LMFDB - Embedded newform 4013.2.a.c.1.17

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:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.39761 q^{2} +0.688358 q^{3} +3.74852 q^{4} +1.63631 q^{5} -1.65041 q^{6} -2.07745 q^{7} -4.19226 q^{8} -2.52616 q^{9} +O(q^{10})$	\(q-2.39761 q^{2} +0.688358 q^{3} +3.74852 q^{4} +1.63631 q^{5} -1.65041 q^{6} -2.07745 q^{7} -4.19226 q^{8} -2.52616 q^{9} -3.92323 q^{10} +3.47719 q^{11} +2.58032 q^{12} -5.71192 q^{13} +4.98092 q^{14} +1.12637 q^{15} +2.55435 q^{16} +5.74198 q^{17} +6.05675 q^{18} -0.556818 q^{19} +6.13374 q^{20} -1.43003 q^{21} -8.33693 q^{22} +5.59281 q^{23} -2.88577 q^{24} -2.32249 q^{25} +13.6949 q^{26} -3.80398 q^{27} -7.78737 q^{28} -1.62783 q^{29} -2.70058 q^{30} +2.48180 q^{31} +2.26018 q^{32} +2.39355 q^{33} -13.7670 q^{34} -3.39936 q^{35} -9.46937 q^{36} +3.64581 q^{37} +1.33503 q^{38} -3.93184 q^{39} -6.85984 q^{40} +9.46476 q^{41} +3.42865 q^{42} +0.434001 q^{43} +13.0343 q^{44} -4.13359 q^{45} -13.4094 q^{46} -7.81409 q^{47} +1.75831 q^{48} -2.68419 q^{49} +5.56841 q^{50} +3.95253 q^{51} -21.4112 q^{52} -0.156015 q^{53} +9.12044 q^{54} +5.68976 q^{55} +8.70922 q^{56} -0.383290 q^{57} +3.90291 q^{58} +0.193204 q^{59} +4.22221 q^{60} -8.46028 q^{61} -5.95037 q^{62} +5.24799 q^{63} -10.5277 q^{64} -9.34647 q^{65} -5.73879 q^{66} -3.38726 q^{67} +21.5239 q^{68} +3.84986 q^{69} +8.15032 q^{70} -13.1300 q^{71} +10.5903 q^{72} +7.44620 q^{73} -8.74122 q^{74} -1.59870 q^{75} -2.08724 q^{76} -7.22370 q^{77} +9.42701 q^{78} -2.91963 q^{79} +4.17972 q^{80} +4.96000 q^{81} -22.6928 q^{82} +12.1030 q^{83} -5.36050 q^{84} +9.39566 q^{85} -1.04056 q^{86} -1.12053 q^{87} -14.5773 q^{88} +11.6955 q^{89} +9.91072 q^{90} +11.8662 q^{91} +20.9648 q^{92} +1.70836 q^{93} +18.7351 q^{94} -0.911127 q^{95} +1.55581 q^{96} +13.2014 q^{97} +6.43563 q^{98} -8.78395 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) $ 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * 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 $

$2$	−2.39761	−1.69536	−0.847682	−	0.530505i	$-0.822002\pi$
$2$	−2.39761	−1.69536	−0.847682	+	0.530505i	$0.822002\pi$
$3$	0.688358	0.397423	0.198712	−	0.980058i	$-0.436324\pi$
$3$	0.688358	0.397423	0.198712	+	0.980058i	$0.436324\pi$
$4$	3.74852	1.87426
$5$	1.63631	0.731780	0.365890	−	0.930658i	$-0.380765\pi$
$5$	1.63631	0.731780	0.365890	+	0.930658i	$0.380765\pi$
$6$	−1.65041	−0.673777
$7$	−2.07745	−0.785204	−0.392602	−	0.919709i	$-0.628425\pi$
$7$	−2.07745	−0.785204	−0.392602	+	0.919709i	$0.628425\pi$
$8$	−4.19226	−1.48219
$9$	−2.52616	−0.842055
$10$	−3.92323	−1.24063
$11$	3.47719	1.04841	0.524206	−	0.851592i	$-0.324362\pi$
$11$	3.47719	1.04841	0.524206	+	0.851592i	$0.324362\pi$
$12$	2.58032	0.744875
$13$	−5.71192	−1.58420	−0.792100	−	0.610391i	$-0.791012\pi$
$13$	−5.71192	−1.58420	−0.792100	+	0.610391i	$0.791012\pi$
$14$	4.98092	1.33121
$15$	1.12637	0.290827
$16$	2.55435	0.638589
$17$	5.74198	1.39263	0.696317	−	0.717734i	$-0.254821\pi$
$17$	5.74198	1.39263	0.696317	+	0.717734i	$0.254821\pi$
$18$	6.05675	1.42759
$19$	−0.556818	−0.127743	−0.0638714	−	0.997958i	$-0.520345\pi$
$19$	−0.556818	−0.127743	−0.0638714	+	0.997958i	$0.520345\pi$
$20$	6.13374	1.37155
$21$	−1.43003	−0.312058
$22$	−8.33693	−1.77744
$23$	5.59281	1.16618	0.583091	−	0.812407i	$-0.301843\pi$
$23$	5.59281	1.16618	0.583091	+	0.812407i	$0.301843\pi$
$24$	−2.88577	−0.589056
$25$	−2.32249	−0.464498
$26$	13.6949	2.68580
$27$	−3.80398	−0.732076
$28$	−7.78737	−1.47168
$29$	−1.62783	−0.302281	−0.151141	−	0.988512i	$-0.548295\pi$
$29$	−1.62783	−0.302281	−0.151141	+	0.988512i	$0.548295\pi$
$30$	−2.70058	−0.493057
$31$	2.48180	0.445744	0.222872	−	0.974848i	$-0.428457\pi$
$31$	2.48180	0.445744	0.222872	+	0.974848i	$0.428457\pi$
$32$	2.26018	0.399548
$33$	2.39355	0.416663
$34$	−13.7670	−2.36102
$35$	−3.39936	−0.574596
$36$	−9.46937	−1.57823
$37$	3.64581	0.599368	0.299684	−	0.954039i	$-0.403119\pi$
$37$	3.64581	0.599368	0.299684	+	0.954039i	$0.403119\pi$
$38$	1.33503	0.216571
$39$	−3.93184	−0.629598
$40$	−6.85984	−1.08464
$41$	9.46476	1.47815	0.739073	−	0.673625i	$-0.235264\pi$
$41$	9.46476	1.47815	0.739073	+	0.673625i	$0.235264\pi$
$42$	3.42865	0.529052
$43$	0.434001	0.0661846	0.0330923	−	0.999452i	$-0.489464\pi$
$43$	0.434001	0.0661846	0.0330923	+	0.999452i	$0.489464\pi$
$44$	13.0343	1.96500
$45$	−4.13359	−0.616199
$46$	−13.4094	−1.97710
$47$	−7.81409	−1.13980	−0.569901	−	0.821713i	$-0.693019\pi$
$47$	−7.81409	−1.13980	−0.569901	+	0.821713i	$0.693019\pi$
$48$	1.75831	0.253790
$49$	−2.68419	−0.383455
$50$	5.56841	0.787493
$51$	3.95253	0.553466
$52$	−21.4112	−2.96920
$53$	−0.156015	−0.0214304	−0.0107152	−	0.999943i	$-0.503411\pi$
$53$	−0.156015	−0.0214304	−0.0107152	+	0.999943i	$0.503411\pi$
$54$	9.12044	1.24113
$55$	5.68976	0.767207
$56$	8.70922	1.16382
$57$	−0.383290	−0.0507680
$58$	3.90291	0.512477
$59$	0.193204	0.0251530	0.0125765	−	0.999921i	$-0.495997\pi$
$59$	0.193204	0.0251530	0.0125765	+	0.999921i	$0.495997\pi$
$60$	4.22221	0.545084
$61$	−8.46028	−1.08323	−0.541614	−	0.840627i	$-0.682187\pi$
$61$	−8.46028	−1.08323	−0.541614	+	0.840627i	$0.682187\pi$
$62$	−5.95037	−0.755698
$63$	5.24799	0.661184
$64$	−10.5277	−1.31597
$65$	−9.34647	−1.15929
$66$	−5.73879	−0.706396
$67$	−3.38726	−0.413820	−0.206910	−	0.978360i	$-0.566341\pi$
$67$	−3.38726	−0.413820	−0.206910	+	0.978360i	$0.566341\pi$
$68$	21.5239	2.61016
$69$	3.84986	0.463468
$70$	8.15032	0.974150
$71$	−13.1300	−1.55824	−0.779122	−	0.626872i	$-0.784335\pi$
$71$	−13.1300	−1.55824	−0.779122	+	0.626872i	$0.784335\pi$
