LMFDB - Embedded newform 4334.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 6 x^{14} - 8 x^{13} + 94 x^{12} - 13 x^{11} - 582 x^{10} + 295 x^{9} + 1814 x^{8} - 1056 x^{7} + \cdots - 45 $ x^15 - 6x^14 - 8x^13 + 94x^12 - 13x^11 - 582x^10 + 295x^9 + 1814x^8 - 1056x^7 - 2966x^6 + 1621x^5 + 2328x^4 - 1160x^3 - 589x^2 + 364x - 45
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$1.97073$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.970726 q^{3} +1.00000 q^{4} +0.208503 q^{5} +0.970726 q^{6} -0.143082 q^{7} +1.00000 q^{8} -2.05769 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.970726 q^{3} +1.00000 q^{4} +0.208503 q^{5} +0.970726 q^{6} -0.143082 q^{7} +1.00000 q^{8} -2.05769 q^{9} +0.208503 q^{10} +1.00000 q^{11} +0.970726 q^{12} -1.77218 q^{13} -0.143082 q^{14} +0.202399 q^{15} +1.00000 q^{16} -5.73447 q^{17} -2.05769 q^{18} -2.88901 q^{19} +0.208503 q^{20} -0.138894 q^{21} +1.00000 q^{22} +1.00120 q^{23} +0.970726 q^{24} -4.95653 q^{25} -1.77218 q^{26} -4.90963 q^{27} -0.143082 q^{28} -5.11255 q^{29} +0.202399 q^{30} -3.84517 q^{31} +1.00000 q^{32} +0.970726 q^{33} -5.73447 q^{34} -0.0298331 q^{35} -2.05769 q^{36} -3.80705 q^{37} -2.88901 q^{38} -1.72030 q^{39} +0.208503 q^{40} -12.4195 q^{41} -0.138894 q^{42} +5.49455 q^{43} +1.00000 q^{44} -0.429035 q^{45} +1.00120 q^{46} +3.77329 q^{47} +0.970726 q^{48} -6.97953 q^{49} -4.95653 q^{50} -5.56660 q^{51} -1.77218 q^{52} +4.68844 q^{53} -4.90963 q^{54} +0.208503 q^{55} -0.143082 q^{56} -2.80444 q^{57} -5.11255 q^{58} +8.09333 q^{59} +0.202399 q^{60} +9.60240 q^{61} -3.84517 q^{62} +0.294419 q^{63} +1.00000 q^{64} -0.369505 q^{65} +0.970726 q^{66} -7.28671 q^{67} -5.73447 q^{68} +0.971891 q^{69} -0.0298331 q^{70} +5.65294 q^{71} -2.05769 q^{72} +7.45826 q^{73} -3.80705 q^{74} -4.81143 q^{75} -2.88901 q^{76} -0.143082 q^{77} -1.72030 q^{78} +12.0430 q^{79} +0.208503 q^{80} +1.40717 q^{81} -12.4195 q^{82} -0.278855 q^{83} -0.138894 q^{84} -1.19566 q^{85} +5.49455 q^{86} -4.96289 q^{87} +1.00000 q^{88} -15.6248 q^{89} -0.429035 q^{90} +0.253567 q^{91} +1.00120 q^{92} -3.73261 q^{93} +3.77329 q^{94} -0.602369 q^{95} +0.970726 q^{96} -10.5404 q^{97} -6.97953 q^{98} -2.05769 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9} - 11 q^{10} + 15 q^{11} - 9 q^{12} - 21 q^{13} - 11 q^{14} - 2 q^{15} + 15 q^{16} - 4 q^{17} + 10 q^{18} - 22 q^{19} - 11 q^{20} - 13 q^{21} + 15 q^{22} - 16 q^{23} - 9 q^{24} + 6 q^{25} - 21 q^{26} - 21 q^{27} - 11 q^{28} - 8 q^{29} - 2 q^{30} - 33 q^{31} + 15 q^{32} - 9 q^{33} - 4 q^{34} - 2 q^{35} + 10 q^{36} - q^{37} - 22 q^{38} + q^{39} - 11 q^{40} - 10 q^{41} - 13 q^{42} - 8 q^{43} + 15 q^{44} - 10 q^{45} - 16 q^{46} - 31 q^{47} - 9 q^{48} + 2 q^{49} + 6 q^{50} + 2 q^{51} - 21 q^{52} - 18 q^{53} - 21 q^{54} - 11 q^{55} - 11 q^{56} + 16 q^{57} - 8 q^{58} - 37 q^{59} - 2 q^{60} - 31 q^{61} - 33 q^{62} - 20 q^{63} + 15 q^{64} - 13 q^{65} - 9 q^{66} + q^{67} - 4 q^{68} - 25 q^{69} - 2 q^{70} - 28 q^{71} + 10 q^{72} - 20 q^{73} - q^{74} - 9 q^{75} - 22 q^{76} - 11 q^{77} + q^{78} - 6 q^{79} - 11 q^{80} + 3 q^{81} - 10 q^{82} - 15 q^{83} - 13 q^{84} - 31 q^{85} - 8 q^{86} - 16 q^{87} + 15 q^{88} - 17 q^{89} - 10 q^{90} - 21 q^{91} - 16 q^{92} + 10 q^{93} - 31 q^{94} - 3 q^{95} - 9 q^{96} - 9 q^{97} + 2 q^{98} + 10 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9 - 11 * q^10 + 15 * q^11 - 9 * q^12 - 21 * q^13 - 11 * q^14 - 2 * q^15 + 15 * q^16 - 4 * q^17 + 10 * q^18 - 22 * q^19 - 11 * q^20 - 13 * q^21 + 15 * q^22 - 16 * q^23 - 9 * q^24 + 6 * q^25 - 21 * q^26 - 21 * q^27 - 11 * q^28 - 8 * q^29 - 2 * q^30 - 33 * q^31 + 15 * q^32 - 9 * q^33 - 4 * q^34 - 2 * q^35 + 10 * q^36 - q^37 - 22 * q^38 + q^39 - 11 * q^40 - 10 * q^41 - 13 * q^42 - 8 * q^43 + 15 * q^44 - 10 * q^45 - 16 * q^46 - 31 * q^47 - 9 * q^48 + 2 * q^49 + 6 * q^50 + 2 * q^51 - 21 * q^52 - 18 * q^53 - 21 * q^54 - 11 * q^55 - 11 * q^56 + 16 * q^57 - 8 * q^58 - 37 * q^59 - 2 * q^60 - 31 * q^61 - 33 * q^62 - 20 * q^63 + 15 * q^64 - 13 * q^65 - 9 * q^66 + q^67 - 4 * q^68 - 25 * q^69 - 2 * q^70 - 28 * q^71 + 10 * q^72 - 20 * q^73 - q^74 - 9 * q^75 - 22 * q^76 - 11 * q^77 + q^78 - 6 * q^79 - 11 * q^80 + 3 * q^81 - 10 * q^82 - 15 * q^83 - 13 * q^84 - 31 * q^85 - 8 * q^86 - 16 * q^87 + 15 * q^88 - 17 * q^89 - 10 * q^90 - 21 * q^91 - 16 * q^92 + 10 * q^93 - 31 * q^94 - 3 * q^95 - 9 * q^96 - 9 * q^97 + 2 * q^98 + 10 * 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
$3$	0.970726	0.560449	0.280224	−	0.959935i	$-0.409591\pi$
$3$	0.970726	0.560449	0.280224	+	0.959935i	$0.409591\pi$
$4$	1.00000	0.500000
$5$	0.208503	0.0932455	0.0466227	−	0.998913i	$-0.485154\pi$
$5$	0.208503	0.0932455	0.0466227	+	0.998913i	$0.485154\pi$
$6$	0.970726	0.396297
$7$	−0.143082	−0.0540800	−0.0270400	−	0.999634i	$-0.508608\pi$
$7$	−0.143082	−0.0540800	−0.0270400	+	0.999634i	$0.508608\pi$
$8$	1.00000	0.353553
$9$	−2.05769	−0.685897
$10$	0.208503	0.0659345
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.970726	0.280224
$13$	−1.77218	−0.491514	−0.245757	−	0.969331i	$-0.579037\pi$
$13$	−1.77218	−0.491514	−0.245757	+	0.969331i	$0.579037\pi$
$14$	−0.143082	−0.0382403
$15$	0.202399	0.0522593
$16$	1.00000	0.250000
$17$	−5.73447	−1.39081	−0.695407	−	0.718616i	$-0.744776\pi$
$17$	−5.73447	−1.39081	−0.695407	+	0.718616i	$0.744776\pi$
$18$	−2.05769	−0.485003
$19$	−2.88901	−0.662785	−0.331392	−	0.943493i	$-0.607518\pi$
$19$	−2.88901	−0.662785	−0.331392	+	0.943493i	$0.607518\pi$
$20$	0.208503	0.0466227
$21$	−0.138894	−0.0303091
$22$	1.00000	0.213201
$23$	1.00120	0.208765	0.104382	−	0.994537i	$-0.466713\pi$
$23$	1.00120	0.208765	0.104382	+	0.994537i	$0.466713\pi$
$24$	0.970726	0.198149
$25$	−4.95653	−0.991305
$26$	−1.77218	−0.347553
$27$	−4.90963	−0.944859
$28$	−0.143082	−0.0270400
$29$	−5.11255	−0.949378	−0.474689	−	0.880154i	$-0.657439\pi$
$29$	−5.11255	−0.949378	−0.474689	+	0.880154i	$0.657439\pi$
$30$	0.202399	0.0369529
$31$	−3.84517	−0.690614	−0.345307	−	0.938490i	$-0.612225\pi$
$31$	−3.84517	−0.690614	−0.345307	+	0.938490i	$0.612225\pi$
$32$	1.00000	0.176777
$33$	0.970726	0.168982
$34$	−5.73447	−0.983454
$35$	−0.0298331	−0.00504271
$36$	−2.05769	−0.342949
$37$	−3.80705	−0.625875	−0.312938	−	0.949774i	$-0.601313\pi$
