LMFDB - Embedded newform 6015.2.a.g.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.108652 q^{2} -1.00000 q^{3} -1.98819 q^{4} +1.00000 q^{5} -0.108652 q^{6} +0.790651 q^{7} -0.433326 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.108652 q^{2} -1.00000 q^{3} -1.98819 q^{4} +1.00000 q^{5} -0.108652 q^{6} +0.790651 q^{7} -0.433326 q^{8} +1.00000 q^{9} +0.108652 q^{10} -0.287481 q^{11} +1.98819 q^{12} +4.64561 q^{13} +0.0859059 q^{14} -1.00000 q^{15} +3.92931 q^{16} +5.99627 q^{17} +0.108652 q^{18} +1.56500 q^{19} -1.98819 q^{20} -0.790651 q^{21} -0.0312354 q^{22} -3.81758 q^{23} +0.433326 q^{24} +1.00000 q^{25} +0.504755 q^{26} -1.00000 q^{27} -1.57197 q^{28} +8.60734 q^{29} -0.108652 q^{30} -7.99069 q^{31} +1.29358 q^{32} +0.287481 q^{33} +0.651508 q^{34} +0.790651 q^{35} -1.98819 q^{36} +5.61956 q^{37} +0.170041 q^{38} -4.64561 q^{39} -0.433326 q^{40} +1.25677 q^{41} -0.0859059 q^{42} +12.1856 q^{43} +0.571569 q^{44} +1.00000 q^{45} -0.414788 q^{46} -1.51573 q^{47} -3.92931 q^{48} -6.37487 q^{49} +0.108652 q^{50} -5.99627 q^{51} -9.23637 q^{52} +7.46173 q^{53} -0.108652 q^{54} -0.287481 q^{55} -0.342609 q^{56} -1.56500 q^{57} +0.935206 q^{58} -9.20088 q^{59} +1.98819 q^{60} +10.1472 q^{61} -0.868205 q^{62} +0.790651 q^{63} -7.71807 q^{64} +4.64561 q^{65} +0.0312354 q^{66} -14.8367 q^{67} -11.9218 q^{68} +3.81758 q^{69} +0.0859059 q^{70} -12.2074 q^{71} -0.433326 q^{72} -4.15457 q^{73} +0.610577 q^{74} -1.00000 q^{75} -3.11153 q^{76} -0.227297 q^{77} -0.504755 q^{78} +6.62160 q^{79} +3.92931 q^{80} +1.00000 q^{81} +0.136551 q^{82} +9.73376 q^{83} +1.57197 q^{84} +5.99627 q^{85} +1.32399 q^{86} -8.60734 q^{87} +0.124573 q^{88} +3.23324 q^{89} +0.108652 q^{90} +3.67306 q^{91} +7.59009 q^{92} +7.99069 q^{93} -0.164688 q^{94} +1.56500 q^{95} -1.29358 q^{96} -14.4387 q^{97} -0.692643 q^{98} -0.287481 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9} + 15 q^{11} - 36 q^{12} + 8 q^{13} + 10 q^{14} - 36 q^{15} + 36 q^{16} + 32 q^{17} + 5 q^{19} + 36 q^{20} + 4 q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + 36 q^{25} + 22 q^{26} - 36 q^{27} + 61 q^{29} + 15 q^{31} - q^{32} - 15 q^{33} + 26 q^{34} - 4 q^{35} + 36 q^{36} + 16 q^{37} + 20 q^{38} - 8 q^{39} - 3 q^{40} + 61 q^{41} - 10 q^{42} - 35 q^{43} + 39 q^{44} + 36 q^{45} + 11 q^{46} - 28 q^{47} - 36 q^{48} + 68 q^{49} - 32 q^{51} + 4 q^{52} + 33 q^{53} + 15 q^{55} + 23 q^{56} - 5 q^{57} + 6 q^{58} + 35 q^{59} - 36 q^{60} + 55 q^{61} + q^{62} - 4 q^{63} + 15 q^{64} + 8 q^{65} - q^{66} - 34 q^{67} + 60 q^{68} + 10 q^{69} + 10 q^{70} + 42 q^{71} - 3 q^{72} + 53 q^{73} + 54 q^{74} - 36 q^{75} + 20 q^{76} + 20 q^{77} - 22 q^{78} + 25 q^{79} + 36 q^{80} + 36 q^{81} - 15 q^{82} - 11 q^{83} + 32 q^{85} + 53 q^{86} - 61 q^{87} + 27 q^{88} + 81 q^{89} + 15 q^{91} - 7 q^{92} - 15 q^{93} + 56 q^{94} + 5 q^{95} + q^{96} + 47 q^{97} - 3 q^{98} + 15 q^{99}+O(q^{100}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9 + 15 * q^11 - 36 * q^12 + 8 * q^13 + 10 * q^14 - 36 * q^15 + 36 * q^16 + 32 * q^17 + 5 * q^19 + 36 * q^20 + 4 * q^21 + q^22 - 10 * q^23 + 3 * q^24 + 36 * q^25 + 22 * q^26 - 36 * q^27 + 61 * q^29 + 15 * q^31 - q^32 - 15 * q^33 + 26 * q^34 - 4 * q^35 + 36 * q^36 + 16 * q^37 + 20 * q^38 - 8 * q^39 - 3 * q^40 + 61 * q^41 - 10 * q^42 - 35 * q^43 + 39 * q^44 + 36 * q^45 + 11 * q^46 - 28 * q^47 - 36 * q^48 + 68 * q^49 - 32 * q^51 + 4 * q^52 + 33 * q^53 + 15 * q^55 + 23 * q^56 - 5 * q^57 + 6 * q^58 + 35 * q^59 - 36 * q^60 + 55 * q^61 + q^62 - 4 * q^63 + 15 * q^64 + 8 * q^65 - q^66 - 34 * q^67 + 60 * q^68 + 10 * q^69 + 10 * q^70 + 42 * q^71 - 3 * q^72 + 53 * q^73 + 54 * q^74 - 36 * q^75 + 20 * q^76 + 20 * q^77 - 22 * q^78 + 25 * q^79 + 36 * q^80 + 36 * q^81 - 15 * q^82 - 11 * q^83 + 32 * q^85 + 53 * q^86 - 61 * q^87 + 27 * q^88 + 81 * q^89 + 15 * q^91 - 7 * q^92 - 15 * q^93 + 56 * q^94 + 5 * q^95 + q^96 + 47 * q^97 - 3 * q^98 + 15 * 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 $

$2$	0.108652	0.0768286	0.0384143	−	0.999262i	$-0.487769\pi$
$2$	0.108652	0.0768286	0.0384143	+	0.999262i	$0.487769\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.98819	−0.994097
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.108652	−0.0443570
$7$	0.790651	0.298838	0.149419	−	0.988774i	$-0.452260\pi$
$7$	0.790651	0.298838	0.149419	+	0.988774i	$0.452260\pi$
$8$	−0.433326	−0.153204
$9$	1.00000	0.333333
$10$	0.108652	0.0343588
$11$	−0.287481	−0.0866789	−0.0433394	−	0.999060i	$-0.513800\pi$
$11$	−0.287481	−0.0866789	−0.0433394	+	0.999060i	$0.513800\pi$
$12$	1.98819	0.573942
$13$	4.64561	1.28846	0.644230	−	0.764832i	$-0.277178\pi$
$13$	4.64561	1.28846	0.644230	+	0.764832i	$0.277178\pi$
$14$	0.0859059	0.0229593
$15$	−1.00000	−0.258199
$16$	3.92931	0.982327
$17$	5.99627	1.45431	0.727155	−	0.686473i	$-0.240842\pi$
$17$	5.99627	1.45431	0.727155	+	0.686473i	$0.240842\pi$
$18$	0.108652	0.0256095
$19$	1.56500	0.359036	0.179518	−	0.983755i	$-0.442546\pi$
$19$	1.56500	0.359036	0.179518	+	0.983755i	$0.442546\pi$
$20$	−1.98819	−0.444574
$21$	−0.790651	−0.172534
$22$	−0.0312354	−0.00665942
$23$	−3.81758	−0.796020	−0.398010	−	0.917381i	$-0.630299\pi$
$23$	−3.81758	−0.796020	−0.398010	+	0.917381i	$0.630299\pi$
$24$	0.433326	0.0884522
$25$	1.00000	0.200000
$26$	0.504755	0.0989906
$27$	−1.00000	−0.192450
$28$	−1.57197	−0.297074
$29$	8.60734	1.59834	0.799172	−	0.601103i	$-0.205272\pi$
$29$	8.60734	1.59834	0.799172	+	0.601103i	$0.205272\pi$
$30$	−0.108652	−0.0198371
$31$	−7.99069	−1.43517	−0.717585	−	0.696471i	$-0.754753\pi$
$31$	−7.99069	−1.43517	−0.717585	+	0.696471i	$0.754753\pi$
$32$	1.29358	0.228675
$33$	0.287481	0.0500441
$34$	0.651508	0.111733
$35$	0.790651	0.133644
$36$	−1.98819	−0.331366
$37$	5.61956	0.923850	0.461925	−	0.886919i	$-0.347159\pi$
$37$	5.61956	0.923850	0.461925	+	0.886919i	$0.347159\pi$
$38$	0.170041	0.0275842
$39$	−4.64561	−0.743893
$40$	−0.433326	−0.0685148
$41$	1.25677	0.196275	0.0981373	−	0.995173i	$-0.468712\pi$
$41$	1.25677	0.196275	0.0981373	+	0.995173i	$0.468712\pi$
$42$	−0.0859059	−0.0132556
$43$	12.1856	1.85829	0.929145	−	0.369715i	$-0.120545\pi$
