LMFDB - Embedded newform 1682.4.a.k.1.3

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			1.3
Root			$-1.68430$ 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)

$f(q)$	$=$	\(q-2.00000 q^{2} -3.04095 q^{3} +4.00000 q^{4} +20.5863 q^{5} +6.08191 q^{6} -7.99437 q^{7} -8.00000 q^{8} -17.7526 q^{9} -41.1726 q^{10} +51.8694 q^{11} -12.1638 q^{12} -66.5113 q^{13} +15.9887 q^{14} -62.6020 q^{15} +16.0000 q^{16} +119.963 q^{17} +35.5052 q^{18} -114.153 q^{19} +82.3453 q^{20} +24.3105 q^{21} -103.739 q^{22} -156.955 q^{23} +24.3276 q^{24} +298.797 q^{25} +133.023 q^{26} +136.091 q^{27} -31.9775 q^{28} +125.204 q^{30} +28.7742 q^{31} -32.0000 q^{32} -157.732 q^{33} -239.925 q^{34} -164.575 q^{35} -71.0104 q^{36} +149.472 q^{37} +228.306 q^{38} +202.258 q^{39} -164.691 q^{40} -16.6204 q^{41} -48.6210 q^{42} -19.8401 q^{43} +207.477 q^{44} -365.461 q^{45} +313.909 q^{46} -277.437 q^{47} -48.6552 q^{48} -279.090 q^{49} -597.593 q^{50} -364.801 q^{51} -266.045 q^{52} -193.075 q^{53} -272.181 q^{54} +1067.80 q^{55} +63.9550 q^{56} +347.134 q^{57} +129.515 q^{59} -250.408 q^{60} -495.263 q^{61} -57.5483 q^{62} +141.921 q^{63} +64.0000 q^{64} -1369.22 q^{65} +315.465 q^{66} -800.451 q^{67} +479.850 q^{68} +477.292 q^{69} +329.149 q^{70} -464.445 q^{71} +142.021 q^{72} -28.9706 q^{73} -298.944 q^{74} -908.626 q^{75} -456.612 q^{76} -414.663 q^{77} -404.515 q^{78} -45.5102 q^{79} +329.381 q^{80} +65.4754 q^{81} +33.2408 q^{82} -136.916 q^{83} +97.2420 q^{84} +2469.59 q^{85} +39.6802 q^{86} -414.955 q^{88} +329.723 q^{89} +730.922 q^{90} +531.716 q^{91} -627.818 q^{92} -87.5009 q^{93} +554.875 q^{94} -2349.99 q^{95} +97.3105 q^{96} +251.136 q^{97} +558.180 q^{98} -920.816 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.04095	−0.585232	−0.292616	−	0.956230i	$-0.594526\pi$
$3$	−3.04095	−0.585232	−0.292616	+	0.956230i	$0.594526\pi$
$4$	4.00000	0.500000
$5$	20.5863	1.84130	0.920648	−	0.390393i	$-0.127661\pi$
$5$	20.5863	1.84130	0.920648	+	0.390393i	$0.127661\pi$
$6$	6.08191	0.413821
$7$	−7.99437	−0.431656	−0.215828	−	0.976431i	$-0.569245\pi$
$7$	−7.99437	−0.431656	−0.215828	+	0.976431i	$0.569245\pi$
$8$	−8.00000	−0.353553
$9$	−17.7526	−0.657504
$10$	−41.1726	−1.30199
$11$	51.8694	1.42175	0.710873	−	0.703321i	$-0.248300\pi$
$11$	51.8694	1.42175	0.710873	+	0.703321i	$0.248300\pi$
$12$	−12.1638	−0.292616
$13$	−66.5113	−1.41899	−0.709497	−	0.704709i	$-0.751078\pi$
$13$	−66.5113	−1.41899	−0.709497	+	0.704709i	$0.751078\pi$
$14$	15.9887	0.305227
$15$	−62.6020	−1.07758
$16$	16.0000	0.250000
$17$	119.963	1.71148	0.855741	−	0.517404i	$-0.173102\pi$
$17$	119.963	1.71148	0.855741	+	0.517404i	$0.173102\pi$
$18$	35.5052	0.464925
$19$	−114.153	−1.37834	−0.689171	−	0.724599i	$-0.742025\pi$
$19$	−114.153	−1.37834	−0.689171	+	0.724599i	$0.742025\pi$
$20$	82.3453	0.920648
$21$	24.3105	0.252618
$22$	−103.739	−1.00533
$23$	−156.955	−1.42293	−0.711463	−	0.702724i	$-0.751967\pi$
$23$	−156.955	−1.42293	−0.711463	+	0.702724i	$0.751967\pi$
$24$	24.3276	0.206911
$25$	298.797	2.39037
$26$	133.023	1.00338
$27$	136.091	0.970024
$28$	−31.9775	−0.215828
$29$	0	0
$29$	0	0
$30$	125.204	0.761968
$31$	28.7742	0.166709	0.0833547	−	0.996520i	$-0.473437\pi$
$31$	28.7742	0.166709	0.0833547	+	0.996520i	$0.473437\pi$
$32$	−32.0000	−0.176777
$33$	−157.732	−0.832050
$34$	−239.925	−1.21020
$35$	−164.575	−0.794806
$36$	−71.0104	−0.328752
$37$	149.472	0.664137	0.332069	−	0.943255i	$-0.392253\pi$
$37$	149.472	0.664137	0.332069	+	0.943255i	$0.392253\pi$
$38$	228.306	0.974635
$39$	202.258	0.830440
$40$	−164.691	−0.650997
$41$	−16.6204	−0.0633090	−0.0316545	−	0.999499i	$-0.510078\pi$
$41$	−16.6204	−0.0633090	−0.0316545	+	0.999499i	$0.510078\pi$
$42$	−48.6210	−0.178628
$43$	−19.8401	−0.0703624	−0.0351812	−	0.999381i	$-0.511201\pi$
$43$	−19.8401	−0.0703624	−0.0351812	+	0.999381i	$0.511201\pi$
$44$	207.477	0.710873
$45$	−365.461	−1.21066
$46$	313.909	1.00616
$47$	−277.437	−0.861029	−0.430515	−	0.902584i	$-0.641668\pi$
$47$	−277.437	−0.861029	−0.430515	+	0.902584i	$0.641668\pi$
$48$	−48.6552	−0.146308
$49$	−279.090	−0.813674
$50$	−597.593	−1.69025
$51$	−364.801	−1.00161
$52$	−266.045	−0.709497
$53$	−193.075	−0.500394	−0.250197	−	0.968195i	$-0.580495\pi$
$53$	−193.075	−0.500394	−0.250197	+	0.968195i	$0.580495\pi$
$54$	−272.181	−0.685910
$55$	1067.80	2.61785
$56$	63.9550	0.152613
$57$	347.134	0.806650
$58$	0	0
$59$	129.515	0.285787	0.142893	−	0.989738i	$-0.454359\pi$
$59$	129.515	0.285787	0.142893	+	0.989738i	$0.454359\pi$
$60$	−250.408	−0.538792
$61$	−495.263	−1.03954	−0.519770	−	0.854306i	$-0.673982\pi$
$61$	−495.263	−1.03954	−0.519770	+	0.854306i	$0.673982\pi$
$62$	−57.5483	−0.117881
$63$	141.921	0.283815
$64$	64.0000	0.125000
$65$	−1369.22	−2.61279
$66$	315.465	0.588348
$67$	−800.451	−1.45956	−0.729781	−	0.683681i	$-0.760378\pi$
$67$	−800.451	−1.45956	−0.729781	+	0.683681i	$0.760378\pi$
$68$	479.850	0.855741
$69$	477.292	0.832741
$70$	329.149	0.562013
$71$	−464.445	−0.776330	−0.388165	−	0.921590i	$-0.626891\pi$
$71$	−464.445	−0.776330	−0.388165	+	0.921590i	$0.626891\pi$
$72$	142.021	0.232463
$73$	−28.9706	−0.0464487	−0.0232244	−	0.999730i	$-0.507393\pi$
$73$	−28.9706	−0.0464487	−0.0232244	+	0.999730i	$0.507393\pi$
$74$	−298.944	−0.469616
$75$	−908.626	−1.39892
$76$	−456.612	−0.689171
$77$	−414.663	−0.613704
$78$	−404.515	−0.587210
$79$	−45.5102	−0.0648139	−0.0324070	−	0.999475i	$-0.510317\pi$
$79$	−45.5102	−0.0648139	−0.0324070	+	0.999475i	$0.510317\pi$
