LMFDB - Embedded newform 8011.2.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8011,2,Mod(1,8011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8011.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:	$63.9681570592$
Analytic rank:	$1$
Dimension:	$309$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74693 q^{2} +2.61520 q^{3} +5.54560 q^{4} -1.49229 q^{5} -7.18376 q^{6} +4.10131 q^{7} -9.73951 q^{8} +3.83927 q^{9} +O(q^{10})$	\(q-2.74693 q^{2} +2.61520 q^{3} +5.54560 q^{4} -1.49229 q^{5} -7.18376 q^{6} +4.10131 q^{7} -9.73951 q^{8} +3.83927 q^{9} +4.09920 q^{10} -0.965756 q^{11} +14.5029 q^{12} +2.92658 q^{13} -11.2660 q^{14} -3.90263 q^{15} +15.6625 q^{16} -5.20957 q^{17} -10.5462 q^{18} -5.19874 q^{19} -8.27563 q^{20} +10.7257 q^{21} +2.65286 q^{22} -9.27155 q^{23} -25.4708 q^{24} -2.77308 q^{25} -8.03911 q^{26} +2.19486 q^{27} +22.7442 q^{28} -0.585517 q^{29} +10.7202 q^{30} -3.53565 q^{31} -23.5447 q^{32} -2.52564 q^{33} +14.3103 q^{34} -6.12033 q^{35} +21.2911 q^{36} +2.51921 q^{37} +14.2806 q^{38} +7.65360 q^{39} +14.5341 q^{40} +8.15740 q^{41} -29.4628 q^{42} +3.06910 q^{43} -5.35570 q^{44} -5.72930 q^{45} +25.4683 q^{46} -6.29545 q^{47} +40.9606 q^{48} +9.82075 q^{49} +7.61744 q^{50} -13.6241 q^{51} +16.2297 q^{52} +14.1181 q^{53} -6.02912 q^{54} +1.44119 q^{55} -39.9447 q^{56} -13.5957 q^{57} +1.60837 q^{58} +0.445533 q^{59} -21.6424 q^{60} +4.89889 q^{61} +9.71216 q^{62} +15.7460 q^{63} +33.3506 q^{64} -4.36730 q^{65} +6.93776 q^{66} -2.62088 q^{67} -28.8902 q^{68} -24.2470 q^{69} +16.8121 q^{70} +3.86065 q^{71} -37.3926 q^{72} -2.28784 q^{73} -6.92009 q^{74} -7.25215 q^{75} -28.8302 q^{76} -3.96087 q^{77} -21.0239 q^{78} -3.13591 q^{79} -23.3730 q^{80} -5.77781 q^{81} -22.4078 q^{82} +3.10779 q^{83} +59.4807 q^{84} +7.77418 q^{85} -8.43059 q^{86} -1.53124 q^{87} +9.40599 q^{88} -4.61049 q^{89} +15.7380 q^{90} +12.0028 q^{91} -51.4163 q^{92} -9.24642 q^{93} +17.2931 q^{94} +7.75802 q^{95} -61.5742 q^{96} +1.19526 q^{97} -26.9769 q^{98} -3.70780 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) $ 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * 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 $

$2$	−2.74693	−1.94237	−0.971185	−	0.238327i	$-0.923401\pi$
$2$	−2.74693	−1.94237	−0.971185	+	0.238327i	$0.923401\pi$
$3$	2.61520	1.50989	0.754943	−	0.655790i	$-0.227664\pi$
$3$	2.61520	1.50989	0.754943	+	0.655790i	$0.227664\pi$
$4$	5.54560	2.77280
$5$	−1.49229	−0.667371	−0.333686	−	0.942684i	$-0.608292\pi$
$5$	−1.49229	−0.667371	−0.333686	+	0.942684i	$0.608292\pi$
$6$	−7.18376	−2.93276
$7$	4.10131	1.55015	0.775075	−	0.631869i	$-0.217712\pi$
$7$	4.10131	1.55015	0.775075	+	0.631869i	$0.217712\pi$
$8$	−9.73951	−3.44344
$9$	3.83927	1.27976
$10$	4.09920	1.29628
$11$	−0.965756	−0.291186	−0.145593	−	0.989345i	$-0.546509\pi$
$11$	−0.965756	−0.291186	−0.145593	+	0.989345i	$0.546509\pi$
$12$	14.5029	4.18661
$13$	2.92658	0.811688	0.405844	−	0.913942i	$-0.366978\pi$
$13$	2.92658	0.811688	0.405844	+	0.913942i	$0.366978\pi$
$14$	−11.2660	−3.01096
$15$	−3.90263	−1.00765
$16$	15.6625	3.91563
$17$	−5.20957	−1.26351	−0.631753	−	0.775169i	$-0.717664\pi$
$17$	−5.20957	−1.26351	−0.631753	+	0.775169i	$0.717664\pi$
$18$	−10.5462	−2.48576
$19$	−5.19874	−1.19267	−0.596336	−	0.802735i	$-0.703378\pi$
$19$	−5.19874	−1.19267	−0.596336	+	0.802735i	$0.703378\pi$
$20$	−8.27563	−1.85049
$21$	10.7257	2.34055
$22$	2.65286	0.565592
$23$	−9.27155	−1.93325	−0.966626	−	0.256193i	$-0.917532\pi$
$23$	−9.27155	−1.93325	−0.966626	+	0.256193i	$0.917532\pi$
$24$	−25.4708	−5.19920
$25$	−2.77308	−0.554616
$26$	−8.03911	−1.57660
$27$	2.19486	0.422401
$28$	22.7442	4.29826
$29$	−0.585517	−0.108728	−0.0543639	−	0.998521i	$-0.517313\pi$
$29$	−0.585517	−0.108728	−0.0543639	+	0.998521i	$0.517313\pi$
$30$	10.7202	1.95724
$31$	−3.53565	−0.635021	−0.317510	−	0.948255i	$-0.602847\pi$
$31$	−3.53565	−0.635021	−0.317510	+	0.948255i	$0.602847\pi$
$32$	−23.5447	−4.16216
$33$	−2.52564	−0.439658
$34$	14.3103	2.45420
$35$	−6.12033	−1.03453
$36$	21.2911	3.54851
$37$	2.51921	0.414156	0.207078	−	0.978324i	$-0.433605\pi$
$37$	2.51921	0.414156	0.207078	+	0.978324i	$0.433605\pi$
$38$	14.2806	2.31661
$39$	7.65360	1.22556
$40$	14.5341	2.29805
$41$	8.15740	1.27397	0.636986	−	0.770876i	$-0.280181\pi$
$41$	8.15740	1.27397	0.636986	+	0.770876i	$0.280181\pi$
$42$	−29.4628	−4.54621
$43$	3.06910	0.468033	0.234017	−	0.972233i	$-0.424813\pi$
$43$	3.06910	0.468033	0.234017	+	0.972233i	$0.424813\pi$
$44$	−5.35570	−0.807402
$45$	−5.72930	−0.854073
$46$	25.4683	3.75509
$47$	−6.29545	−0.918286	−0.459143	−	0.888362i	$-0.651843\pi$
$47$	−6.29545	−0.918286	−0.459143	+	0.888362i	$0.651843\pi$
$48$	40.9606	5.91215
$49$	9.82075	1.40296
$50$	7.61744	1.07727
$51$	−13.6241	−1.90775
$52$	16.2297	2.25065
$53$	14.1181	1.93927	0.969637	−	0.244550i	$-0.0786401\pi$
$53$	14.1181	1.93927	0.969637	+	0.244550i	$0.0786401\pi$
$54$	−6.02912	−0.820459
$55$	1.44119	0.194329
$56$	−39.9447	−5.33784
$57$	−13.5957	−1.80080
$58$	1.60837	0.211190
$59$	0.445533	0.0580034	0.0290017	−	0.999579i	$-0.490767\pi$
$59$	0.445533	0.0580034	0.0290017	+	0.999579i	$0.490767\pi$
$60$	−21.6424	−2.79403
$61$	4.89889	0.627239	0.313619	−	0.949549i	$-0.398458\pi$
$61$	4.89889	0.627239	0.313619	+	0.949549i	$0.398458\pi$
$62$	9.71216	1.23345
$63$	15.7460	1.98381
$64$	33.3506	4.16883
$65$	−4.36730	−0.541697
$66$	6.93776	0.853979
$67$	−2.62088	−0.320192	−0.160096	−	0.987101i	$-0.551180\pi$
$67$	−2.62088	−0.320192	−0.160096	+	0.987101i	$0.551180\pi$
$68$	−28.8902	−3.50345
$69$	−24.2470	−2.91899
$70$	16.8121	2.00943
$71$	3.86065	0.458174	0.229087	−	0.973406i	$-0.426426\pi$
$71$	3.86065	0.458174	0.229087	+	0.973406i	$0.426426\pi$
$72$	−37.3926	−4.40676
$73$	−2.28784	−0.267772	−0.133886	−	0.990997i	$-0.542746\pi$
$73$	−2.28784	−0.267772	−0.133886	+	0.990997i	$0.542746\pi$
