LMFDB - Embedded newform 605.3.c.a.241.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,3,Mod(241,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.241"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	605.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$16.4850559938$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			241.2
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	605.241
Dual form			605.3.c.a.241.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.726543i q^{2} -4.00000 q^{3} +3.47214 q^{4} -2.23607 q^{5} +2.90617i q^{6} -0.277515i q^{7} -5.42882i q^{8} +7.00000 q^{9} +1.62460i q^{10} -13.8885 q^{12} +11.3067i q^{13} -0.201626 q^{14} +8.94427 q^{15} +9.94427 q^{16} +20.2622i q^{17} -5.08580i q^{18} -28.8747i q^{19} -7.76393 q^{20} +1.11006i q^{21} -27.6180 q^{23} +21.7153i q^{24} +5.00000 q^{25} +8.21478 q^{26} +8.00000 q^{27} -0.963568i q^{28} +17.3560i q^{29} -6.49839i q^{30} +34.3607 q^{31} -28.9402i q^{32} +14.7214 q^{34} +0.620541i q^{35} +24.3050 q^{36} +13.2705 q^{37} -20.9787 q^{38} -45.2267i q^{39} +12.1392i q^{40} +18.0576i q^{41} +0.806504 q^{42} +34.7931i q^{43} -15.6525 q^{45} +20.0657i q^{46} +47.4934 q^{47} -39.7771 q^{48} +48.9230 q^{49} -3.63271i q^{50} -81.0489i q^{51} +39.2583i q^{52} +41.5755 q^{53} -5.81234i q^{54} -1.50658 q^{56} +115.499i q^{57} +12.6099 q^{58} +101.743 q^{59} +31.0557 q^{60} -50.9080i q^{61} -24.9645i q^{62} -1.94260i q^{63} +18.7508 q^{64} -25.2825i q^{65} +40.1803 q^{67} +70.3532i q^{68} +110.472 q^{69} +0.450850 q^{70} +28.1803 q^{71} -38.0018i q^{72} -99.8079i q^{73} -9.64159i q^{74} -20.0000 q^{75} -100.257i q^{76} -32.8591 q^{78} -131.614i q^{79} -22.2361 q^{80} -95.0000 q^{81} +13.1196 q^{82} +125.408i q^{83} +3.85427i q^{84} -45.3077i q^{85} +25.2786 q^{86} -69.4242i q^{87} +88.9493 q^{89} +11.3722i q^{90} +3.13777 q^{91} -95.8936 q^{92} -137.443 q^{93} -34.5060i q^{94} +64.5658i q^{95} +115.761i q^{96} +48.3181 q^{97} -35.5446i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{3} - 4 q^{4} + 28 q^{9} + 16 q^{12} - 50 q^{14} + 4 q^{16} - 40 q^{20} - 106 q^{23} + 20 q^{25} - 70 q^{26} + 32 q^{27} + 48 q^{31} - 120 q^{34} - 28 q^{36} - 14 q^{37} + 10 q^{38} + 200 q^{42}+ \cdots - 84 q^{97}+O(q^{100}) $ 4 * q - 16 * q^3 - 4 * q^4 + 28 * q^9 + 16 * q^12 - 50 * q^14 + 4 * q^16 - 40 * q^20 - 106 * q^23 + 20 * q^25 - 70 * q^26 + 32 * q^27 + 48 * q^31 - 120 * q^34 - 28 * q^36 - 14 * q^37 + 10 * q^38 + 200 * q^42 + 266 * q^47 - 16 * q^48 + 66 * q^49 - 26 * q^53 + 70 * q^56 - 200 * q^58 + 322 * q^59 + 160 * q^60 + 236 * q^64 + 116 * q^67 + 424 * q^69 - 110 * q^70 + 68 * q^71 - 80 * q^75 + 280 * q^78 - 80 * q^80 - 380 * q^81 + 370 * q^82 + 280 * q^86 - 78 * q^89 - 220 * q^91 + 86 * q^92 - 192 * q^93 - 84 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 0.726543i	− 0.363271i	−0.983366	−	0.181636i	$-0.941861\pi$
$2$	− 0.726543i	− 0.363271i	0.983366	−	0.181636i	$-0.0581391\pi$
$3$	−4.00000	−1.33333	−0.666667	−	0.745356i	$-0.732280\pi$
$3$	−4.00000	−1.33333	−0.666667	+	0.745356i	$0.732280\pi$
$4$	3.47214	0.868034
$5$	−2.23607	−0.447214
$5$	−2.23607	−0.447214
$6$	2.90617i	0.484362i
$7$	− 0.277515i	− 0.0396449i	−0.999804	−	0.0198225i	$-0.993690\pi$
$7$	− 0.277515i	− 0.0396449i	0.999804	−	0.0198225i	$-0.00631010\pi$
$8$	− 5.42882i	− 0.678603i
$9$	7.00000	0.777778
$10$	1.62460i	0.162460i
$11$	0	0
$11$	0	0
$12$	−13.8885	−1.15738
$13$	11.3067i	0.869744i	0.900492	+	0.434872i	$0.143206\pi$
$13$	11.3067i	0.869744i	−0.900492	+	0.434872i	$0.856794\pi$
$14$	−0.201626	−0.0144019
$15$	8.94427	0.596285
$16$	9.94427	0.621517
$17$	20.2622i	1.19189i	0.803023	+	0.595947i	$0.203223\pi$
$17$	20.2622i	1.19189i	−0.803023	+	0.595947i	$0.796777\pi$
$18$	− 5.08580i	− 0.282544i
$19$	− 28.8747i	− 1.51972i	−0.650085	−	0.759861i	$-0.725267\pi$
$19$	− 28.8747i	− 1.51972i	0.650085	−	0.759861i	$-0.274733\pi$
$20$	−7.76393	−0.388197
$21$	1.11006i	0.0528599i
$22$	0	0
$23$	−27.6180	−1.20078	−0.600392	−	0.799706i	$-0.704989\pi$
$23$	−27.6180	−1.20078	−0.600392	+	0.799706i	$0.704989\pi$
$24$	21.7153i	0.904804i
$25$	5.00000	0.200000
$26$	8.21478	0.315953
$27$	8.00000	0.296296
$28$	− 0.963568i	− 0.0344132i
$29$	17.3560i	0.598484i	0.954177	+	0.299242i	$0.0967338\pi$
$29$	17.3560i	0.598484i	−0.954177	+	0.299242i	$0.903266\pi$
$30$	− 6.49839i	− 0.216613i
$31$	34.3607	1.10841	0.554205	−	0.832381i	$-0.313023\pi$
$31$	34.3607	1.10841	0.554205	+	0.832381i	$0.313023\pi$
$32$	− 28.9402i	− 0.904382i
$33$	0	0
$34$	14.7214	0.432981
$35$	0.620541i	0.0177298i
$36$	24.3050	0.675138
$37$	13.2705	0.358662	0.179331	−	0.983789i	$-0.442607\pi$
$37$	13.2705	0.358662	0.179331	+	0.983789i	$0.442607\pi$
$38$	−20.9787	−0.552071
$39$	− 45.2267i	− 1.15966i
$40$	12.1392i	0.303481i
$41$	18.0576i	0.440428i	0.975452	+	0.220214i	$0.0706756\pi$
$41$	18.0576i	0.440428i	−0.975452	+	0.220214i	$0.929324\pi$
$42$	0.806504	0.0192025
$43$	34.7931i	0.809141i	0.914507	+	0.404571i	$0.132579\pi$
$43$	34.7931i	0.809141i	−0.914507	+	0.404571i	$0.867421\pi$
$44$	0	0
$45$	−15.6525	−0.347833
$46$	20.0657i	0.436210i
$47$	47.4934	1.01050	0.505249	−	0.862974i	$-0.331401\pi$
$47$	47.4934	1.01050	0.505249	+	0.862974i	$0.331401\pi$
$48$	−39.7771	−0.828689
$49$	48.9230	0.998428
$50$	− 3.63271i	− 0.0726543i
$51$	− 81.0489i	− 1.58919i
$52$	39.2583i	0.754968i
$53$	41.5755	0.784443	0.392221	−	0.919871i	$-0.371707\pi$
$53$	41.5755	0.784443	0.392221	+	0.919871i	$0.371707\pi$
$54$	− 5.81234i	− 0.107636i
$55$	0	0
$56$	−1.50658	−0.0269032
$57$	115.499i	2.02630i
$58$	12.6099	0.217412
$59$	101.743	1.72445	0.862226	−	0.506524i	$-0.169070\pi$
$59$	101.743	1.72445	0.862226	+	0.506524i	$0.169070\pi$
$60$	31.0557	0.517595
$61$	− 50.9080i	− 0.834558i	−0.908778	−	0.417279i	$-0.862984\pi$
$61$	− 50.9080i	− 0.834558i	0.908778	−	0.417279i	$-0.137016\pi$
$62$	− 24.9645i	− 0.402653i
