LMFDB - Embedded newform 6047.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, 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("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.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:	$48.2855381023$
Analytic rank:	$1$
Dimension:	$217$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77438 q^{2} -3.26218 q^{3} +5.69718 q^{4} +2.18536 q^{5} +9.05052 q^{6} +2.86186 q^{7} -10.2574 q^{8} +7.64181 q^{9} +O(q^{10})$	\(q-2.77438 q^{2} -3.26218 q^{3} +5.69718 q^{4} +2.18536 q^{5} +9.05052 q^{6} +2.86186 q^{7} -10.2574 q^{8} +7.64181 q^{9} -6.06301 q^{10} +1.00872 q^{11} -18.5852 q^{12} -0.310734 q^{13} -7.93988 q^{14} -7.12903 q^{15} +17.0635 q^{16} -2.88986 q^{17} -21.2013 q^{18} -0.819136 q^{19} +12.4504 q^{20} -9.33590 q^{21} -2.79857 q^{22} +5.98245 q^{23} +33.4614 q^{24} -0.224208 q^{25} +0.862095 q^{26} -15.1424 q^{27} +16.3045 q^{28} +4.28435 q^{29} +19.7786 q^{30} -5.07960 q^{31} -26.8259 q^{32} -3.29063 q^{33} +8.01758 q^{34} +6.25419 q^{35} +43.5368 q^{36} -6.54106 q^{37} +2.27259 q^{38} +1.01367 q^{39} -22.4161 q^{40} +5.84478 q^{41} +25.9013 q^{42} +8.07457 q^{43} +5.74686 q^{44} +16.7001 q^{45} -16.5976 q^{46} +0.356923 q^{47} -55.6643 q^{48} +1.19024 q^{49} +0.622037 q^{50} +9.42725 q^{51} -1.77031 q^{52} +5.30402 q^{53} +42.0108 q^{54} +2.20442 q^{55} -29.3552 q^{56} +2.67217 q^{57} -11.8864 q^{58} +7.92929 q^{59} -40.6154 q^{60} -11.3369 q^{61} +14.0927 q^{62} +21.8698 q^{63} +40.2982 q^{64} -0.679066 q^{65} +9.12944 q^{66} -8.70340 q^{67} -16.4641 q^{68} -19.5158 q^{69} -17.3515 q^{70} -2.88126 q^{71} -78.3850 q^{72} -6.95310 q^{73} +18.1474 q^{74} +0.731405 q^{75} -4.66677 q^{76} +2.88682 q^{77} -2.81231 q^{78} -16.6345 q^{79} +37.2899 q^{80} +26.4718 q^{81} -16.2156 q^{82} -17.8718 q^{83} -53.1883 q^{84} -6.31539 q^{85} -22.4019 q^{86} -13.9763 q^{87} -10.3468 q^{88} -0.0355791 q^{89} -46.3324 q^{90} -0.889278 q^{91} +34.0831 q^{92} +16.5706 q^{93} -0.990239 q^{94} -1.79011 q^{95} +87.5109 q^{96} -11.4073 q^{97} -3.30218 q^{98} +7.70845 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) $ 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * 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 $

$2$	−2.77438	−1.96178	−0.980891	−	0.194556i	$-0.937673\pi$
$2$	−2.77438	−1.96178	−0.980891	+	0.194556i	$0.937673\pi$
$3$	−3.26218	−1.88342	−0.941710	−	0.336426i	$-0.890782\pi$
$3$	−3.26218	−1.88342	−0.941710	+	0.336426i	$0.890782\pi$
$4$	5.69718	2.84859
$5$	2.18536	0.977322	0.488661	−	0.872474i	$-0.337485\pi$
$5$	2.18536	0.977322	0.488661	+	0.872474i	$0.337485\pi$
$6$	9.05052	3.69486
$7$	2.86186	1.08168	0.540841	−	0.841125i	$-0.318106\pi$
$7$	2.86186	1.08168	0.540841	+	0.841125i	$0.318106\pi$
$8$	−10.2574	−3.62653
$9$	7.64181	2.54727
$10$	−6.06301	−1.91729
$11$	1.00872	0.304141	0.152070	−	0.988370i	$-0.451406\pi$
$11$	1.00872	0.304141	0.152070	+	0.988370i	$0.451406\pi$
$12$	−18.5852	−5.36509
$13$	−0.310734	−0.0861822	−0.0430911	−	0.999071i	$-0.513721\pi$
$13$	−0.310734	−0.0861822	−0.0430911	+	0.999071i	$0.513721\pi$
$14$	−7.93988	−2.12202
$15$	−7.12903	−1.84071
$16$	17.0635	4.26588
$17$	−2.88986	−0.700895	−0.350447	−	0.936582i	$-0.613970\pi$
$17$	−2.88986	−0.700895	−0.350447	+	0.936582i	$0.613970\pi$
$18$	−21.2013	−4.99719
$19$	−0.819136	−0.187923	−0.0939614	−	0.995576i	$-0.529953\pi$
$19$	−0.819136	−0.187923	−0.0939614	+	0.995576i	$0.529953\pi$
$20$	12.4504	2.78399
$21$	−9.33590	−2.03726
$22$	−2.79857	−0.596658
$23$	5.98245	1.24743	0.623714	−	0.781653i	$-0.285623\pi$
$23$	5.98245	1.24743	0.623714	+	0.781653i	$0.285623\pi$
$24$	33.4614	6.83029
$25$	−0.224208	−0.0448415
$26$	0.862095	0.169071
$27$	−15.1424	−2.91416
$28$	16.3045	3.08127
$29$	4.28435	0.795584	0.397792	−	0.917476i	$-0.369777\pi$
$29$	4.28435	0.795584	0.397792	+	0.917476i	$0.369777\pi$
$30$	19.7786	3.61107
$31$	−5.07960	−0.912323	−0.456161	−	0.889897i	$-0.650776\pi$
$31$	−5.07960	−0.912323	−0.456161	+	0.889897i	$0.650776\pi$
$32$	−26.8259	−4.74220
$33$	−3.29063	−0.572824
$34$	8.01758	1.37500
$35$	6.25419	1.05715
$36$	43.5368	7.25613
$37$	−6.54106	−1.07534	−0.537672	−	0.843154i	$-0.680696\pi$
$37$	−6.54106	−1.07534	−0.537672	+	0.843154i	$0.680696\pi$
$38$	2.27259	0.368664
$39$	1.01367	0.162317
$40$	−22.4161	−3.54429
$41$	5.84478	0.912801	0.456400	−	0.889775i	$-0.349138\pi$
$41$	5.84478	0.912801	0.456400	+	0.889775i	$0.349138\pi$
$42$	25.9013	3.99666
$43$	8.07457	1.23136	0.615680	−	0.787996i	$-0.288881\pi$
$43$	8.07457	1.23136	0.615680	+	0.787996i	$0.288881\pi$
$44$	5.74686	0.866372
$45$	16.7001	2.48950
$46$	−16.5976	−2.44718
$47$	0.356923	0.0520625	0.0260313	−	0.999661i	$-0.491713\pi$
$47$	0.356923	0.0520625	0.0260313	+	0.999661i	$0.491713\pi$
$48$	−55.6643	−8.03444
$49$	1.19024	0.170034
$50$	0.622037	0.0879693
$51$	9.42725	1.32008
$52$	−1.77031	−0.245498
$53$	5.30402	0.728563	0.364281	−	0.931289i	$-0.381315\pi$
$53$	5.30402	0.728563	0.364281	+	0.931289i	$0.381315\pi$
$54$	42.0108	5.71695
$55$	2.20442	0.297243
$56$	−29.3552	−3.92275
$57$	2.67217	0.353937
$58$	−11.8864	−1.56076
$59$	7.92929	1.03231	0.516153	−	0.856496i	$-0.327364\pi$
$59$	7.92929	1.03231	0.516153	+	0.856496i	$0.327364\pi$
$60$	−40.6154	−5.24342
$61$	−11.3369	−1.45154	−0.725770	−	0.687938i	$-0.758516\pi$
$61$	−11.3369	−1.45154	−0.725770	+	0.687938i	$0.758516\pi$
$62$	14.0927	1.78978
$63$	21.8698	2.75533
$64$	40.2982	5.03728
$65$	−0.679066	−0.0842278
$66$	9.12944	1.12376
$67$	−8.70340	−1.06329	−0.531644	−	0.846968i	$-0.678426\pi$
$67$	−8.70340	−1.06329	−0.531644	+	0.846968i	$0.678426\pi$
