LMFDB - Embedded newform 197.2.a.c.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [197,2,Mod(1,197)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("197.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(197, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	197.a (trivial)

Newform invariants

comment:select newform

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

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

Self dual:	yes
Analytic conductor:	$1.57305291982$
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} - 15x^{8} - x^{7} + 78x^{6} + 7x^{5} - 165x^{4} - 15x^{3} + 123x^{2} + 9x - 26 $ x^10 - 15x^8 - x^7 + 78x^6 + 7x^5 - 165x^4 - 15x^3 + 123x^2 + 9*x - 26
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-2.27104$ of defining polynomial
Character	$\chi$	$=$	197.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.27104 q^{2} +1.58668 q^{3} +3.15762 q^{4} -3.10959 q^{5} +3.60342 q^{6} -0.149594 q^{7} +2.62899 q^{8} -0.482441 q^{9} -7.06199 q^{10} -2.04141 q^{11} +5.01013 q^{12} +0.758286 q^{13} -0.339733 q^{14} -4.93392 q^{15} -0.344687 q^{16} +2.98720 q^{17} -1.09564 q^{18} +4.51557 q^{19} -9.81888 q^{20} -0.237357 q^{21} -4.63612 q^{22} +0.863791 q^{23} +4.17138 q^{24} +4.66952 q^{25} +1.72210 q^{26} -5.52553 q^{27} -0.472359 q^{28} -0.963320 q^{29} -11.2051 q^{30} +0.311286 q^{31} -6.04079 q^{32} -3.23906 q^{33} +6.78405 q^{34} +0.465174 q^{35} -1.52336 q^{36} +11.1450 q^{37} +10.2550 q^{38} +1.20316 q^{39} -8.17508 q^{40} +8.45451 q^{41} -0.539048 q^{42} +5.98358 q^{43} -6.44598 q^{44} +1.50019 q^{45} +1.96170 q^{46} -12.5490 q^{47} -0.546909 q^{48} -6.97762 q^{49} +10.6047 q^{50} +4.73973 q^{51} +2.39438 q^{52} -11.0563 q^{53} -12.5487 q^{54} +6.34793 q^{55} -0.393281 q^{56} +7.16478 q^{57} -2.18774 q^{58} +8.16033 q^{59} -15.5794 q^{60} +2.88942 q^{61} +0.706943 q^{62} +0.0721700 q^{63} -13.0295 q^{64} -2.35796 q^{65} -7.35604 q^{66} -11.2942 q^{67} +9.43243 q^{68} +1.37056 q^{69} +1.05643 q^{70} -8.59142 q^{71} -1.26833 q^{72} +0.890213 q^{73} +25.3108 q^{74} +7.40905 q^{75} +14.2585 q^{76} +0.305381 q^{77} +2.73242 q^{78} -3.39702 q^{79} +1.07183 q^{80} -7.31993 q^{81} +19.2005 q^{82} +12.6851 q^{83} -0.749484 q^{84} -9.28895 q^{85} +13.5889 q^{86} -1.52848 q^{87} -5.36685 q^{88} +6.62161 q^{89} +3.40699 q^{90} -0.113435 q^{91} +2.72752 q^{92} +0.493912 q^{93} -28.4992 q^{94} -14.0416 q^{95} -9.58480 q^{96} -1.57517 q^{97} -15.8465 q^{98} +0.984858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{3} + 10 q^{4} + 2 q^{5} - 4 q^{6} + 11 q^{7} - 3 q^{8} + 12 q^{9} - 2 q^{10} + 2 q^{11} + 4 q^{12} + 8 q^{13} - 9 q^{14} - q^{15} - 2 q^{16} - 3 q^{17} - 9 q^{18} + 17 q^{19} - 2 q^{20} - 2 q^{21}+ \cdots - q^{99}+O(q^{100}) $ 10 * q + 10 * q^3 + 10 * q^4 + 2 * q^5 - 4 * q^6 + 11 * q^7 - 3 * q^8 + 12 * q^9 - 2 * q^10 + 2 * q^11 + 4 * q^12 + 8 * q^13 - 9 * q^14 - q^15 - 2 * q^16 - 3 * q^17 - 9 * q^18 + 17 * q^19 - 2 * q^20 - 2 * q^21 + 3 * q^22 - 4 * q^23 - 15 * q^24 + 6 * q^25 - 13 * q^26 + 19 * q^27 + 16 * q^28 - 9 * q^29 - 19 * q^30 + 20 * q^31 - 16 * q^32 - 2 * q^33 - 8 * q^34 - 12 * q^35 - 12 * q^36 + 12 * q^37 - 15 * q^38 - 9 * q^39 - 15 * q^40 - 18 * q^41 - 31 * q^42 + 11 * q^43 - 24 * q^44 - 15 * q^45 - 13 * q^46 + 5 * q^47 - 22 * q^48 + q^49 - 24 * q^50 - 13 * q^51 + 9 * q^52 - 6 * q^53 - 15 * q^54 - 17 * q^55 - 6 * q^56 + 3 * q^57 - 15 * q^58 - q^59 - 23 * q^60 + 4 * q^61 - 16 * q^62 - 11 * q^63 - 17 * q^64 - 17 * q^65 + 24 * q^66 + 46 * q^67 + 15 * q^68 - 21 * q^69 + 25 * q^70 - 5 * q^71 + 7 * q^72 + 25 * q^73 + 3 * q^74 + 46 * q^75 + 49 * q^76 - 14 * q^77 + 15 * q^78 - q^79 + 9 * q^80 + 22 * q^81 + 52 * q^82 + 28 * q^83 - 14 * q^84 - 30 * q^85 + 27 * q^86 - 7 * q^87 + 9 * q^88 - 6 * q^89 - 10 * q^90 + 51 * q^91 + 32 * q^92 + 15 * q^93 - 3 * q^94 - 13 * q^95 + 75 * q^96 + 2 * q^97 + 22 * q^98 - q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.27104	1.60587	0.802933	−	0.596069i	$-0.203271\pi$
$2$	2.27104	1.60587	0.802933	+	0.596069i	$0.203271\pi$
$3$	1.58668	0.916071	0.458036	−	0.888934i	$-0.348553\pi$
$3$	1.58668	0.916071	0.458036	+	0.888934i	$0.348553\pi$
$4$	3.15762	1.57881
$5$	−3.10959	−1.39065	−0.695324	−	0.718696i	$-0.744739\pi$
$5$	−3.10959	−1.39065	−0.695324	+	0.718696i	$0.744739\pi$
$6$	3.60342	1.47109
$7$	−0.149594	−0.0565410	−0.0282705	−	0.999600i	$-0.509000\pi$
$7$	−0.149594	−0.0565410	−0.0282705	+	0.999600i	$0.509000\pi$
$8$	2.62899	0.929490
$9$	−0.482441	−0.160814
$10$	−7.06199	−2.23320
$11$	−2.04141	−0.615507	−0.307754	−	0.951466i	$-0.599577\pi$
$11$	−2.04141	−0.615507	−0.307754	+	0.951466i	$0.599577\pi$
$12$	5.01013	1.44630
$13$	0.758286	0.210311	0.105155	−	0.994456i	$-0.466466\pi$
$13$	0.758286	0.210311	0.105155	+	0.994456i	$0.466466\pi$
$14$	−0.339733	−0.0907974
$15$	−4.93392	−1.27393
$16$	−0.344687	−0.0861717
$17$	2.98720	0.724502	0.362251	−	0.932081i	$-0.382008\pi$
$17$	2.98720	0.724502	0.362251	+	0.932081i	$0.382008\pi$
$18$	−1.09564	−0.258245
$19$	4.51557	1.03594	0.517972	−	0.855398i	$-0.326687\pi$
$19$	4.51557	1.03594	0.517972	+	0.855398i	$0.326687\pi$
$20$	−9.81888	−2.19557
$21$	−0.237357	−0.0517956
$22$	−4.63612	−0.988423
$23$	0.863791	0.180113	0.0900564	−	0.995937i	$-0.471295\pi$
$23$	0.863791	0.180113	0.0900564	+	0.995937i	$0.471295\pi$
$24$	4.17138	0.851479
$25$	4.66952	0.933905
$26$	1.72210	0.337731
$27$	−5.52553	−1.06339
$28$	−0.472359	−0.0892675
$29$	−0.963320	−0.178884	−0.0894420	−	0.995992i	$-0.528508\pi$
$29$	−0.963320	−0.178884	−0.0894420	+	0.995992i	$0.528508\pi$
$30$	−11.2051	−2.04577
$31$	0.311286	0.0559087	0.0279543	−	0.999609i	$-0.491101\pi$
$31$	0.311286	0.0559087	0.0279543	+	0.999609i	$0.491101\pi$
$32$	−6.04079	−1.06787
$33$	−3.23906	−0.563849
$34$	6.78405	1.16345
$35$	0.465174	0.0786287
$36$	−1.52336	−0.253894
$37$	11.1450	1.83223	0.916115	−	0.400917i	$-0.131308\pi$
$37$	11.1450	1.83223	0.916115	+	0.400917i	$0.131308\pi$
$38$	10.2550	1.66359
$39$	1.20316	0.192660
$40$	−8.17508	−1.29259
