LMFDB - Embedded newform 373.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [373,2,Mod(1,373)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(373, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("373.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 373 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	373.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:	$2.97841999539$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 18 x^{15} + 85 x^{14} + 111 x^{13} - 713 x^{12} - 211 x^{11} + 3017 x^{10} + \cdots - 62 $ x^17 - 4x^16 - 18x^15 + 85x^14 + 111x^13 - 713x^12 - 211x^11 + 3017x^10 - 469x^9 - 6832x^8 + 2513x^7 + 8146x^6 - 3634x^5 - 4743x^4 + 2092x^3 + 1142x^2 - 417x - 62
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$2.09044$ of defining polynomial
Character	$\chi$	$=$	373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.09044 q^{2} -1.65242 q^{3} +2.36995 q^{4} +3.43385 q^{5} -3.45429 q^{6} +0.400775 q^{7} +0.773351 q^{8} -0.269499 q^{9} +O(q^{10})$	\(q+2.09044 q^{2} -1.65242 q^{3} +2.36995 q^{4} +3.43385 q^{5} -3.45429 q^{6} +0.400775 q^{7} +0.773351 q^{8} -0.269499 q^{9} +7.17826 q^{10} +4.33354 q^{11} -3.91615 q^{12} +0.268751 q^{13} +0.837797 q^{14} -5.67417 q^{15} -3.12325 q^{16} -3.37200 q^{17} -0.563372 q^{18} +1.03791 q^{19} +8.13804 q^{20} -0.662250 q^{21} +9.05902 q^{22} +6.35972 q^{23} -1.27790 q^{24} +6.79133 q^{25} +0.561809 q^{26} +5.40259 q^{27} +0.949816 q^{28} -10.0484 q^{29} -11.8615 q^{30} +1.91865 q^{31} -8.07567 q^{32} -7.16085 q^{33} -7.04898 q^{34} +1.37620 q^{35} -0.638699 q^{36} -4.61050 q^{37} +2.16970 q^{38} -0.444091 q^{39} +2.65557 q^{40} -4.88693 q^{41} -1.38440 q^{42} -4.76131 q^{43} +10.2703 q^{44} -0.925420 q^{45} +13.2946 q^{46} -6.28515 q^{47} +5.16092 q^{48} -6.83938 q^{49} +14.1969 q^{50} +5.57198 q^{51} +0.636926 q^{52} -4.74304 q^{53} +11.2938 q^{54} +14.8807 q^{55} +0.309940 q^{56} -1.71507 q^{57} -21.0055 q^{58} -4.07654 q^{59} -13.4475 q^{60} -0.597637 q^{61} +4.01082 q^{62} -0.108009 q^{63} -10.6352 q^{64} +0.922852 q^{65} -14.9693 q^{66} -1.44913 q^{67} -7.99147 q^{68} -10.5089 q^{69} +2.87687 q^{70} +10.1704 q^{71} -0.208418 q^{72} +16.7233 q^{73} -9.63797 q^{74} -11.2221 q^{75} +2.45980 q^{76} +1.73678 q^{77} -0.928346 q^{78} -3.91708 q^{79} -10.7248 q^{80} -8.11887 q^{81} -10.2158 q^{82} +10.4062 q^{83} -1.56950 q^{84} -11.5790 q^{85} -9.95323 q^{86} +16.6042 q^{87} +3.35135 q^{88} -10.6528 q^{89} -1.93454 q^{90} +0.107709 q^{91} +15.0722 q^{92} -3.17042 q^{93} -13.1387 q^{94} +3.56404 q^{95} +13.3444 q^{96} +19.0113 q^{97} -14.2973 q^{98} -1.16789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 4 q^{2} + 14 q^{3} + 18 q^{4} + 9 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) $ 17 * q + 4 * q^2 + 14 * q^3 + 18 * q^4 + 9 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 23 * q^9	\( 17 q + 4 q^{2} + 14 q^{3} + 18 q^{4} + 9 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 23 q^{9} - 7 q^{10} + 16 q^{11} + 19 q^{12} - q^{13} - q^{14} + 3 q^{15} + 8 q^{16} + 16 q^{17} - 5 q^{18} + 5 q^{19} + 10 q^{20} - 10 q^{21} - 15 q^{22} + 32 q^{23} - 10 q^{24} + 12 q^{25} - 2 q^{26} + 47 q^{27} - 26 q^{28} - 7 q^{29} - 44 q^{30} - 6 q^{31} + 7 q^{32} - 16 q^{34} + 41 q^{35} + 8 q^{36} - 13 q^{37} + 18 q^{38} - 11 q^{39} - 29 q^{40} - 5 q^{41} - 12 q^{42} + 9 q^{43} + 5 q^{44} - 5 q^{45} - 25 q^{46} + 42 q^{47} + 18 q^{48} + 8 q^{49} - 15 q^{50} + 6 q^{51} - 17 q^{52} + 16 q^{53} - 18 q^{54} - 4 q^{55} - 30 q^{56} - 27 q^{57} - 5 q^{58} + 55 q^{59} - 57 q^{60} - 20 q^{61} + 30 q^{62} - 19 q^{63} - 15 q^{64} - 24 q^{65} - 49 q^{66} - 6 q^{67} + 39 q^{68} - 4 q^{69} - 38 q^{70} - 7 q^{71} - 68 q^{72} - 6 q^{73} - 36 q^{74} + 6 q^{75} - 34 q^{76} + 7 q^{77} - 14 q^{78} - 23 q^{79} - q^{80} + 33 q^{81} - 36 q^{82} + 98 q^{83} - 113 q^{84} - 40 q^{85} - 32 q^{86} - 8 q^{87} - 86 q^{88} + 4 q^{89} - 108 q^{90} - 45 q^{91} + 45 q^{92} - 36 q^{93} - 22 q^{94} - 24 q^{95} - 63 q^{96} - 13 q^{97} - 2 q^{98} + 12 q^{99}+O(q^{100}) \) 17 * q + 4 * q^2 + 14 * q^3 + 18 * q^4 + 9 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 23 * q^9 - 7 * q^10 + 16 * q^11 + 19 * q^12 - q^13 - q^14 + 3 * q^15 + 8 * q^16 + 16 * q^17 - 5 * q^18 + 5 * q^19 + 10 * q^20 - 10 * q^21 - 15 * q^22 + 32 * q^23 - 10 * q^24 + 12 * q^25 - 2 * q^26 + 47 * q^27 - 26 * q^28 - 7 * q^29 - 44 * q^30 - 6 * q^31 + 7 * q^32 - 16 * q^34 + 41 * q^35 + 8 * q^36 - 13 * q^37 + 18 * q^38 - 11 * q^39 - 29 * q^40 - 5 * q^41 - 12 * q^42 + 9 * q^43 + 5 * q^44 - 5 * q^45 - 25 * q^46 + 42 * q^47 + 18 * q^48 + 8 * q^49 - 15 * q^50 + 6 * q^51 - 17 * q^52 + 16 * q^53 - 18 * q^54 - 4 * q^55 - 30 * q^56 - 27 * q^57 - 5 * q^58 + 55 * q^59 - 57 * q^60 - 20 * q^61 + 30 * q^62 - 19 * q^63 - 15 * q^64 - 24 * q^65 - 49 * q^66 - 6 * q^67 + 39 * q^68 - 4 * q^69 - 38 * q^70 - 7 * q^71 - 68 * q^72 - 6 * q^73 - 36 * q^74 + 6 * q^75 - 34 * q^76 + 7 * q^77 - 14 * q^78 - 23 * q^79 - q^80 + 33 * q^81 - 36 * q^82 + 98 * q^83 - 113 * q^84 - 40 * q^85 - 32 * q^86 - 8 * q^87 - 86 * q^88 + 4 * q^89 - 108 * q^90 - 45 * q^91 + 45 * q^92 - 36 * q^93 - 22 * q^94 - 24 * q^95 - 63 * q^96 - 13 * q^97 - 2 * q^98 + 12 * 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 $

$2$	2.09044	1.47817	0.739083	−	0.673615i	$-0.235259\pi$
$2$	2.09044	1.47817	0.739083	+	0.673615i	$0.235259\pi$
$3$	−1.65242	−0.954027	−0.477013	−	0.878896i	$-0.658281\pi$
$3$	−1.65242	−0.954027	−0.477013	+	0.878896i	$0.658281\pi$
$4$	2.36995	1.18497
$5$	3.43385	1.53566	0.767832	−	0.640651i	$-0.221335\pi$
$5$	3.43385	1.53566	0.767832	+	0.640651i	$0.221335\pi$
$6$	−3.45429	−1.41021
$7$	0.400775	0.151479	0.0757394	−	0.997128i	$-0.475868\pi$
$7$	0.400775	0.151479	0.0757394	+	0.997128i	$0.475868\pi$
$8$	0.773351	0.273421
$9$	−0.269499	−0.0898331
$10$	7.17826	2.26997
$11$	4.33354	1.30661	0.653306	−	0.757094i	$-0.273381\pi$
$11$	4.33354	1.30661	0.653306	+	0.757094i	$0.273381\pi$
$12$	−3.91615	−1.13050
$13$	0.268751	0.0745382	0.0372691	−	0.999305i	$-0.488134\pi$
$13$	0.268751	0.0745382	0.0372691	+	0.999305i	$0.488134\pi$
$14$	0.837797	0.223911
$15$	−5.67417	−1.46507
$16$	−3.12325	−0.780812
$17$	−3.37200	−0.817831	−0.408916	−	0.912572i	$-0.634093\pi$
$17$	−3.37200	−0.817831	−0.408916	+	0.912572i	$0.634093\pi$
$18$	−0.563372	−0.132788
