LMFDB - Embedded newform 8013.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41059 q^{2} +1.00000 q^{3} +3.81094 q^{4} -0.0291843 q^{5} -2.41059 q^{6} -4.28110 q^{7} -4.36543 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.41059 q^{2} +1.00000 q^{3} +3.81094 q^{4} -0.0291843 q^{5} -2.41059 q^{6} -4.28110 q^{7} -4.36543 q^{8} +1.00000 q^{9} +0.0703514 q^{10} -2.79864 q^{11} +3.81094 q^{12} -0.529671 q^{13} +10.3200 q^{14} -0.0291843 q^{15} +2.90137 q^{16} -6.45533 q^{17} -2.41059 q^{18} +3.36076 q^{19} -0.111220 q^{20} -4.28110 q^{21} +6.74637 q^{22} +1.83835 q^{23} -4.36543 q^{24} -4.99915 q^{25} +1.27682 q^{26} +1.00000 q^{27} -16.3150 q^{28} +9.38740 q^{29} +0.0703514 q^{30} -8.61633 q^{31} +1.73684 q^{32} -2.79864 q^{33} +15.5611 q^{34} +0.124941 q^{35} +3.81094 q^{36} +6.02920 q^{37} -8.10140 q^{38} -0.529671 q^{39} +0.127402 q^{40} -5.62171 q^{41} +10.3200 q^{42} +4.91765 q^{43} -10.6654 q^{44} -0.0291843 q^{45} -4.43152 q^{46} -12.7556 q^{47} +2.90137 q^{48} +11.3278 q^{49} +12.0509 q^{50} -6.45533 q^{51} -2.01854 q^{52} -3.08474 q^{53} -2.41059 q^{54} +0.0816764 q^{55} +18.6888 q^{56} +3.36076 q^{57} -22.6292 q^{58} -0.386347 q^{59} -0.111220 q^{60} -13.8054 q^{61} +20.7704 q^{62} -4.28110 q^{63} -9.98955 q^{64} +0.0154581 q^{65} +6.74637 q^{66} +12.4931 q^{67} -24.6008 q^{68} +1.83835 q^{69} -0.301181 q^{70} -8.82238 q^{71} -4.36543 q^{72} +8.57246 q^{73} -14.5339 q^{74} -4.99915 q^{75} +12.8076 q^{76} +11.9812 q^{77} +1.27682 q^{78} -4.68356 q^{79} -0.0846745 q^{80} +1.00000 q^{81} +13.5516 q^{82} +3.14380 q^{83} -16.3150 q^{84} +0.188394 q^{85} -11.8544 q^{86} +9.38740 q^{87} +12.2172 q^{88} -13.1700 q^{89} +0.0703514 q^{90} +2.26757 q^{91} +7.00585 q^{92} -8.61633 q^{93} +30.7486 q^{94} -0.0980815 q^{95} +1.73684 q^{96} +12.5415 q^{97} -27.3066 q^{98} -2.79864 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * 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 $

$2$	−2.41059	−1.70454	−0.852272	−	0.523099i	$-0.824776\pi$
$2$	−2.41059	−1.70454	−0.852272	+	0.523099i	$0.824776\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.81094	1.90547
$5$	−0.0291843	−0.0130516	−0.00652582	−	0.999979i	$-0.502077\pi$
$5$	−0.0291843	−0.0130516	−0.00652582	+	0.999979i	$0.502077\pi$
$6$	−2.41059	−0.984119
$7$	−4.28110	−1.61810	−0.809051	−	0.587738i	$-0.800018\pi$
$7$	−4.28110	−1.61810	−0.809051	+	0.587738i	$0.800018\pi$
$8$	−4.36543	−1.54341
$9$	1.00000	0.333333
$10$	0.0703514	0.0222471
$11$	−2.79864	−0.843821	−0.421911	−	0.906637i	$-0.638640\pi$
$11$	−2.79864	−0.843821	−0.421911	+	0.906637i	$0.638640\pi$
$12$	3.81094	1.10012
$13$	−0.529671	−0.146904	−0.0734522	−	0.997299i	$-0.523402\pi$
$13$	−0.529671	−0.146904	−0.0734522	+	0.997299i	$0.523402\pi$
$14$	10.3200	2.75813
$15$	−0.0291843	−0.00753536
$16$	2.90137	0.725342
$17$	−6.45533	−1.56565	−0.782823	−	0.622244i	$-0.786221\pi$
$17$	−6.45533	−1.56565	−0.782823	+	0.622244i	$0.786221\pi$
$18$	−2.41059	−0.568181
$19$	3.36076	0.771011	0.385505	−	0.922706i	$-0.374027\pi$
$19$	3.36076	0.771011	0.385505	+	0.922706i	$0.374027\pi$
$20$	−0.111220	−0.0248695
$21$	−4.28110	−0.934212
$22$	6.74637	1.43833
$23$	1.83835	0.383323	0.191662	−	0.981461i	$-0.438612\pi$
$23$	1.83835	0.383323	0.191662	+	0.981461i	$0.438612\pi$
$24$	−4.36543	−0.891089
$25$	−4.99915	−0.999830
$26$	1.27682	0.250405
$27$	1.00000	0.192450
$28$	−16.3150	−3.08324
$29$	9.38740	1.74320	0.871599	−	0.490220i	$-0.163084\pi$
$29$	9.38740	1.74320	0.871599	+	0.490220i	$0.163084\pi$
$30$	0.0703514	0.0128444
$31$	−8.61633	−1.54754	−0.773769	−	0.633468i	$-0.781631\pi$
$31$	−8.61633	−1.54754	−0.773769	+	0.633468i	$0.781631\pi$
$32$	1.73684	0.307033
$33$	−2.79864	−0.487181
$34$	15.5611	2.66871
$35$	0.124941	0.0211189
$36$	3.81094	0.635156
$37$	6.02920	0.991195	0.495598	−	0.868552i	$-0.334949\pi$
$37$	6.02920	0.991195	0.495598	+	0.868552i	$0.334949\pi$
$38$	−8.10140	−1.31422
$39$	−0.529671	−0.0848153
$40$	0.127402	0.0201440
$41$	−5.62171	−0.877964	−0.438982	−	0.898496i	$-0.644661\pi$
$41$	−5.62171	−0.877964	−0.438982	+	0.898496i	$0.644661\pi$
$42$	10.3200	1.59240
$43$	4.91765	0.749935	0.374968	−	0.927038i	$-0.377654\pi$
$43$	4.91765	0.749935	0.374968	+	0.927038i	$0.377654\pi$
$44$	−10.6654	−1.60788
$45$	−0.0291843	−0.00435054
$46$	−4.43152	−0.653392
$47$	−12.7556	−1.86060	−0.930301	−	0.366797i	$-0.880455\pi$
$47$	−12.7556	−1.86060	−0.930301	+	0.366797i	$0.880455\pi$
$48$	2.90137	0.418777
$49$	11.3278	1.61825
$50$	12.0509	1.70425
$51$	−6.45533	−0.903926
$52$	−2.01854	−0.279922
$53$	−3.08474	−0.423722	−0.211861	−	0.977300i	$-0.567952\pi$
$53$	−3.08474	−0.423722	−0.211861	+	0.977300i	$0.567952\pi$
$54$	−2.41059	−0.328040
$55$	0.0816764	0.0110132
$56$	18.6888	2.49740
$57$	3.36076	0.445143
$58$	−22.6292	−2.97136
$59$	−0.386347	−0.0502981	−0.0251490	−	0.999684i	$-0.508006\pi$
$59$	−0.386347	−0.0502981	−0.0251490	+	0.999684i	$0.508006\pi$
$60$	−0.111220	−0.0143584
$61$	−13.8054	−1.76760	−0.883802	−	0.467861i	$-0.845025\pi$
$61$	−13.8054	−1.76760	−0.883802	+	0.467861i	$0.845025\pi$
$62$	20.7704	2.63785
$63$	−4.28110	−0.539367
$64$	−9.98955	−1.24869
$65$	0.0154581	0.00191734
$66$	6.74637	0.830420
$67$	12.4931	1.52628	0.763139	−	0.646234i	$-0.223657\pi$
$67$	12.4931	1.52628	0.763139	+	0.646234i	$0.223657\pi$
$68$	−24.6008	−2.98329
$69$	1.83835	0.221312
$70$	−0.301181	−0.0359980
$71$	−8.82238	−1.04702	−0.523512	−	0.852018i	$-0.675379\pi$
$71$	−8.82238	−1.04702	−0.523512	+	0.852018i	$0.675379\pi$
$72$	−4.36543	−0.514470
$73$	8.57246	1.00333	0.501665	−	0.865062i	$-0.332721\pi$