$80$	329.381	0.460324
$81$	65.4754	0.0898154
$82$	33.2408	0.0447662
$83$	−136.916	−0.181066	−0.0905328	−	0.995893i	$-0.528857\pi$
$83$	−136.916	−0.181066	−0.0905328	+	0.995893i	$0.528857\pi$
$84$	97.2420	0.126309
$85$	2469.59	3.15135
$86$	39.6802	0.0497537
$87$	0	0
$88$	−414.955	−0.502663
$89$	329.723	0.392703	0.196351	−	0.980534i	$-0.437091\pi$
$89$	329.723	0.392703	0.196351	+	0.980534i	$0.437091\pi$
$90$	730.922	0.856066
$91$	531.716	0.612516
$92$	−627.818	−0.711463
$93$	−87.5009	−0.0975636
$94$	554.875	0.608840
$95$	−2349.99	−2.53794
$96$	97.3105	0.103455
$97$	251.136	0.262876	0.131438	−	0.991324i	$-0.458041\pi$
$97$	251.136	0.262876	0.131438	+	0.991324i	$0.458041\pi$
$98$	558.180	0.575354
$99$	−920.816	−0.934803
$100$	1195.19	1.19519
$101$	337.700	0.332697	0.166348	−	0.986067i	$-0.446802\pi$
$101$	337.700	0.332697	0.166348	+	0.986067i	$0.446802\pi$
$102$	729.601	0.708248
$103$	1051.61	1.00600	0.503001	−	0.864286i	$-0.332229\pi$
$103$	1051.61	1.00600	0.503001	+	0.864286i	$0.332229\pi$
$104$	532.090	0.501690
$105$	500.464	0.465145
$106$	386.150	0.353832
$107$	−910.584	−0.822705	−0.411353	−	0.911476i	$-0.634944\pi$
$107$	−910.584	−0.822705	−0.411353	+	0.911476i	$0.634944\pi$
$108$	544.362	0.485012
$109$	837.923	0.736316	0.368158	−	0.929763i	$-0.379989\pi$
$109$	837.923	0.736316	0.368158	+	0.929763i	$0.379989\pi$
$110$	−2135.60	−1.85110
$111$	−454.538	−0.388674
$112$	−127.910	−0.107914
$113$	−1522.30	−1.26731	−0.633654	−	0.773617i	$-0.718446\pi$
$113$	−1522.30	−1.26731	−0.633654	+	0.773617i	$0.718446\pi$
$114$	−694.268	−0.570387
$115$	−3231.12	−2.62003
$116$	0	0
$117$	1180.75	0.932994
$118$	−259.030	−0.202082
$119$	−959.026	−0.738771
$120$	500.816	0.380984
$121$	1359.43	1.02136
$122$	990.526	0.735066
$123$	50.5418	0.0370504
$124$	115.097	0.0833547
$125$	3577.83	2.56009
$126$	−283.842	−0.200688
$127$	1664.14	1.16274	0.581372	−	0.813638i	$-0.302516\pi$
$127$	1664.14	1.16274	0.581372	+	0.813638i	$0.302516\pi$
$128$	−128.000	−0.0883883
$129$	60.3328	0.0411783
$130$	2738.45	1.84752
$131$	−668.361	−0.445763	−0.222882	−	0.974846i	$-0.571546\pi$
$131$	−668.361	−0.445763	−0.222882	+	0.974846i	$0.571546\pi$
$132$	−630.929	−0.416025
$133$	912.582	0.594969
$134$	1600.90	1.03207
$135$	2801.60	1.78610
$136$	−959.701	−0.605100
$137$	−2077.97	−1.29586	−0.647931	−	0.761699i	$-0.724366\pi$
$137$	−2077.97	−1.29586	−0.647931	+	0.761699i	$0.724366\pi$
$138$	−954.583	−0.588837
$139$	667.398	0.407251	0.203626	−	0.979049i	$-0.434727\pi$
$139$	667.398	0.407251	0.203626	+	0.979049i	$0.434727\pi$
$140$	−658.299	−0.397403
$141$	843.674	0.503902
$142$	928.889	0.548948
$143$	−3449.90	−2.01745
$144$	−284.042	−0.164376
$145$	0	0
$146$	57.9413	0.0328442
$147$	848.700	0.476187
$148$	597.889	0.332069
$149$	2170.19	1.19321	0.596606	−	0.802534i	$-0.296515\pi$
$149$	2170.19	1.19321	0.596606	+	0.802534i	$0.296515\pi$
$150$	1817.25	0.989187
$151$	−2551.61	−1.37515	−0.687574	−	0.726114i	$-0.741324\pi$
$151$	−2551.61	−1.37515	−0.687574	+	0.726114i	$0.741324\pi$
$152$	913.224	0.487318
$153$	−2129.65	−1.12531
$154$	829.326	0.433954
$155$	592.354	0.306961
$156$	809.031	0.415220
$157$	−985.392	−0.500910	−0.250455	−	0.968128i	$-0.580580\pi$
$157$	−985.392	−0.500910	−0.250455	+	0.968128i	$0.580580\pi$
$158$	91.0204	0.0458304
$159$	587.132	0.292846
$160$	−658.762	−0.325498
$161$	1254.75	0.614214
$162$	−130.951	−0.0635091
$163$	1712.58	0.822940	0.411470	−	0.911423i	$-0.365015\pi$
$163$	1712.58	0.822940	0.411470	+	0.911423i	$0.365015\pi$
$164$	−66.4816	−0.0316545
$165$	−3247.13	−1.53205
$166$	273.831	0.128033
$167$	1947.60	0.902454	0.451227	−	0.892409i	$-0.350987\pi$
$167$	1947.60	0.902454	0.451227	+	0.892409i	$0.350987\pi$
$168$	−194.484	−0.0893141
$169$	2226.75	1.01354
$170$	−4939.18	−2.22834
$171$	2026.51	0.906266
$172$	−79.3603	−0.0351812
$173$	−358.047	−0.157351	−0.0786757	−	0.996900i	$-0.525069\pi$
$173$	−358.047	−0.157351	−0.0786757	+	0.996900i	$0.525069\pi$
$174$	0	0
$175$	−2388.69	−1.03182
$176$	829.910	0.355436
$177$	−393.849	−0.167251
$178$	−659.446	−0.277683
$179$	1365.65	0.570242	0.285121	−	0.958492i	$-0.407966\pi$
$179$	1365.65	0.570242	0.285121	+	0.958492i	$0.407966\pi$
$180$	−1461.84	−0.605330
$181$	−499.158	−0.204984	−0.102492	−	0.994734i	$-0.532682\pi$
$181$	−499.158	−0.204984	−0.102492	+	0.994734i	$0.532682\pi$
$182$	−1063.43	−0.433114
$183$	1506.07	0.608372
$184$	1255.64	0.503080
$185$	3077.08	1.22287
$186$	175.002	0.0689879
$187$	6222.38	2.43329
$188$	−1109.75	−0.430515
$189$	−1087.96	−0.418716
$190$	4699.98	1.79459
$191$	−3904.01	−1.47898	−0.739488	−	0.673170i	$-0.764932\pi$
$191$	−3904.01	−1.47898	−0.739488	+	0.673170i	$0.764932\pi$
$192$	−194.621	−0.0731540
$193$	2899.72	1.08148	0.540742	−	0.841189i	$-0.318144\pi$
$193$	2899.72	1.08148	0.540742	+	0.841189i	$0.318144\pi$
$194$	−502.272	−0.185881
$195$	4163.74	1.52909
$196$	−1116.36	−0.406837
$197$	−2072.98	−0.749715	−0.374858	−	0.927082i	$-0.622308\pi$
$197$	−2072.98	−0.749715	−0.374858	+	0.927082i	$0.622308\pi$
$198$	1841.63	0.661006
$199$	197.139	0.0702253	0.0351127	−	0.999383i	$-0.488821\pi$
$199$	197.139	0.0702253	0.0351127	+	0.999383i	$0.488821\pi$
$200$	−2390.37	−0.845124
$201$	2434.13	0.854182
$202$	−675.399	−0.235252
$203$	0	0
$204$	−1459.20	−0.500807
$205$	−342.153	−0.116571
$206$	−2103.22	−0.711351
$207$	2786.35	0.935579
$208$	−1064.18	−0.354748
$209$	−5921.05	−1.95965
$210$	−1000.93	−0.328908
$211$	−1159.47	−0.378299	−0.189149	−	0.981948i	$-0.560573\pi$