$74$	−6.92009	−0.804444
$75$	−7.25215	−0.837407
$76$	−28.8302	−3.30705
$77$	−3.96087	−0.451382
$78$	−21.0239	−2.38048
$79$	−3.13591	−0.352818	−0.176409	−	0.984317i	$-0.556448\pi$
$79$	−3.13591	−0.352818	−0.176409	+	0.984317i	$0.556448\pi$
$80$	−23.3730	−2.61318
$81$	−5.77781	−0.641979
$82$	−22.4078	−2.47452
$83$	3.10779	0.341125	0.170562	−	0.985347i	$-0.445442\pi$
$83$	3.10779	0.341125	0.170562	+	0.985347i	$0.445442\pi$
$84$	59.4807	6.48988
$85$	7.77418	0.843228
$86$	−8.43059	−0.909094
$87$	−1.53124	−0.164167
$88$	9.40599	1.00268
$89$	−4.61049	−0.488711	−0.244355	−	0.969686i	$-0.578576\pi$
$89$	−4.61049	−0.488711	−0.244355	+	0.969686i	$0.578576\pi$
$90$	15.7380	1.65893
$91$	12.0028	1.25824
$92$	−51.4163	−5.36052
$93$	−9.24642	−0.958809
$94$	17.2931	1.78365
$95$	7.75802	0.795956
$96$	−61.5742	−6.28439
$97$	1.19526	0.121361	0.0606803	−	0.998157i	$-0.480673\pi$
$97$	1.19526	0.121361	0.0606803	+	0.998157i	$0.480673\pi$
$98$	−26.9769	−2.72508
$99$	−3.70780	−0.372648
$100$	−15.3784	−1.53784
$101$	−5.15507	−0.512949	−0.256474	−	0.966551i	$-0.582561\pi$
$101$	−5.15507	−0.512949	−0.256474	+	0.966551i	$0.582561\pi$
$102$	37.4243	3.70556
$103$	−8.01663	−0.789902	−0.394951	−	0.918702i	$-0.629238\pi$
$103$	−8.01663	−0.789902	−0.394951	+	0.918702i	$0.629238\pi$
$104$	−28.5035	−2.79500
$105$	−16.0059	−1.56202
$106$	−38.7814	−3.76679
$107$	−3.77408	−0.364854	−0.182427	−	0.983219i	$-0.558395\pi$
$107$	−3.77408	−0.364854	−0.182427	+	0.983219i	$0.558395\pi$
$108$	12.1718	1.17123
$109$	−4.79811	−0.459575	−0.229788	−	0.973241i	$-0.573803\pi$
$109$	−4.79811	−0.459575	−0.229788	+	0.973241i	$0.573803\pi$
$110$	−3.95883	−0.377460
$111$	6.58824	0.625329
$112$	64.2368	6.06981
$113$	7.95377	0.748227	0.374114	−	0.927383i	$-0.377947\pi$
$113$	7.95377	0.748227	0.374114	+	0.927383i	$0.377947\pi$
$114$	37.3465	3.49782
$115$	13.8358	1.29020
$116$	−3.24705	−0.301481
$117$	11.2359	1.03876
$118$	−1.22385	−0.112664
$119$	−21.3661	−1.95862
$120$	38.0097	3.46979
$121$	−10.0673	−0.915210
$122$	−13.4569	−1.21833
$123$	21.3332	1.92355
$124$	−19.6073	−1.76079
$125$	11.5997	1.03751
$126$	−43.2532	−3.85330
$127$	−3.70386	−0.328665	−0.164332	−	0.986405i	$-0.552547\pi$
$127$	−3.70386	−0.328665	−0.164332	+	0.986405i	$0.552547\pi$
$128$	−44.5222	−3.93524
$129$	8.02631	0.706677
$130$	11.9967	1.05218
$131$	−10.5120	−0.918441	−0.459220	−	0.888322i	$-0.651871\pi$
$131$	−10.5120	−0.918441	−0.459220	+	0.888322i	$0.651871\pi$
$132$	−14.0062	−1.21909
$133$	−21.3217	−1.84882
$134$	7.19937	0.621931
$135$	−3.27536	−0.281898
$136$	50.7387	4.35081
$137$	−17.4339	−1.48948	−0.744738	−	0.667356i	$-0.767426\pi$
$137$	−17.4339	−1.48948	−0.744738	+	0.667356i	$0.767426\pi$
$138$	66.6046	5.66976
$139$	−15.4476	−1.31025	−0.655126	−	0.755520i	$-0.727384\pi$
$139$	−15.4476	−1.31025	−0.655126	+	0.755520i	$0.727384\pi$
$140$	−33.9409	−2.86853
$141$	−16.4639	−1.38651
$142$	−10.6049	−0.889944
$143$	−2.82637	−0.236353
$144$	60.1326	5.01105
$145$	0.873760	0.0725618
$146$	6.28453	0.520112
$147$	25.6832	2.11832
$148$	13.9706	1.14837
$149$	6.85894	0.561906	0.280953	−	0.959722i	$-0.409350\pi$
$149$	6.85894	0.561906	0.280953	+	0.959722i	$0.409350\pi$
$150$	19.9211	1.62655
$151$	−21.5656	−1.75499	−0.877493	−	0.479589i	$-0.840786\pi$
$151$	−21.5656	−1.75499	−0.877493	+	0.479589i	$0.840786\pi$
$152$	50.6332	4.10689
$153$	−20.0010	−1.61698
$154$	10.8802	0.876752
$155$	5.27620	0.423795
$156$	42.4438	3.39823
$157$	−4.50886	−0.359846	−0.179923	−	0.983681i	$-0.557585\pi$
$157$	−4.50886	−0.359846	−0.179923	+	0.983681i	$0.557585\pi$
$158$	8.61412	0.685303
$159$	36.9217	2.92808
$160$	35.1355	2.77770
$161$	−38.0255	−2.99683
$162$	15.8712	1.24696
$163$	16.5437	1.29580	0.647901	−	0.761725i	$-0.275647\pi$
$163$	16.5437	1.29580	0.647901	+	0.761725i	$0.275647\pi$
$164$	45.2377	3.53247
$165$	3.76899	0.293415
$166$	−8.53688	−0.662590
$167$	−6.52404	−0.504845	−0.252422	−	0.967617i	$-0.581227\pi$
$167$	−6.52404	−0.504845	−0.252422	+	0.967617i	$0.581227\pi$
$168$	−104.464	−8.05953
$169$	−4.43511	−0.341162
$170$	−21.3551	−1.63786
$171$	−19.9594	−1.52633
$172$	17.0200	1.29776
$173$	20.0457	1.52405	0.762023	−	0.647549i	$-0.224206\pi$
$173$	20.0457	1.52405	0.762023	+	0.647549i	$0.224206\pi$
$174$	4.20621	0.318872
$175$	−11.3733	−0.859737
$176$	−15.1262	−1.14018
$177$	1.16516	0.0875785
$178$	12.6647	0.949257
$179$	−15.0511	−1.12497	−0.562486	−	0.826807i	$-0.690155\pi$
$179$	−15.0511	−1.12497	−0.562486	+	0.826807i	$0.690155\pi$
$180$	−31.7724	−2.36817
$181$	−26.5739	−1.97522	−0.987611	−	0.156921i	$-0.949843\pi$
$181$	−26.5739	−1.97522	−0.987611	+	0.156921i	$0.949843\pi$
$182$	−32.9709	−2.44396
$183$	12.8116	0.947059
$184$	90.3003	6.65703
$185$	−3.75939	−0.276396
$186$	25.3992	1.86236
$187$	5.03118	0.367916
$188$	−34.9121	−2.54622
$189$	9.00180	0.654785
$190$	−21.3107	−1.54604
$191$	13.7252	0.993120	0.496560	−	0.868002i	$-0.334596\pi$
$191$	13.7252	0.993120	0.496560	+	0.868002i	$0.334596\pi$
$192$	87.2185	6.29445
$193$	−18.1141	−1.30388	−0.651942	−	0.758269i	$-0.726046\pi$
$193$	−18.1141	−1.30388	−0.651942	+	0.758269i	$0.726046\pi$
$194$	−3.28330	−0.235727
$195$	−11.4214	−0.817901
$196$	54.4620	3.89014
$197$	19.5261	1.39118	0.695588	−	0.718441i	$-0.255144\pi$
$197$	19.5261	1.39118	0.695588	+	0.718441i	$0.255144\pi$
$198$	10.1850	0.723820
$199$	3.81690	0.270573	0.135287	−	0.990807i	$-0.456804\pi$
$199$	3.81690	0.270573	0.135287	+	0.990807i	$0.456804\pi$
$200$	27.0084	1.90978
$201$	−6.85413	−0.483453
$202$	14.1606	0.996336
$203$	−2.40139	−0.168544
$204$	−75.5537	−5.28982
$205$	−12.1732	−0.850212
$206$	22.0211	1.53428
$207$	−35.5960	−2.47409
$208$	45.8376	3.17827
$209$	5.02072	0.347290
$210$	43.9670	3.03401
$211$	14.7311	1.01413	0.507067	−	0.861907i	$-0.330730\pi$
$211$	14.7311	1.01413	0.507067	+	0.861907i	$0.330730\pi$
$212$	78.2935	5.37722
$213$	10.0964	0.691791