$63$	− 1.94260i	− 0.0308350i
$64$	18.7508	0.292981
$65$	− 25.2825i	− 0.388962i
$66$	0	0
$67$	40.1803	0.599707	0.299853	−	0.953985i	$-0.403062\pi$
$67$	40.1803	0.599707	0.299853	+	0.953985i	$0.403062\pi$
$68$	70.3532i	1.03461i
$69$	110.472	1.60105
$70$	0.450850	0.00644071
$71$	28.1803	0.396906	0.198453	−	0.980110i	$-0.436408\pi$
$71$	28.1803	0.396906	0.198453	+	0.980110i	$0.436408\pi$
$72$	− 38.0018i	− 0.527802i
$73$	− 99.8079i	− 1.36723i	−0.729842	−	0.683616i	$-0.760406\pi$
$73$	− 99.8079i	− 1.36723i	0.729842	−	0.683616i	$-0.239594\pi$
$74$	− 9.64159i	− 0.130292i
$75$	−20.0000	−0.266667
$76$	− 100.257i	− 1.31917i
$77$	0	0
$78$	−32.8591	−0.421271
$79$	− 131.614i	− 1.66600i	−0.553274	−	0.832999i	$-0.686622\pi$
$79$	− 131.614i	− 1.66600i	0.553274	−	0.832999i	$-0.313378\pi$
$80$	−22.2361	−0.277951
$81$	−95.0000	−1.17284
$82$	13.1196	0.159995
$83$	125.408i	1.51095i	0.655180	+	0.755473i	$0.272593\pi$
$83$	125.408i	1.51095i	−0.655180	+	0.755473i	$0.727407\pi$
$84$	3.85427i	0.0458842i
$85$	− 45.3077i	− 0.533032i
$86$	25.2786	0.293938
$87$	− 69.4242i	− 0.797979i
$88$	0	0
$89$	88.9493	0.999430	0.499715	−	0.866190i	$-0.333438\pi$
$89$	88.9493	0.999430	0.499715	+	0.866190i	$0.333438\pi$
$90$	11.3722i	0.126358i
$91$	3.13777	0.0344810
$92$	−95.8936	−1.04232
$93$	−137.443	−1.47788
$94$	− 34.5060i	− 0.367085i
$95$	64.5658i	0.679640i
$96$	115.761i	1.20584i
$97$	48.3181	0.498125	0.249062	−	0.968487i	$-0.419878\pi$
$97$	48.3181	0.498125	0.249062	+	0.968487i	$0.419878\pi$
$98$	− 35.5446i	− 0.362700i
$99$	0	0
$100$	17.3607	0.173607
$101$	38.4663i	0.380854i	0.981701	+	0.190427i	$0.0609873\pi$
$101$	38.4663i	0.380854i	−0.981701	+	0.190427i	$0.939013\pi$
$102$	−58.8854	−0.577308
$103$	126.172	1.22497	0.612486	−	0.790481i	$-0.290169\pi$
$103$	126.172	1.22497	0.612486	+	0.790481i	$0.290169\pi$
$104$	61.3820	0.590211
$105$	− 2.48217i	− 0.0236397i
$106$	− 30.2063i	− 0.284965i
$107$	− 87.7092i	− 0.819712i	−0.912150	−	0.409856i	$-0.865579\pi$
$107$	− 87.7092i	− 0.819712i	0.912150	−	0.409856i	$-0.134421\pi$
$108$	27.7771	0.257195
$109$	144.692i	1.32745i	0.747978	+	0.663723i	$0.231025\pi$
$109$	144.692i	1.32745i	−0.747978	+	0.663723i	$0.768975\pi$
$110$	0	0
$111$	−53.0820	−0.478217
$112$	− 2.75968i	− 0.0246400i
$113$	−129.623	−1.14711	−0.573553	−	0.819168i	$-0.694435\pi$
$113$	−129.623	−1.14711	−0.573553	+	0.819168i	$0.694435\pi$
$114$	83.9149	0.736095
$115$	61.7558	0.537007
$116$	60.2625i	0.519505i
$117$	79.1467i	0.676468i
$118$	− 73.9204i	− 0.626444i
$119$	5.62306	0.0472526
$120$	− 48.5569i	− 0.404641i
$121$	0	0
$122$	−36.9868	−0.303171
$123$	− 72.2302i	− 0.587238i
$124$	119.305	0.962137
$125$	−11.1803	−0.0894427
$126$	−1.41138	−0.0112015
$127$	154.202i	1.21419i	0.794629	+	0.607095i	$0.207665\pi$
$127$	154.202i	1.21419i	−0.794629	+	0.607095i	$0.792335\pi$
$128$	− 129.384i	− 1.01081i
$129$	− 139.172i	− 1.07885i
$130$	−18.3688	−0.141299
$131$	128.496i	0.980883i	0.871474	+	0.490442i	$0.163164\pi$
$131$	128.496i	0.980883i	−0.871474	+	0.490442i	$0.836836\pi$
$132$	0	0
$133$	−8.01316	−0.0602493
$134$	− 29.1927i	− 0.217856i
$135$	−17.8885	−0.132508
$136$	110.000	0.808824
$137$	−61.9311	−0.452052	−0.226026	−	0.974121i	$-0.572573\pi$
$137$	−61.9311	−0.452052	−0.226026	+	0.974121i	$0.572573\pi$
$138$	− 80.2627i	− 0.581614i
$139$	228.238i	1.64200i	0.570928	+	0.821000i	$0.306584\pi$
$139$	228.238i	1.64200i	−0.570928	+	0.821000i	$0.693416\pi$
$140$	2.15460i	0.0153900i
$141$	−189.974	−1.34733
$142$	− 20.4742i	− 0.144185i
$143$	0	0
$144$	69.6099	0.483402
$145$	− 38.8093i	− 0.267650i
$146$	−72.5147	−0.496676
$147$	−195.692	−1.33124
$148$	46.0770	0.311331
$149$	78.6977i	0.528173i	0.964499	+	0.264086i	$0.0850704\pi$
$149$	78.6977i	0.528173i	−0.964499	+	0.264086i	$0.914930\pi$
$150$	14.5309i	0.0968723i
$151$	− 71.0893i	− 0.470790i	−0.971900	−	0.235395i	$-0.924362\pi$
$151$	− 71.0893i	− 0.470790i	0.971900	−	0.235395i	$-0.0756383\pi$
$152$	−156.756	−1.03129
$153$	141.835i	0.927029i
$154$	0	0
$155$	−76.8328	−0.495696
$156$	− 157.033i	− 1.00662i
$157$	−214.743	−1.36779	−0.683894	−	0.729582i	$-0.739715\pi$
$157$	−214.743	−1.36779	−0.683894	+	0.729582i	$0.739715\pi$
$158$	−95.6231	−0.605209
$159$	−166.302	−1.04592
$160$	64.7123i	0.404452i
$161$	7.66441i	0.0476050i
$162$	69.0215i	0.426059i
$163$	−91.1772	−0.559370	−0.279685	−	0.960092i	$-0.590230\pi$
$163$	−91.1772	−0.559370	−0.279685	+	0.960092i	$0.590230\pi$
$164$	62.6983i	0.382307i
$165$	0	0
$166$	91.1146	0.548883
$167$	45.4137i	0.271938i	0.990713	+	0.135969i	$0.0434148\pi$
$167$	45.4137i	0.271938i	−0.990713	+	0.135969i	$0.956585\pi$
$168$	6.02631	0.0358709
$169$	41.1591	0.243545
$170$	−32.9180	−0.193635
$171$	− 202.123i	− 1.18201i
$172$	120.806i	0.702362i
$173$	151.549i	0.876003i	0.898974	+	0.438001i	$0.144314\pi$
$173$	151.549i	0.876003i	−0.898974	+	0.438001i	$0.855686\pi$
$174$	−50.4396	−0.289883
$175$	− 1.38757i	− 0.00792899i
$176$	0	0
$177$	−406.971	−2.29927
$178$	− 64.6254i	− 0.363064i
$179$	−170.493	−0.952477	−0.476239	−	0.879316i	$-0.658000\pi$
$179$	−170.493	−0.952477	−0.476239	+	0.879316i	$0.658000\pi$
$180$	−54.3475	−0.301931
$181$	−165.984	−0.917037	−0.458519	−	0.888685i	$-0.651620\pi$
$181$	−165.984	−0.917037	−0.458519	+	0.888685i	$0.651620\pi$
$182$	− 2.27972i	− 0.0125259i
$183$	203.632i	1.11274i
$184$	149.933i	0.814856i
$185$	−29.6738	−0.160399
$186$	99.8580i	0.536871i
$187$	0	0
$188$	164.904	0.877147
$189$	− 2.22012i	− 0.0117466i
$190$	46.9098	0.246894
$191$	11.1935	0.0586047	0.0293023	−	0.999571i	$-0.490671\pi$
$191$	11.1935	0.0586047	0.0293023	+	0.999571i	$0.490671\pi$
$192$	−75.0031	−0.390641
$193$	− 125.620i	− 0.650883i	−0.945562	−	0.325442i	$-0.894487\pi$
$193$	− 125.620i	− 0.650883i	0.945562	−	0.325442i	$-0.105513\pi$
$194$	− 35.1052i	− 0.180954i
$195$	101.130i	0.518615i
$196$	169.867	0.866670
$197$	− 361.517i	− 1.83511i	−0.397607	−	0.917556i	$-0.630159\pi$
