LMFDB - Embedded newform 4010.2.a.i.1.5

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 12x^{8} + 34x^{7} + 46x^{6} - 104x^{5} - 90x^{4} + 89x^{3} + 82x^{2} + 12x - 1 $ x^10 - 3x^9 - 12x^8 + 34x^7 + 46x^6 - 104x^5 - 90x^4 + 89x^3 + 82x^2 + 12*x - 1
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			1.5
Root			$-0.557507$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.25862 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.25862 q^{6} +1.88678 q^{7} -1.00000 q^{8} -1.41588 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.25862 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.25862 q^{6} +1.88678 q^{7} -1.00000 q^{8} -1.41588 q^{9} -1.00000 q^{10} -3.48622 q^{11} -1.25862 q^{12} -6.95331 q^{13} -1.88678 q^{14} -1.25862 q^{15} +1.00000 q^{16} +2.07979 q^{17} +1.41588 q^{18} +3.03678 q^{19} +1.00000 q^{20} -2.37474 q^{21} +3.48622 q^{22} +6.09494 q^{23} +1.25862 q^{24} +1.00000 q^{25} +6.95331 q^{26} +5.55791 q^{27} +1.88678 q^{28} -1.90478 q^{29} +1.25862 q^{30} +8.71536 q^{31} -1.00000 q^{32} +4.38782 q^{33} -2.07979 q^{34} +1.88678 q^{35} -1.41588 q^{36} -7.53999 q^{37} -3.03678 q^{38} +8.75157 q^{39} -1.00000 q^{40} +2.87033 q^{41} +2.37474 q^{42} +8.26705 q^{43} -3.48622 q^{44} -1.41588 q^{45} -6.09494 q^{46} -0.387411 q^{47} -1.25862 q^{48} -3.44005 q^{49} -1.00000 q^{50} -2.61766 q^{51} -6.95331 q^{52} +10.1906 q^{53} -5.55791 q^{54} -3.48622 q^{55} -1.88678 q^{56} -3.82216 q^{57} +1.90478 q^{58} -11.5233 q^{59} -1.25862 q^{60} -6.34170 q^{61} -8.71536 q^{62} -2.67145 q^{63} +1.00000 q^{64} -6.95331 q^{65} -4.38782 q^{66} -14.2874 q^{67} +2.07979 q^{68} -7.67121 q^{69} -1.88678 q^{70} -8.46495 q^{71} +1.41588 q^{72} +7.64415 q^{73} +7.53999 q^{74} -1.25862 q^{75} +3.03678 q^{76} -6.57773 q^{77} -8.75157 q^{78} +7.07250 q^{79} +1.00000 q^{80} -2.74766 q^{81} -2.87033 q^{82} +4.66441 q^{83} -2.37474 q^{84} +2.07979 q^{85} -8.26705 q^{86} +2.39740 q^{87} +3.48622 q^{88} +1.33024 q^{89} +1.41588 q^{90} -13.1194 q^{91} +6.09494 q^{92} -10.9693 q^{93} +0.387411 q^{94} +3.03678 q^{95} +1.25862 q^{96} -3.66697 q^{97} +3.44005 q^{98} +4.93606 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9} - 10 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 10 q^{16} + 9 q^{17} - 6 q^{18} - 13 q^{19} + 10 q^{20} - 24 q^{21} + 11 q^{22} - 3 q^{23} + 4 q^{24} + 10 q^{25} - 6 q^{26} - 10 q^{27} - 3 q^{28} - 4 q^{29} + 4 q^{30} - 17 q^{31} - 10 q^{32} - 2 q^{33} - 9 q^{34} - 3 q^{35} + 6 q^{36} - 15 q^{37} + 13 q^{38} - 6 q^{39} - 10 q^{40} - 11 q^{41} + 24 q^{42} - 11 q^{43} - 11 q^{44} + 6 q^{45} + 3 q^{46} + 3 q^{47} - 4 q^{48} - 5 q^{49} - 10 q^{50} - 21 q^{51} + 6 q^{52} + 25 q^{53} + 10 q^{54} - 11 q^{55} + 3 q^{56} + 31 q^{57} + 4 q^{58} - 46 q^{59} - 4 q^{60} - 54 q^{61} + 17 q^{62} - 6 q^{63} + 10 q^{64} + 6 q^{65} + 2 q^{66} - 26 q^{67} + 9 q^{68} - 9 q^{69} + 3 q^{70} - 16 q^{71} - 6 q^{72} + 4 q^{73} + 15 q^{74} - 4 q^{75} - 13 q^{76} + 11 q^{77} + 6 q^{78} - 19 q^{79} + 10 q^{80} - 6 q^{81} + 11 q^{82} + 19 q^{83} - 24 q^{84} + 9 q^{85} + 11 q^{86} + 28 q^{87} + 11 q^{88} - 30 q^{89} - 6 q^{90} - 38 q^{91} - 3 q^{92} - 18 q^{93} - 3 q^{94} - 13 q^{95} + 4 q^{96} - 16 q^{97} + 5 q^{98} - 59 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9 - 10 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 10 * q^16 + 9 * q^17 - 6 * q^18 - 13 * q^19 + 10 * q^20 - 24 * q^21 + 11 * q^22 - 3 * q^23 + 4 * q^24 + 10 * q^25 - 6 * q^26 - 10 * q^27 - 3 * q^28 - 4 * q^29 + 4 * q^30 - 17 * q^31 - 10 * q^32 - 2 * q^33 - 9 * q^34 - 3 * q^35 + 6 * q^36 - 15 * q^37 + 13 * q^38 - 6 * q^39 - 10 * q^40 - 11 * q^41 + 24 * q^42 - 11 * q^43 - 11 * q^44 + 6 * q^45 + 3 * q^46 + 3 * q^47 - 4 * q^48 - 5 * q^49 - 10 * q^50 - 21 * q^51 + 6 * q^52 + 25 * q^53 + 10 * q^54 - 11 * q^55 + 3 * q^56 + 31 * q^57 + 4 * q^58 - 46 * q^59 - 4 * q^60 - 54 * q^61 + 17 * q^62 - 6 * q^63 + 10 * q^64 + 6 * q^65 + 2 * q^66 - 26 * q^67 + 9 * q^68 - 9 * q^69 + 3 * q^70 - 16 * q^71 - 6 * q^72 + 4 * q^73 + 15 * q^74 - 4 * q^75 - 13 * q^76 + 11 * q^77 + 6 * q^78 - 19 * q^79 + 10 * q^80 - 6 * q^81 + 11 * q^82 + 19 * q^83 - 24 * q^84 + 9 * q^85 + 11 * q^86 + 28 * q^87 + 11 * q^88 - 30 * q^89 - 6 * q^90 - 38 * q^91 - 3 * q^92 - 18 * q^93 - 3 * q^94 - 13 * q^95 + 4 * q^96 - 16 * q^97 + 5 * q^98 - 59 * 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
$3$	−1.25862	−0.726664	−0.363332	−	0.931660i	$-0.618361\pi$
$3$	−1.25862	−0.726664	−0.363332	+	0.931660i	$0.618361\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.25862	0.513829
$7$	1.88678	0.713137	0.356568	−	0.934269i	$-0.383947\pi$
$7$	1.88678	0.713137	0.356568	+	0.934269i	$0.383947\pi$
$8$	−1.00000	−0.353553
$9$	−1.41588	−0.471959
$10$	−1.00000	−0.316228
$11$	−3.48622	−1.05113	−0.525567	−	0.850752i	$-0.676147\pi$
$11$	−3.48622	−1.05113	−0.525567	+	0.850752i	$0.676147\pi$
$12$	−1.25862	−0.363332
$13$	−6.95331	−1.92850	−0.964250	−	0.264993i	$-0.914630\pi$
$13$	−6.95331	−1.92850	−0.964250	+	0.264993i	$0.914630\pi$
$14$	−1.88678	−0.504264
$15$	−1.25862	−0.324974
$16$	1.00000	0.250000
$17$	2.07979	0.504422	0.252211	−	0.967672i	$-0.418842\pi$
$17$	2.07979	0.504422	0.252211	+	0.967672i	$0.418842\pi$
$18$	1.41588	0.333725
$19$	3.03678	0.696686	0.348343	−	0.937367i	$-0.386744\pi$
$19$	3.03678	0.696686	0.348343	+	0.937367i	$0.386744\pi$
$20$	1.00000	0.223607
$21$	−2.37474	−0.518211
$22$	3.48622	0.743264
$23$	6.09494	1.27088	0.635441	−	0.772149i	$-0.280818\pi$
$23$	6.09494	1.27088	0.635441	+	0.772149i	$0.280818\pi$
$24$	1.25862	0.256915
$25$	1.00000	0.200000
$26$	6.95331	1.36366
$27$	5.55791	1.06962
$28$	1.88678	0.356568
$29$	−1.90478	−0.353709	−0.176855	−	0.984237i	$-0.556592\pi$
$29$	−1.90478	−0.353709	−0.176855	+	0.984237i	$0.556592\pi$
$30$	1.25862	0.229791
$31$	8.71536	1.56533	0.782663	−	0.622446i	$-0.213861\pi$
$31$	8.71536	1.56533	0.782663	+	0.622446i	$0.213861\pi$
$32$	−1.00000	−0.176777
$33$	4.38782	0.763822
$34$	−2.07979	−0.356680
$35$	1.88678	0.318924
$36$	−1.41588	−0.235980
$37$	−7.53999	−1.23957	−0.619783	−	0.784773i	$-0.712779\pi$
$37$	−7.53999	−1.23957	−0.619783	+	0.784773i	$0.712779\pi$
