LMFDB - Embedded newform 6009.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6009,2,Mod(1,6009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6009, 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("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6009 = 3 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6009.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:	$47.9821065746$
Analytic rank:	$0$
Dimension:	$93$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66976 q^{2} -1.00000 q^{3} +5.12761 q^{4} +3.59325 q^{5} +2.66976 q^{6} +3.20381 q^{7} -8.34997 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.66976 q^{2} -1.00000 q^{3} +5.12761 q^{4} +3.59325 q^{5} +2.66976 q^{6} +3.20381 q^{7} -8.34997 q^{8} +1.00000 q^{9} -9.59311 q^{10} -4.39470 q^{11} -5.12761 q^{12} +0.328869 q^{13} -8.55341 q^{14} -3.59325 q^{15} +12.0372 q^{16} -1.56905 q^{17} -2.66976 q^{18} +8.37189 q^{19} +18.4248 q^{20} -3.20381 q^{21} +11.7328 q^{22} -3.55036 q^{23} +8.34997 q^{24} +7.91144 q^{25} -0.878001 q^{26} -1.00000 q^{27} +16.4279 q^{28} +5.83272 q^{29} +9.59311 q^{30} -0.627775 q^{31} -15.4364 q^{32} +4.39470 q^{33} +4.18900 q^{34} +11.5121 q^{35} +5.12761 q^{36} +0.134448 q^{37} -22.3509 q^{38} -0.328869 q^{39} -30.0035 q^{40} -9.44514 q^{41} +8.55341 q^{42} -7.06029 q^{43} -22.5343 q^{44} +3.59325 q^{45} +9.47860 q^{46} -2.85307 q^{47} -12.0372 q^{48} +3.26441 q^{49} -21.1216 q^{50} +1.56905 q^{51} +1.68631 q^{52} +3.17956 q^{53} +2.66976 q^{54} -15.7913 q^{55} -26.7517 q^{56} -8.37189 q^{57} -15.5720 q^{58} +10.4103 q^{59} -18.4248 q^{60} +9.38025 q^{61} +1.67601 q^{62} +3.20381 q^{63} +17.1372 q^{64} +1.18171 q^{65} -11.7328 q^{66} +5.73997 q^{67} -8.04550 q^{68} +3.55036 q^{69} -30.7345 q^{70} +4.95958 q^{71} -8.34997 q^{72} -13.4311 q^{73} -0.358945 q^{74} -7.91144 q^{75} +42.9278 q^{76} -14.0798 q^{77} +0.878001 q^{78} -0.579997 q^{79} +43.2526 q^{80} +1.00000 q^{81} +25.2162 q^{82} +5.03840 q^{83} -16.4279 q^{84} -5.63800 q^{85} +18.8493 q^{86} -5.83272 q^{87} +36.6956 q^{88} -10.7774 q^{89} -9.59311 q^{90} +1.05363 q^{91} -18.2049 q^{92} +0.627775 q^{93} +7.61702 q^{94} +30.0823 q^{95} +15.4364 q^{96} -1.76040 q^{97} -8.71520 q^{98} -4.39470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) $ 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9} + 19 q^{10} + 10 q^{11} - 114 q^{12} + 20 q^{13} + 13 q^{14} + 20 q^{15} + 148 q^{16} - 43 q^{17} + 2 q^{18} + 50 q^{19} - 31 q^{20} - 28 q^{21} + 36 q^{22} + 21 q^{23} - 6 q^{24} + 137 q^{25} + 2 q^{26} - 93 q^{27} + 62 q^{28} - q^{29} - 19 q^{30} + 58 q^{31} + 19 q^{32} - 10 q^{33} + 30 q^{34} + 30 q^{35} + 114 q^{36} + 42 q^{37} - 6 q^{38} - 20 q^{39} + 53 q^{40} - 7 q^{41} - 13 q^{42} + 60 q^{43} + 25 q^{44} - 20 q^{45} + 57 q^{46} + 9 q^{47} - 148 q^{48} + 145 q^{49} + 41 q^{50} + 43 q^{51} + 71 q^{52} - 45 q^{53} - 2 q^{54} + 78 q^{55} + 44 q^{56} - 50 q^{57} + 40 q^{58} + 42 q^{59} + 31 q^{60} + 69 q^{61} - 42 q^{62} + 28 q^{63} + 230 q^{64} - 4 q^{65} - 36 q^{66} + 76 q^{67} - 91 q^{68} - 21 q^{69} + 57 q^{70} + 92 q^{71} + 6 q^{72} + 29 q^{73} + 59 q^{74} - 137 q^{75} + 131 q^{76} - 98 q^{77} - 2 q^{78} + 215 q^{79} - 37 q^{80} + 93 q^{81} + 50 q^{82} - 27 q^{83} - 62 q^{84} + 52 q^{85} + 82 q^{86} + q^{87} + 136 q^{88} - 14 q^{89} + 19 q^{90} + 101 q^{91} - 14 q^{92} - 58 q^{93} + 112 q^{94} + 59 q^{95} - 19 q^{96} + 38 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9 + 19 * q^10 + 10 * q^11 - 114 * q^12 + 20 * q^13 + 13 * q^14 + 20 * q^15 + 148 * q^16 - 43 * q^17 + 2 * q^18 + 50 * q^19 - 31 * q^20 - 28 * q^21 + 36 * q^22 + 21 * q^23 - 6 * q^24 + 137 * q^25 + 2 * q^26 - 93 * q^27 + 62 * q^28 - q^29 - 19 * q^30 + 58 * q^31 + 19 * q^32 - 10 * q^33 + 30 * q^34 + 30 * q^35 + 114 * q^36 + 42 * q^37 - 6 * q^38 - 20 * q^39 + 53 * q^40 - 7 * q^41 - 13 * q^42 + 60 * q^43 + 25 * q^44 - 20 * q^45 + 57 * q^46 + 9 * q^47 - 148 * q^48 + 145 * q^49 + 41 * q^50 + 43 * q^51 + 71 * q^52 - 45 * q^53 - 2 * q^54 + 78 * q^55 + 44 * q^56 - 50 * q^57 + 40 * q^58 + 42 * q^59 + 31 * q^60 + 69 * q^61 - 42 * q^62 + 28 * q^63 + 230 * q^64 - 4 * q^65 - 36 * q^66 + 76 * q^67 - 91 * q^68 - 21 * q^69 + 57 * q^70 + 92 * q^71 + 6 * q^72 + 29 * q^73 + 59 * q^74 - 137 * q^75 + 131 * q^76 - 98 * q^77 - 2 * q^78 + 215 * q^79 - 37 * q^80 + 93 * q^81 + 50 * q^82 - 27 * q^83 - 62 * q^84 + 52 * q^85 + 82 * q^86 + q^87 + 136 * q^88 - 14 * q^89 + 19 * q^90 + 101 * q^91 - 14 * q^92 - 58 * q^93 + 112 * q^94 + 59 * q^95 - 19 * q^96 + 38 * q^97 - 16 * q^98 + 10 * 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 $

$2$	−2.66976	−1.88780	−0.943902	−	0.330225i	$-0.892875\pi$
$2$	−2.66976	−1.88780	−0.943902	+	0.330225i	$0.892875\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.12761	2.56381
$5$	3.59325	1.60695	0.803475	−	0.595338i	$-0.202982\pi$
$5$	3.59325	1.60695	0.803475	+	0.595338i	$0.202982\pi$
$6$	2.66976	1.08992
$7$	3.20381	1.21093	0.605464	−	0.795873i	$-0.292988\pi$
$7$	3.20381	1.21093	0.605464	+	0.795873i	$0.292988\pi$
$8$	−8.34997	−2.95216
$9$	1.00000	0.333333
$10$	−9.59311	−3.03361
$11$	−4.39470	−1.32505	−0.662526	−	0.749039i	$-0.730516\pi$
$11$	−4.39470	−1.32505	−0.662526	+	0.749039i	$0.730516\pi$
$12$	−5.12761	−1.48021
$13$	0.328869	0.0912118	0.0456059	−	0.998960i	$-0.485478\pi$
$13$	0.328869	0.0912118	0.0456059	+	0.998960i	$0.485478\pi$
$14$	−8.55341	−2.28599
$15$	−3.59325	−0.927773
$16$	12.0372	3.00929
$17$	−1.56905	−0.380551	−0.190276	−	0.981731i	$-0.560938\pi$
$17$	−1.56905	−0.380551	−0.190276	+	0.981731i	$0.560938\pi$
$18$	−2.66976	−0.629268
$19$	8.37189	1.92064	0.960322	−	0.278894i	$-0.0899677\pi$
$19$	8.37189	1.92064	0.960322	+	0.278894i	$0.0899677\pi$
$20$	18.4248	4.11991
$21$	−3.20381	−0.699129
$22$	11.7328	2.50144
$23$	−3.55036	−0.740301	−0.370150	−	0.928972i	$-0.620694\pi$
$23$	−3.55036	−0.740301	−0.370150	+	0.928972i	$0.620694\pi$
$24$	8.34997	1.70443
$25$	7.91144	1.58229
$26$	−0.878001	−0.172190
$27$	−1.00000	−0.192450
$28$	16.4279	3.10458
$29$	5.83272	1.08311	0.541555	−	0.840665i	$-0.317836\pi$
$29$	5.83272	1.08311	0.541555	+	0.840665i	$0.317836\pi$
$30$	9.59311	1.75145
