LMFDB - Embedded newform 595.2.a.f.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [595,2,Mod(1,595)] 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("595.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(595, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 595 = 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	595.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-2,-2,4,-3] 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:	$4.75109892027$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.169.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x - 1 $ x^3 - x^2 - 4*x - 1
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			1.1
Root			$-1.37720$ of defining polynomial
Character	$\chi$	$=$	595.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.37720 q^{2} +1.65109 q^{3} +3.65109 q^{4} -1.00000 q^{5} -3.92498 q^{6} +1.00000 q^{7} -3.92498 q^{8} -0.273891 q^{9} +2.37720 q^{10} -3.00000 q^{11} +6.02830 q^{12} -3.92498 q^{13} -2.37720 q^{14} -1.65109 q^{15} +2.02830 q^{16} +1.00000 q^{17} +0.651093 q^{18} -4.30219 q^{19} -3.65109 q^{20} +1.65109 q^{21} +7.13161 q^{22} -4.09556 q^{23} -6.48052 q^{24} +1.00000 q^{25} +9.33048 q^{26} -5.40550 q^{27} +3.65109 q^{28} -9.37720 q^{29} +3.92498 q^{30} +5.57608 q^{31} +3.02830 q^{32} -4.95328 q^{33} -2.37720 q^{34} -1.00000 q^{35} -1.00000 q^{36} +10.2555 q^{37} +10.2272 q^{38} -6.48052 q^{39} +3.92498 q^{40} -7.58383 q^{41} -3.92498 q^{42} +7.37720 q^{43} -10.9533 q^{44} +0.273891 q^{45} +9.73598 q^{46} +5.95328 q^{47} +3.34891 q^{48} +1.00000 q^{49} -2.37720 q^{50} +1.65109 q^{51} -14.3305 q^{52} -7.93273 q^{53} +12.8500 q^{54} +3.00000 q^{55} -3.92498 q^{56} -7.10331 q^{57} +22.2915 q^{58} -8.50106 q^{59} -6.02830 q^{60} -4.44447 q^{61} -13.2555 q^{62} -0.273891 q^{63} -11.2555 q^{64} +3.92498 q^{65} +11.7750 q^{66} -7.61212 q^{67} +3.65109 q^{68} -6.76216 q^{69} +2.37720 q^{70} -2.44447 q^{71} +1.07502 q^{72} +7.17833 q^{73} -24.3793 q^{74} +1.65109 q^{75} -15.7077 q^{76} -3.00000 q^{77} +15.4055 q^{78} -14.6121 q^{79} -2.02830 q^{80} -8.10331 q^{81} +18.0283 q^{82} -10.7827 q^{83} +6.02830 q^{84} -1.00000 q^{85} -17.5371 q^{86} -15.4826 q^{87} +11.7750 q^{88} +7.75441 q^{89} -0.651093 q^{90} -3.92498 q^{91} -14.9533 q^{92} +9.20662 q^{93} -14.1522 q^{94} +4.30219 q^{95} +5.00000 q^{96} +0.726109 q^{97} -2.37720 q^{98} +0.821672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + q^{9} + 2 q^{10} - 9 q^{11} + 6 q^{12} - 3 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} + 3 q^{17} - 5 q^{18} + q^{19} - 4 q^{20}+ \cdots - 3 q^{99}+O(q^{100}) $ 3 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + q^9 + 2 * q^10 - 9 * q^11 + 6 * q^12 - 3 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 + 3 * q^17 - 5 * q^18 + q^19 - 4 * q^20 - 2 * q^21 + 6 * q^22 - 5 * q^23 - 11 * q^24 + 3 * q^25 + 2 * q^26 + q^27 + 4 * q^28 - 23 * q^29 + 3 * q^30 + q^31 - 3 * q^32 + 6 * q^33 - 2 * q^34 - 3 * q^35 - 3 * q^36 - 4 * q^37 + 8 * q^38 - 11 * q^39 + 3 * q^40 - 11 * q^41 - 3 * q^42 + 17 * q^43 - 12 * q^44 - q^45 - 14 * q^46 - 3 * q^47 + 17 * q^48 + 3 * q^49 - 2 * q^50 - 2 * q^51 - 17 * q^52 - 19 * q^53 + 21 * q^54 + 9 * q^55 - 3 * q^56 - 18 * q^57 + 24 * q^58 - q^59 - 6 * q^60 - 13 * q^61 - 5 * q^62 + q^63 + q^64 + 3 * q^65 + 9 * q^66 + q^67 + 4 * q^68 - 14 * q^69 + 2 * q^70 - 7 * q^71 + 12 * q^72 + 27 * q^73 - 19 * q^74 - 2 * q^75 - 16 * q^76 - 9 * q^77 + 29 * q^78 - 20 * q^79 + 6 * q^80 - 21 * q^81 + 42 * q^82 - 10 * q^83 + 6 * q^84 - 3 * q^85 - 20 * q^86 + 11 * q^87 + 9 * q^88 + 13 * q^89 + 5 * q^90 - 3 * q^91 - 24 * q^92 + 21 * q^93 - 11 * q^94 - q^95 + 15 * q^96 + 4 * q^97 - 2 * q^98 - 3 * 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 $

$2$	−2.37720	−1.68094	−0.840468	−	0.541861i	$-0.817720\pi$
$2$	−2.37720	−1.68094	−0.840468	+	0.541861i	$0.817720\pi$
$3$	1.65109	0.953259	0.476630	−	0.879104i	$-0.341858\pi$
$3$	1.65109	0.953259	0.476630	+	0.879104i	$0.341858\pi$
$4$	3.65109	1.82555
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.92498	−1.60237
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.92498	−1.38769
$9$	−0.273891	−0.0912969
$10$	2.37720	0.751738
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	6.02830	1.74022
$13$	−3.92498	−1.08859	−0.544297	−	0.838892i	$-0.683204\pi$
$13$	−3.92498	−1.08859	−0.544297	+	0.838892i	$0.683204\pi$
$14$	−2.37720	−0.635334
$15$	−1.65109	−0.426310
$16$	2.02830	0.507074
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.651093	0.153464
$19$	−4.30219	−0.986989	−0.493495	−	0.869749i	$-0.664281\pi$
$19$	−4.30219	−0.986989	−0.493495	+	0.869749i	$0.664281\pi$
$20$	−3.65109	−0.816409
$21$	1.65109	0.360298
$22$	7.13161	1.52046
$23$	−4.09556	−0.853984	−0.426992	−	0.904255i	$-0.640427\pi$
$23$	−4.09556	−0.853984	−0.426992	+	0.904255i	$0.640427\pi$
$24$	−6.48052	−1.32283
$25$	1.00000	0.200000
$26$	9.33048	1.82986
$27$	−5.40550	−1.04029
$28$	3.65109	0.689992
$29$	−9.37720	−1.74130	−0.870651	−	0.491900i	$-0.836302\pi$
$29$	−9.37720	−1.74130	−0.870651	+	0.491900i	$0.836302\pi$
$30$	3.92498	0.716601
$31$	5.57608	1.00149	0.500747	−	0.865594i	$-0.333059\pi$
$31$	5.57608	1.00149	0.500747	+	0.865594i	$0.333059\pi$
$32$	3.02830	0.535332
$33$	−4.95328	−0.862255
$34$	−2.37720	−0.407687
$35$	−1.00000	−0.169031
$36$	−1.00000	−0.166667
$37$	10.2555	1.68599	0.842994	−	0.537923i	$-0.180791\pi$
$37$	10.2555	1.68599	0.842994	+	0.537923i	$0.180791\pi$
$38$	10.2272	1.65907
$39$	−6.48052	−1.03771
$40$	3.92498	0.620594
$41$	−7.58383	−1.18439	−0.592197	−	0.805793i	$-0.701739\pi$
$41$	−7.58383	−1.18439	−0.592197	+	0.805793i	$0.701739\pi$
$42$	−3.92498	−0.605638
$43$	7.37720	1.12501	0.562506	−	0.826793i	$-0.309837\pi$
$43$	7.37720	1.12501	0.562506	+	0.826793i	$0.309837\pi$
$44$	−10.9533	−1.65127
$45$	0.273891	0.0408292
$46$	9.73598	1.43549
$47$	5.95328	0.868375	0.434188	−	0.900822i	$-0.357036\pi$