$214$	10.3671	0.708681
$215$	−4.57998	−0.312352
$216$	−21.3769	−1.45451
$217$	−14.5008	−0.984377
$218$	13.1801	0.892666
$219$	−5.98316	−0.404305
$220$	7.99224	0.538837
$221$	−15.2462	−1.02557
$222$	−18.0974	−1.21462
$223$	−5.42578	−0.363337	−0.181669	−	0.983360i	$-0.558150\pi$
$223$	−5.42578	−0.363337	−0.181669	+	0.983360i	$0.558150\pi$
$224$	−96.5642	−6.45197
$225$	−10.6466	−0.709773
$226$	−21.8484	−1.45333
$227$	−0.0308539	−0.00204784	−0.00102392	−	0.999999i	$-0.500326\pi$
$227$	−0.0308539	−0.00204784	−0.00102392	+	0.999999i	$0.500326\pi$
$228$	−75.3966	−4.99326
$229$	19.8315	1.31050	0.655250	−	0.755412i	$-0.272563\pi$
$229$	19.8315	1.31050	0.655250	+	0.755412i	$0.272563\pi$
$230$	−38.0060	−2.50604
$231$	−10.3585	−0.681536
$232$	5.70265	0.374397
$233$	0.178446	0.0116904	0.00584520	−	0.999983i	$-0.498139\pi$
$233$	0.178446	0.0116904	0.00584520	+	0.999983i	$0.498139\pi$
$234$	−30.8643	−2.01766
$235$	9.39462	0.612838
$236$	2.47075	0.160832
$237$	−8.20104	−0.532715
$238$	58.6910	3.80437
$239$	−23.8480	−1.54260	−0.771299	−	0.636473i	$-0.780393\pi$
$239$	−23.8480	−1.54260	−0.771299	+	0.636473i	$0.780393\pi$
$240$	−61.1250	−3.94560
$241$	−24.6900	−1.59042	−0.795210	−	0.606334i	$-0.792640\pi$
$241$	−24.6900	−1.59042	−0.795210	+	0.606334i	$0.792640\pi$
$242$	27.6542	1.77768
$243$	−21.6947	−1.39172
$244$	27.1673	1.73921
$245$	−14.6554	−0.936298
$246$	−58.6008	−3.73625
$247$	−15.2145	−0.968078
$248$	34.4354	2.18665
$249$	8.12750	0.515059
$250$	−31.8634	−2.01522
$251$	11.8219	0.746189	0.373095	−	0.927793i	$-0.378297\pi$
$251$	11.8219	0.746189	0.373095	+	0.927793i	$0.378297\pi$
$252$	87.3213	5.50072
$253$	8.95405	0.562937
$254$	10.1742	0.638389
$255$	20.3310	1.27318
$256$	55.5980	3.47487
$257$	−23.2733	−1.45175	−0.725875	−	0.687827i	$-0.758565\pi$
$257$	−23.2733	−1.45175	−0.725875	+	0.687827i	$0.758565\pi$
$258$	−22.0477	−1.37263
$259$	10.3321	0.642004
$260$	−24.2193	−1.50202
$261$	−2.24796	−0.139145
$262$	28.8758	1.78395
$263$	−16.9960	−1.04802	−0.524010	−	0.851712i	$-0.675564\pi$
$263$	−16.9960	−1.04802	−0.524010	+	0.851712i	$0.675564\pi$
$264$	24.5985	1.51394
$265$	−21.0683	−1.29422
$266$	58.5690	3.59110
$267$	−12.0573	−0.737897
$268$	−14.5344	−0.887828
$269$	−22.4201	−1.36698	−0.683489	−	0.729961i	$-0.739538\pi$
$269$	−22.4201	−1.36698	−0.683489	+	0.729961i	$0.739538\pi$
$270$	8.99718	0.547551
$271$	14.1813	0.861450	0.430725	−	0.902483i	$-0.358258\pi$
$271$	14.1813	0.861450	0.430725	+	0.902483i	$0.358258\pi$
$272$	−81.5949	−4.94742
$273$	31.3898	1.89980
$274$	47.8896	2.89312
$275$	2.67812	0.161497
$276$	−134.464	−8.09378
$277$	−25.9908	−1.56164	−0.780818	−	0.624759i	$-0.785197\pi$
$277$	−25.9908	−1.56164	−0.780818	+	0.624759i	$0.785197\pi$
$278$	42.4335	2.54499
$279$	−13.5743	−0.812672
$280$	59.6090	3.56232
$281$	10.0309	0.598394	0.299197	−	0.954191i	$-0.403281\pi$
$281$	10.0309	0.598394	0.299197	+	0.954191i	$0.403281\pi$
$282$	45.2250	2.69311
$283$	−16.9537	−1.00780	−0.503898	−	0.863763i	$-0.668101\pi$
$283$	−16.9537	−1.00780	−0.503898	+	0.863763i	$0.668101\pi$
$284$	21.4096	1.27043
$285$	20.2888	1.20180
$286$	7.76382	0.459084
$287$	33.4560	1.97485
$288$	−90.3946	−5.32655
$289$	10.1396	0.596450
$290$	−2.40015	−0.140942
$291$	3.12585	0.183241
$292$	−12.6875	−0.742478
$293$	−22.9680	−1.34180	−0.670901	−	0.741547i	$-0.734093\pi$
$293$	−22.9680	−1.34180	−0.670901	+	0.741547i	$0.734093\pi$
$294$	−70.5499	−4.11455
$295$	−0.664863	−0.0387098
$296$	−24.5359	−1.42612
$297$	−2.11970	−0.122997
$298$	−18.8410	−1.09143
$299$	−27.1340	−1.56920
$300$	−40.2176	−2.32196
$301$	12.5873	0.725522
$302$	59.2392	3.40883
$303$	−13.4815	−0.774494
$304$	−81.4253	−4.67006
$305$	−7.31055	−0.418601
$306$	54.9411	3.14078
$307$	13.6728	0.780346	0.390173	−	0.920742i	$-0.372415\pi$
$307$	13.6728	0.780346	0.390173	+	0.920742i	$0.372415\pi$
$308$	−21.9654	−1.25159
$309$	−20.9651	−1.19266
$310$	−14.4933	−0.823166
$311$	28.3130	1.60548	0.802740	−	0.596329i	$-0.203374\pi$
$311$	28.3130	1.60548	0.802740	+	0.596329i	$0.203374\pi$
$312$	−74.5423	−4.22013
$313$	−30.2662	−1.71074	−0.855372	−	0.518014i	$-0.826671\pi$
$313$	−30.2662	−1.71074	−0.855372	+	0.518014i	$0.826671\pi$
$314$	12.3855	0.698954
$315$	−23.4976	−1.32394
$316$	−17.3905	−0.978294
$317$	6.92358	0.388867	0.194433	−	0.980916i	$-0.437713\pi$
$317$	6.92358	0.388867	0.194433	+	0.980916i	$0.437713\pi$
$318$	−101.421	−5.68742
$319$	0.565467	0.0316601
$320$	−49.7687	−2.78215
$321$	−9.86996	−0.550888
$322$	104.453	5.82095
$323$	27.0832	1.50695
$324$	−32.0415	−1.78008
$325$	−8.11564	−0.450175
$326$	−45.4443	−2.51693
$327$	−12.5480	−0.693907
$328$	−79.4491	−4.38684
$329$	−25.8196	−1.42348
$330$	−10.3531	−0.569921
$331$	19.6897	1.08225	0.541123	−	0.840943i	$-0.317999\pi$
$331$	19.6897	1.08225	0.541123	+	0.840943i	$0.317999\pi$
$332$	17.2346	0.945871
$333$	9.67194	0.530019
$334$	17.9210	0.980596
$335$	3.91111	0.213687
$336$	167.992	9.16472
$337$	−26.9697	−1.46913	−0.734567	−	0.678536i	$-0.762615\pi$
$337$	−26.9697	−1.46913	−0.734567	+	0.678536i	$0.762615\pi$
$338$	12.1829	0.662664
$339$	20.8007	1.12974
$340$	43.1125	2.33810
$341$	3.41457	0.184909
$342$	54.8269	2.96470
$343$	11.5688	0.624655
$344$	−29.8915	−1.61164
$345$	36.1834	1.94805
$346$	−55.0641	−2.96026
$347$	14.2324	0.764037	0.382018	−	0.924155i	$-0.375229\pi$
$347$	14.2324	0.764037	0.382018	+	0.924155i	$0.375229\pi$
$348$	−8.49167	−0.455201
$349$	16.9231	0.905872	0.452936	−	0.891543i	$-0.350377\pi$
$349$	16.9231	0.905872	0.452936	+	0.891543i	$0.350377\pi$
$350$	31.2415	1.66993
$351$	6.42344	0.342858
$352$	22.7385	1.21196
$353$	−24.4255	−1.30004	−0.650019	−	0.759918i	$-0.725239\pi$
$353$	−24.4255	−1.30004	−0.650019	+	0.759918i	$0.725239\pi$
$354$	−3.20060	−0.170110
$355$	−5.76119	−0.305772
$356$	−25.5679	−1.35510
$357$	−55.8766	−2.95730
$358$	41.3443	2.18511
$359$	2.60765	0.137626	0.0688132	−	0.997630i	$-0.478079\pi$
