LMFDB - Embedded newform 8017.2.a.a.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, 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("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$1$
Dimension:	$327$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58656 q^{2} +2.73680 q^{3} +4.69031 q^{4} +2.52723 q^{5} -7.07890 q^{6} -4.80679 q^{7} -6.95866 q^{8} +4.49006 q^{9} +O(q^{10})$	\(q-2.58656 q^{2} +2.73680 q^{3} +4.69031 q^{4} +2.52723 q^{5} -7.07890 q^{6} -4.80679 q^{7} -6.95866 q^{8} +4.49006 q^{9} -6.53684 q^{10} +4.35336 q^{11} +12.8364 q^{12} -1.66896 q^{13} +12.4331 q^{14} +6.91651 q^{15} +8.61840 q^{16} -6.78846 q^{17} -11.6138 q^{18} -2.24343 q^{19} +11.8535 q^{20} -13.1552 q^{21} -11.2602 q^{22} -0.637815 q^{23} -19.0444 q^{24} +1.38689 q^{25} +4.31688 q^{26} +4.07798 q^{27} -22.5454 q^{28} +7.24462 q^{29} -17.8900 q^{30} -5.40552 q^{31} -8.37472 q^{32} +11.9143 q^{33} +17.5588 q^{34} -12.1479 q^{35} +21.0598 q^{36} +2.87340 q^{37} +5.80278 q^{38} -4.56761 q^{39} -17.5861 q^{40} +0.103084 q^{41} +34.0268 q^{42} -7.97611 q^{43} +20.4186 q^{44} +11.3474 q^{45} +1.64975 q^{46} +12.4745 q^{47} +23.5868 q^{48} +16.1053 q^{49} -3.58727 q^{50} -18.5786 q^{51} -7.82796 q^{52} -6.27612 q^{53} -10.5480 q^{54} +11.0019 q^{55} +33.4489 q^{56} -6.13981 q^{57} -18.7387 q^{58} +4.99658 q^{59} +32.4406 q^{60} -9.39004 q^{61} +13.9817 q^{62} -21.5828 q^{63} +4.42494 q^{64} -4.21785 q^{65} -30.8170 q^{66} -14.3093 q^{67} -31.8400 q^{68} -1.74557 q^{69} +31.4212 q^{70} -10.2612 q^{71} -31.2448 q^{72} +3.51906 q^{73} -7.43223 q^{74} +3.79563 q^{75} -10.5224 q^{76} -20.9257 q^{77} +11.8144 q^{78} +3.88025 q^{79} +21.7807 q^{80} -2.30957 q^{81} -0.266633 q^{82} -17.9932 q^{83} -61.7021 q^{84} -17.1560 q^{85} +20.6307 q^{86} +19.8271 q^{87} -30.2936 q^{88} +15.7898 q^{89} -29.3508 q^{90} +8.02236 q^{91} -2.99155 q^{92} -14.7938 q^{93} -32.2661 q^{94} -5.66966 q^{95} -22.9199 q^{96} -6.31630 q^{97} -41.6573 q^{98} +19.5468 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) $ 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * 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 $

$2$	−2.58656	−1.82898	−0.914488	−	0.404612i	$-0.867407\pi$
$2$	−2.58656	−1.82898	−0.914488	+	0.404612i	$0.867407\pi$
$3$	2.73680	1.58009	0.790045	−	0.613049i	$-0.210057\pi$
$3$	2.73680	1.58009	0.790045	+	0.613049i	$0.210057\pi$
$4$	4.69031	2.34516
$5$	2.52723	1.13021	0.565106	−	0.825019i	$-0.308835\pi$
$5$	2.52723	1.13021	0.565106	+	0.825019i	$0.308835\pi$
$6$	−7.07890	−2.88995
$7$	−4.80679	−1.81680	−0.908399	−	0.418105i	$-0.862694\pi$
$7$	−4.80679	−1.81680	−0.908399	+	0.418105i	$0.862694\pi$
$8$	−6.95866	−2.46026
$9$	4.49006	1.49669
$10$	−6.53684	−2.06713
$11$	4.35336	1.31259	0.656294	−	0.754506i	$-0.272123\pi$
$11$	4.35336	1.31259	0.656294	+	0.754506i	$0.272123\pi$
$12$	12.8364	3.70556
$13$	−1.66896	−0.462887	−0.231444	−	0.972848i	$-0.574345\pi$
$13$	−1.66896	−0.462887	−0.231444	+	0.972848i	$0.574345\pi$
$14$	12.4331	3.32288
$15$	6.91651	1.78584
$16$	8.61840	2.15460
$17$	−6.78846	−1.64644	−0.823222	−	0.567719i	$-0.807826\pi$
$17$	−6.78846	−1.64644	−0.823222	+	0.567719i	$0.807826\pi$
$18$	−11.6138	−2.73740
$19$	−2.24343	−0.514678	−0.257339	−	0.966321i	$-0.582846\pi$
$19$	−2.24343	−0.514678	−0.257339	+	0.966321i	$0.582846\pi$
$20$	11.8535	2.65052
$21$	−13.1552	−2.87070
$22$	−11.2602	−2.40069
$23$	−0.637815	−0.132994	−0.0664968	−	0.997787i	$-0.521182\pi$
$23$	−0.637815	−0.132994	−0.0664968	+	0.997787i	$0.521182\pi$
$24$	−19.0444	−3.88743
$25$	1.38689	0.277377
$26$	4.31688	0.846610
$27$	4.07798	0.784807
$28$	−22.5454	−4.26067
$29$	7.24462	1.34529	0.672646	−	0.739964i	$-0.265158\pi$
$29$	7.24462	1.34529	0.672646	+	0.739964i	$0.265158\pi$
$30$	−17.8900	−3.26625
$31$	−5.40552	−0.970860	−0.485430	−	0.874276i	$-0.661337\pi$
$31$	−5.40552	−0.970860	−0.485430	+	0.874276i	$0.661337\pi$
$32$	−8.37472	−1.48046
$33$	11.9143	2.07401
$34$	17.5588	3.01131
$35$	−12.1479	−2.05336
$36$	21.0598	3.50996
$37$	2.87340	0.472384	0.236192	−	0.971706i	$-0.424101\pi$
$37$	2.87340	0.472384	0.236192	+	0.971706i	$0.424101\pi$
$38$	5.80278	0.941335
$39$	−4.56761	−0.731404
$40$	−17.5861	−2.78061
$41$	0.103084	0.0160990	0.00804949	−	0.999968i	$-0.497438\pi$
$41$	0.103084	0.0160990	0.00804949	+	0.999968i	$0.497438\pi$
$42$	34.0268	5.25045
$43$	−7.97611	−1.21635	−0.608173	−	0.793805i	$-0.708097\pi$
$43$	−7.97611	−1.21635	−0.608173	+	0.793805i	$0.708097\pi$
$44$	20.4186	3.07822
$45$	11.3474	1.69157
$46$	1.64975	0.243242
$47$	12.4745	1.81959	0.909796	−	0.415056i	$-0.136238\pi$
$47$	12.4745	1.81959	0.909796	+	0.415056i	$0.136238\pi$
$48$	23.5868	3.40446
$49$	16.1053	2.30075
$50$	−3.58727	−0.507317
$51$	−18.5786	−2.60153
$52$	−7.82796	−1.08554
$53$	−6.27612	−0.862092	−0.431046	−	0.902330i	$-0.641855\pi$
$53$	−6.27612	−0.862092	−0.431046	+	0.902330i	$0.641855\pi$
$54$	−10.5480	−1.43539
$55$	11.0019	1.48350
$56$	33.4489	4.46979
$57$	−6.13981	−0.813238
$58$	−18.7387	−2.46051
$59$	4.99658	0.650499	0.325250	−	0.945628i	$-0.394552\pi$
$59$	4.99658	0.650499	0.325250	+	0.945628i	$0.394552\pi$
$60$	32.4406	4.18806
$61$	−9.39004	−1.20227	−0.601136	−	0.799147i	$-0.705285\pi$
$61$	−9.39004	−1.20227	−0.601136	+	0.799147i	$0.705285\pi$
$62$	13.9817	1.77568
$63$	−21.5828	−2.71917
$64$	4.42494	0.553118
$65$	−4.21785	−0.523160
$66$	−30.8170	−3.79331
$67$	−14.3093	−1.74816	−0.874078	−	0.485785i	$-0.838534\pi$
$67$	−14.3093	−1.74816	−0.874078	+	0.485785i	$0.838534\pi$
$68$	−31.8400	−3.86117
$69$	−1.74557	−0.210142
