LMFDB - Embedded newform 6009.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6009 = 3 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6009.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$47.9821065746$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32830 q^{2} -1.00000 q^{3} +3.42098 q^{4} -2.84103 q^{5} +2.32830 q^{6} -3.28939 q^{7} -3.30847 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.32830 q^{2} -1.00000 q^{3} +3.42098 q^{4} -2.84103 q^{5} +2.32830 q^{6} -3.28939 q^{7} -3.30847 q^{8} +1.00000 q^{9} +6.61477 q^{10} -1.14254 q^{11} -3.42098 q^{12} -1.65899 q^{13} +7.65868 q^{14} +2.84103 q^{15} +0.861148 q^{16} +0.888184 q^{17} -2.32830 q^{18} -7.93381 q^{19} -9.71911 q^{20} +3.28939 q^{21} +2.66018 q^{22} -0.322878 q^{23} +3.30847 q^{24} +3.07145 q^{25} +3.86262 q^{26} -1.00000 q^{27} -11.2529 q^{28} +0.544776 q^{29} -6.61477 q^{30} +3.18574 q^{31} +4.61193 q^{32} +1.14254 q^{33} -2.06796 q^{34} +9.34525 q^{35} +3.42098 q^{36} +3.68674 q^{37} +18.4723 q^{38} +1.65899 q^{39} +9.39946 q^{40} +3.85914 q^{41} -7.65868 q^{42} -1.34642 q^{43} -3.90861 q^{44} -2.84103 q^{45} +0.751758 q^{46} -10.3584 q^{47} -0.861148 q^{48} +3.82007 q^{49} -7.15127 q^{50} -0.888184 q^{51} -5.67537 q^{52} +7.59776 q^{53} +2.32830 q^{54} +3.24599 q^{55} +10.8828 q^{56} +7.93381 q^{57} -1.26840 q^{58} +0.618060 q^{59} +9.71911 q^{60} -12.4275 q^{61} -7.41735 q^{62} -3.28939 q^{63} -12.4602 q^{64} +4.71324 q^{65} -2.66018 q^{66} +8.42038 q^{67} +3.03846 q^{68} +0.322878 q^{69} -21.7585 q^{70} +8.88637 q^{71} -3.30847 q^{72} +12.2822 q^{73} -8.58383 q^{74} -3.07145 q^{75} -27.1414 q^{76} +3.75825 q^{77} -3.86262 q^{78} -12.3222 q^{79} -2.44655 q^{80} +1.00000 q^{81} -8.98523 q^{82} +3.19741 q^{83} +11.2529 q^{84} -2.52336 q^{85} +3.13487 q^{86} -0.544776 q^{87} +3.78006 q^{88} +0.605126 q^{89} +6.61477 q^{90} +5.45705 q^{91} -1.10456 q^{92} -3.18574 q^{93} +24.1173 q^{94} +22.5402 q^{95} -4.61193 q^{96} +13.9139 q^{97} -8.89426 q^{98} -1.14254 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 3 q^{2} - 74 q^{3} + 57 q^{4} + 14 q^{5} + 3 q^{6} - 26 q^{7} - 9 q^{8} + 74 q^{9}+O(q^{10}) $ 74 * q - 3 * q^2 - 74 * q^3 + 57 * q^4 + 14 * q^5 + 3 * q^6 - 26 * q^7 - 9 * q^8 + 74 * q^9	\( 74 q - 3 q^{2} - 74 q^{3} + 57 q^{4} + 14 q^{5} + 3 q^{6} - 26 q^{7} - 9 q^{8} + 74 q^{9} - 21 q^{10} - 16 q^{11} - 57 q^{12} - 16 q^{13} - 17 q^{14} - 14 q^{15} + 15 q^{16} + 33 q^{17} - 3 q^{18} - 46 q^{19} + 17 q^{20} + 26 q^{21} - 28 q^{22} - 31 q^{23} + 9 q^{24} + 42 q^{25} - 8 q^{26} - 74 q^{27} - 46 q^{28} - 7 q^{29} + 21 q^{30} - 60 q^{31} - 16 q^{32} + 16 q^{33} - 42 q^{34} - 46 q^{35} + 57 q^{36} - 22 q^{37} + 10 q^{38} + 16 q^{39} - 67 q^{40} - 11 q^{41} + 17 q^{42} - 56 q^{43} - 25 q^{44} + 14 q^{45} - 59 q^{46} - q^{47} - 15 q^{48} + 12 q^{49} - 24 q^{50} - 33 q^{51} - 37 q^{52} + 25 q^{53} + 3 q^{54} - 90 q^{55} - 46 q^{56} + 46 q^{57} - 20 q^{58} - 60 q^{59} - 17 q^{60} - 55 q^{61} + 40 q^{62} - 26 q^{63} - 55 q^{64} - 12 q^{65} + 28 q^{66} - 64 q^{67} + 75 q^{68} + 31 q^{69} - 23 q^{70} - 128 q^{71} - 9 q^{72} - 31 q^{73} - 51 q^{74} - 42 q^{75} - 109 q^{76} + 70 q^{77} + 8 q^{78} - 193 q^{79} + 39 q^{80} + 74 q^{81} - 26 q^{82} - 5 q^{83} + 46 q^{84} - 60 q^{85} - 36 q^{86} + 7 q^{87} - 56 q^{88} - 21 q^{90} - 99 q^{91} - 54 q^{92} + 60 q^{93} - 66 q^{94} - 101 q^{95} + 16 q^{96} - 36 q^{97} - 21 q^{98} - 16 q^{99}+O(q^{100}) \) 74 * q - 3 * q^2 - 74 * q^3 + 57 * q^4 + 14 * q^5 + 3 * q^6 - 26 * q^7 - 9 * q^8 + 74 * q^9 - 21 * q^10 - 16 * q^11 - 57 * q^12 - 16 * q^13 - 17 * q^14 - 14 * q^15 + 15 * q^16 + 33 * q^17 - 3 * q^18 - 46 * q^19 + 17 * q^20 + 26 * q^21 - 28 * q^22 - 31 * q^23 + 9 * q^24 + 42 * q^25 - 8 * q^26 - 74 * q^27 - 46 * q^28 - 7 * q^29 + 21 * q^30 - 60 * q^31 - 16 * q^32 + 16 * q^33 - 42 * q^34 - 46 * q^35 + 57 * q^36 - 22 * q^37 + 10 * q^38 + 16 * q^39 - 67 * q^40 - 11 * q^41 + 17 * q^42 - 56 * q^43 - 25 * q^44 + 14 * q^45 - 59 * q^46 - q^47 - 15 * q^48 + 12 * q^49 - 24 * q^50 - 33 * q^51 - 37 * q^52 + 25 * q^53 + 3 * q^54 - 90 * q^55 - 46 * q^56 + 46 * q^57 - 20 * q^58 - 60 * q^59 - 17 * q^60 - 55 * q^61 + 40 * q^62 - 26 * q^63 - 55 * q^64 - 12 * q^65 + 28 * q^66 - 64 * q^67 + 75 * q^68 + 31 * q^69 - 23 * q^70 - 128 * q^71 - 9 * q^72 - 31 * q^73 - 51 * q^74 - 42 * q^75 - 109 * q^76 + 70 * q^77 + 8 * q^78 - 193 * q^79 + 39 * q^80 + 74 * q^81 - 26 * q^82 - 5 * q^83 + 46 * q^84 - 60 * q^85 - 36 * q^86 + 7 * q^87 - 56 * q^88 - 21 * q^90 - 99 * q^91 - 54 * q^92 + 60 * q^93 - 66 * q^94 - 101 * q^95 + 16 * q^96 - 36 * q^97 - 21 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.32830	−1.64636	−0.823178	−	0.567783i	$-0.807801\pi$
$2$	−2.32830	−1.64636	−0.823178	+	0.567783i	$0.807801\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.42098	1.71049
$5$	−2.84103	−1.27055	−0.635274	−	0.772287i	$-0.719113\pi$
$5$	−2.84103	−1.27055	−0.635274	+	0.772287i	$0.719113\pi$
$6$	2.32830	0.950524
$7$	−3.28939	−1.24327	−0.621636	−	0.783307i	$-0.713532\pi$
$7$	−3.28939	−1.24327	−0.621636	+	0.783307i	$0.713532\pi$
$8$	−3.30847	−1.16972
$9$	1.00000	0.333333
$10$	6.61477	2.09177
$11$	−1.14254	−0.344489	−0.172244	−	0.985054i	$-0.555102\pi$
$11$	−1.14254	−0.344489	−0.172244	+	0.985054i	$0.555102\pi$
$12$	−3.42098	−0.987552
$13$	−1.65899	−0.460120	−0.230060	−	0.973176i	$-0.573892\pi$
$13$	−1.65899	−0.460120	−0.230060	+	0.973176i	$0.573892\pi$
$14$	7.65868	2.04687
$15$	2.84103	0.733551
$16$	0.861148	0.215287
$17$	0.888184	0.215416	0.107708	−	0.994183i	$-0.465649\pi$
$17$	0.888184	0.215416	0.107708	+	0.994183i	$0.465649\pi$
$18$	−2.32830	−0.548786
$19$	−7.93381	−1.82014	−0.910071	−	0.414453i	$-0.863973\pi$
$19$	−7.93381	−1.82014	−0.910071	+	0.414453i	$0.863973\pi$
$20$	−9.71911	−2.17326
$21$	3.28939	0.717803
$22$	2.66018	0.567151
$23$	−0.322878	−0.0673248	−0.0336624	−	0.999433i	$-0.510717\pi$
$23$	−0.322878	−0.0673248	−0.0336624	+	0.999433i	$0.510717\pi$
$24$	3.30847	0.675338
$25$	3.07145	0.614291
$26$	3.86262	0.757522
$27$	−1.00000	−0.192450
$28$	−11.2529	−2.12660
$29$	0.544776	0.101162	0.0505812	−	0.998720i	$-0.483893\pi$
$29$	0.544776	0.101162	0.0505812	+	0.998720i	$0.483893\pi$
$30$	−6.61477	−1.20769
