LMFDB - Embedded newform 4006.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.07158 q^{3} +1.00000 q^{4} +0.0807440 q^{5} +3.07158 q^{6} -2.46915 q^{7} -1.00000 q^{8} +6.43459 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.07158 q^{3} +1.00000 q^{4} +0.0807440 q^{5} +3.07158 q^{6} -2.46915 q^{7} -1.00000 q^{8} +6.43459 q^{9} -0.0807440 q^{10} -4.79480 q^{11} -3.07158 q^{12} +0.832702 q^{13} +2.46915 q^{14} -0.248011 q^{15} +1.00000 q^{16} +3.88839 q^{17} -6.43459 q^{18} -3.52829 q^{19} +0.0807440 q^{20} +7.58419 q^{21} +4.79480 q^{22} -3.78567 q^{23} +3.07158 q^{24} -4.99348 q^{25} -0.832702 q^{26} -10.5496 q^{27} -2.46915 q^{28} +2.91912 q^{29} +0.248011 q^{30} -2.92786 q^{31} -1.00000 q^{32} +14.7276 q^{33} -3.88839 q^{34} -0.199369 q^{35} +6.43459 q^{36} +4.00713 q^{37} +3.52829 q^{38} -2.55771 q^{39} -0.0807440 q^{40} +3.13851 q^{41} -7.58419 q^{42} -1.23659 q^{43} -4.79480 q^{44} +0.519554 q^{45} +3.78567 q^{46} -8.94878 q^{47} -3.07158 q^{48} -0.903297 q^{49} +4.99348 q^{50} -11.9435 q^{51} +0.832702 q^{52} -11.4019 q^{53} +10.5496 q^{54} -0.387152 q^{55} +2.46915 q^{56} +10.8374 q^{57} -2.91912 q^{58} +7.08872 q^{59} -0.248011 q^{60} -6.24134 q^{61} +2.92786 q^{62} -15.8880 q^{63} +1.00000 q^{64} +0.0672356 q^{65} -14.7276 q^{66} +1.67942 q^{67} +3.88839 q^{68} +11.6280 q^{69} +0.199369 q^{70} -7.07799 q^{71} -6.43459 q^{72} +0.958286 q^{73} -4.00713 q^{74} +15.3379 q^{75} -3.52829 q^{76} +11.8391 q^{77} +2.55771 q^{78} +11.6788 q^{79} +0.0807440 q^{80} +13.1002 q^{81} -3.13851 q^{82} -5.63651 q^{83} +7.58419 q^{84} +0.313964 q^{85} +1.23659 q^{86} -8.96630 q^{87} +4.79480 q^{88} -10.3458 q^{89} -0.519554 q^{90} -2.05607 q^{91} -3.78567 q^{92} +8.99316 q^{93} +8.94878 q^{94} -0.284888 q^{95} +3.07158 q^{96} -15.3644 q^{97} +0.903297 q^{98} -30.8526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) $ 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.07158	−1.77338	−0.886688	−	0.462368i	$-0.847000\pi$
$3$	−3.07158	−1.77338	−0.886688	+	0.462368i	$0.847000\pi$
$4$	1.00000	0.500000
$5$	0.0807440	0.0361098	0.0180549	−	0.999837i	$-0.494253\pi$
$5$	0.0807440	0.0361098	0.0180549	+	0.999837i	$0.494253\pi$
$6$	3.07158	1.25397
$7$	−2.46915	−0.933251	−0.466626	−	0.884455i	$-0.654530\pi$
$7$	−2.46915	−0.933251	−0.466626	+	0.884455i	$0.654530\pi$
$8$	−1.00000	−0.353553
$9$	6.43459	2.14486
$10$	−0.0807440	−0.0255335
$11$	−4.79480	−1.44569	−0.722844	−	0.691011i	$-0.757165\pi$
$11$	−4.79480	−1.44569	−0.722844	+	0.691011i	$0.757165\pi$
$12$	−3.07158	−0.886688
$13$	0.832702	0.230950	0.115475	−	0.993310i	$-0.463161\pi$
$13$	0.832702	0.230950	0.115475	+	0.993310i	$0.463161\pi$
$14$	2.46915	0.659908
$15$	−0.248011	−0.0640363
$16$	1.00000	0.250000
$17$	3.88839	0.943072	0.471536	−	0.881847i	$-0.343700\pi$
$17$	3.88839	0.943072	0.471536	+	0.881847i	$0.343700\pi$
$18$	−6.43459	−1.51665
$19$	−3.52829	−0.809444	−0.404722	−	0.914440i	$-0.632632\pi$
$19$	−3.52829	−0.809444	−0.404722	+	0.914440i	$0.632632\pi$
$20$	0.0807440	0.0180549
$21$	7.58419	1.65501
$22$	4.79480	1.02226
$23$	−3.78567	−0.789367	−0.394683	−	0.918817i	$-0.629146\pi$
$23$	−3.78567	−0.789367	−0.394683	+	0.918817i	$0.629146\pi$
$24$	3.07158	0.626983
$25$	−4.99348	−0.998696
$26$	−0.832702	−0.163306
$27$	−10.5496	−2.03027
$28$	−2.46915	−0.466626
$29$	2.91912	0.542067	0.271034	−	0.962570i	$-0.412635\pi$
$29$	2.91912	0.542067	0.271034	+	0.962570i	$0.412635\pi$
$30$	0.248011	0.0452805
$31$	−2.92786	−0.525860	−0.262930	−	0.964815i	$-0.584689\pi$
$31$	−2.92786	−0.525860	−0.262930	+	0.964815i	$0.584689\pi$
$32$	−1.00000	−0.176777
$33$	14.7276	2.56375
$34$	−3.88839	−0.666853
$35$	−0.199369	−0.0336995
$36$	6.43459	1.07243
$37$	4.00713	0.658768	0.329384	−	0.944196i	$-0.393159\pi$
$37$	4.00713	0.658768	0.329384	+	0.944196i	$0.393159\pi$
$38$	3.52829	0.572364
$39$	−2.55771	−0.409561
$40$	−0.0807440	−0.0127667
$41$	3.13851	0.490153	0.245076	−	0.969504i	$-0.421187\pi$
$41$	3.13851	0.490153	0.245076	+	0.969504i	$0.421187\pi$
$42$	−7.58419	−1.17027
$43$	−1.23659	−0.188578	−0.0942889	−	0.995545i	$-0.530058\pi$
$43$	−1.23659	−0.188578	−0.0942889	+	0.995545i	$0.530058\pi$
$44$	−4.79480	−0.722844
$45$	0.519554	0.0774506
$46$	3.78567	0.558167
$47$	−8.94878	−1.30531	−0.652657	−	0.757653i	$-0.726346\pi$
$47$	−8.94878	−1.30531	−0.652657	+	0.757653i	$0.726346\pi$
$48$	−3.07158	−0.443344
$49$	−0.903297	−0.129042
$50$	4.99348	0.706185
$51$	−11.9435	−1.67242
$52$	0.832702	0.115475
$53$	−11.4019	−1.56617	−0.783087	−	0.621912i	$-0.786356\pi$
$53$	−11.4019	−1.56617	−0.783087	+	0.621912i	$0.786356\pi$
$54$	10.5496	1.43562
$55$	−0.387152	−0.0522035
$56$	2.46915	0.329954
$57$	10.8374	1.43545
$58$	−2.91912	−0.383299
$59$	7.08872	0.922873	0.461437	−	0.887173i	$-0.347334\pi$
$59$	7.08872	0.922873	0.461437	+	0.887173i	$0.347334\pi$
$60$	−0.248011	−0.0320181
$61$	−6.24134	−0.799122	−0.399561	−	0.916707i	$-0.630837\pi$
$61$	−6.24134	−0.799122	−0.399561	+	0.916707i	$0.630837\pi$
$62$	2.92786	0.371839
$63$	−15.8880	−2.00170
$64$	1.00000	0.125000
$65$	0.0672356	0.00833955
$66$	−14.7276	−1.81284
$67$	1.67942	0.205173	0.102587	−	0.994724i	$-0.467288\pi$
$67$	1.67942	0.205173	0.102587	+	0.994724i	$0.467288\pi$
$68$	3.88839	0.471536
$69$	11.6280	1.39984
$70$	0.199369	0.0238292
$71$	−7.07799	−0.840003	−0.420001	−	0.907524i	$-0.637970\pi$
$71$	−7.07799	−0.840003	−0.420001	+	0.907524i	$0.637970\pi$
$72$	−6.43459	−0.758323
$73$	0.958286	0.112159	0.0560794	−	0.998426i	$-0.482140\pi$
$73$	0.958286	0.112159	0.0560794	+	0.998426i	$0.482140\pi$
$74$	−4.00713	−0.465819
$75$	15.3379	1.77106