$359$	2.60765	0.137626	0.0688132	+	0.997630i	$0.478079\pi$
$360$	55.8005	2.94095
$361$	8.02691	0.422469
$362$	72.9965	3.83661
$363$	−26.3280	−1.38186
$364$	66.5629	3.48884
$365$	3.41412	0.178703
$366$	−35.1924	−1.83954
$367$	7.50404	0.391708	0.195854	−	0.980633i	$-0.437252\pi$
$367$	7.50404	0.391708	0.195854	+	0.980633i	$0.437252\pi$
$368$	−145.216	−7.56989
$369$	31.3185	1.63037
$370$	10.3268	0.536863
$371$	57.9028	3.00616
$372$	−51.2770	−2.65859
$373$	8.20560	0.424870	0.212435	−	0.977175i	$-0.431861\pi$
$373$	8.20560	0.424870	0.212435	+	0.977175i	$0.431861\pi$
$374$	−13.8203	−0.714629
$375$	30.3354	1.56652
$376$	61.3146	3.16206
$377$	−1.71356	−0.0882531
$378$	−24.7273	−1.27183
$379$	−24.8178	−1.27481	−0.637403	−	0.770530i	$-0.719992\pi$
$379$	−24.8178	−1.27481	−0.637403	+	0.770530i	$0.719992\pi$
$380$	43.0229	2.20703
$381$	−9.68635	−0.496247
$382$	−37.7021	−1.92901
$383$	35.0943	1.79323	0.896617	−	0.442808i	$-0.146018\pi$
$383$	35.0943	1.79323	0.896617	+	0.442808i	$0.146018\pi$
$384$	−116.434	−5.94177
$385$	5.91075	0.301240
$386$	49.7582	2.53263
$387$	11.7831	0.598969
$388$	6.62845	0.336509
$389$	−29.4301	−1.49216	−0.746082	−	0.665854i	$-0.768067\pi$
$389$	−29.4301	−1.49216	−0.746082	+	0.665854i	$0.768067\pi$
$390$	31.3737	1.58867
$391$	48.3008	2.44268
$392$	−95.6493	−4.83102
$393$	−27.4911	−1.38674
$394$	−53.6367	−2.70218
$395$	4.67968	0.235460
$396$	−20.5620	−1.03328
$397$	−9.35155	−0.469341	−0.234670	−	0.972075i	$-0.575401\pi$
$397$	−9.35155	−0.469341	−0.234670	+	0.972075i	$0.575401\pi$
$398$	−10.4848	−0.525553
$399$	−55.7604	−2.79151
$400$	−43.4333	−2.17167
$401$	−30.0594	−1.50110	−0.750548	−	0.660816i	$-0.770211\pi$
$401$	−30.0594	−1.50110	−0.750548	+	0.660816i	$0.770211\pi$
$402$	18.8278	0.939045
$403$	−10.3474	−0.515439
$404$	−28.5880	−1.42230
$405$	8.62216	0.428439
$406$	6.59643	0.327376
$407$	−2.43294	−0.120597
$408$	132.692	6.56922
$409$	11.3842	0.562913	0.281457	−	0.959574i	$-0.409182\pi$
$409$	11.3842	0.562913	0.281457	+	0.959574i	$0.409182\pi$
$410$	33.4388	1.65143
$411$	−45.5931	−2.24894
$412$	−44.4570	−2.19024
$413$	1.82727	0.0899140
$414$	97.7795	4.80560
$415$	−4.63772	−0.227657
$416$	−68.9056	−3.37837
$417$	−40.3987	−1.97833
$418$	−13.7915	−0.674566
$419$	15.1928	0.742218	0.371109	−	0.928589i	$-0.378978\pi$
$419$	15.1928	0.742218	0.371109	+	0.928589i	$0.378978\pi$
$420$	−88.7624	−4.33116
$421$	19.1972	0.935616	0.467808	−	0.883830i	$-0.345044\pi$
$421$	19.1972	0.935616	0.467808	+	0.883830i	$0.345044\pi$
$422$	−40.4653	−1.96982
$423$	−24.1699	−1.17518
$424$	−137.504	−6.67776
$425$	14.4466	0.700761
$426$	−27.7340	−1.34371
$427$	20.0919	0.972314
$428$	−20.9295	−1.01167
$429$	−7.39151	−0.356865
$430$	12.5809	0.606703
$431$	−29.5526	−1.42350	−0.711749	−	0.702434i	$-0.752097\pi$
$431$	−29.5526	−1.42350	−0.711749	+	0.702434i	$0.752097\pi$
$432$	34.3770	1.65396
$433$	−20.8448	−1.00174	−0.500869	−	0.865523i	$-0.666986\pi$
$433$	−20.8448	−1.00174	−0.500869	+	0.865523i	$0.666986\pi$
$434$	39.8326	1.91202
$435$	2.28506	0.109560
$436$	−26.6084	−1.27431
$437$	48.2004	2.30574
$438$	16.4353	0.785309
$439$	31.2103	1.48958	0.744792	−	0.667297i	$-0.232549\pi$
$439$	31.2103	1.48958	0.744792	+	0.667297i	$0.232549\pi$
$440$	−14.0364	−0.669161
$441$	37.7045	1.79545
$442$	41.8803	1.99204
$443$	13.6455	0.648316	0.324158	−	0.946003i	$-0.394919\pi$
$443$	13.6455	0.648316	0.324158	+	0.946003i	$0.394919\pi$
$444$	36.5358	1.73391
$445$	6.88017	0.326151
$446$	14.9042	0.705735
$447$	17.9375	0.848414
$448$	136.781	6.46230
$449$	7.16969	0.338359	0.169179	−	0.985585i	$-0.445888\pi$
$449$	7.16969	0.338359	0.169179	+	0.985585i	$0.445888\pi$
$450$	29.2454	1.37864
$451$	−7.87806	−0.370963
$452$	44.1084	2.07469
$453$	−56.3984	−2.64983
$454$	0.0847533	0.00397767
$455$	−17.9117	−0.839712
$456$	132.416	6.20094
$457$	24.1746	1.13084	0.565421	−	0.824802i	$-0.308714\pi$
$457$	24.1746	1.13084	0.565421	+	0.824802i	$0.308714\pi$
$458$	−54.4756	−2.54548
$459$	−11.4343	−0.533707
$460$	76.7279	3.57746
$461$	24.7640	1.15337	0.576687	−	0.816965i	$-0.304345\pi$
$461$	24.7640	1.15337	0.576687	+	0.816965i	$0.304345\pi$
$462$	28.4539	1.32380
$463$	−22.6170	−1.05110	−0.525551	−	0.850762i	$-0.676141\pi$
$463$	−22.6170	−1.05110	−0.525551	+	0.850762i	$0.676141\pi$
$464$	−9.17066	−0.425737
$465$	13.7983	0.639882
$466$	−0.490179	−0.0227071
$467$	−27.9455	−1.29316	−0.646581	−	0.762845i	$-0.723802\pi$
$467$	−27.9455	−1.29316	−0.646581	+	0.762845i	$0.723802\pi$
$468$	62.3101	2.88028
$469$	−10.7491	−0.496345
$470$	−25.8063	−1.19036
$471$	−11.7916	−0.543327
$472$	−4.33927	−0.199731
$473$	−2.96400	−0.136285
$474$	22.5276	1.03473
$475$	14.4165	0.661475
$476$	−118.488	−5.43088
$477$	54.2033	2.48180
$478$	65.5086	2.99630
$479$	−17.9125	−0.818444	−0.409222	−	0.912435i	$-0.634200\pi$
$479$	−17.9125	−0.818444	−0.409222	+	0.912435i	$0.634200\pi$
$480$	91.8863	4.19402
$481$	7.37269	0.336166
$482$	67.8215	3.08919
$483$	−99.4443	−4.52487
$484$	−55.8293	−2.53770
$485$	−1.78368	−0.0809925
$486$	59.5938	2.70323
$487$	23.4635	1.06323	0.531616	−	0.846985i	$-0.321585\pi$
$487$	23.4635	1.06323	0.531616	+	0.846985i	$0.321585\pi$
$488$	−47.7128	−2.15986
$489$	43.2650	1.95651
$490$	40.2572	1.81864
$491$	10.2845	0.464132	0.232066	−	0.972700i	$-0.425451\pi$
$491$	10.2845	0.464132	0.232066	+	0.972700i	$0.425451\pi$
$492$	118.306	5.33363
$493$	3.05029	0.137378
$494$	41.7932	1.88037
$495$	5.53310	0.248694
$496$	−55.3771	−2.48650
$497$	15.8337	0.710239
$498$	−22.3256	−1.00044
$499$	17.1816	0.769152	0.384576	−	0.923093i	$-0.374348\pi$
$499$	17.1816	0.769152	0.384576	+	0.923093i	$0.374348\pi$
$500$	64.3271	2.87680
$501$	−17.0617	−0.762259
$502$	−32.4738	−1.44938
$503$	9.54480	0.425582	0.212791	−	0.977098i	$-0.431745\pi$
$503$	9.54480	0.425582	0.212791	+	0.977098i	$0.431745\pi$
$504$	−153.359	−6.83114
$505$	7.69285	0.342327
