LMFDB - Embedded newform 4018.2.a.bs.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 17x^{8} + 36x^{7} + 75x^{6} - 174x^{5} - 69x^{4} + 260x^{3} - 104x^{2} - 24x + 14 $ x^10 - 2x^9 - 17x^8 + 36x^7 + 75x^6 - 174x^5 - 69x^4 + 260x^3 - 104x^2 - 24*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.84058$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.68800 q^{3} +1.00000 q^{4} +4.36119 q^{5} -1.68800 q^{6} -1.00000 q^{8} -0.150660 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.68800 q^{3} +1.00000 q^{4} +4.36119 q^{5} -1.68800 q^{6} -1.00000 q^{8} -0.150660 q^{9} -4.36119 q^{10} -0.568251 q^{11} +1.68800 q^{12} -3.23738 q^{13} +7.36168 q^{15} +1.00000 q^{16} +7.22529 q^{17} +0.150660 q^{18} +3.92993 q^{19} +4.36119 q^{20} +0.568251 q^{22} +0.128528 q^{23} -1.68800 q^{24} +14.0200 q^{25} +3.23738 q^{26} -5.31831 q^{27} +0.183326 q^{29} -7.36168 q^{30} -0.398097 q^{31} -1.00000 q^{32} -0.959207 q^{33} -7.22529 q^{34} -0.150660 q^{36} +1.28439 q^{37} -3.92993 q^{38} -5.46469 q^{39} -4.36119 q^{40} +1.00000 q^{41} +6.36258 q^{43} -0.568251 q^{44} -0.657058 q^{45} -0.128528 q^{46} -1.38086 q^{47} +1.68800 q^{48} -14.0200 q^{50} +12.1963 q^{51} -3.23738 q^{52} -4.31697 q^{53} +5.31831 q^{54} -2.47825 q^{55} +6.63372 q^{57} -0.183326 q^{58} -0.102854 q^{59} +7.36168 q^{60} -4.87703 q^{61} +0.398097 q^{62} +1.00000 q^{64} -14.1188 q^{65} +0.959207 q^{66} -2.57453 q^{67} +7.22529 q^{68} +0.216955 q^{69} +10.7148 q^{71} +0.150660 q^{72} -13.9065 q^{73} -1.28439 q^{74} +23.6657 q^{75} +3.92993 q^{76} +5.46469 q^{78} +6.53994 q^{79} +4.36119 q^{80} -8.52532 q^{81} -1.00000 q^{82} +1.98887 q^{83} +31.5109 q^{85} -6.36258 q^{86} +0.309454 q^{87} +0.568251 q^{88} -5.16073 q^{89} +0.657058 q^{90} +0.128528 q^{92} -0.671988 q^{93} +1.38086 q^{94} +17.1392 q^{95} -1.68800 q^{96} +13.2049 q^{97} +0.0856129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 20 * q^17 - 10 * q^18 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 16 * q^27 - 4 * q^29 - 4 * q^30 - 4 * q^31 - 10 * q^32 + 36 * q^33 - 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 - 4 * q^40 + 10 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 4 * q^46 + 24 * q^47 + 4 * q^48 - 6 * q^50 + 20 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^54 + 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 + 4 * q^62 + 10 * q^64 - 12 * q^65 - 36 * q^66 + 8 * q^67 + 20 * q^68 + 4 * q^71 - 10 * q^72 - 24 * q^73 + 16 * q^74 + 48 * q^75 - 20 * q^78 + 24 * q^79 + 4 * q^80 - 18 * q^81 - 10 * q^82 + 48 * q^83 + 8 * q^85 + 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 24 * q^94 - 4 * q^95 - 4 * q^96 + 4 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

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
$3$	1.68800	0.974567	0.487283	−	0.873244i	$-0.337988\pi$
$3$	1.68800	0.974567	0.487283	+	0.873244i	$0.337988\pi$
$4$	1.00000	0.500000
$5$	4.36119	1.95038	0.975191	−	0.221365i	$-0.0710511\pi$
$5$	4.36119	1.95038	0.975191	+	0.221365i	$0.0710511\pi$
$6$	−1.68800	−0.689123
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−0.150660	−0.0502201
$10$	−4.36119	−1.37913
$11$	−0.568251	−0.171334	−0.0856671	−	0.996324i	$-0.527302\pi$
$11$	−0.568251	−0.171334	−0.0856671	+	0.996324i	$0.527302\pi$
$12$	1.68800	0.487283
$13$	−3.23738	−0.897888	−0.448944	−	0.893560i	$-0.648200\pi$
$13$	−3.23738	−0.897888	−0.448944	+	0.893560i	$0.648200\pi$
$14$	0	0
$15$	7.36168	1.90078
$16$	1.00000	0.250000
$17$	7.22529	1.75239	0.876196	−	0.481955i	$-0.160073\pi$
$17$	7.22529	1.75239	0.876196	+	0.481955i	$0.160073\pi$
$18$	0.150660	0.0355110
$19$	3.92993	0.901588	0.450794	−	0.892628i	$-0.351141\pi$
$19$	3.92993	0.901588	0.450794	+	0.892628i	$0.351141\pi$
$20$	4.36119	0.975191
$21$	0	0
$22$	0.568251	0.121152
$23$	0.128528	0.0268000	0.0134000	−	0.999910i	$-0.495735\pi$
$23$	0.128528	0.0268000	0.0134000	+	0.999910i	$0.495735\pi$
$24$	−1.68800	−0.344561
$25$	14.0200	2.80399
$26$	3.23738	0.634903
$27$	−5.31831	−1.02351
$28$	0	0
$29$	0.183326	0.0340428	0.0170214	−	0.999855i	$-0.494582\pi$
$29$	0.183326	0.0340428	0.0170214	+	0.999855i	$0.494582\pi$
$30$	−7.36168	−1.34405
$31$	−0.398097	−0.0715004	−0.0357502	−	0.999361i	$-0.511382\pi$
$31$	−0.398097	−0.0715004	−0.0357502	+	0.999361i	$0.511382\pi$
$32$	−1.00000	−0.176777
$33$	−0.959207	−0.166977
$34$	−7.22529	−1.23913
$35$	0	0
$36$	−0.150660	−0.0251100
$37$	1.28439	0.211152	0.105576	−	0.994411i	$-0.466331\pi$
$37$	1.28439	0.211152	0.105576	+	0.994411i	$0.466331\pi$
$38$	−3.92993	−0.637519
$39$	−5.46469	−0.875051
$40$	−4.36119	−0.689564
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	6.36258	0.970284	0.485142	−	0.874435i	$-0.338768\pi$
$43$	6.36258	0.970284	0.485142	+	0.874435i	$0.338768\pi$
$44$	−0.568251	−0.0856671
$45$	−0.657058	−0.0979484
$46$	−0.128528	−0.0189504
$47$	−1.38086	−0.201419	−0.100710	−	0.994916i	$-0.532111\pi$
$47$	−1.38086	−0.201419	−0.100710	+	0.994916i	$0.532111\pi$
$48$	1.68800	0.243642
$49$	0	0
$50$	−14.0200	−1.98272
$51$	12.1963	1.70782
$52$	−3.23738	−0.448944
$53$	−4.31697	−0.592982	−0.296491	−	0.955036i	$-0.595816\pi$
$53$	−4.31697	−0.592982	−0.296491	+	0.955036i	$0.595816\pi$
$54$	5.31831	0.723730
$55$	−2.47825	−0.334167
$56$	0	0
$57$	6.63372	0.878658
$58$	−0.183326	−0.0240719
$59$	−0.102854	−0.0133904	−0.00669519	−	0.999978i	$-0.502131\pi$
$59$	−0.102854	−0.0133904	−0.00669519	+	0.999978i	$0.502131\pi$
$60$	7.36168	0.950389
$61$	−4.87703	−0.624440	−0.312220	−	0.950010i	$-0.601073\pi$
