.0203779	+	0.999792i	$0.493513\pi$
$114$	22.8576	2.14081
$115$	−3.82405	−0.356595
$116$	0.956262	0.0887867
$117$	7.59862	0.702493
$118$	7.78158	0.716353
$119$	0	0
$120$	30.4534	2.78000
$121$	−10.7062	−0.973292
$122$	4.89945	0.443576
$123$	14.7920	1.33375
$124$	−2.31876	−0.208230
$125$	17.6800	1.58134
$126$	0	0
$127$	8.84149	0.784556	0.392278	−	0.919847i	$-0.371687\pi$
$127$	8.84149	0.784556	0.392278	+	0.919847i	$0.371687\pi$
$128$	−12.9908	−1.14824
$129$	11.0927	0.976655
$130$	−6.98867	−0.612947
$131$	2.54931	0.222735	0.111367	−	0.993779i	$-0.464477\pi$
$131$	2.54931	0.222735	0.111367	+	0.993779i	$0.464477\pi$
$132$	−0.422706	−0.0367918
$133$	0	0
$134$	18.0825	1.56209
$135$	37.7397	3.24812
$136$	9.59352	0.822638
$137$	13.6265	1.16419	0.582095	−	0.813121i	$-0.302233\pi$
$137$	13.6265	1.16419	0.582095	+	0.813121i	$0.302233\pi$
$138$	4.56757	0.388817
$139$	18.0466	1.53069	0.765347	−	0.643618i	$-0.222568\pi$
$139$	18.0466	1.53069	0.765347	+	0.643618i	$0.222568\pi$
$140$	0	0
$141$	−32.3506	−2.72441
$142$	7.95838	0.667852
$143$	−0.659431	−0.0551444
$144$	−27.7756	−2.31464
$145$	14.2576	1.18403
$146$	12.3037	1.01826
$147$	0	0
$148$	−2.33029	−0.191549
$149$	13.8178	1.13200	0.565999	−	0.824406i	$-0.308491\pi$
$149$	13.8178	1.13200	0.565999	+	0.824406i	$0.308491\pi$
$150$	−43.9554	−3.58894
$151$	16.1412	1.31355	0.656777	−	0.754085i	$-0.271919\pi$
$151$	16.1412	1.31355	0.656777	+	0.754085i	$0.271919\pi$
$152$	−13.1065	−1.06308
$153$	22.8778	1.84956
$154$	0	0
$155$	−34.5720	−2.77689
$156$	0.948809	0.0759655
$157$	15.3111	1.22196	0.610979	−	0.791647i	$-0.290776\pi$
$157$	15.3111	1.22196	0.610979	+	0.791647i	$0.290776\pi$
$158$	−15.0652	−1.19853
$159$	22.7656	1.80543
$160$	5.51536	0.436028
$161$	0	0
$162$	−16.9315	−1.33027
$163$	−3.94876	−0.309291	−0.154645	−	0.987970i	$-0.549423\pi$
$163$	−3.94876	−0.309291	−0.154645	+	0.987970i	$0.549423\pi$
$164$	1.24771	0.0974295
$165$	−6.30242	−0.490643
$166$	11.4887	0.891693
$167$	−1.87752	−0.145287	−0.0726433	−	0.997358i	$-0.523143\pi$
$167$	−1.87752	−0.145287	−0.0726433	+	0.997358i	$0.523143\pi$
$168$	0	0
$169$	−11.5198	−0.886141
$170$	−21.0414	−1.61380
$171$	−31.2554	−2.39016
$172$	0.935667	0.0713439
$173$	−10.9246	−0.830582	−0.415291	−	0.909689i	$-0.636320\pi$
$173$	−10.9246	−0.830582	−0.415291	+	0.909689i	$0.636320\pi$
$174$	−17.0297	−1.29102
$175$	0	0
$176$	2.41045	0.181695
$177$	−15.7515	−1.18395
$178$	−7.13079	−0.534475
$179$	4.74253	0.354474	0.177237	−	0.984168i	$-0.443284\pi$
$179$	4.74253	0.354474	0.177237	+	0.984168i	$0.443284\pi$
$180$	6.12573	0.456585
$181$	−2.82837	−0.210231	−0.105115	−	0.994460i	$-0.533521\pi$
$181$	−2.82837	−0.210231	−0.105115	+	0.994460i	$0.533521\pi$
$182$	0	0
$183$	−9.91748	−0.733121
$184$	−2.61904	−0.193078
$185$	−34.7440	−2.55443
$186$	41.2939	3.02782
$187$	−1.98541	−0.145187
$188$	−2.72877	−0.199016
$189$	0	0
$190$	28.7464	2.08549
$191$	−3.56838	−0.258199	−0.129099	−	0.991632i	$-0.541209\pi$
$191$	−3.56838	−0.258199	−0.129099	+	0.991632i	$0.541209\pi$
$192$	20.4571	1.47636
$193$	20.9158	1.50555	0.752777	−	0.658276i	$-0.228714\pi$
$193$	20.9158	1.50555	0.752777	+	0.658276i	$0.228714\pi$
$194$	−16.5079	−1.18520
$195$	14.1465	1.01305
$196$	0	0
$197$	5.54576	0.395119	0.197559	−	0.980291i	$-0.436698\pi$
$197$	5.54576	0.395119	0.197559	+	0.980291i	$0.436698\pi$
$198$	5.08522	0.361391
$199$	7.73808	0.548538	0.274269	−	0.961653i	$-0.411564\pi$
$199$	7.73808	0.548538	0.274269	+	0.961653i	$0.411564\pi$
$200$	25.2040	1.78219
$201$	−36.6027	−2.58175
$202$	5.40570	0.380344
$203$	0	0
$204$	2.85667	0.200007
$205$	18.6029	1.29929
$206$	14.2510	0.992917
$207$	−6.24568	−0.434105
$208$	−5.41053	−0.375153
$209$	2.71243	0.187623
$210$	0	0
$211$	9.43918	0.649820	0.324910	−	0.945745i	$-0.394666\pi$
$211$	9.43918	0.649820	0.324910	+	0.945745i	$0.394666\pi$
$212$	1.92028	0.131885
$213$	−16.1094	−1.10379
$214$	−9.91866	−0.678026
$215$	13.9505	0.951418
$216$	25.8474	1.75870
$217$	0	0
$218$	−1.66329	−0.112652
$219$	−24.9052	−1.68294
$220$	−0.531609	−0.0358411
$221$	4.45647	0.299774
$222$	41.4994	2.78526
$223$	−11.1010	−0.743379	−0.371689	−	0.928357i	$-0.621221\pi$
$223$	−11.1010	−0.743379	−0.371689	+	0.928357i	$0.621221\pi$
$224$	0	0
$225$	60.1044	4.00696
$226$	−0.650797	−0.0432903
$227$	−20.9827	−1.39267	−0.696336	−	0.717716i	$-0.745188\pi$
$227$	−20.9827	−1.39267	−0.696336	+	0.717716i	$0.745188\pi$
$228$	−3.90273	−0.258465
$229$	−4.63545	−0.306319	−0.153159	−	0.988201i	$-0.548945\pi$
$229$	−4.63545	−0.306319	−0.153159	+	0.988201i	$0.548945\pi$
$230$	5.74433	0.378770
$231$	0	0
$232$	9.76484	0.641093
$233$	16.1703	1.05935	0.529675	−	0.848201i	$-0.322314\pi$
