LMFDB - Embedded newform 6031.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.14221 q^{2} +1.83370 q^{3} +2.58905 q^{4} -3.64172 q^{5} -3.92816 q^{6} +3.71202 q^{7} -1.26186 q^{8} +0.362447 q^{9} +O(q^{10})$	\(q-2.14221 q^{2} +1.83370 q^{3} +2.58905 q^{4} -3.64172 q^{5} -3.92816 q^{6} +3.71202 q^{7} -1.26186 q^{8} +0.362447 q^{9} +7.80132 q^{10} -5.02675 q^{11} +4.74753 q^{12} -0.605986 q^{13} -7.95192 q^{14} -6.67782 q^{15} -2.47493 q^{16} -1.90825 q^{17} -0.776437 q^{18} +3.84573 q^{19} -9.42859 q^{20} +6.80673 q^{21} +10.7683 q^{22} +1.83811 q^{23} -2.31387 q^{24} +8.26213 q^{25} +1.29815 q^{26} -4.83647 q^{27} +9.61061 q^{28} +2.71114 q^{29} +14.3053 q^{30} -0.885966 q^{31} +7.82553 q^{32} -9.21755 q^{33} +4.08786 q^{34} -13.5182 q^{35} +0.938393 q^{36} +1.00000 q^{37} -8.23834 q^{38} -1.11119 q^{39} +4.59535 q^{40} -4.53098 q^{41} -14.5814 q^{42} +6.94191 q^{43} -13.0145 q^{44} -1.31993 q^{45} -3.93761 q^{46} +7.47993 q^{47} -4.53827 q^{48} +6.77912 q^{49} -17.6992 q^{50} -3.49915 q^{51} -1.56893 q^{52} -0.557732 q^{53} +10.3607 q^{54} +18.3060 q^{55} -4.68406 q^{56} +7.05190 q^{57} -5.80783 q^{58} +9.04093 q^{59} -17.2892 q^{60} +6.67775 q^{61} +1.89792 q^{62} +1.34541 q^{63} -11.8140 q^{64} +2.20683 q^{65} +19.7459 q^{66} -6.85251 q^{67} -4.94054 q^{68} +3.37054 q^{69} +28.9587 q^{70} -1.94708 q^{71} -0.457358 q^{72} +10.4042 q^{73} -2.14221 q^{74} +15.1503 q^{75} +9.95677 q^{76} -18.6594 q^{77} +2.38041 q^{78} -12.0694 q^{79} +9.01300 q^{80} -9.95597 q^{81} +9.70630 q^{82} -0.0731947 q^{83} +17.6229 q^{84} +6.94931 q^{85} -14.8710 q^{86} +4.97142 q^{87} +6.34306 q^{88} -15.3107 q^{89} +2.82757 q^{90} -2.24943 q^{91} +4.75896 q^{92} -1.62459 q^{93} -16.0235 q^{94} -14.0051 q^{95} +14.3497 q^{96} +4.34874 q^{97} -14.5223 q^{98} -1.82193 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) $ 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * 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 $

$2$	−2.14221	−1.51477	−0.757384	−	0.652969i	$-0.773523\pi$
$2$	−2.14221	−1.51477	−0.757384	+	0.652969i	$0.773523\pi$
$3$	1.83370	1.05869	0.529343	−	0.848408i	$-0.322439\pi$
$3$	1.83370	1.05869	0.529343	+	0.848408i	$0.322439\pi$
$4$	2.58905	1.29452
$5$	−3.64172	−1.62863	−0.814314	−	0.580425i	$-0.802886\pi$
$5$	−3.64172	−1.62863	−0.814314	+	0.580425i	$0.802886\pi$
$6$	−3.92816	−1.60366
$7$	3.71202	1.40301	0.701507	−	0.712663i	$-0.252511\pi$
$7$	3.71202	1.40301	0.701507	+	0.712663i	$0.252511\pi$
$8$	−1.26186	−0.446135
$9$	0.362447	0.120816
$10$	7.80132	2.46699
$11$	−5.02675	−1.51562	−0.757812	−	0.652473i	$-0.773731\pi$
$11$	−5.02675	−1.51562	−0.757812	+	0.652473i	$0.773731\pi$
$12$	4.74753	1.37049
$13$	−0.605986	−0.168070	−0.0840351	−	0.996463i	$-0.526781\pi$
$13$	−0.605986	−0.168070	−0.0840351	+	0.996463i	$0.526781\pi$
$14$	−7.95192	−2.12524
$15$	−6.67782	−1.72420
$16$	−2.47493	−0.618732
$17$	−1.90825	−0.462818	−0.231409	−	0.972857i	$-0.574334\pi$
$17$	−1.90825	−0.462818	−0.231409	+	0.972857i	$0.574334\pi$
$18$	−0.776437	−0.183008
$19$	3.84573	0.882270	0.441135	−	0.897441i	$-0.354576\pi$
$19$	3.84573	0.882270	0.441135	+	0.897441i	$0.354576\pi$
$20$	−9.42859	−2.10830
$21$	6.80673	1.48535
$22$	10.7683	2.29582
$23$	1.83811	0.383273	0.191636	−	0.981466i	$-0.438621\pi$
$23$	1.83811	0.383273	0.191636	+	0.981466i	$0.438621\pi$
$24$	−2.31387	−0.472317
$25$	8.26213	1.65243
$26$	1.29815	0.254587
$27$	−4.83647	−0.930780
$28$	9.61061	1.81623
$29$	2.71114	0.503447	0.251723	−	0.967799i	$-0.419003\pi$
$29$	2.71114	0.503447	0.251723	+	0.967799i	$0.419003\pi$
$30$	14.3053	2.61177
$31$	−0.885966	−0.159124	−0.0795621	−	0.996830i	$-0.525352\pi$
$31$	−0.885966	−0.159124	−0.0795621	+	0.996830i	$0.525352\pi$
$32$	7.82553	1.38337
$33$	−9.21755	−1.60457
$34$	4.08786	0.701062
$35$	−13.5182	−2.28499
$36$	0.938393	0.156399
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−8.23834	−1.33643
$39$	−1.11119	−0.177934
$40$	4.59535	0.726588
$41$	−4.53098	−0.707620	−0.353810	−	0.935317i	$-0.615114\pi$
$41$	−4.53098	−0.707620	−0.353810	+	0.935317i	$0.615114\pi$
$42$	−14.5814	−2.24996
$43$	6.94191	1.05863	0.529315	−	0.848425i	$-0.322449\pi$
$43$	6.94191	1.05863	0.529315	+	0.848425i	$0.322449\pi$
$44$	−13.0145	−1.96201
$45$	−1.31993	−0.196764
$46$	−3.93761	−0.580570
$47$	7.47993	1.09106	0.545530	−	0.838092i	$-0.316329\pi$
$47$	7.47993	1.09106	0.545530	+	0.838092i	$0.316329\pi$
$48$	−4.53827	−0.655043
$49$	6.77912	0.968446
$50$	−17.6992	−2.50304
$51$	−3.49915	−0.489979
$52$	−1.56893	−0.217571
$53$	−0.557732	−0.0766104	−0.0383052	−	0.999266i	$-0.512196\pi$
$53$	−0.557732	−0.0766104	−0.0383052	+	0.999266i	$0.512196\pi$
$54$	10.3607	1.40992
$55$	18.3060	2.46839
$56$	−4.68406	−0.625934
$57$	7.05190	0.934047
$58$	−5.80783	−0.762605
$59$	9.04093	1.17703	0.588514	−	0.808487i	$-0.299713\pi$
$59$	9.04093	1.17703	0.588514	+	0.808487i	$0.299713\pi$
$60$	−17.2892	−2.23202
$61$	6.67775	0.854998	0.427499	−	0.904016i	$-0.359395\pi$
$61$	6.67775	0.854998	0.427499	+	0.904016i	$0.359395\pi$
$62$	1.89792	0.241036
$63$	1.34541	0.169506
$64$	−11.8140	−1.47675
$65$	2.20683	0.273724
$66$	19.7459	2.43055
$67$	−6.85251	−0.837167	−0.418584	−	0.908178i	$-0.637473\pi$
$67$	−6.85251	−0.837167	−0.418584	+	0.908178i	$0.637473\pi$
$68$	−4.94054	−0.599129
$69$	3.37054	0.405765
$70$	28.9587	3.46122
$71$	−1.94708	−0.231076	−0.115538	−	0.993303i	$-0.536859\pi$
$71$	−1.94708	−0.231076	−0.115538	+	0.993303i	$0.536859\pi$
$72$	−0.457358	−0.0539002
$73$	10.4042	1.21772	0.608860	−	0.793278i	$-0.291627\pi$