$47$	5.95328	0.868375	0.434188	+	0.900822i	$0.357036\pi$
$48$	3.34891	0.483373
$49$	1.00000	0.142857
$50$	−2.37720	−0.336187
$51$	1.65109	0.231199
$52$	−14.3305	−1.98728
$53$	−7.93273	−1.08964	−0.544822	−	0.838551i	$-0.683403\pi$
$53$	−7.93273	−1.08964	−0.544822	+	0.838551i	$0.683403\pi$
$54$	12.8500	1.74866
$55$	3.00000	0.404520
$56$	−3.92498	−0.524498
$57$	−7.10331	−0.940857
$58$	22.2915	2.92702
$59$	−8.50106	−1.10674	−0.553372	−	0.832934i	$-0.686659\pi$
$59$	−8.50106	−1.10674	−0.553372	+	0.832934i	$0.686659\pi$
$60$	−6.02830	−0.778250
$61$	−4.44447	−0.569056	−0.284528	−	0.958668i	$-0.591837\pi$
$61$	−4.44447	−0.569056	−0.284528	+	0.958668i	$0.591837\pi$
$62$	−13.2555	−1.68345
$63$	−0.273891	−0.0345070
$64$	−11.2555	−1.40693
$65$	3.92498	0.486834
$66$	11.7750	1.44940
$67$	−7.61212	−0.929969	−0.464984	−	0.885319i	$-0.653940\pi$
$67$	−7.61212	−0.929969	−0.464984	+	0.885319i	$0.653940\pi$
$68$	3.65109	0.442760
$69$	−6.76216	−0.814068
$70$	2.37720	0.284130
$71$	−2.44447	−0.290105	−0.145053	−	0.989424i	$-0.546335\pi$
$71$	−2.44447	−0.290105	−0.145053	+	0.989424i	$0.546335\pi$
$72$	1.07502	0.126692
$73$	7.17833	0.840160	0.420080	−	0.907487i	$-0.362002\pi$
$73$	7.17833	0.840160	0.420080	+	0.907487i	$0.362002\pi$
$74$	−24.3793	−2.83404
$75$	1.65109	0.190652
$76$	−15.7077	−1.80180
$77$	−3.00000	−0.341882
$78$	15.4055	1.74433
$79$	−14.6121	−1.64399	−0.821996	−	0.569493i	$-0.807140\pi$
$79$	−14.6121	−1.64399	−0.821996	+	0.569493i	$0.807140\pi$
$80$	−2.02830	−0.226770
$81$	−8.10331	−0.900368
$82$	18.0283	1.99089
$83$	−10.7827	−1.18356	−0.591778	−	0.806101i	$-0.701574\pi$
$83$	−10.7827	−1.18356	−0.591778	+	0.806101i	$0.701574\pi$
$84$	6.02830	0.657741
$85$	−1.00000	−0.108465
$86$	−17.5371	−1.89107
$87$	−15.4826	−1.65991
$88$	11.7750	1.25521
$89$	7.75441	0.821965	0.410983	−	0.911643i	$-0.365186\pi$
$89$	7.75441	0.821965	0.410983	+	0.911643i	$0.365186\pi$
$90$	−0.651093	−0.0686313
$91$	−3.92498	−0.411450
$92$	−14.9533	−1.55899
$93$	9.20662	0.954682
$94$	−14.1522	−1.45968
$95$	4.30219	0.441395
$96$	5.00000	0.510310
$97$	0.726109	0.0737252	0.0368626	−	0.999320i	$-0.488264\pi$
$97$	0.726109	0.0737252	0.0368626	+	0.999320i	$0.488264\pi$
$98$	−2.37720	−0.240134
$99$	0.821672	0.0825811
$100$	3.65109	0.365109
$101$	10.9816	1.09271	0.546354	−	0.837554i	$-0.316015\pi$
$101$	10.9816	1.09271	0.546354	+	0.837554i	$0.316015\pi$
$102$	−3.92498	−0.388631
$103$	−7.78270	−0.766852	−0.383426	−	0.923572i	$-0.625256\pi$
$103$	−7.78270	−0.766852	−0.383426	+	0.923572i	$0.625256\pi$
$104$	15.4055	1.51063
$105$	−1.65109	−0.161130
$106$	18.8577	1.83162
$107$	−2.51948	−0.243568	−0.121784	−	0.992557i	$-0.538861\pi$
$107$	−2.51948	−0.243568	−0.121784	+	0.992557i	$0.538861\pi$
$108$	−19.7360	−1.89910
$109$	−2.42392	−0.232170	−0.116085	−	0.993239i	$-0.537034\pi$
$109$	−2.42392	−0.232170	−0.116085	+	0.993239i	$0.537034\pi$
$110$	−7.13161	−0.679972
$111$	16.9327	1.60718
$112$	2.02830	0.191656
$113$	15.9816	1.50342	0.751710	−	0.659494i	$-0.229229\pi$
$113$	15.9816	1.50342	0.751710	+	0.659494i	$0.229229\pi$
$114$	16.8860	1.58152
$115$	4.09556	0.381913
$116$	−34.2370	−3.17883
$117$	1.07502	0.0993853
$118$	20.2087	1.86037
$119$	1.00000	0.0916698
$120$	6.48052	0.591587
$121$	−2.00000	−0.181818
$122$	10.5654	0.956547
$123$	−12.5216	−1.12904
$124$	20.3588	1.82827
$125$	−1.00000	−0.0894427
$126$	0.651093	0.0580040
$127$	−0.508811	−0.0451497	−0.0225749	−	0.999745i	$-0.507186\pi$
$127$	−0.508811	−0.0451497	−0.0225749	+	0.999745i	$0.507186\pi$
$128$	20.6999	1.82963
$129$	12.1805	1.07243
$130$	−9.33048	−0.818338
$131$	13.5577	1.18454	0.592269	−	0.805740i	$-0.298232\pi$
$131$	13.5577	1.18454	0.592269	+	0.805740i	$0.298232\pi$
$132$	−18.0849	−1.57409
$133$	−4.30219	−0.373047
$134$	18.0956	1.56322
$135$	5.40550	0.465231
$136$	−3.92498	−0.336565
$137$	12.6249	1.07862	0.539310	−	0.842107i	$-0.318685\pi$
$137$	12.6249	1.07862	0.539310	+	0.842107i	$0.318685\pi$
$138$	16.0750	1.36840
$139$	3.39775	0.288193	0.144097	−	0.989564i	$-0.453972\pi$
$139$	3.39775	0.288193	0.144097	+	0.989564i	$0.453972\pi$
$140$	−3.65109	−0.308574
$141$	9.82942	0.827787
$142$	5.81100	0.487648
$143$	11.7750	0.984671
$144$	−0.555531	−0.0462943
$145$	9.37720	0.778734
$146$	−17.0643	−1.41226
$147$	1.65109	0.136180
$148$	37.4437	3.07785
$149$	1.13161	0.0927050	0.0463525	−	0.998925i	$-0.485240\pi$
$149$	1.13161	0.0927050	0.0463525	+	0.998925i	$0.485240\pi$
$150$	−3.92498	−0.320474
$151$	8.86547	0.721462	0.360731	−	0.932670i	$-0.382527\pi$
$151$	8.86547	0.721462	0.360731	+	0.932670i	$0.382527\pi$
$152$	16.8860	1.36964
$153$	−0.273891	−0.0221427
$154$	7.13161	0.574681
$155$	−5.57608	−0.447881
$156$	−23.6610	−1.89439
$157$	−16.2944	−1.30044	−0.650219	−	0.759747i	$-0.725323\pi$
$157$	−16.2944	−1.30044	−0.650219	+	0.759747i	$0.725323\pi$
$158$	34.7360	2.76345
$159$	−13.0977	−1.03871
$160$	−3.02830	−0.239408
$161$	−4.09556	−0.322776
$162$	19.2632	1.51346
$163$	−2.66177	−0.208486	−0.104243	−	0.994552i	$-0.533242\pi$
$163$	−2.66177	−0.208486	−0.104243	+	0.994552i	$0.533242\pi$
$164$	−27.6893	−2.16217
$165$	4.95328	0.385612
$166$	25.6327	1.98948
$167$	2.31286	0.178974	0.0894872	−	0.995988i	$-0.471477\pi$
$167$	2.31286	0.178974	0.0894872	+	0.995988i	$0.471477\pi$
$168$	−6.48052	−0.499983
$169$	2.40550	0.185038
$170$	2.37720	0.182323
$171$	1.17833	0.0901090
$172$	26.9349	2.05376
$173$	−25.2165	−1.91717	−0.958587	−	0.284799i	$-0.908073\pi$
$173$	−25.2165	−1.91717	−0.958587	+	0.284799i	$0.908073\pi$
$174$	36.8054	2.79021
$175$	1.00000	0.0755929
$176$	−6.08489	−0.458666
$177$	−14.0360	−1.05501
$178$	−18.4338	−1.38167
$179$	19.8315	1.48228	0.741140	−	0.671351i	$-0.234286\pi$
$179$	19.8315	1.48228	0.741140	+	0.671351i	$0.234286\pi$
$180$	1.00000	0.0745356
$181$	−16.7750	−1.24687	−0.623436	−	0.781874i	$-0.714264\pi$
$181$	−16.7750	−1.24687	−0.623436	+	0.781874i	$0.714264\pi$
$182$	9.33048	0.691621
$183$	−7.33823	−0.542458
$184$	16.0750	1.18507
