LMFDB - Embedded newform 161.4.a.b.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [161,4,Mod(1,161)] 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("161.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(161, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$9.49930751092$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 44x^{6} - 23x^{5} + 587x^{4} + 594x^{3} - 2430x^{2} - 3403x + 110 $ x^8 - 44x^6 - 23x^5 + 587x^4 + 594x^3 - 2430x^2 - 3403x + 110
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-3.02588$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.02588 q^{2} -9.11775 q^{3} +1.15594 q^{4} +18.5973 q^{5} -27.5892 q^{6} -7.00000 q^{7} -20.7093 q^{8} +56.1334 q^{9} +56.2732 q^{10} -33.2549 q^{11} -10.5396 q^{12} -64.4205 q^{13} -21.1812 q^{14} -169.566 q^{15} -71.9113 q^{16} -52.2394 q^{17} +169.853 q^{18} -88.3614 q^{19} +21.4974 q^{20} +63.8243 q^{21} -100.625 q^{22} +23.0000 q^{23} +188.822 q^{24} +220.859 q^{25} -194.928 q^{26} -265.631 q^{27} -8.09159 q^{28} +118.211 q^{29} -513.085 q^{30} -255.347 q^{31} -51.9206 q^{32} +303.210 q^{33} -158.070 q^{34} -130.181 q^{35} +64.8870 q^{36} +57.9031 q^{37} -267.371 q^{38} +587.370 q^{39} -385.137 q^{40} -347.026 q^{41} +193.125 q^{42} +477.979 q^{43} -38.4407 q^{44} +1043.93 q^{45} +69.5952 q^{46} +239.666 q^{47} +655.670 q^{48} +49.0000 q^{49} +668.294 q^{50} +476.306 q^{51} -74.4663 q^{52} -402.094 q^{53} -803.769 q^{54} -618.452 q^{55} +144.965 q^{56} +805.657 q^{57} +357.691 q^{58} -587.617 q^{59} -196.008 q^{60} +698.764 q^{61} -772.649 q^{62} -392.934 q^{63} +418.185 q^{64} -1198.05 q^{65} +917.477 q^{66} +126.625 q^{67} -60.3857 q^{68} -209.708 q^{69} -393.912 q^{70} -844.084 q^{71} -1162.48 q^{72} +712.052 q^{73} +175.208 q^{74} -2013.74 q^{75} -102.141 q^{76} +232.784 q^{77} +1777.31 q^{78} -589.839 q^{79} -1337.36 q^{80} +906.360 q^{81} -1050.06 q^{82} +1009.86 q^{83} +73.7771 q^{84} -971.511 q^{85} +1446.31 q^{86} -1077.81 q^{87} +688.686 q^{88} +35.6685 q^{89} +3158.81 q^{90} +450.943 q^{91} +26.5866 q^{92} +2328.19 q^{93} +725.201 q^{94} -1643.28 q^{95} +473.400 q^{96} -127.177 q^{97} +148.268 q^{98} -1866.71 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{3} + 24 q^{4} - 24 q^{5} - 41 q^{6} - 56 q^{7} - 69 q^{8} + 95 q^{9} - 30 q^{10} - 98 q^{11} - 131 q^{12} - 145 q^{13} - 232 q^{15} - 76 q^{16} - 96 q^{17} - 69 q^{18} - 226 q^{19} - 22 q^{20}+ \cdots - 1676 q^{99}+O(q^{100}) $ 8 * q - 3 * q^3 + 24 * q^4 - 24 * q^5 - 41 * q^6 - 56 * q^7 - 69 * q^8 + 95 * q^9 - 30 * q^10 - 98 * q^11 - 131 * q^12 - 145 * q^13 - 232 * q^15 - 76 * q^16 - 96 * q^17 - 69 * q^18 - 226 * q^19 - 22 * q^20 + 21 * q^21 - 98 * q^22 + 184 * q^23 - 216 * q^24 + 60 * q^25 - 185 * q^26 - 531 * q^27 - 168 * q^28 + 73 * q^29 - 416 * q^30 - 987 * q^31 + 118 * q^32 + 16 * q^33 - 846 * q^34 + 168 * q^35 - 69 * q^36 - 2 * q^37 - 454 * q^38 - 675 * q^39 - 640 * q^40 - 907 * q^41 + 287 * q^42 + 636 * q^43 + 126 * q^44 - 126 * q^45 + 421 * q^47 + 2165 * q^48 + 392 * q^49 + 2308 * q^50 - 408 * q^51 - 931 * q^52 + 138 * q^53 + 1717 * q^54 - 90 * q^55 + 483 * q^56 + 984 * q^57 + 1329 * q^58 - 924 * q^59 + 2642 * q^60 - 890 * q^61 + 2175 * q^62 - 665 * q^63 + 303 * q^64 - 392 * q^65 + 408 * q^66 - 1392 * q^67 + 2592 * q^68 - 69 * q^69 + 210 * q^70 + 259 * q^71 + 141 * q^72 - 297 * q^73 + 2314 * q^74 - 851 * q^75 - 428 * q^76 + 686 * q^77 + 6789 * q^78 - 1788 * q^79 - 2104 * q^80 + 2300 * q^81 - 219 * q^82 + 2114 * q^83 + 917 * q^84 + 528 * q^85 - 2360 * q^86 - 2441 * q^87 + 2144 * q^88 - 1040 * q^89 + 4872 * q^90 + 1015 * q^91 + 552 * q^92 - 621 * q^93 - 1009 * q^94 + 1268 * q^95 - 1163 * q^96 - 1452 * q^97 - 1676 * 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 $

$2$	3.02588	1.06981	0.534905	−	0.844912i	$-0.320347\pi$
$2$	3.02588	1.06981	0.534905	+	0.844912i	$0.320347\pi$
$3$	−9.11775	−1.75471	−0.877356	−	0.479840i	$-0.840695\pi$
$3$	−9.11775	−1.75471	−0.877356	+	0.479840i	$0.840695\pi$
$4$	1.15594	0.144493
$5$	18.5973	1.66339	0.831696	−	0.555231i	$-0.187370\pi$
$5$	18.5973	1.66339	0.831696	+	0.555231i	$0.187370\pi$
$6$	−27.5892	−1.87721
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−20.7093	−0.915230
$9$	56.1334	2.07902
$10$	56.2732	1.77951
$11$	−33.2549	−0.911522	−0.455761	−	0.890102i	$-0.650633\pi$
$11$	−33.2549	−0.911522	−0.455761	+	0.890102i	$0.650633\pi$
$12$	−10.5396	−0.253543
$13$	−64.4205	−1.37439	−0.687193	−	0.726475i	$-0.741157\pi$
$13$	−64.4205	−1.37439	−0.687193	+	0.726475i	$0.741157\pi$
$14$	−21.1812	−0.404350
$15$	−169.566	−2.91878
$16$	−71.9113	−1.12361
$17$	−52.2394	−0.745289	−0.372644	−	0.927974i	$-0.621549\pi$
$17$	−52.2394	−0.745289	−0.372644	+	0.927974i	$0.621549\pi$
$18$	169.853	2.22415
$19$	−88.3614	−1.06692	−0.533460	−	0.845825i	$-0.679109\pi$
$19$	−88.3614	−1.06692	−0.533460	+	0.845825i	$0.679109\pi$
$20$	21.4974	0.240348
$21$	63.8243	0.663219
$22$	−100.625	−0.975155
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	188.822	1.60597
$25$	220.859	1.76687
$26$	−194.928	−1.47033
$27$	−265.631	−1.89336
$28$	−8.09159	−0.0546131
$29$	118.211	0.756936	0.378468	−	0.925614i	$-0.376451\pi$
$29$	118.211	0.756936	0.378468	+	0.925614i	$0.376451\pi$
$30$	−513.085	−3.12253
$31$	−255.347	−1.47941	−0.739704	−	0.672932i	$-0.765035\pi$
$31$	−255.347	−1.47941	−0.739704	+	0.672932i	$0.765035\pi$
$32$	−51.9206	−0.286824
$33$	303.210	1.59946
$34$	−158.070	−0.797317
$35$	−130.181	−0.628703
$36$	64.8870	0.300403
$37$	57.9031	0.257276	0.128638	−	0.991692i	$-0.458939\pi$
$37$	57.9031	0.257276	0.128638	+	0.991692i	$0.458939\pi$
$38$	−267.371	−1.14140
$39$	587.370	2.41165
$40$	−385.137	−1.52239
$41$	−347.026	−1.32186	−0.660931	−	0.750446i	$-0.729839\pi$
$41$	−347.026	−1.32186	−0.660931	+	0.750446i	$0.729839\pi$
$42$	193.125	0.709518
$43$	477.979	1.69514	0.847571	−	0.530682i	$-0.178064\pi$
$43$	477.979	1.69514	0.847571	+	0.530682i	$0.178064\pi$
$44$	−38.4407	−0.131708
