LMFDB - Embedded newform 7581.2.a.w.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7581,2,Mod(1,7581)] 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("7581.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7581, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7581 = 3 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7581.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5,-3,5,7,4,-3,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$60.5345897723$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.368464.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 6x^{3} + 6x^{2} + 6x - 4 $ x^5 - 2x^4 - 6x^3 + 6x^2 + 6x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 399)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.552543$ of defining polynomial
Character	$\chi$	$=$	7581.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.447457 q^{2} +1.00000 q^{3} -1.79978 q^{4} +3.78739 q^{5} -0.447457 q^{6} +1.00000 q^{7} +1.70024 q^{8} +1.00000 q^{9} -1.69470 q^{10} -3.77387 q^{11} -1.79978 q^{12} -4.83000 q^{13} -0.447457 q^{14} +3.78739 q^{15} +2.83878 q^{16} +5.09156 q^{17} -0.447457 q^{18} -6.81648 q^{20} +1.00000 q^{21} +1.68865 q^{22} +8.49448 q^{23} +1.70024 q^{24} +9.34434 q^{25} +2.16122 q^{26} +1.00000 q^{27} -1.79978 q^{28} +8.28187 q^{29} -1.69470 q^{30} +1.23044 q^{31} -4.67071 q^{32} -3.77387 q^{33} -2.27826 q^{34} +3.78739 q^{35} -1.79978 q^{36} -0.695831 q^{37} -4.83000 q^{39} +6.43948 q^{40} -7.98404 q^{41} -0.447457 q^{42} -3.25522 q^{43} +6.79214 q^{44} +3.78739 q^{45} -3.80092 q^{46} +1.98648 q^{47} +2.83878 q^{48} +1.00000 q^{49} -4.18120 q^{50} +5.09156 q^{51} +8.69296 q^{52} -3.40292 q^{53} -0.447457 q^{54} -14.2931 q^{55} +1.70024 q^{56} -3.70578 q^{58} +12.2683 q^{59} -6.81648 q^{60} -14.4537 q^{61} -0.550570 q^{62} +1.00000 q^{63} -3.58761 q^{64} -18.2931 q^{65} +1.68865 q^{66} +10.0852 q^{67} -9.16370 q^{68} +8.49448 q^{69} -1.69470 q^{70} -2.50800 q^{71} +1.70024 q^{72} -15.1473 q^{73} +0.311355 q^{74} +9.34434 q^{75} -3.77387 q^{77} +2.16122 q^{78} +0.906002 q^{79} +10.7516 q^{80} +1.00000 q^{81} +3.57252 q^{82} +4.01125 q^{83} -1.79978 q^{84} +19.2837 q^{85} +1.45657 q^{86} +8.28187 q^{87} -6.41648 q^{88} +12.9730 q^{89} -1.69470 q^{90} -4.83000 q^{91} -15.2882 q^{92} +1.23044 q^{93} -0.888863 q^{94} -4.67071 q^{96} +15.6600 q^{97} -0.447457 q^{98} -3.77387 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{2} + 5 q^{3} + 7 q^{4} + 4 q^{5} - 3 q^{6} + 5 q^{7} - 9 q^{8} + 5 q^{9} + 6 q^{10} + 8 q^{11} + 7 q^{12} + 6 q^{13} - 3 q^{14} + 4 q^{15} + 19 q^{16} + 12 q^{17} - 3 q^{18} + 8 q^{20} + 5 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) $ 5 * q - 3 * q^2 + 5 * q^3 + 7 * q^4 + 4 * q^5 - 3 * q^6 + 5 * q^7 - 9 * q^8 + 5 * q^9 + 6 * q^10 + 8 * q^11 + 7 * q^12 + 6 * q^13 - 3 * q^14 + 4 * q^15 + 19 * q^16 + 12 * q^17 - 3 * q^18 + 8 * q^20 + 5 * q^21 + 12 * q^22 + 12 * q^23 - 9 * q^24 + 15 * q^25 + 6 * q^26 + 5 * q^27 + 7 * q^28 - 4 * q^29 + 6 * q^30 + 8 * q^31 - 31 * q^32 + 8 * q^33 - 2 * q^34 + 4 * q^35 + 7 * q^36 - 2 * q^37 + 6 * q^39 + 18 * q^40 - 10 * q^41 - 3 * q^42 - 16 * q^43 - 4 * q^44 + 4 * q^45 - 16 * q^46 - 2 * q^47 + 19 * q^48 + 5 * q^49 + 39 * q^50 + 12 * q^51 + 22 * q^52 - 3 * q^54 - 12 * q^55 - 9 * q^56 + 2 * q^58 + 4 * q^59 + 8 * q^60 - 14 * q^61 - 36 * q^62 + 5 * q^63 + 11 * q^64 - 32 * q^65 + 12 * q^66 + 20 * q^67 + 8 * q^68 + 12 * q^69 + 6 * q^70 + 6 * q^71 - 9 * q^72 + 10 * q^73 - 2 * q^74 + 15 * q^75 + 8 * q^77 + 6 * q^78 - 20 * q^80 + 5 * q^81 - 38 * q^82 + 6 * q^83 + 7 * q^84 + 8 * q^85 + 36 * q^86 - 4 * q^87 + 40 * q^88 - 26 * q^89 + 6 * q^90 + 6 * q^91 - 48 * q^92 + 8 * q^93 - 24 * q^94 - 31 * q^96 + 18 * q^97 - 3 * q^98 + 8 * 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 $

$2$	−0.447457	−0.316400	−0.158200	−	0.987407i	$-0.550569\pi$
$2$	−0.447457	−0.316400	−0.158200	+	0.987407i	$0.550569\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.79978	−0.899891
$5$	3.78739	1.69377	0.846887	−	0.531773i	$-0.178474\pi$
$5$	3.78739	1.69377	0.846887	+	0.531773i	$0.178474\pi$
$6$	−0.447457	−0.182674
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.70024	0.601126
$9$	1.00000	0.333333
$10$	−1.69470	−0.535910
$11$	−3.77387	−1.13786	−0.568932	−	0.822384i	$-0.692643\pi$
$11$	−3.77387	−1.13786	−0.568932	+	0.822384i	$0.692643\pi$
$12$	−1.79978	−0.519552
$13$	−4.83000	−1.33960	−0.669801	−	0.742541i	$-0.733621\pi$
$13$	−4.83000	−1.33960	−0.669801	+	0.742541i	$0.733621\pi$
$14$	−0.447457	−0.119588
$15$	3.78739	0.977901
$16$	2.83878	0.709695
$17$	5.09156	1.23489	0.617443	−	0.786616i	$-0.288169\pi$
$17$	5.09156	1.23489	0.617443	+	0.786616i	$0.288169\pi$
$18$	−0.447457	−0.105467
$19$	0	0
$19$	0	0
$20$	−6.81648	−1.52421
$21$	1.00000	0.218218
$22$	1.68865	0.360020
$23$	8.49448	1.77122	0.885611	−	0.464429i	$-0.153740\pi$
$23$	8.49448	1.77122	0.885611	+	0.464429i	$0.153740\pi$
$24$	1.70024	0.347060
$25$	9.34434	1.86887
$26$	2.16122	0.423850
$27$	1.00000	0.192450
$28$	−1.79978	−0.340127
$29$	8.28187	1.53790	0.768952	−	0.639306i	$-0.220778\pi$
$29$	8.28187	1.53790	0.768952	+	0.639306i	$0.220778\pi$
$30$	−1.69470	−0.309408
$31$	1.23044	0.220994	0.110497	−	0.993876i	$-0.464756\pi$
$31$	1.23044	0.220994	0.110497	+	0.993876i	$0.464756\pi$
$32$	−4.67071	−0.825673
$33$	−3.77387	−0.656946
$34$	−2.27826	−0.390718
$35$	3.78739	0.640186
$36$	−1.79978	−0.299964
$37$	−0.695831	−0.114394	−0.0571969	−	0.998363i	$-0.518216\pi$
$37$	−0.695831	−0.114394	−0.0571969	+	0.998363i	$0.518216\pi$
$38$	0	0
$39$	−4.83000	−0.773420
$40$	6.43948	1.01817
$41$	−7.98404	−1.24690	−0.623449	−	0.781864i	$-0.714269\pi$
$41$	−7.98404	−1.24690	−0.623449	+	0.781864i	$0.714269\pi$
$42$	−0.447457	−0.0690442
$43$	−3.25522	−0.496416	−0.248208	−	0.968707i	$-0.579842\pi$
$43$	−3.25522	−0.496416	−0.248208	+	0.968707i	$0.579842\pi$
$44$	6.79214	1.02395
$45$	3.78739	0.564591