$68$	−16.4641	−1.99656
$69$	−19.5158	−2.34943
$70$	−17.3515	−2.07390
$71$	−2.88126	−0.341943	−0.170971	−	0.985276i	$-0.554691\pi$
$71$	−2.88126	−0.341943	−0.170971	+	0.985276i	$0.554691\pi$
$72$	−78.3850	−9.23776
$73$	−6.95310	−0.813799	−0.406899	−	0.913473i	$-0.633390\pi$
$73$	−6.95310	−0.813799	−0.406899	+	0.913473i	$0.633390\pi$
$74$	18.1474	2.10959
$75$	0.731405	0.0844554
$76$	−4.66677	−0.535315
$77$	2.88682	0.328983
$78$	−2.81231	−0.318431
$79$	−16.6345	−1.87153	−0.935765	−	0.352624i	$-0.885290\pi$
$79$	−16.6345	−1.87153	−0.935765	+	0.352624i	$0.885290\pi$
$80$	37.2899	4.16914
$81$	26.4718	2.94131
$82$	−16.2156	−1.79072
$83$	−17.8718	−1.96168	−0.980840	−	0.194814i	$-0.937590\pi$
$83$	−17.8718	−1.96168	−0.980840	+	0.194814i	$0.937590\pi$
$84$	−53.1883	−5.80332
$85$	−6.31539	−0.685000
$86$	−22.4019	−2.41566
$87$	−13.9763	−1.49842
$88$	−10.3468	−1.10298
$89$	−0.0355791	−0.00377138	−0.00188569	−	0.999998i	$-0.500600\pi$
$89$	−0.0355791	−0.00377138	−0.00188569	+	0.999998i	$0.500600\pi$
$90$	−46.3324	−4.88386
$91$	−0.889278	−0.0932217
$92$	34.0831	3.55341
$93$	16.5706	1.71829
$94$	−0.990239	−0.102135
$95$	−1.79011	−0.183661
$96$	87.5109	8.93155
$97$	−11.4073	−1.15824	−0.579119	−	0.815243i	$-0.696604\pi$
$97$	−11.4073	−1.15824	−0.579119	+	0.815243i	$0.696604\pi$
$98$	−3.30218	−0.333570
$99$	7.70845	0.774728
$100$	−1.27735	−0.127735
$101$	12.6784	1.26155	0.630774	−	0.775966i	$-0.282737\pi$
$101$	12.6784	1.26155	0.630774	+	0.775966i	$0.282737\pi$
$102$	−26.1548	−2.58971
$103$	−1.59186	−0.156850	−0.0784252	−	0.996920i	$-0.524989\pi$
$103$	−1.59186	−0.156850	−0.0784252	+	0.996920i	$0.524989\pi$
$104$	3.18732	0.312543
$105$	−20.4023	−1.99106
$106$	−14.7154	−1.42928
$107$	3.14382	0.303925	0.151962	−	0.988386i	$-0.451441\pi$
$107$	3.14382	0.303925	0.151962	+	0.988386i	$0.451441\pi$
$108$	−86.2691	−8.30125
$109$	−14.3122	−1.37086	−0.685430	−	0.728139i	$-0.740386\pi$
$109$	−14.3122	−1.37086	−0.685430	+	0.728139i	$0.740386\pi$
$110$	−6.11589	−0.583127
$111$	21.3381	2.02532
$112$	48.8334	4.61432
$113$	−8.72018	−0.820326	−0.410163	−	0.912012i	$-0.634528\pi$
$113$	−8.72018	−0.820326	−0.410163	+	0.912012i	$0.634528\pi$
$114$	−7.41361	−0.694348
$115$	13.0738	1.21914
$116$	24.4087	2.26629
$117$	−2.37457	−0.219529
$118$	−21.9989	−2.02516
$119$	−8.27038	−0.758145
$120$	73.1252	6.67539
$121$	−9.98248	−0.907499
$122$	31.4528	2.84761
$123$	−19.0667	−1.71919
$124$	−28.9394	−2.59884
$125$	−11.4168	−1.02115
$126$	−60.6751	−5.40537
$127$	−10.4477	−0.927087	−0.463544	−	0.886074i	$-0.653422\pi$
$127$	−10.4477	−0.927087	−0.463544	+	0.886074i	$0.653422\pi$
$128$	−58.1507	−5.13985
$129$	−26.3407	−2.31917
$130$	1.88399	0.165237
$131$	15.6713	1.36920	0.684602	−	0.728917i	$-0.259976\pi$
$131$	15.6713	1.36920	0.684602	+	0.728917i	$0.259976\pi$
$132$	−18.7473	−1.63174
$133$	−2.34425	−0.203272
$134$	24.1465	2.08594
$135$	−33.0916	−2.84807
$136$	29.6424	2.54182
$137$	−11.0694	−0.945721	−0.472860	−	0.881137i	$-0.656779\pi$
$137$	−11.0694	−0.945721	−0.472860	+	0.881137i	$0.656779\pi$
$138$	54.1443	4.60907
$139$	16.4646	1.39651	0.698253	−	0.715851i	$-0.253961\pi$
$139$	16.4646	1.39651	0.698253	+	0.715851i	$0.253961\pi$
$140$	35.6313	3.01139
$141$	−1.16435	−0.0980556
$142$	7.99371	0.670818
$143$	−0.313444	−0.0262115
$144$	130.396	10.8663
$145$	9.36284	0.777541
$146$	19.2905	1.59650
$147$	−3.88278	−0.320246
$148$	−37.2656	−3.06322
$149$	−8.52165	−0.698121	−0.349060	−	0.937100i	$-0.613499\pi$
$149$	−8.52165	−0.698121	−0.349060	+	0.937100i	$0.613499\pi$
$150$	−2.02920	−0.165683
$151$	0.452528	0.0368262	0.0184131	−	0.999830i	$-0.494139\pi$
$151$	0.452528	0.0368262	0.0184131	+	0.999830i	$0.494139\pi$
$152$	8.40220	0.681508
$153$	−22.0838	−1.78537
$154$	−8.00912	−0.645393
$155$	−11.1007	−0.891633
$156$	5.77507	0.462376
$157$	−22.5475	−1.79949	−0.899743	−	0.436421i	$-0.856246\pi$
$157$	−22.5475	−1.79949	−0.899743	+	0.436421i	$0.856246\pi$
$158$	46.1505	3.67154
$159$	−17.3027	−1.37219
$160$	−58.6242	−4.63465
$161$	17.1209	1.34932
$162$	−73.4429	−5.77022
$163$	−20.6365	−1.61638	−0.808189	−	0.588923i	$-0.799552\pi$
$163$	−20.6365	−1.61638	−0.808189	+	0.588923i	$0.799552\pi$
$164$	33.2988	2.60020
$165$	−7.19120	−0.559834
$166$	49.5830	3.84839
$167$	−1.02741	−0.0795034	−0.0397517	−	0.999210i	$-0.512657\pi$
$167$	−1.02741	−0.0795034	−0.0397517	+	0.999210i	$0.512657\pi$
$168$	95.7619	7.38819
$169$	−12.9034	−0.992573
$170$	17.5213	1.34382
$171$	−6.25968	−0.478690
$172$	46.0023	3.50764
$173$	−13.2993	−1.01113	−0.505563	−	0.862790i	$-0.668715\pi$
$173$	−13.2993	−1.01113	−0.505563	+	0.862790i	$0.668715\pi$
$174$	38.7756	2.93957
$175$	−0.641650	−0.0485042
$176$	17.2123	1.29743
$177$	−25.8668	−1.94427
$178$	0.0987100	0.00739863
$179$	−6.91430	−0.516799	−0.258400	−	0.966038i	$-0.583195\pi$
$179$	−6.91430	−0.516799	−0.258400	+	0.966038i	$0.583195\pi$
$180$	95.1435	7.09158
$181$	4.37093	0.324889	0.162444	−	0.986718i	$-0.448062\pi$
$181$	4.37093	0.324889	0.162444	+	0.986718i	$0.448062\pi$
$182$	2.46719	0.182881
$183$	36.9829	2.73386
$184$	−61.3643	−4.52384
$185$	−14.2946	−1.05096
$186$	−45.9730	−3.37091
$187$	−2.91506	−0.213171
$188$	2.03345	0.148305
$189$	−43.3355	−3.15219
$190$	4.96643	0.360303
$191$	5.48129	0.396612	0.198306	−	0.980140i	$-0.436456\pi$
$191$	5.48129	0.396612	0.198306	+	0.980140i	$0.436456\pi$
$192$	−131.460	−9.48731
$193$	23.0753	1.66100	0.830500	−	0.557019i	$-0.188055\pi$
$193$	23.0753	1.66100	0.830500	+	0.557019i	$0.188055\pi$
$194$	31.6483	2.27221
$195$	2.21523	0.158636
$196$	6.78102	0.484358
