LMFDB - Embedded newform 6010.2.a.g.1.10

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:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.805731 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.805731 q^{6} +2.46129 q^{7} -1.00000 q^{8} -2.35080 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.805731 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.805731 q^{6} +2.46129 q^{7} -1.00000 q^{8} -2.35080 q^{9} -1.00000 q^{10} +2.96697 q^{11} -0.805731 q^{12} +0.253489 q^{13} -2.46129 q^{14} -0.805731 q^{15} +1.00000 q^{16} +2.99046 q^{17} +2.35080 q^{18} +7.75962 q^{19} +1.00000 q^{20} -1.98314 q^{21} -2.96697 q^{22} +5.62801 q^{23} +0.805731 q^{24} +1.00000 q^{25} -0.253489 q^{26} +4.31130 q^{27} +2.46129 q^{28} +2.46565 q^{29} +0.805731 q^{30} -0.0301013 q^{31} -1.00000 q^{32} -2.39058 q^{33} -2.99046 q^{34} +2.46129 q^{35} -2.35080 q^{36} +4.95508 q^{37} -7.75962 q^{38} -0.204244 q^{39} -1.00000 q^{40} +7.67525 q^{41} +1.98314 q^{42} -7.35704 q^{43} +2.96697 q^{44} -2.35080 q^{45} -5.62801 q^{46} -6.21928 q^{47} -0.805731 q^{48} -0.942045 q^{49} -1.00000 q^{50} -2.40950 q^{51} +0.253489 q^{52} +5.55541 q^{53} -4.31130 q^{54} +2.96697 q^{55} -2.46129 q^{56} -6.25217 q^{57} -2.46565 q^{58} -1.78883 q^{59} -0.805731 q^{60} -4.04915 q^{61} +0.0301013 q^{62} -5.78600 q^{63} +1.00000 q^{64} +0.253489 q^{65} +2.39058 q^{66} -5.65828 q^{67} +2.99046 q^{68} -4.53467 q^{69} -2.46129 q^{70} -6.71451 q^{71} +2.35080 q^{72} +11.3798 q^{73} -4.95508 q^{74} -0.805731 q^{75} +7.75962 q^{76} +7.30259 q^{77} +0.204244 q^{78} +10.3652 q^{79} +1.00000 q^{80} +3.57864 q^{81} -7.67525 q^{82} -11.8374 q^{83} -1.98314 q^{84} +2.99046 q^{85} +7.35704 q^{86} -1.98665 q^{87} -2.96697 q^{88} +4.04190 q^{89} +2.35080 q^{90} +0.623910 q^{91} +5.62801 q^{92} +0.0242536 q^{93} +6.21928 q^{94} +7.75962 q^{95} +0.805731 q^{96} -3.40721 q^{97} +0.942045 q^{98} -6.97475 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * 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
$3$	−0.805731	−0.465189	−0.232595	−	0.972574i	$-0.574721\pi$
$3$	−0.805731	−0.465189	−0.232595	+	0.972574i	$0.574721\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.805731	0.328938
$7$	2.46129	0.930281	0.465140	−	0.885237i	$-0.346004\pi$
$7$	2.46129	0.930281	0.465140	+	0.885237i	$0.346004\pi$
$8$	−1.00000	−0.353553
$9$	−2.35080	−0.783599
$10$	−1.00000	−0.316228
$11$	2.96697	0.894576	0.447288	−	0.894390i	$-0.352390\pi$
$11$	2.96697	0.894576	0.447288	+	0.894390i	$0.352390\pi$
$12$	−0.805731	−0.232595
$13$	0.253489	0.0703051	0.0351526	−	0.999382i	$-0.488808\pi$
$13$	0.253489	0.0703051	0.0351526	+	0.999382i	$0.488808\pi$
$14$	−2.46129	−0.657808
$15$	−0.805731	−0.208039
$16$	1.00000	0.250000
$17$	2.99046	0.725293	0.362646	−	0.931927i	$-0.381873\pi$
$17$	2.99046	0.725293	0.362646	+	0.931927i	$0.381873\pi$
$18$	2.35080	0.554088
$19$	7.75962	1.78018	0.890089	−	0.455786i	$-0.150642\pi$
$19$	7.75962	1.78018	0.890089	+	0.455786i	$0.150642\pi$
$20$	1.00000	0.223607
$21$	−1.98314	−0.432756
$22$	−2.96697	−0.632561
$23$	5.62801	1.17352	0.586761	−	0.809760i	$-0.300403\pi$
$23$	5.62801	1.17352	0.586761	+	0.809760i	$0.300403\pi$
$24$	0.805731	0.164469
$25$	1.00000	0.200000
$26$	−0.253489	−0.0497132
$27$	4.31130	0.829711
$28$	2.46129	0.465140
$29$	2.46565	0.457859	0.228930	−	0.973443i	$-0.426477\pi$
$29$	2.46565	0.457859	0.228930	+	0.973443i	$0.426477\pi$
$30$	0.805731	0.147106
$31$	−0.0301013	−0.00540636	−0.00270318	−	0.999996i	$-0.500860\pi$
$31$	−0.0301013	−0.00540636	−0.00270318	+	0.999996i	$0.500860\pi$
$32$	−1.00000	−0.176777
$33$	−2.39058	−0.416147
$34$	−2.99046	−0.512859
$35$	2.46129	0.416034
$36$	−2.35080	−0.391800
$37$	4.95508	0.814610	0.407305	−	0.913292i	$-0.366469\pi$
$37$	4.95508	0.814610	0.407305	+	0.913292i	$0.366469\pi$
$38$	−7.75962	−1.25878
$39$	−0.204244	−0.0327052
$40$	−1.00000	−0.158114
$41$	7.67525	1.19867	0.599336	−	0.800497i	$-0.295431\pi$
$41$	7.67525	1.19867	0.599336	+	0.800497i	$0.295431\pi$
$42$	1.98314	0.306005
$43$	−7.35704	−1.12194	−0.560969	−	0.827837i	$-0.689571\pi$
$43$	−7.35704	−1.12194	−0.560969	+	0.827837i	$0.689571\pi$
$44$	2.96697	0.447288
$45$	−2.35080	−0.350436
$46$	−5.62801	−0.829805
$47$	−6.21928	−0.907175	−0.453587	−	0.891212i	$-0.649856\pi$
$47$	−6.21928	−0.907175	−0.453587	+	0.891212i	$0.649856\pi$
$48$	−0.805731	−0.116297
$49$	−0.942045	−0.134578
$50$	−1.00000	−0.141421
$51$	−2.40950	−0.337398
$52$	0.253489	0.0351526
$53$	5.55541	0.763095	0.381547	−	0.924349i	$-0.375391\pi$
$53$	5.55541	0.763095	0.381547	+	0.924349i	$0.375391\pi$
$54$	−4.31130	−0.586694
$55$	2.96697	0.400067
$56$	−2.46129	−0.328904
$57$	−6.25217	−0.828120
$58$	−2.46565	−0.323755
$59$	−1.78883	−0.232885	−0.116443	−	0.993197i	$-0.537149\pi$
$59$	−1.78883	−0.232885	−0.116443	+	0.993197i	$0.537149\pi$
$60$	−0.805731	−0.104019
$61$	−4.04915	−0.518440	−0.259220	−	0.965818i	$-0.583466\pi$
$61$	−4.04915	−0.518440	−0.259220	+	0.965818i	$0.583466\pi$
$62$	0.0301013	0.00382287
$63$	−5.78600	−0.728967
$64$	1.00000	0.125000
$65$	0.253489	0.0314414
$66$	2.39058	0.294260
$67$	−5.65828	−0.691270	−0.345635	−	0.938369i	$-0.612336\pi$
$67$	−5.65828	−0.691270	−0.345635	+	0.938369i	$0.612336\pi$
$68$	2.99046	0.362646
$69$	−4.53467	−0.545910
$70$	−2.46129	−0.294181
$71$	−6.71451	−0.796865	−0.398433	−	0.917198i	$-0.630446\pi$
$71$	−6.71451	−0.796865	−0.398433	+	0.917198i	$0.630446\pi$
$72$	2.35080	0.277044
$73$	11.3798	1.33190	0.665951	−	0.745995i	$-0.268026\pi$
$73$	11.3798	1.33190	0.665951	+	0.745995i	$0.268026\pi$
$74$	−4.95508	−0.576016
$75$	−0.805731	−0.0930378
