LMFDB - Embedded newform 1690.2.a.w.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(1,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,6,-2,6,6,-2,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.20439713.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 15x^{4} + 22x^{3} + 70x^{2} - 56x - 91 $ x^6 - 2x^5 - 15x^4 + 22x^3 + 70x^2 - 56*x - 91
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.57254$ of defining polynomial
Character	$\chi$	$=$	1690.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +2.57254 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.57254 q^{6} +1.90403 q^{7} +1.00000 q^{8} +3.61798 q^{9} +1.00000 q^{10} +5.17658 q^{11} +2.57254 q^{12} +1.90403 q^{14} +2.57254 q^{15} +1.00000 q^{16} -5.89037 q^{17} +3.61798 q^{18} -8.09045 q^{19} +1.00000 q^{20} +4.89819 q^{21} +5.17658 q^{22} -0.908568 q^{23} +2.57254 q^{24} +1.00000 q^{25} +1.58977 q^{27} +1.90403 q^{28} -5.29954 q^{29} +2.57254 q^{30} -0.0626650 q^{31} +1.00000 q^{32} +13.3170 q^{33} -5.89037 q^{34} +1.90403 q^{35} +3.61798 q^{36} +1.63865 q^{37} -8.09045 q^{38} +1.00000 q^{40} +1.77061 q^{41} +4.89819 q^{42} -8.58977 q^{43} +5.17658 q^{44} +3.61798 q^{45} -0.908568 q^{46} -11.2024 q^{47} +2.57254 q^{48} -3.37468 q^{49} +1.00000 q^{50} -15.1532 q^{51} -8.92525 q^{53} +1.58977 q^{54} +5.17658 q^{55} +1.90403 q^{56} -20.8130 q^{57} -5.29954 q^{58} +10.6767 q^{59} +2.57254 q^{60} -0.681193 q^{61} -0.0626650 q^{62} +6.88873 q^{63} +1.00000 q^{64} +13.3170 q^{66} +14.1492 q^{67} -5.89037 q^{68} -2.33733 q^{69} +1.90403 q^{70} +15.7017 q^{71} +3.61798 q^{72} +0.163089 q^{73} +1.63865 q^{74} +2.57254 q^{75} -8.09045 q^{76} +9.85635 q^{77} +14.7178 q^{79} +1.00000 q^{80} -6.76417 q^{81} +1.77061 q^{82} -1.89246 q^{83} +4.89819 q^{84} -5.89037 q^{85} -8.58977 q^{86} -13.6333 q^{87} +5.17658 q^{88} -0.541298 q^{89} +3.61798 q^{90} -0.908568 q^{92} -0.161208 q^{93} -11.2024 q^{94} -8.09045 q^{95} +2.57254 q^{96} +12.8001 q^{97} -3.37468 q^{98} +18.7287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 3 q^{7} + 6 q^{8} + 16 q^{9} + 6 q^{10} + 15 q^{11} - 2 q^{12} + 3 q^{14} - 2 q^{15} + 6 q^{16} - 3 q^{17} + 16 q^{18} + q^{19} + 6 q^{20} - 2 q^{21}+ \cdots + 55 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 3 * q^7 + 6 * q^8 + 16 * q^9 + 6 * q^10 + 15 * q^11 - 2 * q^12 + 3 * q^14 - 2 * q^15 + 6 * q^16 - 3 * q^17 + 16 * q^18 + q^19 + 6 * q^20 - 2 * q^21 + 15 * q^22 - 3 * q^23 - 2 * q^24 + 6 * q^25 - 20 * q^27 + 3 * q^28 + 7 * q^29 - 2 * q^30 + 6 * q^32 + 4 * q^33 - 3 * q^34 + 3 * q^35 + 16 * q^36 + 6 * q^37 + q^38 + 6 * q^40 + 2 * q^41 - 2 * q^42 - 22 * q^43 + 15 * q^44 + 16 * q^45 - 3 * q^46 + 7 * q^47 - 2 * q^48 + 31 * q^49 + 6 * q^50 - 22 * q^51 - 16 * q^53 - 20 * q^54 + 15 * q^55 + 3 * q^56 + 2 * q^57 + 7 * q^58 + 15 * q^59 - 2 * q^60 + 33 * q^61 + 25 * q^63 + 6 * q^64 + 4 * q^66 - 8 * q^67 - 3 * q^68 - 6 * q^69 + 3 * q^70 + 40 * q^71 + 16 * q^72 + 21 * q^73 + 6 * q^74 - 2 * q^75 + q^76 - 34 * q^77 + 20 * q^79 + 6 * q^80 - 2 * q^81 + 2 * q^82 + 22 * q^83 - 2 * q^84 - 3 * q^85 - 22 * q^86 - 39 * q^87 + 15 * q^88 + 20 * q^89 + 16 * q^90 - 3 * q^92 + 48 * q^93 + 7 * q^94 + q^95 - 2 * q^96 - 7 * q^97 + 31 * q^98 + 55 * 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
$3$	2.57254	1.48526	0.742629	−	0.669703i	$-0.233579\pi$
$3$	2.57254	1.48526	0.742629	+	0.669703i	$0.233579\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.57254	1.05024
$7$	1.90403	0.719655	0.359827	−	0.933019i	$-0.382836\pi$
$7$	1.90403	0.719655	0.359827	+	0.933019i	$0.382836\pi$
$8$	1.00000	0.353553
$9$	3.61798	1.20599
$10$	1.00000	0.316228
$11$	5.17658	1.56080	0.780398	−	0.625283i	$-0.215016\pi$
$11$	5.17658	1.56080	0.780398	+	0.625283i	$0.215016\pi$
$12$	2.57254	0.742629
$13$	0	0
$13$	0	0
$14$	1.90403	0.508873
$15$	2.57254	0.664228
$16$	1.00000	0.250000
$17$	−5.89037	−1.42862	−0.714312	−	0.699827i	$-0.753260\pi$
$17$	−5.89037	−1.42862	−0.714312	+	0.699827i	$0.753260\pi$
$18$	3.61798	0.852765
$19$	−8.09045	−1.85608	−0.928038	−	0.372485i	$-0.878506\pi$
$19$	−8.09045	−1.85608	−0.928038	+	0.372485i	$0.878506\pi$
$20$	1.00000	0.223607
$21$	4.89819	1.06887
$22$	5.17658	1.10365
$23$	−0.908568	−0.189449	−0.0947247	−	0.995504i	$-0.530197\pi$
$23$	−0.908568	−0.189449	−0.0947247	+	0.995504i	$0.530197\pi$
$24$	2.57254	0.525118
$25$	1.00000	0.200000
$26$	0	0
$27$	1.58977	0.305952
$28$	1.90403	0.359827
$29$	−5.29954	−0.984099	−0.492050	−	0.870567i	$-0.663752\pi$
$29$	−5.29954	−0.984099	−0.492050	+	0.870567i	$0.663752\pi$
$30$	2.57254	0.469680
$31$	−0.0626650	−0.0112550	−0.00562748	−	0.999984i	$-0.501791\pi$
$31$	−0.0626650	−0.0112550	−0.00562748	+	0.999984i	$0.501791\pi$
$32$	1.00000	0.176777
$33$	13.3170	2.31819
$34$	−5.89037	−1.01019
$35$	1.90403	0.321839
$36$	3.61798	0.602996
$37$	1.63865	0.269393	0.134696	−	0.990887i	$-0.456994\pi$
$37$	1.63865	0.269393	0.134696	+	0.990887i	$0.456994\pi$
$38$	−8.09045	−1.31244
$39$	0	0
$40$	1.00000	0.158114
$41$	1.77061	0.276522	0.138261	−	0.990396i	$-0.455849\pi$
$41$	1.77061	0.276522	0.138261	+	0.990396i	$0.455849\pi$
$42$	4.89819	0.755808
$43$	−8.58977	−1.30993	−0.654964	−	0.755660i	$-0.727316\pi$
$43$	−8.58977	−1.30993	−0.654964	+	0.755660i	$0.727316\pi$
$44$	5.17658	0.780398
$45$	3.61798	0.539336
$46$	−0.908568	−0.133961
$47$	−11.2024	−1.63404	−0.817018	−	0.576612i	$-0.804374\pi$
$47$	−11.2024	−1.63404	−0.817018	+	0.576612i	$0.804374\pi$
$48$	2.57254	0.371315
$49$	−3.37468	−0.482097
$50$	1.00000	0.141421
$51$	−15.1532	−2.12188
$52$	0	0
$53$	−8.92525	−1.22598	−0.612989	−	0.790092i	$-0.710033\pi$
$53$	−8.92525	−1.22598	−0.612989	+	0.790092i	$0.710033\pi$
$54$	1.58977	0.216341
$55$	5.17658	0.698009
$56$	1.90403	0.254436
$57$	−20.8130	−2.75675
$58$	−5.29954	−0.695863
$59$	10.6767	1.38999	0.694997	−	0.719013i	$-0.255406\pi$