$38$	−3.03678	−0.492631
$39$	8.75157	1.40137
$40$	−1.00000	−0.158114
$41$	2.87033	0.448271	0.224135	−	0.974558i	$-0.428044\pi$
$41$	2.87033	0.448271	0.224135	+	0.974558i	$0.428044\pi$
$42$	2.37474	0.366430
$43$	8.26705	1.26071	0.630357	−	0.776306i	$-0.282909\pi$
$43$	8.26705	1.26071	0.630357	+	0.776306i	$0.282909\pi$
$44$	−3.48622	−0.525567
$45$	−1.41588	−0.211067
$46$	−6.09494	−0.898650
$47$	−0.387411	−0.0565097	−0.0282548	−	0.999601i	$-0.508995\pi$
$47$	−0.387411	−0.0565097	−0.0282548	+	0.999601i	$0.508995\pi$
$48$	−1.25862	−0.181666
$49$	−3.44005	−0.491436
$50$	−1.00000	−0.141421
$51$	−2.61766	−0.366546
$52$	−6.95331	−0.964250
$53$	10.1906	1.39979	0.699893	−	0.714247i	$-0.253231\pi$
$53$	10.1906	1.39979	0.699893	+	0.714247i	$0.253231\pi$
$54$	−5.55791	−0.756336
$55$	−3.48622	−0.470081
$56$	−1.88678	−0.252132
$57$	−3.82216	−0.506257
$58$	1.90478	0.250110
$59$	−11.5233	−1.50020	−0.750101	−	0.661323i	$-0.769995\pi$
$59$	−11.5233	−1.50020	−0.750101	+	0.661323i	$0.769995\pi$
$60$	−1.25862	−0.162487
$61$	−6.34170	−0.811971	−0.405986	−	0.913879i	$-0.633072\pi$
$61$	−6.34170	−0.811971	−0.405986	+	0.913879i	$0.633072\pi$
$62$	−8.71536	−1.10685
$63$	−2.67145	−0.336571
$64$	1.00000	0.125000
$65$	−6.95331	−0.862452
$66$	−4.38782	−0.540103
$67$	−14.2874	−1.74549	−0.872743	−	0.488179i	$-0.837661\pi$
$67$	−14.2874	−1.74549	−0.872743	+	0.488179i	$0.837661\pi$
$68$	2.07979	0.252211
$69$	−7.67121	−0.923505
$70$	−1.88678	−0.225514
$71$	−8.46495	−1.00461	−0.502303	−	0.864692i	$-0.667514\pi$
$71$	−8.46495	−1.00461	−0.502303	+	0.864692i	$0.667514\pi$
$72$	1.41588	0.166863
$73$	7.64415	0.894680	0.447340	−	0.894364i	$-0.352371\pi$
$73$	7.64415	0.894680	0.447340	+	0.894364i	$0.352371\pi$
$74$	7.53999	0.876506
$75$	−1.25862	−0.145333
$76$	3.03678	0.348343
$77$	−6.57773	−0.749602
$78$	−8.75157	−0.990920
$79$	7.07250	0.795718	0.397859	−	0.917447i	$-0.369753\pi$
$79$	7.07250	0.795718	0.397859	+	0.917447i	$0.369753\pi$
$80$	1.00000	0.111803
$81$	−2.74766	−0.305296
$82$	−2.87033	−0.316975
$83$	4.66441	0.511985	0.255993	−	0.966679i	$-0.417598\pi$
$83$	4.66441	0.511985	0.255993	+	0.966679i	$0.417598\pi$
$84$	−2.37474	−0.259105
$85$	2.07979	0.225584
$86$	−8.26705	−0.891459
$87$	2.39740	0.257028
$88$	3.48622	0.371632
$89$	1.33024	0.141005	0.0705023	−	0.997512i	$-0.477540\pi$
$89$	1.33024	0.141005	0.0705023	+	0.997512i	$0.477540\pi$
$90$	1.41588	0.149247
$91$	−13.1194	−1.37528
$92$	6.09494	0.635441
$93$	−10.9693	−1.13747
$94$	0.387411	0.0399584
$95$	3.03678	0.311568
$96$	1.25862	0.128457
$97$	−3.66697	−0.372325	−0.186162	−	0.982519i	$-0.559605\pi$
$97$	−3.66697	−0.372325	−0.186162	+	0.982519i	$0.559605\pi$
$98$	3.44005	0.347498
$99$	4.93606	0.496092
$100$	1.00000	0.100000
$101$	−3.83152	−0.381251	−0.190625	−	0.981663i	$-0.561052\pi$
$101$	−3.83152	−0.381251	−0.190625	+	0.981663i	$0.561052\pi$
$102$	2.61766	0.259187
$103$	−4.52834	−0.446191	−0.223095	−	0.974797i	$-0.571616\pi$
$103$	−4.52834	−0.446191	−0.223095	+	0.974797i	$0.571616\pi$
$104$	6.95331	0.681828
$105$	−2.37474	−0.231751
$106$	−10.1906	−0.989799
$107$	−8.53972	−0.825566	−0.412783	−	0.910829i	$-0.635443\pi$
$107$	−8.53972	−0.825566	−0.412783	+	0.910829i	$0.635443\pi$
$108$	5.55791	0.534810
$109$	−12.6859	−1.21509	−0.607544	−	0.794286i	$-0.707845\pi$
$109$	−12.6859	−1.21509	−0.607544	+	0.794286i	$0.707845\pi$
$110$	3.48622	0.332398
$111$	9.48997	0.900748
$112$	1.88678	0.178284
$113$	1.41079	0.132716	0.0663581	−	0.997796i	$-0.478862\pi$
$113$	1.41079	0.132716	0.0663581	+	0.997796i	$0.478862\pi$
$114$	3.82216	0.357978
$115$	6.09494	0.568356
$116$	−1.90478	−0.176855
$117$	9.84503	0.910174
$118$	11.5233	1.06080
$119$	3.92410	0.359722
$120$	1.25862	0.114896
$121$	1.15371	0.104883
$122$	6.34170	0.574150
$123$	−3.61266	−0.325742
$124$	8.71536	0.782663
$125$	1.00000	0.0894427
$126$	2.67145	0.237992
$127$	−7.44437	−0.660581	−0.330290	−	0.943879i	$-0.607147\pi$
$127$	−7.44437	−0.660581	−0.330290	+	0.943879i	$0.607147\pi$
$128$	−1.00000	−0.0883883
$129$	−10.4051	−0.916115
$130$	6.95331	0.609846
$131$	−0.585301	−0.0511380	−0.0255690	−	0.999673i	$-0.508140\pi$
$131$	−0.585301	−0.0511380	−0.0255690	+	0.999673i	$0.508140\pi$
$132$	4.38782	0.381911
$133$	5.72975	0.496832
$134$	14.2874	1.23425
$135$	5.55791	0.478349
$136$	−2.07979	−0.178340
$137$	−3.90577	−0.333692	−0.166846	−	0.985983i	$-0.553358\pi$
$137$	−3.90577	−0.333692	−0.166846	+	0.985983i	$0.553358\pi$
$138$	7.67121	0.653017
$139$	−17.5948	−1.49237	−0.746185	−	0.665739i	$-0.768117\pi$
$139$	−17.5948	−1.49237	−0.746185	+	0.665739i	$0.768117\pi$
$140$	1.88678	0.159462
$141$	0.487603	0.0410636
$142$	8.46495	0.710363
$143$	24.2407	2.02711
$144$	−1.41588	−0.117990
$145$	−1.90478	−0.158184
$146$	−7.64415	−0.632634
$147$	4.32972	0.357109
$148$	−7.53999	−0.619783
$149$	−9.54635	−0.782067	−0.391034	−	0.920376i	$-0.627882\pi$
$149$	−9.54635	−0.782067	−0.391034	+	0.920376i	$0.627882\pi$
$150$	1.25862	0.102766
$151$	−13.8126	−1.12405	−0.562027	−	0.827119i	$-0.689978\pi$
$151$	−13.8126	−1.12405	−0.562027	+	0.827119i	$0.689978\pi$
$152$	−3.03678	−0.246316
$153$	−2.94472	−0.238067
$154$	6.57773	0.530049
$155$	8.71536	0.700035
$156$	8.75157	0.700686
$157$	3.53365	0.282016	0.141008	−	0.990008i	$-0.454966\pi$
$157$	3.53365	0.282016	0.141008	+	0.990008i	$0.454966\pi$
$158$	−7.07250	−0.562658
$159$	−12.8261	−1.01718
$160$	−1.00000	−0.0790569
$161$	11.4998	0.906313
$162$	2.74766	0.215877
$163$	15.0237	1.17675	0.588373	−	0.808590i	$-0.299769\pi$
$163$	15.0237	1.17675	0.588373	+	0.808590i	$0.299769\pi$
$164$	2.87033	0.224135
$165$	4.38782	0.341591
$166$	−4.66441	−0.362028
$167$	−6.40103	−0.495327	−0.247663	−	0.968846i	$-0.579663\pi$
$167$	−6.40103	−0.495327	−0.247663	+	0.968846i	$0.579663\pi$
$168$	2.37474	0.183215
$169$	35.3485	2.71912
$170$	−2.07979	−0.159512
$171$	−4.29971	−0.328807
$172$	8.26705	0.630357
$173$	−6.47210	−0.492065	−0.246032	−	0.969262i	$-0.579127\pi$
$173$	−6.47210	−0.492065	−0.246032	+	0.969262i	$0.579127\pi$
$174$	−2.39740	−0.181746
$175$	1.88678	0.142627
$176$	−3.48622	−0.262784
$177$	14.5034	1.09014