$211$	−1159.47	−0.378299	−0.189149	+	0.981948i	$0.560573\pi$
$212$	−772.299	−0.250197
$213$	1412.35	0.454333
$214$	1821.17	0.581740
$215$	−408.434	−0.129558
$216$	−1088.72	−0.342955
$217$	−230.031	−0.0719610
$218$	−1675.85	−0.520654
$219$	88.0983	0.0271833
$220$	4271.20	1.30893
$221$	−7978.87	−2.42858
$222$	909.076	0.274834
$223$	−5055.53	−1.51813	−0.759066	−	0.651014i	$-0.774344\pi$
$223$	−5055.53	−1.51813	−0.759066	+	0.651014i	$0.774344\pi$
$224$	255.820	0.0763066
$225$	−5304.42	−1.57168
$226$	3044.60	0.896122
$227$	785.964	0.229807	0.114904	−	0.993377i	$-0.463344\pi$
$227$	785.964	0.229807	0.114904	+	0.993377i	$0.463344\pi$
$228$	1388.54	0.403325
$229$	20.0300	0.00578000	0.00289000	−	0.999996i	$-0.499080\pi$
$229$	20.0300	0.00578000	0.00289000	+	0.999996i	$0.499080\pi$
$230$	6462.24	1.85264
$231$	1260.97	0.359159
$232$	0	0
$233$	−3272.63	−0.920158	−0.460079	−	0.887878i	$-0.652179\pi$
$233$	−3272.63	−0.920158	−0.460079	+	0.887878i	$0.652179\pi$
$234$	−2361.50	−0.659726
$235$	−5711.41	−1.58541
$236$	518.060	0.142893
$237$	138.394	0.0379311
$238$	1918.05	0.522390
$239$	−4597.12	−1.24420	−0.622098	−	0.782939i	$-0.713720\pi$
$239$	−4597.12	−1.24420	−0.622098	+	0.782939i	$0.713720\pi$
$240$	−1001.63	−0.269396
$241$	2126.69	0.568432	0.284216	−	0.958760i	$-0.408267\pi$
$241$	2126.69	0.568432	0.284216	+	0.958760i	$0.408267\pi$
$242$	−2718.86	−0.722211
$243$	−3873.55	−1.02259
$244$	−1981.05	−0.519770
$245$	−5745.44	−1.49821
$246$	−101.084	−0.0261986
$247$	7592.47	1.95586
$248$	−230.193	−0.0589407
$249$	416.354	0.105965
$250$	−7155.67	−1.81026
$251$	1376.21	0.346079	0.173040	−	0.984915i	$-0.444641\pi$
$251$	1376.21	0.346079	0.173040	+	0.984915i	$0.444641\pi$
$252$	567.684	0.141908
$253$	−8141.13	−2.02304
$254$	−3328.28	−0.822184
$255$	−7509.90	−1.84427
$256$	256.000	0.0625000
$257$	−5550.89	−1.34730	−0.673648	−	0.739053i	$-0.735273\pi$
$257$	−5550.89	−1.34730	−0.673648	+	0.739053i	$0.735273\pi$
$258$	−120.666	−0.0291175
$259$	−1194.94	−0.286679
$260$	−5476.89	−1.30639
$261$	0	0
$262$	1336.72	0.315202
$263$	−7922.44	−1.85748	−0.928742	−	0.370725i	$-0.879109\pi$
$263$	−7922.44	−1.85748	−0.928742	+	0.370725i	$0.879109\pi$
$264$	1261.86	0.294174
$265$	−3974.70	−0.921373
$266$	−1825.16	−0.420707
$267$	−1002.67	−0.229822
$268$	−3201.80	−0.729781
$269$	6669.70	1.51174	0.755871	−	0.654721i	$-0.227214\pi$
$269$	6669.70	1.51174	0.755871	+	0.654721i	$0.227214\pi$
$270$	−5603.21	−1.26296
$271$	−6527.79	−1.46323	−0.731614	−	0.681719i	$-0.761233\pi$
$271$	−6527.79	−1.46323	−0.731614	+	0.681719i	$0.761233\pi$
$272$	1919.40	0.427871
$273$	−1616.92	−0.358464
$274$	4155.95	0.916314
$275$	15498.4	3.39850
$276$	1909.17	0.416371
$277$	−8872.44	−1.92453	−0.962263	−	0.272122i	$-0.912274\pi$
$277$	−8872.44	−1.92453	−0.962263	+	0.272122i	$0.912274\pi$
$278$	−1334.80	−0.287970
$279$	−510.816	−0.109612
$280$	1316.60	0.281006
$281$	1700.97	0.361108	0.180554	−	0.983565i	$-0.442211\pi$
$281$	1700.97	0.361108	0.180554	+	0.983565i	$0.442211\pi$
$282$	−1687.35	−0.356312
$283$	−4126.87	−0.866845	−0.433422	−	0.901191i	$-0.642694\pi$
$283$	−4126.87	−0.866845	−0.433422	+	0.901191i	$0.642694\pi$
$284$	−1857.78	−0.388165
$285$	7146.21	1.48528
$286$	6899.80	1.42655
$287$	132.870	0.0273277
$288$	568.083	0.116231
$289$	9478.02	1.92917
$290$	0	0
$291$	−763.692	−0.153843
$292$	−115.883	−0.0232244
$293$	−493.443	−0.0983865	−0.0491932	−	0.998789i	$-0.515665\pi$
$293$	−493.443	−0.0983865	−0.0491932	+	0.998789i	$0.515665\pi$
$294$	−1697.40	−0.336715
$295$	2666.24	0.526218
$296$	−1195.78	−0.234808
$297$	7058.93	1.37913
$298$	−4340.37	−0.843729
$299$	10439.3	2.01912
$300$	−3634.51	−0.699461
$301$	158.609	0.0303723
$302$	5103.23	0.972377
$303$	−1026.93	−0.194705
$304$	−1826.45	−0.344586
$305$	−10195.6	−1.91410
$306$	4259.30	0.795712
$307$	3443.22	0.640114	0.320057	−	0.947398i	$-0.396298\pi$
$307$	3443.22	0.640114	0.320057	+	0.947398i	$0.396298\pi$
$308$	−1658.65	−0.306852
$309$	−3197.90	−0.588744
$310$	−1184.71	−0.217055
$311$	−4228.33	−0.770955	−0.385477	−	0.922717i	$-0.625963\pi$
$311$	−4228.33	−0.770955	−0.385477	+	0.922717i	$0.625963\pi$
$312$	−1618.06	−0.293605
$313$	−3154.43	−0.569644	−0.284822	−	0.958580i	$-0.591935\pi$
$313$	−3154.43	−0.569644	−0.284822	+	0.958580i	$0.591935\pi$
$314$	1970.78	0.354197
$315$	2921.63	0.522588
$316$	−182.041	−0.0324070
$317$	4850.65	0.859431	0.429716	−	0.902964i	$-0.358614\pi$
$317$	4850.65	0.859431	0.429716	+	0.902964i	$0.358614\pi$
$318$	−1174.26	−0.207074
$319$	0	0
$320$	1317.52	0.230162
$321$	2769.04	0.481473
$322$	−2509.51	−0.434315
$323$	−13694.1	−2.35901
$324$	261.902	0.0449077
$325$	−19873.3	−3.39192
$326$	−3425.15	−0.581907
$327$	−2548.08	−0.430915
$328$	132.963	0.0223831
$329$	2217.94	0.371668
$330$	6494.25	1.08332
$331$	−3831.91	−0.636317	−0.318159	−	0.948037i	$-0.603064\pi$
$331$	−3831.91	−0.636317	−0.318159	+	0.948037i	$0.603064\pi$
$332$	−547.663	−0.0905328
$333$	−2653.52	−0.436673
$334$	−3895.20	−0.638131
$335$	−16478.3	−2.68749
$336$	388.968	0.0631546
$337$	4326.31	0.699314	0.349657	−	0.936878i	$-0.386298\pi$
$337$	4326.31	0.699314	0.349657	+	0.936878i	$0.386298\pi$
$338$	−4453.50	−0.716683
$339$	4629.24	0.741668
$340$	9878.35	1.57567
$341$	1492.50	0.237018
$342$	−4053.03	−0.640827
$343$	4973.22	0.782882
$344$	158.721	0.0248769
$345$	9825.68	1.53332
$346$	716.094	0.111264
$347$	−9181.01	−1.42035	−0.710177	−	0.704024i	$-0.751385\pi$
$347$	−9181.01	−1.42035	−0.710177	+	0.704024i	$0.751385\pi$