$70$	31.4212	3.75556
$71$	−10.2612	−1.21779	−0.608893	−	0.793253i	$-0.708386\pi$
$71$	−10.2612	−1.21779	−0.608893	+	0.793253i	$0.708386\pi$
$72$	−31.2448	−3.68223
$73$	3.51906	0.411875	0.205937	−	0.978565i	$-0.433976\pi$
$73$	3.51906	0.411875	0.205937	+	0.978565i	$0.433976\pi$
$74$	−7.43223	−0.863979
$75$	3.79563	0.438281
$76$	−10.5224	−1.20700
$77$	−20.9257	−2.38470
$78$	11.8144	1.33772
$79$	3.88025	0.436562	0.218281	−	0.975886i	$-0.429955\pi$
$79$	3.88025	0.436562	0.218281	+	0.975886i	$0.429955\pi$
$80$	21.7807	2.43515
$81$	−2.30957	−0.256619
$82$	−0.266633	−0.0294447
$83$	−17.9932	−1.97502	−0.987508	−	0.157570i	$-0.949634\pi$
$83$	−17.9932	−1.97502	−0.987508	+	0.157570i	$0.949634\pi$
$84$	−61.7021	−6.73225
$85$	−17.1560	−1.86083
$86$	20.6307	2.22467
$87$	19.8271	2.12568
$88$	−30.2936	−3.22930
$89$	15.7898	1.67372	0.836859	−	0.547418i	$-0.184389\pi$
$89$	15.7898	1.67372	0.836859	+	0.547418i	$0.184389\pi$
$90$	−29.3508	−3.09384
$91$	8.02236	0.840972
$92$	−2.99155	−0.311891
$93$	−14.7938	−1.53405
$94$	−32.2661	−3.32799
$95$	−5.66966	−0.581695
$96$	−22.9199	−2.33925
$97$	−6.31630	−0.641323	−0.320662	−	0.947194i	$-0.603905\pi$
$97$	−6.31630	−0.641323	−0.320662	+	0.947194i	$0.603905\pi$
$98$	−41.6573	−4.20802
$99$	19.5468	1.96453
$100$	6.50493	0.650493
$101$	12.9588	1.28945	0.644726	−	0.764414i	$-0.276971\pi$
$101$	12.9588	1.28945	0.644726	+	0.764414i	$0.276971\pi$
$102$	48.0548	4.75814
$103$	7.29611	0.718907	0.359454	−	0.933163i	$-0.382963\pi$
$103$	7.29611	0.718907	0.359454	+	0.933163i	$0.382963\pi$
$104$	11.6138	1.13882
$105$	−33.2462	−3.24450
$106$	16.2336	1.57675
$107$	8.65597	0.836805	0.418402	−	0.908262i	$-0.362590\pi$
$107$	8.65597	0.836805	0.418402	+	0.908262i	$0.362590\pi$
$108$	19.1270	1.84050
$109$	−10.1037	−0.967759	−0.483879	−	0.875135i	$-0.660773\pi$
$109$	−10.1037	−0.967759	−0.483879	+	0.875135i	$0.660773\pi$
$110$	−28.4572	−2.71329
$111$	7.86391	0.746409
$112$	−41.4269	−3.91447
$113$	9.35925	0.880444	0.440222	−	0.897889i	$-0.354900\pi$
$113$	9.35925	0.880444	0.440222	+	0.897889i	$0.354900\pi$
$114$	15.8810	1.48739
$115$	−1.61190	−0.150311
$116$	33.9795	3.15492
$117$	−7.49374	−0.692797
$118$	−12.9240	−1.18975
$119$	32.6307	2.99126
$120$	−48.1297	−4.39362
$121$	7.95173	0.722885
$122$	24.2879	2.19893
$123$	0.282119	0.0254378
$124$	−25.3536	−2.27682
$125$	−9.13116	−0.816716
$126$	55.8252	4.97330
$127$	−2.96487	−0.263089	−0.131545	−	0.991310i	$-0.541994\pi$
$127$	−2.96487	−0.263089	−0.131545	+	0.991310i	$0.541994\pi$
$128$	5.30404	0.468816
$129$	−21.8290	−1.92194
$130$	10.9097	0.956848
$131$	−5.32515	−0.465260	−0.232630	−	0.972565i	$-0.574733\pi$
$131$	−5.32515	−0.465260	−0.232630	+	0.972565i	$0.574733\pi$
$132$	55.8816	4.86387
$133$	10.7837	0.935066
$134$	37.0119	3.19734
$135$	10.3060	0.886998
$136$	47.2386	4.05068
$137$	−4.18454	−0.357509	−0.178755	−	0.983894i	$-0.557207\pi$
$137$	−4.18454	−0.357509	−0.178755	+	0.983894i	$0.557207\pi$
$138$	4.51502	0.384344
$139$	−6.21825	−0.527425	−0.263713	−	0.964601i	$-0.584947\pi$
$139$	−6.21825	−0.527425	−0.263713	+	0.964601i	$0.584947\pi$
$140$	−56.9773	−4.81546
$141$	34.1401	2.87512
$142$	26.5414	2.22730
$143$	−7.26560	−0.607580
$144$	38.6971	3.22476
$145$	18.3088	1.52046
$146$	−9.10227	−0.753309
$147$	44.0768	3.63539
$148$	13.4771	1.10781
$149$	8.03569	0.658310	0.329155	−	0.944276i	$-0.393236\pi$
$149$	8.03569	0.658310	0.329155	+	0.944276i	$0.393236\pi$
$150$	−9.81763	−0.801606
$151$	−21.2912	−1.73265	−0.866326	−	0.499479i	$-0.833525\pi$
$151$	−21.2912	−1.73265	−0.866326	+	0.499479i	$0.833525\pi$
$152$	15.6113	1.26624
$153$	−30.4806	−2.46421
$154$	54.1256	4.36157
$155$	−13.6610	−1.09728
$156$	−21.4235	−1.71526
$157$	−21.8139	−1.74094	−0.870469	−	0.492224i	$-0.836184\pi$
$157$	−21.8139	−1.74094	−0.870469	+	0.492224i	$0.836184\pi$
$158$	−10.0365	−0.798462
$159$	−17.1765	−1.36218
$160$	−21.1648	−1.67323
$161$	3.06584	0.241622
$162$	5.97385	0.469350
$163$	5.84455	0.457781	0.228890	−	0.973452i	$-0.426490\pi$
$163$	5.84455	0.457781	0.228890	+	0.973452i	$0.426490\pi$
$164$	0.483495	0.0377546
$165$	30.1101	2.34406
$166$	46.5407	3.61226
$167$	−11.8781	−0.919158	−0.459579	−	0.888137i	$-0.652000\pi$
$167$	−11.8781	−0.919158	−0.459579	+	0.888137i	$0.652000\pi$
$168$	91.5427	7.06267
$169$	−10.2146	−0.785735
$170$	44.3751	3.40341
$171$	−10.0731	−0.770311
$172$	−37.4104	−2.85252
$173$	−12.5173	−0.951675	−0.475837	−	0.879533i	$-0.657855\pi$
$173$	−12.5173	−0.951675	−0.475837	+	0.879533i	$0.657855\pi$
$174$	−51.2839	−3.88783
$175$	−6.66648	−0.503938
$176$	37.5190	2.82810
$177$	13.6746	1.02785
$178$	−40.8414	−3.06119
$179$	−18.3645	−1.37263	−0.686314	−	0.727305i	$-0.740773\pi$
$179$	−18.3645	−1.37263	−0.686314	+	0.727305i	$0.740773\pi$
$180$	53.2228	3.96700
$181$	−7.00588	−0.520743	−0.260371	−	0.965509i	$-0.583845\pi$
$181$	−7.00588	−0.520743	−0.260371	+	0.965509i	$0.583845\pi$
$182$	−20.7504	−1.53812
$183$	−25.6986	−1.89970
$184$	4.43834	0.327198
$185$	7.26173	0.533893
$186$	38.2651	2.80573
$187$	−29.5526	−2.16110
$188$	58.5093	4.26723
$189$	−19.6020	−1.42584
$190$	14.6649	1.06391
$191$	−25.3067	−1.83113	−0.915566	−	0.402168i	$-0.868257\pi$
$191$	−25.3067	−1.83113	−0.915566	+	0.402168i	$0.868257\pi$
$192$	12.1102	0.873976
$193$	12.8745	0.926729	0.463365	−	0.886168i	$-0.346642\pi$
$193$	12.8745	0.926729	0.463365	+	0.886168i	$0.346642\pi$
$194$	16.3375	1.17297
$195$	−11.5434	−0.826641
$196$	75.5387	5.39562
$197$	19.9880	1.42409	0.712043	−	0.702136i	$-0.247770\pi$
$197$	19.9880	1.42409	0.712043	+	0.702136i	$0.247770\pi$
