LMFDB - Embedded newform 1849.2.a.q.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 27 x^{18} + 300 x^{16} - 1775 x^{14} + 6037 x^{12} - 11859 x^{10} + 12809 x^{8} - 6823 x^{6} + \cdots + 1 $ x^20 - 27x^18 + 300x^16 - 1775x^14 + 6037x^12 - 11859x^10 + 12809x^8 - 6823x^6 + 1500x^4 - 75*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$1.36200$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.36200 q^{2} +0.149497 q^{3} -0.144951 q^{4} +3.99648 q^{5} +0.203616 q^{6} -3.68871 q^{7} -2.92143 q^{8} -2.97765 q^{9} +O(q^{10})$	\(q+1.36200 q^{2} +0.149497 q^{3} -0.144951 q^{4} +3.99648 q^{5} +0.203616 q^{6} -3.68871 q^{7} -2.92143 q^{8} -2.97765 q^{9} +5.44321 q^{10} -3.00278 q^{11} -0.0216698 q^{12} -0.0960833 q^{13} -5.02403 q^{14} +0.597463 q^{15} -3.68909 q^{16} +1.64946 q^{17} -4.05557 q^{18} -3.24605 q^{19} -0.579294 q^{20} -0.551453 q^{21} -4.08979 q^{22} +0.694235 q^{23} -0.436746 q^{24} +10.9718 q^{25} -0.130866 q^{26} -0.893643 q^{27} +0.534683 q^{28} -6.49105 q^{29} +0.813745 q^{30} -3.45321 q^{31} +0.818311 q^{32} -0.448907 q^{33} +2.24657 q^{34} -14.7419 q^{35} +0.431613 q^{36} -5.35088 q^{37} -4.42112 q^{38} -0.0143642 q^{39} -11.6754 q^{40} -2.50675 q^{41} -0.751080 q^{42} +0.435255 q^{44} -11.9001 q^{45} +0.945549 q^{46} -9.52226 q^{47} -0.551509 q^{48} +6.60660 q^{49} +14.9437 q^{50} +0.246590 q^{51} +0.0139274 q^{52} -3.18885 q^{53} -1.21714 q^{54} -12.0005 q^{55} +10.7763 q^{56} -0.485275 q^{57} -8.84083 q^{58} +7.02691 q^{59} -0.0866028 q^{60} -0.283436 q^{61} -4.70328 q^{62} +10.9837 q^{63} +8.49272 q^{64} -0.383995 q^{65} -0.611412 q^{66} +8.26604 q^{67} -0.239091 q^{68} +0.103786 q^{69} -20.0784 q^{70} -6.89303 q^{71} +8.69899 q^{72} +9.19513 q^{73} -7.28791 q^{74} +1.64026 q^{75} +0.470518 q^{76} +11.0764 q^{77} -0.0195641 q^{78} +2.30820 q^{79} -14.7434 q^{80} +8.79935 q^{81} -3.41420 q^{82} +5.85188 q^{83} +0.0799336 q^{84} +6.59203 q^{85} -0.970395 q^{87} +8.77239 q^{88} +15.6724 q^{89} -16.2080 q^{90} +0.354424 q^{91} -0.100630 q^{92} -0.516246 q^{93} -12.9693 q^{94} -12.9728 q^{95} +0.122335 q^{96} +1.19749 q^{97} +8.99821 q^{98} +8.94122 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9}+O(q^{10}) $ 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9	$ 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9} + 12 q^{10} - 20 q^{11} + 6 q^{13} - 34 q^{14} - 34 q^{15} + 14 q^{16} - 8 q^{17} + 12 q^{21} - 46 q^{23} + 2 q^{24} + 20 q^{25} - 38 q^{31} - 76 q^{35} - 46 q^{36} - 68 q^{38} - 64 q^{40} - 56 q^{41} - 58 q^{44} - 24 q^{47} - 20 q^{49} - 20 q^{52} - 42 q^{53} + 66 q^{54} - 46 q^{56} + 2 q^{57} + 12 q^{58} - 90 q^{59} + 18 q^{60} - 28 q^{64} + 76 q^{66} - 62 q^{67} - 54 q^{68} + 24 q^{74} - 36 q^{78} - 10 q^{79} - 48 q^{81} - 68 q^{83} + 70 q^{84} - 12 q^{87} + 58 q^{90} - 8 q^{92} - 42 q^{95} - 22 q^{96} - 44 q^{97} - 38 q^{99}+O(q^{100}) $ 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9 + 12 * q^10 - 20 * q^11 + 6 * q^13 - 34 * q^14 - 34 * q^15 + 14 * q^16 - 8 * q^17 + 12 * q^21 - 46 * q^23 + 2 * q^24 + 20 * q^25 - 38 * q^31 - 76 * q^35 - 46 * q^36 - 68 * q^38 - 64 * q^40 - 56 * q^41 - 58 * q^44 - 24 * q^47 - 20 * q^49 - 20 * q^52 - 42 * q^53 + 66 * q^54 - 46 * q^56 + 2 * q^57 + 12 * q^58 - 90 * q^59 + 18 * q^60 - 28 * q^64 + 76 * q^66 - 62 * q^67 - 54 * q^68 + 24 * q^74 - 36 * q^78 - 10 * q^79 - 48 * q^81 - 68 * q^83 + 70 * q^84 - 12 * q^87 + 58 * q^90 - 8 * q^92 - 42 * q^95 - 22 * q^96 - 44 * q^97 - 38 * 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 $

$2$	1.36200	0.963081	0.481540	−	0.876424i	$-0.340077\pi$
$2$	1.36200	0.963081	0.481540	+	0.876424i	$0.340077\pi$
$3$	0.149497	0.0863123	0.0431562	−	0.999068i	$-0.486259\pi$
$3$	0.149497	0.0863123	0.0431562	+	0.999068i	$0.486259\pi$
$4$	−0.144951	−0.0724755
$5$	3.99648	1.78728	0.893640	−	0.448785i	$-0.148143\pi$
$5$	3.99648	1.78728	0.893640	+	0.448785i	$0.148143\pi$
$6$	0.203616	0.0831257
$7$	−3.68871	−1.39420	−0.697101	−	0.716973i	$-0.745527\pi$
$7$	−3.68871	−1.39420	−0.697101	+	0.716973i	$0.745527\pi$
$8$	−2.92143	−1.03288
$9$	−2.97765	−0.992550
$10$	5.44321	1.72129
$11$	−3.00278	−0.905371	−0.452686	−	0.891670i	$-0.649534\pi$
$11$	−3.00278	−0.905371	−0.452686	+	0.891670i	$0.649534\pi$
$12$	−0.0216698	−0.00625553
$13$	−0.0960833	−0.0266487	−0.0133244	−	0.999911i	$-0.504241\pi$
$13$	−0.0960833	−0.0266487	−0.0133244	+	0.999911i	$0.504241\pi$
$14$	−5.02403	−1.34273
$15$	0.597463	0.154264
$16$	−3.68909	−0.922272
$17$	1.64946	0.400053	0.200026	−	0.979791i	$-0.435897\pi$
$17$	1.64946	0.400053	0.200026	+	0.979791i	$0.435897\pi$
$18$	−4.05557	−0.955906
$19$	−3.24605	−0.744694	−0.372347	−	0.928094i	$-0.621447\pi$
$19$	−3.24605	−0.744694	−0.372347	+	0.928094i	$0.621447\pi$
$20$	−0.579294	−0.129534
$21$	−0.551453	−0.120337
$22$	−4.08979	−0.871945
$23$	0.694235	0.144758	0.0723790	−	0.997377i	$-0.476941\pi$
$23$	0.694235	0.144758	0.0723790	+	0.997377i	$0.476941\pi$
$24$	−0.436746	−0.0891503
$25$	10.9718	2.19437
$26$	−0.130866	−0.0256649
$27$	−0.893643	−0.171982
$28$	0.534683	0.101046
$29$	−6.49105	−1.20536	−0.602679	−	0.797984i	$-0.705900\pi$
$29$	−6.49105	−1.20536	−0.602679	+	0.797984i	$0.705900\pi$
$30$	0.813745	0.148569
$31$	−3.45321	−0.620215	−0.310108	−	0.950701i	$-0.600365\pi$
$31$	−3.45321	−0.620215	−0.310108	+	0.950701i	$0.600365\pi$
$32$	0.818311	0.144658
$33$	−0.448907	−0.0781447
$34$	2.24657	0.385283
$35$	−14.7419	−2.49183
$36$	0.431613	0.0719356
$37$	−5.35088	−0.879679	−0.439839	−	0.898076i	$-0.644965\pi$
$37$	−5.35088	−0.879679	−0.439839	+	0.898076i	$0.644965\pi$
$38$	−4.42112	−0.717201
$39$	−0.0143642	−0.00230011
$40$	−11.6754	−1.84605
$41$	−2.50675	−0.391488	−0.195744	−	0.980655i	$-0.562712\pi$
$41$	−2.50675	−0.391488	−0.195744	+	0.980655i	$0.562712\pi$
$42$	−0.751080	−0.115894
$43$	0	0
$43$	0	0
$44$	0.435255	0.0656172
$45$	−11.9001	−1.77396
$46$	0.945549	0.139414
$47$	−9.52226	−1.38896	−0.694482	−	0.719510i	$-0.744366\pi$