$197$	−22.1917	−1.58109	−0.790547	−	0.612402i	$-0.790203\pi$
$197$	−22.1917	−1.58109	−0.790547	+	0.612402i	$0.790203\pi$
$198$	−21.3862	−1.51985
$199$	23.9947	1.70094	0.850471	−	0.526022i	$-0.176317\pi$
$199$	23.9947	1.70094	0.850471	+	0.526022i	$0.176317\pi$
$200$	2.29978	0.162619
$201$	28.3920	2.00262
$202$	−35.1747	−2.47488
$203$	12.2612	0.860568
$204$	53.7088	3.76036
$205$	12.7729	0.892100
$206$	4.41642	0.307706
$207$	45.7167	3.17753
$208$	−5.30222	−0.367643
$209$	−0.826279	−0.0571549
$210$	56.6037	3.90603
$211$	16.2234	1.11687	0.558434	−	0.829549i	$-0.311402\pi$
$211$	16.2234	1.11687	0.558434	+	0.829549i	$0.311402\pi$
$212$	30.2180	2.07538
$213$	9.39919	0.644022
$214$	−8.72215	−0.596234
$215$	17.6458	1.20344
$216$	155.322	10.5683
$217$	−14.5371	−0.986843
$218$	39.7075	2.68933
$219$	22.6823	1.53272
$220$	12.5590	0.846725
$221$	0.897980	0.0604046
$222$	−59.2001	−3.97325
$223$	14.5458	0.974058	0.487029	−	0.873386i	$-0.338081\pi$
$223$	14.5458	0.974058	0.487029	+	0.873386i	$0.338081\pi$
$224$	−76.7720	−5.12954
$225$	−1.71335	−0.114223
$226$	24.1931	1.60930
$227$	3.16511	0.210075	0.105038	−	0.994468i	$-0.466504\pi$
$227$	3.16511	0.210075	0.105038	+	0.994468i	$0.466504\pi$
$228$	15.2238	1.00822
$229$	19.7124	1.30263	0.651316	−	0.758807i	$-0.274217\pi$
$229$	19.7124	1.30263	0.651316	+	0.758807i	$0.274217\pi$
$230$	−36.2717	−2.39168
$231$	−9.41731	−0.619613
$232$	−43.9462	−2.88521
$233$	−4.35047	−0.285009	−0.142504	−	0.989794i	$-0.545516\pi$
$233$	−4.35047	−0.285009	−0.142504	+	0.989794i	$0.545516\pi$
$234$	6.58797	0.430669
$235$	0.780004	0.0508819
$236$	45.1746	2.94062
$237$	54.2648	3.52488
$238$	22.9452	1.48731
$239$	−26.9472	−1.74307	−0.871535	−	0.490334i	$-0.836875\pi$
$239$	−26.9472	−1.74307	−0.871535	+	0.490334i	$0.836875\pi$
$240$	−121.646	−7.85224
$241$	1.58736	0.102251	0.0511253	−	0.998692i	$-0.483719\pi$
$241$	1.58736	0.102251	0.0511253	+	0.998692i	$0.483719\pi$
$242$	27.6952	1.78031
$243$	−40.9286	−2.62557
$244$	−64.5883	−4.13484
$245$	2.60110	0.166178
$246$	52.8983	3.37267
$247$	0.254534	0.0161956
$248$	52.1034	3.30857
$249$	58.3009	3.69467
$250$	31.6744	2.00327
$251$	−12.9515	−0.817492	−0.408746	−	0.912648i	$-0.634034\pi$
$251$	−12.9515	−0.817492	−0.408746	+	0.912648i	$0.634034\pi$
$252$	124.596	7.84882
$253$	6.03462	0.379393
$254$	28.9860	1.81874
$255$	20.6019	1.29014
$256$	80.7358	5.04599
$257$	−2.31137	−0.144179	−0.0720896	−	0.997398i	$-0.522967\pi$
$257$	−2.31137	−0.144179	−0.0720896	+	0.997398i	$0.522967\pi$
$258$	73.0791	4.54970
$259$	−18.7196	−1.16318
$260$	−3.86876	−0.239930
$261$	32.7402	2.02657
$262$	−43.4780	−2.68608
$263$	10.5650	0.651467	0.325734	−	0.945462i	$-0.394389\pi$
$263$	10.5650	0.651467	0.325734	+	0.945462i	$0.394389\pi$
$264$	33.7532	2.07737
$265$	11.5912	0.712040
$266$	6.50385	0.398776
$267$	0.116065	0.00710309
$268$	−49.5848	−3.02888
$269$	−1.58441	−0.0966032	−0.0483016	−	0.998833i	$-0.515381\pi$
$269$	−1.58441	−0.0966032	−0.0483016	+	0.998833i	$0.515381\pi$
$270$	91.8087	5.58730
$271$	−7.62050	−0.462912	−0.231456	−	0.972845i	$-0.574349\pi$
$271$	−7.62050	−0.462912	−0.231456	+	0.972845i	$0.574349\pi$
$272$	−49.3112	−2.98993
$273$	2.90098	0.175576
$274$	30.7107	1.85530
$275$	−0.226163	−0.0136381
$276$	−111.185	−6.69256
$277$	2.50785	0.150682	0.0753410	−	0.997158i	$-0.475995\pi$
$277$	2.50785	0.150682	0.0753410	+	0.997158i	$0.475995\pi$
$278$	−45.6789	−2.73964
$279$	−38.8173	−2.32393
$280$	−64.1516	−3.83379
$281$	−10.1495	−0.605471	−0.302736	−	0.953075i	$-0.597900\pi$
$281$	−10.1495	−0.605471	−0.302736	+	0.953075i	$0.597900\pi$
$282$	3.23034	0.192364
$283$	16.5050	0.981120	0.490560	−	0.871407i	$-0.336792\pi$
$283$	16.5050	0.981120	0.490560	+	0.871407i	$0.336792\pi$
$284$	−16.4151	−0.974055
$285$	5.83965	0.345911
$286$	0.869613	0.0514213
$287$	16.7269	0.987359
$288$	−204.999	−12.0797
$289$	−8.64869	−0.508747
$290$	−25.9761	−1.52537
$291$	37.2127	2.18145
$292$	−39.6131	−2.31818
$293$	7.84290	0.458187	0.229093	−	0.973404i	$-0.426424\pi$
$293$	7.84290	0.458187	0.229093	+	0.973404i	$0.426424\pi$
$294$	10.7723	0.628253
$295$	17.3283	1.00890
$296$	67.0942	3.89977
$297$	−15.2745	−0.886314
$298$	23.6423	1.36956
$299$	−1.85895	−0.107506
$300$	4.16695	0.240579
$301$	23.1083	1.33194
$302$	−1.25549	−0.0722450
$303$	−41.3592	−2.37603
$304$	−13.9773	−0.801656
$305$	−24.7752	−1.41862
$306$	61.2688	3.50250
$307$	0.329612	0.0188120	0.00940598	−	0.999956i	$-0.497006\pi$
$307$	0.329612	0.0188120	0.00940598	+	0.999956i	$0.497006\pi$
$308$	16.4467	0.937139
$309$	5.19292	0.295415
$310$	30.7977	1.74919
$311$	−17.4194	−0.987765	−0.493882	−	0.869529i	$-0.664423\pi$
$311$	−17.4194	−0.987765	−0.493882	+	0.869529i	$0.664423\pi$
$312$	−10.3976	−0.588649
$313$	−13.6638	−0.772323	−0.386162	−	0.922431i	$-0.626199\pi$
$313$	−13.6638	−0.772323	−0.386162	+	0.922431i	$0.626199\pi$
$314$	62.5553	3.53020
$315$	47.7933	2.69285
$316$	−94.7699	−5.33123
$317$	−7.30849	−0.410486	−0.205243	−	0.978711i	$-0.565798\pi$
$317$	−7.30849	−0.410486	−0.205243	+	0.978711i	$0.565798\pi$
$318$	48.0041	2.69194
$319$	4.32171	0.241969
$320$	88.0661	4.92304
$321$	−10.2557	−0.572418
$322$	−47.5000	−2.64707
$323$	2.36719	0.131714
$324$	150.815	8.37860
$325$	0.0696690	0.00386454
$326$	57.2536	3.17098
$327$	46.6889	2.58190
$328$	−59.9521	−3.31030
$329$	1.02146	0.0563151
$330$	19.9511	1.09827
$331$	−9.14908	−0.502879	−0.251439	−	0.967873i	$-0.580904\pi$
$331$	−9.14908	−0.502879	−0.251439	+	0.967873i	$0.580904\pi$
$332$	−101.819	−5.58803
$333$	−49.9856	−2.73919
$334$	2.85043	0.155968
$335$	−19.0200	−1.03918
$336$	−159.303	−8.69071