$45$	1043.93	3.45822
$46$	69.5952	0.223071
$47$	239.666	0.743807	0.371903	−	0.928271i	$-0.378705\pi$
$47$	239.666	0.743807	0.371903	+	0.928271i	$0.378705\pi$
$48$	655.670	1.97162
$49$	49.0000	0.142857
$50$	668.294	1.89022
$51$	476.306	1.30777
$52$	−74.4663	−0.198589
$53$	−402.094	−1.04211	−0.521056	−	0.853523i	$-0.674462\pi$
$53$	−402.094	−1.04211	−0.521056	+	0.853523i	$0.674462\pi$
$54$	−803.769	−2.02554
$55$	−618.452	−1.51622
$56$	144.965	0.345924
$57$	805.657	1.87214
$58$	357.691	0.809777
$59$	−587.617	−1.29663	−0.648315	−	0.761372i	$-0.724526\pi$
$59$	−587.617	−1.29663	−0.648315	+	0.761372i	$0.724526\pi$
$60$	−196.008	−0.421742
$61$	698.764	1.46668	0.733341	−	0.679861i	$-0.237960\pi$
$61$	698.764	1.46668	0.733341	+	0.679861i	$0.237960\pi$
$62$	−772.649	−1.58269
$63$	−392.934	−0.785794
$64$	418.185	0.816768
$65$	−1198.05	−2.28614
$66$	917.477	1.71112
$67$	126.625	0.230890	0.115445	−	0.993314i	$-0.463171\pi$
$67$	126.625	0.230890	0.115445	+	0.993314i	$0.463171\pi$
$68$	−60.3857	−0.107689
$69$	−209.708	−0.365883
$70$	−393.912	−0.672593
$71$	−844.084	−1.41091	−0.705453	−	0.708757i	$-0.749256\pi$
$71$	−844.084	−1.41091	−0.705453	+	0.708757i	$0.749256\pi$
$72$	−1162.48	−1.90278
$73$	712.052	1.14164	0.570818	−	0.821077i	$-0.306626\pi$
$73$	712.052	1.14164	0.570818	+	0.821077i	$0.306626\pi$
$74$	175.208	0.275236
$75$	−2013.74	−3.10036
$76$	−102.141	−0.154162
$77$	232.784	0.344523
$78$	1777.31	2.58001
$79$	−589.839	−0.840026	−0.420013	−	0.907518i	$-0.637974\pi$
$79$	−589.839	−0.840026	−0.420013	+	0.907518i	$0.637974\pi$
$80$	−1337.36	−1.86901
$81$	906.360	1.24329
$82$	−1050.06	−1.41414
$83$	1009.86	1.33550	0.667752	−	0.744384i	$-0.267257\pi$
$83$	1009.86	1.33550	0.667752	+	0.744384i	$0.267257\pi$
$84$	73.7771	0.0958303
$85$	−971.511	−1.23971
$86$	1446.31	1.81348
$87$	−1077.81	−1.32820
$88$	688.686	0.834252
$89$	35.6685	0.0424814	0.0212407	−	0.999774i	$-0.493238\pi$
$89$	35.6685	0.0424814	0.0212407	+	0.999774i	$0.493238\pi$
$90$	3158.81	3.69964
$91$	450.943	0.519469
$92$	26.5866	0.0301288
$93$	2328.19	2.59594
$94$	725.201	0.795731
$95$	−1643.28	−1.77471
$96$	473.400	0.503293
$97$	−127.177	−0.133123	−0.0665613	−	0.997782i	$-0.521203\pi$
$97$	−127.177	−0.133123	−0.0665613	+	0.997782i	$0.521203\pi$
$98$	148.268	0.152830
$99$	−1866.71	−1.89507
$100$	255.300	0.255300
$101$	−1376.80	−1.35641	−0.678203	−	0.734875i	$-0.737241\pi$
$101$	−1376.80	−1.35641	−0.678203	+	0.734875i	$0.737241\pi$
$102$	1441.24	1.39906
$103$	−508.618	−0.486559	−0.243280	−	0.969956i	$-0.578223\pi$
$103$	−508.618	−0.486559	−0.243280	+	0.969956i	$0.578223\pi$
$104$	1334.10	1.25788
$105$	1186.96	1.10319
$106$	−1216.69	−1.11486
$107$	435.724	0.393673	0.196837	−	0.980436i	$-0.436933\pi$
$107$	435.724	0.393673	0.196837	+	0.980436i	$0.436933\pi$
$108$	−307.054	−0.273577
$109$	426.303	0.374610	0.187305	−	0.982302i	$-0.440025\pi$
$109$	426.303	0.374610	0.187305	+	0.982302i	$0.440025\pi$
$110$	−1871.36	−1.62206
$111$	−527.947	−0.451446
$112$	503.379	0.424686
$113$	692.534	0.576532	0.288266	−	0.957550i	$-0.406921\pi$
$113$	692.534	0.576532	0.288266	+	0.957550i	$0.406921\pi$
$114$	2437.82	2.00283
$115$	427.738	0.346841
$116$	136.644	0.109372
$117$	−3616.14	−2.85737
$118$	−1778.06	−1.38715
$119$	365.676	0.281693
$120$	3511.58	2.67135
$121$	−225.110	−0.169128
$122$	2114.38	1.56907
$123$	3164.10	2.31949
$124$	−295.166	−0.213764
$125$	1782.72	1.27561
$126$	−1188.97	−0.840650
$127$	−656.335	−0.458585	−0.229293	−	0.973358i	$-0.573641\pi$
$127$	−656.335	−0.458585	−0.229293	+	0.973358i	$0.573641\pi$
$128$	1680.74	1.16061
$129$	−4358.09	−2.97449
$130$	−3625.14	−2.44574
$131$	1575.99	1.05111	0.525553	−	0.850761i	$-0.323858\pi$
$131$	1575.99	1.05111	0.525553	+	0.850761i	$0.323858\pi$
$132$	350.493	0.231110
$133$	618.530	0.403258
$134$	383.151	0.247009
$135$	−4940.03	−3.14941
$136$	1081.84	0.682111
$137$	792.294	0.494089	0.247045	−	0.969004i	$-0.420541\pi$
$137$	792.294	0.494089	0.247045	+	0.969004i	$0.420541\pi$
$138$	−634.552	−0.391425
$139$	−2675.35	−1.63252	−0.816261	−	0.577684i	$-0.803957\pi$
$139$	−2675.35	−1.63252	−0.816261	+	0.577684i	$0.803957\pi$
$140$	−150.482	−0.0908430
$141$	−2185.22	−1.30517
$142$	−2554.10	−1.50940
$143$	2142.30	1.25278
$144$	−4036.63	−2.33601
$145$	2198.40	1.25908
$146$	2154.58	1.22133
$147$	−446.770	−0.250673
$148$	66.9326	0.0371745
$149$	291.225	0.160121	0.0800607	−	0.996790i	$-0.474489\pi$
$149$	291.225	0.160121	0.0800607	+	0.996790i	$0.474489\pi$
$150$	−6093.34	−3.31679
$151$	2204.34	1.18799	0.593995	−	0.804469i	$-0.297550\pi$
$151$	2204.34	1.18799	0.593995	+	0.804469i	$0.297550\pi$
$152$	1829.90	0.976478
$153$	−2932.38	−1.54947
$154$	704.378	0.368574
$155$	−4748.76	−2.46084
$156$	678.965	0.348466
$157$	−1615.90	−0.821422	−0.410711	−	0.911766i	$-0.634719\pi$
$157$	−1615.90	−0.821422	−0.410711	+	0.911766i	$0.634719\pi$
$158$	−1784.78	−0.898668
$159$	3666.20	1.82861
$160$	−965.583	−0.477100
$161$	−161.000	−0.0788110
$162$	2742.53	1.33009
$163$	336.417	0.161658	0.0808288	−	0.996728i	$-0.474243\pi$
$163$	336.417	0.161658	0.0808288	+	0.996728i	$0.474243\pi$
$164$	−401.142	−0.190999
$165$	5638.89	2.66053
$166$	3055.72	1.42874
$167$	−27.3144	−0.0126566	−0.00632831	−	0.999980i	$-0.502014\pi$
$167$	−27.3144	−0.0126566	−0.00632831	+	0.999980i	$0.502014\pi$
$168$	−1321.76	−0.606998
$169$	1953.00	0.888938
$170$	−2939.68	−1.32625
$171$	−4960.03	−2.21815
$172$	552.516	0.244936
$173$	−2690.54	−1.18242	−0.591208	−	0.806519i	$-0.701349\pi$
$173$	−2690.54	−1.18242	−0.591208	+	0.806519i	$0.701349\pi$
$174$	−3261.34	−1.42093
$175$	−1546.02	−0.667816
$176$	2391.41	1.02420
$177$	5357.75	2.27521
$178$	107.928	0.0454471
$179$	−1251.42	−0.522546	−0.261273	−	0.965265i	$-0.584142\pi$
$179$	−1251.42	−0.522546	−0.261273	+	0.965265i	$0.584142\pi$
$180$	1206.72	0.499687
$181$	193.457	0.0794449	0.0397224	−	0.999211i	$-0.487353\pi$
$181$	193.457	0.0794449	0.0397224	+	0.999211i	$0.487353\pi$
