LMFDB - Embedded newform 4013.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, 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("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0439663311$
Analytic rank:	$1$
Dimension:	$157$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28352 q^{2} -2.81571 q^{3} +3.21448 q^{4} +2.96925 q^{5} +6.42974 q^{6} -4.34900 q^{7} -2.77330 q^{8} +4.92822 q^{9} +O(q^{10})$	\(q-2.28352 q^{2} -2.81571 q^{3} +3.21448 q^{4} +2.96925 q^{5} +6.42974 q^{6} -4.34900 q^{7} -2.77330 q^{8} +4.92822 q^{9} -6.78035 q^{10} -3.71586 q^{11} -9.05105 q^{12} +2.94893 q^{13} +9.93105 q^{14} -8.36054 q^{15} -0.0960599 q^{16} -6.18538 q^{17} -11.2537 q^{18} -2.42561 q^{19} +9.54461 q^{20} +12.2455 q^{21} +8.48526 q^{22} +3.19299 q^{23} +7.80882 q^{24} +3.81645 q^{25} -6.73396 q^{26} -5.42930 q^{27} -13.9798 q^{28} +9.27386 q^{29} +19.0915 q^{30} +11.0386 q^{31} +5.76596 q^{32} +10.4628 q^{33} +14.1245 q^{34} -12.9133 q^{35} +15.8417 q^{36} -8.70670 q^{37} +5.53894 q^{38} -8.30333 q^{39} -8.23463 q^{40} -5.58536 q^{41} -27.9630 q^{42} -6.45697 q^{43} -11.9446 q^{44} +14.6331 q^{45} -7.29127 q^{46} -10.9576 q^{47} +0.270477 q^{48} +11.9138 q^{49} -8.71495 q^{50} +17.4162 q^{51} +9.47929 q^{52} +13.6128 q^{53} +12.3979 q^{54} -11.0333 q^{55} +12.0611 q^{56} +6.82981 q^{57} -21.1771 q^{58} +2.74502 q^{59} -26.8748 q^{60} +10.0282 q^{61} -25.2069 q^{62} -21.4328 q^{63} -12.9746 q^{64} +8.75611 q^{65} -23.8920 q^{66} +9.51855 q^{67} -19.8828 q^{68} -8.99053 q^{69} +29.4878 q^{70} -8.82726 q^{71} -13.6674 q^{72} -8.12609 q^{73} +19.8820 q^{74} -10.7460 q^{75} -7.79708 q^{76} +16.1603 q^{77} +18.9609 q^{78} +0.116975 q^{79} -0.285226 q^{80} +0.502677 q^{81} +12.7543 q^{82} +0.119164 q^{83} +39.3631 q^{84} -18.3659 q^{85} +14.7447 q^{86} -26.1125 q^{87} +10.3052 q^{88} -4.67249 q^{89} -33.4151 q^{90} -12.8249 q^{91} +10.2638 q^{92} -31.0814 q^{93} +25.0219 q^{94} -7.20224 q^{95} -16.2353 q^{96} +8.76742 q^{97} -27.2055 q^{98} -18.3126 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) $ 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9 - 61 * q^10 - 27 * q^11 - 93 * q^12 - 97 * q^13 - 12 * q^14 - 36 * q^15 + 105 * q^16 - 45 * q^17 - 68 * q^18 - 128 * q^19 - 30 * q^20 - 26 * q^21 - 68 * q^22 - 41 * q^23 - 40 * q^24 + 102 * q^25 - 5 * q^26 - 189 * q^27 - 115 * q^28 - 26 * q^29 - 12 * q^30 - 88 * q^31 - 89 * q^32 - 52 * q^33 - 61 * q^34 - 87 * q^35 + 110 * q^36 - 62 * q^37 - 37 * q^38 - 20 * q^39 - 161 * q^40 - 34 * q^41 - 53 * q^42 - 254 * q^43 - 19 * q^44 - 46 * q^45 - 52 * q^46 - 76 * q^47 - 162 * q^48 + 96 * q^49 - 54 * q^50 - 76 * q^51 - 259 * q^52 - 48 * q^53 - 12 * q^54 - 194 * q^55 - 10 * q^56 - 30 * q^57 - 52 * q^58 - 64 * q^59 - 31 * q^60 - 107 * q^61 - 51 * q^62 - 106 * q^63 + 54 * q^64 - 17 * q^65 - 13 * q^66 - 193 * q^67 - 118 * q^68 - 55 * q^69 - 86 * q^70 - 11 * q^71 - 172 * q^72 - 173 * q^73 - 11 * q^74 - 209 * q^75 - 213 * q^76 - 84 * q^77 - 30 * q^78 - 111 * q^79 - 6 * q^80 + 157 * q^81 - 117 * q^82 - 154 * q^83 - 6 * q^84 - 91 * q^85 + 28 * q^86 - 165 * q^87 - 165 * q^88 - 32 * q^89 - 103 * q^90 - 200 * q^91 - 86 * q^92 - 39 * q^93 - 118 * q^94 - 22 * q^95 - 28 * q^96 - 151 * q^97 - 38 * q^98 - 91 * 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 $

$2$	−2.28352	−1.61470	−0.807348	−	0.590076i	$-0.799098\pi$
$2$	−2.28352	−1.61470	−0.807348	+	0.590076i	$0.799098\pi$
$3$	−2.81571	−1.62565	−0.812825	−	0.582508i	$-0.802072\pi$
$3$	−2.81571	−1.62565	−0.812825	+	0.582508i	$0.802072\pi$
$4$	3.21448	1.60724
$5$	2.96925	1.32789	0.663944	−	0.747782i	$-0.268881\pi$
$5$	2.96925	1.32789	0.663944	+	0.747782i	$0.268881\pi$
$6$	6.42974	2.62493
$7$	−4.34900	−1.64377	−0.821884	−	0.569655i	$-0.807077\pi$
$7$	−4.34900	−1.64377	−0.821884	+	0.569655i	$0.807077\pi$
$8$	−2.77330	−0.980511
$9$	4.92822	1.64274
$10$	−6.78035	−2.14414
$11$	−3.71586	−1.12037	−0.560187	−	0.828366i	$-0.689271\pi$
$11$	−3.71586	−1.12037	−0.560187	+	0.828366i	$0.689271\pi$
$12$	−9.05105	−2.61281
$13$	2.94893	0.817886	0.408943	−	0.912560i	$-0.365897\pi$
$13$	2.94893	0.817886	0.408943	+	0.912560i	$0.365897\pi$
$14$	9.93105	2.65419
$15$	−8.36054	−2.15868
$16$	−0.0960599	−0.0240150
$17$	−6.18538	−1.50017	−0.750087	−	0.661339i	$-0.769988\pi$
$17$	−6.18538	−1.50017	−0.750087	+	0.661339i	$0.769988\pi$
$18$	−11.2537	−2.65252
$19$	−2.42561	−0.556473	−0.278236	−	0.960513i	$-0.589750\pi$
$19$	−2.42561	−0.556473	−0.278236	+	0.960513i	$0.589750\pi$
$20$	9.54461	2.13424
$21$	12.2455	2.67219
$22$	8.48526	1.80906
$23$	3.19299	0.665784	0.332892	−	0.942965i	$-0.391975\pi$
$23$	3.19299	0.665784	0.332892	+	0.942965i	$0.391975\pi$
$24$	7.80882	1.59397
$25$	3.81645	0.763289
$26$	−6.73396	−1.32064
$27$	−5.42930	−1.04487
$28$	−13.9798	−2.64193
$29$	9.27386	1.72211	0.861056	−	0.508510i	$-0.169803\pi$
$29$	9.27386	1.72211	0.861056	+	0.508510i	$0.169803\pi$
$30$	19.0915	3.48562
$31$	11.0386	1.98259	0.991294	−	0.131670i	$-0.0420339\pi$
$31$	11.0386	1.98259	0.991294	+	0.131670i	$0.0420339\pi$
$32$	5.76596	1.01929
$33$	10.4628	1.82134
$34$	14.1245	2.42232
$35$	−12.9133	−2.18274
$36$	15.8417	2.64028
$37$	−8.70670	−1.43137	−0.715686	−	0.698422i	$-0.753886\pi$
$37$	−8.70670	−1.43137	−0.715686	+	0.698422i	$0.753886\pi$
$38$	5.53894	0.898534
$39$	−8.30333	−1.32960
$40$	−8.23463	−1.30201
$41$	−5.58536	−0.872286	−0.436143	−	0.899877i	$-0.643656\pi$
$41$	−5.58536	−0.872286	−0.436143	+	0.899877i	$0.643656\pi$
$42$	−27.9630	−4.31478
$43$	−6.45697	−0.984679	−0.492339	−	0.870403i	$-0.663858\pi$
$43$	−6.45697	−0.984679	−0.492339	+	0.870403i	$0.663858\pi$
$44$	−11.9446	−1.80071
$45$	14.6331	2.18138
$46$	−7.29127	−1.07504
$47$	−10.9576	−1.59833	−0.799163	−	0.601115i	$-0.794723\pi$
$47$	−10.9576	−1.59833	−0.799163	+	0.601115i	$0.794723\pi$
$48$	0.270477	0.0390400
$49$	11.9138	1.70197
