LMFDB - Embedded newform 2013.4.a.g.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.49324 q^{2} -3.00000 q^{3} +4.20275 q^{4} +11.6764 q^{5} +10.4797 q^{6} -11.9890 q^{7} +13.2647 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.49324 q^{2} -3.00000 q^{3} +4.20275 q^{4} +11.6764 q^{5} +10.4797 q^{6} -11.9890 q^{7} +13.2647 q^{8} +9.00000 q^{9} -40.7884 q^{10} +11.0000 q^{11} -12.6083 q^{12} +6.29471 q^{13} +41.8806 q^{14} -35.0291 q^{15} -79.9589 q^{16} -7.00591 q^{17} -31.4392 q^{18} -84.1888 q^{19} +49.0729 q^{20} +35.9671 q^{21} -38.4257 q^{22} -17.5612 q^{23} -39.7941 q^{24} +11.3375 q^{25} -21.9889 q^{26} -27.0000 q^{27} -50.3869 q^{28} +260.352 q^{29} +122.365 q^{30} -57.2433 q^{31} +173.198 q^{32} -33.0000 q^{33} +24.4733 q^{34} -139.988 q^{35} +37.8248 q^{36} -320.912 q^{37} +294.092 q^{38} -18.8841 q^{39} +154.884 q^{40} -110.802 q^{41} -125.642 q^{42} +147.503 q^{43} +46.2303 q^{44} +105.087 q^{45} +61.3454 q^{46} -54.4895 q^{47} +239.877 q^{48} -199.263 q^{49} -39.6046 q^{50} +21.0177 q^{51} +26.4551 q^{52} +700.883 q^{53} +94.3176 q^{54} +128.440 q^{55} -159.031 q^{56} +252.566 q^{57} -909.471 q^{58} +410.558 q^{59} -147.219 q^{60} +61.0000 q^{61} +199.965 q^{62} -107.901 q^{63} +34.6477 q^{64} +73.4993 q^{65} +115.277 q^{66} +574.828 q^{67} -29.4441 q^{68} +52.6835 q^{69} +489.013 q^{70} +754.444 q^{71} +119.382 q^{72} -843.305 q^{73} +1121.02 q^{74} -34.0125 q^{75} -353.824 q^{76} -131.879 q^{77} +65.9668 q^{78} -375.295 q^{79} -933.629 q^{80} +81.0000 q^{81} +387.060 q^{82} -346.328 q^{83} +151.161 q^{84} -81.8036 q^{85} -515.265 q^{86} -781.055 q^{87} +145.912 q^{88} -272.866 q^{89} -367.095 q^{90} -75.4674 q^{91} -73.8052 q^{92} +171.730 q^{93} +190.345 q^{94} -983.019 q^{95} -519.595 q^{96} -1380.51 q^{97} +696.075 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * 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 $

$2$	−3.49324	−1.23505	−0.617524	−	0.786552i	$-0.711864\pi$
$2$	−3.49324	−1.23505	−0.617524	+	0.786552i	$0.711864\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.20275	0.525344
$5$	11.6764	1.04437	0.522183	−	0.852834i	$-0.325118\pi$
$5$	11.6764	1.04437	0.522183	+	0.852834i	$0.325118\pi$
$6$	10.4797	0.713055
$7$	−11.9890	−0.647347	−0.323673	−	0.946169i	$-0.604918\pi$
$7$	−11.9890	−0.647347	−0.323673	+	0.946169i	$0.604918\pi$
$8$	13.2647	0.586223
$9$	9.00000	0.333333
$10$	−40.7884	−1.28984
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−12.6083	−0.303307
$13$	6.29471	0.134295	0.0671476	−	0.997743i	$-0.478610\pi$
$13$	6.29471	0.134295	0.0671476	+	0.997743i	$0.478610\pi$
$14$	41.8806	0.799504
$15$	−35.0291	−0.602965
$16$	−79.9589	−1.24936
$17$	−7.00591	−0.0999519	−0.0499760	−	0.998750i	$-0.515914\pi$
$17$	−7.00591	−0.0999519	−0.0499760	+	0.998750i	$0.515914\pi$
$18$	−31.4392	−0.411683
$19$	−84.1888	−1.01654	−0.508269	−	0.861198i	$-0.669714\pi$
$19$	−84.1888	−1.01654	−0.508269	+	0.861198i	$0.669714\pi$
$20$	49.0729	0.548651
$21$	35.9671	0.373746
$22$	−38.4257	−0.372381
$23$	−17.5612	−0.159207	−0.0796034	−	0.996827i	$-0.525365\pi$
$23$	−17.5612	−0.159207	−0.0796034	+	0.996827i	$0.525365\pi$
$24$	−39.7941	−0.338456
$25$	11.3375	0.0906999
$26$	−21.9889	−0.165861
$27$	−27.0000	−0.192450
$28$	−50.3869	−0.340080
$29$	260.352	1.66711	0.833553	−	0.552440i	$-0.186303\pi$
$29$	260.352	1.66711	0.833553	+	0.552440i	$0.186303\pi$
$30$	122.365	0.744691
$31$	−57.2433	−0.331652	−0.165826	−	0.986155i	$-0.553029\pi$
$31$	−57.2433	−0.331652	−0.165826	+	0.986155i	$0.553029\pi$
$32$	173.198	0.956794
$33$	−33.0000	−0.174078
$34$	24.4733	0.123445
$35$	−139.988	−0.676067
$36$	37.8248	0.175115
$37$	−320.912	−1.42588	−0.712941	−	0.701225i	$-0.752637\pi$
$37$	−320.912	−1.42588	−0.712941	+	0.701225i	$0.752637\pi$
$38$	294.092	1.25547
$39$	−18.8841	−0.0775354
$40$	154.884	0.612231
$41$	−110.802	−0.422059	−0.211030	−	0.977480i	$-0.567682\pi$
$41$	−110.802	−0.422059	−0.211030	+	0.977480i	$0.567682\pi$
$42$	−125.642	−0.461594
$43$	147.503	0.523117	0.261559	−	0.965188i	$-0.415764\pi$
$43$	147.503	0.523117	0.261559	+	0.965188i	$0.415764\pi$
$44$	46.2303	0.158397
$45$	105.087	0.348122
$46$	61.3454	0.196628
$47$	−54.4895	−0.169109	−0.0845543	−	0.996419i	$-0.526947\pi$
$47$	−54.4895	−0.169109	−0.0845543	+	0.996419i	$0.526947\pi$
$48$	239.877	0.721317
$49$	−199.263	−0.580942
$50$	−39.6046	−0.112019
$51$	21.0177	0.0577073
$52$	26.4551	0.0705512
$53$	700.883	1.81648	0.908242	−	0.418445i	$-0.137425\pi$
$53$	700.883	1.81648	0.908242	+	0.418445i	$0.137425\pi$
$54$	94.3176	0.237685
$55$	128.440	0.314888
$56$	−159.031	−0.379489
$57$	252.566	0.586899
$58$	−909.471	−2.05896
$59$	410.558	0.905933	0.452967	−	0.891528i	$-0.350366\pi$
$59$	410.558	0.905933	0.452967	+	0.891528i	$0.350366\pi$
$60$	−147.219	−0.316764
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	199.965	0.409606
$63$	−107.901	−0.215782
$64$	34.6477	0.0676712
$65$	73.4993	0.140253
$66$	115.277	0.214994
$67$	574.828	1.04816	0.524078	−	0.851670i	$-0.324410\pi$
$67$	574.828	1.04816	0.524078	+	0.851670i	$0.324410\pi$
$68$	−29.4441	−0.0525091
$69$	52.6835	0.0919181
$70$	489.013	0.834975
$71$	754.444	1.26107	0.630536	−	0.776160i	$-0.282835\pi$
$71$	754.444	1.26107	0.630536	+	0.776160i	$0.282835\pi$
$72$	119.382	0.195408
$73$	−843.305	−1.35207	−0.676037	−	0.736868i	$-0.736304\pi$
$73$	−843.305	−1.35207	−0.676037	+	0.736868i	$0.736304\pi$
$74$	1121.02	1.76103
$75$	−34.0125	−0.0523656
$76$	−353.824	−0.534032
$77$	−131.879	−0.195182
$78$	65.9668	0.0957599
