LMFDB - Embedded newform 6015.2.a.g.1.14

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			1.14
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)

$f(q)$	$=$	$q-0.713173 q^{2} -1.00000 q^{3} -1.49138 q^{4} +1.00000 q^{5} +0.713173 q^{6} -4.34956 q^{7} +2.48996 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.713173 q^{2} -1.00000 q^{3} -1.49138 q^{4} +1.00000 q^{5} +0.713173 q^{6} -4.34956 q^{7} +2.48996 q^{8} +1.00000 q^{9} -0.713173 q^{10} -4.21670 q^{11} +1.49138 q^{12} +3.57816 q^{13} +3.10198 q^{14} -1.00000 q^{15} +1.20700 q^{16} +7.48553 q^{17} -0.713173 q^{18} -4.64884 q^{19} -1.49138 q^{20} +4.34956 q^{21} +3.00724 q^{22} +0.401722 q^{23} -2.48996 q^{24} +1.00000 q^{25} -2.55185 q^{26} -1.00000 q^{27} +6.48686 q^{28} +1.07048 q^{29} +0.713173 q^{30} +2.56351 q^{31} -5.84072 q^{32} +4.21670 q^{33} -5.33848 q^{34} -4.34956 q^{35} -1.49138 q^{36} +0.965272 q^{37} +3.31542 q^{38} -3.57816 q^{39} +2.48996 q^{40} -5.24341 q^{41} -3.10198 q^{42} -5.30279 q^{43} +6.28872 q^{44} +1.00000 q^{45} -0.286497 q^{46} +3.69342 q^{47} -1.20700 q^{48} +11.9186 q^{49} -0.713173 q^{50} -7.48553 q^{51} -5.33641 q^{52} -13.3107 q^{53} +0.713173 q^{54} -4.21670 q^{55} -10.8302 q^{56} +4.64884 q^{57} -0.763435 q^{58} -10.7287 q^{59} +1.49138 q^{60} -2.81593 q^{61} -1.82822 q^{62} -4.34956 q^{63} +1.75145 q^{64} +3.57816 q^{65} -3.00724 q^{66} +0.829122 q^{67} -11.1638 q^{68} -0.401722 q^{69} +3.10198 q^{70} +12.4804 q^{71} +2.48996 q^{72} +1.48225 q^{73} -0.688406 q^{74} -1.00000 q^{75} +6.93320 q^{76} +18.3408 q^{77} +2.55185 q^{78} -13.0675 q^{79} +1.20700 q^{80} +1.00000 q^{81} +3.73946 q^{82} -12.6449 q^{83} -6.48686 q^{84} +7.48553 q^{85} +3.78180 q^{86} -1.07048 q^{87} -10.4994 q^{88} -10.6857 q^{89} -0.713173 q^{90} -15.5634 q^{91} -0.599123 q^{92} -2.56351 q^{93} -2.63405 q^{94} -4.64884 q^{95} +5.84072 q^{96} -1.84853 q^{97} -8.50004 q^{98} -4.21670 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.713173	−0.504289	−0.252145	−	0.967690i	$-0.581136\pi$
$2$	−0.713173	−0.504289	−0.252145	+	0.967690i	$0.581136\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.49138	−0.745692
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.713173	0.291152
$7$	−4.34956	−1.64398	−0.821989	−	0.569504i	$-0.807135\pi$
$7$	−4.34956	−1.64398	−0.821989	+	0.569504i	$0.807135\pi$
$8$	2.48996	0.880334
$9$	1.00000	0.333333
$10$	−0.713173	−0.225525
$11$	−4.21670	−1.27138	−0.635691	−	0.771943i	$-0.719285\pi$
$11$	−4.21670	−1.27138	−0.635691	+	0.771943i	$0.719285\pi$
$12$	1.49138	0.430526
$13$	3.57816	0.992403	0.496201	−	0.868207i	$-0.334728\pi$
$13$	3.57816	0.992403	0.496201	+	0.868207i	$0.334728\pi$
$14$	3.10198	0.829040
$15$	−1.00000	−0.258199
$16$	1.20700	0.301749
$17$	7.48553	1.81551	0.907754	−	0.419503i	$-0.137796\pi$
$17$	7.48553	1.81551	0.907754	+	0.419503i	$0.137796\pi$
$18$	−0.713173	−0.168096
$19$	−4.64884	−1.06652	−0.533258	−	0.845953i	$-0.679033\pi$
$19$	−4.64884	−1.06652	−0.533258	+	0.845953i	$0.679033\pi$
$20$	−1.49138	−0.333484
$21$	4.34956	0.949151
$22$	3.00724	0.641145
$23$	0.401722	0.0837649	0.0418825	−	0.999123i	$-0.486664\pi$
$23$	0.401722	0.0837649	0.0418825	+	0.999123i	$0.486664\pi$
$24$	−2.48996	−0.508261
$25$	1.00000	0.200000
$26$	−2.55185	−0.500458
$27$	−1.00000	−0.192450
$28$	6.48686	1.22590
$29$	1.07048	0.198782	0.0993912	−	0.995048i	$-0.468310\pi$
$29$	1.07048	0.198782	0.0993912	+	0.995048i	$0.468310\pi$
$30$	0.713173	0.130207
$31$	2.56351	0.460420	0.230210	−	0.973141i	$-0.426059\pi$
$31$	2.56351	0.460420	0.230210	+	0.973141i	$0.426059\pi$
$32$	−5.84072	−1.03250
$33$	4.21670	0.734033
$34$	−5.33848	−0.915541
$35$	−4.34956	−0.735209
$36$	−1.49138	−0.248564
$37$	0.965272	0.158690	0.0793449	−	0.996847i	$-0.474717\pi$
$37$	0.965272	0.158690	0.0793449	+	0.996847i	$0.474717\pi$
$38$	3.31542	0.537833
$39$	−3.57816	−0.572964
$40$	2.48996	0.393697
$41$	−5.24341	−0.818883	−0.409442	−	0.912336i	$-0.634276\pi$
$41$	−5.24341	−0.818883	−0.409442	+	0.912336i	$0.634276\pi$
$42$	−3.10198	−0.478647
$43$	−5.30279	−0.808668	−0.404334	−	0.914611i	$-0.632497\pi$
$43$	−5.30279	−0.808668	−0.404334	+	0.914611i	$0.632497\pi$
$44$	6.28872	0.948060
$45$	1.00000	0.149071
$46$	−0.286497	−0.0422418
$47$	3.69342	0.538741	0.269370	−	0.963037i	$-0.413184\pi$
$47$	3.69342	0.538741	0.269370	+	0.963037i	$0.413184\pi$
$48$	−1.20700	−0.174215
$49$	11.9186	1.70266
$50$	−0.713173	−0.100858
$51$	−7.48553	−1.04818
$52$	−5.33641	−0.740027
$53$	−13.3107	−1.82837	−0.914184	−	0.405300i	$-0.867167\pi$
$53$	−13.3107	−1.82837	−0.914184	+	0.405300i	$0.867167\pi$
$54$	0.713173	0.0970505
$55$	−4.21670	−0.568580
$56$	−10.8302	−1.44725
$57$	4.64884	0.615754
$58$	−0.763435	−0.100244
$59$	−10.7287	−1.39675	−0.698376	−	0.715731i	$-0.746094\pi$
$59$	−10.7287	−1.39675	−0.698376	+	0.715731i	$0.746094\pi$
$60$	1.49138	0.192537
$61$	−2.81593	−0.360543	−0.180272	−	0.983617i	$-0.557698\pi$
$61$	−2.81593	−0.360543	−0.180272	+	0.983617i	$0.557698\pi$
$62$	−1.82822	−0.232185
$63$	−4.34956	−0.547992
$64$	1.75145	0.218931
$65$	3.57816	0.443816
$66$	−3.00724	−0.370165
$67$	0.829122	0.101293	0.0506467	−	0.998717i	$-0.483872\pi$
$67$	0.829122	0.101293	0.0506467	+	0.998717i	$0.483872\pi$
$68$	−11.1638	−1.35381
$69$	−0.401722	−0.0483617
$70$	3.10198	0.370758
$71$	12.4804	1.48115	0.740574	−	0.671975i	$-0.234554\pi$
$71$	12.4804	1.48115	0.740574	+	0.671975i	$0.234554\pi$
$72$	2.48996	0.293445
$73$	1.48225	0.173484	0.0867419	−	0.996231i	$-0.472354\pi$
$73$	1.48225	0.173484	0.0867419	+	0.996231i	$0.472354\pi$
$74$	−0.688406	−0.0800255
