LMFDB - Embedded newform 4013.2.a.b.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.78653 q^{2} -0.812844 q^{3} +5.76476 q^{4} -1.14246 q^{5} +2.26502 q^{6} -4.07959 q^{7} -10.4906 q^{8} -2.33929 q^{9} +O(q^{10})$	\(q-2.78653 q^{2} -0.812844 q^{3} +5.76476 q^{4} -1.14246 q^{5} +2.26502 q^{6} -4.07959 q^{7} -10.4906 q^{8} -2.33929 q^{9} +3.18350 q^{10} +3.12497 q^{11} -4.68585 q^{12} +1.93748 q^{13} +11.3679 q^{14} +0.928640 q^{15} +17.7030 q^{16} -1.52727 q^{17} +6.51849 q^{18} -0.467077 q^{19} -6.58600 q^{20} +3.31607 q^{21} -8.70783 q^{22} +1.47154 q^{23} +8.52725 q^{24} -3.69479 q^{25} -5.39884 q^{26} +4.34000 q^{27} -23.5179 q^{28} -2.12733 q^{29} -2.58768 q^{30} -1.18770 q^{31} -28.3486 q^{32} -2.54011 q^{33} +4.25580 q^{34} +4.66076 q^{35} -13.4854 q^{36} -9.12735 q^{37} +1.30153 q^{38} -1.57487 q^{39} +11.9851 q^{40} +7.75959 q^{41} -9.24033 q^{42} -2.78347 q^{43} +18.0147 q^{44} +2.67254 q^{45} -4.10050 q^{46} +11.8237 q^{47} -14.3897 q^{48} +9.64305 q^{49} +10.2957 q^{50} +1.24144 q^{51} +11.1691 q^{52} +10.6057 q^{53} -12.0936 q^{54} -3.57015 q^{55} +42.7975 q^{56} +0.379661 q^{57} +5.92787 q^{58} +5.93137 q^{59} +5.35339 q^{60} -6.65091 q^{61} +3.30957 q^{62} +9.54333 q^{63} +43.5885 q^{64} -2.21349 q^{65} +7.07810 q^{66} +6.19050 q^{67} -8.80438 q^{68} -1.19613 q^{69} -12.9874 q^{70} -9.38026 q^{71} +24.5406 q^{72} -6.03468 q^{73} +25.4337 q^{74} +3.00329 q^{75} -2.69259 q^{76} -12.7486 q^{77} +4.38841 q^{78} +3.52159 q^{79} -20.2249 q^{80} +3.49011 q^{81} -21.6224 q^{82} -4.98477 q^{83} +19.1164 q^{84} +1.74485 q^{85} +7.75624 q^{86} +1.72918 q^{87} -32.7829 q^{88} +9.44368 q^{89} -7.44711 q^{90} -7.90411 q^{91} +8.48309 q^{92} +0.965416 q^{93} -32.9472 q^{94} +0.533616 q^{95} +23.0430 q^{96} +8.56412 q^{97} -26.8707 q^{98} -7.31019 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.78653	−1.97038	−0.985188	−	0.171477i	$-0.945146\pi$
$2$	−2.78653	−1.97038	−0.985188	+	0.171477i	$0.945146\pi$
$3$	−0.812844	−0.469295	−0.234648	−	0.972080i	$-0.575394\pi$
$3$	−0.812844	−0.469295	−0.234648	+	0.972080i	$0.575394\pi$
$4$	5.76476	2.88238
$5$	−1.14246	−0.510923	−0.255461	−	0.966819i	$-0.582227\pi$
$5$	−1.14246	−0.510923	−0.255461	+	0.966819i	$0.582227\pi$
$6$	2.26502	0.924689
$7$	−4.07959	−1.54194	−0.770970	−	0.636871i	$-0.780228\pi$
$7$	−4.07959	−1.54194	−0.770970	+	0.636871i	$0.780228\pi$
$8$	−10.4906	−3.70900
$9$	−2.33929	−0.779762
$10$	3.18350	1.00671
$11$	3.12497	0.942214	0.471107	−	0.882076i	$-0.343855\pi$
$11$	3.12497	0.942214	0.471107	+	0.882076i	$0.343855\pi$
$12$	−4.68585	−1.35269
$13$	1.93748	0.537359	0.268680	−	0.963230i	$-0.413413\pi$
$13$	1.93748	0.537359	0.268680	+	0.963230i	$0.413413\pi$
$14$	11.3679	3.03820
$15$	0.928640	0.239774
$16$	17.7030	4.42574
$17$	−1.52727	−0.370418	−0.185209	−	0.982699i	$-0.559296\pi$
$17$	−1.52727	−0.370418	−0.185209	+	0.982699i	$0.559296\pi$
$18$	6.51849	1.53642
$19$	−0.467077	−0.107155	−0.0535775	−	0.998564i	$-0.517062\pi$
$19$	−0.467077	−0.107155	−0.0535775	+	0.998564i	$0.517062\pi$
$20$	−6.58600	−1.47267
$21$	3.31607	0.723625
$22$	−8.70783	−1.85652
$23$	1.47154	0.306838	0.153419	−	0.988161i	$-0.450972\pi$
$23$	1.47154	0.306838	0.153419	+	0.988161i	$0.450972\pi$
$24$	8.52725	1.74062
$25$	−3.69479	−0.738958
$26$	−5.39884	−1.05880
$27$	4.34000	0.835234
$28$	−23.5179	−4.44446
$29$	−2.12733	−0.395035	−0.197517	−	0.980299i	$-0.563288\pi$
$29$	−2.12733	−0.395035	−0.197517	+	0.980299i	$0.563288\pi$
$30$	−2.58768	−0.472444
$31$	−1.18770	−0.213318	−0.106659	−	0.994296i	$-0.534015\pi$
$31$	−1.18770	−0.213318	−0.106659	+	0.994296i	$0.534015\pi$
$32$	−28.3486	−5.01138
$33$	−2.54011	−0.442177
$34$	4.25580	0.729864
$35$	4.66076	0.787812
$36$	−13.4854	−2.24757
$37$	−9.12735	−1.50053	−0.750264	−	0.661139i	$-0.770073\pi$
$37$	−9.12735	−1.50053	−0.750264	+	0.661139i	$0.770073\pi$
$38$	1.30153	0.211135
$39$	−1.57487	−0.252180
$40$	11.9851	1.89501
$41$	7.75959	1.21184	0.605922	−	0.795524i	$-0.292804\pi$
$41$	7.75959	1.21184	0.605922	+	0.795524i	$0.292804\pi$
$42$	−9.24033	−1.42581
$43$	−2.78347	−0.424476	−0.212238	−	0.977218i	$-0.568075\pi$
$43$	−2.78347	−0.424476	−0.212238	+	0.977218i	$0.568075\pi$
$44$	18.0147	2.71582
$45$	2.67254	0.398398
$46$	−4.10050	−0.604586
$47$	11.8237	1.72467	0.862335	−	0.506338i	$-0.169001\pi$
$47$	11.8237	1.72467	0.862335	+	0.506338i	$0.169001\pi$
$48$	−14.3897	−2.07698
$49$	9.64305	1.37758
$50$	10.2957	1.45603
$51$	1.24144	0.173836
$52$	11.1691	1.54887
$53$	10.6057	1.45681	0.728406	−	0.685146i	$-0.240262\pi$
$53$	10.6057	1.45681	0.728406	+	0.685146i	$0.240262\pi$
$54$	−12.0936	−1.64573
$55$	−3.57015	−0.481398
$56$	42.7975	5.71906
$57$	0.379661	0.0502873
$58$	5.92787	0.778367
$59$	5.93137	0.772198	0.386099	−	0.922457i	$-0.373822\pi$
$59$	5.93137	0.772198	0.386099	+	0.922457i	$0.373822\pi$
$60$	5.35339	0.691119
$61$	−6.65091	−0.851561	−0.425781	−	0.904826i	$-0.640000\pi$
$61$	−6.65091	−0.851561	−0.425781	+	0.904826i	$0.640000\pi$
$62$	3.30957	0.420316
$63$	9.54333	1.20235
$64$	43.5885	5.44856
$65$	−2.21349	−0.274549
$66$	7.07810	0.871254
$67$	6.19050	0.756289	0.378145	−	0.925746i	$-0.376562\pi$
$67$	6.19050	0.756289	0.378145	+	0.925746i	$0.376562\pi$
$68$	−8.80438	−1.06769
$69$	−1.19613	−0.143998
$70$	−12.9874	−1.55229
$71$	−9.38026	−1.11323	−0.556616	−	0.830770i	$-0.687901\pi$
$71$	−9.38026	−1.11323	−0.556616	+	0.830770i	$0.687901\pi$
$72$	24.5406	2.89214
$73$	−6.03468	−0.706306	−0.353153	−	0.935566i	$-0.614891\pi$
$73$	−6.03468	−0.706306	−0.353153	+	0.935566i	$0.614891\pi$
