LMFDB - Embedded newform 1682.4.a.k.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1682,4,Mod(1,1682)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1682, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1682.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 1682 = 2 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1682.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,-12,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$99.2412126297$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 97x^{4} - 87x^{3} + 1809x^{2} + 1890x - 1620 $ x^6 - x^5 - 97x^4 - 87x^3 + 1809x^2 + 1890x - 1620
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-5.84101$ of defining polynomial
Character	$\chi$	$=$	1682.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +7.45095 q^{3} +4.00000 q^{4} -7.82664 q^{5} -14.9019 q^{6} +2.70016 q^{7} -8.00000 q^{8} +28.5167 q^{9} +15.6533 q^{10} +27.6893 q^{11} +29.8038 q^{12} +19.8389 q^{13} -5.40031 q^{14} -58.3159 q^{15} +16.0000 q^{16} -105.283 q^{17} -57.0333 q^{18} +119.879 q^{19} -31.3066 q^{20} +20.1187 q^{21} -55.3787 q^{22} -77.4698 q^{23} -59.6076 q^{24} -63.7437 q^{25} -39.6777 q^{26} +11.3006 q^{27} +10.8006 q^{28} +116.632 q^{30} -294.938 q^{31} -32.0000 q^{32} +206.312 q^{33} +210.566 q^{34} -21.1331 q^{35} +114.067 q^{36} -97.3759 q^{37} -239.757 q^{38} +147.818 q^{39} +62.6131 q^{40} -69.2556 q^{41} -40.2374 q^{42} -537.409 q^{43} +110.757 q^{44} -223.190 q^{45} +154.940 q^{46} +168.858 q^{47} +119.215 q^{48} -335.709 q^{49} +127.487 q^{50} -784.459 q^{51} +79.3555 q^{52} -109.193 q^{53} -22.6012 q^{54} -216.714 q^{55} -21.6012 q^{56} +893.211 q^{57} +416.074 q^{59} -233.264 q^{60} +626.162 q^{61} +589.875 q^{62} +76.9994 q^{63} +64.0000 q^{64} -155.272 q^{65} -412.624 q^{66} +286.046 q^{67} -421.133 q^{68} -577.224 q^{69} +42.2663 q^{70} +1066.48 q^{71} -228.133 q^{72} +132.201 q^{73} +194.752 q^{74} -474.951 q^{75} +479.515 q^{76} +74.7655 q^{77} -295.637 q^{78} -206.432 q^{79} -125.226 q^{80} -685.750 q^{81} +138.511 q^{82} +762.855 q^{83} +80.4749 q^{84} +824.013 q^{85} +1074.82 q^{86} -221.515 q^{88} +722.523 q^{89} +446.379 q^{90} +53.5680 q^{91} -309.879 q^{92} -2197.57 q^{93} -337.715 q^{94} -938.248 q^{95} -238.430 q^{96} -647.151 q^{97} +671.418 q^{98} +789.607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 12 q^{2} - 10 q^{3} + 24 q^{4} - 10 q^{5} + 20 q^{6} - 26 q^{7} - 48 q^{8} + 54 q^{9} + 20 q^{10} + 89 q^{11} - 40 q^{12} - 86 q^{13} + 52 q^{14} - 89 q^{15} + 96 q^{16} + 95 q^{17} - 108 q^{18} + 30 q^{19}+ \cdots + 3854 q^{99}+O(q^{100}) $ 6 * q - 12 * q^2 - 10 * q^3 + 24 * q^4 - 10 * q^5 + 20 * q^6 - 26 * q^7 - 48 * q^8 + 54 * q^9 + 20 * q^10 + 89 * q^11 - 40 * q^12 - 86 * q^13 + 52 * q^14 - 89 * q^15 + 96 * q^16 + 95 * q^17 - 108 * q^18 + 30 * q^19 - 40 * q^20 + 346 * q^21 - 178 * q^22 - 377 * q^23 + 80 * q^24 - 66 * q^25 + 172 * q^26 - 115 * q^27 - 104 * q^28 + 178 * q^30 - 454 * q^31 - 192 * q^32 - 85 * q^33 - 190 * q^34 - 322 * q^35 + 216 * q^36 - 50 * q^37 - 60 * q^38 + 1131 * q^39 + 80 * q^40 + 730 * q^41 - 692 * q^42 + 62 * q^43 + 356 * q^44 - 352 * q^45 + 754 * q^46 + 191 * q^47 - 160 * q^48 - 528 * q^49 + 132 * q^50 - 1095 * q^51 - 344 * q^52 + 347 * q^53 + 230 * q^54 + 1468 * q^55 + 208 * q^56 + 648 * q^57 - 49 * q^59 - 356 * q^60 + 616 * q^61 + 908 * q^62 - 2297 * q^63 + 384 * q^64 - 1408 * q^65 + 170 * q^66 + 611 * q^67 + 380 * q^68 + 1826 * q^69 + 644 * q^70 + 214 * q^71 - 432 * q^72 + 865 * q^73 + 100 * q^74 - 29 * q^75 + 120 * q^76 - 2687 * q^77 - 2262 * q^78 - 1134 * q^79 - 160 * q^80 - 78 * q^81 - 1460 * q^82 + 900 * q^83 + 1384 * q^84 + 2454 * q^85 - 124 * q^86 - 712 * q^88 + 293 * q^89 + 704 * q^90 + 1576 * q^91 - 1508 * q^92 - 2360 * q^93 - 382 * q^94 - 4031 * q^95 + 320 * q^96 + 3918 * q^97 + 1056 * q^98 + 3854 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	7.45095	1.43394	0.716968	−	0.697106i	$-0.245529\pi$
$3$	7.45095	1.43394	0.716968	+	0.697106i	$0.245529\pi$
$4$	4.00000	0.500000
$5$	−7.82664	−0.700036	−0.350018	−	0.936743i	$-0.613825\pi$
$5$	−7.82664	−0.700036	−0.350018	+	0.936743i	$0.613825\pi$
$6$	−14.9019	−1.01395
$7$	2.70016	0.145795	0.0728973	−	0.997339i	$-0.476775\pi$
$7$	2.70016	0.145795	0.0728973	+	0.997339i	$0.476775\pi$
$8$	−8.00000	−0.353553
$9$	28.5167	1.05617
$10$	15.6533	0.495000
$11$	27.6893	0.758968	0.379484	−	0.925198i	$-0.376102\pi$
$11$	27.6893	0.758968	0.379484	+	0.925198i	$0.376102\pi$
$12$	29.8038	0.716968
$13$	19.8389	0.423255	0.211627	−	0.977350i	$-0.432124\pi$
$13$	19.8389	0.423255	0.211627	+	0.977350i	$0.432124\pi$
$14$	−5.40031	−0.103092
$15$	−58.3159	−1.00381
$16$	16.0000	0.250000
$17$	−105.283	−1.50205	−0.751027	−	0.660272i	$-0.770441\pi$
$17$	−105.283	−1.50205	−0.751027	+	0.660272i	$0.770441\pi$
$18$	−57.0333	−0.746827
$19$	119.879	1.44748	0.723739	−	0.690074i	$-0.242422\pi$
$19$	119.879	1.44748	0.723739	+	0.690074i	$0.242422\pi$
$20$	−31.3066	−0.350018
$21$	20.1187	0.209060
$22$	−55.3787	−0.536671
$23$	−77.4698	−0.702330	−0.351165	−	0.936314i	$-0.614214\pi$
$23$	−77.4698	−0.702330	−0.351165	+	0.936314i	$0.614214\pi$
$24$	−59.6076	−0.506973
$25$	−63.7437	−0.509950
$26$	−39.6777	−0.299286
$27$	11.3006	0.0805480
$28$	10.8006	0.0728973
$29$	0	0
$29$	0	0
$30$	116.632	0.709799
$31$	−294.938	−1.70879	−0.854393	−	0.519628i	$-0.826071\pi$
$31$	−294.938	−1.70879	−0.854393	+	0.519628i	$0.826071\pi$
$32$	−32.0000	−0.176777
$33$	206.312	1.08831
$34$	210.566	1.06211
$35$	−21.1331	−0.102062
$36$	114.067	0.528086
$37$	−97.3759	−0.432662	−0.216331	−	0.976320i	$-0.569409\pi$
$37$	−97.3759	−0.432662	−0.216331	+	0.976320i	$0.569409\pi$
$38$	−239.757	−1.02352
$39$	147.818	0.606920
$40$	62.6131	0.247500
$41$	−69.2556	−0.263803	−0.131901	−	0.991263i	$-0.542108\pi$
$41$	−69.2556	−0.263803	−0.131901	+	0.991263i	$0.542108\pi$
$42$	−40.2374	−0.147828
$43$	−537.409	−1.90591	−0.952955	−	0.303113i	$-0.901974\pi$