$506$	−24.5961	−1.09343
$507$	−11.5987	−0.515116
$508$	−20.5402	−0.911322
$509$	−24.0642	−1.06663	−0.533313	−	0.845918i	$-0.679053\pi$
$509$	−24.0642	−1.06663	−0.533313	+	0.845918i	$0.679053\pi$
$510$	−55.8478	−2.47298
$511$	−9.38315	−0.415086
$512$	−63.6791	−2.81425
$513$	−11.4105	−0.503786
$514$	63.9301	2.81983
$515$	11.9631	0.527158
$516$	44.5107	1.95948
$517$	6.07987	0.267392
$518$	−28.3814	−1.24701
$519$	52.4235	2.30114
$520$	42.5354	1.86530
$521$	13.7807	0.603743	0.301871	−	0.953349i	$-0.402389\pi$
$521$	13.7807	0.603743	0.301871	+	0.953349i	$0.402389\pi$
$522$	6.17498	0.270271
$523$	−20.1085	−0.879284	−0.439642	−	0.898173i	$-0.644895\pi$
$523$	−20.1085	−0.879284	−0.439642	+	0.898173i	$0.644895\pi$
$524$	−58.2956	−2.54665
$525$	−29.7433	−1.29811
$526$	46.6868	2.03564
$527$	18.4192	0.802353
$528$	−39.5579	−1.72154
$529$	62.9616	2.73746
$530$	57.8731	2.51385
$531$	1.71052	0.0742302
$532$	−118.241	−5.12642
$533$	23.8733	1.03407
$534$	33.1206	1.43327
$535$	5.63201	0.243493
$536$	25.5261	1.10256
$537$	−39.3616	−1.69858
$538$	61.5864	2.65518
$539$	−9.48445	−0.408524
$540$	−18.1639	−0.781648
$541$	−34.6602	−1.49016	−0.745079	−	0.666976i	$-0.767588\pi$
$541$	−34.6602	−1.49016	−0.745079	+	0.666976i	$0.767588\pi$
$542$	−38.9548	−1.67325
$543$	−69.4961	−2.98236
$544$	122.658	5.25892
$545$	7.16016	0.306707
$546$	−86.2254	−3.69011
$547$	−42.1955	−1.80415	−0.902076	−	0.431578i	$-0.857957\pi$
$547$	−42.1955	−1.80415	−0.902076	+	0.431578i	$0.857957\pi$
$548$	−96.6814	−4.13002
$549$	18.8082	0.802713
$550$	−7.35659	−0.313686
$551$	3.04395	0.129677
$552$	236.153	10.0514
$553$	−12.8614	−0.546920
$554$	71.3948	3.03327
$555$	−9.83156	−0.417326
$556$	−85.6665	−3.63307
$557$	6.19374	0.262437	0.131219	−	0.991353i	$-0.458111\pi$
$557$	6.19374	0.262437	0.131219	+	0.991353i	$0.458111\pi$
$558$	37.2876	1.57851
$559$	8.98198	0.379897
$560$	−95.8598	−4.05081
$561$	13.1575	0.555511
$562$	−27.5542	−1.16230
$563$	18.8876	0.796015	0.398008	−	0.917382i	$-0.369702\pi$
$563$	18.8876	0.796015	0.398008	+	0.917382i	$0.369702\pi$
$564$	−91.3020	−3.84451
$565$	−11.8693	−0.499345
$566$	46.5707	1.95751
$567$	−23.6966	−0.995164
$568$	−37.6008	−1.57769
$569$	−26.4905	−1.11054	−0.555270	−	0.831670i	$-0.687385\pi$
$569$	−26.4905	−1.11054	−0.555270	+	0.831670i	$0.687385\pi$
$570$	−55.7317	−2.33435
$571$	42.6884	1.78645	0.893227	−	0.449605i	$-0.148435\pi$
$571$	42.6884	1.78645	0.893227	+	0.449605i	$0.148435\pi$
$572$	−15.6739	−0.655359
$573$	35.8941	1.49950
$574$	−91.9012	−3.83588
$575$	25.7107	1.07221
$576$	128.042	5.33508
$577$	−15.6232	−0.650404	−0.325202	−	0.945645i	$-0.605432\pi$
$577$	−15.6232	−0.650404	−0.325202	+	0.945645i	$0.605432\pi$
$578$	−27.8529	−1.15853
$579$	−47.3721	−1.96872
$580$	4.84553	0.201199
$581$	12.7460	0.528794
$582$	−8.58648	−0.355921
$583$	−13.6347	−0.564690
$584$	22.2825	0.922055
$585$	−16.7673	−0.693241
$586$	63.0913	2.60628
$587$	−21.2005	−0.875039	−0.437519	−	0.899209i	$-0.644143\pi$
$587$	−21.2005	−0.875039	−0.437519	+	0.899209i	$0.644143\pi$
$588$	142.429	5.87367
$589$	18.3809	0.757372
$590$	1.82633	0.0751888
$591$	51.0646	2.10052
$592$	39.4572	1.62168
$593$	34.3948	1.41243	0.706213	−	0.707999i	$-0.250402\pi$
$593$	34.3948	1.41243	0.706213	+	0.707999i	$0.250402\pi$
$594$	5.82266	0.238906
$595$	31.8843	1.30713
$596$	38.0369	1.55805
$597$	9.98197	0.408535
$598$	74.5350	3.04796
$599$	26.7773	1.09409	0.547046	−	0.837103i	$-0.315752\pi$
$599$	26.7773	1.09409	0.547046	+	0.837103i	$0.315752\pi$
$600$	70.6324	2.88356
$601$	34.9887	1.42722	0.713609	−	0.700544i	$-0.247059\pi$
$601$	34.9887	1.42722	0.713609	+	0.700544i	$0.247059\pi$
$602$	−34.5765	−1.40923
$603$	−10.0623	−0.409768
$604$	−119.594	−4.86623
$605$	15.0233	0.610785
$606$	37.0328	1.50435
$607$	−36.9598	−1.50015	−0.750075	−	0.661353i	$-0.769983\pi$
$607$	−36.9598	−1.50015	−0.750075	+	0.661353i	$0.769983\pi$
$608$	122.403	4.96409
$609$	−6.28011	−0.254483
$610$	20.0815	0.813078
$611$	−18.4242	−0.745362
$612$	−110.917	−4.48357
$613$	−2.96088	−0.119589	−0.0597943	−	0.998211i	$-0.519044\pi$
$613$	−2.96088	−0.119589	−0.0597943	+	0.998211i	$0.519044\pi$
$614$	−37.5581	−1.51572
$615$	−31.8353	−1.28372
$616$	38.5769	1.55431
$617$	27.1115	1.09147	0.545734	−	0.837959i	$-0.316251\pi$
$617$	27.1115	1.09147	0.545734	+	0.837959i	$0.316251\pi$
$618$	57.5895	2.31659
$619$	−3.34026	−0.134257	−0.0671283	−	0.997744i	$-0.521384\pi$
$619$	−3.34026	−0.134257	−0.0671283	+	0.997744i	$0.521384\pi$
$620$	29.2597	1.17510
$621$	−20.3497	−0.816607
$622$	−77.7736	−3.11844
$623$	−18.9090	−0.757574
$624$	119.875	4.79882
$625$	−3.44465	−0.137786
$626$	83.1389	3.32290
$627$	13.1302	0.524369
$628$	−25.0043	−0.997782
$629$	−13.1240	−0.523289
$630$	64.5462	2.57158
$631$	17.5881	0.700169	0.350085	−	0.936718i	$-0.386153\pi$
$631$	17.5881	0.700169	0.350085	+	0.936718i	$0.386153\pi$
$632$	30.5423	1.21491
$633$	38.5249	1.53123
$634$	−19.0186	−0.755323
$635$	5.52723	0.219341
$636$	204.753	8.11899
$637$	28.7412	1.13877
$638$	−1.55330	−0.0614955
$639$	14.8221	0.586352
$640$	66.4399	2.62627
$641$	26.2727	1.03771	0.518856	−	0.854862i	$-0.326358\pi$
$641$	26.2727	1.03771	0.518856	+	0.854862i	$0.326358\pi$
$642$	27.1121	1.07003
$643$	22.1263	0.872574	0.436287	−	0.899807i	$-0.356293\pi$
$643$	22.1263	0.872574	0.436287	+	0.899807i	$0.356293\pi$
$644$	−210.874	−8.30961
$645$	−11.9776	−0.471616
$646$	−74.3956	−2.92706
$647$	−13.1508	−0.517010	−0.258505	−	0.966010i	$-0.583230\pi$
$647$	−13.1508	−0.517010	−0.258505	+	0.966010i	$0.583230\pi$
$648$	56.2731	2.21061
$649$	−0.430276	−0.0168898
$650$	22.2931	0.874406
$651$	−37.9224	−1.48630
$652$	91.7447	3.59300
$653$	44.5595	1.74375	0.871873	−	0.489732i	$-0.162905\pi$
$653$	44.5595	1.74375	0.871873	+	0.489732i	$0.162905\pi$
$654$	34.4685	1.34782
$655$	15.6870	0.612941
$656$	127.765	4.98840
$657$	−8.78364	−0.342683