$337$	5.95989	0.324656	0.162328	−	0.986737i	$-0.448100\pi$
$337$	5.95989	0.324656	0.162328	+	0.986737i	$0.448100\pi$
$338$	35.7991	1.94721
$339$	28.4468	1.54502
$340$	−35.9799	−1.95128
$341$	−5.12389	−0.277474
$342$	17.3667	0.939086
$343$	−16.6267	−0.897758
$344$	−82.8240	−4.46557
$345$	−42.6491	−2.29615
$346$	36.8973	1.98361
$347$	12.0883	0.648932	0.324466	−	0.945897i	$-0.394815\pi$
$347$	12.0883	0.648932	0.324466	+	0.945897i	$0.394815\pi$
$348$	−79.6256	−4.26838
$349$	−11.5816	−0.619948	−0.309974	−	0.950745i	$-0.600320\pi$
$349$	−11.5816	−0.619948	−0.309974	+	0.950745i	$0.600320\pi$
$350$	1.78018	0.0951547
$351$	4.70527	0.251149
$352$	−27.0598	−1.44229
$353$	−20.2605	−1.07836	−0.539180	−	0.842190i	$-0.681266\pi$
$353$	−20.2605	−1.07836	−0.539180	+	0.842190i	$0.681266\pi$
$354$	71.7642	3.81423
$355$	−6.29659	−0.334188
$356$	−0.202701	−0.0107431
$357$	26.9795	1.42790
$358$	19.1829	1.01385
$359$	0.617077	0.0325681	0.0162841	−	0.999867i	$-0.494816\pi$
$359$	0.617077	0.0325681	0.0162841	+	0.999867i	$0.494816\pi$
$360$	−171.299	−9.02827
$361$	−18.3290	−0.964685
$362$	−12.1266	−0.637361
$363$	32.5646	1.70920
$364$	−5.06638	−0.265550
$365$	−15.1950	−0.795344
$366$	−102.605	−5.36324
$367$	14.5716	0.760629	0.380315	−	0.924857i	$-0.375816\pi$
$367$	14.5716	0.760629	0.380315	+	0.924857i	$0.375816\pi$
$368$	102.082	5.32138
$369$	44.6647	2.32515
$370$	39.6586	2.06175
$371$	15.1794	0.788073
$372$	94.4055	4.89470
$373$	−0.455180	−0.0235683	−0.0117842	−	0.999931i	$-0.503751\pi$
$373$	−0.455180	−0.0235683	−0.0117842	+	0.999931i	$0.503751\pi$
$374$	8.08749	0.418194
$375$	37.2435	1.92325
$376$	−3.66109	−0.188807
$377$	−1.33129	−0.0685651
$378$	120.229	6.18391
$379$	−37.8095	−1.94214	−0.971072	−	0.238789i	$-0.923250\pi$
$379$	−37.8095	−1.94214	−0.971072	+	0.238789i	$0.923250\pi$
$380$	−10.1986	−0.523175
$381$	34.0824	1.74609
$382$	−15.2072	−0.778067
$383$	31.5926	1.61431	0.807154	−	0.590341i	$-0.201007\pi$
$383$	31.5926	1.61431	0.807154	+	0.590341i	$0.201007\pi$
$384$	189.698	9.68049
$385$	6.30873	0.321523
$386$	−64.0198	−3.25852
$387$	61.7043	3.13661
$388$	−64.9896	−3.29935
$389$	33.4195	1.69444	0.847218	−	0.531245i	$-0.178276\pi$
$389$	33.4195	1.69444	0.847218	+	0.531245i	$0.178276\pi$
$390$	−6.14590	−0.311210
$391$	−17.2885	−0.874315
$392$	−12.2088	−0.616635
$393$	−51.1225	−2.57879
$394$	61.5682	3.10176
$395$	−36.3524	−1.82909
$396$	43.9164	2.20688
$397$	23.8153	1.19526	0.597628	−	0.801773i	$-0.296110\pi$
$397$	23.8153	1.19526	0.597628	+	0.801773i	$0.296110\pi$
$398$	−66.5705	−3.33688
$399$	7.64737	0.382847
$400$	−3.82577	−0.191289
$401$	−13.4744	−0.672879	−0.336440	−	0.941705i	$-0.609223\pi$
$401$	−13.4744	−0.672879	−0.336440	+	0.941705i	$0.609223\pi$
$402$	−78.7703	−3.92870
$403$	1.57841	0.0786260
$404$	72.2312	3.59364
$405$	57.8504	2.87461
$406$	−34.0172	−1.68825
$407$	−6.59810	−0.327056
$408$	−96.6989	−4.78731
$409$	23.0857	1.14151	0.570756	−	0.821119i	$-0.306650\pi$
$409$	23.0857	1.14151	0.570756	+	0.821119i	$0.306650\pi$
$410$	−35.4370	−1.75011
$411$	36.1103	1.78119
$412$	−9.06910	−0.446803
$413$	22.6925	1.11663
$414$	−126.836	−6.23363
$415$	−39.0562	−1.91719
$416$	8.33573	0.408693
$417$	−53.7103	−2.63021
$418$	2.29241	0.112126
$419$	−4.23010	−0.206654	−0.103327	−	0.994647i	$-0.532949\pi$
$419$	−4.23010	−0.206654	−0.103327	+	0.994647i	$0.532949\pi$
$420$	−116.236	−5.67171
$421$	20.9144	1.01930	0.509652	−	0.860380i	$-0.329774\pi$
$421$	20.9144	1.01930	0.509652	+	0.860380i	$0.329774\pi$
$422$	−45.0100	−2.19105
$423$	2.72754	0.132617
$424$	−54.4054	−2.64216
$425$	0.647929	0.0314292
$426$	−26.0769	−1.26343
$427$	−32.4446	−1.57010
$428$	17.9109	0.865757
$429$	1.02251	0.0493673
$430$	−48.9562	−2.36088
$431$	−31.8792	−1.53557	−0.767784	−	0.640709i	$-0.778641\pi$
$431$	−31.8792	−1.53557	−0.767784	+	0.640709i	$0.778641\pi$
$432$	−258.383	−12.4315
$433$	−6.16704	−0.296369	−0.148184	−	0.988960i	$-0.547343\pi$
$433$	−6.16704	−0.296369	−0.148184	+	0.988960i	$0.547343\pi$
$434$	40.3314	1.93597
$435$	−30.5433	−1.46444
$436$	−81.5392	−3.90502
$437$	−4.90044	−0.234420
$438$	−62.9292	−3.00687
$439$	8.98601	0.428879	0.214439	−	0.976737i	$-0.431208\pi$
$439$	8.98601	0.428879	0.214439	+	0.976737i	$0.431208\pi$
$440$	−22.6115	−1.07796
$441$	9.09559	0.433123
$442$	−2.49134	−0.118501
$443$	22.6312	1.07524	0.537621	−	0.843187i	$-0.319323\pi$
$443$	22.6312	1.07524	0.537621	+	0.843187i	$0.319323\pi$
$444$	121.567	5.76932
$445$	−0.0777532	−0.00368585
$446$	−40.3555	−1.91089
$447$	27.7991	1.31485
$448$	115.328	5.44873
$449$	−0.171548	−0.00809587	−0.00404794	−	0.999992i	$-0.501289\pi$
$449$	−0.171548	−0.00809587	−0.00404794	+	0.999992i	$0.501289\pi$
$450$	4.75349	0.224082
$451$	5.89574	0.277620
$452$	−49.6805	−2.33677
$453$	−1.47623	−0.0693592
$454$	−8.78121	−0.412122
$455$	−1.94339	−0.0911076
$456$	−27.4095	−1.28357
$457$	−3.51690	−0.164513	−0.0822567	−	0.996611i	$-0.526213\pi$
$457$	−3.51690	−0.164513	−0.0822567	+	0.996611i	$0.526213\pi$
$458$	−54.6897	−2.55548
$459$	43.7595	2.04252
$460$	74.4838	3.47283
$461$	−20.3090	−0.945884	−0.472942	−	0.881093i	$-0.656808\pi$
$461$	−20.3090	−0.945884	−0.472942	+	0.881093i	$0.656808\pi$
$462$	26.1272	1.21555
$463$	18.1645	0.844175	0.422087	−	0.906555i	$-0.361298\pi$
$463$	18.1645	0.844175	0.422087	+	0.906555i	$0.361298\pi$
$464$	73.1061	3.39386
$465$	36.2126	1.67932
$466$	12.0699	0.559125
$467$	22.1828	1.02650	0.513249	−	0.858240i	$-0.328442\pi$
$467$	22.1828	1.02650	0.513249	+	0.858240i	$0.328442\pi$
$468$	−13.5284	−0.625349
$469$	−24.9079	−1.15014
$470$	−2.16403	−0.0998191
