LMFDB - Embedded newform 6010.2.a.j.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.162499 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.162499 q^{6} -4.01770 q^{7} +1.00000 q^{8} -2.97359 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.162499 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.162499 q^{6} -4.01770 q^{7} +1.00000 q^{8} -2.97359 q^{9} +1.00000 q^{10} -3.71619 q^{11} +0.162499 q^{12} +3.04893 q^{13} -4.01770 q^{14} +0.162499 q^{15} +1.00000 q^{16} +4.01536 q^{17} -2.97359 q^{18} +2.54871 q^{19} +1.00000 q^{20} -0.652872 q^{21} -3.71619 q^{22} -8.21802 q^{23} +0.162499 q^{24} +1.00000 q^{25} +3.04893 q^{26} -0.970703 q^{27} -4.01770 q^{28} -9.46422 q^{29} +0.162499 q^{30} +7.44349 q^{31} +1.00000 q^{32} -0.603876 q^{33} +4.01536 q^{34} -4.01770 q^{35} -2.97359 q^{36} +8.64660 q^{37} +2.54871 q^{38} +0.495448 q^{39} +1.00000 q^{40} +8.16315 q^{41} -0.652872 q^{42} +7.28651 q^{43} -3.71619 q^{44} -2.97359 q^{45} -8.21802 q^{46} +9.14758 q^{47} +0.162499 q^{48} +9.14190 q^{49} +1.00000 q^{50} +0.652492 q^{51} +3.04893 q^{52} +9.01136 q^{53} -0.970703 q^{54} -3.71619 q^{55} -4.01770 q^{56} +0.414163 q^{57} -9.46422 q^{58} +8.42784 q^{59} +0.162499 q^{60} -15.4367 q^{61} +7.44349 q^{62} +11.9470 q^{63} +1.00000 q^{64} +3.04893 q^{65} -0.603876 q^{66} -2.24036 q^{67} +4.01536 q^{68} -1.33542 q^{69} -4.01770 q^{70} -4.30906 q^{71} -2.97359 q^{72} -14.7120 q^{73} +8.64660 q^{74} +0.162499 q^{75} +2.54871 q^{76} +14.9305 q^{77} +0.495448 q^{78} +7.06533 q^{79} +1.00000 q^{80} +8.76304 q^{81} +8.16315 q^{82} -0.676261 q^{83} -0.652872 q^{84} +4.01536 q^{85} +7.28651 q^{86} -1.53793 q^{87} -3.71619 q^{88} +7.94004 q^{89} -2.97359 q^{90} -12.2497 q^{91} -8.21802 q^{92} +1.20956 q^{93} +9.14758 q^{94} +2.54871 q^{95} +0.162499 q^{96} +10.0406 q^{97} +9.14190 q^{98} +11.0504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9} + 33 q^{10} + 12 q^{11} + 6 q^{12} + 20 q^{13} + 4 q^{14} + 6 q^{15} + 33 q^{16} + 33 q^{17} + 49 q^{18} + 17 q^{19} + 33 q^{20} + 26 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 33 q^{25} + 20 q^{26} + 21 q^{27} + 4 q^{28} + 33 q^{29} + 6 q^{30} + 35 q^{31} + 33 q^{32} + 25 q^{33} + 33 q^{34} + 4 q^{35} + 49 q^{36} + 16 q^{37} + 17 q^{38} + 22 q^{39} + 33 q^{40} + 39 q^{41} + 26 q^{42} - 3 q^{43} + 12 q^{44} + 49 q^{45} + 7 q^{46} + 19 q^{47} + 6 q^{48} + 69 q^{49} + 33 q^{50} + 21 q^{51} + 20 q^{52} + 41 q^{53} + 21 q^{54} + 12 q^{55} + 4 q^{56} + 33 q^{58} + 18 q^{59} + 6 q^{60} + 30 q^{61} + 35 q^{62} - 15 q^{63} + 33 q^{64} + 20 q^{65} + 25 q^{66} - 9 q^{67} + 33 q^{68} + 23 q^{69} + 4 q^{70} + 36 q^{71} + 49 q^{72} + 35 q^{73} + 16 q^{74} + 6 q^{75} + 17 q^{76} + 26 q^{77} + 22 q^{78} + 32 q^{79} + 33 q^{80} + 53 q^{81} + 39 q^{82} + 24 q^{83} + 26 q^{84} + 33 q^{85} - 3 q^{86} + 12 q^{87} + 12 q^{88} + 40 q^{89} + 49 q^{90} + 5 q^{91} + 7 q^{92} + 18 q^{93} + 19 q^{94} + 17 q^{95} + 6 q^{96} + 39 q^{97} + 69 q^{98} + 3 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9 + 33 * q^10 + 12 * q^11 + 6 * q^12 + 20 * q^13 + 4 * q^14 + 6 * q^15 + 33 * q^16 + 33 * q^17 + 49 * q^18 + 17 * q^19 + 33 * q^20 + 26 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 33 * q^25 + 20 * q^26 + 21 * q^27 + 4 * q^28 + 33 * q^29 + 6 * q^30 + 35 * q^31 + 33 * q^32 + 25 * q^33 + 33 * q^34 + 4 * q^35 + 49 * q^36 + 16 * q^37 + 17 * q^38 + 22 * q^39 + 33 * q^40 + 39 * q^41 + 26 * q^42 - 3 * q^43 + 12 * q^44 + 49 * q^45 + 7 * q^46 + 19 * q^47 + 6 * q^48 + 69 * q^49 + 33 * q^50 + 21 * q^51 + 20 * q^52 + 41 * q^53 + 21 * q^54 + 12 * q^55 + 4 * q^56 + 33 * q^58 + 18 * q^59 + 6 * q^60 + 30 * q^61 + 35 * q^62 - 15 * q^63 + 33 * q^64 + 20 * q^65 + 25 * q^66 - 9 * q^67 + 33 * q^68 + 23 * q^69 + 4 * q^70 + 36 * q^71 + 49 * q^72 + 35 * q^73 + 16 * q^74 + 6 * q^75 + 17 * q^76 + 26 * q^77 + 22 * q^78 + 32 * q^79 + 33 * q^80 + 53 * q^81 + 39 * q^82 + 24 * q^83 + 26 * q^84 + 33 * q^85 - 3 * q^86 + 12 * q^87 + 12 * q^88 + 40 * q^89 + 49 * q^90 + 5 * q^91 + 7 * q^92 + 18 * q^93 + 19 * q^94 + 17 * q^95 + 6 * q^96 + 39 * q^97 + 69 * q^98 + 3 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.162499	0.0938188	0.0469094	−	0.998899i	$-0.485063\pi$
$3$	0.162499	0.0938188	0.0469094	+	0.998899i	$0.485063\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.162499	0.0663399
$7$	−4.01770	−1.51855	−0.759274	−	0.650772i	$-0.774446\pi$
$7$	−4.01770	−1.51855	−0.759274	+	0.650772i	$0.774446\pi$
$8$	1.00000	0.353553
$9$	−2.97359	−0.991198
$10$	1.00000	0.316228
$11$	−3.71619	−1.12047	−0.560236	−	0.828333i	$-0.689290\pi$
$11$	−3.71619	−1.12047	−0.560236	+	0.828333i	$0.689290\pi$
$12$	0.162499	0.0469094
$13$	3.04893	0.845622	0.422811	−	0.906218i	$-0.361043\pi$
$13$	3.04893	0.845622	0.422811	+	0.906218i	$0.361043\pi$
$14$	−4.01770	−1.07378
$15$	0.162499	0.0419570
$16$	1.00000	0.250000
$17$	4.01536	0.973868	0.486934	−	0.873439i	$-0.338115\pi$
$17$	4.01536	0.973868	0.486934	+	0.873439i	$0.338115\pi$
$18$	−2.97359	−0.700883
$19$	2.54871	0.584714	0.292357	−	0.956309i	$-0.405560\pi$
$19$	2.54871	0.584714	0.292357	+	0.956309i	$0.405560\pi$
$20$	1.00000	0.223607
$21$	−0.652872	−0.142468
$22$	−3.71619	−0.792294
$23$	−8.21802	−1.71358	−0.856788	−	0.515669i	$-0.827543\pi$
$23$	−8.21802	−1.71358	−0.856788	+	0.515669i	$0.827543\pi$
$24$	0.162499	0.0331700
$25$	1.00000	0.200000
$26$	3.04893	0.597945
$27$	−0.970703	−0.186812
$28$	−4.01770	−0.759274
$29$	−9.46422	−1.75746	−0.878730	−	0.477319i	$-0.841609\pi$
$29$	−9.46422	−1.75746	−0.878730	+	0.477319i	$0.841609\pi$
$30$	0.162499	0.0296681
$31$	7.44349	1.33689	0.668445	−	0.743762i	$-0.266960\pi$
$31$	7.44349	1.33689	0.668445	+	0.743762i	$0.266960\pi$
$32$	1.00000	0.176777
$33$	−0.603876	−0.105121
$34$	4.01536	0.688629
$35$	−4.01770	−0.679115
$36$	−2.97359	−0.495599
$37$	8.64660	1.42149	0.710746	−	0.703449i	$-0.248357\pi$
$37$	8.64660	1.42149	0.710746	+	0.703449i	$0.248357\pi$
$38$	2.54871	0.413455
$39$	0.495448	0.0793352
$40$	1.00000	0.158114
$41$	8.16315	1.27487	0.637435	−	0.770504i	$-0.279995\pi$
$41$	8.16315	1.27487	0.637435	+	0.770504i	$0.279995\pi$
