LMFDB - Embedded newform 161.4.a.d.1.6

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 = [12] 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:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 76 x^{10} + 311 x^{9} + 1979 x^{8} - 8466 x^{7} - 19942 x^{6} + 95647 x^{5} + \cdots - 70656 $ x^12 - 4x^11 - 76x^10 + 311x^9 + 1979x^8 - 8466x^7 - 19942x^6 + 95647x^5 + 50294x^4 - 400320x^3 + 178432x^2 + 227072*x - 70656
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.285899$ 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)

$f(q)$	$=$	\(q+0.285899 q^{2} +8.01264 q^{3} -7.91826 q^{4} +1.18183 q^{5} +2.29081 q^{6} +7.00000 q^{7} -4.55102 q^{8} +37.2024 q^{9} +0.337884 q^{10} +31.7112 q^{11} -63.4462 q^{12} +72.6373 q^{13} +2.00129 q^{14} +9.46956 q^{15} +62.0450 q^{16} +20.0013 q^{17} +10.6361 q^{18} +13.6521 q^{19} -9.35802 q^{20} +56.0885 q^{21} +9.06621 q^{22} +23.0000 q^{23} -36.4657 q^{24} -123.603 q^{25} +20.7669 q^{26} +81.7482 q^{27} -55.4278 q^{28} -184.094 q^{29} +2.70734 q^{30} +38.7916 q^{31} +54.1468 q^{32} +254.090 q^{33} +5.71836 q^{34} +8.27280 q^{35} -294.578 q^{36} -275.999 q^{37} +3.90312 q^{38} +582.016 q^{39} -5.37852 q^{40} +369.378 q^{41} +16.0357 q^{42} -146.345 q^{43} -251.098 q^{44} +43.9668 q^{45} +6.57568 q^{46} +28.1535 q^{47} +497.144 q^{48} +49.0000 q^{49} -35.3381 q^{50} +160.263 q^{51} -575.161 q^{52} -159.958 q^{53} +23.3717 q^{54} +37.4772 q^{55} -31.8571 q^{56} +109.389 q^{57} -52.6323 q^{58} -271.921 q^{59} -74.9825 q^{60} +851.565 q^{61} +11.0905 q^{62} +260.417 q^{63} -480.879 q^{64} +85.8448 q^{65} +72.6443 q^{66} -526.926 q^{67} -158.376 q^{68} +184.291 q^{69} +2.36519 q^{70} -518.035 q^{71} -169.309 q^{72} -945.822 q^{73} -78.9079 q^{74} -990.389 q^{75} -108.101 q^{76} +221.978 q^{77} +166.398 q^{78} -291.790 q^{79} +73.3265 q^{80} -349.446 q^{81} +105.605 q^{82} -186.718 q^{83} -444.123 q^{84} +23.6381 q^{85} -41.8400 q^{86} -1475.08 q^{87} -144.318 q^{88} -1594.45 q^{89} +12.5701 q^{90} +508.461 q^{91} -182.120 q^{92} +310.823 q^{93} +8.04906 q^{94} +16.1344 q^{95} +433.858 q^{96} +1491.44 q^{97} +14.0091 q^{98} +1179.73 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * 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 $

$2$	0.285899	0.101081	0.0505403	−	0.998722i	$-0.483906\pi$
$2$	0.285899	0.101081	0.0505403	+	0.998722i	$0.483906\pi$
$3$	8.01264	1.54203	0.771017	−	0.636815i	$-0.219748\pi$
$3$	8.01264	1.54203	0.771017	+	0.636815i	$0.219748\pi$
$4$	−7.91826	−0.989783
$5$	1.18183	0.105706	0.0528530	−	0.998602i	$-0.483169\pi$
$5$	1.18183	0.105706	0.0528530	+	0.998602i	$0.483169\pi$
$6$	2.29081	0.155870
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−4.55102	−0.201129
$9$	37.2024	1.37787
$10$	0.337884	0.0106848
$11$	31.7112	0.869208	0.434604	−	0.900622i	$-0.356888\pi$
$11$	31.7112	0.869208	0.434604	+	0.900622i	$0.356888\pi$
$12$	−63.4462	−1.52628
$13$	72.6373	1.54969	0.774845	−	0.632152i	$-0.217828\pi$
$13$	72.6373	1.54969	0.774845	+	0.632152i	$0.217828\pi$
$14$	2.00129	0.0382049
$15$	9.46956	0.163002
$16$	62.0450	0.969453
$17$	20.0013	0.285355	0.142677	−	0.989769i	$-0.454429\pi$
$17$	20.0013	0.285355	0.142677	+	0.989769i	$0.454429\pi$
$18$	10.6361	0.139276
$19$	13.6521	0.164842	0.0824211	−	0.996598i	$-0.473735\pi$
$19$	13.6521	0.164842	0.0824211	+	0.996598i	$0.473735\pi$
$20$	−9.35802	−0.104626
$21$	56.0885	0.582834
$22$	9.06621	0.0878601
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−36.4657	−0.310147
$25$	−123.603	−0.988826
$26$	20.7669	0.156644
$27$	81.7482	0.582683
$28$	−55.4278	−0.374103
$29$	−184.094	−1.17881	−0.589403	−	0.807839i	$-0.700637\pi$
$29$	−184.094	−1.17881	−0.589403	+	0.807839i	$0.700637\pi$
$30$	2.70734	0.0164764
$31$	38.7916	0.224748	0.112374	−	0.993666i	$-0.464155\pi$
$31$	38.7916	0.224748	0.112374	+	0.993666i	$0.464155\pi$
$32$	54.1468	0.299121
$33$	254.090	1.34035
$34$	5.71836	0.0288438
$35$	8.27280	0.0399531
$36$	−294.578	−1.36379
$37$	−275.999	−1.22632	−0.613162	−	0.789958i	$-0.710103\pi$
$37$	−275.999	−1.22632	−0.613162	+	0.789958i	$0.710103\pi$
$38$	3.90312	0.0166624
$39$	582.016	2.38967
$40$	−5.37852	−0.0212605
$41$	369.378	1.40701	0.703503	−	0.710693i	$-0.251618\pi$
$41$	369.378	1.40701	0.703503	+	0.710693i	$0.251618\pi$
$42$	16.0357	0.0589132
$43$	−146.345	−0.519010	−0.259505	−	0.965742i	$-0.583559\pi$
$43$	−146.345	−0.519010	−0.259505	+	0.965742i	$0.583559\pi$
$44$	−251.098	−0.860327
$45$	43.9668	0.145649
$46$	6.57568	0.0210768
$47$	28.1535	0.0873746	0.0436873	−	0.999045i	$-0.486089\pi$
$47$	28.1535	0.0873746	0.0436873	+	0.999045i	$0.486089\pi$
$48$	497.144	1.49493
$49$	49.0000	0.142857
$50$	−35.3381	−0.0999512
$51$	160.263	0.440027
$52$	−575.161	−1.53386
$53$	−159.958	−0.414565	−0.207282	−	0.978281i	$-0.566462\pi$
$53$	−159.958	−0.414565	−0.207282	+	0.978281i	$0.566462\pi$
$54$	23.3717	0.0588980
$55$	37.4772	0.0918804
$56$	−31.8571	−0.0760194
$57$	109.389	0.254192
$58$	−52.6323	−0.119155
$59$	−271.921	−0.600019	−0.300010	−	0.953936i	$-0.596990\pi$
$59$	−271.921	−0.600019	−0.300010	+	0.953936i	$0.596990\pi$
$60$	−74.9825	−0.161337
$61$	851.565	1.78741	0.893703	−	0.448659i	$-0.148098\pi$
$61$	851.565	1.78741	0.893703	+	0.448659i	$0.148098\pi$
$62$	11.0905	0.0227176
$63$	260.417	0.520785
$64$	−480.879	−0.939217
$65$	85.8448	0.163811
$66$	72.6443	0.135483
$67$	−526.926	−0.960811	−0.480405	−	0.877047i	$-0.659510\pi$
$67$	−526.926	−0.960811	−0.480405	+	0.877047i	$0.659510\pi$
$68$	−158.376	−0.282439
$69$	184.291	0.321536
$70$	2.36519	0.00403848
$71$	−518.035	−0.865908	−0.432954	−	0.901416i	$-0.642529\pi$