$19$	1.03791	0.238114	0.119057	−	0.992887i	$-0.462013\pi$
$19$	1.03791	0.238114	0.119057	+	0.992887i	$0.462013\pi$
$20$	8.13804	1.81972
$21$	−0.662250	−0.144515
$22$	9.05902	1.93139
$23$	6.35972	1.32609	0.663046	−	0.748578i	$-0.269263\pi$
$23$	6.35972	1.32609	0.663046	+	0.748578i	$0.269263\pi$
$24$	−1.27790	−0.260851
$25$	6.79133	1.35827
$26$	0.561809	0.110180
$27$	5.40259	1.03973
$28$	0.949816	0.179498
$29$	−10.0484	−1.86594	−0.932968	−	0.359958i	$-0.882791\pi$
$29$	−10.0484	−1.86594	−0.932968	+	0.359958i	$0.882791\pi$
$30$	−11.8615	−2.16561
$31$	1.91865	0.344600	0.172300	−	0.985045i	$-0.444880\pi$
$31$	1.91865	0.344600	0.172300	+	0.985045i	$0.444880\pi$
$32$	−8.07567	−1.42759
$33$	−7.16085	−1.24654
$34$	−7.04898	−1.20889
$35$	1.37620	0.232621
$36$	−0.638699	−0.106450
$37$	−4.61050	−0.757961	−0.378981	−	0.925405i	$-0.623725\pi$
$37$	−4.61050	−0.757961	−0.378981	+	0.925405i	$0.623725\pi$
$38$	2.16970	0.351972
$39$	−0.444091	−0.0711114
$40$	2.65557	0.419883
$41$	−4.88693	−0.763211	−0.381605	−	0.924325i	$-0.624629\pi$
$41$	−4.88693	−0.763211	−0.381605	+	0.924325i	$0.624629\pi$
$42$	−1.38440	−0.213617
$43$	−4.76131	−0.726093	−0.363046	−	0.931771i	$-0.618263\pi$
$43$	−4.76131	−0.726093	−0.363046	+	0.931771i	$0.618263\pi$
$44$	10.2703	1.54830
$45$	−0.925420	−0.137953
$46$	13.2946	1.96018
$47$	−6.28515	−0.916784	−0.458392	−	0.888750i	$-0.651574\pi$
$47$	−6.28515	−0.916784	−0.458392	+	0.888750i	$0.651574\pi$
$48$	5.16092	0.744915
$49$	−6.83938	−0.977054
$50$	14.1969	2.00774
$51$	5.57198	0.780233
$52$	0.636926	0.0883258
$53$	−4.74304	−0.651507	−0.325753	−	0.945455i	$-0.605618\pi$
$53$	−4.74304	−0.651507	−0.325753	+	0.945455i	$0.605618\pi$
$54$	11.2938	1.53689
$55$	14.8807	2.00652
$56$	0.309940	0.0414175
$57$	−1.71507	−0.227167
$58$	−21.0055	−2.75816
$59$	−4.07654	−0.530721	−0.265360	−	0.964149i	$-0.585491\pi$
$59$	−4.07654	−0.530721	−0.265360	+	0.964149i	$0.585491\pi$
$60$	−13.4475	−1.73606
$61$	−0.597637	−0.0765196	−0.0382598	−	0.999268i	$-0.512181\pi$
$61$	−0.597637	−0.0765196	−0.0382598	+	0.999268i	$0.512181\pi$
$62$	4.01082	0.509375
$63$	−0.108009	−0.0136078
$64$	−10.6352	−1.32940
$65$	0.922852	0.114466
$66$	−14.9693	−1.84260
$67$	−1.44913	−0.177039	−0.0885197	−	0.996074i	$-0.528214\pi$
$67$	−1.44913	−0.177039	−0.0885197	+	0.996074i	$0.528214\pi$
$68$	−7.99147	−0.969108
$69$	−10.5089	−1.26513
$70$	2.87687	0.343852
$71$	10.1704	1.20700	0.603499	−	0.797363i	$-0.293773\pi$
$71$	10.1704	1.20700	0.603499	+	0.797363i	$0.293773\pi$
$72$	−0.208418	−0.0245622
$73$	16.7233	1.95731	0.978656	−	0.205505i	$-0.0658838\pi$
$73$	16.7233	1.95731	0.978656	+	0.205505i	$0.0658838\pi$
$74$	−9.63797	−1.12039
$75$	−11.2221	−1.29582
$76$	2.45980	0.282159
$77$	1.73678	0.197924
$78$	−0.928346	−0.105114
$79$	−3.91708	−0.440706	−0.220353	−	0.975420i	$-0.570721\pi$
$79$	−3.91708	−0.440706	−0.220353	+	0.975420i	$0.570721\pi$
$80$	−10.7248	−1.19907
$81$	−8.11887	−0.902097
$82$	−10.2158	−1.12815
$83$	10.4062	1.14223	0.571116	−	0.820870i	$-0.306511\pi$
$83$	10.4062	1.14223	0.571116	+	0.820870i	$0.306511\pi$
$84$	−1.56950	−0.171246
$85$	−11.5790	−1.25591
$86$	−9.95323	−1.07328
$87$	16.6042	1.78015
$88$	3.35135	0.357255
$89$	−10.6528	−1.12919	−0.564595	−	0.825368i	$-0.690968\pi$
$89$	−10.6528	−1.12919	−0.564595	+	0.825368i	$0.690968\pi$
$90$	−1.93454	−0.203918
$91$	0.107709	0.0112910
$92$	15.0722	1.57138
$93$	−3.17042	−0.328757
$94$	−13.1387	−1.35516
$95$	3.56404	0.365663
$96$	13.3444	1.36196
$97$	19.0113	1.93030	0.965152	−	0.261691i	$-0.0842802\pi$
$97$	19.0113	1.93030	0.965152	+	0.261691i	$0.0842802\pi$
$98$	−14.2973	−1.44425
$99$	−1.16789	−0.117377
$100$	16.0951	1.60951
$101$	−2.35285	−0.234117	−0.117059	−	0.993125i	$-0.537347\pi$
$101$	−2.35285	−0.234117	−0.117059	+	0.993125i	$0.537347\pi$
$102$	11.6479	1.15331
$103$	−5.25439	−0.517730	−0.258865	−	0.965913i	$-0.583348\pi$
$103$	−5.25439	−0.517730	−0.258865	+	0.965913i	$0.583348\pi$
$104$	0.207839	0.0203803
$105$	−2.27407	−0.221926
$106$	−9.91505	−0.963035
$107$	−10.0779	−0.974263	−0.487132	−	0.873329i	$-0.661957\pi$
$107$	−10.0779	−0.974263	−0.487132	+	0.873329i	$0.661957\pi$
$108$	12.8039	1.23205
$109$	7.36874	0.705797	0.352899	−	0.935662i	$-0.385196\pi$
$109$	7.36874	0.705797	0.352899	+	0.935662i	$0.385196\pi$
$110$	31.1073	2.96597
$111$	7.61849	0.723115
$112$	−1.25172	−0.118276
$113$	14.2041	1.33621	0.668105	−	0.744067i	$-0.267106\pi$
$113$	14.2041	1.33621	0.668105	+	0.744067i	$0.267106\pi$
$114$	−3.58526	−0.335790
$115$	21.8383	2.03643
$116$	−23.8141	−2.21108
$117$	−0.0724283	−0.00669600
$118$	−8.52178	−0.784493
$119$	−1.35142	−0.123884
$120$	−4.38813	−0.400579
$121$	7.77960	0.707236
$122$	−1.24933	−0.113109
$123$	8.07528	0.728123
$124$	4.54710	0.408341
$125$	6.15116	0.550177
$126$	−0.225786	−0.0201146
$127$	5.03101	0.446430	0.223215	−	0.974769i	$-0.428345\pi$
$127$	5.03101	0.446430	0.223215	+	0.974769i	$0.428345\pi$
$128$	−6.08097	−0.537487
$129$	7.86769	0.692712
$130$	1.92917	0.169199
$131$	17.6951	1.54602	0.773012	−	0.634391i	$-0.218749\pi$
$131$	17.6951	1.54602	0.773012	+	0.634391i	$0.218749\pi$
$132$	−16.9708	−1.47712
$133$	0.415970	0.0360692
$134$	−3.02932	−0.261694
$135$	18.5517	1.59668
$136$	−2.60774	−0.223612
$137$	−3.37791	−0.288594	−0.144297	−	0.989534i	$-0.546092\pi$
$137$	−3.37791	−0.288594	−0.144297	+	0.989534i	$0.546092\pi$
$138$	−21.9683	−1.87007
$139$	−3.96010	−0.335892	−0.167946	−	0.985796i	$-0.553713\pi$
$139$	−3.96010	−0.335892	−0.167946	+	0.985796i	$0.553713\pi$
$140$	3.26153	0.275649
$141$	10.3857	0.874636
$142$	21.2605	1.78414
$143$	1.16465	0.0973926
$144$	0.841713	0.0701427
$145$	−34.5046	−2.86545
$146$	34.9590	2.89323
$147$	11.3015	0.932136
$148$	−10.9266	−0.898163
$149$	−2.87004	−0.235123	−0.117562	−	0.993066i	$-0.537508\pi$
$149$	−2.87004	−0.235123	−0.117562	+	0.993066i	$0.537508\pi$
$150$	−23.4592	−1.91544
$151$	−17.1607	−1.39651	−0.698257	−	0.715847i	$-0.746041\pi$
$151$	−17.1607	−1.39651	−0.698257	+	0.715847i	$0.746041\pi$
$152$	0.802672	0.0651053
$153$	0.908752	0.0734683
$154$	3.63063	0.292565
$155$	6.58836	0.529189
$156$	−1.05247	−0.0842651
$157$	24.5127	1.95633	0.978164	−	0.207834i	$-0.0666413\pi$
$157$	24.5127	1.95633	0.978164	+	0.207834i	$0.0666413\pi$
$158$	−8.18842	−0.651436
$159$	7.83751	0.621555
$160$	−27.7306	−2.19230
$161$	2.54882	0.200875