$50$	−8.71495	−1.23248
$51$	17.4162	2.43876
$52$	9.47929	1.31454
$53$	13.6128	1.86986	0.934930	−	0.354832i	$-0.115462\pi$
$53$	13.6128	1.86986	0.934930	+	0.354832i	$0.115462\pi$
$54$	12.3979	1.68715
$55$	−11.0333	−1.48773
$56$	12.0611	1.61173
$57$	6.82981	0.904630
$58$	−21.1771	−2.78069
$59$	2.74502	0.357371	0.178685	−	0.983906i	$-0.442816\pi$
$59$	2.74502	0.357371	0.178685	+	0.983906i	$0.442816\pi$
$60$	−26.8748	−3.46953
$61$	10.0282	1.28397	0.641987	−	0.766716i	$-0.278110\pi$
$61$	10.0282	1.28397	0.641987	+	0.766716i	$0.278110\pi$
$62$	−25.2069	−3.20127
$63$	−21.4328	−2.70028
$64$	−12.9746	−1.62182
$65$	8.75611	1.08606
$66$	−23.8920	−2.94091
$67$	9.51855	1.16288	0.581438	−	0.813591i	$-0.302490\pi$
$67$	9.51855	1.16288	0.581438	+	0.813591i	$0.302490\pi$
$68$	−19.8828	−2.41114
$69$	−8.99053	−1.08233
$70$	29.4878	3.52446
$71$	−8.82726	−1.04760	−0.523802	−	0.851840i	$-0.675487\pi$
$71$	−8.82726	−1.04760	−0.523802	+	0.851840i	$0.675487\pi$
$72$	−13.6674	−1.61072
$73$	−8.12609	−0.951086	−0.475543	−	0.879692i	$-0.657748\pi$
$73$	−8.12609	−0.951086	−0.475543	+	0.879692i	$0.657748\pi$
$74$	19.8820	2.31123
$75$	−10.7460	−1.24084
$76$	−7.79708	−0.894386
$77$	16.1603	1.84164
$78$	18.9609	2.14689
$79$	0.116975	0.0131607	0.00658036	−	0.999978i	$-0.497905\pi$
$79$	0.116975	0.0131607	0.00658036	+	0.999978i	$0.497905\pi$
$80$	−0.285226	−0.0318892
$81$	0.502677	0.0558530
$82$	12.7543	1.40848
$83$	0.119164	0.0130800	0.00653999	−	0.999979i	$-0.497918\pi$
$83$	0.119164	0.0130800	0.00653999	+	0.999979i	$0.497918\pi$
$84$	39.3631	4.29486
$85$	−18.3659	−1.99206
$86$	14.7447	1.58996
$87$	−26.1125	−2.79955
$88$	10.3052	1.09854
$89$	−4.67249	−0.495283	−0.247642	−	0.968852i	$-0.579656\pi$
$89$	−4.67249	−0.495283	−0.247642	+	0.968852i	$0.579656\pi$
$90$	−33.4151	−3.52226
$91$	−12.8249	−1.34442
$92$	10.2638	1.07008
$93$	−31.0814	−3.22299
$94$	25.0219	2.58081
$95$	−7.20224	−0.738934
$96$	−16.2353	−1.65701
$97$	8.76742	0.890197	0.445098	−	0.895482i	$-0.353169\pi$
$97$	8.76742	0.890197	0.445098	+	0.895482i	$0.353169\pi$
$98$	−27.2055	−2.74817
$99$	−18.3126	−1.84048
$100$	12.2679	1.22679
$101$	−3.88033	−0.386108	−0.193054	−	0.981188i	$-0.561839\pi$
$101$	−3.88033	−0.386108	−0.193054	+	0.981188i	$0.561839\pi$
$102$	−39.7704	−3.93785
$103$	−7.78638	−0.767215	−0.383608	−	0.923496i	$-0.625318\pi$
$103$	−7.78638	−0.767215	−0.383608	+	0.923496i	$0.625318\pi$
$104$	−8.17828	−0.801947
$105$	36.3600	3.54838
$106$	−31.0851	−3.01926
$107$	7.88304	0.762082	0.381041	−	0.924558i	$-0.375566\pi$
$107$	7.88304	0.762082	0.381041	+	0.924558i	$0.375566\pi$
$108$	−17.4524	−1.67936
$109$	17.9440	1.71872	0.859360	−	0.511371i	$-0.170862\pi$
$109$	17.9440	1.71872	0.859360	+	0.511371i	$0.170862\pi$
$110$	25.1949	2.40224
$111$	24.5155	2.32691
$112$	0.417765	0.0394751
$113$	5.36816	0.504994	0.252497	−	0.967598i	$-0.418748\pi$
$113$	5.36816	0.504994	0.252497	+	0.967598i	$0.418748\pi$
$114$	−15.5960	−1.46070
$115$	9.48078	0.884088
$116$	29.8107	2.76785
$117$	14.5330	1.34357
$118$	−6.26831	−0.577045
$119$	26.9002	2.46594
$120$	23.1863	2.11661
$121$	2.80764	0.255240
$122$	−22.8995	−2.07323
$123$	15.7267	1.41803
$124$	35.4833	3.18650
$125$	−3.51427	−0.314326
$126$	48.9424	4.36014
$127$	9.70248	0.860956	0.430478	−	0.902601i	$-0.358345\pi$
$127$	9.70248	0.860956	0.430478	+	0.902601i	$0.358345\pi$
$128$	18.0959	1.59947
$129$	18.1810	1.60074
$130$	−19.9948	−1.75366
$131$	0.250178	0.0218582	0.0109291	−	0.999940i	$-0.496521\pi$
$131$	0.250178	0.0218582	0.0109291	+	0.999940i	$0.496521\pi$
$132$	33.6325	2.92733
$133$	10.5490	0.914712
$134$	−21.7358	−1.87769
$135$	−16.1210	−1.38747
$136$	17.1539	1.47094
$137$	1.73443	0.148183	0.0740913	−	0.997251i	$-0.476394\pi$
$137$	1.73443	0.148183	0.0740913	+	0.997251i	$0.476394\pi$
$138$	20.5301	1.74764
$139$	−6.42236	−0.544737	−0.272369	−	0.962193i	$-0.587807\pi$
$139$	−6.42236	−0.544737	−0.272369	+	0.962193i	$0.587807\pi$
$140$	−41.5095	−3.50819
$141$	30.8533	2.59832
$142$	20.1573	1.69156
$143$	−10.9578	−0.916339
$144$	−0.473404	−0.0394504
$145$	27.5364	2.28677
$146$	18.5561	1.53572
$147$	−33.5459	−2.76682
$148$	−27.9875	−2.30056
$149$	−0.615968	−0.0504621	−0.0252310	−	0.999682i	$-0.508032\pi$
$149$	−0.615968	−0.0504621	−0.0252310	+	0.999682i	$0.508032\pi$
$150$	24.5388	2.00358
$151$	9.13630	0.743502	0.371751	−	0.928333i	$-0.378758\pi$
$151$	9.13630	0.743502	0.371751	+	0.928333i	$0.378758\pi$
$152$	6.72695	0.545628
$153$	−30.4829	−2.46439
$154$	−36.9024	−2.97368
$155$	32.7763	2.63266
$156$	−26.6909	−2.13698
$157$	0.360765	0.0287922	0.0143961	−	0.999896i	$-0.495417\pi$
$157$	0.360765	0.0287922	0.0143961	+	0.999896i	$0.495417\pi$
$158$	−0.267115	−0.0212506
$159$	−38.3297	−3.03974
$160$	17.1206	1.35350
$161$	−13.8863	−1.09440
$162$	−1.14788	−0.0901857
$163$	−17.5241	−1.37259	−0.686297	−	0.727321i	$-0.740765\pi$
$163$	−17.5241	−1.37259	−0.686297	+	0.727321i	$0.740765\pi$
$164$	−17.9540	−1.40197
$165$	31.0666	2.41853
$166$	−0.272114	−0.0211202
$167$	17.5153	1.35537	0.677686	−	0.735351i	$-0.262983\pi$
$167$	17.5153	1.35537	0.677686	+	0.735351i	$0.262983\pi$
$168$	−33.9606	−2.62012
$169$	−4.30380	−0.331062
$170$	41.9390	3.21658
$171$	−11.9539	−0.914140
$172$	−20.7558	−1.58262
$173$	−16.5563	−1.25875	−0.629376	−	0.777101i	$-0.716689\pi$
$173$	−16.5563	−1.25875	−0.629376	+	0.777101i	$0.716689\pi$
$174$	59.6285	4.52043
$175$	−16.5977	−1.25467
$176$	0.356946	0.0269058
$177$	−7.72917	−0.580960
$178$	10.6698	0.799732
$179$	12.6114	0.942620	0.471310	−	0.881968i	$-0.343781\pi$
$179$	12.6114	0.942620	0.471310	+	0.881968i	$0.343781\pi$
$180$	47.0379	3.50600
$181$	23.6921	1.76102	0.880510	−	0.474028i	$-0.157200\pi$
$181$	23.6921	1.76102	0.880510	+	0.474028i	$0.157200\pi$
$182$	29.2860	2.17082
$183$	−28.2364	−2.08729
$184$	−8.85513	−0.652809
$185$	−25.8524	−1.90070