$185$	−10.2555	−0.753997
$186$	−21.8860	−1.60476
$187$	−3.00000	−0.219382
$188$	21.7360	1.58526
$189$	−5.40550	−0.393192
$190$	−10.2272	−0.741957
$191$	8.80325	0.636981	0.318490	−	0.947926i	$-0.396824\pi$
$191$	8.80325	0.636981	0.318490	+	0.947926i	$0.396824\pi$
$192$	−18.5838	−1.34117
$193$	19.1882	1.38120	0.690598	−	0.723238i	$-0.257347\pi$
$193$	19.1882	1.38120	0.690598	+	0.723238i	$0.257347\pi$
$194$	−1.72611	−0.123927
$195$	6.48052	0.464079
$196$	3.65109	0.260792
$197$	16.4437	1.17156	0.585781	−	0.810469i	$-0.300788\pi$
$197$	16.4437	1.17156	0.585781	+	0.810469i	$0.300788\pi$
$198$	−1.95328	−0.138814
$199$	11.6482	0.825717	0.412858	−	0.910795i	$-0.364530\pi$
$199$	11.6482	0.825717	0.412858	+	0.910795i	$0.364530\pi$
$200$	−3.92498	−0.277538
$201$	−12.5683	−0.886501
$202$	−26.1054	−1.83677
$203$	−9.37720	−0.658151
$204$	6.02830	0.422065
$205$	7.58383	0.529677
$206$	18.5011	1.28903
$207$	1.12174	0.0779660
$208$	−7.96103	−0.551998
$209$	12.9066	0.892765
$210$	3.92498	0.270850
$211$	−18.7437	−1.29037	−0.645186	−	0.764026i	$-0.723220\pi$
$211$	−18.7437	−1.29037	−0.645186	+	0.764026i	$0.723220\pi$
$212$	−28.9632	−1.98920
$213$	−4.03605	−0.276545
$214$	5.98933	0.409422
$215$	−7.37720	−0.503121
$216$	21.2165	1.44360
$217$	5.57608	0.378529
$218$	5.76216	0.390262
$219$	11.8521	0.800890
$220$	10.9533	0.738470
$221$	−3.92498	−0.264023
$222$	−40.2525	−2.70157
$223$	4.34116	0.290705	0.145353	−	0.989380i	$-0.453568\pi$
$223$	4.34116	0.290705	0.145353	+	0.989380i	$0.453568\pi$
$224$	3.02830	0.202337
$225$	−0.273891	−0.0182594
$226$	−37.9914	−2.52715
$227$	18.9349	1.25675	0.628375	−	0.777910i	$-0.283720\pi$
$227$	18.9349	1.25675	0.628375	+	0.777910i	$0.283720\pi$
$228$	−25.9349	−1.71758
$229$	−15.7077	−1.03799	−0.518997	−	0.854776i	$-0.673694\pi$
$229$	−15.7077	−1.03799	−0.518997	+	0.854776i	$0.673694\pi$
$230$	−9.73598	−0.641972
$231$	−4.95328	−0.325902
$232$	36.8054	2.41639
$233$	−18.4933	−1.21154	−0.605769	−	0.795641i	$-0.707134\pi$
$233$	−18.4933	−1.21154	−0.605769	+	0.795641i	$0.707134\pi$
$234$	−2.55553	−0.167060
$235$	−5.95328	−0.388349
$236$	−31.0382	−2.02041
$237$	−24.1260	−1.56715
$238$	−2.37720	−0.154091
$239$	−18.8988	−1.22246	−0.611231	−	0.791452i	$-0.709325\pi$
$239$	−18.8988	−1.22246	−0.611231	+	0.791452i	$0.709325\pi$
$240$	−3.34891	−0.216171
$241$	7.29151	0.469688	0.234844	−	0.972033i	$-0.424542\pi$
$241$	7.29151	0.469688	0.234844	+	0.972033i	$0.424542\pi$
$242$	4.75441	0.305625
$243$	2.83717	0.182005
$244$	−16.2272	−1.03884
$245$	−1.00000	−0.0638877
$246$	29.7664	1.89784
$247$	16.8860	1.07443
$248$	−21.8860	−1.38976
$249$	−17.8032	−1.12824
$250$	2.37720	0.150348
$251$	17.6249	1.11248	0.556238	−	0.831023i	$-0.312244\pi$
$251$	17.6249	1.11248	0.556238	+	0.831023i	$0.312244\pi$
$252$	−1.00000	−0.0629941
$253$	12.2867	0.772457
$254$	1.20955	0.0758938
$255$	−1.65109	−0.103395
$256$	−26.6970	−1.66856
$257$	9.75441	0.608463	0.304232	−	0.952598i	$-0.401600\pi$
$257$	9.75441	0.608463	0.304232	+	0.952598i	$0.401600\pi$
$258$	−28.9554	−1.80268
$259$	10.2555	0.637244
$260$	14.3305	0.888739
$261$	2.56833	0.158975
$262$	−32.2293	−1.99113
$263$	−27.9504	−1.72349	−0.861746	−	0.507339i	$-0.830629\pi$
$263$	−27.9504	−1.72349	−0.861746	+	0.507339i	$0.830629\pi$
$264$	19.4415	1.19654
$265$	7.93273	0.487304
$266$	10.2272	0.627068
$267$	12.8032	0.783546
$268$	−27.7926	−1.69770
$269$	−2.09344	−0.127639	−0.0638196	−	0.997961i	$-0.520328\pi$
$269$	−2.09344	−0.127639	−0.0638196	+	0.997961i	$0.520328\pi$
$270$	−12.8500	−0.782024
$271$	2.11399	0.128415	0.0642077	−	0.997937i	$-0.479548\pi$
$271$	2.11399	0.128415	0.0642077	+	0.997937i	$0.479548\pi$
$272$	2.02830	0.122984
$273$	−6.48052	−0.392219
$274$	−30.0120	−1.81309
$275$	−3.00000	−0.180907
$276$	−24.6893	−1.48612
$277$	−10.9709	−0.659178	−0.329589	−	0.944125i	$-0.606910\pi$
$277$	−10.9709	−0.659178	−0.329589	+	0.944125i	$0.606910\pi$
$278$	−8.07714	−0.484435
$279$	−1.52723	−0.0914332
$280$	3.92498	0.234563
$281$	2.59450	0.154775	0.0773875	−	0.997001i	$-0.475342\pi$
$281$	2.59450	0.154775	0.0773875	+	0.997001i	$0.475342\pi$
$282$	−23.3665	−1.39146
$283$	−20.1620	−1.19851	−0.599254	−	0.800559i	$-0.704536\pi$
$283$	−20.1620	−1.19851	−0.599254	+	0.800559i	$0.704536\pi$
$284$	−8.92498	−0.529600
$285$	7.10331	0.420764
$286$	−27.9914	−1.65517
$287$	−7.58383	−0.447659
$288$	−0.829422	−0.0488741
$289$	1.00000	0.0588235
$290$	−22.2915	−1.30900
$291$	1.19887	0.0702793
$292$	26.2087	1.53375
$293$	14.8548	0.867826	0.433913	−	0.900955i	$-0.357132\pi$
$293$	14.8548	0.867826	0.433913	+	0.900955i	$0.357132\pi$
$294$	−3.92498	−0.228910
$295$	8.50106	0.494951
$296$	−40.2525	−2.33963
$297$	16.2165	0.940977
$298$	−2.69006	−0.155831
$299$	16.0750	0.929642
$300$	6.02830	0.348044
$301$	7.37720	0.425215
$302$	−21.0750	−1.21273
$303$	18.1316	1.04163
$304$	−8.72611	−0.500477
$305$	4.44447	0.254490
$306$	0.651093	0.0372205
$307$	24.0099	1.37032	0.685158	−	0.728395i	$-0.259733\pi$
$307$	24.0099	1.37032	0.685158	+	0.728395i	$0.259733\pi$
$308$	−10.9533	−0.624121
$309$	−12.8500	−0.731009
$310$	13.2555	0.752860
$311$	24.1239	1.36794	0.683969	−	0.729511i	$-0.260252\pi$
$311$	24.1239	1.36794	0.683969	+	0.729511i	$0.260252\pi$
$312$	25.4359	1.44003
$313$	29.5315	1.66922	0.834609	−	0.550843i	$-0.185694\pi$
$313$	29.5315	1.66922	0.834609	+	0.550843i	$0.185694\pi$
$314$	38.7352	2.18595
$315$	0.273891	0.0154320
$316$	−53.3502	−3.00118
$317$	−3.53499	−0.198545	−0.0992723	−	0.995060i	$-0.531651\pi$
$317$	−3.53499	−0.198545	−0.0992723	+	0.995060i	$0.531651\pi$
$318$	31.1359	1.74601
$319$	28.1316	1.57507
$320$	11.2555	0.629200
$321$	−4.15990	−0.232183
$322$	9.73598	0.542565
$323$	−4.30219	−0.239380
$324$	−29.5860	−1.64366
$325$	−3.92498	−0.217719
$326$	6.32756	0.350451
$327$	−4.00212	−0.221318
$328$	29.7664	1.64357
$329$	5.95328	0.328215
$330$	−11.7750	−0.648190
$331$	22.8598	1.25649	0.628245	−	0.778015i	$-0.283773\pi$