$61$	−4.87703	−0.624440	−0.312220	+	0.950010i	$0.601073\pi$
$62$	0.398097	0.0505584
$63$	0	0
$64$	1.00000	0.125000
$65$	−14.1188	−1.75122
$66$	0.959207	0.118070
$67$	−2.57453	−0.314529	−0.157265	−	0.987557i	$-0.550268\pi$
$67$	−2.57453	−0.314529	−0.157265	+	0.987557i	$0.550268\pi$
$68$	7.22529	0.876196
$69$	0.216955	0.0261183
$70$	0	0
$71$	10.7148	1.27162	0.635808	−	0.771848i	$-0.280667\pi$
$71$	10.7148	1.27162	0.635808	+	0.771848i	$0.280667\pi$
$72$	0.150660	0.0177555
$73$	−13.9065	−1.62764	−0.813818	−	0.581120i	$-0.802615\pi$
$73$	−13.9065	−1.62764	−0.813818	+	0.581120i	$0.802615\pi$
$74$	−1.28439	−0.149307
$75$	23.6657	2.73268
$76$	3.92993	0.450794
$77$	0	0
$78$	5.46469	0.618755
$79$	6.53994	0.735801	0.367901	−	0.929865i	$-0.380077\pi$
$79$	6.53994	0.735801	0.367901	+	0.929865i	$0.380077\pi$
$80$	4.36119	0.487596
$81$	−8.52532	−0.947258
$82$	−1.00000	−0.110432
$83$	1.98887	0.218307	0.109154	−	0.994025i	$-0.465186\pi$
$83$	1.98887	0.218307	0.109154	+	0.994025i	$0.465186\pi$
$84$	0	0
$85$	31.5109	3.41783
$86$	−6.36258	−0.686094
$87$	0.309454	0.0331769
$88$	0.568251	0.0605758
$89$	−5.16073	−0.547036	−0.273518	−	0.961867i	$-0.588187\pi$
$89$	−5.16073	−0.547036	−0.273518	+	0.961867i	$0.588187\pi$
$90$	0.657058	0.0692600
$91$	0	0
$92$	0.128528	0.0134000
$93$	−0.671988	−0.0696819
$94$	1.38086	0.142425
$95$	17.1392	1.75844
$96$	−1.68800	−0.172281
$97$	13.2049	1.34075	0.670377	−	0.742021i	$-0.266133\pi$
$97$	13.2049	1.34075	0.670377	+	0.742021i	$0.266133\pi$
$98$	0	0
$99$	0.0856129	0.00860442
$100$	14.0200	1.40200
$101$	−11.2477	−1.11919	−0.559596	−	0.828766i	$-0.689044\pi$
$101$	−11.2477	−1.11919	−0.559596	+	0.828766i	$0.689044\pi$
$102$	−12.1963	−1.20761
$103$	11.3912	1.12241	0.561203	−	0.827678i	$-0.310339\pi$
$103$	11.3912	1.12241	0.561203	+	0.827678i	$0.310339\pi$
$104$	3.23738	0.317451
$105$	0	0
$106$	4.31697	0.419302
$107$	20.5761	1.98917	0.994585	−	0.103923i	$-0.0331394\pi$
$107$	20.5761	1.98917	0.994585	+	0.103923i	$0.0331394\pi$
$108$	−5.31831	−0.511755
$109$	8.94984	0.857239	0.428619	−	0.903485i	$-0.359000\pi$
$109$	8.94984	0.857239	0.428619	+	0.903485i	$0.359000\pi$
$110$	2.47825	0.236292
$111$	2.16804	0.205782
$112$	0	0
$113$	−11.3001	−1.06302	−0.531512	−	0.847051i	$-0.678376\pi$
$113$	−11.3001	−1.06302	−0.531512	+	0.847051i	$0.678376\pi$
$114$	−6.63372	−0.621305
$115$	0.560535	0.0522702
$116$	0.183326	0.0170214
$117$	0.487745	0.0450920
$118$	0.102854	0.00946844
$119$	0	0
$120$	−7.36168	−0.672026
$121$	−10.6771	−0.970645
$122$	4.87703	0.441545
$123$	1.68800	0.152202
$124$	−0.398097	−0.0357502
$125$	39.3377	3.51847
$126$	0	0
$127$	10.9820	0.974491	0.487245	−	0.873265i	$-0.338002\pi$
$127$	10.9820	0.974491	0.487245	+	0.873265i	$0.338002\pi$
$128$	−1.00000	−0.0883883
$129$	10.7400	0.945606
$130$	14.1188	1.23830
$131$	−16.4688	−1.43889	−0.719443	−	0.694552i	$-0.755603\pi$
$131$	−16.4688	−1.43889	−0.719443	+	0.694552i	$0.755603\pi$
$132$	−0.959207	−0.0834883
$133$	0	0
$134$	2.57453	0.222406
$135$	−23.1941	−1.99623
$136$	−7.22529	−0.619564
$137$	0.0388554	0.00331964	0.00165982	−	0.999999i	$-0.499472\pi$
$137$	0.0388554	0.00331964	0.00165982	+	0.999999i	$0.499472\pi$
$138$	−0.216955	−0.0184685
$139$	16.9486	1.43756	0.718780	−	0.695237i	$-0.244701\pi$
$139$	16.9486	1.43756	0.718780	+	0.695237i	$0.244701\pi$
$140$	0	0
$141$	−2.33089	−0.196296
$142$	−10.7148	−0.899168
$143$	1.83965	0.153839
$144$	−0.150660	−0.0125550
$145$	0.799518	0.0663964
$146$	13.9065	1.15091
$147$	0	0
$148$	1.28439	0.105576
$149$	−0.304695	−0.0249616	−0.0124808	−	0.999922i	$-0.503973\pi$
$149$	−0.304695	−0.0249616	−0.0124808	+	0.999922i	$0.503973\pi$
$150$	−23.6657	−1.93229
$151$	18.8515	1.53411	0.767056	−	0.641580i	$-0.221721\pi$
$151$	18.8515	1.53411	0.767056	+	0.641580i	$0.221721\pi$
$152$	−3.92993	−0.318760
$153$	−1.08857	−0.0880053
$154$	0	0
$155$	−1.73618	−0.139453
$156$	−5.46469	−0.437526
$157$	−14.8641	−1.18628	−0.593142	−	0.805098i	$-0.702113\pi$
$157$	−14.8641	−1.18628	−0.593142	+	0.805098i	$0.702113\pi$
$158$	−6.53994	−0.520290
$159$	−7.28705	−0.577900
$160$	−4.36119	−0.344782
$161$	0	0
$162$	8.52532	0.669812
$163$	−18.2525	−1.42964	−0.714822	−	0.699306i	$-0.753492\pi$
$163$	−18.2525	−1.42964	−0.714822	+	0.699306i	$0.753492\pi$
$164$	1.00000	0.0780869
$165$	−4.18328	−0.325668
$166$	−1.98887	−0.154367
$167$	2.25023	0.174128	0.0870639	−	0.996203i	$-0.472252\pi$
$167$	2.25023	0.174128	0.0870639	+	0.996203i	$0.472252\pi$
$168$	0	0
$169$	−2.51937	−0.193798
$170$	−31.5109	−2.41677
$171$	−0.592085	−0.0452779
$172$	6.36258	0.485142
$173$	9.22947	0.701704	0.350852	−	0.936431i	$-0.385892\pi$
$173$	9.22947	0.701704	0.350852	+	0.936431i	$0.385892\pi$
$174$	−0.309454	−0.0234596
$175$	0	0
$176$	−0.568251	−0.0428335
$177$	−0.173617	−0.0130498
$178$	5.16073	0.386813
$179$	−18.1291	−1.35503	−0.677514	−	0.735510i	$-0.736943\pi$
$179$	−18.1291	−1.35503	−0.677514	+	0.735510i	$0.736943\pi$
$180$	−0.657058	−0.0489742
$181$	−3.23967	−0.240803	−0.120401	−	0.992725i	$-0.538418\pi$
$181$	−3.23967	−0.240803	−0.120401	+	0.992725i	$0.538418\pi$
$182$	0	0
$183$	−8.23242	−0.608558
$184$	−0.128528	−0.00947522
$185$	5.60145	0.411827
$186$	0.671988	0.0492725
$187$	−4.10578	−0.300245
$188$	−1.38086	−0.100710
$189$	0	0
$190$	−17.1392	−1.24341
$191$	−23.5363	−1.70302	−0.851512	−	0.524335i	$-0.824314\pi$
$191$	−23.5363	−1.70302	−0.851512	+	0.524335i	$0.824314\pi$
$192$	1.68800	0.121821
$193$	−17.8787	−1.28694	−0.643470	−	0.765471i	$-0.722506\pi$
$193$	−17.8787	−1.28694	−0.643470	+	0.765471i	$0.722506\pi$