$59$	10.6767	1.38999	0.694997	+	0.719013i	$0.255406\pi$
$60$	2.57254	0.332114
$61$	−0.681193	−0.0872179	−0.0436089	−	0.999049i	$-0.513886\pi$
$61$	−0.681193	−0.0872179	−0.0436089	+	0.999049i	$0.513886\pi$
$62$	−0.0626650	−0.00795846
$63$	6.88873	0.867898
$64$	1.00000	0.125000
$65$	0	0
$66$	13.3170	1.63921
$67$	14.1492	1.72860	0.864301	−	0.502975i	$-0.167761\pi$
$67$	14.1492	1.72860	0.864301	+	0.502975i	$0.167761\pi$
$68$	−5.89037	−0.714312
$69$	−2.33733	−0.281381
$70$	1.90403	0.227575
$71$	15.7017	1.86345	0.931725	−	0.363164i	$-0.118304\pi$
$71$	15.7017	1.86345	0.931725	+	0.363164i	$0.118304\pi$
$72$	3.61798	0.426383
$73$	0.163089	0.0190881	0.00954407	−	0.999954i	$-0.496962\pi$
$73$	0.163089	0.0190881	0.00954407	+	0.999954i	$0.496962\pi$
$74$	1.63865	0.190489
$75$	2.57254	0.297052
$76$	−8.09045	−0.928038
$77$	9.85635	1.12323
$78$	0	0
$79$	14.7178	1.65589	0.827943	−	0.560813i	$-0.189511\pi$
$79$	14.7178	1.65589	0.827943	+	0.560813i	$0.189511\pi$
$80$	1.00000	0.111803
$81$	−6.76417	−0.751575
$82$	1.77061	0.195531
$83$	−1.89246	−0.207724	−0.103862	−	0.994592i	$-0.533120\pi$
$83$	−1.89246	−0.207724	−0.103862	+	0.994592i	$0.533120\pi$
$84$	4.89819	0.534437
$85$	−5.89037	−0.638900
$86$	−8.58977	−0.926259
$87$	−13.6333	−1.46164
$88$	5.17658	0.551825
$89$	−0.541298	−0.0573775	−0.0286887	−	0.999588i	$-0.509133\pi$
$89$	−0.541298	−0.0573775	−0.0286887	+	0.999588i	$0.509133\pi$
$90$	3.61798	0.381368
$91$	0	0
$92$	−0.908568	−0.0947247
$93$	−0.161208	−0.0167165
$94$	−11.2024	−1.15544
$95$	−8.09045	−0.830063
$96$	2.57254	0.262559
$97$	12.8001	1.29966	0.649829	−	0.760081i	$-0.274841\pi$
$97$	12.8001	1.29966	0.649829	+	0.760081i	$0.274841\pi$
$98$	−3.37468	−0.340894
$99$	18.7287	1.88231
$100$	1.00000	0.100000
$101$	2.59059	0.257773	0.128886	−	0.991659i	$-0.458860\pi$
$101$	2.59059	0.257773	0.128886	+	0.991659i	$0.458860\pi$
$102$	−15.1532	−1.50039
$103$	−1.77799	−0.175191	−0.0875953	−	0.996156i	$-0.527918\pi$
$103$	−1.77799	−0.175191	−0.0875953	+	0.996156i	$0.527918\pi$
$104$	0	0
$105$	4.89819	0.478015
$106$	−8.92525	−0.866897
$107$	3.56829	0.344959	0.172480	−	0.985013i	$-0.444822\pi$
$107$	3.56829	0.344959	0.172480	+	0.985013i	$0.444822\pi$
$108$	1.58977	0.152976
$109$	−11.4449	−1.09622	−0.548112	−	0.836405i	$-0.684653\pi$
$109$	−11.4449	−1.09622	−0.548112	+	0.836405i	$0.684653\pi$
$110$	5.17658	0.493567
$111$	4.21550	0.400118
$112$	1.90403	0.179914
$113$	11.2334	1.05675	0.528373	−	0.849012i	$-0.322802\pi$
$113$	11.2334	1.05675	0.528373	+	0.849012i	$0.322802\pi$
$114$	−20.8130	−1.94932
$115$	−0.908568	−0.0847244
$116$	−5.29954	−0.492050
$117$	0	0
$118$	10.6767	0.982874
$119$	−11.2154	−1.02812
$120$	2.57254	0.234840
$121$	15.7969	1.43609
$122$	−0.681193	−0.0616724
$123$	4.55496	0.410707
$124$	−0.0626650	−0.00562748
$125$	1.00000	0.0894427
$126$	6.88873	0.613697
$127$	10.8735	0.964870	0.482435	−	0.875932i	$-0.339752\pi$
$127$	10.8735	0.964870	0.482435	+	0.875932i	$0.339752\pi$
$128$	1.00000	0.0883883
$129$	−22.0976	−1.94558
$130$	0	0
$131$	1.13042	0.0987653	0.0493827	−	0.998780i	$-0.484275\pi$
$131$	1.13042	0.0987653	0.0493827	+	0.998780i	$0.484275\pi$
$132$	13.3170	1.15909
$133$	−15.4044	−1.33573
$134$	14.1492	1.22231
$135$	1.58977	0.136826
$136$	−5.89037	−0.505095
$137$	−10.9390	−0.934584	−0.467292	−	0.884103i	$-0.654770\pi$
$137$	−10.9390	−0.934584	−0.467292	+	0.884103i	$0.654770\pi$
$138$	−2.33733	−0.198967
$139$	−4.30562	−0.365198	−0.182599	−	0.983188i	$-0.558451\pi$
$139$	−4.30562	−0.365198	−0.182599	+	0.983188i	$0.558451\pi$
$140$	1.90403	0.160920
$141$	−28.8186	−2.42697
$142$	15.7017	1.31766
$143$	0	0
$144$	3.61798	0.301498
$145$	−5.29954	−0.440103
$146$	0.163089	0.0134974
$147$	−8.68150	−0.716038
$148$	1.63865	0.134696
$149$	−19.2499	−1.57701	−0.788505	−	0.615029i	$-0.789144\pi$
$149$	−19.2499	−1.57701	−0.788505	+	0.615029i	$0.789144\pi$
$150$	2.57254	0.210047
$151$	−7.91349	−0.643990	−0.321995	−	0.946741i	$-0.604354\pi$
$151$	−7.91349	−0.643990	−0.321995	+	0.946741i	$0.604354\pi$
$152$	−8.09045	−0.656222
$153$	−21.3112	−1.72291
$154$	9.85635	0.794247
$155$	−0.0626650	−0.00503337
$156$	0	0
$157$	−0.946176	−0.0755131	−0.0377565	−	0.999287i	$-0.512021\pi$
$157$	−0.946176	−0.0755131	−0.0377565	+	0.999287i	$0.512021\pi$
$158$	14.7178	1.17089
$159$	−22.9606	−1.82089
$160$	1.00000	0.0790569
$161$	−1.72994	−0.136338
$162$	−6.76417	−0.531444
$163$	4.51269	0.353461	0.176731	−	0.984259i	$-0.443448\pi$
$163$	4.51269	0.353461	0.176731	+	0.984259i	$0.443448\pi$
$164$	1.77061	0.138261
$165$	13.3170	1.03672
$166$	−1.89246	−0.146883
$167$	−1.96336	−0.151929	−0.0759647	−	0.997111i	$-0.524204\pi$
$167$	−1.96336	−0.151929	−0.0759647	+	0.997111i	$0.524204\pi$
$168$	4.89819	0.377904
$169$	0	0
$170$	−5.89037	−0.451771
$171$	−29.2711	−2.23841
$172$	−8.58977	−0.654964
$173$	10.2747	0.781171	0.390585	−	0.920567i	$-0.372273\pi$
$173$	10.2747	0.781171	0.390585	+	0.920567i	$0.372273\pi$
$174$	−13.6333	−1.03354
$175$	1.90403	0.143931
$176$	5.17658	0.390199
$177$	27.4664	2.06450
$178$	−0.541298	−0.0405720
$179$	11.3293	0.846790	0.423395	−	0.905945i	$-0.360838\pi$
$179$	11.3293	0.846790	0.423395	+	0.905945i	$0.360838\pi$
$180$	3.61798	0.269668
$181$	16.6110	1.23468	0.617342	−	0.786695i	$-0.288209\pi$
$181$	16.6110	1.23468	0.617342	+	0.786695i	$0.288209\pi$
$182$	0	0
$183$	−1.75240	−0.129541
$184$	−0.908568	−0.0669805
$185$	1.63865	0.120476
$186$	−0.161208	−0.0118204
$187$	−30.4919	−2.22979
$188$	−11.2024	−0.817018
$189$	3.02697	0.220180
$190$	−8.09045	−0.586943
$191$	21.7130	1.57110	0.785550	−	0.618798i	$-0.212380\pi$
$191$	21.7130	1.57110	0.785550	+	0.618798i	$0.212380\pi$
$192$	2.57254	0.185657
$193$	11.3641	0.818006	0.409003	−	0.912533i	$-0.365877\pi$
$193$	11.3641	0.818006	0.409003	+	0.912533i	$0.365877\pi$