$79$	−375.295	−0.534481	−0.267240	−	0.963630i	$-0.586112\pi$
$79$	−375.295	−0.534481	−0.267240	+	0.963630i	$0.586112\pi$
$80$	−933.629	−1.30479
$81$	81.0000	0.111111
$82$	387.060	0.521264
$83$	−346.328	−0.458005	−0.229003	−	0.973426i	$-0.573546\pi$
$83$	−346.328	−0.458005	−0.229003	+	0.973426i	$0.573546\pi$
$84$	151.161	0.196345
$85$	−81.8036	−0.104386
$86$	−515.265	−0.646075
$87$	−781.055	−0.962504
$88$	145.912	0.176753
$89$	−272.866	−0.324985	−0.162493	−	0.986710i	$-0.551953\pi$
$89$	−272.866	−0.324985	−0.162493	+	0.986710i	$0.551953\pi$
$90$	−367.095	−0.429947
$91$	−75.4674	−0.0869355
$92$	−73.8052	−0.0836383
$93$	171.730	0.191479
$94$	190.345	0.208857
$95$	−983.019	−1.06164
$96$	−519.595	−0.552405
$97$	−1380.51	−1.44505	−0.722525	−	0.691344i	$-0.757019\pi$
$97$	−1380.51	−1.44505	−0.722525	+	0.691344i	$0.757019\pi$
$98$	696.075	0.717492
$99$	99.0000	0.100504
$100$	47.6487	0.0476487
$101$	303.749	0.299249	0.149624	−	0.988743i	$-0.452194\pi$
$101$	303.749	0.299249	0.149624	+	0.988743i	$0.452194\pi$
$102$	−73.4200	−0.0712713
$103$	1744.30	1.66865	0.834327	−	0.551269i	$-0.185856\pi$
$103$	1744.30	1.66865	0.834327	+	0.551269i	$0.185856\pi$
$104$	83.4975	0.0787269
$105$	419.965	0.390327
$106$	−2448.36	−2.24345
$107$	244.820	0.221193	0.110596	−	0.993865i	$-0.464724\pi$
$107$	244.820	0.221193	0.110596	+	0.993865i	$0.464724\pi$
$108$	−113.474	−0.101102
$109$	−1358.91	−1.19413	−0.597063	−	0.802194i	$-0.703666\pi$
$109$	−1358.91	−1.19413	−0.597063	+	0.802194i	$0.703666\pi$
$110$	−448.672	−0.388902
$111$	962.736	0.823233
$112$	958.629	0.808767
$113$	1931.92	1.60832	0.804158	−	0.594415i	$-0.202617\pi$
$113$	1931.92	1.60832	0.804158	+	0.594415i	$0.202617\pi$
$114$	−882.276	−0.724848
$115$	−205.051	−0.166270
$116$	1094.19	0.875804
$117$	56.6524	0.0447651
$118$	−1434.18	−1.11887
$119$	83.9940	0.0647035
$120$	−464.651	−0.353472
$121$	121.000	0.0909091
$122$	−213.088	−0.158132
$123$	332.407	0.243676
$124$	−240.579	−0.174231
$125$	−1327.16	−0.949642
$126$	376.925	0.266501
$127$	585.808	0.409307	0.204654	−	0.978834i	$-0.434393\pi$
$127$	585.808	0.409307	0.204654	+	0.978834i	$0.434393\pi$
$128$	−1506.62	−1.04037
$129$	−442.510	−0.302022
$130$	−256.751	−0.173220
$131$	−96.1627	−0.0641357	−0.0320678	−	0.999486i	$-0.510209\pi$
$131$	−96.1627	−0.0641357	−0.0320678	+	0.999486i	$0.510209\pi$
$132$	−138.691	−0.0914506
$133$	1009.34	0.658052
$134$	−2008.01	−1.29452
$135$	−315.262	−0.200988
$136$	−92.9314	−0.0585941
$137$	−1222.12	−0.762137	−0.381068	−	0.924547i	$-0.624444\pi$
$137$	−1222.12	−0.762137	−0.381068	+	0.924547i	$0.624444\pi$
$138$	−184.036	−0.113523
$139$	650.428	0.396896	0.198448	−	0.980111i	$-0.436410\pi$
$139$	650.428	0.396896	0.198448	+	0.980111i	$0.436410\pi$
$140$	−588.336	−0.355167
$141$	163.468	0.0976349
$142$	−2635.46	−1.55748
$143$	69.2418	0.0404915
$144$	−719.630	−0.416453
$145$	3039.96	1.74107
$146$	2945.87	1.66988
$147$	597.790	0.335407
$148$	−1348.71	−0.749078
$149$	−1854.22	−1.01949	−0.509743	−	0.860327i	$-0.670259\pi$
$149$	−1854.22	−1.01949	−0.509743	+	0.860327i	$0.670259\pi$
$150$	118.814	0.0646741
$151$	2633.70	1.41939	0.709694	−	0.704511i	$-0.248833\pi$
$151$	2633.70	1.41939	0.709694	+	0.704511i	$0.248833\pi$
$152$	−1116.74	−0.595918
$153$	−63.0532	−0.0333173
$154$	460.686	0.241060
$155$	−668.394	−0.346366
$156$	−79.3653	−0.0407327
$157$	−1751.05	−0.890123	−0.445062	−	0.895500i	$-0.646818\pi$
$157$	−1751.05	−0.890123	−0.445062	+	0.895500i	$0.646818\pi$
$158$	1311.00	0.660109
$159$	−2102.65	−1.04875
$160$	2022.33	0.999243
$161$	210.541	0.103062
$162$	−282.953	−0.137228
$163$	156.771	0.0753329	0.0376664	−	0.999290i	$-0.488008\pi$
$163$	156.771	0.0753329	0.0376664	+	0.999290i	$0.488008\pi$
$164$	−465.675	−0.221726
$165$	−385.320	−0.181801
$166$	1209.81	0.565658
$167$	1721.63	0.797745	0.398873	−	0.917006i	$-0.369402\pi$
$167$	1721.63	0.797745	0.398873	+	0.917006i	$0.369402\pi$
$168$	477.093	0.219098
$169$	−2157.38	−0.981965
$170$	285.760	0.128922
$171$	−757.699	−0.338846
$172$	619.920	0.274817
$173$	1463.90	0.643341	0.321671	−	0.946852i	$-0.395756\pi$
$173$	1463.90	0.643341	0.321671	+	0.946852i	$0.395756\pi$
$174$	2728.41	1.18874
$175$	−135.925	−0.0587143
$176$	−879.548	−0.376696
$177$	−1231.67	−0.523041
$178$	953.186	0.401372
$179$	−3212.87	−1.34157	−0.670785	−	0.741652i	$-0.734043\pi$
$179$	−3212.87	−1.34157	−0.670785	+	0.741652i	$0.734043\pi$
$180$	441.656	0.182884
$181$	−2132.78	−0.875848	−0.437924	−	0.899012i	$-0.644286\pi$
$181$	−2132.78	−0.875848	−0.437924	+	0.899012i	$0.644286\pi$
$182$	263.626	0.107370
$183$	−183.000	−0.0739221
$184$	−232.944	−0.0933307
$185$	−3747.08	−1.48914
$186$	−599.894	−0.236486
$187$	−77.0650	−0.0301366
$188$	−229.006	−0.0888402
$189$	323.704	0.124582
$190$	3433.92	1.31117
$191$	985.839	0.373470	0.186735	−	0.982410i	$-0.440209\pi$
$191$	985.839	0.373470	0.186735	+	0.982410i	$0.440209\pi$
$192$	−103.943	−0.0390700
$193$	−1720.58	−0.641712	−0.320856	−	0.947128i	$-0.603971\pi$
$193$	−1720.58	−0.641712	−0.320856	+	0.947128i	$0.603971\pi$
$194$	4822.47	1.78471
$195$	−220.498	−0.0809753
$196$	−837.454	−0.305195
$197$	−900.027	−0.325504	−0.162752	−	0.986667i	$-0.552037\pi$
$197$	−900.027	−0.325504	−0.162752	+	0.986667i	$0.552037\pi$
$198$	−345.831	−0.124127
$199$	−5222.17	−1.86025	−0.930124	−	0.367244i	$-0.880301\pi$
$199$	−5222.17	−1.86025	−0.930124	+	0.367244i	$0.880301\pi$
$200$	150.389	0.0531704
$201$	−1724.48	−0.605153
$202$	−1061.07	−0.369587
$203$	−3121.36	−1.07920
$204$	88.3323	0.0303162
$205$	−1293.77	−0.440784
$206$	−6093.28	−2.06087