$76$	7.75962	0.890089
$77$	7.30259	0.832207
$78$	0.204244	0.0231260
$79$	10.3652	1.16617	0.583085	−	0.812411i	$-0.301845\pi$
$79$	10.3652	1.16617	0.583085	+	0.812411i	$0.301845\pi$
$80$	1.00000	0.111803
$81$	3.57864	0.397627
$82$	−7.67525	−0.847590
$83$	−11.8374	−1.29932	−0.649659	−	0.760225i	$-0.725088\pi$
$83$	−11.8374	−1.29932	−0.649659	+	0.760225i	$0.725088\pi$
$84$	−1.98314	−0.216378
$85$	2.99046	0.324361
$86$	7.35704	0.793330
$87$	−1.98665	−0.212991
$88$	−2.96697	−0.316280
$89$	4.04190	0.428440	0.214220	−	0.976785i	$-0.431279\pi$
$89$	4.04190	0.428440	0.214220	+	0.976785i	$0.431279\pi$
$90$	2.35080	0.247796
$91$	0.623910	0.0654035
$92$	5.62801	0.586761
$93$	0.0242536	0.00251498
$94$	6.21928	0.641469
$95$	7.75962	0.796120
$96$	0.805731	0.0822346
$97$	−3.40721	−0.345950	−0.172975	−	0.984926i	$-0.555338\pi$
$97$	−3.40721	−0.345950	−0.172975	+	0.984926i	$0.555338\pi$
$98$	0.942045	0.0951609
$99$	−6.97475	−0.700989
$100$	1.00000	0.100000
$101$	−7.54611	−0.750866	−0.375433	−	0.926849i	$-0.622506\pi$
$101$	−7.54611	−0.750866	−0.375433	+	0.926849i	$0.622506\pi$
$102$	2.40950	0.238577
$103$	−1.87793	−0.185038	−0.0925189	−	0.995711i	$-0.529492\pi$
$103$	−1.87793	−0.185038	−0.0925189	+	0.995711i	$0.529492\pi$
$104$	−0.253489	−0.0248566
$105$	−1.98314	−0.193535
$106$	−5.55541	−0.539590
$107$	0.538613	0.0520697	0.0260348	−	0.999661i	$-0.491712\pi$
$107$	0.538613	0.0520697	0.0260348	+	0.999661i	$0.491712\pi$
$108$	4.31130	0.414855
$109$	−0.0226911	−0.00217341	−0.00108671	−	0.999999i	$-0.500346\pi$
$109$	−0.0226911	−0.00217341	−0.00108671	+	0.999999i	$0.500346\pi$
$110$	−2.96697	−0.282890
$111$	−3.99246	−0.378948
$112$	2.46129	0.232570
$113$	−7.97836	−0.750541	−0.375270	−	0.926915i	$-0.622450\pi$
$113$	−7.97836	−0.750541	−0.375270	+	0.926915i	$0.622450\pi$
$114$	6.25217	0.585569
$115$	5.62801	0.524815
$116$	2.46565	0.228930
$117$	−0.595901	−0.0550910
$118$	1.78883	0.164675
$119$	7.36039	0.674726
$120$	0.805731	0.0735528
$121$	−2.19707	−0.199734
$122$	4.04915	0.366593
$123$	−6.18419	−0.557609
$124$	−0.0301013	−0.00270318
$125$	1.00000	0.0894427
$126$	5.78600	0.515458
$127$	19.2365	1.70696	0.853480	−	0.521125i	$-0.174487\pi$
$127$	19.2365	1.70696	0.853480	+	0.521125i	$0.174487\pi$
$128$	−1.00000	−0.0883883
$129$	5.92780	0.521914
$130$	−0.253489	−0.0222324
$131$	15.7620	1.37713	0.688565	−	0.725174i	$-0.258241\pi$
$131$	15.7620	1.37713	0.688565	+	0.725174i	$0.258241\pi$
$132$	−2.39058	−0.208073
$133$	19.0987	1.65607
$134$	5.65828	0.488801
$135$	4.31130	0.371058
$136$	−2.99046	−0.256430
$137$	3.26606	0.279038	0.139519	−	0.990219i	$-0.455444\pi$
$137$	3.26606	0.279038	0.139519	+	0.990219i	$0.455444\pi$
$138$	4.53467	0.386016
$139$	−6.63356	−0.562651	−0.281326	−	0.959612i	$-0.590774\pi$
$139$	−6.63356	−0.562651	−0.281326	+	0.959612i	$0.590774\pi$
$140$	2.46129	0.208017
$141$	5.01106	0.422008
$142$	6.71451	0.563469
$143$	0.752094	0.0628933
$144$	−2.35080	−0.195900
$145$	2.46565	0.204761
$146$	−11.3798	−0.941798
$147$	0.759035	0.0626041
$148$	4.95508	0.407305
$149$	11.6505	0.954449	0.477224	−	0.878781i	$-0.341643\pi$
$149$	11.6505	0.954449	0.477224	+	0.878781i	$0.341643\pi$
$150$	0.805731	0.0657877
$151$	−19.6807	−1.60159	−0.800796	−	0.598938i	$-0.795590\pi$
$151$	−19.6807	−1.60159	−0.800796	+	0.598938i	$0.795590\pi$
$152$	−7.75962	−0.629388
$153$	−7.02996	−0.568339
$154$	−7.30259	−0.588459
$155$	−0.0301013	−0.00241780
$156$	−0.204244	−0.0163526
$157$	16.0762	1.28302	0.641509	−	0.767115i	$-0.278309\pi$
$157$	16.0762	1.28302	0.641509	+	0.767115i	$0.278309\pi$
$158$	−10.3652	−0.824607
$159$	−4.47617	−0.354983
$160$	−1.00000	−0.0790569
$161$	13.8522	1.09170
$162$	−3.57864	−0.281165
$163$	−14.9132	−1.16809	−0.584044	−	0.811722i	$-0.698531\pi$
$163$	−14.9132	−1.16809	−0.584044	+	0.811722i	$0.698531\pi$
$164$	7.67525	0.599336
$165$	−2.39058	−0.186107
$166$	11.8374	0.918757
$167$	−19.0991	−1.47793	−0.738967	−	0.673742i	$-0.764686\pi$
$167$	−19.0991	−1.47793	−0.738967	+	0.673742i	$0.764686\pi$
$168$	1.98314	0.153002
$169$	−12.9357	−0.995057
$170$	−2.99046	−0.229358
$171$	−18.2413	−1.39495
$172$	−7.35704	−0.560969
$173$	4.49770	0.341954	0.170977	−	0.985275i	$-0.445308\pi$
$173$	4.49770	0.341954	0.170977	+	0.985275i	$0.445308\pi$
$174$	1.98665	0.150607
$175$	2.46129	0.186056
$176$	2.96697	0.223644
$177$	1.44131	0.108336
$178$	−4.04190	−0.302953
$179$	13.2397	0.989584	0.494792	−	0.869012i	$-0.335244\pi$
$179$	13.2397	0.989584	0.494792	+	0.869012i	$0.335244\pi$
$180$	−2.35080	−0.175218
$181$	−16.4699	−1.22419	−0.612097	−	0.790782i	$-0.709674\pi$
$181$	−16.4699	−1.22419	−0.612097	+	0.790782i	$0.709674\pi$
$182$	−0.623910	−0.0462472
$183$	3.26252	0.241173
$184$	−5.62801	−0.414903
$185$	4.95508	0.364305
$186$	−0.0242536	−0.00177836
$187$	8.87261	0.648829
$188$	−6.21928	−0.453587
$189$	10.6114	0.771864
$190$	−7.75962	−0.562942
$191$	2.19134	0.158560	0.0792800	−	0.996852i	$-0.474738\pi$
$191$	2.19134	0.158560	0.0792800	+	0.996852i	$0.474738\pi$
$192$	−0.805731	−0.0581486
$193$	−15.3176	−1.10258	−0.551292	−	0.834312i	$-0.685865\pi$
$193$	−15.3176	−1.10258	−0.551292	+	0.834312i	$0.685865\pi$
$194$	3.40721	0.244624
$195$	−0.204244	−0.0146262
$196$	−0.942045	−0.0672889
$197$	−17.8785	−1.27379	−0.636897	−	0.770949i	$-0.719782\pi$
$197$	−17.8785	−1.27379	−0.636897	+	0.770949i	$0.719782\pi$
$198$	6.97475	0.495674
$199$	3.18520	0.225793	0.112896	−	0.993607i	$-0.463987\pi$
$199$	3.18520	0.225793	0.112896	+	0.993607i	$0.463987\pi$
$200$	−1.00000	−0.0707107
$201$	4.55906	0.321571
$202$	7.54611	0.530943
$203$	6.06867	0.425937
$204$	−2.40950	−0.168699
$205$	7.67525	0.536063
