LMFDB - Embedded newform 8027.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33451 q^{2} +2.56074 q^{3} +3.44993 q^{4} +1.12501 q^{5} -5.97807 q^{6} -4.54116 q^{7} -3.38489 q^{8} +3.55739 q^{9} +O(q^{10})$	\(q-2.33451 q^{2} +2.56074 q^{3} +3.44993 q^{4} +1.12501 q^{5} -5.97807 q^{6} -4.54116 q^{7} -3.38489 q^{8} +3.55739 q^{9} -2.62635 q^{10} +3.09048 q^{11} +8.83438 q^{12} +0.153255 q^{13} +10.6014 q^{14} +2.88086 q^{15} +1.00218 q^{16} -0.319577 q^{17} -8.30475 q^{18} -0.0834454 q^{19} +3.88121 q^{20} -11.6287 q^{21} -7.21475 q^{22} -1.00000 q^{23} -8.66781 q^{24} -3.73435 q^{25} -0.357775 q^{26} +1.42732 q^{27} -15.6667 q^{28} -0.825570 q^{29} -6.72539 q^{30} -4.58063 q^{31} +4.43018 q^{32} +7.91391 q^{33} +0.746055 q^{34} -5.10885 q^{35} +12.2727 q^{36} +9.41792 q^{37} +0.194804 q^{38} +0.392446 q^{39} -3.80803 q^{40} -0.978257 q^{41} +27.1474 q^{42} +8.23209 q^{43} +10.6619 q^{44} +4.00209 q^{45} +2.33451 q^{46} -7.17406 q^{47} +2.56632 q^{48} +13.6222 q^{49} +8.71788 q^{50} -0.818353 q^{51} +0.528719 q^{52} -1.65351 q^{53} -3.33209 q^{54} +3.47682 q^{55} +15.3713 q^{56} -0.213682 q^{57} +1.92730 q^{58} -14.5749 q^{59} +9.93877 q^{60} +5.24204 q^{61} +10.6935 q^{62} -16.1547 q^{63} -12.3466 q^{64} +0.172413 q^{65} -18.4751 q^{66} -4.53843 q^{67} -1.10252 q^{68} -2.56074 q^{69} +11.9267 q^{70} -5.58207 q^{71} -12.0413 q^{72} -3.15692 q^{73} -21.9862 q^{74} -9.56270 q^{75} -0.287881 q^{76} -14.0344 q^{77} -0.916168 q^{78} -0.860171 q^{79} +1.12746 q^{80} -7.01716 q^{81} +2.28375 q^{82} -4.59643 q^{83} -40.1184 q^{84} -0.359527 q^{85} -19.2179 q^{86} -2.11407 q^{87} -10.4609 q^{88} +3.82198 q^{89} -9.34293 q^{90} -0.695955 q^{91} -3.44993 q^{92} -11.7298 q^{93} +16.7479 q^{94} -0.0938769 q^{95} +11.3445 q^{96} +0.769804 q^{97} -31.8011 q^{98} +10.9940 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) $ 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * 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 $

$2$	−2.33451	−1.65075	−0.825374	−	0.564587i	$-0.809036\pi$
$2$	−2.33451	−1.65075	−0.825374	+	0.564587i	$0.809036\pi$
$3$	2.56074	1.47844	0.739222	−	0.673462i	$-0.235194\pi$
$3$	2.56074	1.47844	0.739222	+	0.673462i	$0.235194\pi$
$4$	3.44993	1.72497
$5$	1.12501	0.503120	0.251560	−	0.967842i	$-0.419056\pi$
$5$	1.12501	0.503120	0.251560	+	0.967842i	$0.419056\pi$
$6$	−5.97807	−2.44054
$7$	−4.54116	−1.71640	−0.858199	−	0.513317i	$-0.828417\pi$
$7$	−4.54116	−1.71640	−0.858199	+	0.513317i	$0.828417\pi$
$8$	−3.38489	−1.19674
$9$	3.55739	1.18580
$10$	−2.62635	−0.830524
$11$	3.09048	0.931814	0.465907	−	0.884834i	$-0.345728\pi$
$11$	3.09048	0.931814	0.465907	+	0.884834i	$0.345728\pi$
$12$	8.83438	2.55027
$13$	0.153255	0.0425053	0.0212526	−	0.999774i	$-0.493235\pi$
$13$	0.153255	0.0425053	0.0212526	+	0.999774i	$0.493235\pi$
$14$	10.6014	2.83334
$15$	2.88086	0.743834
$16$	1.00218	0.250544
$17$	−0.319577	−0.0775088	−0.0387544	−	0.999249i	$-0.512339\pi$
$17$	−0.319577	−0.0775088	−0.0387544	+	0.999249i	$0.512339\pi$
$18$	−8.30475	−1.95745
$19$	−0.0834454	−0.0191437	−0.00957184	−	0.999954i	$-0.503047\pi$
$19$	−0.0834454	−0.0191437	−0.00957184	+	0.999954i	$0.503047\pi$
$20$	3.88121	0.867865
$21$	−11.6287	−2.53760
$22$	−7.21475	−1.53819
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−8.66781	−1.76931
$25$	−3.73435	−0.746870
$26$	−0.357775	−0.0701654
$27$	1.42732	0.274688
$28$	−15.6667	−2.96073
$29$	−0.825570	−0.153304	−0.0766522	−	0.997058i	$-0.524423\pi$
$29$	−0.825570	−0.153304	−0.0766522	+	0.997058i	$0.524423\pi$
$30$	−6.72539	−1.22788
$31$	−4.58063	−0.822705	−0.411353	−	0.911476i	$-0.634944\pi$
$31$	−4.58063	−0.822705	−0.411353	+	0.911476i	$0.634944\pi$
$32$	4.43018	0.783152
$33$	7.91391	1.37763
$34$	0.746055	0.127947
$35$	−5.10885	−0.863554
$36$	12.2727	2.04546
$37$	9.41792	1.54830	0.774148	−	0.633004i	$-0.218179\pi$
$37$	9.41792	1.54830	0.774148	+	0.633004i	$0.218179\pi$
$38$	0.194804	0.0316014
$39$	0.392446	0.0628416
$40$	−3.80803	−0.602102
$41$	−0.978257	−0.152778	−0.0763890	−	0.997078i	$-0.524339\pi$
$41$	−0.978257	−0.152778	−0.0763890	+	0.997078i	$0.524339\pi$
$42$	27.1474	4.18893
$43$	8.23209	1.25538	0.627691	−	0.778463i	$-0.284000\pi$
$43$	8.23209	1.25538	0.627691	+	0.778463i	$0.284000\pi$
$44$	10.6619	1.60735
$45$	4.00209	0.596597
$46$	2.33451	0.344205
$47$	−7.17406	−1.04644	−0.523222	−	0.852196i	$-0.675270\pi$
$47$	−7.17406	−1.04644	−0.523222	+	0.852196i	$0.675270\pi$
$48$	2.56632	0.370416
$49$	13.6222	1.94602
$50$	8.71788	1.23289
$51$	−0.818353	−0.114592
$52$	0.528719	0.0733202
$53$	−1.65351	−0.227127	−0.113564	−	0.993531i	$-0.536227\pi$
$53$	−1.65351	−0.227127	−0.113564	+	0.993531i	$0.536227\pi$
$54$	−3.33209	−0.453440
$55$	3.47682	0.468814
$56$	15.3713	2.05408
$57$	−0.213682	−0.0283029
$58$	1.92730	0.253067
$59$	−14.5749	−1.89749	−0.948744	−	0.316047i	$-0.897644\pi$
$59$	−14.5749	−1.89749	−0.948744	+	0.316047i	$0.897644\pi$
$60$	9.93877	1.28309
$61$	5.24204	0.671175	0.335587	−	0.942009i	$-0.391065\pi$
$61$	5.24204	0.671175	0.335587	+	0.942009i	$0.391065\pi$
$62$	10.6935	1.35808
$63$	−16.1547	−2.03530
$64$	−12.3466	−1.54333
$65$	0.172413	0.0213852
$66$	−18.4751	−2.27413
$67$	−4.53843	−0.554458	−0.277229	−	0.960804i	$-0.589416\pi$
$67$	−4.53843	−0.554458	−0.277229	+	0.960804i	$0.589416\pi$
$68$	−1.10252	−0.133700
$69$	−2.56074	−0.308277
$70$	11.9267	1.42551
$71$	−5.58207	−0.662470	−0.331235	−	0.943548i	$-0.607465\pi$
$71$	−5.58207	−0.662470	−0.331235	+	0.943548i	$0.607465\pi$
$72$	−12.0413	−1.41909
$73$	−3.15692	−0.369489	−0.184744	−	0.982787i	$-0.559146\pi$