$31$	−0.627775	−0.112752	−0.0563759	−	0.998410i	$-0.517955\pi$
$31$	−0.627775	−0.112752	−0.0563759	+	0.998410i	$0.517955\pi$
$32$	−15.4364	−2.72880
$33$	4.39470	0.765019
$34$	4.18900	0.718407
$35$	11.5121	1.94590
$36$	5.12761	0.854602
$37$	0.134448	0.0221032	0.0110516	−	0.999939i	$-0.496482\pi$
$37$	0.134448	0.0221032	0.0110516	+	0.999939i	$0.496482\pi$
$38$	−22.3509	−3.62580
$39$	−0.328869	−0.0526612
$40$	−30.0035	−4.74397
$41$	−9.44514	−1.47508	−0.737541	−	0.675302i	$-0.764013\pi$
$41$	−9.44514	−1.47508	−0.737541	+	0.675302i	$0.764013\pi$
$42$	8.55341	1.31982
$43$	−7.06029	−1.07668	−0.538342	−	0.842726i	$-0.680949\pi$
$43$	−7.06029	−1.07668	−0.538342	+	0.842726i	$0.680949\pi$
$44$	−22.5343	−3.39718
$45$	3.59325	0.535650
$46$	9.47860	1.39754
$47$	−2.85307	−0.416164	−0.208082	−	0.978111i	$-0.566722\pi$
$47$	−2.85307	−0.416164	−0.208082	+	0.978111i	$0.566722\pi$
$48$	−12.0372	−1.73742
$49$	3.26441	0.466345
$50$	−21.1216	−2.98705
$51$	1.56905	0.219711
$52$	1.68631	0.233849
$53$	3.17956	0.436746	0.218373	−	0.975865i	$-0.429925\pi$
$53$	3.17956	0.436746	0.218373	+	0.975865i	$0.429925\pi$
$54$	2.66976	0.363308
$55$	−15.7913	−2.12929
$56$	−26.7517	−3.57485
$57$	−8.37189	−1.10888
$58$	−15.5720	−2.04470
$59$	10.4103	1.35530	0.677652	−	0.735383i	$-0.262997\pi$
$59$	10.4103	1.35530	0.677652	+	0.735383i	$0.262997\pi$
$60$	−18.4248	−2.37863
$61$	9.38025	1.20102	0.600509	−	0.799618i	$-0.294965\pi$
$61$	9.38025	1.20102	0.600509	+	0.799618i	$0.294965\pi$
$62$	1.67601	0.212853
$63$	3.20381	0.403642
$64$	17.1372	2.14214
$65$	1.18171	0.146573
$66$	−11.7328	−1.44421
$67$	5.73997	0.701248	0.350624	−	0.936516i	$-0.385969\pi$
$67$	5.73997	0.701248	0.350624	+	0.936516i	$0.385969\pi$
$68$	−8.04550	−0.975660
$69$	3.55036	0.427413
$70$	−30.7345	−3.67348
$71$	4.95958	0.588594	0.294297	−	0.955714i	$-0.404915\pi$
$71$	4.95958	0.588594	0.294297	+	0.955714i	$0.404915\pi$
$72$	−8.34997	−0.984053
$73$	−13.4311	−1.57199	−0.785995	−	0.618233i	$-0.787849\pi$
$73$	−13.4311	−1.57199	−0.785995	+	0.618233i	$0.787849\pi$
$74$	−0.358945	−0.0417265
$75$	−7.91144	−0.913535
$76$	42.9278	4.92416
$77$	−14.0798	−1.60454
$78$	0.878001	0.0994140
$79$	−0.579997	−0.0652548	−0.0326274	−	0.999468i	$-0.510387\pi$
$79$	−0.579997	−0.0652548	−0.0326274	+	0.999468i	$0.510387\pi$
$80$	43.2526	4.83578
$81$	1.00000	0.111111
$82$	25.2162	2.78467
$83$	5.03840	0.553036	0.276518	−	0.961009i	$-0.410819\pi$
$83$	5.03840	0.553036	0.276518	+	0.961009i	$0.410819\pi$
$84$	−16.4279	−1.79243
$85$	−5.63800	−0.611527
$86$	18.8493	2.03257
$87$	−5.83272	−0.625334
$88$	36.6956	3.91176
$89$	−10.7774	−1.14241	−0.571203	−	0.820809i	$-0.693523\pi$
$89$	−10.7774	−1.14241	−0.571203	+	0.820809i	$0.693523\pi$
$90$	−9.59311	−1.01120
$91$	1.05363	0.110451
$92$	−18.2049	−1.89799
$93$	0.627775	0.0650972
$94$	7.61702	0.785636
$95$	30.0823	3.08638
$96$	15.4364	1.57547
$97$	−1.76040	−0.178741	−0.0893707	−	0.995998i	$-0.528486\pi$
$97$	−1.76040	−0.178741	−0.0893707	+	0.995998i	$0.528486\pi$
$98$	−8.71520	−0.880368
$99$	−4.39470	−0.441684
$100$	40.5668	4.05668
$101$	9.59807	0.955043	0.477522	−	0.878620i	$-0.341535\pi$
$101$	9.59807	0.955043	0.477522	+	0.878620i	$0.341535\pi$
$102$	−4.18900	−0.414772
$103$	0.984673	0.0970227	0.0485113	−	0.998823i	$-0.484552\pi$
$103$	0.984673	0.0970227	0.0485113	+	0.998823i	$0.484552\pi$
$104$	−2.74604	−0.269272
$105$	−11.5121	−1.12347
$106$	−8.48866	−0.824492
$107$	19.7948	1.91364	0.956818	−	0.290686i	$-0.0938836\pi$
$107$	19.7948	1.91364	0.956818	+	0.290686i	$0.0938836\pi$
$108$	−5.12761	−0.493405
$109$	−2.56334	−0.245523	−0.122762	−	0.992436i	$-0.539175\pi$
$109$	−2.56334	−0.245523	−0.122762	+	0.992436i	$0.539175\pi$
$110$	42.1588	4.01969
$111$	−0.134448	−0.0127613
$112$	38.5648	3.64404
$113$	16.8712	1.58711	0.793555	−	0.608499i	$-0.208228\pi$
$113$	16.8712	1.58711	0.793555	+	0.608499i	$0.208228\pi$
$114$	22.3509	2.09336
$115$	−12.7573	−1.18963
$116$	29.9079	2.77688
$117$	0.328869	0.0304039
$118$	−27.7930	−2.55855
$119$	−5.02695	−0.460820
$120$	30.0035	2.73893
$121$	8.31338	0.755762
$122$	−25.0430	−2.26729
$123$	9.44514	0.851639
$124$	−3.21899	−0.289073
$125$	10.4615	0.935709
$126$	−8.55341	−0.761998
$127$	14.0952	1.25074	0.625372	−	0.780327i	$-0.284947\pi$
$127$	14.0952	1.25074	0.625372	+	0.780327i	$0.284947\pi$
$128$	−14.8792	−1.31515
$129$	7.06029	0.621624
$130$	−3.15488	−0.276701
$131$	15.0160	1.31196	0.655978	−	0.754780i	$-0.272257\pi$
$131$	15.0160	1.31196	0.655978	+	0.754780i	$0.272257\pi$
$132$	22.5343	1.96136
$133$	26.8220	2.32576
$134$	−15.3243	−1.32382
$135$	−3.59325	−0.309258
$136$	13.1015	1.12345
$137$	−4.03335	−0.344592	−0.172296	−	0.985045i	$-0.555119\pi$
$137$	−4.03335	−0.344592	−0.172296	+	0.985045i	$0.555119\pi$
$138$	−9.47860	−0.806872
$139$	19.5152	1.65526	0.827629	−	0.561275i	$-0.189689\pi$
$139$	19.5152	1.65526	0.827629	+	0.561275i	$0.189689\pi$
$140$	59.0296	4.98891
$141$	2.85307	0.240272
$142$	−13.2409	−1.11115
$143$	−1.44528	−0.120860
$144$	12.0372	1.00310
$145$	20.9584	1.74050
$146$	35.8578	2.96761
$147$	−3.26441	−0.269244
$148$	0.689399	0.0566682
$149$	−16.5449	−1.35541	−0.677707	−	0.735332i	$-0.737026\pi$
$149$	−16.5449	−1.35541	−0.677707	+	0.735332i	$0.737026\pi$
$150$	21.1216	1.72458
$151$	−14.3071	−1.16430	−0.582149	−	0.813082i	$-0.697788\pi$
$151$	−14.3071	−1.16430	−0.582149	+	0.813082i	$0.697788\pi$
$152$	−69.9050	−5.67005
$153$	−1.56905	−0.126850
$154$	37.5896	3.02906
$155$	−2.25575	−0.181186
$156$	−1.68631	−0.135013
$157$	17.1547	1.36910	0.684549	−	0.728967i	$-0.259999\pi$
$157$	17.1547	1.36910	0.684549	+	0.728967i	$0.259999\pi$
$158$	1.54845	0.123188
$159$	−3.17956	−0.252156
$160$	−55.4669	−4.38504
$161$	−11.3747	−0.896450
$162$	−2.66976	−0.209756
$163$	−4.92495	−0.385752	−0.192876	−	0.981223i	$-0.561781\pi$
$163$	−4.92495	−0.385752	−0.192876	+	0.981223i	$0.561781\pi$
$164$	−48.4310	−3.78182
$165$	15.7913	1.22935
$166$	−13.4513	−1.04402
$167$	−3.59401	−0.278113	−0.139057	−	0.990284i	$-0.544407\pi$
$167$	−3.59401	−0.278113	−0.139057	+	0.990284i	$0.544407\pi$
$168$	26.7517	2.06394
$169$	−12.8918	−0.991680
$170$	15.0521	1.15444
$171$	8.37189	0.640215