$74$	25.4337	2.95660
$75$	3.00329	0.346790
$76$	−2.69259	−0.308861
$77$	−12.7486	−1.45284
$78$	4.38841	0.496890
$79$	3.52159	0.396210	0.198105	−	0.980181i	$-0.436521\pi$
$79$	3.52159	0.396210	0.198105	+	0.980181i	$0.436521\pi$
$80$	−20.2249	−2.26121
$81$	3.49011	0.387790
$82$	−21.6224	−2.38779
$83$	−4.98477	−0.547150	−0.273575	−	0.961851i	$-0.588206\pi$
$83$	−4.98477	−0.547150	−0.273575	+	0.961851i	$0.588206\pi$
$84$	19.1164	2.08576
$85$	1.74485	0.189255
$86$	7.75624	0.836377
$87$	1.72918	0.185388
$88$	−32.7829	−3.49467
$89$	9.44368	1.00103	0.500514	−	0.865728i	$-0.333144\pi$
$89$	9.44368	1.00103	0.500514	+	0.865728i	$0.333144\pi$
$90$	−7.44711	−0.784994
$91$	−7.90411	−0.828576
$92$	8.48309	0.884424
$93$	0.965416	0.100109
$94$	−32.9472	−3.39825
$95$	0.533616	0.0547479
$96$	23.0430	2.35182
$97$	8.56412	0.869555	0.434777	−	0.900538i	$-0.356827\pi$
$97$	8.56412	0.869555	0.434777	+	0.900538i	$0.356827\pi$
$98$	−26.8707	−2.71435
$99$	−7.31019	−0.734702
$100$	−21.2996	−2.12996
$101$	1.59782	0.158990	0.0794948	−	0.996835i	$-0.474669\pi$
$101$	1.59782	0.158990	0.0794948	+	0.996835i	$0.474669\pi$
$102$	−3.45930	−0.342522
$103$	−1.71167	−0.168656	−0.0843278	−	0.996438i	$-0.526874\pi$
$103$	−1.71167	−0.168656	−0.0843278	+	0.996438i	$0.526874\pi$
$104$	−20.3254	−1.99307
$105$	−3.78847	−0.369717
$106$	−29.5533	−2.87047
$107$	−7.83071	−0.757024	−0.378512	−	0.925596i	$-0.623564\pi$
$107$	−7.83071	−0.757024	−0.378512	+	0.925596i	$0.623564\pi$
$108$	25.0191	2.40746
$109$	19.9696	1.91274	0.956372	−	0.292153i	$-0.0943717\pi$
$109$	19.9696	1.91274	0.956372	+	0.292153i	$0.0943717\pi$
$110$	9.94833	0.948536
$111$	7.41911	0.704191
$112$	−72.2209	−6.82423
$113$	−4.16182	−0.391511	−0.195756	−	0.980653i	$-0.562716\pi$
$113$	−4.16182	−0.391511	−0.195756	+	0.980653i	$0.562716\pi$
$114$	−1.05794	−0.0990849
$115$	−1.68118	−0.156770
$116$	−12.2635	−1.13864
$117$	−4.53231	−0.419012
$118$	−16.5279	−1.52152
$119$	6.23065	0.571163
$120$	−9.74202	−0.889321
$121$	−1.23457	−0.112233
$122$	18.5330	1.67790
$123$	−6.30733	−0.568713
$124$	−6.84682	−0.614863
$125$	9.93343	0.888473
$126$	−26.5928	−2.36907
$127$	−2.97960	−0.264397	−0.132198	−	0.991223i	$-0.542204\pi$
$127$	−2.97960	−0.264397	−0.132198	+	0.991223i	$0.542204\pi$
$128$	−64.7634	−5.72433
$129$	2.26253	0.199205
$130$	6.16795	0.540965
$131$	14.3896	1.25722	0.628612	−	0.777719i	$-0.283624\pi$
$131$	14.3896	1.25722	0.628612	+	0.777719i	$0.283624\pi$
$132$	−14.6431	−1.27452
$133$	1.90548	0.165226
$134$	−17.2500	−1.49017
$135$	−4.95827	−0.426740
$136$	16.0221	1.37388
$137$	−2.03244	−0.173643	−0.0868217	−	0.996224i	$-0.527671\pi$
$137$	−2.03244	−0.173643	−0.0868217	+	0.996224i	$0.527671\pi$
$138$	3.33306	0.283729
$139$	7.73307	0.655910	0.327955	−	0.944693i	$-0.393640\pi$
$139$	7.73307	0.655910	0.327955	+	0.944693i	$0.393640\pi$
$140$	26.8682	2.27078
$141$	−9.61085	−0.809380
$142$	26.1384	2.19349
$143$	6.05455	0.506307
$144$	−41.4123	−3.45103
$145$	2.43038	0.201832
$146$	16.8158	1.39169
$147$	−7.83829	−0.646492
$148$	−52.6170	−4.32509
$149$	9.47361	0.776109	0.388054	−	0.921636i	$-0.373147\pi$
$149$	9.47361	0.776109	0.388054	+	0.921636i	$0.373147\pi$
$150$	−8.36875	−0.683306
$151$	2.87188	0.233710	0.116855	−	0.993149i	$-0.462719\pi$
$151$	2.87188	0.233710	0.116855	+	0.993149i	$0.462719\pi$
$152$	4.89994	0.397438
$153$	3.57273	0.288838
$154$	35.5244	2.86264
$155$	1.35690	0.108989
$156$	−9.07873	−0.726880
$157$	−5.92978	−0.473248	−0.236624	−	0.971601i	$-0.576041\pi$
$157$	−5.92978	−0.473248	−0.236624	+	0.971601i	$0.576041\pi$
$158$	−9.81303	−0.780683
$159$	−8.62081	−0.683675
$160$	32.3871	2.56043
$161$	−6.00329	−0.473125
$162$	−9.72531	−0.764093
$163$	−2.13584	−0.167292	−0.0836459	−	0.996496i	$-0.526656\pi$
$163$	−2.13584	−0.167292	−0.0836459	+	0.996496i	$0.526656\pi$
$164$	44.7322	3.49300
$165$	2.90197	0.225918
$166$	13.8902	1.07809
$167$	25.1822	1.94866	0.974330	−	0.225124i	$-0.0722787\pi$
$167$	25.1822	1.94866	0.974330	+	0.225124i	$0.0722787\pi$
$168$	−34.7877	−2.68393
$169$	−9.24619	−0.711245
$170$	−4.86207	−0.372904
$171$	1.09263	0.0835553
$172$	−16.0461	−1.22350
$173$	−13.1574	−1.00034	−0.500168	−	0.865928i	$-0.666728\pi$
$173$	−13.1574	−1.00034	−0.500168	+	0.865928i	$0.666728\pi$
$174$	−4.81843	−0.365284
$175$	15.0732	1.13943
$176$	55.3213	4.17000
$177$	−4.82127	−0.362389
$178$	−26.3151	−1.97240
$179$	6.16120	0.460510	0.230255	−	0.973130i	$-0.426044\pi$
$179$	6.16120	0.460510	0.230255	+	0.973130i	$0.426044\pi$
$180$	15.4065	1.14834
$181$	−4.18140	−0.310801	−0.155400	−	0.987852i	$-0.549667\pi$
$181$	−4.18140	−0.310801	−0.155400	+	0.987852i	$0.549667\pi$
$182$	22.0251	1.63261
$183$	5.40615	0.399634
$184$	−15.4374	−1.13806
$185$	10.4276	0.766654
$186$	−2.69016	−0.197252
$187$	−4.77269	−0.349013
$188$	68.1611	4.97116
$189$	−17.7054	−1.28788
$190$	−1.48694	−0.107874
$191$	15.4713	1.11946	0.559731	−	0.828674i	$-0.310904\pi$
$191$	15.4713	1.11946	0.559731	+	0.828674i	$0.310904\pi$
$192$	−35.4306	−2.55698
$193$	−12.0634	−0.868340	−0.434170	−	0.900831i	$-0.642958\pi$
$193$	−12.0634	−0.868340	−0.434170	+	0.900831i	$0.642958\pi$
$194$	−23.8642	−1.71335
$195$	1.79922	0.128845
$196$	55.5899	3.97071
$197$	−21.8884	−1.55948	−0.779742	−	0.626101i	$-0.784650\pi$
$197$	−21.8884	−1.55948	−0.779742	+	0.626101i	$0.784650\pi$
$198$	20.3701	1.44764
$199$	−7.27558	−0.515752	−0.257876	−	0.966178i	$-0.583023\pi$
$199$	−7.27558	−0.515752	−0.257876	+	0.966178i	$0.583023\pi$
$200$	38.7607	2.74080
$201$	−5.03190	−0.354923