$47$	−9.52226	−1.38896	−0.694482	+	0.719510i	$0.744366\pi$
$48$	−0.551509	−0.0796034
$49$	6.60660	0.943800
$50$	14.9437	2.11335
$51$	0.246590	0.0345295
$52$	0.0139274	0.00193138
$53$	−3.18885	−0.438022	−0.219011	−	0.975722i	$-0.570283\pi$
$53$	−3.18885	−0.438022	−0.219011	+	0.975722i	$0.570283\pi$
$54$	−1.21714	−0.165632
$55$	−12.0005	−1.61815
$56$	10.7763	1.44004
$57$	−0.485275	−0.0642763
$58$	−8.84083	−1.16086
$59$	7.02691	0.914826	0.457413	−	0.889254i	$-0.348776\pi$
$59$	7.02691	0.914826	0.457413	+	0.889254i	$0.348776\pi$
$60$	−0.0866028	−0.0111804
$61$	−0.283436	−0.0362903	−0.0181451	−	0.999835i	$-0.505776\pi$
$61$	−0.283436	−0.0362903	−0.0181451	+	0.999835i	$0.505776\pi$
$62$	−4.70328	−0.597317
$63$	10.9837	1.38382
$64$	8.49272	1.06159
$65$	−0.383995	−0.0476287
$66$	−0.611412	−0.0752596
$67$	8.26604	1.00986	0.504929	−	0.863161i	$-0.331519\pi$
$67$	8.26604	1.00986	0.504929	+	0.863161i	$0.331519\pi$
$68$	−0.239091	−0.0289940
$69$	0.103786	0.0124944
$70$	−20.0784	−2.39983
$71$	−6.89303	−0.818052	−0.409026	−	0.912523i	$-0.634132\pi$
$71$	−6.89303	−0.818052	−0.409026	+	0.912523i	$0.634132\pi$
$72$	8.69899	1.02519
$73$	9.19513	1.07621	0.538104	−	0.842878i	$-0.319141\pi$
$73$	9.19513	1.07621	0.538104	+	0.842878i	$0.319141\pi$
$74$	−7.28791	−0.847202
$75$	1.64026	0.189401
$76$	0.470518	0.0539721
$77$	11.0764	1.26227
$78$	−0.0195641	−0.00221519
$79$	2.30820	0.259693	0.129847	−	0.991534i	$-0.458552\pi$
$79$	2.30820	0.259693	0.129847	+	0.991534i	$0.458552\pi$
$80$	−14.7434	−1.64836
$81$	8.79935	0.977706
$82$	−3.41420	−0.377035
$83$	5.85188	0.642327	0.321163	−	0.947024i	$-0.395926\pi$
$83$	5.85188	0.642327	0.321163	+	0.947024i	$0.395926\pi$
$84$	0.0799336	0.00872147
$85$	6.59203	0.715006
$86$	0	0
$87$	−0.970395	−0.104037
$88$	8.77239	0.935140
$89$	15.6724	1.66127	0.830637	−	0.556814i	$-0.187977\pi$
$89$	15.6724	1.66127	0.830637	+	0.556814i	$0.187977\pi$
$90$	−16.2080	−1.70847
$91$	0.354424	0.0371537
$92$	−0.100630	−0.0104914
$93$	−0.516246	−0.0535322
$94$	−12.9693	−1.33768
$95$	−12.9728	−1.33098
$96$	0.122335	0.0124858
$97$	1.19749	0.121586	0.0607931	−	0.998150i	$-0.480637\pi$
$97$	1.19749	0.121586	0.0607931	+	0.998150i	$0.480637\pi$
$98$	8.99821	0.908956
$99$	8.94122	0.898626
$100$	−1.59038	−0.159038
$101$	−14.9598	−1.48856	−0.744280	−	0.667868i	$-0.767207\pi$
$101$	−14.9598	−1.48856	−0.744280	+	0.667868i	$0.767207\pi$
$102$	0.335856	0.0332547
$103$	−12.2291	−1.20497	−0.602484	−	0.798131i	$-0.705822\pi$
$103$	−12.2291	−1.20497	−0.602484	+	0.798131i	$0.705822\pi$
$104$	0.280700	0.0275249
$105$	−2.20387	−0.215076
$106$	−4.34322	−0.421851
$107$	−10.7721	−1.04138	−0.520688	−	0.853747i	$-0.674324\pi$
$107$	−10.7721	−1.04138	−0.520688	+	0.853747i	$0.674324\pi$
$108$	0.129534	0.0124645
$109$	−7.13825	−0.683721	−0.341860	−	0.939751i	$-0.611057\pi$
$109$	−7.13825	−0.683721	−0.341860	+	0.939751i	$0.611057\pi$
$110$	−16.3447	−1.55841
$111$	−0.799942	−0.0759271
$112$	13.6080	1.28583
$113$	1.73938	0.163627	0.0818135	−	0.996648i	$-0.473929\pi$
$113$	1.73938	0.163627	0.0818135	+	0.996648i	$0.473929\pi$
$114$	−0.660946	−0.0619033
$115$	2.77449	0.258723
$116$	0.940885	0.0873590
$117$	0.286102	0.0264502
$118$	9.57067	0.881051
$119$	−6.08438	−0.557754
$120$	−1.74544	−0.159336
$121$	−1.98333	−0.180303
$122$	−0.386040	−0.0349504
$123$	−0.374752	−0.0337903
$124$	0.500547	0.0449504
$125$	23.8663	2.13467
$126$	14.9598	1.33273
$127$	−20.5629	−1.82467	−0.912333	−	0.409450i	$-0.865721\pi$
$127$	−20.5629	−1.82467	−0.912333	+	0.409450i	$0.865721\pi$
$128$	9.93047	0.877738
$129$	0	0
$130$	−0.523002	−0.0458703
$131$	6.14499	0.536891	0.268445	−	0.963295i	$-0.413490\pi$
$131$	6.14499	0.536891	0.268445	+	0.963295i	$0.413490\pi$
$132$	0.0650695	0.00566358
$133$	11.9737	1.03825
$134$	11.2584	0.972575
$135$	−3.57142	−0.307379
$136$	−4.81878	−0.413207
$137$	11.4029	0.974215	0.487108	−	0.873342i	$-0.338052\pi$
$137$	11.4029	0.974215	0.487108	+	0.873342i	$0.338052\pi$
$138$	0.141357	0.0120331
$139$	15.2218	1.29109	0.645547	−	0.763721i	$-0.276630\pi$
$139$	15.2218	1.29109	0.645547	+	0.763721i	$0.276630\pi$
$140$	2.13685	0.180597
$141$	−1.42355	−0.119885
$142$	−9.38832	−0.787850
$143$	0.288517	0.0241270
$144$	10.9848	0.915401
$145$	−25.9414	−2.15431
$146$	12.5238	1.03648
$147$	0.987669	0.0814616
$148$	0.775615	0.0637552
$149$	12.7907	1.04786	0.523928	−	0.851763i	$-0.324466\pi$
$149$	12.7907	1.04786	0.523928	+	0.851763i	$0.324466\pi$
$150$	2.23404	0.182408
$151$	−18.7852	−1.52872	−0.764359	−	0.644790i	$-0.776945\pi$
$151$	−18.7852	−1.52872	−0.764359	+	0.644790i	$0.776945\pi$
$152$	9.48309	0.769180
$153$	−4.91151	−0.397072
$154$	15.0860	1.21567
$155$	−13.8007	−1.10850
$156$	0.00208210	0.000166702 0
$157$	12.7077	1.01418	0.507092	−	0.861892i	$-0.330720\pi$
$157$	12.7077	1.01418	0.507092	+	0.861892i	$0.330720\pi$
$158$	3.14378	0.250105
$159$	−0.476724	−0.0378067
$160$	3.27036	0.258545
$161$	−2.56083	−0.201822
$162$	11.9847	0.941610
$163$	−18.6244	−1.45878	−0.729388	−	0.684100i	$-0.760195\pi$
$163$	−18.6244	−1.45878	−0.729388	+	0.684100i	$0.760195\pi$
$164$	0.363356	0.0283733
$165$	−1.79405	−0.139666
$166$	7.97027	0.618613
$167$	−10.4718	−0.810333	−0.405167	−	0.914243i	$-0.632786\pi$
$167$	−10.4718	−0.810333	−0.405167	+	0.914243i	$0.632786\pi$
$168$	1.61103	0.124294
$169$	−12.9908	−0.999290
$170$	8.97835	0.688608
$171$	9.66560	0.739147
$172$	0	0
$173$	−0.613762	−0.0466634	−0.0233317	−	0.999728i	$-0.507427\pi$
$173$	−0.613762	−0.0466634	−0.0233317	+	0.999728i	$0.507427\pi$
$174$	−1.32168	−0.100196
$175$	−40.4719	−3.05939
$176$	11.0775	0.834998
$177$	1.05050	0.0789608
$178$	21.3459	1.59994
$179$	11.8117	0.882850	0.441425	−	0.897298i	$-0.354473\pi$
$179$	11.8117	0.882850	0.441425	+	0.897298i	$0.354473\pi$
$180$	1.72493	0.128569
$181$	25.1025	1.86585	0.932926	−	0.360068i	$-0.117247\pi$
$181$	25.1025	1.86585	0.932926	+	0.360068i	$0.117247\pi$
$182$	0.482726	0.0357820
$183$	−0.0423729	−0.00313230
