LMFDB - Embedded newform 6009.2.a.c.1.11

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:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-2.23454 q^{2} +1.00000 q^{3} +2.99319 q^{4} +2.17127 q^{5} -2.23454 q^{6} -3.00622 q^{7} -2.21933 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.23454 q^{2} +1.00000 q^{3} +2.99319 q^{4} +2.17127 q^{5} -2.23454 q^{6} -3.00622 q^{7} -2.21933 q^{8} +1.00000 q^{9} -4.85180 q^{10} -2.71370 q^{11} +2.99319 q^{12} -1.05917 q^{13} +6.71754 q^{14} +2.17127 q^{15} -1.02719 q^{16} +0.843009 q^{17} -2.23454 q^{18} +1.17846 q^{19} +6.49902 q^{20} -3.00622 q^{21} +6.06389 q^{22} -7.73376 q^{23} -2.21933 q^{24} -0.285593 q^{25} +2.36677 q^{26} +1.00000 q^{27} -8.99820 q^{28} -7.27552 q^{29} -4.85180 q^{30} -0.0713017 q^{31} +6.73396 q^{32} -2.71370 q^{33} -1.88374 q^{34} -6.52732 q^{35} +2.99319 q^{36} +7.98801 q^{37} -2.63333 q^{38} -1.05917 q^{39} -4.81876 q^{40} +1.03360 q^{41} +6.71754 q^{42} -0.267189 q^{43} -8.12262 q^{44} +2.17127 q^{45} +17.2814 q^{46} +11.3799 q^{47} -1.02719 q^{48} +2.03737 q^{49} +0.638171 q^{50} +0.843009 q^{51} -3.17030 q^{52} -0.634346 q^{53} -2.23454 q^{54} -5.89217 q^{55} +6.67180 q^{56} +1.17846 q^{57} +16.2575 q^{58} -1.03598 q^{59} +6.49902 q^{60} -8.79324 q^{61} +0.159327 q^{62} -3.00622 q^{63} -12.9930 q^{64} -2.29975 q^{65} +6.06389 q^{66} +4.64887 q^{67} +2.52329 q^{68} -7.73376 q^{69} +14.5856 q^{70} +5.75629 q^{71} -2.21933 q^{72} +0.383890 q^{73} -17.8496 q^{74} -0.285593 q^{75} +3.52736 q^{76} +8.15799 q^{77} +2.36677 q^{78} +7.07903 q^{79} -2.23030 q^{80} +1.00000 q^{81} -2.30962 q^{82} +5.93882 q^{83} -8.99820 q^{84} +1.83040 q^{85} +0.597046 q^{86} -7.27552 q^{87} +6.02260 q^{88} +3.69665 q^{89} -4.85180 q^{90} +3.18411 q^{91} -23.1486 q^{92} -0.0713017 q^{93} -25.4288 q^{94} +2.55876 q^{95} +6.73396 q^{96} -12.8821 q^{97} -4.55260 q^{98} -2.71370 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9}+O(q^{10}) $ 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9} + 13 q^{10} + 40 q^{11} + 107 q^{12} + 6 q^{13} + 37 q^{14} + 34 q^{15} + 133 q^{16} + 77 q^{17} + 17 q^{18} + 34 q^{19} + 55 q^{20} + 22 q^{21} + 8 q^{22} + 83 q^{23} + 51 q^{24} + 110 q^{25} + 22 q^{26} + 92 q^{27} + 32 q^{28} + 97 q^{29} + 13 q^{30} + 44 q^{31} + 104 q^{32} + 40 q^{33} + 20 q^{34} + 80 q^{35} + 107 q^{36} + 12 q^{37} + 54 q^{38} + 6 q^{39} + 23 q^{40} + 67 q^{41} + 37 q^{42} + 30 q^{43} + 87 q^{44} + 34 q^{45} + 33 q^{46} + 69 q^{47} + 133 q^{48} + 112 q^{49} + 58 q^{50} + 77 q^{51} - 3 q^{52} + 113 q^{53} + 17 q^{54} + 42 q^{55} + 92 q^{56} + 34 q^{57} - 30 q^{58} + 72 q^{59} + 55 q^{60} + 19 q^{61} + 60 q^{62} + 22 q^{63} + 147 q^{64} + 74 q^{65} + 8 q^{66} + 26 q^{67} + 171 q^{68} + 83 q^{69} - 35 q^{70} + 134 q^{71} + 51 q^{72} - 17 q^{73} + 95 q^{74} + 110 q^{75} + 27 q^{76} + 108 q^{77} + 22 q^{78} + 159 q^{79} + 79 q^{80} + 92 q^{81} - 64 q^{82} + 73 q^{83} + 32 q^{84} - 4 q^{85} + 22 q^{86} + 97 q^{87} - 16 q^{88} + 50 q^{89} + 13 q^{90} + 17 q^{91} + 154 q^{92} + 44 q^{93} + 8 q^{94} + 155 q^{95} + 104 q^{96} - 20 q^{97} + 63 q^{98} + 40 q^{99}+O(q^{100}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9 + 13 * q^10 + 40 * q^11 + 107 * q^12 + 6 * q^13 + 37 * q^14 + 34 * q^15 + 133 * q^16 + 77 * q^17 + 17 * q^18 + 34 * q^19 + 55 * q^20 + 22 * q^21 + 8 * q^22 + 83 * q^23 + 51 * q^24 + 110 * q^25 + 22 * q^26 + 92 * q^27 + 32 * q^28 + 97 * q^29 + 13 * q^30 + 44 * q^31 + 104 * q^32 + 40 * q^33 + 20 * q^34 + 80 * q^35 + 107 * q^36 + 12 * q^37 + 54 * q^38 + 6 * q^39 + 23 * q^40 + 67 * q^41 + 37 * q^42 + 30 * q^43 + 87 * q^44 + 34 * q^45 + 33 * q^46 + 69 * q^47 + 133 * q^48 + 112 * q^49 + 58 * q^50 + 77 * q^51 - 3 * q^52 + 113 * q^53 + 17 * q^54 + 42 * q^55 + 92 * q^56 + 34 * q^57 - 30 * q^58 + 72 * q^59 + 55 * q^60 + 19 * q^61 + 60 * q^62 + 22 * q^63 + 147 * q^64 + 74 * q^65 + 8 * q^66 + 26 * q^67 + 171 * q^68 + 83 * q^69 - 35 * q^70 + 134 * q^71 + 51 * q^72 - 17 * q^73 + 95 * q^74 + 110 * q^75 + 27 * q^76 + 108 * q^77 + 22 * q^78 + 159 * q^79 + 79 * q^80 + 92 * q^81 - 64 * q^82 + 73 * q^83 + 32 * q^84 - 4 * q^85 + 22 * q^86 + 97 * q^87 - 16 * q^88 + 50 * q^89 + 13 * q^90 + 17 * q^91 + 154 * q^92 + 44 * q^93 + 8 * q^94 + 155 * q^95 + 104 * q^96 - 20 * q^97 + 63 * q^98 + 40 * 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 $

$2$	−2.23454	−1.58006	−0.790031	−	0.613067i	$-0.789936\pi$
$2$	−2.23454	−1.58006	−0.790031	+	0.613067i	$0.789936\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.99319	1.49660
$5$	2.17127	0.971021	0.485510	−	0.874231i	$-0.338634\pi$
$5$	2.17127	0.971021	0.485510	+	0.874231i	$0.338634\pi$
$6$	−2.23454	−0.912249
$7$	−3.00622	−1.13625	−0.568123	−	0.822944i	$-0.692330\pi$
$7$	−3.00622	−1.13625	−0.568123	+	0.822944i	$0.692330\pi$
$8$	−2.21933	−0.784652
$9$	1.00000	0.333333
$10$	−4.85180	−1.53427
$11$	−2.71370	−0.818211	−0.409106	−	0.912487i	$-0.634159\pi$
$11$	−2.71370	−0.818211	−0.409106	+	0.912487i	$0.634159\pi$
$12$	2.99319	0.864060
$13$	−1.05917	−0.293761	−0.146881	−	0.989154i	$-0.546923\pi$
$13$	−1.05917	−0.293761	−0.146881	+	0.989154i	$0.546923\pi$
$14$	6.71754	1.79534
$15$	2.17127	0.560619
$16$	−1.02719	−0.256797
$17$	0.843009	0.204460	0.102230	−	0.994761i	$-0.467402\pi$
$17$	0.843009	0.204460	0.102230	+	0.994761i	$0.467402\pi$
$18$	−2.23454	−0.526687
$19$	1.17846	0.270358	0.135179	−	0.990821i	$-0.456839\pi$
$19$	1.17846	0.270358	0.135179	+	0.990821i	$0.456839\pi$
$20$	6.49902	1.45323
$21$	−3.00622	−0.656012
$22$	6.06389	1.29282
$23$	−7.73376	−1.61260	−0.806300	−	0.591506i	$-0.798534\pi$
$23$	−7.73376	−1.61260	−0.806300	+	0.591506i	$0.798534\pi$
$24$	−2.21933	−0.453019
$25$	−0.285593	−0.0571187
$26$	2.36677	0.464161
$27$	1.00000	0.192450
$28$	−8.99820	−1.70050
$29$	−7.27552	−1.35103	−0.675515	−	0.737346i	$-0.736079\pi$
$29$	−7.27552	−1.35103	−0.675515	+	0.737346i	$0.736079\pi$
$30$	−4.85180	−0.885813
$31$	−0.0713017	−0.0128062	−0.00640308	−	0.999980i	$-0.502038\pi$
$31$	−0.0713017	−0.0128062	−0.00640308	+	0.999980i	$0.502038\pi$
$32$	6.73396	1.19041
$33$	−2.71370	−0.472395
$34$	−1.88374	−0.323059
$35$	−6.52732	−1.10332
$36$	2.99319	0.498865