$72$	10.5903	1.24808
$73$	7.44620	0.871512	0.435756	−	0.900065i	$-0.356481\pi$
$73$	7.44620	0.871512	0.435756	+	0.900065i	$0.356481\pi$
$74$	−8.74122	−1.01615
$75$	−1.59870	−0.184602
$76$	−2.08724	−0.239423
$77$	−7.22370	−0.823217
$78$	9.42701	1.06740
$79$	−2.91963	−0.328484	−0.164242	−	0.986420i	$-0.552518\pi$
$79$	−2.91963	−0.328484	−0.164242	+	0.986420i	$0.552518\pi$
$80$	4.17972	0.467306
$81$	4.96000	0.551111
$82$	−22.6928	−2.50600
$83$	12.1030	1.32848	0.664239	−	0.747520i	$-0.268756\pi$
$83$	12.1030	1.32848	0.664239	+	0.747520i	$0.268756\pi$
$84$	−5.36050	−0.584878
$85$	9.39566	1.01910
$86$	−1.04056	−0.112207
$87$	−1.12053	−0.120134
$88$	−14.5773	−1.55394
$89$	11.6955	1.23972	0.619858	−	0.784714i	$-0.287190\pi$
$89$	11.6955	1.23972	0.619858	+	0.784714i	$0.287190\pi$
$90$	9.91072	1.04468
$91$	11.8662	1.24392
$92$	20.9648	2.18573
$93$	1.70836	0.177149
$94$	18.7351	1.93238
$95$	−0.911127	−0.0934797
$96$	1.55581	0.158790
$97$	13.2014	1.34040	0.670201	−	0.742179i	$-0.266208\pi$
$97$	13.2014	1.34040	0.670201	+	0.742179i	$0.266208\pi$
$98$	6.43563	0.650096
$99$	−8.78395	−0.882820
$100$	−8.70589	−0.870589
$101$	−11.4506	−1.13937	−0.569687	−	0.821862i	$-0.692936\pi$
$101$	−11.4506	−1.13937	−0.569687	+	0.821862i	$0.692936\pi$
$102$	−9.47662	−0.938326
$103$	13.3999	1.32033	0.660166	−	0.751119i	$-0.270486\pi$
$103$	13.3999	1.32033	0.660166	+	0.751119i	$0.270486\pi$
$104$	23.9458	2.34808
$105$	−2.33997	−0.228358
$106$	0.374064	0.0363323
$107$	0.553811	0.0535389	0.0267695	−	0.999642i	$-0.491478\pi$
$107$	0.553811	0.0535389	0.0267695	+	0.999642i	$0.491478\pi$
$108$	−14.2593	−1.37210
$109$	10.8899	1.04307	0.521533	−	0.853231i	$-0.325360\pi$
$109$	10.8899	1.04307	0.521533	+	0.853231i	$0.325360\pi$
$110$	−13.6418	−1.30070
$111$	2.50962	0.238203
$112$	−5.30655	−0.501422
$113$	13.4674	1.26691	0.633455	−	0.773780i	$-0.281636\pi$
$113$	13.4674	1.26691	0.633455	+	0.773780i	$0.281636\pi$
$114$	0.918979	0.0860703
$115$	9.15158	0.853389
$116$	−6.10197	−0.566553
$117$	14.4292	1.33398
$118$	−0.463227	−0.0426435
$119$	−11.9287	−1.09350
$120$	−4.72202	−0.431060
$121$	1.09084	0.0991677
$122$	20.2844	1.83647
$123$	6.51514	0.587450
$124$	9.30306	0.835439
$125$	−11.9819	−1.07169
$126$	−12.5826	−1.12095
$127$	4.75207	0.421678	0.210839	−	0.977521i	$-0.432380\pi$
$127$	4.75207	0.421678	0.210839	+	0.977521i	$0.432380\pi$
$128$	20.7210	1.83150
$129$	0.298748	0.0263033
$130$	22.4092	1.96541
$131$	20.8596	1.82251	0.911255	−	0.411844i	$-0.135115\pi$
$131$	20.8596	1.82251	0.911255	+	0.411844i	$0.135115\pi$
$132$	8.97226	0.780935
$133$	1.15676	0.100304
$134$	8.12132	0.701576
$135$	−6.22449	−0.535719
$136$	−24.0719	−2.06415
$137$	4.00978	0.342579	0.171289	−	0.985221i	$-0.445207\pi$
$137$	4.00978	0.342579	0.171289	+	0.985221i	$0.445207\pi$
$138$	−9.23044	−0.785747
$139$	13.3004	1.12813	0.564063	−	0.825732i	$-0.309237\pi$
$139$	13.3004	1.12813	0.564063	+	0.825732i	$0.309237\pi$
$140$	−12.7426	−1.07694
$141$	−5.37889	−0.452984
$142$	31.4806	2.64179
$143$	−19.8614	−1.66089
$144$	−6.45272	−0.537726
$145$	−2.66364	−0.221203
$146$	−17.8531	−1.47753
$147$	−1.84768	−0.152394
$148$	13.6664	1.12337
$149$	−11.9069	−0.975449	−0.487724	−	0.872998i	$-0.662173\pi$
$149$	−11.9069	−0.975449	−0.487724	+	0.872998i	$0.662173\pi$
$150$	3.83306	0.312968
$151$	2.98515	0.242928	0.121464	−	0.992596i	$-0.461241\pi$
$151$	2.98515	0.242928	0.121464	+	0.992596i	$0.461241\pi$
$152$	2.33433	0.189339
$153$	−14.5052	−1.17267
$154$	17.3196	1.39565
$155$	4.06099	0.326186
$156$	−14.7386	−1.18003
$157$	1.67528	0.133702	0.0668509	−	0.997763i	$-0.478705\pi$
$157$	1.67528	0.133702	0.0668509	+	0.997763i	$0.478705\pi$
$158$	7.00013	0.556900
$159$	−0.107394	−0.00851693
$160$	3.69836	0.292381
$161$	−11.6188	−0.915690
$162$	−11.8921	−0.934333
$163$	−14.3375	−1.12300	−0.561500	−	0.827477i	$-0.689776\pi$
$163$	−14.3375	−1.12300	−0.561500	+	0.827477i	$0.689776\pi$
$164$	35.4788	2.77043
$165$	3.91659	0.304906
$166$	−29.0183	−2.25225
$167$	−7.89273	−0.610757	−0.305379	−	0.952231i	$-0.598783\pi$
$167$	−7.89273	−0.610757	−0.305379	+	0.952231i	$0.598783\pi$
$168$	5.99506	0.462529
$169$	19.6260	1.50969
$170$	−22.5271	−1.72775
$171$	1.40661	0.107566
$172$	1.62686	0.124047
$173$	−7.34481	−0.558415	−0.279208	−	0.960231i	$-0.590072\pi$
$173$	−7.34481	−0.558415	−0.279208	+	0.960231i	$0.590072\pi$
$174$	2.68660	0.203670
$175$	4.82486	0.364725
$176$	8.88197	0.669504
$177$	0.132993	0.00999638
$178$	−28.0411	−2.10177
$179$	−0.106852	−0.00798650	−0.00399325	−	0.999992i	$-0.501271\pi$
$179$	−0.106852	−0.00798650	−0.00399325	+	0.999992i	$0.501271\pi$
$180$	−15.4948	−1.15492
$181$	1.94568	0.144622	0.0723108	−	0.997382i	$-0.476963\pi$
$181$	1.94568	0.144622	0.0723108	+	0.997382i	$0.476963\pi$
$182$	−28.4506	−2.10890
$183$	−5.82370	−0.430500
$184$	−23.4465	−1.72850
$185$	5.96568	0.438605
$186$	−4.09598	−0.300332
$187$	19.9659	1.46005
$188$	−29.2913	−2.13629
$189$	7.90258	0.574828
$190$	2.18453	0.158482
$191$	−6.73529	−0.487349	−0.243674	−	0.969857i	$-0.578353\pi$
$191$	−6.73529	−0.487349	−0.243674	+	0.969857i	$0.578353\pi$
$192$	−7.24685	−0.522996
$193$	5.11553	0.368224	0.184112	−	0.982905i	$-0.441059\pi$
$193$	5.11553	0.368224	0.184112	+	0.982905i	$0.441059\pi$
$194$	−31.6519	−2.27247
$195$	−6.43371	−0.460728
$196$	−10.0617	−0.718695
$197$	25.7430	1.83411	0.917056	−	0.398759i	$-0.130559\pi$
$197$	25.7430	1.83411	0.917056	+	0.398759i	$0.130559\pi$
$198$	21.0605	1.49670
$199$	−24.6169	−1.74505	−0.872523	−	0.488573i	$-0.837518\pi$
$199$	−24.6169	−1.74505	−0.872523	+	0.488573i	$0.837518\pi$