$43$	12.1856	1.85829	0.929145	+	0.369715i	$0.120545\pi$
$44$	0.571569	0.0861672
$45$	1.00000	0.149071
$46$	−0.414788	−0.0611571
$47$	−1.51573	−0.221092	−0.110546	−	0.993871i	$-0.535260\pi$
$47$	−1.51573	−0.221092	−0.110546	+	0.993871i	$0.535260\pi$
$48$	−3.92931	−0.567147
$49$	−6.37487	−0.910696
$50$	0.108652	0.0153657
$51$	−5.99627	−0.839646
$52$	−9.23637	−1.28085
$53$	7.46173	1.02495	0.512474	−	0.858703i	$-0.328729\pi$
$53$	7.46173	1.02495	0.512474	+	0.858703i	$0.328729\pi$
$54$	−0.108652	−0.0147857
$55$	−0.287481	−0.0387640
$56$	−0.342609	−0.0457831
$57$	−1.56500	−0.207289
$58$	0.935206	0.122799
$59$	−9.20088	−1.19785	−0.598926	−	0.800804i	$-0.704406\pi$
$59$	−9.20088	−1.19785	−0.598926	+	0.800804i	$0.704406\pi$
$60$	1.98819	0.256675
$61$	10.1472	1.29921	0.649607	−	0.760270i	$-0.274933\pi$
$61$	10.1472	1.29921	0.649607	+	0.760270i	$0.274933\pi$
$62$	−0.868205	−0.110262
$63$	0.790651	0.0996127
$64$	−7.71807	−0.964758
$65$	4.64561	0.576217
$66$	0.0312354	0.00384482
$67$	−14.8367	−1.81260	−0.906298	−	0.422639i	$-0.861104\pi$
$67$	−14.8367	−1.81260	−0.906298	+	0.422639i	$0.861104\pi$
$68$	−11.9218	−1.44573
$69$	3.81758	0.459582
$70$	0.0859059	0.0102677
$71$	−12.2074	−1.44875	−0.724375	−	0.689406i	$-0.757871\pi$
$71$	−12.2074	−1.44875	−0.724375	+	0.689406i	$0.757871\pi$
$72$	−0.433326	−0.0510679
$73$	−4.15457	−0.486255	−0.243128	−	0.969994i	$-0.578173\pi$
$73$	−4.15457	−0.486255	−0.243128	+	0.969994i	$0.578173\pi$
$74$	0.610577	0.0709781
$75$	−1.00000	−0.115470
$76$	−3.11153	−0.356917
$77$	−0.227297	−0.0259029
$78$	−0.504755	−0.0571523
$79$	6.62160	0.744988	0.372494	−	0.928035i	$-0.378503\pi$
$79$	6.62160	0.744988	0.372494	+	0.928035i	$0.378503\pi$
$80$	3.92931	0.439310
$81$	1.00000	0.111111
$82$	0.136551	0.0150795
$83$	9.73376	1.06842	0.534209	−	0.845352i	$-0.320609\pi$
$83$	9.73376	1.06842	0.534209	+	0.845352i	$0.320609\pi$
$84$	1.57197	0.171516
$85$	5.99627	0.650387
$86$	1.32399	0.142770
$87$	−8.60734	−0.922804
$88$	0.124573	0.0132795
$89$	3.23324	0.342722	0.171361	−	0.985208i	$-0.445183\pi$
$89$	3.23324	0.342722	0.171361	+	0.985208i	$0.445183\pi$
$90$	0.108652	0.0114529
$91$	3.67306	0.385041
$92$	7.59009	0.791321
$93$	7.99069	0.828596
$94$	−0.164688	−0.0169862
$95$	1.56500	0.160566
$96$	−1.29358	−0.132025
$97$	−14.4387	−1.46603	−0.733016	−	0.680211i	$-0.761888\pi$
$97$	−14.4387	−1.46603	−0.733016	+	0.680211i	$0.761888\pi$
$98$	−0.692643	−0.0699675
$99$	−0.287481	−0.0288930
$100$	−1.98819	−0.198819
$101$	12.2367	1.21759	0.608797	−	0.793326i	$-0.291652\pi$
$101$	12.2367	1.21759	0.608797	+	0.793326i	$0.291652\pi$
$102$	−0.651508	−0.0645089
$103$	12.9137	1.27243	0.636213	−	0.771513i	$-0.280500\pi$
$103$	12.9137	1.27243	0.636213	+	0.771513i	$0.280500\pi$
$104$	−2.01306	−0.197397
$105$	−0.790651	−0.0771596
$106$	0.810732	0.0787453
$107$	−3.69840	−0.357538	−0.178769	−	0.983891i	$-0.557211\pi$
$107$	−3.69840	−0.357538	−0.178769	+	0.983891i	$0.557211\pi$
$108$	1.98819	0.191314
$109$	−5.25650	−0.503481	−0.251741	−	0.967795i	$-0.581003\pi$
$109$	−5.25650	−0.503481	−0.251741	+	0.967795i	$0.581003\pi$
$110$	−0.0312354	−0.00297818
$111$	−5.61956	−0.533385
$112$	3.10671	0.293557
$113$	3.08073	0.289811	0.144905	−	0.989446i	$-0.453712\pi$
$113$	3.08073	0.289811	0.144905	+	0.989446i	$0.453712\pi$
$114$	−0.170041	−0.0159258
$115$	−3.81758	−0.355991
$116$	−17.1131	−1.58891
$117$	4.64561	0.429487
$118$	−0.999695	−0.0920294
$119$	4.74096	0.434603
$120$	0.433326	0.0395570
$121$	−10.9174	−0.992487
$122$	1.10251	0.0998169
$123$	−1.25677	−0.113319
$124$	15.8871	1.42670
$125$	1.00000	0.0894427
$126$	0.0859059	0.00765310
$127$	−2.84824	−0.252740	−0.126370	−	0.991983i	$-0.540333\pi$
$127$	−2.84824	−0.252740	−0.126370	+	0.991983i	$0.540333\pi$
$128$	−3.42574	−0.302796
$129$	−12.1856	−1.07288
$130$	0.504755	0.0442699
$131$	−19.5417	−1.70737	−0.853684	−	0.520792i	$-0.825637\pi$
$131$	−19.5417	−1.70737	−0.853684	+	0.520792i	$0.825637\pi$
$132$	−0.571569	−0.0497487
$133$	1.23737	0.107294
$134$	−1.61204	−0.139259
$135$	−1.00000	−0.0860663
$136$	−2.59834	−0.222806
$137$	−14.6197	−1.24904	−0.624521	−	0.781008i	$-0.714706\pi$
$137$	−14.6197	−1.24904	−0.624521	+	0.781008i	$0.714706\pi$
$138$	0.414788	0.0353091
$139$	−16.7335	−1.41931	−0.709657	−	0.704547i	$-0.751150\pi$
$139$	−16.7335	−1.41931	−0.709657	+	0.704547i	$0.751150\pi$
$140$	−1.57197	−0.132856
$141$	1.51573	0.127648
$142$	−1.32636	−0.111305
$143$	−1.33553	−0.111682
$144$	3.92931	0.327442
$145$	8.60734	0.714801
$146$	−0.451402	−0.0373583
$147$	6.37487	0.525790
$148$	−11.1728	−0.918397
$149$	22.7861	1.86671	0.933353	−	0.358959i	$-0.116868\pi$
$149$	22.7861	1.86671	0.933353	+	0.358959i	$0.116868\pi$
$150$	−0.108652	−0.00887141
$151$	10.8179	0.880351	0.440175	−	0.897912i	$-0.354916\pi$
$151$	10.8179	0.880351	0.440175	+	0.897912i	$0.354916\pi$
$152$	−0.678155	−0.0550056
$153$	5.99627	0.484770
$154$	−0.0246963	−0.00199009
$155$	−7.99069	−0.641828
$156$	9.23637	0.739502
$157$	9.84949	0.786075	0.393037	−	0.919522i	$-0.371424\pi$
$157$	9.84949	0.786075	0.393037	+	0.919522i	$0.371424\pi$
$158$	0.719450	0.0572364
$159$	−7.46173	−0.591754
$160$	1.29358	0.102266
$161$	−3.01837	−0.237881
$162$	0.108652	0.00853651
$163$	−6.53720	−0.512033	−0.256017	−	0.966672i	$-0.582410\pi$
$163$	−6.53720	−0.512033	−0.256017	+	0.966672i	$0.582410\pi$
$164$	−2.49870	−0.195116
$165$	0.287481	0.0223804
$166$	1.05759	0.0820851
$167$	24.2876	1.87943	0.939716	−	0.341956i	$-0.111089\pi$
$167$	24.2876	1.87943	0.939716	+	0.341956i	$0.111089\pi$
$168$	0.342609	0.0264329
$169$	8.58168	0.660129
$170$	0.651508	0.0499684
$171$	1.56500	0.119679
$172$	−24.2274	−1.84732
$173$	11.7303	0.891836	0.445918	−	0.895074i	$-0.352877\pi$
$173$	11.7303	0.891836	0.445918	+	0.895074i	$0.352877\pi$
$174$	−0.935206	−0.0708978
$175$	0.790651	0.0597676
$176$	−1.12960	−0.0851470
$177$	9.20088	0.691581
$178$	0.351298	0.0263309
$179$	−24.2088	−1.80945	−0.904724	−	0.425998i	$-0.859923\pi$
$179$	−24.2088	−1.80945	−0.904724	+	0.425998i	$0.859923\pi$
$180$	−1.98819	−0.148191
$181$	17.3685	1.29099	0.645495	−	0.763765i	$-0.276651\pi$
$181$	17.3685	1.29099	0.645495	+	0.763765i	$0.276651\pi$
