LMFDB - Embedded newform 4010.2.a.j.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 16 x^{10} + 30 x^{9} + 93 x^{8} - 162 x^{7} - 238 x^{6} + 391 x^{5} + 240 x^{4} + \cdots - 8 $ x^12 - 2x^11 - 16x^10 + 30x^9 + 93x^8 - 162x^7 - 238x^6 + 391x^5 + 240x^4 - 408x^3 - 42x^2 + 120*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-2.50579$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.50579 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.50579 q^{6} -4.61369 q^{7} +1.00000 q^{8} +3.27901 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.50579 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.50579 q^{6} -4.61369 q^{7} +1.00000 q^{8} +3.27901 q^{9} -1.00000 q^{10} -1.79618 q^{11} +2.50579 q^{12} +1.88878 q^{13} -4.61369 q^{14} -2.50579 q^{15} +1.00000 q^{16} -4.96122 q^{17} +3.27901 q^{18} -3.39282 q^{19} -1.00000 q^{20} -11.5610 q^{21} -1.79618 q^{22} -3.88813 q^{23} +2.50579 q^{24} +1.00000 q^{25} +1.88878 q^{26} +0.699137 q^{27} -4.61369 q^{28} +1.77073 q^{29} -2.50579 q^{30} +7.02789 q^{31} +1.00000 q^{32} -4.50086 q^{33} -4.96122 q^{34} +4.61369 q^{35} +3.27901 q^{36} -10.6902 q^{37} -3.39282 q^{38} +4.73289 q^{39} -1.00000 q^{40} +0.471863 q^{41} -11.5610 q^{42} -1.80366 q^{43} -1.79618 q^{44} -3.27901 q^{45} -3.88813 q^{46} -13.1682 q^{47} +2.50579 q^{48} +14.2862 q^{49} +1.00000 q^{50} -12.4318 q^{51} +1.88878 q^{52} -1.34842 q^{53} +0.699137 q^{54} +1.79618 q^{55} -4.61369 q^{56} -8.50172 q^{57} +1.77073 q^{58} -0.0911359 q^{59} -2.50579 q^{60} -2.62310 q^{61} +7.02789 q^{62} -15.1283 q^{63} +1.00000 q^{64} -1.88878 q^{65} -4.50086 q^{66} -6.15633 q^{67} -4.96122 q^{68} -9.74287 q^{69} +4.61369 q^{70} +12.4907 q^{71} +3.27901 q^{72} -7.44735 q^{73} -10.6902 q^{74} +2.50579 q^{75} -3.39282 q^{76} +8.28702 q^{77} +4.73289 q^{78} -10.5899 q^{79} -1.00000 q^{80} -8.08513 q^{81} +0.471863 q^{82} +11.7519 q^{83} -11.5610 q^{84} +4.96122 q^{85} -1.80366 q^{86} +4.43710 q^{87} -1.79618 q^{88} +4.85113 q^{89} -3.27901 q^{90} -8.71423 q^{91} -3.88813 q^{92} +17.6104 q^{93} -13.1682 q^{94} +3.39282 q^{95} +2.50579 q^{96} -4.19615 q^{97} +14.2862 q^{98} -5.88969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q + 12 * q^2 - 2 * q^3 + 12 * q^4 - 12 * q^5 - 2 * q^6 - 9 * q^7 + 12 * q^8	\( 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8} - 12 q^{10} + q^{11} - 2 q^{12} - 6 q^{13} - 9 q^{14} + 2 q^{15} + 12 q^{16} - 11 q^{17} - 13 q^{19} - 12 q^{20} - 14 q^{21} + q^{22} - 21 q^{23} - 2 q^{24} + 12 q^{25} - 6 q^{26} - 2 q^{27} - 9 q^{28} - 10 q^{29} + 2 q^{30} - 11 q^{31} + 12 q^{32} - 22 q^{33} - 11 q^{34} + 9 q^{35} - 29 q^{37} - 13 q^{38} - 2 q^{39} - 12 q^{40} - q^{41} - 14 q^{42} - 23 q^{43} + q^{44} - 21 q^{46} - 17 q^{47} - 2 q^{48} - 3 q^{49} + 12 q^{50} - 19 q^{51} - 6 q^{52} - 47 q^{53} - 2 q^{54} - q^{55} - 9 q^{56} - 11 q^{57} - 10 q^{58} + 14 q^{59} + 2 q^{60} - 22 q^{61} - 11 q^{62} - 28 q^{63} + 12 q^{64} + 6 q^{65} - 22 q^{66} - 28 q^{67} - 11 q^{68} - q^{69} + 9 q^{70} - 18 q^{71} - 2 q^{73} - 29 q^{74} - 2 q^{75} - 13 q^{76} - 11 q^{77} - 2 q^{78} - 39 q^{79} - 12 q^{80} - 44 q^{81} - q^{82} - 5 q^{83} - 14 q^{84} + 11 q^{85} - 23 q^{86} - 6 q^{87} + q^{88} - 8 q^{89} - 12 q^{91} - 21 q^{92} - 30 q^{93} - 17 q^{94} + 13 q^{95} - 2 q^{96} - 32 q^{97} - 3 q^{98} - 13 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 - 2 * q^3 + 12 * q^4 - 12 * q^5 - 2 * q^6 - 9 * q^7 + 12 * q^8 - 12 * q^10 + q^11 - 2 * q^12 - 6 * q^13 - 9 * q^14 + 2 * q^15 + 12 * q^16 - 11 * q^17 - 13 * q^19 - 12 * q^20 - 14 * q^21 + q^22 - 21 * q^23 - 2 * q^24 + 12 * q^25 - 6 * q^26 - 2 * q^27 - 9 * q^28 - 10 * q^29 + 2 * q^30 - 11 * q^31 + 12 * q^32 - 22 * q^33 - 11 * q^34 + 9 * q^35 - 29 * q^37 - 13 * q^38 - 2 * q^39 - 12 * q^40 - q^41 - 14 * q^42 - 23 * q^43 + q^44 - 21 * q^46 - 17 * q^47 - 2 * q^48 - 3 * q^49 + 12 * q^50 - 19 * q^51 - 6 * q^52 - 47 * q^53 - 2 * q^54 - q^55 - 9 * q^56 - 11 * q^57 - 10 * q^58 + 14 * q^59 + 2 * q^60 - 22 * q^61 - 11 * q^62 - 28 * q^63 + 12 * q^64 + 6 * q^65 - 22 * q^66 - 28 * q^67 - 11 * q^68 - q^69 + 9 * q^70 - 18 * q^71 - 2 * q^73 - 29 * q^74 - 2 * q^75 - 13 * q^76 - 11 * q^77 - 2 * q^78 - 39 * q^79 - 12 * q^80 - 44 * q^81 - q^82 - 5 * q^83 - 14 * q^84 + 11 * q^85 - 23 * q^86 - 6 * q^87 + q^88 - 8 * q^89 - 12 * q^91 - 21 * q^92 - 30 * q^93 - 17 * q^94 + 13 * q^95 - 2 * q^96 - 32 * q^97 - 3 * q^98 - 13 * 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
$3$	2.50579	1.44672	0.723361	−	0.690470i	$-0.242596\pi$
$3$	2.50579	1.44672	0.723361	+	0.690470i	$0.242596\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.50579	1.02299
$7$	−4.61369	−1.74381	−0.871906	−	0.489673i	$-0.837116\pi$
$7$	−4.61369	−1.74381	−0.871906	+	0.489673i	$0.837116\pi$
$8$	1.00000	0.353553
$9$	3.27901	1.09300
$10$	−1.00000	−0.316228
$11$	−1.79618	−0.541569	−0.270784	−	0.962640i	$-0.587283\pi$
$11$	−1.79618	−0.541569	−0.270784	+	0.962640i	$0.587283\pi$
$12$	2.50579	0.723361
$13$	1.88878	0.523852	0.261926	−	0.965088i	$-0.415642\pi$
$13$	1.88878	0.523852	0.261926	+	0.965088i	$0.415642\pi$
$14$	−4.61369	−1.23306
$15$	−2.50579	−0.646993
$16$	1.00000	0.250000
$17$	−4.96122	−1.20327	−0.601636	−	0.798770i	$-0.705484\pi$
$17$	−4.96122	−1.20327	−0.601636	+	0.798770i	$0.705484\pi$
$18$	3.27901	0.772870
$19$	−3.39282	−0.778367	−0.389184	−	0.921160i	$-0.627243\pi$
$19$	−3.39282	−0.778367	−0.389184	+	0.921160i	$0.627243\pi$
$20$	−1.00000	−0.223607
$21$	−11.5610	−2.52281
$22$	−1.79618	−0.382947
$23$	−3.88813	−0.810732	−0.405366	−	0.914154i	$-0.632856\pi$
$23$	−3.88813	−0.810732	−0.405366	+	0.914154i	$0.632856\pi$
$24$	2.50579	0.511493
$25$	1.00000	0.200000
$26$	1.88878	0.370419
$27$	0.699137	0.134549
$28$	−4.61369	−0.871906
$29$	1.77073	0.328817	0.164408	−	0.986392i	$-0.447428\pi$
$29$	1.77073	0.328817	0.164408	+	0.986392i	$0.447428\pi$
$30$	−2.50579	−0.457493
$31$	7.02789	1.26225	0.631123	−	0.775683i	$-0.282594\pi$
$31$	7.02789	1.26225	0.631123	+	0.775683i	$0.282594\pi$
$32$	1.00000	0.176777
$33$	−4.50086	−0.783499
$34$	−4.96122	−0.850842
$35$	4.61369	0.779856
$36$	3.27901	0.546501