$202$	−4.45239	−0.313269
$203$	8.67863	0.609120
$204$	7.15658	0.501061
$205$	−8.86501	−0.619159
$206$	4.76962	0.332315
$207$	−3.44236	−0.239260
$208$	34.2991	2.37821
$209$	−1.45960	−0.100963
$210$	10.5567	0.728481
$211$	−20.2610	−1.39483	−0.697413	−	0.716669i	$-0.745666\pi$
$211$	−20.2610	−1.39483	−0.697413	+	0.716669i	$0.745666\pi$
$212$	61.1396	4.19909
$213$	7.62469	0.522435
$214$	21.8205	1.49162
$215$	3.18000	0.216874
$216$	−45.5294	−3.09788
$217$	4.84534	0.328923
$218$	−55.6460	−3.76882
$219$	4.90525	0.331466
$220$	−20.5810	−1.38757
$221$	−2.95906	−0.199048
$222$	−20.6736	−1.38752
$223$	−4.53398	−0.303617	−0.151809	−	0.988410i	$-0.548510\pi$
$223$	−4.53398	−0.303617	−0.151809	+	0.988410i	$0.548510\pi$
$224$	115.651	7.72725
$225$	8.64317	0.576211
$226$	11.5970	0.771424
$227$	1.20505	0.0799823	0.0399911	−	0.999200i	$-0.487267\pi$
$227$	1.20505	0.0799823	0.0399911	+	0.999200i	$0.487267\pi$
$228$	2.18866	0.144947
$229$	6.87648	0.454411	0.227205	−	0.973847i	$-0.427041\pi$
$229$	6.87648	0.454411	0.227205	+	0.973847i	$0.427041\pi$
$230$	4.68465	0.308897
$231$	10.3626	0.681810
$232$	22.3170	1.46518
$233$	−20.0295	−1.31218	−0.656089	−	0.754683i	$-0.727791\pi$
$233$	−20.0295	−1.31218	−0.656089	+	0.754683i	$0.727791\pi$
$234$	12.6294	0.825612
$235$	−13.5081	−0.881173
$236$	34.1929	2.22577
$237$	−2.86250	−0.185940
$238$	−17.3619	−1.12541
$239$	−14.8520	−0.960697	−0.480349	−	0.877078i	$-0.659490\pi$
$239$	−14.8520	−0.960697	−0.480349	+	0.877078i	$0.659490\pi$
$240$	16.4397	1.06118
$241$	20.2211	1.30256	0.651279	−	0.758838i	$-0.274233\pi$
$241$	20.2211	1.30256	0.651279	+	0.758838i	$0.274233\pi$
$242$	3.44017	0.221142
$243$	−15.8569	−1.01722
$244$	−38.3409	−2.45453
$245$	−11.0168	−0.703837
$246$	17.5756	1.12058
$247$	−0.904951	−0.0575807
$248$	12.4598	0.791195
$249$	4.05184	0.256775
$250$	−27.6798	−1.75063
$251$	10.0977	0.637358	0.318679	−	0.947863i	$-0.396761\pi$
$251$	10.0977	0.637358	0.318679	+	0.947863i	$0.396761\pi$
$252$	55.0150	3.46562
$253$	4.59852	0.289107
$254$	8.30275	0.520961
$255$	−1.41829	−0.0888166
$256$	93.2884	5.83053
$257$	−18.0065	−1.12322	−0.561608	−	0.827403i	$-0.689817\pi$
$257$	−18.0065	−1.12322	−0.561608	+	0.827403i	$0.689817\pi$
$258$	−6.30461	−0.392508
$259$	37.2358	2.31372
$260$	−12.7602	−0.791355
$261$	4.97643	0.308033
$262$	−40.0970	−2.47720
$263$	−20.4701	−1.26224	−0.631119	−	0.775686i	$-0.717404\pi$
$263$	−20.4701	−1.26224	−0.631119	+	0.775686i	$0.717404\pi$
$264$	26.6474	1.64003
$265$	−12.1166	−0.744318
$266$	−5.30969	−0.325558
$267$	−7.67623	−0.469778
$268$	35.6867	2.17992
$269$	20.6235	1.25744	0.628718	−	0.777634i	$-0.283580\pi$
$269$	20.6235	1.25744	0.628718	+	0.777634i	$0.283580\pi$
$270$	13.8164	0.840839
$271$	−12.2128	−0.741875	−0.370938	−	0.928658i	$-0.620964\pi$
$271$	−12.2128	−0.741875	−0.370938	+	0.928658i	$0.620964\pi$
$272$	−27.0373	−1.63938
$273$	6.42480	0.388847
$274$	5.66347	0.342143
$275$	−11.5461	−0.696256
$276$	−6.89543	−0.415056
$277$	21.6089	1.29835	0.649175	−	0.760639i	$-0.275114\pi$
$277$	21.6089	1.29835	0.649175	+	0.760639i	$0.275114\pi$
$278$	−21.5485	−1.29239
$279$	2.77838	0.166337
$280$	−48.8943	−2.92200
$281$	5.62891	0.335792	0.167896	−	0.985805i	$-0.446303\pi$
$281$	5.62891	0.335792	0.167896	+	0.985805i	$0.446303\pi$
$282$	26.7810	1.59478
$283$	−24.8623	−1.47791	−0.738954	−	0.673756i	$-0.764680\pi$
$283$	−24.8623	−1.47791	−0.738954	+	0.673756i	$0.764680\pi$
$284$	−54.0750	−3.20876
$285$	−0.433747	−0.0256929
$286$	−16.8712	−0.997616
$287$	−31.6560	−1.86859
$288$	66.3156	3.90768
$289$	−14.6674	−0.862790
$290$	−6.77234	−0.397686
$291$	−6.96129	−0.408078
$292$	−34.7885	−2.03584
$293$	−0.936675	−0.0547211	−0.0273606	−	0.999626i	$-0.508710\pi$
$293$	−0.936675	−0.0547211	−0.0273606	+	0.999626i	$0.508710\pi$
$294$	21.8417	1.27383
$295$	−6.77634	−0.394534
$296$	95.7517	5.56546
$297$	13.5624	0.786969
$298$	−26.3985	−1.52923
$299$	2.85108	0.164882
$300$	17.3132	0.999580
$301$	11.3554	0.654516
$302$	−8.00259	−0.460497
$303$	−1.29878	−0.0746131
$304$	−8.26866	−0.474240
$305$	7.59838	0.435082
$306$	−9.95553	−0.569120
$307$	−25.6113	−1.46171	−0.730857	−	0.682530i	$-0.760879\pi$
$307$	−25.6113	−1.46171	−0.730857	+	0.682530i	$0.760879\pi$
$308$	−73.4926	−4.18763
$309$	1.39132	0.0791493
$310$	−3.78105	−0.214749
$311$	−20.4479	−1.15949	−0.579746	−	0.814797i	$-0.696848\pi$
$311$	−20.4479	−1.15949	−0.579746	+	0.814797i	$0.696848\pi$
$312$	16.5213	0.935337
$313$	31.1241	1.75924	0.879619	−	0.475679i	$-0.157798\pi$
$313$	31.1241	1.75924	0.879619	+	0.475679i	$0.157798\pi$
$314$	16.5235	0.932477
$315$	−10.9028	−0.614306
$316$	20.3011	1.14203
$317$	29.3625	1.64916	0.824581	−	0.565744i	$-0.191411\pi$
$317$	29.3625	1.64916	0.824581	+	0.565744i	$0.191411\pi$
$318$	24.0222	1.34710
$319$	−6.64783	−0.372207
$320$	−49.7980	−2.78379
$321$	6.36515	0.355268
$322$	16.7284	0.932235
$323$	0.713355	0.0396922
$324$	20.1197	1.11776
$325$	−7.15857	−0.397086
$326$	5.95158	0.329628
$327$	−16.2322	−0.897642
$328$	−81.4031	−4.49473
$329$	−48.2360	−2.65934
$330$	−8.08643	−0.445144
$331$	−8.19430	−0.450399	−0.225200	−	0.974313i	$-0.572303\pi$
$331$	−8.19430	−0.450399	−0.225200	+	0.974313i	$0.572303\pi$
$332$	−28.7360	−1.57709
$333$	21.3515	1.17005
$334$	−70.1711	−3.83959
$335$	−7.07238	−0.386405
$336$	58.7043	3.20258
$337$	−2.62336	−0.142903	−0.0714517	−	0.997444i	$-0.522763\pi$
$337$	−2.62336	−0.142903	−0.0714517	+	0.997444i	$0.522763\pi$
$338$	25.7648	1.40142
$339$	3.38291	0.183734
$340$	10.0586	0.545506
$341$	−3.71153	−0.200991