$41$	8.45451	1.32037	0.660186	−	0.751102i	$-0.270477\pi$
$41$	8.45451	1.32037	0.660186	+	0.751102i	$0.270477\pi$
$42$	−0.539048	−0.0831769
$43$	5.98358	0.912487	0.456243	−	0.889855i	$-0.349195\pi$
$43$	5.98358	0.912487	0.456243	+	0.889855i	$0.349195\pi$
$44$	−6.44598	−0.971769
$45$	1.50019	0.223635
$46$	1.96170	0.289237
$47$	−12.5490	−1.83046	−0.915229	−	0.402934i	$-0.867990\pi$
$47$	−12.5490	−1.83046	−0.915229	+	0.402934i	$0.867990\pi$
$48$	−0.546909	−0.0789394
$49$	−6.97762	−0.996803
$50$	10.6047	1.49973
$51$	4.73973	0.663696
$52$	2.39438	0.332040
$53$	−11.0563	−1.51870	−0.759352	−	0.650680i	$-0.774484\pi$
$53$	−11.0563	−1.51870	−0.759352	+	0.650680i	$0.774484\pi$
$54$	−12.5487	−1.70766
$55$	6.34793	0.855955
$56$	−0.393281	−0.0525543
$57$	7.16478	0.948998
$58$	−2.18774	−0.287264
$59$	8.16033	1.06238	0.531192	−	0.847251i	$-0.321744\pi$
$59$	8.16033	1.06238	0.531192	+	0.847251i	$0.321744\pi$
$60$	−15.5794	−2.01130
$61$	2.88942	0.369953	0.184976	−	0.982743i	$-0.440779\pi$
$61$	2.88942	0.369953	0.184976	+	0.982743i	$0.440779\pi$
$62$	0.706943	0.0897819
$63$	0.0721700	0.00909257
$64$	−13.0295	−1.62869
$65$	−2.35796	−0.292468
$66$	−7.35604	−0.905466
$67$	−11.2942	−1.37980	−0.689902	−	0.723902i	$-0.742347\pi$
$67$	−11.2942	−1.37980	−0.689902	+	0.723902i	$0.742347\pi$
$68$	9.43243	1.14385
$69$	1.37056	0.164996
$70$	1.05643	0.126267
$71$	−8.59142	−1.01961	−0.509807	−	0.860289i	$-0.670283\pi$
$71$	−8.59142	−1.01961	−0.509807	+	0.860289i	$0.670283\pi$
$72$	−1.26833	−0.149475
$73$	0.890213	0.104192	0.0520958	−	0.998642i	$-0.483410\pi$
$73$	0.890213	0.104192	0.0520958	+	0.998642i	$0.483410\pi$
$74$	25.3108	2.94232
$75$	7.40905	0.855523
$76$	14.2585	1.63556
$77$	0.305381	0.0348014
$78$	2.73242	0.309386
$79$	−3.39702	−0.382195	−0.191097	−	0.981571i	$-0.561205\pi$
$79$	−3.39702	−0.382195	−0.191097	+	0.981571i	$0.561205\pi$
$80$	1.07183	0.119835
$81$	−7.31993	−0.813325
$82$	19.2005	2.12034
$83$	12.6851	1.39237	0.696184	−	0.717863i	$-0.254880\pi$
$83$	12.6851	1.39237	0.696184	+	0.717863i	$0.254880\pi$
$84$	−0.749484	−0.0817754
$85$	−9.28895	−1.00753
$86$	13.5889	1.46533
$87$	−1.52848	−0.163870
$88$	−5.36685	−0.572108
$89$	6.62161	0.701889	0.350944	−	0.936396i	$-0.385861\pi$
$89$	6.62161	0.701889	0.350944	+	0.936396i	$0.385861\pi$
$90$	3.40699	0.359129
$91$	−0.113435	−0.0118912
$92$	2.72752	0.284364
$93$	0.493912	0.0512163
$94$	−28.4992	−2.93947
$95$	−14.0416	−1.44063
$96$	−9.58480	−0.978245
$97$	−1.57517	−0.159934	−0.0799671	−	0.996798i	$-0.525482\pi$
$97$	−1.57517	−0.159934	−0.0799671	+	0.996798i	$0.525482\pi$
$98$	−15.8465	−1.60073
$99$	0.984858	0.0989820
$100$	14.7446	1.47446
$101$	−14.4642	−1.43924	−0.719622	−	0.694366i	$-0.755685\pi$
$101$	−14.4642	−1.43924	−0.719622	+	0.694366i	$0.755685\pi$
$102$	10.7641	1.06581
$103$	17.4494	1.71934	0.859670	−	0.510850i	$-0.170669\pi$
$103$	17.4494	1.71934	0.859670	+	0.510850i	$0.170669\pi$
$104$	1.99353	0.195482
$105$	0.738083	0.0720295
$106$	−25.1094	−2.43884
$107$	3.90123	0.377146	0.188573	−	0.982059i	$-0.439614\pi$
$107$	3.90123	0.377146	0.188573	+	0.982059i	$0.439614\pi$
$108$	−17.4475	−1.67889
$109$	−4.55943	−0.436715	−0.218357	−	0.975869i	$-0.570070\pi$
$109$	−4.55943	−0.436715	−0.218357	+	0.975869i	$0.570070\pi$
$110$	14.4164	1.37455
$111$	17.6836	1.67845
$112$	0.0515629	0.00487224
$113$	5.88632	0.553738	0.276869	−	0.960908i	$-0.410703\pi$
$113$	5.88632	0.553738	0.276869	+	0.960908i	$0.410703\pi$
$114$	16.2715	1.52396
$115$	−2.68603	−0.250474
$116$	−3.04179	−0.282424
$117$	−0.365828	−0.0338208
$118$	18.5324	1.70605
$119$	−0.446866	−0.0409641
$120$	−12.9713	−1.18411
$121$	−6.83266	−0.621151
$122$	6.56199	0.594095
$123$	13.4146	1.20956
$124$	0.982923	0.0882691
$125$	1.02765	0.0919155
$126$	0.163901	0.0146015
$127$	−3.60748	−0.320112	−0.160056	−	0.987108i	$-0.551168\pi$
$127$	−3.60748	−0.320112	−0.160056	+	0.987108i	$0.551168\pi$
$128$	−17.5089	−1.54758
$129$	9.49403	0.835903
$130$	−5.35501	−0.469665
$131$	18.4534	1.61229	0.806143	−	0.591721i	$-0.201551\pi$
$131$	18.4534	1.61229	0.806143	+	0.591721i	$0.201551\pi$
$132$	−10.2277	−0.890209
$133$	−0.675500	−0.0585733
$134$	−25.6495	−2.21578
$135$	17.1821	1.47880
$136$	7.85333	0.673417
$137$	−21.5440	−1.84063	−0.920316	−	0.391177i	$-0.872068\pi$
$137$	−21.5440	−1.84063	−0.920316	+	0.391177i	$0.872068\pi$
$138$	3.11260	0.264962
$139$	20.9614	1.77792	0.888962	−	0.457981i	$-0.151427\pi$
$139$	20.9614	1.77792	0.888962	+	0.457981i	$0.151427\pi$
$140$	1.46884	0.124140
$141$	−19.9112	−1.67683
$142$	−19.5115	−1.63736
$143$	−1.54797	−0.129448
$144$	0.166291	0.0138576
$145$	2.99552	0.248765
$146$	2.02171	0.167318
$147$	−11.0713	−0.913143
$148$	35.1917	2.89274
$149$	11.7993	0.966634	0.483317	−	0.875445i	$-0.339432\pi$
$149$	11.7993	0.966634	0.483317	+	0.875445i	$0.339432\pi$
$150$	16.8262	1.37386
$151$	10.6885	0.869818	0.434909	−	0.900474i	$-0.356781\pi$
$151$	10.6885	0.869818	0.434909	+	0.900474i	$0.356781\pi$
$152$	11.8714	0.962899
$153$	−1.44115	−0.116510
$154$	0.693533	0.0558865
$155$	−0.967971	−0.0777493
$156$	3.79911	0.304173
$157$	−12.4007	−0.989685	−0.494843	−	0.868983i	$-0.664774\pi$
$157$	−12.4007	−0.989685	−0.494843	+	0.868983i	$0.664774\pi$
$158$	−7.71477	−0.613754
$159$	−17.5429	−1.39124
$160$	18.7843	1.48503
$161$	−0.129218	−0.0101838
$162$	−16.6238	−1.30609
$163$	11.7497	0.920311	0.460155	−	0.887838i	$-0.347794\pi$
$163$	11.7497	0.920311	0.460155	+	0.887838i	$0.347794\pi$
$164$	26.6961	2.08462
$165$	10.0721	0.784116
$166$	28.8083	2.23596
$167$	−16.0874	−1.24488	−0.622441	−	0.782667i	$-0.713859\pi$
$167$	−16.0874	−1.24488	−0.622441	+	0.782667i	$0.713859\pi$
$168$	−0.624011	−0.0481435
$169$	−12.4250	−0.955769
$170$	−21.0956	−1.61796
$171$	−2.17850	−0.166594
$172$	18.8938	1.44064
$173$	−21.1311	−1.60657	−0.803285	−	0.595595i	$-0.796917\pi$
$173$	−21.1311	−1.60657	−0.803285	+	0.595595i	$0.796917\pi$
$174$	−3.47124	−0.263154
$175$	−0.698530	−0.0528039
$176$	0.703646	0.0530393
$177$	12.9478	0.973219
$178$	15.0379	1.12714