$200$	9.73648	0.688473
$201$	−2.33165	−0.164462
$202$	27.4540	1.93165
$203$	3.38175	0.237352
$204$	14.8162	1.03734
$205$	15.4873	1.08168
$206$	−32.1277	−2.23845
$207$	−14.1284	−0.981989
$208$	−14.5903	−1.01165
$209$	−1.93616	−0.133927
$210$	5.61034	0.387150
$211$	3.44407	0.237099	0.118550	−	0.992948i	$-0.462176\pi$
$211$	3.44407	0.237099	0.118550	+	0.992948i	$0.462176\pi$
$212$	−0.584827	−0.0401661
$213$	−9.03813	−0.619283
$214$	−1.32782	−0.0907679
$215$	0.710161	0.0484326
$216$	15.9473	1.08507
$217$	−5.15582	−0.350000
$218$	−26.1098	−1.76838
$219$	5.12565	0.346359
$220$	21.3282	1.43795
$221$	−32.7977	−2.20621
$222$	−6.01709	−0.403840
$223$	12.9521	0.867340	0.433670	−	0.901072i	$-0.357218\pi$
$223$	12.9521	0.867340	0.433670	+	0.901072i	$0.357218\pi$
$224$	−4.69542	−0.313726
$225$	5.86699	0.391132
$226$	−32.2896	−2.14787
$227$	−12.2682	−0.814270	−0.407135	−	0.913368i	$-0.633472\pi$
$227$	−12.2682	−0.814270	−0.407135	+	0.913368i	$0.633472\pi$
$228$	−1.43677	−0.0951524
$229$	12.1858	0.805262	0.402631	−	0.915362i	$-0.368096\pi$
$229$	12.1858	0.805262	0.402631	+	0.915362i	$0.368096\pi$
$230$	−21.9419	−1.44681
$231$	−4.97249	−0.327166
$232$	6.82430	0.448038
$233$	25.3698	1.66203	0.831017	−	0.556247i	$-0.187759\pi$
$233$	25.3698	1.66203	0.831017	+	0.556247i	$0.187759\pi$
$234$	−34.5956	−2.26159
$235$	−12.7863	−0.834085
$236$	0.724228	0.0471432
$237$	−2.00975	−0.130547
$238$	28.6003	1.85388
$239$	20.0715	1.29832	0.649159	−	0.760653i	$-0.275121\pi$
$239$	20.0715	1.29832	0.649159	+	0.760653i	$0.275121\pi$
$240$	2.87714	0.185719
$241$	−8.75217	−0.563777	−0.281888	−	0.959447i	$-0.590961\pi$
$241$	−8.75217	−0.563777	−0.281888	+	0.959447i	$0.590961\pi$
$242$	−2.61542	−0.168125
$243$	14.8262	0.951100
$244$	−31.7135	−2.03025
$245$	−4.39216	−0.280605
$246$	−15.6207	−0.995942
$247$	3.18050	0.202370
$248$	−10.4043	−0.660676
$249$	8.33120	0.527968
$250$	28.7278	1.81691
$251$	28.8403	1.82039	0.910193	−	0.414184i	$-0.135933\pi$
$251$	28.8403	1.82039	0.910193	+	0.414184i	$0.135933\pi$
$252$	19.6722	1.23923
$253$	19.4473	1.22264
$254$	−11.3936	−0.714898
$255$	6.46757	0.405015
$256$	−28.6254	−1.78909
$257$	−21.9727	−1.37062	−0.685311	−	0.728251i	$-0.740334\pi$
$257$	−21.9727	−1.37062	−0.685311	+	0.728251i	$0.740334\pi$
$258$	−0.716280	−0.0445937
$259$	−7.57400	−0.470626
$260$	−35.0354	−2.17280
$261$	4.11218	0.254537
$262$	−50.0130	−3.08982
$263$	16.4558	1.01471	0.507354	−	0.861738i	$-0.330624\pi$
$263$	16.4558	1.01471	0.507354	+	0.861738i	$0.330624\pi$
$264$	−10.0344	−0.617574
$265$	−0.255290	−0.0156823
$266$	−2.77346	−0.170052
$267$	8.05065	0.492692
$268$	−12.6972	−0.775606
$269$	−20.2351	−1.23375	−0.616876	−	0.787060i	$-0.711602\pi$
$269$	−20.2351	−1.23375	−0.616876	+	0.787060i	$0.711602\pi$
$270$	14.9239	0.908238
$271$	−6.00401	−0.364718	−0.182359	−	0.983232i	$-0.558373\pi$
$271$	−6.00401	−0.364718	−0.182359	+	0.983232i	$0.558373\pi$
$272$	14.6670	0.889320
$273$	8.16822	0.494363
$274$	−9.61387	−0.580795
$275$	−8.07573	−0.486985
$276$	14.4313	0.868659
$277$	14.3843	0.864270	0.432135	−	0.901809i	$-0.357760\pi$
$277$	14.3843	0.864270	0.432135	+	0.901809i	$0.357760\pi$
$278$	−31.8892	−1.91259
$279$	−6.26942	−0.375341
$280$	14.2510	0.851660
$281$	11.5509	0.689072	0.344536	−	0.938773i	$-0.388036\pi$
$281$	11.5509	0.689072	0.344536	+	0.938773i	$0.388036\pi$
$282$	12.8965	0.767973
$283$	−14.2418	−0.846584	−0.423292	−	0.905993i	$-0.639126\pi$
$283$	−14.2418	−0.846584	−0.423292	+	0.905993i	$0.639126\pi$
$284$	−49.2180	−2.92055
$285$	−0.627181	−0.0371510
$286$	47.6199	2.81582
$287$	−19.6626	−1.16065
$288$	−5.70959	−0.336441
$289$	15.9703	0.939431
$290$	6.38637	0.375020
$291$	9.08731	0.532707
$292$	27.9122	1.63344
$293$	25.3576	1.48141	0.740704	−	0.671831i	$-0.234492\pi$
$293$	25.3576	1.48141	0.740704	+	0.671831i	$0.234492\pi$
$294$	4.43001	0.258364
$295$	0.316141	0.0184065
$296$	−15.2842	−0.888376
$297$	−13.2271	−0.767517
$298$	28.5480	1.65374
$299$	−31.9457	−1.84747
$300$	−5.99277	−0.345993
$301$	−0.901617	−0.0519684
$302$	−7.15723	−0.411852
$303$	−7.88209	−0.452814
$304$	−1.42231	−0.0815751
$305$	−13.8436	−0.792685
$306$	34.7777	1.98811
$307$	23.6406	1.34924	0.674620	−	0.738165i	$-0.264308\pi$
$307$	23.6406	1.34924	0.674620	+	0.738165i	$0.264308\pi$
$308$	−27.0782	−1.54292
$309$	9.22393	0.524731
$310$	−9.73665	−0.553005
$311$	0.0366607	0.00207884	0.00103942	−	0.999999i	$-0.499669\pi$
$311$	0.0366607	0.00207884	0.00103942	+	0.999999i	$0.499669\pi$
$312$	16.4833	0.933183
$313$	−6.83334	−0.386243	−0.193122	−	0.981175i	$-0.561861\pi$
$313$	−6.83334	−0.386243	−0.193122	+	0.981175i	$0.561861\pi$
$314$	−4.01666	−0.226673
$315$	8.58734	0.483842
$316$	−10.9443	−0.615664
$317$	19.7147	1.10729	0.553644	−	0.832753i	$-0.313237\pi$
$317$	19.7147	1.10729	0.553644	+	0.832753i	$0.313237\pi$
$318$	0.257489	0.0144393
$319$	−5.66029	−0.316915
$320$	−17.2266	−0.962999
$321$	0.381220	0.0212776
$322$	27.8573	1.55243
$323$	−3.19724	−0.177899
$324$	18.5926	1.03292
$325$	13.2659	0.735857
$326$	34.3757	1.90389
$327$	7.49617	0.414539
$328$	−39.6787	−2.19089
$329$	16.2334	0.894977
$330$	−9.39044	−0.516927
$331$	21.2372	1.16730	0.583651	−	0.812005i	$-0.301624\pi$
$331$	21.2372	1.16730	0.583651	+	0.812005i	$0.301624\pi$
$332$	45.3684	2.48991
$333$	−9.20992	−0.504700
$334$	18.9237	1.03546
$335$	−5.54261	−0.302825
$336$	−3.65281	−0.199277
$337$	−22.2017	−1.20941	−0.604703	−	0.796451i	$-0.706708\pi$
$337$	−22.2017	−1.20941	−0.604703	+	0.796451i	$0.706708\pi$
$338$	−47.0554	−2.55948
$339$	9.27041	0.503500