$331$	22.8598	1.25649	0.628245	+	0.778015i	$0.283773\pi$
$332$	−39.3687	−2.16064
$333$	−2.80888	−0.153925
$334$	−5.49814	−0.300845
$335$	7.61212	0.415895
$336$	3.34891	0.182698
$337$	−26.6580	−1.45216	−0.726078	−	0.687612i	$-0.758659\pi$
$337$	−26.6580	−1.45216	−0.726078	+	0.687612i	$0.758659\pi$
$338$	−5.71836	−0.311038
$339$	26.3871	1.43315
$340$	−3.65109	−0.198008
$341$	−16.7282	−0.905885
$342$	−2.80113	−0.151468
$343$	1.00000	0.0539949
$344$	−28.9554	−1.56117
$345$	6.76216	0.364062
$346$	59.9447	3.22265
$347$	−21.7771	−1.16905	−0.584527	−	0.811374i	$-0.698720\pi$
$347$	−21.7771	−1.16905	−0.584527	+	0.811374i	$0.698720\pi$
$348$	−56.5286	−3.03025
$349$	−10.3206	−0.552450	−0.276225	−	0.961093i	$-0.589083\pi$
$349$	−10.3206	−0.552450	−0.276225	+	0.961093i	$0.589083\pi$
$350$	−2.37720	−0.127067
$351$	21.2165	1.13245
$352$	−9.08489	−0.484226
$353$	−29.7176	−1.58171	−0.790853	−	0.612006i	$-0.790363\pi$
$353$	−29.7176	−1.58171	−0.790853	+	0.612006i	$0.790363\pi$
$354$	33.3665	1.77341
$355$	2.44447	0.129739
$356$	28.3121	1.50054
$357$	1.65109	0.0873851
$358$	−47.1436	−2.49162
$359$	−20.2010	−1.06617	−0.533084	−	0.846062i	$-0.678967\pi$
$359$	−20.2010	−1.06617	−0.533084	+	0.846062i	$0.678967\pi$
$360$	−1.07502	−0.0566583
$361$	−0.491189	−0.0258520
$362$	39.8775	2.09591
$363$	−3.30219	−0.173320
$364$	−14.3305	−0.751121
$365$	−7.17833	−0.375731
$366$	17.4445	0.911837
$367$	11.0595	0.577302	0.288651	−	0.957434i	$-0.406793\pi$
$367$	11.0595	0.577302	0.288651	+	0.957434i	$0.406793\pi$
$368$	−8.30701	−0.433033
$369$	2.07714	0.108132
$370$	24.3793	1.26742
$371$	−7.93273	−0.411847
$372$	33.6142	1.74282
$373$	−27.3043	−1.41376	−0.706882	−	0.707332i	$-0.749899\pi$
$373$	−27.3043	−1.41376	−0.706882	+	0.707332i	$0.749899\pi$
$374$	7.13161	0.368767
$375$	−1.65109	−0.0852621
$376$	−23.3665	−1.20504
$377$	36.8054	1.89557
$378$	12.8500	0.660931
$379$	8.92498	0.458446	0.229223	−	0.973374i	$-0.426382\pi$
$379$	8.92498	0.458446	0.229223	+	0.973374i	$0.426382\pi$
$380$	15.7077	0.805787
$381$	−0.840095	−0.0430394
$382$	−20.9271	−1.07072
$383$	0.0955622	0.00488300	0.00244150	−	0.999997i	$-0.499223\pi$
$383$	0.0955622	0.00488300	0.00244150	+	0.999997i	$0.499223\pi$
$384$	34.1775	1.74411
$385$	3.00000	0.152894
$386$	−45.6142	−2.32170
$387$	−2.02055	−0.102710
$388$	2.65109	0.134589
$389$	16.2632	0.824578	0.412289	−	0.911053i	$-0.364729\pi$
$389$	16.2632	0.824578	0.412289	+	0.911053i	$0.364729\pi$
$390$	−15.4055	−0.780088
$391$	−4.09556	−0.207121
$392$	−3.92498	−0.198242
$393$	22.3850	1.12917
$394$	−39.0899	−1.96932
$395$	14.6121	0.735216
$396$	3.00000	0.150756
$397$	3.16283	0.158738	0.0793689	−	0.996845i	$-0.474709\pi$
$397$	3.16283	0.158738	0.0793689	+	0.996845i	$0.474709\pi$
$398$	−27.6901	−1.38798
$399$	−7.10331	−0.355610
$400$	2.02830	0.101415
$401$	−15.4728	−0.772673	−0.386337	−	0.922358i	$-0.626260\pi$
$401$	−15.4728	−0.772673	−0.386337	+	0.922358i	$0.626260\pi$
$402$	29.8775	1.49015
$403$	−21.8860	−1.09022
$404$	40.0948	1.99479
$405$	8.10331	0.402657
$406$	22.2915	1.10631
$407$	−30.7664	−1.52503
$408$	−6.48052	−0.320833
$409$	−29.2739	−1.44750	−0.723750	−	0.690062i	$-0.757583\pi$
$409$	−29.2739	−1.44750	−0.723750	+	0.690062i	$0.757583\pi$
$410$	−18.0283	−0.890354
$411$	20.8449	1.02820
$412$	−28.4154	−1.39992
$413$	−8.50106	−0.418310
$414$	−2.66659	−0.131056
$415$	10.7827	0.529302
$416$	−11.8860	−0.582760
$417$	5.61000	0.274723
$418$	−30.6815	−1.50068
$419$	3.80595	0.185933	0.0929665	−	0.995669i	$-0.470365\pi$
$419$	3.80595	0.185933	0.0929665	+	0.995669i	$0.470365\pi$
$420$	−6.02830	−0.294151
$421$	−0.395626	−0.0192816	−0.00964082	−	0.999954i	$-0.503069\pi$
$421$	−0.395626	−0.0192816	−0.00964082	+	0.999954i	$0.503069\pi$
$422$	44.5577	2.16903
$423$	−1.63055	−0.0792799
$424$	31.1359	1.51209
$425$	1.00000	0.0485071
$426$	9.59450	0.464855
$427$	−4.44447	−0.215083
$428$	−9.19887	−0.444644
$429$	19.4415	0.938647
$430$	17.5371	0.845714
$431$	15.1337	0.728966	0.364483	−	0.931210i	$-0.381246\pi$
$431$	15.1337	0.728966	0.364483	+	0.931210i	$0.381246\pi$
$432$	−10.9640	−0.527503
$433$	34.5422	1.65999	0.829995	−	0.557771i	$-0.188343\pi$
$433$	34.5422	1.65999	0.829995	+	0.557771i	$0.188343\pi$
$434$	−13.2555	−0.636283
$435$	15.4826	0.742336
$436$	−8.84997	−0.423837
$437$	17.6199	0.842873
$438$	−28.1748	−1.34625
$439$	−24.9709	−1.19180	−0.595898	−	0.803060i	$-0.703204\pi$
$439$	−24.9709	−1.19180	−0.595898	+	0.803060i	$0.703204\pi$
$440$	−11.7750	−0.561349
$441$	−0.273891	−0.0130424
$442$	9.33048	0.443806
$443$	8.75653	0.416035	0.208018	−	0.978125i	$-0.433299\pi$
$443$	8.75653	0.416035	0.208018	+	0.978125i	$0.433299\pi$
$444$	61.8230	2.93399
$445$	−7.75441	−0.367594
$446$	−10.3198	−0.488657
$447$	1.86839	0.0883719
$448$	−11.2555	−0.531771
$449$	−29.2944	−1.38249	−0.691245	−	0.722621i	$-0.742937\pi$
$449$	−29.2944	−1.38249	−0.691245	+	0.722621i	$0.742937\pi$
$450$	0.651093	0.0306928
$451$	22.7515	1.07133
$452$	58.3502	2.74456
$453$	14.6377	0.687740
$454$	−45.0120	−2.11252
$455$	3.92498	0.184006
$456$	27.8804	1.30562
$457$	−24.8131	−1.16071	−0.580354	−	0.814364i	$-0.697086\pi$
$457$	−24.8131	−1.16071	−0.580354	+	0.814364i	$0.697086\pi$
$458$	37.3404	1.74480
$459$	−5.40550	−0.252307
$460$	14.9533	0.697200
$461$	−4.15990	−0.193746	−0.0968730	−	0.995297i	$-0.530884\pi$
$461$	−4.15990	−0.193746	−0.0968730	+	0.995297i	$0.530884\pi$
$462$	11.7750	0.547820
$463$	4.87534	0.226576	0.113288	−	0.993562i	$-0.463862\pi$
$463$	4.87534	0.226576	0.113288	+	0.993562i	$0.463862\pi$
$464$	−19.0197	−0.882970
$465$	−9.20662	−0.426947
$466$	43.9624	2.03652
$467$	−10.1834	−0.471230	−0.235615	−	0.971846i	$-0.575710\pi$
$467$	−10.1834	−0.471230	−0.235615	+	0.971846i	$0.575710\pi$
$468$	3.92498	0.181432
$469$	−7.61212	−0.351495
$470$	14.1522	0.652790
$471$	−26.9036	−1.23965
$472$	33.3665	1.53582
$473$	−22.1316	−1.01761
$474$	57.3524	2.63428
$475$	−4.30219	−0.197398
$476$	3.65109	0.167348
$477$	2.17270	0.0994811