$179$	−7.66757	−0.573101	−0.286550	−	0.958065i	$-0.592509\pi$
$179$	−7.66757	−0.573101	−0.286550	+	0.958065i	$0.592509\pi$
$180$	4.73703	0.353077
$181$	10.8909	0.809515	0.404758	−	0.914424i	$-0.367356\pi$
$181$	10.8909	0.809515	0.404758	+	0.914424i	$0.367356\pi$
$182$	−0.257615	−0.0190957
$183$	4.58459	0.338903
$184$	2.27090	0.167413
$185$	−34.6564	−2.54799
$186$	1.12169	0.0822466
$187$	−6.09809	−0.445937
$188$	−39.6249	−2.88994
$189$	0.826583	0.0601251
$190$	−31.8889	−2.31347
$191$	−17.6310	−1.27574	−0.637868	−	0.770145i	$-0.720184\pi$
$191$	−17.6310	−1.27574	−0.637868	+	0.770145i	$0.720184\pi$
$192$	−20.6736	−1.49199
$193$	11.1467	0.802356	0.401178	−	0.916000i	$-0.368601\pi$
$193$	11.1467	0.802356	0.401178	+	0.916000i	$0.368601\pi$
$194$	−3.57727	−0.256833
$195$	−3.74132	−0.267922
$196$	−22.0327	−1.57376
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	2.23665	0.158952
$199$	7.99331	0.566631	0.283315	−	0.959027i	$-0.408566\pi$
$199$	7.99331	0.566631	0.283315	+	0.959027i	$0.408566\pi$
$200$	12.2761	0.868055
$201$	−17.9203	−1.26400
$202$	−32.8488	−2.31124
$203$	0.144106	0.0101143
$204$	14.9663	1.04785
$205$	−26.2900	−1.83618
$206$	39.6283	2.76103
$207$	−0.416728	−0.0289646
$208$	−0.261371	−0.0181228
$209$	−9.21812	−0.637631
$210$	1.67621	0.115670
$211$	−11.6469	−0.801805	−0.400902	−	0.916121i	$-0.631303\pi$
$211$	−11.6469	−0.801805	−0.400902	+	0.916121i	$0.631303\pi$
$212$	−34.9117	−2.39774
$213$	−13.6319	−0.934039
$214$	8.85983	0.605646
$215$	−18.6064	−1.26895
$216$	−14.5266	−0.988408
$217$	−0.0465664	−0.00316113
$218$	−10.3547	−0.701306
$219$	1.41249	0.0954469
$220$	20.0443	1.35139
$221$	2.26515	0.152371
$222$	40.1601	2.69537
$223$	−4.29155	−0.287383	−0.143692	−	0.989623i	$-0.545897\pi$
$223$	−4.29155	−0.287383	−0.143692	+	0.989623i	$0.545897\pi$
$224$	0.903662	0.0603785
$225$	−2.25277	−0.150185
$226$	13.3681	0.889230
$227$	−3.63320	−0.241144	−0.120572	−	0.992705i	$-0.538473\pi$
$227$	−3.63320	−0.241144	−0.120572	+	0.992705i	$0.538473\pi$
$228$	22.6236	1.49829
$229$	−4.77220	−0.315356	−0.157678	−	0.987491i	$-0.550401\pi$
$229$	−4.77220	−0.315356	−0.157678	+	0.987491i	$0.550401\pi$
$230$	−6.10008	−0.402228
$231$	0.484543	0.0318806
$232$	−2.53256	−0.166271
$233$	4.35903	0.285569	0.142785	−	0.989754i	$-0.454394\pi$
$233$	4.35903	0.285569	0.142785	+	0.989754i	$0.454394\pi$
$234$	−0.830810	−0.0543117
$235$	39.0221	2.54552
$236$	25.7672	1.67730
$237$	−5.38999	−0.350118
$238$	−1.01485	−0.0657829
$239$	−2.75071	−0.177929	−0.0889643	−	0.996035i	$-0.528356\pi$
$239$	−2.75071	−0.177929	−0.0889643	+	0.996035i	$0.528356\pi$
$240$	1.70066	0.109777
$241$	−11.3886	−0.733601	−0.366801	−	0.930300i	$-0.619547\pi$
$241$	−11.3886	−0.733601	−0.366801	+	0.930300i	$0.619547\pi$
$242$	−15.5172	−0.997485
$243$	4.96218	0.318324
$244$	9.12369	0.584084
$245$	21.6975	1.38620
$246$	30.4651	1.94239
$247$	3.42410	0.217870
$248$	0.818370	0.0519665
$249$	20.1272	1.27551
$250$	2.33383	0.147604
$251$	−10.5985	−0.668971	−0.334485	−	0.942401i	$-0.608562\pi$
$251$	−10.5985	−0.668971	−0.334485	+	0.942401i	$0.608562\pi$
$252$	0.227885	0.0143554
$253$	−1.76335	−0.110861
$254$	−8.19273	−0.514058
$255$	−14.7386	−0.922968
$256$	−13.7044	−0.856526
$257$	−26.2175	−1.63540	−0.817702	−	0.575642i	$-0.804752\pi$
$257$	−26.2175	−1.63540	−0.817702	+	0.575642i	$0.804752\pi$
$258$	21.5613	1.34235
$259$	−1.66722	−0.103596
$260$	−7.44552	−0.461752
$261$	0.464745	0.0287670
$262$	41.9085	2.58912
$263$	8.76253	0.540321	0.270160	−	0.962815i	$-0.412923\pi$
$263$	8.76253	0.540321	0.270160	+	0.962815i	$0.412923\pi$
$264$	−8.51548	−0.524092
$265$	34.3806	2.11198
$266$	−1.53409	−0.0940610
$267$	10.5064	0.642980
$268$	−35.6627	−2.17845
$269$	2.40305	0.146516	0.0732582	−	0.997313i	$-0.476660\pi$
$269$	2.40305	0.146516	0.0732582	+	0.997313i	$0.476660\pi$
$270$	39.0212	2.37475
$271$	13.2964	0.807700	0.403850	−	0.914825i	$-0.367672\pi$
$271$	13.2964	0.807700	0.403850	+	0.914825i	$0.367672\pi$
$272$	−1.02965	−0.0624316
$273$	−0.179985	−0.0108932
$274$	−48.9273	−2.95581
$275$	−9.53240	−0.574825
$276$	4.32771	0.260497
$277$	−12.9122	−0.775819	−0.387910	−	0.921697i	$-0.626803\pi$
$277$	−12.9122	−0.775819	−0.387910	+	0.921697i	$0.626803\pi$
$278$	47.6042	2.85511
$279$	−0.150177	−0.00899088
$280$	1.22294	0.0730846
$281$	19.3681	1.15540	0.577701	−	0.816249i	$-0.303950\pi$
$281$	19.3681	1.15540	0.577701	+	0.816249i	$0.303950\pi$
$282$	−45.2192	−2.69277
$283$	−6.11007	−0.363206	−0.181603	−	0.983372i	$-0.558129\pi$
$283$	−6.11007	−0.363206	−0.181603	+	0.983372i	$0.558129\pi$
$284$	−27.1284	−1.60978
$285$	−22.2795	−1.31972
$286$	−3.51550	−0.207876
$287$	−1.26474	−0.0746553
$288$	2.91432	0.171728
$289$	−8.07664	−0.475097
$290$	6.80295	0.399483
$291$	−2.49929	−0.146511
$292$	2.81095	0.164499
$293$	25.5735	1.49402	0.747009	−	0.664814i	$-0.231489\pi$
$293$	25.5735	1.49402	0.747009	+	0.664814i	$0.231489\pi$
$294$	−25.1433	−1.46639
$295$	−25.3752	−1.47740
$296$	29.3002	1.70304
$297$	11.2798	0.654523
$298$	26.7966	1.55229
$299$	0.655001	0.0378797
$300$	23.3949	1.35071
$301$	−0.895104	−0.0515929
$302$	24.2740	1.39681
$303$	−22.9501	−1.31845
$304$	−1.55646	−0.0892690
$305$	−8.98490	−0.514474
$306$	−3.27290	−0.187099
$307$	19.6201	1.11978	0.559890	−	0.828567i	$-0.310843\pi$
$307$	19.6201	1.11978	0.559890	+	0.828567i	$0.310843\pi$
$308$	0.964277	0.0549448
$309$	27.6866	1.57504
$310$	−2.19830	−0.124855
$311$	−1.82686	−0.103592	−0.0517958	−	0.998658i	$-0.516495\pi$
$311$	−1.82686	−0.103592	−0.0517958	+	0.998658i	$0.516495\pi$
$312$	3.16310	0.179075
$313$	7.09638	0.401111	0.200556	−	0.979682i	$-0.435725\pi$
$313$	7.09638	0.401111	0.200556	+	0.979682i	$0.435725\pi$
$314$	−28.1625	−1.58930
$315$	−0.224419	−0.0126446
$316$	−10.7265	−0.603413
$317$	14.4595	0.812126	0.406063	−	0.913845i	$-0.366901\pi$
$317$	14.4595	0.812126	0.406063	+	0.913845i	$0.366901\pi$
$318$	−39.8406	−2.23415
$319$	1.96653	0.110104
$320$	40.5163	2.26493
$321$	6.19000	0.345492
$322$	−0.293458	−0.0163538