$194$	12.8001	0.918997
$195$	0	0
$196$	−3.37468	−0.241048
$197$	17.6398	1.25678	0.628390	−	0.777898i	$-0.283714\pi$
$197$	17.6398	1.25678	0.628390	+	0.777898i	$0.283714\pi$
$198$	18.7287	1.33099
$199$	−23.6305	−1.67512	−0.837562	−	0.546342i	$-0.816020\pi$
$199$	−23.6305	−1.67512	−0.837562	+	0.546342i	$0.816020\pi$
$200$	1.00000	0.0707107
$201$	36.3995	2.56742
$202$	2.59059	0.182273
$203$	−10.0905	−0.708212
$204$	−15.1532	−1.06094
$205$	1.77061	0.123664
$206$	−1.77799	−0.123878
$207$	−3.28718	−0.228475
$208$	0	0
$209$	−41.8808	−2.89696
$210$	4.89819	0.338007
$211$	−15.2360	−1.04889	−0.524445	−	0.851444i	$-0.675727\pi$
$211$	−15.2360	−1.04889	−0.524445	+	0.851444i	$0.675727\pi$
$212$	−8.92525	−0.612989
$213$	40.3933	2.76770
$214$	3.56829	0.243923
$215$	−8.58977	−0.585818
$216$	1.58977	0.108170
$217$	−0.119316	−0.00809969
$218$	−11.4449	−0.775148
$219$	0.419554	0.0283508
$220$	5.17658	0.349005
$221$	0	0
$222$	4.21550	0.282926
$223$	−2.78265	−0.186340	−0.0931699	−	0.995650i	$-0.529700\pi$
$223$	−2.78265	−0.186340	−0.0931699	+	0.995650i	$0.529700\pi$
$224$	1.90403	0.127218
$225$	3.61798	0.241198
$226$	11.2334	0.747232
$227$	−3.94347	−0.261737	−0.130869	−	0.991400i	$-0.541777\pi$
$227$	−3.94347	−0.261737	−0.130869	+	0.991400i	$0.541777\pi$
$228$	−20.8130	−1.37838
$229$	10.3809	0.685986	0.342993	−	0.939338i	$-0.388559\pi$
$229$	10.3809	0.685986	0.342993	+	0.939338i	$0.388559\pi$
$230$	−0.908568	−0.0599092
$231$	25.3559	1.66829
$232$	−5.29954	−0.347932
$233$	−13.2410	−0.867449	−0.433725	−	0.901045i	$-0.642801\pi$
$233$	−13.2410	−0.867449	−0.433725	+	0.901045i	$0.642801\pi$
$234$	0	0
$235$	−11.2024	−0.730763
$236$	10.6767	0.694997
$237$	37.8623	2.45942
$238$	−11.2154	−0.726988
$239$	24.3290	1.57371	0.786856	−	0.617137i	$-0.211708\pi$
$239$	24.3290	1.57371	0.786856	+	0.617137i	$0.211708\pi$
$240$	2.57254	0.166057
$241$	−11.1983	−0.721349	−0.360674	−	0.932692i	$-0.617453\pi$
$241$	−11.1983	−0.721349	−0.360674	+	0.932692i	$0.617453\pi$
$242$	15.7969	1.01547
$243$	−22.1704	−1.42223
$244$	−0.681193	−0.0436089
$245$	−3.37468	−0.215600
$246$	4.55496	0.290414
$247$	0	0
$248$	−0.0626650	−0.00397923
$249$	−4.86843	−0.308524
$250$	1.00000	0.0632456
$251$	5.81385	0.366967	0.183483	−	0.983023i	$-0.441263\pi$
$251$	5.81385	0.366967	0.183483	+	0.983023i	$0.441263\pi$
$252$	6.88873	0.433949
$253$	−4.70327	−0.295692
$254$	10.8735	0.682266
$255$	−15.1532	−0.948932
$256$	1.00000	0.0625000
$257$	−29.1850	−1.82051	−0.910254	−	0.414050i	$-0.864114\pi$
$257$	−29.1850	−1.82051	−0.910254	+	0.414050i	$0.864114\pi$
$258$	−22.0976	−1.37573
$259$	3.12004	0.193870
$260$	0	0
$261$	−19.1736	−1.18682
$262$	1.13042	0.0698376
$263$	27.5544	1.69908	0.849538	−	0.527527i	$-0.176881\pi$
$263$	27.5544	1.69908	0.849538	+	0.527527i	$0.176881\pi$
$264$	13.3170	0.819603
$265$	−8.92525	−0.548274
$266$	−15.4044	−0.944507
$267$	−1.39251	−0.0852204
$268$	14.1492	0.864301
$269$	3.97887	0.242596	0.121298	−	0.992616i	$-0.461294\pi$
$269$	3.97887	0.242596	0.121298	+	0.992616i	$0.461294\pi$
$270$	1.58977	0.0967505
$271$	13.6399	0.828567	0.414283	−	0.910148i	$-0.364032\pi$
$271$	13.6399	0.828567	0.414283	+	0.910148i	$0.364032\pi$
$272$	−5.89037	−0.357156
$273$	0	0
$274$	−10.9390	−0.660851
$275$	5.17658	0.312159
$276$	−2.33733	−0.140691
$277$	−2.30543	−0.138520	−0.0692600	−	0.997599i	$-0.522064\pi$
$277$	−2.30543	−0.138520	−0.0692600	+	0.997599i	$0.522064\pi$
$278$	−4.30562	−0.258234
$279$	−0.226720	−0.0135734
$280$	1.90403	0.113787
$281$	−21.0557	−1.25608	−0.628038	−	0.778183i	$-0.716142\pi$
$281$	−21.0557	−1.25608	−0.628038	+	0.778183i	$0.716142\pi$
$282$	−28.8186	−1.71612
$283$	−2.60164	−0.154652	−0.0773258	−	0.997006i	$-0.524638\pi$
$283$	−2.60164	−0.154652	−0.0773258	+	0.997006i	$0.524638\pi$
$284$	15.7017	0.931725
$285$	−20.8130	−1.23286
$286$	0	0
$287$	3.37128	0.199000
$288$	3.61798	0.213191
$289$	17.6964	1.04097
$290$	−5.29954	−0.311200
$291$	32.9289	1.93033
$292$	0.163089	0.00954407
$293$	6.46826	0.377880	0.188940	−	0.981989i	$-0.439495\pi$
$293$	6.46826	0.377880	0.188940	+	0.981989i	$0.439495\pi$
$294$	−8.68150	−0.506316
$295$	10.6767	0.621624
$296$	1.63865	0.0952447
$297$	8.22958	0.477529
$298$	−19.2499	−1.11511
$299$	0	0
$300$	2.57254	0.148526
$301$	−16.3552	−0.942696
$302$	−7.91349	−0.455370
$303$	6.66439	0.382859
$304$	−8.09045	−0.464019
$305$	−0.681193	−0.0390050
$306$	−21.3112	−1.21828
$307$	−11.7707	−0.671789	−0.335894	−	0.941900i	$-0.609039\pi$
$307$	−11.7707	−0.671789	−0.335894	+	0.941900i	$0.609039\pi$
$308$	9.85635	0.561617
$309$	−4.57395	−0.260203
$310$	−0.0626650	−0.00355913
$311$	2.09362	0.118718	0.0593591	−	0.998237i	$-0.481094\pi$
$311$	2.09362	0.118718	0.0593591	+	0.998237i	$0.481094\pi$
$312$	0	0
$313$	−24.7645	−1.39977	−0.699885	−	0.714256i	$-0.746765\pi$
$313$	−24.7645	−1.39977	−0.699885	+	0.714256i	$0.746765\pi$
$314$	−0.946176	−0.0533958
$315$	6.88873	0.388136
$316$	14.7178	0.827943
$317$	20.9473	1.17652	0.588259	−	0.808672i	$-0.299814\pi$
$317$	20.9473	1.17652	0.588259	+	0.808672i	$0.299814\pi$
$318$	−22.9606	−1.28757
$319$	−27.4335	−1.53598
$320$	1.00000	0.0559017
$321$	9.17957	0.512354
$322$	−1.72994	−0.0964057
$323$	47.6557	2.65164
$324$	−6.76417	−0.375787
$325$	0	0
$326$	4.51269	0.249935
$327$	−29.4426	−1.62818
$328$	1.77061	0.0977653
$329$	−21.3297	−1.17594
$330$	13.3170	0.733075
$331$	−21.2478	−1.16789	−0.583944	−	0.811794i	$-0.698491\pi$
$331$	−21.2478	−1.16789	−0.583944	+	0.811794i	$0.698491\pi$
$332$	−1.89246	−0.103862
$333$	5.92861	0.324886
$334$	−1.96336	−0.107430
$335$	14.1492	0.773054
$336$	4.89819	0.267218
$337$	11.8333	0.644603	0.322301	−	0.946637i	$-0.395544\pi$
$337$	11.8333	0.644603	0.322301	+	0.946637i	$0.395544\pi$
$338$	0	0
$339$	28.8983	1.56954
$340$	−5.89037	−0.319450
$341$	−0.324390	−0.0175667
$342$	−29.2711	−1.58280