$342$	−3.04464	−0.164635
$343$	−10.7826	−0.582204
$344$	29.2004	1.57438
$345$	1.36653	0.0735716
$346$	36.6634	1.97104
$347$	34.2269	1.83739	0.918697	−	0.394962i	$-0.129242\pi$
$347$	34.2269	1.83739	0.918697	+	0.394962i	$0.129242\pi$
$348$	9.96834	0.534359
$349$	19.8926	1.06482	0.532412	−	0.846485i	$-0.321286\pi$
$349$	19.8926	1.06482	0.532412	+	0.846485i	$0.321286\pi$
$350$	−42.0020	−2.24510
$351$	8.40865	0.448821
$352$	−88.5886	−4.72179
$353$	−31.6336	−1.68369	−0.841843	−	0.539722i	$-0.818529\pi$
$353$	−31.6336	−1.68369	−0.841843	+	0.539722i	$0.818529\pi$
$354$	13.4346	0.714043
$355$	10.7166	0.568776
$356$	54.4406	2.88535
$357$	−5.06455	−0.268044
$358$	−17.1684	−0.907378
$359$	3.31701	0.175065	0.0875326	−	0.996162i	$-0.472102\pi$
$359$	3.31701	0.175065	0.0875326	+	0.996162i	$0.472102\pi$
$360$	−28.0366	−1.47766
$361$	−18.7818	−0.988518
$362$	11.6516	0.612395
$363$	1.00351	0.0526707
$364$	−45.5653	−2.38827
$365$	6.89437	0.360868
$366$	−15.0644	−0.787429
$367$	8.45581	0.441390	0.220695	−	0.975343i	$-0.429168\pi$
$367$	8.45581	0.441390	0.220695	+	0.975343i	$0.429168\pi$
$368$	26.0507	1.35799
$369$	−18.1519	−0.944950
$370$	−29.0569	−1.51060
$371$	−43.2671	−2.24632
$372$	5.56540	0.288552
$373$	3.16701	0.163981	0.0819907	−	0.996633i	$-0.473872\pi$
$373$	3.16701	0.163981	0.0819907	+	0.996633i	$0.473872\pi$
$374$	13.2992	0.687688
$375$	−8.07433	−0.416956
$376$	−124.039	−6.39680
$377$	−4.12165	−0.212276
$378$	49.3368	2.53761
$379$	−6.18241	−0.317569	−0.158784	−	0.987313i	$-0.550757\pi$
$379$	−6.18241	−0.317569	−0.158784	+	0.987313i	$0.550757\pi$
$380$	3.07617	0.157804
$381$	2.42195	0.124080
$382$	−43.1112	−2.20576
$383$	4.83289	0.246949	0.123475	−	0.992348i	$-0.460596\pi$
$383$	4.83289	0.246949	0.123475	+	0.992348i	$0.460596\pi$
$384$	52.6425	2.68640
$385$	14.5647	0.742287
$386$	33.6149	1.71096
$387$	6.51134	0.330990
$388$	49.3701	2.50639
$389$	26.4693	1.34204	0.671022	−	0.741437i	$-0.265855\pi$
$389$	26.4693	1.34204	0.671022	+	0.741437i	$0.265855\pi$
$390$	−5.01358	−0.253872
$391$	−2.24745	−0.113658
$392$	−101.162	−5.10944
$393$	−11.6965	−0.590009
$394$	60.9927	3.07277
$395$	−4.02327	−0.202433
$396$	−42.1415	−2.11769
$397$	35.0934	1.76129	0.880644	−	0.473779i	$-0.157110\pi$
$397$	35.0934	1.76129	0.880644	+	0.473779i	$0.157110\pi$
$398$	20.2736	1.01623
$399$	−1.54886	−0.0775400
$400$	−65.4088	−3.27044
$401$	1.13880	0.0568688	0.0284344	−	0.999596i	$-0.490948\pi$
$401$	1.13880	0.0568688	0.0284344	+	0.999596i	$0.490948\pi$
$402$	14.0216	0.699332
$403$	−2.30115	−0.114628
$404$	9.21108	0.458269
$405$	−3.98731	−0.198131
$406$	−24.1833	−1.20020
$407$	−28.5227	−1.41382
$408$	−13.0234	−0.644757
$409$	7.28038	0.359991	0.179996	−	0.983667i	$-0.442392\pi$
$409$	7.28038	0.359991	0.179996	+	0.983667i	$0.442392\pi$
$410$	24.7026	1.21998
$411$	1.65206	0.0814900
$412$	−9.86736	−0.486130
$413$	−24.1975	−1.19068
$414$	9.59224	0.471433
$415$	5.69489	0.279551
$416$	−54.9248	−2.69291
$417$	−6.28578	−0.307816
$418$	4.06723	0.198935
$419$	−38.8670	−1.89878	−0.949389	−	0.314102i	$-0.898297\pi$
$419$	−38.8670	−1.89878	−0.949389	+	0.314102i	$0.898297\pi$
$420$	−21.8396	−1.06566
$421$	−25.0396	−1.22035	−0.610177	−	0.792265i	$-0.708902\pi$
$421$	−25.0396	−1.22035	−0.610177	+	0.792265i	$0.708902\pi$
$422$	56.4580	2.74833
$423$	−27.6591	−1.34483
$424$	−111.261	−5.40331
$425$	5.64296	0.273724
$426$	−21.2464	−1.02939
$427$	27.1330	1.31306
$428$	−45.1422	−2.18203
$429$	−4.92141	−0.237608
$430$	−8.86118	−0.427324
$431$	−19.9592	−0.961401	−0.480701	−	0.876885i	$-0.659618\pi$
$431$	−19.9592	−0.961401	−0.480701	+	0.876885i	$0.659618\pi$
$432$	76.8310	3.69653
$433$	−13.5220	−0.649828	−0.324914	−	0.945744i	$-0.605335\pi$
$433$	−13.5220	−0.649828	−0.324914	+	0.945744i	$0.605335\pi$
$434$	−13.5017	−0.648102
$435$	−1.97552	−0.0947190
$436$	115.120	5.51326
$437$	−0.687324	−0.0328792
$438$	−13.6686	−0.653113
$439$	−34.5574	−1.64933	−0.824667	−	0.565619i	$-0.808637\pi$
$439$	−34.5574	−1.64933	−0.824667	+	0.565619i	$0.808637\pi$
$440$	37.4531	1.78551
$441$	−22.5579	−1.07418
$442$	8.24551	0.392199
$443$	11.9023	0.565495	0.282747	−	0.959194i	$-0.408754\pi$
$443$	11.9023	0.565495	0.282747	+	0.959194i	$0.408754\pi$
$444$	42.7694	2.02975
$445$	−10.7890	−0.511448
$446$	12.6341	0.598241
$447$	−7.70057	−0.364224
$448$	−177.823	−8.40135
$449$	−0.890490	−0.0420248	−0.0210124	−	0.999779i	$-0.506689\pi$
$449$	−0.890490	−0.0420248	−0.0210124	+	0.999779i	$0.506689\pi$
$450$	−24.0845	−1.13535
$451$	24.2485	1.14182
$452$	−23.9919	−1.12848
$453$	−2.33439	−0.109679
$454$	−3.35792	−0.157595
$455$	9.03011	0.423338
$456$	−3.98288	−0.186516
$457$	−16.3361	−0.764170	−0.382085	−	0.924127i	$-0.624794\pi$
$457$	−16.3361	−0.764170	−0.382085	+	0.924127i	$0.624794\pi$
$458$	−19.1615	−0.895360
$459$	−6.62838	−0.309386
$460$	−9.69158	−0.451872
$461$	−6.13506	−0.285738	−0.142869	−	0.989742i	$-0.545633\pi$
$461$	−6.13506	−0.285738	−0.142869	+	0.989742i	$0.545633\pi$
$462$	−28.8758	−1.34342
$463$	−8.49318	−0.394712	−0.197356	−	0.980332i	$-0.563235\pi$
$463$	−8.49318	−0.394712	−0.197356	+	0.980332i	$0.563235\pi$
$464$	−37.6600	−1.74832
$465$	−1.10295	−0.0511480
$466$	55.8130	2.58549
$467$	−24.5766	−1.13727	−0.568635	−	0.822590i	$-0.692528\pi$
$467$	−24.5766	−1.13727	−0.568635	+	0.822590i	$0.692528\pi$
$468$	−26.1277	−1.20775
$469$	−25.2547	−1.16615
$470$	37.6408	1.73624
$471$	4.81999	0.222093
$472$	−62.2238	−2.86408
$473$	−8.69827	−0.399947
$474$	7.97646	0.366371
$475$	1.72575	0.0791830
$476$	35.9182	1.64631