$172$	−36.2024	−2.76041
$173$	−16.0006	−1.21650	−0.608252	−	0.793744i	$-0.708129\pi$
$173$	−16.0006	−1.21650	−0.608252	+	0.793744i	$0.708129\pi$
$174$	15.5720	1.18051
$175$	25.3468	1.91604
$176$	−52.8998	−3.98747
$177$	−10.4103	−0.782485
$178$	28.7731	2.15664
$179$	5.53747	0.413890	0.206945	−	0.978353i	$-0.433648\pi$
$179$	5.53747	0.413890	0.206945	+	0.978353i	$0.433648\pi$
$180$	18.4248	1.37330
$181$	6.83281	0.507879	0.253939	−	0.967220i	$-0.418274\pi$
$181$	6.83281	0.507879	0.253939	+	0.967220i	$0.418274\pi$
$182$	−2.81295	−0.208510
$183$	−9.38025	−0.693408
$184$	29.6454	2.18549
$185$	0.483107	0.0355187
$186$	−1.67601	−0.122891
$187$	6.89552	0.504250
$188$	−14.6295	−1.06696
$189$	−3.20381	−0.233043
$190$	−80.3125	−5.82648
$191$	11.6860	0.845572	0.422786	−	0.906230i	$-0.361052\pi$
$191$	11.6860	0.845572	0.422786	+	0.906230i	$0.361052\pi$
$192$	−17.1372	−1.23677
$193$	10.6623	0.767490	0.383745	−	0.923439i	$-0.374634\pi$
$193$	10.6623	0.767490	0.383745	+	0.923439i	$0.374634\pi$
$194$	4.69984	0.337429
$195$	−1.18171	−0.0846239
$196$	16.7386	1.19562
$197$	−1.94123	−0.138307	−0.0691535	−	0.997606i	$-0.522030\pi$
$197$	−1.94123	−0.138307	−0.0691535	+	0.997606i	$0.522030\pi$
$198$	11.7328	0.833813
$199$	10.2086	0.723671	0.361836	−	0.932242i	$-0.382150\pi$
$199$	10.2086	0.723671	0.361836	+	0.932242i	$0.382150\pi$
$200$	−66.0603	−4.67117
$201$	−5.73997	−0.404866
$202$	−25.6245	−1.80293
$203$	18.6870	1.31157
$204$	8.04550	0.563298
$205$	−33.9387	−2.37038
$206$	−2.62884	−0.183160
$207$	−3.55036	−0.246767
$208$	3.95865	0.274483
$209$	−36.7920	−2.54495
$210$	30.7345	2.12088
$211$	18.4893	1.27285	0.636427	−	0.771337i	$-0.280412\pi$
$211$	18.4893	1.27285	0.636427	+	0.771337i	$0.280412\pi$
$212$	16.3036	1.11973
$213$	−4.95958	−0.339825
$214$	−52.8474	−3.61257
$215$	−25.3694	−1.73018
$216$	8.34997	0.568143
$217$	−2.01127	−0.136534
$218$	6.84350	0.463500
$219$	13.4311	0.907589
$220$	−80.9714	−5.45909
$221$	−0.516013	−0.0347108
$222$	0.358945	0.0240908
$223$	18.8393	1.26157	0.630787	−	0.775956i	$-0.282732\pi$
$223$	18.8393	1.26157	0.630787	+	0.775956i	$0.282732\pi$
$224$	−49.4554	−3.30438
$225$	7.91144	0.527430
$226$	−45.0420	−2.99615
$227$	−6.54262	−0.434249	−0.217124	−	0.976144i	$-0.569668\pi$
$227$	−6.54262	−0.434249	−0.217124	+	0.976144i	$0.569668\pi$
$228$	−42.9278	−2.84296
$229$	16.9405	1.11946	0.559731	−	0.828675i	$-0.310905\pi$
$229$	16.9405	1.11946	0.559731	+	0.828675i	$0.310905\pi$
$230$	34.0590	2.24578
$231$	14.0798	0.926382
$232$	−48.7030	−3.19751
$233$	−25.0692	−1.64234	−0.821170	−	0.570684i	$-0.806678\pi$
$233$	−25.0692	−1.64234	−0.821170	+	0.570684i	$0.806678\pi$
$234$	−0.878001	−0.0573967
$235$	−10.2518	−0.668754
$236$	53.3799	3.47474
$237$	0.579997	0.0376749
$238$	13.4208	0.869938
$239$	−2.79610	−0.180865	−0.0904323	−	0.995903i	$-0.528825\pi$
$239$	−2.79610	−0.180865	−0.0904323	+	0.995903i	$0.528825\pi$
$240$	−43.2526	−2.79194
$241$	14.4911	0.933452	0.466726	−	0.884402i	$-0.345433\pi$
$241$	14.4911	0.933452	0.466726	+	0.884402i	$0.345433\pi$
$242$	−22.1947	−1.42673
$243$	−1.00000	−0.0641500
$244$	48.0983	3.07918
$245$	11.7299	0.749393
$246$	−25.2162	−1.60773
$247$	2.75326	0.175185
$248$	5.24190	0.332861
$249$	−5.03840	−0.319296
$250$	−27.9298	−1.76644
$251$	6.36250	0.401598	0.200799	−	0.979632i	$-0.435646\pi$
$251$	6.36250	0.401598	0.200799	+	0.979632i	$0.435646\pi$
$252$	16.4279	1.03486
$253$	15.6028	0.980937
$254$	−37.6307	−2.36116
$255$	5.63800	0.353065
$256$	5.44966	0.340604
$257$	1.45774	0.0909311	0.0454656	−	0.998966i	$-0.485523\pi$
$257$	1.45774	0.0909311	0.0454656	+	0.998966i	$0.485523\pi$
$258$	−18.8493	−1.17350
$259$	0.430747	0.0267653
$260$	6.05934	0.375784
$261$	5.83272	0.361036
$262$	−40.0891	−2.47671
$263$	16.7158	1.03074	0.515370	−	0.856968i	$-0.327654\pi$
$263$	16.7158	1.03074	0.515370	+	0.856968i	$0.327654\pi$
$264$	−36.6956	−2.25846
$265$	11.4250	0.701830
$266$	−71.6082	−4.39058
$267$	10.7774	0.659568
$268$	29.4323	1.79786
$269$	6.10423	0.372181	0.186091	−	0.982533i	$-0.440418\pi$
$269$	6.10423	0.372181	0.186091	+	0.982533i	$0.440418\pi$
$270$	9.59311	0.583818
$271$	−12.7576	−0.774969	−0.387485	−	0.921876i	$-0.626656\pi$
$271$	−12.7576	−0.774969	−0.387485	+	0.921876i	$0.626656\pi$
$272$	−18.8870	−1.14519
$273$	−1.05363	−0.0637689
$274$	10.7681	0.650523
$275$	−34.7684	−2.09661
$276$	18.2049	1.09580
$277$	5.41921	0.325609	0.162804	−	0.986658i	$-0.447946\pi$
$277$	5.41921	0.325609	0.162804	+	0.986658i	$0.447946\pi$
$278$	−52.1009	−3.12480
$279$	−0.627775	−0.0375839
$280$	−96.1256	−5.74461
$281$	25.7270	1.53474	0.767371	−	0.641204i	$-0.221565\pi$
$281$	25.7270	1.53474	0.767371	+	0.641204i	$0.221565\pi$
$282$	−7.61702	−0.453587
$283$	5.75656	0.342192	0.171096	−	0.985254i	$-0.445269\pi$
$283$	5.75656	0.342192	0.171096	+	0.985254i	$0.445269\pi$
$284$	25.4308	1.50904
$285$	−30.0823	−1.78192
$286$	3.85855	0.228161
$287$	−30.2604	−1.78622
$288$	−15.4364	−0.909599
$289$	−14.5381	−0.855181
$290$	−55.9540	−3.28573
$291$	1.76040	0.103196
$292$	−68.8694	−4.03028
$293$	0.835107	0.0487875	0.0243937	−	0.999702i	$-0.492234\pi$
$293$	0.835107	0.0487875	0.0243937	+	0.999702i	$0.492234\pi$
$294$	8.71520	0.508281
$295$	37.4068	2.17791
$296$	−1.12264	−0.0652521
$297$	4.39470	0.255006
$298$	44.1710	2.55876
$299$	−1.16760	−0.0675242
$300$	−40.5668	−2.34213
$301$	−22.6199	−1.30379
$302$	38.1966	2.19797
$303$	−9.59807	−0.551394
$304$	100.774	5.77978
$305$	33.7056	1.92998
$306$	4.18900	0.239469
$307$	1.03572	0.0591115	0.0295558	−	0.999563i	$-0.490591\pi$
$307$	1.03572	0.0591115	0.0295558	+	0.999563i	$0.490591\pi$
$308$	−72.1957	−4.11373
$309$	−0.984673	−0.0560161
$310$	6.02231	0.342044
$311$	−2.60537	−0.147737	−0.0738685	−	0.997268i	$-0.523535\pi$
$311$	−2.60537	−0.147737	−0.0738685	+	0.997268i	$0.523535\pi$
$312$	2.74604	0.155464
$313$	−28.8252	−1.62930	−0.814648	−	0.579956i	$-0.803070\pi$
$313$	−28.8252	−1.62930	−0.814648	+	0.579956i	$0.803070\pi$
$314$	−45.7990	−2.58459
$315$	11.5121	0.648633
$316$	−2.97400	−0.167301
$317$	5.28930	0.297077	0.148538	−	0.988907i	$-0.452543\pi$
$317$	5.28930	0.297077	0.148538	+	0.988907i	$0.452543\pi$