$184$	−2.02816	−0.149518
$185$	−21.3847	−1.57223
$186$	−0.703128	−0.0515558
$187$	−4.95296	−0.362196
$188$	1.38026	0.100666
$189$	3.29639	0.239777
$190$	−17.6689	−1.28184
$191$	0.642179	0.0464664	0.0232332	−	0.999730i	$-0.492604\pi$
$191$	0.642179	0.0464664	0.0232332	+	0.999730i	$0.492604\pi$
$192$	1.26964	0.0916282
$193$	−20.4935	−1.47515	−0.737576	−	0.675264i	$-0.764030\pi$
$193$	−20.4935	−1.47515	−0.737576	+	0.675264i	$0.764030\pi$
$194$	1.63098	0.117097
$195$	−0.0574062	−0.00411094
$196$	−0.957634	−0.0684024
$197$	−11.5903	−0.825777	−0.412888	−	0.910782i	$-0.635480\pi$
$197$	−11.5903	−0.825777	−0.412888	+	0.910782i	$0.635480\pi$
$198$	12.1780	0.865450
$199$	20.8484	1.47791	0.738953	−	0.673757i	$-0.235321\pi$
$199$	20.8484	1.47791	0.738953	+	0.673757i	$0.235321\pi$
$200$	−32.0534	−2.26652
$201$	1.23575	0.0871632
$202$	−20.3753	−1.43360
$203$	23.9436	1.68051
$204$	−0.0357434	−0.00250254
$205$	−10.0182	−0.699699
$206$	−16.6560	−1.16048
$207$	−2.06719	−0.143680
$208$	0.354460	0.0245774
$209$	9.74715	0.674225
$210$	−3.00167	−0.207135
$211$	8.08792	0.556796	0.278398	−	0.960466i	$-0.410197\pi$
$211$	8.08792	0.556796	0.278398	+	0.960466i	$0.410197\pi$
$212$	0.462227	0.0317459
$213$	−1.03049	−0.0706080
$214$	−14.6716	−1.00293
$215$	0	0
$216$	2.61071	0.177636
$217$	12.7379	0.864706
$218$	−9.72231	−0.658478
$219$	1.37465	0.0928900
$220$	1.73949	0.117276
$221$	−0.158485	−0.0106609
$222$	−1.08952	−0.0731239
$223$	−3.21456	−0.215263	−0.107631	−	0.994191i	$-0.534327\pi$
$223$	−3.21456	−0.215263	−0.107631	+	0.994191i	$0.534327\pi$
$224$	−3.01851	−0.201683
$225$	−32.6703	−2.17802
$226$	2.36904	0.157586
$227$	3.58860	0.238184	0.119092	−	0.992883i	$-0.462002\pi$
$227$	3.58860	0.238184	0.119092	+	0.992883i	$0.462002\pi$
$228$	0.0703412	0.00465846
$229$	−6.27639	−0.414756	−0.207378	−	0.978261i	$-0.566493\pi$
$229$	−6.27639	−0.414756	−0.207378	+	0.978261i	$0.566493\pi$
$230$	3.77887	0.249171
$231$	1.65589	0.108950
$232$	18.9631	1.24499
$233$	1.93167	0.126548	0.0632740	−	0.997996i	$-0.479846\pi$
$233$	1.93167	0.126548	0.0632740	+	0.997996i	$0.479846\pi$
$234$	0.389672	0.0254737
$235$	−38.0555	−2.48247
$236$	−1.01856	−0.0663025
$237$	0.345070	0.0224147
$238$	−8.28694	−0.537163
$239$	15.3781	0.994728	0.497364	−	0.867542i	$-0.334301\pi$
$239$	15.3781	0.994728	0.497364	+	0.867542i	$0.334301\pi$
$240$	−2.20409	−0.142274
$241$	2.93466	0.189038	0.0945189	−	0.995523i	$-0.469869\pi$
$241$	2.93466	0.189038	0.0945189	+	0.995523i	$0.469869\pi$
$242$	−2.70131	−0.173647
$243$	3.99641	0.256370
$244$	0.0410843	0.00263016
$245$	26.4031	1.68683
$246$	−0.510413	−0.0325428
$247$	0.311891	0.0198451
$248$	10.0883	0.640608
$249$	0.874840	0.0554407
$250$	32.5060	2.05586
$251$	−18.8631	−1.19063	−0.595313	−	0.803494i	$-0.702972\pi$
$251$	−18.8631	−1.19063	−0.595313	+	0.803494i	$0.702972\pi$
$252$	−1.59210	−0.100293
$253$	−2.08463	−0.131060
$254$	−28.0068	−1.75730
$255$	0.985490	0.0617138
$256$	−3.46011	−0.216257
$257$	−1.01694	−0.0634349	−0.0317174	−	0.999497i	$-0.510098\pi$
$257$	−1.01694	−0.0634349	−0.0317174	+	0.999497i	$0.510098\pi$
$258$	0	0
$259$	19.7379	1.22645
$260$	0.0556604	0.00345191
$261$	19.3281	1.19638
$262$	8.36949	0.517069
$263$	−29.5819	−1.82410	−0.912048	−	0.410083i	$-0.865500\pi$
$263$	−29.5819	−1.82410	−0.912048	+	0.410083i	$0.865500\pi$
$264$	1.31145	0.0807141
$265$	−12.7442	−0.782868
$266$	16.3083	0.999923
$267$	2.34299	0.143388
$268$	−1.19817	−0.0731900
$269$	16.4014	1.00001	0.500005	−	0.866023i	$-0.333332\pi$
$269$	16.4014	1.00001	0.500005	+	0.866023i	$0.333332\pi$
$270$	−4.86429	−0.296031
$271$	6.07180	0.368835	0.184418	−	0.982848i	$-0.440960\pi$
$271$	6.07180	0.368835	0.184418	+	0.982848i	$0.440960\pi$
$272$	−6.08500	−0.368957
$273$	0.0529854	0.00320682
$274$	15.5308	0.938248
$275$	−32.9460	−1.98672
$276$	−0.0150439	−0.000905538 0
$277$	−16.0757	−0.965894	−0.482947	−	0.875650i	$-0.660434\pi$
$277$	−16.0757	−0.965894	−0.482947	+	0.875650i	$0.660434\pi$
$278$	20.7321	1.24343
$279$	10.2825	0.615595
$280$	43.0673	2.57376
$281$	3.62145	0.216038	0.108019	−	0.994149i	$-0.465549\pi$
$281$	3.62145	0.216038	0.108019	+	0.994149i	$0.465549\pi$
$282$	−1.93888	−0.115459
$283$	−23.5005	−1.39696	−0.698480	−	0.715630i	$-0.746140\pi$
$283$	−23.5005	−1.39696	−0.698480	+	0.715630i	$0.746140\pi$
$284$	0.999152	0.0592888
$285$	−1.93939	−0.114880
$286$	0.392960	0.0232362
$287$	9.24668	0.545814
$288$	−2.43664	−0.143581
$289$	−14.2793	−0.839958
$290$	−35.3322	−2.07478
$291$	0.179021	0.0104944
$292$	−1.33284	−0.0779988
$293$	21.4055	1.25053	0.625263	−	0.780414i	$-0.284992\pi$
$293$	21.4055	1.25053	0.625263	+	0.780414i	$0.284992\pi$
$294$	1.34521	0.0784541
$295$	28.0829	1.63505
$296$	15.6322	0.908603
$297$	2.68341	0.155707
$298$	17.4210	1.00917
$299$	−0.0667044	−0.00385761
$300$	−0.237757	−0.0137269
$301$	0	0
$302$	−25.5855	−1.47228
$303$	−2.23645	−0.128481
$304$	11.9750	0.686811
$305$	−1.13275	−0.0648608
$306$	−6.68949	−0.382413
$307$	−10.0621	−0.574272	−0.287136	−	0.957890i	$-0.592703\pi$
$307$	−10.0621	−0.574272	−0.287136	+	0.957890i	$0.592703\pi$
$308$	−1.60553	−0.0914837
$309$	−1.82822	−0.104004
$310$	−18.7966	−1.06757
$311$	4.64457	0.263369	0.131685	−	0.991292i	$-0.457961\pi$
$311$	4.64457	0.263369	0.131685	+	0.991292i	$0.457961\pi$
$312$	0.0419639	0.00237574
$313$	20.8879	1.18065	0.590326	−	0.807165i	$-0.298999\pi$
$313$	20.8879	1.18065	0.590326	+	0.807165i	$0.298999\pi$
$314$	17.3079	0.976741
$315$	43.8961	2.47327
$316$	−0.334576	−0.0188214
$317$	−1.55895	−0.0875594	−0.0437797	−	0.999041i	$-0.513940\pi$
$317$	−1.55895	−0.0875594	−0.0437797	+	0.999041i	$0.513940\pi$
$318$	−0.649299	−0.0364109
$319$	19.4912	1.09130
$320$	33.9409	1.89736
$321$	−1.61040	−0.0898835
$322$	−3.48786	−0.194371
$323$	−5.35422	−0.297917
$324$	−1.27548	−0.0708597
$325$	−1.05421	−0.0584770
$326$	−25.3665	−1.40492
$327$	−1.06715	−0.0590135
$328$	7.32328	0.404361
$329$	35.1249	1.93650
$330$	−2.44350	−0.134510