$658$	70.9245	2.76493
$659$	−39.1880	−1.52655	−0.763275	−	0.646074i	$-0.776410\pi$
$659$	−39.1880	−1.52655	−0.763275	+	0.646074i	$0.776410\pi$
$660$	20.9013	0.813582
$661$	−16.7274	−0.650619	−0.325310	−	0.945608i	$-0.605469\pi$
$661$	−16.7274	−0.650619	−0.325310	+	0.945608i	$0.605469\pi$
$662$	−54.0863	−2.10212
$663$	−39.8720	−1.54850
$664$	−30.2684	−1.17464
$665$	31.8180	1.23385
$666$	−26.5681	−1.02949
$667$	5.42865	0.210198
$668$	−36.1797	−1.39983
$669$	−14.1895	−0.548598
$670$	−10.7435	−0.415059
$671$	−4.73113	−0.182643
$672$	−252.535	−9.74174
$673$	−43.0199	−1.65830	−0.829149	−	0.559028i	$-0.811174\pi$
$673$	−43.0199	−1.65830	−0.829149	+	0.559028i	$0.811174\pi$
$674$	74.0838	2.85360
$675$	−6.08652	−0.234270
$676$	−24.5954	−0.945975
$677$	−8.03402	−0.308772	−0.154386	−	0.988011i	$-0.549340\pi$
$677$	−8.03402	−0.308772	−0.154386	+	0.988011i	$0.549340\pi$
$678$	−57.1379	−2.19437
$679$	4.90214	0.188127
$680$	−75.7167	−2.90360
$681$	−0.0806891	−0.00309201
$682$	−9.37957	−0.359162
$683$	39.7823	1.52223	0.761115	−	0.648617i	$-0.224652\pi$
$683$	39.7823	1.52223	0.761115	+	0.648617i	$0.224652\pi$
$684$	−110.687	−4.23221
$685$	26.0164	0.994034
$686$	−31.7785	−1.21331
$687$	51.8632	1.97871
$688$	48.0698	1.83264
$689$	41.3179	1.57409
$690$	−99.3932	−3.78383
$691$	28.7280	1.09287	0.546433	−	0.837503i	$-0.315985\pi$
$691$	28.7280	1.09287	0.546433	+	0.837503i	$0.315985\pi$
$692$	111.166	4.22588
$693$	−15.2068	−0.577660
$694$	−39.0954	−1.48404
$695$	23.0523	0.874424
$696$	14.9136	0.565297
$697$	−42.4966	−1.60967
$698$	−46.4865	−1.75954
$699$	0.466673	0.0176512
$700$	−63.0715	−2.38388
$701$	−42.4098	−1.60179	−0.800897	−	0.598802i	$-0.795644\pi$
$701$	−42.4098	−1.60179	−0.800897	+	0.598802i	$0.795644\pi$
$702$	−17.6447	−0.665957
$703$	−13.0967	−0.493953
$704$	−32.2085	−1.21391
$705$	24.5688	0.925315
$706$	67.0950	2.52515
$707$	−21.1425	−0.795147
$708$	6.46150	0.242838
$709$	12.3558	0.464031	0.232015	−	0.972712i	$-0.425468\pi$
$709$	12.3558	0.464031	0.232015	+	0.972712i	$0.425468\pi$
$710$	15.8256	0.593923
$711$	−12.0396	−0.451521
$712$	44.9039	1.68284
$713$	32.7809	1.22765
$714$	153.489	5.74417
$715$	4.21775	0.157735
$716$	−83.4674	−3.11932
$717$	−62.3672	−2.32915
$718$	−7.16302	−0.267322
$719$	−0.457595	−0.0170654	−0.00853271	−	0.999964i	$-0.502716\pi$
$719$	−0.457595	−0.0170654	−0.00853271	+	0.999964i	$0.502716\pi$
$720$	−89.7351	−3.34423
$721$	−32.8787	−1.22447
$722$	−22.0493	−0.820591
$723$	−64.5692	−2.40135
$724$	−147.368	−5.47690
$725$	1.62368	0.0603021
$726$	72.3212	2.68409
$727$	22.7280	0.842936	0.421468	−	0.906843i	$-0.361515\pi$
$727$	22.7280	0.842936	0.421468	+	0.906843i	$0.361515\pi$
$728$	−116.902	−4.33266
$729$	−39.4026	−1.45935
$730$	−9.37833	−0.347108
$731$	−15.9887	−0.591364
$732$	71.0479	2.62601
$733$	14.3235	0.529052	0.264526	−	0.964379i	$-0.414785\pi$
$733$	14.3235	0.529052	0.264526	+	0.964379i	$0.414785\pi$
$734$	−20.6130	−0.760842
$735$	−38.3267	−1.41370
$736$	218.296	8.04650
$737$	2.53113	0.0932355
$738$	−86.0295	−3.16679
$739$	2.64412	0.0972655	0.0486327	−	0.998817i	$-0.484514\pi$
$739$	2.64412	0.0972655	0.0486327	+	0.998817i	$0.484514\pi$
$740$	−20.8481	−0.766391
$741$	−39.7891	−1.46169
$742$	−159.055	−5.83908
$743$	−20.0187	−0.734413	−0.367207	−	0.930139i	$-0.619686\pi$
$743$	−20.0187	−0.734413	−0.367207	+	0.930139i	$0.619686\pi$
$744$	90.0556	3.30160
$745$	−10.2355	−0.375000
$746$	−22.5402	−0.825254
$747$	11.9317	0.436557
$748$	27.9009	1.02016
$749$	−15.4787	−0.565578
$750$	−83.3292	−3.04275
$751$	22.2563	0.812144	0.406072	−	0.913841i	$-0.366898\pi$
$751$	22.2563	0.812144	0.406072	+	0.913841i	$0.366898\pi$
$752$	−98.6025	−3.59566
$753$	30.9165	1.12666
$754$	4.70704	0.171420
$755$	32.1821	1.17123
$756$	49.9204	1.81559
$757$	37.7253	1.37115	0.685574	−	0.728003i	$-0.259551\pi$
$757$	37.7253	1.37115	0.685574	+	0.728003i	$0.259551\pi$
$758$	68.1728	2.47615
$759$	23.4166	0.849970
$760$	−75.5593	−2.74082
$761$	−12.6486	−0.458510	−0.229255	−	0.973366i	$-0.573629\pi$
$761$	−12.6486	−0.458510	−0.229255	+	0.973366i	$0.573629\pi$
$762$	26.6077	0.963894
$763$	−19.6785	−0.712411
$764$	76.1144	2.75372
$765$	29.8472	1.07913
$766$	−96.4014	−3.48312
$767$	1.30389	0.0470807
$768$	145.400	5.24666
$769$	−22.9558	−0.827806	−0.413903	−	0.910321i	$-0.635835\pi$
$769$	−22.9558	−0.827806	−0.413903	+	0.910321i	$0.635835\pi$
$770$	−16.2364	−0.585119
$771$	−60.8644	−2.19198
$772$	−100.454	−3.61541
$773$	−15.0778	−0.542311	−0.271155	−	0.962536i	$-0.587406\pi$
$773$	−15.0778	−0.542311	−0.271155	+	0.962536i	$0.587406\pi$
$774$	−32.3673	−1.16342
$775$	9.80462	0.352192
$776$	−11.6413	−0.417897
$777$	27.0204	0.969353
$778$	80.8422	2.89833
$779$	−42.4082	−1.51943
$780$	−63.3384	−2.26788
$781$	−3.72844	−0.133414
$782$	−132.679	−4.74458
$783$	−1.28513	−0.0459267
$784$	153.818	5.49348
$785$	6.72851	0.240151
$786$	75.5160	2.69356
$787$	−8.99372	−0.320591	−0.160296	−	0.987069i	$-0.551245\pi$
$787$	−8.99372	−0.320591	−0.160296	+	0.987069i	$0.551245\pi$
$788$	108.284	3.85745
$789$	−44.4480	−1.58239
$790$	−12.8547	−0.457351
$791$	32.6209	1.15986
$792$	36.1121	1.28319
$793$	14.3370	0.509122
$794$	25.6880	0.911633
$795$	−55.0978	−1.95412
$796$	21.1670	0.750245
$797$	21.5565	0.763570	0.381785	−	0.924251i	$-0.375309\pi$
$797$	21.5565	0.763570	0.381785	+	0.924251i	$0.375309\pi$
$798$	153.170	5.42215
$799$	32.7966	1.16026
$800$	65.2913	2.30840
$801$	−17.7009	−0.625431
$802$	82.5711	2.91569
$803$	2.20950	0.0779715
$804$	−38.0103	−1.34052
$805$	56.7450	2.00000
$806$	28.4234	1.00117
$807$	−58.6331	−2.06398
$808$	50.2078	1.76631
$809$	−36.4396	−1.28115	−0.640574	−	0.767896i	$-0.721304\pi$
$809$	−36.4396	−1.28115	−0.640574	+	0.767896i	$0.721304\pi$
$810$	−23.6844	−0.832186
$811$	−13.3137	−0.467507	−0.233754	−	0.972296i	$-0.575101\pi$
$811$	−13.3137	−0.467507	−0.233754	+	0.972296i	$0.575101\pi$
$812$	−13.3171	−0.467340