$182$	0.399085	0.0295822
$183$	−10.1472	−0.750102
$184$	1.65425	0.121953
$185$	5.61956	0.413158
$186$	0.868205	0.0636599
$187$	−1.72382	−0.126058
$188$	3.01357	0.219787
$189$	−0.790651	−0.0575114
$190$	0.170041	0.0123360
$191$	23.3590	1.69020	0.845099	−	0.534610i	$-0.179541\pi$
$191$	23.3590	1.69020	0.845099	+	0.534610i	$0.179541\pi$
$192$	7.71807	0.557003
$193$	−1.17013	−0.0842278	−0.0421139	−	0.999113i	$-0.513409\pi$
$193$	−1.17013	−0.0842278	−0.0421139	+	0.999113i	$0.513409\pi$
$194$	−1.56880	−0.112633
$195$	−4.64561	−0.332679
$196$	12.6745	0.905320
$197$	8.35785	0.595472	0.297736	−	0.954648i	$-0.403768\pi$
$197$	8.35785	0.595472	0.297736	+	0.954648i	$0.403768\pi$
$198$	−0.0312354	−0.00221981
$199$	8.31585	0.589495	0.294748	−	0.955575i	$-0.404764\pi$
$199$	8.31585	0.589495	0.294748	+	0.955575i	$0.404764\pi$
$200$	−0.433326	−0.0306408
$201$	14.8367	1.04650
$202$	1.32954	0.0935461
$203$	6.80540	0.477646
$204$	11.9218	0.834690
$205$	1.25677	0.0877767
$206$	1.40310	0.0977587
$207$	−3.81758	−0.265340
$208$	18.2540	1.26569
$209$	−0.449909	−0.0311208
$210$	−0.0859059	−0.00592807
$211$	23.6220	1.62621	0.813104	−	0.582118i	$-0.197776\pi$
$211$	23.6220	1.62621	0.813104	+	0.582118i	$0.197776\pi$
$212$	−14.8354	−1.01890
$213$	12.2074	0.836436
$214$	−0.401839	−0.0274691
$215$	12.1856	0.831053
$216$	0.433326	0.0294841
$217$	−6.31785	−0.428884
$218$	−0.571130	−0.0386818
$219$	4.15457	0.280740
$220$	0.571569	0.0385352
$221$	27.8563	1.87382
$222$	−0.610577	−0.0409793
$223$	8.30503	0.556146	0.278073	−	0.960560i	$-0.410304\pi$
$223$	8.30503	0.556146	0.278073	+	0.960560i	$0.410304\pi$
$224$	1.02277	0.0683367
$225$	1.00000	0.0666667
$226$	0.334728	0.0222658
$227$	5.53534	0.367393	0.183697	−	0.982983i	$-0.441194\pi$
$227$	5.53534	0.367393	0.183697	+	0.982983i	$0.441194\pi$
$228$	3.11153	0.206066
$229$	−0.864488	−0.0571270	−0.0285635	−	0.999592i	$-0.509093\pi$
$229$	−0.864488	−0.0571270	−0.0285635	+	0.999592i	$0.509093\pi$
$230$	−0.414788	−0.0273503
$231$	0.227297	0.0149551
$232$	−3.72978	−0.244872
$233$	−6.96581	−0.456345	−0.228173	−	0.973621i	$-0.573275\pi$
$233$	−6.96581	−0.456345	−0.228173	+	0.973621i	$0.573275\pi$
$234$	0.504755	0.0329969
$235$	−1.51573	−0.0988756
$236$	18.2931	1.19078
$237$	−6.62160	−0.430119
$238$	0.515115	0.0333900
$239$	−12.4726	−0.806788	−0.403394	−	0.915026i	$-0.632170\pi$
$239$	−12.4726	−0.806788	−0.403394	+	0.915026i	$0.632170\pi$
$240$	−3.92931	−0.253636
$241$	3.42441	0.220585	0.110293	−	0.993899i	$-0.464821\pi$
$241$	3.42441	0.220585	0.110293	+	0.993899i	$0.464821\pi$
$242$	−1.18619	−0.0762514
$243$	−1.00000	−0.0641500
$244$	−20.1746	−1.29155
$245$	−6.37487	−0.407276
$246$	−0.136551	−0.00870616
$247$	7.27038	0.462603
$248$	3.46257	0.219874
$249$	−9.73376	−0.616852
$250$	0.108652	0.00687176
$251$	−18.7101	−1.18097	−0.590485	−	0.807049i	$-0.701063\pi$
$251$	−18.7101	−1.18097	−0.590485	+	0.807049i	$0.701063\pi$
$252$	−1.57197	−0.0990247
$253$	1.09748	0.0689981
$254$	−0.309467	−0.0194177
$255$	−5.99627	−0.375501
$256$	15.0639	0.941495
$257$	−13.6264	−0.849992	−0.424996	−	0.905195i	$-0.639725\pi$
$257$	−13.6264	−0.849992	−0.424996	+	0.905195i	$0.639725\pi$
$258$	−1.32399	−0.0824282
$259$	4.44311	0.276082
$260$	−9.23637	−0.572816
$261$	8.60734	0.532781
$262$	−2.12325	−0.131175
$263$	−4.91830	−0.303276	−0.151638	−	0.988436i	$-0.548455\pi$
$263$	−4.91830	−0.303276	−0.151638	+	0.988436i	$0.548455\pi$
$264$	−0.124573	−0.00766694
$265$	7.46173	0.458370
$266$	0.134443	0.00824322
$267$	−3.23324	−0.197871
$268$	29.4983	1.80190
$269$	1.47885	0.0901669	0.0450835	−	0.998983i	$-0.485645\pi$
$269$	1.47885	0.0901669	0.0450835	+	0.998983i	$0.485645\pi$
$270$	−0.108652	−0.00661235
$271$	−10.0748	−0.611998	−0.305999	−	0.952032i	$-0.598990\pi$
$271$	−10.0748	−0.611998	−0.305999	+	0.952032i	$0.598990\pi$
$272$	23.5612	1.42861
$273$	−3.67306	−0.222303
$274$	−1.58846	−0.0959621
$275$	−0.287481	−0.0173358
$276$	−7.59009	−0.456870
$277$	11.4078	0.685431	0.342716	−	0.939439i	$-0.388653\pi$
$277$	11.4078	0.685431	0.342716	+	0.939439i	$0.388653\pi$
$278$	−1.81813	−0.109044
$279$	−7.99069	−0.478390
$280$	−0.342609	−0.0204748
$281$	13.0855	0.780615	0.390307	−	0.920685i	$-0.372369\pi$
$281$	13.0855	0.780615	0.390307	+	0.920685i	$0.372369\pi$
$282$	0.164688	0.00980700
$283$	2.47110	0.146892	0.0734459	−	0.997299i	$-0.476600\pi$
$283$	2.47110	0.146892	0.0734459	+	0.997299i	$0.476600\pi$
$284$	24.2707	1.44020
$285$	−1.56500	−0.0927027
$286$	−0.145108	−0.00858039
$287$	0.993667	0.0586543
$288$	1.29358	0.0762249
$289$	18.9553	1.11502
$290$	0.935206	0.0549172
$291$	14.4387	0.846414
$292$	8.26009	0.483385
$293$	13.8680	0.810180	0.405090	−	0.914277i	$-0.367240\pi$
$293$	13.8680	0.810180	0.405090	+	0.914277i	$0.367240\pi$
$294$	0.692643	0.0403958
$295$	−9.20088	−0.535696
$296$	−2.43510	−0.141537
$297$	0.287481	0.0166814
$298$	2.47575	0.143416
$299$	−17.7350	−1.02564
$300$	1.98819	0.114788
$301$	9.63458	0.555328
$302$	1.17539	0.0676361
$303$	−12.2367	−0.702978
$304$	6.14937	0.352691
$305$	10.1472	0.581027
$306$	0.651508	0.0372442
$307$	24.5776	1.40272	0.701358	−	0.712809i	$-0.252577\pi$
$307$	24.5776	1.40272	0.701358	+	0.712809i	$0.252577\pi$
$308$	0.451911	0.0257500
$309$	−12.9137	−0.734635
$310$	−0.868205	−0.0493107
$311$	−13.4371	−0.761949	−0.380974	−	0.924586i	$-0.624411\pi$
$311$	−13.4371	−0.761949	−0.380974	+	0.924586i	$0.624411\pi$
$312$	2.01306	0.113967
$313$	18.7347	1.05895	0.529473	−	0.848327i	$-0.322390\pi$
$313$	18.7347	1.05895	0.529473	+	0.848327i	$0.322390\pi$
$314$	1.07017	0.0603931
$315$	0.790651	0.0445481
$316$	−13.1650	−0.740591
$317$	−9.44436	−0.530448	−0.265224	−	0.964187i	$-0.585446\pi$
$317$	−9.44436	−0.530448	−0.265224	+	0.964187i	$0.585446\pi$
$318$	−0.810732	−0.0454636
$319$	−2.47445	−0.138543
$320$	−7.71807	−0.431453
$321$	3.69840	0.206424
$322$	−0.327952	−0.0182761
$323$	9.38417	0.522149
$324$	−1.98819	−0.110455
$325$	4.64561	0.257692
$326$	−0.710281	−0.0393388
$327$	5.25650	0.290685
$328$	−0.544591	−0.0300700
$329$	−1.19842	−0.0660708
$330$	0.0312354	0.00171945
$331$	29.6408	1.62921	0.814603	−	0.580018i	$-0.196955\pi$