$318$	8.48866	0.476020
$319$	−25.6331	−1.43518
$320$	61.5781	3.44232
$321$	−19.7948	−1.10484
$322$	30.3676	1.69232
$323$	−13.1360	−0.730904
$324$	5.12761	0.284867
$325$	2.60183	0.144323
$326$	13.1484	0.728224
$327$	2.56334	0.141753
$328$	78.8666	4.35468
$329$	−9.14071	−0.503944
$330$	−42.1588	−2.32077
$331$	18.7756	1.03200	0.515999	−	0.856589i	$-0.327421\pi$
$331$	18.7756	1.03200	0.515999	+	0.856589i	$0.327421\pi$
$332$	25.8350	1.41788
$333$	0.134448	0.00736772
$334$	9.59515	0.525023
$335$	20.6251	1.12687
$336$	−38.5648	−2.10388
$337$	4.68017	0.254945	0.127472	−	0.991842i	$-0.459314\pi$
$337$	4.68017	0.254945	0.127472	+	0.991842i	$0.459314\pi$
$338$	34.4181	1.87210
$339$	−16.8712	−0.916318
$340$	−28.9095	−1.56784
$341$	2.75888	0.149402
$342$	−22.3509	−1.20860
$343$	−11.9681	−0.646218
$344$	58.9532	3.17854
$345$	12.7573	0.686831
$346$	42.7178	2.29652
$347$	30.2653	1.62473	0.812363	−	0.583152i	$-0.198181\pi$
$347$	30.2653	1.62473	0.812363	+	0.583152i	$0.198181\pi$
$348$	−29.9079	−1.60323
$349$	21.0554	1.12707	0.563534	−	0.826093i	$-0.309441\pi$
$349$	21.0554	1.12707	0.563534	+	0.826093i	$0.309441\pi$
$350$	−67.6698	−3.61710
$351$	−0.328869	−0.0175537
$352$	67.8384	3.61580
$353$	−7.40884	−0.394333	−0.197166	−	0.980370i	$-0.563174\pi$
$353$	−7.40884	−0.394333	−0.197166	+	0.980370i	$0.563174\pi$
$354$	27.7930	1.47718
$355$	17.8210	0.945841
$356$	−55.2625	−2.92891
$357$	5.02695	0.266055
$358$	−14.7837	−0.781344
$359$	29.7097	1.56802	0.784009	−	0.620750i	$-0.213172\pi$
$359$	29.7097	1.56802	0.784009	+	0.620750i	$0.213172\pi$
$360$	−30.0035	−1.58132
$361$	51.0886	2.68887
$362$	−18.2419	−0.958776
$363$	−8.31338	−0.436340
$364$	5.40263	0.283175
$365$	−48.2613	−2.52611
$366$	25.0430	1.30902
$367$	−30.5353	−1.59393	−0.796965	−	0.604025i	$-0.793563\pi$
$367$	−30.5353	−1.59393	−0.796965	+	0.604025i	$0.793563\pi$
$368$	−42.7363	−2.22778
$369$	−9.44514	−0.491694
$370$	−1.28978	−0.0670524
$371$	10.1867	0.528868
$372$	3.21899	0.166897
$373$	−25.9475	−1.34351	−0.671754	−	0.740774i	$-0.734459\pi$
$373$	−25.9475	−1.34351	−0.671754	+	0.740774i	$0.734459\pi$
$374$	−18.4094	−0.951926
$375$	−10.4615	−0.540232
$376$	23.8231	1.22858
$377$	1.91820	0.0987924
$378$	8.55341	0.439940
$379$	−33.0760	−1.69900	−0.849500	−	0.527589i	$-0.823096\pi$
$379$	−33.0760	−1.69900	−0.849500	+	0.527589i	$0.823096\pi$
$380$	154.250	7.91288
$381$	−14.0952	−0.722118
$382$	−31.1989	−1.59627
$383$	2.27668	0.116333	0.0581664	−	0.998307i	$-0.481475\pi$
$383$	2.27668	0.116333	0.0581664	+	0.998307i	$0.481475\pi$
$384$	14.8792	0.759303
$385$	−50.5922	−2.57842
$386$	−28.4658	−1.44887
$387$	−7.06029	−0.358895
$388$	−9.02664	−0.458258
$389$	9.51643	0.482502	0.241251	−	0.970463i	$-0.422442\pi$
$389$	9.51643	0.482502	0.241251	+	0.970463i	$0.422442\pi$
$390$	3.15488	0.159753
$391$	5.57070	0.281723
$392$	−27.2577	−1.37672
$393$	−15.0160	−0.757458
$394$	5.18262	0.261096
$395$	−2.08408	−0.104861
$396$	−22.5343	−1.13239
$397$	25.5120	1.28041	0.640206	−	0.768203i	$-0.278849\pi$
$397$	25.5120	1.28041	0.640206	+	0.768203i	$0.278849\pi$
$398$	−27.2546	−1.36615
$399$	−26.8220	−1.34278
$400$	95.2314	4.76157
$401$	−17.5219	−0.875002	−0.437501	−	0.899218i	$-0.644136\pi$
$401$	−17.5219	−0.875002	−0.437501	+	0.899218i	$0.644136\pi$
$402$	15.3243	0.764308
$403$	−0.206456	−0.0102843
$404$	49.2151	2.44854
$405$	3.59325	0.178550
$406$	−49.8896	−2.47598
$407$	−0.590860	−0.0292879
$408$	−13.1015	−0.648623
$409$	−27.9118	−1.38015	−0.690074	−	0.723738i	$-0.742422\pi$
$409$	−27.9118	−1.38015	−0.690074	+	0.723738i	$0.742422\pi$
$410$	90.6082	4.47482
$411$	4.03335	0.198951
$412$	5.04902	0.248747
$413$	33.3526	1.64118
$414$	9.47860	0.465848
$415$	18.1042	0.888702
$416$	−5.07656	−0.248899
$417$	−19.5152	−0.955664
$418$	98.2256	4.80437
$419$	−8.60907	−0.420581	−0.210290	−	0.977639i	$-0.567441\pi$
$419$	−8.60907	−0.420581	−0.210290	+	0.977639i	$0.567441\pi$
$420$	−59.0296	−2.88035
$421$	25.3158	1.23382	0.616908	−	0.787035i	$-0.288385\pi$
$421$	25.3158	1.23382	0.616908	+	0.787035i	$0.288385\pi$
$422$	−49.3619	−2.40290
$423$	−2.85307	−0.138721
$424$	−26.5492	−1.28934
$425$	−12.4135	−0.602142
$426$	13.2409	0.641523
$427$	30.0526	1.45435
$428$	101.500	4.90619
$429$	1.44528	0.0697788
$430$	67.7302	3.26624
$431$	19.2030	0.924977	0.462488	−	0.886625i	$-0.346957\pi$
$431$	19.2030	0.924977	0.462488	+	0.886625i	$0.346957\pi$
$432$	−12.0372	−0.579139
$433$	−38.6494	−1.85737	−0.928685	−	0.370869i	$-0.879060\pi$
$433$	−38.6494	−1.85737	−0.928685	+	0.370869i	$0.879060\pi$
$434$	5.36961	0.257750
$435$	−20.9584	−1.00488
$436$	−13.1438	−0.629474
$437$	−29.7232	−1.42185
$438$	−35.8578	−1.71335
$439$	−10.2040	−0.487009	−0.243505	−	0.969900i	$-0.578297\pi$
$439$	−10.2040	−0.487009	−0.243505	+	0.969900i	$0.578297\pi$
$440$	131.856	6.28601
$441$	3.26441	0.155448
$442$	1.37763	0.0655272
$443$	−20.2066	−0.960045	−0.480022	−	0.877256i	$-0.659371\pi$
$443$	−20.2066	−0.960045	−0.480022	+	0.877256i	$0.659371\pi$
$444$	−0.689399	−0.0327174
$445$	−38.7260	−1.83579
$446$	−50.2964	−2.38160
$447$	16.5449	0.782549
$448$	54.9042	2.59398
$449$	−23.6826	−1.11765	−0.558825	−	0.829285i	$-0.688748\pi$
$449$	−23.6826	−1.11765	−0.558825	+	0.829285i	$0.688748\pi$
$450$	−21.1216	−0.995684
$451$	41.5085	1.95456
$452$	86.5090	4.06904
$453$	14.3071	0.672208
$454$	17.4672	0.819776
$455$	3.78597	0.177489
$456$	69.9050	3.27360
$457$	−21.7010	−1.01513	−0.507565	−	0.861614i	$-0.669454\pi$
$457$	−21.7010	−1.01513	−0.507565	+	0.861614i	$0.669454\pi$
$458$	−45.2271	−2.11332
$459$	1.56905	0.0732372
$460$	−65.4146	−3.04997
$461$	−10.1055	−0.470658	−0.235329	−	0.971916i	$-0.575617\pi$
$461$	−10.1055	−0.470658	−0.235329	+	0.971916i	$0.575617\pi$
$462$	−37.5896	−1.74883
$463$	2.71206	0.126040	0.0630202	−	0.998012i	$-0.479927\pi$
$463$	2.71206	0.126040	0.0630202	+	0.998012i	$0.479927\pi$
$464$	70.2095	3.25939
$465$	2.25575	0.104608
$466$	66.9288	3.10042
$467$	−36.4499	−1.68670	−0.843350	−	0.537365i	$-0.819420\pi$
$467$	−36.4499	−1.68670	−0.843350	+	0.537365i	$0.819420\pi$
$468$	1.68631	0.0779498
$469$	18.3898	0.849161
$470$	27.3699	1.26248
$471$	−17.1547	−0.790449