$73$	−3.15692	−0.369489	−0.184744	+	0.982787i	$0.559146\pi$
$74$	−21.9862	−2.55585
$75$	−9.56270	−1.10421
$76$	−0.287881	−0.0330222
$77$	−14.0344	−1.59936
$78$	−0.916168	−0.103736
$79$	−0.860171	−0.0967768	−0.0483884	−	0.998829i	$-0.515409\pi$
$79$	−0.860171	−0.0967768	−0.0483884	+	0.998829i	$0.515409\pi$
$80$	1.12746	0.126054
$81$	−7.01716	−0.779685
$82$	2.28375	0.252198
$83$	−4.59643	−0.504523	−0.252262	−	0.967659i	$-0.581174\pi$
$83$	−4.59643	−0.504523	−0.252262	+	0.967659i	$0.581174\pi$
$84$	−40.1184	−4.37727
$85$	−0.359527	−0.0389962
$86$	−19.2179	−2.07232
$87$	−2.11407	−0.226652
$88$	−10.4609	−1.11514
$89$	3.82198	0.405129	0.202564	−	0.979269i	$-0.435072\pi$
$89$	3.82198	0.405129	0.202564	+	0.979269i	$0.435072\pi$
$90$	−9.34293	−0.984831
$91$	−0.695955	−0.0729559
$92$	−3.44993	−0.359681
$93$	−11.7298	−1.21632
$94$	16.7479	1.72742
$95$	−0.0938769	−0.00963157
$96$	11.3445	1.15785
$97$	0.769804	0.0781618	0.0390809	−	0.999236i	$-0.487557\pi$
$97$	0.769804	0.0781618	0.0390809	+	0.999236i	$0.487557\pi$
$98$	−31.8011	−3.21239
$99$	10.9940	1.10494
$100$	−12.8833	−1.28833
$101$	−2.69965	−0.268626	−0.134313	−	0.990939i	$-0.542883\pi$
$101$	−2.69965	−0.268626	−0.134313	+	0.990939i	$0.542883\pi$
$102$	1.91045	0.189163
$103$	1.58065	0.155746	0.0778729	−	0.996963i	$-0.475187\pi$
$103$	1.58065	0.155746	0.0778729	+	0.996963i	$0.475187\pi$
$104$	−0.518750	−0.0508676
$105$	−13.0824	−1.27672
$106$	3.86014	0.374930
$107$	6.03531	0.583455	0.291728	−	0.956501i	$-0.405770\pi$
$107$	6.03531	0.583455	0.291728	+	0.956501i	$0.405770\pi$
$108$	4.92416	0.473827
$109$	4.72309	0.452390	0.226195	−	0.974082i	$-0.427371\pi$
$109$	4.72309	0.452390	0.226195	+	0.974082i	$0.427371\pi$
$110$	−8.11667	−0.773894
$111$	24.1168	2.28907
$112$	−4.55105	−0.430034
$113$	−13.3293	−1.25391	−0.626957	−	0.779053i	$-0.715700\pi$
$113$	−13.3293	−1.25391	−0.626957	+	0.779053i	$0.715700\pi$
$114$	0.498842	0.0467209
$115$	−1.12501	−0.104908
$116$	−2.84816	−0.264445
$117$	0.545187	0.0504025
$118$	34.0252	3.13227
$119$	1.45125	0.133036
$120$	−9.75137	−0.890174
$121$	−1.44894	−0.131722
$122$	−12.2376	−1.10794
$123$	−2.50506	−0.225874
$124$	−15.8029	−1.41914
$125$	−9.82623	−0.878885
$126$	37.7132	3.35976
$127$	10.0472	0.891548	0.445774	−	0.895146i	$-0.352929\pi$
$127$	10.0472	0.891548	0.445774	+	0.895146i	$0.352929\pi$
$128$	19.9630	1.76450
$129$	21.0802	1.85601
$130$	−0.402500	−0.0353016
$131$	13.3062	1.16257	0.581286	−	0.813700i	$-0.302550\pi$
$131$	13.3062	1.16257	0.581286	+	0.813700i	$0.302550\pi$
$132$	27.3025	2.37637
$133$	0.378939	0.0328582
$134$	10.5950	0.915270
$135$	1.60575	0.138201
$136$	1.08173	0.0927577
$137$	−3.03787	−0.259543	−0.129772	−	0.991544i	$-0.541424\pi$
$137$	−3.03787	−0.259543	−0.129772	+	0.991544i	$0.541424\pi$
$138$	5.97807	0.508887
$139$	−3.17771	−0.269530	−0.134765	−	0.990878i	$-0.543028\pi$
$139$	−3.17771	−0.269530	−0.134765	+	0.990878i	$0.543028\pi$
$140$	−17.6252	−1.48960
$141$	−18.3709	−1.54711
$142$	13.0314	1.09357
$143$	0.473631	0.0396070
$144$	3.56513	0.297094
$145$	−0.928775	−0.0771305
$146$	7.36985	0.609933
$147$	34.8828	2.87709
$148$	32.4912	2.67076
$149$	−6.26153	−0.512965	−0.256482	−	0.966549i	$-0.582564\pi$
$149$	−6.26153	−0.512965	−0.256482	+	0.966549i	$0.582564\pi$
$150$	22.3242	1.82276
$151$	−2.01964	−0.164356	−0.0821779	−	0.996618i	$-0.526188\pi$
$151$	−2.01964	−0.164356	−0.0821779	+	0.996618i	$0.526188\pi$
$152$	0.282453	0.0229100
$153$	−1.13686	−0.0919095
$154$	32.7634	2.64015
$155$	−5.15326	−0.413919
$156$	1.35391	0.108400
$157$	−7.55860	−0.603242	−0.301621	−	0.953428i	$-0.597528\pi$
$157$	−7.55860	−0.603242	−0.301621	+	0.953428i	$0.597528\pi$
$158$	2.00808	0.159754
$159$	−4.23421	−0.335795
$160$	4.98399	0.394019
$161$	4.54116	0.357894
$162$	16.3816	1.28706
$163$	−12.9950	−1.01784	−0.508922	−	0.860812i	$-0.669956\pi$
$163$	−12.9950	−1.01784	−0.508922	+	0.860812i	$0.669956\pi$
$164$	−3.37492	−0.263537
$165$	8.90323	0.693115
$166$	10.7304	0.832841
$167$	21.8177	1.68830	0.844151	−	0.536105i	$-0.180105\pi$
$167$	21.8177	1.68830	0.844151	+	0.536105i	$0.180105\pi$
$168$	39.3619	3.03684
$169$	−12.9765	−0.998193
$170$	0.839320	0.0643729
$171$	−0.296847	−0.0227005
$172$	28.4002	2.16549
$173$	−24.9931	−1.90019	−0.950094	−	0.311965i	$-0.899013\pi$
$173$	−24.9931	−1.90019	−0.950094	+	0.311965i	$0.899013\pi$
$174$	4.93531	0.374145
$175$	16.9583	1.28193
$176$	3.09721	0.233461
$177$	−37.3225	−2.80533
$178$	−8.92244	−0.668765
$179$	20.7487	1.55083	0.775416	−	0.631450i	$-0.217540\pi$
$179$	20.7487	1.55083	0.775416	+	0.631450i	$0.217540\pi$
$180$	13.8070	1.02911
$181$	−19.7964	−1.47145	−0.735727	−	0.677278i	$-0.763159\pi$
$181$	−19.7964	−1.47145	−0.735727	+	0.677278i	$0.763159\pi$
$182$	1.62471	0.120432
$183$	13.4235	0.992294
$184$	3.38489	0.249537
$185$	10.5953	0.778979
$186$	27.3833	2.00784
$187$	−0.987645	−0.0722238
$188$	−24.7500	−1.80508
$189$	−6.48169	−0.471474
$190$	0.219157	0.0158993
$191$	9.53645	0.690033	0.345017	−	0.938597i	$-0.387873\pi$
$191$	9.53645	0.690033	0.345017	+	0.938597i	$0.387873\pi$
$192$	−31.6165	−2.28173
$193$	0.632857	0.0455541	0.0227770	−	0.999741i	$-0.492749\pi$
$193$	0.632857	0.0455541	0.0227770	+	0.999741i	$0.492749\pi$
$194$	−1.79712	−0.129025
$195$	0.441505	0.0316169
$196$	46.9956	3.35683
$197$	−20.5595	−1.46481	−0.732403	−	0.680871i	$-0.761601\pi$
$197$	−20.5595	−1.46481	−0.732403	+	0.680871i	$0.761601\pi$
$198$	−25.6656	−1.82398
$199$	−17.3037	−1.22663	−0.613313	−	0.789840i	$-0.710164\pi$
$199$	−17.3037	−1.22663	−0.613313	+	0.789840i	$0.710164\pi$
$200$	12.6404	0.893808
