LMFDB - Embedded newform 8031.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, 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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44537 q^{2} -1.00000 q^{3} +3.97985 q^{4} +0.860526 q^{5} +2.44537 q^{6} -1.02072 q^{7} -4.84146 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.44537 q^{2} -1.00000 q^{3} +3.97985 q^{4} +0.860526 q^{5} +2.44537 q^{6} -1.02072 q^{7} -4.84146 q^{8} +1.00000 q^{9} -2.10431 q^{10} -0.795174 q^{11} -3.97985 q^{12} +0.110466 q^{13} +2.49603 q^{14} -0.860526 q^{15} +3.87949 q^{16} -4.81272 q^{17} -2.44537 q^{18} -5.53544 q^{19} +3.42476 q^{20} +1.02072 q^{21} +1.94450 q^{22} -1.04997 q^{23} +4.84146 q^{24} -4.25949 q^{25} -0.270131 q^{26} -1.00000 q^{27} -4.06229 q^{28} -8.08014 q^{29} +2.10431 q^{30} -7.41181 q^{31} +0.196136 q^{32} +0.795174 q^{33} +11.7689 q^{34} -0.878352 q^{35} +3.97985 q^{36} -4.32162 q^{37} +13.5362 q^{38} -0.110466 q^{39} -4.16621 q^{40} -0.262618 q^{41} -2.49603 q^{42} -7.10182 q^{43} -3.16467 q^{44} +0.860526 q^{45} +2.56758 q^{46} -1.26244 q^{47} -3.87949 q^{48} -5.95814 q^{49} +10.4161 q^{50} +4.81272 q^{51} +0.439639 q^{52} -9.12695 q^{53} +2.44537 q^{54} -0.684268 q^{55} +4.94175 q^{56} +5.53544 q^{57} +19.7590 q^{58} -3.27129 q^{59} -3.42476 q^{60} -7.27254 q^{61} +18.1246 q^{62} -1.02072 q^{63} -8.23860 q^{64} +0.0950591 q^{65} -1.94450 q^{66} -6.15854 q^{67} -19.1539 q^{68} +1.04997 q^{69} +2.14790 q^{70} +12.3679 q^{71} -4.84146 q^{72} -2.56006 q^{73} +10.5680 q^{74} +4.25949 q^{75} -22.0302 q^{76} +0.811646 q^{77} +0.270131 q^{78} +14.3968 q^{79} +3.33840 q^{80} +1.00000 q^{81} +0.642199 q^{82} -15.6480 q^{83} +4.06229 q^{84} -4.14147 q^{85} +17.3666 q^{86} +8.08014 q^{87} +3.84980 q^{88} +10.6444 q^{89} -2.10431 q^{90} -0.112755 q^{91} -4.17873 q^{92} +7.41181 q^{93} +3.08714 q^{94} -4.76339 q^{95} -0.196136 q^{96} -0.104286 q^{97} +14.5699 q^{98} -0.795174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) $ 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * 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 $

$2$	−2.44537	−1.72914	−0.864570	−	0.502513i	$-0.832409\pi$
$2$	−2.44537	−1.72914	−0.864570	+	0.502513i	$0.832409\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.97985	1.98992
$5$	0.860526	0.384839	0.192419	−	0.981313i	$-0.438367\pi$
$5$	0.860526	0.384839	0.192419	+	0.981313i	$0.438367\pi$
$6$	2.44537	0.998319
$7$	−1.02072	−0.385794	−0.192897	−	0.981219i	$-0.561788\pi$
$7$	−1.02072	−0.385794	−0.192897	+	0.981219i	$0.561788\pi$
$8$	−4.84146	−1.71172
$9$	1.00000	0.333333
$10$	−2.10431	−0.665440
$11$	−0.795174	−0.239754	−0.119877	−	0.992789i	$-0.538250\pi$
$11$	−0.795174	−0.239754	−0.119877	+	0.992789i	$0.538250\pi$
$12$	−3.97985	−1.14888
$13$	0.110466	0.0306378	0.0153189	−	0.999883i	$-0.495124\pi$
$13$	0.110466	0.0306378	0.0153189	+	0.999883i	$0.495124\pi$
$14$	2.49603	0.667092
$15$	−0.860526	−0.222187
$16$	3.87949	0.969872
$17$	−4.81272	−1.16726	−0.583629	−	0.812021i	$-0.698368\pi$
$17$	−4.81272	−1.16726	−0.583629	+	0.812021i	$0.698368\pi$
$18$	−2.44537	−0.576380
$19$	−5.53544	−1.26992	−0.634958	−	0.772546i	$-0.718983\pi$
$19$	−5.53544	−1.26992	−0.634958	+	0.772546i	$0.718983\pi$
$20$	3.42476	0.765800
$21$	1.02072	0.222738
$22$	1.94450	0.414568
$23$	−1.04997	−0.218935	−0.109467	−	0.993990i	$-0.534914\pi$
$23$	−1.04997	−0.218935	−0.109467	+	0.993990i	$0.534914\pi$
$24$	4.84146	0.988259
$25$	−4.25949	−0.851899
$26$	−0.270131	−0.0529771
$27$	−1.00000	−0.192450
$28$	−4.06229	−0.767701
$29$	−8.08014	−1.50044	−0.750222	−	0.661186i	$-0.770054\pi$
$29$	−8.08014	−1.50044	−0.750222	+	0.661186i	$0.770054\pi$
$30$	2.10431	0.384192
$31$	−7.41181	−1.33120	−0.665600	−	0.746309i	$-0.731824\pi$
$31$	−7.41181	−1.33120	−0.665600	+	0.746309i	$0.731824\pi$
$32$	0.196136	0.0346723
$33$	0.795174	0.138422
$34$	11.7689	2.01835
$35$	−0.878352	−0.148469
$36$	3.97985	0.663308
$37$	−4.32162	−0.710470	−0.355235	−	0.934777i	$-0.615599\pi$
$37$	−4.32162	−0.710470	−0.355235	+	0.934777i	$0.615599\pi$
$38$	13.5362	2.19586
$39$	−0.110466	−0.0176888
$40$	−4.16621	−0.658735
$41$	−0.262618	−0.0410141	−0.0205070	−	0.999790i	$-0.506528\pi$
$41$	−0.262618	−0.0410141	−0.0205070	+	0.999790i	$0.506528\pi$
$42$	−2.49603	−0.385146
$43$	−7.10182	−1.08302	−0.541509	−	0.840695i	$-0.682147\pi$
$43$	−7.10182	−1.08302	−0.541509	+	0.840695i	$0.682147\pi$
$44$	−3.16467	−0.477092
$45$	0.860526	0.128280
$46$	2.56758	0.378568
$47$	−1.26244	−0.184146	−0.0920730	−	0.995752i	$-0.529349\pi$
$47$	−1.26244	−0.184146	−0.0920730	+	0.995752i	$0.529349\pi$
$48$	−3.87949	−0.559956
$49$	−5.95814	−0.851163
$50$	10.4161	1.47305
$51$	4.81272	0.673916
$52$	0.439639	0.0609669
$53$	−9.12695	−1.25368	−0.626841	−	0.779147i	$-0.715653\pi$
$53$	−9.12695	−1.25368	−0.626841	+	0.779147i	$0.715653\pi$
$54$	2.44537	0.332773
$55$	−0.684268	−0.0922666
$56$	4.94175	0.660370
$57$	5.53544	0.733187
$58$	19.7590	2.59448
$59$	−3.27129	−0.425885	−0.212943	−	0.977065i	$-0.568305\pi$
$59$	−3.27129	−0.425885	−0.212943	+	0.977065i	$0.568305\pi$
$60$	−3.42476	−0.442135
$61$	−7.27254	−0.931153	−0.465576	−	0.885008i	$-0.654153\pi$
$61$	−7.27254	−0.931153	−0.465576	+	0.885008i	$0.654153\pi$
$62$	18.1246	2.30183
$63$	−1.02072	−0.128598
$64$	−8.23860	−1.02982
$65$	0.0950591	0.0117906
$66$	−1.94450	−0.239351
$67$	−6.15854	−0.752385	−0.376193	−	0.926541i	$-0.622767\pi$
$67$	−6.15854	−0.752385	−0.376193	+	0.926541i	$0.622767\pi$
$68$	−19.1539	−2.32275
$69$	1.04997	0.126402
$70$	2.14790	0.256723
$71$	12.3679	1.46780	0.733899	−	0.679258i	$-0.237698\pi$
$71$	12.3679	1.46780	0.733899	+	0.679258i	$0.237698\pi$
$72$	−4.84146	−0.570572
$73$	−2.56006	−0.299633	−0.149816	−	0.988714i	$-0.547868\pi$
$73$	−2.56006	−0.299633	−0.149816	+	0.988714i	$0.547868\pi$
$74$	10.5680	1.22850
$75$	4.25949	0.491844
$76$	−22.0302	−2.52704
$77$	0.811646	0.0924956
$78$	0.270131	0.0305863
