LMFDB - Embedded newform 4013.2.a.c.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0439663311$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28329 q^{2} +3.29602 q^{3} +3.21343 q^{4} +1.63708 q^{5} -7.52578 q^{6} -3.76844 q^{7} -2.77062 q^{8} +7.86375 q^{9} +O(q^{10})$	\(q-2.28329 q^{2} +3.29602 q^{3} +3.21343 q^{4} +1.63708 q^{5} -7.52578 q^{6} -3.76844 q^{7} -2.77062 q^{8} +7.86375 q^{9} -3.73794 q^{10} +5.13294 q^{11} +10.5915 q^{12} +2.85851 q^{13} +8.60445 q^{14} +5.39585 q^{15} -0.100716 q^{16} +3.51225 q^{17} -17.9553 q^{18} +3.70095 q^{19} +5.26065 q^{20} -12.4208 q^{21} -11.7200 q^{22} -3.14801 q^{23} -9.13203 q^{24} -2.31997 q^{25} -6.52682 q^{26} +16.0310 q^{27} -12.1096 q^{28} +9.94218 q^{29} -12.3203 q^{30} -3.08319 q^{31} +5.77121 q^{32} +16.9183 q^{33} -8.01950 q^{34} -6.16923 q^{35} +25.2696 q^{36} -2.53665 q^{37} -8.45037 q^{38} +9.42170 q^{39} -4.53573 q^{40} -0.363405 q^{41} +28.3604 q^{42} -2.66508 q^{43} +16.4943 q^{44} +12.8736 q^{45} +7.18784 q^{46} +5.01845 q^{47} -0.331961 q^{48} +7.20111 q^{49} +5.29717 q^{50} +11.5764 q^{51} +9.18563 q^{52} +5.54811 q^{53} -36.6035 q^{54} +8.40303 q^{55} +10.4409 q^{56} +12.1984 q^{57} -22.7009 q^{58} -8.02532 q^{59} +17.3392 q^{60} -10.9118 q^{61} +7.03982 q^{62} -29.6340 q^{63} -12.9759 q^{64} +4.67961 q^{65} -38.6294 q^{66} +1.06710 q^{67} +11.2864 q^{68} -10.3759 q^{69} +14.0862 q^{70} -11.3825 q^{71} -21.7875 q^{72} -10.4275 q^{73} +5.79192 q^{74} -7.64666 q^{75} +11.8928 q^{76} -19.3431 q^{77} -21.5125 q^{78} +10.9674 q^{79} -0.164880 q^{80} +29.2473 q^{81} +0.829761 q^{82} +9.75776 q^{83} -39.9135 q^{84} +5.74983 q^{85} +6.08516 q^{86} +32.7696 q^{87} -14.2214 q^{88} -17.8087 q^{89} -29.3942 q^{90} -10.7721 q^{91} -10.1159 q^{92} -10.1622 q^{93} -11.4586 q^{94} +6.05876 q^{95} +19.0220 q^{96} +1.31502 q^{97} -16.4422 q^{98} +40.3641 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.28329	−1.61453	−0.807266	−	0.590187i	$-0.799054\pi$
$2$	−2.28329	−1.61453	−0.807266	+	0.590187i	$0.799054\pi$
$3$	3.29602	1.90296	0.951479	−	0.307714i	$-0.0995639\pi$
$3$	3.29602	1.90296	0.951479	+	0.307714i	$0.0995639\pi$
$4$	3.21343	1.60672
$5$	1.63708	0.732125	0.366062	−	0.930590i	$-0.380706\pi$
$5$	1.63708	0.732125	0.366062	+	0.930590i	$0.380706\pi$
$6$	−7.52578	−3.07239
$7$	−3.76844	−1.42433	−0.712167	−	0.702010i	$-0.752286\pi$
$7$	−3.76844	−1.42433	−0.712167	+	0.702010i	$0.752286\pi$
$8$	−2.77062	−0.979563
$9$	7.86375	2.62125
$10$	−3.73794	−1.18204
$11$	5.13294	1.54764	0.773819	−	0.633406i	$-0.218344\pi$
$11$	5.13294	1.54764	0.773819	+	0.633406i	$0.218344\pi$
$12$	10.5915	3.05751
$13$	2.85851	0.792808	0.396404	−	0.918076i	$-0.370258\pi$
$13$	2.85851	0.792808	0.396404	+	0.918076i	$0.370258\pi$
$14$	8.60445	2.29964
$15$	5.39585	1.39320
$16$	−0.100716	−0.0251789
$17$	3.51225	0.851846	0.425923	−	0.904759i	$-0.359949\pi$
$17$	3.51225	0.851846	0.425923	+	0.904759i	$0.359949\pi$
$18$	−17.9553	−4.23209
$19$	3.70095	0.849057	0.424529	−	0.905415i	$-0.360440\pi$
$19$	3.70095	0.849057	0.424529	+	0.905415i	$0.360440\pi$
$20$	5.26065	1.17632
$21$	−12.4208	−2.71045
$22$	−11.7200	−2.49871
$23$	−3.14801	−0.656406	−0.328203	−	0.944607i	$-0.606443\pi$
$23$	−3.14801	−0.656406	−0.328203	+	0.944607i	$0.606443\pi$
$24$	−9.13203	−1.86407
$25$	−2.31997	−0.463994
$26$	−6.52682	−1.28001
$27$	16.0310	3.08517
$28$	−12.1096	−2.28850
$29$	9.94218	1.84622	0.923109	−	0.384539i	$-0.125640\pi$
$29$	9.94218	1.84622	0.923109	+	0.384539i	$0.125640\pi$
$30$	−12.3203	−2.24937
$31$	−3.08319	−0.553757	−0.276878	−	0.960905i	$-0.589300\pi$
$31$	−3.08319	−0.553757	−0.276878	+	0.960905i	$0.589300\pi$
$32$	5.77121	1.02022
$33$	16.9183	2.94509
$34$	−8.01950	−1.37533
$35$	−6.16923	−1.04279
$36$	25.2696	4.21160
$37$	−2.53665	−0.417023	−0.208511	−	0.978020i	$-0.566862\pi$
$37$	−2.53665	−0.417023	−0.208511	+	0.978020i	$0.566862\pi$
$38$	−8.45037	−1.37083
$39$	9.42170	1.50868
$40$	−4.53573	−0.717162
$41$	−0.363405	−0.0567543	−0.0283772	−	0.999597i	$-0.509034\pi$
$41$	−0.363405	−0.0567543	−0.0283772	+	0.999597i	$0.509034\pi$
$42$	28.3604	4.37611
$43$	−2.66508	−0.406421	−0.203210	−	0.979135i	$-0.565138\pi$
$43$	−2.66508	−0.406421	−0.203210	+	0.979135i	$0.565138\pi$
$44$	16.4943	2.48662
$45$	12.8736	1.91908
$46$	7.18784	1.05979
$47$	5.01845	0.732016	0.366008	−	0.930612i	$-0.380724\pi$
$47$	5.01845	0.732016	0.366008	+	0.930612i	$0.380724\pi$
$48$	−0.331961	−0.0479144
$49$	7.20111	1.02873
$50$	5.29717	0.749133
$51$	11.5764	1.62103
$52$	9.18563	1.27382
$53$	5.54811	0.762092	0.381046	−	0.924556i	$-0.375564\pi$
$53$	5.54811	0.762092	0.381046	+	0.924556i	$0.375564\pi$
$54$	−36.6035	−4.98111
$55$	8.40303	1.13306
$56$	10.4409	1.39523
$57$	12.1984	1.61572
$58$	−22.7009	−2.98078
$59$	−8.02532	−1.04481	−0.522404	−	0.852698i	$-0.674965\pi$
$59$	−8.02532	−1.04481	−0.522404	+	0.852698i	$0.674965\pi$
$60$	17.3392	2.23848
$61$	−10.9118	−1.39712	−0.698558	−	0.715554i	$-0.746174\pi$
$61$	−10.9118	−1.39712	−0.698558	+	0.715554i	$0.746174\pi$
$62$	7.03982	0.894058
$63$	−29.6340	−3.73354
$64$	−12.9759	−1.62199
$65$	4.67961	0.580434
$66$	−38.6294	−4.75495
$67$	1.06710	0.130366	0.0651832	−	0.997873i	$-0.479237\pi$
$67$	1.06710	0.130366	0.0651832	+	0.997873i	$0.479237\pi$
$68$	11.2864	1.36867
$69$	−10.3759	−1.24911
$70$	14.0862	1.68362
$71$	−11.3825	−1.35085	−0.675424	−	0.737429i	$-0.736039\pi$
$71$	−11.3825	−1.35085	−0.675424	+	0.737429i	$0.736039\pi$
$72$	−21.7875	−2.56768
$73$	−10.4275	−1.22045	−0.610225	−	0.792228i	$-0.708921\pi$