$37$	7.98801	1.31322	0.656610	−	0.754230i	$-0.271990\pi$
$37$	7.98801	1.31322	0.656610	+	0.754230i	$0.271990\pi$
$38$	−2.63333	−0.427182
$39$	−1.05917	−0.169603
$40$	−4.81876	−0.761913
$41$	1.03360	0.161421	0.0807104	−	0.996738i	$-0.474281\pi$
$41$	1.03360	0.161421	0.0807104	+	0.996738i	$0.474281\pi$
$42$	6.71754	1.03654
$43$	−0.267189	−0.0407459	−0.0203730	−	0.999792i	$-0.506485\pi$
$43$	−0.267189	−0.0407459	−0.0203730	+	0.999792i	$0.506485\pi$
$44$	−8.12262	−1.22453
$45$	2.17127	0.323674
$46$	17.2814	2.54801
$47$	11.3799	1.65992	0.829962	−	0.557820i	$-0.188362\pi$
$47$	11.3799	1.65992	0.829962	+	0.557820i	$0.188362\pi$
$48$	−1.02719	−0.148262
$49$	2.03737	0.291053
$50$	0.638171	0.0902511
$51$	0.843009	0.118045
$52$	−3.17030	−0.439642
$53$	−0.634346	−0.0871341	−0.0435671	−	0.999051i	$-0.513872\pi$
$53$	−0.634346	−0.0871341	−0.0435671	+	0.999051i	$0.513872\pi$
$54$	−2.23454	−0.304083
$55$	−5.89217	−0.794500
$56$	6.67180	0.891557
$57$	1.17846	0.156091
$58$	16.2575	2.13471
$59$	−1.03598	−0.134873	−0.0674363	−	0.997724i	$-0.521482\pi$
$59$	−1.03598	−0.134873	−0.0674363	+	0.997724i	$0.521482\pi$
$60$	6.49902	0.839020
$61$	−8.79324	−1.12586	−0.562930	−	0.826505i	$-0.690326\pi$
$61$	−8.79324	−1.12586	−0.562930	+	0.826505i	$0.690326\pi$
$62$	0.159327	0.0202345
$63$	−3.00622	−0.378748
$64$	−12.9930	−1.62412
$65$	−2.29975	−0.285248
$66$	6.06389	0.746413
$67$	4.64887	0.567950	0.283975	−	0.958832i	$-0.408347\pi$
$67$	4.64887	0.567950	0.283975	+	0.958832i	$0.408347\pi$
$68$	2.52329	0.305994
$69$	−7.73376	−0.931036
$70$	14.5856	1.74331
$71$	5.75629	0.683146	0.341573	−	0.939855i	$-0.389040\pi$
$71$	5.75629	0.683146	0.341573	+	0.939855i	$0.389040\pi$
$72$	−2.21933	−0.261551
$73$	0.383890	0.0449309	0.0224654	−	0.999748i	$-0.492848\pi$
$73$	0.383890	0.0449309	0.0224654	+	0.999748i	$0.492848\pi$
$74$	−17.8496	−2.07497
$75$	−0.285593	−0.0329775
$76$	3.52736	0.404616
$77$	8.15799	0.929689
$78$	2.36677	0.267984
$79$	7.07903	0.796454	0.398227	−	0.917287i	$-0.369626\pi$
$79$	7.07903	0.796454	0.398227	+	0.917287i	$0.369626\pi$
$80$	−2.23030	−0.249355
$81$	1.00000	0.111111
$82$	−2.30962	−0.255055
$83$	5.93882	0.651870	0.325935	−	0.945392i	$-0.394321\pi$
$83$	5.93882	0.651870	0.325935	+	0.945392i	$0.394321\pi$
$84$	−8.99820	−0.981784
$85$	1.83040	0.198535
$86$	0.597046	0.0643811
$87$	−7.27552	−0.780018
$88$	6.02260	0.642011
$89$	3.69665	0.391844	0.195922	−	0.980619i	$-0.437230\pi$
$89$	3.69665	0.391844	0.195922	+	0.980619i	$0.437230\pi$
$90$	−4.85180	−0.511424
$91$	3.18411	0.333785
$92$	−23.1486	−2.41341
$93$	−0.0713017	−0.00739364
$94$	−25.4288	−2.62278
$95$	2.55876	0.262523
$96$	6.73396	0.687282
$97$	−12.8821	−1.30798	−0.653990	−	0.756504i	$-0.726906\pi$
$97$	−12.8821	−1.30798	−0.653990	+	0.756504i	$0.726906\pi$
$98$	−4.55260	−0.459882
$99$	−2.71370	−0.272737
$100$	−0.854836	−0.0854836
$101$	17.0489	1.69643	0.848213	−	0.529655i	$-0.177679\pi$
$101$	17.0489	1.69643	0.848213	+	0.529655i	$0.177679\pi$
$102$	−1.88374	−0.186518
$103$	−13.1445	−1.29516	−0.647582	−	0.761996i	$-0.724220\pi$
$103$	−13.1445	−1.29516	−0.647582	+	0.761996i	$0.724220\pi$
$104$	2.35065	0.230500
$105$	−6.52732	−0.637001
$106$	1.41747	0.137677
$107$	17.8489	1.72552	0.862761	−	0.505613i	$-0.168733\pi$
$107$	17.8489	1.72552	0.862761	+	0.505613i	$0.168733\pi$
$108$	2.99319	0.288020
$109$	20.3803	1.95207	0.976037	−	0.217603i	$-0.0698240\pi$
$109$	20.3803	1.95207	0.976037	+	0.217603i	$0.0698240\pi$
$110$	13.1663	1.25536
$111$	7.98801	0.758188
$112$	3.08796	0.291784
$113$	−15.7136	−1.47821	−0.739104	−	0.673591i	$-0.764751\pi$
$113$	−15.7136	−1.47821	−0.739104	+	0.673591i	$0.764751\pi$
$114$	−2.63333	−0.246634
$115$	−16.7921	−1.56587
$116$	−21.7770	−2.02195
$117$	−1.05917	−0.0979205
$118$	2.31493	0.213107
$119$	−2.53427	−0.232316
$120$	−4.81876	−0.439891
$121$	−3.63583	−0.330530
$122$	19.6489	1.77893
$123$	1.03360	0.0931963
$124$	−0.213420	−0.0191656
$125$	−11.4764	−1.02648
$126$	6.71754	0.598446
$127$	15.0438	1.33492	0.667459	−	0.744647i	$-0.267382\pi$
$127$	15.0438	1.33492	0.667459	+	0.744647i	$0.267382\pi$
$128$	15.5654	1.37580
$129$	−0.267189	−0.0235247
$130$	5.13889	0.450710
$131$	−0.960260	−0.0838983	−0.0419492	−	0.999120i	$-0.513357\pi$
$131$	−0.960260	−0.0838983	−0.0419492	+	0.999120i	$0.513357\pi$
$132$	−8.12262	−0.706984
$133$	−3.54272	−0.307193
$134$	−10.3881	−0.897396
$135$	2.17127	0.186873
$136$	−1.87092	−0.160430
$137$	3.41803	0.292022	0.146011	−	0.989283i	$-0.453357\pi$
$137$	3.41803	0.292022	0.146011	+	0.989283i	$0.453357\pi$
$138$	17.2814	1.47109
$139$	20.5276	1.74113	0.870563	−	0.492057i	$-0.163755\pi$
$139$	20.5276	1.74113	0.870563	+	0.492057i	$0.163755\pi$
$140$	−19.5375	−1.65122
$141$	11.3799	0.958357
$142$	−12.8627	−1.07941
$143$	2.87428	0.240359
$144$	−1.02719	−0.0855990
$145$	−15.7971	−1.31188
$146$	−0.857819	−0.0709936
$147$	2.03737	0.168040
$148$	23.9096	1.96536
$149$	20.7805	1.70241	0.851204	−	0.524835i	$-0.175873\pi$
$149$	20.7805	1.70241	0.851204	+	0.524835i	$0.175873\pi$
$150$	0.638171	0.0521065
$151$	2.14149	0.174272	0.0871360	−	0.996196i	$-0.472229\pi$
$151$	2.14149	0.174272	0.0871360	+	0.996196i	$0.472229\pi$
$152$	−2.61540	−0.212137
$153$	0.843009	0.0681532
$154$	−18.2294	−1.46897
$155$	−0.154815	−0.0124350
$156$	−3.17030	−0.253827
$157$	17.9089	1.42928	0.714641	−	0.699491i	$-0.246590\pi$
$157$	17.9089	1.42928	0.714641	+	0.699491i	$0.246590\pi$
$158$	−15.8184	−1.25845
$159$	−0.634346	−0.0503069
$160$	14.6212	1.15591
$161$	23.2494	1.83231
$162$	−2.23454	−0.175562
$163$	19.3299	1.51403	0.757017	−	0.653395i	$-0.226656\pi$
$163$	19.3299	1.51403	0.757017	+	0.653395i	$0.226656\pi$
$164$	3.09375	0.241582
$165$	−5.89217	−0.458705
$166$	−13.2706	−1.02999
$167$	13.7497	1.06398	0.531991	−	0.846750i	$-0.321444\pi$
$167$	13.7497	1.06398	0.531991	+	0.846750i	$0.321444\pi$
$168$	6.67180	0.514741
$169$	−11.8782	−0.913704
$170$	−4.09011	−0.313697
$171$	1.17846	0.0901192
$172$	−0.799747	−0.0609802
$173$	1.91565	0.145644	0.0728222	−	0.997345i	$-0.476799\pi$
$173$	1.91565	0.145644	0.0728222	+	0.997345i	$0.476799\pi$
$174$	16.2575	1.23248
$175$	0.858557	0.0649008
$176$	2.78748	0.210114