$182$	1364.50	0.555733
$183$	−6371.16	−2.57361
$184$	−476.314	−0.190839
$185$	1076.84	0.427951
$186$	7044.82	2.77716
$187$	1737.22	0.679347
$188$	277.040	0.107475
$189$	1859.42	0.715624
$190$	−4972.37	−1.89860
$191$	−1795.26	−0.680107	−0.340054	−	0.940406i	$-0.610445\pi$
$191$	−1795.26	−0.680107	−0.340054	+	0.940406i	$0.610445\pi$
$192$	−3812.91	−1.43319
$193$	−861.357	−0.321253	−0.160626	−	0.987015i	$-0.551351\pi$
$193$	−861.357	−0.321253	−0.160626	+	0.987015i	$0.551351\pi$
$194$	−384.823	−0.142416
$195$	10923.5	4.01153
$196$	56.6411	0.0206418
$197$	225.099	0.0814092	0.0407046	−	0.999171i	$-0.487040\pi$
$197$	225.099	0.0814092	0.0407046	+	0.999171i	$0.487040\pi$
$198$	−5648.45	−2.02736
$199$	−223.345	−0.0795603	−0.0397801	−	0.999208i	$-0.512666\pi$
$199$	−223.345	−0.0795603	−0.0397801	+	0.999208i	$0.512666\pi$
$200$	−4573.84	−1.61710
$201$	−1154.53	−0.405146
$202$	−4166.04	−1.45110
$203$	−827.474	−0.286095
$204$	550.582	0.188963
$205$	−6453.75	−2.19878
$206$	−1539.02	−0.520526
$207$	1291.07	0.433505
$208$	4632.56	1.54428
$209$	2938.45	0.972521
$210$	3591.59	1.18021
$211$	1347.64	0.439694	0.219847	−	0.975534i	$-0.429444\pi$
$211$	1347.64	0.439694	0.219847	+	0.975534i	$0.429444\pi$
$212$	−464.797	−0.150577
$213$	7696.15	2.47573
$214$	1318.45	0.421155
$215$	8889.11	2.81969
$216$	5501.04	1.73286
$217$	1787.43	0.559164
$218$	1289.94	0.400761
$219$	−6492.32	−2.00324
$220$	−714.894	−0.219082
$221$	3365.29	1.02431
$222$	−1597.50	−0.482961
$223$	1209.59	0.363228	0.181614	−	0.983370i	$-0.441868\pi$
$223$	1209.59	0.363228	0.181614	+	0.983370i	$0.441868\pi$
$224$	363.444	0.108409
$225$	12397.6	3.67336
$226$	2095.52	0.616780
$227$	−3411.17	−0.997390	−0.498695	−	0.866777i	$-0.666187\pi$
$227$	−3411.17	−0.997390	−0.498695	+	0.866777i	$0.666187\pi$
$228$	931.293	0.270510
$229$	512.486	0.147886	0.0739432	−	0.997262i	$-0.476442\pi$
$229$	512.486	0.147886	0.0739432	+	0.997262i	$0.476442\pi$
$230$	1294.28	0.371054
$231$	−2122.47	−0.604538
$232$	−2448.06	−0.692770
$233$	−3903.84	−1.09763	−0.548817	−	0.835942i	$-0.684922\pi$
$233$	−3903.84	−1.09763	−0.548817	+	0.835942i	$0.684922\pi$
$234$	−10942.0	−3.05684
$235$	4457.14	1.23724
$236$	−679.251	−0.187354
$237$	5378.01	1.47400
$238$	1106.49	0.301358
$239$	1424.61	0.385567	0.192784	−	0.981241i	$-0.438248\pi$
$239$	1424.61	0.385567	0.192784	+	0.981241i	$0.438248\pi$
$240$	12193.7	3.27958
$241$	−6444.69	−1.72257	−0.861285	−	0.508123i	$-0.830340\pi$
$241$	−6444.69	−1.72257	−0.861285	+	0.508123i	$0.830340\pi$
$242$	−681.155	−0.180935
$243$	−1091.92	−0.288257
$244$	807.731	0.211925
$245$	911.267	0.237628
$246$	9574.18	2.48141
$247$	5692.28	1.46636
$248$	5288.05	1.35400
$249$	−9207.68	−2.34343
$250$	5394.31	1.36466
$251$	7062.49	1.77602	0.888008	−	0.459827i	$-0.152089\pi$
$251$	7062.49	1.77602	0.888008	+	0.459827i	$0.152089\pi$
$252$	−454.209	−0.113541
$253$	−764.863	−0.190065
$254$	−1985.99	−0.490599
$255$	8858.00	2.17533
$256$	1740.24	0.424864
$257$	−5900.90	−1.43225	−0.716125	−	0.697972i	$-0.754086\pi$
$257$	−5900.90	−1.43225	−0.716125	+	0.697972i	$0.754086\pi$
$258$	−13187.1	−3.18213
$259$	−405.322	−0.0972412
$260$	−1384.87	−0.330331
$261$	6635.56	1.57368
$262$	4768.75	1.12448
$263$	−1634.09	−0.383127	−0.191564	−	0.981480i	$-0.561356\pi$
$263$	−1634.09	−0.383127	−0.191564	+	0.981480i	$0.561356\pi$
$264$	−6279.27	−1.46387
$265$	−7477.86	−1.73344
$266$	1871.60	0.431409
$267$	−325.216	−0.0745427
$268$	146.371	0.0333620
$269$	−2747.85	−0.622824	−0.311412	−	0.950275i	$-0.600802\pi$
$269$	−2747.85	−0.622824	−0.311412	+	0.950275i	$0.600802\pi$
$270$	−14947.9	−3.36927
$271$	−7298.61	−1.63601	−0.818005	−	0.575211i	$-0.804920\pi$
$271$	−7298.61	−1.63601	−0.818005	+	0.575211i	$0.804920\pi$
$272$	3756.60	0.837418
$273$	−4111.59	−0.911519
$274$	2397.39	0.528582
$275$	−7344.66	−1.61054
$276$	−242.411	−0.0528674
$277$	−6341.50	−1.37554	−0.687769	−	0.725930i	$-0.741410\pi$
$277$	−6341.50	−1.37554	−0.687769	+	0.725930i	$0.741410\pi$
$278$	−8095.29	−1.74649
$279$	−14333.5	−3.07571
$280$	2695.96	0.575408
$281$	−5340.75	−1.13382	−0.566908	−	0.823781i	$-0.691861\pi$
$281$	−5340.75	−1.13382	−0.566908	+	0.823781i	$0.691861\pi$
$282$	−6612.20	−1.39628
$283$	−4744.66	−0.996611	−0.498305	−	0.867002i	$-0.666044\pi$
$283$	−4744.66	−0.996611	−0.498305	+	0.867002i	$0.666044\pi$
$284$	−975.711	−0.203866
$285$	14983.0	3.11410
$286$	6482.33	1.34024
$287$	2429.18	0.499617
$288$	−2914.48	−0.596311
$289$	−2184.05	−0.444544
$290$	6652.08	1.34698
$291$	1159.57	0.233592
$292$	823.090	0.164958
$293$	7990.45	1.59320	0.796599	−	0.604508i	$-0.206630\pi$
$293$	7990.45	1.59320	0.796599	+	0.604508i	$0.206630\pi$
$294$	−1351.87	−0.268173
$295$	−10928.1	−2.15681
$296$	−1199.13	−0.235467
$297$	8833.56	1.72584
$298$	881.212	0.171300
$299$	−1481.67	−0.286579
$300$	−2327.77	−0.447979
$301$	−3345.85	−0.640703
$302$	6670.06	1.27092
$303$	12553.3	2.38010
$304$	6354.18	1.19881
$305$	12995.1	2.43967
$306$	−8873.01	−1.65764
$307$	4925.41	0.915662	0.457831	−	0.889039i	$-0.348627\pi$
$307$	4925.41	0.915662	0.457831	+	0.889039i	$0.348627\pi$
$308$	269.085	0.0497810
$309$	4637.45	0.853771
$310$	−14369.2	−2.63263
$311$	2905.57	0.529774	0.264887	−	0.964279i	$-0.414665\pi$
$311$	2905.57	0.529774	0.264887	+	0.964279i	$0.414665\pi$
$312$	−12164.0	−2.20722
$313$	−2970.69	−0.536464	−0.268232	−	0.963354i	$-0.586439\pi$
$313$	−2970.69	−0.536464	−0.268232	+	0.963354i	$0.586439\pi$
$314$	−4889.53	−0.878765
$315$	−7307.51	−1.30708
$316$	−681.819	−0.121378
$317$	−799.754	−0.141699	−0.0708497	−	0.997487i	$-0.522571\pi$
$317$	−799.754	−0.141699	−0.0708497	+	0.997487i	$0.522571\pi$
$318$	11093.5	1.95626
$319$	−3931.08	−0.689963
$320$	7777.11	1.35861
$321$	−3972.83	−0.690783
$322$	−487.166	−0.0843128
$323$	4615.94	0.795164
$324$	1047.70	0.179647
$325$	−14227.9	−2.42837
$326$	1017.96	0.172943
$327$	−3886.93	−0.657332
$328$	7186.67	1.20981
$329$	−1677.66	−0.281132
$330$	17062.6	2.84626
