LMFDB - Embedded newform 8026.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.27254 q^{3} +1.00000 q^{4} -0.667760 q^{5} -3.27254 q^{6} -3.79895 q^{7} +1.00000 q^{8} +7.70950 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.27254 q^{3} +1.00000 q^{4} -0.667760 q^{5} -3.27254 q^{6} -3.79895 q^{7} +1.00000 q^{8} +7.70950 q^{9} -0.667760 q^{10} +4.80896 q^{11} -3.27254 q^{12} +3.23119 q^{13} -3.79895 q^{14} +2.18527 q^{15} +1.00000 q^{16} +6.34816 q^{17} +7.70950 q^{18} +5.99173 q^{19} -0.667760 q^{20} +12.4322 q^{21} +4.80896 q^{22} +8.46768 q^{23} -3.27254 q^{24} -4.55410 q^{25} +3.23119 q^{26} -15.4120 q^{27} -3.79895 q^{28} +8.48209 q^{29} +2.18527 q^{30} +3.77783 q^{31} +1.00000 q^{32} -15.7375 q^{33} +6.34816 q^{34} +2.53679 q^{35} +7.70950 q^{36} -3.84020 q^{37} +5.99173 q^{38} -10.5742 q^{39} -0.667760 q^{40} +5.05702 q^{41} +12.4322 q^{42} -1.11601 q^{43} +4.80896 q^{44} -5.14810 q^{45} +8.46768 q^{46} -9.40610 q^{47} -3.27254 q^{48} +7.43201 q^{49} -4.55410 q^{50} -20.7746 q^{51} +3.23119 q^{52} +0.645485 q^{53} -15.4120 q^{54} -3.21123 q^{55} -3.79895 q^{56} -19.6082 q^{57} +8.48209 q^{58} +14.7049 q^{59} +2.18527 q^{60} +11.6292 q^{61} +3.77783 q^{62} -29.2880 q^{63} +1.00000 q^{64} -2.15766 q^{65} -15.7375 q^{66} -3.44187 q^{67} +6.34816 q^{68} -27.7108 q^{69} +2.53679 q^{70} -11.4094 q^{71} +7.70950 q^{72} +0.419609 q^{73} -3.84020 q^{74} +14.9034 q^{75} +5.99173 q^{76} -18.2690 q^{77} -10.5742 q^{78} -5.84063 q^{79} -0.667760 q^{80} +27.3079 q^{81} +5.05702 q^{82} -2.65729 q^{83} +12.4322 q^{84} -4.23905 q^{85} -1.11601 q^{86} -27.7579 q^{87} +4.80896 q^{88} +1.28123 q^{89} -5.14810 q^{90} -12.2751 q^{91} +8.46768 q^{92} -12.3631 q^{93} -9.40610 q^{94} -4.00104 q^{95} -3.27254 q^{96} -4.57141 q^{97} +7.43201 q^{98} +37.0747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) $ 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * 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
$3$	−3.27254	−1.88940	−0.944700	−	0.327935i	$-0.893647\pi$
$3$	−3.27254	−1.88940	−0.944700	+	0.327935i	$0.893647\pi$
$4$	1.00000	0.500000
$5$	−0.667760	−0.298631	−0.149316	−	0.988790i	$-0.547707\pi$
$5$	−0.667760	−0.298631	−0.149316	+	0.988790i	$0.547707\pi$
$6$	−3.27254	−1.33601
$7$	−3.79895	−1.43587	−0.717934	−	0.696112i	$-0.754912\pi$
$7$	−3.79895	−1.43587	−0.717934	+	0.696112i	$0.754912\pi$
$8$	1.00000	0.353553
$9$	7.70950	2.56983
$10$	−0.667760	−0.211164
$11$	4.80896	1.44996	0.724978	−	0.688772i	$-0.241850\pi$
$11$	4.80896	1.44996	0.724978	+	0.688772i	$0.241850\pi$
$12$	−3.27254	−0.944700
$13$	3.23119	0.896171	0.448085	−	0.893991i	$-0.352106\pi$
$13$	3.23119	0.896171	0.448085	+	0.893991i	$0.352106\pi$
$14$	−3.79895	−1.01531
$15$	2.18527	0.564234
$16$	1.00000	0.250000
$17$	6.34816	1.53966	0.769828	−	0.638252i	$-0.220342\pi$
$17$	6.34816	1.53966	0.769828	+	0.638252i	$0.220342\pi$
$18$	7.70950	1.81715
$19$	5.99173	1.37460	0.687298	−	0.726375i	$-0.258796\pi$
$19$	5.99173	1.37460	0.687298	+	0.726375i	$0.258796\pi$
$20$	−0.667760	−0.149316
$21$	12.4322	2.71293
$22$	4.80896	1.02527
$23$	8.46768	1.76563	0.882816	−	0.469719i	$-0.155645\pi$
$23$	8.46768	1.76563	0.882816	+	0.469719i	$0.155645\pi$
$24$	−3.27254	−0.668004
$25$	−4.55410	−0.910819
$26$	3.23119	0.633688
$27$	−15.4120	−2.96604
$28$	−3.79895	−0.717934
$29$	8.48209	1.57508	0.787542	−	0.616261i	$-0.211353\pi$
$29$	8.48209	1.57508	0.787542	+	0.616261i	$0.211353\pi$
$30$	2.18527	0.398974
$31$	3.77783	0.678518	0.339259	−	0.940693i	$-0.389824\pi$
$31$	3.77783	0.678518	0.339259	+	0.940693i	$0.389824\pi$
$32$	1.00000	0.176777
$33$	−15.7375	−2.73955
$34$	6.34816	1.08870
$35$	2.53679	0.428795
$36$	7.70950	1.28492
$37$	−3.84020	−0.631326	−0.315663	−	0.948871i	$-0.602227\pi$
$37$	−3.84020	−0.631326	−0.315663	+	0.948871i	$0.602227\pi$
$38$	5.99173	0.971987
$39$	−10.5742	−1.69323
$40$	−0.667760	−0.105582
$41$	5.05702	0.789774	0.394887	−	0.918730i	$-0.370784\pi$
$41$	5.05702	0.789774	0.394887	+	0.918730i	$0.370784\pi$
$42$	12.4322	1.91833
$43$	−1.11601	−0.170190	−0.0850948	−	0.996373i	$-0.527119\pi$
$43$	−1.11601	−0.170190	−0.0850948	+	0.996373i	$0.527119\pi$
$44$	4.80896	0.724978
$45$	−5.14810	−0.767433
$46$	8.46768	1.24849
$47$	−9.40610	−1.37202	−0.686010	−	0.727592i	$-0.740639\pi$
$47$	−9.40610	−1.37202	−0.686010	+	0.727592i	$0.740639\pi$
$48$	−3.27254	−0.472350
$49$	7.43201	1.06172
$50$	−4.55410	−0.644046
$51$	−20.7746	−2.90902
$52$	3.23119	0.448085
$53$	0.645485	0.0886642	0.0443321	−	0.999017i	$-0.485884\pi$
$53$	0.645485	0.0886642	0.0443321	+	0.999017i	$0.485884\pi$
$54$	−15.4120	−2.09731
$55$	−3.21123	−0.433002
$56$	−3.79895	−0.507656
$57$	−19.6082	−2.59716
$58$	8.48209	1.11375
$59$	14.7049	1.91441	0.957205	−	0.289412i	$-0.0934596\pi$
$59$	14.7049	1.91441	0.957205	+	0.289412i	$0.0934596\pi$
$60$	2.18527	0.282117
$61$	11.6292	1.48897	0.744486	−	0.667638i	$-0.232695\pi$
$61$	11.6292	1.48897	0.744486	+	0.667638i	$0.232695\pi$
$62$	3.77783	0.479785
$63$	−29.2880	−3.68994
$64$	1.00000	0.125000
$65$	−2.15766	−0.267625
$66$	−15.7375	−1.93715
$67$	−3.44187	−0.420491	−0.210246	−	0.977649i	$-0.567426\pi$
$67$	−3.44187	−0.420491	−0.210246	+	0.977649i	$0.567426\pi$
$68$	6.34816	0.769828
$69$	−27.7108	−3.33599
$70$	2.53679	0.303204
$71$	−11.4094	−1.35404	−0.677022	−	0.735963i	$-0.736730\pi$
$71$	−11.4094	−1.35404	−0.677022	+	0.735963i	$0.736730\pi$
$72$	7.70950	0.908573
$73$	0.419609	0.0491116	0.0245558	−	0.999698i	$-0.492183\pi$
$73$	0.419609	0.0491116	0.0245558	+	0.999698i	$0.492183\pi$