$472$	−86.9256	−4.00107
$473$	31.0279	1.42666
$474$	−1.54845	−0.0711228
$475$	66.2338	3.03901
$476$	−25.7763	−1.18145
$477$	3.17956	0.145582
$478$	7.46491	0.341437
$479$	−12.4886	−0.570620	−0.285310	−	0.958435i	$-0.592097\pi$
$479$	−12.4886	−0.570620	−0.285310	+	0.958435i	$0.592097\pi$
$480$	55.4669	2.53171
$481$	0.0442159	0.00201607
$482$	−38.6877	−1.76218
$483$	11.3747	0.517566
$484$	42.6278	1.93763
$485$	−6.32555	−0.287228
$486$	2.66976	0.121103
$487$	25.2288	1.14323	0.571614	−	0.820523i	$-0.306317\pi$
$487$	25.2288	1.14323	0.571614	+	0.820523i	$0.306317\pi$
$488$	−78.3248	−3.54560
$489$	4.92495	0.222714
$490$	−31.3159	−1.41471
$491$	−29.1307	−1.31465	−0.657326	−	0.753606i	$-0.728313\pi$
$491$	−29.1307	−1.31465	−0.657326	+	0.753606i	$0.728313\pi$
$492$	48.4310	2.18344
$493$	−9.15186	−0.412179
$494$	−7.35053	−0.330716
$495$	−15.7913	−0.709764
$496$	−7.55664	−0.339303
$497$	15.8896	0.712744
$498$	13.4513	0.602768
$499$	16.2063	0.725492	0.362746	−	0.931888i	$-0.381839\pi$
$499$	16.2063	0.725492	0.362746	+	0.931888i	$0.381839\pi$
$500$	53.6427	2.39898
$501$	3.59401	0.160569
$502$	−16.9864	−0.758138
$503$	14.8140	0.660524	0.330262	−	0.943889i	$-0.392863\pi$
$503$	14.8140	0.660524	0.330262	+	0.943889i	$0.392863\pi$
$504$	−26.7517	−1.19162
$505$	34.4882	1.53471
$506$	−41.6556	−1.85182
$507$	12.8918	0.572547
$508$	72.2746	3.20666
$509$	4.31891	0.191432	0.0957161	−	0.995409i	$-0.469486\pi$
$509$	4.31891	0.191432	0.0957161	+	0.995409i	$0.469486\pi$
$510$	−15.0521	−0.666518
$511$	−43.0307	−1.90357
$512$	15.2092	0.672158
$513$	−8.37189	−0.369628
$514$	−3.89180	−0.171660
$515$	3.53817	0.155911
$516$	36.2024	1.59372
$517$	12.5384	0.551438
$518$	−1.14999	−0.0505277
$519$	16.0006	0.702349
$520$	−9.86723	−0.432706
$521$	23.1922	1.01607	0.508034	−	0.861337i	$-0.330373\pi$
$521$	23.1922	1.01607	0.508034	+	0.861337i	$0.330373\pi$
$522$	−15.5720	−0.681566
$523$	−15.8772	−0.694261	−0.347130	−	0.937817i	$-0.612844\pi$
$523$	−15.8772	−0.694261	−0.347130	+	0.937817i	$0.612844\pi$
$524$	76.9963	3.36360
$525$	−25.3468	−1.10622
$526$	−44.6271	−1.94584
$527$	0.985013	0.0429078
$528$	52.8998	2.30217
$529$	−10.3950	−0.451955
$530$	−30.5019	−1.32492
$531$	10.4103	0.451768
$532$	137.533	5.96280
$533$	−3.10621	−0.134545
$534$	−28.7731	−1.24514
$535$	71.1277	3.07512
$536$	−47.9285	−2.07020
$537$	−5.53747	−0.238960
$538$	−16.2968	−0.702606
$539$	−14.3461	−0.617931
$540$	−18.4248	−0.792877
$541$	−36.6185	−1.57435	−0.787175	−	0.616729i	$-0.788457\pi$
$541$	−36.6185	−1.57435	−0.787175	+	0.616729i	$0.788457\pi$
$542$	34.0597	1.46299
$543$	−6.83281	−0.293224
$544$	24.2206	1.03845
$545$	−9.21072	−0.394544
$546$	2.81295	0.120383
$547$	20.9492	0.895724	0.447862	−	0.894103i	$-0.352186\pi$
$547$	20.9492	0.895724	0.447862	+	0.894103i	$0.352186\pi$
$548$	−20.6815	−0.883468
$549$	9.38025	0.400339
$550$	92.8233	3.95800
$551$	48.8309	2.08027
$552$	−29.6454	−1.26179
$553$	−1.85820	−0.0790188
$554$	−14.4680	−0.614686
$555$	−0.483107	−0.0205067
$556$	100.066	4.24376
$557$	23.1835	0.982317	0.491158	−	0.871070i	$-0.336574\pi$
$557$	23.1835	0.982317	0.491158	+	0.871070i	$0.336574\pi$
$558$	1.67601	0.0709511
$559$	−2.32191	−0.0982064
$560$	138.573	5.85578
$561$	−6.89552	−0.291129
$562$	−68.6848	−2.89729
$563$	−36.9606	−1.55770	−0.778852	−	0.627208i	$-0.784197\pi$
$563$	−36.9606	−1.55770	−0.778852	+	0.627208i	$0.784197\pi$
$564$	14.6295	0.616011
$565$	60.6224	2.55041
$566$	−15.3686	−0.645992
$567$	3.20381	0.134547
$568$	−41.4123	−1.73762
$569$	31.8759	1.33631	0.668155	−	0.744023i	$-0.267085\pi$
$569$	31.8759	1.33631	0.668155	+	0.744023i	$0.267085\pi$
$570$	80.3125	3.36392
$571$	13.3649	0.559303	0.279651	−	0.960102i	$-0.409781\pi$
$571$	13.3649	0.559303	0.279651	+	0.960102i	$0.409781\pi$
$572$	−7.41084	−0.309863
$573$	−11.6860	−0.488191
$574$	80.7881	3.37203
$575$	−28.0885	−1.17137
$576$	17.1372	0.714048
$577$	−18.7586	−0.780932	−0.390466	−	0.920617i	$-0.627686\pi$
$577$	−18.7586	−0.780932	−0.390466	+	0.920617i	$0.627686\pi$
$578$	38.8131	1.61441
$579$	−10.6623	−0.443110
$580$	107.467	4.46231
$581$	16.1421	0.669687
$582$	−4.69984	−0.194815
$583$	−13.9732	−0.578711
$584$	112.149	4.64076
$585$	1.18171	0.0488576
$586$	−2.22953	−0.0921012
$587$	0.462164	0.0190755	0.00953777	−	0.999955i	$-0.496964\pi$
$587$	0.462164	0.0190755	0.00953777	+	0.999955i	$0.496964\pi$
$588$	−16.7386	−0.690290
$589$	−5.25566	−0.216556
$590$	−99.8671	−4.11146
$591$	1.94123	0.0798516
$592$	1.61838	0.0665149
$593$	26.8599	1.10301	0.551503	−	0.834173i	$-0.314055\pi$
$593$	26.8599	1.10301	0.551503	+	0.834173i	$0.314055\pi$
$594$	−11.7328	−0.481402
$595$	−18.0631	−0.740515
$596$	−84.8360	−3.47502
$597$	−10.2086	−0.417812
$598$	3.11722	0.127472
$599$	32.1648	1.31422	0.657109	−	0.753796i	$-0.271779\pi$
$599$	32.1648	1.31422	0.657109	+	0.753796i	$0.271779\pi$
$600$	66.0603	2.69690
$601$	47.9892	1.95752	0.978760	−	0.205007i	$-0.0657219\pi$
$601$	47.9892	1.95752	0.978760	+	0.205007i	$0.0657219\pi$
$602$	60.3896	2.46129
$603$	5.73997	0.233749
$604$	−73.3614	−2.98503
$605$	29.8721	1.21447
$606$	25.6245	1.04092
$607$	−29.8104	−1.20997	−0.604983	−	0.796238i	$-0.706820\pi$
$607$	−29.8104	−1.20997	−0.604983	+	0.796238i	$0.706820\pi$
$608$	−129.232	−5.24105
$609$	−18.6870	−0.757233
$610$	−89.9858	−3.64342
$611$	−0.938288	−0.0379591
$612$	−8.04550	−0.325220
$613$	44.8352	1.81088	0.905439	−	0.424476i	$-0.139542\pi$
$613$	44.8352	1.81088	0.905439	+	0.424476i	$0.139542\pi$
$614$	−2.76511	−0.111591
$615$	33.9387	1.36854
$616$	117.566	4.73686
$617$	5.10023	0.205328	0.102664	−	0.994716i	$-0.467263\pi$
$617$	5.10023	0.205328	0.102664	+	0.994716i	$0.467263\pi$
$618$	2.62884	0.105747
$619$	−10.7379	−0.431591	−0.215796	−	0.976439i	$-0.569234\pi$
$619$	−10.7379	−0.431591	−0.215796	+	0.976439i	$0.569234\pi$
$620$	−11.5666	−0.464527
$621$	3.55036	0.142471
$622$	6.95571	0.278899
$623$	−34.5289	−1.38337
$624$	−3.95865	−0.158473
$625$	−1.96627	−0.0786507
$626$	76.9563	3.07579
$627$	36.7920	1.46933
$628$	87.9628	3.51010
$629$	−0.210957	−0.00841140
$630$	−30.7345	−1.22449
$631$	−42.3970	−1.68780	−0.843898	−	0.536503i	$-0.819745\pi$