$471$	73.5539	3.38919
$472$	−81.3338	−3.74369
$473$	8.14498	0.374507
$474$	−150.551	−6.91504
$475$	0.183657	0.00842674
$476$	−47.1179	−2.15964
$477$	40.5323	1.85585
$478$	74.7618	3.41952
$479$	−22.6777	−1.03617	−0.518085	−	0.855329i	$-0.673355\pi$
$479$	−22.6777	−1.03617	−0.518085	+	0.855329i	$0.673355\pi$
$480$	191.243	8.72900
$481$	2.03253	0.0926756
$482$	−4.40393	−0.200594
$483$	−55.8515	−2.54133
$484$	−56.8720	−2.58509
$485$	−24.9291	−1.13197
$486$	113.551	5.15080
$487$	−37.7175	−1.70914	−0.854572	−	0.519333i	$-0.826181\pi$
$487$	−37.7175	−1.70914	−0.854572	+	0.519333i	$0.826181\pi$
$488$	116.287	5.26406
$489$	67.3201	3.04432
$490$	−7.21644	−0.326006
$491$	−6.09245	−0.274949	−0.137474	−	0.990505i	$-0.543898\pi$
$491$	−6.09245	−0.274949	−0.137474	+	0.990505i	$0.543898\pi$
$492$	−108.626	−4.89726
$493$	−12.3812	−0.557620
$494$	−0.706173	−0.0317722
$495$	16.8457	0.757159
$496$	−86.6759	−3.89186
$497$	−8.24577	−0.369873
$498$	−161.749	−7.24814
$499$	−39.0019	−1.74596	−0.872982	−	0.487752i	$-0.837817\pi$
$499$	−39.0019	−1.74596	−0.872982	+	0.487752i	$0.837817\pi$
$500$	−65.0434	−2.90883
$501$	3.35160	0.149738
$502$	35.9324	1.60374
$503$	−6.74645	−0.300809	−0.150405	−	0.988625i	$-0.548058\pi$
$503$	−6.74645	−0.300809	−0.150405	+	0.988625i	$0.548058\pi$
$504$	−224.327	−9.99231
$505$	27.7069	1.23294
$506$	−16.7423	−0.744287
$507$	42.0933	1.86943
$508$	−59.5227	−2.64089
$509$	−28.5549	−1.26567	−0.632837	−	0.774285i	$-0.718110\pi$
$509$	−28.5549	−1.26567	−0.632837	+	0.774285i	$0.718110\pi$
$510$	−57.1575	−2.53098
$511$	−19.8988	−0.880271
$512$	−107.690	−4.75928
$513$	12.4037	0.547637
$514$	6.41262	0.282848
$515$	−3.47878	−0.153293
$516$	−150.068	−6.60636
$517$	0.360035	0.0158343
$518$	51.9353	2.28191
$519$	43.3847	1.90438
$520$	6.96544	0.305455
$521$	14.1306	0.619071	0.309536	−	0.950888i	$-0.399826\pi$
$521$	14.1306	0.619071	0.309536	+	0.950888i	$0.399826\pi$
$522$	−90.8337	−3.97568
$523$	−2.72062	−0.118965	−0.0594823	−	0.998229i	$-0.518945\pi$
$523$	−2.72062	−0.118965	−0.0594823	+	0.998229i	$0.518945\pi$
$524$	89.2820	3.90030
$525$	2.09318	0.0913538
$526$	−29.3114	−1.27804
$527$	14.6793	0.639442
$528$	−56.1497	−2.44360
$529$	12.7897	0.556074
$530$	−32.1583	−1.39687
$531$	60.5941	2.62956
$532$	−13.3556	−0.579040
$533$	−1.81617	−0.0786672
$534$	−0.322010	−0.0139347
$535$	6.87038	0.297032
$536$	89.2741	3.85605
$537$	22.5557	0.973350
$538$	4.39575	0.189514
$539$	1.20062	0.0517143
$540$	−188.529	−8.11299
$541$	13.9598	0.600177	0.300089	−	0.953911i	$-0.402984\pi$
$541$	13.9598	0.600177	0.300089	+	0.953911i	$0.402984\pi$
$542$	21.1422	0.908133
$543$	−14.2588	−0.611902
$544$	77.5232	3.32378
$545$	−31.2773	−1.33977
$546$	−8.04843	−0.344441
$547$	17.1894	0.734965	0.367483	−	0.930030i	$-0.380220\pi$
$547$	17.1894	0.734965	0.367483	+	0.930030i	$0.380220\pi$
$548$	−63.0643	−2.69397
$549$	−86.6343	−3.69746
$550$	0.627461	0.0267550
$551$	−3.50947	−0.149508
$552$	200.181	8.52028
$553$	−47.6057	−2.02440
$554$	−6.95772	−0.295605
$555$	46.6315	1.97939
$556$	93.8016	3.97807
$557$	−3.53460	−0.149766	−0.0748829	−	0.997192i	$-0.523858\pi$
$557$	−3.53460	−0.149766	−0.0748829	+	0.997192i	$0.523858\pi$
$558$	107.694	4.55905
$559$	−2.50905	−0.106121
$560$	106.719	4.50968
$561$	9.50946	0.401490
$562$	28.1587	1.18780
$563$	28.8229	1.21474	0.607369	−	0.794420i	$-0.292225\pi$
$563$	28.8229	1.21474	0.607369	+	0.794420i	$0.292225\pi$
$564$	−6.63349	−0.279320
$565$	−19.0567	−0.801723
$566$	−45.7911	−1.92474
$567$	75.7586	3.18156
$568$	29.5542	1.24007
$569$	18.7969	0.788005	0.394003	−	0.919109i	$-0.371090\pi$
$569$	18.7969	0.788005	0.394003	+	0.919109i	$0.371090\pi$
$570$	−16.2014	−0.678602
$571$	10.8066	0.452244	0.226122	−	0.974099i	$-0.427395\pi$
$571$	10.8066	0.452244	0.226122	+	0.974099i	$0.427395\pi$
$572$	−1.78575	−0.0746659
$573$	−17.8810	−0.746987
$574$	−46.4068	−1.93698
$575$	−1.34131	−0.0559365
$576$	307.951	12.8313
$577$	14.1539	0.589235	0.294618	−	0.955615i	$-0.404808\pi$
$577$	14.1539	0.589235	0.294618	+	0.955615i	$0.404808\pi$
$578$	23.9948	0.998050
$579$	−75.2759	−3.12836
$580$	53.3418	2.21490
$581$	−51.1465	−2.12191
$582$	−103.242	−4.27953
$583$	5.35027	0.221585
$584$	71.3207	2.95127
$585$	−5.18929	−0.214551
$586$	−21.7592	−0.898863
$587$	21.2805	0.878339	0.439170	−	0.898404i	$-0.355273\pi$
$587$	21.2805	0.878339	0.439170	+	0.898404i	$0.355273\pi$
$588$	−22.1209	−0.912250
$589$	4.16088	0.171446
$590$	−48.0754	−1.97923
$591$	72.3933	2.97786
$592$	−111.614	−4.58729
$593$	−14.3680	−0.590022	−0.295011	−	0.955494i	$-0.595323\pi$
$593$	−14.3680	−0.590022	−0.295011	+	0.955494i	$0.595323\pi$
$594$	42.3771	1.73876
$595$	−18.0737	−0.740951
$596$	−48.5494	−1.98866
$597$	−78.2751	−3.20359
$598$	5.15744	0.210903
$599$	47.7184	1.94972	0.974860	−	0.222819i	$-0.0715259\pi$
$599$	47.7184	1.94972	0.974860	+	0.222819i	$0.0715259\pi$
$600$	−7.50230	−0.306280
$601$	−25.6015	−1.04431	−0.522153	−	0.852852i	$-0.674871\pi$
$601$	−25.6015	−1.04431	−0.522153	+	0.852852i	$0.674871\pi$
$602$	−64.1111	−2.61297
$603$	−66.5097	−2.70848
$604$	2.57814	0.104903
$605$	−21.8153	−0.886918
$606$	114.746	4.66124
$607$	39.3364	1.59662	0.798308	−	0.602249i	$-0.205729\pi$
$607$	39.3364	1.59662	0.798308	+	0.602249i	$0.205729\pi$
$608$	21.9741	0.891166
$609$	−39.9982	−1.62081
$610$	68.7357	2.78303
$611$	−0.110908	−0.00448686
$612$	−125.815	−5.08578
$613$	23.1516	0.935086	0.467543	−	0.883970i	$-0.345139\pi$
$613$	23.1516	0.935086	0.467543	+	0.883970i	$0.345139\pi$
$614$	−0.914470	−0.0369050
$615$	−41.6676	−1.68020
$616$	−29.6112	−1.19307