$42$	−0.652872	−0.100740
$43$	7.28651	1.11118	0.555591	−	0.831456i	$-0.312492\pi$
$43$	7.28651	1.11118	0.555591	+	0.831456i	$0.312492\pi$
$44$	−3.71619	−0.560236
$45$	−2.97359	−0.443277
$46$	−8.21802	−1.21168
$47$	9.14758	1.33431	0.667156	−	0.744918i	$-0.267511\pi$
$47$	9.14758	1.33431	0.667156	+	0.744918i	$0.267511\pi$
$48$	0.162499	0.0234547
$49$	9.14190	1.30599
$50$	1.00000	0.141421
$51$	0.652492	0.0913671
$52$	3.04893	0.422811
$53$	9.01136	1.23781	0.618903	−	0.785467i	$-0.287577\pi$
$53$	9.01136	1.23781	0.618903	+	0.785467i	$0.287577\pi$
$54$	−0.970703	−0.132096
$55$	−3.71619	−0.501091
$56$	−4.01770	−0.536888
$57$	0.414163	0.0548572
$58$	−9.46422	−1.24271
$59$	8.42784	1.09721	0.548606	−	0.836081i	$-0.315159\pi$
$59$	8.42784	1.09721	0.548606	+	0.836081i	$0.315159\pi$
$60$	0.162499	0.0209785
$61$	−15.4367	−1.97646	−0.988230	−	0.152974i	$-0.951115\pi$
$61$	−15.4367	−1.97646	−0.988230	+	0.152974i	$0.951115\pi$
$62$	7.44349	0.945324
$63$	11.9470	1.50518
$64$	1.00000	0.125000
$65$	3.04893	0.378174
$66$	−0.603876	−0.0743321
$67$	−2.24036	−0.273704	−0.136852	−	0.990592i	$-0.543698\pi$
$67$	−2.24036	−0.273704	−0.136852	+	0.990592i	$0.543698\pi$
$68$	4.01536	0.486934
$69$	−1.33542	−0.160766
$70$	−4.01770	−0.480207
$71$	−4.30906	−0.511391	−0.255695	−	0.966757i	$-0.582304\pi$
$71$	−4.30906	−0.511391	−0.255695	+	0.966757i	$0.582304\pi$
$72$	−2.97359	−0.350441
$73$	−14.7120	−1.72191	−0.860954	−	0.508682i	$-0.830133\pi$
$73$	−14.7120	−1.72191	−0.860954	+	0.508682i	$0.830133\pi$
$74$	8.64660	1.00515
$75$	0.162499	0.0187638
$76$	2.54871	0.292357
$77$	14.9305	1.70149
$78$	0.495448	0.0560985
$79$	7.06533	0.794911	0.397456	−	0.917621i	$-0.369893\pi$
$79$	7.06533	0.794911	0.397456	+	0.917621i	$0.369893\pi$
$80$	1.00000	0.111803
$81$	8.76304	0.973672
$82$	8.16315	0.901469
$83$	−0.676261	−0.0742293	−0.0371146	−	0.999311i	$-0.511817\pi$
$83$	−0.676261	−0.0742293	−0.0371146	+	0.999311i	$0.511817\pi$
$84$	−0.652872	−0.0712341
$85$	4.01536	0.435527
$86$	7.28651	0.785725
$87$	−1.53793	−0.164883
$88$	−3.71619	−0.396147
$89$	7.94004	0.841642	0.420821	−	0.907144i	$-0.361742\pi$
$89$	7.94004	0.841642	0.420821	+	0.907144i	$0.361742\pi$
$90$	−2.97359	−0.313444
$91$	−12.2497	−1.28412
$92$	−8.21802	−0.856788
$93$	1.20956	0.125425
$94$	9.14758	0.943501
$95$	2.54871	0.261492
$96$	0.162499	0.0165850
$97$	10.0406	1.01947	0.509734	−	0.860332i	$-0.329744\pi$
$97$	10.0406	1.01947	0.509734	+	0.860332i	$0.329744\pi$
$98$	9.14190	0.923471
$99$	11.0504	1.11061
$100$	1.00000	0.100000
$101$	9.21125	0.916554	0.458277	−	0.888809i	$-0.348467\pi$
$101$	9.21125	0.916554	0.458277	+	0.888809i	$0.348467\pi$
$102$	0.652492	0.0646063
$103$	6.07818	0.598901	0.299450	−	0.954112i	$-0.403197\pi$
$103$	6.07818	0.598901	0.299450	+	0.954112i	$0.403197\pi$
$104$	3.04893	0.298972
$105$	−0.652872	−0.0637138
$106$	9.01136	0.875261
$107$	−6.22728	−0.602014	−0.301007	−	0.953622i	$-0.597323\pi$
$107$	−6.22728	−0.602014	−0.301007	+	0.953622i	$0.597323\pi$
$108$	−0.970703	−0.0934059
$109$	7.03199	0.673543	0.336771	−	0.941586i	$-0.390665\pi$
$109$	7.03199	0.673543	0.336771	+	0.941586i	$0.390665\pi$
$110$	−3.71619	−0.354325
$111$	1.40506	0.133363
$112$	−4.01770	−0.379637
$113$	11.8021	1.11025	0.555123	−	0.831768i	$-0.312671\pi$
$113$	11.8021	1.11025	0.555123	+	0.831768i	$0.312671\pi$
$114$	0.414163	0.0387899
$115$	−8.21802	−0.766334
$116$	−9.46422	−0.878730
$117$	−9.06629	−0.838179
$118$	8.42784	0.775845
$119$	−16.1325	−1.47886
$120$	0.162499	0.0148341
$121$	2.81004	0.255459
$122$	−15.4367	−1.39757
$123$	1.32650	0.119607
$124$	7.44349	0.668445
$125$	1.00000	0.0894427
$126$	11.9470	1.06432
$127$	2.88450	0.255958	0.127979	−	0.991777i	$-0.459151\pi$
$127$	2.88450	0.255958	0.127979	+	0.991777i	$0.459151\pi$
$128$	1.00000	0.0883883
$129$	1.18405	0.104250
$130$	3.04893	0.267409
$131$	−9.69449	−0.847012	−0.423506	−	0.905893i	$-0.639201\pi$
$131$	−9.69449	−0.847012	−0.423506	+	0.905893i	$0.639201\pi$
$132$	−0.603876	−0.0525607
$133$	−10.2399	−0.887916
$134$	−2.24036	−0.193538
$135$	−0.970703	−0.0835448
$136$	4.01536	0.344314
$137$	1.02752	0.0877865	0.0438933	−	0.999036i	$-0.486024\pi$
$137$	1.02752	0.0877865	0.0438933	+	0.999036i	$0.486024\pi$
$138$	−1.33542	−0.113678
$139$	0.351035	0.0297744	0.0148872	−	0.999889i	$-0.495261\pi$
$139$	0.351035	0.0297744	0.0148872	+	0.999889i	$0.495261\pi$
$140$	−4.01770	−0.339557
$141$	1.48647	0.125184
$142$	−4.30906	−0.361608
$143$	−11.3304	−0.947496
$144$	−2.97359	−0.247800
$145$	−9.46422	−0.785960
$146$	−14.7120	−1.21757
$147$	1.48555	0.122526
$148$	8.64660	0.710746
$149$	20.3180	1.66451	0.832256	−	0.554391i	$-0.187049\pi$
$149$	20.3180	1.66451	0.832256	+	0.554391i	$0.187049\pi$
$150$	0.162499	0.0132680
$151$	5.87774	0.478324	0.239162	−	0.970980i	$-0.423127\pi$
$151$	5.87774	0.478324	0.239162	+	0.970980i	$0.423127\pi$
$152$	2.54871	0.206728
$153$	−11.9401	−0.965296
$154$	14.9305	1.20314
$155$	7.44349	0.597875
$156$	0.495448	0.0396676
$157$	−14.9621	−1.19411	−0.597054	−	0.802201i	$-0.703662\pi$
$157$	−14.9621	−1.19411	−0.597054	+	0.802201i	$0.703662\pi$
$158$	7.06533	0.562087
$159$	1.46434	0.116129
$160$	1.00000	0.0790569
$161$	33.0175	2.60215
$162$	8.76304	0.688490
$163$	−3.07847	−0.241124	−0.120562	−	0.992706i	$-0.538470\pi$
$163$	−3.07847	−0.241124	−0.120562	+	0.992706i	$0.538470\pi$
$164$	8.16315	0.637435
$165$	−0.603876	−0.0470117
$166$	−0.676261	−0.0524880
$167$	16.2409	1.25676	0.628378	−	0.777909i	$-0.283719\pi$
$167$	16.2409	1.25676	0.628378	+	0.777909i	$0.283719\pi$
$168$	−0.652872	−0.0503701
$169$	−3.70401	−0.284924
$170$	4.01536	0.307964
$171$	−7.57883	−0.579567
$172$	7.28651	0.555591
$173$	16.0471	1.22004	0.610020	−	0.792386i	$-0.291162\pi$
$173$	16.0471	1.22004	0.610020	+	0.792386i	$0.291162\pi$
$174$	−1.53793	−0.116590
$175$	−4.01770	−0.303709
$176$	−3.71619	−0.280118
$177$	1.36952	0.102939
$178$	7.94004	0.595131
$179$	−4.36346	−0.326140	−0.163070	−	0.986614i	$-0.552140\pi$
$179$	−4.36346	−0.326140	−0.163070	+	0.986614i	$0.552140\pi$
$180$	−2.97359	−0.221639
$181$	−9.51503	−0.707247	−0.353623	−	0.935388i	$-0.615051\pi$