$207$	−158.050	−0.0530689
$208$	−503.318	−0.167783
$209$	−926.076	−0.306498
$210$	−1467.04	−0.482073
$211$	5414.81	1.76669	0.883343	−	0.468727i	$-0.155287\pi$
$211$	5414.81	1.76669	0.883343	+	0.468727i	$0.155287\pi$
$212$	2945.64	0.954279
$213$	−2263.33	−0.728080
$214$	−855.214	−0.273183
$215$	1722.30	0.546326
$216$	−358.147	−0.112819
$217$	686.291	0.214694
$218$	4747.00	1.47480
$219$	2529.91	0.780620
$220$	539.801	0.165425
$221$	−44.1001	−0.0134231
$222$	−3363.07	−1.01673
$223$	4763.90	1.43056	0.715278	−	0.698840i	$-0.246300\pi$
$223$	4763.90	1.43056	0.715278	+	0.698840i	$0.246300\pi$
$224$	−2076.48	−0.619377
$225$	102.037	0.0302333
$226$	−6748.67	−1.98635
$227$	1582.59	0.462732	0.231366	−	0.972867i	$-0.425681\pi$
$227$	1582.59	0.462732	0.231366	+	0.972867i	$0.425681\pi$
$228$	1061.47	0.308324
$229$	−3566.68	−1.02923	−0.514614	−	0.857422i	$-0.672065\pi$
$229$	−3566.68	−1.02923	−0.514614	+	0.857422i	$0.672065\pi$
$230$	716.292	0.205352
$231$	395.638	0.112689
$232$	3453.49	0.977296
$233$	−2488.71	−0.699746	−0.349873	−	0.936797i	$-0.613775\pi$
$233$	−2488.71	−0.699746	−0.349873	+	0.936797i	$0.613775\pi$
$234$	−197.900	−0.0552870
$235$	−636.239	−0.176611
$236$	1725.47	0.475926
$237$	1125.88	0.308583
$238$	−293.412	−0.0799120
$239$	3616.96	0.978918	0.489459	−	0.872026i	$-0.337194\pi$
$239$	3616.96	0.978918	0.489459	+	0.872026i	$0.337194\pi$
$240$	2800.89	0.753319
$241$	4418.19	1.18092	0.590458	−	0.807068i	$-0.298947\pi$
$241$	4418.19	1.18092	0.590458	+	0.807068i	$0.298947\pi$
$242$	−422.682	−0.112277
$243$	−243.000	−0.0641500
$244$	256.368	0.0672634
$245$	−2326.67	−0.606716
$246$	−1161.18	−0.300952
$247$	−529.943	−0.136516
$248$	−759.316	−0.194422
$249$	1038.98	0.264429
$250$	4636.11	1.17285
$251$	−5449.52	−1.37040	−0.685200	−	0.728355i	$-0.740285\pi$
$251$	−5449.52	−1.37040	−0.685200	+	0.728355i	$0.740285\pi$
$252$	−453.482	−0.113360
$253$	−193.173	−0.0480026
$254$	−2046.37	−0.505514
$255$	245.411	0.0602675
$256$	4985.80	1.21724
$257$	−71.4390	−0.0173395	−0.00866973	−	0.999962i	$-0.502760\pi$
$257$	−71.4390	−0.0173395	−0.00866973	+	0.999962i	$0.502760\pi$
$258$	1545.80	0.373012
$259$	3847.42	0.923039
$260$	308.899	0.0736812
$261$	2343.16	0.555702
$262$	335.920	0.0792106
$263$	−6564.45	−1.53909	−0.769546	−	0.638591i	$-0.779518\pi$
$263$	−6564.45	−1.53909	−0.769546	+	0.638591i	$0.779518\pi$
$264$	−437.736	−0.102048
$265$	8183.77	1.89707
$266$	−3525.87	−0.812727
$267$	818.597	0.187630
$268$	2415.86	0.550642
$269$	7800.48	1.76804	0.884021	−	0.467446i	$-0.154826\pi$
$269$	7800.48	1.76804	0.884021	+	0.467446i	$0.154826\pi$
$270$	1101.29	0.248230
$271$	6966.27	1.56151	0.780757	−	0.624834i	$-0.214833\pi$
$271$	6966.27	1.56151	0.780757	+	0.624834i	$0.214833\pi$
$272$	560.185	0.124876
$273$	226.402	0.0501922
$274$	4269.16	0.941275
$275$	124.712	0.0273471
$276$	221.416	0.0482886
$277$	−6136.25	−1.33102	−0.665508	−	0.746390i	$-0.731785\pi$
$277$	−6136.25	−1.33102	−0.665508	+	0.746390i	$0.731785\pi$
$278$	−2272.10	−0.490186
$279$	−515.190	−0.110551
$280$	−1856.90	−0.396326
$281$	−713.541	−0.151482	−0.0757408	−	0.997128i	$-0.524132\pi$
$281$	−713.541	−0.151482	−0.0757408	+	0.997128i	$0.524132\pi$
$282$	−571.035	−0.120584
$283$	8155.48	1.71305	0.856524	−	0.516106i	$-0.172619\pi$
$283$	8155.48	1.71305	0.856524	+	0.516106i	$0.172619\pi$
$284$	3170.74	0.662496
$285$	2949.06	0.612937
$286$	−241.878	−0.0500090
$287$	1328.41	0.273219
$288$	1558.78	0.318931
$289$	−4863.92	−0.990010
$290$	−10619.3	−2.15030
$291$	4141.54	0.834300
$292$	−3544.20	−0.710304
$293$	1533.40	0.305741	0.152871	−	0.988246i	$-0.451148\pi$
$293$	1533.40	0.305741	0.152871	+	0.988246i	$0.451148\pi$
$294$	−2088.23	−0.414244
$295$	4793.82	0.946126
$296$	−4256.81	−0.835884
$297$	−297.000	−0.0580259
$298$	6477.23	1.25911
$299$	−110.542	−0.0213807
$300$	−142.946	−0.0275100
$301$	−1768.42	−0.338638
$302$	−9200.15	−1.75301
$303$	−911.247	−0.172771
$304$	6731.64	1.27002
$305$	712.258	0.133717
$306$	220.260	0.0411485
$307$	1652.37	0.307184	0.153592	−	0.988134i	$-0.450916\pi$
$307$	1652.37	0.307184	0.153592	+	0.988134i	$0.450916\pi$
$308$	−554.256	−0.102538
$309$	−5232.91	−0.963398
$310$	2334.86	0.427778
$311$	8542.00	1.55747	0.778733	−	0.627355i	$-0.215862\pi$
$311$	8542.00	1.55747	0.778733	+	0.627355i	$0.215862\pi$
$312$	−250.492	−0.0454530
$313$	366.598	0.0662024	0.0331012	−	0.999452i	$-0.489462\pi$
$313$	366.598	0.0662024	0.0331012	+	0.999452i	$0.489462\pi$
$314$	6116.86	1.09935
$315$	−1259.89	−0.225356
$316$	−1577.27	−0.280786
$317$	10026.8	1.77653	0.888267	−	0.459328i	$-0.151910\pi$
$317$	10026.8	1.77653	0.888267	+	0.459328i	$0.151910\pi$
$318$	7345.07	1.29525
$319$	2863.87	0.502651
$320$	404.559	0.0706735
$321$	−734.459	−0.127706
$322$	−735.472	−0.127286
$323$	589.819	0.101605
$324$	340.423	0.0583716
$325$	71.3662	0.0121806
$326$	−547.639	−0.0930397
$327$	4076.72	0.689429
$328$	−1469.76	−0.247421
$329$	653.276	0.109472
$330$	1346.02	0.224533
$331$	2094.60	0.347823	0.173911	−	0.984761i	$-0.444359\pi$
$331$	2094.60	0.347823	0.173911	+	0.984761i	$0.444359\pi$
$332$	−1455.53	−0.240610
$333$	−2888.21	−0.475294
$334$	−6014.06	−0.985254
$335$	6711.90	1.09466
$336$	−2875.89	−0.466942
$337$	5025.94	0.812405	0.406203	−	0.913783i	$-0.366853\pi$
$337$	5025.94	0.812405	0.406203	+	0.913783i	$0.366853\pi$
$338$	7536.24	1.21277
$339$	−5795.76	−0.928562
$340$	−343.800	−0.0548387
$341$	−629.676	−0.0999967
$342$	2646.83	0.418491
$343$	6501.21	1.02342
$344$	1956.59	0.306663
$345$	615.152	0.0959961
$346$	−5113.75	−0.794557