$76$	−3.52829	−0.404722
$77$	11.8391	1.34919
$78$	2.55771	0.289603
$79$	11.6788	1.31396	0.656981	−	0.753907i	$-0.271833\pi$
$79$	11.6788	1.31396	0.656981	+	0.753907i	$0.271833\pi$
$80$	0.0807440	0.00902745
$81$	13.1002	1.45557
$82$	−3.13851	−0.346590
$83$	−5.63651	−0.618688	−0.309344	−	0.950950i	$-0.600109\pi$
$83$	−5.63651	−0.618688	−0.309344	+	0.950950i	$0.600109\pi$
$84$	7.58419	0.827503
$85$	0.313964	0.0340542
$86$	1.23659	0.133345
$87$	−8.96630	−0.961289
$88$	4.79480	0.511128
$89$	−10.3458	−1.09666	−0.548328	−	0.836263i	$-0.684736\pi$
$89$	−10.3458	−1.09666	−0.548328	+	0.836263i	$0.684736\pi$
$90$	−0.519554	−0.0547658
$91$	−2.05607	−0.215534
$92$	−3.78567	−0.394683
$93$	8.99316	0.932547
$94$	8.94878	0.922997
$95$	−0.284888	−0.0292289
$96$	3.07158	0.313492
$97$	−15.3644	−1.56002	−0.780008	−	0.625770i	$-0.784785\pi$
$97$	−15.3644	−1.56002	−0.780008	+	0.625770i	$0.784785\pi$
$98$	0.903297	0.0912468
$99$	−30.8526	−3.10080
$100$	−4.99348	−0.499348
$101$	2.49968	0.248728	0.124364	−	0.992237i	$-0.460311\pi$
$101$	2.49968	0.248728	0.124364	+	0.992237i	$0.460311\pi$
$102$	11.9435	1.18258
$103$	−16.6533	−1.64090	−0.820448	−	0.571721i	$-0.806276\pi$
$103$	−16.6533	−1.64090	−0.820448	+	0.571721i	$0.806276\pi$
$104$	−0.832702	−0.0816531
$105$	0.612377	0.0597619
$106$	11.4019	1.10745
$107$	10.9979	1.06321	0.531604	−	0.846993i	$-0.321589\pi$
$107$	10.9979	1.06321	0.531604	+	0.846993i	$0.321589\pi$
$108$	−10.5496	−1.01514
$109$	−2.16182	−0.207065	−0.103532	−	0.994626i	$-0.533015\pi$
$109$	−2.16182	−0.207065	−0.103532	+	0.994626i	$0.533015\pi$
$110$	0.387152	0.0369134
$111$	−12.3082	−1.16824
$112$	−2.46915	−0.233313
$113$	−19.8309	−1.86554	−0.932769	−	0.360474i	$-0.882615\pi$
$113$	−19.8309	−1.86554	−0.932769	+	0.360474i	$0.882615\pi$
$114$	−10.8374	−1.01502
$115$	−0.305670	−0.0285039
$116$	2.91912	0.271034
$117$	5.35809	0.495356
$118$	−7.08872	−0.652570
$119$	−9.60101	−0.880123
$120$	0.248011	0.0226402
$121$	11.9901	1.09001
$122$	6.24134	0.565065
$123$	−9.64017	−0.869225
$124$	−2.92786	−0.262930
$125$	−0.806913	−0.0721725
$126$	15.8880	1.41541
$127$	−13.8355	−1.22771	−0.613853	−	0.789421i	$-0.710381\pi$
$127$	−13.8355	−1.22771	−0.613853	+	0.789421i	$0.710381\pi$
$128$	−1.00000	−0.0883883
$129$	3.79827	0.334419
$130$	−0.0672356	−0.00589695
$131$	−1.35953	−0.118783	−0.0593914	−	0.998235i	$-0.518916\pi$
$131$	−1.35953	−0.118783	−0.0593914	+	0.998235i	$0.518916\pi$
$132$	14.7276	1.28187
$133$	8.71187	0.755415
$134$	−1.67942	−0.145079
$135$	−0.851817	−0.0733127
$136$	−3.88839	−0.333426
$137$	2.86414	0.244700	0.122350	−	0.992487i	$-0.460957\pi$
$137$	2.86414	0.244700	0.122350	+	0.992487i	$0.460957\pi$
$138$	−11.6280	−0.989840
$139$	5.76219	0.488743	0.244371	−	0.969682i	$-0.421418\pi$
$139$	5.76219	0.488743	0.244371	+	0.969682i	$0.421418\pi$
$140$	−0.199369	−0.0168498
$141$	27.4869	2.31481
$142$	7.07799	0.593971
$143$	−3.99264	−0.333881
$144$	6.43459	0.536216
$145$	0.235701	0.0195739
$146$	−0.958286	−0.0793083
$147$	2.77455	0.228841
$148$	4.00713	0.329384
$149$	20.8281	1.70631	0.853154	−	0.521659i	$-0.174687\pi$
$149$	20.8281	1.70631	0.853154	+	0.521659i	$0.174687\pi$
$150$	−15.3379	−1.25233
$151$	8.08628	0.658052	0.329026	−	0.944321i	$-0.393280\pi$
$151$	8.08628	0.658052	0.329026	+	0.944321i	$0.393280\pi$
$152$	3.52829	0.286182
$153$	25.0202	2.02276
$154$	−11.8391	−0.954021
$155$	−0.236407	−0.0189887
$156$	−2.55771	−0.204780
$157$	−3.27924	−0.261712	−0.130856	−	0.991401i	$-0.541773\pi$
$157$	−3.27924	−0.261712	−0.130856	+	0.991401i	$0.541773\pi$
$158$	−11.6788	−0.929112
$159$	35.0219	2.77742
$160$	−0.0807440	−0.00638337
$161$	9.34739	0.736678
$162$	−13.1002	−1.02925
$163$	−6.33277	−0.496021	−0.248010	−	0.968757i	$-0.579777\pi$
$163$	−6.33277	−0.496021	−0.248010	+	0.968757i	$0.579777\pi$
$164$	3.13851	0.245076
$165$	1.18917	0.0925764
$166$	5.63651	0.437478
$167$	12.3118	0.952719	0.476359	−	0.879251i	$-0.341956\pi$
$167$	12.3118	0.952719	0.476359	+	0.879251i	$0.341956\pi$
$168$	−7.58419	−0.585133
$169$	−12.3066	−0.946662
$170$	−0.313964	−0.0240799
$171$	−22.7031	−1.73615
$172$	−1.23659	−0.0942889
$173$	−6.21953	−0.472862	−0.236431	−	0.971648i	$-0.575978\pi$
$173$	−6.21953	−0.472862	−0.236431	+	0.971648i	$0.575978\pi$
$174$	8.96630	0.679734
$175$	12.3297	0.932034
$176$	−4.79480	−0.361422
$177$	−21.7736	−1.63660
$178$	10.3458	0.775453
$179$	−23.9431	−1.78959	−0.894794	−	0.446479i	$-0.852678\pi$
$179$	−23.9431	−1.78959	−0.894794	+	0.446479i	$0.852678\pi$
$180$	0.519554	0.0387253
$181$	−18.4588	−1.37203	−0.686015	−	0.727587i	$-0.740642\pi$
$181$	−18.4588	−1.37203	−0.686015	+	0.727587i	$0.740642\pi$
$182$	2.05607	0.152406
$183$	19.1708	1.41714
$184$	3.78567	0.279083
$185$	0.323551	0.0237880
$186$	−8.99316	−0.659410
$187$	−18.6441	−1.36339
$188$	−8.94878	−0.652657
$189$	26.0486	1.89475
$190$	0.284888	0.0206679
$191$	23.4563	1.69724	0.848618	−	0.529007i	$-0.177435\pi$
$191$	23.4563	1.69724	0.848618	+	0.529007i	$0.177435\pi$
$192$	−3.07158	−0.221672
$193$	−18.7129	−1.34698	−0.673492	−	0.739194i	$-0.735207\pi$
$193$	−18.7129	−1.34698	−0.673492	+	0.739194i	$0.735207\pi$
$194$	15.3644	1.10310
$195$	−0.206519	−0.0147892
$196$	−0.903297	−0.0645212
$197$	12.3245	0.878085	0.439042	−	0.898466i	$-0.355318\pi$
$197$	12.3245	0.878085	0.439042	+	0.898466i	$0.355318\pi$
$198$	30.8526	2.19260
$199$	−2.18874	−0.155156	−0.0775778	−	0.996986i	$-0.524719\pi$
$199$	−2.18874	−0.155156	−0.0775778	+	0.996986i	$0.524719\pi$
$200$	4.99348	0.353092
$201$	−5.15845	−0.363849
$202$	−2.49968	−0.175877
$203$	−7.20775	−0.505885
$204$	−11.9435	−0.836211