$71$	−518.035	−0.865908	−0.432954	+	0.901416i	$0.642529\pi$
$72$	−169.309	−0.277128
$73$	−945.822	−1.51644	−0.758220	−	0.651999i	$-0.773931\pi$
$73$	−945.822	−1.51644	−0.758220	+	0.651999i	$0.773931\pi$
$74$	−78.9079	−0.123958
$75$	−990.389	−1.52480
$76$	−108.101	−0.163158
$77$	221.978	0.328530
$78$	166.398	0.241550
$79$	−291.790	−0.415556	−0.207778	−	0.978176i	$-0.566623\pi$
$79$	−291.790	−0.415556	−0.207778	+	0.978176i	$0.566623\pi$
$80$	73.3265	0.102477
$81$	−349.446	−0.479350
$82$	105.605	0.142221
$83$	−186.718	−0.246927	−0.123463	−	0.992349i	$-0.539400\pi$
$83$	−186.718	−0.246927	−0.123463	+	0.992349i	$0.539400\pi$
$84$	−444.123	−0.576879
$85$	23.6381	0.0301637
$86$	−41.8400	−0.0524618
$87$	−1475.08	−1.81776
$88$	−144.318	−0.174822
$89$	−1594.45	−1.89900	−0.949502	−	0.313762i	$-0.898410\pi$
$89$	−1594.45	−1.89900	−0.949502	+	0.313762i	$0.898410\pi$
$90$	12.5701	0.0147223
$91$	508.461	0.585728
$92$	−182.120	−0.206384
$93$	310.823	0.346568
$94$	8.04906	0.00883188
$95$	16.1344	0.0174248
$96$	433.858	0.461255
$97$	1491.44	1.56116	0.780579	−	0.625057i	$-0.214924\pi$
$97$	1491.44	1.56116	0.780579	+	0.625057i	$0.214924\pi$
$98$	14.0091	0.0144401
$99$	1179.73	1.19765
$100$	978.723	0.978723
$101$	366.255	0.360829	0.180414	−	0.983591i	$-0.442256\pi$
$101$	366.255	0.360829	0.180414	+	0.983591i	$0.442256\pi$
$102$	45.8192	0.0444782
$103$	84.9358	0.0812522	0.0406261	−	0.999174i	$-0.487065\pi$
$103$	84.9358	0.0812522	0.0406261	+	0.999174i	$0.487065\pi$
$104$	−330.574	−0.311687
$105$	66.2869	0.0616090
$106$	−45.7319	−0.0419045
$107$	351.855	0.317898	0.158949	−	0.987287i	$-0.449189\pi$
$107$	351.855	0.317898	0.158949	+	0.987287i	$0.449189\pi$
$108$	−647.303	−0.576730
$109$	600.614	0.527784	0.263892	−	0.964552i	$-0.414994\pi$
$109$	600.614	0.527784	0.263892	+	0.964552i	$0.414994\pi$
$110$	10.7147	0.00928733
$111$	−2211.48	−1.89103
$112$	434.315	0.366419
$113$	1910.01	1.59008	0.795040	−	0.606557i	$-0.207450\pi$
$113$	1910.01	1.59008	0.795040	+	0.606557i	$0.207450\pi$
$114$	31.2743	0.0256939
$115$	27.1820	0.0220412
$116$	1457.70	1.16676
$117$	2702.28	2.13527
$118$	−77.7421	−0.0606504
$119$	140.009	0.107854
$120$	−43.0962	−0.0327844
$121$	−325.400	−0.244478
$122$	243.462	0.180672
$123$	2959.70	2.16965
$124$	−307.162	−0.222451
$125$	−293.806	−0.210231
$126$	74.4530	0.0526412
$127$	1005.09	0.702264	0.351132	−	0.936326i	$-0.385797\pi$
$127$	1005.09	0.702264	0.351132	+	0.936326i	$0.385797\pi$
$128$	−570.657	−0.394058
$129$	−1172.61	−0.800330
$130$	24.5430	0.0165582
$131$	−2320.66	−1.54776	−0.773882	−	0.633329i	$-0.781688\pi$
$131$	−2320.66	−1.54776	−0.773882	+	0.633329i	$0.781688\pi$
$132$	−2011.95	−1.32665
$133$	95.5645	0.0623045
$134$	−150.648	−0.0971194
$135$	96.6123	0.0615930
$136$	−91.0264	−0.0573930
$137$	−205.180	−0.127954	−0.0639771	−	0.997951i	$-0.520378\pi$
$137$	−205.180	−0.127954	−0.0639771	+	0.997951i	$0.520378\pi$
$138$	52.6886	0.0325011
$139$	1770.21	1.08019	0.540097	−	0.841603i	$-0.318388\pi$
$139$	1770.21	1.08019	0.540097	+	0.841603i	$0.318388\pi$
$140$	−65.5062	−0.0395449
$141$	225.584	0.134735
$142$	−148.106	−0.0875265
$143$	2303.42	1.34700
$144$	2308.22	1.33578
$145$	−217.567	−0.124607
$146$	−270.410	−0.153283
$147$	392.619	0.220290
$148$	2185.43	1.21379
$149$	−368.593	−0.202660	−0.101330	−	0.994853i	$-0.532310\pi$
$149$	−368.593	−0.202660	−0.101330	+	0.994853i	$0.532310\pi$
$150$	−283.151	−0.154128
$151$	−2276.05	−1.22664	−0.613319	−	0.789835i	$-0.710166\pi$
$151$	−2276.05	−1.22664	−0.613319	+	0.789835i	$0.710166\pi$
$152$	−62.1309	−0.0331545
$153$	744.097	0.393181
$154$	63.4635	0.0332080
$155$	45.8450	0.0237572
$156$	−4608.56	−2.36526
$157$	−807.171	−0.410314	−0.205157	−	0.978729i	$-0.565770\pi$
$157$	−807.171	−0.410314	−0.205157	+	0.978729i	$0.565770\pi$
$158$	−83.4224	−0.0420046
$159$	−1281.69	−0.639273
$160$	63.9922	0.0316189
$161$	161.000	0.0788110
$162$	−99.9064	−0.0484530
$163$	1437.21	0.690619	0.345310	−	0.938489i	$-0.387774\pi$
$163$	1437.21	0.690619	0.345310	+	0.938489i	$0.387774\pi$
$164$	−2924.84	−1.39263
$165$	300.291	0.141683
$166$	−53.3824	−0.0249595
$167$	−825.363	−0.382446	−0.191223	−	0.981547i	$-0.561245\pi$
$167$	−825.363	−0.382446	−0.191223	+	0.981547i	$0.561245\pi$
$168$	−255.260	−0.117224
$169$	3079.18	1.40154
$170$	6.75812	0.00304897
$171$	507.890	0.227131
$172$	1158.80	0.513707
$173$	−1946.81	−0.855567	−0.427783	−	0.903881i	$-0.640705\pi$
$173$	−1946.81	−0.855567	−0.427783	+	0.903881i	$0.640705\pi$
$174$	−421.724	−0.183740
$175$	−865.223	−0.373741
$176$	1967.52	0.842656
$177$	−2178.81	−0.925250
$178$	−455.852	−0.191952
$179$	−4486.84	−1.87353	−0.936766	−	0.349955i	$-0.886197\pi$
$179$	−4486.84	−1.87353	−0.936766	+	0.349955i	$0.886197\pi$
$180$	−348.141	−0.144161
$181$	3696.70	1.51809	0.759043	−	0.651040i	$-0.225667\pi$
$181$	3696.70	1.51809	0.759043	+	0.651040i	$0.225667\pi$
$182$	145.369	0.0592057
$183$	6823.29	2.75624
$184$	−104.673	−0.0419382
$185$	−326.183	−0.129630
$186$	88.8641	0.0350314
$187$	634.266	0.248033
$188$	−222.927	−0.0864819
$189$	572.237	0.220233
$190$	4.61281	0.00176131
$191$	−476.055	−0.180346	−0.0901732	−	0.995926i	$-0.528742\pi$
$191$	−476.055	−0.180346	−0.0901732	+	0.995926i	$0.528742\pi$
$192$	−3853.11	−1.44830
$193$	2944.00	1.09800	0.548999	−	0.835823i	$-0.315009\pi$
$193$	2944.00	1.09800	0.548999	+	0.835823i	$0.315009\pi$
$194$	426.400	0.157803
$195$	687.843	0.252603
$196$	−387.995	−0.141398
$197$	2016.48	0.729282	0.364641	−	0.931148i	$-0.381192\pi$
$197$	2016.48	0.729282	0.364641	+	0.931148i	$0.381192\pi$
$198$	337.285	0.121059
$199$	4289.24	1.52792	0.763960	−	0.645264i	$-0.223252\pi$