$177$	−1.03598	−0.0778687
$178$	−8.26033	−0.619138
$179$	20.2693	1.51500	0.757498	−	0.652837i	$-0.226421\pi$
$179$	20.2693	1.51500	0.757498	+	0.652837i	$0.226421\pi$
$180$	6.49902	0.484408
$181$	−19.4566	−1.44620	−0.723098	−	0.690746i	$-0.757282\pi$
$181$	−19.4566	−1.44620	−0.723098	+	0.690746i	$0.757282\pi$
$182$	−7.11503	−0.527401
$183$	−8.79324	−0.650015
$184$	17.1638	1.26533
$185$	17.3441	1.27516
$186$	0.159327	0.0116824
$187$	−2.28767	−0.167291
$188$	34.0621	2.48423
$189$	−3.00622	−0.218671
$190$	−5.71766	−0.414802
$191$	15.3949	1.11394	0.556968	−	0.830534i	$-0.311964\pi$
$191$	15.3949	1.11394	0.556968	+	0.830534i	$0.311964\pi$
$192$	−12.9930	−0.937686
$193$	4.66371	0.335701	0.167851	−	0.985812i	$-0.446317\pi$
$193$	4.66371	0.335701	0.167851	+	0.985812i	$0.446317\pi$
$194$	28.7856	2.06669
$195$	−2.29975	−0.164688
$196$	6.09825	0.435589
$197$	−0.745626	−0.0531237	−0.0265618	−	0.999647i	$-0.508456\pi$
$197$	−0.745626	−0.0531237	−0.0265618	+	0.999647i	$0.508456\pi$
$198$	6.06389	0.430942
$199$	−11.8671	−0.841237	−0.420619	−	0.907238i	$-0.638187\pi$
$199$	−11.8671	−0.841237	−0.420619	+	0.907238i	$0.638187\pi$
$200$	0.633826	0.0448183
$201$	4.64887	0.327906
$202$	−38.0965	−2.68046
$203$	21.8718	1.53510
$204$	2.52329	0.176665
$205$	2.24422	0.156743
$206$	29.3719	2.04644
$207$	−7.73376	−0.537534
$208$	1.08797	0.0754371
$209$	−3.19799	−0.221210
$210$	14.5856	1.00650
$211$	16.4886	1.13512	0.567561	−	0.823331i	$-0.307887\pi$
$211$	16.4886	1.13512	0.567561	+	0.823331i	$0.307887\pi$
$212$	−1.89872	−0.130405
$213$	5.75629	0.394415
$214$	−39.8842	−2.72643
$215$	−0.580139	−0.0395651
$216$	−2.21933	−0.151006
$217$	0.214349	0.0145509
$218$	−45.5406	−3.08440
$219$	0.383890	0.0259409
$220$	−17.6364	−1.18905
$221$	−0.892891	−0.0600624
$222$	−17.8496	−1.19798
$223$	−11.9191	−0.798165	−0.399082	−	0.916915i	$-0.630671\pi$
$223$	−11.9191	−0.798165	−0.399082	+	0.916915i	$0.630671\pi$
$224$	−20.2438	−1.35259
$225$	−0.285593	−0.0190396
$226$	35.1127	2.33566
$227$	−8.32680	−0.552669	−0.276334	−	0.961062i	$-0.589120\pi$
$227$	−8.32680	−0.552669	−0.276334	+	0.961062i	$0.589120\pi$
$228$	3.52736	0.233605
$229$	−22.8793	−1.51191	−0.755954	−	0.654624i	$-0.772827\pi$
$229$	−22.8793	−1.51191	−0.755954	+	0.654624i	$0.772827\pi$
$230$	37.5226	2.47417
$231$	8.15799	0.536756
$232$	16.1468	1.06009
$233$	23.8352	1.56149	0.780747	−	0.624847i	$-0.214839\pi$
$233$	23.8352	1.56149	0.780747	+	0.624847i	$0.214839\pi$
$234$	2.36677	0.154720
$235$	24.7087	1.61182
$236$	−3.10087	−0.201850
$237$	7.07903	0.459833
$238$	5.66295	0.367074
$239$	−3.13233	−0.202613	−0.101307	−	0.994855i	$-0.532302\pi$
$239$	−3.13233	−0.202613	−0.101307	+	0.994855i	$0.532302\pi$
$240$	−2.23030	−0.143965
$241$	8.06905	0.519773	0.259887	−	0.965639i	$-0.416315\pi$
$241$	8.06905	0.519773	0.259887	+	0.965639i	$0.416315\pi$
$242$	8.12443	0.522258
$243$	1.00000	0.0641500
$244$	−26.3199	−1.68496
$245$	4.42368	0.282619
$246$	−2.30962	−0.147256
$247$	−1.24819	−0.0794206
$248$	0.158242	0.0100484
$249$	5.93882	0.376357
$250$	25.6446	1.62191
$251$	28.2442	1.78276	0.891381	−	0.453256i	$-0.149737\pi$
$251$	28.2442	1.78276	0.891381	+	0.453256i	$0.149737\pi$
$252$	−8.99820	−0.566833
$253$	20.9871	1.31945
$254$	−33.6159	−2.10925
$255$	1.83040	0.114624
$256$	−8.79574	−0.549734
$257$	−11.7238	−0.731313	−0.365657	−	0.930750i	$-0.619156\pi$
$257$	−11.7238	−0.731313	−0.365657	+	0.930750i	$0.619156\pi$
$258$	0.597046	0.0371704
$259$	−24.0137	−1.49214
$260$	−6.88358	−0.426902
$261$	−7.27552	−0.450344
$262$	2.14574	0.132565
$263$	−0.677767	−0.0417929	−0.0208964	−	0.999782i	$-0.506652\pi$
$263$	−0.677767	−0.0417929	−0.0208964	+	0.999782i	$0.506652\pi$
$264$	6.02260	0.370665
$265$	−1.37734	−0.0846090
$266$	7.91636	0.485383
$267$	3.69665	0.226231
$268$	13.9150	0.849991
$269$	−10.2111	−0.622581	−0.311290	−	0.950315i	$-0.600761\pi$
$269$	−10.2111	−0.622581	−0.311290	+	0.950315i	$0.600761\pi$
$270$	−4.85180	−0.295271
$271$	−23.5987	−1.43352	−0.716760	−	0.697320i	$-0.754376\pi$
$271$	−23.5987	−1.43352	−0.716760	+	0.697320i	$0.754376\pi$
$272$	−0.865929	−0.0525047
$273$	3.18411	0.192711
$274$	−7.63774	−0.461413
$275$	0.775015	0.0467352
$276$	−23.1486	−1.39338
$277$	−24.2019	−1.45415	−0.727075	−	0.686558i	$-0.759121\pi$
$277$	−24.2019	−1.45415	−0.727075	+	0.686558i	$0.759121\pi$
$278$	−45.8698	−2.75109
$279$	−0.0713017	−0.00426872
$280$	14.4863	0.865720
$281$	26.8733	1.60313	0.801563	−	0.597911i	$-0.204002\pi$
$281$	26.8733	1.60313	0.801563	+	0.597911i	$0.204002\pi$
$282$	−25.4288	−1.51426
$283$	−30.5124	−1.81377	−0.906886	−	0.421377i	$-0.861547\pi$
$283$	−30.5124	−1.81377	−0.906886	+	0.421377i	$0.861547\pi$
$284$	17.2297	1.02239
$285$	2.55876	0.151568
$286$	−6.42270	−0.379782
$287$	−3.10722	−0.183414
$288$	6.73396	0.396802
$289$	−16.2893	−0.958196
$290$	35.2994	2.07285
$291$	−12.8821	−0.755162
$292$	1.14906	0.0672434
$293$	−20.1352	−1.17631	−0.588155	−	0.808748i	$-0.700145\pi$
$293$	−20.1352	−1.17631	−0.588155	+	0.808748i	$0.700145\pi$
$294$	−4.55260	−0.265513
$295$	−2.24938	−0.130964
$296$	−17.7280	−1.03042
$297$	−2.71370	−0.157465
$298$	−46.4351	−2.68991
$299$	8.19138	0.473720
$300$	−0.854836	−0.0493540
$301$	0.803229	0.0462974
$302$	−4.78525	−0.275360
$303$	17.0489	0.979432
$304$	−1.21050	−0.0694271
$305$	−19.0925	−1.09323
$306$	−1.88374	−0.107686
$307$	−0.820511	−0.0468290	−0.0234145	−	0.999726i	$-0.507454\pi$
$307$	−0.820511	−0.0468290	−0.0234145	+	0.999726i	$0.507454\pi$
$308$	24.4184	1.39137
$309$	−13.1445	−0.747763
$310$	0.345941	0.0196481
$311$	33.3435	1.89074	0.945369	−	0.326003i	$-0.105702\pi$
$311$	33.3435	1.89074	0.945369	+	0.326003i	$0.105702\pi$
$312$	2.35065	0.133080
$313$	−16.3179	−0.922341	−0.461170	−	0.887312i	$-0.652570\pi$
$313$	−16.3179	−0.922341	−0.461170	+	0.887312i	$0.652570\pi$
$314$	−40.0181	−2.25835
$315$	−6.52732	−0.367773
$316$	21.1889	1.19197
$317$	−4.18915	−0.235286	−0.117643	−	0.993056i	$-0.537534\pi$
$317$	−4.18915	−0.235286	−0.117643	+	0.993056i	$0.537534\pi$
$318$	1.41747	0.0794880
$319$	19.7436	1.10543
$320$	−28.2112	−1.57705
$321$	17.8489	0.996230
$322$	−51.9519	−2.89516
$323$	0.993454	0.0552772
$324$	2.99319	0.166288
