LMFDB - Embedded newform 605.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, 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("605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.65544$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.39593 q^{2} -1.65544 q^{3} -0.0513742 q^{4} -1.00000 q^{5} -2.31088 q^{6} +4.70682 q^{7} -2.86358 q^{8} -0.259511 q^{9} +O(q^{10})$	\(q+1.39593 q^{2} -1.65544 q^{3} -0.0513742 q^{4} -1.00000 q^{5} -2.31088 q^{6} +4.70682 q^{7} -2.86358 q^{8} -0.259511 q^{9} -1.39593 q^{10} +0.0850471 q^{12} +5.05137 q^{13} +6.57040 q^{14} +1.65544 q^{15} -3.89461 q^{16} +5.31088 q^{17} -0.362259 q^{18} +2.25951 q^{19} +0.0513742 q^{20} -7.79186 q^{21} +1.05137 q^{23} +4.74049 q^{24} +1.00000 q^{25} +7.05137 q^{26} +5.39593 q^{27} -0.241809 q^{28} +2.79186 q^{29} +2.31088 q^{30} +3.74049 q^{31} +0.290544 q^{32} +7.41363 q^{34} -4.70682 q^{35} +0.0133322 q^{36} -0.791864 q^{37} +3.15412 q^{38} -8.36226 q^{39} +2.86358 q^{40} -6.15412 q^{41} -10.8769 q^{42} -2.70682 q^{43} +0.259511 q^{45} +1.46765 q^{46} -11.2392 q^{47} +6.44731 q^{48} +15.1541 q^{49} +1.39593 q^{50} -8.79186 q^{51} -0.259511 q^{52} +1.05137 q^{53} +7.53235 q^{54} -13.4783 q^{56} -3.74049 q^{57} +3.89725 q^{58} +4.53235 q^{59} -0.0850471 q^{60} +9.88128 q^{61} +5.22147 q^{62} -1.22147 q^{63} +8.19480 q^{64} -5.05137 q^{65} +10.4473 q^{67} -0.272843 q^{68} -1.74049 q^{69} -6.57040 q^{70} -1.05137 q^{71} +0.743129 q^{72} -10.1027 q^{73} -1.10539 q^{74} -1.65544 q^{75} -0.116081 q^{76} -11.6731 q^{78} -9.41363 q^{79} +3.89461 q^{80} -8.15412 q^{81} -8.59074 q^{82} -3.15412 q^{83} +0.400301 q^{84} -5.31088 q^{85} -3.77853 q^{86} -4.62177 q^{87} -12.5164 q^{89} +0.362259 q^{90} +23.7759 q^{91} -0.0540136 q^{92} -6.19216 q^{93} -15.6891 q^{94} -2.25951 q^{95} -0.480979 q^{96} -17.7759 q^{97} +21.1541 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + q^{3} + 9 q^{4} - 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q + q^2 + q^3 + 9 * q^4 - 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 + 2 * q^9	$ 3 q + q^{2} + q^{3} + 9 q^{4} - 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} + 2 q^{9} - q^{10} + 9 q^{12} + 6 q^{13} + 5 q^{14} - q^{15} + 13 q^{16} + 4 q^{17} + 20 q^{18} + 4 q^{19} - 9 q^{20} - 17 q^{21} - 6 q^{23} + 17 q^{24} + 3 q^{25} + 12 q^{26} + 13 q^{27} - 25 q^{28} + 2 q^{29} - 5 q^{30} + 14 q^{31} - 27 q^{32} - 8 q^{34} + q^{35} + 2 q^{36} + 4 q^{37} - 18 q^{38} - 4 q^{39} + 9 q^{40} + 9 q^{41} - 35 q^{42} + 7 q^{43} - 2 q^{45} + 8 q^{46} - 15 q^{47} + 7 q^{48} + 18 q^{49} + q^{50} - 20 q^{51} + 2 q^{52} - 6 q^{53} + 19 q^{54} - 3 q^{56} - 14 q^{57} + 30 q^{58} + 10 q^{59} - 9 q^{60} + 3 q^{61} + 24 q^{62} - 12 q^{63} + 29 q^{64} - 6 q^{65} + 19 q^{67} - 8 q^{69} - 5 q^{70} + 6 q^{71} + 48 q^{72} - 12 q^{73} - 28 q^{74} + q^{75} + 16 q^{76} - 2 q^{78} + 2 q^{79} - 13 q^{80} + 3 q^{81} - 27 q^{82} + 18 q^{83} - 31 q^{84} - 4 q^{85} - 3 q^{86} + 10 q^{87} + 11 q^{89} - 20 q^{90} + 20 q^{91} - 34 q^{92} + 20 q^{93} - 59 q^{94} - 4 q^{95} - 7 q^{96} - 2 q^{97} + 36 q^{98}+O(q^{100}) $ 3 * q + q^2 + q^3 + 9 * q^4 - 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 + 2 * q^9 - q^10 + 9 * q^12 + 6 * q^13 + 5 * q^14 - q^15 + 13 * q^16 + 4 * q^17 + 20 * q^18 + 4 * q^19 - 9 * q^20 - 17 * q^21 - 6 * q^23 + 17 * q^24 + 3 * q^25 + 12 * q^26 + 13 * q^27 - 25 * q^28 + 2 * q^29 - 5 * q^30 + 14 * q^31 - 27 * q^32 - 8 * q^34 + q^35 + 2 * q^36 + 4 * q^37 - 18 * q^38 - 4 * q^39 + 9 * q^40 + 9 * q^41 - 35 * q^42 + 7 * q^43 - 2 * q^45 + 8 * q^46 - 15 * q^47 + 7 * q^48 + 18 * q^49 + q^50 - 20 * q^51 + 2 * q^52 - 6 * q^53 + 19 * q^54 - 3 * q^56 - 14 * q^57 + 30 * q^58 + 10 * q^59 - 9 * q^60 + 3 * q^61 + 24 * q^62 - 12 * q^63 + 29 * q^64 - 6 * q^65 + 19 * q^67 - 8 * q^69 - 5 * q^70 + 6 * q^71 + 48 * q^72 - 12 * q^73 - 28 * q^74 + q^75 + 16 * q^76 - 2 * q^78 + 2 * q^79 - 13 * q^80 + 3 * q^81 - 27 * q^82 + 18 * q^83 - 31 * q^84 - 4 * q^85 - 3 * q^86 + 10 * q^87 + 11 * q^89 - 20 * q^90 + 20 * q^91 - 34 * q^92 + 20 * q^93 - 59 * q^94 - 4 * q^95 - 7 * q^96 - 2 * q^97 + 36 * q^98

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 $

$2$	1.39593	0.987073	0.493536	−	0.869725i	$-0.335704\pi$
$2$	1.39593	0.987073	0.493536	+	0.869725i	$0.335704\pi$
$3$	−1.65544	−0.955770	−0.477885	−	0.878422i	$-0.658596\pi$
$3$	−1.65544	−0.955770	−0.477885	+	0.878422i	$0.658596\pi$
$4$	−0.0513742	−0.0256871
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.31088	−0.943415
$7$	4.70682	1.77901	0.889505	−	0.456926i	$-0.151050\pi$
$7$	4.70682	1.77901	0.889505	+	0.456926i	$0.151050\pi$
$8$	−2.86358	−1.01243
$9$	−0.259511	−0.0865035
$10$	−1.39593	−0.441432
$11$	0	0
$11$	0	0
$12$	0.0850471	0.0245510
$13$	5.05137	1.40100	0.700500	−	0.713653i	$-0.252961\pi$
$13$	5.05137	1.40100	0.700500	+	0.713653i	$0.252961\pi$
$14$	6.57040	1.75601
$15$	1.65544	0.427433
$16$	−3.89461	−0.973653
$17$	5.31088	1.28808	0.644039	−	0.764992i	$-0.277257\pi$
$17$	5.31088	1.28808	0.644039	+	0.764992i	$0.277257\pi$
$18$	−0.362259	−0.0853853
$19$	2.25951	0.518367	0.259184	−	0.965828i	$-0.416547\pi$
$19$	2.25951	0.518367	0.259184	+	0.965828i	$0.416547\pi$
$20$	0.0513742	0.0114876
$21$	−7.79186	−1.70032
$22$	0	0
$23$	1.05137	0.219227	0.109613	−	0.993974i	$-0.465039\pi$
$23$	1.05137	0.219227	0.109613	+	0.993974i	$0.465039\pi$
$24$	4.74049	0.967648
$25$	1.00000	0.200000
$26$	7.05137	1.38289
$27$	5.39593	1.03845
$28$	−0.241809	−0.0456976
$29$	2.79186	0.518436	0.259218	−	0.965819i	$-0.416535\pi$
$29$	2.79186	0.518436	0.259218	+	0.965819i	$0.416535\pi$
$30$	2.31088	0.421908
$31$	3.74049	0.671812	0.335906	−	0.941896i	$-0.390958\pi$
$31$	3.74049	0.671812	0.335906	+	0.941896i	$0.390958\pi$
$32$	0.290544	0.0513614
$33$	0	0
$34$	7.41363	1.27143
$35$	−4.70682	−0.795597
$36$	0.0133322	0.00222203
$37$	−0.791864	−0.130182	−0.0650908	−	0.997879i	$-0.520734\pi$
$37$	−0.791864	−0.130182	−0.0650908	+	0.997879i	$0.520734\pi$
$38$	3.15412	0.511666
$39$	−8.36226	−1.33903
$40$	2.86358	0.452772
$41$	−6.15412	−0.961112	−0.480556	−	0.876964i	$-0.659565\pi$