$477$	−24.8099	−1.13597
$478$	41.3856	1.89293
$479$	5.70637	0.260731	0.130365	−	0.991466i	$-0.458385\pi$
$479$	5.70637	0.260731	0.130365	+	0.991466i	$0.458385\pi$
$480$	−26.3257	−1.20160
$481$	−17.6840	−0.806322
$482$	−56.3469	−2.56653
$483$	4.87973	0.222036
$484$	−7.11700	−0.323500
$485$	−9.78415	−0.444275
$486$	44.1858	2.00431
$487$	4.70117	0.213031	0.106515	−	0.994311i	$-0.466031\pi$
$487$	4.70117	0.213031	0.106515	+	0.994311i	$0.466031\pi$
$488$	69.7723	3.15844
$489$	1.73610	0.0785092
$490$	30.6986	1.38682
$491$	−42.3561	−1.91150	−0.955752	−	0.294174i	$-0.904956\pi$
$491$	−42.3561	−1.91150	−0.955752	+	0.294174i	$0.904956\pi$
$492$	−36.3603	−1.63925
$493$	3.24901	0.146328
$494$	2.52168	0.113456
$495$	8.35159	0.375376
$496$	−21.0259	−0.944089
$497$	38.2676	1.71654
$498$	−11.2906	−0.505943
$499$	−37.0125	−1.65691	−0.828453	−	0.560058i	$-0.810779\pi$
$499$	−37.0125	−1.65691	−0.828453	+	0.560058i	$0.810779\pi$
$500$	57.2639	2.56092
$501$	−20.4692	−0.914497
$502$	−28.1374	−1.25584
$503$	−36.8503	−1.64307	−0.821536	−	0.570156i	$-0.806883\pi$
$503$	−36.8503	−1.64307	−0.821536	+	0.570156i	$0.806883\pi$
$504$	−100.116	−4.45950
$505$	−1.82545	−0.0812314
$506$	−12.8139	−0.569649
$507$	7.51570	0.333784
$508$	−17.1767	−0.762092
$509$	−24.3300	−1.07841	−0.539204	−	0.842175i	$-0.681275\pi$
$509$	−24.3300	−1.07841	−0.539204	+	0.842175i	$0.681275\pi$
$510$	3.95210	0.175002
$511$	24.6190	1.08908
$512$	−130.424	−5.76400
$513$	−2.02712	−0.0894994
$514$	50.1758	2.21316
$515$	1.95551	0.0861700
$516$	13.0429	0.574184
$517$	36.9488	1.62501
$518$	−103.759	−4.55890
$519$	10.6949	0.469453
$520$	23.2209	1.01830
$521$	−11.2490	−0.492827	−0.246414	−	0.969165i	$-0.579252\pi$
$521$	−11.2490	−0.492827	−0.246414	+	0.969165i	$0.579252\pi$
$522$	−13.8670	−0.606941
$523$	8.34564	0.364929	0.182465	−	0.983212i	$-0.441592\pi$
$523$	8.34564	0.364929	0.182465	+	0.983212i	$0.441592\pi$
$524$	82.9525	3.62380
$525$	−12.2522	−0.534729
$526$	57.0405	2.48708
$527$	1.81395	0.0790168
$528$	−44.9675	−1.95696
$529$	−20.8346	−0.905851
$530$	33.7634	1.46659
$531$	−13.8752	−0.602131
$532$	10.9847	0.476246
$533$	15.0340	0.651196
$534$	21.3901	0.925639
$535$	8.94626	0.386781
$536$	−64.9422	−2.80508
$537$	−5.00809	−0.216115
$538$	−57.4680	−2.47762
$539$	30.1342	1.29797
$540$	−28.5833	−1.23003
$541$	3.86725	0.166266	0.0831329	−	0.996538i	$-0.473507\pi$
$541$	3.86725	0.166266	0.0831329	+	0.996538i	$0.473507\pi$
$542$	34.0314	1.46177
$543$	3.39882	0.145857
$544$	43.2962	1.85631
$545$	−22.8145	−0.977264
$546$	−17.9029	−0.766175
$547$	8.14001	0.348042	0.174021	−	0.984742i	$-0.444324\pi$
$547$	8.14001	0.348042	0.174021	+	0.984742i	$0.444324\pi$
$548$	−11.7166	−0.500506
$549$	15.5584	0.664015
$550$	32.1736	1.37189
$551$	0.993627	0.0423299
$552$	12.5482	0.534087
$553$	−14.3667	−0.610932
$554$	−60.2138	−2.55824
$555$	−8.47602	−0.359787
$556$	44.5793	1.89058
$557$	0.971512	0.0411643	0.0205821	−	0.999788i	$-0.493448\pi$
$557$	0.971512	0.0411643	0.0205821	+	0.999788i	$0.493448\pi$
$558$	−7.74203	−0.327746
$559$	−5.39292	−0.228096
$560$	82.5093	3.48666
$561$	3.87945	0.163790
$562$	−15.6851	−0.661637
$563$	1.65409	0.0697115	0.0348557	−	0.999392i	$-0.488903\pi$
$563$	1.65409	0.0697115	0.0348557	+	0.999392i	$0.488903\pi$
$564$	−55.4043	−2.33294
$565$	4.75470	0.200032
$566$	69.2795	2.91203
$567$	−14.2382	−0.597949
$568$	98.4049	4.12898
$569$	−39.9752	−1.67585	−0.837924	−	0.545787i	$-0.816231\pi$
$569$	−39.9752	−1.67585	−0.837924	+	0.545787i	$0.816231\pi$
$570$	1.20865	0.0506247
$571$	14.9325	0.624906	0.312453	−	0.949933i	$-0.398849\pi$
$571$	14.9325	0.624906	0.312453	+	0.949933i	$0.398849\pi$
$572$	34.9031	1.45937
$573$	−12.5757	−0.525359
$574$	88.2104	3.68183
$575$	−5.43704	−0.226740
$576$	−101.966	−4.24858
$577$	−15.8739	−0.660837	−0.330419	−	0.943834i	$-0.607190\pi$
$577$	−15.8739	−0.660837	−0.330419	+	0.943834i	$0.607190\pi$
$578$	40.8713	1.70002
$579$	9.80562	0.407508
$580$	14.0106	0.581758
$581$	20.3358	0.843672
$582$	19.3979	0.804067
$583$	33.1426	1.37263
$584$	63.3077	2.61969
$585$	5.17797	0.214083
$586$	2.61007	0.107821
$587$	33.8083	1.39542	0.697708	−	0.716382i	$-0.254203\pi$
$587$	33.8083	1.39542	0.697708	+	0.716382i	$0.254203\pi$
$588$	−45.1859	−1.86344
$589$	0.554749	0.0228580
$590$	18.8825	0.777380
$591$	17.7918	0.731859
$592$	−161.581	−6.64095
$593$	7.31116	0.300234	0.150117	−	0.988668i	$-0.452035\pi$
$593$	7.31116	0.300234	0.150117	+	0.988668i	$0.452035\pi$
$594$	−37.7920	−1.55062
$595$	−7.11826	−0.291820
$596$	54.6131	2.23704
$597$	5.91391	0.242040
$598$	−7.94462	−0.324880
$599$	17.9280	0.732517	0.366259	−	0.930513i	$-0.380639\pi$
$599$	17.9280	0.732517	0.366259	+	0.930513i	$0.380639\pi$
$600$	−31.5064	−1.28624
$601$	−5.20241	−0.212211	−0.106105	−	0.994355i	$-0.533838\pi$
$601$	−5.20241	−0.212211	−0.106105	+	0.994355i	$0.533838\pi$
$602$	−31.6423	−1.28964
$603$	−14.4813	−0.589726
$604$	16.5557	0.673642
$605$	1.41044	0.0573426
$606$	3.61910	0.147016
$607$	−40.4980	−1.64376	−0.821881	−	0.569659i	$-0.807075\pi$
$607$	−40.4980	−1.64376	−0.821881	+	0.569659i	$0.807075\pi$
$608$	13.2410	0.536994
$609$	−7.05437	−0.285857
$610$	−21.1731	−0.857275
$611$	22.9082	0.926767
$612$	20.5960	0.832542
$613$	−6.15641	−0.248655	−0.124328	−	0.992241i	$-0.539677\pi$
$613$	−6.15641	−0.248655	−0.124328	+	0.992241i	$0.539677\pi$
$614$	71.3667	2.88013
$615$	7.20587	0.290569
$616$	133.741	5.38857
$617$	42.5497	1.71299	0.856494	−	0.516158i	$-0.172638\pi$
$617$	42.5497	1.71299	0.856494	+	0.516158i	$0.172638\pi$