$205$	0.253416	0.0176993
$206$	16.6533	1.16029
$207$	−24.3592	−1.69308
$208$	0.832702	0.0577375
$209$	16.9174	1.17020
$210$	−0.612377	−0.0422580
$211$	19.1578	1.31888	0.659440	−	0.751757i	$-0.270794\pi$
$211$	19.1578	1.31888	0.659440	+	0.751757i	$0.270794\pi$
$212$	−11.4019	−0.783087
$213$	21.7406	1.48964
$214$	−10.9979	−0.751802
$215$	−0.0998470	−0.00680951
$216$	10.5496	0.717810
$217$	7.22933	0.490759
$218$	2.16182	0.146417
$219$	−2.94345	−0.198900
$220$	−0.387152	−0.0261018
$221$	3.23787	0.217802
$222$	12.3082	0.826072
$223$	−10.6157	−0.710880	−0.355440	−	0.934699i	$-0.615669\pi$
$223$	−10.6157	−0.710880	−0.355440	+	0.934699i	$0.615669\pi$
$224$	2.46915	0.164977
$225$	−32.1310	−2.14207
$226$	19.8309	1.31914
$227$	24.0971	1.59938	0.799692	−	0.600411i	$-0.204996\pi$
$227$	24.0971	1.59938	0.799692	+	0.600411i	$0.204996\pi$
$228$	10.8374	0.717725
$229$	−4.67786	−0.309122	−0.154561	−	0.987983i	$-0.549396\pi$
$229$	−4.67786	−0.309122	−0.154561	+	0.987983i	$0.549396\pi$
$230$	0.305670	0.0201553
$231$	−36.3647	−2.39262
$232$	−2.91912	−0.191650
$233$	−11.2653	−0.738015	−0.369007	−	0.929426i	$-0.620302\pi$
$233$	−11.2653	−0.738015	−0.369007	+	0.929426i	$0.620302\pi$
$234$	−5.35809	−0.350269
$235$	−0.722560	−0.0471346
$236$	7.08872	0.461437
$237$	−35.8722	−2.33015
$238$	9.60101	0.622341
$239$	6.22325	0.402549	0.201274	−	0.979535i	$-0.435492\pi$
$239$	6.22325	0.402549	0.201274	+	0.979535i	$0.435492\pi$
$240$	−0.248011	−0.0160091
$241$	17.0302	1.09701	0.548505	−	0.836147i	$-0.315197\pi$
$241$	17.0302	1.09701	0.548505	+	0.836147i	$0.315197\pi$
$242$	−11.9901	−0.770756
$243$	−8.58934	−0.551006
$244$	−6.24134	−0.399561
$245$	−0.0729358	−0.00465970
$246$	9.64017	0.614635
$247$	−2.93801	−0.186941
$248$	2.92786	0.185919
$249$	17.3130	1.09717
$250$	0.806913	0.0510337
$251$	10.7914	0.681144	0.340572	−	0.940218i	$-0.389379\pi$
$251$	10.7914	0.681144	0.340572	+	0.940218i	$0.389379\pi$
$252$	−15.8880	−1.00085
$253$	18.1516	1.14118
$254$	13.8355	0.868119
$255$	−0.964364	−0.0603908
$256$	1.00000	0.0625000
$257$	13.4173	0.836949	0.418475	−	0.908229i	$-0.362565\pi$
$257$	13.4173	0.836949	0.418475	+	0.908229i	$0.362565\pi$
$258$	−3.79827	−0.236470
$259$	−9.89420	−0.614796
$260$	0.0672356	0.00416978
$261$	18.7833	1.16266
$262$	1.35953	0.0839921
$263$	0.788820	0.0486407	0.0243203	−	0.999704i	$-0.492258\pi$
$263$	0.788820	0.0486407	0.0243203	+	0.999704i	$0.492258\pi$
$264$	−14.7276	−0.906422
$265$	−0.920637	−0.0565543
$266$	−8.71187	−0.534159
$267$	31.7780	1.94478
$268$	1.67942	0.102587
$269$	3.56695	0.217481	0.108741	−	0.994070i	$-0.465318\pi$
$269$	3.56695	0.217481	0.108741	+	0.994070i	$0.465318\pi$
$270$	0.851817	0.0518399
$271$	21.7717	1.32254	0.661270	−	0.750148i	$-0.270018\pi$
$271$	21.7717	1.32254	0.661270	+	0.750148i	$0.270018\pi$
$272$	3.88839	0.235768
$273$	6.31536	0.382223
$274$	−2.86414	−0.173029
$275$	23.9428	1.44380
$276$	11.6280	0.699922
$277$	−8.81695	−0.529759	−0.264880	−	0.964282i	$-0.585332\pi$
$277$	−8.81695	−0.529759	−0.264880	+	0.964282i	$0.585332\pi$
$278$	−5.76219	−0.345593
$279$	−18.8396	−1.12790
$280$	0.199369	0.0119146
$281$	−2.98320	−0.177963	−0.0889814	−	0.996033i	$-0.528361\pi$
$281$	−2.98320	−0.177963	−0.0889814	+	0.996033i	$0.528361\pi$
$282$	−27.4869	−1.63682
$283$	30.5029	1.81321	0.906604	−	0.421983i	$-0.138666\pi$
$283$	30.5029	1.81321	0.906604	+	0.421983i	$0.138666\pi$
$284$	−7.07799	−0.420001
$285$	0.875055	0.0518338
$286$	3.99264	0.236090
$287$	−7.74945	−0.457436
$288$	−6.43459	−0.379162
$289$	−1.88044	−0.110614
$290$	−0.235701	−0.0138409
$291$	47.1929	2.76649
$292$	0.958286	0.0560794
$293$	−8.11918	−0.474328	−0.237164	−	0.971470i	$-0.576218\pi$
$293$	−8.11918	−0.474328	−0.237164	+	0.971470i	$0.576218\pi$
$294$	−2.77455	−0.161815
$295$	0.572372	0.0333248
$296$	−4.00713	−0.232910
$297$	50.5833	2.93514
$298$	−20.8281	−1.20654
$299$	−3.15233	−0.182304
$300$	15.3379	0.885532
$301$	3.05332	0.175990
$302$	−8.08628	−0.465313
$303$	−7.67797	−0.441088
$304$	−3.52829	−0.202361
$305$	−0.503951	−0.0288561
$306$	−25.0202	−1.43031
$307$	8.39116	0.478909	0.239454	−	0.970908i	$-0.423031\pi$
$307$	8.39116	0.478909	0.239454	+	0.970908i	$0.423031\pi$
$308$	11.8391	0.674595
$309$	51.1518	2.90992
$310$	0.236407	0.0134270
$311$	20.0915	1.13929	0.569643	−	0.821892i	$-0.307081\pi$
$311$	20.0915	1.13929	0.569643	+	0.821892i	$0.307081\pi$
$312$	2.55771	0.144802
$313$	6.68783	0.378019	0.189009	−	0.981975i	$-0.439472\pi$
$313$	6.68783	0.378019	0.189009	+	0.981975i	$0.439472\pi$
$314$	3.27924	0.185058
$315$	−1.28286	−0.0722808
$316$	11.6788	0.656981
$317$	6.32130	0.355039	0.177520	−	0.984117i	$-0.443193\pi$
$317$	6.32130	0.355039	0.177520	+	0.984117i	$0.443193\pi$
$318$	−35.0219	−1.96393
$319$	−13.9966	−0.783660
$320$	0.0807440	0.00451373
$321$	−33.7809	−1.88547
$322$	−9.34739	−0.520910
$323$	−13.7193	−0.763365
$324$	13.1002	0.727786
$325$	−4.15808	−0.230649
$326$	6.33277	0.350740
$327$	6.64020	0.367204
$328$	−3.13851	−0.173295
$329$	22.0959	1.21819
$330$	−1.18917	−0.0654614
$331$	24.4884	1.34600	0.673002	−	0.739640i	$-0.265004\pi$
$331$	24.4884	1.34600	0.673002	+	0.739640i	$0.265004\pi$
$332$	−5.63651	−0.309344
$333$	25.7842	1.41297
$334$	−12.3118	−0.673674
$335$	0.135603	0.00740876
$336$	7.58419	0.413751
$337$	−13.3089	−0.724981	−0.362491	−	0.931987i	$-0.618074\pi$
$337$	−13.3089	−0.724981	−0.362491	+	0.931987i	$0.618074\pi$
$338$	12.3066	0.669391
$339$	60.9123	3.30830
$340$	0.313964	0.0170271
$341$	14.0385	0.760229
$342$	22.7031	1.22764
$343$	19.5144	1.05368
$344$	1.23659	0.0666723
$345$	0.938889	0.0505481