$31$	3.18574	0.572175	0.286088	−	0.958203i	$-0.407645\pi$
$31$	3.18574	0.572175	0.286088	+	0.958203i	$0.407645\pi$
$32$	4.61193	0.815281
$33$	1.14254	0.198891
$34$	−2.06796	−0.354652
$35$	9.34525	1.57964
$36$	3.42098	0.570163
$37$	3.68674	0.606096	0.303048	−	0.952975i	$-0.401996\pi$
$37$	3.68674	0.606096	0.303048	+	0.952975i	$0.401996\pi$
$38$	18.4723	2.99660
$39$	1.65899	0.265651
$40$	9.39946	1.48619
$41$	3.85914	0.602696	0.301348	−	0.953514i	$-0.402563\pi$
$41$	3.85914	0.602696	0.301348	+	0.953514i	$0.402563\pi$
$42$	−7.65868	−1.18176
$43$	−1.34642	−0.205327	−0.102664	−	0.994716i	$-0.532737\pi$
$43$	−1.34642	−0.205327	−0.102664	+	0.994716i	$0.532737\pi$
$44$	−3.90861	−0.589245
$45$	−2.84103	−0.423516
$46$	0.751758	0.110841
$47$	−10.3584	−1.51092	−0.755460	−	0.655194i	$-0.772587\pi$
$47$	−10.3584	−1.51092	−0.755460	+	0.655194i	$0.772587\pi$
$48$	−0.861148	−0.124296
$49$	3.82007	0.545724
$50$	−7.15127	−1.01134
$51$	−0.888184	−0.124371
$52$	−5.67537	−0.787032
$53$	7.59776	1.04363	0.521816	−	0.853058i	$-0.325255\pi$
$53$	7.59776	1.04363	0.521816	+	0.853058i	$0.325255\pi$
$54$	2.32830	0.316841
$55$	3.24599	0.437689
$56$	10.8828	1.45428
$57$	7.93381	1.05086
$58$	−1.26840	−0.166549
$59$	0.618060	0.0804646	0.0402323	−	0.999190i	$-0.487190\pi$
$59$	0.618060	0.0804646	0.0402323	+	0.999190i	$0.487190\pi$
$60$	9.71911	1.25473
$61$	−12.4275	−1.59118	−0.795589	−	0.605837i	$-0.792838\pi$
$61$	−12.4275	−1.59118	−0.795589	+	0.605837i	$0.792838\pi$
$62$	−7.41735	−0.942004
$63$	−3.28939	−0.414424
$64$	−12.4602	−1.55753
$65$	4.71324	0.584605
$66$	−2.66018	−0.327445
$67$	8.42038	1.02871	0.514357	−	0.857576i	$-0.328031\pi$
$67$	8.42038	1.02871	0.514357	+	0.857576i	$0.328031\pi$
$68$	3.03846	0.368467
$69$	0.322878	0.0388700
$70$	−21.7585	−2.60064
$71$	8.88637	1.05462	0.527309	−	0.849673i	$-0.323201\pi$
$71$	8.88637	1.05462	0.527309	+	0.849673i	$0.323201\pi$
$72$	−3.30847	−0.389907
$73$	12.2822	1.43753	0.718763	−	0.695255i	$-0.244709\pi$
$73$	12.2822	1.43753	0.718763	+	0.695255i	$0.244709\pi$
$74$	−8.58383	−0.997849
$75$	−3.07145	−0.354661
$76$	−27.1414	−3.11333
$77$	3.75825	0.428293
$78$	−3.86262	−0.437356
$79$	−12.3222	−1.38636	−0.693180	−	0.720765i	$-0.743791\pi$
$79$	−12.3222	−1.38636	−0.693180	+	0.720765i	$0.743791\pi$
$80$	−2.44655	−0.273532
$81$	1.00000	0.111111
$82$	−8.98523	−0.992252
$83$	3.19741	0.350961	0.175481	−	0.984483i	$-0.443852\pi$
$83$	3.19741	0.350961	0.175481	+	0.984483i	$0.443852\pi$
$84$	11.2529	1.22780
$85$	−2.52336	−0.273697
$86$	3.13487	0.338042
$87$	−0.544776	−0.0584061
$88$	3.78006	0.402955
$89$	0.605126	0.0641433	0.0320716	−	0.999486i	$-0.489790\pi$
$89$	0.605126	0.0641433	0.0320716	+	0.999486i	$0.489790\pi$
$90$	6.61477	0.697258
$91$	5.45705	0.572055
$92$	−1.10456	−0.115158
$93$	−3.18574	−0.330345
$94$	24.1173	2.48751
$95$	22.5402	2.31258
$96$	−4.61193	−0.470703
$97$	13.9139	1.41275	0.706374	−	0.707839i	$-0.250330\pi$
$97$	13.9139	1.41275	0.706374	+	0.707839i	$0.250330\pi$
$98$	−8.89426	−0.898456
$99$	−1.14254	−0.114830
$100$	10.5074	1.05074
$101$	14.8564	1.47827	0.739136	−	0.673557i	$-0.235234\pi$
$101$	14.8564	1.47827	0.739136	+	0.673557i	$0.235234\pi$
$102$	2.06796	0.204758
$103$	−5.86201	−0.577601	−0.288800	−	0.957389i	$-0.593256\pi$
$103$	−5.86201	−0.577601	−0.288800	+	0.957389i	$0.593256\pi$
$104$	5.48871	0.538212
$105$	−9.34525	−0.912003
$106$	−17.6899	−1.71819
$107$	−5.19125	−0.501857	−0.250929	−	0.968006i	$-0.580736\pi$
$107$	−5.19125	−0.501857	−0.250929	+	0.968006i	$0.580736\pi$
$108$	−3.42098	−0.329184
$109$	−13.1479	−1.25934	−0.629669	−	0.776863i	$-0.716810\pi$
$109$	−13.1479	−1.25934	−0.629669	+	0.776863i	$0.716810\pi$
$110$	−7.55764	−0.720593
$111$	−3.68674	−0.349929
$112$	−2.83265	−0.267660
$113$	0.515378	0.0484827	0.0242413	−	0.999706i	$-0.492283\pi$
$113$	0.515378	0.0484827	0.0242413	+	0.999706i	$0.492283\pi$
$114$	−18.4723	−1.73009
$115$	0.917307	0.0855394
$116$	1.86367	0.173037
$117$	−1.65899	−0.153373
$118$	−1.43903	−0.132473
$119$	−2.92158	−0.267821
$120$	−9.39946	−0.858050
$121$	−9.69460	−0.881328
$122$	28.9349	2.61965
$123$	−3.85914	−0.347967
$124$	10.8983	0.978700
$125$	5.47906	0.490062
$126$	7.65868	0.682289
$127$	−15.1758	−1.34663	−0.673316	−	0.739355i	$-0.735130\pi$
$127$	−15.1758	−1.34663	−0.673316	+	0.739355i	$0.735130\pi$
$128$	19.7873	1.74897
$129$	1.34642	0.118546
$130$	−10.9738	−0.962468
$131$	1.01644	0.0888070	0.0444035	−	0.999014i	$-0.485861\pi$
$131$	1.01644	0.0888070	0.0444035	+	0.999014i	$0.485861\pi$
$132$	3.90861	0.340201
$133$	26.0974	2.26293
$134$	−19.6052	−1.69363
$135$	2.84103	0.244517
$136$	−2.93853	−0.251977
$137$	22.3756	1.91168	0.955840	−	0.293888i	$-0.0949494\pi$
$137$	22.3756	1.91168	0.955840	+	0.293888i	$0.0949494\pi$
$138$	−0.751758	−0.0639939
$139$	10.7752	0.913938	0.456969	−	0.889483i	$-0.348935\pi$
$139$	10.7752	0.913938	0.456969	+	0.889483i	$0.348935\pi$
$140$	31.9699	2.70195
$141$	10.3584	0.872330
$142$	−20.6901	−1.73628
$143$	1.89546	0.158506
$144$	0.861148	0.0717623
$145$	−1.54772	−0.128532
$146$	−28.5967	−2.36668
$147$	−3.82007	−0.315074
$148$	12.6122	1.03672
$149$	5.30028	0.434215	0.217108	−	0.976148i	$-0.430338\pi$
$149$	5.30028	0.434215	0.217108	+	0.976148i	$0.430338\pi$
$150$	7.15127	0.583899
$151$	4.51709	0.367596	0.183798	−	0.982964i	$-0.441161\pi$
$151$	4.51709	0.367596	0.183798	+	0.982964i	$0.441161\pi$
$152$	26.2488	2.12906
$153$	0.888184	0.0718054
$154$	−8.75034	−0.705123
$155$	−9.05077	−0.726976
$156$	5.67537	0.454393
$157$	20.8651	1.66521	0.832607	−	0.553864i	$-0.186847\pi$
$157$	20.8651	1.66521	0.832607	+	0.553864i	$0.186847\pi$
$158$	28.6898	2.28244
$159$	−7.59776	−0.602541
$160$	−13.1026	−1.03585
$161$	1.06207	0.0837030
$162$	−2.32830	−0.182929
$163$	23.6442	1.85196	0.925979	−	0.377576i	$-0.123242\pi$
$163$	23.6442	1.85196	0.925979	+	0.377576i	$0.123242\pi$
$164$	13.2020	1.03091
$165$	−3.24599	−0.252700
$166$	−7.44453	−0.577807
$167$	20.4386	1.58159	0.790793	−	0.612083i	$-0.209668\pi$
$167$	20.4386	1.58159	0.790793	+	0.612083i	$0.209668\pi$
$168$	−10.8828	−0.839629
$169$	−10.2478	−0.788289
$170$	5.87513	0.450602
$171$	−7.93381	−0.606714
$172$	−4.60608	−0.351210
$173$	11.8676	0.902276	0.451138	−	0.892454i	$-0.351018\pi$