$73$	8.57246	1.00333	0.501665	+	0.865062i	$0.332721\pi$
$74$	−14.5339	−1.68954
$75$	−4.99915	−0.577252
$76$	12.8076	1.46914
$77$	11.9812	1.36539
$78$	1.27682	0.144571
$79$	−4.68356	−0.526942	−0.263471	−	0.964667i	$-0.584867\pi$
$79$	−4.68356	−0.526942	−0.263471	+	0.964667i	$0.584867\pi$
$80$	−0.0846745	−0.00946690
$81$	1.00000	0.111111
$82$	13.5516	1.49653
$83$	3.14380	0.345077	0.172538	−	0.985003i	$-0.444803\pi$
$83$	3.14380	0.345077	0.172538	+	0.985003i	$0.444803\pi$
$84$	−16.3150	−1.78011
$85$	0.188394	0.0204342
$86$	−11.8544	−1.27830
$87$	9.38740	1.00644
$88$	12.2172	1.30236
$89$	−13.1700	−1.39601	−0.698007	−	0.716091i	$-0.745930\pi$
$89$	−13.1700	−1.39601	−0.698007	+	0.716091i	$0.745930\pi$
$90$	0.0703514	0.00741569
$91$	2.26757	0.237706
$92$	7.00585	0.730411
$93$	−8.61633	−0.893471
$94$	30.7486	3.17148
$95$	−0.0980815	−0.0100629
$96$	1.73684	0.177266
$97$	12.5415	1.27340	0.636698	−	0.771113i	$-0.280300\pi$
$97$	12.5415	1.27340	0.636698	+	0.771113i	$0.280300\pi$
$98$	−27.3066	−2.75839
$99$	−2.79864	−0.281274
$100$	−19.0514	−1.90514
$101$	−1.13220	−0.112658	−0.0563292	−	0.998412i	$-0.517940\pi$
$101$	−1.13220	−0.112658	−0.0563292	+	0.998412i	$0.517940\pi$
$102$	15.5611	1.54078
$103$	−10.8243	−1.06655	−0.533276	−	0.845941i	$-0.679039\pi$
$103$	−10.8243	−1.06655	−0.533276	+	0.845941i	$0.679039\pi$
$104$	2.31224	0.226734
$105$	0.124941	0.0121930
$106$	7.43604	0.722252
$107$	−16.3976	−1.58522	−0.792610	−	0.609729i	$-0.791278\pi$
$107$	−16.3976	−1.58522	−0.792610	+	0.609729i	$0.791278\pi$
$108$	3.81094	0.366708
$109$	−4.83098	−0.462724	−0.231362	−	0.972868i	$-0.574318\pi$
$109$	−4.83098	−0.462724	−0.231362	+	0.972868i	$0.574318\pi$
$110$	−0.196888	−0.0187726
$111$	6.02920	0.572267
$112$	−12.4210	−1.17368
$113$	−11.4476	−1.07690	−0.538448	−	0.842659i	$-0.680989\pi$
$113$	−11.4476	−1.07690	−0.538448	+	0.842659i	$0.680989\pi$
$114$	−8.10140	−0.758766
$115$	−0.0536512	−0.00500300
$116$	35.7748	3.32161
$117$	−0.529671	−0.0489681
$118$	0.931323	0.0857352
$119$	27.6359	2.53338
$120$	0.127402	0.0116302
$121$	−3.16762	−0.287965
$122$	33.2792	3.01296
$123$	−5.62171	−0.506893
$124$	−32.8363	−2.94878
$125$	0.291818	0.0261010
$126$	10.3200	0.919375
$127$	−5.91982	−0.525299	−0.262649	−	0.964891i	$-0.584596\pi$
$127$	−5.91982	−0.525299	−0.262649	+	0.964891i	$0.584596\pi$
$128$	20.6070	1.82142
$129$	4.91765	0.432975
$130$	−0.0372631	−0.00326819
$131$	11.0327	0.963929	0.481965	−	0.876191i	$-0.339923\pi$
$131$	11.0327	0.963929	0.481965	+	0.876191i	$0.339923\pi$
$132$	−10.6654	−0.928307
$133$	−14.3877	−1.24757
$134$	−30.1158	−2.60161
$135$	−0.0291843	−0.00251179
$136$	28.1802	2.41644
$137$	−9.59424	−0.819691	−0.409846	−	0.912155i	$-0.634417\pi$
$137$	−9.59424	−0.819691	−0.409846	+	0.912155i	$0.634417\pi$
$138$	−4.43152	−0.377236
$139$	−15.7442	−1.33541	−0.667705	−	0.744426i	$-0.732723\pi$
$139$	−15.7442	−1.33541	−0.667705	+	0.744426i	$0.732723\pi$
$140$	0.476142	0.0402414
$141$	−12.7556	−1.07422
$142$	21.2671	1.78470
$143$	1.48236	0.123961
$144$	2.90137	0.241781
$145$	−0.273965	−0.0227516
$146$	−20.6647	−1.71022
$147$	11.3278	0.934300
$148$	22.9769	1.88869
$149$	−20.2264	−1.65701	−0.828504	−	0.559983i	$-0.810808\pi$
$149$	−20.2264	−1.65701	−0.828504	+	0.559983i	$0.810808\pi$
$150$	12.0509	0.983951
$151$	10.0513	0.817962	0.408981	−	0.912543i	$-0.365884\pi$
$151$	10.0513	0.817962	0.408981	+	0.912543i	$0.365884\pi$
$152$	−14.6711	−1.18999
$153$	−6.45533	−0.521882
$154$	−28.8818	−2.32737
$155$	0.251462	0.0201979
$156$	−2.01854	−0.161613
$157$	11.6302	0.928191	0.464096	−	0.885785i	$-0.346379\pi$
$157$	11.6302	0.928191	0.464096	+	0.885785i	$0.346379\pi$
$158$	11.2901	0.898195
$159$	−3.08474	−0.244636
$160$	−0.0506886	−0.00400729
$161$	−7.87017	−0.620257
$162$	−2.41059	−0.189394
$163$	23.1152	1.81052	0.905262	−	0.424854i	$-0.139675\pi$
$163$	23.1152	1.81052	0.905262	+	0.424854i	$0.139675\pi$
$164$	−21.4240	−1.67293
$165$	0.0816764	0.00635850
$166$	−7.57841	−0.588199
$167$	12.0948	0.935924	0.467962	−	0.883749i	$-0.344988\pi$
$167$	12.0948	0.935924	0.467962	+	0.883749i	$0.344988\pi$
$168$	18.6888	1.44187
$169$	−12.7194	−0.978419
$170$	−0.454141	−0.0348311
$171$	3.36076	0.257004
$172$	18.7409	1.42898
$173$	−14.0029	−1.06462	−0.532309	−	0.846550i	$-0.678676\pi$
$173$	−14.0029	−1.06462	−0.532309	+	0.846550i	$0.678676\pi$
$174$	−22.6292	−1.71551
$175$	21.4018	1.61783
$176$	−8.11988	−0.612059
$177$	−0.386347	−0.0290396
$178$	31.7474	2.37957
$179$	7.71284	0.576485	0.288243	−	0.957557i	$-0.406929\pi$
$179$	7.71284	0.576485	0.288243	+	0.957557i	$0.406929\pi$
$180$	−0.111220	−0.00828982
$181$	−16.7560	−1.24547	−0.622733	−	0.782434i	$-0.713978\pi$
$181$	−16.7560	−1.24547	−0.622733	+	0.782434i	$0.713978\pi$
$182$	−5.46619	−0.405181
$183$	−13.8054	−1.02053
$184$	−8.02520	−0.591626
$185$	−0.175958	−0.0129367
$186$	20.7704	1.52296
$187$	18.0661	1.32113
$188$	−48.6110	−3.54532
$189$	−4.28110	−0.311404
$190$	0.236434	0.0171527
$191$	−2.11723	−0.153197	−0.0765985	−	0.997062i	$-0.524406\pi$
$191$	−2.11723	−0.153197	−0.0765985	+	0.997062i	$0.524406\pi$
$192$	−9.98955	−0.720934
$193$	21.7998	1.56919	0.784593	−	0.620011i	$-0.212872\pi$
$193$	21.7998	1.56919	0.784593	+	0.620011i	$0.212872\pi$
$194$	−30.2324	−2.17056
$195$	0.0154581	0.00110698
$196$	43.1695	3.08353
$197$	12.6763	0.903151	0.451575	−	0.892233i	$-0.350862\pi$
$197$	12.6763	0.903151	0.451575	+	0.892233i	$0.350862\pi$
$198$	6.74637	0.479443
$199$	−2.54320	−0.180283	−0.0901413	−	0.995929i	$-0.528732\pi$
$199$	−2.54320	−0.180283	−0.0901413	+	0.995929i	$0.528732\pi$
$200$	21.8234	1.54315
$201$	12.4931	0.881197