$201$	−11.6217	−0.819734
$202$	6.30237	0.443433
$203$	3.74905	0.263132
$204$	−2.82326	−0.197668
$205$	−1.10055	−0.0768657
$206$	−3.69003	−0.257097
$207$	−3.55739	−0.247255
$208$	0.153589	0.0106495
$209$	−0.257886	−0.0178384
$210$	30.5411	2.10754
$211$	−7.17893	−0.494218	−0.247109	−	0.968988i	$-0.579481\pi$
$211$	−7.17893	−0.494218	−0.247109	+	0.968988i	$0.579481\pi$
$212$	−5.70451	−0.391787
$213$	−14.2942	−0.979424
$214$	−14.0895	−0.963138
$215$	9.26119	0.631608
$216$	−4.83131	−0.328729
$217$	20.8014	1.41209
$218$	−11.0261	−0.746782
$219$	−8.08404	−0.546269
$220$	11.9948	0.808689
$221$	−0.0489767	−0.00329453
$222$	−56.3010	−3.77867
$223$	4.59129	0.307456	0.153728	−	0.988113i	$-0.450872\pi$
$223$	4.59129	0.307456	0.153728	+	0.988113i	$0.450872\pi$
$224$	−20.1182	−1.34420
$225$	−13.2845	−0.885635
$226$	31.1174	2.06990
$227$	−9.45958	−0.627855	−0.313927	−	0.949447i	$-0.601645\pi$
$227$	−9.45958	−0.627855	−0.313927	+	0.949447i	$0.601645\pi$
$228$	−0.737189	−0.0488215
$229$	−22.1728	−1.46522	−0.732609	−	0.680649i	$-0.761698\pi$
$229$	−22.1728	−1.46522	−0.732609	+	0.680649i	$0.761698\pi$
$230$	2.62635	0.173176
$231$	−35.9384	−2.36457
$232$	2.79446	0.183465
$233$	10.3516	0.678157	0.339079	−	0.940758i	$-0.389885\pi$
$233$	10.3516	0.678157	0.339079	+	0.940758i	$0.389885\pi$
$234$	−1.27274	−0.0832018
$235$	−8.07089	−0.526487
$236$	−50.2824	−3.27310
$237$	−2.20267	−0.143079
$238$	−3.38796	−0.219609
$239$	3.13312	0.202665	0.101332	−	0.994853i	$-0.467689\pi$
$239$	3.13312	0.202665	0.101332	+	0.994853i	$0.467689\pi$
$240$	2.88713	0.186364
$241$	0.228526	0.0147207	0.00736033	−	0.999973i	$-0.497657\pi$
$241$	0.228526	0.0147207	0.00736033	+	0.999973i	$0.497657\pi$
$242$	3.38258	0.217440
$243$	−22.2511	−1.42741
$244$	18.0847	1.15775
$245$	15.3251	0.979083
$246$	5.84809	0.372860
$247$	−0.0127884	−0.000813707 0
$248$	15.5049	0.984563
$249$	−11.7703	−0.745909
$250$	22.9394	1.45082
$251$	16.6504	1.05096	0.525481	−	0.850805i	$-0.323885\pi$
$251$	16.6504	1.05096	0.525481	+	0.850805i	$0.323885\pi$
$252$	−55.7325	−3.51082
$253$	−3.09048	−0.194297
$254$	−23.4554	−1.47172
$255$	−0.920656	−0.0576537
$256$	−21.9105	−1.36941
$257$	−2.85520	−0.178102	−0.0890512	−	0.996027i	$-0.528383\pi$
$257$	−2.85520	−0.178102	−0.0890512	+	0.996027i	$0.528383\pi$
$258$	−49.2120	−3.06381
$259$	−42.7683	−2.65749
$260$	0.594814	0.0368888
$261$	−2.93687	−0.181788
$262$	−31.0635	−1.91911
$263$	−11.8941	−0.733420	−0.366710	−	0.930335i	$-0.619516\pi$
$263$	−11.8941	−0.733420	−0.366710	+	0.930335i	$0.619516\pi$
$264$	−26.7877	−1.64867
$265$	−1.86022	−0.114272
$266$	−0.884637	−0.0542406
$267$	9.78709	0.598960
$268$	−15.6573	−0.956421
$269$	21.9589	1.33885	0.669427	−	0.742877i	$-0.266539\pi$
$269$	21.9589	1.33885	0.669427	+	0.742877i	$0.266539\pi$
$270$	−3.74864	−0.228135
$271$	−1.39177	−0.0845438	−0.0422719	−	0.999106i	$-0.513460\pi$
$271$	−1.39177	−0.0845438	−0.0422719	+	0.999106i	$0.513460\pi$
$272$	−0.320273	−0.0194194
$273$	−1.78216	−0.107861
$274$	7.09194	0.428440
$275$	−11.5409	−0.695944
$276$	−8.83438	−0.531767
$277$	−4.05948	−0.243911	−0.121955	−	0.992536i	$-0.538916\pi$
$277$	−4.05948	−0.243911	−0.121955	+	0.992536i	$0.538916\pi$
$278$	7.41839	0.444925
$279$	−16.2951	−0.975560
$280$	17.2929	1.03345
$281$	17.8855	1.06696	0.533479	−	0.845813i	$-0.320884\pi$
$281$	17.8855	1.06696	0.533479	+	0.845813i	$0.320884\pi$
$282$	42.8870	2.55389
$283$	9.59338	0.570267	0.285134	−	0.958488i	$-0.407962\pi$
$283$	9.59338	0.570267	0.285134	+	0.958488i	$0.407962\pi$
$284$	−19.2578	−1.14274
$285$	−0.240394	−0.0142397
$286$	−1.10570	−0.0653812
$287$	4.44242	0.262228
$288$	15.7598	0.928658
$289$	−16.8979	−0.993992
$290$	2.16823	0.127323
$291$	1.97127	0.115558
$292$	−10.8911	−0.637356
$293$	−32.6952	−1.91008	−0.955038	−	0.296482i	$-0.904186\pi$
$293$	−32.6952	−1.91008	−0.955038	+	0.296482i	$0.904186\pi$
$294$	−81.4342	−4.74934
$295$	−16.3969	−0.954664
$296$	−31.8786	−1.85290
$297$	4.41110	0.255958
$298$	14.6176	0.846775
$299$	−0.153255	−0.00886296
$300$	−32.9907	−1.90472
$301$	−37.3833	−2.15474
$302$	4.71486	0.271310
$303$	−6.91311	−0.397148
$304$	−0.0836271	−0.00479635
$305$	5.89735	0.337681
$306$	2.65401	0.151719
$307$	10.4406	0.595875	0.297938	−	0.954585i	$-0.403701\pi$
$307$	10.4406	0.595875	0.297938	+	0.954585i	$0.403701\pi$
$308$	−48.4176	−2.75885
$309$	4.04762	0.230261
$310$	12.0303	0.683276
$311$	−2.63083	−0.149181	−0.0745904	−	0.997214i	$-0.523765\pi$
$311$	−2.63083	−0.149181	−0.0745904	+	0.997214i	$0.523765\pi$
$312$	−1.32838	−0.0752049
$313$	−4.63941	−0.262235	−0.131118	−	0.991367i	$-0.541857\pi$
$313$	−4.63941	−0.262235	−0.131118	+	0.991367i	$0.541857\pi$
$314$	17.6456	0.995800
$315$	−18.1742	−1.02400
$316$	−2.96753	−0.166937
$317$	13.9787	0.785122	0.392561	−	0.919726i	$-0.371589\pi$
$317$	13.9787	0.785122	0.392561	+	0.919726i	$0.371589\pi$
$318$	9.88481	0.554313
$319$	−2.55141	−0.142851
$320$	−13.8901	−0.776480
$321$	15.4549	0.862606
$322$	−10.6014	−0.590792
$323$	0.0266672	0.00148380
$324$	−24.2088	−1.34493
$325$	−0.572308	−0.0317459
$326$	30.3369	1.68020
$327$	12.0946	0.668834
$328$	3.31129	0.182835
$329$	32.5786	1.79612
$330$	−20.7847	−1.14416
$331$	25.1177	1.38060	0.690298	−	0.723525i	$-0.257479\pi$
$331$	25.1177	1.38060	0.690298	+	0.723525i	$0.257479\pi$
$332$	−15.8574	−0.870286
$333$	33.5032	1.83596
$334$	−50.9336	−2.78696
$335$	−5.10578	−0.278959
$336$	−11.6541	−0.635781
$337$	−5.62271	−0.306288	−0.153144	−	0.988204i	$-0.548940\pi$
$337$	−5.62271	−0.306288	−0.153144	+	0.988204i	$0.548940\pi$
$338$	30.2938	1.64777
