LMFDB - Embedded newform 8027.2.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70691 q^{2} +1.62616 q^{3} +5.32735 q^{4} -1.60888 q^{5} -4.40186 q^{6} -2.81542 q^{7} -9.00682 q^{8} -0.355610 q^{9} +O(q^{10})$	\(q-2.70691 q^{2} +1.62616 q^{3} +5.32735 q^{4} -1.60888 q^{5} -4.40186 q^{6} -2.81542 q^{7} -9.00682 q^{8} -0.355610 q^{9} +4.35510 q^{10} -4.89128 q^{11} +8.66311 q^{12} +3.47170 q^{13} +7.62109 q^{14} -2.61630 q^{15} +13.7259 q^{16} -3.90665 q^{17} +0.962604 q^{18} +6.58894 q^{19} -8.57109 q^{20} -4.57832 q^{21} +13.2402 q^{22} -1.00000 q^{23} -14.6465 q^{24} -2.41149 q^{25} -9.39756 q^{26} -5.45675 q^{27} -14.9987 q^{28} -9.82564 q^{29} +7.08208 q^{30} +0.728263 q^{31} -19.1412 q^{32} -7.95399 q^{33} +10.5749 q^{34} +4.52969 q^{35} -1.89446 q^{36} -3.17967 q^{37} -17.8356 q^{38} +5.64553 q^{39} +14.4909 q^{40} -0.541771 q^{41} +12.3931 q^{42} -12.6996 q^{43} -26.0575 q^{44} +0.572136 q^{45} +2.70691 q^{46} -6.96170 q^{47} +22.3205 q^{48} +0.926600 q^{49} +6.52768 q^{50} -6.35283 q^{51} +18.4949 q^{52} +12.6258 q^{53} +14.7709 q^{54} +7.86951 q^{55} +25.3580 q^{56} +10.7147 q^{57} +26.5971 q^{58} -11.5645 q^{59} -13.9379 q^{60} +6.55611 q^{61} -1.97134 q^{62} +1.00119 q^{63} +24.3615 q^{64} -5.58556 q^{65} +21.5307 q^{66} +2.21097 q^{67} -20.8121 q^{68} -1.62616 q^{69} -12.2614 q^{70} +4.39852 q^{71} +3.20292 q^{72} +11.6701 q^{73} +8.60708 q^{74} -3.92146 q^{75} +35.1016 q^{76} +13.7710 q^{77} -15.2819 q^{78} -14.7063 q^{79} -22.0834 q^{80} -7.80671 q^{81} +1.46652 q^{82} -11.2565 q^{83} -24.3903 q^{84} +6.28535 q^{85} +34.3765 q^{86} -15.9780 q^{87} +44.0549 q^{88} -2.36321 q^{89} -1.54872 q^{90} -9.77429 q^{91} -5.32735 q^{92} +1.18427 q^{93} +18.8447 q^{94} -10.6008 q^{95} -31.1266 q^{96} +15.8398 q^{97} -2.50822 q^{98} +1.73939 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) $ 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * 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 $

$2$	−2.70691	−1.91407	−0.957036	−	0.289968i	$-0.906355\pi$
$2$	−2.70691	−1.91407	−0.957036	+	0.289968i	$0.906355\pi$
$3$	1.62616	0.938863	0.469431	−	0.882969i	$-0.344459\pi$
$3$	1.62616	0.938863	0.469431	+	0.882969i	$0.344459\pi$
$4$	5.32735	2.66367
$5$	−1.60888	−0.719515	−0.359758	−	0.933046i	$-0.617141\pi$
$5$	−1.60888	−0.719515	−0.359758	+	0.933046i	$0.617141\pi$
$6$	−4.40186	−1.79705
$7$	−2.81542	−1.06413	−0.532065	−	0.846704i	$-0.678584\pi$
$7$	−2.81542	−1.06413	−0.532065	+	0.846704i	$0.678584\pi$
$8$	−9.00682	−3.18439
$9$	−0.355610	−0.118537
$10$	4.35510	1.37720
$11$	−4.89128	−1.47478	−0.737388	−	0.675469i	$-0.763941\pi$