$37$	−3.80705	−0.625875	−0.312938	+	0.949774i	$0.601313\pi$
$38$	−2.88901	−0.468660
$39$	−1.72030	−0.275469
$40$	0.208503	0.0329673
$41$	−12.4195	−1.93960	−0.969798	−	0.243910i	$-0.921570\pi$
$41$	−12.4195	−1.93960	−0.969798	+	0.243910i	$0.921570\pi$
$42$	−0.138894	−0.0214317
$43$	5.49455	0.837911	0.418956	−	0.908007i	$-0.362396\pi$
$43$	5.49455	0.837911	0.418956	+	0.908007i	$0.362396\pi$
$44$	1.00000	0.150756
$45$	−0.429035	−0.0639568
$46$	1.00120	0.147619
$47$	3.77329	0.550391	0.275195	−	0.961388i	$-0.411257\pi$
$47$	3.77329	0.550391	0.275195	+	0.961388i	$0.411257\pi$
$48$	0.970726	0.140112
$49$	−6.97953	−0.997075
$50$	−4.95653	−0.700959
$51$	−5.56660	−0.779480
$52$	−1.77218	−0.245757
$53$	4.68844	0.644007	0.322004	−	0.946738i	$-0.395644\pi$
$53$	4.68844	0.644007	0.322004	+	0.946738i	$0.395644\pi$
$54$	−4.90963	−0.668116
$55$	0.208503	0.0281146
$56$	−0.143082	−0.0191202
$57$	−2.80444	−0.371457
$58$	−5.11255	−0.671311
$59$	8.09333	1.05366	0.526831	−	0.849970i	$-0.323380\pi$
$59$	8.09333	1.05366	0.526831	+	0.849970i	$0.323380\pi$
$60$	0.202399	0.0261297
$61$	9.60240	1.22946	0.614730	−	0.788737i	$-0.289265\pi$
$61$	9.60240	1.22946	0.614730	+	0.788737i	$0.289265\pi$
$62$	−3.84517	−0.488338
$63$	0.294419	0.0370933
$64$	1.00000	0.125000
$65$	−0.369505	−0.0458315
$66$	0.970726	0.119488
$67$	−7.28671	−0.890213	−0.445106	−	0.895478i	$-0.646834\pi$
$67$	−7.28671	−0.890213	−0.445106	+	0.895478i	$0.646834\pi$
$68$	−5.73447	−0.695407
$69$	0.971891	0.117002
$70$	−0.0298331	−0.00356574
$71$	5.65294	0.670881	0.335440	−	0.942061i	$-0.391115\pi$
$71$	5.65294	0.670881	0.335440	+	0.942061i	$0.391115\pi$
$72$	−2.05769	−0.242501
$73$	7.45826	0.872923	0.436462	−	0.899723i	$-0.356232\pi$
$73$	7.45826	0.872923	0.436462	+	0.899723i	$0.356232\pi$
$74$	−3.80705	−0.442561
$75$	−4.81143	−0.555576
$76$	−2.88901	−0.331392
$77$	−0.143082	−0.0163057
$78$	−1.72030	−0.194786
$79$	12.0430	1.35494	0.677472	−	0.735549i	$-0.263076\pi$
$79$	12.0430	1.35494	0.677472	+	0.735549i	$0.263076\pi$
$80$	0.208503	0.0233114
$81$	1.40717	0.156352
$82$	−12.4195	−1.37150
$83$	−0.278855	−0.0306083	−0.0153042	−	0.999883i	$-0.504872\pi$
$83$	−0.278855	−0.0306083	−0.0153042	+	0.999883i	$0.504872\pi$
$84$	−0.138894	−0.0151545
$85$	−1.19566	−0.129687
$86$	5.49455	0.592493
$87$	−4.96289	−0.532077
$88$	1.00000	0.106600
$89$	−15.6248	−1.65622	−0.828112	−	0.560563i	$-0.810585\pi$
$89$	−15.6248	−1.65622	−0.828112	+	0.560563i	$0.810585\pi$
$90$	−0.429035	−0.0452243
$91$	0.253567	0.0265811
$92$	1.00120	0.104382
$93$	−3.73261	−0.387053
$94$	3.77329	0.389185
$95$	−0.602369	−0.0618017
$96$	0.970726	0.0990743
$97$	−10.5404	−1.07021	−0.535107	−	0.844784i	$-0.679729\pi$
$97$	−10.5404	−1.07021	−0.535107	+	0.844784i	$0.679729\pi$
$98$	−6.97953	−0.705039
$99$	−2.05769	−0.206806
$100$	−4.95653	−0.495653
$101$	12.2180	1.21574	0.607870	−	0.794036i	$-0.292024\pi$
$101$	12.2180	1.21574	0.607870	+	0.794036i	$0.292024\pi$
$102$	−5.56660	−0.551175
$103$	9.61981	0.947868	0.473934	−	0.880560i	$-0.342833\pi$
$103$	9.61981	0.947868	0.473934	+	0.880560i	$0.342833\pi$
$104$	−1.77218	−0.173777
$105$	−0.0289598	−0.00282618
$106$	4.68844	0.455382
$107$	1.97065	0.190510	0.0952551	−	0.995453i	$-0.469633\pi$
$107$	1.97065	0.190510	0.0952551	+	0.995453i	$0.469633\pi$
$108$	−4.90963	−0.472429
$109$	−9.35913	−0.896442	−0.448221	−	0.893923i	$-0.647942\pi$
$109$	−9.35913	−0.896442	−0.448221	+	0.893923i	$0.647942\pi$
$110$	0.208503	0.0198800
$111$	−3.69560	−0.350771
$112$	−0.143082	−0.0135200
$113$	−7.09760	−0.667686	−0.333843	−	0.942629i	$-0.608346\pi$
$113$	−7.09760	−0.667686	−0.333843	+	0.942629i	$0.608346\pi$
$114$	−2.80444	−0.262660
$115$	0.208754	0.0194664
$116$	−5.11255	−0.474689
$117$	3.64660	0.337128
$118$	8.09333	0.745052
$119$	0.820500	0.0752152
$120$	0.202399	0.0184765
$121$	1.00000	0.0909091
$122$	9.60240	0.869360
$123$	−12.0559	−1.08704
$124$	−3.84517	−0.345307
$125$	−2.07597	−0.185680
$126$	0.294419	0.0262289
$127$	5.69119	0.505012	0.252506	−	0.967595i	$-0.418745\pi$
$127$	5.69119	0.505012	0.252506	+	0.967595i	$0.418745\pi$
$128$	1.00000	0.0883883
$129$	5.33370	0.469606
$130$	−0.369505	−0.0324078
$131$	−17.1130	−1.49517	−0.747583	−	0.664168i	$-0.768786\pi$
$131$	−17.1130	−1.49517	−0.747583	+	0.664168i	$0.768786\pi$
$132$	0.970726	0.0844908
$133$	0.413366	0.0358434
$134$	−7.28671	−0.629476
$135$	−1.02367	−0.0881038
$136$	−5.73447	−0.491727
$137$	−2.00802	−0.171556	−0.0857782	−	0.996314i	$-0.527338\pi$
$137$	−2.00802	−0.171556	−0.0857782	+	0.996314i	$0.527338\pi$
$138$	0.971891	0.0827329
$139$	14.1098	1.19678	0.598391	−	0.801205i	$-0.295807\pi$
$139$	14.1098	1.19678	0.598391	+	0.801205i	$0.295807\pi$
$140$	−0.0298331	−0.00252136
$141$	3.66283	0.308466
$142$	5.65294	0.474384
$143$	−1.77218	−0.148197
$144$	−2.05769	−0.171474
$145$	−1.06598	−0.0885252
$146$	7.45826	0.617250
$147$	−6.77521	−0.558810
$148$	−3.80705	−0.312938
$149$	13.6119	1.11513	0.557564	−	0.830134i	$-0.311736\pi$
$149$	13.6119	1.11513	0.557564	+	0.830134i	$0.311736\pi$
$150$	−4.81143	−0.392851
$151$	−13.3154	−1.08359	−0.541797	−	0.840509i	$-0.682256\pi$
$151$	−13.3154	−1.08359	−0.541797	+	0.840509i	$0.682256\pi$
$152$	−2.88901	−0.234330
$153$	11.7998	0.953955
$154$	−0.143082	−0.0115299
$155$	−0.801731	−0.0643966
$156$	−1.72030	−0.137734
$157$	−15.5532	−1.24128	−0.620642	−	0.784094i	$-0.713128\pi$
$157$	−15.5532	−1.24128	−0.620642	+	0.784094i	$0.713128\pi$
$158$	12.0430	0.958090
$159$	4.55119	0.360933
$160$	0.208503	0.0164836
$161$	−0.143254	−0.0112900
$162$	1.40717	0.110558
$163$	4.23053	0.331360	0.165680	−	0.986180i	$-0.447018\pi$
$163$	4.23053	0.331360	0.165680	+	0.986180i	$0.447018\pi$
$164$	−12.4195	−0.969798
$165$	0.202399	0.0157568
$166$	−0.278855	−0.0216433
$167$	−2.96447	−0.229398	−0.114699	−	0.993400i	$-0.536590\pi$
$167$	−2.96447	−0.229398	−0.114699	+	0.993400i	$0.536590\pi$
$168$	−0.138894	−0.0107159
$169$	−9.85938	−0.758414
$170$	−1.19566	−0.0917026
$171$	5.94470	0.454602
$172$	5.49455	0.418956
$173$	−1.67435	−0.127298	−0.0636491	−	0.997972i	$-0.520274\pi$
$173$	−1.67435	−0.127298	−0.0636491	+	0.997972i	$0.520274\pi$
$174$	−4.96289	−0.376236
$175$	0.709191	0.0536098
$176$	1.00000	0.0753778