$41$	−6.15412	−0.961112	−0.480556	+	0.876964i	$0.659565\pi$
$42$	−10.8769	−1.67834
$43$	−2.70682	−0.412786	−0.206393	−	0.978469i	$-0.566172\pi$
$43$	−2.70682	−0.412786	−0.206393	+	0.978469i	$0.566172\pi$
$44$	0	0
$45$	0.259511	0.0386855
$46$	1.46765	0.216393
$47$	−11.2392	−1.63940	−0.819701	−	0.572792i	$-0.805860\pi$
$47$	−11.2392	−1.63940	−0.819701	+	0.572792i	$0.805860\pi$
$48$	6.44731	0.930588
$49$	15.1541	2.16487
$50$	1.39593	0.197415
$51$	−8.79186	−1.23111
$52$	−0.259511	−0.0359876
$53$	1.05137	0.144417	0.0722087	−	0.997390i	$-0.476995\pi$
$53$	1.05137	0.144417	0.0722087	+	0.997390i	$0.476995\pi$
$54$	7.53235	1.02502
$55$	0	0
$56$	−13.4783	−1.80112
$57$	−3.74049	−0.495440
$58$	3.89725	0.511734
$59$	4.53235	0.590062	0.295031	−	0.955488i	$-0.404670\pi$
$59$	4.53235	0.590062	0.295031	+	0.955488i	$0.404670\pi$
$60$	−0.0850471	−0.0109795
$61$	9.88128	1.26517	0.632584	−	0.774492i	$-0.281994\pi$
$61$	9.88128	1.26517	0.632584	+	0.774492i	$0.281994\pi$
$62$	5.22147	0.663127
$63$	−1.22147	−0.153891
$64$	8.19480	1.02435
$65$	−5.05137	−0.626546
$66$	0	0
$67$	10.4473	1.27634	0.638171	−	0.769895i	$-0.279691\pi$
$67$	10.4473	1.27634	0.638171	+	0.769895i	$0.279691\pi$
$68$	−0.272843	−0.0330870
$69$	−1.74049	−0.209530
$70$	−6.57040	−0.785312
$71$	−1.05137	−0.124775	−0.0623876	−	0.998052i	$-0.519871\pi$
$71$	−1.05137	−0.124775	−0.0623876	+	0.998052i	$0.519871\pi$
$72$	0.743129	0.0875786
$73$	−10.1027	−1.18244	−0.591219	−	0.806511i	$-0.701353\pi$
$73$	−10.1027	−1.18244	−0.591219	+	0.806511i	$0.701353\pi$
$74$	−1.10539	−0.128499
$75$	−1.65544	−0.191154
$76$	−0.116081	−0.0133154
$77$	0	0
$78$	−11.6731	−1.32172
$79$	−9.41363	−1.05912	−0.529558	−	0.848274i	$-0.677642\pi$
$79$	−9.41363	−1.05912	−0.529558	+	0.848274i	$0.677642\pi$
$80$	3.89461	0.435431
$81$	−8.15412	−0.906014
$82$	−8.59074	−0.948688
$83$	−3.15412	−0.346210	−0.173105	−	0.984903i	$-0.555380\pi$
$83$	−3.15412	−0.346210	−0.173105	+	0.984903i	$0.555380\pi$
$84$	0.400301	0.0436764
$85$	−5.31088	−0.576046
$86$	−3.77853	−0.407450
$87$	−4.62177	−0.495506
$88$	0	0
$89$	−12.5164	−1.32673	−0.663367	−	0.748294i	$-0.730873\pi$
$89$	−12.5164	−1.32673	−0.663367	+	0.748294i	$0.730873\pi$
$90$	0.362259	0.0381855
$91$	23.7759	2.49239
$92$	−0.0540136	−0.00563130
$93$	−6.19216	−0.642098
$94$	−15.6891	−1.61821
$95$	−2.25951	−0.231821
$96$	−0.480979	−0.0490897
$97$	−17.7759	−1.80487	−0.902434	−	0.430828i	$-0.858222\pi$
$97$	−17.7759	−1.80487	−0.902434	+	0.430828i	$0.858222\pi$
$98$	21.1541	2.13689
$99$	0	0
$100$	−0.0513742	−0.00513742
$101$	−3.68912	−0.367081	−0.183540	−	0.983012i	$-0.558756\pi$
$101$	−3.68912	−0.367081	−0.183540	+	0.983012i	$0.558756\pi$
$102$	−12.2728	−1.21519
$103$	−0.0133322	−0.00131366	−0.000656828	−	1.00000i	$-0.500209\pi$
$103$	−0.0133322	−0.00131366	−0.000656828		1.00000i	$0.500209\pi$
$104$	−14.4650	−1.41841
$105$	7.79186	0.760408
$106$	1.46765	0.142550
$107$	11.6554	1.12677	0.563387	−	0.826193i	$-0.309498\pi$
$107$	11.6554	1.12677	0.563387	+	0.826193i	$0.309498\pi$
$108$	−0.277212	−0.0266747
$109$	12.9460	1.24000	0.620000	−	0.784602i	$-0.287132\pi$
$109$	12.9460	1.24000	0.620000	+	0.784602i	$0.287132\pi$
$110$	0	0
$111$	1.31088	0.124424
$112$	−18.3312	−1.73214
$113$	−16.6218	−1.56364	−0.781822	−	0.623501i	$-0.785710\pi$
$113$	−16.6218	−1.56364	−0.781822	+	0.623501i	$0.785710\pi$
$114$	−5.22147	−0.489035
$115$	−1.05137	−0.0980412
$116$	−0.143430	−0.0133171
$117$	−1.31088	−0.121191
$118$	6.32686	0.582434
$119$	24.9974	2.29150
$120$	−4.74049	−0.432746
$121$	0	0
$122$	13.7936	1.24881
$123$	10.1878	0.918603
$124$	−0.192165	−0.0172569
$125$	−1.00000	−0.0894427
$126$	−1.70509	−0.151901
$127$	−4.17446	−0.370424	−0.185212	−	0.982699i	$-0.559297\pi$
$127$	−4.17446	−0.370424	−0.185212	+	0.982699i	$0.559297\pi$
$128$	10.8583	0.959747
$129$	4.48098	0.394528
$130$	−7.05137	−0.618446
$131$	8.88128	0.775961	0.387981	−	0.921668i	$-0.373173\pi$
$131$	8.88128	0.775961	0.387981	+	0.921668i	$0.373173\pi$
$132$	0	0
$133$	10.6351	0.922180
$134$	14.5837	1.25984
$135$	−5.39593	−0.464408
$136$	−15.2081	−1.30409
$137$	0.778532	0.0665144	0.0332572	−	0.999447i	$-0.489412\pi$
$137$	0.778532	0.0665144	0.0332572	+	0.999447i	$0.489412\pi$
$138$	−2.42960	−0.206822
$139$	−8.77853	−0.744585	−0.372293	−	0.928115i	$-0.621428\pi$
$139$	−8.77853	−0.744585	−0.372293	+	0.928115i	$0.621428\pi$
$140$	0.241809	0.0204366
$141$	18.6058	1.56689
$142$	−1.46765	−0.123162
$143$	0	0
$144$	1.01069	0.0842244
$145$	−2.79186	−0.231852
$146$	−14.1027	−1.16715
$147$	−25.0868	−2.06912
$148$	0.0406814	0.00334399
$149$	10.0514	0.823441	0.411720	−	0.911310i	$-0.364928\pi$
$149$	10.0514	0.823441	0.411720	+	0.911310i	$0.364928\pi$
$150$	−2.31088	−0.188683
$151$	10.6351	0.865472	0.432736	−	0.901521i	$-0.357548\pi$
$151$	10.6351	0.865472	0.432736	+	0.901521i	$0.357548\pi$
$152$	−6.47029	−0.524810
$153$	−1.37823	−0.111423
$154$	0	0
$155$	−3.74049	−0.300443
$156$	0.429605	0.0343959
$157$	−0.519021	−0.0414224	−0.0207112	−	0.999786i	$-0.506593\pi$
$157$	−0.519021	−0.0414224	−0.0207112	+	0.999786i	$0.506593\pi$
$158$	−13.1408	−1.04543
$159$	−1.74049	−0.138030
$160$	−0.290544	−0.0229695
$161$	4.94863	0.390006
$162$	−11.3826	−0.894301
$163$	19.7449	1.54654	0.773268	−	0.634079i	$-0.218621\pi$
$163$	19.7449	1.54654	0.773268	+	0.634079i	$0.218621\pi$
$164$	0.316163	0.0246882
$165$	0	0
$166$	−4.40294	−0.341734
$167$	1.81220	0.140233	0.0701163	−	0.997539i	$-0.477663\pi$
$167$	1.81220	0.140233	0.0701163	+	0.997539i	$0.477663\pi$
$168$	22.3126	1.72146
$169$	12.5164	0.962799
$170$	−7.41363	−0.568600
$171$	−0.586367	−0.0448406
$172$	0.139061	0.0106033
$173$	4.53235	0.344588	0.172294	−	0.985046i	$-0.444882\pi$
$173$	4.53235	0.344588	0.172294	+	0.985046i	$0.444882\pi$
$174$	−6.45168	−0.489100
$175$	4.70682	0.355802
$176$	0	0
$177$	−7.50305	−0.563964
$178$	−17.4720	−1.30958
$179$	0.416273	0.0311137	0.0155568	−	0.999879i	$-0.495048\pi$
$179$	0.416273	0.0311137	0.0155568	+	0.999879i	$0.495048\pi$
$180$	−0.0133322	−0.000993720 0
$181$	−3.79186	−0.281847	−0.140924	−	0.990020i	$-0.545007\pi$