$162$	−16.9720	−1.33345
$163$	−7.79820	−0.610802	−0.305401	−	0.952224i	$-0.598791\pi$
$163$	−7.79820	−0.610802	−0.305401	+	0.952224i	$0.598791\pi$
$164$	−11.5818	−0.904384
$165$	−24.5893	−1.91427
$166$	21.7536	1.68841
$167$	3.29824	0.255226	0.127613	−	0.991824i	$-0.459268\pi$
$167$	3.29824	0.255226	0.127613	+	0.991824i	$0.459268\pi$
$168$	−0.512152	−0.0395134
$169$	−12.9278	−0.994444
$170$	−24.2051	−1.85645
$171$	−0.279717	−0.0213905
$172$	−11.2840	−0.860400
$173$	1.32722	0.100907	0.0504535	−	0.998726i	$-0.483933\pi$
$173$	1.32722	0.100907	0.0504535	+	0.998726i	$0.483933\pi$
$174$	34.7100	2.63136
$175$	2.72180	0.205749
$176$	−13.5347	−1.02022
$177$	6.73618	0.506322
$178$	−22.2690	−1.66913
$179$	6.82417	0.510062	0.255031	−	0.966933i	$-0.417914\pi$
$179$	6.82417	0.510062	0.255031	+	0.966933i	$0.417914\pi$
$180$	−2.19320	−0.163471
$181$	13.2423	0.984293	0.492147	−	0.870512i	$-0.336212\pi$
$181$	13.2423	0.984293	0.492147	+	0.870512i	$0.336212\pi$
$182$	0.225159	0.0166899
$183$	0.987549	0.0730017
$184$	4.91829	0.362581
$185$	−15.8318	−1.16397
$186$	−6.62758	−0.485958
$187$	−14.6127	−1.06859
$188$	−14.8955	−1.08636
$189$	2.16523	0.157497
$190$	7.45042	0.540510
$191$	16.8587	1.21985	0.609926	−	0.792458i	$-0.291199\pi$
$191$	16.8587	1.21985	0.609926	+	0.792458i	$0.291199\pi$
$192$	17.5739	1.26829
$193$	−27.7428	−1.99697	−0.998485	−	0.0550212i	$-0.982477\pi$
$193$	−27.7428	−1.99697	−0.998485	+	0.0550212i	$0.982477\pi$
$194$	39.7420	2.85331
$195$	−1.52494	−0.109203
$196$	−16.2090	−1.15778
$197$	25.0058	1.78159	0.890793	−	0.454409i	$-0.150149\pi$
$197$	25.0058	1.78159	0.890793	+	0.454409i	$0.150149\pi$
$198$	−2.44140	−0.173503
$199$	8.51567	0.603660	0.301830	−	0.953362i	$-0.402403\pi$
$199$	8.51567	0.603660	0.301830	+	0.953362i	$0.402403\pi$
$200$	5.25208	0.371378
$201$	2.39458	0.168900
$202$	−4.91850	−0.346064
$203$	−4.02714	−0.282650
$204$	13.2053	0.924555
$205$	−16.7810	−1.17204
$206$	−10.9840	−0.765291
$207$	−1.71394	−0.119127
$208$	−0.839377	−0.0582003
$209$	4.49785	0.311123
$210$	−4.75381	−0.328044
$211$	−10.8123	−0.744346	−0.372173	−	0.928163i	$-0.621387\pi$
$211$	−10.8123	−0.744346	−0.372173	+	0.928163i	$0.621387\pi$
$212$	−11.2408	−0.772018
$213$	−16.8057	−1.15151
$214$	−21.0672	−1.44012
$215$	−16.3496	−1.11503
$216$	4.17810	0.284284
$217$	0.768947	0.0521995
$218$	15.4039	1.04329
$219$	−27.6339	−1.86733
$220$	35.2666	2.37767
$221$	−0.906231	−0.0609597
$222$	15.9260	1.06888
$223$	22.9979	1.54006	0.770028	−	0.638010i	$-0.220242\pi$
$223$	22.9979	1.54006	0.770028	+	0.638010i	$0.220242\pi$
$224$	−3.23653	−0.216250
$225$	−1.83026	−0.122017
$226$	29.6929	1.97514
$227$	9.35683	0.621034	0.310517	−	0.950568i	$-0.399498\pi$
$227$	9.35683	0.621034	0.310517	+	0.950568i	$0.399498\pi$
$228$	−4.06463	−0.269187
$229$	−8.17442	−0.540181	−0.270090	−	0.962835i	$-0.587054\pi$
$229$	−8.17442	−0.540181	−0.270090	+	0.962835i	$0.587054\pi$
$230$	45.6517	3.01019
$231$	−2.86989	−0.188825
$232$	−7.77092	−0.510186
$233$	2.85911	0.187307	0.0936534	−	0.995605i	$-0.470145\pi$
$233$	2.85911	0.187307	0.0936534	+	0.995605i	$0.470145\pi$
$234$	−0.151407	−0.00989779
$235$	−21.5823	−1.40787
$236$	−9.66119	−0.628890
$237$	6.47267	0.420445
$238$	−2.82506	−0.183121
$239$	−20.8929	−1.35145	−0.675725	−	0.737154i	$-0.736169\pi$
$239$	−20.8929	−1.35145	−0.675725	+	0.737154i	$0.736169\pi$
$240$	17.7218	1.14394
$241$	18.4911	1.19111	0.595557	−	0.803313i	$-0.296931\pi$
$241$	18.4911	1.19111	0.595557	+	0.803313i	$0.296931\pi$
$242$	16.2628	1.04541
$243$	−2.79198	−0.179105
$244$	−1.41637	−0.0906737
$245$	−23.4854	−1.50043
$246$	16.8809	1.07629
$247$	0.278941	0.0177486
$248$	1.48379	0.0942207
$249$	−17.1955	−1.08972
$250$	12.8586	0.813252
$251$	5.55357	0.350538	0.175269	−	0.984521i	$-0.443920\pi$
$251$	5.55357	0.350538	0.175269	+	0.984521i	$0.443920\pi$
$252$	−0.255975	−0.0161249
$253$	27.5601	1.73269
$254$	10.5170	0.659898
$255$	19.1333	1.19818
$256$	8.55853	0.534908
$257$	−5.24725	−0.327315	−0.163657	−	0.986517i	$-0.552329\pi$
$257$	−5.24725	−0.327315	−0.163657	+	0.986517i	$0.552329\pi$
$258$	16.4470	1.02394
$259$	−1.84777	−0.114815
$260$	2.18711	0.135639
$261$	2.70803	0.167623
$262$	36.9905	2.28528
$263$	−2.95705	−0.182339	−0.0911697	−	0.995835i	$-0.529061\pi$
$263$	−2.95705	−0.182339	−0.0911697	+	0.995835i	$0.529061\pi$
$264$	−5.53785	−0.340831
$265$	−16.2869	−1.00050
$266$	0.869562	0.0533162
$267$	17.6029	1.07728
$268$	−3.43436	−0.209787
$269$	12.6731	0.772692	0.386346	−	0.922354i	$-0.373737\pi$
$269$	12.6731	0.772692	0.386346	+	0.922354i	$0.373737\pi$
$270$	38.7813	2.36015
$271$	15.7547	0.957031	0.478515	−	0.878079i	$-0.341175\pi$
$271$	15.7547	0.957031	0.478515	+	0.878079i	$0.341175\pi$
$272$	10.5316	0.638572
$273$	−0.177981	−0.0107719
$274$	−7.06132	−0.426590
$275$	29.4305	1.77473
$276$	−24.9056	−1.49914
$277$	−13.5536	−0.814356	−0.407178	−	0.913349i	$-0.633487\pi$
$277$	−13.5536	−0.814356	−0.407178	+	0.913349i	$0.633487\pi$
$278$	−8.27837	−0.496504
$279$	−0.517075	−0.0309564
$280$	1.06429	0.0636034
$281$	−7.00486	−0.417875	−0.208938	−	0.977929i	$-0.567001\pi$
$281$	−7.00486	−0.417875	−0.208938	+	0.977929i	$0.567001\pi$
$282$	21.7108	1.29286
$283$	−27.2503	−1.61986	−0.809930	−	0.586527i	$-0.800495\pi$
$283$	−27.2503	−1.61986	−0.809930	+	0.586527i	$0.800495\pi$
$284$	24.1032	1.43026
$285$	−5.88930	−0.348852
$286$	2.43462	0.143962
$287$	−1.95856	−0.115610
$288$	2.17639	0.128245
$289$	−5.62959	−0.331152
$290$	−72.1299	−4.23561
$291$	−31.4147	−1.84156
$292$	39.6333	2.31936
$293$	5.42918	0.317176	0.158588	−	0.987345i	$-0.449306\pi$
$293$	5.42918	0.317176	0.158588	+	0.987345i	$0.449306\pi$
$294$	23.6252	1.37785
$295$	−13.9982	−0.815009
$296$	−3.56553	−0.207242
$297$	23.4124	1.35852
$298$	−5.99966	−0.347551
$299$	1.70918	0.0988446
$300$	−26.5959	−1.53551
$301$	−1.90821	−0.109988
$302$	−35.8733	−2.06428
$303$	3.88790	0.223354
$304$	−3.24166	−0.185922
$305$	−2.05220	−0.117508
$306$	1.89969	0.108598
$307$	−18.0464	−1.02996	−0.514982	−	0.857201i	$-0.672201\pi$
$307$	−18.0464	−1.02996	−0.514982	+	0.857201i	$0.672201\pi$
$308$	4.11607	0.234535
$309$	8.68247	0.493928
$310$	13.7726	0.782230
$311$	−31.1918	−1.76872	−0.884362	−	0.466801i	$-0.845406\pi$
$311$	−31.1918	−1.76872	−0.884362	+	0.466801i	$0.845406\pi$
$312$	−0.343438	−0.0194434
$313$	13.0770	0.739158	0.369579	−	0.929199i	$-0.379502\pi$