$199$	4289.24	1.52792	0.763960	+	0.645264i	$0.223252\pi$
$200$	562.521	0.198881
$201$	−4222.07	−1.48160
$202$	104.712	0.0364728
$203$	−1288.66	−0.445547
$204$	−1269.01	−0.435531
$205$	436.542	0.148729
$206$	24.2831	0.00821302
$207$	855.655	0.287305
$208$	4506.78	1.50235
$209$	432.924	0.143282
$210$	18.9514	0.00622748
$211$	1988.13	0.648665	0.324332	−	0.945943i	$-0.394860\pi$
$211$	1988.13	0.648665	0.324332	+	0.945943i	$0.394860\pi$
$212$	1266.59	0.410329
$213$	−4150.83	−1.33526
$214$	100.595	0.0321334
$215$	−172.955	−0.0548624
$216$	−372.037	−0.117194
$217$	271.541	0.0849466
$218$	171.715	0.0533487
$219$	−7578.53	−2.33840
$220$	−296.754	−0.0909417
$221$	1452.84	0.442211
$222$	−632.261	−0.191147
$223$	1580.63	0.474648	0.237324	−	0.971430i	$-0.423730\pi$
$223$	1580.63	0.474648	0.237324	+	0.971430i	$0.423730\pi$
$224$	379.027	0.113057
$225$	−4598.34	−1.36247
$226$	546.072	0.160726
$227$	−2405.09	−0.703223	−0.351611	−	0.936146i	$-0.614366\pi$
$227$	−2405.09	−0.703223	−0.351611	+	0.936146i	$0.614366\pi$
$228$	−866.172	−0.251595
$229$	−907.778	−0.261955	−0.130977	−	0.991385i	$-0.541812\pi$
$229$	−907.778	−0.261955	−0.130977	+	0.991385i	$0.541812\pi$
$230$	7.77133	0.00222794
$231$	1778.63	0.506604
$232$	837.815	0.237092
$233$	1225.43	0.344551	0.172275	−	0.985049i	$-0.444888\pi$
$233$	1225.43	0.344551	0.172275	+	0.985049i	$0.444888\pi$
$234$	772.580	0.215834
$235$	33.2726	0.00923601
$236$	2153.14	0.593889
$237$	−2338.01	−0.640801
$238$	40.0285	0.0109019
$239$	−3705.62	−1.00292	−0.501458	−	0.865182i	$-0.667203\pi$
$239$	−3705.62	−1.00292	−0.501458	+	0.865182i	$0.667203\pi$
$240$	587.539	0.158023
$241$	−4555.74	−1.21768	−0.608840	−	0.793293i	$-0.708365\pi$
$241$	−4555.74	−1.21768	−0.608840	+	0.793293i	$0.708365\pi$
$242$	−93.0315	−0.0247120
$243$	−5007.19	−1.32186
$244$	−6742.92	−1.76914
$245$	57.9096	0.0151008
$246$	846.175	0.219310
$247$	991.650	0.255454
$248$	−176.541	−0.0452032
$249$	−1496.10	−0.380769
$250$	−83.9990	−0.0212503
$251$	3971.26	0.998659	0.499330	−	0.866412i	$-0.333580\pi$
$251$	3971.26	0.998659	0.499330	+	0.866412i	$0.333580\pi$
$252$	−2062.05	−0.515464
$253$	729.358	0.181242
$254$	287.355	0.0709853
$255$	189.404	0.0465134
$256$	3683.88	0.899385
$257$	−7259.92	−1.76211	−0.881054	−	0.473016i	$-0.843165\pi$
$257$	−7259.92	−1.76211	−0.881054	+	0.473016i	$0.843165\pi$
$258$	−335.249	−0.0808979
$259$	−1931.99	−0.463507
$260$	−679.742	−0.162138
$261$	−6848.74	−1.62424
$262$	−663.476	−0.156449
$263$	4800.96	1.12563	0.562813	−	0.826584i	$-0.309719\pi$
$263$	4800.96	1.12563	0.562813	+	0.826584i	$0.309719\pi$
$264$	−1156.37	−0.269582
$265$	−189.043	−0.0438219
$266$	27.3218	0.00629778
$267$	−12775.7	−2.92833
$268$	4172.34	0.950994
$269$	−1420.11	−0.321879	−0.160939	−	0.986964i	$-0.551452\pi$
$269$	−1420.11	−0.321879	−0.160939	+	0.986964i	$0.551452\pi$
$270$	27.6214	0.00622586
$271$	2645.39	0.592975	0.296487	−	0.955037i	$-0.404185\pi$
$271$	2645.39	0.592975	0.296487	+	0.955037i	$0.404185\pi$
$272$	1240.98	0.276638
$273$	4074.12	0.903211
$274$	−58.6608	−0.0129337
$275$	−3919.61	−0.859496
$276$	−1459.26	−0.318251
$277$	−5695.33	−1.23538	−0.617688	−	0.786424i	$-0.711930\pi$
$277$	−5695.33	−1.23538	−0.617688	+	0.786424i	$0.711930\pi$
$278$	506.100	0.109187
$279$	1443.14	0.309672
$280$	−37.6497	−0.00803570
$281$	−4990.88	−1.05954	−0.529770	−	0.848141i	$-0.677722\pi$
$281$	−4990.88	−1.05954	−0.529770	+	0.848141i	$0.677722\pi$
$282$	64.4942	0.0136191
$283$	7756.10	1.62916	0.814580	−	0.580052i	$-0.196968\pi$
$283$	7756.10	1.62916	0.814580	+	0.580052i	$0.196968\pi$
$284$	4101.94	0.857061
$285$	129.279	0.0268696
$286$	658.545	0.136156
$287$	2585.65	0.531798
$288$	2014.39	0.412149
$289$	−4512.95	−0.918573
$290$	−62.2024	−0.0125953
$291$	11950.3	2.40736
$292$	7489.27	1.50095
$293$	6638.53	1.32364	0.661821	−	0.749662i	$-0.269784\pi$
$293$	6638.53	1.32364	0.661821	+	0.749662i	$0.269784\pi$
$294$	112.250	0.0222671
$295$	−321.364	−0.0634256
$296$	1256.08	0.246649
$297$	2592.33	0.506473
$298$	−105.381	−0.0204850
$299$	1670.66	0.323133
$300$	7842.16	1.50922
$301$	−1024.42	−0.196167
$302$	−650.721	−0.123989
$303$	2934.67	0.556410
$304$	847.043	0.159807
$305$	1006.40	0.188939
$306$	212.737	0.0397430
$307$	1231.52	0.228946	0.114473	−	0.993426i	$-0.463482\pi$
$307$	1231.52	0.228946	0.114473	+	0.993426i	$0.463482\pi$
$308$	−1757.68	−0.325173
$309$	680.560	0.125294
$310$	13.1071	0.00240139
$311$	−2628.36	−0.479230	−0.239615	−	0.970868i	$-0.577021\pi$
$311$	−2628.36	−0.479230	−0.239615	+	0.970868i	$0.577021\pi$
$312$	−2648.77	−0.480631
$313$	−209.150	−0.0377695	−0.0188847	−	0.999822i	$-0.506012\pi$
$313$	−209.150	−0.0377695	−0.0188847	+	0.999822i	$0.506012\pi$
$314$	−230.769	−0.0414748
$315$	307.768	0.0550500
$316$	2310.47	0.411310
$317$	7266.50	1.28747	0.643734	−	0.765250i	$-0.277385\pi$
$317$	7266.50	1.28747	0.643734	+	0.765250i	$0.277385\pi$
$318$	−366.433	−0.0646181
$319$	−5837.84	−1.02463
$320$	−568.317	−0.0992808
$321$	2819.29	0.490210
$322$	46.0298	0.00796627
$323$	273.059	0.0470385
$324$	2767.01	0.474452
$325$	−8978.21	−1.53237
$326$	410.897	0.0698082
$327$	4812.51	0.813860
$328$	−1681.05	−0.282989
$329$	197.074	0.0330245
$330$	85.8530	0.0143214
$331$	1454.36	0.241506	0.120753	−	0.992683i	$-0.461469\pi$
$331$	1454.36	0.241506	0.120753	+	0.992683i	$0.461469\pi$
$332$	1478.48	0.244404
$333$	−10267.8	−1.68971
$334$	−235.971	−0.0386579
$335$	−622.737	−0.101563
$336$	3480.01	0.565030
$337$	−3890.15	−0.628812	−0.314406	−	0.949289i	$-0.601805\pi$
$337$	−3890.15	−0.628812	−0.314406	+	0.949289i	$0.601805\pi$