$73$	−10.4275	−1.22045	−0.610225	+	0.792228i	$0.708921\pi$
$74$	5.79192	0.673297
$75$	−7.64666	−0.882961
$76$	11.8928	1.36419
$77$	−19.3431	−2.20436
$78$	−21.5125	−2.43581
$79$	10.9674	1.23393	0.616967	−	0.786989i	$-0.288361\pi$
$79$	10.9674	1.23393	0.616967	+	0.786989i	$0.288361\pi$
$80$	−0.164880	−0.0184341
$81$	29.2473	3.24970
$82$	0.829761	0.0916317
$83$	9.75776	1.07105	0.535527	−	0.844518i	$-0.320113\pi$
$83$	9.75776	1.07105	0.535527	+	0.844518i	$0.320113\pi$
$84$	−39.9135	−4.35492
$85$	5.74983	0.623657
$86$	6.08516	0.656180
$87$	32.7696	3.51327
$88$	−14.2214	−1.51601
$89$	−17.8087	−1.88771	−0.943857	−	0.330355i	$-0.892831\pi$
$89$	−17.8087	−1.88771	−0.943857	+	0.330355i	$0.892831\pi$
$90$	−29.3942	−3.09842
$91$	−10.7721	−1.12922
$92$	−10.1159	−1.05466
$93$	−10.1622	−1.05378
$94$	−11.4586	−1.18186
$95$	6.05876	0.621616
$96$	19.0220	1.94143
$97$	1.31502	0.133520	0.0667599	−	0.997769i	$-0.478734\pi$
$97$	1.31502	0.133520	0.0667599	+	0.997769i	$0.478734\pi$
$98$	−16.4422	−1.66092
$99$	40.3641	4.05675
$100$	−7.45506	−0.745506
$101$	−16.1334	−1.60534	−0.802669	−	0.596425i	$-0.796587\pi$
$101$	−16.1334	−1.60534	−0.802669	+	0.596425i	$0.796587\pi$
$102$	−26.4324	−2.61720
$103$	−18.6026	−1.83297	−0.916486	−	0.400066i	$-0.868987\pi$
$103$	−18.6026	−1.83297	−0.916486	+	0.400066i	$0.868987\pi$
$104$	−7.91985	−0.776606
$105$	−20.3339	−1.98439
$106$	−12.6680	−1.23042
$107$	17.2356	1.66623	0.833114	−	0.553101i	$-0.186556\pi$
$107$	17.2356	1.66623	0.833114	+	0.553101i	$0.186556\pi$
$108$	51.5146	4.95699
$109$	9.94141	0.952214	0.476107	−	0.879387i	$-0.342047\pi$
$109$	9.94141	0.952214	0.476107	+	0.879387i	$0.342047\pi$
$110$	−19.1866	−1.82937
$111$	−8.36085	−0.793577
$112$	0.379540	0.0358632
$113$	8.94228	0.841219	0.420609	−	0.907242i	$-0.361816\pi$
$113$	8.94228	0.841219	0.420609	+	0.907242i	$0.361816\pi$
$114$	−27.8526	−2.60863
$115$	−5.15355	−0.480571
$116$	31.9485	2.96635
$117$	22.4786	2.07815
$118$	18.3242	1.68688
$119$	−13.2357	−1.21331
$120$	−14.9499	−1.36473
$121$	15.3470	1.39519
$122$	24.9149	2.25569
$123$	−1.19779	−0.108001
$124$	−9.90761	−0.889730
$125$	−11.9834	−1.07183
$126$	67.6632	6.02792
$127$	3.31157	0.293855	0.146927	−	0.989147i	$-0.453062\pi$
$127$	3.31157	0.293855	0.146927	+	0.989147i	$0.453062\pi$
$128$	18.0855	1.59855
$129$	−8.78416	−0.773402
$130$	−10.6849	−0.937130
$131$	7.84864	0.685739	0.342870	−	0.939383i	$-0.388601\pi$
$131$	7.84864	0.685739	0.342870	+	0.939383i	$0.388601\pi$
$132$	54.3657	4.73193
$133$	−13.9468	−1.20934
$134$	−2.43649	−0.210481
$135$	26.2441	2.25873
$136$	−9.73112	−0.834437
$137$	−12.4804	−1.06627	−0.533137	−	0.846029i	$-0.678987\pi$
$137$	−12.4804	−1.06627	−0.533137	+	0.846029i	$0.678987\pi$
$138$	23.6913	2.01673
$139$	−11.8117	−1.00186	−0.500928	−	0.865489i	$-0.667008\pi$
$139$	−11.8117	−1.00186	−0.500928	+	0.865489i	$0.667008\pi$
$140$	−19.8244	−1.67547
$141$	16.5409	1.39300
$142$	25.9895	2.18099
$143$	14.6725	1.22698
$144$	−0.792002	−0.0660002
$145$	16.2762	1.35166
$146$	23.8091	1.97046
$147$	23.7350	1.95763
$148$	−8.15136	−0.670037
$149$	7.94855	0.651171	0.325585	−	0.945513i	$-0.394439\pi$
$149$	7.94855	0.651171	0.325585	+	0.945513i	$0.394439\pi$
$150$	17.4596	1.42557
$151$	−13.0129	−1.05897	−0.529487	−	0.848318i	$-0.677616\pi$
$151$	−13.0129	−1.05897	−0.529487	+	0.848318i	$0.677616\pi$
$152$	−10.2540	−0.831706
$153$	27.6194	2.23290
$154$	44.1661	3.55900
$155$	−5.04742	−0.405419
$156$	30.2760	2.42402
$157$	18.9910	1.51564	0.757822	−	0.652461i	$-0.226263\pi$
$157$	18.9910	1.51564	0.757822	+	0.652461i	$0.226263\pi$
$158$	−25.0419	−1.99223
$159$	18.2867	1.45023
$160$	9.44794	0.746925
$161$	11.8631	0.934942
$162$	−66.7802	−5.24675
$163$	18.7431	1.46807	0.734036	−	0.679111i	$-0.237635\pi$
$163$	18.7431	1.46807	0.734036	+	0.679111i	$0.237635\pi$
$164$	−1.16778	−0.0911881
$165$	27.6965	2.15617
$166$	−22.2798	−1.72925
$167$	−2.35619	−0.182327	−0.0911637	−	0.995836i	$-0.529059\pi$
$167$	−2.35619	−0.182327	−0.0911637	+	0.995836i	$0.529059\pi$
$168$	34.4135	2.65506
$169$	−4.82893	−0.371456
$170$	−13.1286	−1.00691
$171$	29.1034	2.22559
$172$	−8.56405	−0.653003
$173$	8.19758	0.623251	0.311625	−	0.950205i	$-0.399127\pi$
$173$	8.19758	0.623251	0.311625	+	0.950205i	$0.399127\pi$
$174$	−74.8227	−5.67230
$175$	8.74265	0.660882
$176$	−0.516967	−0.0389678
$177$	−26.4516	−1.98822
$178$	40.6624	3.04778
$179$	13.0810	0.977717	0.488859	−	0.872363i	$-0.337413\pi$
$179$	13.0810	0.977717	0.488859	+	0.872363i	$0.337413\pi$
$180$	41.3684	3.08342
$181$	−22.9222	−1.70380	−0.851898	−	0.523707i	$-0.824549\pi$
$181$	−22.9222	−1.70380	−0.851898	+	0.523707i	$0.824549\pi$
$182$	24.5959	1.82317
$183$	−35.9656	−2.65865
$184$	8.72196	0.642991
$185$	−4.15270	−0.305313
$186$	23.2034	1.70136
$187$	18.0282	1.31835
$188$	16.1264	1.17614
$189$	−60.4118	−4.39431
$190$	−13.8339	−1.00362
$191$	−5.40971	−0.391433	−0.195716	−	0.980661i	$-0.562703\pi$
$191$	−5.40971	−0.391433	−0.195716	+	0.980661i	$0.562703\pi$
$192$	−42.7690	−3.08658
$193$	7.06741	0.508724	0.254362	−	0.967109i	$-0.418135\pi$
$193$	7.06741	0.508724	0.254362	+	0.967109i	$0.418135\pi$
$194$	−3.00257	−0.215572
$195$	15.4241	1.10454
$196$	23.1403	1.65288
$197$	−12.7431	−0.907909	−0.453955	−	0.891025i	$-0.649987\pi$
$197$	−12.7431	−0.907909	−0.453955	+	0.891025i	$0.649987\pi$
$198$	−92.1632	−6.54975
$199$	−1.60695	−0.113913	−0.0569567	−	0.998377i	$-0.518140\pi$
$199$	−1.60695	−0.113913	−0.0569567	+	0.998377i	$0.518140\pi$
$200$	6.42776	0.454511
$201$	3.51717	0.248082