$197$	− 361.517i	− 1.83511i	0.397607	−	0.917556i	$-0.369841\pi$
$198$	0	0
$199$	267.692	1.34519	0.672593	−	0.740013i	$-0.265181\pi$
$199$	267.692	1.34519	0.672593	+	0.740013i	$0.265181\pi$
$200$	− 27.1441i	− 0.135721i
$201$	−160.721	−0.799609
$202$	27.9474	0.138353
$203$	4.81655	0.0237269
$204$	− 281.413i	− 1.37947i
$205$	− 40.3779i	− 0.196966i
$206$	− 91.6695i	− 0.444997i
$207$	−193.326	−0.933943
$208$	112.437i	0.540561i
$209$	0	0
$210$	−1.80340	−0.00858761
$211$	− 226.033i	− 1.07125i	−0.844456	−	0.535624i	$-0.820076\pi$
$211$	− 226.033i	− 1.07125i	0.844456	−	0.535624i	$-0.179924\pi$
$212$	144.356	0.680923
$213$	−112.721	−0.529208
$214$	−63.7245	−0.297778
$215$	− 77.7997i	− 0.361859i
$216$	− 43.4306i	− 0.201068i
$217$	− 9.53559i	− 0.0439428i
$218$	105.125	0.482223
$219$	399.232i	1.82298i
$220$	0	0
$221$	−229.098	−1.03664
$222$	38.5664i	0.173722i
$223$	280.116	1.25613	0.628064	−	0.778162i	$-0.283848\pi$
$223$	280.116	1.25613	0.628064	+	0.778162i	$0.283848\pi$
$224$	−8.03134	−0.0358542
$225$	35.0000	0.155556
$226$	94.1767i	0.416711i
$227$	87.1733i	0.384023i	0.981393	+	0.192012i	$0.0615011\pi$
$227$	87.1733i	0.384023i	−0.981393	+	0.192012i	$0.938499\pi$
$228$	401.028i	1.75889i
$229$	107.348	0.468766	0.234383	−	0.972144i	$-0.424693\pi$
$229$	107.348	0.468766	0.234383	+	0.972144i	$0.424693\pi$
$230$	− 44.8682i	− 0.195079i
$231$	0	0
$232$	94.2229	0.406133
$233$	− 131.776i	− 0.565561i	−0.959185	−	0.282781i	$-0.908743\pi$
$233$	− 131.776i	− 0.565561i	0.959185	−	0.282781i	$-0.0912569\pi$
$234$	57.5035	0.245741
$235$	−106.199	−0.451909
$236$	353.264	1.49688
$237$	526.455i	2.22133i
$238$	− 4.08539i	− 0.0171655i
$239$	92.0375i	0.385094i	0.981288	+	0.192547i	$0.0616748\pi$
$239$	92.0375i	0.385094i	−0.981288	+	0.192547i	$0.938325\pi$
$240$	88.9443	0.370601
$241$	− 26.5140i	− 0.110017i	−0.998486	−	0.0550083i	$-0.982481\pi$
$241$	− 26.5140i	− 0.110017i	0.998486	−	0.0550083i	$-0.0175185\pi$
$242$	0	0
$243$	308.000	1.26749
$244$	− 176.760i	− 0.724425i
$245$	−109.395	−0.446511
$246$	−52.4783	−0.213327
$247$	326.477	1.32177
$248$	− 186.538i	− 0.752170i
$249$	− 501.634i	− 2.01459i
$250$	8.12299i	0.0324920i
$251$	−135.034	−0.537986	−0.268993	−	0.963142i	$-0.586691\pi$
$251$	−135.034	−0.537986	−0.268993	+	0.963142i	$0.586691\pi$
$252$	− 6.74498i	− 0.0267658i
$253$	0	0
$254$	112.034	0.441080
$255$	181.231i	0.710709i
$256$	−19.0000	−0.0742188
$257$	−244.292	−0.950552	−0.475276	−	0.879837i	$-0.657652\pi$
$257$	−244.292	−0.950552	−0.475276	+	0.879837i	$0.657652\pi$
$258$	−101.115	−0.391917
$259$	− 3.68276i	− 0.0142191i
$260$	− 87.7843i	− 0.337632i
$261$	121.492i	0.465488i
$262$	93.3576	0.356327
$263$	1.93304i	0.00734998i	0.999993	+	0.00367499i	$0.00116979\pi$
$263$	1.93304i	0.00734998i	−0.999993	+	0.00367499i	$0.998830\pi$
$264$	0	0
$265$	−92.9656	−0.350813
$266$	5.82190i	0.0218868i
$267$	−355.797	−1.33257
$268$	139.512	0.520566
$269$	−183.210	−0.681077	−0.340539	−	0.940231i	$-0.610609\pi$
$269$	−183.210	−0.681077	−0.340539	+	0.940231i	$0.610609\pi$
$270$	12.9968i	0.0481363i
$271$	507.565i	1.87293i	0.350755	+	0.936467i	$0.385925\pi$
$271$	507.565i	1.87293i	−0.350755	+	0.936467i	$0.614075\pi$
$272$	201.493i	0.740783i
$273$	−12.5511	−0.0459746
$274$	44.9956i	0.164217i
$275$	0	0
$276$	383.574	1.38976
$277$	35.4327i	0.127916i	0.997953	+	0.0639580i	$0.0203724\pi$
$277$	35.4327i	0.127916i	−0.997953	+	0.0639580i	$0.979628\pi$
$278$	165.825	0.596492
$279$	240.525	0.862096
$280$	3.36881	0.0120315
$281$	341.794i	1.21635i	0.793803	+	0.608175i	$0.208098\pi$
$281$	341.794i	1.21635i	−0.793803	+	0.608175i	$0.791902\pi$
$282$	138.024i	0.489447i
$283$	− 413.420i	− 1.46085i	−0.682995	−	0.730423i	$-0.739323\pi$
$283$	− 413.420i	− 1.46085i	0.682995	−	0.730423i	$-0.260677\pi$
$284$	97.8460	0.344528
$285$	− 258.263i	− 0.906187i
$286$	0	0
$287$	5.01124	0.0174608
$288$	− 202.582i	− 0.703408i
$289$	−121.557	−0.420613
$290$	−28.1966	−0.0972297
$291$	−193.272	−0.664166
$292$	− 346.547i	− 1.18680i
$293$	192.859i	0.658222i	0.944291	+	0.329111i	$0.106749\pi$
$293$	192.859i	0.658222i	−0.944291	+	0.329111i	$0.893251\pi$
$294$	142.179i	0.483600i
$295$	−227.503	−0.771198
$296$	− 72.0433i	− 0.243389i
$297$	0	0
$298$	57.1772	0.191870
$299$	− 312.268i	− 1.04438i
$300$	−69.4427	−0.231476
$301$	9.65558	0.0320783
$302$	−51.6494	−0.171024
$303$	− 153.865i	− 0.507805i
$304$	− 287.138i	− 0.944533i
$305$	113.834i	0.373226i
$306$	103.050	0.336763
$307$	− 335.115i	− 1.09158i	−0.837922	−	0.545790i	$-0.816230\pi$
$307$	− 335.115i	− 1.09158i	0.837922	−	0.545790i	$-0.183770\pi$
$308$	0	0
$309$	−504.689	−1.63330
$310$	55.8223i	0.180072i
$311$	217.161	0.698267	0.349133	−	0.937073i	$-0.386476\pi$
$311$	217.161	0.698267	0.349133	+	0.937073i	$0.386476\pi$
$312$	−245.528	−0.786948
$313$	594.636	1.89980	0.949898	−	0.312560i	$-0.101186\pi$
$313$	594.636	1.89980	0.949898	+	0.312560i	$0.101186\pi$
$314$	156.020i	0.496878i
$315$	4.34379i	0.0137898i
$316$	− 456.981i	− 1.44614i
$317$	−71.7953	−0.226483	−0.113242	−	0.993567i	$-0.536123\pi$
$317$	−71.7953	−0.226483	−0.113242	+	0.993567i	$0.536123\pi$
$318$	120.825i	0.379954i
$319$	0	0
$320$	−41.9280	−0.131025
$321$	350.837i	1.09295i
$322$	5.56852	0.0172935
$323$	585.066	1.81135
$324$	−329.853	−1.01806
$325$	56.5334i	0.173949i
$326$	66.2441i	0.203203i
$327$	− 578.766i	− 1.76993i
$328$	98.0313	0.298876
$329$	− 13.1801i	− 0.0400611i
$330$	0	0
$331$	−292.681	−0.884232	−0.442116	−	0.896958i	$-0.645772\pi$
$331$	−292.681	−0.884232	−0.442116	+	0.896958i	$0.645772\pi$
$332$	435.435i	1.31155i
$333$	92.8936	0.278960
$334$	32.9950	0.0987874
$335$	−89.8460	−0.268197
$336$	11.0387i	0.0328533i
$337$	391.997i	1.16320i	0.813476	+	0.581598i	$0.197572\pi$
$337$	391.997i	1.16320i	−0.813476	+	0.581598i	$0.802428\pi$
$338$	− 29.9038i	− 0.0884728i
$339$	518.492	1.52948
$340$	− 157.314i	− 0.462690i
$341$	0	0