$346$	6.21953	0.334364
$347$	3.17394	0.170386	0.0851931	−	0.996364i	$-0.472849\pi$
$347$	3.17394	0.170386	0.0851931	+	0.996364i	$0.472849\pi$
$348$	−8.96630	−0.480644
$349$	1.53393	0.0821095	0.0410547	−	0.999157i	$-0.486928\pi$
$349$	1.53393	0.0821095	0.0410547	+	0.999157i	$0.486928\pi$
$350$	−12.3297	−0.659048
$351$	−8.78467	−0.468891
$352$	4.79480	0.255564
$353$	23.6923	1.26101	0.630507	−	0.776184i	$-0.282847\pi$
$353$	23.6923	1.26101	0.630507	+	0.776184i	$0.282847\pi$
$354$	21.7736	1.15725
$355$	−0.571505	−0.0303323
$356$	−10.3458	−0.548328
$357$	29.4903	1.56079
$358$	23.9431	1.26543
$359$	11.4062	0.601996	0.300998	−	0.953625i	$-0.402680\pi$
$359$	11.4062	0.601996	0.300998	+	0.953625i	$0.402680\pi$
$360$	−0.519554	−0.0273829
$361$	−6.55120	−0.344800
$362$	18.4588	0.970172
$363$	−36.8287	−1.93300
$364$	−2.05607	−0.107767
$365$	0.0773758	0.00405003
$366$	−19.1708	−1.00207
$367$	−30.4298	−1.58842	−0.794211	−	0.607642i	$-0.792116\pi$
$367$	−30.4298	−1.58842	−0.794211	+	0.607642i	$0.792116\pi$
$368$	−3.78567	−0.197342
$369$	20.1950	1.05131
$370$	−0.323551	−0.0168206
$371$	28.1531	1.46163
$372$	8.99316	0.466273
$373$	−3.64341	−0.188649	−0.0943244	−	0.995542i	$-0.530069\pi$
$373$	−3.64341	−0.188649	−0.0943244	+	0.995542i	$0.530069\pi$
$374$	18.6441	0.964061
$375$	2.47850	0.127989
$376$	8.94878	0.461498
$377$	2.43076	0.125190
$378$	−26.0486	−1.33979
$379$	12.7096	0.652847	0.326424	−	0.945224i	$-0.394156\pi$
$379$	12.7096	0.652847	0.326424	+	0.945224i	$0.394156\pi$
$380$	−0.284888	−0.0146144
$381$	42.4969	2.17718
$382$	−23.4563	−1.20013
$383$	7.40039	0.378142	0.189071	−	0.981963i	$-0.439452\pi$
$383$	7.40039	0.378142	0.189071	+	0.981963i	$0.439452\pi$
$384$	3.07158	0.156746
$385$	0.955935	0.0487190
$386$	18.7129	0.952462
$387$	−7.95693	−0.404474
$388$	−15.3644	−0.780008
$389$	25.0506	1.27012	0.635058	−	0.772464i	$-0.280976\pi$
$389$	25.0506	1.27012	0.635058	+	0.772464i	$0.280976\pi$
$390$	0.206519	0.0104575
$391$	−14.7202	−0.744430
$392$	0.903297	0.0456234
$393$	4.17591	0.210647
$394$	−12.3245	−0.620900
$395$	0.942989	0.0474469
$396$	−30.8526	−1.55040
$397$	6.34783	0.318589	0.159294	−	0.987231i	$-0.449078\pi$
$397$	6.34783	0.318589	0.159294	+	0.987231i	$0.449078\pi$
$398$	2.18874	0.109712
$399$	−26.7592	−1.33963
$400$	−4.99348	−0.249674
$401$	−12.9909	−0.648737	−0.324368	−	0.945931i	$-0.605152\pi$
$401$	−12.9909	−0.648737	−0.324368	+	0.945931i	$0.605152\pi$
$402$	5.15845	0.257280
$403$	−2.43804	−0.121447
$404$	2.49968	0.124364
$405$	1.05776	0.0525605
$406$	7.20775	0.357714
$407$	−19.2134	−0.952372
$408$	11.9435	0.591291
$409$	3.12372	0.154458	0.0772290	−	0.997013i	$-0.475393\pi$
$409$	3.12372	0.154458	0.0772290	+	0.997013i	$0.475393\pi$
$410$	−0.253416	−0.0125153
$411$	−8.79743	−0.433945
$412$	−16.6533	−0.820448
$413$	−17.5031	−0.861272
$414$	24.3592	1.19719
$415$	−0.455114	−0.0223407
$416$	−0.832702	−0.0408266
$417$	−17.6990	−0.866725
$418$	−16.9174	−0.827459
$419$	24.8412	1.21357	0.606787	−	0.794865i	$-0.292458\pi$
$419$	24.8412	1.21357	0.606787	+	0.794865i	$0.292458\pi$
$420$	0.612377	0.0298810
$421$	15.8720	0.773553	0.386777	−	0.922173i	$-0.373588\pi$
$421$	15.8720	0.773553	0.386777	+	0.922173i	$0.373588\pi$
$422$	−19.1578	−0.932589
$423$	−57.5817	−2.79972
$424$	11.4019	0.553726
$425$	−19.4166	−0.941843
$426$	−21.7406	−1.05333
$427$	15.4108	0.745782
$428$	10.9979	0.531604
$429$	12.2637	0.592097
$430$	0.0998470	0.00481505
$431$	−6.72883	−0.324116	−0.162058	−	0.986781i	$-0.551813\pi$
$431$	−6.72883	−0.324116	−0.162058	+	0.986781i	$0.551813\pi$
$432$	−10.5496	−0.507568
$433$	−22.3051	−1.07191	−0.535957	−	0.844245i	$-0.680049\pi$
$433$	−22.3051	−1.07191	−0.535957	+	0.844245i	$0.680049\pi$
$434$	−7.22933	−0.347019
$435$	−0.723975	−0.0347119
$436$	−2.16182	−0.103532
$437$	13.3569	0.638949
$438$	2.94345	0.140643
$439$	21.7139	1.03635	0.518174	−	0.855275i	$-0.326612\pi$
$439$	21.7139	1.03635	0.518174	+	0.855275i	$0.326612\pi$
$440$	0.387152	0.0184567
$441$	−5.81235	−0.276778
$442$	−3.23787	−0.154010
$443$	24.6967	1.17337	0.586687	−	0.809814i	$-0.300432\pi$
$443$	24.6967	1.17337	0.586687	+	0.809814i	$0.300432\pi$
$444$	−12.3082	−0.584121
$445$	−0.835364	−0.0396001
$446$	10.6157	0.502668
$447$	−63.9753	−3.02593
$448$	−2.46915	−0.116656
$449$	9.60108	0.453103	0.226551	−	0.973999i	$-0.427255\pi$
$449$	9.60108	0.453103	0.226551	+	0.973999i	$0.427255\pi$
$450$	32.1310	1.51467
$451$	−15.0485	−0.708608
$452$	−19.8309	−0.932769
$453$	−24.8376	−1.16697
$454$	−24.0971	−1.13093
$455$	−0.166015	−0.00778290
$456$	−10.8374	−0.507508
$457$	31.9164	1.49299	0.746493	−	0.665393i	$-0.231736\pi$
$457$	31.9164	1.49299	0.746493	+	0.665393i	$0.231736\pi$
$458$	4.67786	0.218582
$459$	−41.0209	−1.91469
$460$	−0.305670	−0.0142519
$461$	−35.1428	−1.63677	−0.818383	−	0.574674i	$-0.805129\pi$
$461$	−35.1428	−1.63677	−0.818383	+	0.574674i	$0.805129\pi$
$462$	36.3647	1.69184
$463$	−27.6982	−1.28724	−0.643622	−	0.765344i	$-0.722569\pi$
$463$	−27.6982	−1.28724	−0.643622	+	0.765344i	$0.722569\pi$
$464$	2.91912	0.135517
$465$	0.726143	0.0336741
$466$	11.2653	0.521855
$467$	7.36990	0.341038	0.170519	−	0.985354i	$-0.445456\pi$
$467$	7.36990	0.341038	0.170519	+	0.985354i	$0.445456\pi$
$468$	5.35809	0.247678
$469$	−4.14673	−0.191478
$470$	0.722560	0.0333292
$471$	10.0724	0.464114
$472$	−7.08872	−0.326285
$473$	5.92920	0.272625
$474$	35.8722	1.64766
$475$	17.6184	0.808389
$476$	−9.60101	−0.440062
$477$	−73.3667	−3.35923
$478$	−6.22325	−0.284645
$479$	−8.49258	−0.388036	−0.194018	−	0.980998i	$-0.562152\pi$
