LMFDB - Embedded newform 1682.2.a.r.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1682,2,Mod(1,1682)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1682.1"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

sage:traces = [6,-6,8,6,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$13.4308376200$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{28})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 7x^{4} + 14x^{2} - 7 $ x^6 - 7x^4 + 14x^2 - 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.94986$ 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)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.44504 q^{3} +1.00000 q^{4} -0.613807 q^{5} -1.44504 q^{6} +2.87647 q^{7} -1.00000 q^{8} -0.911854 q^{9} +0.613807 q^{10} +4.34475 q^{11} +1.44504 q^{12} +0.478274 q^{13} -2.87647 q^{14} -0.886977 q^{15} +1.00000 q^{16} -0.259558 q^{17} +0.911854 q^{18} +8.42322 q^{19} -0.613807 q^{20} +4.15662 q^{21} -4.34475 q^{22} -0.142575 q^{23} -1.44504 q^{24} -4.62324 q^{25} -0.478274 q^{26} -5.65279 q^{27} +2.87647 q^{28} +0.886977 q^{30} -6.62704 q^{31} -1.00000 q^{32} +6.27835 q^{33} +0.259558 q^{34} -1.76560 q^{35} -0.911854 q^{36} +9.60431 q^{37} -8.42322 q^{38} +0.691125 q^{39} +0.613807 q^{40} +4.28236 q^{41} -4.15662 q^{42} +3.25912 q^{43} +4.34475 q^{44} +0.559702 q^{45} +0.142575 q^{46} -5.08365 q^{47} +1.44504 q^{48} +1.27409 q^{49} +4.62324 q^{50} -0.375073 q^{51} +0.478274 q^{52} +9.26256 q^{53} +5.65279 q^{54} -2.66684 q^{55} -2.87647 q^{56} +12.1719 q^{57} -10.2463 q^{59} -0.886977 q^{60} +9.93996 q^{61} +6.62704 q^{62} -2.62292 q^{63} +1.00000 q^{64} -0.293568 q^{65} -6.27835 q^{66} +1.86332 q^{67} -0.259558 q^{68} -0.206027 q^{69} +1.76560 q^{70} -9.58445 q^{71} +0.911854 q^{72} -2.98180 q^{73} -9.60431 q^{74} -6.68078 q^{75} +8.42322 q^{76} +12.4976 q^{77} -0.691125 q^{78} +13.5549 q^{79} -0.613807 q^{80} -5.43296 q^{81} -4.28236 q^{82} +1.05487 q^{83} +4.15662 q^{84} +0.159319 q^{85} -3.25912 q^{86} -4.34475 q^{88} -2.57596 q^{89} -0.559702 q^{90} +1.37574 q^{91} -0.142575 q^{92} -9.57635 q^{93} +5.08365 q^{94} -5.17023 q^{95} -1.44504 q^{96} +16.6449 q^{97} -1.27409 q^{98} -3.96178 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 8 q^{3} + 6 q^{4} - 6 q^{5} - 8 q^{6} + 2 q^{7} - 6 q^{8} + 2 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} - 8 q^{13} - 2 q^{14} - 8 q^{15} + 6 q^{16} + 12 q^{17} - 2 q^{18} + 4 q^{19} - 6 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 8 * q^3 + 6 * q^4 - 6 * q^5 - 8 * q^6 + 2 * q^7 - 6 * q^8 + 2 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 - 8 * q^13 - 2 * q^14 - 8 * q^15 + 6 * q^16 + 12 * q^17 - 2 * q^18 + 4 * q^19 - 6 * q^20 + 12 * q^21 - 2 * q^22 + 6 * q^23 - 8 * q^24 + 4 * q^25 + 8 * q^26 + 2 * q^27 + 2 * q^28 + 8 * q^30 + 26 * q^31 - 6 * q^32 + 12 * q^33 - 12 * q^34 - 16 * q^35 + 2 * q^36 + 20 * q^37 - 4 * q^38 - 6 * q^39 + 6 * q^40 + 24 * q^41 - 12 * q^42 + 26 * q^43 + 2 * q^44 - 2 * q^45 - 6 * q^46 + 18 * q^47 + 8 * q^48 - 4 * q^49 - 4 * q^50 + 16 * q^51 - 8 * q^52 + 8 * q^53 - 2 * q^54 + 26 * q^55 - 2 * q^56 + 10 * q^57 - 24 * q^59 - 8 * q^60 + 18 * q^61 - 26 * q^62 + 24 * q^63 + 6 * q^64 - 6 * q^65 - 12 * q^66 + 8 * q^67 + 12 * q^68 + 22 * q^69 + 16 * q^70 + 20 * q^71 - 2 * q^72 + 12 * q^73 - 20 * q^74 + 10 * q^75 + 4 * q^76 + 10 * q^77 + 6 * q^78 + 20 * q^79 - 6 * q^80 + 6 * q^81 - 24 * q^82 - 28 * q^83 + 12 * q^84 + 16 * q^85 - 26 * q^86 - 2 * q^88 + 2 * q^90 - 12 * q^91 + 6 * q^92 + 30 * q^93 - 18 * q^94 - 32 * q^95 - 8 * q^96 + 44 * q^97 + 4 * q^98 + 24 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.44504	0.834295	0.417148	−	0.908839i	$-0.363030\pi$
$3$	1.44504	0.834295	0.417148	+	0.908839i	$0.363030\pi$
$4$	1.00000	0.500000
$5$	−0.613807	−0.274503	−0.137251	−	0.990536i	$-0.543827\pi$
$5$	−0.613807	−0.274503	−0.137251	+	0.990536i	$0.543827\pi$
$6$	−1.44504	−0.589936
$7$	2.87647	1.08720	0.543602	−	0.839343i	$-0.317060\pi$
$7$	2.87647	1.08720	0.543602	+	0.839343i	$0.317060\pi$
$8$	−1.00000	−0.353553
$9$	−0.911854	−0.303951
$10$	0.613807	0.194103
$11$	4.34475	1.30999	0.654996	−	0.755632i	$-0.272670\pi$
$11$	4.34475	1.30999	0.654996	+	0.755632i	$0.272670\pi$
$12$	1.44504	0.417148
$13$	0.478274	0.132649	0.0663246	−	0.997798i	$-0.478873\pi$
$13$	0.478274	0.132649	0.0663246	+	0.997798i	$0.478873\pi$
$14$	−2.87647	−0.768770
$15$	−0.886977	−0.229016
$16$	1.00000	0.250000
$17$	−0.259558	−0.0629522	−0.0314761	−	0.999505i	$-0.510021\pi$
$17$	−0.259558	−0.0629522	−0.0314761	+	0.999505i	$0.510021\pi$
$18$	0.911854	0.214926
$19$	8.42322	1.93242	0.966210	−	0.257756i	$-0.0829832\pi$
$19$	8.42322	1.93242	0.966210	+	0.257756i	$0.0829832\pi$
$20$	−0.613807	−0.137251
$21$	4.15662	0.907049
$22$	−4.34475	−0.926305
$23$	−0.142575	−0.0297289	−0.0148645	−	0.999890i	$-0.504732\pi$
$23$	−0.142575	−0.0297289	−0.0148645	+	0.999890i	$0.504732\pi$
$24$	−1.44504	−0.294968
$25$	−4.62324	−0.924648
$26$	−0.478274	−0.0937972
$27$	−5.65279	−1.08788
$28$	2.87647	0.543602
$29$	0	0
$29$	0	0
$30$	0.886977	0.161939
$31$	−6.62704	−1.19025	−0.595126	−	0.803633i	$-0.702898\pi$
$31$	−6.62704	−1.19025	−0.595126	+	0.803633i	$0.702898\pi$
$32$	−1.00000	−0.176777
$33$	6.27835	1.09292
$34$	0.259558	0.0445139
$35$	−1.76560	−0.298441
$36$	−0.911854	−0.151976
$37$	9.60431	1.57894	0.789470	−	0.613790i	$-0.210356\pi$
$37$	9.60431	1.57894	0.789470	+	0.613790i	$0.210356\pi$
$38$	−8.42322	−1.36643
$39$	0.691125	0.110669
$40$	0.613807	0.0970514
$41$	4.28236	0.668792	0.334396	−	0.942433i	$-0.391468\pi$
$41$	4.28236	0.668792	0.334396	+	0.942433i	$0.391468\pi$
$42$	−4.15662	−0.641381
$43$	3.25912	0.497011	0.248506	−	0.968630i	$-0.420061\pi$
$43$	3.25912	0.497011	0.248506	+	0.968630i	$0.420061\pi$
$44$	4.34475	0.654996
$45$	0.559702	0.0834355
$46$	0.142575	0.0210215
$47$	−5.08365	−0.741527	−0.370763	−	0.928727i	$-0.620904\pi$
$47$	−5.08365	−0.741527	−0.370763	+	0.928727i	$0.620904\pi$
$48$	1.44504	0.208574
