LMFDB - Embedded newform 483.2.a.j.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(1,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("483.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,2,-4,4,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.15317.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 2 $ x^4 - 2x^3 - 4x^2 + 5*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.69353$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.69353 q^{2} -1.00000 q^{3} +5.25508 q^{4} +1.04900 q^{5} -2.69353 q^{6} -1.00000 q^{7} +8.76763 q^{8} +1.00000 q^{9} +2.82550 q^{10} +0.180969 q^{11} -5.25508 q^{12} -4.89961 q^{13} -2.69353 q^{14} -1.04900 q^{15} +13.1057 q^{16} +2.82550 q^{17} +2.69353 q^{18} -0.180969 q^{19} +5.51256 q^{20} +1.00000 q^{21} +0.487443 q^{22} +1.00000 q^{23} -8.76763 q^{24} -3.89961 q^{25} -13.1972 q^{26} -1.00000 q^{27} -5.25508 q^{28} -5.68466 q^{29} -2.82550 q^{30} -0.825498 q^{31} +17.7652 q^{32} -0.180969 q^{33} +7.61055 q^{34} -1.04900 q^{35} +5.25508 q^{36} +6.46356 q^{37} -0.487443 q^{38} +4.89961 q^{39} +9.19722 q^{40} -3.47003 q^{41} +2.69353 q^{42} +0.125506 q^{43} +0.951004 q^{44} +1.04900 q^{45} +2.69353 q^{46} -12.0316 q^{47} -13.1057 q^{48} +1.00000 q^{49} -10.5037 q^{50} -2.82550 q^{51} -25.7478 q^{52} +8.55269 q^{53} -2.69353 q^{54} +0.189835 q^{55} -8.76763 q^{56} +0.180969 q^{57} -15.3118 q^{58} -4.30647 q^{59} -5.51256 q^{60} +9.01625 q^{61} -2.22350 q^{62} -1.00000 q^{63} +21.6397 q^{64} -5.13967 q^{65} -0.487443 q^{66} -15.7074 q^{67} +14.8482 q^{68} -1.00000 q^{69} -2.82550 q^{70} -2.22350 q^{71} +8.76763 q^{72} +13.0717 q^{73} +17.4098 q^{74} +3.89961 q^{75} -0.951004 q^{76} -0.180969 q^{77} +13.1972 q^{78} -16.1948 q^{79} +13.7478 q^{80} +1.00000 q^{81} -9.34660 q^{82} +10.8757 q^{83} +5.25508 q^{84} +2.96394 q^{85} +0.338054 q^{86} +5.68466 q^{87} +1.58667 q^{88} -14.7466 q^{89} +2.82550 q^{90} +4.89961 q^{91} +5.25508 q^{92} +0.825498 q^{93} -32.4074 q^{94} -0.189835 q^{95} -17.7652 q^{96} +10.4636 q^{97} +2.69353 q^{98} +0.180969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{3} + 4 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} + 4 q^{9} + 2 q^{10} + q^{11} - 4 q^{12} + 7 q^{13} - 2 q^{14} - 5 q^{15} + 8 q^{16} + 2 q^{17} + 2 q^{18} - q^{19} + 13 q^{20}+ \cdots + q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 + 4 * q^9 + 2 * q^10 + q^11 - 4 * q^12 + 7 * q^13 - 2 * q^14 - 5 * q^15 + 8 * q^16 + 2 * q^17 + 2 * q^18 - q^19 + 13 * q^20 + 4 * q^21 + 11 * q^22 + 4 * q^23 - 9 * q^24 + 11 * q^25 - 19 * q^26 - 4 * q^27 - 4 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 20 * q^32 - q^33 + 23 * q^34 - 5 * q^35 + 4 * q^36 + 16 * q^37 - 11 * q^38 - 7 * q^39 + 3 * q^40 + 5 * q^41 + 2 * q^42 + 9 * q^43 + 3 * q^44 + 5 * q^45 + 2 * q^46 - 21 * q^47 - 8 * q^48 + 4 * q^49 - 17 * q^50 - 2 * q^51 - 24 * q^52 + 10 * q^53 - 2 * q^54 + 17 * q^55 - 9 * q^56 + q^57 + q^58 - 26 * q^59 - 13 * q^60 + 2 * q^61 - 19 * q^62 - 4 * q^63 + 27 * q^64 + 26 * q^65 - 11 * q^66 + 5 * q^67 + 7 * q^68 - 4 * q^69 - 2 * q^70 - 19 * q^71 + 9 * q^72 + 10 * q^73 + 9 * q^74 - 11 * q^75 - 3 * q^76 - q^77 + 19 * q^78 - 6 * q^79 - 24 * q^80 + 4 * q^81 - 31 * q^82 - 2 * q^83 + 4 * q^84 - 7 * q^85 - 17 * q^86 - 2 * q^87 - 20 * q^88 - 17 * q^89 + 2 * q^90 - 7 * q^91 + 4 * q^92 - 6 * q^93 - 44 * q^94 - 17 * q^95 - 20 * q^96 + 32 * q^97 + 2 * q^98 + q^99

Coefficient data

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

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

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

$2$	2.69353	1.90461	0.952305	−	0.305148i	$-0.0987059\pi$
$2$	2.69353	1.90461	0.952305	+	0.305148i	$0.0987059\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.25508	2.62754
$5$	1.04900	0.469125	0.234563	−	0.972101i	$-0.424634\pi$
$5$	1.04900	0.469125	0.234563	+	0.972101i	$0.424634\pi$
$6$	−2.69353	−1.09963
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	8.76763	3.09983
$9$	1.00000	0.333333
$10$	2.82550	0.893501
$11$	0.180969	0.0545641	0.0272820	−	0.999628i	$-0.491315\pi$
$11$	0.180969	0.0545641	0.0272820	+	0.999628i	$0.491315\pi$
$12$	−5.25508	−1.51701
$13$	−4.89961	−1.35891	−0.679453	−	0.733719i	$-0.737783\pi$
$13$	−4.89961	−1.35891	−0.679453	+	0.733719i	$0.737783\pi$
$14$	−2.69353	−0.719875
$15$	−1.04900	−0.270850
$16$	13.1057	3.27642
$17$	2.82550	0.685284	0.342642	−	0.939466i	$-0.388678\pi$
$17$	2.82550	0.685284	0.342642	+	0.939466i	$0.388678\pi$
$18$	2.69353	0.634870
$19$	−0.180969	−0.0415170	−0.0207585	−	0.999785i	$-0.506608\pi$
$19$	−0.180969	−0.0415170	−0.0207585	+	0.999785i	$0.506608\pi$
$20$	5.51256	1.23265
$21$	1.00000	0.218218
$22$	0.487443	0.103923
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−8.76763	−1.78969
$25$	−3.89961	−0.779921
$26$	−13.1972	−2.58819
$27$	−1.00000	−0.192450
$28$	−5.25508	−0.993116
$29$	−5.68466	−1.05561	−0.527807	−	0.849364i	$-0.676986\pi$
$29$	−5.68466	−1.05561	−0.527807	+	0.849364i	$0.676986\pi$
$30$	−2.82550	−0.515863
$31$	−0.825498	−0.148264	−0.0741319	−	0.997248i	$-0.523619\pi$
$31$	−0.825498	−0.148264	−0.0741319	+	0.997248i	$0.523619\pi$
$32$	17.7652	3.14048
$33$	−0.180969	−0.0315026
$34$	7.61055	1.30520
$35$	−1.04900	−0.177313
$36$	5.25508	0.875846
$37$	6.46356	1.06260	0.531301	−	0.847183i	$-0.321703\pi$
$37$	6.46356	1.06260	0.531301	+	0.847183i	$0.321703\pi$
$38$	−0.487443	−0.0790738
$39$	4.89961	0.784565
$40$	9.19722	1.45421
$41$	−3.47003	−0.541927	−0.270964	−	0.962590i	$-0.587342\pi$
$41$	−3.47003	−0.541927	−0.270964	+	0.962590i	$0.587342\pi$
$42$	2.69353	0.415620
$43$	0.125506	0.0191395	0.00956976	−	0.999954i	$-0.496954\pi$
$43$	0.125506	0.0191395	0.00956976	+	0.999954i	$0.496954\pi$
$44$	0.951004	0.143369
$45$	1.04900	0.156375
$46$	2.69353	0.397139
$47$	−12.0316	−1.75499	−0.877493	−	0.479589i	$-0.840786\pi$
$47$	−12.0316	−1.75499	−0.877493	+	0.479589i	$0.840786\pi$
$48$	−13.1057	−1.89164