$11$	−4.89128	−1.47478	−0.737388	+	0.675469i	$0.763941\pi$
$12$	8.66311	2.50082
$13$	3.47170	0.962876	0.481438	−	0.876480i	$-0.340115\pi$
$13$	3.47170	0.962876	0.481438	+	0.876480i	$0.340115\pi$
$14$	7.62109	2.03682
$15$	−2.61630	−0.675526
$16$	13.7259	3.43148
$17$	−3.90665	−0.947501	−0.473751	−	0.880659i	$-0.657100\pi$
$17$	−3.90665	−0.947501	−0.473751	+	0.880659i	$0.657100\pi$
$18$	0.962604	0.226888
$19$	6.58894	1.51161	0.755803	−	0.654799i	$-0.227247\pi$
$19$	6.58894	1.51161	0.755803	+	0.654799i	$0.227247\pi$
$20$	−8.57109	−1.91655
$21$	−4.57832	−0.999071
$22$	13.2402	2.82283
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−14.6465	−2.98971
$25$	−2.41149	−0.482298
$26$	−9.39756	−1.84301
$27$	−5.45675	−1.05015
$28$	−14.9987	−2.83449
$29$	−9.82564	−1.82458	−0.912288	−	0.409550i	$-0.865686\pi$
$29$	−9.82564	−1.82458	−0.912288	+	0.409550i	$0.865686\pi$
$30$	7.08208	1.29301
$31$	0.728263	0.130800	0.0653999	−	0.997859i	$-0.479168\pi$
$31$	0.728263	0.130800	0.0653999	+	0.997859i	$0.479168\pi$
$32$	−19.1412	−3.38371
$33$	−7.95399	−1.38461
$34$	10.5749	1.81359
$35$	4.52969	0.765657
$36$	−1.89446	−0.315743
$37$	−3.17967	−0.522735	−0.261367	−	0.965239i	$-0.584173\pi$
$37$	−3.17967	−0.522735	−0.261367	+	0.965239i	$0.584173\pi$
$38$	−17.8356	−2.89332
$39$	5.64553	0.904008
$40$	14.4909	2.29122
$41$	−0.541771	−0.0846104	−0.0423052	−	0.999105i	$-0.513470\pi$
$41$	−0.541771	−0.0846104	−0.0423052	+	0.999105i	$0.513470\pi$
$42$	12.3931	1.91230
$43$	−12.6996	−1.93666	−0.968332	−	0.249665i	$-0.919679\pi$
$43$	−12.6996	−1.93666	−0.968332	+	0.249665i	$0.919679\pi$
$44$	−26.0575	−3.92832
$45$	0.572136	0.0852890
$46$	2.70691	0.399112
$47$	−6.96170	−1.01547	−0.507734	−	0.861514i	$-0.669517\pi$
$47$	−6.96170	−1.01547	−0.507734	+	0.861514i	$0.669517\pi$
$48$	22.3205	3.22169
$49$	0.926600	0.132371
$50$	6.52768	0.923153
$51$	−6.35283	−0.889574
$52$	18.4949	2.56479
$53$	12.6258	1.73428	0.867141	−	0.498063i	$-0.165955\pi$
$53$	12.6258	1.73428	0.867141	+	0.498063i	$0.165955\pi$
$54$	14.7709	2.01007
$55$	7.86951	1.06112
$56$	25.3580	3.38860
$57$	10.7147	1.41919
$58$	26.5971	3.49237
$59$	−11.5645	−1.50557	−0.752787	−	0.658264i	$-0.771291\pi$
$59$	−11.5645	−1.50557	−0.752787	+	0.658264i	$0.771291\pi$
$60$	−13.9379	−1.79938
$61$	6.55611	0.839424	0.419712	−	0.907657i	$-0.362131\pi$
$61$	6.55611	0.839424	0.419712	+	0.907657i	$0.362131\pi$
$62$	−1.97134	−0.250360
$63$	1.00119	0.126138
$64$	24.3615	3.04519
$65$	−5.58556	−0.692804
$66$	21.5307	2.65025
$67$	2.21097	0.270113	0.135057	−	0.990838i	$-0.456878\pi$
$67$	2.21097	0.270113	0.135057	+	0.990838i	$0.456878\pi$
$68$	−20.8121	−2.52383
$69$	−1.62616	−0.195766