$617$	−18.9182	−0.761617	−0.380809	−	0.924654i	$-0.624354\pi$
$617$	−18.9182	−0.761617	−0.380809	+	0.924654i	$0.624354\pi$
$618$	−14.4071	−0.579540
$619$	−3.95811	−0.159090	−0.0795449	−	0.996831i	$-0.525347\pi$
$619$	−3.95811	−0.159090	−0.0795449	+	0.996831i	$0.525347\pi$
$620$	−63.2430	−2.53990
$621$	−90.5887	−3.63520
$622$	48.3281	1.93778
$623$	−0.101822	−0.00407943
$624$	17.2968	0.692426
$625$	−23.8287	−0.953148
$626$	37.9086	1.51513
$627$	2.69547	0.107647
$628$	−128.457	−5.12600
$629$	18.9028	0.753703
$630$	−132.597	−5.28278
$631$	3.24478	0.129173	0.0645863	−	0.997912i	$-0.479427\pi$
$631$	3.24478	0.129173	0.0645863	+	0.997912i	$0.479427\pi$
$632$	170.627	6.78717
$633$	−52.9238	−2.10353
$634$	20.2765	0.805284
$635$	−22.8321	−0.906063
$636$	−98.5764	−3.90881
$637$	−0.369849	−0.0146539
$638$	−11.9901	−0.474691
$639$	−22.0181	−0.871021
$640$	−127.080	−5.02329
$641$	39.6131	1.56462	0.782312	−	0.622887i	$-0.214040\pi$
$641$	39.6131	1.56462	0.782312	+	0.622887i	$0.214040\pi$
$642$	28.4532	1.12296
$643$	20.8230	0.821180	0.410590	−	0.911820i	$-0.365323\pi$
$643$	20.8230	0.821180	0.410590	+	0.911820i	$0.365323\pi$
$644$	97.5411	3.84366
$645$	−57.5638	−2.26657
$646$	−6.56749	−0.258394
$647$	15.1733	0.596526	0.298263	−	0.954484i	$-0.403593\pi$
$647$	15.1733	0.596526	0.298263	+	0.954484i	$0.403593\pi$
$648$	−271.532	−10.6668
$649$	7.99844	0.313966
$650$	−0.193288	−0.00758139
$651$	47.4226	1.85864
$652$	−117.570	−4.60440
$653$	−26.4551	−1.03527	−0.517635	−	0.855602i	$-0.673187\pi$
$653$	−26.4551	−1.03527	−0.517635	+	0.855602i	$0.673187\pi$
$654$	−129.533	−5.06513
$655$	34.2473	1.33815
$656$	99.7325	3.89390
$657$	−53.1343	−2.07297
$658$	−2.83392	−0.110478
$659$	2.44877	0.0953907	0.0476953	−	0.998862i	$-0.484812\pi$
$659$	2.44877	0.0953907	0.0476953	+	0.998862i	$0.484812\pi$
$660$	−40.9696	−1.59474
$661$	27.8714	1.08407	0.542037	−	0.840355i	$-0.317653\pi$
$661$	27.8714	1.08407	0.542037	+	0.840355i	$0.317653\pi$
$662$	25.3830	0.986539
$663$	−2.92937	−0.113767
$664$	183.318	7.11410
$665$	−5.12303	−0.198663
$666$	138.679	5.37370
$667$	25.6309	0.992433
$668$	−5.85334	−0.226473
$669$	−47.4510	−1.83456
$670$	52.7688	2.03864
$671$	−11.4357	−0.441472
$672$	250.444	9.66109
$673$	−44.9781	−1.73378	−0.866889	−	0.498502i	$-0.833884\pi$
$673$	−44.9781	−1.73378	−0.866889	+	0.498502i	$0.833884\pi$
$674$	−16.5350	−0.636904
$675$	3.39504	0.130675
$676$	−73.5133	−2.82743
$677$	38.5268	1.48070	0.740352	−	0.672220i	$-0.234659\pi$
$677$	38.5268	1.48070	0.740352	+	0.672220i	$0.234659\pi$
$678$	−78.9222	−3.03099
$679$	−32.6462	−1.25285
$680$	64.7794	2.48418
$681$	−10.3251	−0.395660
$682$	14.2156	0.544344
$683$	0.0349168	0.00133605	0.000668026	−	1.00000i	$-0.499787\pi$
$683$	0.0349168	0.00133605	0.000668026		1.00000i	$0.499787\pi$
$684$	−35.6626	−1.36359
$685$	−24.1906	−0.924274
$686$	46.1288	1.76121
$687$	−64.3054	−2.45340
$688$	137.781	5.25283
$689$	−1.64814	−0.0627891
$690$	118.325	4.50454
$691$	35.7472	1.35989	0.679943	−	0.733265i	$-0.262005\pi$
$691$	35.7472	1.35989	0.679943	+	0.733265i	$0.262005\pi$
$692$	−75.7685	−2.88029
$693$	22.0605	0.838009
$694$	−33.5374	−1.27306
$695$	35.9810	1.36484
$696$	143.360	5.43406
$697$	−16.8906	−0.639777
$698$	32.1317	1.21620
$699$	14.1920	0.536791
$700$	−3.65560	−0.138169
$701$	−22.0960	−0.834554	−0.417277	−	0.908779i	$-0.637015\pi$
$701$	−22.0960	−0.834554	−0.417277	+	0.908779i	$0.637015\pi$
$702$	−13.0542	−0.492699
$703$	5.35802	0.202082
$704$	40.6496	1.53204
$705$	−2.54451	−0.0958319
$706$	56.2105	2.11551
$707$	36.2838	1.36459
$708$	−147.368	−5.53842
$709$	−27.6601	−1.03880	−0.519399	−	0.854532i	$-0.673844\pi$
$709$	−27.6601	−1.03880	−0.519399	+	0.854532i	$0.673844\pi$
$710$	17.4691	0.655605
$711$	−127.118	−4.76729
$712$	0.364949	0.0136770
$713$	−30.3884	−1.13806
$714$	−74.8513	−2.80124
$715$	−0.684988	−0.0256171
$716$	−39.3920	−1.47215
$717$	87.9066	3.28293
$718$	−1.71201	−0.0638915
$719$	9.99841	0.372878	0.186439	−	0.982467i	$-0.440305\pi$
$719$	9.99841	0.372878	0.186439	+	0.982467i	$0.440305\pi$
$720$	284.962	10.6199
$721$	−4.55567	−0.169662
$722$	50.8516	1.89250
$723$	−5.17824	−0.192581
$724$	24.9020	0.925475
$725$	−0.960583	−0.0356752
$726$	−90.3467	−3.35308
$727$	−50.3564	−1.86761	−0.933807	−	0.357778i	$-0.883535\pi$
$727$	−50.3564	−1.86761	−0.933807	+	0.357778i	$0.883535\pi$
$728$	9.12167	0.338072
$729$	54.1009	2.00374
$730$	42.1568	1.56029
$731$	−23.3344	−0.863054
$732$	210.699	7.78764
$733$	35.7919	1.32200	0.661002	−	0.750385i	$-0.270132\pi$
$733$	35.7919	1.32200	0.661002	+	0.750385i	$0.270132\pi$
$734$	−40.4270	−1.49219
$735$	−8.48526	−0.312983
$736$	−160.485	−5.91554
$737$	−8.77929	−0.323389
$738$	−123.917	−4.56144
$739$	16.4371	0.604650	0.302325	−	0.953205i	$-0.402237\pi$
$739$	16.4371	0.604650	0.302325	+	0.953205i	$0.402237\pi$
$740$	−81.4388	−2.99375
$741$	−0.830335	−0.0305031
$742$	−42.1133	−1.54603
$743$	46.7796	1.71618	0.858089	−	0.513500i	$-0.171652\pi$
$743$	46.7796	1.71618	0.858089	+	0.513500i	$0.171652\pi$
$744$	−169.971	−6.23143
$745$	−18.6229	−0.682289
$746$	1.26284	0.0462359
$747$	−136.573	−4.99693
$748$	−16.6076	−0.607236
$749$	8.99718	0.328750
$750$	−103.328	−3.77299
$751$	−38.4969	−1.40477	−0.702385	−	0.711797i	$-0.747882\pi$
$751$	−38.4969	−1.40477	−0.702385	+	0.711797i	$0.747882\pi$
$752$	6.09036	0.222093
$753$	42.2501	1.53968
$754$	3.69352	0.134510
$755$	0.988936	0.0359911
$756$	−246.890	−8.97930
$757$	−48.4461	−1.76080	−0.880402	−	0.474228i	$-0.842727\pi$
$757$	−48.4461	−1.76080	−0.880402	+	0.474228i	$0.842727\pi$
$758$	104.898	3.81006