$331$	−27.5922	−1.51661	−0.758303	−	0.651902i	$-0.773971\pi$
$331$	−27.5922	−1.51661	−0.758303	+	0.651902i	$0.773971\pi$
$332$	−0.848235	−0.0465530
$333$	15.9330	0.873125
$334$	−14.2626	−0.780416
$335$	33.0351	1.80490
$336$	2.03436	0.110983
$337$	16.4955	0.898570	0.449285	−	0.893389i	$-0.351679\pi$
$337$	16.4955	0.898570	0.449285	+	0.893389i	$0.351679\pi$
$338$	−17.6934	−0.962397
$339$	0.260033	0.0141230
$340$	−0.955521	−0.0518204
$341$	10.3692	0.561525
$342$	13.1646	0.711858
$343$	1.45113	0.0783535
$344$	0	0
$345$	0.414779	0.0223310
$346$	−0.835944	−0.0449406
$347$	18.6276	0.999983	0.499991	−	0.866030i	$-0.333337\pi$
$347$	18.6276	0.999983	0.499991	+	0.866030i	$0.333337\pi$
$348$	0.140660	0.00754015
$349$	5.36281	0.287065	0.143532	−	0.989646i	$-0.454154\pi$
$349$	5.36281	0.287065	0.143532	+	0.989646i	$0.454154\pi$
$350$	−55.1229	−2.94644
$351$	0.0858641	0.00458309
$352$	−2.45720	−0.130969
$353$	33.4984	1.78294	0.891470	−	0.453080i	$-0.149675\pi$
$353$	33.4984	1.78294	0.891470	+	0.453080i	$0.149675\pi$
$354$	1.43079	0.0760456
$355$	−27.5478	−1.46209
$356$	−2.27173	−0.120402
$357$	−0.909599	−0.0481411
$358$	16.0876	0.850255
$359$	22.4857	1.18675	0.593376	−	0.804925i	$-0.297795\pi$
$359$	22.4857	1.18675	0.593376	+	0.804925i	$0.297795\pi$
$360$	34.7653	1.83229
$361$	−8.46318	−0.445430
$362$	34.1896	1.79697
$363$	−0.296503	−0.0155624
$364$	−0.0513741	−0.00269273
$365$	36.7481	1.92348
$366$	−0.0577120	−0.00301665
$367$	16.3965	0.855893	0.427946	−	0.903804i	$-0.359237\pi$
$367$	16.3965	0.855893	0.427946	+	0.903804i	$0.359237\pi$
$368$	−2.56109	−0.133506
$369$	7.46422	0.388572
$370$	−29.1260	−1.51419
$371$	11.7627	0.610691
$372$	0.0748304	0.00387977
$373$	−19.7641	−1.02335	−0.511674	−	0.859180i	$-0.670974\pi$
$373$	−19.7641	−1.02335	−0.511674	+	0.859180i	$0.670974\pi$
$374$	−6.74594	−0.348824
$375$	3.56795	0.184248
$376$	27.8186	1.43463
$377$	0.623682	0.0321212
$378$	4.48969	0.230925
$379$	−35.3709	−1.81688	−0.908442	−	0.418012i	$-0.862727\pi$
$379$	−35.3709	−1.81688	−0.908442	+	0.418012i	$0.862727\pi$
$380$	1.88041	0.0964632
$381$	−3.07410	−0.157491
$382$	0.874648	0.0447509
$383$	−11.3532	−0.580123	−0.290061	−	0.957008i	$-0.593676\pi$
$383$	−11.3532	−0.580123	−0.290061	+	0.957008i	$0.593676\pi$
$384$	1.48458	0.0757596
$385$	44.2665	2.25603
$386$	−27.9121	−1.42069
$387$	0	0
$388$	−0.173577	−0.00881203
$389$	−23.1419	−1.17334	−0.586670	−	0.809826i	$-0.699562\pi$
$389$	−23.1419	−1.17334	−0.586670	+	0.809826i	$0.699562\pi$
$390$	−0.0781873	−0.00395917
$391$	1.14511	0.0579108
$392$	−19.3007	−0.974833
$393$	0.918660	0.0463403
$394$	−15.7861	−0.795290
$395$	9.22468	0.464144
$396$	−1.29604	−0.0651284
$397$	−16.9247	−0.849428	−0.424714	−	0.905328i	$-0.639625\pi$
$397$	−16.9247	−0.849428	−0.424714	+	0.905328i	$0.639625\pi$
$398$	28.3956	1.42334
$399$	1.79004	0.0896142
$400$	−40.4761	−2.02380
$401$	−5.72124	−0.285705	−0.142852	−	0.989744i	$-0.545627\pi$
$401$	−5.72124	−0.285705	−0.142852	+	0.989744i	$0.545627\pi$
$402$	1.68310	0.0839452
$403$	0.331796	0.0165279
$404$	2.16844	0.107884
$405$	35.1664	1.74743
$406$	32.6113	1.61847
$407$	16.0675	0.796436
$408$	−0.720394	−0.0356648
$409$	−12.5607	−0.621086	−0.310543	−	0.950559i	$-0.600511\pi$
$409$	−12.5607	−0.621086	−0.310543	+	0.950559i	$0.600511\pi$
$410$	−13.6448	−0.673867
$411$	1.70470	0.0840868
$412$	1.77262	0.0873307
$413$	−25.9203	−1.27545
$414$	−2.81551	−0.138375
$415$	23.3869	1.14802
$416$	−0.0786260	−0.00385496
$417$	2.27561	0.111437
$418$	13.2756	0.649333
$419$	−7.74319	−0.378280	−0.189140	−	0.981950i	$-0.560570\pi$
$419$	−7.74319	−0.378280	−0.189140	+	0.981950i	$0.560570\pi$
$420$	0.319453	0.0155877
$421$	−10.3499	−0.504421	−0.252211	−	0.967672i	$-0.581158\pi$
$421$	−10.3499	−0.504421	−0.252211	+	0.967672i	$0.581158\pi$
$422$	11.0158	0.536239
$423$	28.3540	1.37862
$424$	9.31599	0.452424
$425$	18.0976	0.877862
$426$	−1.40353	−0.0680012
$427$	1.04551	0.0505960
$428$	1.56142	0.0754742
$429$	0.0431325	0.00208245
$430$	0	0
$431$	−33.4240	−1.60998	−0.804988	−	0.593291i	$-0.797828\pi$
$431$	−33.4240	−1.60998	−0.804988	+	0.593291i	$0.797828\pi$
$432$	3.29673	0.158614
$433$	−12.5622	−0.603701	−0.301851	−	0.953355i	$-0.597604\pi$
$433$	−12.5622	−0.603701	−0.301851	+	0.953355i	$0.597604\pi$
$434$	17.3491	0.832781
$435$	−3.87816	−0.185944
$436$	1.03470	0.0495530
$437$	−2.25352	−0.107800
$438$	1.87227	0.0894606
$439$	−23.8989	−1.14063	−0.570316	−	0.821426i	$-0.693179\pi$
$439$	−23.8989	−1.14063	−0.570316	+	0.821426i	$0.693179\pi$
$440$	35.0587	1.67136
$441$	−19.6722	−0.936769
$442$	−0.215858	−0.0102673
$443$	15.5764	0.740058	0.370029	−	0.929020i	$-0.379348\pi$
$443$	15.5764	0.740058	0.370029	+	0.929020i	$0.379348\pi$
$444$	0.115952	0.00550286
$445$	62.6345	2.96916
$446$	−4.37823	−0.207315
$447$	1.91218	0.0904428
$448$	−31.3272	−1.48007
$449$	13.3440	0.629741	0.314870	−	0.949135i	$-0.398039\pi$
$449$	13.3440	0.629741	0.314870	+	0.949135i	$0.398039\pi$
$450$	−44.4970	−2.09761
$451$	7.52721	0.354442
$452$	−0.252125	−0.0118590
$453$	−2.80834	−0.131947
$454$	4.88768	0.229390
$455$	1.41645	0.0664040
$456$	1.41770	0.0663897
$457$	23.4076	1.09496	0.547481	−	0.836818i	$-0.315587\pi$
$457$	23.4076	1.09496	0.547481	+	0.836818i	$0.315587\pi$
$458$	−8.54846	−0.399443
$459$	−1.47403	−0.0688017
$460$	−0.402166	−0.0187511
$461$	−7.54626	−0.351464	−0.175732	−	0.984438i	$-0.556229\pi$
$461$	−7.54626	−0.351464	−0.175732	+	0.984438i	$0.556229\pi$
$462$	2.25532	0.104927
$463$	22.7895	1.05912	0.529558	−	0.848274i	$-0.322358\pi$
$463$	22.7895	1.05912	0.529558	+	0.848274i	$0.322358\pi$
$464$	23.9461	1.11167
$465$	−2.06317	−0.0956770
$466$	2.63094	0.121876
$467$	29.8419	1.38092	0.690458	−	0.723372i	$-0.257409\pi$
$467$	29.8419	1.38092	0.690458	+	0.723372i	$0.257409\pi$
$468$	−0.0414708	−0.00191699
$469$	−30.4911	−1.40795
$470$	−51.8316	−2.39082
$471$	1.89977	0.0875366
$472$	−20.5286	−0.944906
$473$	0	0
$474$	0.469986	0.0215872
$475$	−35.6151	−1.63413