$618$	−3.87695	−0.155954
$619$	20.9182	0.840772	0.420386	−	0.907345i	$-0.361895\pi$
$619$	20.9182	0.840772	0.420386	+	0.907345i	$0.361895\pi$
$620$	7.82221	0.314148
$621$	6.38650	0.256281
$622$	56.9786	2.28464
$623$	−38.5263	−1.54353
$624$	−27.8798	−1.11609
$625$	7.12542	0.285017
$626$	−86.7283	−3.46636
$627$	1.18643	0.0473814
$628$	−34.1838	−1.36408
$629$	13.9400	0.555823
$630$	30.3811	1.21041
$631$	−9.98459	−0.397480	−0.198740	−	0.980052i	$-0.563685\pi$
$631$	−9.98459	−0.397480	−0.198740	+	0.980052i	$0.563685\pi$
$632$	−36.9437	−1.46954
$633$	16.4690	0.654586
$634$	−81.8195	−3.24947
$635$	3.40407	0.135086
$636$	−49.6970	−1.97061
$637$	18.6832	0.740255
$638$	18.5244	0.733388
$639$	21.9431	0.868056
$640$	73.9895	2.92469
$641$	−17.5102	−0.691611	−0.345805	−	0.938306i	$-0.612394\pi$
$641$	−17.5102	−0.691611	−0.345805	+	0.938306i	$0.612394\pi$
$642$	−17.7367	−0.700011
$643$	−25.5510	−1.00763	−0.503817	−	0.863811i	$-0.668071\pi$
$643$	−25.5510	−1.00763	−0.503817	+	0.863811i	$0.668071\pi$
$644$	−34.6075	−1.36373
$645$	−2.58484	−0.101778
$646$	−1.98779	−0.0782085
$647$	46.0276	1.80953	0.904766	−	0.425909i	$-0.140045\pi$
$647$	46.0276	1.80953	0.904766	+	0.425909i	$0.140045\pi$
$648$	−36.6135	−1.43831
$649$	18.5353	0.727576
$650$	19.9476	0.782409
$651$	−3.93850	−0.154362
$652$	−12.3126	−0.482199
$653$	47.8078	1.87087	0.935433	−	0.353505i	$-0.115010\pi$
$653$	47.8078	1.87087	0.935433	+	0.353505i	$0.115010\pi$
$654$	45.2315	1.76869
$655$	−16.4395	−0.642344
$656$	137.368	5.36331
$657$	14.1168	0.550750
$658$	134.411	5.23990
$659$	−19.1662	−0.746608	−0.373304	−	0.927709i	$-0.621775\pi$
$659$	−19.1662	−0.746608	−0.373304	+	0.927709i	$0.621775\pi$
$660$	16.7292	0.651182
$661$	−46.0332	−1.79048	−0.895242	−	0.445580i	$-0.852997\pi$
$661$	−46.0332	−1.79048	−0.895242	+	0.445580i	$0.852997\pi$
$662$	22.8337	0.887456
$663$	2.40525	0.0934122
$664$	52.2934	2.02938
$665$	−2.17694	−0.0844180
$666$	−59.4966	−2.30545
$667$	−3.13045	−0.121212
$668$	145.170	5.61678
$669$	3.68541	0.142486
$670$	19.7074	0.761364
$671$	−20.7839	−0.802353
$672$	−94.0060	−3.62636
$673$	37.1622	1.43250	0.716249	−	0.697845i	$-0.245858\pi$
$673$	37.1622	1.43250	0.716249	+	0.697845i	$0.245858\pi$
$674$	7.31007	0.281573
$675$	−16.0354	−0.617203
$676$	−53.3021	−2.05008
$677$	−6.31557	−0.242727	−0.121363	−	0.992608i	$-0.538727\pi$
$677$	−6.31557	−0.242727	−0.121363	+	0.992608i	$0.538727\pi$
$678$	−9.42658	−0.362026
$679$	−34.9381	−1.34080
$680$	−18.3046	−0.701948
$681$	−0.979521	−0.0375353
$682$	10.3423	0.396027
$683$	−45.0073	−1.72216	−0.861079	−	0.508472i	$-0.830211\pi$
$683$	−45.0073	−1.72216	−0.861079	+	0.508472i	$0.830211\pi$
$684$	6.29874	0.240838
$685$	2.32198	0.0887183
$686$	30.0460	1.14716
$687$	−5.58950	−0.213253
$688$	−49.2758	−1.87862
$689$	20.5484	0.782831
$690$	−3.80789	−0.144964
$691$	−0.649718	−0.0247164	−0.0123582	−	0.999924i	$-0.503934\pi$
$691$	−0.649718	−0.0247164	−0.0123582	+	0.999924i	$0.503934\pi$
$692$	−75.8491	−2.88335
$693$	29.8226	1.13287
$694$	−95.3743	−3.62036
$695$	−8.83471	−0.335120
$696$	−18.1403	−0.687605
$697$	−11.8510	−0.448890
$698$	−55.4313	−2.09811
$699$	16.2809	0.615800
$700$	86.8936	3.28427
$701$	−50.4677	−1.90614	−0.953070	−	0.302751i	$-0.902095\pi$
$701$	−50.4677	−1.90614	−0.953070	+	0.302751i	$0.902095\pi$
$702$	−23.4310	−0.884346
$703$	4.26318	0.160789
$704$	136.213	5.13371
$705$	10.9800	0.413531
$706$	88.1480	3.31749
$707$	−6.51847	−0.245152
$708$	−27.7935	−1.04454
$709$	34.0120	1.27735	0.638673	−	0.769478i	$-0.279484\pi$
$709$	34.0120	1.27735	0.638673	+	0.769478i	$0.279484\pi$
$710$	−29.8620	−1.12070
$711$	−8.23801	−0.308949
$712$	−99.0702	−3.71281
$713$	−1.74775	−0.0654539
$714$	14.1125	0.528148
$715$	−6.91707	−0.258684
$716$	35.5179	1.32737
$717$	12.0724	0.450851
$718$	−9.24296	−0.344944
$719$	31.3412	1.16883	0.584416	−	0.811454i	$-0.301324\pi$
$719$	31.3412	1.16883	0.584416	+	0.811454i	$0.301324\pi$
$720$	47.3118	1.76321
$721$	6.98290	0.260057
$722$	52.3362	1.94775
$723$	−16.4366	−0.611284
$724$	−24.1048	−0.895847
$725$	7.86003	0.291914
$726$	−2.79632	−0.103781
$727$	−47.6884	−1.76866	−0.884332	−	0.466859i	$-0.845385\pi$
$727$	−47.6884	−1.76866	−0.884332	+	0.466859i	$0.845385\pi$
$728$	82.9191	3.07319
$729$	2.41886	0.0895875
$730$	−19.2114	−0.711045
$731$	4.25113	0.157234
$732$	31.1652	1.15190
$733$	5.61582	0.207425	0.103712	−	0.994607i	$-0.466928\pi$
$733$	5.61582	0.207425	0.103712	+	0.994607i	$0.466928\pi$
$734$	−23.5624	−0.869704
$735$	8.95492	0.330307
$736$	−41.7162	−1.53768
$737$	19.3451	0.712586
$738$	50.5809	1.86191
$739$	−18.1269	−0.666810	−0.333405	−	0.942784i	$-0.608198\pi$
$739$	−18.1269	−0.666810	−0.333405	+	0.942784i	$0.608198\pi$
$740$	60.1127	2.20979
$741$	0.735584	0.0270224
$742$	120.565	4.42609
$743$	−21.3366	−0.782763	−0.391381	−	0.920229i	$-0.628003\pi$
$743$	−21.3366	−0.782763	−0.391381	+	0.920229i	$0.628003\pi$
$744$	−10.1278	−0.371304
$745$	−10.8232	−0.396532
$746$	−8.82497	−0.323105
$747$	11.6608	0.426646
$748$	−27.5134	−1.00599
$749$	31.9461	1.16729
$750$	22.4994	0.821561
$751$	2.63544	0.0961685	0.0480842	−	0.998843i	$-0.484688\pi$
$751$	2.63544	0.0961685	0.0480842	+	0.998843i	$0.484688\pi$
$752$	209.315	7.63295
$753$	−8.20781	−0.299109
$754$	11.4851	0.418263
$755$	−3.28100	−0.119408
$756$	−102.068	−3.71216
$757$	−32.0937	−1.16647	−0.583233	−	0.812305i	$-0.698212\pi$
$757$	−32.0937	−1.16647	−0.583233	+	0.812305i	$0.698212\pi$
$758$	17.2275	0.625730
$759$	−3.73788	−0.135676
$760$	−5.59798	−0.203060
