LMFDB - Embedded newform 8013.2.a.d.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.21092 q^{2} +1.00000 q^{3} +2.88816 q^{4} +1.51753 q^{5} -2.21092 q^{6} +0.0486600 q^{7} -1.96364 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.21092 q^{2} +1.00000 q^{3} +2.88816 q^{4} +1.51753 q^{5} -2.21092 q^{6} +0.0486600 q^{7} -1.96364 q^{8} +1.00000 q^{9} -3.35514 q^{10} +6.56010 q^{11} +2.88816 q^{12} +0.517879 q^{13} -0.107583 q^{14} +1.51753 q^{15} -1.43486 q^{16} -4.76722 q^{17} -2.21092 q^{18} -0.00792509 q^{19} +4.38287 q^{20} +0.0486600 q^{21} -14.5038 q^{22} +4.25244 q^{23} -1.96364 q^{24} -2.69710 q^{25} -1.14499 q^{26} +1.00000 q^{27} +0.140538 q^{28} -7.88822 q^{29} -3.35514 q^{30} -3.05936 q^{31} +7.09965 q^{32} +6.56010 q^{33} +10.5399 q^{34} +0.0738431 q^{35} +2.88816 q^{36} +7.82698 q^{37} +0.0175217 q^{38} +0.517879 q^{39} -2.97989 q^{40} -7.47610 q^{41} -0.107583 q^{42} -8.77561 q^{43} +18.9466 q^{44} +1.51753 q^{45} -9.40180 q^{46} +1.80651 q^{47} -1.43486 q^{48} -6.99763 q^{49} +5.96306 q^{50} -4.76722 q^{51} +1.49571 q^{52} +5.72962 q^{53} -2.21092 q^{54} +9.95516 q^{55} -0.0955509 q^{56} -0.00792509 q^{57} +17.4402 q^{58} +0.207025 q^{59} +4.38287 q^{60} +12.1014 q^{61} +6.76400 q^{62} +0.0486600 q^{63} -12.8270 q^{64} +0.785897 q^{65} -14.5038 q^{66} -8.59573 q^{67} -13.7685 q^{68} +4.25244 q^{69} -0.163261 q^{70} +0.245324 q^{71} -1.96364 q^{72} +9.82368 q^{73} -17.3048 q^{74} -2.69710 q^{75} -0.0228889 q^{76} +0.319215 q^{77} -1.14499 q^{78} +16.6551 q^{79} -2.17745 q^{80} +1.00000 q^{81} +16.5290 q^{82} +6.64959 q^{83} +0.140538 q^{84} -7.23440 q^{85} +19.4022 q^{86} -7.88822 q^{87} -12.8817 q^{88} +14.6852 q^{89} -3.35514 q^{90} +0.0252000 q^{91} +12.2817 q^{92} -3.05936 q^{93} -3.99404 q^{94} -0.0120266 q^{95} +7.09965 q^{96} +12.1718 q^{97} +15.4712 q^{98} +6.56010 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.21092	−1.56335	−0.781677	−	0.623683i	$-0.785636\pi$
$2$	−2.21092	−1.56335	−0.781677	+	0.623683i	$0.785636\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.88816	1.44408
$5$	1.51753	0.678661	0.339330	−	0.940667i	$-0.389800\pi$
$5$	1.51753	0.678661	0.339330	+	0.940667i	$0.389800\pi$
$6$	−2.21092	−0.902603
$7$	0.0486600	0.0183918	0.00919588	−	0.999958i	$-0.497073\pi$
$7$	0.0486600	0.0183918	0.00919588	+	0.999958i	$0.497073\pi$
$8$	−1.96364	−0.694253
$9$	1.00000	0.333333
$10$	−3.35514	−1.06099
$11$	6.56010	1.97794	0.988972	−	0.148100i	$-0.0473157\pi$
$11$	6.56010	1.97794	0.988972	+	0.148100i	$0.0473157\pi$
$12$	2.88816	0.833739
$13$	0.517879	0.143634	0.0718168	−	0.997418i	$-0.477120\pi$
$13$	0.517879	0.143634	0.0718168	+	0.997418i	$0.477120\pi$
$14$	−0.107583	−0.0287528
$15$	1.51753	0.391825
$16$	−1.43486	−0.358715
$17$	−4.76722	−1.15622	−0.578110	−	0.815959i	$-0.696210\pi$
$17$	−4.76722	−1.15622	−0.578110	+	0.815959i	$0.696210\pi$
$18$	−2.21092	−0.521118
$19$	−0.00792509	−0.00181814	−0.000909070	−	1.00000i	$-0.500289\pi$
$19$	−0.00792509	−0.00181814	−0.000909070		1.00000i	$0.500289\pi$
$20$	4.38287	0.980040
$21$	0.0486600	0.0106185
$22$	−14.5038	−3.09223
$23$	4.25244	0.886695	0.443348	−	0.896350i	$-0.353791\pi$
$23$	4.25244	0.886695	0.443348	+	0.896350i	$0.353791\pi$
$24$	−1.96364	−0.400827
$25$	−2.69710	−0.539420
$26$	−1.14499	−0.224550
$27$	1.00000	0.192450
$28$	0.140538	0.0265591
$29$	−7.88822	−1.46480	−0.732402	−	0.680872i	$-0.761601\pi$
$29$	−7.88822	−1.46480	−0.732402	+	0.680872i	$0.761601\pi$
$30$	−3.35514	−0.612562
$31$	−3.05936	−0.549477	−0.274739	−	0.961519i	$-0.588591\pi$
$31$	−3.05936	−0.549477	−0.274739	+	0.961519i	$0.588591\pi$
$32$	7.09965	1.25505
$33$	6.56010	1.14197
$34$	10.5399	1.80758
$35$	0.0738431	0.0124818
$36$	2.88816	0.481360
$37$	7.82698	1.28675	0.643374	−	0.765552i	$-0.277534\pi$
$37$	7.82698	1.28675	0.643374	+	0.765552i	$0.277534\pi$
$38$	0.0175217	0.00284240
$39$	0.517879	0.0829269
$40$	−2.97989	−0.471162
$41$	−7.47610	−1.16757	−0.583785	−	0.811908i	$-0.698429\pi$
$41$	−7.47610	−1.16757	−0.583785	+	0.811908i	$0.698429\pi$
$42$	−0.107583	−0.0166005
$43$	−8.77561	−1.33827	−0.669134	−	0.743142i	$-0.733335\pi$
$43$	−8.77561	−1.33827	−0.669134	+	0.743142i	$0.733335\pi$
$44$	18.9466	2.85631
$45$	1.51753	0.226220
$46$	−9.40180	−1.38622
$47$	1.80651	0.263506	0.131753	−	0.991283i	$-0.457939\pi$
$47$	1.80651	0.263506	0.131753	+	0.991283i	$0.457939\pi$
$48$	−1.43486	−0.207104
$49$	−6.99763	−0.999662
$50$	5.96306	0.843304
$51$	−4.76722	−0.667544
$52$	1.49571	0.207418
$53$	5.72962	0.787024	0.393512	−	0.919319i	$-0.371260\pi$
$53$	5.72962	0.787024	0.393512	+	0.919319i	$0.371260\pi$
$54$	−2.21092	−0.300868
$55$	9.95516	1.34235
$56$	−0.0955509	−0.0127685
$57$	−0.00792509	−0.00104970
$58$	17.4402	2.29001
$59$	0.207025	0.0269524	0.0134762	−	0.999909i	$-0.495710\pi$
$59$	0.207025	0.0269524	0.0134762	+	0.999909i	$0.495710\pi$
$60$	4.38287	0.565826
$61$	12.1014	1.54943	0.774713	−	0.632313i	$-0.217894\pi$
$61$	12.1014	1.54943	0.774713	+	0.632313i	$0.217894\pi$
$62$	6.76400	0.859028
$63$	0.0486600	0.00613058
$64$	−12.8270	−1.60338
$65$	0.785897	0.0974785
$66$	−14.5038	−1.78530
$67$	−8.59573	−1.05014	−0.525068	−	0.851060i	$-0.675960\pi$
$67$	−8.59573	−1.05014	−0.525068	+	0.851060i	$0.675960\pi$
$68$	−13.7685	−1.66967
$69$	4.25244	0.511934
$70$	−0.163261	−0.0195134
$71$	0.245324	0.0291147	0.0145573	−	0.999894i	$-0.495366\pi$
$71$	0.245324	0.0291147	0.0145573	+	0.999894i	$0.495366\pi$
$72$	−1.96364	−0.231418
$73$	9.82368	1.14977	0.574887	−	0.818233i	$-0.305046\pi$
$73$	9.82368	1.14977	0.574887	+	0.818233i	$0.305046\pi$
$74$	−17.3048	−2.01164
$75$	−2.69710	−0.311434
$76$	−0.0228889	−0.00262554