$340$	35.2198	1.91006
$341$	8.62967	0.467323
$342$	−3.37251	−0.182364
$343$	20.1184	1.08629
$344$	−1.81945	−0.0980979
$345$	6.29956	0.339157
$346$	17.6100	0.946717
$347$	9.81721	0.527015	0.263508	−	0.964657i	$-0.415121\pi$
$347$	9.81721	0.527015	0.263508	+	0.964657i	$0.415121\pi$
$348$	−4.20034	−0.225162
$349$	−14.1074	−0.755151	−0.377576	−	0.925979i	$-0.623242\pi$
$349$	−14.1074	−0.755151	−0.377576	+	0.925979i	$0.623242\pi$
$350$	−11.5681	−0.618342
$351$	21.7280	1.15975
$352$	7.85908	0.418891
$353$	−3.95307	−0.210401	−0.105200	−	0.994451i	$-0.533548\pi$
$353$	−3.95307	−0.210401	−0.105200	+	0.994451i	$0.533548\pi$
$354$	−0.318866	−0.0169475
$355$	−21.4847	−1.14029
$356$	43.8406	2.32355
$357$	−8.21121	−0.434583
$358$	0.256189	0.0135400
$359$	10.5139	0.554901	0.277451	−	0.960740i	$-0.410511\pi$
$359$	10.5139	0.554901	0.277451	+	0.960740i	$0.410511\pi$
$360$	17.3291	0.913322
$361$	−18.6900	−0.983682
$362$	−4.66499	−0.245186
$363$	0.750891	0.0394116
$364$	44.4808	2.33143
$365$	12.1843	0.637755
$366$	13.9629	0.729855
$367$	−29.7848	−1.55476	−0.777378	−	0.629034i	$-0.783451\pi$
$367$	−29.7848	−1.55476	−0.777378	+	0.629034i	$0.783451\pi$
$368$	14.2860	0.744711
$369$	−23.9095	−1.24468
$370$	−14.3034	−0.743596
$371$	0.324115	0.0168272
$372$	6.40383	0.332023
$373$	16.9715	0.878752	0.439376	−	0.898303i	$-0.355200\pi$
$373$	16.9715	0.878752	0.439376	+	0.898303i	$0.355200\pi$
$374$	−47.8705	−2.47532
$375$	−8.24781	−0.425915
$376$	32.7587	1.68940
$377$	9.29805	0.478874
$378$	−18.9473	−0.974543
$379$	−28.9585	−1.48750	−0.743749	−	0.668460i	$-0.766954\pi$
$379$	−28.9585	−1.48750	−0.743749	+	0.668460i	$0.766954\pi$
$380$	−3.41538	−0.175205
$381$	3.27112	0.167585
$382$	16.1486	0.826234
$383$	−18.5438	−0.947541	−0.473771	−	0.880648i	$-0.657107\pi$
$383$	−18.5438	−0.947541	−0.473771	+	0.880648i	$0.657107\pi$
$384$	14.2635	0.727879
$385$	−11.8202	−0.602414
$386$	−12.2650	−0.624273
$387$	−1.09636	−0.0557310
$388$	49.4858	2.51226
$389$	12.5661	0.637127	0.318563	−	0.947902i	$-0.396800\pi$
$389$	12.5661	0.637127	0.318563	+	0.947902i	$0.396800\pi$
$390$	15.4255	0.781101
$391$	32.1138	1.62407
$392$	11.2528	0.568353
$393$	14.3588	0.724308
$394$	−61.7215	−3.10949
$395$	−4.77742	−0.240378
$396$	−32.9268	−1.65463
$397$	21.2213	1.06507	0.532533	−	0.846409i	$-0.321240\pi$
$397$	21.2213	1.06507	0.532533	+	0.846409i	$0.321240\pi$
$398$	59.0217	2.95849
$399$	0.796267	0.0398632
$400$	−5.93246	−0.296623
$401$	−16.9201	−0.844947	−0.422474	−	0.906375i	$-0.638838\pi$
$401$	−16.9201	−0.844947	−0.422474	+	0.906375i	$0.638838\pi$
$402$	5.59038	0.278823
$403$	−14.1758	−0.706147
$404$	−42.9227	−2.13548
$405$	8.11609	0.403292
$406$	−8.10811	−0.402399
$407$	12.6772	0.628384
$408$	−16.5701	−0.820340
$409$	4.54723	0.224846	0.112423	−	0.993660i	$-0.464139\pi$
$409$	4.54723	0.224846	0.112423	+	0.993660i	$0.464139\pi$
$410$	−37.1324	−1.83384
$411$	2.76016	0.136149
$412$	50.2298	2.47465
$413$	−0.401372	−0.0197502
$414$	33.8743	1.66483
$415$	19.8043	0.972154
$416$	−12.9100	−0.632964
$417$	9.15544	0.448344
$418$	4.64216	0.227055
$419$	16.1807	0.790480	0.395240	−	0.918578i	$-0.370661\pi$
$419$	16.1807	0.790480	0.395240	+	0.918578i	$0.370661\pi$
$420$	−8.77144	−0.428002
$421$	33.0192	1.60926	0.804629	−	0.593778i	$-0.202364\pi$
$421$	33.0192	1.60926	0.804629	+	0.593778i	$0.202364\pi$
$422$	−8.25752	−0.401970
$423$	19.7397	0.959776
$424$	0.654057	0.0317638
$425$	−13.3357	−0.646876
$426$	21.6699	1.04991
$427$	17.5758	0.850555
$428$	2.07597	0.100346
$429$	−13.6718	−0.660078
$430$	−1.70269	−0.0821108
$431$	−9.00351	−0.433684	−0.216842	−	0.976207i	$-0.569576\pi$
$431$	−9.00351	−0.433684	−0.216842	+	0.976207i	$0.569576\pi$
$432$	−9.71670	−0.467495
$433$	38.9541	1.87201	0.936006	−	0.351983i	$-0.114492\pi$
$433$	38.9541	1.87201	0.936006	+	0.351983i	$0.114492\pi$
$434$	12.3616	0.593377
$435$	−1.83354	−0.0879114
$436$	40.8211	1.95498
$437$	−3.11418	−0.148971
$438$	−12.2893	−0.587205
$439$	35.1280	1.67657	0.838284	−	0.545234i	$-0.183559\pi$
$439$	35.1280	1.67657	0.838284	+	0.545234i	$0.183559\pi$
$440$	−23.8530	−1.13715
$441$	6.78070	0.322890
$442$	78.6360	3.74033
$443$	11.4493	0.543971	0.271986	−	0.962301i	$-0.412320\pi$
$443$	11.4493	0.543971	0.271986	+	0.962301i	$0.412320\pi$
$444$	9.40737	0.446454
$445$	19.1374	0.907199
$446$	−31.0542	−1.47046
$447$	−8.19618	−0.387666
$448$	21.8709	1.03330
$449$	−17.4637	−0.824162	−0.412081	−	0.911147i	$-0.635198\pi$
$449$	−17.4637	−0.824162	−0.412081	+	0.911147i	$0.635198\pi$
$450$	−14.0667	−0.663112
$451$	32.9108	1.54971
$452$	50.4829	2.37452
$453$	2.05485	0.0965455
$454$	29.4144	1.38048
$455$	19.4168	0.910276
$456$	1.60685	0.0752477
$457$	12.7074	0.594429	0.297215	−	0.954811i	$-0.403942\pi$
$457$	12.7074	0.594429	0.297215	+	0.954811i	$0.403942\pi$
$458$	−29.2168	−1.36521
$459$	−21.8424	−1.01951
$460$	34.3049	1.59947
$461$	−15.3858	−0.716589	−0.358295	−	0.933609i	$-0.616642\pi$
$461$	−15.3858	−0.716589	−0.358295	+	0.933609i	$0.616642\pi$
$462$	11.9221	0.554665
$463$	18.4453	0.857227	0.428614	−	0.903488i	$-0.359002\pi$
$463$	18.4453	0.857227	0.428614	+	0.903488i	$0.359002\pi$
$464$	−4.15807	−0.193033
$465$	2.79541	0.129634
$466$	−60.8269	−2.81775
$467$	35.8605	1.65943	0.829714	−	0.558189i	$-0.188503\pi$
$467$	35.8605	1.65943	0.829714	+	0.558189i	$0.188503\pi$
$468$	54.0883	2.50023
$469$	7.03688	0.324933
$470$	30.6565	1.41408
$471$	1.15319	0.0531362
$472$	−0.809960	−0.0372814
$473$	1.50910	0.0693887
$474$	4.81859	0.221325
$475$	1.29320	0.0593363
$476$	−44.7149	−2.04951
$477$	0.394120	0.0180455
$478$	−48.1236	−2.20112