$79$	14.3968	1.61977	0.809884	−	0.586590i	$-0.199530\pi$
$79$	14.3968	1.61977	0.809884	+	0.586590i	$0.199530\pi$
$80$	3.33840	0.373244
$81$	1.00000	0.111111
$82$	0.642199	0.0709190
$83$	−15.6480	−1.71759	−0.858794	−	0.512321i	$-0.828786\pi$
$83$	−15.6480	−1.71759	−0.858794	+	0.512321i	$0.828786\pi$
$84$	4.06229	0.443232
$85$	−4.14147	−0.449206
$86$	17.3666	1.87269
$87$	8.08014	0.866282
$88$	3.84980	0.410390
$89$	10.6444	1.12830	0.564152	−	0.825671i	$-0.309203\pi$
$89$	10.6444	1.12830	0.564152	+	0.825671i	$0.309203\pi$
$90$	−2.10431	−0.221813
$91$	−0.112755	−0.0118199
$92$	−4.17873	−0.435663
$93$	7.41181	0.768569
$94$	3.08714	0.318414
$95$	−4.76339	−0.488713
$96$	−0.196136	−0.0200181
$97$	−0.104286	−0.0105886	−0.00529432	−	0.999986i	$-0.501685\pi$
$97$	−0.104286	−0.0105886	−0.00529432	+	0.999986i	$0.501685\pi$
$98$	14.5699	1.47178
$99$	−0.795174	−0.0799180
$100$	−16.9521	−1.69521
$101$	9.14044	0.909508	0.454754	−	0.890617i	$-0.349727\pi$
$101$	9.14044	0.909508	0.454754	+	0.890617i	$0.349727\pi$
$102$	−11.7689	−1.16530
$103$	9.46237	0.932355	0.466178	−	0.884691i	$-0.345631\pi$
$103$	9.46237	0.932355	0.466178	+	0.884691i	$0.345631\pi$
$104$	−0.534818	−0.0524432
$105$	0.878352	0.0857184
$106$	22.3188	2.16779
$107$	−10.1862	−0.984735	−0.492367	−	0.870388i	$-0.663868\pi$
$107$	−10.1862	−0.984735	−0.492367	+	0.870388i	$0.663868\pi$
$108$	−3.97985	−0.382961
$109$	−1.61446	−0.154638	−0.0773188	−	0.997006i	$-0.524636\pi$
$109$	−1.61446	−0.154638	−0.0773188	+	0.997006i	$0.524636\pi$
$110$	1.67329	0.159542
$111$	4.32162	0.410190
$112$	−3.95985	−0.374171
$113$	7.97243	0.749983	0.374991	−	0.927028i	$-0.377646\pi$
$113$	7.97243	0.749983	0.374991	+	0.927028i	$0.377646\pi$
$114$	−13.5362	−1.26778
$115$	−0.903529	−0.0842546
$116$	−32.1577	−2.98577
$117$	0.110466	0.0102126
$118$	7.99951	0.736415
$119$	4.91242	0.450321
$120$	4.16621	0.380321
$121$	−10.3677	−0.942518
$122$	17.7841	1.61009
$123$	0.262618	0.0236795
$124$	−29.4979	−2.64899
$125$	−7.96804	−0.712683
$126$	2.49603	0.222364
$127$	−6.94216	−0.616017	−0.308009	−	0.951384i	$-0.599663\pi$
$127$	−6.94216	−0.616017	−0.308009	+	0.951384i	$0.599663\pi$
$128$	19.7542	1.74604
$129$	7.10182	0.625281
$130$	−0.232455	−0.0203876
$131$	10.0190	0.875366	0.437683	−	0.899129i	$-0.355799\pi$
$131$	10.0190	0.875366	0.437683	+	0.899129i	$0.355799\pi$
$132$	3.16467	0.275449
$133$	5.65010	0.489926
$134$	15.0599	1.30098
$135$	−0.860526	−0.0740623
$136$	23.3006	1.99801
$137$	2.08917	0.178490	0.0892448	−	0.996010i	$-0.471555\pi$
$137$	2.08917	0.178490	0.0892448	+	0.996010i	$0.471555\pi$
$138$	−2.56758	−0.218567
$139$	−2.79449	−0.237025	−0.118513	−	0.992953i	$-0.537813\pi$
$139$	−2.79449	−0.237025	−0.118513	+	0.992953i	$0.537813\pi$
$140$	−3.49571	−0.295441
$141$	1.26244	0.106317
$142$	−30.2441	−2.53803
$143$	−0.0878398	−0.00734554
$144$	3.87949	0.323291
$145$	−6.95317	−0.577430
$146$	6.26031	0.518107
$147$	5.95814	0.491419
$148$	−17.1994	−1.41378
$149$	19.8148	1.62329	0.811647	−	0.584149i	$-0.198572\pi$
$149$	19.8148	1.62329	0.811647	+	0.584149i	$0.198572\pi$
$150$	−10.4161	−0.850467
$151$	12.4786	1.01549	0.507747	−	0.861506i	$-0.330479\pi$
$151$	12.4786	1.01549	0.507747	+	0.861506i	$0.330479\pi$
$152$	26.7996	2.17374
$153$	−4.81272	−0.389086
$154$	−1.98478	−0.159938
$155$	−6.37805	−0.512298
$156$	−0.439639	−0.0351993
$157$	17.8464	1.42429	0.712147	−	0.702030i	$-0.247723\pi$
$157$	17.8464	1.42429	0.712147	+	0.702030i	$0.247723\pi$
$158$	−35.2056	−2.80080
$159$	9.12695	0.723814
$160$	0.168780	0.0133433
$161$	1.07172	0.0844636
$162$	−2.44537	−0.192127
$163$	−9.24643	−0.724236	−0.362118	−	0.932132i	$-0.617946\pi$
$163$	−9.24643	−0.724236	−0.362118	+	0.932132i	$0.617946\pi$
$164$	−1.04518	−0.0816148
$165$	0.684268	0.0532702
$166$	38.2651	2.96995
$167$	21.4184	1.65740	0.828702	−	0.559690i	$-0.189080\pi$
$167$	21.4184	1.65740	0.828702	+	0.559690i	$0.189080\pi$
$168$	−4.94175	−0.381265
$169$	−12.9878	−0.999061
$170$	10.1274	0.776740
$171$	−5.53544	−0.423306
$172$	−28.2642	−2.15512
$173$	12.5065	0.950848	0.475424	−	0.879757i	$-0.342295\pi$
$173$	12.5065	0.950848	0.475424	+	0.879757i	$0.342295\pi$
$174$	−19.7590	−1.49792
$175$	4.34773	0.328658
$176$	−3.08487	−0.232530
$177$	3.27129	0.245885
$178$	−26.0295	−1.95099
$179$	14.3574	1.07312	0.536560	−	0.843862i	$-0.319723\pi$
$179$	14.3574	1.07312	0.536560	+	0.843862i	$0.319723\pi$
$180$	3.42476	0.255267
$181$	−6.90968	−0.513592	−0.256796	−	0.966466i	$-0.582667\pi$
$181$	−6.90968	−0.513592	−0.256796	+	0.966466i	$0.582667\pi$
$182$	0.275727	0.0204382
$183$	7.27254	0.537601
$184$	5.08341	0.374754
$185$	−3.71887	−0.273417
$186$	−18.1246	−1.32896
$187$	3.82695	0.279854
$188$	−5.02433	−0.366437
$189$	1.02072	0.0742461
$190$	11.6483	0.845054
$191$	1.99244	0.144168	0.0720839	−	0.997399i	$-0.477035\pi$
$191$	1.99244	0.144168	0.0720839	+	0.997399i	$0.477035\pi$
$192$	8.23860	0.594570
$193$	2.14373	0.154309	0.0771544	−	0.997019i	$-0.475417\pi$
$193$	2.14373	0.154309	0.0771544	+	0.997019i	$0.475417\pi$
$194$	0.255018	0.0183092
$195$	−0.0950591	−0.00680732
$196$	−23.7125	−1.69375
$197$	−0.128300	−0.00914103	−0.00457051	−	0.999990i	$-0.501455\pi$
$197$	−0.128300	−0.00914103	−0.00457051	+	0.999990i	$0.501455\pi$
$198$	1.94450	0.138189
$199$	−9.87856	−0.700272	−0.350136	−	0.936699i	$-0.613865\pi$
$199$	−9.87856	−0.700272	−0.350136	+	0.936699i	$0.613865\pi$
$200$	20.6222	1.45821
$201$	6.15854	0.434390
$202$	−22.3518	−1.57267
$203$	8.24752	0.578863
$204$	19.1539	1.34104
$205$	−0.225990	−0.0157838
$206$	−23.1390	−1.61217
$207$	−1.04997	−0.0729782
$208$	0.428552	0.0297148
$209$	4.40163	0.304467
$210$	−2.14790	−0.148219
$211$	−2.53674	−0.174636	−0.0873182	−	0.996180i	$-0.527830\pi$
$211$	−2.53674	−0.174636	−0.0873182	+	0.996180i	$0.527830\pi$
$212$	−36.3239	−2.49473
$213$	−12.3679	−0.847434
$214$	24.9090	1.70274
$215$	−6.11130	−0.416787
$216$	4.84146	0.329420
$217$	7.56534	0.513569
$218$	3.94796	0.267390