$339$	−34.1329	−1.85384
$340$	−1.24035	−0.0672672
$341$	−14.1563	−0.766609
$342$	0.692993	0.0374728
$343$	−30.0723	−1.62375
$344$	−27.8647	−1.50236
$345$	−2.88086	−0.155100
$346$	58.3465	3.13673
$347$	−8.52659	−0.457731	−0.228866	−	0.973458i	$-0.573502\pi$
$347$	−8.52659	−0.457731	−0.228866	+	0.973458i	$0.573502\pi$
$348$	−7.29340	−0.390967
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−39.5893	−2.11614
$351$	0.218744	0.0116757
$352$	13.6914	0.729752
$353$	−6.21291	−0.330680	−0.165340	−	0.986237i	$-0.552872\pi$
$353$	−6.21291	−0.330680	−0.165340	+	0.986237i	$0.552872\pi$
$354$	87.1296	4.63089
$355$	−6.27988	−0.333302
$356$	13.1856	0.698834
$357$	3.71628	0.196686
$358$	−48.4381	−2.56003
$359$	−23.9263	−1.26278	−0.631390	−	0.775465i	$-0.717515\pi$
$359$	−23.9263	−1.26278	−0.631390	+	0.775465i	$0.717515\pi$
$360$	−13.5466	−0.713970
$361$	−18.9930	−0.999634
$362$	46.2149	2.42900
$363$	−3.71037	−0.194744
$364$	−2.40100	−0.125847
$365$	−3.55156	−0.185897
$366$	−31.3373	−1.63803
$367$	19.7166	1.02920	0.514600	−	0.857430i	$-0.327940\pi$
$367$	19.7166	1.02920	0.514600	+	0.857430i	$0.327940\pi$
$368$	−1.00218	−0.0522421
$369$	−3.48004	−0.181163
$370$	−24.7347	−1.28590
$371$	7.50887	0.389841
$372$	−40.4670	−2.09812
$373$	−32.7035	−1.69332	−0.846661	−	0.532133i	$-0.821391\pi$
$373$	−32.7035	−1.69332	−0.846661	+	0.532133i	$0.821391\pi$
$374$	2.30567	0.119223
$375$	−25.1624	−1.29938
$376$	24.2834	1.25232
$377$	−0.126523	−0.00651625
$378$	15.1316	0.778284
$379$	22.8697	1.17474	0.587368	−	0.809320i	$-0.300164\pi$
$379$	22.8697	1.17474	0.587368	+	0.809320i	$0.300164\pi$
$380$	−0.323869	−0.0166141
$381$	25.7283	1.31810
$382$	−22.2629	−1.13907
$383$	−34.2676	−1.75099	−0.875495	−	0.483226i	$-0.839465\pi$
$383$	−34.2676	−1.75099	−0.875495	+	0.483226i	$0.839465\pi$
$384$	51.1201	2.60871
$385$	−15.7888	−0.804672
$386$	−1.47741	−0.0751983
$387$	29.2847	1.48863
$388$	2.65577	0.134827
$389$	−0.536671	−0.0272103	−0.0136051	−	0.999907i	$-0.504331\pi$
$389$	−0.536671	−0.0272103	−0.0136051	+	0.999907i	$0.504331\pi$
$390$	−1.03070	−0.0521915
$391$	0.319577	0.0161617
$392$	−46.1095	−2.32888
$393$	34.0738	1.71880
$394$	47.9964	2.41802
$395$	−0.967701	−0.0486903
$396$	37.9287	1.90599
$397$	−21.2566	−1.06684	−0.533418	−	0.845852i	$-0.679093\pi$
$397$	−21.2566	−1.06684	−0.533418	+	0.845852i	$0.679093\pi$
$398$	40.3956	2.02485
$399$	0.970365	0.0485790
$400$	−3.74248	−0.187124
$401$	21.5928	1.07829	0.539146	−	0.842212i	$-0.318747\pi$
$401$	21.5928	1.07829	0.539146	+	0.842212i	$0.318747\pi$
$402$	27.1311	1.35317
$403$	−0.702004	−0.0349693
$404$	−9.31363	−0.463370
$405$	−7.89438	−0.392275
$406$	−8.75219	−0.434364
$407$	29.1059	1.44272
$408$	2.77003	0.137137
$409$	−30.5020	−1.50823	−0.754114	−	0.656743i	$-0.771933\pi$
$409$	−30.5020	−1.50823	−0.754114	+	0.656743i	$0.771933\pi$
$410$	2.56924	0.126886
$411$	−7.77920	−0.383720
$412$	5.45313	0.268656
$413$	66.1869	3.25684
$414$	8.30475	0.408156
$415$	−5.17103	−0.253836
$416$	0.678946	0.0332881
$417$	−8.13728	−0.398484
$418$	0.602038	0.0294466
$419$	−12.0352	−0.587956	−0.293978	−	0.955812i	$-0.594979\pi$
$419$	−12.0352	−0.587956	−0.293978	+	0.955812i	$0.594979\pi$
$420$	−45.1336	−2.20229
$421$	−1.27221	−0.0620038	−0.0310019	−	0.999519i	$-0.509870\pi$
$421$	−1.27221	−0.0620038	−0.0310019	+	0.999519i	$0.509870\pi$
$422$	16.7593	0.815829
$423$	−25.5209	−1.24087
$424$	5.59695	0.271812
$425$	1.19341	0.0578890
$426$	33.3700	1.61678
$427$	−23.8050	−1.15200
$428$	20.8214	1.00644
$429$	1.21285	0.0585567
$430$	−21.6203	−1.04262
$431$	−4.64634	−0.223806	−0.111903	−	0.993719i	$-0.535695\pi$
$431$	−4.64634	−0.223806	−0.111903	+	0.993719i	$0.535695\pi$
$432$	1.43043	0.0688215
$433$	−35.4138	−1.70188	−0.850940	−	0.525264i	$-0.823967\pi$
$433$	−35.4138	−1.70188	−0.850940	+	0.525264i	$0.823967\pi$
$434$	−48.5610	−2.33100
$435$	−2.37835	−0.114033
$436$	16.2944	0.780359
$437$	0.0834454	0.00399174
$438$	18.8723	0.901751
$439$	21.9764	1.04888	0.524439	−	0.851448i	$-0.324275\pi$
$439$	21.9764	1.04888	0.524439	+	0.851448i	$0.324275\pi$
$440$	−11.7686	−0.561048
$441$	48.4593	2.30759
$442$	0.114337	0.00543844
$443$	−17.1169	−0.813250	−0.406625	−	0.913595i	$-0.633294\pi$
$443$	−17.1169	−0.813250	−0.406625	+	0.913595i	$0.633294\pi$
$444$	83.2015	3.94857
$445$	4.29976	0.203828
$446$	−10.7184	−0.507532
$447$	−16.0342	−0.758389
$448$	56.0681	2.64897
$449$	6.19173	0.292206	0.146103	−	0.989269i	$-0.453327\pi$
$449$	6.19173	0.292206	0.146103	+	0.989269i	$0.453327\pi$
$450$	31.0129	1.46196
$451$	−3.02328	−0.142361
$452$	−45.9852	−2.16296
$453$	−5.17177	−0.242991
$454$	22.0835	1.03643
$455$	−0.782957	−0.0367056
$456$	0.723289	0.0338711
$457$	0.604449	0.0282749	0.0141375	−	0.999900i	$-0.495500\pi$
$457$	0.604449	0.0282749	0.0141375	+	0.999900i	$0.495500\pi$
$458$	51.7626	2.41871
$459$	−0.456138	−0.0212907
$460$	−3.88121	−0.180962
$461$	27.4474	1.27835	0.639176	−	0.769060i	$-0.279275\pi$
$461$	27.4474	1.27835	0.639176	+	0.769060i	$0.279275\pi$
$462$	83.8984	3.90331
$463$	−24.0060	−1.11565	−0.557826	−	0.829958i	$-0.688365\pi$
$463$	−24.0060	−1.11565	−0.557826	+	0.829958i	$0.688365\pi$
$464$	−0.827368	−0.0384096
$465$	−13.1961	−0.611956
$466$	−24.1660	−1.11947
$467$	8.28812	0.383529	0.191764	−	0.981441i	$-0.438579\pi$
$467$	8.28812	0.383529	0.191764	+	0.981441i	$0.438579\pi$
$468$	1.88086	0.0869427
$469$	20.6098	0.951670
$470$	18.8416	0.869097
$471$	−19.3556	−0.891859
$472$	49.3343	2.27079
$473$	25.4411	1.16978
$474$	5.14216	0.236187
$475$	0.311615	0.0142979
$476$	5.00672	0.229483
$477$	−5.88218	−0.269327