$331$	29.6408	1.62921	0.814603	+	0.580018i	$0.196955\pi$
$332$	−19.3526	−1.06211
$333$	5.61956	0.307950
$334$	2.63890	0.144394
$335$	−14.8367	−0.810618
$336$	−3.10671	−0.169485
$337$	−35.1215	−1.91319	−0.956596	−	0.291417i	$-0.905873\pi$
$337$	−35.1215	−1.91319	−0.956596	+	0.291417i	$0.905873\pi$
$338$	0.932417	0.0507168
$339$	−3.08073	−0.167322
$340$	−11.9218	−0.646548
$341$	2.29717	0.124399
$342$	0.170041	0.00919474
$343$	−10.5749	−0.570989
$344$	−5.28034	−0.284697
$345$	3.81758	0.205531
$346$	1.27452	0.0685185
$347$	20.1169	1.07993	0.539965	−	0.841687i	$-0.318437\pi$
$347$	20.1169	1.07993	0.539965	+	0.841687i	$0.318437\pi$
$348$	17.1131	0.917357
$349$	−2.24309	−0.120070	−0.0600350	−	0.998196i	$-0.519121\pi$
$349$	−2.24309	−0.120070	−0.0600350	+	0.998196i	$0.519121\pi$
$350$	0.0859059	0.00459186
$351$	−4.64561	−0.247964
$352$	−0.371880	−0.0198213
$353$	2.03366	0.108241	0.0541204	−	0.998534i	$-0.482765\pi$
$353$	2.03366	0.108241	0.0541204	+	0.998534i	$0.482765\pi$
$354$	0.999695	0.0531332
$355$	−12.2074	−0.647901
$356$	−6.42830	−0.340699
$357$	−4.74096	−0.250918
$358$	−2.63033	−0.139017
$359$	−3.00063	−0.158367	−0.0791837	−	0.996860i	$-0.525231\pi$
$359$	−3.00063	−0.158367	−0.0791837	+	0.996860i	$0.525231\pi$
$360$	−0.433326	−0.0228383
$361$	−16.5508	−0.871093
$362$	1.88712	0.0991849
$363$	10.9174	0.573013
$364$	−7.30275	−0.382768
$365$	−4.15457	−0.217460
$366$	−1.10251	−0.0576293
$367$	23.4960	1.22648	0.613240	−	0.789897i	$-0.289866\pi$
$367$	23.4960	1.22648	0.613240	+	0.789897i	$0.289866\pi$
$368$	−15.0004	−0.781952
$369$	1.25677	0.0654249
$370$	0.610577	0.0317424
$371$	5.89962	0.306293
$372$	−15.8871	−0.823705
$373$	6.32035	0.327255	0.163628	−	0.986522i	$-0.447680\pi$
$373$	6.32035	0.327255	0.163628	+	0.986522i	$0.447680\pi$
$374$	−0.187296	−0.00968486
$375$	−1.00000	−0.0516398
$376$	0.656806	0.0338722
$377$	39.9863	2.05940
$378$	−0.0859059	−0.00441852
$379$	22.9058	1.17659	0.588296	−	0.808646i	$-0.299799\pi$
$379$	22.9058	1.17659	0.588296	+	0.808646i	$0.299799\pi$
$380$	−3.11153	−0.159618
$381$	2.84824	0.145920
$382$	2.53800	0.129856
$383$	−10.9136	−0.557660	−0.278830	−	0.960340i	$-0.589947\pi$
$383$	−10.9136	−0.557660	−0.278830	+	0.960340i	$0.589947\pi$
$384$	3.42574	0.174819
$385$	−0.227297	−0.0115841
$386$	−0.127137	−0.00647110
$387$	12.1856	0.619430
$388$	28.7070	1.45738
$389$	−2.26185	−0.114680	−0.0573402	−	0.998355i	$-0.518262\pi$
$389$	−2.26185	−0.114680	−0.0573402	+	0.998355i	$0.518262\pi$
$390$	−0.504755	−0.0255593
$391$	−22.8912	−1.15766
$392$	2.76240	0.139522
$393$	19.5417	0.985749
$394$	0.908098	0.0457493
$395$	6.62160	0.333169
$396$	0.571569	0.0287224
$397$	4.10769	0.206159	0.103079	−	0.994673i	$-0.467130\pi$
$397$	4.10769	0.206159	0.103079	+	0.994673i	$0.467130\pi$
$398$	0.903535	0.0452901
$399$	−1.23737	−0.0619460
$400$	3.92931	0.196465
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	1.61204	0.0804014
$403$	−37.1216	−1.84916
$404$	−24.3289	−1.21041
$405$	1.00000	0.0496904
$406$	0.739421	0.0366969
$407$	−1.61552	−0.0800783
$408$	2.59834	0.128637
$409$	−21.9572	−1.08572	−0.542858	−	0.839824i	$-0.682658\pi$
$409$	−21.9572	−1.08572	−0.542858	+	0.839824i	$0.682658\pi$
$410$	0.136551	0.00674376
$411$	14.6197	0.721134
$412$	−25.6750	−1.26492
$413$	−7.27469	−0.357964
$414$	−0.414788	−0.0203857
$415$	9.73376	0.477811
$416$	6.00946	0.294638
$417$	16.7335	0.819441
$418$	−0.0488835	−0.00239097
$419$	28.9091	1.41230	0.706150	−	0.708062i	$-0.250430\pi$
$419$	28.9091	1.41230	0.706150	+	0.708062i	$0.250430\pi$
$420$	1.57197	0.0767042
$421$	−1.08193	−0.0527300	−0.0263650	−	0.999652i	$-0.508393\pi$
$421$	−1.08193	−0.0527300	−0.0263650	+	0.999652i	$0.508393\pi$
$422$	2.56658	0.124939
$423$	−1.51573	−0.0736975
$424$	−3.23336	−0.157026
$425$	5.99627	0.290862
$426$	1.32636	0.0642622
$427$	8.02289	0.388255
$428$	7.35314	0.355427
$429$	1.33553	0.0644798
$430$	1.32399	0.0638486
$431$	33.4648	1.61194	0.805972	−	0.591954i	$-0.201643\pi$
$431$	33.4648	1.61194	0.805972	+	0.591954i	$0.201643\pi$
$432$	−3.92931	−0.189049
$433$	−10.6757	−0.513040	−0.256520	−	0.966539i	$-0.582576\pi$
$433$	−10.6757	−0.513040	−0.256520	+	0.966539i	$0.582576\pi$
$434$	−0.686447	−0.0329505
$435$	−8.60734	−0.412690
$436$	10.4509	0.500509
$437$	−5.97451	−0.285800
$438$	0.451402	0.0215688
$439$	−14.5280	−0.693381	−0.346691	−	0.937980i	$-0.612695\pi$
$439$	−14.5280	−0.693381	−0.346691	+	0.937980i	$0.612695\pi$
$440$	0.124573	0.00593879
$441$	−6.37487	−0.303565
$442$	3.02665	0.143963
$443$	−27.2500	−1.29468	−0.647342	−	0.762199i	$-0.724120\pi$
$443$	−27.2500	−1.29468	−0.647342	+	0.762199i	$0.724120\pi$
$444$	11.1728	0.530237
$445$	3.23324	0.153270
$446$	0.902359	0.0427279
$447$	−22.7861	−1.07774
$448$	−6.10230	−0.288306
$449$	−13.0813	−0.617345	−0.308672	−	0.951168i	$-0.599885\pi$
$449$	−13.0813	−0.617345	−0.308672	+	0.951168i	$0.599885\pi$
$450$	0.108652	0.00512191
$451$	−0.361298	−0.0170129
$452$	−6.12509	−0.288100
$453$	−10.8179	−0.508271
$454$	0.601426	0.0282263
$455$	3.67306	0.172195
$456$	0.678155	0.0317575
$457$	−35.2953	−1.65104	−0.825522	−	0.564370i	$-0.809119\pi$
$457$	−35.2953	−1.65104	−0.825522	+	0.564370i	$0.809119\pi$
$458$	−0.0939284	−0.00438899
$459$	−5.99627	−0.279882
$460$	7.59009	0.353890
$461$	7.28391	0.339245	0.169623	−	0.985509i	$-0.445745\pi$
$461$	7.28391	0.339245	0.169623	+	0.985509i	$0.445745\pi$
$462$	0.0246963	0.00114898
$463$	4.30964	0.200286	0.100143	−	0.994973i	$-0.468070\pi$
$463$	4.30964	0.200286	0.100143	+	0.994973i	$0.468070\pi$
$464$	33.8209	1.57010
$465$	7.99069	0.370559
$466$	−0.756849	−0.0350604
$467$	33.0676	1.53018	0.765092	−	0.643921i	$-0.222693\pi$
$467$	33.0676	1.53018	0.765092	+	0.643921i	$0.222693\pi$
$468$	−9.23637	−0.426952
$469$	−11.7307	−0.541673
$470$	−0.164688	−0.00759647
$471$	−9.84949	−0.453841
$472$	3.98698	0.183516
$473$	−3.50314	−0.161074
$474$	−0.719450	−0.0330454
$475$	1.56500	0.0718072
$476$	−9.42595	−0.432038
$477$	7.46173	0.341649
$478$	−1.35518	−0.0619844
$479$	−27.8521	−1.27260	−0.636298	−	0.771444i	$-0.719535\pi$
$479$	−27.8521	−1.27260	−0.636298	+	0.771444i	$0.719535\pi$