$37$	−10.6902	−1.75746	−0.878728	−	0.477322i	$-0.841607\pi$
$37$	−10.6902	−1.75746	−0.878728	+	0.477322i	$0.841607\pi$
$38$	−3.39282	−0.550389
$39$	4.73289	0.757868
$40$	−1.00000	−0.158114
$41$	0.471863	0.0736927	0.0368463	−	0.999321i	$-0.488269\pi$
$41$	0.471863	0.0736927	0.0368463	+	0.999321i	$0.488269\pi$
$42$	−11.5610	−1.78390
$43$	−1.80366	−0.275056	−0.137528	−	0.990498i	$-0.543916\pi$
$43$	−1.80366	−0.275056	−0.137528	+	0.990498i	$0.543916\pi$
$44$	−1.79618	−0.270784
$45$	−3.27901	−0.488806
$46$	−3.88813	−0.573274
$47$	−13.1682	−1.92078	−0.960390	−	0.278658i	$-0.910110\pi$
$47$	−13.1682	−1.92078	−0.960390	+	0.278658i	$0.910110\pi$
$48$	2.50579	0.361680
$49$	14.2862	2.04088
$50$	1.00000	0.141421
$51$	−12.4318	−1.74080
$52$	1.88878	0.261926
$53$	−1.34842	−0.185220	−0.0926099	−	0.995702i	$-0.529521\pi$
$53$	−1.34842	−0.185220	−0.0926099	+	0.995702i	$0.529521\pi$
$54$	0.699137	0.0951405
$55$	1.79618	0.242197
$56$	−4.61369	−0.616531
$57$	−8.50172	−1.12608
$58$	1.77073	0.232509
$59$	−0.0911359	−0.0118649	−0.00593244	−	0.999982i	$-0.501888\pi$
$59$	−0.0911359	−0.0118649	−0.00593244	+	0.999982i	$0.501888\pi$
$60$	−2.50579	−0.323497
$61$	−2.62310	−0.335853	−0.167927	−	0.985799i	$-0.553707\pi$
$61$	−2.62310	−0.335853	−0.167927	+	0.985799i	$0.553707\pi$
$62$	7.02789	0.892542
$63$	−15.1283	−1.90599
$64$	1.00000	0.125000
$65$	−1.88878	−0.234274
$66$	−4.50086	−0.554017
$67$	−6.15633	−0.752115	−0.376058	−	0.926596i	$-0.622721\pi$
$67$	−6.15633	−0.752115	−0.376058	+	0.926596i	$0.622721\pi$
$68$	−4.96122	−0.601636
$69$	−9.74287	−1.17290
$70$	4.61369	0.551442
$71$	12.4907	1.48238	0.741190	−	0.671296i	$-0.234262\pi$
$71$	12.4907	1.48238	0.741190	+	0.671296i	$0.234262\pi$
$72$	3.27901	0.386435
$73$	−7.44735	−0.871647	−0.435823	−	0.900032i	$-0.643543\pi$
$73$	−7.44735	−0.871647	−0.435823	+	0.900032i	$0.643543\pi$
$74$	−10.6902	−1.24271
$75$	2.50579	0.289344
$76$	−3.39282	−0.389184
$77$	8.28702	0.944394
$78$	4.73289	0.535894
$79$	−10.5899	−1.19145	−0.595727	−	0.803187i	$-0.703136\pi$
$79$	−10.5899	−1.19145	−0.595727	+	0.803187i	$0.703136\pi$
$80$	−1.00000	−0.111803
$81$	−8.08513	−0.898348
$82$	0.471863	0.0521086
$83$	11.7519	1.28994	0.644969	−	0.764209i	$-0.276870\pi$
$83$	11.7519	1.28994	0.644969	+	0.764209i	$0.276870\pi$
$84$	−11.5610	−1.26140
$85$	4.96122	0.538120
$86$	−1.80366	−0.194494
$87$	4.43710	0.475707
$88$	−1.79618	−0.191473
$89$	4.85113	0.514218	0.257109	−	0.966382i	$-0.417230\pi$
$89$	4.85113	0.514218	0.257109	+	0.966382i	$0.417230\pi$
$90$	−3.27901	−0.345638
$91$	−8.71423	−0.913500
$92$	−3.88813	−0.405366
$93$	17.6104	1.82612
$94$	−13.1682	−1.35820
$95$	3.39282	0.348096
$96$	2.50579	0.255747
$97$	−4.19615	−0.426054	−0.213027	−	0.977046i	$-0.568332\pi$
$97$	−4.19615	−0.426054	−0.213027	+	0.977046i	$0.568332\pi$
$98$	14.2862	1.44312
$99$	−5.88969	−0.591936
$100$	1.00000	0.100000
$101$	−3.25338	−0.323723	−0.161862	−	0.986813i	$-0.551750\pi$
$101$	−3.25338	−0.323723	−0.161862	+	0.986813i	$0.551750\pi$
$102$	−12.4318	−1.23093
$103$	8.34824	0.822576	0.411288	−	0.911505i	$-0.365079\pi$
$103$	8.34824	0.822576	0.411288	+	0.911505i	$0.365079\pi$
$104$	1.88878	0.185210
$105$	11.5610	1.12823
$106$	−1.34842	−0.130970
$107$	−0.616692	−0.0596178	−0.0298089	−	0.999556i	$-0.509490\pi$
$107$	−0.616692	−0.0596178	−0.0298089	+	0.999556i	$0.509490\pi$
$108$	0.699137	0.0672745
$109$	4.29776	0.411651	0.205825	−	0.978589i	$-0.434012\pi$
$109$	4.29776	0.411651	0.205825	+	0.978589i	$0.434012\pi$
$110$	1.79618	0.171259
$111$	−26.7874	−2.54255
$112$	−4.61369	−0.435953
$113$	7.38301	0.694535	0.347268	−	0.937766i	$-0.387110\pi$
$113$	7.38301	0.694535	0.347268	+	0.937766i	$0.387110\pi$
$114$	−8.50172	−0.796259
$115$	3.88813	0.362570
$116$	1.77073	0.164408
$117$	6.19331	0.572572
$118$	−0.0911359	−0.00838974
$119$	22.8895	2.09828
$120$	−2.50579	−0.228747
$121$	−7.77374	−0.706704
$122$	−2.62310	−0.237484
$123$	1.18239	0.106613
$124$	7.02789	0.631123
$125$	−1.00000	−0.0894427
$126$	−15.1283	−1.34774
$127$	4.40821	0.391166	0.195583	−	0.980687i	$-0.437340\pi$
$127$	4.40821	0.391166	0.195583	+	0.980687i	$0.437340\pi$
$128$	1.00000	0.0883883
$129$	−4.51961	−0.397929
$130$	−1.88878	−0.165657
$131$	4.14777	0.362392	0.181196	−	0.983447i	$-0.442003\pi$
$131$	4.14777	0.362392	0.181196	+	0.983447i	$0.442003\pi$
$132$	−4.50086	−0.391749
$133$	15.6534	1.35733
$134$	−6.15633	−0.531826
$135$	−0.699137	−0.0601721
$136$	−4.96122	−0.425421
$137$	−8.58617	−0.733566	−0.366783	−	0.930307i	$-0.619541\pi$
$137$	−8.58617	−0.733566	−0.366783	+	0.930307i	$0.619541\pi$
$138$	−9.74287	−0.829368
$139$	12.9892	1.10173	0.550864	−	0.834595i	$-0.314298\pi$
$139$	12.9892	1.10173	0.550864	+	0.834595i	$0.314298\pi$
$140$	4.61369	0.389928
$141$	−32.9968	−2.77883
$142$	12.4907	1.04820
$143$	−3.39258	−0.283702
$144$	3.27901	0.273251
$145$	−1.77073	−0.147051
$146$	−7.44735	−0.616347
$147$	35.7982	2.95258
$148$	−10.6902	−0.878728
$149$	12.0696	0.988779	0.494389	−	0.869241i	$-0.335392\pi$
$149$	12.0696	0.988779	0.494389	+	0.869241i	$0.335392\pi$
$150$	2.50579	0.204597
$151$	9.19767	0.748496	0.374248	−	0.927329i	$-0.377901\pi$
$151$	9.19767	0.748496	0.374248	+	0.927329i	$0.377901\pi$
$152$	−3.39282	−0.275194
$153$	−16.2679	−1.31518
$154$	8.28702	0.667787
$155$	−7.02789	−0.564493
$156$	4.73289	0.378934
$157$	−13.4576	−1.07403	−0.537015	−	0.843573i	$-0.680448\pi$
$157$	−13.4576	−1.07403	−0.537015	+	0.843573i	$0.680448\pi$
$158$	−10.5899	−0.842485
$159$	−3.37886	−0.267961
$160$	−1.00000	−0.0790569
$161$	17.9387	1.41376
$162$	−8.08513	−0.635228
$163$	5.71056	0.447286	0.223643	−	0.974671i	$-0.428205\pi$
$163$	5.71056	0.447286	0.223643	+	0.974671i	$0.428205\pi$
$164$	0.471863	0.0368463
$165$	4.50086	0.350391
$166$	11.7519	0.912124
$167$	−18.4736	−1.42953	−0.714767	−	0.699363i	$-0.753467\pi$
$167$	−18.4736	−1.42953	−0.714767	+	0.699363i	$0.753467\pi$
$168$	−11.5610	−0.891948
$169$	−9.43253	−0.725579
$170$	4.96122	0.380508
$171$	−11.1251	−0.850757
$172$	−1.80366	−0.137528
$173$	−17.5797	−1.33656	−0.668280	−	0.743910i	$-0.732969\pi$
$173$	−17.5797	−1.33656	−0.668280	+	0.743910i	$0.732969\pi$
$174$	4.43710	0.336375