$338$	880.334	0.141668
$339$	15304.3	2.45196
$340$	−187.173	−0.0298555
$341$	1230.13	0.195352
$342$	145.205	0.0229585
$343$	343.000	0.0539949
$344$	666.019	0.104388
$345$	217.800	0.0339883
$346$	−556.591	−0.0864812
$347$	−9933.78	−1.53681	−0.768406	−	0.639963i	$-0.778950\pi$
$347$	−9933.78	−1.53681	−0.768406	+	0.639963i	$0.778950\pi$
$348$	11680.1	1.79919
$349$	468.885	0.0719164	0.0359582	−	0.999353i	$-0.488552\pi$
$349$	468.885	0.0719164	0.0359582	+	0.999353i	$0.488552\pi$
$350$	−247.367	−0.0377780
$351$	5937.96	0.902978
$352$	1717.06	0.259999
$353$	−12345.7	−1.86146	−0.930732	−	0.365703i	$-0.880829\pi$
$353$	−12345.7	−1.86146	−0.930732	+	0.365703i	$0.880829\pi$
$354$	−622.920	−0.0935249
$355$	−612.229	−0.0915316
$356$	12625.3	1.87960
$357$	1121.84	0.166314
$358$	−1282.78	−0.189378
$359$	10663.2	1.56764	0.783821	−	0.620986i	$-0.213268\pi$
$359$	10663.2	1.56764	0.783821	+	0.620986i	$0.213268\pi$
$360$	−200.094	−0.0292941
$361$	−6672.62	−0.972827
$362$	1056.88	0.153449
$363$	−2607.31	−0.376993
$364$	−4026.13	−0.579743
$365$	−1117.80	−0.160297
$366$	1950.77	0.278602
$367$	1906.29	0.271138	0.135569	−	0.990768i	$-0.456714\pi$
$367$	1906.29	0.271138	0.135569	+	0.990768i	$0.456714\pi$
$368$	1427.03	0.202145
$369$	13741.8	1.93867
$370$	−93.2556	−0.0131030
$371$	−1119.71	−0.156691
$372$	−2461.18	−0.343027
$373$	8444.04	1.17216	0.586080	−	0.810253i	$-0.300670\pi$
$373$	8444.04	1.17216	0.586080	+	0.810253i	$0.300670\pi$
$374$	181.336	0.0250713
$375$	−2354.16	−0.324183
$376$	−128.127	−0.0175735
$377$	−13372.1	−1.82678
$378$	163.602	0.0222613
$379$	13721.8	1.85974	0.929868	−	0.367894i	$-0.119921\pi$
$379$	13721.8	1.85974	0.929868	+	0.367894i	$0.119921\pi$
$380$	−127.756	−0.0172468
$381$	8053.45	1.08291
$382$	−136.104	−0.0182295
$383$	−7050.47	−0.940632	−0.470316	−	0.882498i	$-0.655860\pi$
$383$	−7050.47	−0.940632	−0.470316	+	0.882498i	$0.655860\pi$
$384$	−4572.47	−0.607651
$385$	262.340	0.0347275
$386$	841.687	0.110986
$387$	−5444.39	−0.715126
$388$	−11809.6	−1.54521
$389$	−4881.00	−0.636187	−0.318093	−	0.948059i	$-0.603043\pi$
$389$	−4881.00	−0.636187	−0.318093	+	0.948059i	$0.603043\pi$
$390$	196.654	0.0255332
$391$	460.030	0.0595006
$392$	−223.000	−0.0287326
$393$	−18594.6	−2.38671
$394$	576.511	0.0737163
$395$	−344.845	−0.0439267
$396$	−9341.43	−1.18542
$397$	3455.14	0.436798	0.218399	−	0.975860i	$-0.429917\pi$
$397$	3455.14	0.436798	0.218399	+	0.975860i	$0.429917\pi$
$398$	1226.29	0.154443
$399$	765.724	0.0960756
$400$	−7668.96	−0.958620
$401$	−13705.6	−1.70680	−0.853401	−	0.521256i	$-0.825464\pi$
$401$	−13705.6	−1.70680	−0.853401	+	0.521256i	$0.825464\pi$
$402$	−1207.09	−0.149761
$403$	2817.72	0.348289
$404$	−2900.10	−0.357142
$405$	−412.985	−0.0506701
$406$	−368.426	−0.0450362
$407$	−8752.26	−1.06593
$408$	−729.362	−0.0885019
$409$	−2353.28	−0.284504	−0.142252	−	0.989830i	$-0.545434\pi$
$409$	−2353.28	−0.284504	−0.142252	+	0.989830i	$0.545434\pi$
$410$	124.807	0.0150336
$411$	−1644.03	−0.197310
$412$	−672.544	−0.0804220
$413$	−1903.45	−0.226786
$414$	244.631	0.0290410
$415$	−220.668	−0.0261016
$416$	3933.07	0.463545
$417$	14184.0	1.66569
$418$	123.773	0.0144830
$419$	−10660.2	−1.24292	−0.621461	−	0.783445i	$-0.713460\pi$
$419$	−10660.2	−1.24292	−0.621461	+	0.783445i	$0.713460\pi$
$420$	−524.877	−0.0609795
$421$	9970.25	1.15421	0.577103	−	0.816672i	$-0.304183\pi$
$421$	9970.25	1.15421	0.577103	+	0.816672i	$0.304183\pi$
$422$	568.404	0.0655674
$423$	1047.38	0.120391
$424$	727.972	0.0833808
$425$	−2472.23	−0.282166
$426$	−1186.72	−0.134969
$427$	5960.96	0.675576
$428$	−2786.08	−0.314650
$429$	18456.4	2.07712
$430$	−49.4476	−0.00554553
$431$	16523.6	1.84667	0.923334	−	0.383999i	$-0.125453\pi$
$431$	16523.6	1.84667	0.923334	+	0.383999i	$0.125453\pi$
$432$	5072.06	0.564883
$433$	−13056.1	−1.44904	−0.724522	−	0.689251i	$-0.757940\pi$
$433$	−13056.1	−1.44904	−0.724522	+	0.689251i	$0.757940\pi$
$434$	77.6334	0.00858646
$435$	−1743.29	−0.192148
$436$	−4755.82	−0.522391
$437$	313.998	0.0343720
$438$	−2166.70	−0.236367
$439$	494.593	0.0537714	0.0268857	−	0.999639i	$-0.491441\pi$
$439$	494.593	0.0537714	0.0268857	+	0.999639i	$0.491441\pi$
$440$	−170.559	−0.0184798
$441$	1822.92	0.196838
$442$	415.366	0.0446990
$443$	16371.6	1.75584	0.877919	−	0.478809i	$-0.158931\pi$
$443$	16371.6	1.75584	0.877919	+	0.478809i	$0.158931\pi$
$444$	17511.1	1.87171
$445$	−1884.36	−0.200736
$446$	451.900	0.0479778
$447$	−2953.41	−0.312509
$448$	−3366.15	−0.354991
$449$	7720.56	0.811483	0.405742	−	0.913988i	$-0.367013\pi$
$449$	7720.56	0.811483	0.405742	+	0.913988i	$0.367013\pi$
$450$	−1314.66	−0.137719
$451$	11713.4	1.22298
$452$	−15124.0	−1.57383
$453$	−18237.2	−1.89152
$454$	−687.614	−0.0710822
$455$	600.914	0.0619149
$456$	−497.832	−0.0511253
$457$	6228.11	0.637503	0.318751	−	0.947838i	$-0.396736\pi$
$457$	6228.11	0.637503	0.318751	+	0.947838i	$0.396736\pi$
$458$	−259.533	−0.0264786
$459$	1635.07	0.166271
$460$	−215.235	−0.0218160
$461$	−7684.61	−0.776373	−0.388186	−	0.921581i	$-0.626898\pi$
$461$	−7684.61	−0.776373	−0.388186	+	0.921581i	$0.626898\pi$
$462$	508.510	0.0512078
$463$	112.473	0.0112896	0.00564479	−	0.999984i	$-0.498203\pi$
$463$	112.473	0.0112896	0.00564479	+	0.999984i	$0.498203\pi$
$464$	−11422.1	−1.14280
$465$	367.339	0.0366343
$466$	350.348	0.0348274
$467$	15068.1	1.49309	0.746543	−	0.665338i	$-0.231712\pi$
$467$	15068.1	1.49309	0.746543	+	0.665338i	$0.231712\pi$
$468$	−21397.4	−2.11345
$469$	−3688.49	−0.363152
$470$	9.51260	0.000933582 0
$471$	−6467.57	−0.632717
$472$	1237.52	0.120681
$473$	−4640.78	−0.451127
$474$	−668.434	−0.0647726