$73$	10.4042	1.21772	0.608860	+	0.793278i	$0.291627\pi$
$74$	−2.14221	−0.249026
$75$	15.1503	1.74940
$76$	9.95677	1.14212
$77$	−18.6594	−2.12644
$78$	2.38041	0.269528
$79$	−12.0694	−1.35791	−0.678956	−	0.734179i	$-0.737567\pi$
$79$	−12.0694	−1.35791	−0.678956	+	0.734179i	$0.737567\pi$
$80$	9.01300	1.00768
$81$	−9.95597	−1.10622
$82$	9.70630	1.07188
$83$	−0.0731947	−0.00803416	−0.00401708	−	0.999992i	$-0.501279\pi$
$83$	−0.0731947	−0.00803416	−0.00401708	+	0.999992i	$0.501279\pi$
$84$	17.6229	1.92282
$85$	6.94931	0.753758
$86$	−14.8710	−1.60358
$87$	4.97142	0.532992
$88$	6.34306	0.676173
$89$	−15.3107	−1.62293	−0.811464	−	0.584402i	$-0.801329\pi$
$89$	−15.3107	−1.62293	−0.811464	+	0.584402i	$0.801329\pi$
$90$	2.82757	0.298052
$91$	−2.24943	−0.235805
$92$	4.75896	0.496156
$93$	−1.62459	−0.168463
$94$	−16.0235	−1.65270
$95$	−14.0051	−1.43689
$96$	14.3497	1.46456
$97$	4.34874	0.441547	0.220774	−	0.975325i	$-0.429142\pi$
$97$	4.34874	0.441547	0.220774	+	0.975325i	$0.429142\pi$
$98$	−14.5223	−1.46697
$99$	−1.82193	−0.183111
$100$	21.3911	2.13911
$101$	−1.09555	−0.109011	−0.0545055	−	0.998513i	$-0.517358\pi$
$101$	−1.09555	−0.109011	−0.0545055	+	0.998513i	$0.517358\pi$
$102$	7.49590	0.742205
$103$	−6.03515	−0.594661	−0.297331	−	0.954775i	$-0.596096\pi$
$103$	−6.03515	−0.594661	−0.297331	+	0.954775i	$0.596096\pi$
$104$	0.764670	0.0749820
$105$	−24.7882	−2.41908
$106$	1.19478	0.116047
$107$	−5.58628	−0.540046	−0.270023	−	0.962854i	$-0.587031\pi$
$107$	−5.58628	−0.540046	−0.270023	+	0.962854i	$0.587031\pi$
$108$	−12.5219	−1.20492
$109$	−10.4236	−0.998398	−0.499199	−	0.866488i	$-0.666372\pi$
$109$	−10.4236	−0.998398	−0.499199	+	0.866488i	$0.666372\pi$
$110$	−39.2153	−3.73903
$111$	1.83370	0.174047
$112$	−9.18699	−0.868089
$113$	0.569617	0.0535850	0.0267925	−	0.999641i	$-0.491471\pi$
$113$	0.569617	0.0535850	0.0267925	+	0.999641i	$0.491471\pi$
$114$	−15.1066	−1.41486
$115$	−6.69389	−0.624208
$116$	7.01928	0.651724
$117$	−0.219638	−0.0203055
$118$	−19.3675	−1.78293
$119$	−7.08346	−0.649340
$120$	8.42647	0.769228
$121$	14.2683	1.29711
$122$	−14.3051	−1.29512
$123$	−8.30845	−0.749148
$124$	−2.29381	−0.205990
$125$	−11.8798	−1.06256
$126$	−2.88215	−0.256762
$127$	−15.3922	−1.36584	−0.682919	−	0.730494i	$-0.739290\pi$
$127$	−15.3922	−1.36584	−0.682919	+	0.730494i	$0.739290\pi$
$128$	9.65705	0.853571
$129$	12.7294	1.12076
$130$	−4.72749	−0.414628
$131$	16.6055	1.45083	0.725415	−	0.688312i	$-0.241648\pi$
$131$	16.6055	1.45083	0.725415	+	0.688312i	$0.241648\pi$
$132$	−23.8647	−2.07715
$133$	14.2754	1.23784
$134$	14.6795	1.26811
$135$	17.6131	1.51589
$136$	2.40794	0.206479
$137$	−18.2082	−1.55563	−0.777817	−	0.628491i	$-0.783673\pi$
$137$	−18.2082	−1.55563	−0.777817	+	0.628491i	$0.783673\pi$
$138$	−7.22039	−0.614641
$139$	10.2672	0.870850	0.435425	−	0.900225i	$-0.356598\pi$
$139$	10.2672	0.870850	0.435425	+	0.900225i	$0.356598\pi$
$140$	−34.9991	−2.95797
$141$	13.7159	1.15509
$142$	4.17105	0.350027
$143$	3.04614	0.254731
$144$	−0.897031	−0.0747526
$145$	−9.87323	−0.819927
$146$	−22.2879	−1.84456
$147$	12.4309	1.02528
$148$	2.58905	0.212818
$149$	−8.31623	−0.681292	−0.340646	−	0.940192i	$-0.610646\pi$
$149$	−8.31623	−0.681292	−0.340646	+	0.940192i	$0.610646\pi$
$150$	−32.4550	−2.64994
$151$	2.52505	0.205486	0.102743	−	0.994708i	$-0.467238\pi$
$151$	2.52505	0.205486	0.102743	+	0.994708i	$0.467238\pi$
$152$	−4.85277	−0.393612
$153$	−0.691639	−0.0559157
$154$	39.9723	3.22106
$155$	3.22644	0.259154
$156$	−2.87694	−0.230339
$157$	−10.4741	−0.835921	−0.417960	−	0.908465i	$-0.637255\pi$
$157$	−10.4741	−0.835921	−0.417960	+	0.908465i	$0.637255\pi$
$158$	25.8551	2.05692
$159$	−1.02271	−0.0811063
$160$	−28.4984	−2.25300
$161$	6.82311	0.537737
$162$	21.3277	1.67567
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	−11.7309	−0.916031
$165$	33.5677	2.61324
$166$	0.156798	0.0121699
$167$	15.1154	1.16966	0.584832	−	0.811154i	$-0.301160\pi$
$167$	15.1154	1.16966	0.584832	+	0.811154i	$0.301160\pi$
$168$	−8.58915	−0.662667
$169$	−12.6328	−0.971752
$170$	−14.8868	−1.14177
$171$	1.39387	0.106592
$172$	17.9729	1.37042
$173$	−5.58827	−0.424868	−0.212434	−	0.977175i	$-0.568139\pi$
$173$	−5.58827	−0.424868	−0.212434	+	0.977175i	$0.568139\pi$
$174$	−10.6498	−0.807359
$175$	30.6692	2.31838
$176$	12.4409	0.937765
$177$	16.5783	1.24610
$178$	32.7986	2.45836
$179$	2.97615	0.222448	0.111224	−	0.993795i	$-0.464523\pi$
$179$	2.97615	0.222448	0.111224	+	0.993795i	$0.464523\pi$
$180$	−3.41737	−0.254715
$181$	3.22550	0.239750	0.119875	−	0.992789i	$-0.461751\pi$
$181$	3.22550	0.239750	0.119875	+	0.992789i	$0.461751\pi$
$182$	4.81875	0.357190
$183$	12.2450	0.905174
$184$	−2.31944	−0.170991
$185$	−3.64172	−0.267745
$186$	3.48022	0.255182
$187$	9.59229	0.701458
$188$	19.3659	1.41240
$189$	−17.9531	−1.30590
$190$	30.0017	2.17655
$191$	−19.8200	−1.43412	−0.717062	−	0.697010i	$-0.754513\pi$
$191$	−19.8200	−1.43412	−0.717062	+	0.697010i	$0.754513\pi$
$192$	−21.6634	−1.56342
$193$	1.16580	0.0839160	0.0419580	−	0.999119i	$-0.486640\pi$
$193$	1.16580	0.0839160	0.0419580	+	0.999119i	$0.486640\pi$
$194$	−9.31589	−0.668842
$195$	4.04666	0.289787
$196$	17.5515	1.25368
$197$	−14.2336	−1.01410	−0.507050	−	0.861916i	$-0.669264\pi$
$197$	−14.2336	−1.01410	−0.507050	+	0.861916i	$0.669264\pi$
$198$	3.90296	0.277371
$199$	1.58343	0.112246	0.0561231	−	0.998424i	$-0.482126\pi$
$199$	1.58343	0.112246	0.0561231	+	0.998424i	$0.482126\pi$
$200$	−10.4257	−0.737206
$201$	−12.5654	−0.886297
$202$	2.34689	0.165126
$203$	10.0638	0.706342