$175$	−4.61369	−0.348762
$176$	−1.79618	−0.135392
$177$	−0.228368	−0.0171652
$178$	4.85113	0.363607
$179$	11.0591	0.826597	0.413299	−	0.910596i	$-0.364377\pi$
$179$	11.0591	0.826597	0.413299	+	0.910596i	$0.364377\pi$
$180$	−3.27901	−0.244403
$181$	0.675734	0.0502269	0.0251135	−	0.999685i	$-0.492005\pi$
$181$	0.675734	0.0502269	0.0251135	+	0.999685i	$0.492005\pi$
$182$	−8.71423	−0.645942
$183$	−6.57295	−0.485886
$184$	−3.88813	−0.286637
$185$	10.6902	0.785958
$186$	17.6104	1.29126
$187$	8.91124	0.651654
$188$	−13.1682	−0.960390
$189$	−3.22560	−0.234628
$190$	3.39282	0.246141
$191$	0.909046	0.0657762	0.0328881	−	0.999459i	$-0.489529\pi$
$191$	0.909046	0.0657762	0.0328881	+	0.999459i	$0.489529\pi$
$192$	2.50579	0.180840
$193$	3.89430	0.280318	0.140159	−	0.990129i	$-0.455239\pi$
$193$	3.89430	0.280318	0.140159	+	0.990129i	$0.455239\pi$
$194$	−4.19615	−0.301266
$195$	−4.73289	−0.338929
$196$	14.2862	1.02044
$197$	−20.9893	−1.49542	−0.747712	−	0.664023i	$-0.768848\pi$
$197$	−20.9893	−1.49542	−0.747712	+	0.664023i	$0.768848\pi$
$198$	−5.88969	−0.418562
$199$	−10.6981	−0.758365	−0.379182	−	0.925322i	$-0.623795\pi$
$199$	−10.6981	−0.758365	−0.379182	+	0.925322i	$0.623795\pi$
$200$	1.00000	0.0707107
$201$	−15.4265	−1.08810
$202$	−3.25338	−0.228907
$203$	−8.16962	−0.573395
$204$	−12.4318	−0.870400
$205$	−0.471863	−0.0329564
$206$	8.34824	0.581649
$207$	−12.7492	−0.886132
$208$	1.88878	0.130963
$209$	6.09412	0.421539
$210$	11.5610	0.797782
$211$	11.1320	0.766356	0.383178	−	0.923675i	$-0.374830\pi$
$211$	11.1320	0.766356	0.383178	+	0.923675i	$0.374830\pi$
$212$	−1.34842	−0.0926099
$213$	31.2993	2.14459
$214$	−0.616692	−0.0421562
$215$	1.80366	0.123009
$216$	0.699137	0.0475702
$217$	−32.4245	−2.20112
$218$	4.29776	0.291081
$219$	−18.6615	−1.26103
$220$	1.79618	0.121098
$221$	−9.37063	−0.630337
$222$	−26.7874	−1.79785
$223$	−5.38697	−0.360738	−0.180369	−	0.983599i	$-0.557729\pi$
$223$	−5.38697	−0.360738	−0.180369	+	0.983599i	$0.557729\pi$
$224$	−4.61369	−0.308265
$225$	3.27901	0.218601
$226$	7.38301	0.491110
$227$	26.7131	1.77301	0.886504	−	0.462721i	$-0.153127\pi$
$227$	26.7131	1.77301	0.886504	+	0.462721i	$0.153127\pi$
$228$	−8.50172	−0.563040
$229$	−23.3817	−1.54511	−0.772555	−	0.634948i	$-0.781021\pi$
$229$	−23.3817	−1.54511	−0.772555	+	0.634948i	$0.781021\pi$
$230$	3.88813	0.256376
$231$	20.7656	1.36627
$232$	1.77073	0.116254
$233$	−14.6055	−0.956839	−0.478420	−	0.878131i	$-0.658790\pi$
$233$	−14.6055	−0.956839	−0.478420	+	0.878131i	$0.658790\pi$
$234$	6.19331	0.404869
$235$	13.1682	0.858999
$236$	−0.0911359	−0.00593244
$237$	−26.5361	−1.72370
$238$	22.8895	1.48371
$239$	14.9618	0.967799	0.483900	−	0.875123i	$-0.339220\pi$
$239$	14.9618	0.967799	0.483900	+	0.875123i	$0.339220\pi$
$240$	−2.50579	−0.161748
$241$	9.18041	0.591362	0.295681	−	0.955287i	$-0.404453\pi$
$241$	9.18041	0.591362	0.295681	+	0.955287i	$0.404453\pi$
$242$	−7.77374	−0.499715
$243$	−22.3571	−1.43421
$244$	−2.62310	−0.167927
$245$	−14.2862	−0.912709
$246$	1.18239	0.0753866
$247$	−6.40828	−0.407749
$248$	7.02789	0.446271
$249$	29.4478	1.86618
$250$	−1.00000	−0.0632456
$251$	10.4300	0.658335	0.329167	−	0.944272i	$-0.393232\pi$
$251$	10.4300	0.658335	0.329167	+	0.944272i	$0.393232\pi$
$252$	−15.1283	−0.952995
$253$	6.98379	0.439067
$254$	4.40821	0.276596
$255$	12.4318	0.778509
$256$	1.00000	0.0625000
$257$	17.6872	1.10330	0.551649	−	0.834077i	$-0.313999\pi$
$257$	17.6872	1.10330	0.551649	+	0.834077i	$0.313999\pi$
$258$	−4.51961	−0.281379
$259$	49.3213	3.06467
$260$	−1.88878	−0.117137
$261$	5.80625	0.359398
$262$	4.14777	0.256250
$263$	7.49119	0.461927	0.230963	−	0.972962i	$-0.425812\pi$
$263$	7.49119	0.461927	0.230963	+	0.972962i	$0.425812\pi$
$264$	−4.50086	−0.277009
$265$	1.34842	0.0828328
$266$	15.6534	0.959774
$267$	12.1559	0.743931
$268$	−6.15633	−0.376058
$269$	−15.9134	−0.970257	−0.485129	−	0.874443i	$-0.661227\pi$
$269$	−15.9134	−0.970257	−0.485129	+	0.874443i	$0.661227\pi$
$270$	−0.699137	−0.0425481
$271$	−28.4556	−1.72855	−0.864276	−	0.503018i	$-0.832223\pi$
$271$	−28.4556	−1.72855	−0.864276	+	0.503018i	$0.832223\pi$
$272$	−4.96122	−0.300818
$273$	−21.8361	−1.32158
$274$	−8.58617	−0.518709
$275$	−1.79618	−0.108314
$276$	−9.74287	−0.586452
$277$	24.1977	1.45390	0.726950	−	0.686690i	$-0.240937\pi$
$277$	24.1977	1.45390	0.726950	+	0.686690i	$0.240937\pi$
$278$	12.9892	0.779040
$279$	23.0445	1.37964
$280$	4.61369	0.275721
$281$	−4.27541	−0.255050	−0.127525	−	0.991835i	$-0.540703\pi$
$281$	−4.27541	−0.255050	−0.127525	+	0.991835i	$0.540703\pi$
$282$	−32.9968	−1.96493
$283$	26.2887	1.56270	0.781349	−	0.624094i	$-0.214532\pi$
$283$	26.2887	1.56270	0.781349	+	0.624094i	$0.214532\pi$
$284$	12.4907	0.741190
$285$	8.50172	0.503599
$286$	−3.39258	−0.200608
$287$	−2.17703	−0.128506
$288$	3.27901	0.193217
$289$	7.61369	0.447864
$290$	−1.77073	−0.103981
$291$	−10.5147	−0.616382
$292$	−7.44735	−0.435823
$293$	21.7103	1.26833	0.634163	−	0.773199i	$-0.281345\pi$
$293$	21.7103	1.26833	0.634163	+	0.773199i	$0.281345\pi$
$294$	35.7982	2.08779
$295$	0.0911359	0.00530613
$296$	−10.6902	−0.621355
$297$	−1.25578	−0.0728675
$298$	12.0696	0.699172
$299$	−7.34381	−0.424704
$300$	2.50579	0.144672
$301$	8.32155	0.479646
$302$	9.19767	0.529266
$303$	−8.15230	−0.468337
$304$	−3.39282	−0.194592
$305$	2.62310	0.150198
$306$	−16.2679	−0.929973
$307$	6.65352	0.379737	0.189868	−	0.981810i	$-0.439194\pi$
$307$	6.65352	0.379737	0.189868	+	0.981810i	$0.439194\pi$
$308$	8.28702	0.472197
$309$	20.9190	1.19004
$310$	−7.02789	−0.399157
$311$	30.3156	1.71904	0.859521	−	0.511100i	$-0.170762\pi$
$311$	30.3156	1.71904	0.859521	+	0.511100i	$0.170762\pi$
$312$	4.73289	0.267947
$313$	32.6442	1.84516	0.922580	−	0.385806i	$-0.126077\pi$
$313$	32.6442	1.84516	0.922580	+	0.385806i	$0.126077\pi$
$314$	−13.4576	−0.759454
$315$	15.1283	0.852385
$316$	−10.5899	−0.595727
$317$	−20.9310	−1.17560	−0.587802	−	0.809005i	$-0.700007\pi$
$317$	−20.9310	−1.17560	−0.587802	+	0.809005i	$0.700007\pi$
$318$	−3.37886	−0.189477
$319$	−3.18056	−0.178077
$320$	−1.00000	−0.0559017
$321$	−1.54530	−0.0862504
$322$	17.9387	0.999682