$43$	−537.409	−1.90591	−0.952955	+	0.303113i	$0.901974\pi$
$44$	110.757	0.379484
$45$	−223.190	−0.739359
$46$	154.940	0.496622
$47$	168.858	0.524052	0.262026	−	0.965061i	$-0.415609\pi$
$47$	168.858	0.524052	0.262026	+	0.965061i	$0.415609\pi$
$48$	119.215	0.358484
$49$	−335.709	−0.978744
$50$	127.487	0.360589
$51$	−784.459	−2.15385
$52$	79.3555	0.211627
$53$	−109.193	−0.282997	−0.141499	−	0.989938i	$-0.545192\pi$
$53$	−109.193	−0.282997	−0.141499	+	0.989938i	$0.545192\pi$
$54$	−22.6012	−0.0569561
$55$	−216.714	−0.531305
$56$	−21.6012	−0.0515462
$57$	893.211	2.07559
$58$	0	0
$59$	416.074	0.918105	0.459052	−	0.888409i	$-0.348189\pi$
$59$	416.074	0.918105	0.459052	+	0.888409i	$0.348189\pi$
$60$	−233.264	−0.501903
$61$	626.162	1.31429	0.657146	−	0.753764i	$-0.271764\pi$
$61$	626.162	1.31429	0.657146	+	0.753764i	$0.271764\pi$
$62$	589.875	1.20829
$63$	76.9994	0.153984
$64$	64.0000	0.125000
$65$	−155.272	−0.296294
$66$	−412.624	−0.769552
$67$	286.046	0.521583	0.260792	−	0.965395i	$-0.416016\pi$
$67$	286.046	0.521583	0.260792	+	0.965395i	$0.416016\pi$
$68$	−421.133	−0.751027
$69$	−577.224	−1.00710
$70$	42.2663	0.0721684
$71$	1066.48	1.78265	0.891325	−	0.453365i	$-0.149777\pi$
$71$	1066.48	1.78265	0.891325	+	0.453365i	$0.149777\pi$
$72$	−228.133	−0.373413
$73$	132.201	0.211958	0.105979	−	0.994368i	$-0.466202\pi$
$73$	132.201	0.211958	0.105979	+	0.994368i	$0.466202\pi$
$74$	194.752	0.305938
$75$	−474.951	−0.731235
$76$	479.515	0.723739
$77$	74.7655	0.110653
$78$	−295.637	−0.429157
$79$	−206.432	−0.293993	−0.146997	−	0.989137i	$-0.546961\pi$
$79$	−206.432	−0.293993	−0.146997	+	0.989137i	$0.546961\pi$
$80$	−125.226	−0.175009
$81$	−685.750	−0.940672
$82$	138.511	0.186537
$83$	762.855	1.00885	0.504423	−	0.863457i	$-0.331705\pi$
$83$	762.855	1.00885	0.504423	+	0.863457i	$0.331705\pi$
$84$	80.4749	0.104530
$85$	824.013	1.05149
$86$	1074.82	1.34768
$87$	0	0
$88$	−221.515	−0.268336
$89$	722.523	0.860532	0.430266	−	0.902702i	$-0.358420\pi$
$89$	722.523	0.860532	0.430266	+	0.902702i	$0.358420\pi$
$90$	446.379	0.522806
$91$	53.5680	0.0617083
$92$	−309.879	−0.351165
$93$	−2197.57	−2.45029
$94$	−337.715	−0.370560
$95$	−938.248	−1.01329
$96$	−238.430	−0.253486
$97$	−647.151	−0.677404	−0.338702	−	0.940894i	$-0.609988\pi$
$97$	−647.151	−0.677404	−0.338702	+	0.940894i	$0.609988\pi$
$98$	671.418	0.692076
$99$	789.607	0.801601
$100$	−254.975	−0.254975
$101$	−630.176	−0.620840	−0.310420	−	0.950600i	$-0.600470\pi$
$101$	−630.176	−0.620840	−0.310420	+	0.950600i	$0.600470\pi$
$102$	1568.92	1.52300
$103$	−1988.72	−1.90247	−0.951233	−	0.308473i	$-0.900182\pi$
$103$	−1988.72	−1.90247	−0.951233	+	0.308473i	$0.900182\pi$
$104$	−158.711	−0.149643
$105$	−157.462	−0.146350
$106$	218.387	0.200109
$107$	−2045.12	−1.84775	−0.923876	−	0.382693i	$-0.874997\pi$
$107$	−2045.12	−1.84775	−0.923876	+	0.382693i	$0.874997\pi$
$108$	45.2023	0.0402740
$109$	−2182.87	−1.91817	−0.959086	−	0.283115i	$-0.908632\pi$
$109$	−2182.87	−1.91817	−0.959086	+	0.283115i	$0.908632\pi$
$110$	433.429	0.375689
$111$	−725.543	−0.620410
$112$	43.2025	0.0364487
$113$	543.377	0.452360	0.226180	−	0.974086i	$-0.427376\pi$
$113$	543.377	0.452360	0.226180	+	0.974086i	$0.427376\pi$
$114$	−1786.42	−1.46766
$115$	606.329	0.491656
$116$	0	0
$117$	565.738	0.447030
$118$	−832.147	−0.649198
$119$	−284.281	−0.218991
$120$	466.527	0.354899
$121$	−564.301	−0.423968
$122$	−1252.32	−0.929344
$123$	−516.020	−0.378276
$124$	−1179.75	−0.854393
$125$	1477.23	1.05702
$126$	−153.999	−0.108883
$127$	−1410.18	−0.985300	−0.492650	−	0.870228i	$-0.663972\pi$
$127$	−1410.18	−0.985300	−0.492650	+	0.870228i	$0.663972\pi$
$128$	−128.000	−0.0883883
$129$	−4004.21	−2.73295
$130$	310.543	0.209511
$131$	2398.82	1.59989	0.799946	−	0.600072i	$-0.204861\pi$
$131$	2398.82	1.59989	0.799946	+	0.600072i	$0.204861\pi$
$132$	825.247	0.544156
$133$	323.691	0.211034
$134$	−572.092	−0.368815
$135$	−88.4456	−0.0563865
$136$	842.265	0.531056
$137$	1246.70	0.777466	0.388733	−	0.921351i	$-0.372913\pi$
$137$	1246.70	0.777466	0.388733	+	0.921351i	$0.372913\pi$
$138$	1154.45	0.712124
$139$	918.664	0.560576	0.280288	−	0.959916i	$-0.409570\pi$
$139$	918.664	0.560576	0.280288	+	0.959916i	$0.409570\pi$
$140$	−84.5326	−0.0510308
$141$	1258.15	0.751456
$142$	−2132.96	−1.26052
$143$	549.325	0.321237
$144$	456.267	0.264043
$145$	0	0
$146$	−264.401	−0.149877
$147$	−2501.35	−1.40346
$148$	−389.503	−0.216331
$149$	−2383.79	−1.31065	−0.655327	−	0.755345i	$-0.727469\pi$
$149$	−2383.79	−1.31065	−0.655327	+	0.755345i	$0.727469\pi$
$150$	949.902	0.517061
$151$	867.644	0.467602	0.233801	−	0.972284i	$-0.424884\pi$
$151$	867.644	0.467602	0.233801	+	0.972284i	$0.424884\pi$
$152$	−959.030	−0.511760
$153$	−3002.32	−1.58643
$154$	−149.531	−0.0782438
$155$	2308.37	1.19621
$156$	591.274	0.303460
$157$	−1167.80	−0.593636	−0.296818	−	0.954934i	$-0.595926\pi$
$157$	−1167.80	−0.593636	−0.296818	+	0.954934i	$0.595926\pi$
$158$	412.865	0.207885
$159$	−813.595	−0.405800
$160$	250.452	0.123750
$161$	−209.181	−0.102396
$162$	1371.50	0.665156
$163$	−205.787	−0.0988863	−0.0494432	−	0.998777i	$-0.515745\pi$
$163$	−205.787	−0.0988863	−0.0494432	+	0.998777i	$0.515745\pi$
$164$	−277.022	−0.131901
$165$	−1614.73	−0.761857
$166$	−1525.71	−0.713362
$167$	−1143.63	−0.529919	−0.264960	−	0.964259i	$-0.585359\pi$
$167$	−1143.63	−0.529919	−0.264960	+	0.964259i	$0.585359\pi$
$168$	−160.950	−0.0739140
$169$	−1803.42	−0.820855
$170$	−1648.03	−0.743517
$171$	3418.54	1.52879
$172$	−2149.64	−0.952955
$173$	−812.968	−0.357276	−0.178638	−	0.983915i	$-0.557169\pi$
$173$	−812.968	−0.357276	−0.178638	+	0.983915i	$0.557169\pi$
$174$	0	0
$175$	−172.118	−0.0743479
$176$	443.029	0.189742
$177$	3100.14	1.31650
$178$	−1445.05	−0.608488
$179$	−2131.38	−0.889981	−0.444991	−	0.895535i	$-0.646793\pi$
$179$	−2131.38	−0.889981	−0.444991	+	0.895535i	$0.646793\pi$
$180$	−892.759	−0.369679
