LMFDB - Embedded newform 4010.2.a.j.1.6

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			1.6
Root			$0.803872$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.803872 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.803872 q^{6} +1.44710 q^{7} +1.00000 q^{8} -2.35379 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.803872 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.803872 q^{6} +1.44710 q^{7} +1.00000 q^{8} -2.35379 q^{9} -1.00000 q^{10} -0.326178 q^{11} -0.803872 q^{12} -2.95206 q^{13} +1.44710 q^{14} +0.803872 q^{15} +1.00000 q^{16} +3.19340 q^{17} -2.35379 q^{18} -2.71870 q^{19} -1.00000 q^{20} -1.16329 q^{21} -0.326178 q^{22} +7.05099 q^{23} -0.803872 q^{24} +1.00000 q^{25} -2.95206 q^{26} +4.30376 q^{27} +1.44710 q^{28} -7.21197 q^{29} +0.803872 q^{30} -3.42146 q^{31} +1.00000 q^{32} +0.262206 q^{33} +3.19340 q^{34} -1.44710 q^{35} -2.35379 q^{36} +6.36496 q^{37} -2.71870 q^{38} +2.37308 q^{39} -1.00000 q^{40} -0.336080 q^{41} -1.16329 q^{42} -4.62681 q^{43} -0.326178 q^{44} +2.35379 q^{45} +7.05099 q^{46} -8.73635 q^{47} -0.803872 q^{48} -4.90589 q^{49} +1.00000 q^{50} -2.56709 q^{51} -2.95206 q^{52} -2.27959 q^{53} +4.30376 q^{54} +0.326178 q^{55} +1.44710 q^{56} +2.18549 q^{57} -7.21197 q^{58} -4.52983 q^{59} +0.803872 q^{60} +2.03696 q^{61} -3.42146 q^{62} -3.40618 q^{63} +1.00000 q^{64} +2.95206 q^{65} +0.262206 q^{66} -0.347703 q^{67} +3.19340 q^{68} -5.66810 q^{69} -1.44710 q^{70} -13.4678 q^{71} -2.35379 q^{72} -5.02082 q^{73} +6.36496 q^{74} -0.803872 q^{75} -2.71870 q^{76} -0.472014 q^{77} +2.37308 q^{78} -11.5208 q^{79} -1.00000 q^{80} +3.60169 q^{81} -0.336080 q^{82} +2.99172 q^{83} -1.16329 q^{84} -3.19340 q^{85} -4.62681 q^{86} +5.79750 q^{87} -0.326178 q^{88} -7.54354 q^{89} +2.35379 q^{90} -4.27194 q^{91} +7.05099 q^{92} +2.75041 q^{93} -8.73635 q^{94} +2.71870 q^{95} -0.803872 q^{96} +11.3139 q^{97} -4.90589 q^{98} +0.767755 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.803872	−0.464116	−0.232058	−	0.972702i	$-0.574546\pi$
$3$	−0.803872	−0.464116	−0.232058	+	0.972702i	$0.574546\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.803872	−0.328179
$7$	1.44710	0.546954	0.273477	−	0.961879i	$-0.411826\pi$
$7$	1.44710	0.546954	0.273477	+	0.961879i	$0.411826\pi$
$8$	1.00000	0.353553
$9$	−2.35379	−0.784596
$10$	−1.00000	−0.316228
$11$	−0.326178	−0.0983464	−0.0491732	−	0.998790i	$-0.515659\pi$
$11$	−0.326178	−0.0983464	−0.0491732	+	0.998790i	$0.515659\pi$
$12$	−0.803872	−0.232058
$13$	−2.95206	−0.818755	−0.409377	−	0.912365i	$-0.634254\pi$
$13$	−2.95206	−0.818755	−0.409377	+	0.912365i	$0.634254\pi$
$14$	1.44710	0.386755
$15$	0.803872	0.207559
$16$	1.00000	0.250000
$17$	3.19340	0.774513	0.387257	−	0.921972i	$-0.373423\pi$
$17$	3.19340	0.774513	0.387257	+	0.921972i	$0.373423\pi$
$18$	−2.35379	−0.554793
$19$	−2.71870	−0.623713	−0.311857	−	0.950129i	$-0.600951\pi$
$19$	−2.71870	−0.623713	−0.311857	+	0.950129i	$0.600951\pi$
$20$	−1.00000	−0.223607
$21$	−1.16329	−0.253850
$22$	−0.326178	−0.0695414
$23$	7.05099	1.47023	0.735117	−	0.677940i	$-0.237127\pi$
$23$	7.05099	1.47023	0.735117	+	0.677940i	$0.237127\pi$
$24$	−0.803872	−0.164090
$25$	1.00000	0.200000
$26$	−2.95206	−0.578947
$27$	4.30376	0.828260
$28$	1.44710	0.273477
$29$	−7.21197	−1.33923	−0.669614	−	0.742709i	$-0.733541\pi$
$29$	−7.21197	−1.33923	−0.669614	+	0.742709i	$0.733541\pi$
$30$	0.803872	0.146766
$31$	−3.42146	−0.614512	−0.307256	−	0.951627i	$-0.599411\pi$
$31$	−3.42146	−0.614512	−0.307256	+	0.951627i	$0.599411\pi$
$32$	1.00000	0.176777
$33$	0.262206	0.0456441
$34$	3.19340	0.547664
$35$	−1.44710	−0.244605
$36$	−2.35379	−0.392298
$37$	6.36496	1.04639	0.523196	−	0.852212i	$-0.324739\pi$
$37$	6.36496	1.04639	0.523196	+	0.852212i	$0.324739\pi$
$38$	−2.71870	−0.441032
$39$	2.37308	0.379997
$40$	−1.00000	−0.158114
$41$	−0.336080	−0.0524869	−0.0262434	−	0.999656i	$-0.508355\pi$
$41$	−0.336080	−0.0524869	−0.0262434	+	0.999656i	$0.508355\pi$
$42$	−1.16329	−0.179499
$43$	−4.62681	−0.705581	−0.352791	−	0.935702i	$-0.614767\pi$
$43$	−4.62681	−0.705581	−0.352791	+	0.935702i	$0.614767\pi$
$44$	−0.326178	−0.0491732
$45$	2.35379	0.350882
$46$	7.05099	1.03961
$47$	−8.73635	−1.27433	−0.637164	−	0.770728i	$-0.719893\pi$
$47$	−8.73635	−1.27433	−0.637164	+	0.770728i	$0.719893\pi$
$48$	−0.803872	−0.116029
$49$	−4.90589	−0.700841
$50$	1.00000	0.141421
$51$	−2.56709	−0.359464
$52$	−2.95206	−0.409377
$53$	−2.27959	−0.313126	−0.156563	−	0.987668i	$-0.550041\pi$
$53$	−2.27959	−0.313126	−0.156563	+	0.987668i	$0.550041\pi$
$54$	4.30376	0.585668
$55$	0.326178	0.0439819
$56$	1.44710	0.193377
$57$	2.18549	0.289475
$58$	−7.21197	−0.946978
$59$	−4.52983	−0.589734	−0.294867	−	0.955538i	$-0.595275\pi$
$59$	−4.52983	−0.589734	−0.294867	+	0.955538i	$0.595275\pi$
$60$	0.803872	0.103779
$61$	2.03696	0.260806	0.130403	−	0.991461i	$-0.458373\pi$
$61$	2.03696	0.260806	0.130403	+	0.991461i	$0.458373\pi$
$62$	−3.42146	−0.434526
$63$	−3.40618	−0.429138
$64$	1.00000	0.125000
$65$	2.95206	0.366158
$66$	0.262206	0.0322753
$67$	−0.347703	−0.0424786	−0.0212393	−	0.999774i	$-0.506761\pi$
$67$	−0.347703	−0.0424786	−0.0212393	+	0.999774i	$0.506761\pi$
$68$	3.19340	0.387257
$69$	−5.66810	−0.682359
$70$	−1.44710	−0.172962
$71$	−13.4678	−1.59834	−0.799169	−	0.601107i	$-0.794727\pi$
$71$	−13.4678	−1.59834	−0.799169	+	0.601107i	$0.794727\pi$
$72$	−2.35379	−0.277397
$73$	−5.02082	−0.587642	−0.293821	−	0.955860i	$-0.594927\pi$
$73$	−5.02082	−0.587642	−0.293821	+	0.955860i	$0.594927\pi$
$74$	6.36496	0.739911
$75$	−0.803872	−0.0928232