$186$	70.9752	5.20415
$187$	22.9840	1.68076
$188$	−35.2229	−2.56890
$189$	23.6120	1.71752
$190$	16.4465	1.19315
$191$	0.547334	0.0396037	0.0198019	−	0.999804i	$-0.493696\pi$
$191$	0.547334	0.0396037	0.0198019	+	0.999804i	$0.493696\pi$
$192$	36.5327	2.63652
$193$	−8.90032	−0.640659	−0.320330	−	0.947306i	$-0.603794\pi$
$193$	−8.90032	−0.640659	−0.320330	+	0.947306i	$0.603794\pi$
$194$	−20.0206	−1.43740
$195$	−24.6547	−1.76556
$196$	38.2968	2.73549
$197$	22.0786	1.57303	0.786517	−	0.617568i	$-0.211882\pi$
$197$	22.0786	1.57303	0.786517	+	0.617568i	$0.211882\pi$
$198$	41.8172	2.97182
$199$	13.4282	0.951899	0.475950	−	0.879473i	$-0.342104\pi$
$199$	13.4282	0.951899	0.475950	+	0.879473i	$0.342104\pi$
$200$	−10.5842	−0.748413
$201$	−26.8015	−1.89043
$202$	8.86084	0.623446
$203$	−40.3320	−2.83075
$204$	55.9842	3.91967
$205$	−16.5843	−1.15830
$206$	17.7804	1.23882
$207$	15.7357	1.09371
$208$	−0.283274	−0.0196415
$209$	9.01323	0.623458
$210$	−83.0290	−5.72955
$211$	−11.8190	−0.813653	−0.406826	−	0.913505i	$-0.633365\pi$
$211$	−11.8190	−0.813653	−0.406826	+	0.913505i	$0.633365\pi$
$212$	43.7581	3.00532
$213$	24.8550	1.70304
$214$	−18.0011	−1.23053
$215$	−19.1724	−1.30754
$216$	15.0571	1.02451
$217$	−48.0068	−3.25891
$218$	−40.9755	−2.77521
$219$	22.8807	1.54613
$220$	−35.4665	−2.39115
$221$	−18.2402	−1.22697
$222$	−55.9818	−3.75725
$223$	−1.51829	−0.101672	−0.0508360	−	0.998707i	$-0.516189\pi$
$223$	−1.51829	−0.101672	−0.0508360	+	0.998707i	$0.516189\pi$
$224$	−25.0762	−1.67547
$225$	18.8083	1.25388
$226$	−12.2583	−0.815411
$227$	8.99403	0.596955	0.298477	−	0.954417i	$-0.403521\pi$
$227$	8.99403	0.596955	0.298477	+	0.954417i	$0.403521\pi$
$228$	21.9543	1.45396
$229$	1.07637	0.0711286	0.0355643	−	0.999367i	$-0.488677\pi$
$229$	1.07637	0.0711286	0.0355643	+	0.999367i	$0.488677\pi$
$230$	−21.6496	−1.42753
$231$	−45.5027	−2.99386
$232$	−25.7192	−1.68855
$233$	14.7239	0.964598	0.482299	−	0.876007i	$-0.339802\pi$
$233$	14.7239	0.964598	0.482299	+	0.876007i	$0.339802\pi$
$234$	−33.1864	−2.16946
$235$	−32.5357	−2.12240
$236$	8.82381	0.574381
$237$	−0.329368	−0.0213947
$238$	−61.4273	−3.98174
$239$	24.3278	1.57364	0.786818	−	0.617185i	$-0.211727\pi$
$239$	24.3278	1.57364	0.786818	+	0.617185i	$0.211727\pi$
$240$	0.803113	0.0518407
$241$	−4.15595	−0.267709	−0.133854	−	0.991001i	$-0.542735\pi$
$241$	−4.15595	−0.267709	−0.133854	+	0.991001i	$0.542735\pi$
$242$	−6.41131	−0.412135
$243$	14.8725	0.954072
$244$	32.2353	2.06366
$245$	35.3751	2.26003
$246$	−35.9124	−2.28969
$247$	−7.15295	−0.455131
$248$	−30.6133	−1.94395
$249$	−0.335532	−0.0212635
$250$	8.02492	0.507541
$251$	16.7162	1.05512	0.527558	−	0.849519i	$-0.323108\pi$
$251$	16.7162	1.05512	0.527558	+	0.849519i	$0.323108\pi$
$252$	−68.8955	−4.34001
$253$	−11.8647	−0.745928
$254$	−22.1558	−1.39018
$255$	51.7131	3.23840
$256$	−15.3732	−0.960825
$257$	−24.8606	−1.55076	−0.775380	−	0.631495i	$-0.782441\pi$
$257$	−24.8606	−1.55076	−0.775380	+	0.631495i	$0.782441\pi$
$258$	−41.5167	−2.58471
$259$	37.8655	2.35285
$260$	28.1464	1.74556
$261$	45.7036	2.82898
$262$	−0.571288	−0.0352943
$263$	−22.6009	−1.39363	−0.696815	−	0.717250i	$-0.745400\pi$
$263$	−22.6009	−1.39363	−0.696815	+	0.717250i	$0.745400\pi$
$264$	−29.0165	−1.78584
$265$	40.4198	2.48297
$266$	−24.0889	−1.47698
$267$	13.1564	0.805157
$268$	30.5972	1.86902
$269$	−27.2618	−1.66218	−0.831091	−	0.556137i	$-0.812283\pi$
$269$	−27.2618	−1.66218	−0.831091	+	0.556137i	$0.812283\pi$
$270$	36.8126	2.24034
$271$	−3.75445	−0.228067	−0.114033	−	0.993477i	$-0.536377\pi$
$271$	−3.75445	−0.228067	−0.114033	+	0.993477i	$0.536377\pi$
$272$	0.594167	0.0360266
$273$	36.1112	2.18555
$274$	−3.96062	−0.239270
$275$	−14.1814	−0.855170
$276$	−28.8999	−1.73957
$277$	−13.0089	−0.781628	−0.390814	−	0.920470i	$-0.627806\pi$
$277$	−13.0089	−0.781628	−0.390814	+	0.920470i	$0.627806\pi$
$278$	14.6656	0.879585
$279$	54.4005	3.25687
$280$	35.8124	2.14020
$281$	−19.9500	−1.19012	−0.595059	−	0.803682i	$-0.702871\pi$
$281$	−19.9500	−1.19012	−0.595059	+	0.803682i	$0.702871\pi$
$282$	−70.4543	−4.19549
$283$	−26.6243	−1.58265	−0.791325	−	0.611396i	$-0.790608\pi$
$283$	−26.6243	−1.58265	−0.791325	+	0.611396i	$0.790608\pi$
$284$	−28.3751	−1.68375
$285$	20.2794	1.20125
$286$	25.0225	1.47961
$287$	24.2907	1.43384
$288$	28.4159	1.67442
$289$	21.2589	1.25052
$290$	−62.8801	−3.69244
$291$	−24.6865	−1.44715
$292$	−26.1212	−1.52863
$293$	16.4693	0.962145	0.481073	−	0.876681i	$-0.340247\pi$
$293$	16.4693	0.962145	0.481073	+	0.876681i	$0.340247\pi$
$294$	76.6028	4.46757
$295$	8.15064	0.474549
$296$	24.1463	1.40348
$297$	20.1745	1.17065
$298$	1.40658	0.0814809
$299$	9.41591	0.544536
$300$	−34.5428	−1.99433
$301$	28.0814	1.61858
$302$	−20.8630	−1.20053
$303$	10.9259	0.627676
$304$	0.233004	0.0133637
$305$	29.7761	1.70497
$306$	69.6084	3.97925
$307$	−9.36682	−0.534593	−0.267296	−	0.963614i	$-0.586130\pi$
$307$	−9.36682	−0.534593	−0.267296	+	0.963614i	$0.586130\pi$
$308$	51.9470	2.95996
$309$	21.9242	1.24722
$310$	−74.8455	−4.25094
$311$	−21.6747	−1.22906	−0.614530	−	0.788893i	$-0.710654\pi$
$311$	−21.6747	−1.22906	−0.614530	+	0.788893i	$0.710654\pi$
$312$	23.0277	1.30368
$313$	−16.0001	−0.904378	−0.452189	−	0.891922i	$-0.649357\pi$
$313$	−16.0001	−0.904378	−0.452189	+	0.891922i	$0.649357\pi$
$314$	−0.823815	−0.0464906
$315$	−63.6394	−3.58568
$316$	0.376015	0.0211525
$317$	18.9761	1.06580	0.532902	−	0.846177i	$-0.321102\pi$
$317$	18.9761	1.06580	0.532902	+	0.846177i	$0.321102\pi$
$318$	87.5267	4.90825
$319$	−34.4604	−1.92941
$320$	−38.5248	−2.15360
$321$	−22.1963	−1.23888
$322$	31.7098	1.76712
$323$	15.0033	0.834806
$324$	1.61585	0.0897694
$325$	11.2544	0.624284
$326$	40.0167	2.21632
$327$	−50.5250	−2.79404
$328$	15.4899	0.855286
$329$	47.6545	2.62728
$330$	−70.9414	−3.90520