$202$	36.8374	2.59187
$203$	−37.4665	−2.62963
$204$	37.2001	2.60453
$205$	−0.594923	−0.0415512
$206$	42.4753	2.95939
$207$	−24.7552	−1.72060
$208$	−0.287896	−0.0199620
$209$	18.9968	1.31403
$210$	46.4283	3.20386
$211$	0.0339444	0.00233683	0.00116841	−	0.999999i	$-0.499628\pi$
$211$	0.0339444	0.00233683	0.00116841	+	0.999999i	$0.499628\pi$
$212$	17.8285	1.22447
$213$	−37.5168	−2.57061
$214$	−39.3539	−2.69018
$215$	−4.36295	−0.297551
$216$	−44.4159	−3.02212
$217$	11.6188	0.788735
$218$	−22.6992	−1.53738
$219$	−34.3694	−2.32247
$220$	27.0026	1.82051
$221$	10.0398	0.675350
$222$	19.0903	1.28126
$223$	26.2717	1.75928	0.879641	−	0.475638i	$-0.157783\pi$
$223$	26.2717	1.75928	0.879641	+	0.475638i	$0.157783\pi$
$224$	−21.7484	−1.45313
$225$	−18.2436	−1.21624
$226$	−20.4179	−1.35818
$227$	14.0582	0.933076	0.466538	−	0.884501i	$-0.345501\pi$
$227$	14.0582	0.933076	0.466538	+	0.884501i	$0.345501\pi$
$228$	39.1988	2.59600
$229$	22.3464	1.47669	0.738347	−	0.674421i	$-0.235607\pi$
$229$	22.3464	1.47669	0.738347	+	0.674421i	$0.235607\pi$
$230$	11.7671	0.775898
$231$	−63.7554	−4.19480
$232$	−27.5461	−1.80849
$233$	20.8020	1.36278	0.681391	−	0.731919i	$-0.261375\pi$
$233$	20.8020	1.36278	0.681391	+	0.731919i	$0.261375\pi$
$234$	−51.3252	−3.35524
$235$	8.21560	0.535927
$236$	−25.7888	−1.67871
$237$	36.1489	2.34812
$238$	30.2210	1.95893
$239$	−18.1966	−1.17704	−0.588520	−	0.808483i	$-0.700289\pi$
$239$	−18.1966	−1.17704	−0.588520	+	0.808483i	$0.700289\pi$
$240$	−0.543446	−0.0350793
$241$	−16.0843	−1.03608	−0.518042	−	0.855355i	$-0.673339\pi$
$241$	−16.0843	−1.03608	−0.518042	+	0.855355i	$0.673339\pi$
$242$	−35.0418	−2.25257
$243$	48.3066	3.09887
$244$	−35.0644	−2.24477
$245$	11.7888	0.753158
$246$	2.73491	0.174371
$247$	10.5792	0.673139
$248$	8.54235	0.542440
$249$	32.1618	2.03817
$250$	27.3616	1.73050
$251$	−0.185824	−0.0117291	−0.00586456	−	0.999983i	$-0.501867\pi$
$251$	−0.185824	−0.0117291	−0.00586456	+	0.999983i	$0.501867\pi$
$252$	−95.2270	−5.99873
$253$	−16.1586	−1.01588
$254$	−7.56130	−0.474438
$255$	18.9516	1.18679
$256$	−15.3426	−0.958911
$257$	−13.4681	−0.840114	−0.420057	−	0.907498i	$-0.637990\pi$
$257$	−13.4681	−0.840114	−0.420057	+	0.907498i	$0.637990\pi$
$258$	20.0568	1.24868
$259$	9.55920	0.593980
$260$	15.0376	0.932593
$261$	78.1828	4.83940
$262$	−17.9208	−1.10715
$263$	−18.3684	−1.13264	−0.566322	−	0.824184i	$-0.691634\pi$
$263$	−18.3684	−1.13264	−0.566322	+	0.824184i	$0.691634\pi$
$264$	−46.8741	−2.88490
$265$	9.08271	0.557946
$266$	31.8447	1.95252
$267$	−58.6977	−3.59224
$268$	3.42904	0.209462
$269$	−7.99628	−0.487542	−0.243771	−	0.969833i	$-0.578385\pi$
$269$	−7.99628	−0.487542	−0.243771	+	0.969833i	$0.578385\pi$
$270$	−59.9229	−3.64679
$271$	5.52016	0.335326	0.167663	−	0.985844i	$-0.446378\pi$
$271$	5.52016	0.335326	0.167663	+	0.985844i	$0.446378\pi$
$272$	−0.353738	−0.0214485
$273$	−35.5051	−2.14887
$274$	28.4965	1.72153
$275$	−11.9083	−0.718095
$276$	−33.3423	−2.00697
$277$	7.52874	0.452358	0.226179	−	0.974086i	$-0.427377\pi$
$277$	7.52874	0.452358	0.226179	+	0.974086i	$0.427377\pi$
$278$	26.9696	1.61753
$279$	−24.2454	−1.45153
$280$	17.0926	1.02148
$281$	−14.4707	−0.863248	−0.431624	−	0.902054i	$-0.642059\pi$
$281$	−14.4707	−0.863248	−0.431624	+	0.902054i	$0.642059\pi$
$282$	−37.7678	−2.24904
$283$	19.1969	1.14114	0.570569	−	0.821250i	$-0.306723\pi$
$283$	19.1969	1.14114	0.570569	+	0.821250i	$0.306723\pi$
$284$	−36.5767	−2.17043
$285$	19.9698	1.18291
$286$	−33.5017	−1.98100
$287$	1.36947	0.0808372
$288$	45.3834	2.67424
$289$	−4.66410	−0.274359
$290$	−37.1632	−2.18230
$291$	4.33432	0.254082
$292$	−33.5082	−1.96092
$293$	−3.42031	−0.199817	−0.0999084	−	0.994997i	$-0.531855\pi$
$293$	−3.42031	−0.199817	−0.0999084	+	0.994997i	$0.531855\pi$
$294$	−54.1940	−3.16066
$295$	−13.1381	−0.764929
$296$	7.02811	0.408500
$297$	82.2862	4.77473
$298$	−18.1489	−1.05134
$299$	−8.99862	−0.520404
$300$	−24.5720	−1.41867
$301$	10.0432	0.578879
$302$	29.7123	1.70975
$303$	−53.1762	−3.05489
$304$	−0.372744	−0.0213783
$305$	−17.8635	−1.02286
$306$	−63.0633	−3.60509
$307$	15.3531	0.876247	0.438124	−	0.898915i	$-0.355643\pi$
$307$	15.3531	0.876247	0.438124	+	0.898915i	$0.355643\pi$
$308$	−62.1579	−3.54177
$309$	−61.3147	−3.48807
$310$	11.5248	0.654562
$311$	19.4322	1.10190	0.550951	−	0.834538i	$-0.314265\pi$
$311$	19.4322	1.10190	0.550951	+	0.834538i	$0.314265\pi$
$312$	−26.1040	−1.47785
$313$	−17.9419	−1.01414	−0.507069	−	0.861905i	$-0.669271\pi$
$313$	−17.9419	−1.01414	−0.507069	+	0.861905i	$0.669271\pi$
$314$	−43.3620	−2.44706
$315$	−48.5133	−2.73341
$316$	35.2431	1.98258
$317$	−18.8700	−1.05985	−0.529923	−	0.848046i	$-0.677779\pi$
$317$	−18.8700	−1.05985	−0.529923	+	0.848046i	$0.677779\pi$
$318$	−41.7539	−2.34144
$319$	51.0326	2.85728
$320$	−21.2427	−1.18750
$321$	56.8089	3.17076
$322$	−27.0869	−1.50949
$323$	12.9987	0.723266
$324$	93.9842	5.22134
$325$	−6.63165	−0.367858
$326$	−42.7960	−2.37025
$327$	32.7671	1.81202
$328$	1.00686	0.0555945
$329$	−18.9117	−1.04264
$330$	−63.2394	−3.48121
$331$	−7.46185	−0.410141	−0.205070	−	0.978747i	$-0.565742\pi$
$331$	−7.46185	−0.410141	−0.205070	+	0.978747i	$0.565742\pi$
$332$	31.3559	1.72088
$333$	−19.9476	−1.09312
$334$	5.37987	0.294374
$335$	1.74692	0.0954445
$336$	1.25097	0.0682461
$337$	2.06760	0.112630	0.0563148	−	0.998413i	$-0.482065\pi$
$337$	2.06760	0.112630	0.0563148	+	0.998413i	$0.482065\pi$
$338$	11.0259	0.599728
$339$	29.4739	1.60080
$340$	18.4767	1.00204
$341$	−15.8258	−0.857015