$323$	13.4889	0.750543
$324$	−23.1135	−1.28409
$325$	3.54083	0.196410
$326$	26.6841	1.47790
$327$	−7.23437	−0.400062
$328$	22.2269	1.22727
$329$	1.87725	0.103496
$330$	22.8742	1.25919
$331$	17.7067	0.973249	0.486625	−	0.873611i	$-0.338228\pi$
$331$	17.7067	0.973249	0.486625	+	0.873611i	$0.338228\pi$
$332$	40.0546	2.19828
$333$	−5.37681	−0.294647
$334$	−36.5351	−1.99911
$335$	35.1203	1.91882
$336$	0.0818140	0.00446332
$337$	2.94729	0.160549	0.0802746	−	0.996773i	$-0.474420\pi$
$337$	2.94729	0.160549	0.0802746	+	0.996773i	$0.474420\pi$
$338$	−28.2177	−1.53484
$339$	9.33971	0.507264
$340$	−29.3310	−1.59069
$341$	−0.635462	−0.0344122
$342$	−4.94745	−0.267528
$343$	2.09096	0.112901
$344$	15.7308	0.848147
$345$	−4.26188	−0.229452
$346$	−47.9896	−2.57994
$347$	32.6398	1.75219	0.876097	−	0.482135i	$-0.160139\pi$
$347$	32.6398	1.75219	0.876097	+	0.482135i	$0.160139\pi$
$348$	−4.82636	−0.258720
$349$	−18.0069	−0.963890	−0.481945	−	0.876202i	$-0.660069\pi$
$349$	−18.0069	−0.963890	−0.481945	+	0.876202i	$0.660069\pi$
$350$	−1.58639	−0.0847961
$351$	−4.18993	−0.223642
$352$	12.3317	0.657282
$353$	9.30547	0.495280	0.247640	−	0.968852i	$-0.420345\pi$
$353$	9.30547	0.495280	0.247640	+	0.968852i	$0.420345\pi$
$354$	29.4051	1.56286
$355$	26.7158	1.41793
$356$	20.9085	1.10815
$357$	−0.709034	−0.0375260
$358$	−17.4133	−0.920324
$359$	2.82343	0.149015	0.0745076	−	0.997220i	$-0.476261\pi$
$359$	2.82343	0.149015	0.0745076	+	0.997220i	$0.476261\pi$
$360$	3.94399	0.207867
$361$	1.39040	0.0731788
$362$	24.7337	1.29997
$363$	−10.8413	−0.569018
$364$	−0.358183	−0.0187739
$365$	−2.76819	−0.144894
$366$	10.4118	0.544233
$367$	16.7063	0.872063	0.436031	−	0.899931i	$-0.356384\pi$
$367$	16.7063	0.872063	0.436031	+	0.899931i	$0.356384\pi$
$368$	−0.297737	−0.0155206
$369$	−4.07880	−0.212334
$370$	−78.7060	−4.09173
$371$	1.65396	0.0858691
$372$	1.55959	0.0808608
$373$	20.9544	1.08498	0.542490	−	0.840062i	$-0.317482\pi$
$373$	20.9544	1.08498	0.542490	+	0.840062i	$0.317482\pi$
$374$	−13.8490	−0.716115
$375$	1.63055	0.0842011
$376$	−32.9912	−1.70139
$377$	−0.730472	−0.0376212
$378$	1.87720	0.0965528
$379$	6.08388	0.312508	0.156254	−	0.987717i	$-0.450058\pi$
$379$	6.08388	0.312508	0.156254	+	0.987717i	$0.450058\pi$
$380$	−44.3379	−2.27449
$381$	−5.72393	−0.293246
$382$	−40.0408	−2.04866
$383$	−20.0586	−1.02494	−0.512472	−	0.858704i	$-0.671270\pi$
$383$	−20.0586	−1.02494	−0.512472	+	0.858704i	$0.671270\pi$
$384$	−27.7810	−1.41770
$385$	−0.949609	−0.0483966
$386$	25.3145	1.28848
$387$	−2.88672	−0.146740
$388$	−4.97378	−0.252505
$389$	−20.8648	−1.05789	−0.528945	−	0.848656i	$-0.677412\pi$
$389$	−20.8648	−1.05789	−0.528945	+	0.848656i	$0.677412\pi$
$390$	−8.49669	−0.430247
$391$	2.58032	0.130492
$392$	−18.3441	−0.926518
$393$	29.2798	1.47697
$394$	2.27104	0.114413
$395$	10.5633	0.531499
$396$	3.10981	0.156274
$397$	−33.2509	−1.66881	−0.834407	−	0.551148i	$-0.814190\pi$
$397$	−33.2509	−1.66881	−0.834407	+	0.551148i	$0.814190\pi$
$398$	18.1531	0.909934
$399$	−1.07180	−0.0536573
$400$	−1.60952	−0.0804762
$401$	19.4355	0.970563	0.485282	−	0.874358i	$-0.338717\pi$
$401$	19.4355	0.970563	0.485282	+	0.874358i	$0.338717\pi$
$402$	−40.6977	−2.02982
$403$	0.236044	0.0117582
$404$	−45.6725	−2.27229
$405$	22.7619	1.13105
$406$	0.327271	0.0162422
$407$	−22.7515	−1.12775
$408$	12.4607	0.616898
$409$	12.3242	0.609391	0.304695	−	0.952450i	$-0.401445\pi$
$409$	12.3242	0.609391	0.304695	+	0.952450i	$0.401445\pi$
$410$	−59.7057	−2.94865
$411$	−34.1835	−1.68615
$412$	55.0985	2.71451
$413$	−1.22073	−0.0600683
$414$	−0.946406	−0.0465133
$415$	−39.4453	−1.93630
$416$	−4.58064	−0.224585
$417$	33.2591	1.62870
$418$	−20.9347	−1.02395
$419$	−32.3778	−1.58176	−0.790879	−	0.611973i	$-0.790376\pi$
$419$	−32.3778	−1.58176	−0.790879	+	0.611973i	$0.790376\pi$
$420$	2.33058	0.113721
$421$	−9.55814	−0.465835	−0.232918	−	0.972496i	$-0.574827\pi$
$421$	−9.55814	−0.465835	−0.232918	+	0.972496i	$0.574827\pi$
$422$	−26.4505	−1.28759
$423$	6.05414	0.294363
$424$	−29.0670	−1.41162
$425$	13.9488	0.676616
$426$	−30.9585	−1.49994
$427$	−0.432239	−0.0209175
$428$	12.3186	0.595441
$429$	−2.45614	−0.118583
$430$	−42.2559	−2.03776
$431$	−4.32795	−0.208470	−0.104235	−	0.994553i	$-0.533239\pi$
$431$	−4.32795	−0.208470	−0.104235	+	0.994553i	$0.533239\pi$
$432$	1.90458	0.0916340
$433$	18.3407	0.881399	0.440700	−	0.897655i	$-0.354730\pi$
$433$	18.3407	0.881399	0.440700	+	0.897655i	$0.354730\pi$
$434$	−0.105754	−0.00507636
$435$	4.75294	0.227886
$436$	−14.3969	−0.689489
$437$	3.90051	0.186587
$438$	3.20781	0.153275
$439$	−1.41079	−0.0673333	−0.0336666	−	0.999433i	$-0.510718\pi$
$439$	−1.41079	−0.0673333	−0.0336666	+	0.999433i	$0.510718\pi$
$440$	16.6887	0.795601
$441$	3.36629	0.160300
$442$	5.14425	0.244687
$443$	4.09086	0.194363	0.0971813	−	0.995267i	$-0.469017\pi$
$443$	4.09086	0.194363	0.0971813	+	0.995267i	$0.469017\pi$
$444$	55.8380	2.64996
$445$	−20.5905	−0.976081
$446$	−9.74627	−0.461499
$447$	18.7217	0.885505
$448$	1.94913	0.0920876
$449$	30.2781	1.42891	0.714456	−	0.699680i	$-0.246674\pi$
$449$	30.2781	1.42891	0.714456	+	0.699680i	$0.246674\pi$
$450$	−5.11613	−0.241176
$451$	−17.2591	−0.812699
$452$	18.5867	0.874247
$453$	16.9593	0.796815
$454$	−8.25113	−0.387245
$455$	0.352735	0.0165365
$456$	18.8362	0.882084
$457$	−25.5350	−1.19448	−0.597238	−	0.802064i	$-0.703735\pi$
$457$	−25.5350	−1.19448	−0.597238	+	0.802064i	$0.703735\pi$
$458$	−10.8378	−0.506419
$459$	−16.5058	−0.770427
$460$	−8.48146	−0.395450
$461$	20.4572	0.952785	0.476392	−	0.879233i	$-0.341944\pi$
$461$	20.4572	0.952785	0.476392	+	0.879233i	$0.341944\pi$
$462$	1.10042	0.0511960
$463$	34.1826	1.58860	0.794301	−	0.607525i	$-0.207838\pi$
$463$	34.1826	1.58860	0.794301	+	0.607525i	$0.207838\pi$
$464$	0.332044	0.0154147
$465$	−1.53586	−0.0712239
$466$	9.89952	0.458586
$467$	35.5139	1.64339	0.821695	−	0.569928i	$-0.193029\pi$
$467$	35.5139	1.64339	0.821695	+	0.569928i	$0.193029\pi$
$468$	−1.15515	−0.0533966
$469$	1.68954	0.0780156