$331$	7735.22	1.28449	0.642245	−	0.766500i	$-0.278003\pi$
$331$	7735.22	1.28449	0.642245	+	0.766500i	$0.278003\pi$
$332$	1167.34	0.192971
$333$	3250.30	0.534881
$334$	−82.6502	−0.0135402
$335$	2354.88	0.384061
$336$	−4589.69	−0.745203
$337$	11779.0	1.90398	0.951990	−	0.306128i	$-0.0990337\pi$
$337$	11779.0	1.90398	0.951990	+	0.306128i	$0.0990337\pi$
$338$	5909.53	0.950994
$339$	−6314.36	−1.01165
$340$	−1123.01	−0.179129
$341$	8491.54	1.34851
$342$	−15008.4	−2.37299
$343$	−343.000	−0.0539949
$344$	−9898.60	−1.55144
$345$	−3900.01	−0.608607
$346$	−8141.25	−1.26496
$347$	5624.50	0.870141	0.435071	−	0.900396i	$-0.356723\pi$
$347$	5624.50	0.870141	0.435071	+	0.900396i	$0.356723\pi$
$348$	−1245.89	−0.191916
$349$	−3023.16	−0.463684	−0.231842	−	0.972753i	$-0.574475\pi$
$349$	−3023.16	−0.463684	−0.231842	+	0.972753i	$0.574475\pi$
$350$	−4678.05	−0.714436
$351$	17112.1	2.60221
$352$	1726.62	0.261446
$353$	404.183	0.0609419	0.0304709	−	0.999536i	$-0.490299\pi$
$353$	404.183	0.0609419	0.0304709	+	0.999536i	$0.490299\pi$
$354$	16211.9	2.43405
$355$	−15697.7	−2.34689
$356$	41.2306	0.00613826
$357$	−3334.14	−0.494290
$358$	−3786.65	−0.559024
$359$	2268.39	0.333485	0.166742	−	0.986001i	$-0.446675\pi$
$359$	2268.39	0.333485	0.166742	+	0.986001i	$0.446675\pi$
$360$	−21619.0	−3.16507
$361$	948.734	0.138320
$362$	585.377	0.0849909
$363$	2052.50	0.296772
$364$	521.264	0.0750595
$365$	13242.2	1.89899
$366$	−19278.4	−2.75327
$367$	−129.076	−0.0183589	−0.00917945	−	0.999958i	$-0.502922\pi$
$367$	−129.076	−0.0183589	−0.00917945	+	0.999958i	$0.502922\pi$
$368$	−1653.96	−0.234290
$369$	−19479.8	−2.74817
$370$	3258.39	0.457826
$371$	2814.66	0.393881
$372$	2691.25	0.375094
$373$	1354.27	0.187994	0.0939969	−	0.995572i	$-0.470036\pi$
$373$	1354.27	0.187994	0.0939969	+	0.995572i	$0.470036\pi$
$374$	5256.61	0.726772
$375$	−16254.4	−2.23834
$376$	−4963.32	−0.680754
$377$	−7615.18	−1.04032
$378$	5626.38	0.765581
$379$	−10233.1	−1.38691	−0.693455	−	0.720500i	$-0.743912\pi$
$379$	−10233.1	−1.38691	−0.693455	+	0.720500i	$0.743912\pi$
$380$	−1899.54	−0.256432
$381$	5984.30	0.804685
$382$	−5432.24	−0.727585
$383$	5780.40	0.771188	0.385594	−	0.922669i	$-0.373997\pi$
$383$	5780.40	0.771188	0.385594	+	0.922669i	$0.373997\pi$
$384$	−15324.6	−2.03654
$385$	4329.16	0.573077
$386$	−2606.36	−0.343679
$387$	26830.6	3.52423
$388$	−147.009	−0.0192352
$389$	11762.5	1.53311	0.766556	−	0.642177i	$-0.221969\pi$
$389$	11762.5	1.53311	0.766556	+	0.642177i	$0.221969\pi$
$390$	33053.2	4.29157
$391$	−1201.51	−0.155403
$392$	−1014.76	−0.130747
$393$	−14369.5	−1.84439
$394$	681.121	0.0870924
$395$	−10969.4	−1.39729
$396$	−2157.81	−0.273823
$397$	−454.539	−0.0574626	−0.0287313	−	0.999587i	$-0.509147\pi$
$397$	−454.539	−0.0574626	−0.0287313	+	0.999587i	$0.509147\pi$
$398$	−675.814	−0.0851144
$399$	−5639.60	−0.707602
$400$	−15882.3	−1.98529
$401$	−11330.2	−1.41098	−0.705491	−	0.708719i	$-0.749273\pi$
$401$	−11330.2	−1.41098	−0.705491	+	0.708719i	$0.749273\pi$
$402$	−3493.47	−0.433429
$403$	16449.6	2.03328
$404$	−1591.50	−0.195991
$405$	16855.8	2.06808
$406$	−2503.83	−0.306067
$407$	−1925.56	−0.234513
$408$	−9863.96	−1.19691
$409$	−1009.32	−0.122024	−0.0610121	−	0.998137i	$-0.519433\pi$
$409$	−1009.32	−0.122024	−0.0610121	+	0.998137i	$0.519433\pi$
$410$	−19528.3	−2.35227
$411$	−7223.94	−0.866985
$412$	−587.932	−0.0703042
$413$	4113.32	0.490080
$414$	3906.62	0.463768
$415$	18780.7	2.22147
$416$	3344.75	0.394206
$417$	24393.2	2.86461
$418$	8891.40	1.04041
$419$	−14056.5	−1.63891	−0.819455	−	0.573143i	$-0.805724\pi$
$419$	−14056.5	−1.63891	−0.819455	+	0.573143i	$0.805724\pi$
$420$	1372.05	0.159403
$421$	−3217.99	−0.372531	−0.186265	−	0.982499i	$-0.559638\pi$
$421$	−3217.99	−0.372531	−0.186265	+	0.982499i	$0.559638\pi$
$422$	4077.80	0.470389
$423$	13453.3	1.54639
$424$	8327.09	0.953771
$425$	−11537.6	−1.31683
$426$	23287.6	2.64856
$427$	−4891.35	−0.554354
$428$	503.671	0.0568829
$429$	−19532.9	−2.19827
$430$	26897.4	3.01653
$431$	872.562	0.0975170	0.0487585	−	0.998811i	$-0.484474\pi$
$431$	872.562	0.0975170	0.0487585	+	0.998811i	$0.484474\pi$
$432$	19101.9	2.12741
$433$	−9665.82	−1.07277	−0.536385	−	0.843973i	$-0.680211\pi$
$433$	−9665.82	−1.07277	−0.536385	+	0.843973i	$0.680211\pi$
$434$	5408.54	0.598199
$435$	−20044.4	−2.20933
$436$	492.782	0.0541284
$437$	−2032.31	−0.222468
$438$	−19645.0	−2.14309
$439$	15457.9	1.68055	0.840277	−	0.542158i	$-0.182392\pi$
$439$	15457.9	1.68055	0.840277	+	0.542158i	$0.182392\pi$
$440$	12807.7	1.38769
$441$	2750.54	0.297002
$442$	10182.9	1.09582
$443$	−10487.1	−1.12473	−0.562365	−	0.826889i	$-0.690108\pi$
$443$	−10487.1	−1.12473	−0.562365	+	0.826889i	$0.690108\pi$
$444$	−610.275	−0.0652306
$445$	663.337	0.0706633
$446$	3660.06	0.388585
$447$	−2655.32	−0.280967
$448$	−2927.30	−0.308709
$449$	6169.92	0.648500	0.324250	−	0.945971i	$-0.394888\pi$
$449$	6169.92	0.648500	0.324250	+	0.945971i	$0.394888\pi$
$450$	37513.6	3.92980
$451$	11540.3	1.20491
$452$	800.529	0.0833047
$453$	−20098.6	−2.08458
$454$	−10321.8	−1.06702
$455$	8386.32	0.864081
$456$	−16684.6	−1.71344
$457$	−16296.4	−1.66808	−0.834039	−	0.551706i	$-0.813977\pi$
$457$	−16296.4	−1.66808	−0.834039	+	0.551706i	$0.813977\pi$
$458$	1550.72	0.158210
$459$	13876.4	1.41110
$460$	494.440	0.0501160
$461$	18404.0	1.85935	0.929673	−	0.368386i	$-0.120089\pi$
$461$	18404.0	1.85935	0.929673	+	0.368386i	$0.120089\pi$
$462$	−6422.34	−0.646741
$463$	−13024.1	−1.30730	−0.653650	−	0.756797i	$-0.726763\pi$
$463$	−13024.1	−1.30730	−0.653650	+	0.756797i	$0.726763\pi$
$464$	−8500.68	−0.850504
$465$	43298.0	4.31806
$466$	−11812.5	−1.17426
$467$	−2332.68	−0.231142	−0.115571	−	0.993299i	$-0.536870\pi$
$467$	−2332.68	−0.231142	−0.115571	+	0.993299i	$0.536870\pi$
$468$	−4180.05	−0.412869
$469$	−886.372	−0.0872684
$470$	13486.8	1.32361
$471$	14733.4	1.44136
$472$	12169.1	1.18672
$473$	−15895.2	−1.54516
$474$	16273.2	1.57690