$181$	−3490.64	−1.43346	−0.716732	−	0.697348i	$-0.754363\pi$
$181$	−3490.64	−1.43346	−0.716732	+	0.697348i	$0.754363\pi$
$182$	−107.136	−0.0436344
$183$	4665.50	1.88461
$184$	619.759	0.248311
$185$	762.126	0.302879
$186$	4395.13	1.73262
$187$	−2915.22	−1.14001
$188$	675.431	0.262026
$189$	30.5133	0.0117435
$190$	1876.50	0.716502
$191$	−1260.70	−0.477596	−0.238798	−	0.971069i	$-0.576753\pi$
$191$	−1260.70	−0.477596	−0.238798	+	0.971069i	$0.576753\pi$
$192$	476.861	0.179242
$193$	−4972.54	−1.85457	−0.927283	−	0.374361i	$-0.877862\pi$
$193$	−4972.54	−1.85457	−0.927283	+	0.374361i	$0.877862\pi$
$194$	1294.30	0.478997
$195$	−1156.92	−0.424866
$196$	−1342.84	−0.489372
$197$	1255.57	0.454089	0.227044	−	0.973884i	$-0.427094\pi$
$197$	1255.57	0.454089	0.227044	+	0.973884i	$0.427094\pi$
$198$	−1579.21	−0.566818
$199$	318.115	0.113319	0.0566596	−	0.998394i	$-0.481955\pi$
$199$	318.115	0.113319	0.0566596	+	0.998394i	$0.481955\pi$
$200$	509.950	0.180294
$201$	2131.32	0.747917
$202$	1260.35	0.439000
$203$	0	0
$204$	−3137.84	−1.07692
$205$	542.039	0.184671
$206$	3977.43	1.34525
$207$	−2209.18	−0.741781
$208$	317.422	0.105814
$209$	3319.36	1.09859
$210$	314.924	0.103485
$211$	4006.23	1.30711	0.653555	−	0.756879i	$-0.273277\pi$
$211$	4006.23	1.30711	0.653555	+	0.756879i	$0.273277\pi$
$212$	−436.774	−0.141499
$213$	7946.30	2.55621
$214$	4090.24	1.30656
$215$	4206.11	1.33421
$216$	−90.4046	−0.0284780
$217$	−796.377	−0.249132
$218$	4365.73	1.35635
$219$	985.021	0.303934
$220$	−866.858	−0.265652
$221$	−2088.70	−0.635751
$222$	1451.09	0.438696
$223$	1037.20	0.311463	0.155731	−	0.987799i	$-0.450227\pi$
$223$	1037.20	0.311463	0.155731	+	0.987799i	$0.450227\pi$
$224$	−86.4050	−0.0257731
$225$	−1817.76	−0.538595
$226$	−1086.75	−0.319867
$227$	−4530.34	−1.32462	−0.662311	−	0.749229i	$-0.730424\pi$
$227$	−4530.34	−1.32462	−0.662311	+	0.749229i	$0.730424\pi$
$228$	3572.84	1.03779
$229$	4748.77	1.37034	0.685169	−	0.728384i	$-0.259728\pi$
$229$	4748.77	1.37034	0.685169	+	0.728384i	$0.259728\pi$
$230$	−1212.66	−0.347653
$231$	557.074	0.158670
$232$	0	0
$233$	−4354.21	−1.22427	−0.612133	−	0.790755i	$-0.709688\pi$
$233$	−4354.21	−1.22427	−0.612133	+	0.790755i	$0.709688\pi$
$234$	−1131.48	−0.316098
$235$	−1321.59	−0.366855
$236$	1664.29	0.459052
$237$	−1538.12	−0.421567
$238$	568.562	0.154850
$239$	−1279.38	−0.346261	−0.173130	−	0.984899i	$-0.555388\pi$
$239$	−1279.38	−0.346261	−0.173130	+	0.984899i	$0.555388\pi$
$240$	−933.055	−0.250952
$241$	−3967.87	−1.06055	−0.530276	−	0.847825i	$-0.677912\pi$
$241$	−3967.87	−1.06055	−0.530276	+	0.847825i	$0.677912\pi$
$242$	1128.60	0.299790
$243$	−5414.60	−1.42941
$244$	2504.65	0.657146
$245$	2627.47	0.685156
$246$	1032.04	0.267482
$247$	2378.26	0.612652
$248$	2359.50	0.604147
$249$	5683.99	1.44662
$250$	−2954.46	−0.747425
$251$	−1819.29	−0.457500	−0.228750	−	0.973485i	$-0.573464\pi$
$251$	−1819.29	−0.457500	−0.228750	+	0.973485i	$0.573464\pi$
$252$	307.998	0.0769922
$253$	−2145.09	−0.533046
$254$	2820.36	0.696712
$255$	6139.68	1.50777
$256$	256.000	0.0625000
$257$	2589.18	0.628439	0.314219	−	0.949350i	$-0.398257\pi$
$257$	2589.18	0.628439	0.314219	+	0.949350i	$0.398257\pi$
$258$	8008.41	1.93249
$259$	−262.930	−0.0630798
$260$	−621.087	−0.148147
$261$	0	0
$262$	−4797.64	−1.13129
$263$	−5085.92	−1.19244	−0.596219	−	0.802822i	$-0.703331\pi$
$263$	−5085.92	−1.19244	−0.596219	+	0.802822i	$0.703331\pi$
$264$	−1650.49	−0.384776
$265$	854.617	0.198108
$266$	−647.382	−0.149224
$267$	5383.49	1.23395
$268$	1144.18	0.260792
$269$	5503.30	1.24737	0.623684	−	0.781677i	$-0.285635\pi$
$269$	5503.30	1.24737	0.623684	+	0.781677i	$0.285635\pi$
$270$	176.891	0.0398713
$271$	4290.11	0.961644	0.480822	−	0.876818i	$-0.340338\pi$
$271$	4290.11	0.961644	0.480822	+	0.876818i	$0.340338\pi$
$272$	−1684.53	−0.375513
$273$	399.133	0.0884858
$274$	−2493.40	−0.549751
$275$	−1765.02	−0.387035
$276$	−2308.90	−0.503548
$277$	−2858.15	−0.619963	−0.309982	−	0.950743i	$-0.600323\pi$
$277$	−2858.15	−0.619963	−0.309982	+	0.950743i	$0.600323\pi$
$278$	−1837.33	−0.396387
$279$	−8410.64	−1.80477
$280$	169.065	0.0360842
$281$	3597.56	0.763746	0.381873	−	0.924215i	$-0.375279\pi$
$281$	3597.56	0.763746	0.381873	+	0.924215i	$0.375279\pi$
$282$	−2516.30	−0.531360
$283$	5914.47	1.24233	0.621164	−	0.783681i	$-0.286660\pi$
$283$	5914.47	1.24233	0.621164	+	0.783681i	$0.286660\pi$
$284$	4265.93	0.891325
$285$	−6990.84	−1.45299
$286$	−1098.65	−0.227149
$287$	−187.001	−0.0384610
$288$	−912.533	−0.186707
$289$	6171.54	1.25616
$290$	0	0
$291$	−4821.89	−0.971355
$292$	528.803	0.105979
$293$	1978.09	0.394408	0.197204	−	0.980363i	$-0.436814\pi$
$293$	1978.09	0.394408	0.197204	+	0.980363i	$0.436814\pi$
$294$	5002.70	0.992393
$295$	−3256.46	−0.642706
$296$	779.007	0.152969
$297$	312.905	0.0611334
$298$	4767.58	0.926773
$299$	−1536.91	−0.297264
$300$	−1899.80	−0.365618
$301$	−1451.09	−0.277871
$302$	−1735.29	−0.330644
$303$	−4695.41	−0.890245
$304$	1918.06	0.361869
$305$	−4900.74	−0.920051
$306$	6004.65	1.12177
$307$	1536.32	0.285610	0.142805	−	0.989751i	$-0.454388\pi$
$307$	1536.32	0.285610	0.142805	+	0.989751i	$0.454388\pi$
$308$	299.062	0.0553267
$309$	−14817.8	−2.72801
$310$	−4616.74	−0.845849
$311$	5510.16	1.00467	0.502335	−	0.864673i	$-0.332474\pi$
$311$	5510.16	1.00467	0.502335	+	0.864673i	$0.332474\pi$
$312$	−1182.55	−0.214579
$313$	−2183.22	−0.394259	−0.197130	−	0.980377i	$-0.563162\pi$
$313$	−2183.22	−0.394259	−0.197130	+	0.980377i	$0.563162\pi$
$314$	2335.61	0.419764
$315$	−602.647	−0.107795
$316$	−825.730	−0.146997
$317$	−4983.23	−0.882921	−0.441460	−	0.897281i	$-0.645539\pi$
$317$	−4983.23	−0.882921	−0.441460	+	0.897281i	$0.645539\pi$
$318$	1627.19	0.286944
$319$	0	0
$320$	−500.905	−0.0875045
$321$	−15238.1	−2.64956
$322$	418.361	0.0724048
$323$	−12621.2	−2.17419
$324$	−2743.00	−0.470336
$325$	−1264.60	−0.215839
$326$	411.574	0.0699232