$342$	−146.851	−0.429389
$343$	− 27.1751i	− 0.0792276i
$344$	188.885	0.549086
$345$	−247.023	−0.716009
$346$	110.106	0.318227
$347$	− 63.6118i	− 0.183319i	−0.995790	−	0.0916597i	$-0.970783\pi$
$347$	− 63.6118i	− 0.183319i	0.995790	−	0.0916597i	$-0.0292172\pi$
$348$	− 241.050i	− 0.692673i
$349$	− 245.479i	− 0.703377i	−0.936117	−	0.351689i	$-0.885608\pi$
$349$	− 245.479i	− 0.703377i	0.936117	−	0.351689i	$-0.114392\pi$
$350$	−1.00813	−0.00288037
$351$	90.4534i	0.257702i
$352$	0	0
$353$	216.535	0.613413	0.306707	−	0.951804i	$-0.400773\pi$
$353$	216.535	0.613413	0.306707	+	0.951804i	$0.400773\pi$
$354$	295.681i	0.835258i
$355$	−63.0132	−0.177502
$356$	308.844	0.867539
$357$	−22.4922	−0.0630035
$358$	123.871i	0.346008i
$359$	− 682.934i	− 1.90232i	−0.308695	−	0.951161i	$-0.599892\pi$
$359$	− 682.934i	− 1.90232i	0.308695	−	0.951161i	$-0.400108\pi$
$360$	84.9745i	0.236040i
$361$	−472.750	−1.30956
$362$	120.594i	0.333133i
$363$	0	0
$364$	10.8948	0.0299306
$365$	223.177i	0.611445i
$366$	147.947	0.404228
$367$	73.6919	0.200795	0.100398	−	0.994947i	$-0.467988\pi$
$367$	73.6919	0.200795	0.100398	+	0.994947i	$0.467988\pi$
$368$	−274.641	−0.746308
$369$	126.403i	0.342555i
$370$	21.5593i	0.0582682i
$371$	− 11.5378i	− 0.0310992i
$372$	−477.220	−1.28285
$373$	58.3795i	0.156514i	0.996933	+	0.0782568i	$0.0249354\pi$
$373$	58.3795i	0.156514i	−0.996933	+	0.0782568i	$0.975065\pi$
$374$	0	0
$375$	44.7214	0.119257
$376$	− 257.833i	− 0.685727i
$377$	−196.239	−0.520528
$378$	−1.61301	−0.00426722
$379$	−187.480	−0.494671	−0.247335	−	0.968930i	$-0.579555\pi$
$379$	−187.480	−0.494671	−0.247335	+	0.968930i	$0.579555\pi$
$380$	224.181i	0.589951i
$381$	− 616.809i	− 1.61892i
$382$	− 8.13255i	− 0.0212894i
$383$	−6.12269	−0.0159861	−0.00799307	−	0.999968i	$-0.502544\pi$
$383$	−6.12269	−0.0159861	−0.00799307	+	0.999968i	$0.502544\pi$
$384$	517.537i	1.34775i
$385$	0	0
$386$	−91.2686	−0.236447
$387$	243.551i	0.629332i
$388$	167.767	0.432389
$389$	−226.105	−0.581247	−0.290624	−	0.956837i	$-0.593863\pi$
$389$	−226.105	−0.581247	−0.290624	+	0.956837i	$0.593863\pi$
$390$	73.4752	0.188398
$391$	− 559.602i	− 1.43121i
$392$	− 265.594i	− 0.677536i
$393$	− 513.983i	− 1.30784i
$394$	−262.658	−0.666643
$395$	294.298i	0.745057i
$396$	0	0
$397$	−215.123	−0.541873	−0.270936	−	0.962597i	$-0.587333\pi$
$397$	−215.123	−0.541873	−0.270936	+	0.962597i	$0.587333\pi$
$398$	− 194.490i	− 0.488667i
$399$	32.0526	0.0803324
$400$	49.7214	0.124303
$401$	−541.068	−1.34930	−0.674648	−	0.738140i	$-0.735705\pi$
$401$	−541.068	−1.34930	−0.674648	+	0.738140i	$0.735705\pi$
$402$	116.771i	0.290475i
$403$	388.505i	0.964033i
$404$	133.560i	0.330594i
$405$	212.426	0.524510
$406$	− 3.49943i	− 0.00861929i
$407$	0	0
$408$	−440.000	−1.07843
$409$	366.734i	0.896660i	0.893868	+	0.448330i	$0.147981\pi$
$409$	366.734i	0.896660i	−0.893868	+	0.448330i	$0.852019\pi$
$410$	−29.3363	−0.0715519
$411$	247.724	0.602736
$412$	438.087	1.06332
$413$	− 28.2351i	− 0.0683658i
$414$	140.460i	0.339275i
$415$	− 280.422i	− 0.675715i
$416$	327.218	0.786581
$417$	− 912.952i	− 2.18933i
$418$	0	0
$419$	164.543	0.392704	0.196352	−	0.980533i	$-0.437090\pi$
$419$	164.543	0.392704	0.196352	+	0.980533i	$0.437090\pi$
$420$	− 8.61842i	− 0.0205200i
$421$	120.255	0.285642	0.142821	−	0.989749i	$-0.454383\pi$
$421$	120.255	0.285642	0.142821	+	0.989749i	$0.454383\pi$
$422$	−164.223	−0.389154
$423$	332.454	0.785943
$424$	− 225.706i	− 0.532325i
$425$	101.311i	0.238379i
$426$	81.8969i	0.192246i
$427$	−14.1277	−0.0330860
$428$	− 304.538i	− 0.711538i
$429$	0	0
$430$	−56.5248	−0.131453
$431$	540.593i	1.25428i	0.778908	+	0.627138i	$0.215774\pi$
$431$	540.593i	1.25428i	−0.778908	+	0.627138i	$0.784226\pi$
$432$	79.5542	0.184153
$433$	213.368	0.492766	0.246383	−	0.969173i	$-0.420758\pi$
$433$	213.368	0.492766	0.246383	+	0.969173i	$0.420758\pi$
$434$	−6.92801	−0.0159632
$435$	155.237i	0.356867i
$436$	502.389i	1.15227i
$437$	797.463i	1.82486i
$438$	290.059	0.662235
$439$	29.8597i	0.0680175i	0.999422	+	0.0340087i	$0.0108274\pi$
$439$	29.8597i	0.0680175i	−0.999422	+	0.0340087i	$0.989173\pi$
$440$	0	0
$441$	342.461	0.776555
$442$	166.450i	0.376583i
$443$	−57.2624	−0.129260	−0.0646302	−	0.997909i	$-0.520587\pi$
$443$	−57.2624	−0.129260	−0.0646302	+	0.997909i	$0.520587\pi$
$444$	−184.308	−0.415108
$445$	−198.897	−0.446959
$446$	− 203.517i	− 0.456315i
$447$	− 314.791i	− 0.704230i
$448$	− 5.20361i	− 0.0116152i
$449$	594.697	1.32449	0.662246	−	0.749286i	$-0.269603\pi$
$449$	594.697	1.32449	0.662246	+	0.749286i	$0.269603\pi$
$450$	− 25.4290i	− 0.0565089i
$451$	0	0
$452$	−450.069	−0.995728
$453$	284.357i	0.627720i
$454$	63.3351	0.139505
$455$	−7.01626	−0.0154204
$456$	627.023	1.37505
$457$	475.154i	1.03972i	0.854250	+	0.519862i	$0.174017\pi$
$457$	475.154i	1.03972i	−0.854250	+	0.519862i	$0.825983\pi$
$458$	− 77.9925i	− 0.170289i
$459$	162.098i	0.353154i
$460$	214.425	0.466140
$461$	290.362i	0.629853i	0.949116	+	0.314927i	$0.101980\pi$
$461$	290.362i	0.629853i	−0.949116	+	0.314927i	$0.898020\pi$
$462$	0	0
$463$	86.1358	0.186039	0.0930193	−	0.995664i	$-0.470348\pi$
$463$	86.1358	0.186039	0.0930193	+	0.995664i	$0.470348\pi$
$464$	172.593i	0.371968i
$465$	307.331	0.660927
$466$	−95.7407	−0.205452
$467$	225.935	0.483801	0.241900	−	0.970301i	$-0.422229\pi$
$467$	225.935	0.483801	0.241900	+	0.970301i	$0.422229\pi$
$468$	274.808i	0.587197i
$469$	− 11.1506i	− 0.0237753i
$470$	77.1577i	0.164165i
$471$	858.971	1.82372
$472$	− 552.343i	− 1.17022i
$473$	0	0
$474$	382.492	0.806946
$475$	− 144.374i	− 0.303944i
$476$	19.5240	0.0410169
$477$	291.028	0.610122
$478$	66.8692	0.139894
$479$	− 84.1052i	− 0.175585i	−0.996139	−	0.0877924i	$-0.972019\pi$
$479$	− 84.1052i	− 0.175585i	0.996139	−	0.0877924i	$-0.0279812\pi$
$480$	− 258.849i	− 0.539269i
$481$	150.045i	0.311945i
$482$	−19.2636	−0.0399659
$483$	− 30.6576i	− 0.0634733i