$323$	16.8325	0.936588
$324$	−8.08513	−0.449174
$325$	1.88878	0.104770
$326$	5.71056	0.316279
$327$	10.7693	0.595544
$328$	0.471863	0.0260543
$329$	60.7541	3.34948
$330$	4.50086	0.247764
$331$	−4.43176	−0.243592	−0.121796	−	0.992555i	$-0.538865\pi$
$331$	−4.43176	−0.243592	−0.121796	+	0.992555i	$0.538865\pi$
$332$	11.7519	0.644969
$333$	−35.0532	−1.92090
$334$	−18.4736	−1.01083
$335$	6.15633	0.336356
$336$	−11.5610	−0.630702
$337$	8.89593	0.484592	0.242296	−	0.970202i	$-0.422099\pi$
$337$	8.89593	0.484592	0.242296	+	0.970202i	$0.422099\pi$
$338$	−9.43253	−0.513062
$339$	18.5003	1.00480
$340$	4.96122	0.269060
$341$	−12.6233	−0.683592
$342$	−11.1251	−0.601576
$343$	−33.6161	−1.81510
$344$	−1.80366	−0.0972470
$345$	9.74287	0.524538
$346$	−17.5797	−0.945090
$347$	30.6867	1.64735	0.823674	−	0.567064i	$-0.191921\pi$
$347$	30.6867	1.64735	0.823674	+	0.567064i	$0.191921\pi$
$348$	4.43710	0.237853
$349$	7.93953	0.424994	0.212497	−	0.977162i	$-0.431841\pi$
$349$	7.93953	0.424994	0.212497	+	0.977162i	$0.431841\pi$
$350$	−4.61369	−0.246612
$351$	1.32051	0.0704837
$352$	−1.79618	−0.0957367
$353$	−26.6194	−1.41681	−0.708405	−	0.705806i	$-0.750585\pi$
$353$	−26.6194	−1.41681	−0.708405	+	0.705806i	$0.750585\pi$
$354$	−0.228368	−0.0121376
$355$	−12.4907	−0.662940
$356$	4.85113	0.257109
$357$	57.3565	3.03563
$358$	11.0591	0.584492
$359$	−8.52119	−0.449731	−0.224866	−	0.974390i	$-0.572194\pi$
$359$	−8.52119	−0.449731	−0.224866	+	0.974390i	$0.572194\pi$
$360$	−3.27901	−0.172819
$361$	−7.48874	−0.394144
$362$	0.675734	0.0355158
$363$	−19.4794	−1.02240
$364$	−8.71423	−0.456750
$365$	7.44735	0.389812
$366$	−6.57295	−0.343573
$367$	−18.9605	−0.989731	−0.494866	−	0.868970i	$-0.664783\pi$
$367$	−18.9605	−0.989731	−0.494866	+	0.868970i	$0.664783\pi$
$368$	−3.88813	−0.202683
$369$	1.54724	0.0805463
$370$	10.6902	0.555757
$371$	6.22120	0.322988
$372$	17.6104	0.913059
$373$	−23.7217	−1.22826	−0.614131	−	0.789204i	$-0.710493\pi$
$373$	−23.7217	−1.22826	−0.614131	+	0.789204i	$0.710493\pi$
$374$	8.91124	0.460789
$375$	−2.50579	−0.129399
$376$	−13.1682	−0.679099
$377$	3.34452	0.172252
$378$	−3.22560	−0.165907
$379$	−1.65550	−0.0850374	−0.0425187	−	0.999096i	$-0.513538\pi$
$379$	−1.65550	−0.0850374	−0.0425187	+	0.999096i	$0.513538\pi$
$380$	3.39282	0.174048
$381$	11.0461	0.565908
$382$	0.909046	0.0465108
$383$	−21.8794	−1.11799	−0.558994	−	0.829172i	$-0.688812\pi$
$383$	−21.8794	−1.11799	−0.558994	+	0.829172i	$0.688812\pi$
$384$	2.50579	0.127873
$385$	−8.28702	−0.422346
$386$	3.89430	0.198215
$387$	−5.91422	−0.300637
$388$	−4.19615	−0.213027
$389$	−23.5936	−1.19624	−0.598122	−	0.801405i	$-0.704086\pi$
$389$	−23.5936	−1.19624	−0.598122	+	0.801405i	$0.704086\pi$
$390$	−4.73289	−0.239659
$391$	19.2899	0.975531
$392$	14.2862	0.721560
$393$	10.3935	0.524280
$394$	−20.9893	−1.05742
$395$	10.5899	0.532834
$396$	−5.88969	−0.295968
$397$	−8.64570	−0.433915	−0.216958	−	0.976181i	$-0.569613\pi$
$397$	−8.64570	−0.433915	−0.216958	+	0.976181i	$0.569613\pi$
$398$	−10.6981	−0.536245
$399$	39.2243	1.96367
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−15.4265	−0.769404
$403$	13.2741	0.661230
$404$	−3.25338	−0.161862
$405$	8.08513	0.401753
$406$	−8.16962	−0.405451
$407$	19.2015	0.951783
$408$	−12.4318	−0.615466
$409$	33.2815	1.64566	0.822831	−	0.568286i	$-0.192393\pi$
$409$	33.2815	1.64566	0.822831	+	0.568286i	$0.192393\pi$
$410$	−0.471863	−0.0233037
$411$	−21.5152	−1.06127
$412$	8.34824	0.411288
$413$	0.420473	0.0206901
$414$	−12.7492	−0.626590
$415$	−11.7519	−0.576878
$416$	1.88878	0.0926049
$417$	32.5482	1.59389
$418$	6.09412	0.298073
$419$	−21.3709	−1.04404	−0.522019	−	0.852934i	$-0.674821\pi$
$419$	−21.3709	−1.04404	−0.522019	+	0.852934i	$0.674821\pi$
$420$	11.5610	0.564117
$421$	−34.2108	−1.66733	−0.833666	−	0.552270i	$-0.813762\pi$
$421$	−34.2108	−1.66733	−0.833666	+	0.552270i	$0.813762\pi$
$422$	11.1320	0.541896
$423$	−43.1787	−2.09942
$424$	−1.34842	−0.0654851
$425$	−4.96122	−0.240654
$426$	31.2993	1.51645
$427$	12.1022	0.585665
$428$	−0.616692	−0.0298089
$429$	−8.50111	−0.410438
$430$	1.80366	0.0869803
$431$	17.8172	0.858224	0.429112	−	0.903251i	$-0.358827\pi$
$431$	17.8172	0.858224	0.429112	+	0.903251i	$0.358827\pi$
$432$	0.699137	0.0336372
$433$	−1.57894	−0.0758792	−0.0379396	−	0.999280i	$-0.512079\pi$
$433$	−1.57894	−0.0758792	−0.0379396	+	0.999280i	$0.512079\pi$
$434$	−32.4245	−1.55643
$435$	−4.43710	−0.212742
$436$	4.29776	0.205825
$437$	13.1918	0.631047
$438$	−18.6615	−0.891683
$439$	−10.7072	−0.511028	−0.255514	−	0.966805i	$-0.582245\pi$
$439$	−10.7072	−0.511028	−0.255514	+	0.966805i	$0.582245\pi$
$440$	1.79618	0.0856295
$441$	46.8444	2.23069
$442$	−9.37063	−0.445715
$443$	3.63162	0.172544	0.0862718	−	0.996272i	$-0.472505\pi$
$443$	3.63162	0.172544	0.0862718	+	0.996272i	$0.472505\pi$
$444$	−26.7874	−1.27127
$445$	−4.85113	−0.229965
$446$	−5.38697	−0.255081
$447$	30.2439	1.43049
$448$	−4.61369	−0.217976
$449$	−35.5661	−1.67847	−0.839233	−	0.543772i	$-0.816996\pi$
$449$	−35.5661	−1.67847	−0.839233	+	0.543772i	$0.816996\pi$
$450$	3.27901	0.154574
$451$	−0.847551	−0.0399096
$452$	7.38301	0.347268
$453$	23.0475	1.08286
$454$	26.7131	1.25371
$455$	8.71423	0.408529
$456$	−8.50172	−0.398130
$457$	30.3816	1.42119	0.710596	−	0.703601i	$-0.248426\pi$
$457$	30.3816	1.42119	0.710596	+	0.703601i	$0.248426\pi$
$458$	−23.3817	−1.09256
$459$	−3.46857	−0.161899
$460$	3.88813	0.181285
$461$	−11.6805	−0.544014	−0.272007	−	0.962295i	$-0.587687\pi$
$461$	−11.6805	−0.544014	−0.272007	+	0.962295i	$0.587687\pi$
$462$	20.7656	0.966102
$463$	−3.22349	−0.149808	−0.0749042	−	0.997191i	$-0.523865\pi$
$463$	−3.22349	−0.149808	−0.0749042	+	0.997191i	$0.523865\pi$
$464$	1.77073	0.0822042
$465$	−17.6104	−0.816665
$466$	−14.6055	−0.676587
$467$	−0.767334	−0.0355080	−0.0177540	−	0.999842i	$-0.505652\pi$
$467$	−0.767334	−0.0355080	−0.0177540	+	0.999842i	$0.505652\pi$
$468$	6.19331	0.286286
$469$	28.4034	1.31155
$470$	13.1682	0.607404
$471$	−33.7219	−1.55382
$472$	−0.0911359	−0.00419487
$473$	3.23970	0.148962
$474$	−26.5361	−1.21884
$475$	−3.39282	−0.155673
$476$	22.8895	1.04914