$181$	−3.79186	−0.281847	−0.140924	+	0.990020i	$0.545007\pi$
$182$	33.1895	2.46017
$183$	−16.3579	−1.20921
$184$	−3.01069	−0.221951
$185$	0.791864	0.0582190
$186$	−8.64384	−0.633797
$187$	0	0
$188$	0.577404	0.0421115
$189$	25.3977	1.84741
$190$	−3.15412	−0.228824
$191$	19.7759	1.43093	0.715467	−	0.698647i	$-0.246214\pi$
$191$	19.7759	1.43093	0.715467	+	0.698647i	$0.246214\pi$
$192$	−13.5660	−0.979044
$193$	−8.03540	−0.578401	−0.289200	−	0.957269i	$-0.593389\pi$
$193$	−8.03540	−0.578401	−0.289200	+	0.957269i	$0.593389\pi$
$194$	−24.8139	−1.78154
$195$	8.36226	0.598834
$196$	−0.778532	−0.0556094
$197$	−14.7919	−1.05388	−0.526938	−	0.849904i	$-0.676660\pi$
$197$	−14.7919	−1.05388	−0.526938	+	0.849904i	$0.676660\pi$
$198$	0	0
$199$	−9.16745	−0.649864	−0.324932	−	0.945737i	$-0.605341\pi$
$199$	−9.16745	−0.649864	−0.324932	+	0.945737i	$0.605341\pi$
$200$	−2.86358	−0.202486
$201$	−17.2949	−1.21989
$202$	−5.14975	−0.362335
$203$	13.1408	0.922303
$204$	0.451675	0.0316236
$205$	6.15412	0.429823
$206$	−0.0186108	−0.00129667
$207$	−0.272843	−0.0189639
$208$	−19.6731	−1.36409
$209$	0	0
$210$	10.8769	0.750578
$211$	−8.77853	−0.604339	−0.302170	−	0.953254i	$-0.597711\pi$
$211$	−8.77853	−0.604339	−0.302170	+	0.953254i	$0.597711\pi$
$212$	−0.0540136	−0.00370967
$213$	1.74049	0.119256
$214$	16.2702	1.11221
$215$	2.70682	0.184603
$216$	−15.4517	−1.05135
$217$	17.6058	1.19516
$218$	18.0717	1.22397
$219$	16.7245	1.13014
$220$	0	0
$221$	26.8273	1.80460
$222$	1.82991	0.122815
$223$	23.8069	1.59423	0.797115	−	0.603828i	$-0.206359\pi$
$223$	23.8069	1.59423	0.797115	+	0.603828i	$0.206359\pi$
$224$	1.36754	0.0913725
$225$	−0.259511	−0.0173007
$226$	−23.2029	−1.54343
$227$	8.53672	0.566602	0.283301	−	0.959031i	$-0.408570\pi$
$227$	8.53672	0.566602	0.283301	+	0.959031i	$0.408570\pi$
$228$	0.192165	0.0127264
$229$	−14.8299	−0.979988	−0.489994	−	0.871726i	$-0.663001\pi$
$229$	−14.8299	−0.979988	−0.489994	+	0.871726i	$0.663001\pi$
$230$	−1.46765	−0.0967738
$231$	0	0
$232$	−7.99472	−0.524879
$233$	−6.36226	−0.416805	−0.208403	−	0.978043i	$-0.566826\pi$
$233$	−6.36226	−0.416805	−0.208403	+	0.978043i	$0.566826\pi$
$234$	−1.82991	−0.119625
$235$	11.2392	0.733163
$236$	−0.232846	−0.0151570
$237$	15.5837	1.01227
$238$	34.8946	2.26188
$239$	−4.67578	−0.302451	−0.151226	−	0.988499i	$-0.548322\pi$
$239$	−4.67578	−0.302451	−0.151226	+	0.988499i	$0.548322\pi$
$240$	−6.44731	−0.416172
$241$	7.63510	0.491820	0.245910	−	0.969293i	$-0.420913\pi$
$241$	7.63510	0.491820	0.245910	+	0.969293i	$0.420913\pi$
$242$	0	0
$243$	−2.68912	−0.172507
$244$	−0.507643	−0.0324985
$245$	−15.1541	−0.968161
$246$	14.2215	0.906728
$247$	11.4136	0.726232
$248$	−10.7112	−0.680161
$249$	5.22147	0.330897
$250$	−1.39593	−0.0882865
$251$	−21.4624	−1.35469	−0.677346	−	0.735664i	$-0.736870\pi$
$251$	−21.4624	−1.35469	−0.677346	+	0.735664i	$0.736870\pi$
$252$	0.0627520	0.00395301
$253$	0	0
$254$	−5.82727	−0.365635
$255$	8.79186	0.550568
$256$	−1.23216	−0.0770101
$257$	16.8406	1.05049	0.525244	−	0.850952i	$-0.323974\pi$
$257$	16.8406	1.05049	0.525244	+	0.850952i	$0.323974\pi$
$258$	6.25514	0.389428
$259$	−3.72716	−0.231594
$260$	0.259511	0.0160942
$261$	−0.724518	−0.0448465
$262$	12.3977	0.765930
$263$	11.2215	0.691945	0.345973	−	0.938245i	$-0.387549\pi$
$263$	11.2215	0.691945	0.345973	+	0.938245i	$0.387549\pi$
$264$	0	0
$265$	−1.05137	−0.0645854
$266$	14.8459	0.910259
$267$	20.7201	1.26805
$268$	−0.536722	−0.0327855
$269$	−12.4270	−0.757685	−0.378843	−	0.925461i	$-0.623678\pi$
$269$	−12.4270	−0.757685	−0.378843	+	0.925461i	$0.623678\pi$
$270$	−7.53235	−0.458404
$271$	17.8299	1.08309	0.541545	−	0.840672i	$-0.317840\pi$
$271$	17.8299	1.08309	0.541545	+	0.840672i	$0.317840\pi$
$272$	−20.6838	−1.25414
$273$	−39.3596	−2.38215
$274$	1.08678	0.0656546
$275$	0	0
$276$	0.0894163	0.00538223
$277$	−17.2081	−1.03394	−0.516968	−	0.856005i	$-0.672940\pi$
$277$	−17.2081	−1.03394	−0.516968	+	0.856005i	$0.672940\pi$
$278$	−12.2542	−0.734960
$279$	−0.970696	−0.0581141
$280$	13.4783	0.805485
$281$	−26.4110	−1.57555	−0.787774	−	0.615965i	$-0.788766\pi$
$281$	−26.4110	−1.57555	−0.787774	+	0.615965i	$0.788766\pi$
$282$	25.9724	1.54664
$283$	−18.2772	−1.08647	−0.543234	−	0.839582i	$-0.682800\pi$
$283$	−18.2772	−1.08647	−0.543234	+	0.839582i	$0.682800\pi$
$284$	0.0540136	0.00320511
$285$	3.74049	0.221567
$286$	0	0
$287$	−28.9663	−1.70983
$288$	−0.0753992	−0.00444294
$289$	11.2055	0.659147
$290$	−3.89725	−0.228854
$291$	29.4270	1.72504
$292$	0.519021	0.0303734
$293$	−25.6325	−1.49746	−0.748732	−	0.662873i	$-0.769337\pi$
$293$	−25.6325	−1.49746	−0.748732	+	0.662873i	$0.769337\pi$
$294$	−35.0194	−2.04237
$295$	−4.53235	−0.263884
$296$	2.26756	0.131799
$297$	0	0
$298$	14.0310	0.812796
$299$	5.31088	0.307136
$300$	0.0850471	0.00491020
$301$	−12.7405	−0.734350
$302$	14.8459	0.854284
$303$	6.10712	0.350845
$304$	−8.79992	−0.504710
$305$	−9.88128	−0.565800
$306$	−1.92392	−0.109983
$307$	−27.3596	−1.56150	−0.780748	−	0.624846i	$-0.785162\pi$
$307$	−27.3596	−1.56150	−0.780748	+	0.624846i	$0.785162\pi$
$308$	0	0
$309$	0.0220706	0.00125555
$310$	−5.22147	−0.296559
$311$	19.5030	1.10592	0.552958	−	0.833209i	$-0.313499\pi$
$311$	19.5030	1.10592	0.552958	+	0.833209i	$0.313499\pi$
$312$	23.9460	1.35567
$313$	−7.53499	−0.425903	−0.212951	−	0.977063i	$-0.568308\pi$
$313$	−7.53499	−0.425903	−0.212951	+	0.977063i	$0.568308\pi$
$314$	−0.724518	−0.0408869
$315$	1.22147	0.0688219
$316$	0.483618	0.0272057
$317$	−11.5837	−0.650607	−0.325303	−	0.945610i	$-0.605466\pi$
$317$	−11.5837	−0.650607	−0.325303	+	0.945610i	$0.605466\pi$
$318$	−2.42960	−0.136245
$319$	0	0
$320$	−8.19480	−0.458103
$321$	−19.2949	−1.07694
$322$	6.90794	0.384965
$323$	12.0000	0.667698
$324$	0.418912	0.0232729
$325$	5.05137	0.280200
$326$	27.5625	1.52654
$327$	−21.4313	−1.18516
$328$	17.6228	0.973057
$329$	−52.9007	−2.91651
$330$	0	0
$331$	18.5324	1.01863	0.509315	−	0.860580i	$-0.329899\pi$
$331$	18.5324	1.01863	0.509315	+	0.860580i	$0.329899\pi$
$332$	0.162041	0.00889314
$333$	0.205497	0.0112612
$334$	2.52971	0.138420