$347$	−4828.88	−0.747054	−0.373527	−	0.927619i	$-0.621852\pi$
$347$	−4828.88	−0.747054	−0.373527	+	0.927619i	$0.621852\pi$
$348$	−3282.58	−0.505646
$349$	12769.8	1.95861	0.979303	−	0.202398i	$-0.0648733\pi$
$349$	12769.8	1.95861	0.979303	+	0.202398i	$0.0648733\pi$
$350$	474.821	0.0725150
$351$	−169.957	−0.0258451
$352$	1905.18	0.288484
$353$	3126.06	0.471342	0.235671	−	0.971833i	$-0.424271\pi$
$353$	3126.06	0.471342	0.235671	+	0.971833i	$0.424271\pi$
$354$	4302.53	0.645980
$355$	8809.17	1.31702
$356$	−1146.79	−0.170729
$357$	−251.982	−0.0373566
$358$	11223.3	1.65690
$359$	9569.10	1.40679	0.703395	−	0.710799i	$-0.251666\pi$
$359$	9569.10	1.40679	0.703395	+	0.710799i	$0.251666\pi$
$360$	1393.95	0.204077
$361$	228.747	0.0333500
$362$	7450.33	1.08171
$363$	−363.000	−0.0524864
$364$	−317.171	−0.0456710
$365$	−9846.73	−1.41206
$366$	639.264	0.0912974
$367$	1057.14	0.150361	0.0751803	−	0.997170i	$-0.476047\pi$
$367$	1057.14	0.150361	0.0751803	+	0.997170i	$0.476047\pi$
$368$	1404.17	0.198906
$369$	−997.222	−0.140686
$370$	13089.5	1.83916
$371$	−8402.90	−1.17590
$372$	721.738	0.100592
$373$	−2709.89	−0.376173	−0.188087	−	0.982152i	$-0.560229\pi$
$373$	−2709.89	−0.376173	−0.188087	+	0.982152i	$0.560229\pi$
$374$	269.207	0.0372202
$375$	3981.49	0.548276
$376$	−722.787	−0.0991354
$377$	1638.84	0.223884
$378$	−1130.78	−0.153865
$379$	−2361.71	−0.320087	−0.160044	−	0.987110i	$-0.551164\pi$
$379$	−2361.71	−0.320087	−0.160044	+	0.987110i	$0.551164\pi$
$380$	−4131.38	−0.557725
$381$	−1757.42	−0.236314
$382$	−3443.78	−0.461254
$383$	−3237.63	−0.431946	−0.215973	−	0.976399i	$-0.569292\pi$
$383$	−3237.63	−0.431946	−0.215973	+	0.976399i	$0.569292\pi$
$384$	4519.85	0.600659
$385$	−1539.87	−0.203842
$386$	6010.42	0.792545
$387$	1327.53	0.174372
$388$	−5801.96	−0.759149
$389$	5823.40	0.759018	0.379509	−	0.925188i	$-0.376093\pi$
$389$	5823.40	0.759018	0.379509	+	0.925188i	$0.376093\pi$
$390$	770.253	0.100008
$391$	123.032	0.0159130
$392$	−2643.17	−0.340562
$393$	288.488	0.0370287
$394$	3144.01	0.402013
$395$	−4382.08	−0.558193
$396$	416.072	0.0527991
$397$	9877.27	1.24868	0.624340	−	0.781153i	$-0.285368\pi$
$397$	9877.27	1.24868	0.624340	+	0.781153i	$0.285368\pi$
$398$	18242.3	2.29750
$399$	−3028.02	−0.379927
$400$	−906.533	−0.113317
$401$	−11583.1	−1.44247	−0.721235	−	0.692691i	$-0.756425\pi$
$401$	−11583.1	−1.44247	−0.721235	+	0.692691i	$0.756425\pi$
$402$	6024.04	0.747393
$403$	−360.330	−0.0445392
$404$	1276.58	0.157209
$405$	945.786	0.116041
$406$	10903.7	1.33286
$407$	−3530.03	−0.429919
$408$	278.794	0.0338293
$409$	2640.55	0.319234	0.159617	−	0.987179i	$-0.448974\pi$
$409$	2640.55	0.319234	0.159617	+	0.987179i	$0.448974\pi$
$410$	4519.45	0.544390
$411$	3666.36	0.440020
$412$	7330.88	0.876618
$413$	−4922.19	−0.586453
$414$	552.109	0.0655427
$415$	−4043.85	−0.478325
$416$	1090.23	0.128493
$417$	−1951.28	−0.229148
$418$	3235.01	0.378540
$419$	−12749.0	−1.48646	−0.743232	−	0.669034i	$-0.766708\pi$
$419$	−12749.0	−1.48646	−0.743232	+	0.669034i	$0.766708\pi$
$420$	1765.01	0.205056
$421$	4305.17	0.498388	0.249194	−	0.968454i	$-0.419834\pi$
$421$	4305.17	0.498388	0.249194	+	0.968454i	$0.419834\pi$
$422$	−18915.2	−2.18194
$423$	−490.405	−0.0563695
$424$	9297.01	1.06487
$425$	−79.4294	−0.00906563
$426$	7906.38	0.899214
$427$	−731.331	−0.0828842
$428$	1028.92	0.116202
$429$	−207.725	−0.0233778
$430$	−6016.42	−0.674739
$431$	13576.0	1.51725	0.758624	−	0.651529i	$-0.225872\pi$
$431$	13576.0	1.51725	0.758624	+	0.651529i	$0.225872\pi$
$432$	2158.89	0.240439
$433$	11867.8	1.31716	0.658579	−	0.752512i	$-0.271158\pi$
$433$	11867.8	1.31716	0.658579	+	0.752512i	$0.271158\pi$
$434$	−2397.38	−0.265157
$435$	−9119.88	−1.00521
$436$	−5711.15	−0.627327
$437$	1478.45	0.161840
$438$	−8837.61	−0.964103
$439$	9001.17	0.978593	0.489297	−	0.872117i	$-0.337254\pi$
$439$	9001.17	0.978593	0.489297	+	0.872117i	$0.337254\pi$
$440$	1703.72	0.184595
$441$	−1793.37	−0.193647
$442$	154.053	0.0165781
$443$	14264.5	1.52986	0.764931	−	0.644112i	$-0.222773\pi$
$443$	14264.5	1.52986	0.764931	+	0.644112i	$0.222773\pi$
$444$	4046.14	0.432480
$445$	−3186.08	−0.339404
$446$	−16641.4	−1.76681
$447$	5562.65	0.588600
$448$	−415.392	−0.0438067
$449$	12013.8	1.26273	0.631364	−	0.775486i	$-0.282495\pi$
$449$	12013.8	1.26273	0.631364	+	0.775486i	$0.282495\pi$
$450$	−356.442	−0.0373396
$451$	−1218.83	−0.127256
$452$	8119.38	0.844919
$453$	−7901.10	−0.819483
$454$	−5528.37	−0.571496
$455$	−881.185	−0.0907925
$456$	3350.22	0.344054
$457$	−2243.76	−0.229669	−0.114835	−	0.993385i	$-0.536634\pi$
$457$	−2243.76	−0.229669	−0.114835	+	0.993385i	$0.536634\pi$
$458$	12459.3	1.27115
$459$	189.160	0.0192358
$460$	−861.777	−0.0873490
$461$	−1369.29	−0.138339	−0.0691695	−	0.997605i	$-0.522035\pi$
$461$	−1369.29	−0.138339	−0.0691695	+	0.997605i	$0.522035\pi$
$462$	−1382.06	−0.139176
$463$	13556.2	1.36071	0.680355	−	0.732883i	$-0.261826\pi$
$463$	13556.2	1.36071	0.680355	+	0.732883i	$0.261826\pi$
$464$	−20817.4	−2.08281
$465$	2005.18	0.199974
$466$	8693.67	0.864220
$467$	−3916.59	−0.388090	−0.194045	−	0.980993i	$-0.562161\pi$
$467$	−3916.59	−0.388090	−0.194045	+	0.980993i	$0.562161\pi$
$468$	238.096	0.0235171
$469$	−6891.63	−0.678520
$470$	2222.54	0.218123
$471$	5253.16	0.513913
$472$	5445.93	0.531079
$473$	1622.54	0.157726
$474$	−3932.99	−0.381114
$475$	−954.489	−0.0922000
$476$	353.006	0.0339916
$477$	6307.95	0.605495
$478$	−12634.9	−1.20901
$479$	−438.919	−0.0418679	−0.0209339	−	0.999781i	$-0.506664\pi$