$198$	−50.5591	−3.59308
$199$	9.05610	0.641970	0.320985	−	0.947084i	$-0.395986\pi$
$199$	9.05610	0.641970	0.320985	+	0.947084i	$0.395986\pi$
$200$	−9.65088	−0.682420
$201$	−39.1616	−2.76225
$202$	−33.5189	−2.35838
$203$	−34.8234	−2.44412
$204$	−87.1396	−6.10100
$205$	0.260516	0.0181952
$206$	−18.8719	−1.31486
$207$	−2.86382	−0.199049
$208$	−14.3838	−0.997337
$209$	−9.76646	−0.675560
$210$	85.9935	5.93412
$211$	25.1047	1.72828	0.864140	−	0.503252i	$-0.167863\pi$
$211$	25.1047	1.72828	0.864140	+	0.503252i	$0.167863\pi$
$212$	−29.4370	−2.02174
$213$	−28.0829	−1.92421
$214$	−22.3892	−1.53050
$215$	−20.1575	−1.37473
$216$	−28.3773	−1.93083
$217$	25.9832	1.76386
$218$	26.1339	1.77001
$219$	9.63095	0.650799
$220$	51.6025	3.47904
$221$	11.3297	0.762118
$222$	−20.3405	−1.36516
$223$	−0.339274	−0.0227195	−0.0113597	−	0.999935i	$-0.503616\pi$
$223$	−0.339274	−0.0227195	−0.0113597	+	0.999935i	$0.503616\pi$
$224$	40.2555	2.68969
$225$	6.22720	0.415147
$226$	−24.2083	−1.61031
$227$	−7.03306	−0.466801	−0.233400	−	0.972381i	$-0.574985\pi$
$227$	−7.03306	−0.466801	−0.233400	+	0.972381i	$0.574985\pi$
$228$	−28.7976	−1.90717
$229$	−7.58283	−0.501087	−0.250544	−	0.968105i	$-0.580609\pi$
$229$	−7.58283	−0.501087	−0.250544	+	0.968105i	$0.580609\pi$
$230$	4.16929	0.274915
$231$	−57.2694	−3.76805
$232$	−50.4129	−3.30977
$233$	20.9509	1.37254	0.686268	−	0.727349i	$-0.259248\pi$
$233$	20.9509	1.37254	0.686268	+	0.727349i	$0.259248\pi$
$234$	19.3830	1.26711
$235$	31.5259	2.05652
$236$	23.4355	1.52552
$237$	10.6195	0.689807
$238$	−84.4015	−5.47094
$239$	5.38937	0.348609	0.174305	−	0.984692i	$-0.444232\pi$
$239$	5.38937	0.348609	0.174305	+	0.984692i	$0.444232\pi$
$240$	59.6093	3.84776
$241$	−7.92498	−0.510493	−0.255246	−	0.966876i	$-0.582157\pi$
$241$	−7.92498	−0.510493	−0.255246	+	0.966876i	$0.582157\pi$
$242$	−20.5677	−1.32214
$243$	−18.5548	−1.19029
$244$	−44.0422	−2.81951
$245$	40.7017	2.60034
$246$	−0.729720	−0.0465252
$247$	3.74420	0.238238
$248$	37.6152	2.38857
$249$	−49.2439	−3.12070
$250$	23.6183	1.49375
$251$	5.67293	0.358072	0.179036	−	0.983842i	$-0.442702\pi$
$251$	5.67293	0.358072	0.179036	+	0.983842i	$0.442702\pi$
$252$	−101.230	−6.37688
$253$	−2.77664	−0.174566
$254$	7.66882	0.481185
$255$	−46.9525	−2.94028
$256$	−22.5691	−1.41057
$257$	−9.18590	−0.573001	−0.286500	−	0.958080i	$-0.592492\pi$
$257$	−9.18590	−0.573001	−0.286500	+	0.958080i	$0.592492\pi$
$258$	56.4621	3.51518
$259$	−13.8118	−0.858225
$260$	−19.7831	−1.22689
$261$	32.5287	2.01348
$262$	13.7738	0.850950
$263$	−25.1650	−1.55174	−0.775870	−	0.630893i	$-0.782689\pi$
$263$	−25.1650	−1.55174	−0.775870	+	0.630893i	$0.782689\pi$
$264$	−82.9073	−5.10259
$265$	−15.8612	−0.974346
$266$	−27.8927	−1.71021
$267$	43.2135	2.64463
$268$	−67.1150	−4.09970
$269$	−17.6606	−1.07678	−0.538392	−	0.842695i	$-0.680968\pi$
$269$	−17.6606	−1.07678	−0.538392	+	0.842695i	$0.680968\pi$
$270$	−26.6571	−1.62230
$271$	−16.8313	−1.02243	−0.511214	−	0.859454i	$-0.670804\pi$
$271$	−16.8313	−1.02243	−0.511214	+	0.859454i	$0.670804\pi$
$272$	−58.5057	−3.54743
$273$	21.9556	1.32881
$274$	10.8236	0.653876
$275$	6.03762	0.364082
$276$	−8.18726	−0.492815
$277$	11.5819	0.695888	0.347944	−	0.937515i	$-0.386880\pi$
$277$	11.5819	0.695888	0.347944	+	0.937515i	$0.386880\pi$
$278$	16.0839	0.964648
$279$	−24.2711	−1.45307
$280$	84.5329	5.05181
$281$	1.41379	0.0843397	0.0421698	−	0.999110i	$-0.486573\pi$
$281$	1.41379	0.0843397	0.0421698	+	0.999110i	$0.486573\pi$
$282$	−88.3057	−5.25853
$283$	−22.8658	−1.35923	−0.679614	−	0.733570i	$-0.737853\pi$
$283$	−22.8658	−1.35923	−0.679614	+	0.733570i	$0.737853\pi$
$284$	−48.1284	−2.85590
$285$	−15.5167	−0.919131
$286$	18.7929	1.11125
$287$	−0.495502	−0.0292486
$288$	−37.6030	−2.21578
$289$	29.0832	1.71078
$290$	−47.3569	−2.78089
$291$	−17.2864	−1.01335
$292$	16.5055	0.965910
$293$	5.01524	0.292994	0.146497	−	0.989211i	$-0.453200\pi$
$293$	5.01524	0.292994	0.146497	+	0.989211i	$0.453200\pi$
$294$	−114.008	−6.64905
$295$	12.6275	0.735202
$296$	−19.9950	−1.16219
$297$	17.7529	1.03013
$298$	−20.7848	−1.20403
$299$	1.06449	0.0615610
$300$	17.8027	1.02784
$301$	38.3395	2.20985
$302$	55.0710	3.16898
$303$	35.4657	2.03745
$304$	−19.3348	−1.10893
$305$	−23.7308	−1.35882
$306$	78.8400	4.50698
$307$	14.5763	0.831916	0.415958	−	0.909384i	$-0.363446\pi$
$307$	14.5763	0.831916	0.415958	+	0.909384i	$0.363446\pi$
$308$	−98.1480	−5.59250
$309$	19.9680	1.13594
$310$	35.3350	2.00689
$311$	−0.203859	−0.0115598	−0.00577989	−	0.999983i	$-0.501840\pi$
$311$	−0.203859	−0.0115598	−0.00577989	+	0.999983i	$0.501840\pi$
$312$	31.7845	1.79944
$313$	−18.3410	−1.03670	−0.518348	−	0.855170i	$-0.673453\pi$
$313$	−18.3410	−1.03670	−0.518348	+	0.855170i	$0.673453\pi$
$314$	56.4230	3.18413
$315$	−54.5446	−3.07324
$316$	18.1996	1.02381
$317$	−34.4470	−1.93474	−0.967369	−	0.253370i	$-0.918461\pi$
$317$	−34.4470	−1.93474	−0.967369	+	0.253370i	$0.918461\pi$
$318$	44.4280	2.49140
$319$	31.5384	1.76581
$320$	11.1828	0.625140
$321$	23.6896	1.32223
$322$	−7.93000	−0.441921
$323$	15.2294	0.847389
$324$	−10.8326	−0.601811
$325$	−2.31466	−0.128394
$326$	−15.1173	−0.837270
$327$	−27.6518	−1.52915
$328$	−0.717325	−0.0396077
$329$	−59.9623	−3.30583
$330$	−77.8816	−4.28724
$331$	−30.1796	−1.65882	−0.829412	−	0.558638i	$-0.811324\pi$
$331$	−30.1796	−1.65882	−0.829412	+	0.558638i	$0.811324\pi$
$332$	−84.3939	−4.63172
$333$	12.9017	0.707010
$334$	30.7236	1.68112
$335$	−36.1628	−1.97579
$336$	−113.377	−6.18522