$335$	−10.4473	−0.570797
$336$	30.3463	1.65553
$337$	−7.67314	−0.417983	−0.208991	−	0.977917i	$-0.567018\pi$
$337$	−7.67314	−0.417983	−0.208991	+	0.977917i	$0.567018\pi$
$338$	17.4720	0.950352
$339$	27.5164	1.49448
$340$	0.272843	0.0147970
$341$	0	0
$342$	−0.818528	−0.0442609
$343$	38.3800	2.07232
$344$	7.75118	0.417916
$345$	1.74049	0.0937048
$346$	6.32686	0.340134
$347$	−28.1878	−1.51320	−0.756600	−	0.653878i	$-0.773141\pi$
$347$	−28.1878	−1.51320	−0.756600	+	0.653878i	$0.773141\pi$
$348$	0.237440	0.0127281
$349$	8.89461	0.476118	0.238059	−	0.971251i	$-0.423489\pi$
$349$	8.89461	0.476118	0.238059	+	0.971251i	$0.423489\pi$
$350$	6.57040	0.351202
$351$	27.2569	1.45486
$352$	0	0
$353$	−28.0221	−1.49146	−0.745732	−	0.666246i	$-0.767900\pi$
$353$	−28.0221	−1.49146	−0.745732	+	0.666246i	$0.767900\pi$
$354$	−10.4737	−0.556673
$355$	1.05137	0.0558012
$356$	0.643020	0.0340800
$357$	−41.3817	−2.19015
$358$	0.581088	0.0307115
$359$	11.2569	0.594115	0.297057	−	0.954860i	$-0.403995\pi$
$359$	11.2569	0.594115	0.297057	+	0.954860i	$0.403995\pi$
$360$	−0.743129	−0.0391663
$361$	−13.8946	−0.731295
$362$	−5.29318	−0.278204
$363$	0	0
$364$	−1.22147	−0.0640223
$365$	10.1027	0.528802
$366$	−22.8345	−1.19358
$367$	5.55269	0.289848	0.144924	−	0.989443i	$-0.453706\pi$
$367$	5.55269	0.289848	0.144924	+	0.989443i	$0.453706\pi$
$368$	−4.09469	−0.213451
$369$	1.59706	0.0831396
$370$	1.10539	0.0574664
$371$	4.94863	0.256920
$372$	0.318118	0.0164936
$373$	−6.80520	−0.352360	−0.176180	−	0.984358i	$-0.556374\pi$
$373$	−6.80520	−0.352360	−0.176180	+	0.984358i	$0.556374\pi$
$374$	0	0
$375$	1.65544	0.0854867
$376$	32.1842	1.65978
$377$	14.1027	0.726328
$378$	35.4534	1.82353
$379$	−12.5544	−0.644877	−0.322439	−	0.946590i	$-0.604503\pi$
$379$	−12.5544	−0.644877	−0.322439	+	0.946590i	$0.604503\pi$
$380$	0.116081	0.00595481
$381$	6.91058	0.354040
$382$	27.6058	1.41244
$383$	−36.6705	−1.87378	−0.936888	−	0.349631i	$-0.886307\pi$
$383$	−36.6705	−1.87378	−0.936888	+	0.349631i	$0.886307\pi$
$384$	−17.9753	−0.917298
$385$	0	0
$386$	−11.2169	−0.570924
$387$	0.702447	0.0357074
$388$	0.913223	0.0463619
$389$	6.87864	0.348761	0.174380	−	0.984678i	$-0.444208\pi$
$389$	6.87864	0.348761	0.174380	+	0.984678i	$0.444208\pi$
$390$	11.6731	0.591093
$391$	5.58373	0.282381
$392$	−43.3950	−2.19178
$393$	−14.7024	−0.741640
$394$	−20.6484	−1.04025
$395$	9.41363	0.473651
$396$	0	0
$397$	37.7626	1.89525	0.947624	−	0.319387i	$-0.103477\pi$
$397$	37.7626	1.89525	0.947624	+	0.319387i	$0.103477\pi$
$398$	−12.7971	−0.641463
$399$	−17.6058	−0.881392
$400$	−3.89461	−0.194731
$401$	19.2055	0.959077	0.479538	−	0.877521i	$-0.340804\pi$
$401$	19.2055	0.959077	0.479538	+	0.877521i	$0.340804\pi$
$402$	−24.1425	−1.20412
$403$	18.8946	0.941208
$404$	0.189525	0.00942925
$405$	8.15412	0.405182
$406$	18.3436	0.910380
$407$	0	0
$408$	25.1762	1.24641
$409$	−27.1161	−1.34080	−0.670402	−	0.741998i	$-0.733878\pi$
$409$	−27.1161	−1.34080	−0.670402	+	0.741998i	$0.733878\pi$
$410$	8.59074	0.424266
$411$	−1.28881	−0.0635725
$412$	0.000684929 0	3.37441e−5 0
$413$	21.3330	1.04973
$414$	−0.380870	−0.0187187
$415$	3.15412	0.154830
$416$	1.46765	0.0719573
$417$	14.5324	0.711652
$418$	0	0
$419$	11.9106	0.581870	0.290935	−	0.956743i	$-0.406034\pi$
$419$	11.9106	0.581870	0.290935	+	0.956743i	$0.406034\pi$
$420$	−0.400301	−0.0195327
$421$	−3.19216	−0.155577	−0.0777883	−	0.996970i	$-0.524786\pi$
$421$	−3.19216	−0.155577	−0.0777883	+	0.996970i	$0.524786\pi$
$422$	−12.2542	−0.596527
$423$	2.91668	0.141814
$424$	−3.01069	−0.146212
$425$	5.31088	0.257616
$426$	2.42960	0.117715
$427$	46.5094	2.25075
$428$	−0.598790	−0.0289436
$429$	0	0
$430$	3.77853	0.182217
$431$	36.0354	1.73576	0.867882	−	0.496770i	$-0.165481\pi$
$431$	36.0354	1.73576	0.867882	+	0.496770i	$0.165481\pi$
$432$	−21.0151	−1.01109
$433$	−25.8786	−1.24365	−0.621824	−	0.783157i	$-0.713608\pi$
$433$	−25.8786	−1.24365	−0.621824	+	0.783157i	$0.713608\pi$
$434$	24.5765	1.17971
$435$	4.62177	0.221597
$436$	−0.665090	−0.0318520
$437$	2.37559	0.113640
$438$	23.3463	1.11553
$439$	12.0673	0.575943	0.287971	−	0.957639i	$-0.407019\pi$
$439$	12.0673	0.575943	0.287971	+	0.957639i	$0.407019\pi$
$440$	0	0
$441$	−3.93265	−0.187269
$442$	37.4490	1.78127
$443$	−18.2905	−0.869010	−0.434505	−	0.900669i	$-0.643077\pi$
$443$	−18.2905	−0.869010	−0.434505	+	0.900669i	$0.643077\pi$
$444$	−0.0673457	−0.00319609
$445$	12.5164	0.593333
$446$	33.2328	1.57362
$447$	−16.6395	−0.787020
$448$	38.5714	1.82233
$449$	0.426965	0.0201497	0.0100749	−	0.999949i	$-0.496793\pi$
$449$	0.426965	0.0201497	0.0100749	+	0.999949i	$0.496793\pi$
$450$	−0.362259	−0.0170771
$451$	0	0
$452$	0.853931	0.0401655
$453$	−17.6058	−0.827193
$454$	11.9167	0.559278
$455$	−23.7759	−1.11463
$456$	10.7112	0.501597
$457$	15.3649	0.718740	0.359370	−	0.933195i	$-0.382992\pi$
$457$	15.3649	0.718740	0.359370	+	0.933195i	$0.382992\pi$
$458$	−20.7015	−0.967319
$459$	28.6572	1.33760
$460$	0.0540136	0.00251839
$461$	−20.6191	−0.960329	−0.480164	−	0.877179i	$-0.659423\pi$
$461$	−20.6191	−0.960329	−0.480164	+	0.877179i	$0.659423\pi$
$462$	0	0
$463$	−1.64211	−0.0763153	−0.0381577	−	0.999272i	$-0.512149\pi$
$463$	−1.64211	−0.0763153	−0.0381577	+	0.999272i	$0.512149\pi$
$464$	−10.8732	−0.504777
$465$	6.19216	0.287155
$466$	−8.88128	−0.411417
$467$	−3.13642	−0.145136	−0.0725681	−	0.997363i	$-0.523119\pi$
$467$	−3.13642	−0.145136	−0.0725681	+	0.997363i	$0.523119\pi$
$468$	0.0673457	0.00311306
$469$	49.1736	2.27062
$470$	15.6891	0.723685
$471$	0.859209	0.0395903
$472$	−12.9787	−0.597395
$473$	0	0
$474$	21.7538	0.999186
$475$	2.25951	0.103673
$476$	−1.28422	−0.0588621
$477$	−0.272843	−0.0124926
$478$	−6.52707	−0.298541
$479$	9.93265	0.453835	0.226917	−	0.973914i	$-0.427135\pi$
$479$	9.93265	0.453835	0.226917	+	0.973914i	$0.427135\pi$
$480$	0.480979	0.0219536
$481$	−4.00000	−0.182384
$482$	10.6581	0.485462
$483$	−8.19216	−0.372756
$484$	0	0
$485$	17.7759	0.807162
$486$	−3.75382	−0.170277
$487$	4.84588	0.219588	0.109794	−	0.993954i	$-0.464981\pi$
$487$	4.84588	0.219588	0.109794	+	0.993954i	$0.464981\pi$