$204$	−9.05947	−0.634289
$205$	16.5006	1.15245
$206$	12.9285	0.900774
$207$	0.666218	0.0463054
$208$	1.49977	0.103990
$209$	−19.3315	−1.33719
$210$	53.1015	3.66435
$211$	−15.3819	−1.05894	−0.529468	−	0.848330i	$-0.677608\pi$
$211$	−15.3819	−1.05894	−0.529468	+	0.848330i	$0.677608\pi$
$212$	−1.44399	−0.0991739
$213$	−3.57036	−0.244637
$214$	11.9670	0.818045
$215$	−25.2805	−1.72411
$216$	6.10296	0.415254
$217$	−3.28873	−0.223253
$218$	22.3294	1.51234
$219$	19.0782	1.28918
$220$	47.3952	3.19538
$221$	1.15637	0.0777859
$222$	−3.92816	−0.263641
$223$	−22.5512	−1.51014	−0.755068	−	0.655646i	$-0.772396\pi$
$223$	−22.5512	−1.51014	−0.755068	+	0.655646i	$0.772396\pi$
$224$	29.0486	1.94089
$225$	2.99459	0.199639
$226$	−1.22024	−0.0811689
$227$	−17.4414	−1.15763	−0.578814	−	0.815460i	$-0.696484\pi$
$227$	−17.4414	−1.15763	−0.578814	+	0.815460i	$0.696484\pi$
$228$	18.2577	1.20915
$229$	−5.67980	−0.375331	−0.187666	−	0.982233i	$-0.560092\pi$
$229$	−5.67980	−0.375331	−0.187666	+	0.982233i	$0.560092\pi$
$230$	14.3397	0.945531
$231$	−34.2158	−2.25123
$232$	−3.42109	−0.224605
$233$	−20.7250	−1.35774	−0.678869	−	0.734259i	$-0.737530\pi$
$233$	−20.7250	−1.35774	−0.678869	+	0.734259i	$0.737530\pi$
$234$	0.470510	0.0307582
$235$	−27.2398	−1.77693
$236$	23.4074	1.52369
$237$	−22.1316	−1.43760
$238$	15.1742	0.983600
$239$	5.48923	0.355069	0.177534	−	0.984115i	$-0.443188\pi$
$239$	5.48923	0.355069	0.177534	+	0.984115i	$0.443188\pi$
$240$	16.5271	1.06682
$241$	15.3398	0.988122	0.494061	−	0.869427i	$-0.335512\pi$
$241$	15.3398	0.988122	0.494061	+	0.869427i	$0.335512\pi$
$242$	−30.5655	−1.96483
$243$	−3.74682	−0.240359
$244$	17.2890	1.10681
$245$	−24.6877	−1.57724
$246$	17.7984	1.13479
$247$	−2.33046	−0.148283
$248$	1.11797	0.0709909
$249$	−0.134217	−0.00850565
$250$	25.4489	1.60953
$251$	11.3715	0.717762	0.358881	−	0.933383i	$-0.383158\pi$
$251$	11.3715	0.717762	0.358881	+	0.933383i	$0.383158\pi$
$252$	3.48334	0.219430
$253$	−9.23973	−0.580897
$254$	32.9733	2.06893
$255$	12.7429	0.797993
$256$	2.94068	0.183793
$257$	21.1508	1.31935	0.659675	−	0.751551i	$-0.270694\pi$
$257$	21.1508	1.31935	0.659675	+	0.751551i	$0.270694\pi$
$258$	−27.2689	−1.69769
$259$	3.71202	0.230654
$260$	5.71359	0.354342
$261$	0.982646	0.0608243
$262$	−35.5724	−2.19767
$263$	−5.20303	−0.320832	−0.160416	−	0.987049i	$-0.551284\pi$
$263$	−5.20303	−0.320832	−0.160416	+	0.987049i	$0.551284\pi$
$264$	11.6313	0.715855
$265$	2.03110	0.124770
$266$	−30.5809	−1.87504
$267$	−28.0751	−1.71817
$268$	−17.7415	−1.08373
$269$	−15.3747	−0.937414	−0.468707	−	0.883354i	$-0.655280\pi$
$269$	−15.3747	−0.937414	−0.468707	+	0.883354i	$0.655280\pi$
$270$	−37.7309	−2.29623
$271$	9.34983	0.567962	0.283981	−	0.958830i	$-0.408345\pi$
$271$	9.34983	0.567962	0.283981	+	0.958830i	$0.408345\pi$
$272$	4.72278	0.286360
$273$	−4.12478	−0.249643
$274$	39.0058	2.35643
$275$	−41.5317	−2.50446
$276$	8.72649	0.525273
$277$	−17.9031	−1.07569	−0.537846	−	0.843043i	$-0.680762\pi$
$277$	−17.9031	−1.07569	−0.537846	+	0.843043i	$0.680762\pi$
$278$	−21.9944	−1.31914
$279$	−0.321116	−0.0192247
$280$	17.0580	1.01941
$281$	31.4080	1.87365	0.936823	−	0.349803i	$-0.113751\pi$
$281$	31.4080	1.87365	0.936823	+	0.349803i	$0.113751\pi$
$282$	−29.3823	−1.74969
$283$	20.6381	1.22681	0.613404	−	0.789769i	$-0.289800\pi$
$283$	20.6381	1.22681	0.613404	+	0.789769i	$0.289800\pi$
$284$	−5.04109	−0.299133
$285$	−25.6810	−1.52121
$286$	−6.52546	−0.385859
$287$	−16.8191	−0.992801
$288$	2.83634	0.167133
$289$	−13.3586	−0.785799
$290$	21.1505	1.24200
$291$	7.97427	0.467460
$292$	26.9370	1.57637
$293$	0.188418	0.0110075	0.00550375	−	0.999985i	$-0.498248\pi$
$293$	0.188418	0.0110075	0.00550375	+	0.999985i	$0.498248\pi$
$294$	−26.6295	−1.55306
$295$	−32.9245	−1.91694
$296$	−1.26186	−0.0733442
$297$	24.3118	1.41071
$298$	17.8151	1.03200
$299$	−1.11387	−0.0644167
$300$	39.2247	2.26464
$301$	25.7685	1.48527
$302$	−5.40918	−0.311264
$303$	−2.00890	−0.115408
$304$	−9.51790	−0.545889
$305$	−24.3185	−1.39247
$306$	1.48163	0.0846994
$307$	−6.22454	−0.355253	−0.177627	−	0.984098i	$-0.556842\pi$
$307$	−6.22454	−0.355253	−0.177627	+	0.984098i	$0.556842\pi$
$308$	−48.3101	−2.75273
$309$	−11.0666	−0.629559
$310$	−6.91170	−0.392558
$311$	16.1536	0.915985	0.457992	−	0.888956i	$-0.348569\pi$
$311$	16.1536	0.915985	0.457992	+	0.888956i	$0.348569\pi$
$312$	1.40217	0.0793824
$313$	−26.6523	−1.50648	−0.753239	−	0.657747i	$-0.771509\pi$
$313$	−26.6523	−1.50648	−0.753239	+	0.657747i	$0.771509\pi$
$314$	22.4376	1.26623
$315$	−4.89962	−0.276062
$316$	−31.2482	−1.75785
$317$	−10.2349	−0.574848	−0.287424	−	0.957803i	$-0.592799\pi$
$317$	−10.2349	−0.574848	−0.287424	+	0.957803i	$0.592799\pi$
$318$	2.19086	0.122857
$319$	−13.6282	−0.763035
$320$	43.0234	2.40508
$321$	−10.2435	−0.571739
$322$	−14.6165	−0.814547
$323$	−7.33860	−0.408331
$324$	−25.7765	−1.43203
$325$	−5.00674	−0.277724
$326$	−2.14221	−0.118646
$327$	−19.1137	−1.05699
$328$	5.71747	0.315694
$329$	27.7657	1.53077
$330$	−71.9090	−3.95846
$331$	−4.57311	−0.251361	−0.125681	−	0.992071i	$-0.540111\pi$
$331$	−4.57311	−0.251361	−0.125681	+	0.992071i	$0.540111\pi$
$332$	−0.189505	−0.0104004
$333$	0.362447	0.0198620
$334$	−32.3803	−1.77177
$335$	24.9549	1.36343
$336$	−16.8462	−0.919034
$337$	16.1477	0.879622	0.439811	−	0.898090i	$-0.355045\pi$
$337$	16.1477	0.879622	0.439811	+	0.898090i	$0.355045\pi$
$338$	27.0620	1.47198
$339$	1.04450	0.0567297
$340$	17.9921	0.975758
$341$	4.45353	0.241172
$342$	−2.98596	−0.161462
$343$	−0.819905	−0.0442707