$202$	2.72927	0.192031
$203$	−40.1884	−2.82067
$204$	−24.6008	−1.72240
$205$	0.164066	0.0114589
$206$	26.0930	1.81798
$207$	1.83835	0.127774
$208$	−1.53677	−0.106556
$209$	−9.40555	−0.650595
$210$	−0.301181	−0.0207835
$211$	13.6475	0.939535	0.469768	−	0.882790i	$-0.344338\pi$
$211$	13.6475	0.939535	0.469768	+	0.882790i	$0.344338\pi$
$212$	−11.7557	−0.807388
$213$	−8.82238	−0.604500
$214$	39.5280	2.70208
$215$	−0.143518	−0.00978788
$216$	−4.36543	−0.297030
$217$	36.8873	2.50407
$218$	11.6455	0.788733
$219$	8.57246	0.579273
$220$	0.311264	0.0209854
$221$	3.41920	0.230000
$222$	−14.5339	−0.975454
$223$	15.0731	1.00937	0.504683	−	0.863305i	$-0.331609\pi$
$223$	15.0731	1.00937	0.504683	+	0.863305i	$0.331609\pi$
$224$	−7.43559	−0.496811
$225$	−4.99915	−0.333277
$226$	27.5954	1.83562
$227$	23.3873	1.55227	0.776134	−	0.630568i	$-0.217178\pi$
$227$	23.3873	1.55227	0.776134	+	0.630568i	$0.217178\pi$
$228$	12.8076	0.848206
$229$	29.9193	1.97712	0.988562	−	0.150812i	$-0.0481889\pi$
$229$	29.9193	1.97712	0.988562	+	0.150812i	$0.0481889\pi$
$230$	0.129331	0.00852782
$231$	11.9812	0.788308
$232$	−40.9800	−2.69047
$233$	−13.7713	−0.902185	−0.451092	−	0.892477i	$-0.648965\pi$
$233$	−13.7713	−0.902185	−0.451092	+	0.892477i	$0.648965\pi$
$234$	1.27682	0.0834683
$235$	0.372265	0.0242839
$236$	−1.47234	−0.0958414
$237$	−4.68356	−0.304230
$238$	−66.6187	−4.31825
$239$	10.4291	0.674604	0.337302	−	0.941397i	$-0.390486\pi$
$239$	10.4291	0.674604	0.337302	+	0.941397i	$0.390486\pi$
$240$	−0.0846745	−0.00546572
$241$	−6.11450	−0.393870	−0.196935	−	0.980417i	$-0.563099\pi$
$241$	−6.11450	−0.393870	−0.196935	+	0.980417i	$0.563099\pi$
$242$	7.63583	0.490850
$243$	1.00000	0.0641500
$244$	−52.6116	−3.36811
$245$	−0.330594	−0.0211209
$246$	13.5516	0.864021
$247$	−1.78010	−0.113265
$248$	37.6139	2.38849
$249$	3.14380	0.199230
$250$	−0.703454	−0.0444904
$251$	20.3582	1.28500	0.642500	−	0.766285i	$-0.277897\pi$
$251$	20.3582	1.28500	0.642500	+	0.766285i	$0.277897\pi$
$252$	−16.3150	−1.02775
$253$	−5.14489	−0.323457
$254$	14.2702	0.895395
$255$	0.188394	0.0117977
$256$	−29.6959	−1.85600
$257$	−11.1357	−0.694624	−0.347312	−	0.937750i	$-0.612906\pi$
$257$	−11.1357	−0.694624	−0.347312	+	0.937750i	$0.612906\pi$
$258$	−11.8544	−0.738025
$259$	−25.8116	−1.60386
$260$	0.0589098	0.00365343
$261$	9.38740	0.581066
$262$	−26.5952	−1.64306
$263$	22.0849	1.36181	0.680906	−	0.732371i	$-0.261586\pi$
$263$	22.0849	1.36181	0.680906	+	0.732371i	$0.261586\pi$
$264$	12.2172	0.751920
$265$	0.0900261	0.00553026
$266$	34.6829	2.12654
$267$	−13.1700	−0.805989
$268$	47.6105	2.90828
$269$	−24.7147	−1.50688	−0.753441	−	0.657516i	$-0.771607\pi$
$269$	−24.7147	−1.50688	−0.753441	+	0.657516i	$0.771607\pi$
$270$	0.0703514	0.00428145
$271$	19.4297	1.18027	0.590134	−	0.807305i	$-0.299075\pi$
$271$	19.4297	1.18027	0.590134	+	0.807305i	$0.299075\pi$
$272$	−18.7293	−1.13563
$273$	2.26757	0.137240
$274$	23.1278	1.39720
$275$	13.9908	0.843678
$276$	7.00585	0.421703
$277$	19.7316	1.18556	0.592778	−	0.805366i	$-0.298031\pi$
$277$	19.7316	1.18556	0.592778	+	0.805366i	$0.298031\pi$
$278$	37.9529	2.27626
$279$	−8.61633	−0.515846
$280$	−0.545420	−0.0325951
$281$	15.5789	0.929361	0.464680	−	0.885478i	$-0.346169\pi$
$281$	15.5789	0.929361	0.464680	+	0.885478i	$0.346169\pi$
$282$	30.7486	1.83105
$283$	22.0000	1.30776	0.653882	−	0.756597i	$-0.273139\pi$
$283$	22.0000	1.30776	0.653882	+	0.756597i	$0.273139\pi$
$284$	−33.6216	−1.99507
$285$	−0.0980815	−0.00580984
$286$	−3.57336	−0.211297
$287$	24.0671	1.42064
$288$	1.73684	0.102344
$289$	24.6712	1.45125
$290$	0.660417	0.0387810
$291$	12.5415	0.735196
$292$	32.6691	1.91182
$293$	30.8227	1.80068	0.900342	−	0.435183i	$-0.143316\pi$
$293$	30.8227	1.80068	0.900342	+	0.435183i	$0.143316\pi$
$294$	−27.3066	−1.59255
$295$	0.0112753	0.000656472 0
$296$	−26.3200	−1.52982
$297$	−2.79864	−0.162394
$298$	48.7574	2.82444
$299$	−0.973723	−0.0563119
$300$	−19.0514	−1.09994
$301$	−21.0530	−1.21347
$302$	−24.2295	−1.39425
$303$	−1.13220	−0.0650433
$304$	9.75080	0.559247
$305$	0.402902	0.0230701
$306$	15.5611	0.889571
$307$	−9.68555	−0.552783	−0.276392	−	0.961045i	$-0.589139\pi$
$307$	−9.68555	−0.552783	−0.276392	+	0.961045i	$0.589139\pi$
$308$	45.6598	2.60171
$309$	−10.8243	−0.615774
$310$	−0.606171	−0.0344282
$311$	4.90114	0.277918	0.138959	−	0.990298i	$-0.455624\pi$
$311$	4.90114	0.277918	0.138959	+	0.990298i	$0.455624\pi$
$312$	2.31224	0.130905
$313$	5.44833	0.307958	0.153979	−	0.988074i	$-0.450791\pi$
$313$	5.44833	0.307958	0.153979	+	0.988074i	$0.450791\pi$
$314$	−28.0356	−1.58214
$315$	0.124941	0.00703962
$316$	−17.8488	−1.00407
$317$	13.9208	0.781868	0.390934	−	0.920419i	$-0.372152\pi$
$317$	13.9208	0.781868	0.390934	+	0.920419i	$0.372152\pi$
$318$	7.43604	0.416992
$319$	−26.2720	−1.47095
$320$	0.291538	0.0162975
$321$	−16.3976	−0.915227
$322$	18.9717	1.05725
$323$	−21.6948	−1.20713
$324$	3.81094	0.211719
$325$	2.64790	0.146879
$326$	−55.7213	−3.08612
$327$	−4.83098	−0.267154
$328$	24.5412	1.35506
$329$	54.6082	3.01064
$330$	−0.196888	−0.0108383
$331$	−20.0851	−1.10398	−0.551989	−	0.833852i	$-0.686131\pi$
$331$	−20.0851	−1.10398	−0.551989	+	0.833852i	$0.686131\pi$
$332$	11.9808	0.657533
$333$	6.02920	0.330398
$334$	−29.1556	−1.59532
$335$	−0.364604	−0.0199204
$336$	−12.4210	−0.677623
$337$	12.3695	0.673808	0.336904	−	0.941539i	$-0.390620\pi$
$337$	12.3695	0.673808	0.336904	+	0.941539i	$0.390620\pi$
$338$	30.6614	1.66776
$339$	−11.4476	−0.621746
$340$	0.717959	0.0389368
$341$	24.1140	1.30585
$342$	−8.10140	−0.438074
$343$	−18.5277	−1.00040