$331$	16.2630	0.893896	0.446948	−	0.894560i	$-0.352511\pi$
$331$	16.2630	0.893896	0.446948	+	0.894560i	$0.352511\pi$
$332$	0.383051	0.0210227
$333$	−42.9085	−2.35137
$334$	−39.9966	−2.18851
$335$	28.2630	1.54417
$336$	−1.17630	−0.0641727
$337$	−24.8183	−1.35194	−0.675969	−	0.736930i	$-0.736275\pi$
$337$	−24.8183	−1.35194	−0.675969	+	0.736930i	$0.736275\pi$
$338$	9.82784	0.534564
$339$	−15.1152	−0.820944
$340$	−59.0370	−3.20173
$341$	−41.0178	−2.22124
$342$	27.2971	1.47606
$343$	−21.3702	−1.15388
$344$	17.9071	0.965489
$345$	−26.6951	−1.43722
$346$	37.8067	2.03250
$347$	−9.70783	−0.521144	−0.260572	−	0.965454i	$-0.583911\pi$
$347$	−9.70783	−0.521144	−0.260572	+	0.965454i	$0.583911\pi$
$348$	−83.9382	−4.49956
$349$	−19.4011	−1.03852	−0.519258	−	0.854618i	$-0.673792\pi$
$349$	−19.4011	−1.03852	−0.519258	+	0.854618i	$0.673792\pi$
$350$	37.9013	2.02591
$351$	−16.0106	−0.854584
$352$	−21.4255	−1.14198
$353$	18.7497	0.997947	0.498973	−	0.866617i	$-0.333711\pi$
$353$	18.7497	0.997947	0.498973	+	0.866617i	$0.333711\pi$
$354$	17.6497	0.938073
$355$	−26.2103	−1.39110
$356$	−15.0197	−0.796040
$357$	−75.7432	−4.00875
$358$	−28.7984	−1.52204
$359$	15.6638	0.826701	0.413351	−	0.910572i	$-0.364358\pi$
$359$	15.6638	0.826701	0.413351	+	0.910572i	$0.364358\pi$
$360$	−40.5821	−2.13886
$361$	−13.1164	−0.690338
$362$	−54.1015	−2.84351
$363$	−7.90550	−0.414931
$364$	−41.2255	−2.16080
$365$	−24.1284	−1.26294
$366$	64.4784	3.37034
$367$	−8.92655	−0.465962	−0.232981	−	0.972481i	$-0.574848\pi$
$367$	−8.92655	−0.465962	−0.232981	+	0.972481i	$0.574848\pi$
$368$	−0.306718	−0.0159888
$369$	−27.5259	−1.43294
$370$	59.0345	3.06906
$371$	−59.2021	−3.07362
$372$	−99.9108	−5.18013
$373$	−35.0806	−1.81640	−0.908202	−	0.418533i	$-0.862545\pi$
$373$	−35.0806	−1.81640	−0.908202	+	0.418533i	$0.862545\pi$
$374$	−52.4845	−2.71391
$375$	9.89516	0.510984
$376$	30.3887	1.56718
$377$	27.3480	1.40849
$378$	−53.9187	−2.77328
$379$	−3.82857	−0.196660	−0.0983302	−	0.995154i	$-0.531350\pi$
$379$	−3.82857	−0.196660	−0.0983302	+	0.995154i	$0.531350\pi$
$380$	−23.1515	−1.18765
$381$	−27.3194	−1.39961
$382$	−1.24985	−0.0639480
$383$	22.2643	1.13765	0.568825	−	0.822458i	$-0.307398\pi$
$383$	22.2643	1.13765	0.568825	+	0.822458i	$0.307398\pi$
$384$	−50.9528	−2.60017
$385$	47.9840	2.44549
$386$	20.3241	1.03447
$387$	−31.8214	−1.61757
$388$	28.1827	1.43076
$389$	−26.7538	−1.35647	−0.678235	−	0.734846i	$-0.737255\pi$
$389$	−26.7538	−1.35647	−0.678235	+	0.734846i	$0.737255\pi$
$390$	56.2995	2.85084
$391$	−19.7498	−0.998792
$392$	−33.0407	−1.66881
$393$	−0.704429	−0.0355337
$394$	−50.4170	−2.53997
$395$	0.347328	0.0174760
$396$	−58.8655	−2.95810
$397$	−14.0995	−0.707634	−0.353817	−	0.935315i	$-0.615116\pi$
$397$	−14.0995	−0.707634	−0.353817	+	0.935315i	$0.615116\pi$
$398$	−30.6636	−1.53703
$399$	−29.7029	−1.48700
$400$	−0.366607	−0.0183304
$401$	−10.1473	−0.506731	−0.253365	−	0.967371i	$-0.581538\pi$
$401$	−10.1473	−0.506731	−0.253365	+	0.967371i	$0.581538\pi$
$402$	61.2018	3.05247
$403$	32.5520	1.62153
$404$	−12.4733	−0.620568
$405$	1.49257	0.0741666
$406$	92.0992	4.57081
$407$	32.3529	1.60367
$408$	−48.3005	−2.39123
$409$	−29.9257	−1.47973	−0.739866	−	0.672754i	$-0.765111\pi$
$409$	−29.9257	−1.47973	−0.739866	+	0.672754i	$0.765111\pi$
$410$	37.8707	1.87030
$411$	−4.88366	−0.240893
$412$	−25.0292	−1.23310
$413$	−11.9381	−0.587435
$414$	−35.9330	−1.76601
$415$	0.353828	0.0173687
$416$	17.0034	0.833662
$417$	18.0835	0.885553
$418$	−20.5819	−1.00670
$419$	15.1207	0.738695	0.369348	−	0.929291i	$-0.379581\pi$
$419$	15.1207	0.738695	0.369348	+	0.929291i	$0.379581\pi$
$420$	116.879	5.70310
$421$	22.8631	1.11428	0.557141	−	0.830418i	$-0.311898\pi$
$421$	22.8631	1.11428	0.557141	+	0.830418i	$0.311898\pi$
$422$	26.9890	1.31380
$423$	−54.0013	−2.62563
$424$	−37.7524	−1.83342
$425$	−23.6061	−1.14507
$426$	−56.7570	−2.74989
$427$	−43.6125	−2.11055
$428$	25.3399	1.22485
$429$	30.8540	1.48965
$430$	43.7806	2.11129
$431$	−26.0514	−1.25485	−0.627426	−	0.778676i	$-0.715892\pi$
$431$	−26.0514	−1.25485	−0.627426	+	0.778676i	$0.715892\pi$
$432$	0.521538	0.0250925
$433$	−15.9356	−0.765816	−0.382908	−	0.923787i	$-0.625077\pi$
$433$	−15.9356	−0.765816	−0.382908	+	0.923787i	$0.625077\pi$
$434$	109.625	5.26215
$435$	−77.5345	−3.71749
$436$	57.6806	2.76240
$437$	−7.74494	−0.370491
$438$	−52.2486	−2.49654
$439$	−24.6134	−1.17473	−0.587367	−	0.809321i	$-0.699835\pi$
$439$	−24.6134	−1.17473	−0.587367	+	0.809321i	$0.699835\pi$
$440$	30.5988	1.45874
$441$	58.7139	2.79590
$442$	41.6520	1.98119
$443$	40.8079	1.93884	0.969422	−	0.245401i	$-0.0789195\pi$
$443$	40.8079	1.93884	0.969422	+	0.245401i	$0.0789195\pi$
$444$	78.8048	3.73991
$445$	−13.8738	−0.657681
$446$	3.46705	0.164169
$447$	1.73439	0.0820337
$448$	56.4266	2.66590
$449$	22.6176	1.06739	0.533694	−	0.845677i	$-0.320803\pi$
$449$	22.6176	1.06739	0.533694	+	0.845677i	$0.320803\pi$
$450$	−42.9492	−2.02464
$451$	20.7544	0.977287
$452$	17.2559	0.811647
$453$	−25.7252	−1.20867
$454$	−20.5381	−0.963900
$455$	−38.0804	−1.78523
$456$	−18.9411	−0.887000
$457$	−12.7325	−0.595600	−0.297800	−	0.954628i	$-0.596253\pi$
$457$	−12.7325	−0.595600	−0.297800	+	0.954628i	$0.596253\pi$
$458$	−2.45792	−0.114851
$459$	33.5823	1.56749
$460$	30.4758	1.42094
$461$	9.10264	0.423952	0.211976	−	0.977275i	$-0.432010\pi$
$461$	9.10264	0.423952	0.211976	+	0.977275i	$0.432010\pi$
$462$	103.907	4.83417
$463$	4.37036	0.203108	0.101554	−	0.994830i	$-0.467619\pi$
$463$	4.37036	0.203108	0.101554	+	0.994830i	$0.467619\pi$
$464$	−0.890846	−0.0413565
$465$	−92.2885	−4.27978
$466$	−33.6225	−1.55753
$467$	−7.65936	−0.354433	−0.177217	−	0.984172i	$-0.556709\pi$
$467$	−7.65936	−0.354433	−0.177217	+	0.984172i	$0.556709\pi$
$468$	46.7160	2.15945
$469$	−41.3962	−1.91150
$470$	74.2962	3.42703
$471$	−1.01581	−0.0468060
$472$	−7.61277	−0.350406