$327$	−16264.4	−2.75054
$328$	554.045	0.0932683
$329$	455.942	0.0764039
$330$	3229.46	0.538714
$331$	7707.45	1.27988	0.639939	−	0.768426i	$-0.278960\pi$
$331$	7707.45	1.27988	0.639939	+	0.768426i	$0.278960\pi$
$332$	3051.42	0.504423
$333$	−2776.83	−0.456966
$334$	2287.25	0.374710
$335$	−2238.78	−0.365127
$336$	321.900	0.0522651
$337$	−1078.53	−0.174337	−0.0871685	−	0.996194i	$-0.527782\pi$
$337$	−1078.53	−0.174337	−0.0871685	+	0.996194i	$0.527782\pi$
$338$	3606.84	0.580432
$339$	4048.68	0.648655
$340$	3296.05	0.525746
$341$	−8166.62	−1.29691
$342$	−6837.08	−1.08101
$343$	−1832.62	−0.288490
$344$	4299.27	0.673841
$345$	4517.72	0.705003
$346$	1625.94	0.252633
$347$	579.489	0.0896501	0.0448250	−	0.998995i	$-0.485727\pi$
$347$	579.489	0.0896501	0.0448250	+	0.998995i	$0.485727\pi$
$348$	0	0
$349$	−6151.86	−0.943558	−0.471779	−	0.881717i	$-0.656388\pi$
$349$	−6151.86	−0.943558	−0.471779	+	0.881717i	$0.656388\pi$
$350$	344.236	0.0525719
$351$	224.191	0.0340923
$352$	−886.059	−0.134168
$353$	−453.612	−0.0683947	−0.0341973	−	0.999415i	$-0.510887\pi$
$353$	−453.612	−0.0683947	−0.0341973	+	0.999415i	$0.510887\pi$
$354$	−6200.29	−0.930909
$355$	−8346.97	−1.24792
$356$	2890.09	0.430266
$357$	−2118.16	−0.314020
$358$	4262.76	0.629312
$359$	−6543.18	−0.961938	−0.480969	−	0.876738i	$-0.659715\pi$
$359$	−6543.18	−0.961938	−0.480969	+	0.876738i	$0.659715\pi$
$360$	1785.52	0.261403
$361$	7511.91	1.09519
$362$	6981.28	1.01361
$363$	−4204.58	−0.607943
$364$	214.272	0.0308541
$365$	−1034.69	−0.148378
$366$	−9331.00	−1.33262
$367$	4378.09	0.622709	0.311355	−	0.950294i	$-0.399217\pi$
$367$	4378.09	0.622709	0.311355	+	0.950294i	$0.399217\pi$
$368$	−1239.52	−0.175582
$369$	−1974.94	−0.278621
$370$	−1524.25	−0.214168
$371$	−294.839	−0.0412595
$372$	−8790.26	−1.22514
$373$	−10463.6	−1.45251	−0.726253	−	0.687428i	$-0.758740\pi$
$373$	−10463.6	−1.45251	−0.726253	+	0.687428i	$0.758740\pi$
$374$	5830.44	0.806109
$375$	11006.8	1.51570
$376$	−1350.86	−0.185280
$377$	0	0
$378$	−61.0266	−0.00830389
$379$	353.637	0.0479291	0.0239646	−	0.999713i	$-0.492371\pi$
$379$	353.637	0.0479291	0.0239646	+	0.999713i	$0.492371\pi$
$380$	−3752.99	−0.506643
$381$	−10507.2	−1.41286
$382$	2521.39	0.337711
$383$	4249.67	0.566966	0.283483	−	0.958977i	$-0.408510\pi$
$383$	4249.67	0.566966	0.283483	+	0.958977i	$0.408510\pi$
$384$	−953.722	−0.126743
$385$	−585.163	−0.0774614
$386$	9945.08	1.31138
$387$	−15325.1	−2.01297
$388$	−2588.60	−0.338702
$389$	−13792.1	−1.79766	−0.898828	−	0.438301i	$-0.855580\pi$
$389$	−13792.1	−1.79766	−0.898828	+	0.438301i	$0.855580\pi$
$390$	2313.84	0.300426
$391$	8156.27	1.05494
$392$	2685.67	0.346038
$393$	17873.5	2.29414
$394$	−2511.13	−0.321089
$395$	1615.67	0.205806
$396$	3158.43	0.400801
$397$	−13329.6	−1.68513	−0.842563	−	0.538598i	$-0.818954\pi$
$397$	−13329.6	−1.68513	−0.842563	+	0.538598i	$0.818954\pi$
$398$	−636.229	−0.0801288
$399$	2411.81	0.302610
$400$	−1019.90	−0.127487
$401$	14184.8	1.76647	0.883235	−	0.468930i	$-0.155360\pi$
$401$	14184.8	1.76647	0.883235	+	0.468930i	$0.155360\pi$
$402$	−4262.63	−0.528857
$403$	−5851.23	−0.723252
$404$	−2520.70	−0.310420
$405$	5367.12	0.658504
$406$	0	0
$407$	−2696.27	−0.328377
$408$	6275.67	0.761500
$409$	4863.90	0.588030	0.294015	−	0.955801i	$-0.405008\pi$
$409$	4863.90	0.588030	0.294015	+	0.955801i	$0.405008\pi$
$410$	−1084.08	−0.130582
$411$	9289.10	1.11484
$412$	−7954.86	−0.951233
$413$	1123.46	0.133855
$414$	4418.36	0.524519
$415$	−5970.59	−0.706228
$416$	−634.844	−0.0748216
$417$	6844.92	0.803830
$418$	−6638.72	−0.776820
$419$	−6829.43	−0.796275	−0.398138	−	0.917326i	$-0.630343\pi$
$419$	−6829.43	−0.796275	−0.398138	+	0.917326i	$0.630343\pi$
$420$	−629.848	−0.0731748
$421$	−1648.06	−0.190787	−0.0953935	−	0.995440i	$-0.530411\pi$
$421$	−1648.06	−0.190787	−0.0953935	+	0.995440i	$0.530411\pi$
$422$	−8012.46	−0.924266
$423$	4815.26	0.553489
$424$	873.547	0.100055
$425$	6711.14	0.765972
$426$	−15892.6	−1.80751
$427$	1690.73	0.191617
$428$	−8180.49	−0.923876
$429$	4092.99	0.460633
$430$	−8412.21	−0.943425
$431$	8779.43	0.981184	0.490592	−	0.871389i	$-0.336781\pi$
$431$	8779.43	0.981184	0.490592	+	0.871389i	$0.336781\pi$
$432$	180.809	0.0201370
$433$	−1893.58	−0.210161	−0.105080	−	0.994464i	$-0.533510\pi$
$433$	−1893.58	−0.210161	−0.105080	+	0.994464i	$0.533510\pi$
$434$	1592.75	0.176163
$435$	0	0
$436$	−8731.47	−0.959086
$437$	−9286.99	−1.01661
$438$	−1970.04	−0.214914
$439$	4926.54	0.535605	0.267803	−	0.963474i	$-0.413702\pi$
$439$	4926.54	0.535605	0.267803	+	0.963474i	$0.413702\pi$
$440$	1733.72	0.187845
$441$	−9573.30	−1.03372
$442$	4177.40	0.449544
$443$	−6588.02	−0.706561	−0.353280	−	0.935517i	$-0.614934\pi$
$443$	−6588.02	−0.706561	−0.353280	+	0.935517i	$0.614934\pi$
$444$	−2902.17	−0.310205
$445$	−5654.93	−0.602403
$446$	−2074.40	−0.220237
$447$	−17761.5	−1.87939
$448$	172.810	0.0182243
$449$	1244.84	0.130841	0.0654206	−	0.997858i	$-0.479161\pi$
$449$	1244.84	0.130841	0.0654206	+	0.997858i	$0.479161\pi$
$450$	3635.52	0.380844
$451$	−1917.64	−0.200218
$452$	2173.51	0.226180
$453$	6464.77	0.670511
$454$	9060.68	0.936649
$455$	−419.258	−0.0431980
$456$	−7145.68	−0.733832
$457$	−6434.37	−0.658615	−0.329307	−	0.944223i	$-0.606815\pi$
$457$	−6434.37	−0.658615	−0.329307	+	0.944223i	$0.606815\pi$
$458$	−9497.53	−0.968975
$459$	−1189.76	−0.120987
$460$	2425.31	0.245828
$461$	−11626.6	−1.17463	−0.587316	−	0.809358i	$-0.699816\pi$
$461$	−11626.6	−1.17463	−0.587316	+	0.809358i	$0.699816\pi$
$462$	−1114.15	−0.112197
$463$	1438.84	0.144424	0.0722122	−	0.997389i	$-0.476994\pi$
$463$	1438.84	0.144424	0.0722122	+	0.997389i	$0.476994\pi$
$464$	0	0
$465$	17199.6	1.71529
$466$	8708.42	0.865686
$467$	13557.6	1.34341	0.671704	−	0.740820i	$-0.265563\pi$
$467$	13557.6	1.34341	0.671704	+	0.740820i	$0.265563\pi$
$468$	2262.95	0.223515
$469$	772.369	0.0760441
$470$	2643.18	0.259406
$471$	−8701.25	−0.851237