$206$	1.87793	0.130841
$207$	−13.2303	−0.919571
$208$	0.253489	0.0175763
$209$	23.0226	1.59251
$210$	1.98314	0.136850
$211$	17.8783	1.23079	0.615397	−	0.788218i	$-0.288996\pi$
$211$	17.8783	1.23079	0.615397	+	0.788218i	$0.288996\pi$
$212$	5.55541	0.381547
$213$	5.41009	0.370693
$214$	−0.538613	−0.0368188
$215$	−7.35704	−0.501746
$216$	−4.31130	−0.293347
$217$	−0.0740882	−0.00502943
$218$	0.0226911	0.00153683
$219$	−9.16904	−0.619587
$220$	2.96697	0.200033
$221$	0.758047	0.0509918
$222$	3.99246	0.267957
$223$	−22.5791	−1.51201	−0.756004	−	0.654567i	$-0.772851\pi$
$223$	−22.5791	−1.51201	−0.756004	+	0.654567i	$0.772851\pi$
$224$	−2.46129	−0.164452
$225$	−2.35080	−0.156720
$226$	7.97836	0.530713
$227$	−0.488383	−0.0324151	−0.0162076	−	0.999869i	$-0.505159\pi$
$227$	−0.488383	−0.0324151	−0.0162076	+	0.999869i	$0.505159\pi$
$228$	−6.25217	−0.414060
$229$	28.7548	1.90017	0.950086	−	0.311989i	$-0.100995\pi$
$229$	28.7548	1.90017	0.950086	+	0.311989i	$0.100995\pi$
$230$	−5.62801	−0.371100
$231$	−5.88392	−0.387133
$232$	−2.46565	−0.161878
$233$	9.33928	0.611837	0.305918	−	0.952058i	$-0.401037\pi$
$233$	9.33928	0.611837	0.305918	+	0.952058i	$0.401037\pi$
$234$	0.595901	0.0389552
$235$	−6.21928	−0.405701
$236$	−1.78883	−0.116443
$237$	−8.35152	−0.542490
$238$	−7.36039	−0.477103
$239$	23.8586	1.54329	0.771644	−	0.636055i	$-0.219435\pi$
$239$	23.8586	1.54329	0.771644	+	0.636055i	$0.219435\pi$
$240$	−0.805731	−0.0520097
$241$	−4.96156	−0.319602	−0.159801	−	0.987149i	$-0.551085\pi$
$241$	−4.96156	−0.319602	−0.159801	+	0.987149i	$0.551085\pi$
$242$	2.19707	0.141233
$243$	−15.8173	−1.01468
$244$	−4.04915	−0.259220
$245$	−0.942045	−0.0601850
$246$	6.18419	0.394289
$247$	1.96698	0.125156
$248$	0.0301013	0.00191144
$249$	9.53772	0.604429
$250$	−1.00000	−0.0632456
$251$	21.4738	1.35541	0.677706	−	0.735333i	$-0.262974\pi$
$251$	21.4738	1.35541	0.677706	+	0.735333i	$0.262974\pi$
$252$	−5.78600	−0.364484
$253$	16.6982	1.04980
$254$	−19.2365	−1.20700
$255$	−2.40950	−0.150889
$256$	1.00000	0.0625000
$257$	12.7069	0.792633	0.396317	−	0.918114i	$-0.370288\pi$
$257$	12.7069	0.792633	0.396317	+	0.918114i	$0.370288\pi$
$258$	−5.92780	−0.369049
$259$	12.1959	0.757816
$260$	0.253489	0.0157207
$261$	−5.79624	−0.358778
$262$	−15.7620	−0.973779
$263$	−11.4642	−0.706911	−0.353455	−	0.935451i	$-0.614993\pi$
$263$	−11.4642	−0.706911	−0.353455	+	0.935451i	$0.614993\pi$
$264$	2.39058	0.147130
$265$	5.55541	0.341266
$266$	−19.0987	−1.17102
$267$	−3.25668	−0.199306
$268$	−5.65828	−0.345635
$269$	−5.29850	−0.323055	−0.161528	−	0.986868i	$-0.551642\pi$
$269$	−5.29850	−0.323055	−0.161528	+	0.986868i	$0.551642\pi$
$270$	−4.31130	−0.262378
$271$	−29.4701	−1.79018	−0.895089	−	0.445887i	$-0.852888\pi$
$271$	−29.4701	−1.79018	−0.895089	+	0.445887i	$0.852888\pi$
$272$	2.99046	0.181323
$273$	−0.502703	−0.0304250
$274$	−3.26606	−0.197310
$275$	2.96697	0.178915
$276$	−4.53467	−0.272955
$277$	−9.58667	−0.576007	−0.288003	−	0.957629i	$-0.592991\pi$
$277$	−9.58667	−0.576007	−0.288003	+	0.957629i	$0.592991\pi$
$278$	6.63356	0.397854
$279$	0.0707622	0.00423642
$280$	−2.46129	−0.147090
$281$	−20.1363	−1.20123	−0.600615	−	0.799539i	$-0.705077\pi$
$281$	−20.1363	−1.20123	−0.600615	+	0.799539i	$0.705077\pi$
$282$	−5.01106	−0.298405
$283$	−15.3926	−0.914994	−0.457497	−	0.889211i	$-0.651254\pi$
$283$	−15.3926	−0.914994	−0.457497	+	0.889211i	$0.651254\pi$
$284$	−6.71451	−0.398433
$285$	−6.25217	−0.370346
$286$	−0.752094	−0.0444723
$287$	18.8910	1.11510
$288$	2.35080	0.138522
$289$	−8.05716	−0.473951
$290$	−2.46565	−0.144788
$291$	2.74530	0.160932
$292$	11.3798	0.665951
$293$	−1.83720	−0.107331	−0.0536653	−	0.998559i	$-0.517090\pi$
$293$	−1.83720	−0.107331	−0.0536653	+	0.998559i	$0.517090\pi$
$294$	−0.759035	−0.0442678
$295$	−1.78883	−0.104149
$296$	−4.95508	−0.288008
$297$	12.7915	0.742239
$298$	−11.6505	−0.674897
$299$	1.42664	0.0825046
$300$	−0.805731	−0.0465189
$301$	−18.1078	−1.04372
$302$	19.6807	1.13250
$303$	6.08014	0.349295
$304$	7.75962	0.445045
$305$	−4.04915	−0.231854
$306$	7.02996	0.401876
$307$	−8.99338	−0.513279	−0.256640	−	0.966507i	$-0.582615\pi$
$307$	−8.99338	−0.513279	−0.256640	+	0.966507i	$0.582615\pi$
$308$	7.30259	0.416103
$309$	1.51311	0.0860776
$310$	0.0301013	0.00170964
$311$	28.3587	1.60807	0.804037	−	0.594579i	$-0.202681\pi$
$311$	28.3587	1.60807	0.804037	+	0.594579i	$0.202681\pi$
$312$	0.204244	0.0115630
$313$	−10.1585	−0.574190	−0.287095	−	0.957902i	$-0.592690\pi$
$313$	−10.1585	−0.574190	−0.287095	+	0.957902i	$0.592690\pi$
$314$	−16.0762	−0.907231
$315$	−5.78600	−0.326004
$316$	10.3652	0.583085
$317$	−10.7405	−0.603244	−0.301622	−	0.953428i	$-0.597528\pi$
$317$	−10.7405	−0.603244	−0.301622	+	0.953428i	$0.597528\pi$
$318$	4.47617	0.251011
$319$	7.31551	0.409590
$320$	1.00000	0.0559017
$321$	−0.433977	−0.0242222
$322$	−13.8522	−0.771952
$323$	23.2048	1.29115
$324$	3.57864	0.198813
$325$	0.253489	0.0140610
$326$	14.9132	0.825963
$327$	0.0182829	0.00101105
$328$	−7.67525	−0.423795
$329$	−15.3075	−0.843927
$330$	2.39058	0.131597
$331$	5.90708	0.324683	0.162341	−	0.986735i	$-0.448095\pi$
$331$	5.90708	0.324683	0.162341	+	0.986735i	$0.448095\pi$
$332$	−11.8374	−0.649659
$333$	−11.6484	−0.638328
$334$	19.0991	1.04506
$335$	−5.65828	−0.309145
$336$	−1.98314	−0.108189
$337$	18.6918	1.01821	0.509103	−	0.860706i	$-0.329977\pi$
$337$	18.6918	1.01821	0.509103	+	0.860706i	$0.329977\pi$
$338$	12.9357	0.703612
$339$	6.42841	0.349143
$340$	2.99046	0.162180
$341$	−0.0893099	−0.00483640
$342$	18.2413	0.986376
$343$	−19.5477	−1.05548
$344$	7.35704	0.396665