$325$	0.302493	0.0167793
$326$	−43.1935	−2.39227
$327$	20.3803	1.12703
$328$	−2.29389	−0.126659
$329$	−34.2104	−1.88608
$330$	13.1663	0.724782
$331$	−23.6586	−1.30039	−0.650197	−	0.759766i	$-0.725314\pi$
$331$	−23.6586	−1.30039	−0.650197	+	0.759766i	$0.725314\pi$
$332$	17.7760	0.975585
$333$	7.98801	0.437740
$334$	−30.7243	−1.68116
$335$	10.0939	0.551491
$336$	3.08796	0.168462
$337$	−7.45430	−0.406062	−0.203031	−	0.979172i	$-0.565079\pi$
$337$	−7.45430	−0.406062	−0.203031	+	0.979172i	$0.565079\pi$
$338$	26.5423	1.44371
$339$	−15.7136	−0.853444
$340$	5.47873	0.297126
$341$	0.193491	0.0104781
$342$	−2.63333	−0.142394
$343$	14.9188	0.805537
$344$	0.592980	0.0319714
$345$	−16.7921	−0.904055
$346$	−4.28061	−0.230127
$347$	15.2901	0.820814	0.410407	−	0.911903i	$-0.365387\pi$
$347$	15.2901	0.820814	0.410407	+	0.911903i	$0.365387\pi$
$348$	−21.7770	−1.16737
$349$	20.8015	1.11348	0.556738	−	0.830688i	$-0.312053\pi$
$349$	20.8015	1.11348	0.556738	+	0.830688i	$0.312053\pi$
$350$	−1.91849	−0.102547
$351$	−1.05917	−0.0565344
$352$	−18.2739	−0.974005
$353$	−9.52844	−0.507148	−0.253574	−	0.967316i	$-0.581606\pi$
$353$	−9.52844	−0.507148	−0.253574	+	0.967316i	$0.581606\pi$
$354$	2.31493	0.123037
$355$	12.4985	0.663349
$356$	11.0648	0.586432
$357$	−2.53427	−0.134128
$358$	−45.2926	−2.39379
$359$	29.7533	1.57032	0.785159	−	0.619294i	$-0.212581\pi$
$359$	29.7533	1.57032	0.785159	+	0.619294i	$0.212581\pi$
$360$	−4.81876	−0.253971
$361$	−17.6112	−0.926907
$362$	43.4766	2.28508
$363$	−3.63583	−0.190832
$364$	9.53064	0.499541
$365$	0.833527	0.0436288
$366$	19.6489	1.02706
$367$	2.82989	0.147719	0.0738595	−	0.997269i	$-0.476468\pi$
$367$	2.82989	0.147719	0.0738595	+	0.997269i	$0.476468\pi$
$368$	7.94403	0.414111
$369$	1.03360	0.0538069
$370$	−38.7562	−2.01484
$371$	1.90699	0.0990057
$372$	−0.213420	−0.0110653
$373$	5.41530	0.280394	0.140197	−	0.990124i	$-0.455226\pi$
$373$	5.41530	0.280394	0.140197	+	0.990124i	$0.455226\pi$
$374$	5.11191	0.264331
$375$	−11.4764	−0.592641
$376$	−25.2557	−1.30246
$377$	7.70603	0.396881
$378$	6.71754	0.345513
$379$	16.0054	0.822143	0.411072	−	0.911603i	$-0.365155\pi$
$379$	16.0054	0.822143	0.411072	+	0.911603i	$0.365155\pi$
$380$	7.65885	0.392891
$381$	15.0438	0.770715
$382$	−34.4006	−1.76009
$383$	−31.4122	−1.60509	−0.802544	−	0.596593i	$-0.796521\pi$
$383$	−31.4122	−1.60509	−0.802544	+	0.596593i	$0.796521\pi$
$384$	15.5654	0.794320
$385$	17.7132	0.902747
$386$	−10.4213	−0.530429
$387$	−0.267189	−0.0135820
$388$	−38.5586	−1.95752
$389$	25.0904	1.27213	0.636066	−	0.771635i	$-0.280561\pi$
$389$	25.0904	1.27213	0.636066	+	0.771635i	$0.280561\pi$
$390$	5.13889	0.260218
$391$	−6.51963	−0.329712
$392$	−4.52160	−0.228376
$393$	−0.960260	−0.0484387
$394$	1.66614	0.0839387
$395$	15.3705	0.773373
$396$	−8.12262	−0.408177
$397$	−33.0139	−1.65692	−0.828461	−	0.560047i	$-0.810783\pi$
$397$	−33.0139	−1.65692	−0.828461	+	0.560047i	$0.810783\pi$
$398$	26.5176	1.32921
$399$	−3.54272	−0.177358
$400$	0.293358	0.0146679
$401$	16.1447	0.806228	0.403114	−	0.915150i	$-0.367928\pi$
$401$	16.1447	0.806228	0.403114	+	0.915150i	$0.367928\pi$
$402$	−10.3881	−0.518112
$403$	0.0755207	0.00376196
$404$	51.0305	2.53886
$405$	2.17127	0.107891
$406$	−48.8736	−2.42556
$407$	−21.6771	−1.07449
$408$	−1.87092	−0.0926241
$409$	5.29851	0.261994	0.130997	−	0.991383i	$-0.458182\pi$
$409$	5.29851	0.261994	0.130997	+	0.991383i	$0.458182\pi$
$410$	−5.01480	−0.247664
$411$	3.41803	0.168599
$412$	−39.3439	−1.93834
$413$	3.11437	0.153248
$414$	17.2814	0.849336
$415$	12.8948	0.632979
$416$	−7.13242	−0.349696
$417$	20.5276	1.00524
$418$	7.14606	0.349525
$419$	−27.3792	−1.33756	−0.668780	−	0.743460i	$-0.733183\pi$
$419$	−27.3792	−1.33756	−0.668780	+	0.743460i	$0.733183\pi$
$420$	−19.5375	−0.953333
$421$	31.5346	1.53690	0.768451	−	0.639909i	$-0.221028\pi$
$421$	31.5346	1.53690	0.768451	+	0.639909i	$0.221028\pi$
$422$	−36.8445	−1.79356
$423$	11.3799	0.553308
$424$	1.40782	0.0683700
$425$	−0.240758	−0.0116785
$426$	−12.8627	−0.623199
$427$	26.4344	1.27925
$428$	53.4253	2.58241
$429$	2.87428	0.138771
$430$	1.29635	0.0625154
$431$	−30.6518	−1.47644	−0.738222	−	0.674558i	$-0.764334\pi$
$431$	−30.6518	−1.47644	−0.738222	+	0.674558i	$0.764334\pi$
$432$	−1.02719	−0.0494206
$433$	14.4507	0.694459	0.347229	−	0.937780i	$-0.387123\pi$
$433$	14.4507	0.694459	0.347229	+	0.937780i	$0.387123\pi$
$434$	−0.478972	−0.0229914
$435$	−15.7971	−0.757414
$436$	61.0020	2.92147
$437$	−9.11394	−0.435979
$438$	−0.857819	−0.0409882
$439$	25.3770	1.21118	0.605590	−	0.795777i	$-0.292937\pi$
$439$	25.3770	1.21118	0.605590	+	0.795777i	$0.292937\pi$
$440$	13.0767	0.623406
$441$	2.03737	0.0970178
$442$	1.99521	0.0949023
$443$	−1.90956	−0.0907261	−0.0453630	−	0.998971i	$-0.514444\pi$
$443$	−1.90956	−0.0907261	−0.0453630	+	0.998971i	$0.514444\pi$
$444$	23.9096	1.13470
$445$	8.02642	0.380489
$446$	26.6339	1.26115
$447$	20.7805	0.982886
$448$	39.0597	1.84540
$449$	7.65608	0.361313	0.180656	−	0.983546i	$-0.442178\pi$
$449$	7.65608	0.361313	0.180656	+	0.983546i	$0.442178\pi$
$450$	0.638171	0.0300837
$451$	−2.80487	−0.132076
$452$	−47.0337	−2.21228
$453$	2.14149	0.100616
$454$	18.6066	0.873251
$455$	6.91355	0.324112
$456$	−2.61540	−0.122477
$457$	−23.4267	−1.09586	−0.547928	−	0.836525i	$-0.684583\pi$
$457$	−23.4267	−1.09586	−0.547928	+	0.836525i	$0.684583\pi$
$458$	51.1249	2.38891
$459$	0.843009	0.0393483
$460$	−50.2619	−2.34347
$461$	3.48667	0.162390	0.0811951	−	0.996698i	$-0.474126\pi$
$461$	3.48667	0.162390	0.0811951	+	0.996698i	$0.474126\pi$
$462$	−18.2294	−0.848108
$463$	−11.6758	−0.542619	−0.271310	−	0.962492i	$-0.587457\pi$
$463$	−11.6758	−0.542619	−0.271310	+	0.962492i	$0.587457\pi$
$464$	7.47333	0.346941
$465$	−0.154815	−0.00717938
$466$	−53.2608	−2.46726
$467$	0.218650	0.0101179	0.00505896	−	0.999987i	$-0.498390\pi$
$467$	0.218650	0.0101179	0.00505896	+	0.999987i	$0.498390\pi$
$468$	−3.17030	−0.146547
$469$	−13.9755	−0.645330
$470$	−55.2128	−2.54678
$471$	17.9089	0.825196
$472$	2.29917	0.105828
$473$	0.725071	0.0333388
$474$	−15.8184	−0.726564
$475$	−0.336561	−0.0154425
$476$	−7.58556	−0.347684
$477$	−0.634346	−0.0290447