$337$	−22.6513	−1.23390	−0.616948	−	0.787004i	$-0.711631\pi$
$337$	−22.6513	−1.23390	−0.616948	+	0.787004i	$0.711631\pi$
$338$	26.4206	1.43709
$339$	25.6144	1.39118
$340$	−80.4670	−4.36394
$341$	−23.5322	−1.27434
$342$	26.0548	1.40888
$343$	−43.7671	−2.36320
$344$	55.5031	2.99252
$345$	−4.41145	−0.237505
$346$	32.3769	1.74059
$347$	24.8404	1.33350	0.666751	−	0.745281i	$-0.267685\pi$
$347$	24.8404	1.33350	0.666751	+	0.745281i	$0.267685\pi$
$348$	92.9951	4.98506
$349$	3.02869	0.162122	0.0810610	−	0.996709i	$-0.474169\pi$
$349$	3.02869	0.162122	0.0810610	+	0.996709i	$0.474169\pi$
$350$	17.2433	0.921692
$351$	−6.80600	−0.363277
$352$	−36.4582	−1.94323
$353$	22.3881	1.19160	0.595800	−	0.803133i	$-0.296835\pi$
$353$	22.3881	1.19160	0.595800	+	0.803133i	$0.296835\pi$
$354$	−35.3703	−1.87991
$355$	−25.9325	−1.37635
$356$	74.0592	3.92513
$357$	89.3037	4.72645
$358$	47.5010	2.51051
$359$	1.55366	0.0819990	0.0409995	−	0.999159i	$-0.486946\pi$
$359$	1.55366	0.0819990	0.0409995	+	0.999159i	$0.486946\pi$
$360$	−78.9627	−4.16170
$361$	−13.9670	−0.735106
$362$	18.1211	0.952426
$363$	21.7623	1.14222
$364$	37.6274	1.97221
$365$	8.89347	0.465505
$366$	66.4712	3.47450
$367$	−2.50398	−0.130707	−0.0653533	−	0.997862i	$-0.520817\pi$
$367$	−2.50398	−0.130707	−0.0653533	+	0.997862i	$0.520817\pi$
$368$	−5.49694	−0.286548
$369$	0.462852	0.0240951
$370$	−18.7829	−0.976479
$371$	30.1680	1.56625
$372$	−69.3876	−3.59758
$373$	−1.97885	−0.102461	−0.0512305	−	0.998687i	$-0.516314\pi$
$373$	−1.97885	−0.102461	−0.0512305	+	0.998687i	$0.516314\pi$
$374$	76.4397	3.95260
$375$	−24.9901	−1.29049
$376$	−86.8058	−4.47667
$377$	−12.0910	−0.622719
$378$	50.7018	2.60782
$379$	25.1298	1.29083	0.645415	−	0.763832i	$-0.276685\pi$
$379$	25.1298	1.29083	0.645415	+	0.763832i	$0.276685\pi$
$380$	−26.5925	−1.36417
$381$	−8.11424	−0.415705
$382$	65.4575	3.34910
$383$	−19.4708	−0.994910	−0.497455	−	0.867490i	$-0.665732\pi$
$383$	−19.4708	−0.994910	−0.497455	+	0.867490i	$0.665732\pi$
$384$	14.5161	0.740771
$385$	−52.8840	−2.69522
$386$	−33.3008	−1.69497
$387$	−35.8132	−1.82049
$388$	−29.6254	−1.50400
$389$	−27.4524	−1.39189	−0.695947	−	0.718093i	$-0.745015\pi$
$389$	−27.4524	−1.39189	−0.695947	+	0.718093i	$0.745015\pi$
$390$	29.8578	1.51191
$391$	4.32978	0.218966
$392$	−112.071	−5.66044
$393$	−14.5738	−0.735153
$394$	−51.7002	−2.60462
$395$	9.80628	0.493407
$396$	91.6807	4.60713
$397$	−1.34022	−0.0672637	−0.0336318	−	0.999434i	$-0.510707\pi$
$397$	−1.34022	−0.0672637	−0.0336318	+	0.999434i	$0.510707\pi$
$398$	−23.4242	−1.17415
$399$	29.5128	1.47749
$400$	11.9527	0.597637
$401$	5.19580	0.259466	0.129733	−	0.991549i	$-0.458588\pi$
$401$	5.19580	0.259466	0.129733	+	0.991549i	$0.458588\pi$
$402$	101.294	5.05208
$403$	9.02162	0.449399
$404$	60.7810	3.02397
$405$	−5.83681	−0.290033
$406$	90.0729	4.47024
$407$	12.5089	0.620045
$408$	129.283	6.40044
$409$	36.9735	1.82822	0.914111	−	0.405465i	$-0.132890\pi$
$409$	36.9735	1.82822	0.914111	+	0.405465i	$0.132890\pi$
$410$	−0.673842	−0.0332787
$411$	−11.4522	−0.564897
$412$	34.2210	1.68595
$413$	−24.0175	−1.18183
$414$	7.40746	0.364057
$415$	−45.4731	−2.23218
$416$	13.9771	0.685284
$417$	−17.0181	−0.833379
$418$	25.2616	1.23558
$419$	−11.8010	−0.576515	−0.288257	−	0.957553i	$-0.593076\pi$
$419$	−11.8010	−0.576515	−0.288257	+	0.957553i	$0.593076\pi$
$420$	−155.935	−7.60886
$421$	29.6203	1.44361	0.721803	−	0.692098i	$-0.243313\pi$
$421$	29.6203	1.44361	0.721803	+	0.692098i	$0.243313\pi$
$422$	−64.9349	−3.16098
$423$	56.0112	2.72336
$424$	43.6734	2.12097
$425$	−9.41483	−0.456686
$426$	72.6383	3.51934
$427$	45.1360	2.18428
$428$	40.5992	1.96244
$429$	−19.8845	−0.960031
$430$	52.1385	2.51434
$431$	5.91215	0.284778	0.142389	−	0.989811i	$-0.454522\pi$
$431$	5.91215	0.284778	0.142389	+	0.989811i	$0.454522\pi$
$432$	35.1457	1.69095
$433$	−13.6420	−0.655592	−0.327796	−	0.944749i	$-0.606306\pi$
$433$	−13.6420	−0.655592	−0.327796	+	0.944749i	$0.606306\pi$
$434$	−67.2072	−3.22605
$435$	50.1075	2.40247
$436$	−47.3895	−2.26955
$437$	1.43089	0.0684489
$438$	−24.9111	−1.19030
$439$	11.6541	0.556219	0.278109	−	0.960549i	$-0.410292\pi$
$439$	11.6541	0.556219	0.278109	+	0.960549i	$0.410292\pi$
$440$	−76.5588	−3.64980
$441$	72.3135	3.44350
$442$	−29.3050	−1.39390
$443$	24.9529	1.18555	0.592773	−	0.805369i	$-0.298033\pi$
$443$	24.9529	1.18555	0.592773	+	0.805369i	$0.298033\pi$
$444$	36.8842	1.75045
$445$	39.9045	1.89165
$446$	0.877555	0.0415534
$447$	21.9921	1.04019
$448$	−21.2698	−1.00490
$449$	−26.0203	−1.22797	−0.613986	−	0.789317i	$-0.710435\pi$
$449$	−26.0203	−1.22797	−0.613986	+	0.789317i	$0.710435\pi$
$450$	−16.1070	−0.759294
$451$	0.448761	0.0211313
$452$	43.8978	2.06478
$453$	−58.2697	−2.73775
$454$	18.1915	0.853768
$455$	20.2744	0.950476
$456$	42.7249	2.00078
$457$	−2.98903	−0.139821	−0.0699104	−	0.997553i	$-0.522271\pi$
$457$	−2.98903	−0.139821	−0.0699104	+	0.997553i	$0.522271\pi$
$458$	19.6135	0.916477
$459$	−27.6832	−1.29214
$460$	−7.56033	−0.352502
$461$	−12.1700	−0.566813	−0.283407	−	0.959000i	$-0.591465\pi$
$461$	−12.1700	−0.566813	−0.283407	+	0.959000i	$0.591465\pi$
$462$	148.131	6.89167
$463$	2.50224	0.116289	0.0581444	−	0.998308i	$-0.481482\pi$
$463$	2.50224	0.116289	0.0581444	+	0.998308i	$0.481482\pi$
$464$	62.4371	2.89857
$465$	−37.3873	−1.73380
$466$	−54.1907	−2.51034
$467$	−26.4870	−1.22567	−0.612836	−	0.790210i	$-0.709971\pi$
$467$	−26.4870	−1.22567	−0.612836	+	0.790210i	$0.709971\pi$
$468$	−35.1480	−1.62472
$469$	68.7818	3.17605
$470$	−81.5437	−3.76133
$471$	−59.7002	−2.75084