$74$	−3.84020	−0.446415
$75$	14.9034	1.72090
$76$	5.99173	0.687298
$77$	−18.2690	−2.08194
$78$	−10.5742	−1.19729
$79$	−5.84063	−0.657122	−0.328561	−	0.944483i	$-0.606564\pi$
$79$	−5.84063	−0.657122	−0.328561	+	0.944483i	$0.606564\pi$
$80$	−0.667760	−0.0746579
$81$	27.3079	3.03421
$82$	5.05702	0.558454
$83$	−2.65729	−0.291676	−0.145838	−	0.989309i	$-0.546588\pi$
$83$	−2.65729	−0.291676	−0.145838	+	0.989309i	$0.546588\pi$
$84$	12.4322	1.35646
$85$	−4.23905	−0.459789
$86$	−1.11601	−0.120342
$87$	−27.7579	−2.97596
$88$	4.80896	0.512637
$89$	1.28123	0.135811	0.0679053	−	0.997692i	$-0.478368\pi$
$89$	1.28123	0.135811	0.0679053	+	0.997692i	$0.478368\pi$
$90$	−5.14810	−0.542657
$91$	−12.2751	−1.28678
$92$	8.46768	0.882816
$93$	−12.3631	−1.28199
$94$	−9.40610	−0.970165
$95$	−4.00104	−0.410498
$96$	−3.27254	−0.334002
$97$	−4.57141	−0.464156	−0.232078	−	0.972697i	$-0.574552\pi$
$97$	−4.57141	−0.464156	−0.232078	+	0.972697i	$0.574552\pi$
$98$	7.43201	0.750746
$99$	37.0747	3.72614
$100$	−4.55410	−0.455410
$101$	−12.0643	−1.20044	−0.600220	−	0.799835i	$-0.704920\pi$
$101$	−12.0643	−1.20044	−0.600220	+	0.799835i	$0.704920\pi$
$102$	−20.7746	−2.05699
$103$	14.8401	1.46224	0.731121	−	0.682247i	$-0.238997\pi$
$103$	14.8401	1.46224	0.731121	+	0.682247i	$0.238997\pi$
$104$	3.23119	0.316844
$105$	−8.30173	−0.810166
$106$	0.645485	0.0626951
$107$	−20.0740	−1.94062	−0.970312	−	0.241858i	$-0.922243\pi$
$107$	−20.0740	−1.94062	−0.970312	+	0.241858i	$0.922243\pi$
$108$	−15.4120	−1.48302
$109$	15.5426	1.48871	0.744357	−	0.667781i	$-0.232756\pi$
$109$	15.5426	1.48871	0.744357	+	0.667781i	$0.232756\pi$
$110$	−3.21123	−0.306179
$111$	12.5672	1.19283
$112$	−3.79895	−0.358967
$113$	5.20127	0.489294	0.244647	−	0.969612i	$-0.421328\pi$
$113$	5.20127	0.489294	0.244647	+	0.969612i	$0.421328\pi$
$114$	−19.6082	−1.83647
$115$	−5.65438	−0.527273
$116$	8.48209	0.787542
$117$	24.9109	2.30301
$118$	14.7049	1.35369
$119$	−24.1163	−2.21074
$120$	2.18527	0.199487
$121$	12.1261	1.10237
$122$	11.6292	1.05286
$123$	−16.5493	−1.49220
$124$	3.77783	0.339259
$125$	6.37985	0.570631
$126$	−29.2880	−2.60918
$127$	17.3493	1.53950	0.769750	−	0.638346i	$-0.220381\pi$
$127$	17.3493	1.53950	0.769750	+	0.638346i	$0.220381\pi$
$128$	1.00000	0.0883883
$129$	3.65218	0.321556
$130$	−2.15766	−0.189239
$131$	−5.37860	−0.469930	−0.234965	−	0.972004i	$-0.575498\pi$
$131$	−5.37860	−0.469930	−0.234965	+	0.972004i	$0.575498\pi$
$132$	−15.7375	−1.36977
$133$	−22.7623	−1.97374
$134$	−3.44187	−0.297332
$135$	10.2915	0.885754
$136$	6.34816	0.544350
$137$	2.60962	0.222955	0.111478	−	0.993767i	$-0.464442\pi$
$137$	2.60962	0.222955	0.111478	+	0.993767i	$0.464442\pi$
$138$	−27.7108	−2.35890
$139$	6.36234	0.539647	0.269823	−	0.962910i	$-0.413035\pi$
$139$	6.36234	0.539647	0.269823	+	0.962910i	$0.413035\pi$
$140$	2.53679	0.214398
$141$	30.7818	2.59230
$142$	−11.4094	−0.957454
$143$	15.5387	1.29941
$144$	7.70950	0.642458
$145$	−5.66400	−0.470370
$146$	0.419609	0.0347271
$147$	−24.3215	−2.00600
$148$	−3.84020	−0.315663
$149$	12.6023	1.03242	0.516211	−	0.856461i	$-0.327342\pi$
$149$	12.6023	1.03242	0.516211	+	0.856461i	$0.327342\pi$
$150$	14.9034	1.21686
$151$	−19.0252	−1.54825	−0.774124	−	0.633035i	$-0.781809\pi$
$151$	−19.0252	−1.54825	−0.774124	+	0.633035i	$0.781809\pi$
$152$	5.99173	0.485993
$153$	48.9411	3.95666
$154$	−18.2690	−1.47216
$155$	−2.52268	−0.202627
$156$	−10.5742	−0.846613
$157$	12.0659	0.962962	0.481481	−	0.876457i	$-0.340099\pi$
$157$	12.0659	0.962962	0.481481	+	0.876457i	$0.340099\pi$
$158$	−5.84063	−0.464656
$159$	−2.11238	−0.167522
$160$	−0.667760	−0.0527911
$161$	−32.1683	−2.53521
$162$	27.3079	2.14551
$163$	10.1260	0.793129	0.396564	−	0.918007i	$-0.370202\pi$
$163$	10.1260	0.793129	0.396564	+	0.918007i	$0.370202\pi$
$164$	5.05702	0.394887
$165$	10.5089	0.818115
$166$	−2.65729	−0.206246
$167$	18.7718	1.45261	0.726304	−	0.687373i	$-0.241236\pi$
$167$	18.7718	1.45261	0.726304	+	0.687373i	$0.241236\pi$
$168$	12.4322	0.959165
$169$	−2.55941	−0.196878
$170$	−4.23905	−0.325120
$171$	46.1932	3.53249
$172$	−1.11601	−0.0850948
$173$	−10.8651	−0.826061	−0.413030	−	0.910717i	$-0.635530\pi$
$173$	−10.8651	−0.826061	−0.413030	+	0.910717i	$0.635530\pi$
$174$	−27.7579	−2.10432
$175$	17.3008	1.30782
$176$	4.80896	0.362489
$177$	−48.1222	−3.61709
$178$	1.28123	0.0960326
$179$	−15.4889	−1.15769	−0.578847	−	0.815436i	$-0.696497\pi$
$179$	−15.4889	−1.15769	−0.578847	+	0.815436i	$0.696497\pi$
$180$	−5.14810	−0.383717
$181$	9.61659	0.714795	0.357398	−	0.933952i	$-0.383664\pi$
$181$	9.61659	0.714795	0.357398	+	0.933952i	$0.383664\pi$
$182$	−12.2751	−0.909893
$183$	−38.0571	−2.81326
$184$	8.46768	0.624245
$185$	2.56434	0.188534
$186$	−12.3631	−0.906505
$187$	30.5280	2.23243
$188$	−9.40610	−0.686010
$189$	58.5494	4.25885
$190$	−4.00104	−0.290266
$191$	−13.2091	−0.955776	−0.477888	−	0.878421i	$-0.658598\pi$
$191$	−13.2091	−0.955776	−0.477888	+	0.878421i	$0.658598\pi$
$192$	−3.27254	−0.236175
$193$	−6.10556	−0.439488	−0.219744	−	0.975558i	$-0.570522\pi$
$193$	−6.10556	−0.439488	−0.219744	+	0.975558i	$0.570522\pi$
$194$	−4.57141	−0.328208
$195$	7.06102	0.505650
$196$	7.43201	0.530858
$197$	−5.03868	−0.358991	−0.179495	−	0.983759i	$-0.557447\pi$
$197$	−5.03868	−0.358991	−0.179495	+	0.983759i	$0.557447\pi$
$198$	37.0747	2.63478
$199$	−23.6408	−1.67585	−0.837927	−	0.545783i	$-0.816232\pi$
$199$	−23.6408	−1.67585	−0.837927	+	0.545783i	$0.816232\pi$
$200$	−4.55410	−0.322023
$201$	11.2636	0.794476
$202$	−12.0643	−0.848839
$203$	−32.2230	−2.26161