$344$	−21.4677	−1.15746
$345$	−0.0536512	−0.00288848
$346$	33.7552	1.81469
$347$	−23.5795	−1.26582	−0.632908	−	0.774227i	$-0.718139\pi$
$347$	−23.5795	−1.26582	−0.632908	+	0.774227i	$0.718139\pi$
$348$	35.7748	1.91773
$349$	10.7755	0.576798	0.288399	−	0.957510i	$-0.406877\pi$
$349$	10.7755	0.576798	0.288399	+	0.957510i	$0.406877\pi$
$350$	−51.5910	−2.75766
$351$	−0.529671	−0.0282718
$352$	−4.86080	−0.259081
$353$	9.91438	0.527689	0.263845	−	0.964565i	$-0.415009\pi$
$353$	9.91438	0.527689	0.263845	+	0.964565i	$0.415009\pi$
$354$	0.931323	0.0494993
$355$	0.257475	0.0136654
$356$	−50.1899	−2.66006
$357$	27.6359	1.46265
$358$	−18.5925	−0.982644
$359$	−29.9928	−1.58296	−0.791480	−	0.611196i	$-0.790689\pi$
$359$	−29.9928	−1.58296	−0.791480	+	0.611196i	$0.790689\pi$
$360$	0.127402	0.00671468
$361$	−7.70531	−0.405543
$362$	40.3919	2.12295
$363$	−3.16762	−0.166257
$364$	8.64158	0.452942
$365$	−0.250182	−0.0130951
$366$	33.2792	1.73953
$367$	27.9195	1.45738	0.728692	−	0.684842i	$-0.240129\pi$
$367$	27.9195	1.45738	0.728692	+	0.684842i	$0.240129\pi$
$368$	5.33375	0.278041
$369$	−5.62171	−0.292655
$370$	0.424163	0.0220512
$371$	13.2061	0.685625
$372$	−32.8363	−1.70248
$373$	6.98536	0.361688	0.180844	−	0.983512i	$-0.442117\pi$
$373$	6.98536	0.361688	0.180844	+	0.983512i	$0.442117\pi$
$374$	−43.5500	−2.25192
$375$	0.291818	0.0150694
$376$	55.6838	2.87167
$377$	−4.97224	−0.256083
$378$	10.3200	0.530802
$379$	−3.13295	−0.160929	−0.0804644	−	0.996757i	$-0.525640\pi$
$379$	−3.13295	−0.160929	−0.0804644	+	0.996757i	$0.525640\pi$
$380$	−0.373782	−0.0191746
$381$	−5.91982	−0.303281
$382$	5.10376	0.261131
$383$	−7.43540	−0.379931	−0.189966	−	0.981791i	$-0.560838\pi$
$383$	−7.43540	−0.379931	−0.189966	+	0.981791i	$0.560838\pi$
$384$	20.6070	1.05160
$385$	−0.349665	−0.0178206
$386$	−52.5504	−2.67475
$387$	4.91765	0.249978
$388$	47.7949	2.42642
$389$	−11.1293	−0.564277	−0.282139	−	0.959374i	$-0.591044\pi$
$389$	−11.1293	−0.564277	−0.282139	+	0.959374i	$0.591044\pi$
$390$	−0.0372631	−0.00188689
$391$	−11.8672	−0.600149
$392$	−49.4506	−2.49763
$393$	11.0327	0.556525
$394$	−30.5574	−1.53946
$395$	0.136687	0.00687745
$396$	−10.6654	−0.535958
$397$	−4.70184	−0.235979	−0.117989	−	0.993015i	$-0.537645\pi$
$397$	−4.70184	−0.235979	−0.117989	+	0.993015i	$0.537645\pi$
$398$	6.13060	0.307299
$399$	−14.3877	−0.720287
$400$	−14.5044	−0.725219
$401$	13.0422	0.651297	0.325649	−	0.945491i	$-0.394417\pi$
$401$	13.0422	0.651297	0.325649	+	0.945491i	$0.394417\pi$
$402$	−30.1158	−1.50204
$403$	4.56382	0.227340
$404$	−4.31475	−0.214667
$405$	−0.0291843	−0.00145018
$406$	96.8776	4.80796
$407$	−16.8736	−0.836392
$408$	28.1802	1.39513
$409$	18.5050	0.915011	0.457505	−	0.889207i	$-0.348743\pi$
$409$	18.5050	0.915011	0.457505	+	0.889207i	$0.348743\pi$
$410$	−0.395495	−0.0195321
$411$	−9.59424	−0.473249
$412$	−41.2508	−2.03228
$413$	1.65399	0.0813874
$414$	−4.43152	−0.217797
$415$	−0.0917497	−0.00450382
$416$	−0.919955	−0.0451045
$417$	−15.7442	−0.770999
$418$	22.6729	1.10897
$419$	−21.6029	−1.05537	−0.527686	−	0.849439i	$-0.676940\pi$
$419$	−21.6029	−1.05537	−0.527686	+	0.849439i	$0.676940\pi$
$420$	0.476142	0.0232334
$421$	−13.6903	−0.667222	−0.333611	−	0.942711i	$-0.608267\pi$
$421$	−13.6903	−0.667222	−0.333611	+	0.942711i	$0.608267\pi$
$422$	−32.8986	−1.60148
$423$	−12.7556	−0.620201
$424$	13.4662	0.653976
$425$	32.2711	1.56538
$426$	21.2671	1.03040
$427$	59.1024	2.86016
$428$	−62.4904	−3.02059
$429$	1.48236	0.0715689
$430$	0.345964	0.0166839
$431$	8.11749	0.391006	0.195503	−	0.980703i	$-0.437366\pi$
$431$	8.11749	0.391006	0.195503	+	0.980703i	$0.437366\pi$
$432$	2.90137	0.139592
$433$	−1.57598	−0.0757367	−0.0378684	−	0.999283i	$-0.512057\pi$
$433$	−1.57598	−0.0757367	−0.0378684	+	0.999283i	$0.512057\pi$
$434$	−88.9202	−4.26830
$435$	−0.273965	−0.0131356
$436$	−18.4106	−0.881706
$437$	6.17826	0.295546
$438$	−20.6647	−0.987397
$439$	18.3362	0.875139	0.437570	−	0.899185i	$-0.355839\pi$
$439$	18.3362	0.875139	0.437570	+	0.899185i	$0.355839\pi$
$440$	−0.356552	−0.0169980
$441$	11.3278	0.539418
$442$	−8.24228	−0.392045
$443$	−34.6421	−1.64590	−0.822948	−	0.568117i	$-0.807672\pi$
$443$	−34.6421	−1.64590	−0.822948	+	0.568117i	$0.807672\pi$
$444$	22.9769	1.09044
$445$	0.384357	0.0182203
$446$	−36.3349	−1.72051
$447$	−20.2264	−0.956674
$448$	42.7662	2.02051
$449$	2.54242	0.119984	0.0599922	−	0.998199i	$-0.480892\pi$
$449$	2.54242	0.119984	0.0599922	+	0.998199i	$0.480892\pi$
$450$	12.0509	0.568084
$451$	15.7331	0.740845
$452$	−43.6259	−2.05199
$453$	10.0513	0.472251
$454$	−56.3771	−2.64591
$455$	−0.0661776	−0.00310245
$456$	−14.6711	−0.687039
$457$	−18.9791	−0.887805	−0.443902	−	0.896075i	$-0.646406\pi$
$457$	−18.9791	−0.887805	−0.443902	+	0.896075i	$0.646406\pi$
$458$	−72.1232	−3.37010
$459$	−6.45533	−0.301309
$460$	−0.204461	−0.00953305
$461$	−9.74527	−0.453882	−0.226941	−	0.973908i	$-0.572873\pi$
$461$	−9.74527	−0.453882	−0.226941	+	0.973908i	$0.572873\pi$
$462$	−28.8818	−1.34371
$463$	26.6543	1.23873	0.619366	−	0.785102i	$-0.287390\pi$
$463$	26.6543	1.23873	0.619366	+	0.785102i	$0.287390\pi$
$464$	27.2363	1.26441
$465$	0.251462	0.0116613
$466$	33.1968	1.53781
$467$	−1.80488	−0.0835201	−0.0417600	−	0.999128i	$-0.513296\pi$
$467$	−1.80488	−0.0835201	−0.0417600	+	0.999128i	$0.513296\pi$
$468$	−2.01854	−0.0933072
$469$	−53.4843	−2.46967
$470$	−0.897378	−0.0413930
$471$	11.6302	0.535891
$472$	1.68657	0.0776306
$473$	−13.7627	−0.632811
$474$	11.2901	0.518573
$475$	−16.8009	−0.770879
$476$	105.319	4.82727
$477$	−3.08474	−0.141241
$478$	−25.1403	−1.14989