$49$	1.00000	0.142857
$50$	−10.5037	−1.48545
$51$	−2.82550	−0.395649
$52$	−25.7478	−3.57058
$53$	8.55269	1.17480	0.587401	−	0.809296i	$-0.300151\pi$
$53$	8.55269	1.17480	0.587401	+	0.809296i	$0.300151\pi$
$54$	−2.69353	−0.366542
$55$	0.189835	0.0255974
$56$	−8.76763	−1.17162
$57$	0.180969	0.0239699
$58$	−15.3118	−2.01053
$59$	−4.30647	−0.560655	−0.280328	−	0.959904i	$-0.590443\pi$
$59$	−4.30647	−0.560655	−0.280328	+	0.959904i	$0.590443\pi$
$60$	−5.51256	−0.711668
$61$	9.01625	1.15441	0.577206	−	0.816599i	$-0.304143\pi$
$61$	9.01625	1.15441	0.577206	+	0.816599i	$0.304143\pi$
$62$	−2.22350	−0.282385
$63$	−1.00000	−0.125988
$64$	21.6397	2.70497
$65$	−5.13967	−0.637497
$66$	−0.487443	−0.0600001
$67$	−15.7074	−1.91896	−0.959480	−	0.281775i	$-0.909077\pi$
$67$	−15.7074	−1.91896	−0.959480	+	0.281775i	$0.909077\pi$
$68$	14.8482	1.80061
$69$	−1.00000	−0.120386
$70$	−2.82550	−0.337712
$71$	−2.22350	−0.263881	−0.131940	−	0.991258i	$-0.542121\pi$
$71$	−2.22350	−0.263881	−0.131940	+	0.991258i	$0.542121\pi$
$72$	8.76763	1.03328
$73$	13.0717	1.52993	0.764964	−	0.644073i	$-0.222757\pi$
$73$	13.0717	1.52993	0.764964	+	0.644073i	$0.222757\pi$
$74$	17.4098	2.02384
$75$	3.89961	0.450288
$76$	−0.951004	−0.109088
$77$	−0.180969	−0.0206233
$78$	13.1972	1.49429
$79$	−16.1948	−1.82206	−0.911029	−	0.412341i	$-0.864711\pi$
$79$	−16.1948	−1.82206	−0.911029	+	0.412341i	$0.864711\pi$
$80$	13.7478	1.53705
$81$	1.00000	0.111111
$82$	−9.34660	−1.03216
$83$	10.8757	1.19377	0.596883	−	0.802328i	$-0.296406\pi$
$83$	10.8757	1.19377	0.596883	+	0.802328i	$0.296406\pi$
$84$	5.25508	0.573376
$85$	2.96394	0.321484
$86$	0.338054	0.0364533
$87$	5.68466	0.609459
$88$	1.58667	0.169139
$89$	−14.7466	−1.56314	−0.781568	−	0.623821i	$-0.785580\pi$
$89$	−14.7466	−1.56314	−0.781568	+	0.623821i	$0.785580\pi$
$90$	2.82550	0.297834
$91$	4.89961	0.513618
$92$	5.25508	0.547880
$93$	0.825498	0.0856001
$94$	−32.4074	−3.34256
$95$	−0.189835	−0.0194767
$96$	−17.7652	−1.81316
$97$	10.4636	1.06241	0.531207	−	0.847242i	$-0.321739\pi$
$97$	10.4636	1.06241	0.531207	+	0.847242i	$0.321739\pi$
$98$	2.69353	0.272087
$99$	0.180969	0.0181880
$100$	−20.4927	−2.04927
$101$	14.7316	1.46585	0.732923	−	0.680312i	$-0.238156\pi$
$101$	14.7316	1.46585	0.732923	+	0.680312i	$0.238156\pi$
$102$	−7.61055	−0.753557
$103$	5.96362	0.587613	0.293806	−	0.955865i	$-0.405078\pi$
$103$	5.96362	0.587613	0.293806	+	0.955865i	$0.405078\pi$
$104$	−42.9580	−4.21238
$105$	1.04900	0.102372
$106$	23.0369	2.23754
$107$	−8.55060	−0.826618	−0.413309	−	0.910591i	$-0.635627\pi$
$107$	−8.55060	−0.826618	−0.413309	+	0.910591i	$0.635627\pi$
$108$	−5.25508	−0.505670
$109$	9.00123	0.862162	0.431081	−	0.902313i	$-0.358132\pi$
$109$	9.00123	0.862162	0.431081	+	0.902313i	$0.358132\pi$
$110$	0.511326	0.0487530
$111$	−6.46356	−0.613494
$112$	−13.1057	−1.23837
$113$	9.81016	0.922863	0.461431	−	0.887176i	$-0.347336\pi$
$113$	9.81016	0.922863	0.461431	+	0.887176i	$0.347336\pi$
$114$	0.487443	0.0456533
$115$	1.04900	0.0978194
$116$	−29.8733	−2.77367
$117$	−4.89961	−0.452969
$118$	−11.5996	−1.06783
$119$	−2.82550	−0.259013
$120$	−9.19722	−0.839587
$121$	−10.9673	−0.997023
$122$	24.2855	2.19870
$123$	3.47003	0.312882
$124$	−4.33805	−0.389569
$125$	−9.33565	−0.835006
$126$	−2.69353	−0.239958
$127$	13.6421	1.21054	0.605272	−	0.796019i	$-0.293065\pi$
$127$	13.6421	1.21054	0.605272	+	0.796019i	$0.293065\pi$
$128$	22.7567	2.01143
$129$	−0.125506	−0.0110502
$130$	−13.8438	−1.21418
$131$	−9.72104	−0.849331	−0.424666	−	0.905350i	$-0.639608\pi$
$131$	−9.72104	−0.849331	−0.424666	+	0.905350i	$0.639608\pi$
$132$	−0.951004	−0.0827743
$133$	0.180969	0.0156920
$134$	−42.3082	−3.65487
$135$	−1.04900	−0.0902832
$136$	24.7729	2.12426
$137$	−5.96725	−0.509817	−0.254908	−	0.966965i	$-0.582045\pi$
$137$	−5.96725	−0.509817	−0.254908	+	0.966965i	$0.582045\pi$
$138$	−2.69353	−0.229288
$139$	7.36317	0.624536	0.312268	−	0.949994i	$-0.398911\pi$
$139$	7.36317	0.624536	0.312268	+	0.949994i	$0.398911\pi$
$140$	−5.51256	−0.465896
$141$	12.0316	1.01324
$142$	−5.98905	−0.502590
$143$	−0.886675	−0.0741475
$144$	13.1057	1.09214
$145$	−5.96318	−0.495216
$146$	35.2090	2.91392
$147$	−1.00000	−0.0824786
$148$	33.9665	2.79203
$149$	21.9288	1.79648	0.898238	−	0.439509i	$-0.144848\pi$
$149$	21.9288	1.79648	0.898238	+	0.439509i	$0.144848\pi$
$150$	10.5037	0.857623
$151$	16.7927	1.36657	0.683287	−	0.730150i	$-0.260550\pi$
$151$	16.7927	1.36657	0.683287	+	0.730150i	$0.260550\pi$
$152$	−1.58667	−0.128696
$153$	2.82550	0.228428
$154$	−0.487443	−0.0392793
$155$	−0.865944	−0.0695543
$156$	25.7478	2.06148
$157$	16.7425	1.33620	0.668099	−	0.744072i	$-0.267108\pi$
$157$	16.7425	1.33620	0.668099	+	0.744072i	$0.267108\pi$
$158$	−43.6211	−3.47031
$159$	−8.55269	−0.678272
$160$	18.6357	1.47328
$161$	−1.00000	−0.0788110
$162$	2.69353	0.211623
$163$	25.1308	1.96840	0.984198	−	0.177070i	$-0.0566621\pi$
$163$	25.1308	1.96840	0.984198	+	0.177070i	$0.0566621\pi$
$164$	−18.2353	−1.42393
$165$	−0.189835	−0.0147787
$166$	29.2940	2.27366
$167$	9.98018	0.772290	0.386145	−	0.922438i	$-0.373806\pi$
$167$	9.98018	0.772290	0.386145	+	0.922438i	$0.373806\pi$
$168$	8.76763	0.676438
$169$	11.0061	0.846627
$170$	7.98344	0.612302
$171$	−0.180969	−0.0138390
$172$	0.659545	0.0502898
$173$	−12.5065	−0.950853	−0.475427	−	0.879755i	$-0.657706\pi$
$173$	−12.5065	−0.950853	−0.475427	+	0.879755i	$0.657706\pi$
$174$	15.3118	1.16078
$175$	3.89961	0.294783
$176$	2.37172	0.178775
$177$	4.30647	0.323694
$178$	−39.7203	−2.97716
$179$	−19.3081	−1.44316	−0.721579	−	0.692332i	$-0.756583\pi$
$179$	−19.3081	−1.44316	−0.721579	+	0.692332i	$0.756583\pi$
$180$	5.51256	0.410882
$181$	17.7656	1.32050	0.660251	−	0.751045i	$-0.270450\pi$
$181$	17.7656	1.32050	0.660251	+	0.751045i	$0.270450\pi$
$182$	13.1972	0.978243
$183$	−9.01625	−0.666500
$184$	8.76763	0.646359
$185$	6.78025	0.498494
$186$	2.22350	0.163035
$187$	0.511326	0.0373919