$475$	−1687.44	−0.163000
$476$	−1108.63	−0.106752
$477$	−5950.82	−0.571215
$478$	−1059.43	−0.101375
$479$	11841.5	1.12954	0.564771	−	0.825247i	$-0.308964\pi$
$479$	11841.5	1.12954	0.564771	+	0.825247i	$0.308964\pi$
$480$	512.746	0.0487574
$481$	−20047.8	−1.90042
$482$	−1302.48	−0.123084
$483$	1290.04	0.121529
$484$	2576.60	0.241980
$485$	1762.62	0.165024
$486$	−1431.55	−0.133614
$487$	2475.57	0.230346	0.115173	−	0.993345i	$-0.463258\pi$
$487$	2475.57	0.230346	0.115173	+	0.993345i	$0.463258\pi$
$488$	−3875.49	−0.359498
$489$	11515.8	1.06496
$490$	16.5563	0.00152640
$491$	−15348.6	−1.41074	−0.705370	−	0.708839i	$-0.749219\pi$
$491$	−15348.6	−1.41074	−0.705370	+	0.708839i	$0.749219\pi$
$492$	−23435.7	−2.14748
$493$	−3682.12	−0.336378
$494$	283.512	0.0258215
$495$	1394.24	0.126599
$496$	2406.82	0.217882
$497$	−3626.25	−0.327282
$498$	−427.734	−0.0384884
$499$	11367.2	1.01977	0.509884	−	0.860243i	$-0.329688\pi$
$499$	11367.2	1.01977	0.509884	+	0.860243i	$0.329688\pi$
$500$	2326.44	0.208083
$501$	−6613.34	−0.589745
$502$	1135.38	0.100945
$503$	5193.92	0.460408	0.230204	−	0.973142i	$-0.426061\pi$
$503$	5193.92	0.460408	0.230204	+	0.973142i	$0.426061\pi$
$504$	−1185.16	−0.104745
$505$	432.850	0.0381417
$506$	208.523	0.0183201
$507$	24672.3	2.16122
$508$	−7958.59	−0.695089
$509$	−977.024	−0.0850803	−0.0425401	−	0.999095i	$-0.513545\pi$
$509$	−977.024	−0.0850803	−0.0425401	+	0.999095i	$0.513545\pi$
$510$	54.1504	0.00470161
$511$	−6620.76	−0.573161
$512$	5618.48	0.484969
$513$	1116.03	0.0960507
$514$	−2075.61	−0.178115
$515$	100.380	0.00858884
$516$	9285.04	0.792153
$517$	892.781	0.0759467
$518$	−552.355	−0.0468515
$519$	−15599.1	−1.31931
$520$	−390.681	−0.0329471
$521$	4297.99	0.361417	0.180709	−	0.983537i	$-0.442161\pi$
$521$	4297.99	0.361417	0.180709	+	0.983537i	$0.442161\pi$
$522$	−1958.05	−0.164179
$523$	−3663.60	−0.306306	−0.153153	−	0.988203i	$-0.548943\pi$
$523$	−3663.60	−0.306306	−0.153153	+	0.988203i	$0.548943\pi$
$524$	18375.6	1.53195
$525$	−6932.72	−0.576321
$526$	1372.59	0.113779
$527$	775.883	0.0641328
$528$	15765.0	1.29940
$529$	529.000	0.0434783
$530$	−54.0472	−0.00442955
$531$	−10116.1	−0.826747
$532$	−756.705	−0.0616679
$533$	26830.7	2.18042
$534$	−3652.58	−0.295997
$535$	415.832	0.0336037
$536$	2398.05	0.193246
$537$	−35951.5	−2.88905
$538$	−406.007	−0.0325357
$539$	1553.85	0.124173
$540$	−765.001	−0.0609637
$541$	−13974.1	−1.11052	−0.555260	−	0.831677i	$-0.687381\pi$
$541$	−13974.1	−1.11052	−0.555260	+	0.831677i	$0.687381\pi$
$542$	756.316	0.0599383
$543$	29620.3	2.34094
$544$	1083.01	0.0853557
$545$	709.823	0.0557898
$546$	1164.79	0.0912972
$547$	6016.30	0.470271	0.235136	−	0.971963i	$-0.424447\pi$
$547$	6016.30	0.470271	0.235136	+	0.971963i	$0.424447\pi$
$548$	1624.67	0.126647
$549$	31680.3	2.46281
$550$	−1120.61	−0.0868784
$551$	−2513.26	−0.194317
$552$	−838.711	−0.0646701
$553$	−2042.53	−0.157065
$554$	−1628.29	−0.124873
$555$	−2613.59	−0.199893
$556$	−14017.0	−1.06916
$557$	−21806.8	−1.65886	−0.829429	−	0.558612i	$-0.811334\pi$
$557$	−21806.8	−1.65886	−0.829429	+	0.558612i	$0.811334\pi$
$558$	412.593	0.0313019
$559$	−10630.1	−0.804304
$560$	513.285	0.0387326
$561$	5082.14	0.382475
$562$	−1426.89	−0.107099
$563$	−18584.8	−1.39122	−0.695610	−	0.718420i	$-0.744866\pi$
$563$	−18584.8	−1.39122	−0.695610	+	0.718420i	$0.744866\pi$
$564$	−1786.23	−0.133358
$565$	2257.31	0.168081
$566$	2217.46	0.164676
$567$	−2446.12	−0.181177
$568$	2357.59	0.174159
$569$	24992.8	1.84140	0.920698	−	0.390275i	$-0.127620\pi$
$569$	24992.8	1.84140	0.920698	+	0.390275i	$0.127620\pi$
$570$	36.9608	0.00271600
$571$	−17594.5	−1.28950	−0.644752	−	0.764392i	$-0.723039\pi$
$571$	−17594.5	−1.28950	−0.644752	+	0.764392i	$0.723039\pi$
$572$	−18239.0	−1.33324
$573$	−3814.46	−0.278100
$574$	739.235	0.0537545
$575$	−2842.88	−0.206185
$576$	−17889.9	−1.29412
$577$	−1666.39	−0.120230	−0.0601149	−	0.998191i	$-0.519147\pi$
$577$	−1666.39	−0.120230	−0.0601149	+	0.998191i	$0.519147\pi$
$578$	−1290.25	−0.0928499
$579$	23589.2	1.69315
$580$	1722.76	0.123334
$581$	−1307.02	−0.0933296
$582$	3416.59	0.243337
$583$	−5072.46	−0.360343
$584$	4304.46	0.304999
$585$	3193.63	0.225710
$586$	1897.95	0.133795
$587$	−6573.88	−0.462237	−0.231119	−	0.972926i	$-0.574239\pi$
$587$	−6573.88	−0.462237	−0.231119	+	0.972926i	$0.574239\pi$
$588$	−3108.86	−0.218040
$589$	529.586	0.0370479
$590$	−91.8778	−0.00641110
$591$	16157.4	1.12458
$592$	−17124.3	−1.18886
$593$	5066.72	0.350869	0.175434	−	0.984491i	$-0.443867\pi$
$593$	5066.72	0.350869	0.175434	+	0.984491i	$0.443867\pi$
$594$	741.146	0.0511946
$595$	165.467	0.0114008
$596$	2918.62	0.200589
$597$	34368.1	2.35610
$598$	477.640	0.0326624
$599$	17004.2	1.15989	0.579944	−	0.814656i	$-0.303074\pi$
$599$	17004.2	1.15989	0.579944	+	0.814656i	$0.303074\pi$
$600$	4507.28	0.306681
$601$	16323.7	1.10791	0.553956	−	0.832546i	$-0.313117\pi$
$601$	16323.7	1.10791	0.553956	+	0.832546i	$0.313117\pi$
$602$	−292.880	−0.0198287
$603$	−19602.9	−1.32387
$604$	18022.4	1.21411
$605$	−384.567	−0.0258427
$606$	839.019	0.0562423
$607$	11372.7	0.760470	0.380235	−	0.924890i	$-0.375843\pi$
$607$	11372.7	0.760470	0.380235	+	0.924890i	$0.375843\pi$
$608$	739.216	0.0493078
$609$	−10325.5	−0.687048
$610$	287.730	0.0190981
$611$	2044.99	0.135404
$612$	−5891.95	−0.389164
$613$	12777.6	0.841898	0.420949	−	0.907084i	$-0.361697\pi$
$613$	12777.6	0.841898	0.420949	+	0.907084i	$0.361697\pi$
$614$	352.090	0.0231420
$615$	3497.85	0.229345
$616$	−1010.23	−0.0660767
$617$	−5633.07	−0.367551	−0.183775	−	0.982968i	$-0.558832\pi$
$617$	−5633.07	−0.367551	−0.183775	+	0.982968i	$0.558832\pi$