$348$	0	0
$349$	−9402.78	−1.44218	−0.721088	−	0.692843i	$-0.756358\pi$
$349$	−9402.78	−1.44218	−0.721088	+	0.692843i	$0.756358\pi$
$350$	4777.38	0.729605
$351$	−9051.56	−1.37646
$352$	−1659.82	−0.251331
$353$	−12799.3	−1.92985	−0.964927	−	0.262519i	$-0.915447\pi$
$353$	−12799.3	−1.92985	−0.964927	+	0.262519i	$0.915447\pi$
$354$	787.698	0.118265
$355$	−9561.21	−1.42945
$356$	1318.89	0.196351
$357$	2916.35	0.432352
$358$	−2731.30	−0.403222
$359$	5065.31	0.744671	0.372335	−	0.928098i	$-0.378557\pi$
$359$	5065.31	0.744671	0.372335	+	0.928098i	$0.378557\pi$
$360$	2923.69	0.428033
$361$	6171.92	0.899828
$362$	998.317	0.144946
$363$	−4133.96	−0.597732
$364$	2126.86	0.306258
$365$	−596.399	−0.0855258
$366$	−3012.14	−0.430184
$367$	2782.74	0.395798	0.197899	−	0.980222i	$-0.436588\pi$
$367$	2782.74	0.395798	0.197899	+	0.980222i	$0.436588\pi$
$368$	−2511.27	−0.355732
$369$	295.055	0.0416259
$370$	−6154.17	−0.864702
$371$	1543.51	0.215998
$372$	−350.003	−0.0487818
$373$	−2444.52	−0.339336	−0.169668	−	0.985501i	$-0.554270\pi$
$373$	−2444.52	−0.339336	−0.169668	+	0.985501i	$0.554270\pi$
$374$	−12444.8	−1.72060
$375$	−10880.0	−1.49824
$376$	2219.50	0.304420
$377$	0	0
$378$	2175.92	0.296077
$379$	−12278.3	−1.66410	−0.832050	−	0.554701i	$-0.812833\pi$
$379$	−12278.3	−1.66410	−0.832050	+	0.554701i	$0.812833\pi$
$380$	−9399.97	−1.26897
$381$	−5060.57	−0.680475
$382$	7808.02	1.04579
$383$	11979.5	1.59823	0.799115	−	0.601179i	$-0.205302\pi$
$383$	11979.5	1.59823	0.799115	+	0.601179i	$0.205302\pi$
$384$	389.242	0.0517277
$385$	−8536.38	−1.13001
$386$	−5799.44	−0.764725
$387$	352.213	0.0462636
$388$	1004.54	0.131438
$389$	5010.85	0.653111	0.326555	−	0.945178i	$-0.394112\pi$
$389$	5010.85	0.653111	0.326555	+	0.945178i	$0.394112\pi$
$390$	−8327.48	−1.08123
$391$	−18828.7	−2.43531
$392$	2232.72	0.287677
$393$	2032.45	0.260875
$394$	4145.96	0.530129
$395$	−936.888	−0.119342
$396$	−3683.27	−0.467402
$397$	−6756.58	−0.854163	−0.427082	−	0.904213i	$-0.640458\pi$
$397$	−6756.58	−0.854163	−0.427082	+	0.904213i	$0.640458\pi$
$398$	−394.279	−0.0496568
$399$	−2775.12	−0.348195
$400$	4780.75	0.597593
$401$	−2492.08	−0.310346	−0.155173	−	0.987887i	$-0.549593\pi$
$401$	−2492.08	−0.310346	−0.155173	+	0.987887i	$0.549593\pi$
$402$	−4868.27	−0.603998
$403$	−1913.81	−0.236560
$404$	1350.80	0.166348
$405$	1347.90	0.165377
$406$	0	0
$407$	7753.03	0.944234
$408$	2918.40	0.354124
$409$	4780.34	0.577928	0.288964	−	0.957340i	$-0.406689\pi$
$409$	4780.34	0.577928	0.288964	+	0.957340i	$0.406689\pi$
$410$	684.305	0.0824279
$411$	6319.02	0.758380
$412$	4206.44	0.503001
$413$	−1035.39	−0.123361
$414$	−5572.71	−0.661555
$415$	−2818.59	−0.333396
$416$	2128.36	0.250845
$417$	−2029.52	−0.238336
$418$	11842.1	1.38568
$419$	7779.43	0.907041	0.453520	−	0.891246i	$-0.350168\pi$
$419$	7779.43	0.907041	0.453520	+	0.891246i	$0.350168\pi$
$420$	2001.86	0.232573
$421$	2927.91	0.338949	0.169474	−	0.985535i	$-0.445793\pi$
$421$	2927.91	0.338949	0.169474	+	0.985535i	$0.445793\pi$
$422$	2318.94	0.267498
$423$	4925.23	0.566130
$424$	1544.60	0.176916
$425$	35844.4	4.09108
$426$	−2824.71	−0.321262
$427$	3959.32	0.448723
$428$	−3642.34	−0.411353
$429$	10491.0	1.18067
$430$	816.869	0.0916114
$431$	−889.746	−0.0994374	−0.0497187	−	0.998763i	$-0.515832\pi$
$431$	−889.746	−0.0994374	−0.0497187	+	0.998763i	$0.515832\pi$
$432$	2177.45	0.242506
$433$	−6554.79	−0.727490	−0.363745	−	0.931499i	$-0.618502\pi$
$433$	−6554.79	−0.727490	−0.363745	+	0.931499i	$0.618502\pi$
$434$	460.063	0.0508841
$435$	0	0
$436$	3351.69	0.368158
$437$	17916.8	1.96128
$438$	−176.197	−0.0192215
$439$	17685.8	1.92277	0.961384	−	0.275209i	$-0.0887471\pi$
$439$	17685.8	1.92277	0.961384	+	0.275209i	$0.0887471\pi$
$440$	−8542.39	−0.925551
$441$	4954.58	0.534994
$442$	15957.7	1.71727
$443$	−7658.61	−0.821380	−0.410690	−	0.911775i	$-0.634712\pi$
$443$	−7658.61	−0.821380	−0.410690	+	0.911775i	$0.634712\pi$
$444$	−1818.15	−0.194337
$445$	6787.78	0.723082
$446$	10111.1	1.07348
$447$	−6599.44	−0.698306
$448$	−511.640	−0.0539569
$449$	14612.4	1.53587	0.767933	−	0.640530i	$-0.221285\pi$
$449$	14612.4	1.53587	0.767933	+	0.640530i	$0.221285\pi$
$450$	10608.8	1.11135
$451$	−862.089	−0.0900093
$452$	−6089.19	−0.633654
$453$	7759.34	0.804780
$454$	−1571.93	−0.162498
$455$	10946.1	1.12782
$456$	−2777.07	−0.285194
$457$	16770.0	1.71656	0.858280	−	0.513181i	$-0.171533\pi$
$457$	16770.0	1.71656	0.858280	+	0.513181i	$0.171533\pi$
$458$	−40.0600	−0.00408708
$459$	16325.8	1.66018
$460$	−12924.5	−1.31001
$461$	−16965.6	−1.71403	−0.857016	−	0.515290i	$-0.827684\pi$
$461$	−16965.6	−1.71403	−0.857016	+	0.515290i	$0.827684\pi$
$462$	−2521.94	−0.253964
$463$	−1022.91	−0.102675	−0.0513376	−	0.998681i	$-0.516348\pi$
$463$	−1022.91	−0.102675	−0.0513376	+	0.998681i	$0.516348\pi$
$464$	0	0
$465$	−1801.32	−0.179644
$466$	6545.25	0.650650
$467$	−5522.03	−0.547171	−0.273586	−	0.961848i	$-0.588210\pi$
$467$	−5522.03	−0.547171	−0.273586	+	0.961848i	$0.588210\pi$
$468$	4723.00	0.466497
$469$	6399.10	0.630028
$470$	11422.8	1.12105
$471$	2996.53	0.293148
$472$	−1036.12	−0.101041
$473$	−1029.09	−0.100037
$474$	−276.789	−0.0268214
$475$	−34108.5	−3.29475
$476$	−3836.10	−0.369385
$477$	3427.58	0.329011
$478$	9194.24	0.879780
$479$	−8813.93	−0.840749	−0.420374	−	0.907351i	$-0.638101\pi$
$479$	−8813.93	−0.840749	−0.420374	+	0.907351i	$0.638101\pi$
$480$	2003.26	0.190492
$481$	−9941.59	−0.942407
$482$	−4253.38	−0.401942
$483$	−3815.65	−0.359457