$344$	−8.75972	−0.472293
$345$	−12.2746	−0.660841
$346$	11.9712	0.643577
$347$	−24.5747	−1.31924	−0.659620	−	0.751600i	$-0.729283\pi$
$347$	−24.5747	−1.31924	−0.659620	+	0.751600i	$0.729283\pi$
$348$	12.8712	0.689971
$349$	19.3442	1.03547	0.517736	−	0.855540i	$-0.326775\pi$
$349$	19.3442	1.03547	0.517736	+	0.855540i	$0.326775\pi$
$350$	−65.6998	−3.51180
$351$	2.93083	0.156436
$352$	−39.3370	−2.09667
$353$	−34.7856	−1.85145	−0.925725	−	0.378198i	$-0.876544\pi$
$353$	−34.7856	−1.85145	−0.925725	+	0.378198i	$0.876544\pi$
$354$	−35.5142	−1.88756
$355$	7.09073	0.376337
$356$	−39.6401	−2.10092
$357$	−12.9889	−0.687447
$358$	−6.37552	−0.336957
$359$	6.73170	0.355285	0.177643	−	0.984095i	$-0.443153\pi$
$359$	6.73170	0.355285	0.177643	+	0.984095i	$0.443153\pi$
$360$	1.66557	0.0877833
$361$	−4.21040	−0.221600
$362$	−6.90969	−0.363165
$363$	26.1637	1.37324
$364$	−5.82389	−0.305255
$365$	−37.8892	−1.98321
$366$	−26.2312	−1.37113
$367$	10.8382	0.565749	0.282874	−	0.959157i	$-0.408712\pi$
$367$	10.8382	0.565749	0.282874	+	0.959157i	$0.408712\pi$
$368$	−4.54919	−0.237143
$369$	−1.64224	−0.0854917
$370$	7.80132	0.405571
$371$	−2.07031	−0.107485
$372$	−4.20615	−0.218079
$373$	19.9848	1.03477	0.517387	−	0.855752i	$-0.326905\pi$
$373$	19.9848	1.03477	0.517387	+	0.855752i	$0.326905\pi$
$374$	−20.5487	−1.06255
$375$	−21.7839	−1.12492
$376$	−9.43863	−0.486760
$377$	−1.64291	−0.0846144
$378$	38.4593	1.97813
$379$	2.99305	0.153742	0.0768712	−	0.997041i	$-0.475507\pi$
$379$	2.99305	0.153742	0.0768712	+	0.997041i	$0.475507\pi$
$380$	−36.2598	−1.86009
$381$	−28.2247	−1.44599
$382$	42.4585	2.17236
$383$	−7.32975	−0.374533	−0.187266	−	0.982309i	$-0.559963\pi$
$383$	−7.32975	−0.374533	−0.187266	+	0.982309i	$0.559963\pi$
$384$	17.7081	0.903663
$385$	67.9524	3.46318
$386$	−2.49738	−0.127113
$387$	2.51607	0.127899
$388$	11.2591	0.571593
$389$	−20.3476	−1.03166	−0.515831	−	0.856690i	$-0.672517\pi$
$389$	−20.3476	−1.03166	−0.515831	+	0.856690i	$0.672517\pi$
$390$	−8.66878	−0.438961
$391$	−3.50757	−0.177386
$392$	−8.55431	−0.432058
$393$	30.4495	1.53597
$394$	30.4913	1.53613
$395$	43.9533	2.21153
$396$	−4.71707	−0.237042
$397$	16.0348	0.804761	0.402381	−	0.915472i	$-0.368183\pi$
$397$	16.0348	0.804761	0.402381	+	0.915472i	$0.368183\pi$
$398$	−3.39203	−0.170027
$399$	26.1768	1.31048
$400$	−20.4482	−1.02241
$401$	−12.0144	−0.599970	−0.299985	−	0.953944i	$-0.596982\pi$
$401$	−12.0144	−0.599970	−0.299985	+	0.953944i	$0.596982\pi$
$402$	26.9177	1.34253
$403$	0.536883	0.0267440
$404$	−2.83642	−0.141117
$405$	36.2569	1.80162
$406$	−21.5588	−1.06994
$407$	−5.02675	−0.249167
$408$	4.41544	0.218597
$409$	1.89395	0.0936497	0.0468248	−	0.998903i	$-0.485090\pi$
$409$	1.89395	0.0936497	0.0468248	+	0.998903i	$0.485090\pi$
$410$	−35.3476	−1.74569
$411$	−33.3884	−1.64693
$412$	−15.6253	−0.769803
$413$	33.5601	1.65139
$414$	−1.42718	−0.0701419
$415$	0.266555	0.0130847
$416$	−4.74216	−0.232503
$417$	18.8269	0.921957
$418$	41.4121	2.02553
$419$	11.7530	0.574172	0.287086	−	0.957905i	$-0.407313\pi$
$419$	11.7530	0.574172	0.287086	+	0.957905i	$0.407313\pi$
$420$	−64.1779	−3.13156
$421$	−30.4242	−1.48278	−0.741391	−	0.671073i	$-0.765834\pi$
$421$	−30.4242	−1.48278	−0.741391	+	0.671073i	$0.765834\pi$
$422$	32.9513	1.60404
$423$	2.71108	0.131817
$424$	0.703780	0.0341786
$425$	−15.7662	−0.764773
$426$	7.64844	0.370568
$427$	24.7880	1.19957
$428$	−14.4631	−0.699102
$429$	5.58570	0.269680
$430$	54.1560	2.61164
$431$	8.38501	0.403892	0.201946	−	0.979397i	$-0.435274\pi$
$431$	8.38501	0.403892	0.201946	+	0.979397i	$0.435274\pi$
$432$	11.9699	0.575903
$433$	−16.6152	−0.798474	−0.399237	−	0.916848i	$-0.630725\pi$
$433$	−16.6152	−0.798474	−0.399237	+	0.916848i	$0.630725\pi$
$434$	7.04513	0.338177
$435$	−18.1045	−0.868045
$436$	−26.9871	−1.29245
$437$	7.06887	0.338150
$438$	−40.8693	−1.95281
$439$	−39.7234	−1.89590	−0.947948	−	0.318425i	$-0.896846\pi$
$439$	−39.7234	−1.89590	−0.947948	+	0.318425i	$0.896846\pi$
$440$	−23.0997	−1.10123
$441$	2.45707	0.117004
$442$	−2.47719	−0.117828
$443$	−16.6087	−0.789104	−0.394552	−	0.918874i	$-0.629100\pi$
$443$	−16.6087	−0.789104	−0.394552	+	0.918874i	$0.629100\pi$
$444$	4.74753	0.225308
$445$	55.7572	2.64314
$446$	48.3092	2.28751
$447$	−15.2494	−0.721274
$448$	−43.8540	−2.07191
$449$	−3.32520	−0.156926	−0.0784630	−	0.996917i	$-0.525001\pi$
$449$	−3.32520	−0.156926	−0.0784630	+	0.996917i	$0.525001\pi$
$450$	−6.41502	−0.302407
$451$	22.7761	1.07249
$452$	1.47476	0.0693671
$453$	4.63018	0.217545
$454$	37.3631	1.75354
$455$	8.19181	0.384038
$456$	−8.89851	−0.416711
$457$	−10.0365	−0.469486	−0.234743	−	0.972058i	$-0.575425\pi$
$457$	−10.0365	−0.469486	−0.234743	+	0.972058i	$0.575425\pi$
$458$	12.1673	0.568540
$459$	9.22919	0.430782
$460$	−17.3308	−0.808053
$461$	32.5172	1.51447	0.757237	−	0.653140i	$-0.226549\pi$
$461$	32.5172	1.51447	0.757237	+	0.653140i	$0.226549\pi$
$462$	73.2972	3.41009
$463$	−14.6340	−0.680099	−0.340050	−	0.940408i	$-0.610444\pi$
$463$	−14.6340	−0.680099	−0.340050	+	0.940408i	$0.610444\pi$
$464$	−6.70988	−0.311499
$465$	5.91632	0.274363
$466$	44.3972	2.05666
$467$	−13.6855	−0.633290	−0.316645	−	0.948544i	$-0.602556\pi$
$467$	−13.6855	−0.633290	−0.316645	+	0.948544i	$0.602556\pi$
$468$	−0.568653	−0.0262860
$469$	−25.4367	−1.17456
$470$	58.3533	2.69164
$471$	−19.2063	−0.884978
$472$	−11.4084	−0.525114
$473$	−34.8953	−1.60449
$474$	47.4105	2.17764
$475$	31.7739	1.45789
$476$	−18.3394	−0.840586
$477$	−0.202148	−0.00925574
$478$	−11.7591	−0.537847