$479$	35.0893	1.60327	0.801636	−	0.597813i	$-0.203963\pi$
$479$	35.0893	1.60327	0.801636	+	0.597813i	$0.203963\pi$
$480$	−0.0506886	−0.00231361
$481$	−3.19350	−0.145611
$482$	14.7396	0.671368
$483$	−7.87017	−0.358105
$484$	−12.0716	−0.548709
$485$	−0.366015	−0.0166199
$486$	−2.41059	−0.109347
$487$	−12.0195	−0.544653	−0.272327	−	0.962205i	$-0.587793\pi$
$487$	−12.0195	−0.544653	−0.272327	+	0.962205i	$0.587793\pi$
$488$	60.2666	2.72814
$489$	23.1152	1.04531
$490$	0.796926	0.0360014
$491$	−10.3636	−0.467704	−0.233852	−	0.972272i	$-0.575133\pi$
$491$	−10.3636	−0.467704	−0.233852	+	0.972272i	$0.575133\pi$
$492$	−21.4240	−0.965868
$493$	−60.5988	−2.72923
$494$	4.29108	0.193065
$495$	0.0816764	0.00367108
$496$	−24.9991	−1.12249
$497$	37.7695	1.69419
$498$	−7.57841	−0.339597
$499$	10.4650	0.468479	0.234239	−	0.972179i	$-0.424740\pi$
$499$	10.4650	0.468479	0.234239	+	0.972179i	$0.424740\pi$
$500$	1.11210	0.0497347
$501$	12.0948	0.540356
$502$	−49.0753	−2.19034
$503$	−42.0914	−1.87676	−0.938380	−	0.345604i	$-0.887674\pi$
$503$	−42.0914	−1.87676	−0.938380	+	0.345604i	$0.887674\pi$
$504$	18.6888	0.832465
$505$	0.0330426	0.00147037
$506$	12.4022	0.551346
$507$	−12.7194	−0.564891
$508$	−22.5601	−1.00094
$509$	9.02358	0.399963	0.199982	−	0.979800i	$-0.435912\pi$
$509$	9.02358	0.399963	0.199982	+	0.979800i	$0.435912\pi$
$510$	−0.454141	−0.0201097
$511$	−36.6995	−1.62349
$512$	30.3706	1.34221
$513$	3.36076	0.148381
$514$	26.8435	1.18402
$515$	0.315900	0.0139202
$516$	18.7409	0.825021
$517$	35.6985	1.57002
$518$	62.2212	2.73384
$519$	−14.0029	−0.614658
$520$	−0.0674812	−0.00295924
$521$	13.1280	0.575150	0.287575	−	0.957758i	$-0.407151\pi$
$521$	13.1280	0.575150	0.287575	+	0.957758i	$0.407151\pi$
$522$	−22.6292	−0.990452
$523$	18.3421	0.802046	0.401023	−	0.916068i	$-0.368655\pi$
$523$	18.3421	0.802046	0.401023	+	0.916068i	$0.368655\pi$
$524$	42.0448	1.83674
$525$	21.4018	0.934053
$526$	−53.2375	−2.32127
$527$	55.6212	2.42290
$528$	−8.11988	−0.353373
$529$	−19.6205	−0.853063
$530$	−0.217016	−0.00942656
$531$	−0.386347	−0.0167660
$532$	−54.8307	−2.37721
$533$	2.97766	0.128977
$534$	31.7474	1.37384
$535$	0.478554	0.0206897
$536$	−54.5378	−2.35567
$537$	7.71284	0.332834
$538$	59.5770	2.56855
$539$	−31.7024	−1.36552
$540$	−0.111220	−0.00478613
$541$	−36.9626	−1.58915	−0.794573	−	0.607168i	$-0.792305\pi$
$541$	−36.9626	−1.58915	−0.794573	+	0.607168i	$0.792305\pi$
$542$	−46.8369	−2.01182
$543$	−16.7560	−0.719070
$544$	−11.2119	−0.480706
$545$	0.140989	0.00603930
$546$	−5.46619	−0.233931
$547$	15.8891	0.679370	0.339685	−	0.940539i	$-0.389680\pi$
$547$	15.8891	0.679370	0.339685	+	0.940539i	$0.389680\pi$
$548$	−36.5631	−1.56190
$549$	−13.8054	−0.589201
$550$	−33.7261	−1.43809
$551$	31.5488	1.34402
$552$	−8.02520	−0.341575
$553$	20.0508	0.852646
$554$	−47.5647	−2.02083
$555$	−0.175958	−0.00746902
$556$	−60.0003	−2.54458
$557$	1.39247	0.0590010	0.0295005	−	0.999565i	$-0.490608\pi$
$557$	1.39247	0.0590010	0.0295005	+	0.999565i	$0.490608\pi$
$558$	20.7704	0.879282
$559$	−2.60474	−0.110169
$560$	0.362500	0.0153184
$561$	18.0661	0.762753
$562$	−37.5544	−1.58414
$563$	−2.08672	−0.0879446	−0.0439723	−	0.999033i	$-0.514001\pi$
$563$	−2.08672	−0.0879446	−0.0439723	+	0.999033i	$0.514001\pi$
$564$	−48.6110	−2.04689
$565$	0.334090	0.0140553
$566$	−53.0329	−2.22914
$567$	−4.28110	−0.179789
$568$	38.5135	1.61599
$569$	4.35134	0.182418	0.0912088	−	0.995832i	$-0.470927\pi$
$569$	4.35134	0.182418	0.0912088	+	0.995832i	$0.470927\pi$
$570$	0.236434	0.00990313
$571$	32.5669	1.36288	0.681442	−	0.731872i	$-0.261353\pi$
$571$	32.5669	1.36288	0.681442	+	0.731872i	$0.261353\pi$
$572$	5.64917	0.236204
$573$	−2.11723	−0.0884483
$574$	−58.0158	−2.42153
$575$	−9.19021	−0.383258
$576$	−9.98955	−0.416231
$577$	12.2346	0.509332	0.254666	−	0.967029i	$-0.418034\pi$
$577$	12.2346	0.509332	0.254666	+	0.967029i	$0.418034\pi$
$578$	−59.4722	−2.47372
$579$	21.7998	0.905970
$580$	−1.04406	−0.0433524
$581$	−13.4589	−0.558370
$582$	−30.2324	−1.25317
$583$	8.63307	0.357545
$584$	−37.4224	−1.54855
$585$	0.0154581	0.000639114 0
$586$	−74.3010	−3.06934
$587$	13.3537	0.551166	0.275583	−	0.961277i	$-0.411129\pi$
$587$	13.3537	0.551166	0.275583	+	0.961277i	$0.411129\pi$
$588$	43.1695	1.78028
$589$	−28.9574	−1.19317
$590$	−0.0271800	−0.00111898
$591$	12.6763	0.521434
$592$	17.4929	0.718956
$593$	−26.6548	−1.09458	−0.547290	−	0.836943i	$-0.684341\pi$
$593$	−26.6548	−1.09458	−0.547290	+	0.836943i	$0.684341\pi$
$594$	6.74637	0.276807
$595$	−0.806535	−0.0330647
$596$	−77.0814	−3.15738
$597$	−2.54320	−0.104086
$598$	2.34725	0.0959860
$599$	−25.5806	−1.04519	−0.522597	−	0.852580i	$-0.675037\pi$
$599$	−25.5806	−1.04519	−0.522597	+	0.852580i	$0.675037\pi$
$600$	21.8234	0.890937
$601$	14.1037	0.575301	0.287650	−	0.957735i	$-0.407126\pi$
$601$	14.1037	0.575301	0.287650	+	0.957735i	$0.407126\pi$
$602$	50.7500	2.06842
$603$	12.4931	0.508760
$604$	38.3048	1.55860
$605$	0.0924449	0.00375842
$606$	2.72927	0.110869
$607$	28.9805	1.17628	0.588141	−	0.808759i	$-0.299860\pi$
$607$	28.9805	1.17628	0.588141	+	0.808759i	$0.299860\pi$
$608$	5.83711	0.236726
$609$	−40.1884	−1.62852
$610$	−0.971232	−0.0393240
$611$	6.75630	0.273331
$612$	−24.6008	−0.994430
$613$	−9.41225	−0.380157	−0.190079	−	0.981769i	$-0.560874\pi$
$613$	−9.41225	−0.380157	−0.190079	+	0.981769i	$0.560874\pi$
$614$	23.3479	0.942244
$615$	0.164066	0.00661578
$616$	−52.3032	−2.10736
$617$	27.4211	1.10393	0.551965	−	0.833867i	$-0.313878\pi$
$617$	27.4211	1.10393	0.551965	+	0.833867i	$0.313878\pi$
$618$	26.0930	1.04961