$631$	−42.3970	−1.68780	−0.843898	+	0.536503i	$0.819745\pi$
$632$	4.84296	0.192643
$633$	−18.4893	−0.734882
$634$	−14.1212	−0.560823
$635$	50.6475	2.00988
$636$	−16.3036	−0.646478
$637$	1.07356	0.0425362
$638$	68.4341	2.70933
$639$	4.95958	0.196198
$640$	−53.4648	−2.11338
$641$	30.9839	1.22379	0.611895	−	0.790939i	$-0.290408\pi$
$641$	30.9839	1.22379	0.611895	+	0.790939i	$0.290408\pi$
$642$	52.8474	2.08572
$643$	−18.2491	−0.719674	−0.359837	−	0.933015i	$-0.617168\pi$
$643$	−18.2491	−0.719674	−0.359837	+	0.933015i	$0.617168\pi$
$644$	−58.3249	−2.29832
$645$	25.3694	0.998919
$646$	35.0698	1.37980
$647$	−22.7919	−0.896041	−0.448020	−	0.894023i	$-0.647871\pi$
$647$	−22.7919	−0.896041	−0.448020	+	0.894023i	$0.647871\pi$
$648$	−8.34997	−0.328018
$649$	−45.7501	−1.79585
$650$	−6.94625	−0.272455
$651$	2.01127	0.0788280
$652$	−25.2532	−0.988992
$653$	−43.1867	−1.69003	−0.845013	−	0.534745i	$-0.820408\pi$
$653$	−43.1867	−1.69003	−0.845013	+	0.534745i	$0.820408\pi$
$654$	−6.84350	−0.267602
$655$	53.9563	2.10825
$656$	−113.693	−4.43896
$657$	−13.4311	−0.523997
$658$	24.4035	0.951347
$659$	−12.2706	−0.477996	−0.238998	−	0.971020i	$-0.576819\pi$
$659$	−12.2706	−0.477996	−0.238998	+	0.971020i	$0.576819\pi$
$660$	80.9714	3.15181
$661$	34.5593	1.34420	0.672100	−	0.740461i	$-0.265393\pi$
$661$	34.5593	1.34420	0.672100	+	0.740461i	$0.265393\pi$
$662$	−50.1262	−1.94821
$663$	0.516013	0.0200403
$664$	−42.0705	−1.63265
$665$	96.3781	3.73738
$666$	−0.358945	−0.0139088
$667$	−20.7083	−0.801827
$668$	−18.4287	−0.713028
$669$	−18.8393	−0.728370
$670$	−55.0641	−2.12731
$671$	−41.2234	−1.59141
$672$	49.4554	1.90778
$673$	7.90840	0.304846	0.152423	−	0.988315i	$-0.451292\pi$
$673$	7.90840	0.304846	0.152423	+	0.988315i	$0.451292\pi$
$674$	−12.4949	−0.481286
$675$	−7.91144	−0.304512
$676$	−66.1044	−2.54248
$677$	−33.1584	−1.27438	−0.637191	−	0.770706i	$-0.719904\pi$
$677$	−33.1584	−1.27438	−0.637191	+	0.770706i	$0.719904\pi$
$678$	45.0420	1.72983
$679$	−5.63999	−0.216443
$680$	47.0771	1.80533
$681$	6.54262	0.250714
$682$	−7.36555	−0.282041
$683$	17.6763	0.676367	0.338183	−	0.941080i	$-0.390188\pi$
$683$	17.6763	0.676367	0.338183	+	0.941080i	$0.390188\pi$
$684$	42.9278	1.64139
$685$	−14.4928	−0.553743
$686$	31.9520	1.21993
$687$	−16.9405	−0.646321
$688$	−84.9860	−3.24006
$689$	1.04566	0.0398364
$690$	−34.0590	−1.29660
$691$	−0.619179	−0.0235547	−0.0117773	−	0.999931i	$-0.503749\pi$
$691$	−0.619179	−0.0235547	−0.0117773	+	0.999931i	$0.503749\pi$
$692$	−82.0449	−3.11888
$693$	−14.0798	−0.534847
$694$	−80.8010	−3.06716
$695$	70.1230	2.65992
$696$	48.7030	1.84608
$697$	14.8199	0.561345
$698$	−56.2127	−2.12768
$699$	25.0692	0.948205
$700$	129.968	4.91235
$701$	13.5165	0.510512	0.255256	−	0.966874i	$-0.417840\pi$
$701$	13.5165	0.510512	0.255256	+	0.966874i	$0.417840\pi$
$702$	0.878001	0.0331380
$703$	1.12559	0.0424523
$704$	−75.3126	−2.83845
$705$	10.2518	0.386105
$706$	19.7798	0.744423
$707$	30.7504	1.15649
$708$	−53.3799	−2.00614
$709$	−5.96223	−0.223916	−0.111958	−	0.993713i	$-0.535712\pi$
$709$	−5.96223	−0.223916	−0.111958	+	0.993713i	$0.535712\pi$
$710$	−47.5778	−1.78556
$711$	−0.579997	−0.0217516
$712$	89.9912	3.37256
$713$	2.22883	0.0834702
$714$	−13.4208	−0.502259
$715$	−5.19325	−0.194217
$716$	28.3940	1.06113
$717$	2.79610	0.104422
$718$	−79.3177	−2.96011
$719$	−32.8414	−1.22478	−0.612390	−	0.790556i	$-0.709792\pi$
$719$	−32.8414	−1.22478	−0.612390	+	0.790556i	$0.709792\pi$
$720$	43.2526	1.61193
$721$	3.15471	0.117487
$722$	−136.394	−5.07607
$723$	−14.4911	−0.538929
$724$	35.0360	1.30210
$725$	46.1453	1.71379
$726$	22.1947	0.823724
$727$	4.65685	0.172713	0.0863565	−	0.996264i	$-0.472478\pi$
$727$	4.65685	0.172713	0.0863565	+	0.996264i	$0.472478\pi$
$728$	−8.79781	−0.326069
$729$	1.00000	0.0370370
$730$	128.846	4.76880
$731$	11.0780	0.409734
$732$	−48.0983	−1.77776
$733$	−6.10031	−0.225320	−0.112660	−	0.993634i	$-0.535937\pi$
$733$	−6.10031	−0.225320	−0.112660	+	0.993634i	$0.535937\pi$
$734$	81.5219	3.00903
$735$	−11.7299	−0.432662
$736$	54.8048	2.02013
$737$	−25.2254	−0.929191
$738$	25.2162	0.928222
$739$	−18.4556	−0.678899	−0.339450	−	0.940624i	$-0.610241\pi$
$739$	−18.4556	−0.678899	−0.339450	+	0.940624i	$0.610241\pi$
$740$	2.47718	0.0910630
$741$	−2.75326	−0.101143
$742$	−27.1961	−0.998399
$743$	−30.9693	−1.13615	−0.568077	−	0.822975i	$-0.692313\pi$
$743$	−30.9693	−1.13615	−0.568077	+	0.822975i	$0.692313\pi$
$744$	−5.24190	−0.192177
$745$	−59.4501	−2.17808
$746$	69.2734	2.53628
$747$	5.03840	0.184345
$748$	35.3575	1.29280
$749$	63.4189	2.31727
$750$	27.9298	1.01985
$751$	24.7998	0.904959	0.452480	−	0.891775i	$-0.350540\pi$
$751$	24.7998	0.904959	0.452480	+	0.891775i	$0.350540\pi$
$752$	−34.3429	−1.25236
$753$	−6.36250	−0.231863
$754$	−5.12114	−0.186501
$755$	−51.4091	−1.87097
$756$	−16.4279	−0.597477
$757$	−14.8505	−0.539751	−0.269876	−	0.962895i	$-0.586983\pi$
$757$	−14.8505	−0.539751	−0.269876	+	0.962895i	$0.586983\pi$
$758$	88.3049	3.20738
$759$	−15.6028	−0.566344
$760$	−251.186	−9.11148
$761$	20.7367	0.751704	0.375852	−	0.926680i	$-0.377350\pi$
$761$	20.7367	0.751704	0.375852	+	0.926680i	$0.377350\pi$
$762$	37.6307	1.36322
$763$	−8.21246	−0.297311
$764$	59.9214	2.16788
$765$	−5.63800	−0.203842
$766$	−6.07818	−0.219614
$767$	3.42362	0.123620
$768$	−5.44966	−0.196648
$769$	19.6971	0.710297	0.355149	−	0.934810i	$-0.384430\pi$
$769$	19.6971	0.710297	0.355149	+	0.934810i	$0.384430\pi$
$770$	135.069	4.86755
$771$	−1.45774	−0.0524991
$772$	54.6722	1.96769
$773$	1.66652	0.0599405	0.0299702	−	0.999551i	$-0.490459\pi$
$773$	1.66652	0.0599405	0.0299702	+	0.999551i	$0.490459\pi$
$774$	18.8493	0.677523
$775$	−4.96661	−0.178406
$776$	14.6993	0.527673
$777$	−0.430747	−0.0154530
$778$	−25.4066	−0.910870
$779$	−79.0737	−2.83311
$780$	−6.05934	−0.216959
$781$	−21.7959	−0.779917
$782$	−14.8724	−0.531837
$783$	−5.83272	−0.208445
$784$	39.2943	1.40337
$785$	61.6413	2.20007
$786$	40.0891	1.42993
$787$	−0.115056	−0.00410131	−0.00205066	−	0.999998i	$-0.500653\pi$
$787$	−0.115056	−0.00410131	−0.00205066	+	0.999998i	$0.500653\pi$
$788$	−9.95387	−0.354592
$789$	−16.7158	−0.595098
$790$	5.56398	0.197957