$204$	−20.7746	−1.45451
$205$	−3.37688	−0.235851
$206$	14.8401	1.03396
$207$	65.2815	4.53738
$208$	3.23119	0.224043
$209$	28.8140	1.99310
$210$	−8.30173	−0.572874
$211$	−22.7901	−1.56894	−0.784469	−	0.620168i	$-0.787064\pi$
$211$	−22.7901	−1.56894	−0.784469	+	0.620168i	$0.787064\pi$
$212$	0.645485	0.0443321
$213$	37.3376	2.55833
$214$	−20.0740	−1.37223
$215$	0.745225	0.0508239
$216$	−15.4120	−1.04865
$217$	−14.3518	−0.974262
$218$	15.5426	1.05268
$219$	−1.37319	−0.0927914
$220$	−3.21123	−0.216501
$221$	20.5121	1.37979
$222$	12.5672	0.843456
$223$	12.1585	0.814196	0.407098	−	0.913384i	$-0.366541\pi$
$223$	12.1585	0.814196	0.407098	+	0.913384i	$0.366541\pi$
$224$	−3.79895	−0.253828
$225$	−35.1098	−2.34065
$226$	5.20127	0.345983
$227$	−18.6243	−1.23614	−0.618069	−	0.786124i	$-0.712085\pi$
$227$	−18.6243	−1.23614	−0.618069	+	0.786124i	$0.712085\pi$
$228$	−19.6082	−1.29858
$229$	26.4354	1.74690	0.873452	−	0.486911i	$-0.161876\pi$
$229$	26.4354	1.74690	0.873452	+	0.486911i	$0.161876\pi$
$230$	−5.65438	−0.372839
$231$	59.7859	3.93363
$232$	8.48209	0.556876
$233$	−19.5055	−1.27785	−0.638925	−	0.769269i	$-0.720621\pi$
$233$	−19.5055	−1.27785	−0.638925	+	0.769269i	$0.720621\pi$
$234$	24.9109	1.62847
$235$	6.28102	0.409728
$236$	14.7049	0.957205
$237$	19.1137	1.24157
$238$	−24.1163	−1.56323
$239$	−17.3070	−1.11950	−0.559748	−	0.828663i	$-0.689102\pi$
$239$	−17.3070	−1.11950	−0.559748	+	0.828663i	$0.689102\pi$
$240$	2.18527	0.141059
$241$	17.2294	1.10984	0.554922	−	0.831902i	$-0.312748\pi$
$241$	17.2294	1.10984	0.554922	+	0.831902i	$0.312748\pi$
$242$	12.1261	0.779494
$243$	−43.1301	−2.76679
$244$	11.6292	0.744486
$245$	−4.96280	−0.317062
$246$	−16.5493	−1.05514
$247$	19.3604	1.23187
$248$	3.77783	0.239892
$249$	8.69609	0.551092
$250$	6.37985	0.403497
$251$	16.0934	1.01581	0.507903	−	0.861414i	$-0.330421\pi$
$251$	16.0934	1.01581	0.507903	+	0.861414i	$0.330421\pi$
$252$	−29.2880	−1.84497
$253$	40.7207	2.56009
$254$	17.3493	1.08859
$255$	13.8724	0.868726
$256$	1.00000	0.0625000
$257$	11.4524	0.714379	0.357190	−	0.934032i	$-0.383735\pi$
$257$	11.4524	0.714379	0.357190	+	0.934032i	$0.383735\pi$
$258$	3.65218	0.227375
$259$	14.5887	0.906500
$260$	−2.15766	−0.133812
$261$	65.3926	4.04770
$262$	−5.37860	−0.332291
$263$	−13.7320	−0.846750	−0.423375	−	0.905955i	$-0.639155\pi$
$263$	−13.7320	−0.846750	−0.423375	+	0.905955i	$0.639155\pi$
$264$	−15.7375	−0.968576
$265$	−0.431030	−0.0264779
$266$	−22.7623	−1.39564
$267$	−4.19289	−0.256600
$268$	−3.44187	−0.210246
$269$	−11.2478	−0.685792	−0.342896	−	0.939373i	$-0.611408\pi$
$269$	−11.2478	−0.685792	−0.342896	+	0.939373i	$0.611408\pi$
$270$	10.2915	0.626323
$271$	5.84501	0.355059	0.177530	−	0.984115i	$-0.443189\pi$
$271$	5.84501	0.355059	0.177530	+	0.984115i	$0.443189\pi$
$272$	6.34816	0.384914
$273$	40.1708	2.43125
$274$	2.60962	0.157653
$275$	−21.9005	−1.32065
$276$	−27.7108	−1.66799
$277$	2.01383	0.121000	0.0604998	−	0.998168i	$-0.480731\pi$
$277$	2.01383	0.121000	0.0604998	+	0.998168i	$0.480731\pi$
$278$	6.36234	0.381588
$279$	29.1252	1.74368
$280$	2.53679	0.151602
$281$	−0.612156	−0.0365181	−0.0182591	−	0.999833i	$-0.505812\pi$
$281$	−0.612156	−0.0365181	−0.0182591	+	0.999833i	$0.505812\pi$
$282$	30.7818	1.83303
$283$	23.6658	1.40679	0.703393	−	0.710801i	$-0.251668\pi$
$283$	23.6658	1.40679	0.703393	+	0.710801i	$0.251668\pi$
$284$	−11.4094	−0.677022
$285$	13.0935	0.775595
$286$	15.5387	0.918820
$287$	−19.2114	−1.13401
$288$	7.70950	0.454287
$289$	23.2991	1.37054
$290$	−5.66400	−0.332602
$291$	14.9601	0.876977
$292$	0.419609	0.0245558
$293$	25.8978	1.51297	0.756484	−	0.654013i	$-0.226916\pi$
$293$	25.8978	1.51297	0.756484	+	0.654013i	$0.226916\pi$
$294$	−24.3215	−1.41846
$295$	−9.81932	−0.571703
$296$	−3.84020	−0.223207
$297$	−74.1158	−4.30063
$298$	12.6023	0.730033
$299$	27.3607	1.58231
$300$	14.9034	0.860451
$301$	4.23965	0.244370
$302$	−19.0252	−1.09478
$303$	39.4808	2.26811
$304$	5.99173	0.343649
$305$	−7.76554	−0.444654
$306$	48.9411	2.79778
$307$	−29.6424	−1.69178	−0.845891	−	0.533356i	$-0.820931\pi$
$307$	−29.6424	−1.69178	−0.845891	+	0.533356i	$0.820931\pi$
$308$	−18.2690	−1.04097
$309$	−48.5649	−2.76276
$310$	−2.52268	−0.143279
$311$	11.6194	0.658878	0.329439	−	0.944177i	$-0.393140\pi$
$311$	11.6194	0.658878	0.329439	+	0.944177i	$0.393140\pi$
$312$	−10.5742	−0.598646
$313$	−9.38993	−0.530750	−0.265375	−	0.964145i	$-0.585496\pi$
$313$	−9.38993	−0.530750	−0.265375	+	0.964145i	$0.585496\pi$
$314$	12.0659	0.680917
$315$	19.5574	1.10193
$316$	−5.84063	−0.328561
$317$	−28.7679	−1.61577	−0.807884	−	0.589342i	$-0.799387\pi$
$317$	−28.7679	−1.61577	−0.807884	+	0.589342i	$0.799387\pi$
$318$	−2.11238	−0.118456
$319$	40.7900	2.28380
$320$	−0.667760	−0.0373289
$321$	65.6928	3.66661
$322$	−32.1683	−1.79267
$323$	38.0365	2.11641
$324$	27.3079	1.51711
$325$	−14.7151	−0.816250
$326$	10.1260	0.560827
$327$	−50.8639	−2.81278
$328$	5.05702	0.279227
$329$	35.7333	1.97004
$330$	10.5089	0.578495
$331$	−6.90949	−0.379780	−0.189890	−	0.981805i	$-0.560813\pi$
$331$	−6.90949	−0.379780	−0.189890	+	0.981805i	$0.560813\pi$
$332$	−2.65729	−0.145838
$333$	−29.6060	−1.62240
$334$	18.7718	1.02715
$335$	2.29834	0.125572
$336$	12.4322	0.678232
$337$	7.86453	0.428408	0.214204	−	0.976789i	$-0.431284\pi$
$337$	7.86453	0.428408	0.214204	+	0.976789i	$0.431284\pi$
$338$	−2.55941	−0.139214
$339$	−17.0213	−0.924473
$340$	−4.23905	−0.229895
$341$	18.1674	0.983821
$342$	46.1932	2.49784
$343$	−1.64117	−0.0886147
$344$	−1.11601	−0.0601711