$619$	−2.44299	−0.0981921	−0.0490961	−	0.998794i	$-0.515634\pi$
$619$	−2.44299	−0.0981921	−0.0490961	+	0.998794i	$0.515634\pi$
$620$	0.958305	0.0384865
$621$	1.83835	0.0737706
$622$	−11.8146	−0.473723
$623$	56.3819	2.25889
$624$	−1.53677	−0.0615201
$625$	24.9872	0.999489
$626$	−13.1337	−0.524927
$627$	−9.40555	−0.375621
$628$	44.3220	1.76864
$629$	−38.9205	−1.55186
$630$	−0.301181	−0.0119993
$631$	17.0681	0.679469	0.339734	−	0.940521i	$-0.389663\pi$
$631$	17.0681	0.679469	0.339734	+	0.940521i	$0.389663\pi$
$632$	20.4457	0.813288
$633$	13.6475	0.542441
$634$	−33.5572	−1.33273
$635$	0.172766	0.00685601
$636$	−11.7557	−0.466146
$637$	−6.00000	−0.237729
$638$	63.3309	2.50729
$639$	−8.82238	−0.349008
$640$	−0.601402	−0.0237725
$641$	−2.09322	−0.0826772	−0.0413386	−	0.999145i	$-0.513162\pi$
$641$	−2.09322	−0.0826772	−0.0413386	+	0.999145i	$0.513162\pi$
$642$	39.5280	1.56004
$643$	−42.4852	−1.67545	−0.837726	−	0.546090i	$-0.816116\pi$
$643$	−42.4852	−1.67545	−0.837726	+	0.546090i	$0.816116\pi$
$644$	−29.9927	−1.18188
$645$	−0.143518	−0.00565103
$646$	52.2972	2.05761
$647$	−15.3077	−0.601806	−0.300903	−	0.953655i	$-0.597288\pi$
$647$	−15.3077	−0.601806	−0.300903	+	0.953655i	$0.597288\pi$
$648$	−4.36543	−0.171490
$649$	1.08125	0.0424426
$650$	−6.38301	−0.250362
$651$	36.8873	1.44573
$652$	88.0907	3.44990
$653$	11.8262	0.462796	0.231398	−	0.972859i	$-0.425670\pi$
$653$	11.8262	0.462796	0.231398	+	0.972859i	$0.425670\pi$
$654$	11.6455	0.455375
$655$	−0.321981	−0.0125808
$656$	−16.3107	−0.636824
$657$	8.57246	0.334444
$658$	−131.638	−5.13178
$659$	48.4642	1.88790	0.943949	−	0.330090i	$-0.107079\pi$
$659$	48.4642	1.88790	0.943949	+	0.330090i	$0.107079\pi$
$660$	0.311264	0.0121159
$661$	−10.2091	−0.397089	−0.198544	−	0.980092i	$-0.563621\pi$
$661$	−10.2091	−0.397089	−0.198544	+	0.980092i	$0.563621\pi$
$662$	48.4169	1.88178
$663$	3.41920	0.132791
$664$	−13.7240	−0.532595
$665$	0.419896	0.0162829
$666$	−14.5339	−0.563178
$667$	17.2574	0.668208
$668$	46.0925	1.78337
$669$	15.0731	0.582758
$670$	0.878909	0.0339552
$671$	38.6364	1.49154
$672$	−7.43559	−0.286834
$673$	49.9748	1.92639	0.963193	−	0.268812i	$-0.0866310\pi$
$673$	49.9748	1.92639	0.963193	+	0.268812i	$0.0866310\pi$
$674$	−29.8177	−1.14853
$675$	−4.99915	−0.192417
$676$	−48.4730	−1.86435
$677$	31.1471	1.19708	0.598540	−	0.801093i	$-0.295748\pi$
$677$	31.1471	1.19708	0.598540	+	0.801093i	$0.295748\pi$
$678$	27.5954	1.05979
$679$	−53.6914	−2.06049
$680$	−0.822422	−0.0315384
$681$	23.3873	0.896202
$682$	−58.1289	−2.22587
$683$	31.1306	1.19118	0.595590	−	0.803288i	$-0.296918\pi$
$683$	31.1306	1.19118	0.595590	+	0.803288i	$0.296918\pi$
$684$	12.8076	0.489712
$685$	0.280002	0.0106983
$686$	44.6626	1.70522
$687$	29.9193	1.14149
$688$	14.2679	0.543960
$689$	1.63390	0.0622465
$690$	0.129331	0.00492354
$691$	−45.6611	−1.73703	−0.868515	−	0.495664i	$-0.834925\pi$
$691$	−45.6611	−1.73703	−0.868515	+	0.495664i	$0.834925\pi$
$692$	−53.3641	−2.02860
$693$	11.9812	0.455130
$694$	56.8406	2.15764
$695$	0.459485	0.0174293
$696$	−40.9800	−1.55334
$697$	36.2900	1.37458
$698$	−25.9752	−0.983176
$699$	−13.7713	−0.520877
$700$	81.5610	3.08272
$701$	11.9171	0.450102	0.225051	−	0.974347i	$-0.427745\pi$
$701$	11.9171	0.450102	0.225051	+	0.974347i	$0.427745\pi$
$702$	1.27682	0.0481904
$703$	20.2627	0.764222
$704$	27.9571	1.05367
$705$	0.372265	0.0140203
$706$	−23.8995	−0.899470
$707$	4.84707	0.182293
$708$	−1.47234	−0.0553341
$709$	−2.16116	−0.0811640	−0.0405820	−	0.999176i	$-0.512921\pi$
$709$	−2.16116	−0.0811640	−0.0405820	+	0.999176i	$0.512921\pi$
$710$	−0.620667	−0.0232932
$711$	−4.68356	−0.175647
$712$	57.4925	2.15462
$713$	−15.8399	−0.593208
$714$	−66.6187	−2.49314
$715$	−0.0432616	−0.00161789
$716$	29.3932	1.09847
$717$	10.4291	0.389483
$718$	72.3003	2.69822
$719$	1.95244	0.0728138	0.0364069	−	0.999337i	$-0.488409\pi$
$719$	1.95244	0.0728138	0.0364069	+	0.999337i	$0.488409\pi$
$720$	−0.0846745	−0.00315563
$721$	46.3399	1.72579
$722$	18.5743	0.691265
$723$	−6.11450	−0.227401
$724$	−63.8562	−2.37320
$725$	−46.9290	−1.74290
$726$	7.63583	0.283392
$727$	−14.0829	−0.522305	−0.261153	−	0.965298i	$-0.584103\pi$
$727$	−14.0829	−0.522305	−0.261153	+	0.965298i	$0.584103\pi$
$728$	−9.89892	−0.366878
$729$	1.00000	0.0370370
$730$	0.603085	0.0223212
$731$	−31.7451	−1.17413
$732$	−52.6116	−1.94458
$733$	15.4869	0.572023	0.286011	−	0.958226i	$-0.407670\pi$
$733$	15.4869	0.572023	0.286011	+	0.958226i	$0.407670\pi$
$734$	−67.3023	−2.48417
$735$	−0.330594	−0.0121941
$736$	3.19293	0.117693
$737$	−34.9638	−1.28791
$738$	13.5516	0.498843
$739$	35.3675	1.30101	0.650507	−	0.759501i	$-0.274557\pi$
$739$	35.3675	1.30101	0.650507	+	0.759501i	$0.274557\pi$
$740$	−0.670566	−0.0246505
$741$	−1.78010	−0.0653935
$742$	−31.8344	−1.16868
$743$	−12.9234	−0.474115	−0.237058	−	0.971496i	$-0.576183\pi$
$743$	−12.9234	−0.474115	−0.237058	+	0.971496i	$0.576183\pi$
$744$	37.6139	1.37899
$745$	0.590293	0.0216267
$746$	−16.8388	−0.616514
$747$	3.14380	0.115026
$748$	68.8489	2.51736
$749$	70.1999	2.56505
$750$	−0.703454	−0.0256865
$751$	33.6245	1.22698	0.613488	−	0.789704i	$-0.289766\pi$
$751$	33.6245	1.22698	0.613488	+	0.789704i	$0.289766\pi$
$752$	−37.0088	−1.34957
$753$	20.3582	0.741896
$754$	11.9860	0.436505
$755$	−0.293340	−0.0106757
$756$	−16.3150	−0.593370
$757$	−17.1319	−0.622669	−0.311335	−	0.950300i	$-0.600776\pi$
$757$	−17.1319	−0.622669	−0.311335	+	0.950300i	$0.600776\pi$
$758$	7.55225	0.274310
$759$	−5.14489	−0.186748
$760$	0.428167	0.0155313
$761$	−46.0391	−1.66892	−0.834458	−	0.551071i	$-0.814219\pi$