$479$	34.2918	1.56683	0.783415	−	0.621498i	$-0.213476\pi$
$479$	34.2918	1.56683	0.783415	+	0.621498i	$0.213476\pi$
$480$	−52.2574	−2.38521
$481$	−0.605986	−0.0276306
$482$	−32.8610	−1.49678
$483$	12.5115	0.569294
$484$	36.9412	1.67914
$485$	−15.8369	−0.719116
$486$	8.02647	0.364088
$487$	−18.3228	−0.830286	−0.415143	−	0.909756i	$-0.636268\pi$
$487$	−18.3228	−0.830286	−0.415143	+	0.909756i	$0.636268\pi$
$488$	−8.42639	−0.381445
$489$	1.83370	0.0829227
$490$	52.8861	2.38915
$491$	4.16764	0.188083	0.0940416	−	0.995568i	$-0.470021\pi$
$491$	4.16764	0.188083	0.0940416	+	0.995568i	$0.470021\pi$
$492$	−21.5110	−0.969789
$493$	−5.17353	−0.233004
$494$	4.99232	0.224615
$495$	6.63497	0.298220
$496$	2.19270	0.0984553
$497$	−7.22761	−0.324203
$498$	0.287520	0.0128841
$499$	−18.2088	−0.815137	−0.407569	−	0.913175i	$-0.633623\pi$
$499$	−18.2088	−0.815137	−0.407569	+	0.913175i	$0.633623\pi$
$500$	−30.7573	−1.37551
$501$	27.7171	1.23831
$502$	−24.3601	−1.08724
$503$	−8.05949	−0.359355	−0.179677	−	0.983726i	$-0.557505\pi$
$503$	−8.05949	−0.359355	−0.179677	+	0.983726i	$0.557505\pi$
$504$	−1.69772	−0.0756226
$505$	3.98967	0.177538
$506$	19.7934	0.879925
$507$	−23.1647	−1.02878
$508$	−39.8512	−1.76811
$509$	−21.5490	−0.955143	−0.477572	−	0.878593i	$-0.658483\pi$
$509$	−21.5490	−0.955143	−0.477572	+	0.878593i	$0.658483\pi$
$510$	−27.2980	−1.20877
$511$	38.6206	1.70848
$512$	−25.6137	−1.13197
$513$	−18.5998	−0.821199
$514$	−45.3093	−1.99851
$515$	21.9783	0.968481
$516$	32.9569	1.45085
$517$	−37.5997	−1.65363
$518$	−7.95192	−0.349387
$519$	−10.2472	−0.449802
$520$	−2.78471	−0.122118
$521$	35.7218	1.56500	0.782499	−	0.622651i	$-0.213945\pi$
$521$	35.7218	1.56500	0.782499	+	0.622651i	$0.213945\pi$
$522$	−2.10503	−0.0921347
$523$	35.0820	1.53403	0.767015	−	0.641629i	$-0.221741\pi$
$523$	35.0820	1.53403	0.767015	+	0.641629i	$0.221741\pi$
$524$	42.9925	1.87813
$525$	56.2381	2.45443
$526$	11.1460	0.485987
$527$	1.69064	0.0736456
$528$	22.8128	0.992798
$529$	−19.6213	−0.853102
$530$	−4.35104	−0.188997
$531$	3.27686	0.142204
$532$	36.9598	1.60241
$533$	2.74571	0.118930
$534$	60.1427	2.60263
$535$	20.3437	0.879533
$536$	8.64691	0.373490
$537$	5.45735	0.235502
$538$	32.9359	1.41997
$539$	−34.0770	−1.46780
$540$	45.6011	1.96236
$541$	30.0077	1.29013	0.645067	−	0.764126i	$-0.276830\pi$
$541$	30.0077	1.29013	0.645067	+	0.764126i	$0.276830\pi$
$542$	−20.0293	−0.860330
$543$	5.91460	0.253820
$544$	−14.9331	−0.640249
$545$	37.9598	1.62602
$546$	8.83613	0.378152
$547$	−8.31544	−0.355542	−0.177771	−	0.984072i	$-0.556889\pi$
$547$	−8.31544	−0.355542	−0.177771	+	0.984072i	$0.556889\pi$
$548$	−47.1420	−2.01381
$549$	2.42033	0.103297
$550$	88.9695	3.79367
$551$	10.4263	0.444176
$552$	−4.25315	−0.181026
$553$	−44.8019	−1.90517
$554$	38.3521	1.62942
$555$	−6.67782	−0.283457
$556$	26.5822	1.12734
$557$	35.5039	1.50435	0.752175	−	0.658963i	$-0.229005\pi$
$557$	35.5039	1.50435	0.752175	+	0.658963i	$0.229005\pi$
$558$	0.687897	0.0291210
$559$	−4.20670	−0.177924
$560$	33.4565	1.41379
$561$	17.5894	0.742624
$562$	−67.2825	−2.83814
$563$	−0.224564	−0.00946425	−0.00473212	−	0.999989i	$-0.501506\pi$
$563$	−0.224564	−0.00946425	−0.00473212	+	0.999989i	$0.501506\pi$
$564$	35.5112	1.49529
$565$	−2.07438	−0.0872700
$566$	−44.2111	−1.85833
$567$	−36.9568	−1.55204
$568$	2.45695	0.103091
$569$	−35.2108	−1.47611	−0.738056	−	0.674739i	$-0.764256\pi$
$569$	−35.2108	−1.47611	−0.738056	+	0.674739i	$0.764256\pi$
$570$	55.0141	2.30429
$571$	−11.3268	−0.474011	−0.237005	−	0.971508i	$-0.576166\pi$
$571$	−11.3268	−0.474011	−0.237005	+	0.971508i	$0.576166\pi$
$572$	7.88660	0.329755
$573$	−36.3438	−1.51829
$574$	36.0300	1.50386
$575$	15.1867	0.633330
$576$	−4.28197	−0.178415
$577$	−8.81518	−0.366981	−0.183490	−	0.983022i	$-0.558740\pi$
$577$	−8.81518	−0.366981	−0.183490	+	0.983022i	$0.558740\pi$
$578$	28.6169	1.19030
$579$	2.13772	0.0888407
$580$	−25.5623	−1.06141
$581$	−0.271700	−0.0112720
$582$	−17.0825	−0.708093
$583$	2.80358	0.116112
$584$	−13.1287	−0.543267
$585$	0.799860	0.0330701
$586$	−0.403631	−0.0166738
$587$	−26.0722	−1.07611	−0.538057	−	0.842909i	$-0.680841\pi$
$587$	−26.0722	−1.07611	−0.538057	+	0.842909i	$0.680841\pi$
$588$	32.1841	1.32725
$589$	−3.40718	−0.140391
$590$	70.5311	2.90372
$591$	−26.1001	−1.07361
$592$	−2.47493	−0.101719
$593$	27.7171	1.13820	0.569102	−	0.822267i	$-0.307291\pi$
$593$	27.7171	1.13820	0.569102	+	0.822267i	$0.307291\pi$
$594$	−52.0808	−2.13690
$595$	25.7960	1.05753
$596$	−21.5311	−0.881948
$597$	2.90353	0.118834
$598$	2.38614	0.0975764
$599$	−32.3285	−1.32091	−0.660454	−	0.750866i	$-0.729636\pi$
$599$	−32.3285	−1.32091	−0.660454	+	0.750866i	$0.729636\pi$
$600$	−19.1175	−0.780469
$601$	−19.6954	−0.803393	−0.401697	−	0.915773i	$-0.631579\pi$
$601$	−19.6954	−0.803393	−0.401697	+	0.915773i	$0.631579\pi$
$602$	−55.2015	−2.24984
$603$	−2.48367	−0.101143
$604$	6.53748	0.266006
$605$	−51.9610	−2.11251
$606$	4.30348	0.174817
$607$	−23.0743	−0.936557	−0.468279	−	0.883581i	$-0.655126\pi$
$607$	−23.0743	−0.936557	−0.468279	+	0.883581i	$0.655126\pi$
$608$	30.0948	1.22051
$609$	18.4540	0.747795
$610$	52.0952	2.10927
$611$	−4.53273	−0.183375
$612$	−1.79069	−0.0723842
$613$	24.6414	0.995256	0.497628	−	0.867391i	$-0.334205\pi$
$613$	24.6414	0.995256	0.497628	+	0.867391i	$0.334205\pi$
$614$	13.3342	0.538126
$615$	30.2571	1.22008
$616$	23.5456	0.948680
$617$	−1.62554	−0.0654416	−0.0327208	−	0.999465i	$-0.510417\pi$
$617$	−1.62554	−0.0654416	−0.0327208	+	0.999465i	$0.510417\pi$
$618$	23.7070	0.953637