$194$	−13.2049	−0.948056
$195$	−23.8326	−1.70668
$196$	0	0
$197$	−4.64590	−0.331006	−0.165503	−	0.986209i	$-0.552925\pi$
$197$	−4.64590	−0.331006	−0.165503	+	0.986209i	$0.552925\pi$
$198$	−0.0856129	−0.00608424
$199$	23.6435	1.67604	0.838022	−	0.545637i	$-0.183712\pi$
$199$	23.6435	1.67604	0.838022	+	0.545637i	$0.183712\pi$
$200$	−14.0200	−0.991361
$201$	−4.34581	−0.306530
$202$	11.2477	0.791388
$203$	0	0
$204$	12.1963	0.853911
$205$	4.36119	0.304599
$206$	−11.3912	−0.793660
$207$	−0.0193641	−0.00134590
$208$	−3.23738	−0.224472
$209$	−2.23319	−0.154473
$210$	0	0
$211$	−9.32982	−0.642291	−0.321146	−	0.947030i	$-0.604068\pi$
$211$	−9.32982	−0.642291	−0.321146	+	0.947030i	$0.604068\pi$
$212$	−4.31697	−0.296491
$213$	18.0866	1.23927
$214$	−20.5761	−1.40656
$215$	27.7484	1.89242
$216$	5.31831	0.361865
$217$	0	0
$218$	−8.94984	−0.606159
$219$	−23.4742	−1.58624
$220$	−2.47825	−0.167084
$221$	−23.3910	−1.57345
$222$	−2.16804	−0.145510
$223$	12.1819	0.815760	0.407880	−	0.913036i	$-0.366268\pi$
$223$	12.1819	0.815760	0.407880	+	0.913036i	$0.366268\pi$
$224$	0	0
$225$	−2.11225	−0.140817
$226$	11.3001	0.751672
$227$	−27.8669	−1.84959	−0.924795	−	0.380465i	$-0.875764\pi$
$227$	−27.8669	−1.84959	−0.924795	+	0.380465i	$0.875764\pi$
$228$	6.63372	0.439329
$229$	−16.4877	−1.08954	−0.544770	−	0.838586i	$-0.683383\pi$
$229$	−16.4877	−1.08954	−0.544770	+	0.838586i	$0.683383\pi$
$230$	−0.560535	−0.0369606
$231$	0	0
$232$	−0.183326	−0.0120359
$233$	21.5069	1.40896	0.704481	−	0.709723i	$-0.251180\pi$
$233$	21.5069	1.40896	0.704481	+	0.709723i	$0.251180\pi$
$234$	−0.487745	−0.0318849
$235$	−6.02219	−0.392844
$236$	−0.102854	−0.00669519
$237$	11.0394	0.717087
$238$	0	0
$239$	20.7553	1.34255	0.671276	−	0.741208i	$-0.265747\pi$
$239$	20.7553	1.34255	0.671276	+	0.741208i	$0.265747\pi$
$240$	7.36168	0.475194
$241$	28.2920	1.82245	0.911224	−	0.411912i	$-0.135139\pi$
$241$	28.2920	1.82245	0.911224	+	0.411912i	$0.135139\pi$
$242$	10.6771	0.686349
$243$	1.56420	0.100344
$244$	−4.87703	−0.312220
$245$	0	0
$246$	−1.68800	−0.107623
$247$	−12.7227	−0.809525
$248$	0.398097	0.0252792
$249$	3.35722	0.212755
$250$	−39.3377	−2.48794
$251$	−13.8593	−0.874788	−0.437394	−	0.899270i	$-0.644098\pi$
$251$	−13.8593	−0.874788	−0.437394	+	0.899270i	$0.644098\pi$
$252$	0	0
$253$	−0.0730362	−0.00459175
$254$	−10.9820	−0.689069
$255$	53.1903	3.33091
$256$	1.00000	0.0625000
$257$	29.2267	1.82311	0.911557	−	0.411173i	$-0.134881\pi$
$257$	29.2267	1.82311	0.911557	+	0.411173i	$0.134881\pi$
$258$	−10.7400	−0.668644
$259$	0	0
$260$	−14.1188	−0.875612
$261$	−0.0276199	−0.00170963
$262$	16.4688	1.01745
$263$	−11.9224	−0.735166	−0.367583	−	0.929991i	$-0.619815\pi$
$263$	−11.9224	−0.735166	−0.367583	+	0.929991i	$0.619815\pi$
$264$	0.959207	0.0590351
$265$	−18.8271	−1.15654
$266$	0	0
$267$	−8.71130	−0.533123
$268$	−2.57453	−0.157265
$269$	−10.4083	−0.634606	−0.317303	−	0.948324i	$-0.602777\pi$
$269$	−10.4083	−0.634606	−0.317303	+	0.948324i	$0.602777\pi$
$270$	23.1941	1.41155
$271$	−21.1785	−1.28650	−0.643252	−	0.765654i	$-0.722415\pi$
$271$	−21.1785	−1.28650	−0.643252	+	0.765654i	$0.722415\pi$
$272$	7.22529	0.438098
$273$	0	0
$274$	−0.0388554	−0.00234734
$275$	−7.96686	−0.480419
$276$	0.216955	0.0130592
$277$	−13.3077	−0.799580	−0.399790	−	0.916607i	$-0.630917\pi$
$277$	−13.3077	−0.799580	−0.399790	+	0.916607i	$0.630917\pi$
$278$	−16.9486	−1.01651
$279$	0.0599775	0.00359076
$280$	0	0
$281$	8.66253	0.516763	0.258382	−	0.966043i	$-0.416811\pi$
$281$	8.66253	0.516763	0.258382	+	0.966043i	$0.416811\pi$
$282$	2.33089	0.138803
$283$	3.72440	0.221393	0.110696	−	0.993854i	$-0.464692\pi$
$283$	3.72440	0.221393	0.110696	+	0.993854i	$0.464692\pi$
$284$	10.7148	0.635808
$285$	28.9309	1.71372
$286$	−1.83965	−0.108780
$287$	0	0
$288$	0.150660	0.00887774
$289$	35.2049	2.07088
$290$	−0.799518	−0.0469493
$291$	22.2898	1.30665
$292$	−13.9065	−0.813818
$293$	10.1937	0.595523	0.297762	−	0.954640i	$-0.403760\pi$
$293$	10.1937	0.595523	0.297762	+	0.954640i	$0.403760\pi$
$294$	0	0
$295$	−0.448564	−0.0261164
$296$	−1.28439	−0.0746535
$297$	3.02214	0.175362
$298$	0.304695	0.0176505
$299$	−0.416094	−0.0240634
$300$	23.6657	1.36634
$301$	0	0
$302$	−18.8515	−1.08478
$303$	−18.9862	−1.09073
$304$	3.92993	0.225397
$305$	−21.2696	−1.21790
$306$	1.08857	0.0622291
$307$	−30.8317	−1.75966	−0.879828	−	0.475291i	$-0.842343\pi$
$307$	−30.8317	−1.75966	−0.879828	+	0.475291i	$0.842343\pi$
$308$	0	0
$309$	19.2283	1.09386
$310$	1.73618	0.0986082
$311$	16.7139	0.947756	0.473878	−	0.880591i	$-0.342854\pi$
$311$	16.7139	0.947756	0.473878	+	0.880591i	$0.342854\pi$
$312$	5.46469	0.309377
$313$	−17.2890	−0.977232	−0.488616	−	0.872499i	$-0.662498\pi$
$313$	−17.2890	−0.977232	−0.488616	+	0.872499i	$0.662498\pi$
$314$	14.8641	0.838829
$315$	0	0
$316$	6.53994	0.367901
$317$	−7.85240	−0.441035	−0.220517	−	0.975383i	$-0.570775\pi$
$317$	−7.85240	−0.441035	−0.220517	+	0.975383i	$0.570775\pi$
$318$	7.28705	0.408637
$319$	−0.104175	−0.00583269
$320$	4.36119	0.243798
$321$	34.7325	1.93858
$322$	0	0
$323$	28.3949	1.57994
$324$	−8.52532	−0.473629
$325$	−45.3879	−2.51767
$326$	18.2525	1.01091
$327$	15.1073	0.835436
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	4.18328	0.230282
$331$	7.63292	0.419543	0.209772	−	0.977750i	$-0.432728\pi$
$331$	7.63292	0.419543	0.209772	+	0.977750i	$0.432728\pi$
$332$	1.98887	0.109154
$333$	−0.193506	−0.0106041
$334$	−2.25023	−0.123127
$335$	−11.2280	−0.613452
$336$	0	0