$479$	−8.49258	−0.388036	−0.194018	+	0.980998i	$0.562152\pi$
$480$	0.248011	0.0113201
$481$	3.33674	0.152142
$482$	−17.0302	−0.775704
$483$	−28.7112	−1.30641
$484$	11.9901	0.545007
$485$	−1.24058	−0.0563318
$486$	8.58934	0.389620
$487$	8.60314	0.389845	0.194923	−	0.980819i	$-0.437554\pi$
$487$	8.60314	0.389845	0.194923	+	0.980819i	$0.437554\pi$
$488$	6.24134	0.282532
$489$	19.4516	0.879632
$490$	0.0729358	0.00329490
$491$	1.89124	0.0853504	0.0426752	−	0.999089i	$-0.486412\pi$
$491$	1.89124	0.0853504	0.0426752	+	0.999089i	$0.486412\pi$
$492$	−9.64017	−0.434613
$493$	11.3507	0.511208
$494$	2.93801	0.132187
$495$	−2.49116	−0.111969
$496$	−2.92786	−0.131465
$497$	17.4766	0.783933
$498$	−17.3130	−0.775813
$499$	−2.22949	−0.0998058	−0.0499029	−	0.998754i	$-0.515891\pi$
$499$	−2.22949	−0.0998058	−0.0499029	+	0.998754i	$0.515891\pi$
$500$	−0.806913	−0.0360863
$501$	−37.8168	−1.68953
$502$	−10.7914	−0.481642
$503$	15.0267	0.670008	0.335004	−	0.942217i	$-0.391262\pi$
$503$	15.0267	0.670008	0.335004	+	0.942217i	$0.391262\pi$
$504$	15.8880	0.707706
$505$	0.201834	0.00898151
$506$	−18.1516	−0.806935
$507$	37.8007	1.67879
$508$	−13.8355	−0.613853
$509$	35.8963	1.59107	0.795537	−	0.605905i	$-0.207189\pi$
$509$	35.8963	1.59107	0.795537	+	0.605905i	$0.207189\pi$
$510$	0.964364	0.0427028
$511$	−2.36615	−0.104672
$512$	−1.00000	−0.0441942
$513$	37.2220	1.64339
$514$	−13.4173	−0.591812
$515$	−1.34465	−0.0592524
$516$	3.79827	0.167210
$517$	42.9077	1.88708
$518$	9.89420	0.434726
$519$	19.1038	0.838562
$520$	−0.0672356	−0.00294848
$521$	−6.47607	−0.283722	−0.141861	−	0.989887i	$-0.545309\pi$
$521$	−6.47607	−0.283722	−0.141861	+	0.989887i	$0.545309\pi$
$522$	−18.7833	−0.822124
$523$	−5.71048	−0.249702	−0.124851	−	0.992176i	$-0.539845\pi$
$523$	−5.71048	−0.249702	−0.124851	+	0.992176i	$0.539845\pi$
$524$	−1.35953	−0.0593914
$525$	−37.8715	−1.65285
$526$	−0.788820	−0.0343942
$527$	−11.3847	−0.495924
$528$	14.7276	0.640937
$529$	−8.66870	−0.376900
$530$	0.920637	0.0399899
$531$	45.6130	1.97944
$532$	8.71187	0.377707
$533$	2.61344	0.113201
$534$	−31.7780	−1.37517
$535$	0.888015	0.0383922
$536$	−1.67942	−0.0725397
$537$	73.5430	3.17361
$538$	−3.56695	−0.153782
$539$	4.33113	0.186555
$540$	−0.851817	−0.0366564
$541$	18.6423	0.801496	0.400748	−	0.916188i	$-0.368750\pi$
$541$	18.6423	0.801496	0.400748	+	0.916188i	$0.368750\pi$
$542$	−21.7717	−0.935177
$543$	56.6976	2.43313
$544$	−3.88839	−0.166713
$545$	−0.174554	−0.00747707
$546$	−6.31536	−0.270273
$547$	28.6008	1.22288	0.611440	−	0.791291i	$-0.290591\pi$
$547$	28.6008	1.22288	0.611440	+	0.791291i	$0.290591\pi$
$548$	2.86414	0.122350
$549$	−40.1605	−1.71401
$550$	−23.9428	−1.02092
$551$	−10.2995	−0.438773
$552$	−11.6280	−0.494920
$553$	−28.8366	−1.22626
$554$	8.81695	0.374596
$555$	−0.993813	−0.0421850
$556$	5.76219	0.244371
$557$	22.8236	0.967066	0.483533	−	0.875326i	$-0.339353\pi$
$557$	22.8236	0.967066	0.483533	+	0.875326i	$0.339353\pi$
$558$	18.8396	0.797543
$559$	−1.02971	−0.0435520
$560$	−0.199369	−0.00842488
$561$	57.2667	2.41780
$562$	2.98320	0.125839
$563$	−30.5692	−1.28834	−0.644170	−	0.764882i	$-0.722797\pi$
$563$	−30.5692	−1.28834	−0.644170	+	0.764882i	$0.722797\pi$
$564$	27.4869	1.15741
$565$	−1.60123	−0.0673642
$566$	−30.5029	−1.28213
$567$	−32.3463	−1.35842
$568$	7.07799	0.296986
$569$	31.4721	1.31938	0.659690	−	0.751538i	$-0.270688\pi$
$569$	31.4721	1.31938	0.659690	+	0.751538i	$0.270688\pi$
$570$	−0.875055	−0.0366520
$571$	−29.7575	−1.24531	−0.622655	−	0.782496i	$-0.713946\pi$
$571$	−29.7575	−1.24531	−0.622655	+	0.782496i	$0.713946\pi$
$572$	−3.99264	−0.166941
$573$	−72.0477	−3.00984
$574$	7.74945	0.323456
$575$	18.9037	0.788338
$576$	6.43459	0.268108
$577$	−36.0350	−1.50016	−0.750079	−	0.661348i	$-0.769985\pi$
$577$	−36.0350	−1.50016	−0.750079	+	0.661348i	$0.769985\pi$
$578$	1.88044	0.0782161
$579$	57.4781	2.38871
$580$	0.235701	0.00978697
$581$	13.9174	0.577391
$582$	−47.1929	−1.95621
$583$	54.6700	2.26420
$584$	−0.958286	−0.0396542
$585$	0.432634	0.0178872
$586$	8.11918	0.335400
$587$	−11.2612	−0.464800	−0.232400	−	0.972620i	$-0.574658\pi$
$587$	−11.2612	−0.464800	−0.232400	+	0.972620i	$0.574658\pi$
$588$	2.77455	0.114420
$589$	10.3303	0.425654
$590$	−0.572372	−0.0235642
$591$	−37.8557	−1.55717
$592$	4.00713	0.164692
$593$	8.35470	0.343087	0.171543	−	0.985177i	$-0.445125\pi$
$593$	8.35470	0.343087	0.171543	+	0.985177i	$0.445125\pi$
$594$	−50.5833	−2.07546
$595$	−0.775224	−0.0317811
$596$	20.8281	0.853154
$597$	6.72288	0.275149
$598$	3.15233	0.128909
$599$	−14.1343	−0.577510	−0.288755	−	0.957403i	$-0.593241\pi$
$599$	−14.1343	−0.577510	−0.288755	+	0.957403i	$0.593241\pi$
$600$	−15.3379	−0.626166
$601$	−23.6034	−0.962802	−0.481401	−	0.876500i	$-0.659872\pi$
$601$	−23.6034	−0.962802	−0.481401	+	0.876500i	$0.659872\pi$
$602$	−3.05332	−0.124444
$603$	10.8063	0.440068
$604$	8.08628	0.329026
$605$	0.968132	0.0393602
$606$	7.67797	0.311896
$607$	1.05332	0.0427528	0.0213764	−	0.999771i	$-0.493195\pi$
$607$	1.05332	0.0427528	0.0213764	+	0.999771i	$0.493195\pi$
$608$	3.52829	0.143091
$609$	22.1392	0.897124
$610$	0.503951	0.0204044
$611$	−7.45167	−0.301462
$612$	25.0202	1.01138
$613$	−18.0789	−0.730200	−0.365100	−	0.930968i	$-0.618965\pi$
$613$	−18.0789	−0.730200	−0.365100	+	0.930968i	$0.618965\pi$
$614$	−8.39116	−0.338639
$615$	−0.778386	−0.0313875
$616$	−11.8391	−0.477011
$617$	−20.3236	−0.818197	−0.409099	−	0.912490i	$-0.634157\pi$
$617$	−20.3236	−0.818197	−0.409099	+	0.912490i	$0.634157\pi$
$618$	−51.1518	−2.05763
$619$	−10.8112	−0.434540	−0.217270	−	0.976112i	$-0.569715\pi$