$484$	5437.72	0.510680
$485$	5169.96	0.484033
$486$	7747.11	0.723078
$487$	−18961.3	−1.76431	−0.882155	−	0.470959i	$-0.843908\pi$
$487$	−18961.3	−1.76431	−0.882155	+	0.470959i	$0.843908\pi$
$488$	3962.10	0.367533
$489$	−5207.86	−0.481611
$490$	11490.9	1.05940
$491$	5187.74	0.476822	0.238411	−	0.971164i	$-0.423373\pi$
$491$	5187.74	0.476822	0.238411	+	0.971164i	$0.423373\pi$
$492$	202.167	0.0185252
$493$	0	0
$494$	−15184.9	−1.38300
$495$	−18956.2	−1.72125
$496$	460.387	0.0416774
$497$	3712.94	0.335107
$498$	−832.708	−0.0749288
$499$	−6000.25	−0.538293	−0.269147	−	0.963099i	$-0.586742\pi$
$499$	−6000.25	−0.538293	−0.269147	+	0.963099i	$0.586742\pi$
$500$	14311.3	1.28004
$501$	−5922.56	−0.528145
$502$	−2752.43	−0.244715
$503$	6117.69	0.542295	0.271147	−	0.962538i	$-0.412597\pi$
$503$	6117.69	0.542295	0.271147	+	0.962538i	$0.412597\pi$
$504$	−1135.37	−0.100344
$505$	6951.99	0.612593
$506$	16282.3	1.43050
$507$	−6771.45	−0.593157
$508$	6656.56	0.581372
$509$	−1138.83	−0.0991706	−0.0495853	−	0.998770i	$-0.515790\pi$
$509$	−1138.83	−0.0991706	−0.0495853	+	0.998770i	$0.515790\pi$
$510$	15019.8	1.30409
$511$	231.602	0.0200498
$512$	−512.000	−0.0441942
$513$	−15535.2	−1.33702
$514$	11101.8	0.952682
$515$	21648.8	1.85235
$516$	241.331	0.0205892
$517$	−14390.5	−1.22416
$518$	2389.87	0.202712
$519$	1088.80	0.0920870
$520$	10953.8	0.923760
$521$	21662.2	1.82157	0.910785	−	0.412881i	$-0.135477\pi$
$521$	21662.2	1.82157	0.910785	+	0.412881i	$0.135477\pi$
$522$	0	0
$523$	12784.9	1.06892	0.534460	−	0.845194i	$-0.320515\pi$
$523$	12784.9	1.06892	0.534460	+	0.845194i	$0.320515\pi$
$524$	−2673.44	−0.222882
$525$	7263.90	0.603852
$526$	15844.9	1.31344
$527$	3451.82	0.285320
$528$	−2523.72	−0.208013
$529$	12467.7	1.02472
$530$	7949.40	0.651509
$531$	−2299.23	−0.187906
$532$	3650.33	0.297485
$533$	1105.44	0.0898350
$534$	2005.34	0.162509
$535$	−18745.6	−1.51484
$536$	6403.61	0.516033
$537$	−4152.87	−0.333724
$538$	−13339.4	−1.06896
$539$	−14476.2	−1.15684
$540$	11206.4	0.893051
$541$	4491.84	0.356967	0.178484	−	0.983943i	$-0.442881\pi$
$541$	4491.84	0.356967	0.178484	+	0.983943i	$0.442881\pi$
$542$	13055.6	1.03466
$543$	1517.92	0.119963
$544$	−3838.80	−0.302550
$545$	17249.7	1.35578
$546$	3233.85	0.253472
$547$	3041.09	0.237710	0.118855	−	0.992912i	$-0.462078\pi$
$547$	3041.09	0.237710	0.118855	+	0.992912i	$0.462078\pi$
$548$	−8311.89	−0.647931
$549$	8792.21	0.683502
$550$	−30996.8	−2.40310
$551$	0	0
$552$	−3818.33	−0.294419
$553$	363.826	0.0279773
$554$	17744.9	1.36084
$555$	−9357.27	−0.715665
$556$	2669.59	0.203626
$557$	−5354.83	−0.407345	−0.203673	−	0.979039i	$-0.565288\pi$
$557$	−5354.83	−0.407345	−0.203673	+	0.979039i	$0.565288\pi$
$558$	1021.63	0.0775075
$559$	1319.59	0.0998438
$560$	−2633.20	−0.198701
$561$	−18922.0	−1.42404
$562$	−3401.94	−0.255342
$563$	−13225.9	−0.990063	−0.495031	−	0.868875i	$-0.664843\pi$
$563$	−13225.9	−0.990063	−0.495031	+	0.868875i	$0.664843\pi$
$564$	3374.69	0.251951
$565$	−31338.5	−2.33349
$566$	8253.75	0.612952
$567$	−523.435	−0.0387693
$568$	3715.56	0.274474
$569$	26652.9	1.96371	0.981854	−	0.189641i	$-0.0607323\pi$
$569$	26652.9	1.96371	0.981854	+	0.189641i	$0.0607323\pi$
$570$	−14292.4	−1.05025
$571$	−6229.77	−0.456581	−0.228291	−	0.973593i	$-0.573314\pi$
$571$	−6229.77	−0.456581	−0.228291	+	0.973593i	$0.573314\pi$
$572$	−13799.6	−1.00872
$573$	11871.9	0.865543
$574$	−265.739	−0.0193236
$575$	−46897.5	−3.40132
$576$	−1136.17	−0.0821880
$577$	−552.312	−0.0398493	−0.0199247	−	0.999801i	$-0.506343\pi$
$577$	−552.312	−0.0398493	−0.0199247	+	0.999801i	$0.506343\pi$
$578$	−18956.0	−1.36413
$579$	−8817.91	−0.632919
$580$	0	0
$581$	1094.55	0.0781580
$582$	1527.38	0.108784
$583$	−10014.7	−0.711433
$584$	231.765	0.0164221
$585$	24307.3	1.71792
$586$	986.886	0.0695697
$587$	−18891.1	−1.32831	−0.664155	−	0.747595i	$-0.731208\pi$
$587$	−18891.1	−1.32831	−0.664155	+	0.747595i	$0.731208\pi$
$588$	3394.80	0.238094
$589$	−3284.66	−0.229783
$590$	−5332.47	−0.372092
$591$	6303.84	0.438757
$592$	2391.56	0.166034
$593$	−16037.3	−1.11058	−0.555289	−	0.831658i	$-0.687392\pi$
$593$	−16037.3	−1.11058	−0.555289	+	0.831658i	$0.687392\pi$
$594$	−14117.9	−0.975190
$595$	−19742.8	−1.36030
$596$	8680.75	0.596606
$597$	−599.492	−0.0410981
$598$	−20878.5	−1.42774
$599$	−10407.9	−0.709943	−0.354971	−	0.934877i	$-0.615509\pi$
$599$	−10407.9	−0.709943	−0.354971	+	0.934877i	$0.615509\pi$
$600$	7269.01	0.494594
$601$	3011.45	0.204392	0.102196	−	0.994764i	$-0.467413\pi$
$601$	3011.45	0.204392	0.102196	+	0.994764i	$0.467413\pi$
$602$	−317.218	−0.0214765
$603$	14210.1	0.959668
$604$	−10206.5	−0.687574
$605$	27985.7	1.88063
$606$	2053.86	0.137677
$607$	−20731.9	−1.38630	−0.693148	−	0.720795i	$-0.743777\pi$
$607$	−20731.9	−1.38630	−0.693148	+	0.720795i	$0.743777\pi$
$608$	3652.90	0.243659
$609$	0	0
$610$	20391.3	1.35347
$611$	18452.7	1.22180
$612$	−8518.59	−0.562653
$613$	−7118.56	−0.469031	−0.234515	−	0.972112i	$-0.575350\pi$
$613$	−7118.56	−0.469031	−0.234515	+	0.972112i	$0.575350\pi$
$614$	−6886.44	−0.452629
$615$	1040.47	0.0682208
$616$	3317.30	0.216977
$617$	3451.80	0.225226	0.112613	−	0.993639i	$-0.464078\pi$
$617$	3451.80	0.225226	0.112613	+	0.993639i	$0.464078\pi$
$618$	6395.79	0.416305
$619$	−9388.26	−0.609606	−0.304803	−	0.952415i	$-0.598591\pi$
$619$	−9388.26	−0.609606	−0.304803	+	0.952415i	$0.598591\pi$
$620$	2369.42	0.153481
$621$	−21360.0	−1.38027
$622$	8456.67	0.545147
$623$	−2635.93	−0.169512