$619$	20.6595	0.830374	0.415187	−	0.909736i	$-0.363716\pi$
$619$	20.6595	0.830374	0.415187	+	0.909736i	$0.363716\pi$
$620$	8.35341	0.335481
$621$	−8.88998	−0.356743
$622$	−34.6043	−1.38751
$623$	−56.8336	−2.27699
$624$	2.75013	0.110093
$625$	1.95218	0.0780870
$626$	57.0947	2.28196
$627$	−35.4482	−1.41566
$628$	−27.1178	−1.08212
$629$	−1.90825	−0.0760868
$630$	10.4960	0.418170
$631$	−29.2395	−1.16401	−0.582004	−	0.813186i	$-0.697731\pi$
$631$	−29.2395	−1.16401	−0.582004	+	0.813186i	$0.697731\pi$
$632$	15.2299	0.605813
$633$	−28.2058	−1.12108
$634$	21.9252	0.870761
$635$	56.0541	2.22444
$636$	−2.64785	−0.104994
$637$	−4.10805	−0.162767
$638$	29.1945	1.15582
$639$	−0.705714	−0.0279176
$640$	−35.1683	−1.39015
$641$	9.88104	0.390277	0.195139	−	0.980776i	$-0.437484\pi$
$641$	9.88104	0.390277	0.195139	+	0.980776i	$0.437484\pi$
$642$	21.9438	0.866052
$643$	−30.8188	−1.21538	−0.607688	−	0.794176i	$-0.707903\pi$
$643$	−30.8188	−1.21538	−0.607688	+	0.794176i	$0.707903\pi$
$644$	17.6654	0.696113
$645$	−46.3568	−1.82530
$646$	15.7208	0.618526
$647$	−38.4563	−1.51187	−0.755937	−	0.654645i	$-0.772818\pi$
$647$	−38.4563	−1.51187	−0.755937	+	0.654645i	$0.772818\pi$
$648$	12.5631	0.493523
$649$	−45.4465	−1.78393
$650$	10.7255	0.420687
$651$	−6.03053	−0.236355
$652$	2.58905	0.101395
$653$	−27.5722	−1.07898	−0.539492	−	0.841991i	$-0.681384\pi$
$653$	−27.5722	−1.07898	−0.539492	+	0.841991i	$0.681384\pi$
$654$	40.9455	1.60109
$655$	−60.4726	−2.36286
$656$	11.2139	0.437827
$657$	3.77097	0.147120
$658$	−59.4798	−2.31876
$659$	−9.56340	−0.372537	−0.186269	−	0.982499i	$-0.559639\pi$
$659$	−9.56340	−0.372537	−0.186269	+	0.982499i	$0.559639\pi$
$660$	86.9085	3.38291
$661$	29.5518	1.14943	0.574717	−	0.818352i	$-0.305112\pi$
$661$	29.5518	1.14943	0.574717	+	0.818352i	$0.305112\pi$
$662$	9.79655	0.380754
$663$	2.12044	0.0823509
$664$	0.0923615	0.00358432
$665$	−51.9871	−2.01597
$666$	−0.776437	−0.0300863
$667$	4.98338	0.192957
$668$	39.1345	1.51416
$669$	−41.3520	−1.59876
$670$	−53.4586	−2.06529
$671$	−33.5674	−1.29585
$672$	53.2663	2.05479
$673$	8.34794	0.321789	0.160895	−	0.986972i	$-0.448562\pi$
$673$	8.34794	0.321789	0.160895	+	0.986972i	$0.448562\pi$
$674$	−34.5917	−1.33242
$675$	−39.9596	−1.53805
$676$	−32.7069	−1.25796
$677$	−1.31673	−0.0506061	−0.0253031	−	0.999680i	$-0.508055\pi$
$677$	−1.31673	−0.0506061	−0.0253031	+	0.999680i	$0.508055\pi$
$678$	−2.23754	−0.0859324
$679$	16.1426	0.619497
$680$	−8.76906	−0.336278
$681$	−31.9823	−1.22556
$682$	−9.54039	−0.365320
$683$	26.4013	1.01022	0.505108	−	0.863056i	$-0.331453\pi$
$683$	26.4013	1.01022	0.505108	+	0.863056i	$0.331453\pi$
$684$	3.60880	0.137986
$685$	66.3093	2.53355
$686$	1.75640	0.0670599
$687$	−10.4150	−0.397358
$688$	−17.1807	−0.655009
$689$	0.337978	0.0128759
$690$	26.2947	1.00102
$691$	−2.12153	−0.0807067	−0.0403534	−	0.999185i	$-0.512848\pi$
$691$	−2.12153	−0.0807067	−0.0403534	+	0.999185i	$0.512848\pi$
$692$	−14.4683	−0.550002
$693$	−6.76306	−0.256907
$694$	52.6441	1.99834
$695$	−37.3902	−1.41829
$696$	−6.27324	−0.237786
$697$	8.64624	0.327500
$698$	−41.4393	−1.56850
$699$	−38.0033	−1.43742
$700$	79.4041	3.00119
$701$	16.8578	0.636710	0.318355	−	0.947972i	$-0.396870\pi$
$701$	16.8578	0.636710	0.318355	+	0.947972i	$0.396870\pi$
$702$	−6.27845	−0.236965
$703$	3.84573	0.145044
$704$	59.3863	2.23820
$705$	−49.9496	−1.88121
$706$	74.5179	2.80452
$707$	−4.06669	−0.152944
$708$	42.9221	1.61311
$709$	−1.39506	−0.0523924	−0.0261962	−	0.999657i	$-0.508339\pi$
$709$	−1.39506	−0.0523924	−0.0261962	+	0.999657i	$0.508339\pi$
$710$	−15.1898	−0.570063
$711$	−4.37452	−0.164057
$712$	19.3199	0.724045
$713$	−1.62850	−0.0609880
$714$	27.8250	1.04132
$715$	−11.0932	−0.414862
$716$	7.70539	0.287964
$717$	10.0656	0.375906
$718$	−14.4207	−0.538175
$719$	30.1869	1.12578	0.562891	−	0.826531i	$-0.309689\pi$
$719$	30.1869	1.12578	0.562891	+	0.826531i	$0.309689\pi$
$720$	3.26674	0.121744
$721$	−22.4026	−0.834318
$722$	9.01954	0.335672
$723$	28.1285	1.04611
$724$	8.35098	0.310362
$725$	22.3998	0.831909
$726$	−56.0480	−2.08013
$727$	−15.3679	−0.569966	−0.284983	−	0.958533i	$-0.591988\pi$
$727$	−15.3679	−0.569966	−0.284983	+	0.958533i	$0.591988\pi$
$728$	2.83847	0.105201
$729$	22.9974	0.851755
$730$	81.1665	3.00411
$731$	−13.2469	−0.489954
$732$	31.7028	1.17177
$733$	−20.2903	−0.749439	−0.374720	−	0.927138i	$-0.622261\pi$
$733$	−20.2903	−0.749439	−0.374720	+	0.927138i	$0.622261\pi$
$734$	−23.2176	−0.856978
$735$	−45.2697	−1.66980
$736$	14.3842	0.530208
$737$	34.4459	1.26883
$738$	3.51802	0.129500
$739$	−26.5949	−0.978308	−0.489154	−	0.872197i	$-0.662694\pi$
$739$	−26.5949	−0.978308	−0.489154	+	0.872197i	$0.662694\pi$
$740$	−9.42859	−0.346602
$741$	−4.27335	−0.156985
$742$	4.43504	0.162815
$743$	7.76515	0.284876	0.142438	−	0.989804i	$-0.454506\pi$
$743$	7.76515	0.284876	0.142438	+	0.989804i	$0.454506\pi$
$744$	2.05001	0.0751571
$745$	30.2854	1.10957
$746$	−42.8115	−1.56744
$747$	−0.0265292	−0.000970653 0
$748$	24.8349	0.908054
$749$	−20.7364	−0.757692
$750$	46.6657	1.70399
$751$	1.21960	0.0445037	0.0222518	−	0.999752i	$-0.492916\pi$
$751$	1.21960	0.0445037	0.0222518	+	0.999752i	$0.492916\pi$
$752$	−18.5123	−0.675073
$753$	20.8519	0.759884
$754$	3.51946	0.128171
$755$	−9.19554	−0.334660
$756$	−46.4815	−1.69051
$757$	15.6406	0.568467	0.284233	−	0.958755i	$-0.408261\pi$
$757$	15.6406	0.568467	0.284233	+	0.958755i	$0.408261\pi$
$758$	−6.41172	−0.232884
$759$	−16.9429	−0.614988
$760$	17.6724	0.641047
$761$	−37.0255	−1.34217	−0.671087	−	0.741379i	$-0.734172\pi$