$619$	−10.8112	−0.434540	−0.217270	+	0.976112i	$0.569715\pi$
$620$	−0.236407	−0.00949434
$621$	39.9373	1.60263
$622$	−20.0915	−0.805597
$623$	25.5454	1.02346
$624$	−2.55771	−0.102390
$625$	24.9022	0.996090
$626$	−6.68783	−0.267300
$627$	−51.9632	−2.07521
$628$	−3.27924	−0.130856
$629$	15.5813	0.621266
$630$	1.28286	0.0511103
$631$	−42.9981	−1.71173	−0.855863	−	0.517203i	$-0.826973\pi$
$631$	−42.9981	−1.71173	−0.855863	+	0.517203i	$0.826973\pi$
$632$	−11.6788	−0.464556
$633$	−58.8448	−2.33887
$634$	−6.32130	−0.251051
$635$	−1.11714	−0.0443322
$636$	35.0219	1.38871
$637$	−0.752177	−0.0298023
$638$	13.9966	0.554131
$639$	−45.5439	−1.80169
$640$	−0.0807440	−0.00319169
$641$	−25.9198	−1.02377	−0.511886	−	0.859053i	$-0.671053\pi$
$641$	−25.9198	−1.02377	−0.511886	+	0.859053i	$0.671053\pi$
$642$	33.7809	1.33323
$643$	−32.0851	−1.26531	−0.632657	−	0.774432i	$-0.718036\pi$
$643$	−32.0851	−1.26531	−0.632657	+	0.774432i	$0.718036\pi$
$644$	9.34739	0.368339
$645$	0.306688	0.0120758
$646$	13.7193	0.539780
$647$	−14.3531	−0.564278	−0.282139	−	0.959374i	$-0.591044\pi$
$647$	−14.3531	−0.564278	−0.282139	+	0.959374i	$0.591044\pi$
$648$	−13.1002	−0.514623
$649$	−33.9890	−1.33419
$650$	4.15808	0.163093
$651$	−22.2055	−0.870300
$652$	−6.33277	−0.248010
$653$	−17.0715	−0.668060	−0.334030	−	0.942562i	$-0.608409\pi$
$653$	−17.0715	−0.668060	−0.334030	+	0.942562i	$0.608409\pi$
$654$	−6.64020	−0.259652
$655$	−0.109774	−0.00428922
$656$	3.13851	0.122538
$657$	6.16617	0.240565
$658$	−22.0959	−0.861387
$659$	−43.3880	−1.69016	−0.845078	−	0.534644i	$-0.820446\pi$
$659$	−43.3880	−1.69016	−0.845078	+	0.534644i	$0.820446\pi$
$660$	1.18917	0.0462882
$661$	0.516011	0.0200705	0.0100352	−	0.999950i	$-0.496806\pi$
$661$	0.516011	0.0200705	0.0100352	+	0.999950i	$0.496806\pi$
$662$	−24.4884	−0.951769
$663$	−9.94536	−0.386246
$664$	5.63651	0.218739
$665$	0.703431	0.0272779
$666$	−25.7842	−0.999118
$667$	−11.0508	−0.427890
$668$	12.3118	0.476359
$669$	32.6070	1.26066
$670$	−0.135603	−0.00523879
$671$	29.9260	1.15528
$672$	−7.58419	−0.292566
$673$	−1.44514	−0.0557060	−0.0278530	−	0.999612i	$-0.508867\pi$
$673$	−1.44514	−0.0557060	−0.0278530	+	0.999612i	$0.508867\pi$
$674$	13.3089	0.512639
$675$	52.6792	2.02762
$676$	−12.3066	−0.473331
$677$	25.8902	0.995041	0.497520	−	0.867452i	$-0.334244\pi$
$677$	25.8902	0.995041	0.497520	+	0.867452i	$0.334244\pi$
$678$	−60.9123	−2.33932
$679$	37.9369	1.45589
$680$	−0.313964	−0.0120400
$681$	−74.0162	−2.83631
$682$	−14.0385	−0.537563
$683$	−15.5245	−0.594028	−0.297014	−	0.954873i	$-0.595991\pi$
$683$	−15.5245	−0.594028	−0.297014	+	0.954873i	$0.595991\pi$
$684$	−22.7031	−0.868074
$685$	0.231262	0.00883607
$686$	−19.5144	−0.745064
$687$	14.3684	0.548189
$688$	−1.23659	−0.0471445
$689$	−9.49440	−0.361708
$690$	−0.938889	−0.0357429
$691$	−6.94498	−0.264200	−0.132100	−	0.991236i	$-0.542172\pi$
$691$	−6.94498	−0.264200	−0.132100	+	0.991236i	$0.542172\pi$
$692$	−6.21953	−0.236431
$693$	76.1797	2.89383
$694$	−3.17394	−0.120481
$695$	0.465262	0.0176484
$696$	8.96630	0.339867
$697$	12.2037	0.462250
$698$	−1.53393	−0.0580602
$699$	34.6023	1.30878
$700$	12.3297	0.466017
$701$	29.6468	1.11975	0.559873	−	0.828579i	$-0.310850\pi$
$701$	29.6468	1.11975	0.559873	+	0.828579i	$0.310850\pi$
$702$	8.78467	0.331556
$703$	−14.1383	−0.533236
$704$	−4.79480	−0.180711
$705$	2.21940	0.0835874
$706$	−23.6923	−0.891671
$707$	−6.17209	−0.232125
$708$	−21.7736	−0.818301
$709$	−2.21985	−0.0833682	−0.0416841	−	0.999131i	$-0.513272\pi$
$709$	−2.21985	−0.0833682	−0.0416841	+	0.999131i	$0.513272\pi$
$710$	0.571505	0.0214482
$711$	75.1480	2.81827
$712$	10.3458	0.387727
$713$	11.0839	0.415096
$714$	−29.4903	−1.10364
$715$	−0.322382	−0.0120564
$716$	−23.9431	−0.894794
$717$	−19.1152	−0.713870
$718$	−11.4062	−0.425676
$719$	−22.6847	−0.845997	−0.422999	−	0.906130i	$-0.639023\pi$
$719$	−22.6847	−0.845997	−0.422999	+	0.906130i	$0.639023\pi$
$720$	0.519554	0.0193626
$721$	41.1194	1.53137
$722$	6.55120	0.243810
$723$	−52.3095	−1.94541
$724$	−18.4588	−0.686015
$725$	−14.5766	−0.541360
$726$	36.8287	1.36684
$727$	19.1762	0.711207	0.355603	−	0.934637i	$-0.384275\pi$
$727$	19.1762	0.711207	0.355603	+	0.934637i	$0.384275\pi$
$728$	2.05607	0.0762028
$729$	−12.9177	−0.478432
$730$	−0.0773758	−0.00286381
$731$	−4.80833	−0.177843
$732$	19.1708	0.708572
$733$	−20.2089	−0.746433	−0.373217	−	0.927744i	$-0.621745\pi$
$733$	−20.2089	−0.746433	−0.373217	+	0.927744i	$0.621745\pi$
$734$	30.4298	1.12318
$735$	0.224028	0.00826340
$736$	3.78567	0.139542
$737$	−8.05247	−0.296616
$738$	−20.1950	−0.743389
$739$	−32.2086	−1.18481	−0.592406	−	0.805640i	$-0.701822\pi$
$739$	−32.2086	−1.18481	−0.592406	+	0.805640i	$0.701822\pi$
$740$	0.323551	0.0118940
$741$	9.02432	0.331517
$742$	−28.1531	−1.03353
$743$	−31.9424	−1.17185	−0.585926	−	0.810364i	$-0.699269\pi$
$743$	−31.9424	−1.17185	−0.585926	+	0.810364i	$0.699269\pi$
$744$	−8.99316	−0.329705
$745$	1.68175	0.0616145
$746$	3.64341	0.133395
$747$	−36.2686	−1.32700
$748$	−18.6441	−0.681694
$749$	−27.1555	−0.992240
$750$	−2.47850	−0.0905019
$751$	34.8788	1.27274	0.636372	−	0.771382i	$-0.280434\pi$
$751$	34.8788	1.27274	0.636372	+	0.771382i	$0.280434\pi$
$752$	−8.94878	−0.326329
$753$	−33.1465	−1.20792
$754$	−2.43076	−0.0885229
$755$	0.652919	0.0237621
$756$	26.0486	0.947377
$757$	−13.9421	−0.506736	−0.253368	−	0.967370i	$-0.581538\pi$
$757$	−13.9421	−0.506736	−0.253368	+	0.967370i	$0.581538\pi$
$758$	−12.7096	−0.461633
$759$	−55.7539	−2.02374
$760$	0.284888	0.0103340
$761$	46.8756	1.69924	0.849620	−	0.527396i	$-0.176831\pi$