$178$	−1.33024	−0.0997054
$179$	−10.5935	−0.791798	−0.395899	−	0.918294i	$-0.629567\pi$
$179$	−10.5935	−0.791798	−0.395899	+	0.918294i	$0.629567\pi$
$180$	−1.41588	−0.105533
$181$	0.882166	0.0655709	0.0327854	−	0.999462i	$-0.489562\pi$
$181$	0.882166	0.0655709	0.0327854	+	0.999462i	$0.489562\pi$
$182$	13.1194	0.972473
$183$	7.98178	0.590030
$184$	−6.09494	−0.449325
$185$	−7.53999	−0.554351
$186$	10.9693	0.804310
$187$	−7.25059	−0.530215
$188$	−0.387411	−0.0282548
$189$	10.4866	0.762785
$190$	−3.03678	−0.220312
$191$	22.7634	1.64710	0.823550	−	0.567243i	$-0.191990\pi$
$191$	22.7634	1.64710	0.823550	+	0.567243i	$0.191990\pi$
$192$	−1.25862	−0.0908330
$193$	−6.26949	−0.451288	−0.225644	−	0.974210i	$-0.572449\pi$
$193$	−6.26949	−0.451288	−0.225644	+	0.974210i	$0.572449\pi$
$194$	3.66697	0.263273
$195$	8.75157	0.626713
$196$	−3.44005	−0.245718
$197$	16.9202	1.20551	0.602756	−	0.797925i	$-0.294069\pi$
$197$	16.9202	1.20551	0.602756	+	0.797925i	$0.294069\pi$
$198$	−4.93606	−0.350790
$199$	−23.9409	−1.69713	−0.848563	−	0.529095i	$-0.822532\pi$
$199$	−23.9409	−1.69713	−0.848563	+	0.529095i	$0.822532\pi$
$200$	−1.00000	−0.0707107
$201$	17.9824	1.26838
$202$	3.83152	0.269585
$203$	−3.59391	−0.252243
$204$	−2.61766	−0.183273
$205$	2.87033	0.200473
$206$	4.52834	0.315504
$207$	−8.62968	−0.599805
$208$	−6.95331	−0.482125
$209$	−10.5869	−0.732311
$210$	2.37474	0.163873
$211$	4.80818	0.331009	0.165505	−	0.986209i	$-0.447075\pi$
$211$	4.80818	0.331009	0.165505	+	0.986209i	$0.447075\pi$
$212$	10.1906	0.699893
$213$	10.6542	0.730011
$214$	8.53972	0.583763
$215$	8.26705	0.563808
$216$	−5.55791	−0.378168
$217$	16.4440	1.11629
$218$	12.6859	0.859197
$219$	−9.62107	−0.650132
$220$	−3.48622	−0.235041
$221$	−14.4614	−0.972778
$222$	−9.48997	−0.636925
$223$	−21.4209	−1.43445	−0.717226	−	0.696841i	$-0.754588\pi$
$223$	−21.4209	−1.43445	−0.717226	+	0.696841i	$0.754588\pi$
$224$	−1.88678	−0.126066
$225$	−1.41588	−0.0943918
$226$	−1.41079	−0.0938446
$227$	−17.0216	−1.12976	−0.564880	−	0.825173i	$-0.691078\pi$
$227$	−17.0216	−1.12976	−0.564880	+	0.825173i	$0.691078\pi$
$228$	−3.82216	−0.253128
$229$	−16.2986	−1.07704	−0.538520	−	0.842613i	$-0.681016\pi$
$229$	−16.2986	−1.07704	−0.538520	+	0.842613i	$0.681016\pi$
$230$	−6.09494	−0.401888
$231$	8.27886	0.544709
$232$	1.90478	0.125055
$233$	3.22300	0.211146	0.105573	−	0.994412i	$-0.466332\pi$
$233$	3.22300	0.211146	0.105573	+	0.994412i	$0.466332\pi$
$234$	−9.84503	−0.643590
$235$	−0.387411	−0.0252719
$236$	−11.5233	−0.750101
$237$	−8.90158	−0.578220
$238$	−3.92410	−0.254362
$239$	−4.21601	−0.272711	−0.136355	−	0.990660i	$-0.543539\pi$
$239$	−4.21601	−0.272711	−0.136355	+	0.990660i	$0.543539\pi$
$240$	−1.25862	−0.0812435
$241$	13.6898	0.881837	0.440919	−	0.897547i	$-0.354653\pi$
$241$	13.6898	0.881837	0.440919	+	0.897547i	$0.354653\pi$
$242$	−1.15371	−0.0741635
$243$	−13.2155	−0.847773
$244$	−6.34170	−0.405986
$245$	−3.44005	−0.219777
$246$	3.61266	0.230335
$247$	−21.1157	−1.34356
$248$	−8.71536	−0.553426
$249$	−5.87072	−0.372042
$250$	−1.00000	−0.0632456
$251$	−25.3286	−1.59872	−0.799362	−	0.600849i	$-0.794829\pi$
$251$	−25.3286	−1.59872	−0.799362	+	0.600849i	$0.794829\pi$
$252$	−2.67145	−0.168286
$253$	−21.2483	−1.33587
$254$	7.44437	0.467101
$255$	−2.61766	−0.163924
$256$	1.00000	0.0625000
$257$	15.7819	0.984447	0.492223	−	0.870469i	$-0.336184\pi$
$257$	15.7819	0.984447	0.492223	+	0.870469i	$0.336184\pi$
$258$	10.4051	0.647791
$259$	−14.2263	−0.883980
$260$	−6.95331	−0.431226
$261$	2.69694	0.166936
$262$	0.585301	0.0361600
$263$	9.08680	0.560316	0.280158	−	0.959954i	$-0.409613\pi$
$263$	9.08680	0.560316	0.280158	+	0.959954i	$0.409613\pi$
$264$	−4.38782	−0.270052
$265$	10.1906	0.626004
$266$	−5.72975	−0.351314
$267$	−1.67426	−0.102463
$268$	−14.2874	−0.872743
$269$	−12.6123	−0.768988	−0.384494	−	0.923127i	$-0.625624\pi$
$269$	−12.6123	−0.768988	−0.384494	+	0.923127i	$0.625624\pi$
$270$	−5.55791	−0.338244
$271$	−22.6668	−1.37691	−0.688454	−	0.725280i	$-0.741710\pi$
$271$	−22.6668	−1.37691	−0.688454	+	0.725280i	$0.741710\pi$
$272$	2.07979	0.126106
$273$	16.5123	0.999370
$274$	3.90577	0.235956
$275$	−3.48622	−0.210227
$276$	−7.67121	−0.461752
$277$	−3.47620	−0.208865	−0.104432	−	0.994532i	$-0.533303\pi$
$277$	−3.47620	−0.208865	−0.104432	+	0.994532i	$0.533303\pi$
$278$	17.5948	1.05526
$279$	−12.3399	−0.738770
$280$	−1.88678	−0.112757
$281$	−16.1204	−0.961661	−0.480830	−	0.876814i	$-0.659665\pi$
$281$	−16.1204	−0.961661	−0.480830	+	0.876814i	$0.659665\pi$
$282$	−0.487603	−0.0290363
$283$	−11.4837	−0.682636	−0.341318	−	0.939948i	$-0.610873\pi$
$283$	−11.4837	−0.682636	−0.341318	+	0.939948i	$0.610873\pi$
$284$	−8.46495	−0.502303
$285$	−3.82216	−0.226405
$286$	−24.2407	−1.43339
$287$	5.41569	0.319678
$288$	1.41588	0.0834314
$289$	−12.6745	−0.745558
$290$	1.90478	0.111853
$291$	4.61532	0.270555
$292$	7.64415	0.447340
$293$	32.6546	1.90770	0.953852	−	0.300276i	$-0.0970789\pi$
$293$	32.6546	1.90770	0.953852	+	0.300276i	$0.0970789\pi$
$294$	−4.32972	−0.252514
$295$	−11.5233	−0.670911
$296$	7.53999	0.438253
$297$	−19.3761	−1.12431
$298$	9.54635	0.553005
$299$	−42.3800	−2.45090
$300$	−1.25862	−0.0726664
$301$	15.5981	0.899061
$302$	13.8126	0.794827
$303$	4.82243	0.277041
$304$	3.03678	0.174172
$305$	−6.34170	−0.363125
$306$	2.94472	0.168339
$307$	−33.4934	−1.91157	−0.955783	−	0.294072i	$-0.904990\pi$
$307$	−33.4934	−1.91157	−0.955783	+	0.294072i	$0.904990\pi$
$308$	−6.57773	−0.374801
$309$	5.69946	0.324231
$310$	−8.71536	−0.494999
$311$	23.5276	1.33413	0.667064	−	0.745000i	$-0.267551\pi$
$311$	23.5276	1.33413	0.667064	+	0.745000i	$0.267551\pi$
$312$	−8.75157	−0.495460
$313$	0.110421	0.00624134	0.00312067	−	0.999995i	$-0.499007\pi$
$313$	0.110421	0.00624134	0.00312067	+	0.999995i	$0.499007\pi$
$314$	−3.53365	−0.199415
$315$	−2.67145	−0.150519
$316$	7.07250	0.397859
$317$	27.3570	1.53652	0.768260	−	0.640137i	$-0.221123\pi$
$317$	27.3570	1.53652	0.768260	+	0.640137i	$0.221123\pi$
$318$	12.8261	0.719251
$319$	6.64049	0.371796
$320$	1.00000	0.0559017
$321$	10.7483	0.599909
$322$	−11.4998	−0.640860