$624$	3236.12	0.207610
$625$	36304.8	2.32351
$626$	6308.85	0.402799
$627$	18005.6	1.14685
$628$	−3941.57	−0.250455
$629$	17931.1	1.13666
$630$	−5843.26	−0.369525
$631$	−24265.2	−1.53087	−0.765437	−	0.643510i	$-0.777477\pi$
$631$	−24265.2	−1.53087	−0.765437	+	0.643510i	$0.777477\pi$
$632$	364.082	0.0229152
$633$	3525.89	0.221392
$634$	−9701.30	−0.607710
$635$	34258.5	2.14096
$636$	2348.53	0.146423
$637$	18562.6	1.15460
$638$	0	0
$639$	8245.10	0.510440
$640$	−2635.05	−0.162749
$641$	19402.3	1.19554	0.597772	−	0.801666i	$-0.296053\pi$
$641$	19402.3	1.19554	0.597772	+	0.801666i	$0.296053\pi$
$642$	−5538.08	−0.340453
$643$	−27872.0	−1.70943	−0.854715	−	0.519098i	$-0.826268\pi$
$643$	−27872.0	−1.70943	−0.854715	+	0.519098i	$0.826268\pi$
$644$	5019.01	0.307107
$645$	1242.03	0.0758215
$646$	27388.2	1.66807
$647$	−20345.5	−1.23627	−0.618134	−	0.786073i	$-0.712111\pi$
$647$	−20345.5	−1.23627	−0.618134	+	0.786073i	$0.712111\pi$
$648$	−523.803	−0.0317545
$649$	6717.86	0.406316
$650$	39746.7	2.39845
$651$	699.515	0.0421139
$652$	6850.30	0.411470
$653$	7147.67	0.428346	0.214173	−	0.976796i	$-0.431294\pi$
$653$	7147.67	0.428346	0.214173	+	0.976796i	$0.431294\pi$
$654$	5096.17	0.304703
$655$	−13759.1	−0.820782
$656$	−265.926	−0.0158272
$657$	514.304	0.0305402
$658$	−4435.87	−0.262809
$659$	−22380.0	−1.32291	−0.661457	−	0.749983i	$-0.730062\pi$
$659$	−22380.0	−1.32291	−0.661457	+	0.749983i	$0.730062\pi$
$660$	−12988.5	−0.766026
$661$	−10398.3	−0.611869	−0.305935	−	0.952053i	$-0.598969\pi$
$661$	−10398.3	−0.611869	−0.305935	+	0.952053i	$0.598969\pi$
$662$	7663.83	0.449944
$663$	24263.4	1.42128
$664$	1095.33	0.0640164
$665$	18786.7	1.09551
$666$	5307.04	0.308774
$667$	0	0
$668$	7790.40	0.451227
$669$	15373.6	0.888459
$670$	32956.7	1.90034
$671$	−25689.0	−1.47796
$672$	−777.936	−0.0446571
$673$	12529.0	0.717618	0.358809	−	0.933411i	$-0.383183\pi$
$673$	12529.0	0.717618	0.358809	+	0.933411i	$0.383183\pi$
$674$	−8652.61	−0.494490
$675$	40663.4	2.31872
$676$	8907.01	0.506771
$677$	14538.7	0.825360	0.412680	−	0.910876i	$-0.364593\pi$
$677$	14538.7	0.825360	0.412680	+	0.910876i	$0.364593\pi$
$678$	−9258.47	−0.524439
$679$	−2007.67	−0.113472
$680$	−19756.7	−1.11417
$681$	−2390.08	−0.134491
$682$	−2984.99	−0.167597
$683$	−42.6821	−0.00239119	−0.00119560	−	0.999999i	$-0.500381\pi$
$683$	−42.6821	−0.00239119	−0.00119560	+	0.999999i	$0.500381\pi$
$684$	8106.06	0.453133
$685$	−42777.8	−2.38607
$686$	−9946.44	−0.553581
$687$	−60.9103	−0.00338264
$688$	−317.441	−0.0175906
$689$	12841.7	0.710055
$690$	−19651.4	−1.08422
$691$	−3802.43	−0.209336	−0.104668	−	0.994507i	$-0.533378\pi$
$691$	−3802.43	−0.209336	−0.104668	+	0.994507i	$0.533378\pi$
$692$	−1432.19	−0.0786757
$693$	7361.35	0.403513
$694$	18362.0	1.00434
$695$	13739.3	0.749870
$696$	0	0
$697$	−1993.82	−0.108352
$698$	18805.6	1.01977
$699$	9951.90	0.538506
$700$	−9554.77	−0.515909
$701$	−28718.5	−1.54734	−0.773668	−	0.633592i	$-0.781580\pi$
$701$	−28718.5	−1.54734	−0.773668	+	0.633592i	$0.781580\pi$
$702$	18103.1	0.973302
$703$	−17062.7	−0.915409
$704$	3319.64	0.177718
$705$	17368.1	0.927832
$706$	25598.6	1.36461
$707$	−2699.70	−0.143610
$708$	−1575.40	−0.0836257
$709$	−2335.31	−0.123702	−0.0618509	−	0.998085i	$-0.519700\pi$
$709$	−2335.31	−0.123702	−0.0618509	+	0.998085i	$0.519700\pi$
$710$	19122.4	1.01078
$711$	807.925	0.0426154
$712$	−2637.78	−0.138841
$713$	−4516.24	−0.237215
$714$	−5832.70	−0.305719
$715$	−71020.7	−3.71472
$716$	5462.59	0.285121
$717$	13979.6	0.728143
$718$	−10130.6	−0.526562
$719$	9359.27	0.485455	0.242727	−	0.970095i	$-0.421958\pi$
$719$	9359.27	0.485455	0.242727	+	0.970095i	$0.421958\pi$
$720$	−5847.37	−0.302665
$721$	−8406.96	−0.434246
$722$	−12343.8	−0.636274
$723$	−6467.16	−0.332664
$724$	−1996.63	−0.102492
$725$	0	0
$726$	8267.93	0.422660
$727$	−12187.4	−0.621741	−0.310870	−	0.950452i	$-0.600620\pi$
$727$	−12187.4	−0.621741	−0.310870	+	0.950452i	$0.600620\pi$
$728$	−4253.73	−0.216557
$729$	10011.5	0.508635
$730$	1192.80	0.0604759
$731$	−2380.07	−0.120424
$732$	6024.29	0.304186
$733$	17055.8	0.859440	0.429720	−	0.902962i	$-0.358612\pi$
$733$	17055.8	0.859440	0.429720	+	0.902962i	$0.358612\pi$
$734$	−5565.48	−0.279871
$735$	17471.6	0.876802
$736$	5022.55	0.251540
$737$	−41518.9	−2.07513
$738$	−590.110	−0.0294340
$739$	−15358.8	−0.764522	−0.382261	−	0.924054i	$-0.624854\pi$
$739$	−15358.8	−0.764522	−0.382261	+	0.924054i	$0.624854\pi$
$740$	12308.3	0.611437
$741$	−23088.3	−1.14463
$742$	−3087.02	−0.152733
$743$	12103.5	0.597621	0.298811	−	0.954312i	$-0.403410\pi$
$743$	12103.5	0.597621	0.298811	+	0.954312i	$0.403410\pi$
$744$	700.007	0.0344940
$745$	44676.2	2.19706
$746$	4889.04	0.239947
$747$	2430.61	0.119051
$748$	24889.5	1.21665
$749$	7279.55	0.355125
$750$	21760.0	1.05942
$751$	8013.04	0.389348	0.194674	−	0.980868i	$-0.437635\pi$
$751$	8013.04	0.389348	0.194674	+	0.980868i	$0.437635\pi$
$752$	−4439.00	−0.215257
$753$	−4185.00	−0.202536
$754$	0	0
$755$	−52528.3	−2.53206
$756$	−4351.83	−0.209358
$757$	27546.0	1.32256	0.661279	−	0.750140i	$-0.270014\pi$
$757$	27546.0	1.32256	0.661279	+	0.750140i	$0.270014\pi$
$758$	24556.6	1.17670
$759$	24756.8	1.18395
$760$	18799.9	0.897296
$761$	−29739.3	−1.41662	−0.708310	−	0.705902i	$-0.750542\pi$
$761$	−29739.3	−1.41662	−0.708310	+	0.705902i	$0.750542\pi$
$762$	10121.1	0.481168
$763$	−6698.67	−0.317835
$764$	−15616.0	−0.739488
$765$	−43841.6	−2.07202
$766$	−23958.9	−1.13012
$767$	−8614.21	−0.405529