$488$	−28.2958	−1.28089
$489$	−32.6865	−1.47813
$490$	−21.1541	−0.955646
$491$	−10.4783	−0.472881	−0.236440	−	0.971646i	$-0.575981\pi$
$491$	−10.4783	−0.472881	−0.236440	+	0.971646i	$0.575981\pi$
$492$	−0.523390	−0.0235963
$493$	14.8273	0.667786
$494$	15.9327	0.716844
$495$	0	0
$496$	−14.5678	−0.654112
$497$	−4.94863	−0.221976
$498$	7.28881	0.326620
$499$	−14.9300	−0.668359	−0.334180	−	0.942509i	$-0.608459\pi$
$499$	−14.9300	−0.668359	−0.334180	+	0.942509i	$0.608459\pi$
$500$	0.0513742	0.00229753
$501$	−3.00000	−0.134030
$502$	−29.9600	−1.33718
$503$	−39.1718	−1.74659	−0.873293	−	0.487196i	$-0.838020\pi$
$503$	−39.1718	−1.74659	−0.873293	+	0.487196i	$0.838020\pi$
$504$	3.49777	0.155803
$505$	3.68912	0.164163
$506$	0	0
$507$	−20.7201	−0.920214
$508$	0.214460	0.00951512
$509$	−16.9593	−0.751709	−0.375854	−	0.926679i	$-0.622651\pi$
$509$	−16.9593	−0.751709	−0.375854	+	0.926679i	$0.622651\pi$
$510$	12.2728	0.543451
$511$	−47.5518	−2.10357
$512$	−23.4366	−1.03576
$513$	12.1922	0.538297
$514$	23.5083	1.03691
$515$	0.0133322	0.000587485 0
$516$	−0.230207	−0.0101343
$517$	0	0
$518$	−5.20286	−0.228600
$519$	−7.50305	−0.329347
$520$	14.4650	0.634333
$521$	−25.6572	−1.12406	−0.562031	−	0.827116i	$-0.689980\pi$
$521$	−25.6572	−1.12406	−0.562031	+	0.827116i	$0.689980\pi$
$522$	−1.01138	−0.0442668
$523$	3.94599	0.172546	0.0862730	−	0.996272i	$-0.472504\pi$
$523$	3.94599	0.172546	0.0862730	+	0.996272i	$0.472504\pi$
$524$	−0.456269	−0.0199322
$525$	−7.79186	−0.340065
$526$	15.6644	0.683001
$527$	19.8653	0.865346
$528$	0	0
$529$	−21.8946	−0.951940
$530$	−1.46765	−0.0637505
$531$	−1.17619	−0.0510424
$532$	−0.546370	−0.0236882
$533$	−31.0868	−1.34652
$534$	28.9239	1.25166
$535$	−11.6554	−0.503909
$536$	−29.9167	−1.29220
$537$	−0.689115	−0.0297375
$538$	−17.3472	−0.747891
$539$	0	0
$540$	0.277212	0.0119293
$541$	−45.3843	−1.95122	−0.975612	−	0.219501i	$-0.929557\pi$
$541$	−45.3843	−1.95122	−0.975612	+	0.219501i	$0.929557\pi$
$542$	24.8893	1.06909
$543$	6.27721	0.269381
$544$	1.54305	0.0661576
$545$	−12.9460	−0.554545
$546$	−54.9433	−2.35136
$547$	−17.4624	−0.746637	−0.373318	−	0.927703i	$-0.621780\pi$
$547$	−17.4624	−0.746637	−0.373318	+	0.927703i	$0.621780\pi$
$548$	−0.0399965	−0.00170856
$549$	−2.56430	−0.109441
$550$	0	0
$551$	6.30825	0.268740
$552$	4.98403	0.212134
$553$	−44.3082	−1.88418
$554$	−24.0214	−1.02057
$555$	−1.31088	−0.0556440
$556$	0.450990	0.0191263
$557$	25.8299	1.09445	0.547224	−	0.836986i	$-0.315685\pi$
$557$	25.8299	1.09445	0.547224	+	0.836986i	$0.315685\pi$
$558$	−1.35503	−0.0573628
$559$	−13.6731	−0.578312
$560$	18.3312	0.774636
$561$	0	0
$562$	−36.8679	−1.55518
$563$	−10.7335	−0.452362	−0.226181	−	0.974085i	$-0.572624\pi$
$563$	−10.7335	−0.452362	−0.226181	+	0.974085i	$0.572624\pi$
$564$	−0.955859	−0.0402489
$565$	16.6218	0.699283
$566$	−25.5137	−1.07242
$567$	−38.3800	−1.61181
$568$	3.01069	0.126326
$569$	26.4003	1.10676	0.553379	−	0.832930i	$-0.313338\pi$
$569$	26.4003	1.10676	0.553379	+	0.832930i	$0.313338\pi$
$570$	5.22147	0.218703
$571$	−2.45168	−0.102599	−0.0512997	−	0.998683i	$-0.516336\pi$
$571$	−2.45168	−0.102599	−0.0512997	+	0.998683i	$0.516336\pi$
$572$	0	0
$573$	−32.7379	−1.36764
$574$	−40.4350	−1.68773
$575$	1.05137	0.0438453
$576$	−2.12664	−0.0886099
$577$	27.3950	1.14047	0.570235	−	0.821482i	$-0.306852\pi$
$577$	27.3950	1.14047	0.570235	+	0.821482i	$0.306852\pi$
$578$	15.6421	0.650626
$579$	13.3021	0.552818
$580$	0.143430	0.00595560
$581$	−14.8459	−0.615911
$582$	41.0780	1.70274
$583$	0	0
$584$	28.9300	1.19713
$585$	1.31088	0.0541984
$586$	−35.7812	−1.47811
$587$	14.1559	0.584275	0.292137	−	0.956376i	$-0.405634\pi$
$587$	14.1559	0.584275	0.292137	+	0.956376i	$0.405634\pi$
$588$	1.28881	0.0531498
$589$	8.45168	0.348245
$590$	−6.32686	−0.260473
$591$	24.4871	1.00726
$592$	3.08400	0.126752
$593$	23.0194	0.945295	0.472647	−	0.881252i	$-0.343298\pi$
$593$	23.0194	0.945295	0.472647	+	0.881252i	$0.343298\pi$
$594$	0	0
$595$	−24.9974	−1.02479
$596$	−0.516382	−0.0211518
$597$	15.1762	0.621120
$598$	7.41363	0.303166
$599$	7.32422	0.299259	0.149630	−	0.988742i	$-0.452192\pi$
$599$	7.32422	0.299259	0.149630	+	0.988742i	$0.452192\pi$
$600$	4.74049	0.193530
$601$	13.9327	0.568325	0.284162	−	0.958776i	$-0.408285\pi$
$601$	13.9327	0.568325	0.284162	+	0.958776i	$0.408285\pi$
$602$	−17.7849	−0.724857
$603$	−2.71119	−0.110408
$604$	−0.546370	−0.0222315
$605$	0	0
$606$	8.52512	0.346309
$607$	11.1948	0.454383	0.227192	−	0.973850i	$-0.427046\pi$
$607$	11.1948	0.454383	0.227192	+	0.973850i	$0.427046\pi$
$608$	0.656487	0.0266241
$609$	−21.7538	−0.881509
$610$	−13.7936	−0.558486
$611$	−56.7733	−2.29680
$612$	0.0708055	0.00286214
$613$	−12.8946	−0.520808	−0.260404	−	0.965500i	$-0.583856\pi$
$613$	−12.8946	−0.520808	−0.260404	+	0.965500i	$0.583856\pi$
$614$	−38.1922	−1.54131
$615$	−10.1878	−0.410812
$616$	0	0
$617$	20.8813	0.840649	0.420324	−	0.907374i	$-0.361916\pi$
$617$	20.8813	0.840649	0.420324	+	0.907374i	$0.361916\pi$
$618$	0.0308091	0.00123932
$619$	22.9353	0.921847	0.460924	−	0.887440i	$-0.347518\pi$
$619$	22.9353	0.921847	0.460924	+	0.887440i	$0.347518\pi$
$620$	0.192165	0.00771752
$621$	5.67314	0.227655
$622$	27.2249	1.09162
$623$	−58.9123	−2.36027
$624$	32.5678	1.30375
$625$	1.00000	0.0400000
$626$	−10.5183	−0.420397
$627$	0	0
$628$	0.0266643	0.00106402
$629$	−4.20550	−0.167684
$630$	1.70509	0.0679323
$631$	16.5190	0.657612	0.328806	−	0.944398i	$-0.393354\pi$
$631$	16.5190	0.657612	0.328806	+	0.944398i	$0.393354\pi$
$632$	26.9567	1.07228
$633$	14.5324	0.577609
$634$	−16.1701	−0.642196
$635$	4.17446	0.165659
$636$	0.0894163	0.00354559
$637$	76.5491	3.03299
$638$	0	0
$639$	0.272843	0.0107935
$640$	−10.8583	−0.429212
$641$	19.5571	0.772458	0.386229	−	0.922403i	$-0.373778\pi$
$641$	19.5571	0.772458	0.386229	+	0.922403i	$0.373778\pi$
$642$	−26.9344	−1.06302
$643$	−1.22584	−0.0483423	−0.0241712	−	0.999708i	$-0.507695\pi$
$643$	−1.22584	−0.0483423	−0.0241712	+	0.999708i	$0.507695\pi$
$644$	−0.254232	−0.0100181
$645$	−4.48098	−0.176438
$646$	16.7512	0.659066