$480$	−1.29358	−0.0590435
$481$	26.1063	1.19034
$482$	0.372069	0.0169473
$483$	3.01837	0.137341
$484$	21.7058	0.986628
$485$	−14.4387	−0.655629
$486$	−0.108652	−0.00492856
$487$	−12.4330	−0.563391	−0.281695	−	0.959504i	$-0.590897\pi$
$487$	−12.4330	−0.563391	−0.281695	+	0.959504i	$0.590897\pi$
$488$	−4.39704	−0.199045
$489$	6.53720	0.295623
$490$	−0.692643	−0.0312904
$491$	39.8955	1.80046	0.900230	−	0.435414i	$-0.143398\pi$
$491$	39.8955	1.80046	0.900230	+	0.435414i	$0.143398\pi$
$492$	2.49870	0.112650
$493$	51.6120	2.32449
$494$	0.789942	0.0355412
$495$	−0.287481	−0.0129213
$496$	−31.3979	−1.40981
$497$	−9.65178	−0.432941
$498$	−1.05759	−0.0473919
$499$	18.1122	0.810813	0.405406	−	0.914137i	$-0.367130\pi$
$499$	18.1122	0.810813	0.405406	+	0.914137i	$0.367130\pi$
$500$	−1.98819	−0.0889148
$501$	−24.2876	−1.08509
$502$	−2.03289	−0.0907323
$503$	40.4607	1.80405	0.902026	−	0.431682i	$-0.142080\pi$
$503$	40.4607	1.80405	0.902026	+	0.431682i	$0.142080\pi$
$504$	−0.342609	−0.0152610
$505$	12.2367	0.544525
$506$	0.119244	0.00530103
$507$	−8.58168	−0.381126
$508$	5.66285	0.251248
$509$	34.9879	1.55081	0.775405	−	0.631464i	$-0.217546\pi$
$509$	34.9879	1.55081	0.775405	+	0.631464i	$0.217546\pi$
$510$	−0.651508	−0.0288492
$511$	−3.28481	−0.145312
$512$	8.48821	0.375129
$513$	−1.56500	−0.0690965
$514$	−1.48054	−0.0653037
$515$	12.9137	0.569046
$516$	24.2274	1.06655
$517$	0.435745	0.0191640
$518$	0.482753	0.0212110
$519$	−11.7303	−0.514902
$520$	−2.01306	−0.0882786
$521$	−1.69079	−0.0740749	−0.0370375	−	0.999314i	$-0.511792\pi$
$521$	−1.69079	−0.0740749	−0.0370375	+	0.999314i	$0.511792\pi$
$522$	0.935206	0.0409328
$523$	−9.53370	−0.416880	−0.208440	−	0.978035i	$-0.566839\pi$
$523$	−9.53370	−0.416880	−0.208440	+	0.978035i	$0.566839\pi$
$524$	38.8527	1.69729
$525$	−0.790651	−0.0345068
$526$	−0.534384	−0.0233002
$527$	−47.9144	−2.08718
$528$	1.12960	0.0491596
$529$	−8.42610	−0.366352
$530$	0.810732	0.0352160
$531$	−9.20088	−0.399284
$532$	−2.46013	−0.106660
$533$	5.83846	0.252892
$534$	−0.351298	−0.0152021
$535$	−3.69840	−0.159896
$536$	6.42914	0.277697
$537$	24.2088	1.04469
$538$	0.160680	0.00692740
$539$	1.83266	0.0789381
$540$	1.98819	0.0855583
$541$	−3.52748	−0.151658	−0.0758290	−	0.997121i	$-0.524160\pi$
$541$	−3.52748	−0.151658	−0.0758290	+	0.997121i	$0.524160\pi$
$542$	−1.09464	−0.0470190
$543$	−17.3685	−0.745353
$544$	7.75665	0.332564
$545$	−5.25650	−0.225164
$546$	−0.399085	−0.0170793
$547$	−25.4688	−1.08897	−0.544484	−	0.838771i	$-0.683275\pi$
$547$	−25.4688	−1.08897	−0.544484	+	0.838771i	$0.683275\pi$
$548$	29.0667	1.24167
$549$	10.1472	0.433072
$550$	−0.0312354	−0.00133188
$551$	13.4705	0.573863
$552$	−1.65425	−0.0704097
$553$	5.23537	0.222631
$554$	1.23949	0.0526607
$555$	−5.61956	−0.238537
$556$	33.2694	1.41094
$557$	−8.30879	−0.352055	−0.176027	−	0.984385i	$-0.556325\pi$
$557$	−8.30879	−0.352055	−0.176027	+	0.984385i	$0.556325\pi$
$558$	−0.868205	−0.0367541
$559$	56.6096	2.39433
$560$	3.10671	0.131283
$561$	1.72382	0.0727796
$562$	1.42177	0.0599735
$563$	10.5108	0.442976	0.221488	−	0.975163i	$-0.428909\pi$
$563$	10.5108	0.442976	0.221488	+	0.975163i	$0.428909\pi$
$564$	−3.01357	−0.126894
$565$	3.08073	0.129607
$566$	0.268491	0.0112855
$567$	0.790651	0.0332042
$568$	5.28977	0.221954
$569$	16.9125	0.709008	0.354504	−	0.935055i	$-0.384650\pi$
$569$	16.9125	0.709008	0.354504	+	0.935055i	$0.384650\pi$
$570$	−0.170041	−0.00712222
$571$	16.1287	0.674966	0.337483	−	0.941332i	$-0.390424\pi$
$571$	16.1287	0.674966	0.337483	+	0.941332i	$0.390424\pi$
$572$	2.65528	0.111023
$573$	−23.3590	−0.975836
$574$	0.107964	0.00450633
$575$	−3.81758	−0.159204
$576$	−7.71807	−0.321586
$577$	−42.4950	−1.76909	−0.884544	−	0.466457i	$-0.845530\pi$
$577$	−42.4950	−1.76909	−0.884544	+	0.466457i	$0.845530\pi$
$578$	2.05953	0.0856653
$579$	1.17013	0.0486289
$580$	−17.1131	−0.710582
$581$	7.69600	0.319284
$582$	1.56880	0.0650288
$583$	−2.14511	−0.0888413
$584$	1.80028	0.0744961
$585$	4.64561	0.192072
$586$	1.50679	0.0622450
$587$	−14.3590	−0.592658	−0.296329	−	0.955086i	$-0.595762\pi$
$587$	−14.3590	−0.592658	−0.296329	+	0.955086i	$0.595762\pi$
$588$	−12.6745	−0.522687
$589$	−12.5054	−0.515278
$590$	−0.999695	−0.0411568
$591$	−8.35785	−0.343796
$592$	22.0810	0.907523
$593$	−1.43877	−0.0590832	−0.0295416	−	0.999564i	$-0.509405\pi$
$593$	−1.43877	−0.0590832	−0.0295416	+	0.999564i	$0.509405\pi$
$594$	0.0312354	0.00128161
$595$	4.74096	0.194360
$596$	−45.3031	−1.85569
$597$	−8.31585	−0.340345
$598$	−1.92694	−0.0787985
$599$	14.8751	0.607781	0.303891	−	0.952707i	$-0.401714\pi$
$599$	14.8751	0.607781	0.303891	+	0.952707i	$0.401714\pi$
$600$	0.433326	0.0176904
$601$	−13.0653	−0.532944	−0.266472	−	0.963843i	$-0.585858\pi$
$601$	−13.0653	−0.532944	−0.266472	+	0.963843i	$0.585858\pi$
$602$	1.04682	0.0426651
$603$	−14.8367	−0.604199
$604$	−21.5081	−0.875154
$605$	−10.9174	−0.443854
$606$	−1.32954	−0.0540088
$607$	−26.0739	−1.05831	−0.529154	−	0.848526i	$-0.677491\pi$
$607$	−26.0739	−1.05831	−0.529154	+	0.848526i	$0.677491\pi$
$608$	2.02445	0.0821024
$609$	−6.80540	−0.275769
$610$	1.10251	0.0446395
$611$	−7.04151	−0.284869
$612$	−11.9218	−0.481909
$613$	17.0027	0.686733	0.343367	−	0.939201i	$-0.388433\pi$
$613$	17.0027	0.686733	0.343367	+	0.939201i	$0.388433\pi$
$614$	2.67041	0.107769
$615$	−1.25677	−0.0506779
$616$	0.0984938	0.00396843
$617$	24.7957	0.998235	0.499118	−	0.866534i	$-0.333658\pi$
$617$	24.7957	0.998235	0.499118	+	0.866534i	$0.333658\pi$
$618$	−1.40310	−0.0564410
$619$	8.33355	0.334954	0.167477	−	0.985876i	$-0.446438\pi$
$619$	8.33355	0.334954	0.167477	+	0.985876i	$0.446438\pi$
$620$	15.8871	0.638039
$621$	3.81758	0.153194
$622$	−1.45997	−0.0585395
$623$	2.55636	0.102418
$624$	−18.2540	−0.730746
$625$	1.00000	0.0400000
$626$	2.03556	0.0813574
$627$	0.449909	0.0179676
$628$	−19.5827	−0.781435
$629$	33.6964	1.34356
$630$	0.0859059	0.00342257
$631$	−17.2292	−0.685885	−0.342942	−	0.939356i	$-0.611424\pi$
$631$	−17.2292	−0.685885	−0.342942	+	0.939356i	$0.611424\pi$
$632$	−2.86931	−0.114135
$633$	−23.6220	−0.938892
$634$	−1.02615	−0.0407536