$813$	37.0868	1.30069
$814$	6.68312	0.234243
$815$	−24.6879	−0.864781
$816$	−213.387	−7.47004
$817$	−15.9555	−0.558211
$818$	−31.2716	−1.09339
$819$	46.0821	1.61024
$820$	−67.5076	−2.35747
$821$	−28.9711	−1.01110	−0.505549	−	0.862798i	$-0.668710\pi$
$821$	−28.9711	−1.01110	−0.505549	+	0.862798i	$0.668710\pi$
$822$	125.241	4.36828
$823$	−6.15609	−0.214588	−0.107294	−	0.994227i	$-0.534219\pi$
$823$	−6.15609	−0.214588	−0.107294	+	0.994227i	$0.534219\pi$
$824$	78.0780	2.71998
$825$	7.00381	0.243841
$826$	−5.01937	−0.174646
$827$	44.6319	1.55200	0.776002	−	0.630730i	$-0.217244\pi$
$827$	44.6319	1.55200	0.776002	+	0.630730i	$0.217244\pi$
$828$	−197.401	−6.86016
$829$	−38.8568	−1.34955	−0.674776	−	0.738022i	$-0.735760\pi$
$829$	−38.8568	−1.34955	−0.674776	+	0.738022i	$0.735760\pi$
$830$	12.7395	0.442194
$831$	−67.9711	−2.35789
$832$	97.6033	3.38379
$833$	−51.1619	−1.77265
$834$	110.972	3.84265
$835$	9.73574	0.336919
$836$	27.8429	0.962967
$837$	−7.76025	−0.268233
$838$	−41.7336	−1.44166
$839$	25.5515	0.882137	0.441068	−	0.897474i	$-0.354600\pi$
$839$	25.5515	0.882137	0.441068	+	0.897474i	$0.354600\pi$
$840$	155.890	5.37870
$841$	−28.6572	−0.988178
$842$	−52.7334	−1.81731
$843$	26.2329	0.903507
$844$	81.6930	2.81199
$845$	6.61846	0.227682
$846$	66.3930	2.28264
$847$	−41.2892	−1.41871
$848$	221.125	7.59347
$849$	−44.3374	−1.52166
$850$	−39.6836	−1.36114
$851$	−23.3570	−0.800668
$852$	55.9904	1.91820
$853$	27.3228	0.935515	0.467757	−	0.883857i	$-0.345062\pi$
$853$	27.3228	0.935515	0.467757	+	0.883857i	$0.345062\pi$
$854$	−55.1909	−1.88859
$855$	29.7851	1.01863
$856$	36.7576	1.25635
$857$	22.9166	0.782817	0.391409	−	0.920217i	$-0.371988\pi$
$857$	22.9166	0.782817	0.391409	+	0.920217i	$0.371988\pi$
$858$	20.3039	0.693165
$859$	13.1521	0.448743	0.224371	−	0.974504i	$-0.427967\pi$
$859$	13.1521	0.448743	0.224371	+	0.974504i	$0.427967\pi$
$860$	−25.3988	−0.866090
$861$	87.4942	2.98179
$862$	81.1788	2.76496
$863$	−23.2276	−0.790676	−0.395338	−	0.918536i	$-0.629373\pi$
$863$	−23.2276	−0.790676	−0.395338	+	0.918536i	$0.629373\pi$
$864$	−51.6774	−1.75810
$865$	−29.9140	−1.01711
$866$	57.2592	1.94575
$867$	26.5172	0.900571
$868$	−80.4156	−2.72948
$869$	3.02853	0.102736
$870$	−6.27688	−0.212806
$871$	−7.67023	−0.259896
$872$	46.7312	1.58252
$873$	4.58894	0.155312
$874$	−132.403	−4.47859
$875$	47.5738	1.60829
$876$	−33.1802	−1.12106
$877$	−20.7274	−0.699914	−0.349957	−	0.936766i	$-0.613804\pi$
$877$	−20.7274	−0.699914	−0.349957	+	0.936766i	$0.613804\pi$
$878$	−85.7322	−2.89332
$879$	−60.0658	−2.02597
$880$	22.5726	0.760921
$881$	−3.86646	−0.130264	−0.0651321	−	0.997877i	$-0.520747\pi$
$881$	−3.86646	−0.130264	−0.0651321	+	0.997877i	$0.520747\pi$
$882$	−103.571	−3.48743
$883$	38.4112	1.29264	0.646319	−	0.763067i	$-0.276307\pi$
$883$	38.4112	1.29264	0.646319	+	0.763067i	$0.276307\pi$
$884$	−84.5496	−2.84371
$885$	−1.73875	−0.0584474
$886$	−37.4831	−1.25927
$887$	−15.1409	−0.508382	−0.254191	−	0.967154i	$-0.581809\pi$
$887$	−15.1409	−0.508382	−0.254191	+	0.967154i	$0.581809\pi$
$888$	−64.1663	−2.15328
$889$	−15.1907	−0.509480
$890$	−18.8993	−0.633507
$891$	5.57996	0.186936
$892$	−30.0892	−1.00746
$893$	32.7284	1.09521
$894$	−49.2730	−1.64793
$895$	22.4606	0.750774
$896$	−182.599	−6.10022
$897$	−70.9607	−2.36931
$898$	−19.6946	−0.657218
$899$	2.07018	0.0690444
$900$	−59.0418	−1.96806
$901$	−73.5494	−2.45029
$902$	21.6404	0.720548
$903$	32.9184	1.09546
$904$	−77.4658	−2.57647
$905$	39.6559	1.31821
$906$	154.922	5.14695
$907$	−21.3784	−0.709857	−0.354928	−	0.934893i	$-0.615495\pi$
$907$	−21.3784	−0.709857	−0.354928	+	0.934893i	$0.615495\pi$
$908$	−0.171103	−0.00567826
$909$	−19.7917	−0.656449
$910$	49.2020	1.63103
$911$	−12.2953	−0.407362	−0.203681	−	0.979037i	$-0.565291\pi$
$911$	−12.2953	−0.407362	−0.203681	+	0.979037i	$0.565291\pi$
$912$	−212.943	−7.05126
$913$	−3.00137	−0.0993308
$914$	−66.4060	−2.19651
$915$	−19.1186	−0.632040
$916$	109.977	3.63376
$917$	−43.1131	−1.42372
$918$	31.4091	1.03666
$919$	−28.1225	−0.927675	−0.463838	−	0.885920i	$-0.653528\pi$
$919$	−28.1225	−0.927675	−0.463838	+	0.885920i	$0.653528\pi$
$920$	−134.754	−4.44271
$921$	35.7570	1.17823
$922$	−68.0249	−2.24028
$923$	11.2985	0.371895
$924$	−57.4439	−1.88976
$925$	−6.98597	−0.229697
$926$	62.1273	2.04163
$927$	−30.7780	−1.01088
$928$	13.7858	0.452542
$929$	14.3011	0.469205	0.234602	−	0.972091i	$-0.424621\pi$
$929$	14.3011	0.469205	0.234602	+	0.972091i	$0.424621\pi$
$930$	−37.9030	−1.24289
$931$	−51.0555	−1.67328
$932$	0.989592	0.0324152
$933$	74.0441	2.42409
$934$	76.7641	2.51180
$935$	−7.50796	−0.245537
$936$	−109.433	−3.57692
$937$	−35.6739	−1.16541	−0.582707	−	0.812682i	$-0.698006\pi$
$937$	−35.6739	−1.16541	−0.582707	+	0.812682i	$0.698006\pi$
$938$	29.5269	0.964086
$939$	−79.1520	−2.58303
$940$	52.0988	1.69928
$941$	54.6310	1.78092	0.890460	−	0.455062i	$-0.150383\pi$
$941$	54.6310	1.78092	0.890460	+	0.455062i	$0.150383\pi$
$942$	32.3906	1.05534
$943$	−75.6317	−2.46291
$944$	6.97816	0.227120
$945$	−13.4333	−0.436985
$946$	8.14190	0.264716
$947$	10.6364	0.345636	0.172818	−	0.984954i	$-0.444713\pi$
$947$	10.6364	0.345636	0.172818	+	0.984954i	$0.444713\pi$
$948$	−45.4797	−1.47711
$949$	−6.69556	−0.217347
$950$	−39.6011	−1.28483
$951$	18.1065	0.587145
$952$	208.095	6.74440
$953$	−7.13518	−0.231131	−0.115566	−	0.993300i	$-0.536868\pi$
$953$	−7.13518	−0.231131	−0.115566	+	0.993300i	$0.536868\pi$
$954$	−148.892	−4.82057
$955$	−20.4819	−0.662780
$956$	−132.251	−4.27732
$957$	1.47881	0.0478031
$958$	49.2044	1.58972
$959$	−71.5018	−2.30891
$960$	−130.155	−4.20074
$961$	−18.4992	−0.596749
$962$	−20.2522	−0.652958
$963$	−14.4897	−0.466924
$964$	−136.921	−4.40992
$965$	27.0315	0.870175
$966$	273.166	8.78897
$967$	46.3976	1.49205	0.746024	−	0.665919i	$-0.231960\pi$
$967$	46.3976	1.49205	0.746024	+	0.665919i	$0.231960\pi$