$181$	−9.51503	−0.707247	−0.353623	+	0.935388i	$0.615051\pi$
$182$	−12.2497	−0.908007
$183$	−2.50844	−0.185429
$184$	−8.21802	−0.605841
$185$	8.64660	0.635711
$186$	1.20956	0.0886892
$187$	−14.9218	−1.09119
$188$	9.14758	0.667156
$189$	3.89999	0.283683
$190$	2.54871	0.184903
$191$	−5.46772	−0.395630	−0.197815	−	0.980239i	$-0.563385\pi$
$191$	−5.46772	−0.395630	−0.197815	+	0.980239i	$0.563385\pi$
$192$	0.162499	0.0117274
$193$	10.4602	0.752940	0.376470	−	0.926429i	$-0.377138\pi$
$193$	10.4602	0.752940	0.376470	+	0.926429i	$0.377138\pi$
$194$	10.0406	0.720872
$195$	0.495448	0.0354798
$196$	9.14190	0.652993
$197$	25.9045	1.84562	0.922811	−	0.385254i	$-0.125886\pi$
$197$	25.9045	1.84562	0.922811	+	0.385254i	$0.125886\pi$
$198$	11.0504	0.785320
$199$	16.8914	1.19740	0.598701	−	0.800973i	$-0.295684\pi$
$199$	16.8914	1.19740	0.598701	+	0.800973i	$0.295684\pi$
$200$	1.00000	0.0707107
$201$	−0.364057	−0.0256786
$202$	9.21125	0.648101
$203$	38.0244	2.66879
$204$	0.652492	0.0456836
$205$	8.16315	0.570139
$206$	6.07818	0.423487
$207$	24.4371	1.69849
$208$	3.04893	0.211405
$209$	−9.47148	−0.655156
$210$	−0.652872	−0.0450524
$211$	−13.4570	−0.926416	−0.463208	−	0.886250i	$-0.653302\pi$
$211$	−13.4570	−0.926416	−0.463208	+	0.886250i	$0.653302\pi$
$212$	9.01136	0.618903
$213$	−0.700217	−0.0479781
$214$	−6.22728	−0.425688
$215$	7.28651	0.496936
$216$	−0.970703	−0.0660480
$217$	−29.9057	−2.03013
$218$	7.03199	0.476266
$219$	−2.39068	−0.161547
$220$	−3.71619	−0.250545
$221$	12.2426	0.823524
$222$	1.40506	0.0943017
$223$	−23.5669	−1.57816	−0.789080	−	0.614291i	$-0.789442\pi$
$223$	−23.5669	−1.57816	−0.789080	+	0.614291i	$0.789442\pi$
$224$	−4.01770	−0.268444
$225$	−2.97359	−0.198240
$226$	11.8021	0.785063
$227$	−13.8825	−0.921411	−0.460705	−	0.887553i	$-0.652404\pi$
$227$	−13.8825	−0.921411	−0.460705	+	0.887553i	$0.652404\pi$
$228$	0.414163	0.0274286
$229$	−3.02352	−0.199800	−0.0998998	−	0.994997i	$-0.531852\pi$
$229$	−3.02352	−0.199800	−0.0998998	+	0.994997i	$0.531852\pi$
$230$	−8.21802	−0.541880
$231$	2.42619	0.159632
$232$	−9.46422	−0.621356
$233$	12.2433	0.802083	0.401042	−	0.916060i	$-0.368648\pi$
$233$	12.2433	0.802083	0.401042	+	0.916060i	$0.368648\pi$
$234$	−9.06629	−0.592682
$235$	9.14758	0.596722
$236$	8.42784	0.548606
$237$	1.14811	0.0745777
$238$	−16.1325	−1.04572
$239$	−3.06773	−0.198435	−0.0992173	−	0.995066i	$-0.531634\pi$
$239$	−3.06773	−0.198435	−0.0992173	+	0.995066i	$0.531634\pi$
$240$	0.162499	0.0104893
$241$	14.4540	0.931066	0.465533	−	0.885030i	$-0.345863\pi$
$241$	14.4540	0.931066	0.465533	+	0.885030i	$0.345863\pi$
$242$	2.81004	0.180637
$243$	4.33609	0.278161
$244$	−15.4367	−0.988230
$245$	9.14190	0.584054
$246$	1.32650	0.0845748
$247$	7.77084	0.494447
$248$	7.44349	0.472662
$249$	−0.109892	−0.00696410
$250$	1.00000	0.0632456
$251$	−27.7181	−1.74955	−0.874776	−	0.484528i	$-0.838991\pi$
$251$	−27.7181	−1.74955	−0.874776	+	0.484528i	$0.838991\pi$
$252$	11.9470	0.752590
$253$	30.5397	1.92001
$254$	2.88450	0.180990
$255$	0.652492	0.0408606
$256$	1.00000	0.0625000
$257$	0.246378	0.0153686	0.00768431	−	0.999970i	$-0.497554\pi$
$257$	0.246378	0.0153686	0.00768431	+	0.999970i	$0.497554\pi$
$258$	1.18405	0.0737157
$259$	−34.7394	−2.15860
$260$	3.04893	0.189087
$261$	28.1427	1.74199
$262$	−9.69449	−0.598928
$263$	−6.13280	−0.378165	−0.189082	−	0.981961i	$-0.560551\pi$
$263$	−6.13280	−0.378165	−0.189082	+	0.981961i	$0.560551\pi$
$264$	−0.603876	−0.0371660
$265$	9.01136	0.553564
$266$	−10.2399	−0.627851
$267$	1.29025	0.0789619
$268$	−2.24036	−0.136852
$269$	22.8312	1.39205	0.696023	−	0.718020i	$-0.254951\pi$
$269$	22.8312	1.39205	0.696023	+	0.718020i	$0.254951\pi$
$270$	−0.970703	−0.0590751
$271$	−3.15356	−0.191565	−0.0957825	−	0.995402i	$-0.530535\pi$
$271$	−3.15356	−0.191565	−0.0957825	+	0.995402i	$0.530535\pi$
$272$	4.01536	0.243467
$273$	−1.99056	−0.120474
$274$	1.02752	0.0620745
$275$	−3.71619	−0.224094
$276$	−1.33542	−0.0803828
$277$	−8.37602	−0.503266	−0.251633	−	0.967823i	$-0.580968\pi$
$277$	−8.37602	−0.503266	−0.251633	+	0.967823i	$0.580968\pi$
$278$	0.351035	0.0210537
$279$	−22.1339	−1.32512
$280$	−4.01770	−0.240103
$281$	31.4835	1.87815	0.939073	−	0.343718i	$-0.111687\pi$
$281$	31.4835	1.87815	0.939073	+	0.343718i	$0.111687\pi$
$282$	1.48647	0.0885181
$283$	−11.4101	−0.678259	−0.339130	−	0.940740i	$-0.610133\pi$
$283$	−11.4101	−0.678259	−0.339130	+	0.940740i	$0.610133\pi$
$284$	−4.30906	−0.255695
$285$	0.414163	0.0245329
$286$	−11.3304	−0.669981
$287$	−32.7971	−1.93595
$288$	−2.97359	−0.175221
$289$	−0.876876	−0.0515810
$290$	−9.46422	−0.555758
$291$	1.63159	0.0956452
$292$	−14.7120	−0.860954
$293$	1.89860	0.110917	0.0554586	−	0.998461i	$-0.482338\pi$
$293$	1.89860	0.110917	0.0554586	+	0.998461i	$0.482338\pi$
$294$	1.48555	0.0866390
$295$	8.42784	0.490688
$296$	8.64660	0.502573
$297$	3.60731	0.209318
$298$	20.3180	1.17699
$299$	−25.0562	−1.44904
$300$	0.162499	0.00938188
$301$	−29.2750	−1.68738
$302$	5.87774	0.338226
$303$	1.49682	0.0859900
$304$	2.54871	0.146179
$305$	−15.4367	−0.883900
$306$	−11.9401	−0.682567
$307$	22.0500	1.25846	0.629231	−	0.777218i	$-0.283370\pi$
$307$	22.0500	1.25846	0.629231	+	0.777218i	$0.283370\pi$
$308$	14.9305	0.850745
$309$	0.987698	0.0561882
$310$	7.44349	0.422762
$311$	−7.56193	−0.428798	−0.214399	−	0.976746i	$-0.568779\pi$
$311$	−7.56193	−0.428798	−0.214399	+	0.976746i	$0.568779\pi$
$312$	0.495448	0.0280492
$313$	−22.6377	−1.27956	−0.639779	−	0.768559i	$-0.720974\pi$
$313$	−22.6377	−1.27956	−0.639779	+	0.768559i	$0.720974\pi$
$314$	−14.9621	−0.844362
$315$	11.9470	0.673137
$316$	7.06533	0.397456
$317$	−13.2659	−0.745085	−0.372542	−	0.928015i	$-0.621514\pi$
$317$	−13.2659	−0.745085	−0.372542	+	0.928015i	$0.621514\pi$
$318$	1.46434	0.0821160
$319$	35.1708	1.96919
$320$	1.00000	0.0559017
$321$	−1.01193	−0.0564802
$322$	33.0175	1.83999
$323$	10.2340	0.569434
$324$	8.76304	0.486836
$325$	3.04893	0.169124
$326$	−3.07847	−0.170500
$327$	1.14269	0.0631910
$328$	8.16315	0.450735
$329$	−36.7522	−2.02622
$330$	−0.603876	−0.0332423
$331$	−33.6742	−1.85090	−0.925451	−	0.378867i	$-0.876314\pi$