$313$	13.0770	0.739158	0.369579	+	0.929199i	$0.379502\pi$
$314$	51.2424	2.89178
$315$	−0.370885	−0.0208970
$316$	−9.28327	−0.522225
$317$	6.45305	0.362439	0.181220	−	0.983443i	$-0.441996\pi$
$317$	6.45305	0.362439	0.181220	+	0.983443i	$0.441996\pi$
$318$	16.3839	0.918761
$319$	−43.5451	−2.43806
$320$	−36.5198	−2.04152
$321$	16.6529	0.929473
$322$	5.32815	0.296926
$323$	−3.49985	−0.194737
$324$	−19.2413	−1.06896
$325$	1.82518	0.101243
$326$	−16.3017	−0.902867
$327$	−12.1763	−0.673349
$328$	−3.77932	−0.208678
$329$	−2.51893	−0.138873
$330$	−51.4024	−2.82961
$331$	−15.5347	−0.853864	−0.426932	−	0.904284i	$-0.640406\pi$
$331$	−15.5347	−0.853864	−0.426932	+	0.904284i	$0.640406\pi$
$332$	24.6622	1.35351
$333$	1.24253	0.0680900
$334$	6.89479	0.377266
$335$	−4.97610	−0.271873
$336$	2.06837	0.112839
$337$	−24.9692	−1.36016	−0.680080	−	0.733138i	$-0.738055\pi$
$337$	−24.9692	−1.36016	−0.680080	+	0.733138i	$0.738055\pi$
$338$	−27.0248	−1.46995
$339$	−23.4712	−1.27478
$340$	−27.4415	−1.48822
$341$	8.31455	0.450258
$342$	−0.584732	−0.0316187
$343$	−5.54648	−0.299482
$344$	−3.68216	−0.198529
$345$	−36.0861	−1.94281
$346$	2.77448	0.149157
$347$	26.0325	1.39750	0.698749	−	0.715367i	$-0.253740\pi$
$347$	26.0325	1.39750	0.698749	+	0.715367i	$0.253740\pi$
$348$	39.3510	2.10943
$349$	−15.1152	−0.809096	−0.404548	−	0.914517i	$-0.632571\pi$
$349$	−15.1152	−0.809096	−0.404548	+	0.914517i	$0.632571\pi$
$350$	5.68976	0.304130
$351$	1.45195	0.0774996
$352$	−34.9963	−1.86531
$353$	27.6881	1.47369	0.736845	−	0.676061i	$-0.236315\pi$
$353$	27.6881	1.47369	0.736845	+	0.676061i	$0.236315\pi$
$354$	14.0816	0.748428
$355$	34.9235	1.85355
$356$	−25.2465	−1.33806
$357$	2.23311	0.118189
$358$	14.2655	0.753956
$359$	17.2181	0.908735	0.454368	−	0.890814i	$-0.349865\pi$
$359$	17.2181	0.908735	0.454368	+	0.890814i	$0.349865\pi$
$360$	−0.715675	−0.0377194
$361$	−17.9227	−0.943302
$362$	27.6823	1.45495
$363$	−12.8552	−0.674722
$364$	0.255264	0.0133795
$365$	57.4252	3.00577
$366$	2.06441	0.107909
$367$	−21.7087	−1.13318	−0.566592	−	0.823999i	$-0.691738\pi$
$367$	−21.7087	−1.13318	−0.566592	+	0.823999i	$0.691738\pi$
$368$	−19.8630	−1.03543
$369$	1.31702	0.0685616
$370$	−33.0954	−1.72055
$371$	−1.90089	−0.0986895
$372$	−7.51372	−0.389568
$373$	1.00000	0.0517780
$373$	1.00000	0.0517780
$374$	−30.5470	−1.57955
$375$	−10.1643	−0.524883
$376$	−4.86063	−0.250668
$377$	−2.70051	−0.139084
$378$	4.52628	0.232807
$379$	23.3912	1.20153	0.600764	−	0.799427i	$-0.294863\pi$
$379$	23.3912	1.20153	0.600764	+	0.799427i	$0.294863\pi$
$380$	8.44659	0.433301
$381$	−8.31336	−0.425906
$382$	35.2421	1.80314
$383$	26.0851	1.33289	0.666444	−	0.745555i	$-0.267816\pi$
$383$	26.0851	1.33289	0.666444	+	0.745555i	$0.267816\pi$
$384$	10.0483	0.512777
$385$	5.96383	0.303945
$386$	−57.9947	−2.95185
$387$	1.28317	0.0652271
$388$	45.0557	2.28736
$389$	36.5077	1.85101	0.925507	−	0.378730i	$-0.123639\pi$
$389$	36.5077	1.85101	0.925507	+	0.378730i	$0.123639\pi$
$390$	−3.18780	−0.161421
$391$	−21.4450	−1.08452
$392$	−5.28924	−0.267147
$393$	−29.2397	−1.47495
$394$	52.2731	2.63348
$395$	−13.4507	−0.676776
$396$	−2.76783	−0.139089
$397$	−18.2698	−0.916935	−0.458467	−	0.888711i	$-0.651601\pi$
$397$	−18.2698	−0.916935	−0.458467	+	0.888711i	$0.651601\pi$
$398$	17.8015	0.892309
$399$	−0.687359	−0.0344110
$400$	−21.2110	−1.06055
$401$	−9.78719	−0.488749	−0.244374	−	0.969681i	$-0.578583\pi$
$401$	−9.78719	−0.488749	−0.244374	+	0.969681i	$0.578583\pi$
$402$	5.00572	0.249663
$403$	0.515640	0.0256858
$404$	−5.57613	−0.277423
$405$	−27.8790	−1.38532
$406$	−8.41850	−0.417803
$407$	−19.9798	−0.990361
$408$	4.30909	0.213332
$409$	−16.1472	−0.798428	−0.399214	−	0.916858i	$-0.630717\pi$
$409$	−16.1472	−0.798428	−0.399214	+	0.916858i	$0.630717\pi$
$410$	−35.0797	−1.73246
$411$	5.58173	0.275327
$412$	−12.4526	−0.613496
$413$	−1.63378	−0.0803930
$414$	−3.58289	−0.176089
$415$	35.7334	1.75408
$416$	−2.17035	−0.106410
$417$	6.54377	0.320450
$418$	9.40248	0.459891
$419$	21.6006	1.05526	0.527630	−	0.849474i	$-0.323081\pi$
$419$	21.6006	1.05526	0.527630	+	0.849474i	$0.323081\pi$
$420$	−5.38942	−0.262977
$421$	−19.1359	−0.932627	−0.466313	−	0.884620i	$-0.654418\pi$
$421$	−19.1359	−0.932627	−0.466313	+	0.884620i	$0.654418\pi$
$422$	−22.6024	−1.10027
$423$	1.69384	0.0823575
$424$	−3.66804	−0.178136
$425$	−22.9004	−1.11083
$426$	−35.1314	−1.70212
$427$	−0.239518	−0.0115911
$428$	−23.8840	−1.15448
$429$	−1.92449	−0.0929151
$430$	−34.1779	−1.64821
$431$	−5.20168	−0.250556	−0.125278	−	0.992122i	$-0.539982\pi$
$431$	−5.20168	−0.250556	−0.125278	+	0.992122i	$0.539982\pi$
$432$	−16.8736	−0.811833
$433$	−27.7351	−1.33286	−0.666432	−	0.745566i	$-0.732179\pi$
$433$	−27.7351	−1.33286	−0.666432	+	0.745566i	$0.732179\pi$
$434$	1.60744	0.0771595
$435$	57.0162	2.73372
$436$	17.4635	0.836351
$437$	6.60084	0.315761
$438$	−57.7671	−2.76022
$439$	−5.79421	−0.276543	−0.138271	−	0.990394i	$-0.544155\pi$
$439$	−5.79421	−0.276543	−0.138271	+	0.990394i	$0.544155\pi$
$440$	11.5080	0.548624
$441$	1.84321	0.0877718
$442$	−1.89442	−0.0901085
$443$	−10.4008	−0.494159	−0.247079	−	0.968995i	$-0.579471\pi$
$443$	−10.4008	−0.494159	−0.247079	+	0.968995i	$0.579471\pi$
$444$	18.0554	0.856872
$445$	−36.5800	−1.73406
$446$	48.0759	2.27646
$447$	4.74252	0.224314
$448$	−4.26233	−0.201376
$449$	−10.3816	−0.489936	−0.244968	−	0.969531i	$-0.578777\pi$
$449$	−10.3816	−0.489936	−0.244968	+	0.969531i	$0.578777\pi$
$450$	−3.82605	−0.180362
$451$	−21.1777	−0.997221
$452$	33.6630	1.58337
$453$	28.3567	1.33231
$454$	19.5599	0.917992
$455$	0.369856	0.0173391
$456$	−1.32635	−0.0621122
$457$	33.3514	1.56011	0.780057	−	0.625708i	$-0.215190\pi$
$457$	33.3514	1.56011	0.780057	+	0.625708i	$0.215190\pi$
$458$	−17.0881	−0.798477
$459$	−18.2176	−0.850323
$460$	51.7556	2.41312
$461$	−4.22890	−0.196959	−0.0984797	−	0.995139i	$-0.531398\pi$
$461$	−4.22890	−0.196959	−0.0984797	+	0.995139i	$0.531398\pi$
$462$	−5.99934	−0.279114
$463$	−11.2351	−0.522137	−0.261069	−	0.965320i	$-0.584075\pi$
$463$	−11.2351	−0.522137	−0.261069	+	0.965320i	$0.584075\pi$
$464$	31.3836	1.45695
$465$	−10.8867	−0.504861
$466$	5.97681	0.276870
$467$	33.2008	1.53635	0.768174	−	0.640241i	$-0.221166\pi$
$467$	33.2008	1.53635	0.768174	+	0.640241i	$0.221166\pi$
$468$	−0.171651	−0.00793458