$173$	11.8676	0.902276	0.451138	+	0.892454i	$0.351018\pi$
$174$	1.26840	0.0961573
$175$	−10.1032	−0.763730
$176$	−0.983895	−0.0741639
$177$	−0.618060	−0.0464563
$178$	−1.40892	−0.105603
$179$	15.0544	1.12522	0.562609	−	0.826723i	$-0.309798\pi$
$179$	15.0544	1.12522	0.562609	+	0.826723i	$0.309798\pi$
$180$	−9.71911	−0.724420
$181$	15.7344	1.16953	0.584764	−	0.811203i	$-0.301187\pi$
$181$	15.7344	1.16953	0.584764	+	0.811203i	$0.301187\pi$
$182$	−12.7057	−0.941806
$183$	12.4275	0.918667
$184$	1.06823	0.0787512
$185$	−10.4741	−0.770073
$186$	7.41735	0.543867
$187$	−1.01479	−0.0742084
$188$	−35.4357	−2.58442
$189$	3.28939	0.239268
$190$	−52.4803	−3.80732
$191$	−20.4709	−1.48122	−0.740611	−	0.671934i	$-0.765464\pi$
$191$	−20.4709	−1.48122	−0.740611	+	0.671934i	$0.765464\pi$
$192$	12.4602	0.899241
$193$	−24.9892	−1.79876	−0.899380	−	0.437167i	$-0.855982\pi$
$193$	−24.9892	−1.79876	−0.899380	+	0.437167i	$0.855982\pi$
$194$	−32.3958	−2.32589
$195$	−4.71324	−0.337522
$196$	13.0684	0.933455
$197$	−12.5542	−0.894450	−0.447225	−	0.894421i	$-0.647588\pi$
$197$	−12.5542	−0.894450	−0.447225	+	0.894421i	$0.647588\pi$
$198$	2.66018	0.189050
$199$	−20.8004	−1.47450	−0.737251	−	0.675619i	$-0.763876\pi$
$199$	−20.8004	−1.47450	−0.737251	+	0.675619i	$0.763876\pi$
$200$	−10.1618	−0.718549
$201$	−8.42038	−0.593928
$202$	−34.5903	−2.43376
$203$	−1.79198	−0.125772
$204$	−3.03846	−0.212735
$205$	−10.9639	−0.765754
$206$	13.6485	0.950936
$207$	−0.322878	−0.0224416
$208$	−1.42863	−0.0990579
$209$	9.06469	0.627018
$210$	21.7585	1.50148
$211$	−2.27900	−0.156893	−0.0784465	−	0.996918i	$-0.524996\pi$
$211$	−2.27900	−0.156893	−0.0784465	+	0.996918i	$0.524996\pi$
$212$	25.9918	1.78512
$213$	−8.88637	−0.608884
$214$	12.0868	0.826236
$215$	3.82522	0.260878
$216$	3.30847	0.225113
$217$	−10.4791	−0.711369
$218$	30.6122	2.07332
$219$	−12.2822	−0.829956
$220$	11.1045	0.748663
$221$	−1.47349	−0.0991174
$222$	8.58383	0.576109
$223$	−1.19418	−0.0799682	−0.0399841	−	0.999200i	$-0.512731\pi$
$223$	−1.19418	−0.0799682	−0.0399841	+	0.999200i	$0.512731\pi$
$224$	−15.1704	−1.01362
$225$	3.07145	0.204764
$226$	−1.19995	−0.0798198
$227$	−21.4471	−1.42349	−0.711747	−	0.702436i	$-0.752096\pi$
$227$	−21.4471	−1.42349	−0.711747	+	0.702436i	$0.752096\pi$
$228$	27.1414	1.79748
$229$	−23.1942	−1.53272	−0.766359	−	0.642412i	$-0.777934\pi$
$229$	−23.1942	−1.53272	−0.766359	+	0.642412i	$0.777934\pi$
$230$	−2.13577	−0.140828
$231$	−3.75825	−0.247275
$232$	−1.80237	−0.118332
$233$	−17.8685	−1.17061	−0.585303	−	0.810815i	$-0.699024\pi$
$233$	−17.8685	−1.17061	−0.585303	+	0.810815i	$0.699024\pi$
$234$	3.86262	0.252507
$235$	29.4284	1.91970
$236$	2.11437	0.137634
$237$	12.3222	0.800415
$238$	6.80232	0.440929
$239$	19.0004	1.22903	0.614516	−	0.788904i	$-0.289351\pi$
$239$	19.0004	1.22903	0.614516	+	0.788904i	$0.289351\pi$
$240$	2.44655	0.157924
$241$	9.39297	0.605054	0.302527	−	0.953141i	$-0.402170\pi$
$241$	9.39297	0.605054	0.302527	+	0.953141i	$0.402170\pi$
$242$	22.5719	1.45098
$243$	−1.00000	−0.0641500
$244$	−42.5142	−2.72169
$245$	−10.8529	−0.693368
$246$	8.98523	0.572877
$247$	13.1621	0.837484
$248$	−10.5399	−0.669285
$249$	−3.19741	−0.202628
$250$	−12.7569	−0.806816
$251$	16.3721	1.03340	0.516700	−	0.856167i	$-0.327160\pi$
$251$	16.3721	1.03340	0.516700	+	0.856167i	$0.327160\pi$
$252$	−11.2529	−0.708868
$253$	0.368901	0.0231926
$254$	35.3337	2.21704
$255$	2.52336	0.158019
$256$	−21.1504	−1.32190
$257$	29.2695	1.82578	0.912890	−	0.408206i	$-0.133845\pi$
$257$	29.2695	1.82578	0.912890	+	0.408206i	$0.133845\pi$
$258$	−3.13487	−0.195169
$259$	−12.1271	−0.753541
$260$	16.1239	0.999961
$261$	0.544776	0.0337208
$262$	−2.36658	−0.146208
$263$	7.08720	0.437016	0.218508	−	0.975835i	$-0.429881\pi$
$263$	7.08720	0.437016	0.218508	+	0.975835i	$0.429881\pi$
$264$	−3.78006	−0.232646
$265$	−21.5855	−1.32598
$266$	−60.7625	−3.72559
$267$	−0.605126	−0.0370331
$268$	28.8060	1.75960
$269$	5.68187	0.346430	0.173215	−	0.984884i	$-0.444584\pi$
$269$	5.68187	0.346430	0.173215	+	0.984884i	$0.444584\pi$
$270$	−6.61477	−0.402562
$271$	1.61529	0.0981218	0.0490609	−	0.998796i	$-0.484377\pi$
$271$	1.61529	0.0981218	0.0490609	+	0.998796i	$0.484377\pi$
$272$	0.764858	0.0463763
$273$	−5.45705	−0.330276
$274$	−52.0972	−3.14731
$275$	−3.50926	−0.211616
$276$	1.10456	0.0664867
$277$	−12.7932	−0.768671	−0.384336	−	0.923193i	$-0.625569\pi$
$277$	−12.7932	−0.768671	−0.384336	+	0.923193i	$0.625569\pi$
$278$	−25.0878	−1.50467
$279$	3.18574	0.190725
$280$	−30.9185	−1.84773
$281$	−1.37266	−0.0818861	−0.0409430	−	0.999161i	$-0.513036\pi$
$281$	−1.37266	−0.0818861	−0.0409430	+	0.999161i	$0.513036\pi$
$282$	−24.1173	−1.43617
$283$	8.21804	0.488512	0.244256	−	0.969711i	$-0.421456\pi$
$283$	8.21804	0.488512	0.244256	+	0.969711i	$0.421456\pi$
$284$	30.4001	1.80391
$285$	−22.5402	−1.33517
$286$	−4.41320	−0.260958
$287$	−12.6942	−0.749315
$288$	4.61193	0.271760
$289$	−16.2111	−0.953596
$290$	3.60357	0.211609
$291$	−13.9139	−0.815650
$292$	42.0173	2.45887
$293$	11.6721	0.681893	0.340947	−	0.940083i	$-0.389252\pi$
$293$	11.6721	0.681893	0.340947	+	0.940083i	$0.389252\pi$
$294$	8.89426	0.518724
$295$	−1.75593	−0.102234
$296$	−12.1975	−0.708962
$297$	1.14254	0.0662969
$298$	−12.3406	−0.714874
$299$	0.535651	0.0309775
$300$	−10.5074	−0.606644
$301$	4.42890	0.255277
$302$	−10.5171	−0.605194
$303$	−14.8564	−0.853480
$304$	−6.83218	−0.391853
$305$	35.3069	2.02167
$306$	−2.06796	−0.118217
$307$	20.0674	1.14531	0.572654	−	0.819797i	$-0.305914\pi$
$307$	20.0674	1.14531	0.572654	+	0.819797i	$0.305914\pi$
$308$	12.8569	0.732591
$309$	5.86201	0.333478
$310$	21.0729	1.19686
$311$	−26.9316	−1.52715	−0.763574	−	0.645720i	$-0.776557\pi$
$311$	−26.9316	−1.52715	−0.763574	+	0.645720i	$0.776557\pi$
$312$	−5.48871	−0.310737
$313$	23.0761	1.30434	0.652170	−	0.758073i	$-0.273859\pi$
$313$	23.0761	1.30434	0.652170	+	0.758073i	$0.273859\pi$
$314$	−48.5801	−2.74154
$315$	9.34525	0.526545
$316$	−42.1541	−2.37135
$317$	13.7605	0.772867	0.386433	−	0.922317i	$-0.373707\pi$
$317$	13.7605	0.772867	0.386433	+	0.922317i	$0.373707\pi$
$318$	17.6899	0.991998
$319$	−0.622428	−0.0348493
$320$	35.3999	1.97892
$321$	5.19125	0.289748