$219$	2.56006	0.172993
$220$	−2.72328	−0.183604
$221$	−0.531644	−0.0357622
$222$	−10.5680	−0.709276
$223$	−7.72444	−0.517267	−0.258633	−	0.965976i	$-0.583272\pi$
$223$	−7.72444	−0.517267	−0.258633	+	0.965976i	$0.583272\pi$
$224$	−0.200199	−0.0133764
$225$	−4.25949	−0.283966
$226$	−19.4956	−1.29682
$227$	−8.62126	−0.572213	−0.286107	−	0.958198i	$-0.592361\pi$
$227$	−8.62126	−0.572213	−0.286107	+	0.958198i	$0.592361\pi$
$228$	22.0302	1.45899
$229$	15.2371	1.00690	0.503449	−	0.864025i	$-0.332064\pi$
$229$	15.2371	1.00690	0.503449	+	0.864025i	$0.332064\pi$
$230$	2.20947	0.145688
$231$	−0.811646	−0.0534024
$232$	39.1197	2.56833
$233$	11.0146	0.721592	0.360796	−	0.932645i	$-0.382505\pi$
$233$	11.0146	0.721592	0.360796	+	0.932645i	$0.382505\pi$
$234$	−0.270131	−0.0176590
$235$	−1.08636	−0.0708666
$236$	−13.0192	−0.847479
$237$	−14.3968	−0.935173
$238$	−12.0127	−0.778667
$239$	−0.126083	−0.00815565	−0.00407782	−	0.999992i	$-0.501298\pi$
$239$	−0.126083	−0.00815565	−0.00407782	+	0.999992i	$0.501298\pi$
$240$	−3.33840	−0.215493
$241$	26.6917	1.71936	0.859681	−	0.510831i	$-0.170662\pi$
$241$	26.6917	1.71936	0.859681	+	0.510831i	$0.170662\pi$
$242$	25.3529	1.62975
$243$	−1.00000	−0.0641500
$244$	−28.9436	−1.85292
$245$	−5.12714	−0.327561
$246$	−0.642199	−0.0409451
$247$	−0.611479	−0.0389075
$248$	35.8840	2.27864
$249$	15.6480	0.991650
$250$	19.4848	1.23233
$251$	−30.4642	−1.92289	−0.961443	−	0.275005i	$-0.911320\pi$
$251$	−30.4642	−1.92289	−0.961443	+	0.275005i	$0.911320\pi$
$252$	−4.06229	−0.255900
$253$	0.834911	0.0524904
$254$	16.9762	1.06518
$255$	4.14147	0.259349
$256$	−31.8291	−1.98932
$257$	−0.111262	−0.00694031	−0.00347015	−	0.999994i	$-0.501105\pi$
$257$	−0.111262	−0.00694031	−0.00347015	+	0.999994i	$0.501105\pi$
$258$	−17.3666	−1.08120
$259$	4.41114	0.274095
$260$	0.378321	0.0234624
$261$	−8.08014	−0.500148
$262$	−24.5002	−1.51363
$263$	20.4311	1.25984	0.629919	−	0.776661i	$-0.283088\pi$
$263$	20.4311	1.25984	0.629919	+	0.776661i	$0.283088\pi$
$264$	−3.84980	−0.236939
$265$	−7.85398	−0.482466
$266$	−13.8166	−0.847151
$267$	−10.6444	−0.651426
$268$	−24.5100	−1.49719
$269$	28.9703	1.76635	0.883174	−	0.469045i	$-0.155402\pi$
$269$	28.9703	1.76635	0.883174	+	0.469045i	$0.155402\pi$
$270$	2.10431	0.128064
$271$	25.6150	1.55600	0.778001	−	0.628262i	$-0.216234\pi$
$271$	25.6150	1.55600	0.778001	+	0.628262i	$0.216234\pi$
$272$	−18.6709	−1.13209
$273$	0.112755	0.00682422
$274$	−5.10879	−0.308633
$275$	3.38704	0.204246
$276$	4.17873	0.251530
$277$	24.1411	1.45050	0.725249	−	0.688486i	$-0.241725\pi$
$277$	24.1411	1.45050	0.725249	+	0.688486i	$0.241725\pi$
$278$	6.83357	0.409850
$279$	−7.41181	−0.443733
$280$	4.25251	0.254136
$281$	3.00933	0.179522	0.0897609	−	0.995963i	$-0.471390\pi$
$281$	3.00933	0.179522	0.0897609	+	0.995963i	$0.471390\pi$
$282$	−3.08714	−0.183837
$283$	1.82002	0.108189	0.0540944	−	0.998536i	$-0.482773\pi$
$283$	1.82002	0.108189	0.0540944	+	0.998536i	$0.482773\pi$
$284$	49.2223	2.92081
$285$	4.76339	0.282159
$286$	0.214801	0.0127015
$287$	0.268058	0.0158230
$288$	0.196136	0.0115574
$289$	6.16231	0.362489
$290$	17.0031	0.998456
$291$	0.104286	0.00611335
$292$	−10.1887	−0.596246
$293$	−0.273111	−0.0159553	−0.00797766	−	0.999968i	$-0.502539\pi$
$293$	−0.273111	−0.0159553	−0.00797766	+	0.999968i	$0.502539\pi$
$294$	−14.5699	−0.849732
$295$	−2.81503	−0.163897
$296$	20.9230	1.21612
$297$	0.795174	0.0461407
$298$	−48.4546	−2.80690
$299$	−0.115987	−0.00670768
$300$	16.9521	0.978732
$301$	7.24894	0.417822
$302$	−30.5148	−1.75593
$303$	−9.14044	−0.525104
$304$	−21.4747	−1.23166
$305$	−6.25821	−0.358344
$306$	11.7689	0.672783
$307$	−28.1333	−1.60565	−0.802827	−	0.596212i	$-0.796672\pi$
$307$	−28.1333	−1.60565	−0.802827	+	0.596212i	$0.796672\pi$
$308$	3.23023	0.184059
$309$	−9.46237	−0.538296
$310$	15.5967	0.885834
$311$	−4.06661	−0.230596	−0.115298	−	0.993331i	$-0.536782\pi$
$311$	−4.06661	−0.230596	−0.115298	+	0.993331i	$0.536782\pi$
$312$	0.534818	0.0302781
$313$	−3.90040	−0.220463	−0.110232	−	0.993906i	$-0.535159\pi$
$313$	−3.90040	−0.220463	−0.110232	+	0.993906i	$0.535159\pi$
$314$	−43.6410	−2.46280
$315$	−0.878352	−0.0494895
$316$	57.2971	3.22321
$317$	−24.1830	−1.35825	−0.679125	−	0.734022i	$-0.737641\pi$
$317$	−24.1830	−1.35825	−0.679125	+	0.734022i	$0.737641\pi$
$318$	−22.3188	−1.25158
$319$	6.42512	0.359737
$320$	−7.08953	−0.396317
$321$	10.1862	0.568537
$322$	−2.62076	−0.146049
$323$	26.6405	1.48232
$324$	3.97985	0.221103
$325$	−0.470530	−0.0261003
$326$	22.6110	1.25231
$327$	1.61446	0.0892800
$328$	1.27146	0.0702044
$329$	1.28859	0.0710425
$330$	−1.67329	−0.0921115
$331$	−23.0378	−1.26627	−0.633137	−	0.774039i	$-0.718233\pi$
$331$	−23.0378	−1.26627	−0.633137	+	0.774039i	$0.718233\pi$
$332$	−62.2765	−3.41787
$333$	−4.32162	−0.236823
$334$	−52.3759	−2.86588
$335$	−5.29958	−0.289547
$336$	3.95985	0.216028
$337$	4.97081	0.270777	0.135389	−	0.990793i	$-0.456772\pi$
$337$	4.97081	0.270777	0.135389	+	0.990793i	$0.456772\pi$
$338$	31.7600	1.72752
$339$	−7.97243	−0.433003
$340$	−16.4824	−0.893885
$341$	5.89367	0.319160
$342$	13.5362	0.731954
$343$	13.2266	0.714168
$344$	34.3832	1.85382
$345$	0.903529	0.0486444
$346$	−30.5829	−1.64415
$347$	−26.6034	−1.42814	−0.714072	−	0.700073i	$-0.753151\pi$
$347$	−26.6034	−1.42814	−0.714072	+	0.700073i	$0.753151\pi$
$348$	32.1577	1.72384
$349$	−23.3953	−1.25232	−0.626161	−	0.779693i	$-0.715375\pi$
$349$	−23.3953	−1.25232	−0.626161	+	0.779693i	$0.715375\pi$
$350$	−10.6318	−0.568295
$351$	−0.110466	−0.00589625
$352$	−0.155962	−0.00831282
$353$	−12.4323	−0.661705	−0.330852	−	0.943683i	$-0.607336\pi$
$353$	−12.4323	−0.661705	−0.330852	+	0.943683i	$0.607336\pi$
$354$	−7.99951	−0.425169
$355$	10.6429	0.564866
$356$	42.3631	2.24524
$357$	−4.91242	−0.259993
$358$	−35.1091	−1.85558
$359$	−14.1253	−0.745505	−0.372752	−	0.927931i	$-0.621586\pi$
$359$	−14.1253	−0.745505	−0.372752	+	0.927931i	$0.621586\pi$