$188$	−63.2269	−4.61129
$189$	1.00000	0.0727393
$190$	−0.511326	−0.0370955
$191$	−8.79275	−0.636221	−0.318110	−	0.948054i	$-0.603048\pi$
$191$	−8.79275	−0.636221	−0.318110	+	0.948054i	$0.603048\pi$
$192$	−21.6397	−1.56171
$193$	−6.79275	−0.488953	−0.244476	−	0.969655i	$-0.578616\pi$
$193$	−6.79275	−0.488953	−0.244476	+	0.969655i	$0.578616\pi$
$194$	28.1839	2.02348
$195$	5.13967	0.368059
$196$	5.25508	0.375363
$197$	14.6534	1.04401	0.522006	−	0.852942i	$-0.325184\pi$
$197$	14.6534	1.04401	0.522006	+	0.852942i	$0.325184\pi$
$198$	0.487443	0.0346411
$199$	−4.45469	−0.315785	−0.157892	−	0.987456i	$-0.550470\pi$
$199$	−4.45469	−0.315785	−0.157892	+	0.987456i	$0.550470\pi$
$200$	−34.1903	−2.41762
$201$	15.7074	1.10791
$202$	39.6799	2.79187
$203$	5.68466	0.398985
$204$	−14.8482	−1.03958
$205$	−3.64004	−0.254232
$206$	16.0632	1.11917
$207$	1.00000	0.0695048
$208$	−64.2127	−4.45235
$209$	−0.0327496	−0.00226534
$210$	2.82550	0.194978
$211$	−4.59793	−0.316535	−0.158267	−	0.987396i	$-0.550591\pi$
$211$	−4.59793	−0.316535	−0.158267	+	0.987396i	$0.550591\pi$
$212$	44.9450	3.08684
$213$	2.22350	0.152352
$214$	−23.0313	−1.57438
$215$	0.131656	0.00897884
$216$	−8.76763	−0.596562
$217$	0.825498	0.0560384
$218$	24.2450	1.64208
$219$	−13.0717	−0.883304
$220$	0.997599	0.0672581
$221$	−13.8438	−0.931237
$222$	−17.4098	−1.16847
$223$	13.0442	0.873504	0.436752	−	0.899582i	$-0.356129\pi$
$223$	13.0442	0.873504	0.436752	+	0.899582i	$0.356129\pi$
$224$	−17.7652	−1.18699
$225$	−3.89961	−0.259974
$226$	26.4239	1.75769
$227$	−0.320321	−0.0212604	−0.0106302	−	0.999943i	$-0.503384\pi$
$227$	−0.320321	−0.0212604	−0.0106302	+	0.999943i	$0.503384\pi$
$228$	0.951004	0.0629818
$229$	8.88459	0.587110	0.293555	−	0.955942i	$-0.405162\pi$
$229$	8.88459	0.587110	0.293555	+	0.955942i	$0.405162\pi$
$230$	2.82550	0.186308
$231$	0.180969	0.0119069
$232$	−49.8410	−3.27222
$233$	−0.418313	−0.0274046	−0.0137023	−	0.999906i	$-0.504362\pi$
$233$	−0.418313	−0.0274046	−0.0137023	+	0.999906i	$0.504362\pi$
$234$	−13.1972	−0.862729
$235$	−12.6211	−0.823309
$236$	−22.6309	−1.47314
$237$	16.1948	1.05197
$238$	−7.61055	−0.493319
$239$	−15.0571	−0.973965	−0.486982	−	0.873412i	$-0.661902\pi$
$239$	−15.0571	−0.973965	−0.486982	+	0.873412i	$0.661902\pi$
$240$	−13.7478	−0.887418
$241$	5.31701	0.342498	0.171249	−	0.985228i	$-0.445220\pi$
$241$	5.31701	0.342498	0.171249	+	0.985228i	$0.445220\pi$
$242$	−29.5406	−1.89894
$243$	−1.00000	−0.0641500
$244$	47.3811	3.03326
$245$	1.04900	0.0670179
$246$	9.34660	0.595918
$247$	0.886675	0.0564178
$248$	−7.23766	−0.459592
$249$	−10.8757	−0.689221
$250$	−25.1458	−1.59036
$251$	−7.19107	−0.453896	−0.226948	−	0.973907i	$-0.572875\pi$
$251$	−7.19107	−0.453896	−0.226948	+	0.973907i	$0.572875\pi$
$252$	−5.25508	−0.331039
$253$	0.180969	0.0113774
$254$	36.7454	2.30561
$255$	−2.96394	−0.185609
$256$	18.0162	1.12602
$257$	−8.77255	−0.547217	−0.273608	−	0.961841i	$-0.588217\pi$
$257$	−8.77255	−0.547217	−0.273608	+	0.961841i	$0.588217\pi$
$258$	−0.338054	−0.0210463
$259$	−6.46356	−0.401626
$260$	−27.0094	−1.67505
$261$	−5.68466	−0.351872
$262$	−26.1839	−1.61764
$263$	16.0304	0.988477	0.494239	−	0.869326i	$-0.335447\pi$
$263$	16.0304	0.988477	0.494239	+	0.869326i	$0.335447\pi$
$264$	−1.58667	−0.0976525
$265$	8.97173	0.551129
$266$	0.487443	0.0298871
$267$	14.7466	0.902476
$268$	−82.5435	−5.04214
$269$	6.27373	0.382516	0.191258	−	0.981540i	$-0.438743\pi$
$269$	6.27373	0.382516	0.191258	+	0.981540i	$0.438743\pi$
$270$	−2.82550	−0.171954
$271$	−17.1397	−1.04116	−0.520580	−	0.853813i	$-0.674284\pi$
$271$	−17.1397	−1.04116	−0.520580	+	0.853813i	$0.674284\pi$
$272$	37.0301	2.24528
$273$	−4.89961	−0.296538
$274$	−16.0729	−0.971002
$275$	−0.705706	−0.0425557
$276$	−5.25508	−0.316319
$277$	−23.9563	−1.43939	−0.719697	−	0.694288i	$-0.755719\pi$
$277$	−23.9563	−1.43939	−0.719697	+	0.694288i	$0.755719\pi$
$278$	19.8329	1.18950
$279$	−0.825498	−0.0494212
$280$	−9.19722	−0.549639
$281$	−7.27132	−0.433771	−0.216885	−	0.976197i	$-0.569590\pi$
$281$	−7.27132	−0.433771	−0.216885	+	0.976197i	$0.569590\pi$
$282$	32.4074	1.92983
$283$	26.5365	1.57743	0.788716	−	0.614758i	$-0.210746\pi$
$283$	26.5365	1.57743	0.788716	+	0.614758i	$0.210746\pi$
$284$	−11.6847	−0.693357
$285$	0.189835	0.0112449
$286$	−2.38828	−0.141222
$287$	3.47003	0.204829
$288$	17.7652	1.04683
$289$	−9.01656	−0.530386
$290$	−16.0620	−0.943192
$291$	−10.4636	−0.613385
$292$	68.6928	4.01994
$293$	−32.7086	−1.91086	−0.955428	−	0.295223i	$-0.904606\pi$
$293$	−32.7086	−1.91086	−0.955428	+	0.295223i	$0.904606\pi$
$294$	−2.69353	−0.157090
$295$	−4.51748	−0.263018
$296$	56.6701	3.29388
$297$	−0.180969	−0.0105009
$298$	59.0657	3.42159
$299$	−4.89961	−0.283352
$300$	20.4927	1.18315
$301$	−0.125506	−0.00723406
$302$	45.2317	2.60279
$303$	−14.7316	−0.846307
$304$	−2.37172	−0.136027
$305$	9.45801	0.541564
$306$	7.61055	0.435066
$307$	−20.4281	−1.16589	−0.582946	−	0.812511i	$-0.698100\pi$
$307$	−20.4281	−1.16589	−0.582946	+	0.812511i	$0.698100\pi$
$308$	−0.951004	−0.0541885
$309$	−5.96362	−0.339258
$310$	−2.33244	−0.132474
$311$	15.9515	0.904526	0.452263	−	0.891884i	$-0.350617\pi$
$311$	15.9515	0.904526	0.452263	+	0.891884i	$0.350617\pi$
$312$	42.9580	2.43202
$313$	−2.91328	−0.164668	−0.0823340	−	0.996605i	$-0.526237\pi$
$313$	−2.91328	−0.164668	−0.0823340	+	0.996605i	$0.526237\pi$
$314$	45.0964	2.54494
$315$	−1.04900	−0.0591042
$316$	−85.1050	−4.78753
$317$	0.295090	0.0165739	0.00828695	−	0.999966i	$-0.497362\pi$
$317$	0.295090	0.0165739	0.00828695	+	0.999966i	$0.497362\pi$
$318$	−23.0369	−1.29184
$319$	−1.02874	−0.0575986
$320$	22.7000	1.26897
$321$	8.55060	0.477248
$322$	−2.69353	−0.150104
$323$	−0.511326	−0.0284510
$324$	5.25508	0.291949
$325$	19.1065	1.05984
$326$	67.6904	3.74903
$327$	−9.00123	−0.497769
$328$	−30.4239	−1.67988
$329$	12.0316	0.663322
$330$	−0.511326	−0.0281476
$331$	10.8907	0.598609	0.299305	−	0.954158i	$-0.403245\pi$