$46$	−3.80092	−0.560415
$47$	1.98648	0.289757	0.144879	−	0.989449i	$-0.453721\pi$
$47$	1.98648	0.289757	0.144879	+	0.989449i	$0.453721\pi$
$48$	2.83878	0.409742
$49$	1.00000	0.142857
$50$	−4.18120	−0.591310
$51$	5.09156	0.712961
$52$	8.69296	1.20550
$53$	−3.40292	−0.467427	−0.233713	−	0.972306i	$-0.575088\pi$
$53$	−3.40292	−0.467427	−0.233713	+	0.972306i	$0.575088\pi$
$54$	−0.447457	−0.0608912
$55$	−14.2931	−1.92728
$56$	1.70024	0.227204
$57$	0	0
$58$	−3.70578	−0.486593
$59$	12.2683	1.59720	0.798601	−	0.601860i	$-0.205574\pi$
$59$	12.2683	1.59720	0.798601	+	0.601860i	$0.205574\pi$
$60$	−6.81648	−0.880004
$61$	−14.4537	−1.85061	−0.925306	−	0.379222i	$-0.876192\pi$
$61$	−14.4537	−1.85061	−0.925306	+	0.379222i	$0.876192\pi$
$62$	−0.550570	−0.0699224
$63$	1.00000	0.125988
$64$	−3.58761	−0.448452
$65$	−18.2931	−2.26898
$66$	1.68865	0.207858
$67$	10.0852	1.23211	0.616053	−	0.787705i	$-0.288731\pi$
$67$	10.0852	1.23211	0.616053	+	0.787705i	$0.288731\pi$
$68$	−9.16370	−1.11126
$69$	8.49448	1.02262
$70$	−1.69470	−0.202555
$71$	−2.50800	−0.297645	−0.148823	−	0.988864i	$-0.547548\pi$
$71$	−2.50800	−0.297645	−0.148823	+	0.988864i	$0.547548\pi$
$72$	1.70024	0.200375
$73$	−15.1473	−1.77286	−0.886429	−	0.462865i	$-0.846822\pi$
$73$	−15.1473	−1.77286	−0.886429	+	0.462865i	$0.846822\pi$
$74$	0.311355	0.0361942
$75$	9.34434	1.07899
$76$	0	0
$77$	−3.77387	−0.430072
$78$	2.16122	0.244710
$79$	0.906002	0.101933	0.0509666	−	0.998700i	$-0.483770\pi$
$79$	0.906002	0.101933	0.0509666	+	0.998700i	$0.483770\pi$
$80$	10.7516	1.20206
$81$	1.00000	0.111111
$82$	3.57252	0.394519
$83$	4.01125	0.440292	0.220146	−	0.975467i	$-0.429347\pi$
$83$	4.01125	0.440292	0.220146	+	0.975467i	$0.429347\pi$
$84$	−1.79978	−0.196372
$85$	19.2837	2.09162
$86$	1.45657	0.157066
$87$	8.28187	0.887910
$88$	−6.41648	−0.684000
$89$	12.9730	1.37513	0.687567	−	0.726120i	$-0.258679\pi$
$89$	12.9730	1.37513	0.687567	+	0.726120i	$0.258679\pi$
$90$	−1.69470	−0.178637
$91$	−4.83000	−0.506322
$92$	−15.2882	−1.59391
$93$	1.23044	0.127591
$94$	−0.888863	−0.0916793
$95$	0	0
$96$	−4.67071	−0.476703
$97$	15.6600	1.59003	0.795017	−	0.606588i	$-0.207462\pi$
$97$	15.6600	1.59003	0.795017	+	0.606588i	$0.207462\pi$
$98$	−0.447457	−0.0452000
$99$	−3.77387	−0.379288
$100$	−16.8178	−1.68178
$101$	18.4562	1.83646	0.918229	−	0.396050i	$-0.129619\pi$
$101$	18.4562	1.83646	0.918229	+	0.396050i	$0.129619\pi$
$102$	−2.27826	−0.225581
$103$	−7.54774	−0.743701	−0.371850	−	0.928293i	$-0.621277\pi$
$103$	−7.54774	−0.743701	−0.371850	+	0.928293i	$0.621277\pi$
$104$	−8.21217	−0.805269
$105$	3.78739	0.369612
$106$	1.52266	0.147894
$107$	−1.72695	−0.166950	−0.0834751	−	0.996510i	$-0.526602\pi$
$107$	−1.72695	−0.166950	−0.0834751	+	0.996510i	$0.526602\pi$
$108$	−1.79978	−0.173184
$109$	−6.39329	−0.612367	−0.306183	−	0.951973i	$-0.599052\pi$
$109$	−6.39329	−0.612367	−0.306183	+	0.951973i	$0.599052\pi$
$110$	6.39556	0.609793
$111$	−0.695831	−0.0660453
$112$	2.83878	0.268239
$113$	4.28187	0.402805	0.201402	−	0.979509i	$-0.435450\pi$
$113$	4.28187	0.402805	0.201402	+	0.979509i	$0.435450\pi$
$114$	0	0
$115$	32.1719	3.00005
$116$	−14.9056	−1.38395
$117$	−4.83000	−0.446534
$118$	−5.48956	−0.505355
$119$	5.09156	0.466743
$120$	6.43948	0.587841
$121$	3.24209	0.294735
$122$	6.46743	0.585534
$123$	−7.98404	−0.719897
$124$	−2.21453	−0.198870
$125$	16.4537	1.47167
$126$	−0.447457	−0.0398627
$127$	−15.8431	−1.40585	−0.702925	−	0.711264i	$-0.748123\pi$
$127$	−15.8431	−1.40585	−0.702925	+	0.711264i	$0.748123\pi$
$128$	10.9467	0.967563
$129$	−3.25522	−0.286606
$130$	8.18539	0.717906
$131$	10.7675	0.940764	0.470382	−	0.882463i	$-0.344116\pi$
$131$	10.7675	0.940764	0.470382	+	0.882463i	$0.344116\pi$
$132$	6.79214	0.591180
$133$	0	0
$134$	−4.51271	−0.389839
$135$	3.78739	0.325967
$136$	8.65688	0.742321
$137$	−2.42034	−0.206784	−0.103392	−	0.994641i	$-0.532970\pi$
$137$	−2.42034	−0.206784	−0.103392	+	0.994641i	$0.532970\pi$
$138$	−3.80092	−0.323555
$139$	−1.94817	−0.165242	−0.0826210	−	0.996581i	$-0.526329\pi$
$139$	−1.94817	−0.165242	−0.0826210	+	0.996581i	$0.526329\pi$
$140$	−6.81648	−0.576098
$141$	1.98648	0.167292
$142$	1.12222	0.0941749
$143$	18.2278	1.52429
$144$	2.83878	0.236565
$145$	31.3667	2.60486
$146$	6.77777	0.560932
$147$	1.00000	0.0824786
$148$	1.25234	0.102942
$149$	1.30644	0.107028	0.0535138	−	0.998567i	$-0.482958\pi$
$149$	1.30644	0.107028	0.0535138	+	0.998567i	$0.482958\pi$
$150$	−4.18120	−0.341393
$151$	−4.48079	−0.364641	−0.182321	−	0.983239i	$-0.558361\pi$
$151$	−4.48079	−0.364641	−0.182321	+	0.983239i	$0.558361\pi$
$152$	0	0
$153$	5.09156	0.411628
$154$	1.68865	0.136075
$155$	4.66016	0.374313
$156$	8.69296	0.695993
$157$	11.5725	0.923587	0.461794	−	0.886987i	$-0.347206\pi$
$157$	11.5725	0.923587	0.461794	+	0.886987i	$0.347206\pi$
$158$	−0.405397	−0.0322517
$159$	−3.40292	−0.269869
$160$	−17.6898	−1.39850
$161$	8.49448	0.669459
$162$	−0.447457	−0.0351556
$163$	−11.1254	−0.871409	−0.435704	−	0.900090i	$-0.643501\pi$
$163$	−11.1254	−0.871409	−0.435704	+	0.900090i	$0.643501\pi$
$164$	14.3695	1.12207
$165$	−14.2931	−1.11272
$166$	−1.79487	−0.139309
$167$	−2.08522	−0.161359	−0.0806797	−	0.996740i	$-0.525709\pi$
$167$	−2.08522	−0.161359	−0.0806797	+	0.996740i	$0.525709\pi$
$168$	1.70024	0.131176
$169$	10.3289	0.794534
$170$	−8.62865	−0.661787
$171$	0	0
$172$	5.85868	0.446721
$173$	7.26343	0.552228	0.276114	−	0.961125i	$-0.410953\pi$
$173$	7.26343	0.552228	0.276114	+	0.961125i	$0.410953\pi$
$174$	−3.70578	−0.280935
$175$	9.34434	0.706366
$176$	−10.7132	−0.807536
$177$	12.2683	0.922145
$178$	−5.80486	−0.435093
$179$	9.84784	0.736062	0.368031	−	0.929814i	$-0.380032\pi$
$179$	9.84784	0.736062	0.368031	+	0.929814i	$0.380032\pi$
$180$	−6.81648	−0.508071
$181$	5.60183	0.416381	0.208190	−	0.978088i	$-0.433243\pi$
$181$	5.60183	0.416381	0.208190	+	0.978088i	$0.433243\pi$
$182$	2.16122	0.160200