$342$	−66.4516	−3.59329
$343$	−0.757855	−0.0409203
$344$	7.38393	0.398115
$345$	−16.9862	−0.914506
$346$	−18.7175	−1.00626
$347$	5.77489	0.310012	0.155006	−	0.987914i	$-0.450460\pi$
$347$	5.77489	0.310012	0.155006	+	0.987914i	$0.450460\pi$
$348$	105.303	5.64484
$349$	−21.8963	−1.17208	−0.586040	−	0.810282i	$-0.699314\pi$
$349$	−21.8963	−1.17208	−0.586040	+	0.810282i	$0.699314\pi$
$350$	−19.9620	−1.06702
$351$	45.8248	2.44595
$352$	29.6233	1.57893
$353$	11.9751	0.637369	0.318684	−	0.947861i	$-0.396759\pi$
$353$	11.9751	0.637369	0.318684	+	0.947861i	$0.396759\pi$
$354$	60.3968	3.21005
$355$	−18.6340	−0.988989
$356$	−57.2269	−3.03302
$357$	−43.6251	−2.30888
$358$	−29.8677	−1.57856
$359$	−13.9784	−0.737752	−0.368876	−	0.929479i	$-0.620257\pi$
$359$	−13.9784	−0.737752	−0.368876	+	0.929479i	$0.620257\pi$
$360$	−35.6679	−1.87986
$361$	−5.30293	−0.279102
$362$	52.3382	2.75084
$363$	50.5841	2.65498
$364$	−34.6154	−1.81434
$365$	−17.0707	−0.893521
$366$	82.1200	4.29248
$367$	−4.47719	−0.233708	−0.116854	−	0.993149i	$-0.537281\pi$
$367$	−4.47719	−0.233708	−0.116854	+	0.993149i	$0.537281\pi$
$368$	0.317054	0.0165276
$369$	−2.85773	−0.148767
$370$	9.48184	0.492937
$371$	−20.9077	−1.08547
$372$	−32.6557	−1.69312
$373$	24.8617	1.28729	0.643645	−	0.765324i	$-0.277421\pi$
$373$	24.8617	1.28729	0.643645	+	0.765324i	$0.277421\pi$
$374$	−41.1636	−2.12852
$375$	−39.4974	−2.03964
$376$	−13.9042	−0.717056
$377$	28.4198	1.46370
$378$	137.938	7.09476
$379$	7.97855	0.409831	0.204915	−	0.978780i	$-0.434308\pi$
$379$	7.97855	0.409831	0.204915	+	0.978780i	$0.434308\pi$
$380$	19.4694	0.998760
$381$	10.9150	0.559193
$382$	12.3520	0.631981
$383$	6.24247	0.318975	0.159488	−	0.987200i	$-0.449016\pi$
$383$	6.24247	0.318975	0.159488	+	0.987200i	$0.449016\pi$
$384$	59.6101	3.04196
$385$	−31.6663	−1.61386
$386$	−16.1370	−0.821351
$387$	−20.9575	−1.06533
$388$	4.22572	0.214528
$389$	2.96325	0.150243	0.0751213	−	0.997174i	$-0.476066\pi$
$389$	2.96325	0.150243	0.0751213	+	0.997174i	$0.476066\pi$
$390$	−35.2177	−1.78332
$391$	−11.0566	−0.559157
$392$	−19.9516	−1.00771
$393$	25.8693	1.30493
$394$	29.0963	1.46585
$395$	17.9546	0.903393
$396$	129.707	6.51804
$397$	33.9047	1.70163	0.850815	−	0.525465i	$-0.176109\pi$
$397$	33.9047	1.70163	0.850815	+	0.525465i	$0.176109\pi$
$398$	3.66913	0.183917
$399$	−45.9690	−2.30133
$400$	0.233657	0.0116829
$401$	−16.1848	−0.808230	−0.404115	−	0.914708i	$-0.632420\pi$
$401$	−16.1848	−0.808230	−0.404115	+	0.914708i	$0.632420\pi$
$402$	−8.03073	−0.400536
$403$	−8.81332	−0.439023
$404$	−51.8437	−2.57932
$405$	47.8802	2.37918
$406$	85.5470	4.24563
$407$	−13.0205	−0.645401
$408$	−32.0740	−1.58790
$409$	−14.5898	−0.721421	−0.360711	−	0.932678i	$-0.617466\pi$
$409$	−14.5898	−0.721421	−0.360711	+	0.932678i	$0.617466\pi$
$410$	1.35838	0.0670858
$411$	−41.1357	−2.02907
$412$	−59.7783	−2.94507
$413$	30.2429	1.48816
$414$	56.5234	2.77797
$415$	15.9742	0.784144
$416$	16.4971	0.808835
$417$	−38.9316	−1.90649
$418$	−43.3752	−2.12155
$419$	13.1140	0.640659	0.320330	−	0.947306i	$-0.396206\pi$
$419$	13.1140	0.640659	0.320330	+	0.947306i	$0.396206\pi$
$420$	−65.3416	−3.18835
$421$	−8.17586	−0.398467	−0.199233	−	0.979952i	$-0.563845\pi$
$421$	−8.17586	−0.398467	−0.199233	+	0.979952i	$0.563845\pi$
$422$	−0.0775050	−0.00377288
$423$	39.4638	1.91880
$424$	−15.3717	−0.746517
$425$	−8.14831	−0.395251
$426$	85.6619	4.15033
$427$	41.1205	1.98996
$428$	55.3854	2.67716
$429$	48.3610	2.33489
$430$	9.96190	0.480405
$431$	−14.0633	−0.677406	−0.338703	−	0.940893i	$-0.609988\pi$
$431$	−14.0633	−0.677406	−0.338703	+	0.940893i	$0.609988\pi$
$432$	−1.61457	−0.0776812
$433$	−26.9613	−1.29568	−0.647839	−	0.761777i	$-0.724327\pi$
$433$	−26.9613	−1.29568	−0.647839	+	0.761777i	$0.724327\pi$
$434$	−26.5291	−1.27344
$435$	53.6465	2.57215
$436$	31.9460	1.52994
$437$	−11.6507	−0.557326
$438$	78.4753	3.74970
$439$	−14.5376	−0.693843	−0.346921	−	0.937894i	$-0.612773\pi$
$439$	−14.5376	−0.693843	−0.346921	+	0.937894i	$0.612773\pi$
$440$	−23.2816	−1.10991
$441$	56.6277	2.69656
$442$	−22.9238	−1.09037
$443$	7.55542	0.358969	0.179484	−	0.983761i	$-0.442557\pi$
$443$	7.55542	0.358969	0.179484	+	0.983761i	$0.442557\pi$
$444$	−26.8670	−1.27505
$445$	−29.1542	−1.38204
$446$	−59.9860	−2.84042
$447$	26.1986	1.23915
$448$	48.8990	2.31026
$449$	18.7459	0.884676	0.442338	−	0.896849i	$-0.354149\pi$
$449$	18.7459	0.884676	0.442338	+	0.896849i	$0.354149\pi$
$450$	41.6556	1.96366
$451$	−1.86533	−0.0878352
$452$	28.7354	1.35160
$453$	−42.8908	−2.01518
$454$	−32.0990	−1.50648
$455$	−17.6348	−0.826732
$456$	−33.7972	−1.58270
$457$	2.22557	0.104108	0.0520539	−	0.998644i	$-0.483423\pi$
$457$	2.22557	0.104108	0.0520539	+	0.998644i	$0.483423\pi$
$458$	−51.0235	−2.38417
$459$	56.3049	2.62809
$460$	−16.5606	−0.772141
$461$	4.90364	0.228385	0.114193	−	0.993459i	$-0.463572\pi$
$461$	4.90364	0.228385	0.114193	+	0.993459i	$0.463572\pi$
$462$	145.572	6.77264
$463$	−2.33333	−0.108439	−0.0542195	−	0.998529i	$-0.517267\pi$
$463$	−2.33333	−0.108439	−0.0542195	+	0.998529i	$0.517267\pi$
$464$	−1.00133	−0.0464857
$465$	−16.6364	−0.771495
$466$	−47.4970	−2.20026
$467$	23.3795	1.08187	0.540937	−	0.841063i	$-0.318070\pi$
$467$	23.3795	1.08187	0.540937	+	0.841063i	$0.318070\pi$
$468$	72.2334	3.33899
$469$	−4.02128	−0.185685
$470$	−18.7586	−0.865271
$471$	62.5946	2.88421
$472$	22.2351	1.02346
$473$	−13.6797	−0.628993
$474$	−82.5386	−3.79112
$475$	−8.58610	−0.393957
$476$	−42.5320	−1.94945
$477$	43.6290	1.99763