$469$	−0.580775	−0.0268177
$470$	−45.1165	−2.08107
$471$	−40.5054	−1.86639
$472$	−3.15260	−0.145110
$473$	−20.6333	−0.948722
$474$	13.5307	0.621487
$475$	7.04882	0.323422
$476$	−3.20278	−0.146799
$477$	1.27825	0.0585269
$478$	−43.6754	−1.99767
$479$	−25.1418	−1.14876	−0.574378	−	0.818590i	$-0.694756\pi$
$479$	−25.1418	−1.14876	−0.574378	+	0.818590i	$0.694756\pi$
$480$	45.8227	2.09151
$481$	−1.23908	−0.0564971
$482$	38.6545	1.76066
$483$	−4.21172	−0.191640
$484$	18.4372	0.838056
$485$	65.2819	2.96430
$486$	−5.83646	−0.264747
$487$	30.6630	1.38947	0.694736	−	0.719265i	$-0.255521\pi$
$487$	30.6630	1.38947	0.694736	+	0.719265i	$0.255521\pi$
$488$	−0.462183	−0.0209221
$489$	12.8859	0.582722
$490$	−49.0949	−2.21788
$491$	−13.1653	−0.594139	−0.297070	−	0.954856i	$-0.596009\pi$
$491$	−13.1653	−0.594139	−0.297070	+	0.954856i	$0.596009\pi$
$492$	19.1380	0.862807
$493$	33.8832	1.52602
$494$	0.583110	0.0262353
$495$	−4.01035	−0.180252
$496$	−5.99242	−0.269067
$497$	4.07603	0.182835
$498$	−35.9461	−1.61079
$499$	32.3923	1.45008	0.725040	−	0.688707i	$-0.241821\pi$
$499$	32.3923	1.45008	0.725040	+	0.688707i	$0.241821\pi$
$500$	14.5779	0.651945
$501$	−5.45009	−0.243492
$502$	11.6094	0.518153
$503$	22.0458	0.982972	0.491486	−	0.870886i	$-0.336454\pi$
$503$	22.0458	0.982972	0.491486	+	0.870886i	$0.336454\pi$
$504$	−0.0835286	−0.00372066
$505$	−8.07934	−0.359526
$506$	57.6128	2.56120
$507$	21.3621	0.948726
$508$	11.9232	0.529008
$509$	12.9013	0.571839	0.285919	−	0.958254i	$-0.407701\pi$
$509$	12.9013	0.571839	0.285919	+	0.958254i	$0.407701\pi$
$510$	39.9971	1.77110
$511$	6.70228	0.296491
$512$	30.0530	1.32817
$513$	5.60743	0.247574
$514$	−10.9691	−0.483825
$515$	−18.0428	−0.795060
$516$	18.6460	0.820845
$517$	−27.2370	−1.19788
$518$	−3.86266	−0.169716
$519$	−2.19313	−0.0962679
$520$	0.713689	0.0312973
$521$	−19.1868	−0.840589	−0.420295	−	0.907388i	$-0.638073\pi$
$521$	−19.1868	−0.840589	−0.420295	+	0.907388i	$0.638073\pi$
$522$	5.66098	0.247774
$523$	26.2476	1.14773	0.573864	−	0.818951i	$-0.305444\pi$
$523$	26.2476	1.14773	0.573864	+	0.818951i	$0.305444\pi$
$524$	41.9363	1.83200
$525$	−4.49756	−0.196290
$526$	−6.18154	−0.269528
$527$	−6.46969	−0.281824
$528$	22.3651	0.973316
$529$	17.4460	0.758521
$530$	−34.0468	−1.47890
$531$	1.09863	0.0476763
$532$	0.985827	0.0427410
$533$	−1.31337	−0.0568884
$534$	36.7978	1.59240
$535$	−34.6059	−1.49614
$536$	−1.12069	−0.0484063
$537$	−11.2764	−0.486613
$538$	26.4923	1.14217
$539$	−29.6387	−1.27663
$540$	43.9665	1.89202
$541$	−5.38780	−0.231640	−0.115820	−	0.993270i	$-0.536950\pi$
$541$	−5.38780	−0.231640	−0.115820	+	0.993270i	$0.536950\pi$
$542$	32.9343	1.41465
$543$	−21.8819	−0.939042
$544$	27.2312	1.16753
$545$	25.3032	1.08387
$546$	−0.372058	−0.0159226
$547$	−24.2210	−1.03562	−0.517808	−	0.855497i	$-0.673252\pi$
$547$	−24.2210	−1.03562	−0.517808	+	0.855497i	$0.673252\pi$
$548$	−8.00546	−0.341976
$549$	0.161063	0.00687399
$550$	61.5228	2.62334
$551$	−10.4294	−0.444305
$552$	−8.12710	−0.345912
$553$	−1.56987	−0.0667576
$554$	−28.3330	−1.20375
$555$	26.1608	1.11046
$556$	−9.38524	−0.398023
$557$	−8.06117	−0.341563	−0.170781	−	0.985309i	$-0.554629\pi$
$557$	−8.06117	−0.341563	−0.170781	+	0.985309i	$0.554629\pi$
$558$	−1.08091	−0.0457587
$559$	−1.27961	−0.0541216
$560$	−4.29822	−0.181633
$561$	24.1464	1.01946
$562$	−14.6433	−0.617689
$563$	37.0038	1.55953	0.779763	−	0.626075i	$-0.215340\pi$
$563$	37.0038	1.55953	0.779763	+	0.626075i	$0.215340\pi$
$564$	24.6136	1.03642
$565$	48.7748	2.05197
$566$	−56.9651	−2.39442
$567$	−3.25384	−0.136649
$568$	7.86525	0.330019
$569$	−23.4220	−0.981901	−0.490950	−	0.871188i	$-0.663350\pi$
$569$	−23.4220	−0.981901	−0.490950	+	0.871188i	$0.663350\pi$
$570$	−12.3112	−0.515661
$571$	39.3660	1.64742	0.823708	−	0.567014i	$-0.191902\pi$
$571$	39.3660	1.64742	0.823708	+	0.567014i	$0.191902\pi$
$572$	2.76015	0.115408
$573$	−27.8577	−1.16377
$574$	−4.09426	−0.170891
$575$	43.1909	1.80119
$576$	2.86618	0.119424
$577$	−42.0970	−1.75252	−0.876261	−	0.481837i	$-0.839970\pi$
$577$	−42.0970	−1.75252	−0.876261	+	0.481837i	$0.839970\pi$
$578$	−11.7683	−0.489498
$579$	45.8428	1.90516
$580$	−81.7741	−3.39549
$581$	4.17056	0.173024
$582$	−65.6705	−2.72213
$583$	−20.5542	−0.851267
$584$	12.9330	0.535170
$585$	−0.248708	−0.0102828
$586$	11.3494	0.468839
$587$	6.50779	0.268605	0.134303	−	0.990940i	$-0.457121\pi$
$587$	6.50779	0.268605	0.134303	+	0.990940i	$0.457121\pi$
$588$	26.7841	1.10456
$589$	1.99139	0.0820539
$590$	−29.2625	−1.20472
$591$	−41.3201	−1.69968
$592$	14.3997	0.591825
$593$	38.3044	1.57297	0.786486	−	0.617609i	$-0.211898\pi$
$593$	38.3044	1.57297	0.786486	+	0.617609i	$0.211898\pi$
$594$	48.9422	2.00812
$595$	−4.64056	−0.190244
$596$	−6.80185	−0.278615
$597$	−14.0715	−0.575908
$598$	3.57295	0.146109
$599$	21.3902	0.873980	0.436990	−	0.899466i	$-0.356045\pi$
$599$	21.3902	0.873980	0.436990	+	0.899466i	$0.356045\pi$
$600$	−8.67866	−0.354305
$601$	−40.0064	−1.63190	−0.815948	−	0.578125i	$-0.803785\pi$
$601$	−40.0064	−1.63190	−0.815948	+	0.578125i	$0.803785\pi$
$602$	−3.98901	−0.162580
$603$	0.390539	0.0159040
$604$	−40.6698	−1.65483
$605$	26.7140	1.08608
$606$	8.12744	0.330155
$607$	−21.4476	−0.870529	−0.435265	−	0.900303i	$-0.643345\pi$
$607$	−21.4476	−0.870529	−0.435265	+	0.900303i	$0.643345\pi$
$608$	−8.38185	−0.339929
$609$	6.65454	0.269655
$610$	−4.29000	−0.173697
$611$	−1.68914	−0.0683354
$612$	2.15369	0.0870579
$613$	−29.9219	−1.20853	−0.604267	−	0.796782i	$-0.706534\pi$
$613$	−29.9219	−1.20853	−0.604267	+	0.796782i	$0.706534\pi$
$614$	−37.7250	−1.52246
$615$	27.7293	1.11815
$616$	1.34314	0.0541166
$617$	6.31743	0.254330	0.127165	−	0.991882i	$-0.459412\pi$
$617$	6.31743	0.254330	0.127165	+	0.991882i	$0.459412\pi$
$618$	18.1502	0.730108
$619$	47.3943	1.90494	0.952469	−	0.304634i	$-0.0985342\pi$
$619$	47.3943	1.90494	0.952469	+	0.304634i	$0.0985342\pi$
$620$	15.6140	0.627075
$621$	34.3590	1.37878
$622$	−65.2046	−2.61447
$623$	−4.26936	−0.171048
$624$	1.38701	0.0555247
$625$	−12.8345	−0.513379
$626$	27.3368	1.09260
$627$	−7.43234	−0.296819
$628$	58.0938	2.31820
$629$	15.5466	0.619884
$630$	−0.775314	−0.0308893
$631$	48.5119	1.93123	0.965615	−	0.259977i	$-0.0837150\pi$
$631$	48.5119	1.93123	0.965615	+	0.259977i	$0.0837150\pi$
$632$	−3.02928	−0.120498