$472$	−34.7695	−1.60040
$473$	−34.7229	−1.59656
$474$	−27.4679	−1.26164
$475$	−3.11138	−0.142760
$476$	153.048	7.01496
$477$	−28.1801	−1.29028
$478$	−13.9399	−0.637598
$479$	9.88182	0.451512	0.225756	−	0.974184i	$-0.427515\pi$
$479$	9.88182	0.451512	0.225756	+	0.974184i	$0.427515\pi$
$480$	−57.9238	−2.64385
$481$	−4.79560	−0.218660
$482$	20.4985	0.933680
$483$	8.39059	0.381785
$484$	37.2961	1.69528
$485$	−15.9627	−0.724831
$486$	47.9931	2.17701
$487$	7.52229	0.340867	0.170434	−	0.985369i	$-0.445483\pi$
$487$	7.52229	0.340867	0.170434	+	0.985369i	$0.445483\pi$
$488$	65.3421	2.95790
$489$	15.9954	0.723335
$490$	−105.277	−4.75595
$491$	39.6252	1.78826	0.894130	−	0.447808i	$-0.147795\pi$
$491$	39.6252	1.78826	0.894130	+	0.447808i	$0.147795\pi$
$492$	1.32323	0.0596557
$493$	−49.1798	−2.21495
$494$	−9.68462	−0.435732
$495$	49.3993	2.22033
$496$	−46.5869	−2.09182
$497$	49.3237	2.21247
$498$	127.372	5.70769
$499$	−1.31527	−0.0588796	−0.0294398	−	0.999567i	$-0.509372\pi$
$499$	−1.31527	−0.0588796	−0.0294398	+	0.999567i	$0.509372\pi$
$500$	−42.8280	−1.91533
$501$	−32.5080	−1.45235
$502$	−14.6734	−0.654906
$503$	−15.2417	−0.679595	−0.339797	−	0.940499i	$-0.610359\pi$
$503$	−15.2417	−0.679595	−0.339797	+	0.940499i	$0.610359\pi$
$504$	150.187	6.68987
$505$	32.7499	1.45735
$506$	7.18194	0.319276
$507$	−27.9552	−1.24153
$508$	−13.9062	−0.616986
$509$	2.34854	0.104097	0.0520487	−	0.998645i	$-0.483425\pi$
$509$	2.34854	0.104097	0.0520487	+	0.998645i	$0.483425\pi$
$510$	121.446	5.37770
$511$	−16.9154	−0.748293
$512$	47.7684	2.11109
$513$	−9.14866	−0.403923
$514$	23.7599	1.04800
$515$	18.4389	0.812517
$516$	−102.385	−4.50724
$517$	54.3059	2.38837
$518$	35.7252	1.56967
$519$	−34.2574	−1.50373
$520$	29.3506	1.28711
$521$	18.5541	0.812871	0.406435	−	0.913680i	$-0.366772\pi$
$521$	18.5541	0.812871	0.406435	+	0.913680i	$0.366772\pi$
$522$	−84.1377	−3.68261
$523$	−11.9823	−0.523951	−0.261976	−	0.965074i	$-0.584374\pi$
$523$	−11.9823	−0.523951	−0.261976	+	0.965074i	$0.584374\pi$
$524$	−24.9766	−1.09111
$525$	−18.2448	−0.796268
$526$	65.0908	2.83810
$527$	36.6952	1.59847
$528$	102.682	4.46865
$529$	−22.5932	−0.982313
$530$	41.0260	1.78206
$531$	22.4349	0.973593
$532$	50.5790	2.19288
$533$	−0.172043	−0.00745201
$534$	−111.775	−4.83696
$535$	21.8756	0.945766
$536$	99.5735	4.30092
$537$	−50.2599	−2.16888
$538$	45.6802	1.96941
$539$	70.1120	3.01994
$540$	48.3383	2.08015
$541$	3.64730	0.156810	0.0784048	−	0.996922i	$-0.475017\pi$
$541$	3.64730	0.156810	0.0784048	+	0.996922i	$0.475017\pi$
$542$	43.5352	1.87000
$543$	−19.1737	−0.822820
$544$	56.8515	2.43749
$545$	−25.5344	−1.09377
$546$	−56.7895	−2.43037
$547$	3.69779	0.158106	0.0790531	−	0.996870i	$-0.474810\pi$
$547$	3.69779	0.158106	0.0790531	+	0.996870i	$0.474810\pi$
$548$	−19.6268	−0.838415
$549$	−42.1618	−1.79942
$550$	−15.6167	−0.665897
$551$	−16.2528	−0.692393
$552$	12.1468	0.517003
$553$	−18.6516	−0.793145
$554$	−29.9573	−1.27276
$555$	19.8739	0.843600
$556$	−29.1655	−1.23689
$557$	−44.2838	−1.87636	−0.938182	−	0.346141i	$-0.887492\pi$
$557$	−44.2838	−1.87636	−0.938182	+	0.346141i	$0.887492\pi$
$558$	62.7787	2.65763
$559$	13.3118	0.563031
$560$	−104.695	−4.42418
$561$	−80.8795	−3.41474
$562$	−3.65686	−0.154255
$563$	−33.5792	−1.41519	−0.707597	−	0.706616i	$-0.750221\pi$
$563$	−33.5792	−1.41519	−0.707597	+	0.706616i	$0.750221\pi$
$564$	160.128	6.74260
$565$	23.6530	0.995088
$566$	59.1437	2.48600
$567$	11.1016	0.466224
$568$	71.4045	2.99607
$569$	−17.2361	−0.722576	−0.361288	−	0.932454i	$-0.617663\pi$
$569$	−17.2361	−0.722576	−0.361288	+	0.932454i	$0.617663\pi$
$570$	40.1350	1.68107
$571$	28.7318	1.20239	0.601194	−	0.799103i	$-0.294692\pi$
$571$	28.7318	1.20239	0.601194	+	0.799103i	$0.294692\pi$
$572$	−34.0779	−1.42487
$573$	−69.2594	−2.89335
$574$	1.28165	0.0534950
$575$	−0.884577	−0.0368894
$576$	19.8682	0.827843
$577$	24.5080	1.02028	0.510140	−	0.860091i	$-0.329594\pi$
$577$	24.5080	1.02028	0.510140	+	0.860091i	$0.329594\pi$
$578$	−75.2257	−3.12898
$579$	35.2350	1.46432
$580$	85.8741	3.56573
$581$	86.4898	3.58820
$582$	44.7125	1.85339
$583$	−27.3222	−1.13157
$584$	−24.4879	−1.01332
$585$	−18.9384	−0.783006
$586$	−12.9722	−0.535878
$587$	−5.63539	−0.232597	−0.116299	−	0.993214i	$-0.537103\pi$
$587$	−5.63539	−0.232597	−0.116299	+	0.993214i	$0.537103\pi$
$588$	206.734	8.52557
$589$	12.1269	0.499681
$590$	−32.6618	−1.34467
$591$	54.7031	2.25018
$592$	24.7641	1.01780
$593$	−2.65132	−0.108877	−0.0544383	−	0.998517i	$-0.517337\pi$
$593$	−2.65132	−0.108877	−0.0544383	+	0.998517i	$0.517337\pi$
$594$	−45.9190	−1.88408
$595$	82.4654	3.38075
$596$	37.6899	1.54384
$597$	24.7847	1.01437
$598$	−2.75337	−0.112594
$599$	−16.6995	−0.682322	−0.341161	−	0.940005i	$-0.610820\pi$
$599$	−16.6995	−0.682322	−0.341161	+	0.940005i	$0.610820\pi$
$600$	−26.4125	−1.07829
$601$	−7.75044	−0.316147	−0.158074	−	0.987427i	$-0.550528\pi$
$601$	−7.75044	−0.316147	−0.158074	+	0.987427i	$0.550528\pi$
$602$	−99.1676	−4.04177
$603$	−64.2495	−2.61644
$604$	−99.8623	−4.06334
$605$	20.0958	0.817012
$606$	−91.7343	−3.72645
$607$	33.3192	1.35238	0.676191	−	0.736726i	$-0.263629\pi$
$607$	33.3192	1.35238	0.676191	+	0.736726i	$0.263629\pi$
$608$	18.7881	0.761958
$609$	−95.3045	−3.86194
$610$	61.3812	2.48525
$611$	−20.8195	−0.842266
$612$	−142.963	−5.77895
$613$	15.5990	0.630039	0.315019	−	0.949085i	$-0.397989\pi$
$613$	15.5990	0.630039	0.315019	+	0.949085i	$0.397989\pi$
$614$	−37.7026	−1.52155
$615$	0.712980	0.0287501
$616$	145.615	5.86699