$635$	−2.84824	−0.113029
$636$	14.8354	0.588261
$637$	−29.6152	−1.17340
$638$	−0.268854	−0.0106440
$639$	−12.2074	−0.482917
$640$	−3.42574	−0.135414
$641$	38.7425	1.53024	0.765118	−	0.643890i	$-0.222681\pi$
$641$	38.7425	1.53024	0.765118	+	0.643890i	$0.222681\pi$
$642$	0.401839	0.0158593
$643$	31.3036	1.23450	0.617248	−	0.786769i	$-0.288248\pi$
$643$	31.3036	1.23450	0.617248	+	0.786769i	$0.288248\pi$
$644$	6.00111	0.236477
$645$	−12.1856	−0.479808
$646$	1.01961	0.0401160
$647$	21.2335	0.834777	0.417388	−	0.908728i	$-0.362945\pi$
$647$	21.2335	0.834777	0.417388	+	0.908728i	$0.362945\pi$
$648$	−0.433326	−0.0170226
$649$	2.64508	0.103829
$650$	0.504755	0.0197981
$651$	6.31785	0.247616
$652$	12.9972	0.509011
$653$	19.7298	0.772089	0.386044	−	0.922480i	$-0.373841\pi$
$653$	19.7298	0.772089	0.386044	+	0.922480i	$0.373841\pi$
$654$	0.571130	0.0223329
$655$	−19.5417	−0.763558
$656$	4.93824	0.192806
$657$	−4.15457	−0.162085
$658$	−0.130210	−0.00507613
$659$	36.8068	1.43379	0.716896	−	0.697181i	$-0.245562\pi$
$659$	36.8068	1.43379	0.716896	+	0.697181i	$0.245562\pi$
$660$	−0.571569	−0.0222483
$661$	−16.2071	−0.630384	−0.315192	−	0.949028i	$-0.602069\pi$
$661$	−16.2071	−0.630384	−0.315192	+	0.949028i	$0.602069\pi$
$662$	3.22054	0.125170
$663$	−27.8563	−1.08185
$664$	−4.21789	−0.163686
$665$	1.23737	0.0479831
$666$	0.610577	0.0236594
$667$	−32.8592	−1.27231
$668$	−48.2885	−1.86834
$669$	−8.30503	−0.321091
$670$	−1.61204	−0.0622786
$671$	−2.91713	−0.112614
$672$	−1.02277	−0.0394542
$673$	−12.8213	−0.494224	−0.247112	−	0.968987i	$-0.579482\pi$
$673$	−12.8213	−0.494224	−0.247112	+	0.968987i	$0.579482\pi$
$674$	−3.81603	−0.146988
$675$	−1.00000	−0.0384900
$676$	−17.0620	−0.656233
$677$	−37.1952	−1.42953	−0.714763	−	0.699366i	$-0.753466\pi$
$677$	−37.1952	−1.42953	−0.714763	+	0.699366i	$0.753466\pi$
$678$	−0.334728	−0.0128551
$679$	−11.4160	−0.438106
$680$	−2.59834	−0.0996418
$681$	−5.53534	−0.212115
$682$	0.249593	0.00955740
$683$	7.94430	0.303980	0.151990	−	0.988382i	$-0.451432\pi$
$683$	7.94430	0.303980	0.151990	+	0.988382i	$0.451432\pi$
$684$	−3.11153	−0.118972
$685$	−14.6197	−0.558588
$686$	−1.14898	−0.0438683
$687$	0.864488	0.0329823
$688$	47.8811	1.82545
$689$	34.6643	1.32060
$690$	0.414788	0.0157907
$691$	37.8931	1.44152	0.720760	−	0.693184i	$-0.243793\pi$
$691$	37.8931	1.44152	0.720760	+	0.693184i	$0.243793\pi$
$692$	−23.3221	−0.886571
$693$	−0.227297	−0.00863431
$694$	2.18574	0.0829696
$695$	−16.7335	−0.634736
$696$	3.72978	0.141377
$697$	7.53594	0.285444
$698$	−0.243717	−0.00922481
$699$	6.96581	0.263471
$700$	−1.57197	−0.0594148
$701$	38.4360	1.45171	0.725854	−	0.687849i	$-0.241445\pi$
$701$	38.4360	1.45171	0.725854	+	0.687849i	$0.241445\pi$
$702$	−0.504755	−0.0190508
$703$	8.79462	0.331695
$704$	2.21880	0.0836241
$705$	1.51573	0.0570858
$706$	0.220961	0.00831599
$707$	9.67493	0.363863
$708$	−18.2931	−0.687498
$709$	−11.1272	−0.417891	−0.208945	−	0.977927i	$-0.567003\pi$
$709$	−11.1272	−0.417891	−0.208945	+	0.977927i	$0.567003\pi$
$710$	−1.32636	−0.0497773
$711$	6.62160	0.248329
$712$	−1.40104	−0.0525064
$713$	30.5051	1.14242
$714$	−0.515115	−0.0192777
$715$	−1.33553	−0.0499458
$716$	48.1317	1.79877
$717$	12.4726	0.465799
$718$	−0.326025	−0.0121672
$719$	28.9259	1.07876	0.539378	−	0.842064i	$-0.318660\pi$
$719$	28.9259	1.07876	0.539378	+	0.842064i	$0.318660\pi$
$720$	3.92931	0.146437
$721$	10.2102	0.380249
$722$	−1.79828	−0.0669249
$723$	−3.42441	−0.127355
$724$	−34.5319	−1.28337
$725$	8.60734	0.319669
$726$	1.18619	0.0440238
$727$	−28.3209	−1.05036	−0.525182	−	0.850990i	$-0.676003\pi$
$727$	−28.3209	−1.05036	−0.525182	+	0.850990i	$0.676003\pi$
$728$	−1.59163	−0.0589897
$729$	1.00000	0.0370370
$730$	−0.451402	−0.0167071
$731$	73.0683	2.70253
$732$	20.1746	0.745675
$733$	−38.5067	−1.42228	−0.711139	−	0.703052i	$-0.751820\pi$
$733$	−38.5067	−1.42228	−0.711139	+	0.703052i	$0.751820\pi$
$734$	2.55289	0.0942287
$735$	6.37487	0.235141
$736$	−4.93834	−0.182030
$737$	4.26528	0.157114
$738$	0.136551	0.00502650
$739$	11.9813	0.440739	0.220369	−	0.975416i	$-0.429274\pi$
$739$	11.9813	0.440739	0.220369	+	0.975416i	$0.429274\pi$
$740$	−11.1728	−0.410720
$741$	−7.27038	−0.267084
$742$	0.641006	0.0235321
$743$	6.69026	0.245442	0.122721	−	0.992441i	$-0.460838\pi$
$743$	6.69026	0.245442	0.122721	+	0.992441i	$0.460838\pi$
$744$	−3.46257	−0.126944
$745$	22.7861	0.834817
$746$	0.686719	0.0251426
$747$	9.73376	0.356140
$748$	3.42728	0.125314
$749$	−2.92414	−0.106846
$750$	−0.108652	−0.00396741
$751$	−47.3255	−1.72693	−0.863467	−	0.504406i	$-0.831712\pi$
$751$	−47.3255	−1.72693	−0.863467	+	0.504406i	$0.831712\pi$
$752$	−5.95578	−0.217185
$753$	18.7101	0.681833
$754$	4.34460	0.158221
$755$	10.8179	0.393705
$756$	1.57197	0.0571719
$757$	−45.4651	−1.65246	−0.826229	−	0.563335i	$-0.809518\pi$
$757$	−45.4651	−1.65246	−0.826229	+	0.563335i	$0.809518\pi$
$758$	2.48876	0.0903959
$759$	−1.09748	−0.0398361
$760$	−0.678155	−0.0245993
$761$	−45.8618	−1.66249	−0.831245	−	0.555906i	$-0.812371\pi$
$761$	−45.8618	−1.66249	−0.831245	+	0.555906i	$0.812371\pi$
$762$	0.309467	0.0112108
$763$	−4.15606	−0.150459
$764$	−46.4422	−1.68022
$765$	5.99627	0.216796
$766$	−1.18579	−0.0428443
$767$	−42.7437	−1.54339
$768$	−15.0639	−0.543572
$769$	0.726271	0.0261900	0.0130950	−	0.999914i	$-0.495832\pi$
$769$	0.726271	0.0261900	0.0130950	+	0.999914i	$0.495832\pi$
$770$	−0.0246963	−0.000889994 0
$771$	13.6264	0.490743
$772$	2.32645	0.0837306
$773$	−27.6566	−0.994740	−0.497370	−	0.867538i	$-0.665701\pi$
$773$	−27.6566	−0.994740	−0.497370	+	0.867538i	$0.665701\pi$
$774$	1.32399	0.0475900
$775$	−7.99069	−0.287034
$776$	6.25668	0.224602
$777$	−4.44311	−0.159396
$778$	−0.245755	−0.00881073
$779$	1.96685	0.0704696
$780$	9.23637	0.330715
$781$	3.50939	0.125576
$782$	−2.48718	−0.0889414
$783$	−8.60734	−0.307601
$784$	−25.0488	−0.894601
$785$	9.84949	0.351543
$786$	2.12325	0.0757337
$787$	3.79663	0.135335	0.0676676	−	0.997708i	$-0.478444\pi$
$787$	3.79663	0.135335	0.0676676	+	0.997708i	$0.478444\pi$
$788$	−16.6170	−0.591958
$789$	4.91830	0.175096
$790$	0.719450	0.0255969