$177$	7.85641	0.590524
$178$	−15.6248	−1.17113
$179$	7.14221	0.533834	0.266917	−	0.963720i	$-0.413995\pi$
$179$	7.14221	0.533834	0.266917	+	0.963720i	$0.413995\pi$
$180$	−0.429035	−0.0319784
$181$	6.58062	0.489133	0.244567	−	0.969632i	$-0.421354\pi$
$181$	6.58062	0.489133	0.244567	+	0.969632i	$0.421354\pi$
$182$	0.253567	0.0187957
$183$	9.32129	0.689050
$184$	1.00120	0.0738095
$185$	−0.793783	−0.0583601
$186$	−3.73261	−0.273688
$187$	−5.73447	−0.419346
$188$	3.77329	0.275195
$189$	0.702481	0.0510980
$190$	−0.602369	−0.0437004
$191$	0.837571	0.0606045	0.0303023	−	0.999541i	$-0.490353\pi$
$191$	0.837571	0.0606045	0.0303023	+	0.999541i	$0.490353\pi$
$192$	0.970726	0.0700561
$193$	−4.20151	−0.302431	−0.151216	−	0.988501i	$-0.548319\pi$
$193$	−4.20151	−0.302431	−0.151216	+	0.988501i	$0.548319\pi$
$194$	−10.5404	−0.756755
$195$	−0.358688	−0.0256862
$196$	−6.97953	−0.498538
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	−2.05769	−0.146234
$199$	1.38808	0.0983984	0.0491992	−	0.998789i	$-0.484333\pi$
$199$	1.38808	0.0983984	0.0491992	+	0.998789i	$0.484333\pi$
$200$	−4.95653	−0.350479
$201$	−7.07339	−0.498919
$202$	12.2180	0.859658
$203$	0.731515	0.0513423
$204$	−5.56660	−0.389740
$205$	−2.58950	−0.180859
$206$	9.61981	0.670244
$207$	−2.06016	−0.143191
$208$	−1.77218	−0.122879
$209$	−2.88901	−0.199837
$210$	−0.0289598	−0.00199841
$211$	13.3512	0.919135	0.459568	−	0.888143i	$-0.348004\pi$
$211$	13.3512	0.919135	0.459568	+	0.888143i	$0.348004\pi$
$212$	4.68844	0.322004
$213$	5.48746	0.375994
$214$	1.97065	0.134711
$215$	1.14563	0.0781315
$216$	−4.90963	−0.334058
$217$	0.550176	0.0373484
$218$	−9.35913	−0.633880
$219$	7.23992	0.489229
$220$	0.208503	0.0140573
$221$	10.1625	0.683605
$222$	−3.69560	−0.248033
$223$	−15.0754	−1.00952	−0.504762	−	0.863259i	$-0.668420\pi$
$223$	−15.0754	−1.00952	−0.504762	+	0.863259i	$0.668420\pi$
$224$	−0.143082	−0.00956008
$225$	10.1990	0.679933
$226$	−7.09760	−0.472126
$227$	−22.1561	−1.47056	−0.735278	−	0.677766i	$-0.762948\pi$
$227$	−22.1561	−1.47056	−0.735278	+	0.677766i	$0.762948\pi$
$228$	−2.80444	−0.185728
$229$	−10.1473	−0.670550	−0.335275	−	0.942120i	$-0.608829\pi$
$229$	−10.1473	−0.670550	−0.335275	+	0.942120i	$0.608829\pi$
$230$	0.208754	0.0137648
$231$	−0.138894	−0.00913852
$232$	−5.11255	−0.335656
$233$	8.39797	0.550169	0.275085	−	0.961420i	$-0.411294\pi$
$233$	8.39797	0.550169	0.275085	+	0.961420i	$0.411294\pi$
$234$	3.64660	0.238386
$235$	0.786743	0.0513214
$236$	8.09333	0.526831
$237$	11.6904	0.759376
$238$	0.820500	0.0531851
$239$	7.39000	0.478019	0.239010	−	0.971017i	$-0.423177\pi$
$239$	7.39000	0.478019	0.239010	+	0.971017i	$0.423177\pi$
$240$	0.202399	0.0130648
$241$	−7.30760	−0.470724	−0.235362	−	0.971908i	$-0.575628\pi$
$241$	−7.30760	−0.470724	−0.235362	+	0.971908i	$0.575628\pi$
$242$	1.00000	0.0642824
$243$	16.0949	1.03249
$244$	9.60240	0.614730
$245$	−1.45525	−0.0929728
$246$	−12.0559	−0.768656
$247$	5.11985	0.325768
$248$	−3.84517	−0.244169
$249$	−0.270692	−0.0171544
$250$	−2.07597	−0.131296
$251$	22.4519	1.41715	0.708576	−	0.705635i	$-0.249338\pi$
$251$	22.4519	1.41715	0.708576	+	0.705635i	$0.249338\pi$
$252$	0.294419	0.0185467
$253$	1.00120	0.0629450
$254$	5.69119	0.357097
$255$	−1.16065	−0.0726830
$256$	1.00000	0.0625000
$257$	−17.6478	−1.10084	−0.550421	−	0.834887i	$-0.685533\pi$
$257$	−17.6478	−1.10084	−0.550421	+	0.834887i	$0.685533\pi$
$258$	5.33370	0.332062
$259$	0.544721	0.0338473
$260$	−0.369505	−0.0229157
$261$	10.5201	0.651175
$262$	−17.1130	−1.05724
$263$	−26.9808	−1.66371	−0.831855	−	0.554993i	$-0.812721\pi$
$263$	−26.9808	−1.66371	−0.831855	+	0.554993i	$0.812721\pi$
$264$	0.970726	0.0597440
$265$	0.977556	0.0600508
$266$	0.413366	0.0253451
$267$	−15.1674	−0.928228
$268$	−7.28671	−0.445106
$269$	−7.95754	−0.485180	−0.242590	−	0.970129i	$-0.577997\pi$
$269$	−7.95754	−0.485180	−0.242590	+	0.970129i	$0.577997\pi$
$270$	−1.02367	−0.0622988
$271$	−6.69184	−0.406500	−0.203250	−	0.979127i	$-0.565150\pi$
$271$	−6.69184	−0.406500	−0.203250	+	0.979127i	$0.565150\pi$
$272$	−5.73447	−0.347703
$273$	0.246144	0.0148973
$274$	−2.00802	−0.121309
$275$	−4.95653	−0.298890
$276$	0.971891	0.0585010
$277$	3.82220	0.229654	0.114827	−	0.993386i	$-0.463369\pi$
$277$	3.82220	0.229654	0.114827	+	0.993386i	$0.463369\pi$
$278$	14.1098	0.846252
$279$	7.91218	0.473690
$280$	−0.0298331	−0.00178287
$281$	12.9086	0.770062	0.385031	−	0.922904i	$-0.374191\pi$
$281$	12.9086	0.770062	0.385031	+	0.922904i	$0.374191\pi$
$282$	3.66283	0.218118
$283$	6.26048	0.372147	0.186073	−	0.982536i	$-0.440424\pi$
$283$	6.26048	0.372147	0.186073	+	0.982536i	$0.440424\pi$
$284$	5.65294	0.335440
$285$	−0.584735	−0.0346367
$286$	−1.77218	−0.104791
$287$	1.77700	0.104893
$288$	−2.05769	−0.121251
$289$	15.8841	0.934362
$290$	−1.06598	−0.0625968
$291$	−10.2318	−0.599800
$292$	7.45826	0.436462
$293$	−9.13646	−0.533758	−0.266879	−	0.963730i	$-0.585992\pi$
$293$	−9.13646	−0.533758	−0.266879	+	0.963730i	$0.585992\pi$
$294$	−6.77521	−0.395138
$295$	1.68749	0.0982493
$296$	−3.80705	−0.221280
$297$	−4.90963	−0.284886
$298$	13.6119	0.788515
$299$	−1.77431	−0.102611
$300$	−4.81143	−0.277788
$301$	−0.786173	−0.0453142
$302$	−13.3154	−0.766217
$303$	11.8604	0.681360
$304$	−2.88901	−0.165696
$305$	2.00213	0.114642
$306$	11.7998	0.674548
$307$	26.8219	1.53081	0.765403	−	0.643552i	$-0.222540\pi$
$307$	26.8219	1.53081	0.765403	+	0.643552i	$0.222540\pi$
$308$	−0.143082	−0.00815286
$309$	9.33820	0.531232
$310$	−0.801731	−0.0455353
$311$	−28.8083	−1.63357	−0.816784	−	0.576944i	$-0.804245\pi$
$311$	−28.8083	−1.63357	−0.816784	+	0.576944i	$0.804245\pi$
$312$	−1.72030	−0.0973928
$313$	−15.6425	−0.884167	−0.442083	−	0.896974i	$-0.645760\pi$
$313$	−15.6425	−0.884167	−0.442083	+	0.896974i	$0.645760\pi$
$314$	−15.5532	−0.877720
$315$	0.0613873	0.00345878
$316$	12.0430	0.677472
$317$	1.21582	0.0682873	0.0341436	−	0.999417i	$-0.489130\pi$
$317$	1.21582	0.0682873	0.0341436	+	0.999417i	$0.489130\pi$
$318$	4.55119	0.255218
$319$	−5.11255	−0.286248
$320$	0.208503	0.0116557
$321$	1.91296	0.106771
$322$	−0.143254	−0.00798323
$323$	16.5670	0.921810
$324$	1.40717	0.0781761
$325$	8.78386	0.487241
$326$	4.23053	0.234307