$647$	7.43133	0.292156	0.146078	−	0.989273i	$-0.453335\pi$
$647$	7.43133	0.292156	0.146078	+	0.989273i	$0.453335\pi$
$648$	23.3500	0.917274
$649$	0	0
$650$	7.05137	0.276578
$651$	−29.1454	−1.14230
$652$	−1.01438	−0.0397261
$653$	−42.3436	−1.65704	−0.828518	−	0.559963i	$-0.810815\pi$
$653$	−42.3436	−1.65704	−0.828518	+	0.559963i	$0.810815\pi$
$654$	−29.9167	−1.16983
$655$	−8.88128	−0.347020
$656$	23.9679	0.935790
$657$	2.62177	0.102285
$658$	−73.8458	−2.87881
$659$	35.4897	1.38248	0.691242	−	0.722624i	$-0.257064\pi$
$659$	35.4897	1.38248	0.691242	+	0.722624i	$0.257064\pi$
$660$	0	0
$661$	−19.2188	−0.747526	−0.373763	−	0.927524i	$-0.621933\pi$
$661$	−19.2188	−0.747526	−0.373763	+	0.927524i	$0.621933\pi$
$662$	25.8699	1.00546
$663$	−44.4110	−1.72478
$664$	9.03208	0.350513
$665$	−10.6351	−0.412412
$666$	0.286860	0.0111156
$667$	2.93529	0.113655
$668$	−0.0931006	−0.00360217
$669$	−39.4110	−1.52372
$670$	−14.5837	−0.563419
$671$	0	0
$672$	−2.26388	−0.0873311
$673$	43.4624	1.67535	0.837676	−	0.546168i	$-0.183914\pi$
$673$	43.4624	1.67535	0.837676	+	0.546168i	$0.183914\pi$
$674$	−10.7112	−0.412579
$675$	5.39593	0.207690
$676$	−0.643020	−0.0247315
$677$	−17.5837	−0.675798	−0.337899	−	0.941182i	$-0.609716\pi$
$677$	−17.5837	−0.675798	−0.337899	+	0.941182i	$0.609716\pi$
$678$	38.4110	1.47517
$679$	−83.6679	−3.21088
$680$	15.2081	0.583205
$681$	−14.1321	−0.541541
$682$	0	0
$683$	12.0177	0.459845	0.229922	−	0.973209i	$-0.426153\pi$
$683$	12.0177	0.459845	0.229922	+	0.973209i	$0.426153\pi$
$684$	0.0301241	0.00115183
$685$	−0.778532	−0.0297462
$686$	53.5758	2.04553
$687$	24.5501	0.936643
$688$	10.5420	0.401910
$689$	5.31088	0.202329
$690$	2.42960	0.0924935
$691$	34.9167	1.32829	0.664147	−	0.747602i	$-0.268795\pi$
$691$	34.9167	1.32829	0.664147	+	0.747602i	$0.268795\pi$
$692$	−0.232846	−0.00885148
$693$	0	0
$694$	−39.3482	−1.49364
$695$	8.77853	0.332989
$696$	13.2348	0.501664
$697$	−32.6838	−1.23799
$698$	12.4163	0.469963
$699$	10.5324	0.398370
$700$	−0.241809	−0.00913953
$701$	−17.4403	−0.658711	−0.329355	−	0.944206i	$-0.606831\pi$
$701$	−17.4403	−0.658711	−0.329355	+	0.944206i	$0.606831\pi$
$702$	38.0487	1.43606
$703$	−1.78922	−0.0674819
$704$	0	0
$705$	−18.6058	−0.700735
$706$	−39.1169	−1.47218
$707$	−17.3640	−0.653040
$708$	0.385463	0.0144866
$709$	51.8220	1.94622	0.973108	−	0.230350i	$-0.0739872\pi$
$709$	51.8220	1.94622	0.973108	+	0.230350i	$0.0739872\pi$
$710$	1.46765	0.0550798
$711$	2.44294	0.0916173
$712$	35.8416	1.34322
$713$	3.93265	0.147279
$714$	−57.7660	−2.16184
$715$	0	0
$716$	−0.0213857	−0.000799221 0
$717$	7.74049	0.289074
$718$	15.7138	0.586435
$719$	−26.9167	−1.00382	−0.501911	−	0.864919i	$-0.667370\pi$
$719$	−26.9167	−1.00382	−0.501911	+	0.864919i	$0.667370\pi$
$720$	−1.01069	−0.0376663
$721$	−0.0627520	−0.00233701
$722$	−19.3959	−0.721842
$723$	−12.6395	−0.470067
$724$	0.194804	0.00723984
$725$	2.79186	0.103687
$726$	0	0
$727$	−21.7449	−0.806472	−0.403236	−	0.915096i	$-0.632115\pi$
$727$	−21.7449	−0.806472	−0.403236	+	0.915096i	$0.632115\pi$
$728$	−68.0841	−2.52337
$729$	28.9140	1.07089
$730$	14.1027	0.521966
$731$	−14.3756	−0.531700
$732$	0.840374	0.0310611
$733$	4.81853	0.177976	0.0889882	−	0.996033i	$-0.471637\pi$
$733$	4.81853	0.177976	0.0889882	+	0.996033i	$0.471637\pi$
$734$	7.75118	0.286101
$735$	25.0868	0.925340
$736$	0.305471	0.0112598
$737$	0	0
$738$	2.22939	0.0820648
$739$	−48.2409	−1.77457	−0.887285	−	0.461221i	$-0.847411\pi$
$739$	−48.2409	−1.77457	−0.887285	+	0.461221i	$0.847411\pi$
$740$	−0.0406814	−0.00149548
$741$	−18.8946	−0.694111
$742$	6.90794	0.253599
$743$	−26.7910	−0.982865	−0.491432	−	0.870916i	$-0.663527\pi$
$743$	−26.7910	−0.982865	−0.491432	+	0.870916i	$0.663527\pi$
$744$	17.7318	0.650078
$745$	−10.0514	−0.368254
$746$	−9.49959	−0.347805
$747$	0.818528	0.0299484
$748$	0	0
$749$	54.8600	2.00454
$750$	2.31088	0.0843816
$751$	0.442937	0.0161630	0.00808150	−	0.999967i	$-0.497428\pi$
$751$	0.442937	0.0161630	0.00808150	+	0.999967i	$0.497428\pi$
$752$	43.7722	1.59621
$753$	35.5297	1.29477
$754$	19.6865	0.716939
$755$	−10.6351	−0.387051
$756$	−1.30479	−0.0474546
$757$	27.6325	1.00432	0.502159	−	0.864775i	$-0.332539\pi$
$757$	27.6325	1.00432	0.502159	+	0.864775i	$0.332539\pi$
$758$	−17.5251	−0.636541
$759$	0	0
$760$	6.47029	0.234702
$761$	1.86531	0.0676174	0.0338087	−	0.999428i	$-0.489236\pi$
$761$	1.86531	0.0676174	0.0338087	+	0.999428i	$0.489236\pi$
$762$	9.64670	0.349463
$763$	60.9344	2.20597
$764$	−1.01597	−0.0367566
$765$	1.37823	0.0498300
$766$	−51.1895	−1.84955
$767$	22.8946	0.826677
$768$	2.03977	0.0736039
$769$	−47.5872	−1.71604	−0.858019	−	0.513618i	$-0.828305\pi$
$769$	−47.5872	−1.71604	−0.858019	+	0.513618i	$0.828305\pi$
$770$	0	0
$771$	−27.8786	−1.00402
$772$	0.412813	0.0148575
$773$	42.0168	1.51124	0.755619	−	0.655011i	$-0.227336\pi$
$773$	42.0168	1.51124	0.755619	+	0.655011i	$0.227336\pi$
$774$	0.980569	0.0352458
$775$	3.74049	0.134362
$776$	50.9027	1.82730
$777$	6.17009	0.221351
$778$	9.60211	0.344252
$779$	−13.9053	−0.498209
$780$	−0.429605	−0.0153823
$781$	0	0
$782$	7.79450	0.278731
$783$	15.0647	0.538369
$784$	−59.0194	−2.10784
$785$	0.519021	0.0185247
$786$	−20.5236	−0.732053
$787$	−17.4093	−0.620573	−0.310287	−	0.950643i	$-0.600425\pi$
$787$	−17.4093	−0.620573	−0.310287	+	0.950643i	$0.600425\pi$
$788$	0.759921	0.0270711
$789$	−18.5765	−0.661341
$790$	13.1408	0.467528
$791$	−78.2356	−2.78174
$792$	0	0
$793$	49.9140	1.77250
$794$	52.7140	1.87075
$795$	1.74049	0.0617288
$796$	0.470971	0.0166931
$797$	5.94599	0.210618	0.105309	−	0.994440i	$-0.466417\pi$
$797$	5.94599	0.210618	0.105309	+	0.994440i	$0.466417\pi$
$798$	−24.5765	−0.869998
$799$	−59.6899	−2.11168
$800$	0.290544	0.0102723
$801$	3.24813	0.114767
$802$	26.8096	0.946679
$803$	0	0
$804$	0.888513	0.0313354
$805$	−4.94863	−0.174416
$806$	26.3756	0.929041
$807$	20.5721	0.724173
$808$	10.5641	0.371643
$809$	−20.3756	−0.716368	−0.358184	−	0.933651i	$-0.616604\pi$
$809$	−20.3756	−0.716368	−0.358184	+	0.933651i	$0.616604\pi$
$810$	11.3826	0.399944