$477$	−4.42148	−0.202446
$478$	14.9618	0.684338
$479$	−14.0589	−0.642367	−0.321183	−	0.947017i	$-0.604081\pi$
$479$	−14.0589	−0.642367	−0.321183	+	0.947017i	$0.604081\pi$
$480$	−2.50579	−0.114373
$481$	−20.1914	−0.920648
$482$	9.18041	0.418156
$483$	44.9506	2.04532
$484$	−7.77374	−0.353352
$485$	4.19615	0.190537
$486$	−22.3571	−1.01414
$487$	12.6928	0.575166	0.287583	−	0.957756i	$-0.407148\pi$
$487$	12.6928	0.575166	0.287583	+	0.957756i	$0.407148\pi$
$488$	−2.62310	−0.118742
$489$	14.3095	0.647098
$490$	−14.2862	−0.645383
$491$	3.57159	0.161183	0.0805917	−	0.996747i	$-0.474319\pi$
$491$	3.57159	0.161183	0.0805917	+	0.996747i	$0.474319\pi$
$492$	1.18239	0.0533064
$493$	−8.78500	−0.395656
$494$	−6.40828	−0.288322
$495$	5.88969	0.264722
$496$	7.02789	0.315561
$497$	−57.6285	−2.58499
$498$	29.4478	1.31959
$499$	26.3712	1.18054	0.590269	−	0.807207i	$-0.299022\pi$
$499$	26.3712	1.18054	0.590269	+	0.807207i	$0.299022\pi$
$500$	−1.00000	−0.0447214
$501$	−46.2912	−2.06814
$502$	10.4300	0.465513
$503$	5.70768	0.254493	0.127246	−	0.991871i	$-0.459386\pi$
$503$	5.70768	0.254493	0.127246	+	0.991871i	$0.459386\pi$
$504$	−15.1283	−0.673870
$505$	3.25338	0.144773
$506$	6.98379	0.310467
$507$	−23.6360	−1.04971
$508$	4.40821	0.195583
$509$	−4.04746	−0.179400	−0.0897002	−	0.995969i	$-0.528591\pi$
$509$	−4.04746	−0.179400	−0.0897002	+	0.995969i	$0.528591\pi$
$510$	12.4318	0.550489
$511$	34.3598	1.51999
$512$	1.00000	0.0441942
$513$	−2.37205	−0.104728
$514$	17.6872	0.780149
$515$	−8.34824	−0.367867
$516$	−4.51961	−0.198965
$517$	23.6525	1.04023
$518$	49.3213	2.16705
$519$	−44.0511	−1.93363
$520$	−1.88878	−0.0828283
$521$	30.4321	1.33326	0.666628	−	0.745391i	$-0.267737\pi$
$521$	30.4321	1.33326	0.666628	+	0.745391i	$0.267737\pi$
$522$	5.80625	0.254133
$523$	−13.8151	−0.604091	−0.302045	−	0.953294i	$-0.597669\pi$
$523$	−13.8151	−0.604091	−0.302045	+	0.953294i	$0.597669\pi$
$524$	4.14777	0.181196
$525$	−11.5610	−0.504562
$526$	7.49119	0.326632
$527$	−34.8669	−1.51883
$528$	−4.50086	−0.195875
$529$	−7.88241	−0.342714
$530$	1.34842	0.0585716
$531$	−0.298835	−0.0129683
$532$	15.6534	0.678663
$533$	0.891244	0.0386041
$534$	12.1559	0.526038
$535$	0.616692	0.0266619
$536$	−6.15633	−0.265913
$537$	27.7119	1.19586
$538$	−15.9134	−0.686076
$539$	−25.6605	−1.10528
$540$	−0.699137	−0.0300861
$541$	12.0438	0.517804	0.258902	−	0.965904i	$-0.416639\pi$
$541$	12.0438	0.517804	0.258902	+	0.965904i	$0.416639\pi$
$542$	−28.4556	−1.22227
$543$	1.69325	0.0726644
$544$	−4.96122	−0.212711
$545$	−4.29776	−0.184096
$546$	−21.8361	−0.934498
$547$	−27.3727	−1.17037	−0.585185	−	0.810900i	$-0.698978\pi$
$547$	−27.3727	−1.17037	−0.585185	+	0.810900i	$0.698978\pi$
$548$	−8.58617	−0.366783
$549$	−8.60116	−0.367089
$550$	−1.79618	−0.0765894
$551$	−6.00779	−0.255940
$552$	−9.74287	−0.414684
$553$	48.8584	2.07767
$554$	24.1977	1.02806
$555$	26.7874	1.13706
$556$	12.9892	0.550864
$557$	−3.35604	−0.142200	−0.0710999	−	0.997469i	$-0.522651\pi$
$557$	−3.35604	−0.142200	−0.0710999	+	0.997469i	$0.522651\pi$
$558$	23.0445	0.975551
$559$	−3.40671	−0.144089
$560$	4.61369	0.194964
$561$	22.3297	0.942762
$562$	−4.27541	−0.180347
$563$	−39.5032	−1.66486	−0.832430	−	0.554130i	$-0.813051\pi$
$563$	−39.5032	−1.66486	−0.832430	+	0.554130i	$0.813051\pi$
$564$	−32.9968	−1.38942
$565$	−7.38301	−0.310606
$566$	26.2887	1.10499
$567$	37.3023	1.56655
$568$	12.4907	0.524100
$569$	5.51394	0.231156	0.115578	−	0.993298i	$-0.463128\pi$
$569$	5.51394	0.231156	0.115578	+	0.993298i	$0.463128\pi$
$570$	8.50172	0.356098
$571$	−1.29147	−0.0540465	−0.0270232	−	0.999635i	$-0.508603\pi$
$571$	−1.29147	−0.0540465	−0.0270232	+	0.999635i	$0.508603\pi$
$572$	−3.39258	−0.141851
$573$	2.27788	0.0951599
$574$	−2.17703	−0.0908676
$575$	−3.88813	−0.162146
$576$	3.27901	0.136625
$577$	−5.91243	−0.246137	−0.123069	−	0.992398i	$-0.539274\pi$
$577$	−5.91243	−0.246137	−0.123069	+	0.992398i	$0.539274\pi$
$578$	7.61369	0.316688
$579$	9.75832	0.405542
$580$	−1.77073	−0.0735257
$581$	−54.2196	−2.24941
$582$	−10.5147	−0.435848
$583$	2.42200	0.100309
$584$	−7.44735	−0.308174
$585$	−6.19331	−0.256062
$586$	21.7103	0.896843
$587$	−18.5118	−0.764063	−0.382032	−	0.924149i	$-0.624775\pi$
$587$	−18.5118	−0.764063	−0.382032	+	0.924149i	$0.624775\pi$
$588$	35.7982	1.47629
$589$	−23.8444	−0.982491
$590$	0.0911359	0.00375200
$591$	−52.5948	−2.16346
$592$	−10.6902	−0.439364
$593$	−24.1946	−0.993551	−0.496776	−	0.867879i	$-0.665483\pi$
$593$	−24.1946	−0.993551	−0.496776	+	0.867879i	$0.665483\pi$
$594$	−1.25578	−0.0515251
$595$	−22.8895	−0.938380
$596$	12.0696	0.494389
$597$	−26.8071	−1.09714
$598$	−7.34381	−0.300311
$599$	−28.1795	−1.15139	−0.575693	−	0.817666i	$-0.695267\pi$
$599$	−28.1795	−1.15139	−0.575693	+	0.817666i	$0.695267\pi$
$600$	2.50579	0.102299
$601$	36.7347	1.49844	0.749219	−	0.662322i	$-0.230429\pi$
$601$	36.7347	1.49844	0.749219	+	0.662322i	$0.230429\pi$
$602$	8.32155	0.339161
$603$	−20.1866	−0.822064
$604$	9.19767	0.374248
$605$	7.77374	0.316047
$606$	−8.15230	−0.331164
$607$	−10.1092	−0.410322	−0.205161	−	0.978728i	$-0.565772\pi$
$607$	−10.1092	−0.410322	−0.205161	+	0.978728i	$0.565772\pi$
$608$	−3.39282	−0.137597
$609$	−20.4714	−0.829543
$610$	2.62310	0.106206
$611$	−24.8718	−1.00621
$612$	−16.2679	−0.657590
$613$	11.8095	0.476980	0.238490	−	0.971145i	$-0.423348\pi$
$613$	11.8095	0.476980	0.238490	+	0.971145i	$0.423348\pi$
$614$	6.65352	0.268514
$615$	−1.18239	−0.0476787
$616$	8.28702	0.333894
$617$	17.2472	0.694348	0.347174	−	0.937801i	$-0.387141\pi$
$617$	17.2472	0.694348	0.347174	+	0.937801i	$0.387141\pi$
$618$	20.9190	0.841484
$619$	−15.1807	−0.610164	−0.305082	−	0.952326i	$-0.598684\pi$
$619$	−15.1807	−0.610164	−0.305082	+	0.952326i	$0.598684\pi$
$620$	−7.02789	−0.282247
$621$	−2.71834	−0.109083
$622$	30.3156	1.21555
$623$	−22.3816	−0.896700
$624$	4.73289	0.189467
$625$	1.00000	0.0400000
$626$	32.6442	1.30472
$627$	15.2706	0.609850
$628$	−13.4576	−0.537015
$629$	53.0364	2.11470
$630$	15.1283	0.602727
$631$	−36.7766	−1.46405	−0.732027	−	0.681276i	$-0.761425\pi$
$631$	−36.7766	−1.46405	−0.732027	+	0.681276i	$0.761425\pi$