$331$	10.8907	0.598609	0.299305	+	0.954158i	$0.403245\pi$
$332$	57.1528	3.13667
$333$	6.46356	0.354201
$334$	26.8819	1.47091
$335$	−16.4770	−0.900233
$336$	13.1057	0.714974
$337$	1.29884	0.0707522	0.0353761	−	0.999374i	$-0.488737\pi$
$337$	1.29884	0.0707522	0.0353761	+	0.999374i	$0.488737\pi$
$338$	29.6453	1.61249
$339$	−9.81016	−0.532815
$340$	15.5757	0.844712
$341$	−0.149389	−0.00808987
$342$	−0.487443	−0.0263579
$343$	−1.00000	−0.0539949
$344$	1.10039	0.0593292
$345$	−1.04900	−0.0564761
$346$	−33.6866	−1.81100
$347$	18.2928	0.982009	0.491005	−	0.871157i	$-0.336630\pi$
$347$	18.2928	0.982009	0.491005	+	0.871157i	$0.336630\pi$
$348$	29.8733	1.60138
$349$	−22.9333	−1.22759	−0.613795	−	0.789466i	$-0.710358\pi$
$349$	−22.9333	−1.22759	−0.613795	+	0.789466i	$0.710358\pi$
$350$	10.5037	0.561446
$351$	4.89961	0.261522
$352$	3.21495	0.171357
$353$	15.5867	0.829595	0.414797	−	0.909914i	$-0.363853\pi$
$353$	15.5867	0.829595	0.414797	+	0.909914i	$0.363853\pi$
$354$	11.5996	0.616512
$355$	−2.33244	−0.123793
$356$	−77.4945	−4.10720
$357$	2.82550	0.149541
$358$	−52.0070	−2.74865
$359$	−21.6094	−1.14050	−0.570250	−	0.821471i	$-0.693154\pi$
$359$	−21.6094	−1.14050	−0.570250	+	0.821471i	$0.693154\pi$
$360$	9.19722	0.484736
$361$	−18.9673	−0.998276
$362$	47.8520	2.51504
$363$	10.9673	0.575631
$364$	25.7478	1.34955
$365$	13.7122	0.717728
$366$	−24.2855	−1.26942
$367$	−4.46399	−0.233019	−0.116509	−	0.993190i	$-0.537170\pi$
$367$	−4.46399	−0.233019	−0.116509	+	0.993190i	$0.537170\pi$
$368$	13.1057	0.683181
$369$	−3.47003	−0.180642
$370$	18.2628	0.949436
$371$	−8.55269	−0.444033
$372$	4.33805	0.224918
$373$	−30.7527	−1.59232	−0.796158	−	0.605089i	$-0.793138\pi$
$373$	−30.7527	−1.59232	−0.796158	+	0.605089i	$0.793138\pi$
$374$	1.37727	0.0712169
$375$	9.33565	0.482091
$376$	−105.488	−5.44015
$377$	27.8526	1.43448
$378$	2.69353	0.138540
$379$	22.7013	1.16609	0.583045	−	0.812440i	$-0.301861\pi$
$379$	22.7013	1.16609	0.583045	+	0.812440i	$0.301861\pi$
$380$	−0.997599	−0.0511758
$381$	−13.6421	−0.698907
$382$	−23.6835	−1.21175
$383$	−18.3478	−0.937531	−0.468765	−	0.883323i	$-0.655301\pi$
$383$	−18.3478	−0.937531	−0.468765	+	0.883323i	$0.655301\pi$
$384$	−22.7567	−1.16130
$385$	−0.189835	−0.00967490
$386$	−18.2964	−0.931264
$387$	0.125506	0.00637984
$388$	54.9868	2.79153
$389$	−22.0620	−1.11859	−0.559294	−	0.828970i	$-0.688928\pi$
$389$	−22.0620	−1.11859	−0.559294	+	0.828970i	$0.688928\pi$
$390$	13.8438	0.701009
$391$	2.82550	0.142892
$392$	8.76763	0.442832
$393$	9.72104	0.490362
$394$	39.4693	1.98843
$395$	−16.9883	−0.854774
$396$	0.951004	0.0477897
$397$	23.3045	1.16962	0.584808	−	0.811171i	$-0.301170\pi$
$397$	23.3045	1.16962	0.584808	+	0.811171i	$0.301170\pi$
$398$	−11.9988	−0.601447
$399$	−0.180969	−0.00905976
$400$	−51.1070	−2.55535
$401$	14.2087	0.709547	0.354773	−	0.934952i	$-0.384558\pi$
$401$	14.2087	0.709547	0.354773	+	0.934952i	$0.384558\pi$
$402$	42.3082	2.11014
$403$	4.04461	0.201477
$404$	77.4156	3.85157
$405$	1.04900	0.0521250
$406$	15.3118	0.759910
$407$	1.16970	0.0579799
$408$	−24.7729	−1.22644
$409$	−33.2758	−1.64538	−0.822692	−	0.568488i	$-0.807529\pi$
$409$	−33.2758	−1.64538	−0.822692	+	0.568488i	$0.807529\pi$
$410$	−9.80455	−0.484212
$411$	5.96725	0.294343
$412$	31.3393	1.54398
$413$	4.30647	0.211908
$414$	2.69353	0.132380
$415$	11.4086	0.560026
$416$	−87.0427	−4.26762
$417$	−7.36317	−0.360576
$418$	−0.0882119	−0.00431459
$419$	1.93819	0.0946867	0.0473434	−	0.998879i	$-0.484925\pi$
$419$	1.93819	0.0946867	0.0473434	+	0.998879i	$0.484925\pi$
$420$	5.51256	0.268985
$421$	−3.10852	−0.151500	−0.0757501	−	0.997127i	$-0.524135\pi$
$421$	−3.10852	−0.151500	−0.0757501	+	0.997127i	$0.524135\pi$
$422$	−12.3846	−0.602875
$423$	−12.0316	−0.584995
$424$	74.9868	3.64168
$425$	−11.0183	−0.534468
$426$	5.98905	0.290170
$427$	−9.01625	−0.436327
$428$	−44.9341	−2.17197
$429$	0.886675	0.0428091
$430$	0.354618	0.0171012
$431$	−27.2204	−1.31116	−0.655579	−	0.755126i	$-0.727576\pi$
$431$	−27.2204	−1.31116	−0.655579	+	0.755126i	$0.727576\pi$
$432$	−13.1057	−0.630548
$433$	−12.2146	−0.586998	−0.293499	−	0.955959i	$-0.594820\pi$
$433$	−12.2146	−0.586998	−0.293499	+	0.955959i	$0.594820\pi$
$434$	2.22350	0.106731
$435$	5.96318	0.285913
$436$	47.3022	2.26536
$437$	−0.180969	−0.00865690
$438$	−35.2090	−1.68235
$439$	28.7859	1.37387	0.686937	−	0.726717i	$-0.258955\pi$
$439$	28.7859	1.37387	0.686937	+	0.726717i	$0.258955\pi$
$440$	1.66441	0.0793475
$441$	1.00000	0.0476190
$442$	−37.2887	−1.77364
$443$	−32.1005	−1.52514	−0.762569	−	0.646907i	$-0.776062\pi$
$443$	−32.1005	−1.52514	−0.762569	+	0.646907i	$0.776062\pi$
$444$	−33.9665	−1.61198
$445$	−15.4691	−0.733306
$446$	35.1349	1.66368
$447$	−21.9288	−1.03720
$448$	−21.6397	−1.02238
$449$	−25.6596	−1.21095	−0.605476	−	0.795864i	$-0.707017\pi$
$449$	−25.6596	−1.21095	−0.605476	+	0.795864i	$0.707017\pi$
$450$	−10.5037	−0.495149
$451$	−0.627966	−0.0295697
$452$	51.5532	2.42486
$453$	−16.7927	−0.788992
$454$	−0.862792	−0.0404928
$455$	5.13967	0.240951
$456$	1.58667	0.0743024
$457$	16.8061	0.786157	0.393078	−	0.919505i	$-0.371410\pi$
$457$	16.8061	0.786157	0.393078	+	0.919505i	$0.371410\pi$
$458$	23.9309	1.11822
$459$	−2.82550	−0.131883
$460$	5.51256	0.257024
$461$	8.73248	0.406712	0.203356	−	0.979105i	$-0.434815\pi$
$461$	8.73248	0.406712	0.203356	+	0.979105i	$0.434815\pi$
$462$	0.487443	0.0226779
$463$	18.2312	0.847275	0.423638	−	0.905832i	$-0.360753\pi$
$463$	18.2312	0.847275	0.423638	+	0.905832i	$0.360753\pi$
$464$	−74.5014	−3.45864
$465$	0.865944	0.0401572
$466$	−1.12674	−0.0521951
$467$	13.8127	0.639175	0.319587	−	0.947557i	$-0.396456\pi$
$467$	13.8127	0.639175	0.319587	+	0.947557i	$0.396456\pi$
$468$	−25.7478	−1.19019
$469$	15.7074	0.725299
$470$	−33.9952	−1.56808
$471$	−16.7425	−0.771455
$472$	−37.7576	−1.73793
$473$	0.0227127	0.00104433
$474$	43.6211	2.00359
$475$	0.705706	0.0323800
