LMFDB - Embedded newform 119.4.a.e.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [119,4,Mod(1,119)] 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("119.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(119, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	119.a (trivial)

Newform invariants

comment:select newform

sage:traces = [9] 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:	$7.02122729068$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 53x^{7} + 90x^{6} + 880x^{5} - 1087x^{4} - 4674x^{3} + 2515x^{2} + 1814x + 36 $ x^9 - 2x^8 - 53x^7 + 90x^6 + 880x^5 - 1087x^4 - 4674x^3 + 2515x^2 + 1814x + 36
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			1.3
Root			$-2.64062$ of defining polynomial
Character	$\chi$	$=$	119.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.64062 q^{2} +8.72657 q^{3} -1.02714 q^{4} -19.5792 q^{5} -23.0435 q^{6} +7.00000 q^{7} +23.8372 q^{8} +49.1531 q^{9} +51.7011 q^{10} +41.9498 q^{11} -8.96337 q^{12} +72.2591 q^{13} -18.4843 q^{14} -170.859 q^{15} -54.7279 q^{16} +17.0000 q^{17} -129.794 q^{18} +30.1510 q^{19} +20.1105 q^{20} +61.0860 q^{21} -110.773 q^{22} +27.6705 q^{23} +208.017 q^{24} +258.344 q^{25} -190.809 q^{26} +193.320 q^{27} -7.18995 q^{28} -213.732 q^{29} +451.173 q^{30} +144.223 q^{31} -46.1822 q^{32} +366.078 q^{33} -44.8905 q^{34} -137.054 q^{35} -50.4869 q^{36} +7.12836 q^{37} -79.6172 q^{38} +630.574 q^{39} -466.713 q^{40} -328.205 q^{41} -161.305 q^{42} +256.119 q^{43} -43.0882 q^{44} -962.376 q^{45} -73.0673 q^{46} +285.932 q^{47} -477.587 q^{48} +49.0000 q^{49} -682.187 q^{50} +148.352 q^{51} -74.2199 q^{52} -21.6411 q^{53} -510.485 q^{54} -821.342 q^{55} +166.861 q^{56} +263.115 q^{57} +564.386 q^{58} +533.837 q^{59} +175.495 q^{60} -598.521 q^{61} -380.839 q^{62} +344.072 q^{63} +559.773 q^{64} -1414.77 q^{65} -966.673 q^{66} +32.5622 q^{67} -17.4613 q^{68} +241.469 q^{69} +361.908 q^{70} -891.162 q^{71} +1171.67 q^{72} +103.142 q^{73} -18.8233 q^{74} +2254.45 q^{75} -30.9692 q^{76} +293.649 q^{77} -1665.11 q^{78} +380.784 q^{79} +1071.53 q^{80} +359.892 q^{81} +866.664 q^{82} +931.499 q^{83} -62.7436 q^{84} -332.846 q^{85} -676.313 q^{86} -1865.15 q^{87} +999.967 q^{88} -1283.26 q^{89} +2541.27 q^{90} +505.814 q^{91} -28.4214 q^{92} +1258.58 q^{93} -755.037 q^{94} -590.331 q^{95} -403.013 q^{96} +980.656 q^{97} -129.390 q^{98} +2061.96 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 2 q^{2} + 11 q^{3} + 38 q^{4} - 3 q^{5} + 9 q^{6} + 63 q^{7} + 24 q^{8} + 74 q^{9} + 134 q^{10} - 8 q^{11} + 56 q^{12} + 164 q^{13} + 14 q^{14} + 34 q^{15} + 178 q^{16} + 153 q^{17} + 98 q^{18} + 244 q^{19}+ \cdots - 2396 q^{99}+O(q^{100}) $ 9 * q + 2 * q^2 + 11 * q^3 + 38 * q^4 - 3 * q^5 + 9 * q^6 + 63 * q^7 + 24 * q^8 + 74 * q^9 + 134 * q^10 - 8 * q^11 + 56 * q^12 + 164 * q^13 + 14 * q^14 + 34 * q^15 + 178 * q^16 + 153 * q^17 + 98 * q^18 + 244 * q^19 - 41 * q^20 + 77 * q^21 - 80 * q^22 - 14 * q^23 + 298 * q^24 + 684 * q^25 + 326 * q^26 + 218 * q^27 + 266 * q^28 - 234 * q^29 - 335 * q^30 + 555 * q^31 - 181 * q^32 + 458 * q^33 + 34 * q^34 - 21 * q^35 - 1221 * q^36 - 364 * q^37 - 714 * q^38 - 52 * q^39 + 123 * q^40 - 45 * q^41 + 63 * q^42 - 135 * q^43 - 748 * q^44 - 844 * q^45 - 1576 * q^46 - 172 * q^47 - 949 * q^48 + 441 * q^49 - 2901 * q^50 + 187 * q^51 - 1596 * q^52 + 101 * q^53 - 1163 * q^54 + 1260 * q^55 + 168 * q^56 - 602 * q^57 + 1062 * q^58 + 280 * q^59 - 1727 * q^60 + 639 * q^61 - 1708 * q^62 + 518 * q^63 - 2390 * q^64 + 638 * q^65 - 2476 * q^66 + 35 * q^67 + 646 * q^68 + 1288 * q^69 + 938 * q^70 - 1616 * q^71 + 1335 * q^72 + 1049 * q^73 - 370 * q^74 + 1260 * q^75 + 4964 * q^76 - 56 * q^77 - 4714 * q^78 + 2304 * q^79 - 3996 * q^80 - 791 * q^81 - 215 * q^82 + 2508 * q^83 + 392 * q^84 - 51 * q^85 + 623 * q^86 + 166 * q^87 - 416 * q^88 + 2762 * q^89 + 2935 * q^90 + 1148 * q^91 - 2392 * q^92 + 2784 * q^93 - 862 * q^94 - 3462 * q^95 + 2928 * q^96 + 3107 * q^97 + 98 * q^98 - 2396 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.64062	−0.933600	−0.466800	−	0.884363i	$-0.654593\pi$
$2$	−2.64062	−0.933600	−0.466800	+	0.884363i	$0.654593\pi$
$3$	8.72657	1.67943	0.839715	−	0.543028i	$-0.182722\pi$
$3$	8.72657	1.67943	0.839715	+	0.543028i	$0.182722\pi$
$4$	−1.02714	−0.128392
$5$	−19.5792	−1.75121	−0.875607	−	0.483025i	$-0.839538\pi$
$5$	−19.5792	−1.75121	−0.875607	+	0.483025i	$0.839538\pi$
$6$	−23.0435	−1.56791
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	23.8372	1.05347
$9$	49.1531	1.82048
$10$	51.7011	1.63493
$11$	41.9498	1.14985	0.574925	−	0.818206i	$-0.305031\pi$
$11$	41.9498	1.14985	0.574925	+	0.818206i	$0.305031\pi$
$12$	−8.96337	−0.215625
$13$	72.2591	1.54162	0.770810	−	0.637065i	$-0.219852\pi$
$13$	72.2591	1.54162	0.770810	+	0.637065i	$0.219852\pi$
$14$	−18.4843	−0.352867
$15$	−170.859	−2.94104
$16$	−54.7279	−0.855124
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	−129.794	−1.69960
$19$	30.1510	0.364058	0.182029	−	0.983293i	$-0.441733\pi$
$19$	30.1510	0.364058	0.182029	+	0.983293i	$0.441733\pi$
$20$	20.1105	0.224842
$21$	61.0860	0.634765
$22$	−110.773	−1.07350
$23$	27.6705	0.250857	0.125428	−	0.992103i	$-0.459970\pi$
$23$	27.6705	0.250857	0.125428	+	0.992103i	$0.459970\pi$
$24$	208.017	1.76922
$25$	258.344	2.06675
$26$	−190.809	−1.43926
$27$	193.320	1.37795
$28$	−7.18995	−0.0485276
$29$	−213.732	−1.36859	−0.684295	−	0.729205i	$-0.739890\pi$
$29$	−213.732	−1.36859	−0.684295	+	0.729205i	$0.739890\pi$
$30$	451.173	2.74575
$31$	144.223	0.835590	0.417795	−	0.908541i	$-0.362803\pi$
$31$	144.223	0.835590	0.417795	+	0.908541i	$0.362803\pi$
$32$	−46.1822	−0.255123
$33$	366.078	1.93109
$34$	−44.8905	−0.226431
$35$	−137.054	−0.661896
$36$	−50.4869	−0.233736
$37$	7.12836	0.0316728	0.0158364	−	0.999875i	$-0.494959\pi$
$37$	7.12836	0.0316728	0.0158364	+	0.999875i	$0.494959\pi$
$38$	−79.6172	−0.339885
$39$	630.574	2.58904
$40$	−466.713	−1.84484
$41$	−328.205	−1.25017	−0.625086	−	0.780556i	$-0.714936\pi$