$49$	1.27409	0.182013
$50$	4.62324	0.653825
$51$	−0.375073	−0.0525207
$52$	0.478274	0.0663246
$53$	9.26256	1.27231	0.636155	−	0.771561i	$-0.280524\pi$
$53$	9.26256	1.27231	0.636155	+	0.771561i	$0.280524\pi$
$54$	5.65279	0.769248
$55$	−2.66684	−0.359597
$56$	−2.87647	−0.384385
$57$	12.1719	1.61221
$58$	0	0
$59$	−10.2463	−1.33395	−0.666977	−	0.745078i	$-0.732412\pi$
$59$	−10.2463	−1.33395	−0.666977	+	0.745078i	$0.732412\pi$
$60$	−0.886977	−0.114508
$61$	9.93996	1.27268	0.636341	−	0.771408i	$-0.280447\pi$
$61$	9.93996	1.27268	0.636341	+	0.771408i	$0.280447\pi$
$62$	6.62704	0.841635
$63$	−2.62292	−0.330457
$64$	1.00000	0.125000
$65$	−0.293568	−0.0364126
$66$	−6.27835	−0.772812
$67$	1.86332	0.227640	0.113820	−	0.993501i	$-0.463691\pi$
$67$	1.86332	0.227640	0.113820	+	0.993501i	$0.463691\pi$
$68$	−0.259558	−0.0314761
$69$	−0.206027	−0.0248027
$70$	1.76560	0.211029
$71$	−9.58445	−1.13746	−0.568732	−	0.822523i	$-0.692566\pi$
$71$	−9.58445	−1.13746	−0.568732	+	0.822523i	$0.692566\pi$
$72$	0.911854	0.107463
$73$	−2.98180	−0.348993	−0.174497	−	0.984658i	$-0.555830\pi$
$73$	−2.98180	−0.348993	−0.174497	+	0.984658i	$0.555830\pi$
$74$	−9.60431	−1.11648
$75$	−6.68078	−0.771430
$76$	8.42322	0.966210
$77$	12.4976	1.42423
$78$	−0.691125	−0.0782545
$79$	13.5549	1.52505	0.762525	−	0.646959i	$-0.223959\pi$
$79$	13.5549	1.52505	0.762525	+	0.646959i	$0.223959\pi$
$80$	−0.613807	−0.0686257
$81$	−5.43296	−0.603662
$82$	−4.28236	−0.472908
$83$	1.05487	0.115787	0.0578933	−	0.998323i	$-0.481562\pi$
$83$	1.05487	0.115787	0.0578933	+	0.998323i	$0.481562\pi$
$84$	4.15662	0.453525
$85$	0.159319	0.0172806
$86$	−3.25912	−0.351440
$87$	0	0
$88$	−4.34475	−0.463152
$89$	−2.57596	−0.273051	−0.136526	−	0.990637i	$-0.543594\pi$
$89$	−2.57596	−0.273051	−0.136526	+	0.990637i	$0.543594\pi$
$90$	−0.559702	−0.0589978
$91$	1.37574	0.144217
$92$	−0.142575	−0.0148645
$93$	−9.57635	−0.993021
$94$	5.08365	0.524338
$95$	−5.17023	−0.530455
$96$	−1.44504	−0.147484
$97$	16.6449	1.69003	0.845015	−	0.534742i	$-0.179591\pi$
$97$	16.6449	1.69003	0.845015	+	0.534742i	$0.179591\pi$
$98$	−1.27409	−0.128703
$99$	−3.96178	−0.398174
$100$	−4.62324	−0.462324
$101$	16.8855	1.68017	0.840084	−	0.542456i	$-0.182506\pi$
$101$	16.8855	1.68017	0.840084	+	0.542456i	$0.182506\pi$
$102$	0.375073	0.0371377
$103$	−2.65015	−0.261127	−0.130563	−	0.991440i	$-0.541679\pi$
$103$	−2.65015	−0.261127	−0.130563	+	0.991440i	$0.541679\pi$
$104$	−0.478274	−0.0468986
$105$	−2.55136	−0.248988
$106$	−9.26256	−0.899659
$107$	15.7119	1.51893	0.759464	−	0.650549i	$-0.225461\pi$
$107$	15.7119	1.51893	0.759464	+	0.650549i	$0.225461\pi$
$108$	−5.65279	−0.543940
$109$	−10.1709	−0.974191	−0.487096	−	0.873349i	$-0.661944\pi$
$109$	−10.1709	−0.974191	−0.487096	+	0.873349i	$0.661944\pi$
$110$	2.66684	0.254273
$111$	13.8786	1.31730
$112$	2.87647	0.271801
$113$	−17.0447	−1.60343	−0.801714	−	0.597708i	$-0.796078\pi$
$113$	−17.0447	−1.60343	−0.801714	+	0.597708i	$0.796078\pi$
$114$	−12.1719	−1.14000
$115$	0.0875136	0.00816068
$116$	0	0
$117$	−0.436116	−0.0403189
$118$	10.2463	0.943248
$119$	−0.746613	−0.0684419
$120$	0.886977	0.0809696
$121$	7.87688	0.716080
$122$	−9.93996	−0.899922
$123$	6.18819	0.557970
$124$	−6.62704	−0.595126
$125$	5.90681	0.528321
$126$	2.62292	0.233669
$127$	−3.42505	−0.303924	−0.151962	−	0.988386i	$-0.548559\pi$
$127$	−3.42505	−0.303924	−0.151962	+	0.988386i	$0.548559\pi$
$128$	−1.00000	−0.0883883
$129$	4.70957	0.414654
$130$	0.293568	0.0257476
$131$	−2.93793	−0.256688	−0.128344	−	0.991730i	$-0.540966\pi$
$131$	−2.93793	−0.256688	−0.128344	+	0.991730i	$0.540966\pi$
$132$	6.27835	0.546460
$133$	24.2292	2.10094
$134$	−1.86332	−0.160966
$135$	3.46972	0.298626
$136$	0.259558	0.0222570
$137$	−16.9899	−1.45154	−0.725772	−	0.687935i	$-0.758517\pi$
$137$	−16.9899	−1.45154	−0.725772	+	0.687935i	$0.758517\pi$
$138$	0.206027	0.0175382
$139$	−0.365574	−0.0310076	−0.0155038	−	0.999880i	$-0.504935\pi$
$139$	−0.365574	−0.0310076	−0.0155038	+	0.999880i	$0.504935\pi$
$140$	−1.76560	−0.149220
$141$	−7.34609	−0.618652
$142$	9.58445	0.804309
$143$	2.07798	0.173770
$144$	−0.911854	−0.0759878
$145$	0	0
$146$	2.98180	0.246776
$147$	1.84112	0.151853
$148$	9.60431	0.789470
$149$	−5.32915	−0.436581	−0.218291	−	0.975884i	$-0.570048\pi$
$149$	−5.32915	−0.436581	−0.218291	+	0.975884i	$0.570048\pi$
$150$	6.68078	0.545483
$151$	6.73362	0.547974	0.273987	−	0.961733i	$-0.411657\pi$
$151$	6.73362	0.547974	0.273987	+	0.961733i	$0.411657\pi$
$152$	−8.42322	−0.683214
$153$	0.236679	0.0191344
$154$	−12.4976	−1.00708
$155$	4.06772	0.326727
$156$	0.691125	0.0553343
$157$	4.45167	0.355282	0.177641	−	0.984095i	$-0.443153\pi$
$157$	4.45167	0.355282	0.177641	+	0.984095i	$0.443153\pi$
$158$	−13.5549	−1.07837
$159$	13.3848	1.06148
$160$	0.613807	0.0485257
$161$	−0.410113	−0.0323214
$162$	5.43296	0.426854
$163$	8.12268	0.636218	0.318109	−	0.948054i	$-0.396952\pi$
$163$	8.12268	0.636218	0.318109	+	0.948054i	$0.396952\pi$
$164$	4.28236	0.334396
$165$	−3.85370	−0.300010
$166$	−1.05487	−0.0818734
$167$	−0.399378	−0.0309048	−0.0154524	−	0.999881i	$-0.504919\pi$
$167$	−0.399378	−0.0309048	−0.0154524	+	0.999881i	$0.504919\pi$
$168$	−4.15662	−0.320690
$169$	−12.7713	−0.982404
$170$	−0.159319	−0.0122192
$171$	−7.68075	−0.587362
$172$	3.25912	0.248506
$173$	−4.70045	−0.357368	−0.178684	−	0.983906i	$-0.557184\pi$
$173$	−4.70045	−0.357368	−0.178684	+	0.983906i	$0.557184\pi$
$174$	0	0
$175$	−13.2986	−1.00528
$176$	4.34475	0.327498
$177$	−14.8063	−1.11291
$178$	2.57596	0.193076
$179$	−4.66359	−0.348573	−0.174287	−	0.984695i	$-0.555762\pi$
$179$	−4.66359	−0.348573	−0.174287	+	0.984695i	$0.555762\pi$
$180$	0.559702	0.0417178
$181$	9.43759	0.701490	0.350745	−	0.936471i	$-0.385928\pi$
$181$	9.43759	0.701490	0.350745	+	0.936471i	$0.385928\pi$
$182$	−1.37574	−0.101977
$183$	14.3637	1.06179
$184$	0.142575	0.0105108
$185$	−5.89520	−0.433423
$186$	9.57635	0.702172
$187$	−1.12772	−0.0824669
$188$	−5.08365	−0.370763