$233$	16.1703	1.05935	0.529675	+	0.848201i	$0.322314\pi$
$234$	−11.4143	−0.746178
$235$	−40.6852	−2.65401
$236$	−1.32864	−0.0864869
$237$	30.4951	1.98087
$238$	0	0
$239$	1.26610	0.0818973	0.0409486	−	0.999161i	$-0.486962\pi$
$239$	1.26610	0.0818973	0.0409486	+	0.999161i	$0.486962\pi$
$240$	−51.7104	−3.33789
$241$	2.09623	0.135030	0.0675150	−	0.997718i	$-0.478493\pi$
$241$	2.09623	0.135030	0.0675150	+	0.997718i	$0.478493\pi$
$242$	16.0824	1.03382
$243$	4.66568	0.299304
$244$	−0.836539	−0.0535539
$245$	0	0
$246$	−22.2200	−1.41669
$247$	−6.08835	−0.387393
$248$	−23.6779	−1.50355
$249$	−23.2554	−1.47375
$250$	−26.5581	−1.67968
$251$	−11.5365	−0.728179	−0.364089	−	0.931364i	$-0.618620\pi$
$251$	−11.5365	−0.728179	−0.364089	+	0.931364i	$0.618620\pi$
$252$	0	0
$253$	0.542019	0.0340764
$254$	−13.2813	−0.833345
$255$	42.5921	2.66722
$256$	6.05863	0.378664
$257$	−14.6546	−0.914131	−0.457066	−	0.889433i	$-0.651100\pi$
$257$	−14.6546	−0.914131	−0.457066	+	0.889433i	$0.651100\pi$
$258$	−16.6630	−1.03739
$259$	0	0
$260$	1.19325	0.0740025
$261$	23.2864	1.44139
$262$	−3.82947	−0.236586
$263$	−22.7133	−1.40056	−0.700282	−	0.713866i	$-0.746942\pi$
$263$	−22.7133	−1.40056	−0.700282	+	0.713866i	$0.746942\pi$
$264$	−4.31645	−0.265659
$265$	28.6308	1.75878
$266$	0	0
$267$	14.4341	0.883355
$268$	−3.08743	−0.188595
$269$	−25.0855	−1.52949	−0.764746	−	0.644332i	$-0.777135\pi$
$269$	−25.0855	−1.52949	−0.764746	+	0.644332i	$0.777135\pi$
$270$	−56.6910	−3.45011
$271$	28.0232	1.70229	0.851145	−	0.524930i	$-0.175909\pi$
$271$	28.0232	1.70229	0.851145	+	0.524930i	$0.175909\pi$
$272$	−16.2900	−0.987724
$273$	0	0
$274$	−20.4692	−1.23659
$275$	−5.21604	−0.314539
$276$	−0.779873	−0.0469428
$277$	−16.2692	−0.977524	−0.488762	−	0.872417i	$-0.662551\pi$
$277$	−16.2692	−0.977524	−0.488762	+	0.872417i	$0.662551\pi$
$278$	−27.1089	−1.62588
$279$	−56.4651	−3.38048
$280$	0	0
$281$	−13.4694	−0.803518	−0.401759	−	0.915745i	$-0.631601\pi$
$281$	−13.4694	−0.803518	−0.401759	+	0.915745i	$0.631601\pi$
$282$	48.5957	2.89383
$283$	−18.0516	−1.07305	−0.536527	−	0.843883i	$-0.680264\pi$
$283$	−18.0516	−1.07305	−0.536527	+	0.843883i	$0.680264\pi$
$284$	−1.35882	−0.0806314
$285$	−58.1886	−3.44679
$286$	0.990570	0.0585736
$287$	0	0
$288$	9.00803	0.530803
$289$	−3.58251	−0.210736
$290$	−21.4172	−1.25766
$291$	33.4152	1.95884
$292$	−2.10075	−0.122937
$293$	−23.1521	−1.35256	−0.676280	−	0.736644i	$-0.736409\pi$
$293$	−23.1521	−1.35256	−0.676280	+	0.736644i	$0.736409\pi$
$294$	0	0
$295$	−19.8096	−1.15336
$296$	−23.7957	−1.38310
$297$	−5.34920	−0.310392
$298$	−20.7565	−1.20239
$299$	−1.21662	−0.0703590
$300$	7.50500	0.433301
$301$	0	0
$302$	−24.2467	−1.39524
$303$	−10.9422	−0.628614
$304$	22.2551	1.27642
$305$	−12.4726	−0.714176
$306$	−34.3662	−1.96458
$307$	1.14301	0.0652353	0.0326176	−	0.999468i	$-0.489616\pi$
$307$	1.14301	0.0652353	0.0326176	+	0.999468i	$0.489616\pi$
$308$	0	0
$309$	−28.8470	−1.64105
$310$	51.9326	2.94957
$311$	19.3196	1.09551	0.547757	−	0.836638i	$-0.315482\pi$
$311$	19.3196	1.09551	0.547757	+	0.836638i	$0.315482\pi$
$312$	9.68874	0.548517
$313$	17.4140	0.984299	0.492150	−	0.870511i	$-0.336211\pi$
$313$	17.4140	0.984299	0.492150	+	0.870511i	$0.336211\pi$
$314$	−22.9997	−1.29795
$315$	0	0
$316$	2.57226	0.144701
$317$	1.42612	0.0800989	0.0400495	−	0.999198i	$-0.487248\pi$
$317$	1.42612	0.0800989	0.0400495	+	0.999198i	$0.487248\pi$
$318$	−34.1976	−1.91770
$319$	−2.02086	−0.113147
$320$	25.7275	1.43821
$321$	20.0774	1.12061
$322$	0	0
$323$	−18.3308	−1.01995
$324$	2.89091	0.160606
$325$	11.7080	0.649442
$326$	5.93166	0.328524
$327$	3.36682	0.186186
$328$	12.7409	0.703499
$329$	0	0
$330$	9.46723	0.521154
$331$	3.91690	0.215292	0.107646	−	0.994189i	$-0.465669\pi$
$331$	3.91690	0.215292	0.107646	+	0.994189i	$0.465669\pi$
$332$	−1.96159	−0.107656
$333$	−56.7461	−3.10967
$334$	2.82033	0.154321
$335$	−46.0327	−2.51504
$336$	0	0
$337$	7.73646	0.421432	0.210716	−	0.977547i	$-0.432421\pi$
$337$	7.73646	0.421432	0.210716	+	0.977547i	$0.432421\pi$
$338$	17.3046	0.941247
$339$	1.31734	0.0715482
$340$	3.59264	0.194838
$341$	4.90021	0.265361
$342$	46.9505	2.53879
$343$	0	0
$344$	9.55453	0.515146
$345$	−11.6277	−0.626013
$346$	16.4105	0.882233
$347$	−32.0316	−1.71955	−0.859773	−	0.510677i	$-0.829395\pi$
$347$	−32.0316	−1.71955	−0.859773	+	0.510677i	$0.829395\pi$
$348$	2.90768	0.155868
$349$	−29.0447	−1.55473	−0.777363	−	0.629052i	$-0.783443\pi$
$349$	−29.0447	−1.55473	−0.777363	+	0.629052i	$0.783443\pi$
$350$	0	0
$351$	12.0069	0.640880
$352$	−0.781744	−0.0416671
$353$	−14.1412	−0.752661	−0.376331	−	0.926485i	$-0.622814\pi$
$353$	−14.1412	−0.752661	−0.376331	+	0.926485i	$0.622814\pi$