$476$	−14.8482	−0.680567
$477$	8.55269	0.391601
$478$	−40.5568	−1.85502
$479$	−19.4814	−0.890128	−0.445064	−	0.895499i	$-0.646819\pi$
$479$	−19.4814	−0.890128	−0.445064	+	0.895499i	$0.646819\pi$
$480$	−18.6357	−0.850598
$481$	−31.6689	−1.44398
$482$	14.3215	0.652326
$483$	1.00000	0.0455016
$484$	−57.6338	−2.61972
$485$	10.9762	0.498405
$486$	−2.69353	−0.122181
$487$	27.5268	1.24736	0.623680	−	0.781680i	$-0.285637\pi$
$487$	27.5268	1.24736	0.623680	+	0.781680i	$0.285637\pi$
$488$	79.0512	3.57848
$489$	−25.1308	−1.13645
$490$	2.82550	0.127643
$491$	15.3547	0.692950	0.346475	−	0.938059i	$-0.387379\pi$
$491$	15.3547	0.692950	0.346475	+	0.938059i	$0.387379\pi$
$492$	18.2353	0.822109
$493$	−16.0620	−0.723396
$494$	2.38828	0.107454
$495$	0.189835	0.00853246
$496$	−10.8187	−0.485775
$497$	2.22350	0.0997375
$498$	−29.2940	−1.31270
$499$	−8.11621	−0.363331	−0.181666	−	0.983360i	$-0.558149\pi$
$499$	−8.11621	−0.363331	−0.181666	+	0.983360i	$0.558149\pi$
$500$	−49.0596	−2.19401
$501$	−9.98018	−0.445882
$502$	−19.3693	−0.864495
$503$	−19.1576	−0.854194	−0.427097	−	0.904206i	$-0.640464\pi$
$503$	−19.1576	−0.854194	−0.427097	+	0.904206i	$0.640464\pi$
$504$	−8.76763	−0.390541
$505$	15.4534	0.687666
$506$	0.487443	0.0216695
$507$	−11.0061	−0.488800
$508$	71.6904	3.18075
$509$	−3.87856	−0.171914	−0.0859571	−	0.996299i	$-0.527395\pi$
$509$	−3.87856	−0.171914	−0.0859571	+	0.996299i	$0.527395\pi$
$510$	−7.98344	−0.353513
$511$	−13.0717	−0.578258
$512$	3.01385	0.133194
$513$	0.180969	0.00798996
$514$	−23.6291	−1.04223
$515$	6.25581	0.275664
$516$	−0.659545	−0.0290349
$517$	−2.17734	−0.0957592
$518$	−17.4098	−0.764941
$519$	12.5065	0.548976
$520$	−45.0627	−1.97613
$521$	35.3522	1.54881	0.774404	−	0.632691i	$-0.218050\pi$
$521$	35.3522	1.54881	0.774404	+	0.632691i	$0.218050\pi$
$522$	−15.3118	−0.670178
$523$	−39.3231	−1.71948	−0.859740	−	0.510733i	$-0.829374\pi$
$523$	−39.3231	−1.71948	−0.859740	+	0.510733i	$0.829374\pi$
$524$	−51.0848	−2.23165
$525$	−3.89961	−0.170193
$526$	43.1783	1.88266
$527$	−2.33244	−0.101603
$528$	−2.37172	−0.103216
$529$	1.00000	0.0434783
$530$	24.1656	1.04969
$531$	−4.30647	−0.186885
$532$	0.951004	0.0412312
$533$	17.0018	0.736428
$534$	39.7203	1.71887
$535$	−8.96955	−0.387787
$536$	−137.716	−5.94845
$537$	19.3081	0.833208
$538$	16.8984	0.728543
$539$	0.180969	0.00779487
$540$	−5.51256	−0.237223
$541$	−2.43081	−0.104509	−0.0522544	−	0.998634i	$-0.516641\pi$
$541$	−2.43081	−0.104509	−0.0522544	+	0.998634i	$0.516641\pi$
$542$	−46.1661	−1.98301
$543$	−17.7656	−0.762393
$544$	50.1956	2.15212
$545$	9.44226	0.404462
$546$	−13.1972	−0.564789
$547$	−20.0320	−0.856507	−0.428254	−	0.903659i	$-0.640871\pi$
$547$	−20.0320	−0.856507	−0.428254	+	0.903659i	$0.640871\pi$
$548$	−31.3584	−1.33956
$549$	9.01625	0.384804
$550$	−1.90084	−0.0810520
$551$	1.02874	0.0438260
$552$	−8.76763	−0.373175
$553$	16.1948	0.688674
$554$	−64.5269	−2.74149
$555$	−6.78025	−0.287806
$556$	38.6940	1.64099
$557$	34.5733	1.46492	0.732459	−	0.680811i	$-0.238372\pi$
$557$	34.5733	1.46492	0.732459	+	0.680811i	$0.238372\pi$
$558$	−2.22350	−0.0941282
$559$	−0.614931	−0.0260088
$560$	−13.7478	−0.580951
$561$	−0.511326	−0.0215882
$562$	−19.5855	−0.826164
$563$	11.6307	0.490177	0.245089	−	0.969501i	$-0.421183\pi$
$563$	11.6307	0.490177	0.245089	+	0.969501i	$0.421183\pi$
$564$	63.2269	2.66233
$565$	10.2908	0.432938
$566$	71.4767	3.00439
$567$	−1.00000	−0.0419961
$568$	−19.4948	−0.817985
$569$	20.0340	0.839871	0.419935	−	0.907554i	$-0.362053\pi$
$569$	20.0340	0.839871	0.419935	+	0.907554i	$0.362053\pi$
$570$	0.511326	0.0214171
$571$	−30.6328	−1.28194	−0.640972	−	0.767564i	$-0.721469\pi$
$571$	−30.6328	−1.28194	−0.640972	+	0.767564i	$0.721469\pi$
$572$	−4.65955	−0.194825
$573$	8.79275	0.367322
$574$	9.34660	0.390120
$575$	−3.89961	−0.162625
$576$	21.6397	0.901655
$577$	6.02586	0.250860	0.125430	−	0.992102i	$-0.459969\pi$
$577$	6.02586	0.250860	0.125430	+	0.992102i	$0.459969\pi$
$578$	−24.2863	−1.01018
$579$	6.79275	0.282297
$580$	−31.3370	−1.30120
$581$	−10.8757	−0.451201
$582$	−28.1839	−1.16826
$583$	1.54777	0.0641020
$584$	114.608	4.74251
$585$	−5.13967	−0.212499
$586$	−88.1014	−3.63944
$587$	−0.00886676	−0.000365971 0	−0.000182985	−	1.00000i	$-0.500058\pi$
$587$	−0.00886676	−0.000365971 0	−0.000182985		1.00000i	$0.500058\pi$
$588$	−5.25508	−0.216716
$589$	0.149389	0.00615547
$590$	−12.1679	−0.500946
$591$	−14.6534	−0.602760
$592$	84.7094	3.48154
$593$	−46.0454	−1.89086	−0.945429	−	0.325827i	$-0.894357\pi$
$593$	−46.0454	−1.89086	−0.945429	+	0.325827i	$0.894357\pi$
$594$	−0.487443	−0.0200000
$595$	−2.96394	−0.121510
$596$	115.237	4.72031
$597$	4.45469	0.182318
$598$	−13.1972	−0.539674
$599$	−24.6357	−1.00659	−0.503293	−	0.864116i	$-0.667878\pi$
$599$	−24.6357	−1.00659	−0.503293	+	0.864116i	$0.667878\pi$
$600$	34.1903	1.39581
$601$	−32.4037	−1.32177	−0.660887	−	0.750486i	$-0.729820\pi$
$601$	−32.4037	−1.32177	−0.660887	+	0.750486i	$0.729820\pi$
$602$	−0.338054	−0.0137781
$603$	−15.7074	−0.639654
$604$	88.2472	3.59073
$605$	−11.5046	−0.467729
$606$	−39.6799	−1.61188
$607$	10.5554	0.428431	0.214215	−	0.976786i	$-0.431281\pi$
$607$	10.5554	0.428431	0.214215	+	0.976786i	$0.431281\pi$
$608$	−3.21495	−0.130383
$609$	−5.68466	−0.230354
$610$	25.4754	1.03147
$611$	58.9500	2.38486
$612$	14.8482	0.600203
$613$	4.26511	0.172266	0.0861332	−	0.996284i	$-0.472549\pi$
$613$	4.26511	0.172266	0.0861332	+	0.996284i	$0.472549\pi$
$614$	−55.0236	−2.22057
$615$	3.64004	0.146781
$616$	−1.58667	−0.0639286
$617$	−9.32470	−0.375398	−0.187699	−	0.982227i	$-0.560103\pi$
$617$	−9.32470	−0.375398	−0.187699	+	0.982227i	$0.560103\pi$
$618$	−16.0632	−0.646155
$619$	3.64538	0.146520	0.0732601	−	0.997313i	$-0.476660\pi$
$619$	3.64538	0.146520	0.0732601	+	0.997313i	$0.476660\pi$
$620$	−4.55060	−0.182757
$621$	−1.00000	−0.0401286
$622$	42.9658	1.72277
$623$	14.7466	0.590810
$624$	64.2127	2.57057