$327$	−9.08515	−0.502410
$328$	−12.4195	−0.685751
$329$	−0.539890	−0.0297651
$330$	0.202399	0.0111417
$331$	−26.5484	−1.45923	−0.729615	−	0.683858i	$-0.760301\pi$
$331$	−26.5484	−1.45923	−0.729615	+	0.683858i	$0.760301\pi$
$332$	−0.278855	−0.0153042
$333$	7.83374	0.429286
$334$	−2.96447	−0.162209
$335$	−1.51930	−0.0830083
$336$	−0.138894	−0.00757726
$337$	−28.6799	−1.56229	−0.781147	−	0.624347i	$-0.785365\pi$
$337$	−28.6799	−1.56229	−0.781147	+	0.624347i	$0.785365\pi$
$338$	−9.85938	−0.536279
$339$	−6.88983	−0.374204
$340$	−1.19566	−0.0648435
$341$	−3.84517	−0.208228
$342$	5.94470	0.321452
$343$	2.00022	0.108002
$344$	5.49455	0.296246
$345$	0.202643	0.0109099
$346$	−1.67435	−0.0900135
$347$	18.3561	0.985406	0.492703	−	0.870198i	$-0.336009\pi$
$347$	18.3561	0.985406	0.492703	+	0.870198i	$0.336009\pi$
$348$	−4.96289	−0.266039
$349$	29.7354	1.59170	0.795849	−	0.605495i	$-0.207025\pi$
$349$	29.7354	1.59170	0.795849	+	0.605495i	$0.207025\pi$
$350$	0.709191	0.0379078
$351$	8.70075	0.464412
$352$	1.00000	0.0533002
$353$	27.2794	1.45193	0.725967	−	0.687730i	$-0.241392\pi$
$353$	27.2794	1.45193	0.725967	+	0.687730i	$0.241392\pi$
$354$	7.85641	0.417563
$355$	1.17866	0.0625566
$356$	−15.6248	−0.828112
$357$	0.796481	0.0421542
$358$	7.14221	0.377477
$359$	12.0825	0.637691	0.318845	−	0.947807i	$-0.396705\pi$
$359$	12.0825	0.637691	0.318845	+	0.947807i	$0.396705\pi$
$360$	−0.429035	−0.0226122
$361$	−10.6536	−0.560716
$362$	6.58062	0.345869
$363$	0.970726	0.0509499
$364$	0.253567	0.0132905
$365$	1.55507	0.0813961
$366$	9.32129	0.487232
$367$	31.2347	1.63044	0.815218	−	0.579154i	$-0.196617\pi$
$367$	31.2347	1.63044	0.815218	+	0.579154i	$0.196617\pi$
$368$	1.00120	0.0521912
$369$	25.5554	1.33036
$370$	−0.793783	−0.0412668
$371$	−0.670833	−0.0348279
$372$	−3.73261	−0.193527
$373$	1.39014	0.0719785	0.0359893	−	0.999352i	$-0.488542\pi$
$373$	1.39014	0.0719785	0.0359893	+	0.999352i	$0.488542\pi$
$374$	−5.73447	−0.296522
$375$	−2.01520	−0.104064
$376$	3.77329	0.194592
$377$	9.06037	0.466633
$378$	0.702481	0.0361317
$379$	6.34767	0.326058	0.163029	−	0.986621i	$-0.447874\pi$
$379$	6.34767	0.326058	0.163029	+	0.986621i	$0.447874\pi$
$380$	−0.602369	−0.0309009
$381$	5.52459	0.283033
$382$	0.837571	0.0428539
$383$	−31.0460	−1.58638	−0.793188	−	0.608977i	$-0.791580\pi$
$383$	−31.0460	−1.58638	−0.793188	+	0.608977i	$0.791580\pi$
$384$	0.970726	0.0495371
$385$	−0.0298331	−0.00152044
$386$	−4.20151	−0.213851
$387$	−11.3061	−0.574721
$388$	−10.5404	−0.535107
$389$	4.19052	0.212468	0.106234	−	0.994341i	$-0.466121\pi$
$389$	4.19052	0.212468	0.106234	+	0.994341i	$0.466121\pi$
$390$	−0.358688	−0.0181629
$391$	−5.74136	−0.290353
$392$	−6.97953	−0.352519
$393$	−16.6120	−0.837964
$394$	−1.00000	−0.0503793
$395$	2.51100	0.126342
$396$	−2.05769	−0.103403
$397$	−20.2561	−1.01663	−0.508313	−	0.861173i	$-0.669731\pi$
$397$	−20.2561	−1.01663	−0.508313	+	0.861173i	$0.669731\pi$
$398$	1.38808	0.0695782
$399$	0.401265	0.0200884
$400$	−4.95653	−0.247826
$401$	35.2086	1.75823	0.879116	−	0.476608i	$-0.158134\pi$
$401$	35.2086	1.75823	0.879116	+	0.476608i	$0.158134\pi$
$402$	−7.07339	−0.352789
$403$	6.81434	0.339446
$404$	12.2180	0.607870
$405$	0.293399	0.0145791
$406$	0.731515	0.0363045
$407$	−3.80705	−0.188709
$408$	−5.56660	−0.275588
$409$	−13.3582	−0.660521	−0.330261	−	0.943890i	$-0.607137\pi$
$409$	−13.3582	−0.660521	−0.330261	+	0.943890i	$0.607137\pi$
$410$	−2.58950	−0.127886
$411$	−1.94923	−0.0961486
$412$	9.61981	0.473934
$413$	−1.15801	−0.0569820
$414$	−2.06016	−0.101251
$415$	−0.0581422	−0.00285409
$416$	−1.77218	−0.0868883
$417$	13.6968	0.670734
$418$	−2.88901	−0.141306
$419$	−14.7650	−0.721316	−0.360658	−	0.932698i	$-0.617448\pi$
$419$	−14.7650	−0.721316	−0.360658	+	0.932698i	$0.617448\pi$
$420$	−0.0289598	−0.00141309
$421$	−2.74704	−0.133882	−0.0669412	−	0.997757i	$-0.521324\pi$
$421$	−2.74704	−0.133882	−0.0669412	+	0.997757i	$0.521324\pi$
$422$	13.3512	0.649927
$423$	−7.76426	−0.377511
$424$	4.68844	0.227691
$425$	28.4231	1.37872
$426$	5.48746	0.265868
$427$	−1.37393	−0.0664892
$428$	1.97065	0.0952551
$429$	−1.72030	−0.0830569
$430$	1.14563	0.0552473
$431$	21.2869	1.02535	0.512676	−	0.858582i	$-0.328654\pi$
$431$	21.2869	1.02535	0.512676	+	0.858582i	$0.328654\pi$
$432$	−4.90963	−0.236215
$433$	14.6467	0.703874	0.351937	−	0.936024i	$-0.385523\pi$
$433$	14.6467	0.703874	0.351937	+	0.936024i	$0.385523\pi$
$434$	0.550176	0.0264093
$435$	−1.03478	−0.0496138
$436$	−9.35913	−0.448221
$437$	−2.89248	−0.138366
$438$	7.23992	0.345937
$439$	18.2258	0.869871	0.434936	−	0.900462i	$-0.356771\pi$
$439$	18.2258	0.869871	0.434936	+	0.900462i	$0.356771\pi$
$440$	0.208503	0.00994000
$441$	14.3617	0.683891
$442$	10.1625	0.483381
$443$	23.6493	1.12361	0.561806	−	0.827269i	$-0.310107\pi$
$443$	23.6493	1.12361	0.561806	+	0.827269i	$0.310107\pi$
$444$	−3.69560	−0.175386
$445$	−3.25782	−0.154435
$446$	−15.0754	−0.713841
$447$	13.2134	0.624973
$448$	−0.143082	−0.00676000
$449$	11.5912	0.547022	0.273511	−	0.961869i	$-0.411815\pi$
$449$	11.5912	0.547022	0.273511	+	0.961869i	$0.411815\pi$
$450$	10.1990	0.480786
$451$	−12.4195	−0.584810
$452$	−7.09760	−0.333843
$453$	−12.9256	−0.607299
$454$	−22.1561	−1.03984
$455$	0.0528696	0.00247857
$456$	−2.80444	−0.131330
$457$	−34.8460	−1.63003	−0.815013	−	0.579443i	$-0.803270\pi$
$457$	−34.8460	−1.63003	−0.815013	+	0.579443i	$0.803270\pi$
$458$	−10.1473	−0.474150
$459$	28.1541	1.31412
$460$	0.208754	0.00973319
$461$	−34.4558	−1.60477	−0.802384	−	0.596808i	$-0.796435\pi$
$461$	−34.4558	−1.60477	−0.802384	+	0.596808i	$0.796435\pi$
$462$	−0.138894	−0.00646191
$463$	−35.7701	−1.66238	−0.831188	−	0.555992i	$-0.812339\pi$
$463$	−35.7701	−1.66238	−0.831188	+	0.555992i	$0.812339\pi$
$464$	−5.11255	−0.237344
$465$	−0.778261	−0.0360910
$466$	8.39797	0.389028
$467$	1.93858	0.0897068	0.0448534	−	0.998994i	$-0.485718\pi$
$467$	1.93858	0.0897068	0.0448534	+	0.998994i	$0.485718\pi$
$468$	3.64660	0.168564
$469$	1.04260	0.0481427
$470$	0.786743	0.0362897
$471$	−15.0979	−0.695676
$472$	8.09333	0.372526
$473$	5.49455	0.252640
$474$	11.6904	0.536960
$475$	14.3195	0.657022
$476$	0.820500	0.0376076
$477$	−9.64737	−0.441723
$478$	7.39000	0.338011