$322$	−2.47282	−0.137805
$323$	−7.04668	−0.392088
$324$	3.42098	0.190054
$325$	−5.09551	−0.282648
$326$	−55.0508	−3.04898
$327$	13.1479	0.727079
$328$	−12.7678	−0.704986
$329$	34.0726	1.87848
$330$	7.55764	0.416034
$331$	6.70734	0.368669	0.184334	−	0.982864i	$-0.440987\pi$
$331$	6.70734	0.368669	0.184334	+	0.982864i	$0.440987\pi$
$332$	10.9383	0.600316
$333$	3.68674	0.202032
$334$	−47.5872	−2.60386
$335$	−23.9226	−1.30703
$336$	2.83265	0.154534
$337$	13.2432	0.721405	0.360703	−	0.932681i	$-0.382537\pi$
$337$	13.2432	0.721405	0.360703	+	0.932681i	$0.382537\pi$
$338$	23.8599	1.29781
$339$	−0.515378	−0.0279915
$340$	−8.63236	−0.468155
$341$	−3.63983	−0.197108
$342$	18.4723	0.998867
$343$	10.4600	0.564789
$344$	4.45459	0.240175
$345$	−0.917307	−0.0493862
$346$	−27.6313	−1.48547
$347$	−16.4977	−0.885644	−0.442822	−	0.896610i	$-0.646023\pi$
$347$	−16.4977	−0.885644	−0.442822	+	0.896610i	$0.646023\pi$
$348$	−1.86367	−0.0999031
$349$	26.7572	1.43228	0.716141	−	0.697955i	$-0.245907\pi$
$349$	26.7572	1.43228	0.716141	+	0.697955i	$0.245907\pi$
$350$	23.5233	1.25737
$351$	1.65899	0.0885502
$352$	−5.26931	−0.280855
$353$	−20.8124	−1.10773	−0.553867	−	0.832605i	$-0.686848\pi$
$353$	−20.8124	−1.10773	−0.553867	+	0.832605i	$0.686848\pi$
$354$	1.43903	0.0764836
$355$	−25.2465	−1.33994
$356$	2.07013	0.109716
$357$	2.92158	0.154626
$358$	−35.0511	−1.85251
$359$	−0.713624	−0.0376636	−0.0188318	−	0.999823i	$-0.505995\pi$
$359$	−0.713624	−0.0376636	−0.0188318	+	0.999823i	$0.505995\pi$
$360$	9.39946	0.495395
$361$	43.9454	2.31291
$362$	−36.6344	−1.92546
$363$	9.69460	0.508835
$364$	18.6685	0.978494
$365$	−34.8942	−1.82644
$366$	−28.9349	−1.51245
$367$	−22.0537	−1.15119	−0.575596	−	0.817734i	$-0.695230\pi$
$367$	−22.0537	−1.15119	−0.575596	+	0.817734i	$0.695230\pi$
$368$	−0.278046	−0.0144942
$369$	3.85914	0.200899
$370$	24.3869	1.26782
$371$	−24.9920	−1.29752
$372$	−10.8983	−0.565053
$373$	10.5119	0.544286	0.272143	−	0.962257i	$-0.412268\pi$
$373$	10.5119	0.544286	0.272143	+	0.962257i	$0.412268\pi$
$374$	2.36272	0.122174
$375$	−5.47906	−0.282937
$376$	34.2703	1.76736
$377$	−0.903777	−0.0465469
$378$	−7.65868	−0.393920
$379$	34.2872	1.76122	0.880608	−	0.473846i	$-0.157135\pi$
$379$	34.2872	1.76122	0.880608	+	0.473846i	$0.157135\pi$
$380$	77.1096	3.95564
$381$	15.1758	0.777478
$382$	47.6624	2.43862
$383$	12.8515	0.656679	0.328339	−	0.944560i	$-0.393511\pi$
$383$	12.8515	0.656679	0.328339	+	0.944560i	$0.393511\pi$
$384$	−19.7873	−1.00977
$385$	−10.6773	−0.544166
$386$	58.1823	2.96140
$387$	−1.34642	−0.0684424
$388$	47.5993	2.41649
$389$	−26.2755	−1.33222	−0.666111	−	0.745852i	$-0.732042\pi$
$389$	−26.2755	−1.33222	−0.666111	+	0.745852i	$0.732042\pi$
$390$	10.9738	0.555681
$391$	−0.286775	−0.0145029
$392$	−12.6386	−0.638344
$393$	−1.01644	−0.0512727
$394$	29.2300	1.47258
$395$	35.0078	1.76144
$396$	−3.90861	−0.196415
$397$	12.8875	0.646805	0.323403	−	0.946261i	$-0.395173\pi$
$397$	12.8875	0.646805	0.323403	+	0.946261i	$0.395173\pi$
$398$	48.4296	2.42756
$399$	−26.0974	−1.30650
$400$	2.64498	0.132249
$401$	−13.4402	−0.671172	−0.335586	−	0.942010i	$-0.608934\pi$
$401$	−13.4402	−0.671172	−0.335586	+	0.942010i	$0.608934\pi$
$402$	19.6052	0.977817
$403$	−5.28510	−0.263269
$404$	50.8236	2.52857
$405$	−2.84103	−0.141172
$406$	4.17226	0.207066
$407$	−4.21224	−0.208793
$408$	2.93853	0.145479
$409$	−3.17547	−0.157017	−0.0785084	−	0.996913i	$-0.525016\pi$
$409$	−3.17547	−0.157017	−0.0785084	+	0.996913i	$0.525016\pi$
$410$	25.5273	1.26070
$411$	−22.3756	−1.10371
$412$	−20.0538	−0.987980
$413$	−2.03304	−0.100039
$414$	0.751758	0.0369469
$415$	−9.08393	−0.445913
$416$	−7.65113	−0.375128
$417$	−10.7752	−0.527662
$418$	−21.1053	−1.03230
$419$	9.66436	0.472135	0.236067	−	0.971737i	$-0.424141\pi$
$419$	9.66436	0.472135	0.236067	+	0.971737i	$0.424141\pi$
$420$	−31.9699	−1.55997
$421$	10.3530	0.504576	0.252288	−	0.967652i	$-0.418817\pi$
$421$	10.3530	0.504576	0.252288	+	0.967652i	$0.418817\pi$
$422$	5.30620	0.258302
$423$	−10.3584	−0.503640
$424$	−25.1369	−1.22076
$425$	2.72802	0.132328
$426$	20.6901	1.00244
$427$	40.8788	1.97827
$428$	−17.7592	−0.858422
$429$	−1.89546	−0.0915136
$430$	−8.90626	−0.429498
$431$	−14.3386	−0.690665	−0.345333	−	0.938480i	$-0.612234\pi$
$431$	−14.3386	−0.690665	−0.345333	+	0.938480i	$0.612234\pi$
$432$	−0.861148	−0.0414320
$433$	−10.5328	−0.506176	−0.253088	−	0.967443i	$-0.581446\pi$
$433$	−10.5328	−0.506176	−0.253088	+	0.967443i	$0.581446\pi$
$434$	24.3985	1.17117
$435$	1.54772	0.0742077
$436$	−44.9786	−2.15409
$437$	2.56166	0.122541
$438$	28.5967	1.36640
$439$	−28.8458	−1.37674	−0.688368	−	0.725362i	$-0.741673\pi$
$439$	−28.8458	−1.37674	−0.688368	+	0.725362i	$0.741673\pi$
$440$	−10.7393	−0.511974
$441$	3.82007	0.181908
$442$	3.43072	0.163183
$443$	−20.0961	−0.954794	−0.477397	−	0.878688i	$-0.658420\pi$
$443$	−20.0961	−0.954794	−0.477397	+	0.878688i	$0.658420\pi$
$444$	−12.6122	−0.598551
$445$	−1.71918	−0.0814971
$446$	2.78041	0.131656
$447$	−5.30028	−0.250694
$448$	40.9866	1.93643
$449$	−12.7224	−0.600408	−0.300204	−	0.953875i	$-0.597055\pi$
$449$	−12.7224	−0.600408	−0.300204	+	0.953875i	$0.597055\pi$
$450$	−7.15127	−0.337114
$451$	−4.40922	−0.207622
$452$	1.76310	0.0829291
$453$	−4.51709	−0.212232
$454$	49.9353	2.34358
$455$	−15.5037	−0.726822
$456$	−26.2488	−1.22921
$457$	−6.75887	−0.316167	−0.158083	−	0.987426i	$-0.550531\pi$
$457$	−6.75887	−0.316167	−0.158083	+	0.987426i	$0.550531\pi$
$458$	54.0031	2.52340
$459$	−0.888184	−0.0414569
$460$	3.13809	0.146314
$461$	20.7086	0.964496	0.482248	−	0.876035i	$-0.339820\pi$
$461$	20.7086	0.964496	0.482248	+	0.876035i	$0.339820\pi$
$462$	8.75034	0.407103
$463$	−8.91484	−0.414308	−0.207154	−	0.978308i	$-0.566420\pi$
$463$	−8.91484	−0.414308	−0.207154	+	0.978308i	$0.566420\pi$
$464$	0.469133	0.0217789
$465$	9.05077	0.419720
$466$	41.6033	1.92723
$467$	−12.2219	−0.565561	−0.282780	−	0.959185i	$-0.591257\pi$
$467$	−12.2219	−0.565561	−0.282780	+	0.959185i	$0.591257\pi$
$468$	−5.67537	−0.262344
$469$	−27.6979	−1.27897
$470$	−68.5181	−3.16051
$471$	−20.8651	−0.961412
$472$	−2.04483	−0.0941211
$473$	1.53834	0.0707329
$474$	−28.6898	−1.31777
$475$	−24.3683	−1.11810