$75$	−1.00000	−0.115470
$76$	6.93320	0.795293
$77$	18.3408	2.09012
$78$	2.55185	0.288940
$79$	−13.0675	−1.47021	−0.735106	−	0.677952i	$-0.762868\pi$
$79$	−13.0675	−1.47021	−0.735106	+	0.677952i	$0.762868\pi$
$80$	1.20700	0.134946
$81$	1.00000	0.111111
$82$	3.73946	0.412954
$83$	−12.6449	−1.38796	−0.693979	−	0.719996i	$-0.744144\pi$
$83$	−12.6449	−1.38796	−0.693979	+	0.719996i	$0.744144\pi$
$84$	−6.48686	−0.707774
$85$	7.48553	0.811920
$86$	3.78180	0.407802
$87$	−1.07048	−0.114767
$88$	−10.4994	−1.11924
$89$	−10.6857	−1.13268	−0.566341	−	0.824171i	$-0.691641\pi$
$89$	−10.6857	−1.13268	−0.566341	+	0.824171i	$0.691641\pi$
$90$	−0.713173	−0.0751750
$91$	−15.5634	−1.63149
$92$	−0.599123	−0.0624629
$93$	−2.56351	−0.265823
$94$	−2.63405	−0.271681
$95$	−4.64884	−0.476961
$96$	5.84072	0.596116
$97$	−1.84853	−0.187690	−0.0938451	−	0.995587i	$-0.529916\pi$
$97$	−1.84853	−0.187690	−0.0938451	+	0.995587i	$0.529916\pi$
$98$	−8.50004	−0.858634
$99$	−4.21670	−0.423794
$100$	−1.49138	−0.149138
$101$	0.826064	0.0821964	0.0410982	−	0.999155i	$-0.486914\pi$
$101$	0.826064	0.0821964	0.0410982	+	0.999155i	$0.486914\pi$
$102$	5.33848	0.528588
$103$	12.7987	1.26109	0.630547	−	0.776151i	$-0.282831\pi$
$103$	12.7987	1.26109	0.630547	+	0.776151i	$0.282831\pi$
$104$	8.90948	0.873646
$105$	4.34956	0.424473
$106$	9.49284	0.922026
$107$	10.9849	1.06195	0.530973	−	0.847389i	$-0.321827\pi$
$107$	10.9849	1.06195	0.530973	+	0.847389i	$0.321827\pi$
$108$	1.49138	0.143509
$109$	10.5513	1.01063	0.505316	−	0.862934i	$-0.331376\pi$
$109$	10.5513	1.01063	0.505316	+	0.862934i	$0.331376\pi$
$110$	3.00724	0.286729
$111$	−0.965272	−0.0916196
$112$	−5.24990	−0.496069
$113$	−15.8792	−1.49379	−0.746894	−	0.664943i	$-0.768456\pi$
$113$	−15.8792	−1.49379	−0.746894	+	0.664943i	$0.768456\pi$
$114$	−3.31542	−0.310518
$115$	0.401722	0.0374608
$116$	−1.59649	−0.148231
$117$	3.57816	0.330801
$118$	7.65139	0.704367
$119$	−32.5587	−2.98465
$120$	−2.48996	−0.227301
$121$	6.78056	0.616414
$122$	2.00825	0.181818
$123$	5.24341	0.472782
$124$	−3.82318	−0.343331
$125$	1.00000	0.0894427
$126$	3.10198	0.276347
$127$	16.3807	1.45356	0.726778	−	0.686872i	$-0.241017\pi$
$127$	16.3807	1.45356	0.726778	+	0.686872i	$0.241017\pi$
$128$	10.4324	0.922098
$129$	5.30279	0.466884
$130$	−2.55185	−0.223812
$131$	14.3864	1.25695	0.628474	−	0.777830i	$-0.283680\pi$
$131$	14.3864	1.25695	0.628474	+	0.777830i	$0.283680\pi$
$132$	−6.28872	−0.547363
$133$	20.2204	1.75333
$134$	−0.591307	−0.0510811
$135$	−1.00000	−0.0860663
$136$	18.6387	1.59825
$137$	−15.2937	−1.30663	−0.653313	−	0.757088i	$-0.726621\pi$
$137$	−15.2937	−1.30663	−0.653313	+	0.757088i	$0.726621\pi$
$138$	0.286497	0.0243883
$139$	−13.2468	−1.12358	−0.561788	−	0.827281i	$-0.689886\pi$
$139$	−13.2468	−1.12358	−0.561788	+	0.827281i	$0.689886\pi$
$140$	6.48686	0.548240
$141$	−3.69342	−0.311042
$142$	−8.90066	−0.746927
$143$	−15.0880	−1.26172
$144$	1.20700	0.100583
$145$	1.07048	0.0888982
$146$	−1.05710	−0.0874860
$147$	−11.9186	−0.983032
$148$	−1.43959	−0.118334
$149$	14.6285	1.19841	0.599206	−	0.800595i	$-0.295483\pi$
$149$	14.6285	1.19841	0.599206	+	0.800595i	$0.295483\pi$
$150$	0.713173	0.0582303
$151$	−0.537868	−0.0437711	−0.0218855	−	0.999760i	$-0.506967\pi$
$151$	−0.537868	−0.0437711	−0.0218855	+	0.999760i	$0.506967\pi$
$152$	−11.5754	−0.938891
$153$	7.48553	0.605169
$154$	−13.0801	−1.05403
$155$	2.56351	0.205906
$156$	5.33641	0.427255
$157$	8.83853	0.705392	0.352696	−	0.935738i	$-0.385265\pi$
$157$	8.83853	0.705392	0.352696	+	0.935738i	$0.385265\pi$
$158$	9.31940	0.741412
$159$	13.3107	1.05561
$160$	−5.84072	−0.461749
$161$	−1.74731	−0.137708
$162$	−0.713173	−0.0560321
$163$	−5.86049	−0.459029	−0.229514	−	0.973305i	$-0.573714\pi$
$163$	−5.86049	−0.459029	−0.229514	+	0.973305i	$0.573714\pi$
$164$	7.81994	0.610635
$165$	4.21670	0.328270
$166$	9.01799	0.699932
$167$	0.0647144	0.00500775	0.00250388	−	0.999997i	$-0.499203\pi$
$167$	0.0647144	0.00500775	0.00250388	+	0.999997i	$0.499203\pi$
$168$	10.8302	0.835570
$169$	−0.196776	−0.0151366
$170$	−5.33848	−0.409442
$171$	−4.64884	−0.355505
$172$	7.90850	0.603017
$173$	12.4895	0.949556	0.474778	−	0.880105i	$-0.342528\pi$
$173$	12.4895	0.949556	0.474778	+	0.880105i	$0.342528\pi$
$174$	0.763435	0.0578758
$175$	−4.34956	−0.328795
$176$	−5.08954	−0.383639
$177$	10.7287	0.806415
$178$	7.62075	0.571199
$179$	−21.8323	−1.63182	−0.815912	−	0.578176i	$-0.803765\pi$
$179$	−21.8323	−1.63182	−0.815912	+	0.578176i	$0.803765\pi$
$180$	−1.49138	−0.111161
$181$	−3.94727	−0.293398	−0.146699	−	0.989181i	$-0.546865\pi$
$181$	−3.94727	−0.293398	−0.146699	+	0.989181i	$0.546865\pi$
$182$	11.0994	0.822742
$183$	2.81593	0.208160
$184$	1.00027	0.0737411
$185$	0.965272	0.0709682
$186$	1.82822	0.134052
$187$	−31.5642	−2.30821
$188$	−5.50831	−0.401735
$189$	4.34956	0.316384
$190$	3.31542	0.240526
$191$	26.2855	1.90195	0.950977	−	0.309262i	$-0.100082\pi$
$191$	26.2855	1.90195	0.950977	+	0.309262i	$0.100082\pi$
$192$	−1.75145	−0.126400
$193$	−7.56503	−0.544543	−0.272272	−	0.962220i	$-0.587775\pi$
$193$	−7.56503	−0.544543	−0.272272	+	0.962220i	$0.587775\pi$
$194$	1.31832	0.0946502
$195$	−3.57816	−0.256237
$196$	−17.7753	−1.26966
$197$	−10.2667	−0.731470	−0.365735	−	0.930719i	$-0.619182\pi$
$197$	−10.2667	−0.731470	−0.365735	+	0.930719i	$0.619182\pi$
$198$	3.00724	0.213715
$199$	23.7547	1.68393	0.841963	−	0.539535i	$-0.181400\pi$
$199$	23.7547	1.68393	0.841963	+	0.539535i	$0.181400\pi$
$200$	2.48996	0.176067
$201$	−0.829122	−0.0584817
$202$	−0.589126	−0.0414508
$203$	−4.65610	−0.326794