$343$	−19.7537	−1.06660
$344$	−8.58977	−0.463130
$345$	−2.33733	−0.125838
$346$	10.2747	0.552371
$347$	−21.3904	−1.14830	−0.574149	−	0.818751i	$-0.694667\pi$
$347$	−21.3904	−1.14830	−0.574149	+	0.818751i	$0.694667\pi$
$348$	−13.6333	−0.730821
$349$	−18.5446	−0.992670	−0.496335	−	0.868131i	$-0.665321\pi$
$349$	−18.5446	−0.992670	−0.496335	+	0.868131i	$0.665321\pi$
$350$	1.90403	0.101775
$351$	0	0
$352$	5.17658	0.275912
$353$	11.2265	0.597527	0.298764	−	0.954327i	$-0.403426\pi$
$353$	11.2265	0.597527	0.298764	+	0.954327i	$0.403426\pi$
$354$	27.4664	1.45982
$355$	15.7017	0.833360
$356$	−0.541298	−0.0286887
$357$	−28.8522	−1.52702
$358$	11.3293	0.598771
$359$	−7.97148	−0.420719	−0.210359	−	0.977624i	$-0.567463\pi$
$359$	−7.97148	−0.420719	−0.210359	+	0.977624i	$0.567463\pi$
$360$	3.61798	0.190684
$361$	46.4554	2.44502
$362$	16.6110	0.873054
$363$	40.6383	2.13296
$364$	0	0
$365$	0.163089	0.00853648
$366$	−1.75240	−0.0915994
$367$	−20.4864	−1.06938	−0.534690	−	0.845048i	$-0.679572\pi$
$367$	−20.4864	−1.06938	−0.534690	+	0.845048i	$0.679572\pi$
$368$	−0.908568	−0.0473624
$369$	6.40601	0.333484
$370$	1.63865	0.0851895
$371$	−16.9939	−0.882281
$372$	−0.161208	−0.00835826
$373$	14.4319	0.747254	0.373627	−	0.927579i	$-0.378114\pi$
$373$	14.4319	0.747254	0.373627	+	0.927579i	$0.378114\pi$
$374$	−30.4919	−1.57670
$375$	2.57254	0.132846
$376$	−11.2024	−0.577719
$377$	0	0
$378$	3.02697	0.155691
$379$	0.607528	0.0312066	0.0156033	−	0.999878i	$-0.495033\pi$
$379$	0.607528	0.0312066	0.0156033	+	0.999878i	$0.495033\pi$
$380$	−8.09045	−0.415031
$381$	27.9726	1.43308
$382$	21.7130	1.11094
$383$	14.6778	0.749998	0.374999	−	0.927025i	$-0.377643\pi$
$383$	14.6778	0.749998	0.374999	+	0.927025i	$0.377643\pi$
$384$	2.57254	0.131280
$385$	9.85635	0.502326
$386$	11.3641	0.578418
$387$	−31.0776	−1.57976
$388$	12.8001	0.649829
$389$	18.6299	0.944572	0.472286	−	0.881445i	$-0.343429\pi$
$389$	18.6299	0.944572	0.472286	+	0.881445i	$0.343429\pi$
$390$	0	0
$391$	5.35180	0.270652
$392$	−3.37468	−0.170447
$393$	2.90806	0.146692
$394$	17.6398	0.888678
$395$	14.7178	0.740535
$396$	18.7287	0.941154
$397$	7.96619	0.399811	0.199906	−	0.979815i	$-0.435936\pi$
$397$	7.96619	0.399811	0.199906	+	0.979815i	$0.435936\pi$
$398$	−23.6305	−1.18449
$399$	−39.6286	−1.98391
$400$	1.00000	0.0500000
$401$	−4.76351	−0.237878	−0.118939	−	0.992902i	$-0.537949\pi$
$401$	−4.76351	−0.237878	−0.118939	+	0.992902i	$0.537949\pi$
$402$	36.3995	1.81544
$403$	0	0
$404$	2.59059	0.128886
$405$	−6.76417	−0.336114
$406$	−10.0905	−0.500782
$407$	8.48261	0.420467
$408$	−15.1532	−0.750196
$409$	−9.59521	−0.474452	−0.237226	−	0.971454i	$-0.576238\pi$
$409$	−9.59521	−0.474452	−0.237226	+	0.971454i	$0.576238\pi$
$410$	1.77061	0.0874440
$411$	−28.1411	−1.38810
$412$	−1.77799	−0.0875953
$413$	20.3288	1.00032
$414$	−3.28718	−0.161556
$415$	−1.89246	−0.0928971
$416$	0	0
$417$	−11.0764	−0.542413
$418$	−41.8808	−2.04846
$419$	17.0041	0.830707	0.415353	−	0.909660i	$-0.363658\pi$
$419$	17.0041	0.830707	0.415353	+	0.909660i	$0.363658\pi$
$420$	4.89819	0.239007
$421$	−11.3647	−0.553882	−0.276941	−	0.960887i	$-0.589321\pi$
$421$	−11.3647	−0.553882	−0.276941	+	0.960887i	$0.589321\pi$
$422$	−15.2360	−0.741677
$423$	−40.5300	−1.97064
$424$	−8.92525	−0.433449
$425$	−5.89037	−0.285725
$426$	40.3933	1.95706
$427$	−1.29701	−0.0627668
$428$	3.56829	0.172480
$429$	0	0
$430$	−8.58977	−0.414236
$431$	22.6058	1.08888	0.544441	−	0.838799i	$-0.316742\pi$
$431$	22.6058	1.08888	0.544441	+	0.838799i	$0.316742\pi$
$432$	1.58977	0.0764880
$433$	2.99497	0.143929	0.0719645	−	0.997407i	$-0.477073\pi$
$433$	2.99497	0.143929	0.0719645	+	0.997407i	$0.477073\pi$
$434$	−0.119316	−0.00572734
$435$	−13.6333	−0.653666
$436$	−11.4449	−0.548112
$437$	7.35072	0.351633
$438$	0.419554	0.0200471
$439$	13.4489	0.641881	0.320940	−	0.947099i	$-0.396001\pi$
$439$	13.4489	0.641881	0.320940	+	0.947099i	$0.396001\pi$
$440$	5.17658	0.246784
$441$	−12.2095	−0.581405
$442$	0	0
$443$	−16.6206	−0.789671	−0.394835	−	0.918752i	$-0.629198\pi$
$443$	−16.6206	−0.789671	−0.394835	+	0.918752i	$0.629198\pi$
$444$	4.21550	0.200059
$445$	−0.541298	−0.0256600
$446$	−2.78265	−0.131762
$447$	−49.5211	−2.34227
$448$	1.90403	0.0899569
$449$	14.0974	0.665298	0.332649	−	0.943051i	$-0.392058\pi$
$449$	14.0974	0.665298	0.332649	+	0.943051i	$0.392058\pi$
$450$	3.61798	0.170553
$451$	9.16567	0.431595
$452$	11.2334	0.528373
$453$	−20.3578	−0.956492
$454$	−3.94347	−0.185076
$455$	0	0
$456$	−20.8130	−0.974660
$457$	−26.2785	−1.22926	−0.614628	−	0.788817i	$-0.710694\pi$
$457$	−26.2785	−1.22926	−0.614628	+	0.788817i	$0.710694\pi$
$458$	10.3809	0.485066
$459$	−9.36435	−0.437090
$460$	−0.908568	−0.0423622
$461$	−2.52721	−0.117704	−0.0588520	−	0.998267i	$-0.518744\pi$
$461$	−2.52721	−0.117704	−0.0588520	+	0.998267i	$0.518744\pi$
$462$	25.3559	1.17966
$463$	20.9477	0.973522	0.486761	−	0.873535i	$-0.338178\pi$
$463$	20.9477	0.973522	0.486761	+	0.873535i	$0.338178\pi$
$464$	−5.29954	−0.246025
$465$	−0.161208	−0.00747586
$466$	−13.2410	−0.613379
$467$	−19.2552	−0.891023	−0.445511	−	0.895276i	$-0.646978\pi$
$467$	−19.2552	−0.891023	−0.445511	+	0.895276i	$0.646978\pi$
$468$	0	0
$469$	26.9405	1.24400
$470$	−11.2024	−0.516728
$471$	−2.43408	−0.112156
$472$	10.6767	0.491437
$473$	−44.4656	−2.04453
$474$	37.8623	1.73907
$475$	−8.09045	−0.371215
$476$	−11.2154	−0.514058
$477$	−32.2914	−1.47852
$478$	24.3290	1.11278
$479$	−22.9230	−1.04738	−0.523689	−	0.851910i	$-0.675445\pi$
$479$	−22.9230	−1.04738	−0.523689	+	0.851910i	$0.675445\pi$
$480$	2.57254	0.117420
$481$	0	0
$482$	−11.1983	−0.510071
$483$	−4.45034	−0.202498
$484$	15.7969	0.718043
$485$	12.8001	0.581225
$486$	−22.1704	−1.00567
$487$	−27.0722	−1.22676	−0.613379	−	0.789789i	$-0.710190\pi$
$487$	−27.0722	−1.22676	−0.613379	+	0.789789i	$0.710190\pi$