$360$	−4.16621	−0.219578
$361$	11.6411	0.612688
$362$	16.8967	0.888073
$363$	10.3677	0.544163
$364$	−0.448746	−0.0235207
$365$	−2.20300	−0.115310
$366$	−17.7841	−0.929588
$367$	−22.3848	−1.16848	−0.584239	−	0.811582i	$-0.698607\pi$
$367$	−22.3848	−1.16848	−0.584239	+	0.811582i	$0.698607\pi$
$368$	−4.07336	−0.212338
$369$	−0.262618	−0.0136714
$370$	9.09402	0.472775
$371$	9.31601	0.483663
$372$	29.4979	1.52939
$373$	−29.3805	−1.52126	−0.760632	−	0.649183i	$-0.775111\pi$
$373$	−29.3805	−1.52126	−0.760632	+	0.649183i	$0.775111\pi$
$374$	−9.35832	−0.483907
$375$	7.96804	0.411468
$376$	6.11207	0.315206
$377$	−0.892583	−0.0459704
$378$	−2.49603	−0.128382
$379$	0.602123	0.0309290	0.0154645	−	0.999880i	$-0.495077\pi$
$379$	0.602123	0.0309290	0.0154645	+	0.999880i	$0.495077\pi$
$380$	−18.9576	−0.972502
$381$	6.94216	0.355658
$382$	−4.87226	−0.249286
$383$	−6.66801	−0.340719	−0.170360	−	0.985382i	$-0.554493\pi$
$383$	−6.66801	−0.340719	−0.170360	+	0.985382i	$0.554493\pi$
$384$	−19.7542	−1.00808
$385$	0.698442	0.0355959
$386$	−5.24221	−0.266821
$387$	−7.10182	−0.361006
$388$	−0.415042	−0.0210706
$389$	24.5472	1.24459	0.622297	−	0.782781i	$-0.286200\pi$
$389$	24.5472	1.24459	0.622297	+	0.782781i	$0.286200\pi$
$390$	0.232455	0.0117708
$391$	5.05323	0.255553
$392$	28.8461	1.45695
$393$	−10.0190	−0.505393
$394$	0.313742	0.0158061
$395$	12.3888	0.623350
$396$	−3.16467	−0.159031
$397$	−38.4795	−1.93123	−0.965615	−	0.259975i	$-0.916286\pi$
$397$	−38.4795	−1.93123	−0.965615	+	0.259975i	$0.916286\pi$
$398$	24.1568	1.21087
$399$	−5.65010	−0.282859
$400$	−16.5247	−0.826233
$401$	−12.3824	−0.618348	−0.309174	−	0.951005i	$-0.600053\pi$
$401$	−12.3824	−0.618348	−0.309174	+	0.951005i	$0.600053\pi$
$402$	−15.0599	−0.751121
$403$	−0.818755	−0.0407851
$404$	36.3775	1.80985
$405$	0.860526	0.0427599
$406$	−20.1683	−1.00093
$407$	3.43644	0.170338
$408$	−23.3006	−1.15355
$409$	0.995303	0.0492146	0.0246073	−	0.999697i	$-0.492166\pi$
$409$	0.995303	0.0492146	0.0246073	+	0.999697i	$0.492166\pi$
$410$	0.552629	0.0272924
$411$	−2.08917	−0.103051
$412$	37.6588	1.85532
$413$	3.33905	0.164304
$414$	2.56758	0.126189
$415$	−13.4655	−0.660995
$416$	0.0216664	0.00106228
$417$	2.79449	0.136847
$418$	−10.7636	−0.526467
$419$	−27.0441	−1.32119	−0.660595	−	0.750743i	$-0.729696\pi$
$419$	−27.0441	−1.32119	−0.660595	+	0.750743i	$0.729696\pi$
$420$	3.49571	0.170573
$421$	31.1663	1.51895	0.759475	−	0.650536i	$-0.225456\pi$
$421$	31.1663	1.51895	0.759475	+	0.650536i	$0.225456\pi$
$422$	6.20327	0.301971
$423$	−1.26244	−0.0613820
$424$	44.1878	2.14595
$425$	20.4998	0.994385
$426$	30.2441	1.46533
$427$	7.42319	0.359233
$428$	−40.5394	−1.95955
$429$	0.0878398	0.00424095
$430$	14.9444	0.720684
$431$	33.5832	1.61765	0.808824	−	0.588051i	$-0.200104\pi$
$431$	33.5832	1.61765	0.808824	+	0.588051i	$0.200104\pi$
$432$	−3.87949	−0.186652
$433$	−29.3004	−1.40809	−0.704043	−	0.710157i	$-0.748624\pi$
$433$	−29.3004	−1.40809	−0.704043	+	0.710157i	$0.748624\pi$
$434$	−18.5001	−0.888032
$435$	6.95317	0.333379
$436$	−6.42532	−0.307717
$437$	5.81206	0.278029
$438$	−6.26031	−0.299129
$439$	−23.4143	−1.11750	−0.558752	−	0.829335i	$-0.688720\pi$
$439$	−23.4143	−1.11750	−0.558752	+	0.829335i	$0.688720\pi$
$440$	3.31286	0.157934
$441$	−5.95814	−0.283721
$442$	1.30007	0.0618379
$443$	−14.9908	−0.712235	−0.356117	−	0.934441i	$-0.615900\pi$
$443$	−14.9908	−0.712235	−0.356117	+	0.934441i	$0.615900\pi$
$444$	17.1994	0.816247
$445$	9.15978	0.434215
$446$	18.8891	0.894426
$447$	−19.8148	−0.937209
$448$	8.40926	0.397300
$449$	−25.3356	−1.19566	−0.597830	−	0.801623i	$-0.703970\pi$
$449$	−25.3356	−1.19566	−0.597830	+	0.801623i	$0.703970\pi$
$450$	10.4161	0.491017
$451$	0.208827	0.00983328
$452$	31.7290	1.49241
$453$	−12.4786	−0.586295
$454$	21.0822	0.989436
$455$	−0.0970283	−0.00454875
$456$	−26.7996	−1.25501
$457$	37.6061	1.75914	0.879570	−	0.475770i	$-0.157830\pi$
$457$	37.6061	1.75914	0.879570	+	0.475770i	$0.157830\pi$
$458$	−37.2605	−1.74107
$459$	4.81272	0.224639
$460$	−3.59591	−0.167660
$461$	18.1552	0.845573	0.422786	−	0.906229i	$-0.361052\pi$
$461$	18.1552	0.845573	0.422786	+	0.906229i	$0.361052\pi$
$462$	1.98478	0.0923401
$463$	−11.9452	−0.555142	−0.277571	−	0.960705i	$-0.589529\pi$
$463$	−11.9452	−0.555142	−0.277571	+	0.960705i	$0.589529\pi$
$464$	−31.3468	−1.45524
$465$	6.37805	0.295775
$466$	−26.9349	−1.24773
$467$	−30.3932	−1.40643	−0.703216	−	0.710977i	$-0.748253\pi$
$467$	−30.3932	−1.40643	−0.703216	+	0.710977i	$0.748253\pi$
$468$	0.439639	0.0203223
$469$	6.28611	0.290266
$470$	2.65657	0.122538
$471$	−17.8464	−0.822317
$472$	15.8378	0.728994
$473$	5.64718	0.259658
$474$	35.2056	1.61705
$475$	23.5782	1.08184
$476$	19.5507	0.896104
$477$	−9.12695	−0.417894
$478$	0.308321	0.0141023
$479$	−3.60796	−0.164852	−0.0824259	−	0.996597i	$-0.526267\pi$
$479$	−3.60796	−0.164852	−0.0824259	+	0.996597i	$0.526267\pi$
$480$	−0.168780	−0.00770373
$481$	−0.477393	−0.0217673
$482$	−65.2711	−2.97302
$483$	−1.07172	−0.0487651
$484$	−41.2619	−1.87554
$485$	−0.0897408	−0.00407492
$486$	2.44537	0.110924
$487$	−28.6546	−1.29846	−0.649232	−	0.760591i	$-0.724909\pi$
$487$	−28.6546	−1.29846	−0.649232	+	0.760591i	$0.724909\pi$
$488$	35.2097	1.59387
$489$	9.24643	0.418138
$490$	12.5378	0.566398
$491$	32.7821	1.47944	0.739718	−	0.672917i	$-0.234959\pi$
$491$	32.7821	1.47944	0.739718	+	0.672917i	$0.234959\pi$
$492$	1.04518	0.0471203
$493$	38.8875	1.75140
$494$	1.49529	0.0672765
$495$	−0.684268	−0.0307555
$496$	−28.7540	−1.29109
$497$	−12.6241	−0.566268
$498$	−38.2651	−1.71470
$499$	−27.1513	−1.21546	−0.607729	−	0.794144i	$-0.707919\pi$
$499$	−27.1513	−1.21546	−0.607729	+	0.794144i	$0.707919\pi$
$500$	−31.7116	−1.41818
$501$	−21.4184	−0.956902
$502$	74.4964	3.32494
$503$	−16.6896	−0.744150	−0.372075	−	0.928203i	$-0.621354\pi$
$503$	−16.6896	−0.744150	−0.372075	+	0.928203i	$0.621354\pi$
$504$	4.94175	0.220123