$76$	−2.71870	−0.311857
$77$	−0.472014	−0.0537910
$78$	2.37308	0.268699
$79$	−11.5208	−1.29619	−0.648094	−	0.761560i	$-0.724434\pi$
$79$	−11.5208	−1.29619	−0.648094	+	0.761560i	$0.724434\pi$
$80$	−1.00000	−0.111803
$81$	3.60169	0.400188
$82$	−0.336080	−0.0371138
$83$	2.99172	0.328384	0.164192	−	0.986428i	$-0.447498\pi$
$83$	2.99172	0.328384	0.164192	+	0.986428i	$0.447498\pi$
$84$	−1.16329	−0.126925
$85$	−3.19340	−0.346373
$86$	−4.62681	−0.498921
$87$	5.79750	0.621557
$88$	−0.326178	−0.0347707
$89$	−7.54354	−0.799614	−0.399807	−	0.916599i	$-0.630923\pi$
$89$	−7.54354	−0.799614	−0.399807	+	0.916599i	$0.630923\pi$
$90$	2.35379	0.248111
$91$	−4.27194	−0.447821
$92$	7.05099	0.735117
$93$	2.75041	0.285205
$94$	−8.73635	−0.901086
$95$	2.71870	0.278933
$96$	−0.803872	−0.0820449
$97$	11.3139	1.14875	0.574377	−	0.818591i	$-0.305244\pi$
$97$	11.3139	1.14875	0.574377	+	0.818591i	$0.305244\pi$
$98$	−4.90589	−0.495570
$99$	0.767755	0.0771623
$100$	1.00000	0.100000
$101$	15.9703	1.58911	0.794553	−	0.607194i	$-0.207705\pi$
$101$	15.9703	1.58911	0.794553	+	0.607194i	$0.207705\pi$
$102$	−2.56709	−0.254179
$103$	−11.5971	−1.14270	−0.571350	−	0.820707i	$-0.693580\pi$
$103$	−11.5971	−1.14270	−0.571350	+	0.820707i	$0.693580\pi$
$104$	−2.95206	−0.289474
$105$	1.16329	0.113525
$106$	−2.27959	−0.221414
$107$	−16.0736	−1.55390	−0.776948	−	0.629564i	$-0.783233\pi$
$107$	−16.0736	−1.55390	−0.776948	+	0.629564i	$0.783233\pi$
$108$	4.30376	0.414130
$109$	−4.81094	−0.460805	−0.230402	−	0.973095i	$-0.574004\pi$
$109$	−4.81094	−0.460805	−0.230402	+	0.973095i	$0.574004\pi$
$110$	0.326178	0.0310999
$111$	−5.11661	−0.485647
$112$	1.44710	0.136738
$113$	−5.77952	−0.543692	−0.271846	−	0.962341i	$-0.587634\pi$
$113$	−5.77952	−0.543692	−0.271846	+	0.962341i	$0.587634\pi$
$114$	2.18549	0.204690
$115$	−7.05099	−0.657508
$116$	−7.21197	−0.669614
$117$	6.94853	0.642392
$118$	−4.52983	−0.417005
$119$	4.62118	0.423623
$120$	0.803872	0.0733832
$121$	−10.8936	−0.990328
$122$	2.03696	0.184417
$123$	0.270165	0.0243600
$124$	−3.42146	−0.307256
$125$	−1.00000	−0.0894427
$126$	−3.40618	−0.303446
$127$	9.62589	0.854159	0.427080	−	0.904214i	$-0.359542\pi$
$127$	9.62589	0.854159	0.427080	+	0.904214i	$0.359542\pi$
$128$	1.00000	0.0883883
$129$	3.71936	0.327471
$130$	2.95206	0.258913
$131$	−0.642895	−0.0561700	−0.0280850	−	0.999606i	$-0.508941\pi$
$131$	−0.642895	−0.0561700	−0.0280850	+	0.999606i	$0.508941\pi$
$132$	0.262206	0.0228221
$133$	−3.93425	−0.341142
$134$	−0.347703	−0.0300369
$135$	−4.30376	−0.370409
$136$	3.19340	0.273832
$137$	−13.9212	−1.18937	−0.594685	−	0.803959i	$-0.702723\pi$
$137$	−13.9212	−1.18937	−0.594685	+	0.803959i	$0.702723\pi$
$138$	−5.66810	−0.482501
$139$	17.1300	1.45295	0.726473	−	0.687195i	$-0.241158\pi$
$139$	17.1300	1.45295	0.726473	+	0.687195i	$0.241158\pi$
$140$	−1.44710	−0.122303
$141$	7.02291	0.591436
$142$	−13.4678	−1.13020
$143$	0.962899	0.0805216
$144$	−2.35379	−0.196149
$145$	7.21197	0.598921
$146$	−5.02082	−0.415526
$147$	3.94371	0.325272
$148$	6.36496	0.523196
$149$	−4.47380	−0.366508	−0.183254	−	0.983066i	$-0.558663\pi$
$149$	−4.47380	−0.366508	−0.183254	+	0.983066i	$0.558663\pi$
$150$	−0.803872	−0.0656359
$151$	−16.1863	−1.31722	−0.658611	−	0.752484i	$-0.728856\pi$
$151$	−16.1863	−1.31722	−0.658611	+	0.752484i	$0.728856\pi$
$152$	−2.71870	−0.220516
$153$	−7.51659	−0.607681
$154$	−0.472014	−0.0380360
$155$	3.42146	0.274818
$156$	2.37308	0.189999
$157$	9.85298	0.786353	0.393177	−	0.919463i	$-0.371376\pi$
$157$	9.85298	0.786353	0.393177	+	0.919463i	$0.371376\pi$
$158$	−11.5208	−0.916543
$159$	1.83250	0.145327
$160$	−1.00000	−0.0790569
$161$	10.2035	0.804150
$162$	3.60169	0.282976
$163$	2.10378	0.164781	0.0823903	−	0.996600i	$-0.473745\pi$
$163$	2.10378	0.164781	0.0823903	+	0.996600i	$0.473745\pi$
$164$	−0.336080	−0.0262434
$165$	−0.262206	−0.0204127
$166$	2.99172	0.232202
$167$	−15.6767	−1.21310	−0.606550	−	0.795045i	$-0.707447\pi$
$167$	−15.6767	−1.21310	−0.606550	+	0.795045i	$0.707447\pi$
$168$	−1.16329	−0.0897495
$169$	−4.28532	−0.329640
$170$	−3.19340	−0.244923
$171$	6.39926	0.489363
$172$	−4.62681	−0.352791
$173$	−8.43117	−0.641010	−0.320505	−	0.947247i	$-0.603853\pi$
$173$	−8.43117	−0.641010	−0.320505	+	0.947247i	$0.603853\pi$
$174$	5.79750	0.439507
$175$	1.44710	0.109391
$176$	−0.326178	−0.0245866
$177$	3.64140	0.273705
$178$	−7.54354	−0.565413
$179$	6.33439	0.473455	0.236727	−	0.971576i	$-0.423925\pi$
$179$	6.33439	0.473455	0.236727	+	0.971576i	$0.423925\pi$
$180$	2.35379	0.175441
$181$	19.5010	1.44950	0.724750	−	0.689012i	$-0.241955\pi$
$181$	19.5010	1.44950	0.724750	+	0.689012i	$0.241955\pi$
$182$	−4.27194	−0.316657
$183$	−1.63745	−0.121044
$184$	7.05099	0.519806
$185$	−6.36496	−0.467961
$186$	2.75041	0.201670
$187$	−1.04162	−0.0761706
$188$	−8.73635	−0.637164
$189$	6.22799	0.453020
$190$	2.71870	0.197236
$191$	17.3779	1.25742	0.628709	−	0.777640i	$-0.283584\pi$
$191$	17.3779	1.25742	0.628709	+	0.777640i	$0.283584\pi$
$192$	−0.803872	−0.0580145
$193$	−9.67293	−0.696273	−0.348136	−	0.937444i	$-0.613185\pi$
$193$	−9.67293	−0.696273	−0.348136	+	0.937444i	$0.613185\pi$
$194$	11.3139	0.812292
$195$	−2.37308	−0.169940
$196$	−4.90589	−0.350421
$197$	−15.4129	−1.09812	−0.549061	−	0.835782i	$-0.685014\pi$
$197$	−15.4129	−1.09812	−0.549061	+	0.835782i	$0.685014\pi$
$198$	0.767755	0.0545620
$199$	−11.1048	−0.787201	−0.393600	−	0.919282i	$-0.628771\pi$
$199$	−11.1048	−0.787201	−0.393600	+	0.919282i	$0.628771\pi$
$200$	1.00000	0.0707107
$201$	0.279509	0.0197150
$202$	15.9703	1.12367
$203$	−10.4365	−0.732496