$479$	−16.5274	−0.755157	−0.377578	−	0.925978i	$-0.623243\pi$
$479$	−16.5274	−0.755157	−0.377578	+	0.925978i	$0.623243\pi$
$480$	0.202399	0.00923823
$481$	6.74678	0.307627
$482$	−7.30760	−0.332852
$483$	−0.139060	−0.00632746
$484$	1.00000	0.0454545
$485$	−2.19770	−0.0997926
$486$	16.0949	0.730078
$487$	14.7480	0.668298	0.334149	−	0.942520i	$-0.391551\pi$
$487$	14.7480	0.668298	0.334149	+	0.942520i	$0.391551\pi$
$488$	9.60240	0.434680
$489$	4.10668	0.185711
$490$	−1.45525	−0.0657417
$491$	−16.0296	−0.723407	−0.361704	−	0.932293i	$-0.617805\pi$
$491$	−16.0296	−0.723407	−0.361704	+	0.932293i	$0.617805\pi$
$492$	−12.0559	−0.543522
$493$	29.3178	1.32041
$494$	5.11985	0.230353
$495$	−0.429035	−0.0192837
$496$	−3.84517	−0.172653
$497$	−0.808835	−0.0362812
$498$	−0.270692	−0.0121300
$499$	3.39195	0.151845	0.0759223	−	0.997114i	$-0.475810\pi$
$499$	3.39195	0.151845	0.0759223	+	0.997114i	$0.475810\pi$
$500$	−2.07597	−0.0928401
$501$	−2.87769	−0.128566
$502$	22.4519	1.00208
$503$	−3.44141	−0.153445	−0.0767224	−	0.997052i	$-0.524446\pi$
$503$	−3.44141	−0.153445	−0.0767224	+	0.997052i	$0.524446\pi$
$504$	0.294419	0.0131145
$505$	2.54750	0.113362
$506$	1.00120	0.0445088
$507$	−9.57075	−0.425052
$508$	5.69119	0.252506
$509$	−26.5994	−1.17900	−0.589499	−	0.807769i	$-0.700675\pi$
$509$	−26.5994	−1.17900	−0.589499	+	0.807769i	$0.700675\pi$
$510$	−1.16065	−0.0513946
$511$	−1.06714	−0.0472077
$512$	1.00000	0.0441942
$513$	14.1840	0.626238
$514$	−17.6478	−0.778413
$515$	2.00576	0.0883844
$516$	5.33370	0.234803
$517$	3.77329	0.165949
$518$	0.544721	0.0239337
$519$	−1.62533	−0.0713441
$520$	−0.369505	−0.0162039
$521$	−5.54395	−0.242885	−0.121442	−	0.992598i	$-0.538752\pi$
$521$	−5.54395	−0.242885	−0.121442	+	0.992598i	$0.538752\pi$
$522$	10.5201	0.460451
$523$	13.1482	0.574933	0.287466	−	0.957791i	$-0.407187\pi$
$523$	13.1482	0.574933	0.287466	+	0.957791i	$0.407187\pi$
$524$	−17.1130	−0.747583
$525$	0.688430	0.0300455
$526$	−26.9808	−1.17642
$527$	22.0500	0.960515
$528$	0.970726	0.0422454
$529$	−21.9976	−0.956417
$530$	0.977556	0.0424623
$531$	−16.6536	−0.722704
$532$	0.413366	0.0179217
$533$	22.0095	0.953339
$534$	−15.1674	−0.656357
$535$	0.410888	0.0177642
$536$	−7.28671	−0.314738
$537$	6.93313	0.299186
$538$	−7.95754	−0.343074
$539$	−6.97953	−0.300630
$540$	−1.02367	−0.0440519
$541$	−9.49978	−0.408427	−0.204214	−	0.978926i	$-0.565464\pi$
$541$	−9.49978	−0.408427	−0.204214	+	0.978926i	$0.565464\pi$
$542$	−6.69184	−0.287439
$543$	6.38797	0.274134
$544$	−5.73447	−0.245863
$545$	−1.95141	−0.0835892
$546$	0.246144	0.0105340
$547$	23.9797	1.02530	0.512649	−	0.858598i	$-0.328664\pi$
$547$	23.9797	1.02530	0.512649	+	0.858598i	$0.328664\pi$
$548$	−2.00802	−0.0857782
$549$	−19.7588	−0.843284
$550$	−4.95653	−0.211347
$551$	14.7702	0.629233
$552$	0.971891	0.0413664
$553$	−1.72314	−0.0732753
$554$	3.82220	0.162390
$555$	−0.770545	−0.0327078
$556$	14.1098	0.598391
$557$	−8.66752	−0.367254	−0.183627	−	0.982996i	$-0.558784\pi$
$557$	−8.66752	−0.367254	−0.183627	+	0.982996i	$0.558784\pi$
$558$	7.91218	0.334949
$559$	−9.73734	−0.411845
$560$	−0.0298331	−0.00126068
$561$	−5.56660	−0.235022
$562$	12.9086	0.544516
$563$	−9.14641	−0.385475	−0.192738	−	0.981250i	$-0.561737\pi$
$563$	−9.14641	−0.385475	−0.192738	+	0.981250i	$0.561737\pi$
$564$	3.66283	0.154233
$565$	−1.47987	−0.0622588
$566$	6.26048	0.263148
$567$	−0.201341	−0.00845552
$568$	5.65294	0.237192
$569$	29.9968	1.25753	0.628766	−	0.777594i	$-0.283560\pi$
$569$	29.9968	1.25753	0.628766	+	0.777594i	$0.283560\pi$
$570$	−0.584735	−0.0244918
$571$	−20.0210	−0.837852	−0.418926	−	0.908020i	$-0.637593\pi$
$571$	−20.0210	−0.837852	−0.418926	+	0.908020i	$0.637593\pi$
$572$	−1.77218	−0.0740986
$573$	0.813052	0.0339657
$574$	1.77700	0.0741708
$575$	−4.96248	−0.206950
$576$	−2.05769	−0.0857371
$577$	−36.4802	−1.51869	−0.759346	−	0.650687i	$-0.774481\pi$
$577$	−36.4802	−1.51869	−0.759346	+	0.650687i	$0.774481\pi$
$578$	15.8841	0.660694
$579$	−4.07852	−0.169497
$580$	−1.06598	−0.0442626
$581$	0.0398992	0.00165530
$582$	−10.2318	−0.424122
$583$	4.68844	0.194175
$584$	7.45826	0.308625
$585$	0.760328	0.0314357
$586$	−9.13646	−0.377424
$587$	−13.8797	−0.572878	−0.286439	−	0.958099i	$-0.592472\pi$
$587$	−13.8797	−0.572878	−0.286439	+	0.958099i	$0.592472\pi$
$588$	−6.77521	−0.279405
$589$	11.1088	0.457728
$590$	1.68749	0.0694727
$591$	−0.970726	−0.0399303
$592$	−3.80705	−0.156469
$593$	17.4116	0.715007	0.357503	−	0.933912i	$-0.383628\pi$
$593$	17.4116	0.715007	0.357503	+	0.933912i	$0.383628\pi$
$594$	−4.90963	−0.201445
$595$	0.171077	0.00701347
$596$	13.6119	0.557564
$597$	1.34744	0.0551473
$598$	−1.77431	−0.0725568
$599$	16.0441	0.655545	0.327773	−	0.944757i	$-0.393702\pi$
$599$	16.0441	0.655545	0.327773	+	0.944757i	$0.393702\pi$
$600$	−4.81143	−0.196426
$601$	−32.5020	−1.32578	−0.662891	−	0.748716i	$-0.730671\pi$
$601$	−32.5020	−1.32578	−0.662891	+	0.748716i	$0.730671\pi$
$602$	−0.786173	−0.0320420
$603$	14.9938	0.610595
$604$	−13.3154	−0.541797
$605$	0.208503	0.00847686
$606$	11.8604	0.481794
$607$	−1.15015	−0.0466831	−0.0233416	−	0.999728i	$-0.507431\pi$
$607$	−1.15015	−0.0466831	−0.0233416	+	0.999728i	$0.507431\pi$
$608$	−2.88901	−0.117165
$609$	0.710101	0.0287747
$610$	2.00213	0.0810639
$611$	−6.68694	−0.270525
$612$	11.7998	0.476977
$613$	9.08936	0.367116	0.183558	−	0.983009i	$-0.441239\pi$
$613$	9.08936	0.367116	0.183558	+	0.983009i	$0.441239\pi$
$614$	26.8219	1.08244
$615$	−2.51369	−0.101362
$616$	−0.143082	−0.00576495
$617$	−11.1298	−0.448069	−0.224034	−	0.974581i	$-0.571923\pi$
$617$	−11.1298	−0.448069	−0.224034	+	0.974581i	$0.571923\pi$
$618$	9.33820	0.375637
$619$	19.5100	0.784172	0.392086	−	0.919928i	$-0.371753\pi$
$619$	19.5100	0.784172	0.392086	+	0.919928i	$0.371753\pi$
$620$	−0.801731	−0.0321983
$621$	−4.91553	−0.197253
$622$	−28.8083	−1.15511
$623$	2.23563	0.0895685
$624$	−1.72030	−0.0688671
$625$	24.3498	0.973991
$626$	−15.6425	−0.625200
$627$	−2.80444	−0.111998
$628$	−15.5532	−0.620642
$629$	21.8314	0.870476
$630$	0.0613873	0.00244573
$631$	6.02997	0.240049	0.120025	−	0.992771i	$-0.461703\pi$
$631$	6.02997	0.240049	0.120025	+	0.992771i	$0.461703\pi$
$632$	12.0430	0.479045
$633$	12.9604	0.515128