$479$	−11.6142	−0.530668	−0.265334	−	0.964157i	$-0.585482\pi$
$479$	−11.6142	−0.530668	−0.265334	+	0.964157i	$0.585482\pi$
$480$	2.54579	0.116199
$481$	−20.8246	−0.949519
$482$	20.9843	0.955807
$483$	−7.99790	−0.363917
$484$	4.08905	0.185866
$485$	21.6016	0.980880
$486$	−35.5474	−1.61246
$487$	−14.9852	−0.679045	−0.339523	−	0.940598i	$-0.610266\pi$
$487$	−14.9852	−0.679045	−0.339523	+	0.940598i	$0.610266\pi$
$488$	35.4677	1.60555
$489$	−9.86933	−0.446307
$490$	10.5307	0.475728
$491$	37.9761	1.71384	0.856919	−	0.515451i	$-0.172376\pi$
$491$	37.9761	1.71384	0.856919	+	0.515451i	$0.172376\pi$
$492$	24.4221	1.10103
$493$	−9.34699	−0.420967
$494$	−7.62559	−0.343091
$495$	−14.3733	−0.646030
$496$	6.33939	0.284647
$497$	27.2770	1.22354
$498$	−19.9749	−0.895098
$499$	−34.9215	−1.56330	−0.781651	−	0.623717i	$-0.785622\pi$
$499$	−34.9215	−1.56330	−0.781651	+	0.623717i	$0.785622\pi$
$500$	−44.9142	−2.00863
$501$	−5.43302	−0.242729
$502$	−69.1478	−3.08622
$503$	15.2727	0.680977	0.340489	−	0.940249i	$-0.389408\pi$
$503$	15.2727	0.680977	0.340489	+	0.940249i	$0.389408\pi$
$504$	−22.0009	−0.979999
$505$	−18.7367	−0.833772
$506$	−46.6269	−2.07282
$507$	13.5097	0.599987
$508$	17.8132	0.790334
$509$	17.8801	0.792522	0.396261	−	0.918138i	$-0.370308\pi$
$509$	17.8801	0.792522	0.396261	+	0.918138i	$0.370308\pi$
$510$	−15.5067	−0.686648
$511$	−15.4691	−0.684314
$512$	27.1903	1.20165
$513$	2.11812	0.0935174
$514$	52.6820	2.32370
$515$	21.9264	0.966194
$516$	1.11986	0.0492992
$517$	−27.1711	−1.19498
$518$	18.1595	0.797882
$519$	−5.05585	−0.221927
$520$	39.1828	1.71828
$521$	26.0074	1.13941	0.569703	−	0.821850i	$-0.307058\pi$
$521$	26.0074	1.13941	0.569703	+	0.821850i	$0.307058\pi$
$522$	−9.85938	−0.431533
$523$	−24.9531	−1.09112	−0.545562	−	0.838070i	$-0.683684\pi$
$523$	−24.9531	−1.09112	−0.545562	+	0.838070i	$0.683684\pi$
$524$	78.1925	3.41585
$525$	3.32123	0.144950
$526$	−39.4546	−1.72030
$527$	14.2504	0.620758
$528$	6.11397	0.266077
$529$	8.27956	0.359981
$530$	0.612084	0.0265872
$531$	−0.488064	−0.0211802
$532$	4.33615	0.187996
$533$	−54.0619	−2.34168
$534$	−19.3023	−0.835292
$535$	0.906206	0.0391787
$536$	14.2003	0.613359
$537$	−0.0735524	−0.00317402
$538$	48.5157	2.09166
$539$	−9.33343	−0.402019
$540$	−23.3326	−1.00408
$541$	−4.55188	−0.195701	−0.0978504	−	0.995201i	$-0.531197\pi$
$541$	−4.55188	−0.195701	−0.0978504	+	0.995201i	$0.531197\pi$
$542$	14.3953	0.618330
$543$	1.33933	0.0574760
$544$	12.9779	0.556424
$545$	17.8193	0.763295
$546$	−19.5842	−0.838125
$547$	4.16248	0.177975	0.0889874	−	0.996033i	$-0.471637\pi$
$547$	4.16248	0.177975	0.0889874	+	0.996033i	$0.471637\pi$
$548$	15.0307	0.642081
$549$	21.3721	0.912137
$550$	19.3624	0.825617
$551$	0.906408	0.0386143
$552$	−16.1396	−0.686947
$553$	6.06540	0.257927
$554$	−34.4879	−1.46525
$555$	4.10652	0.174312
$556$	49.8569	2.11440
$557$	21.5715	0.914012	0.457006	−	0.889464i	$-0.348922\pi$
$557$	21.5715	0.914012	0.457006	+	0.889464i	$0.348922\pi$
$558$	15.0316	0.636339
$559$	−2.47898	−0.104850
$560$	−8.68317	−0.366931
$561$	13.7437	0.580260
$562$	−27.6946	−1.16823
$563$	−0.927812	−0.0391026	−0.0195513	−	0.999809i	$-0.506224\pi$
$563$	−0.927812	−0.0391026	−0.0195513	+	0.999809i	$0.506224\pi$
$564$	−20.1629	−0.849010
$565$	22.0369	0.927100
$566$	34.1461	1.43527
$567$	−10.3042	−0.432734
$568$	55.0444	2.30961
$569$	−16.4566	−0.689895	−0.344948	−	0.938622i	$-0.612103\pi$
$569$	−16.4566	−0.689895	−0.344948	+	0.938622i	$0.612103\pi$
$570$	1.50373	0.0629845
$571$	39.7430	1.66319	0.831597	−	0.555380i	$-0.187427\pi$
$571$	39.7430	1.66319	0.831597	+	0.555380i	$0.187427\pi$
$572$	−74.4509	−3.11295
$573$	−4.63629	−0.193684
$574$	47.1432	1.96772
$575$	−12.9892	−0.541689
$576$	26.5948	1.10812
$577$	−23.4697	−0.977056	−0.488528	−	0.872548i	$-0.662466\pi$
$577$	−23.4697	−0.977056	−0.488528	+	0.872548i	$0.662466\pi$
$578$	−38.2906	−1.59268
$579$	3.52131	0.146341
$580$	−9.98471	−0.414593
$581$	−25.1434	−1.04313
$582$	−21.7878	−0.903133
$583$	−0.542495	−0.0224678
$584$	−31.2164	−1.29174
$585$	23.6107	0.976183
$586$	−60.7976	−2.51153
$587$	−25.0725	−1.03485	−0.517426	−	0.855728i	$-0.673110\pi$
$587$	−25.0725	−1.03485	−0.517426	+	0.855728i	$0.673110\pi$
$588$	−6.92607	−0.285626
$589$	−1.38191	−0.0569406
$590$	−0.757982	−0.0312056
$591$	17.7204	0.728919
$592$	9.31269	0.382749
$593$	−11.1270	−0.456931	−0.228466	−	0.973552i	$-0.573371\pi$
$593$	−11.1270	−0.456931	−0.228466	+	0.973552i	$0.573371\pi$
$594$	31.7135	1.30122
$595$	−19.5190	−0.800203
$596$	−44.6331	−1.82824
$597$	−16.9452	−0.693522
$598$	76.5932	3.13213
$599$	−17.1400	−0.700322	−0.350161	−	0.936690i	$-0.613873\pi$
$599$	−17.1400	−0.700322	−0.350161	+	0.936690i	$0.613873\pi$
$600$	6.70218	0.273615
$601$	−15.4224	−0.629093	−0.314547	−	0.949242i	$-0.601853\pi$
$601$	−15.4224	−0.629093	−0.314547	+	0.949242i	$0.601853\pi$
$602$	2.16172	0.0881053
$603$	8.55678	0.348459
$604$	11.1899	0.455311
$605$	1.78496	0.0725689
$606$	18.8981	0.767685
$607$	11.5752	0.469824	0.234912	−	0.972017i	$-0.424520\pi$
$607$	11.5752	0.469824	0.234912	+	0.972017i	$0.424520\pi$
$608$	−1.25851	−0.0510394
$609$	2.32785	0.0943294
$610$	33.1916	1.34389
$611$	44.6334	1.80568
$612$	−54.3729	−2.19790
$613$	−5.34574	−0.215912	−0.107956	−	0.994156i	$-0.534431\pi$
$613$	−5.34574	−0.215912	−0.107956	+	0.994156i	$0.534431\pi$
$614$	−56.6809	−2.28745
$615$	10.6608	0.429884
$616$	30.2836	1.22016
$617$	−38.7858	−1.56146	−0.780729	−	0.624869i	$-0.785152\pi$
$617$	−38.7858	−1.56146	−0.780729	+	0.624869i	$0.785152\pi$
$618$	−22.1154	−0.889611