$70$	−12.2614	−1.46552
$71$	4.39852	0.522008	0.261004	−	0.965338i	$-0.415946\pi$
$71$	4.39852	0.522008	0.261004	+	0.965338i	$0.415946\pi$
$72$	3.20292	0.377467
$73$	11.6701	1.36588	0.682939	−	0.730475i	$-0.260701\pi$
$73$	11.6701	1.36588	0.682939	+	0.730475i	$0.260701\pi$
$74$	8.60708	1.00055
$75$	−3.92146	−0.452812
$76$	35.1016	4.02643
$77$	13.7710	1.56935
$78$	−15.2819	−1.73034
$79$	−14.7063	−1.65459	−0.827294	−	0.561769i	$-0.810121\pi$
$79$	−14.7063	−1.65459	−0.827294	+	0.561769i	$0.810121\pi$
$80$	−22.0834	−2.46900
$81$	−7.80671	−0.867412
$82$	1.46652	0.161950
$83$	−11.2565	−1.23556	−0.617780	−	0.786351i	$-0.711968\pi$
$83$	−11.2565	−1.23556	−0.617780	+	0.786351i	$0.711968\pi$
$84$	−24.3903	−2.66120
$85$	6.28535	0.681741
$86$	34.3765	3.70692
$87$	−15.9780	−1.71303
$88$	44.0549	4.69627
$89$	−2.36321	−0.250500	−0.125250	−	0.992125i	$-0.539973\pi$
$89$	−2.36321	−0.250500	−0.125250	+	0.992125i	$0.539973\pi$
$90$	−1.54872	−0.163249
$91$	−9.77429	−1.02462
$92$	−5.32735	−0.555414
$93$	1.18427	0.122803
$94$	18.8447	1.94368
$95$	−10.6008	−1.08762
$96$	−31.1266	−3.17684
$97$	15.8398	1.60829	0.804143	−	0.594436i	$-0.202625\pi$
$97$	15.8398	1.60829	0.804143	+	0.594436i	$0.202625\pi$
$98$	−2.50822	−0.253369
$99$	1.73939	0.174815
$100$	−12.8468	−1.28468
$101$	1.00300	0.0998027	0.0499013	−	0.998754i	$-0.484109\pi$
$101$	1.00300	0.0998027	0.0499013	+	0.998754i	$0.484109\pi$
$102$	17.1965	1.70271
$103$	−13.0357	−1.28445	−0.642224	−	0.766517i	$-0.721988\pi$
$103$	−13.0357	−1.28445	−0.642224	+	0.766517i	$0.721988\pi$
$104$	−31.2690	−3.06617
$105$	7.36599	0.718847
$106$	−34.1768	−3.31954
$107$	12.1577	1.17533	0.587663	−	0.809106i	$-0.300048\pi$
$107$	12.1577	1.17533	0.587663	+	0.809106i	$0.300048\pi$
$108$	−29.0700	−2.79726
$109$	−5.83786	−0.559165	−0.279583	−	0.960122i	$-0.590196\pi$
$109$	−5.83786	−0.559165	−0.279583	+	0.960122i	$0.590196\pi$
$110$	−21.3020	−2.03107
$111$	−5.17065	−0.490776
$112$	−38.6443	−3.65154
$113$	14.5695	1.37058	0.685292	−	0.728268i	$-0.259674\pi$
$113$	14.5695	1.37058	0.685292	+	0.728268i	$0.259674\pi$
$114$	−29.0036	−2.71643
$115$	1.60888	0.150029
$116$	−52.3446	−4.86007
$117$	−1.23457	−0.114136
$118$	31.3041	2.88178
$119$	10.9989	1.00826
$120$	23.5645	2.15114
$121$	12.9246	1.17497
$122$	−17.7468	−1.60672
$123$	−0.881005	−0.0794376
$124$	3.87971	0.348408
$125$	11.9242	1.06654
$126$	−2.71014	−0.241438
$127$	−4.63193	−0.411018	−0.205509	−	0.978655i	$-0.565885\pi$
$127$	−4.63193	−0.411018	−0.205509	+	0.978655i	$0.565885\pi$
$128$	−27.6621	−2.44500
$129$	−20.6515	−1.81826
$130$	15.1196	1.32608
$131$	−3.51411	−0.307029	−0.153515	−	0.988146i	$-0.549059\pi$