$204$	−2.56709	−0.179732
$205$	0.336080	0.0234728
$206$	−11.5971	−0.808011
$207$	−16.5966	−1.15354
$208$	−2.95206	−0.204689
$209$	0.886782	0.0613400
$210$	1.16329	0.0802744
$211$	15.8281	1.08965	0.544827	−	0.838548i	$-0.316595\pi$
$211$	15.8281	1.08965	0.544827	+	0.838548i	$0.316595\pi$
$212$	−2.27959	−0.156563
$213$	10.8264	0.741814
$214$	−16.0736	−1.09877
$215$	4.62681	0.315546
$216$	4.30376	0.292834
$217$	−4.95120	−0.336110
$218$	−4.81094	−0.325838
$219$	4.03610	0.272734
$220$	0.326178	0.0219909
$221$	−9.42712	−0.634137
$222$	−5.11661	−0.343405
$223$	1.52201	0.101922	0.0509608	−	0.998701i	$-0.483772\pi$
$223$	1.52201	0.101922	0.0509608	+	0.998701i	$0.483772\pi$
$224$	1.44710	0.0966887
$225$	−2.35379	−0.156919
$226$	−5.77952	−0.384448
$227$	12.3837	0.821937	0.410969	−	0.911649i	$-0.365191\pi$
$227$	12.3837	0.821937	0.410969	+	0.911649i	$0.365191\pi$
$228$	2.18549	0.144738
$229$	−1.32183	−0.0873489	−0.0436744	−	0.999046i	$-0.513906\pi$
$229$	−1.32183	−0.0873489	−0.0436744	+	0.999046i	$0.513906\pi$
$230$	−7.05099	−0.464929
$231$	0.379439	0.0249652
$232$	−7.21197	−0.473489
$233$	−2.91551	−0.191001	−0.0955006	−	0.995429i	$-0.530445\pi$
$233$	−2.91551	−0.191001	−0.0955006	+	0.995429i	$0.530445\pi$
$234$	6.94853	0.454240
$235$	8.73635	0.569897
$236$	−4.52983	−0.294867
$237$	9.26123	0.601581
$238$	4.62118	0.299547
$239$	−12.4037	−0.802326	−0.401163	−	0.916007i	$-0.631394\pi$
$239$	−12.4037	−0.802326	−0.401163	+	0.916007i	$0.631394\pi$
$240$	0.803872	0.0518897
$241$	−16.3856	−1.05549	−0.527745	−	0.849403i	$-0.676962\pi$
$241$	−16.3856	−1.05549	−0.527745	+	0.849403i	$0.676962\pi$
$242$	−10.8936	−0.700268
$243$	−15.8066	−1.01399
$244$	2.03696	0.130403
$245$	4.90589	0.313426
$246$	0.270165	0.0172251
$247$	8.02579	0.510668
$248$	−3.42146	−0.217263
$249$	−2.40496	−0.152408
$250$	−1.00000	−0.0632456
$251$	23.7542	1.49935	0.749677	−	0.661803i	$-0.230209\pi$
$251$	23.7542	1.49935	0.749677	+	0.661803i	$0.230209\pi$
$252$	−3.40618	−0.214569
$253$	−2.29988	−0.144592
$254$	9.62589	0.603982
$255$	2.56709	0.160757
$256$	1.00000	0.0625000
$257$	1.33683	0.0833890	0.0416945	−	0.999130i	$-0.486724\pi$
$257$	1.33683	0.0833890	0.0416945	+	0.999130i	$0.486724\pi$
$258$	3.71936	0.231557
$259$	9.21075	0.572328
$260$	2.95206	0.183079
$261$	16.9755	1.05075
$262$	−0.642895	−0.0397182
$263$	1.67561	0.103322	0.0516612	−	0.998665i	$-0.483548\pi$
$263$	1.67561	0.103322	0.0516612	+	0.998665i	$0.483548\pi$
$264$	0.262206	0.0161376
$265$	2.27959	0.140034
$266$	−3.93425	−0.241224
$267$	6.06405	0.371114
$268$	−0.347703	−0.0212393
$269$	−6.97178	−0.425077	−0.212538	−	0.977153i	$-0.568173\pi$
$269$	−6.97178	−0.425077	−0.212538	+	0.977153i	$0.568173\pi$
$270$	−4.30376	−0.261919
$271$	−7.54704	−0.458450	−0.229225	−	0.973373i	$-0.573619\pi$
$271$	−7.54704	−0.458450	−0.229225	+	0.973373i	$0.573619\pi$
$272$	3.19340	0.193628
$273$	3.43410	0.207841
$274$	−13.9212	−0.841011
$275$	−0.326178	−0.0196693
$276$	−5.66810	−0.341179
$277$	−0.194382	−0.0116793	−0.00583965	−	0.999983i	$-0.501859\pi$
$277$	−0.194382	−0.0116793	−0.00583965	+	0.999983i	$0.501859\pi$
$278$	17.1300	1.02739
$279$	8.05339	0.482144
$280$	−1.44710	−0.0864810
$281$	−4.70689	−0.280790	−0.140395	−	0.990096i	$-0.544837\pi$
$281$	−4.70689	−0.280790	−0.140395	+	0.990096i	$0.544837\pi$
$282$	7.02291	0.418208
$283$	2.64595	0.157285	0.0786426	−	0.996903i	$-0.474941\pi$
$283$	2.64595	0.157285	0.0786426	+	0.996903i	$0.474941\pi$
$284$	−13.4678	−0.799169
$285$	−2.18549	−0.129457
$286$	0.962899	0.0569374
$287$	−0.486342	−0.0287079
$288$	−2.35379	−0.138698
$289$	−6.80219	−0.400129
$290$	7.21197	0.423501
$291$	−9.09494	−0.533155
$292$	−5.02082	−0.293821
$293$	−19.3301	−1.12927	−0.564637	−	0.825339i	$-0.690984\pi$
$293$	−19.3301	−1.12927	−0.564637	+	0.825339i	$0.690984\pi$
$294$	3.94371	0.230002
$295$	4.52983	0.263737
$296$	6.36496	0.369956
$297$	−1.40379	−0.0814564
$298$	−4.47380	−0.259160
$299$	−20.8150	−1.20376
$300$	−0.803872	−0.0464116
$301$	−6.69547	−0.385920
$302$	−16.1863	−0.931416
$303$	−12.8381	−0.737530
$304$	−2.71870	−0.155928
$305$	−2.03696	−0.116636
$306$	−7.51659	−0.429695
$307$	22.5481	1.28689	0.643444	−	0.765493i	$-0.277505\pi$
$307$	22.5481	1.28689	0.643444	+	0.765493i	$0.277505\pi$
$308$	−0.472014	−0.0268955
$309$	9.32262	0.530345
$310$	3.42146	0.194326
$311$	15.8569	0.899164	0.449582	−	0.893239i	$-0.351573\pi$
$311$	15.8569	0.899164	0.449582	+	0.893239i	$0.351573\pi$
$312$	2.37308	0.134349
$313$	−11.8259	−0.668442	−0.334221	−	0.942495i	$-0.608473\pi$
$313$	−11.8259	−0.668442	−0.334221	+	0.942495i	$0.608473\pi$
$314$	9.85298	0.556036
$315$	3.40618	0.191916
$316$	−11.5208	−0.648094
$317$	3.60645	0.202559	0.101279	−	0.994858i	$-0.467706\pi$
$317$	3.60645	0.202559	0.101279	+	0.994858i	$0.467706\pi$
$318$	1.83250	0.102762
$319$	2.35239	0.131708
$320$	−1.00000	−0.0559017
$321$	12.9211	0.721188
$322$	10.2035	0.568620
$323$	−8.68191	−0.483074
$324$	3.60169	0.200094
$325$	−2.95206	−0.163751
$326$	2.10378	0.116517
$327$	3.86738	0.213867
$328$	−0.336080	−0.0185569
$329$	−12.6424	−0.696999
$330$	−0.262206	−0.0144339
$331$	−26.8302	−1.47472	−0.737361	−	0.675499i	$-0.763928\pi$
$331$	−26.8302	−1.47472	−0.737361	+	0.675499i	$0.763928\pi$
$332$	2.99172	0.164192
$333$	−14.9818	−0.820996
$334$	−15.6767	−0.857791
$335$	0.347703	0.0189970
$336$	−1.16329	−0.0634625
$337$	−14.5166	−0.790769	−0.395384	−	0.918516i	$-0.629389\pi$
$337$	−14.5166	−0.790769	−0.395384	+	0.918516i	$0.629389\pi$
$338$	−4.28532	−0.233091
$339$	4.64600	0.252336
$340$	−3.19340	−0.173186
$341$	1.11600	0.0604351
$342$	6.39926	0.346032