$633$	17.8664	0.710126
$634$	13.4897	0.535745
$635$	17.2758	0.685567
$636$	18.5745	0.736526
$637$	−1.83809	−0.0728279
$638$	−91.0284	−3.60385
$639$	−2.74090	−0.108428
$640$	−20.8811	−0.825399
$641$	−28.9536	−1.14360	−0.571799	−	0.820394i	$-0.693754\pi$
$641$	−28.9536	−1.14360	−0.571799	+	0.820394i	$0.693754\pi$
$642$	34.8119	1.37392
$643$	34.0612	1.34324	0.671621	−	0.740895i	$-0.265598\pi$
$643$	34.0612	1.34324	0.671621	+	0.740895i	$0.265598\pi$
$644$	6.04056	0.238031
$645$	27.0165	1.06377
$646$	−7.31623	−0.287853
$647$	−19.2598	−0.757179	−0.378590	−	0.925565i	$-0.623591\pi$
$647$	−19.2598	−0.757179	−0.378590	+	0.925565i	$0.623591\pi$
$648$	−6.27874	−0.246652
$649$	−17.6659	−0.693447
$650$	3.81543	0.149654
$651$	−1.27063	−0.0497997
$652$	−18.4813	−0.723784
$653$	−34.2591	−1.34066	−0.670332	−	0.742061i	$-0.733848\pi$
$653$	−34.2591	−1.34066	−0.670332	+	0.742061i	$0.733848\pi$
$654$	−25.4538	−0.995322
$655$	60.7622	2.37418
$656$	15.2631	0.595924
$657$	−4.50691	−0.175831
$658$	−5.26569	−0.205278
$659$	−19.5511	−0.761603	−0.380801	−	0.924657i	$-0.624352\pi$
$659$	−19.5511	−0.761603	−0.380801	+	0.924657i	$0.624352\pi$
$660$	−58.2753	−2.26836
$661$	−13.5824	−0.528294	−0.264147	−	0.964482i	$-0.585090\pi$
$661$	−13.5824	−0.528294	−0.264147	+	0.964482i	$0.585090\pi$
$662$	−32.4744	−1.26215
$663$	1.49748	0.0581571
$664$	8.04767	0.312310
$665$	1.42838	0.0553902
$666$	2.59743	0.100648
$667$	−63.9048	−2.47440
$668$	7.81666	0.302436
$669$	−38.0023	−1.46925
$670$	−10.4022	−0.401873
$671$	−2.58989	−0.0999815
$672$	5.34811	0.206308
$673$	3.30120	0.127252	0.0636260	−	0.997974i	$-0.479734\pi$
$673$	3.30120	0.127252	0.0636260	+	0.997974i	$0.479734\pi$
$674$	−52.1967	−2.01054
$675$	36.6908	1.41223
$676$	−30.6381	−1.17839
$677$	20.3739	0.783034	0.391517	−	0.920171i	$-0.371950\pi$
$677$	20.3739	0.783034	0.391517	+	0.920171i	$0.371950\pi$
$678$	−49.0652	−1.88434
$679$	7.61925	0.292400
$680$	−8.95460	−0.343393
$681$	−15.4614	−0.592483
$682$	17.3811	0.665556
$683$	−2.28839	−0.0875627	−0.0437814	−	0.999041i	$-0.513940\pi$
$683$	−2.28839	−0.0875627	−0.0437814	+	0.999041i	$0.513940\pi$
$684$	−0.662914	−0.0253472
$685$	−11.5992	−0.443184
$686$	−11.5946	−0.442684
$687$	13.5076	0.515347
$688$	14.8707	0.566942
$689$	−1.27470	−0.0485621
$690$	−75.4359	−2.87180
$691$	−15.7349	−0.598583	−0.299292	−	0.954162i	$-0.596750\pi$
$691$	−15.7349	−0.598583	−0.299292	+	0.954162i	$0.596750\pi$
$692$	3.14545	0.119572
$693$	−0.468060	−0.0177801
$694$	54.4194	2.06573
$695$	−13.5984	−0.515817
$696$	12.8409	0.486731
$697$	16.4788	0.624178
$698$	−31.5974	−1.19598
$699$	−4.72446	−0.178696
$700$	6.45051	0.243806
$701$	8.97574	0.339009	0.169505	−	0.985529i	$-0.445783\pi$
$701$	8.97574	0.339009	0.169505	+	0.985529i	$0.445783\pi$
$702$	3.03523	0.114557
$703$	−4.78530	−0.180481
$704$	−46.0882	−1.73701
$705$	35.6631	1.34315
$706$	57.8804	2.17836
$707$	−0.942964	−0.0354638
$708$	15.9644	0.599978
$709$	−18.0577	−0.678170	−0.339085	−	0.940756i	$-0.610117\pi$
$709$	−18.0577	−0.678170	−0.339085	+	0.940756i	$0.610117\pi$
$710$	73.0055	2.73985
$711$	1.05565	0.0395900
$712$	−8.23833	−0.308744
$713$	12.2021	0.456971
$714$	4.66819	0.174702
$715$	3.99922	0.149562
$716$	16.1729	0.604410
$717$	34.5239	1.28932
$718$	35.9934	1.34326
$719$	−53.4274	−1.99251	−0.996253	−	0.0864852i	$-0.972436\pi$
$719$	−53.4274	−1.99251	−0.996253	+	0.0864852i	$0.972436\pi$
$720$	2.89032	0.107716
$721$	−2.10583	−0.0784251
$722$	−37.4664	−1.39436
$723$	−30.5550	−1.13635
$724$	31.3836	1.16636
$725$	−68.2418	−2.53444
$726$	−26.8730	−0.997351
$727$	−2.00534	−0.0743739	−0.0371870	−	0.999308i	$-0.511840\pi$
$727$	−2.00534	−0.0743739	−0.0371870	+	0.999308i	$0.511840\pi$
$728$	0.0832968	0.00308718
$729$	28.9701	1.07297
$730$	120.044	4.44303
$731$	16.0551	0.593821
$732$	2.34044	0.0865051
$733$	−36.4524	−1.34640	−0.673201	−	0.739460i	$-0.735081\pi$
$733$	−36.4524	−1.34640	−0.673201	+	0.739460i	$0.735081\pi$
$734$	−45.3807	−1.67503
$735$	38.8078	1.43145
$736$	−51.3590	−1.89312
$737$	−6.27987	−0.231322
$738$	2.75316	0.101345
$739$	39.8350	1.46535	0.732677	−	0.680576i	$-0.238270\pi$
$739$	39.8350	1.46535	0.732677	+	0.680576i	$0.238270\pi$
$740$	−37.5204	−1.37928
$741$	−0.460928	−0.0169326
$742$	−3.97371	−0.145879
$743$	10.8323	0.397398	0.198699	−	0.980061i	$-0.436328\pi$
$743$	10.8323	0.397398	0.198699	+	0.980061i	$0.436328\pi$
$744$	−2.45185	−0.0898891
$745$	−9.85530	−0.361070
$746$	2.09044	0.0765365
$747$	−2.80447	−0.102610
$748$	−34.6314	−1.26625
$749$	−4.03896	−0.147580
$750$	−21.2479	−0.775864
$751$	10.2129	0.372676	0.186338	−	0.982486i	$-0.440338\pi$
$751$	10.2129	0.372676	0.186338	+	0.982486i	$0.440338\pi$
$752$	19.6301	0.715836
$753$	−9.17684	−0.334423
$754$	−5.64527	−0.205589
$755$	−58.9271	−2.14458
$756$	5.13147	0.186630
$757$	46.0236	1.67276	0.836378	−	0.548154i	$-0.184669\pi$
$757$	46.0236	1.67276	0.836378	+	0.548154i	$0.184669\pi$
$758$	48.8980	1.77606
$759$	−45.5409	−1.65303
$760$	2.75626	0.0999799
$761$	−5.55997	−0.201549	−0.100774	−	0.994909i	$-0.532132\pi$
$761$	−5.55997	−0.201549	−0.100774	+	0.994909i	$0.532132\pi$
$762$	−17.3786	−0.629560
$763$	2.95321	0.106913
$764$	39.9542	1.44549
$765$	3.12052	0.112823
$766$	54.5294	1.97023
$767$	−1.09558	−0.0395590
$768$	−14.1423	−0.510317
$769$	−1.62022	−0.0584268	−0.0292134	−	0.999573i	$-0.509300\pi$
$769$	−1.62022	−0.0584268	−0.0292134	+	0.999573i	$0.509300\pi$
$770$	12.4670	0.449281
$771$	8.67068	0.312267
$772$	−65.7489	−2.36636
$773$	−40.9432	−1.47262	−0.736312	−	0.676642i	$-0.763435\pi$
$773$	−40.9432	−1.47262	−0.736312	+	0.676642i	$0.763435\pi$
$774$	2.68239	0.0964165
$775$	13.0302	0.468058
$776$	14.7024	0.527785
$777$	3.05330	0.109537
$778$	76.3172	2.73611
$779$	−5.07222	−0.181731
$780$	−3.61403	−0.129403
$781$	44.0737	1.57708
$782$	−44.8295	−1.60310
$783$	−54.2873	−1.94007
$784$	21.3611	0.762895
$785$	84.1730	3.00426
$786$	−61.1239	−2.18022
$787$	8.77264	0.312711	0.156355	−	0.987701i	$-0.450025\pi$
$787$	8.77264	0.312711	0.156355	+	0.987701i	$0.450025\pi$
$788$	59.2623	2.11113
$789$	4.88630	0.173957
$790$	−28.1178	−1.00039
$791$	5.69266	0.202408
$792$	−0.903186	−0.0320933
$793$	−0.160616	−0.00570363
$794$	−38.1919	−1.35538
$795$	26.9128	0.954500
$796$	20.1817	0.715321
$797$	7.61080	0.269588	0.134794	−	0.990874i	$-0.456963\pi$