$478$	44.9263	2.05488
$479$	14.1890	0.648312	0.324156	−	0.946004i	$-0.394920\pi$
$479$	14.1890	0.648312	0.324156	+	0.946004i	$0.394920\pi$
$480$	−5.00000	−0.228218
$481$	−40.2525	−1.83536
$482$	−17.3334	−0.789515
$483$	−6.76216	−0.307689
$484$	−7.30219	−0.331918
$485$	−0.726109	−0.0329709
$486$	−6.74453	−0.305938
$487$	0.235722	0.0106816	0.00534078	−	0.999986i	$-0.498300\pi$
$487$	0.235722	0.0106816	0.00534078	+	0.999986i	$0.498300\pi$
$488$	17.4445	0.789674
$489$	−4.39483	−0.198741
$490$	2.37720	0.107391
$491$	−16.6220	−0.750140	−0.375070	−	0.926996i	$-0.622381\pi$
$491$	−16.6220	−0.750140	−0.375070	+	0.926996i	$0.622381\pi$
$492$	−45.7176	−2.06111
$493$	−9.37720	−0.422328
$494$	−40.1415	−1.80605
$495$	−0.821672	−0.0369314
$496$	11.3099	0.507831
$497$	−2.44447	−0.109649
$498$	42.3219	1.89649
$499$	30.4671	1.36390	0.681948	−	0.731400i	$-0.261133\pi$
$499$	30.4671	1.36390	0.681948	+	0.731400i	$0.261133\pi$
$500$	−3.65109	−0.163282
$501$	3.81875	0.170609
$502$	−41.8980	−1.87000
$503$	15.1209	0.674209	0.337105	−	0.941467i	$-0.390552\pi$
$503$	15.1209	0.674209	0.337105	+	0.941467i	$0.390552\pi$
$504$	1.07502	0.0478850
$505$	−10.9816	−0.488674
$506$	−29.2079	−1.29845
$507$	3.97170	0.176390
$508$	−1.85772	−0.0824229
$509$	−20.8959	−0.926194	−0.463097	−	0.886308i	$-0.653262\pi$
$509$	−20.8959	−0.926194	−0.463097	+	0.886308i	$0.653262\pi$
$510$	3.92498	0.173801
$511$	7.17833	0.317551
$512$	22.0643	0.975115
$513$	23.2555	1.02675
$514$	−23.1882	−1.02279
$515$	7.78270	0.342947
$516$	44.4720	1.95777
$517$	−17.8598	−0.785475
$518$	−24.3793	−1.07117
$519$	−41.6348	−1.82756
$520$	−15.4055	−0.675576
$521$	34.2165	1.49905	0.749526	−	0.661975i	$-0.230281\pi$
$521$	34.2165	1.49905	0.749526	+	0.661975i	$0.230281\pi$
$522$	−6.10543	−0.267228
$523$	7.15508	0.312870	0.156435	−	0.987688i	$-0.450000\pi$
$523$	7.15508	0.312870	0.156435	+	0.987688i	$0.450000\pi$
$524$	49.5003	2.16243
$525$	1.65109	0.0720596
$526$	66.4437	2.89708
$527$	5.57608	0.242898
$528$	−10.0467	−0.437227
$529$	−6.22637	−0.270712
$530$	−18.8577	−0.819127
$531$	2.32836	0.101042
$532$	−15.7077	−0.681015
$533$	29.7664	1.28933
$534$	−30.4359	−1.31709
$535$	2.51948	0.108927
$536$	29.8775	1.29051
$537$	32.7437	1.41300
$538$	4.97653	0.214553
$539$	−3.00000	−0.129219
$540$	19.7360	0.849301
$541$	−21.7154	−0.933620	−0.466810	−	0.884358i	$-0.654597\pi$
$541$	−21.7154	−0.933620	−0.466810	+	0.884358i	$0.654597\pi$
$542$	−5.02537	−0.215858
$543$	−27.6970	−1.18859
$544$	3.02830	0.129837
$545$	2.42392	0.103829
$546$	15.4055	0.659294
$547$	−43.1124	−1.84335	−0.921676	−	0.387960i	$-0.873180\pi$
$547$	−43.1124	−1.84335	−0.921676	+	0.387960i	$0.873180\pi$
$548$	46.0948	1.96907
$549$	1.21730	0.0519530
$550$	7.13161	0.304093
$551$	40.3425	1.71865
$552$	26.5414	1.12968
$553$	−14.6121	−0.621371
$554$	26.0801	1.10804
$555$	−16.9327	−0.718755
$556$	12.4055	0.526110
$557$	1.40045	0.0593391	0.0296696	−	0.999560i	$-0.490555\pi$
$557$	1.40045	0.0593391	0.0296696	+	0.999560i	$0.490555\pi$
$558$	3.63055	0.153693
$559$	−28.9554	−1.22468
$560$	−2.02830	−0.0857112
$561$	−4.95328	−0.209128
$562$	−6.16765	−0.260167
$563$	21.0438	0.886890	0.443445	−	0.896302i	$-0.353756\pi$
$563$	21.0438	0.886890	0.443445	+	0.896302i	$0.353756\pi$
$564$	35.8881	1.51116
$565$	−15.9816	−0.672350
$566$	47.9292	2.01462
$567$	−8.10331	−0.340307
$568$	9.59450	0.402576
$569$	11.7467	0.492445	0.246223	−	0.969213i	$-0.420811\pi$
$569$	11.7467	0.492445	0.246223	+	0.969213i	$0.420811\pi$
$570$	−16.8860	−0.707277
$571$	15.8470	0.663178	0.331589	−	0.943424i	$-0.392415\pi$
$571$	15.8470	0.663178	0.331589	+	0.943424i	$0.392415\pi$
$572$	42.9914	1.79756
$573$	14.5350	0.607208
$574$	18.0283	0.752487
$575$	−4.09556	−0.170797
$576$	3.08277	0.128449
$577$	−2.47277	−0.102943	−0.0514713	−	0.998674i	$-0.516391\pi$
$577$	−2.47277	−0.102943	−0.0514713	+	0.998674i	$0.516391\pi$
$578$	−2.37720	−0.0988786
$579$	31.6815	1.31664
$580$	34.2370	1.42162
$581$	−10.7827	−0.447342
$582$	−2.84997	−0.118135
$583$	23.7982	0.985621
$584$	−28.1748	−1.16588
$585$	−1.07502	−0.0444464
$586$	−35.3129	−1.45876
$587$	20.4162	0.842666	0.421333	−	0.906906i	$-0.361562\pi$
$587$	20.4162	0.842666	0.421333	+	0.906906i	$0.361562\pi$
$588$	6.02830	0.248603
$589$	−23.9893	−0.988463
$590$	−20.2087	−0.831981
$591$	27.1500	1.11680
$592$	20.8011	0.854921
$593$	−24.2760	−0.996896	−0.498448	−	0.866919i	$-0.666097\pi$
$593$	−24.2760	−0.996896	−0.498448	+	0.866919i	$0.666097\pi$
$594$	−38.5499	−1.58172
$595$	−1.00000	−0.0409960
$596$	4.13161	0.169237
$597$	19.2322	0.787122
$598$	−38.2136	−1.56267
$599$	1.50398	0.0614511	0.0307256	−	0.999528i	$-0.490218\pi$
$599$	1.50398	0.0614511	0.0307256	+	0.999528i	$0.490218\pi$
$600$	−6.48052	−0.264566
$601$	−13.6241	−0.555739	−0.277870	−	0.960619i	$-0.589628\pi$
$601$	−13.6241	−0.555739	−0.277870	+	0.960619i	$0.589628\pi$
$602$	−17.5371	−0.714759
$603$	2.08489	0.0849032
$604$	32.3687	1.31706
$605$	2.00000	0.0813116
$606$	−43.1025	−1.75092
$607$	−19.2349	−0.780721	−0.390361	−	0.920662i	$-0.627650\pi$
$607$	−19.2349	−0.780721	−0.390361	+	0.920662i	$0.627650\pi$
$608$	−13.0283	−0.528367
$609$	−15.4826	−0.627388
$610$	−10.5654	−0.427781
$611$	−23.3665	−0.945309
$612$	−1.00000	−0.0404226
$613$	42.2341	1.70582	0.852910	−	0.522058i	$-0.174836\pi$
$613$	42.2341	1.70582	0.852910	+	0.522058i	$0.174836\pi$
$614$	−57.0763	−2.30341
$615$	12.5216	0.504920
$616$	11.7750	0.474426
$617$	−35.5675	−1.43189	−0.715947	−	0.698154i	$-0.754005\pi$
$617$	−35.5675	−1.43189	−0.715947	+	0.698154i	$0.754005\pi$
$618$	30.5470	1.22878
$619$	−8.60145	−0.345721	−0.172861	−	0.984946i	$-0.555301\pi$
$619$	−8.60145	−0.345721	−0.172861	+	0.984946i	$0.555301\pi$
$620$	−20.3588	−0.817628
$621$	22.1386	0.888390
$622$	−57.3473	−2.29942
$623$	7.75441	0.310674
$624$	−13.1444	−0.526197
$625$	1.00000	0.0400000
$626$	−70.2023	−2.80585
$627$	21.3099	0.851037
$628$	−59.4925	−2.37401