$632$	−10.5899	−0.421243
$633$	27.8944	1.10870
$634$	−20.9310	−0.831277
$635$	−4.40821	−0.174935
$636$	−3.37886	−0.133981
$637$	26.9834	1.06912
$638$	−3.18056	−0.125919
$639$	40.9573	1.62024
$640$	−1.00000	−0.0395285
$641$	−14.1360	−0.558337	−0.279168	−	0.960242i	$-0.590059\pi$
$641$	−14.1360	−0.558337	−0.279168	+	0.960242i	$0.590059\pi$
$642$	−1.54530	−0.0609883
$643$	−40.4321	−1.59449	−0.797243	−	0.603658i	$-0.793709\pi$
$643$	−40.4321	−1.59449	−0.797243	+	0.603658i	$0.793709\pi$
$644$	17.9387	0.706882
$645$	4.51961	0.177959
$646$	16.8325	0.662268
$647$	44.8800	1.76441	0.882207	−	0.470861i	$-0.156057\pi$
$647$	44.8800	1.76441	0.882207	+	0.470861i	$0.156057\pi$
$648$	−8.08513	−0.317614
$649$	0.163696	0.00642564
$650$	1.88878	0.0740839
$651$	−81.2492	−3.18441
$652$	5.71056	0.223643
$653$	46.3155	1.81247	0.906233	−	0.422780i	$-0.138946\pi$
$653$	46.3155	1.81247	0.906233	+	0.422780i	$0.138946\pi$
$654$	10.7693	0.421113
$655$	−4.14777	−0.162067
$656$	0.471863	0.0184232
$657$	−24.4199	−0.952712
$658$	60.7541	2.36844
$659$	−16.9956	−0.662053	−0.331027	−	0.943621i	$-0.607395\pi$
$659$	−16.9956	−0.662053	−0.331027	+	0.943621i	$0.607395\pi$
$660$	4.50086	0.175196
$661$	19.1052	0.743105	0.371553	−	0.928412i	$-0.378826\pi$
$661$	19.1052	0.743105	0.371553	+	0.928412i	$0.378826\pi$
$662$	−4.43176	−0.172245
$663$	−23.4809	−0.911922
$664$	11.7519	0.456062
$665$	−15.6534	−0.607015
$666$	−35.0532	−1.35828
$667$	−6.88485	−0.266582
$668$	−18.4736	−0.714767
$669$	−13.4986	−0.521888
$670$	6.15633	0.237840
$671$	4.71156	0.181888
$672$	−11.5610	−0.445974
$673$	20.5699	0.792911	0.396456	−	0.918054i	$-0.370240\pi$
$673$	20.5699	0.792911	0.396456	+	0.918054i	$0.370240\pi$
$674$	8.89593	0.342659
$675$	0.699137	0.0269098
$676$	−9.43253	−0.362789
$677$	21.0872	0.810445	0.405223	−	0.914218i	$-0.367194\pi$
$677$	21.0872	0.810445	0.405223	+	0.914218i	$0.367194\pi$
$678$	18.5003	0.710500
$679$	19.3597	0.742958
$680$	4.96122	0.190254
$681$	66.9374	2.56505
$682$	−12.6233	−0.483373
$683$	29.7096	1.13681	0.568403	−	0.822750i	$-0.307562\pi$
$683$	29.7096	1.13681	0.568403	+	0.822750i	$0.307562\pi$
$684$	−11.1251	−0.425379
$685$	8.58617	0.328061
$686$	−33.6161	−1.28347
$687$	−58.5899	−2.23534
$688$	−1.80366	−0.0687640
$689$	−2.54686	−0.0970278
$690$	9.74287	0.370905
$691$	−37.5875	−1.42989	−0.714947	−	0.699178i	$-0.753549\pi$
$691$	−37.5875	−1.42989	−0.714947	+	0.699178i	$0.753549\pi$
$692$	−17.5797	−0.668280
$693$	27.1732	1.03222
$694$	30.6867	1.16485
$695$	−12.9892	−0.492708
$696$	4.43710	0.168188
$697$	−2.34102	−0.0886723
$698$	7.93953	0.300516
$699$	−36.5984	−1.38428
$700$	−4.61369	−0.174381
$701$	−14.5634	−0.550052	−0.275026	−	0.961437i	$-0.588687\pi$
$701$	−14.5634	−0.550052	−0.275026	+	0.961437i	$0.588687\pi$
$702$	1.32051	0.0498395
$703$	36.2699	1.36795
$704$	−1.79618	−0.0676961
$705$	32.9968	1.24273
$706$	−26.6194	−1.00184
$707$	15.0101	0.564512
$708$	−0.228368	−0.00858259
$709$	−36.8671	−1.38457	−0.692287	−	0.721622i	$-0.743397\pi$
$709$	−36.8671	−1.38457	−0.692287	+	0.721622i	$0.743397\pi$
$710$	−12.4907	−0.468769
$711$	−34.7243	−1.30226
$712$	4.85113	0.181804
$713$	−27.3254	−1.02334
$714$	57.3565	2.14651
$715$	3.39258	0.126875
$716$	11.0591	0.413299
$717$	37.4912	1.40014
$718$	−8.52119	−0.318008
$719$	−12.7522	−0.475576	−0.237788	−	0.971317i	$-0.576422\pi$
$719$	−12.7522	−0.475576	−0.237788	+	0.971317i	$0.576422\pi$
$720$	−3.27901	−0.122201
$721$	−38.5162	−1.43442
$722$	−7.48874	−0.278702
$723$	23.0042	0.855536
$724$	0.675734	0.0251135
$725$	1.77073	0.0657634
$726$	−19.4794	−0.722948
$727$	14.6674	0.543985	0.271992	−	0.962299i	$-0.412317\pi$
$727$	14.6674	0.543985	0.271992	+	0.962299i	$0.412317\pi$
$728$	−8.71423	−0.322971
$729$	−31.7669	−1.17655
$730$	7.44735	0.275639
$731$	8.94837	0.330967
$732$	−6.57295	−0.242943
$733$	−30.3903	−1.12249	−0.561245	−	0.827650i	$-0.689678\pi$
$733$	−30.3903	−1.12249	−0.561245	+	0.827650i	$0.689678\pi$
$734$	−18.9605	−0.699846
$735$	−35.7982	−1.32044
$736$	−3.88813	−0.143319
$737$	11.0579	0.407322
$738$	1.54724	0.0569548
$739$	−27.2195	−1.00129	−0.500643	−	0.865654i	$-0.666903\pi$
$739$	−27.2195	−1.00129	−0.500643	+	0.865654i	$0.666903\pi$
$740$	10.6902	0.392979
$741$	−16.0578	−0.589900
$742$	6.22120	0.228387
$743$	−47.6184	−1.74695	−0.873474	−	0.486871i	$-0.838138\pi$
$743$	−47.6184	−1.74695	−0.873474	+	0.486871i	$0.838138\pi$
$744$	17.6104	0.645630
$745$	−12.0696	−0.442195
$746$	−23.7217	−0.868512
$747$	38.5346	1.40991
$748$	8.91124	0.325827
$749$	2.84523	0.103962
$750$	−2.50579	−0.0914987
$751$	37.1863	1.35695	0.678474	−	0.734624i	$-0.262642\pi$
$751$	37.1863	1.35695	0.678474	+	0.734624i	$0.262642\pi$
$752$	−13.1682	−0.480195
$753$	26.1354	0.952427
$754$	3.34452	0.121800
$755$	−9.19767	−0.334737
$756$	−3.22560	−0.117314
$757$	−47.4634	−1.72509	−0.862544	−	0.505983i	$-0.831130\pi$
$757$	−47.4634	−1.72509	−0.862544	+	0.505983i	$0.831130\pi$
$758$	−1.65550	−0.0601305
$759$	17.4999	0.635208
$760$	3.39282	0.123071
$761$	20.3601	0.738054	0.369027	−	0.929419i	$-0.379691\pi$
$761$	20.3601	0.738054	0.369027	+	0.929419i	$0.379691\pi$
$762$	11.0461	0.400157
$763$	−19.8285	−0.717841
$764$	0.909046	0.0328881
$765$	16.2679	0.588166
$766$	−21.8794	−0.790536
$767$	−0.172135	−0.00621544
$768$	2.50579	0.0904201
$769$	−10.7985	−0.389402	−0.194701	−	0.980863i	$-0.562374\pi$
$769$	−10.7985	−0.389402	−0.194701	+	0.980863i	$0.562374\pi$
$770$	−8.28702	−0.298643
$771$	44.3205	1.59616
$772$	3.89430	0.140159
$773$	−32.0705	−1.15349	−0.576747	−	0.816923i	$-0.695678\pi$
$773$	−32.0705	−1.15349	−0.576747	+	0.816923i	$0.695678\pi$
$774$	−5.91422	−0.212582
$775$	7.02789	0.252449
$776$	−4.19615	−0.150633
$777$	123.589	4.43373
$778$	−23.5936	−0.845872
$779$	−1.60095	−0.0573600
$780$	−4.73289	−0.169464
$781$	−22.4356	−0.802810
$782$	19.2899	0.689805
$783$	1.23798	0.0442420
$784$	14.2862	0.510220
$785$	13.4576	0.480321
$786$	10.3935	0.370722
$787$	−10.7456	−0.383039	−0.191520	−	0.981489i	$-0.561342\pi$
$787$	−10.7456	−0.383039	−0.191520	+	0.981489i	$0.561342\pi$
$788$	−20.9893	−0.747712
$789$	18.7714	0.668279
$790$	10.5899	0.376771