$343$	−17.2291	−0.930282
$344$	−4.62681	−0.249461
$345$	5.66810	0.305160
$346$	−8.43117	−0.453263
$347$	7.99374	0.429126	0.214563	−	0.976710i	$-0.431167\pi$
$347$	7.99374	0.429126	0.214563	+	0.976710i	$0.431167\pi$
$348$	5.79750	0.310779
$349$	4.19436	0.224519	0.112260	−	0.993679i	$-0.464191\pi$
$349$	4.19436	0.224519	0.112260	+	0.993679i	$0.464191\pi$
$350$	1.44710	0.0773510
$351$	−12.7050	−0.678142
$352$	−0.326178	−0.0173854
$353$	20.2335	1.07692	0.538461	−	0.842650i	$-0.319006\pi$
$353$	20.2335	1.07692	0.538461	+	0.842650i	$0.319006\pi$
$354$	3.64140	0.193538
$355$	13.4678	0.714798
$356$	−7.54354	−0.399807
$357$	−3.71484	−0.196610
$358$	6.33439	0.334783
$359$	26.4895	1.39806	0.699031	−	0.715092i	$-0.253615\pi$
$359$	26.4895	1.39806	0.699031	+	0.715092i	$0.253615\pi$
$360$	2.35379	0.124056
$361$	−11.6086	−0.610982
$362$	19.5010	1.02495
$363$	8.75707	0.459627
$364$	−4.27194	−0.223911
$365$	5.02082	0.262802
$366$	−1.63745	−0.0855911
$367$	−18.7944	−0.981058	−0.490529	−	0.871425i	$-0.663196\pi$
$367$	−18.7944	−0.981058	−0.490529	+	0.871425i	$0.663196\pi$
$368$	7.05099	0.367558
$369$	0.791061	0.0411810
$370$	−6.36496	−0.330898
$371$	−3.29881	−0.171266
$372$	2.75041	0.142602
$373$	4.42813	0.229280	0.114640	−	0.993407i	$-0.463429\pi$
$373$	4.42813	0.229280	0.114640	+	0.993407i	$0.463429\pi$
$374$	−1.04162	−0.0538608
$375$	0.803872	0.0415118
$376$	−8.73635	−0.450543
$377$	21.2902	1.09650
$378$	6.22799	0.320333
$379$	−23.5429	−1.20932	−0.604658	−	0.796485i	$-0.706690\pi$
$379$	−23.5429	−1.20932	−0.604658	+	0.796485i	$0.706690\pi$
$380$	2.71870	0.139467
$381$	−7.73798	−0.396429
$382$	17.3779	0.889129
$383$	15.0196	0.767464	0.383732	−	0.923444i	$-0.374639\pi$
$383$	15.0196	0.767464	0.383732	+	0.923444i	$0.374639\pi$
$384$	−0.803872	−0.0410224
$385$	0.472014	0.0240560
$386$	−9.67293	−0.492339
$387$	10.8905	0.553597
$388$	11.3139	0.574377
$389$	26.9914	1.36852	0.684258	−	0.729240i	$-0.260126\pi$
$389$	26.9914	1.36852	0.684258	+	0.729240i	$0.260126\pi$
$390$	−2.37308	−0.120166
$391$	22.5166	1.13872
$392$	−4.90589	−0.247785
$393$	0.516806	0.0260694
$394$	−15.4129	−0.776489
$395$	11.5208	0.579673
$396$	0.767755	0.0385811
$397$	−9.63708	−0.483671	−0.241836	−	0.970317i	$-0.577749\pi$
$397$	−9.63708	−0.483671	−0.241836	+	0.970317i	$0.577749\pi$
$398$	−11.1048	−0.556635
$399$	3.16263	0.158330
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	0.279509	0.0139406
$403$	10.1004	0.503135
$404$	15.9703	0.794553
$405$	−3.60169	−0.178970
$406$	−10.4365	−0.517953
$407$	−2.07611	−0.102909
$408$	−2.56709	−0.127090
$409$	−27.8993	−1.37953	−0.689766	−	0.724032i	$-0.742287\pi$
$409$	−27.8993	−1.37953	−0.689766	+	0.724032i	$0.742287\pi$
$410$	0.336080	0.0165978
$411$	11.1909	0.552005
$412$	−11.5971	−0.571350
$413$	−6.55513	−0.322557
$414$	−16.5966	−0.815676
$415$	−2.99172	−0.146858
$416$	−2.95206	−0.144737
$417$	−13.7703	−0.674336
$418$	0.886782	0.0433739
$419$	−6.31040	−0.308283	−0.154142	−	0.988049i	$-0.549261\pi$
$419$	−6.31040	−0.308283	−0.154142	+	0.988049i	$0.549261\pi$
$420$	1.16329	0.0567626
$421$	15.0719	0.734557	0.367279	−	0.930111i	$-0.380290\pi$
$421$	15.0719	0.734557	0.367279	+	0.930111i	$0.380290\pi$
$422$	15.8281	0.770502
$423$	20.5635	0.999833
$424$	−2.27959	−0.110707
$425$	3.19340	0.154903
$426$	10.8264	0.524542
$427$	2.94769	0.142649
$428$	−16.0736	−0.776948
$429$	−0.774047	−0.0373714
$430$	4.62681	0.223124
$431$	5.55855	0.267746	0.133873	−	0.990998i	$-0.457259\pi$
$431$	5.55855	0.267746	0.133873	+	0.990998i	$0.457259\pi$
$432$	4.30376	0.207065
$433$	15.1803	0.729519	0.364760	−	0.931102i	$-0.381151\pi$
$433$	15.1803	0.729519	0.364760	+	0.931102i	$0.381151\pi$
$434$	−4.95120	−0.237665
$435$	−5.79750	−0.277969
$436$	−4.81094	−0.230402
$437$	−19.1696	−0.917005
$438$	4.03610	0.192852
$439$	−12.5804	−0.600430	−0.300215	−	0.953872i	$-0.597058\pi$
$439$	−12.5804	−0.600430	−0.300215	+	0.953872i	$0.597058\pi$
$440$	0.326178	0.0155499
$441$	11.5474	0.549878
$442$	−9.42712	−0.448402
$443$	9.27470	0.440654	0.220327	−	0.975426i	$-0.429288\pi$
$443$	9.27470	0.440654	0.220327	+	0.975426i	$0.429288\pi$
$444$	−5.11661	−0.242824
$445$	7.54354	0.357598
$446$	1.52201	0.0720694
$447$	3.59637	0.170102
$448$	1.44710	0.0683692
$449$	−13.0290	−0.614877	−0.307438	−	0.951568i	$-0.599472\pi$
$449$	−13.0290	−0.614877	−0.307438	+	0.951568i	$0.599472\pi$
$450$	−2.35379	−0.110959
$451$	0.109622	0.00516190
$452$	−5.77952	−0.271846
$453$	13.0117	0.611343
$454$	12.3837	0.581198
$455$	4.27194	0.200272
$456$	2.18549	0.102345
$457$	20.7626	0.971236	0.485618	−	0.874171i	$-0.338595\pi$
$457$	20.7626	0.971236	0.485618	+	0.874171i	$0.338595\pi$
$458$	−1.32183	−0.0617650
$459$	13.7436	0.641498
$460$	−7.05099	−0.328754
$461$	0.355841	0.0165732	0.00828658	−	0.999966i	$-0.497362\pi$
$461$	0.355841	0.0165732	0.00828658	+	0.999966i	$0.497362\pi$
$462$	0.379439	0.0176531
$463$	−14.7129	−0.683767	−0.341883	−	0.939742i	$-0.611065\pi$
$463$	−14.7129	−0.683767	−0.341883	+	0.939742i	$0.611065\pi$
$464$	−7.21197	−0.334807
$465$	−2.75041	−0.127547
$466$	−2.91551	−0.135058
$467$	37.4942	1.73502	0.867512	−	0.497417i	$-0.165718\pi$
$467$	37.4942	1.73502	0.867512	+	0.497417i	$0.165718\pi$
$468$	6.94853	0.321196
$469$	−0.503162	−0.0232339
$470$	8.73635	0.402978
$471$	−7.92053	−0.364959
$472$	−4.52983	−0.208502
$473$	1.50916	0.0693914
$474$	9.26123	0.425382
$475$	−2.71870	−0.124743
$476$	4.62118	0.211812
$477$	5.36568	0.245678
$478$	−12.4037	−0.567330
$479$	35.6215	1.62759	0.813795	−	0.581152i	$-0.197398\pi$
$479$	35.6215	1.62759	0.813795	+	0.581152i	$0.197398\pi$