$204$	11.1638	0.781623
$205$	−5.24341	−0.366216
$206$	−9.12768	−0.635956
$207$	0.401722	0.0279216
$208$	4.31883	0.299457
$209$	19.6028	1.35595
$210$	−3.10198	−0.214057
$211$	−3.73397	−0.257057	−0.128529	−	0.991706i	$-0.541025\pi$
$211$	−3.73397	−0.257057	−0.128529	+	0.991706i	$0.541025\pi$
$212$	19.8514	1.36340
$213$	−12.4804	−0.855141
$214$	−7.83410	−0.535528
$215$	−5.30279	−0.361647
$216$	−2.48996	−0.169420
$217$	−11.1501	−0.756919
$218$	−7.52491	−0.509651
$219$	−1.48225	−0.100161
$220$	6.28872	0.423985
$221$	26.7844	1.80171
$222$	0.688406	0.0462028
$223$	13.3287	0.892558	0.446279	−	0.894894i	$-0.352749\pi$
$223$	13.3287	0.892558	0.446279	+	0.894894i	$0.352749\pi$
$224$	25.4045	1.69741
$225$	1.00000	0.0666667
$226$	11.3246	0.753301
$227$	−2.92349	−0.194039	−0.0970195	−	0.995282i	$-0.530931\pi$
$227$	−2.92349	−0.194039	−0.0970195	+	0.995282i	$0.530931\pi$
$228$	−6.93320	−0.459163
$229$	12.1607	0.803602	0.401801	−	0.915727i	$-0.368384\pi$
$229$	12.1607	0.803602	0.401801	+	0.915727i	$0.368384\pi$
$230$	−0.286497	−0.0188911
$231$	−18.3408	−1.20673
$232$	2.66544	0.174995
$233$	−7.57219	−0.496070	−0.248035	−	0.968751i	$-0.579785\pi$
$233$	−7.57219	−0.496070	−0.248035	+	0.968751i	$0.579785\pi$
$234$	−2.55185	−0.166819
$235$	3.69342	0.240932
$236$	16.0006	1.04155
$237$	13.0675	0.848827
$238$	23.2200	1.50513
$239$	10.2154	0.660779	0.330389	−	0.943845i	$-0.392820\pi$
$239$	10.2154	0.660779	0.330389	+	0.943845i	$0.392820\pi$
$240$	−1.20700	−0.0779113
$241$	9.51513	0.612923	0.306462	−	0.951883i	$-0.400855\pi$
$241$	9.51513	0.612923	0.306462	+	0.951883i	$0.400855\pi$
$242$	−4.83571	−0.310851
$243$	−1.00000	−0.0641500
$244$	4.19964	0.268854
$245$	11.9186	0.761453
$246$	−3.73946	−0.238419
$247$	−16.6343	−1.05841
$248$	6.38303	0.405323
$249$	12.6449	0.801338
$250$	−0.713173	−0.0451050
$251$	5.85091	0.369306	0.184653	−	0.982804i	$-0.440884\pi$
$251$	5.85091	0.369306	0.184653	+	0.982804i	$0.440884\pi$
$252$	6.48686	0.408634
$253$	−1.69394	−0.106497
$254$	−11.6823	−0.733013
$255$	−7.48553	−0.468762
$256$	−10.9430	−0.683935
$257$	20.8994	1.30367	0.651836	−	0.758360i	$-0.273999\pi$
$257$	20.8994	1.30367	0.651836	+	0.758360i	$0.273999\pi$
$258$	−3.78180	−0.235445
$259$	−4.19850	−0.260882
$260$	−5.33641	−0.330950
$261$	1.07048	0.0662608
$262$	−10.2600	−0.633866
$263$	−16.2380	−1.00128	−0.500639	−	0.865656i	$-0.666902\pi$
$263$	−16.2380	−1.00128	−0.500639	+	0.865656i	$0.666902\pi$
$264$	10.4994	0.646194
$265$	−13.3107	−0.817671
$266$	−14.4206	−0.884185
$267$	10.6857	0.653954
$268$	−1.23654	−0.0755337
$269$	1.04395	0.0636505	0.0318253	−	0.999493i	$-0.489868\pi$
$269$	1.04395	0.0636505	0.0318253	+	0.999493i	$0.489868\pi$
$270$	0.713173	0.0434023
$271$	−0.0829088	−0.00503635	−0.00251817	−	0.999997i	$-0.500802\pi$
$271$	−0.0829088	−0.00503635	−0.00251817	+	0.999997i	$0.500802\pi$
$272$	9.03501	0.547828
$273$	15.5634	0.941940
$274$	10.9070	0.658918
$275$	−4.21670	−0.254277
$276$	0.599123	0.0360629
$277$	−9.76548	−0.586751	−0.293375	−	0.955997i	$-0.594779\pi$
$277$	−9.76548	−0.586751	−0.293375	+	0.955997i	$0.594779\pi$
$278$	9.44723	0.566607
$279$	2.56351	0.153473
$280$	−10.8302	−0.647229
$281$	30.3180	1.80862	0.904311	−	0.426874i	$-0.140385\pi$
$281$	30.3180	1.80862	0.904311	+	0.426874i	$0.140385\pi$
$282$	2.63405	0.156855
$283$	9.73914	0.578932	0.289466	−	0.957188i	$-0.406522\pi$
$283$	9.73914	0.578932	0.289466	+	0.957188i	$0.406522\pi$
$284$	−18.6130	−1.10448
$285$	4.64884	0.275373
$286$	10.7604	0.636274
$287$	22.8065	1.34623
$288$	−5.84072	−0.344168
$289$	39.0332	2.29607
$290$	−0.763435	−0.0448304
$291$	1.84853	0.108363
$292$	−2.21060	−0.129366
$293$	−12.8276	−0.749394	−0.374697	−	0.927147i	$-0.622253\pi$
$293$	−12.8276	−0.749394	−0.374697	+	0.927147i	$0.622253\pi$
$294$	8.50004	0.495733
$295$	−10.7287	−0.624647
$296$	2.40349	0.139700
$297$	4.21670	0.244678
$298$	−10.4326	−0.604347
$299$	1.43743	0.0831285
$300$	1.49138	0.0861051
$301$	23.0648	1.32943
$302$	0.383593	0.0220733
$303$	−0.826064	−0.0474561
$304$	−5.61113	−0.321821
$305$	−2.81593	−0.161240
$306$	−5.33848	−0.305180
$307$	−29.5137	−1.68443	−0.842217	−	0.539139i	$-0.818750\pi$
$307$	−29.5137	−1.68443	−0.842217	+	0.539139i	$0.818750\pi$
$308$	−27.3531	−1.55859
$309$	−12.7987	−0.728093
$310$	−1.82822	−0.103836
$311$	24.4617	1.38710	0.693548	−	0.720410i	$-0.256046\pi$
$311$	24.4617	1.38710	0.693548	+	0.720410i	$0.256046\pi$
$312$	−8.90948	−0.504400
$313$	−14.5404	−0.821874	−0.410937	−	0.911664i	$-0.634798\pi$
$313$	−14.5404	−0.821874	−0.410937	+	0.911664i	$0.634798\pi$
$314$	−6.30340	−0.355722
$315$	−4.34956	−0.245070
$316$	19.4887	1.09633
$317$	−29.6893	−1.66751	−0.833757	−	0.552131i	$-0.813815\pi$
$317$	−29.6893	−1.66751	−0.833757	+	0.552131i	$0.813815\pi$
$318$	−9.49284	−0.532332
$319$	−4.51388	−0.252729
$320$	1.75145	0.0979089
$321$	−10.9849	−0.613115
$322$	1.24614	0.0694445
$323$	−34.7990	−1.93627
$324$	−1.49138	−0.0828547
$325$	3.57816	0.198481
$326$	4.17954	0.231483
$327$	−10.5513	−0.583489
$328$	−13.0559	−0.720891
$329$	−16.0647	−0.885678
$330$	−3.00724	−0.165543
$331$	−27.4419	−1.50834	−0.754172	−	0.656677i	$-0.771962\pi$
$331$	−27.4419	−1.50834	−0.754172	+	0.656677i	$0.771962\pi$
$332$	18.8584	1.03499
$333$	0.965272	0.0528966
$334$	−0.0461526	−0.00252536
$335$	0.829122	0.0452998
$336$	5.24990	0.286406
$337$	25.2813	1.37716	0.688579	−	0.725161i	$-0.258235\pi$
$337$	25.2813	1.37716	0.688579	+	0.725161i	$0.258235\pi$
$338$	0.140335	0.00763322
$339$	15.8792	0.862439
$340$	−11.1638	−0.605442
$341$	−10.8095	−0.585369
$342$	3.31542	0.179278