$629$	10.2555	0.408912
$630$	−0.651093	−0.0259402
$631$	−39.4407	−1.57011	−0.785056	−	0.619425i	$-0.787366\pi$
$631$	−39.4407	−1.57011	−0.785056	+	0.619425i	$0.787366\pi$
$632$	57.3524	2.28135
$633$	−30.9477	−1.23006
$634$	8.40338	0.333741
$635$	0.508811	0.0201916
$636$	−47.8209	−1.89622
$637$	−3.92498	−0.155514
$638$	−66.8745	−2.64759
$639$	0.669517	0.0264857
$640$	−20.6999	−0.818237
$641$	−42.1690	−1.66557	−0.832787	−	0.553593i	$-0.813256\pi$
$641$	−42.1690	−1.66557	−0.832787	+	0.553593i	$0.813256\pi$
$642$	9.88894	0.390285
$643$	22.1981	0.875407	0.437703	−	0.899119i	$-0.355792\pi$
$643$	22.1981	0.875407	0.437703	+	0.899119i	$0.355792\pi$
$644$	−14.9533	−0.589242
$645$	−12.1805	−0.479605
$646$	10.2272	0.402383
$647$	41.7557	1.64159	0.820794	−	0.571225i	$-0.193532\pi$
$647$	41.7557	1.64159	0.820794	+	0.571225i	$0.193532\pi$
$648$	31.8054	1.24943
$649$	25.5032	1.00109
$650$	9.33048	0.365972
$651$	9.20662	0.360836
$652$	−9.71836	−0.380600
$653$	−19.9250	−0.779725	−0.389862	−	0.920873i	$-0.627477\pi$
$653$	−19.9250	−0.779725	−0.389862	+	0.920873i	$0.627477\pi$
$654$	9.51386	0.372021
$655$	−13.5577	−0.529741
$656$	−15.3822	−0.600576
$657$	−1.96608	−0.0767039
$658$	−14.1522	−0.551708
$659$	−8.45726	−0.329448	−0.164724	−	0.986340i	$-0.552673\pi$
$659$	−8.45726	−0.329448	−0.164724	+	0.986340i	$0.552673\pi$
$660$	18.0849	0.703953
$661$	−21.6172	−0.840810	−0.420405	−	0.907336i	$-0.638112\pi$
$661$	−21.6172	−0.840810	−0.420405	+	0.907336i	$0.638112\pi$
$662$	−54.3425	−2.11208
$663$	−6.48052	−0.251682
$664$	42.3219	1.64241
$665$	4.30219	0.166832
$666$	6.67727	0.258739
$667$	38.4049	1.48704
$668$	8.44447	0.326726
$669$	7.16765	0.277118
$670$	−18.0956	−0.699093
$671$	13.3334	0.514730
$672$	5.00000	0.192879
$673$	−37.4097	−1.44204	−0.721020	−	0.692914i	$-0.756326\pi$
$673$	−37.4097	−1.44204	−0.721020	+	0.692914i	$0.756326\pi$
$674$	63.3716	2.44098
$675$	−5.40550	−0.208058
$676$	8.78270	0.337796
$677$	−14.9765	−0.575595	−0.287797	−	0.957691i	$-0.592923\pi$
$677$	−14.9765	−0.575595	−0.287797	+	0.957691i	$0.592923\pi$
$678$	−62.7274	−2.40903
$679$	0.726109	0.0278655
$680$	3.92498	0.150516
$681$	31.2632	1.19801
$682$	39.7664	1.52273
$683$	24.5011	0.937507	0.468754	−	0.883329i	$-0.344703\pi$
$683$	24.5011	0.937507	0.468754	+	0.883329i	$0.344703\pi$
$684$	4.30219	0.164498
$685$	−12.6249	−0.482373
$686$	−2.37720	−0.0907620
$687$	−25.9349	−0.989477
$688$	14.9632	0.570465
$689$	31.1359	1.18618
$690$	−16.0750	−0.611965
$691$	37.5958	1.43021	0.715106	−	0.699016i	$-0.246378\pi$
$691$	37.5958	1.43021	0.715106	+	0.699016i	$0.246378\pi$
$692$	−92.0678	−3.49989
$693$	0.821672	0.0312127
$694$	51.7685	1.96511
$695$	−3.39775	−0.128884
$696$	60.7691	2.30345
$697$	−7.58383	−0.287258
$698$	24.5342	0.928633
$699$	−30.5342	−1.15491
$700$	3.65109	0.137998
$701$	−41.1386	−1.55378	−0.776891	−	0.629635i	$-0.783204\pi$
$701$	−41.1386	−1.55378	−0.776891	+	0.629635i	$0.783204\pi$
$702$	−50.4359	−1.90358
$703$	−44.1209	−1.66405
$704$	33.7664	1.27262
$705$	−9.82942	−0.370197
$706$	70.6447	2.65875
$707$	10.9816	0.413005
$708$	−51.2469	−1.92598
$709$	−36.1677	−1.35830	−0.679152	−	0.733997i	$-0.737652\pi$
$709$	−36.1677	−1.35830	−0.679152	+	0.733997i	$0.737652\pi$
$710$	−5.81100	−0.218083
$711$	4.00212	0.150091
$712$	−30.4359	−1.14063
$713$	−22.8372	−0.855259
$714$	−3.92498	−0.146889
$715$	−11.7750	−0.440358
$716$	72.4068	2.70597
$717$	−31.2037	−1.16532
$718$	48.0219	1.79216
$719$	−3.31074	−0.123470	−0.0617348	−	0.998093i	$-0.519663\pi$
$719$	−3.31074	−0.123470	−0.0617348	+	0.998093i	$0.519663\pi$
$720$	0.555531	0.0207034
$721$	−7.78270	−0.289843
$722$	1.16765	0.0434556
$723$	12.0390	0.447734
$724$	−61.2469	−2.27622
$725$	−9.37720	−0.348261
$726$	7.84997	0.291340
$727$	15.3404	0.568942	0.284471	−	0.958685i	$-0.408182\pi$
$727$	15.3404	0.568942	0.284471	+	0.958685i	$0.408182\pi$
$728$	15.4055	0.570966
$729$	28.9944	1.07387
$730$	17.0643	0.631580
$731$	7.37720	0.272856
$732$	−26.7926	−0.990282
$733$	−14.3665	−0.530640	−0.265320	−	0.964160i	$-0.585478\pi$
$733$	−14.3665	−0.530640	−0.265320	+	0.964160i	$0.585478\pi$
$734$	−26.2907	−0.970408
$735$	−1.65109	−0.0609015
$736$	−12.4026	−0.457165
$737$	22.8364	0.841189
$738$	−4.93778	−0.181762
$739$	−0.198875	−0.00731572	−0.00365786	−	0.999993i	$-0.501164\pi$
$739$	−0.198875	−0.00731572	−0.00365786	+	0.999993i	$0.501164\pi$
$740$	−37.4437	−1.37646
$741$	27.8804	1.02421
$742$	18.8577	0.692289
$743$	2.04804	0.0751354	0.0375677	−	0.999294i	$-0.488039\pi$
$743$	2.04804	0.0751354	0.0375677	+	0.999294i	$0.488039\pi$
$744$	−36.1359	−1.32480
$745$	−1.13161	−0.0414589
$746$	64.9079	2.37645
$747$	2.95328	0.108055
$748$	−10.9533	−0.400492
$749$	−2.51948	−0.0920600
$750$	3.92498	0.143320
$751$	−47.1415	−1.72022	−0.860109	−	0.510111i	$-0.829604\pi$
$751$	−47.1415	−1.72022	−0.860109	+	0.510111i	$0.829604\pi$
$752$	12.0750	0.440331
$753$	29.1004	1.06048
$754$	−87.4938	−3.18634
$755$	−8.86547	−0.322647
$756$	−19.7360	−0.717791
$757$	5.46209	0.198523	0.0992615	−	0.995061i	$-0.468352\pi$
$757$	5.46209	0.198523	0.0992615	+	0.995061i	$0.468352\pi$
$758$	−21.2165	−0.770618
$759$	20.2865	0.736352
$760$	−16.8860	−0.612520
$761$	23.5080	0.852165	0.426082	−	0.904684i	$-0.359893\pi$
$761$	23.5080	0.852165	0.426082	+	0.904684i	$0.359893\pi$
$762$	1.99708	0.0723465
$763$	−2.42392	−0.0877519
$764$	32.1415	1.16284
$765$	0.273891	0.00990253
$766$	−0.227171	−0.00820801
$767$	33.3665	1.20480
$768$	−44.0793	−1.59057
$769$	−1.98933	−0.0717370	−0.0358685	−	0.999357i	$-0.511420\pi$
$769$	−1.98933	−0.0717370	−0.0358685	+	0.999357i	$0.511420\pi$
$770$	−7.13161	−0.257005
$771$	16.1054	0.580023
$772$	70.0579	2.52144
$773$	−14.0977	−0.507058	−0.253529	−	0.967328i	$-0.581591\pi$
$773$	−14.0977	−0.507058	−0.253529	+	0.967328i	$0.581591\pi$
$774$	4.80325	0.172649
$775$	5.57608	0.200299
$776$	−2.84997	−0.102308
$777$	16.9327	0.607458
$778$	−38.6610	−1.38606
$779$	32.6270	1.16899