$619$	6.68061	0.268516	0.134258	−	0.990946i	$-0.457135\pi$
$619$	6.68061	0.268516	0.134258	+	0.990946i	$0.457135\pi$
$620$	15.2227	0.611358
$621$	−21.2749	−0.853734
$622$	−0.0878979	−0.00352439
$623$	−24.2968	−0.973429
$624$	−10.0433	−0.402054
$625$	−7.99360	−0.319744
$626$	16.3837	0.654823
$627$	−1.33277	−0.0532258
$628$	6.27981	0.250592
$629$	20.9342	0.834700
$630$	−20.5891	−0.820288
$631$	−27.1805	−1.08204	−0.541020	−	0.841010i	$-0.681962\pi$
$631$	−27.1805	−1.08204	−0.541020	+	0.841010i	$0.681962\pi$
$632$	12.2399	0.486875
$633$	2.37075	0.0942288
$634$	−47.2681	−1.87726
$635$	7.77586	0.308576
$636$	−0.402570	−0.0159629
$637$	15.3319	0.607470
$638$	13.5711	0.537287
$639$	33.1685	1.31213
$640$	33.9060	1.34025
$641$	14.5946	0.576452	0.288226	−	0.957562i	$-0.406935\pi$
$641$	14.5946	0.576452	0.288226	+	0.957562i	$0.406935\pi$
$642$	−0.914015	−0.0360733
$643$	34.3380	1.35416	0.677078	−	0.735911i	$-0.263246\pi$
$643$	34.3380	1.35416	0.677078	+	0.735911i	$0.263246\pi$
$644$	−43.5533	−1.71624
$645$	0.488844	0.0192482
$646$	7.66572	0.301604
$647$	39.3705	1.54782	0.773908	−	0.633298i	$-0.218299\pi$
$647$	39.3705	1.54782	0.773908	+	0.633298i	$0.218299\pi$
$648$	−20.7936	−0.816849
$649$	0.671806	0.0263707
$650$	−31.8063	−1.24755
$651$	−3.54905	−0.139098
$652$	−53.7444	−2.10479
$653$	39.2073	1.53430	0.767150	−	0.641468i	$-0.221674\pi$
$653$	39.2073	1.53430	0.767150	+	0.641468i	$0.221674\pi$
$654$	−17.9729	−0.702795
$655$	34.1327	1.33368
$656$	24.1763	0.943928
$657$	−18.8103	−0.733861
$658$	−38.9213	−1.51731
$659$	−2.10909	−0.0821583	−0.0410792	−	0.999156i	$-0.513080\pi$
$659$	−2.10909	−0.0821583	−0.0410792	+	0.999156i	$0.513080\pi$
$660$	14.6814	0.571473
$661$	34.8350	1.35492	0.677462	−	0.735557i	$-0.263080\pi$
$661$	34.8350	1.35492	0.677462	+	0.735557i	$0.263080\pi$
$662$	−50.9184	−1.97900
$663$	−22.5765	−0.876800
$664$	−50.7390	−1.96905
$665$	1.89282	0.0734006
$666$	22.0818	0.855651
$667$	−9.10417	−0.352515
$668$	−29.5860	−1.14472
$669$	8.91571	0.344701
$670$	13.2890	0.513399
$671$	−29.4180	−1.13567
$672$	−3.23213	−0.124682
$673$	50.0494	1.92926	0.964632	−	0.263601i	$-0.0849103\pi$
$673$	50.0494	1.92926	0.964632	+	0.263601i	$0.0849103\pi$
$674$	53.2310	2.05038
$675$	8.83469	0.340047
$676$	73.5684	2.82955
$677$	−33.6312	−1.29255	−0.646276	−	0.763104i	$-0.723675\pi$
$677$	−33.6312	−1.29255	−0.646276	+	0.763104i	$0.723675\pi$
$678$	−22.2268	−0.853615
$679$	−27.4254	−1.05249
$680$	−39.3890	−1.51050
$681$	−8.44492	−0.323610
$682$	−20.6906	−0.792283
$683$	−9.55340	−0.365551	−0.182775	−	0.983155i	$-0.558508\pi$
$683$	−9.55340	−0.365551	−0.182775	+	0.983155i	$0.558508\pi$
$684$	5.27272	0.201607
$685$	6.56124	0.250692
$686$	−48.2361	−1.84166
$687$	8.38821	0.320030
$688$	1.10859	0.0422647
$689$	0.891147	0.0339500
$690$	−15.1039	−0.574994
$691$	−31.8951	−1.21335	−0.606673	−	0.794952i	$-0.707496\pi$
$691$	−31.8951	−1.21335	−0.606673	+	0.794952i	$0.707496\pi$
$692$	−27.5321	−1.04661
$693$	18.2482	0.693194
$694$	−23.5378	−0.893483
$695$	21.7636	0.825541
$696$	4.69756	0.178061
$697$	54.3464	2.05852
$698$	33.8240	1.28026
$699$	17.4635	0.660531
$700$	18.0861	0.683590
$701$	−34.2974	−1.29539	−0.647697	−	0.761898i	$-0.724268\pi$
$701$	−34.2974	−1.29539	−0.647697	+	0.761898i	$0.724268\pi$
$702$	−52.0952	−1.96621
$703$	−2.03005	−0.0765649
$704$	−36.6069	−1.37968
$705$	−8.80153	−0.331485
$706$	9.47791	0.356706
$707$	23.7880	0.894641
$708$	0.498528	0.0187358
$709$	−0.626918	−0.0235444	−0.0117722	−	0.999931i	$-0.503747\pi$
$709$	−0.626918	−0.0235444	−0.0117722	+	0.999931i	$0.503747\pi$
$710$	51.5120	1.93321
$711$	7.37547	0.276602
$712$	−49.0304	−1.83749
$713$	13.8802	0.519818
$714$	19.6872	0.736777
$715$	−32.4994	−1.21541
$716$	−0.400537	−0.0149688
$717$	13.8164	0.515982
$718$	−25.2081	−0.940759
$719$	7.73239	0.288369	0.144185	−	0.989551i	$-0.453944\pi$
$719$	7.73239	0.288369	0.144185	+	0.989551i	$0.453944\pi$
$720$	−10.5586	−0.393498
$721$	−27.8377	−1.03673
$722$	44.8112	1.66770
$723$	−6.02462	−0.224058
$724$	7.29343	0.271058
$725$	3.78063	0.140409
$726$	−1.80034	−0.0668169
$727$	30.9028	1.14612	0.573061	−	0.819513i	$-0.305756\pi$
$727$	30.9028	1.14612	0.573061	+	0.819513i	$0.305756\pi$
$728$	−49.7464	−1.84372
$729$	−4.67427	−0.173121
$730$	−29.2132	−1.08123
$731$	2.49203	0.0921709
$732$	−21.8302	−0.806869
$733$	−34.3662	−1.26934	−0.634672	−	0.772782i	$-0.718865\pi$
$733$	−34.3662	−1.26934	−0.634672	+	0.772782i	$0.718865\pi$
$734$	71.4123	2.63588
$735$	−3.02338	−0.111519
$736$	12.6408	0.465945
$737$	−11.7782	−0.433854
$738$	57.3256	2.11019
$739$	34.4120	1.26586	0.632932	−	0.774207i	$-0.281851\pi$
$739$	34.4120	1.26586	0.632932	+	0.774207i	$0.281851\pi$
$740$	22.3625	0.822060
$741$	2.18932	0.0804267
$742$	−0.777100	−0.0285282
$743$	−0.344871	−0.0126521	−0.00632605	−	0.999980i	$-0.502014\pi$
$743$	−0.344871	−0.0126521	−0.00632605	+	0.999980i	$0.502014\pi$
$744$	−7.16190	−0.262568
$745$	−19.4833	−0.713814
$746$	−40.6910	−1.48980
$747$	−30.5742	−1.11865
$748$	74.8427	2.73652
$749$	−1.15052	−0.0420389
$750$	19.7750	0.722081
$751$	−21.4127	−0.781360	−0.390680	−	0.920526i	$-0.627760\pi$
$751$	−21.4127	−0.781360	−0.390680	+	0.920526i	$0.627760\pi$
$752$	−19.9600	−0.727865
$753$	19.8525	0.723464
$754$	−22.2931	−0.811866
$755$	4.88464	0.177770
$756$	29.6230	1.07738
$757$	−5.60307	−0.203647	−0.101824	−	0.994802i	$-0.532468\pi$
$757$	−5.60307	−0.203647	−0.101824	+	0.994802i	$0.532468\pi$
$758$	69.4310	2.52185
$759$	13.3867	0.485906
$760$	3.81968	0.138554
$761$	40.0422	1.45153	0.725764	−	0.687944i	$-0.241486\pi$