$337$	−15.7465	−0.857764	−0.428882	−	0.903361i	$-0.641092\pi$
$337$	−15.7465	−0.857764	−0.428882	+	0.903361i	$0.641092\pi$
$338$	2.51937	0.137036
$339$	−19.0746	−1.03599
$340$	31.5109	1.70892
$341$	0.226219	0.0122505
$342$	0.592085	0.0320163
$343$	0	0
$344$	−6.36258	−0.343047
$345$	0.946182	0.0509408
$346$	−9.22947	−0.496180
$347$	5.04569	0.270867	0.135433	−	0.990786i	$-0.456757\pi$
$347$	5.04569	0.270867	0.135433	+	0.990786i	$0.456757\pi$
$348$	0.309454	0.0165885
$349$	23.5627	1.26128	0.630640	−	0.776075i	$-0.282792\pi$
$349$	23.5627	1.26128	0.630640	+	0.776075i	$0.282792\pi$
$350$	0	0
$351$	17.2174	0.918997
$352$	0.568251	0.0302879
$353$	−32.1346	−1.71035	−0.855176	−	0.518338i	$-0.826551\pi$
$353$	−32.1346	−1.71035	−0.855176	+	0.518338i	$0.826551\pi$
$354$	0.173617	0.00922762
$355$	46.7293	2.48014
$356$	−5.16073	−0.273518
$357$	0	0
$358$	18.1291	0.958150
$359$	−11.1055	−0.586125	−0.293062	−	0.956093i	$-0.594674\pi$
$359$	−11.1055	−0.586125	−0.293062	+	0.956093i	$0.594674\pi$
$360$	0.657058	0.0346300
$361$	−3.55563	−0.187139
$362$	3.23967	0.170273
$363$	−18.0229	−0.945958
$364$	0	0
$365$	−60.6490	−3.17451
$366$	8.23242	0.430315
$367$	27.9981	1.46149	0.730744	−	0.682651i	$-0.239173\pi$
$367$	27.9981	1.46149	0.730744	+	0.682651i	$0.239173\pi$
$368$	0.128528	0.00669999
$369$	−0.150660	−0.00784306
$370$	−5.60145	−0.291206
$371$	0	0
$372$	−0.671988	−0.0348409
$373$	−11.8648	−0.614335	−0.307168	−	0.951655i	$-0.599381\pi$
$373$	−11.8648	−0.614335	−0.307168	+	0.951655i	$0.599381\pi$
$374$	4.10578	0.212305
$375$	66.4020	3.42899
$376$	1.38086	0.0712124
$377$	−0.593495	−0.0305666
$378$	0	0
$379$	−26.8697	−1.38021	−0.690103	−	0.723712i	$-0.742435\pi$
$379$	−26.8697	−1.38021	−0.690103	+	0.723712i	$0.742435\pi$
$380$	17.1392	0.879221
$381$	18.5375	0.949706
$382$	23.5363	1.20422
$383$	24.2386	1.23853	0.619266	−	0.785181i	$-0.287430\pi$
$383$	24.2386	1.23853	0.619266	+	0.785181i	$0.287430\pi$
$384$	−1.68800	−0.0861403
$385$	0	0
$386$	17.8787	0.910004
$387$	−0.958588	−0.0487277
$388$	13.2049	0.670377
$389$	−8.45054	−0.428459	−0.214230	−	0.976783i	$-0.568724\pi$
$389$	−8.45054	−0.428459	−0.214230	+	0.976783i	$0.568724\pi$
$390$	23.8326	1.20681
$391$	0.928653	0.0469640
$392$	0	0
$393$	−27.7993	−1.40229
$394$	4.64590	0.234057
$395$	28.5219	1.43509
$396$	0.0856129	0.00430221
$397$	−26.7709	−1.34359	−0.671796	−	0.740737i	$-0.734477\pi$
$397$	−26.7709	−1.34359	−0.671796	+	0.740737i	$0.734477\pi$
$398$	−23.6435	−1.18514
$399$	0	0
$400$	14.0200	0.700998
$401$	2.26458	0.113088	0.0565438	−	0.998400i	$-0.481992\pi$
$401$	2.26458	0.113088	0.0565438	+	0.998400i	$0.481992\pi$
$402$	4.34581	0.216749
$403$	1.28879	0.0641993
$404$	−11.2477	−0.559596
$405$	−37.1805	−1.84751
$406$	0	0
$407$	−0.729854	−0.0361775
$408$	−12.1963	−0.603806
$409$	−0.808014	−0.0399537	−0.0199769	−	0.999800i	$-0.506359\pi$
$409$	−0.808014	−0.0399537	−0.0199769	+	0.999800i	$0.506359\pi$
$410$	−4.36119	−0.215384
$411$	0.0655878	0.00323521
$412$	11.3912	0.561203
$413$	0	0
$414$	0.0193641	0.000951693 0
$415$	8.67385	0.425783
$416$	3.23738	0.158726
$417$	28.6092	1.40100
$418$	2.23319	0.109229
$419$	−8.94624	−0.437052	−0.218526	−	0.975831i	$-0.570125\pi$
$419$	−8.94624	−0.437052	−0.218526	+	0.975831i	$0.570125\pi$
$420$	0	0
$421$	23.7303	1.15654	0.578271	−	0.815844i	$-0.303727\pi$
$421$	23.7303	1.15654	0.578271	+	0.815844i	$0.303727\pi$
$422$	9.32982	0.454168
$423$	0.208041	0.0101153
$424$	4.31697	0.209651
$425$	101.298	4.91369
$426$	−18.0866	−0.876299
$427$	0	0
$428$	20.5761	0.994585
$429$	3.10532	0.149926
$430$	−27.7484	−1.33815
$431$	−23.2112	−1.11804	−0.559021	−	0.829153i	$-0.688823\pi$
$431$	−23.2112	−1.11804	−0.559021	+	0.829153i	$0.688823\pi$
$432$	−5.31831	−0.255877
$433$	19.9734	0.959859	0.479930	−	0.877307i	$-0.340662\pi$
$433$	19.9734	0.959859	0.479930	+	0.877307i	$0.340662\pi$
$434$	0	0
$435$	1.34959	0.0647077
$436$	8.94984	0.428619
$437$	0.505107	0.0241625
$438$	23.4742	1.12164
$439$	−30.0376	−1.43362	−0.716808	−	0.697270i	$-0.754398\pi$
$439$	−30.0376	−1.43362	−0.716808	+	0.697270i	$0.754398\pi$
$440$	2.47825	0.118146
$441$	0	0
$442$	23.3910	1.11260
$443$	−2.84568	−0.135202	−0.0676011	−	0.997712i	$-0.521535\pi$
$443$	−2.84568	−0.135202	−0.0676011	+	0.997712i	$0.521535\pi$
$444$	2.16804	0.102891
$445$	−22.5069	−1.06693
$446$	−12.1819	−0.576830
$447$	−0.514324	−0.0243267
$448$	0	0
$449$	−10.4593	−0.493607	−0.246804	−	0.969066i	$-0.579380\pi$
$449$	−10.4593	−0.493607	−0.246804	+	0.969066i	$0.579380\pi$
$450$	2.11225	0.0995724
$451$	−0.568251	−0.0267579
$452$	−11.3001	−0.531512
$453$	31.8213	1.49509
$454$	27.8669	1.30786
$455$	0	0
$456$	−6.63372	−0.310652
$457$	−13.7405	−0.642755	−0.321377	−	0.946951i	$-0.604146\pi$
$457$	−13.7405	−0.642755	−0.321377	+	0.946951i	$0.604146\pi$
$458$	16.4877	0.770421
$459$	−38.4264	−1.79359
$460$	0.560535	0.0261351
$461$	−14.1512	−0.659087	−0.329543	−	0.944140i	$-0.606895\pi$
$461$	−14.1512	−0.659087	−0.329543	+	0.944140i	$0.606895\pi$
$462$	0	0
$463$	−4.16820	−0.193713	−0.0968563	−	0.995298i	$-0.530879\pi$
$463$	−4.16820	−0.193713	−0.0968563	+	0.995298i	$0.530879\pi$
$464$	0.183326	0.00851069
$465$	−2.93066	−0.135906
$466$	−21.5069	−0.996287
$467$	37.7772	1.74812	0.874060	−	0.485818i	$-0.161478\pi$
$467$	37.7772	1.74812	0.874060	+	0.485818i	$0.161478\pi$
$468$	0.487745	0.0225460
$469$	0	0
$470$	6.02219	0.277783
$471$	−25.0906	−1.15611
$472$	0.102854	0.00473422
$473$	−3.61554	−0.166243
$474$	−11.0394	−0.507057
$475$	55.0975	2.52805
$476$	0	0
$477$	0.650397	0.0297796