$470$	88.6208	4.08777
$471$	−19.6760	−0.906622
$472$	21.4535	0.987475
$473$	−12.2149	−0.561642
$474$	−12.2409	−0.562242
$475$	21.0856	0.967472
$476$	−1.41103	−0.0646745
$477$	5.33403	0.244228
$478$	−6.24697	−0.285730
$479$	−14.2527	−0.651223	−0.325611	−	0.945504i	$-0.605570\pi$
$479$	−14.2527	−0.651223	−0.325611	+	0.945504i	$0.605570\pi$
$480$	29.8048	1.36040
$481$	8.45111	0.385337
$482$	−25.8638	−1.17807
$483$	−0.205027	−0.00932906
$484$	−21.5749	−0.980678
$485$	4.89812	0.222412
$486$	11.2693	0.511186
$487$	27.1058	1.22828	0.614141	−	0.789196i	$-0.289502\pi$
$487$	27.1058	1.22828	0.614141	+	0.789196i	$0.289502\pi$
$488$	7.59627	0.343867
$489$	18.6431	0.843070
$490$	49.2759	2.22606
$491$	−26.3562	−1.18944	−0.594720	−	0.803933i	$-0.702737\pi$
$491$	−26.3562	−1.18944	−0.594720	+	0.803933i	$0.702737\pi$
$492$	42.3582	1.90966
$493$	−2.87763	−0.129602
$494$	7.77625	0.349870
$495$	−3.06250	−0.137649
$496$	−0.107296	−0.00481775
$497$	1.28522	0.0576500
$498$	45.7096	2.04830
$499$	−33.1003	−1.48177	−0.740887	−	0.671630i	$-0.765595\pi$
$499$	−33.1003	−1.48177	−0.740887	+	0.671630i	$0.765595\pi$
$500$	3.24491	0.145117
$501$	−25.5256	−1.14040
$502$	−24.0696	−1.07428
$503$	22.3052	0.994540	0.497270	−	0.867596i	$-0.334336\pi$
$503$	22.3052	0.994540	0.497270	+	0.867596i	$0.334336\pi$
$504$	0.189735	0.00845145
$505$	44.9778	2.00148
$506$	−4.00463	−0.178028
$507$	−19.7145	−0.875553
$508$	−11.3911	−0.505396
$509$	30.9032	1.36976	0.684881	−	0.728655i	$-0.259854\pi$
$509$	30.9032	1.36976	0.684881	+	0.728655i	$0.259854\pi$
$510$	−33.4720	−1.48216
$511$	−0.133170	−0.00589110
$512$	3.89454	0.172116
$513$	−24.9509	−1.10161
$514$	−59.5410	−2.62624
$515$	−54.2604	−2.39100
$516$	29.9785	1.31973
$517$	25.6176	1.12666
$518$	−3.78633	−0.166362
$519$	−33.5284	−1.47173
$520$	−6.19905	−0.271846
$521$	−26.9897	−1.18244	−0.591219	−	0.806511i	$-0.701353\pi$
$521$	−26.9897	−1.18244	−0.591219	+	0.806511i	$0.701353\pi$
$522$	1.05545	0.0461959
$523$	−5.34197	−0.233588	−0.116794	−	0.993156i	$-0.537262\pi$
$523$	−5.34197	−0.233588	−0.116794	+	0.993156i	$0.537262\pi$
$524$	58.2689	2.54549
$525$	−1.10835	−0.0483722
$526$	19.9000	0.867683
$527$	0.929874	0.0405060
$528$	1.11646	0.0485878
$529$	−22.2539	−0.967559
$530$	78.0797	3.39157
$531$	−3.93687	−0.170846
$532$	−2.13297	−0.0924761
$533$	6.41094	0.277689
$534$	23.8604	1.03254
$535$	−12.1312	−0.524477
$536$	−29.6924	−1.28251
$537$	−12.1660	−0.525001
$538$	5.45742	0.235286
$539$	14.2442	0.613540
$540$	54.2545	2.33474
$541$	−3.93668	−0.169251	−0.0846256	−	0.996413i	$-0.526969\pi$
$541$	−3.93668	−0.169251	−0.0846256	+	0.996413i	$0.526969\pi$
$542$	30.1967	1.29706
$543$	17.2804	0.741574
$544$	−18.0450	−0.773674
$545$	14.1780	0.607317
$546$	−0.408752	−0.0174930
$547$	28.4145	1.21492	0.607458	−	0.794352i	$-0.292189\pi$
$547$	28.4145	1.21492	0.607458	+	0.794352i	$0.292189\pi$
$548$	−68.0278	−2.90600
$549$	−1.39398	−0.0594934
$550$	−21.6484	−0.923093
$551$	−4.34994	−0.185314
$552$	3.60320	0.153362
$553$	0.508173	0.0216097
$554$	−29.3241	−1.24586
$555$	−54.9886	−2.33414
$556$	66.1881	2.80700
$557$	46.9688	1.99013	0.995066	−	0.0992132i	$-0.0316326\pi$
$557$	46.9688	1.99013	0.995066	+	0.0992132i	$0.0316326\pi$
$558$	−0.341058	−0.0144382
$559$	4.53726	0.191906
$560$	−0.160339	−0.00677557
$561$	−9.67573	−0.408510
$562$	43.9856	1.85542
$563$	18.8864	0.795966	0.397983	−	0.917393i	$-0.369710\pi$
$563$	18.8864	0.795966	0.397983	+	0.917393i	$0.369710\pi$
$564$	−62.8721	−2.64739
$565$	−18.3040	−0.770055
$566$	−13.8762	−0.583261
$567$	1.09501	0.0459863
$568$	−22.5868	−0.947721
$569$	−12.5338	−0.525443	−0.262721	−	0.964872i	$-0.584620\pi$
$569$	−12.5338	−0.525443	−0.262721	+	0.964872i	$0.584620\pi$
$570$	−50.5976	−2.11930
$571$	−2.83681	−0.118717	−0.0593585	−	0.998237i	$-0.518906\pi$
$571$	−2.83681	−0.118717	−0.0593585	+	0.998237i	$0.518906\pi$
$572$	−4.88790	−0.204373
$573$	−27.9748	−1.16867
$574$	−2.87227	−0.119886
$575$	4.03349	0.168208
$576$	6.28596	0.261915
$577$	−41.8016	−1.74022	−0.870112	−	0.492854i	$-0.835954\pi$
$577$	−41.8016	−1.74022	−0.870112	+	0.492854i	$0.835954\pi$
$578$	−18.3424	−0.762942
$579$	17.6862	0.735015
$580$	9.45872	0.392752
$581$	−1.89761	−0.0787259
$582$	−5.67599	−0.235277
$583$	22.5705	0.934774
$584$	2.34037	0.0968450
$585$	1.13757	0.0470329
$586$	58.0783	2.39919
$587$	−3.47959	−0.143618	−0.0718091	−	0.997418i	$-0.522877\pi$
$587$	−3.47959	−0.143618	−0.0718091	+	0.997418i	$0.522877\pi$
$588$	−34.9588	−1.44168
$589$	1.40564	0.0579182
$590$	−57.6281	−2.37251
$591$	1.58668	0.0652674
$592$	−3.84154	−0.157886
$593$	−6.94185	−0.285068	−0.142534	−	0.989790i	$-0.545525\pi$
$593$	−6.94185	−0.285068	−0.142534	+	0.989790i	$0.545525\pi$
$594$	25.6170	1.05108
$595$	1.38957	0.0569667
$596$	37.2576	1.52613
$597$	12.6828	0.519074
$598$	1.48753	0.0608297
$599$	16.5945	0.678034	0.339017	−	0.940780i	$-0.389906\pi$
$599$	16.5945	0.678034	0.339017	+	0.940780i	$0.389906\pi$
$600$	19.4783	0.795200
$601$	−45.3204	−1.84866	−0.924329	−	0.381597i	$-0.875374\pi$
$601$	−45.3204	−1.84866	−0.924329	+	0.381597i	$0.875374\pi$
$602$	−2.03282	−0.0828514
$603$	5.44878	0.221891
$604$	33.7502	1.37328
$605$	21.2467	0.863802
$606$	−52.1206	−2.11726
$607$	−27.6690	−1.12305	−0.561525	−	0.827460i	$-0.689785\pi$
$607$	−27.6690	−1.12305	−0.561525	+	0.827460i	$0.689785\pi$
$608$	−27.2776	−1.10625
$609$	0.228651	0.00926540
$610$	−20.4051	−0.826177
$611$	−9.51572	−0.384965
$612$	−4.55059	−0.183947
$613$	26.5900	1.07396	0.536981	−	0.843594i	$-0.319565\pi$
$613$	26.5900	1.07396	0.536981	+	0.843594i	$0.319565\pi$
$614$	44.5581	1.79822
$615$	−41.7139	−1.68207
$616$	0.802846	0.0323476
$617$	6.83991	0.275364	0.137682	−	0.990476i	$-0.456035\pi$
$617$	6.83991	0.275364	0.137682	+	0.990476i	$0.456035\pi$
$618$	62.8774	2.52930
$619$	12.4016	0.498464	0.249232	−	0.968444i	$-0.419822\pi$
$619$	12.4016	0.498464	0.249232	+	0.968444i	$0.419822\pi$
$620$	−3.05648	−0.122751
$621$	−4.77290	−0.191530
$622$	−4.14887	−0.166354
$623$	−0.990550	−0.0396855