$189$	−16.2601	−1.18275
$190$	5.17023	0.375088
$191$	−19.7596	−1.42975	−0.714877	−	0.699251i	$-0.753517\pi$
$191$	−19.7596	−1.42975	−0.714877	+	0.699251i	$0.753517\pi$
$192$	1.44504	0.104287
$193$	−2.00731	−0.144489	−0.0722446	−	0.997387i	$-0.523016\pi$
$193$	−2.00731	−0.144489	−0.0722446	+	0.997387i	$0.523016\pi$
$194$	−16.6449	−1.19503
$195$	−0.424218	−0.0303789
$196$	1.27409	0.0910066
$197$	1.62857	0.116031	0.0580154	−	0.998316i	$-0.481523\pi$
$197$	1.62857	0.116031	0.0580154	+	0.998316i	$0.481523\pi$
$198$	3.96178	0.281552
$199$	9.36362	0.663770	0.331885	−	0.943320i	$-0.392315\pi$
$199$	9.36362	0.663770	0.331885	+	0.943320i	$0.392315\pi$
$200$	4.62324	0.326912
$201$	2.69257	0.189919
$202$	−16.8855	−1.18806
$203$	0	0
$204$	−0.375073	−0.0262604
$205$	−2.62854	−0.183585
$206$	2.65015	0.184644
$207$	0.130008	0.00903615
$208$	0.478274	0.0331623
$209$	36.5968	2.53146
$210$	2.55136	0.176061
$211$	6.35245	0.437321	0.218660	−	0.975801i	$-0.429831\pi$
$211$	6.35245	0.437321	0.218660	+	0.975801i	$0.429831\pi$
$212$	9.26256	0.636155
$213$	−13.8499	−0.948982
$214$	−15.7119	−1.07404
$215$	−2.00047	−0.136431
$216$	5.65279	0.384624
$217$	−19.0625	−1.29405
$218$	10.1709	0.688857
$219$	−4.30883	−0.291163
$220$	−2.66684	−0.179798
$221$	−0.124140	−0.00835056
$222$	−13.8786	−0.931473
$223$	6.77523	0.453703	0.226852	−	0.973929i	$-0.427157\pi$
$223$	6.77523	0.453703	0.226852	+	0.973929i	$0.427157\pi$
$224$	−2.87647	−0.192192
$225$	4.21572	0.281048
$226$	17.0447	1.13379
$227$	16.6240	1.10338	0.551688	−	0.834050i	$-0.313984\pi$
$227$	16.6240	1.10338	0.551688	+	0.834050i	$0.313984\pi$
$228$	12.1719	0.806104
$229$	6.48836	0.428763	0.214382	−	0.976750i	$-0.431226\pi$
$229$	6.48836	0.428763	0.214382	+	0.976750i	$0.431226\pi$
$230$	−0.0875136	−0.00577047
$231$	18.0595	1.18823
$232$	0	0
$233$	19.9763	1.30869	0.654346	−	0.756195i	$-0.272944\pi$
$233$	19.9763	1.30869	0.654346	+	0.756195i	$0.272944\pi$
$234$	0.436116	0.0285098
$235$	3.12038	0.203551
$236$	−10.2463	−0.666977
$237$	19.5875	1.27234
$238$	0.746613	0.0483957
$239$	1.85655	0.120090	0.0600452	−	0.998196i	$-0.480876\pi$
$239$	1.85655	0.120090	0.0600452	+	0.998196i	$0.480876\pi$
$240$	−0.886977	−0.0572541
$241$	−2.38694	−0.153757	−0.0768783	−	0.997040i	$-0.524495\pi$
$241$	−2.38694	−0.153757	−0.0768783	+	0.997040i	$0.524495\pi$
$242$	−7.87688	−0.506345
$243$	9.10752	0.584248
$244$	9.93996	0.636341
$245$	−0.782047	−0.0499632
$246$	−6.18819	−0.394545
$247$	4.02861	0.256334
$248$	6.62704	0.420817
$249$	1.52432	0.0966002
$250$	−5.90681	−0.373580
$251$	−18.2524	−1.15208	−0.576040	−	0.817421i	$-0.695403\pi$
$251$	−18.2524	−1.15208	−0.576040	+	0.817421i	$0.695403\pi$
$252$	−2.62292	−0.165229
$253$	−0.619453	−0.0389447
$254$	3.42505	0.214907
$255$	0.230222	0.0144171
$256$	1.00000	0.0625000
$257$	−12.7119	−0.792944	−0.396472	−	0.918047i	$-0.629766\pi$
$257$	−12.7119	−0.792944	−0.396472	+	0.918047i	$0.629766\pi$
$258$	−4.70957	−0.293205
$259$	27.6265	1.71663
$260$	−0.293568	−0.0182063
$261$	0	0
$262$	2.93793	0.181506
$263$	−1.89993	−0.117155	−0.0585774	−	0.998283i	$-0.518656\pi$
$263$	−1.89993	−0.117155	−0.0585774	+	0.998283i	$0.518656\pi$
$264$	−6.27835	−0.386406
$265$	−5.68542	−0.349253
$266$	−24.2292	−1.48559
$267$	−3.72237	−0.227805
$268$	1.86332	0.113820
$269$	25.6366	1.56309	0.781545	−	0.623849i	$-0.214432\pi$
$269$	25.6366	1.56309	0.781545	+	0.623849i	$0.214432\pi$
$270$	−3.46972	−0.211161
$271$	−7.82313	−0.475221	−0.237611	−	0.971360i	$-0.576364\pi$
$271$	−7.82313	−0.475221	−0.237611	+	0.971360i	$0.576364\pi$
$272$	−0.259558	−0.0157380
$273$	1.98800	0.120319
$274$	16.9899	1.02640
$275$	−20.0868	−1.21128
$276$	−0.206027	−0.0124014
$277$	12.7302	0.764886	0.382443	−	0.923979i	$-0.375083\pi$
$277$	12.7302	0.764886	0.382443	+	0.923979i	$0.375083\pi$
$278$	0.365574	0.0219257
$279$	6.04289	0.361778
$280$	1.76560	0.105515
$281$	5.74861	0.342933	0.171467	−	0.985190i	$-0.445149\pi$
$281$	5.74861	0.342933	0.171467	+	0.985190i	$0.445149\pi$
$282$	7.34609	0.437453
$283$	24.7442	1.47089	0.735445	−	0.677585i	$-0.236973\pi$
$283$	24.7442	1.47089	0.735445	+	0.677585i	$0.236973\pi$
$284$	−9.58445	−0.568732
$285$	−7.47121	−0.442556
$286$	−2.07798	−0.122874
$287$	12.3181	0.727114
$288$	0.911854	0.0537315
$289$	−16.9326	−0.996037
$290$	0	0
$291$	24.0525	1.40998
$292$	−2.98180	−0.174497
$293$	−25.1721	−1.47057	−0.735285	−	0.677758i	$-0.762952\pi$
$293$	−25.1721	−1.47057	−0.735285	+	0.677758i	$0.762952\pi$
$294$	−1.84112	−0.107376
$295$	6.28925	0.366174
$296$	−9.60431	−0.558239
$297$	−24.5600	−1.42512
$298$	5.32915	0.308710
$299$	−0.0681899	−0.00394352
$300$	−6.68078	−0.385715
$301$	9.37477	0.540353
$302$	−6.73362	−0.387476
$303$	24.4002	1.40176
$304$	8.42322	0.483105
$305$	−6.10122	−0.349355
$306$	−0.236679	−0.0135301
$307$	−15.0768	−0.860480	−0.430240	−	0.902715i	$-0.641571\pi$
$307$	−15.0768	−0.860480	−0.430240	+	0.902715i	$0.641571\pi$
$308$	12.4976	0.712115
$309$	−3.82957	−0.217857
$310$	−4.06772	−0.231031
$311$	−18.5916	−1.05423	−0.527117	−	0.849793i	$-0.676727\pi$
$311$	−18.5916	−1.05423	−0.527117	+	0.849793i	$0.676727\pi$
$312$	−0.691125	−0.0391273
$313$	−20.4199	−1.15420	−0.577101	−	0.816672i	$-0.695816\pi$
$313$	−20.4199	−1.15420	−0.577101	+	0.816672i	$0.695816\pi$
$314$	−4.45167	−0.251222
$315$	1.60997	0.0907115
$316$	13.5549	0.762525
$317$	−8.41935	−0.472878	−0.236439	−	0.971646i	$-0.575980\pi$
$317$	−8.41935	−0.472878	−0.236439	+	0.971646i	$0.575980\pi$
$318$	−13.3848	−0.750581
$319$	0	0
$320$	−0.613807	−0.0343129
$321$	22.7044	1.26723
$322$	0.410113	0.0228547
$323$	−2.18632	−0.121650
$324$	−5.43296	−0.301831
$325$	−2.21117	−0.122654
$326$	−8.12268	−0.449874
$327$	−14.6973	−0.812763
$328$	−4.28236	−0.236454
$329$	−14.6230	−0.806191
$330$	3.85370	0.212139
$331$	−31.5696	−1.73522	−0.867610	−	0.497246i	$-0.834345\pi$
$331$	−31.5696	−1.73522	−0.867610	+	0.497246i	$0.834345\pi$
$332$	1.05487	0.0578933
$333$	−8.75773	−0.479921
$334$	0.399378	0.0218530