$618$	194.572	0.0126648
$619$	−14391.6	−0.934488	−0.467244	−	0.884128i	$-0.654753\pi$
$619$	−14391.6	−0.934488	−0.467244	+	0.884128i	$0.654753\pi$
$620$	−363.013	−0.0235144
$621$	1880.21	0.121498
$622$	−751.446	−0.0484409
$623$	−11161.1	−0.717756
$624$	36111.2	2.31667
$625$	15103.2	0.966604
$626$	−59.7958	−0.00381776
$627$	3468.86	0.220946
$628$	6391.39	0.406121
$629$	−5520.34	−0.349937
$630$	87.9906	0.00556449
$631$	−10258.1	−0.647178	−0.323589	−	0.946198i	$-0.604889\pi$
$631$	−10258.1	−0.647178	−0.323589	+	0.946198i	$0.604889\pi$
$632$	1327.94	0.0835801
$633$	15930.1	1.00026
$634$	2077.49	0.130138
$635$	1187.85	0.0742335
$636$	10148.7	0.632741
$637$	3559.23	0.221384
$638$	−1669.03	−0.103570
$639$	−19272.2	−1.19311
$640$	−674.419	−0.0416543
$641$	13645.9	0.840841	0.420421	−	0.907329i	$-0.361883\pi$
$641$	13645.9	0.840841	0.420421	+	0.907329i	$0.361883\pi$
$642$	806.033	0.0495507
$643$	−963.797	−0.0591111	−0.0295555	−	0.999563i	$-0.509409\pi$
$643$	−963.797	−0.0591111	−0.0295555	+	0.999563i	$0.509409\pi$
$644$	−1274.84	−0.0780058
$645$	−1385.82	−0.0845997
$646$	78.0675	0.00475468
$647$	19063.8	1.15839	0.579194	−	0.815190i	$-0.303367\pi$
$647$	19063.8	1.15839	0.579194	+	0.815190i	$0.303367\pi$
$648$	1590.34	0.0964110
$649$	−8622.95	−0.521542
$650$	−2566.86	−0.154893
$651$	2175.76	0.130991
$652$	−11380.2	−0.683563
$653$	−18110.9	−1.08535	−0.542676	−	0.839942i	$-0.682589\pi$
$653$	−18110.9	−1.08535	−0.542676	+	0.839942i	$0.682589\pi$
$654$	1375.89	0.0822655
$655$	−2742.62	−0.163608
$656$	22918.1	1.36402
$657$	−35186.9	−2.08945
$658$	56.3434	0.00333814
$659$	14235.4	0.841479	0.420739	−	0.907182i	$-0.361771\pi$
$659$	14235.4	0.841479	0.420739	+	0.907182i	$0.361771\pi$
$660$	−2377.78	−0.140235
$661$	19106.5	1.12429	0.562145	−	0.827039i	$-0.309976\pi$
$661$	19106.5	1.12429	0.562145	+	0.827039i	$0.309976\pi$
$662$	415.799	0.0244116
$663$	11641.1	0.681905
$664$	849.756	0.0496640
$665$	112.941	0.00658595
$666$	−2935.56	−0.170797
$667$	−4234.16	−0.245798
$668$	6535.44	0.378539
$669$	12665.0	0.731924
$670$	−178.040	−0.0102661
$671$	27004.2	1.55363
$672$	3037.01	0.174338
$673$	−17515.0	−1.00320	−0.501599	−	0.865100i	$-0.667255\pi$
$673$	−17515.0	−1.00320	−0.501599	+	0.865100i	$0.667255\pi$
$674$	−1112.19	−0.0635608
$675$	−10104.3	−0.576172
$676$	−24381.7	−1.38722
$677$	−16056.4	−0.911519	−0.455760	−	0.890103i	$-0.650632\pi$
$677$	−16056.4	−0.911519	−0.455760	+	0.890103i	$0.650632\pi$
$678$	4375.47	0.247845
$679$	10440.0	0.590062
$680$	−107.578	−0.00606678
$681$	−19271.1	−1.08439
$682$	351.693	0.0197463
$683$	32998.3	1.84867	0.924337	−	0.381578i	$-0.124619\pi$
$683$	32998.3	1.84867	0.924337	+	0.381578i	$0.124619\pi$
$684$	−4021.61	−0.224810
$685$	−242.488	−0.0135255
$686$	98.0634	0.00545784
$687$	−7273.70	−0.403943
$688$	−9079.98	−0.503155
$689$	−11618.9	−0.642446
$690$	62.2688	0.00343556
$691$	17674.3	0.973025	0.486512	−	0.873674i	$-0.338269\pi$
$691$	17674.3	0.973025	0.486512	+	0.873674i	$0.338269\pi$
$692$	15415.3	0.846825
$693$	8258.13	0.452670
$694$	−2840.06	−0.155342
$695$	2092.08	0.114183
$696$	6713.11	0.365603
$697$	7388.06	0.401496
$698$	134.054	0.00726935
$699$	9818.89	0.531309
$700$	6851.06	0.369923
$701$	4964.87	0.267505	0.133752	−	0.991015i	$-0.457297\pi$
$701$	4964.87	0.267505	0.133752	+	0.991015i	$0.457297\pi$
$702$	1697.66	0.0912736
$703$	−3767.96	−0.202150
$704$	−15249.3	−0.816375
$705$	266.601	0.0142422
$706$	−3529.63	−0.188158
$707$	2563.78	0.136380
$708$	17252.4	0.915796
$709$	17982.2	0.952518	0.476259	−	0.879305i	$-0.341993\pi$
$709$	17982.2	0.952518	0.476259	+	0.879305i	$0.341993\pi$
$710$	−175.036	−0.00925207
$711$	−10855.3	−0.572580
$712$	7256.37	0.381944
$713$	892.207	0.0468631
$714$	320.734	0.0168112
$715$	2722.24	0.142386
$716$	35528.0	1.85439
$717$	−29691.8	−1.54653
$718$	3048.61	0.158458
$719$	−13551.7	−0.702913	−0.351457	−	0.936204i	$-0.614314\pi$
$719$	−13551.7	−0.702913	−0.351457	+	0.936204i	$0.614314\pi$
$720$	2727.92	0.141199
$721$	594.551	0.0307104
$722$	−1907.70	−0.0983340
$723$	−36503.5	−1.87770
$724$	−29271.5	−1.50258
$725$	22754.6	1.16563
$726$	−745.428	−0.0381067
$727$	−12568.5	−0.641185	−0.320592	−	0.947217i	$-0.603882\pi$
$727$	−12568.5	−0.641185	−0.320592	+	0.947217i	$0.603882\pi$
$728$	−2314.02	−0.117807
$729$	−30685.7	−1.55900
$730$	−319.578	−0.0162029
$731$	−2927.10	−0.148102
$732$	−54028.6	−2.72808
$733$	−600.152	−0.0302416	−0.0151208	−	0.999886i	$-0.504813\pi$
$733$	−600.152	−0.0302416	−0.0151208	+	0.999886i	$0.504813\pi$
$734$	545.007	0.0274068
$735$	464.009	0.0232860
$736$	1245.38	0.0623711
$737$	−16709.5	−0.835144
$738$	3928.76	0.195962
$739$	−26422.8	−1.31526	−0.657631	−	0.753340i	$-0.728441\pi$
$739$	−26422.8	−1.31526	−0.657631	+	0.753340i	$0.728441\pi$
$740$	2582.81	0.128305
$741$	7945.73	0.393919
$742$	−320.123	−0.0158384
$743$	−16071.3	−0.793539	−0.396770	−	0.917918i	$-0.629869\pi$
$743$	−16071.3	−0.793539	−0.396770	+	0.917918i	$0.629869\pi$
$744$	−1414.56	−0.0697048
$745$	−435.614	−0.0214224
$746$	2414.14	0.118483
$747$	−6946.35	−0.340232
$748$	−5022.28	−0.245498
$749$	2462.99	0.120154
$750$	−673.054	−0.0327686
$751$	15571.2	0.756592	0.378296	−	0.925685i	$-0.376510\pi$
$751$	15571.2	0.756592	0.378296	+	0.925685i	$0.376510\pi$
$752$	1746.78	0.0847055
$753$	31820.2	1.53997
$754$	−3823.07	−0.184652
$755$	−2689.90	−0.129663
$756$	−4531.12	−0.217983
$757$	−2225.91	−0.106872	−0.0534360	−	0.998571i	$-0.517017\pi$
$757$	−2225.91	−0.106872	−0.0534360	+	0.998571i	$0.517017\pi$
$758$	3923.04	0.187983
$759$	5844.08	0.279482
$760$	−73.4280	−0.00350462