$761$	46.8756	1.69924	0.849620	+	0.527396i	$0.176831\pi$
$762$	−42.4969	−1.53950
$763$	5.33786	0.193243
$764$	23.4563	0.848618
$765$	2.02023	0.0730415
$766$	−7.40039	−0.267387
$767$	5.90279	0.213137
$768$	−3.07158	−0.110836
$769$	25.9606	0.936163	0.468081	−	0.883685i	$-0.344945\pi$
$769$	25.9606	0.936163	0.468081	+	0.883685i	$0.344945\pi$
$770$	−0.955935	−0.0344495
$771$	−41.2123	−1.48423
$772$	−18.7129	−0.673492
$773$	−51.9283	−1.86773	−0.933865	−	0.357626i	$-0.883586\pi$
$773$	−51.9283	−1.86773	−0.933865	+	0.357626i	$0.883586\pi$
$774$	7.95693	0.286006
$775$	14.6202	0.525174
$776$	15.3644	0.551549
$777$	30.3908	1.09026
$778$	−25.0506	−0.898108
$779$	−11.0736	−0.396751
$780$	−0.206519	−0.00739458
$781$	33.9376	1.21438
$782$	14.7202	0.526392
$783$	−30.7956	−1.10054
$784$	−0.903297	−0.0322606
$785$	−0.264779	−0.00945037
$786$	−4.17591	−0.148950
$787$	31.9210	1.13786	0.568930	−	0.822386i	$-0.307358\pi$
$787$	31.9210	1.13786	0.568930	+	0.822386i	$0.307358\pi$
$788$	12.3245	0.439042
$789$	−2.42292	−0.0862582
$790$	−0.942989	−0.0335500
$791$	48.9656	1.74102
$792$	30.8526	1.09630
$793$	−5.19718	−0.184557
$794$	−6.34783	−0.225276
$795$	2.82781	0.100292
$796$	−2.18874	−0.0775778
$797$	36.3848	1.28882	0.644409	−	0.764681i	$-0.277104\pi$
$797$	36.3848	1.28882	0.644409	+	0.764681i	$0.277104\pi$
$798$	26.7592	0.947265
$799$	−34.7963	−1.23101
$800$	4.99348	0.176546
$801$	−66.5712	−2.35218
$802$	12.9909	0.458726
$803$	−4.59479	−0.162147
$804$	−5.15845	−0.181925
$805$	0.754745	0.0266013
$806$	2.43804	0.0858761
$807$	−10.9562	−0.385676
$808$	−2.49968	−0.0879385
$809$	−12.7035	−0.446630	−0.223315	−	0.974746i	$-0.571688\pi$
$809$	−12.7035	−0.446630	−0.223315	+	0.974746i	$0.571688\pi$
$810$	−1.05776	−0.0371659
$811$	−11.2054	−0.393475	−0.196737	−	0.980456i	$-0.563035\pi$
$811$	−11.2054	−0.393475	−0.196737	+	0.980456i	$0.563035\pi$
$812$	−7.20775	−0.252942
$813$	−66.8736	−2.34536
$814$	19.2134	0.673429
$815$	−0.511333	−0.0179112
$816$	−11.9435	−0.418106
$817$	4.36304	0.152643
$818$	−3.12372	−0.109218
$819$	−13.2299	−0.462291
$820$	0.253416	0.00884966
$821$	21.2452	0.741463	0.370731	−	0.928740i	$-0.379107\pi$
$821$	21.2452	0.741463	0.370731	+	0.928740i	$0.379107\pi$
$822$	8.79743	0.306846
$823$	10.7871	0.376014	0.188007	−	0.982168i	$-0.439797\pi$
$823$	10.7871	0.376014	0.188007	+	0.982168i	$0.439797\pi$
$824$	16.6533	0.580144
$825$	−73.5420	−2.56041
$826$	17.5031	0.609012
$827$	14.9920	0.521324	0.260662	−	0.965430i	$-0.416059\pi$
$827$	14.9920	0.521324	0.260662	+	0.965430i	$0.416059\pi$
$828$	−24.3592	−0.846542
$829$	44.7112	1.55288	0.776441	−	0.630190i	$-0.217023\pi$
$829$	44.7112	1.55288	0.776441	+	0.630190i	$0.217023\pi$
$830$	0.455114	0.0157973
$831$	27.0819	0.939462
$832$	0.832702	0.0288687
$833$	−3.51237	−0.121696
$834$	17.6990	0.612867
$835$	0.994107	0.0344025
$836$	16.9174	0.585102
$837$	30.8878	1.06764
$838$	−24.8412	−0.858126
$839$	−6.78155	−0.234125	−0.117063	−	0.993125i	$-0.537348\pi$
$839$	−6.78155	−0.234125	−0.117063	+	0.993125i	$0.537348\pi$
$840$	−0.612377	−0.0211290
$841$	−20.4787	−0.706163
$842$	−15.8720	−0.546985
$843$	9.16313	0.315595
$844$	19.1578	0.659440
$845$	−0.993684	−0.0341838
$846$	57.5817	1.97970
$847$	−29.6055	−1.01726
$848$	−11.4019	−0.391544
$849$	−93.6919	−3.21550
$850$	19.4166	0.665983
$851$	−15.1697	−0.520009
$852$	21.7406	0.744820
$853$	−12.9134	−0.442145	−0.221072	−	0.975257i	$-0.570956\pi$
$853$	−12.9134	−0.442145	−0.221072	+	0.975257i	$0.570956\pi$
$854$	−15.4108	−0.527347
$855$	−1.83314	−0.0626919
$856$	−10.9979	−0.375901
$857$	6.43280	0.219740	0.109870	−	0.993946i	$-0.464957\pi$
$857$	6.43280	0.219740	0.109870	+	0.993946i	$0.464957\pi$
$858$	−12.2637	−0.418676
$859$	−19.9285	−0.679950	−0.339975	−	0.940434i	$-0.610419\pi$
$859$	−19.9285	−0.679950	−0.339975	+	0.940434i	$0.610419\pi$
$860$	−0.0998470	−0.00340475
$861$	23.8030	0.811205
$862$	6.72883	0.229185
$863$	−10.6384	−0.362135	−0.181068	−	0.983471i	$-0.557955\pi$
$863$	−10.6384	−0.362135	−0.181068	+	0.983471i	$0.557955\pi$
$864$	10.5496	0.358905
$865$	−0.502189	−0.0170749
$866$	22.3051	0.757958
$867$	5.77593	0.196161
$868$	7.22933	0.245380
$869$	−55.9973	−1.89958
$870$	0.723975	0.0245451
$871$	1.39845	0.0473847
$872$	2.16182	0.0732084
$873$	−98.8634	−3.34602
$874$	−13.3569	−0.451805
$875$	1.99239	0.0673551
$876$	−2.94345	−0.0994499
$877$	−4.26755	−0.144105	−0.0720524	−	0.997401i	$-0.522955\pi$
$877$	−4.26755	−0.144105	−0.0720524	+	0.997401i	$0.522955\pi$
$878$	−21.7139	−0.732809
$879$	24.9387	0.841161
$880$	−0.387152	−0.0130509
$881$	42.3384	1.42642	0.713208	−	0.700952i	$-0.247241\pi$
$881$	42.3384	1.42642	0.713208	+	0.700952i	$0.247241\pi$
$882$	5.81235	0.195712
$883$	34.0984	1.14750	0.573751	−	0.819030i	$-0.305488\pi$
$883$	34.0984	1.14750	0.573751	+	0.819030i	$0.305488\pi$
$884$	3.23787	0.108901
$885$	−1.75808	−0.0590973
$886$	−24.6967	−0.829701
$887$	23.1153	0.776136	0.388068	−	0.921631i	$-0.373143\pi$
$887$	23.1153	0.776136	0.388068	+	0.921631i	$0.373143\pi$
$888$	12.3082	0.413036
$889$	34.1620	1.14576
$890$	0.835364	0.0280015
$891$	−62.8127	−2.10430
$892$	−10.6157	−0.355440
$893$	31.5739	1.05658
$894$	63.9753	2.13965
$895$	−1.93326	−0.0646217
$896$	2.46915	0.0824885
$897$	9.68264	0.323294
$898$	−9.60108	−0.320392
$899$	−8.54678	−0.285051
$900$	−32.1310	−1.07103
$901$	−44.3351	−1.47702
$902$	15.0485	0.501061
$903$	−9.37851	−0.312097
$904$	19.8309	0.659568
$905$	−1.49044	−0.0495437
$906$	24.8376	0.825175
$907$	36.6524	1.21702	0.608511	−	0.793546i	$-0.291767\pi$
$907$	36.6524	1.21702	0.608511	+	0.793546i	$0.291767\pi$