$780$	23.6610	0.847198
$781$	7.33341	0.262410
$782$	9.73598	0.348158
$783$	50.6885	1.81146
$784$	2.02830	0.0724392
$785$	16.2944	0.581573
$786$	−53.2136	−1.89807
$787$	33.1444	1.18147	0.590735	−	0.806865i	$-0.298838\pi$
$787$	33.1444	1.18147	0.590735	+	0.806865i	$0.298838\pi$
$788$	60.0374	2.13874
$789$	−46.1487	−1.64294
$790$	−34.7360	−1.23585
$791$	15.9816	0.568239
$792$	−3.22505	−0.114597
$793$	17.4445	0.619471
$794$	−7.51868	−0.266828
$795$	13.0977	0.464527
$796$	42.5286	1.50738
$797$	−8.07019	−0.285861	−0.142930	−	0.989733i	$-0.545653\pi$
$797$	−8.07019	−0.285861	−0.142930	+	0.989733i	$0.545653\pi$
$798$	16.8860	0.597758
$799$	5.95328	0.210612
$800$	3.02830	0.107066
$801$	−2.12386	−0.0750428
$802$	36.7819	1.29881
$803$	−21.5350	−0.759953
$804$	−45.8881	−1.61835
$805$	4.09556	0.144350
$806$	52.0275	1.83259
$807$	−3.45646	−0.121673
$808$	−43.1025	−1.51634
$809$	20.8783	0.734041	0.367020	−	0.930213i	$-0.380378\pi$
$809$	20.8783	0.734041	0.367020	+	0.930213i	$0.380378\pi$
$810$	−19.2632	−0.676840
$811$	42.3318	1.48647	0.743235	−	0.669030i	$-0.233290\pi$
$811$	42.3318	1.48647	0.743235	+	0.669030i	$0.233290\pi$
$812$	−34.2370	−1.20148
$813$	3.49039	0.122413
$814$	73.1380	2.56348
$815$	2.66177	0.0932376
$816$	3.34891	0.117235
$817$	−31.7381	−1.11038
$818$	69.5900	2.43316
$819$	1.07502	0.0375641
$820$	27.6893	0.966951
$821$	−31.7918	−1.10954	−0.554770	−	0.832004i	$-0.687194\pi$
$821$	−31.7918	−1.10954	−0.554770	+	0.832004i	$0.687194\pi$
$822$	−49.5526	−1.72835
$823$	29.1463	1.01598	0.507988	−	0.861364i	$-0.330389\pi$
$823$	29.1463	1.01598	0.507988	+	0.861364i	$0.330389\pi$
$824$	30.5470	1.06415
$825$	−4.95328	−0.172451
$826$	20.2087	0.703152
$827$	−9.99225	−0.347465	−0.173732	−	0.984793i	$-0.555583\pi$
$827$	−9.99225	−0.347465	−0.173732	+	0.984793i	$0.555583\pi$
$828$	4.09556	0.142331
$829$	45.5675	1.58263	0.791313	−	0.611412i	$-0.209398\pi$
$829$	45.5675	1.58263	0.791313	+	0.611412i	$0.209398\pi$
$830$	−25.6327	−0.889723
$831$	−18.1140	−0.628367
$832$	44.1775	1.53158
$833$	1.00000	0.0346479
$834$	−13.3361	−0.461792
$835$	−2.31286	−0.0800398
$836$	47.1231	1.62979
$837$	−30.1415	−1.04184
$838$	−9.04752	−0.312541
$839$	−49.8131	−1.71974	−0.859870	−	0.510513i	$-0.829455\pi$
$839$	−49.8131	−1.71974	−0.859870	+	0.510513i	$0.829455\pi$
$840$	6.48052	0.223599
$841$	58.9319	2.03214
$842$	0.940484	0.0324112
$843$	4.28376	0.147541
$844$	−68.4351	−2.35563
$845$	−2.40550	−0.0827517
$846$	3.87614	0.133264
$847$	−2.00000	−0.0687208
$848$	−16.0899	−0.552531
$849$	−33.2894	−1.14249
$850$	−2.37720	−0.0815374
$851$	−42.0019	−1.43981
$852$	−14.7360	−0.504846
$853$	−21.1442	−0.723963	−0.361982	−	0.932185i	$-0.617900\pi$
$853$	−21.1442	−0.723963	−0.361982	+	0.932185i	$0.617900\pi$
$854$	10.5654	0.361541
$855$	−1.17833	−0.0402980
$856$	9.88894	0.337997
$857$	−45.1669	−1.54287	−0.771435	−	0.636308i	$-0.780461\pi$
$857$	−45.1669	−1.54287	−0.771435	+	0.636308i	$0.780461\pi$
$858$	−46.2165	−1.57781
$859$	−29.4309	−1.00417	−0.502084	−	0.864819i	$-0.667433\pi$
$859$	−29.4309	−1.00417	−0.502084	+	0.864819i	$0.667433\pi$
$860$	−26.9349	−0.918471
$861$	−12.5216	−0.426735
$862$	−35.9759	−1.22535
$863$	−16.2322	−0.552551	−0.276276	−	0.961078i	$-0.589100\pi$
$863$	−16.2322	−0.552551	−0.276276	+	0.961078i	$0.589100\pi$
$864$	−16.3695	−0.556900
$865$	25.2165	0.857387
$866$	−82.1137	−2.79034
$867$	1.65109	0.0560741
$868$	20.3588	0.691022
$869$	43.8364	1.48705
$870$	−36.8054	−1.24782
$871$	29.8775	1.01236
$872$	9.51386	0.322180
$873$	−0.198875	−0.00673088
$874$	−41.8860	−1.41682
$875$	−1.00000	−0.0338062
$876$	43.2731	1.46206
$877$	26.6842	0.901062	0.450531	−	0.892761i	$-0.351235\pi$
$877$	26.6842	0.901062	0.450531	+	0.892761i	$0.351235\pi$
$878$	59.3609	2.00333
$879$	24.5267	0.827263
$880$	6.08489	0.205122
$881$	10.0184	0.337529	0.168765	−	0.985656i	$-0.446022\pi$
$881$	10.0184	0.337529	0.168765	+	0.985656i	$0.446022\pi$
$882$	0.651093	0.0219235
$883$	−35.7976	−1.20469	−0.602343	−	0.798237i	$-0.705766\pi$
$883$	−35.7976	−1.20469	−0.602343	+	0.798237i	$0.705766\pi$
$884$	−14.3305	−0.481986
$885$	14.0360	0.471817
$886$	−20.8160	−0.699329
$887$	57.4202	1.92798	0.963991	−	0.265936i	$-0.0856809\pi$
$887$	57.4202	1.92798	0.963991	+	0.265936i	$0.0856809\pi$
$888$	−66.4607	−2.23028
$889$	−0.508811	−0.0170650
$890$	18.4338	0.617902
$891$	24.3099	0.814414
$892$	15.8500	0.530696
$893$	−25.6121	−0.857077
$894$	−4.44155	−0.148548
$895$	−19.8315	−0.662895
$896$	20.6999	0.691536
$897$	26.5414	0.886190
$898$	69.6388	2.32388
$899$	−52.2880	−1.74390
$900$	−1.00000	−0.0333333
$901$	−7.93273	−0.264278
$902$	−54.0849	−1.80083
$903$	12.1805	0.405340
$904$	−62.7274	−2.08628
$905$	16.7750	0.557618
$906$	−34.7968	−1.15605
$907$	−48.5088	−1.61071	−0.805354	−	0.592794i	$-0.798025\pi$
$907$	−48.5088	−1.61071	−0.805354	+	0.592794i	$0.798025\pi$
$908$	69.1329	2.29426
$909$	−3.00775	−0.0997608
$910$	−9.33048	−0.309303
$911$	−37.8881	−1.25529	−0.627645	−	0.778500i	$-0.715981\pi$
$911$	−37.8881	−1.25529	−0.627645	+	0.778500i	$0.715981\pi$
$912$	−14.4076	−0.477084
$913$	32.3481	1.07057
$914$	58.9858	1.95108
$915$	7.33823	0.242595
$916$	−57.3502	−1.89490
$917$	13.5577	0.447713
$918$	12.8500	0.424112
$919$	−43.8521	−1.44655	−0.723273	−	0.690562i	$-0.757363\pi$
$919$	−43.8521	−1.44655	−0.723273	+	0.690562i	$0.757363\pi$
$920$	−16.0750	−0.529978
$921$	39.6425	1.30627
$922$	9.88894	0.325675
$923$	9.59450	0.315807
$924$	−18.0849	−0.594949
$925$	10.2555	0.337198
$926$	−11.5897	−0.380860
$927$	2.13161	0.0700112
$928$	−28.3969	−0.932175
$929$	15.7614	0.517113	0.258557	−	0.965996i	$-0.416753\pi$
$929$	15.7614	0.517113	0.258557	+	0.965996i	$0.416753\pi$
$930$	21.8860	0.717671
$931$	−4.30219	−0.140998
$932$	−67.5208	−2.21172
$933$	39.8307	1.30400
$934$	24.2079	0.792108
$935$	3.00000	0.0981105
$936$	−4.21942	−0.137916
$937$	58.0502	1.89642	0.948208	−	0.317650i	$-0.102894\pi$