$41$	−328.205	−1.25017	−0.625086	+	0.780556i	$0.714936\pi$
$42$	−161.305	−0.592616
$43$	256.119	0.908321	0.454161	−	0.890920i	$-0.349939\pi$
$43$	256.119	0.908321	0.454161	+	0.890920i	$0.349939\pi$
$44$	−43.0882	−0.147631
$45$	−962.376	−3.18806
$46$	−73.0673	−0.234200
$47$	285.932	0.887393	0.443696	−	0.896177i	$-0.353667\pi$
$47$	285.932	0.887393	0.443696	+	0.896177i	$0.353667\pi$
$48$	−477.587	−1.43612
$49$	49.0000	0.142857
$50$	−682.187	−1.92951
$51$	148.352	0.407322
$52$	−74.2199	−0.197932
$53$	−21.6411	−0.0560875	−0.0280438	−	0.999607i	$-0.508928\pi$
$53$	−21.6411	−0.0560875	−0.0280438	+	0.999607i	$0.508928\pi$
$54$	−510.485	−1.28645
$55$	−821.342	−2.01363
$56$	166.861	0.398173
$57$	263.115	0.611411
$58$	564.386	1.27771
$59$	533.837	1.17796	0.588980	−	0.808147i	$-0.299530\pi$
$59$	533.837	1.17796	0.588980	+	0.808147i	$0.299530\pi$
$60$	175.495	0.377606
$61$	−598.521	−1.25627	−0.628137	−	0.778102i	$-0.716182\pi$
$61$	−598.521	−1.25627	−0.628137	+	0.778102i	$0.716182\pi$
$62$	−380.839	−0.780106
$63$	344.072	0.688078
$64$	559.773	1.09331
$65$	−1414.77	−2.69971
$66$	−966.673	−1.80287
$67$	32.5622	0.0593748	0.0296874	−	0.999559i	$-0.490549\pi$
$67$	32.5622	0.0593748	0.0296874	+	0.999559i	$0.490549\pi$
$68$	−17.4613	−0.0311396
$69$	241.469	0.421296
$70$	361.908	0.617946
$71$	−891.162	−1.48960	−0.744799	−	0.667289i	$-0.767455\pi$
$71$	−891.162	−1.48960	−0.744799	+	0.667289i	$0.767455\pi$
$72$	1171.67	1.91782
$73$	103.142	0.165368	0.0826840	−	0.996576i	$-0.473651\pi$
$73$	103.142	0.165368	0.0826840	+	0.996576i	$0.473651\pi$
$74$	−18.8233	−0.0295697
$75$	2254.45	3.47096
$76$	−30.9692	−0.0467422
$77$	293.649	0.434602
$78$	−1665.11	−2.41713
$79$	380.784	0.542298	0.271149	−	0.962537i	$-0.412596\pi$
$79$	380.784	0.542298	0.271149	+	0.962537i	$0.412596\pi$
$80$	1071.53	1.49750
$81$	359.892	0.493678
$82$	866.664	1.16716
$83$	931.499	1.23187	0.615936	−	0.787796i	$-0.288778\pi$
$83$	931.499	1.23187	0.615936	+	0.787796i	$0.288778\pi$
$84$	−62.7436	−0.0814987
$85$	−332.846	−0.424732
$86$	−676.313	−0.848008
$87$	−1865.15	−2.29845
$88$	999.967	1.21133
$89$	−1283.26	−1.52837	−0.764184	−	0.644998i	$-0.776858\pi$
$89$	−1283.26	−1.52837	−0.764184	+	0.644998i	$0.776858\pi$
$90$	2541.27	2.97637
$91$	505.814	0.582678
$92$	−28.4214	−0.0322080
$93$	1258.58	1.40331
$94$	−755.037	−0.828469
$95$	−590.331	−0.637544
$96$	−403.013	−0.428462
$97$	980.656	1.02650	0.513250	−	0.858239i	$-0.328441\pi$
$97$	980.656	1.02650	0.513250	+	0.858239i	$0.328441\pi$
$98$	−129.390	−0.133371
$99$	2061.96	2.09328
$100$	−265.354	−0.265354
$101$	−1673.35	−1.64856	−0.824278	−	0.566185i	$-0.808419\pi$
$101$	−1673.35	−1.64856	−0.824278	+	0.566185i	$0.808419\pi$
$102$	−391.740	−0.380275
$103$	408.737	0.391010	0.195505	−	0.980703i	$-0.437365\pi$
$103$	408.737	0.391010	0.195505	+	0.980703i	$0.437365\pi$
$104$	1722.46	1.62405
$105$	−1196.01	−1.11161
$106$	57.1460	0.0523633
$107$	−220.099	−0.198857	−0.0994287	−	0.995045i	$-0.531702\pi$
$107$	−220.099	−0.198857	−0.0994287	+	0.995045i	$0.531702\pi$
$108$	−198.566	−0.176917
$109$	−1239.63	−1.08931	−0.544655	−	0.838660i	$-0.683339\pi$
$109$	−1239.63	−1.08931	−0.544655	+	0.838660i	$0.683339\pi$
$110$	2168.85	1.87993
$111$	62.2061	0.0531923
$112$	−383.095	−0.323206
$113$	1213.86	1.01054	0.505268	−	0.862963i	$-0.331394\pi$
$113$	1213.86	1.01054	0.505268	+	0.862963i	$0.331394\pi$
$114$	−694.786	−0.570813
$115$	−541.765	−0.439303
$116$	219.532	0.175716
$117$	3551.76	2.80650
$118$	−1409.66	−1.09974
$119$	119.000	0.0916698
$120$	−4072.80	−3.09829
$121$	428.787	0.322154
$122$	1580.47	1.17286
$123$	−2864.11	−2.09957
$124$	−148.137	−0.107283
$125$	−2610.75	−1.86810
$126$	−908.561	−0.642390
$127$	−2307.15	−1.61202	−0.806010	−	0.591902i	$-0.798377\pi$
$127$	−2307.15	−1.61202	−0.806010	+	0.591902i	$0.798377\pi$
$128$	−1108.69	−0.765587
$129$	2235.04	1.52546
$130$	3735.87	2.52045
$131$	34.6301	0.0230965	0.0115483	−	0.999933i	$-0.496324\pi$
$131$	34.6301	0.0230965	0.0115483	+	0.999933i	$0.496324\pi$
$132$	−376.012	−0.247937
$133$	211.057	0.137601
$134$	−85.9844	−0.0554323
$135$	−3785.05	−2.41308
$136$	405.233	0.255503
$137$	−1937.12	−1.20803	−0.604013	−	0.796974i	$-0.706433\pi$
$137$	−1937.12	−1.20803	−0.604013	+	0.796974i	$0.706433\pi$
$138$	−637.627	−0.393322
$139$	1681.10	1.02582	0.512910	−	0.858442i	$-0.328567\pi$
$139$	1681.10	1.02582	0.512910	+	0.858442i	$0.328567\pi$
$140$	140.773	0.0849822
$141$	2495.21	1.49031
$142$	2353.22	1.39069
$143$	3031.26	1.77263
$144$	−2690.04	−1.55674
$145$	4184.70	2.39669
$146$	−272.359	−0.154387
$147$	427.602	0.239919
$148$	−7.32179	−0.00406654
$149$	1835.05	1.00895	0.504473	−	0.863427i	$-0.331687\pi$
$149$	1835.05	1.00895	0.504473	+	0.863427i	$0.331687\pi$
$150$	−5953.15	−3.24048
$151$	3463.37	1.86652	0.933261	−	0.359199i	$-0.116950\pi$
$151$	3463.37	1.86652	0.933261	+	0.359199i	$0.116950\pi$
$152$	718.716	0.383523
$153$	835.602	0.441532
$154$	−775.414	−0.405745
$155$	−2823.77	−1.46330
$156$	−647.685	−0.332412
$157$	−798.838	−0.406078	−0.203039	−	0.979171i	$-0.565082\pi$
$157$	−798.838	−0.406078	−0.203039	+	0.979171i	$0.565082\pi$
$158$	−1005.51	−0.506289
$159$	−188.853	−0.0941951
$160$	904.210	0.446775
$161$	193.694	0.0948149
$162$	−950.336	−0.460898
$163$	−408.551	−0.196320	−0.0981602	−	0.995171i	$-0.531296\pi$
$163$	−408.551	−0.196320	−0.0981602	+	0.995171i	$0.531296\pi$
$164$	337.111	0.160512
$165$	−7167.50	−3.38175
$166$	−2459.73	−1.15007
$167$	3331.83	1.54386	0.771930	−	0.635708i	$-0.219292\pi$
$167$	3331.83	1.54386	0.771930	+	0.635708i	$0.219292\pi$
$168$	1456.12	0.668703
$169$	3024.38	1.37659
$170$	878.918	0.396529
$171$	1482.01	0.662763
$172$	−263.069	−0.116621
$173$	−2925.48	−1.28566	−0.642832	−	0.766007i	$-0.722241\pi$
$173$	−2925.48	−1.28566	−0.642832	+	0.766007i	$0.722241\pi$
$174$	4925.15	2.14583
$175$	1808.40	0.781157
$176$	−2295.83	−0.983263
$177$	4658.57	1.97830
$178$	3388.59	1.42688
$179$	−755.972	−0.315665	−0.157832	−	0.987466i	$-0.550451\pi$
$179$	−755.972	−0.315665	−0.157832	+	0.987466i	$0.550451\pi$