$797$	7.61080	0.269588	0.134794	+	0.990874i	$0.456963\pi$
$798$	−1.43688	−0.0508651
$799$	21.1936	0.749775
$800$	−54.8445	−1.93905
$801$	2.87091	0.101439
$802$	−20.4595	−0.722452
$803$	72.4711	2.55745
$804$	5.67501	0.200142
$805$	8.75226	0.308476
$806$	1.07791	0.0379679
$807$	−20.9413	−0.737168
$808$	−1.81958	−0.0640126
$809$	−35.8654	−1.26096	−0.630479	−	0.776206i	$-0.717142\pi$
$809$	−35.8654	−1.26096	−0.630479	+	0.776206i	$0.717142\pi$
$810$	−58.2794	−2.04773
$811$	−15.2870	−0.536798	−0.268399	−	0.963308i	$-0.586495\pi$
$811$	−15.2870	−0.536798	−0.268399	+	0.963308i	$0.586495\pi$
$812$	−9.54411	−0.334932
$813$	−26.0334	−0.913033
$814$	−41.7666	−1.46392
$815$	−26.7779	−0.937988
$816$	−17.4027	−0.609215
$817$	−4.94183	−0.172893
$818$	−33.7548	−1.18021
$819$	−0.0290275	−0.00101430
$820$	−39.7701	−1.38883
$821$	−6.73198	−0.234948	−0.117474	−	0.993076i	$-0.537480\pi$
$821$	−6.73198	−0.234948	−0.117474	+	0.993076i	$0.537480\pi$
$822$	11.6683	0.406978
$823$	22.2084	0.774138	0.387069	−	0.922051i	$-0.373488\pi$
$823$	22.2084	0.774138	0.387069	+	0.922051i	$0.373488\pi$
$824$	−4.06349	−0.141558
$825$	−48.6317	−1.69314
$826$	−3.41532	−0.118834
$827$	−16.4189	−0.570941	−0.285470	−	0.958388i	$-0.592150\pi$
$827$	−16.4189	−0.570941	−0.285470	+	0.958388i	$0.592150\pi$
$828$	−4.06194	−0.141162
$829$	−10.5602	−0.366770	−0.183385	−	0.983041i	$-0.558705\pi$
$829$	−10.5602	−0.366770	−0.183385	+	0.983041i	$0.558705\pi$
$830$	74.6986	2.59283
$831$	22.3963	0.776918
$832$	−2.85823	−0.0990913
$833$	23.0624	0.799065
$834$	13.6794	0.473678
$835$	11.3257	0.391941
$836$	10.6597	0.368672
$837$	10.3657	0.358290
$838$	45.1549	1.55985
$839$	−0.506451	−0.0174846	−0.00874232	−	0.999962i	$-0.502783\pi$
$839$	−0.506451	−0.0174846	−0.00874232	+	0.999962i	$0.502783\pi$
$840$	−1.75865	−0.0606793
$841$	71.9699	2.48172
$842$	−40.0025	−1.37858
$843$	11.5750	0.398664
$844$	−25.6245	−0.882030
$845$	−44.3920	−1.52713
$846$	3.54088	0.121738
$847$	3.11787	0.107131
$848$	14.8137	0.508704
$849$	45.0289	1.54539
$850$	−47.8719	−1.64199
$851$	−29.3214	−1.00513
$852$	−39.8287	−1.36451
$853$	24.4764	0.838058	0.419029	−	0.907973i	$-0.362371\pi$
$853$	24.4764	0.838058	0.419029	+	0.907973i	$0.362371\pi$
$854$	−0.500699	−0.0171336
$855$	−0.960507	−0.0328486
$856$	−7.79372	−0.266384
$857$	−29.9286	−1.02234	−0.511171	−	0.859479i	$-0.670788\pi$
$857$	−29.9286	−1.02234	−0.511171	+	0.859479i	$0.670788\pi$
$858$	−4.02303	−0.137344
$859$	−42.8390	−1.46165	−0.730824	−	0.682566i	$-0.760864\pi$
$859$	−42.8390	−1.46165	−0.730824	+	0.682566i	$0.760864\pi$
$860$	−38.7477	−1.32129
$861$	3.23637	0.110295
$862$	−10.8738	−0.370364
$863$	17.0825	0.581495	0.290748	−	0.956800i	$-0.406096\pi$
$863$	17.0825	0.581495	0.290748	+	0.956800i	$0.406096\pi$
$864$	−43.6296	−1.48431
$865$	4.55749	0.154959
$866$	−57.9786	−1.97019
$867$	9.30246	0.315928
$868$	1.82236	0.0618550
$869$	−16.9748	−0.575832
$870$	119.189	4.04089
$871$	−0.389456	−0.0131962
$872$	5.69862	0.192980
$873$	−5.12353	−0.173405
$874$	13.7987	0.466747
$875$	2.46523	0.0833401
$876$	−65.4909	−2.21273
$877$	48.0928	1.62398	0.811989	−	0.583673i	$-0.198385\pi$
$877$	48.0928	1.62398	0.811989	+	0.583673i	$0.198385\pi$
$878$	−12.1125	−0.408776
$879$	−8.97131	−0.302595
$880$	−46.4762	−1.56671
$881$	1.57030	0.0529046	0.0264523	−	0.999650i	$-0.491579\pi$
$881$	1.57030	0.0529046	0.0264523	+	0.999650i	$0.491579\pi$
$882$	3.85312	0.129741
$883$	16.8027	0.565457	0.282729	−	0.959200i	$-0.408760\pi$
$883$	16.8027	0.565457	0.282729	+	0.959200i	$0.408760\pi$
$884$	−2.14772	−0.0722356
$885$	23.1310	0.777541
$886$	−21.7423	−0.730448
$887$	−8.31097	−0.279055	−0.139528	−	0.990218i	$-0.544558\pi$
$887$	−8.31097	−0.279055	−0.139528	+	0.990218i	$0.544558\pi$
$888$	5.89177	0.197715
$889$	2.01631	0.0676247
$890$	−76.4684	−2.56323
$891$	−35.1835	−1.17869
$892$	54.5039	1.82493
$893$	−6.52345	−0.218299
$894$	9.91397	0.331573
$895$	23.4332	0.783285
$896$	−2.43710	−0.0814178
$897$	−2.82429	−0.0943003
$898$	−21.7020	−0.724206
$899$	−19.2793	−0.643001
$900$	−4.33761	−0.144587
$901$	15.9936	0.532822
$902$	−44.2708	−1.47406
$903$	3.15318	0.104931
$904$	10.9848	0.365348
$905$	45.4721	1.51154
$906$	59.2779	1.96938
$907$	−46.8874	−1.55687	−0.778436	−	0.627724i	$-0.783987\pi$
$907$	−46.8874	−1.55687	−0.778436	+	0.627724i	$0.783987\pi$
$908$	22.1752	0.735909
$909$	0.634092	0.0210315
$910$	0.773163	0.0256301
$911$	38.8966	1.28870	0.644350	−	0.764731i	$-0.277128\pi$
$911$	38.8966	1.28870	0.644350	+	0.764731i	$0.277128\pi$
$912$	5.35660	0.177375
$913$	45.0958	1.49245
$914$	69.7192	2.30611
$915$	3.39110	0.112106
$916$	−19.3729	−0.640100
$917$	7.09174	0.234190
$918$	−38.0828	−1.25692
$919$	−31.7673	−1.04791	−0.523953	−	0.851747i	$-0.675543\pi$
$919$	−31.7673	−1.04791	−0.523953	+	0.851747i	$0.675543\pi$
$920$	16.8887	0.556803
$921$	29.8203	0.982613
$922$	−8.84026	−0.291139
$923$	2.73330	0.0899675
$924$	−6.80148	−0.223752
$925$	−31.3114	−1.02951
$926$	−23.4862	−0.771806
$927$	1.41605	0.0465093
$928$	81.1474	2.66379
$929$	−43.4004	−1.42392	−0.711960	−	0.702220i	$-0.752192\pi$
$929$	−43.4004	−1.42392	−0.711960	+	0.702220i	$0.752192\pi$
$930$	−22.7581	−0.746268
$931$	−7.09869	−0.232650
$932$	6.77594	0.221953
$933$	51.5420	1.68741
$934$	69.4042	2.27098
$935$	−50.1779	−1.64099
$936$	−0.0560125	−0.00183083
$937$	35.4866	1.15930	0.579648	−	0.814867i	$-0.303190\pi$
$937$	35.4866	1.15930	0.579648	+	0.814867i	$0.303190\pi$
$938$	−1.21408	−0.0396410
$939$	−21.6088	−0.705176
$940$	−51.1489	−1.66829
$941$	−37.9274	−1.23640	−0.618200	−	0.786021i	$-0.712138\pi$
$941$	−37.9274	−1.23640	−0.618200	+	0.786021i	$0.712138\pi$
$942$	−84.6741	−2.75883
$943$	−31.0795	−1.01209
$944$	12.7321	0.414393
$945$	7.43506	0.241863
$946$	−43.1328	−1.40237
$947$	51.3928	1.67004	0.835021	−	0.550219i	$-0.185456\pi$
$947$	51.3928	1.67004	0.835021	+	0.550219i	$0.185456\pi$
$948$	15.3399	0.498216
$949$	4.49440	0.145895
$950$	14.7351	0.478071
$951$	−10.6632	−0.345777
$952$	−1.04512	−0.0338725
$953$	20.3040	0.657711	0.328855	−	0.944380i	$-0.393337\pi$
$953$	20.3040	0.657711	0.328855	+	0.944380i	$0.393337\pi$
$954$	2.67210	0.0865124
$955$	57.8903	1.87329
$956$	−49.5150	−1.60143
$957$	71.9549	2.32597
$958$	−52.5574	−1.69805
$959$	−1.35378	−0.0437159
$960$	60.3461	1.94766
$961$	−27.3188	−0.881251
$962$	−2.59022	−0.0835120
$963$	2.71597	0.0875211