$761$	40.0422	1.45153	0.725764	+	0.687944i	$0.241486\pi$
$762$	−7.84287	−0.284117
$763$	−22.6233	−0.819019
$764$	−25.2474	−0.913418
$765$	−23.7350	−0.858140
$766$	44.4606	1.60643
$767$	−1.10356	−0.0398474
$768$	−19.7045	−0.711024
$769$	−22.1127	−0.797405	−0.398703	−	0.917080i	$-0.630539\pi$
$769$	−22.1127	−0.797405	−0.398703	+	0.917080i	$0.630539\pi$
$770$	28.3402	1.02131
$771$	−15.1251	−0.544717
$772$	19.1756	0.690146
$773$	−38.3017	−1.37762	−0.688808	−	0.724944i	$-0.741866\pi$
$773$	−38.3017	−1.37762	−0.688808	+	0.724944i	$0.741866\pi$
$774$	2.62864	0.0944844
$775$	−5.76394	−0.207047
$776$	−55.3438	−1.98673
$777$	−5.21362	−0.187038
$778$	−30.1286	−1.08016
$779$	−5.27015	−0.188823
$780$	−24.1169	−0.863523
$781$	−45.6555	−1.63368
$782$	−76.9963	−2.75338
$783$	6.19224	0.221293
$784$	−6.85637	−0.244870
$785$	2.74127	0.0978403
$786$	−34.4269	−1.22797
$787$	46.2019	1.64692	0.823460	−	0.567374i	$-0.192041\pi$
$787$	46.2019	1.64692	0.823460	+	0.567374i	$0.192041\pi$
$788$	96.4980	3.43760
$789$	11.3275	0.403269
$790$	11.4544	0.407529
$791$	−27.9780	−0.994782
$792$	36.8246	1.30851
$793$	48.3244	1.71605
$794$	−50.8803	−1.80568
$795$	−0.175731	−0.00623252
$796$	−92.2769	−3.27067
$797$	−6.99050	−0.247616	−0.123808	−	0.992306i	$-0.539511\pi$
$797$	−6.99050	−0.247616	−0.123808	+	0.992306i	$0.539511\pi$
$798$	−1.90914	−0.0675827
$799$	−44.8684	−1.58733
$800$	−5.24925	−0.185589
$801$	−29.5446	−1.04391
$802$	40.5677	1.43249
$803$	25.8919	0.913704
$804$	−8.74023	−0.308244
$805$	−19.0120	−0.670084
$806$	33.9880	1.19718
$807$	−13.9290	−0.490322
$808$	48.0038	1.68877
$809$	4.32237	0.151966	0.0759832	−	0.997109i	$-0.475790\pi$
$809$	4.32237	0.151966	0.0759832	+	0.997109i	$0.475790\pi$
$810$	−19.4592	−0.683726
$811$	−19.3037	−0.677845	−0.338923	−	0.940814i	$-0.610062\pi$
$811$	−19.3037	−0.677845	−0.338923	+	0.940814i	$0.610062\pi$
$812$	12.6766	0.444860
$813$	−4.13291	−0.144947
$814$	−30.3949	−1.06534
$815$	−23.4606	−0.821789
$816$	10.0962	0.353437
$817$	−0.241660	−0.00845461
$818$	−10.9025	−0.381196
$819$	−29.9761	−1.04745
$820$	58.0544	2.02735
$821$	−21.0455	−0.734495	−0.367247	−	0.930123i	$-0.619700\pi$
$821$	−21.0455	−0.734495	−0.367247	+	0.930123i	$0.619700\pi$
$822$	−6.61778	−0.230822
$823$	−55.7629	−1.94377	−0.971887	−	0.235448i	$-0.924344\pi$
$823$	−55.7629	−1.94377	−0.971887	+	0.235448i	$0.924344\pi$
$824$	−56.1759	−1.95698
$825$	−5.55899	−0.193539
$826$	0.962332	0.0334838
$827$	−4.37738	−0.152216	−0.0761081	−	0.997100i	$-0.524249\pi$
$827$	−4.37738	−0.152216	−0.0761081	+	0.997100i	$0.524249\pi$
$828$	−52.9604	−1.84050
$829$	3.32468	0.115471	0.0577354	−	0.998332i	$-0.481612\pi$
$829$	3.32468	0.115471	0.0577354	+	0.998332i	$0.481612\pi$
$830$	−47.4829	−1.64815
$831$	9.90155	0.343481
$832$	60.1336	2.08476
$833$	−15.4125	−0.534013
$834$	−21.9512	−0.760106
$835$	−12.9149	−0.446940
$836$	−7.25774	−0.251014
$837$	−9.44070	−0.326318
$838$	−38.7950	−1.34015
$839$	25.4285	0.877891	0.438945	−	0.898514i	$-0.355352\pi$
$839$	25.4285	0.877891	0.438945	+	0.898514i	$0.355352\pi$
$840$	9.80978	0.338470
$841$	−26.3502	−0.908626
$842$	−79.1671	−2.72828
$843$	7.95118	0.273853
$844$	12.9101	0.444385
$845$	32.1142	1.10476
$846$	−47.3280	−1.62717
$847$	−2.26618	−0.0778668
$848$	−0.398519	−0.0136852
$849$	−9.80342	−0.336453
$850$	31.9737	1.09669
$851$	20.3903	0.698972
$852$	−33.8796	−1.16070
$853$	−40.1533	−1.37482	−0.687412	−	0.726268i	$-0.741253\pi$
$853$	−40.1533	−1.37482	−0.687412	+	0.726268i	$0.741253\pi$
$854$	−42.1400	−1.44200
$855$	2.30166	0.0787150
$856$	−2.32172	−0.0793547
$857$	−55.9859	−1.91244	−0.956221	−	0.292646i	$-0.905464\pi$
$857$	−55.9859	−1.91244	−0.956221	+	0.292646i	$0.905464\pi$
$858$	32.7795	1.11907
$859$	9.55017	0.325847	0.162924	−	0.986639i	$-0.447908\pi$
$859$	9.55017	0.325847	0.162924	+	0.986639i	$0.447908\pi$
$860$	2.66205	0.0907752
$861$	−13.5349	−0.461268
$862$	21.5869	0.735252
$863$	44.1300	1.50220	0.751101	−	0.660187i	$-0.229523\pi$
$863$	44.1300	1.50220	0.751101	+	0.660187i	$0.229523\pi$
$864$	−8.59768	−0.292499
$865$	−12.0184	−0.408637
$866$	−93.3965	−3.17374
$867$	10.9933	0.373352
$868$	−19.3267	−0.655990
$869$	−10.1521	−0.344387
$870$	4.39610	0.149042
$871$	19.3478	0.655574
$872$	−45.6534	−1.54602
$873$	−33.3490	−1.12869
$874$	7.46658	0.252561
$875$	24.8918	0.841495
$876$	19.2136	0.649167
$877$	19.2148	0.648837	0.324418	−	0.945914i	$-0.394831\pi$
$877$	19.2148	0.648837	0.324418	+	0.945914i	$0.394831\pi$
$878$	−84.2231	−2.84239
$879$	17.4551	0.588746
$880$	14.5337	0.489930
$881$	8.33683	0.280875	0.140437	−	0.990090i	$-0.455149\pi$
$881$	8.33683	0.280875	0.140437	+	0.990090i	$0.455149\pi$
$882$	−16.2574	−0.547417
$883$	−24.6875	−0.830801	−0.415400	−	0.909639i	$-0.636358\pi$
$883$	−24.6875	−0.830801	−0.415400	+	0.909639i	$0.636358\pi$
$884$	−122.943	−4.13501
$885$	0.217618	0.00731516
$886$	−27.4509	−0.922229
$887$	−33.8982	−1.13819	−0.569094	−	0.822272i	$-0.692706\pi$
$887$	−33.8982	−1.13819	−0.569094	+	0.822272i	$0.692706\pi$
$888$	−10.5210	−0.353061
$889$	−9.87221	−0.331103
$890$	−45.8839	−1.53803
$891$	17.2468	0.577791
$892$	48.5514	1.62562
$893$	4.35103	0.145602
$894$	19.6512	0.657235
$895$	−0.174843	−0.00584436
$896$	−43.0469	−1.43810
$897$	−21.9901	−0.734226
$898$	41.8710	1.39725
$899$	−4.03995	−0.134740
$900$	21.9925	0.733084
$901$	−0.895837	−0.0298447
$902$	−78.9070	−2.62732
$903$	−0.620635	−0.0206534
$904$	−56.4590	−1.87780
$905$	3.18374	0.105831
$906$	−4.92673	−0.163680
$907$	−25.8498	−0.858329	−0.429165	−	0.903226i	$-0.641192\pi$
$907$	−25.8498	−0.858329	−0.429165	+	0.903226i	$0.641192\pi$