$343$	−21.3939	−1.15516
$344$	−13.2037	−0.711898
$345$	−0.401722	−0.0216280
$346$	−8.90715	−0.478851
$347$	−12.0899	−0.649019	−0.324509	−	0.945883i	$-0.605199\pi$
$347$	−12.0899	−0.649019	−0.324509	+	0.945883i	$0.605199\pi$
$348$	1.59649	0.0855810
$349$	−7.46517	−0.399601	−0.199801	−	0.979837i	$-0.564029\pi$
$349$	−7.46517	−0.399601	−0.199801	+	0.979837i	$0.564029\pi$
$350$	3.10198	0.165808
$351$	−3.57816	−0.190988
$352$	24.6286	1.31271
$353$	6.27079	0.333760	0.166880	−	0.985977i	$-0.446631\pi$
$353$	6.27079	0.333760	0.166880	+	0.985977i	$0.446631\pi$
$354$	−7.65139	−0.406667
$355$	12.4804	0.662390
$356$	15.9365	0.844632
$357$	32.5587	1.72319
$358$	15.5702	0.822911
$359$	15.4196	0.813813	0.406907	−	0.913470i	$-0.366607\pi$
$359$	15.4196	0.813813	0.406907	+	0.913470i	$0.366607\pi$
$360$	2.48996	0.131232
$361$	2.61169	0.137457
$362$	2.81509	0.147958
$363$	−6.78056	−0.355887
$364$	23.2110	1.21659
$365$	1.48225	0.0775843
$366$	−2.00825	−0.104973
$367$	6.57078	0.342992	0.171496	−	0.985185i	$-0.445140\pi$
$367$	6.57078	0.342992	0.171496	+	0.985185i	$0.445140\pi$
$368$	0.484878	0.0252760
$369$	−5.24341	−0.272961
$370$	−0.688406	−0.0357885
$371$	57.8957	3.00580
$372$	3.82318	0.198222
$373$	−0.950442	−0.0492120	−0.0246060	−	0.999697i	$-0.507833\pi$
$373$	−0.950442	−0.0492120	−0.0246060	+	0.999697i	$0.507833\pi$
$374$	22.5107	1.16400
$375$	−1.00000	−0.0516398
$376$	9.19647	0.474272
$377$	3.83034	0.197272
$378$	−3.10198	−0.159549
$379$	−7.16036	−0.367803	−0.183901	−	0.982945i	$-0.558873\pi$
$379$	−7.16036	−0.367803	−0.183901	+	0.982945i	$0.558873\pi$
$380$	6.93320	0.355666
$381$	−16.3807	−0.839211
$382$	−18.7461	−0.959135
$383$	17.0637	0.871915	0.435958	−	0.899967i	$-0.356410\pi$
$383$	17.0637	0.871915	0.435958	+	0.899967i	$0.356410\pi$
$384$	−10.4324	−0.532374
$385$	18.3408	0.934732
$386$	5.39518	0.274607
$387$	−5.30279	−0.269556
$388$	2.75688	0.139959
$389$	24.6936	1.25202	0.626008	−	0.779816i	$-0.284688\pi$
$389$	24.6936	1.25202	0.626008	+	0.779816i	$0.284688\pi$
$390$	2.55185	0.129218
$391$	3.00711	0.152076
$392$	29.6769	1.49891
$393$	−14.3864	−0.725700
$394$	7.32191	0.368873
$395$	−13.0675	−0.657499
$396$	6.28872	0.316020
$397$	−14.5719	−0.731342	−0.365671	−	0.930744i	$-0.619160\pi$
$397$	−14.5719	−0.731342	−0.365671	+	0.930744i	$0.619160\pi$
$398$	−16.9412	−0.849186
$399$	−20.2204	−1.01228
$400$	1.20700	0.0603499
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	0.591307	0.0294917
$403$	9.17264	0.456922
$404$	−1.23198	−0.0612932
$405$	1.00000	0.0496904
$406$	3.32060	0.164799
$407$	−4.07026	−0.201755
$408$	−18.6387	−0.922752
$409$	9.64723	0.477025	0.238513	−	0.971139i	$-0.423340\pi$
$409$	9.64723	0.477025	0.238513	+	0.971139i	$0.423340\pi$
$410$	3.73946	0.184679
$411$	15.2937	0.754381
$412$	−19.0878	−0.940388
$413$	46.6649	2.29623
$414$	−0.286497	−0.0140806
$415$	−12.6449	−0.620713
$416$	−20.8990	−1.02466
$417$	13.2468	0.648697
$418$	−13.9801	−0.683791
$419$	9.20194	0.449544	0.224772	−	0.974411i	$-0.427836\pi$
$419$	9.20194	0.449544	0.224772	+	0.974411i	$0.427836\pi$
$420$	−6.48686	−0.316526
$421$	28.0860	1.36883	0.684414	−	0.729093i	$-0.260058\pi$
$421$	28.0860	1.36883	0.684414	+	0.729093i	$0.260058\pi$
$422$	2.66297	0.129631
$423$	3.69342	0.179580
$424$	−33.1432	−1.60957
$425$	7.48553	0.363102
$426$	8.90066	0.431239
$427$	12.2481	0.592725
$428$	−16.3826	−0.791885
$429$	15.0880	0.728457
$430$	3.78180	0.182375
$431$	16.7659	0.807584	0.403792	−	0.914851i	$-0.367692\pi$
$431$	16.7659	0.807584	0.403792	+	0.914851i	$0.367692\pi$
$432$	−1.20700	−0.0580717
$433$	14.5039	0.697012	0.348506	−	0.937307i	$-0.386689\pi$
$433$	14.5039	0.697012	0.348506	+	0.937307i	$0.386689\pi$
$434$	7.95196	0.381706
$435$	−1.07048	−0.0513254
$436$	−15.7361	−0.753621
$437$	−1.86754	−0.0893367
$438$	1.05710	0.0505101
$439$	−33.5482	−1.60117	−0.800585	−	0.599219i	$-0.795478\pi$
$439$	−33.5482	−1.60117	−0.800585	+	0.599219i	$0.795478\pi$
$440$	−10.4994	−0.500540
$441$	11.9186	0.567554
$442$	−19.1019	−0.908586
$443$	18.8498	0.895582	0.447791	−	0.894138i	$-0.352211\pi$
$443$	18.8498	0.895582	0.447791	+	0.894138i	$0.352211\pi$
$444$	1.43959	0.0683200
$445$	−10.6857	−0.506550
$446$	−9.50569	−0.450108
$447$	−14.6285	−0.691904
$448$	−7.61801	−0.359917
$449$	32.1992	1.51958	0.759788	−	0.650171i	$-0.225303\pi$
$449$	32.1992	1.51958	0.759788	+	0.650171i	$0.225303\pi$
$450$	−0.713173	−0.0336193
$451$	22.1099	1.04111
$452$	23.6820	1.11391
$453$	0.537868	0.0252713
$454$	2.08496	0.0978518
$455$	−15.5634	−0.729624
$456$	11.5754	0.542069
$457$	9.69225	0.453384	0.226692	−	0.973966i	$-0.427209\pi$
$457$	9.69225	0.453384	0.226692	+	0.973966i	$0.427209\pi$
$458$	−8.67269	−0.405248
$459$	−7.48553	−0.349395
$460$	−0.599123	−0.0279342
$461$	−2.38892	−0.111263	−0.0556315	−	0.998451i	$-0.517717\pi$
$461$	−2.38892	−0.111263	−0.0556315	+	0.998451i	$0.517717\pi$
$462$	13.0801	0.608543
$463$	16.0508	0.745944	0.372972	−	0.927843i	$-0.378339\pi$
$463$	16.0508	0.745944	0.372972	+	0.927843i	$0.378339\pi$
$464$	1.29206	0.0599825
$465$	−2.56351	−0.118880
$466$	5.40028	0.250163
$467$	18.8004	0.869978	0.434989	−	0.900436i	$-0.356752\pi$
$467$	18.8004	0.869978	0.434989	+	0.900436i	$0.356752\pi$
$468$	−5.33641	−0.246676
$469$	−3.60631	−0.166524
$470$	−2.63405	−0.121500
$471$	−8.83853	−0.407258
$472$	−26.7139	−1.22961
$473$	22.3603	1.02813
$474$	−9.31940	−0.428054
$475$	−4.64884	−0.213303
$476$	48.5576	2.22563
$477$	−13.3107	−0.609456
$478$	−7.28534	−0.333224
$479$	10.0557	0.459458	0.229729	−	0.973255i	$-0.426216\pi$