$183$	−14.4537	−1.06845
$184$	14.4427	1.06473
$185$	−2.63539	−0.193757
$186$	−0.550570	−0.0403697
$187$	−19.2149	−1.40513
$188$	−3.57522	−0.260750
$189$	1.00000	0.0727393
$190$	0	0
$191$	8.74519	0.632780	0.316390	−	0.948629i	$-0.397529\pi$
$191$	8.74519	0.632780	0.316390	+	0.948629i	$0.397529\pi$
$192$	−3.58761	−0.258914
$193$	26.7221	1.92350	0.961749	−	0.273932i	$-0.0883244\pi$
$193$	26.7221	1.92350	0.961749	+	0.273932i	$0.0883244\pi$
$194$	−7.00719	−0.503087
$195$	−18.2931	−1.31000
$196$	−1.79978	−0.128556
$197$	15.3597	1.09434	0.547168	−	0.837023i	$-0.315706\pi$
$197$	15.3597	1.09434	0.547168	+	0.837023i	$0.315706\pi$
$198$	1.68865	0.120007
$199$	−3.97295	−0.281635	−0.140818	−	0.990036i	$-0.544973\pi$
$199$	−3.97295	−0.281635	−0.140818	+	0.990036i	$0.544973\pi$
$200$	15.8876	1.12343
$201$	10.0852	0.711357
$202$	−8.25835	−0.581056
$203$	8.28187	0.581273
$204$	−9.16370	−0.641587
$205$	−30.2387	−2.11196
$206$	3.37729	0.235307
$207$	8.49448	0.590407
$208$	−13.7113	−0.950709
$209$	0	0
$210$	−1.69470	−0.116945
$211$	9.48956	0.653288	0.326644	−	0.945147i	$-0.394082\pi$
$211$	9.48956	0.653288	0.326644	+	0.945147i	$0.394082\pi$
$212$	6.12451	0.420633
$213$	−2.50800	−0.171845
$214$	0.772735	0.0528231
$215$	−12.3288	−0.840817
$216$	1.70024	0.115687
$217$	1.23044	0.0835278
$218$	2.86073	0.193753
$219$	−15.1473	−1.02356
$220$	25.7245	1.73435
$221$	−24.5923	−1.65426
$222$	0.311355	0.0208968
$223$	−7.61106	−0.509674	−0.254837	−	0.966984i	$-0.582022\pi$
$223$	−7.61106	−0.509674	−0.254837	+	0.966984i	$0.582022\pi$
$224$	−4.67071	−0.312075
$225$	9.34434	0.622956
$226$	−1.91595	−0.127447
$227$	5.36461	0.356062	0.178031	−	0.984025i	$-0.443027\pi$
$227$	5.36461	0.356062	0.178031	+	0.984025i	$0.443027\pi$
$228$	0	0
$229$	−11.1139	−0.734427	−0.367214	−	0.930137i	$-0.619688\pi$
$229$	−11.1139	−0.734427	−0.367214	+	0.930137i	$0.619688\pi$
$230$	−14.3956	−0.949215
$231$	−3.77387	−0.248302
$232$	14.0812	0.924474
$233$	10.9664	0.718436	0.359218	−	0.933254i	$-0.383043\pi$
$233$	10.9664	0.718436	0.359218	+	0.933254i	$0.383043\pi$
$234$	2.16122	0.141283
$235$	7.52357	0.490783
$236$	−22.0804	−1.43731
$237$	0.906002	0.0588511
$238$	−2.27826	−0.147677
$239$	−0.101184	−0.00654503	−0.00327252	−	0.999995i	$-0.501042\pi$
$239$	−0.101184	−0.00654503	−0.00327252	+	0.999995i	$0.501042\pi$
$240$	10.7516	0.694011
$241$	−3.78983	−0.244124	−0.122062	−	0.992522i	$-0.538951\pi$
$241$	−3.78983	−0.244124	−0.122062	+	0.992522i	$0.538951\pi$
$242$	−1.45070	−0.0932543
$243$	1.00000	0.0641500
$244$	26.0136	1.66535
$245$	3.78739	0.241968
$246$	3.57252	0.227775
$247$	0	0
$248$	2.09205	0.132845
$249$	4.01125	0.254203
$250$	−7.36235	−0.465636
$251$	7.42769	0.468832	0.234416	−	0.972136i	$-0.424682\pi$
$251$	7.42769	0.468832	0.234416	+	0.972136i	$0.424682\pi$
$252$	−1.79978	−0.113376
$253$	−32.0571	−2.01541
$254$	7.08913	0.444811
$255$	19.2837	1.20759
$256$	2.27703	0.142315
$257$	−7.13848	−0.445286	−0.222643	−	0.974900i	$-0.571468\pi$
$257$	−7.13848	−0.445286	−0.222643	+	0.974900i	$0.571468\pi$
$258$	1.45657	0.0906822
$259$	−0.695831	−0.0432368
$260$	32.9236	2.04184
$261$	8.28187	0.512635
$262$	−4.81801	−0.297658
$263$	5.55883	0.342772	0.171386	−	0.985204i	$-0.445175\pi$
$263$	5.55883	0.342772	0.171386	+	0.985204i	$0.445175\pi$
$264$	−6.41648	−0.394907
$265$	−12.8882	−0.791715
$266$	0	0
$267$	12.9730	0.793935
$268$	−18.1512	−1.10876
$269$	16.2299	0.989553	0.494777	−	0.869020i	$-0.335250\pi$
$269$	16.2299	0.989553	0.494777	+	0.869020i	$0.335250\pi$
$270$	−1.69470	−0.103136
$271$	−24.3735	−1.48058	−0.740292	−	0.672286i	$-0.765313\pi$
$271$	−24.3735	−1.48058	−0.740292	+	0.672286i	$0.765313\pi$
$272$	14.4538	0.876392
$273$	−4.83000	−0.292325
$274$	1.08300	0.0654264
$275$	−35.2643	−2.12652
$276$	−15.2882	−0.920242
$277$	−6.80523	−0.408886	−0.204443	−	0.978878i	$-0.565538\pi$
$277$	−6.80523	−0.408886	−0.204443	+	0.978878i	$0.565538\pi$
$278$	0.871725	0.0522826
$279$	1.23044	0.0736646
$280$	6.43948	0.384832
$281$	10.5525	0.629509	0.314754	−	0.949173i	$-0.398078\pi$
$281$	10.5525	0.629509	0.314754	+	0.949173i	$0.398078\pi$
$282$	−0.888863	−0.0529310
$283$	−17.4625	−1.03804	−0.519019	−	0.854762i	$-0.673703\pi$
$283$	−17.4625	−1.03804	−0.519019	+	0.854762i	$0.673703\pi$
$284$	4.51386	0.267848
$285$	0	0
$286$	−8.15617	−0.482284
$287$	−7.98404	−0.471283
$288$	−4.67071	−0.275224
$289$	8.92400	0.524941
$290$	−14.0353	−0.824179
$291$	15.6600	0.918006
$292$	27.2618	1.59538
$293$	−2.09631	−0.122468	−0.0612339	−	0.998123i	$-0.519504\pi$
$293$	−2.09631	−0.122468	−0.0612339	+	0.998123i	$0.519504\pi$
$294$	−0.447457	−0.0260962
$295$	46.4651	2.70530
$296$	−1.18308	−0.0687651
$297$	−3.77387	−0.218982
$298$	−0.584575	−0.0338635
$299$	−41.0284	−2.37273
$300$	−16.8178	−0.970975
$301$	−3.25522	−0.187628
$302$	2.00496	0.115373
$303$	18.4562	1.06028
$304$	0	0
$305$	−54.7420	−3.13452
$306$	−2.27826	−0.130239
$307$	26.3173	1.50201	0.751004	−	0.660298i	$-0.229570\pi$
$307$	26.3173	1.50201	0.751004	+	0.660298i	$0.229570\pi$
$308$	6.79214	0.387018
$309$	−7.54774	−0.429376
$310$	−2.08522	−0.118433
$311$	16.9236	0.959650	0.479825	−	0.877364i	$-0.340700\pi$
$311$	16.9236	0.959650	0.479825	+	0.877364i	$0.340700\pi$
$312$	−8.21217	−0.464922
$313$	17.0137	0.961673	0.480837	−	0.876810i	$-0.340333\pi$
$313$	17.0137	0.961673	0.480837	+	0.876810i	$0.340333\pi$
$314$	−5.17821	−0.292223
$315$	3.78739	0.213395
$316$	−1.63061	−0.0917287
$317$	0.734133	0.0412330	0.0206165	−	0.999787i	$-0.493437\pi$
$317$	0.734133	0.0412330	0.0206165	+	0.999787i	$0.493437\pi$
$318$	1.52266	0.0853865
$319$	−31.2547	−1.74993
$320$	−13.5877	−0.759576
$321$	−1.72695	−0.0963888
$322$	−3.80092	−0.211817
$323$	0	0
$324$	−1.79978	−0.0999879
$325$	−45.1332	−2.50354
$326$	4.97814	0.275714
$327$	−6.39329	−0.353550
$328$	−13.5748	−0.749542
$329$	1.98648	0.109518
$330$	6.39556	0.352064
$331$	−13.7700	−0.756868	−0.378434	−	0.925628i	$-0.623537\pi$