$472$	−3328.59	−0.324599
$473$	−14880.5	−1.44652
$474$	3076.24	0.298093
$475$	−7641.51	−0.738140
$476$	−1137.12	−0.109496
$477$	−3113.83	−0.298894
$478$	2558.76	0.244843
$479$	15103.6	1.44071	0.720355	−	0.693605i	$-0.243979\pi$
$479$	15103.6	1.44071	0.720355	+	0.693605i	$0.243979\pi$
$480$	1866.11	0.177450
$481$	−1931.83	−0.183126
$482$	7935.75	0.749924
$483$	−1558.59	−0.146829
$484$	−2257.20	−0.211984
$485$	5065.02	0.474207
$486$	10829.2	1.01075
$487$	12514.7	1.16447	0.582235	−	0.813021i	$-0.302178\pi$
$487$	12514.7	1.16447	0.582235	+	0.813021i	$0.302178\pi$
$488$	−5009.29	−0.464672
$489$	−1533.31	−0.141797
$490$	−5254.95	−0.484478
$491$	331.462	0.0304657	0.0152328	−	0.999884i	$-0.495151\pi$
$491$	331.462	0.0304657	0.0152328	+	0.999884i	$0.495151\pi$
$492$	−2064.08	−0.189138
$493$	0	0
$494$	−4756.52	−0.433210
$495$	−6179.97	−0.561150
$496$	−4719.00	−0.427196
$497$	2879.67	0.259901
$498$	−11368.0	−1.02292
$499$	352.716	0.0316427	0.0158214	−	0.999875i	$-0.494964\pi$
$499$	352.716	0.0316427	0.0158214	+	0.999875i	$0.494964\pi$
$500$	5908.92	0.528510
$501$	−8521.11	−0.759870
$502$	3638.58	0.323502
$503$	−15380.5	−1.36338	−0.681692	−	0.731639i	$-0.738756\pi$
$503$	−15380.5	−1.36338	−0.681692	+	0.731639i	$0.738756\pi$
$504$	−615.995	−0.0544417
$505$	4932.16	0.434610
$506$	4290.18	0.376920
$507$	−13437.2	−1.17705
$508$	−5640.71	−0.492650
$509$	−17668.3	−1.53857	−0.769286	−	0.638905i	$-0.779388\pi$
$509$	−17668.3	−1.53857	−0.769286	+	0.638905i	$0.779388\pi$
$510$	−12279.4	−1.06616
$511$	356.962	0.0309023
$512$	−512.000	−0.0441942
$513$	1354.70	0.116591
$514$	−5178.36	−0.444373
$515$	15565.0	1.33179
$516$	−16016.8	−1.36648
$517$	4675.56	0.397738
$518$	525.860	0.0446042
$519$	−6057.38	−0.512311
$520$	1242.17	0.104756
$521$	16812.2	1.41373	0.706867	−	0.707346i	$-0.250108\pi$
$521$	16812.2	1.41373	0.706867	+	0.707346i	$0.250108\pi$
$522$	0	0
$523$	14123.2	1.18081	0.590407	−	0.807106i	$-0.298967\pi$
$523$	14123.2	1.18081	0.590407	+	0.807106i	$0.298967\pi$
$524$	9595.28	0.799946
$525$	−1282.44	−0.106610
$526$	10171.8	0.843182
$527$	31052.0	2.56669
$528$	3300.99	0.272078
$529$	−6165.42	−0.506733
$530$	−1709.23	−0.140084
$531$	11865.0	0.969677
$532$	1294.76	0.105517
$533$	−1373.95	−0.111656
$534$	−10767.0	−0.872533
$535$	16006.4	1.29349
$536$	−2288.37	−0.184408
$537$	−15880.8	−1.27618
$538$	−11006.6	−0.882022
$539$	−9295.56	−0.742835
$540$	−353.782	−0.0281933
$541$	−10361.2	−0.823405	−0.411703	−	0.911318i	$-0.635066\pi$
$541$	−10361.2	−0.823405	−0.411703	+	0.911318i	$0.635066\pi$
$542$	−8580.22	−0.679985
$543$	−26008.6	−2.05550
$544$	3369.06	0.265528
$545$	17084.5	1.34279
$546$	−798.265	−0.0625689
$547$	−2753.45	−0.215227	−0.107613	−	0.994193i	$-0.534321\pi$
$547$	−2753.45	−0.215227	−0.107613	+	0.994193i	$0.534321\pi$
$548$	4986.80	0.388733
$549$	17856.0	1.38812
$550$	3530.04	0.273675
$551$	0	0
$552$	4617.79	0.356062
$553$	−557.400	−0.0428626
$554$	5716.31	0.438380
$555$	5678.56	0.434309
$556$	3674.65	0.280288
$557$	−2444.50	−0.185955	−0.0929773	−	0.995668i	$-0.529638\pi$
$557$	−2444.50	−0.185955	−0.0929773	+	0.995668i	$0.529638\pi$
$558$	16821.3	1.27617
$559$	−10661.6	−0.806685
$560$	−338.130	−0.0255154
$561$	−21721.2	−1.63470
$562$	−7195.12	−0.540050
$563$	16269.4	1.21789	0.608944	−	0.793213i	$-0.291593\pi$
$563$	16269.4	1.21789	0.608944	+	0.793213i	$0.291593\pi$
$564$	5032.60	0.375728
$565$	−4252.82	−0.316668
$566$	−11828.9	−0.878458
$567$	−1851.63	−0.137145
$568$	−8531.86	−0.630262
$569$	3904.41	0.287665	0.143832	−	0.989602i	$-0.454057\pi$
$569$	3904.41	0.287665	0.143832	+	0.989602i	$0.454057\pi$
$570$	13981.7	1.02742
$571$	20389.6	1.49436	0.747180	−	0.664622i	$-0.231407\pi$
$571$	20389.6	1.49436	0.747180	+	0.664622i	$0.231407\pi$
$572$	2197.30	0.160618
$573$	−9393.38	−0.684841
$574$	374.002	0.0271961
$575$	4938.21	0.358153
$576$	1825.07	0.132022
$577$	−18371.0	−1.32547	−0.662734	−	0.748855i	$-0.730604\pi$
$577$	−18371.0	−1.32547	−0.662734	+	0.748855i	$0.730604\pi$
$578$	−12343.1	−0.888242
$579$	−37050.2	−2.65933
$580$	0	0
$581$	2059.83	0.147084
$582$	9643.78	0.686851
$583$	−3023.49	−0.214786
$584$	−1057.61	−0.0749384
$585$	−4427.83	−0.312937
$586$	−3956.19	−0.278888
$587$	−18033.3	−1.26799	−0.633997	−	0.773336i	$-0.718587\pi$
$587$	−18033.3	−1.26799	−0.633997	+	0.773336i	$0.718587\pi$
$588$	−10005.4	−0.701728
$589$	−35356.7	−2.47343
$590$	6512.92	0.454462
$591$	9355.17	0.651134
$592$	−1558.01	−0.108165
$593$	20415.1	1.41374	0.706870	−	0.707343i	$-0.250107\pi$
$593$	20415.1	1.41374	0.706870	+	0.707343i	$0.250107\pi$
$594$	−625.811	−0.0432278
$595$	2224.96	0.153302
$596$	−9535.15	−0.655327
$597$	2370.26	0.162493
$598$	3073.83	0.210198
$599$	15554.6	1.06101	0.530505	−	0.847682i	$-0.322002\pi$
$599$	15554.6	1.06101	0.530505	+	0.847682i	$0.322002\pi$
$600$	3799.61	0.258531
$601$	14493.0	0.983667	0.491833	−	0.870689i	$-0.336327\pi$
$601$	14493.0	0.983667	0.491833	+	0.870689i	$0.336327\pi$
$602$	2902.18	0.196485
$603$	8157.08	0.550882
$604$	3470.58	0.233801
$605$	4416.58	0.296793
$606$	9390.82	0.629498
$607$	6646.81	0.444457	0.222229	−	0.974995i	$-0.428667\pi$
$607$	6646.81	0.444457	0.222229	+	0.974995i	$0.428667\pi$
$608$	−3836.12	−0.255880
$609$	0	0
$610$	9801.48	0.650574
$611$	3349.95	0.221807
$612$	−12009.3	−0.793214
$613$	−1306.48	−0.0860819	−0.0430409	−	0.999073i	$-0.513705\pi$
$613$	−1306.48	−0.0860819	−0.0430409	+	0.999073i	$0.513705\pi$
$614$	−3072.64	−0.201957
$615$	4038.70	0.264807
$616$	−598.124	−0.0391219
$617$	21689.4	1.41521	0.707604	−	0.706609i	$-0.249776\pi$
$617$	21689.4	1.41521	0.707604	+	0.706609i	$0.249776\pi$
$618$	29635.6	1.92900
$619$	25914.9	1.68272	0.841362	−	0.540472i	$-0.181754\pi$
$619$	25914.9	1.68272	0.841362	+	0.540472i	$0.181754\pi$
$620$	9233.48	0.598106
$621$	−875.454	−0.0565713
$622$	−11020.3	−0.710409
$623$	1950.93	0.125461
$624$	2365.09	0.151730
$625$	−3593.78	−0.230002
$626$	4366.45	0.278783