$354$	23.6612	1.25758
$355$	−20.2597	−1.07527
$356$	1.21752	0.0645284
$357$	0	0
$358$	−7.12404	−0.376517
$359$	7.25851	0.383089	0.191545	−	0.981484i	$-0.438650\pi$
$359$	7.25851	0.383089	0.191545	+	0.981484i	$0.438650\pi$
$360$	62.5527	3.29681
$361$	6.04319	0.318063
$362$	4.24866	0.223304
$363$	−32.5541	−1.70865
$364$	0	0
$365$	−31.3216	−1.63945
$366$	14.8976	0.778711
$367$	15.7667	0.823015	0.411507	−	0.911406i	$-0.365002\pi$
$367$	15.7667	0.823015	0.411507	+	0.911406i	$0.365002\pi$
$368$	4.44718	0.231825
$369$	30.3835	1.58170
$370$	52.1910	2.71328
$371$	0	0
$372$	−7.05057	−0.365555
$373$	4.16807	0.215815	0.107907	−	0.994161i	$-0.465585\pi$
$373$	4.16807	0.215815	0.107907	+	0.994161i	$0.465585\pi$
$374$	2.98240	0.154216
$375$	53.7589	2.77610
$376$	−27.8648	−1.43702
$377$	4.53605	0.233618
$378$	0	0
$379$	18.6572	0.958356	0.479178	−	0.877718i	$-0.340935\pi$
$379$	18.6572	0.958356	0.479178	+	0.877718i	$0.340935\pi$
$380$	−4.90821	−0.251786
$381$	26.8841	1.37731
$382$	5.36027	0.274255
$383$	30.2829	1.54738	0.773692	−	0.633562i	$-0.218408\pi$
$383$	30.2829	1.54738	0.773692	+	0.633562i	$0.218408\pi$
$384$	−39.5008	−2.01577
$385$	0	0
$386$	−31.4189	−1.59918
$387$	22.7849	1.15822
$388$	2.81857	0.143091
$389$	−14.0727	−0.713515	−0.356757	−	0.934197i	$-0.616118\pi$
$389$	−14.0727	−0.713515	−0.356757	+	0.934197i	$0.616118\pi$
$390$	−21.2502	−1.07605
$391$	−3.66299	−0.185245
$392$	0	0
$393$	7.75163	0.391018
$394$	−8.33061	−0.419690
$395$	38.3516	1.92968
$396$	−0.868257	−0.0436316
$397$	−30.2423	−1.51782	−0.758908	−	0.651198i	$-0.774267\pi$
$397$	−30.2423	−1.51782	−0.758908	+	0.651198i	$0.774267\pi$
$398$	−11.6238	−0.582649
$399$	0	0
$400$	−42.7968	−2.13984
$401$	−0.668630	−0.0333898	−0.0166949	−	0.999861i	$-0.505314\pi$
$401$	−0.668630	−0.0333898	−0.0166949	+	0.999861i	$0.505314\pi$
$402$	54.9830	2.74230
$403$	−10.9991	−0.547902
$404$	−0.922976	−0.0459198
$405$	43.1026	2.14179
$406$	0	0
$407$	4.92460	0.244103
$408$	29.1707	1.44417
$409$	9.05602	0.447791	0.223896	−	0.974613i	$-0.428122\pi$
$409$	9.05602	0.447791	0.223896	+	0.974613i	$0.428122\pi$
$410$	−27.9446	−1.38008
$411$	41.4337	2.04377
$412$	−2.43324	−0.119877
$413$	0	0
$414$	9.38200	0.461100
$415$	−29.2467	−1.43567
$416$	1.75471	0.0860318
$417$	54.8738	2.68718
$418$	−4.07451	−0.199291
$419$	19.9592	0.975068	0.487534	−	0.873104i	$-0.337896\pi$
$419$	19.9592	0.975068	0.487534	+	0.873104i	$0.337896\pi$
$420$	0	0
$421$	−6.86296	−0.334480	−0.167240	−	0.985916i	$-0.553486\pi$
$421$	−6.86296	−0.334480	−0.167240	+	0.985916i	$0.553486\pi$
$422$	−14.1791	−0.690230
$423$	−66.4496	−3.23089
$424$	19.6089	0.952291
$425$	35.2503	1.70989
$426$	24.1988	1.17244
$427$	0	0
$428$	1.69352	0.0818596
$429$	−2.00511	−0.0968078
$430$	−20.9559	−1.01058
$431$	4.52160	0.217798	0.108899	−	0.994053i	$-0.465268\pi$
$431$	4.52160	0.217798	0.108899	+	0.994053i	$0.465268\pi$
$432$	−43.8894	−2.11163
$433$	−14.5170	−0.697641	−0.348820	−	0.937190i	$-0.613418\pi$
$433$	−14.5170	−0.697641	−0.348820	+	0.937190i	$0.613418\pi$
$434$	0	0
$435$	43.3526	2.07860
$436$	0.283992	0.0136007
$437$	5.00432	0.239389
$438$	37.4116	1.78759
$439$	−25.5058	−1.21732	−0.608662	−	0.793430i	$-0.708293\pi$
$439$	−25.5058	−1.21732	−0.608662	+	0.793430i	$0.708293\pi$
$440$	−5.42851	−0.258794
$441$	0	0
$442$	−6.69432	−0.318416
$443$	13.9434	0.662469	0.331235	−	0.943548i	$-0.392535\pi$
$443$	13.9434	0.662469	0.331235	+	0.943548i	$0.392535\pi$
$444$	−7.08566	−0.336270
$445$	18.1529	0.860528
$446$	16.6755	0.789607
$447$	42.0154	1.98726
$448$	0	0
$449$	−22.5307	−1.06329	−0.531644	−	0.846968i	$-0.678426\pi$
$449$	−22.5307	−1.06329	−0.531644	+	0.846968i	$0.678426\pi$
$450$	−90.2864	−4.25614
$451$	−2.63677	−0.124161
$452$	0.111118	0.00522654
$453$	49.0801	2.30599
$454$	31.5194	1.47928
$455$	0	0
$456$	−39.8526	−1.86627
$457$	−12.9589	−0.606191	−0.303096	−	0.952960i	$-0.598020\pi$
$457$	−12.9589	−0.606191	−0.303096	+	0.952960i	$0.598020\pi$
$458$	6.96317	0.325368
$459$	36.1502	1.68735
$460$	−0.980794	−0.0457298
$461$	−14.9315	−0.695428	−0.347714	−	0.937601i	$-0.613042\pi$
$461$	−14.9315	−0.695428	−0.347714	+	0.937601i	$0.613042\pi$
$462$	0	0
$463$	17.4941	0.813018	0.406509	−	0.913647i	$-0.366746\pi$
$463$	17.4941	0.813018	0.406509	+	0.913647i	$0.366746\pi$
$464$	−16.5809	−0.769747
$465$	−105.122	−4.87492
$466$	−24.2903	−1.12523
$467$	17.6281	0.815732	0.407866	−	0.913042i	$-0.366273\pi$
$467$	17.6281	0.815732	0.407866	+	0.913042i	$0.366273\pi$
$468$	1.94890	0.0900878
$469$	0	0
$470$	61.1156	2.81905
$471$	46.5560	2.14519
$472$	−13.5673	−0.624487
$473$	−1.97734	−0.0909181
$474$	−45.8084	−2.10405
$475$	−48.1583	−2.20966