$335$	−1.14372	−0.0624879
$336$	4.15662	0.226762
$337$	−17.1433	−0.933856	−0.466928	−	0.884295i	$-0.654639\pi$
$337$	−17.1433	−0.933856	−0.466928	+	0.884295i	$0.654639\pi$
$338$	12.7713	0.694665
$339$	−24.6303	−1.33773
$340$	0.159319	0.00864028
$341$	−28.7929	−1.55922
$342$	7.68075	0.415327
$343$	−16.4704	−0.889319
$344$	−3.25912	−0.175720
$345$	0.126461	0.00680842
$346$	4.70045	0.252698
$347$	−15.2643	−0.819433	−0.409717	−	0.912213i	$-0.634372\pi$
$347$	−15.2643	−0.819433	−0.409717	+	0.912213i	$0.634372\pi$
$348$	0	0
$349$	−27.7100	−1.48328	−0.741641	−	0.670797i	$-0.765952\pi$
$349$	−27.7100	−1.48328	−0.741641	+	0.670797i	$0.765952\pi$
$350$	13.2986	0.710841
$351$	−2.70358	−0.144307
$352$	−4.34475	−0.231576
$353$	−26.1989	−1.39443	−0.697214	−	0.716863i	$-0.745577\pi$
$353$	−26.1989	−1.39443	−0.697214	+	0.716863i	$0.745577\pi$
$354$	14.8063	0.786947
$355$	5.88300	0.312237
$356$	−2.57596	−0.136526
$357$	−1.07889	−0.0571007
$358$	4.66359	0.246479
$359$	11.8516	0.625503	0.312751	−	0.949835i	$-0.398749\pi$
$359$	11.8516	0.625503	0.312751	+	0.949835i	$0.398749\pi$
$360$	−0.559702	−0.0294989
$361$	51.9507	2.73425
$362$	−9.43759	−0.496029
$363$	11.3824	0.597422
$364$	1.37574	0.0721084
$365$	1.83025	0.0957997
$366$	−14.3637	−0.750800
$367$	−26.0651	−1.36059	−0.680293	−	0.732940i	$-0.738147\pi$
$367$	−26.0651	−1.36059	−0.680293	+	0.732940i	$0.738147\pi$
$368$	−0.142575	−0.00743224
$369$	−3.90489	−0.203280
$370$	5.89520	0.306477
$371$	26.6435	1.38326
$372$	−9.57635	−0.496511
$373$	−23.2397	−1.20331	−0.601653	−	0.798758i	$-0.705491\pi$
$373$	−23.2397	−1.20331	−0.601653	+	0.798758i	$0.705491\pi$
$374$	1.12772	0.0583129
$375$	8.53559	0.440776
$376$	5.08365	0.262169
$377$	0	0
$378$	16.2601	0.836329
$379$	−30.9906	−1.59188	−0.795941	−	0.605374i	$-0.793024\pi$
$379$	−30.9906	−1.59188	−0.795941	+	0.605374i	$0.793024\pi$
$380$	−5.17023	−0.265227
$381$	−4.94935	−0.253563
$382$	19.7596	1.01099
$383$	−23.7304	−1.21257	−0.606283	−	0.795249i	$-0.707340\pi$
$383$	−23.7304	−1.21257	−0.606283	+	0.795249i	$0.707340\pi$
$384$	−1.44504	−0.0737420
$385$	−7.67109	−0.390955
$386$	2.00731	0.102169
$387$	−2.97184	−0.151067
$388$	16.6449	0.845015
$389$	−1.08756	−0.0551416	−0.0275708	−	0.999620i	$-0.508777\pi$
$389$	−1.08756	−0.0551416	−0.0275708	+	0.999620i	$0.508777\pi$
$390$	0.424218	0.0214811
$391$	0.0370065	0.00187150
$392$	−1.27409	−0.0643514
$393$	−4.24543	−0.214154
$394$	−1.62857	−0.0820462
$395$	−8.32012	−0.418631
$396$	−3.96178	−0.199087
$397$	6.38613	0.320511	0.160255	−	0.987076i	$-0.448768\pi$
$397$	6.38613	0.320511	0.160255	+	0.987076i	$0.448768\pi$
$398$	−9.36362	−0.469356
$399$	35.0122	1.75280
$400$	−4.62324	−0.231162
$401$	−30.1679	−1.50651	−0.753256	−	0.657728i	$-0.771518\pi$
$401$	−30.1679	−1.50651	−0.753256	+	0.657728i	$0.771518\pi$
$402$	−2.69257	−0.134293
$403$	−3.16954	−0.157886
$404$	16.8855	0.840084
$405$	3.33479	0.165707
$406$	0	0
$407$	41.7284	2.06840
$408$	0.375073	0.0185689
$409$	4.76753	0.235739	0.117870	−	0.993029i	$-0.462393\pi$
$409$	4.76753	0.235739	0.117870	+	0.993029i	$0.462393\pi$
$410$	2.62854	0.129815
$411$	−24.5511	−1.21102
$412$	−2.65015	−0.130563
$413$	−29.4732	−1.45028
$414$	−0.130008	−0.00638952
$415$	−0.647484	−0.0317837
$416$	−0.478274	−0.0234493
$417$	−0.528269	−0.0258695
$418$	−36.5968	−1.79001
$419$	−27.2149	−1.32953	−0.664767	−	0.747051i	$-0.731469\pi$
$419$	−27.2149	−1.32953	−0.664767	+	0.747051i	$0.731469\pi$
$420$	−2.55136	−0.124494
$421$	18.9520	0.923665	0.461833	−	0.886967i	$-0.347192\pi$
$421$	18.9520	0.923665	0.461833	+	0.886967i	$0.347192\pi$
$422$	−6.35245	−0.309233
$423$	4.63555	0.225388
$424$	−9.26256	−0.449829
$425$	1.20000	0.0582086
$426$	13.8499	0.671031
$427$	28.5920	1.38366
$428$	15.7119	0.759464
$429$	3.00277	0.144975
$430$	2.00047	0.0964713
$431$	20.6248	0.993461	0.496730	−	0.867905i	$-0.334534\pi$
$431$	20.6248	0.993461	0.496730	+	0.867905i	$0.334534\pi$
$432$	−5.65279	−0.271970
$433$	4.85408	0.233272	0.116636	−	0.993175i	$-0.462789\pi$
$433$	4.85408	0.233272	0.116636	+	0.993175i	$0.462789\pi$
$434$	19.0625	0.915029
$435$	0	0
$436$	−10.1709	−0.487096
$437$	−1.20094	−0.0574488
$438$	4.30883	0.205884
$439$	−27.2748	−1.30176	−0.650878	−	0.759183i	$-0.725599\pi$
$439$	−27.2748	−1.30176	−0.650878	+	0.759183i	$0.725599\pi$
$440$	2.66684	0.127137
$441$	−1.16179	−0.0553232
$442$	0.124140	0.00590474
$443$	−22.5925	−1.07340	−0.536700	−	0.843773i	$-0.680329\pi$
$443$	−22.5925	−1.07340	−0.536700	+	0.843773i	$0.680329\pi$
$444$	13.8786	0.658651
$445$	1.58114	0.0749534
$446$	−6.77523	−0.320817
$447$	−7.70085	−0.364238
$448$	2.87647	0.135901
$449$	6.15402	0.290426	0.145213	−	0.989400i	$-0.453613\pi$
$449$	6.15402	0.290426	0.145213	+	0.989400i	$0.453613\pi$
$450$	−4.21572	−0.198731
$451$	18.6058	0.876113
$452$	−17.0447	−0.801714
$453$	9.73036	0.457172
$454$	−16.6240	−0.780205
$455$	−0.844440	−0.0395879
$456$	−12.1719	−0.570002
$457$	15.7924	0.738737	0.369369	−	0.929283i	$-0.379574\pi$
$457$	15.7924	0.738737	0.369369	+	0.929283i	$0.379574\pi$
$458$	−6.48836	−0.303181
$459$	1.46723	0.0684844
$460$	0.0875136	0.00408034
$461$	8.27739	0.385516	0.192758	−	0.981246i	$-0.438257\pi$
$461$	8.27739	0.385516	0.192758	+	0.981246i	$0.438257\pi$
$462$	−18.0595	−0.840204
$463$	9.93980	0.461942	0.230971	−	0.972961i	$-0.425810\pi$
$463$	9.93980	0.461942	0.230971	+	0.972961i	$0.425810\pi$
$464$	0	0
$465$	5.87803	0.272587
$466$	−19.9763	−0.925385
$467$	17.6952	0.818837	0.409419	−	0.912347i	$-0.365732\pi$
$467$	17.6952	0.818837	0.409419	+	0.912347i	$0.365732\pi$
$468$	−0.436116	−0.0201595
$469$	5.35978	0.247491
$470$	−3.12038	−0.143932
$471$	6.43285	0.296410
$472$	10.2463	0.471624
$473$	14.1601	0.651081
$474$	−19.5875	−0.899682
$475$	−38.9426	−1.78681
$476$	−0.746613	−0.0342209
$477$	−8.44610	−0.386720
$478$	−1.85655	−0.0849167
$479$	23.2355	1.06166	0.530828	−	0.847480i	$-0.321881\pi$
$479$	23.2355	1.06166	0.530828	+	0.847480i	$0.321881\pi$
$480$	0.886977	0.0404848
$481$	4.59349	0.209445