$345$	18.5042	0.996230
$346$	−10.8651	−0.584113
$347$	−23.1991	−1.24539	−0.622696	−	0.782464i	$-0.713963\pi$
$347$	−23.1991	−1.24539	−0.622696	+	0.782464i	$0.713963\pi$
$348$	−27.7579	−1.48798
$349$	−23.6477	−1.26583	−0.632915	−	0.774221i	$-0.718142\pi$
$349$	−23.6477	−1.26583	−0.632915	+	0.774221i	$0.718142\pi$
$350$	17.3008	0.924765
$351$	−49.7991	−2.65808
$352$	4.80896	0.256318
$353$	−9.16693	−0.487907	−0.243953	−	0.969787i	$-0.578444\pi$
$353$	−9.16693	−0.487907	−0.243953	+	0.969787i	$0.578444\pi$
$354$	−48.1222	−2.55767
$355$	7.61873	0.404360
$356$	1.28123	0.0679053
$357$	78.9216	4.17697
$358$	−15.4889	−0.818614
$359$	24.8324	1.31061	0.655303	−	0.755366i	$-0.272541\pi$
$359$	24.8324	1.31061	0.655303	+	0.755366i	$0.272541\pi$
$360$	−5.14810	−0.271329
$361$	16.9008	0.889517
$362$	9.61659	0.505436
$363$	−39.6831	−2.08282
$364$	−12.2751	−0.643391
$365$	−0.280198	−0.0146663
$366$	−38.0571	−1.98928
$367$	−33.2978	−1.73813	−0.869067	−	0.494695i	$-0.835280\pi$
$367$	−33.2978	−1.73813	−0.869067	+	0.494695i	$0.835280\pi$
$368$	8.46768	0.441408
$369$	38.9871	2.02959
$370$	2.56434	0.133313
$371$	−2.45217	−0.127310
$372$	−12.3631	−0.640996
$373$	−19.3511	−1.00196	−0.500981	−	0.865458i	$-0.667027\pi$
$373$	−19.3511	−1.00196	−0.500981	+	0.865458i	$0.667027\pi$
$374$	30.5280	1.57857
$375$	−20.8783	−1.07815
$376$	−9.40610	−0.485082
$377$	27.4072	1.41154
$378$	58.5494	3.01146
$379$	−3.35265	−0.172214	−0.0861070	−	0.996286i	$-0.527443\pi$
$379$	−3.35265	−0.172214	−0.0861070	+	0.996286i	$0.527443\pi$
$380$	−4.00104	−0.205249
$381$	−56.7762	−2.90873
$382$	−13.2091	−0.675836
$383$	10.5090	0.536987	0.268493	−	0.963282i	$-0.413474\pi$
$383$	10.5090	0.536987	0.268493	+	0.963282i	$0.413474\pi$
$384$	−3.27254	−0.167001
$385$	12.1993	0.621734
$386$	−6.10556	−0.310765
$387$	−8.60386	−0.437359
$388$	−4.57141	−0.232078
$389$	2.50279	0.126897	0.0634483	−	0.997985i	$-0.479790\pi$
$389$	2.50279	0.126897	0.0634483	+	0.997985i	$0.479790\pi$
$390$	7.06102	0.357549
$391$	53.7542	2.71846
$392$	7.43201	0.375373
$393$	17.6017	0.887886
$394$	−5.03868	−0.253845
$395$	3.90014	0.196237
$396$	37.0747	1.86307
$397$	−19.1629	−0.961759	−0.480879	−	0.876787i	$-0.659683\pi$
$397$	−19.1629	−0.961759	−0.480879	+	0.876787i	$0.659683\pi$
$398$	−23.6408	−1.18501
$399$	74.4904	3.72918
$400$	−4.55410	−0.227705
$401$	−20.2868	−1.01308	−0.506538	−	0.862218i	$-0.669075\pi$
$401$	−20.2868	−1.01308	−0.506538	+	0.862218i	$0.669075\pi$
$402$	11.2636	0.561779
$403$	12.2069	0.608068
$404$	−12.0643	−0.600220
$405$	−18.2351	−0.906111
$406$	−32.2230	−1.59920
$407$	−18.4674	−0.915394
$408$	−20.7746	−1.02850
$409$	0.880267	0.0435264	0.0217632	−	0.999763i	$-0.493072\pi$
$409$	0.880267	0.0435264	0.0217632	+	0.999763i	$0.493072\pi$
$410$	−3.37688	−0.166772
$411$	−8.54009	−0.421252
$412$	14.8401	0.731121
$413$	−55.8630	−2.74884
$414$	65.2815	3.20841
$415$	1.77443	0.0871035
$416$	3.23119	0.158422
$417$	−20.8210	−1.01961
$418$	28.8140	1.40934
$419$	−30.0784	−1.46943	−0.734713	−	0.678378i	$-0.762683\pi$
$419$	−30.0784	−1.46943	−0.734713	+	0.678378i	$0.762683\pi$
$420$	−8.30173	−0.405083
$421$	−15.7736	−0.768760	−0.384380	−	0.923175i	$-0.625585\pi$
$421$	−15.7736	−0.768760	−0.384380	+	0.923175i	$0.625585\pi$
$422$	−22.7901	−1.10941
$423$	−72.5163	−3.52586
$424$	0.645485	0.0313475
$425$	−28.9101	−1.40235
$426$	37.3376	1.80901
$427$	−44.1789	−2.13797
$428$	−20.0740	−0.970312
$429$	−50.8508	−2.45510
$430$	0.745225	0.0359380
$431$	27.0422	1.30258	0.651289	−	0.758830i	$-0.274228\pi$
$431$	27.0422	1.30258	0.651289	+	0.758830i	$0.274228\pi$
$432$	−15.4120	−0.741511
$433$	14.6612	0.704574	0.352287	−	0.935892i	$-0.385404\pi$
$433$	14.6612	0.704574	0.352287	+	0.935892i	$0.385404\pi$
$434$	−14.3518	−0.688907
$435$	18.5357	0.888716
$436$	15.5426	0.744357
$437$	50.7360	2.42703
$438$	−1.37319	−0.0656134
$439$	−29.9967	−1.43166	−0.715831	−	0.698273i	$-0.753952\pi$
$439$	−29.9967	−1.43166	−0.715831	+	0.698273i	$0.753952\pi$
$440$	−3.21123	−0.153089
$441$	57.2971	2.72843
$442$	20.5121	0.975662
$443$	−0.128286	−0.00609505	−0.00304753	−	0.999995i	$-0.500970\pi$
$443$	−0.128286	−0.00609505	−0.00304753	+	0.999995i	$0.500970\pi$
$444$	12.5672	0.596413
$445$	−0.855557	−0.0405573
$446$	12.1585	0.575724
$447$	−41.2415	−1.95066
$448$	−3.79895	−0.179483
$449$	−13.5017	−0.637186	−0.318593	−	0.947892i	$-0.603210\pi$
$449$	−13.5017	−0.637186	−0.318593	+	0.947892i	$0.603210\pi$
$450$	−35.1098	−1.65509
$451$	24.3190	1.14514
$452$	5.20127	0.244647
$453$	62.2606	2.92526
$454$	−18.6243	−0.874082
$455$	8.19684	0.384274
$456$	−19.6082	−0.918236
$457$	24.5376	1.14782	0.573911	−	0.818918i	$-0.305425\pi$
$457$	24.5376	1.14782	0.573911	+	0.818918i	$0.305425\pi$
$458$	26.4354	1.23525
$459$	−97.8379	−4.56668
$460$	−5.65438	−0.263637
$461$	9.72513	0.452944	0.226472	−	0.974018i	$-0.427281\pi$
$461$	9.72513	0.452944	0.226472	+	0.974018i	$0.427281\pi$
$462$	59.7859	2.78149
$463$	−19.9671	−0.927948	−0.463974	−	0.885849i	$-0.653577\pi$
$463$	−19.9671	−0.927948	−0.463974	+	0.885849i	$0.653577\pi$
$464$	8.48209	0.393771
$465$	8.25558	0.382843
$466$	−19.5055	−0.903577
$467$	9.95812	0.460807	0.230404	−	0.973095i	$-0.425995\pi$
$467$	9.95812	0.460807	0.230404	+	0.973095i	$0.425995\pi$
$468$	24.9109	1.15150
$469$	13.0755	0.603770
$470$	6.28102	0.289722
$471$	−39.4860	−1.81942
$472$	14.7049	0.676846
$473$	−5.36683	−0.246767
$474$	19.1137	0.877920
$475$	−27.2869	−1.25201
$476$	−24.1163	−1.10537
$477$	4.97637	0.227852
$478$	−17.3070	−0.791603