$476$	0	0
$477$	46.7616	2.14107
$478$	−1.90188	−0.0869902
$479$	11.7457	0.536673	0.268336	−	0.963325i	$-0.413526\pi$
$479$	11.7457	0.536673	0.268336	+	0.963325i	$0.413526\pi$
$480$	16.7704	0.765460
$481$	−11.0538	−0.504010
$482$	−3.14887	−0.143427
$483$	0	0
$484$	−2.74594	−0.124815
$485$	42.0241	1.90822
$486$	−7.00860	−0.317916
$487$	22.9380	1.03942	0.519710	−	0.854342i	$-0.326040\pi$
$487$	22.9380	1.03942	0.519710	+	0.854342i	$0.326040\pi$
$488$	−8.54229	−0.386691
$489$	−12.0069	−0.542970
$490$	0	0
$491$	11.5682	0.522067	0.261034	−	0.965330i	$-0.415937\pi$
$491$	11.5682	0.522067	0.261034	+	0.965330i	$0.415937\pi$
$492$	3.79386	0.171041
$493$	13.6571	0.615084
$494$	9.14567	0.411483
$495$	−12.9455	−0.581855
$496$	40.2055	1.80528
$497$	0	0
$498$	34.9332	1.56540
$499$	25.0063	1.11943	0.559717	−	0.828684i	$-0.310910\pi$
$499$	25.0063	1.11943	0.559717	+	0.828684i	$0.310910\pi$
$500$	4.53457	0.202792
$501$	−5.70891	−0.255055
$502$	17.3297	0.773462
$503$	−16.1238	−0.718925	−0.359463	−	0.933160i	$-0.617040\pi$
$503$	−16.1238	−0.718925	−0.359463	+	0.933160i	$0.617040\pi$
$504$	0	0
$505$	−13.7613	−0.612370
$506$	−0.814198	−0.0361955
$507$	−35.0280	−1.55565
$508$	2.26767	0.100612
$509$	1.46604	0.0649809	0.0324905	−	0.999472i	$-0.489656\pi$
$509$	1.46604	0.0649809	0.0324905	+	0.999472i	$0.489656\pi$
$510$	−63.9800	−2.83308
$511$	0	0
$512$	16.8806	0.746025
$513$	−49.3878	−2.18052
$514$	22.0136	0.970978
$515$	−36.2789	−1.59864
$516$	2.84505	0.125247
$517$	5.76669	0.253619
$518$	0	0
$519$	−33.2181	−1.45811
$520$	12.1849	0.534342
$521$	31.1921	1.36655	0.683276	−	0.730160i	$-0.260554\pi$
$521$	31.1921	1.36655	0.683276	+	0.730160i	$0.260554\pi$
$522$	−34.9798	−1.53103
$523$	25.0064	1.09345	0.546727	−	0.837311i	$-0.315874\pi$
$523$	25.0064	1.09345	0.546727	+	0.837311i	$0.315874\pi$
$524$	0.653850	0.0285636
$525$	0	0
$526$	34.1190	1.48766
$527$	−33.1159	−1.44255
$528$	7.32940	0.318971
$529$	1.00000	0.0434783
$530$	−43.0080	−1.86815
$531$	−32.3543	−1.40406
$532$	0	0
$533$	5.91852	0.256360
$534$	−21.6824	−0.938288
$535$	25.2500	1.09165
$536$	−31.5272	−1.36177
$537$	14.4205	0.622290
$538$	37.6824	1.62460
$539$	0	0
$540$	9.67950	0.416539
$541$	−29.8577	−1.28368	−0.641842	−	0.766837i	$-0.721829\pi$
$541$	−29.8577	−1.28368	−0.641842	+	0.766837i	$0.721829\pi$
$542$	−42.0954	−1.80815
$543$	−8.60013	−0.369067
$544$	5.28306	0.226510
$545$	4.23423	0.181375
$546$	0	0
$547$	29.1669	1.24708	0.623542	−	0.781789i	$-0.285693\pi$
$547$	29.1669	1.24708	0.623542	+	0.781789i	$0.285693\pi$
$548$	3.49493	0.149296
$549$	−20.3710	−0.869411
$550$	7.83532	0.334099
$551$	−18.6581	−0.794862
$552$	−7.96365	−0.338955
$553$	0	0
$554$	24.4390	1.03831
$555$	−105.645	−4.48439
$556$	4.62860	0.196297
$557$	40.2543	1.70563	0.852814	−	0.522214i	$-0.174894\pi$
$557$	40.2543	1.70563	0.852814	+	0.522214i	$0.174894\pi$
$558$	84.8196	3.59070
$559$	4.43835	0.187722
$560$	0	0
$561$	−6.03697	−0.254881
$562$	20.2332	0.853486
$563$	22.5130	0.948808	0.474404	−	0.880307i	$-0.342664\pi$
$563$	22.5130	0.948808	0.474404	+	0.880307i	$0.342664\pi$
$564$	−8.29729	−0.349379
$565$	1.65673	0.0696994
$566$	27.1163	1.13978
$567$	0	0
$568$	−13.8756	−0.582207
$569$	6.81862	0.285852	0.142926	−	0.989733i	$-0.454349\pi$
$569$	6.81862	0.285852	0.142926	+	0.989733i	$0.454349\pi$
$570$	87.4085	3.66114
$571$	−0.873495	−0.0365546	−0.0182773	−	0.999833i	$-0.505818\pi$
$571$	−0.873495	−0.0365546	−0.0182773	+	0.999833i	$0.505818\pi$
$572$	−0.169131	−0.00707173
$573$	−10.8503	−0.453276
$574$	0	0
$575$	−9.62336	−0.401322
$576$	42.0198	1.75083
$577$	16.4150	0.683366	0.341683	−	0.939815i	$-0.389003\pi$
$577$	16.4150	0.683366	0.341683	+	0.939815i	$0.389003\pi$
$578$	5.38150	0.223841
$579$	63.5981	2.64305
$580$	3.65679	0.151840
$581$	0	0
$582$	−50.1950	−2.08065
$583$	−4.05812	−0.168070
$584$	−21.4518	−0.887681
$585$	29.0575	1.20138
$586$	34.7781	1.43667
$587$	9.97331	0.411643	0.205821	−	0.978590i	$-0.434013\pi$
$587$	9.97331	0.411643	0.205821	+	0.978590i	$0.434013\pi$
$588$	0	0
$589$	45.2424	1.86418
$590$	29.7572	1.22508
$591$	16.8628	0.693644
$592$	40.4055	1.66066
$593$	20.5516	0.843951	0.421976	−	0.906607i	$-0.361337\pi$
$593$	20.5516	0.843951	0.421976	+	0.906607i	$0.361337\pi$
$594$	8.03535	0.329694
$595$	0	0
$596$	3.54400	0.145168
$597$	23.5289	0.962975
$598$	1.82756	0.0747344
$599$	15.5468	0.635224	0.317612	−	0.948221i	$-0.397119\pi$
$599$	15.5468	0.635224	0.317612	+	0.948221i	$0.397119\pi$
$600$	76.6370	3.12869
$601$	29.3814	1.19849	0.599246	−	0.800565i	$-0.295467\pi$
$601$	29.3814	1.19849	0.599246	+	0.800565i	$0.295467\pi$
$602$	0	0
$603$	−75.1836	−3.06171
$604$	4.13991	0.168450
$605$	−40.9411	−1.66449