$478$	6.99932	0.320142
$479$	26.3410	1.20355	0.601776	−	0.798665i	$-0.294460\pi$
$479$	26.3410	1.20355	0.601776	+	0.798665i	$0.294460\pi$
$480$	14.6212	0.667365
$481$	−8.46067	−0.385773
$482$	−18.0307	−0.821274
$483$	23.2494	1.05788
$484$	−10.8827	−0.494670
$485$	−27.9705	−1.27007
$486$	−2.23454	−0.101361
$487$	2.35686	0.106800	0.0533998	−	0.998573i	$-0.482994\pi$
$487$	2.35686	0.106800	0.0533998	+	0.998573i	$0.482994\pi$
$488$	19.5151	0.883408
$489$	19.3299	0.874128
$490$	−9.88492	−0.446555
$491$	−10.5762	−0.477299	−0.238650	−	0.971106i	$-0.576705\pi$
$491$	−10.5762	−0.477299	−0.238650	+	0.971106i	$0.576705\pi$
$492$	3.09375	0.139477
$493$	−6.13333	−0.276231
$494$	2.78914	0.125490
$495$	−5.89217	−0.264833
$496$	0.0732403	0.00328858
$497$	−17.3047	−0.776221
$498$	−13.2706	−0.594668
$499$	37.4467	1.67634	0.838172	−	0.545406i	$-0.183625\pi$
$499$	37.4467	1.67634	0.838172	+	0.545406i	$0.183625\pi$
$500$	−34.3512	−1.53623
$501$	13.7497	0.614290
$502$	−63.1130	−2.81687
$503$	1.00185	0.0446704	0.0223352	−	0.999751i	$-0.492890\pi$
$503$	1.00185	0.0446704	0.0223352	+	0.999751i	$0.492890\pi$
$504$	6.67180	0.297186
$505$	37.0177	1.64727
$506$	−46.8966	−2.08481
$507$	−11.8782	−0.527527
$508$	45.0288	1.99783
$509$	18.7494	0.831054	0.415527	−	0.909581i	$-0.363597\pi$
$509$	18.7494	0.831054	0.415527	+	0.909581i	$0.363597\pi$
$510$	−4.09011	−0.181113
$511$	−1.15406	−0.0510525
$512$	−11.4764	−0.507189
$513$	1.17846	0.0520304
$514$	26.1975	1.15552
$515$	−28.5402	−1.25763
$516$	−0.799747	−0.0352069
$517$	−30.8815	−1.35817
$518$	53.6598	2.35767
$519$	1.91565	0.0840878
$520$	5.10390	0.223821
$521$	−27.6804	−1.21270	−0.606349	−	0.795198i	$-0.707367\pi$
$521$	−27.6804	−1.21270	−0.606349	+	0.795198i	$0.707367\pi$
$522$	16.2575	0.711571
$523$	−20.2887	−0.887165	−0.443582	−	0.896234i	$-0.646293\pi$
$523$	−20.2887	−0.887165	−0.443582	+	0.896234i	$0.646293\pi$
$524$	−2.87424	−0.125562
$525$	0.858557	0.0374705
$526$	1.51450	0.0660354
$527$	−0.0601080	−0.00261834
$528$	2.78748	0.121310
$529$	36.8111	1.60048
$530$	3.07772	0.133688
$531$	−1.03598	−0.0449575
$532$	−10.6040	−0.459743
$533$	−1.09476	−0.0474192
$534$	−8.26033	−0.357460
$535$	38.7548	1.67552
$536$	−10.3174	−0.445643
$537$	20.2693	0.874684
$538$	22.8171	0.983716
$539$	−5.52882	−0.238143
$540$	6.49902	0.279673
$541$	1.54478	0.0664155	0.0332077	−	0.999448i	$-0.489428\pi$
$541$	1.54478	0.0664155	0.0332077	+	0.999448i	$0.489428\pi$
$542$	52.7324	2.26505
$543$	−19.4566	−0.834961
$544$	5.67679	0.243390
$545$	44.2510	1.89550
$546$	−7.11503	−0.304495
$547$	27.6488	1.18218	0.591089	−	0.806607i	$-0.298698\pi$
$547$	27.6488	1.18218	0.591089	+	0.806607i	$0.298698\pi$
$548$	10.2308	0.437039
$549$	−8.79324	−0.375286
$550$	−1.73181	−0.0738445
$551$	−8.57392	−0.365261
$552$	17.1638	0.730539
$553$	−21.2811	−0.904967
$554$	54.0802	2.29765
$555$	17.3441	0.736216
$556$	61.4430	2.60576
$557$	−1.16550	−0.0493839	−0.0246920	−	0.999695i	$-0.507860\pi$
$557$	−1.16550	−0.0493839	−0.0246920	+	0.999695i	$0.507860\pi$
$558$	0.159327	0.00674484
$559$	0.282999	0.0119696
$560$	6.70478	0.283329
$561$	−2.28767	−0.0965857
$562$	−60.0496	−2.53304
$563$	23.3117	0.982472	0.491236	−	0.871027i	$-0.336545\pi$
$563$	23.3117	0.982472	0.491236	+	0.871027i	$0.336545\pi$
$564$	34.0621	1.43427
$565$	−34.1184	−1.43537
$566$	68.1812	2.86587
$567$	−3.00622	−0.126249
$568$	−12.7751	−0.536032
$569$	−11.0559	−0.463487	−0.231743	−	0.972777i	$-0.574443\pi$
$569$	−11.0559	−0.463487	−0.231743	+	0.972777i	$0.574443\pi$
$570$	−5.71766	−0.239486
$571$	22.1261	0.925949	0.462974	−	0.886372i	$-0.346782\pi$
$571$	22.1261	0.925949	0.462974	+	0.886372i	$0.346782\pi$
$572$	8.60326	0.359720
$573$	15.3949	0.643132
$574$	6.94323	0.289805
$575$	2.20871	0.0921097
$576$	−12.9930	−0.541373
$577$	−29.5857	−1.23167	−0.615835	−	0.787875i	$-0.711181\pi$
$577$	−29.5857	−1.23167	−0.615835	+	0.787875i	$0.711181\pi$
$578$	36.3993	1.51401
$579$	4.66371	0.193817
$580$	−47.2838	−1.96335
$581$	−17.8534	−0.740684
$582$	28.7856	1.19320
$583$	1.72142	0.0712941
$584$	−0.851978	−0.0352551
$585$	−2.29975	−0.0950828
$586$	44.9930	1.85864
$587$	−30.6345	−1.26442	−0.632211	−	0.774797i	$-0.717852\pi$
$587$	−30.6345	−1.26442	−0.632211	+	0.774797i	$0.717852\pi$
$588$	6.09825	0.251487
$589$	−0.0840263	−0.00346224
$590$	5.02634	0.206931
$591$	−0.745626	−0.0306710
$592$	−8.20519	−0.337231
$593$	4.77619	0.196135	0.0980673	−	0.995180i	$-0.468734\pi$
$593$	4.77619	0.196135	0.0980673	+	0.995180i	$0.468734\pi$
$594$	6.06389	0.248804
$595$	−5.50259	−0.225584
$596$	62.2001	2.54782
$597$	−11.8671	−0.485689
$598$	−18.3040	−0.748507
$599$	35.5834	1.45390	0.726948	−	0.686692i	$-0.240938\pi$
$599$	35.5834	1.45390	0.726948	+	0.686692i	$0.240938\pi$
$600$	0.633826	0.0258759
$601$	−7.26146	−0.296201	−0.148101	−	0.988972i	$-0.547316\pi$
$601$	−7.26146	−0.296201	−0.148101	+	0.988972i	$0.547316\pi$
$602$	−1.79485	−0.0731527
$603$	4.64887	0.189317
$604$	6.40989	0.260815
$605$	−7.89436	−0.320952
$606$	−38.0965	−1.54756
$607$	−34.8635	−1.41506	−0.707532	−	0.706681i	$-0.750192\pi$
$607$	−34.8635	−1.41506	−0.707532	+	0.706681i	$0.750192\pi$
$608$	7.93571	0.321836
$609$	21.8718	0.886292
$610$	42.6630	1.72738
$611$	−12.0532	−0.487622
$612$	2.52329	0.101998
$613$	14.2106	0.573962	0.286981	−	0.957936i	$-0.407348\pi$
$613$	14.2106	0.573962	0.286981	+	0.957936i	$0.407348\pi$
$614$	1.83347	0.0739928
$615$	2.24422	0.0904956
$616$	−18.1053	−0.729482
$617$	12.1480	0.489061	0.244530	−	0.969642i	$-0.421366\pi$
$617$	12.1480	0.489061	0.244530	+	0.969642i	$0.421366\pi$
$618$	29.3719	1.18151
$619$	14.5396	0.584395	0.292197	−	0.956358i	$-0.405614\pi$
$619$	14.5396	0.584395	0.292197	+	0.956358i	$0.405614\pi$
$620$	−0.463391	−0.0186102
$621$	−7.73376	−0.310345
$622$	−74.5076	−2.98748
$623$	−11.1130	−0.445231
$624$	1.08797	0.0435536
$625$	−23.4905	−0.939619
$626$	36.4630	1.45736
$627$	−3.19799	−0.127715
$628$	53.6046	2.13906
$629$	6.73396	0.268501
$630$	14.5856	0.581103
$631$	2.54643	0.101372	0.0506859	−	0.998715i	$-0.483859\pi$
$631$	2.54643	0.101372	0.0506859	+	0.998715i	$0.483859\pi$
$632$	−15.7107	−0.624939
$633$	16.4886	0.655363