$484$	0	0
$485$	−108.043	−0.222768
$486$	− 223.775i	− 0.460443i
$487$	661.712	1.35875	0.679376	−	0.733791i	$-0.262251\pi$
$487$	661.712	1.35875	0.679376	+	0.733791i	$0.262251\pi$
$488$	−276.371	−0.566333
$489$	364.709	0.745826
$490$	79.4802i	0.162205i
$491$	− 745.268i	− 1.51786i	−0.651174	−	0.758928i	$-0.725723\pi$
$491$	− 745.268i	− 1.51786i	0.651174	−	0.758928i	$-0.274277\pi$
$492$	− 250.793i	− 0.509742i
$493$	−351.672	−0.713330
$494$	− 237.200i	− 0.480161i
$495$	0	0
$496$	341.692	0.688895
$497$	− 7.82045i	− 0.0157353i
$498$	−364.458	−0.731844
$499$	278.025	0.557165	0.278582	−	0.960412i	$-0.410136\pi$
$499$	278.025	0.557165	0.278582	+	0.960412i	$0.410136\pi$
$500$	−38.8197	−0.0776393
$501$	− 181.655i	− 0.362584i
$502$	98.1083i	0.195435i
$503$	− 269.427i	− 0.535641i	−0.963469	−	0.267820i	$-0.913697\pi$
$503$	− 269.427i	− 0.535641i	0.963469	−	0.267820i	$-0.0863033\pi$
$504$	−10.5460	−0.0209247
$505$	− 86.0132i	− 0.170323i
$506$	0	0
$507$	−164.636	−0.324726
$508$	535.411i	1.05396i
$509$	524.312	1.03008	0.515041	−	0.857165i	$-0.327777\pi$
$509$	524.312	1.03008	0.515041	+	0.857165i	$0.327777\pi$
$510$	131.672	0.258180
$511$	−27.6982	−0.0542038
$512$	− 503.732i	− 0.983852i
$513$	− 230.998i	− 0.450288i
$514$	177.488i	0.345308i
$515$	−282.130	−0.547825
$516$	− 483.225i	− 0.936483i
$517$	0	0
$518$	−2.67568	−0.00516541
$519$	− 606.194i	− 1.16800i
$520$	−137.254	−0.263950
$521$	−381.500	−0.732246	−0.366123	−	0.930566i	$-0.619315\pi$
$521$	−381.500	−0.732246	−0.366123	+	0.930566i	$0.619315\pi$
$522$	88.2693	0.169098
$523$	− 638.767i	− 1.22135i	−0.791881	−	0.610676i	$-0.790898\pi$
$523$	− 638.767i	− 1.22135i	0.791881	−	0.610676i	$-0.209102\pi$
$524$	446.154i	0.851440i
$525$	5.55029i	0.0105720i
$526$	1.40444	0.00267004
$527$	696.223i	1.32111i
$528$	0	0
$529$	233.756	0.441882
$530$	67.5434i	0.127440i
$531$	712.199	1.34124
$532$	−27.8228	−0.0522984
$533$	−204.171	−0.383060
$534$	258.502i	0.484086i
$535$	196.124i	0.366586i
$536$	− 218.132i	− 0.406963i
$537$	681.974	1.26997
$538$	133.110i	0.247416i
$539$	0	0
$540$	−62.1115	−0.115021
$541$	123.269i	0.227855i	0.993489	+	0.113927i	$0.0363431\pi$
$541$	123.269i	0.227855i	−0.993489	+	0.113927i	$0.963657\pi$
$542$	368.768	0.680383
$543$	663.935	1.22272
$544$	586.393	1.07793
$545$	− 323.540i	− 0.593652i
$546$	9.11889i	0.0167013i
$547$	339.474i	0.620611i	0.950637	+	0.310305i	$0.100431\pi$
$547$	339.474i	0.620611i	−0.950637	+	0.310305i	$0.899569\pi$
$548$	−215.033	−0.392396
$549$	− 356.356i	− 0.649100i
$550$	0	0
$551$	501.151	0.909530
$552$	− 599.734i	− 1.08647i
$553$	−36.5248	−0.0660484
$554$	25.7434	0.0464682
$555$	118.695	0.213865
$556$	792.474i	1.42531i
$557$	− 528.107i	− 0.948128i	−0.880490	−	0.474064i	$-0.842787\pi$
$557$	− 528.107i	− 0.948128i	0.880490	−	0.474064i	$-0.157213\pi$
$558$	− 174.751i	− 0.313175i
$559$	−393.394	−0.703746
$560$	6.17083i	0.0110193i
$561$	0	0
$562$	248.328	0.441865
$563$	− 256.648i	− 0.455858i	−0.973678	−	0.227929i	$-0.926805\pi$
$563$	− 256.648i	− 0.455858i	0.973678	−	0.227929i	$-0.0731955\pi$
$564$	−659.614	−1.16953
$565$	289.846	0.513002
$566$	−300.367	−0.530684
$567$	26.3639i	0.0464971i
$568$	− 152.986i	− 0.269342i
$569$	− 248.963i	− 0.437544i	−0.975776	−	0.218772i	$-0.929795\pi$
$569$	− 248.963i	− 0.437544i	0.975776	−	0.218772i	$-0.0702051\pi$
$570$	−187.639	−0.329192
$571$	393.435i	0.689028i	0.938781	+	0.344514i	$0.111956\pi$
$571$	393.435i	0.689028i	−0.938781	+	0.344514i	$0.888044\pi$
$572$	0	0
$573$	−44.7740	−0.0781396
$574$	− 3.64088i	− 0.00634299i
$575$	−138.090	−0.240157
$576$	131.255	0.227874
$577$	248.604	0.430856	0.215428	−	0.976520i	$-0.430885\pi$
$577$	248.604	0.430856	0.215428	+	0.976520i	$0.430885\pi$
$578$	88.3165i	0.152797i
$579$	502.482i	0.867844i
$580$	− 134.751i	− 0.232330i
$581$	34.8027	0.0599013
$582$	140.421i	0.241273i
$583$	0	0
$584$	−541.840	−0.927808
$585$	− 176.977i	− 0.302526i
$586$	140.120	0.239113
$587$	−381.895	−0.650587	−0.325294	−	0.945613i	$-0.605463\pi$
$587$	−381.895	−0.650587	−0.325294	+	0.945613i	$0.605463\pi$
$588$	−679.469	−1.15556
$589$	− 992.155i	− 1.68447i
$590$	165.291i	0.280154i
$591$	1446.07i	2.44682i
$592$	131.966	0.222915
$593$	467.858i	0.788968i	0.918903	+	0.394484i	$0.129077\pi$
$593$	467.858i	0.788968i	−0.918903	+	0.394484i	$0.870923\pi$
$594$	0	0
$595$	−12.5735	−0.0211320
$596$	273.249i	0.458472i
$597$	−1070.77	−1.79358
$598$	−226.876	−0.379392
$599$	582.780	0.972922	0.486461	−	0.873702i	$-0.338288\pi$
$599$	582.780	0.972922	0.486461	+	0.873702i	$0.338288\pi$
$600$	108.576i	0.180961i
$601$	748.529i	1.24547i	0.782432	+	0.622736i	$0.213979\pi$
$601$	748.529i	1.24547i	−0.782432	+	0.622736i	$0.786021\pi$
$602$	− 7.01519i	− 0.0116531i
$603$	281.262	0.466438
$604$	− 246.832i	− 0.408662i
$605$	0	0
$606$	−111.790	−0.184471
$607$	− 751.965i	− 1.23882i	−0.785067	−	0.619411i	$-0.787372\pi$
$607$	− 751.965i	− 1.23882i	0.785067	−	0.619411i	$-0.212628\pi$
$608$	−835.641	−1.37441
$609$	−19.2662	−0.0316358
$610$	82.7051	0.135582
$611$	536.993i	0.878875i
$612$	492.472i	0.804693i
$613$	1002.92i	1.63608i	0.575158	+	0.818042i	$0.304941\pi$
$613$	1002.92i	1.63608i	−0.575158	+	0.818042i	$0.695059\pi$
$614$	−243.475	−0.396539
$615$	161.512i	0.262621i
$616$	0	0
$617$	436.456	0.707384	0.353692	−	0.935362i	$-0.384926\pi$
$617$	436.456	0.707384	0.353692	+	0.935362i	$0.384926\pi$
$618$	366.678i	0.593330i
$619$	127.116	0.205358	0.102679	−	0.994715i	$-0.467259\pi$
$619$	127.116	0.205358	0.102679	+	0.994715i	$0.467259\pi$
$620$	−266.774	−0.430281
$621$	−220.944	−0.355788
$622$	− 157.777i	− 0.253660i
$623$	− 24.6847i	− 0.0396224i
$624$	− 449.747i	− 0.720748i
$625$	25.0000	0.0400000
$626$	− 432.028i	− 0.690141i
$627$	0	0
$628$	−745.616	−1.18729
$629$	268.890i	0.427488i
$630$	3.15595	0.00500944
$631$	−225.155	−0.356822	−0.178411	−	0.983956i	$-0.557096\pi$