$180$	988.491	0.409321
$181$	−2746.60	−1.12792	−0.563960	−	0.825802i	$-0.690723\pi$
$181$	−2746.60	−1.12792	−0.563960	+	0.825802i	$0.690723\pi$
$182$	−1335.66	−0.543988
$183$	−5223.04	−2.10983
$184$	659.588	0.264269
$185$	−139.567	−0.0554659
$186$	−3323.42	−1.31013
$187$	713.147	0.278879
$188$	−293.691	−0.113934
$189$	1353.24	0.520814
$190$	1558.84	0.595211
$191$	−2634.45	−0.998023	−0.499012	−	0.866595i	$-0.666304\pi$
$191$	−2634.45	−0.998023	−0.499012	+	0.866595i	$0.666304\pi$
$192$	4884.90	1.83613
$193$	−3066.96	−1.14386	−0.571929	−	0.820303i	$-0.693805\pi$
$193$	−3066.96	−1.14386	−0.571929	+	0.820303i	$0.693805\pi$
$194$	−2589.54	−0.958341
$195$	−12346.1	−4.53397
$196$	−50.3296	−0.0183417
$197$	114.780	0.0415112	0.0207556	−	0.999785i	$-0.493393\pi$
$197$	114.780	0.0415112	0.0207556	+	0.999785i	$0.493393\pi$
$198$	−5444.86	−1.95429
$199$	−2987.11	−1.06407	−0.532037	−	0.846721i	$-0.678573\pi$
$199$	−2987.11	−1.06407	−0.532037	+	0.846721i	$0.678573\pi$
$200$	6158.19	2.17725
$201$	284.157	0.0997158
$202$	4418.67	1.53909
$203$	−1496.13	−0.517278
$204$	−152.377	−0.0522968
$205$	6425.98	2.18932
$206$	−1079.32	−0.365047
$207$	1360.09	0.456680
$208$	−3954.59	−1.31828
$209$	1264.83	0.418613
$210$	3158.21	1.03780
$211$	−479.732	−0.156522	−0.0782609	−	0.996933i	$-0.524937\pi$
$211$	−479.732	−0.156522	−0.0782609	+	0.996933i	$0.524937\pi$
$212$	22.2284	0.00720119
$213$	−7776.79	−2.50168
$214$	581.197	0.185653
$215$	−5014.60	−1.59066
$216$	4608.22	1.45162
$217$	1009.56	0.315823
$218$	3273.38	1.01698
$219$	900.076	0.277724
$220$	843.630	0.258534
$221$	1228.40	0.373898
$222$	−164.263	−0.0496603
$223$	−2067.78	−0.620937	−0.310469	−	0.950584i	$-0.600486\pi$
$223$	−2067.78	−0.620937	−0.310469	+	0.950584i	$0.600486\pi$
$224$	−323.276	−0.0964275
$225$	12698.4	3.76248
$226$	−3205.34	−0.943435
$227$	5488.28	1.60471	0.802357	−	0.596845i	$-0.203579\pi$
$227$	5488.28	1.60471	0.802357	+	0.596845i	$0.203579\pi$
$228$	−270.255	−0.0785002
$229$	314.178	0.0906614	0.0453307	−	0.998972i	$-0.485566\pi$
$229$	314.178	0.0906614	0.0453307	+	0.998972i	$0.485566\pi$
$230$	1430.60	0.410133
$231$	2562.55	0.729884
$232$	−5094.78	−1.44176
$233$	−5880.46	−1.65340	−0.826699	−	0.562644i	$-0.809784\pi$
$233$	−5880.46	−1.65340	−0.826699	+	0.562644i	$0.809784\pi$
$234$	−9378.83	−2.62014
$235$	−5598.31	−1.55401
$236$	−548.323	−0.151241
$237$	3322.94	0.910751
$238$	−314.234	−0.0855829
$239$	−4859.82	−1.31530	−0.657648	−	0.753326i	$-0.728448\pi$
$239$	−4859.82	−1.31530	−0.657648	+	0.753326i	$0.728448\pi$
$240$	9350.75	2.51495
$241$	4791.46	1.28069	0.640343	−	0.768089i	$-0.278792\pi$
$241$	4791.46	1.28069	0.640343	+	0.768089i	$0.278792\pi$
$242$	−1132.26	−0.300763
$243$	−2079.03	−0.548847
$244$	614.762	0.161296
$245$	−959.379	−0.250173
$246$	7563.01	1.96016
$247$	2178.68	0.561240
$248$	3437.88	0.880265
$249$	8128.80	2.06884
$250$	6894.00	1.74406
$251$	1159.03	0.291464	0.145732	−	0.989324i	$-0.453446\pi$
$251$	1159.03	0.291464	0.145732	+	0.989324i	$0.453446\pi$
$252$	−353.408	−0.0883437
$253$	1160.77	0.288447
$254$	6092.30	1.50498
$255$	−2904.60	−0.713307
$256$	−1550.56	−0.378555
$257$	−4490.45	−1.08991	−0.544955	−	0.838466i	$-0.683453\pi$
$257$	−4490.45	−1.08991	−0.544955	+	0.838466i	$0.683453\pi$
$258$	−5901.90	−1.42417
$259$	49.8985	0.0119712
$260$	1453.16	0.346621
$261$	−10505.6	−2.49150
$262$	−91.4448	−0.0215629
$263$	6133.75	1.43811	0.719055	−	0.694953i	$-0.244575\pi$
$263$	6133.75	1.43811	0.719055	+	0.694953i	$0.244575\pi$
$264$	8726.28	2.03434
$265$	423.715	0.0982213
$266$	−557.321	−0.128464
$267$	−11198.4	−2.56679
$268$	−33.4458	−0.00762324
$269$	4927.18	1.11679	0.558393	−	0.829577i	$-0.311418\pi$
$269$	4927.18	1.11679	0.558393	+	0.829577i	$0.311418\pi$
$270$	9994.87	2.25285
$271$	−205.364	−0.0460331	−0.0230166	−	0.999735i	$-0.507327\pi$
$271$	−205.364	−0.0460331	−0.0230166	+	0.999735i	$0.507327\pi$
$272$	−930.374	−0.207398
$273$	4414.02	0.978567
$274$	5115.20	1.12781
$275$	10837.5	2.37645
$276$	−248.021	−0.0540910
$277$	−6869.88	−1.49015	−0.745074	−	0.666982i	$-0.767586\pi$
$277$	−6869.88	−1.49015	−0.745074	+	0.666982i	$0.767586\pi$
$278$	−4439.14	−0.957705
$279$	7089.02	1.52118
$280$	−3266.99	−0.697285
$281$	2396.97	0.508866	0.254433	−	0.967090i	$-0.418111\pi$
$281$	2396.97	0.508866	0.254433	+	0.967090i	$0.418111\pi$
$282$	−6588.89	−1.39136
$283$	−3548.07	−0.745268	−0.372634	−	0.927978i	$-0.621545\pi$
$283$	−3548.07	−0.745268	−0.372634	+	0.927978i	$0.621545\pi$
$284$	915.344	0.191252
$285$	−5151.57	−1.07071
$286$	−8004.39	−1.65493
$287$	−2297.44	−0.472520
$288$	−2270.00	−0.464448
$289$	289.000	0.0588235
$290$	−11050.2	−2.23755
$291$	8557.77	1.72394
$292$	−105.941	−0.0212319
$293$	2328.13	0.464200	0.232100	−	0.972692i	$-0.425440\pi$
$293$	2328.13	0.464200	0.232100	+	0.972692i	$0.425440\pi$
$294$	−1129.13	−0.223988
$295$	−10452.1	−2.06286
$296$	169.920	0.0333663
$297$	8109.76	1.58443
$298$	−4845.66	−0.941952
$299$	1999.45	0.386726
$300$	−2315.63	−0.445643
$301$	1792.83	0.343313
$302$	−9145.43	−1.74258
$303$	−14602.6	−2.76863
$304$	−1650.10	−0.311315
$305$	11718.5	2.20001
$306$	−2206.51	−0.412214
$307$	265.106	0.0492846	0.0246423	−	0.999696i	$-0.492155\pi$
$307$	265.106	0.0492846	0.0246423	+	0.999696i	$0.492155\pi$
$308$	−301.617	−0.0557994
$309$	3566.87	0.656674
$310$	7456.50	1.36613
$311$	8763.04	1.59777	0.798885	−	0.601484i	$-0.205424\pi$
$311$	8763.04	1.59777	0.798885	+	0.601484i	$0.205424\pi$
$312$	15031.1	2.72747
$313$	−3465.27	−0.625779	−0.312889	−	0.949790i	$-0.601297\pi$
$313$	−3465.27	−0.625779	−0.312889	+	0.949790i	$0.601297\pi$
$314$	2109.43	0.379114
$315$	−6736.63	−1.20497
$316$	−391.117	−0.0696267
$317$	−2756.68	−0.488424	−0.244212	−	0.969722i	$-0.578529\pi$
$317$	−2756.68	−0.488424	−0.244212	+	0.969722i	$0.578529\pi$
$318$	498.689	0.0879405
$319$	−8966.03	−1.57367
$320$	−10959.9	−1.91461
$321$	−1920.71	−0.333967
$322$	−511.471	−0.0885191
$323$	512.567	0.0882972
$324$	−369.657	−0.0633843
$325$	18667.7	3.18614
$326$	1078.83	0.183285