$634$	9.36083	0.371766
$635$	32.6640	1.29623
$636$	−1.89872	−0.0752891
$637$	−2.15793	−0.0855002
$638$	−44.1179	−1.74665
$639$	5.75629	0.227715
$640$	33.7967	1.33593
$641$	−41.0017	−1.61947	−0.809735	−	0.586796i	$-0.800389\pi$
$641$	−41.0017	−1.61947	−0.809735	+	0.586796i	$0.800389\pi$
$642$	−39.8842	−1.57411
$643$	7.40524	0.292034	0.146017	−	0.989282i	$-0.453355\pi$
$643$	7.40524	0.292034	0.146017	+	0.989282i	$0.453355\pi$
$644$	69.5899	2.74223
$645$	−0.580139	−0.0228429
$646$	−2.21992	−0.0873415
$647$	1.79642	0.0706245	0.0353122	−	0.999376i	$-0.488757\pi$
$647$	1.79642	0.0706245	0.0353122	+	0.999376i	$0.488757\pi$
$648$	−2.21933	−0.0871835
$649$	2.81133	0.110354
$650$	−0.675933	−0.0265123
$651$	0.214349	0.00840099
$652$	57.8581	2.26590
$653$	−13.8728	−0.542883	−0.271441	−	0.962455i	$-0.587500\pi$
$653$	−13.8728	−0.542883	−0.271441	+	0.962455i	$0.587500\pi$
$654$	−45.5406	−1.78078
$655$	−2.08498	−0.0814670
$656$	−1.06170	−0.0414524
$657$	0.383890	0.0149770
$658$	76.4447	2.98012
$659$	−40.5615	−1.58005	−0.790026	−	0.613074i	$-0.789933\pi$
$659$	−40.5615	−1.58005	−0.790026	+	0.613074i	$0.789933\pi$
$660$	−17.6364	−0.686496
$661$	−2.37057	−0.0922047	−0.0461023	−	0.998937i	$-0.514680\pi$
$661$	−2.37057	−0.0922047	−0.0461023	+	0.998937i	$0.514680\pi$
$662$	52.8662	2.05470
$663$	−0.892891	−0.0346770
$664$	−13.1802	−0.511491
$665$	−7.69219	−0.298290
$666$	−17.8496	−0.691657
$667$	56.2672	2.17867
$668$	41.1554	1.59235
$669$	−11.9191	−0.460821
$670$	−22.5554	−0.871390
$671$	23.8622	0.921191
$672$	−20.2438	−0.780921
$673$	−24.7252	−0.953085	−0.476543	−	0.879151i	$-0.658110\pi$
$673$	−24.7252	−0.953085	−0.476543	+	0.879151i	$0.658110\pi$
$674$	16.6570	0.641603
$675$	−0.285593	−0.0109925
$676$	−35.5536	−1.36745
$677$	−37.1902	−1.42934	−0.714668	−	0.699464i	$-0.753422\pi$
$677$	−37.1902	−1.42934	−0.714668	+	0.699464i	$0.753422\pi$
$678$	35.1127	1.34849
$679$	38.7265	1.48619
$680$	−4.06226	−0.155781
$681$	−8.32680	−0.319083
$682$	−0.432365	−0.0165561
$683$	23.5583	0.901432	0.450716	−	0.892667i	$-0.351169\pi$
$683$	23.5583	0.901432	0.450716	+	0.892667i	$0.351169\pi$
$684$	3.52736	0.134872
$685$	7.42146	0.283559
$686$	−33.3366	−1.27280
$687$	−22.8793	−0.872901
$688$	0.274453	0.0104634
$689$	0.671881	0.0255966
$690$	37.5226	1.42846
$691$	−4.87301	−0.185378	−0.0926891	−	0.995695i	$-0.529546\pi$
$691$	−4.87301	−0.185378	−0.0926891	+	0.995695i	$0.529546\pi$
$692$	5.73391	0.217971
$693$	8.15799	0.309896
$694$	−34.1663	−1.29694
$695$	44.5709	1.69067
$696$	16.1468	0.612043
$697$	0.871332	0.0330040
$698$	−46.4818	−1.75936
$699$	23.8352	0.901529
$700$	2.56983	0.0971303
$701$	8.78465	0.331792	0.165896	−	0.986143i	$-0.446948\pi$
$701$	8.78465	0.331792	0.165896	+	0.986143i	$0.446948\pi$
$702$	2.36677	0.0893279
$703$	9.41356	0.355039
$704$	35.2590	1.32887
$705$	24.7087	0.930585
$706$	21.2917	0.801324
$707$	−51.2527	−1.92756
$708$	−3.10087	−0.116538
$709$	8.24939	0.309812	0.154906	−	0.987929i	$-0.450492\pi$
$709$	8.24939	0.309812	0.154906	+	0.987929i	$0.450492\pi$
$710$	−27.9284	−1.04813
$711$	7.07903	0.265485
$712$	−8.20409	−0.307461
$713$	0.551430	0.0206512
$714$	5.66295	0.211930
$715$	6.24082	0.233394
$716$	60.6698	2.26734
$717$	−3.13233	−0.116979
$718$	−66.4850	−2.48120
$719$	14.6762	0.547331	0.273665	−	0.961825i	$-0.411764\pi$
$719$	14.6762	0.547331	0.273665	+	0.961825i	$0.411764\pi$
$720$	−2.23030	−0.0831184
$721$	39.5152	1.47162
$722$	39.3531	1.46457
$723$	8.06905	0.300091
$724$	−58.2372	−2.16437
$725$	2.07784	0.0771691
$726$	8.12443	0.301526
$727$	26.6258	0.987495	0.493747	−	0.869605i	$-0.335627\pi$
$727$	26.6258	0.987495	0.493747	+	0.869605i	$0.335627\pi$
$728$	−7.06658	−0.261905
$729$	1.00000	0.0370370
$730$	−1.86255	−0.0689362
$731$	−0.225243	−0.00833090
$732$	−26.3199	−0.972810
$733$	41.1848	1.52120	0.760598	−	0.649223i	$-0.224906\pi$
$733$	41.1848	1.52120	0.760598	+	0.649223i	$0.224906\pi$
$734$	−6.32351	−0.233405
$735$	4.42368	0.163170
$736$	−52.0788	−1.91965
$737$	−12.6156	−0.464703
$738$	−2.30962	−0.0850183
$739$	−27.3928	−1.00766	−0.503831	−	0.863802i	$-0.668076\pi$
$739$	−27.3928	−1.00766	−0.503831	+	0.863802i	$0.668076\pi$
$740$	51.9142	1.90841
$741$	−1.24819	−0.0458535
$742$	−4.26124	−0.156435
$743$	15.5158	0.569221	0.284610	−	0.958643i	$-0.408136\pi$
$743$	15.5158	0.569221	0.284610	+	0.958643i	$0.408136\pi$
$744$	0.158242	0.00580143
$745$	45.1201	1.65307
$746$	−12.1007	−0.443039
$747$	5.93882	0.217290
$748$	−6.84745	−0.250367
$749$	−53.6579	−1.96062
$750$	25.6446	0.936409
$751$	33.1551	1.20985	0.604924	−	0.796283i	$-0.293203\pi$
$751$	33.1551	1.20985	0.604924	+	0.796283i	$0.293203\pi$
$752$	−11.6893	−0.426264
$753$	28.2442	1.02928
$754$	−17.2195	−0.627096
$755$	4.64975	0.169222
$756$	−8.99820	−0.327261
$757$	48.6441	1.76800	0.884000	−	0.467487i	$-0.154841\pi$
$757$	48.6441	1.76800	0.884000	+	0.467487i	$0.154841\pi$
$758$	−35.7648	−1.29904
$759$	20.9871	0.761784
$760$	−5.67873	−0.205989
$761$	−34.7525	−1.25978	−0.629889	−	0.776685i	$-0.716900\pi$
$761$	−34.7525	−1.25978	−0.629889	+	0.776685i	$0.716900\pi$
$762$	−33.6159	−1.21778
$763$	−61.2676	−2.21804
$764$	46.0799	1.66711
$765$	1.83040	0.0661782
$766$	70.1920	2.53614
$767$	1.09728	0.0396203
$768$	−8.79574	−0.317389
$769$	48.9863	1.76649	0.883246	−	0.468910i	$-0.155353\pi$
$769$	48.9863	1.76649	0.883246	+	0.468910i	$0.155353\pi$
$770$	−39.5809	−1.42640
$771$	−11.7238	−0.422224
$772$	13.9594	0.502409
$773$	43.8665	1.57777	0.788885	−	0.614541i	$-0.210659\pi$
$773$	43.8665	1.57777	0.788885	+	0.614541i	$0.210659\pi$
$774$	0.597046	0.0214604
$775$	0.0203633	0.000731471 0
$776$	28.5896	1.02631
$777$	−24.0137	−0.861488
$778$	−56.0655	−2.01005
$779$	1.21805	0.0436413
$780$	−6.88358	−0.246472
$781$	−15.6208	−0.558958
$782$	14.5684	0.520965
$783$	−7.27552	−0.260006
$784$	−2.09277	−0.0747416
$785$	38.8849	1.38786
$786$	2.14574	0.0765362
$787$	−29.2788	−1.04368	−0.521838	−	0.853044i	$-0.674754\pi$
$787$	−29.2788	−1.04368	−0.521838	+	0.853044i	$0.674754\pi$
$788$	−2.23180	−0.0795047
$789$	−0.677767	−0.0241291
$790$	−34.3460	−1.22198
$791$	47.2385	1.67961
$792$	6.02260	0.214004
$793$	9.31355	0.330734
$794$	73.7711	2.61804