$631$	−225.155	−0.356822	−0.178411	+	0.983956i	$0.557096\pi$
$632$	−714.508	−1.13055
$633$	904.134i	1.42833i
$634$	52.1623i	0.0822749i
$635$	− 344.807i	− 0.543002i
$636$	−577.423	−0.907897
$637$	553.156i	0.868377i
$638$	0	0
$639$	197.262	0.308705
$640$	289.312i	0.452050i
$641$	−1053.43	−1.64341	−0.821707	−	0.569910i	$-0.806978\pi$
$641$	−1053.43	−1.64341	−0.821707	+	0.569910i	$0.806978\pi$
$642$	254.898	0.397037
$643$	−840.964	−1.30788	−0.653938	−	0.756548i	$-0.726884\pi$
$643$	−840.964	−1.30788	−0.653938	+	0.756548i	$0.726884\pi$
$644$	26.6119i	0.0413228i
$645$	311.199i	0.482478i
$646$	− 425.075i	− 0.658011i
$647$	64.3219	0.0994157	0.0497078	−	0.998764i	$-0.484171\pi$
$647$	64.3219	0.0994157	0.0497078	+	0.998764i	$0.484171\pi$
$648$	515.738i	0.795892i
$649$	0	0
$650$	41.0739	0.0631906
$651$	38.1424i	0.0585904i
$652$	−316.580	−0.485552
$653$	−1069.20	−1.63737	−0.818684	−	0.574244i	$-0.805296\pi$
$653$	−1069.20	−1.63737	−0.818684	+	0.574244i	$0.805296\pi$
$654$	−420.498	−0.642964
$655$	− 287.325i	− 0.438664i
$656$	179.569i	0.273734i
$657$	− 698.656i	− 1.06340i
$658$	−9.57591	−0.0145531
$659$	283.355i	0.429978i	0.976617	+	0.214989i	$0.0689715\pi$
$659$	283.355i	0.429978i	−0.976617	+	0.214989i	$0.931028\pi$
$660$	0	0
$661$	−845.155	−1.27860	−0.639300	−	0.768957i	$-0.720776\pi$
$661$	−845.155	−1.27860	−0.639300	+	0.768957i	$0.720776\pi$
$662$	212.645i	0.321216i
$663$	916.393	1.38219
$664$	680.820	1.02533
$665$	17.9180	0.0269443
$666$	− 67.4911i	− 0.101338i
$667$	− 479.340i	− 0.718650i
$668$	157.682i	0.236052i
$669$	−1120.47	−1.67484
$670$	65.2769i	0.0974282i
$671$	0	0
$672$	32.1253	0.0478056
$673$	− 443.780i	− 0.659405i	−0.944085	−	0.329703i	$-0.893052\pi$
$673$	− 443.780i	− 0.659405i	0.944085	−	0.329703i	$-0.106948\pi$
$674$	284.803	0.422556
$675$	40.0000	0.0592593
$676$	142.910	0.211405
$677$	− 961.671i	− 1.42049i	−0.703955	−	0.710245i	$-0.748584\pi$
$677$	− 961.671i	− 1.42049i	0.703955	−	0.710245i	$-0.251416\pi$
$678$	− 376.707i	− 0.555615i
$679$	− 13.4090i	− 0.0197481i
$680$	−245.967	−0.361717
$681$	− 348.693i	− 0.512031i
$682$	0	0
$683$	−488.033	−0.714542	−0.357271	−	0.934001i	$-0.616293\pi$
$683$	−488.033	−0.714542	−0.357271	+	0.934001i	$0.616293\pi$
$684$	− 701.799i	− 1.02602i
$685$	138.482	0.202164
$686$	−19.7438	−0.0287811
$687$	−429.390	−0.625022
$688$	345.992i	0.502895i
$689$	470.080i	0.682265i
$690$	179.473i	0.260106i
$691$	−496.647	−0.718737	−0.359369	−	0.933196i	$-0.617008\pi$
$691$	−496.647	−0.718737	−0.359369	+	0.933196i	$0.617008\pi$
$692$	526.197i	0.760400i
$693$	0	0
$694$	−46.2167	−0.0665947
$695$	− 510.356i	− 0.734325i
$696$	−376.892	−0.541511
$697$	−365.886	−0.524944
$698$	−178.351	−0.255517
$699$	527.103i	0.754082i
$700$	− 4.81784i	− 0.00688263i
$701$	− 501.060i	− 0.714778i	−0.933956	−	0.357389i	$-0.883667\pi$
$701$	− 501.060i	− 0.714778i	0.933956	−	0.357389i	$-0.116333\pi$
$702$	65.7183	0.0936157
$703$	− 383.182i	− 0.545067i
$704$	0	0
$705$	424.794	0.602545
$706$	− 157.322i	− 0.222835i
$707$	10.6749	0.0150989
$708$	−1413.06	−1.99584
$709$	−2.08131	−0.00293555	−0.00146778	−	0.999999i	$-0.500467\pi$
$709$	−2.08131	−0.00293555	−0.00146778	+	0.999999i	$0.500467\pi$
$710$	45.7817i	0.0644813i
$711$	− 921.297i	− 1.29578i
$712$	− 482.890i	− 0.678216i
$713$	−948.974	−1.33096
$714$	16.3416i	0.0228873i
$715$	0	0
$716$	−591.976	−0.826783
$717$	− 368.150i	− 0.513459i
$718$	−496.180	−0.691059
$719$	702.875	0.977574	0.488787	−	0.872403i	$-0.337440\pi$
$719$	702.875	0.977574	0.488787	+	0.872403i	$0.337440\pi$
$720$	−155.652	−0.216184
$721$	− 35.0146i	− 0.0485640i
$722$	343.473i	0.475724i
$723$	106.056i	0.146689i
$724$	−576.318	−0.796019
$725$	86.7802i	0.119697i
$726$	0	0
$727$	1163.47	1.60037	0.800184	−	0.599754i	$-0.204735\pi$
$727$	1163.47	1.60037	0.800184	+	0.599754i	$0.204735\pi$
$728$	− 17.0344i	− 0.0233989i
$729$	−377.000	−0.517147
$730$	162.148	0.222120
$731$	−704.984	−0.964411
$732$	707.038i	0.965899i
$733$	1308.04i	1.78451i	0.451534	+	0.892254i	$0.350877\pi$
$733$	1308.04i	1.78451i	−0.451534	+	0.892254i	$0.649123\pi$
$734$	− 53.5403i	− 0.0729432i
$735$	437.580	0.595348
$736$	799.272i	1.08597i
$737$	0	0
$738$	91.8371	0.124441
$739$	− 1141.81i	− 1.54507i	−0.634972	−	0.772535i	$-0.718988\pi$
$739$	− 1141.81i	− 1.54507i	0.634972	−	0.772535i	$-0.281012\pi$
$740$	−103.031	−0.139232
$741$	−1305.91	−1.76236
$742$	−8.38270	−0.0112974
$743$	570.888i	0.768355i	0.923259	+	0.384178i	$0.125515\pi$
$743$	570.888i	0.768355i	−0.923259	+	0.384178i	$0.874485\pi$
$744$	746.152i	1.00289i
$745$	− 175.973i	− 0.236206i
$746$	42.4152	0.0568569
$747$	877.859i	1.17518i
$748$	0	0
$749$	−24.3406	−0.0324974
$750$	− 32.4920i	− 0.0433226i
$751$	−613.827	−0.817347	−0.408673	−	0.912681i	$-0.634008\pi$
$751$	−613.827	−0.817347	−0.408673	+	0.912681i	$0.634008\pi$
$752$	472.288	0.628042
$753$	540.138	0.717314
$754$	142.576i	0.189093i
$755$	158.960i	0.210544i
$756$	− 7.70855i	− 0.0101965i
$757$	−815.438	−1.07720	−0.538599	−	0.842562i	$-0.681046\pi$
$757$	−815.438	−1.07720	−0.538599	+	0.842562i	$0.681046\pi$
$758$	136.212i	0.179700i
$759$	0	0
$760$	350.517	0.461206
$761$	− 513.721i	− 0.675060i	−0.941315	−	0.337530i	$-0.890409\pi$
$761$	− 513.721i	− 0.675060i	0.941315	−	0.337530i	$-0.109591\pi$
$762$	−448.138	−0.588107
$763$	40.1540	0.0526265
$764$	38.8653	0.0508709
$765$	− 317.154i	− 0.414580i
$766$	4.44840i	0.00580731i
$767$	1150.37i	1.49983i
$768$	76.0000	0.0989583
$769$	− 501.416i	− 0.652036i	−0.945364	−	0.326018i	$-0.894293\pi$
$769$	− 501.416i	− 0.652036i	0.945364	−	0.326018i	$-0.105707\pi$
$770$	0	0
$771$	977.167	1.26740
$772$	− 436.171i	− 0.564989i
$773$	−449.458	−0.581446	−0.290723	−	0.956807i	$-0.593896\pi$
$773$	−449.458	−0.581446	−0.290723	+	0.956807i	$0.593896\pi$
$774$	176.950	0.228618
$775$	171.803	0.221682
$776$	− 262.311i	− 0.338029i
$777$	14.7310i	0.0189589i
$778$	164.275i	0.211150i
$779$	521.407	0.669329