$476$	0.881937	0.0404235
$477$	9.49528	0.434759
$478$	20.9450	0.958003
$479$	−20.3122	−0.928090	−0.464045	−	0.885812i	$-0.653602\pi$
$479$	−20.3122	−0.928090	−0.464045	+	0.885812i	$0.653602\pi$
$480$	0.488910	0.0223156
$481$	0.514130	0.0234423
$482$	3.99701	0.182059
$483$	−0.382838	−0.0174197
$484$	0.287486	0.0130676
$485$	4.78573	0.217309
$486$	5.44312	0.246905
$487$	−20.9785	−0.950626	−0.475313	−	0.879817i	$-0.657665\pi$
$487$	−20.9785	−0.950626	−0.475313	+	0.879817i	$0.657665\pi$
$488$	0.828038	0.0374835
$489$	−2.78430	−0.125910
$490$	35.9611	1.62456
$491$	−36.8398	−1.66256	−0.831278	−	0.555857i	$-0.812390\pi$
$491$	−36.8398	−1.66256	−0.831278	+	0.555857i	$0.812390\pi$
$492$	0.0543207	0.00244897
$493$	−10.7067	−0.482207
$494$	0.424796	0.0191125
$495$	35.7334	1.60610
$496$	12.7392	0.572007
$497$	25.4264	1.14053
$498$	1.19153	0.0533939
$499$	12.0099	0.537637	0.268819	−	0.963191i	$-0.413367\pi$
$499$	12.0099	0.537637	0.268819	+	0.963191i	$0.413367\pi$
$500$	−3.45945	−0.154711
$501$	−1.56551	−0.0699417
$502$	−25.6915	−1.14667
$503$	−3.96188	−0.176652	−0.0883258	−	0.996092i	$-0.528152\pi$
$503$	−3.96188	−0.176652	−0.0883258	+	0.996092i	$0.528152\pi$
$504$	−32.0881	−1.42932
$505$	−59.7866	−2.66047
$506$	−2.83927	−0.126221
$507$	−1.94209	−0.0862510
$508$	2.98062	0.132244
$509$	−38.8022	−1.71988	−0.859939	−	0.510396i	$-0.829499\pi$
$509$	−38.8022	−1.71988	−0.859939	+	0.510396i	$0.829499\pi$
$510$	1.34224	0.0594354
$511$	−33.9182	−1.50045
$512$	−24.5736	−1.08601
$513$	2.90081	0.128074
$514$	−1.38507	−0.0610929
$515$	−48.8733	−2.15361
$516$	0	0
$517$	28.5932	1.25753
$518$	26.8830	1.18117
$519$	−0.0917557	−0.00402763
$520$	1.12181	0.0491947
$521$	15.7157	0.688515	0.344258	−	0.938875i	$-0.388131\pi$
$521$	15.7157	0.688515	0.344258	+	0.938875i	$0.388131\pi$
$522$	26.3249	1.15221
$523$	−38.3640	−1.67754	−0.838771	−	0.544485i	$-0.816725\pi$
$523$	−38.3640	−1.67754	−0.838771	+	0.544485i	$0.816725\pi$
$524$	−0.890723	−0.0389114
$525$	−6.05045	−0.264063
$526$	−40.2906	−1.75675
$527$	−5.69593	−0.248119
$528$	1.65606	0.0720706
$529$	−22.5180	−0.979045
$530$	−17.3576	−0.753965
$531$	−20.9237	−0.908011
$532$	−1.73561	−0.0752480
$533$	0.240857	0.0104327
$534$	3.19115	0.138095
$535$	−43.0503	−1.86123
$536$	−24.1486	−1.04306
$537$	1.76582	0.0762008
$538$	22.3387	0.963089
$539$	−19.8382	−0.854490
$540$	0.517681	0.0222775
$541$	16.0723	0.691003	0.345501	−	0.938418i	$-0.387709\pi$
$541$	16.0723	0.691003	0.345501	+	0.938418i	$0.387709\pi$
$542$	8.26980	0.355218
$543$	3.75275	0.161046
$544$	1.34977	0.0578709
$545$	−28.5279	−1.22200
$546$	0.0721662	0.00308843
$547$	−1.61333	−0.0689810	−0.0344905	−	0.999405i	$-0.510981\pi$
$547$	−1.61333	−0.0689810	−0.0344905	+	0.999405i	$0.510981\pi$
$548$	−1.65286	−0.0706067
$549$	0.843973	0.0360199
$550$	−44.8725	−1.91337
$551$	21.0703	0.897624
$552$	−0.303204	−0.0129052
$553$	−8.51430	−0.362065
$554$	−21.8951	−0.930234
$555$	−3.19695	−0.135703
$556$	−2.20641	−0.0935727
$557$	5.06661	0.214679	0.107340	−	0.994222i	$-0.465767\pi$
$557$	5.06661	0.214679	0.107340	+	0.994222i	$0.465767\pi$
$558$	14.0047	0.592867
$559$	0	0
$560$	54.3840	2.29814
$561$	−0.740454	−0.0312620
$562$	4.93242	0.208062
$563$	10.0547	0.423757	0.211878	−	0.977296i	$-0.432042\pi$
$563$	10.0547	0.423757	0.211878	+	0.977296i	$0.432042\pi$
$564$	0.206345	0.00868870
$565$	6.95139	0.292447
$566$	−32.0077	−1.34538
$567$	−32.4583	−1.36312
$568$	20.1375	0.844950
$569$	23.2842	0.976124	0.488062	−	0.872809i	$-0.337704\pi$
$569$	23.2842	0.976124	0.488062	+	0.872809i	$0.337704\pi$
$570$	−2.64146	−0.110638
$571$	3.30299	0.138226	0.0691129	−	0.997609i	$-0.477983\pi$
$571$	3.30299	0.138226	0.0691129	+	0.997609i	$0.477983\pi$
$572$	−0.0418208	−0.00174861
$573$	0.0960040	0.00401062
$574$	12.5940	0.525663
$575$	7.61703	0.317652
$576$	−25.2883	−1.05368
$577$	−17.9484	−0.747203	−0.373601	−	0.927589i	$-0.621877\pi$
$577$	−17.9484	−0.747203	−0.373601	+	0.927589i	$0.621877\pi$
$578$	−19.4484	−0.808947
$579$	−3.06372	−0.127324
$580$	3.76023	0.156135
$581$	−21.5859	−0.895534
$582$	0.243827	0.0101069
$583$	9.57540	0.396573
$584$	−26.8629	−1.11159
$585$	1.14340	0.0472739
$586$	29.1544	1.20436
$587$	−26.3793	−1.08879	−0.544396	−	0.838828i	$-0.683241\pi$
$587$	−26.3793	−1.08879	−0.544396	+	0.838828i	$0.683241\pi$
$588$	−0.143164	−0.00590397
$589$	11.2093	0.461871
$590$	38.2490	1.57468
$591$	−1.73272	−0.0712747
$592$	19.7399	0.811303
$593$	33.2362	1.36485	0.682423	−	0.730957i	$-0.260926\pi$
$593$	33.2362	1.36485	0.682423	+	0.730957i	$0.260926\pi$
$594$	3.65481	0.149959
$595$	−24.3161	−0.996863
$596$	−1.85403	−0.0759438
$597$	3.11678	0.127561
$598$	−0.0908515	−0.00371519
$599$	−16.8959	−0.690348	−0.345174	−	0.938539i	$-0.612180\pi$
$599$	−16.8959	−0.690348	−0.345174	+	0.938539i	$0.612180\pi$
$600$	−4.79190	−0.195628
$601$	28.4356	1.15991	0.579956	−	0.814648i	$-0.303070\pi$
$601$	28.4356	1.15991	0.579956	+	0.814648i	$0.303070\pi$
$602$	0	0
$603$	−24.6134	−1.00233
$604$	2.72294	0.110795
$605$	−7.92635	−0.322252
$606$	−3.04606	−0.123738
$607$	11.6409	0.472489	0.236245	−	0.971694i	$-0.424083\pi$
$607$	11.6409	0.472489	0.236245	+	0.971694i	$0.424083\pi$
$608$	−2.65628	−0.107726
$609$	3.57951	0.145049
$610$	−1.54280	−0.0624662
$611$	0.914930	0.0370141
$612$	0.711929	0.0287780
$613$	−32.9560	−1.33108	−0.665541	−	0.746361i	$-0.731799\pi$
$613$	−32.9560	−1.33108	−0.665541	+	0.746361i	$0.731799\pi$
$614$	−13.7045	−0.553070
$615$	−1.49769	−0.0603926
$616$	−32.3588	−1.30377
$617$	−30.4527	−1.22598	−0.612990	−	0.790091i	$-0.710033\pi$
$617$	−30.4527	−1.22598	−0.612990	+	0.790091i	$0.710033\pi$
$618$	−2.49003	−0.100164
$619$	42.7298	1.71746	0.858728	−	0.512431i	$-0.171255\pi$
$619$	42.7298	1.71746	0.858728	+	0.512431i	$0.171255\pi$
$620$	2.00042	0.0803389
$621$	−0.620398	−0.0248957
$622$	6.32591	0.253646
$623$	−57.8111	−2.31615
$624$	0.0529908	0.00212133
$625$	40.5220	1.62088
$626$	28.4493	1.13706