$473$	23.9932	1.10321
$474$	0.752119	0.0345460
$475$	−9.25720	−0.424750
$476$	86.4703	3.96336
$477$	67.0868	3.07169
$478$	−55.5532	−2.54094
$479$	−1.13952	−0.0520660	−0.0260330	−	0.999661i	$-0.508287\pi$
$479$	−1.13952	−0.0520660	−0.0260330	+	0.999661i	$0.508287\pi$
$480$	−48.2066	−2.20032
$481$	−25.6755	−1.17070
$482$	9.49022	0.432268
$483$	39.0998	1.77910
$484$	9.02511	0.410232
$485$	26.0327	1.18208
$486$	−33.9617	−1.54054
$487$	0.427854	0.0193879	0.00969395	−	0.999953i	$-0.496914\pi$
$487$	0.427854	0.0193879	0.00969395	+	0.999953i	$0.496914\pi$
$488$	−27.8111	−1.25895
$489$	49.3428	2.23136
$490$	−80.7800	−3.64927
$491$	6.74088	0.304212	0.152106	−	0.988364i	$-0.451395\pi$
$491$	6.74088	0.304212	0.152106	+	0.988364i	$0.451395\pi$
$492$	50.5533	2.27912
$493$	−57.3623	−2.58347
$494$	16.3339	0.734899
$495$	−54.3746	−2.44396
$496$	−1.06036	−0.0476118
$497$	38.3898	1.72202
$498$	0.766195	0.0343340
$499$	12.4044	0.555297	0.277648	−	0.960683i	$-0.410445\pi$
$499$	12.4044	0.555297	0.277648	+	0.960683i	$0.410445\pi$
$500$	−11.2966	−0.505198
$501$	−49.3179	−2.20336
$502$	−38.1718	−1.70369
$503$	−19.8350	−0.884399	−0.442199	−	0.896917i	$-0.645802\pi$
$503$	−19.8350	−0.884399	−0.442199	+	0.896917i	$0.645802\pi$
$504$	59.4398	2.64766
$505$	−11.5217	−0.512708
$506$	27.0934	1.20445
$507$	12.1183	0.538191
$508$	31.1885	1.38376
$509$	31.5751	1.39954	0.699772	−	0.714367i	$-0.253285\pi$
$509$	31.5751	1.39954	0.699772	+	0.714367i	$0.253285\pi$
$510$	−118.088	−5.22903
$511$	35.3404	1.56337
$512$	−1.08668	−0.0480251
$513$	13.1694	0.581441
$514$	56.7697	2.50400
$515$	−23.1197	−1.01878
$516$	58.4424	2.57278
$517$	40.7168	1.79072
$518$	−86.4667	−3.79913
$519$	46.6177	2.04629
$520$	−24.2834	−1.06490
$521$	−5.91934	−0.259331	−0.129665	−	0.991558i	$-0.541390\pi$
$521$	−5.91934	−0.259331	−0.129665	+	0.991558i	$0.541390\pi$
$522$	−104.365	−4.56794
$523$	−19.3927	−0.847985	−0.423993	−	0.905666i	$-0.639372\pi$
$523$	−19.3927	−0.847985	−0.423993	+	0.905666i	$0.639372\pi$
$524$	0.804193	0.0351314
$525$	46.7344	2.03966
$526$	51.6097	2.25029
$527$	−68.2777	−2.97423
$528$	−1.00505	−0.0437394
$529$	−12.8048	−0.556731
$530$	−92.2995	−4.00924
$531$	13.5280	0.587067
$532$	33.9095	1.47016
$533$	−16.4708	−0.713431
$534$	−30.0429	−1.30008
$535$	23.4067	1.01196
$536$	−26.3978	−1.14021
$537$	−35.5100	−1.53237
$538$	62.2530	2.68392
$539$	−44.2701	−1.90685
$540$	−51.8205	−2.23000
$541$	−31.6558	−1.36099	−0.680494	−	0.732754i	$-0.738235\pi$
$541$	−31.6558	−1.36099	−0.680494	+	0.732754i	$0.738235\pi$
$542$	8.57339	0.368258
$543$	−66.7101	−2.86280
$544$	−35.6646	−1.52911
$545$	53.2801	2.28227
$546$	−82.4608	−3.52900
$547$	−24.2846	−1.03834	−0.519168	−	0.854672i	$-0.673758\pi$
$547$	−24.2846	−1.03834	−0.519168	+	0.854672i	$0.673758\pi$
$548$	5.57530	0.238165
$549$	49.4209	2.10923
$550$	32.3835	1.38084
$551$	−22.4947	−0.958309
$552$	24.9335	1.06124
$553$	−0.508725	−0.0216332
$554$	29.7061	1.26209
$555$	72.7927	3.08988
$556$	−20.6446	−0.875525
$557$	7.55673	0.320189	0.160095	−	0.987102i	$-0.448820\pi$
$557$	7.55673	0.320189	0.160095	+	0.987102i	$0.448820\pi$
$558$	−124.225	−5.25886
$559$	−19.0412	−0.805355
$560$	1.24045	0.0524185
$561$	−64.7163	−2.73232
$562$	45.5563	1.92168
$563$	−8.03658	−0.338701	−0.169351	−	0.985556i	$-0.554167\pi$
$563$	−8.03658	−0.338701	−0.169351	+	0.985556i	$0.554167\pi$
$564$	99.1775	4.17613
$565$	15.9394	0.670576
$566$	60.7972	2.55550
$567$	−2.18615	−0.0918095
$568$	24.4807	1.02719
$569$	−8.02812	−0.336556	−0.168278	−	0.985740i	$-0.553821\pi$
$569$	−8.02812	−0.336556	−0.168278	+	0.985740i	$0.553821\pi$
$570$	−46.3085	−1.93965
$571$	−33.3271	−1.39469	−0.697347	−	0.716733i	$-0.745637\pi$
$571$	−33.3271	−1.39469	−0.697347	+	0.716733i	$0.745637\pi$
$572$	−35.2238	−1.47278
$573$	−1.54113	−0.0643818
$574$	−55.4685	−2.31521
$575$	12.1859	0.508186
$576$	−63.9417	−2.66424
$577$	−2.16398	−0.0900877	−0.0450438	−	0.998985i	$-0.514343\pi$
$577$	−2.16398	−0.0900877	−0.0450438	+	0.998985i	$0.514343\pi$
$578$	−48.5451	−2.01921
$579$	25.0607	1.04149
$580$	88.5153	3.67540
$581$	−0.518245	−0.0215004
$582$	56.3723	2.33671
$583$	−50.5833	−2.09494
$584$	22.5361	0.932551
$585$	43.1520	1.78412
$586$	−37.6080	−1.55357
$587$	28.4305	1.17345	0.586727	−	0.809785i	$-0.300416\pi$
$587$	28.4305	1.17345	0.586727	+	0.809785i	$0.300416\pi$
$588$	−107.833	−4.44694
$589$	−26.7753	−1.10326
$590$	−18.6122	−0.766252
$591$	−62.1669	−2.55720
$592$	0.836365	0.0343744
$593$	31.6790	1.30090	0.650450	−	0.759549i	$-0.274580\pi$
$593$	31.6790	1.30090	0.650450	+	0.759549i	$0.274580\pi$
$594$	−46.0691	−1.89024
$595$	79.8735	3.27449
$596$	−1.98002	−0.0811048
$597$	−37.8099	−1.54746
$598$	−21.5015	−0.879260
$599$	−19.4351	−0.794099	−0.397049	−	0.917797i	$-0.629966\pi$
$599$	−19.4351	−0.794099	−0.397049	+	0.917797i	$0.629966\pi$
$600$	29.8019	1.21666
$601$	15.5693	0.635085	0.317543	−	0.948244i	$-0.397142\pi$
$601$	15.5693	0.635085	0.317543	+	0.948244i	$0.397142\pi$
$602$	−64.1245	−2.61352
$603$	46.9095	1.91030
$604$	29.3685	1.19499
$605$	8.33658	0.338930
$606$	−24.9495	−1.01351
$607$	1.62637	0.0660121	0.0330061	−	0.999455i	$-0.489492\pi$
$607$	1.62637	0.0660121	0.0330061	+	0.999455i	$0.489492\pi$
$608$	−13.9860	−0.567206
$609$	113.563	4.60182
$610$	−67.9944	−2.75301
$611$	−32.3131	−1.30725
$612$	−97.9867	−3.96088
$613$	−22.1344	−0.894001	−0.447001	−	0.894534i	$-0.647508\pi$
$613$	−22.1344	−0.894001	−0.447001	+	0.894534i	$0.647508\pi$
$614$	21.3894	0.863205
$615$	46.6966	1.88299
$616$	−44.8174	−1.80575
$617$	17.1457	0.690261	0.345130	−	0.938555i	$-0.387835\pi$
$617$	17.1457	0.690261	0.345130	+	0.938555i	$0.387835\pi$
$618$	−50.0644	−2.01389
$619$	1.79827	0.0722786	0.0361393	−	0.999347i	$-0.488494\pi$
$619$	1.79827	0.0722786	0.0361393	+	0.999347i	$0.488494\pi$
$620$	105.359	4.23131
$621$	−17.3357	−0.695658