$505$	7.86559	0.350014
$506$	−2.04167	−0.0907632
$507$	12.9878	0.576808
$508$	−27.6287	−1.22583
$509$	−24.2717	−1.07583	−0.537913	−	0.843000i	$-0.680787\pi$
$509$	−24.2717	−1.07583	−0.537913	+	0.843000i	$0.680787\pi$
$510$	−10.1274	−0.448451
$511$	2.61310	0.115597
$512$	38.3257	1.69377
$513$	5.53544	0.244396
$514$	0.272076	0.0120008
$515$	8.14262	0.358807
$516$	28.2642	1.24426
$517$	1.00386	0.0441497
$518$	−10.7869	−0.473949
$519$	−12.5065	−0.548972
$520$	−0.460225	−0.0201822
$521$	31.0836	1.36180	0.680898	−	0.732378i	$-0.261589\pi$
$521$	31.0836	1.36180	0.680898	+	0.732378i	$0.261589\pi$
$522$	19.7590	0.864826
$523$	−14.3829	−0.628919	−0.314460	−	0.949271i	$-0.601823\pi$
$523$	−14.3829	−0.628919	−0.314460	+	0.949271i	$0.601823\pi$
$524$	39.8742	1.74191
$525$	−4.34773	−0.189751
$526$	−49.9617	−2.17843
$527$	35.6710	1.55385
$528$	3.08487	0.134252
$529$	−21.8976	−0.952068
$530$	19.2059	0.834251
$531$	−3.27129	−0.141962
$532$	22.4866	0.974916
$533$	−0.0290104	−0.00125658
$534$	26.0295	1.12641
$535$	−8.76547	−0.378964
$536$	29.8163	1.28787
$537$	−14.3574	−0.619566
$538$	−70.8431	−3.05426
$539$	4.73776	0.204070
$540$	−3.42476	−0.147378
$541$	−22.5073	−0.967665	−0.483832	−	0.875161i	$-0.660756\pi$
$541$	−22.5073	−0.967665	−0.483832	+	0.875161i	$0.660756\pi$
$542$	−62.6383	−2.69055
$543$	6.90968	0.296523
$544$	−0.943949	−0.0404715
$545$	−1.38929	−0.0595106
$546$	−0.275727	−0.0118000
$547$	−3.16610	−0.135373	−0.0676863	−	0.997707i	$-0.521562\pi$
$547$	−3.16610	−0.135373	−0.0676863	+	0.997707i	$0.521562\pi$
$548$	8.31456	0.355181
$549$	−7.27254	−0.310384
$550$	−8.28257	−0.353170
$551$	44.7271	1.90544
$552$	−5.08341	−0.216364
$553$	−14.6950	−0.624897
$554$	−59.0340	−2.50811
$555$	3.71887	0.157857
$556$	−11.1216	−0.471662
$557$	−11.2064	−0.474831	−0.237416	−	0.971408i	$-0.576300\pi$
$557$	−11.2064	−0.474831	−0.237416	+	0.971408i	$0.576300\pi$
$558$	18.1246	0.767277
$559$	−0.784512	−0.0331813
$560$	−3.40755	−0.143995
$561$	−3.82695	−0.161574
$562$	−7.35894	−0.310418
$563$	−10.0865	−0.425096	−0.212548	−	0.977151i	$-0.568176\pi$
$563$	−10.0865	−0.425096	−0.212548	+	0.977151i	$0.568176\pi$
$564$	5.02433	0.211562
$565$	6.86048	0.288623
$566$	−4.45062	−0.187074
$567$	−1.02072	−0.0428660
$568$	−59.8787	−2.51245
$569$	−6.89338	−0.288986	−0.144493	−	0.989506i	$-0.546155\pi$
$569$	−6.89338	−0.288986	−0.144493	+	0.989506i	$0.546155\pi$
$570$	−11.6483	−0.487892
$571$	−21.0015	−0.878886	−0.439443	−	0.898270i	$-0.644824\pi$
$571$	−21.0015	−0.878886	−0.439443	+	0.898270i	$0.644824\pi$
$572$	−0.349589	−0.0146171
$573$	−1.99244	−0.0832354
$574$	−0.655502	−0.0273601
$575$	4.47236	0.186510
$576$	−8.23860	−0.343275
$577$	46.7214	1.94504	0.972518	−	0.232829i	$-0.0747981\pi$
$577$	46.7214	1.94504	0.972518	+	0.232829i	$0.0747981\pi$
$578$	−15.0691	−0.626794
$579$	−2.14373	−0.0890902
$580$	−27.6726	−1.14904
$581$	15.9721	0.662635
$582$	−0.255018	−0.0105708
$583$	7.25751	0.300575
$584$	12.3945	0.512886
$585$	0.0950591	0.00393021
$586$	0.667859	0.0275890
$587$	21.3732	0.882165	0.441083	−	0.897466i	$-0.354595\pi$
$587$	21.3732	0.882165	0.441083	+	0.897466i	$0.354595\pi$
$588$	23.7125	0.977886
$589$	41.0276	1.69051
$590$	6.88379	0.283401
$591$	0.128300	0.00527758
$592$	−16.7657	−0.689065
$593$	12.2795	0.504257	0.252129	−	0.967694i	$-0.418869\pi$
$593$	12.2795	0.504257	0.252129	+	0.967694i	$0.418869\pi$
$594$	−1.94450	−0.0797836
$595$	4.22727	0.173301
$596$	78.8599	3.23023
$597$	9.87856	0.404303
$598$	0.283630	0.0115985
$599$	34.9316	1.42726	0.713632	−	0.700520i	$-0.247049\pi$
$599$	34.9316	1.42726	0.713632	+	0.700520i	$0.247049\pi$
$600$	−20.6222	−0.841897
$601$	22.5250	0.918812	0.459406	−	0.888226i	$-0.348062\pi$
$601$	22.5250	0.918812	0.459406	+	0.888226i	$0.348062\pi$
$602$	−17.7264	−0.722472
$603$	−6.15854	−0.250795
$604$	49.6629	2.02075
$605$	−8.92168	−0.362718
$606$	22.3518	0.907979
$607$	−10.4881	−0.425701	−0.212850	−	0.977085i	$-0.568275\pi$
$607$	−10.4881	−0.425701	−0.212850	+	0.977085i	$0.568275\pi$
$608$	−1.08570	−0.0440309
$609$	−8.24752	−0.334207
$610$	15.3036	0.619627
$611$	−0.139457	−0.00564184
$612$	−19.1539	−0.774251
$613$	24.8761	1.00474	0.502368	−	0.864654i	$-0.332462\pi$
$613$	24.8761	1.00474	0.502368	+	0.864654i	$0.332462\pi$
$614$	68.7965	2.77640
$615$	0.225990	0.00911278
$616$	−3.92955	−0.158326
$617$	24.7997	0.998399	0.499199	−	0.866487i	$-0.333628\pi$
$617$	24.7997	0.998399	0.499199	+	0.866487i	$0.333628\pi$
$618$	23.1390	0.930788
$619$	17.1525	0.689416	0.344708	−	0.938710i	$-0.387978\pi$
$619$	17.1525	0.689416	0.344708	+	0.938710i	$0.387978\pi$
$620$	−25.3837	−1.01943
$621$	1.04997	0.0421340
$622$	9.94438	0.398733
$623$	−10.8649	−0.435293
$624$	−0.428552	−0.0171558
$625$	14.4408	0.577631
$626$	9.53792	0.381212
$627$	−4.40163	−0.175784
$628$	71.0257	2.83424
$629$	20.7988	0.829301
$630$	2.14790	0.0855743
$631$	−18.8023	−0.748507	−0.374254	−	0.927326i	$-0.622101\pi$
$631$	−18.8023	−0.748507	−0.374254	+	0.927326i	$0.622101\pi$
$632$	−69.7016	−2.77258
$633$	2.53674	0.100826
$634$	59.1363	2.34860
$635$	−5.97391	−0.237067
$636$	36.3239	1.44033
$637$	−0.658173	−0.0260778
$638$	−15.7118	−0.622036
$639$	12.3679	0.489266
$640$	16.9990	0.671944
$641$	−16.4522	−0.649822	−0.324911	−	0.945745i	$-0.605334\pi$
$641$	−16.4522	−0.649822	−0.324911	+	0.945745i	$0.605334\pi$
$642$	−24.9090	−0.983079
$643$	−6.63386	−0.261614	−0.130807	−	0.991408i	$-0.541757\pi$
$643$	−6.63386	−0.261614	−0.130807	+	0.991408i	$0.541757\pi$
$644$	4.26530	0.168076
$645$	6.11130	0.240632
$646$	−65.1460	−2.56314
$647$	2.52861	0.0994101	0.0497051	−	0.998764i	$-0.484172\pi$
$647$	2.52861	0.0994101	0.0497051	+	0.998764i	$0.484172\pi$
$648$	−4.84146	−0.190191
$649$	2.60124	0.102108
$650$	1.15062	0.0451311
$651$	−7.56534	−0.296509
$652$	−36.7994	−1.44117
$653$	7.11507	0.278434	0.139217	−	0.990262i	$-0.455541\pi$
$653$	7.11507	0.278434	0.139217	+	0.990262i	$0.455541\pi$