$617$	−8.16519	−0.328718	−0.164359	−	0.986401i	$-0.552556\pi$
$617$	−8.16519	−0.328718	−0.164359	+	0.986401i	$0.552556\pi$
$618$	−51.6484	−2.07760
$619$	24.6560	0.991010	0.495505	−	0.868605i	$-0.334983\pi$
$619$	24.6560	0.991010	0.495505	+	0.868605i	$0.334983\pi$
$620$	−64.0743	−2.57329
$621$	−2.60099	−0.104374
$622$	0.527294	0.0211426
$623$	−75.8984	−3.04081
$624$	−39.3655	−1.57588
$625$	−30.0110	−1.20044
$626$	47.4402	1.89609
$627$	−26.7288	−1.06745
$628$	−102.314	−4.08277
$629$	−19.5060	−0.777754
$630$	141.083	5.62088
$631$	37.5826	1.49614	0.748070	−	0.663620i	$-0.230981\pi$
$631$	37.5826	1.49614	0.748070	+	0.663620i	$0.230981\pi$
$632$	−27.0013	−1.07406
$633$	68.7065	2.73084
$634$	89.0995	3.53859
$635$	−7.49290	−0.297347
$636$	−80.5630	−3.19453
$637$	−26.8791	−1.06499
$638$	−81.5762	−3.22963
$639$	−46.0735	−1.82264
$640$	13.4045	0.529861
$641$	−26.9096	−1.06287	−0.531433	−	0.847101i	$-0.678346\pi$
$641$	−26.9096	−1.06287	−0.531433	+	0.847101i	$0.678346\pi$
$642$	−61.2748	−2.41832
$643$	5.78494	0.228136	0.114068	−	0.993473i	$-0.463612\pi$
$643$	5.78494	0.228136	0.114068	+	0.993473i	$0.463612\pi$
$644$	14.3798	0.566642
$645$	−55.1669	−2.17219
$646$	−39.3919	−1.54986
$647$	9.33793	0.367112	0.183556	−	0.983009i	$-0.441239\pi$
$647$	9.33793	0.367112	0.183556	+	0.983009i	$0.441239\pi$
$648$	16.0715	0.631349
$649$	21.7519	0.853837
$650$	5.98703	0.234831
$651$	71.1108	2.78705
$652$	27.4128	1.07357
$653$	21.6576	0.847526	0.423763	−	0.905773i	$-0.360709\pi$
$653$	21.6576	0.847526	0.423763	+	0.905773i	$0.360709\pi$
$654$	71.5231	2.79677
$655$	−13.4579	−0.525843
$656$	0.888417	0.0346869
$657$	15.8008	0.616447
$658$	155.096	6.04628
$659$	11.1543	0.434511	0.217255	−	0.976115i	$-0.430290\pi$
$659$	11.1543	0.434511	0.217255	+	0.976115i	$0.430290\pi$
$660$	141.226	5.49720
$661$	17.1719	0.667908	0.333954	−	0.942589i	$-0.391617\pi$
$661$	17.1719	0.667908	0.333954	+	0.942589i	$0.391617\pi$
$662$	78.0616	3.03395
$663$	31.0071	1.20422
$664$	125.209	4.85905
$665$	27.2529	1.05682
$666$	−33.3711	−1.29310
$667$	−4.62072	−0.178915
$668$	−55.7122	−2.15557
$669$	−0.928525	−0.0358989
$670$	93.5375	3.61367
$671$	−40.8782	−1.57809
$672$	110.171	4.24995
$673$	−3.92265	−0.151207	−0.0756035	−	0.997138i	$-0.524088\pi$
$673$	−3.92265	−0.151207	−0.0756035	+	0.997138i	$0.524088\pi$
$674$	58.5891	2.25677
$675$	5.65570	0.217688
$676$	−47.9095	−1.84267
$677$	1.57935	0.0606992	0.0303496	−	0.999539i	$-0.490338\pi$
$677$	1.57935	0.0606992	0.0303496	+	0.999539i	$0.490338\pi$
$678$	−66.2532	−2.54444
$679$	30.3611	1.16515
$680$	119.383	4.57812
$681$	−19.2481	−0.737587
$682$	60.8674	2.33073
$683$	4.00120	0.153102	0.0765509	−	0.997066i	$-0.475609\pi$
$683$	4.00120	0.153102	0.0765509	+	0.997066i	$0.475609\pi$
$684$	−47.2461	−1.80650
$685$	−10.5753	−0.404061
$686$	113.206	4.32224
$687$	−20.7527	−0.791763
$688$	−68.7413	−2.62074
$689$	10.4746	0.399051
$690$	11.4105	0.434390
$691$	51.0790	1.94314	0.971569	−	0.236757i	$-0.0760846\pi$
$691$	51.0790	1.94314	0.971569	+	0.236757i	$0.0760846\pi$
$692$	−58.7102	−2.23183
$693$	−93.9575	−3.56915
$694$	−64.2512	−2.43894
$695$	−15.7149	−0.596102
$696$	−137.970	−5.22973
$697$	−0.699781	−0.0265061
$698$	−7.83390	−0.296517
$699$	57.3382	2.16873
$700$	−31.2679	−1.18181
$701$	19.1467	0.723160	0.361580	−	0.932341i	$-0.382237\pi$
$701$	19.1467	0.723160	0.361580	+	0.932341i	$0.382237\pi$
$702$	17.6042	0.664426
$703$	−6.44627	−0.243126
$704$	19.2634	0.726015
$705$	86.2800	3.24949
$706$	−57.9084	−2.17941
$707$	−62.2904	−2.34267
$708$	64.1383	2.41046
$709$	20.1881	0.758180	0.379090	−	0.925360i	$-0.376237\pi$
$709$	20.1881	0.758180	0.379090	+	0.925360i	$0.376237\pi$
$710$	67.0761	2.51732
$711$	17.4225	0.653396
$712$	−109.876	−4.11778
$713$	3.44772	0.129118
$714$	−230.990	−8.64457
$715$	−18.3618	−0.686694
$716$	−86.1353	−3.21903
$717$	14.7496	0.550834
$718$	−4.01864	−0.149974
$719$	14.9976	0.559315	0.279657	−	0.960100i	$-0.409779\pi$
$719$	14.9976	0.559315	0.279657	+	0.960100i	$0.409779\pi$
$720$	97.7964	3.64466
$721$	−35.0709	−1.30611
$722$	36.1266	1.34449
$723$	−21.6891	−0.806625
$724$	−32.8597	−1.22122
$725$	10.0475	0.373154
$726$	−56.2895	−2.08910
$727$	43.9578	1.63031	0.815153	−	0.579246i	$-0.196653\pi$
$727$	43.9578	1.63031	0.815153	+	0.579246i	$0.196653\pi$
$728$	−55.8249	−2.06901
$729$	−43.8519	−1.62414
$730$	−23.0035	−0.851398
$731$	54.1455	2.00265
$732$	−120.535	−4.45509
$733$	−5.91075	−0.218319	−0.109159	−	0.994024i	$-0.534816\pi$
$733$	−5.91075	−0.218319	−0.109159	+	0.994024i	$0.534816\pi$
$734$	6.47670	0.239060
$735$	111.392	4.10876
$736$	5.34152	0.196891
$737$	−62.2934	−2.29461
$738$	−1.19720	−0.0440694
$739$	−36.4172	−1.33963	−0.669815	−	0.742528i	$-0.733626\pi$
$739$	−36.4172	−1.33963	−0.669815	+	0.742528i	$0.733626\pi$
$740$	34.0598	1.25206
$741$	10.2471	0.376438
$742$	−78.0315	−2.86463
$743$	−27.7210	−1.01698	−0.508492	−	0.861067i	$-0.669797\pi$
$743$	−27.7210	−1.01698	−0.508492	+	0.861067i	$0.669797\pi$
$744$	102.945	3.77415
$745$	20.3080	0.744029
$746$	5.11842	0.187399
$747$	−80.7907	−2.95598
$748$	−138.611	−5.06812
$749$	−41.6075	−1.52030
$750$	64.6386	2.36027
$751$	19.6745	0.717933	0.358966	−	0.933350i	$-0.383129\pi$
$751$	19.6745	0.717933	0.358966	+	0.933350i	$0.383129\pi$
$752$	107.510	3.92049
$753$	15.5257	0.565787
$754$	31.2742	1.13894
$755$	−53.8077	−1.95826
$756$	−91.9395	−3.34381
$757$	7.77920	0.282740	0.141370	−	0.989957i	$-0.454849\pi$
$757$	7.77920	0.282740	0.141370	+	0.989957i	$0.454849\pi$
$758$	−64.9997	−2.36090
$759$	−7.59909	−0.275829