$634$	1.21582	0.0482864
$635$	1.18663	0.0470901
$636$	4.55119	0.180466
$637$	12.3690	0.490077
$638$	−5.11255	−0.202408
$639$	−11.6320	−0.460155
$640$	0.208503	0.00824182
$641$	23.2326	0.917634	0.458817	−	0.888531i	$-0.348273\pi$
$641$	23.2326	0.917634	0.458817	+	0.888531i	$0.348273\pi$
$642$	1.91296	0.0754987
$643$	1.12137	0.0442224	0.0221112	−	0.999756i	$-0.492961\pi$
$643$	1.12137	0.0442224	0.0221112	+	0.999756i	$0.492961\pi$
$644$	−0.143254	−0.00564500
$645$	1.11209	0.0437887
$646$	16.5670	0.651818
$647$	−12.7900	−0.502827	−0.251413	−	0.967880i	$-0.580895\pi$
$647$	−12.7900	−0.502827	−0.251413	+	0.967880i	$0.580895\pi$
$648$	1.40717	0.0552788
$649$	8.09333	0.317691
$650$	8.78386	0.344531
$651$	0.534070	0.0209318
$652$	4.23053	0.165680
$653$	47.2949	1.85079	0.925397	−	0.378999i	$-0.123732\pi$
$653$	47.2949	1.85079	0.925397	+	0.378999i	$0.123732\pi$
$654$	−9.08515	−0.355257
$655$	−3.56811	−0.139418
$656$	−12.4195	−0.484899
$657$	−15.3468	−0.598735
$658$	−0.539890	−0.0210471
$659$	−29.9210	−1.16556	−0.582778	−	0.812631i	$-0.698034\pi$
$659$	−29.9210	−1.16556	−0.582778	+	0.812631i	$0.698034\pi$
$660$	0.202399	0.00787839
$661$	30.5715	1.18909	0.594547	−	0.804061i	$-0.297331\pi$
$661$	30.5715	1.18909	0.594547	+	0.804061i	$0.297331\pi$
$662$	−26.5484	−1.03183
$663$	9.86501	0.383125
$664$	−0.278855	−0.0108217
$665$	0.0861882	0.00334224
$666$	7.83374	0.303551
$667$	−5.11869	−0.198197
$668$	−2.96447	−0.114699
$669$	−14.6341	−0.565786
$670$	−1.51930	−0.0586958
$671$	9.60240	0.370696
$672$	−0.138894	−0.00535794
$673$	−4.40746	−0.169895	−0.0849475	−	0.996385i	$-0.527072\pi$
$673$	−4.40746	−0.169895	−0.0849475	+	0.996385i	$0.527072\pi$
$674$	−28.6799	−1.10471
$675$	24.3347	0.936644
$676$	−9.85938	−0.379207
$677$	13.2251	0.508282	0.254141	−	0.967167i	$-0.418207\pi$
$677$	13.2251	0.508282	0.254141	+	0.967167i	$0.418207\pi$
$678$	−6.88983	−0.264602
$679$	1.50814	0.0578771
$680$	−1.19566	−0.0458513
$681$	−21.5075	−0.824171
$682$	−3.84517	−0.147239
$683$	−15.3705	−0.588137	−0.294068	−	0.955784i	$-0.595009\pi$
$683$	−15.3705	−0.588137	−0.294068	+	0.955784i	$0.595009\pi$
$684$	5.94470	0.227301
$685$	−0.418678	−0.0159969
$686$	2.00022	0.0763688
$687$	−9.85021	−0.375809
$688$	5.49455	0.209478
$689$	−8.30876	−0.316539
$690$	0.202643	0.00771447
$691$	−34.0812	−1.29651	−0.648255	−	0.761423i	$-0.724501\pi$
$691$	−34.0812	−1.29651	−0.648255	+	0.761423i	$0.724501\pi$
$692$	−1.67435	−0.0636491
$693$	0.294419	0.0111841
$694$	18.3561	0.696787
$695$	2.94195	0.111594
$696$	−4.96289	−0.188118
$697$	71.2191	2.69762
$698$	29.7354	1.12550
$699$	8.15212	0.308342
$700$	0.709191	0.0268049
$701$	−27.4725	−1.03762	−0.518811	−	0.854889i	$-0.673625\pi$
$701$	−27.4725	−1.03762	−0.518811	+	0.854889i	$0.673625\pi$
$702$	8.70075	0.328389
$703$	10.9986	0.414821
$704$	1.00000	0.0376889
$705$	0.763712	0.0287630
$706$	27.2794	1.02667
$707$	−1.74818	−0.0657472
$708$	7.85641	0.295262
$709$	−22.1463	−0.831721	−0.415861	−	0.909428i	$-0.636520\pi$
$709$	−22.1463	−0.831721	−0.415861	+	0.909428i	$0.636520\pi$
$710$	1.17866	0.0442342
$711$	−24.7808	−0.929352
$712$	−15.6248	−0.585563
$713$	−3.84979	−0.144176
$714$	0.796481	0.0298076
$715$	−0.369505	−0.0138187
$716$	7.14221	0.266917
$717$	7.17366	0.267905
$718$	12.0825	0.450915
$719$	−28.3188	−1.05611	−0.528057	−	0.849209i	$-0.677079\pi$
$719$	−28.3188	−1.05611	−0.528057	+	0.849209i	$0.677079\pi$
$720$	−0.429035	−0.0159892
$721$	−1.37642	−0.0512607
$722$	−10.6536	−0.396486
$723$	−7.09368	−0.263817
$724$	6.58062	0.244567
$725$	25.3405	0.941123
$726$	0.970726	0.0360270
$727$	14.9654	0.555034	0.277517	−	0.960721i	$-0.410488\pi$
$727$	14.9654	0.555034	0.277517	+	0.960721i	$0.410488\pi$
$728$	0.253567	0.00939783
$729$	11.4022	0.422304
$730$	1.55507	0.0575558
$731$	−31.5084	−1.16538
$732$	9.32129	0.344525
$733$	16.7088	0.617152	0.308576	−	0.951200i	$-0.400148\pi$
$733$	16.7088	0.617152	0.308576	+	0.951200i	$0.400148\pi$
$734$	31.2347	1.15289
$735$	−1.41265	−0.0521065
$736$	1.00120	0.0369047
$737$	−7.28671	−0.268409
$738$	25.5554	0.940709
$739$	13.4848	0.496047	0.248024	−	0.968754i	$-0.420219\pi$
$739$	13.4848	0.496047	0.248024	+	0.968754i	$0.420219\pi$
$740$	−0.793783	−0.0291800
$741$	4.96997	0.182576
$742$	−0.670833	−0.0246270
$743$	18.7465	0.687741	0.343870	−	0.939017i	$-0.388262\pi$
$743$	18.7465	0.687741	0.343870	+	0.939017i	$0.388262\pi$
$744$	−3.73261	−0.136844
$745$	2.83812	0.103981
$746$	1.39014	0.0508965
$747$	0.573797	0.0209942
$748$	−5.73447	−0.209673
$749$	−0.281965	−0.0103028
$750$	−2.01520	−0.0735845
$751$	−50.6432	−1.84800	−0.923999	−	0.382395i	$-0.875099\pi$
$751$	−50.6432	−1.84800	−0.923999	+	0.382395i	$0.875099\pi$
$752$	3.77329	0.137598
$753$	21.7946	0.794241
$754$	9.06037	0.329959
$755$	−2.77631	−0.101040
$756$	0.702481	0.0255490
$757$	27.5904	1.00279	0.501395	−	0.865218i	$-0.332820\pi$
$757$	27.5904	1.00279	0.501395	+	0.865218i	$0.332820\pi$
$758$	6.34767	0.230558
$759$	0.971891	0.0352774
$760$	−0.602369	−0.0218502
$761$	47.8444	1.73436	0.867180	−	0.497995i	$-0.165930\pi$
$761$	47.8444	1.73436	0.867180	+	0.497995i	$0.165930\pi$
$762$	5.52459	0.200135
$763$	1.33912	0.0484796
$764$	0.837571	0.0303023
$765$	2.46029	0.0889520
$766$	−31.0460	−1.12174
$767$	−14.3428	−0.517890
$768$	0.970726	0.0350280
$769$	−17.1884	−0.619829	−0.309915	−	0.950764i	$-0.600300\pi$
$769$	−17.1884	−0.619829	−0.309915	+	0.950764i	$0.600300\pi$
$770$	−0.0298331	−0.00107511
$771$	−17.1312	−0.616966
$772$	−4.20151	−0.151216
$773$	9.11275	0.327763	0.163881	−	0.986480i	$-0.447599\pi$
$773$	9.11275	0.327763	0.163881	+	0.986480i	$0.447599\pi$
$774$	−11.3061	−0.406389
$775$	19.0587	0.684609
$776$	−10.5404	−0.378378
$777$	0.528775	0.0189697
$778$	4.19052	0.150237
$779$	35.8800	1.28553
$780$	−0.358688	−0.0128431
$781$	5.65294	0.202278
$782$	−5.74136	−0.205310
$783$	25.1008	0.897028
$784$	−6.97953	−0.249269
$785$	−3.24290	−0.115744
$786$	−16.6120	−0.592530
$787$	−26.7501	−0.953537	−0.476769	−	0.879029i	$-0.658192\pi$
$787$	−26.7501	−0.953537	−0.476769	+	0.879029i	$0.658192\pi$
$788$	−1.00000	−0.0356235
$789$	−26.1910	−0.932424
$790$	2.51100	0.0893375
$791$	1.01554	0.0361085
$792$	−2.05769	−0.0731169
$793$	−17.0172	−0.604298
$794$	−20.2561	−0.718863