$476$	−9.99467	−0.458105
$477$	7.59776	0.347877
$478$	−44.2386	−2.02343
$479$	−23.9662	−1.09505	−0.547523	−	0.836791i	$-0.684429\pi$
$479$	−23.9662	−1.09505	−0.547523	+	0.836791i	$0.684429\pi$
$480$	13.1026	0.598050
$481$	−6.11625	−0.278877
$482$	−21.8696	−0.996135
$483$	−1.06207	−0.0483259
$484$	−33.1651	−1.50750
$485$	−39.5300	−1.79496
$486$	2.32830	0.105614
$487$	8.05820	0.365152	0.182576	−	0.983192i	$-0.441556\pi$
$487$	8.05820	0.365152	0.182576	+	0.983192i	$0.441556\pi$
$488$	41.1160	1.86123
$489$	−23.6442	−1.06923
$490$	25.2689	1.14153
$491$	−22.7494	−1.02667	−0.513334	−	0.858189i	$-0.671590\pi$
$491$	−22.7494	−1.02667	−0.513334	+	0.858189i	$0.671590\pi$
$492$	−13.2020	−0.595194
$493$	0.483861	0.0217920
$494$	−30.6453	−1.37880
$495$	3.24599	0.145896
$496$	2.74339	0.123182
$497$	−29.2307	−1.31118
$498$	7.44453	0.333597
$499$	6.94709	0.310995	0.155497	−	0.987836i	$-0.450302\pi$
$499$	6.94709	0.310995	0.155497	+	0.987836i	$0.450302\pi$
$500$	18.7437	0.838246
$501$	−20.4386	−0.913129
$502$	−38.1192	−1.70134
$503$	−18.1265	−0.808220	−0.404110	−	0.914710i	$-0.632419\pi$
$503$	−18.1265	−0.808220	−0.404110	+	0.914710i	$0.632419\pi$
$504$	10.8828	0.484760
$505$	−42.2076	−1.87821
$506$	−0.858913	−0.0381833
$507$	10.2478	0.455119
$508$	−51.9160	−2.30340
$509$	22.7723	1.00937	0.504683	−	0.863305i	$-0.331609\pi$
$509$	22.7723	1.00937	0.504683	+	0.863305i	$0.331609\pi$
$510$	−5.87513	−0.260155
$511$	−40.4010	−1.78723
$512$	9.66971	0.427345
$513$	7.93381	0.350286
$514$	−68.1481	−3.00589
$515$	16.6541	0.733869
$516$	4.60608	0.202771
$517$	11.8348	0.520495
$518$	28.2355	1.24060
$519$	−11.8676	−0.520929
$520$	−15.5936	−0.683824
$521$	−3.63656	−0.159321	−0.0796604	−	0.996822i	$-0.525384\pi$
$521$	−3.63656	−0.159321	−0.0796604	+	0.996822i	$0.525384\pi$
$522$	−1.26840	−0.0555164
$523$	−16.9667	−0.741901	−0.370951	−	0.928653i	$-0.620968\pi$
$523$	−16.9667	−0.741901	−0.370951	+	0.928653i	$0.620968\pi$
$524$	3.47723	0.151903
$525$	10.1032	0.440940
$526$	−16.5011	−0.719483
$527$	2.82952	0.123256
$528$	0.983895	0.0428186
$529$	−22.8957	−0.995467
$530$	50.2574	2.18304
$531$	0.618060	0.0268215
$532$	89.2786	3.87072
$533$	−6.40226	−0.277313
$534$	1.40892	0.0609697
$535$	14.7485	0.637634
$536$	−27.8586	−1.20331
$537$	−15.0544	−0.649645
$538$	−13.2291	−0.570347
$539$	−4.36458	−0.187996
$540$	9.71911	0.418244
$541$	−31.1222	−1.33805	−0.669023	−	0.743242i	$-0.733287\pi$
$541$	−31.1222	−1.33805	−0.669023	+	0.743242i	$0.733287\pi$
$542$	−3.76088	−0.161544
$543$	−15.7344	−0.675227
$544$	4.09624	0.175625
$545$	37.3535	1.60005
$546$	12.7057	0.543752
$547$	−11.0844	−0.473933	−0.236967	−	0.971518i	$-0.576153\pi$
$547$	−11.0844	−0.473933	−0.236967	+	0.971518i	$0.576153\pi$
$548$	76.5466	3.26991
$549$	−12.4275	−0.530392
$550$	8.17061	0.348396
$551$	−4.32215	−0.184130
$552$	−1.06823	−0.0454670
$553$	40.5326	1.72362
$554$	29.7865	1.26551
$555$	10.4741	0.444602
$556$	36.8617	1.56328
$557$	−5.05445	−0.214164	−0.107082	−	0.994250i	$-0.534151\pi$
$557$	−5.05445	−0.214164	−0.107082	+	0.994250i	$0.534151\pi$
$558$	−7.41735	−0.314001
$559$	2.23370	0.0944752
$560$	8.04764	0.340075
$561$	1.01479	0.0428443
$562$	3.19597	0.134814
$563$	−1.85310	−0.0780991	−0.0390495	−	0.999237i	$-0.512433\pi$
$563$	−1.85310	−0.0780991	−0.0390495	+	0.999237i	$0.512433\pi$
$564$	35.4357	1.49211
$565$	−1.46420	−0.0615995
$566$	−19.1341	−0.804265
$567$	−3.28939	−0.138141
$568$	−29.4003	−1.23361
$569$	−8.54746	−0.358328	−0.179164	−	0.983819i	$-0.557339\pi$
$569$	−8.54746	−0.358328	−0.179164	+	0.983819i	$0.557339\pi$
$570$	52.4803	2.19816
$571$	27.0460	1.13184	0.565919	−	0.824461i	$-0.308521\pi$
$571$	27.0460	1.13184	0.565919	+	0.824461i	$0.308521\pi$
$572$	6.48433	0.271123
$573$	20.4709	0.855184
$574$	29.5559	1.23364
$575$	−0.991706	−0.0413570
$576$	−12.4602	−0.519177
$577$	−25.2241	−1.05009	−0.525047	−	0.851073i	$-0.675952\pi$
$577$	−25.2241	−1.05009	−0.525047	+	0.851073i	$0.675952\pi$
$578$	37.7444	1.56996
$579$	24.9892	1.03852
$580$	−5.29474	−0.219852
$581$	−10.5175	−0.436340
$582$	32.3958	1.34285
$583$	−8.68074	−0.359519
$584$	−40.6354	−1.68150
$585$	4.71324	0.194868
$586$	−27.1762	−1.12264
$587$	29.0009	1.19700	0.598498	−	0.801124i	$-0.295764\pi$
$587$	29.0009	1.19700	0.598498	+	0.801124i	$0.295764\pi$
$588$	−13.0684	−0.538931
$589$	−25.2750	−1.04144
$590$	4.08833	0.168314
$591$	12.5542	0.516411
$592$	3.17482	0.130484
$593$	−44.5002	−1.82740	−0.913701	−	0.406386i	$-0.866789\pi$
$593$	−44.5002	−1.82740	−0.913701	+	0.406386i	$0.866789\pi$
$594$	−2.66018	−0.109148
$595$	8.30030	0.340279
$596$	18.1321	0.742721
$597$	20.8004	0.851304
$598$	−1.24716	−0.0510000
$599$	−3.00072	−0.122606	−0.0613031	−	0.998119i	$-0.519526\pi$
$599$	−3.00072	−0.122606	−0.0613031	+	0.998119i	$0.519526\pi$
$600$	10.1618	0.414854
$601$	11.5848	0.472555	0.236277	−	0.971686i	$-0.424073\pi$
$601$	11.5848	0.472555	0.236277	+	0.971686i	$0.424073\pi$
$602$	−10.3118	−0.420278
$603$	8.42038	0.342904
$604$	15.4529	0.628769
$605$	27.5427	1.11977
$606$	34.5903	1.40513
$607$	26.5123	1.07610	0.538051	−	0.842912i	$-0.319161\pi$
$607$	26.5123	1.07610	0.538051	+	0.842912i	$0.319161\pi$
$608$	−36.5902	−1.48393
$609$	1.79198	0.0726146
$610$	−82.2050	−3.32838
$611$	17.1844	0.695205
$612$	3.03846	0.122822
$613$	−45.7512	−1.84787	−0.923937	−	0.382544i	$-0.875048\pi$
$613$	−45.7512	−1.84787	−0.923937	+	0.382544i	$0.875048\pi$
$614$	−46.7230	−1.88559
$615$	10.9639	0.442108
$616$	−12.4341	−0.500983
$617$	−12.9316	−0.520605	−0.260303	−	0.965527i	$-0.583822\pi$
$617$	−12.9316	−0.520605	−0.260303	+	0.965527i	$0.583822\pi$
$618$	−13.6485	−0.549023
$619$	−6.94298	−0.279062	−0.139531	−	0.990218i	$-0.544560\pi$
$619$	−6.94298	−0.279062	−0.139531	+	0.990218i	$0.544560\pi$
$620$	−30.9625	−1.24348
$621$	0.322878	0.0129567
$622$	62.7047	2.51423
$623$	−1.99049	−0.0797475
$624$	1.42863	0.0571911
$625$	−30.9234	−1.23694
$626$	−53.7281	−2.14741
$627$	−9.06469	−0.362009
$628$	71.3790	2.84833
$629$	3.27450	0.130563
$630$	−21.7585	−0.866881
$631$	−37.1777	−1.48002	−0.740011	−	0.672594i	$-0.765180\pi$
$631$	−37.1777	−1.48002	−0.740011	+	0.672594i	$0.765180\pi$
$632$	40.7677	1.62165
$633$	2.27900	0.0905822
$634$	−32.0386	−1.27241