$791$	2.43578	0.0866064
$792$	0.124573	0.00442651
$793$	47.1399	1.67399
$794$	0.446309	0.0158389
$795$	−7.46173	−0.264640
$796$	−16.5335	−0.586016
$797$	−14.7902	−0.523895	−0.261947	−	0.965082i	$-0.584365\pi$
$797$	−14.7902	−0.523895	−0.261947	+	0.965082i	$0.584365\pi$
$798$	−0.134443	−0.00475922
$799$	−9.08875	−0.321537
$800$	1.29358	0.0457349
$801$	3.23324	0.114241
$802$	−0.108652	−0.00383664
$803$	1.19436	0.0421481
$804$	−29.4983	−1.04033
$805$	−3.01837	−0.106384
$806$	−4.03334	−0.142068
$807$	−1.47885	−0.0520579
$808$	−5.30246	−0.186540
$809$	−14.5997	−0.513300	−0.256650	−	0.966504i	$-0.582619\pi$
$809$	−14.5997	−0.513300	−0.256650	+	0.966504i	$0.582619\pi$
$810$	0.108652	0.00381764
$811$	−43.6546	−1.53292	−0.766459	−	0.642293i	$-0.777983\pi$
$811$	−43.6546	−1.53292	−0.766459	+	0.642293i	$0.777983\pi$
$812$	−13.5305	−0.474826
$813$	10.0748	0.353337
$814$	−0.175529	−0.00615231
$815$	−6.53720	−0.228988
$816$	−23.5612	−0.824807
$817$	19.0705	0.667193
$818$	−2.38570	−0.0834141
$819$	3.67306	0.128347
$820$	−2.49870	−0.0872586
$821$	52.3430	1.82678	0.913392	−	0.407081i	$-0.133453\pi$
$821$	52.3430	1.82678	0.913392	+	0.407081i	$0.133453\pi$
$822$	1.58846	0.0554037
$823$	14.7290	0.513420	0.256710	−	0.966489i	$-0.417362\pi$
$823$	14.7290	0.513420	0.256710	+	0.966489i	$0.417362\pi$
$824$	−5.59584	−0.194940
$825$	0.287481	0.0100088
$826$	−0.790410	−0.0275019
$827$	25.1706	0.875269	0.437634	−	0.899153i	$-0.355816\pi$
$827$	25.1706	0.875269	0.437634	+	0.899153i	$0.355816\pi$
$828$	7.59009	0.263774
$829$	−23.4288	−0.813716	−0.406858	−	0.913491i	$-0.633376\pi$
$829$	−23.4288	−0.813716	−0.406858	+	0.913491i	$0.633376\pi$
$830$	1.05759	0.0367096
$831$	−11.4078	−0.395734
$832$	−35.8551	−1.24305
$833$	−38.2255	−1.32443
$834$	1.81813	0.0629565
$835$	24.2876	0.840508
$836$	0.894506	0.0309371
$837$	7.99069	0.276199
$838$	3.14103	0.108505
$839$	−35.9932	−1.24262	−0.621312	−	0.783563i	$-0.713400\pi$
$839$	−35.9932	−1.24262	−0.621312	+	0.783563i	$0.713400\pi$
$840$	0.342609	0.0118211
$841$	45.0863	1.55470
$842$	−0.117554	−0.00405118
$843$	−13.0855	−0.450688
$844$	−46.9652	−1.61661
$845$	8.58168	0.295219
$846$	−0.164688	−0.00566208
$847$	−8.63182	−0.296593
$848$	29.3194	1.00683
$849$	−2.47110	−0.0848081
$850$	0.651508	0.0223465
$851$	−21.4531	−0.735403
$852$	−24.2707	−0.831499
$853$	−42.5739	−1.45770	−0.728851	−	0.684673i	$-0.759945\pi$
$853$	−42.5739	−1.45770	−0.728851	+	0.684673i	$0.759945\pi$
$854$	0.871704	0.0298291
$855$	1.56500	0.0535219
$856$	1.60261	0.0547761
$857$	−10.6634	−0.364255	−0.182128	−	0.983275i	$-0.558298\pi$
$857$	−10.6634	−0.364255	−0.182128	+	0.983275i	$0.558298\pi$
$858$	0.145108	0.00495389
$859$	−22.6074	−0.771354	−0.385677	−	0.922634i	$-0.626032\pi$
$859$	−22.6074	−0.771354	−0.385677	+	0.922634i	$0.626032\pi$
$860$	−24.2274	−0.826147
$861$	−0.993667	−0.0338641
$862$	3.63602	0.123843
$863$	19.6471	0.668795	0.334397	−	0.942432i	$-0.391467\pi$
$863$	19.6471	0.668795	0.334397	+	0.942432i	$0.391467\pi$
$864$	−1.29358	−0.0440084
$865$	11.7303	0.398841
$866$	−1.15993	−0.0394162
$867$	−18.9553	−0.643756
$868$	12.5611	0.426352
$869$	−1.90359	−0.0645747
$870$	−0.935206	−0.0317064
$871$	−68.9257	−2.33546
$872$	2.27778	0.0771352
$873$	−14.4387	−0.488677
$874$	−0.649143	−0.0219576
$875$	0.790651	0.0267289
$876$	−8.26009	−0.279082
$877$	23.3046	0.786940	0.393470	−	0.919338i	$-0.371275\pi$
$877$	23.3046	0.786940	0.393470	+	0.919338i	$0.371275\pi$
$878$	−1.57849	−0.0532715
$879$	−13.8680	−0.467758
$880$	−1.12960	−0.0380789
$881$	30.9601	1.04307	0.521536	−	0.853229i	$-0.325359\pi$
$881$	30.9601	1.04307	0.521536	+	0.853229i	$0.325359\pi$
$882$	−0.692643	−0.0233225
$883$	−5.34180	−0.179766	−0.0898829	−	0.995952i	$-0.528649\pi$
$883$	−5.34180	−0.179766	−0.0898829	+	0.995952i	$0.528649\pi$
$884$	−55.3838	−1.86276
$885$	9.20088	0.309284
$886$	−2.96077	−0.0994688
$887$	5.55590	0.186549	0.0932743	−	0.995640i	$-0.470267\pi$
$887$	5.55590	0.186549	0.0932743	+	0.995640i	$0.470267\pi$
$888$	2.43510	0.0817166
$889$	−2.25196	−0.0755283
$890$	0.351298	0.0117755
$891$	−0.287481	−0.00963099
$892$	−16.5120	−0.552863
$893$	−2.37212	−0.0793801
$894$	−2.47575	−0.0828016
$895$	−24.2088	−0.809210
$896$	−2.70857	−0.0904868
$897$	17.7350	0.592153
$898$	−1.42131	−0.0474298
$899$	−68.7786	−2.29390
$900$	−1.98819	−0.0662732
$901$	44.7426	1.49059
$902$	−0.0392558	−0.00130707
$903$	−9.63458	−0.320619
$904$	−1.33496	−0.0444001
$905$	17.3685	0.577348
$906$	−1.17539	−0.0390497
$907$	−58.6869	−1.94867	−0.974333	−	0.225111i	$-0.927726\pi$
$907$	−58.6869	−1.94867	−0.974333	+	0.225111i	$0.927726\pi$
$908$	−11.0053	−0.365225
$909$	12.2367	0.405865
$910$	0.399085	0.0132295
$911$	38.1362	1.26351	0.631755	−	0.775168i	$-0.282335\pi$
$911$	38.1362	1.26351	0.631755	+	0.775168i	$0.282335\pi$
$912$	−6.14937	−0.203626
$913$	−2.79827	−0.0926093
$914$	−3.83490	−0.126847
$915$	−10.1472	−0.335456
$916$	1.71877	0.0567898
$917$	−15.4507	−0.510226
$918$	−0.651508	−0.0215030
$919$	55.2949	1.82401	0.912005	−	0.410179i	$-0.134534\pi$
$919$	55.2949	1.82401	0.912005	+	0.410179i	$0.134534\pi$
$920$	1.65425	0.0545392
$921$	−24.5776	−0.809859
$922$	0.791412	0.0260638
$923$	−56.7107	−1.86666
$924$	−0.451911	−0.0148668
$925$	5.61956	0.184770
$926$	0.468252	0.0153877
$927$	12.9137	0.424142
$928$	11.1343	0.365500
$929$	−49.5912	−1.62703	−0.813517	−	0.581542i	$-0.802450\pi$
$929$	−49.5912	−1.62703	−0.813517	+	0.581542i	$0.802450\pi$
$930$	0.868205	0.0284696
$931$	−9.97668	−0.326972
$932$	13.8494	0.453651
$933$	13.4371	0.439911
$934$	3.59286	0.117562
$935$	−1.72382	−0.0563748
$936$	−2.01306	−0.0657990
$937$	−30.1566	−0.985172	−0.492586	−	0.870264i	$-0.663948\pi$
$937$	−30.1566	−0.985172	−0.492586	+	0.870264i	$0.663948\pi$
$938$	−1.27456	−0.0416160
$939$	−18.7347	−0.611383
$940$	3.01357	0.0982919
$941$	−19.0623	−0.621414	−0.310707	−	0.950506i	$-0.600566\pi$
$941$	−19.0623	−0.621414	−0.310707	+	0.950506i	$0.600566\pi$
$942$	−1.07017	−0.0348679
$943$	−4.79782	−0.156239
$944$	−36.1531	−1.17668
$945$	−0.790651	−0.0257199
$946$	−0.380623	−0.0123751
$947$	−5.22804	−0.169888	−0.0849442	−	0.996386i	$-0.527071\pi$