$479$	−438.919	−0.0418679	−0.0209339	+	0.999781i	$0.506664\pi$
$480$	−6066.98	−0.576913
$481$	−2020.05	−0.191489
$482$	−15433.8	−1.45849
$483$	−631.624	−0.0595028
$484$	508.533	0.0477585
$485$	−16119.4	−1.50916
$486$	848.858	0.0792284
$487$	−9644.17	−0.897370	−0.448685	−	0.893690i	$-0.648107\pi$
$487$	−9644.17	−0.897370	−0.448685	+	0.893690i	$0.648107\pi$
$488$	809.148	0.0750582
$489$	−470.313	−0.0434934
$490$	8127.63	0.749324
$491$	16603.5	1.52608	0.763041	−	0.646351i	$-0.223706\pi$
$491$	16603.5	1.52608	0.763041	+	0.646351i	$0.223706\pi$
$492$	1397.03	0.128014
$493$	−1824.00	−0.166630
$494$	1851.22	0.168604
$495$	1155.96	0.104963
$496$	4577.11	0.414351
$497$	−9045.05	−0.816350
$498$	−3629.42	−0.326583
$499$	−9473.72	−0.849904	−0.424952	−	0.905216i	$-0.639709\pi$
$499$	−9473.72	−0.849904	−0.424952	+	0.905216i	$0.639709\pi$
$500$	−5577.74	−0.498889
$501$	−5164.88	−0.460579
$502$	19036.5	1.69251
$503$	−4229.50	−0.374919	−0.187459	−	0.982272i	$-0.560025\pi$
$503$	−4229.50	−0.374919	−0.187459	+	0.982272i	$0.560025\pi$
$504$	−1431.28	−0.126496
$505$	3546.68	0.312525
$506$	674.800	0.0592856
$507$	6472.13	0.566938
$508$	2462.01	0.215027
$509$	−20665.8	−1.79959	−0.899797	−	0.436309i	$-0.856286\pi$
$509$	−20665.8	−1.79959	−0.899797	+	0.436309i	$0.856286\pi$
$510$	−857.279	−0.0744333
$511$	10110.4	0.875260
$512$	−5363.68	−0.462975
$513$	2273.10	0.195633
$514$	249.554	0.0214151
$515$	20367.1	1.74269
$516$	−1859.76	−0.158665
$517$	−599.384	−0.0509882
$518$	−13440.0	−1.14000
$519$	−4391.69	−0.371433
$520$	974.947	0.0822197
$521$	19860.7	1.67008	0.835041	−	0.550187i	$-0.185444\pi$
$521$	19860.7	1.67008	0.835041	+	0.550187i	$0.185444\pi$
$522$	−8185.24	−0.686319
$523$	−3924.38	−0.328109	−0.164054	−	0.986451i	$-0.552457\pi$
$523$	−3924.38	−0.328109	−0.164054	+	0.986451i	$0.552457\pi$
$524$	−404.148	−0.0336933
$525$	407.776	0.0338987
$526$	22931.2	1.90085
$527$	401.041	0.0331492
$528$	2638.64	0.217485
$529$	−11858.6	−0.974653
$530$	−28587.9	−2.34298
$531$	3695.02	0.301978
$532$	4242.01	0.345704
$533$	−697.469	−0.0566805
$534$	−2859.56	−0.231733
$535$	2858.60	0.231006
$536$	7624.93	0.614453
$537$	9638.60	0.774556
$538$	−27249.0	−2.18362
$539$	−2191.90	−0.175161
$540$	−1324.97	−0.105588
$541$	6396.23	0.508310	0.254155	−	0.967164i	$-0.418203\pi$
$541$	6396.23	0.508310	0.254155	+	0.967164i	$0.418203\pi$
$542$	−24334.9	−1.92855
$543$	6398.35	0.505671
$544$	−1213.41	−0.0956334
$545$	−15867.1	−1.24710
$546$	−790.878	−0.0619898
$547$	3958.85	0.309448	0.154724	−	0.987958i	$-0.450551\pi$
$547$	3958.85	0.309448	0.154724	+	0.987958i	$0.450551\pi$
$548$	−5136.26	−0.400384
$549$	549.000	0.0426790
$550$	−435.651	−0.0337749
$551$	−21918.7	−1.69468
$552$	698.831	0.0538845
$553$	4499.42	0.345994
$554$	21435.4	1.64387
$555$	11241.3	0.859756
$556$	2733.59	0.208507
$557$	16233.9	1.23492	0.617461	−	0.786602i	$-0.288161\pi$
$557$	16233.9	1.23492	0.617461	+	0.786602i	$0.288161\pi$
$558$	1799.68	0.136535
$559$	928.490	0.0702521
$560$	11193.3	0.844649
$561$	231.195	0.0173994
$562$	2492.57	0.187087
$563$	6492.56	0.486019	0.243010	−	0.970024i	$-0.421865\pi$
$563$	6492.56	0.486019	0.243010	+	0.970024i	$0.421865\pi$
$564$	687.017	0.0512919
$565$	22557.8	1.67967
$566$	−28489.1	−2.11570
$567$	−971.111	−0.0719274
$568$	10007.5	0.739269
$569$	15180.6	1.11846	0.559229	−	0.829013i	$-0.311097\pi$
$569$	15180.6	1.11846	0.559229	+	0.829013i	$0.311097\pi$
$570$	−10301.8	−0.757007
$571$	−11261.7	−0.825370	−0.412685	−	0.910874i	$-0.635409\pi$
$571$	−11261.7	−0.825370	−0.412685	+	0.910874i	$0.635409\pi$
$572$	291.006	0.0212720
$573$	−2957.52	−0.215623
$574$	−4640.47	−0.337438
$575$	−199.100	−0.0144400
$576$	311.829	0.0225571
$577$	26859.4	1.93791	0.968954	−	0.247242i	$-0.0795244\pi$
$577$	26859.4	1.93791	0.968954	+	0.247242i	$0.0795244\pi$
$578$	16990.8	1.22271
$579$	5161.75	0.370493
$580$	12776.2	0.914660
$581$	4152.13	0.296488
$582$	−14467.4	−1.03040
$583$	7709.71	0.547691
$584$	−11186.2	−0.792617
$585$	661.494	0.0467511
$586$	−5356.54	−0.377605
$587$	−9883.43	−0.694945	−0.347473	−	0.937690i	$-0.612960\pi$
$587$	−9883.43	−0.694945	−0.347473	+	0.937690i	$0.612960\pi$
$588$	2512.36	0.176204
$589$	4819.24	0.337137
$590$	−16746.0	−1.16851
$591$	2700.08	0.187930
$592$	25659.8	1.78144
$593$	17690.5	1.22506	0.612530	−	0.790448i	$-0.290152\pi$
$593$	17690.5	1.22506	0.612530	+	0.790448i	$0.290152\pi$
$594$	1037.49	0.0716648
$595$	980.745	0.0675742
$596$	−7792.81	−0.535580
$597$	15666.5	1.07402
$598$	386.151	0.0264062
$599$	−12474.1	−0.850881	−0.425440	−	0.904986i	$-0.639881\pi$
$599$	−12474.1	−0.850881	−0.425440	+	0.904986i	$0.639881\pi$
$600$	−451.166	−0.0306979
$601$	19831.8	1.34602	0.673010	−	0.739633i	$-0.265001\pi$
$601$	19831.8	1.34602	0.673010	+	0.739633i	$0.265001\pi$
$602$	6177.53	0.418235
$603$	5173.45	0.349385
$604$	11068.8	0.745666
$605$	1412.84	0.0949423
$606$	3183.21	0.213381
$607$	9702.60	0.648792	0.324396	−	0.945921i	$-0.394839\pi$
$607$	9702.60	0.648792	0.324396	+	0.945921i	$0.394839\pi$
$608$	−14581.3	−0.972617
$609$	9364.08	0.623074
$610$	−2488.09	−0.165147
$611$	−342.995	−0.0227105
$612$	−264.997	−0.0175030
$613$	−14011.7	−0.923207	−0.461604	−	0.887086i	$-0.652726\pi$
$613$	−14011.7	−0.923207	−0.461604	+	0.887086i	$0.652726\pi$
$614$	−5772.12	−0.379387
$615$	3881.31	0.254487
$616$	−1749.34	−0.114420
$617$	−9121.56	−0.595170	−0.297585	−	0.954695i	$-0.596181\pi$
$617$	−9121.56	−0.595170	−0.297585	+	0.954695i	$0.596181\pi$
$618$	18279.8	1.18984
$619$	−8923.61	−0.579435	−0.289717	−	0.957112i	$-0.593561\pi$