$331$	−13.7700	−0.756868	−0.378434	+	0.925628i	$0.623537\pi$
$332$	−7.21938	−0.396215
$333$	−0.695831	−0.0381313
$334$	0.933049	0.0510542
$335$	38.1967	2.08691
$336$	2.83878	0.154868
$337$	−24.3217	−1.32488	−0.662442	−	0.749113i	$-0.730480\pi$
$337$	−24.3217	−1.32488	−0.662442	+	0.749113i	$0.730480\pi$
$338$	−4.62176	−0.251391
$339$	4.28187	0.232559
$340$	−34.7065	−1.88223
$341$	−4.64352	−0.251461
$342$	0	0
$343$	1.00000	0.0539949
$344$	−5.53465	−0.298409
$345$	32.1719	1.73208
$346$	−3.25008	−0.174725
$347$	3.89882	0.209299	0.104650	−	0.994509i	$-0.466628\pi$
$347$	3.89882	0.209299	0.104650	+	0.994509i	$0.466628\pi$
$348$	−14.9056	−0.799022
$349$	−14.6887	−0.786268	−0.393134	−	0.919481i	$-0.628609\pi$
$349$	−14.6887	−0.786268	−0.393134	+	0.919481i	$0.628609\pi$
$350$	−4.18120	−0.223494
$351$	−4.83000	−0.257807
$352$	17.6267	0.939504
$353$	−21.5453	−1.14674	−0.573370	−	0.819296i	$-0.694364\pi$
$353$	−21.5453	−1.14674	−0.573370	+	0.819296i	$0.694364\pi$
$354$	−5.48956	−0.291767
$355$	−9.49879	−0.504143
$356$	−23.3486	−1.23747
$357$	5.09156	0.269474
$358$	−4.40649	−0.232890
$359$	3.82343	0.201793	0.100896	−	0.994897i	$-0.467829\pi$
$359$	3.82343	0.201793	0.100896	+	0.994897i	$0.467829\pi$
$360$	6.43948	0.339390
$361$	0	0
$362$	−2.50658	−0.131743
$363$	3.24209	0.170166
$364$	8.69296	0.455635
$365$	−57.3688	−3.00282
$366$	6.46743	0.338058
$367$	10.8542	0.566583	0.283292	−	0.959034i	$-0.408574\pi$
$367$	10.8542	0.566583	0.283292	+	0.959034i	$0.408574\pi$
$368$	24.1139	1.25703
$369$	−7.98404	−0.415633
$370$	1.17922	0.0613048
$371$	−3.40292	−0.176671
$372$	−2.21453	−0.114818
$373$	−27.0779	−1.40204	−0.701021	−	0.713141i	$-0.747272\pi$
$373$	−27.0779	−1.40204	−0.701021	+	0.713141i	$0.747272\pi$
$374$	8.59784	0.444584
$375$	16.4537	0.849668
$376$	3.37749	0.174181
$377$	−40.0015	−2.06018
$378$	−0.447457	−0.0230147
$379$	37.4378	1.92305	0.961526	−	0.274714i	$-0.0885832\pi$
$379$	37.4378	1.92305	0.961526	+	0.274714i	$0.0885832\pi$
$380$	0	0
$381$	−15.8431	−0.811668
$382$	−3.91310	−0.200212
$383$	9.49443	0.485143	0.242571	−	0.970134i	$-0.422009\pi$
$383$	9.49443	0.485143	0.242571	+	0.970134i	$0.422009\pi$
$384$	10.9467	0.558623
$385$	−14.2931	−0.728445
$386$	−11.9570	−0.608595
$387$	−3.25522	−0.165472
$388$	−28.1846	−1.43086
$389$	−11.1139	−0.563497	−0.281749	−	0.959488i	$-0.590914\pi$
$389$	−11.1139	−0.563497	−0.281749	+	0.959488i	$0.590914\pi$
$390$	8.18539	0.414483
$391$	43.2502	2.18725
$392$	1.70024	0.0858751
$393$	10.7675	0.543150
$394$	−6.87283	−0.346248
$395$	3.43138	0.172652
$396$	6.79214	0.341318
$397$	19.3278	0.970036	0.485018	−	0.874504i	$-0.338813\pi$
$397$	19.3278	0.970036	0.485018	+	0.874504i	$0.338813\pi$
$398$	1.77773	0.0891094
$399$	0	0
$400$	26.5265	1.32633
$401$	−10.9728	−0.547957	−0.273978	−	0.961736i	$-0.588340\pi$
$401$	−10.9728	−0.547957	−0.273978	+	0.961736i	$0.588340\pi$
$402$	−4.51271	−0.225073
$403$	−5.94304	−0.296044
$404$	−33.2171	−1.65261
$405$	3.78739	0.188197
$406$	−3.70578	−0.183915
$407$	2.62598	0.130165
$408$	8.65688	0.428579
$409$	−3.12165	−0.154356	−0.0771779	−	0.997017i	$-0.524591\pi$
$409$	−3.12165	−0.154356	−0.0771779	+	0.997017i	$0.524591\pi$
$410$	13.5305	0.668225
$411$	−2.42034	−0.119387
$412$	13.5843	0.669250
$413$	12.2683	0.603686
$414$	−3.80092	−0.186805
$415$	15.1922	0.745756
$416$	22.5596	1.10607
$417$	−1.94817	−0.0954025
$418$	0	0
$419$	15.7219	0.768064	0.384032	−	0.923320i	$-0.374535\pi$
$419$	15.7219	0.768064	0.384032	+	0.923320i	$0.374535\pi$
$420$	−6.81648	−0.332610
$421$	−33.3575	−1.62574	−0.812872	−	0.582443i	$-0.802097\pi$
$421$	−33.3575	−1.62574	−0.812872	+	0.582443i	$0.802097\pi$
$422$	−4.24617	−0.206700
$423$	1.98648	0.0965858
$424$	−5.78578	−0.280982
$425$	47.5773	2.30784
$426$	1.12222	0.0543719
$427$	−14.4537	−0.699466
$428$	3.10813	0.150237
$429$	18.2278	0.880047
$430$	5.51661	0.266034
$431$	20.5677	0.990709	0.495355	−	0.868691i	$-0.335038\pi$
$431$	20.5677	0.990709	0.495355	+	0.868691i	$0.335038\pi$
$432$	2.83878	0.136581
$433$	34.8108	1.67290	0.836450	−	0.548043i	$-0.184627\pi$
$433$	34.8108	1.67290	0.836450	+	0.548043i	$0.184627\pi$
$434$	−0.550570	−0.0264282
$435$	31.3667	1.50392
$436$	11.5065	0.551063
$437$	0	0
$438$	6.77777	0.323854
$439$	0.509832	0.0243329	0.0121665	−	0.999926i	$-0.496127\pi$
$439$	0.509832	0.0243329	0.0121665	+	0.999926i	$0.496127\pi$
$440$	−24.3017	−1.15854
$441$	1.00000	0.0476190
$442$	11.0040	0.523406
$443$	2.65997	0.126379	0.0631894	−	0.998002i	$-0.479873\pi$
$443$	2.65997	0.126379	0.0631894	+	0.998002i	$0.479873\pi$
$444$	1.25234	0.0594336
$445$	49.1338	2.32917
$446$	3.40562	0.161261
$447$	1.30644	0.0617924
$448$	−3.58761	−0.169499
$449$	−0.762659	−0.0359921	−0.0179960	−	0.999838i	$-0.505729\pi$
$449$	−0.762659	−0.0359921	−0.0179960	+	0.999838i	$0.505729\pi$
$450$	−4.18120	−0.197103
$451$	30.1307	1.41880
$452$	−7.70643	−0.362480
$453$	−4.48079	−0.210526
$454$	−2.40044	−0.112658
$455$	−18.2931	−0.857595
$456$	0	0
$457$	−16.8810	−0.789662	−0.394831	−	0.918754i	$-0.629197\pi$
$457$	−16.8810	−0.789662	−0.394831	+	0.918754i	$0.629197\pi$
$458$	4.97300	0.232373
$459$	5.09156	0.237654
$460$	−57.9025	−2.69972
$461$	−5.86051	−0.272951	−0.136476	−	0.990643i	$-0.543578\pi$
$461$	−5.86051	−0.272951	−0.136476	+	0.990643i	$0.543578\pi$
$462$	1.68865	0.0785629
$463$	19.1991	0.892259	0.446130	−	0.894968i	$-0.352802\pi$
$463$	19.1991	0.892259	0.446130	+	0.894968i	$0.352802\pi$
$464$	23.5104	1.09144
$465$	4.66016	0.216110
$466$	−4.90702	−0.227313
$467$	22.7897	1.05458	0.527291	−	0.849685i	$-0.323208\pi$
$467$	22.7897	1.05458	0.527291	+	0.849685i	$0.323208\pi$
$468$	8.69296	0.401832
$469$	10.0852	0.465692
$470$	−3.36647	−0.155284
$471$	11.5725	0.533233
$472$	20.8591	0.960120
$473$	12.2848	0.564854
$474$	−0.405397	−0.0186205
$475$	0	0
$476$	−9.16370	−0.420018
$477$	−3.40292	−0.155809
$478$	0.0452754	0.00207085