$791$	54.0522	1.92187
$792$	36.6956	1.30392
$793$	3.08487	0.109547
$794$	−68.1110	−2.41717
$795$	−11.4250	−0.405201
$796$	52.3459	1.85535
$797$	−12.6598	−0.448435	−0.224217	−	0.974539i	$-0.571983\pi$
$797$	−12.6598	−0.448435	−0.224217	+	0.974539i	$0.571983\pi$
$798$	71.6082	2.53490
$799$	4.47663	0.158372
$800$	−122.124	−4.31775
$801$	−10.7774	−0.380802
$802$	46.7792	1.65183
$803$	59.0256	2.08297
$804$	−29.4323	−1.03800
$805$	−40.8721	−1.44055
$806$	0.551187	0.0194147
$807$	−6.10423	−0.214879
$808$	−80.1435	−2.81944
$809$	−50.6327	−1.78015	−0.890075	−	0.455814i	$-0.849348\pi$
$809$	−50.6327	−1.78015	−0.890075	+	0.455814i	$0.849348\pi$
$810$	−9.59311	−0.337068
$811$	46.6300	1.63740	0.818700	−	0.574222i	$-0.194695\pi$
$811$	46.6300	1.63740	0.818700	+	0.574222i	$0.194695\pi$
$812$	95.8194	3.36260
$813$	12.7576	0.447429
$814$	1.57745	0.0552897
$815$	−17.6966	−0.619884
$816$	18.8870	0.661176
$817$	−59.1080	−2.06793
$818$	74.5177	2.60545
$819$	1.05363	0.0368170
$820$	−174.025	−6.07720
$821$	40.5086	1.41376	0.706880	−	0.707333i	$-0.250102\pi$
$821$	40.5086	1.41376	0.706880	+	0.707333i	$0.250102\pi$
$822$	−10.7681	−0.375580
$823$	21.7040	0.756553	0.378276	−	0.925693i	$-0.376517\pi$
$823$	21.7040	0.756553	0.378276	+	0.925693i	$0.376517\pi$
$824$	−8.22198	−0.286426
$825$	34.7684	1.21048
$826$	−89.0434	−3.09822
$827$	−19.0784	−0.663423	−0.331711	−	0.943381i	$-0.607626\pi$
$827$	−19.0784	−0.663423	−0.331711	+	0.943381i	$0.607626\pi$
$828$	−18.2049	−0.632662
$829$	−12.8573	−0.446552	−0.223276	−	0.974755i	$-0.571675\pi$
$829$	−12.8573	−0.446552	−0.223276	+	0.974755i	$0.571675\pi$
$830$	−48.3339	−1.67770
$831$	−5.41921	−0.187990
$832$	5.63588	0.195389
$833$	−5.12204	−0.177468
$834$	52.1009	1.80411
$835$	−12.9142	−0.446914
$836$	−188.655	−6.52476
$837$	0.627775	0.0216991
$838$	22.9841	0.793974
$839$	−14.0443	−0.484864	−0.242432	−	0.970168i	$-0.577945\pi$
$839$	−14.0443	−0.484864	−0.242432	+	0.970168i	$0.577945\pi$
$840$	96.1256	3.31665
$841$	5.02066	0.173126
$842$	−67.5870	−2.32920
$843$	−25.7270	−0.886083
$844$	94.8058	3.26335
$845$	−46.3236	−1.59358
$846$	7.61702	0.261879
$847$	26.6345	0.915173
$848$	38.2729	1.31430
$849$	−5.75656	−0.197565
$850$	33.1410	1.13673
$851$	−0.477340	−0.0163630
$852$	−25.4308	−0.871245
$853$	−41.2180	−1.41128	−0.705640	−	0.708571i	$-0.749340\pi$
$853$	−41.2180	−1.41128	−0.705640	+	0.708571i	$0.749340\pi$
$854$	−80.2331	−2.74552
$855$	30.0823	1.02879
$856$	−165.286	−5.64936
$857$	−29.2904	−1.00054	−0.500271	−	0.865869i	$-0.666766\pi$
$857$	−29.2904	−1.00054	−0.500271	+	0.865869i	$0.666766\pi$
$858$	−3.85855	−0.131729
$859$	−22.6303	−0.772135	−0.386068	−	0.922470i	$-0.626167\pi$
$859$	−22.6303	−0.772135	−0.386068	+	0.922470i	$0.626167\pi$
$860$	−130.084	−4.43584
$861$	30.2604	1.03127
$862$	−51.2674	−1.74618
$863$	−31.6107	−1.07604	−0.538021	−	0.842931i	$-0.680828\pi$
$863$	−31.6107	−1.07604	−0.538021	+	0.842931i	$0.680828\pi$
$864$	15.4364	0.525157
$865$	−57.4942	−1.95486
$866$	103.185	3.50635
$867$	14.5381	0.493739
$868$	−10.3130	−0.350047
$869$	2.54891	0.0864660
$870$	55.9540	1.89702
$871$	1.88770	0.0639622
$872$	21.4038	0.724824
$873$	−1.76040	−0.0595805
$874$	79.3538	2.68418
$875$	33.5168	1.13308
$876$	68.8694	2.32688
$877$	4.57985	0.154650	0.0773252	−	0.997006i	$-0.475362\pi$
$877$	4.57985	0.154650	0.0773252	+	0.997006i	$0.475362\pi$
$878$	27.2422	0.919379
$879$	−0.835107	−0.0281675
$880$	−190.082	−6.40767
$881$	−0.514375	−0.0173297	−0.00866487	−	0.999962i	$-0.502758\pi$
$881$	−0.514375	−0.0173297	−0.00866487	+	0.999962i	$0.502758\pi$
$882$	−8.71520	−0.293456
$883$	−53.1494	−1.78862	−0.894309	−	0.447449i	$-0.852333\pi$
$883$	−53.1494	−1.78862	−0.894309	+	0.447449i	$0.852333\pi$
$884$	−2.64591	−0.0889917
$885$	−37.4068	−1.25742
$886$	53.9468	1.81238
$887$	57.6916	1.93709	0.968547	−	0.248829i	$-0.0800458\pi$
$887$	57.6916	1.93709	0.968547	+	0.248829i	$0.0800458\pi$
$888$	1.12264	0.0376733
$889$	45.1583	1.51456
$890$	103.389	3.46561
$891$	−4.39470	−0.147228
$892$	96.6006	3.23443
$893$	−23.8856	−0.799302
$894$	−44.1710	−1.47730
$895$	19.8975	0.665101
$896$	−47.6703	−1.59255
$897$	1.16760	0.0389851
$898$	63.2268	2.10991
$899$	−3.66164	−0.122122
$900$	40.5668	1.35223
$901$	−4.98890	−0.166204
$902$	−110.818	−3.68983
$903$	22.6199	0.752742
$904$	−140.874	−4.68540
$905$	24.5520	0.816136
$906$	−38.1966	−1.26900
$907$	56.0893	1.86242	0.931208	−	0.364489i	$-0.118756\pi$
$907$	56.0893	1.86242	0.931208	+	0.364489i	$0.118756\pi$
$908$	−33.5480	−1.11333
$909$	9.59807	0.318348
$910$	−10.1076	−0.335065
$911$	58.9050	1.95161	0.975805	−	0.218641i	$-0.0701623\pi$
$911$	58.9050	1.95161	0.975805	+	0.218641i	$0.0701623\pi$
$912$	−100.774	−3.33696
$913$	−22.1423	−0.732802
$914$	57.9364	1.91637
$915$	−33.7056	−1.11427
$916$	86.8644	2.87008
$917$	48.1085	1.58868
$918$	−4.18900	−0.138257
$919$	47.0153	1.55089	0.775446	−	0.631414i	$-0.217525\pi$
$919$	47.0153	1.55089	0.775446	+	0.631414i	$0.217525\pi$
$920$	106.523	3.51197
$921$	−1.03572	−0.0341280
$922$	26.9791	0.888510
$923$	1.63105	0.0536867
$924$	72.1957	2.37506
$925$	1.06368	0.0349736
$926$	−7.24056	−0.237940
$927$	0.984673	0.0323409
$928$	−90.0363	−2.95559
$929$	18.4434	0.605110	0.302555	−	0.953132i	$-0.402160\pi$
$929$	18.4434	0.605110	0.302555	+	0.953132i	$0.402160\pi$
$930$	−6.02231	−0.197479
$931$	27.3293	0.895682
$932$	−128.545	−4.21064
$933$	2.60537	0.0852960
$934$	97.3124	3.18416
$935$	24.7773	0.810305
$936$	−2.74604	−0.0897573
$937$	43.1334	1.40911	0.704554	−	0.709650i	$-0.251147\pi$
$937$	43.1334	1.40911	0.704554	+	0.709650i	$0.251147\pi$
$938$	−49.0963	−1.60305
$939$	28.8252	0.940674
$940$	−52.5673	−1.71456
$941$	41.5401	1.35417	0.677084	−	0.735906i	$-0.263244\pi$
$941$	41.5401	1.35417	0.677084	+	0.735906i	$0.263244\pi$
$942$	45.7990	1.49221
$943$	33.5336	1.09200
$944$	125.310	4.07851
$945$	−11.5121	−0.374489
$946$	−82.8369	−2.69326
$947$	28.9928	0.942139	0.471070	−	0.882096i	$-0.343868\pi$
$947$	28.9928	0.942139	0.471070	+	0.882096i	$0.343868\pi$
$948$	2.97400	0.0965911
$949$	−4.41707	−0.143384
$950$	−176.828	−5.73706
$951$	−5.28930	−0.171517
$952$	41.9749	1.36041