$327$	−10817.7	−1.82942
$328$	−7823.50	−1.31701
$329$	2001.52	0.335403
$330$	18926.6	3.15720
$331$	−968.107	−0.160761	−0.0803807	−	0.996764i	$-0.525614\pi$
$331$	−968.107	−0.160761	−0.0803807	+	0.996764i	$0.525614\pi$
$332$	−956.776	−0.158162
$333$	350.381	0.0576599
$334$	−8798.08	−1.44135
$335$	−637.541	−0.103978
$336$	−3343.11	−0.542802
$337$	−1193.83	−0.192974	−0.0964871	−	0.995334i	$-0.530761\pi$
$337$	−1193.83	−0.192974	−0.0964871	+	0.995334i	$0.530761\pi$
$338$	−7986.23	−1.28519
$339$	10592.8	1.69712
$340$	341.878	0.0545321
$341$	6050.14	0.960802
$342$	−3913.43	−0.618755
$343$	343.000	0.0539949
$344$	6105.17	0.956886
$345$	−4727.76	−0.737779
$346$	7725.07	1.20030
$347$	−6030.71	−0.932984	−0.466492	−	0.884526i	$-0.654482\pi$
$347$	−6030.71	−0.932984	−0.466492	+	0.884526i	$0.654482\pi$
$348$	1915.76	0.295103
$349$	−7489.05	−1.14865	−0.574326	−	0.818627i	$-0.694736\pi$
$349$	−7489.05	−1.14865	−0.574326	+	0.818627i	$0.694736\pi$
$350$	−4775.31	−0.729288
$351$	13969.2	2.12427
$352$	−1937.34	−0.293353
$353$	5367.84	0.809352	0.404676	−	0.914460i	$-0.367384\pi$
$353$	5367.84	0.809352	0.404676	+	0.914460i	$0.367384\pi$
$354$	−12301.5	−1.84694
$355$	17448.2	2.60860
$356$	1318.08	0.196230
$357$	1038.46	0.153953
$358$	1996.23	0.294705
$359$	1533.95	0.225512	0.112756	−	0.993623i	$-0.464032\pi$
$359$	1533.95	0.225512	0.112756	+	0.993623i	$0.464032\pi$
$360$	−22940.4	−3.35851
$361$	−5949.92	−0.867461
$362$	7252.73	1.05302
$363$	3741.84	0.541035
$364$	−519.539	−0.0748112
$365$	−2019.43	−0.289594
$366$	13792.0	1.96973
$367$	−916.137	−0.130305	−0.0651525	−	0.997875i	$-0.520753\pi$
$367$	−916.137	−0.130305	−0.0651525	+	0.997875i	$0.520753\pi$
$368$	−1514.35	−0.214513
$369$	−16132.3	−2.27592
$370$	368.544	0.0517829
$371$	−151.488	−0.0211991
$372$	−1292.73	−0.180174
$373$	−5872.02	−0.815125	−0.407563	−	0.913177i	$-0.633621\pi$
$373$	−5872.02	−0.815125	−0.407563	+	0.913177i	$0.633621\pi$
$374$	−1883.15	−0.260362
$375$	−22782.9	−3.13735
$376$	6815.82	0.934838
$377$	−15444.1	−2.10985
$378$	−3573.40	−0.486232
$379$	−6661.89	−0.902899	−0.451449	−	0.892297i	$-0.649093\pi$
$379$	−6661.89	−0.902899	−0.451449	+	0.892297i	$0.649093\pi$
$380$	606.350	0.0818555
$381$	−20133.5	−2.70727
$382$	6956.59	0.931754
$383$	7607.86	1.01500	0.507498	−	0.861653i	$-0.330570\pi$
$383$	7607.86	1.01500	0.507498	+	0.861653i	$0.330570\pi$
$384$	−9675.05	−1.28575
$385$	−5749.40	−0.761081
$386$	8098.67	1.06791
$387$	12589.0	1.65358
$388$	−1007.27	−0.131794
$389$	−5344.30	−0.696573	−0.348286	−	0.937388i	$-0.613236\pi$
$389$	−5344.30	−0.696573	−0.348286	+	0.937388i	$0.613236\pi$
$390$	32601.4	4.23291
$391$	470.399	0.0608417
$392$	1168.02	0.150495
$393$	302.202	0.0387890
$394$	−303.089	−0.0387548
$395$	−7455.43	−0.949680
$396$	−2117.92	−0.268761
$397$	8153.05	1.03070	0.515352	−	0.856979i	$-0.327661\pi$
$397$	8153.05	1.03070	0.515352	+	0.856979i	$0.327661\pi$
$398$	7887.82	0.993419
$399$	1841.80	0.231091
$400$	−14138.6	−1.76732
$401$	−2060.49	−0.256599	−0.128299	−	0.991735i	$-0.540952\pi$
$401$	−2060.49	−0.256599	−0.128299	+	0.991735i	$0.540952\pi$
$402$	−750.349	−0.0930946
$403$	10421.5	1.28816
$404$	1718.75	0.211661
$405$	−7046.37	−0.864536
$406$	3950.70	0.482931
$407$	299.033	0.0364190
$408$	3536.29	0.429099
$409$	−2965.19	−0.358482	−0.179241	−	0.983805i	$-0.557364\pi$
$409$	−2965.19	−0.358482	−0.179241	+	0.983805i	$0.557364\pi$
$410$	−16968.6	−2.04394
$411$	−16904.4	−2.02880
$412$	−419.828	−0.0502026
$413$	3736.86	0.445227
$414$	−3591.48	−0.426357
$415$	−18238.0	−2.15727
$416$	−3337.09	−0.393303
$417$	14670.2	1.72279
$418$	−3339.93	−0.390816
$419$	−2430.26	−0.283356	−0.141678	−	0.989913i	$-0.545250\pi$
$419$	−2430.26	−0.283356	−0.141678	+	0.989913i	$0.545250\pi$
$420$	1228.47	0.142722
$421$	−2080.44	−0.240841	−0.120421	−	0.992723i	$-0.538424\pi$
$421$	−2080.44	−0.240841	−0.120421	+	0.992723i	$0.538424\pi$
$422$	1266.79	0.146129
$423$	14054.4	1.61548
$424$	−515.865	−0.0590863
$425$	4391.84	0.501260
$426$	20535.5	2.33556
$427$	−4189.65	−0.474827
$428$	226.071	0.0255317
$429$	26452.5	2.97701
$430$	13241.6	1.48504
$431$	3973.72	0.444101	0.222050	−	0.975035i	$-0.428725\pi$
$431$	3973.72	0.444101	0.222050	+	0.975035i	$0.428725\pi$
$432$	−10580.0	−1.17831
$433$	1071.48	0.118919	0.0594596	−	0.998231i	$-0.481062\pi$
$433$	1071.48	0.118919	0.0594596	+	0.998231i	$0.481062\pi$
$434$	−2665.87	−0.294852
$435$	36518.1	4.02508
$436$	1273.27	0.139859
$437$	834.293	0.0913265
$438$	−2376.76	−0.259283
$439$	10684.3	1.16158	0.580789	−	0.814054i	$-0.302744\pi$
$439$	10684.3	1.16158	0.580789	+	0.814054i	$0.302744\pi$
$440$	−19578.5	−2.12129
$441$	2408.50	0.260069
$442$	−3243.75	−0.349071
$443$	−3351.08	−0.359401	−0.179700	−	0.983721i	$-0.557513\pi$
$443$	−3351.08	−0.359401	−0.179700	+	0.983721i	$0.557513\pi$
$444$	−63.8942	−0.00682946
$445$	25125.1	2.67650
$446$	5460.23	0.579707
$447$	16013.7	1.69445
$448$	3918.41	0.413231
$449$	13818.1	1.45237	0.726185	−	0.687499i	$-0.241291\pi$
$449$	13818.1	1.45237	0.726185	+	0.687499i	$0.241291\pi$
$450$	−33531.6	−3.51265
$451$	−13768.1	−1.43751
$452$	−1246.80	−0.129745
$453$	30223.3	3.13469
$454$	−14492.4	−1.49816
$455$	−9903.41	−1.02039
$456$	6271.92	0.644100
$457$	−4162.65	−0.426084	−0.213042	−	0.977043i	$-0.568337\pi$
$457$	−4162.65	−0.426084	−0.213042	+	0.977043i	$0.568337\pi$
$458$	−829.624	−0.0846415
$459$	3286.45	0.334201
$460$	556.467	0.0564030
$461$	15252.6	1.54096	0.770480	−	0.637464i	$-0.220017\pi$
$461$	15252.6	1.54096	0.770480	+	0.637464i	$0.220017\pi$
$462$	−6766.71	−0.681419
$463$	−4408.08	−0.442464	−0.221232	−	0.975221i	$-0.571008\pi$
$463$	−4408.08	−0.442464	−0.221232	+	0.975221i	$0.571008\pi$
$464$	11697.1	1.17031
$465$	−24641.9	−2.45750
$466$	15528.1	1.54361
$467$	−4160.91	−0.412300	−0.206150	−	0.978520i	$-0.566093\pi$
$467$	−4160.91	−0.412300	−0.206150	+	0.978520i	$0.566093\pi$
$468$	−3648.14	−0.360332
$469$	227.936	0.0224416
$470$	14783.0	1.45083
$471$	−6971.11	−0.681979
$472$	12725.2	1.24094
$473$	10744.2	1.04443