$331$	−33.6742	−1.85090	−0.925451	+	0.378867i	$0.876314\pi$
$332$	−0.676261	−0.0371146
$333$	−25.7115	−1.40898
$334$	16.2409	0.888660
$335$	−2.24036	−0.122404
$336$	−0.652872	−0.0356171
$337$	18.0082	0.980968	0.490484	−	0.871450i	$-0.336820\pi$
$337$	18.0082	0.980968	0.490484	+	0.871450i	$0.336820\pi$
$338$	−3.70401	−0.201472
$339$	1.91783	0.104162
$340$	4.01536	0.217764
$341$	−27.6614	−1.49795
$342$	−7.57883	−0.409816
$343$	−8.60550	−0.464653
$344$	7.28651	0.392862
$345$	−1.33542	−0.0718966
$346$	16.0471	0.862698
$347$	−17.6675	−0.948441	−0.474221	−	0.880406i	$-0.657270\pi$
$347$	−17.6675	−0.948441	−0.474221	+	0.880406i	$0.657270\pi$
$348$	−1.53793	−0.0824414
$349$	32.0864	1.71754	0.858772	−	0.512359i	$-0.171228\pi$
$349$	32.0864	1.71754	0.858772	+	0.512359i	$0.171228\pi$
$350$	−4.01770	−0.214755
$351$	−2.95961	−0.157972
$352$	−3.71619	−0.198073
$353$	−21.0996	−1.12302	−0.561509	−	0.827471i	$-0.689779\pi$
$353$	−21.0996	−1.12302	−0.561509	+	0.827471i	$0.689779\pi$
$354$	1.36952	0.0727889
$355$	−4.30906	−0.228701
$356$	7.94004	0.420821
$357$	−2.62152	−0.138745
$358$	−4.36346	−0.230616
$359$	−6.63845	−0.350364	−0.175182	−	0.984536i	$-0.556051\pi$
$359$	−6.63845	−0.350364	−0.175182	+	0.984536i	$0.556051\pi$
$360$	−2.97359	−0.156722
$361$	−12.5041	−0.658109
$362$	−9.51503	−0.500099
$363$	0.456629	0.0239668
$364$	−12.2497	−0.642058
$365$	−14.7120	−0.770061
$366$	−2.50844	−0.131118
$367$	−33.2657	−1.73646	−0.868228	−	0.496165i	$-0.834741\pi$
$367$	−33.2657	−1.73646	−0.868228	+	0.496165i	$0.834741\pi$
$368$	−8.21802	−0.428394
$369$	−24.2739	−1.26365
$370$	8.64660	0.449515
$371$	−36.2049	−1.87967
$372$	1.20956	0.0627127
$373$	−20.4603	−1.05939	−0.529697	−	0.848187i	$-0.677694\pi$
$373$	−20.4603	−1.05939	−0.529697	+	0.848187i	$0.677694\pi$
$374$	−14.9218	−0.771590
$375$	0.162499	0.00839141
$376$	9.14758	0.471751
$377$	−28.8558	−1.48615
$378$	3.89999	0.200594
$379$	35.9565	1.84696	0.923481	−	0.383644i	$-0.125331\pi$
$379$	35.9565	1.84696	0.923481	+	0.383644i	$0.125331\pi$
$380$	2.54871	0.130746
$381$	0.468729	0.0240137
$382$	−5.46772	−0.279753
$383$	27.4831	1.40432	0.702160	−	0.712019i	$-0.252219\pi$
$383$	27.4831	1.40432	0.702160	+	0.712019i	$0.252219\pi$
$384$	0.162499	0.00829249
$385$	14.9305	0.760930
$386$	10.4602	0.532409
$387$	−21.6671	−1.10140
$388$	10.0406	0.509734
$389$	−0.276799	−0.0140343	−0.00701714	−	0.999975i	$-0.502234\pi$
$389$	−0.276799	−0.0140343	−0.00701714	+	0.999975i	$0.502234\pi$
$390$	0.495448	0.0250880
$391$	−32.9983	−1.66880
$392$	9.14190	0.461736
$393$	−1.57534	−0.0794656
$394$	25.9045	1.30505
$395$	7.06533	0.355495
$396$	11.0504	0.555305
$397$	7.52441	0.377639	0.188820	−	0.982012i	$-0.439534\pi$
$397$	7.52441	0.377639	0.188820	+	0.982012i	$0.439534\pi$
$398$	16.8914	0.846691
$399$	−1.66398	−0.0833032
$400$	1.00000	0.0500000
$401$	8.13331	0.406158	0.203079	−	0.979162i	$-0.434905\pi$
$401$	8.13331	0.406158	0.203079	+	0.979162i	$0.434905\pi$
$402$	−0.364057	−0.0181575
$403$	22.6947	1.13050
$404$	9.21125	0.458277
$405$	8.76304	0.435439
$406$	38.0244	1.88712
$407$	−32.1324	−1.59274
$408$	0.652492	0.0323032
$409$	20.6702	1.02208	0.511038	−	0.859558i	$-0.329261\pi$
$409$	20.6702	1.02208	0.511038	+	0.859558i	$0.329261\pi$
$410$	8.16315	0.403149
$411$	0.166970	0.00823603
$412$	6.07818	0.299450
$413$	−33.8605	−1.66617
$414$	24.4371	1.20102
$415$	−0.676261	−0.0331963
$416$	3.04893	0.149486
$417$	0.0570428	0.00279340
$418$	−9.47148	−0.463265
$419$	18.5644	0.906932	0.453466	−	0.891274i	$-0.350187\pi$
$419$	18.5644	0.906932	0.453466	+	0.891274i	$0.350187\pi$
$420$	−0.652872	−0.0318569
$421$	−1.56717	−0.0763793	−0.0381897	−	0.999271i	$-0.512159\pi$
$421$	−1.56717	−0.0763793	−0.0381897	+	0.999271i	$0.512159\pi$
$422$	−13.4570	−0.655075
$423$	−27.2012	−1.32257
$424$	9.01136	0.437631
$425$	4.01536	0.194774
$426$	−0.700217	−0.0339256
$427$	62.0198	3.00135
$428$	−6.22728	−0.301007
$429$	−1.84118	−0.0888929
$430$	7.28651	0.351387
$431$	−7.42840	−0.357813	−0.178907	−	0.983866i	$-0.557256\pi$
$431$	−7.42840	−0.357813	−0.178907	+	0.983866i	$0.557256\pi$
$432$	−0.970703	−0.0467030
$433$	3.15489	0.151614	0.0758072	−	0.997122i	$-0.475847\pi$
$433$	3.15489	0.151614	0.0758072	+	0.997122i	$0.475847\pi$
$434$	−29.9057	−1.43552
$435$	−1.53793	−0.0737379
$436$	7.03199	0.336771
$437$	−20.9453	−1.00195
$438$	−2.39068	−0.114231
$439$	−2.91854	−0.139295	−0.0696473	−	0.997572i	$-0.522187\pi$
$439$	−2.91854	−0.139295	−0.0696473	+	0.997572i	$0.522187\pi$
$440$	−3.71619	−0.177162
$441$	−27.1843	−1.29449
$442$	12.2426	0.582319
$443$	28.4210	1.35032	0.675162	−	0.737669i	$-0.264074\pi$
$443$	28.4210	1.35032	0.675162	+	0.737669i	$0.264074\pi$
$444$	1.40506	0.0666814
$445$	7.94004	0.376394
$446$	−23.5669	−1.11593
$447$	3.30165	0.156163
$448$	−4.01770	−0.189818
$449$	−15.0273	−0.709181	−0.354591	−	0.935022i	$-0.615380\pi$
$449$	−15.0273	−0.709181	−0.354591	+	0.935022i	$0.615380\pi$
$450$	−2.97359	−0.140177
$451$	−30.3358	−1.42846
$452$	11.8021	0.555123
$453$	0.955126	0.0448758
$454$	−13.8825	−0.651536
$455$	−12.2497	−0.574274
$456$	0.414163	0.0193949
$457$	15.5897	0.729255	0.364628	−	0.931153i	$-0.381196\pi$
$457$	15.5897	0.729255	0.364628	+	0.931153i	$0.381196\pi$
$458$	−3.02352	−0.141280
$459$	−3.89772	−0.181930
$460$	−8.21802	−0.383167
$461$	−16.4034	−0.763984	−0.381992	−	0.924166i	$-0.624762\pi$
$461$	−16.4034	−0.763984	−0.381992	+	0.924166i	$0.624762\pi$
$462$	2.42619	0.112877
$463$	−17.4454	−0.810758	−0.405379	−	0.914149i	$-0.632860\pi$
$463$	−17.4454	−0.810758	−0.405379	+	0.914149i	$0.632860\pi$
$464$	−9.46422	−0.439365
$465$	1.20956	0.0560920
$466$	12.2433	0.567158
$467$	1.51957	0.0703173	0.0351587	−	0.999382i	$-0.488806\pi$
$467$	1.51957	0.0703173	0.0351587	+	0.999382i	$0.488806\pi$
$468$	−9.06629	−0.419089
$469$	9.00110	0.415632
$470$	9.14758	0.421946
$471$	−2.43133	−0.112030
$472$	8.42784	0.387923
$473$	−27.0780	−1.24505
$474$	1.14811	0.0527344
$475$	2.54871	0.116943
$476$	−16.1325	−0.739432
$477$	−26.7961	−1.22691
$478$	−3.06773	−0.140314
$479$	0.155854	0.00712115	0.00356058	−	0.999994i	$-0.498867\pi$