$478$	−20.7553	−0.949328
$479$	26.3641	1.20461	0.602304	−	0.798267i	$-0.294250\pi$
$479$	26.3641	1.20461	0.602304	+	0.798267i	$0.294250\pi$
$480$	−7.36168	−0.336013
$481$	−4.15805	−0.189591
$482$	−28.2920	−1.28867
$483$	0	0
$484$	−10.6771	−0.485322
$485$	57.5890	2.61498
$486$	−1.56420	−0.0709536
$487$	−21.6225	−0.979809	−0.489904	−	0.871776i	$-0.662968\pi$
$487$	−21.6225	−0.979809	−0.489904	+	0.871776i	$0.662968\pi$
$488$	4.87703	0.220773
$489$	−30.8102	−1.39328
$490$	0	0
$491$	35.1542	1.58649	0.793243	−	0.608905i	$-0.208391\pi$
$491$	35.1542	1.58649	0.793243	+	0.608905i	$0.208391\pi$
$492$	1.68800	0.0761009
$493$	1.32458	0.0596562
$494$	12.7227	0.572421
$495$	0.373374	0.0167819
$496$	−0.398097	−0.0178751
$497$	0	0
$498$	−3.35722	−0.150441
$499$	−18.6545	−0.835091	−0.417545	−	0.908656i	$-0.637109\pi$
$499$	−18.6545	−0.835091	−0.417545	+	0.908656i	$0.637109\pi$
$500$	39.3377	1.75924
$501$	3.79838	0.169699
$502$	13.8593	0.618569
$503$	30.3997	1.35545	0.677727	−	0.735313i	$-0.262965\pi$
$503$	30.3997	1.35545	0.677727	+	0.735313i	$0.262965\pi$
$504$	0	0
$505$	−49.0535	−2.18285
$506$	0.0730362	0.00324686
$507$	−4.25269	−0.188869
$508$	10.9820	0.487245
$509$	−35.5496	−1.57571	−0.787853	−	0.615863i	$-0.788808\pi$
$509$	−35.5496	−1.57571	−0.787853	+	0.615863i	$0.788808\pi$
$510$	−53.1903	−2.35531
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−20.9006	−0.922784
$514$	−29.2267	−1.28914
$515$	49.6790	2.18912
$516$	10.7400	0.472803
$517$	0.784676	0.0345100
$518$	0	0
$519$	15.5793	0.683857
$520$	14.1188	0.619151
$521$	−28.8828	−1.26538	−0.632689	−	0.774406i	$-0.718049\pi$
$521$	−28.8828	−1.26538	−0.632689	+	0.774406i	$0.718049\pi$
$522$	0.0276199	0.00120889
$523$	3.28831	0.143788	0.0718939	−	0.997412i	$-0.477096\pi$
$523$	3.28831	0.143788	0.0718939	+	0.997412i	$0.477096\pi$
$524$	−16.4688	−0.719443
$525$	0	0
$526$	11.9224	0.519841
$527$	−2.87637	−0.125297
$528$	−0.959207	−0.0417441
$529$	−22.9835	−0.999282
$530$	18.8271	0.817799
$531$	0.0154959	0.000672467 0
$532$	0	0
$533$	−3.23738	−0.140227
$534$	8.71130	0.376975
$535$	89.7364	3.87964
$536$	2.57453	0.111203
$537$	−30.6018	−1.32057
$538$	10.4083	0.448734
$539$	0	0
$540$	−23.1941	−0.998117
$541$	36.9446	1.58837	0.794187	−	0.607674i	$-0.207897\pi$
$541$	36.9446	1.58837	0.794187	+	0.607674i	$0.207897\pi$
$542$	21.1785	0.909696
$543$	−5.46856	−0.234678
$544$	−7.22529	−0.309782
$545$	39.0319	1.67194
$546$	0	0
$547$	−38.3036	−1.63774	−0.818871	−	0.573977i	$-0.805400\pi$
$547$	−38.3036	−1.63774	−0.818871	+	0.573977i	$0.805400\pi$
$548$	0.0388554	0.00165982
$549$	0.734775	0.0313594
$550$	7.96686	0.339708
$551$	0.720458	0.0306925
$552$	−0.216955	−0.00923423
$553$	0	0
$554$	13.3077	0.565389
$555$	9.45524	0.401353
$556$	16.9486	0.718780
$557$	7.92940	0.335979	0.167990	−	0.985789i	$-0.446272\pi$
$557$	7.92940	0.335979	0.167990	+	0.985789i	$0.446272\pi$
$558$	−0.0599775	−0.00253905
$559$	−20.5981	−0.871206
$560$	0	0
$561$	−6.93055	−0.292608
$562$	−8.66253	−0.365407
$563$	41.8418	1.76342	0.881710	−	0.471792i	$-0.156393\pi$
$563$	41.8418	1.76342	0.881710	+	0.471792i	$0.156393\pi$
$564$	−2.33089	−0.0981482
$565$	−49.2819	−2.07330
$566$	−3.72440	−0.156548
$567$	0	0
$568$	−10.7148	−0.449584
$569$	36.0079	1.50953	0.754764	−	0.655996i	$-0.227751\pi$
$569$	36.0079	1.50953	0.754764	+	0.655996i	$0.227751\pi$
$570$	−28.9309	−1.21178
$571$	23.3915	0.978903	0.489452	−	0.872030i	$-0.337197\pi$
$571$	23.3915	0.978903	0.489452	+	0.872030i	$0.337197\pi$
$572$	1.83965	0.0769194
$573$	−39.7292	−1.65971
$574$	0	0
$575$	1.80196	0.0751468
$576$	−0.150660	−0.00627751
$577$	−2.89328	−0.120449	−0.0602244	−	0.998185i	$-0.519182\pi$
$577$	−2.89328	−0.120449	−0.0602244	+	0.998185i	$0.519182\pi$
$578$	−35.2049	−1.46433
$579$	−30.1793	−1.25421
$580$	0.799518	0.0331982
$581$	0	0
$582$	−22.2898	−0.923943
$583$	2.45313	0.101598
$584$	13.9065	0.575456
$585$	2.12715	0.0879467
$586$	−10.1937	−0.421099
$587$	−7.85541	−0.324228	−0.162114	−	0.986772i	$-0.551831\pi$
$587$	−7.85541	−0.324228	−0.162114	+	0.986772i	$0.551831\pi$
$588$	0	0
$589$	−1.56450	−0.0644639
$590$	0.448564	0.0184671
$591$	−7.84226	−0.322588
$592$	1.28439	0.0527880
$593$	−29.3046	−1.20340	−0.601698	−	0.798724i	$-0.705509\pi$
$593$	−29.3046	−1.20340	−0.601698	+	0.798724i	$0.705509\pi$
$594$	−3.02214	−0.124000
$595$	0	0
$596$	−0.304695	−0.0124808
$597$	39.9102	1.63342
$598$	0.416094	0.0170154
$599$	−14.7799	−0.603891	−0.301946	−	0.953325i	$-0.597636\pi$
$599$	−14.7799	−0.603891	−0.301946	+	0.953325i	$0.597636\pi$
$600$	−23.6657	−0.966147
$601$	−43.5647	−1.77704	−0.888522	−	0.458835i	$-0.848267\pi$
$601$	−43.5647	−1.77704	−0.888522	+	0.458835i	$0.848267\pi$
$602$	0	0
$603$	0.387880	0.0157957
$604$	18.8515	0.767056
$605$	−46.5648	−1.89313
$606$	18.9862	0.771260
$607$	−46.1066	−1.87141	−0.935705	−	0.352784i	$-0.885235\pi$
$607$	−46.1066	−1.87141	−0.935705	+	0.352784i	$0.885235\pi$
$608$	−3.92993	−0.159380
$609$	0	0
$610$	21.2696	0.861182
$611$	4.47037	0.180852
$612$	−1.08857	−0.0440026
$613$	−35.6409	−1.43952	−0.719761	−	0.694222i	$-0.755748\pi$
$613$	−35.6409	−1.43952	−0.719761	+	0.694222i	$0.755748\pi$
$614$	30.8317	1.24427
$615$	7.36168	0.296852
$616$	0	0
$617$	−23.0135	−0.926488	−0.463244	−	0.886231i	$-0.653315\pi$
$617$	−23.0135	−0.926488	−0.463244	+	0.886231i	$0.653315\pi$
$618$	−19.2283	−0.773475
$619$	−46.6228	−1.87393	−0.936965	−	0.349423i	$-0.886378\pi$
$619$	−46.6228	−1.87393	−0.936965	+	0.349423i	$0.886378\pi$
$620$	−1.73618	−0.0697265