$478$	41.5482	1.90037
$479$	9.73443	0.444777	0.222389	−	0.974958i	$-0.428615\pi$
$479$	9.73443	0.444777	0.222389	+	0.974958i	$0.428615\pi$
$480$	31.1406	1.42137
$481$	−7.25104	−0.330619
$482$	36.7253	1.67279
$483$	39.1010	1.77916
$484$	49.3167	2.24167
$485$	2.15279	0.0977531
$486$	−110.298	−5.00323
$487$	−33.6652	−1.52552	−0.762758	−	0.646684i	$-0.776155\pi$
$487$	−33.6652	−1.52552	−0.762758	+	0.646684i	$0.776155\pi$
$488$	30.2326	1.36856
$489$	61.7776	2.79368
$490$	−26.9173	−1.21600
$491$	19.9862	0.901966	0.450983	−	0.892533i	$-0.351074\pi$
$491$	19.9862	0.901966	0.450983	+	0.892533i	$0.351074\pi$
$492$	−3.84902	−0.173527
$493$	34.9194	1.57269
$494$	−24.1555	−1.08681
$495$	66.0793	2.97004
$496$	0.310525	0.0139430
$497$	42.8940	1.92406
$498$	−73.4348	−3.29069
$499$	−1.48867	−0.0666418	−0.0333209	−	0.999445i	$-0.510608\pi$
$499$	−1.48867	−0.0666418	−0.0333209	+	0.999445i	$0.510608\pi$
$500$	−38.5078	−1.72212
$501$	−7.76605	−0.346961
$502$	0.424291	0.0189370
$503$	10.1764	0.453744	0.226872	−	0.973925i	$-0.427150\pi$
$503$	10.1764	0.453744	0.226872	+	0.973925i	$0.427150\pi$
$504$	82.1047	3.65724
$505$	−26.4117	−1.17531
$506$	36.8947	1.64017
$507$	−15.9162	−0.706865
$508$	10.6415	0.472141
$509$	−32.4034	−1.43625	−0.718127	−	0.695912i	$-0.755000\pi$
$509$	−32.4034	−1.43625	−0.718127	+	0.695912i	$0.755000\pi$
$510$	−43.2720	−1.91612
$511$	39.2955	1.73833
$512$	−1.13934	−0.0503522
$513$	59.3300	2.61949
$514$	30.7515	1.35639
$515$	−30.4540	−1.34196
$516$	−28.2273	−1.24264
$517$	25.7594	1.13290
$518$	−21.8265	−0.959000
$519$	27.0194	1.18602
$520$	−12.9654	−0.568572
$521$	14.4186	0.631691	0.315845	−	0.948811i	$-0.397712\pi$
$521$	14.4186	0.631691	0.315845	+	0.948811i	$0.397712\pi$
$522$	−178.514	−7.81336
$523$	−4.01025	−0.175356	−0.0876780	−	0.996149i	$-0.527945\pi$
$523$	−4.01025	−0.175356	−0.0876780	+	0.996149i	$0.527945\pi$
$524$	25.2211	1.10179
$525$	28.8160	1.25763
$526$	41.9405	1.82869
$527$	−10.8289	−0.471715
$528$	−1.70393	−0.0741542
$529$	−13.0900	−0.569131
$530$	−20.7385	−0.900822
$531$	−63.1091	−2.73870
$532$	−44.8171	−1.94307
$533$	−1.03880	−0.0449953
$534$	134.024	5.79979
$535$	28.2161	1.21989
$536$	−2.95652	−0.127702
$537$	43.1151	1.86055
$538$	18.2579	0.787153
$539$	36.9628	1.59210
$540$	84.3335	3.62914
$541$	16.1624	0.694874	0.347437	−	0.937703i	$-0.387052\pi$
$541$	16.1624	0.694874	0.347437	+	0.937703i	$0.387052\pi$
$542$	−12.6042	−0.541395
$543$	−75.5522	−3.24225
$544$	20.2699	0.869066
$545$	16.2749	0.697139
$546$	81.0685	3.46941
$547$	18.2662	0.781004	0.390502	−	0.920602i	$-0.372301\pi$
$547$	18.2662	0.781004	0.390502	+	0.920602i	$0.372301\pi$
$548$	−40.1050	−1.71320
$549$	−85.8078	−3.66219
$550$	27.1900	1.15939
$551$	36.7956	1.56754
$552$	28.7478	1.22359
$553$	−41.3301	−1.75753
$554$	−17.1903	−0.730347
$555$	−13.6874	−0.580997
$556$	−37.9561	−1.60970
$557$	−35.6456	−1.51035	−0.755177	−	0.655521i	$-0.772449\pi$
$557$	−35.6456	−1.51035	−0.755177	+	0.655521i	$0.772449\pi$
$558$	55.3594	2.34355
$559$	−7.61815	−0.322214
$560$	0.621338	0.0262563
$561$	59.4212	2.50876
$562$	33.0408	1.39374
$563$	41.3464	1.74254	0.871272	−	0.490800i	$-0.163295\pi$
$563$	41.3464	1.74254	0.871272	+	0.490800i	$0.163295\pi$
$564$	53.1531	2.23815
$565$	14.6392	0.615877
$566$	−43.8322	−1.84240
$567$	−110.217	−4.62866
$568$	31.5365	1.32324
$569$	−32.9630	−1.38188	−0.690940	−	0.722912i	$-0.742803\pi$
$569$	−32.9630	−1.38188	−0.690940	+	0.722912i	$0.742803\pi$
$570$	−45.5969	−1.90984
$571$	7.25059	0.303428	0.151714	−	0.988424i	$-0.451521\pi$
$571$	7.25059	0.303428	0.151714	+	0.988424i	$0.451521\pi$
$572$	47.1492	1.97141
$573$	−17.8305	−0.744881
$574$	−3.12690	−0.130514
$575$	7.30329	0.304568
$576$	−102.040	−4.25165
$577$	9.44890	0.393363	0.196681	−	0.980467i	$-0.436984\pi$
$577$	9.44890	0.393363	0.196681	+	0.980467i	$0.436984\pi$
$578$	10.6495	0.442961
$579$	23.2943	0.968080
$580$	52.3023	2.17174
$581$	−36.7715	−1.52554
$582$	−9.89653	−0.410225
$583$	28.4781	1.17944
$584$	28.8908	1.19551
$585$	36.7993	1.52146
$586$	7.80958	0.322611
$587$	−37.5331	−1.54916	−0.774578	−	0.632478i	$-0.782038\pi$
$587$	−37.5331	−1.54916	−0.774578	+	0.632478i	$0.782038\pi$
$588$	76.2708	3.14535
$589$	−11.4107	−0.470171
$590$	29.9981	1.23500
$591$	−42.0015	−1.72771
$592$	0.255480	0.0105002
$593$	−35.9118	−1.47472	−0.737360	−	0.675500i	$-0.763928\pi$
$593$	−35.9118	−1.47472	−0.737360	+	0.675500i	$0.763928\pi$
$594$	−187.884	−7.70895
$595$	−21.6679	−0.888297
$596$	25.5421	1.04625
$597$	−5.29653	−0.216772
$598$	20.5465	0.840209
$599$	−18.1333	−0.740907	−0.370453	−	0.928851i	$-0.620798\pi$
$599$	−18.1333	−0.740907	−0.370453	+	0.928851i	$0.620798\pi$
$600$	21.1860	0.864916
$601$	41.8194	1.70585	0.852925	−	0.522034i	$-0.174827\pi$
$601$	41.8194	1.70585	0.852925	+	0.522034i	$0.174827\pi$
$602$	−22.9315	−0.934620
$603$	8.39137	0.341723
$604$	−41.8161	−1.70147
$605$	25.1243	1.02145
$606$	121.417	4.93222
$607$	−33.6433	−1.36554	−0.682770	−	0.730633i	$-0.739225\pi$
$607$	−33.6433	−1.36554	−0.682770	+	0.730633i	$0.739225\pi$
$608$	21.3590	0.866222
$609$	−123.490	−5.00408
$610$	40.7877	1.65145
$611$	14.3453	0.580348
$612$	88.7532	3.58764
$613$	−35.2659	−1.42437	−0.712187	−	0.701989i	$-0.752295\pi$
$613$	−35.2659	−1.42437	−0.712187	+	0.701989i	$0.752295\pi$
$614$	−35.0556	−1.41473
$615$	−1.96088	−0.0790703
$616$	53.5926	2.15931
$617$	−25.0474	−1.00837	−0.504186	−	0.863595i	$-0.668207\pi$
$617$	−25.0474	−1.00837	−0.504186	+	0.863595i	$0.668207\pi$
$618$	139.999	5.63160