$761$	30.0282	1.08852	0.544260	−	0.838916i	$-0.316810\pi$
$761$	30.0282	1.08852	0.544260	+	0.838916i	$0.316810\pi$
$762$	−6.74884	−0.244485
$763$	−81.4679	−2.94934
$764$	89.1883	3.22672
$765$	−4.08170	−0.147574
$766$	−13.4670	−0.486583
$767$	11.4919	0.414948
$768$	−75.8289	−2.73624
$769$	20.6940	0.746243	0.373122	−	0.927782i	$-0.378287\pi$
$769$	20.6940	0.746243	0.373122	+	0.927782i	$0.378287\pi$
$770$	−40.5851	−1.46259
$771$	14.6365	0.527120
$772$	−69.5424	−2.50289
$773$	−8.11561	−0.291898	−0.145949	−	0.989292i	$-0.546624\pi$
$773$	−8.11561	−0.291898	−0.145949	+	0.989292i	$0.546624\pi$
$774$	−18.1441	−0.652175
$775$	4.38831	0.157633
$776$	−89.8431	−3.22518
$777$	−30.2669	−1.08582
$778$	−73.7574	−2.64433
$779$	−3.62433	−0.129855
$780$	10.3721	0.371379
$781$	−29.3130	−1.04890
$782$	6.26259	0.223950
$783$	−9.23261	−0.329947
$784$	170.711	6.09681
$785$	6.77453	0.241793
$786$	32.5926	1.16254
$787$	17.3710	0.619210	0.309605	−	0.950865i	$-0.399803\pi$
$787$	17.3710	0.619210	0.309605	+	0.950865i	$0.399803\pi$
$788$	−126.181	−4.49503
$789$	16.6390	0.592363
$790$	11.2110	0.398869
$791$	16.9785	0.603687
$792$	76.6886	2.72501
$793$	−12.8860	−0.457594
$794$	−97.7889	−3.47040
$795$	9.84892	0.349305
$796$	−41.9420	−1.48660
$797$	22.7928	0.807363	0.403682	−	0.914900i	$-0.367730\pi$
$797$	22.7928	0.807363	0.403682	+	0.914900i	$0.367730\pi$
$798$	4.31595	0.152783
$799$	−18.0581	−0.638850
$800$	104.742	3.70320
$801$	−22.0915	−0.780563
$802$	−3.17329	−0.112053
$803$	−18.8582	−0.665491
$804$	−29.0077	−1.02302
$805$	6.85850	0.241731
$806$	6.41222	0.225861
$807$	−16.7637	−0.590109
$808$	−16.7622	−0.589692
$809$	−40.6864	−1.43046	−0.715229	−	0.698891i	$-0.753677\pi$
$809$	−40.6864	−1.43046	−0.715229	+	0.698891i	$0.753677\pi$
$810$	11.1108	0.390392
$811$	−15.8101	−0.555168	−0.277584	−	0.960701i	$-0.589534\pi$
$811$	−15.8101	−0.555168	−0.277584	+	0.960701i	$0.589534\pi$
$812$	50.0302	1.75572
$813$	9.92710	0.348159
$814$	79.4794	2.78575
$815$	2.44011	0.0854732
$816$	21.9771	0.769352
$817$	1.30010	0.0454847
$818$	−20.2870	−0.709318
$819$	18.4900	0.646092
$820$	−51.1047	−1.78465
$821$	10.5874	0.369503	0.184752	−	0.982785i	$-0.440852\pi$
$821$	10.5874	0.369503	0.184752	+	0.982785i	$0.440852\pi$
$822$	−4.60351	−0.160566
$823$	22.7196	0.791956	0.395978	−	0.918260i	$-0.370406\pi$
$823$	22.7196	0.791956	0.395978	+	0.918260i	$0.370406\pi$
$824$	17.9565	0.625544
$825$	9.38518	0.326750
$826$	67.4272	2.34609
$827$	5.66866	0.197119	0.0985594	−	0.995131i	$-0.468577\pi$
$827$	5.66866	0.197119	0.0985594	+	0.995131i	$0.468577\pi$
$828$	−19.8444	−0.689640
$829$	−44.0785	−1.53091	−0.765456	−	0.643489i	$-0.777486\pi$
$829$	−44.0785	−1.53091	−0.765456	+	0.643489i	$0.777486\pi$
$830$	−15.8690	−0.550821
$831$	−17.5646	−0.609310
$832$	84.4516	2.92783
$833$	−14.7276	−0.510281
$834$	17.5155	0.606513
$835$	−28.7697	−0.995615
$836$	−8.41426	−0.291013
$837$	−5.15463	−0.178170
$838$	108.304	3.74131
$839$	−16.9363	−0.584705	−0.292352	−	0.956311i	$-0.594438\pi$
$839$	−16.9363	−0.584705	−0.292352	+	0.956311i	$0.594438\pi$
$840$	39.7435	1.37128
$841$	−24.4745	−0.843947
$842$	69.7736	2.40456
$843$	−4.57542	−0.157586
$844$	−116.800	−4.02042
$845$	10.5634	0.363391
$846$	77.0730	2.64982
$847$	5.03653	0.173057
$848$	187.753	6.44747
$849$	20.2091	0.693575
$850$	−15.7243	−0.539339
$851$	−13.4313	−0.460418
$852$	43.9545	1.50586
$853$	37.4930	1.28374	0.641869	−	0.766815i	$-0.278159\pi$
$853$	37.4930	1.28374	0.641869	+	0.766815i	$0.278159\pi$
$854$	−75.6069	−2.58722
$855$	−1.24828	−0.0426903
$856$	82.1492	2.80780
$857$	−38.3433	−1.30978	−0.654891	−	0.755724i	$-0.727285\pi$
$857$	−38.3433	−1.30978	−0.654891	+	0.755724i	$0.727285\pi$
$858$	13.7137	0.468176
$859$	31.3432	1.06942	0.534708	−	0.845037i	$-0.320421\pi$
$859$	31.3432	1.06942	0.534708	+	0.845037i	$0.320421\pi$
$860$	18.3320	0.625115
$861$	25.7313	0.876922
$862$	55.6170	1.89432
$863$	15.0560	0.512514	0.256257	−	0.966609i	$-0.417511\pi$
$863$	15.0560	0.512514	0.256257	+	0.966609i	$0.417511\pi$
$864$	−123.033	−4.18568
$865$	15.0317	0.511094
$866$	37.6796	1.28041
$867$	11.9223	0.404903
$868$	27.9322	0.948082
$869$	11.0049	0.373315
$870$	5.50485	0.186632
$871$	11.9939	0.406399
$872$	−209.494	−7.09437
$873$	−20.0339	−0.678046
$874$	1.91525	0.0647843
$875$	−40.5243	−1.36997
$876$	28.2776	0.955412
$877$	−7.06194	−0.238465	−0.119232	−	0.992866i	$-0.538043\pi$
$877$	−7.06194	−0.238465	−0.119232	+	0.992866i	$0.538043\pi$
$878$	96.2952	3.24981
$879$	0.761370	0.0256804
$880$	−63.2022	−2.13055
$881$	1.61656	0.0544631	0.0272316	−	0.999629i	$-0.491331\pi$
$881$	1.61656	0.0544631	0.0272316	+	0.999629i	$0.491331\pi$
$882$	62.8582	2.11655
$883$	4.86401	0.163687	0.0818434	−	0.996645i	$-0.473919\pi$
$883$	4.86401	0.163687	0.0818434	+	0.996645i	$0.473919\pi$
$884$	−17.0583	−0.573732
$885$	5.50810	0.185153
$886$	−33.1661	−1.11424
$887$	2.58523	0.0868036	0.0434018	−	0.999058i	$-0.486180\pi$
$887$	2.58523	0.0868036	0.0434018	+	0.999058i	$0.486180\pi$
$888$	−77.8312	−2.61184
$889$	12.1555	0.407684
$890$	30.0639	1.00774
$891$	10.9065	0.365381
$892$	−26.1373	−0.875142
$893$	−5.52260	−0.184807
$894$	21.4579	0.717659
$895$	−7.03891	−0.235285
$896$	264.208	8.82657
$897$	−2.31748	−0.0773784
$898$	2.48138	0.0828047
$899$	2.52663	0.0842679
$900$	49.8258	1.66086
$901$	−16.1979	−0.539630
$902$	−67.5692	−2.24981
$903$	−9.23019	−0.307161
$904$	43.6601	1.45211
$905$	4.77707	0.158795
$906$	6.50485	0.216109
$907$	26.4976	0.879837	0.439918	−	0.898038i	$-0.355007\pi$