$761$	−46.0391	−1.66892	−0.834458	+	0.551071i	$0.814219\pi$
$762$	14.2702	0.516956
$763$	20.6819	0.748735
$764$	−8.06861	−0.291912
$765$	0.188394	0.00681141
$766$	17.9237	0.647609
$767$	0.204637	0.00738900
$768$	−29.6959	−1.07156
$769$	37.7773	1.36228	0.681142	−	0.732151i	$-0.261484\pi$
$769$	37.7773	1.36228	0.681142	+	0.732151i	$0.261484\pi$
$770$	0.842897	0.0303759
$771$	−11.1357	−0.401042
$772$	83.0778	2.99004
$773$	−10.8062	−0.388672	−0.194336	−	0.980935i	$-0.562255\pi$
$773$	−10.8062	−0.388672	−0.194336	+	0.980935i	$0.562255\pi$
$774$	−11.8544	−0.426099
$775$	43.0743	1.54727
$776$	−54.7490	−1.96537
$777$	−25.8116	−0.925986
$778$	26.8281	0.961835
$779$	−18.8932	−0.676919
$780$	0.0589098	0.00210931
$781$	24.6907	0.883502
$782$	28.6069	1.02298
$783$	9.38740	0.335478
$784$	32.8661	1.17379
$785$	−0.339420	−0.0121144
$786$	−26.5952	−0.948621
$787$	−46.3487	−1.65215	−0.826076	−	0.563559i	$-0.809432\pi$
$787$	−46.3487	−1.65215	−0.826076	+	0.563559i	$0.809432\pi$
$788$	48.3087	1.72093
$789$	22.0849	0.786242
$790$	−0.329495	−0.0117229
$791$	49.0081	1.74253
$792$	12.2172	0.434121
$793$	7.31234	0.259669
$794$	11.3342	0.402236
$795$	0.0900261	0.00319290
$796$	−9.69197	−0.343523
$797$	−18.0995	−0.641118	−0.320559	−	0.947229i	$-0.603871\pi$
$797$	−18.0995	−0.641118	−0.320559	+	0.947229i	$0.603871\pi$
$798$	34.6829	1.22776
$799$	82.3419	2.91305
$800$	−8.68273	−0.306981
$801$	−13.1700	−0.465338
$802$	−31.4394	−1.11016
$803$	−23.9912	−0.846632
$804$	47.6105	1.67909
$805$	0.229686	0.00809536
$806$	−11.0015	−0.387511
$807$	−24.7147	−0.869999
$808$	4.94254	0.173878
$809$	−21.0268	−0.739264	−0.369632	−	0.929178i	$-0.620516\pi$
$809$	−21.0268	−0.739264	−0.369632	+	0.929178i	$0.620516\pi$
$810$	0.0703514	0.00247190
$811$	−0.497548	−0.0174713	−0.00873563	−	0.999962i	$-0.502781\pi$
$811$	−0.497548	−0.0174713	−0.00873563	+	0.999962i	$0.502781\pi$
$812$	−153.155	−5.37470
$813$	19.4297	0.681428
$814$	40.6752	1.42567
$815$	−0.674602	−0.0236303
$816$	−18.7293	−0.655656
$817$	16.5270	0.578208
$818$	−44.6078	−1.55968
$819$	2.26757	0.0792354
$820$	0.625245	0.0218345
$821$	−42.3686	−1.47867	−0.739337	−	0.673335i	$-0.764861\pi$
$821$	−42.3686	−1.47867	−0.739337	+	0.673335i	$0.764861\pi$
$822$	23.1278	0.806674
$823$	−36.5864	−1.27532	−0.637660	−	0.770318i	$-0.720098\pi$
$823$	−36.5864	−1.27532	−0.637660	+	0.770318i	$0.720098\pi$
$824$	47.2527	1.64613
$825$	13.9908	0.487098
$826$	−3.98708	−0.138728
$827$	33.7534	1.17372	0.586861	−	0.809688i	$-0.300364\pi$
$827$	33.7534	1.17372	0.586861	+	0.809688i	$0.300364\pi$
$828$	7.00585	0.243470
$829$	−27.0039	−0.937886	−0.468943	−	0.883229i	$-0.655365\pi$
$829$	−27.0039	−0.937886	−0.468943	+	0.883229i	$0.655365\pi$
$830$	0.221171	0.00767695
$831$	19.7316	0.684481
$832$	5.29118	0.183439
$833$	−73.1245	−2.53362
$834$	37.9529	1.31420
$835$	−0.352979	−0.0122153
$836$	−35.8439	−1.23969
$837$	−8.61633	−0.297824
$838$	52.0758	1.79893
$839$	30.4241	1.05036	0.525179	−	0.850992i	$-0.323998\pi$
$839$	30.4241	1.05036	0.525179	+	0.850992i	$0.323998\pi$
$840$	−0.545420	−0.0188188
$841$	59.1233	2.03874
$842$	33.0016	1.13731
$843$	15.5789	0.536567
$844$	52.0099	1.79025
$845$	0.371209	0.0127700
$846$	30.7486	1.05716
$847$	13.5609	0.465957
$848$	−8.94997	−0.307343
$849$	22.0000	0.755038
$850$	−77.7924	−2.66826
$851$	11.0838	0.379948
$852$	−33.6216	−1.15186
$853$	−26.8765	−0.920232	−0.460116	−	0.887859i	$-0.652192\pi$
$853$	−26.8765	−0.920232	−0.460116	+	0.887859i	$0.652192\pi$
$854$	−142.472	−4.87527
$855$	−0.0980815	−0.00335431
$856$	71.5827	2.44665
$857$	−3.71644	−0.126951	−0.0634755	−	0.997983i	$-0.520218\pi$
$857$	−3.71644	−0.126951	−0.0634755	+	0.997983i	$0.520218\pi$
$858$	−3.57336	−0.121992
$859$	−35.4170	−1.20841	−0.604206	−	0.796828i	$-0.706510\pi$
$859$	−35.4170	−1.20841	−0.604206	+	0.796828i	$0.706510\pi$
$860$	−0.546940	−0.0186505
$861$	24.0671	0.820204
$862$	−19.5679	−0.666486
$863$	15.5705	0.530027	0.265013	−	0.964245i	$-0.414624\pi$
$863$	15.5705	0.530027	0.265013	+	0.964245i	$0.414624\pi$
$864$	1.73684	0.0590886
$865$	0.408664	0.0138950
$866$	3.79904	0.129097
$867$	24.6712	0.837879
$868$	140.575	4.77144
$869$	13.1076	0.444645
$870$	0.660417	0.0223902
$871$	−6.61725	−0.224217
$872$	21.0893	0.714173
$873$	12.5415	0.424466
$874$	−14.8933	−0.503772
$875$	−1.24930	−0.0422341
$876$	32.6691	1.10379
$877$	−19.3818	−0.654478	−0.327239	−	0.944942i	$-0.606118\pi$
$877$	−19.3818	−0.654478	−0.327239	+	0.944942i	$0.606118\pi$
$878$	−44.2010	−1.49171
$879$	30.8227	1.03963
$880$	0.236973	0.00798837
$881$	−22.3823	−0.754080	−0.377040	−	0.926197i	$-0.623058\pi$
$881$	−22.3823	−0.754080	−0.377040	+	0.926197i	$0.623058\pi$
$882$	−27.3066	−0.919462
$883$	−45.7562	−1.53982	−0.769909	−	0.638154i	$-0.779698\pi$
$883$	−45.7562	−1.53982	−0.769909	+	0.638154i	$0.779698\pi$
$884$	13.0304	0.438258
$885$	0.0112753	0.000379014 0
$886$	83.5078	2.80550
$887$	−7.67423	−0.257675	−0.128838	−	0.991666i	$-0.541125\pi$
$887$	−7.67423	−0.257675	−0.128838	+	0.991666i	$0.541125\pi$
$888$	−26.3200	−0.883243
$889$	25.3433	0.849987
$890$	−0.926526	−0.0310572
$891$	−2.79864	−0.0937579
$892$	57.4425	1.92332
$893$	−42.8686	−1.43454
$894$	48.7574	1.63069
$895$	−0.225094	−0.00752407
$896$	−88.2206	−2.94724
$897$	−0.973723	−0.0325117
$898$	−6.12874	−0.204519
$899$	−80.8849	−2.69766
$900$	−19.0514	−0.635048
$901$	19.9130	0.663398
$902$	−37.9261	−1.26280
$903$	−21.0530	−0.700598
$904$	49.9735	1.66209
$905$	0.489014	0.0162554
$906$	−24.2295	−0.804972
$907$	22.3182	0.741064	0.370532	−	0.928820i	$-0.379175\pi$