$479$	0.155854	0.00712115	0.00356058	+	0.999994i	$0.498867\pi$
$480$	0.162499	0.00741703
$481$	26.3629	1.20204
$482$	14.4540	0.658363
$483$	5.36531	0.244130
$484$	2.81004	0.127729
$485$	10.0406	0.455920
$486$	4.33609	0.196689
$487$	−7.09497	−0.321504	−0.160752	−	0.986995i	$-0.551392\pi$
$487$	−7.09497	−0.321504	−0.160752	+	0.986995i	$0.551392\pi$
$488$	−15.4367	−0.698784
$489$	−0.500247	−0.0226220
$490$	9.14190	0.412989
$491$	7.30688	0.329755	0.164877	−	0.986314i	$-0.447277\pi$
$491$	7.30688	0.329755	0.164877	+	0.986314i	$0.447277\pi$
$492$	1.32650	0.0598034
$493$	−38.0022	−1.71153
$494$	7.77084	0.349627
$495$	11.0504	0.496680
$496$	7.44349	0.334223
$497$	17.3125	0.776571
$498$	−0.109892	−0.00492436
$499$	1.07376	0.0480681	0.0240341	−	0.999711i	$-0.492349\pi$
$499$	1.07376	0.0480681	0.0240341	+	0.999711i	$0.492349\pi$
$500$	1.00000	0.0447214
$501$	2.63912	0.117907
$502$	−27.7181	−1.23712
$503$	15.8245	0.705581	0.352791	−	0.935702i	$-0.385233\pi$
$503$	15.8245	0.705581	0.352791	+	0.935702i	$0.385233\pi$
$504$	11.9470	0.532162
$505$	9.21125	0.409895
$506$	30.5397	1.35766
$507$	−0.601898	−0.0267312
$508$	2.88450	0.127979
$509$	21.2193	0.940529	0.470264	−	0.882526i	$-0.344159\pi$
$509$	21.2193	0.940529	0.470264	+	0.882526i	$0.344159\pi$
$510$	0.652492	0.0288928
$511$	59.1083	2.61480
$512$	1.00000	0.0441942
$513$	−2.47404	−0.109232
$514$	0.246378	0.0108673
$515$	6.07818	0.267837
$516$	1.18405	0.0521249
$517$	−33.9941	−1.49506
$518$	−34.7394	−1.52636
$519$	2.60764	0.114463
$520$	3.04893	0.133705
$521$	7.34273	0.321691	0.160845	−	0.986980i	$-0.448578\pi$
$521$	7.34273	0.321691	0.160845	+	0.986980i	$0.448578\pi$
$522$	28.1427	1.23177
$523$	−27.6355	−1.20841	−0.604207	−	0.796827i	$-0.706510\pi$
$523$	−27.6355	−1.20841	−0.604207	+	0.796827i	$0.706510\pi$
$524$	−9.69449	−0.423506
$525$	−0.652872	−0.0284937
$526$	−6.13280	−0.267403
$527$	29.8883	1.30195
$528$	−0.603876	−0.0262803
$529$	44.5359	1.93634
$530$	9.01136	0.391429
$531$	−25.0610	−1.08755
$532$	−10.2399	−0.443958
$533$	24.8889	1.07806
$534$	1.29025	0.0558345
$535$	−6.22728	−0.269229
$536$	−2.24036	−0.0967689
$537$	−0.709057	−0.0305981
$538$	22.8312	0.984325
$539$	−33.9730	−1.46332
$540$	−0.970703	−0.0417724
$541$	41.3980	1.77984	0.889920	−	0.456116i	$-0.150760\pi$
$541$	41.3980	1.77984	0.889920	+	0.456116i	$0.150760\pi$
$542$	−3.15356	−0.135457
$543$	−1.54618	−0.0663531
$544$	4.01536	0.172157
$545$	7.03199	0.301217
$546$	−1.99056	−0.0851882
$547$	30.4807	1.30326	0.651631	−	0.758536i	$-0.274085\pi$
$547$	30.4807	1.30326	0.651631	+	0.758536i	$0.274085\pi$
$548$	1.02752	0.0438933
$549$	45.9023	1.95906
$550$	−3.71619	−0.158459
$551$	−24.1215	−1.02761
$552$	−1.33542	−0.0568392
$553$	−28.3864	−1.20711
$554$	−8.37602	−0.355863
$555$	1.40506	0.0596416
$556$	0.351035	0.0148872
$557$	21.8210	0.924585	0.462293	−	0.886727i	$-0.347027\pi$
$557$	21.8210	0.924585	0.462293	+	0.886727i	$0.347027\pi$
$558$	−22.1339	−0.937003
$559$	22.2161	0.939640
$560$	−4.01770	−0.169779
$561$	−2.42478	−0.102374
$562$	31.4835	1.32805
$563$	−39.4503	−1.66263	−0.831316	−	0.555801i	$-0.812412\pi$
$563$	−39.4503	−1.66263	−0.831316	+	0.555801i	$0.812412\pi$
$564$	1.48647	0.0625918
$565$	11.8021	0.496517
$566$	−11.4101	−0.479602
$567$	−35.2073	−1.47857
$568$	−4.30906	−0.180804
$569$	18.6427	0.781544	0.390772	−	0.920487i	$-0.372208\pi$
$569$	18.6427	0.781544	0.390772	+	0.920487i	$0.372208\pi$
$570$	0.414163	0.0173474
$571$	24.5641	1.02798	0.513988	−	0.857797i	$-0.328167\pi$
$571$	24.5641	1.02798	0.513988	+	0.857797i	$0.328167\pi$
$572$	−11.3304	−0.473748
$573$	−0.888498	−0.0371175
$574$	−32.7971	−1.36892
$575$	−8.21802	−0.342715
$576$	−2.97359	−0.123900
$577$	17.2294	0.717269	0.358634	−	0.933478i	$-0.383242\pi$
$577$	17.2294	0.717269	0.358634	+	0.933478i	$0.383242\pi$
$578$	−0.876876	−0.0364732
$579$	1.69977	0.0706400
$580$	−9.46422	−0.392980
$581$	2.71701	0.112721
$582$	1.63159	0.0676314
$583$	−33.4879	−1.38693
$584$	−14.7120	−0.608787
$585$	−9.06629	−0.374845
$586$	1.89860	0.0784303
$587$	19.9870	0.824954	0.412477	−	0.910968i	$-0.364664\pi$
$587$	19.9870	0.824954	0.412477	+	0.910968i	$0.364664\pi$
$588$	1.48555	0.0612630
$589$	18.9713	0.781698
$590$	8.42784	0.346969
$591$	4.20946	0.173154
$592$	8.64660	0.355373
$593$	−28.4123	−1.16675	−0.583377	−	0.812202i	$-0.698269\pi$
$593$	−28.4123	−1.16675	−0.583377	+	0.812202i	$0.698269\pi$
$594$	3.60731	0.148010
$595$	−16.1325	−0.661368
$596$	20.3180	0.832256
$597$	2.74484	0.112339
$598$	−25.0562	−1.02462
$599$	41.7057	1.70405	0.852025	−	0.523502i	$-0.175375\pi$
$599$	41.7057	1.70405	0.852025	+	0.523502i	$0.175375\pi$
$600$	0.162499	0.00663399
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	−29.2750	−1.19316
$603$	6.66193	0.271295
$604$	5.87774	0.239162
$605$	2.81004	0.114245
$606$	1.49682	0.0608041
$607$	−19.5084	−0.791821	−0.395910	−	0.918289i	$-0.629571\pi$
$607$	−19.5084	−0.791821	−0.395910	+	0.918289i	$0.629571\pi$
$608$	2.54871	0.103364
$609$	6.17892	0.250382
$610$	−15.4367	−0.625012
$611$	27.8904	1.12832
$612$	−11.9401	−0.482648
$613$	−37.7975	−1.52663	−0.763314	−	0.646028i	$-0.776429\pi$
$613$	−37.7975	−1.52663	−0.763314	+	0.646028i	$0.776429\pi$
$614$	22.0500	0.889868
$615$	1.32650	0.0534898
$616$	14.9305	0.601568
$617$	−24.6941	−0.994148	−0.497074	−	0.867708i	$-0.665592\pi$
$617$	−24.6941	−0.994148	−0.497074	+	0.867708i	$0.665592\pi$
$618$	0.987698	0.0397310
$619$	−28.4032	−1.14162	−0.570811	−	0.821081i	$-0.693371\pi$
$619$	−28.4032	−1.14162	−0.570811	+	0.821081i	$0.693371\pi$
$620$	7.44349	0.298938
$621$	7.97726	0.320116
$622$	−7.56193	−0.303206
$623$	−31.9007	−1.27807
$624$	0.495448	0.0198338
$625$	1.00000	0.0400000
$626$	−22.6377	−0.904784
$627$	−1.53911	−0.0614660
$628$	−14.9621	−0.597054
$629$	34.7192	1.38435
$630$	11.9470	0.475980
$631$	47.8154	1.90350	0.951751	−	0.306872i	$-0.0992823\pi$
$631$	47.8154	1.90350	0.951751	+	0.306872i	$0.0992823\pi$
$632$	7.06533	0.281044
$633$	−2.18674	−0.0869153
$634$	−13.2659	−0.526854
$635$	2.88450	0.114468
$636$	1.46434	0.0580647
$637$	27.8730	1.10437
$638$	35.1708	1.39242