$606$	16.4369	0.667705
$607$	−31.1108	−1.26275	−0.631374	−	0.775478i	$-0.717509\pi$
$607$	−31.1108	−1.26275	−0.631374	+	0.775478i	$0.717509\pi$
$608$	−7.21764	−0.292714
$609$	0	0
$610$	18.7358	0.758589
$611$	−12.9440	−0.523657
$612$	5.86772	0.237189
$613$	−27.7365	−1.12026	−0.560132	−	0.828403i	$-0.689250\pi$
$613$	−27.7365	−1.12026	−0.560132	+	0.828403i	$0.689250\pi$
$614$	−1.71699	−0.0692920
$615$	56.5654	2.28094
$616$	0	0
$617$	−20.6041	−0.829490	−0.414745	−	0.909938i	$-0.636129\pi$
$617$	−20.6041	−0.829490	−0.414745	+	0.909938i	$0.636129\pi$
$618$	43.3327	1.74310
$619$	9.83894	0.395460	0.197730	−	0.980256i	$-0.436643\pi$
$619$	9.83894	0.395460	0.197730	+	0.980256i	$0.436643\pi$
$620$	−8.86704	−0.356109
$621$	−9.86904	−0.396031
$622$	−29.0211	−1.16364
$623$	0	0
$624$	−16.4516	−0.658593
$625$	19.4923	0.779690
$626$	−26.1586	−1.04551
$627$	8.24762	0.329378
$628$	3.92700	0.156704
$629$	−33.2807	−1.32699
$630$	0	0
$631$	2.65314	0.105620	0.0528098	−	0.998605i	$-0.483182\pi$
$631$	2.65314	0.105620	0.0528098	+	0.998605i	$0.483182\pi$
$632$	26.2665	1.04483
$633$	28.7014	1.14078
$634$	−2.14226	−0.0850800
$635$	33.8103	1.34172
$636$	5.83894	0.231529
$637$	0	0
$638$	3.03566	0.120183
$639$	−33.0894	−1.30899
$640$	−49.6775	−1.96368
$641$	−46.9550	−1.85461	−0.927306	−	0.374304i	$-0.877882\pi$
$641$	−46.9550	−1.85461	−0.927306	+	0.374304i	$0.877882\pi$
$642$	−30.1594	−1.19030
$643$	8.01924	0.316248	0.158124	−	0.987419i	$-0.449455\pi$
$643$	8.01924	0.316248	0.158124	+	0.987419i	$0.449455\pi$
$644$	0	0
$645$	42.4189	1.67024
$646$	27.5357	1.08338
$647$	−20.3950	−0.801810	−0.400905	−	0.916120i	$-0.631304\pi$
$647$	−20.3950	−0.801810	−0.400905	+	0.916120i	$0.631304\pi$
$648$	29.5204	1.15967
$649$	2.80780	0.110216
$650$	−17.5872	−0.689828
$651$	0	0
$652$	−1.01278	−0.0396635
$653$	−30.9134	−1.20973	−0.604867	−	0.796326i	$-0.706774\pi$
$653$	−30.9134	−1.20973	−0.604867	+	0.796326i	$0.706774\pi$
$654$	−5.05750	−0.197764
$655$	9.74871	0.380913
$656$	−21.6343	−0.844677
$657$	−51.1565	−1.99580
$658$	0	0
$659$	8.74476	0.340647	0.170324	−	0.985388i	$-0.445519\pi$
$659$	8.74476	0.340647	0.170324	+	0.985388i	$0.445519\pi$
$660$	−1.61645	−0.0629201
$661$	−36.1030	−1.40424	−0.702121	−	0.712057i	$-0.747764\pi$
$661$	−36.1030	−1.40424	−0.702121	+	0.712057i	$0.747764\pi$
$662$	−5.88380	−0.228680
$663$	13.5506	0.526264
$664$	−20.0307	−0.777342
$665$	0	0
$666$	85.2416	3.30305
$667$	−3.72840	−0.144364
$668$	−0.481546	−0.0186316
$669$	−33.7545	−1.30502
$670$	69.1485	2.67144
$671$	1.76785	0.0682472
$672$	0	0
$673$	−37.5762	−1.44845	−0.724227	−	0.689561i	$-0.757803\pi$
$673$	−37.5762	−1.44845	−0.724227	+	0.689561i	$0.757803\pi$
$674$	−11.6214	−0.447639
$675$	94.9733	3.65552
$676$	−2.95461	−0.113639
$677$	21.5389	0.827807	0.413904	−	0.910321i	$-0.364165\pi$
$677$	21.5389	0.827807	0.413904	+	0.910321i	$0.364165\pi$
$678$	−1.97886	−0.0759976
$679$	0	0
$680$	36.6861	1.40685
$681$	−63.8015	−2.44488
$682$	−7.36090	−0.281863
$683$	20.0545	0.767364	0.383682	−	0.923465i	$-0.374656\pi$
$683$	20.0545	0.767364	0.383682	+	0.923465i	$0.374656\pi$
$684$	−8.01639	−0.306514
$685$	52.1084	1.99096
$686$	0	0
$687$	−14.0949	−0.537753
$688$	−16.2238	−0.618525
$689$	9.10888	0.347021
$690$	17.4666	0.664943
$691$	−36.3245	−1.38185	−0.690925	−	0.722927i	$-0.742796\pi$
$691$	−36.3245	−1.38185	−0.690925	+	0.722927i	$0.742796\pi$
$692$	−2.80195	−0.106514
$693$	0	0
$694$	48.1165	1.82648
$695$	69.0111	2.61774
$696$	29.6917	1.12546
$697$	17.8194	0.674959
$698$	43.6297	1.65141
$699$	49.1685	1.85972
$700$	0	0
$701$	28.3217	1.06969	0.534847	−	0.844949i	$-0.320369\pi$
$701$	28.3217	1.06969	0.534847	+	0.844949i	$0.320369\pi$
$702$	−18.0362	−0.680734
$703$	45.4675	1.71484
$704$	−3.64660	−0.137437
$705$	−123.710	−4.65920
$706$	21.2424	0.799466
$707$	0	0
$708$	−4.03995	−0.151831
$709$	21.4326	0.804919	0.402460	−	0.915438i	$-0.368155\pi$
$709$	21.4326	0.804919	0.402460	+	0.915438i	$0.368155\pi$
$710$	30.4332	1.14214
$711$	62.6383	2.34912
$712$	12.4327	0.465934
$713$	9.04067	0.338576
$714$	0	0
$715$	−2.52170	−0.0943061
$716$	1.21637	0.0454578
$717$	3.84980	0.143773
$718$	−10.9034	−0.406912
$719$	−46.7125	−1.74208	−0.871040	−	0.491212i	$-0.836554\pi$
$719$	−46.7125	−1.74208	−0.871040	+	0.491212i	$0.836554\pi$
$720$	−106.215	−3.95842
$721$	0	0
$722$	−9.07783	−0.337842
$723$	6.37394	0.237050
$724$	−0.725421	−0.0269601
$725$	35.8797	1.33254
$726$	48.9014	1.81490
$727$	−17.3705	−0.644237	−0.322119	−	0.946699i	$-0.604395\pi$
$727$	−17.3705	−0.644237	−0.322119	+	0.946699i	$0.604395\pi$
$728$	0	0
$729$	−19.6276	−0.726947
$730$	47.0501	1.74140
$731$	13.3630	0.494247