$77$	0.319215	0.0363779
$78$	−1.14499	−0.129644
$79$	16.6551	1.87385	0.936924	−	0.349534i	$-0.113660\pi$
$79$	16.6551	1.87385	0.936924	+	0.349534i	$0.113660\pi$
$80$	−2.17745	−0.243446
$81$	1.00000	0.111111
$82$	16.5290	1.82533
$83$	6.64959	0.729887	0.364944	−	0.931030i	$-0.381088\pi$
$83$	6.64959	0.729887	0.364944	+	0.931030i	$0.381088\pi$
$84$	0.140538	0.0153339
$85$	−7.23440	−0.784681
$86$	19.4022	2.09219
$87$	−7.88822	−0.845706
$88$	−12.8817	−1.37319
$89$	14.6852	1.55663	0.778314	−	0.627876i	$-0.216075\pi$
$89$	14.6852	1.55663	0.778314	+	0.627876i	$0.216075\pi$
$90$	−3.35514	−0.353663
$91$	0.0252000	0.00264167
$92$	12.2817	1.28046
$93$	−3.05936	−0.317241
$94$	−3.99404	−0.411953
$95$	−0.0120266	−0.00123390
$96$	7.09965	0.724605
$97$	12.1718	1.23585	0.617927	−	0.786235i	$-0.287973\pi$
$97$	12.1718	1.23585	0.617927	+	0.786235i	$0.287973\pi$
$98$	15.4712	1.56283
$99$	6.56010	0.659315
$100$	−7.78964	−0.778964
$101$	11.2638	1.12079	0.560393	−	0.828227i	$-0.310650\pi$
$101$	11.2638	1.12079	0.560393	+	0.828227i	$0.310650\pi$
$102$	10.5399	1.04361
$103$	2.01512	0.198556	0.0992779	−	0.995060i	$-0.468347\pi$
$103$	2.01512	0.198556	0.0992779	+	0.995060i	$0.468347\pi$
$104$	−1.01693	−0.0997181
$105$	0.0738431	0.00720635
$106$	−12.6677	−1.23040
$107$	3.71150	0.358804	0.179402	−	0.983776i	$-0.442584\pi$
$107$	3.71150	0.358804	0.179402	+	0.983776i	$0.442584\pi$
$108$	2.88816	0.277913
$109$	−0.616748	−0.0590738	−0.0295369	−	0.999564i	$-0.509403\pi$
$109$	−0.616748	−0.0590738	−0.0295369	+	0.999564i	$0.509403\pi$
$110$	−22.0100	−2.09858
$111$	7.82698	0.742904
$112$	−0.0698203	−0.00659740
$113$	−15.6247	−1.46985	−0.734923	−	0.678150i	$-0.762782\pi$
$113$	−15.6247	−1.46985	−0.734923	+	0.678150i	$0.762782\pi$
$114$	0.0175217	0.00164106
$115$	6.45321	0.601765
$116$	−22.7824	−2.11529
$117$	0.517879	0.0478779
$118$	−0.457715	−0.0421361
$119$	−0.231973	−0.0212649
$120$	−2.97989	−0.272026
$121$	32.0349	2.91227
$122$	−26.7552	−2.42230
$123$	−7.47610	−0.674097
$124$	−8.83592	−0.793489
$125$	−11.6806	−1.04474
$126$	−0.107583	−0.00958428
$127$	11.6821	1.03662	0.518310	−	0.855193i	$-0.326561\pi$
$127$	11.6821	1.03662	0.518310	+	0.855193i	$0.326561\pi$
$128$	14.1602	1.25159
$129$	−8.77561	−0.772649
$130$	−1.73755	−0.152394
$131$	0.423746	0.0370229	0.0185114	−	0.999829i	$-0.494107\pi$
$131$	0.423746	0.0370229	0.0185114	+	0.999829i	$0.494107\pi$
$132$	18.9466	1.64909
$133$	−0.000385635 0	−3.34388e−5 0
$134$	19.0044	1.64173
$135$	1.51753	0.130608
$136$	9.36112	0.802709
$137$	−11.1143	−0.949556	−0.474778	−	0.880105i	$-0.657472\pi$
$137$	−11.1143	−0.949556	−0.474778	+	0.880105i	$0.657472\pi$
$138$	−9.40180	−0.800334
$139$	−4.99898	−0.424008	−0.212004	−	0.977269i	$-0.567999\pi$
$139$	−4.99898	−0.424008	−0.212004	+	0.977269i	$0.567999\pi$
$140$	0.213270	0.0180246
$141$	1.80651	0.152135
$142$	−0.542392	−0.0455166
$143$	3.39734	0.284099
$144$	−1.43486	−0.119572
$145$	−11.9706	−0.994106
$146$	−21.7193	−1.79751
$147$	−6.99763	−0.577155
$148$	22.6056	1.85817
$149$	19.7415	1.61729	0.808643	−	0.588299i	$-0.200202\pi$
$149$	19.7415	1.61729	0.808643	+	0.588299i	$0.200202\pi$
$150$	5.96306	0.486882
$151$	17.1896	1.39887	0.699434	−	0.714697i	$-0.253435\pi$
$151$	17.1896	1.39887	0.699434	+	0.714697i	$0.253435\pi$
$152$	0.0155621	0.00126225
$153$	−4.76722	−0.385407
$154$	−0.705757	−0.0568715
$155$	−4.64268	−0.372909
$156$	1.49571	0.119753
$157$	17.1097	1.36550	0.682752	−	0.730650i	$-0.260783\pi$
$157$	17.1097	1.36550	0.682752	+	0.730650i	$0.260783\pi$
$158$	−36.8231	−2.92949
$159$	5.72962	0.454389
$160$	10.7739	0.851755
$161$	0.206924	0.0163079
$162$	−2.21092	−0.173706
$163$	10.6059	0.830720	0.415360	−	0.909657i	$-0.363656\pi$
$163$	10.6059	0.830720	0.415360	+	0.909657i	$0.363656\pi$
$164$	−21.5922	−1.68606
$165$	9.95516	0.775008
$166$	−14.7017	−1.14107
$167$	−9.14480	−0.707646	−0.353823	−	0.935312i	$-0.615119\pi$
$167$	−9.14480	−0.707646	−0.353823	+	0.935312i	$0.615119\pi$
$168$	−0.0955509	−0.00737191
$169$	−12.7318	−0.979369
$170$	15.9947	1.22674
$171$	−0.00792509	−0.000606047 0
$172$	−25.3453	−1.93256
$173$	19.9013	1.51307	0.756534	−	0.653955i	$-0.226891\pi$
$173$	19.9013	1.51307	0.756534	+	0.653955i	$0.226891\pi$
$174$	17.4402	1.32214
$175$	−0.131241	−0.00992087
$176$	−9.41283	−0.709519
$177$	0.207025	0.0155610
$178$	−32.4678	−2.43356
$179$	−19.8729	−1.48537	−0.742684	−	0.669642i	$-0.766447\pi$
$179$	−19.8729	−1.48537	−0.742684	+	0.669642i	$0.766447\pi$
$180$	4.38287	0.326680
$181$	0.0914433	0.00679693	0.00339846	−	0.999994i	$-0.498918\pi$
$181$	0.0914433	0.00679693	0.00339846	+	0.999994i	$0.498918\pi$
$182$	−0.0557151	−0.00412988
$183$	12.1014	0.894561
$184$	−8.35028	−0.615591
$185$	11.8777	0.873265
$186$	6.76400	0.495960
$187$	−31.2734	−2.28694
$188$	5.21747	0.380523
$189$	0.0486600	0.00353949
$190$	0.0265898	0.00192902
$191$	19.5935	1.41774	0.708869	−	0.705340i	$-0.249206\pi$
$191$	19.5935	1.41774	0.708869	+	0.705340i	$0.249206\pi$
$192$	−12.8270	−0.925710
$193$	17.7064	1.27454	0.637268	−	0.770642i	$-0.280065\pi$
$193$	17.7064	1.27454	0.637268	+	0.770642i	$0.280065\pi$
$194$	−26.9108	−1.93208
$195$	0.785897	0.0562793
$196$	−20.2103	−1.44359
$197$	−4.40320	−0.313715	−0.156857	−	0.987621i	$-0.550136\pi$
$197$	−4.40320	−0.313715	−0.156857	+	0.987621i	$0.550136\pi$
$198$	−14.5038	−1.03074
$199$	−7.26491	−0.514996	−0.257498	−	0.966279i	$-0.582898\pi$
$199$	−7.26491	−0.514996	−0.257498	+	0.966279i	$0.582898\pi$
$200$	5.29614	0.374494
$201$	−8.59573	−0.606296
$202$	−24.9033	−1.75219
$203$	−0.383841	−0.0269403
$204$	−13.7685	−0.963986
$205$	−11.3452	−0.792384