$964$	43.8228	1.41144
$965$	−95.2646	−3.06668
$966$	−8.80436	−0.283276
$967$	−5.38543	−0.173184	−0.0865918	−	0.996244i	$-0.527598\pi$
$967$	−5.38543	−0.173184	−0.0865918	+	0.996244i	$0.527598\pi$
$968$	6.01636	0.193373
$969$	5.78323	0.185784
$970$	136.468	4.38172
$971$	−6.67206	−0.214117	−0.107058	−	0.994253i	$-0.534143\pi$
$971$	−6.67206	−0.214117	−0.107058	+	0.994253i	$0.534143\pi$
$972$	−6.61683	−0.212235
$973$	−1.58711	−0.0508805
$974$	64.0992	2.05387
$975$	−3.01597	−0.0965883
$976$	1.86657	0.0597474
$977$	27.3010	0.873436	0.436718	−	0.899599i	$-0.356141\pi$
$977$	27.3010	0.873436	0.436718	+	0.899599i	$0.356141\pi$
$978$	26.9373	0.861359
$979$	−46.1642	−1.47541
$980$	−55.6592	−1.77797
$981$	−1.98587	−0.0634039
$982$	−27.5212	−0.878236
$983$	21.3227	0.680090	0.340045	−	0.940409i	$-0.389558\pi$
$983$	21.3227	0.680090	0.340045	+	0.940409i	$0.389558\pi$
$984$	6.24503	0.199084
$985$	85.8660	2.73592
$986$	70.8308	2.25571
$987$	4.16234	0.132489
$988$	0.661075	0.0210316
$989$	−30.2806	−0.962866
$990$	−8.38340	−0.266442
$991$	−57.3286	−1.82110	−0.910551	−	0.413396i	$-0.864343\pi$
$991$	−57.3286	−1.82110	−0.910551	+	0.413396i	$0.864343\pi$
$992$	−15.4944	−0.491947
$993$	25.6699	0.814609
$994$	8.52069	0.270260
$995$	29.2415	0.927019
$996$	−40.7524	−1.29129
$997$	15.3880	0.487343	0.243671	−	0.969858i	$-0.421648\pi$
$997$	15.3880	0.487343	0.243671	+	0.969858i	$0.421648\pi$
$998$	67.7143	2.14346
$999$	−24.9086	−0.788075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	373.2.a.c.1.14	✓	17
3.2	odd	2		3357.2.a.e.1.4		17
4.3	odd	2		5968.2.a.l.1.14		17
5.4	even	2		9325.2.a.m.1.4		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
373.2.a.c.1.14	✓	17	1.1	even	1	trivial
3357.2.a.e.1.4		17	3.2	odd	2
5968.2.a.l.1.14		17	4.3	odd	2
9325.2.a.m.1.4		17	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 373 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	373.a (trivial)

\(f(q)\)	\(=\)	\(q+2.09044 q^{2} -1.65242 q^{3} +2.36995 q^{4} +3.43385 q^{5} -3.45429 q^{6} +0.400775 q^{7} +0.773351 q^{8} -0.269499 q^{9} +O(q^{10})\)	\(q+2.09044 q^{2} -1.65242 q^{3} +2.36995 q^{4} +3.43385 q^{5} -3.45429 q^{6} +0.400775 q^{7} +0.773351 q^{8} -0.269499 q^{9} +7.17826 q^{10} +4.33354 q^{11} -3.91615 q^{12} +0.268751 q^{13} +0.837797 q^{14} -5.67417 q^{15} -3.12325 q^{16} -3.37200 q^{17} -0.563372 q^{18} +1.03791 q^{19} +8.13804 q^{20} -0.662250 q^{21} +9.05902 q^{22} +6.35972 q^{23} -1.27790 q^{24} +6.79133 q^{25} +0.561809 q^{26} +5.40259 q^{27} +0.949816 q^{28} -10.0484 q^{29} -11.8615 q^{30} +1.91865 q^{31} -8.07567 q^{32} -7.16085 q^{33} -7.04898 q^{34} +1.37620 q^{35} -0.638699 q^{36} -4.61050 q^{37} +2.16970 q^{38} -0.444091 q^{39} +2.65557 q^{40} -4.88693 q^{41} -1.38440 q^{42} -4.76131 q^{43} +10.2703 q^{44} -0.925420 q^{45} +13.2946 q^{46} -6.28515 q^{47} +5.16092 q^{48} -6.83938 q^{49} +14.1969 q^{50} +5.57198 q^{51} +0.636926 q^{52} -4.74304 q^{53} +11.2938 q^{54} +14.8807 q^{55} +0.309940 q^{56} -1.71507 q^{57} -21.0055 q^{58} -4.07654 q^{59} -13.4475 q^{60} -0.597637 q^{61} +4.01082 q^{62} -0.108009 q^{63} -10.6352 q^{64} +0.922852 q^{65} -14.9693 q^{66} -1.44913 q^{67} -7.99147 q^{68} -10.5089 q^{69} +2.87687 q^{70} +10.1704 q^{71} -0.208418 q^{72} +16.7233 q^{73} -9.63797 q^{74} -11.2221 q^{75} +2.45980 q^{76} +1.73678 q^{77} -0.928346 q^{78} -3.91708 q^{79} -10.7248 q^{80} -8.11887 q^{81} -10.2158 q^{82} +10.4062 q^{83} -1.56950 q^{84} -11.5790 q^{85} -9.95323 q^{86} +16.6042 q^{87} +3.35135 q^{88} -10.6528 q^{89} -1.93454 q^{90} +0.107709 q^{91} +15.0722 q^{92} -3.17042 q^{93} -13.1387 q^{94} +3.56404 q^{95} +13.3444 q^{96} +19.0113 q^{97} -14.2973 q^{98} -1.16789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 4 q^{2} + 14 q^{3} + 18 q^{4} + 9 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 17 * q + 4 * q^2 + 14 * q^3 + 18 * q^4 + 9 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 23 * q^9	\( 17 q + 4 q^{2} + 14 q^{3} + 18 q^{4} + 9 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 23 q^{9} - 7 q^{10} + 16 q^{11} + 19 q^{12} - q^{13} - q^{14} + 3 q^{15} + 8 q^{16} + 16 q^{17} - 5 q^{18} + 5 q^{19} + 10 q^{20} - 10 q^{21} - 15 q^{22} + 32 q^{23} - 10 q^{24} + 12 q^{25} - 2 q^{26} + 47 q^{27} - 26 q^{28} - 7 q^{29} - 44 q^{30} - 6 q^{31} + 7 q^{32} - 16 q^{34} + 41 q^{35} + 8 q^{36} - 13 q^{37} + 18 q^{38} - 11 q^{39} - 29 q^{40} - 5 q^{41} - 12 q^{42} + 9 q^{43} + 5 q^{44} - 5 q^{45} - 25 q^{46} + 42 q^{47} + 18 q^{48} + 8 q^{49} - 15 q^{50} + 6 q^{51} - 17 q^{52} + 16 q^{53} - 18 q^{54} - 4 q^{55} - 30 q^{56} - 27 q^{57} - 5 q^{58} + 55 q^{59} - 57 q^{60} - 20 q^{61} + 30 q^{62} - 19 q^{63} - 15 q^{64} - 24 q^{65} - 49 q^{66} - 6 q^{67} + 39 q^{68} - 4 q^{69} - 38 q^{70} - 7 q^{71} - 68 q^{72} - 6 q^{73} - 36 q^{74} + 6 q^{75} - 34 q^{76} + 7 q^{77} - 14 q^{78} - 23 q^{79} - q^{80} + 33 q^{81} - 36 q^{82} + 98 q^{83} - 113 q^{84} - 40 q^{85} - 32 q^{86} - 8 q^{87} - 86 q^{88} + 4 q^{89} - 108 q^{90} - 45 q^{91} + 45 q^{92} - 36 q^{93} - 22 q^{94} - 24 q^{95} - 63 q^{96} - 13 q^{97} - 2 q^{98} + 12 q^{99}+O(q^{100}) \) 17 * q + 4 * q^2 + 14 * q^3 + 18 * q^4 + 9 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 23 * q^9 - 7 * q^10 + 16 * q^11 + 19 * q^12 - q^13 - q^14 + 3 * q^15 + 8 * q^16 + 16 * q^17 - 5 * q^18 + 5 * q^19 + 10 * q^20 - 10 * q^21 - 15 * q^22 + 32 * q^23 - 10 * q^24 + 12 * q^25 - 2 * q^26 + 47 * q^27 - 26 * q^28 - 7 * q^29 - 44 * q^30 - 6 * q^31 + 7 * q^32 - 16 * q^34 + 41 * q^35 + 8 * q^36 - 13 * q^37 + 18 * q^38 - 11 * q^39 - 29 * q^40 - 5 * q^41 - 12 * q^42 + 9 * q^43 + 5 * q^44 - 5 * q^45 - 25 * q^46 + 42 * q^47 + 18 * q^48 + 8 * q^49 - 15 * q^50 + 6 * q^51 - 17 * q^52 + 16 * q^53 - 18 * q^54 - 4 * q^55 - 30 * q^56 - 27 * q^57 - 5 * q^58 + 55 * q^59 - 57 * q^60 - 20 * q^61 + 30 * q^62 - 19 * q^63 - 15 * q^64 - 24 * q^65 - 49 * q^66 - 6 * q^67 + 39 * q^68 - 4 * q^69 - 38 * q^70 - 7 * q^71 - 68 * q^72 - 6 * q^73 - 36 * q^74 + 6 * q^75 - 34 * q^76 + 7 * q^77 - 14 * q^78 - 23 * q^79 - q^80 + 33 * q^81 - 36 * q^82 + 98 * q^83 - 113 * q^84 - 40 * q^85 - 32 * q^86 - 8 * q^87 - 86 * q^88 + 4 * q^89 - 108 * q^90 - 45 * q^91 + 45 * q^92 - 36 * q^93 - 22 * q^94 - 24 * q^95 - 63 * q^96 - 13 * q^97 - 2 * q^98 + 12 * q^99

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