$480$	0.803872	0.0366916
$481$	−18.7898	−0.856739
$482$	−16.3856	−0.746344
$483$	−8.20233	−0.373219
$484$	−10.8936	−0.495164
$485$	−11.3139	−0.513738
$486$	−15.8066	−0.717001
$487$	−21.2978	−0.965094	−0.482547	−	0.875870i	$-0.660288\pi$
$487$	−21.2978	−0.965094	−0.482547	+	0.875870i	$0.660288\pi$
$488$	2.03696	0.0922087
$489$	−1.69117	−0.0764773
$490$	4.90589	0.221626
$491$	21.0042	0.947907	0.473953	−	0.880550i	$-0.342827\pi$
$491$	21.0042	0.947907	0.473953	+	0.880550i	$0.342827\pi$
$492$	0.270165	0.0121800
$493$	−23.0307	−1.03725
$494$	8.02579	0.361097
$495$	−0.767755	−0.0345080
$496$	−3.42146	−0.153628
$497$	−19.4894	−0.874217
$498$	−2.40496	−0.107769
$499$	30.4121	1.36143	0.680717	−	0.732547i	$-0.261668\pi$
$499$	30.4121	1.36143	0.680717	+	0.732547i	$0.261668\pi$
$500$	−1.00000	−0.0447214
$501$	12.6021	0.563019
$502$	23.7542	1.06020
$503$	−16.4435	−0.733178	−0.366589	−	0.930383i	$-0.619474\pi$
$503$	−16.4435	−0.733178	−0.366589	+	0.930383i	$0.619474\pi$
$504$	−3.40618	−0.151723
$505$	−15.9703	−0.710670
$506$	−2.29988	−0.102242
$507$	3.44485	0.152991
$508$	9.62589	0.427080
$509$	32.5560	1.44302	0.721509	−	0.692405i	$-0.243449\pi$
$509$	32.5560	1.44302	0.721509	+	0.692405i	$0.243449\pi$
$510$	2.56709	0.113672
$511$	−7.26565	−0.321413
$512$	1.00000	0.0441942
$513$	−11.7007	−0.516597
$514$	1.33683	0.0589649
$515$	11.5971	0.511031
$516$	3.71936	0.163736
$517$	2.84961	0.125326
$518$	9.21075	0.404697
$519$	6.77758	0.297503
$520$	2.95206	0.129457
$521$	−13.8205	−0.605488	−0.302744	−	0.953072i	$-0.597903\pi$
$521$	−13.8205	−0.605488	−0.302744	+	0.953072i	$0.597903\pi$
$522$	16.9755	0.742995
$523$	−8.52986	−0.372985	−0.186492	−	0.982456i	$-0.559712\pi$
$523$	−8.52986	−0.372985	−0.186492	+	0.982456i	$0.559712\pi$
$524$	−0.642895	−0.0280850
$525$	−1.16329	−0.0507700
$526$	1.67561	0.0730600
$527$	−10.9261	−0.475948
$528$	0.262206	0.0114110
$529$	26.7165	1.16159
$530$	2.27959	0.0990192
$531$	10.6623	0.462703
$532$	−3.93425	−0.170571
$533$	0.992129	0.0429739
$534$	6.06405	0.262417
$535$	16.0736	0.694924
$536$	−0.347703	−0.0150185
$537$	−5.09204	−0.219738
$538$	−6.97178	−0.300575
$539$	1.60019	0.0689253
$540$	−4.30376	−0.185204
$541$	24.6341	1.05910	0.529551	−	0.848278i	$-0.322361\pi$
$541$	24.6341	1.05910	0.529551	+	0.848278i	$0.322361\pi$
$542$	−7.54704	−0.324173
$543$	−15.6763	−0.672736
$544$	3.19340	0.136916
$545$	4.81094	0.206078
$546$	3.43410	0.146966
$547$	−15.7174	−0.672030	−0.336015	−	0.941857i	$-0.609079\pi$
$547$	−15.7174	−0.672030	−0.336015	+	0.941857i	$0.609079\pi$
$548$	−13.9212	−0.594685
$549$	−4.79457	−0.204627
$550$	−0.326178	−0.0139083
$551$	19.6072	0.835295
$552$	−5.66810	−0.241250
$553$	−16.6717	−0.708955
$554$	−0.194382	−0.00825852
$555$	5.11661	0.217188
$556$	17.1300	0.726473
$557$	32.1545	1.36243	0.681215	−	0.732084i	$-0.261452\pi$
$557$	32.1545	1.36243	0.681215	+	0.732084i	$0.261452\pi$
$558$	8.05339	0.340927
$559$	13.6586	0.577698
$560$	−1.44710	−0.0611513
$561$	0.837328	0.0353520
$562$	−4.70689	−0.198548
$563$	16.5422	0.697171	0.348585	−	0.937277i	$-0.386662\pi$
$563$	16.5422	0.697171	0.348585	+	0.937277i	$0.386662\pi$
$564$	7.02291	0.295718
$565$	5.77952	0.243146
$566$	2.64595	0.111217
$567$	5.21202	0.218884
$568$	−13.4678	−0.565098
$569$	17.2773	0.724304	0.362152	−	0.932119i	$-0.382042\pi$
$569$	17.2773	0.724304	0.362152	+	0.932119i	$0.382042\pi$
$570$	−2.18549	−0.0915401
$571$	−5.93114	−0.248211	−0.124105	−	0.992269i	$-0.539606\pi$
$571$	−5.93114	−0.248211	−0.124105	+	0.992269i	$0.539606\pi$
$572$	0.962899	0.0402608
$573$	−13.9696	−0.583588
$574$	−0.486342	−0.0202995
$575$	7.05099	0.294047
$576$	−2.35379	−0.0980746
$577$	−10.6009	−0.441321	−0.220661	−	0.975351i	$-0.570821\pi$
$577$	−10.6009	−0.441321	−0.220661	+	0.975351i	$0.570821\pi$
$578$	−6.80219	−0.282934
$579$	7.77580	0.323151
$580$	7.21197	0.299461
$581$	4.32933	0.179611
$582$	−9.09494	−0.376997
$583$	0.743554	0.0307948
$584$	−5.02082	−0.207763
$585$	−6.94853	−0.287287
$586$	−19.3301	−0.798518
$587$	−5.00024	−0.206382	−0.103191	−	0.994662i	$-0.532905\pi$
$587$	−5.00024	−0.206382	−0.103191	+	0.994662i	$0.532905\pi$
$588$	3.94371	0.162636
$589$	9.30193	0.383279
$590$	4.52983	0.186490
$591$	12.3900	0.509656
$592$	6.36496	0.261598
$593$	−5.38669	−0.221205	−0.110602	−	0.993865i	$-0.535278\pi$
$593$	−5.38669	−0.221205	−0.110602	+	0.993865i	$0.535278\pi$
$594$	−1.40379	−0.0575984
$595$	−4.62118	−0.189450
$596$	−4.47380	−0.183254
$597$	8.92687	0.365352
$598$	−20.8150	−0.851188
$599$	−9.60063	−0.392271	−0.196136	−	0.980577i	$-0.562839\pi$
$599$	−9.60063	−0.392271	−0.196136	+	0.980577i	$0.562839\pi$
$600$	−0.803872	−0.0328179
$601$	−4.45095	−0.181558	−0.0907790	−	0.995871i	$-0.528936\pi$
$601$	−4.45095	−0.181558	−0.0907790	+	0.995871i	$0.528936\pi$
$602$	−6.69547	−0.272887
$603$	0.818419	0.0333286
$604$	−16.1863	−0.658611
$605$	10.8936	0.442888
$606$	−12.8381	−0.521512
$607$	33.4240	1.35664	0.678319	−	0.734768i	$-0.262709\pi$
$607$	33.4240	1.35664	0.678319	+	0.734768i	$0.262709\pi$
$608$	−2.71870	−0.110258
$609$	8.38958	0.339963
$610$	−2.03696	−0.0824740
$611$	25.7903	1.04336
$612$	−7.51659	−0.303840
$613$	−14.1004	−0.569508	−0.284754	−	0.958601i	$-0.591912\pi$
$613$	−14.1004	−0.569508	−0.284754	+	0.958601i	$0.591912\pi$
$614$	22.5481	0.909967
$615$	−0.270165	−0.0108941
$616$	−0.472014	−0.0190180
$617$	20.6375	0.830833	0.415417	−	0.909631i	$-0.363636\pi$
$617$	20.6375	0.830833	0.415417	+	0.909631i	$0.363636\pi$
$618$	9.32262	0.375011
$619$	47.4493	1.90715	0.953574	−	0.301160i	$-0.0973739\pi$
$619$	47.4493	1.90715	0.953574	+	0.301160i	$0.0973739\pi$