$795$	−1.37734	−0.0488491
$796$	−35.5205	−1.25899
$797$	33.6320	1.19131	0.595654	−	0.803241i	$-0.296893\pi$
$797$	33.6320	1.19131	0.595654	+	0.803241i	$0.296893\pi$
$798$	7.91636	0.280236
$799$	9.59333	0.339388
$800$	−1.92317	−0.0679945
$801$	3.69665	0.130615
$802$	−36.0761	−1.27389
$803$	−1.04176	−0.0367630
$804$	13.9150	0.490743
$805$	50.4807	1.77921
$806$	−0.168754	−0.00594412
$807$	−10.2111	−0.359447
$808$	−37.8371	−1.33110
$809$	29.8040	1.04785	0.523926	−	0.851764i	$-0.324467\pi$
$809$	29.8040	1.04785	0.523926	+	0.851764i	$0.324467\pi$
$810$	−4.85180	−0.170475
$811$	19.6149	0.688774	0.344387	−	0.938828i	$-0.388087\pi$
$811$	19.6149	0.688774	0.344387	+	0.938828i	$0.388087\pi$
$812$	65.4666	2.29743
$813$	−23.5987	−0.827643
$814$	48.4384	1.69776
$815$	41.9704	1.47016
$816$	−0.865929	−0.0303136
$817$	−0.314872	−0.0110160
$818$	−11.8398	−0.413967
$819$	3.18411	0.111262
$820$	6.71737	0.234581
$821$	−5.81442	−0.202925	−0.101462	−	0.994839i	$-0.532352\pi$
$821$	−5.81442	−0.202925	−0.101462	+	0.994839i	$0.532352\pi$
$822$	−7.63774	−0.266397
$823$	22.6172	0.788387	0.394193	−	0.919028i	$-0.371024\pi$
$823$	22.6172	0.788387	0.394193	+	0.919028i	$0.371024\pi$
$824$	29.1719	1.01625
$825$	0.775015	0.0269826
$826$	−6.95921	−0.242142
$827$	47.4721	1.65077	0.825384	−	0.564572i	$-0.190959\pi$
$827$	47.4721	1.65077	0.825384	+	0.564572i	$0.190959\pi$
$828$	−23.1486	−0.804470
$829$	29.9138	1.03895	0.519474	−	0.854486i	$-0.326128\pi$
$829$	29.9138	1.03895	0.519474	+	0.854486i	$0.326128\pi$
$830$	−28.8139	−1.00015
$831$	−24.2019	−0.839554
$832$	13.7618	0.477104
$833$	1.71752	0.0595087
$834$	−45.8698	−1.58834
$835$	29.8542	1.03315
$836$	−9.57220	−0.331062
$837$	−0.0713017	−0.00246455
$838$	61.1800	2.11343
$839$	−1.68659	−0.0582276	−0.0291138	−	0.999576i	$-0.509269\pi$
$839$	−1.68659	−0.0582276	−0.0291138	+	0.999576i	$0.509269\pi$
$840$	14.4863	0.499824
$841$	23.9332	0.825284
$842$	−70.4655	−2.42840
$843$	26.8733	0.925565
$844$	49.3535	1.69882
$845$	−25.7907	−0.887226
$846$	−25.4288	−0.874261
$847$	10.9301	0.375563
$848$	0.651593	0.0223758
$849$	−30.5124	−1.04718
$850$	0.537984	0.0184527
$851$	−61.7774	−2.11770
$852$	17.2297	0.590279
$853$	51.4258	1.76079	0.880394	−	0.474244i	$-0.157278\pi$
$853$	51.4258	1.76079	0.880394	+	0.474244i	$0.157278\pi$
$854$	−59.0689	−2.02130
$855$	2.55876	0.0875076
$856$	−39.6127	−1.35393
$857$	−27.9023	−0.953125	−0.476562	−	0.879141i	$-0.658117\pi$
$857$	−27.9023	−0.953125	−0.476562	+	0.879141i	$0.658117\pi$
$858$	−6.42270	−0.219267
$859$	42.3635	1.44543	0.722713	−	0.691149i	$-0.242895\pi$
$859$	42.3635	1.44543	0.722713	+	0.691149i	$0.242895\pi$
$860$	−1.73647	−0.0592130
$861$	−3.10722	−0.105894
$862$	68.4928	2.33287
$863$	5.81970	0.198105	0.0990524	−	0.995082i	$-0.468419\pi$
$863$	5.81970	0.198105	0.0990524	+	0.995082i	$0.468419\pi$
$864$	6.73396	0.229094
$865$	4.15940	0.141424
$866$	−32.2908	−1.09729
$867$	−16.2893	−0.553215
$868$	0.641587	0.0217769
$869$	−19.2104	−0.651667
$870$	35.2994	1.19676
$871$	−4.92395	−0.166842
$872$	−45.2305	−1.53170
$873$	−12.8821	−0.435993
$874$	20.3655	0.688874
$875$	34.5007	1.16634
$876$	1.14906	0.0388230
$877$	43.9205	1.48309	0.741544	−	0.670904i	$-0.234094\pi$
$877$	43.9205	1.48309	0.741544	+	0.670904i	$0.234094\pi$
$878$	−56.7061	−1.91374
$879$	−20.1352	−0.679143
$880$	6.05237	0.204025
$881$	28.5723	0.962625	0.481312	−	0.876549i	$-0.340160\pi$
$881$	28.5723	0.962625	0.481312	+	0.876549i	$0.340160\pi$
$882$	−4.55260	−0.153294
$883$	−46.6723	−1.57065	−0.785323	−	0.619086i	$-0.787503\pi$
$883$	−46.6723	−1.57065	−0.785323	+	0.619086i	$0.787503\pi$
$884$	−2.67259	−0.0898891
$885$	−2.24938	−0.0756121
$886$	4.26700	0.143353
$887$	30.9407	1.03889	0.519444	−	0.854505i	$-0.326139\pi$
$887$	30.9407	1.03889	0.519444	+	0.854505i	$0.326139\pi$
$888$	−17.7280	−0.594914
$889$	−45.2249	−1.51679
$890$	−17.9354	−0.601196
$891$	−2.71370	−0.0909124
$892$	−35.6763	−1.19453
$893$	13.4107	0.448773
$894$	−46.4351	−1.55302
$895$	44.0100	1.47109
$896$	−46.7932	−1.56325
$897$	8.19138	0.273502
$898$	−17.1079	−0.570897
$899$	0.518757	0.0173015
$900$	−0.854836	−0.0284945
$901$	−0.534759	−0.0178154
$902$	6.26762	0.208689
$903$	0.803229	0.0267298
$904$	34.8736	1.15988
$905$	−42.2454	−1.40429
$906$	−4.78525	−0.158979
$907$	−39.3134	−1.30538	−0.652690	−	0.757625i	$-0.726360\pi$
$907$	−39.3134	−1.30538	−0.652690	+	0.757625i	$0.726360\pi$
$908$	−24.9237	−0.827122
$909$	17.0489	0.565475
$910$	−15.4486	−0.512117
$911$	−11.8232	−0.391719	−0.195859	−	0.980632i	$-0.562750\pi$
$911$	−11.8232	−0.391719	−0.195859	+	0.980632i	$0.562750\pi$
$912$	−1.21050	−0.0400837
$913$	−16.1162	−0.533367
$914$	52.3481	1.73152
$915$	−19.0925	−0.631178
$916$	−68.4822	−2.26272
$917$	2.88676	0.0953290
$918$	−1.88374	−0.0621727
$919$	−8.18203	−0.269900	−0.134950	−	0.990852i	$-0.543087\pi$
$919$	−8.18203	−0.269900	−0.134950	+	0.990852i	$0.543087\pi$
$920$	37.2672	1.22866
$921$	−0.820511	−0.0270368
$922$	−7.79111	−0.256587
$923$	−6.09690	−0.200682
$924$	24.4184	0.803307
$925$	−2.28132	−0.0750094
$926$	26.0900	0.857372
$927$	−13.1445	−0.431721
$928$	−48.9931	−1.60828
$929$	−6.82276	−0.223848	−0.111924	−	0.993717i	$-0.535701\pi$
$929$	−6.82276	−0.223848	−0.111924	+	0.993717i	$0.535701\pi$
$930$	0.345941	0.0113439
$931$	2.40097	0.0786885
$932$	71.3432	2.33693
$933$	33.3435	1.09162
$934$	−0.488583	−0.0159869
$935$	−4.96715	−0.162443
$936$	2.35065	0.0768335
$937$	26.3041	0.859319	0.429659	−	0.902991i	$-0.358634\pi$
$937$	26.3041	0.859319	0.429659	+	0.902991i	$0.358634\pi$
$938$	31.2290	1.01966
$939$	−16.3179	−0.532514
$940$	73.9580	2.41224
$941$	−52.5680	−1.71367	−0.856834	−	0.515593i	$-0.827572\pi$
$941$	−52.5680	−1.71367	−0.856834	+	0.515593i	$0.827572\pi$
$942$	−40.0181	−1.30386
$943$	−7.99359	−0.260307
$944$	1.06414	0.0346349
$945$	−6.52732	−0.212334
$946$	−1.62020	−0.0526773
$947$	−36.9825	−1.20177	−0.600885	−	0.799335i	$-0.705185\pi$
$947$	−36.9825	−1.20177	−0.600885	+	0.799335i	$0.705185\pi$
$948$	21.1889	0.688184
$949$	−0.406605	−0.0131990
$950$	0.752061	0.0244001
$951$	−4.18915	−0.135842
$952$	5.62439	0.182287
$953$	−31.2425	−1.01204	−0.506022	−	0.862521i	$-0.668884\pi$