$761$	−23803.6	−1.13388	−0.566938	−	0.823761i	$-0.691872\pi$
$761$	−23803.6	−1.13388	−0.566938	+	0.823761i	$0.691872\pi$
$762$	2302.47	0.109462
$763$	4204.30	0.199483
$764$	3769.53	0.178504
$765$	879.395	0.0415615
$766$	−2015.72	−0.0950797
$767$	−19751.6	−0.929844
$768$	29517.6	1.38688
$769$	−20561.7	−0.964208	−0.482104	−	0.876114i	$-0.660127\pi$
$769$	−20561.7	−0.964208	−0.482104	+	0.876114i	$0.660127\pi$
$770$	75.0029	0.00351028
$771$	−58171.1	−2.71723
$772$	−23311.4	−1.08678
$773$	33772.8	1.57144	0.785719	−	0.618583i	$-0.212293\pi$
$773$	33772.8	1.57144	0.785719	+	0.618583i	$0.212293\pi$
$774$	−1556.55	−0.0722854
$775$	−4794.77	−0.222236
$776$	−6787.55	−0.313993
$777$	−15480.4	−0.714742
$778$	−1395.47	−0.0643062
$779$	5042.78	0.231934
$780$	−5446.52	−0.250022
$781$	−16427.5	−0.752654
$782$	131.522	0.00601436
$783$	−15049.3	−0.686870
$784$	3040.20	0.138493
$785$	−953.937	−0.0433726
$786$	−5316.19	−0.241250
$787$	−19747.7	−0.894448	−0.447224	−	0.894422i	$-0.647587\pi$
$787$	−19747.7	−0.894448	−0.447224	+	0.894422i	$0.647587\pi$
$788$	−15967.1	−0.721831
$789$	38468.3	1.73575
$790$	−98.5910	−0.00444014
$791$	13370.1	0.600994
$792$	−5368.99	−0.240882
$793$	61855.4	2.76992
$794$	987.823	0.0441518
$795$	−1514.73	−0.0675749
$796$	−33963.3	−1.51231
$797$	39699.9	1.76442	0.882209	−	0.470858i	$-0.156056\pi$
$797$	39699.9	1.76442	0.882209	+	0.470858i	$0.156056\pi$
$798$	218.920	0.00971138
$799$	563.107	0.0249328
$800$	−6692.72	−0.295779
$801$	−59317.3	−2.61657
$802$	−3918.43	−0.172525
$803$	−29993.2	−1.31810
$804$	33431.5	1.46646
$805$	190.274	0.00833079
$806$	805.583	0.0352053
$807$	−11378.8	−0.496348
$808$	−1666.83	−0.0725729
$809$	2046.60	0.0889426	0.0444713	−	0.999011i	$-0.485840\pi$
$809$	2046.60	0.0889426	0.0444713	+	0.999011i	$0.485840\pi$
$810$	−118.072	−0.00512177
$811$	32153.8	1.39220	0.696099	−	0.717946i	$-0.254918\pi$
$811$	32153.8	1.39220	0.696099	+	0.717946i	$0.254918\pi$
$812$	10203.9	0.440995
$813$	21196.6	0.914387
$814$	−2502.26	−0.107745
$815$	1698.53	0.0730025
$816$	9943.53	0.426585
$817$	−1997.91	−0.0855547
$818$	−672.801	−0.0287579
$819$	18916.0	0.807054
$820$	−3456.65	−0.147209
$821$	29207.4	1.24159	0.620796	−	0.783972i	$-0.286810\pi$
$821$	29207.4	1.24159	0.620796	+	0.783972i	$0.286810\pi$
$822$	−470.028	−0.0199442
$823$	−1692.71	−0.0716939	−0.0358470	−	0.999357i	$-0.511413\pi$
$823$	−1692.71	−0.0716939	−0.0358470	+	0.999357i	$0.511413\pi$
$824$	−386.545	−0.0163421
$825$	−31406.4	−1.32537
$826$	−544.195	−0.0229237
$827$	4139.01	0.174036	0.0870179	−	0.996207i	$-0.472266\pi$
$827$	4139.01	0.174036	0.0870179	+	0.996207i	$0.472266\pi$
$828$	−6775.30	−0.284370
$829$	1063.54	0.0445577	0.0222789	−	0.999752i	$-0.492908\pi$
$829$	1063.54	0.0445577	0.0222789	+	0.999752i	$0.492908\pi$
$830$	−63.0889	−0.00263837
$831$	−45634.6	−1.90499
$832$	−34929.8	−1.45549
$833$	980.065	0.0407650
$834$	4055.20	0.168369
$835$	−975.437	−0.0404268
$836$	−3428.00	−0.141818
$837$	3171.14	0.130957
$838$	−3047.74	−0.125635
$839$	25032.6	1.03006	0.515030	−	0.857172i	$-0.327781\pi$
$839$	25032.6	1.03006	0.515030	+	0.857172i	$0.327781\pi$
$840$	−301.673	−0.0123913
$841$	9501.58	0.389585
$842$	2850.49	0.116668
$843$	−39990.1	−1.63385
$844$	−15742.5	−0.642037
$845$	3639.06	0.148151
$846$	299.444	0.0121692
$847$	−2277.80	−0.0924039
$848$	−9924.59	−0.401901
$849$	62146.8	2.51222
$850$	−706.808	−0.0285216
$851$	−6347.98	−0.255706
$852$	32867.4	1.32162
$853$	−13526.9	−0.542967	−0.271484	−	0.962443i	$-0.587514\pi$
$853$	−13526.9	−0.542967	−0.271484	+	0.962443i	$0.587514\pi$
$854$	1704.23	0.0682877
$855$	600.239	0.0240090
$856$	−1601.30	−0.0639384
$857$	−9459.85	−0.377062	−0.188531	−	0.982067i	$-0.560373\pi$
$857$	−9459.85	−0.377062	−0.188531	+	0.982067i	$0.560373\pi$
$858$	5276.68	0.209957
$859$	35172.1	1.39704	0.698520	−	0.715591i	$-0.253842\pi$
$859$	35172.1	1.39704	0.698520	+	0.715591i	$0.253842\pi$
$860$	1369.50	0.0543019
$861$	20717.9	0.820050
$862$	4724.08	0.186662
$863$	−46996.6	−1.85375	−0.926873	−	0.375376i	$-0.877514\pi$
$863$	−46996.6	−1.85375	−0.926873	+	0.375376i	$0.877514\pi$
$864$	4426.40	0.174293
$865$	−2300.79	−0.0904385
$866$	−3732.73	−0.146470
$867$	−36160.6	−1.41647
$868$	−2150.13	−0.0840787
$869$	−9253.00	−0.361204
$870$	−498.405	−0.0194224
$871$	−38274.5	−1.48896
$872$	−2733.41	−0.106152
$873$	55485.0	2.15107
$874$	89.7717	0.00347434
$875$	−2056.64	−0.0794597
$876$	60008.8	2.31451
$877$	10896.9	0.419570	0.209785	−	0.977748i	$-0.432724\pi$
$877$	10896.9	0.419570	0.209785	+	0.977748i	$0.432724\pi$
$878$	141.404	0.00543524
$879$	53192.2	2.04110
$880$	2325.27	0.0890737
$881$	17667.1	0.675617	0.337809	−	0.941215i	$-0.390314\pi$
$881$	17667.1	0.675617	0.337809	+	0.941215i	$0.390314\pi$
$882$	521.171	0.0198965
$883$	−23576.2	−0.898531	−0.449265	−	0.893398i	$-0.648314\pi$
$883$	−23576.2	−0.898531	−0.449265	+	0.893398i	$0.648314\pi$
$884$	−11504.0	−0.437693
$885$	−2574.98	−0.0978044
$886$	4680.62	0.177481
$887$	16348.3	0.618853	0.309427	−	0.950923i	$-0.399863\pi$
$887$	16348.3	0.618853	0.309427	+	0.950923i	$0.399863\pi$
$888$	10064.5	0.380340
$889$	7035.65	0.265431
$890$	−538.738	−0.0202905
$891$	−11081.4	−0.416655
$892$	−12515.8	−0.469799
$893$	384.353	0.0144030
$894$	−844.377	−0.0315886
$895$	−5302.68	−0.198044
$896$	−3994.60	−0.148940
$897$	13386.4	0.498281
$898$	2207.30	0.0820252
$899$	−7141.30	−0.264934
$900$	36410.8	1.34855
$901$	−3199.37	−0.118298
$902$	3348.86	0.123620
$903$	−8208.28	−0.302496
$904$	−8692.51	−0.319810
$905$	4368.87	0.160471
$906$	−5214.00	−0.191196
$907$	26708.2	0.977764	0.488882	−	0.872350i	$-0.337405\pi$