$482$	2.38694	0.108722
$483$	−0.592631	−0.0269656
$484$	7.87688	0.358040
$485$	−10.2167	−0.463918
$486$	−9.10752	−0.413126
$487$	−5.79395	−0.262549	−0.131274	−	0.991346i	$-0.541907\pi$
$487$	−5.79395	−0.262549	−0.131274	+	0.991346i	$0.541907\pi$
$488$	−9.93996	−0.449961
$489$	11.7376	0.530793
$490$	0.782047	0.0353293
$491$	8.40728	0.379415	0.189708	−	0.981841i	$-0.439246\pi$
$491$	8.40728	0.379415	0.189708	+	0.981841i	$0.439246\pi$
$492$	6.18819	0.278985
$493$	0	0
$494$	−4.02861	−0.181256
$495$	2.43177	0.109300
$496$	−6.62704	−0.297563
$497$	−27.5694	−1.23666
$498$	−1.52432	−0.0683066
$499$	17.5998	0.787876	0.393938	−	0.919137i	$-0.371112\pi$
$499$	17.5998	0.787876	0.393938	+	0.919137i	$0.371112\pi$
$500$	5.90681	0.264161
$501$	−0.577119	−0.0257838
$502$	18.2524	0.814644
$503$	−21.5416	−0.960494	−0.480247	−	0.877133i	$-0.659453\pi$
$503$	−21.5416	−0.960494	−0.480247	+	0.877133i	$0.659453\pi$
$504$	2.62292	0.116834
$505$	−10.3644	−0.461211
$506$	0.619453	0.0275381
$507$	−18.4550	−0.819615
$508$	−3.42505	−0.151962
$509$	−25.7945	−1.14332	−0.571660	−	0.820491i	$-0.693700\pi$
$509$	−25.7945	−1.14332	−0.571660	+	0.820491i	$0.693700\pi$
$510$	−0.230222	−0.0101944
$511$	−8.57707	−0.379427
$512$	−1.00000	−0.0441942
$513$	−47.6147	−2.10224
$514$	12.7119	0.560696
$515$	1.62668	0.0716800
$516$	4.70957	0.207327
$517$	−22.0872	−0.971394
$518$	−27.6265	−1.21384
$519$	−6.79234	−0.298151
$520$	0.293568	0.0128738
$521$	−22.3082	−0.977341	−0.488670	−	0.872468i	$-0.662518\pi$
$521$	−22.3082	−0.977341	−0.488670	+	0.872468i	$0.662518\pi$
$522$	0	0
$523$	−40.0895	−1.75299	−0.876496	−	0.481408i	$-0.840125\pi$
$523$	−40.0895	−1.75299	−0.876496	+	0.481408i	$0.840125\pi$
$524$	−2.93793	−0.128344
$525$	−19.2171	−0.838702
$526$	1.89993	0.0828410
$527$	1.72010	0.0749289
$528$	6.27835	0.273230
$529$	−22.9797	−0.999116
$530$	5.68542	0.246959
$531$	9.34313	0.405457
$532$	24.2292	1.05047
$533$	2.04814	0.0887148
$534$	3.72237	0.161083
$535$	−9.64408	−0.416950
$536$	−1.86332	−0.0804830
$537$	−6.73909	−0.290813
$538$	−25.6366	−1.10527
$539$	5.53562	0.238436
$540$	3.46972	0.149313
$541$	6.98308	0.300226	0.150113	−	0.988669i	$-0.452036\pi$
$541$	6.98308	0.300226	0.150113	+	0.988669i	$0.452036\pi$
$542$	7.82313	0.336032
$543$	13.6377	0.585250
$544$	0.259558	0.0111285
$545$	6.24294	0.267418
$546$	−1.98800	−0.0850787
$547$	6.38811	0.273136	0.136568	−	0.990631i	$-0.456393\pi$
$547$	6.38811	0.273136	0.136568	+	0.990631i	$0.456393\pi$
$548$	−16.9899	−0.725772
$549$	−9.06379	−0.386833
$550$	20.0868	0.856506
$551$	0	0
$552$	0.206027	0.00876908
$553$	38.9904	1.65804
$554$	−12.7302	−0.540856
$555$	−8.51880	−0.361603
$556$	−0.365574	−0.0155038
$557$	−10.1321	−0.429309	−0.214655	−	0.976690i	$-0.568863\pi$
$557$	−10.1321	−0.429309	−0.214655	+	0.976690i	$0.568863\pi$
$558$	−6.04289	−0.255816
$559$	1.55875	0.0659282
$560$	−1.76560	−0.0746102
$561$	−1.62960	−0.0688017
$562$	−5.74861	−0.242490
$563$	17.1419	0.722445	0.361222	−	0.932480i	$-0.382359\pi$
$563$	17.1419	0.722445	0.361222	+	0.932480i	$0.382359\pi$
$564$	−7.34609	−0.309326
$565$	10.4621	0.440145
$566$	−24.7442	−1.04008
$567$	−15.6278	−0.656304
$568$	9.58445	0.402155
$569$	−42.5607	−1.78424	−0.892118	−	0.451802i	$-0.850781\pi$
$569$	−42.5607	−1.78424	−0.892118	+	0.451802i	$0.850781\pi$
$570$	7.47121	0.312934
$571$	18.9512	0.793081	0.396540	−	0.918017i	$-0.370211\pi$
$571$	18.9512	0.793081	0.396540	+	0.918017i	$0.370211\pi$
$572$	2.07798	0.0868848
$573$	−28.5534	−1.19284
$574$	−12.3181	−0.514147
$575$	0.659159	0.0274888
$576$	−0.911854	−0.0379939
$577$	40.9378	1.70426	0.852131	−	0.523329i	$-0.175310\pi$
$577$	40.9378	1.70426	0.852131	+	0.523329i	$0.175310\pi$
$578$	16.9326	0.704305
$579$	−2.90064	−0.120547
$580$	0	0
$581$	3.03429	0.125884
$582$	−24.0525	−0.997010
$583$	40.2435	1.66672
$584$	2.98180	0.123388
$585$	0.267691	0.0110677
$586$	25.1721	1.03985
$587$	−7.34441	−0.303136	−0.151568	−	0.988447i	$-0.548432\pi$
$587$	−7.34441	−0.303136	−0.151568	+	0.988447i	$0.548432\pi$
$588$	1.84112	0.0759264
$589$	−55.8210	−2.30007
$590$	−6.28925	−0.258924
$591$	2.35335	0.0968039
$592$	9.60431	0.394735
$593$	4.59131	0.188543	0.0942713	−	0.995547i	$-0.469948\pi$
$593$	4.59131	0.188543	0.0942713	+	0.995547i	$0.469948\pi$
$594$	24.5600	1.00771
$595$	0.458276	0.0187875
$596$	−5.32915	−0.218291
$597$	13.5308	0.553780
$598$	0.0681899	0.00278849
$599$	−20.4115	−0.833990	−0.416995	−	0.908909i	$-0.636917\pi$
$599$	−20.4115	−0.833990	−0.416995	+	0.908909i	$0.636917\pi$
$600$	6.68078	0.272742
$601$	−10.4206	−0.425067	−0.212533	−	0.977154i	$-0.568171\pi$
$601$	−10.4206	−0.425067	−0.212533	+	0.977154i	$0.568171\pi$
$602$	−9.37477	−0.382087
$603$	−1.69907	−0.0691915
$604$	6.73362	0.273987
$605$	−4.83489	−0.196566
$606$	−24.4002	−0.991191
$607$	−18.7398	−0.760623	−0.380312	−	0.924858i	$-0.624183\pi$
$607$	−18.7398	−0.760623	−0.380312	+	0.924858i	$0.624183\pi$
$608$	−8.42322	−0.341607
$609$	0	0
$610$	6.10122	0.247031
$611$	−2.43138	−0.0983629
$612$	0.236679	0.00956720
$613$	37.8044	1.52690	0.763452	−	0.645864i	$-0.223503\pi$
$613$	37.8044	1.52690	0.763452	+	0.645864i	$0.223503\pi$
$614$	15.0768	0.608451
$615$	−3.79836	−0.153164
$616$	−12.4976	−0.503541
$617$	4.16490	0.167673	0.0838363	−	0.996480i	$-0.473283\pi$
$617$	4.16490	0.167673	0.0838363	+	0.996480i	$0.473283\pi$
$618$	3.82957	0.154048
$619$	11.9265	0.479366	0.239683	−	0.970851i	$-0.422956\pi$
$619$	11.9265	0.479366	0.239683	+	0.970851i	$0.422956\pi$
$620$	4.06772	0.163364
$621$	0.805947	0.0323415
$622$	18.5916	0.745456
$623$	−7.40968	−0.296863
$624$	0.691125	0.0276672
$625$	19.4906	0.779622
$626$	20.4199	0.816145
$627$	52.8839	2.11198
$628$	4.45167	0.177641
$629$	−2.49288	−0.0993976
$630$	−1.60997	−0.0641427
$631$	−4.56341	−0.181666	−0.0908332	−	0.995866i	$-0.528953\pi$
$631$	−4.56341	−0.181666	−0.0908332	+	0.995866i	$0.528953\pi$
$632$	−13.5549	−0.539187
$633$	9.17956	0.364855
$634$	8.41935	0.334375
$635$	2.10232	0.0834281