$654$	−3.94796	−0.154378
$655$	8.62163	0.336875
$656$	−1.01882	−0.0397784
$657$	−2.56006	−0.0998776
$658$	−3.15109	−0.122842
$659$	−16.5231	−0.643648	−0.321824	−	0.946800i	$-0.604296\pi$
$659$	−16.5231	−0.643648	−0.321824	+	0.946800i	$0.604296\pi$
$660$	2.72328	0.106004
$661$	12.3354	0.479790	0.239895	−	0.970799i	$-0.422887\pi$
$661$	12.3354	0.479790	0.239895	+	0.970799i	$0.422887\pi$
$662$	56.3361	2.18957
$663$	0.531644	0.0206473
$664$	75.7590	2.94002
$665$	4.86206	0.188543
$666$	10.5680	0.409501
$667$	8.48393	0.328499
$668$	85.2419	3.29811
$669$	7.72444	0.298644
$670$	12.9595	0.500667
$671$	5.78293	0.223248
$672$	0.200199	0.00772285
$673$	−17.4271	−0.671767	−0.335883	−	0.941904i	$-0.609035\pi$
$673$	−17.4271	−0.671767	−0.335883	+	0.941904i	$0.609035\pi$
$674$	−12.1555	−0.468211
$675$	4.25949	0.163948
$676$	−51.6894	−1.98806
$677$	22.9645	0.882599	0.441299	−	0.897360i	$-0.354518\pi$
$677$	22.9645	0.882599	0.441299	+	0.897360i	$0.354518\pi$
$678$	19.4956	0.748722
$679$	0.106446	0.00408503
$680$	20.0508	0.768913
$681$	8.62126	0.330367
$682$	−14.4122	−0.551873
$683$	11.4725	0.438982	0.219491	−	0.975615i	$-0.429560\pi$
$683$	11.4725	0.438982	0.219491	+	0.975615i	$0.429560\pi$
$684$	−22.0302	−0.842346
$685$	1.79778	0.0686897
$686$	−32.3439	−1.23490
$687$	−15.2371	−0.581333
$688$	−27.5514	−1.05039
$689$	−1.00822	−0.0384101
$690$	−2.20947	−0.0841129
$691$	15.9005	0.604885	0.302442	−	0.953168i	$-0.402198\pi$
$691$	15.9005	0.604885	0.302442	+	0.953168i	$0.402198\pi$
$692$	49.7738	1.89211
$693$	0.811646	0.0308319
$694$	65.0551	2.46946
$695$	−2.40473	−0.0912166
$696$	−39.1197	−1.48283
$697$	1.26391	0.0478739
$698$	57.2103	2.16544
$699$	−11.0146	−0.416611
$700$	17.3033	0.654003
$701$	0.932076	0.0352040	0.0176020	−	0.999845i	$-0.494397\pi$
$701$	0.932076	0.0352040	0.0176020	+	0.999845i	$0.494397\pi$
$702$	0.270131	0.0101954
$703$	23.9221	0.902238
$704$	6.55112	0.246904
$705$	1.08636	0.0409148
$706$	30.4016	1.14418
$707$	−9.32978	−0.350883
$708$	13.0192	0.489292
$709$	23.8165	0.894446	0.447223	−	0.894422i	$-0.352413\pi$
$709$	23.8165	0.894446	0.447223	+	0.894422i	$0.352413\pi$
$710$	−26.0258	−0.976732
$711$	14.3968	0.539923
$712$	−51.5344	−1.93134
$713$	7.78220	0.291446
$714$	12.0127	0.449564
$715$	−0.0755885	−0.00282685
$716$	57.1401	2.13543
$717$	0.126083	0.00470867
$718$	34.5416	1.28908
$719$	1.53359	0.0571933	0.0285967	−	0.999591i	$-0.490896\pi$
$719$	1.53359	0.0571933	0.0285967	+	0.999591i	$0.490896\pi$
$720$	3.33840	0.124415
$721$	−9.65839	−0.359697
$722$	−28.4668	−1.05942
$723$	−26.6917	−0.992674
$724$	−27.4995	−1.02201
$725$	34.4173	1.27823
$726$	−25.3529	−0.940934
$727$	−5.84650	−0.216835	−0.108417	−	0.994105i	$-0.534578\pi$
$727$	−5.84650	−0.216835	−0.108417	+	0.994105i	$0.534578\pi$
$728$	0.545897	0.0202323
$729$	1.00000	0.0370370
$730$	5.38716	0.199388
$731$	34.1791	1.26416
$732$	28.9436	1.06979
$733$	−40.4682	−1.49473	−0.747364	−	0.664415i	$-0.768681\pi$
$733$	−40.4682	−1.49473	−0.747364	+	0.664415i	$0.768681\pi$
$734$	54.7392	2.02046
$735$	5.12714	0.189117
$736$	−0.205938	−0.00759096
$737$	4.89711	0.180387
$738$	0.642199	0.0236397
$739$	−18.1960	−0.669350	−0.334675	−	0.942334i	$-0.608627\pi$
$739$	−18.1960	−0.669350	−0.334675	+	0.942334i	$0.608627\pi$
$740$	−14.8005	−0.544078
$741$	0.611479	0.0224632
$742$	−22.7811	−0.836321
$743$	−47.5035	−1.74273	−0.871367	−	0.490632i	$-0.836766\pi$
$743$	−47.5035	−1.74273	−0.871367	+	0.490632i	$0.836766\pi$
$744$	−35.8840	−1.31557
$745$	17.0512	0.624706
$746$	71.8462	2.63048
$747$	−15.6480	−0.572529
$748$	15.2307	0.556889
$749$	10.3972	0.379905
$750$	−19.4848	−0.711485
$751$	−27.6076	−1.00742	−0.503708	−	0.863874i	$-0.668031\pi$
$751$	−27.6076	−1.00742	−0.503708	+	0.863874i	$0.668031\pi$
$752$	−4.89763	−0.178598
$753$	30.4642	1.11018
$754$	2.18270	0.0794892
$755$	10.7382	0.390801
$756$	4.06229	0.147744
$757$	45.2700	1.64536	0.822682	−	0.568502i	$-0.192477\pi$
$757$	45.2700	1.64536	0.822682	+	0.568502i	$0.192477\pi$
$758$	−1.47242	−0.0534806
$759$	−0.834911	−0.0303054
$760$	23.0618	0.836538
$761$	2.27563	0.0824917	0.0412458	−	0.999149i	$-0.486867\pi$
$761$	2.27563	0.0824917	0.0412458	+	0.999149i	$0.486867\pi$
$762$	−16.9762	−0.614982
$763$	1.64791	0.0596582
$764$	7.92960	0.286883
$765$	−4.14147	−0.149735
$766$	16.3058	0.589151
$767$	−0.361367	−0.0130482
$768$	31.8291	1.14853
$769$	51.2775	1.84911	0.924557	−	0.381045i	$-0.124436\pi$
$769$	51.2775	1.84911	0.924557	+	0.381045i	$0.124436\pi$
$770$	−1.70795	−0.0615503
$771$	0.111262	0.00400699
$772$	8.53170	0.307063
$773$	−26.8705	−0.966466	−0.483233	−	0.875492i	$-0.660538\pi$
$773$	−26.8705	−0.966466	−0.483233	+	0.875492i	$0.660538\pi$
$774$	17.3666	0.624230
$775$	31.5706	1.13405
$776$	0.504896	0.0181247
$777$	−4.41114	−0.158249
$778$	−60.0271	−2.15208
$779$	1.45371	0.0520844
$780$	−0.378321	−0.0135461
$781$	−9.83462	−0.351910
$782$	−12.3570	−0.441887
$783$	8.08014	0.288761
$784$	−23.1145	−0.825519
$785$	15.3573	0.548124
$786$	24.5002	0.873894
$787$	39.4212	1.40521	0.702606	−	0.711579i	$-0.252019\pi$
$787$	39.4212	1.40521	0.702606	+	0.711579i	$0.252019\pi$
$788$	−0.510616	−0.0181899
$789$	−20.4311	−0.727368
$790$	−30.2953	−1.07786
$791$	−8.13758	−0.289339
$792$	3.84980	0.136797
$793$	−0.803370	−0.0285285
$794$	94.0967	3.33937
$795$	7.85398	0.278552
$796$	−39.3152	−1.39349
$797$	−27.4436	−0.972101	−0.486051	−	0.873931i	$-0.661563\pi$
$797$	−27.4436	−0.972101	−0.486051	+	0.873931i	$0.661563\pi$
$798$	13.8166	0.489103
$799$	6.07579	0.214946
$800$	−0.835441	−0.0295373
$801$	10.6444	0.376101
$802$	30.2796	1.06921
$803$	2.03570	0.0718381
$804$	24.5100	0.864402
$805$	0.922246	0.0325049
$806$	2.00216	0.0705231
$807$	−28.9703	−1.01980
$808$	−44.2531	−1.55682
$809$	16.8702	0.593126	0.296563	−	0.955013i	$-0.404159\pi$
$809$	16.8702	0.593126	0.296563	+	0.955013i	$0.404159\pi$
$810$	−2.10431	−0.0739378
$811$	3.20383	0.112502	0.0562509	−	0.998417i	$-0.482085\pi$