$323$	6.31586	0.351424
$324$	−2.74766	−0.152648
$325$	−6.95331	−0.385700
$326$	−15.0237	−0.832085
$327$	15.9667	0.882961
$328$	−2.87033	−0.158488
$329$	−0.730960	−0.0402991
$330$	−4.38782	−0.241542
$331$	−18.3665	−1.00952	−0.504758	−	0.863261i	$-0.668418\pi$
$331$	−18.3665	−1.00952	−0.504758	+	0.863261i	$0.668418\pi$
$332$	4.66441	0.255993
$333$	10.6757	0.585025
$334$	6.40103	0.350249
$335$	−14.2874	−0.780605
$336$	−2.37474	−0.129553
$337$	−14.8058	−0.806521	−0.403260	−	0.915085i	$-0.632123\pi$
$337$	−14.8058	−0.806521	−0.403260	+	0.915085i	$0.632123\pi$
$338$	−35.3485	−1.92271
$339$	−1.77565	−0.0964402
$340$	2.07979	0.112792
$341$	−30.3837	−1.64537
$342$	4.29971	0.232502
$343$	−19.6981	−1.06360
$344$	−8.26705	−0.445729
$345$	−7.67121	−0.413004
$346$	6.47210	0.347942
$347$	18.7785	1.00808	0.504042	−	0.863679i	$-0.331846\pi$
$347$	18.7785	1.00808	0.504042	+	0.863679i	$0.331846\pi$
$348$	2.39740	0.128514
$349$	6.81508	0.364803	0.182401	−	0.983224i	$-0.441613\pi$
$349$	6.81508	0.364803	0.182401	+	0.983224i	$0.441613\pi$
$350$	−1.88678	−0.100853
$351$	−38.6459	−2.06276
$352$	3.48622	0.185816
$353$	−24.6282	−1.31083	−0.655413	−	0.755271i	$-0.727505\pi$
$353$	−24.6282	−1.31083	−0.655413	+	0.755271i	$0.727505\pi$
$354$	−14.5034	−0.770847
$355$	−8.46495	−0.449273
$356$	1.33024	0.0705023
$357$	−4.93895	−0.261397
$358$	10.5935	0.559885
$359$	1.95793	0.103335	0.0516677	−	0.998664i	$-0.483546\pi$
$359$	1.95793	0.103335	0.0516677	+	0.998664i	$0.483546\pi$
$360$	1.41588	0.0746233
$361$	−9.77794	−0.514628
$362$	−0.882166	−0.0463656
$363$	−1.45209	−0.0762147
$364$	−13.1194	−0.687642
$365$	7.64415	0.400113
$366$	−7.98178	−0.417215
$367$	23.1187	1.20679	0.603393	−	0.797444i	$-0.293815\pi$
$367$	23.1187	1.20679	0.603393	+	0.797444i	$0.293815\pi$
$368$	6.09494	0.317721
$369$	−4.06404	−0.211565
$370$	7.53999	0.391985
$371$	19.2274	0.998239
$372$	−10.9693	−0.568733
$373$	36.1412	1.87132	0.935659	−	0.352905i	$-0.114806\pi$
$373$	36.1412	1.87132	0.935659	+	0.352905i	$0.114806\pi$
$374$	7.25059	0.374919
$375$	−1.25862	−0.0649948
$376$	0.387411	0.0199792
$377$	13.2445	0.682129
$378$	−10.4866	−0.539371
$379$	3.64173	0.187063	0.0935316	−	0.995616i	$-0.470184\pi$
$379$	3.64173	0.187063	0.0935316	+	0.995616i	$0.470184\pi$
$380$	3.03678	0.155784
$381$	9.36963	0.480020
$382$	−22.7634	−1.16468
$383$	7.17961	0.366861	0.183430	−	0.983033i	$-0.441280\pi$
$383$	7.17961	0.366861	0.183430	+	0.983033i	$0.441280\pi$
$384$	1.25862	0.0642287
$385$	−6.57773	−0.335232
$386$	6.26949	0.319109
$387$	−11.7051	−0.595005
$388$	−3.66697	−0.186162
$389$	−16.5162	−0.837404	−0.418702	−	0.908124i	$-0.637515\pi$
$389$	−16.5162	−0.837404	−0.418702	+	0.908124i	$0.637515\pi$
$390$	−8.75157	−0.443153
$391$	12.6762	0.641061
$392$	3.44005	0.173749
$393$	0.736671	0.0371602
$394$	−16.9202	−0.852426
$395$	7.07250	0.355856
$396$	4.93606	0.248046
$397$	−10.1468	−0.509253	−0.254627	−	0.967039i	$-0.581953\pi$
$397$	−10.1468	−0.509253	−0.254627	+	0.967039i	$0.581953\pi$
$398$	23.9409	1.20005
$399$	−7.21158	−0.361030
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−17.9824	−0.896882
$403$	−60.6006	−3.01873
$404$	−3.83152	−0.190625
$405$	−2.74766	−0.136532
$406$	3.59391	0.178363
$407$	26.2860	1.30295
$408$	2.61766	0.129593
$409$	−6.66002	−0.329317	−0.164658	−	0.986351i	$-0.552652\pi$
$409$	−6.66002	−0.329317	−0.164658	+	0.986351i	$0.552652\pi$
$410$	−2.87033	−0.141756
$411$	4.91587	0.242482
$412$	−4.52834	−0.223095
$413$	−21.7419	−1.06985
$414$	8.62968	0.424126
$415$	4.66441	0.228967
$416$	6.95331	0.340914
$417$	22.1451	1.08445
$418$	10.5869	0.517822
$419$	−2.49145	−0.121715	−0.0608577	−	0.998146i	$-0.519384\pi$
$419$	−2.49145	−0.121715	−0.0608577	+	0.998146i	$0.519384\pi$
$420$	−2.37474	−0.115875
$421$	−6.59406	−0.321375	−0.160687	−	0.987005i	$-0.551371\pi$
$421$	−6.59406	−0.321375	−0.160687	+	0.987005i	$0.551371\pi$
$422$	−4.80818	−0.234059
$423$	0.548526	0.0266703
$424$	−10.1906	−0.494899
$425$	2.07979	0.100884
$426$	−10.6542	−0.516195
$427$	−11.9654	−0.579047
$428$	−8.53972	−0.412783
$429$	−30.5099	−1.47303
$430$	−8.26705	−0.398673
$431$	−18.1593	−0.874702	−0.437351	−	0.899291i	$-0.644083\pi$
$431$	−18.1593	−0.874702	−0.437351	+	0.899291i	$0.644083\pi$
$432$	5.55791	0.267405
$433$	19.1718	0.921338	0.460669	−	0.887572i	$-0.347610\pi$
$433$	19.1718	0.921338	0.460669	+	0.887572i	$0.347610\pi$
$434$	−16.4440	−0.789337
$435$	2.39740	0.114946
$436$	−12.6859	−0.607544
$437$	18.5090	0.885406
$438$	9.62107	0.459713
$439$	29.0910	1.38844	0.694218	−	0.719765i	$-0.255750\pi$
$439$	29.0910	1.38844	0.694218	+	0.719765i	$0.255750\pi$
$440$	3.48622	0.166199
$441$	4.87069	0.231938
$442$	14.4614	0.687858
$443$	−8.67590	−0.412205	−0.206102	−	0.978530i	$-0.566078\pi$
$443$	−8.67590	−0.412205	−0.206102	+	0.978530i	$0.566078\pi$
$444$	9.48997	0.450374
$445$	1.33024	0.0630592
$446$	21.4209	1.01431
$447$	12.0152	0.568300
$448$	1.88678	0.0891421
$449$	−33.8132	−1.59574	−0.797872	−	0.602826i	$-0.794041\pi$
$449$	−33.8132	−1.59574	−0.797872	+	0.602826i	$0.794041\pi$
$450$	1.41588	0.0667451
$451$	−10.0066	−0.471193
$452$	1.41079	0.0663581
$453$	17.3848	0.816811
$454$	17.0216	0.798861
$455$	−13.1194	−0.615046
$456$	3.82216	0.178989
$457$	13.2145	0.618146	0.309073	−	0.951038i	$-0.399981\pi$
$457$	13.2145	0.618146	0.309073	+	0.951038i	$0.399981\pi$
$458$	16.2986	0.761582
$459$	11.5593	0.539540
$460$	6.09494	0.284178
$461$	−2.10624	−0.0980975	−0.0490488	−	0.998796i	$-0.515619\pi$
$461$	−2.10624	−0.0980975	−0.0490488	+	0.998796i	$0.515619\pi$
$462$	−8.27886	−0.385168
$463$	−1.56942	−0.0729374	−0.0364687	−	0.999335i	$-0.511611\pi$
$463$	−1.56942	−0.0729374	−0.0364687	+	0.999335i	$0.511611\pi$
$464$	−1.90478	−0.0884274
$465$	−10.9693	−0.508690
$466$	−3.22300	−0.149302
$467$	38.9296	1.80145	0.900725	−	0.434391i	$-0.143036\pi$
$467$	38.9296	1.80145	0.900725	+	0.434391i	$0.143036\pi$
$468$	9.84503	0.455087
$469$	−26.9573	−1.24477
$470$	0.387411	0.0178699
$471$	−4.44752	−0.204931
$472$	11.5233	0.530401
$473$	−28.8207	−1.32518
$474$	8.90158	0.408863
$475$	3.03678	0.139337
$476$	3.92410	0.179861