$479$	10.0557	0.459458	0.229729	+	0.973255i	$0.426216\pi$
$480$	5.84072	0.266591
$481$	3.45390	0.157484
$482$	−6.78593	−0.309091
$483$	1.74731	0.0795055
$484$	−10.1124	−0.459655
$485$	−1.84853	−0.0839376
$486$	0.713173	0.0323502
$487$	−3.68442	−0.166957	−0.0834785	−	0.996510i	$-0.526603\pi$
$487$	−3.68442	−0.166957	−0.0834785	+	0.996510i	$0.526603\pi$
$488$	−7.01156	−0.317398
$489$	5.86049	0.265020
$490$	−8.50004	−0.383993
$491$	−7.92208	−0.357518	−0.178759	−	0.983893i	$-0.557208\pi$
$491$	−7.92208	−0.357518	−0.178759	+	0.983893i	$0.557208\pi$
$492$	−7.81994	−0.352550
$493$	8.01308	0.360891
$494$	11.8631	0.533747
$495$	−4.21670	−0.189527
$496$	3.09415	0.138931
$497$	−54.2841	−2.43497
$498$	−9.01799	−0.404106
$499$	3.96381	0.177444	0.0887222	−	0.996056i	$-0.471722\pi$
$499$	3.96381	0.177444	0.0887222	+	0.996056i	$0.471722\pi$
$500$	−1.49138	−0.0666967
$501$	−0.0647144	−0.00289123
$502$	−4.17271	−0.186237
$503$	−16.4807	−0.734838	−0.367419	−	0.930056i	$-0.619758\pi$
$503$	−16.4807	−0.734838	−0.367419	+	0.930056i	$0.619758\pi$
$504$	−10.8302	−0.482416
$505$	0.826064	0.0367594
$506$	1.20807	0.0537054
$507$	0.196776	0.00873912
$508$	−24.4300	−1.08391
$509$	9.68755	0.429393	0.214697	−	0.976681i	$-0.431124\pi$
$509$	9.68755	0.429393	0.214697	+	0.976681i	$0.431124\pi$
$510$	5.33848	0.236392
$511$	−6.44711	−0.285203
$512$	−13.0605	−0.577197
$513$	4.64884	0.205251
$514$	−14.9049	−0.657428
$515$	12.7987	0.563978
$516$	−7.90850	−0.348152
$517$	−15.5740	−0.684946
$518$	2.99426	0.131560
$519$	−12.4895	−0.548227
$520$	8.90948	0.390706
$521$	9.45182	0.414092	0.207046	−	0.978331i	$-0.433615\pi$
$521$	9.45182	0.414092	0.207046	+	0.978331i	$0.433615\pi$
$522$	−0.763435	−0.0334146
$523$	−15.8393	−0.692605	−0.346303	−	0.938123i	$-0.612563\pi$
$523$	−15.8393	−0.692605	−0.346303	+	0.938123i	$0.612563\pi$
$524$	−21.4557	−0.937297
$525$	4.34956	0.189830
$526$	11.5805	0.504934
$527$	19.1892	0.835895
$528$	5.08954	0.221494
$529$	−22.8386	−0.992983
$530$	9.49284	0.412343
$531$	−10.7287	−0.465584
$532$	−30.1564	−1.30744
$533$	−18.7618	−0.812662
$534$	−7.62075	−0.329782
$535$	10.9849	0.474917
$536$	2.06448	0.0891720
$537$	21.8323	0.942134
$538$	−0.744514	−0.0320983
$539$	−50.2573	−2.16473
$540$	1.49138	0.0641790
$541$	24.2525	1.04270	0.521349	−	0.853343i	$-0.325429\pi$
$541$	24.2525	1.04270	0.521349	+	0.853343i	$0.325429\pi$
$542$	0.0591283	0.00253978
$543$	3.94727	0.169394
$544$	−43.7209	−1.87452
$545$	10.5513	0.451969
$546$	−11.0994	−0.475010
$547$	35.5580	1.52035	0.760175	−	0.649719i	$-0.225113\pi$
$547$	35.5580	1.52035	0.760175	+	0.649719i	$0.225113\pi$
$548$	22.8087	0.974341
$549$	−2.81593	−0.120181
$550$	3.00724	0.128229
$551$	−4.97647	−0.212005
$552$	−1.00027	−0.0425744
$553$	56.8379	2.41699
$554$	6.96447	0.295892
$555$	−0.965272	−0.0409735
$556$	19.7560	0.837842
$557$	18.1316	0.768259	0.384129	−	0.923279i	$-0.374502\pi$
$557$	18.1316	0.768259	0.384129	+	0.923279i	$0.374502\pi$
$558$	−1.82822	−0.0773949
$559$	−18.9742	−0.802524
$560$	−5.24990	−0.221849
$561$	31.5642	1.33264
$562$	−21.6220	−0.912069
$563$	0.374635	0.0157890	0.00789450	−	0.999969i	$-0.497487\pi$
$563$	0.374635	0.0157890	0.00789450	+	0.999969i	$0.497487\pi$
$564$	5.50831	0.231942
$565$	−15.8792	−0.668042
$566$	−6.94569	−0.291949
$567$	−4.34956	−0.182664
$568$	31.0756	1.30390
$569$	39.2019	1.64343	0.821715	−	0.569899i	$-0.193018\pi$
$569$	39.2019	1.64343	0.821715	+	0.569899i	$0.193018\pi$
$570$	−3.31542	−0.138868
$571$	15.1736	0.634996	0.317498	−	0.948259i	$-0.397157\pi$
$571$	15.1736	0.634996	0.317498	+	0.948259i	$0.397157\pi$
$572$	22.5020	0.940858
$573$	−26.2855	−1.09809
$574$	−16.2650	−0.678887
$575$	0.401722	0.0167530
$576$	1.75145	0.0729770
$577$	6.40478	0.266635	0.133317	−	0.991073i	$-0.457437\pi$
$577$	6.40478	0.266635	0.133317	+	0.991073i	$0.457437\pi$
$578$	−27.8374	−1.15788
$579$	7.56503	0.314392
$580$	−1.59649	−0.0662907
$581$	54.9997	2.28177
$582$	−1.31832	−0.0546463
$583$	56.1273	2.32456
$584$	3.69073	0.152724
$585$	3.57816	0.147939
$586$	9.14827	0.377911
$587$	−14.1516	−0.584099	−0.292050	−	0.956403i	$-0.594337\pi$
$587$	−14.1516	−0.584099	−0.292050	+	0.956403i	$0.594337\pi$
$588$	17.7753	0.733039
$589$	−11.9173	−0.491045
$590$	7.65139	0.315003
$591$	10.2667	0.422315
$592$	1.16508	0.0478845
$593$	27.6664	1.13612	0.568061	−	0.822986i	$-0.307694\pi$
$593$	27.6664	1.13612	0.568061	+	0.822986i	$0.307694\pi$
$594$	−3.00724	−0.123388
$595$	−32.5587	−1.33478
$596$	−21.8167	−0.893647
$597$	−23.7547	−0.972215
$598$	−1.02513	−0.0419208
$599$	−7.68592	−0.314038	−0.157019	−	0.987596i	$-0.550188\pi$
$599$	−7.68592	−0.314038	−0.157019	+	0.987596i	$0.550188\pi$
$600$	−2.48996	−0.101652
$601$	28.9706	1.18174	0.590868	−	0.806768i	$-0.298785\pi$
$601$	28.9706	1.18174	0.590868	+	0.806768i	$0.298785\pi$
$602$	−16.4492	−0.670418
$603$	0.829122	0.0337644
$604$	0.802168	0.0326398
$605$	6.78056	0.275669
$606$	0.589126	0.0239316
$607$	21.6323	0.878026	0.439013	−	0.898481i	$-0.355328\pi$
$607$	21.6323	0.878026	0.439013	+	0.898481i	$0.355328\pi$
$608$	27.1525	1.10118
$609$	4.65610	0.188675
$610$	2.00825	0.0813115
$611$	13.2156	0.534648
$612$	−11.1638	−0.451270
$613$	−10.1365	−0.409408	−0.204704	−	0.978824i	$-0.565623\pi$
$613$	−10.1365	−0.409408	−0.204704	+	0.978824i	$0.565623\pi$
$614$	21.0483	0.849442
$615$	5.24341	0.211435
$616$	45.6678	1.84001
$617$	32.4334	1.30572	0.652860	−	0.757478i	$-0.273569\pi$
$617$	32.4334	1.30572	0.652860	+	0.757478i	$0.273569\pi$
$618$	9.12768	0.367169
$619$	−34.0744	−1.36956	−0.684782	−	0.728748i	$-0.740103\pi$