$475$	−19515.4	−1.88512
$476$	422.700	0.0407025
$477$	−22570.9	−2.16657
$478$	4310.71	0.412484
$479$	16019.5	1.52808	0.764040	−	0.645169i	$-0.223213\pi$
$479$	16019.5	1.52808	0.764040	+	0.645169i	$0.223213\pi$
$480$	8803.95	0.837174
$481$	−3730.15	−0.353597
$482$	−19500.9	−1.84282
$483$	1467.96	0.138291
$484$	−260.214	−0.0244378
$485$	−2365.15	−0.221435
$486$	−3304.00	−0.308380
$487$	−1579.85	−0.147002	−0.0735010	−	0.997295i	$-0.523417\pi$
$487$	−1579.85	−0.147002	−0.0735010	+	0.997295i	$0.523417\pi$
$488$	−14470.9	−1.34235
$489$	−3067.36	−0.283663
$490$	2757.38	0.254216
$491$	−20545.3	−1.88838	−0.944191	−	0.329399i	$-0.893154\pi$
$491$	−20545.3	−1.88838	−0.944191	+	0.329399i	$0.893154\pi$
$492$	3657.51	0.335149
$493$	−6175.24	−0.564136
$494$	17224.2	1.56873
$495$	−34715.8	−3.15224
$496$	18362.3	1.66228
$497$	5908.59	0.533272
$498$	−27861.3	−2.50702
$499$	−1331.47	−0.119448	−0.0597242	−	0.998215i	$-0.519022\pi$
$499$	−1331.47	−0.119448	−0.0597242	+	0.998215i	$0.519022\pi$
$500$	2060.72	0.184317
$501$	249.046	0.0222087
$502$	21370.2	1.90000
$503$	−927.686	−0.0822335	−0.0411168	−	0.999154i	$-0.513092\pi$
$503$	−927.686	−0.0822335	−0.0411168	+	0.999154i	$0.513092\pi$
$504$	8137.39	0.719182
$505$	−25604.8	−2.25624
$506$	−2314.38	−0.203334
$507$	−17806.9	−1.55983
$508$	−758.685	−0.0662622
$509$	6991.85	0.608857	0.304429	−	0.952535i	$-0.401534\pi$
$509$	6991.85	0.608857	0.304429	+	0.952535i	$0.401534\pi$
$510$	26803.2	2.32719
$511$	−4984.36	−0.431498
$512$	−8180.18	−0.706086
$513$	23471.6	2.02007
$514$	−17855.4	−1.53223
$515$	−9458.91	−0.809339
$516$	−5037.70	−0.429792
$517$	−7970.08	−0.677996
$518$	−1226.45	−0.104030
$519$	24531.7	2.07480
$520$	24810.7	2.09235
$521$	15300.3	1.28660	0.643302	−	0.765613i	$-0.277564\pi$
$521$	15300.3	1.28660	0.643302	+	0.765613i	$0.277564\pi$
$522$	20078.4	1.68354
$523$	13089.8	1.09441	0.547206	−	0.836998i	$-0.315691\pi$
$523$	13089.8	1.09441	0.547206	+	0.836998i	$0.315691\pi$
$524$	1821.75	0.151877
$525$	14096.2	1.17182
$526$	−4944.57	−0.409873
$527$	13339.2	1.10259
$528$	−21804.3	−1.79717
$529$	529.000	0.0434783
$530$	−22627.1	−1.85445
$531$	−32985.0	−2.69572
$532$	714.984	0.0582678
$533$	22355.6	1.81675
$534$	−984.065	−0.0797465
$535$	8103.29	0.654833
$536$	−2622.31	−0.211318
$537$	11410.2	0.916917
$538$	−8314.68	−0.666303
$539$	−1629.49	−0.130217
$540$	−5710.38	−0.455066
$541$	1599.69	0.127128	0.0635638	−	0.997978i	$-0.479753\pi$
$541$	1599.69	0.127128	0.0635638	+	0.997978i	$0.479753\pi$
$542$	−22084.7	−1.75022
$543$	−1763.89	−0.139403
$544$	2712.30	0.213767
$545$	7928.09	0.623123
$546$	−12441.2	−0.975152
$547$	18730.5	1.46409	0.732045	−	0.681256i	$-0.238566\pi$
$547$	18730.5	1.46409	0.732045	+	0.681256i	$0.238566\pi$
$548$	915.845	0.0713923
$549$	39224.0	3.04926
$550$	−22224.1	−1.72298
$551$	−10445.2	−0.807591
$552$	4342.91	0.334867
$553$	4128.87	0.317500
$554$	−19188.6	−1.47156
$555$	−9818.38	−0.750931
$556$	−3092.55	−0.235887
$557$	−5488.44	−0.417509	−0.208755	−	0.977968i	$-0.566941\pi$
$557$	−5488.44	−0.417509	−0.208755	+	0.977968i	$0.566941\pi$
$558$	−43371.4	−3.29043
$559$	−30791.6	−2.32978
$560$	9361.49	0.706420
$561$	−15839.5	−1.19206
$562$	−16160.5	−1.21297
$563$	−8122.20	−0.608010	−0.304005	−	0.952670i	$-0.598324\pi$
$563$	−8122.20	−0.608010	−0.304005	+	0.952670i	$0.598324\pi$
$564$	−2525.98	−0.188587
$565$	12879.3	0.958999
$566$	−14356.8	−1.06618
$567$	−6344.52	−0.469920
$568$	17480.4	1.29130
$569$	−15394.8	−1.13424	−0.567120	−	0.823635i	$-0.691943\pi$
$569$	−15394.8	−1.13424	−0.567120	+	0.823635i	$0.691943\pi$
$570$	45336.9	3.33150
$571$	1704.64	0.124934	0.0624668	−	0.998047i	$-0.480103\pi$
$571$	1704.64	0.124934	0.0624668	+	0.998047i	$0.480103\pi$
$572$	2476.37	0.181018
$573$	16368.7	1.19339
$574$	7350.41	0.534495
$575$	5079.76	0.368419
$576$	23474.2	1.69807
$577$	−2603.58	−0.187848	−0.0939241	−	0.995579i	$-0.529941\pi$
$577$	−2603.58	−0.187848	−0.0939241	+	0.995579i	$0.529941\pi$
$578$	−6608.66	−0.475578
$579$	7853.64	0.563706
$580$	2541.22	0.181928
$581$	−7069.04	−0.504773
$582$	3508.72	0.249899
$583$	13371.6	0.949907
$584$	−14746.1	−1.04486
$585$	−67250.5	−4.75293
$586$	24178.1	1.70442
$587$	8901.60	0.625909	0.312954	−	0.949768i	$-0.398681\pi$
$587$	8901.60	0.625909	0.312954	+	0.949768i	$0.398681\pi$
$588$	−516.440	−0.0362204
$589$	22562.8	1.57841
$590$	−33067.1	−2.30737
$591$	−2052.39	−0.142850
$592$	−4163.89	−0.289079
$593$	−642.837	−0.0445163	−0.0222581	−	0.999752i	$-0.507086\pi$
$593$	−642.837	−0.0445163	−0.0222581	+	0.999752i	$0.507086\pi$
$594$	26729.3	1.84632
$595$	6800.58	0.468566
$596$	336.639	0.0231364
$597$	2036.40	0.139605
$598$	−4483.36	−0.306585
$599$	−14923.7	−1.01797	−0.508987	−	0.860774i	$-0.669980\pi$
$599$	−14923.7	−1.01797	−0.508987	+	0.860774i	$0.669980\pi$
$600$	41703.1	2.83754
$601$	−9190.75	−0.623791	−0.311896	−	0.950116i	$-0.600964\pi$
$601$	−9190.75	−0.623791	−0.311896	+	0.950116i	$0.600964\pi$
$602$	−10124.1	−0.685431
$603$	7107.88	0.480025
$604$	2548.09	0.171656
$605$	−4186.43	−0.281327
$606$	37984.9	2.54626
$607$	−16137.4	−1.07907	−0.539535	−	0.841963i	$-0.681400\pi$
$607$	−16137.4	−1.07907	−0.539535	+	0.841963i	$0.681400\pi$
$608$	4587.78	0.306018
$609$	7544.70	0.502014
$610$	39321.7	2.60998
$611$	−15439.4	−1.02228
$612$	−3389.65	−0.223887
$613$	−12316.5	−0.811516	−0.405758	−	0.913981i	$-0.632992\pi$
$613$	−12316.5	−0.811516	−0.405758	+	0.913981i	$0.632992\pi$
$614$	14903.7	0.979584
$615$	58843.7	3.85822
$616$	−4820.80	−0.315318
$617$	−11398.5	−0.743735	−0.371868	−	0.928286i	$-0.621282\pi$
$617$	−11398.5	−0.743735	−0.371868	+	0.928286i	$0.621282\pi$
$618$	14032.4	0.913373
$619$	7815.13	0.507458	0.253729	−	0.967275i	$-0.418343\pi$
$619$	7815.13	0.507458	0.253729	+	0.967275i	$0.418343\pi$
$620$	−5489.29	−0.355573
$621$	−6109.52	−0.394794
$622$	8791.90	0.566758
$623$	−249.679	−0.0160565
$624$	−42238.6	−2.70977
$625$	5546.43	0.354971
$626$	−8988.94	−0.573914