$619$	−8923.61	−0.579435	−0.289717	+	0.957112i	$0.593561\pi$
$620$	−2809.09	−0.181961
$621$	474.151	0.0306394
$622$	−29839.3	−1.92355
$623$	3271.39	0.210378
$624$	1509.95	0.0968694
$625$	−16913.6	−1.08247
$626$	−1280.62	−0.0817631
$627$	2778.23	0.176957
$628$	−7359.25	−0.467621
$629$	2248.28	0.142520
$630$	4401.12	0.278325
$631$	2262.81	0.142759	0.0713795	−	0.997449i	$-0.477260\pi$
$631$	2262.81	0.142759	0.0713795	+	0.997449i	$0.477260\pi$
$632$	−4978.18	−0.313325
$633$	−16244.4	−1.02000
$634$	−35026.0	−2.19410
$635$	6840.11	0.427467
$636$	−8836.91	−0.550953
$637$	−1254.30	−0.0780178
$638$	−10004.2	−0.620799
$639$	6790.00	0.420357
$640$	−17591.8	−1.08653
$641$	−29792.7	−1.83579	−0.917895	−	0.396823i	$-0.870113\pi$
$641$	−29792.7	−1.83579	−0.917895	+	0.396823i	$0.870113\pi$
$642$	2565.64	0.157723
$643$	−871.804	−0.0534691	−0.0267345	−	0.999643i	$-0.508511\pi$
$643$	−871.804	−0.0534691	−0.0267345	+	0.999643i	$0.508511\pi$
$644$	884.853	0.0541430
$645$	−5166.91	−0.315421
$646$	−2060.38	−0.125487
$647$	20827.2	1.26554	0.632768	−	0.774342i	$-0.281919\pi$
$647$	20827.2	1.26554	0.632768	+	0.774342i	$0.281919\pi$
$648$	1074.44	0.0651359
$649$	4516.13	0.273149
$650$	−249.299	−0.0150436
$651$	−2058.87	−0.123953
$652$	658.870	0.0395757
$653$	23754.1	1.42354	0.711768	−	0.702415i	$-0.247895\pi$
$653$	23754.1	1.42354	0.711768	+	0.702415i	$0.247895\pi$
$654$	−14241.0	−0.851478
$655$	−1122.83	−0.0669811
$656$	8859.64	0.527303
$657$	−7589.74	−0.450691
$658$	−2282.05	−0.135203
$659$	−8777.71	−0.518864	−0.259432	−	0.965761i	$-0.583535\pi$
$659$	−8777.71	−0.518864	−0.259432	+	0.965761i	$0.583535\pi$
$660$	−1619.40	−0.0955079
$661$	4529.91	0.266556	0.133278	−	0.991079i	$-0.457450\pi$
$661$	4529.91	0.266556	0.133278	+	0.991079i	$0.457450\pi$
$662$	−7316.93	−0.429578
$663$	132.300	0.00774981
$664$	−4593.94	−0.268493
$665$	11785.4	0.687248
$666$	10089.2	0.587011
$667$	−4572.08	−0.265415
$668$	7235.57	0.419091
$669$	−14291.7	−0.825932
$670$	−23446.3	−1.35196
$671$	671.000	0.0386046
$672$	6229.43	0.357598
$673$	−30273.0	−1.73394	−0.866969	−	0.498362i	$-0.833935\pi$
$673$	−30273.0	−1.73394	−0.866969	+	0.498362i	$0.833935\pi$
$674$	−17556.8	−1.00336
$675$	−306.112	−0.0174552
$676$	−9066.92	−0.515869
$677$	10205.8	0.579380	0.289690	−	0.957120i	$-0.406448\pi$
$677$	10205.8	0.579380	0.289690	+	0.957120i	$0.406448\pi$
$678$	20246.0	1.14682
$679$	16551.0	0.935449
$680$	−1085.10	−0.0611937
$681$	−4747.76	−0.267158
$682$	2199.61	0.123501
$683$	1704.60	0.0954971	0.0477486	−	0.998859i	$-0.484795\pi$
$683$	1704.60	0.0954971	0.0477486	+	0.998859i	$0.484795\pi$
$684$	−3184.42	−0.178011
$685$	−14269.9	−0.795949
$686$	−22710.3	−1.26397
$687$	10700.0	0.594225
$688$	−11794.2	−0.653561
$689$	4411.85	0.243945
$690$	−2148.87	−0.118560
$691$	−29576.4	−1.62827	−0.814137	−	0.580672i	$-0.802790\pi$
$691$	−29576.4	−1.62827	−0.814137	+	0.580672i	$0.802790\pi$
$692$	6152.40	0.337975
$693$	−1186.91	−0.0650608
$694$	16868.4	0.922648
$695$	7594.63	0.414505
$696$	−10360.5	−0.564242
$697$	776.272	0.0421856
$698$	−44608.2	−2.41897
$699$	7466.13	0.403998
$700$	−571.261	−0.0308452
$701$	−21938.5	−1.18203	−0.591017	−	0.806659i	$-0.701273\pi$
$701$	−21938.5	−1.18203	−0.591017	+	0.806659i	$0.701273\pi$
$702$	593.701	0.0319200
$703$	27017.2	1.44946
$704$	381.124	0.0204036
$705$	1908.72	0.101967
$706$	−10920.1	−0.582129
$707$	−3641.65	−0.193718
$708$	−5176.42	−0.274776
$709$	−8397.47	−0.444815	−0.222407	−	0.974954i	$-0.571392\pi$
$709$	−8397.47	−0.444815	−0.222407	+	0.974954i	$0.571392\pi$
$710$	−30772.6	−1.62658
$711$	−3377.65	−0.178160
$712$	−3619.48	−0.190514
$713$	1005.26	0.0528012
$714$	880.235	0.0461372
$715$	808.492	0.0422880
$716$	−13502.9	−0.704786
$717$	−10850.9	−0.565179
$718$	−33427.2	−1.73745
$719$	−18172.5	−0.942587	−0.471294	−	0.881976i	$-0.656213\pi$
$719$	−18172.5	−0.942587	−0.471294	+	0.881976i	$0.656213\pi$
$720$	−8402.66	−0.434929
$721$	−20912.5	−1.08020
$722$	−799.070	−0.0411888
$723$	−13254.6	−0.681802
$724$	−8963.55	−0.460121
$725$	2951.73	0.151206
$726$	1268.05	0.0648232
$727$	−4399.93	−0.224463	−0.112231	−	0.993682i	$-0.535800\pi$
$727$	−4399.93	−0.224463	−0.112231	+	0.993682i	$0.535800\pi$
$728$	−1001.05	−0.0509636
$729$	729.000	0.0370370
$730$	34397.0	1.74396
$731$	−1033.39	−0.0522866
$732$	−769.104	−0.0388345
$733$	31179.5	1.57113	0.785567	−	0.618776i	$-0.212371\pi$
$733$	31179.5	1.57113	0.785567	+	0.618776i	$0.212371\pi$
$734$	−3692.85	−0.185702
$735$	6980.01	0.350288
$736$	−3041.56	−0.152328
$737$	6323.11	0.316031
$738$	3483.54	0.173755
$739$	9946.79	0.495127	0.247563	−	0.968872i	$-0.420370\pi$
$739$	9946.79	0.495127	0.247563	+	0.968872i	$0.420370\pi$
$740$	−15748.1	−0.782311
$741$	1589.83	0.0788177
$742$	29353.4	1.45229
$743$	29652.8	1.46414	0.732069	−	0.681231i	$-0.238555\pi$
$743$	29652.8	1.46414	0.732069	+	0.681231i	$0.238555\pi$
$744$	2277.95	0.112249
$745$	−21650.5	−1.06472
$746$	9466.30	0.464592
$747$	−3116.95	−0.152668
$748$	−323.885	−0.0158321
$749$	−2935.15	−0.143188
$750$	−13908.3	−0.677147
$751$	−33990.5	−1.65157	−0.825785	−	0.563985i	$-0.809268\pi$
$751$	−33990.5	−1.65157	−0.825785	+	0.563985i	$0.809268\pi$
$752$	4356.92	0.211277
$753$	16348.6	0.791201
$754$	−5724.86	−0.276508
$755$	30752.0	1.48236
$756$	1360.45	0.0654483
$757$	5083.66	0.244080	0.122040	−	0.992525i	$-0.461056\pi$
$757$	5083.66	0.244080	0.122040	+	0.992525i	$0.461056\pi$
$758$	8250.04	0.395323
$759$	579.518	0.0277143
$760$	−13039.5	−0.622357
$761$	2944.33	0.140252	0.0701260	−	0.997538i	$-0.477660\pi$