$621$	−0.683552	−0.0274300
$622$	−16.7139	−0.670165
$623$	0	0
$624$	−5.46469	−0.218763
$625$	101.459	4.05837
$626$	17.2890	0.691007
$627$	−3.76962	−0.150544
$628$	−14.8641	−0.593142
$629$	9.28007	0.370021
$630$	0	0
$631$	29.5402	1.17598	0.587988	−	0.808869i	$-0.299920\pi$
$631$	29.5402	1.17598	0.587988	+	0.808869i	$0.299920\pi$
$632$	−6.53994	−0.260145
$633$	−15.7487	−0.625955
$634$	7.85240	0.311859
$635$	47.8944	1.90063
$636$	−7.28705	−0.288950
$637$	0	0
$638$	0.104175	0.00412433
$639$	−1.61430	−0.0638606
$640$	−4.36119	−0.172391
$641$	23.4659	0.926849	0.463424	−	0.886137i	$-0.346621\pi$
$641$	23.4659	0.926849	0.463424	+	0.886137i	$0.346621\pi$
$642$	−34.7325	−1.37078
$643$	41.8961	1.65222	0.826111	−	0.563507i	$-0.190548\pi$
$643$	41.8961	1.65222	0.826111	+	0.563507i	$0.190548\pi$
$644$	0	0
$645$	46.8392	1.84429
$646$	−28.3949	−1.11718
$647$	−19.6761	−0.773549	−0.386775	−	0.922174i	$-0.626411\pi$
$647$	−19.6761	−0.773549	−0.386775	+	0.922174i	$0.626411\pi$
$648$	8.52532	0.334906
$649$	0.0584466	0.00229423
$650$	45.3879	1.78026
$651$	0	0
$652$	−18.2525	−0.714822
$653$	−19.8798	−0.777958	−0.388979	−	0.921247i	$-0.627172\pi$
$653$	−19.8798	−0.777958	−0.388979	+	0.921247i	$0.627172\pi$
$654$	−15.1073	−0.590743
$655$	−71.8235	−2.80638
$656$	1.00000	0.0390434
$657$	2.09516	0.0817401
$658$	0	0
$659$	3.59248	0.139943	0.0699715	−	0.997549i	$-0.477709\pi$
$659$	3.59248	0.139943	0.0699715	+	0.997549i	$0.477709\pi$
$660$	−4.18328	−0.162834
$661$	−45.1177	−1.75488	−0.877438	−	0.479690i	$-0.840749\pi$
$661$	−45.1177	−1.75488	−0.877438	+	0.479690i	$0.840749\pi$
$662$	−7.63292	−0.296662
$663$	−39.4840	−1.53343
$664$	−1.98887	−0.0771833
$665$	0	0
$666$	0.193506	0.00749821
$667$	0.0235625	0.000912344 0
$668$	2.25023	0.0870639
$669$	20.5630	0.795013
$670$	11.2280	0.433776
$671$	2.77138	0.106988
$672$	0	0
$673$	22.3852	0.862888	0.431444	−	0.902140i	$-0.358004\pi$
$673$	22.3852	0.862888	0.431444	+	0.902140i	$0.358004\pi$
$674$	15.7465	0.606531
$675$	−74.5625	−2.86991
$676$	−2.51937	−0.0968988
$677$	3.76034	0.144521	0.0722607	−	0.997386i	$-0.476979\pi$
$677$	3.76034	0.144521	0.0722607	+	0.997386i	$0.476979\pi$
$678$	19.0746	0.732554
$679$	0	0
$680$	−31.5109	−1.20839
$681$	−47.0393	−1.80255
$682$	−0.226219	−0.00866238
$683$	−4.74458	−0.181546	−0.0907731	−	0.995872i	$-0.528934\pi$
$683$	−4.74458	−0.181546	−0.0907731	+	0.995872i	$0.528934\pi$
$684$	−0.592085	−0.0226389
$685$	0.169455	0.00647456
$686$	0	0
$687$	−27.8313	−1.06183
$688$	6.36258	0.242571
$689$	13.9757	0.532431
$690$	−0.946182	−0.0360206
$691$	5.34750	0.203428	0.101714	−	0.994814i	$-0.467567\pi$
$691$	5.34750	0.203428	0.101714	+	0.994814i	$0.467567\pi$
$692$	9.22947	0.350852
$693$	0	0
$694$	−5.04569	−0.191532
$695$	73.9160	2.80379
$696$	−0.309454	−0.0117298
$697$	7.22529	0.273678
$698$	−23.5627	−0.891860
$699$	36.3036	1.37313
$700$	0	0
$701$	8.93266	0.337382	0.168691	−	0.985669i	$-0.446046\pi$
$701$	8.93266	0.337382	0.168691	+	0.985669i	$0.446046\pi$
$702$	−17.2174	−0.649829
$703$	5.04755	0.190372
$704$	−0.568251	−0.0214168
$705$	−10.1655	−0.382853
$706$	32.1346	1.20940
$707$	0	0
$708$	−0.173617	−0.00652491
$709$	−4.58157	−0.172064	−0.0860322	−	0.996292i	$-0.527419\pi$
$709$	−4.58157	−0.172064	−0.0860322	+	0.996292i	$0.527419\pi$
$710$	−46.7293	−1.75372
$711$	−0.985310	−0.0369520
$712$	5.16073	0.193406
$713$	−0.0511667	−0.00191621
$714$	0	0
$715$	8.02304	0.300045
$716$	−18.1291	−0.677514
$717$	35.0350	1.30841
$718$	11.1055	0.414453
$719$	8.83296	0.329414	0.164707	−	0.986343i	$-0.447332\pi$
$719$	8.83296	0.329414	0.164707	+	0.986343i	$0.447332\pi$
$720$	−0.657058	−0.0244871
$721$	0	0
$722$	3.55563	0.132327
$723$	47.7568	1.77610
$724$	−3.23967	−0.120401
$725$	2.57022	0.0954556
$726$	18.0229	0.668893
$727$	−5.18597	−0.192337	−0.0961684	−	0.995365i	$-0.530659\pi$
$727$	−5.18597	−0.192337	−0.0961684	+	0.995365i	$0.530659\pi$
$728$	0	0
$729$	28.2163	1.04505
$730$	60.6490	2.24472
$731$	45.9715	1.70032
$732$	−8.23242	−0.304279
$733$	13.2137	0.488059	0.244030	−	0.969768i	$-0.421531\pi$
$733$	13.2137	0.488059	0.244030	+	0.969768i	$0.421531\pi$
$734$	−27.9981	−1.03343
$735$	0	0
$736$	−0.128528	−0.00473761
$737$	1.46298	0.0538896
$738$	0.150660	0.00554588
$739$	−8.01330	−0.294774	−0.147387	−	0.989079i	$-0.547086\pi$
$739$	−8.01330	−0.294774	−0.147387	+	0.989079i	$0.547086\pi$
$740$	5.60145	0.205913
$741$	−21.4759	−0.788936
$742$	0	0
$743$	32.9682	1.20949	0.604743	−	0.796420i	$-0.293276\pi$
$743$	32.9682	1.20949	0.604743	+	0.796420i	$0.293276\pi$
$744$	0.671988	0.0246363
$745$	−1.32883	−0.0486846
$746$	11.8648	0.434401
$747$	−0.299644	−0.0109634
$748$	−4.10578	−0.150122
$749$	0	0
$750$	−66.4020	−2.42466
$751$	−37.8431	−1.38091	−0.690457	−	0.723373i	$-0.742591\pi$
$751$	−37.8431	−1.38091	−0.690457	+	0.723373i	$0.742591\pi$
$752$	−1.38086	−0.0503548
$753$	−23.3944	−0.852539
$754$	0.593495	0.0216138
$755$	82.2148	2.99210
$756$	0	0
$757$	−5.55902	−0.202046	−0.101023	−	0.994884i	$-0.532212\pi$
$757$	−5.55902	−0.202046	−0.101023	+	0.994884i	$0.532212\pi$
$758$	26.8697	0.975952
$759$	−0.123285	−0.00447496
$760$	−17.1392	−0.621703
$761$	0.0200574	0.000727079 0	0.000363540	−	1.00000i	$-0.499884\pi$
$761$	0.0200574	0.000727079 0	0.000363540		1.00000i	$0.499884\pi$
$762$	−18.5375	−0.671544
$763$	0	0
$764$	−23.5363	−0.851512
$765$	−4.74744	−0.171644
$766$	−24.2386	−0.875775
$767$	0.332976	0.0120231
$768$	1.68800	0.0609104
$769$	30.5326	1.10104	0.550518	−	0.834824i	$-0.314430\pi$
$769$	30.5326	1.10104	0.550518	+	0.834824i	$0.314430\pi$