$759$	−19.6860	−0.714557
$760$	18.3618	0.666053
$761$	−5.33776	−0.193494	−0.0967469	−	0.995309i	$-0.530844\pi$
$761$	−5.33776	−0.193494	−0.0967469	+	0.995309i	$0.530844\pi$
$762$	−94.5575	−3.42546
$763$	−40.9595	−1.48283
$764$	31.2279	1.12979
$765$	−48.2610	−1.74488
$766$	−87.6500	−3.16692
$767$	−2.46390	−0.0889664
$768$	−263.375	−9.50371
$769$	53.0873	1.91438	0.957188	−	0.289468i	$-0.0934784\pi$
$769$	53.0873	1.91438	0.957188	+	0.289468i	$0.0934784\pi$
$770$	−17.5028	−0.630757
$771$	7.54010	0.271550
$772$	131.464	4.73151
$773$	−12.4277	−0.446995	−0.223498	−	0.974704i	$-0.571747\pi$
$773$	−12.4277	−0.446995	−0.223498	+	0.974704i	$0.571747\pi$
$774$	−171.191	−6.15334
$775$	1.13888	0.0409099
$776$	117.009	4.20039
$777$	61.0667	2.19076
$778$	−92.7184	−3.32412
$779$	−4.78767	−0.171536
$780$	12.6206	0.451890
$781$	−2.90639	−0.103999
$782$	47.9648	1.71522
$783$	−64.8754	−2.31846
$784$	20.3097	0.725346
$785$	−49.2743	−1.75868
$786$	141.833	5.05902
$787$	23.1385	0.824798	0.412399	−	0.911003i	$-0.364691\pi$
$787$	23.1385	0.824798	0.412399	+	0.911003i	$0.364691\pi$
$788$	−126.430	−4.50389
$789$	−34.4650	−1.22699
$790$	100.855	3.58827
$791$	−24.9559	−0.887331
$792$	−79.0685	−2.80958
$793$	3.52276	0.125097
$794$	−66.0727	−2.34483
$795$	−37.8125	−1.34107
$796$	136.702	4.84529
$797$	15.9583	0.565271	0.282636	−	0.959227i	$-0.408791\pi$
$797$	15.9583	0.565271	0.282636	+	0.959227i	$0.408791\pi$
$798$	−21.2167	−0.751063
$799$	−1.03146	−0.0364903
$800$	6.01457	0.212647
$801$	−0.271889	−0.00960672
$802$	37.3831	1.32004
$803$	−7.01373	−0.247509
$804$	161.755	5.70464
$805$	37.4154	1.31872
$806$	−4.37910	−0.154247
$807$	5.16863	0.181944
$808$	−130.047	−4.57505
$809$	−6.87759	−0.241803	−0.120902	−	0.992664i	$-0.538579\pi$
$809$	−6.87759	−0.241803	−0.120902	+	0.992664i	$0.538579\pi$
$810$	−160.499	−5.63936
$811$	−1.45082	−0.0509453	−0.0254726	−	0.999676i	$-0.508109\pi$
$811$	−1.45082	−0.0509453	−0.0254726	+	0.999676i	$0.508109\pi$
$812$	69.8543	2.45141
$813$	24.8594	0.871858
$814$	18.3056	0.641613
$815$	−45.0982	−1.57972
$816$	160.862	5.63130
$817$	−6.61417	−0.231401
$818$	−64.0484	−2.23940
$819$	−6.79569	−0.237461
$820$	72.7697	2.54123
$821$	29.4821	1.02893	0.514466	−	0.857511i	$-0.327990\pi$
$821$	29.4821	1.02893	0.514466	+	0.857511i	$0.327990\pi$
$822$	−100.184	−3.49431
$823$	−20.9623	−0.730698	−0.365349	−	0.930871i	$-0.619050\pi$
$823$	−20.9623	−0.730698	−0.365349	+	0.930871i	$0.619050\pi$
$824$	16.3283	0.568823
$825$	0.737783	0.0256863
$826$	−62.9577	−2.19058
$827$	−51.9104	−1.80510	−0.902550	−	0.430585i	$-0.858307\pi$
$827$	−51.9104	−1.80510	−0.902550	+	0.430585i	$0.858307\pi$
$828$	260.457	9.05149
$829$	35.9236	1.24768	0.623840	−	0.781552i	$-0.285572\pi$
$829$	35.9236	1.24768	0.623840	+	0.781552i	$0.285572\pi$
$830$	108.357	3.76112
$831$	−8.18105	−0.283798
$832$	−12.5220	−0.434124
$833$	−3.43963	−0.119176
$834$	149.013	5.15989
$835$	−2.24526	−0.0777004
$836$	−4.70746	−0.162811
$837$	76.9174	2.65865
$838$	11.7359	0.405410
$839$	−1.52939	−0.0528003	−0.0264002	−	0.999651i	$-0.508404\pi$
$839$	−1.52939	−0.0528003	−0.0264002	+	0.999651i	$0.508404\pi$
$840$	209.274	7.22064
$841$	−10.6444	−0.367047
$842$	−58.0244	−1.99965
$843$	33.1096	1.14036
$844$	92.4279	3.18150
$845$	−28.1987	−0.970063
$846$	−7.56722	−0.260166
$847$	−28.5685	−0.981624
$848$	90.5052	3.10796
$849$	−53.8422	−1.84786
$850$	−1.79760	−0.0616572
$851$	−39.1316	−1.34141
$852$	53.5489	1.83456
$853$	−24.1138	−0.825642	−0.412821	−	0.910812i	$-0.635456\pi$
$853$	−24.1138	−0.825642	−0.412821	+	0.910812i	$0.635456\pi$
$854$	90.0136	3.08020
$855$	−13.6797	−0.467834
$856$	−32.2474	−1.10219
$857$	7.86522	0.268671	0.134335	−	0.990936i	$-0.457110\pi$
$857$	7.86522	0.268671	0.134335	+	0.990936i	$0.457110\pi$
$858$	−2.83683	−0.0968478
$859$	44.2552	1.50997	0.754985	−	0.655742i	$-0.227644\pi$
$859$	44.2552	1.50997	0.754985	+	0.655742i	$0.227644\pi$
$860$	100.531	3.42810
$861$	−54.5662	−1.85961
$862$	88.4451	3.01245
$863$	−15.5694	−0.529989	−0.264994	−	0.964250i	$-0.585370\pi$
$863$	−15.5694	−0.529989	−0.264994	+	0.964250i	$0.585370\pi$
$864$	406.209	13.8195
$865$	−29.0637	−0.988196
$866$	17.1097	0.581411
$867$	28.2136	0.958184
$868$	−82.8205	−2.81111
$869$	−16.7796	−0.569208
$870$	84.7386	2.87291
$871$	2.70444	0.0916366
$872$	146.806	4.97147
$873$	−87.1726	−2.95035
$874$	13.5957	0.459881
$875$	−32.6732	−1.10456
$876$	129.225	4.36611
$877$	18.8844	0.637681	0.318840	−	0.947808i	$-0.396707\pi$
$877$	18.8844	0.637681	0.318840	+	0.947808i	$0.396707\pi$
$878$	−24.9306	−0.841367
$879$	−25.5849	−0.862958
$880$	37.6151	1.26800
$881$	−15.9961	−0.538923	−0.269462	−	0.963011i	$-0.586846\pi$
$881$	−15.9961	−0.538923	−0.269462	+	0.963011i	$0.586846\pi$
$882$	−25.2346	−0.849694
$883$	−5.71942	−0.192474	−0.0962370	−	0.995358i	$-0.530681\pi$
$883$	−5.71942	−0.192474	−0.0962370	+	0.995358i	$0.530681\pi$
$884$	5.11595	0.172068
$885$	−56.5282	−1.90017
$886$	−62.7876	−2.10939
$887$	48.9667	1.64414	0.822071	−	0.569385i	$-0.192819\pi$
$887$	48.9667	1.64414	0.822071	+	0.569385i	$0.192819\pi$
$888$	−218.873	−7.34491
$889$	−29.9000	−1.00281
$890$	0.215717	0.00723084
$891$	26.7027	0.894573
$892$	82.8700	2.77469
$893$	−0.292368	−0.00978373
$894$	−77.1254	−2.57946
$895$	−15.1102	−0.505079
$896$	−166.419	−5.55968
$897$	6.06424	0.202479
$898$	0.475941	0.0158823
$899$	−21.7628	−0.725829
$900$	−9.76127	−0.325376
$901$	−15.3279	−0.510646
$902$	−16.3570	−0.544630
$903$	−75.3833	−2.50860
$904$	89.4463	2.97494
$905$	9.55205	0.317521
$906$	4.09562	0.136068
$907$	37.1397	1.23320	0.616602	−	0.787275i	$-0.288509\pi$