$619$	−34.0744	−1.36956	−0.684782	+	0.728748i	$0.740103\pi$
$620$	−3.82318	−0.153542
$621$	−0.401722	−0.0161206
$622$	−17.4454	−0.699498
$623$	46.4780	1.86210
$624$	−4.31883	−0.172892
$625$	1.00000	0.0400000
$626$	10.3698	0.414462
$627$	−19.6028	−0.782858
$628$	−13.1817	−0.526005
$629$	7.22557	0.288102
$630$	3.10198	0.123586
$631$	−5.39349	−0.214711	−0.107356	−	0.994221i	$-0.534238\pi$
$631$	−5.39349	−0.214711	−0.107356	+	0.994221i	$0.534238\pi$
$632$	−32.5376	−1.29428
$633$	3.73397	0.148412
$634$	21.1736	0.840910
$635$	16.3807	0.650050
$636$	−19.8514	−0.787159
$637$	42.6468	1.68973
$638$	3.21917	0.127448
$639$	12.4804	0.493716
$640$	10.4324	0.412375
$641$	−5.54726	−0.219103	−0.109552	−	0.993981i	$-0.534942\pi$
$641$	−5.54726	−0.219103	−0.109552	+	0.993981i	$0.534942\pi$
$642$	7.83410	0.309187
$643$	14.4375	0.569359	0.284680	−	0.958623i	$-0.408113\pi$
$643$	14.4375	0.569359	0.284680	+	0.958623i	$0.408113\pi$
$644$	2.60592	0.102688
$645$	5.30279	0.208797
$646$	24.8177	0.976440
$647$	−36.4002	−1.43104	−0.715519	−	0.698593i	$-0.753810\pi$
$647$	−36.4002	−1.43104	−0.715519	+	0.698593i	$0.753810\pi$
$648$	2.48996	0.0978149
$649$	45.2395	1.77581
$650$	−2.55185	−0.100092
$651$	11.1501	0.437008
$652$	8.74024	0.342294
$653$	−11.5953	−0.453760	−0.226880	−	0.973923i	$-0.572852\pi$
$653$	−11.5953	−0.453760	−0.226880	+	0.973923i	$0.572852\pi$
$654$	7.52491	0.294247
$655$	14.3864	0.562125
$656$	−6.32878	−0.247097
$657$	1.48225	0.0578279
$658$	11.4569	0.446638
$659$	34.9833	1.36275	0.681377	−	0.731933i	$-0.261381\pi$
$659$	34.9833	1.36275	0.681377	+	0.731933i	$0.261381\pi$
$660$	−6.28872	−0.244788
$661$	−9.10958	−0.354321	−0.177161	−	0.984182i	$-0.556691\pi$
$661$	−9.10958	−0.354321	−0.177161	+	0.984182i	$0.556691\pi$
$662$	19.5708	0.760642
$663$	−26.7844	−1.04022
$664$	−31.4853	−1.22187
$665$	20.2204	0.784112
$666$	−0.688406	−0.0266752
$667$	0.430034	0.0166510
$668$	−0.0965141	−0.00373424
$669$	−13.3287	−0.515319
$670$	−0.591307	−0.0228442
$671$	11.8739	0.458388
$672$	−25.4045	−0.980001
$673$	15.1972	0.585810	0.292905	−	0.956142i	$-0.405378\pi$
$673$	15.1972	0.585810	0.292905	+	0.956142i	$0.405378\pi$
$674$	−18.0299	−0.694486
$675$	−1.00000	−0.0384900
$676$	0.293468	0.0112872
$677$	−16.2389	−0.624112	−0.312056	−	0.950064i	$-0.601018\pi$
$677$	−16.2389	−0.624112	−0.312056	+	0.950064i	$0.601018\pi$
$678$	−11.3246	−0.434919
$679$	8.04030	0.308559
$680$	18.6387	0.714760
$681$	2.92349	0.112028
$682$	7.70907	0.295196
$683$	10.9617	0.419439	0.209720	−	0.977762i	$-0.432745\pi$
$683$	10.9617	0.419439	0.209720	+	0.977762i	$0.432745\pi$
$684$	6.93320	0.265098
$685$	−15.2937	−0.584341
$686$	15.2575	0.582535
$687$	−12.1607	−0.463960
$688$	−6.40045	−0.244015
$689$	−47.6279	−1.81448
$690$	0.286497	0.0109068
$691$	12.2887	0.467483	0.233741	−	0.972299i	$-0.424903\pi$
$691$	12.2887	0.467483	0.233741	+	0.972299i	$0.424903\pi$
$692$	−18.6266	−0.708077
$693$	18.3408	0.696708
$694$	8.62217	0.327293
$695$	−13.2468	−0.502478
$696$	−2.66544	−0.101033
$697$	−39.2497	−1.48669
$698$	5.32396	0.201515
$699$	7.57219	0.286406
$700$	6.48686	0.245180
$701$	40.9950	1.54836	0.774181	−	0.632965i	$-0.218162\pi$
$701$	40.9950	1.54836	0.774181	+	0.632965i	$0.218162\pi$
$702$	2.55185	0.0963132
$703$	−4.48739	−0.169245
$704$	−7.38533	−0.278345
$705$	−3.69342	−0.139102
$706$	−4.47215	−0.168312
$707$	−3.59301	−0.135129
$708$	−16.0006	−0.601338
$709$	−32.2473	−1.21107	−0.605537	−	0.795817i	$-0.707041\pi$
$709$	−32.2473	−1.21107	−0.605537	+	0.795817i	$0.707041\pi$
$710$	−8.90066	−0.334036
$711$	−13.0675	−0.490071
$712$	−26.6070	−0.997138
$713$	1.02982	0.0385670
$714$	−23.2200	−0.868986
$715$	−15.0880	−0.564260
$716$	32.5604	1.21684
$717$	−10.2154	−0.381501
$718$	−10.9968	−0.410397
$719$	29.6454	1.10559	0.552793	−	0.833318i	$-0.313562\pi$
$719$	29.6454	1.10559	0.552793	+	0.833318i	$0.313562\pi$
$720$	1.20700	0.0449821
$721$	−55.6687	−2.07321
$722$	−1.86259	−0.0693182
$723$	−9.51513	−0.353871
$724$	5.88690	0.218785
$725$	1.07048	0.0397565
$726$	4.83571	0.179470
$727$	−23.9255	−0.887347	−0.443673	−	0.896189i	$-0.646325\pi$
$727$	−23.9255	−0.887347	−0.443673	+	0.896189i	$0.646325\pi$
$728$	−38.7523	−1.43625
$729$	1.00000	0.0370370
$730$	−1.05710	−0.0391249
$731$	−39.6942	−1.46814
$732$	−4.19964	−0.155223
$733$	12.9024	0.476561	0.238280	−	0.971196i	$-0.423416\pi$
$733$	12.9024	0.476561	0.238280	+	0.971196i	$0.423416\pi$
$734$	−4.68610	−0.172967
$735$	−11.9186	−0.439625
$736$	−2.34635	−0.0864875
$737$	−3.49616	−0.128783
$738$	3.73946	0.137651
$739$	−10.8648	−0.399668	−0.199834	−	0.979830i	$-0.564040\pi$
$739$	−10.8648	−0.399668	−0.199834	+	0.979830i	$0.564040\pi$
$740$	−1.43959	−0.0529205
$741$	16.6343	0.611076
$742$	−41.2896	−1.51579
$743$	28.6478	1.05099	0.525494	−	0.850797i	$-0.323881\pi$
$743$	28.6478	1.05099	0.525494	+	0.850797i	$0.323881\pi$
$744$	−6.38303	−0.234013
$745$	14.6285	0.535946
$746$	0.677829	0.0248171
$747$	−12.6449	−0.462652
$748$	47.0744	1.72121
$749$	−47.7792	−1.74582
$750$	0.713173	0.0260414
$751$	23.0288	0.840332	0.420166	−	0.907447i	$-0.361972\pi$
$751$	23.0288	0.840332	0.420166	+	0.907447i	$0.361972\pi$
$752$	4.45795	0.162565
$753$	−5.85091	−0.213219
$754$	−2.73169	−0.0994823
$755$	−0.537868	−0.0195750
$756$	−6.48686	−0.235925
$757$	−23.3087	−0.847169	−0.423585	−	0.905857i	$-0.639228\pi$
$757$	−23.3087	−0.847169	−0.423585	+	0.905857i	$0.639228\pi$
$758$	5.10657	0.185479
$759$	1.69394	0.0614862
$760$	−11.5754	−0.419885
$761$	26.1952	0.949576	0.474788	−	0.880100i	$-0.342525\pi$
$761$	26.1952	0.949576	0.474788	+	0.880100i	$0.342525\pi$