$620$	3.42146	0.137409
$621$	30.3458	1.21774
$622$	15.8569	0.635805
$623$	−10.9163	−0.437352
$624$	2.37308	0.0949993
$625$	1.00000	0.0400000
$626$	−11.8259	−0.472660
$627$	−0.712859	−0.0284689
$628$	9.85298	0.393177
$629$	20.3259	0.810445
$630$	3.40618	0.135705
$631$	−11.4304	−0.455038	−0.227519	−	0.973774i	$-0.573061\pi$
$631$	−11.4304	−0.455038	−0.227519	+	0.973774i	$0.573061\pi$
$632$	−11.5208	−0.458272
$633$	−12.7238	−0.505726
$634$	3.60645	0.143231
$635$	−9.62589	−0.381992
$636$	1.83250	0.0726634
$637$	14.4825	0.573817
$638$	2.35239	0.0931319
$639$	31.7004	1.25405
$640$	−1.00000	−0.0395285
$641$	31.6893	1.25165	0.625826	−	0.779962i	$-0.284762\pi$
$641$	31.6893	1.25165	0.625826	+	0.779962i	$0.284762\pi$
$642$	12.9211	0.509957
$643$	−15.7795	−0.622282	−0.311141	−	0.950364i	$-0.600711\pi$
$643$	−15.7795	−0.622282	−0.311141	+	0.950364i	$0.600711\pi$
$644$	10.2035	0.402075
$645$	−3.71936	−0.146450
$646$	−8.68191	−0.341585
$647$	29.0571	1.14235	0.571177	−	0.820827i	$-0.306487\pi$
$647$	29.0571	1.14235	0.571177	+	0.820827i	$0.306487\pi$
$648$	3.60169	0.141488
$649$	1.47753	0.0579982
$650$	−2.95206	−0.115789
$651$	3.98014	0.155994
$652$	2.10378	0.0823903
$653$	10.8619	0.425059	0.212529	−	0.977155i	$-0.431830\pi$
$653$	10.8619	0.425059	0.212529	+	0.977155i	$0.431830\pi$
$654$	3.86738	0.151227
$655$	0.642895	0.0251200
$656$	−0.336080	−0.0131217
$657$	11.8180	0.461062
$658$	−12.6424	−0.492852
$659$	39.8398	1.55194	0.775969	−	0.630771i	$-0.217261\pi$
$659$	39.8398	1.55194	0.775969	+	0.630771i	$0.217261\pi$
$660$	−0.262206	−0.0102063
$661$	−10.5056	−0.408622	−0.204311	−	0.978906i	$-0.565495\pi$
$661$	−10.5056	−0.408622	−0.204311	+	0.978906i	$0.565495\pi$
$662$	−26.8302	−1.04279
$663$	7.57820	0.294313
$664$	2.99172	0.116101
$665$	3.93425	0.152564
$666$	−14.9818	−0.580532
$667$	−50.8515	−1.96898
$668$	−15.6767	−0.606550
$669$	−1.22350	−0.0473034
$670$	0.347703	0.0134329
$671$	−0.664411	−0.0256493
$672$	−1.16329	−0.0448748
$673$	−0.987095	−0.0380497	−0.0190249	−	0.999819i	$-0.506056\pi$
$673$	−0.987095	−0.0380497	−0.0190249	+	0.999819i	$0.506056\pi$
$674$	−14.5166	−0.559158
$675$	4.30376	0.165652
$676$	−4.28532	−0.164820
$677$	38.8848	1.49446	0.747231	−	0.664564i	$-0.231383\pi$
$677$	38.8848	1.49446	0.747231	+	0.664564i	$0.231383\pi$
$678$	4.64600	0.178429
$679$	16.3724	0.628315
$680$	−3.19340	−0.122461
$681$	−9.95494	−0.381474
$682$	1.11600	0.0427340
$683$	−25.5822	−0.978876	−0.489438	−	0.872038i	$-0.662798\pi$
$683$	−25.5822	−0.978876	−0.489438	+	0.872038i	$0.662798\pi$
$684$	6.39926	0.244682
$685$	13.9212	0.531902
$686$	−17.2291	−0.657809
$687$	1.06258	0.0405400
$688$	−4.62681	−0.176395
$689$	6.72950	0.256374
$690$	5.66810	0.215781
$691$	10.3243	0.392753	0.196377	−	0.980529i	$-0.437082\pi$
$691$	10.3243	0.392753	0.196377	+	0.980529i	$0.437082\pi$
$692$	−8.43117	−0.320505
$693$	1.11102	0.0422042
$694$	7.99374	0.303438
$695$	−17.1300	−0.649777
$696$	5.79750	0.219754
$697$	−1.07324	−0.0406518
$698$	4.19436	0.158759
$699$	2.34369	0.0886466
$700$	1.44710	0.0546954
$701$	14.1826	0.535668	0.267834	−	0.963465i	$-0.413692\pi$
$701$	14.1826	0.535668	0.267834	+	0.963465i	$0.413692\pi$
$702$	−12.7050	−0.479519
$703$	−17.3044	−0.652649
$704$	−0.326178	−0.0122933
$705$	−7.02291	−0.264498
$706$	20.2335	0.761499
$707$	23.1107	0.869168
$708$	3.64140	0.136852
$709$	−38.0349	−1.42843	−0.714215	−	0.699927i	$-0.753216\pi$
$709$	−38.0349	−1.42843	−0.714215	+	0.699927i	$0.753216\pi$
$710$	13.4678	0.505439
$711$	27.1175	1.01698
$712$	−7.54354	−0.282706
$713$	−24.1247	−0.903476
$714$	−3.71484	−0.139024
$715$	−0.962899	−0.0360104
$716$	6.33439	0.236727
$717$	9.97095	0.372372
$718$	26.4895	0.988579
$719$	−50.6743	−1.88983	−0.944916	−	0.327314i	$-0.893857\pi$
$719$	−50.6743	−1.88983	−0.944916	+	0.327314i	$0.893857\pi$
$720$	2.35379	0.0877206
$721$	−16.7823	−0.625004
$722$	−11.6086	−0.432029
$723$	13.1719	0.489870
$724$	19.5010	0.724750
$725$	−7.21197	−0.267846
$726$	8.75707	0.325005
$727$	−12.3826	−0.459246	−0.229623	−	0.973280i	$-0.573749\pi$
$727$	−12.3826	−0.459246	−0.229623	+	0.973280i	$0.573749\pi$
$728$	−4.27194	−0.158329
$729$	1.90140	0.0704222
$730$	5.02082	0.185829
$731$	−14.7752	−0.546482
$732$	−1.63745	−0.0605220
$733$	−8.97770	−0.331599	−0.165799	−	0.986159i	$-0.553020\pi$
$733$	−8.97770	−0.331599	−0.165799	+	0.986159i	$0.553020\pi$
$734$	−18.7944	−0.693713
$735$	−3.94371	−0.145466
$736$	7.05099	0.259903
$737$	0.113413	0.00417762
$738$	0.791061	0.0291194
$739$	5.89861	0.216984	0.108492	−	0.994097i	$-0.465398\pi$
$739$	5.89861	0.216984	0.108492	+	0.994097i	$0.465398\pi$
$740$	−6.36496	−0.233980
$741$	−6.45171	−0.237009
$742$	−3.29881	−0.121103
$743$	26.3869	0.968043	0.484022	−	0.875056i	$-0.339176\pi$
$743$	26.3869	0.968043	0.484022	+	0.875056i	$0.339176\pi$
$744$	2.75041	0.100835
$745$	4.47380	0.163907
$746$	4.42813	0.162126
$747$	−7.04188	−0.257649
$748$	−1.04162	−0.0380853
$749$	−23.2602	−0.849910
$750$	0.803872	0.0293533
$751$	−28.1776	−1.02821	−0.514107	−	0.857726i	$-0.671877\pi$
$751$	−28.1776	−1.02821	−0.514107	+	0.857726i	$0.671877\pi$
$752$	−8.73635	−0.318582
$753$	−19.0954	−0.695874
$754$	21.2902	0.775343
$755$	16.1863	0.589079
$756$	6.22799	0.226510
$757$	7.47421	0.271655	0.135827	−	0.990733i	$-0.456631\pi$
$757$	7.47421	0.271655	0.135827	+	0.990733i	$0.456631\pi$
$758$	−23.5429	−0.855115
$759$	1.84881	0.0671075
$760$	2.71870	0.0986178
$761$	−19.8789	−0.720608	−0.360304	−	0.932835i	$-0.617327\pi$
$761$	−19.8789	−0.720608	−0.360304	+	0.932835i	$0.617327\pi$
$762$	−7.73798	−0.280318