$636$	13.3848	0.530741
$637$	0.609365	0.0241439
$638$	0	0
$639$	8.73962	0.345734
$640$	0.613807	0.0242629
$641$	−6.57727	−0.259786	−0.129893	−	0.991528i	$-0.541463\pi$
$641$	−6.57727	−0.259786	−0.129893	+	0.991528i	$0.541463\pi$
$642$	−22.7044	−0.896070
$643$	−7.68578	−0.303098	−0.151549	−	0.988450i	$-0.548426\pi$
$643$	−7.68578	−0.303098	−0.151549	+	0.988450i	$0.548426\pi$
$644$	−0.410113	−0.0161607
$645$	−2.89077	−0.113824
$646$	2.18632	0.0860196
$647$	30.9479	1.21669	0.608343	−	0.793674i	$-0.291834\pi$
$647$	30.9479	1.21669	0.608343	+	0.793674i	$0.291834\pi$
$648$	5.43296	0.213427
$649$	−44.5176	−1.74747
$650$	2.21117	0.0867294
$651$	−27.5461	−1.07962
$652$	8.12268	0.318109
$653$	−10.7195	−0.419487	−0.209743	−	0.977756i	$-0.567263\pi$
$653$	−10.7195	−0.419487	−0.209743	+	0.977756i	$0.567263\pi$
$654$	14.6973	0.574710
$655$	1.80332	0.0704617
$656$	4.28236	0.167198
$657$	2.71897	0.106077
$658$	14.6230	0.570063
$659$	−29.9298	−1.16590	−0.582950	−	0.812508i	$-0.698102\pi$
$659$	−29.9298	−1.16590	−0.582950	+	0.812508i	$0.698102\pi$
$660$	−3.85370	−0.150005
$661$	−16.9946	−0.661012	−0.330506	−	0.943804i	$-0.607219\pi$
$661$	−16.9946	−0.661012	−0.330506	+	0.943804i	$0.607219\pi$
$662$	31.5696	1.22699
$663$	−0.179387	−0.00696683
$664$	−1.05487	−0.0409367
$665$	−14.8720	−0.576713
$666$	8.75773	0.339355
$667$	0	0
$668$	−0.399378	−0.0154524
$669$	9.79049	0.378522
$670$	1.14372	0.0441856
$671$	43.1867	1.66720
$672$	−4.15662	−0.160345
$673$	−35.6523	−1.37429	−0.687147	−	0.726518i	$-0.741137\pi$
$673$	−35.6523	−1.37429	−0.687147	+	0.726518i	$0.741137\pi$
$674$	17.1433	0.660336
$675$	26.1342	1.00591
$676$	−12.7713	−0.491202
$677$	39.4582	1.51650	0.758250	−	0.651964i	$-0.226055\pi$
$677$	39.4582	1.51650	0.758250	+	0.651964i	$0.226055\pi$
$678$	24.6303	0.945919
$679$	47.8785	1.83741
$680$	−0.159319	−0.00610960
$681$	24.0224	0.920542
$682$	28.7929	1.10254
$683$	−3.49900	−0.133886	−0.0669428	−	0.997757i	$-0.521324\pi$
$683$	−3.49900	−0.133886	−0.0669428	+	0.997757i	$0.521324\pi$
$684$	−7.68075	−0.293681
$685$	10.4285	0.398453
$686$	16.4704	0.628843
$687$	9.37596	0.357715
$688$	3.25912	0.124253
$689$	4.43004	0.168771
$690$	−0.126461	−0.00481428
$691$	−5.37007	−0.204287	−0.102143	−	0.994770i	$-0.532570\pi$
$691$	−5.37007	−0.204287	−0.102143	+	0.994770i	$0.532570\pi$
$692$	−4.70045	−0.178684
$693$	−11.3960	−0.432896
$694$	15.2643	0.579427
$695$	0.224392	0.00851166
$696$	0	0
$697$	−1.11152	−0.0421019
$698$	27.7100	1.04884
$699$	28.8666	1.09184
$700$	−13.2986	−0.502641
$701$	16.7002	0.630758	0.315379	−	0.948966i	$-0.397868\pi$
$701$	16.7002	0.630758	0.315379	+	0.948966i	$0.397868\pi$
$702$	2.70358	0.102040
$703$	80.8993	3.05117
$704$	4.34475	0.163749
$705$	4.50908	0.169822
$706$	26.1989	0.986009
$707$	48.5706	1.82669
$708$	−14.8063	−0.556456
$709$	−19.0888	−0.716893	−0.358447	−	0.933550i	$-0.616694\pi$
$709$	−19.0888	−0.716893	−0.358447	+	0.933550i	$0.616694\pi$
$710$	−5.88300	−0.220785
$711$	−12.3601	−0.463541
$712$	2.57596	0.0965382
$713$	0.944850	0.0353849
$714$	1.07889	0.0403763
$715$	−1.27548	−0.0477002
$716$	−4.66359	−0.174287
$717$	2.68280	0.100191
$718$	−11.8516	−0.442297
$719$	25.3990	0.947224	0.473612	−	0.880734i	$-0.342950\pi$
$719$	25.3990	0.947224	0.473612	+	0.880734i	$0.342950\pi$
$720$	0.559702	0.0208589
$721$	−7.62307	−0.283898
$722$	−51.9507	−1.93340
$723$	−3.44924	−0.128278
$724$	9.43759	0.350745
$725$	0	0
$726$	−11.3824	−0.422441
$727$	14.6165	0.542097	0.271049	−	0.962566i	$-0.412630\pi$
$727$	14.6165	0.542097	0.271049	+	0.962566i	$0.412630\pi$
$728$	−1.37574	−0.0509883
$729$	29.4596	1.09110
$730$	−1.83025	−0.0677406
$731$	−0.845933	−0.0312879
$732$	14.3637	0.530896
$733$	−39.3020	−1.45165	−0.725827	−	0.687877i	$-0.758543\pi$
$733$	−39.3020	−1.45165	−0.725827	+	0.687877i	$0.758543\pi$
$734$	26.0651	0.962079
$735$	−1.13009	−0.0416840
$736$	0.142575	0.00525538
$737$	8.09565	0.298207
$738$	3.90489	0.143741
$739$	−34.2467	−1.25979	−0.629893	−	0.776682i	$-0.716901\pi$
$739$	−34.2467	−1.25979	−0.629893	+	0.776682i	$0.716901\pi$
$740$	−5.89520	−0.216712
$741$	5.82150	0.213858
$742$	−26.6435	−0.978113
$743$	35.0885	1.28727	0.643636	−	0.765332i	$-0.277425\pi$
$743$	35.0885	1.28727	0.643636	+	0.765332i	$0.277425\pi$
$744$	9.57635	0.351086
$745$	3.27107	0.119843
$746$	23.2397	0.850866
$747$	−0.961883	−0.0351935
$748$	−1.12772	−0.0412334
$749$	45.1949	1.65138
$750$	−8.53559	−0.311676
$751$	48.2274	1.75984	0.879922	−	0.475118i	$-0.157595\pi$
$751$	48.2274	1.75984	0.879922	+	0.475118i	$0.157595\pi$
$752$	−5.08365	−0.185382
$753$	−26.3755	−0.961176
$754$	0	0
$755$	−4.13314	−0.150420
$756$	−16.2601	−0.591374
$757$	−9.91374	−0.360321	−0.180161	−	0.983637i	$-0.557662\pi$
$757$	−9.91374	−0.360321	−0.180161	+	0.983637i	$0.557662\pi$
$758$	30.9906	1.12563
$759$	−0.895136	−0.0324914
$760$	5.17023	0.187544
$761$	−2.71944	−0.0985798	−0.0492899	−	0.998785i	$-0.515696\pi$
$761$	−2.71944	−0.0985798	−0.0492899	+	0.998785i	$0.515696\pi$
$762$	4.94935	0.179296
$763$	−29.2562	−1.05914
$764$	−19.7596	−0.714877
$765$	−0.145276	−0.00525245
$766$	23.7304	0.857414
$767$	−4.90053	−0.176948
$768$	1.44504	0.0521435
$769$	5.75037	0.207364	0.103682	−	0.994611i	$-0.466938\pi$
$769$	5.75037	0.207364	0.103682	+	0.994611i	$0.466938\pi$
$770$	7.67109	0.276447
$771$	−18.3692	−0.661550
$772$	−2.00731	−0.0722446
$773$	37.6903	1.35563	0.677813	−	0.735235i	$-0.262928\pi$
$773$	37.6903	1.35563	0.677813	+	0.735235i	$0.262928\pi$
$774$	2.97184	0.106821
$775$	30.6384	1.10056
$776$	−16.6449	−0.597516
$777$	39.9215	1.43218
$778$	1.08756	0.0389910
$779$	36.0713	1.29239
$780$	−0.424218	−0.0151894
$781$	−41.6421	−1.49007
$782$	−0.0370065	−0.00132335
$783$	0	0
$784$	1.27409	0.0455033
$785$	−2.73247	−0.0975260
$786$	4.24543	0.151430
$787$	2.22168	0.0791943	0.0395972	−	0.999216i	$-0.487393\pi$
$787$	2.22168	0.0791943	0.0395972	+	0.999216i	$0.487393\pi$
$788$	1.62857	0.0580154
$789$	−2.74548	−0.0977417
$790$	8.32012	0.296017