$791$	−34.0629	−1.21114
$792$	−5.88969	−0.209281
$793$	−4.95445	−0.175938
$794$	−8.64570	−0.306824
$795$	3.37886	0.119836
$796$	−10.6981	−0.379182
$797$	50.3702	1.78421	0.892103	−	0.451832i	$-0.149230\pi$
$797$	50.3702	1.78421	0.892103	+	0.451832i	$0.149230\pi$
$798$	39.2243	1.38853
$799$	65.3304	2.31122
$800$	1.00000	0.0353553
$801$	15.9069	0.562042
$802$	1.00000	0.0353112
$803$	13.3768	0.472057
$804$	−15.4265	−0.544051
$805$	−17.9387	−0.632254
$806$	13.2741	0.467560
$807$	−39.8757	−1.40369
$808$	−3.25338	−0.114453
$809$	−35.6119	−1.25205	−0.626025	−	0.779803i	$-0.715319\pi$
$809$	−35.6119	−1.25205	−0.626025	+	0.779803i	$0.715319\pi$
$810$	8.08513	0.284083
$811$	−1.61741	−0.0567949	−0.0283975	−	0.999597i	$-0.509040\pi$
$811$	−1.61741	−0.0567949	−0.0283975	+	0.999597i	$0.509040\pi$
$812$	−8.16962	−0.286697
$813$	−71.3038	−2.50073
$814$	19.2015	0.673012
$815$	−5.71056	−0.200032
$816$	−12.4318	−0.435200
$817$	6.11951	0.214095
$818$	33.2815	1.16366
$819$	−28.5740	−0.998458
$820$	−0.471863	−0.0164782
$821$	5.02885	0.175508	0.0877541	−	0.996142i	$-0.472031\pi$
$821$	5.02885	0.175508	0.0877541	+	0.996142i	$0.472031\pi$
$822$	−21.5152	−0.750428
$823$	−22.6671	−0.790125	−0.395062	−	0.918654i	$-0.629277\pi$
$823$	−22.6671	−0.790125	−0.395062	+	0.918654i	$0.629277\pi$
$824$	8.34824	0.290825
$825$	−4.50086	−0.156700
$826$	0.420473	0.0146301
$827$	46.8068	1.62763	0.813815	−	0.581124i	$-0.197387\pi$
$827$	46.8068	1.62763	0.813815	+	0.581124i	$0.197387\pi$
$828$	−12.7492	−0.443066
$829$	−42.6531	−1.48140	−0.740701	−	0.671835i	$-0.765506\pi$
$829$	−42.6531	−1.48140	−0.740701	+	0.671835i	$0.765506\pi$
$830$	−11.7519	−0.407914
$831$	60.6345	2.10339
$832$	1.88878	0.0654815
$833$	−70.8768	−2.45573
$834$	32.5482	1.12705
$835$	18.4736	0.639307
$836$	6.09412	0.210770
$837$	4.91345	0.169834
$838$	−21.3709	−0.738246
$839$	44.7177	1.54383	0.771914	−	0.635727i	$-0.219300\pi$
$839$	44.7177	1.54383	0.771914	+	0.635727i	$0.219300\pi$
$840$	11.5610	0.398891
$841$	−25.8645	−0.891879
$842$	−34.2108	−1.17898
$843$	−10.7133	−0.368986
$844$	11.1320	0.383178
$845$	9.43253	0.324489
$846$	−43.1787	−1.48451
$847$	35.8656	1.23236
$848$	−1.34842	−0.0463049
$849$	65.8740	2.26079
$850$	−4.96122	−0.170168
$851$	41.5649	1.42483
$852$	31.2993	1.07229
$853$	−19.4774	−0.666894	−0.333447	−	0.942769i	$-0.608212\pi$
$853$	−19.4774	−0.666894	−0.333447	+	0.942769i	$0.608212\pi$
$854$	12.1022	0.414128
$855$	11.1251	0.380470
$856$	−0.616692	−0.0210781
$857$	−27.4983	−0.939326	−0.469663	−	0.882846i	$-0.655624\pi$
$857$	−27.4983	−0.939326	−0.469663	+	0.882846i	$0.655624\pi$
$858$	−8.50111	−0.290223
$859$	−4.27730	−0.145940	−0.0729698	−	0.997334i	$-0.523248\pi$
$859$	−4.27730	−0.145940	−0.0729698	+	0.997334i	$0.523248\pi$
$860$	1.80366	0.0615044
$861$	−5.45520	−0.185913
$862$	17.8172	0.606856
$863$	−31.3864	−1.06841	−0.534203	−	0.845356i	$-0.679388\pi$
$863$	−31.3864	−1.06841	−0.534203	+	0.845356i	$0.679388\pi$
$864$	0.699137	0.0237851
$865$	17.5797	0.597727
$866$	−1.57894	−0.0536547
$867$	19.0784	0.647935
$868$	−32.4245	−1.10056
$869$	19.0213	0.645254
$870$	−4.43710	−0.150432
$871$	−11.6279	−0.393997
$872$	4.29776	0.145540
$873$	−13.7592	−0.465678
$874$	13.1918	0.446218
$875$	4.61369	0.155971
$876$	−18.6615	−0.630515
$877$	−23.5398	−0.794881	−0.397440	−	0.917628i	$-0.630101\pi$
$877$	−23.5398	−0.794881	−0.397440	+	0.917628i	$0.630101\pi$
$878$	−10.7072	−0.361351
$879$	54.4015	1.83492
$880$	1.79618	0.0605492
$881$	33.2639	1.12069	0.560344	−	0.828260i	$-0.310669\pi$
$881$	33.2639	1.12069	0.560344	+	0.828260i	$0.310669\pi$
$882$	46.8444	1.57733
$883$	−19.7730	−0.665414	−0.332707	−	0.943030i	$-0.607962\pi$
$883$	−19.7730	−0.665414	−0.332707	+	0.943030i	$0.607962\pi$
$884$	−9.37063	−0.315168
$885$	0.228368	0.00767650
$886$	3.63162	0.122007
$887$	37.3152	1.25292	0.626461	−	0.779453i	$-0.284503\pi$
$887$	37.3152	1.25292	0.626461	+	0.779453i	$0.284503\pi$
$888$	−26.7874	−0.898927
$889$	−20.3381	−0.682119
$890$	−4.85113	−0.162610
$891$	14.5223	0.486517
$892$	−5.38697	−0.180369
$893$	44.6774	1.49507
$894$	30.2439	1.01151
$895$	−11.0591	−0.369665
$896$	−4.61369	−0.154133
$897$	−18.4021	−0.614428
$898$	−35.5661	−1.18686
$899$	12.4445	0.415048
$900$	3.27901	0.109300
$901$	6.68981	0.222870
$902$	−0.847551	−0.0282204
$903$	20.8521	0.693914
$904$	7.38301	0.245555
$905$	−0.675734	−0.0224622
$906$	23.0475	0.765701
$907$	−32.2080	−1.06945	−0.534724	−	0.845027i	$-0.679585\pi$
$907$	−32.2080	−1.06945	−0.534724	+	0.845027i	$0.679585\pi$
$908$	26.7131	0.886504
$909$	−10.6679	−0.353830
$910$	8.71423	0.288874
$911$	51.6207	1.71027	0.855135	−	0.518405i	$-0.173474\pi$
$911$	51.6207	1.71027	0.855135	+	0.518405i	$0.173474\pi$
$912$	−8.50172	−0.281520
$913$	−21.1085	−0.698590
$914$	30.3816	1.00493
$915$	6.57295	0.217295
$916$	−23.3817	−0.772555
$917$	−19.1365	−0.631943
$918$	−3.46857	−0.114480
$919$	−13.0543	−0.430623	−0.215311	−	0.976545i	$-0.569077\pi$
$919$	−13.0543	−0.430623	−0.215311	+	0.976545i	$0.569077\pi$
$920$	3.88813	0.128188
$921$	16.6724	0.549373
$922$	−11.6805	−0.384676
$923$	23.5922	0.776548
$924$	20.7656	0.683137
$925$	−10.6902	−0.351491
$926$	−3.22349	−0.105931
$927$	27.3739	0.899078
$928$	1.77073	0.0581272
$929$	−45.1036	−1.47980	−0.739900	−	0.672717i	$-0.765127\pi$
$929$	−45.1036	−1.47980	−0.739900	+	0.672717i	$0.765127\pi$
$930$	−17.6104	−0.577469
$931$	−48.4704	−1.58855
$932$	−14.6055	−0.478420
$933$	75.9648	2.48698
$934$	−0.767334	−0.0251079
$935$	−8.91124	−0.291429
$936$	6.19331	0.202435
$937$	46.7479	1.52719	0.763593	−	0.645697i	$-0.223433\pi$
$937$	46.7479	1.52719	0.763593	+	0.645697i	$0.223433\pi$
$938$	28.4034	0.927404
$939$	81.7997	2.66943
$940$	13.1682	0.429500
$941$	3.53780	0.115329	0.0576645	−	0.998336i	$-0.481635\pi$
$941$	3.53780	0.115329	0.0576645	+	0.998336i	$0.481635\pi$
$942$	−33.7219	−1.09872
$943$	−1.83467	−0.0597450
$944$	−0.0911359	−0.00296622
$945$	3.22560	0.104929
$946$	3.23970	0.105332
$947$	31.8542	1.03512	0.517562	−	0.855646i	$-0.326840\pi$
$947$	31.8542	1.03512	0.517562	+	0.855646i	$0.326840\pi$
$948$	−26.5361	−0.861851
$949$	−14.0664	−0.456614
$950$	−3.39282	−0.110078