$479$	8.00644	0.365823	0.182912	−	0.983129i	$-0.441448\pi$
$479$	8.00644	0.365823	0.182912	+	0.983129i	$0.441448\pi$
$480$	2.18527	0.0997435
$481$	−12.4084	−0.565775
$482$	17.2294	0.784779
$483$	105.272	4.79003
$484$	12.1261	0.551186
$485$	3.05260	0.138612
$486$	−43.1301	−1.95642
$487$	−7.92502	−0.359117	−0.179559	−	0.983747i	$-0.557467\pi$
$487$	−7.92502	−0.359117	−0.179559	+	0.983747i	$0.557467\pi$
$488$	11.6292	0.526431
$489$	−33.1377	−1.49854
$490$	−4.96280	−0.224196
$491$	20.2865	0.915519	0.457759	−	0.889076i	$-0.348652\pi$
$491$	20.2865	0.915519	0.457759	+	0.889076i	$0.348652\pi$
$492$	−16.5493	−0.746099
$493$	53.8456	2.42509
$494$	19.3604	0.871066
$495$	−24.7570	−1.11274
$496$	3.77783	0.169630
$497$	43.3436	1.94423
$498$	8.69609	0.389681
$499$	−14.7364	−0.659693	−0.329846	−	0.944035i	$-0.606997\pi$
$499$	−14.7364	−0.659693	−0.329846	+	0.944035i	$0.606997\pi$
$500$	6.37985	0.285315
$501$	−61.4316	−2.74456
$502$	16.0934	0.718283
$503$	−15.1178	−0.674071	−0.337036	−	0.941492i	$-0.609424\pi$
$503$	−15.1178	−0.674071	−0.337036	+	0.941492i	$0.609424\pi$
$504$	−29.2880	−1.30459
$505$	8.05604	0.358489
$506$	40.7207	1.81026
$507$	8.37578	0.371981
$508$	17.3493	0.769750
$509$	−4.85205	−0.215063	−0.107532	−	0.994202i	$-0.534295\pi$
$509$	−4.85205	−0.215063	−0.107532	+	0.994202i	$0.534295\pi$
$510$	13.8724	0.614282
$511$	−1.59407	−0.0705177
$512$	1.00000	0.0441942
$513$	−92.3446	−4.07711
$514$	11.4524	0.505142
$515$	−9.90966	−0.436672
$516$	3.65218	0.160778
$517$	−45.2335	−1.98937
$518$	14.5887	0.640992
$519$	35.5565	1.56076
$520$	−2.15766	−0.0946197
$521$	−3.33949	−0.146306	−0.0731529	−	0.997321i	$-0.523306\pi$
$521$	−3.33949	−0.146306	−0.0731529	+	0.997321i	$0.523306\pi$
$522$	65.3926	2.86216
$523$	−17.9858	−0.786464	−0.393232	−	0.919439i	$-0.628643\pi$
$523$	−17.9858	−0.786464	−0.393232	+	0.919439i	$0.628643\pi$
$524$	−5.37860	−0.234965
$525$	−56.6174	−2.47099
$526$	−13.7320	−0.598742
$527$	23.9823	1.04468
$528$	−15.7375	−0.684887
$529$	48.7015	2.11746
$530$	−0.431030	−0.0187227
$531$	113.367	4.91971
$532$	−22.7623	−0.986869
$533$	16.3402	0.707772
$534$	−4.19289	−0.181444
$535$	13.4046	0.579531
$536$	−3.44187	−0.148666
$537$	50.6880	2.18735
$538$	−11.2478	−0.484928
$539$	35.7402	1.53944
$540$	10.2915	0.442877
$541$	45.6402	1.96223	0.981113	−	0.193435i	$-0.0619628\pi$
$541$	45.6402	1.96223	0.981113	+	0.193435i	$0.0619628\pi$
$542$	5.84501	0.251065
$543$	−31.4706	−1.35053
$544$	6.34816	0.272175
$545$	−10.3788	−0.444577
$546$	40.1708	1.71915
$547$	−11.8915	−0.508446	−0.254223	−	0.967146i	$-0.581820\pi$
$547$	−11.8915	−0.508446	−0.254223	+	0.967146i	$0.581820\pi$
$548$	2.60962	0.111478
$549$	89.6556	3.82641
$550$	−21.9005	−0.933839
$551$	50.8224	2.16511
$552$	−27.7108	−1.17945
$553$	22.1882	0.943540
$554$	2.01383	0.0855596
$555$	−8.39188	−0.356216
$556$	6.36234	0.269823
$557$	−0.0825288	−0.00349686	−0.00174843	−	0.999998i	$-0.500557\pi$
$557$	−0.0825288	−0.00349686	−0.00174843	+	0.999998i	$0.500557\pi$
$558$	29.1252	1.23297
$559$	−3.60603	−0.152519
$560$	2.53679	0.107199
$561$	−99.9042	−4.21796
$562$	−0.612156	−0.0258222
$563$	17.8324	0.751545	0.375772	−	0.926712i	$-0.377377\pi$
$563$	17.8324	0.751545	0.375772	+	0.926712i	$0.377377\pi$
$564$	30.7818	1.29615
$565$	−3.47320	−0.146119
$566$	23.6658	0.994748
$567$	−103.741	−4.35672
$568$	−11.4094	−0.478727
$569$	26.1121	1.09468	0.547338	−	0.836912i	$-0.315641\pi$
$569$	26.1121	1.09468	0.547338	+	0.836912i	$0.315641\pi$
$570$	13.0935	0.548428
$571$	10.8738	0.455054	0.227527	−	0.973772i	$-0.426936\pi$
$571$	10.8738	0.455054	0.227527	+	0.973772i	$0.426936\pi$
$572$	15.5387	0.649704
$573$	43.2272	1.80584
$574$	−19.2114	−0.801866
$575$	−38.5626	−1.60817
$576$	7.70950	0.321229
$577$	−5.25472	−0.218757	−0.109378	−	0.994000i	$-0.534886\pi$
$577$	−5.25472	−0.218757	−0.109378	+	0.994000i	$0.534886\pi$
$578$	23.2991	0.969116
$579$	19.9807	0.830368
$580$	−5.66400	−0.235185
$581$	10.0949	0.418808
$582$	14.9601	0.620116
$583$	3.10411	0.128559
$584$	0.419609	0.0173636
$585$	−16.6345	−0.687751
$586$	25.8978	1.06983
$587$	−21.4026	−0.883378	−0.441689	−	0.897168i	$-0.645621\pi$
$587$	−21.4026	−0.883378	−0.441689	+	0.897168i	$0.645621\pi$
$588$	−24.3215	−1.00300
$589$	22.6357	0.932689
$590$	−9.81932	−0.404255
$591$	16.4893	0.678277
$592$	−3.84020	−0.157831
$593$	−2.67168	−0.109713	−0.0548563	−	0.998494i	$-0.517470\pi$
$593$	−2.67168	−0.109713	−0.0548563	+	0.998494i	$0.517470\pi$
$594$	−74.1158	−3.04101
$595$	16.1039	0.660197
$596$	12.6023	0.516211
$597$	77.3655	3.16636
$598$	27.3607	1.11886
$599$	19.6414	0.802526	0.401263	−	0.915963i	$-0.368571\pi$
$599$	19.6414	0.802526	0.401263	+	0.915963i	$0.368571\pi$
$600$	14.9034	0.608431
$601$	−42.8599	−1.74829	−0.874145	−	0.485665i	$-0.838577\pi$
$601$	−42.8599	−1.74829	−0.874145	+	0.485665i	$0.838577\pi$
$602$	4.23965	0.172795
$603$	−26.5351	−1.08059
$604$	−19.0252	−0.774124
$605$	−8.09732	−0.329203
$606$	39.4808	1.60380
$607$	−12.4150	−0.503911	−0.251955	−	0.967739i	$-0.581074\pi$
$607$	−12.4150	−0.503911	−0.251955	+	0.967739i	$0.581074\pi$
$608$	5.99173	0.242997
$609$	105.451	4.27309
$610$	−7.76554	−0.314418
$611$	−30.3929	−1.22956
$612$	48.9411	1.97833
$613$	−15.5298	−0.627243	−0.313622	−	0.949548i	$-0.601542\pi$
$613$	−15.5298	−0.627243	−0.313622	+	0.949548i	$0.601542\pi$
$614$	−29.6424	−1.19627
$615$	11.0510	0.445617
$616$	−18.2690	−0.736078
$617$	−31.1212	−1.25289	−0.626445	−	0.779465i	$-0.715491\pi$
$617$	−31.1212	−1.25289	−0.626445	+	0.779465i	$0.715491\pi$
$618$	−48.5649	−1.95357