$791$	−49.0285	−1.74325
$792$	3.96178	0.140776
$793$	4.75402	0.168820
$794$	−6.38613	−0.226635
$795$	−8.21567	−0.291380
$796$	9.36362	0.331885
$797$	37.9020	1.34256	0.671279	−	0.741205i	$-0.265745\pi$
$797$	37.9020	1.34256	0.671279	+	0.741205i	$0.265745\pi$
$798$	−35.0122	−1.23942
$799$	1.31950	0.0466807
$800$	4.62324	0.163456
$801$	2.34890	0.0829943
$802$	30.1679	1.06526
$803$	−12.9552	−0.457179
$804$	2.69257	0.0949596
$805$	0.251730	0.00887233
$806$	3.16954	0.111642
$807$	37.0459	1.30408
$808$	−16.8855	−0.594029
$809$	2.24431	0.0789059	0.0394529	−	0.999221i	$-0.487438\pi$
$809$	2.24431	0.0789059	0.0394529	+	0.999221i	$0.487438\pi$
$810$	−3.33479	−0.117173
$811$	−21.1074	−0.741180	−0.370590	−	0.928797i	$-0.620844\pi$
$811$	−21.1074	−0.741180	−0.370590	+	0.928797i	$0.620844\pi$
$812$	0	0
$813$	−11.3048	−0.396475
$814$	−41.7284	−1.46258
$815$	−4.98576	−0.174644
$816$	−0.375073	−0.0131302
$817$	27.4523	0.960435
$818$	−4.76753	−0.166693
$819$	−1.25447	−0.0438349
$820$	−2.62854	−0.0917927
$821$	−48.0167	−1.67580	−0.837898	−	0.545827i	$-0.816216\pi$
$821$	−48.0167	−1.67580	−0.837898	+	0.545827i	$0.816216\pi$
$822$	24.5511	0.856318
$823$	−7.22912	−0.251991	−0.125996	−	0.992031i	$-0.540213\pi$
$823$	−7.22912	−0.251991	−0.125996	+	0.992031i	$0.540213\pi$
$824$	2.65015	0.0923222
$825$	−29.0263	−1.01057
$826$	29.4732	1.02550
$827$	6.73227	0.234104	0.117052	−	0.993126i	$-0.462656\pi$
$827$	6.73227	0.234104	0.117052	+	0.993126i	$0.462656\pi$
$828$	0.130008	0.00451808
$829$	4.80413	0.166854	0.0834271	−	0.996514i	$-0.473413\pi$
$829$	4.80413	0.166854	0.0834271	+	0.996514i	$0.473413\pi$
$830$	0.647484	0.0224745
$831$	18.3957	0.638141
$832$	0.478274	0.0165812
$833$	−0.330702	−0.0114581
$834$	0.528269	0.0182925
$835$	0.245141	0.00848347
$836$	36.5968	1.26573
$837$	37.4613	1.29485
$838$	27.2149	0.940122
$839$	−16.9749	−0.586038	−0.293019	−	0.956107i	$-0.594660\pi$
$839$	−16.9749	−0.586038	−0.293019	+	0.956107i	$0.594660\pi$
$840$	2.55136	0.0880304
$841$	0	0
$842$	−18.9520	−0.653130
$843$	8.30698	0.286108
$844$	6.35245	0.218660
$845$	7.83909	0.269673
$846$	−4.63555	−0.159373
$847$	22.6576	0.778526
$848$	9.26256	0.318077
$849$	35.7564	1.22716
$850$	−1.20000	−0.0411597
$851$	−1.36933	−0.0469402
$852$	−13.8499	−0.474491
$853$	28.3800	0.971713	0.485857	−	0.874039i	$-0.338508\pi$
$853$	28.3800	0.971713	0.485857	+	0.874039i	$0.338508\pi$
$854$	−28.5920	−0.978399
$855$	4.71450	0.161232
$856$	−15.7119	−0.537022
$857$	44.1365	1.50767	0.753836	−	0.657062i	$-0.228201\pi$
$857$	44.1365	1.50767	0.753836	+	0.657062i	$0.228201\pi$
$858$	−3.00277	−0.102513
$859$	1.50569	0.0513733	0.0256867	−	0.999670i	$-0.491823\pi$
$859$	1.50569	0.0513733	0.0256867	+	0.999670i	$0.491823\pi$
$860$	−2.00047	−0.0682155
$861$	17.8002	0.606628
$862$	−20.6248	−0.702483
$863$	−39.5912	−1.34770	−0.673851	−	0.738868i	$-0.735361\pi$
$863$	−39.5912	−1.34770	−0.673851	+	0.738868i	$0.735361\pi$
$864$	5.65279	0.192312
$865$	2.88517	0.0980986
$866$	−4.85408	−0.164948
$867$	−24.4684	−0.830989
$868$	−19.0625	−0.647023
$869$	58.8929	1.99780
$870$	0	0
$871$	0.891175	0.0301963
$872$	10.1709	0.344429
$873$	−15.1777	−0.513687
$874$	1.20094	0.0406224
$875$	16.9908	0.574393
$876$	−4.30883	−0.145582
$877$	41.2160	1.39177	0.695883	−	0.718155i	$-0.255013\pi$
$877$	41.2160	1.39177	0.695883	+	0.718155i	$0.255013\pi$
$878$	27.2748	0.920480
$879$	−36.3747	−1.22689
$880$	−2.66684	−0.0898992
$881$	35.6727	1.20184	0.600921	−	0.799308i	$-0.294801\pi$
$881$	35.6727	1.20184	0.600921	+	0.799308i	$0.294801\pi$
$882$	1.16179	0.0391194
$883$	−24.4491	−0.822777	−0.411389	−	0.911460i	$-0.634956\pi$
$883$	−24.4491	−0.822777	−0.411389	+	0.911460i	$0.634956\pi$
$884$	−0.124140	−0.00417528
$885$	9.08823	0.305498
$886$	22.5925	0.759008
$887$	−3.56621	−0.119742	−0.0598708	−	0.998206i	$-0.519069\pi$
$887$	−3.56621	−0.119742	−0.0598708	+	0.998206i	$0.519069\pi$
$888$	−13.8786	−0.465736
$889$	−9.85208	−0.330428
$890$	−1.58114	−0.0530000
$891$	−23.6049	−0.790793
$892$	6.77523	0.226852
$893$	−42.8207	−1.43294
$894$	7.70085	0.257555
$895$	2.86255	0.0956844
$896$	−2.87647	−0.0960962
$897$	−0.0985372	−0.00329006
$898$	−6.15402	−0.205362
$899$	0	0
$900$	4.21572	0.140524
$901$	−2.40417	−0.0800947
$902$	−18.6058	−0.619506
$903$	13.5469	0.450814
$904$	17.0447	0.566897
$905$	−5.79286	−0.192561
$906$	−9.73036	−0.323269
$907$	9.34921	0.310436	0.155218	−	0.987880i	$-0.450392\pi$
$907$	9.34921	0.310436	0.155218	+	0.987880i	$0.450392\pi$
$908$	16.6240	0.551688
$909$	−15.3971	−0.510689
$910$	0.844440	0.0279929
$911$	28.1951	0.934145	0.467073	−	0.884219i	$-0.345309\pi$
$911$	28.1951	0.934145	0.467073	+	0.884219i	$0.345309\pi$
$912$	12.1719	0.403052
$913$	4.58313	0.151679
$914$	−15.7924	−0.522366
$915$	−8.81651	−0.291465
$916$	6.48836	0.214382
$917$	−8.45088	−0.279073
$918$	−1.46723	−0.0484258
$919$	−52.9307	−1.74602	−0.873011	−	0.487700i	$-0.837836\pi$
$919$	−52.9307	−1.74602	−0.873011	+	0.487700i	$0.837836\pi$
$920$	−0.0875136	−0.00288524
$921$	−21.7866	−0.717894
$922$	−8.27739	−0.272601
$923$	−4.58399	−0.150884
$924$	18.0595	0.594114
$925$	−44.4030	−1.45996
$926$	−9.93980	−0.326642
$927$	2.41655	0.0793698
$928$	0	0
$929$	−19.2831	−0.632657	−0.316329	−	0.948650i	$-0.602450\pi$
$929$	−19.2831	−0.632657	−0.316329	+	0.948650i	$0.602450\pi$
$930$	−5.87803	−0.192748
$931$	10.7320	0.351726
$932$	19.9763	0.654346
$933$	−26.8657	−0.879543
$934$	−17.6952	−0.579005
$935$	0.692201	0.0226374
$936$	0.436116	0.0142549
$937$	−30.1635	−0.985397	−0.492699	−	0.870200i	$-0.663989\pi$
$937$	−30.1635	−0.985397	−0.492699	+	0.870200i	$0.663989\pi$
$938$	−5.35978	−0.175003
$939$	−29.5077	−0.962946
$940$	3.12038	0.101776
$941$	19.5496	0.637299	0.318649	−	0.947873i	$-0.396771\pi$
$941$	19.5496	0.637299	0.318649	+	0.947873i	$0.396771\pi$
$942$	−6.43285	−0.209594
$943$	−0.610558	−0.0198825
$944$	−10.2463	−0.333489
$945$	9.98057	0.324668
$946$	−14.1601	−0.460384
$947$	27.2788	0.886443	0.443222	−	0.896412i	$-0.353835\pi$