$639$	12.8134	0.506890
$640$	1.00000	0.0395285
$641$	−15.2838	−0.603674	−0.301837	−	0.953360i	$-0.597600\pi$
$641$	−15.2838	−0.603674	−0.301837	+	0.953360i	$0.597600\pi$
$642$	−1.01193	−0.0399375
$643$	−26.6128	−1.04951	−0.524753	−	0.851254i	$-0.675842\pi$
$643$	−26.6128	−1.04951	−0.524753	+	0.851254i	$0.675842\pi$
$644$	33.0175	1.30107
$645$	1.18405	0.0466219
$646$	10.2340	0.402651
$647$	3.71468	0.146039	0.0730196	−	0.997331i	$-0.476736\pi$
$647$	3.71468	0.146039	0.0730196	+	0.997331i	$0.476736\pi$
$648$	8.76304	0.344245
$649$	−31.3194	−1.22939
$650$	3.04893	0.119589
$651$	−4.85964	−0.190464
$652$	−3.07847	−0.120562
$653$	−18.5218	−0.724815	−0.362407	−	0.932020i	$-0.618045\pi$
$653$	−18.5218	−0.724815	−0.362407	+	0.932020i	$0.618045\pi$
$654$	1.14269	0.0446828
$655$	−9.69449	−0.378795
$656$	8.16315	0.318718
$657$	43.7475	1.70675
$658$	−36.7522	−1.43275
$659$	−27.4796	−1.07045	−0.535227	−	0.844709i	$-0.679774\pi$
$659$	−27.4796	−1.07045	−0.535227	+	0.844709i	$0.679774\pi$
$660$	−0.603876	−0.0235059
$661$	33.3531	1.29729	0.648643	−	0.761093i	$-0.275337\pi$
$661$	33.3531	1.29729	0.648643	+	0.761093i	$0.275337\pi$
$662$	−33.6742	−1.30879
$663$	1.98940	0.0772620
$664$	−0.676261	−0.0262440
$665$	−10.2399	−0.397088
$666$	−25.7115	−0.996300
$667$	77.7771	3.01154
$668$	16.2409	0.628378
$669$	−3.82960	−0.148061
$670$	−2.24036	−0.0865528
$671$	57.3655	2.21457
$672$	−0.652872	−0.0251851
$673$	−9.66688	−0.372631	−0.186315	−	0.982490i	$-0.559655\pi$
$673$	−9.66688	−0.372631	−0.186315	+	0.982490i	$0.559655\pi$
$674$	18.0082	0.693649
$675$	−0.970703	−0.0373624
$676$	−3.70401	−0.142462
$677$	40.1833	1.54437	0.772185	−	0.635397i	$-0.219164\pi$
$677$	40.1833	1.54437	0.772185	+	0.635397i	$0.219164\pi$
$678$	1.91783	0.0736537
$679$	−40.3401	−1.54811
$680$	4.01536	0.153982
$681$	−2.25588	−0.0864457
$682$	−27.6614	−1.05921
$683$	18.8927	0.722910	0.361455	−	0.932389i	$-0.382280\pi$
$683$	18.8927	0.722910	0.361455	+	0.932389i	$0.382280\pi$
$684$	−7.57883	−0.289784
$685$	1.02752	0.0392593
$686$	−8.60550	−0.328560
$687$	−0.491318	−0.0187450
$688$	7.28651	0.277796
$689$	27.4750	1.04672
$690$	−1.33542	−0.0508386
$691$	−15.1476	−0.576241	−0.288121	−	0.957594i	$-0.593030\pi$
$691$	−15.1476	−0.576241	−0.288121	+	0.957594i	$0.593030\pi$
$692$	16.0471	0.610020
$693$	−44.3973	−1.68651
$694$	−17.6675	−0.670649
$695$	0.351035	0.0133155
$696$	−1.53793	−0.0582949
$697$	32.7780	1.24156
$698$	32.0864	1.21449
$699$	1.98952	0.0752505
$700$	−4.01770	−0.151855
$701$	−8.45843	−0.319471	−0.159735	−	0.987160i	$-0.551064\pi$
$701$	−8.45843	−0.319471	−0.159735	+	0.987160i	$0.551064\pi$
$702$	−2.95961	−0.111703
$703$	22.0377	0.831167
$704$	−3.71619	−0.140059
$705$	1.48647	0.0559838
$706$	−21.0996	−0.794094
$707$	−37.0080	−1.39183
$708$	1.36952	0.0514695
$709$	−15.0076	−0.563621	−0.281811	−	0.959470i	$-0.590935\pi$
$709$	−15.0076	−0.563621	−0.281811	+	0.959470i	$0.590935\pi$
$710$	−4.30906	−0.161716
$711$	−21.0094	−0.787915
$712$	7.94004	0.297566
$713$	−61.1708	−2.29086
$714$	−2.62152	−0.0981078
$715$	−11.3304	−0.423733
$716$	−4.36346	−0.163070
$717$	−0.498502	−0.0186169
$718$	−6.63845	−0.247745
$719$	1.88068	0.0701375	0.0350687	−	0.999385i	$-0.488835\pi$
$719$	1.88068	0.0701375	0.0350687	+	0.999385i	$0.488835\pi$
$720$	−2.97359	−0.110819
$721$	−24.4203	−0.909459
$722$	−12.5041	−0.465354
$723$	2.34877	0.0873515
$724$	−9.51503	−0.353623
$725$	−9.46422	−0.351492
$726$	0.456629	0.0169471
$727$	−29.5087	−1.09442	−0.547208	−	0.836997i	$-0.684309\pi$
$727$	−29.5087	−1.09442	−0.547208	+	0.836997i	$0.684309\pi$
$728$	−12.2497	−0.454004
$729$	−25.5845	−0.947575
$730$	−14.7120	−0.544515
$731$	29.2580	1.08214
$732$	−2.50844	−0.0927146
$733$	38.8212	1.43389	0.716946	−	0.697129i	$-0.245539\pi$
$733$	38.8212	1.43389	0.716946	+	0.697129i	$0.245539\pi$
$734$	−33.2657	−1.22786
$735$	1.48555	0.0547953
$736$	−8.21802	−0.302920
$737$	8.32561	0.306678
$738$	−24.2739	−0.893535
$739$	−19.7297	−0.725767	−0.362884	−	0.931834i	$-0.618208\pi$
$739$	−19.7297	−0.725767	−0.362884	+	0.931834i	$0.618208\pi$
$740$	8.64660	0.317855
$741$	1.26275	0.0463884
$742$	−36.2049	−1.32913
$743$	22.3419	0.819645	0.409823	−	0.912165i	$-0.365591\pi$
$743$	22.3419	0.819645	0.409823	+	0.912165i	$0.365591\pi$
$744$	1.20956	0.0443446
$745$	20.3180	0.744392
$746$	−20.4603	−0.749104
$747$	2.01092	0.0735759
$748$	−14.9218	−0.545596
$749$	25.0193	0.914186
$750$	0.162499	0.00593362
$751$	2.43714	0.0889324	0.0444662	−	0.999011i	$-0.485841\pi$
$751$	2.43714	0.0889324	0.0444662	+	0.999011i	$0.485841\pi$
$752$	9.14758	0.333578
$753$	−4.50416	−0.164141
$754$	−28.8558	−1.05086
$755$	5.87774	0.213913
$756$	3.89999	0.141841
$757$	−27.9232	−1.01489	−0.507444	−	0.861685i	$-0.669410\pi$
$757$	−27.9232	−1.01489	−0.507444	+	0.861685i	$0.669410\pi$
$758$	35.9565	1.30600
$759$	4.96267	0.180133
$760$	2.54871	0.0924514
$761$	−15.0077	−0.544027	−0.272014	−	0.962293i	$-0.587690\pi$
$761$	−15.0077	−0.544027	−0.272014	+	0.962293i	$0.587690\pi$
$762$	0.468729	0.0169802
$763$	−28.2524	−1.02281
$764$	−5.46772	−0.197815
$765$	−11.9401	−0.431694
$766$	27.4831	0.993004
$767$	25.6959	0.927826
$768$	0.162499	0.00586368
$769$	5.21964	0.188225	0.0941126	−	0.995562i	$-0.469999\pi$
$769$	5.21964	0.188225	0.0941126	+	0.995562i	$0.469999\pi$
$770$	14.9305	0.538058
$771$	0.0400361	0.00144187
$772$	10.4602	0.376470
$773$	23.7841	0.855453	0.427727	−	0.903908i	$-0.359315\pi$
$773$	23.7841	0.855453	0.427727	+	0.903908i	$0.359315\pi$
$774$	−21.6671	−0.778809
$775$	7.44349	0.267378
$776$	10.0406	0.360436
$777$	−5.64512	−0.202518
$778$	−0.276799	−0.00992374
$779$	20.8055	0.745434
$780$	0.495448	0.0177399
$781$	16.0133	0.573000
$782$	−32.9983	−1.18002
$783$	9.18694	0.328314
$784$	9.14190	0.326496
$785$	−14.9621	−0.534021
$786$	−1.57534	−0.0561907
$787$	−48.0931	−1.71433	−0.857167	−	0.515039i	$-0.827777\pi$
$787$	−48.0931	−1.71433	−0.857167	+	0.515039i	$0.827777\pi$
$788$	25.9045	0.922811
$789$	−0.996574	−0.0354790
$790$	7.06533	0.251373
$791$	−47.4172	−1.68596
$792$	11.0504	0.392660
$793$	−47.0653	−1.67134
$794$	7.52441	0.267031
$795$	1.46434	0.0519347