$479$	26.9706	1.23232	0.616158	−	0.787622i	$-0.288688\pi$
$479$	26.9706	1.23232	0.616158	+	0.787622i	$0.288688\pi$
$480$	−17.6898	−0.807426
$481$	3.36087	0.153242
$482$	1.69579	0.0772410
$483$	8.49448	0.386512
$484$	−5.83506	−0.265230
$485$	59.3106	2.69316
$486$	−0.447457	−0.0202971
$487$	23.1450	1.04880	0.524401	−	0.851472i	$-0.324289\pi$
$487$	23.1450	1.04880	0.524401	+	0.851472i	$0.324289\pi$
$488$	−24.5748	−1.11245
$489$	−11.1254	−0.503108
$490$	−1.69470	−0.0765586
$491$	−27.8415	−1.25647	−0.628236	−	0.778023i	$-0.716223\pi$
$491$	−27.8415	−1.25647	−0.628236	+	0.778023i	$0.716223\pi$
$492$	14.3695	0.647829
$493$	42.1677	1.89914
$494$	0	0
$495$	−14.2931	−0.642428
$496$	3.49295	0.156838
$497$	−2.50800	−0.112499
$498$	−1.79487	−0.0804298
$499$	−9.53019	−0.426630	−0.213315	−	0.976983i	$-0.568426\pi$
$499$	−9.53019	−0.426630	−0.213315	+	0.976983i	$0.568426\pi$
$500$	−29.6131	−1.32434
$501$	−2.08522	−0.0931609
$502$	−3.32358	−0.148338
$503$	18.2166	0.812236	0.406118	−	0.913821i	$-0.366882\pi$
$503$	18.2166	0.812236	0.406118	+	0.913821i	$0.366882\pi$
$504$	1.70024	0.0757347
$505$	69.9008	3.11054
$506$	14.3442	0.637676
$507$	10.3289	0.458725
$508$	28.5142	1.26511
$509$	−5.16178	−0.228792	−0.114396	−	0.993435i	$-0.536493\pi$
$509$	−5.16178	−0.228792	−0.114396	+	0.993435i	$0.536493\pi$
$510$	−8.62865	−0.382083
$511$	−15.1473	−0.670077
$512$	−22.9123	−1.01259
$513$	0	0
$514$	3.19417	0.140889
$515$	−28.5863	−1.25966
$516$	5.85868	0.257914
$517$	−7.49670	−0.329705
$518$	0.311355	0.0136801
$519$	7.26343	0.318829
$520$	−31.1027	−1.36394
$521$	1.76900	0.0775012	0.0387506	−	0.999249i	$-0.487662\pi$
$521$	1.76900	0.0775012	0.0387506	+	0.999249i	$0.487662\pi$
$522$	−3.70578	−0.162198
$523$	−21.7671	−0.951810	−0.475905	−	0.879497i	$-0.657879\pi$
$523$	−21.7671	−0.951810	−0.475905	+	0.879497i	$0.657879\pi$
$524$	−19.3792	−0.846585
$525$	9.34434	0.407821
$526$	−2.48734	−0.108453
$527$	6.26487	0.272902
$528$	−10.7132	−0.466231
$529$	49.1562	2.13722
$530$	5.76691	0.250499
$531$	12.2683	0.532401
$532$	0	0
$533$	38.5630	1.67035
$534$	−5.80486	−0.251201
$535$	−6.54063	−0.282776
$536$	17.1473	0.740651
$537$	9.84784	0.424966
$538$	−7.26218	−0.313095
$539$	−3.77387	−0.162552
$540$	−6.81648	−0.293335
$541$	13.2253	0.568600	0.284300	−	0.958735i	$-0.408239\pi$
$541$	13.2253	0.568600	0.284300	+	0.958735i	$0.408239\pi$
$542$	10.9061	0.468457
$543$	5.60183	0.240398
$544$	−23.7812	−1.01961
$545$	−24.2139	−1.03721
$546$	2.16122	0.0924917
$547$	−3.56390	−0.152381	−0.0761906	−	0.997093i	$-0.524276\pi$
$547$	−3.56390	−0.152381	−0.0761906	+	0.997093i	$0.524276\pi$
$548$	4.35609	0.186083
$549$	−14.4537	−0.616871
$550$	15.7793	0.672831
$551$	0	0
$552$	14.4427	0.614720
$553$	0.906002	0.0385271
$554$	3.04505	0.129372
$555$	−2.63539	−0.111866
$556$	3.50629	0.148700
$557$	13.3471	0.565533	0.282767	−	0.959189i	$-0.408748\pi$
$557$	13.3471	0.565533	0.282767	+	0.959189i	$0.408748\pi$
$558$	−0.550570	−0.0233075
$559$	15.7227	0.665000
$560$	10.7516	0.454337
$561$	−19.2149	−0.811253
$562$	−4.72179	−0.199177
$563$	−9.98157	−0.420673	−0.210337	−	0.977629i	$-0.567456\pi$
$563$	−9.98157	−0.420673	−0.210337	+	0.977629i	$0.567456\pi$
$564$	−3.57522	−0.150544
$565$	16.2171	0.682260
$566$	7.81373	0.328436
$567$	1.00000	0.0419961
$568$	−4.26421	−0.178922
$569$	−41.3583	−1.73383	−0.866916	−	0.498455i	$-0.833901\pi$
$569$	−41.3583	−1.73383	−0.866916	+	0.498455i	$0.833901\pi$
$570$	0	0
$571$	4.51906	0.189117	0.0945584	−	0.995519i	$-0.469856\pi$
$571$	4.51906	0.189117	0.0945584	+	0.995519i	$0.469856\pi$
$572$	−32.8061	−1.37169
$573$	8.74519	0.365336
$574$	3.57252	0.149114
$575$	79.3753	3.31018
$576$	−3.58761	−0.149484
$577$	−27.0388	−1.12564	−0.562820	−	0.826580i	$-0.690283\pi$
$577$	−27.0388	−1.12564	−0.562820	+	0.826580i	$0.690283\pi$
$578$	−3.99311	−0.166091
$579$	26.7221	1.11053
$580$	−56.4532	−2.34409
$581$	4.01125	0.166415
$582$	−7.00719	−0.290457
$583$	12.8422	0.531868
$584$	−25.7541	−1.06571
$585$	−18.2931	−0.756328
$586$	0.938010	0.0387488
$587$	−22.9706	−0.948097	−0.474048	−	0.880499i	$-0.657208\pi$
$587$	−22.9706	−0.948097	−0.474048	+	0.880499i	$0.657208\pi$
$588$	−1.79978	−0.0742218
$589$	0	0
$590$	−20.7911	−0.855957
$591$	15.3597	0.631815
$592$	−1.97531	−0.0811848
$593$	25.1922	1.03452	0.517259	−	0.855829i	$-0.326952\pi$
$593$	25.1922	1.03452	0.517259	+	0.855829i	$0.326952\pi$
$594$	1.68865	0.0692860
$595$	19.2837	0.790556
$596$	−2.35130	−0.0963131
$597$	−3.97295	−0.162602
$598$	18.3584	0.750733
$599$	−23.7491	−0.970364	−0.485182	−	0.874413i	$-0.661247\pi$
$599$	−23.7491	−0.970364	−0.485182	+	0.874413i	$0.661247\pi$
$600$	15.8876	0.648610
$601$	−16.5994	−0.677104	−0.338552	−	0.940948i	$-0.609937\pi$
$601$	−16.5994	−0.677104	−0.338552	+	0.940948i	$0.609937\pi$
$602$	1.45657	0.0593654
$603$	10.0852	0.410702
$604$	8.06444	0.328137
$605$	12.2791	0.499215
$606$	−8.25835	−0.335473
$607$	3.12740	0.126937	0.0634686	−	0.997984i	$-0.479784\pi$
$607$	3.12740	0.126937	0.0634686	+	0.997984i	$0.479784\pi$
$608$	0	0
$609$	8.28187	0.335598
$610$	24.4947	0.991762
$611$	−9.59469	−0.388160
$612$	−9.16370	−0.370421
$613$	−12.0219	−0.485560	−0.242780	−	0.970081i	$-0.578059\pi$
$613$	−12.0219	−0.485560	−0.242780	+	0.970081i	$0.578059\pi$
$614$	−11.7759	−0.475235
$615$	−30.2387	−1.21934
$616$	−6.41648	−0.258528
$617$	−16.0263	−0.645193	−0.322596	−	0.946537i	$-0.604556\pi$
$617$	−16.0263	−0.645193	−0.322596	+	0.946537i	$0.604556\pi$
$618$	3.37729	0.135855
$619$	−8.50696	−0.341923	−0.170962	−	0.985278i	$-0.554687\pi$
$619$	−8.50696	−0.341923	−0.170962	+	0.985278i	$0.554687\pi$
$620$	−8.38728	−0.336841
$621$	8.49448	0.340872
$622$	−7.57259	−0.303633
$623$	12.9730	0.519752
$624$	−13.7113	−0.548892
$625$	15.5951	0.623802
$626$	−7.61292	−0.304273
$627$	0	0
$628$	−20.8280	−0.831128
$629$	−3.54287	−0.141263
$630$	−1.69470	−0.0675183
$631$	42.8162	1.70449	0.852243	−	0.523146i	$-0.175242\pi$