$907$	37.1397	1.23320	0.616602	+	0.787275i	$0.288509\pi$
$908$	18.0322	0.598419
$909$	96.8859	3.21350
$910$	5.39171	0.178733
$911$	−10.4871	−0.347453	−0.173726	−	0.984794i	$-0.555581\pi$
$911$	−10.4871	−0.347453	−0.173726	+	0.984794i	$0.555581\pi$
$912$	45.5966	1.50985
$913$	−18.0276	−0.596627
$914$	9.75720	0.322740
$915$	80.8210	2.67186
$916$	112.305	3.71067
$917$	44.8490	1.48104
$918$	−121.405	−4.00698
$919$	−56.6739	−1.86950	−0.934750	−	0.355307i	$-0.884376\pi$
$919$	−56.6739	−1.86950	−0.934750	+	0.355307i	$0.884376\pi$
$920$	−134.103	−4.42125
$921$	−1.07525	−0.0354308
$922$	56.3449	1.85562
$923$	0.895307	0.0294694
$924$	−53.6521	−1.76503
$925$	1.46656	0.0482201
$926$	−50.3952	−1.65609
$927$	−12.1647	−0.399540
$928$	−114.932	−3.77281
$929$	2.95513	0.0969545	0.0484773	−	0.998824i	$-0.484563\pi$
$929$	2.95513	0.0969545	0.0484773	+	0.998824i	$0.484563\pi$
$930$	−100.468	−3.29446
$931$	−0.974969	−0.0319533
$932$	−24.7854	−0.811874
$933$	56.8253	1.86038
$934$	−61.5436	−2.01377
$935$	−6.37046	−0.208336
$936$	24.3569	0.796131
$937$	55.1764	1.80253	0.901267	−	0.433264i	$-0.142638\pi$
$937$	55.1764	1.80253	0.901267	+	0.433264i	$0.142638\pi$
$938$	69.1040	2.25632
$939$	44.5737	1.45461
$940$	4.44383	0.144942
$941$	12.9030	0.420625	0.210312	−	0.977634i	$-0.432552\pi$
$941$	12.9030	0.420625	0.210312	+	0.977634i	$0.432552\pi$
$942$	−204.067	−6.64885
$943$	34.9661	1.13865
$944$	135.302	4.40369
$945$	−94.7035	−3.08071
$946$	−22.5973	−0.734700
$947$	−31.6465	−1.02837	−0.514186	−	0.857679i	$-0.671906\pi$
$947$	−31.6465	−1.02837	−0.514186	+	0.857679i	$0.671906\pi$
$948$	309.156	10.0409
$949$	2.16057	0.0701350
$950$	−0.509533	−0.0165314
$951$	23.8416	0.773117
$952$	84.8325	2.74944
$953$	−32.8076	−1.06274	−0.531371	−	0.847139i	$-0.678323\pi$
$953$	−32.8076	−1.06274	−0.531371	+	0.847139i	$0.678323\pi$
$954$	−112.452	−3.64077
$955$	11.9786	0.387618
$956$	−153.523	−4.96529
$957$	−14.0982	−0.455730
$958$	62.9165	2.03274
$959$	−31.6790	−1.02297
$960$	−287.287	−9.27216
$961$	−5.19767	−0.167667
$962$	−5.63902	−0.181809
$963$	24.0245	0.774178
$964$	9.04346	0.291270
$965$	50.4279	1.62333
$966$	154.953	4.98554
$967$	15.2763	0.491254	0.245627	−	0.969364i	$-0.421006\pi$
$967$	15.2763	0.491254	0.245627	+	0.969364i	$0.421006\pi$
$968$	102.394	3.29107
$969$	−7.72220	−0.248073
$970$	69.1628	2.22068
$971$	−21.6320	−0.694203	−0.347101	−	0.937828i	$-0.612834\pi$
$971$	−21.6320	−0.694203	−0.347101	+	0.937828i	$0.612834\pi$
$972$	−233.178	−7.47918
$973$	47.1193	1.51057
$974$	104.643	3.35297
$975$	−0.227273	−0.00727855
$976$	−193.447	−6.19209
$977$	−25.1584	−0.804889	−0.402445	−	0.915444i	$-0.631839\pi$
$977$	−25.1584	−0.804889	−0.402445	+	0.915444i	$0.631839\pi$
$978$	−186.771	−5.97229
$979$	−0.0358894	−0.00114703
$980$	14.8190	0.473374
$981$	−109.371	−3.49195
$982$	16.9028	0.539389
$983$	24.2438	0.773258	0.386629	−	0.922235i	$-0.373639\pi$
$983$	24.2438	0.773258	0.386629	+	0.922235i	$0.373639\pi$
$984$	195.575	6.23469
$985$	−48.4968	−1.54524
$986$	34.3501	1.09393
$987$	−3.33219	−0.106065
$988$	1.45013	0.0461346
$989$	48.3057	1.53603
$990$	−46.7364	−1.48538
$991$	5.90834	0.187685	0.0938423	−	0.995587i	$-0.470085\pi$
$991$	5.90834	0.187685	0.0938423	+	0.995587i	$0.470085\pi$
$992$	136.265	4.32641
$993$	29.8459	0.947132
$994$	22.8769	0.725611
$995$	52.4371	1.66237
$996$	332.151	10.5246
$997$	43.7386	1.38522	0.692608	−	0.721314i	$-0.256461\pi$
$997$	43.7386	1.38522	0.692608	+	0.721314i	$0.256461\pi$
$998$	108.206	3.42520
$999$	99.0475	3.13372

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.a.1.3	✓	217

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.a.1.3	✓	217	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77438 q^{2} -3.26218 q^{3} +5.69718 q^{4} +2.18536 q^{5} +9.05052 q^{6} +2.86186 q^{7} -10.2574 q^{8} +7.64181 q^{9} +O(q^{10})\)	\(q-2.77438 q^{2} -3.26218 q^{3} +5.69718 q^{4} +2.18536 q^{5} +9.05052 q^{6} +2.86186 q^{7} -10.2574 q^{8} +7.64181 q^{9} -6.06301 q^{10} +1.00872 q^{11} -18.5852 q^{12} -0.310734 q^{13} -7.93988 q^{14} -7.12903 q^{15} +17.0635 q^{16} -2.88986 q^{17} -21.2013 q^{18} -0.819136 q^{19} +12.4504 q^{20} -9.33590 q^{21} -2.79857 q^{22} +5.98245 q^{23} +33.4614 q^{24} -0.224208 q^{25} +0.862095 q^{26} -15.1424 q^{27} +16.3045 q^{28} +4.28435 q^{29} +19.7786 q^{30} -5.07960 q^{31} -26.8259 q^{32} -3.29063 q^{33} +8.01758 q^{34} +6.25419 q^{35} +43.5368 q^{36} -6.54106 q^{37} +2.27259 q^{38} +1.01367 q^{39} -22.4161 q^{40} +5.84478 q^{41} +25.9013 q^{42} +8.07457 q^{43} +5.74686 q^{44} +16.7001 q^{45} -16.5976 q^{46} +0.356923 q^{47} -55.6643 q^{48} +1.19024 q^{49} +0.622037 q^{50} +9.42725 q^{51} -1.77031 q^{52} +5.30402 q^{53} +42.0108 q^{54} +2.20442 q^{55} -29.3552 q^{56} +2.67217 q^{57} -11.8864 q^{58} +7.92929 q^{59} -40.6154 q^{60} -11.3369 q^{61} +14.0927 q^{62} +21.8698 q^{63} +40.2982 q^{64} -0.679066 q^{65} +9.12944 q^{66} -8.70340 q^{67} -16.4641 q^{68} -19.5158 q^{69} -17.3515 q^{70} -2.88126 q^{71} -78.3850 q^{72} -6.95310 q^{73} +18.1474 q^{74} +0.731405 q^{75} -4.66677 q^{76} +2.88682 q^{77} -2.81231 q^{78} -16.6345 q^{79} +37.2899 q^{80} +26.4718 q^{81} -16.2156 q^{82} -17.8718 q^{83} -53.1883 q^{84} -6.31539 q^{85} -22.4019 q^{86} -13.9763 q^{87} -10.3468 q^{88} -0.0355791 q^{89} -46.3324 q^{90} -0.889278 q^{91} +34.0831 q^{92} +16.5706 q^{93} -0.990239 q^{94} -1.79011 q^{95} +87.5109 q^{96} -11.4073 q^{97} -3.30218 q^{98} +7.70845 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * q^99

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