$635$	43.1148	1.71096
$636$	−25.9918	−1.03064
$637$	−6.33744	−0.251099
$638$	1.44920	0.0573743
$639$	8.88637	0.351539
$640$	−56.2164	−2.22215
$641$	−7.42424	−0.293240	−0.146620	−	0.989193i	$-0.546839\pi$
$641$	−7.42424	−0.293240	−0.146620	+	0.989193i	$0.546839\pi$
$642$	−12.0868	−0.477028
$643$	−18.3708	−0.724475	−0.362238	−	0.932086i	$-0.617987\pi$
$643$	−18.3708	−0.724475	−0.362238	+	0.932086i	$0.617987\pi$
$644$	3.63333	0.143173
$645$	−3.82522	−0.150618
$646$	16.4068	0.645517
$647$	−32.2522	−1.26797	−0.633983	−	0.773347i	$-0.718581\pi$
$647$	−32.2522	−1.26797	−0.633983	+	0.773347i	$0.718581\pi$
$648$	−3.30847	−0.129969
$649$	−0.706158	−0.0277191
$650$	11.8639	0.465339
$651$	10.4791	0.410709
$652$	80.8864	3.16776
$653$	5.04594	0.197463	0.0987315	−	0.995114i	$-0.468522\pi$
$653$	5.04594	0.197463	0.0987315	+	0.995114i	$0.468522\pi$
$654$	−30.6122	−1.19703
$655$	−2.88774	−0.112833
$656$	3.32329	0.129753
$657$	12.2822	0.479175
$658$	−79.3313	−3.09266
$659$	−4.61835	−0.179905	−0.0899527	−	0.995946i	$-0.528672\pi$
$659$	−4.61835	−0.179905	−0.0899527	+	0.995946i	$0.528672\pi$
$660$	−11.1045	−0.432241
$661$	18.4822	0.718876	0.359438	−	0.933169i	$-0.382968\pi$
$661$	18.4822	0.718876	0.359438	+	0.933169i	$0.382968\pi$
$662$	−15.6167	−0.606960
$663$	1.47349	0.0572255
$664$	−10.5785	−0.410526
$665$	−74.1434	−2.87516
$666$	−8.58383	−0.332616
$667$	−0.175896	−0.00681073
$668$	69.9201	2.70529
$669$	1.19418	0.0461697
$670$	55.6989	2.15184
$671$	14.1989	0.548143
$672$	15.1704	0.585212
$673$	31.1363	1.20022	0.600108	−	0.799919i	$-0.295124\pi$
$673$	31.1363	1.20022	0.600108	+	0.799919i	$0.295124\pi$
$674$	−30.8342	−1.18769
$675$	−3.07145	−0.118220
$676$	−35.0574	−1.34836
$677$	24.9614	0.959346	0.479673	−	0.877447i	$-0.340755\pi$
$677$	24.9614	0.959346	0.479673	+	0.877447i	$0.340755\pi$
$678$	1.19995	0.0460840
$679$	−45.7684	−1.75643
$680$	8.34845	0.320148
$681$	21.4471	0.821855
$682$	8.47462	0.324510
$683$	−44.4683	−1.70153	−0.850765	−	0.525546i	$-0.823861\pi$
$683$	−44.4683	−1.70153	−0.850765	+	0.525546i	$0.823861\pi$
$684$	−27.1414	−1.03778
$685$	−63.5699	−2.42888
$686$	−24.3541	−0.929844
$687$	23.1942	0.884915
$688$	−1.15947	−0.0442043
$689$	−12.6046	−0.480196
$690$	2.13577	0.0813073
$691$	−41.5127	−1.57922	−0.789609	−	0.613610i	$-0.789717\pi$
$691$	−41.5127	−1.57922	−0.789609	+	0.613610i	$0.789717\pi$
$692$	40.5988	1.54333
$693$	3.75825	0.142764
$694$	38.4116	1.45809
$695$	−30.6126	−1.16120
$696$	1.80237	0.0683188
$697$	3.42762	0.129830
$698$	−62.2989	−2.35805
$699$	17.8685	0.675849
$700$	−34.5629	−1.30635
$701$	−13.4151	−0.506682	−0.253341	−	0.967377i	$-0.581530\pi$
$701$	−13.4151	−0.506682	−0.253341	+	0.967377i	$0.581530\pi$
$702$	−3.86262	−0.145785
$703$	−29.2499	−1.10318
$704$	14.2363	0.536552
$705$	−29.4284	−1.10834
$706$	48.4576	1.82372
$707$	−48.8686	−1.83789
$708$	−2.11437	−0.0794630
$709$	−47.2728	−1.77537	−0.887684	−	0.460453i	$-0.847687\pi$
$709$	−47.2728	−1.77537	−0.887684	+	0.460453i	$0.847687\pi$
$710$	58.7813	2.20602
$711$	−12.3222	−0.462120
$712$	−2.00204	−0.0750297
$713$	−1.02861	−0.0385216
$714$	−6.80232	−0.254570
$715$	−5.38506	−0.201390
$716$	51.5008	1.92467
$717$	−19.0004	−0.709583
$718$	1.66153	0.0620078
$719$	34.8082	1.29813	0.649063	−	0.760735i	$-0.275161\pi$
$719$	34.8082	1.29813	0.649063	+	0.760735i	$0.275161\pi$
$720$	−2.44655	−0.0911774
$721$	19.2824	0.718114
$722$	−102.318	−3.80788
$723$	−9.39297	−0.349328
$724$	53.8271	2.00047
$725$	1.67325	0.0621431
$726$	−22.5719	−0.837723
$727$	16.5225	0.612785	0.306393	−	0.951905i	$-0.400878\pi$
$727$	16.5225	0.612785	0.306393	+	0.951905i	$0.400878\pi$
$728$	−18.0545	−0.669144
$729$	1.00000	0.0370370
$730$	81.2441	3.00698
$731$	−1.19587	−0.0442308
$732$	42.5142	1.57137
$733$	2.40152	0.0887022	0.0443511	−	0.999016i	$-0.485878\pi$
$733$	2.40152	0.0887022	0.0443511	+	0.999016i	$0.485878\pi$
$734$	51.3475	1.89527
$735$	10.8529	0.400316
$736$	−1.48909	−0.0548887
$737$	−9.62062	−0.354380
$738$	−8.98523	−0.330751
$739$	29.1795	1.07338	0.536692	−	0.843778i	$-0.319674\pi$
$739$	29.1795	1.07338	0.536692	+	0.843778i	$0.319674\pi$
$740$	−35.8318	−1.31720
$741$	−13.1621	−0.483522
$742$	58.1888	2.13618
$743$	−43.5314	−1.59701	−0.798507	−	0.601986i	$-0.794376\pi$
$743$	−43.5314	−1.59701	−0.798507	+	0.601986i	$0.794376\pi$
$744$	10.5399	0.386412
$745$	−15.0582	−0.551691
$746$	−24.4749	−0.896090
$747$	3.19741	0.116987
$748$	−3.47156	−0.126933
$749$	17.0760	0.623945
$750$	12.7569	0.465816
$751$	14.9924	0.547082	0.273541	−	0.961860i	$-0.411805\pi$
$751$	14.9924	0.547082	0.273541	+	0.961860i	$0.411805\pi$
$752$	−8.92007	−0.325281
$753$	−16.3721	−0.596634
$754$	2.10426	0.0766327
$755$	−12.8332	−0.467048
$756$	11.2529	0.409265
$757$	20.6589	0.750860	0.375430	−	0.926851i	$-0.377495\pi$
$757$	20.6589	0.750860	0.375430	+	0.926851i	$0.377495\pi$
$758$	−79.8309	−2.89959
$759$	−0.368901	−0.0133903
$760$	−74.5736	−2.70507
$761$	16.7685	0.607856	0.303928	−	0.952695i	$-0.401702\pi$
$761$	16.7685	0.607856	0.303928	+	0.952695i	$0.401702\pi$
$762$	−35.3337	−1.28001
$763$	43.2485	1.56570
$764$	−70.0305	−2.53362
$765$	−2.52336	−0.0912322
$766$	−29.9220	−1.08113
$767$	−1.02535	−0.0370234
$768$	21.1504	0.763198
$769$	2.02844	0.0731474	0.0365737	−	0.999331i	$-0.488356\pi$
$769$	2.02844	0.0731474	0.0365737	+	0.999331i	$0.488356\pi$
$770$	24.8600	0.895892
$771$	−29.2695	−1.05411
$772$	−85.4875	−3.07676
$773$	19.8684	0.714615	0.357307	−	0.933987i	$-0.383695\pi$
$773$	19.8684	0.714615	0.357307	+	0.933987i	$0.383695\pi$
$774$	3.13487	0.112681
$775$	9.78484	0.351482
$776$	−46.0339	−1.65252
$777$	12.1271	0.435057
$778$	61.1773	2.19331
$779$	−30.6177	−1.09699
$780$	−16.1239	−0.577328
$781$	−10.1530	−0.363304
$782$	0.667699	0.0238769
$783$	−0.544776	−0.0194687
$784$	3.28964	0.117487
$785$	−59.2783	−2.11573
$786$	2.36658	0.0844132
$787$	16.4543	0.586533	0.293267	−	0.956031i	$-0.405258\pi$
$787$	16.4543	0.586533	0.293267	+	0.956031i	$0.405258\pi$
$788$	−42.9477	−1.52995
$789$	−7.08720	−0.252311
$790$	−81.5087	−2.89995
$791$	−1.69528	−0.0602771
$792$	3.78006	0.134318
$793$	20.6171	0.732133
$794$	−30.0060	−1.06487
$795$	21.5855	0.765557
$796$	−71.1578	−2.52212
$797$	−30.8755	−1.09367	−0.546833	−	0.837242i	$-0.684167\pi$