$474$	−8774.61	−0.850277
$475$	7789.31	0.752417
$476$	−122.229	−0.0117697
$477$	−1063.73	−0.102106
$478$	12832.9	1.22796
$479$	877.914	0.0837430	0.0418715	−	0.999123i	$-0.486668\pi$
$479$	877.914	0.0837430	0.0418715	+	0.999123i	$0.486668\pi$
$480$	7890.65	0.750328
$481$	515.089	0.0488275
$482$	−12652.4	−1.19565
$483$	1690.28	0.159235
$484$	−440.423	−0.0413620
$485$	−19200.4	−1.79762
$486$	5489.93	0.512404
$487$	−13389.2	−1.24583	−0.622917	−	0.782288i	$-0.714053\pi$
$487$	−13389.2	−1.24583	−0.622917	+	0.782288i	$0.714053\pi$
$488$	−14267.1	−1.32344
$489$	−3565.25	−0.329706
$490$	2533.35	0.233562
$491$	7277.08	0.668860	0.334430	−	0.942421i	$-0.391456\pi$
$491$	7277.08	0.668860	0.334430	+	0.942421i	$0.391456\pi$
$492$	2941.82	0.269568
$493$	−3633.45	−0.331932
$494$	−5753.07	−0.523974
$495$	−40371.5	−3.66579
$496$	−7893.04	−0.714532
$497$	−6238.14	−0.563015
$498$	−21465.0	−1.93147
$499$	−5495.10	−0.492975	−0.246487	−	0.969146i	$-0.579276\pi$
$499$	−5495.10	−0.492975	−0.246487	+	0.969146i	$0.579276\pi$
$500$	2681.60	0.239849
$501$	29075.4	2.59280
$502$	−3060.56	−0.272111
$503$	−10238.0	−0.907530	−0.453765	−	0.891121i	$-0.649919\pi$
$503$	−10238.0	−0.907530	−0.453765	+	0.891121i	$0.649919\pi$
$504$	8201.71	0.724867
$505$	32762.7	2.88697
$506$	−3065.16	−0.269294
$507$	26392.5	2.31189
$508$	2369.76	0.206970
$509$	−12601.6	−1.09736	−0.548678	−	0.836034i	$-0.684869\pi$
$509$	−12601.6	−1.09736	−0.548678	+	0.836034i	$0.684869\pi$
$510$	7669.95	0.665943
$511$	721.994	0.0625032
$512$	12963.9	1.11901
$513$	5828.80	0.501653
$514$	11857.6	1.01754
$515$	−8002.73	−0.684742
$516$	−2295.69	−0.195857
$517$	11994.8	1.02037
$518$	−131.763	−0.0111763
$519$	−25529.4	−2.15918
$520$	−33724.2	−2.84405
$521$	4259.75	0.358201	0.179101	−	0.983831i	$-0.442681\pi$
$521$	4259.75	0.358201	0.179101	+	0.983831i	$0.442681\pi$
$522$	27741.3	2.32606
$523$	1112.98	0.0930542	0.0465271	−	0.998917i	$-0.485185\pi$
$523$	1112.98	0.0930542	0.0465271	+	0.998917i	$0.485185\pi$
$524$	−35.5698	−0.00296541
$525$	15781.2	1.31190
$526$	−16196.9	−1.34262
$527$	2451.80	0.202660
$528$	−20034.7	−1.65132
$529$	−11401.3	−0.937071
$530$	−1118.87	−0.0916993
$531$	26239.7	2.14446
$532$	−216.784	−0.0176669
$533$	−23715.8	−1.92729
$534$	29570.8	2.39635
$535$	4309.35	0.348242
$536$	776.193	0.0625493
$537$	−6597.05	−0.530137
$538$	−13010.8	−1.04263
$539$	2055.54	0.164264
$540$	3887.76	0.309820
$541$	−8653.47	−0.687692	−0.343846	−	0.939026i	$-0.611730\pi$
$541$	−8653.47	−0.687692	−0.343846	+	0.939026i	$0.611730\pi$
$542$	542.288	0.0429765
$543$	−23968.4	−1.89426
$544$	−785.098	−0.0618765
$545$	24270.9	1.90761
$546$	−11655.7	−0.913589
$547$	−9978.05	−0.779946	−0.389973	−	0.920826i	$-0.627516\pi$
$547$	−9978.05	−0.779946	−0.389973	+	0.920826i	$0.627516\pi$
$548$	1989.69	0.155101
$549$	−29419.1	−2.28703
$550$	−28617.6	−2.21865
$551$	−6444.24	−0.498247
$552$	5755.94	0.443821
$553$	2665.49	0.204969
$554$	18140.7	1.39120
$555$	−1217.94	−0.0931511
$556$	−1726.72	−0.131707
$557$	−14884.6	−1.13228	−0.566141	−	0.824308i	$-0.691564\pi$
$557$	−14884.6	−1.13228	−0.566141	+	0.824308i	$0.691564\pi$
$558$	−18719.4	−1.42017
$559$	18506.9	1.40029
$560$	7500.69	0.566003
$561$	6223.33	0.468359
$562$	−6329.49	−0.475077
$563$	23544.1	1.76246	0.881230	−	0.472688i	$-0.156716\pi$
$563$	23544.1	1.76246	0.881230	+	0.472688i	$0.156716\pi$
$564$	−2562.91	−0.191344
$565$	−23766.4	−1.76966
$566$	9369.10	0.695782
$567$	2519.24	0.186593
$568$	−21242.8	−1.56924
$569$	15326.6	1.12922	0.564610	−	0.825358i	$-0.309027\pi$
$569$	15326.6	1.12922	0.564610	+	0.825358i	$0.309027\pi$
$570$	13603.3	0.999615
$571$	528.927	0.0387651	0.0193826	−	0.999812i	$-0.493830\pi$
$571$	528.927	0.0387651	0.0193826	+	0.999812i	$0.493830\pi$
$572$	−3113.51	−0.227592
$573$	−22989.8	−1.67611
$574$	6066.65	0.441145
$575$	7148.50	0.518457
$576$	27514.6	1.99035
$577$	−5913.14	−0.426633	−0.213317	−	0.976983i	$-0.568427\pi$
$577$	−5913.14	−0.426633	−0.213317	+	0.976983i	$0.568427\pi$
$578$	−763.139	−0.0549176
$579$	−26764.1	−1.92103
$580$	−4298.25	−0.307716
$581$	6520.49	0.465604
$582$	−22597.8	−1.60947
$583$	−907.842	−0.0644922
$584$	2458.62	0.174210
$585$	−69540.4	−4.91477
$586$	−6147.69	−0.433377
$587$	7875.31	0.553746	0.276873	−	0.960907i	$-0.410702\pi$
$587$	7875.31	0.553746	0.276873	+	0.960907i	$0.410702\pi$
$588$	−439.205	−0.0308036
$589$	4348.48	0.304203
$590$	27600.0	1.92589
$591$	1001.63	0.0697152
$592$	−390.120	−0.0270842
$593$	−13993.1	−0.969019	−0.484510	−	0.874786i	$-0.661002\pi$
$593$	−13993.1	−0.969019	−0.484510	+	0.874786i	$0.661002\pi$
$594$	−21414.8	−1.47922
$595$	−2329.92	−0.160533
$596$	−1884.84	−0.129541
$597$	−26067.3	−1.78704
$598$	−5279.78	−0.361047
$599$	−15156.8	−1.03387	−0.516937	−	0.856024i	$-0.672928\pi$
$599$	−15156.8	−1.03387	−0.516937	+	0.856024i	$0.672928\pi$
$600$	53739.9	3.65654
$601$	−7509.86	−0.509707	−0.254853	−	0.966980i	$-0.582027\pi$
$601$	−7509.86	−0.509707	−0.254853	+	0.966980i	$0.582027\pi$
$602$	−4734.19	−0.320517
$603$	1600.53	0.108091
$604$	−3557.35	−0.239646
$605$	−8395.29	−0.564161
$606$	38559.8	2.58480
$607$	20812.3	1.39167	0.695837	−	0.718200i	$-0.255034\pi$
$607$	20812.3	1.39167	0.695837	+	0.718200i	$0.255034\pi$
$608$	−1392.44	−0.0928798
$609$	−13056.1	−0.868732
$610$	−30944.2	−2.05392
$611$	20661.2	1.36802
$612$	−858.277	−0.0566892
$613$	25261.4	1.66444	0.832218	−	0.554449i	$-0.187071\pi$
$613$	25261.4	1.66444	0.832218	+	0.554449i	$0.187071\pi$
$614$	−700.043	−0.0460121
$615$	56076.8	3.67680
$616$	6999.77	0.457839
$617$	3947.07	0.257542	0.128771	−	0.991674i	$-0.458897\pi$
$617$	3947.07	0.257542	0.128771	+	0.991674i	$0.458897\pi$
$618$	−9418.75	−0.613071
$619$	−800.441	−0.0519749	−0.0259874	−	0.999662i	$-0.508273\pi$
$619$	−800.441	−0.0519749	−0.0259874	+	0.999662i	$0.508273\pi$
$620$	2900.40	0.187875
$621$	5349.27	0.345667
$622$	−23139.8	−1.49168
$623$	−8982.79	−0.577669
$624$	−34510.0	−2.21395
$625$	18823.4	1.20470
$626$	9150.46	0.584227
$627$	11037.6	0.703030
$628$	820.515	0.0521371