$947$	−5.22804	−0.169888	−0.0849442	+	0.996386i	$0.527071\pi$
$948$	13.1650	0.427580
$949$	−19.3005	−0.626520
$950$	0.170041	0.00551685
$951$	9.44436	0.306254
$952$	−2.05438	−0.0665828
$953$	3.57458	0.115792	0.0578959	−	0.998323i	$-0.481561\pi$
$953$	3.57458	0.115792	0.0578959	+	0.998323i	$0.481561\pi$
$954$	0.810732	0.0262484
$955$	23.3590	0.755879
$956$	24.7980	0.802026
$957$	2.47445	0.0799876
$958$	−3.02619	−0.0977717
$959$	−11.5590	−0.373261
$960$	7.71807	0.249099
$961$	32.8512	1.05971
$962$	2.83650	0.0914525
$963$	−3.69840	−0.119179
$964$	−6.80839	−0.219283
$965$	−1.17013	−0.0376678
$966$	0.327952	0.0105517
$967$	−38.3616	−1.23363	−0.616813	−	0.787110i	$-0.711577\pi$
$967$	−38.3616	−1.23363	−0.616813	+	0.787110i	$0.711577\pi$
$968$	4.73077	0.152053
$969$	−9.38417	−0.301463
$970$	−1.56880	−0.0503711
$971$	34.3998	1.10394	0.551972	−	0.833863i	$-0.313876\pi$
$971$	34.3998	1.10394	0.551972	+	0.833863i	$0.313876\pi$
$972$	1.98819	0.0637714
$973$	−13.2303	−0.424145
$974$	−1.35087	−0.0432846
$975$	−4.64561	−0.148779
$976$	39.8714	1.27625
$977$	−13.2292	−0.423238	−0.211619	−	0.977352i	$-0.567874\pi$
$977$	−13.2292	−0.423238	−0.211619	+	0.977352i	$0.567874\pi$
$978$	0.710281	0.0227123
$979$	−0.929495	−0.0297068
$980$	12.6745	0.404872
$981$	−5.25650	−0.167827
$982$	4.33473	0.138327
$983$	8.68184	0.276908	0.138454	−	0.990369i	$-0.455787\pi$
$983$	8.68184	0.276908	0.138454	+	0.990369i	$0.455787\pi$
$984$	0.544591	0.0173609
$985$	8.35785	0.266303
$986$	5.60775	0.178587
$987$	1.19842	0.0381460
$988$	−14.4549	−0.459873
$989$	−46.5196	−1.47924
$990$	−0.0312354	−0.000992727 0
$991$	0.849320	0.0269795	0.0134898	−	0.999909i	$-0.495706\pi$
$991$	0.849320	0.0269795	0.0134898	+	0.999909i	$0.495706\pi$
$992$	−10.3366	−0.328187
$993$	−29.6408	−0.940623
$994$	−1.04869	−0.0332623
$995$	8.31585	0.263630
$996$	19.3526	0.613211
$997$	−20.3232	−0.643643	−0.321821	−	0.946800i	$-0.604295\pi$
$997$	−20.3232	−0.643643	−0.321821	+	0.946800i	$0.604295\pi$
$998$	1.96793	0.0622936
$999$	−5.61956	−0.177795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.g.1.18	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.g.1.18	✓	36	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.108652 q^{2} -1.00000 q^{3} -1.98819 q^{4} +1.00000 q^{5} -0.108652 q^{6} +0.790651 q^{7} -0.433326 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.108652 q^{2} -1.00000 q^{3} -1.98819 q^{4} +1.00000 q^{5} -0.108652 q^{6} +0.790651 q^{7} -0.433326 q^{8} +1.00000 q^{9} +0.108652 q^{10} -0.287481 q^{11} +1.98819 q^{12} +4.64561 q^{13} +0.0859059 q^{14} -1.00000 q^{15} +3.92931 q^{16} +5.99627 q^{17} +0.108652 q^{18} +1.56500 q^{19} -1.98819 q^{20} -0.790651 q^{21} -0.0312354 q^{22} -3.81758 q^{23} +0.433326 q^{24} +1.00000 q^{25} +0.504755 q^{26} -1.00000 q^{27} -1.57197 q^{28} +8.60734 q^{29} -0.108652 q^{30} -7.99069 q^{31} +1.29358 q^{32} +0.287481 q^{33} +0.651508 q^{34} +0.790651 q^{35} -1.98819 q^{36} +5.61956 q^{37} +0.170041 q^{38} -4.64561 q^{39} -0.433326 q^{40} +1.25677 q^{41} -0.0859059 q^{42} +12.1856 q^{43} +0.571569 q^{44} +1.00000 q^{45} -0.414788 q^{46} -1.51573 q^{47} -3.92931 q^{48} -6.37487 q^{49} +0.108652 q^{50} -5.99627 q^{51} -9.23637 q^{52} +7.46173 q^{53} -0.108652 q^{54} -0.287481 q^{55} -0.342609 q^{56} -1.56500 q^{57} +0.935206 q^{58} -9.20088 q^{59} +1.98819 q^{60} +10.1472 q^{61} -0.868205 q^{62} +0.790651 q^{63} -7.71807 q^{64} +4.64561 q^{65} +0.0312354 q^{66} -14.8367 q^{67} -11.9218 q^{68} +3.81758 q^{69} +0.0859059 q^{70} -12.2074 q^{71} -0.433326 q^{72} -4.15457 q^{73} +0.610577 q^{74} -1.00000 q^{75} -3.11153 q^{76} -0.227297 q^{77} -0.504755 q^{78} +6.62160 q^{79} +3.92931 q^{80} +1.00000 q^{81} +0.136551 q^{82} +9.73376 q^{83} +1.57197 q^{84} +5.99627 q^{85} +1.32399 q^{86} -8.60734 q^{87} +0.124573 q^{88} +3.23324 q^{89} +0.108652 q^{90} +3.67306 q^{91} +7.59009 q^{92} +7.99069 q^{93} -0.164688 q^{94} +1.56500 q^{95} -1.29358 q^{96} -14.4387 q^{97} -0.692643 q^{98} -0.287481 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9} + 15 q^{11} - 36 q^{12} + 8 q^{13} + 10 q^{14} - 36 q^{15} + 36 q^{16} + 32 q^{17} + 5 q^{19} + 36 q^{20} + 4 q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + 36 q^{25} + 22 q^{26} - 36 q^{27} + 61 q^{29} + 15 q^{31} - q^{32} - 15 q^{33} + 26 q^{34} - 4 q^{35} + 36 q^{36} + 16 q^{37} + 20 q^{38} - 8 q^{39} - 3 q^{40} + 61 q^{41} - 10 q^{42} - 35 q^{43} + 39 q^{44} + 36 q^{45} + 11 q^{46} - 28 q^{47} - 36 q^{48} + 68 q^{49} - 32 q^{51} + 4 q^{52} + 33 q^{53} + 15 q^{55} + 23 q^{56} - 5 q^{57} + 6 q^{58} + 35 q^{59} - 36 q^{60} + 55 q^{61} + q^{62} - 4 q^{63} + 15 q^{64} + 8 q^{65} - q^{66} - 34 q^{67} + 60 q^{68} + 10 q^{69} + 10 q^{70} + 42 q^{71} - 3 q^{72} + 53 q^{73} + 54 q^{74} - 36 q^{75} + 20 q^{76} + 20 q^{77} - 22 q^{78} + 25 q^{79} + 36 q^{80} + 36 q^{81} - 15 q^{82} - 11 q^{83} + 32 q^{85} + 53 q^{86} - 61 q^{87} + 27 q^{88} + 81 q^{89} + 15 q^{91} - 7 q^{92} - 15 q^{93} + 56 q^{94} + 5 q^{95} + q^{96} + 47 q^{97} - 3 q^{98} + 15 q^{99}+O(q^{100}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9 + 15 * q^11 - 36 * q^12 + 8 * q^13 + 10 * q^14 - 36 * q^15 + 36 * q^16 + 32 * q^17 + 5 * q^19 + 36 * q^20 + 4 * q^21 + q^22 - 10 * q^23 + 3 * q^24 + 36 * q^25 + 22 * q^26 - 36 * q^27 + 61 * q^29 + 15 * q^31 - q^32 - 15 * q^33 + 26 * q^34 - 4 * q^35 + 36 * q^36 + 16 * q^37 + 20 * q^38 - 8 * q^39 - 3 * q^40 + 61 * q^41 - 10 * q^42 - 35 * q^43 + 39 * q^44 + 36 * q^45 + 11 * q^46 - 28 * q^47 - 36 * q^48 + 68 * q^49 - 32 * q^51 + 4 * q^52 + 33 * q^53 + 15 * q^55 + 23 * q^56 - 5 * q^57 + 6 * q^58 + 35 * q^59 - 36 * q^60 + 55 * q^61 + q^62 - 4 * q^63 + 15 * q^64 + 8 * q^65 - q^66 - 34 * q^67 + 60 * q^68 + 10 * q^69 + 10 * q^70 + 42 * q^71 - 3 * q^72 + 53 * q^73 + 54 * q^74 - 36 * q^75 + 20 * q^76 + 20 * q^77 - 22 * q^78 + 25 * q^79 + 36 * q^80 + 36 * q^81 - 15 * q^82 - 11 * q^83 + 32 * q^85 + 53 * q^86 - 61 * q^87 + 27 * q^88 + 81 * q^89 + 15 * q^91 - 7 * q^92 - 15 * q^93 + 56 * q^94 + 5 * q^95 + q^96 + 47 * q^97 - 3 * q^98 + 15 * q^99

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