$206$	−4.45527	−0.310413
$207$	4.25244	0.295565
$208$	−0.743084	−0.0515236
$209$	−0.0519894	−0.00359618
$210$	−0.163261	−0.0112661
$211$	25.8895	1.78231	0.891155	−	0.453699i	$-0.149896\pi$
$211$	25.8895	1.78231	0.891155	+	0.453699i	$0.149896\pi$
$212$	16.5480	1.13652
$213$	0.245324	0.0168094
$214$	−8.20583	−0.560939
$215$	−13.3173	−0.908230
$216$	−1.96364	−0.133609
$217$	−0.148869	−0.0101059
$218$	1.36358	0.0923533
$219$	9.82368	0.663823
$220$	28.7521	1.93846
$221$	−2.46884	−0.166072
$222$	−17.3048	−1.16142
$223$	−26.2779	−1.75970	−0.879850	−	0.475252i	$-0.842357\pi$
$223$	−26.2779	−1.75970	−0.879850	+	0.475252i	$0.842357\pi$
$224$	0.345469	0.0230826
$225$	−2.69710	−0.179807
$226$	34.5449	2.29789
$227$	5.41646	0.359503	0.179752	−	0.983712i	$-0.442471\pi$
$227$	5.41646	0.359503	0.179752	+	0.983712i	$0.442471\pi$
$228$	−0.0228889	−0.00151586
$229$	17.2949	1.14288	0.571440	−	0.820644i	$-0.306385\pi$
$229$	17.2949	1.14288	0.571440	+	0.820644i	$0.306385\pi$
$230$	−14.2675	−0.940772
$231$	0.319215	0.0210028
$232$	15.4896	1.01694
$233$	−6.86948	−0.450034	−0.225017	−	0.974355i	$-0.572244\pi$
$233$	−6.86948	−0.450034	−0.225017	+	0.974355i	$0.572244\pi$
$234$	−1.14499	−0.0748501
$235$	2.74143	0.178831
$236$	0.597921	0.0389213
$237$	16.6551	1.08187
$238$	0.512873	0.0332446
$239$	−4.77560	−0.308908	−0.154454	−	0.988000i	$-0.549362\pi$
$239$	−4.77560	−0.308908	−0.154454	+	0.988000i	$0.549362\pi$
$240$	−2.17745	−0.140554
$241$	14.1647	0.912428	0.456214	−	0.889870i	$-0.349205\pi$
$241$	14.1647	0.912428	0.456214	+	0.889870i	$0.349205\pi$
$242$	−70.8266	−4.55291
$243$	1.00000	0.0641500
$244$	34.9507	2.23749
$245$	−10.6191	−0.678431
$246$	16.5290	1.05385
$247$	−0.00410423	−0.000261146 0
$248$	6.00749	0.381476
$249$	6.64959	0.421401
$250$	25.8248	1.63331
$251$	15.7111	0.991676	0.495838	−	0.868415i	$-0.334861\pi$
$251$	15.7111	0.991676	0.495838	+	0.868415i	$0.334861\pi$
$252$	0.140538	0.00885305
$253$	27.8964	1.75383
$254$	−25.8282	−1.62060
$255$	−7.23440	−0.453036
$256$	−5.65297	−0.353310
$257$	−0.410524	−0.0256078	−0.0128039	−	0.999918i	$-0.504076\pi$
$257$	−0.410524	−0.0256078	−0.0128039	+	0.999918i	$0.504076\pi$
$258$	19.4022	1.20793
$259$	0.380861	0.0236655
$260$	2.26979	0.140767
$261$	−7.88822	−0.488268
$262$	−0.936868	−0.0578799
$263$	10.6161	0.654618	0.327309	−	0.944917i	$-0.393858\pi$
$263$	10.6161	0.654618	0.327309	+	0.944917i	$0.393858\pi$
$264$	−12.8817	−0.792814
$265$	8.69488	0.534122
$266$	0.000852607 0	5.22767e−5 0
$267$	14.6852	0.898719
$268$	−24.8258	−1.51648
$269$	−14.4471	−0.880853	−0.440427	−	0.897789i	$-0.645173\pi$
$269$	−14.4471	−0.880853	−0.440427	+	0.897789i	$0.645173\pi$
$270$	−3.35514	−0.204187
$271$	23.7878	1.44501	0.722503	−	0.691368i	$-0.242991\pi$
$271$	23.7878	1.44501	0.722503	+	0.691368i	$0.242991\pi$
$272$	6.84030	0.414754
$273$	0.0252000	0.00152517
$274$	24.5727	1.48449
$275$	−17.6932	−1.06694
$276$	12.2817	0.739272
$277$	16.6659	1.00136	0.500678	−	0.865634i	$-0.333084\pi$
$277$	16.6659	1.00136	0.500678	+	0.865634i	$0.333084\pi$
$278$	11.0523	0.662875
$279$	−3.05936	−0.183159
$280$	−0.145002	−0.00866550
$281$	−21.2038	−1.26491	−0.632455	−	0.774597i	$-0.717953\pi$
$281$	−21.2038	−1.26491	−0.632455	+	0.774597i	$0.717953\pi$
$282$	−3.99404	−0.237841
$283$	21.0479	1.25117	0.625584	−	0.780157i	$-0.284861\pi$
$283$	21.0479	1.25117	0.625584	+	0.780157i	$0.284861\pi$
$284$	0.708536	0.0420439
$285$	−0.0120266	−0.000712393 0
$286$	−7.51123	−0.444148
$287$	−0.363787	−0.0214737
$288$	7.09965	0.418351
$289$	5.72637	0.336845
$290$	26.4661	1.55414
$291$	12.1718	0.713521
$292$	28.3723	1.66036
$293$	14.3585	0.838835	0.419417	−	0.907794i	$-0.362234\pi$
$293$	14.3585	0.838835	0.419417	+	0.907794i	$0.362234\pi$
$294$	15.4712	0.902298
$295$	0.314167	0.0182915
$296$	−15.3694	−0.893328
$297$	6.56010	0.380656
$298$	−43.6468	−2.52839
$299$	2.20225	0.127359
$300$	−7.78964	−0.449735
$301$	−0.427021	−0.0246131
$302$	−38.0048	−2.18693
$303$	11.2638	0.647087
$304$	0.0113714	0.000652195 0
$305$	18.3643	1.05153
$306$	10.5399	0.602528
$307$	−15.4896	−0.884039	−0.442019	−	0.897006i	$-0.645738\pi$
$307$	−15.4896	−0.884039	−0.442019	+	0.897006i	$0.645738\pi$
$308$	0.921942	0.0525325
$309$	2.01512	0.114636
$310$	10.2646	0.582989
$311$	−4.07764	−0.231222	−0.115611	−	0.993295i	$-0.536883\pi$
$311$	−4.07764	−0.231222	−0.115611	+	0.993295i	$0.536883\pi$
$312$	−1.01693	−0.0575723
$313$	−16.5977	−0.938155	−0.469077	−	0.883157i	$-0.655413\pi$
$313$	−16.5977	−0.938155	−0.469077	+	0.883157i	$0.655413\pi$
$314$	−37.8282	−2.13477
$315$	0.0738431	0.00416059
$316$	48.1026	2.70598
$317$	9.72846	0.546405	0.273202	−	0.961957i	$-0.411917\pi$
$317$	9.72846	0.546405	0.273202	+	0.961957i	$0.411917\pi$
$318$	−12.6677	−0.710371
$319$	−51.7475	−2.89730
$320$	−19.4654	−1.08815
$321$	3.71150	0.207156
$322$	−0.457491	−0.0254950
$323$	0.0377806	0.00210217
$324$	2.88816	0.160453
$325$	−1.39677	−0.0774788
$326$	−23.4488	−1.29871
$327$	−0.616748	−0.0341063
$328$	14.6804	0.810589
$329$	0.0879046	0.00484634
$330$	−22.0100	−1.21161
$331$	4.23416	0.232731	0.116365	−	0.993206i	$-0.462876\pi$
$331$	4.23416	0.232731	0.116365	+	0.993206i	$0.462876\pi$
$332$	19.2051	1.05401
$333$	7.82698	0.428916
$334$	20.2184	1.10630
$335$	−13.0443	−0.712686
$336$	−0.0698203	−0.00380901
$337$	29.5595	1.61021	0.805105	−	0.593133i	$-0.202109\pi$
$337$	29.5595	1.61021	0.805105	+	0.593133i	$0.202109\pi$
$338$	28.1490	1.53110
$339$	−15.6247	−0.848616
$340$	−20.8941	−1.13314
$341$	−20.0697	−1.08684
$342$	0.0175217	0.000947466 0
$343$	−0.681125	−0.0367773
$344$	17.2322	0.929096
$345$	6.45321	0.347429
$346$	−44.0001	−2.36546