$627$	−26792.1	−1.70650
$628$	−1867.89	−0.118689
$629$	−3024.82	−0.191745
$630$	−22111.6	−1.39833
$631$	−30593.9	−1.93015	−0.965073	−	0.261982i	$-0.915624\pi$
$631$	−30593.9	−1.93015	−0.965073	+	0.261982i	$0.915624\pi$
$632$	12215.1	0.768817
$633$	−12287.5	−0.771536
$634$	−2419.96	−0.151591
$635$	−12206.1	−0.762807
$636$	4237.91	0.264220
$637$	−3156.60	−0.196341
$638$	−11895.0	−0.738130
$639$	−47381.3	−2.93330
$640$	31257.3	1.93055
$641$	22556.1	1.38988	0.694938	−	0.719069i	$-0.255432\pi$
$641$	22556.1	1.38988	0.694938	+	0.719069i	$0.255432\pi$
$642$	−12021.3	−0.739007
$643$	17917.3	1.09890	0.549448	−	0.835528i	$-0.314838\pi$
$643$	17917.3	1.09890	0.549448	+	0.835528i	$0.314838\pi$
$644$	−186.107	−0.0113876
$645$	−81048.8	−4.94774
$646$	13967.3	0.850674
$647$	−13444.1	−0.816911	−0.408455	−	0.912778i	$-0.633932\pi$
$647$	−13444.1	−0.816911	−0.408455	+	0.912778i	$0.633932\pi$
$648$	−18770.1	−1.13790
$649$	19541.2	1.18191
$650$	−43051.8	−2.59789
$651$	−16297.3	−0.981172
$652$	388.878	0.0233583
$653$	14177.3	0.849616	0.424808	−	0.905283i	$-0.360342\pi$
$653$	14177.3	0.849616	0.424808	+	0.905283i	$0.360342\pi$
$654$	−11761.4	−0.703221
$655$	29309.1	1.74840
$656$	24955.1	1.48526
$657$	39969.9	2.37348
$658$	−5076.41	−0.300758
$659$	12726.7	0.752292	0.376146	−	0.926560i	$-0.377249\pi$
$659$	12726.7	0.752292	0.376146	+	0.926560i	$0.377249\pi$
$660$	6518.23	0.384427
$661$	18860.6	1.10982	0.554911	−	0.831909i	$-0.312752\pi$
$661$	18860.6	1.10982	0.554911	+	0.831909i	$0.312752\pi$
$662$	23405.8	1.37416
$663$	−30683.8	−1.79738
$664$	−20913.5	−1.22229
$665$	11503.0	0.670776
$666$	9835.02	0.572221
$667$	2718.84	0.157832
$668$	−31.5739	−0.00182879
$669$	−11028.7	−0.637361
$670$	7125.57	0.410873
$671$	−23237.4	−1.33691
$672$	−3313.80	−0.190227
$673$	22067.4	1.26395	0.631974	−	0.774989i	$-0.282245\pi$
$673$	22067.4	1.26395	0.631974	+	0.774989i	$0.282245\pi$
$674$	35641.7	2.03690
$675$	−58667.2	−3.34534
$676$	2257.55	0.128445
$677$	19136.3	1.08636	0.543181	−	0.839616i	$-0.317220\pi$
$677$	19136.3	1.08636	0.543181	+	0.839616i	$0.317220\pi$
$678$	−19106.5	−1.08227
$679$	890.240	0.0503156
$680$	20119.3	1.13462
$681$	31102.2	1.75013
$682$	25694.4	1.44265
$683$	27945.8	1.56562	0.782808	−	0.622263i	$-0.213787\pi$
$683$	27945.8	1.56562	0.782808	+	0.622263i	$0.213787\pi$
$684$	−5733.50	−0.320506
$685$	14734.5	0.821865
$686$	−1037.88	−0.0577643
$687$	−4672.72	−0.259498
$688$	−34372.1	−1.90469
$689$	25903.1	1.43226
$690$	−11800.9	−0.651093
$691$	−28123.0	−1.54826	−0.774131	−	0.633025i	$-0.781813\pi$
$691$	−28123.0	−1.54826	−0.774131	+	0.633025i	$0.781813\pi$
$692$	−3110.11	−0.170850
$693$	13067.0	0.716268
$694$	17019.1	0.930885
$695$	−49754.3	−2.71552
$696$	22320.8	1.21561
$697$	18128.4	0.985170
$698$	−9147.70	−0.496054
$699$	35594.2	1.92603
$700$	−1787.10	−0.0964945
$701$	3602.16	0.194082	0.0970410	−	0.995280i	$-0.469062\pi$
$701$	3602.16	0.194082	0.0970410	+	0.995280i	$0.469062\pi$
$702$	51779.1	2.78387
$703$	−5116.40	−0.274493
$704$	−13906.7	−0.744502
$705$	−40639.1	−2.17100
$706$	1223.01	0.0651962
$707$	9637.62	0.512673
$708$	6193.24	0.328752
$709$	−2994.24	−0.158605	−0.0793025	−	0.996851i	$-0.525269\pi$
$709$	−2994.24	−0.158605	−0.0793025	+	0.996851i	$0.525269\pi$
$710$	−47499.3	−2.51073
$711$	−33109.7	−1.74643
$712$	−738.668	−0.0388803
$713$	−5872.98	−0.308478
$714$	−10088.7	−0.528796
$715$	39840.9	2.08387
$716$	−1446.57	−0.0755040
$717$	−12989.3	−0.676560
$718$	6863.87	0.356765
$719$	29085.7	1.50864	0.754321	−	0.656506i	$-0.227966\pi$
$719$	29085.7	1.50864	0.754321	+	0.656506i	$0.227966\pi$
$720$	−75070.4	−3.88571
$721$	3560.32	0.183902
$722$	2870.75	0.147976
$723$	58761.1	3.02261
$724$	223.625	0.0114792
$725$	26107.9	1.33741
$726$	6210.60	0.317489
$727$	−15224.7	−0.776691	−0.388346	−	0.921514i	$-0.626953\pi$
$727$	−15224.7	−0.776691	−0.388346	+	0.921514i	$0.626953\pi$
$728$	−9338.71	−0.475434
$729$	−14515.9	−0.737484
$730$	40069.4	2.03156
$731$	−24969.3	−1.26337
$732$	−7364.69	−0.371867
$733$	26889.5	1.35496	0.677480	−	0.735542i	$-0.263072\pi$
$733$	26889.5	1.35496	0.677480	+	0.735542i	$0.263072\pi$
$734$	−390.569	−0.0196405
$735$	−8308.71	−0.416968
$736$	−1194.17	−0.0598069
$737$	−4210.89	−0.210462
$738$	−58943.4	−2.94002
$739$	−26240.9	−1.30621	−0.653104	−	0.757269i	$-0.726533\pi$
$739$	−26240.9	−1.30621	−0.653104	+	0.757269i	$0.726533\pi$
$740$	1244.77	0.0618358
$741$	−51900.8	−2.57304
$742$	8516.82	0.421378
$743$	16294.7	0.804571	0.402285	−	0.915514i	$-0.368216\pi$
$743$	16294.7	0.804571	0.402285	+	0.915514i	$0.368216\pi$
$744$	−48215.2	−2.37588
$745$	5416.00	0.266345
$746$	4097.87	0.201118
$747$	56687.1	2.77653
$748$	2008.12	0.0981607
$749$	−3050.07	−0.148795
$750$	−49184.0	−2.39459
$751$	10383.4	0.504522	0.252261	−	0.967659i	$-0.418826\pi$
$751$	10383.4	0.504522	0.252261	+	0.967659i	$0.418826\pi$
$752$	−17234.7	−0.835752
$753$	−64394.0	−3.11640
$754$	−23042.6	−1.11295
$755$	40994.7	1.97609
$756$	2149.38	0.103402
$757$	7102.44	0.341008	0.170504	−	0.985357i	$-0.445460\pi$
$757$	7102.44	0.341008	0.170504	+	0.985357i	$0.445460\pi$
$758$	−30964.1	−1.48373
$759$	6973.84	0.333510
$760$	34031.2	1.62427
$761$	−7096.71	−0.338049	−0.169025	−	0.985612i	$-0.554062\pi$
$761$	−7096.71	−0.338049	−0.169025	+	0.985612i	$0.554062\pi$
$762$	18107.8	0.860860
$763$	−2984.12	−0.141589
$764$	−2075.22	−0.0982705
$765$	−54534.3	−2.57737
$766$	17490.8	0.825024
$767$	37854.5	1.78207
$768$	−15867.1	−0.745514
$769$	17765.5	0.833080	0.416540	−	0.909117i	$-0.363243\pi$
$769$	17765.5	0.833080	0.416540	+	0.909117i	$0.363243\pi$
$770$	13099.5	0.613083
$771$	53803.0	2.51319
$772$	−995.678	−0.0464187
$773$	−22105.9	−1.02858	−0.514291	−	0.857616i	$-0.671945\pi$
$773$	−22105.9	−1.02858	−0.514291	+	0.857616i	$0.671945\pi$
$774$	81186.1	3.77025
$775$	−56395.7	−2.61393
$776$	2633.75	0.121838
$777$	3695.63	0.170630
$778$	35591.8	1.64014
$779$	30663.7	1.41032
$780$	12626.9	0.579636