$908$	−45.9876	−1.52615
$909$	28.9260	0.959415
$910$	−46.5540	−1.54325
$911$	12.8436	0.425527	0.212763	−	0.977104i	$-0.431754\pi$
$911$	12.8436	0.425527	0.212763	+	0.977104i	$0.431754\pi$
$912$	−0.979058	−0.0324199
$913$	42.0845	1.39279
$914$	−30.4675	−1.00777
$915$	−9.52938	−0.315032
$916$	45.6788	1.50927
$917$	−43.3348	−1.43104
$918$	52.3694	1.72845
$919$	−23.7654	−0.783948	−0.391974	−	0.919976i	$-0.628208\pi$
$919$	−23.7654	−0.783948	−0.391974	+	0.919976i	$0.628208\pi$
$920$	−38.3658	−1.26488
$921$	16.2732	0.536220
$922$	36.8892	1.21488
$923$	74.9974	2.46857
$924$	−18.6395	−0.613193
$925$	−8.46736	−0.278405
$926$	−44.2247	−1.45331
$927$	−33.8504	−1.11179
$928$	−3.67920	−0.120776
$929$	−57.9961	−1.90279	−0.951395	−	0.307974i	$-0.900349\pi$
$929$	−57.9961	−1.90279	−0.951395	+	0.307974i	$0.900349\pi$
$930$	−6.70230	−0.219777
$931$	1.49460	0.0489837
$932$	95.0993	3.11508
$933$	0.0252357	0.000826179 0
$934$	−85.9795	−2.81333
$935$	32.6705	1.06844
$936$	−60.4911	−1.97721
$937$	−13.4028	−0.437850	−0.218925	−	0.975742i	$-0.570255\pi$
$937$	−13.4028	−0.437850	−0.218925	+	0.975742i	$0.570255\pi$
$938$	−16.8717	−0.550880
$939$	−4.70378	−0.153502
$940$	−47.9296	−1.56329
$941$	−2.47859	−0.0807999	−0.0403999	−	0.999184i	$-0.512863\pi$
$941$	−2.47859	−0.0807999	−0.0403999	+	0.999184i	$0.512863\pi$
$942$	−2.76490	−0.0900852
$943$	52.9346	1.72379
$944$	0.493511	0.0160624
$945$	12.9311	0.420648
$946$	−3.61824	−0.117639
$947$	4.56159	0.148232	0.0741159	−	0.997250i	$-0.476387\pi$
$947$	4.56159	0.148232	0.0741159	+	0.997250i	$0.476387\pi$
$948$	−7.53358	−0.244679
$949$	−42.5321	−1.38065
$950$	−3.10059	−0.100597
$951$	13.5708	0.440062
$952$	50.0082	1.62077
$953$	50.9687	1.65104	0.825519	−	0.564374i	$-0.190883\pi$
$953$	50.9687	1.65104	0.825519	+	0.564374i	$0.190883\pi$
$954$	−0.944946	−0.0305937
$955$	−11.0210	−0.356632
$956$	75.2384	2.43338
$957$	−3.89630	−0.125950
$958$	27.8464	0.899676
$959$	−8.33013	−0.268994
$960$	−11.8581	−0.382718
$961$	−24.8407	−0.801312
$962$	49.9291	1.60978
$963$	−1.39902	−0.0450827
$964$	−32.8077	−1.05666
$965$	8.37059	0.269459
$966$	19.1758	0.616972
$967$	44.5686	1.43323	0.716615	−	0.697469i	$-0.245690\pi$
$967$	44.5686	1.43323	0.716615	+	0.697469i	$0.245690\pi$
$968$	−4.57310	−0.146985
$969$	−2.20084	−0.0707013
$970$	−51.7923	−1.66295
$971$	16.5537	0.531233	0.265616	−	0.964079i	$-0.414425\pi$
$971$	16.5537	0.531233	0.265616	+	0.964079i	$0.414425\pi$
$972$	55.5762	1.78261
$973$	−27.6310	−0.885809
$974$	35.9287	1.15123
$975$	9.13165	0.292447
$976$	−21.6106	−0.691737
$977$	−12.8157	−0.410009	−0.205005	−	0.978761i	$-0.565721\pi$
$977$	−12.8157	−0.410009	−0.205005	+	0.978761i	$0.565721\pi$
$978$	23.6628	0.756652
$979$	40.6673	1.29973
$980$	−16.4641	−0.525927
$981$	−27.5098	−0.878319
$982$	−91.0518	−2.90558
$983$	−26.9296	−0.858921	−0.429461	−	0.903086i	$-0.641296\pi$
$983$	−26.9296	−0.858921	−0.429461	+	0.903086i	$0.641296\pi$
$984$	−27.3132	−0.870711
$985$	42.1235	1.34217
$986$	22.4104	0.713693
$987$	11.1744	0.355685
$988$	11.9222	0.379294
$989$	2.42729	0.0771833
$990$	34.4614	1.09526
$991$	24.4697	0.777307	0.388653	−	0.921384i	$-0.372940\pi$
$991$	24.4697	0.777307	0.388653	+	0.921384i	$0.372940\pi$
$992$	5.60931	0.178096
$993$	14.6188	0.463913
$994$	−65.3994	−2.07434
$995$	−40.2809	−1.27699
$996$	31.2297	0.989549
$997$	−54.2250	−1.71732	−0.858661	−	0.512544i	$-0.828703\pi$
$997$	−54.2250	−1.71732	−0.858661	+	0.512544i	$0.828703\pi$
$998$	83.7280	2.65036
$999$	−13.8686	−0.438783

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.c.1.17	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.c.1.17	✓	176	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)

\(f(q)\)	\(=\)	\(q-2.39761 q^{2} +0.688358 q^{3} +3.74852 q^{4} +1.63631 q^{5} -1.65041 q^{6} -2.07745 q^{7} -4.19226 q^{8} -2.52616 q^{9} +O(q^{10})\)	\(q-2.39761 q^{2} +0.688358 q^{3} +3.74852 q^{4} +1.63631 q^{5} -1.65041 q^{6} -2.07745 q^{7} -4.19226 q^{8} -2.52616 q^{9} -3.92323 q^{10} +3.47719 q^{11} +2.58032 q^{12} -5.71192 q^{13} +4.98092 q^{14} +1.12637 q^{15} +2.55435 q^{16} +5.74198 q^{17} +6.05675 q^{18} -0.556818 q^{19} +6.13374 q^{20} -1.43003 q^{21} -8.33693 q^{22} +5.59281 q^{23} -2.88577 q^{24} -2.32249 q^{25} +13.6949 q^{26} -3.80398 q^{27} -7.78737 q^{28} -1.62783 q^{29} -2.70058 q^{30} +2.48180 q^{31} +2.26018 q^{32} +2.39355 q^{33} -13.7670 q^{34} -3.39936 q^{35} -9.46937 q^{36} +3.64581 q^{37} +1.33503 q^{38} -3.93184 q^{39} -6.85984 q^{40} +9.46476 q^{41} +3.42865 q^{42} +0.434001 q^{43} +13.0343 q^{44} -4.13359 q^{45} -13.4094 q^{46} -7.81409 q^{47} +1.75831 q^{48} -2.68419 q^{49} +5.56841 q^{50} +3.95253 q^{51} -21.4112 q^{52} -0.156015 q^{53} +9.12044 q^{54} +5.68976 q^{55} +8.70922 q^{56} -0.383290 q^{57} +3.90291 q^{58} +0.193204 q^{59} +4.22221 q^{60} -8.46028 q^{61} -5.95037 q^{62} +5.24799 q^{63} -10.5277 q^{64} -9.34647 q^{65} -5.73879 q^{66} -3.38726 q^{67} +21.5239 q^{68} +3.84986 q^{69} +8.15032 q^{70} -13.1300 q^{71} +10.5903 q^{72} +7.44620 q^{73} -8.74122 q^{74} -1.59870 q^{75} -2.08724 q^{76} -7.22370 q^{77} +9.42701 q^{78} -2.91963 q^{79} +4.17972 q^{80} +4.96000 q^{81} -22.6928 q^{82} +12.1030 q^{83} -5.36050 q^{84} +9.39566 q^{85} -1.04056 q^{86} -1.12053 q^{87} -14.5773 q^{88} +11.6955 q^{89} +9.91072 q^{90} +11.8662 q^{91} +20.9648 q^{92} +1.70836 q^{93} +18.7351 q^{94} -0.911127 q^{95} +1.55581 q^{96} +13.2014 q^{97} +6.43563 q^{98} -8.78395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * q^99

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