$907$	26.4976	0.879837	0.439918	+	0.898038i	$0.355007\pi$
$908$	6.94685	0.230539
$909$	−3.73777	−0.123974
$910$	−25.1627	−0.834136
$911$	−23.0920	−0.765073	−0.382537	−	0.923940i	$-0.624949\pi$
$911$	−23.0920	−0.765073	−0.382537	+	0.923940i	$0.624949\pi$
$912$	6.72113	0.222559
$913$	−15.5772	−0.515532
$914$	45.5210	1.50570
$915$	−6.17630	−0.204182
$916$	39.6413	1.30978
$917$	−58.7036	−1.93856
$918$	18.4702	0.609607
$919$	−34.4152	−1.13525	−0.567627	−	0.823286i	$-0.692138\pi$
$919$	−34.4152	−1.13525	−0.567627	+	0.823286i	$0.692138\pi$
$920$	17.6366	0.581461
$921$	20.8180	0.685976
$922$	17.0956	0.563012
$923$	−18.1740	−0.598206
$924$	59.7380	1.96524
$925$	33.7236	1.10883
$926$	23.6665	0.777731
$927$	4.00408	0.131511
$928$	60.3069	1.97967
$929$	40.5580	1.33066	0.665332	−	0.746547i	$-0.268290\pi$
$929$	40.5580	1.33066	0.665332	+	0.746547i	$0.268290\pi$
$930$	3.07340	0.100781
$931$	−4.50405	−0.147614
$932$	−115.466	−3.78220
$933$	16.6209	0.544144
$934$	68.4836	2.24085
$935$	5.45259	0.178319
$936$	47.5468	1.55412
$937$	−16.2229	−0.529980	−0.264990	−	0.964251i	$-0.585369\pi$
$937$	−16.2229	−0.529980	−0.264990	+	0.964251i	$0.585369\pi$
$938$	70.3730	2.29776
$939$	−25.2990	−0.825602
$940$	−77.8712	−2.53988
$941$	−11.0764	−0.361079	−0.180539	−	0.983568i	$-0.557784\pi$
$941$	−11.0764	−0.361079	−0.180539	+	0.983568i	$0.557784\pi$
$942$	−13.4311	−0.437607
$943$	11.4186	0.371840
$944$	105.003	3.41755
$945$	20.2277	0.658008
$946$	24.2380	0.788046
$947$	−29.4681	−0.957585	−0.478793	−	0.877928i	$-0.658925\pi$
$947$	−29.4681	−0.957585	−0.478793	+	0.877928i	$0.658925\pi$
$948$	−16.5017	−0.535949
$949$	−11.6921	−0.379540
$950$	−4.80887	−0.156020
$951$	−23.8671	−0.773944
$952$	−65.3635	−2.11844
$953$	39.1010	1.26661	0.633303	−	0.773904i	$-0.281699\pi$
$953$	39.1010	1.26661	0.633303	+	0.773904i	$0.281699\pi$
$954$	69.1335	2.23828
$955$	−17.6753	−0.571959
$956$	−85.6184	−2.76910
$957$	5.40365	0.174675
$958$	−15.9010	−0.513737
$959$	8.29154	0.267748
$960$	40.4780	1.30642
$961$	−29.5894	−0.954496
$962$	49.2771	1.58876
$963$	18.3183	0.590298
$964$	116.570	3.75447
$965$	13.7819	0.443655
$966$	−13.5975	−0.437494
$967$	−52.3783	−1.68437	−0.842187	−	0.539186i	$-0.818732\pi$
$967$	−52.3783	−1.68437	−0.842187	+	0.539186i	$0.818732\pi$
$968$	12.9514	0.416274
$969$	−0.579846	−0.0186273
$970$	27.2638	0.875389
$971$	23.2589	0.746413	0.373206	−	0.927748i	$-0.378258\pi$
$971$	23.2589	0.746413	0.373206	+	0.927748i	$0.378258\pi$
$972$	−91.4114	−2.93202
$973$	−31.5478	−1.01137
$974$	−13.1000	−0.419750
$975$	5.81880	0.186351
$976$	−117.741	−3.76879
$977$	−7.67683	−0.245604	−0.122802	−	0.992431i	$-0.539188\pi$
$977$	−7.67683	−0.245604	−0.122802	+	0.992431i	$0.539188\pi$
$978$	−4.83770	−0.154693
$979$	29.5112	0.943182
$980$	−63.5092	−2.02873
$981$	−46.7146	−1.49148
$982$	118.027	3.76638
$983$	3.96363	0.126420	0.0632102	−	0.998000i	$-0.479866\pi$
$983$	3.96363	0.126420	0.0632102	+	0.998000i	$0.479866\pi$
$984$	66.1680	2.10936
$985$	25.0066	0.796776
$986$	−9.05348	−0.288322
$987$	39.2083	1.24802
$988$	−5.21683	−0.165970
$989$	−4.09600	−0.130245
$990$	−23.2720	−0.739632
$991$	−40.4033	−1.28345	−0.641727	−	0.766934i	$-0.721782\pi$
$991$	−40.4033	−1.28345	−0.641727	+	0.766934i	$0.721782\pi$
$992$	33.6698	1.06902
$993$	6.66068	0.211370
$994$	−106.634	−3.38222
$995$	8.31205	0.263510
$996$	23.3579	0.740123
$997$	23.6168	0.747952	0.373976	−	0.927438i	$-0.377994\pi$
$997$	23.6168	0.747952	0.373976	+	0.927438i	$0.377994\pi$
$998$	103.137	3.26473
$999$	−39.6127	−1.25329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.b.1.2	✓	157

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.78653 q^{2} -0.812844 q^{3} +5.76476 q^{4} -1.14246 q^{5} +2.26502 q^{6} -4.07959 q^{7} -10.4906 q^{8} -2.33929 q^{9} +O(q^{10})\)	\(q-2.78653 q^{2} -0.812844 q^{3} +5.76476 q^{4} -1.14246 q^{5} +2.26502 q^{6} -4.07959 q^{7} -10.4906 q^{8} -2.33929 q^{9} +3.18350 q^{10} +3.12497 q^{11} -4.68585 q^{12} +1.93748 q^{13} +11.3679 q^{14} +0.928640 q^{15} +17.7030 q^{16} -1.52727 q^{17} +6.51849 q^{18} -0.467077 q^{19} -6.58600 q^{20} +3.31607 q^{21} -8.70783 q^{22} +1.47154 q^{23} +8.52725 q^{24} -3.69479 q^{25} -5.39884 q^{26} +4.34000 q^{27} -23.5179 q^{28} -2.12733 q^{29} -2.58768 q^{30} -1.18770 q^{31} -28.3486 q^{32} -2.54011 q^{33} +4.25580 q^{34} +4.66076 q^{35} -13.4854 q^{36} -9.12735 q^{37} +1.30153 q^{38} -1.57487 q^{39} +11.9851 q^{40} +7.75959 q^{41} -9.24033 q^{42} -2.78347 q^{43} +18.0147 q^{44} +2.67254 q^{45} -4.10050 q^{46} +11.8237 q^{47} -14.3897 q^{48} +9.64305 q^{49} +10.2957 q^{50} +1.24144 q^{51} +11.1691 q^{52} +10.6057 q^{53} -12.0936 q^{54} -3.57015 q^{55} +42.7975 q^{56} +0.379661 q^{57} +5.92787 q^{58} +5.93137 q^{59} +5.35339 q^{60} -6.65091 q^{61} +3.30957 q^{62} +9.54333 q^{63} +43.5885 q^{64} -2.21349 q^{65} +7.07810 q^{66} +6.19050 q^{67} -8.80438 q^{68} -1.19613 q^{69} -12.9874 q^{70} -9.38026 q^{71} +24.5406 q^{72} -6.03468 q^{73} +25.4337 q^{74} +3.00329 q^{75} -2.69259 q^{76} -12.7486 q^{77} +4.38841 q^{78} +3.52159 q^{79} -20.2249 q^{80} +3.49011 q^{81} -21.6224 q^{82} -4.98477 q^{83} +19.1164 q^{84} +1.74485 q^{85} +7.75624 q^{86} +1.72918 q^{87} -32.7829 q^{88} +9.44368 q^{89} -7.44711 q^{90} -7.90411 q^{91} +8.48309 q^{92} +0.965416 q^{93} -32.9472 q^{94} +0.533616 q^{95} +23.0430 q^{96} +8.56412 q^{97} -26.8707 q^{98} -7.31019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) \) 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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