$131$	−3.51411	−0.307029	−0.153515	+	0.988146i	$0.549059\pi$
$132$	−42.3737	−3.68816
$133$	−18.5506	−1.60854
$134$	−5.98490	−0.517017
$135$	8.77929	0.755601
$136$	35.1865	3.01721
$137$	−15.7771	−1.34793	−0.673965	−	0.738763i	$-0.735410\pi$
$137$	−15.7771	−1.34793	−0.673965	+	0.738763i	$0.735410\pi$
$138$	4.40186	0.374711
$139$	−18.4964	−1.56885	−0.784424	−	0.620225i	$-0.787041\pi$
$139$	−18.4964	−1.56885	−0.784424	+	0.620225i	$0.787041\pi$
$140$	24.1312	2.03946
$141$	−11.3208	−0.953386
$142$	−11.9064	−0.999162
$143$	−16.9810	−1.42003
$144$	−4.88108	−0.406757
$145$	15.8083	1.31281
$146$	−31.5898	−2.61439
$147$	1.50680	0.124279
$148$	−16.9392	−1.39239
$149$	9.64441	0.790101	0.395050	−	0.918659i	$-0.370727\pi$
$149$	9.64441	0.790101	0.395050	+	0.918659i	$0.370727\pi$
$150$	10.6150	0.866714
$151$	0.853573	0.0694628	0.0347314	−	0.999397i	$-0.488942\pi$
$151$	0.853573	0.0694628	0.0347314	+	0.999397i	$0.488942\pi$
$152$	−59.3454	−4.81355
$153$	1.38924	0.112314
$154$	−37.2769	−3.00386
$155$	−1.17169	−0.0941125
$156$	30.0757	2.40798
$157$	8.61976	0.687932	0.343966	−	0.938982i	$-0.388230\pi$
$157$	8.61976	0.687932	0.343966	+	0.938982i	$0.388230\pi$
$158$	39.8086	3.16700
$159$	20.5315	1.62825
$160$	30.7959	2.43463
$161$	2.81542	0.221886
$162$	21.1320	1.66029
$163$	20.8368	1.63206	0.816032	−	0.578006i	$-0.196169\pi$
$163$	20.8368	1.63206	0.816032	+	0.578006i	$0.196169\pi$
$164$	−2.88620	−0.225375
$165$	12.7971	0.996250
$166$	30.4703	2.36495
$167$	−14.7120	−1.13845	−0.569225	−	0.822182i	$-0.692757\pi$
$167$	−14.7120	−1.13845	−0.569225	+	0.822182i	$0.692757\pi$
$168$	41.2361	3.18143
$169$	−0.947315	−0.0728704
$170$	−17.0138	−1.30490
$171$	−2.34309	−0.179181
$172$	−67.6549	−5.15864
$173$	0.204125	0.0155194	0.00775968	−	0.999970i	$-0.497530\pi$
$173$	0.204125	0.0155194	0.00775968	+	0.999970i	$0.497530\pi$
$174$	43.2511	3.27886
$175$	6.78936	0.513227
$176$	−67.1374	−5.06067
$177$	−18.8058	−1.41353
$178$	6.39700	0.479475
$179$	9.76765	0.730069	0.365034	−	0.930994i	$-0.381057\pi$
$179$	9.76765	0.730069	0.365034	+	0.930994i	$0.381057\pi$
$180$	3.04797	0.227182
$181$	−18.2504	−1.35654	−0.678269	−	0.734814i	$-0.737270\pi$
$181$	−18.2504	−1.35654	−0.678269	+	0.734814i	$0.737270\pi$
$182$	26.4581	1.96121
$183$	10.6613	0.788104
$184$	9.00682	0.663991
$185$	5.11573	0.376116
$186$	−3.20571	−0.235054
$187$	19.1085	1.39735
$188$	−37.0874	−2.70488
$189$	15.3631	1.11750
$190$	28.6955	2.08179
$191$	−4.63365	−0.335279	−0.167640	−	0.985848i	$-0.553615\pi$
$191$	−4.63365	−0.335279	−0.167640	+	0.985848i	$0.553615\pi$
$192$	39.6157	2.85902
$193$	5.51440	0.396935	0.198468	−	0.980107i	$-0.436404\pi$