$624$	−0.414713	−0.0166018
$625$	−26.5432	−1.06173
$626$	16.1162	0.644131
$627$	−14.6262	−0.584115
$628$	−39.1567	−1.56252
$629$	33.2924	1.32745
$630$	−0.509664	−0.0203055
$631$	−1.32218	−0.0526350	−0.0263175	−	0.999654i	$-0.508378\pi$
$631$	−1.32218	−0.0526350	−0.0263175	+	0.999654i	$0.508378\pi$
$632$	−8.93075	−0.355246
$633$	−18.4799	−0.734510
$634$	32.8380	1.30417
$635$	11.2178	0.445164
$636$	−55.3937	−2.19650
$637$	−5.29103	−0.209638
$638$	4.46606	0.176813
$639$	4.14485	0.163968
$640$	54.4454	2.15214
$641$	−41.1382	−1.62486	−0.812431	−	0.583057i	$-0.801856\pi$
$641$	−41.1382	−1.62486	−0.812431	+	0.583057i	$0.801856\pi$
$642$	14.0577	0.554815
$643$	37.6607	1.48519	0.742596	−	0.669739i	$-0.233594\pi$
$643$	37.6607	1.48519	0.742596	+	0.669739i	$0.233594\pi$
$644$	−0.408020	−0.0160782
$645$	−29.5225	−1.16245
$646$	30.6339	1.20527
$647$	19.6152	0.771153	0.385577	−	0.922676i	$-0.374003\pi$
$647$	19.6152	0.771153	0.385577	+	0.922676i	$0.374003\pi$
$648$	−19.2440	−0.755978
$649$	−16.6586	−0.653905
$650$	8.04137	0.315409
$651$	−0.0738861	−0.00289582
$652$	37.1012	1.45299
$653$	15.1389	0.592432	0.296216	−	0.955121i	$-0.404275\pi$
$653$	15.1389	0.592432	0.296216	+	0.955121i	$0.404275\pi$
$654$	−16.4295	−0.642446
$655$	−57.3826	−2.24212
$656$	−2.91416	−0.113779
$657$	−0.429475	−0.0167554
$658$	4.26330	0.166201
$659$	−19.0534	−0.742217	−0.371108	−	0.928590i	$-0.621022\pi$
$659$	−19.0534	−0.742217	−0.371108	+	0.928590i	$0.621022\pi$
$660$	31.8040	1.23797
$661$	−1.14523	−0.0445444	−0.0222722	−	0.999752i	$-0.507090\pi$
$661$	−1.14523	−0.0445444	−0.0222722	+	0.999752i	$0.507090\pi$
$662$	40.2127	1.56291
$663$	3.59407	0.139582
$664$	33.3490	1.29419
$665$	2.10053	0.0814549
$666$	−12.2109	−0.473165
$667$	−0.832107	−0.0322193
$668$	−50.7979	−1.96543
$669$	−6.80932	−0.263263
$670$	79.7595	3.08138
$671$	−5.89849	−0.227709
$672$	1.43382	0.0553110
$673$	−26.2697	−1.01262	−0.506310	−	0.862351i	$-0.668991\pi$
$673$	−26.2697	−1.01262	−0.506310	+	0.862351i	$0.668991\pi$
$674$	6.69341	0.257821
$675$	−25.8016	−0.993103
$676$	−39.2334	−1.50898
$677$	25.5460	0.981813	0.490906	−	0.871212i	$-0.336666\pi$
$677$	25.5460	0.981813	0.490906	+	0.871212i	$0.336666\pi$
$678$	21.2109	0.814598
$679$	0.235635	0.00904284
$680$	−24.4206	−0.936487
$681$	−5.76473	−0.220905
$682$	−1.44316	−0.0552614
$683$	−18.3347	−0.701557	−0.350778	−	0.936458i	$-0.614083\pi$
$683$	−18.3347	−0.701557	−0.350778	+	0.936458i	$0.614083\pi$
$684$	−6.87886	−0.263020
$685$	66.9930	2.55967
$686$	4.74866	0.181304
$687$	−7.57196	−0.288888
$688$	−2.06246	−0.0786306
$689$	−8.38387	−0.319400
$690$	−9.67889	−0.368469
$691$	26.2087	0.997024	0.498512	−	0.866883i	$-0.333880\pi$
$691$	26.2087	0.997024	0.498512	+	0.866883i	$0.333880\pi$
$692$	−66.7240	−2.53647
$693$	−0.147328	−0.00559654
$694$	74.1261	2.81379
$695$	−65.1813	−2.47247
$696$	−4.01837	−0.152316
$697$	25.2553	0.956613
$698$	−40.8945	−1.54788
$699$	6.91639	0.261602
$700$	−2.20569	−0.0833673
$701$	−38.6044	−1.45807	−0.729033	−	0.684478i	$-0.760030\pi$
$701$	−38.6044	−1.45807	−0.729033	+	0.684478i	$0.760030\pi$
$702$	−9.51549	−0.359139
$703$	50.3261	1.89809
$704$	26.5985	1.00247
$705$	61.9157	2.33188
$706$	21.1331	0.795354
$707$	2.16375	0.0813764
$708$	40.8843	1.53653
$709$	22.2848	0.836923	0.418462	−	0.908234i	$-0.362569\pi$
$709$	22.2848	0.836923	0.418462	+	0.908234i	$0.362569\pi$
$710$	60.6725	2.27700
$711$	1.63886	0.0614621
$712$	17.4082	0.652399
$713$	0.268886	0.0100699
$714$	−1.61024	−0.0602618
$715$	4.81355	0.180016
$716$	−24.2112	−0.904817
$717$	−4.36450	−0.162995
$718$	6.41213	0.239299
$719$	−8.39863	−0.313216	−0.156608	−	0.987661i	$-0.550056\pi$
$719$	−8.39863	−0.313216	−0.156608	+	0.987661i	$0.550056\pi$
$720$	−0.517096	−0.0192710
$721$	−2.61032	−0.0972133
$722$	3.15765	0.117515
$723$	−18.0700	−0.672031
$724$	34.3893	1.27807
$725$	−4.49824	−0.167061
$726$	−24.6209	−0.913767
$727$	11.1345	0.412956	0.206478	−	0.978451i	$-0.433800\pi$
$727$	11.1345	0.412956	0.206478	+	0.978451i	$0.433800\pi$
$728$	−0.298219	−0.0110527
$729$	29.8332	1.10493
$730$	−6.28668	−0.232680
$731$	17.8741	0.661099
$732$	14.4764	0.535063
$733$	−48.5244	−1.79229	−0.896144	−	0.443763i	$-0.853643\pi$
$733$	−48.5244	−1.79229	−0.896144	+	0.443763i	$0.853643\pi$
$734$	37.9407	1.40042
$735$	34.4270	1.26986
$736$	−5.21798	−0.192337
$737$	23.0560	0.849280
$738$	−9.26312	−0.340980
$739$	−12.7441	−0.468798	−0.234399	−	0.972140i	$-0.575312\pi$
$739$	−12.7441	−0.468798	−0.234399	+	0.972140i	$0.575312\pi$
$740$	−109.432	−4.02279
$741$	5.43295	0.199584
$742$	3.75620	0.137894
$743$	−20.9237	−0.767617	−0.383808	−	0.923413i	$-0.625388\pi$
$743$	−20.9237	−0.767617	−0.383808	+	0.923413i	$0.625388\pi$
$744$	1.29849	0.0476050
$745$	−36.6908	−1.34425
$746$	47.5884	1.74233
$747$	−6.11980	−0.223912
$748$	−19.2554	−0.704048
$749$	−0.583598	−0.0213242
$750$	3.70304	0.135216
$751$	−52.6802	−1.92233	−0.961165	−	0.275975i	$-0.910999\pi$
$751$	−52.6802	−1.92233	−0.961165	+	0.275975i	$0.910999\pi$
$752$	4.32547	0.157734
$753$	−16.8164	−0.612825
$754$	−1.65893	−0.0604147
$755$	−33.2368	−1.20961
$756$	2.61003	0.0949260
$757$	32.8341	1.19337	0.596687	−	0.802474i	$-0.296483\pi$
$757$	32.8341	1.19337	0.596687	+	0.802474i	$0.296483\pi$
$758$	13.8167	0.501846
$759$	−2.79787	−0.101556
$760$	−36.9152	−1.33905
$761$	26.5174	0.961256	0.480628	−	0.876925i	$-0.340409\pi$
$761$	26.5174	0.961256	0.480628	+	0.876925i	$0.340409\pi$
$762$	−12.9993	−0.470914
$763$	0.682062	0.0246923
$764$	−55.6721	−2.01414
$765$	4.48137	0.162024
$766$	−45.5538	−1.64592
$767$	6.18786	0.223431
$768$	−21.7445	−0.784639
$769$	−4.12397	−0.148714	−0.0743570	−	0.997232i	$-0.523690\pi$
$769$	−4.12397	−0.148714	−0.0743570	+	0.997232i	$0.523690\pi$
$770$	−2.15660	−0.0777185
$771$	−41.5989	−1.49815
$772$	35.1969	1.26677
$773$	−44.8179	−1.61199	−0.805994	−	0.591924i	$-0.798369\pi$
$773$	−44.8179	−1.61199	−0.805994	+	0.591924i	$0.798369\pi$
$774$	−6.55586	−0.235645
$775$	1.45356	0.0522134
$776$	−4.14111	−0.148657