$732$	−2.54364	−0.0940156
$733$	−15.4702	−0.571404	−0.285702	−	0.958318i	$-0.592227\pi$
$733$	−15.4702	−0.571404	−0.285702	+	0.958318i	$0.592227\pi$
$734$	−23.6841	−0.874195
$735$	0	0
$736$	−1.44228	−0.0531632
$737$	6.52465	0.240339
$738$	−45.6408	−1.68006
$739$	−17.5944	−0.647221	−0.323611	−	0.946190i	$-0.604897\pi$
$739$	−17.5944	−0.647221	−0.323611	+	0.946190i	$0.604897\pi$
$740$	−8.91116	−0.327581
$741$	−18.5127	−0.680080
$742$	0	0
$743$	−32.0161	−1.17456	−0.587278	−	0.809385i	$-0.699801\pi$
$743$	−32.0161	−1.17456	−0.587278	+	0.809385i	$0.699801\pi$
$744$	−71.9967	−2.63953
$745$	52.8399	1.93591
$746$	−6.26111	−0.229236
$747$	−47.7676	−1.74772
$748$	−0.509219	−0.0186189
$749$	0	0
$750$	−80.7545	−2.94874
$751$	38.1097	1.39064	0.695321	−	0.718700i	$-0.255262\pi$
$751$	38.1097	1.39064	0.695321	+	0.718700i	$0.255262\pi$
$752$	47.3148	1.72539
$753$	−35.0788	−1.27834
$754$	−6.81386	−0.248146
$755$	61.7248	2.24640
$756$	0	0
$757$	19.5846	0.711814	0.355907	−	0.934521i	$-0.384172\pi$
$757$	19.5846	0.711814	0.355907	+	0.934521i	$0.384172\pi$
$758$	−28.0261	−1.01795
$759$	1.64810	0.0598223
$760$	−50.1200	−1.81804
$761$	1.99465	0.0723058	0.0361529	−	0.999346i	$-0.488490\pi$
$761$	1.99465	0.0723058	0.0361529	+	0.999346i	$0.488490\pi$
$762$	−40.3841	−1.46296
$763$	0	0
$764$	−0.915220	−0.0331115
$765$	87.4860	3.16306
$766$	−45.4897	−1.64361
$767$	−6.30242	−0.227567
$768$	18.4223	0.664757
$769$	−11.5731	−0.417338	−0.208669	−	0.977986i	$-0.566913\pi$
$769$	−11.5731	−0.417338	−0.208669	+	0.977986i	$0.566913\pi$
$770$	0	0
$771$	−44.5599	−1.60479
$772$	5.36450	0.193073
$773$	47.3961	1.70472	0.852360	−	0.522955i	$-0.175170\pi$
$773$	47.3961	1.70472	0.852360	+	0.522955i	$0.175170\pi$
$774$	−34.2265	−1.23025
$775$	−87.0016	−3.12519
$776$	28.7818	1.03321
$777$	0	0
$778$	21.1394	0.757886
$779$	−24.3446	−0.872236
$780$	3.62829	0.129914
$781$	2.87159	0.102754
$782$	5.50239	0.196765
$783$	36.7957	1.31497
$784$	0	0
$785$	58.5504	2.08975
$786$	−11.6442	−0.415334
$787$	30.1964	1.07639	0.538193	−	0.842822i	$-0.319107\pi$
$787$	30.1964	1.07639	0.538193	+	0.842822i	$0.319107\pi$
$788$	1.42238	0.0506701
$789$	−69.0638	−2.45874
$790$	−57.6102	−2.04968
$791$	0	0
$792$	−8.86618	−0.315046
$793$	−3.96814	−0.140913
$794$	45.4287	1.61220
$795$	87.0569	3.08759
$796$	1.98467	0.0703446
$797$	41.0916	1.45554	0.727770	−	0.685821i	$-0.240557\pi$
$797$	41.0916	1.45554	0.727770	+	0.685821i	$0.240557\pi$
$798$	0	0
$799$	−38.9716	−1.37872
$800$	13.8796	0.490718
$801$	29.6484	1.04757
$802$	1.00439	0.0354662
$803$	4.43951	0.156667
$804$	−9.38787	−0.331085
$805$	0	0
$806$	16.5223	0.581975
$807$	−76.2768	−2.68507
$808$	−9.42494	−0.331568
$809$	17.9154	0.629870	0.314935	−	0.949113i	$-0.398017\pi$
$809$	17.9154	0.629870	0.314935	+	0.949113i	$0.398017\pi$
$810$	−64.7470	−2.27498
$811$	−10.1577	−0.356686	−0.178343	−	0.983968i	$-0.557074\pi$
$811$	−10.1577	−0.356686	−0.178343	+	0.983968i	$0.557074\pi$
$812$	0	0
$813$	85.2095	2.98843
$814$	−7.39753	−0.259283
$815$	−15.1003	−0.528939
$816$	−49.5324	−1.73398
$817$	−18.2563	−0.638705
$818$	−13.6036	−0.475638
$819$	0	0
$820$	4.77129	0.166621
$821$	−15.2289	−0.531491	−0.265745	−	0.964043i	$-0.585618\pi$
$821$	−15.2289	−0.531491	−0.265745	+	0.964043i	$0.585618\pi$
$822$	−62.2400	−2.17087
$823$	−20.0090	−0.697468	−0.348734	−	0.937222i	$-0.613388\pi$
$823$	−20.0090	−0.697468	−0.348734	+	0.937222i	$0.613388\pi$
$824$	−24.8470	−0.865585
$825$	−15.8603	−0.552184
$826$	0	0
$827$	18.0259	0.626822	0.313411	−	0.949618i	$-0.398528\pi$
$827$	18.0259	0.626822	0.313411	+	0.949618i	$0.398528\pi$
$828$	−1.60189	−0.0556697
$829$	−14.2616	−0.495327	−0.247664	−	0.968846i	$-0.579663\pi$
$829$	−14.2616	−0.495327	−0.247664	+	0.968846i	$0.579663\pi$
$830$	43.9332	1.52494
$831$	−49.4694	−1.71607
$832$	8.18520	0.283771
$833$	0	0
$834$	−82.4291	−2.85429
$835$	−7.17971	−0.248464
$836$	0.695686	0.0240608
$837$	−89.2227	−3.08399
$838$	−29.9818	−1.03570
$839$	−51.5877	−1.78101	−0.890503	−	0.454977i	$-0.849647\pi$
$839$	−51.5877	−1.78101	−0.890503	+	0.454977i	$0.849647\pi$
$840$	0	0
$841$	−15.0990	−0.520656
$842$	10.3093	0.355280
$843$	−40.9561	−1.41060
$844$	2.42097	0.0833331
$845$	−44.0524	−1.51545
$846$	99.8178	3.43181
$847$	0	0
$848$	−33.2962	−1.14340
$849$	−54.8889	−1.88378
$850$	−52.9515	−1.81622
$851$	9.08566	0.311452
$852$	−4.13174	−0.141551
$853$	−48.2610	−1.65243	−0.826213	−	0.563358i	$-0.809509\pi$
$853$	−48.2610	−1.65243	−0.826213	+	0.563358i	$0.809509\pi$
$854$	0	0
$855$	−119.522	−4.08757
$856$	17.2934	0.591075
$857$	1.37665	0.0470256	0.0235128	−	0.999724i	$-0.492515\pi$
$857$	1.37665	0.0470256	0.0235128	+	0.999724i	$0.492515\pi$
$858$	3.01200	0.102828