$761$	−37.0255	−1.34217	−0.671087	+	0.741379i	$0.734172\pi$
$762$	60.4630	2.19035
$763$	−38.6926	−1.40076
$764$	−51.3149	−1.85651
$765$	2.51876	0.0910658
$766$	15.7018	0.567330
$767$	−5.47867	−0.197823
$768$	5.39233	0.194579
$769$	12.3594	0.445690	0.222845	−	0.974854i	$-0.428466\pi$
$769$	12.3594	0.445690	0.222845	+	0.974854i	$0.428466\pi$
$770$	−145.568	−5.24591
$771$	38.7841	1.39678
$772$	3.01831	0.108631
$773$	17.9412	0.645298	0.322649	−	0.946519i	$-0.395427\pi$
$773$	17.9412	0.645298	0.322649	+	0.946519i	$0.395427\pi$
$774$	−5.38995	−0.193738
$775$	−7.31997	−0.262941
$776$	−5.48750	−0.196990
$777$	6.80673	0.244190
$778$	43.5887	1.56273
$779$	−17.4249	−0.624312
$780$	10.4770	0.375137
$781$	9.78750	0.350224
$782$	7.51394	0.268698
$783$	−13.1124	−0.468598
$784$	−16.7778	−0.599209
$785$	38.1436	1.36140
$786$	−65.2291	−2.32664
$787$	−36.8063	−1.31200	−0.656001	−	0.754760i	$-0.727753\pi$
$787$	−36.8063	−1.31200	−0.656001	+	0.754760i	$0.727753\pi$
$788$	−36.8514	−1.31278
$789$	−9.54078	−0.339661
$790$	−94.1571	−3.34996
$791$	2.11443	0.0751805
$792$	2.29903	0.0816923
$793$	−4.04662	−0.143700
$794$	−34.3497	−1.21903
$795$	3.72443	0.132092
$796$	4.09957	0.145305
$797$	27.4722	0.973117	0.486558	−	0.873648i	$-0.338252\pi$
$797$	27.4722	0.973117	0.486558	+	0.873648i	$0.338252\pi$
$798$	−56.0761	−1.98507
$799$	−14.2736	−0.504962
$800$	64.6556	2.28592
$801$	−5.54931	−0.196075
$802$	25.7373	0.908816
$803$	−52.2993	−1.84560
$804$	−32.5325	−1.14733
$805$	−24.8479	−0.875773
$806$	−1.15011	−0.0405110
$807$	−28.1926	−0.992427
$808$	1.38243	0.0486336
$809$	27.4470	0.964985	0.482492	−	0.875900i	$-0.339732\pi$
$809$	27.4470	0.964985	0.482492	+	0.875900i	$0.339732\pi$
$810$	−77.6697	−2.72904
$811$	−27.6991	−0.972647	−0.486323	−	0.873779i	$-0.661662\pi$
$811$	−27.6991	−0.972647	−0.486323	+	0.873779i	$0.661662\pi$
$812$	26.0557	0.914377
$813$	17.1448	0.601293
$814$	10.7683	0.377430
$815$	−3.64172	−0.127564
$816$	8.66015	0.303166
$817$	26.6967	0.933998
$818$	−4.05723	−0.141858
$819$	−0.815301	−0.0284889
$820$	42.7208	1.49187
$821$	−44.6775	−1.55925	−0.779627	−	0.626244i	$-0.784592\pi$
$821$	−44.6775	−1.55925	−0.779627	+	0.626244i	$0.784592\pi$
$822$	71.5248	2.49471
$823$	7.11798	0.248117	0.124059	−	0.992275i	$-0.460409\pi$
$823$	7.11798	0.248117	0.124059	+	0.992275i	$0.460409\pi$
$824$	7.61552	0.265299
$825$	−76.1566	−2.65143
$826$	−71.8927	−2.50147
$827$	39.0419	1.35762	0.678810	−	0.734314i	$-0.262496\pi$
$827$	39.0419	1.35762	0.678810	+	0.734314i	$0.262496\pi$
$828$	1.72487	0.0599434
$829$	22.7626	0.790578	0.395289	−	0.918557i	$-0.370644\pi$
$829$	22.7626	0.790578	0.395289	+	0.918557i	$0.370644\pi$
$830$	−0.571015	−0.0198202
$831$	−32.8288	−1.13882
$832$	7.15914	0.248199
$833$	−12.9362	−0.448214
$834$	−40.3311	−1.39655
$835$	−55.0460	−1.90495
$836$	−50.0502	−1.73102
$837$	4.28495	0.148110
$838$	−25.1774	−0.869738
$839$	−34.2425	−1.18218	−0.591092	−	0.806604i	$-0.701303\pi$
$839$	−34.2425	−1.18218	−0.591092	+	0.806604i	$0.701303\pi$
$840$	31.2793	1.07924
$841$	−21.6497	−0.746542
$842$	65.1748	2.24607
$843$	57.5929	1.98360
$844$	−39.8245	−1.37082
$845$	46.0051	1.58262
$846$	−5.80769	−0.199672
$847$	52.9641	1.81987
$848$	1.38035	0.0474013
$849$	37.8441	1.29880
$850$	33.7744	1.15845
$851$	1.83811	0.0630097
$852$	−9.24383	−0.316688
$853$	−27.6206	−0.945710	−0.472855	−	0.881140i	$-0.656777\pi$
$853$	−27.6206	−0.945710	−0.472855	+	0.881140i	$0.656777\pi$
$854$	−53.1009	−1.81708
$855$	−5.07609	−0.173599
$856$	7.04911	0.240934
$857$	3.73358	0.127537	0.0637684	−	0.997965i	$-0.479688\pi$
$857$	3.73358	0.127537	0.0637684	+	0.997965i	$0.479688\pi$
$858$	−11.9657	−0.408503
$859$	−58.5685	−1.99833	−0.999166	−	0.0408277i	$-0.987001\pi$
$859$	−58.5685	−1.99833	−0.999166	+	0.0408277i	$0.987001\pi$
$860$	−65.4524	−2.23191
$861$	−30.8412	−1.05106
$862$	−17.9624	−0.611802
$863$	−3.35701	−0.114274	−0.0571370	−	0.998366i	$-0.518197\pi$
$863$	−3.35701	−0.114274	−0.0571370	+	0.998366i	$0.518197\pi$
$864$	−37.8480	−1.28761
$865$	20.3509	0.691952
$866$	35.5931	1.20950
$867$	−24.4956	−0.831915
$868$	−8.51467	−0.289007
$869$	60.6698	2.05808
$870$	38.7836	1.31489
$871$	4.15252	0.140703
$872$	13.1531	0.445420
$873$	1.57619	0.0533458
$874$	−15.1430	−0.512219
$875$	−44.0980	−1.49079
$876$	49.3942	1.66888
$877$	30.2977	1.02308	0.511541	−	0.859259i	$-0.329075\pi$
$877$	30.2977	1.02308	0.511541	+	0.859259i	$0.329075\pi$
$878$	85.0958	2.87184
$879$	0.345502	0.0116535
$880$	−45.3061	−1.52727
$881$	−13.7132	−0.462011	−0.231005	−	0.972952i	$-0.574201\pi$
$881$	−13.7132	−0.462011	−0.231005	+	0.972952i	$0.574201\pi$
$882$	−5.26356	−0.177233
$883$	−17.9899	−0.605407	−0.302704	−	0.953085i	$-0.597889\pi$
$883$	−17.9899	−0.605407	−0.302704	+	0.953085i	$0.597889\pi$
$884$	2.99390	0.100696
$885$	−60.3736	−2.02944
$886$	35.5793	1.19531
$887$	−22.6269	−0.759738	−0.379869	−	0.925040i	$-0.624031\pi$
$887$	−22.6269	−0.759738	−0.379869	+	0.925040i	$0.624031\pi$
$888$	−2.31387	−0.0776484
$889$	−57.1363	−1.91629
$890$	−119.443	−4.00375
$891$	50.0462	1.67661
$892$	−58.3860	−1.95491
$893$	28.7657	0.962609
$894$	32.6675	1.09256
$895$	−10.8383	−0.362284
$896$	35.8472	1.19757
$897$	−2.04250	−0.0681971
$898$	7.12327	0.237707
$899$	−2.40198	−0.0801106
$900$	7.75313	0.258438
$901$	1.06429	0.0354567
$902$	−48.7912	−1.62457
$903$	47.2517	1.57244
$904$	−0.718777	−0.0239062
$905$	−11.7464	−0.390463
$906$	−9.91881	−0.329530
$907$	−23.1033	−0.767132	−0.383566	−	0.923513i	$-0.625304\pi$
$907$	−23.1033	−0.767132	−0.383566	+	0.923513i	$0.625304\pi$