$622$	49.4948	1.98456
$623$	20.3207	0.814131
$624$	0.797617	0.0319303
$625$	−29.5170	−1.18068
$626$	36.5366	1.46030
$627$	−25.3786	−1.01352
$628$	1.15967	0.0462760
$629$	53.8542	2.14731
$630$	145.322	5.78978
$631$	−14.8897	−0.592751	−0.296376	−	0.955071i	$-0.595778\pi$
$631$	−14.8897	−0.592751	−0.296376	+	0.955071i	$0.595778\pi$
$632$	−0.324407	−0.0129042
$633$	33.2788	1.32272
$634$	−43.3324	−1.72095
$635$	28.8091	1.14325
$636$	−123.210	−4.88560
$637$	35.1330	1.39202
$638$	78.6911	3.11541
$639$	−43.5027	−1.72094
$640$	53.7312	2.12391
$641$	32.1996	1.27181	0.635903	−	0.771769i	$-0.280628\pi$
$641$	32.1996	1.27181	0.635903	+	0.771769i	$0.280628\pi$
$642$	50.6859	2.00041
$643$	5.52674	0.217953	0.108977	−	0.994044i	$-0.465243\pi$
$643$	5.52674	0.217953	0.108977	+	0.994044i	$0.465243\pi$
$644$	−44.6374	−1.75896
$645$	53.9838	2.12561
$646$	−34.2604	−1.34796
$647$	−34.3668	−1.35110	−0.675550	−	0.737314i	$-0.736094\pi$
$647$	−34.3668	−1.35110	−0.675550	+	0.737314i	$0.736094\pi$
$648$	−1.39408	−0.0547645
$649$	−10.2001	−0.400389
$650$	−25.6998	−1.00803
$651$	135.173	5.29786
$652$	−56.3310	−2.20609
$653$	−0.889150	−0.0347951	−0.0173976	−	0.999849i	$-0.505538\pi$
$653$	−0.889150	−0.0347951	−0.0173976	+	0.999849i	$0.505538\pi$
$654$	115.375	4.51152
$655$	0.742841	0.0290252
$656$	0.536529	0.0209479
$657$	−40.0471	−1.56239
$658$	−108.820	−4.24225
$659$	7.55941	0.294473	0.147236	−	0.989101i	$-0.452962\pi$
$659$	7.55941	0.294473	0.147236	+	0.989101i	$0.452962\pi$
$660$	99.8632	3.88717
$661$	33.2318	1.29257	0.646283	−	0.763098i	$-0.276322\pi$
$661$	33.2318	1.29257	0.646283	+	0.763098i	$0.276322\pi$
$662$	−37.1370	−1.44337
$663$	51.3592	1.99463
$664$	−0.330479	−0.0128251
$665$	31.3226	1.21464
$666$	97.9826	3.79675
$667$	29.6113	1.14656
$668$	56.3026	2.17841
$669$	4.27506	0.165283
$670$	−64.5391	−2.49336
$671$	−37.2632	−1.43853
$672$	70.6073	2.72373
$673$	−12.3141	−0.474672	−0.237336	−	0.971428i	$-0.576274\pi$
$673$	−12.3141	−0.474672	−0.237336	+	0.971428i	$0.576274\pi$
$674$	56.6731	2.18297
$675$	−20.7206	−0.797537
$676$	−13.8345	−0.532097
$677$	−3.23474	−0.124321	−0.0621605	−	0.998066i	$-0.519799\pi$
$677$	−3.23474	−0.124321	−0.0621605	+	0.998066i	$0.519799\pi$
$678$	34.5159	1.32557
$679$	−38.1295	−1.46328
$680$	50.9343	1.95324
$681$	−25.3246	−0.970440
$682$	93.6653	3.58663
$683$	−19.6873	−0.753314	−0.376657	−	0.926353i	$-0.622926\pi$
$683$	−19.6873	−0.753314	−0.376657	+	0.926353i	$0.622926\pi$
$684$	−38.4257	−1.46924
$685$	5.14996	0.196770
$686$	48.7995	1.86317
$687$	−3.03075	−0.115630
$688$	0.620256	0.0236470
$689$	40.1432	1.52933
$690$	60.9590	2.32067
$691$	−7.16987	−0.272755	−0.136377	−	0.990657i	$-0.543546\pi$
$691$	−7.16987	−0.272755	−0.136377	+	0.990657i	$0.543546\pi$
$692$	−53.2199	−2.02312
$693$	79.6415	3.02533
$694$	22.1681	0.841488
$695$	−19.0696	−0.723351
$696$	72.4179	2.74499
$697$	34.5475	1.30858
$698$	44.3028	1.67689
$699$	−41.4583	−1.56810
$700$	−53.3531	−2.01656
$701$	17.3062	0.653645	0.326822	−	0.945086i	$-0.394022\pi$
$701$	17.3062	0.653645	0.326822	+	0.945086i	$0.394022\pi$
$702$	36.5607	1.37989
$703$	21.1190	0.796520
$704$	48.2118	1.81705
$705$	91.6112	3.45028
$706$	−42.8154	−1.61138
$707$	16.8756	0.634672
$708$	−24.8453	−0.933743
$709$	−14.6719	−0.551015	−0.275508	−	0.961299i	$-0.588846\pi$
$709$	−14.6719	−0.551015	−0.275508	+	0.961299i	$0.588846\pi$
$710$	59.8520	2.24620
$711$	0.576479	0.0216196
$712$	12.9582	0.485631
$713$	35.2461	1.31998
$714$	172.961	6.47292
$715$	−32.5365	−1.21680
$716$	40.5391	1.51502
$717$	−68.5001	−2.55818
$718$	−35.7686	−1.33487
$719$	−50.7652	−1.89322	−0.946611	−	0.322378i	$-0.895518\pi$
$719$	−50.7652	−1.89322	−0.946611	+	0.322378i	$0.895518\pi$
$720$	−1.40566	−0.0523857
$721$	33.8630	1.26112
$722$	29.9517	1.11469
$723$	11.7020	0.435201
$724$	76.1579	2.83039
$725$	35.3932	1.31447
$726$	18.0524	0.669987
$727$	−28.0707	−1.04109	−0.520543	−	0.853836i	$-0.674270\pi$
$727$	−28.0707	−1.04109	−0.520543	+	0.853836i	$0.674270\pi$
$728$	35.5674	1.31821
$729$	−43.3847	−1.60684
$730$	55.0977	2.03926
$731$	39.9388	1.47719
$732$	−90.7653	−3.35478
$733$	10.0927	0.372782	0.186391	−	0.982476i	$-0.440321\pi$
$733$	10.0927	0.372782	0.186391	+	0.982476i	$0.440321\pi$
$734$	20.3840	0.752387
$735$	−99.6061	−3.67402
$736$	18.4107	0.678626
$737$	−35.3696	−1.30286
$738$	62.8560	2.31376
$739$	15.0117	0.552214	0.276107	−	0.961127i	$-0.410956\pi$
$739$	15.0117	0.552214	0.276107	+	0.961127i	$0.410956\pi$
$740$	−83.1020	−3.05489
$741$	20.1406	0.739885
$742$	135.189	4.96296
$743$	−34.6067	−1.26960	−0.634799	−	0.772678i	$-0.718917\pi$
$743$	−34.6067	−1.26960	−0.634799	+	0.772678i	$0.718917\pi$
$744$	86.1983	3.16018
$745$	−1.82896	−0.0670080
$746$	80.1074	2.93294
$747$	0.587267	0.0214870
$748$	73.8817	2.70138
$749$	−34.2833	−1.25269
$750$	−22.5958	−0.825084
$751$	−15.5084	−0.565909	−0.282955	−	0.959133i	$-0.591315\pi$
$751$	−15.5084	−0.565909	−0.282955	+	0.959133i	$0.591315\pi$
$752$	1.05258	0.0383837
$753$	−47.0679	−1.71525
$754$	−62.4498	−2.27429
$755$	27.1280	0.987287
$756$	75.9005	2.76048
$757$	16.5219	0.600498	0.300249	−	0.953861i	$-0.402930\pi$
$757$	16.5219	0.600498	0.300249	+	0.953861i	$0.402930\pi$
$758$	8.74263	0.317547
$759$	33.4076	1.21262
$760$	19.9740	0.724533
$761$	−28.4668	−1.03192	−0.515960	−	0.856613i	$-0.672565\pi$
$761$	−28.4668	−1.03192	−0.515960	+	0.856613i	$0.672565\pi$
$762$	62.3844	2.25995
$763$	−78.0384	−2.82518
$764$	1.75940	0.0636528
$765$	−90.5113	−3.27244
$766$	−50.8410	−1.83696
$767$	8.09487	0.292289
$768$	43.2865	1.56197
$769$	−29.9861	−1.08133	−0.540664	−	0.841239i	$-0.681827\pi$
$769$	−29.9861	−1.08133	−0.540664	+	0.841239i	$0.681827\pi$
$770$	−109.573	−3.94872
$771$	70.0001	2.52099
$772$	−28.6100	−1.02969
$773$	−1.72912	−0.0621921	−0.0310961	−	0.999516i	$-0.509900\pi$