$907$	26708.2	0.977764	0.488882	+	0.872350i	$0.337405\pi$
$908$	19044.1	0.696038
$909$	13625.5	0.497174
$910$	171.801	0.00625839
$911$	34641.5	1.25985	0.629926	−	0.776655i	$-0.283085\pi$
$911$	34641.5	1.25985	0.629926	+	0.776655i	$0.283085\pi$
$912$	6787.05	0.246427
$913$	−5921.04	−0.214631
$914$	1780.61	0.0644392
$915$	8063.95	0.291351
$916$	7188.03	0.259278
$917$	−16244.6	−0.585000
$918$	467.465	0.0168068
$919$	−21866.1	−0.784871	−0.392435	−	0.919780i	$-0.628367\pi$
$919$	−21866.1	−0.784871	−0.392435	+	0.919780i	$0.628367\pi$
$920$	−123.706	−0.00443312
$921$	9867.72	0.353043
$922$	−2197.02	−0.0784762
$923$	−37628.7	−1.34189
$924$	−14083.7	−0.501428
$925$	34114.4	1.21262
$926$	32.1560	0.00114116
$927$	3159.82	0.111955
$928$	−9968.09	−0.352606
$929$	26857.0	0.948491	0.474245	−	0.880393i	$-0.342721\pi$
$929$	26857.0	0.948491	0.474245	+	0.880393i	$0.342721\pi$
$930$	105.022	0.00370302
$931$	668.952	0.0235489
$932$	−9703.24	−0.341030
$933$	−21060.1	−0.738989
$934$	4307.97	0.150922
$935$	749.593	0.0262185
$936$	−12298.1	−0.429463
$937$	−8735.68	−0.304570	−0.152285	−	0.988337i	$-0.548663\pi$
$937$	−8735.68	−0.304570	−0.152285	+	0.988337i	$0.548663\pi$
$938$	−1054.54	−0.0367077
$939$	−1675.84	−0.0582418
$940$	−263.461	−0.00914165
$941$	−49431.8	−1.71247	−0.856233	−	0.516590i	$-0.827201\pi$
$941$	−49431.8	−1.71247	−0.856233	+	0.516590i	$0.827201\pi$
$942$	−1849.07	−0.0639555
$943$	8495.70	0.293381
$944$	−16871.4	−0.581690
$945$	676.286	0.0232800
$946$	−1326.80	−0.0456003
$947$	−1469.30	−0.0504180	−0.0252090	−	0.999682i	$-0.508025\pi$
$947$	−1469.30	−0.0504180	−0.0252090	+	0.999682i	$0.508025\pi$
$948$	18512.9	0.634254
$949$	−68702.0	−2.35001
$950$	−482.438	−0.0164762
$951$	58223.8	1.98532
$952$	−637.185	−0.0216925
$953$	−39795.3	−1.35267	−0.676336	−	0.736593i	$-0.736433\pi$
$953$	−39795.3	−1.35267	−0.676336	+	0.736593i	$0.736433\pi$
$954$	−1701.34	−0.0577388
$955$	−562.616	−0.0190637
$956$	29342.1	0.992668
$957$	−46776.5	−1.58001
$958$	3385.47	0.114175
$959$	−1436.26	−0.0483621
$960$	−4553.72	−0.153094
$961$	−28286.2	−0.949489
$962$	−5731.66	−0.192096
$963$	13089.9	0.438022
$964$	36073.5	1.20524
$965$	3479.30	0.116065
$966$	368.820	0.0122843
$967$	50334.2	1.67388	0.836938	−	0.547298i	$-0.184343\pi$
$967$	50334.2	1.67388	0.836938	+	0.547298i	$0.184343\pi$
$968$	1480.90	0.0491714
$969$	2187.93	0.0725349
$970$	503.932	0.0166807
$971$	−48446.8	−1.60116	−0.800582	−	0.599223i	$-0.795476\pi$
$971$	−48446.8	−1.60116	−0.800582	+	0.599223i	$0.795476\pi$
$972$	39648.2	1.30835
$973$	12391.4	0.408275
$974$	707.763	0.0232836
$975$	−71939.1	−2.36297
$976$	52835.3	1.73281
$977$	−14711.2	−0.481734	−0.240867	−	0.970558i	$-0.577432\pi$
$977$	−14711.2	−0.481734	−0.240867	+	0.970558i	$0.577432\pi$
$978$	3292.37	0.107647
$979$	−50561.9	−1.65063
$980$	−458.543	−0.0149466
$981$	22344.3	0.727215
$982$	−4388.16	−0.142599
$983$	−7190.14	−0.233296	−0.116648	−	0.993173i	$-0.537215\pi$
$983$	−7190.14	−0.233296	−0.116648	+	0.993173i	$0.537215\pi$
$984$	−13469.6	−0.436378
$985$	2383.14	0.0770894
$986$	−1052.72	−0.0340013
$987$	1579.09	0.0509249
$988$	−7852.14	−0.252844
$989$	−3365.94	−0.108221
$990$	398.613	0.0127967
$991$	41963.2	1.34511	0.672555	−	0.740047i	$-0.265197\pi$
$991$	41963.2	1.34511	0.672555	+	0.740047i	$0.265197\pi$
$992$	2100.44	0.0672268
$993$	11653.2	0.372411
$994$	−1036.74	−0.0330819
$995$	5069.14	0.161510
$996$	11846.5	0.376879
$997$	61082.8	1.94033	0.970166	−	0.242443i	$-0.0779488\pi$
$997$	61082.8	1.94033	0.970166	+	0.242443i	$0.0779488\pi$
$998$	3249.86	0.103079
$999$	−22562.4	−0.714558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.d.1.6	✓	12
3.2	odd	2		1449.4.a.o.1.7		12
7.6	odd	2		1127.4.a.h.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.d.1.6	✓	12	1.1	even	1	trivial
1127.4.a.h.1.6		12	7.6	odd	2
1449.4.a.o.1.7		12	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)

\(f(q)\)	\(=\)	\(q+0.285899 q^{2} +8.01264 q^{3} -7.91826 q^{4} +1.18183 q^{5} +2.29081 q^{6} +7.00000 q^{7} -4.55102 q^{8} +37.2024 q^{9} +0.337884 q^{10} +31.7112 q^{11} -63.4462 q^{12} +72.6373 q^{13} +2.00129 q^{14} +9.46956 q^{15} +62.0450 q^{16} +20.0013 q^{17} +10.6361 q^{18} +13.6521 q^{19} -9.35802 q^{20} +56.0885 q^{21} +9.06621 q^{22} +23.0000 q^{23} -36.4657 q^{24} -123.603 q^{25} +20.7669 q^{26} +81.7482 q^{27} -55.4278 q^{28} -184.094 q^{29} +2.70734 q^{30} +38.7916 q^{31} +54.1468 q^{32} +254.090 q^{33} +5.71836 q^{34} +8.27280 q^{35} -294.578 q^{36} -275.999 q^{37} +3.90312 q^{38} +582.016 q^{39} -5.37852 q^{40} +369.378 q^{41} +16.0357 q^{42} -146.345 q^{43} -251.098 q^{44} +43.9668 q^{45} +6.57568 q^{46} +28.1535 q^{47} +497.144 q^{48} +49.0000 q^{49} -35.3381 q^{50} +160.263 q^{51} -575.161 q^{52} -159.958 q^{53} +23.3717 q^{54} +37.4772 q^{55} -31.8571 q^{56} +109.389 q^{57} -52.6323 q^{58} -271.921 q^{59} -74.9825 q^{60} +851.565 q^{61} +11.0905 q^{62} +260.417 q^{63} -480.879 q^{64} +85.8448 q^{65} +72.6443 q^{66} -526.926 q^{67} -158.376 q^{68} +184.291 q^{69} +2.36519 q^{70} -518.035 q^{71} -169.309 q^{72} -945.822 q^{73} -78.9079 q^{74} -990.389 q^{75} -108.101 q^{76} +221.978 q^{77} +166.398 q^{78} -291.790 q^{79} +73.3265 q^{80} -349.446 q^{81} +105.605 q^{82} -186.718 q^{83} -444.123 q^{84} +23.6381 q^{85} -41.8400 q^{86} -1475.08 q^{87} -144.318 q^{88} -1594.45 q^{89} +12.5701 q^{90} +508.461 q^{91} -182.120 q^{92} +310.823 q^{93} +8.04906 q^{94} +16.1344 q^{95} +433.858 q^{96} +1491.44 q^{97} +14.0091 q^{98} +1179.73 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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