$619$	25.9404	1.04263	0.521317	−	0.853363i	$-0.325441\pi$
$619$	25.9404	1.04263	0.521317	+	0.853363i	$0.325441\pi$
$620$	−2.52268	−0.101313
$621$	−130.504	−5.23694
$622$	11.6194	0.465897
$623$	−4.86734	−0.195006
$624$	−10.5742	−0.423306
$625$	18.5103	0.740411
$626$	−9.38993	−0.375297
$627$	−94.2948	−3.76577
$628$	12.0659	0.481481
$629$	−24.3782	−0.972024
$630$	19.5574	0.779184
$631$	−39.7380	−1.58195	−0.790973	−	0.611851i	$-0.790425\pi$
$631$	−39.7380	−1.58195	−0.790973	+	0.611851i	$0.790425\pi$
$632$	−5.84063	−0.232328
$633$	74.5816	2.96435
$634$	−28.7679	−1.14252
$635$	−11.5852	−0.459743
$636$	−2.11238	−0.0837611
$637$	24.0142	0.951478
$638$	40.7900	1.61489
$639$	−87.9606	−3.47967
$640$	−0.667760	−0.0263955
$641$	−33.7761	−1.33407	−0.667037	−	0.745025i	$-0.732438\pi$
$641$	−33.7761	−1.33407	−0.667037	+	0.745025i	$0.732438\pi$
$642$	65.6928	2.59269
$643$	16.4438	0.648481	0.324240	−	0.945975i	$-0.394891\pi$
$643$	16.4438	0.648481	0.324240	+	0.945975i	$0.394891\pi$
$644$	−32.1683	−1.26761
$645$	−2.43878	−0.0960268
$646$	38.0365	1.49652
$647$	7.42788	0.292020	0.146010	−	0.989283i	$-0.453357\pi$
$647$	7.42788	0.292020	0.146010	+	0.989283i	$0.453357\pi$
$648$	27.3079	1.07276
$649$	70.7151	2.77581
$650$	−14.7151	−0.577176
$651$	46.9667	1.84077
$652$	10.1260	0.396564
$653$	38.8234	1.51928	0.759638	−	0.650346i	$-0.225376\pi$
$653$	38.8234	1.51928	0.759638	+	0.650346i	$0.225376\pi$
$654$	−50.8639	−1.98893
$655$	3.59161	0.140336
$656$	5.05702	0.197443
$657$	3.23498	0.126209
$658$	35.7333	1.39303
$659$	−7.06168	−0.275084	−0.137542	−	0.990496i	$-0.543920\pi$
$659$	−7.06168	−0.275084	−0.137542	+	0.990496i	$0.543920\pi$
$660$	10.5089	0.409057
$661$	−36.2420	−1.40965	−0.704824	−	0.709382i	$-0.748974\pi$
$661$	−36.2420	−1.40965	−0.704824	+	0.709382i	$0.748974\pi$
$662$	−6.90949	−0.268545
$663$	−67.1266	−2.60698
$664$	−2.65729	−0.103123
$665$	15.1997	0.589421
$666$	−29.6060	−1.14721
$667$	71.8235	2.78102
$668$	18.7718	0.726304
$669$	−39.7893	−1.53834
$670$	2.29834	0.0887927
$671$	55.9245	2.15894
$672$	12.4322	0.479582
$673$	33.4889	1.29090	0.645452	−	0.763801i	$-0.276669\pi$
$673$	33.4889	1.29090	0.645452	+	0.763801i	$0.276669\pi$
$674$	7.86453	0.302930
$675$	70.1878	2.70153
$676$	−2.55941	−0.0984390
$677$	−17.1853	−0.660483	−0.330242	−	0.943896i	$-0.607130\pi$
$677$	−17.1853	−0.660483	−0.330242	+	0.943896i	$0.607130\pi$
$678$	−17.0213	−0.653701
$679$	17.3665	0.666467
$680$	−4.23905	−0.162560
$681$	60.9487	2.33556
$682$	18.1674	0.695667
$683$	22.9138	0.876771	0.438385	−	0.898787i	$-0.355551\pi$
$683$	22.9138	0.876771	0.438385	+	0.898787i	$0.355551\pi$
$684$	46.1932	1.76624
$685$	−1.74260	−0.0665814
$686$	−1.64117	−0.0626601
$687$	−86.5110	−3.30060
$688$	−1.11601	−0.0425474
$689$	2.08569	0.0794583
$690$	18.5042	0.704441
$691$	43.3761	1.65011	0.825053	−	0.565055i	$-0.191145\pi$
$691$	43.3761	1.65011	0.825053	+	0.565055i	$0.191145\pi$
$692$	−10.8651	−0.413030
$693$	−140.845	−5.35025
$694$	−23.1991	−0.880625
$695$	−4.24852	−0.161155
$696$	−27.7579	−1.05216
$697$	32.1028	1.21598
$698$	−23.6477	−0.895078
$699$	63.8326	2.41437
$700$	17.3008	0.653908
$701$	18.7385	0.707742	0.353871	−	0.935294i	$-0.384865\pi$
$701$	18.7385	0.707742	0.353871	+	0.935294i	$0.384865\pi$
$702$	−49.7991	−1.87955
$703$	−23.0095	−0.867818
$704$	4.80896	0.181244
$705$	−20.5549	−0.774141
$706$	−9.16693	−0.345002
$707$	45.8315	1.72367
$708$	−48.1222	−1.80854
$709$	3.54361	0.133083	0.0665415	−	0.997784i	$-0.478804\pi$
$709$	3.54361	0.133083	0.0665415	+	0.997784i	$0.478804\pi$
$710$	7.61873	0.285926
$711$	−45.0283	−1.68869
$712$	1.28123	0.0480163
$713$	31.9894	1.19801
$714$	78.9216	2.95357
$715$	−10.3761	−0.388044
$716$	−15.4889	−0.578847
$717$	56.6377	2.11517
$718$	24.8324	0.926738
$719$	−13.2243	−0.493184	−0.246592	−	0.969119i	$-0.579311\pi$
$719$	−13.2243	−0.493184	−0.246592	+	0.969119i	$0.579311\pi$
$720$	−5.14810	−0.191858
$721$	−56.3769	−2.09959
$722$	16.9008	0.628983
$723$	−56.3839	−2.09694
$724$	9.61659	0.357398
$725$	−38.6282	−1.43462
$726$	−39.6831	−1.47278
$727$	15.5192	0.575575	0.287788	−	0.957694i	$-0.407080\pi$
$727$	15.5192	0.575575	0.287788	+	0.957694i	$0.407080\pi$
$728$	−12.2751	−0.454946
$729$	59.2210	2.19337
$730$	−0.280198	−0.0103706
$731$	−7.08459	−0.262033
$732$	−38.0571	−1.40663
$733$	3.19095	0.117860	0.0589302	−	0.998262i	$-0.481231\pi$
$733$	3.19095	0.117860	0.0589302	+	0.998262i	$0.481231\pi$
$734$	−33.2978	−1.22905
$735$	16.2409	0.599056
$736$	8.46768	0.312123
$737$	−16.5518	−0.609694
$738$	38.9871	1.43513
$739$	−13.1830	−0.484944	−0.242472	−	0.970158i	$-0.577958\pi$
$739$	−13.1830	−0.484944	−0.242472	+	0.970158i	$0.577958\pi$
$740$	2.56434	0.0942668
$741$	−63.3577	−2.32750
$742$	−2.45217	−0.0900218
$743$	31.3635	1.15062	0.575308	−	0.817937i	$-0.304882\pi$
$743$	31.3635	1.15062	0.575308	+	0.817937i	$0.304882\pi$
$744$	−12.3631	−0.453253
$745$	−8.41533	−0.308314
$746$	−19.3511	−0.708495
$747$	−20.4864	−0.749558
$748$	30.5280	1.11622
$749$	76.2600	2.78648
$750$	−20.8783	−0.762367
$751$	11.6080	0.423583	0.211791	−	0.977315i	$-0.432070\pi$
$751$	11.6080	0.423583	0.211791	+	0.977315i	$0.432070\pi$
$752$	−9.40610	−0.343005
$753$	−52.6662	−1.91926
$754$	27.4072	0.998112
$755$	12.7043	0.462355
$756$	58.5494	2.12942
$757$	16.2587	0.590931	0.295465	−	0.955353i	$-0.404525\pi$
$757$	16.2587	0.590931	0.295465	+	0.955353i	$0.404525\pi$
$758$	−3.35265	−0.121774
$759$	−133.260	−4.83703
$760$	−4.00104	−0.145133
$761$	34.9229	1.26596	0.632978	−	0.774170i	$-0.281832\pi$