$773$	−1.72912	−0.0621921	−0.0310961	+	0.999516i	$0.509900\pi$
$774$	72.6649	2.61188
$775$	42.1281	1.51329
$776$	−24.3147	−0.872848
$777$	−106.618	−3.82490
$778$	61.0928	2.19028
$779$	13.5479	0.485403
$780$	−79.2520	−2.83768
$781$	32.8009	1.17371
$782$	45.0992	1.61275
$783$	−50.3506	−1.79938
$784$	−1.14444	−0.0408729
$785$	1.07120	0.0382328
$786$	1.60858	0.0573762
$787$	32.7010	1.16566	0.582832	−	0.812593i	$-0.301945\pi$
$787$	32.7010	1.16566	0.582832	+	0.812593i	$0.301945\pi$
$788$	70.9713	2.52825
$789$	63.6375	2.26556
$790$	−0.793133	−0.0282184
$791$	−23.3461	−0.830093
$792$	50.7864	1.80461
$793$	29.5723	1.05014
$794$	32.1966	1.14261
$795$	−113.810	−4.03644
$796$	43.1647	1.52993
$797$	0.393768	0.0139480	0.00697400	−	0.999976i	$-0.497780\pi$
$797$	0.393768	0.0139480	0.00697400	+	0.999976i	$0.497780\pi$
$798$	67.8272	2.40106
$799$	67.7766	2.39777
$800$	22.0055	0.778011
$801$	−23.0271	−0.813621
$802$	23.1716	0.818216
$803$	30.1954	1.06557
$804$	−86.1529	−3.03838
$805$	−41.2320	−1.45324
$806$	−74.3333	−2.61828
$807$	76.7613	2.70213
$808$	10.7613	0.378583
$809$	−23.1146	−0.812666	−0.406333	−	0.913725i	$-0.633193\pi$
$809$	−23.1146	−0.812666	−0.406333	+	0.913725i	$0.633193\pi$
$810$	−3.40833	−0.119757
$811$	−27.4995	−0.965638	−0.482819	−	0.875720i	$-0.660387\pi$
$811$	−27.4995	−0.965638	−0.482819	+	0.875720i	$0.660387\pi$
$812$	−129.647	−4.54971
$813$	10.5714	0.370757
$814$	−73.8786	−2.58945
$815$	−52.0335	−1.82265
$816$	−1.67300	−0.0585667
$817$	15.6621	0.547947
$818$	68.3361	2.38932
$819$	−63.2039	−2.20852
$820$	−53.3100	−1.86167
$821$	−48.0667	−1.67754	−0.838770	−	0.544486i	$-0.816725\pi$
$821$	−48.0667	−1.67754	−0.838770	+	0.544486i	$0.816725\pi$
$822$	11.1519	0.388969
$823$	20.9325	0.729660	0.364830	−	0.931074i	$-0.381127\pi$
$823$	20.9325	0.729660	0.364830	+	0.931074i	$0.381127\pi$
$824$	21.5940	0.752263
$825$	39.9307	1.39021
$826$	27.2609	0.948528
$827$	8.84591	0.307603	0.153801	−	0.988102i	$-0.450848\pi$
$827$	8.84591	0.307603	0.153801	+	0.988102i	$0.450848\pi$
$828$	50.5823	1.75786
$829$	37.8022	1.31292	0.656462	−	0.754359i	$-0.272052\pi$
$829$	37.8022	1.31292	0.656462	+	0.754359i	$0.272052\pi$
$830$	−0.807976	−0.0280452
$831$	36.6292	1.27065
$832$	−38.2612	−1.32647
$833$	−73.6915	−2.55326
$834$	−41.2941	−1.42990
$835$	52.0072	1.79978
$836$	28.9729	1.00205
$837$	−59.9318	−2.07154
$838$	−34.5285	−1.19277
$839$	33.8604	1.16899	0.584495	−	0.811397i	$-0.301293\pi$
$839$	33.8604	1.16899	0.584495	+	0.811397i	$0.301293\pi$
$840$	−100.837	−3.47922
$841$	57.0044	1.96567
$842$	−52.2085	−1.79922
$843$	56.1734	1.93472
$844$	−37.9920	−1.30774
$845$	−12.7791	−0.439613
$846$	123.313	4.23960
$847$	−12.2104	−0.419555
$848$	−1.30764	−0.0449047
$849$	74.9663	2.57284
$850$	53.9052	1.84893
$851$	−27.8004	−0.952985
$852$	79.8960	2.73719
$853$	−18.3453	−0.628132	−0.314066	−	0.949401i	$-0.601691\pi$
$853$	−18.3453	−0.628132	−0.314066	+	0.949401i	$0.601691\pi$
$854$	99.5901	3.40790
$855$	−35.4942	−1.21388
$856$	−21.8621	−0.747230
$857$	−30.6377	−1.04656	−0.523281	−	0.852160i	$-0.675292\pi$
$857$	−30.6377	−1.04656	−0.523281	+	0.852160i	$0.675292\pi$
$858$	−70.4560	−2.40533
$859$	−38.1791	−1.30265	−0.651326	−	0.758798i	$-0.725787\pi$
$859$	−38.1791	−1.30265	−0.651326	+	0.758798i	$0.725787\pi$
$860$	−61.6293	−2.10154
$861$	−68.3956	−2.33092
$862$	59.4890	2.02620
$863$	−45.1469	−1.53682	−0.768410	−	0.639958i	$-0.778952\pi$
$863$	−45.1469	−1.53682	−0.768410	+	0.639958i	$0.778952\pi$
$864$	−31.3052	−1.06502
$865$	−49.1598	−1.67148
$866$	36.3893	1.23656
$867$	−59.8588	−2.03291
$868$	−154.317	−5.23786
$869$	−0.434663	−0.0147449
$870$	177.052	6.00262
$871$	28.0695	0.951100
$872$	−49.7641	−1.68522
$873$	43.2078	1.46236
$874$	17.6858	0.598230
$875$	15.2836	0.516679
$876$	73.5496	2.48501
$877$	−52.3121	−1.76646	−0.883228	−	0.468944i	$-0.844635\pi$
$877$	−52.3121	−1.76646	−0.883228	+	0.468944i	$0.844635\pi$
$878$	56.2053	1.89684
$879$	−46.3727	−1.56411
$880$	1.05986	0.0357279
$881$	−1.21455	−0.0409193	−0.0204597	−	0.999791i	$-0.506513\pi$
$881$	−1.21455	−0.0409193	−0.0204597	+	0.999791i	$0.506513\pi$
$882$	−134.075	−4.51453
$883$	−3.57343	−0.120255	−0.0601277	−	0.998191i	$-0.519151\pi$
$883$	−3.57343	−0.120255	−0.0601277	+	0.998191i	$0.519151\pi$
$884$	−58.6330	−1.97204
$885$	−22.9498	−0.771450
$886$	−93.1859	−3.13064
$887$	29.7886	1.00020	0.500101	−	0.865967i	$-0.333296\pi$
$887$	29.7886	1.00020	0.500101	+	0.865967i	$0.333296\pi$
$888$	−67.9890	−2.28156
$889$	−42.1961	−1.41521
$890$	31.6812	1.06195
$891$	−1.86788	−0.0625763
$892$	−4.88051	−0.163412
$893$	26.5788	0.889424
$894$	−3.96052	−0.132459
$895$	37.4464	1.25170
$896$	−78.6991	−2.62915
$897$	−26.5125	−0.885225
$898$	−51.6478	−1.72351
$899$	102.370	3.41424
$900$	60.4589	2.01530
$901$	−84.2002	−2.80512
$902$	−47.3932	−1.57802
$903$	−79.0690	−2.63125
$904$	−14.8875	−0.495152
$905$	70.3478	2.33844
$906$	58.7440	1.95164
$907$	57.4281	1.90687	0.953435	−	0.301599i	$-0.0975204\pi$
$907$	57.4281	1.90687	0.953435	+	0.301599i	$0.0975204\pi$
$908$	28.9112	0.959451
$909$	−19.1231	−0.634274
$910$	86.9574	2.88261
$911$	11.3733	0.376813	0.188407	−	0.982091i	$-0.439668\pi$
$911$	11.3733	0.376813	0.188407	+	0.982091i	$0.439668\pi$
$912$	−0.656071	−0.0217247
$913$	−0.442798	−0.0146545
$914$	29.0749	0.961713
$915$	−83.8408	−2.77169
$916$	3.45998	0.114321
$917$	−1.08803	−0.0359298
$918$	−76.6859	−2.53101
$919$	−14.8342	−0.489336	−0.244668	−	0.969607i	$-0.578679\pi$
$919$	−14.8342	−0.489336	−0.244668	+	0.969607i	$0.578679\pi$
$920$	−26.2931	−0.866858
$921$	26.3742	0.869061
$922$	−20.7861	−0.684554
$923$	−26.0310	−0.856820
$924$	−146.268	−4.81185
$925$	−33.2286	−1.09255
$926$	−9.97982	−0.327957
$927$	−38.3730	−1.26033
$928$	53.4727	1.75533
$929$	−43.8162	−1.43756	−0.718781	−	0.695236i	$-0.755300\pi$
$929$	−43.8162	−1.43756	−0.718781	+	0.695236i	$0.755300\pi$