$859$	36.3622	1.24066	0.620331	−	0.784340i	$-0.286998\pi$
$859$	36.3622	1.24066	0.620331	+	0.784340i	$0.286998\pi$
$860$	3.57804	0.122010
$861$	0	0
$862$	−6.79215	−0.231342
$863$	44.8731	1.52750	0.763749	−	0.645514i	$-0.223357\pi$
$863$	44.8731	1.52750	0.763749	+	0.645514i	$0.223357\pi$
$864$	14.2339	0.484248
$865$	−41.7762	−1.42043
$866$	21.8068	0.741025
$867$	−10.8932	−0.369954
$868$	0	0
$869$	−5.43594	−0.184402
$870$	−65.1225	−2.20786
$871$	−14.6453	−0.496237
$872$	2.89997	0.0982054
$873$	68.6364	2.32299
$874$	−7.51728	−0.254276
$875$	0	0
$876$	−6.38770	−0.215820
$877$	42.2559	1.42688	0.713441	−	0.700716i	$-0.247136\pi$
$877$	42.2559	1.42688	0.713441	+	0.700716i	$0.247136\pi$
$878$	38.3137	1.29303
$879$	−70.3979	−2.37446
$880$	9.21770	0.310729
$881$	−51.1432	−1.72306	−0.861529	−	0.507708i	$-0.830493\pi$
$881$	−51.1432	−1.72306	−0.861529	+	0.507708i	$0.830493\pi$
$882$	0	0
$883$	52.6889	1.77312	0.886562	−	0.462610i	$-0.153087\pi$
$883$	52.6889	1.77312	0.886562	+	0.462610i	$0.153087\pi$
$884$	1.14300	0.0384432
$885$	−60.2345	−2.02476
$886$	−20.9451	−0.703666
$887$	42.9102	1.44078	0.720391	−	0.693568i	$-0.243962\pi$
$887$	42.9102	1.44078	0.720391	+	0.693568i	$0.243962\pi$
$888$	−72.3550	−2.42807
$889$	0	0
$890$	−27.2685	−0.914042
$891$	−6.10934	−0.204671
$892$	−2.84719	−0.0953311
$893$	53.2424	1.78169
$894$	−63.1137	−2.11084
$895$	18.1357	0.606209
$896$	0	0
$897$	−3.69934	−0.123517
$898$	33.8446	1.12941
$899$	−33.7072	−1.12420
$900$	15.4156	0.513854
$901$	27.4249	0.913657
$902$	3.96085	0.131882
$903$	0	0
$904$	1.13468	0.0377388
$905$	−10.8158	−0.359530
$906$	−73.7261	−2.44939
$907$	−24.5213	−0.814217	−0.407108	−	0.913380i	$-0.633463\pi$
$907$	−24.5213	−0.814217	−0.407108	+	0.913380i	$0.633463\pi$
$908$	−5.38166	−0.178597
$909$	−22.4758	−0.745476
$910$	0	0
$911$	−31.6347	−1.04810	−0.524052	−	0.851686i	$-0.675580\pi$
$911$	−31.6347	−1.04810	−0.524052	+	0.851686i	$0.675580\pi$
$912$	67.6704	2.24079
$913$	4.14541	0.137193
$914$	19.4663	0.643888
$915$	−37.9249	−1.25376
$916$	−1.18890	−0.0392824
$917$	0	0
$918$	−54.3033	−1.79228
$919$	−43.7293	−1.44250	−0.721249	−	0.692676i	$-0.756431\pi$
$919$	−43.7293	−1.44250	−0.721249	+	0.692676i	$0.756431\pi$
$920$	−10.0154	−0.330196
$921$	3.47553	0.114523
$922$	22.4294	0.738674
$923$	−6.44561	−0.212160
$924$	0	0
$925$	−87.4346	−2.87483
$926$	−26.2788	−0.863576
$927$	−59.2530	−1.94612
$928$	5.37741	0.176522
$929$	−3.63411	−0.119231	−0.0596157	−	0.998221i	$-0.518988\pi$
$929$	−3.63411	−0.119231	−0.0596157	+	0.998221i	$0.518988\pi$
$930$	157.910	5.17807
$931$	0	0
$932$	4.14736	0.135851
$933$	58.7445	1.92321
$934$	−26.4802	−0.866460
$935$	−7.59230	−0.248295
$936$	19.9011	0.650488
$937$	10.3649	0.338606	0.169303	−	0.985564i	$-0.445848\pi$
$937$	10.3649	0.338606	0.169303	+	0.985564i	$0.445848\pi$
$938$	0	0
$939$	52.9503	1.72797
$940$	−10.4350	−0.340351
$941$	29.8720	0.973800	0.486900	−	0.873458i	$-0.338128\pi$
$941$	29.8720	0.973800	0.486900	+	0.873458i	$0.338128\pi$
$942$	−69.9345	−2.27859
$943$	−4.86472	−0.158417
$944$	23.0376	0.749809
$945$	0	0
$946$	2.97028	0.0965720
$947$	7.17017	0.232999	0.116500	−	0.993191i	$-0.462833\pi$
$947$	7.17017	0.232999	0.116500	+	0.993191i	$0.462833\pi$
$948$	7.82139	0.254027
$949$	−9.96497	−0.323477
$950$	72.3415	2.34707
$951$	4.33636	0.140616
$952$	0	0
$953$	16.0495	0.519894	0.259947	−	0.965623i	$-0.416295\pi$
$953$	16.0495	0.519894	0.259947	+	0.965623i	$0.416295\pi$
$954$	−70.2434	−2.27421
$955$	−13.6457	−0.441563
$956$	0.324730	0.0105025
$957$	−6.14478	−0.198632
$958$	−17.6438	−0.570046
$959$	0	0
$960$	78.2289	2.52483
$961$	50.7337	1.63657
$962$	16.6046	0.535352
$963$	41.2398	1.32893
$964$	0.537642	0.0173163
$965$	79.9832	2.57475
$966$	0	0
$967$	33.5360	1.07845	0.539223	−	0.842163i	$-0.318718\pi$
$967$	33.5360	1.07845	0.539223	+	0.842163i	$0.318718\pi$
$968$	−28.0400	−0.901241
$969$	−55.7378	−1.79056
$970$	−63.1269	−2.02688
$971$	17.5189	0.562208	0.281104	−	0.959677i	$-0.409299\pi$
$971$	17.5189	0.562208	0.281104	+	0.959677i	$0.409299\pi$
$972$	1.19666	0.0383828
$973$	0	0
$974$	−34.4565	−1.10406
$975$	35.6001	1.14012
$976$	14.5050	0.464292
$977$	50.1902	1.60573	0.802863	−	0.596163i	$-0.203309\pi$
$977$	50.1902	1.60573	0.802863	+	0.596163i	$0.203309\pi$
$978$	18.0362	0.576735
$979$	−2.57298	−0.0822327
$980$	0	0
$981$	6.91561	0.220798
$982$	−17.3773	−0.554533
$983$	22.7924	0.726966	0.363483	−	0.931601i	$-0.381587\pi$
$983$	22.7924	0.726966	0.363483	+	0.931601i	$0.381587\pi$
$984$	38.7409	1.23502
$985$	21.2073	0.675719
$986$	−20.5151	−0.653334
$987$	0	0
$988$	−1.56154	−0.0496793
$989$	−3.64810	−0.116003
$990$	19.4461	0.618039