$627$	1.45717	0.0581939
$628$	−1.84199	−0.0735035
$629$	−8.82606	−0.351918
$630$	59.7866	2.38195
$631$	5.74867	0.228851	0.114425	−	0.993432i	$-0.463497\pi$
$631$	5.74867	0.228851	0.114425	+	0.993432i	$0.463497\pi$
$632$	−6.74325	−0.268232
$633$	1.20912	0.0480583
$634$	−2.12329	−0.0843268
$635$	−82.1793	−3.26119
$636$	0.0691017	0.00274006
$637$	−0.634784	−0.0251511
$638$	26.5470	1.05101
$639$	20.5250	0.811958
$640$	39.6869	1.56876
$641$	−7.80317	−0.308207	−0.154103	−	0.988055i	$-0.549249\pi$
$641$	−7.80317	−0.308207	−0.154103	+	0.988055i	$0.549249\pi$
$642$	−2.19336	−0.0865651
$643$	18.3112	0.722123	0.361062	−	0.932542i	$-0.382414\pi$
$643$	18.3112	0.722123	0.361062	+	0.932542i	$0.382414\pi$
$644$	0.371195	0.0146271
$645$	0	0
$646$	−7.29246	−0.286918
$647$	−11.5035	−0.452251	−0.226125	−	0.974098i	$-0.572606\pi$
$647$	−11.5035	−0.452251	−0.226125	+	0.974098i	$0.572606\pi$
$648$	−25.7067	−1.00985
$649$	−21.1002	−0.828257
$650$	−1.43584	−0.0563181
$651$	1.90428	0.0746347
$652$	2.69963	0.105726
$653$	24.8615	0.972905	0.486453	−	0.873707i	$-0.338291\pi$
$653$	24.8615	0.972905	0.486453	+	0.873707i	$0.338291\pi$
$654$	−1.45346	−0.0568348
$655$	24.5583	0.959573
$656$	9.24762	0.361059
$657$	−27.3799	−1.06819
$658$	47.8401	1.86500
$659$	19.1936	0.747676	0.373838	−	0.927494i	$-0.378042\pi$
$659$	19.1936	0.747676	0.373838	+	0.927494i	$0.378042\pi$
$660$	0.260049	0.0101224
$661$	3.36075	0.130718	0.0653591	−	0.997862i	$-0.479181\pi$
$661$	3.36075	0.130718	0.0653591	+	0.997862i	$0.479181\pi$
$662$	−37.5807	−1.46061
$663$	−0.0236932	−0.000920166 0
$664$	−17.0958	−0.663447
$665$	47.8528	1.85565
$666$	21.7008	0.840890
$667$	−4.50632	−0.174485
$668$	1.51790	0.0587293
$669$	−0.480567	−0.0185798
$670$	44.9938	1.73826
$671$	0.851095	0.0328562
$672$	−0.451260	−0.0174077
$673$	−30.3659	−1.17052	−0.585261	−	0.810845i	$-0.699008\pi$
$673$	−30.3659	−1.17052	−0.585261	+	0.810845i	$0.699008\pi$
$674$	22.4670	0.865395
$675$	−9.80490	−0.377391
$676$	1.88303	0.0724240
$677$	13.9894	0.537657	0.268829	−	0.963188i	$-0.413364\pi$
$677$	13.9894	0.537657	0.268829	+	0.963188i	$0.413364\pi$
$678$	0.354165	0.0136016
$679$	−4.41718	−0.169516
$680$	−19.2581	−0.738516
$681$	0.536486	0.0205582
$682$	14.1229	0.540794
$683$	−0.0759021	−0.00290431	−0.00145216	−	0.999999i	$-0.500462\pi$
$683$	−0.0759021	−0.00290431	−0.00145216	+	0.999999i	$0.500462\pi$
$684$	−1.40104	−0.0535700
$685$	45.5714	1.74119
$686$	1.97644	0.0754608
$687$	−0.938304	−0.0357985
$688$	0	0
$689$	0.306395	0.0116727
$690$	0.564930	0.0215065
$691$	18.3671	0.698716	0.349358	−	0.936989i	$-0.386400\pi$
$691$	18.3671	0.698716	0.349358	+	0.936989i	$0.386400\pi$
$692$	0.0889654	0.00338196
$693$	−32.9816	−1.25287
$694$	25.3708	0.963064
$695$	60.8335	2.30754
$696$	2.83494	0.107458
$697$	−4.13478	−0.156616
$698$	7.30416	0.276466
$699$	0.288780	0.0109227
$700$	5.86645	0.221731
$701$	−47.1374	−1.78035	−0.890177	−	0.455615i	$-0.849419\pi$
$701$	−47.1374	−1.78035	−0.890177	+	0.455615i	$0.849419\pi$
$702$	0.116947	0.00441388
$703$	17.3692	0.655092
$704$	−25.5017	−0.961132
$705$	−5.68919	−0.214267
$706$	45.6249	1.71712
$707$	55.1825	2.07535
$708$	−0.152272	−0.00572272
$709$	−11.8697	−0.445775	−0.222888	−	0.974844i	$-0.571548\pi$
$709$	−11.8697	−0.445775	−0.222888	+	0.974844i	$0.571548\pi$
$710$	−37.5202	−1.40811
$711$	−6.87302	−0.257759
$712$	−45.7859	−1.71590
$713$	−2.39734	−0.0897811
$714$	−1.23888	−0.0463637
$715$	1.15305	0.0431216
$716$	−1.71212	−0.0639850
$717$	2.29899	0.0858572
$718$	30.6256	1.14294
$719$	−15.1572	−0.565269	−0.282634	−	0.959228i	$-0.591208\pi$
$719$	−15.1572	−0.565269	−0.282634	+	0.959228i	$0.591208\pi$
$720$	43.9006	1.63608
$721$	45.1096	1.67997
$722$	−11.5269	−0.428985
$723$	0.438723	0.0163163
$724$	−3.63863	−0.135229
$725$	−71.2188	−2.64500
$726$	−0.403838	−0.0149878
$727$	47.0803	1.74611	0.873056	−	0.487620i	$-0.162135\pi$
$727$	47.0803	1.74611	0.873056	+	0.487620i	$0.162135\pi$
$728$	−1.03542	−0.0383753
$729$	−25.8006	−0.955578
$730$	50.0510	1.85247
$731$	0	0
$732$	0.00614200	0.000227015 0
$733$	32.2221	1.19015	0.595075	−	0.803670i	$-0.297122\pi$
$733$	32.2221	1.19015	0.595075	+	0.803670i	$0.297122\pi$
$734$	22.3321	0.824294
$735$	3.94720	0.145595
$736$	0.568100	0.0209404
$737$	−24.8211	−0.914296
$738$	10.1663	0.374226
$739$	10.7278	0.394628	0.197314	−	0.980340i	$-0.436778\pi$
$739$	10.7278	0.394628	0.197314	+	0.980340i	$0.436778\pi$
$740$	3.09973	0.113948
$741$	0.0466269	0.00171288
$742$	16.0209	0.588145
$743$	35.8364	1.31471	0.657355	−	0.753581i	$-0.271675\pi$
$743$	35.8364	1.31471	0.657355	+	0.753581i	$0.271675\pi$
$744$	1.50817	0.0552924
$745$	51.1178	1.87281
$746$	−26.9188	−0.985567
$747$	−17.4248	−0.637542
$748$	0.717936	0.0262503
$749$	39.7351	1.45189
$750$	4.85955	0.177446
$751$	31.6920	1.15646	0.578229	−	0.815875i	$-0.303744\pi$
$751$	31.6920	1.15646	0.578229	+	0.815875i	$0.303744\pi$
$752$	35.1284	1.28100
$753$	−2.81998	−0.102766
$754$	0.849456	0.0309354
$755$	−75.0747	−2.73225
$756$	−0.477815	−0.0173780
$757$	11.4389	0.415752	0.207876	−	0.978155i	$-0.433345\pi$
$757$	11.4389	0.415752	0.207876	+	0.978155i	$0.433345\pi$
$758$	−48.1753	−1.74981
$759$	−0.311647	−0.0113121
$760$	37.8990	1.37474
$761$	−35.7779	−1.29695	−0.648475	−	0.761236i	$-0.724593\pi$
$761$	−35.7779	−1.29695	−0.648475	+	0.761236i	$0.724593\pi$
$762$	−4.18693	−0.151677
$763$	26.3310	0.953245
$764$	−0.0930844	−0.00336768
$765$	−19.6288	−0.709679
$766$	−15.4631	−0.558705
$767$	−0.675169	−0.0243789
$768$	−0.517277	−0.0186656
$769$	−21.0006	−0.757302	−0.378651	−	0.925539i	$-0.623612\pi$
$769$	−21.0006	−0.757302	−0.378651	+	0.925539i	$0.623612\pi$
$770$	60.2911	2.17274
$771$	−0.152030	−0.00547521
$772$	2.97055	0.106912
$773$	−12.8725	−0.462992	−0.231496	−	0.972836i	$-0.574362\pi$
$773$	−12.8725	−0.462992	−0.231496	+	0.972836i	$0.574362\pi$
$774$	0	0
$775$	−37.8881	−1.36098
$776$	−3.49837	−0.125584
$777$	2.95076	0.105858
$778$	−31.5193	−1.13002