$625$	9.70497	0.388199
$626$	−7.84698	−0.313628
$627$	0.0327496	0.00130789
$628$	87.9833	3.51091
$629$	18.2628	0.728185
$630$	−2.82550	−0.112571
$631$	15.3155	0.609699	0.304849	−	0.952401i	$-0.401394\pi$
$631$	15.3155	0.609699	0.304849	+	0.952401i	$0.401394\pi$
$632$	−141.990	−5.64807
$633$	4.59793	0.182751
$634$	0.794832	0.0315668
$635$	14.3105	0.567896
$636$	−44.9450	−1.78219
$637$	−4.89961	−0.194129
$638$	−2.77095	−0.109703
$639$	−2.22350	−0.0879602
$640$	23.8717	0.943611
$641$	17.8252	0.704052	0.352026	−	0.935990i	$-0.385493\pi$
$641$	17.8252	0.704052	0.352026	+	0.935990i	$0.385493\pi$
$642$	23.0313	0.908971
$643$	−10.2196	−0.403022	−0.201511	−	0.979486i	$-0.564585\pi$
$643$	−10.2196	−0.403022	−0.201511	+	0.979486i	$0.564585\pi$
$644$	−5.25508	−0.207079
$645$	−0.131656	−0.00518393
$646$	−1.37727	−0.0541880
$647$	−1.71217	−0.0673124	−0.0336562	−	0.999433i	$-0.510715\pi$
$647$	−1.71217	−0.0673124	−0.0336562	+	0.999433i	$0.510715\pi$
$648$	8.76763	0.344425
$649$	−0.779336	−0.0305916
$650$	51.4640	2.01858
$651$	−0.825498	−0.0323538
$652$	132.064	5.17204
$653$	−2.80044	−0.109590	−0.0547949	−	0.998498i	$-0.517451\pi$
$653$	−2.80044	−0.109590	−0.0547949	+	0.998498i	$0.517451\pi$
$654$	−24.2450	−0.948056
$655$	−10.1973	−0.398443
$656$	−45.4771	−1.77558
$657$	13.0717	0.509976
$658$	32.4074	1.26337
$659$	25.7153	1.00173	0.500863	−	0.865526i	$-0.333016\pi$
$659$	25.7153	1.00173	0.500863	+	0.865526i	$0.333016\pi$
$660$	−0.997599	−0.0388315
$661$	10.5129	0.408903	0.204452	−	0.978877i	$-0.434459\pi$
$661$	10.5129	0.408903	0.204452	+	0.978877i	$0.434459\pi$
$662$	29.3345	1.14012
$663$	13.8438	0.537650
$664$	95.3544	3.70047
$665$	0.189835	0.00736150
$666$	17.4098	0.674615
$667$	−5.68466	−0.220111
$668$	52.4466	2.02922
$669$	−13.0442	−0.504318
$670$	−44.3811	−1.71459
$671$	1.63166	0.0629894
$672$	17.7652	0.685309
$673$	23.1235	0.891345	0.445672	−	0.895196i	$-0.352965\pi$
$673$	23.1235	0.891345	0.445672	+	0.895196i	$0.352965\pi$
$674$	3.49845	0.134755
$675$	3.89961	0.150096
$676$	57.8382	2.22455
$677$	−44.2843	−1.70198	−0.850992	−	0.525178i	$-0.823999\pi$
$677$	−44.2843	−1.70198	−0.850992	+	0.525178i	$0.823999\pi$
$678$	−26.4239	−1.01480
$679$	−10.4636	−0.401555
$680$	25.9867	0.996545
$681$	0.320321	0.0122747
$682$	−0.402383	−0.0154081
$683$	25.9663	0.993574	0.496787	−	0.867872i	$-0.334513\pi$
$683$	25.9663	0.993574	0.496787	+	0.867872i	$0.334513\pi$
$684$	−0.951004	−0.0363625
$685$	−6.25962	−0.239168
$686$	−2.69353	−0.102839
$687$	−8.88459	−0.338968
$688$	1.64485	0.0627092
$689$	−41.9048	−1.59645
$690$	−2.82550	−0.107565
$691$	−11.2697	−0.428719	−0.214359	−	0.976755i	$-0.568766\pi$
$691$	−11.2697	−0.428719	−0.214359	+	0.976755i	$0.568766\pi$
$692$	−65.7228	−2.49840
$693$	−0.180969	−0.00687443
$694$	49.2721	1.87034
$695$	7.72393	0.292986
$696$	49.8410	1.88922
$697$	−9.80455	−0.371374
$698$	−61.7713	−2.33808
$699$	0.418313	0.0158221
$700$	20.4927	0.774553
$701$	41.4152	1.56423	0.782115	−	0.623134i	$-0.214141\pi$
$701$	41.4152	1.56423	0.782115	+	0.623134i	$0.214141\pi$
$702$	13.1972	0.498097
$703$	−1.16970	−0.0441161
$704$	3.91611	0.147594
$705$	12.6211	0.475337
$706$	41.9831	1.58005
$707$	−14.7316	−0.554038
$708$	22.6309	0.850520
$709$	27.9629	1.05017	0.525084	−	0.851050i	$-0.324034\pi$
$709$	27.9629	1.05017	0.525084	+	0.851050i	$0.324034\pi$
$710$	−6.28249	−0.235778
$711$	−16.1948	−0.607353
$712$	−129.293	−4.84545
$713$	−0.825498	−0.0309151
$714$	7.61055	0.284818
$715$	−0.930118	−0.0347845
$716$	−101.466	−3.79195
$717$	15.0571	0.562319
$718$	−58.2054	−2.17221
$719$	−39.1607	−1.46045	−0.730224	−	0.683207i	$-0.760585\pi$
$719$	−39.1607	−1.46045	−0.730224	+	0.683207i	$0.760585\pi$
$720$	13.7478	0.512351
$721$	−5.96362	−0.222097
$722$	−51.0888	−1.90133
$723$	−5.31701	−0.197742
$724$	93.3594	3.46967
$725$	22.1679	0.823296
$726$	29.5406	1.09635
$727$	−39.7139	−1.47291	−0.736453	−	0.676488i	$-0.763501\pi$
$727$	−39.7139	−1.47291	−0.736453	+	0.676488i	$0.763501\pi$
$728$	42.9580	1.59213
$729$	1.00000	0.0370370
$730$	36.9341	1.36699
$731$	0.354618	0.0131160
$732$	−47.3811	−1.75126
$733$	−19.6633	−0.726280	−0.363140	−	0.931735i	$-0.618295\pi$
$733$	−19.6633	−0.726280	−0.363140	+	0.931735i	$0.618295\pi$
$734$	−12.0239	−0.443810
$735$	−1.04900	−0.0386928
$736$	17.7652	0.654835
$737$	−2.84254	−0.104706
$738$	−9.34660	−0.344053
$739$	−7.05398	−0.259485	−0.129742	−	0.991548i	$-0.541415\pi$
$739$	−7.05398	−0.259485	−0.129742	+	0.991548i	$0.541415\pi$
$740$	35.6307	1.30981
$741$	−0.886675	−0.0325728
$742$	−23.0369	−0.845710
$743$	−33.3545	−1.22366	−0.611829	−	0.790990i	$-0.709566\pi$
$743$	−33.3545	−1.22366	−0.611829	+	0.790990i	$0.709566\pi$
$744$	7.23766	0.265346
$745$	23.0032	0.842772
$746$	−82.8333	−3.03274
$747$	10.8757	0.397922
$748$	2.68706	0.0982486
$749$	8.55060	0.312432
$750$	25.1458	0.918195
$751$	5.86039	0.213849	0.106924	−	0.994267i	$-0.465900\pi$
$751$	5.86039	0.213849	0.106924	+	0.994267i	$0.465900\pi$
$752$	−157.682	−5.75008
$753$	7.19107	0.262057
$754$	75.0217	2.73213
$755$	17.6155	0.641095
$756$	5.25508	0.191125
$757$	−4.25464	−0.154638	−0.0773188	−	0.997006i	$-0.524636\pi$
$757$	−4.25464	−0.154638	−0.0773188	+	0.997006i	$0.524636\pi$
$758$	61.1466	2.22095
$759$	−0.180969	−0.00656874
$760$	−1.66441	−0.0603744
$761$	16.2300	0.588338	0.294169	−	0.955753i	$-0.404957\pi$
$761$	16.2300	0.588338	0.294169	+	0.955753i	$0.404957\pi$
$762$	−36.7454	−1.33115
$763$	−9.00123	−0.325866
$764$	−46.2066	−1.67170
$765$	2.96394	0.107161
$766$	−49.4204	−1.78563
$767$	21.1000	0.761878
$768$	−18.0162	−0.650105
$769$	−34.4633	−1.24278	−0.621388	−	0.783503i	$-0.713431\pi$
$769$	−34.4633	−1.24278	−0.621388	+	0.783503i	$0.713431\pi$
$770$	−0.511326	−0.0184269
$771$	8.77255	0.315936
$772$	−35.6964	−1.28474
$773$	40.0968	1.44218	0.721091	−	0.692840i	$-0.243641\pi$
$773$	40.0968	1.44218	0.721091	+	0.692840i	$0.243641\pi$
$774$	0.338054	0.0121511
$775$	3.21912	0.115634