$627$	24732.4	1.57531
$628$	−4671.22	−0.296818
$629$	10252.0	0.649881
$630$	1205.29	0.0762223
$631$	−7391.94	−0.466353	−0.233176	−	0.972434i	$-0.574912\pi$
$631$	−7391.94	−0.466353	−0.233176	+	0.972434i	$0.574912\pi$
$632$	1651.46	0.103942
$633$	29850.2	1.87431
$634$	9966.45	0.624319
$635$	11037.0	0.689745
$636$	−3254.38	−0.202900
$637$	−6660.09	−0.414258
$638$	0	0
$639$	30412.5	1.88279
$640$	1001.81	0.0618750
$641$	−15884.7	−0.978796	−0.489398	−	0.872060i	$-0.662783\pi$
$641$	−15884.7	−0.978796	−0.489398	+	0.872060i	$0.662783\pi$
$642$	30476.2	1.87352
$643$	20569.7	1.26157	0.630786	−	0.775957i	$-0.282733\pi$
$643$	20569.7	1.26157	0.630786	+	0.775957i	$0.282733\pi$
$644$	−836.722	−0.0511980
$645$	31339.5	1.91316
$646$	25242.4	1.53738
$647$	31285.7	1.90103	0.950515	−	0.310679i	$-0.100557\pi$
$647$	31285.7	1.90103	0.950515	+	0.310679i	$0.100557\pi$
$648$	5486.00	0.332578
$649$	11520.8	0.696812
$650$	2529.21	0.152621
$651$	−5933.77	−0.357239
$652$	−823.148	−0.0494432
$653$	−1670.67	−0.100120	−0.0500601	−	0.998746i	$-0.515941\pi$
$653$	−1670.67	−0.100120	−0.0500601	+	0.998746i	$0.515941\pi$
$654$	32528.9	1.94492
$655$	−18774.7	−1.11998
$656$	−1108.09	−0.0659507
$657$	3769.92	0.223864
$658$	−911.884	−0.0540257
$659$	23871.6	1.41109	0.705543	−	0.708667i	$-0.250703\pi$
$659$	23871.6	1.41109	0.705543	+	0.708667i	$0.250703\pi$
$660$	−6458.91	−0.380929
$661$	−22952.4	−1.35060	−0.675298	−	0.737545i	$-0.735985\pi$
$661$	−22952.4	−1.35060	−0.675298	+	0.737545i	$0.735985\pi$
$662$	−15414.9	−0.905010
$663$	−15562.8	−0.911627
$664$	−6102.84	−0.356681
$665$	−2533.41	−0.147732
$666$	5553.67	0.323124
$667$	0	0
$668$	−4574.51	−0.264960
$669$	7728.14	0.446618
$670$	4477.56	0.258184
$671$	17338.0	0.997505
$672$	−643.799	−0.0369570
$673$	8493.54	0.486481	0.243241	−	0.969966i	$-0.421790\pi$
$673$	8493.54	0.486481	0.243241	+	0.969966i	$0.421790\pi$
$674$	2157.07	0.123275
$675$	−720.341	−0.0410754
$676$	−7213.68	−0.410428
$677$	−11636.2	−0.660583	−0.330291	−	0.943879i	$-0.607147\pi$
$677$	−11636.2	−0.660583	−0.330291	+	0.943879i	$0.607147\pi$
$678$	−8097.36	−0.458668
$679$	−1747.41	−0.0987620
$680$	−6592.11	−0.371758
$681$	−33755.3	−1.89942
$682$	16333.2	0.917056
$683$	−1137.88	−0.0637476	−0.0318738	−	0.999492i	$-0.510147\pi$
$683$	−1137.88	−0.0637476	−0.0318738	+	0.999492i	$0.510147\pi$
$684$	13674.2	0.764393
$685$	−9757.47	−0.544254
$686$	3665.24	0.203993
$687$	35382.8	1.96498
$688$	−8598.54	−0.476477
$689$	−2166.27	−0.119780
$690$	−9035.45	−0.498513
$691$	22693.1	1.24933	0.624664	−	0.780893i	$-0.285236\pi$
$691$	22693.1	1.24933	0.624664	+	0.780893i	$0.285236\pi$
$692$	−3251.87	−0.178638
$693$	2132.06	0.116869
$694$	−1158.98	−0.0633922
$695$	−7190.05	−0.392423
$696$	0	0
$697$	7291.45	0.396246
$698$	12303.7	0.667196
$699$	−32443.0	−1.75552
$700$	−688.472	−0.0371740
$701$	−36528.2	−1.96812	−0.984058	−	0.177847i	$-0.943087\pi$
$701$	−36528.2	−1.96812	−0.984058	+	0.177847i	$0.943087\pi$
$702$	−448.381	−0.0241069
$703$	−11673.3	−0.626268
$704$	1772.12	0.0948710
$705$	−9847.09	−0.526047
$706$	907.224	0.0483623
$707$	−1701.57	−0.0905152
$708$	12400.6	0.658252
$709$	−31880.9	−1.68873	−0.844367	−	0.535765i	$-0.820023\pi$
$709$	−31880.9	−1.68873	−0.844367	+	0.535765i	$0.820023\pi$
$710$	16693.9	0.882412
$711$	−5886.76	−0.310508
$712$	−5780.19	−0.304244
$713$	22848.8	1.20013
$714$	4236.32	0.222045
$715$	−4299.37	−0.224877
$716$	−8525.51	−0.444991
$717$	−9532.61	−0.496516
$718$	13086.4	0.680193
$719$	−16242.8	−0.842495	−0.421247	−	0.906946i	$-0.638408\pi$
$719$	−16242.8	−0.842495	−0.421247	+	0.906946i	$0.638408\pi$
$720$	−3571.03	−0.184840
$721$	−5369.84	−0.277369
$722$	−15023.8	−0.774417
$723$	−29564.4	−1.52077
$724$	−13962.6	−0.716732
$725$	0	0
$726$	8409.16	0.429880
$727$	26846.7	1.36959	0.684793	−	0.728738i	$-0.259893\pi$
$727$	26846.7	1.36959	0.684793	+	0.728738i	$0.259893\pi$
$728$	−428.544	−0.0218172
$729$	−21828.7	−1.10901
$730$	2069.37	0.104919
$731$	56580.1	2.86278
$732$	18662.0	0.942305
$733$	14320.2	0.721595	0.360797	−	0.932644i	$-0.382505\pi$
$733$	14320.2	0.721595	0.360797	+	0.932644i	$0.382505\pi$
$734$	−8756.18	−0.440322
$735$	19577.2	0.982470
$736$	2479.04	0.124155
$737$	7920.42	0.395865
$738$	3949.88	0.197015
$739$	12378.3	0.616162	0.308081	−	0.951360i	$-0.400313\pi$
$739$	12378.3	0.616162	0.308081	+	0.951360i	$0.400313\pi$
$740$	3048.50	0.151439
$741$	17720.3	0.878503
$742$	589.678	0.0291749
$743$	28092.1	1.38708	0.693539	−	0.720419i	$-0.256050\pi$
$743$	28092.1	1.38708	0.693539	+	0.720419i	$0.256050\pi$
$744$	17580.5	0.866308
$745$	18657.0	0.917505
$746$	20927.2	1.02708
$747$	21754.1	1.06552
$748$	−11660.9	−0.570005
$749$	−5522.15	−0.269392
$750$	−22013.5	−1.07176
$751$	−38866.6	−1.88850	−0.944249	−	0.329232i	$-0.893210\pi$
$751$	−38866.6	−1.88850	−0.944249	+	0.329232i	$0.893210\pi$
$752$	2701.72	0.131013
$753$	−13555.4	−0.656026
$754$	0	0
$755$	−6790.74	−0.327338
$756$	122.053	0.00587174
$757$	27780.9	1.33384	0.666918	−	0.745131i	$-0.267613\pi$
$757$	27780.9	1.33384	0.666918	+	0.745131i	$0.267613\pi$
$758$	−707.275	−0.0338910
$759$	−15982.9	−0.764353
$760$	7505.98	0.358251
$761$	32674.1	1.55642	0.778209	−	0.628006i	$-0.216129\pi$
$761$	32674.1	1.55642	0.778209	+	0.628006i	$0.216129\pi$
$762$	21014.3	0.999040
$763$	−5894.08	−0.279659
$764$	−5042.78	−0.238798
$765$	23498.1	1.11056
$766$	−8499.33	−0.400905
$767$	8254.43	0.388592
$768$	1907.44	0.0896210
$769$	−27268.7	−1.27872	−0.639359	−	0.768908i	$-0.720800\pi$
$769$	−27268.7	−1.27872	−0.639359	+	0.768908i	$0.720800\pi$
$770$	1170.33	0.0547735
$771$	19291.9	0.901141
$772$	−19890.2	−0.927283
$773$	−19081.8	−0.887871	−0.443936	−	0.896059i	$-0.646418\pi$
$773$	−19081.8	−0.887871	−0.443936	+	0.896059i	$0.646418\pi$
$774$	30650.2	1.42338
$775$	18800.4	0.871395
$776$	5177.21	0.239499
$777$	−1959.08	−0.0904524
$778$	27584.2	1.27114
$779$	−8302.28	−0.381848
$780$	−4627.69	−0.212433