$477$	−14.4286	−0.660642
$478$	4.21601	0.192836
$479$	10.4833	0.478994	0.239497	−	0.970897i	$-0.423017\pi$
$479$	10.4833	0.478994	0.239497	+	0.970897i	$0.423017\pi$
$480$	1.25862	0.0574479
$481$	52.4279	2.39050
$482$	−13.6898	−0.623553
$483$	−14.4739	−0.658585
$484$	1.15371	0.0524415
$485$	−3.66697	−0.166509
$486$	13.2155	0.599466
$487$	−24.6487	−1.11694	−0.558471	−	0.829524i	$-0.688612\pi$
$487$	−24.6487	−1.11694	−0.558471	+	0.829524i	$0.688612\pi$
$488$	6.34170	0.287075
$489$	−18.9091	−0.855099
$490$	3.44005	0.155406
$491$	14.8353	0.669509	0.334754	−	0.942305i	$-0.391347\pi$
$491$	14.8353	0.669509	0.334754	+	0.942305i	$0.391347\pi$
$492$	−3.61266	−0.162871
$493$	−3.96154	−0.178419
$494$	21.1157	0.950040
$495$	4.93606	0.221859
$496$	8.71536	0.391331
$497$	−15.9715	−0.716421
$498$	5.87072	0.263073
$499$	−5.40224	−0.241837	−0.120919	−	0.992662i	$-0.538584\pi$
$499$	−5.40224	−0.241837	−0.120919	+	0.992662i	$0.538584\pi$
$500$	1.00000	0.0447214
$501$	8.05647	0.359936
$502$	25.3286	1.13047
$503$	−16.4494	−0.733440	−0.366720	−	0.930331i	$-0.619519\pi$
$503$	−16.4494	−0.733440	−0.366720	+	0.930331i	$0.619519\pi$
$504$	2.67145	0.118996
$505$	−3.83152	−0.170500
$506$	21.2483	0.944601
$507$	−44.4903	−1.97588
$508$	−7.44437	−0.330290
$509$	−32.7990	−1.45379	−0.726894	−	0.686749i	$-0.759037\pi$
$509$	−32.7990	−1.45379	−0.726894	+	0.686749i	$0.759037\pi$
$510$	2.61766	0.115912
$511$	14.4228	0.638029
$512$	−1.00000	−0.0441942
$513$	16.8782	0.745189
$514$	−15.7819	−0.696109
$515$	−4.52834	−0.199543
$516$	−10.4051	−0.458058
$517$	1.35060	0.0593992
$518$	14.2263	0.625068
$519$	8.14591	0.357566
$520$	6.95331	0.304923
$521$	37.5053	1.64314	0.821568	−	0.570111i	$-0.193100\pi$
$521$	37.5053	1.64314	0.821568	+	0.570111i	$0.193100\pi$
$522$	−2.69694	−0.118042
$523$	26.1649	1.14411	0.572055	−	0.820215i	$-0.306146\pi$
$523$	26.1649	1.14411	0.572055	+	0.820215i	$0.306146\pi$
$524$	−0.585301	−0.0255690
$525$	−2.37474	−0.103642
$526$	−9.08680	−0.396203
$527$	18.1261	0.789585
$528$	4.38782	0.190955
$529$	14.1483	0.615142
$530$	−10.1906	−0.442651
$531$	16.3155	0.708034
$532$	5.72975	0.248416
$533$	−19.9583	−0.864491
$534$	1.67426	0.0724523
$535$	−8.53972	−0.369204
$536$	14.2874	0.617123
$537$	13.3332	0.575371
$538$	12.6123	0.543757
$539$	11.9928	0.516565
$540$	5.55791	0.239174
$541$	−38.6718	−1.66263	−0.831315	−	0.555802i	$-0.812411\pi$
$541$	−38.6718	−1.66263	−0.831315	+	0.555802i	$0.812411\pi$
$542$	22.6668	0.973621
$543$	−1.11031	−0.0476480
$544$	−2.07979	−0.0891701
$545$	−12.6859	−0.543404
$546$	−16.5123	−0.706661
$547$	−7.45495	−0.318751	−0.159375	−	0.987218i	$-0.550948\pi$
$547$	−7.45495	−0.318751	−0.159375	+	0.987218i	$0.550948\pi$
$548$	−3.90577	−0.166846
$549$	8.97907	0.383217
$550$	3.48622	0.148653
$551$	−5.78442	−0.246424
$552$	7.67121	0.326508
$553$	13.3443	0.567456
$554$	3.47620	0.147690
$555$	9.48997	0.402827
$556$	−17.5948	−0.746185
$557$	22.7958	0.965889	0.482944	−	0.875651i	$-0.339567\pi$
$557$	22.7958	0.965889	0.482944	+	0.875651i	$0.339567\pi$
$558$	12.3399	0.522389
$559$	−57.4833	−2.43129
$560$	1.88678	0.0797311
$561$	9.12573	0.385288
$562$	16.1204	0.679997
$563$	−10.1923	−0.429552	−0.214776	−	0.976663i	$-0.568902\pi$
$563$	−10.1923	−0.429552	−0.214776	+	0.976663i	$0.568902\pi$
$564$	0.487603	0.0205318
$565$	1.41079	0.0593525
$566$	11.4837	0.482696
$567$	−5.18424	−0.217717
$568$	8.46495	0.355182
$569$	23.4550	0.983286	0.491643	−	0.870797i	$-0.336396\pi$
$569$	23.4550	0.983286	0.491643	+	0.870797i	$0.336396\pi$
$570$	3.82216	0.160092
$571$	14.7947	0.619138	0.309569	−	0.950877i	$-0.399815\pi$
$571$	14.7947	0.619138	0.309569	+	0.950877i	$0.399815\pi$
$572$	24.2407	1.01356
$573$	−28.6504	−1.19689
$574$	−5.41569	−0.226047
$575$	6.09494	0.254176
$576$	−1.41588	−0.0589949
$577$	−4.14266	−0.172461	−0.0862305	−	0.996275i	$-0.527482\pi$
$577$	−4.14266	−0.172461	−0.0862305	+	0.996275i	$0.527482\pi$
$578$	12.6745	0.527189
$579$	7.89091	0.327935
$580$	−1.90478	−0.0790918
$581$	8.80073	0.365116
$582$	−4.61532	−0.191311
$583$	−35.5267	−1.47136
$584$	−7.64415	−0.316317
$585$	9.84503	0.407042
$586$	−32.6546	−1.34895
$587$	9.09515	0.375397	0.187698	−	0.982227i	$-0.439897\pi$
$587$	9.09515	0.375397	0.187698	+	0.982227i	$0.439897\pi$
$588$	4.32972	0.178555
$589$	26.4667	1.09054
$590$	11.5233	0.474405
$591$	−21.2961	−0.876003
$592$	−7.53999	−0.309892
$593$	1.36584	0.0560883	0.0280442	−	0.999607i	$-0.491072\pi$
$593$	1.36584	0.0560883	0.0280442	+	0.999607i	$0.491072\pi$
$594$	19.3761	0.795010
$595$	3.92410	0.160873
$596$	−9.54635	−0.391034
$597$	30.1325	1.23324
$598$	42.3800	1.73305
$599$	31.3707	1.28177	0.640886	−	0.767636i	$-0.278567\pi$
$599$	31.3707	1.28177	0.640886	+	0.767636i	$0.278567\pi$
$600$	1.25862	0.0513829
$601$	−20.6139	−0.840860	−0.420430	−	0.907325i	$-0.638121\pi$
$601$	−20.6139	−0.840860	−0.420430	+	0.907325i	$0.638121\pi$
$602$	−15.5981	−0.635732
$603$	20.2292	0.823798
$604$	−13.8126	−0.562027
$605$	1.15371	0.0469051
$606$	−4.82243	−0.195898
$607$	−12.9985	−0.527594	−0.263797	−	0.964578i	$-0.584975\pi$
$607$	−12.9985	−0.527594	−0.263797	+	0.964578i	$0.584975\pi$
$608$	−3.03678	−0.123158
$609$	4.52337	0.183296
$610$	6.34170	0.256768
$611$	2.69379	0.108979
$612$	−2.94472	−0.119033
$613$	−2.88549	−0.116544	−0.0582720	−	0.998301i	$-0.518559\pi$
$613$	−2.88549	−0.116544	−0.0582720	+	0.998301i	$0.518559\pi$
$614$	33.4934	1.35168
$615$	−3.61266	−0.145676
$616$	6.57773	0.265024
$617$	−1.94625	−0.0783532	−0.0391766	−	0.999232i	$-0.512473\pi$
$617$	−1.94625	−0.0783532	−0.0391766	+	0.999232i	$0.512473\pi$
$618$	−5.69946	−0.229266
$619$	32.9784	1.32551	0.662757	−	0.748834i	$-0.269386\pi$
$619$	32.9784	1.32551	0.662757	+	0.748834i	$0.269386\pi$
$620$	8.71536	0.350017
$621$	33.8751	1.35936
$622$	−23.5276	−0.943371
$623$	2.50986	0.100556
$624$	8.75157	0.350343
$625$	1.00000	0.0400000
$626$	−0.110421	−0.00441329
$627$	13.3249	0.532144
$628$	3.53365	0.141008
$629$	−15.6816	−0.625265
$630$	2.67145	0.106433
$631$	10.4077	0.414324	0.207162	−	0.978307i	$-0.433577\pi$
$631$	10.4077	0.414324	0.207162	+	0.978307i	$0.433577\pi$
$632$	−7.07250	−0.281329