$908$	24.0971	0.799692
$909$	16.0844	0.533487
$910$	0.166015	0.00550334
$911$	40.0521	1.32698	0.663492	−	0.748183i	$-0.269074\pi$
$911$	40.0521	1.32698	0.663492	+	0.748183i	$0.269074\pi$
$912$	10.8374	0.358862
$913$	27.0260	0.894429
$914$	−31.9164	−1.05570
$915$	1.54792	0.0511728
$916$	−4.67786	−0.154561
$917$	3.35689	0.110854
$918$	41.0209	1.35389
$919$	−28.0166	−0.924182	−0.462091	−	0.886833i	$-0.652901\pi$
$919$	−28.0166	−0.924182	−0.462091	+	0.886833i	$0.652901\pi$
$920$	0.305670	0.0100776
$921$	−25.7741	−0.849285
$922$	35.1428	1.15737
$923$	−5.89385	−0.193998
$924$	−36.3647	−1.19631
$925$	−20.0095	−0.657909
$926$	27.6982	0.910218
$927$	−107.157	−3.51950
$928$	−2.91912	−0.0958248
$929$	34.9235	1.14580	0.572901	−	0.819624i	$-0.305818\pi$
$929$	34.9235	1.14580	0.572901	+	0.819624i	$0.305818\pi$
$930$	−0.726143	−0.0238112
$931$	3.18709	0.104453
$932$	−11.2653	−0.369007
$933$	−61.7127	−2.02038
$934$	−7.36990	−0.241151
$935$	−1.50540	−0.0492317
$936$	−5.35809	−0.175135
$937$	11.2635	0.367963	0.183982	−	0.982930i	$-0.441101\pi$
$937$	11.2635	0.367963	0.183982	+	0.982930i	$0.441101\pi$
$938$	4.14673	0.135395
$939$	−20.5422	−0.670369
$940$	−0.722560	−0.0235673
$941$	−18.5935	−0.606129	−0.303065	−	0.952970i	$-0.598010\pi$
$941$	−18.5935	−0.606129	−0.303065	+	0.952970i	$0.598010\pi$
$942$	−10.0724	−0.328178
$943$	−11.8814	−0.386910
$944$	7.08872	0.230718
$945$	2.10326	0.0684192
$946$	−5.92920	−0.192775
$947$	4.71902	0.153348	0.0766738	−	0.997056i	$-0.475570\pi$
$947$	4.71902	0.153348	0.0766738	+	0.997056i	$0.475570\pi$
$948$	−35.8722	−1.16507
$949$	0.797966	0.0259031
$950$	−17.6184	−0.571617
$951$	−19.4164	−0.629618
$952$	9.60101	0.311171
$953$	−28.1369	−0.911442	−0.455721	−	0.890123i	$-0.650619\pi$
$953$	−28.1369	−0.911442	−0.455721	+	0.890123i	$0.650619\pi$
$954$	73.3667	2.37533
$955$	1.89395	0.0612868
$956$	6.22325	0.201274
$957$	42.9917	1.38972
$958$	8.49258	0.274383
$959$	−7.07199	−0.228367
$960$	−0.248011	−0.00800453
$961$	−22.4276	−0.723472
$962$	−3.33674	−0.107581
$963$	70.7670	2.28044
$964$	17.0302	0.548505
$965$	−1.51095	−0.0486393
$966$	28.7112	0.923769
$967$	−1.51846	−0.0488305	−0.0244153	−	0.999702i	$-0.507772\pi$
$967$	−1.51846	−0.0488305	−0.0244153	+	0.999702i	$0.507772\pi$
$968$	−11.9901	−0.385378
$969$	42.1400	1.35373
$970$	1.24058	0.0398326
$971$	3.84651	0.123440	0.0617201	−	0.998093i	$-0.480341\pi$
$971$	3.84651	0.123440	0.0617201	+	0.998093i	$0.480341\pi$
$972$	−8.58934	−0.275503
$973$	−14.2277	−0.456120
$974$	−8.60314	−0.275662
$975$	12.7719	0.409027
$976$	−6.24134	−0.199781
$977$	−16.4607	−0.526625	−0.263312	−	0.964711i	$-0.584815\pi$
$977$	−16.4607	−0.526625	−0.263312	+	0.964711i	$0.584815\pi$
$978$	−19.4516	−0.621993
$979$	49.6063	1.58542
$980$	−0.0729358	−0.00232985
$981$	−13.9104	−0.444125
$982$	−1.89124	−0.0603518
$983$	−5.46972	−0.174457	−0.0872284	−	0.996188i	$-0.527801\pi$
$983$	−5.46972	−0.174457	−0.0872284	+	0.996188i	$0.527801\pi$
$984$	9.64017	0.307317
$985$	0.995130	0.0317075
$986$	−11.3507	−0.361479
$987$	−67.8692	−2.16030
$988$	−2.93801	−0.0934705
$989$	4.68131	0.148857
$990$	2.49116	0.0791743
$991$	−50.7292	−1.61147	−0.805733	−	0.592279i	$-0.798228\pi$
$991$	−50.7292	−1.61147	−0.805733	+	0.592279i	$0.798228\pi$
$992$	2.92786	0.0929597
$993$	−75.2181	−2.38697
$994$	−17.4766	−0.554325
$995$	−0.176727	−0.00560264
$996$	17.3130	0.548583
$997$	−45.7089	−1.44761	−0.723807	−	0.690002i	$-0.757610\pi$
$997$	−45.7089	−1.44761	−0.723807	+	0.690002i	$0.757610\pi$
$998$	2.22949	0.0705734
$999$	−42.2736	−1.33748

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.h.1.2	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.h.1.2	✓	42	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.07158 q^{3} +1.00000 q^{4} +0.0807440 q^{5} +3.07158 q^{6} -2.46915 q^{7} -1.00000 q^{8} +6.43459 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.07158 q^{3} +1.00000 q^{4} +0.0807440 q^{5} +3.07158 q^{6} -2.46915 q^{7} -1.00000 q^{8} +6.43459 q^{9} -0.0807440 q^{10} -4.79480 q^{11} -3.07158 q^{12} +0.832702 q^{13} +2.46915 q^{14} -0.248011 q^{15} +1.00000 q^{16} +3.88839 q^{17} -6.43459 q^{18} -3.52829 q^{19} +0.0807440 q^{20} +7.58419 q^{21} +4.79480 q^{22} -3.78567 q^{23} +3.07158 q^{24} -4.99348 q^{25} -0.832702 q^{26} -10.5496 q^{27} -2.46915 q^{28} +2.91912 q^{29} +0.248011 q^{30} -2.92786 q^{31} -1.00000 q^{32} +14.7276 q^{33} -3.88839 q^{34} -0.199369 q^{35} +6.43459 q^{36} +4.00713 q^{37} +3.52829 q^{38} -2.55771 q^{39} -0.0807440 q^{40} +3.13851 q^{41} -7.58419 q^{42} -1.23659 q^{43} -4.79480 q^{44} +0.519554 q^{45} +3.78567 q^{46} -8.94878 q^{47} -3.07158 q^{48} -0.903297 q^{49} +4.99348 q^{50} -11.9435 q^{51} +0.832702 q^{52} -11.4019 q^{53} +10.5496 q^{54} -0.387152 q^{55} +2.46915 q^{56} +10.8374 q^{57} -2.91912 q^{58} +7.08872 q^{59} -0.248011 q^{60} -6.24134 q^{61} +2.92786 q^{62} -15.8880 q^{63} +1.00000 q^{64} +0.0672356 q^{65} -14.7276 q^{66} +1.67942 q^{67} +3.88839 q^{68} +11.6280 q^{69} +0.199369 q^{70} -7.07799 q^{71} -6.43459 q^{72} +0.958286 q^{73} -4.00713 q^{74} +15.3379 q^{75} -3.52829 q^{76} +11.8391 q^{77} +2.55771 q^{78} +11.6788 q^{79} +0.0807440 q^{80} +13.1002 q^{81} -3.13851 q^{82} -5.63651 q^{83} +7.58419 q^{84} +0.313964 q^{85} +1.23659 q^{86} -8.96630 q^{87} +4.79480 q^{88} -10.3458 q^{89} -0.519554 q^{90} -2.05607 q^{91} -3.78567 q^{92} +8.99316 q^{93} +8.94878 q^{94} -0.284888 q^{95} +3.07158 q^{96} -15.3644 q^{97} +0.903297 q^{98} -30.8526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

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