$619$	30.7684	1.23669	0.618344	−	0.785907i	$-0.287804\pi$
$619$	30.7684	1.23669	0.618344	+	0.785907i	$0.287804\pi$
$620$	−16.2196	−0.651393
$621$	−50.4658	−2.02512
$622$	−44.3695	−1.77906
$623$	67.1108	2.68874
$624$	−0.948912	−0.0379869
$625$	−8.01790	−0.320716
$626$	40.9667	1.63736
$627$	62.6137	2.50055
$628$	61.0262	2.43521
$629$	−8.90935	−0.355239
$630$	110.770	4.41319
$631$	20.3617	0.810586	0.405293	−	0.914187i	$-0.367169\pi$
$631$	20.3617	0.810586	0.405293	+	0.914187i	$0.367169\pi$
$632$	−30.3867	−1.20872
$633$	0.111881	0.00444688
$634$	43.0858	1.71116
$635$	5.42131	0.215138
$636$	58.7631	2.33011
$637$	20.5844	0.815585
$638$	−116.522	−4.61317
$639$	−89.5087	−3.54091
$640$	29.6074	1.17033
$641$	−21.9937	−0.868699	−0.434349	−	0.900744i	$-0.643022\pi$
$641$	−21.9937	−0.868699	−0.434349	+	0.900744i	$0.643022\pi$
$642$	−129.711	−5.11930
$643$	19.9641	0.787306	0.393653	−	0.919259i	$-0.371211\pi$
$643$	19.9641	0.787306	0.393653	+	0.919259i	$0.371211\pi$
$644$	38.1212	1.50219
$645$	−14.3804	−0.566226
$646$	−29.6798	−1.16774
$647$	−29.9391	−1.17703	−0.588514	−	0.808487i	$-0.700287\pi$
$647$	−29.9391	−1.17703	−0.588514	+	0.808487i	$0.700287\pi$
$648$	−81.0332	−3.18329
$649$	−41.1934	−1.61698
$650$	15.1420	0.593918
$651$	38.2958	1.50093
$652$	60.2296	2.35877
$653$	−20.6601	−0.808491	−0.404245	−	0.914651i	$-0.632466\pi$
$653$	−20.6601	−0.808491	−0.404245	+	0.914651i	$0.632466\pi$
$654$	−74.8169	−2.92557
$655$	12.8489	0.502046
$656$	0.0366006	0.00142901
$657$	−81.9995	−3.19910
$658$	43.1810	1.68337
$659$	−26.4658	−1.03096	−0.515481	−	0.856901i	$-0.672387\pi$
$659$	−26.4658	−1.03096	−0.515481	+	0.856901i	$0.672387\pi$
$660$	89.0010	3.46436
$661$	−46.1650	−1.79561	−0.897805	−	0.440392i	$-0.854839\pi$
$661$	−46.1650	−1.79561	−0.897805	+	0.440392i	$0.854839\pi$
$662$	17.0376	0.662185
$663$	33.0914	1.28516
$664$	−27.0351	−1.04916
$665$	−22.8320	−0.885389
$666$	45.5462	1.76488
$667$	−31.2981	−1.21187
$668$	−7.57146	−0.292948
$669$	86.5920	3.34784
$670$	−3.98873	−0.154098
$671$	−56.0097	−2.16223
$672$	−71.6833	−2.76524
$673$	49.2852	1.89981	0.949903	−	0.312544i	$-0.101181\pi$
$673$	49.2852	1.89981	0.949903	+	0.312544i	$0.101181\pi$
$674$	−4.72095	−0.181844
$675$	−37.1914	−1.43150
$676$	−15.5174	−0.596824
$677$	21.5234	0.827212	0.413606	−	0.910456i	$-0.364269\pi$
$677$	21.5234	0.827212	0.413606	+	0.910456i	$0.364269\pi$
$678$	−67.2977	−2.58455
$679$	−4.95556	−0.190177
$680$	−15.9306	−0.610912
$681$	46.3361	1.77560
$682$	36.1350	1.38368
$683$	−5.40060	−0.206648	−0.103324	−	0.994648i	$-0.532948\pi$
$683$	−5.40060	−0.206648	−0.103324	+	0.994648i	$0.532948\pi$
$684$	93.5217	3.57589
$685$	−20.4314	−0.780645
$686$	1.73041	0.0660672
$687$	73.6543	2.81009
$688$	0.268415	0.0102332
$689$	15.8593	0.604192
$690$	38.7845	1.47650
$691$	25.3093	0.962810	0.481405	−	0.876498i	$-0.340127\pi$
$691$	25.3093	0.962810	0.481405	+	0.876498i	$0.340127\pi$
$692$	26.3424	1.00139
$693$	−152.110	−5.77816
$694$	−13.1858	−0.500525
$695$	−19.3367	−0.733483
$696$	−90.7923	−3.44148
$697$	−1.27637	−0.0483459
$698$	49.9956	1.89236
$699$	68.5637	2.59332
$700$	28.0939	1.06185
$701$	37.1682	1.40382	0.701912	−	0.712263i	$-0.252330\pi$
$701$	37.1682	1.40382	0.701912	+	0.712263i	$0.252330\pi$
$702$	−104.631	−3.94906
$703$	−9.38803	−0.354076
$704$	−66.6047	−2.51026
$705$	27.0788	1.01985
$706$	−27.3426	−1.02905
$707$	60.7978	2.28654
$708$	−85.0005	−3.19451
$709$	−45.5242	−1.70970	−0.854848	−	0.518879i	$-0.826350\pi$
$709$	−45.5242	−1.70970	−0.854848	+	0.518879i	$0.826350\pi$
$710$	42.5469	1.59676
$711$	86.2452	3.23445
$712$	49.3411	1.84914
$713$	9.70591	0.363489
$714$	99.6089	3.72777
$715$	24.0201	0.898302
$716$	42.0348	1.57091
$717$	−59.9763	−2.23986
$718$	31.9168	1.19113
$719$	46.8971	1.74897	0.874483	−	0.485056i	$-0.161201\pi$
$719$	46.8971	1.74897	0.874483	+	0.485056i	$0.161201\pi$
$720$	−1.29657	−0.0483203
$721$	70.1029	2.61077
$722$	12.1082	0.450619
$723$	−53.0143	−1.97162
$724$	−73.6591	−2.73752
$725$	−23.0656	−0.856633
$726$	−115.498	−4.28655
$727$	8.99395	0.333567	0.166783	−	0.985994i	$-0.446662\pi$
$727$	8.99395	0.333567	0.166783	+	0.985994i	$0.446662\pi$
$728$	29.8455	1.10615
$729$	71.4777	2.64732
$730$	38.9774	1.44262
$731$	−9.36043	−0.346208
$732$	−115.573	−4.27170
$733$	33.6204	1.24180	0.620900	−	0.783890i	$-0.286767\pi$
$733$	33.6204	1.24180	0.620900	+	0.783890i	$0.286767\pi$
$734$	10.2228	0.377329
$735$	38.8561	1.43323
$736$	−18.1678	−0.669676
$737$	5.47733	0.201760
$738$	6.52503	0.240190
$739$	−25.9949	−0.956239	−0.478120	−	0.878295i	$-0.658681\pi$
$739$	−25.9949	−0.956239	−0.478120	+	0.878295i	$0.658681\pi$
$740$	−13.3444	−0.490551
$741$	34.8693	1.28096
$742$	47.7384	1.75253
$743$	21.7692	0.798633	0.399317	−	0.916813i	$-0.369247\pi$
$743$	21.7692	0.798633	0.399317	+	0.916813i	$0.369247\pi$
$744$	28.1558	1.03224
$745$	13.0124	0.476738
$746$	−56.7666	−2.07837
$747$	76.7326	2.80750
$748$	57.9323	2.11821
$749$	−64.9512	−2.37327
$750$	90.1843	3.29306
$751$	−1.40449	−0.0512507	−0.0256254	−	0.999672i	$-0.508158\pi$
$751$	−1.40449	−0.0512507	−0.0256254	+	0.999672i	$0.508158\pi$
$752$	−0.505436	−0.0184314
$753$	−0.612480	−0.0223200
$754$	−64.8908	−2.36318
$755$	−21.3032	−0.775302
$756$	−194.129	−7.06042
$757$	−21.5289	−0.782480	−0.391240	−	0.920289i	$-0.627954\pi$
$757$	−21.5289	−0.782480	−0.391240	+	0.920289i	$0.627954\pi$
$758$	−18.2174	−0.661685
$759$	−53.2589	−1.93318
$760$	−16.7865	−0.608912
$761$	−45.5741	−1.65206	−0.826031	−	0.563625i	$-0.809406\pi$