$478$	−7.31430	−0.334548
$479$	17.2816	0.789619	0.394809	−	0.918763i	$-0.370811\pi$
$479$	17.2816	0.789619	0.394809	+	0.918763i	$0.370811\pi$
$480$	12.7627	0.582535
$481$	1.44334	0.0658107
$482$	−0.533496	−0.0243001
$483$	11.6287	0.529126
$484$	−4.99876	−0.227217
$485$	0.866038	0.0393247
$486$	51.9454	2.35629
$487$	−11.0341	−0.500001	−0.250000	−	0.968246i	$-0.580431\pi$
$487$	−11.0341	−0.500001	−0.250000	+	0.968246i	$0.580431\pi$
$488$	−17.7437	−0.803220
$489$	−33.2767	−1.50483
$490$	−35.7765	−1.61622
$491$	−10.3214	−0.465797	−0.232898	−	0.972501i	$-0.574821\pi$
$491$	−10.3214	−0.465797	−0.232898	+	0.972501i	$0.574821\pi$
$492$	−8.64229	−0.389625
$493$	0.263833	0.0118824
$494$	0.0298547	0.00134323
$495$	12.3684	0.555918
$496$	−4.59061	−0.206124
$497$	25.3491	1.13706
$498$	27.4778	1.23131
$499$	−4.47196	−0.200192	−0.100096	−	0.994978i	$-0.531915\pi$
$499$	−4.47196	−0.200192	−0.100096	+	0.994978i	$0.531915\pi$
$500$	−33.8999	−1.51605
$501$	55.8694	2.49606
$502$	−38.8704	−1.73487
$503$	−17.0138	−0.758609	−0.379304	−	0.925272i	$-0.623837\pi$
$503$	−17.0138	−0.758609	−0.379304	+	0.925272i	$0.623837\pi$
$504$	54.6817	2.43572
$505$	−3.03714	−0.135151
$506$	7.21475	0.320735
$507$	−33.2295	−1.47577
$508$	34.6623	1.53789
$509$	−3.44603	−0.152743	−0.0763714	−	0.997079i	$-0.524333\pi$
$509$	−3.44603	−0.152743	−0.0763714	+	0.997079i	$0.524333\pi$
$510$	2.14928	0.0951717
$511$	14.3361	0.634190
$512$	11.2243	0.496050
$513$	−0.119103	−0.00525854
$514$	6.66549	0.294002
$515$	1.77824	0.0783588
$516$	72.7254	3.20156
$517$	−22.1713	−0.975092
$518$	99.8430	4.38685
$519$	−64.0007	−2.80932
$520$	−0.583599	−0.0255925
$521$	38.1650	1.67204	0.836019	−	0.548700i	$-0.184877\pi$
$521$	38.1650	1.67204	0.836019	+	0.548700i	$0.184877\pi$
$522$	6.85615	0.300086
$523$	−24.9547	−1.09119	−0.545596	−	0.838048i	$-0.683697\pi$
$523$	−24.9547	−1.09119	−0.545596	+	0.838048i	$0.683697\pi$
$524$	45.9056	2.00540
$525$	43.4258	1.89526
$526$	27.7668	1.21069
$527$	1.46386	0.0637669
$528$	7.93114	0.345159
$529$	1.00000	0.0434783
$530$	4.34270	0.188635
$531$	−51.8485	−2.25003
$532$	1.30732	0.0566793
$533$	−0.149923	−0.00649387
$534$	−22.8480	−0.988732
$535$	6.78978	0.293548
$536$	15.3621	0.663540
$537$	53.1321	2.29282
$538$	−51.2632	−2.21011
$539$	42.0990	1.81333
$540$	5.53973	0.238392
$541$	−12.6394	−0.543411	−0.271705	−	0.962380i	$-0.587588\pi$
$541$	−12.6394	−0.543411	−0.271705	+	0.962380i	$0.587588\pi$
$542$	3.24909	0.139561
$543$	−50.6934	−2.17546
$544$	−1.41578	−0.0607012
$545$	5.31353	0.227607
$546$	4.16047	0.178052
$547$	12.1065	0.517638	0.258819	−	0.965926i	$-0.416667\pi$
$547$	12.1065	0.517638	0.258819	+	0.965926i	$0.416667\pi$
$548$	−10.4805	−0.447703
$549$	18.6480	0.795876
$550$	26.9424	1.14883
$551$	0.0688900	0.00293481
$552$	8.66781	0.368926
$553$	3.90618	0.166107
$554$	9.47690	0.402635
$555$	27.1317	1.15168
$556$	−10.9629	−0.464930
$557$	−27.5514	−1.16739	−0.583696	−	0.811973i	$-0.698394\pi$
$557$	−27.5514	−1.16739	−0.583696	+	0.811973i	$0.698394\pi$
$558$	38.0410	1.61040
$559$	1.26161	0.0533603
$560$	−5.11998	−0.216359
$561$	−2.52910	−0.106779
$562$	−41.7538	−1.76128
$563$	3.78440	0.159493	0.0797467	−	0.996815i	$-0.474589\pi$
$563$	3.78440	0.159493	0.0797467	+	0.996815i	$0.474589\pi$
$564$	−63.3784	−2.66871
$565$	−14.9956	−0.630869
$566$	−22.3958	−0.941368
$567$	31.8661	1.33825
$568$	18.8947	0.792802
$569$	16.8678	0.707136	0.353568	−	0.935409i	$-0.384968\pi$
$569$	16.8678	0.707136	0.353568	+	0.935409i	$0.384968\pi$
$570$	0.561203	0.0235062
$571$	−3.62850	−0.151848	−0.0759241	−	0.997114i	$-0.524191\pi$
$571$	−3.62850	−0.151848	−0.0759241	+	0.997114i	$0.524191\pi$
$572$	1.63400	0.0683208
$573$	24.4204	1.02018
$574$	−10.3709	−0.432872
$575$	3.73435	0.155733
$576$	−43.9218	−1.83007
$577$	−18.6816	−0.777727	−0.388863	−	0.921295i	$-0.627132\pi$
$577$	−18.6816	−0.777727	−0.388863	+	0.921295i	$0.627132\pi$
$578$	39.4482	1.64083
$579$	1.62058	0.0673491
$580$	−3.20421	−0.133048
$581$	20.8731	0.865963
$582$	−4.60194	−0.190757
$583$	−5.11014	−0.211641
$584$	10.6858	0.442181
$585$	0.613341	0.0253585
$586$	76.3274	3.15305
$587$	26.5938	1.09764	0.548822	−	0.835939i	$-0.315077\pi$
$587$	26.5938	1.09764	0.548822	+	0.835939i	$0.315077\pi$
$588$	120.343	4.96288
$589$	0.382233	0.0157496
$590$	38.2787	1.57591
$591$	−52.6476	−2.16563
$592$	9.43843	0.387917
$593$	−8.92257	−0.366406	−0.183203	−	0.983075i	$-0.558647\pi$
$593$	−8.92257	−0.366406	−0.183203	+	0.983075i	$0.558647\pi$
$594$	−10.2978	−0.422522
$595$	1.63267	0.0669330
$596$	−21.6019	−0.884847
$597$	−44.3103	−1.81350
$598$	0.357775	0.0146305
$599$	6.14389	0.251032	0.125516	−	0.992092i	$-0.459941\pi$
$599$	6.14389	0.251032	0.125516	+	0.992092i	$0.459941\pi$
$600$	32.3686	1.32144
$601$	45.9285	1.87346	0.936732	−	0.350048i	$-0.113835\pi$
$601$	45.9285	1.87346	0.936732	+	0.350048i	$0.113835\pi$
$602$	87.2716	3.55692
$603$	−16.1450	−0.657473
$604$	−6.96762	−0.283508
$605$	−1.63008	−0.0662721
$606$	16.1387	0.655591
$607$	−25.6043	−1.03924	−0.519622	−	0.854396i	$-0.673927\pi$
$607$	−25.6043	−1.03924	−0.519622	+	0.854396i	$0.673927\pi$
$608$	−0.369678	−0.0149924
$609$	9.60033	0.389025
$610$	−13.7674	−0.557426
$611$	−1.09946	−0.0444794
$612$	−3.92209	−0.158541
$613$	17.1765	0.693753	0.346877	−	0.937911i	$-0.387242\pi$
$613$	17.1765	0.693753	0.346877	+	0.937911i	$0.387242\pi$
$614$	−24.3736	−0.983639
$615$	−2.81822	−0.113642
$616$	47.5047	1.91402
$617$	−49.6047	−1.99701	−0.998504	−	0.0546715i	$-0.982589\pi$
$617$	−49.6047	−1.99701	−0.998504	+	0.0546715i	$0.982589\pi$
$618$	−9.44921	−0.380103