$762$	11.6823	0.423205
$763$	−45.8935	−1.66146
$764$	−39.2018	−1.41827
$765$	7.48553	0.270640
$766$	−12.1694	−0.439697
$767$	−38.3888	−1.38614
$768$	10.9430	0.394870
$769$	−39.7835	−1.43463	−0.717315	−	0.696749i	$-0.754629\pi$
$769$	−39.7835	−1.43463	−0.717315	+	0.696749i	$0.754629\pi$
$770$	−13.0801	−0.471375
$771$	−20.8994	−0.752675
$772$	11.2824	0.406062
$773$	47.2915	1.70096	0.850479	−	0.526008i	$-0.176312\pi$
$773$	47.2915	1.70096	0.850479	+	0.526008i	$0.176312\pi$
$774$	3.78180	0.135934
$775$	2.56351	0.0920839
$776$	−4.60278	−0.165230
$777$	4.19850	0.150620
$778$	−17.6108	−0.631379
$779$	24.3758	0.873352
$780$	5.33641	0.191074
$781$	−52.6260	−1.88311
$782$	−2.14459	−0.0766902
$783$	−1.07048	−0.0382557
$784$	14.3858	0.513777
$785$	8.83853	0.315461
$786$	10.2600	0.365963
$787$	−28.7618	−1.02525	−0.512623	−	0.858614i	$-0.671326\pi$
$787$	−28.7618	−1.02525	−0.512623	+	0.858614i	$0.671326\pi$
$788$	15.3116	0.545452
$789$	16.2380	0.578088
$790$	9.31940	0.331570
$791$	69.0674	2.45575
$792$	−10.4994	−0.373080
$793$	−10.0759	−0.357804
$794$	10.3923	0.368808
$795$	13.3107	0.472083
$796$	−35.4274	−1.25569
$797$	27.3148	0.967541	0.483770	−	0.875195i	$-0.339267\pi$
$797$	27.3148	0.967541	0.483770	+	0.875195i	$0.339267\pi$
$798$	14.4206	0.510484
$799$	27.6472	0.978088
$800$	−5.84072	−0.206501
$801$	−10.6857	−0.377560
$802$	0.713173	0.0251830
$803$	−6.25019	−0.220564
$804$	1.23654	0.0436094
$805$	−1.74731	−0.0615847
$806$	−6.54168	−0.230421
$807$	−1.04395	−0.0367486
$808$	2.05687	0.0723603
$809$	48.1317	1.69222	0.846109	−	0.533009i	$-0.178939\pi$
$809$	48.1317	1.69222	0.846109	+	0.533009i	$0.178939\pi$
$810$	−0.713173	−0.0250583
$811$	−20.7543	−0.728781	−0.364391	−	0.931246i	$-0.618723\pi$
$811$	−20.7543	−0.728781	−0.364391	+	0.931246i	$0.618723\pi$
$812$	6.94403	0.243688
$813$	0.0829088	0.00290774
$814$	2.90280	0.101743
$815$	−5.86049	−0.205284
$816$	−9.03501	−0.316289
$817$	24.6518	0.862457
$818$	−6.88014	−0.240559
$819$	−15.5634	−0.543829
$820$	7.81994	0.273084
$821$	−9.02144	−0.314851	−0.157425	−	0.987531i	$-0.550319\pi$
$821$	−9.02144	−0.314851	−0.157425	+	0.987531i	$0.550319\pi$
$822$	−10.9070	−0.380426
$823$	25.5544	0.890770	0.445385	−	0.895339i	$-0.353067\pi$
$823$	25.5544	0.890770	0.445385	+	0.895339i	$0.353067\pi$
$824$	31.8683	1.11018
$825$	4.21670	0.146807
$826$	−33.2801	−1.15796
$827$	−13.4048	−0.466131	−0.233066	−	0.972461i	$-0.574876\pi$
$827$	−13.4048	−0.466131	−0.233066	+	0.972461i	$0.574876\pi$
$828$	−0.599123	−0.0208210
$829$	28.3933	0.986141	0.493071	−	0.869989i	$-0.335874\pi$
$829$	28.3933	0.986141	0.493071	+	0.869989i	$0.335874\pi$
$830$	9.01799	0.313019
$831$	9.76548	0.338761
$832$	6.26696	0.217268
$833$	89.2173	3.09119
$834$	−9.44723	−0.327131
$835$	0.0647144	0.00223953
$836$	−29.2352	−1.01112
$837$	−2.56351	−0.0886078
$838$	−6.56257	−0.226700
$839$	20.7536	0.716495	0.358247	−	0.933627i	$-0.383374\pi$
$839$	20.7536	0.716495	0.358247	+	0.933627i	$0.383374\pi$
$840$	10.8302	0.373678
$841$	−27.8541	−0.960486
$842$	−20.0302	−0.690286
$843$	−30.3180	−1.04421
$844$	5.56879	0.191686
$845$	−0.196776	−0.00676929
$846$	−2.63405	−0.0905604
$847$	−29.4924	−1.01337
$848$	−16.0660	−0.551709
$849$	−9.73914	−0.334246
$850$	−5.33848	−0.183108
$851$	0.387771	0.0132926
$852$	18.6130	0.637672
$853$	−13.7895	−0.472143	−0.236071	−	0.971736i	$-0.575860\pi$
$853$	−13.7895	−0.472143	−0.236071	+	0.971736i	$0.575860\pi$
$854$	−8.73498	−0.298905
$855$	−4.64884	−0.158987
$856$	27.3519	0.934867
$857$	2.42488	0.0828324	0.0414162	−	0.999142i	$-0.486813\pi$
$857$	2.42488	0.0828324	0.0414162	+	0.999142i	$0.486813\pi$
$858$	−10.7604	−0.367353
$859$	30.8785	1.05356	0.526780	−	0.850002i	$-0.323399\pi$
$859$	30.8785	1.05356	0.526780	+	0.850002i	$0.323399\pi$
$860$	7.90850	0.269677
$861$	−22.8065	−0.777244
$862$	−11.9570	−0.407256
$863$	−43.6924	−1.48731	−0.743653	−	0.668566i	$-0.766908\pi$
$863$	−43.6924	−1.48731	−0.743653	+	0.668566i	$0.766908\pi$
$864$	5.84072	0.198705
$865$	12.4895	0.424655
$866$	−10.3438	−0.351496
$867$	−39.0332	−1.32564
$868$	16.6291	0.564429
$869$	55.1018	1.86920
$870$	0.763435	0.0258829
$871$	2.96673	0.100524
$872$	26.2724	0.889694
$873$	−1.84853	−0.0625634
$874$	1.33188	0.0450515
$875$	−4.34956	−0.147042
$876$	2.21060	0.0746892
$877$	16.5518	0.558916	0.279458	−	0.960158i	$-0.409845\pi$
$877$	16.5518	0.558916	0.279458	+	0.960158i	$0.409845\pi$
$878$	23.9257	0.807453
$879$	12.8276	0.432663
$880$	−5.08954	−0.171569
$881$	−6.24526	−0.210408	−0.105204	−	0.994451i	$-0.533550\pi$
$881$	−6.24526	−0.210408	−0.105204	+	0.994451i	$0.533550\pi$
$882$	−8.50004	−0.286211
$883$	−32.8117	−1.10420	−0.552101	−	0.833777i	$-0.686174\pi$
$883$	−32.8117	−1.10420	−0.552101	+	0.833777i	$0.686174\pi$
$884$	−39.9459	−1.34352
$885$	10.7287	0.360640
$886$	−13.4432	−0.451632
$887$	−19.8032	−0.664928	−0.332464	−	0.943116i	$-0.607880\pi$
$887$	−19.8032	−0.664928	−0.332464	+	0.943116i	$0.607880\pi$
$888$	−2.40349	−0.0806558
$889$	−71.2490	−2.38961
$890$	7.62075	0.255448
$891$	−4.21670	−0.141265
$892$	−19.8783	−0.665574
$893$	−17.1701	−0.574576
$894$	10.4326	0.348920
$895$	−21.8323	−0.729774
$896$	−45.3761	−1.51591
$897$	−1.43743	−0.0479943
$898$	−22.9636	−0.766306
$899$	2.74417	0.0915233
$900$	−1.49138	−0.0497128
$901$	−99.6378	−3.31942
$902$	−15.7682	−0.525023
$903$	−23.0648	−0.767547
$904$	−39.5385	−1.31503
$905$	−3.94727	−0.131212
$906$	−0.383593	−0.0127440
$907$	41.5257	1.37884	0.689419	−	0.724363i	$-0.257866\pi$
$907$	41.5257	1.37884	0.689419	+	0.724363i	$0.257866\pi$
$908$	4.36005	0.144693