$347$	−13.1968	−0.708440	−0.354220	−	0.935162i	$-0.615254\pi$
$347$	−13.1968	−0.708440	−0.354220	+	0.935162i	$0.615254\pi$
$348$	−22.7824	−1.22127
$349$	−21.0082	−1.12454	−0.562272	−	0.826953i	$-0.690072\pi$
$349$	−21.0082	−1.12454	−0.562272	+	0.826953i	$0.690072\pi$
$350$	0.290163	0.0155098
$351$	0.517879	0.0276423
$352$	46.5744	2.48242
$353$	7.10103	0.377950	0.188975	−	0.981982i	$-0.439484\pi$
$353$	7.10103	0.377950	0.188975	+	0.981982i	$0.439484\pi$
$354$	−0.457715	−0.0243273
$355$	0.372288	0.0197590
$356$	42.4131	2.24789
$357$	−0.231973	−0.0122773
$358$	43.9373	2.32216
$359$	−12.6459	−0.667424	−0.333712	−	0.942675i	$-0.608301\pi$
$359$	−12.6459	−0.667424	−0.333712	+	0.942675i	$0.608301\pi$
$360$	−2.97989	−0.157054
$361$	−18.9999	−0.999997
$362$	−0.202174	−0.0106260
$363$	32.0349	1.68140
$364$	0.0727815	0.00381479
$365$	14.9077	0.780307
$366$	−26.7552	−1.39852
$367$	−13.9430	−0.727820	−0.363910	−	0.931434i	$-0.618559\pi$
$367$	−13.9430	−0.727820	−0.363910	+	0.931434i	$0.618559\pi$
$368$	−6.10166	−0.318071
$369$	−7.47610	−0.389190
$370$	−26.2606	−1.36522
$371$	0.278803	0.0144748
$372$	−8.83592	−0.458121
$373$	35.5550	1.84097	0.920483	−	0.390783i	$-0.127796\pi$
$373$	35.5550	1.84097	0.920483	+	0.390783i	$0.127796\pi$
$374$	69.1430	3.57530
$375$	−11.6806	−0.603183
$376$	−3.54733	−0.182940
$377$	−4.08514	−0.210395
$378$	−0.107583	−0.00553349
$379$	5.72818	0.294237	0.147118	−	0.989119i	$-0.453000\pi$
$379$	5.72818	0.294237	0.147118	+	0.989119i	$0.453000\pi$
$380$	−0.0347346	−0.00178185
$381$	11.6821	0.598493
$382$	−43.3197	−2.21643
$383$	−28.8842	−1.47591	−0.737957	−	0.674848i	$-0.764209\pi$
$383$	−28.8842	−1.47591	−0.737957	+	0.674848i	$0.764209\pi$
$384$	14.1602	0.722609
$385$	0.484418	0.0246882
$386$	−39.1474	−1.99255
$387$	−8.77561	−0.446089
$388$	35.1539	1.78467
$389$	−3.49871	−0.177391	−0.0886957	−	0.996059i	$-0.528270\pi$
$389$	−3.49871	−0.177391	−0.0886957	+	0.996059i	$0.528270\pi$
$390$	−1.73755	−0.0879844
$391$	−20.2723	−1.02521
$392$	13.7409	0.694018
$393$	0.423746	0.0213752
$394$	9.73510	0.490447
$395$	25.2747	1.27171
$396$	18.9466	0.952103
$397$	7.78680	0.390808	0.195404	−	0.980723i	$-0.437398\pi$
$397$	7.78680	0.390808	0.195404	+	0.980723i	$0.437398\pi$
$398$	16.0621	0.805121
$399$	−0.000385635 0	−1.93059e−5 0
$400$	3.86996	0.193498
$401$	−31.3985	−1.56797	−0.783983	−	0.620782i	$-0.786815\pi$
$401$	−31.3985	−1.56797	−0.783983	+	0.620782i	$0.786815\pi$
$402$	19.0044	0.947856
$403$	−1.58438	−0.0789235
$404$	32.5315	1.61850
$405$	1.51753	0.0754067
$406$	0.848640	0.0421173
$407$	51.3458	2.54512
$408$	9.36112	0.463444
$409$	2.38174	0.117769	0.0588846	−	0.998265i	$-0.481246\pi$
$409$	2.38174	0.117769	0.0588846	+	0.998265i	$0.481246\pi$
$410$	25.0833	1.23878
$411$	−11.1143	−0.548227
$412$	5.81999	0.286730
$413$	0.0100738	0.000495701 0
$414$	−9.40180	−0.462073
$415$	10.0910	0.495346
$416$	3.67675	0.180268
$417$	−4.99898	−0.244801
$418$	0.114944	0.00562211
$419$	1.79343	0.0876145	0.0438073	−	0.999040i	$-0.486051\pi$
$419$	1.79343	0.0876145	0.0438073	+	0.999040i	$0.486051\pi$
$420$	0.213270	0.0104065
$421$	8.14268	0.396850	0.198425	−	0.980116i	$-0.436417\pi$
$421$	8.14268	0.396850	0.198425	+	0.980116i	$0.436417\pi$
$422$	−57.2397	−2.78638
$423$	1.80651	0.0878353
$424$	−11.2509	−0.546394
$425$	12.8577	0.623688
$426$	−0.542392	−0.0262790
$427$	0.588854	0.0284967
$428$	10.7194	0.518142
$429$	3.39734	0.164025
$430$	29.4434	1.41989
$431$	1.98300	0.0955177	0.0477589	−	0.998859i	$-0.484792\pi$
$431$	1.98300	0.0955177	0.0477589	+	0.998859i	$0.484792\pi$
$432$	−1.43486	−0.0690348
$433$	6.78933	0.326275	0.163137	−	0.986603i	$-0.447839\pi$
$433$	6.78933	0.326275	0.163137	+	0.986603i	$0.447839\pi$
$434$	0.329136	0.0157990
$435$	−11.9706	−0.573947
$436$	−1.78127	−0.0853072
$437$	−0.0337010	−0.00161214
$438$	−21.7193	−1.03779
$439$	29.1166	1.38966	0.694829	−	0.719175i	$-0.255480\pi$
$439$	29.1166	1.38966	0.694829	+	0.719175i	$0.255480\pi$
$440$	−19.5484	−0.931933
$441$	−6.99763	−0.333221
$442$	5.45840	0.259630
$443$	−14.7084	−0.698818	−0.349409	−	0.936970i	$-0.613618\pi$
$443$	−14.7084	−0.698818	−0.349409	+	0.936970i	$0.613618\pi$
$444$	22.6056	1.07281
$445$	22.2852	1.05642
$446$	58.0983	2.75103
$447$	19.7415	0.933741
$448$	−0.624163	−0.0294889
$449$	−25.1731	−1.18799	−0.593996	−	0.804468i	$-0.702450\pi$
$449$	−25.1731	−1.18799	−0.593996	+	0.804468i	$0.702450\pi$
$450$	5.96306	0.281101
$451$	−49.0440	−2.30939
$452$	−45.1265	−2.12257
$453$	17.1896	0.807637
$454$	−11.9753	−0.562031
$455$	0.0382418	0.00179280
$456$	0.0155621	0.000728760 0
$457$	−6.08006	−0.284413	−0.142207	−	0.989837i	$-0.545420\pi$
$457$	−6.08006	−0.284413	−0.142207	+	0.989837i	$0.545420\pi$
$458$	−38.2376	−1.78673
$459$	−4.76722	−0.222515
$460$	18.6379	0.868996
$461$	−11.5469	−0.537795	−0.268897	−	0.963169i	$-0.586659\pi$
$461$	−11.5469	−0.537795	−0.268897	+	0.963169i	$0.586659\pi$
$462$	−0.705757	−0.0328348
$463$	−14.2169	−0.660715	−0.330358	−	0.943856i	$-0.607169\pi$
$463$	−14.2169	−0.660715	−0.330358	+	0.943856i	$0.607169\pi$
$464$	11.3185	0.525448
$465$	−4.64268	−0.215299
$466$	15.1879	0.703564
$467$	22.8859	1.05903	0.529516	−	0.848300i	$-0.322373\pi$
$467$	22.8859	1.05903	0.529516	+	0.848300i	$0.322373\pi$
$468$	1.49571	0.0691394
$469$	−0.418268	−0.0193138
$470$	−6.06108	−0.279577
$471$	17.1097	0.788374
$472$	−0.406523	−0.0187118
$473$	−57.5689	−2.64702
$474$	−36.8231	−1.69134
$475$	0.0213747	0.000980741 0
$476$	−0.669974	−0.0307082
$477$	5.72962	0.262341
$478$	10.5585	0.482933
$479$	−31.6380	−1.44558	−0.722788	−	0.691070i	$-0.757140\pi$