$631$	42.8162	1.70449	0.852243	+	0.523146i	$0.175242\pi$
$632$	1.54042	0.0612746
$633$	9.48956	0.377176
$634$	−0.328493	−0.0130461
$635$	−60.0042	−2.38119
$636$	6.12451	0.242853
$637$	−4.83000	−0.191372
$638$	13.9851	0.553677
$639$	−2.50800	−0.0992150
$640$	41.4596	1.63883
$641$	15.4409	0.609877	0.304939	−	0.952372i	$-0.401364\pi$
$641$	15.4409	0.609877	0.304939	+	0.952372i	$0.401364\pi$
$642$	0.772735	0.0304974
$643$	−26.2283	−1.03434	−0.517171	−	0.855882i	$-0.673015\pi$
$643$	−26.2283	−1.03434	−0.517171	+	0.855882i	$0.673015\pi$
$644$	−15.2882	−0.602440
$645$	−12.3288	−0.485446
$646$	0	0
$647$	−42.8416	−1.68428	−0.842138	−	0.539262i	$-0.818703\pi$
$647$	−42.8416	−1.68428	−0.842138	+	0.539262i	$0.818703\pi$
$648$	1.70024	0.0667917
$649$	−46.2991	−1.81740
$650$	20.1952	0.792121
$651$	1.23044	0.0482248
$652$	20.0233	0.784173
$653$	14.2200	0.556472	0.278236	−	0.960513i	$-0.410250\pi$
$653$	14.2200	0.556472	0.278236	+	0.960513i	$0.410250\pi$
$654$	2.86073	0.111863
$655$	40.7809	1.59344
$656$	−22.6649	−0.884917
$657$	−15.1473	−0.590953
$658$	−0.888863	−0.0346515
$659$	13.2053	0.514406	0.257203	−	0.966357i	$-0.417199\pi$
$659$	13.2053	0.514406	0.257203	+	0.966357i	$0.417199\pi$
$660$	25.7245	1.00133
$661$	−0.529737	−0.0206044	−0.0103022	−	0.999947i	$-0.503279\pi$
$661$	−0.529737	−0.0206044	−0.0103022	+	0.999947i	$0.503279\pi$
$662$	6.16149	0.239473
$663$	−24.5923	−0.955085
$664$	6.82010	0.264671
$665$	0	0
$666$	0.311355	0.0120647
$667$	70.3502	2.72397
$668$	3.75295	0.145206
$669$	−7.61106	−0.294261
$670$	−17.0914	−0.660298
$671$	54.5465	2.10575
$672$	−4.67071	−0.180177
$673$	−3.95758	−0.152554	−0.0762768	−	0.997087i	$-0.524303\pi$
$673$	−3.95758	−0.152554	−0.0762768	+	0.997087i	$0.524303\pi$
$674$	10.8829	0.419194
$675$	9.34434	0.359664
$676$	−18.5899	−0.714994
$677$	34.9108	1.34173	0.670865	−	0.741580i	$-0.265923\pi$
$677$	34.9108	1.34173	0.670865	+	0.741580i	$0.265923\pi$
$678$	−1.91595	−0.0735818
$679$	15.6600	0.600976
$680$	32.7870	1.25732
$681$	5.36461	0.205572
$682$	2.07778	0.0795622
$683$	29.8433	1.14192	0.570961	−	0.820977i	$-0.306571\pi$
$683$	29.8433	1.14192	0.570961	+	0.820977i	$0.306571\pi$
$684$	0	0
$685$	−9.16678	−0.350245
$686$	−0.447457	−0.0170840
$687$	−11.1139	−0.424022
$688$	−9.24085	−0.352304
$689$	16.4361	0.626166
$690$	−14.3956	−0.548030
$691$	34.4624	1.31101	0.655505	−	0.755191i	$-0.272456\pi$
$691$	34.4624	1.31101	0.655505	+	0.755191i	$0.272456\pi$
$692$	−13.0726	−0.496945
$693$	−3.77387	−0.143357
$694$	−1.74455	−0.0662224
$695$	−7.37850	−0.279883
$696$	14.0812	0.533745
$697$	−40.6512	−1.53978
$698$	6.57256	0.248775
$699$	10.9664	0.414789
$700$	−16.8178	−0.635652
$701$	−24.0484	−0.908297	−0.454148	−	0.890926i	$-0.650056\pi$
$701$	−24.0484	−0.908297	−0.454148	+	0.890926i	$0.650056\pi$
$702$	2.16122	0.0815700
$703$	0	0
$704$	13.5392	0.510277
$705$	7.52357	0.283354
$706$	9.64060	0.362829
$707$	18.4562	0.694116
$708$	−22.0804	−0.829830
$709$	46.9216	1.76218	0.881088	−	0.472951i	$-0.156811\pi$
$709$	46.9216	1.76218	0.881088	+	0.472951i	$0.156811\pi$
$710$	4.25030	0.159511
$711$	0.906002	0.0339777
$712$	22.0572	0.826629
$713$	10.4520	0.391429
$714$	−2.27826	−0.0852616
$715$	69.0359	2.58180
$716$	−17.7240	−0.662376
$717$	−0.101184	−0.00377878
$718$	−1.71082	−0.0638472
$719$	−42.7532	−1.59443	−0.797214	−	0.603697i	$-0.793694\pi$
$719$	−42.7532	−1.59443	−0.797214	+	0.603697i	$0.793694\pi$
$720$	10.7516	0.400687
$721$	−7.54774	−0.281092
$722$	0	0
$723$	−3.78983	−0.140945
$724$	−10.0821	−0.374697
$725$	77.3887	2.87414
$726$	−1.45070	−0.0538404
$727$	−29.9126	−1.10940	−0.554698	−	0.832052i	$-0.687166\pi$
$727$	−29.9126	−1.10940	−0.554698	+	0.832052i	$0.687166\pi$
$728$	−8.21217	−0.304363
$729$	1.00000	0.0370370
$730$	25.6701	0.950092
$731$	−16.5741	−0.613017
$732$	26.0136	0.961490
$733$	−1.63929	−0.0605484	−0.0302742	−	0.999542i	$-0.509638\pi$
$733$	−1.63929	−0.0605484	−0.0302742	+	0.999542i	$0.509638\pi$
$734$	−4.85678	−0.179267
$735$	3.78739	0.139700
$736$	−39.6753	−1.46245
$737$	−38.0603	−1.40197
$738$	3.57252	0.131506
$739$	31.1692	1.14658	0.573289	−	0.819353i	$-0.305667\pi$
$739$	31.1692	1.14658	0.573289	+	0.819353i	$0.305667\pi$
$740$	4.74312	0.174361
$741$	0	0
$742$	1.52266	0.0558986
$743$	28.6218	1.05003	0.525015	−	0.851093i	$-0.324060\pi$
$743$	28.6218	1.05003	0.525015	+	0.851093i	$0.324060\pi$
$744$	2.09205	0.0766981
$745$	4.94799	0.181280
$746$	12.1162	0.443606
$747$	4.01125	0.146764
$748$	34.5826	1.26447
$749$	−1.72695	−0.0631013
$750$	−7.36235	−0.268835
$751$	10.4730	0.382165	0.191082	−	0.981574i	$-0.438800\pi$
$751$	10.4730	0.382165	0.191082	+	0.981574i	$0.438800\pi$
$752$	5.63917	0.205639
$753$	7.42769	0.270680
$754$	17.8990	0.651841
$755$	−16.9705	−0.617620
$756$	−1.79978	−0.0654574
$757$	−40.7907	−1.48256	−0.741281	−	0.671195i	$-0.765781\pi$
$757$	−40.7907	−1.48256	−0.741281	+	0.671195i	$0.765781\pi$
$758$	−16.7518	−0.608454
$759$	−32.0571	−1.16360
$760$	0	0
$761$	−39.8989	−1.44633	−0.723167	−	0.690674i	$-0.757314\pi$
$761$	−39.8989	−1.44633	−0.723167	+	0.690674i	$0.757314\pi$
$762$	7.08913	0.256812
$763$	−6.39329	−0.231453
$764$	−15.7394	−0.569433
$765$	19.2837	0.697205
$766$	−4.24835	−0.153499
$767$	−59.2562	−2.13962
$768$	2.27703	0.0821654
$769$	0.847825	0.0305733	0.0152867	−	0.999883i	$-0.495134\pi$
$769$	0.847825	0.0305733	0.0152867	+	0.999883i	$0.495134\pi$
$770$	6.39556	0.230480
$771$	−7.13848	−0.257086
$772$	−48.0939	−1.73094
$773$	−13.6395	−0.490579	−0.245290	−	0.969450i	$-0.578883\pi$
$773$	−13.6395	−0.490579	−0.245290	+	0.969450i	$0.578883\pi$
$774$	1.45657	0.0523554
$775$	11.4977	0.413008
$776$	26.6258	0.955810
$777$	−0.695831	−0.0249628
$778$	4.97300	0.178291
$779$	0	0
$780$	32.9236	1.17886
$781$	9.46487	0.338680
$782$	−19.3526	−0.692048
$783$	8.28187	0.295970
$784$	2.83878	0.101385
$785$	43.8297	1.56435
$786$	−4.81801	−0.171853
$787$	22.6717	0.808157	0.404079	−	0.914724i	$-0.367592\pi$