$953$	−31.2425	−1.01204	−0.506022	+	0.862521i	$0.668884\pi$
$954$	1.41747	0.0458924
$955$	33.4265	1.08166
$956$	−9.37565	−0.303230
$957$	19.7436	0.638220
$958$	−58.8602	−1.90169
$959$	−10.2754	−0.331808
$960$	−28.2112	−0.910513
$961$	−30.9949	−0.999836
$962$	18.9058	0.609546
$963$	17.8489	0.575174
$964$	24.1522	0.777890
$965$	10.1262	0.325973
$966$	−51.9519	−1.67152
$967$	−54.0050	−1.73668	−0.868342	−	0.495966i	$-0.834814\pi$
$967$	−54.0050	−1.73668	−0.868342	+	0.495966i	$0.834814\pi$
$968$	8.06911	0.259351
$969$	0.993454	0.0319143
$970$	62.5013	2.00680
$971$	34.4112	1.10431	0.552153	−	0.833743i	$-0.313806\pi$
$971$	34.4112	1.10431	0.552153	+	0.833743i	$0.313806\pi$
$972$	2.99319	0.0960067
$973$	−61.7105	−1.97835
$974$	−5.26651	−0.168750
$975$	0.302493	0.00968752
$976$	9.03232	0.289117
$977$	12.1473	0.388626	0.194313	−	0.980940i	$-0.437752\pi$
$977$	12.1473	0.388626	0.194313	+	0.980940i	$0.437752\pi$
$978$	−43.1935	−1.38118
$979$	−10.0316	−0.320611
$980$	13.2409	0.422966
$981$	20.3803	0.650692
$982$	23.6331	0.754163
$983$	39.2530	1.25198	0.625988	−	0.779832i	$-0.284696\pi$
$983$	39.2530	1.25198	0.625988	+	0.779832i	$0.284696\pi$
$984$	−2.29389	−0.0731267
$985$	−1.61895	−0.0515842
$986$	13.7052	0.436463
$987$	−34.2104	−1.08893
$988$	−3.73608	−0.118861
$989$	2.06638	0.0657069
$990$	13.1663	0.418453
$991$	11.1775	0.355065	0.177532	−	0.984115i	$-0.443189\pi$
$991$	11.1775	0.355065	0.177532	+	0.984115i	$0.443189\pi$
$992$	−0.480143	−0.0152445
$993$	−23.6586	−0.750783
$994$	38.6681	1.22648
$995$	−25.7667	−0.816859
$996$	17.7760	0.563255
$997$	43.5646	1.37970	0.689852	−	0.723951i	$-0.257676\pi$
$997$	43.5646	1.37970	0.689852	+	0.723951i	$0.257676\pi$
$998$	−83.6763	−2.64873
$999$	7.98801	0.252729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.c.1.11	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.c.1.11	✓	92	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)

\(f(q)\)	\(=\)	\(q-2.23454 q^{2} +1.00000 q^{3} +2.99319 q^{4} +2.17127 q^{5} -2.23454 q^{6} -3.00622 q^{7} -2.21933 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.23454 q^{2} +1.00000 q^{3} +2.99319 q^{4} +2.17127 q^{5} -2.23454 q^{6} -3.00622 q^{7} -2.21933 q^{8} +1.00000 q^{9} -4.85180 q^{10} -2.71370 q^{11} +2.99319 q^{12} -1.05917 q^{13} +6.71754 q^{14} +2.17127 q^{15} -1.02719 q^{16} +0.843009 q^{17} -2.23454 q^{18} +1.17846 q^{19} +6.49902 q^{20} -3.00622 q^{21} +6.06389 q^{22} -7.73376 q^{23} -2.21933 q^{24} -0.285593 q^{25} +2.36677 q^{26} +1.00000 q^{27} -8.99820 q^{28} -7.27552 q^{29} -4.85180 q^{30} -0.0713017 q^{31} +6.73396 q^{32} -2.71370 q^{33} -1.88374 q^{34} -6.52732 q^{35} +2.99319 q^{36} +7.98801 q^{37} -2.63333 q^{38} -1.05917 q^{39} -4.81876 q^{40} +1.03360 q^{41} +6.71754 q^{42} -0.267189 q^{43} -8.12262 q^{44} +2.17127 q^{45} +17.2814 q^{46} +11.3799 q^{47} -1.02719 q^{48} +2.03737 q^{49} +0.638171 q^{50} +0.843009 q^{51} -3.17030 q^{52} -0.634346 q^{53} -2.23454 q^{54} -5.89217 q^{55} +6.67180 q^{56} +1.17846 q^{57} +16.2575 q^{58} -1.03598 q^{59} +6.49902 q^{60} -8.79324 q^{61} +0.159327 q^{62} -3.00622 q^{63} -12.9930 q^{64} -2.29975 q^{65} +6.06389 q^{66} +4.64887 q^{67} +2.52329 q^{68} -7.73376 q^{69} +14.5856 q^{70} +5.75629 q^{71} -2.21933 q^{72} +0.383890 q^{73} -17.8496 q^{74} -0.285593 q^{75} +3.52736 q^{76} +8.15799 q^{77} +2.36677 q^{78} +7.07903 q^{79} -2.23030 q^{80} +1.00000 q^{81} -2.30962 q^{82} +5.93882 q^{83} -8.99820 q^{84} +1.83040 q^{85} +0.597046 q^{86} -7.27552 q^{87} +6.02260 q^{88} +3.69665 q^{89} -4.85180 q^{90} +3.18411 q^{91} -23.1486 q^{92} -0.0713017 q^{93} -25.4288 q^{94} +2.55876 q^{95} +6.73396 q^{96} -12.8821 q^{97} -4.55260 q^{98} -2.71370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9}+O(q^{10}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9} + 13 q^{10} + 40 q^{11} + 107 q^{12} + 6 q^{13} + 37 q^{14} + 34 q^{15} + 133 q^{16} + 77 q^{17} + 17 q^{18} + 34 q^{19} + 55 q^{20} + 22 q^{21} + 8 q^{22} + 83 q^{23} + 51 q^{24} + 110 q^{25} + 22 q^{26} + 92 q^{27} + 32 q^{28} + 97 q^{29} + 13 q^{30} + 44 q^{31} + 104 q^{32} + 40 q^{33} + 20 q^{34} + 80 q^{35} + 107 q^{36} + 12 q^{37} + 54 q^{38} + 6 q^{39} + 23 q^{40} + 67 q^{41} + 37 q^{42} + 30 q^{43} + 87 q^{44} + 34 q^{45} + 33 q^{46} + 69 q^{47} + 133 q^{48} + 112 q^{49} + 58 q^{50} + 77 q^{51} - 3 q^{52} + 113 q^{53} + 17 q^{54} + 42 q^{55} + 92 q^{56} + 34 q^{57} - 30 q^{58} + 72 q^{59} + 55 q^{60} + 19 q^{61} + 60 q^{62} + 22 q^{63} + 147 q^{64} + 74 q^{65} + 8 q^{66} + 26 q^{67} + 171 q^{68} + 83 q^{69} - 35 q^{70} + 134 q^{71} + 51 q^{72} - 17 q^{73} + 95 q^{74} + 110 q^{75} + 27 q^{76} + 108 q^{77} + 22 q^{78} + 159 q^{79} + 79 q^{80} + 92 q^{81} - 64 q^{82} + 73 q^{83} + 32 q^{84} - 4 q^{85} + 22 q^{86} + 97 q^{87} - 16 q^{88} + 50 q^{89} + 13 q^{90} + 17 q^{91} + 154 q^{92} + 44 q^{93} + 8 q^{94} + 155 q^{95} + 104 q^{96} - 20 q^{97} + 63 q^{98} + 40 q^{99}+O(q^{100}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9 + 13 * q^10 + 40 * q^11 + 107 * q^12 + 6 * q^13 + 37 * q^14 + 34 * q^15 + 133 * q^16 + 77 * q^17 + 17 * q^18 + 34 * q^19 + 55 * q^20 + 22 * q^21 + 8 * q^22 + 83 * q^23 + 51 * q^24 + 110 * q^25 + 22 * q^26 + 92 * q^27 + 32 * q^28 + 97 * q^29 + 13 * q^30 + 44 * q^31 + 104 * q^32 + 40 * q^33 + 20 * q^34 + 80 * q^35 + 107 * q^36 + 12 * q^37 + 54 * q^38 + 6 * q^39 + 23 * q^40 + 67 * q^41 + 37 * q^42 + 30 * q^43 + 87 * q^44 + 34 * q^45 + 33 * q^46 + 69 * q^47 + 133 * q^48 + 112 * q^49 + 58 * q^50 + 77 * q^51 - 3 * q^52 + 113 * q^53 + 17 * q^54 + 42 * q^55 + 92 * q^56 + 34 * q^57 - 30 * q^58 + 72 * q^59 + 55 * q^60 + 19 * q^61 + 60 * q^62 + 22 * q^63 + 147 * q^64 + 74 * q^65 + 8 * q^66 + 26 * q^67 + 171 * q^68 + 83 * q^69 - 35 * q^70 + 134 * q^71 + 51 * q^72 - 17 * q^73 + 95 * q^74 + 110 * q^75 + 27 * q^76 + 108 * q^77 + 22 * q^78 + 159 * q^79 + 79 * q^80 + 92 * q^81 - 64 * q^82 + 73 * q^83 + 32 * q^84 - 4 * q^85 + 22 * q^86 + 97 * q^87 - 16 * q^88 + 50 * q^89 + 13 * q^90 + 17 * q^91 + 154 * q^92 + 44 * q^93 + 8 * q^94 + 155 * q^95 + 104 * q^96 - 20 * q^97 + 63 * q^98 + 40 * q^99

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