$968$	98.0507	3.15147
$969$	70.8280	2.27532
$970$	4.89962	0.157317
$971$	−45.9771	−1.47547	−0.737737	−	0.675088i	$-0.764106\pi$
$971$	−45.9771	−1.47547	−0.737737	+	0.675088i	$0.764106\pi$
$972$	−120.310	−3.85895
$973$	−63.3556	−2.03109
$974$	−64.4525	−2.06519
$975$	−21.2240	−0.679713
$976$	76.7289	2.45603
$977$	17.3966	0.556568	0.278284	−	0.960499i	$-0.410234\pi$
$977$	17.3966	0.556568	0.278284	+	0.960499i	$0.410234\pi$
$978$	−118.846	−3.80027
$979$	4.45260	0.142306
$980$	−81.2729	−2.59617
$981$	−18.4212	−0.588145
$982$	−28.2507	−0.901517
$983$	36.9474	1.17844	0.589220	−	0.807972i	$-0.299435\pi$
$983$	36.9474	1.17844	0.589220	+	0.807972i	$0.299435\pi$
$984$	−207.775	−6.62363
$985$	−29.1385	−0.928431
$986$	−8.37893	−0.266840
$987$	−67.5234	−2.14929
$988$	−84.3738	−2.68429
$989$	−28.4553	−0.904826
$990$	−15.1990	−0.483057
$991$	19.4463	0.617733	0.308866	−	0.951105i	$-0.400050\pi$
$991$	19.4463	0.617733	0.308866	+	0.951105i	$0.400050\pi$
$992$	83.2458	2.64306
$993$	51.4926	1.63407
$994$	−43.4940	−1.37955
$995$	−5.69592	−0.180573
$996$	45.0719	1.42816
$997$	49.0119	1.55222	0.776111	−	0.630597i	$-0.217190\pi$
$997$	49.0119	1.55222	0.776111	+	0.630597i	$0.217190\pi$
$998$	−47.1965	−1.49398
$999$	5.52932	0.174940

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.a.1.6	✓	309

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.a.1.6	✓	309	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:	\( N \)	\(=\)	\( 8011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74693 q^{2} +2.61520 q^{3} +5.54560 q^{4} -1.49229 q^{5} -7.18376 q^{6} +4.10131 q^{7} -9.73951 q^{8} +3.83927 q^{9} +O(q^{10})\)	\(q-2.74693 q^{2} +2.61520 q^{3} +5.54560 q^{4} -1.49229 q^{5} -7.18376 q^{6} +4.10131 q^{7} -9.73951 q^{8} +3.83927 q^{9} +4.09920 q^{10} -0.965756 q^{11} +14.5029 q^{12} +2.92658 q^{13} -11.2660 q^{14} -3.90263 q^{15} +15.6625 q^{16} -5.20957 q^{17} -10.5462 q^{18} -5.19874 q^{19} -8.27563 q^{20} +10.7257 q^{21} +2.65286 q^{22} -9.27155 q^{23} -25.4708 q^{24} -2.77308 q^{25} -8.03911 q^{26} +2.19486 q^{27} +22.7442 q^{28} -0.585517 q^{29} +10.7202 q^{30} -3.53565 q^{31} -23.5447 q^{32} -2.52564 q^{33} +14.3103 q^{34} -6.12033 q^{35} +21.2911 q^{36} +2.51921 q^{37} +14.2806 q^{38} +7.65360 q^{39} +14.5341 q^{40} +8.15740 q^{41} -29.4628 q^{42} +3.06910 q^{43} -5.35570 q^{44} -5.72930 q^{45} +25.4683 q^{46} -6.29545 q^{47} +40.9606 q^{48} +9.82075 q^{49} +7.61744 q^{50} -13.6241 q^{51} +16.2297 q^{52} +14.1181 q^{53} -6.02912 q^{54} +1.44119 q^{55} -39.9447 q^{56} -13.5957 q^{57} +1.60837 q^{58} +0.445533 q^{59} -21.6424 q^{60} +4.89889 q^{61} +9.71216 q^{62} +15.7460 q^{63} +33.3506 q^{64} -4.36730 q^{65} +6.93776 q^{66} -2.62088 q^{67} -28.8902 q^{68} -24.2470 q^{69} +16.8121 q^{70} +3.86065 q^{71} -37.3926 q^{72} -2.28784 q^{73} -6.92009 q^{74} -7.25215 q^{75} -28.8302 q^{76} -3.96087 q^{77} -21.0239 q^{78} -3.13591 q^{79} -23.3730 q^{80} -5.77781 q^{81} -22.4078 q^{82} +3.10779 q^{83} +59.4807 q^{84} +7.77418 q^{85} -8.43059 q^{86} -1.53124 q^{87} +9.40599 q^{88} -4.61049 q^{89} +15.7380 q^{90} +12.0028 q^{91} -51.4163 q^{92} -9.24642 q^{93} +17.2931 q^{94} +7.75802 q^{95} -61.5742 q^{96} +1.19526 q^{97} -26.9769 q^{98} -3.70780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9}+O(q^{10}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9	\( 309 q - 33 q^{2} - 15 q^{3} + 273 q^{4} - 74 q^{5} - 32 q^{6} - 19 q^{7} - 93 q^{8} + 214 q^{9} - 23 q^{10} - 72 q^{11} - 42 q^{12} - 57 q^{13} - 77 q^{14} - 44 q^{15} + 205 q^{16} - 86 q^{17} - 82 q^{18} - 58 q^{19} - 134 q^{20} - 123 q^{21} - 31 q^{22} - 94 q^{23} - 84 q^{24} + 225 q^{25} - 92 q^{26} - 48 q^{27} - 36 q^{28} - 345 q^{29} - 85 q^{30} - 36 q^{31} - 199 q^{32} - 56 q^{33} - 28 q^{34} - 168 q^{35} + 65 q^{36} - 79 q^{37} - 66 q^{38} - 145 q^{39} - 54 q^{40} - 176 q^{41} - 48 q^{42} - 58 q^{43} - 194 q^{44} - 192 q^{45} - 44 q^{46} - 82 q^{47} - 81 q^{48} + 186 q^{49} - 206 q^{50} - 145 q^{51} - 86 q^{52} - 223 q^{53} - 117 q^{54} - 58 q^{55} - 216 q^{56} - 124 q^{57} - 151 q^{59} - 91 q^{60} - 184 q^{61} - 124 q^{62} - 78 q^{63} + 101 q^{64} - 194 q^{65} - 112 q^{66} - 53 q^{67} - 182 q^{68} - 243 q^{69} - 193 q^{71} - 208 q^{72} - 69 q^{73} - 236 q^{74} - 62 q^{75} - 142 q^{76} - 324 q^{77} - 20 q^{78} - 91 q^{79} - 223 q^{80} - 27 q^{81} + 2 q^{82} - 117 q^{83} - 157 q^{84} - 171 q^{85} - 203 q^{86} - 69 q^{87} - 36 q^{88} - 172 q^{89} - 10 q^{90} - 84 q^{91} - 226 q^{92} - 220 q^{93} - 96 q^{94} - 166 q^{95} - 118 q^{96} - 12 q^{97} - 116 q^{98} - 154 q^{99}+O(q^{100}) \) 309 * q - 33 * q^2 - 15 * q^3 + 273 * q^4 - 74 * q^5 - 32 * q^6 - 19 * q^7 - 93 * q^8 + 214 * q^9 - 23 * q^10 - 72 * q^11 - 42 * q^12 - 57 * q^13 - 77 * q^14 - 44 * q^15 + 205 * q^16 - 86 * q^17 - 82 * q^18 - 58 * q^19 - 134 * q^20 - 123 * q^21 - 31 * q^22 - 94 * q^23 - 84 * q^24 + 225 * q^25 - 92 * q^26 - 48 * q^27 - 36 * q^28 - 345 * q^29 - 85 * q^30 - 36 * q^31 - 199 * q^32 - 56 * q^33 - 28 * q^34 - 168 * q^35 + 65 * q^36 - 79 * q^37 - 66 * q^38 - 145 * q^39 - 54 * q^40 - 176 * q^41 - 48 * q^42 - 58 * q^43 - 194 * q^44 - 192 * q^45 - 44 * q^46 - 82 * q^47 - 81 * q^48 + 186 * q^49 - 206 * q^50 - 145 * q^51 - 86 * q^52 - 223 * q^53 - 117 * q^54 - 58 * q^55 - 216 * q^56 - 124 * q^57 - 151 * q^59 - 91 * q^60 - 184 * q^61 - 124 * q^62 - 78 * q^63 + 101 * q^64 - 194 * q^65 - 112 * q^66 - 53 * q^67 - 182 * q^68 - 243 * q^69 - 193 * q^71 - 208 * q^72 - 69 * q^73 - 236 * q^74 - 62 * q^75 - 142 * q^76 - 324 * q^77 - 20 * q^78 - 91 * q^79 - 223 * q^80 - 27 * q^81 + 2 * q^82 - 117 * q^83 - 157 * q^84 - 171 * q^85 - 203 * q^86 - 69 * q^87 - 36 * q^88 - 172 * q^89 - 10 * q^90 - 84 * q^91 - 226 * q^92 - 220 * q^93 - 96 * q^94 - 166 * q^95 - 118 * q^96 - 12 * q^97 - 116 * q^98 - 154 * q^99

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