$951$	−52.4489	−1.70077
$952$	22.8895	0.741854
$953$	−32.0636	−1.03864	−0.519322	−	0.854579i	$-0.673815\pi$
$953$	−32.0636	−1.03864	−0.519322	+	0.854579i	$0.673815\pi$
$954$	−4.42148	−0.143151
$955$	−0.909046	−0.0294160
$956$	14.9618	0.483900
$957$	−7.96982	−0.257628
$958$	−14.0589	−0.454222
$959$	39.6139	1.27920
$960$	−2.50579	−0.0808742
$961$	18.3912	0.593264
$962$	−20.1914	−0.650996
$963$	−2.02214	−0.0651625
$964$	9.18041	0.295681
$965$	−3.89430	−0.125362
$966$	44.9506	1.44626
$967$	−25.2209	−0.811051	−0.405525	−	0.914084i	$-0.632911\pi$
$967$	−25.2209	−0.811051	−0.405525	+	0.914084i	$0.632911\pi$
$968$	−7.77374	−0.249857
$969$	42.1789	1.35498
$970$	4.19615	0.134730
$971$	−34.8551	−1.11855	−0.559277	−	0.828981i	$-0.688921\pi$
$971$	−34.8551	−1.11855	−0.559277	+	0.828981i	$0.688921\pi$
$972$	−22.3571	−0.717104
$973$	−59.9281	−1.92121
$974$	12.6928	0.406704
$975$	4.73289	0.151574
$976$	−2.62310	−0.0839633
$977$	−30.3162	−0.969900	−0.484950	−	0.874542i	$-0.661162\pi$
$977$	−30.3162	−0.969900	−0.484950	+	0.874542i	$0.661162\pi$
$978$	14.3095	0.457567
$979$	−8.71349	−0.278484
$980$	−14.2862	−0.456355
$981$	14.0924	0.449935
$982$	3.57159	0.113974
$983$	2.53239	0.0807708	0.0403854	−	0.999184i	$-0.487141\pi$
$983$	2.53239	0.0807708	0.0403854	+	0.999184i	$0.487141\pi$
$984$	1.18239	0.0376933
$985$	20.9893	0.668774
$986$	−8.78500	−0.279771
$987$	152.237	4.84576
$988$	−6.40828	−0.203875
$989$	7.01288	0.222997
$990$	5.88969	0.187187
$991$	1.37530	0.0436877	0.0218439	−	0.999761i	$-0.493046\pi$
$991$	1.37530	0.0436877	0.0218439	+	0.999761i	$0.493046\pi$
$992$	7.02789	0.223136
$993$	−11.1051	−0.352409
$994$	−57.6285	−1.82786
$995$	10.6981	0.339151
$996$	29.4478	0.933090
$997$	39.7642	1.25934	0.629672	−	0.776861i	$-0.283189\pi$
$997$	39.7642	1.25934	0.629672	+	0.776861i	$0.283189\pi$
$998$	26.3712	0.834766
$999$	−7.47390	−0.236464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.j.1.12	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.j.1.12	✓	12	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.50579 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.50579 q^{6} -4.61369 q^{7} +1.00000 q^{8} +3.27901 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.50579 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.50579 q^{6} -4.61369 q^{7} +1.00000 q^{8} +3.27901 q^{9} -1.00000 q^{10} -1.79618 q^{11} +2.50579 q^{12} +1.88878 q^{13} -4.61369 q^{14} -2.50579 q^{15} +1.00000 q^{16} -4.96122 q^{17} +3.27901 q^{18} -3.39282 q^{19} -1.00000 q^{20} -11.5610 q^{21} -1.79618 q^{22} -3.88813 q^{23} +2.50579 q^{24} +1.00000 q^{25} +1.88878 q^{26} +0.699137 q^{27} -4.61369 q^{28} +1.77073 q^{29} -2.50579 q^{30} +7.02789 q^{31} +1.00000 q^{32} -4.50086 q^{33} -4.96122 q^{34} +4.61369 q^{35} +3.27901 q^{36} -10.6902 q^{37} -3.39282 q^{38} +4.73289 q^{39} -1.00000 q^{40} +0.471863 q^{41} -11.5610 q^{42} -1.80366 q^{43} -1.79618 q^{44} -3.27901 q^{45} -3.88813 q^{46} -13.1682 q^{47} +2.50579 q^{48} +14.2862 q^{49} +1.00000 q^{50} -12.4318 q^{51} +1.88878 q^{52} -1.34842 q^{53} +0.699137 q^{54} +1.79618 q^{55} -4.61369 q^{56} -8.50172 q^{57} +1.77073 q^{58} -0.0911359 q^{59} -2.50579 q^{60} -2.62310 q^{61} +7.02789 q^{62} -15.1283 q^{63} +1.00000 q^{64} -1.88878 q^{65} -4.50086 q^{66} -6.15633 q^{67} -4.96122 q^{68} -9.74287 q^{69} +4.61369 q^{70} +12.4907 q^{71} +3.27901 q^{72} -7.44735 q^{73} -10.6902 q^{74} +2.50579 q^{75} -3.39282 q^{76} +8.28702 q^{77} +4.73289 q^{78} -10.5899 q^{79} -1.00000 q^{80} -8.08513 q^{81} +0.471863 q^{82} +11.7519 q^{83} -11.5610 q^{84} +4.96122 q^{85} -1.80366 q^{86} +4.43710 q^{87} -1.79618 q^{88} +4.85113 q^{89} -3.27901 q^{90} -8.71423 q^{91} -3.88813 q^{92} +17.6104 q^{93} -13.1682 q^{94} +3.39282 q^{95} +2.50579 q^{96} -4.19615 q^{97} +14.2862 q^{98} -5.88969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q + 12 * q^2 - 2 * q^3 + 12 * q^4 - 12 * q^5 - 2 * q^6 - 9 * q^7 + 12 * q^8	\( 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8} - 12 q^{10} + q^{11} - 2 q^{12} - 6 q^{13} - 9 q^{14} + 2 q^{15} + 12 q^{16} - 11 q^{17} - 13 q^{19} - 12 q^{20} - 14 q^{21} + q^{22} - 21 q^{23} - 2 q^{24} + 12 q^{25} - 6 q^{26} - 2 q^{27} - 9 q^{28} - 10 q^{29} + 2 q^{30} - 11 q^{31} + 12 q^{32} - 22 q^{33} - 11 q^{34} + 9 q^{35} - 29 q^{37} - 13 q^{38} - 2 q^{39} - 12 q^{40} - q^{41} - 14 q^{42} - 23 q^{43} + q^{44} - 21 q^{46} - 17 q^{47} - 2 q^{48} - 3 q^{49} + 12 q^{50} - 19 q^{51} - 6 q^{52} - 47 q^{53} - 2 q^{54} - q^{55} - 9 q^{56} - 11 q^{57} - 10 q^{58} + 14 q^{59} + 2 q^{60} - 22 q^{61} - 11 q^{62} - 28 q^{63} + 12 q^{64} + 6 q^{65} - 22 q^{66} - 28 q^{67} - 11 q^{68} - q^{69} + 9 q^{70} - 18 q^{71} - 2 q^{73} - 29 q^{74} - 2 q^{75} - 13 q^{76} - 11 q^{77} - 2 q^{78} - 39 q^{79} - 12 q^{80} - 44 q^{81} - q^{82} - 5 q^{83} - 14 q^{84} + 11 q^{85} - 23 q^{86} - 6 q^{87} + q^{88} - 8 q^{89} - 12 q^{91} - 21 q^{92} - 30 q^{93} - 17 q^{94} + 13 q^{95} - 2 q^{96} - 32 q^{97} - 3 q^{98} - 13 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 - 2 * q^3 + 12 * q^4 - 12 * q^5 - 2 * q^6 - 9 * q^7 + 12 * q^8 - 12 * q^10 + q^11 - 2 * q^12 - 6 * q^13 - 9 * q^14 + 2 * q^15 + 12 * q^16 - 11 * q^17 - 13 * q^19 - 12 * q^20 - 14 * q^21 + q^22 - 21 * q^23 - 2 * q^24 + 12 * q^25 - 6 * q^26 - 2 * q^27 - 9 * q^28 - 10 * q^29 + 2 * q^30 - 11 * q^31 + 12 * q^32 - 22 * q^33 - 11 * q^34 + 9 * q^35 - 29 * q^37 - 13 * q^38 - 2 * q^39 - 12 * q^40 - q^41 - 14 * q^42 - 23 * q^43 + q^44 - 21 * q^46 - 17 * q^47 - 2 * q^48 - 3 * q^49 + 12 * q^50 - 19 * q^51 - 6 * q^52 - 47 * q^53 - 2 * q^54 - q^55 - 9 * q^56 - 11 * q^57 - 10 * q^58 + 14 * q^59 + 2 * q^60 - 22 * q^61 - 11 * q^62 - 28 * q^63 + 12 * q^64 + 6 * q^65 - 22 * q^66 - 28 * q^67 - 11 * q^68 - q^69 + 9 * q^70 - 18 * q^71 - 2 * q^73 - 29 * q^74 - 2 * q^75 - 13 * q^76 - 11 * q^77 - 2 * q^78 - 39 * q^79 - 12 * q^80 - 44 * q^81 - q^82 - 5 * q^83 - 14 * q^84 + 11 * q^85 - 23 * q^86 - 6 * q^87 + q^88 - 8 * q^89 - 12 * q^91 - 21 * q^92 - 30 * q^93 - 17 * q^94 + 13 * q^95 - 2 * q^96 - 32 * q^97 - 3 * q^98 - 13 * q^99

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