$629$	121.182	0.00768179
$630$	17788.9	1.12496
$631$	20505.4	1.29367	0.646837	−	0.762628i	$-0.276091\pi$
$631$	20505.4	1.29367	0.646837	+	0.762628i	$0.276091\pi$
$632$	9076.83	0.571293
$633$	−4186.41	−0.262867
$634$	7279.33	0.455993
$635$	45172.1	2.82299
$636$	193.978	0.0120939
$637$	3540.70	0.220232
$638$	23675.9	1.46918
$639$	−43803.4	−2.71179
$640$	21707.2	1.34071
$641$	−15289.2	−0.942101	−0.471050	−	0.882106i	$-0.656125\pi$
$641$	−15289.2	−0.942101	−0.471050	+	0.882106i	$0.656125\pi$
$642$	5071.86	0.311792
$643$	9845.41	0.603834	0.301917	−	0.953334i	$-0.402374\pi$
$643$	9845.41	0.603834	0.301917	+	0.953334i	$0.402374\pi$
$644$	−198.950	−0.0121735
$645$	−43760.3	−2.67141
$646$	−1353.49	−0.0824342
$647$	30137.3	1.83125	0.915625	−	0.402034i	$-0.131696\pi$
$647$	30137.3	1.83125	0.915625	+	0.402034i	$0.131696\pi$
$648$	8578.81	0.520073
$649$	22394.4	1.35448
$650$	−49294.2	−2.97458
$651$	8810.03	0.530403
$652$	419.638	0.0252060
$653$	17680.2	1.05954	0.529769	−	0.848142i	$-0.322279\pi$
$653$	17680.2	1.05954	0.529769	+	0.848142i	$0.322279\pi$
$654$	28565.4	1.70794
$655$	−678.028	−0.0404469
$656$	17962.0	1.06905
$657$	5069.75	0.301050
$658$	−5285.26	−0.313132
$659$	−9959.15	−0.588700	−0.294350	−	0.955698i	$-0.595103\pi$
$659$	−9959.15	−0.588700	−0.294350	+	0.955698i	$0.595103\pi$
$660$	7362.00	0.434190
$661$	−5660.03	−0.333056	−0.166528	−	0.986037i	$-0.553256\pi$
$661$	−5660.03	−0.333056	−0.166528	+	0.986037i	$0.553256\pi$
$662$	2556.40	0.150087
$663$	10719.8	0.627935
$664$	22204.3	1.29773
$665$	−4132.32	−0.240969
$666$	−925.222	−0.0538313
$667$	−5914.08	−0.343320
$668$	−3422.24	−0.198219
$669$	−18044.7	−1.04282
$670$	1683.50	0.0970737
$671$	−25107.8	−1.44453
$672$	−2821.09	−0.161943
$673$	8237.78	0.471832	0.235916	−	0.971773i	$-0.424191\pi$
$673$	8237.78	0.471832	0.235916	+	0.971773i	$0.424191\pi$
$674$	3152.46	0.180161
$675$	49943.1	2.84787
$676$	−3106.45	−0.176744
$677$	−31531.4	−1.79003	−0.895015	−	0.446035i	$-0.852836\pi$
$677$	−31531.4	−1.79003	−0.895015	+	0.446035i	$0.852836\pi$
$678$	−27971.7	−1.58443
$679$	6864.59	0.387981
$680$	−7934.12	−0.447440
$681$	47893.9	2.69500
$682$	−15976.1	−0.897005
$683$	−23706.5	−1.32812	−0.664059	−	0.747681i	$-0.731167\pi$
$683$	−23706.5	−1.32812	−0.664059	+	0.747681i	$0.731167\pi$
$684$	−1522.23	−0.0850934
$685$	37927.3	2.11551
$686$	−905.732	−0.0504096
$687$	2741.70	0.152259
$688$	−14016.9	−0.776727
$689$	−1563.77	−0.0864657
$690$	12484.2	0.688790
$691$	−23330.9	−1.28444	−0.642221	−	0.766519i	$-0.721987\pi$
$691$	−23330.9	−1.28444	−0.642221	+	0.766519i	$0.721987\pi$
$692$	3004.86	0.165069
$693$	14433.7	0.791187
$694$	15924.8	0.871033
$695$	−32914.5	−1.79643
$696$	−44460.0	−2.42134
$697$	−5579.49	−0.303211
$698$	19775.7	1.07238
$699$	−51316.3	−2.77677
$700$	−1857.48	−0.100294
$701$	10586.4	0.570387	0.285193	−	0.958470i	$-0.407942\pi$
$701$	10586.4	0.570387	0.285193	+	0.958470i	$0.407942\pi$
$702$	−36887.2	−1.98322
$703$	214.927	0.0115308
$704$	23482.4	1.25714
$705$	−48854.0	−2.60986
$706$	−14174.4	−0.755611
$707$	−11713.4	−0.623096
$708$	−4784.98	−0.253998
$709$	15057.2	0.797581	0.398791	−	0.917042i	$-0.369430\pi$
$709$	15057.2	0.797581	0.398791	+	0.917042i	$0.369430\pi$
$710$	−46074.1	−2.43539
$711$	18716.7	0.987245
$712$	−30589.2	−1.61008
$713$	3990.73	0.209613
$714$	−2742.18	−0.143731
$715$	−59349.5	−3.10426
$716$	776.486	0.0405288
$717$	−42409.6	−2.20895
$718$	−4050.58	−0.210538
$719$	6018.52	0.312174	0.156087	−	0.987743i	$-0.450112\pi$
$719$	6018.52	0.312174	0.156087	+	0.987743i	$0.450112\pi$
$720$	52668.8	2.72618
$721$	2861.16	0.147788
$722$	15711.5	0.809862
$723$	41813.1	2.15082
$724$	2821.13	0.144816
$725$	−55216.4	−2.82853
$726$	−9880.78	−0.505110
$727$	22036.3	1.12418	0.562090	−	0.827076i	$-0.309997\pi$
$727$	22036.3	1.12418	0.562090	+	0.827076i	$0.309997\pi$
$728$	12057.2	0.613831
$729$	−27859.9	−1.41543
$730$	5332.55	0.270365
$731$	4354.03	0.220300
$732$	5364.77	0.270885
$733$	15512.8	0.781688	0.390844	−	0.920457i	$-0.372183\pi$
$733$	15512.8	0.781688	0.390844	+	0.920457i	$0.372183\pi$
$734$	2419.17	0.121653
$735$	−8372.09	−0.420149
$736$	−1277.89	−0.0639993
$737$	1365.98	0.0682721
$738$	42599.2	2.12479
$739$	13157.0	0.654921	0.327461	−	0.944865i	$-0.393807\pi$
$739$	13157.0	0.654921	0.327461	+	0.944865i	$0.393807\pi$
$740$	143.355	0.00712138
$741$	19012.4	0.942563
$742$	400.022	0.0197915
$743$	22042.4	1.08837	0.544184	−	0.838966i	$-0.316839\pi$
$743$	22042.4	1.08837	0.544184	+	0.838966i	$0.316839\pi$
$744$	30000.9	1.47834
$745$	−35928.7	−1.76688
$746$	15505.8	0.761000
$747$	45786.0	2.24260
$748$	−732.499	−0.0358059
$749$	−1540.69	−0.0751610
$750$	60161.0	2.92903
$751$	22833.3	1.10945	0.554726	−	0.832033i	$-0.312823\pi$
$751$	22833.3	1.10945	0.554726	+	0.832033i	$0.312823\pi$
$752$	−15648.5	−0.758830
$753$	10114.4	0.489493
$754$	40782.0	1.96975
$755$	−67809.8	−3.26868
$756$	−1389.96	−0.0668684
$757$	−15095.8	−0.724792	−0.362396	−	0.932024i	$-0.618041\pi$
$757$	−15095.8	−0.724792	−0.362396	+	0.932024i	$0.618041\pi$
$758$	17591.5	0.842946
$759$	10129.6	0.484427
$760$	−14071.8	−0.671631
$761$	19033.7	0.906662	0.453331	−	0.891342i	$-0.350236\pi$
$761$	19033.7	0.906662	0.453331	+	0.891342i	$0.350236\pi$
$762$	53164.9	2.52751
$763$	−8677.39	−0.411720
$764$	2705.94	0.128138
$765$	−16360.4	−0.773217
$766$	−20089.5	−0.947600
$767$	38574.6	1.81597
$768$	−13531.1	−0.635756
$769$	16419.8	0.769980	0.384990	−	0.922921i	$-0.374205\pi$
$769$	16419.8	0.769980	0.384990	+	0.922921i	$0.374205\pi$
$770$	15182.0	0.710545
$771$	−39186.2	−1.83043
$772$	3150.18	0.146862
$773$	17271.0	0.803614	0.401807	−	0.915724i	$-0.368382\pi$
$773$	17271.0	0.803614	0.401807	+	0.915724i	$0.368382\pi$
$774$	−33242.9	−1.54379
$775$	37259.2	1.72695
$776$	23376.1	1.08138
$777$	435.443	0.0201048
$778$	14112.3	0.650320
$779$	−9895.71	−0.455135
$780$	12681.1	0.582125
$781$	−37384.1	−1.71281
$782$	−1242.14	−0.0568017
$783$	−41318.8	−1.88584
$784$	−2681.67	−0.122161
$785$	15640.6	0.711128