$488$	−0.681193	−0.0308362
$489$	11.6091	0.524981
$490$	−3.37468	−0.152452
$491$	−14.7213	−0.664363	−0.332182	−	0.943215i	$-0.607785\pi$
$491$	−14.7213	−0.664363	−0.332182	+	0.943215i	$0.607785\pi$
$492$	4.55496	0.205353
$493$	31.2162	1.40591
$494$	0	0
$495$	18.7287	0.841794
$496$	−0.0626650	−0.00281374
$497$	29.8965	1.34104
$498$	−4.86843	−0.218160
$499$	−4.24391	−0.189984	−0.0949918	−	0.995478i	$-0.530282\pi$
$499$	−4.24391	−0.189984	−0.0949918	+	0.995478i	$0.530282\pi$
$500$	1.00000	0.0447214
$501$	−5.05083	−0.225654
$502$	5.81385	0.259485
$503$	−9.57492	−0.426925	−0.213462	−	0.976951i	$-0.568474\pi$
$503$	−9.57492	−0.426925	−0.213462	+	0.976951i	$0.568474\pi$
$504$	6.88873	0.306848
$505$	2.59059	0.115280
$506$	−4.70327	−0.209086
$507$	0	0
$508$	10.8735	0.482435
$509$	33.5783	1.48833	0.744165	−	0.667995i	$-0.232847\pi$
$509$	33.5783	1.48833	0.744165	+	0.667995i	$0.232847\pi$
$510$	−15.1532	−0.670996
$511$	0.310526	0.0137369
$512$	1.00000	0.0441942
$513$	−12.8620	−0.567870
$514$	−29.1850	−1.28729
$515$	−1.77799	−0.0783476
$516$	−22.0976	−0.972791
$517$	−57.9900	−2.55040
$518$	3.12004	0.137087
$519$	26.4321	1.16024
$520$	0	0
$521$	2.45328	0.107480	0.0537400	−	0.998555i	$-0.482886\pi$
$521$	2.45328	0.107480	0.0537400	+	0.998555i	$0.482886\pi$
$522$	−19.1736	−0.839206
$523$	−28.1579	−1.23126	−0.615630	−	0.788035i	$-0.711098\pi$
$523$	−28.1579	−1.23126	−0.615630	+	0.788035i	$0.711098\pi$
$524$	1.13042	0.0493827
$525$	4.89819	0.213775
$526$	27.5544	1.20143
$527$	0.369120	0.0160791
$528$	13.3170	0.579546
$529$	−22.1745	−0.964109
$530$	−8.92525	−0.387688
$531$	38.6282	1.67632
$532$	−15.4044	−0.667867
$533$	0	0
$534$	−1.39251	−0.0602599
$535$	3.56829	0.154271
$536$	14.1492	0.611153
$537$	29.1450	1.25770
$538$	3.97887	0.171541
$539$	−17.4693	−0.752455
$540$	1.58977	0.0684130
$541$	21.4643	0.922820	0.461410	−	0.887187i	$-0.347344\pi$
$541$	21.4643	0.922820	0.461410	+	0.887187i	$0.347344\pi$
$542$	13.6399	0.585885
$543$	42.7325	1.83383
$544$	−5.89037	−0.252547
$545$	−11.4449	−0.490247
$546$	0	0
$547$	17.0076	0.727192	0.363596	−	0.931557i	$-0.381549\pi$
$547$	17.0076	0.727192	0.363596	+	0.931557i	$0.381549\pi$
$548$	−10.9390	−0.467292
$549$	−2.46454	−0.105184
$550$	5.17658	0.220730
$551$	42.8756	1.82656
$552$	−2.33733	−0.0994834
$553$	28.0232	1.19167
$554$	−2.30543	−0.0979484
$555$	4.21550	0.178938
$556$	−4.30562	−0.182599
$557$	3.62480	0.153588	0.0767938	−	0.997047i	$-0.475532\pi$
$557$	3.62480	0.153588	0.0767938	+	0.997047i	$0.475532\pi$
$558$	−0.226720	−0.00959784
$559$	0	0
$560$	1.90403	0.0804599
$561$	−78.4418	−3.31182
$562$	−21.0557	−0.888180
$563$	−40.7538	−1.71757	−0.858783	−	0.512339i	$-0.828779\pi$
$563$	−40.7538	−1.71757	−0.858783	+	0.512339i	$0.828779\pi$
$564$	−28.8186	−1.21348
$565$	11.2334	0.472591
$566$	−2.60164	−0.109355
$567$	−12.8792	−0.540874
$568$	15.7017	0.658829
$569$	31.7297	1.33018	0.665089	−	0.746764i	$-0.268394\pi$
$569$	31.7297	1.33018	0.665089	+	0.746764i	$0.268394\pi$
$570$	−20.8130	−0.871762
$571$	−14.5697	−0.609722	−0.304861	−	0.952397i	$-0.598610\pi$
$571$	−14.5697	−0.609722	−0.304861	+	0.952397i	$0.598610\pi$
$572$	0	0
$573$	55.8577	2.33349
$574$	3.37128	0.140715
$575$	−0.908568	−0.0378899
$576$	3.61798	0.150749
$577$	−5.78013	−0.240630	−0.120315	−	0.992736i	$-0.538390\pi$
$577$	−5.78013	−0.240630	−0.120315	+	0.992736i	$0.538390\pi$
$578$	17.6964	0.736075
$579$	29.2347	1.21495
$580$	−5.29954	−0.220051
$581$	−3.60329	−0.149490
$582$	32.9289	1.36495
$583$	−46.2023	−1.91350
$584$	0.163089	0.00674868
$585$	0	0
$586$	6.46826	0.267201
$587$	−1.46614	−0.0605139	−0.0302570	−	0.999542i	$-0.509633\pi$
$587$	−1.46614	−0.0605139	−0.0302570	+	0.999542i	$0.509633\pi$
$588$	−8.68150	−0.358019
$589$	0.506988	0.0208901
$590$	10.6767	0.439554
$591$	45.3790	1.86664
$592$	1.63865	0.0673482
$593$	25.7264	1.05646	0.528228	−	0.849103i	$-0.322857\pi$
$593$	25.7264	1.05646	0.528228	+	0.849103i	$0.322857\pi$
$594$	8.22958	0.337664
$595$	−11.2154	−0.459788
$596$	−19.2499	−0.788505
$597$	−60.7906	−2.48799
$598$	0	0
$599$	−26.7207	−1.09178	−0.545890	−	0.837857i	$-0.683808\pi$
$599$	−26.7207	−1.09178	−0.545890	+	0.837857i	$0.683808\pi$
$600$	2.57254	0.105024
$601$	26.9562	1.09956	0.549782	−	0.835308i	$-0.314711\pi$
$601$	26.9562	1.09956	0.549782	+	0.835308i	$0.314711\pi$
$602$	−16.3552	−0.666587
$603$	51.1915	2.08468
$604$	−7.91349	−0.321995
$605$	15.7969	0.642237
$606$	6.66439	0.270722
$607$	−32.3286	−1.31218	−0.656088	−	0.754684i	$-0.727790\pi$
$607$	−32.3286	−1.31218	−0.656088	+	0.754684i	$0.727790\pi$
$608$	−8.09045	−0.328111
$609$	−25.9582	−1.05188
$610$	−0.681193	−0.0275807
$611$	0	0
$612$	−21.3112	−0.861455
$613$	10.2117	0.412447	0.206224	−	0.978505i	$-0.433883\pi$
$613$	10.2117	0.412447	0.206224	+	0.978505i	$0.433883\pi$
$614$	−11.7707	−0.475027
$615$	4.55496	0.183674
$616$	9.85635	0.397123
$617$	−32.6071	−1.31271	−0.656356	−	0.754452i	$-0.727903\pi$
$617$	−32.6071	−1.31271	−0.656356	+	0.754452i	$0.727903\pi$
$618$	−4.57395	−0.183991
$619$	−8.49492	−0.341440	−0.170720	−	0.985320i	$-0.554609\pi$
$619$	−8.49492	−0.341440	−0.170720	+	0.985320i	$0.554609\pi$
$620$	−0.0626650	−0.00251669
$621$	−1.44442	−0.0579625
$622$	2.09362	0.0839465
$623$	−1.03065	−0.0412920
$624$	0	0
$625$	1.00000	0.0400000
$626$	−24.7645	−0.989787
$627$	−107.740	−4.30273
$628$	−0.946176	−0.0377565
$629$	−9.65226	−0.384861
$630$	6.88873	0.274454
$631$	41.4992	1.65206	0.826029	−	0.563628i	$-0.190595\pi$
$631$	41.4992	1.65206	0.826029	+	0.563628i	$0.190595\pi$
$632$	14.7178	0.585444
$633$	−39.1953	−1.55787
$634$	20.9473	0.831924
$635$	10.8735	0.431503
$636$	−22.9606	−0.910447
$637$	0	0
$638$	−27.4335	−1.08610
$639$	56.8084	2.24731
$640$	1.00000	0.0395285
$641$	17.9976	0.710862	0.355431	−	0.934703i	$-0.384334\pi$