$795$	0.948938	0.0336554
$796$	1.38808	0.0491992
$797$	25.2725	0.895199	0.447599	−	0.894234i	$-0.352279\pi$
$797$	25.2725	0.895199	0.447599	+	0.894234i	$0.352279\pi$
$798$	0.401265	0.0142046
$799$	−21.6378	−0.765491
$800$	−4.95653	−0.175240
$801$	32.1510	1.13600
$802$	35.2086	1.24326
$803$	7.45826	0.263196
$804$	−7.07339	−0.249459
$805$	−0.0298689	−0.00105274
$806$	6.81434	0.240025
$807$	−7.72459	−0.271918
$808$	12.2180	0.429829
$809$	−13.2987	−0.467557	−0.233779	−	0.972290i	$-0.575109\pi$
$809$	−13.2987	−0.467557	−0.233779	+	0.972290i	$0.575109\pi$
$810$	0.293399	0.0103090
$811$	−22.3574	−0.785075	−0.392537	−	0.919736i	$-0.628403\pi$
$811$	−22.3574	−0.785075	−0.392537	+	0.919736i	$0.628403\pi$
$812$	0.731515	0.0256712
$813$	−6.49594	−0.227823
$814$	−3.80705	−0.133437
$815$	0.882079	0.0308979
$816$	−5.56660	−0.194870
$817$	−15.8738	−0.555355
$818$	−13.3582	−0.467059
$819$	−0.521763	−0.0182319
$820$	−2.58950	−0.0904293
$821$	15.3829	0.536868	0.268434	−	0.963298i	$-0.413494\pi$
$821$	15.3829	0.536868	0.268434	+	0.963298i	$0.413494\pi$
$822$	−1.94923	−0.0679873
$823$	11.0048	0.383604	0.191802	−	0.981434i	$-0.438567\pi$
$823$	11.0048	0.383604	0.191802	+	0.981434i	$0.438567\pi$
$824$	9.61981	0.335122
$825$	−4.81143	−0.167512
$826$	−1.15801	−0.0402924
$827$	17.3463	0.603188	0.301594	−	0.953436i	$-0.402481\pi$
$827$	17.3463	0.603188	0.301594	+	0.953436i	$0.402481\pi$
$828$	−2.06016	−0.0715956
$829$	37.0040	1.28520	0.642601	−	0.766201i	$-0.277855\pi$
$829$	37.0040	1.28520	0.642601	+	0.766201i	$0.277855\pi$
$830$	−0.0581422	−0.00201814
$831$	3.71031	0.128709
$832$	−1.77218	−0.0614393
$833$	40.0239	1.38675
$834$	13.6968	0.474281
$835$	−0.618102	−0.0213903
$836$	−2.88901	−0.0999186
$837$	18.8784	0.652532
$838$	−14.7650	−0.510048
$839$	1.58726	0.0547982	0.0273991	−	0.999625i	$-0.491278\pi$
$839$	1.58726	0.0547982	0.0273991	+	0.999625i	$0.491278\pi$
$840$	−0.0289598	−0.000999207 0
$841$	−2.86179	−0.0986824
$842$	−2.74704	−0.0946691
$843$	12.5307	0.431580
$844$	13.3512	0.459568
$845$	−2.05571	−0.0707187
$846$	−7.76426	−0.266941
$847$	−0.143082	−0.00491636
$848$	4.68844	0.161002
$849$	6.07721	0.208569
$850$	28.4231	0.974903
$851$	−3.81162	−0.130661
$852$	5.48746	0.187997
$853$	−27.3798	−0.937467	−0.468733	−	0.883340i	$-0.655289\pi$
$853$	−27.3798	−0.937467	−0.468733	+	0.883340i	$0.655289\pi$
$854$	−1.37393	−0.0470150
$855$	1.23949	0.0423896
$856$	1.97065	0.0673556
$857$	23.9159	0.816950	0.408475	−	0.912769i	$-0.366061\pi$
$857$	23.9159	0.816950	0.408475	+	0.912769i	$0.366061\pi$
$858$	−1.72030	−0.0587301
$859$	24.1939	0.825485	0.412743	−	0.910848i	$-0.364571\pi$
$859$	24.1939	0.825485	0.412743	+	0.910848i	$0.364571\pi$
$860$	1.14563	0.0390657
$861$	1.72498	0.0587873
$862$	21.2869	0.725033
$863$	−5.43358	−0.184961	−0.0924806	−	0.995714i	$-0.529480\pi$
$863$	−5.43358	−0.184961	−0.0924806	+	0.995714i	$0.529480\pi$
$864$	−4.90963	−0.167029
$865$	−0.349107	−0.0118700
$866$	14.6467	0.497714
$867$	15.4192	0.523662
$868$	0.550176	0.0186742
$869$	12.0430	0.408531
$870$	−1.03478	−0.0350823
$871$	12.9134	0.437552
$872$	−9.35913	−0.316940
$873$	21.6889	0.734056
$874$	−2.89248	−0.0978396
$875$	0.297034	0.0100416
$876$	7.23992	0.244614
$877$	33.7161	1.13851	0.569256	−	0.822161i	$-0.307232\pi$
$877$	33.7161	1.13851	0.569256	+	0.822161i	$0.307232\pi$
$878$	18.2258	0.615092
$879$	−8.86900	−0.299144
$880$	0.208503	0.00702864
$881$	20.6883	0.697007	0.348504	−	0.937307i	$-0.386690\pi$
$881$	20.6883	0.697007	0.348504	+	0.937307i	$0.386690\pi$
$882$	14.3617	0.483584
$883$	10.6831	0.359514	0.179757	−	0.983711i	$-0.442469\pi$
$883$	10.6831	0.359514	0.179757	+	0.983711i	$0.442469\pi$
$884$	10.1625	0.341802
$885$	1.63809	0.0550637
$886$	23.6493	0.794513
$887$	−8.59057	−0.288443	−0.144222	−	0.989545i	$-0.546068\pi$
$887$	−8.59057	−0.288443	−0.144222	+	0.989545i	$0.546068\pi$
$888$	−3.69560	−0.124016
$889$	−0.814308	−0.0273110
$890$	−3.25782	−0.109202
$891$	1.40717	0.0471419
$892$	−15.0754	−0.504762
$893$	−10.9011	−0.364791
$894$	13.2134	0.441922
$895$	1.48917	0.0497776
$896$	−0.143082	−0.00478004
$897$	−1.72237	−0.0575081
$898$	11.5912	0.386803
$899$	19.6587	0.655653
$900$	10.1990	0.339967
$901$	−26.8857	−0.895694
$902$	−12.4195	−0.413523
$903$	−0.763158	−0.0253963
$904$	−7.09760	−0.236063
$905$	1.37208	0.0456095
$906$	−12.9256	−0.429426
$907$	−24.8909	−0.826489	−0.413245	−	0.910620i	$-0.635605\pi$
$907$	−24.8909	−0.826489	−0.413245	+	0.910620i	$0.635605\pi$
$908$	−22.1561	−0.735278
$909$	−25.1410	−0.833873
$910$	0.0528696	0.00175261
$911$	−25.7647	−0.853621	−0.426811	−	0.904341i	$-0.640363\pi$
$911$	−25.7647	−0.853621	−0.426811	+	0.904341i	$0.640363\pi$
$912$	−2.80444	−0.0928642
$913$	−0.278855	−0.00922875
$914$	−34.8460	−1.15260
$915$	1.94352	0.0642508
$916$	−10.1473	−0.335275
$917$	2.44856	0.0808586
$918$	28.1541	0.929225
$919$	−20.9706	−0.691757	−0.345879	−	0.938279i	$-0.612419\pi$
$919$	−20.9706	−0.691757	−0.345879	+	0.938279i	$0.612419\pi$
$920$	0.208754	0.00688240
$921$	26.0367	0.857938
$922$	−34.4558	−1.13474
$923$	−10.0180	−0.329747
$924$	−0.138894	−0.00456926
$925$	18.8698	0.620434
$926$	−35.7701	−1.17548
$927$	−19.7946	−0.650140
$928$	−5.11255	−0.167828
$929$	−33.1352	−1.08713	−0.543566	−	0.839367i	$-0.682926\pi$
$929$	−33.1352	−1.08713	−0.543566	+	0.839367i	$0.682926\pi$
$930$	−0.778261	−0.0255202
$931$	20.1639	0.660847
$932$	8.39797	0.275085
$933$	−27.9649	−0.915531
$934$	1.93858	0.0634323
$935$	−1.19566	−0.0391021
$936$	3.64660	0.119193
$937$	−9.51689	−0.310903	−0.155452	−	0.987844i	$-0.549683\pi$
$937$	−9.51689	−0.310903	−0.155452	+	0.987844i	$0.549683\pi$
$938$	1.04260	0.0340420
$939$	−15.1846	−0.495530
$940$	0.786743	0.0256607
$941$	−12.7635	−0.416078	−0.208039	−	0.978120i	$-0.566708\pi$
$941$	−12.7635	−0.416078	−0.208039	+	0.978120i	$0.566708\pi$
$942$	−15.0979	−0.491917
$943$	−12.4344	−0.404919
$944$	8.09333	0.263416
$945$	0.146470	0.00476465
$946$	5.49455	0.178643
$947$	−7.12533	−0.231542	−0.115771	−	0.993276i	$-0.536934\pi$
$947$	−7.12533	−0.231542	−0.115771	+	0.993276i	$0.536934\pi$
$948$	11.6904	0.379688
$949$	−13.2174	−0.429054
$950$	14.3195	0.464585
$951$	1.18023	0.0382715
$952$	0.820500	0.0265926