$797$	−30.8755	−1.09367	−0.546833	+	0.837242i	$0.684167\pi$
$798$	60.7625	2.15097
$799$	−9.20012	−0.325477
$800$	14.1653	0.500820
$801$	0.605126	0.0213811
$802$	31.2928	1.10499
$803$	−14.0329	−0.495211
$804$	−28.8060	−1.01591
$805$	−3.01738	−0.106349
$806$	12.3053	0.433435
$807$	−5.68187	−0.200011
$808$	−49.1521	−1.72916
$809$	−28.7093	−1.00937	−0.504683	−	0.863305i	$-0.668391\pi$
$809$	−28.7093	−1.00937	−0.504683	+	0.863305i	$0.668391\pi$
$810$	6.61477	0.232419
$811$	30.7108	1.07840	0.539201	−	0.842177i	$-0.318726\pi$
$811$	30.7108	1.07840	0.539201	+	0.842177i	$0.318726\pi$
$812$	−6.13032	−0.215132
$813$	−1.61529	−0.0566507
$814$	9.80736	0.343748
$815$	−67.1739	−2.35300
$816$	−0.764858	−0.0267754
$817$	10.6822	0.373724
$818$	7.39344	0.258506
$819$	5.45705	0.190685
$820$	−37.5074	−1.30981
$821$	−10.9975	−0.383814	−0.191907	−	0.981413i	$-0.561467\pi$
$821$	−10.9975	−0.383814	−0.191907	+	0.981413i	$0.561467\pi$
$822$	52.0972	1.81710
$823$	−14.3800	−0.501255	−0.250628	−	0.968084i	$-0.580637\pi$
$823$	−14.3800	−0.501255	−0.250628	+	0.968084i	$0.580637\pi$
$824$	19.3943	0.675631
$825$	3.50926	0.122177
$826$	4.73353	0.164700
$827$	22.0394	0.766385	0.383192	−	0.923669i	$-0.374825\pi$
$827$	22.0394	0.766385	0.383192	+	0.923669i	$0.374825\pi$
$828$	−1.10456	−0.0383861
$829$	32.2098	1.11869	0.559346	−	0.828934i	$-0.311052\pi$
$829$	32.2098	1.11869	0.559346	+	0.828934i	$0.311052\pi$
$830$	21.1501	0.734131
$831$	12.7932	0.443793
$832$	20.6714	0.716652
$833$	3.39292	0.117558
$834$	25.0878	0.868720
$835$	−58.0667	−2.00948
$836$	31.0101	1.07251
$837$	−3.18574	−0.110115
$838$	−22.5015	−0.777302
$839$	5.50370	0.190009	0.0950044	−	0.995477i	$-0.469713\pi$
$839$	5.50370	0.190009	0.0950044	+	0.995477i	$0.469713\pi$
$840$	30.9185	1.06679
$841$	−28.7032	−0.989766
$842$	−24.1050	−0.830712
$843$	1.37266	0.0472770
$844$	−7.79642	−0.268364
$845$	29.1142	1.00156
$846$	24.1173	0.829171
$847$	31.8893	1.09573
$848$	6.54279	0.224680
$849$	−8.21804	−0.282042
$850$	−6.35164	−0.217859
$851$	−1.19037	−0.0408053
$852$	−30.4001	−1.04149
$853$	−14.1766	−0.485396	−0.242698	−	0.970102i	$-0.578032\pi$
$853$	−14.1766	−0.485396	−0.242698	+	0.970102i	$0.578032\pi$
$854$	−95.1782	−3.25693
$855$	22.5402	0.770859
$856$	17.1751	0.587033
$857$	19.6256	0.670397	0.335199	−	0.942147i	$-0.391197\pi$
$857$	19.6256	0.670397	0.335199	+	0.942147i	$0.391197\pi$
$858$	4.41320	0.150664
$859$	−18.8304	−0.642484	−0.321242	−	0.946997i	$-0.604100\pi$
$859$	−18.8304	−0.642484	−0.321242	+	0.946997i	$0.604100\pi$
$860$	13.0860	0.446229
$861$	12.6942	0.432617
$862$	33.3845	1.13708
$863$	−46.3705	−1.57847	−0.789236	−	0.614090i	$-0.789523\pi$
$863$	−46.3705	−1.57847	−0.789236	+	0.614090i	$0.789523\pi$
$864$	−4.61193	−0.156901
$865$	−33.7162	−1.14638
$866$	24.5236	0.833347
$867$	16.2111	0.550559
$868$	−35.8489	−1.21679
$869$	14.0786	0.477585
$870$	−3.60357	−0.122172
$871$	−13.9693	−0.473332
$872$	43.4994	1.47307
$873$	13.9139	0.470916
$874$	−5.96430	−0.201746
$875$	−18.0227	−0.609280
$876$	−42.0173	−1.41963
$877$	5.59672	0.188988	0.0944939	−	0.995525i	$-0.469877\pi$
$877$	5.59672	0.188988	0.0944939	+	0.995525i	$0.469877\pi$
$878$	67.1617	2.26660
$879$	−11.6721	−0.393691
$880$	2.79528	0.0942288
$881$	33.5471	1.13023	0.565115	−	0.825012i	$-0.308832\pi$
$881$	33.5471	1.13023	0.565115	+	0.825012i	$0.308832\pi$
$882$	−8.89426	−0.299485
$883$	−15.4322	−0.519334	−0.259667	−	0.965698i	$-0.583613\pi$
$883$	−15.4322	−0.519334	−0.259667	+	0.965698i	$0.583613\pi$
$884$	−5.04077	−0.169539
$885$	1.75593	0.0590249
$886$	46.7897	1.57193
$887$	−4.27979	−0.143701	−0.0718506	−	0.997415i	$-0.522890\pi$
$887$	−4.27979	−0.143701	−0.0718506	+	0.997415i	$0.522890\pi$
$888$	12.1975	0.409320
$889$	49.9190	1.67423
$890$	4.00277	0.134173
$891$	−1.14254	−0.0382765
$892$	−4.08527	−0.136785
$893$	82.1812	2.75009
$894$	12.3406	0.412732
$895$	−42.7700	−1.42964
$896$	−65.0882	−2.17444
$897$	−0.535651	−0.0178849
$898$	29.6216	0.988486
$899$	1.73551	0.0578826
$900$	10.5074	0.350246
$901$	6.74820	0.224815
$902$	10.2660	0.341820
$903$	−4.42890	−0.147384
$904$	−1.70511	−0.0567112
$905$	−44.7019	−1.48594
$906$	10.5171	0.349409
$907$	−7.92747	−0.263227	−0.131614	−	0.991301i	$-0.542016\pi$
$907$	−7.92747	−0.263227	−0.131614	+	0.991301i	$0.542016\pi$
$908$	−73.3701	−2.43487
$909$	14.8564	0.492757
$910$	36.0972	1.19661
$911$	38.4461	1.27378	0.636888	−	0.770956i	$-0.280221\pi$
$911$	38.4461	1.27378	0.636888	+	0.770956i	$0.280221\pi$
$912$	6.83218	0.226236
$913$	−3.65317	−0.120902
$914$	15.7367	0.520523
$915$	−35.3069	−1.16721
$916$	−79.3470	−2.62170
$917$	−3.34347	−0.110411
$918$	2.06796	0.0682528
$919$	9.62956	0.317650	0.158825	−	0.987307i	$-0.449229\pi$
$919$	9.62956	0.317650	0.158825	+	0.987307i	$0.449229\pi$
$920$	−3.03488	−0.100057
$921$	−20.0674	−0.661244
$922$	−48.2159	−1.58790
$923$	−14.7424	−0.485251
$924$	−12.8569	−0.422962
$925$	11.3236	0.372319
$926$	20.7564	0.682098
$927$	−5.86201	−0.192534
$928$	2.51247	0.0824758
$929$	−56.1650	−1.84271	−0.921357	−	0.388717i	$-0.872918\pi$
$929$	−56.1650	−1.84271	−0.921357	+	0.388717i	$0.872918\pi$
$930$	−21.0729	−0.691008
$931$	−30.3077	−0.993294
$932$	−61.1279	−2.00231
$933$	26.9316	0.881700
$934$	28.4562	0.931115
$935$	2.88304	0.0942854
$936$	5.48871	0.179404
$937$	−11.0667	−0.361532	−0.180766	−	0.983526i	$-0.557858\pi$
$937$	−11.0667	−0.361532	−0.180766	+	0.983526i	$0.557858\pi$
$938$	64.4890	2.10564
$939$	−23.0761	−0.753061
$940$	100.674	3.28362
$941$	45.3760	1.47922	0.739608	−	0.673038i	$-0.235011\pi$
$941$	45.3760	1.47922	0.739608	+	0.673038i	$0.235011\pi$
$942$	48.5801	1.58283
$943$	−1.24603	−0.0405764
$944$	0.532241	0.0173230
$945$	−9.34525	−0.304001
$946$	−3.58171	−0.116452
$947$	38.8301	1.26181	0.630905	−	0.775860i	$-0.282684\pi$
$947$	38.8301	1.26181	0.630905	+	0.775860i	$0.282684\pi$
$948$	42.1541	1.36910
$949$	−20.3761	−0.661435
$950$	56.7368	1.84078
$951$	−13.7605	−0.446215
$952$	9.66596	0.313276
$953$	−11.5533	−0.374249	−0.187124	−	0.982336i	$-0.559917\pi$
$953$	−11.5533	−0.374249	−0.187124	+	0.982336i	$0.559917\pi$
$954$	−17.6899	−0.572730
$955$	58.1584	1.88196
$956$	65.0000	2.10225
$957$	0.622428	0.0201202