$345$	−4.53467	−0.244138
$346$	−4.49770	−0.241798
$347$	10.2806	0.551893	0.275946	−	0.961173i	$-0.411009\pi$
$347$	10.2806	0.551893	0.275946	+	0.961173i	$0.411009\pi$
$348$	−1.98665	−0.106495
$349$	18.9515	1.01445	0.507225	−	0.861814i	$-0.330671\pi$
$349$	18.9515	1.01445	0.507225	+	0.861814i	$0.330671\pi$
$350$	−2.46129	−0.131562
$351$	1.09287	0.0583329
$352$	−2.96697	−0.158140
$353$	17.0773	0.908932	0.454466	−	0.890764i	$-0.349830\pi$
$353$	17.0773	0.908932	0.454466	+	0.890764i	$0.349830\pi$
$354$	−1.44131	−0.0766049
$355$	−6.71451	−0.356369
$356$	4.04190	0.214220
$357$	−5.93049	−0.313875
$358$	−13.2397	−0.699741
$359$	6.22653	0.328623	0.164312	−	0.986408i	$-0.447460\pi$
$359$	6.22653	0.328623	0.164312	+	0.986408i	$0.447460\pi$
$360$	2.35080	0.123898
$361$	41.2117	2.16904
$362$	16.4699	0.865637
$363$	1.77025	0.0929139
$364$	0.623910	0.0327017
$365$	11.3798	0.595645
$366$	−3.26252	−0.170535
$367$	5.83252	0.304455	0.152227	−	0.988345i	$-0.451355\pi$
$367$	5.83252	0.304455	0.152227	+	0.988345i	$0.451355\pi$
$368$	5.62801	0.293381
$369$	−18.0430	−0.939279
$370$	−4.95508	−0.257602
$371$	13.6735	0.709892
$372$	0.0242536	0.00125749
$373$	−34.2494	−1.77336	−0.886682	−	0.462379i	$-0.846996\pi$
$373$	−34.2494	−1.77336	−0.886682	+	0.462379i	$0.846996\pi$
$374$	−8.87261	−0.458792
$375$	−0.805731	−0.0416078
$376$	6.21928	0.320735
$377$	0.625013	0.0321898
$378$	−10.6114	−0.545790
$379$	13.3407	0.685265	0.342632	−	0.939470i	$-0.388682\pi$
$379$	13.3407	0.685265	0.342632	+	0.939470i	$0.388682\pi$
$380$	7.75962	0.398060
$381$	−15.4994	−0.794059
$382$	−2.19134	−0.112119
$383$	20.5402	1.04955	0.524777	−	0.851240i	$-0.324149\pi$
$383$	20.5402	1.04955	0.524777	+	0.851240i	$0.324149\pi$
$384$	0.805731	0.0411173
$385$	7.30259	0.372174
$386$	15.3176	0.779645
$387$	17.2949	0.879150
$388$	−3.40721	−0.172975
$389$	−17.3789	−0.881144	−0.440572	−	0.897717i	$-0.645224\pi$
$389$	−17.3789	−0.881144	−0.440572	+	0.897717i	$0.645224\pi$
$390$	0.204244	0.0103423
$391$	16.8303	0.851147
$392$	0.942045	0.0475804
$393$	−12.6999	−0.640626
$394$	17.8785	0.900708
$395$	10.3652	0.521527
$396$	−6.97475	−0.350495
$397$	−39.2496	−1.96988	−0.984941	−	0.172893i	$-0.944689\pi$
$397$	−39.2496	−1.96988	−0.984941	+	0.172893i	$0.944689\pi$
$398$	−3.18520	−0.159660
$399$	−15.3884	−0.770384
$400$	1.00000	0.0500000
$401$	−0.214587	−0.0107159	−0.00535797	−	0.999986i	$-0.501706\pi$
$401$	−0.214587	−0.0107159	−0.00535797	+	0.999986i	$0.501706\pi$
$402$	−4.55906	−0.227385
$403$	−0.00763035	−0.000380095 0
$404$	−7.54611	−0.375433
$405$	3.57864	0.177824
$406$	−6.06867	−0.301183
$407$	14.7016	0.728731
$408$	2.40950	0.119288
$409$	33.2261	1.64293	0.821464	−	0.570261i	$-0.193158\pi$
$409$	33.2261	1.64293	0.821464	+	0.570261i	$0.193158\pi$
$410$	−7.67525	−0.379054
$411$	−2.63156	−0.129805
$412$	−1.87793	−0.0925189
$413$	−4.40282	−0.216649
$414$	13.2303	0.650235
$415$	−11.8374	−0.581073
$416$	−0.253489	−0.0124283
$417$	5.34486	0.261739
$418$	−23.0226	−1.12607
$419$	3.61884	0.176792	0.0883959	−	0.996085i	$-0.471826\pi$
$419$	3.61884	0.176792	0.0883959	+	0.996085i	$0.471826\pi$
$420$	−1.98314	−0.0967673
$421$	11.2779	0.549649	0.274824	−	0.961494i	$-0.411380\pi$
$421$	11.2779	0.549649	0.274824	+	0.961494i	$0.411380\pi$
$422$	−17.8783	−0.870302
$423$	14.6203	0.710861
$424$	−5.55541	−0.269795
$425$	2.99046	0.145059
$426$	−5.41009	−0.262120
$427$	−9.96614	−0.482295
$428$	0.538613	0.0260348
$429$	−0.605986	−0.0292573
$430$	7.35704	0.354788
$431$	10.5233	0.506888	0.253444	−	0.967350i	$-0.418437\pi$
$431$	10.5233	0.506888	0.253444	+	0.967350i	$0.418437\pi$
$432$	4.31130	0.207428
$433$	−10.9362	−0.525562	−0.262781	−	0.964856i	$-0.584640\pi$
$433$	−10.9362	−0.525562	−0.262781	+	0.964856i	$0.584640\pi$
$434$	0.0740882	0.00355635
$435$	−1.98665	−0.0952525
$436$	−0.0226911	−0.00108671
$437$	43.6712	2.08908
$438$	9.16904	0.438114
$439$	38.9122	1.85718	0.928588	−	0.371111i	$-0.121023\pi$
$439$	38.9122	1.85718	0.928588	+	0.371111i	$0.121023\pi$
$440$	−2.96697	−0.141445
$441$	2.21456	0.105455
$442$	−0.758047	−0.0360566
$443$	−5.40883	−0.256981	−0.128491	−	0.991711i	$-0.541013\pi$
$443$	−5.40883	−0.256981	−0.128491	+	0.991711i	$0.541013\pi$
$444$	−3.99246	−0.189474
$445$	4.04190	0.191604
$446$	22.5791	1.06915
$447$	−9.38720	−0.443999
$448$	2.46129	0.116285
$449$	20.3460	0.960185	0.480093	−	0.877218i	$-0.340603\pi$
$449$	20.3460	0.960185	0.480093	+	0.877218i	$0.340603\pi$
$450$	2.35080	0.110818
$451$	22.7723	1.07230
$452$	−7.97836	−0.375270
$453$	15.8573	0.745043
$454$	0.488383	0.0229209
$455$	0.623910	0.0292493
$456$	6.25217	0.292784
$457$	−1.98930	−0.0930556	−0.0465278	−	0.998917i	$-0.514816\pi$
$457$	−1.98930	−0.0930556	−0.0465278	+	0.998917i	$0.514816\pi$
$458$	−28.7548	−1.34362
$459$	12.8928	0.601783
$460$	5.62801	0.262408
$461$	−17.5399	−0.816917	−0.408458	−	0.912777i	$-0.633933\pi$
$461$	−17.5399	−0.816917	−0.408458	+	0.912777i	$0.633933\pi$
$462$	5.88392	0.273745
$463$	31.3019	1.45472	0.727362	−	0.686254i	$-0.240746\pi$
$463$	31.3019	1.45472	0.727362	+	0.686254i	$0.240746\pi$
$464$	2.46565	0.114465
$465$	0.0242536	0.00112473
$466$	−9.33928	−0.432634
$467$	19.2457	0.890585	0.445292	−	0.895385i	$-0.353100\pi$
$467$	19.2457	0.890585	0.445292	+	0.895385i	$0.353100\pi$
$468$	−0.595901	−0.0275455
$469$	−13.9267	−0.643075
$470$	6.21928	0.286874
$471$	−12.9531	−0.596846
$472$	1.78883	0.0823374
$473$	−21.8281	−1.00366
$474$	8.35152	0.383598
$475$	7.75962	0.356036
$476$	7.36039	0.337363
$477$	−13.0597	−0.597961
$478$	−23.8586	−1.09127
$479$	−19.8308	−0.906094	−0.453047	−	0.891487i	$-0.649663\pi$