$908$	−45.1567	−1.49858
$909$	−0.397078	−0.0131702
$910$	−17.5485	−0.581729
$911$	0.183002	0.00606314	0.00303157	−	0.999995i	$-0.499035\pi$
$911$	0.183002	0.00606314	0.00303157	+	0.999995i	$0.499035\pi$
$912$	−17.4529	−0.577925
$913$	0.367932	0.0121768
$914$	21.5002	0.711162
$915$	−44.5928	−1.47419
$916$	−14.7053	−0.485875
$917$	61.6401	2.03553
$918$	−19.7708	−0.652535
$919$	−25.1344	−0.829107	−0.414553	−	0.910025i	$-0.636062\pi$
$919$	−25.1344	−0.829107	−0.414553	+	0.910025i	$0.636062\pi$
$920$	8.44676	0.278481
$921$	−11.4139	−0.376101
$922$	−69.6585	−2.29408
$923$	1.17990	0.0388370
$924$	−88.5862	−2.91427
$925$	8.26213	0.271657
$926$	31.3490	1.03019
$927$	−2.18742	−0.0718444
$928$	21.2161	0.696453
$929$	−18.3485	−0.601994	−0.300997	−	0.953625i	$-0.597319\pi$
$929$	−18.3485	−0.601994	−0.300997	+	0.953625i	$0.597319\pi$
$930$	−12.6740	−0.415596
$931$	26.0706	0.854431
$932$	−53.6580	−1.75762
$933$	29.6208	0.969740
$934$	29.3172	0.959287
$935$	−34.9325	−1.14241
$936$	0.277152	0.00905901
$937$	−9.74790	−0.318450	−0.159225	−	0.987242i	$-0.550900\pi$
$937$	−9.74790	−0.318450	−0.159225	+	0.987242i	$0.550900\pi$
$938$	54.4906	1.77918
$939$	−48.8723	−1.59489
$940$	−70.5251	−2.30028
$941$	14.3744	0.468591	0.234296	−	0.972165i	$-0.424722\pi$
$941$	14.3744	0.468591	0.234296	+	0.972165i	$0.424722\pi$
$942$	41.1438	1.34054
$943$	−8.32845	−0.271212
$944$	−22.3756	−0.728265
$945$	65.3802	2.12682
$946$	74.7528	2.43042
$947$	−51.8120	−1.68367	−0.841833	−	0.539739i	$-0.818523\pi$
$947$	−51.8120	−1.68367	−0.841833	+	0.539739i	$0.818523\pi$
$948$	−57.2998	−1.86101
$949$	−6.30480	−0.204662
$950$	−68.0662	−2.20836
$951$	−18.7677	−0.608583
$952$	8.93834	0.289693
$953$	30.6999	0.994466	0.497233	−	0.867617i	$-0.334349\pi$
$953$	30.6999	0.994466	0.497233	+	0.867617i	$0.334349\pi$
$954$	0.433043	0.0140203
$955$	72.1788	2.33565
$956$	14.2119	0.459645
$957$	−24.9901	−0.807815
$958$	−73.4600	−2.37339
$959$	−67.5894	−2.18258
$960$	78.8920	2.54623
$961$	−30.2151	−0.974679
$962$	1.29815	0.0418539
$963$	−2.02473	−0.0652460
$964$	39.7154	1.27915
$965$	−4.24551	−0.136668
$966$	−26.8023	−0.862349
$967$	22.5453	0.725007	0.362503	−	0.931982i	$-0.381922\pi$
$967$	22.5453	0.725007	0.362503	+	0.931982i	$0.381922\pi$
$968$	−18.0046	−0.578688
$969$	−13.4568	−0.432294
$970$	33.9259	1.08929
$971$	−6.56473	−0.210672	−0.105336	−	0.994437i	$-0.533592\pi$
$971$	−6.56473	−0.210672	−0.105336	+	0.994437i	$0.533592\pi$
$972$	−9.70070	−0.311150
$973$	38.1120	1.22181
$974$	39.2512	1.25769
$975$	−9.18084	−0.294022
$976$	−16.5269	−0.529015
$977$	13.2751	0.424709	0.212355	−	0.977193i	$-0.431887\pi$
$977$	13.2751	0.424709	0.212355	+	0.977193i	$0.431887\pi$
$978$	−3.92816	−0.125609
$979$	76.9630	2.45975
$980$	−63.9176	−2.04177
$981$	−3.77800	−0.120622
$982$	−8.92795	−0.284902
$983$	1.00373	0.0320140	0.0160070	−	0.999872i	$-0.494905\pi$
$983$	1.00373	0.0320140	0.0160070	+	0.999872i	$0.494905\pi$
$984$	10.4841	0.334221
$985$	51.8347	1.65159
$986$	11.0828	0.352947
$987$	50.9138	1.62061
$988$	−6.03366	−0.191956
$989$	12.7600	0.405744
$990$	−14.2135	−0.451734
$991$	25.9342	0.823828	0.411914	−	0.911223i	$-0.364860\pi$
$991$	25.9342	0.823828	0.411914	+	0.911223i	$0.364860\pi$
$992$	−6.93315	−0.220128
$993$	−8.38571	−0.266112
$994$	15.4830	0.491092
$995$	−5.76640	−0.182807
$996$	−0.347494	−0.0110108
$997$	−12.9841	−0.411210	−0.205605	−	0.978635i	$-0.565916\pi$
$997$	−12.9841	−0.411210	−0.205605	+	0.978635i	$0.565916\pi$
$998$	39.0070	1.23474
$999$	−4.83647	−0.153019

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.b.1.17	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.b.1.17	✓	109	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.14221 q^{2} +1.83370 q^{3} +2.58905 q^{4} -3.64172 q^{5} -3.92816 q^{6} +3.71202 q^{7} -1.26186 q^{8} +0.362447 q^{9} +O(q^{10})\)	\(q-2.14221 q^{2} +1.83370 q^{3} +2.58905 q^{4} -3.64172 q^{5} -3.92816 q^{6} +3.71202 q^{7} -1.26186 q^{8} +0.362447 q^{9} +7.80132 q^{10} -5.02675 q^{11} +4.74753 q^{12} -0.605986 q^{13} -7.95192 q^{14} -6.67782 q^{15} -2.47493 q^{16} -1.90825 q^{17} -0.776437 q^{18} +3.84573 q^{19} -9.42859 q^{20} +6.80673 q^{21} +10.7683 q^{22} +1.83811 q^{23} -2.31387 q^{24} +8.26213 q^{25} +1.29815 q^{26} -4.83647 q^{27} +9.61061 q^{28} +2.71114 q^{29} +14.3053 q^{30} -0.885966 q^{31} +7.82553 q^{32} -9.21755 q^{33} +4.08786 q^{34} -13.5182 q^{35} +0.938393 q^{36} +1.00000 q^{37} -8.23834 q^{38} -1.11119 q^{39} +4.59535 q^{40} -4.53098 q^{41} -14.5814 q^{42} +6.94191 q^{43} -13.0145 q^{44} -1.31993 q^{45} -3.93761 q^{46} +7.47993 q^{47} -4.53827 q^{48} +6.77912 q^{49} -17.6992 q^{50} -3.49915 q^{51} -1.56893 q^{52} -0.557732 q^{53} +10.3607 q^{54} +18.3060 q^{55} -4.68406 q^{56} +7.05190 q^{57} -5.80783 q^{58} +9.04093 q^{59} -17.2892 q^{60} +6.67775 q^{61} +1.89792 q^{62} +1.34541 q^{63} -11.8140 q^{64} +2.20683 q^{65} +19.7459 q^{66} -6.85251 q^{67} -4.94054 q^{68} +3.37054 q^{69} +28.9587 q^{70} -1.94708 q^{71} -0.457358 q^{72} +10.4042 q^{73} -2.14221 q^{74} +15.1503 q^{75} +9.95677 q^{76} -18.6594 q^{77} +2.38041 q^{78} -12.0694 q^{79} +9.01300 q^{80} -9.95597 q^{81} +9.70630 q^{82} -0.0731947 q^{83} +17.6229 q^{84} +6.94931 q^{85} -14.8710 q^{86} +4.97142 q^{87} +6.34306 q^{88} -15.3107 q^{89} +2.82757 q^{90} -2.24943 q^{91} +4.75896 q^{92} -1.62459 q^{93} -16.0235 q^{94} -14.0051 q^{95} +14.3497 q^{96} +4.34874 q^{97} -14.5223 q^{98} -1.82193 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * q^99

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