$777$	−2.64535	−0.0949014
$778$	−47.3849	−1.69883
$779$	38.1770	1.36783
$780$	−11.8137	−0.422997
$781$	17.5386	0.627580
$782$	5.86000	0.209553
$783$	5.32285	0.190223
$784$	2.40510	0.0858963
$785$	38.5611	1.37630
$786$	66.4955	2.37181
$787$	−3.62405	−0.129183	−0.0645917	−	0.997912i	$-0.520575\pi$
$787$	−3.62405	−0.129183	−0.0645917	+	0.997912i	$0.520575\pi$
$788$	3.15762	0.112485
$789$	13.9033	0.494972
$790$	23.9897	0.853517
$791$	−0.880555	−0.0313089
$792$	2.58919	0.0920027
$793$	2.19101	0.0778050
$794$	−75.5141	−2.67989
$795$	54.5511	1.93473
$796$	25.2398	0.894602
$797$	−23.4545	−0.830800	−0.415400	−	0.909639i	$-0.636358\pi$
$797$	−23.4545	−0.830800	−0.415400	+	0.909639i	$0.636358\pi$
$798$	−2.43411	−0.0861665
$799$	−37.4863	−1.32617
$800$	−28.2076	−0.997289
$801$	−3.19453	−0.112873
$802$	44.1388	1.55860
$803$	−1.81729	−0.0641307
$804$	−56.5854	−1.99561
$805$	0.401813	0.0141620
$806$	0.536065	0.0188821
$807$	3.81287	0.134220
$808$	−38.0264	−1.33776
$809$	26.3278	0.925636	0.462818	−	0.886453i	$-0.346838\pi$
$809$	26.3278	0.925636	0.462818	+	0.886453i	$0.346838\pi$
$810$	51.6933	1.81632
$811$	−55.1858	−1.93783	−0.968917	−	0.247386i	$-0.920428\pi$
$811$	−55.1858	−1.93783	−0.968917	+	0.247386i	$0.920428\pi$
$812$	0.455033	0.0159685
$813$	21.0972	0.739911
$814$	−51.6696	−1.81102
$815$	−36.5368	−1.27983
$816$	−1.63372	−0.0571918
$817$	27.0193	0.945285
$818$	27.9886	0.978600
$819$	0.0547255	0.00191226
$820$	−83.0139	−2.89897
$821$	48.6965	1.69952	0.849759	−	0.527171i	$-0.176747\pi$
$821$	48.6965	1.69952	0.849759	+	0.527171i	$0.176747\pi$
$822$	−77.6321	−2.70773
$823$	−16.4203	−0.572376	−0.286188	−	0.958173i	$-0.592388\pi$
$823$	−16.4203	−0.572376	−0.286188	+	0.958173i	$0.592388\pi$
$824$	45.8744	1.59811
$825$	−15.1249	−0.526581
$826$	−2.77233	−0.0964617
$827$	49.4264	1.71872	0.859361	−	0.511369i	$-0.170861\pi$
$827$	49.4264	1.71872	0.859361	+	0.511369i	$0.170861\pi$
$828$	−1.31587	−0.0457296
$829$	12.1454	0.421826	0.210913	−	0.977505i	$-0.432356\pi$
$829$	12.1454	0.421826	0.210913	+	0.977505i	$0.432356\pi$
$830$	−89.5819	−3.10943
$831$	−20.4876	−0.710706
$832$	−9.88008	−0.342530
$833$	−20.8435	−0.722186
$834$	75.5327	2.61548
$835$	50.0252	1.73119
$836$	−29.1073	−1.00670
$837$	−1.72002	−0.0594526
$838$	−73.5312	−2.54009
$839$	40.4060	1.39497	0.697484	−	0.716600i	$-0.254303\pi$
$839$	40.4060	1.39497	0.697484	+	0.716600i	$0.254303\pi$
$840$	1.94042	0.0669507
$841$	−28.0720	−0.968001
$842$	−21.7069	−0.748069
$843$	30.7309	1.05843
$844$	−36.7764	−1.26590
$845$	38.6366	1.32914
$846$	13.7492	0.472707
$847$	1.02212	0.0351205
$848$	3.81097	0.130869
$849$	−9.69474	−0.332723
$850$	31.6783	1.08656
$851$	9.62696	0.330008
$852$	−43.0442	−1.47467
$853$	36.0359	1.23385	0.616924	−	0.787023i	$-0.288379\pi$
$853$	36.0359	1.23385	0.616924	+	0.787023i	$0.288379\pi$
$854$	−0.981631	−0.0335907
$855$	6.77422	0.231674
$856$	10.2563	0.350553
$857$	−57.0697	−1.94946	−0.974731	−	0.223380i	$-0.928291\pi$
$857$	−57.0697	−1.94946	−0.974731	+	0.223380i	$0.928291\pi$
$858$	−5.57798	−0.190429
$859$	2.93679	0.100202	0.0501010	−	0.998744i	$-0.484046\pi$
$859$	2.93679	0.100202	0.0501010	+	0.998744i	$0.484046\pi$
$860$	−58.7520	−2.00343
$861$	−2.00674	−0.0683895
$862$	−9.82894	−0.334775
$863$	−40.7560	−1.38735	−0.693675	−	0.720288i	$-0.744010\pi$
$863$	−40.7560	−1.38735	−0.693675	+	0.720288i	$0.744010\pi$
$864$	33.3785	1.13556
$865$	65.7091	2.23418
$866$	41.6525	1.41541
$867$	−12.8151	−0.435222
$868$	−0.147039	−0.00499083
$869$	6.93471	0.235244
$870$	10.7941	0.365955
$871$	−8.56423	−0.290188
$872$	−11.9867	−0.405922
$873$	0.759926	0.0257196
$874$	8.85821	0.299633
$875$	−0.153729	−0.00519700
$876$	4.46009	0.150692
$877$	53.7864	1.81624	0.908118	−	0.418713i	$-0.137519\pi$
$877$	53.7864	1.81624	0.908118	+	0.418713i	$0.137519\pi$
$878$	−3.20396	−0.108128
$879$	40.5769	1.36863
$880$	−2.18805	−0.0737591
$881$	24.3409	0.820065	0.410032	−	0.912071i	$-0.365517\pi$
$881$	24.3409	0.820065	0.410032	+	0.912071i	$0.365517\pi$
$882$	7.64497	0.257420
$883$	−29.9957	−1.00943	−0.504717	−	0.863285i	$-0.668403\pi$
$883$	−29.9957	−1.00943	−0.504717	+	0.863285i	$0.668403\pi$
$884$	7.15248	0.240564
$885$	−40.2624	−1.35341
$886$	9.29051	0.312121
$887$	27.8139	0.933900	0.466950	−	0.884284i	$-0.345353\pi$
$887$	27.8139	0.933900	0.466950	+	0.884284i	$0.345353\pi$
$888$	46.4901	1.56010
$889$	0.539656	0.0180995
$890$	−46.7617	−1.56746
$891$	14.9430	0.500608
$892$	−13.5511	−0.453723
$893$	−56.6659	−1.89625
$894$	42.5177	1.42200
$895$	23.8430	0.796982
$896$	2.61922	0.0875019
$897$	1.03928	0.0347005
$898$	68.7627	2.29464
$899$	−0.299868	−0.0100012
$900$	−7.11338	−0.237113
$901$	−33.0275	−1.10030
$902$	−39.1961	−1.30509
$903$	−1.42025	−0.0472628
$904$	15.4751	0.514694
$905$	−33.8662	−1.12575
$906$	38.5151	1.27958
$907$	−52.0834	−1.72940	−0.864700	−	0.502288i	$-0.832492\pi$
$907$	−52.0834	−1.72940	−0.864700	+	0.502288i	$0.832492\pi$
$908$	−11.4722	−0.380720
$909$	6.97813	0.231450
$910$	0.801075	0.0265554
$911$	5.82160	0.192878	0.0964392	−	0.995339i	$-0.469255\pi$
$911$	5.82160	0.192878	0.0964392	+	0.995339i	$0.469255\pi$
$912$	−2.46961	−0.0817768
$913$	−25.8954	−0.857013
$914$	−57.9909	−1.91817
$915$	−14.2562	−0.471295
$916$	−15.0688	−0.497886
$917$	−2.76052	−0.0911603
$918$	−37.4854	−1.23720
$919$	−32.5191	−1.07271	−0.536353	−	0.843994i	$-0.680198\pi$
$919$	−32.5191	−1.07271	−0.536353	+	0.843994i	$0.680198\pi$
$920$	−7.06156	−0.232813
$921$	31.1309	1.02580
$922$	46.4590	1.53005
$923$	−6.51475	−0.214436
$924$	1.53000	0.0503333
$925$	52.0419	1.71113
$926$	77.6301	2.55108
$927$	−8.41830	−0.276493
$928$	5.81921	0.191025
$929$	−53.9917	−1.77141	−0.885706	−	0.464247i	$-0.846325\pi$
$929$	−53.9917	−1.77141	−0.885706	+	0.464247i	$0.846325\pi$
$930$	−3.48800	−0.114376
$931$	−31.5080	−1.03263
$932$	13.7641	0.450859
$933$	−2.89864	−0.0948973
$934$	80.6535	2.63906
$935$	18.9625	0.620141
$936$	−0.961760	−0.0314361
$937$	−4.74365	−0.154968	−0.0774842	−	0.996994i	$-0.524689\pi$