$479$	−19.8308	−0.906094	−0.453047	+	0.891487i	$0.649663\pi$
$480$	0.805731	0.0367764
$481$	1.25606	0.0572713
$482$	4.96156	0.225993
$483$	−11.1611	−0.507849
$484$	−2.19707	−0.0998668
$485$	−3.40721	−0.154714
$486$	15.8173	0.717489
$487$	6.05063	0.274180	0.137090	−	0.990559i	$-0.456225\pi$
$487$	6.05063	0.274180	0.137090	+	0.990559i	$0.456225\pi$
$488$	4.04915	0.183296
$489$	12.0160	0.543382
$490$	0.942045	0.0425572
$491$	39.8293	1.79747	0.898735	−	0.438492i	$-0.144487\pi$
$491$	39.8293	1.79747	0.898735	+	0.438492i	$0.144487\pi$
$492$	−6.18419	−0.278805
$493$	7.37341	0.332082
$494$	−1.96698	−0.0884984
$495$	−6.97475	−0.313492
$496$	−0.0301013	−0.00135159
$497$	−16.5264	−0.741309
$498$	−9.53772	−0.427396
$499$	18.1737	0.813566	0.406783	−	0.913525i	$-0.366650\pi$
$499$	18.1737	0.813566	0.406783	+	0.913525i	$0.366650\pi$
$500$	1.00000	0.0447214
$501$	15.3887	0.687518
$502$	−21.4738	−0.958422
$503$	33.3084	1.48515	0.742574	−	0.669764i	$-0.233605\pi$
$503$	33.3084	1.48515	0.742574	+	0.669764i	$0.233605\pi$
$504$	5.78600	0.257729
$505$	−7.54611	−0.335798
$506$	−16.6982	−0.742324
$507$	10.4227	0.462890
$508$	19.2365	0.853480
$509$	−3.94016	−0.174644	−0.0873222	−	0.996180i	$-0.527831\pi$
$509$	−3.94016	−0.174644	−0.0873222	+	0.996180i	$0.527831\pi$
$510$	2.40950	0.106695
$511$	28.0090	1.23904
$512$	−1.00000	−0.0441942
$513$	33.4541	1.47703
$514$	−12.7069	−0.560476
$515$	−1.87793	−0.0827514
$516$	5.92780	0.260957
$517$	−18.4524	−0.811537
$518$	−12.1959	−0.535857
$519$	−3.62393	−0.159073
$520$	−0.253489	−0.0111162
$521$	−7.03558	−0.308234	−0.154117	−	0.988053i	$-0.549253\pi$
$521$	−7.03558	−0.308234	−0.154117	+	0.988053i	$0.549253\pi$
$522$	5.79624	0.253694
$523$	−7.66946	−0.335362	−0.167681	−	0.985841i	$-0.553628\pi$
$523$	−7.66946	−0.335362	−0.167681	+	0.985841i	$0.553628\pi$
$524$	15.7620	0.688565
$525$	−1.98314	−0.0865513
$526$	11.4642	0.499862
$527$	−0.0900168	−0.00392119
$528$	−2.39058	−0.104037
$529$	8.67454	0.377154
$530$	−5.55541	−0.241312
$531$	4.20517	0.182489
$532$	19.0987	0.828033
$533$	1.94559	0.0842728
$534$	3.25668	0.140930
$535$	0.538613	0.0232863
$536$	5.65828	0.244401
$537$	−10.6677	−0.460343
$538$	5.29850	0.228435
$539$	−2.79502	−0.120390
$540$	4.31130	0.185529
$541$	−12.3970	−0.532990	−0.266495	−	0.963836i	$-0.585866\pi$
$541$	−12.3970	−0.532990	−0.266495	+	0.963836i	$0.585866\pi$
$542$	29.4701	1.26585
$543$	13.2703	0.569482
$544$	−2.99046	−0.128215
$545$	−0.0226911	−0.000971980 0
$546$	0.502703	0.0215137
$547$	−23.4786	−1.00387	−0.501936	−	0.864905i	$-0.667379\pi$
$547$	−23.4786	−1.00387	−0.501936	+	0.864905i	$0.667379\pi$
$548$	3.26606	0.139519
$549$	9.51873	0.406249
$550$	−2.96697	−0.126512
$551$	19.1325	0.815071
$552$	4.53467	0.193008
$553$	25.5117	1.08487
$554$	9.58667	0.407298
$555$	−3.99246	−0.169471
$556$	−6.63356	−0.281326
$557$	7.99487	0.338754	0.169377	−	0.985551i	$-0.445825\pi$
$557$	7.99487	0.338754	0.169377	+	0.985551i	$0.445825\pi$
$558$	−0.0707622	−0.00299560
$559$	−1.86493	−0.0788780
$560$	2.46129	0.104009
$561$	−7.14894	−0.301828
$562$	20.1363	0.849397
$563$	−36.5016	−1.53836	−0.769179	−	0.639034i	$-0.779334\pi$
$563$	−36.5016	−1.53836	−0.769179	+	0.639034i	$0.779334\pi$
$564$	5.01106	0.211004
$565$	−7.97836	−0.335652
$566$	15.3926	0.646999
$567$	8.80808	0.369905
$568$	6.71451	0.281734
$569$	−17.5430	−0.735442	−0.367721	−	0.929936i	$-0.619862\pi$
$569$	−17.5430	−0.735442	−0.367721	+	0.929936i	$0.619862\pi$
$570$	6.25217	0.261874
$571$	−35.5959	−1.48964	−0.744822	−	0.667263i	$-0.767466\pi$
$571$	−35.5959	−1.48964	−0.744822	+	0.667263i	$0.767466\pi$
$572$	0.752094	0.0314466
$573$	−1.76563	−0.0737604
$574$	−18.8910	−0.788496
$575$	5.62801	0.234704
$576$	−2.35080	−0.0979499
$577$	−22.5122	−0.937195	−0.468597	−	0.883412i	$-0.655241\pi$
$577$	−22.5122	−0.937195	−0.468597	+	0.883412i	$0.655241\pi$
$578$	8.05716	0.335134
$579$	12.3419	0.512910
$580$	2.46565	0.102380
$581$	−29.1352	−1.20873
$582$	−2.74530	−0.113796
$583$	16.4828	0.682646
$584$	−11.3798	−0.470899
$585$	−0.595901	−0.0246375
$586$	1.83720	0.0758942
$587$	−21.7024	−0.895753	−0.447876	−	0.894095i	$-0.647820\pi$
$587$	−21.7024	−0.895753	−0.447876	+	0.894095i	$0.647820\pi$
$588$	0.759035	0.0313021
$589$	−0.233575	−0.00962429
$590$	1.78883	0.0736448
$591$	14.4053	0.592555
$592$	4.95508	0.203653
$593$	12.8951	0.529540	0.264770	−	0.964312i	$-0.414704\pi$
$593$	12.8951	0.529540	0.264770	+	0.964312i	$0.414704\pi$
$594$	−12.7915	−0.524842
$595$	7.36039	0.301747
$596$	11.6505	0.477224
$597$	−2.56641	−0.105036
$598$	−1.42664	−0.0583396
$599$	34.6920	1.41748	0.708738	−	0.705471i	$-0.249265\pi$
$599$	34.6920	1.41748	0.708738	+	0.705471i	$0.249265\pi$
$600$	0.805731	0.0328938
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	18.1078	0.738020
$603$	13.3015	0.541678
$604$	−19.6807	−0.800796
$605$	−2.19707	−0.0893236
$606$	−6.08014	−0.246989
$607$	16.8544	0.684101	0.342050	−	0.939682i	$-0.388879\pi$
$607$	16.8544	0.684101	0.342050	+	0.939682i	$0.388879\pi$
$608$	−7.75962	−0.314694
$609$	−4.88972	−0.198141
$610$	4.04915	0.163945
$611$	−1.57652	−0.0637790
$612$	−7.02996	−0.284169
$613$	−1.82154	−0.0735714	−0.0367857	−	0.999323i	$-0.511712\pi$
$613$	−1.82154	−0.0735714	−0.0367857	+	0.999323i	$0.511712\pi$
$614$	8.99338	0.362943
$615$	−6.18419	−0.249371
$616$	−7.30259	−0.294230
$617$	−9.33100	−0.375652	−0.187826	−	0.982202i	$-0.560144\pi$
$617$	−9.33100	−0.375652	−0.187826	+	0.982202i	$0.560144\pi$
$618$	−1.51311	−0.0608660
$619$	44.2932	1.78029	0.890147	−	0.455674i	$-0.150602\pi$
$619$	44.2932	1.78029	0.890147	+	0.455674i	$0.150602\pi$