$763$	−6.96194	−0.252039
$764$	17.3779	0.628709
$765$	7.51659	0.271763
$766$	15.0196	0.542679
$767$	13.3723	0.482847
$768$	−0.803872	−0.0290072
$769$	4.14990	0.149649	0.0748247	−	0.997197i	$-0.476160\pi$
$769$	4.14990	0.149649	0.0748247	+	0.997197i	$0.476160\pi$
$770$	0.472014	0.0170102
$771$	−1.07464	−0.0387021
$772$	−9.67293	−0.348136
$773$	2.71934	0.0978077	0.0489039	−	0.998803i	$-0.484427\pi$
$773$	2.71934	0.0978077	0.0489039	+	0.998803i	$0.484427\pi$
$774$	10.8905	0.391452
$775$	−3.42146	−0.122902
$776$	11.3139	0.406146
$777$	−7.40427	−0.265627
$778$	26.9914	0.967687
$779$	0.913702	0.0327368
$780$	−2.37308	−0.0849699
$781$	4.39291	0.157191
$782$	22.5166	0.805194
$783$	−31.0386	−1.10923
$784$	−4.90589	−0.175210
$785$	−9.85298	−0.351668
$786$	0.516806	0.0184338
$787$	−6.36771	−0.226984	−0.113492	−	0.993539i	$-0.536204\pi$
$787$	−6.36771	−0.226984	−0.113492	+	0.993539i	$0.536204\pi$
$788$	−15.4129	−0.549061
$789$	−1.34698	−0.0479536
$790$	11.5208	0.409891
$791$	−8.36357	−0.297374
$792$	0.767755	0.0272810
$793$	−6.01323	−0.213536
$794$	−9.63708	−0.342007
$795$	−1.83250	−0.0649921
$796$	−11.1048	−0.393600
$797$	−12.0101	−0.425419	−0.212709	−	0.977115i	$-0.568229\pi$
$797$	−12.0101	−0.425419	−0.212709	+	0.977115i	$0.568229\pi$
$798$	3.16263	0.111956
$799$	−27.8987	−0.986984
$800$	1.00000	0.0353553
$801$	17.7559	0.627374
$802$	1.00000	0.0353112
$803$	1.63768	0.0577925
$804$	0.279509	0.00985751
$805$	−10.2035	−0.359627
$806$	10.1004	0.355770
$807$	5.60442	0.197285
$808$	15.9703	0.561834
$809$	51.9096	1.82504	0.912522	−	0.409029i	$-0.134132\pi$
$809$	51.9096	1.82504	0.912522	+	0.409029i	$0.134132\pi$
$810$	−3.60169	−0.126551
$811$	27.3118	0.959048	0.479524	−	0.877529i	$-0.340809\pi$
$811$	27.3118	0.959048	0.479524	+	0.877529i	$0.340809\pi$
$812$	−10.4365	−0.366248
$813$	6.06685	0.212774
$814$	−2.07611	−0.0727676
$815$	−2.10378	−0.0736921
$816$	−2.56709	−0.0898660
$817$	12.5789	0.440080
$818$	−27.8993	−0.975477
$819$	10.0553	0.351359
$820$	0.336080	0.0117364
$821$	−54.2610	−1.89372	−0.946861	−	0.321644i	$-0.895765\pi$
$821$	−54.2610	−1.89372	−0.946861	+	0.321644i	$0.895765\pi$
$822$	11.1909	0.390327
$823$	14.6977	0.512330	0.256165	−	0.966633i	$-0.417541\pi$
$823$	14.6977	0.512330	0.256165	+	0.966633i	$0.417541\pi$
$824$	−11.5971	−0.404005
$825$	0.262206	0.00912883
$826$	−6.55513	−0.228082
$827$	−38.9738	−1.35525	−0.677625	−	0.735407i	$-0.736991\pi$
$827$	−38.9738	−1.35525	−0.677625	+	0.735407i	$0.736991\pi$
$828$	−16.5966	−0.576770
$829$	−55.5200	−1.92829	−0.964145	−	0.265376i	$-0.914504\pi$
$829$	−55.5200	−1.92829	−0.964145	+	0.265376i	$0.914504\pi$
$830$	−2.99172	−0.103844
$831$	0.156259	0.00542055
$832$	−2.95206	−0.102344
$833$	−15.6665	−0.542811
$834$	−13.7703	−0.476827
$835$	15.6767	0.542515
$836$	0.886782	0.0306700
$837$	−14.7251	−0.508975
$838$	−6.31040	−0.217989
$839$	47.0870	1.62562	0.812812	−	0.582526i	$-0.197936\pi$
$839$	47.0870	1.62562	0.812812	+	0.582526i	$0.197936\pi$
$840$	1.16329	0.0401372
$841$	23.0125	0.793533
$842$	15.0719	0.519411
$843$	3.78374	0.130319
$844$	15.8281	0.544827
$845$	4.28532	0.147420
$846$	20.5635	0.706989
$847$	−15.7642	−0.541664
$848$	−2.27959	−0.0782816
$849$	−2.12700	−0.0729985
$850$	3.19340	0.109533
$851$	44.8793	1.53844
$852$	10.8264	0.370907
$853$	−38.3245	−1.31220	−0.656102	−	0.754672i	$-0.727796\pi$
$853$	−38.3245	−1.31220	−0.656102	+	0.754672i	$0.727796\pi$
$854$	2.94769	0.100868
$855$	−6.39926	−0.218850
$856$	−16.0736	−0.549385
$857$	−37.2582	−1.27272	−0.636359	−	0.771393i	$-0.719560\pi$
$857$	−37.2582	−1.27272	−0.636359	+	0.771393i	$0.719560\pi$
$858$	−0.774047	−0.0264255
$859$	−38.6399	−1.31838	−0.659188	−	0.751978i	$-0.729100\pi$
$859$	−38.6399	−1.31838	−0.659188	+	0.751978i	$0.729100\pi$
$860$	4.62681	0.157773
$861$	0.390957	0.0133238
$862$	5.55855	0.189325
$863$	−3.58191	−0.121930	−0.0609648	−	0.998140i	$-0.519418\pi$
$863$	−3.58191	−0.121930	−0.0609648	+	0.998140i	$0.519418\pi$
$864$	4.30376	0.146417
$865$	8.43117	0.286668
$866$	15.1803	0.515848
$867$	5.46809	0.185706
$868$	−4.95120	−0.168055
$869$	3.75782	0.127475
$870$	−5.79750	−0.196554
$871$	1.02644	0.0347796
$872$	−4.81094	−0.162919
$873$	−26.6306	−0.901308
$874$	−19.1696	−0.648420
$875$	−1.44710	−0.0489210
$876$	4.03610	0.136367
$877$	14.3105	0.483232	0.241616	−	0.970372i	$-0.422323\pi$
$877$	14.3105	0.483232	0.241616	+	0.970372i	$0.422323\pi$
$878$	−12.5804	−0.424568
$879$	15.5389	0.524114
$880$	0.326178	0.0109955
$881$	−40.0096	−1.34796	−0.673978	−	0.738751i	$-0.735416\pi$
$881$	−40.0096	−1.34796	−0.673978	+	0.738751i	$0.735416\pi$
$882$	11.5474	0.388822
$883$	−15.4419	−0.519660	−0.259830	−	0.965654i	$-0.583667\pi$
$883$	−15.4419	−0.519660	−0.259830	+	0.965654i	$0.583667\pi$
$884$	−9.42712	−0.317068
$885$	−3.64140	−0.122404
$886$	9.27470	0.311590
$887$	34.9459	1.17337	0.586684	−	0.809816i	$-0.300433\pi$
$887$	34.9459	1.17337	0.586684	+	0.809816i	$0.300433\pi$
$888$	−5.11661	−0.171702
$889$	13.9297	0.467186
$890$	7.54354	0.252860
$891$	−1.17479	−0.0393571
$892$	1.52201	0.0509608
$893$	23.7516	0.794815
$894$	3.59637	0.120280
$895$	−6.33439	−0.211735
$896$	1.44710	0.0483443
$897$	16.7326	0.558685
$898$	−13.0290	−0.434783
$899$	24.6754	0.822972
$900$	−2.35379	−0.0784596
$901$	−7.27966	−0.242520
$902$	0.109622	0.00365001
$903$	5.38230	0.179112
$904$	−5.77952	−0.192224
$905$	−19.5010	−0.648236
$906$	13.0117	0.432285
$907$	−12.0825	−0.401192	−0.200596	−	0.979674i	$-0.564288\pi$
$907$	−12.0825	−0.401192	−0.200596	+	0.979674i	$0.564288\pi$
$908$	12.3837	0.410969
$909$	−37.5908	−1.24681
$910$	4.27194	0.141613