$781$	29530.2	1.35297
$782$	−16312.5	−0.745953
$783$	0	0
$784$	−5371.35	−0.244686
$785$	9139.98	0.415567
$786$	−35747.0	−1.62220
$787$	−26279.8	−1.19031	−0.595155	−	0.803611i	$-0.702909\pi$
$787$	−26279.8	−1.19031	−0.595155	+	0.803611i	$0.702909\pi$
$788$	5022.27	0.227044
$789$	−37895.0	−1.70988
$790$	−3231.34	−0.145527
$791$	1467.20	0.0659516
$792$	−6316.86	−0.283409
$793$	12422.3	0.556280
$794$	26659.3	1.19156
$795$	6367.71	0.284075
$796$	1272.46	0.0566596
$797$	26431.8	1.17473	0.587367	−	0.809320i	$-0.300164\pi$
$797$	26431.8	1.17473	0.587367	+	0.809320i	$0.300164\pi$
$798$	−4823.61	−0.213978
$799$	−17777.9	−0.787153
$800$	2039.80	0.0901472
$801$	20604.0	0.908870
$802$	−28369.6	−1.24908
$803$	3660.55	0.160869
$804$	8525.26	0.373959
$805$	1637.18	0.0716808
$806$	11702.5	0.511416
$807$	41004.8	1.78865
$808$	5041.41	0.219500
$809$	−25378.2	−1.10290	−0.551452	−	0.834207i	$-0.685926\pi$
$809$	−25378.2	−1.10290	−0.551452	+	0.834207i	$0.685926\pi$
$810$	−10734.2	−0.465633
$811$	−495.143	−0.0214387	−0.0107194	−	0.999943i	$-0.503412\pi$
$811$	−495.143	−0.0214387	−0.0107194	+	0.999943i	$0.503412\pi$
$812$	0	0
$813$	31965.4	1.37894
$814$	5392.54	0.232197
$815$	1610.62	0.0692240
$816$	−12551.3	−0.538462
$817$	−64423.9	−2.75876
$818$	−9727.80	−0.415800
$819$	1527.58	0.0651746
$820$	2168.16	0.0923357
$821$	34011.8	1.44582	0.722912	−	0.690940i	$-0.242803\pi$
$821$	34011.8	1.44582	0.722912	+	0.690940i	$0.242803\pi$
$822$	−18578.2	−0.788308
$823$	−27126.3	−1.14892	−0.574462	−	0.818531i	$-0.694789\pi$
$823$	−27126.3	−1.14892	−0.574462	+	0.818531i	$0.694789\pi$
$824$	15909.7	0.672623
$825$	−13151.1	−0.554984
$826$	−2246.93	−0.0946496
$827$	−15540.8	−0.653455	−0.326727	−	0.945119i	$-0.605946\pi$
$827$	−15540.8	−0.653455	−0.326727	+	0.945119i	$0.605946\pi$
$828$	−8836.73	−0.370891
$829$	3273.46	0.137144	0.0685718	−	0.997646i	$-0.478156\pi$
$829$	3273.46	0.137144	0.0685718	+	0.997646i	$0.478156\pi$
$830$	11941.2	0.499379
$831$	−21296.0	−0.888988
$832$	1269.69	0.0529068
$833$	35344.5	1.47013
$834$	−13689.8	−0.568393
$835$	8950.76	0.370963
$836$	13277.4	0.549294
$837$	−3332.97	−0.137639
$838$	13658.9	0.563052
$839$	6745.29	0.277561	0.138780	−	0.990323i	$-0.455682\pi$
$839$	6745.29	0.277561	0.138780	+	0.990323i	$0.455682\pi$
$840$	1259.70	0.0517424
$841$	0	0
$842$	3296.11	0.134907
$843$	26805.3	1.09516
$844$	16024.9	0.653555
$845$	14114.7	0.574628
$846$	−9630.52	−0.391376
$847$	−1523.70	−0.0618122
$848$	−1747.09	−0.0707494
$849$	44068.4	1.78142
$850$	−13422.3	−0.541624
$851$	7543.69	0.303871
$852$	31785.2	1.27810
$853$	19431.9	0.779993	0.389996	−	0.920816i	$-0.372476\pi$
$853$	19431.9	0.779993	0.389996	+	0.920816i	$0.372476\pi$
$854$	−3381.47	−0.135493
$855$	−26755.7	−1.07021
$856$	16361.0	0.653279
$857$	−19332.2	−0.770564	−0.385282	−	0.922799i	$-0.625896\pi$
$857$	−19332.2	−0.770564	−0.385282	+	0.922799i	$0.625896\pi$
$858$	−8185.99	−0.325717
$859$	−39352.8	−1.56310	−0.781549	−	0.623844i	$-0.785570\pi$
$859$	−39352.8	−1.56310	−0.781549	+	0.623844i	$0.785570\pi$
$860$	16824.4	0.667103
$861$	−1393.33	−0.0551507
$862$	−17558.9	−0.693802
$863$	24745.8	0.976082	0.488041	−	0.872821i	$-0.337712\pi$
$863$	24745.8	0.976082	0.488041	+	0.872821i	$0.337712\pi$
$864$	−361.619	−0.0142390
$865$	6362.81	0.250106
$866$	3787.16	0.148606
$867$	45983.8	1.80126
$868$	−3185.51	−0.124566
$869$	−5715.97	−0.223131
$870$	0	0
$871$	5674.83	0.220763
$872$	17462.9	0.678176
$873$	−18454.6	−0.715456
$874$	18574.0	0.718849
$875$	3988.75	0.154108
$876$	3940.08	0.151967
$877$	4421.63	0.170248	0.0851241	−	0.996370i	$-0.472871\pi$
$877$	4421.63	0.170248	0.0851241	+	0.996370i	$0.472871\pi$
$878$	−9853.07	−0.378730
$879$	14738.7	0.565555
$880$	−3467.43	−0.132826
$881$	4152.92	0.158814	0.0794072	−	0.996842i	$-0.474697\pi$
$881$	4152.92	0.158814	0.0794072	+	0.996842i	$0.474697\pi$
$882$	19146.6	0.730952
$883$	−18620.4	−0.709654	−0.354827	−	0.934932i	$-0.615460\pi$
$883$	−18620.4	−0.709654	−0.354827	+	0.934932i	$0.615460\pi$
$884$	−8354.79	−0.317876
$885$	−24263.7	−0.921600
$886$	13176.0	0.499614
$887$	21286.9	0.805798	0.402899	−	0.915244i	$-0.368003\pi$
$887$	21286.9	0.805798	0.402899	+	0.915244i	$0.368003\pi$
$888$	5804.34	0.219348
$889$	−3807.70	−0.143651
$890$	11309.9	0.425963
$891$	−18988.0	−0.713940
$892$	4148.81	0.155731
$893$	20242.4	0.758553
$894$	35523.0	1.32893
$895$	16681.5	0.623019
$896$	−345.620	−0.0128866
$897$	−11451.5	−0.426258
$898$	−2489.68	−0.0925186
$899$	0	0
$900$	−7271.03	−0.269297
$901$	11496.2	0.425077
$902$	3835.28	0.141575
$903$	−10812.0	−0.398450
$904$	−4347.02	−0.159933
$905$	27320.0	1.00348
$906$	−12929.5	−0.474123
$907$	14695.2	0.537977	0.268989	−	0.963143i	$-0.413311\pi$
$907$	14695.2	0.537977	0.268989	+	0.963143i	$0.413311\pi$
$908$	−18121.4	−0.662311
$909$	−17970.5	−0.655714
$910$	838.515	0.0305456
$911$	−7441.79	−0.270645	−0.135322	−	0.990802i	$-0.543207\pi$
$911$	−7441.79	−0.270645	−0.135322	+	0.990802i	$0.543207\pi$
$912$	14291.4	0.518897
$913$	21122.9	0.765682
$914$	12868.7	0.465711
$915$	−36515.2	−1.31929
$916$	18995.1	0.685169
$917$	6477.19	0.233256
$918$	2379.52	0.0855511
$919$	−2936.26	−0.105395	−0.0526976	−	0.998611i	$-0.516782\pi$
$919$	−2936.26	−0.105395	−0.0526976	+	0.998611i	$0.516782\pi$
$920$	−4850.63	−0.173827
$921$	11447.0	0.409547
$922$	23253.2	0.830591
$923$	21157.8	0.754515
$924$	2228.30	0.0793350
$925$	6207.10	0.220636
$926$	−2877.68	−0.102123
$927$	−56711.5	−2.00933
$928$	0	0
$929$	−883.298	−0.0311949	−0.0155974	−	0.999878i	$-0.504965\pi$
$929$	−883.298	−0.0311949	−0.0155974	+	0.999878i	$0.504965\pi$
$930$	−34399.1	−1.21289
$931$	−40244.4	−1.41671
$932$	−17416.8	−0.612133
$933$	41055.9	1.44063
$934$	−27115.2	−0.949932
$935$	22816.4	0.798048
$936$	−4525.91	−0.158049
$937$	−9935.94	−0.346417	−0.173209	−	0.984885i	$-0.555414\pi$
$937$	−9935.94	−0.346417	−0.173209	+	0.984885i	$0.555414\pi$
$938$	−1544.74	−0.0537713