$620$	−0.0301013	−0.00120890
$621$	24.2641	0.973684
$622$	−28.3587	−1.13708
$623$	9.94828	0.398570
$624$	−0.204244	−0.00817629
$625$	1.00000	0.0400000
$626$	10.1585	0.406014
$627$	−18.5500	−0.740816
$628$	16.0762	0.641509
$629$	14.8180	0.590831
$630$	5.78600	0.230520
$631$	0.644410	0.0256535	0.0128268	−	0.999918i	$-0.495917\pi$
$631$	0.644410	0.0256535	0.0128268	+	0.999918i	$0.495917\pi$
$632$	−10.3652	−0.412304
$633$	−14.4051	−0.572552
$634$	10.7405	0.426558
$635$	19.2365	0.763376
$636$	−4.47617	−0.177492
$637$	−0.238798	−0.00946151
$638$	−7.31551	−0.289624
$639$	15.7844	0.624423
$640$	−1.00000	−0.0395285
$641$	41.7930	1.65072	0.825362	−	0.564604i	$-0.190971\pi$
$641$	41.7930	1.65072	0.825362	+	0.564604i	$0.190971\pi$
$642$	0.433977	0.0171277
$643$	−19.4332	−0.766370	−0.383185	−	0.923672i	$-0.625173\pi$
$643$	−19.4332	−0.766370	−0.383185	+	0.923672i	$0.625173\pi$
$644$	13.8522	0.545852
$645$	5.92780	0.233407
$646$	−23.2048	−0.912981
$647$	−18.7712	−0.737971	−0.368986	−	0.929435i	$-0.620295\pi$
$647$	−18.7712	−0.737971	−0.368986	+	0.929435i	$0.620295\pi$
$648$	−3.57864	−0.140582
$649$	−5.30740	−0.208334
$650$	−0.253489	−0.00994264
$651$	0.0596951	0.00233964
$652$	−14.9132	−0.584044
$653$	22.7523	0.890364	0.445182	−	0.895440i	$-0.353139\pi$
$653$	22.7523	0.890364	0.445182	+	0.895440i	$0.353139\pi$
$654$	−0.0182829	−0.000714919 0
$655$	15.7620	0.615872
$656$	7.67525	0.299668
$657$	−26.7516	−1.04368
$658$	15.3075	0.596747
$659$	18.4462	0.718560	0.359280	−	0.933230i	$-0.383022\pi$
$659$	18.4462	0.718560	0.359280	+	0.933230i	$0.383022\pi$
$660$	−2.39058	−0.0930533
$661$	−13.0244	−0.506591	−0.253295	−	0.967389i	$-0.581514\pi$
$661$	−13.0244	−0.506591	−0.253295	+	0.967389i	$0.581514\pi$
$662$	−5.90708	−0.229585
$663$	−0.610782	−0.0237208
$664$	11.8374	0.459379
$665$	19.0987	0.740615
$666$	11.6484	0.451366
$667$	13.8767	0.537308
$668$	−19.0991	−0.738967
$669$	18.1927	0.703369
$670$	5.65828	0.218599
$671$	−12.0137	−0.463784
$672$	1.98314	0.0765012
$673$	27.2167	1.04913	0.524564	−	0.851371i	$-0.324228\pi$
$673$	27.2167	1.04913	0.524564	+	0.851371i	$0.324228\pi$
$674$	−18.6918	−0.719980
$675$	4.31130	0.165942
$676$	−12.9357	−0.497529
$677$	−0.493812	−0.0189787	−0.00948937	−	0.999955i	$-0.503021\pi$
$677$	−0.493812	−0.0189787	−0.00948937	+	0.999955i	$0.503021\pi$
$678$	−6.42841	−0.246882
$679$	−8.38615	−0.321831
$680$	−2.99046	−0.114679
$681$	0.393505	0.0150792
$682$	0.0893099	0.00341985
$683$	35.5289	1.35948	0.679738	−	0.733455i	$-0.262093\pi$
$683$	35.5289	1.35948	0.679738	+	0.733455i	$0.262093\pi$
$684$	−18.2413	−0.697473
$685$	3.26606	0.124790
$686$	19.5477	0.746334
$687$	−23.1686	−0.883939
$688$	−7.35704	−0.280485
$689$	1.40823	0.0536495
$690$	4.53467	0.172632
$691$	0.0611603	0.00232665	0.00116332	−	0.999999i	$-0.499630\pi$
$691$	0.0611603	0.00232665	0.00116332	+	0.999999i	$0.499630\pi$
$692$	4.49770	0.170977
$693$	−17.1669	−0.652117
$694$	−10.2806	−0.390247
$695$	−6.63356	−0.251625
$696$	1.98665	0.0753037
$697$	22.9525	0.869389
$698$	−18.9515	−0.717325
$699$	−7.52495	−0.284620
$700$	2.46129	0.0930281
$701$	−34.0413	−1.28572	−0.642861	−	0.765983i	$-0.722253\pi$
$701$	−34.0413	−1.28572	−0.642861	+	0.765983i	$0.722253\pi$
$702$	−1.09287	−0.0412476
$703$	38.4495	1.45015
$704$	2.96697	0.111822
$705$	5.01106	0.188728
$706$	−17.0773	−0.642712
$707$	−18.5732	−0.698516
$708$	1.44131	0.0541678
$709$	−8.02140	−0.301250	−0.150625	−	0.988591i	$-0.548129\pi$
$709$	−8.02140	−0.301250	−0.150625	+	0.988591i	$0.548129\pi$
$710$	6.71451	0.251991
$711$	−24.3664	−0.913810
$712$	−4.04190	−0.151476
$713$	−0.169411	−0.00634448
$714$	5.93049	0.221943
$715$	0.752094	0.0281267
$716$	13.2397	0.494792
$717$	−19.2236	−0.717920
$718$	−6.22653	−0.232372
$719$	−21.4882	−0.801373	−0.400687	−	0.916215i	$-0.631228\pi$
$719$	−21.4882	−0.801373	−0.400687	+	0.916215i	$0.631228\pi$
$720$	−2.35080	−0.0876091
$721$	−4.62213	−0.172137
$722$	−41.2117	−1.53374
$723$	3.99768	0.148676
$724$	−16.4699	−0.612097
$725$	2.46565	0.0915718
$726$	−1.77025	−0.0657001
$727$	2.24591	0.0832961	0.0416480	−	0.999132i	$-0.486739\pi$
$727$	2.24591	0.0832961	0.0416480	+	0.999132i	$0.486739\pi$
$728$	−0.623910	−0.0231236
$729$	2.00859	0.0743922
$730$	−11.3798	−0.421185
$731$	−22.0009	−0.813734
$732$	3.26252	0.120586
$733$	28.7932	1.06350	0.531751	−	0.846901i	$-0.321534\pi$
$733$	28.7932	1.06350	0.531751	+	0.846901i	$0.321534\pi$
$734$	−5.83252	−0.215282
$735$	0.759035	0.0279974
$736$	−5.62801	−0.207451
$737$	−16.7880	−0.618393
$738$	18.0430	0.664171
$739$	−18.2412	−0.671012	−0.335506	−	0.942038i	$-0.608907\pi$
$739$	−18.2412	−0.671012	−0.335506	+	0.942038i	$0.608907\pi$
$740$	4.95508	0.182152
$741$	−1.58485	−0.0582210
$742$	−13.6735	−0.501970
$743$	14.9616	0.548888	0.274444	−	0.961603i	$-0.411506\pi$
$743$	14.9616	0.548888	0.274444	+	0.961603i	$0.411506\pi$
$744$	−0.0242536	−0.000889180 0
$745$	11.6505	0.426843
$746$	34.2494	1.25396
$747$	27.8272	1.01815
$748$	8.87261	0.324415
$749$	1.32568	0.0484394
$750$	0.805731	0.0294211
$751$	6.71445	0.245014	0.122507	−	0.992468i	$-0.460907\pi$
$751$	6.71445	0.245014	0.122507	+	0.992468i	$0.460907\pi$
$752$	−6.21928	−0.226794
$753$	−17.3021	−0.630523
$754$	−0.625013	−0.0227616
$755$	−19.6807	−0.716253
$756$	10.6114	0.385932
$757$	−17.2749	−0.627867	−0.313933	−	0.949445i	$-0.601647\pi$
$757$	−17.2749	−0.627867	−0.313933	+	0.949445i	$0.601647\pi$
$758$	−13.3407	−0.484555
$759$	−13.4542	−0.488358
$760$	−7.75962	−0.281471
$761$	27.4400	0.994698	0.497349	−	0.867551i	$-0.334307\pi$
$761$	27.4400	0.994698	0.497349	+	0.867551i	$0.334307\pi$
$762$	15.4994	0.561485