$633$	−6.05167	−0.240532
$634$	−27.3570	−1.08648
$635$	−7.44437	−0.295421
$636$	−12.8261	−0.508588
$637$	23.9197	0.947735
$638$	−6.64049	−0.262900
$639$	11.9853	0.474133
$640$	−1.00000	−0.0395285
$641$	−23.2972	−0.920184	−0.460092	−	0.887871i	$-0.652183\pi$
$641$	−23.2972	−0.920184	−0.460092	+	0.887871i	$0.652183\pi$
$642$	−10.7483	−0.424200
$643$	12.0025	0.473333	0.236667	−	0.971591i	$-0.423945\pi$
$643$	12.0025	0.473333	0.236667	+	0.971591i	$0.423945\pi$
$644$	11.4998	0.453156
$645$	−10.4051	−0.409699
$646$	−6.31586	−0.248494
$647$	−36.7478	−1.44470	−0.722352	−	0.691526i	$-0.756939\pi$
$647$	−36.7478	−1.44470	−0.722352	+	0.691526i	$0.756939\pi$
$648$	2.74766	0.107938
$649$	40.1726	1.57691
$650$	6.95331	0.272731
$651$	−20.6967	−0.811169
$652$	15.0237	0.588373
$653$	22.6251	0.885389	0.442695	−	0.896672i	$-0.354023\pi$
$653$	22.6251	0.885389	0.442695	+	0.896672i	$0.354023\pi$
$654$	−15.9667	−0.624348
$655$	−0.585301	−0.0228696
$656$	2.87033	0.112068
$657$	−10.8232	−0.422252
$658$	0.730960	0.0284958
$659$	−23.5581	−0.917692	−0.458846	−	0.888516i	$-0.651737\pi$
$659$	−23.5581	−0.917692	−0.458846	+	0.888516i	$0.651737\pi$
$660$	4.38782	0.170796
$661$	−22.5040	−0.875304	−0.437652	−	0.899144i	$-0.644190\pi$
$661$	−22.5040	−0.875304	−0.437652	+	0.899144i	$0.644190\pi$
$662$	18.3665	0.713835
$663$	18.2014	0.706883
$664$	−4.66441	−0.181014
$665$	5.72975	0.222190
$666$	−10.6757	−0.413675
$667$	−11.6095	−0.449523
$668$	−6.40103	−0.247663
$669$	26.9608	1.04236
$670$	14.2874	0.551971
$671$	22.1085	0.853491
$672$	2.37474	0.0916076
$673$	−44.0253	−1.69705	−0.848524	−	0.529156i	$-0.822509\pi$
$673$	−44.0253	−1.69705	−0.848524	+	0.529156i	$0.822509\pi$
$674$	14.8058	0.570296
$675$	5.55791	0.213924
$676$	35.3485	1.35956
$677$	0.560216	0.0215308	0.0107654	−	0.999942i	$-0.496573\pi$
$677$	0.560216	0.0215308	0.0107654	+	0.999942i	$0.496573\pi$
$678$	1.77565	0.0681935
$679$	−6.91878	−0.265518
$680$	−2.07979	−0.0797561
$681$	21.4237	0.820956
$682$	30.3837	1.16345
$683$	−3.23259	−0.123692	−0.0618458	−	0.998086i	$-0.519699\pi$
$683$	−3.23259	−0.123692	−0.0618458	+	0.998086i	$0.519699\pi$
$684$	−4.29971	−0.164404
$685$	−3.90577	−0.149232
$686$	19.6981	0.752077
$687$	20.5137	0.782646
$688$	8.26705	0.315178
$689$	−70.8584	−2.69949
$690$	7.67121	0.292038
$691$	−13.2122	−0.502615	−0.251307	−	0.967907i	$-0.580860\pi$
$691$	−13.2122	−0.502615	−0.251307	+	0.967907i	$0.580860\pi$
$692$	−6.47210	−0.246032
$693$	9.31326	0.353782
$694$	−18.7785	−0.712822
$695$	−17.5948	−0.667408
$696$	−2.39740	−0.0908731
$697$	5.96968	0.226118
$698$	−6.81508	−0.257955
$699$	−4.05653	−0.153432
$700$	1.88678	0.0713137
$701$	−11.2730	−0.425777	−0.212888	−	0.977077i	$-0.568287\pi$
$701$	−11.2730	−0.425777	−0.212888	+	0.977077i	$0.568287\pi$
$702$	38.6459	1.45859
$703$	−22.8973	−0.863589
$704$	−3.48622	−0.131392
$705$	0.487603	0.0183642
$706$	24.6282	0.926894
$707$	−7.22925	−0.271884
$708$	14.5034	0.545071
$709$	−33.0445	−1.24101	−0.620505	−	0.784202i	$-0.713073\pi$
$709$	−33.0445	−1.24101	−0.620505	+	0.784202i	$0.713073\pi$
$710$	8.46495	0.317684
$711$	−10.0138	−0.375546
$712$	−1.33024	−0.0498527
$713$	53.1196	1.98935
$714$	4.93895	0.184836
$715$	24.2407	0.906553
$716$	−10.5935	−0.395899
$717$	5.30635	0.198169
$718$	−1.95793	−0.0730691
$719$	−1.88027	−0.0701222	−0.0350611	−	0.999385i	$-0.511163\pi$
$719$	−1.88027	−0.0701222	−0.0350611	+	0.999385i	$0.511163\pi$
$720$	−1.41588	−0.0527666
$721$	−8.54399	−0.318195
$722$	9.77794	0.363897
$723$	−17.2302	−0.640800
$724$	0.882166	0.0327854
$725$	−1.90478	−0.0707419
$726$	1.45209	0.0538919
$727$	−49.2235	−1.82560	−0.912799	−	0.408409i	$-0.866084\pi$
$727$	−49.2235	−1.82560	−0.912799	+	0.408409i	$0.866084\pi$
$728$	13.1194	0.486237
$729$	24.8762	0.921342
$730$	−7.64415	−0.282923
$731$	17.1937	0.635932
$732$	7.98178	0.295015
$733$	−36.7645	−1.35793	−0.678964	−	0.734172i	$-0.737571\pi$
$733$	−36.7645	−1.35793	−0.678964	+	0.734172i	$0.737571\pi$
$734$	−23.1187	−0.853327
$735$	4.32972	0.159704
$736$	−6.09494	−0.224662
$737$	49.8091	1.83474
$738$	4.06404	0.149599
$739$	−38.4371	−1.41393	−0.706966	−	0.707248i	$-0.749936\pi$
$739$	−38.4371	−1.41393	−0.706966	+	0.707248i	$0.749936\pi$
$740$	−7.53999	−0.277175
$741$	26.5766	0.976317
$742$	−19.2274	−0.705862
$743$	12.3760	0.454031	0.227016	−	0.973891i	$-0.427103\pi$
$743$	12.3760	0.454031	0.227016	+	0.973891i	$0.427103\pi$
$744$	10.9693	0.402155
$745$	−9.54635	−0.349751
$746$	−36.1412	−1.32322
$747$	−6.60423	−0.241636
$748$	−7.25059	−0.265108
$749$	−16.1126	−0.588741
$750$	1.25862	0.0459583
$751$	−42.3955	−1.54703	−0.773517	−	0.633775i	$-0.781504\pi$
$751$	−42.3955	−1.54703	−0.773517	+	0.633775i	$0.781504\pi$
$752$	−0.387411	−0.0141274
$753$	31.8790	1.16174
$754$	−13.2445	−0.482338
$755$	−13.8126	−0.502693
$756$	10.4866	0.381393
$757$	−44.3231	−1.61095	−0.805476	−	0.592629i	$-0.798090\pi$
$757$	−44.3231	−1.61095	−0.805476	+	0.592629i	$0.798090\pi$
$758$	−3.64173	−0.132274
$759$	26.7435	0.970727
$760$	−3.03678	−0.110156
$761$	2.39114	0.0866788	0.0433394	−	0.999060i	$-0.486200\pi$
$761$	2.39114	0.0866788	0.0433394	+	0.999060i	$0.486200\pi$
$762$	−9.36963	−0.339426
$763$	−23.9355	−0.866524
$764$	22.7634	0.823550
$765$	−2.94472	−0.106467
$766$	−7.17961	−0.259410
$767$	80.1248	2.89314
$768$	−1.25862	−0.0454165
$769$	15.5486	0.560698	0.280349	−	0.959898i	$-0.409550\pi$
$769$	15.5486	0.560698	0.280349	+	0.959898i	$0.409550\pi$
$770$	6.57773	0.237045
$771$	−19.8634	−0.715362
$772$	−6.26949	−0.225644
$773$	−9.15143	−0.329154	−0.164577	−	0.986364i	$-0.552626\pi$
$773$	−9.15143	−0.329154	−0.164577	+	0.986364i	$0.552626\pi$
$774$	11.7051	0.420732
$775$	8.71536	0.313065
$776$	3.66697	0.131637
$777$	17.9055	0.642357
$778$	16.5162	0.592134
$779$	8.71658	0.312304
$780$	8.75157	0.313356
$781$	29.5107	1.05597
$782$	−12.6762	−0.453299
$783$	−10.5866	−0.378335
$784$	−3.44005	−0.122859
$785$	3.53365	0.126121
$786$	−0.736671	−0.0262762
$787$	−47.1340	−1.68014	−0.840072	−	0.542475i	$-0.817487\pi$
$787$	−47.1340	−1.68014	−0.840072	+	0.542475i	$0.817487\pi$
$788$	16.9202	0.602756
$789$	−11.4368	−0.407162