$770$	0	0
$771$	49.3347	1.77675
$772$	−17.8787	−0.643470
$773$	−30.2748	−1.08891	−0.544454	−	0.838791i	$-0.683263\pi$
$773$	−30.2748	−1.08891	−0.544454	+	0.838791i	$0.683263\pi$
$774$	0.958588	0.0344557
$775$	−5.58131	−0.200486
$776$	−13.2049	−0.474028
$777$	0	0
$778$	8.45054	0.302966
$779$	3.92993	0.140804
$780$	−23.8326	−0.853342
$781$	−6.08871	−0.217871
$782$	−0.928653	−0.0332086
$783$	−0.974984	−0.0348431
$784$	0	0
$785$	−64.8251	−2.31371
$786$	27.7993	0.991569
$787$	−2.82193	−0.100591	−0.0502955	−	0.998734i	$-0.516016\pi$
$787$	−2.82193	−0.100591	−0.0502955	+	0.998734i	$0.516016\pi$
$788$	−4.64590	−0.165503
$789$	−20.1250	−0.716468
$790$	−28.5219	−1.01476
$791$	0	0
$792$	−0.0856129	−0.00304212
$793$	15.7888	0.560677
$794$	26.7709	0.950062
$795$	−31.7802	−1.12713
$796$	23.6435	0.838022
$797$	2.31160	0.0818811	0.0409406	−	0.999162i	$-0.486965\pi$
$797$	2.31160	0.0818811	0.0409406	+	0.999162i	$0.486965\pi$
$798$	0	0
$799$	−9.97712	−0.352965
$800$	−14.0200	−0.495680
$801$	0.777517	0.0274722
$802$	−2.26458	−0.0799650
$803$	7.90240	0.278870
$804$	−4.34581	−0.153265
$805$	0	0
$806$	−1.28879	−0.0453958
$807$	−17.5692	−0.618466
$808$	11.2477	0.395694
$809$	−33.9029	−1.19196	−0.595981	−	0.802998i	$-0.703237\pi$
$809$	−33.9029	−1.19196	−0.595981	+	0.802998i	$0.703237\pi$
$810$	37.1805	1.30639
$811$	−28.1783	−0.989476	−0.494738	−	0.869042i	$-0.664736\pi$
$811$	−28.1783	−0.989476	−0.494738	+	0.869042i	$0.664736\pi$
$812$	0	0
$813$	−35.7494	−1.25378
$814$	0.729854	0.0255814
$815$	−79.6025	−2.78835
$816$	12.1963	0.426956
$817$	25.0045	0.874797
$818$	0.808014	0.0282516
$819$	0	0
$820$	4.36119	0.152299
$821$	20.9197	0.730103	0.365052	−	0.930987i	$-0.381051\pi$
$821$	20.9197	0.730103	0.365052	+	0.930987i	$0.381051\pi$
$822$	−0.0655878	−0.00228764
$823$	−30.3907	−1.05935	−0.529677	−	0.848200i	$-0.677687\pi$
$823$	−30.3907	−1.05935	−0.529677	+	0.848200i	$0.677687\pi$
$824$	−11.3912	−0.396830
$825$	−13.4480	−0.468201
$826$	0	0
$827$	−1.70417	−0.0592599	−0.0296300	−	0.999561i	$-0.509433\pi$
$827$	−1.70417	−0.0592599	−0.0296300	+	0.999561i	$0.509433\pi$
$828$	−0.0193641	−0.000672948 0
$829$	8.57439	0.297801	0.148900	−	0.988852i	$-0.452427\pi$
$829$	8.57439	0.297801	0.148900	+	0.988852i	$0.452427\pi$
$830$	−8.67385	−0.301074
$831$	−22.4633	−0.779244
$832$	−3.23738	−0.112236
$833$	0	0
$834$	−28.6092	−0.990656
$835$	9.81366	0.339616
$836$	−2.23319	−0.0772364
$837$	2.11721	0.0731813
$838$	8.94624	0.309043
$839$	9.44150	0.325957	0.162978	−	0.986630i	$-0.447890\pi$
$839$	9.44150	0.325957	0.162978	+	0.986630i	$0.447890\pi$
$840$	0	0
$841$	−28.9664	−0.998841
$842$	−23.7303	−0.817799
$843$	14.6223	0.503620
$844$	−9.32982	−0.321146
$845$	−10.9874	−0.377979
$846$	−0.208041	−0.00715259
$847$	0	0
$848$	−4.31697	−0.148246
$849$	6.28678	0.215762
$850$	−101.298	−3.47450
$851$	0.165080	0.00565886
$852$	18.0866	0.619637
$853$	26.0781	0.892895	0.446448	−	0.894810i	$-0.352689\pi$
$853$	26.0781	0.892895	0.446448	+	0.894810i	$0.352689\pi$
$854$	0	0
$855$	−2.58219	−0.0883091
$856$	−20.5761	−0.703278
$857$	27.4455	0.937519	0.468760	−	0.883326i	$-0.344701\pi$
$857$	27.4455	0.937519	0.468760	+	0.883326i	$0.344701\pi$
$858$	−3.10532	−0.106014
$859$	−35.0173	−1.19478	−0.597388	−	0.801953i	$-0.703795\pi$
$859$	−35.0173	−1.19478	−0.597388	+	0.801953i	$0.703795\pi$
$860$	27.7484	0.946212
$861$	0	0
$862$	23.2112	0.790575
$863$	16.6224	0.565834	0.282917	−	0.959144i	$-0.408698\pi$
$863$	16.6224	0.565834	0.282917	+	0.959144i	$0.408698\pi$
$864$	5.31831	0.180933
$865$	40.2515	1.36859
$866$	−19.9734	−0.678723
$867$	59.4258	2.01821
$868$	0	0
$869$	−3.71633	−0.126068
$870$	−1.34959	−0.0457552
$871$	8.33474	0.282412
$872$	−8.94984	−0.303080
$873$	−1.98945	−0.0673328
$874$	−0.505107	−0.0170855
$875$	0	0
$876$	−23.4742	−0.793120
$877$	28.6256	0.966616	0.483308	−	0.875450i	$-0.339435\pi$
$877$	28.6256	0.966616	0.483308	+	0.875450i	$0.339435\pi$
$878$	30.0376	1.01372
$879$	17.2070	0.580377
$880$	−2.47825	−0.0835418
$881$	−4.02960	−0.135761	−0.0678804	−	0.997693i	$-0.521624\pi$
$881$	−4.02960	−0.135761	−0.0678804	+	0.997693i	$0.521624\pi$
$882$	0	0
$883$	−7.10888	−0.239233	−0.119616	−	0.992820i	$-0.538166\pi$
$883$	−7.10888	−0.239233	−0.119616	+	0.992820i	$0.538166\pi$
$884$	−23.3910	−0.786725
$885$	−0.757175	−0.0254521
$886$	2.84568	0.0956023
$887$	51.5825	1.73197	0.865985	−	0.500070i	$-0.166692\pi$
$887$	51.5825	1.73197	0.865985	+	0.500070i	$0.166692\pi$
$888$	−2.16804	−0.0727548
$889$	0	0
$890$	22.5069	0.754433
$891$	4.84452	0.162298
$892$	12.1819	0.407880
$893$	−5.42669	−0.181597
$894$	0.514324	0.0172016
$895$	−79.0642	−2.64282
$896$	0	0
$897$	−0.702367	−0.0234513
$898$	10.4593	0.349033
$899$	−0.0729815	−0.00243407
$900$	−2.11225	−0.0704084
$901$	−31.1914	−1.03914
$902$	0.568251	0.0189207
$903$	0	0
$904$	11.3001	0.375836
$905$	−14.1288	−0.469658
$906$	−31.8213	−1.05719
$907$	−36.0029	−1.19546	−0.597728	−	0.801699i	$-0.703930\pi$
$907$	−36.0029	−1.19546	−0.597728	+	0.801699i	$0.703930\pi$
$908$	−27.8669	−0.924795
$909$	1.69459	0.0562059
$910$	0	0
$911$	−50.2728	−1.66561	−0.832806	−	0.553564i	$-0.813267\pi$
$911$	−50.2728	−1.66561	−0.832806	+	0.553564i	$0.813267\pi$
$912$	6.63372	0.219664
$913$	−1.13018	−0.0374035
$914$	13.7405	0.454496
$915$	−35.9031	−1.18692
$916$	−16.4877	−0.544770
$917$	0	0
$918$	38.4264	1.26826
$919$	38.5154	1.27050	0.635252	−	0.772305i	$-0.280896\pi$
$919$	38.5154	1.27050	0.635252	+	0.772305i	$0.280896\pi$
$920$	−0.560535	−0.0184803