$763$	−0.0558494	−0.00202188
$764$	2.19134	0.0792800
$765$	−7.02996	−0.254169
$766$	−20.5402	−0.742146
$767$	−0.453447	−0.0163730
$768$	−0.805731	−0.0290743
$769$	−4.46646	−0.161065	−0.0805323	−	0.996752i	$-0.525662\pi$
$769$	−4.46646	−0.161065	−0.0805323	+	0.996752i	$0.525662\pi$
$770$	−7.30259	−0.263167
$771$	−10.2383	−0.368724
$772$	−15.3176	−0.551292
$773$	−1.00643	−0.0361989	−0.0180995	−	0.999836i	$-0.505762\pi$
$773$	−1.00643	−0.0361989	−0.0180995	+	0.999836i	$0.505762\pi$
$774$	−17.2949	−0.621653
$775$	−0.0301013	−0.00108127
$776$	3.40721	0.122312
$777$	−9.82661	−0.352528
$778$	17.3789	0.623063
$779$	59.5570	2.13385
$780$	−0.204244	−0.00731310
$781$	−19.9218	−0.712857
$782$	−16.8303	−0.601852
$783$	10.6302	0.379891
$784$	−0.942045	−0.0336445
$785$	16.0762	0.573783
$786$	12.6999	0.452991
$787$	−12.3244	−0.439316	−0.219658	−	0.975577i	$-0.570494\pi$
$787$	−12.3244	−0.439316	−0.219658	+	0.975577i	$0.570494\pi$
$788$	−17.8785	−0.636897
$789$	9.23704	0.328847
$790$	−10.3652	−0.368776
$791$	−19.6371	−0.698214
$792$	6.97475	0.247837
$793$	−1.02641	−0.0364490
$794$	39.2496	1.39292
$795$	−4.47617	−0.158753
$796$	3.18520	0.112896
$797$	26.7740	0.948385	0.474192	−	0.880421i	$-0.342740\pi$
$797$	26.7740	0.948385	0.474192	+	0.880421i	$0.342740\pi$
$798$	15.3884	0.544743
$799$	−18.5985	−0.657967
$800$	−1.00000	−0.0353553
$801$	−9.50168	−0.335725
$802$	0.214587	0.00757732
$803$	33.7635	1.19149
$804$	4.55906	0.160785
$805$	13.8522	0.488225
$806$	0.00763035	0.000268768 0
$807$	4.26916	0.150282
$808$	7.54611	0.265471
$809$	10.1965	0.358491	0.179245	−	0.983804i	$-0.442634\pi$
$809$	10.1965	0.358491	0.179245	+	0.983804i	$0.442634\pi$
$810$	−3.57864	−0.125741
$811$	36.3389	1.27603	0.638016	−	0.770023i	$-0.279755\pi$
$811$	36.3389	1.27603	0.638016	+	0.770023i	$0.279755\pi$
$812$	6.06867	0.212969
$813$	23.7449	0.832772
$814$	−14.7016	−0.515291
$815$	−14.9132	−0.522385
$816$	−2.40950	−0.0843495
$817$	−57.0879	−1.99725
$818$	−33.2261	−1.16172
$819$	−1.46668	−0.0512501
$820$	7.67525	0.268031
$821$	−32.3674	−1.12963	−0.564815	−	0.825218i	$-0.691052\pi$
$821$	−32.3674	−1.12963	−0.564815	+	0.825218i	$0.691052\pi$
$822$	2.63156	0.0917863
$823$	38.1658	1.33038	0.665189	−	0.746675i	$-0.268351\pi$
$823$	38.1658	1.33038	0.665189	+	0.746675i	$0.268351\pi$
$824$	1.87793	0.0654207
$825$	−2.39058	−0.0832294
$826$	4.40282	0.153194
$827$	1.58200	0.0550114	0.0275057	−	0.999622i	$-0.491244\pi$
$827$	1.58200	0.0550114	0.0275057	+	0.999622i	$0.491244\pi$
$828$	−13.2303	−0.459785
$829$	−3.87882	−0.134717	−0.0673586	−	0.997729i	$-0.521457\pi$
$829$	−3.87882	−0.134717	−0.0673586	+	0.997729i	$0.521457\pi$
$830$	11.8374	0.410881
$831$	7.72427	0.267952
$832$	0.253489	0.00878814
$833$	−2.81715	−0.0976083
$834$	−5.34486	−0.185078
$835$	−19.0991	−0.660952
$836$	23.0226	0.796253
$837$	−0.129776	−0.00448572
$838$	−3.61884	−0.125011
$839$	−47.4156	−1.63697	−0.818484	−	0.574529i	$-0.805185\pi$
$839$	−47.4156	−1.63697	−0.818484	+	0.574529i	$0.805185\pi$
$840$	1.98314	0.0684248
$841$	−22.9206	−0.790365
$842$	−11.2779	−0.388660
$843$	16.2244	0.558799
$844$	17.8783	0.615397
$845$	−12.9357	−0.445003
$846$	−14.6203	−0.502655
$847$	−5.40763	−0.185808
$848$	5.55541	0.190774
$849$	12.4023	0.425645
$850$	−2.99046	−0.102572
$851$	27.8873	0.955963
$852$	5.41009	0.185347
$853$	−5.66351	−0.193915	−0.0969574	−	0.995289i	$-0.530911\pi$
$853$	−5.66351	−0.193915	−0.0969574	+	0.995289i	$0.530911\pi$
$854$	9.96614	0.341034
$855$	−18.2413	−0.623839
$856$	−0.538613	−0.0184094
$857$	−43.4723	−1.48499	−0.742493	−	0.669854i	$-0.766357\pi$
$857$	−43.4723	−1.48499	−0.742493	+	0.669854i	$0.766357\pi$
$858$	0.605986	0.0206880
$859$	−27.3227	−0.932239	−0.466120	−	0.884722i	$-0.654348\pi$
$859$	−27.3227	−0.932239	−0.466120	+	0.884722i	$0.654348\pi$
$860$	−7.35704	−0.250873
$861$	−15.2211	−0.518733
$862$	−10.5233	−0.358424
$863$	44.0696	1.50015	0.750073	−	0.661355i	$-0.230018\pi$
$863$	44.0696	1.50015	0.750073	+	0.661355i	$0.230018\pi$
$864$	−4.31130	−0.146674
$865$	4.49770	0.152926
$866$	10.9362	0.371628
$867$	6.49190	0.220477
$868$	−0.0740882	−0.00251472
$869$	30.7531	1.04323
$870$	1.98665	0.0673537
$871$	−1.43431	−0.0485998
$872$	0.0226911	0.000768417 0
$873$	8.00967	0.271086
$874$	−43.6712	−1.47720
$875$	2.46129	0.0832068
$876$	−9.16904	−0.309793
$877$	−2.37030	−0.0800393	−0.0400196	−	0.999199i	$-0.512742\pi$
$877$	−2.37030	−0.0800393	−0.0400196	+	0.999199i	$0.512742\pi$
$878$	−38.9122	−1.31322
$879$	1.48029	0.0499290
$880$	2.96697	0.100017
$881$	15.5862	0.525112	0.262556	−	0.964917i	$-0.415435\pi$
$881$	15.5862	0.525112	0.262556	+	0.964917i	$0.415435\pi$
$882$	−2.21456	−0.0745680
$883$	−49.2081	−1.65598	−0.827992	−	0.560739i	$-0.810517\pi$
$883$	−49.2081	−1.65598	−0.827992	+	0.560739i	$0.810517\pi$
$884$	0.758047	0.0254959
$885$	1.44131	0.0484492
$886$	5.40883	0.181713
$887$	−21.7984	−0.731917	−0.365959	−	0.930631i	$-0.619259\pi$
$887$	−21.7984	−0.731917	−0.365959	+	0.930631i	$0.619259\pi$
$888$	3.99246	0.133978
$889$	47.3466	1.58795
$890$	−4.04190	−0.135485
$891$	10.6177	0.355707
$892$	−22.5791	−0.756004
$893$	−48.2592	−1.61493
$894$	9.38720	0.313955
$895$	13.2397	0.442555
$896$	−2.46129	−0.0822260
$897$	−1.14949	−0.0383802
$898$	−20.3460	−0.678953
$899$	−0.0742193	−0.00247535
$900$	−2.35080	−0.0783599
$901$	16.6132	0.553467
$902$	−22.7723	−0.758234
$903$	14.5900	0.485526
$904$	7.97836	0.265356
$905$	−16.4699	−0.547477
$906$	−15.8573	−0.526825
$907$	13.2840	0.441088	0.220544	−	0.975377i	$-0.429217\pi$
$907$	13.2840	0.441088	0.220544	+	0.975377i	$0.429217\pi$
$908$	−0.488383	−0.0162076