$790$	−7.07250	−0.251628
$791$	2.66186	0.0946448
$792$	−4.93606	−0.175395
$793$	44.0958	1.56589
$794$	10.1468	0.360096
$795$	−12.8261	−0.454894
$796$	−23.9409	−0.848563
$797$	−14.3376	−0.507864	−0.253932	−	0.967222i	$-0.581724\pi$
$797$	−14.3376	−0.507864	−0.253932	+	0.967222i	$0.581724\pi$
$798$	7.21158	0.255287
$799$	−0.805731	−0.0285047
$800$	−1.00000	−0.0353553
$801$	−1.88345	−0.0665484
$802$	−1.00000	−0.0353112
$803$	−26.6492	−0.940428
$804$	17.9824	0.634191
$805$	11.4998	0.405315
$806$	60.6006	2.13457
$807$	15.8741	0.558796
$808$	3.83152	0.134792
$809$	17.9724	0.631876	0.315938	−	0.948780i	$-0.397681\pi$
$809$	17.9724	0.631876	0.315938	+	0.948780i	$0.397681\pi$
$810$	2.74766	0.0965429
$811$	−23.5508	−0.826980	−0.413490	−	0.910509i	$-0.635690\pi$
$811$	−23.5508	−0.826980	−0.413490	+	0.910509i	$0.635690\pi$
$812$	−3.59391	−0.126122
$813$	28.5288	1.00055
$814$	−26.2860	−0.921325
$815$	15.0237	0.526257
$816$	−2.61766	−0.0916364
$817$	25.1052	0.878321
$818$	6.66002	0.232862
$819$	18.5754	0.649078
$820$	2.87033	0.100236
$821$	−35.9550	−1.25484	−0.627419	−	0.778682i	$-0.715888\pi$
$821$	−35.9550	−1.25484	−0.627419	+	0.778682i	$0.715888\pi$
$822$	−4.91587	−0.171461
$823$	34.0074	1.18542	0.592712	−	0.805414i	$-0.298057\pi$
$823$	34.0074	1.18542	0.592712	+	0.805414i	$0.298057\pi$
$824$	4.52834	0.157752
$825$	4.38782	0.152764
$826$	21.7419	0.756497
$827$	−3.97871	−0.138353	−0.0691766	−	0.997604i	$-0.522037\pi$
$827$	−3.97871	−0.138353	−0.0691766	+	0.997604i	$0.522037\pi$
$828$	−8.62968	−0.299902
$829$	21.7250	0.754540	0.377270	−	0.926103i	$-0.376863\pi$
$829$	21.7250	0.754540	0.377270	+	0.926103i	$0.376863\pi$
$830$	−4.66441	−0.161904
$831$	4.37521	0.151775
$832$	−6.95331	−0.241063
$833$	−7.15457	−0.247891
$834$	−22.1451	−0.766823
$835$	−6.40103	−0.221517
$836$	−10.5869	−0.366155
$837$	48.4392	1.67430
$838$	2.49145	0.0860658
$839$	−22.9960	−0.793912	−0.396956	−	0.917838i	$-0.629933\pi$
$839$	−22.9960	−0.793912	−0.396956	+	0.917838i	$0.629933\pi$
$840$	2.37474	0.0819363
$841$	−25.3718	−0.874890
$842$	6.59406	0.227246
$843$	20.2894	0.698804
$844$	4.80818	0.165505
$845$	35.3485	1.21603
$846$	−0.548526	−0.0188587
$847$	2.17680	0.0747959
$848$	10.1906	0.349947
$849$	14.4536	0.496047
$850$	−2.07979	−0.0713361
$851$	−45.9558	−1.57534
$852$	10.6542	0.365005
$853$	43.9999	1.50653	0.753263	−	0.657719i	$-0.228479\pi$
$853$	43.9999	1.50653	0.753263	+	0.657719i	$0.228479\pi$
$854$	11.9654	0.409448
$855$	−4.29971	−0.147047
$856$	8.53972	0.291882
$857$	46.2326	1.57927	0.789637	−	0.613574i	$-0.210269\pi$
$857$	46.2326	1.57927	0.789637	+	0.613574i	$0.210269\pi$
$858$	30.5099	1.04159
$859$	19.4465	0.663506	0.331753	−	0.943366i	$-0.392360\pi$
$859$	19.4465	0.663506	0.331753	+	0.943366i	$0.392360\pi$
$860$	8.26705	0.281904
$861$	−6.81630	−0.232299
$862$	18.1593	0.618508
$863$	31.9882	1.08889	0.544446	−	0.838796i	$-0.316740\pi$
$863$	31.9882	1.08889	0.544446	+	0.838796i	$0.316740\pi$
$864$	−5.55791	−0.189084
$865$	−6.47210	−0.220058
$866$	−19.1718	−0.651484
$867$	15.9524	0.541771
$868$	16.4440	0.558146
$869$	−24.6563	−0.836407
$870$	−2.39740	−0.0812794
$871$	99.3449	3.36617
$872$	12.6859	0.429599
$873$	5.19198	0.175722
$874$	−18.5090	−0.626077
$875$	1.88678	0.0637849
$876$	−9.62107	−0.325066
$877$	53.2785	1.79909	0.899544	−	0.436830i	$-0.143899\pi$
$877$	53.2785	1.79909	0.899544	+	0.436830i	$0.143899\pi$
$878$	−29.0910	−0.981772
$879$	−41.0998	−1.38626
$880$	−3.48622	−0.117520
$881$	51.1456	1.72314	0.861569	−	0.507640i	$-0.169482\pi$
$881$	51.1456	1.72314	0.861569	+	0.507640i	$0.169482\pi$
$882$	−4.87069	−0.164005
$883$	36.1378	1.21613	0.608066	−	0.793886i	$-0.291945\pi$
$883$	36.1378	1.21613	0.608066	+	0.793886i	$0.291945\pi$
$884$	−14.4614	−0.486389
$885$	14.5034	0.487527
$886$	8.67590	0.291473
$887$	−13.8667	−0.465599	−0.232800	−	0.972525i	$-0.574789\pi$
$887$	−13.8667	−0.465599	−0.232800	+	0.972525i	$0.574789\pi$
$888$	−9.48997	−0.318463
$889$	−14.0459	−0.471084
$890$	−1.33024	−0.0445896
$891$	9.57894	0.320907
$892$	−21.4209	−0.717226
$893$	−1.17648	−0.0393695
$894$	−12.0152	−0.401849
$895$	−10.5935	−0.354103
$896$	−1.88678	−0.0630330
$897$	53.3403	1.78098
$898$	33.8132	1.12836
$899$	−16.6009	−0.553671
$900$	−1.41588	−0.0471959
$901$	21.1943	0.706083
$902$	10.0066	0.333184
$903$	−19.6321	−0.653315
$904$	−1.41079	−0.0469223
$905$	0.882166	0.0293242
$906$	−17.3848	−0.577572
$907$	19.6834	0.653577	0.326788	−	0.945098i	$-0.394034\pi$
$907$	19.6834	0.653577	0.326788	+	0.945098i	$0.394034\pi$
$908$	−17.0216	−0.564880
$909$	5.42496	0.179935
$910$	13.1194	0.434903
$911$	−4.58554	−0.151926	−0.0759628	−	0.997111i	$-0.524203\pi$
$911$	−4.58554	−0.151926	−0.0759628	+	0.997111i	$0.524203\pi$
$912$	−3.82216	−0.126564
$913$	−16.2611	−0.538165
$914$	−13.2145	−0.437095
$915$	7.98178	0.263870
$916$	−16.2986	−0.538520
$917$	−1.10434	−0.0364684
$918$	−11.5593	−0.381512
$919$	−13.3272	−0.439623	−0.219812	−	0.975542i	$-0.570544\pi$
$919$	−13.3272	−0.439623	−0.219812	+	0.975542i	$0.570544\pi$
$920$	−6.09494	−0.200944
$921$	42.1554	1.38907
$922$	2.10624	0.0693654
$923$	58.8594	1.93738
$924$	8.27886	0.272355
$925$	−7.53999	−0.247913
$926$	1.56942	0.0515745
$927$	6.41158	0.210584
$928$	1.90478	0.0625276
$929$	−22.5902	−0.741160	−0.370580	−	0.928801i	$-0.620841\pi$
$929$	−22.5902	−0.741160	−0.370580	+	0.928801i	$0.620841\pi$
$930$	10.9693	0.359698
$931$	−10.4467	−0.342377
$932$	3.22300	0.105573
$933$	−29.6123	−0.969463
$934$	−38.9296	−1.27382
$935$	−7.25059	−0.237119
$936$	−9.84503	−0.321795
$937$	−40.3554	−1.31835	−0.659177	−	0.751988i	$-0.729095\pi$
$937$	−40.3554	−1.31835	−0.659177	+	0.751988i	$0.729095\pi$
$938$	26.9573	0.880186
$939$	−0.138977	−0.00453536
$940$	−0.387411	−0.0126359
$941$	20.8444	0.679509	0.339755	−	0.940514i	$-0.389656\pi$
$941$	20.8444	0.679509	0.339755	+	0.940514i	$0.389656\pi$
$942$	4.44752	0.144908
$943$	17.4945	0.569699
$944$	−11.5233	−0.375050
$945$	10.4866	0.341128
$946$	28.8207	0.937043
$947$	−29.5450	−0.960082	−0.480041	−	0.877246i	$-0.659378\pi$
$947$	−29.5450	−0.960082	−0.480041	+	0.877246i	$0.659378\pi$