$991$	−0.965443	−0.0306683	−0.0153342	−	0.999882i	$-0.504881\pi$
$991$	−0.965443	−0.0306683	−0.0153342	+	0.999882i	$0.504881\pi$
$992$	−13.0392	−0.413995
$993$	11.9100	0.377952
$994$	0	0
$995$	29.5908	0.938091
$996$	−5.96455	−0.188994
$997$	4.22619	0.133845	0.0669224	−	0.997758i	$-0.478682\pi$
$997$	4.22619	0.133845	0.0669224	+	0.997758i	$0.478682\pi$
$998$	−37.5634	−1.18905
$999$	−89.6667	−2.83693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1127.2.a.h.1.2		5
7.6	odd	2		161.2.a.d.1.2	✓	5
21.20	even	2		1449.2.a.r.1.4		5
28.27	even	2		2576.2.a.bd.1.5		5
35.34	odd	2		4025.2.a.p.1.4		5
161.160	even	2		3703.2.a.j.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.a.d.1.2	✓	5	7.6	odd	2
1127.2.a.h.1.2		5	1.1	even	1	trivial
1449.2.a.r.1.4		5	21.20	even	2
2576.2.a.bd.1.5		5	28.27	even	2
3703.2.a.j.1.2		5	161.160	even	2
4025.2.a.p.1.4		5	35.34	odd	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:	\( N \)	\(=\)	\( 1127 = 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1127.a (trivial)

\(f(q)\)	\(=\)	\(q-1.50216 q^{2} +3.04067 q^{3} +0.256481 q^{4} +3.82405 q^{5} -4.56757 q^{6} +2.61904 q^{8} +6.24568 q^{9} +O(q^{10})\)	\(q-1.50216 q^{2} +3.04067 q^{3} +0.256481 q^{4} +3.82405 q^{5} -4.56757 q^{6} +2.61904 q^{8} +6.24568 q^{9} -5.74433 q^{10} -0.542019 q^{11} +0.779873 q^{12} +1.21662 q^{13} +11.6277 q^{15} -4.44718 q^{16} +3.66299 q^{17} -9.38200 q^{18} -5.00432 q^{19} +0.980794 q^{20} +0.814198 q^{22} -1.00000 q^{23} +7.96365 q^{24} +9.62336 q^{25} -1.82756 q^{26} +9.86904 q^{27} +3.72840 q^{29} -17.4666 q^{30} -9.04067 q^{31} +1.44228 q^{32} -1.64810 q^{33} -5.50239 q^{34} +1.60189 q^{36} -9.08566 q^{37} +7.51728 q^{38} +3.69934 q^{39} +10.0154 q^{40} +4.86472 q^{41} +3.64810 q^{43} -0.139017 q^{44} +23.8838 q^{45} +1.50216 q^{46} -10.6393 q^{47} -13.5224 q^{48} -14.4558 q^{50} +11.1379 q^{51} +0.312039 q^{52} +7.48704 q^{53} -14.8249 q^{54} -2.07271 q^{55} -15.2165 q^{57} -5.60065 q^{58} -5.18027 q^{59} +2.98227 q^{60} -3.26161 q^{61} +13.5805 q^{62} +6.72782 q^{64} +4.65242 q^{65} +2.47571 q^{66} -12.0377 q^{67} +0.939485 q^{68} -3.04067 q^{69} -5.29796 q^{71} +16.3577 q^{72} -8.19070 q^{73} +13.6481 q^{74} +29.2615 q^{75} -1.28351 q^{76} -5.55700 q^{78} +10.0291 q^{79} -17.0062 q^{80} +11.2715 q^{81} -7.30758 q^{82} -7.64810 q^{83} +14.0075 q^{85} -5.48003 q^{86} +11.3368 q^{87} -1.41957 q^{88} +4.74703 q^{89} -35.8772 q^{90} -0.256481 q^{92} -27.4897 q^{93} +15.9819 q^{94} -19.1368 q^{95} +4.38551 q^{96} +10.9894 q^{97} -3.38527 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} + 12 q^{4} + 4 q^{5} + 3 q^{6} + 3 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 + 12 * q^4 + 4 * q^5 + 3 * q^6 + 3 * q^8 + 11 * q^9	\( 5 q + 2 q^{2} + 12 q^{4} + 4 q^{5} + 3 q^{6} + 3 q^{8} + 11 q^{9} + 8 q^{10} - 4 q^{11} - 3 q^{12} + 6 q^{13} + 10 q^{15} + 10 q^{16} + 12 q^{17} - 19 q^{18} - 6 q^{19} + 14 q^{22} - 5 q^{23} + 36 q^{24} + 19 q^{25} - q^{26} - 4 q^{29} - 48 q^{30} - 30 q^{31} + 8 q^{32} + 22 q^{33} - 6 q^{34} - q^{36} + 4 q^{37} + 40 q^{38} + 16 q^{39} + 50 q^{40} - 6 q^{41} - 12 q^{43} - 26 q^{44} + 12 q^{45} - 2 q^{46} - 10 q^{47} - 25 q^{48} - 2 q^{50} - 4 q^{51} + 21 q^{52} + 16 q^{53} - 33 q^{54} - 18 q^{55} + 6 q^{57} + 13 q^{58} - 22 q^{59} + 30 q^{60} + 18 q^{61} - 15 q^{62} + 25 q^{64} - 26 q^{65} - 4 q^{66} - 2 q^{67} - 12 q^{68} + 4 q^{71} - 41 q^{72} + 2 q^{73} + 38 q^{74} + 30 q^{75} - 10 q^{76} + 41 q^{78} + 30 q^{79} + 10 q^{80} - 3 q^{81} + 7 q^{82} - 8 q^{83} - 12 q^{85} + 8 q^{86} + 12 q^{87} + 4 q^{88} + 20 q^{89} - 34 q^{90} - 12 q^{92} - 26 q^{93} + 25 q^{94} + 8 q^{95} + q^{96} + 12 q^{97} - 8 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 + 12 * q^4 + 4 * q^5 + 3 * q^6 + 3 * q^8 + 11 * q^9 + 8 * q^10 - 4 * q^11 - 3 * q^12 + 6 * q^13 + 10 * q^15 + 10 * q^16 + 12 * q^17 - 19 * q^18 - 6 * q^19 + 14 * q^22 - 5 * q^23 + 36 * q^24 + 19 * q^25 - q^26 - 4 * q^29 - 48 * q^30 - 30 * q^31 + 8 * q^32 + 22 * q^33 - 6 * q^34 - q^36 + 4 * q^37 + 40 * q^38 + 16 * q^39 + 50 * q^40 - 6 * q^41 - 12 * q^43 - 26 * q^44 + 12 * q^45 - 2 * q^46 - 10 * q^47 - 25 * q^48 - 2 * q^50 - 4 * q^51 + 21 * q^52 + 16 * q^53 - 33 * q^54 - 18 * q^55 + 6 * q^57 + 13 * q^58 - 22 * q^59 + 30 * q^60 + 18 * q^61 - 15 * q^62 + 25 * q^64 - 26 * q^65 - 4 * q^66 - 2 * q^67 - 12 * q^68 + 4 * q^71 - 41 * q^72 + 2 * q^73 + 38 * q^74 + 30 * q^75 - 10 * q^76 + 41 * q^78 + 30 * q^79 + 10 * q^80 - 3 * q^81 + 7 * q^82 - 8 * q^83 - 12 * q^85 + 8 * q^86 + 12 * q^87 + 4 * q^88 + 20 * q^89 - 34 * q^90 - 12 * q^92 - 26 * q^93 + 25 * q^94 + 8 * q^95 + q^96 + 12 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more