$761$	34.9229	1.26596	0.632978	+	0.774170i	$0.281832\pi$
$762$	−56.7762	−2.05678
$763$	−59.0457	−2.13760
$764$	−13.2091	−0.477888
$765$	−32.6810	−1.18158
$766$	10.5090	0.379707
$767$	47.5142	1.71564
$768$	−3.27254	−0.118088
$769$	−15.7906	−0.569424	−0.284712	−	0.958613i	$-0.591898\pi$
$769$	−15.7906	−0.569424	−0.284712	+	0.958613i	$0.591898\pi$
$770$	12.1993	0.439632
$771$	−37.4783	−1.34975
$772$	−6.10556	−0.219744
$773$	36.0281	1.29584	0.647920	−	0.761708i	$-0.275639\pi$
$773$	36.0281	1.29584	0.647920	+	0.761708i	$0.275639\pi$
$774$	−8.60386	−0.309259
$775$	−17.2046	−0.618007
$776$	−4.57141	−0.164104
$777$	−47.7422	−1.71274
$778$	2.50279	0.0897295
$779$	30.3003	1.08562
$780$	7.06102	0.252825
$781$	−54.8672	−1.96330
$782$	53.7542	1.92224
$783$	−130.726	−4.67177
$784$	7.43201	0.265429
$785$	−8.05711	−0.287571
$786$	17.6017	0.627830
$787$	−45.4736	−1.62096	−0.810479	−	0.585767i	$-0.800793\pi$
$787$	−45.4736	−1.62096	−0.810479	+	0.585767i	$0.800793\pi$
$788$	−5.03868	−0.179495
$789$	44.9384	1.59985
$790$	3.90014	0.138761
$791$	−19.7594	−0.702562
$792$	37.0747	1.31739
$793$	37.5763	1.33437
$794$	−19.1629	−0.680066
$795$	1.41056	0.0500274
$796$	−23.6408	−0.837927
$797$	−8.19432	−0.290258	−0.145129	−	0.989413i	$-0.546360\pi$
$797$	−8.19432	−0.290258	−0.145129	+	0.989413i	$0.546360\pi$
$798$	74.4904	2.63693
$799$	−59.7114	−2.11244
$800$	−4.55410	−0.161012
$801$	9.87768	0.349010
$802$	−20.2868	−0.716353
$803$	2.01788	0.0712096
$804$	11.2636	0.397238
$805$	21.4807	0.757095
$806$	12.2069	0.429969
$807$	36.8089	1.29574
$808$	−12.0643	−0.424420
$809$	−25.0709	−0.881447	−0.440723	−	0.897643i	$-0.645278\pi$
$809$	−25.0709	−0.881447	−0.440723	+	0.897643i	$0.645278\pi$
$810$	−18.2351	−0.640717
$811$	12.8953	0.452814	0.226407	−	0.974033i	$-0.427302\pi$
$811$	12.8953	0.452814	0.226407	+	0.974033i	$0.427302\pi$
$812$	−32.2230	−1.13081
$813$	−19.1280	−0.670849
$814$	−18.4674	−0.647281
$815$	−6.76174	−0.236853
$816$	−20.7746	−0.727256
$817$	−6.68681	−0.233942
$818$	0.880267	0.0307778
$819$	−94.6351	−3.30682
$820$	−3.37688	−0.117926
$821$	12.5762	0.438913	0.219457	−	0.975622i	$-0.429572\pi$
$821$	12.5762	0.438913	0.219457	+	0.975622i	$0.429572\pi$
$822$	−8.54009	−0.297870
$823$	−14.7300	−0.513456	−0.256728	−	0.966484i	$-0.582645\pi$
$823$	−14.7300	−0.513456	−0.256728	+	0.966484i	$0.582645\pi$
$824$	14.8401	0.516981
$825$	71.6701	2.49523
$826$	−55.8630	−1.94372
$827$	−11.2773	−0.392150	−0.196075	−	0.980589i	$-0.562820\pi$
$827$	−11.2773	−0.392150	−0.196075	+	0.980589i	$0.562820\pi$
$828$	65.2815	2.26869
$829$	36.1342	1.25499	0.627497	−	0.778619i	$-0.284079\pi$
$829$	36.1342	1.25499	0.627497	+	0.778619i	$0.284079\pi$
$830$	1.77443	0.0615915
$831$	−6.59035	−0.228617
$832$	3.23119	0.112021
$833$	47.1796	1.63468
$834$	−20.8210	−0.720972
$835$	−12.5351	−0.433795
$836$	28.8140	0.996552
$837$	−58.2240	−2.01251
$838$	−30.0784	−1.03904
$839$	−42.4430	−1.46529	−0.732647	−	0.680609i	$-0.761715\pi$
$839$	−42.4430	−1.46529	−0.732647	+	0.680609i	$0.761715\pi$
$840$	−8.30173	−0.286437
$841$	42.9458	1.48089
$842$	−15.7736	−0.543596
$843$	2.00330	0.0689974
$844$	−22.7901	−0.784469
$845$	1.70907	0.0587940
$846$	−72.5163	−2.49316
$847$	−46.0664	−1.58286
$848$	0.645485	0.0221661
$849$	−77.4472	−2.65798
$850$	−28.9101	−0.991609
$851$	−32.5176	−1.11469
$852$	37.3376	1.27917
$853$	−46.6850	−1.59846	−0.799232	−	0.601023i	$-0.794760\pi$
$853$	−46.6850	−1.59846	−0.799232	+	0.601023i	$0.794760\pi$
$854$	−44.1789	−1.51177
$855$	−30.8460	−1.05491
$856$	−20.0740	−0.686114
$857$	39.4498	1.34758	0.673789	−	0.738923i	$-0.264665\pi$
$857$	39.4498	1.34758	0.673789	+	0.738923i	$0.264665\pi$
$858$	−50.8508	−1.73602
$859$	−39.7058	−1.35475	−0.677373	−	0.735640i	$-0.736882\pi$
$859$	−39.7058	−1.35475	−0.677373	+	0.735640i	$0.736882\pi$
$860$	0.745225	0.0254120
$861$	62.8699	2.14260
$862$	27.0422	0.921062
$863$	14.0701	0.478950	0.239475	−	0.970902i	$-0.423025\pi$
$863$	14.0701	0.478950	0.239475	+	0.970902i	$0.423025\pi$
$864$	−15.4120	−0.524327
$865$	7.25530	0.246688
$866$	14.6612	0.498209
$867$	−76.2473	−2.58949
$868$	−14.3518	−0.487131
$869$	−28.0873	−0.952798
$870$	18.5357	0.628417
$871$	−11.1213	−0.376832
$872$	15.5426	0.526340
$873$	−35.2433	−1.19280
$874$	50.7360	1.71617
$875$	−24.2367	−0.819350
$876$	−1.37319	−0.0463957
$877$	8.99196	0.303637	0.151818	−	0.988408i	$-0.451487\pi$
$877$	8.99196	0.303637	0.151818	+	0.988408i	$0.451487\pi$
$878$	−29.9967	−1.01234
$879$	−84.7516	−2.85860
$880$	−3.21123	−0.108251
$881$	0.165408	0.00557273	0.00278637	−	0.999996i	$-0.499113\pi$
$881$	0.165408	0.00557273	0.00278637	+	0.999996i	$0.499113\pi$
$882$	57.2971	1.92929
$883$	−0.0232673	−0.000783008 0	−0.000391504	−	1.00000i	$-0.500125\pi$
$883$	−0.0232673	−0.000783008 0	−0.000391504		1.00000i	$0.500125\pi$
$884$	20.5121	0.689897
$885$	32.1341	1.08018
$886$	−0.128286	−0.00430985
$887$	3.53896	0.118827	0.0594133	−	0.998233i	$-0.481077\pi$
$887$	3.53896	0.118827	0.0594133	+	0.998233i	$0.481077\pi$
$888$	12.5672	0.421728
$889$	−65.9090	−2.21052
$890$	−0.855557	−0.0286783
$891$	131.323	4.39947
$892$	12.1585	0.407098
$893$	−56.3588	−1.88597
$894$	−41.2415	−1.37932
$895$	10.3429	0.345724
$896$	−3.79895	−0.126914
$897$	−89.5388	−2.98961
$898$	−13.5017	−0.450559
$899$	32.0439	1.06872
$900$	−35.1098	−1.17033
$901$	4.09764	0.136512
$902$	24.3190	0.809734
$903$	−13.8744	−0.461712
$904$	5.20127	0.172992
$905$	−6.42157	−0.213460
$906$	62.2606	2.06847
$907$	14.0926	0.467936	0.233968	−	0.972244i	$-0.424829\pi$