$761$	−45.5741	−1.65206	−0.826031	+	0.563625i	$0.809406\pi$
$762$	−24.9222	−0.902836
$763$	−37.4636	−1.35627
$764$	−17.3837	−0.628922
$765$	45.2153	1.63476
$766$	−14.2534	−0.514996
$767$	−22.9404	−0.828331
$768$	−50.5694	−1.82477
$769$	21.5276	0.776304	0.388152	−	0.921595i	$-0.373114\pi$
$769$	21.5276	0.776304	0.388152	+	0.921595i	$0.373114\pi$
$770$	72.3034	2.60563
$771$	−44.3910	−1.59870
$772$	22.7107	0.817374
$773$	−45.1311	−1.62325	−0.811627	−	0.584176i	$-0.801418\pi$
$773$	−45.1311	−1.62325	−0.811627	+	0.584176i	$0.801418\pi$
$774$	47.8522	1.72001
$775$	7.15289	0.256940
$776$	−3.64342	−0.130791
$777$	31.5073	1.13032
$778$	−6.76597	−0.242572
$779$	−1.34495	−0.0481877
$780$	49.5643	1.77468
$781$	−58.4254	−2.09062
$782$	25.2455	0.902777
$783$	159.383	5.69589
$784$	−0.725264	−0.0259023
$785$	31.0897	1.10964
$786$	−59.0672	−2.10686
$787$	−33.0502	−1.17811	−0.589056	−	0.808092i	$-0.700500\pi$
$787$	−33.0502	−1.17811	−0.589056	+	0.808092i	$0.700500\pi$
$788$	−40.9491	−1.45875
$789$	−60.5426	−2.15537
$790$	−40.9956	−1.45856
$791$	−33.6984	−1.19818
$792$	−111.834	−3.97384
$793$	−31.1915	−1.10764
$794$	−77.4145	−2.74734
$795$	29.9368	1.06175
$796$	−5.16381	−0.183026
$797$	18.4507	0.653556	0.326778	−	0.945101i	$-0.394037\pi$
$797$	18.4507	0.653556	0.326778	+	0.945101i	$0.394037\pi$
$798$	104.961	3.71557
$799$	17.6260	0.623565
$800$	−13.3890	−0.473374
$801$	−140.043	−4.94817
$802$	36.9546	1.30491
$803$	−53.5239	−1.88882
$804$	11.3022	0.398597
$805$	19.4208	0.684494
$806$	20.1234	0.708816
$807$	−26.3559	−0.927772
$808$	44.6997	1.57253
$809$	−19.3848	−0.681533	−0.340766	−	0.940148i	$-0.610687\pi$
$809$	−19.3848	−0.681533	−0.340766	+	0.940148i	$0.610687\pi$
$810$	−109.324	−3.84127
$811$	32.7629	1.15046	0.575231	−	0.817991i	$-0.304912\pi$
$811$	32.7629	1.15046	0.575231	+	0.817991i	$0.304912\pi$
$812$	−120.396	−4.22507
$813$	18.1946	0.638111
$814$	29.7296	1.04202
$815$	30.6839	1.07481
$816$	−1.16593	−0.0408157
$817$	−9.86334	−0.345075
$818$	33.3129	1.16476
$819$	−84.7091	−2.95998
$820$	−1.91175	−0.0667611
$821$	−2.09671	−0.0731759	−0.0365879	−	0.999330i	$-0.511649\pi$
$821$	−2.09671	−0.0731759	−0.0365879	+	0.999330i	$0.511649\pi$
$822$	93.9249	3.27601
$823$	17.6566	0.615471	0.307735	−	0.951472i	$-0.400429\pi$
$823$	17.6566	0.615471	0.307735	+	0.951472i	$0.400429\pi$
$824$	51.5409	1.79551
$825$	−39.2498	−1.36650
$826$	−69.0534	−2.40268
$827$	34.3471	1.19437	0.597183	−	0.802105i	$-0.296287\pi$
$827$	34.3471	1.19437	0.597183	+	0.802105i	$0.296287\pi$
$828$	−79.5491	−2.76452
$829$	−26.1867	−0.909500	−0.454750	−	0.890619i	$-0.650271\pi$
$829$	−26.1867	−0.909500	−0.454750	+	0.890619i	$0.650271\pi$
$830$	−36.4739	−1.26603
$831$	24.8149	0.860819
$832$	−37.0918	−1.28593
$833$	25.2921	0.876319
$834$	88.8924	3.07809
$835$	−3.85727	−0.133486
$836$	61.0448	2.11128
$837$	−49.4266	−1.70843
$838$	−29.9431	−1.03437
$839$	53.0055	1.82995	0.914977	−	0.403505i	$-0.132208\pi$
$839$	53.0055	1.82995	0.914977	+	0.403505i	$0.132208\pi$
$840$	56.3376	1.94383
$841$	69.8470	2.40852
$842$	18.6679	0.643338
$843$	−47.6956	−1.64272
$844$	0.109078	0.00375462
$845$	−7.90534	−0.271952
$846$	−90.1075	−3.09796
$847$	−57.8343	−1.98721
$848$	−0.558782	−0.0191886
$849$	63.2734	2.17154
$850$	18.6050	0.638146
$851$	7.98541	0.273736
$852$	−120.558	−4.13024
$853$	−40.0441	−1.37108	−0.685541	−	0.728034i	$-0.740434\pi$
$853$	−40.0441	−1.37108	−0.685541	+	0.728034i	$0.740434\pi$
$854$	−93.8902	−3.21286
$855$	47.6446	1.62941
$856$	−47.7534	−1.63218
$857$	46.7166	1.59581	0.797904	−	0.602785i	$-0.205942\pi$
$857$	46.7166	1.59581	0.797904	+	0.602785i	$0.205942\pi$
$858$	−110.422	−3.76976
$859$	43.6258	1.48849	0.744246	−	0.667905i	$-0.232809\pi$
$859$	43.6258	1.48849	0.744246	+	0.667905i	$0.232809\pi$
$860$	−14.0200	−0.478080
$861$	4.51380	0.153830
$862$	32.1107	1.09369
$863$	−0.794422	−0.0270424	−0.0135212	−	0.999909i	$-0.504304\pi$
$863$	−0.794422	−0.0270424	−0.0135212	+	0.999909i	$0.504304\pi$
$864$	92.5184	3.14754
$865$	13.4201	0.456297
$866$	61.5606	2.09192
$867$	−15.3730	−0.522093
$868$	37.3362	1.26727
$869$	56.2952	1.90968
$870$	−122.491	−4.15283
$871$	3.05030	0.103356
$872$	−27.5439	−0.932754
$873$	10.3410	0.349989
$874$	26.6019	0.899822
$875$	45.1586	1.52664
$876$	−110.444	−3.73154
$877$	52.8026	1.78302	0.891509	−	0.453004i	$-0.149648\pi$
$877$	52.8026	1.78302	0.891509	+	0.453004i	$0.149648\pi$
$878$	33.1937	1.12023
$879$	−11.2734	−0.380243
$880$	−0.846316	−0.0285293
$881$	45.2748	1.52535	0.762674	−	0.646784i	$-0.223886\pi$
$881$	45.2748	1.52535	0.762674	+	0.646784i	$0.223886\pi$
$882$	−129.298	−4.35368
$883$	26.8943	0.905064	0.452532	−	0.891748i	$-0.350521\pi$
$883$	26.8943	0.905064	0.452532	+	0.891748i	$0.350521\pi$
$884$	32.2622	1.08510
$885$	−43.3034	−1.45563
$886$	−17.2512	−0.579567
$887$	−7.64584	−0.256722	−0.128361	−	0.991727i	$-0.540972\pi$
$887$	−7.64584	−0.256722	−0.128361	+	0.991727i	$0.540972\pi$
$888$	23.1648	0.777359
$889$	−12.4795	−0.418547
$890$	66.5676	2.23135
$891$	150.124	5.02936
$892$	84.4223	2.82667
$893$	18.5731	0.621523
$894$	−59.8191	−2.00065
$895$	21.4146	0.715811
$896$	−68.1539	−2.27686
$897$	−29.6596	−0.990307
$898$	−42.8025	−1.42834
$899$	−30.6536	−1.02236
$900$	−58.6247	−1.95416
$901$	19.4864	0.649185
$902$	4.25911	0.141813
$903$	33.1025	1.10158
$904$	−24.7757	−0.824027
$905$	−37.5255	−1.24739
$906$	97.9323	3.25358
$907$	−13.3095	−0.441935	−0.220967	−	0.975281i	$-0.570921\pi$
$907$	−13.3095	−0.441935	−0.220967	+	0.975281i	$0.570921\pi$