$768$	−778.484	−0.0365770
$769$	35529.8	1.66611	0.833054	−	0.553192i	$-0.186590\pi$
$769$	35529.8	1.66611	0.833054	+	0.553192i	$0.186590\pi$
$770$	17072.8	0.799039
$771$	16880.0	0.788480
$772$	11598.9	0.540742
$773$	−24008.3	−1.11710	−0.558549	−	0.829471i	$-0.688642\pi$
$773$	−24008.3	−1.11710	−0.558549	+	0.829471i	$0.688642\pi$
$774$	−704.426	−0.0327133
$775$	8597.62	0.398498
$776$	−2009.09	−0.0929407
$777$	3633.75	0.167773
$778$	−10021.7	−0.461819
$779$	1897.27	0.0872615
$780$	16655.0	0.764543
$781$	−24090.4	−1.10374
$782$	37657.4	1.72203
$783$	0	0
$784$	−4465.44	−0.203418
$785$	−20285.6	−0.922323
$786$	−4064.91	−0.184466
$787$	20459.4	0.926683	0.463342	−	0.886180i	$-0.346650\pi$
$787$	20459.4	0.926683	0.463342	+	0.886180i	$0.346650\pi$
$788$	−8291.93	−0.374858
$789$	24091.8	1.08706
$790$	1873.78	0.0843873
$791$	12169.8	0.547040
$792$	7366.53	0.330503
$793$	32940.6	1.47510
$794$	13513.2	0.603985
$795$	12086.9	0.539217
$796$	788.558	0.0351127
$797$	−15412.1	−0.684976	−0.342488	−	0.939522i	$-0.611270\pi$
$797$	−15412.1	−0.684976	−0.342488	+	0.939522i	$0.611270\pi$
$798$	5550.24	0.246211
$799$	−33282.1	−1.47364
$800$	−9561.49	−0.422562
$801$	−5853.44	−0.258204
$802$	4984.17	0.219448
$803$	−1502.69	−0.0660382
$804$	9736.53	0.427091
$805$	25830.8	1.13095
$806$	3827.61	0.167273
$807$	−20282.2	−0.884719
$808$	−2701.60	−0.117626
$809$	−23857.1	−1.03680	−0.518399	−	0.855139i	$-0.673472\pi$
$809$	−23857.1	−1.03680	−0.518399	+	0.855139i	$0.673472\pi$
$810$	−2695.80	−0.116939
$811$	29129.5	1.26125	0.630626	−	0.776087i	$-0.282798\pi$
$811$	29129.5	1.26125	0.630626	+	0.776087i	$0.282798\pi$
$812$	0	0
$813$	19850.7	0.856327
$814$	−15506.1	−0.667675
$815$	35255.6	1.51528
$816$	−5836.81	−0.250403
$817$	2264.81	0.0969835
$818$	−9560.68	−0.408657
$819$	−9439.35	−0.402732
$820$	−1368.61	−0.0582853
$821$	13095.6	0.556686	0.278343	−	0.960482i	$-0.410215\pi$
$821$	13095.6	0.556686	0.278343	+	0.960482i	$0.410215\pi$
$822$	−12638.0	−0.536256
$823$	9664.63	0.409341	0.204671	−	0.978831i	$-0.434388\pi$
$823$	9664.63	0.409341	0.204671	+	0.978831i	$0.434388\pi$
$824$	−8412.88	−0.355675
$825$	−47129.9	−1.98891
$826$	2070.78	0.0872297
$827$	−11008.9	−0.462899	−0.231450	−	0.972847i	$-0.574347\pi$
$827$	−11008.9	−0.462899	−0.231450	+	0.972847i	$0.574347\pi$
$828$	11145.4	0.467790
$829$	−683.366	−0.0286300	−0.0143150	−	0.999898i	$-0.504557\pi$
$829$	−683.366	−0.0286300	−0.0143150	+	0.999898i	$0.504557\pi$
$830$	5637.18	0.235746
$831$	26980.7	1.12629
$832$	−4256.72	−0.177374
$833$	−33480.4	−1.39259
$834$	4059.05	0.168529
$835$	40093.9	1.66169
$836$	−23684.2	−0.979826
$837$	3915.89	0.161712
$838$	−15558.9	−0.641375
$839$	37980.0	1.56283	0.781416	−	0.624011i	$-0.214498\pi$
$839$	37980.0	1.56283	0.781416	+	0.624011i	$0.214498\pi$
$840$	−4003.71	−0.164454
$841$	0	0
$842$	−5855.81	−0.239673
$843$	−5172.57	−0.211332
$844$	−4637.87	−0.189149
$845$	45840.6	1.86623
$846$	−9850.47	−0.400315
$847$	−10867.8	−0.440876
$848$	−3089.20	−0.125098
$849$	12549.6	0.507305
$850$	−71688.8	−2.89283
$851$	−23460.4	−0.945018
$852$	5649.42	0.227167
$853$	9838.50	0.394917	0.197458	−	0.980311i	$-0.436731\pi$
$853$	9838.50	0.394917	0.197458	+	0.980311i	$0.436731\pi$
$854$	−7918.63	−0.317295
$855$	41718.5	1.66870
$856$	7284.67	0.290870
$857$	28719.5	1.14474	0.572368	−	0.819997i	$-0.306025\pi$
$857$	28719.5	1.14474	0.572368	+	0.819997i	$0.306025\pi$
$858$	−20982.0	−0.834863
$859$	40759.0	1.61895	0.809476	−	0.587153i	$-0.199751\pi$
$859$	40759.0	1.61895	0.809476	+	0.587153i	$0.199751\pi$
$860$	−1633.74	−0.0647790
$861$	−404.050	−0.0159930
$862$	1779.49	0.0703129
$863$	8994.82	0.354794	0.177397	−	0.984139i	$-0.443232\pi$
$863$	8994.82	0.354794	0.177397	+	0.984139i	$0.443232\pi$
$864$	−4354.90	−0.171478
$865$	−7370.87	−0.289731
$866$	13109.6	0.514413
$867$	−28822.2	−1.12901
$868$	−920.125	−0.0359805
$869$	−2360.59	−0.0921489
$870$	0	0
$871$	53239.0	2.07111
$872$	−6703.38	−0.260327
$873$	−4458.31	−0.172842
$874$	−35833.7	−1.38683
$875$	−28602.5	−1.10508
$876$	352.393	0.0135916
$877$	−10503.2	−0.404412	−0.202206	−	0.979343i	$-0.564811\pi$
$877$	−10503.2	−0.404412	−0.202206	+	0.979343i	$0.564811\pi$
$878$	−35371.5	−1.35960
$879$	1500.54	0.0575789
$880$	17084.8	0.654464
$881$	−42642.0	−1.63070	−0.815350	−	0.578968i	$-0.803456\pi$
$881$	−42642.0	−1.63070	−0.815350	+	0.578968i	$0.803456\pi$
$882$	−9909.15	−0.378298
$883$	39816.2	1.51747	0.758733	−	0.651402i	$-0.225819\pi$
$883$	39816.2	1.51747	0.758733	+	0.651402i	$0.225819\pi$
$884$	−31915.5	−1.21429
$885$	−8107.90	−0.307959
$886$	15317.2	0.580804
$887$	−33823.8	−1.28037	−0.640187	−	0.768219i	$-0.721143\pi$
$887$	−33823.8	−1.28037	−0.640187	+	0.768219i	$0.721143\pi$
$888$	3636.30	0.137417
$889$	−13303.8	−0.501905
$890$	−13575.6	−0.511297
$891$	3396.17	0.127695
$892$	−20222.1	−0.759066
$893$	31670.3	1.18679
$894$	13198.9	0.493777
$895$	28113.7	1.04998
$896$	1023.28	0.0381533
$897$	−31745.3	−1.18165
$898$	−29224.9	−1.08602
$899$	0	0
$900$	−21217.7	−0.785840
$901$	−23161.8	−0.856415
$902$	1724.18	0.0636462
$903$	−482.322	−0.0177748
$904$	12178.4	0.448061
$905$	−10275.8	−0.377437
$906$	−15518.7	−0.569066
$907$	−47756.3	−1.74831	−0.874157	−	0.485643i	$-0.838585\pi$
$907$	−47756.3	−1.74831	−0.874157	+	0.485643i	$0.838585\pi$
$908$	3143.86	0.114904
$909$	−5995.05	−0.218749
$910$	−21892.2	−0.797492
$911$	42015.9	1.52804	0.764022	−	0.645190i	$-0.223222\pi$
$911$	42015.9	1.52804	0.764022	+	0.645190i	$0.223222\pi$