$907$	22.3182	0.741064	0.370532	+	0.928820i	$0.379175\pi$
$908$	89.1274	2.95780
$909$	−1.13220	−0.0375528
$910$	0.159527	0.00528827
$911$	56.8629	1.88395	0.941976	−	0.335681i	$-0.108966\pi$
$911$	56.8629	1.88395	0.941976	+	0.335681i	$0.108966\pi$
$912$	9.75080	0.322881
$913$	−8.79836	−0.291183
$914$	45.7508	1.51330
$915$	0.402902	0.0133195
$916$	114.021	3.76735
$917$	−47.2319	−1.55974
$918$	15.5611	0.513594
$919$	14.2808	0.471080	0.235540	−	0.971865i	$-0.424314\pi$
$919$	14.2808	0.471080	0.235540	+	0.971865i	$0.424314\pi$
$920$	0.234210	0.00772168
$921$	−9.68555	−0.319150
$922$	23.4918	0.773662
$923$	4.67296	0.153812
$924$	45.6598	1.50210
$925$	−30.1409	−0.991026
$926$	−64.2526	−2.11147
$927$	−10.8243	−0.355517
$928$	16.3044	0.535220
$929$	12.4699	0.409125	0.204563	−	0.978853i	$-0.434423\pi$
$929$	12.4699	0.409125	0.204563	+	0.978853i	$0.434423\pi$
$930$	−0.606171	−0.0198771
$931$	38.0699	1.24769
$932$	−52.4814	−1.71908
$933$	4.90114	0.160456
$934$	4.35083	0.142364
$935$	−0.527248	−0.0172429
$936$	2.31224	0.0755779
$937$	−54.6711	−1.78603	−0.893013	−	0.450030i	$-0.851413\pi$
$937$	−54.6711	−1.78603	−0.893013	+	0.450030i	$0.851413\pi$
$938$	128.929	4.20967
$939$	5.44833	0.177800
$940$	1.41868	0.0462722
$941$	14.5029	0.472780	0.236390	−	0.971658i	$-0.424036\pi$
$941$	14.5029	0.472780	0.236390	+	0.971658i	$0.424036\pi$
$942$	−28.0356	−0.913450
$943$	−10.3347	−0.336544
$944$	−1.12093	−0.0364833
$945$	0.124941	0.00406433
$946$	33.1763	1.07865
$947$	42.9697	1.39633	0.698164	−	0.715938i	$-0.254001\pi$
$947$	42.9697	1.39633	0.698164	+	0.715938i	$0.254001\pi$
$948$	−17.8488	−0.579701
$949$	−4.54059	−0.147394
$950$	40.5001	1.31400
$951$	13.9208	0.451412
$952$	−120.642	−3.91004
$953$	−21.4599	−0.695155	−0.347578	−	0.937651i	$-0.612996\pi$
$953$	−21.4599	−0.695155	−0.347578	+	0.937651i	$0.612996\pi$
$954$	7.43604	0.240751
$955$	0.0617898	0.00199947
$956$	39.7447	1.28544
$957$	−26.2720	−0.849252
$958$	−84.5859	−2.73285
$959$	41.0739	1.32634
$960$	0.291538	0.00940936
$961$	43.2411	1.39487
$962$	7.69820	0.248200
$963$	−16.3976	−0.528407
$964$	−23.3020	−0.750506
$965$	−0.636214	−0.0204804
$966$	18.9717	0.610406
$967$	46.9208	1.50887	0.754436	−	0.656373i	$-0.227910\pi$
$967$	46.9208	1.50887	0.754436	+	0.656373i	$0.227910\pi$
$968$	13.8280	0.444449
$969$	−21.6948	−0.696937
$970$	0.882313	0.0283294
$971$	−0.890351	−0.0285727	−0.0142864	−	0.999898i	$-0.504548\pi$
$971$	−0.890351	−0.0285727	−0.0142864	+	0.999898i	$0.504548\pi$
$972$	3.81094	0.122236
$973$	67.4026	2.16083
$974$	28.9740	0.928385
$975$	2.64790	0.0848008
$976$	−40.0546	−1.28212
$977$	40.7041	1.30224	0.651120	−	0.758974i	$-0.274299\pi$
$977$	40.7041	1.30224	0.651120	+	0.758974i	$0.274299\pi$
$978$	−55.7213	−1.78177
$979$	36.8580	1.17799
$980$	−1.25987	−0.0402451
$981$	−4.83098	−0.154241
$982$	24.9824	0.797222
$983$	−12.8908	−0.411153	−0.205576	−	0.978641i	$-0.565907\pi$
$983$	−12.8908	−0.411153	−0.205576	+	0.978641i	$0.565907\pi$
$984$	24.5412	0.782344
$985$	−0.369950	−0.0117876
$986$	146.079	4.65209
$987$	54.6082	1.73820
$988$	−6.78383	−0.215822
$989$	9.04039	0.287468
$990$	−0.196888	−0.00625752
$991$	44.1812	1.40346	0.701731	−	0.712442i	$-0.252411\pi$
$991$	44.1812	1.40346	0.701731	+	0.712442i	$0.252411\pi$
$992$	−14.9652	−0.475146
$993$	−20.0851	−0.637382
$994$	−91.0467	−2.88782
$995$	0.0742215	0.00235298
$996$	11.9808	0.379627
$997$	28.7888	0.911750	0.455875	−	0.890044i	$-0.349326\pi$
$997$	28.7888	0.911750	0.455875	+	0.890044i	$0.349326\pi$
$998$	−25.2269	−0.798542
$999$	6.02920	0.190756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.d.1.13	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.d.1.13	✓	129	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41059 q^{2} +1.00000 q^{3} +3.81094 q^{4} -0.0291843 q^{5} -2.41059 q^{6} -4.28110 q^{7} -4.36543 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.41059 q^{2} +1.00000 q^{3} +3.81094 q^{4} -0.0291843 q^{5} -2.41059 q^{6} -4.28110 q^{7} -4.36543 q^{8} +1.00000 q^{9} +0.0703514 q^{10} -2.79864 q^{11} +3.81094 q^{12} -0.529671 q^{13} +10.3200 q^{14} -0.0291843 q^{15} +2.90137 q^{16} -6.45533 q^{17} -2.41059 q^{18} +3.36076 q^{19} -0.111220 q^{20} -4.28110 q^{21} +6.74637 q^{22} +1.83835 q^{23} -4.36543 q^{24} -4.99915 q^{25} +1.27682 q^{26} +1.00000 q^{27} -16.3150 q^{28} +9.38740 q^{29} +0.0703514 q^{30} -8.61633 q^{31} +1.73684 q^{32} -2.79864 q^{33} +15.5611 q^{34} +0.124941 q^{35} +3.81094 q^{36} +6.02920 q^{37} -8.10140 q^{38} -0.529671 q^{39} +0.127402 q^{40} -5.62171 q^{41} +10.3200 q^{42} +4.91765 q^{43} -10.6654 q^{44} -0.0291843 q^{45} -4.43152 q^{46} -12.7556 q^{47} +2.90137 q^{48} +11.3278 q^{49} +12.0509 q^{50} -6.45533 q^{51} -2.01854 q^{52} -3.08474 q^{53} -2.41059 q^{54} +0.0816764 q^{55} +18.6888 q^{56} +3.36076 q^{57} -22.6292 q^{58} -0.386347 q^{59} -0.111220 q^{60} -13.8054 q^{61} +20.7704 q^{62} -4.28110 q^{63} -9.98955 q^{64} +0.0154581 q^{65} +6.74637 q^{66} +12.4931 q^{67} -24.6008 q^{68} +1.83835 q^{69} -0.301181 q^{70} -8.82238 q^{71} -4.36543 q^{72} +8.57246 q^{73} -14.5339 q^{74} -4.99915 q^{75} +12.8076 q^{76} +11.9812 q^{77} +1.27682 q^{78} -4.68356 q^{79} -0.0846745 q^{80} +1.00000 q^{81} +13.5516 q^{82} +3.14380 q^{83} -16.3150 q^{84} +0.188394 q^{85} -11.8544 q^{86} +9.38740 q^{87} +12.2172 q^{88} -13.1700 q^{89} +0.0703514 q^{90} +2.26757 q^{91} +7.00585 q^{92} -8.61633 q^{93} +30.7486 q^{94} -0.0980815 q^{95} +1.73684 q^{96} +12.5415 q^{97} -27.3066 q^{98} -2.79864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * q^99

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