$760$	39.4533	1.43112
$761$	24.5917	0.891450	0.445725	−	0.895170i	$-0.352946\pi$
$761$	24.5917	0.891450	0.445725	+	0.895170i	$0.352946\pi$
$762$	20.9880	0.760315
$763$	48.5664	1.75822
$764$	−118.697	−4.29429
$765$	−77.0314	−2.78508
$766$	50.3624	1.81967
$767$	−8.33911	−0.301108
$768$	−61.7671	−2.22883
$769$	−11.8793	−0.428380	−0.214190	−	0.976792i	$-0.568711\pi$
$769$	−11.8793	−0.428380	−0.214190	+	0.976792i	$0.568711\pi$
$770$	136.788	4.92949
$771$	−25.1399	−0.905393
$772$	60.3856	2.17332
$773$	15.1963	0.546573	0.273286	−	0.961933i	$-0.411889\pi$
$773$	15.1963	0.546573	0.273286	+	0.961933i	$0.411889\pi$
$774$	92.6331	3.32963
$775$	−7.49684	−0.269295
$776$	43.9530	1.57782
$777$	−37.8002	−1.35607
$778$	71.0075	2.54574
$779$	−0.231261	−0.00828580
$780$	−54.1422	−1.93860
$781$	−44.6709	−1.59845
$782$	−11.1993	−0.400485
$783$	29.5434	1.05580
$784$	138.802	4.95720
$785$	−55.1287	−1.96763
$786$	37.6962	1.34458
$787$	44.6013	1.58986	0.794932	−	0.606699i	$-0.207507\pi$
$787$	44.6013	1.58986	0.794932	+	0.606699i	$0.207507\pi$
$788$	93.7499	3.33970
$789$	−68.8714	−2.45189
$790$	−25.3646	−0.902431
$791$	−44.9880	−1.59959
$792$	−136.020	−4.83325
$793$	15.6716	0.556516
$794$	3.46656	0.123024
$795$	−43.4089	−1.53955
$796$	42.4759	1.50552
$797$	18.7035	0.662513	0.331257	−	0.943541i	$-0.392527\pi$
$797$	18.7035	0.662513	0.331257	+	0.943541i	$0.392527\pi$
$798$	−76.3368	−2.70229
$799$	−84.6826	−2.99586
$800$	−11.6148	−0.410645
$801$	70.8972	2.50503
$802$	−13.4393	−0.474557
$803$	15.3197	0.540621
$804$	−183.680	−6.47790
$805$	7.74809	0.273084
$806$	−23.3350	−0.821940
$807$	−48.3334	−1.70141
$808$	−90.1762	−3.17239
$809$	−0.973112	−0.0342128	−0.0171064	−	0.999854i	$-0.505445\pi$
$809$	−0.973112	−0.0342128	−0.0171064	+	0.999854i	$0.505445\pi$
$810$	15.0973	0.530464
$811$	−2.35379	−0.0826529	−0.0413264	−	0.999146i	$-0.513158\pi$
$811$	−2.35379	−0.0826529	−0.0413264	+	0.999146i	$0.513158\pi$
$812$	−163.333	−5.73185
$813$	−46.0638	−1.61553
$814$	−32.3551	−1.13405
$815$	14.7705	0.517389
$816$	−160.118	−5.60526
$817$	17.8939	0.626027
$818$	−95.6343	−3.34377
$819$	36.0209	1.25867
$820$	1.22190	0.0426707
$821$	26.1970	0.914281	0.457140	−	0.889395i	$-0.348874\pi$
$821$	26.1970	0.914281	0.457140	+	0.889395i	$0.348874\pi$
$822$	29.6219	1.03318
$823$	−29.5046	−1.02846	−0.514232	−	0.857651i	$-0.671923\pi$
$823$	−29.5046	−1.02846	−0.514232	+	0.857651i	$0.671923\pi$
$824$	−50.7712	−1.76870
$825$	16.5237	0.575282
$826$	62.1229	2.16153
$827$	31.1113	1.08185	0.540923	−	0.841072i	$-0.318075\pi$
$827$	31.1113	1.08185	0.540923	+	0.841072i	$0.318075\pi$
$828$	−13.4322	−0.466802
$829$	23.8383	0.827939	0.413969	−	0.910291i	$-0.364142\pi$
$829$	23.8383	0.827939	0.413969	+	0.910291i	$0.364142\pi$
$830$	117.619	4.08261
$831$	31.6973	1.09957
$832$	−7.38507	−0.256031
$833$	−109.330	−3.78806
$834$	44.0184	1.52423
$835$	−30.0188	−1.03884
$836$	−45.8077	−1.58429
$837$	−22.0436	−0.761938
$838$	30.5239	1.05443
$839$	29.7335	1.02651	0.513257	−	0.858235i	$-0.328439\pi$
$839$	29.7335	1.02651	0.513257	+	0.858235i	$0.328439\pi$
$840$	231.349	7.98231
$841$	23.4845	0.809811
$842$	−76.6149	−2.64032
$843$	3.86926	0.133264
$844$	117.749	4.05308
$845$	−25.8145	−0.888047
$846$	−144.876	−4.98095
$847$	−38.2223	−1.31333
$848$	−54.0902	−1.85746
$849$	−62.5789	−2.14770
$850$	24.3521	0.835269
$851$	−1.83269	−0.0628240
$852$	−131.718	−4.51257
$853$	1.52980	0.0523794	0.0261897	−	0.999657i	$-0.491663\pi$
$853$	1.52980	0.0523794	0.0261897	+	0.999657i	$0.491663\pi$
$854$	−116.747	−3.99500
$855$	−25.4571	−0.870615
$856$	−60.2340	−2.05876
$857$	39.7855	1.35905	0.679523	−	0.733655i	$-0.262187\pi$
$857$	39.7855	1.35905	0.679523	+	0.733655i	$0.262187\pi$
$858$	51.4324	1.75587
$859$	−0.708969	−0.0241897	−0.0120949	−	0.999927i	$-0.503850\pi$
$859$	−0.708969	−0.0241897	−0.0120949	+	0.999927i	$0.503850\pi$
$860$	−94.5448	−3.22395
$861$	−1.35609	−0.0462154
$862$	−15.2922	−0.520853
$863$	48.2268	1.64166	0.820829	−	0.571173i	$-0.193512\pi$
$863$	48.2268	1.64166	0.820829	+	0.571173i	$0.193512\pi$
$864$	−34.1519	−1.16187
$865$	−31.6342	−1.07559
$866$	35.2858	1.19906
$867$	79.5949	2.70319
$868$	121.869	4.13652
$869$	16.8921	0.573026
$870$	−129.606	−4.39406
$871$	23.8817	0.809200
$872$	70.3082	2.38094
$873$	−28.3605	−0.959859
$874$	−3.70110	−0.125191
$875$	43.8916	1.48381
$876$	45.1721	1.52623
$877$	16.5727	0.559620	0.279810	−	0.960055i	$-0.409729\pi$
$877$	16.5727	0.559620	0.279810	+	0.960055i	$0.409729\pi$
$878$	−30.1440	−1.01731
$879$	13.7257	0.462956
$880$	94.8191	3.19635
$881$	40.9522	1.37971	0.689857	−	0.723946i	$-0.257674\pi$
$881$	40.9522	1.37971	0.689857	+	0.723946i	$0.257674\pi$
$882$	−187.043	−6.29808
$883$	57.4899	1.93469	0.967345	−	0.253462i	$-0.0815694\pi$
$883$	57.4899	1.93469	0.967345	+	0.253462i	$0.0815694\pi$
$884$	53.1398	1.78729
$885$	34.5589	1.16169
$886$	−64.5422	−2.16834
$887$	−57.3417	−1.92535	−0.962673	−	0.270668i	$-0.912755\pi$
$887$	−57.3417	−1.92535	−0.962673	+	0.270668i	$0.912755\pi$
$888$	−54.7223	−1.83636
$889$	14.2515	0.477980
$890$	−103.216	−3.45979
$891$	−10.0544	−0.336834
$892$	−1.59130	−0.0532808
$893$	−27.9857	−0.936504
$894$	−56.8839	−1.90248
$895$	−46.4113	−1.55136
$896$	−25.4954	−0.851743
$897$	2.91329	0.0972720
$898$	67.3031	2.24593
$899$	−39.1609	−1.30609
$900$	29.2075	0.973584
$901$	42.6052	1.41939
$902$	−1.16075	−0.0386487
$903$	104.927	3.49177
$904$	−65.1279	−2.16612
$905$	−17.7055	−0.588549
$906$	150.718	5.00728
$907$	−47.2202	−1.56792	−0.783960	−	0.620812i	$-0.786803\pi$