$912$	5554.14	0.201662
$913$	−7101.73	−0.257429
$914$	−33540.0	−1.21379
$915$	31004.5	1.12019
$916$	80.1200	0.00289000
$917$	5343.13	0.192416
$918$	−32651.6	−1.17392
$919$	−21834.8	−0.783748	−0.391874	−	0.920019i	$-0.628173\pi$
$919$	−21834.8	−0.783748	−0.391874	+	0.920019i	$0.628173\pi$
$920$	25848.9	0.926320
$921$	−10470.7	−0.374615
$922$	33931.3	1.21200
$923$	30890.8	1.10161
$924$	5043.88	0.179580
$925$	44661.8	1.58754
$926$	2045.82	0.0726024
$927$	−18668.8	−0.661450
$928$	0	0
$929$	44670.5	1.57760	0.788801	−	0.614648i	$-0.210702\pi$
$929$	44670.5	1.57760	0.788801	+	0.614648i	$0.210702\pi$
$930$	3602.64	0.127027
$931$	31859.0	1.12152
$932$	−13090.5	−0.460079
$933$	12858.2	0.451187
$934$	11044.1	0.386908
$935$	128096.	4.48041
$936$	−9445.99	−0.329863
$937$	4476.33	0.156068	0.0780339	−	0.996951i	$-0.475136\pi$
$937$	4476.33	0.156068	0.0780339	+	0.996951i	$0.475136\pi$
$938$	−12798.2	−0.445497
$939$	9592.46	0.333374
$940$	−22845.7	−0.792705
$941$	18114.9	0.627553	0.313777	−	0.949497i	$-0.398406\pi$
$941$	18114.9	0.627553	0.313777	+	0.949497i	$0.398406\pi$
$942$	−5993.06	−0.207287
$943$	2608.65	0.0900840
$944$	2072.24	0.0714467
$945$	−22397.1	−0.770980
$946$	2058.18	0.0707372
$947$	−14778.7	−0.507122	−0.253561	−	0.967319i	$-0.581602\pi$
$947$	−14778.7	−0.507122	−0.253561	+	0.967319i	$0.581602\pi$
$948$	553.578	0.0189656
$949$	1926.87	0.0659104
$950$	68217.1	2.32974
$951$	−14750.6	−0.502966
$952$	7672.20	0.261195
$953$	−43564.1	−1.48078	−0.740389	−	0.672179i	$-0.765358\pi$
$953$	−43564.1	−1.48078	−0.740389	+	0.672179i	$0.765358\pi$
$954$	−6855.16	−0.232646
$955$	−80369.2	−2.72323
$956$	−18388.5	−0.622098
$957$	0	0
$958$	17627.9	0.594499
$959$	16612.1	0.559366
$960$	−4006.53	−0.134698
$961$	−28963.0	−0.972208
$962$	19883.2	0.666382
$963$	16165.2	0.540932
$964$	8506.76	0.284216
$965$	59694.6	1.99133
$966$	7631.29	0.254175
$967$	34229.1	1.13830	0.569148	−	0.822235i	$-0.307273\pi$
$967$	34229.1	1.13830	0.569148	+	0.822235i	$0.307273\pi$
$968$	−10875.4	−0.361105
$969$	41643.1	1.38057
$970$	−10339.9	−0.342263
$971$	26279.2	0.868528	0.434264	−	0.900786i	$-0.357008\pi$
$971$	26279.2	0.868528	0.434264	+	0.900786i	$0.357008\pi$
$972$	−15494.2	−0.511293
$973$	−5335.42	−0.175792
$974$	37922.6	1.24756
$975$	60433.9	1.98506
$976$	−7924.21	−0.259885
$977$	−27095.0	−0.887254	−0.443627	−	0.896211i	$-0.646309\pi$
$977$	−27095.0	−0.887254	−0.443627	+	0.896211i	$0.646309\pi$
$978$	10415.7	0.340550
$979$	17102.5	0.558324
$980$	−22981.7	−0.749107
$981$	−14875.3	−0.484131
$982$	−10375.5	−0.337164
$983$	−45364.5	−1.47193	−0.735963	−	0.677022i	$-0.763270\pi$
$983$	−45364.5	−1.47193	−0.735963	+	0.677022i	$0.763270\pi$
$984$	−404.335	−0.0130993
$985$	−42675.1	−1.38045
$986$	0	0
$987$	−6744.64	−0.217512
$988$	30369.9	0.977929
$989$	3113.99	0.100121
$990$	37912.4	1.21711
$991$	−18082.0	−0.579611	−0.289805	−	0.957086i	$-0.593591\pi$
$991$	−18082.0	−0.579611	−0.289805	+	0.957086i	$0.593591\pi$
$992$	−920.773	−0.0294703
$993$	11652.7	0.372393
$994$	−7425.89	−0.236957
$995$	4058.38	0.129306
$996$	1665.42	0.0529827
$997$	26432.3	0.839640	0.419820	−	0.907607i	$-0.362093\pi$
$997$	26432.3	0.839640	0.419820	+	0.907607i	$0.362093\pi$
$998$	12000.5	0.380631
$999$	20341.8	0.644229

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1682.4.a.k.1.3	✓	6
29.28	even	2		1682.4.a.l.1.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1682.4.a.k.1.3	✓	6	1.1	even	1	trivial
1682.4.a.l.1.4	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.04095 q^{3} +4.00000 q^{4} +20.5863 q^{5} +6.08191 q^{6} -7.99437 q^{7} -8.00000 q^{8} -17.7526 q^{9} -41.1726 q^{10} +51.8694 q^{11} -12.1638 q^{12} -66.5113 q^{13} +15.9887 q^{14} -62.6020 q^{15} +16.0000 q^{16} +119.963 q^{17} +35.5052 q^{18} -114.153 q^{19} +82.3453 q^{20} +24.3105 q^{21} -103.739 q^{22} -156.955 q^{23} +24.3276 q^{24} +298.797 q^{25} +133.023 q^{26} +136.091 q^{27} -31.9775 q^{28} +125.204 q^{30} +28.7742 q^{31} -32.0000 q^{32} -157.732 q^{33} -239.925 q^{34} -164.575 q^{35} -71.0104 q^{36} +149.472 q^{37} +228.306 q^{38} +202.258 q^{39} -164.691 q^{40} -16.6204 q^{41} -48.6210 q^{42} -19.8401 q^{43} +207.477 q^{44} -365.461 q^{45} +313.909 q^{46} -277.437 q^{47} -48.6552 q^{48} -279.090 q^{49} -597.593 q^{50} -364.801 q^{51} -266.045 q^{52} -193.075 q^{53} -272.181 q^{54} +1067.80 q^{55} +63.9550 q^{56} +347.134 q^{57} +129.515 q^{59} -250.408 q^{60} -495.263 q^{61} -57.5483 q^{62} +141.921 q^{63} +64.0000 q^{64} -1369.22 q^{65} +315.465 q^{66} -800.451 q^{67} +479.850 q^{68} +477.292 q^{69} +329.149 q^{70} -464.445 q^{71} +142.021 q^{72} -28.9706 q^{73} -298.944 q^{74} -908.626 q^{75} -456.612 q^{76} -414.663 q^{77} -404.515 q^{78} -45.5102 q^{79} +329.381 q^{80} +65.4754 q^{81} +33.2408 q^{82} -136.916 q^{83} +97.2420 q^{84} +2469.59 q^{85} +39.6802 q^{86} -414.955 q^{88} +329.723 q^{89} +730.922 q^{90} +531.716 q^{91} -627.818 q^{92} -87.5009 q^{93} +554.875 q^{94} -2349.99 q^{95} +97.3105 q^{96} +251.136 q^{97} +558.180 q^{98} -920.816 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 12 q^{2} - 10 q^{3} + 24 q^{4} - 10 q^{5} + 20 q^{6} - 26 q^{7} - 48 q^{8} + 54 q^{9} + 20 q^{10} + 89 q^{11} - 40 q^{12} - 86 q^{13} + 52 q^{14} - 89 q^{15} + 96 q^{16} + 95 q^{17} - 108 q^{18} + 30 q^{19}+ \cdots + 3854 q^{99}+O(q^{100}) \) 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

Representations

Groups

Database

Properties

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