$193$	5.51440	0.396935	0.198468	+	0.980107i	$0.436404\pi$
$194$	−42.8768	−3.07838
$195$	−9.08301	−0.650448
$196$	4.93632	0.352594
$197$	−18.3417	−1.30679	−0.653396	−	0.757016i	$-0.726656\pi$
$197$	−18.3417	−1.30679	−0.653396	+	0.757016i	$0.726656\pi$
$198$	−4.70837	−0.334609
$199$	−20.4421	−1.44911	−0.724553	−	0.689219i	$-0.757954\pi$
$199$	−20.4421	−1.44911	−0.724553	+	0.689219i	$0.757954\pi$
$200$	21.7198	1.53583
$201$	3.59539	0.253599
$202$	−2.71504	−0.191030
$203$	27.6633	1.94158
$204$	−33.8437	−2.36953
$205$	0.871647	0.0608785
$206$	35.2865	2.45853
$207$	0.355610	0.0247166
$208$	47.6523	3.30409
$209$	−32.2283	−2.22928
$210$	−19.9391	−1.37593
$211$	−12.0840	−0.831894	−0.415947	−	0.909389i	$-0.636550\pi$
$211$	−12.0840	−0.831894	−0.415947	+	0.909389i	$0.636550\pi$
$212$	67.2618	4.61956
$213$	7.15269	0.490094
$214$	−32.9097	−2.24966
$215$	20.4321	1.39346
$216$	49.1480	3.34410
$217$	−2.05037	−0.139188
$218$	15.8025	1.07028
$219$	18.9774	1.28237
$220$	41.9236	2.82649
$221$	−13.5627	−0.912326
$222$	13.9965	0.939381
$223$	4.11756	0.275732	0.137866	−	0.990451i	$-0.455976\pi$
$223$	4.11756	0.275732	0.137866	+	0.990451i	$0.455976\pi$
$224$	53.8905	3.60071
$225$	0.857550	0.0571700
$226$	−39.4383	−2.62340
$227$	24.7918	1.64549	0.822745	−	0.568410i	$-0.192441\pi$
$227$	24.7918	1.64549	0.822745	+	0.568410i	$0.192441\pi$
$228$	57.0807	3.78026
$229$	−13.5570	−0.895870	−0.447935	−	0.894066i	$-0.647840\pi$
$229$	−13.5570	−0.895870	−0.447935	+	0.894066i	$0.647840\pi$
$230$	−4.35510	−0.287167
$231$	22.3939	1.47341
$232$	88.4978	5.81016
$233$	17.3535	1.13687	0.568434	−	0.822729i	$-0.307549\pi$
$233$	17.3535	1.13687	0.568434	+	0.822729i	$0.307549\pi$
$234$	3.34187	0.218465
$235$	11.2006	0.730645
$236$	−61.6083	−4.01036
$237$	−23.9148	−1.55343
$238$	−29.7729	−1.92989
$239$	5.80852	0.375722	0.187861	−	0.982196i	$-0.439845\pi$
$239$	5.80852	0.375722	0.187861	+	0.982196i	$0.439845\pi$
$240$	−35.9112	−2.31806
$241$	21.4491	1.38166	0.690828	−	0.723019i	$-0.257246\pi$
$241$	21.4491	1.38166	0.690828	+	0.723019i	$0.257246\pi$
$242$	−34.9858	−2.24897
$243$	3.67531	0.235771
$244$	34.9267	2.23595
$245$	−1.49079	−0.0952433
$246$	2.38480	0.152049
$247$	22.8748	1.45549
$248$	−6.55933	−0.416518
$249$	−18.3048	−1.16002
$250$	−32.2778	−2.04143
$251$	−4.13923	−0.261266	−0.130633	−	0.991431i	$-0.541701\pi$
$251$	−4.13923	−0.261266	−0.130633	+	0.991431i	$0.541701\pi$
$252$	5.33370	0.335992
$253$	4.89128	0.307512
$254$	12.5382	0.786717
$255$	10.2210	0.640062
$256$	26.1555	1.63472
$257$	7.68184	0.479180	0.239590	−	0.970874i	$-0.422987\pi$