$908$	45.1751	1.49919
$909$	−126.869	−4.20799
$910$	40.2654	1.33479
$911$	−47.9770	−1.58955	−0.794775	−	0.606905i	$-0.792411\pi$
$911$	−47.9770	−1.58955	−0.794775	+	0.606905i	$0.792411\pi$
$912$	−1.22857	−0.0406821
$913$	50.0860	1.65760
$914$	−5.08164	−0.168086
$915$	−58.8785	−1.94646
$916$	71.8088	2.37263
$917$	−29.5771	−0.976722
$918$	−128.561	−4.24314
$919$	6.62689	0.218601	0.109300	−	0.994009i	$-0.465139\pi$
$919$	6.62689	0.218601	0.109300	+	0.994009i	$0.465139\pi$
$920$	14.2785	0.470750
$921$	50.6041	1.66746
$922$	−11.1965	−0.368736
$923$	−32.5368	−1.07096
$924$	−204.874	−6.73985
$925$	5.88495	0.193496
$926$	5.32768	0.175078
$927$	−146.286	−4.80468
$928$	57.3784	1.88354
$929$	40.6974	1.33524	0.667619	−	0.744503i	$-0.267313\pi$
$929$	40.6974	1.33524	0.667619	+	0.744503i	$0.267313\pi$
$930$	37.9858	1.24560
$931$	26.6510	0.873450
$932$	66.8457	2.18960
$933$	64.0490	2.09687
$934$	−53.3822	−1.74672
$935$	29.5135	0.965196
$936$	−62.2797	−2.03568
$937$	31.2175	1.01983	0.509916	−	0.860224i	$-0.329676\pi$
$937$	31.2175	1.01983	0.509916	+	0.860224i	$0.329676\pi$
$938$	9.18177	0.299795
$939$	−59.1370	−1.92986
$940$	26.4003	0.861082
$941$	−28.5586	−0.930985	−0.465492	−	0.885052i	$-0.654123\pi$
$941$	−28.5586	−0.930985	−0.465492	+	0.885052i	$0.654123\pi$
$942$	−142.922	−4.65665
$943$	1.14400	0.0372539
$944$	0.808275	0.0263071
$945$	−98.8990	−3.21719
$946$	31.2347	1.01553
$947$	−9.73656	−0.316396	−0.158198	−	0.987407i	$-0.550568\pi$
$947$	−9.73656	−0.316396	−0.158198	+	0.987407i	$0.550568\pi$
$948$	116.162	3.77277
$949$	−29.8072	−0.967582
$950$	19.6046	0.636057
$951$	−62.1960	−2.01684
$952$	36.6711	1.18852
$953$	−17.6316	−0.571143	−0.285572	−	0.958357i	$-0.592183\pi$
$953$	−17.6316	−0.571143	−0.285572	+	0.958357i	$0.592183\pi$
$954$	−99.6178	−3.22524
$955$	−8.85613	−0.286578
$956$	−58.4735	−1.89117
$957$	168.204	5.43728
$958$	−22.2266	−0.718107
$959$	47.0316	1.51873
$960$	−70.0162	−2.25976
$961$	−21.4940	−0.693354
$962$	16.5563	0.533795
$963$	135.536	4.36760
$964$	−51.6860	−1.66469
$965$	11.5699	0.372449
$966$	−89.2790	−2.87251
$967$	−39.3413	−1.26513	−0.632566	−	0.774507i	$-0.717998\pi$
$967$	−39.3413	−1.26513	−0.632566	+	0.774507i	$0.717998\pi$
$968$	−42.5209	−1.36667
$969$	42.8439	1.37634
$970$	−4.91545	−0.157826
$971$	13.6537	0.438170	0.219085	−	0.975706i	$-0.429693\pi$
$971$	13.6537	0.438170	0.219085	+	0.975706i	$0.429693\pi$
$972$	155.230	4.97901
$973$	44.5117	1.42698
$974$	76.8675	2.46300
$975$	−21.8581	−0.700018
$976$	1.09899	0.0351778
$977$	41.6611	1.33286	0.666429	−	0.745568i	$-0.267822\pi$
$977$	41.6611	1.33286	0.666429	+	0.745568i	$0.267822\pi$
$978$	−141.056	−4.51048
$979$	−91.4107	−2.92150
$980$	37.8825	1.21011
$981$	78.1767	2.49599
$982$	−45.6344	−1.45625
$983$	18.8571	0.601448	0.300724	−	0.953711i	$-0.402772\pi$
$983$	18.8571	0.601448	0.300724	+	0.953711i	$0.402772\pi$
$984$	3.31863	0.105794
$985$	−20.8615	−0.664702
$986$	−79.7314	−2.53916
$987$	−62.3333	−1.98409
$988$	33.9956	1.08154
$989$	8.38971	0.266777
$990$	−150.878	−4.79523
$991$	−42.5792	−1.35257	−0.676287	−	0.736639i	$-0.736412\pi$
$991$	−42.5792	−1.35257	−0.676287	+	0.736639i	$0.736412\pi$
$992$	−17.7937	−0.564951
$993$	−24.5944	−0.780480
$994$	−97.9397	−3.10646
$995$	−2.63070	−0.0833988
$996$	103.350	3.27476
$997$	23.8641	0.755782	0.377891	−	0.925850i	$-0.376649\pi$
$997$	23.8641	0.755782	0.377891	+	0.925850i	$0.376649\pi$
$998$	3.39906	0.107595
$999$	−40.6651	−1.28659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.c.1.20	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.c.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-2.28329 q^{2} +3.29602 q^{3} +3.21343 q^{4} +1.63708 q^{5} -7.52578 q^{6} -3.76844 q^{7} -2.77062 q^{8} +7.86375 q^{9} +O(q^{10})\)	\(q-2.28329 q^{2} +3.29602 q^{3} +3.21343 q^{4} +1.63708 q^{5} -7.52578 q^{6} -3.76844 q^{7} -2.77062 q^{8} +7.86375 q^{9} -3.73794 q^{10} +5.13294 q^{11} +10.5915 q^{12} +2.85851 q^{13} +8.60445 q^{14} +5.39585 q^{15} -0.100716 q^{16} +3.51225 q^{17} -17.9553 q^{18} +3.70095 q^{19} +5.26065 q^{20} -12.4208 q^{21} -11.7200 q^{22} -3.14801 q^{23} -9.13203 q^{24} -2.31997 q^{25} -6.52682 q^{26} +16.0310 q^{27} -12.1096 q^{28} +9.94218 q^{29} -12.3203 q^{30} -3.08319 q^{31} +5.77121 q^{32} +16.9183 q^{33} -8.01950 q^{34} -6.16923 q^{35} +25.2696 q^{36} -2.53665 q^{37} -8.45037 q^{38} +9.42170 q^{39} -4.53573 q^{40} -0.363405 q^{41} +28.3604 q^{42} -2.66508 q^{43} +16.4943 q^{44} +12.8736 q^{45} +7.18784 q^{46} +5.01845 q^{47} -0.331961 q^{48} +7.20111 q^{49} +5.29717 q^{50} +11.5764 q^{51} +9.18563 q^{52} +5.54811 q^{53} -36.6035 q^{54} +8.40303 q^{55} +10.4409 q^{56} +12.1984 q^{57} -22.7009 q^{58} -8.02532 q^{59} +17.3392 q^{60} -10.9118 q^{61} +7.03982 q^{62} -29.6340 q^{63} -12.9759 q^{64} +4.67961 q^{65} -38.6294 q^{66} +1.06710 q^{67} +11.2864 q^{68} -10.3759 q^{69} +14.0862 q^{70} -11.3825 q^{71} -21.7875 q^{72} -10.4275 q^{73} +5.79192 q^{74} -7.64666 q^{75} +11.8928 q^{76} -19.3431 q^{77} -21.5125 q^{78} +10.9674 q^{79} -0.164880 q^{80} +29.2473 q^{81} +0.829761 q^{82} +9.75776 q^{83} -39.9135 q^{84} +5.74983 q^{85} +6.08516 q^{86} +32.7696 q^{87} -14.2214 q^{88} -17.8087 q^{89} -29.3942 q^{90} -10.7721 q^{91} -10.1159 q^{92} -10.1622 q^{93} -11.4586 q^{94} +6.05876 q^{95} +19.0220 q^{96} +1.31502 q^{97} -16.4422 q^{98} +40.3641 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) \) 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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