$619$	−15.7187	−0.631790	−0.315895	−	0.948794i	$-0.602305\pi$
$619$	−15.7187	−0.631790	−0.315895	+	0.948794i	$0.602305\pi$
$620$	−17.7784	−0.713997
$621$	−1.42732	−0.0572763
$622$	6.14170	0.246260
$623$	−17.3562	−0.695362
$624$	0.393300	0.0157446
$625$	7.61715	0.304686
$626$	10.8308	0.432884
$627$	−0.660379	−0.0263730
$628$	−26.0767	−1.04057
$629$	−3.00975	−0.120007
$630$	42.4278	1.69036
$631$	23.1633	0.922118	0.461059	−	0.887369i	$-0.347470\pi$
$631$	23.1633	0.922118	0.461059	+	0.887369i	$0.347470\pi$
$632$	2.91158	0.115816
$633$	−18.3834	−0.730673
$634$	−32.6334	−1.29604
$635$	11.3032	0.448555
$636$	−14.6078	−0.579235
$637$	2.08766	0.0827162
$638$	5.95628	0.235811
$639$	−19.8576	−0.785553
$640$	22.4586	0.887753
$641$	19.2102	0.758757	0.379379	−	0.925241i	$-0.376138\pi$
$641$	19.2102	0.758757	0.379379	+	0.925241i	$0.376138\pi$
$642$	−36.0795	−1.42394
$643$	17.5307	0.691341	0.345671	−	0.938356i	$-0.387651\pi$
$643$	17.5307	0.691341	0.345671	+	0.938356i	$0.387651\pi$
$644$	15.6667	0.617355
$645$	23.7155	0.933796
$646$	−0.0622549	−0.00244939
$647$	−13.5795	−0.533864	−0.266932	−	0.963715i	$-0.586010\pi$
$647$	−13.5795	−0.533864	−0.266932	+	0.963715i	$0.586010\pi$
$648$	23.7523	0.933078
$649$	−45.0433	−1.76811
$650$	1.33606	0.0524045
$651$	53.2669	2.08770
$652$	−44.8318	−1.75575
$653$	−14.5539	−0.569538	−0.284769	−	0.958596i	$-0.591917\pi$
$653$	−14.5539	−0.569538	−0.284769	+	0.958596i	$0.591917\pi$
$654$	−28.2350	−1.10408
$655$	14.9697	0.584913
$656$	−0.980387	−0.0382777
$657$	−11.2304	−0.438138
$658$	−76.0550	−2.96493
$659$	44.5317	1.73471	0.867355	−	0.497690i	$-0.165818\pi$
$659$	44.5317	1.73471	0.867355	+	0.497690i	$0.165818\pi$
$660$	30.7156	1.19560
$661$	28.8353	1.12156	0.560782	−	0.827963i	$-0.310501\pi$
$661$	28.8353	1.12156	0.560782	+	0.827963i	$0.310501\pi$
$662$	−58.6376	−2.27901
$663$	−0.125417	−0.00487078
$664$	15.5584	0.603782
$665$	0.426310	0.0165316
$666$	−78.2135	−3.03071
$667$	0.825570	0.0319662
$668$	75.2695	2.91227
$669$	11.7571	0.454556
$670$	11.9195	0.460490
$671$	16.2004	0.625410
$672$	−51.5174	−1.98733
$673$	−9.25601	−0.356793	−0.178396	−	0.983959i	$-0.557091\pi$
$673$	−9.25601	−0.356793	−0.178396	+	0.983959i	$0.557091\pi$
$674$	13.1263	0.505605
$675$	−5.33011	−0.205156
$676$	−44.7681	−1.72185
$677$	18.2800	0.702559	0.351279	−	0.936271i	$-0.385747\pi$
$677$	18.2800	0.702559	0.351279	+	0.936271i	$0.385747\pi$
$678$	79.6835	3.06023
$679$	−3.49581	−0.134157
$680$	1.21696	0.0466682
$681$	−24.2235	−0.928248
$682$	33.0481	1.26548
$683$	−27.4915	−1.05193	−0.525966	−	0.850506i	$-0.676296\pi$
$683$	−27.4915	−1.05193	−0.525966	+	0.850506i	$0.676296\pi$
$684$	−1.02410	−0.0391576
$685$	−3.41764	−0.130581
$686$	70.2041	2.68041
$687$	−56.7787	−2.16624
$688$	8.25002	0.314529
$689$	−0.253409	−0.00965411
$690$	6.72539	0.256031
$691$	33.3055	1.26700	0.633501	−	0.773742i	$-0.281617\pi$
$691$	33.3055	1.26700	0.633501	+	0.773742i	$0.281617\pi$
$692$	−86.2244	−3.27776
$693$	−49.9257	−1.89652
$694$	19.9054	0.755598
$695$	−3.57495	−0.135606
$696$	7.15588	0.271243
$697$	0.312628	0.0118416
$698$	2.33451	0.0883625
$699$	26.5078	1.00262
$700$	58.5050	2.21128
$701$	−7.34683	−0.277486	−0.138743	−	0.990328i	$-0.544306\pi$
$701$	−7.34683	−0.277486	−0.138743	+	0.990328i	$0.544306\pi$
$702$	−0.510659	−0.0192736
$703$	−0.785882	−0.0296401
$704$	−38.1570	−1.43810
$705$	−20.6674	−0.778381
$706$	14.5041	0.545869
$707$	12.2596	0.461068
$708$	−128.760	−4.83910
$709$	−29.0789	−1.09208	−0.546041	−	0.837759i	$-0.683866\pi$
$709$	−29.0789	−1.09208	−0.546041	+	0.837759i	$0.683866\pi$
$710$	14.6604	0.550197
$711$	−3.05996	−0.114757
$712$	−12.9370	−0.484833
$713$	4.58063	0.171546
$714$	−8.67568	−0.324679
$715$	0.532839	0.0199271
$716$	71.5817	2.67514
$717$	8.02310	0.299628
$718$	55.8561	2.08453
$719$	28.0947	1.04776	0.523878	−	0.851793i	$-0.324485\pi$
$719$	28.0947	1.04776	0.523878	+	0.851793i	$0.324485\pi$
$720$	4.01081	0.149474
$721$	−7.17797	−0.267322
$722$	44.3394	1.65014
$723$	0.585196	0.0217637
$724$	−68.2962	−2.53821
$725$	3.08297	0.114499
$726$	8.66189	0.321473
$727$	16.4264	0.609221	0.304610	−	0.952477i	$-0.401474\pi$
$727$	16.4264	0.609221	0.304610	+	0.952477i	$0.401474\pi$
$728$	2.35573	0.0873091
$729$	−35.9277	−1.33066
$730$	8.29115	0.306869
$731$	−2.63079	−0.0973031
$732$	46.3102	1.71167
$733$	−32.5817	−1.20343	−0.601717	−	0.798709i	$-0.705516\pi$
$733$	−32.5817	−1.20343	−0.601717	+	0.798709i	$0.705516\pi$
$734$	−46.0287	−1.69895
$735$	39.2435	1.44752
$736$	−4.43018	−0.163298
$737$	−14.0259	−0.516652
$738$	8.12418	0.299055
$739$	20.4512	0.752308	0.376154	−	0.926557i	$-0.377246\pi$
$739$	20.4512	0.752308	0.376154	+	0.926557i	$0.377246\pi$
$740$	36.5529	1.34371
$741$	−0.0327478	−0.00120302
$742$	−17.5295	−0.643529
$743$	−0.322443	−0.0118293	−0.00591464	−	0.999983i	$-0.501883\pi$
$743$	−0.322443	−0.0118293	−0.00591464	+	0.999983i	$0.501883\pi$
$744$	39.7040	1.45562
$745$	−7.04429	−0.258083
$746$	76.3466	2.79525
$747$	−16.3513	−0.598261
$748$	−3.40731	−0.124584
$749$	−27.4073	−1.00144
$750$	58.7419	2.14495
$751$	20.8968	0.762536	0.381268	−	0.924464i	$-0.375487\pi$
$751$	20.8968	0.762536	0.381268	+	0.924464i	$0.375487\pi$
$752$	−7.18968	−0.262181
$753$	42.6372	1.55379
$754$	0.295368	0.0107567
$755$	−2.27211	−0.0826907
$756$	−22.3614	−0.813276
$757$	22.1902	0.806515	0.403257	−	0.915087i	$-0.367878\pi$
$757$	22.1902	0.806515	0.403257	+	0.915087i	$0.367878\pi$
$758$	−53.3894	−1.93919
$759$	−7.91391	−0.287257
$760$	0.317763	0.0115265
$761$	36.9179	1.33827	0.669136	−	0.743140i	$-0.266664\pi$