$907$	−47.2202	−1.56792	−0.783960	+	0.620812i	$0.786803\pi$
$908$	−32.9873	−1.09472
$909$	58.1859	1.92990
$910$	−52.4409	−1.73840
$911$	−7.13677	−0.236452	−0.118226	−	0.992987i	$-0.537721\pi$
$911$	−7.13677	−0.236452	−0.118226	+	0.992987i	$0.537721\pi$
$912$	−52.9154	−1.75220
$913$	−78.3311	−2.59238
$914$	7.73131	0.255729
$915$	−64.9463	−2.14706
$916$	−35.5658	−1.17513
$917$	25.5969	0.845284
$918$	71.6044	2.36330
$919$	52.1917	1.72164	0.860822	−	0.508906i	$-0.169950\pi$
$919$	52.1917	1.72164	0.860822	+	0.508906i	$0.169950\pi$
$920$	11.2167	0.369803
$921$	39.8925	1.31450
$922$	31.4785	1.03669
$923$	17.1256	0.563697
$924$	−268.611	−8.83666
$925$	3.98508	0.131029
$926$	−6.47220	−0.212690
$927$	32.7599	1.07598
$928$	−60.6717	−1.99165
$929$	1.37412	0.0450833	0.0225417	−	0.999746i	$-0.492824\pi$
$929$	1.37412	0.0450833	0.0225417	+	0.999746i	$0.492824\pi$
$930$	96.7047	3.17107
$931$	−36.1310	−1.18415
$932$	98.2660	3.21881
$933$	−0.557920	−0.0182655
$934$	68.5103	2.24172
$935$	−74.6862	−2.44250
$936$	52.1464	1.70446
$937$	−18.4149	−0.601588	−0.300794	−	0.953689i	$-0.597252\pi$
$937$	−18.4149	−0.601588	−0.300794	+	0.953689i	$0.597252\pi$
$938$	−177.908	−5.80891
$939$	−50.1956	−1.63807
$940$	147.866	4.82287
$941$	26.6119	0.867524	0.433762	−	0.901027i	$-0.357186\pi$
$941$	26.6119	0.867524	0.433762	+	0.901027i	$0.357186\pi$
$942$	154.418	5.03122
$943$	−0.0657483	−0.00214106
$944$	43.0625	1.40157
$945$	−49.5387	−1.61150
$946$	89.8129	2.92007
$947$	23.9395	0.777929	0.388965	−	0.921253i	$-0.372833\pi$
$947$	23.9395	0.777929	0.388965	+	0.921253i	$0.372833\pi$
$948$	49.8085	1.61771
$949$	−5.87318	−0.190652
$950$	8.04780	0.261105
$951$	−94.2745	−3.05706
$952$	−227.066	−7.35926
$953$	36.5692	1.18459	0.592297	−	0.805720i	$-0.298221\pi$
$953$	36.5692	1.18459	0.592297	+	0.805720i	$0.298221\pi$
$954$	72.8897	2.35989
$955$	−63.9559	−2.06957
$956$	25.2778	0.817543
$957$	86.3143	2.79014
$958$	−25.5600	−0.825805
$959$	20.1142	0.649522
$960$	30.6052	0.987777
$961$	−1.78036	−0.0574311
$962$	12.4041	0.399925
$963$	38.8658	1.25243
$964$	−37.1706	−1.19719
$965$	32.5369	1.04740
$966$	−21.7028	−0.698276
$967$	−11.6415	−0.374364	−0.187182	−	0.982325i	$-0.559935\pi$
$967$	−11.6415	−0.374364	−0.187182	+	0.982325i	$0.559935\pi$
$968$	−55.3334	−1.77848
$969$	41.6799	1.33895
$970$	41.2886	1.32570
$971$	−31.9729	−1.02606	−0.513030	−	0.858371i	$-0.671477\pi$
$971$	−31.9729	−1.02606	−0.513030	+	0.858371i	$0.671477\pi$
$972$	−87.0276	−2.79141
$973$	29.8898	0.958224
$974$	−19.4569	−0.623438
$975$	−6.33477	−0.202875
$976$	−80.9272	−2.59041
$977$	46.0841	1.47436	0.737180	−	0.675697i	$-0.236157\pi$
$977$	46.0841	1.47436	0.737180	+	0.675697i	$0.236157\pi$
$978$	−41.3730	−1.32296
$979$	68.7388	2.19690
$980$	190.904	6.09819
$981$	−45.3662	−1.44843
$982$	−102.493	−3.27069
$983$	−53.0628	−1.69244	−0.846220	−	0.532834i	$-0.821127\pi$
$983$	−53.0628	−1.69244	−0.846220	+	0.532834i	$0.821127\pi$
$984$	−1.96317	−0.0625837
$985$	50.5142	1.60952
$986$	127.207	4.05109
$987$	−164.105	−5.22351
$988$	17.5615	0.558705
$989$	5.08728	0.161766
$990$	−127.774	−4.06094
$991$	−35.1291	−1.11591	−0.557956	−	0.829870i	$-0.688414\pi$
$991$	−35.1291	−1.11591	−0.557956	+	0.829870i	$0.688414\pi$
$992$	45.2697	1.43731
$993$	−82.5956	−2.62109
$994$	−127.579	−4.04655
$995$	22.8868	0.725561
$996$	−230.969	−7.31853
$997$	−39.6494	−1.25571	−0.627854	−	0.778331i	$-0.716066\pi$
$997$	−39.6494	−1.25571	−0.627854	+	0.778331i	$0.716066\pi$
$998$	3.40203	0.107689
$999$	11.7177	0.370730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.a.1.19	✓	327

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.a.1.19	✓	327	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58656 q^{2} +2.73680 q^{3} +4.69031 q^{4} +2.52723 q^{5} -7.07890 q^{6} -4.80679 q^{7} -6.95866 q^{8} +4.49006 q^{9} +O(q^{10})\)	\(q-2.58656 q^{2} +2.73680 q^{3} +4.69031 q^{4} +2.52723 q^{5} -7.07890 q^{6} -4.80679 q^{7} -6.95866 q^{8} +4.49006 q^{9} -6.53684 q^{10} +4.35336 q^{11} +12.8364 q^{12} -1.66896 q^{13} +12.4331 q^{14} +6.91651 q^{15} +8.61840 q^{16} -6.78846 q^{17} -11.6138 q^{18} -2.24343 q^{19} +11.8535 q^{20} -13.1552 q^{21} -11.2602 q^{22} -0.637815 q^{23} -19.0444 q^{24} +1.38689 q^{25} +4.31688 q^{26} +4.07798 q^{27} -22.5454 q^{28} +7.24462 q^{29} -17.8900 q^{30} -5.40552 q^{31} -8.37472 q^{32} +11.9143 q^{33} +17.5588 q^{34} -12.1479 q^{35} +21.0598 q^{36} +2.87340 q^{37} +5.80278 q^{38} -4.56761 q^{39} -17.5861 q^{40} +0.103084 q^{41} +34.0268 q^{42} -7.97611 q^{43} +20.4186 q^{44} +11.3474 q^{45} +1.64975 q^{46} +12.4745 q^{47} +23.5868 q^{48} +16.1053 q^{49} -3.58727 q^{50} -18.5786 q^{51} -7.82796 q^{52} -6.27612 q^{53} -10.5480 q^{54} +11.0019 q^{55} +33.4489 q^{56} -6.13981 q^{57} -18.7387 q^{58} +4.99658 q^{59} +32.4406 q^{60} -9.39004 q^{61} +13.9817 q^{62} -21.5828 q^{63} +4.42494 q^{64} -4.21785 q^{65} -30.8170 q^{66} -14.3093 q^{67} -31.8400 q^{68} -1.74557 q^{69} +31.4212 q^{70} -10.2612 q^{71} -31.2448 q^{72} +3.51906 q^{73} -7.43223 q^{74} +3.79563 q^{75} -10.5224 q^{76} -20.9257 q^{77} +11.8144 q^{78} +3.88025 q^{79} +21.7807 q^{80} -2.30957 q^{81} -0.266633 q^{82} -17.9932 q^{83} -61.7021 q^{84} -17.1560 q^{85} +20.6307 q^{86} +19.8271 q^{87} -30.2936 q^{88} +15.7898 q^{89} -29.3508 q^{90} +8.02236 q^{91} -2.99155 q^{92} -14.7938 q^{93} -32.2661 q^{94} -5.66966 q^{95} -22.9199 q^{96} -6.31630 q^{97} -41.6573 q^{98} +19.5468 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * q^99

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