$937$	−4.74365	−0.154968	−0.0774842	+	0.996994i	$0.524689\pi$
$938$	3.83701	0.125283
$939$	11.2597	0.367446
$940$	123.217	4.01890
$941$	−34.5465	−1.12618	−0.563092	−	0.826394i	$-0.690388\pi$
$941$	−34.5465	−1.12618	−0.563092	+	0.826394i	$0.690388\pi$
$942$	−44.6849	−1.45591
$943$	7.30293	0.237816
$944$	−2.81276	−0.0915475
$945$	−2.57033	−0.0836128
$946$	−27.7405	−0.901923
$947$	48.5831	1.57874	0.789369	−	0.613919i	$-0.210408\pi$
$947$	48.5831	1.57874	0.789369	+	0.613919i	$0.210408\pi$
$948$	−17.0195	−0.552769
$949$	0.675036	0.0219126
$950$	47.8862	1.55363
$951$	22.9426	0.743965
$952$	−1.17481	−0.0380757
$953$	−2.67338	−0.0865992	−0.0432996	−	0.999062i	$-0.513787\pi$
$953$	−2.67338	−0.0865992	−0.0432996	+	0.999062i	$0.513787\pi$
$954$	12.1138	0.392198
$955$	54.8252	1.77410
$956$	−8.68569	−0.280915
$957$	3.12025	0.100863
$958$	−32.3684	−1.04578
$959$	3.22285	0.104071
$960$	64.2865	2.07484
$961$	−30.9031	−0.996874
$962$	19.1928	0.618801
$963$	−1.88211	−0.0606502
$964$	−35.9607	−1.15822
$965$	−34.6616	−1.11579
$966$	−0.465624	−0.0149812
$967$	6.68133	0.214857	0.107429	−	0.994213i	$-0.465738\pi$
$967$	6.68133	0.214857	0.107429	+	0.994213i	$0.465738\pi$
$968$	−17.9630	−0.577353
$969$	21.4026	0.687551
$970$	11.1238	0.357165
$971$	24.0388	0.771442	0.385721	−	0.922615i	$-0.373953\pi$
$971$	24.0388	0.771442	0.385721	+	0.922615i	$0.373953\pi$
$972$	15.6687	0.502573
$973$	−3.13569	−0.100526
$974$	61.5584	1.97246
$975$	5.61818	0.179926
$976$	−0.995946	−0.0318795
$977$	−2.00773	−0.0642329	−0.0321165	−	0.999484i	$-0.510225\pi$
$977$	−2.00773	−0.0642329	−0.0321165	+	0.999484i	$0.510225\pi$
$978$	42.3392	1.35386
$979$	−13.5174	−0.432018
$980$	68.5124	2.18855
$981$	2.19966	0.0702296
$982$	−59.8560	−1.91008
$983$	−1.01793	−0.0324670	−0.0162335	−	0.999868i	$-0.505168\pi$
$983$	−1.01793	−0.0324670	−0.0162335	+	0.999868i	$0.505168\pi$
$984$	35.2670	1.12427
$985$	−3.10959	−0.0990796
$986$	−6.53520	−0.208123
$987$	2.97859	0.0948097
$988$	10.8120	0.343975
$989$	5.16856	0.164351
$990$	−6.95506	−0.221046
$991$	12.6352	0.401372	0.200686	−	0.979656i	$-0.435683\pi$
$991$	12.6352	0.401372	0.200686	+	0.979656i	$0.435683\pi$
$992$	−1.88041	−0.0597032
$993$	28.0949	0.891566
$994$	2.91879	0.0925783
$995$	−24.8559	−0.787985
$996$	63.5539	2.01378
$997$	−10.5892	−0.335363	−0.167681	−	0.985841i	$-0.553628\pi$
$997$	−10.5892	−0.335363	−0.167681	+	0.985841i	$0.553628\pi$
$998$	−75.1721	−2.37953
$999$	−61.5821	−1.94837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.2.a.c.1.10	✓	10
3.2	odd	2		1773.2.a.f.1.1		10
4.3	odd	2		3152.2.a.m.1.5		10
5.4	even	2		4925.2.a.i.1.1		10
7.6	odd	2		9653.2.a.j.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.2.a.c.1.10	✓	10	1.1	even	1	trivial
1773.2.a.f.1.1		10	3.2	odd	2
3152.2.a.m.1.5		10	4.3	odd	2
4925.2.a.i.1.1		10	5.4	even	2
9653.2.a.j.1.10		10	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q+2.27104 q^{2} +1.58668 q^{3} +3.15762 q^{4} -3.10959 q^{5} +3.60342 q^{6} -0.149594 q^{7} +2.62899 q^{8} -0.482441 q^{9} -7.06199 q^{10} -2.04141 q^{11} +5.01013 q^{12} +0.758286 q^{13} -0.339733 q^{14} -4.93392 q^{15} -0.344687 q^{16} +2.98720 q^{17} -1.09564 q^{18} +4.51557 q^{19} -9.81888 q^{20} -0.237357 q^{21} -4.63612 q^{22} +0.863791 q^{23} +4.17138 q^{24} +4.66952 q^{25} +1.72210 q^{26} -5.52553 q^{27} -0.472359 q^{28} -0.963320 q^{29} -11.2051 q^{30} +0.311286 q^{31} -6.04079 q^{32} -3.23906 q^{33} +6.78405 q^{34} +0.465174 q^{35} -1.52336 q^{36} +11.1450 q^{37} +10.2550 q^{38} +1.20316 q^{39} -8.17508 q^{40} +8.45451 q^{41} -0.539048 q^{42} +5.98358 q^{43} -6.44598 q^{44} +1.50019 q^{45} +1.96170 q^{46} -12.5490 q^{47} -0.546909 q^{48} -6.97762 q^{49} +10.6047 q^{50} +4.73973 q^{51} +2.39438 q^{52} -11.0563 q^{53} -12.5487 q^{54} +6.34793 q^{55} -0.393281 q^{56} +7.16478 q^{57} -2.18774 q^{58} +8.16033 q^{59} -15.5794 q^{60} +2.88942 q^{61} +0.706943 q^{62} +0.0721700 q^{63} -13.0295 q^{64} -2.35796 q^{65} -7.35604 q^{66} -11.2942 q^{67} +9.43243 q^{68} +1.37056 q^{69} +1.05643 q^{70} -8.59142 q^{71} -1.26833 q^{72} +0.890213 q^{73} +25.3108 q^{74} +7.40905 q^{75} +14.2585 q^{76} +0.305381 q^{77} +2.73242 q^{78} -3.39702 q^{79} +1.07183 q^{80} -7.31993 q^{81} +19.2005 q^{82} +12.6851 q^{83} -0.749484 q^{84} -9.28895 q^{85} +13.5889 q^{86} -1.52848 q^{87} -5.36685 q^{88} +6.62161 q^{89} +3.40699 q^{90} -0.113435 q^{91} +2.72752 q^{92} +0.493912 q^{93} -28.4992 q^{94} -14.0416 q^{95} -9.58480 q^{96} -1.57517 q^{97} -15.8465 q^{98} +0.984858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{3} + 10 q^{4} + 2 q^{5} - 4 q^{6} + 11 q^{7} - 3 q^{8} + 12 q^{9} - 2 q^{10} + 2 q^{11} + 4 q^{12} + 8 q^{13} - 9 q^{14} - q^{15} - 2 q^{16} - 3 q^{17} - 9 q^{18} + 17 q^{19} - 2 q^{20} - 2 q^{21}+ \cdots - q^{99}+O(q^{100}) \) 10 * q + 10 * q^3 + 10 * q^4 + 2 * q^5 - 4 * q^6 + 11 * q^7 - 3 * q^8 + 12 * q^9 - 2 * q^10 + 2 * q^11 + 4 * q^12 + 8 * q^13 - 9 * q^14 - q^15 - 2 * q^16 - 3 * q^17 - 9 * q^18 + 17 * q^19 - 2 * q^20 - 2 * q^21 + 3 * q^22 - 4 * q^23 - 15 * q^24 + 6 * q^25 - 13 * q^26 + 19 * q^27 + 16 * q^28 - 9 * q^29 - 19 * q^30 + 20 * q^31 - 16 * q^32 - 2 * q^33 - 8 * q^34 - 12 * q^35 - 12 * q^36 + 12 * q^37 - 15 * q^38 - 9 * q^39 - 15 * q^40 - 18 * q^41 - 31 * q^42 + 11 * q^43 - 24 * q^44 - 15 * q^45 - 13 * q^46 + 5 * q^47 - 22 * q^48 + q^49 - 24 * q^50 - 13 * q^51 + 9 * q^52 - 6 * q^53 - 15 * q^54 - 17 * q^55 - 6 * q^56 + 3 * q^57 - 15 * q^58 - q^59 - 23 * q^60 + 4 * q^61 - 16 * q^62 - 11 * q^63 - 17 * q^64 - 17 * q^65 + 24 * q^66 + 46 * q^67 + 15 * q^68 - 21 * q^69 + 25 * q^70 - 5 * q^71 + 7 * q^72 + 25 * q^73 + 3 * q^74 + 46 * q^75 + 49 * q^76 - 14 * q^77 + 15 * q^78 - q^79 + 9 * q^80 + 22 * q^81 + 52 * q^82 + 28 * q^83 - 14 * q^84 - 30 * q^85 + 27 * q^86 - 7 * q^87 + 9 * q^88 - 6 * q^89 - 10 * q^90 + 51 * q^91 + 32 * q^92 + 15 * q^93 - 3 * q^94 - 13 * q^95 + 75 * q^96 + 2 * q^97 + 22 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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