$479$	−31.6380	−1.44558	−0.722788	+	0.691070i	$0.757140\pi$
$480$	10.7739	0.491761
$481$	4.05343	0.184820
$482$	−31.3170	−1.42645
$483$	0.206924	0.00941536
$484$	92.5219	4.20554
$485$	18.4710	0.838726
$486$	−2.21092	−0.100289
$487$	−24.3308	−1.10253	−0.551266	−	0.834329i	$-0.685855\pi$
$487$	−24.3308	−1.10253	−0.551266	+	0.834329i	$0.685855\pi$
$488$	−23.7628	−1.07569
$489$	10.6059	0.479617
$490$	23.4780	1.06063
$491$	−27.6273	−1.24680	−0.623402	−	0.781901i	$-0.714250\pi$
$491$	−27.6273	−1.24680	−0.623402	+	0.781901i	$0.714250\pi$
$492$	−21.5922	−0.973450
$493$	37.6049	1.69364
$494$	0.00907412	0.000408264 0
$495$	9.95516	0.447451
$496$	4.38976	0.197106
$497$	0.0119375	0.000535470 0
$498$	−14.7017	−0.658799
$499$	−22.3250	−0.999404	−0.499702	−	0.866197i	$-0.666557\pi$
$499$	−22.3250	−0.999404	−0.499702	+	0.866197i	$0.666557\pi$
$500$	−33.7354	−1.50869
$501$	−9.14480	−0.408560
$502$	−34.7360	−1.55034
$503$	−16.2498	−0.724542	−0.362271	−	0.932073i	$-0.617999\pi$
$503$	−16.2498	−0.724542	−0.362271	+	0.932073i	$0.617999\pi$
$504$	−0.0955509	−0.00425618
$505$	17.0931	0.760634
$506$	−61.6767	−2.74186
$507$	−12.7318	−0.565439
$508$	33.7398	1.49696
$509$	−26.0708	−1.15557	−0.577785	−	0.816189i	$-0.696083\pi$
$509$	−26.0708	−1.15557	−0.577785	+	0.816189i	$0.696083\pi$
$510$	15.9947	0.708256
$511$	0.478020	0.0211464
$512$	−15.8221	−0.699245
$513$	−0.00792509	−0.000349901 0
$514$	0.907636	0.0400341
$515$	3.05801	0.134752
$516$	−25.3453	−1.11577
$517$	11.8509	0.521200
$518$	−0.842052	−0.0369977
$519$	19.9013	0.873570
$520$	−1.54322	−0.0676747
$521$	3.39487	0.148732	0.0743660	−	0.997231i	$-0.476307\pi$
$521$	3.39487	0.148732	0.0743660	+	0.997231i	$0.476307\pi$
$522$	17.4402	0.763337
$523$	−13.5447	−0.592268	−0.296134	−	0.955146i	$-0.595698\pi$
$523$	−13.5447	−0.592268	−0.296134	+	0.955146i	$0.595698\pi$
$524$	1.22385	0.0534640
$525$	−0.131241	−0.00572782
$526$	−23.4714	−1.02340
$527$	14.5846	0.635317
$528$	−9.41283	−0.409641
$529$	−4.91675	−0.213772
$530$	−19.2237	−0.835023
$531$	0.207025	0.00898412
$532$	−0.00111377	−4.82882e−5 0
$533$	−3.87171	−0.167702
$534$	−32.4678	−1.40502
$535$	5.63232	0.243506
$536$	16.8789	0.729059
$537$	−19.8729	−0.857577
$538$	31.9413	1.37709
$539$	−45.9052	−1.97728
$540$	4.38287	0.188609
$541$	−22.4670	−0.965932	−0.482966	−	0.875639i	$-0.660441\pi$
$541$	−22.4670	−0.965932	−0.482966	+	0.875639i	$0.660441\pi$
$542$	−52.5929	−2.25906
$543$	0.0914433	0.00392421
$544$	−33.8456	−1.45112
$545$	−0.935935	−0.0400911
$546$	−0.0557151	−0.00238438
$547$	−21.3346	−0.912203	−0.456101	−	0.889928i	$-0.650755\pi$
$547$	−21.3346	−0.912203	−0.456101	+	0.889928i	$0.650755\pi$
$548$	−32.0998	−1.37123
$549$	12.1014	0.516475
$550$	39.1183	1.66801
$551$	0.0625148	0.00266322
$552$	−8.35028	−0.355411
$553$	0.810438	0.0344633
$554$	−36.8469	−1.56547
$555$	11.8777	0.504180
$556$	−14.4379	−0.612301
$557$	0.733346	0.0310729	0.0155364	−	0.999879i	$-0.495054\pi$
$557$	0.733346	0.0310729	0.0155364	+	0.999879i	$0.495054\pi$
$558$	6.76400	0.286343
$559$	−4.54470	−0.192220
$560$	−0.105955	−0.00447740
$561$	−31.2734	−1.32037
$562$	46.8798	1.97750
$563$	13.2132	0.556869	0.278435	−	0.960455i	$-0.410184\pi$
$563$	13.2132	0.556869	0.278435	+	0.960455i	$0.410184\pi$
$564$	5.21747	0.219695
$565$	−23.7109	−0.997527
$566$	−46.5352	−1.95602
$567$	0.0486600	0.00204353
$568$	−0.481730	−0.0202129
$569$	15.0982	0.632951	0.316475	−	0.948601i	$-0.397501\pi$
$569$	15.0982	0.632951	0.316475	+	0.948601i	$0.397501\pi$
$570$	0.0265898	0.00111372
$571$	−44.3027	−1.85401	−0.927005	−	0.375049i	$-0.877626\pi$
$571$	−44.3027	−1.85401	−0.927005	+	0.375049i	$0.877626\pi$
$572$	9.81204	0.410262
$573$	19.5935	0.818531
$574$	0.804303	0.0335710
$575$	−11.4692	−0.478301
$576$	−12.8270	−0.534459
$577$	25.5653	1.06430	0.532149	−	0.846650i	$-0.321384\pi$
$577$	25.5653	1.06430	0.532149	+	0.846650i	$0.321384\pi$
$578$	−12.6605	−0.526609
$579$	17.7064	0.735853
$580$	−34.5730	−1.43557
$581$	0.323569	0.0134239
$582$	−26.9108	−1.11549
$583$	37.5869	1.55669
$584$	−19.2902	−0.798234
$585$	0.785897	0.0324928
$586$	−31.7455	−1.31140
$587$	28.5191	1.17711	0.588555	−	0.808457i	$-0.299697\pi$
$587$	28.5191	1.17711	0.588555	+	0.808457i	$0.299697\pi$
$588$	−20.2103	−0.833457
$589$	0.0242457	0.000999027 0
$590$	−0.694598	−0.0285961
$591$	−4.40320	−0.181123
$592$	−11.2306	−0.461576
$593$	−0.865407	−0.0355380	−0.0177690	−	0.999842i	$-0.505656\pi$
$593$	−0.865407	−0.0355380	−0.0177690	+	0.999842i	$0.505656\pi$
$594$	−14.5038	−0.595100
$595$	−0.352026	−0.0144317
$596$	57.0166	2.33549
$597$	−7.26491	−0.297333
$598$	−4.86899	−0.199108
$599$	−38.0892	−1.55628	−0.778140	−	0.628090i	$-0.783837\pi$
$599$	−38.0892	−1.55628	−0.778140	+	0.628090i	$0.783837\pi$
$600$	5.29614	0.216214
$601$	2.33696	0.0953266	0.0476633	−	0.998863i	$-0.484823\pi$
$601$	2.33696	0.0953266	0.0476633	+	0.998863i	$0.484823\pi$
$602$	0.944109	0.0384790
$603$	−8.59573	−0.350045
$604$	49.6462	2.02008
$605$	48.6140	1.97644
$606$	−24.9033	−1.01163
$607$	6.65273	0.270026	0.135013	−	0.990844i	$-0.456892\pi$
$607$	6.65273	0.270026	0.135013	+	0.990844i	$0.456892\pi$
$608$	−0.0562653	−0.00228186
$609$	−0.383841	−0.0155540
$610$	−40.6019	−1.64392
$611$	0.935551	0.0378483
$612$	−13.7685	−0.556558
$613$	35.9524	1.45211	0.726053	−	0.687639i	$-0.241353\pi$
$613$	35.9524	1.45211	0.726053	+	0.687639i	$0.241353\pi$
$614$	34.2462	1.38207
$615$	−11.3452	−0.457483
$616$	−0.626824	−0.0252554
$617$	45.7483	1.84176	0.920879	−	0.389849i	$-0.127473\pi$
$617$	45.7483	1.84176	0.920879	+	0.389849i	$0.127473\pi$
$618$	−4.45527	−0.179217
$619$	15.3104	0.615376	0.307688	−	0.951487i	$-0.400445\pi$