$779$	8.13703	0.291539
$780$	0.00832108	0.000297943 0
$781$	20.6982	0.740641
$782$	1.55964	0.0557728
$783$	5.80068	0.207300
$784$	−24.3723	−0.870441
$785$	50.7860	1.81263
$786$	1.25122	0.0446294
$787$	32.4115	1.15535	0.577673	−	0.816268i	$-0.303961\pi$
$787$	32.4115	1.15535	0.577673	+	0.816268i	$0.303961\pi$
$788$	1.68003	0.0598486
$789$	−4.42241	−0.157442
$790$	12.5640	0.447008
$791$	−6.41607	−0.228129
$792$	−26.1211	−0.928174
$793$	0.0272335	0.000967089 0
$794$	−23.0515	−0.818068
$795$	−1.90522	−0.0675711
$796$	−3.02200	−0.107112
$797$	−48.1828	−1.70672	−0.853361	−	0.521320i	$-0.825440\pi$
$797$	−48.1828	−1.70672	−0.853361	+	0.521320i	$0.825440\pi$
$798$	2.43804	0.0863057
$799$	−15.7066	−0.555659
$800$	8.97837	0.317433
$801$	−46.6670	−1.64890
$802$	−7.79233	−0.275157
$803$	−27.6109	−0.974368
$804$	−0.179123	−0.00631720
$805$	−10.2343	−0.360712
$806$	0.451907	0.0159177
$807$	2.45196	0.0863131
$808$	43.7041	1.53750
$809$	−27.9088	−0.981223	−0.490611	−	0.871378i	$-0.663227\pi$
$809$	−27.9088	−0.981223	−0.490611	+	0.871378i	$0.663227\pi$
$810$	47.8967	1.68292
$811$	−24.3363	−0.854563	−0.427281	−	0.904119i	$-0.640529\pi$
$811$	−24.3363	−0.854563	−0.427281	+	0.904119i	$0.640529\pi$
$812$	−3.47065	−0.121796
$813$	0.907718	0.0318350
$814$	21.8839	0.767032
$815$	−74.4320	−2.60724
$816$	−0.909691	−0.0318456
$817$	0	0
$818$	−17.1077	−0.598156
$819$	−1.05535	−0.0368769
$820$	1.45214	0.0507110
$821$	0.193942	0.00676863	0.00338431	−	0.999994i	$-0.498923\pi$
$821$	0.193942	0.00676863	0.00338431	+	0.999994i	$0.498923\pi$
$822$	2.32181	0.0809823
$823$	5.64777	0.196869	0.0984345	−	0.995144i	$-0.468617\pi$
$823$	5.64777	0.196869	0.0984345	+	0.995144i	$0.468617\pi$
$824$	35.7264	1.24459
$825$	−4.92533	−0.171478
$826$	−35.3034	−1.22836
$827$	−17.5913	−0.611710	−0.305855	−	0.952078i	$-0.598942\pi$
$827$	−17.5913	−0.611710	−0.305855	+	0.952078i	$0.598942\pi$
$828$	0.299641	0.0104132
$829$	−31.9473	−1.10957	−0.554787	−	0.831992i	$-0.687200\pi$
$829$	−31.9473	−1.10957	−0.554787	+	0.831992i	$0.687200\pi$
$830$	31.8530	1.10563
$831$	−2.40327	−0.0833686
$832$	−0.816008	−0.0282900
$833$	10.8973	0.377570
$834$	3.09939	0.107323
$835$	−41.8504	−1.44829
$836$	−1.41286	−0.0488648
$837$	3.08594	0.106666
$838$	−10.5462	−0.364314
$839$	37.1144	1.28133	0.640665	−	0.767821i	$-0.278659\pi$
$839$	37.1144	1.28133	0.640665	+	0.767821i	$0.278659\pi$
$840$	6.43844	0.222147
$841$	13.1338	0.452889
$842$	−14.0965	−0.485798
$843$	0.541397	0.0186467
$844$	−1.17235	−0.0403541
$845$	−51.9173	−1.78601
$846$	38.6181	1.32772
$847$	7.31595	0.251379
$848$	11.7639	0.403975
$849$	−3.51326	−0.120575
$850$	24.6490	0.845452
$851$	−3.71477	−0.127341
$852$	0.149371	0.00511735
$853$	15.3643	0.526065	0.263033	−	0.964787i	$-0.415277\pi$
$853$	15.3643	0.526065	0.263033	+	0.964787i	$0.415277\pi$
$854$	1.42399	0.0487280
$855$	38.6283	1.32106
$856$	31.4698	1.07562
$857$	17.7539	0.606461	0.303231	−	0.952917i	$-0.401935\pi$
$857$	17.7539	0.606461	0.303231	+	0.952917i	$0.401935\pi$
$858$	0.0587465	0.00200557
$859$	51.4177	1.75435	0.877175	−	0.480172i	$-0.159426\pi$
$859$	51.4177	1.75435	0.877175	+	0.480172i	$0.159426\pi$
$860$	0	0
$861$	1.38235	0.0471105
$862$	−45.5235	−1.55054
$863$	−18.1983	−0.619477	−0.309738	−	0.950822i	$-0.600241\pi$
$863$	−18.1983	−0.619477	−0.309738	+	0.950822i	$0.600241\pi$
$864$	−0.731278	−0.0248786
$865$	−2.45288	−0.0834006
$866$	−17.1098	−0.581413
$867$	−2.13471	−0.0724987
$868$	−1.84637	−0.0626700
$869$	−6.93102	−0.235119
$870$	−5.28206	−0.179079
$871$	−0.794229	−0.0269114
$872$	20.8539	0.706202
$873$	−3.56570	−0.120681
$874$	−3.06930	−0.103821
$875$	−88.0359	−2.97616
$876$	−0.199256	−0.00673225
$877$	−24.6836	−0.833505	−0.416752	−	0.909020i	$-0.636832\pi$
$877$	−24.6836	−0.833505	−0.416752	+	0.909020i	$0.636832\pi$
$878$	−32.5503	−1.09852
$879$	3.20007	0.107936
$880$	44.2710	1.49237
$881$	11.1686	0.376280	0.188140	−	0.982142i	$-0.439754\pi$
$881$	11.1686	0.376280	0.188140	+	0.982142i	$0.439754\pi$
$882$	−26.7935	−0.902184
$883$	−42.8540	−1.44215	−0.721075	−	0.692857i	$-0.756352\pi$
$883$	−42.8540	−1.44215	−0.721075	+	0.692857i	$0.756352\pi$
$884$	0.0229726	0.000772653 0
$885$	4.19832	0.141125
$886$	21.2151	0.712735
$887$	−9.29942	−0.312244	−0.156122	−	0.987738i	$-0.549899\pi$
$887$	−9.29942	−0.312244	−0.156122	+	0.987738i	$0.549899\pi$
$888$	2.33697	0.0784236
$889$	75.8508	2.54395
$890$	85.3083	2.85954
$891$	−26.4225	−0.885187
$892$	0.465953	0.0156013
$893$	30.9097	1.03435
$894$	2.60439	0.0871037
$895$	47.2053	1.57790
$896$	−36.6307	−1.22374
$897$	−0.00997212	−0.000332960 0
$898$	18.1745	0.606491
$899$	22.4150	0.747582
$900$	4.73559	0.157853
$901$	−5.25988	−0.175232
$902$	10.2521	0.341357
$903$	0	0
$904$	−5.08147	−0.169007
$905$	100.321	3.33480
$906$	−3.82496	−0.127076
$907$	7.20123	0.239113	0.119556	−	0.992827i	$-0.461853\pi$
$907$	7.20123	0.239113	0.119556	+	0.992827i	$0.461853\pi$
$908$	−0.520171	−0.0172625
$909$	44.5452	1.47747
$910$	1.92920	0.0639524
$911$	−51.9215	−1.72024	−0.860118	−	0.510096i	$-0.829610\pi$
$911$	−51.9215	−1.72024	−0.860118	+	0.510096i	$0.829610\pi$
$912$	1.79022	0.0592802
$913$	−17.5719	−0.581544
$914$	31.8812	1.05454
$915$	−0.169342	−0.00559829
$916$	0.909770	0.0300596
$917$	−22.6671	−0.748534
$918$	−2.00763	−0.0662616
$919$	−21.8800	−0.721755	−0.360877	−	0.932613i	$-0.617523\pi$
$919$	−21.8800	−0.721755	−0.360877	+	0.932613i	$0.617523\pi$
$920$	−8.10548	−0.267230
$921$	−1.50425	−0.0495667
$922$	−10.2780	−0.338488
$923$	0.662305	0.0218000
$924$	−0.240023	−0.00789617
$925$	−58.7089	−1.93034
$926$	31.0393	1.02001
$927$	36.4140	1.19599
$928$	−5.31170	−0.174365
$929$	−23.7570	−0.779443	−0.389722	−	0.920933i	$-0.627429\pi$
$929$	−23.7570	−0.779443	−0.389722	+	0.920933i	$0.627429\pi$
$930$	−2.81004	−0.0921447
$931$	−21.4453	−0.702843
$932$	−0.279998	−0.00917163
$933$	0.694351	0.0227320
$934$	40.6447	1.32993
$935$	−19.7944	−0.647346
$936$	−0.835828	−0.0273199