$796$	16.8914	0.598701
$797$	26.8786	0.952090	0.476045	−	0.879421i	$-0.342070\pi$
$797$	26.8786	0.952090	0.476045	+	0.879421i	$0.342070\pi$
$798$	−1.66398	−0.0589043
$799$	36.7308	1.29944
$800$	1.00000	0.0353553
$801$	−23.6105	−0.834234
$802$	8.13331	0.287197
$803$	54.6725	1.92935
$804$	−0.364057	−0.0128393
$805$	33.0175	1.16371
$806$	22.6947	0.799387
$807$	3.71005	0.130600
$808$	9.21125	0.324051
$809$	−20.6607	−0.726391	−0.363195	−	0.931713i	$-0.618314\pi$
$809$	−20.6607	−0.726391	−0.363195	+	0.931713i	$0.618314\pi$
$810$	8.76304	0.307902
$811$	44.9325	1.57779	0.788896	−	0.614527i	$-0.210653\pi$
$811$	44.9325	1.57779	0.788896	+	0.614527i	$0.210653\pi$
$812$	38.0244	1.33439
$813$	−0.512450	−0.0179724
$814$	−32.1324	−1.12624
$815$	−3.07847	−0.107834
$816$	0.652492	0.0228418
$817$	18.5712	0.649724
$818$	20.6702	0.722716
$819$	36.4256	1.27281
$820$	8.16315	0.285070
$821$	−15.3764	−0.536640	−0.268320	−	0.963330i	$-0.586469\pi$
$821$	−15.3764	−0.536640	−0.268320	+	0.963330i	$0.586469\pi$
$822$	0.166970	0.00582375
$823$	−9.09159	−0.316913	−0.158457	−	0.987366i	$-0.550652\pi$
$823$	−9.09159	−0.316913	−0.158457	+	0.987366i	$0.550652\pi$
$824$	6.07818	0.211743
$825$	−0.603876	−0.0210243
$826$	−33.8605	−1.17816
$827$	−9.48812	−0.329934	−0.164967	−	0.986299i	$-0.552752\pi$
$827$	−9.48812	−0.329934	−0.164967	+	0.986299i	$0.552752\pi$
$828$	24.4371	0.849247
$829$	31.6964	1.10086	0.550430	−	0.834881i	$-0.314464\pi$
$829$	31.6964	1.10086	0.550430	+	0.834881i	$0.314464\pi$
$830$	−0.676261	−0.0234734
$831$	−1.36109	−0.0472159
$832$	3.04893	0.105703
$833$	36.7080	1.27186
$834$	0.0570428	0.00197523
$835$	16.2409	0.562038
$836$	−9.47148	−0.327578
$837$	−7.22542	−0.249747
$838$	18.5644	0.641298
$839$	−45.6281	−1.57526	−0.787629	−	0.616149i	$-0.788692\pi$
$839$	−45.6281	−1.57526	−0.787629	+	0.616149i	$0.788692\pi$
$840$	−0.652872	−0.0225262
$841$	60.5714	2.08867
$842$	−1.56717	−0.0540084
$843$	5.11603	0.176205
$844$	−13.4570	−0.463208
$845$	−3.70401	−0.127422
$846$	−27.2012	−0.935196
$847$	−11.2899	−0.387926
$848$	9.01136	0.309452
$849$	−1.85413	−0.0636335
$850$	4.01536	0.137726
$851$	−71.0579	−2.43584
$852$	−0.700217	−0.0239890
$853$	−46.0866	−1.57797	−0.788987	−	0.614409i	$-0.789394\pi$
$853$	−46.0866	−1.57797	−0.788987	+	0.614409i	$0.789394\pi$
$854$	62.0198	2.12227
$855$	−7.57883	−0.259190
$856$	−6.22728	−0.212844
$857$	4.91330	0.167835	0.0839175	−	0.996473i	$-0.473257\pi$
$857$	4.91330	0.167835	0.0839175	+	0.996473i	$0.473257\pi$
$858$	−1.84118	−0.0628568
$859$	44.4850	1.51781	0.758904	−	0.651202i	$-0.225735\pi$
$859$	44.4850	1.51781	0.758904	+	0.651202i	$0.225735\pi$
$860$	7.28651	0.248468
$861$	−5.32949	−0.181629
$862$	−7.42840	−0.253012
$863$	6.12298	0.208429	0.104214	−	0.994555i	$-0.466767\pi$
$863$	6.12298	0.208429	0.104214	+	0.994555i	$0.466767\pi$
$864$	−0.970703	−0.0330240
$865$	16.0471	0.545618
$866$	3.15489	0.107208
$867$	−0.142491	−0.00483926
$868$	−29.9057	−1.01507
$869$	−26.2561	−0.890676
$870$	−1.53793	−0.0521405
$871$	−6.83072	−0.231450
$872$	7.03199	0.238133
$873$	−29.8566	−1.01049
$874$	−20.9453	−0.708487
$875$	−4.01770	−0.135823
$876$	−2.39068	−0.0807737
$877$	5.82410	0.196666	0.0983330	−	0.995154i	$-0.468649\pi$
$877$	5.82410	0.196666	0.0983330	+	0.995154i	$0.468649\pi$
$878$	−2.91854	−0.0984961
$879$	0.308520	0.0104061
$880$	−3.71619	−0.125273
$881$	40.8210	1.37529	0.687647	−	0.726045i	$-0.258644\pi$
$881$	40.8210	1.37529	0.687647	+	0.726045i	$0.258644\pi$
$882$	−27.1843	−0.915343
$883$	−46.5712	−1.56725	−0.783623	−	0.621237i	$-0.786630\pi$
$883$	−46.5712	−1.56725	−0.783623	+	0.621237i	$0.786630\pi$
$884$	12.2426	0.411762
$885$	1.36952	0.0460357
$886$	28.4210	0.954823
$887$	−24.1436	−0.810664	−0.405332	−	0.914170i	$-0.632844\pi$
$887$	−24.1436	−0.810664	−0.405332	+	0.914170i	$0.632844\pi$
$888$	1.40506	0.0471508
$889$	−11.5891	−0.388685
$890$	7.94004	0.266151
$891$	−32.5651	−1.09097
$892$	−23.5669	−0.789080
$893$	23.3145	0.780191
$894$	3.30165	0.110424
$895$	−4.36346	−0.145854
$896$	−4.01770	−0.134222
$897$	−4.07160	−0.135947
$898$	−15.0273	−0.501467
$899$	−70.4468	−2.34953
$900$	−2.97359	−0.0991198
$901$	36.1839	1.20546
$902$	−30.3358	−1.01007
$903$	−4.75716	−0.158308
$904$	11.8021	0.392531
$905$	−9.51503	−0.316290
$906$	0.955126	0.0317320
$907$	32.9014	1.09247	0.546237	−	0.837631i	$-0.316060\pi$
$907$	32.9014	1.09247	0.546237	+	0.837631i	$0.316060\pi$
$908$	−13.8825	−0.460705
$909$	−27.3905	−0.908486
$910$	−12.2497	−0.406073
$911$	−12.3805	−0.410184	−0.205092	−	0.978743i	$-0.565749\pi$
$911$	−12.3805	−0.410184	−0.205092	+	0.978743i	$0.565749\pi$
$912$	0.414163	0.0137143
$913$	2.51311	0.0831718
$914$	15.5897	0.515661
$915$	−2.50844	−0.0829264
$916$	−3.02352	−0.0998998
$917$	38.9495	1.28623
$918$	−3.89772	−0.128644
$919$	−41.9610	−1.38417	−0.692084	−	0.721817i	$-0.743307\pi$
$919$	−41.9610	−1.38417	−0.692084	+	0.721817i	$0.743307\pi$
$920$	−8.21802	−0.270940
$921$	3.58311	0.118067
$922$	−16.4034	−0.540218
$923$	−13.1380	−0.432443
$924$	2.42619	0.0798159
$925$	8.64660	0.284298
$926$	−17.4454	−0.573293
$927$	−18.0740	−0.593629
$928$	−9.46422	−0.310678
$929$	−18.8963	−0.619968	−0.309984	−	0.950742i	$-0.600324\pi$
$929$	−18.8963	−0.619968	−0.309984	+	0.950742i	$0.600324\pi$
$930$	1.20956	0.0396630
$931$	23.3000	0.763628
$932$	12.2433	0.401042
$933$	−1.22881	−0.0402293
$934$	1.51957	0.0497219
$935$	−14.9218	−0.487996
$936$	−9.06629	−0.296341
$937$	3.12183	0.101986	0.0509929	−	0.998699i	$-0.483761\pi$
$937$	3.12183	0.101986	0.0509929	+	0.998699i	$0.483761\pi$
$938$	9.00110	0.293896
$939$	−3.67860	−0.120047
$940$	9.14758	0.298361
$941$	7.92308	0.258285	0.129143	−	0.991626i	$-0.458778\pi$
$941$	7.92308	0.258285	0.129143	+	0.991626i	$0.458778\pi$
$942$	−2.43133	−0.0792170
$943$	−67.0850	−2.18459
$944$	8.42784	0.274303
$945$	3.89999	0.126867
$946$	−27.0780	−0.880383
$947$	56.1997	1.82625	0.913123	−	0.407685i	$-0.133664\pi$
$947$	56.1997	1.82625	0.913123	+	0.407685i	$0.133664\pi$
$948$	1.14811	0.0372888
$949$	−44.8559	−1.45608
$950$	2.54871	0.0826911
$951$	−2.15569	−0.0699030
$952$	−16.1325	−0.522858