$781$	28069.9	1.28607
$782$	−3635.61	−0.166252
$783$	−31400.4	−1.43315
$784$	−3523.66	−0.160516
$785$	−30051.5	−1.36635
$786$	−43480.3	−1.97314
$787$	42605.5	1.92976	0.964881	−	0.262686i	$-0.0846085\pi$
$787$	42605.5	1.92976	0.964881	+	0.262686i	$0.0846085\pi$
$788$	260.201	0.0117630
$789$	14899.3	0.672278
$790$	−33192.1	−1.49484
$791$	−4847.74	−0.217909
$792$	38658.3	1.73442
$793$	−45014.7	−2.01579
$794$	−1375.38	−0.0614741
$795$	68181.3	3.04169
$796$	−258.174	−0.0114959
$797$	−24457.1	−1.08697	−0.543485	−	0.839419i	$-0.682895\pi$
$797$	−24457.1	−1.08697	−0.543485	+	0.839419i	$0.682895\pi$
$798$	−17064.7	−0.756999
$799$	−12520.0	−0.554351
$800$	−11467.2	−0.506781
$801$	2002.19	0.0883196
$802$	−34283.8	−1.50948
$803$	−23679.2	−1.04063
$804$	−1334.57	−0.0585407
$805$	−2994.16	−0.131094
$806$	49774.4	2.17522
$807$	25054.3	1.09288
$808$	28512.6	1.24142
$809$	15019.4	0.652725	0.326362	−	0.945245i	$-0.394177\pi$
$809$	15019.4	0.652725	0.326362	+	0.945245i	$0.394177\pi$
$810$	51003.7	2.21245
$811$	−4964.25	−0.214943	−0.107471	−	0.994208i	$-0.534275\pi$
$811$	−4964.25	−0.214943	−0.107471	+	0.994208i	$0.534275\pi$
$812$	−956.511	−0.0413386
$813$	66546.9	2.87073
$814$	−5826.52	−0.250884
$815$	6256.44	0.268900
$816$	−34251.8	−1.46943
$817$	−42234.9	−1.80858
$818$	−3054.09	−0.130543
$819$	25313.0	1.07998
$820$	−7460.15	−0.317707
$821$	−40616.6	−1.72659	−0.863293	−	0.504703i	$-0.831602\pi$
$821$	−40616.6	−1.72659	−0.863293	+	0.504703i	$0.831602\pi$
$822$	−21858.8	−0.927509
$823$	1222.42	0.0517752	0.0258876	−	0.999665i	$-0.491759\pi$
$823$	1222.42	0.0517752	0.0258876	+	0.999665i	$0.491759\pi$
$824$	10533.1	0.445313
$825$	66966.8	2.82604
$826$	12446.4	0.524293
$827$	726.223	0.0305360	0.0152680	−	0.999883i	$-0.495140\pi$
$827$	726.223	0.0305360	0.0152680	+	0.999883i	$0.495140\pi$
$828$	1492.40	0.0626383
$829$	36946.4	1.54789	0.773945	−	0.633253i	$-0.218281\pi$
$829$	36946.4	1.54789	0.773945	+	0.633253i	$0.218281\pi$
$830$	56828.2	2.37655
$831$	57820.2	2.41367
$832$	−26939.7	−1.12255
$833$	−2559.73	−0.106470
$834$	73810.9	3.06458
$835$	−507.975	−0.0210529
$836$	3396.68	0.140522
$837$	67828.2	2.80106
$838$	−42533.2	−1.75332
$839$	−3592.55	−0.147829	−0.0739145	−	0.997265i	$-0.523549\pi$
$839$	−3592.55	−0.147829	−0.0739145	+	0.997265i	$0.523549\pi$
$840$	−24581.1	−1.00968
$841$	−10415.3	−0.427048
$842$	−9737.26	−0.398537
$843$	48695.6	1.98952
$844$	1557.79	0.0635325
$845$	36320.4	1.47865
$846$	40708.0	1.65434
$847$	1575.77	0.0639245
$848$	28915.1	1.17093
$849$	43260.6	1.74877
$850$	−34911.2	−1.40876
$851$	1331.77	0.0536458
$852$	8896.30	0.357725
$853$	18955.7	0.760880	0.380440	−	0.924806i	$-0.375773\pi$
$853$	18955.7	0.760880	0.380440	+	0.924806i	$0.375773\pi$
$854$	−14800.6	−0.593053
$855$	−92243.1	−3.68965
$856$	−9023.54	−0.360302
$857$	26150.7	1.04235	0.521174	−	0.853451i	$-0.325494\pi$
$857$	26150.7	1.04235	0.521174	+	0.853451i	$0.325494\pi$
$858$	−59104.3	−2.35173
$859$	18422.9	0.731757	0.365879	−	0.930663i	$-0.380768\pi$
$859$	18422.9	0.731757	0.365879	+	0.930663i	$0.380768\pi$
$860$	10275.3	0.407424
$861$	−22148.7	−0.876685
$862$	2640.27	0.104325
$863$	23731.6	0.936077	0.468038	−	0.883708i	$-0.344961\pi$
$863$	23731.6	0.936077	0.468038	+	0.883708i	$0.344961\pi$
$864$	13791.8	0.543061
$865$	−50036.8	−1.96682
$866$	−29247.6	−1.14766
$867$	19913.6	0.780048
$868$	2066.16	0.0807951
$869$	19615.0	0.765702
$870$	−60652.0	−2.36356
$871$	−8157.22	−0.317333
$872$	−8828.44	−0.342854
$873$	−7138.89	−0.276764
$874$	−6149.53	−0.237999
$875$	−12479.1	−0.482137
$876$	−7504.74	−0.289454
$877$	−27340.9	−1.05272	−0.526360	−	0.850262i	$-0.676444\pi$
$877$	−27340.9	−1.05272	−0.526360	+	0.850262i	$0.676444\pi$
$878$	46773.6	1.79787
$879$	−72855.0	−2.79561
$880$	44473.7	1.70364
$881$	−29829.5	−1.14073	−0.570363	−	0.821393i	$-0.693198\pi$
$881$	−29829.5	−1.14073	−0.570363	+	0.821393i	$0.693198\pi$
$882$	8322.80	0.317736
$883$	28971.8	1.10417	0.552084	−	0.833789i	$-0.313833\pi$
$883$	28971.8	1.10417	0.552084	+	0.833789i	$0.313833\pi$
$884$	3890.07	0.148006
$885$	99639.6	3.78457
$886$	−31732.6	−1.20325
$887$	13412.2	0.507708	0.253854	−	0.967243i	$-0.418302\pi$
$887$	13412.2	0.507708	0.253854	+	0.967243i	$0.418302\pi$
$888$	10933.4	0.413177
$889$	4594.34	0.173329
$890$	2007.18	0.0755963
$891$	−30140.9	−1.13329
$892$	1398.21	0.0524838
$893$	−21177.2	−0.793583
$894$	−8034.68	−0.300581
$895$	−23273.1	−0.869198
$896$	−11765.2	−0.438669
$897$	13509.5	0.502864
$898$	18669.4	0.693772
$899$	−30184.7	−1.11982
$900$	14330.9	0.530774
$901$	21005.2	0.776674
$902$	34919.6	1.28902
$903$	30506.7	1.12425
$904$	−14341.9	−0.527660
$905$	3597.77	0.132148
$906$	−60816.0	−2.23010
$907$	−21692.1	−0.794129	−0.397064	−	0.917791i	$-0.629971\pi$
$907$	−21692.1	−0.794129	−0.397064	+	0.917791i	$0.629971\pi$
$908$	−3943.12	−0.144116
$909$	−77284.7	−2.81999
$910$	25376.0	0.924402
$911$	−6922.04	−0.251742	−0.125871	−	0.992047i	$-0.540173\pi$
$911$	−6922.04	−0.251742	−0.125871	+	0.992047i	$0.540173\pi$
$912$	−57935.9	−2.10356
$913$	−33582.9	−1.21734
$914$	−49310.8	−1.78453
$915$	−118486.	−4.28092
$916$	592.403	0.0213685
$917$	−11031.9	−0.397281
$918$	41988.4	1.50961
$919$	−32716.2	−1.17433	−0.587164	−	0.809468i	$-0.699755\pi$
$919$	−32716.2	−1.17433	−0.587164	+	0.809468i	$0.699755\pi$
$920$	−8858.15	−0.317440
$921$	−44908.7	−1.60672
$922$	55688.2	1.98915
$923$	54376.3	1.93913
$924$	−2453.45	−0.0873514
$925$	12788.4	0.454575
$926$	−39409.2	−1.39856
$927$	−28550.5	−1.01156
$928$	−6137.56	−0.217107
$929$	9370.01	0.330915	0.165458	−	0.986217i	$-0.447090\pi$
$929$	9370.01	0.330915	0.165458	+	0.986217i	$0.447090\pi$
$930$	131015.	4.61950
$931$	−4329.71	−0.152417
$932$	−4512.60	−0.158600
$933$	−26492.3	−0.929602
$934$	−7058.40	−0.247278
$935$	32307.5	1.13002
$936$	74887.7	2.61515
$937$	−50755.5	−1.76960	−0.884798	−	0.465975i	$-0.845704\pi$
$937$	−50755.5	−1.76960	−0.884798	+	0.465975i	$0.845704\pi$
$938$	−2682.06	−0.0933606