$948$	−8.90158	−0.289110
$949$	−53.1521	−1.72539
$950$	−3.03678	−0.0985263
$951$	−34.4320	−1.11653
$952$	−3.92410	−0.127181
$953$	−27.8195	−0.901162	−0.450581	−	0.892735i	$-0.648783\pi$
$953$	−27.8195	−0.901162	−0.450581	+	0.892735i	$0.648783\pi$
$954$	14.4286	0.467145
$955$	22.7634	0.736606
$956$	−4.21601	−0.136355
$957$	−8.35785	−0.270171
$958$	−10.4833	−0.338700
$959$	−7.36933	−0.237968
$960$	−1.25862	−0.0406218
$961$	44.9576	1.45024
$962$	−52.4279	−1.69034
$963$	12.0912	0.389633
$964$	13.6898	0.440919
$965$	−6.26949	−0.201822
$966$	14.4739	0.465690
$967$	17.5961	0.565853	0.282926	−	0.959142i	$-0.408695\pi$
$967$	17.5961	0.565853	0.282926	+	0.959142i	$0.408695\pi$
$968$	−1.15371	−0.0370817
$969$	−7.94926	−0.255367
$970$	3.66697	0.117739
$971$	43.5488	1.39755	0.698774	−	0.715343i	$-0.253729\pi$
$971$	43.5488	1.39755	0.698774	+	0.715343i	$0.253729\pi$
$972$	−13.2155	−0.423886
$973$	−33.1975	−1.06426
$974$	24.6487	0.789797
$975$	8.75157	0.280275
$976$	−6.34170	−0.202993
$977$	10.0435	0.321321	0.160661	−	0.987010i	$-0.448638\pi$
$977$	10.0435	0.321321	0.160661	+	0.987010i	$0.448638\pi$
$978$	18.9091	0.604646
$979$	−4.63749	−0.148215
$980$	−3.44005	−0.109888
$981$	17.9617	0.573472
$982$	−14.8353	−0.473414
$983$	−41.6833	−1.32949	−0.664745	−	0.747070i	$-0.731460\pi$
$983$	−41.6833	−1.32949	−0.664745	+	0.747070i	$0.731460\pi$
$984$	3.61266	0.115167
$985$	16.9202	0.539122
$986$	3.96154	0.126161
$987$	0.920000	0.0292839
$988$	−21.1157	−0.671780
$989$	50.3872	1.60222
$990$	−4.93606	−0.156878
$991$	−50.7125	−1.61094	−0.805468	−	0.592640i	$-0.798086\pi$
$991$	−50.7125	−1.61094	−0.805468	+	0.592640i	$0.798086\pi$
$992$	−8.71536	−0.276713
$993$	23.1165	0.733579
$994$	15.9715	0.506586
$995$	−23.9409	−0.758978
$996$	−5.87072	−0.186021
$997$	17.9887	0.569707	0.284853	−	0.958571i	$-0.408055\pi$
$997$	17.9887	0.569707	0.284853	+	0.958571i	$0.408055\pi$
$998$	5.40224	0.171005
$999$	−41.9066	−1.32586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.i.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.i.1.5	✓	10	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.25862 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.25862 q^{6} +1.88678 q^{7} -1.00000 q^{8} -1.41588 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.25862 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.25862 q^{6} +1.88678 q^{7} -1.00000 q^{8} -1.41588 q^{9} -1.00000 q^{10} -3.48622 q^{11} -1.25862 q^{12} -6.95331 q^{13} -1.88678 q^{14} -1.25862 q^{15} +1.00000 q^{16} +2.07979 q^{17} +1.41588 q^{18} +3.03678 q^{19} +1.00000 q^{20} -2.37474 q^{21} +3.48622 q^{22} +6.09494 q^{23} +1.25862 q^{24} +1.00000 q^{25} +6.95331 q^{26} +5.55791 q^{27} +1.88678 q^{28} -1.90478 q^{29} +1.25862 q^{30} +8.71536 q^{31} -1.00000 q^{32} +4.38782 q^{33} -2.07979 q^{34} +1.88678 q^{35} -1.41588 q^{36} -7.53999 q^{37} -3.03678 q^{38} +8.75157 q^{39} -1.00000 q^{40} +2.87033 q^{41} +2.37474 q^{42} +8.26705 q^{43} -3.48622 q^{44} -1.41588 q^{45} -6.09494 q^{46} -0.387411 q^{47} -1.25862 q^{48} -3.44005 q^{49} -1.00000 q^{50} -2.61766 q^{51} -6.95331 q^{52} +10.1906 q^{53} -5.55791 q^{54} -3.48622 q^{55} -1.88678 q^{56} -3.82216 q^{57} +1.90478 q^{58} -11.5233 q^{59} -1.25862 q^{60} -6.34170 q^{61} -8.71536 q^{62} -2.67145 q^{63} +1.00000 q^{64} -6.95331 q^{65} -4.38782 q^{66} -14.2874 q^{67} +2.07979 q^{68} -7.67121 q^{69} -1.88678 q^{70} -8.46495 q^{71} +1.41588 q^{72} +7.64415 q^{73} +7.53999 q^{74} -1.25862 q^{75} +3.03678 q^{76} -6.57773 q^{77} -8.75157 q^{78} +7.07250 q^{79} +1.00000 q^{80} -2.74766 q^{81} -2.87033 q^{82} +4.66441 q^{83} -2.37474 q^{84} +2.07979 q^{85} -8.26705 q^{86} +2.39740 q^{87} +3.48622 q^{88} +1.33024 q^{89} +1.41588 q^{90} -13.1194 q^{91} +6.09494 q^{92} -10.9693 q^{93} +0.387411 q^{94} +3.03678 q^{95} +1.25862 q^{96} -3.66697 q^{97} +3.44005 q^{98} +4.93606 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9} - 10 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 10 q^{16} + 9 q^{17} - 6 q^{18} - 13 q^{19} + 10 q^{20} - 24 q^{21} + 11 q^{22} - 3 q^{23} + 4 q^{24} + 10 q^{25} - 6 q^{26} - 10 q^{27} - 3 q^{28} - 4 q^{29} + 4 q^{30} - 17 q^{31} - 10 q^{32} - 2 q^{33} - 9 q^{34} - 3 q^{35} + 6 q^{36} - 15 q^{37} + 13 q^{38} - 6 q^{39} - 10 q^{40} - 11 q^{41} + 24 q^{42} - 11 q^{43} - 11 q^{44} + 6 q^{45} + 3 q^{46} + 3 q^{47} - 4 q^{48} - 5 q^{49} - 10 q^{50} - 21 q^{51} + 6 q^{52} + 25 q^{53} + 10 q^{54} - 11 q^{55} + 3 q^{56} + 31 q^{57} + 4 q^{58} - 46 q^{59} - 4 q^{60} - 54 q^{61} + 17 q^{62} - 6 q^{63} + 10 q^{64} + 6 q^{65} + 2 q^{66} - 26 q^{67} + 9 q^{68} - 9 q^{69} + 3 q^{70} - 16 q^{71} - 6 q^{72} + 4 q^{73} + 15 q^{74} - 4 q^{75} - 13 q^{76} + 11 q^{77} + 6 q^{78} - 19 q^{79} + 10 q^{80} - 6 q^{81} + 11 q^{82} + 19 q^{83} - 24 q^{84} + 9 q^{85} + 11 q^{86} + 28 q^{87} + 11 q^{88} - 30 q^{89} - 6 q^{90} - 38 q^{91} - 3 q^{92} - 18 q^{93} - 3 q^{94} - 13 q^{95} + 4 q^{96} - 16 q^{97} + 5 q^{98} - 59 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9 - 10 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 10 * q^16 + 9 * q^17 - 6 * q^18 - 13 * q^19 + 10 * q^20 - 24 * q^21 + 11 * q^22 - 3 * q^23 + 4 * q^24 + 10 * q^25 - 6 * q^26 - 10 * q^27 - 3 * q^28 - 4 * q^29 + 4 * q^30 - 17 * q^31 - 10 * q^32 - 2 * q^33 - 9 * q^34 - 3 * q^35 + 6 * q^36 - 15 * q^37 + 13 * q^38 - 6 * q^39 - 10 * q^40 - 11 * q^41 + 24 * q^42 - 11 * q^43 - 11 * q^44 + 6 * q^45 + 3 * q^46 + 3 * q^47 - 4 * q^48 - 5 * q^49 - 10 * q^50 - 21 * q^51 + 6 * q^52 + 25 * q^53 + 10 * q^54 - 11 * q^55 + 3 * q^56 + 31 * q^57 + 4 * q^58 - 46 * q^59 - 4 * q^60 - 54 * q^61 + 17 * q^62 - 6 * q^63 + 10 * q^64 + 6 * q^65 + 2 * q^66 - 26 * q^67 + 9 * q^68 - 9 * q^69 + 3 * q^70 - 16 * q^71 - 6 * q^72 + 4 * q^73 + 15 * q^74 - 4 * q^75 - 13 * q^76 + 11 * q^77 + 6 * q^78 - 19 * q^79 + 10 * q^80 - 6 * q^81 + 11 * q^82 + 19 * q^83 - 24 * q^84 + 9 * q^85 + 11 * q^86 + 28 * q^87 + 11 * q^88 - 30 * q^89 - 6 * q^90 - 38 * q^91 - 3 * q^92 - 18 * q^93 - 3 * q^94 - 13 * q^95 + 4 * q^96 - 16 * q^97 + 5 * q^98 - 59 * q^99

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