$787$	22.6717	0.808157	0.404079	+	0.914724i	$0.367592\pi$
$788$	−27.6442	−0.984783
$789$	5.55883	0.197899
$790$	−1.53540	−0.0546270
$791$	4.28187	0.152246
$792$	−6.41648	−0.228000
$793$	69.8116	2.47908
$794$	−8.64838	−0.306919
$795$	−12.8882	−0.457097
$796$	7.15045	0.253441
$797$	−42.5032	−1.50554	−0.752770	−	0.658284i	$-0.771283\pi$
$797$	−42.5032	−1.50554	−0.752770	+	0.658284i	$0.771283\pi$
$798$	0	0
$799$	10.1143	0.357817
$800$	−43.6447	−1.54307
$801$	12.9730	0.458378
$802$	4.90987	0.173374
$803$	57.1639	2.01727
$804$	−18.1512	−0.640144
$805$	32.1719	1.13391
$806$	2.65925	0.0936683
$807$	16.2299	0.571319
$808$	31.3799	1.10394
$809$	−56.8194	−1.99766	−0.998832	−	0.0483155i	$-0.984615\pi$
$809$	−56.8194	−1.99766	−0.998832	+	0.0483155i	$0.984615\pi$
$810$	−1.69470	−0.0595456
$811$	−11.1319	−0.390895	−0.195448	−	0.980714i	$-0.562616\pi$
$811$	−11.1319	−0.390895	−0.195448	+	0.980714i	$0.562616\pi$
$812$	−14.9056	−0.523083
$813$	−24.3735	−0.854815
$814$	−1.17501	−0.0411841
$815$	−42.1363	−1.47597
$816$	14.4538	0.505985
$817$	0	0
$818$	1.39681	0.0488382
$819$	−4.83000	−0.168774
$820$	54.4231	1.90054
$821$	−22.3495	−0.780003	−0.390001	−	0.920814i	$-0.627525\pi$
$821$	−22.3495	−0.780003	−0.390001	+	0.920814i	$0.627525\pi$
$822$	1.08300	0.0377739
$823$	44.7797	1.56092	0.780460	−	0.625205i	$-0.214985\pi$
$823$	44.7797	1.56092	0.780460	+	0.625205i	$0.214985\pi$
$824$	−12.8330	−0.447058
$825$	−35.2643	−1.22775
$826$	−5.48956	−0.191006
$827$	−31.7960	−1.10566	−0.552828	−	0.833295i	$-0.686451\pi$
$827$	−31.7960	−1.10566	−0.552828	+	0.833295i	$0.686451\pi$
$828$	−15.2882	−0.531302
$829$	−0.129908	−0.00451189	−0.00225594	−	0.999997i	$-0.500718\pi$
$829$	−0.129908	−0.00451189	−0.00225594	+	0.999997i	$0.500718\pi$
$830$	−6.79786	−0.235957
$831$	−6.80523	−0.236071
$832$	17.3282	0.600747
$833$	5.09156	0.176412
$834$	0.871725	0.0301854
$835$	−7.89756	−0.273306
$836$	0	0
$837$	1.23044	0.0425303
$838$	−7.03487	−0.243015
$839$	46.2508	1.59675	0.798377	−	0.602157i	$-0.205692\pi$
$839$	46.2508	1.59675	0.798377	+	0.602157i	$0.205692\pi$
$840$	6.43948	0.222183
$841$	39.5894	1.36515
$842$	14.9260	0.514385
$843$	10.5525	0.363447
$844$	−17.0791	−0.587888
$845$	39.1198	1.34576
$846$	−0.888863	−0.0305598
$847$	3.24209	0.111400
$848$	−9.66013	−0.331730
$849$	−17.4625	−0.599312
$850$	−21.2888	−0.730200
$851$	−5.91072	−0.202617
$852$	4.51386	0.154642
$853$	−1.67756	−0.0574385	−0.0287192	−	0.999588i	$-0.509143\pi$
$853$	−1.67756	−0.0574385	−0.0287192	+	0.999588i	$0.509143\pi$
$854$	6.46743	0.221311
$855$	0	0
$856$	−2.93622	−0.100358
$857$	20.3909	0.696540	0.348270	−	0.937394i	$-0.386769\pi$
$857$	20.3909	0.696540	0.348270	+	0.937394i	$0.386769\pi$
$858$	−8.15617	−0.278447
$859$	−34.2508	−1.16862	−0.584311	−	0.811530i	$-0.698635\pi$
$859$	−34.2508	−1.16862	−0.584311	+	0.811530i	$0.698635\pi$
$860$	22.1891	0.756643
$861$	−7.98404	−0.272095
$862$	−9.20315	−0.313460
$863$	0.402083	0.0136871	0.00684353	−	0.999977i	$-0.497822\pi$
$863$	0.402083	0.0136871	0.00684353	+	0.999977i	$0.497822\pi$
$864$	−4.67071	−0.158901
$865$	27.5095	0.935350
$866$	−15.5763	−0.529306
$867$	8.92400	0.303075
$868$	−2.21453	−0.0751659
$869$	−3.41913	−0.115986
$870$	−14.0353	−0.475840
$871$	−48.7117	−1.65053
$872$	−10.8701	−0.368109
$873$	15.6600	0.530011
$874$	0	0
$875$	16.4537	0.556238
$876$	27.2618	0.921092
$877$	−36.4949	−1.23235	−0.616173	−	0.787611i	$-0.711318\pi$
$877$	−36.4949	−1.23235	−0.616173	+	0.787611i	$0.711318\pi$
$878$	−0.228128	−0.00769895
$879$	−2.09631	−0.0707068
$880$	−40.5750	−1.36778
$881$	−0.808269	−0.0272313	−0.0136156	−	0.999907i	$-0.504334\pi$
$881$	−0.808269	−0.0272313	−0.0136156	+	0.999907i	$0.504334\pi$
$882$	−0.447457	−0.0150667
$883$	0.501818	0.0168875	0.00844375	−	0.999964i	$-0.497312\pi$
$883$	0.501818	0.0168875	0.00844375	+	0.999964i	$0.497312\pi$
$884$	44.2607	1.48865
$885$	46.4651	1.56191
$886$	−1.19022	−0.0399863
$887$	−21.0336	−0.706241	−0.353120	−	0.935578i	$-0.614879\pi$
$887$	−21.0336	−0.706241	−0.353120	+	0.935578i	$0.614879\pi$
$888$	−1.18308	−0.0397016
$889$	−15.8431	−0.531362
$890$	−21.9853	−0.736949
$891$	−3.77387	−0.126429
$892$	13.6982	0.458651
$893$	0	0
$894$	−0.584575	−0.0195511
$895$	37.2976	1.24672
$896$	10.9467	0.365705
$897$	−41.0284	−1.36990
$898$	0.341257	0.0113879
$899$	10.1904	0.339867
$900$	−16.8178	−0.560593
$901$	−17.3262	−0.577218
$902$	−13.4822	−0.448909
$903$	−3.25522	−0.108327
$904$	7.28021	0.242136
$905$	21.2163	0.705255
$906$	2.00496	0.0666104
$907$	5.77219	0.191662	0.0958312	−	0.995398i	$-0.469449\pi$
$907$	5.77219	0.191662	0.0958312	+	0.995398i	$0.469449\pi$
$908$	−9.65514	−0.320417
$909$	18.4562	0.612153
$910$	8.18539	0.271343
$911$	−56.0333	−1.85647	−0.928233	−	0.371998i	$-0.878673\pi$
$911$	−56.0333	−1.85647	−0.928233	+	0.371998i	$0.878673\pi$
$912$	0	0
$913$	−15.1380	−0.500993
$914$	7.55354	0.249849
$915$	−54.7420	−1.80971
$916$	20.0026	0.660905
$917$	10.7675	0.355575
$918$	−2.27826	−0.0751937
$919$	47.4364	1.56478	0.782391	−	0.622788i	$-0.214000\pi$
$919$	47.4364	1.56478	0.782391	+	0.622788i	$0.214000\pi$
$920$	54.7000	1.80341
$921$	26.3173	0.867184
$922$	2.62233	0.0863618
$923$	12.1137	0.398726
$924$	6.79214	0.223445
$925$	−6.50208	−0.213787
$926$	−8.59079	−0.282311
$927$	−7.54774	−0.247900
$928$	−38.6822	−1.26981
$929$	−29.2748	−0.960474	−0.480237	−	0.877139i	$-0.659449\pi$
$929$	−29.2748	−0.960474	−0.480237	+	0.877139i	$0.659449\pi$
$930$	−2.08522	−0.0683772
$931$	0	0
$932$	−19.7372	−0.646514
$933$	16.9236	0.554054
$934$	−10.1974	−0.333670
$935$	−72.7743	−2.37998
$936$	−8.21217	−0.268423
$937$	18.3167	0.598380	0.299190	−	0.954194i	$-0.403284\pi$
$937$	18.3167	0.598380	0.299190	+	0.954194i	$0.403284\pi$
$938$	−4.51271	−0.147345
$939$	17.0137	0.555222
$940$	−13.5408	−0.441652
$941$	−37.1705	−1.21172	−0.605862	−	0.795570i	$-0.707172\pi$