$939$	27086.0	0.941340
$940$	5152.20	0.178772
$941$	1528.30	0.0529449	0.0264724	−	0.999650i	$-0.491573\pi$
$941$	1528.30	0.0529449	0.0264724	+	0.999650i	$0.491573\pi$
$942$	44581.5	1.54198
$943$	−7981.60	−0.275627
$944$	42256.3	1.45691
$945$	34580.2	1.19036
$946$	−48096.8	−1.65303
$947$	14564.9	0.499786	0.249893	−	0.968274i	$-0.419605\pi$
$947$	14564.9	0.499786	0.249893	+	0.968274i	$0.419605\pi$
$948$	6216.66	0.212983
$949$	−45870.7	−1.56905
$950$	−59051.3	−2.01671
$951$	7291.96	0.248642
$952$	−7572.88	−0.257814
$953$	−26605.3	−0.904334	−0.452167	−	0.891933i	$-0.649349\pi$
$953$	−26605.3	−0.904334	−0.452167	+	0.891933i	$0.649349\pi$
$954$	−68296.9	−2.31781
$955$	−33387.0	−1.13129
$956$	1646.77	0.0557117
$957$	35842.6	1.21069
$958$	48473.1	1.63475
$959$	−5546.06	−0.186748
$960$	−70909.8	−2.38396
$961$	35411.0	1.18865
$962$	−11287.0	−0.378281
$963$	24458.7	0.818453
$964$	−7449.69	−0.248899
$965$	−16018.9	−0.534370
$966$	4441.86	0.147945
$967$	−13268.4	−0.441244	−0.220622	−	0.975359i	$-0.570809\pi$
$967$	−13268.4	−0.441244	−0.220622	+	0.975359i	$0.570809\pi$
$968$	4661.86	0.154791
$969$	−42087.0	−1.39528
$970$	−7156.66	−0.236893
$971$	−40126.2	−1.32617	−0.663085	−	0.748544i	$-0.730753\pi$
$971$	−40126.2	−1.32617	−0.663085	+	0.748544i	$0.730753\pi$
$972$	−1262.19	−0.0416510
$973$	18727.5	0.617035
$974$	−4780.44	−0.157264
$975$	129726.	4.26109
$976$	−50249.1	−1.64799
$977$	997.072	0.0326501	0.0163251	−	0.999867i	$-0.494803\pi$
$977$	997.072	0.0326501	0.0163251	+	0.999867i	$0.494803\pi$
$978$	−9281.47	−0.303465
$979$	−1186.15	−0.0387228
$980$	1053.37	0.0343354
$981$	23929.9	0.778820
$982$	−62167.5	−2.02021
$983$	−20022.9	−0.649677	−0.324838	−	0.945770i	$-0.605310\pi$
$983$	−20022.9	−0.649677	−0.324838	+	0.945770i	$0.605310\pi$
$984$	−65526.2	−2.12287
$985$	4186.23	0.135415
$986$	−18685.5	−0.603518
$987$	15296.5	0.493307
$988$	6579.94	0.211878
$989$	10993.5	0.353462
$990$	−105046.	−3.37230
$991$	1277.26	0.0409419	0.0204710	−	0.999790i	$-0.493483\pi$
$991$	1277.26	0.0409419	0.0204710	+	0.999790i	$0.493483\pi$
$992$	13257.8	0.424329
$993$	−70527.8	−2.25391
$994$	17878.7	0.570500
$995$	−4153.61	−0.132340
$996$	−10643.5	−0.338608
$997$	59113.7	1.87778	0.938891	−	0.344215i	$-0.111855\pi$
$997$	59113.7	1.87778	0.938891	+	0.344215i	$0.111855\pi$
$998$	−4028.87	−0.127787
$999$	−15380.9	−0.487117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.b.1.7	✓	8
3.2	odd	2		1449.4.a.i.1.2		8
7.6	odd	2		1127.4.a.e.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.b.1.7	✓	8	1.1	even	1	trivial
1127.4.a.e.1.7		8	7.6	odd	2
1449.4.a.i.1.2		8	3.2	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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q+3.02588 q^{2} -9.11775 q^{3} +1.15594 q^{4} +18.5973 q^{5} -27.5892 q^{6} -7.00000 q^{7} -20.7093 q^{8} +56.1334 q^{9} +56.2732 q^{10} -33.2549 q^{11} -10.5396 q^{12} -64.4205 q^{13} -21.1812 q^{14} -169.566 q^{15} -71.9113 q^{16} -52.2394 q^{17} +169.853 q^{18} -88.3614 q^{19} +21.4974 q^{20} +63.8243 q^{21} -100.625 q^{22} +23.0000 q^{23} +188.822 q^{24} +220.859 q^{25} -194.928 q^{26} -265.631 q^{27} -8.09159 q^{28} +118.211 q^{29} -513.085 q^{30} -255.347 q^{31} -51.9206 q^{32} +303.210 q^{33} -158.070 q^{34} -130.181 q^{35} +64.8870 q^{36} +57.9031 q^{37} -267.371 q^{38} +587.370 q^{39} -385.137 q^{40} -347.026 q^{41} +193.125 q^{42} +477.979 q^{43} -38.4407 q^{44} +1043.93 q^{45} +69.5952 q^{46} +239.666 q^{47} +655.670 q^{48} +49.0000 q^{49} +668.294 q^{50} +476.306 q^{51} -74.4663 q^{52} -402.094 q^{53} -803.769 q^{54} -618.452 q^{55} +144.965 q^{56} +805.657 q^{57} +357.691 q^{58} -587.617 q^{59} -196.008 q^{60} +698.764 q^{61} -772.649 q^{62} -392.934 q^{63} +418.185 q^{64} -1198.05 q^{65} +917.477 q^{66} +126.625 q^{67} -60.3857 q^{68} -209.708 q^{69} -393.912 q^{70} -844.084 q^{71} -1162.48 q^{72} +712.052 q^{73} +175.208 q^{74} -2013.74 q^{75} -102.141 q^{76} +232.784 q^{77} +1777.31 q^{78} -589.839 q^{79} -1337.36 q^{80} +906.360 q^{81} -1050.06 q^{82} +1009.86 q^{83} +73.7771 q^{84} -971.511 q^{85} +1446.31 q^{86} -1077.81 q^{87} +688.686 q^{88} +35.6685 q^{89} +3158.81 q^{90} +450.943 q^{91} +26.5866 q^{92} +2328.19 q^{93} +725.201 q^{94} -1643.28 q^{95} +473.400 q^{96} -127.177 q^{97} +148.268 q^{98} -1866.71 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{3} + 24 q^{4} - 24 q^{5} - 41 q^{6} - 56 q^{7} - 69 q^{8} + 95 q^{9} - 30 q^{10} - 98 q^{11} - 131 q^{12} - 145 q^{13} - 232 q^{15} - 76 q^{16} - 96 q^{17} - 69 q^{18} - 226 q^{19} - 22 q^{20}+ \cdots - 1676 q^{99}+O(q^{100}) \) 8 * q - 3 * q^3 + 24 * q^4 - 24 * q^5 - 41 * q^6 - 56 * q^7 - 69 * q^8 + 95 * q^9 - 30 * q^10 - 98 * q^11 - 131 * q^12 - 145 * q^13 - 232 * q^15 - 76 * q^16 - 96 * q^17 - 69 * q^18 - 226 * q^19 - 22 * q^20 + 21 * q^21 - 98 * q^22 + 184 * q^23 - 216 * q^24 + 60 * q^25 - 185 * q^26 - 531 * q^27 - 168 * q^28 + 73 * q^29 - 416 * q^30 - 987 * q^31 + 118 * q^32 + 16 * q^33 - 846 * q^34 + 168 * q^35 - 69 * q^36 - 2 * q^37 - 454 * q^38 - 675 * q^39 - 640 * q^40 - 907 * q^41 + 287 * q^42 + 636 * q^43 + 126 * q^44 - 126 * q^45 + 421 * q^47 + 2165 * q^48 + 392 * q^49 + 2308 * q^50 - 408 * q^51 - 931 * q^52 + 138 * q^53 + 1717 * q^54 - 90 * q^55 + 483 * q^56 + 984 * q^57 + 1329 * q^58 - 924 * q^59 + 2642 * q^60 - 890 * q^61 + 2175 * q^62 - 665 * q^63 + 303 * q^64 - 392 * q^65 + 408 * q^66 - 1392 * q^67 + 2592 * q^68 - 69 * q^69 + 210 * q^70 + 259 * q^71 + 141 * q^72 - 297 * q^73 + 2314 * q^74 - 851 * q^75 - 428 * q^76 + 686 * q^77 + 6789 * q^78 - 1788 * q^79 - 2104 * q^80 + 2300 * q^81 - 219 * q^82 + 2114 * q^83 + 917 * q^84 + 528 * q^85 - 2360 * q^86 - 2441 * q^87 + 2144 * q^88 - 1040 * q^89 + 4872 * q^90 + 1015 * q^91 + 552 * q^92 - 621 * q^93 - 1009 * q^94 + 1268 * q^95 - 1163 * q^96 - 1452 * q^97 - 1676 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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