$953$	−43.0418	−1.39426	−0.697130	−	0.716945i	$-0.745540\pi$
$953$	−43.0418	−1.39426	−0.697130	+	0.716945i	$0.745540\pi$
$954$	−9.64737	−0.312345
$955$	0.174636	0.00565110
$956$	7.39000	0.239010
$957$	−4.96289	−0.160427
$958$	−16.5274	−0.533977
$959$	0.287311	0.00927777
$960$	0.202399	0.00653242
$961$	−16.2146	−0.523053
$962$	6.74678	0.217525
$963$	−4.05500	−0.130670
$964$	−7.30760	−0.235362
$965$	−0.876029	−0.0282004
$966$	−0.139060	−0.00447419
$967$	−30.9063	−0.993880	−0.496940	−	0.867785i	$-0.665543\pi$
$967$	−30.9063	−0.993880	−0.496940	+	0.867785i	$0.665543\pi$
$968$	1.00000	0.0321412
$969$	16.0820	0.516627
$970$	−2.19770	−0.0705640
$971$	19.6780	0.631498	0.315749	−	0.948843i	$-0.397744\pi$
$971$	19.6780	0.631498	0.315749	+	0.948843i	$0.397744\pi$
$972$	16.0949	0.516243
$973$	−2.01887	−0.0647219
$974$	14.7480	0.472558
$975$	8.52672	0.273073
$976$	9.60240	0.307365
$977$	−9.34813	−0.299073	−0.149537	−	0.988756i	$-0.547778\pi$
$977$	−9.34813	−0.299073	−0.149537	+	0.988756i	$0.547778\pi$
$978$	4.10668	0.131317
$979$	−15.6248	−0.499370
$980$	−1.45525	−0.0464864
$981$	19.2582	0.614867
$982$	−16.0296	−0.511526
$983$	26.2009	0.835680	0.417840	−	0.908521i	$-0.362787\pi$
$983$	26.2009	0.835680	0.417840	+	0.908521i	$0.362787\pi$
$984$	−12.0559	−0.384328
$985$	−0.208503	−0.00664347
$986$	29.3178	0.933669
$987$	−0.524085	−0.0166818
$988$	5.11985	0.162884
$989$	5.50115	0.174926
$990$	−0.429035	−0.0136356
$991$	−2.47717	−0.0786898	−0.0393449	−	0.999226i	$-0.512527\pi$
$991$	−2.47717	−0.0786898	−0.0393449	+	0.999226i	$0.512527\pi$
$992$	−3.84517	−0.122084
$993$	−25.7712	−0.817823
$994$	−0.808835	−0.0256547
$995$	0.289419	0.00917521
$996$	−0.270692	−0.00857719
$997$	−7.57534	−0.239913	−0.119957	−	0.992779i	$-0.538276\pi$
$997$	−7.57534	−0.239913	−0.119957	+	0.992779i	$0.538276\pi$
$998$	3.39195	0.107370
$999$	18.6912	0.591364

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.b.1.12	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.b.1.12	✓	15	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.970726 q^{3} +1.00000 q^{4} +0.208503 q^{5} +0.970726 q^{6} -0.143082 q^{7} +1.00000 q^{8} -2.05769 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.970726 q^{3} +1.00000 q^{4} +0.208503 q^{5} +0.970726 q^{6} -0.143082 q^{7} +1.00000 q^{8} -2.05769 q^{9} +0.208503 q^{10} +1.00000 q^{11} +0.970726 q^{12} -1.77218 q^{13} -0.143082 q^{14} +0.202399 q^{15} +1.00000 q^{16} -5.73447 q^{17} -2.05769 q^{18} -2.88901 q^{19} +0.208503 q^{20} -0.138894 q^{21} +1.00000 q^{22} +1.00120 q^{23} +0.970726 q^{24} -4.95653 q^{25} -1.77218 q^{26} -4.90963 q^{27} -0.143082 q^{28} -5.11255 q^{29} +0.202399 q^{30} -3.84517 q^{31} +1.00000 q^{32} +0.970726 q^{33} -5.73447 q^{34} -0.0298331 q^{35} -2.05769 q^{36} -3.80705 q^{37} -2.88901 q^{38} -1.72030 q^{39} +0.208503 q^{40} -12.4195 q^{41} -0.138894 q^{42} +5.49455 q^{43} +1.00000 q^{44} -0.429035 q^{45} +1.00120 q^{46} +3.77329 q^{47} +0.970726 q^{48} -6.97953 q^{49} -4.95653 q^{50} -5.56660 q^{51} -1.77218 q^{52} +4.68844 q^{53} -4.90963 q^{54} +0.208503 q^{55} -0.143082 q^{56} -2.80444 q^{57} -5.11255 q^{58} +8.09333 q^{59} +0.202399 q^{60} +9.60240 q^{61} -3.84517 q^{62} +0.294419 q^{63} +1.00000 q^{64} -0.369505 q^{65} +0.970726 q^{66} -7.28671 q^{67} -5.73447 q^{68} +0.971891 q^{69} -0.0298331 q^{70} +5.65294 q^{71} -2.05769 q^{72} +7.45826 q^{73} -3.80705 q^{74} -4.81143 q^{75} -2.88901 q^{76} -0.143082 q^{77} -1.72030 q^{78} +12.0430 q^{79} +0.208503 q^{80} +1.40717 q^{81} -12.4195 q^{82} -0.278855 q^{83} -0.138894 q^{84} -1.19566 q^{85} +5.49455 q^{86} -4.96289 q^{87} +1.00000 q^{88} -15.6248 q^{89} -0.429035 q^{90} +0.253567 q^{91} +1.00120 q^{92} -3.73261 q^{93} +3.77329 q^{94} -0.602369 q^{95} +0.970726 q^{96} -10.5404 q^{97} -6.97953 q^{98} -2.05769 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9	\( 15 q + 15 q^{2} - 9 q^{3} + 15 q^{4} - 11 q^{5} - 9 q^{6} - 11 q^{7} + 15 q^{8} + 10 q^{9} - 11 q^{10} + 15 q^{11} - 9 q^{12} - 21 q^{13} - 11 q^{14} - 2 q^{15} + 15 q^{16} - 4 q^{17} + 10 q^{18} - 22 q^{19} - 11 q^{20} - 13 q^{21} + 15 q^{22} - 16 q^{23} - 9 q^{24} + 6 q^{25} - 21 q^{26} - 21 q^{27} - 11 q^{28} - 8 q^{29} - 2 q^{30} - 33 q^{31} + 15 q^{32} - 9 q^{33} - 4 q^{34} - 2 q^{35} + 10 q^{36} - q^{37} - 22 q^{38} + q^{39} - 11 q^{40} - 10 q^{41} - 13 q^{42} - 8 q^{43} + 15 q^{44} - 10 q^{45} - 16 q^{46} - 31 q^{47} - 9 q^{48} + 2 q^{49} + 6 q^{50} + 2 q^{51} - 21 q^{52} - 18 q^{53} - 21 q^{54} - 11 q^{55} - 11 q^{56} + 16 q^{57} - 8 q^{58} - 37 q^{59} - 2 q^{60} - 31 q^{61} - 33 q^{62} - 20 q^{63} + 15 q^{64} - 13 q^{65} - 9 q^{66} + q^{67} - 4 q^{68} - 25 q^{69} - 2 q^{70} - 28 q^{71} + 10 q^{72} - 20 q^{73} - q^{74} - 9 q^{75} - 22 q^{76} - 11 q^{77} + q^{78} - 6 q^{79} - 11 q^{80} + 3 q^{81} - 10 q^{82} - 15 q^{83} - 13 q^{84} - 31 q^{85} - 8 q^{86} - 16 q^{87} + 15 q^{88} - 17 q^{89} - 10 q^{90} - 21 q^{91} - 16 q^{92} + 10 q^{93} - 31 q^{94} - 3 q^{95} - 9 q^{96} - 9 q^{97} + 2 q^{98} + 10 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 9 * q^3 + 15 * q^4 - 11 * q^5 - 9 * q^6 - 11 * q^7 + 15 * q^8 + 10 * q^9 - 11 * q^10 + 15 * q^11 - 9 * q^12 - 21 * q^13 - 11 * q^14 - 2 * q^15 + 15 * q^16 - 4 * q^17 + 10 * q^18 - 22 * q^19 - 11 * q^20 - 13 * q^21 + 15 * q^22 - 16 * q^23 - 9 * q^24 + 6 * q^25 - 21 * q^26 - 21 * q^27 - 11 * q^28 - 8 * q^29 - 2 * q^30 - 33 * q^31 + 15 * q^32 - 9 * q^33 - 4 * q^34 - 2 * q^35 + 10 * q^36 - q^37 - 22 * q^38 + q^39 - 11 * q^40 - 10 * q^41 - 13 * q^42 - 8 * q^43 + 15 * q^44 - 10 * q^45 - 16 * q^46 - 31 * q^47 - 9 * q^48 + 2 * q^49 + 6 * q^50 + 2 * q^51 - 21 * q^52 - 18 * q^53 - 21 * q^54 - 11 * q^55 - 11 * q^56 + 16 * q^57 - 8 * q^58 - 37 * q^59 - 2 * q^60 - 31 * q^61 - 33 * q^62 - 20 * q^63 + 15 * q^64 - 13 * q^65 - 9 * q^66 + q^67 - 4 * q^68 - 25 * q^69 - 2 * q^70 - 28 * q^71 + 10 * q^72 - 20 * q^73 - q^74 - 9 * q^75 - 22 * q^76 - 11 * q^77 + q^78 - 6 * q^79 - 11 * q^80 + 3 * q^81 - 10 * q^82 - 15 * q^83 - 13 * q^84 - 31 * q^85 - 8 * q^86 - 16 * q^87 + 15 * q^88 - 17 * q^89 - 10 * q^90 - 21 * q^91 - 16 * q^92 + 10 * q^93 - 31 * q^94 - 3 * q^95 - 9 * q^96 - 9 * q^97 + 2 * q^98 + 10 * q^99

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