$811$	3.20383	0.112502	0.0562509	+	0.998417i	$0.482085\pi$
$812$	32.8239	1.15189
$813$	−25.6150	−0.898359
$814$	−8.40337	−0.294538
$815$	−7.95679	−0.278714
$816$	18.6709	0.653612
$817$	39.3117	1.37534
$818$	−2.43389	−0.0850989
$819$	−0.112755	−0.00393996
$820$	−0.899404	−0.0314086
$821$	3.42846	0.119654	0.0598271	−	0.998209i	$-0.480945\pi$
$821$	3.42846	0.119654	0.0598271	+	0.998209i	$0.480945\pi$
$822$	5.10879	0.178190
$823$	−32.8910	−1.14651	−0.573255	−	0.819377i	$-0.694319\pi$
$823$	−32.8910	−1.14651	−0.573255	+	0.819377i	$0.694319\pi$
$824$	−45.8117	−1.59593
$825$	−3.38704	−0.117922
$826$	−8.16522	−0.284104
$827$	−9.91405	−0.344745	−0.172373	−	0.985032i	$-0.555143\pi$
$827$	−9.91405	−0.344745	−0.172373	+	0.985032i	$0.555143\pi$
$828$	−4.17873	−0.145221
$829$	−19.9160	−0.691710	−0.345855	−	0.938288i	$-0.612411\pi$
$829$	−19.9160	−0.691710	−0.345855	+	0.938288i	$0.612411\pi$
$830$	32.9281	1.14295
$831$	−24.1411	−0.837446
$832$	−0.910087	−0.0315516
$833$	28.6749	0.993526
$834$	−6.83357	−0.236627
$835$	18.4311	0.637834
$836$	17.5178	0.605867
$837$	7.41181	0.256190
$838$	66.1328	2.28452
$839$	43.9283	1.51657	0.758287	−	0.651921i	$-0.226037\pi$
$839$	43.9283	1.51657	0.758287	+	0.651921i	$0.226037\pi$
$840$	−4.25251	−0.146725
$841$	36.2887	1.25133
$842$	−76.2131	−2.62648
$843$	−3.00933	−0.103647
$844$	−10.0958	−0.347513
$845$	−11.1763	−0.384478
$846$	3.08714	0.106138
$847$	10.5825	0.363618
$848$	−35.4079	−1.21591
$849$	−1.82002	−0.0624629
$850$	−50.1296	−1.71943
$851$	4.53759	0.155546
$852$	−49.2223	−1.68633
$853$	13.5700	0.464628	0.232314	−	0.972641i	$-0.425370\pi$
$853$	13.5700	0.464628	0.232314	+	0.972641i	$0.425370\pi$
$854$	−18.1525	−0.621164
$855$	−4.76339	−0.162904
$856$	49.3160	1.68559
$857$	−50.1377	−1.71267	−0.856335	−	0.516421i	$-0.827264\pi$
$857$	−50.1377	−1.71267	−0.856335	+	0.516421i	$0.827264\pi$
$858$	−0.214801	−0.00733319
$859$	−30.1260	−1.02789	−0.513943	−	0.857824i	$-0.671816\pi$
$859$	−30.1260	−1.02789	−0.513943	+	0.857824i	$0.671816\pi$
$860$	−24.3221	−0.829375
$861$	−0.268058	−0.00913540
$862$	−82.1236	−2.79714
$863$	−54.2324	−1.84609	−0.923047	−	0.384688i	$-0.874309\pi$
$863$	−54.2324	−1.84609	−0.923047	+	0.384688i	$0.874309\pi$
$864$	−0.196136	−0.00667269
$865$	10.7621	0.365923
$866$	71.6504	2.43478
$867$	−6.16231	−0.209283
$868$	30.1089	1.02196
$869$	−11.4480	−0.388346
$870$	−17.0031	−0.576459
$871$	−0.680311	−0.0230514
$872$	7.81636	0.264695
$873$	−0.104286	−0.00352954
$874$	−14.2127	−0.480750
$875$	8.13310	0.274949
$876$	10.1887	0.344243
$877$	−7.64978	−0.258315	−0.129157	−	0.991624i	$-0.541227\pi$
$877$	−7.64978	−0.258315	−0.129157	+	0.991624i	$0.541227\pi$
$878$	57.2567	1.93232
$879$	0.273111	0.00921181
$880$	−2.65461	−0.0894868
$881$	13.6135	0.458649	0.229325	−	0.973350i	$-0.426348\pi$
$881$	13.6135	0.458649	0.229325	+	0.973350i	$0.426348\pi$
$882$	14.5699	0.490593
$883$	55.0582	1.85285	0.926427	−	0.376474i	$-0.122863\pi$
$883$	55.0582	1.85285	0.926427	+	0.376474i	$0.122863\pi$
$884$	−2.11586	−0.0711641
$885$	2.81503	0.0946261
$886$	36.6581	1.23155
$887$	−3.20651	−0.107664	−0.0538320	−	0.998550i	$-0.517144\pi$
$887$	−3.20651	−0.107664	−0.0538320	+	0.998550i	$0.517144\pi$
$888$	−20.9230	−0.702129
$889$	7.08597	0.237656
$890$	−22.3991	−0.750819
$891$	−0.795174	−0.0266393
$892$	−30.7421	−1.02932
$893$	6.98817	0.233850
$894$	48.4546	1.62056
$895$	12.3549	0.412979
$896$	−20.1634	−0.673611
$897$	0.115987	0.00387268
$898$	61.9549	2.06746
$899$	59.8885	1.99739
$900$	−16.9521	−0.565071
$901$	43.9255	1.46337
$902$	−0.510660	−0.0170031
$903$	−7.24894	−0.241230
$904$	−38.5982	−1.28376
$905$	−5.94596	−0.197650
$906$	30.5148	1.01379
$907$	−24.1986	−0.803502	−0.401751	−	0.915749i	$-0.631598\pi$
$907$	−24.1986	−0.803502	−0.401751	+	0.915749i	$0.631598\pi$
$908$	−34.3113	−1.13866
$909$	9.14044	0.303169
$910$	0.237270	0.00786543
$911$	24.1209	0.799159	0.399580	−	0.916698i	$-0.369156\pi$
$911$	24.1209	0.799159	0.399580	+	0.916698i	$0.369156\pi$
$912$	21.4747	0.711097
$913$	12.4428	0.411798
$914$	−91.9610	−3.04180
$915$	6.25821	0.206890
$916$	60.6415	2.00365
$917$	−10.2266	−0.337711
$918$	−11.7689	−0.388432
$919$	−56.8545	−1.87546	−0.937728	−	0.347370i	$-0.887075\pi$
$919$	−56.8545	−1.87546	−0.937728	+	0.347370i	$0.887075\pi$
$920$	4.37440	0.144220
$921$	28.1333	0.927025
$922$	−44.3963	−1.46211
$923$	1.36623	0.0449702
$924$	−3.23023	−0.106267
$925$	18.4079	0.605249
$926$	29.2105	0.959918
$927$	9.46237	0.310785
$928$	−1.58481	−0.0520239
$929$	36.0327	1.18219	0.591097	−	0.806601i	$-0.298695\pi$
$929$	36.0327	1.18219	0.591097	+	0.806601i	$0.298695\pi$
$930$	−15.5967	−0.511436
$931$	32.9809	1.08091
$932$	43.8365	1.43591
$933$	4.06661	0.133135
$934$	74.3228	2.43192
$935$	3.29319	0.107699
$936$	−0.534818	−0.0174811
$937$	39.5931	1.29345	0.646726	−	0.762723i	$-0.276138\pi$
$937$	39.5931	1.29345	0.646726	+	0.762723i	$0.276138\pi$
$938$	−15.3719	−0.501910
$939$	3.90040	0.127285
$940$	−4.32356	−0.141019
$941$	−35.6459	−1.16202	−0.581012	−	0.813895i	$-0.697343\pi$
$941$	−35.6459	−1.16202	−0.581012	+	0.813895i	$0.697343\pi$
$942$	43.6410	1.42190
$943$	0.275742	0.00897939
$944$	−12.6909	−0.413054
$945$	0.878352	0.0285728
$946$	−13.8095	−0.448984
$947$	11.4309	0.371455	0.185727	−	0.982601i	$-0.440536\pi$
$947$	11.4309	0.371455	0.185727	+	0.982601i	$0.440536\pi$
$948$	−57.2971	−1.86092
$949$	−0.282801	−0.00918010
$950$	−57.6574	−1.87065
$951$	24.1830	0.784186
$952$	−23.7833	−0.770821
$953$	−15.8403	−0.513117	−0.256558	−	0.966529i	$-0.582589\pi$
$953$	−15.8403	−0.513117	−0.256558	+	0.966529i	$0.582589\pi$
$954$	22.3188	0.722597
$955$	1.71455	0.0554814
$956$	−0.501792	−0.0162291
$957$	−6.42512	−0.207695
$958$	8.82280	0.285052
$959$	−2.13244	−0.0688602
$960$	7.08953	0.228814
$961$	23.9349	0.772093
$962$	1.16740	0.0376386
$963$	−10.1862	−0.328245
$964$	106.229	3.42140
$965$	1.84473	0.0593840
$966$	2.62076	0.0843217