$761$	36.9179	1.33827	0.669136	+	0.743140i	$0.266664\pi$
$762$	−60.0631	−2.17586
$763$	−21.4483	−0.776482
$764$	32.9001	1.19028
$765$	−1.27898	−0.0462415
$766$	79.9980	2.89044
$767$	−2.23367	−0.0806532
$768$	−56.1072	−2.02459
$769$	30.4989	1.09982	0.549909	−	0.835225i	$-0.314663\pi$
$769$	30.4989	1.09982	0.549909	+	0.835225i	$0.314663\pi$
$770$	36.8591	1.32831
$771$	−7.31142	−0.263314
$772$	2.18332	0.0785793
$773$	−34.6612	−1.24668	−0.623338	−	0.781952i	$-0.714224\pi$
$773$	−34.6612	−1.24668	−0.623338	+	0.781952i	$0.714224\pi$
$774$	−68.3655	−2.45735
$775$	17.1057	0.614454
$776$	−2.60570	−0.0935391
$777$	−109.518	−3.92895
$778$	1.25286	0.0449173
$779$	0.0816310	0.00292474
$780$	1.52316	0.0545380
$781$	−17.2513	−0.617299
$782$	−0.746055	−0.0266789
$783$	−1.17835	−0.0421109
$784$	13.6518	0.487565
$785$	−8.50350	−0.303503
$786$	−79.5456	−2.83730
$787$	−9.46318	−0.337326	−0.168663	−	0.985674i	$-0.553945\pi$
$787$	−9.46318	−0.337326	−0.168663	+	0.985674i	$0.553945\pi$
$788$	−70.9290	−2.52674
$789$	−30.4576	−1.08432
$790$	2.25911	0.0803754
$791$	60.5305	2.15222
$792$	−37.2135	−1.32232
$793$	0.803368	0.0285284
$794$	49.6236	1.76108
$795$	−4.76353	−0.168945
$796$	−59.6966	−2.11589
$797$	−32.5326	−1.15236	−0.576182	−	0.817321i	$-0.695458\pi$
$797$	−32.5326	−1.15236	−0.576182	+	0.817321i	$0.695458\pi$
$798$	−2.26533	−0.0801916
$799$	2.29266	0.0811086
$800$	−16.5438	−0.584913
$801$	13.5962	0.480400
$802$	−50.4086	−1.77999
$803$	−9.75638	−0.344295
$804$	−40.0942	−1.41401
$805$	5.10885	0.180063
$806$	1.63883	0.0577255
$807$	56.2309	1.97942
$808$	9.13802	0.321474
$809$	33.7717	1.18735	0.593675	−	0.804705i	$-0.297677\pi$
$809$	33.7717	1.18735	0.593675	+	0.804705i	$0.297677\pi$
$810$	18.4295	0.647547
$811$	−32.0403	−1.12509	−0.562543	−	0.826768i	$-0.690177\pi$
$811$	−32.0403	−1.12509	−0.562543	+	0.826768i	$0.690177\pi$
$812$	12.9340	0.453893
$813$	−3.56395	−0.124993
$814$	−67.9479	−2.38157
$815$	−14.6195	−0.512098
$816$	−0.820135	−0.0287105
$817$	−0.686930	−0.0240326
$818$	71.2073	2.48970
$819$	−2.47578	−0.0865108
$820$	−3.79682	−0.132591
$821$	33.9856	1.18611	0.593053	−	0.805163i	$-0.297922\pi$
$821$	33.9856	1.18611	0.593053	+	0.805163i	$0.297922\pi$
$822$	18.1606	0.633424
$823$	−41.5561	−1.44855	−0.724277	−	0.689509i	$-0.757826\pi$
$823$	−41.5561	−1.44855	−0.724277	+	0.689509i	$0.757826\pi$
$824$	−5.35031	−0.186387
$825$	−29.5533	−1.02891
$826$	−154.514	−5.37623
$827$	−54.5442	−1.89669	−0.948343	−	0.317246i	$-0.897242\pi$
$827$	−54.5442	−1.89669	−0.948343	+	0.317246i	$0.897242\pi$
$828$	−12.2727	−0.426507
$829$	−41.3119	−1.43482	−0.717411	−	0.696650i	$-0.754673\pi$
$829$	−41.3119	−1.43482	−0.717411	+	0.696650i	$0.754673\pi$
$830$	12.0718	0.419019
$831$	−10.3953	−0.360608
$832$	−1.89218	−0.0655997
$833$	−4.35333	−0.150834
$834$	18.9966	0.657797
$835$	24.5451	0.849418
$836$	−0.889690	−0.0307706
$837$	−6.53802	−0.225987
$838$	28.0962	0.970567
$839$	−9.00378	−0.310845	−0.155422	−	0.987848i	$-0.549674\pi$
$839$	−9.00378	−0.310845	−0.155422	+	0.987848i	$0.549674\pi$
$840$	44.2826	1.52789
$841$	−28.3184	−0.976498
$842$	2.96999	0.102353
$843$	45.8000	1.57744
$844$	−24.7668	−0.852510
$845$	−14.5987	−0.502211
$846$	59.5788	2.04836
$847$	6.57990	0.226088
$848$	−1.65711	−0.0569055
$849$	24.5662	0.843108
$850$	−2.78603	−0.0955602
$851$	−9.41792	−0.322842
$852$	−49.3141	−1.68947
$853$	17.5794	0.601908	0.300954	−	0.953639i	$-0.402695\pi$
$853$	17.5794	0.601908	0.300954	+	0.953639i	$0.402695\pi$
$854$	55.5729	1.90167
$855$	−0.333956	−0.0114211
$856$	−20.4288	−0.698243
$857$	47.9772	1.63887	0.819435	−	0.573172i	$-0.194287\pi$
$857$	47.9772	1.63887	0.819435	+	0.573172i	$0.194287\pi$
$858$	−2.83140	−0.0966623
$859$	14.7560	0.503467	0.251734	−	0.967797i	$-0.418999\pi$
$859$	14.7560	0.503467	0.251734	+	0.967797i	$0.418999\pi$
$860$	31.9505	1.08950
$861$	11.3759	0.387689
$862$	10.8469	0.369448
$863$	−25.2894	−0.860860	−0.430430	−	0.902624i	$-0.641638\pi$
$863$	−25.2894	−0.860860	−0.430430	+	0.902624i	$0.641638\pi$
$864$	6.32328	0.215122
$865$	−28.1174	−0.956022
$866$	82.6739	2.80937
$867$	−43.2710	−1.46956
$868$	71.7634	2.43581
$869$	−2.65834	−0.0901780
$870$	5.55228	0.188240
$871$	−0.695537	−0.0235674
$872$	−15.9871	−0.541393
$873$	2.73849	0.0926839
$874$	−0.194804	−0.00658935
$875$	44.6225	1.50852
$876$	−27.8894	−0.942295
$877$	−2.32871	−0.0786348	−0.0393174	−	0.999227i	$-0.512518\pi$
$877$	−2.32871	−0.0786348	−0.0393174	+	0.999227i	$0.512518\pi$
$878$	−51.3042	−1.73143
$879$	−83.7240	−2.82394
$880$	3.48439	0.117459
$881$	48.3506	1.62897	0.814487	−	0.580182i	$-0.197019\pi$
$881$	48.3506	1.62897	0.814487	+	0.580182i	$0.197019\pi$
$882$	−113.129	−3.80924
$883$	32.9068	1.10740	0.553701	−	0.832715i	$-0.313215\pi$
$883$	32.9068	1.10740	0.553701	+	0.832715i	$0.313215\pi$
$884$	−0.168966	−0.00568296
$885$	−41.9881	−1.41142
$886$	39.9596	1.34247
$887$	2.88989	0.0970329	0.0485165	−	0.998822i	$-0.484551\pi$
$887$	2.88989	0.0970329	0.0485165	+	0.998822i	$0.484551\pi$
$888$	−81.6327	−2.73941
$889$	−45.6261	−1.53025
$890$	−10.0378	−0.336469
$891$	−21.6864	−0.726522
$892$	15.8397	0.530351
$893$	0.598642	0.0200328
$894$	37.4319	1.25191
$895$	23.3425	0.780255
$896$	−90.6553	−3.02858
$897$	−0.392446	−0.0131034
$898$	−14.4547	−0.482358
$899$	3.78163	0.126124
$900$	−45.8308	−1.52769
$901$	0.528424	0.0176044
$902$	7.05788	0.235002
$903$	−95.7288	−3.18566
$904$	45.1181	1.50061
$905$	−22.2711	−0.740318
$906$	12.0735	0.401116
$907$	34.6403	1.15021	0.575106	−	0.818079i	$-0.304961\pi$
$907$	34.6403	1.15021	0.575106	+	0.818079i	$0.304961\pi$