$641$	17.9976	0.710862	0.355431	+	0.934703i	$0.384334\pi$
$642$	9.17957	0.362289
$643$	24.9350	0.983342	0.491671	−	0.870781i	$-0.336386\pi$
$643$	24.9350	0.983342	0.491671	+	0.870781i	$0.336386\pi$
$644$	−1.72994	−0.0681691
$645$	−22.0976	−0.870091
$646$	47.6557	1.87499
$647$	−31.5515	−1.24042	−0.620209	−	0.784437i	$-0.712952\pi$
$647$	−31.5515	−1.24042	−0.620209	+	0.784437i	$0.712952\pi$
$648$	−6.76417	−0.265722
$649$	55.2690	2.16950
$650$	0	0
$651$	−0.306945	−0.0120301
$652$	4.51269	0.176731
$653$	8.31180	0.325266	0.162633	−	0.986687i	$-0.448001\pi$
$653$	8.31180	0.325266	0.162633	+	0.986687i	$0.448001\pi$
$654$	−29.4426	−1.15130
$655$	1.13042	0.0441692
$656$	1.77061	0.0691305
$657$	0.590053	0.0230202
$658$	−21.3297	−0.831517
$659$	−4.11647	−0.160355	−0.0801774	−	0.996781i	$-0.525549\pi$
$659$	−4.11647	−0.160355	−0.0801774	+	0.996781i	$0.525549\pi$
$660$	13.3170	0.518362
$661$	−39.4880	−1.53591	−0.767953	−	0.640506i	$-0.778724\pi$
$661$	−39.4880	−1.53591	−0.767953	+	0.640506i	$0.778724\pi$
$662$	−21.2478	−0.825821
$663$	0	0
$664$	−1.89246	−0.0734416
$665$	−15.4044	−0.597359
$666$	5.92861	0.229729
$667$	4.81499	0.186437
$668$	−1.96336	−0.0759647
$669$	−7.15847	−0.276763
$670$	14.1492	0.546632
$671$	−3.52625	−0.136129
$672$	4.89819	0.188952
$673$	−30.1004	−1.16028	−0.580142	−	0.814515i	$-0.697003\pi$
$673$	−30.1004	−1.16028	−0.580142	+	0.814515i	$0.697003\pi$
$674$	11.8333	0.455803
$675$	1.58977	0.0611904
$676$	0	0
$677$	15.8446	0.608959	0.304479	−	0.952519i	$-0.401518\pi$
$677$	15.8446	0.608959	0.304479	+	0.952519i	$0.401518\pi$
$678$	28.8983	1.10983
$679$	24.3718	0.935305
$680$	−5.89037	−0.225885
$681$	−10.1447	−0.388747
$682$	−0.324390	−0.0124215
$683$	3.74741	0.143391	0.0716954	−	0.997427i	$-0.477159\pi$
$683$	3.74741	0.143391	0.0716954	+	0.997427i	$0.477159\pi$
$684$	−29.2711	−1.11921
$685$	−10.9390	−0.417959
$686$	−19.7537	−0.754199
$687$	26.7052	1.01887
$688$	−8.58977	−0.327482
$689$	0	0
$690$	−2.33733	−0.0889806
$691$	49.7932	1.89422	0.947111	−	0.320905i	$-0.103987\pi$
$691$	49.7932	1.89422	0.947111	+	0.320905i	$0.103987\pi$
$692$	10.2747	0.390585
$693$	35.6600	1.35461
$694$	−21.3904	−0.811969
$695$	−4.30562	−0.163321
$696$	−13.6333	−0.516768
$697$	−10.4295	−0.395046
$698$	−18.5446	−0.701924
$699$	−34.0631	−1.28839
$700$	1.90403	0.0719655
$701$	32.9089	1.24295	0.621476	−	0.783434i	$-0.286534\pi$
$701$	32.9089	1.24295	0.621476	+	0.783434i	$0.286534\pi$
$702$	0	0
$703$	−13.2574	−0.500014
$704$	5.17658	0.195100
$705$	−28.8186	−1.08537
$706$	11.2265	0.422515
$707$	4.93255	0.185508
$708$	27.4664	1.03225
$709$	−23.1678	−0.870083	−0.435042	−	0.900410i	$-0.643266\pi$
$709$	−23.1678	−0.870083	−0.435042	+	0.900410i	$0.643266\pi$
$710$	15.7017	0.589275
$711$	53.2488	1.99699
$712$	−0.541298	−0.0202860
$713$	0.0569354	0.00213225
$714$	−28.8522	−1.07977
$715$	0	0
$716$	11.3293	0.423395
$717$	62.5874	2.33737
$718$	−7.97148	−0.297493
$719$	4.76483	0.177698	0.0888491	−	0.996045i	$-0.471681\pi$
$719$	4.76483	0.177698	0.0888491	+	0.996045i	$0.471681\pi$
$720$	3.61798	0.134834
$721$	−3.38534	−0.126077
$722$	46.4554	1.72889
$723$	−28.8082	−1.07139
$724$	16.6110	0.617342
$725$	−5.29954	−0.196820
$726$	40.6383	1.50823
$727$	42.5004	1.57625	0.788127	−	0.615513i	$-0.211051\pi$
$727$	42.5004	1.57625	0.788127	+	0.615513i	$0.211051\pi$
$728$	0	0
$729$	−36.7419	−1.36081
$730$	0.163089	0.00603620
$731$	50.5969	1.87139
$732$	−1.75240	−0.0647705
$733$	−10.3609	−0.382689	−0.191345	−	0.981523i	$-0.561285\pi$
$733$	−10.3609	−0.382689	−0.191345	+	0.981523i	$0.561285\pi$
$734$	−20.4864	−0.756166
$735$	−8.68150	−0.320222
$736$	−0.908568	−0.0334903
$737$	73.2445	2.69800
$738$	6.40601	0.235808
$739$	−25.9157	−0.953324	−0.476662	−	0.879087i	$-0.658154\pi$
$739$	−25.9157	−0.953324	−0.476662	+	0.879087i	$0.658154\pi$
$740$	1.63865	0.0602380
$741$	0	0
$742$	−16.9939	−0.623867
$743$	9.84397	0.361140	0.180570	−	0.983562i	$-0.442206\pi$
$743$	9.84397	0.361140	0.180570	+	0.983562i	$0.442206\pi$
$744$	−0.161208	−0.00591018
$745$	−19.2499	−0.705260
$746$	14.4319	0.528388
$747$	−6.84687	−0.250514
$748$	−30.4919	−1.11490
$749$	6.79412	0.248252
$750$	2.57254	0.0939360
$751$	−48.3807	−1.76544	−0.882718	−	0.469903i	$-0.844289\pi$
$751$	−48.3807	−1.76544	−0.882718	+	0.469903i	$0.844289\pi$
$752$	−11.2024	−0.408509
$753$	14.9564	0.545041
$754$	0	0
$755$	−7.91349	−0.288001
$756$	3.02697	0.110090
$757$	−10.3630	−0.376649	−0.188324	−	0.982107i	$-0.560306\pi$
$757$	−10.3630	−0.376649	−0.188324	+	0.982107i	$0.560306\pi$
$758$	0.607528	0.0220664
$759$	−12.0994	−0.439179
$760$	−8.09045	−0.293471
$761$	−24.0420	−0.871521	−0.435760	−	0.900063i	$-0.643520\pi$
$761$	−24.0420	−0.871521	−0.435760	+	0.900063i	$0.643520\pi$
$762$	27.9726	1.01334
$763$	−21.7915	−0.788904
$764$	21.7130	0.785550
$765$	−21.3112	−0.770509
$766$	14.6778	0.530329
$767$	0	0
$768$	2.57254	0.0928286
$769$	11.4605	0.413277	0.206639	−	0.978417i	$-0.433748\pi$
$769$	11.4605	0.413277	0.206639	+	0.978417i	$0.433748\pi$
$770$	9.85635	0.355198
$771$	−75.0796	−2.70393
$772$	11.3641	0.409003
$773$	−0.507988	−0.0182711	−0.00913553	−	0.999958i	$-0.502908\pi$
$773$	−0.507988	−0.0182711	−0.00913553	+	0.999958i	$0.502908\pi$
$774$	−31.0776	−1.11706
$775$	−0.0626650	−0.00225099
$776$	12.8001	0.459498
$777$	8.02643	0.287947
$778$	18.6299	0.667914
$779$	−14.3250	−0.513246
$780$	0	0
$781$	81.2811	2.90847
$782$	5.35180	0.191380
$783$	−8.42506	−0.301087
$784$	−3.37468	−0.120524
$785$	−0.946176	−0.0337705
$786$	2.90806	0.103727
$787$	−27.4018	−0.976769	−0.488384	−	0.872629i	$-0.662414\pi$
$787$	−27.4018	−0.976769	−0.488384	+	0.872629i	$0.662414\pi$
$788$	17.6398	0.628390
$789$	70.8849	2.52357
$790$	14.7178	0.523637
$791$	21.3886	0.760493
$792$	18.7287	0.665497
$793$	0	0
$794$	7.96619	0.282709
$795$	−22.9606	−0.814328