$907$	14.0926	0.467936	0.233968	+	0.972244i	$0.424829\pi$
$908$	−18.6243	−0.618069
$909$	−93.0095	−3.08493
$910$	8.19684	0.271723
$911$	31.6772	1.04951	0.524756	−	0.851253i	$-0.324157\pi$
$911$	31.6772	1.04951	0.524756	+	0.851253i	$0.324157\pi$
$912$	−19.6082	−0.649291
$913$	−12.7788	−0.422917
$914$	24.5376	0.811633
$915$	25.4130	0.840129
$916$	26.4354	0.873452
$917$	20.4330	0.674758
$918$	−97.8379	−3.22913
$919$	0.446103	0.0147156	0.00735778	−	0.999973i	$-0.497658\pi$
$919$	0.446103	0.0147156	0.00735778	+	0.999973i	$0.497658\pi$
$920$	−5.65438	−0.186419
$921$	97.0059	3.19645
$922$	9.72513	0.320280
$923$	−36.8659	−1.21345
$924$	59.7859	1.96681
$925$	17.4887	0.575023
$926$	−19.9671	−0.656158
$927$	114.410	3.75772
$928$	8.48209	0.278438
$929$	29.9902	0.983946	0.491973	−	0.870610i	$-0.336276\pi$
$929$	29.9902	0.983946	0.491973	+	0.870610i	$0.336276\pi$
$930$	8.25558	0.270711
$931$	44.5306	1.45943
$932$	−19.5055	−0.638925
$933$	−38.0251	−1.24488
$934$	9.95812	0.325840
$935$	−20.3854	−0.666674
$936$	24.9109	0.814237
$937$	26.8981	0.878722	0.439361	−	0.898311i	$-0.355205\pi$
$937$	26.8981	0.878722	0.439361	+	0.898311i	$0.355205\pi$
$938$	13.0755	0.426930
$939$	30.7289	1.00280
$940$	6.28102	0.204864
$941$	−49.2687	−1.60611	−0.803056	−	0.595903i	$-0.796794\pi$
$941$	−49.2687	−1.60611	−0.803056	+	0.595903i	$0.796794\pi$
$942$	−39.4860	−1.28652
$943$	42.8212	1.39445
$944$	14.7049	0.478602
$945$	−39.0970	−1.27183
$946$	−5.36683	−0.174491
$947$	−54.6459	−1.77575	−0.887877	−	0.460080i	$-0.847821\pi$
$947$	−54.6459	−1.77575	−0.887877	+	0.460080i	$0.847821\pi$
$948$	19.1137	0.620783
$949$	1.35584	0.0440123
$950$	−27.2869	−0.885304
$951$	94.1441	3.05283
$952$	−24.1163	−0.781615
$953$	19.8232	0.642137	0.321068	−	0.947056i	$-0.395958\pi$
$953$	19.8232	0.642137	0.321068	+	0.947056i	$0.395958\pi$
$954$	4.97637	0.161116
$955$	8.82051	0.285425
$956$	−17.3070	−0.559748
$957$	−133.487	−4.31502
$958$	8.00644	0.258676
$959$	−9.91382	−0.320134
$960$	2.18527	0.0705293
$961$	−16.7280	−0.539613
$962$	−12.4084	−0.400064
$963$	−154.760	−4.98708
$964$	17.2294	0.554922
$965$	4.07705	0.131245
$966$	105.272	3.38707
$967$	42.7360	1.37430	0.687149	−	0.726517i	$-0.258862\pi$
$967$	42.7360	1.37430	0.687149	+	0.726517i	$0.258862\pi$
$968$	12.1261	0.389747
$969$	−124.476	−3.99874
$970$	3.05260	0.0980132
$971$	−21.8825	−0.702242	−0.351121	−	0.936330i	$-0.614199\pi$
$971$	−21.8825	−0.702242	−0.351121	+	0.936330i	$0.614199\pi$
$972$	−43.1301	−1.38340
$973$	−24.1702	−0.774861
$974$	−7.92502	−0.253934
$975$	48.1559	1.54222
$976$	11.6292	0.372243
$977$	0.0636777	0.00203723	0.00101861	−	0.999999i	$-0.499676\pi$
$977$	0.0636777	0.00203723	0.00101861	+	0.999999i	$0.499676\pi$
$978$	−33.1377	−1.05963
$979$	6.16140	0.196919
$980$	−4.96280	−0.158531
$981$	119.826	3.82575
$982$	20.2865	0.647370
$983$	−3.95651	−0.126193	−0.0630965	−	0.998007i	$-0.520098\pi$
$983$	−3.95651	−0.126193	−0.0630965	+	0.998007i	$0.520098\pi$
$984$	−16.5493	−0.527572
$985$	3.36463	0.107206
$986$	53.8456	1.71479
$987$	−116.938	−3.72219
$988$	19.3604	0.615937
$989$	−9.44999	−0.300492
$990$	−24.7570	−0.786829
$991$	11.2246	0.356562	0.178281	−	0.983980i	$-0.442946\pi$
$991$	11.2246	0.356562	0.178281	+	0.983980i	$0.442946\pi$
$992$	3.77783	0.119946
$993$	22.6116	0.717556
$994$	43.3436	1.37478
$995$	15.7864	0.500463
$996$	8.69609	0.275546
$997$	−23.8535	−0.755449	−0.377725	−	0.925918i	$-0.623293\pi$
$997$	−23.8535	−0.755449	−0.377725	+	0.925918i	$0.623293\pi$
$998$	−14.7364	−0.466473
$999$	59.1853	1.87254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.4	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.4	✓	96	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.27254 q^{3} +1.00000 q^{4} -0.667760 q^{5} -3.27254 q^{6} -3.79895 q^{7} +1.00000 q^{8} +7.70950 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.27254 q^{3} +1.00000 q^{4} -0.667760 q^{5} -3.27254 q^{6} -3.79895 q^{7} +1.00000 q^{8} +7.70950 q^{9} -0.667760 q^{10} +4.80896 q^{11} -3.27254 q^{12} +3.23119 q^{13} -3.79895 q^{14} +2.18527 q^{15} +1.00000 q^{16} +6.34816 q^{17} +7.70950 q^{18} +5.99173 q^{19} -0.667760 q^{20} +12.4322 q^{21} +4.80896 q^{22} +8.46768 q^{23} -3.27254 q^{24} -4.55410 q^{25} +3.23119 q^{26} -15.4120 q^{27} -3.79895 q^{28} +8.48209 q^{29} +2.18527 q^{30} +3.77783 q^{31} +1.00000 q^{32} -15.7375 q^{33} +6.34816 q^{34} +2.53679 q^{35} +7.70950 q^{36} -3.84020 q^{37} +5.99173 q^{38} -10.5742 q^{39} -0.667760 q^{40} +5.05702 q^{41} +12.4322 q^{42} -1.11601 q^{43} +4.80896 q^{44} -5.14810 q^{45} +8.46768 q^{46} -9.40610 q^{47} -3.27254 q^{48} +7.43201 q^{49} -4.55410 q^{50} -20.7746 q^{51} +3.23119 q^{52} +0.645485 q^{53} -15.4120 q^{54} -3.21123 q^{55} -3.79895 q^{56} -19.6082 q^{57} +8.48209 q^{58} +14.7049 q^{59} +2.18527 q^{60} +11.6292 q^{61} +3.77783 q^{62} -29.2880 q^{63} +1.00000 q^{64} -2.15766 q^{65} -15.7375 q^{66} -3.44187 q^{67} +6.34816 q^{68} -27.7108 q^{69} +2.53679 q^{70} -11.4094 q^{71} +7.70950 q^{72} +0.419609 q^{73} -3.84020 q^{74} +14.9034 q^{75} +5.99173 q^{76} -18.2690 q^{77} -10.5742 q^{78} -5.84063 q^{79} -0.667760 q^{80} +27.3079 q^{81} +5.05702 q^{82} -2.65729 q^{83} +12.4322 q^{84} -4.23905 q^{85} -1.11601 q^{86} -27.7579 q^{87} +4.80896 q^{88} +1.28123 q^{89} -5.14810 q^{90} -12.2751 q^{91} +8.46768 q^{92} -12.3631 q^{93} -9.40610 q^{94} -4.00104 q^{95} -3.27254 q^{96} -4.57141 q^{97} +7.43201 q^{98} +37.0747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

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