$776$	91.7407	3.29330
$777$	6.46356	0.231879
$778$	−59.4245	−2.13047
$779$	0.627966	0.0224992
$780$	27.0094	0.967090
$781$	−0.402383	−0.0143984
$782$	7.61055	0.272153
$783$	5.68466	0.203153
$784$	13.1057	0.468060
$785$	17.5628	0.626845
$786$	26.1839	0.933947
$787$	−10.7641	−0.383697	−0.191849	−	0.981425i	$-0.561448\pi$
$787$	−10.7641	−0.383697	−0.191849	+	0.981425i	$0.561448\pi$
$788$	77.0047	2.74318
$789$	−16.0304	−0.570698
$790$	−45.7584	−1.62801
$791$	−9.81016	−0.348809
$792$	1.58667	0.0563797
$793$	−44.1761	−1.56874
$794$	62.7711	2.22766
$795$	−8.97173	−0.318195
$796$	−23.4098	−0.829737
$797$	28.7263	1.01754	0.508769	−	0.860903i	$-0.330101\pi$
$797$	28.7263	1.01754	0.508769	+	0.860903i	$0.330101\pi$
$798$	−0.487443	−0.0172553
$799$	−33.9952	−1.20266
$800$	−69.2774	−2.44933
$801$	−14.7466	−0.521045
$802$	38.2714	1.35141
$803$	2.36557	0.0834791
$804$	82.5435	2.91108
$805$	−1.04900	−0.0369723
$806$	10.8943	0.383734
$807$	−6.27373	−0.220846
$808$	129.161	4.54387
$809$	−7.02676	−0.247048	−0.123524	−	0.992342i	$-0.539420\pi$
$809$	−7.02676	−0.247048	−0.123524	+	0.992342i	$0.539420\pi$
$810$	2.82550	0.0992779
$811$	29.3729	1.03142	0.515712	−	0.856762i	$-0.327528\pi$
$811$	29.3729	1.03142	0.515712	+	0.856762i	$0.327528\pi$
$812$	29.8733	1.04835
$813$	17.1397	0.601114
$814$	3.15062	0.110429
$815$	26.3621	0.923425
$816$	−37.0301	−1.29631
$817$	−0.0227127	−0.000794616 0
$818$	−89.6293	−3.13381
$819$	4.89961	0.171206
$820$	−19.1287	−0.668004
$821$	−20.8592	−0.727990	−0.363995	−	0.931401i	$-0.618587\pi$
$821$	−20.8592	−0.727990	−0.363995	+	0.931401i	$0.618587\pi$
$822$	16.0729	0.560608
$823$	8.32421	0.290164	0.145082	−	0.989420i	$-0.453655\pi$
$823$	8.32421	0.290164	0.145082	+	0.989420i	$0.453655\pi$
$824$	52.2868	1.82150
$825$	0.705706	0.0245695
$826$	11.5996	0.403602
$827$	26.0102	0.904462	0.452231	−	0.891901i	$-0.350628\pi$
$827$	26.0102	0.904462	0.452231	+	0.891901i	$0.350628\pi$
$828$	5.25508	0.182627
$829$	20.5616	0.714132	0.357066	−	0.934079i	$-0.383777\pi$
$829$	20.5616	0.714132	0.357066	+	0.934079i	$0.383777\pi$
$830$	30.7293	1.06663
$831$	23.9563	0.831035
$832$	−106.026	−3.67580
$833$	2.82550	0.0978977
$834$	−19.8329	−0.686756
$835$	10.4692	0.362301
$836$	−0.172102	−0.00595226
$837$	0.825498	0.0285334
$838$	5.22056	0.180341
$839$	11.8568	0.409341	0.204670	−	0.978831i	$-0.434388\pi$
$839$	11.8568	0.409341	0.204670	+	0.978831i	$0.434388\pi$
$840$	9.19722	0.317334
$841$	3.31534	0.114322
$842$	−8.37289	−0.288549
$843$	7.27132	0.250438
$844$	−24.1625	−0.831708
$845$	11.5454	0.397174
$846$	−32.4074	−1.11419
$847$	10.9673	0.376839
$848$	112.089	3.84915
$849$	−26.5365	−0.910730
$850$	−29.6782	−1.01795
$851$	6.46356	0.221568
$852$	11.6847	0.400310
$853$	30.2041	1.03417	0.517085	−	0.855934i	$-0.327017\pi$
$853$	30.2041	1.03417	0.517085	+	0.855934i	$0.327017\pi$
$854$	−24.2855	−0.831032
$855$	−0.189835	−0.00649223
$856$	−74.9686	−2.56237
$857$	−50.5499	−1.72675	−0.863375	−	0.504562i	$-0.831654\pi$
$857$	−50.5499	−1.72675	−0.863375	+	0.504562i	$0.831654\pi$
$858$	2.38828	0.0815346
$859$	10.0834	0.344040	0.172020	−	0.985093i	$-0.444971\pi$
$859$	10.0834	0.344040	0.172020	+	0.985093i	$0.444971\pi$
$860$	0.691860	0.0235922
$861$	−3.47003	−0.118258
$862$	−73.3187	−2.49725
$863$	39.8098	1.35514	0.677571	−	0.735458i	$-0.263033\pi$
$863$	39.8098	1.35514	0.677571	+	0.735458i	$0.263033\pi$
$864$	−17.7652	−0.604386
$865$	−13.1193	−0.446069
$866$	−32.9004	−1.11800
$867$	9.01656	0.306219
$868$	4.33805	0.147243
$869$	−2.93075	−0.0994190
$870$	16.0620	0.544552
$871$	76.9599	2.60769
$872$	78.9195	2.67255
$873$	10.4636	0.354138
$874$	−0.487443	−0.0164880
$875$	9.33565	0.315603
$876$	−68.6928	−2.32092
$877$	−30.8941	−1.04322	−0.521609	−	0.853184i	$-0.674668\pi$
$877$	−30.8941	−1.04322	−0.521609	+	0.853184i	$0.674668\pi$
$878$	77.5354	2.61669
$879$	32.7086	1.10323
$880$	2.48792	0.0838679
$881$	15.2972	0.515375	0.257688	−	0.966228i	$-0.417039\pi$
$881$	15.2972	0.515375	0.257688	+	0.966228i	$0.417039\pi$
$882$	2.69353	0.0906957
$883$	3.35890	0.113036	0.0565180	−	0.998402i	$-0.482000\pi$
$883$	3.35890	0.113036	0.0565180	+	0.998402i	$0.482000\pi$
$884$	−72.7504	−2.44686
$885$	4.51748	0.151853
$886$	−86.4634	−2.90479
$887$	−51.2123	−1.71954	−0.859770	−	0.510681i	$-0.829393\pi$
$887$	−51.2123	−1.71954	−0.859770	+	0.510681i	$0.829393\pi$
$888$	−56.6701	−1.90173
$889$	−13.6421	−0.457542
$890$	−41.6664	−1.39666
$891$	0.180969	0.00606267
$892$	68.5483	2.29517
$893$	2.17734	0.0728618
$894$	−59.0657	−1.97545
$895$	−20.2542	−0.677022
$896$	−22.7567	−0.760247
$897$	4.89961	0.163593
$898$	−69.1148	−2.30639
$899$	4.69267	0.156509
$900$	−20.4927	−0.683091
$901$	24.1656	0.805073
$902$	−1.69144	−0.0563188
$903$	0.125506	0.00417659
$904$	86.0119	2.86071
$905$	18.6360	0.619481
$906$	−45.2317	−1.50272
$907$	27.1380	0.901103	0.450552	−	0.892750i	$-0.351227\pi$
$907$	27.1380	0.901103	0.450552	+	0.892750i	$0.351227\pi$
$908$	−1.68331	−0.0558626
$909$	14.7316	0.488615
$910$	13.8438	0.458918
$911$	−0.642982	−0.0213029	−0.0106515	−	0.999943i	$-0.503391\pi$
$911$	−0.642982	−0.0213029	−0.0106515	+	0.999943i	$0.503391\pi$
$912$	2.37172	0.0785354
$913$	1.96816	0.0651367
$914$	45.2677	1.49732
$915$	−9.45801	−0.312672
$916$	46.6892	1.54266
$917$	9.72104	0.321017
$918$	−7.61055	−0.251186
$919$	51.8741	1.71117	0.855585	−	0.517662i	$-0.173198\pi$
$919$	51.8741	1.71117	0.855585	+	0.517662i	$0.173198\pi$
$920$	9.19722	0.303223
$921$	20.4281	0.673129
$922$	23.5212	0.774628
$923$	10.8943	0.358589
$924$	0.951004	0.0312857
$925$	−25.2053	−0.828747
$926$	49.1062	1.61373
$927$	5.96362	0.195871
$928$	−100.989	−3.31514
$929$	−2.08704	−0.0684736	−0.0342368	−	0.999414i	$-0.510900\pi$
$929$	−2.08704	−0.0684736	−0.0342368	+	0.999414i	$0.510900\pi$
$930$	2.33244	0.0764838
$931$	−0.180969	−0.00593100
$932$	−2.19827	−0.0720067
$933$	−15.9515	−0.522229
$934$	37.2048	1.21738
$935$	0.536379	0.0175415