$780$	351.137i	0.450176i
$781$	0	0
$782$	−406.575	−0.519917
$783$	138.848i	0.177329i
$784$	486.503	0.620540
$785$	480.179	0.611693
$786$	−373.430	−0.475102
$787$	− 575.548i	− 0.731319i	−0.930749	−	0.365660i	$-0.880843\pi$
$787$	− 575.548i	− 0.731319i	0.930749	−	0.365660i	$-0.119157\pi$
$788$	− 1255.24i	− 1.59294i
$789$	− 7.73217i	− 0.00979997i
$790$	213.820	0.270658
$791$	35.9723i	0.0454770i
$792$	0	0
$793$	575.601	0.725852
$794$	156.296i	0.196847i
$795$	371.862	0.467751
$796$	929.463	1.16767
$797$	24.9787	0.0313409	0.0156705	−	0.999877i	$-0.495012\pi$
$797$	24.9787	0.0313409	0.0156705	+	0.999877i	$0.495012\pi$
$798$	− 23.2876i	− 0.0291824i
$799$	962.322i	1.20441i
$800$	− 144.701i	− 0.180876i
$801$	622.645	0.777335
$802$	393.109i	0.490160i
$803$	0	0
$804$	−558.046	−0.694088
$805$	− 17.1381i	− 0.0212896i
$806$	282.265	0.350205
$807$	732.839	0.908103
$808$	208.827	0.258449
$809$	748.617i	0.925361i	0.886525	+	0.462680i	$0.153112\pi$
$809$	748.617i	0.925361i	−0.886525	+	0.462680i	$0.846888\pi$
$810$	− 154.337i	− 0.190539i
$811$	− 235.122i	− 0.289916i	−0.989438	−	0.144958i	$-0.953695\pi$
$811$	− 235.122i	− 0.289916i	0.989438	−	0.144958i	$-0.0463048\pi$
$812$	16.7237	0.0205957
$813$	− 2030.26i	− 2.49725i
$814$	0	0
$815$	203.878	0.250158
$816$	− 805.972i	− 0.987711i
$817$	1004.64	1.22967
$818$	266.448	0.325731
$819$	21.9644	0.0268185
$820$	− 140.198i	− 0.170973i
$821$	− 153.529i	− 0.187003i	−0.995619	−	0.0935014i	$-0.970194\pi$
$821$	− 153.529i	− 0.187003i	0.995619	−	0.0935014i	$-0.0298060\pi$
$822$	− 179.982i	− 0.218957i
$823$	1292.70	1.57071	0.785357	−	0.619044i	$-0.212480\pi$
$823$	1292.70	1.57071	0.785357	+	0.619044i	$0.212480\pi$
$824$	− 684.967i	− 0.831270i
$825$	0	0
$826$	−20.5140	−0.0248353
$827$	624.829i	0.755537i	0.925900	+	0.377769i	$0.123309\pi$
$827$	624.829i	0.755537i	−0.925900	+	0.377769i	$0.876691\pi$
$828$	−671.255	−0.810694
$829$	−1473.40	−1.77732	−0.888661	−	0.458565i	$-0.848364\pi$
$829$	−1473.40	−1.77732	−0.888661	+	0.458565i	$0.848364\pi$
$830$	−203.738	−0.245468
$831$	− 141.731i	− 0.170555i
$832$	212.009i	0.254818i
$833$	991.288i	1.19002i
$834$	−663.299	−0.795322
$835$	− 101.548i	− 0.121614i
$836$	0	0
$837$	274.885	0.328417
$838$	− 119.547i	− 0.142658i
$839$	−1339.44	−1.59647	−0.798236	−	0.602345i	$-0.794233\pi$
$839$	−1339.44	−1.59647	−0.798236	+	0.602345i	$0.794233\pi$
$840$	−13.4752	−0.0160420
$841$	539.768	0.641817
$842$	− 87.3707i	− 0.103766i
$843$	− 1367.18i	− 1.62180i
$844$	− 784.819i	− 0.929880i
$845$	−92.0344	−0.108916
$846$	− 241.542i	− 0.285511i
$847$	0	0
$848$	413.438	0.487544
$849$	1653.68i	1.94780i
$850$	73.6068	0.0865962
$851$	−366.505	−0.430676
$852$	−391.384	−0.459371
$853$	− 1163.63i	− 1.36417i	−0.731274	−	0.682084i	$-0.761074\pi$
$853$	− 1163.63i	− 1.36417i	0.731274	−	0.682084i	$-0.238926\pi$
$854$	10.2644i	0.0120192i
$855$	451.961i	0.528609i
$856$	−476.158	−0.556259
$857$	− 1069.27i	− 1.24769i	−0.781549	−	0.623844i	$-0.785570\pi$
$857$	− 1069.27i	− 1.24769i	0.781549	−	0.623844i	$-0.214430\pi$
$858$	0	0
$859$	998.288	1.16215	0.581076	−	0.813849i	$-0.302632\pi$
$859$	998.288	1.16215	0.581076	+	0.813849i	$0.302632\pi$
$860$	− 270.131i	− 0.314106i
$861$	−20.0449	−0.0232810
$862$	392.764	0.455643
$863$	703.517	0.815200	0.407600	−	0.913161i	$-0.366366\pi$
$863$	703.517	0.815200	0.407600	+	0.913161i	$0.366366\pi$
$864$	− 231.522i	− 0.267965i
$865$	− 338.873i	− 0.391760i
$866$	− 155.021i	− 0.179008i
$867$	486.229	0.560818
$868$	− 33.1089i	− 0.0381438i
$869$	0	0
$870$	112.786	0.129640
$871$	454.306i	0.521591i
$872$	785.505	0.900809
$873$	338.227	0.387430
$874$	579.391	0.662919
$875$	3.10271i	0.00354595i
$876$	1386.19i	1.58241i
$877$	337.498i	0.384833i	0.981313	+	0.192416i	$0.0616324\pi$
$877$	337.498i	0.384833i	−0.981313	+	0.192416i	$0.938368\pi$
$878$	21.6943	0.0247088
$879$	− 771.436i	− 0.877629i
$880$	0	0
$881$	−1011.82	−1.14849	−0.574246	−	0.818682i	$-0.694705\pi$
$881$	−1011.82	−1.14849	−0.574246	+	0.818682i	$0.694705\pi$
$882$	− 248.812i	− 0.282100i
$883$	322.085	0.364762	0.182381	−	0.983228i	$-0.441620\pi$
$883$	322.085	0.364762	0.182381	+	0.983228i	$0.441620\pi$
$884$	−795.460	−0.899842
$885$	910.014	1.02826
$886$	41.6036i	0.0469566i
$887$	− 744.410i	− 0.839245i	−0.907699	−	0.419622i	$-0.862163\pi$
$887$	− 744.410i	− 0.839245i	0.907699	−	0.419622i	$-0.137837\pi$
$888$	288.173i	0.324519i
$889$	42.7933	0.0481365
$890$	144.507i	0.162367i
$891$	0	0
$892$	972.603	1.09036
$893$	− 1371.36i	− 1.53568i
$894$	−228.709	−0.255827
$895$	381.235	0.425961
$896$	−35.9060	−0.0400737
$897$	1249.07i	1.39250i
$898$	− 432.073i	− 0.481150i
$899$	596.365i	0.663365i
$900$	121.525	0.135028
$901$	842.411i	0.934973i
$902$	0	0
$903$	−38.6223	−0.0427711
$904$	703.701i	0.778430i
$905$	371.151	0.410112
$906$	206.597	0.228033
$907$	−562.502	−0.620179	−0.310089	−	0.950707i	$-0.600359\pi$
$907$	−562.502	−0.620179	−0.310089	+	0.950707i	$0.600359\pi$
$908$	302.678i	0.333345i
$909$	269.264i	0.296220i
$910$	5.09761i	0.00560177i
$911$	−70.9404	−0.0778709	−0.0389355	−	0.999242i	$-0.512397\pi$
$911$	−70.9404	−0.0778709	−0.0389355	+	0.999242i	$0.512397\pi$
$912$	1148.55i	1.25938i
$913$	0	0
$914$	345.220	0.377702
$915$	− 455.335i	− 0.497634i
$916$	372.725	0.406905
$917$	35.6594	0.0388870
$918$	117.771	0.128291
$919$	− 67.7163i	− 0.0736848i	−0.999321	−	0.0368424i	$-0.988270\pi$
$919$	− 67.7163i	− 0.0736848i	0.999321	−	0.0368424i	$-0.0117300\pi$
$920$	− 335.261i	− 0.364415i
$921$	1340.46i	1.45544i
$922$	210.961	0.228808
$923$	318.626i	0.345207i
$924$	0	0
$925$	66.3525	0.0717325
$926$	− 62.5814i	− 0.0675825i
$927$	883.205	0.952757
$928$	502.288	0.541259
$929$	1248.95	1.34440	0.672201	−	0.740369i	$-0.265349\pi$
$929$	1248.95	1.34440	0.672201	+	0.740369i	$0.265349\pi$
$930$	− 223.289i	− 0.240096i
$931$	− 1412.64i	− 1.51733i
$932$	− 457.544i	− 0.490927i