$953$	−12.6123	−0.408554	−0.204277	−	0.978913i	$-0.565484\pi$
$953$	−12.6123	−0.408554	−0.204277	+	0.978913i	$0.565484\pi$
$954$	−8.48866	−0.274831
$955$	41.9908	1.35879
$956$	−14.3373	−0.463702
$957$	25.6331	0.828599
$958$	33.3416	1.07722
$959$	−12.9221	−0.417276
$960$	−61.5781	−1.98742
$961$	−30.6059	−0.987287
$962$	−0.118046	−0.00380595
$963$	19.7948	0.637879
$964$	74.3046	2.39319
$965$	38.3123	1.23332
$966$	−30.3676	−0.977063
$967$	−32.8161	−1.05530	−0.527648	−	0.849463i	$-0.676926\pi$
$967$	−32.8161	−1.05530	−0.527648	+	0.849463i	$0.676926\pi$
$968$	−69.4165	−2.23113
$969$	13.1360	0.421988
$970$	16.8877	0.542231
$971$	2.50550	0.0804053	0.0402027	−	0.999192i	$-0.487200\pi$
$971$	2.50550	0.0804053	0.0402027	+	0.999192i	$0.487200\pi$
$972$	−5.12761	−0.164468
$973$	62.5231	2.00440
$974$	−67.3549	−2.15819
$975$	−2.60183	−0.0833252
$976$	112.912	3.61422
$977$	−40.7462	−1.30359	−0.651794	−	0.758396i	$-0.725983\pi$
$977$	−40.7462	−1.30359	−0.651794	+	0.758396i	$0.725983\pi$
$978$	−13.1484	−0.420440
$979$	47.3636	1.51375
$980$	60.1461	1.92130
$981$	−2.56334	−0.0818411
$982$	77.7721	2.48181
$983$	−2.10635	−0.0671820	−0.0335910	−	0.999436i	$-0.510694\pi$
$983$	−2.10635	−0.0671820	−0.0335910	+	0.999436i	$0.510694\pi$
$984$	−78.8666	−2.51417
$985$	−6.97533	−0.222252
$986$	24.4332	0.778113
$987$	9.14071	0.290952
$988$	14.1176	0.449141
$989$	25.0666	0.797070
$990$	42.1588	1.33990
$991$	8.90102	0.282750	0.141375	−	0.989956i	$-0.454848\pi$
$991$	8.90102	0.282750	0.141375	+	0.989956i	$0.454848\pi$
$992$	9.69059	0.307677
$993$	−18.7756	−0.595824
$994$	−42.4213	−1.34552
$995$	36.6822	1.16290
$996$	−25.8350	−0.818612
$997$	41.7657	1.32273	0.661367	−	0.750062i	$-0.269977\pi$
$997$	41.7657	1.32273	0.661367	+	0.750062i	$0.269977\pi$
$998$	−43.2668	−1.36959
$999$	−0.134448	−0.00425376

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.d.1.5	✓	93

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.d.1.5	✓	93	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:	\( N \)	\(=\)	\( 6009 = 3 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66976 q^{2} -1.00000 q^{3} +5.12761 q^{4} +3.59325 q^{5} +2.66976 q^{6} +3.20381 q^{7} -8.34997 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.66976 q^{2} -1.00000 q^{3} +5.12761 q^{4} +3.59325 q^{5} +2.66976 q^{6} +3.20381 q^{7} -8.34997 q^{8} +1.00000 q^{9} -9.59311 q^{10} -4.39470 q^{11} -5.12761 q^{12} +0.328869 q^{13} -8.55341 q^{14} -3.59325 q^{15} +12.0372 q^{16} -1.56905 q^{17} -2.66976 q^{18} +8.37189 q^{19} +18.4248 q^{20} -3.20381 q^{21} +11.7328 q^{22} -3.55036 q^{23} +8.34997 q^{24} +7.91144 q^{25} -0.878001 q^{26} -1.00000 q^{27} +16.4279 q^{28} +5.83272 q^{29} +9.59311 q^{30} -0.627775 q^{31} -15.4364 q^{32} +4.39470 q^{33} +4.18900 q^{34} +11.5121 q^{35} +5.12761 q^{36} +0.134448 q^{37} -22.3509 q^{38} -0.328869 q^{39} -30.0035 q^{40} -9.44514 q^{41} +8.55341 q^{42} -7.06029 q^{43} -22.5343 q^{44} +3.59325 q^{45} +9.47860 q^{46} -2.85307 q^{47} -12.0372 q^{48} +3.26441 q^{49} -21.1216 q^{50} +1.56905 q^{51} +1.68631 q^{52} +3.17956 q^{53} +2.66976 q^{54} -15.7913 q^{55} -26.7517 q^{56} -8.37189 q^{57} -15.5720 q^{58} +10.4103 q^{59} -18.4248 q^{60} +9.38025 q^{61} +1.67601 q^{62} +3.20381 q^{63} +17.1372 q^{64} +1.18171 q^{65} -11.7328 q^{66} +5.73997 q^{67} -8.04550 q^{68} +3.55036 q^{69} -30.7345 q^{70} +4.95958 q^{71} -8.34997 q^{72} -13.4311 q^{73} -0.358945 q^{74} -7.91144 q^{75} +42.9278 q^{76} -14.0798 q^{77} +0.878001 q^{78} -0.579997 q^{79} +43.2526 q^{80} +1.00000 q^{81} +25.2162 q^{82} +5.03840 q^{83} -16.4279 q^{84} -5.63800 q^{85} +18.8493 q^{86} -5.83272 q^{87} +36.6956 q^{88} -10.7774 q^{89} -9.59311 q^{90} +1.05363 q^{91} -18.2049 q^{92} +0.627775 q^{93} +7.61702 q^{94} +30.0823 q^{95} +15.4364 q^{96} -1.76040 q^{97} -8.71520 q^{98} -4.39470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9} + 19 q^{10} + 10 q^{11} - 114 q^{12} + 20 q^{13} + 13 q^{14} + 20 q^{15} + 148 q^{16} - 43 q^{17} + 2 q^{18} + 50 q^{19} - 31 q^{20} - 28 q^{21} + 36 q^{22} + 21 q^{23} - 6 q^{24} + 137 q^{25} + 2 q^{26} - 93 q^{27} + 62 q^{28} - q^{29} - 19 q^{30} + 58 q^{31} + 19 q^{32} - 10 q^{33} + 30 q^{34} + 30 q^{35} + 114 q^{36} + 42 q^{37} - 6 q^{38} - 20 q^{39} + 53 q^{40} - 7 q^{41} - 13 q^{42} + 60 q^{43} + 25 q^{44} - 20 q^{45} + 57 q^{46} + 9 q^{47} - 148 q^{48} + 145 q^{49} + 41 q^{50} + 43 q^{51} + 71 q^{52} - 45 q^{53} - 2 q^{54} + 78 q^{55} + 44 q^{56} - 50 q^{57} + 40 q^{58} + 42 q^{59} + 31 q^{60} + 69 q^{61} - 42 q^{62} + 28 q^{63} + 230 q^{64} - 4 q^{65} - 36 q^{66} + 76 q^{67} - 91 q^{68} - 21 q^{69} + 57 q^{70} + 92 q^{71} + 6 q^{72} + 29 q^{73} + 59 q^{74} - 137 q^{75} + 131 q^{76} - 98 q^{77} - 2 q^{78} + 215 q^{79} - 37 q^{80} + 93 q^{81} + 50 q^{82} - 27 q^{83} - 62 q^{84} + 52 q^{85} + 82 q^{86} + q^{87} + 136 q^{88} - 14 q^{89} + 19 q^{90} + 101 q^{91} - 14 q^{92} - 58 q^{93} + 112 q^{94} + 59 q^{95} - 19 q^{96} + 38 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9 + 19 * q^10 + 10 * q^11 - 114 * q^12 + 20 * q^13 + 13 * q^14 + 20 * q^15 + 148 * q^16 - 43 * q^17 + 2 * q^18 + 50 * q^19 - 31 * q^20 - 28 * q^21 + 36 * q^22 + 21 * q^23 - 6 * q^24 + 137 * q^25 + 2 * q^26 - 93 * q^27 + 62 * q^28 - q^29 - 19 * q^30 + 58 * q^31 + 19 * q^32 - 10 * q^33 + 30 * q^34 + 30 * q^35 + 114 * q^36 + 42 * q^37 - 6 * q^38 - 20 * q^39 + 53 * q^40 - 7 * q^41 - 13 * q^42 + 60 * q^43 + 25 * q^44 - 20 * q^45 + 57 * q^46 + 9 * q^47 - 148 * q^48 + 145 * q^49 + 41 * q^50 + 43 * q^51 + 71 * q^52 - 45 * q^53 - 2 * q^54 + 78 * q^55 + 44 * q^56 - 50 * q^57 + 40 * q^58 + 42 * q^59 + 31 * q^60 + 69 * q^61 - 42 * q^62 + 28 * q^63 + 230 * q^64 - 4 * q^65 - 36 * q^66 + 76 * q^67 - 91 * q^68 - 21 * q^69 + 57 * q^70 + 92 * q^71 + 6 * q^72 + 29 * q^73 + 59 * q^74 - 137 * q^75 + 131 * q^76 - 98 * q^77 - 2 * q^78 + 215 * q^79 - 37 * q^80 + 93 * q^81 + 50 * q^82 - 27 * q^83 - 62 * q^84 + 52 * q^85 + 82 * q^86 + q^87 + 136 * q^88 - 14 * q^89 + 19 * q^90 + 101 * q^91 - 14 * q^92 - 58 * q^93 + 112 * q^94 + 59 * q^95 - 19 * q^96 + 38 * q^97 - 16 * q^98 + 10 * q^99

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