$967$	−57.1866	−1.83900	−0.919499	−	0.393093i	$-0.871405\pi$
$967$	−57.1866	−1.83900	−0.919499	+	0.393093i	$0.871405\pi$
$968$	50.1948	1.61332
$969$	−26.6405	−0.855817
$970$	0.219450	0.00704610
$971$	7.93135	0.254529	0.127265	−	0.991869i	$-0.459380\pi$
$971$	7.93135	0.254529	0.127265	+	0.991869i	$0.459380\pi$
$972$	−3.97985	−0.127654
$973$	2.85238	0.0914430
$974$	70.0712	2.24522
$975$	0.470530	0.0150690
$976$	−28.2137	−0.903099
$977$	−30.3511	−0.971017	−0.485509	−	0.874232i	$-0.661366\pi$
$977$	−30.3511	−0.971017	−0.485509	+	0.874232i	$0.661366\pi$
$978$	−22.6110	−0.723019
$979$	−8.46414	−0.270515
$980$	−20.4052	−0.651821
$981$	−1.61446	−0.0515458
$982$	−80.1644	−2.55815
$983$	13.5639	0.432620	0.216310	−	0.976325i	$-0.430598\pi$
$983$	13.5639	0.432620	0.216310	+	0.976325i	$0.430598\pi$
$984$	−1.27146	−0.0405325
$985$	−0.110406	−0.00351782
$986$	−95.0944	−3.02842
$987$	−1.28859	−0.0410164
$988$	−2.43359	−0.0774229
$989$	7.45672	0.237110
$990$	1.67329	0.0531806
$991$	−24.9379	−0.792178	−0.396089	−	0.918212i	$-0.629633\pi$
$991$	−24.9379	−0.792178	−0.396089	+	0.918212i	$0.629633\pi$
$992$	−1.45372	−0.0461558
$993$	23.0378	0.731084
$994$	30.8706	0.979156
$995$	−8.50076	−0.269492
$996$	62.2765	1.97331
$997$	22.9963	0.728299	0.364150	−	0.931341i	$-0.381360\pi$
$997$	22.9963	0.728299	0.364150	+	0.931341i	$0.381360\pi$
$998$	66.3950	2.10170
$999$	4.32162	0.136730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.c.1.9	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.c.1.9	✓	121	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44537 q^{2} -1.00000 q^{3} +3.97985 q^{4} +0.860526 q^{5} +2.44537 q^{6} -1.02072 q^{7} -4.84146 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.44537 q^{2} -1.00000 q^{3} +3.97985 q^{4} +0.860526 q^{5} +2.44537 q^{6} -1.02072 q^{7} -4.84146 q^{8} +1.00000 q^{9} -2.10431 q^{10} -0.795174 q^{11} -3.97985 q^{12} +0.110466 q^{13} +2.49603 q^{14} -0.860526 q^{15} +3.87949 q^{16} -4.81272 q^{17} -2.44537 q^{18} -5.53544 q^{19} +3.42476 q^{20} +1.02072 q^{21} +1.94450 q^{22} -1.04997 q^{23} +4.84146 q^{24} -4.25949 q^{25} -0.270131 q^{26} -1.00000 q^{27} -4.06229 q^{28} -8.08014 q^{29} +2.10431 q^{30} -7.41181 q^{31} +0.196136 q^{32} +0.795174 q^{33} +11.7689 q^{34} -0.878352 q^{35} +3.97985 q^{36} -4.32162 q^{37} +13.5362 q^{38} -0.110466 q^{39} -4.16621 q^{40} -0.262618 q^{41} -2.49603 q^{42} -7.10182 q^{43} -3.16467 q^{44} +0.860526 q^{45} +2.56758 q^{46} -1.26244 q^{47} -3.87949 q^{48} -5.95814 q^{49} +10.4161 q^{50} +4.81272 q^{51} +0.439639 q^{52} -9.12695 q^{53} +2.44537 q^{54} -0.684268 q^{55} +4.94175 q^{56} +5.53544 q^{57} +19.7590 q^{58} -3.27129 q^{59} -3.42476 q^{60} -7.27254 q^{61} +18.1246 q^{62} -1.02072 q^{63} -8.23860 q^{64} +0.0950591 q^{65} -1.94450 q^{66} -6.15854 q^{67} -19.1539 q^{68} +1.04997 q^{69} +2.14790 q^{70} +12.3679 q^{71} -4.84146 q^{72} -2.56006 q^{73} +10.5680 q^{74} +4.25949 q^{75} -22.0302 q^{76} +0.811646 q^{77} +0.270131 q^{78} +14.3968 q^{79} +3.33840 q^{80} +1.00000 q^{81} +0.642199 q^{82} -15.6480 q^{83} +4.06229 q^{84} -4.14147 q^{85} +17.3666 q^{86} +8.08014 q^{87} +3.84980 q^{88} +10.6444 q^{89} -2.10431 q^{90} -0.112755 q^{91} -4.17873 q^{92} +7.41181 q^{93} +3.08714 q^{94} -4.76339 q^{95} -0.196136 q^{96} -0.104286 q^{97} +14.5699 q^{98} -0.795174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9}+O(q^{10}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9	\( 121 q + 7 q^{2} - 121 q^{3} + 123 q^{4} + 24 q^{5} - 7 q^{6} - 14 q^{7} + 18 q^{8} + 121 q^{9} + 18 q^{10} + 32 q^{11} - 123 q^{12} + 2 q^{13} + 37 q^{14} - 24 q^{15} + 131 q^{16} + 87 q^{17} + 7 q^{18} - 10 q^{19} + 60 q^{20} + 14 q^{21} - 22 q^{22} + 31 q^{23} - 18 q^{24} + 147 q^{25} + 37 q^{26} - 121 q^{27} - 29 q^{28} + 68 q^{29} - 18 q^{30} + 25 q^{31} + 43 q^{32} - 32 q^{33} + 27 q^{34} + 51 q^{35} + 123 q^{36} - 4 q^{37} + 36 q^{38} - 2 q^{39} + 61 q^{40} + 132 q^{41} - 37 q^{42} - 91 q^{43} + 94 q^{44} + 24 q^{45} + 39 q^{47} - 131 q^{48} + 217 q^{49} + 54 q^{50} - 87 q^{51} - 12 q^{52} + 55 q^{53} - 7 q^{54} + 7 q^{55} + 104 q^{56} + 10 q^{57} - 3 q^{58} + 58 q^{59} - 60 q^{60} + 126 q^{61} + 74 q^{62} - 14 q^{63} + 122 q^{64} + 128 q^{65} + 22 q^{66} - 139 q^{67} + 190 q^{68} - 31 q^{69} - 18 q^{70} + 37 q^{71} + 18 q^{72} + 84 q^{73} + 79 q^{74} - 147 q^{75} + 23 q^{76} + 95 q^{77} - 37 q^{78} - 14 q^{79} + 145 q^{80} + 121 q^{81} + 9 q^{82} + 58 q^{83} + 29 q^{84} + 32 q^{85} + 28 q^{86} - 68 q^{87} - 84 q^{88} + 198 q^{89} + 18 q^{90} + 5 q^{91} + 98 q^{92} - 25 q^{93} + 9 q^{94} + 42 q^{95} - 43 q^{96} + 73 q^{97} + 69 q^{98} + 32 q^{99}+O(q^{100}) \) 121 * q + 7 * q^2 - 121 * q^3 + 123 * q^4 + 24 * q^5 - 7 * q^6 - 14 * q^7 + 18 * q^8 + 121 * q^9 + 18 * q^10 + 32 * q^11 - 123 * q^12 + 2 * q^13 + 37 * q^14 - 24 * q^15 + 131 * q^16 + 87 * q^17 + 7 * q^18 - 10 * q^19 + 60 * q^20 + 14 * q^21 - 22 * q^22 + 31 * q^23 - 18 * q^24 + 147 * q^25 + 37 * q^26 - 121 * q^27 - 29 * q^28 + 68 * q^29 - 18 * q^30 + 25 * q^31 + 43 * q^32 - 32 * q^33 + 27 * q^34 + 51 * q^35 + 123 * q^36 - 4 * q^37 + 36 * q^38 - 2 * q^39 + 61 * q^40 + 132 * q^41 - 37 * q^42 - 91 * q^43 + 94 * q^44 + 24 * q^45 + 39 * q^47 - 131 * q^48 + 217 * q^49 + 54 * q^50 - 87 * q^51 - 12 * q^52 + 55 * q^53 - 7 * q^54 + 7 * q^55 + 104 * q^56 + 10 * q^57 - 3 * q^58 + 58 * q^59 - 60 * q^60 + 126 * q^61 + 74 * q^62 - 14 * q^63 + 122 * q^64 + 128 * q^65 + 22 * q^66 - 139 * q^67 + 190 * q^68 - 31 * q^69 - 18 * q^70 + 37 * q^71 + 18 * q^72 + 84 * q^73 + 79 * q^74 - 147 * q^75 + 23 * q^76 + 95 * q^77 - 37 * q^78 - 14 * q^79 + 145 * q^80 + 121 * q^81 + 9 * q^82 + 58 * q^83 + 29 * q^84 + 32 * q^85 + 28 * q^86 - 68 * q^87 - 84 * q^88 + 198 * q^89 + 18 * q^90 + 5 * q^91 + 98 * q^92 - 25 * q^93 + 9 * q^94 + 42 * q^95 - 43 * q^96 + 73 * q^97 + 69 * q^98 + 32 * q^99

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