$933$	−868.644	−0.931022
$934$	− 164.151i	− 0.175751i
$935$	0	0
$936$	429.674	0.459053
$937$	− 541.722i	− 0.578146i	−0.957307	−	0.289073i	$-0.906653\pi$
$937$	− 541.722i	− 0.578146i	0.957307	−	0.289073i	$-0.0933470\pi$
$938$	−8.10141	−0.00863689
$939$	−2378.54	−2.53306
$940$	−368.736	−0.392272
$941$	590.098i	0.627097i	0.949572	+	0.313548i	$0.101518\pi$
$941$	590.098i	0.627097i	−0.949572	+	0.313548i	$0.898482\pi$
$942$	− 624.079i	− 0.662504i
$943$	− 498.714i	− 0.528859i
$944$	1011.76	1.07178
$945$	4.96433i	0.00525326i
$946$	0	0
$947$	−527.364	−0.556878	−0.278439	−	0.960454i	$-0.589817\pi$
$947$	−527.364	−0.556878	−0.278439	+	0.960454i	$0.589817\pi$
$948$	1827.92i	1.92819i
$949$	1128.50	1.18914
$950$	−104.894	−0.110414
$951$	287.181	0.301978
$952$	− 30.5266i	− 0.0320658i
$953$	1766.63i	1.85375i	0.375367	+	0.926876i	$0.377517\pi$
$953$	1766.63i	1.85375i	−0.375367	+	0.926876i	$0.622483\pi$
$954$	− 211.444i	− 0.221640i
$955$	−25.0294	−0.0262088
$956$	319.567i	0.334275i
$957$	0	0
$958$	−61.1060	−0.0637849
$959$	17.1868i	0.0179216i
$960$	167.712	0.174700
$961$	219.656	0.228571
$962$	109.014	0.113321
$963$	− 613.964i	− 0.637554i
$964$	− 92.0603i	− 0.0954982i
$965$	280.896i	0.291084i
$966$	−22.2741	−0.0230580
$967$	1457.23i	1.50696i	0.657470	+	0.753481i	$0.271627\pi$
$967$	1457.23i	1.50696i	−0.657470	+	0.753481i	$0.728373\pi$
$968$	0	0
$969$	−2340.26	−2.41513
$970$	78.4975i	0.0809253i
$971$	187.861	0.193472	0.0967359	−	0.995310i	$-0.469160\pi$
$971$	187.861	0.193472	0.0967359	+	0.995310i	$0.469160\pi$
$972$	1069.42	1.10022
$973$	63.3394	0.0650970
$974$	− 480.762i	− 0.493595i
$975$	− 226.134i	− 0.231932i
$976$	− 506.243i	− 0.518692i
$977$	1259.39	1.28904	0.644518	−	0.764589i	$-0.277058\pi$
$977$	1259.39	1.28904	0.644518	+	0.764589i	$0.277058\pi$
$978$	− 264.977i	− 0.270937i
$979$	0	0
$980$	−379.835	−0.387586
$981$	1012.84i	1.03246i
$982$	−541.469	−0.551394
$983$	−1041.78	−1.05980	−0.529899	−	0.848061i	$-0.677770\pi$
$983$	−1041.78	−1.05980	−0.529899	+	0.848061i	$0.677770\pi$
$984$	−392.125	−0.398501
$985$	808.377i	0.820687i
$986$	255.505i	0.259132i
$987$	52.7205i	0.0534149i
$988$	1133.57	1.14734
$989$	− 960.916i	− 0.971604i
$990$	0	0
$991$	−664.312	−0.670345	−0.335173	−	0.942157i	$-0.608795\pi$
$991$	−664.312	−0.670345	−0.335173	+	0.942157i	$0.608795\pi$
$992$	− 994.406i	− 1.00243i
$993$	1170.72	1.17898
$994$	−5.68189	−0.00571619
$995$	−598.577	−0.601585
$996$	− 1741.74i	− 1.74874i
$997$	− 197.396i	− 0.197990i	−0.995088	−	0.0989949i	$-0.968437\pi$
$997$	− 197.396i	− 0.197990i	0.995088	−	0.0989949i	$-0.0315627\pi$
$998$	− 201.997i	− 0.202402i
$999$	106.164	0.106270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.3.c.a.241.2		4
11.3	even	5		55.3.i.a.46.1	yes	4
11.7	odd	10		55.3.i.a.6.1	✓	4
11.10	odd	2	inner	605.3.c.a.241.3		4
55.3	odd	20		275.3.q.c.24.1		8
55.7	even	20		275.3.q.c.149.1		8
55.14	even	10		275.3.x.d.101.1		4
55.18	even	20		275.3.q.c.149.2		8
55.29	odd	10		275.3.x.d.226.1		4
55.47	odd	20		275.3.q.c.24.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.a.6.1	✓	4	11.7	odd	10
55.3.i.a.46.1	yes	4	11.3	even	5
275.3.q.c.24.1		8	55.3	odd	20
275.3.q.c.24.2		8	55.47	odd	20
275.3.q.c.149.1		8	55.7	even	20
275.3.q.c.149.2		8	55.18	even	20
275.3.x.d.101.1		4	55.14	even	10
275.3.x.d.226.1		4	55.29	odd	10
605.3.c.a.241.2		4	1.1	even	1	trivial
605.3.c.a.241.3		4	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	605.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.726543i q^{2} -4.00000 q^{3} +3.47214 q^{4} -2.23607 q^{5} +2.90617i q^{6} -0.277515i q^{7} -5.42882i q^{8} +7.00000 q^{9} +1.62460i q^{10} -13.8885 q^{12} +11.3067i q^{13} -0.201626 q^{14} +8.94427 q^{15} +9.94427 q^{16} +20.2622i q^{17} -5.08580i q^{18} -28.8747i q^{19} -7.76393 q^{20} +1.11006i q^{21} -27.6180 q^{23} +21.7153i q^{24} +5.00000 q^{25} +8.21478 q^{26} +8.00000 q^{27} -0.963568i q^{28} +17.3560i q^{29} -6.49839i q^{30} +34.3607 q^{31} -28.9402i q^{32} +14.7214 q^{34} +0.620541i q^{35} +24.3050 q^{36} +13.2705 q^{37} -20.9787 q^{38} -45.2267i q^{39} +12.1392i q^{40} +18.0576i q^{41} +0.806504 q^{42} +34.7931i q^{43} -15.6525 q^{45} +20.0657i q^{46} +47.4934 q^{47} -39.7771 q^{48} +48.9230 q^{49} -3.63271i q^{50} -81.0489i q^{51} +39.2583i q^{52} +41.5755 q^{53} -5.81234i q^{54} -1.50658 q^{56} +115.499i q^{57} +12.6099 q^{58} +101.743 q^{59} +31.0557 q^{60} -50.9080i q^{61} -24.9645i q^{62} -1.94260i q^{63} +18.7508 q^{64} -25.2825i q^{65} +40.1803 q^{67} +70.3532i q^{68} +110.472 q^{69} +0.450850 q^{70} +28.1803 q^{71} -38.0018i q^{72} -99.8079i q^{73} -9.64159i q^{74} -20.0000 q^{75} -100.257i q^{76} -32.8591 q^{78} -131.614i q^{79} -22.2361 q^{80} -95.0000 q^{81} +13.1196 q^{82} +125.408i q^{83} +3.85427i q^{84} -45.3077i q^{85} +25.2786 q^{86} -69.4242i q^{87} +88.9493 q^{89} +11.3722i q^{90} +3.13777 q^{91} -95.8936 q^{92} -137.443 q^{93} -34.5060i q^{94} +64.5658i q^{95} +115.761i q^{96} +48.3181 q^{97} -35.5446i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{3} - 4 q^{4} + 28 q^{9} + 16 q^{12} - 50 q^{14} + 4 q^{16} - 40 q^{20} - 106 q^{23} + 20 q^{25} - 70 q^{26} + 32 q^{27} + 48 q^{31} - 120 q^{34} - 28 q^{36} - 14 q^{37} + 10 q^{38} + 200 q^{42}+ \cdots - 84 q^{97}+O(q^{100}) \) 4 * q - 16 * q^3 - 4 * q^4 + 28 * q^9 + 16 * q^12 - 50 * q^14 + 4 * q^16 - 40 * q^20 - 106 * q^23 + 20 * q^25 - 70 * q^26 + 32 * q^27 + 48 * q^31 - 120 * q^34 - 28 * q^36 - 14 * q^37 + 10 * q^38 + 200 * q^42 + 266 * q^47 - 16 * q^48 + 66 * q^49 - 26 * q^53 + 70 * q^56 - 200 * q^58 + 322 * q^59 + 160 * q^60 + 236 * q^64 + 116 * q^67 + 424 * q^69 - 110 * q^70 + 68 * q^71 - 80 * q^75 + 280 * q^78 - 80 * q^80 - 380 * q^81 + 370 * q^82 + 280 * q^86 - 78 * q^89 - 220 * q^91 + 86 * q^92 - 192 * q^93 - 84 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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