$921$	−52.0438	−1.71490
$922$	14.1512	0.466045
$923$	−34.6880	−1.14177
$924$	0	0
$925$	18.0070	0.592068
$926$	4.16820	0.136975
$927$	−1.71620	−0.0563673
$928$	−0.183326	−0.00601797
$929$	0.511234	0.0167730	0.00838652	−	0.999965i	$-0.497330\pi$
$929$	0.511234	0.0167730	0.00838652	+	0.999965i	$0.497330\pi$
$930$	2.93066	0.0961003
$931$	0	0
$932$	21.5069	0.704481
$933$	28.2130	0.923651
$934$	−37.7772	−1.23611
$935$	−17.9061	−0.585592
$936$	−0.487745	−0.0159424
$937$	−14.6852	−0.479743	−0.239872	−	0.970805i	$-0.577105\pi$
$937$	−14.6852	−0.479743	−0.239872	+	0.970805i	$0.577105\pi$
$938$	0	0
$939$	−29.1838	−0.952377
$940$	−6.02219	−0.196422
$941$	−35.5393	−1.15855	−0.579275	−	0.815132i	$-0.696664\pi$
$941$	−35.5393	−1.15855	−0.579275	+	0.815132i	$0.696664\pi$
$942$	25.0906	0.817494
$943$	0.128528	0.00418545
$944$	−0.102854	−0.00334760
$945$	0	0
$946$	3.61554	0.117551
$947$	−20.4441	−0.664344	−0.332172	−	0.943219i	$-0.607781\pi$
$947$	−20.4441	−0.664344	−0.332172	+	0.943219i	$0.607781\pi$
$948$	11.0394	0.358544
$949$	45.0207	1.46143
$950$	−55.0975	−1.78760
$951$	−13.2548	−0.429818
$952$	0	0
$953$	39.0938	1.26637	0.633187	−	0.773999i	$-0.281747\pi$
$953$	39.0938	1.26637	0.633187	+	0.773999i	$0.281747\pi$
$954$	−0.650397	−0.0210574
$955$	−102.646	−3.32155
$956$	20.7553	0.671276
$957$	−0.175847	−0.00568434
$958$	−26.3641	−0.851786
$959$	0	0
$960$	7.36168	0.237597
$961$	−30.8415	−0.994888
$962$	4.15805	0.134061
$963$	−3.10001	−0.0998964
$964$	28.2920	0.911224
$965$	−77.9726	−2.51003
$966$	0	0
$967$	−47.1360	−1.51579	−0.757896	−	0.652376i	$-0.773772\pi$
$967$	−47.1360	−1.51579	−0.757896	+	0.652376i	$0.773772\pi$
$968$	10.6771	0.343175
$969$	47.9306	1.53975
$970$	−57.5890	−1.84907
$971$	−1.06893	−0.0343037	−0.0171518	−	0.999853i	$-0.505460\pi$
$971$	−1.06893	−0.0343037	−0.0171518	+	0.999853i	$0.505460\pi$
$972$	1.56420	0.0501718
$973$	0	0
$974$	21.6225	0.692829
$975$	−76.6148	−2.45364
$976$	−4.87703	−0.156110
$977$	−7.08437	−0.226649	−0.113325	−	0.993558i	$-0.536150\pi$
$977$	−7.08437	−0.226649	−0.113325	+	0.993558i	$0.536150\pi$
$978$	30.8102	0.985200
$979$	2.93259	0.0937260
$980$	0	0
$981$	−1.34839	−0.0430506
$982$	−35.1542	−1.12182
$983$	35.4215	1.12977	0.564885	−	0.825170i	$-0.308921\pi$
$983$	35.4215	1.12977	0.564885	+	0.825170i	$0.308921\pi$
$984$	−1.68800	−0.0538114
$985$	−20.2616	−0.645589
$986$	−1.32458	−0.0421833
$987$	0	0
$988$	−12.7227	−0.404763
$989$	0.817770	0.0260036
$990$	−0.373374	−0.0118666
$991$	32.2317	1.02387	0.511937	−	0.859023i	$-0.328928\pi$
$991$	32.2317	1.02387	0.511937	+	0.859023i	$0.328928\pi$
$992$	0.398097	0.0126396
$993$	12.8844	0.408873
$994$	0	0
$995$	103.114	3.26893
$996$	3.35722	0.106378
$997$	13.2775	0.420502	0.210251	−	0.977647i	$-0.432572\pi$
$997$	13.2775	0.420502	0.210251	+	0.977647i	$0.432572\pi$
$998$	18.6545	0.590498
$999$	−6.83077	−0.216116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bs.1.7	yes	10
7.6	odd	2		4018.2.a.br.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.br.1.4	✓	10	7.6	odd	2
4018.2.a.bs.1.7	yes	10	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.68800 q^{3} +1.00000 q^{4} +4.36119 q^{5} -1.68800 q^{6} -1.00000 q^{8} -0.150660 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.68800 q^{3} +1.00000 q^{4} +4.36119 q^{5} -1.68800 q^{6} -1.00000 q^{8} -0.150660 q^{9} -4.36119 q^{10} -0.568251 q^{11} +1.68800 q^{12} -3.23738 q^{13} +7.36168 q^{15} +1.00000 q^{16} +7.22529 q^{17} +0.150660 q^{18} +3.92993 q^{19} +4.36119 q^{20} +0.568251 q^{22} +0.128528 q^{23} -1.68800 q^{24} +14.0200 q^{25} +3.23738 q^{26} -5.31831 q^{27} +0.183326 q^{29} -7.36168 q^{30} -0.398097 q^{31} -1.00000 q^{32} -0.959207 q^{33} -7.22529 q^{34} -0.150660 q^{36} +1.28439 q^{37} -3.92993 q^{38} -5.46469 q^{39} -4.36119 q^{40} +1.00000 q^{41} +6.36258 q^{43} -0.568251 q^{44} -0.657058 q^{45} -0.128528 q^{46} -1.38086 q^{47} +1.68800 q^{48} -14.0200 q^{50} +12.1963 q^{51} -3.23738 q^{52} -4.31697 q^{53} +5.31831 q^{54} -2.47825 q^{55} +6.63372 q^{57} -0.183326 q^{58} -0.102854 q^{59} +7.36168 q^{60} -4.87703 q^{61} +0.398097 q^{62} +1.00000 q^{64} -14.1188 q^{65} +0.959207 q^{66} -2.57453 q^{67} +7.22529 q^{68} +0.216955 q^{69} +10.7148 q^{71} +0.150660 q^{72} -13.9065 q^{73} -1.28439 q^{74} +23.6657 q^{75} +3.92993 q^{76} +5.46469 q^{78} +6.53994 q^{79} +4.36119 q^{80} -8.52532 q^{81} -1.00000 q^{82} +1.98887 q^{83} +31.5109 q^{85} -6.36258 q^{86} +0.309454 q^{87} +0.568251 q^{88} -5.16073 q^{89} +0.657058 q^{90} +0.128528 q^{92} -0.671988 q^{93} +1.38086 q^{94} +17.1392 q^{95} -1.68800 q^{96} +13.2049 q^{97} +0.0856129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 20 * q^17 - 10 * q^18 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 16 * q^27 - 4 * q^29 - 4 * q^30 - 4 * q^31 - 10 * q^32 + 36 * q^33 - 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 - 4 * q^40 + 10 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 4 * q^46 + 24 * q^47 + 4 * q^48 - 6 * q^50 + 20 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^54 + 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 + 4 * q^62 + 10 * q^64 - 12 * q^65 - 36 * q^66 + 8 * q^67 + 20 * q^68 + 4 * q^71 - 10 * q^72 - 24 * q^73 + 16 * q^74 + 48 * q^75 - 20 * q^78 + 24 * q^79 + 4 * q^80 - 18 * q^81 - 10 * q^82 + 48 * q^83 + 8 * q^85 + 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 24 * q^94 - 4 * q^95 - 4 * q^96 + 4 * q^97 + 32 * q^99

Introduction

L-functions

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