$796$	−23.6305	−0.837562
$797$	−2.46568	−0.0873388	−0.0436694	−	0.999046i	$-0.513905\pi$
$797$	−2.46568	−0.0873388	−0.0436694	+	0.999046i	$0.513905\pi$
$798$	−39.6286	−1.40284
$799$	65.9862	2.33442
$800$	1.00000	0.0353553
$801$	−1.95840	−0.0691968
$802$	−4.76351	−0.168205
$803$	0.844244	0.0297927
$804$	36.3995	1.28371
$805$	−1.72994	−0.0609723
$806$	0	0
$807$	10.2358	0.360318
$808$	2.59059	0.0911365
$809$	1.54477	0.0543112	0.0271556	−	0.999631i	$-0.491355\pi$
$809$	1.54477	0.0543112	0.0271556	+	0.999631i	$0.491355\pi$
$810$	−6.76417	−0.237669
$811$	26.1714	0.919003	0.459502	−	0.888177i	$-0.348028\pi$
$811$	26.1714	0.919003	0.459502	+	0.888177i	$0.348028\pi$
$812$	−10.0905	−0.354106
$813$	35.0893	1.23064
$814$	8.48261	0.297315
$815$	4.51269	0.158073
$816$	−15.1532	−0.530469
$817$	69.4951	2.43133
$818$	−9.59521	−0.335489
$819$	0	0
$820$	1.77061	0.0618322
$821$	41.5128	1.44881	0.724403	−	0.689377i	$-0.242116\pi$
$821$	41.5128	1.44881	0.724403	+	0.689377i	$0.242116\pi$
$822$	−28.1411	−0.981534
$823$	−17.6447	−0.615056	−0.307528	−	0.951539i	$-0.599502\pi$
$823$	−17.6447	−0.615056	−0.307528	+	0.951539i	$0.599502\pi$
$824$	−1.77799	−0.0619392
$825$	13.3170	0.463637
$826$	20.3288	0.707330
$827$	30.1723	1.04919	0.524596	−	0.851351i	$-0.324216\pi$
$827$	30.1723	1.04919	0.524596	+	0.851351i	$0.324216\pi$
$828$	−3.28718	−0.114237
$829$	19.3250	0.671185	0.335593	−	0.942007i	$-0.391063\pi$
$829$	19.3250	0.671185	0.335593	+	0.942007i	$0.391063\pi$
$830$	−1.89246	−0.0656882
$831$	−5.93082	−0.205738
$832$	0	0
$833$	19.8781	0.688735
$834$	−11.0764	−0.383544
$835$	−1.96336	−0.0679449
$836$	−41.8808	−1.44848
$837$	−0.0996231	−0.00344348
$838$	17.0041	0.587398
$839$	−3.98927	−0.137725	−0.0688625	−	0.997626i	$-0.521937\pi$
$839$	−3.98927	−0.137725	−0.0688625	+	0.997626i	$0.521937\pi$
$840$	4.89819	0.169004
$841$	−0.914902	−0.0315483
$842$	−11.3647	−0.391654
$843$	−54.1666	−1.86560
$844$	−15.2360	−0.524445
$845$	0	0
$846$	−40.5300	−1.39345
$847$	30.0778	1.03349
$848$	−8.92525	−0.306494
$849$	−6.69283	−0.229697
$850$	−5.89037	−0.202038
$851$	−1.48883	−0.0510363
$852$	40.3933	1.38385
$853$	0.0825760	0.00282735	0.00141367	−	0.999999i	$-0.499550\pi$
$853$	0.0825760	0.00282735	0.00141367	+	0.999999i	$0.499550\pi$
$854$	−1.29701	−0.0443828
$855$	−29.2711	−1.00105
$856$	3.56829	0.121962
$857$	−33.2315	−1.13517	−0.567584	−	0.823316i	$-0.692122\pi$
$857$	−33.2315	−1.13517	−0.567584	+	0.823316i	$0.692122\pi$
$858$	0	0
$859$	−11.0394	−0.376658	−0.188329	−	0.982106i	$-0.560307\pi$
$859$	−11.0394	−0.376658	−0.188329	+	0.982106i	$0.560307\pi$
$860$	−8.58977	−0.292909
$861$	8.67277	0.295567
$862$	22.6058	0.769957
$863$	22.7798	0.775432	0.387716	−	0.921779i	$-0.373264\pi$
$863$	22.7798	0.775432	0.387716	+	0.921779i	$0.373264\pi$
$864$	1.58977	0.0540852
$865$	10.2747	0.349350
$866$	2.99497	0.101773
$867$	45.5248	1.54610
$868$	−0.119316	−0.00404984
$869$	76.1880	2.58450
$870$	−13.6333	−0.462212
$871$	0	0
$872$	−11.4449	−0.387574
$873$	46.3106	1.56738
$874$	7.35072	0.248642
$875$	1.90403	0.0643679
$876$	0.419554	0.0141754
$877$	−33.3282	−1.12541	−0.562706	−	0.826657i	$-0.690240\pi$
$877$	−33.3282	−1.12541	−0.562706	+	0.826657i	$0.690240\pi$
$878$	13.4489	0.453878
$879$	16.6399	0.561249
$880$	5.17658	0.174502
$881$	20.8588	0.702750	0.351375	−	0.936235i	$-0.385714\pi$
$881$	20.8588	0.702750	0.351375	+	0.936235i	$0.385714\pi$
$882$	−12.2095	−0.411115
$883$	−38.2565	−1.28743	−0.643716	−	0.765264i	$-0.722608\pi$
$883$	−38.2565	−1.28743	−0.643716	+	0.765264i	$0.722608\pi$
$884$	0	0
$885$	27.4664	0.923272
$886$	−16.6206	−0.558382
$887$	42.9534	1.44223	0.721117	−	0.692814i	$-0.243629\pi$
$887$	42.9534	1.44223	0.721117	+	0.692814i	$0.243629\pi$
$888$	4.21550	0.141463
$889$	20.7035	0.694373
$890$	−0.541298	−0.0181444
$891$	−35.0152	−1.17305
$892$	−2.78265	−0.0931699
$893$	90.6324	3.03290
$894$	−49.5211	−1.65623
$895$	11.3293	0.378696
$896$	1.90403	0.0636091
$897$	0	0
$898$	14.0974	0.470437
$899$	0.332095	0.0110760
$900$	3.61798	0.120599
$901$	52.5730	1.75146
$902$	9.16567	0.305184
$903$	−42.0744	−1.40015
$904$	11.2334	0.373616
$905$	16.6110	0.552168
$906$	−20.3578	−0.676342
$907$	−15.3490	−0.509656	−0.254828	−	0.966986i	$-0.582019\pi$
$907$	−15.3490	−0.509656	−0.254828	+	0.966986i	$0.582019\pi$
$908$	−3.94347	−0.130869
$909$	9.37268	0.310872
$910$	0	0
$911$	−7.48652	−0.248040	−0.124020	−	0.992280i	$-0.539579\pi$
$911$	−7.48652	−0.248040	−0.124020	+	0.992280i	$0.539579\pi$
$912$	−20.8130	−0.689188
$913$	−9.79646	−0.324215
$914$	−26.2785	−0.869216
$915$	−1.75240	−0.0579325
$916$	10.3809	0.342993
$917$	2.15235	0.0710769
$918$	−9.36435	−0.309070
$919$	−12.4412	−0.410396	−0.205198	−	0.978720i	$-0.565784\pi$
$919$	−12.4412	−0.410396	−0.205198	+	0.978720i	$0.565784\pi$
$920$	−0.908568	−0.0299546
$921$	−30.2806	−0.997780
$922$	−2.52721	−0.0832293
$923$	0	0
$924$	25.3559	0.834147
$925$	1.63865	0.0538785
$926$	20.9477	0.688384
$927$	−6.43273	−0.211278
$928$	−5.29954	−0.173966
$929$	22.5855	0.741007	0.370504	−	0.928831i	$-0.379185\pi$
$929$	22.5855	0.741007	0.370504	+	0.928831i	$0.379185\pi$
$930$	−0.161208	−0.00528623
$931$	27.3027	0.894809
$932$	−13.2410	−0.433725
$933$	5.38592	0.176327
$934$	−19.2552	−0.630048
$935$	−30.4919	−0.997193
$936$	0	0
$937$	−20.5615	−0.671714	−0.335857	−	0.941913i	$-0.609026\pi$
$937$	−20.5615	−0.671714	−0.335857	+	0.941913i	$0.609026\pi$
$938$	26.9405	0.879639
$939$	−63.7076	−2.07902
$940$	−11.2024	−0.365382
$941$	35.6763	1.16301	0.581506	−	0.813542i	$-0.302464\pi$
$941$	35.6763	1.16301	0.581506	+	0.813542i	$0.302464\pi$
$942$	−2.43408	−0.0793066
$943$	−1.60871	−0.0523870
$944$	10.6767	0.347498
$945$	3.02697	0.0984674
$946$	−44.4656	−1.44570
$947$	−16.0381	−0.521167	−0.260584	−	0.965451i	$-0.583915\pi$