$930$	210.743	6.91054
$931$	−28.8983	−0.947103
$932$	47.3299	1.55034
$933$	61.0297	1.99802
$934$	17.4903	0.572301
$935$	68.2453	2.23186
$936$	−40.3044	−1.31739
$937$	32.7271	1.06915	0.534575	−	0.845121i	$-0.320472\pi$
$937$	32.7271	1.06915	0.534575	+	0.845121i	$0.320472\pi$
$938$	94.5292	3.08649
$939$	45.0516	1.47020
$940$	−104.586	−3.41121
$941$	19.4652	0.634548	0.317274	−	0.948334i	$-0.397233\pi$
$941$	19.4652	0.634548	0.317274	+	0.948334i	$0.397233\pi$
$942$	2.31962	0.0755775
$943$	−17.8340	−0.580754
$944$	−0.263686	−0.00858225
$945$	70.1101	2.28068
$946$	−54.7891	−1.78135
$947$	35.0484	1.13892	0.569460	−	0.822019i	$-0.307152\pi$
$947$	35.0484	1.13892	0.569460	+	0.822019i	$0.307152\pi$
$948$	−1.05875	−0.0343865
$949$	−23.9633	−0.777881
$950$	21.1390	0.685841
$951$	−53.4311	−1.73262
$952$	−74.6025	−2.41788
$953$	−12.2018	−0.395255	−0.197627	−	0.980277i	$-0.563324\pi$
$953$	−12.2018	−0.395255	−0.197627	+	0.980277i	$0.563324\pi$
$954$	−153.194	−4.95985
$955$	1.62517	0.0525894
$956$	78.2014	2.52922
$957$	97.0304	3.13655
$958$	2.60212	0.0840707
$959$	−7.54305	−0.243578
$960$	108.475	3.50101
$961$	90.8502	2.93065
$962$	58.6305	1.89032
$963$	38.8493	1.25190
$964$	−13.3592	−0.430272
$965$	−26.4273	−0.850725
$966$	−89.2854	−2.87271
$967$	2.02994	0.0652785	0.0326393	−	0.999467i	$-0.489609\pi$
$967$	2.02994	0.0652785	0.0326393	+	0.999467i	$0.489609\pi$
$968$	−7.78644	−0.250266
$969$	−42.2449	−1.35710
$970$	−59.4462	−1.90870
$971$	−35.4722	−1.13836	−0.569178	−	0.822214i	$-0.692738\pi$
$971$	−35.4722	−1.13836	−0.569178	+	0.822214i	$0.692738\pi$
$972$	47.8074	1.53342
$973$	27.9309	0.895422
$974$	−0.977015	−0.0313056
$975$	−31.6892	−1.01487
$976$	−0.963303	−0.0308346
$977$	−29.0640	−0.929841	−0.464920	−	0.885352i	$-0.653917\pi$
$977$	−29.0640	−0.929841	−0.464920	+	0.885352i	$0.653917\pi$
$978$	−112.676	−3.60297
$979$	17.3623	0.554903
$980$	113.713	3.63242
$981$	88.4318	2.82341
$982$	−15.3930	−0.491209
$983$	−15.6517	−0.499211	−0.249606	−	0.968348i	$-0.580301\pi$
$983$	−15.6517	−0.499211	−0.249606	+	0.968348i	$0.580301\pi$
$984$	−43.6150	−1.39040
$985$	65.5568	2.08881
$986$	130.988	4.17151
$987$	−134.181	−4.27103
$988$	−22.9931	−0.731506
$989$	−20.6170	−0.655584
$990$	124.166	3.94625
$991$	−33.7780	−1.07299	−0.536496	−	0.843903i	$-0.680253\pi$
$991$	−33.7780	−1.07299	−0.536496	+	0.843903i	$0.680253\pi$
$992$	63.6480	2.02083
$993$	−45.7919	−1.45316
$994$	−87.6640	−2.78053
$995$	39.8716	1.26402
$996$	−1.07856	−0.0341755
$997$	−53.5690	−1.69655	−0.848274	−	0.529558i	$-0.822358\pi$
$997$	−53.5690	−1.69655	−0.848274	+	0.529558i	$0.822358\pi$
$998$	−28.3257	−0.896635
$999$	47.2713	1.49560

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.b.1.20	✓	157

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.b.1.20	✓	157	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28352 q^{2} -2.81571 q^{3} +3.21448 q^{4} +2.96925 q^{5} +6.42974 q^{6} -4.34900 q^{7} -2.77330 q^{8} +4.92822 q^{9} +O(q^{10})\)	\(q-2.28352 q^{2} -2.81571 q^{3} +3.21448 q^{4} +2.96925 q^{5} +6.42974 q^{6} -4.34900 q^{7} -2.77330 q^{8} +4.92822 q^{9} -6.78035 q^{10} -3.71586 q^{11} -9.05105 q^{12} +2.94893 q^{13} +9.93105 q^{14} -8.36054 q^{15} -0.0960599 q^{16} -6.18538 q^{17} -11.2537 q^{18} -2.42561 q^{19} +9.54461 q^{20} +12.2455 q^{21} +8.48526 q^{22} +3.19299 q^{23} +7.80882 q^{24} +3.81645 q^{25} -6.73396 q^{26} -5.42930 q^{27} -13.9798 q^{28} +9.27386 q^{29} +19.0915 q^{30} +11.0386 q^{31} +5.76596 q^{32} +10.4628 q^{33} +14.1245 q^{34} -12.9133 q^{35} +15.8417 q^{36} -8.70670 q^{37} +5.53894 q^{38} -8.30333 q^{39} -8.23463 q^{40} -5.58536 q^{41} -27.9630 q^{42} -6.45697 q^{43} -11.9446 q^{44} +14.6331 q^{45} -7.29127 q^{46} -10.9576 q^{47} +0.270477 q^{48} +11.9138 q^{49} -8.71495 q^{50} +17.4162 q^{51} +9.47929 q^{52} +13.6128 q^{53} +12.3979 q^{54} -11.0333 q^{55} +12.0611 q^{56} +6.82981 q^{57} -21.1771 q^{58} +2.74502 q^{59} -26.8748 q^{60} +10.0282 q^{61} -25.2069 q^{62} -21.4328 q^{63} -12.9746 q^{64} +8.75611 q^{65} -23.8920 q^{66} +9.51855 q^{67} -19.8828 q^{68} -8.99053 q^{69} +29.4878 q^{70} -8.82726 q^{71} -13.6674 q^{72} -8.12609 q^{73} +19.8820 q^{74} -10.7460 q^{75} -7.79708 q^{76} +16.1603 q^{77} +18.9609 q^{78} +0.116975 q^{79} -0.285226 q^{80} +0.502677 q^{81} +12.7543 q^{82} +0.119164 q^{83} +39.3631 q^{84} -18.3659 q^{85} +14.7447 q^{86} -26.1125 q^{87} +10.3052 q^{88} -4.67249 q^{89} -33.4151 q^{90} -12.8249 q^{91} +10.2638 q^{92} -31.0814 q^{93} +25.0219 q^{94} -7.20224 q^{95} -16.2353 q^{96} +8.76742 q^{97} -27.2055 q^{98} -18.3126 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9 - 61 * q^10 - 27 * q^11 - 93 * q^12 - 97 * q^13 - 12 * q^14 - 36 * q^15 + 105 * q^16 - 45 * q^17 - 68 * q^18 - 128 * q^19 - 30 * q^20 - 26 * q^21 - 68 * q^22 - 41 * q^23 - 40 * q^24 + 102 * q^25 - 5 * q^26 - 189 * q^27 - 115 * q^28 - 26 * q^29 - 12 * q^30 - 88 * q^31 - 89 * q^32 - 52 * q^33 - 61 * q^34 - 87 * q^35 + 110 * q^36 - 62 * q^37 - 37 * q^38 - 20 * q^39 - 161 * q^40 - 34 * q^41 - 53 * q^42 - 254 * q^43 - 19 * q^44 - 46 * q^45 - 52 * q^46 - 76 * q^47 - 162 * q^48 + 96 * q^49 - 54 * q^50 - 76 * q^51 - 259 * q^52 - 48 * q^53 - 12 * q^54 - 194 * q^55 - 10 * q^56 - 30 * q^57 - 52 * q^58 - 64 * q^59 - 31 * q^60 - 107 * q^61 - 51 * q^62 - 106 * q^63 + 54 * q^64 - 17 * q^65 - 13 * q^66 - 193 * q^67 - 118 * q^68 - 55 * q^69 - 86 * q^70 - 11 * q^71 - 172 * q^72 - 173 * q^73 - 11 * q^74 - 209 * q^75 - 213 * q^76 - 84 * q^77 - 30 * q^78 - 111 * q^79 - 6 * q^80 + 157 * q^81 - 117 * q^82 - 154 * q^83 - 6 * q^84 - 91 * q^85 + 28 * q^86 - 165 * q^87 - 165 * q^88 - 32 * q^89 - 103 * q^90 - 200 * q^91 - 86 * q^92 - 39 * q^93 - 118 * q^94 - 22 * q^95 - 28 * q^96 - 151 * q^97 - 38 * q^98 - 91 * q^99

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