$811$	3.22147	0.113121	0.0565605	−	0.998399i	$-0.481987\pi$
$811$	3.22147	0.113121	0.0565605	+	0.998399i	$0.481987\pi$
$812$	−0.675098	−0.0236913
$813$	−29.5164	−1.03518
$814$	0	0
$815$	−19.7449	−0.691632
$816$	34.2409	1.19867
$817$	−6.11608	−0.213975
$818$	−37.8522	−1.32347
$819$	−6.17009	−0.215601
$820$	−0.316163	−0.0110409
$821$	−5.91668	−0.206494	−0.103247	−	0.994656i	$-0.532923\pi$
$821$	−5.91668	−0.206494	−0.103247	+	0.994656i	$0.532923\pi$
$822$	−1.79910	−0.0627507
$823$	12.8229	0.446978	0.223489	−	0.974706i	$-0.428255\pi$
$823$	12.8229	0.446978	0.223489	+	0.974706i	$0.428255\pi$
$824$	0.0381777	0.00132998
$825$	0	0
$826$	29.7794	1.03616
$827$	39.4801	1.37286	0.686428	−	0.727198i	$-0.259178\pi$
$827$	39.4801	1.37286	0.686428	+	0.727198i	$0.259178\pi$
$828$	0.0140171	0.000487127 0
$829$	22.6731	0.787471	0.393735	−	0.919224i	$-0.371183\pi$
$829$	22.6731	0.787471	0.393735	+	0.919224i	$0.371183\pi$
$830$	4.40294	0.152828
$831$	28.4871	0.988206
$832$	41.3950	1.43511
$833$	80.4818	2.78853
$834$	20.2862	0.702453
$835$	−1.81220	−0.0627139
$836$	0	0
$837$	20.1834	0.697641
$838$	16.6264	0.574348
$839$	−44.2816	−1.52877	−0.764385	−	0.644760i	$-0.776957\pi$
$839$	−44.2816	−1.52877	−0.764385	+	0.644760i	$0.776957\pi$
$840$	−22.3126	−0.769858
$841$	−21.2055	−0.731224
$842$	−4.45604	−0.153565
$843$	43.7219	1.50586
$844$	0.450990	0.0155237
$845$	−12.5164	−0.430577
$846$	4.07149	0.139981
$847$	0	0
$848$	−4.09469	−0.140612
$849$	30.2569	1.03841
$850$	7.41363	0.254286
$851$	−0.832545	−0.0285393
$852$	−0.0894163	−0.00306335
$853$	37.7892	1.29388	0.646939	−	0.762542i	$-0.276049\pi$
$853$	37.7892	1.29388	0.646939	+	0.762542i	$0.276049\pi$
$854$	64.9239	2.22165
$855$	0.586367	0.0200533
$856$	−33.3763	−1.14078
$857$	−12.0354	−0.411122	−0.205561	−	0.978644i	$-0.565902\pi$
$857$	−12.0354	−0.411122	−0.205561	+	0.978644i	$0.565902\pi$
$858$	0	0
$859$	24.9486	0.851236	0.425618	−	0.904903i	$-0.360057\pi$
$859$	24.9486	0.851236	0.425618	+	0.904903i	$0.360057\pi$
$860$	−0.139061	−0.00474193
$861$	47.9521	1.63420
$862$	50.3030	1.71333
$863$	−56.9698	−1.93927	−0.969637	−	0.244549i	$-0.921360\pi$
$863$	−56.9698	−1.93927	−0.969637	+	0.244549i	$0.921360\pi$
$864$	1.56776	0.0533361
$865$	−4.53235	−0.154105
$866$	−36.1248	−1.22757
$867$	−18.5501	−0.629993
$868$	−0.904485	−0.0307002
$869$	0	0
$870$	6.45168	0.218732
$871$	52.7733	1.78815
$872$	−37.0719	−1.25541
$873$	4.61303	0.156127
$874$	3.31616	0.112171
$875$	−4.70682	−0.159119
$876$	−0.859209	−0.0290300
$877$	−58.3570	−1.97058	−0.985288	−	0.170904i	$-0.945331\pi$
$877$	−58.3570	−1.97058	−0.985288	+	0.170904i	$0.945331\pi$
$878$	16.8452	0.568498
$879$	42.4331	1.43123
$880$	0	0
$881$	−31.7466	−1.06957	−0.534785	−	0.844988i	$-0.679607\pi$
$881$	−31.7466	−1.06957	−0.534785	+	0.844988i	$0.679607\pi$
$882$	−5.48972	−0.184848
$883$	26.0894	0.877979	0.438989	−	0.898492i	$-0.355337\pi$
$883$	26.0894	0.877979	0.438989	+	0.898492i	$0.355337\pi$
$884$	−1.37823	−0.0463549
$885$	7.50305	0.252212
$886$	−25.5324	−0.857776
$887$	11.8743	0.398699	0.199350	−	0.979928i	$-0.436117\pi$
$887$	11.8743	0.398699	0.199350	+	0.979928i	$0.436117\pi$
$888$	−3.75382	−0.125970
$889$	−19.6484	−0.658987
$890$	17.4720	0.585663
$891$	0	0
$892$	−1.22306	−0.0409512
$893$	−25.3950	−0.849812
$894$	−23.2276	−0.776846
$895$	−0.416273	−0.0139145
$896$	51.1080	1.70740
$897$	−8.79186	−0.293552
$898$	0.596015	0.0198893
$899$	10.4429	0.348291
$900$	0.0133322	0.000444405 0
$901$	5.58373	0.186021
$902$	0	0
$903$	21.0911	0.701869
$904$	47.5977	1.58308
$905$	3.79186	0.126046
$906$	−24.5765	−0.816499
$907$	−1.53408	−0.0509384	−0.0254692	−	0.999676i	$-0.508108\pi$
$907$	−1.53408	−0.0509384	−0.0254692	+	0.999676i	$0.508108\pi$
$908$	−0.438568	−0.0145544
$909$	0.957364	0.0317538
$910$	−33.1895	−1.10022
$911$	32.3756	1.07265	0.536326	−	0.844011i	$-0.319812\pi$
$911$	32.3756	1.07265	0.536326	+	0.844011i	$0.319812\pi$
$912$	14.5678	0.482387
$913$	0	0
$914$	21.4484	0.709448
$915$	16.3579	0.540775
$916$	0.761875	0.0251731
$917$	41.8026	1.38044
$918$	40.0035	1.32031
$919$	35.2302	1.16214	0.581069	−	0.813855i	$-0.302635\pi$
$919$	35.2302	1.16214	0.581069	+	0.813855i	$0.302635\pi$
$920$	3.01069	0.0992596
$921$	45.2923	1.49243
$922$	−28.7829	−0.947914
$923$	−5.31088	−0.174810
$924$	0	0
$925$	−0.791864	−0.0260363
$926$	−2.29227	−0.0753288
$927$	0.00345983	0.000113636 0
$928$	0.811159	0.0266276
$929$	−4.51374	−0.148091	−0.0740455	−	0.997255i	$-0.523591\pi$
$929$	−4.51374	−0.148091	−0.0740455	+	0.997255i	$0.523591\pi$
$930$	8.64384	0.283443
$931$	34.2409	1.12220
$932$	0.326856	0.0107065
$933$	−32.2862	−1.05700
$934$	−4.37823	−0.143260
$935$	0	0
$936$	3.75382	0.122697
$937$	11.7219	0.382937	0.191469	−	0.981499i	$-0.438675\pi$
$937$	11.7219	0.382937	0.191469	+	0.981499i	$0.438675\pi$
$938$	68.6429	2.24127
$939$	12.4737	0.407065
$940$	−0.577404	−0.0188328
$941$	39.0708	1.27367	0.636836	−	0.770999i	$-0.280243\pi$
$941$	39.0708	1.27367	0.636836	+	0.770999i	$0.280243\pi$
$942$	1.19940	0.0390785
$943$	−6.47029	−0.210702
$944$	−17.6518	−0.574516
$945$	−25.3977	−0.826186
$946$	0	0
$947$	26.7733	0.870014	0.435007	−	0.900427i	$-0.356746\pi$
$947$	26.7733	0.870014	0.435007	+	0.900427i	$0.356746\pi$
$948$	−0.800602	−0.0260024
$949$	−51.0328	−1.65659
$950$	3.15412	0.102333
$951$	19.1762	0.621831
$952$	−71.5819	−2.31998
$953$	11.4403	0.370588	0.185294	−	0.982683i	$-0.440676\pi$
$953$	11.4403	0.370588	0.185294	+	0.982683i	$0.440676\pi$
$954$	−0.380870	−0.0123311
$955$	−19.7759	−0.639933
$956$	0.240215	0.00776910
$957$	0	0
$958$	13.8653	0.447968
$959$	3.66441	0.118330
$960$	13.5660	0.437842
$961$	−17.0087	−0.548669
$962$	−5.58373	−0.180027
$963$	−3.02471	−0.0974699
$964$	−0.392248	−0.0126334
$965$	8.03540	0.258669
$966$	−11.4357	−0.367938
$967$	−3.28881	−0.105761	−0.0528806	−	0.998601i	$-0.516840\pi$
$967$	−3.28881	−0.105761	−0.0528806	+	0.998601i	$0.516840\pi$
$968$	0	0
$969$	−19.8653	−0.638166
$970$	24.8139	0.796727
$971$	38.5544	1.23727	0.618635	−	0.785678i	$-0.287686\pi$
$971$	38.5544	1.23727	0.618635	+	0.785678i	$0.287686\pi$
$972$	0.138151	0.00443120