$937$	−42.0621	−1.37411	−0.687054	−	0.726606i	$-0.741096\pi$
$937$	−42.0621	−1.37411	−0.687054	+	0.726606i	$0.741096\pi$
$938$	−41.5289	−1.35597
$939$	3.12268	0.101905
$940$	5.51618	0.179918
$941$	−28.9925	−0.945129	−0.472565	−	0.881296i	$-0.656672\pi$
$941$	−28.9925	−0.945129	−0.472565	+	0.881296i	$0.656672\pi$
$942$	2.58748	0.0843048
$943$	−1.74027	−0.0566711
$944$	−25.9229	−0.843718
$945$	13.1740	0.428549
$946$	0	0
$947$	11.1970	0.363854	0.181927	−	0.983312i	$-0.441767\pi$
$947$	11.1970	0.363854	0.181927	+	0.983312i	$0.441767\pi$
$948$	−0.0500183	−0.00162452
$949$	−0.883498	−0.0286796
$950$	−48.5078	−1.57380
$951$	−0.233059	−0.00755746
$952$	17.7751	0.576094
$953$	5.29221	0.171431	0.0857157	−	0.996320i	$-0.472682\pi$
$953$	5.29221	0.171431	0.0857157	+	0.996320i	$0.472682\pi$
$954$	12.9326	0.418708
$955$	2.56645	0.0830485
$956$	−2.22907	−0.0720934
$957$	2.91388	0.0941923
$958$	−27.6653	−0.893825
$959$	−42.0620	−1.35825
$960$	5.07408	0.163765
$961$	−19.0753	−0.615333
$962$	0.700246	0.0225768
$963$	32.0755	1.03362
$964$	−0.425381	−0.0137006
$965$	−81.9017	−2.63651
$966$	−0.521426	−0.0167766
$967$	−9.29771	−0.298994	−0.149497	−	0.988762i	$-0.547765\pi$
$967$	−9.29771	−0.298994	−0.149497	+	0.988762i	$0.547765\pi$
$968$	5.79417	0.186232
$969$	−0.800442	−0.0257139
$970$	6.51817	0.209286
$971$	0.731911	0.0234881	0.0117441	−	0.999931i	$-0.496262\pi$
$971$	0.731911	0.0234881	0.0117441	+	0.999931i	$0.496262\pi$
$972$	−0.579283	−0.0185805
$973$	−56.1487	−1.80005
$974$	−28.5727	−0.915530
$975$	−0.157602	−0.00504729
$976$	1.04562	0.0334695
$977$	−20.0256	−0.640675	−0.320338	−	0.947303i	$-0.603796\pi$
$977$	−20.0256	−0.640675	−0.320338	+	0.947303i	$0.603796\pi$
$978$	−3.79222	−0.121262
$979$	−47.0608	−1.50407
$980$	−3.82716	−0.122254
$981$	21.2552	0.678627
$982$	−50.1759	−1.60118
$983$	−29.4397	−0.938982	−0.469491	−	0.882937i	$-0.655562\pi$
$983$	−29.4397	−0.938982	−0.469491	+	0.882937i	$0.655562\pi$
$984$	1.09481	0.0349013
$985$	−46.3205	−1.47589
$986$	−14.5826	−0.464404
$987$	5.25107	0.167144
$988$	−0.0452089	−0.00143829
$989$	0	0
$990$	48.6689	1.54680
$991$	−44.8944	−1.42612	−0.713058	−	0.701105i	$-0.752691\pi$
$991$	−44.8944	−1.42612	−0.713058	+	0.701105i	$0.752691\pi$
$992$	−2.82580	−0.0897193
$993$	−4.12497	−0.130902
$994$	34.6308	1.09842
$995$	83.3203	2.64143
$996$	−0.126809	−0.00401809
$997$	4.57412	0.144864	0.0724319	−	0.997373i	$-0.476924\pi$
$997$	4.57412	0.144864	0.0724319	+	0.997373i	$0.476924\pi$
$998$	16.3575	0.517788
$999$	4.78177	0.151289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.q.1.15	yes	20
43.42	odd	2	inner	1849.2.a.q.1.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.q.1.6	✓	20	43.42	odd	2	inner
1849.2.a.q.1.15	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.36200 q^{2} +0.149497 q^{3} -0.144951 q^{4} +3.99648 q^{5} +0.203616 q^{6} -3.68871 q^{7} -2.92143 q^{8} -2.97765 q^{9} +O(q^{10})\)	\(q+1.36200 q^{2} +0.149497 q^{3} -0.144951 q^{4} +3.99648 q^{5} +0.203616 q^{6} -3.68871 q^{7} -2.92143 q^{8} -2.97765 q^{9} +5.44321 q^{10} -3.00278 q^{11} -0.0216698 q^{12} -0.0960833 q^{13} -5.02403 q^{14} +0.597463 q^{15} -3.68909 q^{16} +1.64946 q^{17} -4.05557 q^{18} -3.24605 q^{19} -0.579294 q^{20} -0.551453 q^{21} -4.08979 q^{22} +0.694235 q^{23} -0.436746 q^{24} +10.9718 q^{25} -0.130866 q^{26} -0.893643 q^{27} +0.534683 q^{28} -6.49105 q^{29} +0.813745 q^{30} -3.45321 q^{31} +0.818311 q^{32} -0.448907 q^{33} +2.24657 q^{34} -14.7419 q^{35} +0.431613 q^{36} -5.35088 q^{37} -4.42112 q^{38} -0.0143642 q^{39} -11.6754 q^{40} -2.50675 q^{41} -0.751080 q^{42} +0.435255 q^{44} -11.9001 q^{45} +0.945549 q^{46} -9.52226 q^{47} -0.551509 q^{48} +6.60660 q^{49} +14.9437 q^{50} +0.246590 q^{51} +0.0139274 q^{52} -3.18885 q^{53} -1.21714 q^{54} -12.0005 q^{55} +10.7763 q^{56} -0.485275 q^{57} -8.84083 q^{58} +7.02691 q^{59} -0.0866028 q^{60} -0.283436 q^{61} -4.70328 q^{62} +10.9837 q^{63} +8.49272 q^{64} -0.383995 q^{65} -0.611412 q^{66} +8.26604 q^{67} -0.239091 q^{68} +0.103786 q^{69} -20.0784 q^{70} -6.89303 q^{71} +8.69899 q^{72} +9.19513 q^{73} -7.28791 q^{74} +1.64026 q^{75} +0.470518 q^{76} +11.0764 q^{77} -0.0195641 q^{78} +2.30820 q^{79} -14.7434 q^{80} +8.79935 q^{81} -3.41420 q^{82} +5.85188 q^{83} +0.0799336 q^{84} +6.59203 q^{85} -0.970395 q^{87} +8.77239 q^{88} +15.6724 q^{89} -16.2080 q^{90} +0.354424 q^{91} -0.100630 q^{92} -0.516246 q^{93} -12.9693 q^{94} -12.9728 q^{95} +0.122335 q^{96} +1.19749 q^{97} +8.99821 q^{98} +8.94122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9}+O(q^{10}) \) 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9	\( 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9} + 12 q^{10} - 20 q^{11} + 6 q^{13} - 34 q^{14} - 34 q^{15} + 14 q^{16} - 8 q^{17} + 12 q^{21} - 46 q^{23} + 2 q^{24} + 20 q^{25} - 38 q^{31} - 76 q^{35} - 46 q^{36} - 68 q^{38} - 64 q^{40} - 56 q^{41} - 58 q^{44} - 24 q^{47} - 20 q^{49} - 20 q^{52} - 42 q^{53} + 66 q^{54} - 46 q^{56} + 2 q^{57} + 12 q^{58} - 90 q^{59} + 18 q^{60} - 28 q^{64} + 76 q^{66} - 62 q^{67} - 54 q^{68} + 24 q^{74} - 36 q^{78} - 10 q^{79} - 48 q^{81} - 68 q^{83} + 70 q^{84} - 12 q^{87} + 58 q^{90} - 8 q^{92} - 42 q^{95} - 22 q^{96} - 44 q^{97} - 38 q^{99}+O(q^{100}) \) 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9 + 12 * q^10 - 20 * q^11 + 6 * q^13 - 34 * q^14 - 34 * q^15 + 14 * q^16 - 8 * q^17 + 12 * q^21 - 46 * q^23 + 2 * q^24 + 20 * q^25 - 38 * q^31 - 76 * q^35 - 46 * q^36 - 68 * q^38 - 64 * q^40 - 56 * q^41 - 58 * q^44 - 24 * q^47 - 20 * q^49 - 20 * q^52 - 42 * q^53 + 66 * q^54 - 46 * q^56 + 2 * q^57 + 12 * q^58 - 90 * q^59 + 18 * q^60 - 28 * q^64 + 76 * q^66 - 62 * q^67 - 54 * q^68 + 24 * q^74 - 36 * q^78 - 10 * q^79 - 48 * q^81 - 68 * q^83 + 70 * q^84 - 12 * q^87 + 58 * q^90 - 8 * q^92 - 42 * q^95 - 22 * q^96 - 44 * q^97 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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