$909$	0.826064	0.0273988
$910$	11.0994	0.367941
$911$	7.44122	0.246539	0.123269	−	0.992373i	$-0.460662\pi$
$911$	7.44122	0.246539	0.123269	+	0.992373i	$0.460662\pi$
$912$	5.61113	0.185803
$913$	53.3197	1.76463
$914$	−6.91225	−0.228637
$915$	2.81593	0.0930919
$916$	−18.1363	−0.599240
$917$	−62.5746	−2.06640
$918$	5.33848	0.176196
$919$	−57.4892	−1.89639	−0.948197	−	0.317683i	$-0.897095\pi$
$919$	−57.4892	−1.89639	−0.948197	+	0.317683i	$0.897095\pi$
$920$	1.00027	0.0329780
$921$	29.5137	0.972508
$922$	1.70371	0.0561087
$923$	44.6568	1.46990
$924$	27.3531	0.899852
$925$	0.965272	0.0317379
$926$	−11.4470	−0.376171
$927$	12.7987	0.420364
$928$	−6.25235	−0.205243
$929$	−39.9132	−1.30951	−0.654754	−	0.755842i	$-0.727228\pi$
$929$	−39.9132	−1.30951	−0.654754	+	0.755842i	$0.727228\pi$
$930$	1.82822	0.0599498
$931$	−55.4078	−1.81592
$932$	11.2930	0.369916
$933$	−24.4617	−0.800840
$934$	−13.4079	−0.438720
$935$	−31.5642	−1.03226
$936$	8.90948	0.291215
$937$	−41.1287	−1.34362	−0.671809	−	0.740725i	$-0.734482\pi$
$937$	−41.1287	−1.34362	−0.671809	+	0.740725i	$0.734482\pi$
$938$	2.57192	0.0839762
$939$	14.5404	0.474509
$940$	−5.50831	−0.179661
$941$	53.3218	1.73824	0.869121	−	0.494600i	$-0.164685\pi$
$941$	53.3218	1.73824	0.869121	+	0.494600i	$0.164685\pi$
$942$	6.30340	0.205376
$943$	−2.10640	−0.0685937
$944$	−12.9495	−0.421469
$945$	4.34956	0.141491
$946$	−15.9467	−0.518473
$947$	0.549834	0.0178672	0.00893360	−	0.999960i	$-0.497156\pi$
$947$	0.549834	0.0178672	0.00893360	+	0.999960i	$0.497156\pi$
$948$	−19.4887	−0.632964
$949$	5.30371	0.172166
$950$	3.31542	0.107567
$951$	29.6893	0.962740
$952$	−81.0699	−2.62749
$953$	22.3991	0.725577	0.362789	−	0.931871i	$-0.381825\pi$
$953$	22.3991	0.725577	0.362789	+	0.931871i	$0.381825\pi$
$954$	9.49284	0.307342
$955$	26.2855	0.850579
$956$	−15.2351	−0.492738
$957$	4.51388	0.145913
$958$	−7.17148	−0.231700
$959$	66.5207	2.14806
$960$	−1.75145	−0.0565277
$961$	−24.4284	−0.788014
$962$	−2.46323	−0.0794176
$963$	10.9849	0.353982
$964$	−14.1907	−0.457052
$965$	−7.56503	−0.243527
$966$	−1.24614	−0.0400938
$967$	28.3558	0.911862	0.455931	−	0.890015i	$-0.349306\pi$
$967$	28.3558	0.911862	0.455931	+	0.890015i	$0.349306\pi$
$968$	16.8833	0.542650
$969$	34.7990	1.11791
$970$	1.31832	0.0423289
$971$	−34.2188	−1.09813	−0.549066	−	0.835779i	$-0.685017\pi$
$971$	−34.2188	−1.09813	−0.549066	+	0.835779i	$0.685017\pi$
$972$	1.49138	0.0478362
$973$	57.6175	1.84713
$974$	2.62763	0.0841946
$975$	−3.57816	−0.114593
$976$	−3.39882	−0.108794
$977$	−48.4538	−1.55017	−0.775087	−	0.631855i	$-0.782294\pi$
$977$	−48.4538	−1.55017	−0.775087	+	0.631855i	$0.782294\pi$
$978$	−4.17954	−0.133647
$979$	45.0584	1.44007
$980$	−17.7753	−0.567810
$981$	10.5513	0.336878
$982$	5.64981	0.180293
$983$	−47.9881	−1.53058	−0.765291	−	0.643684i	$-0.777405\pi$
$983$	−47.9881	−1.53058	−0.765291	+	0.643684i	$0.777405\pi$
$984$	13.0559	0.416206
$985$	−10.2667	−0.327123
$986$	−5.71471	−0.181994
$987$	16.0647	0.511346
$988$	24.8081	0.789251
$989$	−2.13025	−0.0677380
$990$	3.00724	0.0955762
$991$	32.3832	1.02869	0.514344	−	0.857584i	$-0.328036\pi$
$991$	32.3832	1.02869	0.514344	+	0.857584i	$0.328036\pi$
$992$	−14.9727	−0.475384
$993$	27.4419	0.870843
$994$	38.7139	1.22793
$995$	23.7547	0.753074
$996$	−18.8584	−0.597551
$997$	−50.3479	−1.59453	−0.797267	−	0.603627i	$-0.793721\pi$
$997$	−50.3479	−1.59453	−0.797267	+	0.603627i	$0.793721\pi$
$998$	−2.82688	−0.0894833
$999$	−0.965272	−0.0305399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.g.1.14	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.g.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-0.713173 q^{2} -1.00000 q^{3} -1.49138 q^{4} +1.00000 q^{5} +0.713173 q^{6} -4.34956 q^{7} +2.48996 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.713173 q^{2} -1.00000 q^{3} -1.49138 q^{4} +1.00000 q^{5} +0.713173 q^{6} -4.34956 q^{7} +2.48996 q^{8} +1.00000 q^{9} -0.713173 q^{10} -4.21670 q^{11} +1.49138 q^{12} +3.57816 q^{13} +3.10198 q^{14} -1.00000 q^{15} +1.20700 q^{16} +7.48553 q^{17} -0.713173 q^{18} -4.64884 q^{19} -1.49138 q^{20} +4.34956 q^{21} +3.00724 q^{22} +0.401722 q^{23} -2.48996 q^{24} +1.00000 q^{25} -2.55185 q^{26} -1.00000 q^{27} +6.48686 q^{28} +1.07048 q^{29} +0.713173 q^{30} +2.56351 q^{31} -5.84072 q^{32} +4.21670 q^{33} -5.33848 q^{34} -4.34956 q^{35} -1.49138 q^{36} +0.965272 q^{37} +3.31542 q^{38} -3.57816 q^{39} +2.48996 q^{40} -5.24341 q^{41} -3.10198 q^{42} -5.30279 q^{43} +6.28872 q^{44} +1.00000 q^{45} -0.286497 q^{46} +3.69342 q^{47} -1.20700 q^{48} +11.9186 q^{49} -0.713173 q^{50} -7.48553 q^{51} -5.33641 q^{52} -13.3107 q^{53} +0.713173 q^{54} -4.21670 q^{55} -10.8302 q^{56} +4.64884 q^{57} -0.763435 q^{58} -10.7287 q^{59} +1.49138 q^{60} -2.81593 q^{61} -1.82822 q^{62} -4.34956 q^{63} +1.75145 q^{64} +3.57816 q^{65} -3.00724 q^{66} +0.829122 q^{67} -11.1638 q^{68} -0.401722 q^{69} +3.10198 q^{70} +12.4804 q^{71} +2.48996 q^{72} +1.48225 q^{73} -0.688406 q^{74} -1.00000 q^{75} +6.93320 q^{76} +18.3408 q^{77} +2.55185 q^{78} -13.0675 q^{79} +1.20700 q^{80} +1.00000 q^{81} +3.73946 q^{82} -12.6449 q^{83} -6.48686 q^{84} +7.48553 q^{85} +3.78180 q^{86} -1.07048 q^{87} -10.4994 q^{88} -10.6857 q^{89} -0.713173 q^{90} -15.5634 q^{91} -0.599123 q^{92} -2.56351 q^{93} -2.63405 q^{94} -4.64884 q^{95} +5.84072 q^{96} -1.84853 q^{97} -8.50004 q^{98} -4.21670 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) \) 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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