$911$	18.1295	0.600659	0.300329	−	0.953836i	$-0.402903\pi$
$911$	18.1295	0.600659	0.300329	+	0.953836i	$0.402903\pi$
$912$	2.18549	0.0723688
$913$	−0.975834	−0.0322954
$914$	20.7626	0.686767
$915$	1.63745	0.0541325
$916$	−1.32183	−0.0436744
$917$	−0.930336	−0.0307224
$918$	13.7436	0.453608
$919$	6.62348	0.218489	0.109244	−	0.994015i	$-0.465157\pi$
$919$	6.62348	0.218489	0.109244	+	0.994015i	$0.465157\pi$
$920$	−7.05099	−0.232464
$921$	−18.1258	−0.597265
$922$	0.355841	0.0117190
$923$	39.7579	1.30865
$924$	0.379439	0.0124826
$925$	6.36496	0.209278
$926$	−14.7129	−0.483496
$927$	27.2972	0.896558
$928$	−7.21197	−0.236744
$929$	11.7995	0.387129	0.193564	−	0.981088i	$-0.437995\pi$
$929$	11.7995	0.387129	0.193564	+	0.981088i	$0.437995\pi$
$930$	−2.75041	−0.0901897
$931$	13.3377	0.437124
$932$	−2.91551	−0.0955006
$933$	−12.7469	−0.417316
$934$	37.4942	1.22685
$935$	1.04162	0.0340645
$936$	6.94853	0.227120
$937$	14.2075	0.464138	0.232069	−	0.972699i	$-0.425450\pi$
$937$	14.2075	0.464138	0.232069	+	0.972699i	$0.425450\pi$
$938$	−0.503162	−0.0164288
$939$	9.50655	0.310235
$940$	8.73635	0.284948
$941$	−28.8763	−0.941342	−0.470671	−	0.882309i	$-0.655988\pi$
$941$	−28.8763	−0.941342	−0.470671	+	0.882309i	$0.655988\pi$
$942$	−7.92053	−0.258065
$943$	−2.36970	−0.0771679
$944$	−4.52983	−0.147433
$945$	−6.22799	−0.202597
$946$	1.50916	0.0490671
$947$	19.2741	0.626325	0.313163	−	0.949700i	$-0.398612\pi$
$947$	19.2741	0.626325	0.313163	+	0.949700i	$0.398612\pi$
$948$	9.26123	0.300791
$949$	14.8218	0.481135
$950$	−2.71870	−0.0882064
$951$	−2.89913	−0.0940107
$952$	4.62118	0.149773
$953$	−32.1130	−1.04024	−0.520121	−	0.854092i	$-0.674113\pi$
$953$	−32.1130	−1.04024	−0.520121	+	0.854092i	$0.674113\pi$
$954$	5.36568	0.173720
$955$	−17.3779	−0.562335
$956$	−12.4037	−0.401163
$957$	−1.89102	−0.0611279
$958$	35.6215	1.15088
$959$	−20.1454	−0.650530
$960$	0.803872	0.0259449
$961$	−19.2936	−0.622375
$962$	−18.7898	−0.605806
$963$	37.8339	1.21918
$964$	−16.3856	−0.527745
$965$	9.67293	0.311383
$966$	−8.20233	−0.263906
$967$	47.4304	1.52526	0.762630	−	0.646836i	$-0.223908\pi$
$967$	47.4304	1.52526	0.762630	+	0.646836i	$0.223908\pi$
$968$	−10.8936	−0.350134
$969$	6.97915	0.224203
$970$	−11.3139	−0.363268
$971$	−6.58921	−0.211458	−0.105729	−	0.994395i	$-0.533718\pi$
$971$	−6.58921	−0.211458	−0.105729	+	0.994395i	$0.533718\pi$
$972$	−15.8066	−0.506997
$973$	24.7889	0.794695
$974$	−21.2978	−0.682424
$975$	2.37308	0.0759994
$976$	2.03696	0.0652014
$977$	−13.7289	−0.439225	−0.219612	−	0.975587i	$-0.570479\pi$
$977$	−13.7289	−0.439225	−0.219612	+	0.975587i	$0.570479\pi$
$978$	−1.69117	−0.0540776
$979$	2.46054	0.0786392
$980$	4.90589	0.156713
$981$	11.3239	0.361546
$982$	21.0042	0.670271
$983$	−12.0390	−0.383983	−0.191992	−	0.981397i	$-0.561495\pi$
$983$	−12.0390	−0.383983	−0.191992	+	0.981397i	$0.561495\pi$
$984$	0.270165	0.00861255
$985$	15.4129	0.491095
$986$	−23.0307	−0.733447
$987$	10.1629	0.323488
$988$	8.02579	0.255334
$989$	−32.6236	−1.03737
$990$	−0.767755	−0.0244008
$991$	13.7130	0.435608	0.217804	−	0.975993i	$-0.430111\pi$
$991$	13.7130	0.435608	0.217804	+	0.975993i	$0.430111\pi$
$992$	−3.42146	−0.108631
$993$	21.5681	0.684442
$994$	−19.4894	−0.618165
$995$	11.1048	0.352047
$996$	−2.40496	−0.0762041
$997$	2.51290	0.0795843	0.0397921	−	0.999208i	$-0.487330\pi$
$997$	2.51290	0.0795843	0.0397921	+	0.999208i	$0.487330\pi$
$998$	30.4121	0.962679
$999$	27.3933	0.866684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.j.1.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.j.1.6	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.803872 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.803872 q^{6} +1.44710 q^{7} +1.00000 q^{8} -2.35379 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.803872 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.803872 q^{6} +1.44710 q^{7} +1.00000 q^{8} -2.35379 q^{9} -1.00000 q^{10} -0.326178 q^{11} -0.803872 q^{12} -2.95206 q^{13} +1.44710 q^{14} +0.803872 q^{15} +1.00000 q^{16} +3.19340 q^{17} -2.35379 q^{18} -2.71870 q^{19} -1.00000 q^{20} -1.16329 q^{21} -0.326178 q^{22} +7.05099 q^{23} -0.803872 q^{24} +1.00000 q^{25} -2.95206 q^{26} +4.30376 q^{27} +1.44710 q^{28} -7.21197 q^{29} +0.803872 q^{30} -3.42146 q^{31} +1.00000 q^{32} +0.262206 q^{33} +3.19340 q^{34} -1.44710 q^{35} -2.35379 q^{36} +6.36496 q^{37} -2.71870 q^{38} +2.37308 q^{39} -1.00000 q^{40} -0.336080 q^{41} -1.16329 q^{42} -4.62681 q^{43} -0.326178 q^{44} +2.35379 q^{45} +7.05099 q^{46} -8.73635 q^{47} -0.803872 q^{48} -4.90589 q^{49} +1.00000 q^{50} -2.56709 q^{51} -2.95206 q^{52} -2.27959 q^{53} +4.30376 q^{54} +0.326178 q^{55} +1.44710 q^{56} +2.18549 q^{57} -7.21197 q^{58} -4.52983 q^{59} +0.803872 q^{60} +2.03696 q^{61} -3.42146 q^{62} -3.40618 q^{63} +1.00000 q^{64} +2.95206 q^{65} +0.262206 q^{66} -0.347703 q^{67} +3.19340 q^{68} -5.66810 q^{69} -1.44710 q^{70} -13.4678 q^{71} -2.35379 q^{72} -5.02082 q^{73} +6.36496 q^{74} -0.803872 q^{75} -2.71870 q^{76} -0.472014 q^{77} +2.37308 q^{78} -11.5208 q^{79} -1.00000 q^{80} +3.60169 q^{81} -0.336080 q^{82} +2.99172 q^{83} -1.16329 q^{84} -3.19340 q^{85} -4.62681 q^{86} +5.79750 q^{87} -0.326178 q^{88} -7.54354 q^{89} +2.35379 q^{90} -4.27194 q^{91} +7.05099 q^{92} +2.75041 q^{93} -8.73635 q^{94} +2.71870 q^{95} -0.803872 q^{96} +11.3139 q^{97} -4.90589 q^{98} +0.767755 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8}+O(q^{10}) \) 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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