$958$	55.8006	1.80284
$959$	−73.6021	−2.37674
$960$	−35.3999	−1.14253
$961$	−20.8511	−0.672616
$962$	14.2405	0.459131
$963$	−5.19125	−0.167286
$964$	32.1332	1.03494
$965$	70.9950	2.28541
$966$	2.47282	0.0795618
$967$	13.1206	0.421930	0.210965	−	0.977494i	$-0.432339\pi$
$967$	13.1206	0.421930	0.210965	+	0.977494i	$0.432339\pi$
$968$	32.0743	1.03091
$969$	7.04668	0.226372
$970$	92.0376	2.95515
$971$	37.1142	1.19105	0.595525	−	0.803337i	$-0.296944\pi$
$971$	37.1142	1.19105	0.595525	+	0.803337i	$0.296944\pi$
$972$	−3.42098	−0.109728
$973$	−35.4437	−1.13627
$974$	−18.7619	−0.601170
$975$	5.09551	0.163187
$976$	−10.7019	−0.342560
$977$	46.0417	1.47301	0.736503	−	0.676435i	$-0.236476\pi$
$977$	46.0417	1.47301	0.736503	+	0.676435i	$0.236476\pi$
$978$	55.0508	1.76033
$979$	−0.691381	−0.0220966
$980$	−37.1276	−1.18600
$981$	−13.1479	−0.419780
$982$	52.9675	1.69026
$983$	55.8445	1.78116	0.890581	−	0.454825i	$-0.150298\pi$
$983$	55.8445	1.78116	0.890581	+	0.454825i	$0.150298\pi$
$984$	12.7678	0.407024
$985$	35.6669	1.13644
$986$	−1.12657	−0.0358774
$987$	−34.0726	−1.08454
$988$	45.0273	1.43251
$989$	0.434730	0.0138236
$990$	−7.55764	−0.240198
$991$	50.6859	1.61009	0.805045	−	0.593213i	$-0.202141\pi$
$991$	50.6859	1.61009	0.805045	+	0.593213i	$0.202141\pi$
$992$	14.6924	0.466484
$993$	−6.70734	−0.212851
$994$	68.0579	2.15866
$995$	59.0946	1.87342
$996$	−10.9383	−0.346592
$997$	36.0361	1.14128	0.570638	−	0.821202i	$-0.306696\pi$
$997$	36.0361	1.14128	0.570638	+	0.821202i	$0.306696\pi$
$998$	−16.1749	−0.512008
$999$	−3.68674	−0.116643

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.b.1.7	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.b.1.7	✓	74	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6009 = 3 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32830 q^{2} -1.00000 q^{3} +3.42098 q^{4} -2.84103 q^{5} +2.32830 q^{6} -3.28939 q^{7} -3.30847 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.32830 q^{2} -1.00000 q^{3} +3.42098 q^{4} -2.84103 q^{5} +2.32830 q^{6} -3.28939 q^{7} -3.30847 q^{8} +1.00000 q^{9} +6.61477 q^{10} -1.14254 q^{11} -3.42098 q^{12} -1.65899 q^{13} +7.65868 q^{14} +2.84103 q^{15} +0.861148 q^{16} +0.888184 q^{17} -2.32830 q^{18} -7.93381 q^{19} -9.71911 q^{20} +3.28939 q^{21} +2.66018 q^{22} -0.322878 q^{23} +3.30847 q^{24} +3.07145 q^{25} +3.86262 q^{26} -1.00000 q^{27} -11.2529 q^{28} +0.544776 q^{29} -6.61477 q^{30} +3.18574 q^{31} +4.61193 q^{32} +1.14254 q^{33} -2.06796 q^{34} +9.34525 q^{35} +3.42098 q^{36} +3.68674 q^{37} +18.4723 q^{38} +1.65899 q^{39} +9.39946 q^{40} +3.85914 q^{41} -7.65868 q^{42} -1.34642 q^{43} -3.90861 q^{44} -2.84103 q^{45} +0.751758 q^{46} -10.3584 q^{47} -0.861148 q^{48} +3.82007 q^{49} -7.15127 q^{50} -0.888184 q^{51} -5.67537 q^{52} +7.59776 q^{53} +2.32830 q^{54} +3.24599 q^{55} +10.8828 q^{56} +7.93381 q^{57} -1.26840 q^{58} +0.618060 q^{59} +9.71911 q^{60} -12.4275 q^{61} -7.41735 q^{62} -3.28939 q^{63} -12.4602 q^{64} +4.71324 q^{65} -2.66018 q^{66} +8.42038 q^{67} +3.03846 q^{68} +0.322878 q^{69} -21.7585 q^{70} +8.88637 q^{71} -3.30847 q^{72} +12.2822 q^{73} -8.58383 q^{74} -3.07145 q^{75} -27.1414 q^{76} +3.75825 q^{77} -3.86262 q^{78} -12.3222 q^{79} -2.44655 q^{80} +1.00000 q^{81} -8.98523 q^{82} +3.19741 q^{83} +11.2529 q^{84} -2.52336 q^{85} +3.13487 q^{86} -0.544776 q^{87} +3.78006 q^{88} +0.605126 q^{89} +6.61477 q^{90} +5.45705 q^{91} -1.10456 q^{92} -3.18574 q^{93} +24.1173 q^{94} +22.5402 q^{95} -4.61193 q^{96} +13.9139 q^{97} -8.89426 q^{98} -1.14254 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 3 q^{2} - 74 q^{3} + 57 q^{4} + 14 q^{5} + 3 q^{6} - 26 q^{7} - 9 q^{8} + 74 q^{9}+O(q^{10}) \) 74 * q - 3 * q^2 - 74 * q^3 + 57 * q^4 + 14 * q^5 + 3 * q^6 - 26 * q^7 - 9 * q^8 + 74 * q^9	\( 74 q - 3 q^{2} - 74 q^{3} + 57 q^{4} + 14 q^{5} + 3 q^{6} - 26 q^{7} - 9 q^{8} + 74 q^{9} - 21 q^{10} - 16 q^{11} - 57 q^{12} - 16 q^{13} - 17 q^{14} - 14 q^{15} + 15 q^{16} + 33 q^{17} - 3 q^{18} - 46 q^{19} + 17 q^{20} + 26 q^{21} - 28 q^{22} - 31 q^{23} + 9 q^{24} + 42 q^{25} - 8 q^{26} - 74 q^{27} - 46 q^{28} - 7 q^{29} + 21 q^{30} - 60 q^{31} - 16 q^{32} + 16 q^{33} - 42 q^{34} - 46 q^{35} + 57 q^{36} - 22 q^{37} + 10 q^{38} + 16 q^{39} - 67 q^{40} - 11 q^{41} + 17 q^{42} - 56 q^{43} - 25 q^{44} + 14 q^{45} - 59 q^{46} - q^{47} - 15 q^{48} + 12 q^{49} - 24 q^{50} - 33 q^{51} - 37 q^{52} + 25 q^{53} + 3 q^{54} - 90 q^{55} - 46 q^{56} + 46 q^{57} - 20 q^{58} - 60 q^{59} - 17 q^{60} - 55 q^{61} + 40 q^{62} - 26 q^{63} - 55 q^{64} - 12 q^{65} + 28 q^{66} - 64 q^{67} + 75 q^{68} + 31 q^{69} - 23 q^{70} - 128 q^{71} - 9 q^{72} - 31 q^{73} - 51 q^{74} - 42 q^{75} - 109 q^{76} + 70 q^{77} + 8 q^{78} - 193 q^{79} + 39 q^{80} + 74 q^{81} - 26 q^{82} - 5 q^{83} + 46 q^{84} - 60 q^{85} - 36 q^{86} + 7 q^{87} - 56 q^{88} - 21 q^{90} - 99 q^{91} - 54 q^{92} + 60 q^{93} - 66 q^{94} - 101 q^{95} + 16 q^{96} - 36 q^{97} - 21 q^{98} - 16 q^{99}+O(q^{100}) \) 74 * q - 3 * q^2 - 74 * q^3 + 57 * q^4 + 14 * q^5 + 3 * q^6 - 26 * q^7 - 9 * q^8 + 74 * q^9 - 21 * q^10 - 16 * q^11 - 57 * q^12 - 16 * q^13 - 17 * q^14 - 14 * q^15 + 15 * q^16 + 33 * q^17 - 3 * q^18 - 46 * q^19 + 17 * q^20 + 26 * q^21 - 28 * q^22 - 31 * q^23 + 9 * q^24 + 42 * q^25 - 8 * q^26 - 74 * q^27 - 46 * q^28 - 7 * q^29 + 21 * q^30 - 60 * q^31 - 16 * q^32 + 16 * q^33 - 42 * q^34 - 46 * q^35 + 57 * q^36 - 22 * q^37 + 10 * q^38 + 16 * q^39 - 67 * q^40 - 11 * q^41 + 17 * q^42 - 56 * q^43 - 25 * q^44 + 14 * q^45 - 59 * q^46 - q^47 - 15 * q^48 + 12 * q^49 - 24 * q^50 - 33 * q^51 - 37 * q^52 + 25 * q^53 + 3 * q^54 - 90 * q^55 - 46 * q^56 + 46 * q^57 - 20 * q^58 - 60 * q^59 - 17 * q^60 - 55 * q^61 + 40 * q^62 - 26 * q^63 - 55 * q^64 - 12 * q^65 + 28 * q^66 - 64 * q^67 + 75 * q^68 + 31 * q^69 - 23 * q^70 - 128 * q^71 - 9 * q^72 - 31 * q^73 - 51 * q^74 - 42 * q^75 - 109 * q^76 + 70 * q^77 + 8 * q^78 - 193 * q^79 + 39 * q^80 + 74 * q^81 - 26 * q^82 - 5 * q^83 + 46 * q^84 - 60 * q^85 - 36 * q^86 + 7 * q^87 - 56 * q^88 - 21 * q^90 - 99 * q^91 - 54 * q^92 + 60 * q^93 - 66 * q^94 - 101 * q^95 + 16 * q^96 - 36 * q^97 - 21 * q^98 - 16 * q^99

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