$786$	−798.000	−0.0362134
$787$	−28856.3	−1.30701	−0.653504	−	0.756923i	$-0.726702\pi$
$787$	−28856.3	−1.30701	−0.653504	+	0.756923i	$0.726702\pi$
$788$	−117.894	−0.00532971
$789$	53526.6	2.41521
$790$	19686.9	0.886620
$791$	8497.03	0.381946
$792$	49151.4	2.20520
$793$	−43248.6	−1.93670
$794$	−21529.1	−0.962265
$795$	3697.58	0.164956
$796$	3068.17	0.136619
$797$	19199.7	0.853309	0.426654	−	0.904415i	$-0.359692\pi$
$797$	19199.7	0.853309	0.426654	+	0.904415i	$0.359692\pi$
$798$	−4863.50	−0.215747
$799$	4860.84	0.215224
$800$	−11930.9	−0.527275
$801$	−63075.9	−2.78237
$802$	5440.98	0.239561
$803$	4326.79	0.190148
$804$	−291.868	−0.0128027
$805$	−3792.36	−0.166041
$806$	−27519.1	−1.20263
$807$	42997.4	1.87556
$808$	−39887.9	−1.73670
$809$	−15459.9	−0.671867	−0.335933	−	0.941886i	$-0.609052\pi$
$809$	−15459.9	−0.671867	−0.335933	+	0.941886i	$0.609052\pi$
$810$	18606.8	0.807130
$811$	−26525.2	−1.14849	−0.574245	−	0.818684i	$-0.694704\pi$
$811$	−26525.2	−1.14849	−0.574245	+	0.818684i	$0.694704\pi$
$812$	1536.72	0.0664144
$813$	−1792.12	−0.0773094
$814$	−789.633	−0.0340008
$815$	7999.09	0.343799
$816$	−8118.98	−0.348310
$817$	7722.25	0.330682
$818$	7829.94	0.334679
$819$	24862.3	1.06076
$820$	−6600.35	−0.281091
$821$	−14151.2	−0.601560	−0.300780	−	0.953694i	$-0.597247\pi$
$821$	−14151.2	−0.601560	−0.300780	+	0.953694i	$0.597247\pi$
$822$	44638.2	1.89408
$823$	−1706.12	−0.0722619	−0.0361309	−	0.999347i	$-0.511503\pi$
$823$	−1706.12	−0.0722619	−0.0361309	+	0.999347i	$0.511503\pi$
$824$	9743.15	0.411916
$825$	94573.9	3.99108
$826$	−9867.62	−0.415664
$827$	−7176.88	−0.301771	−0.150886	−	0.988551i	$-0.548212\pi$
$827$	−7176.88	−0.301771	−0.150886	+	0.988551i	$0.548212\pi$
$828$	−1397.00	−0.0586341
$829$	43183.4	1.80919	0.904596	−	0.426270i	$-0.140173\pi$
$829$	43183.4	1.80919	0.904596	+	0.426270i	$0.140173\pi$
$830$	48159.5	2.01403
$831$	−59950.5	−2.50260
$832$	40448.7	1.68546
$833$	833.000	0.0346479
$834$	−38738.5	−1.60840
$835$	−65234.4	−2.70363
$836$	−1299.15	−0.0537465
$837$	27881.3	1.15140
$838$	6417.39	0.264541
$839$	5362.69	0.220668	0.110334	−	0.993895i	$-0.464808\pi$
$839$	5362.69	0.220668	0.110334	+	0.993895i	$0.464808\pi$
$840$	−28509.6	−1.17104
$841$	21292.5	0.873038
$842$	5493.63	0.224849
$843$	20917.4	0.854605
$844$	492.750	0.0200961
$845$	−59214.8	−2.41071
$846$	−37112.4	−1.50822
$847$	3001.51	0.121763
$848$	1184.37	0.0479618
$849$	−30962.5	−1.25163
$850$	−11597.2	−0.467976
$851$	197.245	0.00794534
$852$	7987.82	0.321195
$853$	−15094.3	−0.605884	−0.302942	−	0.953009i	$-0.597969\pi$
$853$	−15094.3	−0.605884	−0.302942	+	0.953009i	$0.597969\pi$
$854$	11063.3	0.443299
$855$	−29016.6	−1.16064
$856$	−5246.54	−0.209490
$857$	20220.7	0.805983	0.402991	−	0.915204i	$-0.367970\pi$
$857$	20220.7	0.805983	0.402991	+	0.915204i	$0.367970\pi$
$858$	−69850.9	−2.77934
$859$	5596.92	0.222310	0.111155	−	0.993803i	$-0.464545\pi$
$859$	5596.92	0.222310	0.111155	+	0.993803i	$0.464545\pi$
$860$	5150.67	0.204229
$861$	−20048.7	−0.793565
$862$	−10493.1	−0.414612
$863$	−21623.0	−0.852901	−0.426451	−	0.904511i	$-0.640236\pi$
$863$	−21623.0	−0.852901	−0.426451	+	0.904511i	$0.640236\pi$
$864$	−8927.97	−0.351546
$865$	57278.4	2.25147
$866$	−2829.37	−0.111023
$867$	2521.98	0.0987900
$868$	−1036.96	−0.0405492
$869$	15973.8	0.623561
$870$	−96430.3	−3.75781
$871$	2352.92	0.0915334
$872$	−29549.3	−1.14755
$873$	48202.3	1.86873
$874$	−2203.05	−0.0852623
$875$	−18275.3	−0.706077
$876$	−924.500	−0.0356575
$877$	6883.48	0.265039	0.132519	−	0.991180i	$-0.457693\pi$
$877$	6883.48	0.265039	0.132519	+	0.991180i	$0.457693\pi$
$878$	−28213.1	−1.08445
$879$	20316.6	0.779591
$880$	44950.3	1.72190
$881$	−17892.1	−0.684222	−0.342111	−	0.939660i	$-0.611142\pi$
$881$	−17892.1	−0.684222	−0.342111	+	0.939660i	$0.611142\pi$
$882$	−6359.93	−0.242800
$883$	40546.5	1.54530	0.772649	−	0.634833i	$-0.218931\pi$
$883$	40546.5	1.54530	0.772649	+	0.634833i	$0.218931\pi$
$884$	−1261.74	−0.0480055
$885$	−91210.9	−3.46443
$886$	8848.92	0.335537
$887$	−36470.9	−1.38058	−0.690289	−	0.723534i	$-0.742516\pi$
$887$	−36470.9	−1.38058	−0.690289	+	0.723534i	$0.742516\pi$
$888$	1482.82	0.0560363
$889$	−16150.1	−0.609286
$890$	−66345.7	−2.49878
$891$	15097.4	0.567656
$892$	2123.89	0.0797233
$893$	8621.13	0.323063
$894$	−42286.0	−1.58194
$895$	14801.3	0.552797
$896$	−7760.82	−0.289365
$897$	17448.3	0.649479
$898$	−36488.2	−1.35593
$899$	−30825.2	−1.14358
$900$	−13043.0	−0.483072
$901$	−367.899	−0.0136032
$902$	36356.4	1.34206
$903$	15645.3	0.576570
$904$	28935.1	1.06456
$905$	53776.2	1.97523
$906$	−79808.3	−2.92655
$907$	16.6105	0.000608095 0	0.000304047	−	1.00000i	$-0.499903\pi$
$907$	16.6105	0.000608095 0	0.000304047		1.00000i	$0.499903\pi$
$908$	−5637.21	−0.206032
$909$	−82250.1	−3.00117
$910$	26151.1	0.952639
$911$	19566.1	0.711586	0.355793	−	0.934565i	$-0.384211\pi$
$911$	19566.1	0.711586	0.355793	+	0.934565i	$0.384211\pi$
$912$	−14399.7	−0.522832
$913$	39076.2	1.41647
$914$	10992.0	0.397792
$915$	102263.	3.69475
$916$	−322.703	−0.0116402
$917$	242.411	0.00872966
$918$	−8678.25	−0.312010
$919$	7912.68	0.284021	0.142010	−	0.989865i	$-0.454643\pi$
$919$	7912.68	0.284021	0.142010	+	0.989865i	$0.454643\pi$
$920$	−12914.2	−0.462791
$921$	2313.46	0.0827700
$922$	−40276.2	−1.43864
$923$	−64394.6	−2.29640
$924$	−2632.08	−0.0937112
$925$	1841.57	0.0654598
$926$	11640.1	0.413084
$927$	20090.7	0.711828
$928$	9870.64	0.349159
$929$	9268.53	0.327331	0.163665	−	0.986516i	$-0.447668\pi$
$929$	9268.53	0.327331	0.163665	+	0.986516i	$0.447668\pi$
$930$	65069.7	2.29432
$931$	1477.40	0.0520084
$932$	6040.03	0.212283
$933$	76471.3	2.68334
$934$	10987.4	0.384923
$935$	−13962.8	−0.488377
$936$	84664.0	2.95655
$937$	−13796.6	−0.481019	−0.240510	−	0.970647i	$-0.577315\pi$
$937$	−13796.6	−0.481019	−0.240510	+	0.970647i	$0.577315\pi$
$938$	−601.891	−0.0209514
$939$	−30239.9	−1.05095
$940$	5750.22	0.199523
$941$	18812.8	0.651732	0.325866	−	0.945416i	$-0.394344\pi$
$941$	18812.8	0.651732	0.325866	+	0.945416i	$0.394344\pi$