$619$	15.3104	0.615376	0.307688	+	0.951487i	$0.400445\pi$
$620$	−13.4088	−0.538510
$621$	4.25244	0.170645
$622$	9.01532	0.361482
$623$	0.714582	0.0286291
$624$	−0.743084	−0.0297472
$625$	−4.24017	−0.169607
$626$	36.6960	1.46667
$627$	−0.0519894	−0.00207626
$628$	49.4156	1.97190
$629$	−37.3129	−1.48776
$630$	−0.163261	−0.00650447
$631$	−32.1331	−1.27920	−0.639600	−	0.768708i	$-0.720900\pi$
$631$	−32.1331	−1.27920	−0.639600	+	0.768708i	$0.720900\pi$
$632$	−32.7047	−1.30092
$633$	25.8895	1.02902
$634$	−21.5088	−0.854224
$635$	17.7280	0.703513
$636$	16.5480	0.656173
$637$	−3.62392	−0.143585
$638$	114.409	4.52951
$639$	0.245324	0.00970489
$640$	21.4885	0.849408
$641$	17.5518	0.693255	0.346627	−	0.938003i	$-0.387327\pi$
$641$	17.5518	0.693255	0.346627	+	0.938003i	$0.387327\pi$
$642$	−8.20583	−0.323858
$643$	17.7933	0.701699	0.350849	−	0.936432i	$-0.385893\pi$
$643$	17.7933	0.701699	0.350849	+	0.936432i	$0.385893\pi$
$644$	0.597628	0.0235499
$645$	−13.3173	−0.524367
$646$	−0.0835299	−0.00328644
$647$	23.2101	0.912481	0.456241	−	0.889856i	$-0.349196\pi$
$647$	23.2101	0.912481	0.456241	+	0.889856i	$0.349196\pi$
$648$	−1.96364	−0.0771392
$649$	1.35811	0.0533103
$650$	3.08814	0.121127
$651$	−0.148869	−0.00583462
$652$	30.6316	1.19963
$653$	1.42891	0.0559174	0.0279587	−	0.999609i	$-0.491099\pi$
$653$	1.42891	0.0559174	0.0279587	+	0.999609i	$0.491099\pi$
$654$	1.36358	0.0533202
$655$	0.643048	0.0251260
$656$	10.7272	0.418825
$657$	9.82368	0.383258
$658$	−0.194350	−0.00757655
$659$	−24.6133	−0.958798	−0.479399	−	0.877597i	$-0.659145\pi$
$659$	−24.6133	−0.958798	−0.479399	+	0.877597i	$0.659145\pi$
$660$	28.7521	1.11917
$661$	0.564346	0.0219505	0.0109753	−	0.999940i	$-0.496506\pi$
$661$	0.564346	0.0219505	0.0109753	+	0.999940i	$0.496506\pi$
$662$	−9.36138	−0.363840
$663$	−2.46884	−0.0958818
$664$	−13.0574	−0.506726
$665$	−0.000585213 0	−2.26936e−5 0
$666$	−17.3048	−0.670548
$667$	−33.5442	−1.29884
$668$	−26.4116	−1.02190
$669$	−26.2779	−1.01596
$670$	28.8399	1.11418
$671$	79.3864	3.06468
$672$	0.345469	0.0133267
$673$	−12.0503	−0.464504	−0.232252	−	0.972656i	$-0.574609\pi$
$673$	−12.0503	−0.464504	−0.232252	+	0.972656i	$0.574609\pi$
$674$	−65.3536	−2.51733
$675$	−2.69710	−0.103811
$676$	−36.7715	−1.41429
$677$	5.32663	0.204719	0.102359	−	0.994747i	$-0.467361\pi$
$677$	5.32663	0.204719	0.102359	+	0.994747i	$0.467361\pi$
$678$	34.5449	1.32669
$679$	0.592278	0.0227295
$680$	14.2058	0.544767
$681$	5.41646	0.207559
$682$	44.3725	1.69911
$683$	19.8034	0.757757	0.378879	−	0.925446i	$-0.376310\pi$
$683$	19.8034	0.757757	0.378879	+	0.925446i	$0.376310\pi$
$684$	−0.0228889	−0.000875179 0
$685$	−16.8663	−0.644427
$686$	1.50591	0.0574960
$687$	17.2949	0.659842
$688$	12.5918	0.480057
$689$	2.96725	0.113043
$690$	−14.2675	−0.543155
$691$	−40.6129	−1.54499	−0.772493	−	0.635023i	$-0.780991\pi$
$691$	−40.6129	−1.54499	−0.772493	+	0.635023i	$0.780991\pi$
$692$	57.4781	2.18499
$693$	0.319215	0.0121260
$694$	29.1770	1.10754
$695$	−7.58611	−0.287758
$696$	15.4896	0.587133
$697$	35.6402	1.34997
$698$	46.4474	1.75806
$699$	−6.86948	−0.259828
$700$	−0.379044	−0.0143265
$701$	4.20374	0.158773	0.0793866	−	0.996844i	$-0.474704\pi$
$701$	4.20374	0.158773	0.0793866	+	0.996844i	$0.474704\pi$
$702$	−1.14499	−0.0432147
$703$	−0.0620295	−0.00233949
$704$	−84.1465	−3.17139
$705$	2.74143	0.103248
$706$	−15.6998	−0.590870
$707$	0.548095	0.0206132
$708$	0.597921	0.0224712
$709$	−1.39593	−0.0524254	−0.0262127	−	0.999656i	$-0.508345\pi$
$709$	−1.39593	−0.0524254	−0.0262127	+	0.999656i	$0.508345\pi$
$710$	−0.823097	−0.0308903
$711$	16.6551	0.624616
$712$	−28.8365	−1.08069
$713$	−13.0097	−0.487219
$714$	0.512873	0.0191938
$715$	5.15556	0.192807
$716$	−57.3960	−2.14499
$717$	−4.77560	−0.178348
$718$	27.9590	1.04342
$719$	36.6266	1.36594	0.682970	−	0.730446i	$-0.260688\pi$
$719$	36.6266	1.36594	0.682970	+	0.730446i	$0.260688\pi$
$720$	−2.17745	−0.0811486
$721$	0.0980558	0.00365179
$722$	42.0073	1.56335
$723$	14.1647	0.526790
$724$	0.264103	0.00981530
$725$	21.2753	0.790145
$726$	−70.8266	−2.62862
$727$	10.3952	0.385537	0.192769	−	0.981244i	$-0.438253\pi$
$727$	10.3952	0.385537	0.192769	+	0.981244i	$0.438253\pi$
$728$	−0.0494838	−0.00183399
$729$	1.00000	0.0370370
$730$	−32.9598	−1.21990
$731$	41.8353	1.54733
$732$	34.9507	1.29182
$733$	13.4529	0.496896	0.248448	−	0.968645i	$-0.420080\pi$
$733$	13.4529	0.496896	0.248448	+	0.968645i	$0.420080\pi$
$734$	30.8269	1.13784
$735$	−10.6191	−0.391692
$736$	30.1908	1.11285
$737$	−56.3888	−2.07711
$738$	16.5290	0.608442
$739$	22.6655	0.833764	0.416882	−	0.908961i	$-0.363123\pi$
$739$	22.6655	0.833764	0.416882	+	0.908961i	$0.363123\pi$
$740$	34.3046	1.26106
$741$	−0.00410423	−0.000150773 0
$742$	−0.616411	−0.0226292
$743$	12.7971	0.469479	0.234740	−	0.972058i	$-0.424576\pi$
$743$	12.7971	0.469479	0.234740	+	0.972058i	$0.424576\pi$
$744$	6.00749	0.220245
$745$	29.9584	1.09759
$746$	−78.6091	−2.87808
$747$	6.64959	0.243296
$748$	−90.3226	−3.30252
$749$	0.180602	0.00659904
$750$	25.8248	0.942989
$751$	15.7404	0.574375	0.287187	−	0.957874i	$-0.407280\pi$
$751$	15.7404	0.574375	0.287187	+	0.957874i	$0.407280\pi$
$752$	−2.59208	−0.0945236
$753$	15.7111	0.572544
$754$	9.03190	0.328923
$755$	26.0857	0.949357
$756$	0.140538	0.00511131
$757$	−31.9693	−1.16195	−0.580973	−	0.813923i	$-0.697328\pi$
$757$	−31.9693	−1.16195	−0.580973	+	0.813923i	$0.697328\pi$
$758$	−12.6645	−0.459997
$759$	27.8964	1.01258
$760$	0.0236159	0.000856639 0
$761$	49.4640	1.79307	0.896534	−	0.442976i	$-0.146077\pi$
$761$	49.4640	1.79307	0.896534	+	0.442976i	$0.146077\pi$
$762$	−25.8282	−0.935656