$761$	2944.33	0.140252	0.0701260	+	0.997538i	$0.477660\pi$
$762$	6139.11	0.291859
$763$	16292.0	0.773013
$764$	4143.24	0.196200
$765$	−736.232	−0.0347955
$766$	11309.8	0.533474
$767$	2584.34	0.121662
$768$	−14957.4	−0.702772
$769$	−37245.6	−1.74657	−0.873284	−	0.487212i	$-0.838014\pi$
$769$	−37245.6	−1.74657	−0.873284	+	0.487212i	$0.838014\pi$
$770$	5379.14	0.251754
$771$	214.317	0.0100109
$772$	−7231.19	−0.337120
$773$	10617.4	0.494024	0.247012	−	0.969012i	$-0.420551\pi$
$773$	10617.4	0.494024	0.247012	+	0.969012i	$0.420551\pi$
$774$	−4637.39	−0.215358
$775$	−648.995	−0.0300808
$776$	−18312.1	−0.847122
$777$	−11542.3	−0.532917
$778$	−20342.6	−0.937424
$779$	9328.32	0.429039
$780$	−926.698	−0.0425399
$781$	8298.89	0.380227
$782$	−429.780	−0.0196533
$783$	−7029.49	−0.320835
$784$	15932.9	0.725805
$785$	−20445.9	−0.929614
$786$	−1007.76	−0.0457323
$787$	−17536.5	−0.794295	−0.397148	−	0.917755i	$-0.630000\pi$
$787$	−17536.5	−0.794295	−0.397148	+	0.917755i	$0.630000\pi$
$788$	−3782.59	−0.171001
$789$	19693.4	0.888596
$790$	15307.7	0.689396
$791$	−23161.8	−1.04114
$792$	1313.21	0.0589176
$793$	383.977	0.0171947
$794$	−34503.7	−1.54218
$795$	−24551.3	−1.09528
$796$	−21947.5	−0.977271
$797$	13512.5	0.600548	0.300274	−	0.953853i	$-0.402922\pi$
$797$	13512.5	0.600548	0.300274	+	0.953853i	$0.402922\pi$
$798$	10577.6	0.469228
$799$	381.748	0.0169027
$800$	1963.63	0.0867811
$801$	−2455.79	−0.108328
$802$	40462.4	1.78152
$803$	−9276.35	−0.407665
$804$	−7247.58	−0.317913
$805$	2458.36	0.107634
$806$	1258.72	0.0550081
$807$	−23401.4	−1.02078
$808$	4029.14	0.175427
$809$	−42286.3	−1.83771	−0.918855	−	0.394596i	$-0.870885\pi$
$809$	−42286.3	−1.83771	−0.918855	+	0.394596i	$0.870885\pi$
$810$	−3303.86	−0.143316
$811$	12986.4	0.562288	0.281144	−	0.959666i	$-0.409286\pi$
$811$	12986.4	0.562288	0.281144	+	0.959666i	$0.409286\pi$
$812$	−13118.3	−0.566949
$813$	−20898.8	−0.901541
$814$	12331.3	0.530971
$815$	1830.52	0.0786751
$816$	−1680.55	−0.0720970
$817$	−12418.1	−0.531769
$818$	−9224.07	−0.394269
$819$	−679.207	−0.0289785
$820$	−5437.39	−0.231563
$821$	11271.2	0.479133	0.239566	−	0.970880i	$-0.422995\pi$
$821$	11271.2	0.479133	0.239566	+	0.970880i	$0.422995\pi$
$822$	−12807.5	−0.543446
$823$	−8183.89	−0.346625	−0.173313	−	0.984867i	$-0.555447\pi$
$823$	−8183.89	−0.346625	−0.173313	+	0.984867i	$0.555447\pi$
$824$	23137.7	0.978204
$825$	−374.137	−0.0157888
$826$	17194.4	0.724297
$827$	24547.5	1.03216	0.516082	−	0.856539i	$-0.327390\pi$
$827$	24547.5	1.03216	0.516082	+	0.856539i	$0.327390\pi$
$828$	−664.247	−0.0278794
$829$	−1642.77	−0.0688248	−0.0344124	−	0.999408i	$-0.510956\pi$
$829$	−1642.77	−0.0688248	−0.0344124	+	0.999408i	$0.510956\pi$
$830$	14126.2	0.590754
$831$	18408.8	0.768463
$832$	218.097	0.00908792
$833$	1396.02	0.0580663
$834$	6816.31	0.283009
$835$	20102.3	0.833138
$836$	−3892.07	−0.161017
$837$	1545.57	0.0638264
$838$	44535.3	1.83585
$839$	31472.3	1.29505	0.647523	−	0.762046i	$-0.275805\pi$
$839$	31472.3	1.29505	0.647523	+	0.762046i	$0.275805\pi$
$840$	5570.71	0.228819
$841$	43393.9	1.77924
$842$	−15039.0	−0.615533
$843$	2140.62	0.0874579
$844$	22757.1	0.928118
$845$	−25190.3	−1.02553
$846$	1713.10	0.0696191
$847$	−1450.67	−0.0588497
$848$	−56041.8	−2.26944
$849$	−24466.4	−0.989029
$850$	277.466	0.0111965
$851$	5635.59	0.227010
$852$	−9512.23	−0.382492
$853$	38933.9	1.56280	0.781401	−	0.624029i	$-0.214505\pi$
$853$	38933.9	1.56280	0.781401	+	0.624029i	$0.214505\pi$
$854$	2554.72	0.102366
$855$	−8847.17	−0.353879
$856$	3247.46	0.129668
$857$	36418.8	1.45162	0.725812	−	0.687893i	$-0.241464\pi$
$857$	36418.8	1.45162	0.725812	+	0.687893i	$0.241464\pi$
$858$	725.635	0.0288727
$859$	21973.7	0.872798	0.436399	−	0.899753i	$-0.356254\pi$
$859$	21973.7	0.872798	0.436399	+	0.899753i	$0.356254\pi$
$860$	7238.41	0.287009
$861$	−3985.24	−0.157743
$862$	−47424.3	−1.87387
$863$	16934.9	0.667986	0.333993	−	0.942576i	$-0.391604\pi$
$863$	16934.9	0.667986	0.333993	+	0.942576i	$0.391604\pi$
$864$	−4676.35	−0.184135
$865$	17093.0	0.671884
$866$	−41457.1	−1.62675
$867$	14591.8	0.571582
$868$	2884.31	0.112788
$869$	−4128.24	−0.161152
$870$	31858.0	1.24148
$871$	3618.37	0.140762
$872$	−18025.5	−0.700024
$873$	−12424.6	−0.481684
$874$	−5164.60	−0.199880
$875$	15911.4	0.614747
$876$	10632.6	0.410094
$877$	−21530.7	−0.829009	−0.414504	−	0.910047i	$-0.636045\pi$
$877$	−21530.7	−0.829009	−0.414504	+	0.910047i	$0.636045\pi$
$878$	−31443.3	−1.20861
$879$	−4600.20	−0.176520
$880$	−10269.9	−0.393408
$881$	41321.2	1.58019	0.790094	−	0.612986i	$-0.210032\pi$
$881$	41321.2	1.58019	0.790094	+	0.612986i	$0.210032\pi$
$882$	6264.68	0.239164
$883$	−43827.2	−1.67033	−0.835166	−	0.549998i	$-0.814628\pi$
$883$	−43827.2	−1.67033	−0.835166	+	0.549998i	$0.814628\pi$
$884$	−185.342	−0.00705172
$885$	−14381.5	−0.546246
$886$	−49829.5	−1.88945
$887$	−14863.6	−0.562650	−0.281325	−	0.959613i	$-0.590774\pi$
$887$	−14863.6	−0.562650	−0.281325	+	0.959613i	$0.590774\pi$
$888$	12770.4	0.482598
$889$	−7023.27	−0.264964
$890$	11129.7	0.419180
$891$	891.000	0.0335013
$892$	20021.5	0.751534
$893$	4587.40	0.171905
$894$	−19431.7	−0.726950
$895$	−37514.6	−1.40109
$896$	18062.9	0.673481
$897$	331.627	0.0123442
$898$	−41967.0	−1.55953
$899$	−14903.4	−0.552898
$900$	428.838	0.0158829
$901$	−4910.32	−0.181561
$902$	4257.66	0.157167
$903$	5305.26	0.195513
$904$	25626.4	0.942832
$905$	−24903.1	−0.914705
$906$	27600.5	1.01210
$907$	33379.4	1.22199	0.610995	−	0.791634i	$-0.290770\pi$
$907$	33379.4	1.22199	0.610995	+	0.791634i	$0.290770\pi$