$942$	18408.1	0.636695
$943$	−9081.60	−0.313614
$944$	−29215.8	−1.00730
$945$	−26495.4	−0.912057
$946$	−28371.2	−0.975082
$947$	−1398.42	−0.0479857	−0.0239928	−	0.999712i	$-0.507638\pi$
$947$	−1398.42	−0.0479857	−0.0239928	+	0.999712i	$0.507638\pi$
$948$	−3413.11	−0.116933
$949$	7452.95	0.254935
$950$	−20568.6	−0.702456
$951$	−24056.3	−0.820274
$952$	2836.63	0.0965711
$953$	−5165.69	−0.175586	−0.0877928	−	0.996139i	$-0.527981\pi$
$953$	−5165.69	−0.175586	−0.0877928	+	0.996139i	$0.527981\pi$
$954$	2808.90	0.0953266
$955$	51580.4	1.74775
$956$	4991.69	0.168873
$957$	−78242.7	−2.64287
$958$	−2318.24	−0.0781825
$959$	−13559.9	−0.456591
$960$	−95642.2	−3.21546
$961$	−8990.63	−0.301790
$962$	−1360.15	−0.0455853
$963$	−10818.5	−0.362017
$964$	−4921.48	−0.164430
$965$	60048.5	2.00314
$966$	−4463.39	−0.148662
$967$	−8767.85	−0.291577	−0.145789	−	0.989316i	$-0.546572\pi$
$967$	−8767.85	−0.291577	−0.145789	+	0.989316i	$0.546572\pi$
$968$	10221.1	0.339379
$969$	4472.95	0.148289
$970$	50701.0	1.67826
$971$	−22934.1	−0.757973	−0.378986	−	0.925402i	$-0.623727\pi$
$971$	−22934.1	−0.757973	−0.378986	+	0.925402i	$0.623727\pi$
$972$	2135.45	0.0704676
$973$	11767.7	0.387724
$974$	35355.7	1.16311
$975$	162905.	5.35090
$976$	32755.8	1.07427
$977$	8730.94	0.285903	0.142952	−	0.989730i	$-0.454341\pi$
$977$	8730.94	0.285903	0.142952	+	0.989730i	$0.454341\pi$
$978$	9414.47	0.307814
$979$	−53832.3	−1.75739
$980$	985.412	0.0321202
$981$	−60931.5	−1.98307
$982$	−19216.0	−0.624447
$983$	−28904.7	−0.937860	−0.468930	−	0.883235i	$-0.655360\pi$
$983$	−28904.7	−0.937860	−0.468930	+	0.883235i	$0.655360\pi$
$984$	−68272.3	−2.21183
$985$	−2247.29	−0.0726950
$986$	9594.55	0.309891
$987$	17466.4	0.563286
$988$	−2237.80	−0.0720587
$989$	7086.95	0.227858
$990$	106606.	3.42238
$991$	19912.8	0.638295	0.319147	−	0.947705i	$-0.396603\pi$
$991$	19912.8	0.638295	0.319147	+	0.947705i	$0.396603\pi$
$992$	−6660.56	−0.213178
$993$	−8448.26	−0.269987
$994$	16472.5	0.525631
$995$	58485.1	1.86342
$996$	−8349.38	−0.265623
$997$	9279.98	0.294784	0.147392	−	0.989078i	$-0.452912\pi$
$997$	9279.98	0.294784	0.147392	+	0.989078i	$0.452912\pi$
$998$	14510.5	0.460241
$999$	1378.06	0.0436434

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.4.a.e.1.3	✓	9
3.2	odd	2		1071.4.a.r.1.7		9
4.3	odd	2		1904.4.a.s.1.1		9
7.6	odd	2		833.4.a.g.1.3		9
17.16	even	2		2023.4.a.h.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.4.a.e.1.3	✓	9	1.1	even	1	trivial
833.4.a.g.1.3		9	7.6	odd	2
1071.4.a.r.1.7		9	3.2	odd	2
1904.4.a.s.1.1		9	4.3	odd	2
2023.4.a.h.1.3		9	17.16	even	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:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	119.a (trivial)

\(f(q)\)	\(=\)	\(q-2.64062 q^{2} +8.72657 q^{3} -1.02714 q^{4} -19.5792 q^{5} -23.0435 q^{6} +7.00000 q^{7} +23.8372 q^{8} +49.1531 q^{9} +51.7011 q^{10} +41.9498 q^{11} -8.96337 q^{12} +72.2591 q^{13} -18.4843 q^{14} -170.859 q^{15} -54.7279 q^{16} +17.0000 q^{17} -129.794 q^{18} +30.1510 q^{19} +20.1105 q^{20} +61.0860 q^{21} -110.773 q^{22} +27.6705 q^{23} +208.017 q^{24} +258.344 q^{25} -190.809 q^{26} +193.320 q^{27} -7.18995 q^{28} -213.732 q^{29} +451.173 q^{30} +144.223 q^{31} -46.1822 q^{32} +366.078 q^{33} -44.8905 q^{34} -137.054 q^{35} -50.4869 q^{36} +7.12836 q^{37} -79.6172 q^{38} +630.574 q^{39} -466.713 q^{40} -328.205 q^{41} -161.305 q^{42} +256.119 q^{43} -43.0882 q^{44} -962.376 q^{45} -73.0673 q^{46} +285.932 q^{47} -477.587 q^{48} +49.0000 q^{49} -682.187 q^{50} +148.352 q^{51} -74.2199 q^{52} -21.6411 q^{53} -510.485 q^{54} -821.342 q^{55} +166.861 q^{56} +263.115 q^{57} +564.386 q^{58} +533.837 q^{59} +175.495 q^{60} -598.521 q^{61} -380.839 q^{62} +344.072 q^{63} +559.773 q^{64} -1414.77 q^{65} -966.673 q^{66} +32.5622 q^{67} -17.4613 q^{68} +241.469 q^{69} +361.908 q^{70} -891.162 q^{71} +1171.67 q^{72} +103.142 q^{73} -18.8233 q^{74} +2254.45 q^{75} -30.9692 q^{76} +293.649 q^{77} -1665.11 q^{78} +380.784 q^{79} +1071.53 q^{80} +359.892 q^{81} +866.664 q^{82} +931.499 q^{83} -62.7436 q^{84} -332.846 q^{85} -676.313 q^{86} -1865.15 q^{87} +999.967 q^{88} -1283.26 q^{89} +2541.27 q^{90} +505.814 q^{91} -28.4214 q^{92} +1258.58 q^{93} -755.037 q^{94} -590.331 q^{95} -403.013 q^{96} +980.656 q^{97} -129.390 q^{98} +2061.96 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 2 q^{2} + 11 q^{3} + 38 q^{4} - 3 q^{5} + 9 q^{6} + 63 q^{7} + 24 q^{8} + 74 q^{9} + 134 q^{10} - 8 q^{11} + 56 q^{12} + 164 q^{13} + 14 q^{14} + 34 q^{15} + 178 q^{16} + 153 q^{17} + 98 q^{18} + 244 q^{19}+ \cdots - 2396 q^{99}+O(q^{100}) \) 9 * q + 2 * q^2 + 11 * q^3 + 38 * q^4 - 3 * q^5 + 9 * q^6 + 63 * q^7 + 24 * q^8 + 74 * q^9 + 134 * q^10 - 8 * q^11 + 56 * q^12 + 164 * q^13 + 14 * q^14 + 34 * q^15 + 178 * q^16 + 153 * q^17 + 98 * q^18 + 244 * q^19 - 41 * q^20 + 77 * q^21 - 80 * q^22 - 14 * q^23 + 298 * q^24 + 684 * q^25 + 326 * q^26 + 218 * q^27 + 266 * q^28 - 234 * q^29 - 335 * q^30 + 555 * q^31 - 181 * q^32 + 458 * q^33 + 34 * q^34 - 21 * q^35 - 1221 * q^36 - 364 * q^37 - 714 * q^38 - 52 * q^39 + 123 * q^40 - 45 * q^41 + 63 * q^42 - 135 * q^43 - 748 * q^44 - 844 * q^45 - 1576 * q^46 - 172 * q^47 - 949 * q^48 + 441 * q^49 - 2901 * q^50 + 187 * q^51 - 1596 * q^52 + 101 * q^53 - 1163 * q^54 + 1260 * q^55 + 168 * q^56 - 602 * q^57 + 1062 * q^58 + 280 * q^59 - 1727 * q^60 + 639 * q^61 - 1708 * q^62 + 518 * q^63 - 2390 * q^64 + 638 * q^65 - 2476 * q^66 + 35 * q^67 + 646 * q^68 + 1288 * q^69 + 938 * q^70 - 1616 * q^71 + 1335 * q^72 + 1049 * q^73 - 370 * q^74 + 1260 * q^75 + 4964 * q^76 - 56 * q^77 - 4714 * q^78 + 2304 * q^79 - 3996 * q^80 - 791 * q^81 - 215 * q^82 + 2508 * q^83 + 392 * q^84 - 51 * q^85 + 623 * q^86 + 166 * q^87 - 416 * q^88 + 2762 * q^89 + 2935 * q^90 + 1148 * q^91 - 2392 * q^92 + 2784 * q^93 - 862 * q^94 - 3462 * q^95 + 2928 * q^96 + 3107 * q^97 + 98 * q^98 - 2396 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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