$939$	−16267.1	−0.565342
$940$	−5286.35	−0.183427
$941$	25025.2	0.866948	0.433474	−	0.901166i	$-0.357288\pi$
$941$	25025.2	0.866948	0.433474	+	0.901166i	$0.357288\pi$
$942$	17402.5	0.601915
$943$	5365.22	0.185276
$944$	6657.18	0.229526
$945$	−238.817	−0.00822086
$946$	29761.0	1.02285
$947$	−24752.3	−0.849359	−0.424679	−	0.905344i	$-0.639613\pi$
$947$	−24752.3	−0.849359	−0.424679	+	0.905344i	$0.639613\pi$
$948$	−6152.47	−0.210784
$949$	2622.71	0.0897122
$950$	15283.0	0.521944
$951$	−37129.8	−1.26605
$952$	2274.25	0.0774252
$953$	−12603.7	−0.428410	−0.214205	−	0.976789i	$-0.568716\pi$
$953$	−12603.7	−0.428410	−0.214205	+	0.976789i	$0.568716\pi$
$954$	6227.66	0.211350
$955$	9867.01	0.334334
$956$	−5117.53	−0.173130
$957$	0	0
$958$	−30207.2	−1.01874
$959$	3366.28	0.113350
$960$	−3732.22	−0.125476
$961$	57197.2	1.91995
$962$	3863.65	0.129490
$963$	−58320.1	−1.95154
$964$	−15871.5	−0.530276
$965$	38918.3	1.29826
$966$	3117.19	0.103824
$967$	−19128.6	−0.636127	−0.318064	−	0.948069i	$-0.603033\pi$
$967$	−19128.6	−0.636127	−0.318064	+	0.948069i	$0.603033\pi$
$968$	4514.41	0.149895
$969$	−94040.0	−3.11765
$970$	−10130.0	−0.335315
$971$	9196.54	0.303945	0.151973	−	0.988385i	$-0.451437\pi$
$971$	9196.54	0.303945	0.151973	+	0.988385i	$0.451437\pi$
$972$	−21658.4	−0.714706
$973$	2480.53	0.0817290
$974$	−25029.5	−0.823404
$975$	−9422.49	−0.309499
$976$	10018.6	0.328573
$977$	−39845.4	−1.30478	−0.652389	−	0.757884i	$-0.726233\pi$
$977$	−39845.4	−1.30478	−0.652389	+	0.757884i	$0.726233\pi$
$978$	3066.62	0.100265
$979$	20006.2	0.653116
$980$	10509.9	0.342578
$981$	−62248.1	−2.02592
$982$	−662.923	−0.0215425
$983$	−20134.4	−0.653294	−0.326647	−	0.945146i	$-0.605919\pi$
$983$	−20134.4	−0.653294	−0.326647	+	0.945146i	$0.605919\pi$
$984$	4128.16	0.133741
$985$	−9826.87	−0.317878
$986$	0	0
$987$	3397.20	0.109558
$988$	9513.03	0.306326
$989$	41633.0	1.33858
$990$	12359.9	0.396793
$991$	10908.3	0.349662	0.174831	−	0.984598i	$-0.444062\pi$
$991$	10908.3	0.349662	0.174831	+	0.984598i	$0.444062\pi$
$992$	9438.00	0.302073
$993$	57427.8	1.83526
$994$	−5759.33	−0.183778
$995$	−2489.77	−0.0793276
$996$	22736.0	0.723310
$997$	26941.1	0.855799	0.427900	−	0.903826i	$-0.359254\pi$
$997$	26941.1	0.855799	0.427900	+	0.903826i	$0.359254\pi$
$998$	−705.432	−0.0223748
$999$	−1100.40	−0.0348501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1682.4.a.k.1.6	✓	6
29.28	even	2		1682.4.a.l.1.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1682.4.a.k.1.6	✓	6	1.1	even	1	trivial
1682.4.a.l.1.1	yes	6	29.28	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:	\( N \)	\(=\)	\( 1682 = 2 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1682.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +7.45095 q^{3} +4.00000 q^{4} -7.82664 q^{5} -14.9019 q^{6} +2.70016 q^{7} -8.00000 q^{8} +28.5167 q^{9} +15.6533 q^{10} +27.6893 q^{11} +29.8038 q^{12} +19.8389 q^{13} -5.40031 q^{14} -58.3159 q^{15} +16.0000 q^{16} -105.283 q^{17} -57.0333 q^{18} +119.879 q^{19} -31.3066 q^{20} +20.1187 q^{21} -55.3787 q^{22} -77.4698 q^{23} -59.6076 q^{24} -63.7437 q^{25} -39.6777 q^{26} +11.3006 q^{27} +10.8006 q^{28} +116.632 q^{30} -294.938 q^{31} -32.0000 q^{32} +206.312 q^{33} +210.566 q^{34} -21.1331 q^{35} +114.067 q^{36} -97.3759 q^{37} -239.757 q^{38} +147.818 q^{39} +62.6131 q^{40} -69.2556 q^{41} -40.2374 q^{42} -537.409 q^{43} +110.757 q^{44} -223.190 q^{45} +154.940 q^{46} +168.858 q^{47} +119.215 q^{48} -335.709 q^{49} +127.487 q^{50} -784.459 q^{51} +79.3555 q^{52} -109.193 q^{53} -22.6012 q^{54} -216.714 q^{55} -21.6012 q^{56} +893.211 q^{57} +416.074 q^{59} -233.264 q^{60} +626.162 q^{61} +589.875 q^{62} +76.9994 q^{63} +64.0000 q^{64} -155.272 q^{65} -412.624 q^{66} +286.046 q^{67} -421.133 q^{68} -577.224 q^{69} +42.2663 q^{70} +1066.48 q^{71} -228.133 q^{72} +132.201 q^{73} +194.752 q^{74} -474.951 q^{75} +479.515 q^{76} +74.7655 q^{77} -295.637 q^{78} -206.432 q^{79} -125.226 q^{80} -685.750 q^{81} +138.511 q^{82} +762.855 q^{83} +80.4749 q^{84} +824.013 q^{85} +1074.82 q^{86} -221.515 q^{88} +722.523 q^{89} +446.379 q^{90} +53.5680 q^{91} -309.879 q^{92} -2197.57 q^{93} -337.715 q^{94} -938.248 q^{95} -238.430 q^{96} -647.151 q^{97} +671.418 q^{98} +789.607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 12 q^{2} - 10 q^{3} + 24 q^{4} - 10 q^{5} + 20 q^{6} - 26 q^{7} - 48 q^{8} + 54 q^{9} + 20 q^{10} + 89 q^{11} - 40 q^{12} - 86 q^{13} + 52 q^{14} - 89 q^{15} + 96 q^{16} + 95 q^{17} - 108 q^{18} + 30 q^{19}+ \cdots + 3854 q^{99}+O(q^{100}) \) 6 * q - 12 * q^2 - 10 * q^3 + 24 * q^4 - 10 * q^5 + 20 * q^6 - 26 * q^7 - 48 * q^8 + 54 * q^9 + 20 * q^10 + 89 * q^11 - 40 * q^12 - 86 * q^13 + 52 * q^14 - 89 * q^15 + 96 * q^16 + 95 * q^17 - 108 * q^18 + 30 * q^19 - 40 * q^20 + 346 * q^21 - 178 * q^22 - 377 * q^23 + 80 * q^24 - 66 * q^25 + 172 * q^26 - 115 * q^27 - 104 * q^28 + 178 * q^30 - 454 * q^31 - 192 * q^32 - 85 * q^33 - 190 * q^34 - 322 * q^35 + 216 * q^36 - 50 * q^37 - 60 * q^38 + 1131 * q^39 + 80 * q^40 + 730 * q^41 - 692 * q^42 + 62 * q^43 + 356 * q^44 - 352 * q^45 + 754 * q^46 + 191 * q^47 - 160 * q^48 - 528 * q^49 + 132 * q^50 - 1095 * q^51 - 344 * q^52 + 347 * q^53 + 230 * q^54 + 1468 * q^55 + 208 * q^56 + 648 * q^57 - 49 * q^59 - 356 * q^60 + 616 * q^61 + 908 * q^62 - 2297 * q^63 + 384 * q^64 - 1408 * q^65 + 170 * q^66 + 611 * q^67 + 380 * q^68 + 1826 * q^69 + 644 * q^70 + 214 * q^71 - 432 * q^72 + 865 * q^73 + 100 * q^74 - 29 * q^75 + 120 * q^76 - 2687 * q^77 - 2262 * q^78 - 1134 * q^79 - 160 * q^80 - 78 * q^81 - 1460 * q^82 + 900 * q^83 + 1384 * q^84 + 2454 * q^85 - 124 * q^86 - 712 * q^88 + 293 * q^89 + 704 * q^90 + 1576 * q^91 - 1508 * q^92 - 2360 * q^93 - 382 * q^94 - 4031 * q^95 + 320 * q^96 + 3918 * q^97 + 1056 * q^98 + 3854 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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