$908$	6651.22	0.243093
$909$	2733.74	0.0997496
$910$	3078.19	0.112133
$911$	−22415.6	−0.815214	−0.407607	−	0.913157i	$-0.633637\pi$
$911$	−22415.6	−0.815214	−0.407607	+	0.913157i	$0.633637\pi$
$912$	−20194.9	−0.733246
$913$	−3809.61	−0.138094
$914$	7838.01	0.283652
$915$	−2136.77	−0.0772017
$916$	−14989.9	−0.540698
$917$	1152.90	0.0415180
$918$	−660.780	−0.0237571
$919$	49721.3	1.78472	0.892359	−	0.451326i	$-0.149049\pi$
$919$	49721.3	1.78472	0.892359	+	0.451326i	$0.149049\pi$
$920$	−2719.94	−0.0974714
$921$	−4957.10	−0.177353
$922$	4783.27	0.170855
$923$	4749.01	0.169356
$924$	1662.77	0.0592003
$925$	−3638.34	−0.129327
$926$	−47355.0	−1.68054
$927$	15698.7	0.556218
$928$	45092.4	1.59508
$929$	44569.1	1.57402	0.787010	−	0.616940i	$-0.211628\pi$
$929$	44569.1	1.57402	0.787010	+	0.616940i	$0.211628\pi$
$930$	−7004.59	−0.246978
$931$	16775.7	0.590550
$932$	−10459.4	−0.367607
$933$	−25626.0	−0.899204
$934$	13681.6	0.479310
$935$	−899.839	−0.0314737
$936$	751.477	0.0262423
$937$	−15739.1	−0.548746	−0.274373	−	0.961623i	$-0.588470\pi$
$937$	−15739.1	−0.548746	−0.274373	+	0.961623i	$0.588470\pi$
$938$	24074.1	0.838005
$939$	−1099.79	−0.0382220
$940$	−2673.95	−0.0927816
$941$	8969.35	0.310725	0.155363	−	0.987858i	$-0.450345\pi$
$941$	8969.35	0.310725	0.155363	+	0.987858i	$0.450345\pi$
$942$	−18350.6	−0.634707
$943$	1945.82	0.0671947
$944$	−32827.7	−1.13183
$945$	3779.68	0.130109
$946$	−5667.92	−0.194799
$947$	−12380.5	−0.424828	−0.212414	−	0.977180i	$-0.568133\pi$
$947$	−12380.5	−0.424828	−0.212414	+	0.977180i	$0.568133\pi$
$948$	4731.81	0.162112
$949$	−5308.36	−0.181577
$950$	3334.26	0.113871
$951$	−30080.4	−1.02568
$952$	1114.16	0.0379307
$953$	28374.0	0.964454	0.482227	−	0.876046i	$-0.339828\pi$
$953$	28374.0	0.964454	0.482227	+	0.876046i	$0.339828\pi$
$954$	−22035.2	−0.747815
$955$	11511.0	0.390039
$956$	15201.2	0.514269
$957$	−8591.60	−0.290206
$958$	1533.25	0.0517089
$959$	14652.0	0.493366
$960$	−1213.68	−0.0408034
$961$	−26514.2	−0.890007
$962$	7056.51	0.236498
$963$	2203.38	0.0737309
$964$	18568.6	0.620387
$965$	−20090.2	−0.670182
$966$	2206.42	0.0734889
$967$	−43332.7	−1.44104	−0.720520	−	0.693434i	$-0.756097\pi$
$967$	−43332.7	−1.44104	−0.720520	+	0.693434i	$0.756097\pi$
$968$	1605.03	0.0532930
$969$	−1769.46	−0.0586616
$970$	56308.9	1.86389
$971$	28831.2	0.952871	0.476436	−	0.879209i	$-0.341929\pi$
$971$	28831.2	0.952871	0.476436	+	0.879209i	$0.341929\pi$
$972$	−1021.27	−0.0337008
$973$	−7798.00	−0.256929
$974$	33689.4	1.10829
$975$	−214.099	−0.00703245
$976$	−4877.49	−0.159964
$977$	−27701.6	−0.907116	−0.453558	−	0.891227i	$-0.649846\pi$
$977$	−27701.6	−0.907116	−0.453558	+	0.891227i	$0.649846\pi$
$978$	1642.92	0.0537165
$979$	−3001.52	−0.0979867
$980$	−9778.42	−0.318735
$981$	−12230.2	−0.398042
$982$	−58000.1	−1.88478
$983$	33874.4	1.09911	0.549555	−	0.835458i	$-0.314797\pi$
$983$	33874.4	1.09911	0.549555	+	0.835458i	$0.314797\pi$
$984$	4409.29	0.142849
$985$	−10509.0	−0.339945
$986$	6371.67	0.205797
$987$	−1959.83	−0.0632036
$988$	−2227.22	−0.0717180
$989$	−2590.33	−0.0832838
$990$	−4038.05	−0.129634
$991$	−18374.0	−0.588969	−0.294485	−	0.955656i	$-0.595148\pi$
$991$	−18374.0	−0.588969	−0.294485	+	0.955656i	$0.595148\pi$
$992$	−9914.44	−0.317322
$993$	−6283.79	−0.200816
$994$	31596.6	1.00823
$995$	−60975.9	−1.94278
$996$	4366.59	0.138916
$997$	50747.8	1.61203	0.806017	−	0.591892i	$-0.201619\pi$
$997$	50747.8	1.61203	0.806017	+	0.591892i	$0.201619\pi$
$998$	33094.0	1.04967
$999$	8664.62	0.274411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.g.1.9	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.g.1.9	✓	39	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-3.49324 q^{2} -3.00000 q^{3} +4.20275 q^{4} +11.6764 q^{5} +10.4797 q^{6} -11.9890 q^{7} +13.2647 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.49324 q^{2} -3.00000 q^{3} +4.20275 q^{4} +11.6764 q^{5} +10.4797 q^{6} -11.9890 q^{7} +13.2647 q^{8} +9.00000 q^{9} -40.7884 q^{10} +11.0000 q^{11} -12.6083 q^{12} +6.29471 q^{13} +41.8806 q^{14} -35.0291 q^{15} -79.9589 q^{16} -7.00591 q^{17} -31.4392 q^{18} -84.1888 q^{19} +49.0729 q^{20} +35.9671 q^{21} -38.4257 q^{22} -17.5612 q^{23} -39.7941 q^{24} +11.3375 q^{25} -21.9889 q^{26} -27.0000 q^{27} -50.3869 q^{28} +260.352 q^{29} +122.365 q^{30} -57.2433 q^{31} +173.198 q^{32} -33.0000 q^{33} +24.4733 q^{34} -139.988 q^{35} +37.8248 q^{36} -320.912 q^{37} +294.092 q^{38} -18.8841 q^{39} +154.884 q^{40} -110.802 q^{41} -125.642 q^{42} +147.503 q^{43} +46.2303 q^{44} +105.087 q^{45} +61.3454 q^{46} -54.4895 q^{47} +239.877 q^{48} -199.263 q^{49} -39.6046 q^{50} +21.0177 q^{51} +26.4551 q^{52} +700.883 q^{53} +94.3176 q^{54} +128.440 q^{55} -159.031 q^{56} +252.566 q^{57} -909.471 q^{58} +410.558 q^{59} -147.219 q^{60} +61.0000 q^{61} +199.965 q^{62} -107.901 q^{63} +34.6477 q^{64} +73.4993 q^{65} +115.277 q^{66} +574.828 q^{67} -29.4441 q^{68} +52.6835 q^{69} +489.013 q^{70} +754.444 q^{71} +119.382 q^{72} -843.305 q^{73} +1121.02 q^{74} -34.0125 q^{75} -353.824 q^{76} -131.879 q^{77} +65.9668 q^{78} -375.295 q^{79} -933.629 q^{80} +81.0000 q^{81} +387.060 q^{82} -346.328 q^{83} +151.161 q^{84} -81.8036 q^{85} -515.265 q^{86} -781.055 q^{87} +145.912 q^{88} -272.866 q^{89} -367.095 q^{90} -75.4674 q^{91} -73.8052 q^{92} +171.730 q^{93} +190.345 q^{94} -983.019 q^{95} -519.595 q^{96} -1380.51 q^{97} +696.075 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * q^99

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