$947$	27.2788	0.886443	0.443222	+	0.896412i	$0.353835\pi$
$948$	19.5875	0.636171
$949$	−1.42612	−0.0462937
$950$	38.9426	1.26346
$951$	−12.1663	−0.394520
$952$	0.746613	0.0241979
$953$	24.9572	0.808444	0.404222	−	0.914661i	$-0.367542\pi$
$953$	24.9572	0.808444	0.404222	+	0.914661i	$0.367542\pi$
$954$	8.44610	0.273453
$955$	12.1286	0.392471
$956$	1.85655	0.0600452
$957$	0	0
$958$	−23.2355	−0.750704
$959$	−48.8709	−1.57812
$960$	−0.886977	−0.0286271
$961$	12.9176	0.416698
$962$	−4.59349	−0.148100
$963$	−14.3270	−0.461680
$964$	−2.38694	−0.0768783
$965$	1.23210	0.0396627
$966$	0.592631	0.0190676
$967$	14.6917	0.472452	0.236226	−	0.971698i	$-0.424089\pi$
$967$	14.6917	0.472452	0.236226	+	0.971698i	$0.424089\pi$
$968$	−7.87688	−0.253173
$969$	−3.15932	−0.101492
$970$	10.2167	0.328040
$971$	18.0880	0.580470	0.290235	−	0.956955i	$-0.406267\pi$
$971$	18.0880	0.580470	0.290235	+	0.956955i	$0.406267\pi$
$972$	9.10752	0.292124
$973$	−1.05156	−0.0337115
$974$	5.79395	0.185650
$975$	−3.19524	−0.102330
$976$	9.93996	0.318170
$977$	43.1498	1.38048	0.690242	−	0.723579i	$-0.257504\pi$
$977$	43.1498	1.38048	0.690242	+	0.723579i	$0.257504\pi$
$978$	−11.7376	−0.375328
$979$	−11.1919	−0.357695
$980$	−0.782047	−0.0249816
$981$	9.27433	0.296107
$982$	−8.40728	−0.268287
$983$	7.09060	0.226155	0.113077	−	0.993586i	$-0.463929\pi$
$983$	7.09060	0.226155	0.113077	+	0.993586i	$0.463929\pi$
$984$	−6.18819	−0.197272
$985$	−0.999628	−0.0318508
$986$	0	0
$987$	−21.1308	−0.672601
$988$	4.02861	0.128167
$989$	−0.464669	−0.0147756
$990$	−2.43177	−0.0772867
$991$	30.8015	0.978443	0.489221	−	0.872160i	$-0.337281\pi$
$991$	30.8015	0.978443	0.489221	+	0.872160i	$0.337281\pi$
$992$	6.62704	0.210409
$993$	−45.6193	−1.44769
$994$	27.5694	0.874448
$995$	−5.74746	−0.182207
$996$	1.52432	0.0483001
$997$	−29.2486	−0.926313	−0.463156	−	0.886277i	$-0.653283\pi$
$997$	−29.2486	−0.926313	−0.463156	+	0.886277i	$0.653283\pi$
$998$	−17.5998	−0.557112
$999$	−54.2912	−1.71770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1682.2.a.r.1.4		6
29.12	odd	4		1682.2.b.j.1681.3		12
29.14	odd	28		58.2.e.a.51.2	yes	12
29.17	odd	4		1682.2.b.j.1681.9		12
29.27	odd	28		58.2.e.a.33.2	✓	12
29.28	even	2		1682.2.a.s.1.4		6
87.14	even	28		522.2.n.a.109.1		12
87.56	even	28		522.2.n.a.91.1		12
116.27	even	28		464.2.y.c.33.2		12
116.43	even	28		464.2.y.c.225.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.e.a.33.2	✓	12	29.27	odd	28
58.2.e.a.51.2	yes	12	29.14	odd	28
464.2.y.c.33.2		12	116.27	even	28
464.2.y.c.225.2		12	116.43	even	28
522.2.n.a.91.1		12	87.56	even	28
522.2.n.a.109.1		12	87.14	even	28
1682.2.a.r.1.4		6	1.1	even	1	trivial
1682.2.a.s.1.4		6	29.28	even	2
1682.2.b.j.1681.3		12	29.12	odd	4
1682.2.b.j.1681.9		12	29.17	odd	4

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1682.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.44504 q^{3} +1.00000 q^{4} -0.613807 q^{5} -1.44504 q^{6} +2.87647 q^{7} -1.00000 q^{8} -0.911854 q^{9} +0.613807 q^{10} +4.34475 q^{11} +1.44504 q^{12} +0.478274 q^{13} -2.87647 q^{14} -0.886977 q^{15} +1.00000 q^{16} -0.259558 q^{17} +0.911854 q^{18} +8.42322 q^{19} -0.613807 q^{20} +4.15662 q^{21} -4.34475 q^{22} -0.142575 q^{23} -1.44504 q^{24} -4.62324 q^{25} -0.478274 q^{26} -5.65279 q^{27} +2.87647 q^{28} +0.886977 q^{30} -6.62704 q^{31} -1.00000 q^{32} +6.27835 q^{33} +0.259558 q^{34} -1.76560 q^{35} -0.911854 q^{36} +9.60431 q^{37} -8.42322 q^{38} +0.691125 q^{39} +0.613807 q^{40} +4.28236 q^{41} -4.15662 q^{42} +3.25912 q^{43} +4.34475 q^{44} +0.559702 q^{45} +0.142575 q^{46} -5.08365 q^{47} +1.44504 q^{48} +1.27409 q^{49} +4.62324 q^{50} -0.375073 q^{51} +0.478274 q^{52} +9.26256 q^{53} +5.65279 q^{54} -2.66684 q^{55} -2.87647 q^{56} +12.1719 q^{57} -10.2463 q^{59} -0.886977 q^{60} +9.93996 q^{61} +6.62704 q^{62} -2.62292 q^{63} +1.00000 q^{64} -0.293568 q^{65} -6.27835 q^{66} +1.86332 q^{67} -0.259558 q^{68} -0.206027 q^{69} +1.76560 q^{70} -9.58445 q^{71} +0.911854 q^{72} -2.98180 q^{73} -9.60431 q^{74} -6.68078 q^{75} +8.42322 q^{76} +12.4976 q^{77} -0.691125 q^{78} +13.5549 q^{79} -0.613807 q^{80} -5.43296 q^{81} -4.28236 q^{82} +1.05487 q^{83} +4.15662 q^{84} +0.159319 q^{85} -3.25912 q^{86} -4.34475 q^{88} -2.57596 q^{89} -0.559702 q^{90} +1.37574 q^{91} -0.142575 q^{92} -9.57635 q^{93} +5.08365 q^{94} -5.17023 q^{95} -1.44504 q^{96} +16.6449 q^{97} -1.27409 q^{98} -3.96178 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 8 q^{3} + 6 q^{4} - 6 q^{5} - 8 q^{6} + 2 q^{7} - 6 q^{8} + 2 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} - 8 q^{13} - 2 q^{14} - 8 q^{15} + 6 q^{16} + 12 q^{17} - 2 q^{18} + 4 q^{19} - 6 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 8 * q^3 + 6 * q^4 - 6 * q^5 - 8 * q^6 + 2 * q^7 - 6 * q^8 + 2 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 - 8 * q^13 - 2 * q^14 - 8 * q^15 + 6 * q^16 + 12 * q^17 - 2 * q^18 + 4 * q^19 - 6 * q^20 + 12 * q^21 - 2 * q^22 + 6 * q^23 - 8 * q^24 + 4 * q^25 + 8 * q^26 + 2 * q^27 + 2 * q^28 + 8 * q^30 + 26 * q^31 - 6 * q^32 + 12 * q^33 - 12 * q^34 - 16 * q^35 + 2 * q^36 + 20 * q^37 - 4 * q^38 - 6 * q^39 + 6 * q^40 + 24 * q^41 - 12 * q^42 + 26 * q^43 + 2 * q^44 - 2 * q^45 - 6 * q^46 + 18 * q^47 + 8 * q^48 - 4 * q^49 - 4 * q^50 + 16 * q^51 - 8 * q^52 + 8 * q^53 - 2 * q^54 + 26 * q^55 - 2 * q^56 + 10 * q^57 - 24 * q^59 - 8 * q^60 + 18 * q^61 - 26 * q^62 + 24 * q^63 + 6 * q^64 - 6 * q^65 - 12 * q^66 + 8 * q^67 + 12 * q^68 + 22 * q^69 + 16 * q^70 + 20 * q^71 - 2 * q^72 + 12 * q^73 - 20 * q^74 + 10 * q^75 + 4 * q^76 + 10 * q^77 + 6 * q^78 + 20 * q^79 - 6 * q^80 + 6 * q^81 - 24 * q^82 - 28 * q^83 + 12 * q^84 + 16 * q^85 - 26 * q^86 - 2 * q^88 + 2 * q^90 - 12 * q^91 + 6 * q^92 + 30 * q^93 - 18 * q^94 - 32 * q^95 - 8 * q^96 + 44 * q^97 + 4 * q^98 + 24 * q^99

Introduction

L-functions

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Database

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