$909$	17.7394	0.588378
$910$	−0.623910	−0.0206824
$911$	28.4263	0.941807	0.470903	−	0.882185i	$-0.343928\pi$
$911$	28.4263	0.941807	0.470903	+	0.882185i	$0.343928\pi$
$912$	−6.25217	−0.207030
$913$	−35.1211	−1.16234
$914$	1.98930	0.0658003
$915$	3.26252	0.107856
$916$	28.7548	0.950086
$917$	38.7948	1.28112
$918$	−12.8928	−0.425525
$919$	47.6713	1.57253	0.786265	−	0.617889i	$-0.212012\pi$
$919$	47.6713	1.57253	0.786265	+	0.617889i	$0.212012\pi$
$920$	−5.62801	−0.185550
$921$	7.24624	0.238772
$922$	17.5399	0.577647
$923$	−1.70205	−0.0560237
$924$	−5.88392	−0.193567
$925$	4.95508	0.162922
$926$	−31.3019	−1.02865
$927$	4.41463	0.144995
$928$	−2.46565	−0.0809388
$929$	−18.2103	−0.597461	−0.298731	−	0.954337i	$-0.596563\pi$
$929$	−18.2103	−0.597461	−0.298731	+	0.954337i	$0.596563\pi$
$930$	−0.0242536	−0.000795306 0
$931$	−7.30991	−0.239573
$932$	9.33928	0.305918
$933$	−22.8495	−0.748058
$934$	−19.2457	−0.629739
$935$	8.87261	0.290165
$936$	0.595901	0.0194776
$937$	−58.9624	−1.92622	−0.963108	−	0.269115i	$-0.913269\pi$
$937$	−58.9624	−1.92622	−0.963108	+	0.269115i	$0.913269\pi$
$938$	13.9267	0.454722
$939$	8.18498	0.267107
$940$	−6.21928	−0.202850
$941$	−37.7301	−1.22997	−0.614984	−	0.788540i	$-0.710837\pi$
$941$	−37.7301	−1.22997	−0.614984	+	0.788540i	$0.710837\pi$
$942$	12.9531	0.422034
$943$	43.1964	1.40667
$944$	−1.78883	−0.0582213
$945$	10.6114	0.345188
$946$	21.8281	0.709694
$947$	−4.76401	−0.154810	−0.0774048	−	0.997000i	$-0.524663\pi$
$947$	−4.76401	−0.154810	−0.0774048	+	0.997000i	$0.524663\pi$
$948$	−8.35152	−0.271245
$949$	2.88465	0.0936396
$950$	−7.75962	−0.251755
$951$	8.65392	0.280623
$952$	−7.36039	−0.238552
$953$	−1.09131	−0.0353510	−0.0176755	−	0.999844i	$-0.505627\pi$
$953$	−1.09131	−0.0353510	−0.0176755	+	0.999844i	$0.505627\pi$
$954$	13.0597	0.422822
$955$	2.19134	0.0709102
$956$	23.8586	0.771644
$957$	−5.89433	−0.190537
$958$	19.8308	0.640705
$959$	8.03871	0.259584
$960$	−0.805731	−0.0260049
$961$	−30.9991	−0.999971
$962$	−1.25606	−0.0404969
$963$	−1.26617	−0.0408018
$964$	−4.96156	−0.159801
$965$	−15.3176	−0.493091
$966$	11.1611	0.359104
$967$	−14.9160	−0.479666	−0.239833	−	0.970814i	$-0.577093\pi$
$967$	−14.9160	−0.479666	−0.239833	+	0.970814i	$0.577093\pi$
$968$	2.19707	0.0706165
$969$	−18.6968	−0.600629
$970$	3.40721	0.109399
$971$	−32.3140	−1.03701	−0.518503	−	0.855076i	$-0.673510\pi$
$971$	−32.3140	−1.03701	−0.518503	+	0.855076i	$0.673510\pi$
$972$	−15.8173	−0.507341
$973$	−16.3271	−0.523423
$974$	−6.05063	−0.193875
$975$	−0.204244	−0.00654103
$976$	−4.04915	−0.129610
$977$	−28.0369	−0.896980	−0.448490	−	0.893788i	$-0.648038\pi$
$977$	−28.0369	−0.896980	−0.448490	+	0.893788i	$0.648038\pi$
$978$	−12.0160	−0.384229
$979$	11.9922	0.383272
$980$	−0.942045	−0.0300925
$981$	0.0533422	0.00170308
$982$	−39.8293	−1.27100
$983$	−57.8523	−1.84520	−0.922602	−	0.385754i	$-0.873941\pi$
$983$	−57.8523	−1.84520	−0.922602	+	0.385754i	$0.873941\pi$
$984$	6.18419	0.197145
$985$	−17.8785	−0.569658
$986$	−7.37341	−0.234817
$987$	12.3337	0.392586
$988$	1.96698	0.0625778
$989$	−41.4055	−1.31662
$990$	6.97475	0.221672
$991$	−33.9423	−1.07821	−0.539106	−	0.842238i	$-0.681238\pi$
$991$	−33.9423	−1.07821	−0.539106	+	0.842238i	$0.681238\pi$
$992$	0.0301013	0.000955719 0
$993$	−4.75952	−0.151039
$994$	16.5264	0.524184
$995$	3.18520	0.100978
$996$	9.53772	0.302214
$997$	27.4734	0.870093	0.435046	−	0.900408i	$-0.356732\pi$
$997$	27.4734	0.870093	0.435046	+	0.900408i	$0.356732\pi$
$998$	−18.1737	−0.575278
$999$	21.3629	0.675891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.g.1.10	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.g.1.10	✓	27	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.805731 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.805731 q^{6} +2.46129 q^{7} -1.00000 q^{8} -2.35080 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.805731 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.805731 q^{6} +2.46129 q^{7} -1.00000 q^{8} -2.35080 q^{9} -1.00000 q^{10} +2.96697 q^{11} -0.805731 q^{12} +0.253489 q^{13} -2.46129 q^{14} -0.805731 q^{15} +1.00000 q^{16} +2.99046 q^{17} +2.35080 q^{18} +7.75962 q^{19} +1.00000 q^{20} -1.98314 q^{21} -2.96697 q^{22} +5.62801 q^{23} +0.805731 q^{24} +1.00000 q^{25} -0.253489 q^{26} +4.31130 q^{27} +2.46129 q^{28} +2.46565 q^{29} +0.805731 q^{30} -0.0301013 q^{31} -1.00000 q^{32} -2.39058 q^{33} -2.99046 q^{34} +2.46129 q^{35} -2.35080 q^{36} +4.95508 q^{37} -7.75962 q^{38} -0.204244 q^{39} -1.00000 q^{40} +7.67525 q^{41} +1.98314 q^{42} -7.35704 q^{43} +2.96697 q^{44} -2.35080 q^{45} -5.62801 q^{46} -6.21928 q^{47} -0.805731 q^{48} -0.942045 q^{49} -1.00000 q^{50} -2.40950 q^{51} +0.253489 q^{52} +5.55541 q^{53} -4.31130 q^{54} +2.96697 q^{55} -2.46129 q^{56} -6.25217 q^{57} -2.46565 q^{58} -1.78883 q^{59} -0.805731 q^{60} -4.04915 q^{61} +0.0301013 q^{62} -5.78600 q^{63} +1.00000 q^{64} +0.253489 q^{65} +2.39058 q^{66} -5.65828 q^{67} +2.99046 q^{68} -4.53467 q^{69} -2.46129 q^{70} -6.71451 q^{71} +2.35080 q^{72} +11.3798 q^{73} -4.95508 q^{74} -0.805731 q^{75} +7.75962 q^{76} +7.30259 q^{77} +0.204244 q^{78} +10.3652 q^{79} +1.00000 q^{80} +3.57864 q^{81} -7.67525 q^{82} -11.8374 q^{83} -1.98314 q^{84} +2.99046 q^{85} +7.35704 q^{86} -1.98665 q^{87} -2.96697 q^{88} +4.04190 q^{89} +2.35080 q^{90} +0.623910 q^{91} +5.62801 q^{92} +0.0242536 q^{93} +6.21928 q^{94} +7.75962 q^{95} +0.805731 q^{96} -3.40721 q^{97} +0.942045 q^{98} -6.97475 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * q^99

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