$763$	−0.0300110	−0.00108647
$764$	56.5892	2.04732
$765$	−7.23440	−0.261560
$766$	63.8606	2.30738
$767$	0.107214	0.00387127
$768$	−5.65297	−0.203984
$769$	10.8605	0.391640	0.195820	−	0.980640i	$-0.437263\pi$
$769$	10.8605	0.391640	0.195820	+	0.980640i	$0.437263\pi$
$770$	−1.07101	−0.0385965
$771$	−0.410524	−0.0147847
$772$	51.1389	1.84053
$773$	−39.5604	−1.42289	−0.711444	−	0.702743i	$-0.751958\pi$
$773$	−39.5604	−1.42289	−0.711444	+	0.702743i	$0.751958\pi$
$774$	19.4022	0.697396
$775$	8.25140	0.296399
$776$	−23.9010	−0.857995
$777$	0.380861	0.0136633
$778$	7.73535	0.277326
$779$	0.0592488	0.00212281
$780$	2.26979	0.0812717
$781$	1.60935	0.0575872
$782$	44.8204	1.60277
$783$	−7.88822	−0.281902
$784$	10.0406	0.358594
$785$	25.9645	0.926714
$786$	−0.936868	−0.0334170
$787$	−15.1489	−0.540000	−0.270000	−	0.962860i	$-0.587024\pi$
$787$	−15.1489	−0.540000	−0.270000	+	0.962860i	$0.587024\pi$
$788$	−12.7171	−0.453029
$789$	10.6161	0.377944
$790$	−55.8802	−1.98813
$791$	−0.760297	−0.0270330
$792$	−12.8817	−0.457731
$793$	6.26705	0.222550
$794$	−17.2160	−0.610972
$795$	8.69488	0.308376
$796$	−20.9822	−0.743695
$797$	−47.6030	−1.68618	−0.843092	−	0.537769i	$-0.819267\pi$
$797$	−47.6030	−1.68618	−0.843092	+	0.537769i	$0.819267\pi$
$798$	0.000852607 0	3.01820e−5 0
$799$	−8.61201	−0.304671
$800$	−19.1484	−0.677000
$801$	14.6852	0.518876
$802$	69.4195	2.45129
$803$	64.4443	2.27419
$804$	−24.8258	−0.875539
$805$	0.314013	0.0110675
$806$	3.50293	0.123385
$807$	−14.4471	−0.508561
$808$	−22.1180	−0.778109
$809$	19.4279	0.683049	0.341524	−	0.939873i	$-0.389057\pi$
$809$	19.4279	0.683049	0.341524	+	0.939873i	$0.389057\pi$
$810$	−3.35514	−0.117888
$811$	−25.0850	−0.880854	−0.440427	−	0.897788i	$-0.645173\pi$
$811$	−25.0850	−0.880854	−0.440427	+	0.897788i	$0.645173\pi$
$812$	−1.10859	−0.0389040
$813$	23.7878	0.834275
$814$	−113.521	−3.97892
$815$	16.0948	0.563777
$816$	6.84030	0.239458
$817$	0.0695475	0.00243316
$818$	−5.26582	−0.184115
$819$	0.0252000	0.000880558 0
$820$	−32.7668	−1.14427
$821$	28.4946	0.994468	0.497234	−	0.867617i	$-0.334349\pi$
$821$	28.4946	0.994468	0.497234	+	0.867617i	$0.334349\pi$
$822$	24.5727	0.857073
$823$	43.0968	1.50226	0.751130	−	0.660154i	$-0.229509\pi$
$823$	43.0968	1.50226	0.751130	+	0.660154i	$0.229509\pi$
$824$	−3.95698	−0.137848
$825$	−17.6932	−0.615999
$826$	−0.0222724	−0.000774957 0
$827$	−6.73989	−0.234369	−0.117185	−	0.993110i	$-0.537387\pi$
$827$	−6.73989	−0.234369	−0.117185	+	0.993110i	$0.537387\pi$
$828$	12.2817	0.426819
$829$	−20.1494	−0.699816	−0.349908	−	0.936784i	$-0.613787\pi$
$829$	−20.1494	−0.699816	−0.349908	+	0.936784i	$0.613787\pi$
$830$	−22.3103	−0.774401
$831$	16.6659	0.578133
$832$	−6.64283	−0.230299
$833$	33.3592	1.15583
$834$	11.0523	0.382711
$835$	−13.8775	−0.480252
$836$	−0.150154	−0.00519317
$837$	−3.05936	−0.105747
$838$	−3.96512	−0.136973
$839$	−30.7280	−1.06085	−0.530423	−	0.847733i	$-0.677967\pi$
$839$	−30.7280	−1.06085	−0.530423	+	0.847733i	$0.677967\pi$
$840$	−0.145002	−0.00500303
$841$	33.2240	1.14565
$842$	−18.0028	−0.620417
$843$	−21.2038	−0.730297
$844$	74.7731	2.57380
$845$	−19.3209	−0.664660
$846$	−3.99404	−0.137318
$847$	1.55882	0.0535617
$848$	−8.22121	−0.282318
$849$	21.0479	0.722362
$850$	−28.4272	−0.975046
$851$	33.2838	1.14095
$852$	0.708536	0.0242740
$853$	−42.4080	−1.45202	−0.726012	−	0.687682i	$-0.758628\pi$
$853$	−42.4080	−1.45202	−0.726012	+	0.687682i	$0.758628\pi$
$854$	−1.30191	−0.0445504
$855$	−0.0120266	−0.000411300 0
$856$	−7.28807	−0.249101
$857$	1.17247	0.0400507	0.0200253	−	0.999799i	$-0.493625\pi$
$857$	1.17247	0.0400507	0.0200253	+	0.999799i	$0.493625\pi$
$858$	−7.51123	−0.256429
$859$	−3.43890	−0.117334	−0.0586670	−	0.998278i	$-0.518685\pi$
$859$	−3.43890	−0.117334	−0.0586670	+	0.998278i	$0.518685\pi$
$860$	−38.4624	−1.31156
$861$	−0.363787	−0.0123978
$862$	−4.38425	−0.149328
$863$	−43.5007	−1.48078	−0.740391	−	0.672176i	$-0.765360\pi$
$863$	−43.5007	−1.48078	−0.740391	+	0.672176i	$0.765360\pi$
$864$	7.09965	0.241535
$865$	30.2008	1.02686
$866$	−15.0107	−0.510083
$867$	5.72637	0.194478
$868$	−0.429956	−0.0145936
$869$	109.259	3.70637
$870$	26.4661	0.897283
$871$	−4.45154	−0.150835
$872$	1.21107	0.0410121
$873$	12.1718	0.411952
$874$	0.0745101	0.00252034
$875$	−0.568378	−0.0192147
$876$	28.3723	0.958612
$877$	19.9045	0.672128	0.336064	−	0.941839i	$-0.390904\pi$
$877$	19.9045	0.672128	0.336064	+	0.941839i	$0.390904\pi$
$878$	−64.3743	−2.17253
$879$	14.3585	0.484302
$880$	−14.2843	−0.481523
$881$	−18.8910	−0.636454	−0.318227	−	0.948014i	$-0.603087\pi$
$881$	−18.8910	−0.636454	−0.318227	+	0.948014i	$0.603087\pi$
$882$	15.4712	0.520942
$883$	−44.9266	−1.51190	−0.755950	−	0.654630i	$-0.772825\pi$
$883$	−44.9266	−1.51190	−0.755950	+	0.654630i	$0.772825\pi$
$884$	−7.13040	−0.239821
$885$	0.314167	0.0105606
$886$	32.5191	1.09250
$887$	−2.15229	−0.0722670	−0.0361335	−	0.999347i	$-0.511504\pi$
$887$	−2.15229	−0.0722670	−0.0361335	+	0.999347i	$0.511504\pi$
$888$	−15.3694	−0.515763
$889$	0.568451	0.0190652
$890$	−49.2708	−1.65156
$891$	6.56010	0.219772
$892$	−75.8948	−2.54114
$893$	−0.0143167	−0.000479091 0
$894$	−43.6468	−1.45977
$895$	−30.1577	−1.00806
$896$	0.689034	0.0230190
$897$	2.20225	0.0735309
$898$	55.6556	1.85725
$899$	24.1329	0.804877
$900$	−7.78964	−0.259655
$901$	−27.3144	−0.909973
$902$	108.432	3.61040
$903$	−0.427021	−0.0142104
$904$	30.6813	1.02044
$905$	0.138768	0.00461281
$906$	−38.0048	−1.26262
$907$	7.25645	0.240946	0.120473	−	0.992717i	$-0.461559\pi$
$907$	7.25645	0.240946	0.120473	+	0.992717i	$0.461559\pi$
$908$	15.6436	0.519151