$953$	−18.7282	−0.606666	−0.303333	−	0.952885i	$-0.598099\pi$
$953$	−18.7282	−0.606666	−0.303333	+	0.952885i	$0.598099\pi$
$954$	−26.7961	−0.867557
$955$	−5.46772	−0.176931
$956$	−3.06773	−0.0992173
$957$	5.71522	0.184747
$958$	0.155854	0.00503542
$959$	−4.12825	−0.133308
$960$	0.162499	0.00524463
$961$	24.4055	0.787275
$962$	26.3629	0.849974
$963$	18.5174	0.596715
$964$	14.4540	0.465533
$965$	10.4602	0.336725
$966$	5.36531	0.172626
$967$	43.9456	1.41320	0.706598	−	0.707615i	$-0.250229\pi$
$967$	43.9456	1.41320	0.706598	+	0.707615i	$0.250229\pi$
$968$	2.81004	0.0903183
$969$	1.66301	0.0534237
$970$	10.0406	0.322384
$971$	2.31592	0.0743214	0.0371607	−	0.999309i	$-0.488169\pi$
$971$	2.31592	0.0743214	0.0371607	+	0.999309i	$0.488169\pi$
$972$	4.33609	0.139080
$973$	−1.41035	−0.0452138
$974$	−7.09497	−0.227338
$975$	0.495448	0.0158670
$976$	−15.4367	−0.494115
$977$	0.932486	0.0298329	0.0149164	−	0.999889i	$-0.495252\pi$
$977$	0.932486	0.0298329	0.0149164	+	0.999889i	$0.495252\pi$
$978$	−0.500247	−0.0159961
$979$	−29.5067	−0.943037
$980$	9.14190	0.292027
$981$	−20.9103	−0.667614
$982$	7.30688	0.233172
$983$	−3.13390	−0.0999557	−0.0499779	−	0.998750i	$-0.515915\pi$
$983$	−3.13390	−0.0999557	−0.0499779	+	0.998750i	$0.515915\pi$
$984$	1.32650	0.0422874
$985$	25.9045	0.825387
$986$	−38.0022	−1.21024
$987$	−5.97220	−0.190097
$988$	7.77084	0.247223
$989$	−59.8807	−1.90410
$990$	11.0504	0.351206
$991$	−11.5446	−0.366726	−0.183363	−	0.983045i	$-0.558698\pi$
$991$	−11.5446	−0.366726	−0.183363	+	0.983045i	$0.558698\pi$
$992$	7.44349	0.236331
$993$	−5.47203	−0.173649
$994$	17.3125	0.549119
$995$	16.8914	0.535494
$996$	−0.109892	−0.00348205
$997$	17.7913	0.563456	0.281728	−	0.959494i	$-0.409092\pi$
$997$	17.7913	0.563456	0.281728	+	0.959494i	$0.409092\pi$
$998$	1.07376	0.0339893
$999$	−8.39328	−0.265552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.j.1.17	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.j.1.17	✓	33	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.162499 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.162499 q^{6} -4.01770 q^{7} +1.00000 q^{8} -2.97359 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.162499 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.162499 q^{6} -4.01770 q^{7} +1.00000 q^{8} -2.97359 q^{9} +1.00000 q^{10} -3.71619 q^{11} +0.162499 q^{12} +3.04893 q^{13} -4.01770 q^{14} +0.162499 q^{15} +1.00000 q^{16} +4.01536 q^{17} -2.97359 q^{18} +2.54871 q^{19} +1.00000 q^{20} -0.652872 q^{21} -3.71619 q^{22} -8.21802 q^{23} +0.162499 q^{24} +1.00000 q^{25} +3.04893 q^{26} -0.970703 q^{27} -4.01770 q^{28} -9.46422 q^{29} +0.162499 q^{30} +7.44349 q^{31} +1.00000 q^{32} -0.603876 q^{33} +4.01536 q^{34} -4.01770 q^{35} -2.97359 q^{36} +8.64660 q^{37} +2.54871 q^{38} +0.495448 q^{39} +1.00000 q^{40} +8.16315 q^{41} -0.652872 q^{42} +7.28651 q^{43} -3.71619 q^{44} -2.97359 q^{45} -8.21802 q^{46} +9.14758 q^{47} +0.162499 q^{48} +9.14190 q^{49} +1.00000 q^{50} +0.652492 q^{51} +3.04893 q^{52} +9.01136 q^{53} -0.970703 q^{54} -3.71619 q^{55} -4.01770 q^{56} +0.414163 q^{57} -9.46422 q^{58} +8.42784 q^{59} +0.162499 q^{60} -15.4367 q^{61} +7.44349 q^{62} +11.9470 q^{63} +1.00000 q^{64} +3.04893 q^{65} -0.603876 q^{66} -2.24036 q^{67} +4.01536 q^{68} -1.33542 q^{69} -4.01770 q^{70} -4.30906 q^{71} -2.97359 q^{72} -14.7120 q^{73} +8.64660 q^{74} +0.162499 q^{75} +2.54871 q^{76} +14.9305 q^{77} +0.495448 q^{78} +7.06533 q^{79} +1.00000 q^{80} +8.76304 q^{81} +8.16315 q^{82} -0.676261 q^{83} -0.652872 q^{84} +4.01536 q^{85} +7.28651 q^{86} -1.53793 q^{87} -3.71619 q^{88} +7.94004 q^{89} -2.97359 q^{90} -12.2497 q^{91} -8.21802 q^{92} +1.20956 q^{93} +9.14758 q^{94} +2.54871 q^{95} +0.162499 q^{96} +10.0406 q^{97} +9.14190 q^{98} +11.0504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9} + 33 q^{10} + 12 q^{11} + 6 q^{12} + 20 q^{13} + 4 q^{14} + 6 q^{15} + 33 q^{16} + 33 q^{17} + 49 q^{18} + 17 q^{19} + 33 q^{20} + 26 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 33 q^{25} + 20 q^{26} + 21 q^{27} + 4 q^{28} + 33 q^{29} + 6 q^{30} + 35 q^{31} + 33 q^{32} + 25 q^{33} + 33 q^{34} + 4 q^{35} + 49 q^{36} + 16 q^{37} + 17 q^{38} + 22 q^{39} + 33 q^{40} + 39 q^{41} + 26 q^{42} - 3 q^{43} + 12 q^{44} + 49 q^{45} + 7 q^{46} + 19 q^{47} + 6 q^{48} + 69 q^{49} + 33 q^{50} + 21 q^{51} + 20 q^{52} + 41 q^{53} + 21 q^{54} + 12 q^{55} + 4 q^{56} + 33 q^{58} + 18 q^{59} + 6 q^{60} + 30 q^{61} + 35 q^{62} - 15 q^{63} + 33 q^{64} + 20 q^{65} + 25 q^{66} - 9 q^{67} + 33 q^{68} + 23 q^{69} + 4 q^{70} + 36 q^{71} + 49 q^{72} + 35 q^{73} + 16 q^{74} + 6 q^{75} + 17 q^{76} + 26 q^{77} + 22 q^{78} + 32 q^{79} + 33 q^{80} + 53 q^{81} + 39 q^{82} + 24 q^{83} + 26 q^{84} + 33 q^{85} - 3 q^{86} + 12 q^{87} + 12 q^{88} + 40 q^{89} + 49 q^{90} + 5 q^{91} + 7 q^{92} + 18 q^{93} + 19 q^{94} + 17 q^{95} + 6 q^{96} + 39 q^{97} + 69 q^{98} + 3 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9 + 33 * q^10 + 12 * q^11 + 6 * q^12 + 20 * q^13 + 4 * q^14 + 6 * q^15 + 33 * q^16 + 33 * q^17 + 49 * q^18 + 17 * q^19 + 33 * q^20 + 26 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 33 * q^25 + 20 * q^26 + 21 * q^27 + 4 * q^28 + 33 * q^29 + 6 * q^30 + 35 * q^31 + 33 * q^32 + 25 * q^33 + 33 * q^34 + 4 * q^35 + 49 * q^36 + 16 * q^37 + 17 * q^38 + 22 * q^39 + 33 * q^40 + 39 * q^41 + 26 * q^42 - 3 * q^43 + 12 * q^44 + 49 * q^45 + 7 * q^46 + 19 * q^47 + 6 * q^48 + 69 * q^49 + 33 * q^50 + 21 * q^51 + 20 * q^52 + 41 * q^53 + 21 * q^54 + 12 * q^55 + 4 * q^56 + 33 * q^58 + 18 * q^59 + 6 * q^60 + 30 * q^61 + 35 * q^62 - 15 * q^63 + 33 * q^64 + 20 * q^65 + 25 * q^66 - 9 * q^67 + 33 * q^68 + 23 * q^69 + 4 * q^70 + 36 * q^71 + 49 * q^72 + 35 * q^73 + 16 * q^74 + 6 * q^75 + 17 * q^76 + 26 * q^77 + 22 * q^78 + 32 * q^79 + 33 * q^80 + 53 * q^81 + 39 * q^82 + 24 * q^83 + 26 * q^84 + 33 * q^85 - 3 * q^86 + 12 * q^87 + 12 * q^88 + 40 * q^89 + 49 * q^90 + 5 * q^91 + 7 * q^92 + 18 * q^93 + 19 * q^94 + 17 * q^95 + 6 * q^96 + 39 * q^97 + 69 * q^98 + 3 * q^99

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