$941$	−37.1705	−1.21172	−0.605862	+	0.795570i	$0.707172\pi$
$942$	−5.17821	−0.168715
$943$	−67.8203	−2.20853
$944$	34.8271	1.13353
$945$	3.78739	0.123204
$946$	−5.49691	−0.178720
$947$	48.7220	1.58325	0.791626	−	0.611006i	$-0.209235\pi$
$947$	48.7220	1.58325	0.791626	+	0.611006i	$0.209235\pi$
$948$	−1.63061	−0.0529596
$949$	73.1615	2.37492
$950$	0	0
$951$	0.734133	0.0238059
$952$	8.65688	0.280571
$953$	41.7422	1.35216	0.676081	−	0.736827i	$-0.263677\pi$
$953$	41.7422	1.35216	0.676081	+	0.736827i	$0.263677\pi$
$954$	1.52266	0.0492979
$955$	33.1215	1.07179
$956$	0.182109	0.00588982
$957$	−31.2547	−1.01032
$958$	−12.0682	−0.389905
$959$	−2.42034	−0.0781569
$960$	−13.5877	−0.438541
$961$	−29.4860	−0.951162
$962$	−1.50384	−0.0484859
$963$	−1.72695	−0.0556501
$964$	6.82087	0.219685
$965$	101.207	3.25797
$966$	−3.80092	−0.122292
$967$	40.1803	1.29211	0.646056	−	0.763290i	$-0.276417\pi$
$967$	40.1803	1.29211	0.646056	+	0.763290i	$0.276417\pi$
$968$	5.51233	0.177173
$969$	0	0
$970$	−26.5390	−0.852115
$971$	7.32895	0.235197	0.117599	−	0.993061i	$-0.462480\pi$
$971$	7.32895	0.235197	0.117599	+	0.993061i	$0.462480\pi$
$972$	−1.79978	−0.0577280
$973$	−1.94817	−0.0624556
$974$	−10.3564	−0.331841
$975$	−45.1332	−1.44542
$976$	−41.0310	−1.31337
$977$	−34.9855	−1.11929	−0.559643	−	0.828734i	$-0.689062\pi$
$977$	−34.9855	−1.11929	−0.559643	+	0.828734i	$0.689062\pi$
$978$	4.97814	0.159183
$979$	−48.9584	−1.56472
$980$	−6.81648	−0.217745
$981$	−6.39329	−0.204122
$982$	12.4579	0.397548
$983$	−47.7039	−1.52152	−0.760759	−	0.649034i	$-0.775173\pi$
$983$	−47.7039	−1.52152	−0.760759	+	0.649034i	$0.775173\pi$
$984$	−13.5748	−0.432748
$985$	58.1734	1.85356
$986$	−18.8682	−0.600887
$987$	1.98648	0.0632302
$988$	0	0
$989$	−27.6514	−0.879263
$990$	6.39556	0.203264
$991$	−26.4080	−0.838878	−0.419439	−	0.907784i	$-0.637773\pi$
$991$	−26.4080	−0.838878	−0.419439	+	0.907784i	$0.637773\pi$
$992$	−5.74704	−0.182469
$993$	−13.7700	−0.436978
$994$	1.12222	0.0355948
$995$	−15.0471	−0.477026
$996$	−7.21938	−0.228755
$997$	−11.4263	−0.361874	−0.180937	−	0.983495i	$-0.557913\pi$
$997$	−11.4263	−0.361874	−0.180937	+	0.983495i	$0.557913\pi$
$998$	4.26435	0.134986
$999$	−0.695831	−0.0220151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7581.2.a.w.1.3		5
19.18	odd	2		399.2.a.g.1.3	✓	5
57.56	even	2		1197.2.a.o.1.3		5
76.75	even	2		6384.2.a.cf.1.5		5
95.94	odd	2		9975.2.a.bp.1.3		5
133.132	even	2		2793.2.a.bg.1.3		5
399.398	odd	2		8379.2.a.cb.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.a.g.1.3	✓	5	19.18	odd	2
1197.2.a.o.1.3		5	57.56	even	2
2793.2.a.bg.1.3		5	133.132	even	2
6384.2.a.cf.1.5		5	76.75	even	2
7581.2.a.w.1.3		5	1.1	even	1	trivial
8379.2.a.cb.1.3		5	399.398	odd	2
9975.2.a.bp.1.3		5	95.94	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:	\( N \)	\(=\)	\( 7581 = 3 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7581.a (trivial)

\(f(q)\)	\(=\)	\(q-0.447457 q^{2} +1.00000 q^{3} -1.79978 q^{4} +3.78739 q^{5} -0.447457 q^{6} +1.00000 q^{7} +1.70024 q^{8} +1.00000 q^{9} -1.69470 q^{10} -3.77387 q^{11} -1.79978 q^{12} -4.83000 q^{13} -0.447457 q^{14} +3.78739 q^{15} +2.83878 q^{16} +5.09156 q^{17} -0.447457 q^{18} -6.81648 q^{20} +1.00000 q^{21} +1.68865 q^{22} +8.49448 q^{23} +1.70024 q^{24} +9.34434 q^{25} +2.16122 q^{26} +1.00000 q^{27} -1.79978 q^{28} +8.28187 q^{29} -1.69470 q^{30} +1.23044 q^{31} -4.67071 q^{32} -3.77387 q^{33} -2.27826 q^{34} +3.78739 q^{35} -1.79978 q^{36} -0.695831 q^{37} -4.83000 q^{39} +6.43948 q^{40} -7.98404 q^{41} -0.447457 q^{42} -3.25522 q^{43} +6.79214 q^{44} +3.78739 q^{45} -3.80092 q^{46} +1.98648 q^{47} +2.83878 q^{48} +1.00000 q^{49} -4.18120 q^{50} +5.09156 q^{51} +8.69296 q^{52} -3.40292 q^{53} -0.447457 q^{54} -14.2931 q^{55} +1.70024 q^{56} -3.70578 q^{58} +12.2683 q^{59} -6.81648 q^{60} -14.4537 q^{61} -0.550570 q^{62} +1.00000 q^{63} -3.58761 q^{64} -18.2931 q^{65} +1.68865 q^{66} +10.0852 q^{67} -9.16370 q^{68} +8.49448 q^{69} -1.69470 q^{70} -2.50800 q^{71} +1.70024 q^{72} -15.1473 q^{73} +0.311355 q^{74} +9.34434 q^{75} -3.77387 q^{77} +2.16122 q^{78} +0.906002 q^{79} +10.7516 q^{80} +1.00000 q^{81} +3.57252 q^{82} +4.01125 q^{83} -1.79978 q^{84} +19.2837 q^{85} +1.45657 q^{86} +8.28187 q^{87} -6.41648 q^{88} +12.9730 q^{89} -1.69470 q^{90} -4.83000 q^{91} -15.2882 q^{92} +1.23044 q^{93} -0.888863 q^{94} -4.67071 q^{96} +15.6600 q^{97} -0.447457 q^{98} -3.77387 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{2} + 5 q^{3} + 7 q^{4} + 4 q^{5} - 3 q^{6} + 5 q^{7} - 9 q^{8} + 5 q^{9} + 6 q^{10} + 8 q^{11} + 7 q^{12} + 6 q^{13} - 3 q^{14} + 4 q^{15} + 19 q^{16} + 12 q^{17} - 3 q^{18} + 8 q^{20} + 5 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 + 5 * q^3 + 7 * q^4 + 4 * q^5 - 3 * q^6 + 5 * q^7 - 9 * q^8 + 5 * q^9 + 6 * q^10 + 8 * q^11 + 7 * q^12 + 6 * q^13 - 3 * q^14 + 4 * q^15 + 19 * q^16 + 12 * q^17 - 3 * q^18 + 8 * q^20 + 5 * q^21 + 12 * q^22 + 12 * q^23 - 9 * q^24 + 15 * q^25 + 6 * q^26 + 5 * q^27 + 7 * q^28 - 4 * q^29 + 6 * q^30 + 8 * q^31 - 31 * q^32 + 8 * q^33 - 2 * q^34 + 4 * q^35 + 7 * q^36 - 2 * q^37 + 6 * q^39 + 18 * q^40 - 10 * q^41 - 3 * q^42 - 16 * q^43 - 4 * q^44 + 4 * q^45 - 16 * q^46 - 2 * q^47 + 19 * q^48 + 5 * q^49 + 39 * q^50 + 12 * q^51 + 22 * q^52 - 3 * q^54 - 12 * q^55 - 9 * q^56 + 2 * q^58 + 4 * q^59 + 8 * q^60 - 14 * q^61 - 36 * q^62 + 5 * q^63 + 11 * q^64 - 32 * q^65 + 12 * q^66 + 20 * q^67 + 8 * q^68 + 12 * q^69 + 6 * q^70 + 6 * q^71 - 9 * q^72 + 10 * q^73 - 2 * q^74 + 15 * q^75 + 8 * q^77 + 6 * q^78 - 20 * q^80 + 5 * q^81 - 38 * q^82 + 6 * q^83 + 7 * q^84 + 8 * q^85 + 36 * q^86 - 4 * q^87 + 40 * q^88 - 26 * q^89 + 6 * q^90 + 6 * q^91 - 48 * q^92 + 8 * q^93 - 24 * q^94 - 31 * q^96 + 18 * q^97 - 3 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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Database

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