$947$	−16.0381	−0.521167	−0.260584	+	0.965451i	$0.583915\pi$
$948$	37.8623	1.22971
$949$	0	0
$950$	−8.09045	−0.262489
$951$	53.8879	1.74743
$952$	−11.2154	−0.363494
$953$	−35.6022	−1.15327	−0.576634	−	0.817002i	$-0.695634\pi$
$953$	−35.6022	−1.15327	−0.576634	+	0.817002i	$0.695634\pi$
$954$	−32.2914	−1.04547
$955$	21.7130	0.702617
$956$	24.3290	0.786856
$957$	−70.5738	−2.28133
$958$	−22.9230	−0.740608
$959$	−20.8282	−0.672578
$960$	2.57254	0.0830285
$961$	−30.9961	−0.999873
$962$	0	0
$963$	12.9100	0.416018
$964$	−11.1983	−0.360674
$965$	11.3641	0.365824
$966$	−4.45034	−0.143187
$967$	8.36719	0.269071	0.134535	−	0.990909i	$-0.457046\pi$
$967$	8.36719	0.269071	0.134535	+	0.990909i	$0.457046\pi$
$968$	15.7969	0.507733
$969$	122.596	3.93836
$970$	12.8001	0.410988
$971$	29.0504	0.932270	0.466135	−	0.884714i	$-0.345646\pi$
$971$	29.0504	0.932270	0.466135	+	0.884714i	$0.345646\pi$
$972$	−22.1704	−0.711117
$973$	−8.19802	−0.262816
$974$	−27.0722	−0.867449
$975$	0	0
$976$	−0.681193	−0.0218045
$977$	−14.1557	−0.452880	−0.226440	−	0.974025i	$-0.572709\pi$
$977$	−14.1557	−0.452880	−0.226440	+	0.974025i	$0.572709\pi$
$978$	11.6091	0.371218
$979$	−2.80207	−0.0895546
$980$	−3.37468	−0.107800
$981$	−41.4075	−1.32204
$982$	−14.7213	−0.469776
$983$	−7.74156	−0.246917	−0.123459	−	0.992350i	$-0.539399\pi$
$983$	−7.74156	−0.246917	−0.123459	+	0.992350i	$0.539399\pi$
$984$	4.55496	0.145207
$985$	17.6398	0.562049
$986$	31.2162	0.994127
$987$	−54.8715	−1.74658
$988$	0	0
$989$	7.80439	0.248165
$990$	18.7287	0.595238
$991$	−20.8876	−0.663517	−0.331759	−	0.943364i	$-0.607642\pi$
$991$	−20.8876	−0.663517	−0.331759	+	0.943364i	$0.607642\pi$
$992$	−0.0626650	−0.00198961
$993$	−54.6610	−1.73461
$994$	29.8965	0.948259
$995$	−23.6305	−0.749138
$996$	−4.86843	−0.154262
$997$	−33.3691	−1.05681	−0.528406	−	0.848992i	$-0.677210\pi$
$997$	−33.3691	−1.05681	−0.528406	+	0.848992i	$0.677210\pi$
$998$	−4.24391	−0.134339
$999$	2.60509	0.0824213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.a.w.1.6	yes	6
5.4	even	2		8450.2.a.cp.1.1		6
13.2	odd	12		1690.2.l.n.1161.10		24
13.3	even	3		1690.2.e.u.191.1		12
13.4	even	6		1690.2.e.v.991.1		12
13.5	odd	4		1690.2.d.l.1351.6		12
13.6	odd	12		1690.2.l.n.361.6		24
13.7	odd	12		1690.2.l.n.361.10		24
13.8	odd	4		1690.2.d.l.1351.12		12
13.9	even	3		1690.2.e.u.991.1		12
13.10	even	6		1690.2.e.v.191.1		12
13.11	odd	12		1690.2.l.n.1161.6		24
13.12	even	2		1690.2.a.v.1.6	✓	6
65.64	even	2		8450.2.a.cq.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.a.v.1.6	✓	6	13.12	even	2
1690.2.a.w.1.6	yes	6	1.1	even	1	trivial
1690.2.d.l.1351.6		12	13.5	odd	4
1690.2.d.l.1351.12		12	13.8	odd	4
1690.2.e.u.191.1		12	13.3	even	3
1690.2.e.u.991.1		12	13.9	even	3
1690.2.e.v.191.1		12	13.10	even	6
1690.2.e.v.991.1		12	13.4	even	6
1690.2.l.n.361.6		24	13.6	odd	12
1690.2.l.n.361.10		24	13.7	odd	12
1690.2.l.n.1161.6		24	13.11	odd	12
1690.2.l.n.1161.10		24	13.2	odd	12
8450.2.a.cp.1.1		6	5.4	even	2
8450.2.a.cq.1.1		6	65.64	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.57254 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.57254 q^{6} +1.90403 q^{7} +1.00000 q^{8} +3.61798 q^{9} +1.00000 q^{10} +5.17658 q^{11} +2.57254 q^{12} +1.90403 q^{14} +2.57254 q^{15} +1.00000 q^{16} -5.89037 q^{17} +3.61798 q^{18} -8.09045 q^{19} +1.00000 q^{20} +4.89819 q^{21} +5.17658 q^{22} -0.908568 q^{23} +2.57254 q^{24} +1.00000 q^{25} +1.58977 q^{27} +1.90403 q^{28} -5.29954 q^{29} +2.57254 q^{30} -0.0626650 q^{31} +1.00000 q^{32} +13.3170 q^{33} -5.89037 q^{34} +1.90403 q^{35} +3.61798 q^{36} +1.63865 q^{37} -8.09045 q^{38} +1.00000 q^{40} +1.77061 q^{41} +4.89819 q^{42} -8.58977 q^{43} +5.17658 q^{44} +3.61798 q^{45} -0.908568 q^{46} -11.2024 q^{47} +2.57254 q^{48} -3.37468 q^{49} +1.00000 q^{50} -15.1532 q^{51} -8.92525 q^{53} +1.58977 q^{54} +5.17658 q^{55} +1.90403 q^{56} -20.8130 q^{57} -5.29954 q^{58} +10.6767 q^{59} +2.57254 q^{60} -0.681193 q^{61} -0.0626650 q^{62} +6.88873 q^{63} +1.00000 q^{64} +13.3170 q^{66} +14.1492 q^{67} -5.89037 q^{68} -2.33733 q^{69} +1.90403 q^{70} +15.7017 q^{71} +3.61798 q^{72} +0.163089 q^{73} +1.63865 q^{74} +2.57254 q^{75} -8.09045 q^{76} +9.85635 q^{77} +14.7178 q^{79} +1.00000 q^{80} -6.76417 q^{81} +1.77061 q^{82} -1.89246 q^{83} +4.89819 q^{84} -5.89037 q^{85} -8.58977 q^{86} -13.6333 q^{87} +5.17658 q^{88} -0.541298 q^{89} +3.61798 q^{90} -0.908568 q^{92} -0.161208 q^{93} -11.2024 q^{94} -8.09045 q^{95} +2.57254 q^{96} +12.8001 q^{97} -3.37468 q^{98} +18.7287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 3 q^{7} + 6 q^{8} + 16 q^{9} + 6 q^{10} + 15 q^{11} - 2 q^{12} + 3 q^{14} - 2 q^{15} + 6 q^{16} - 3 q^{17} + 16 q^{18} + q^{19} + 6 q^{20} - 2 q^{21}+ \cdots + 55 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 3 * q^7 + 6 * q^8 + 16 * q^9 + 6 * q^10 + 15 * q^11 - 2 * q^12 + 3 * q^14 - 2 * q^15 + 6 * q^16 - 3 * q^17 + 16 * q^18 + q^19 + 6 * q^20 - 2 * q^21 + 15 * q^22 - 3 * q^23 - 2 * q^24 + 6 * q^25 - 20 * q^27 + 3 * q^28 + 7 * q^29 - 2 * q^30 + 6 * q^32 + 4 * q^33 - 3 * q^34 + 3 * q^35 + 16 * q^36 + 6 * q^37 + q^38 + 6 * q^40 + 2 * q^41 - 2 * q^42 - 22 * q^43 + 15 * q^44 + 16 * q^45 - 3 * q^46 + 7 * q^47 - 2 * q^48 + 31 * q^49 + 6 * q^50 - 22 * q^51 - 16 * q^53 - 20 * q^54 + 15 * q^55 + 3 * q^56 + 2 * q^57 + 7 * q^58 + 15 * q^59 - 2 * q^60 + 33 * q^61 + 25 * q^63 + 6 * q^64 + 4 * q^66 - 8 * q^67 - 3 * q^68 - 6 * q^69 + 3 * q^70 + 40 * q^71 + 16 * q^72 + 21 * q^73 + 6 * q^74 - 2 * q^75 + q^76 - 34 * q^77 + 20 * q^79 + 6 * q^80 - 2 * q^81 + 2 * q^82 + 22 * q^83 - 2 * q^84 - 3 * q^85 - 22 * q^86 - 39 * q^87 + 15 * q^88 + 20 * q^89 + 16 * q^90 - 3 * q^92 + 48 * q^93 + 7 * q^94 + q^95 - 2 * q^96 - 7 * q^97 + 31 * q^98 + 55 * q^99

Introduction

L-functions

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