$973$	−41.3189	−1.32462
$974$	6.76451	0.216749
$975$	−8.36226	−0.267807
$976$	−38.4838	−1.23183
$977$	53.3817	1.70783	0.853916	−	0.520411i	$-0.174221\pi$
$977$	53.3817	1.70783	0.853916	+	0.520411i	$0.174221\pi$
$978$	−45.6281	−1.45903
$979$	0	0
$980$	0.778532	0.0248693
$981$	−3.35962	−0.107264
$982$	−14.6270	−0.466768
$983$	21.4801	0.685108	0.342554	−	0.939498i	$-0.388708\pi$
$983$	21.4801	0.685108	0.342554	+	0.939498i	$0.388708\pi$
$984$	−29.1736	−0.930019
$985$	14.7919	0.471308
$986$	20.6979	0.659154
$987$	87.5741	2.78751
$988$	−0.586367	−0.0186548
$989$	−2.84588	−0.0904936
$990$	0	0
$991$	−2.87600	−0.0913592	−0.0456796	−	0.998956i	$-0.514545\pi$
$991$	−2.87600	−0.0913592	−0.0456796	+	0.998956i	$0.514545\pi$
$992$	1.08678	0.0345052
$993$	−30.6792	−0.973576
$994$	−6.90794	−0.219107
$995$	9.16745	0.290628
$996$	−0.268249	−0.00849979
$997$	−12.9132	−0.408966	−0.204483	−	0.978870i	$-0.565551\pi$
$997$	−12.9132	−0.408966	−0.204483	+	0.978870i	$0.565551\pi$
$998$	−20.8413	−0.659719
$999$	−4.27284	−0.135187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.h.1.2	yes	3
3.2	odd	2		5445.2.a.bb.1.2		3
4.3	odd	2		9680.2.a.cb.1.3		3
5.4	even	2		3025.2.a.p.1.2		3
11.2	odd	10		605.2.g.p.81.2		12
11.3	even	5		605.2.g.o.251.2		12
11.4	even	5		605.2.g.o.511.2		12
11.5	even	5		605.2.g.o.366.2		12
11.6	odd	10		605.2.g.p.366.2		12
11.7	odd	10		605.2.g.p.511.2		12
11.8	odd	10		605.2.g.p.251.2		12
11.9	even	5		605.2.g.o.81.2		12
11.10	odd	2		605.2.a.g.1.2	✓	3
33.32	even	2		5445.2.a.bd.1.2		3
44.43	even	2		9680.2.a.bz.1.3		3
55.54	odd	2		3025.2.a.u.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.g.1.2	✓	3	11.10	odd	2
605.2.a.h.1.2	yes	3	1.1	even	1	trivial
605.2.g.o.81.2		12	11.9	even	5
605.2.g.o.251.2		12	11.3	even	5
605.2.g.o.366.2		12	11.5	even	5
605.2.g.o.511.2		12	11.4	even	5
605.2.g.p.81.2		12	11.2	odd	10
605.2.g.p.251.2		12	11.8	odd	10
605.2.g.p.366.2		12	11.6	odd	10
605.2.g.p.511.2		12	11.7	odd	10
3025.2.a.p.1.2		3	5.4	even	2
3025.2.a.u.1.2		3	55.54	odd	2
5445.2.a.bb.1.2		3	3.2	odd	2
5445.2.a.bd.1.2		3	33.32	even	2
9680.2.a.bz.1.3		3	44.43	even	2
9680.2.a.cb.1.3		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q+1.39593 q^{2} -1.65544 q^{3} -0.0513742 q^{4} -1.00000 q^{5} -2.31088 q^{6} +4.70682 q^{7} -2.86358 q^{8} -0.259511 q^{9} +O(q^{10})\)	\(q+1.39593 q^{2} -1.65544 q^{3} -0.0513742 q^{4} -1.00000 q^{5} -2.31088 q^{6} +4.70682 q^{7} -2.86358 q^{8} -0.259511 q^{9} -1.39593 q^{10} +0.0850471 q^{12} +5.05137 q^{13} +6.57040 q^{14} +1.65544 q^{15} -3.89461 q^{16} +5.31088 q^{17} -0.362259 q^{18} +2.25951 q^{19} +0.0513742 q^{20} -7.79186 q^{21} +1.05137 q^{23} +4.74049 q^{24} +1.00000 q^{25} +7.05137 q^{26} +5.39593 q^{27} -0.241809 q^{28} +2.79186 q^{29} +2.31088 q^{30} +3.74049 q^{31} +0.290544 q^{32} +7.41363 q^{34} -4.70682 q^{35} +0.0133322 q^{36} -0.791864 q^{37} +3.15412 q^{38} -8.36226 q^{39} +2.86358 q^{40} -6.15412 q^{41} -10.8769 q^{42} -2.70682 q^{43} +0.259511 q^{45} +1.46765 q^{46} -11.2392 q^{47} +6.44731 q^{48} +15.1541 q^{49} +1.39593 q^{50} -8.79186 q^{51} -0.259511 q^{52} +1.05137 q^{53} +7.53235 q^{54} -13.4783 q^{56} -3.74049 q^{57} +3.89725 q^{58} +4.53235 q^{59} -0.0850471 q^{60} +9.88128 q^{61} +5.22147 q^{62} -1.22147 q^{63} +8.19480 q^{64} -5.05137 q^{65} +10.4473 q^{67} -0.272843 q^{68} -1.74049 q^{69} -6.57040 q^{70} -1.05137 q^{71} +0.743129 q^{72} -10.1027 q^{73} -1.10539 q^{74} -1.65544 q^{75} -0.116081 q^{76} -11.6731 q^{78} -9.41363 q^{79} +3.89461 q^{80} -8.15412 q^{81} -8.59074 q^{82} -3.15412 q^{83} +0.400301 q^{84} -5.31088 q^{85} -3.77853 q^{86} -4.62177 q^{87} -12.5164 q^{89} +0.362259 q^{90} +23.7759 q^{91} -0.0540136 q^{92} -6.19216 q^{93} -15.6891 q^{94} -2.25951 q^{95} -0.480979 q^{96} -17.7759 q^{97} +21.1541 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + q^{3} + 9 q^{4} - 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q + q^2 + q^3 + 9 * q^4 - 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 + 2 * q^9	\( 3 q + q^{2} + q^{3} + 9 q^{4} - 3 q^{5} + 5 q^{6} - q^{7} - 9 q^{8} + 2 q^{9} - q^{10} + 9 q^{12} + 6 q^{13} + 5 q^{14} - q^{15} + 13 q^{16} + 4 q^{17} + 20 q^{18} + 4 q^{19} - 9 q^{20} - 17 q^{21} - 6 q^{23} + 17 q^{24} + 3 q^{25} + 12 q^{26} + 13 q^{27} - 25 q^{28} + 2 q^{29} - 5 q^{30} + 14 q^{31} - 27 q^{32} - 8 q^{34} + q^{35} + 2 q^{36} + 4 q^{37} - 18 q^{38} - 4 q^{39} + 9 q^{40} + 9 q^{41} - 35 q^{42} + 7 q^{43} - 2 q^{45} + 8 q^{46} - 15 q^{47} + 7 q^{48} + 18 q^{49} + q^{50} - 20 q^{51} + 2 q^{52} - 6 q^{53} + 19 q^{54} - 3 q^{56} - 14 q^{57} + 30 q^{58} + 10 q^{59} - 9 q^{60} + 3 q^{61} + 24 q^{62} - 12 q^{63} + 29 q^{64} - 6 q^{65} + 19 q^{67} - 8 q^{69} - 5 q^{70} + 6 q^{71} + 48 q^{72} - 12 q^{73} - 28 q^{74} + q^{75} + 16 q^{76} - 2 q^{78} + 2 q^{79} - 13 q^{80} + 3 q^{81} - 27 q^{82} + 18 q^{83} - 31 q^{84} - 4 q^{85} - 3 q^{86} + 10 q^{87} + 11 q^{89} - 20 q^{90} + 20 q^{91} - 34 q^{92} + 20 q^{93} - 59 q^{94} - 4 q^{95} - 7 q^{96} - 2 q^{97} + 36 q^{98}+O(q^{100}) \) 3 * q + q^2 + q^3 + 9 * q^4 - 3 * q^5 + 5 * q^6 - q^7 - 9 * q^8 + 2 * q^9 - q^10 + 9 * q^12 + 6 * q^13 + 5 * q^14 - q^15 + 13 * q^16 + 4 * q^17 + 20 * q^18 + 4 * q^19 - 9 * q^20 - 17 * q^21 - 6 * q^23 + 17 * q^24 + 3 * q^25 + 12 * q^26 + 13 * q^27 - 25 * q^28 + 2 * q^29 - 5 * q^30 + 14 * q^31 - 27 * q^32 - 8 * q^34 + q^35 + 2 * q^36 + 4 * q^37 - 18 * q^38 - 4 * q^39 + 9 * q^40 + 9 * q^41 - 35 * q^42 + 7 * q^43 - 2 * q^45 + 8 * q^46 - 15 * q^47 + 7 * q^48 + 18 * q^49 + q^50 - 20 * q^51 + 2 * q^52 - 6 * q^53 + 19 * q^54 - 3 * q^56 - 14 * q^57 + 30 * q^58 + 10 * q^59 - 9 * q^60 + 3 * q^61 + 24 * q^62 - 12 * q^63 + 29 * q^64 - 6 * q^65 + 19 * q^67 - 8 * q^69 - 5 * q^70 + 6 * q^71 + 48 * q^72 - 12 * q^73 - 28 * q^74 + q^75 + 16 * q^76 - 2 * q^78 + 2 * q^79 - 13 * q^80 + 3 * q^81 - 27 * q^82 + 18 * q^83 - 31 * q^84 - 4 * q^85 - 3 * q^86 + 10 * q^87 + 11 * q^89 - 20 * q^90 + 20 * q^91 - 34 * q^92 + 20 * q^93 - 59 * q^94 - 4 * q^95 - 7 * q^96 - 2 * q^97 + 36 * q^98

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