$936$	−42.9580	−1.40413
$937$	−35.6141	−1.16346	−0.581731	−	0.813382i	$-0.697624\pi$
$937$	−35.6141	−1.16346	−0.581731	+	0.813382i	$0.697624\pi$
$938$	42.3082	1.38141
$939$	2.91328	0.0950711
$940$	−66.3248	−2.16328
$941$	−19.5524	−0.637389	−0.318695	−	0.947857i	$-0.603244\pi$
$941$	−19.5524	−0.637389	−0.318695	+	0.947857i	$0.603244\pi$
$942$	−45.0964	−1.46932
$943$	−3.47003	−0.113000
$944$	−56.4393	−1.83694
$945$	1.04900	0.0341238
$946$	0.0611772	0.00198904
$947$	−14.2793	−0.464016	−0.232008	−	0.972714i	$-0.574530\pi$
$947$	−14.2793	−0.464016	−0.232008	+	0.972714i	$0.574530\pi$
$948$	85.1050	2.76408
$949$	−64.0462	−2.07903
$950$	1.90084	0.0616713
$951$	−0.295090	−0.00956894
$952$	−24.7729	−0.802895
$953$	36.6697	1.18785	0.593924	−	0.804521i	$-0.297578\pi$
$953$	36.6697	1.18785	0.593924	+	0.804521i	$0.297578\pi$
$954$	23.0369	0.745846
$955$	−9.22356	−0.298467
$956$	−79.1264	−2.55913
$957$	1.02874	0.0332546
$958$	−52.4737	−1.69535
$959$	5.96725	0.192693
$960$	−22.7000	−0.732639
$961$	−30.3186	−0.978018
$962$	−85.3010	−2.75021
$963$	−8.55060	−0.275539
$964$	27.9413	0.899928
$965$	−7.12557	−0.229380
$966$	2.69353	0.0866628
$967$	3.23340	0.103979	0.0519895	−	0.998648i	$-0.483444\pi$
$967$	3.23340	0.103979	0.0519895	+	0.998648i	$0.483444\pi$
$968$	−96.1568	−3.09060
$969$	0.511326	0.0164262
$970$	29.5648	0.949267
$971$	35.0009	1.12323	0.561617	−	0.827398i	$-0.310180\pi$
$971$	35.0009	1.12323	0.561617	+	0.827398i	$0.310180\pi$
$972$	−5.25508	−0.168557
$973$	−7.36317	−0.236052
$974$	74.1442	2.37573
$975$	−19.1065	−0.611899
$976$	118.164	3.78234
$977$	11.1142	0.355576	0.177788	−	0.984069i	$-0.443106\pi$
$977$	11.1142	0.355576	0.177788	+	0.984069i	$0.443106\pi$
$978$	−67.6904	−2.16450
$979$	−2.66867	−0.0852910
$980$	5.51256	0.176092
$981$	9.00123	0.287387
$982$	41.3584	1.31980
$983$	12.0343	0.383834	0.191917	−	0.981411i	$-0.438529\pi$
$983$	12.0343	0.383834	0.191917	+	0.981411i	$0.438529\pi$
$984$	30.4239	0.969879
$985$	15.3714	0.489772
$986$	−43.2634	−1.37779
$987$	−12.0316	−0.382969
$988$	4.65955	0.148240
$989$	0.125506	0.00399087
$990$	0.511326	0.0162510
$991$	59.7732	1.89876	0.949380	−	0.314130i	$-0.101713\pi$
$991$	59.7732	1.89876	0.949380	+	0.314130i	$0.101713\pi$
$992$	−14.6652	−0.465619
$993$	−10.8907	−0.345607
$994$	5.98905	0.189961
$995$	−4.67296	−0.148143
$996$	−57.1528	−1.81096
$997$	24.4287	0.773666	0.386833	−	0.922150i	$-0.373569\pi$
$997$	24.4287	0.773666	0.386833	+	0.922150i	$0.373569\pi$
$998$	−21.8612	−0.692004
$999$	−6.46356	−0.204498

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.a.j.1.4	✓	4
3.2	odd	2		1449.2.a.o.1.1		4
4.3	odd	2		7728.2.a.ce.1.2		4
7.6	odd	2		3381.2.a.x.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.j.1.4	✓	4	1.1	even	1	trivial
1449.2.a.o.1.1		4	3.2	odd	2
3381.2.a.x.1.4		4	7.6	odd	2
7728.2.a.ce.1.2		4	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q+2.69353 q^{2} -1.00000 q^{3} +5.25508 q^{4} +1.04900 q^{5} -2.69353 q^{6} -1.00000 q^{7} +8.76763 q^{8} +1.00000 q^{9} +2.82550 q^{10} +0.180969 q^{11} -5.25508 q^{12} -4.89961 q^{13} -2.69353 q^{14} -1.04900 q^{15} +13.1057 q^{16} +2.82550 q^{17} +2.69353 q^{18} -0.180969 q^{19} +5.51256 q^{20} +1.00000 q^{21} +0.487443 q^{22} +1.00000 q^{23} -8.76763 q^{24} -3.89961 q^{25} -13.1972 q^{26} -1.00000 q^{27} -5.25508 q^{28} -5.68466 q^{29} -2.82550 q^{30} -0.825498 q^{31} +17.7652 q^{32} -0.180969 q^{33} +7.61055 q^{34} -1.04900 q^{35} +5.25508 q^{36} +6.46356 q^{37} -0.487443 q^{38} +4.89961 q^{39} +9.19722 q^{40} -3.47003 q^{41} +2.69353 q^{42} +0.125506 q^{43} +0.951004 q^{44} +1.04900 q^{45} +2.69353 q^{46} -12.0316 q^{47} -13.1057 q^{48} +1.00000 q^{49} -10.5037 q^{50} -2.82550 q^{51} -25.7478 q^{52} +8.55269 q^{53} -2.69353 q^{54} +0.189835 q^{55} -8.76763 q^{56} +0.180969 q^{57} -15.3118 q^{58} -4.30647 q^{59} -5.51256 q^{60} +9.01625 q^{61} -2.22350 q^{62} -1.00000 q^{63} +21.6397 q^{64} -5.13967 q^{65} -0.487443 q^{66} -15.7074 q^{67} +14.8482 q^{68} -1.00000 q^{69} -2.82550 q^{70} -2.22350 q^{71} +8.76763 q^{72} +13.0717 q^{73} +17.4098 q^{74} +3.89961 q^{75} -0.951004 q^{76} -0.180969 q^{77} +13.1972 q^{78} -16.1948 q^{79} +13.7478 q^{80} +1.00000 q^{81} -9.34660 q^{82} +10.8757 q^{83} +5.25508 q^{84} +2.96394 q^{85} +0.338054 q^{86} +5.68466 q^{87} +1.58667 q^{88} -14.7466 q^{89} +2.82550 q^{90} +4.89961 q^{91} +5.25508 q^{92} +0.825498 q^{93} -32.4074 q^{94} -0.189835 q^{95} -17.7652 q^{96} +10.4636 q^{97} +2.69353 q^{98} +0.180969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{3} + 4 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} + 4 q^{9} + 2 q^{10} + q^{11} - 4 q^{12} + 7 q^{13} - 2 q^{14} - 5 q^{15} + 8 q^{16} + 2 q^{17} + 2 q^{18} - q^{19} + 13 q^{20}+ \cdots + q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 + 4 * q^9 + 2 * q^10 + q^11 - 4 * q^12 + 7 * q^13 - 2 * q^14 - 5 * q^15 + 8 * q^16 + 2 * q^17 + 2 * q^18 - q^19 + 13 * q^20 + 4 * q^21 + 11 * q^22 + 4 * q^23 - 9 * q^24 + 11 * q^25 - 19 * q^26 - 4 * q^27 - 4 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 20 * q^32 - q^33 + 23 * q^34 - 5 * q^35 + 4 * q^36 + 16 * q^37 - 11 * q^38 - 7 * q^39 + 3 * q^40 + 5 * q^41 + 2 * q^42 + 9 * q^43 + 3 * q^44 + 5 * q^45 + 2 * q^46 - 21 * q^47 - 8 * q^48 + 4 * q^49 - 17 * q^50 - 2 * q^51 - 24 * q^52 + 10 * q^53 - 2 * q^54 + 17 * q^55 - 9 * q^56 + q^57 + q^58 - 26 * q^59 - 13 * q^60 + 2 * q^61 - 19 * q^62 - 4 * q^63 + 27 * q^64 + 26 * q^65 - 11 * q^66 + 5 * q^67 + 7 * q^68 - 4 * q^69 - 2 * q^70 - 19 * q^71 + 9 * q^72 + 10 * q^73 + 9 * q^74 - 11 * q^75 - 3 * q^76 - q^77 + 19 * q^78 - 6 * q^79 - 24 * q^80 + 4 * q^81 - 31 * q^82 - 2 * q^83 + 4 * q^84 - 7 * q^85 - 17 * q^86 - 2 * q^87 - 20 * q^88 - 17 * q^89 + 2 * q^90 - 7 * q^91 + 4 * q^92 - 6 * q^93 - 44 * q^94 - 17 * q^95 - 20 * q^96 + 32 * q^97 + 2 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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