$908$	−32.6349	−1.08303
$909$	−9.60371	−0.318535
$910$	1.82782	0.0605916
$911$	−44.4504	−1.47271	−0.736354	−	0.676597i	$-0.763454\pi$
$911$	−44.4504	−1.47271	−0.736354	+	0.676597i	$0.763454\pi$
$912$	−0.214147	−0.00709113
$913$	−14.2052	−0.470122
$914$	−1.41109	−0.0466748
$915$	15.1016	0.499243
$916$	−76.4946	−2.52745
$917$	−60.4258	−1.99544
$918$	1.06486	0.0351456
$919$	−37.1005	−1.22383	−0.611916	−	0.790923i	$-0.709601\pi$
$919$	−37.1005	−1.22383	−0.611916	+	0.790923i	$0.709601\pi$
$920$	3.80803	0.125547
$921$	26.7356	0.880968
$922$	−64.0762	−2.11024
$923$	−0.855479	−0.0281584
$924$	−123.985	−4.07881
$925$	−35.1698	−1.15638
$926$	56.0422	1.84166
$927$	5.62297	0.184683
$928$	−3.65742	−0.120061
$929$	6.70601	0.220017	0.110008	−	0.993931i	$-0.464912\pi$
$929$	6.70601	0.220017	0.110008	+	0.993931i	$0.464912\pi$
$930$	30.8065	1.01019
$931$	−1.13671	−0.0372541
$932$	35.7124	1.16980
$933$	−6.73687	−0.220555
$934$	−19.3487	−0.633109
$935$	−1.11111	−0.0363372
$936$	−1.84539	−0.0603186
$937$	46.4960	1.51896	0.759479	−	0.650532i	$-0.225454\pi$
$937$	46.4960	1.51896	0.759479	+	0.650532i	$0.225454\pi$
$938$	−48.1137	−1.57097
$939$	−11.8803	−0.387700
$940$	−27.8440	−0.908173
$941$	−22.4665	−0.732387	−0.366194	−	0.930539i	$-0.619339\pi$
$941$	−22.4665	−0.732387	−0.366194	+	0.930539i	$0.619339\pi$
$942$	45.1858	1.47223
$943$	0.978257	0.0318564
$944$	−14.6066	−0.475405
$945$	−7.29197	−0.237208
$946$	−59.3925	−1.93102
$947$	11.7964	0.383331	0.191665	−	0.981460i	$-0.438611\pi$
$947$	11.7964	0.383331	0.191665	+	0.981460i	$0.438611\pi$
$948$	−7.59908	−0.246807
$949$	−0.483813	−0.0157052
$950$	−0.727467	−0.0236021
$951$	35.7958	1.16076
$952$	−4.91232	−0.159209
$953$	−14.4475	−0.467999	−0.234000	−	0.972237i	$-0.575181\pi$
$953$	−14.4475	−0.467999	−0.234000	+	0.972237i	$0.575181\pi$
$954$	13.7320	0.444590
$955$	10.7286	0.347170
$956$	10.8091	0.349590
$957$	−6.53349	−0.211198
$958$	−40.3442	−1.30346
$959$	13.7955	0.445479
$960$	−35.5689	−1.14798
$961$	−10.0178	−0.323156
$962$	−3.36950	−0.108637
$963$	21.4699	0.691859
$964$	0.788400	0.0253927
$965$	0.711971	0.0229192
$966$	−27.1474	−0.873453
$967$	5.10961	0.164314	0.0821570	−	0.996619i	$-0.473819\pi$
$967$	5.10961	0.164314	0.0821570	+	0.996619i	$0.473819\pi$
$968$	4.90451	0.157637
$969$	0.0682878	0.00219372
$970$	−2.02177	−0.0649152
$971$	−52.2438	−1.67658	−0.838292	−	0.545221i	$-0.816446\pi$
$971$	−52.2438	−1.67658	−0.838292	+	0.545221i	$0.816446\pi$
$972$	−76.7648	−2.46223
$973$	14.4305	0.462620
$974$	25.7591	0.825375
$975$	−1.46553	−0.0469345
$976$	5.25346	0.168159
$977$	−5.00226	−0.160036	−0.0800182	−	0.996793i	$-0.525498\pi$
$977$	−5.00226	−0.160036	−0.0800182	+	0.996793i	$0.525498\pi$
$978$	77.6849	2.48409
$979$	11.8117	0.377505
$980$	52.8705	1.68889
$981$	16.8019	0.536442
$982$	24.0953	0.768913
$983$	2.83315	0.0903635	0.0451817	−	0.998979i	$-0.485613\pi$
$983$	2.83315	0.0903635	0.0451817	+	0.998979i	$0.485613\pi$
$984$	8.47934	0.270312
$985$	−23.1297	−0.736973
$986$	−0.615921	−0.0196149
$987$	83.4253	2.65546
$988$	−0.0441192	−0.00140362
$989$	−8.23209	−0.261765
$990$	−28.8741	−0.917680
$991$	5.85782	0.186080	0.0930399	−	0.995662i	$-0.470342\pi$
$991$	5.85782	0.186080	0.0930399	+	0.995662i	$0.470342\pi$
$992$	−20.2930	−0.644303
$993$	64.3200	2.04113
$994$	−59.1777	−1.87700
$995$	−19.4668	−0.617140
$996$	−40.6066	−1.28667
$997$	53.6948	1.70053	0.850266	−	0.526353i	$-0.176441\pi$
$997$	53.6948	1.70053	0.850266	+	0.526353i	$0.176441\pi$
$998$	10.4398	0.330467
$999$	13.4424	0.425298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.d.1.15	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.d.1.15	✓	149	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33451 q^{2} +2.56074 q^{3} +3.44993 q^{4} +1.12501 q^{5} -5.97807 q^{6} -4.54116 q^{7} -3.38489 q^{8} +3.55739 q^{9} +O(q^{10})\)	\(q-2.33451 q^{2} +2.56074 q^{3} +3.44993 q^{4} +1.12501 q^{5} -5.97807 q^{6} -4.54116 q^{7} -3.38489 q^{8} +3.55739 q^{9} -2.62635 q^{10} +3.09048 q^{11} +8.83438 q^{12} +0.153255 q^{13} +10.6014 q^{14} +2.88086 q^{15} +1.00218 q^{16} -0.319577 q^{17} -8.30475 q^{18} -0.0834454 q^{19} +3.88121 q^{20} -11.6287 q^{21} -7.21475 q^{22} -1.00000 q^{23} -8.66781 q^{24} -3.73435 q^{25} -0.357775 q^{26} +1.42732 q^{27} -15.6667 q^{28} -0.825570 q^{29} -6.72539 q^{30} -4.58063 q^{31} +4.43018 q^{32} +7.91391 q^{33} +0.746055 q^{34} -5.10885 q^{35} +12.2727 q^{36} +9.41792 q^{37} +0.194804 q^{38} +0.392446 q^{39} -3.80803 q^{40} -0.978257 q^{41} +27.1474 q^{42} +8.23209 q^{43} +10.6619 q^{44} +4.00209 q^{45} +2.33451 q^{46} -7.17406 q^{47} +2.56632 q^{48} +13.6222 q^{49} +8.71788 q^{50} -0.818353 q^{51} +0.528719 q^{52} -1.65351 q^{53} -3.33209 q^{54} +3.47682 q^{55} +15.3713 q^{56} -0.213682 q^{57} +1.92730 q^{58} -14.5749 q^{59} +9.93877 q^{60} +5.24204 q^{61} +10.6935 q^{62} -16.1547 q^{63} -12.3466 q^{64} +0.172413 q^{65} -18.4751 q^{66} -4.53843 q^{67} -1.10252 q^{68} -2.56074 q^{69} +11.9267 q^{70} -5.58207 q^{71} -12.0413 q^{72} -3.15692 q^{73} -21.9862 q^{74} -9.56270 q^{75} -0.287881 q^{76} -14.0344 q^{77} -0.916168 q^{78} -0.860171 q^{79} +1.12746 q^{80} -7.01716 q^{81} +2.28375 q^{82} -4.59643 q^{83} -40.1184 q^{84} -0.359527 q^{85} -19.2179 q^{86} -2.11407 q^{87} -10.4609 q^{88} +3.82198 q^{89} -9.34293 q^{90} -0.695955 q^{91} -3.44993 q^{92} -11.7298 q^{93} +16.7479 q^{94} -0.0938769 q^{95} +11.3445 q^{96} +0.769804 q^{97} -31.8011 q^{98} +10.9940 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * q^99

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