$937$	58.0502	1.89642	0.948208	+	0.317650i	$0.102894\pi$
$938$	18.0956	0.590841
$939$	48.7592	1.59120
$940$	−21.7360	−0.708950
$941$	−52.8435	−1.72265	−0.861325	−	0.508054i	$-0.830365\pi$
$941$	−52.8435	−1.72265	−0.861325	+	0.508054i	$0.830365\pi$
$942$	63.9554	2.08378
$943$	31.0600	1.01145
$944$	−17.2427	−0.561201
$945$	5.40550	0.175841
$946$	52.6113	1.71054
$947$	−43.7402	−1.42137	−0.710683	−	0.703512i	$-0.751614\pi$
$947$	−43.7402	−1.42137	−0.710683	+	0.703512i	$0.751614\pi$
$948$	−88.0862	−2.86091
$949$	−28.1748	−0.914593
$950$	10.2272	0.331813
$951$	−5.83659	−0.189264
$952$	−3.92498	−0.127209
$953$	44.3863	1.43781	0.718906	−	0.695107i	$-0.244643\pi$
$953$	44.3863	1.43781	0.718906	+	0.695107i	$0.244643\pi$
$954$	−5.16495	−0.167221
$955$	−8.80325	−0.284866
$956$	−69.0013	−2.23166
$957$	46.4479	1.50145
$958$	−33.7301	−1.08977
$959$	12.6249	0.407680
$960$	18.5838	0.599790
$961$	0.0926389	0.00298835
$962$	95.6885	3.08512
$963$	0.690063	0.0222370
$964$	26.6220	0.857437
$965$	−19.1882	−0.617690
$966$	16.0750	0.517205
$967$	12.9512	0.416481	0.208241	−	0.978078i	$-0.433226\pi$
$967$	12.9512	0.416481	0.208241	+	0.978078i	$0.433226\pi$
$968$	7.84997	0.252308
$969$	−7.10331	−0.228191
$970$	1.72611	0.0554220
$971$	35.3969	1.13594	0.567971	−	0.823049i	$-0.307729\pi$
$971$	35.3969	1.13594	0.567971	+	0.823049i	$0.307729\pi$
$972$	10.3588	0.332258
$973$	3.39775	0.108927
$974$	−0.560358	−0.0179550
$975$	−6.48052	−0.207543
$976$	−9.01470	−0.288553
$977$	40.3072	1.28954	0.644771	−	0.764376i	$-0.276953\pi$
$977$	40.3072	1.28954	0.644771	+	0.764376i	$0.276953\pi$
$978$	10.4474	0.334071
$979$	−23.2632	−0.743496
$980$	−3.65109	−0.116630
$981$	0.663890	0.0211964
$982$	39.5139	1.26094
$983$	−33.0275	−1.05341	−0.526707	−	0.850047i	$-0.676573\pi$
$983$	−33.0275	−1.05341	−0.526707	+	0.850047i	$0.676573\pi$
$984$	49.1471	1.56675
$985$	−16.4437	−0.523939
$986$	22.2915	0.709906
$987$	9.82942	0.312874
$988$	61.6524	1.96142
$989$	−30.2138	−0.960743
$990$	1.95328	0.0620793
$991$	3.30994	0.105144	0.0525718	−	0.998617i	$-0.483258\pi$
$991$	3.30994	0.105144	0.0525718	+	0.998617i	$0.483258\pi$
$992$	16.8860	0.536131
$993$	37.7437	1.19776
$994$	5.81100	0.184314
$995$	−11.6482	−0.369272
$996$	−65.0013	−2.05965
$997$	29.5667	0.936388	0.468194	−	0.883626i	$-0.344905\pi$
$997$	29.5667	0.936388	0.468194	+	0.883626i	$0.344905\pi$
$998$	−72.4266	−2.29262
$999$	−55.4359	−1.75391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	595.2.a.f.1.1	✓	3
3.2	odd	2		5355.2.a.bf.1.3		3
4.3	odd	2		9520.2.a.ba.1.1		3
5.4	even	2		2975.2.a.f.1.3		3
7.6	odd	2		4165.2.a.z.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
595.2.a.f.1.1	✓	3	1.1	even	1	trivial
2975.2.a.f.1.3		3	5.4	even	2
4165.2.a.z.1.1		3	7.6	odd	2
5355.2.a.bf.1.3		3	3.2	odd	2
9520.2.a.ba.1.1		3	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:	\( N \)	\(=\)	\( 595 = 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	595.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37720 q^{2} +1.65109 q^{3} +3.65109 q^{4} -1.00000 q^{5} -3.92498 q^{6} +1.00000 q^{7} -3.92498 q^{8} -0.273891 q^{9} +2.37720 q^{10} -3.00000 q^{11} +6.02830 q^{12} -3.92498 q^{13} -2.37720 q^{14} -1.65109 q^{15} +2.02830 q^{16} +1.00000 q^{17} +0.651093 q^{18} -4.30219 q^{19} -3.65109 q^{20} +1.65109 q^{21} +7.13161 q^{22} -4.09556 q^{23} -6.48052 q^{24} +1.00000 q^{25} +9.33048 q^{26} -5.40550 q^{27} +3.65109 q^{28} -9.37720 q^{29} +3.92498 q^{30} +5.57608 q^{31} +3.02830 q^{32} -4.95328 q^{33} -2.37720 q^{34} -1.00000 q^{35} -1.00000 q^{36} +10.2555 q^{37} +10.2272 q^{38} -6.48052 q^{39} +3.92498 q^{40} -7.58383 q^{41} -3.92498 q^{42} +7.37720 q^{43} -10.9533 q^{44} +0.273891 q^{45} +9.73598 q^{46} +5.95328 q^{47} +3.34891 q^{48} +1.00000 q^{49} -2.37720 q^{50} +1.65109 q^{51} -14.3305 q^{52} -7.93273 q^{53} +12.8500 q^{54} +3.00000 q^{55} -3.92498 q^{56} -7.10331 q^{57} +22.2915 q^{58} -8.50106 q^{59} -6.02830 q^{60} -4.44447 q^{61} -13.2555 q^{62} -0.273891 q^{63} -11.2555 q^{64} +3.92498 q^{65} +11.7750 q^{66} -7.61212 q^{67} +3.65109 q^{68} -6.76216 q^{69} +2.37720 q^{70} -2.44447 q^{71} +1.07502 q^{72} +7.17833 q^{73} -24.3793 q^{74} +1.65109 q^{75} -15.7077 q^{76} -3.00000 q^{77} +15.4055 q^{78} -14.6121 q^{79} -2.02830 q^{80} -8.10331 q^{81} +18.0283 q^{82} -10.7827 q^{83} +6.02830 q^{84} -1.00000 q^{85} -17.5371 q^{86} -15.4826 q^{87} +11.7750 q^{88} +7.75441 q^{89} -0.651093 q^{90} -3.92498 q^{91} -14.9533 q^{92} +9.20662 q^{93} -14.1522 q^{94} +4.30219 q^{95} +5.00000 q^{96} +0.726109 q^{97} -2.37720 q^{98} +0.821672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + q^{9} + 2 q^{10} - 9 q^{11} + 6 q^{12} - 3 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} + 3 q^{17} - 5 q^{18} + q^{19} - 4 q^{20}+ \cdots - 3 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + q^9 + 2 * q^10 - 9 * q^11 + 6 * q^12 - 3 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 + 3 * q^17 - 5 * q^18 + q^19 - 4 * q^20 - 2 * q^21 + 6 * q^22 - 5 * q^23 - 11 * q^24 + 3 * q^25 + 2 * q^26 + q^27 + 4 * q^28 - 23 * q^29 + 3 * q^30 + q^31 - 3 * q^32 + 6 * q^33 - 2 * q^34 - 3 * q^35 - 3 * q^36 - 4 * q^37 + 8 * q^38 - 11 * q^39 + 3 * q^40 - 11 * q^41 - 3 * q^42 + 17 * q^43 - 12 * q^44 - q^45 - 14 * q^46 - 3 * q^47 + 17 * q^48 + 3 * q^49 - 2 * q^50 - 2 * q^51 - 17 * q^52 - 19 * q^53 + 21 * q^54 + 9 * q^55 - 3 * q^56 - 18 * q^57 + 24 * q^58 - q^59 - 6 * q^60 - 13 * q^61 - 5 * q^62 + q^63 + q^64 + 3 * q^65 + 9 * q^66 + q^67 + 4 * q^68 - 14 * q^69 + 2 * q^70 - 7 * q^71 + 12 * q^72 + 27 * q^73 - 19 * q^74 - 2 * q^75 - 16 * q^76 - 9 * q^77 + 29 * q^78 - 20 * q^79 + 6 * q^80 - 21 * q^81 + 42 * q^82 - 10 * q^83 + 6 * q^84 - 3 * q^85 - 20 * q^86 + 11 * q^87 + 9 * q^88 + 13 * q^89 + 5 * q^90 - 3 * q^91 - 24 * q^92 + 21 * q^93 - 11 * q^94 - q^95 + 15 * q^96 + 4 * q^97 - 2 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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