$909$	11.2638	0.373596
$910$	−0.0845494	−0.00280278
$911$	15.6873	0.519742	0.259871	−	0.965643i	$-0.416320\pi$
$911$	15.6873	0.519742	0.259871	+	0.965643i	$0.416320\pi$
$912$	0.0113714	0.000376545 0
$913$	43.6220	1.44368
$914$	13.4425	0.444639
$915$	18.3643	0.607104
$916$	49.9504	1.65041
$917$	0.0206195	0.000680916 0
$918$	10.5399	0.347869
$919$	−13.7237	−0.452704	−0.226352	−	0.974046i	$-0.572680\pi$
$919$	−13.7237	−0.452704	−0.226352	+	0.974046i	$0.572680\pi$
$920$	−12.6718	−0.417777
$921$	−15.4896	−0.510400
$922$	25.5293	0.840764
$923$	0.127048	0.00418185
$924$	0.921942	0.0303297
$925$	−21.1101	−0.694097
$926$	31.4324	1.03293
$927$	2.01512	0.0661853
$928$	−56.0035	−1.83841
$929$	−45.0360	−1.47758	−0.738792	−	0.673934i	$-0.764603\pi$
$929$	−45.0360	−1.47758	−0.738792	+	0.673934i	$0.764603\pi$
$930$	10.2646	0.336589
$931$	0.0554569	0.00181753
$932$	−19.8401	−0.649885
$933$	−4.07764	−0.133496
$934$	−50.5988	−1.65564
$935$	−47.4584	−1.55206
$936$	−1.01693	−0.0332394
$937$	17.3038	0.565291	0.282646	−	0.959224i	$-0.408788\pi$
$937$	17.3038	0.565291	0.282646	+	0.959224i	$0.408788\pi$
$938$	0.924757	0.0301944
$939$	−16.5977	−0.541644
$940$	7.91768	0.258246
$941$	−42.0530	−1.37089	−0.685445	−	0.728125i	$-0.740392\pi$
$941$	−42.0530	−1.37089	−0.685445	+	0.728125i	$0.740392\pi$
$942$	−37.8282	−1.23251
$943$	−31.7917	−1.03528
$944$	−0.297052	−0.00966822
$945$	0.0738431	0.00240212
$946$	127.280	4.13823
$947$	45.1348	1.46668	0.733341	−	0.679861i	$-0.237960\pi$
$947$	45.1348	1.46668	0.733341	+	0.679861i	$0.237960\pi$
$948$	48.1026	1.56230
$949$	5.08747	0.165146
$950$	−0.0472578	−0.00153325
$951$	9.72846	0.315467
$952$	0.455512	0.0147632
$953$	26.2750	0.851131	0.425565	−	0.904928i	$-0.360075\pi$
$953$	26.2750	0.851131	0.425565	+	0.904928i	$0.360075\pi$
$954$	−12.6677	−0.410133
$955$	29.7338	0.962163
$956$	−13.7927	−0.446087
$957$	−51.7475	−1.67276
$958$	69.9489	2.25995
$959$	−0.540821	−0.0174640
$960$	−19.4654	−0.628243
$961$	−21.6403	−0.698075
$962$	−8.96179	−0.288940
$963$	3.71150	0.119601
$964$	40.9099	1.31762
$965$	26.8700	0.864977
$966$	−0.457491	−0.0147195
$967$	−35.7448	−1.14948	−0.574738	−	0.818337i	$-0.694896\pi$
$967$	−35.7448	−1.14948	−0.574738	+	0.818337i	$0.694896\pi$
$968$	−62.9052	−2.02185
$969$	0.0377806	0.00121369
$970$	−40.8379	−1.31123
$971$	−3.11135	−0.0998478	−0.0499239	−	0.998753i	$-0.515898\pi$
$971$	−3.11135	−0.0998478	−0.0499239	+	0.998753i	$0.515898\pi$
$972$	2.88816	0.0926377
$973$	−0.243251	−0.00779825
$974$	53.7933	1.72365
$975$	−1.39677	−0.0447324
$976$	−17.3638	−0.555802
$977$	24.5561	0.785621	0.392810	−	0.919620i	$-0.371503\pi$
$977$	24.5561	0.785621	0.392810	+	0.919620i	$0.371503\pi$
$978$	−23.4488	−0.749811
$979$	96.3363	3.07892
$980$	−30.6697	−0.979708
$981$	−0.616748	−0.0196913
$982$	61.0818	1.94920
$983$	56.7505	1.81006	0.905030	−	0.425347i	$-0.139848\pi$
$983$	56.7505	1.81006	0.905030	+	0.425347i	$0.139848\pi$
$984$	14.6804	0.467994
$985$	−6.68199	−0.212906
$986$	−83.1412	−2.64776
$987$	0.0879046	0.00279803
$988$	−0.0118537	−0.000377116 0
$989$	−37.3178	−1.18664
$990$	−22.0100	−0.699525
$991$	31.4474	0.998960	0.499480	−	0.866325i	$-0.333524\pi$
$991$	31.4474	0.998960	0.499480	+	0.866325i	$0.333524\pi$
$992$	−21.7204	−0.689623
$993$	4.23416	0.134367
$994$	−0.0263928	−0.000837129 0
$995$	−11.0247	−0.349507
$996$	19.2051	0.608536
$997$	25.5631	0.809591	0.404795	−	0.914407i	$-0.367343\pi$
$997$	25.5631	0.809591	0.404795	+	0.914407i	$0.367343\pi$
$998$	49.3587	1.56242
$999$	7.82698	0.247635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.d.1.16	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.d.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.21092 q^{2} +1.00000 q^{3} +2.88816 q^{4} +1.51753 q^{5} -2.21092 q^{6} +0.0486600 q^{7} -1.96364 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.21092 q^{2} +1.00000 q^{3} +2.88816 q^{4} +1.51753 q^{5} -2.21092 q^{6} +0.0486600 q^{7} -1.96364 q^{8} +1.00000 q^{9} -3.35514 q^{10} +6.56010 q^{11} +2.88816 q^{12} +0.517879 q^{13} -0.107583 q^{14} +1.51753 q^{15} -1.43486 q^{16} -4.76722 q^{17} -2.21092 q^{18} -0.00792509 q^{19} +4.38287 q^{20} +0.0486600 q^{21} -14.5038 q^{22} +4.25244 q^{23} -1.96364 q^{24} -2.69710 q^{25} -1.14499 q^{26} +1.00000 q^{27} +0.140538 q^{28} -7.88822 q^{29} -3.35514 q^{30} -3.05936 q^{31} +7.09965 q^{32} +6.56010 q^{33} +10.5399 q^{34} +0.0738431 q^{35} +2.88816 q^{36} +7.82698 q^{37} +0.0175217 q^{38} +0.517879 q^{39} -2.97989 q^{40} -7.47610 q^{41} -0.107583 q^{42} -8.77561 q^{43} +18.9466 q^{44} +1.51753 q^{45} -9.40180 q^{46} +1.80651 q^{47} -1.43486 q^{48} -6.99763 q^{49} +5.96306 q^{50} -4.76722 q^{51} +1.49571 q^{52} +5.72962 q^{53} -2.21092 q^{54} +9.95516 q^{55} -0.0955509 q^{56} -0.00792509 q^{57} +17.4402 q^{58} +0.207025 q^{59} +4.38287 q^{60} +12.1014 q^{61} +6.76400 q^{62} +0.0486600 q^{63} -12.8270 q^{64} +0.785897 q^{65} -14.5038 q^{66} -8.59573 q^{67} -13.7685 q^{68} +4.25244 q^{69} -0.163261 q^{70} +0.245324 q^{71} -1.96364 q^{72} +9.82368 q^{73} -17.3048 q^{74} -2.69710 q^{75} -0.0228889 q^{76} +0.319215 q^{77} -1.14499 q^{78} +16.6551 q^{79} -2.17745 q^{80} +1.00000 q^{81} +16.5290 q^{82} +6.64959 q^{83} +0.140538 q^{84} -7.23440 q^{85} +19.4022 q^{86} -7.88822 q^{87} -12.8817 q^{88} +14.6852 q^{89} -3.35514 q^{90} +0.0252000 q^{91} +12.2817 q^{92} -3.05936 q^{93} -3.99404 q^{94} -0.0120266 q^{95} +7.09965 q^{96} +12.1718 q^{97} +15.4712 q^{98} +6.56010 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) \) 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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