$257$	7.68184	0.479180	0.239590	+	0.970874i	$0.422987\pi$
$258$	55.9017	3.48029
$259$	8.95212	0.556257
$260$	−29.7562	−1.84540
$261$	3.49410	0.216279
$262$	9.51237	0.587676
$263$	−13.0439	−0.804323	−0.402161	−	0.915569i	$-0.631741\pi$
$263$	−13.0439	−0.804323	−0.402161	+	0.915569i	$0.631741\pi$
$264$	71.6402	4.40915
$265$	−20.3134	−1.24784
$266$	50.2149	3.07887
$267$	−3.84296	−0.235185
$268$	11.7786	0.719494
$269$	20.6935	1.26170	0.630851	−	0.775904i	$-0.282706\pi$
$269$	20.6935	1.26170	0.630851	+	0.775904i	$0.282706\pi$
$270$	−23.7647	−1.44627
$271$	−16.2557	−0.987463	−0.493732	−	0.869614i	$-0.664367\pi$
$271$	−16.2557	−0.987463	−0.493732	+	0.869614i	$0.664367\pi$
$272$	−53.6224	−3.25133
$273$	−15.8945	−0.961982
$274$	42.7072	2.58004
$275$	11.7953	0.711282
$276$	−8.66311	−0.521458
$277$	−14.5691	−0.875372	−0.437686	−	0.899128i	$-0.644202\pi$
$277$	−14.5691	−0.875372	−0.437686	+	0.899128i	$0.644202\pi$
$278$	50.0682	3.00289
$279$	−0.258978	−0.0155046
$280$	−40.7981	−2.43815
$281$	24.9398	1.48778	0.743892	−	0.668300i	$-0.232978\pi$
$281$	24.9398	1.48778	0.743892	+	0.668300i	$0.232978\pi$
$282$	30.6444	1.82485
$283$	5.62722	0.334504	0.167252	−	0.985914i	$-0.446511\pi$
$283$	5.62722	0.334504	0.167252	+	0.985914i	$0.446511\pi$
$284$	23.4324	1.39046
$285$	−17.2386	−1.02113
$286$	45.9661	2.71803
$287$	1.52531	0.0900365
$288$	6.80680	0.401094
$289$	−1.73811	−0.102242
$290$	−42.7917	−2.51281
$291$	25.7580	1.50996
$292$	62.1705	3.63825
$293$	−0.985441	−0.0575701	−0.0287850	−	0.999586i	$-0.509164\pi$
$293$	−0.985441	−0.0575701	−0.0287850	+	0.999586i	$0.509164\pi$
$294$	−4.07876	−0.237878
$295$	18.6060	1.08328
$296$	28.6387	1.66459
$297$	26.6905	1.54874
$298$	−26.1065	−1.51231
$299$	−3.47170	−0.200773
$300$	−20.8910	−1.20614
$301$	35.7546	2.06086
$302$	−2.31054	−0.132957
$303$	1.63104	0.0937010
$304$	90.4393	5.18705
$305$	−10.5480	−0.603978
$306$	−3.76055	−0.214977
$307$	−19.2342	−1.09776	−0.548878	−	0.835902i	$-0.684945\pi$
$307$	−19.2342	−1.09776	−0.548878	+	0.835902i	$0.684945\pi$
$308$	73.3630	4.18024
$309$	−21.1981	−1.20592
$310$	3.17166	0.180138
$311$	−2.66410	−0.151067	−0.0755335	−	0.997143i	$-0.524066\pi$
$311$	−2.66410	−0.151067	−0.0755335	+	0.997143i	$0.524066\pi$
$312$	−50.8483	−2.87872
$313$	−32.7006	−1.84835	−0.924174	−	0.381971i	$-0.875245\pi$
$313$	−32.7006	−1.84835	−0.924174	+	0.381971i	$0.875245\pi$
$314$	−23.3329	−1.31675
$315$	−1.61080	−0.0907585
$316$	−78.3455	−4.40728
$317$	2.48826	0.139754	0.0698772	−	0.997556i	$-0.477739\pi$
$317$	2.48826	0.139754	0.0698772	+	0.997556i	$0.477739\pi$
$318$	−55.5768	−3.11659
$319$	48.0600	2.69084
$320$	−39.1949	−2.19106
$321$	19.7703	1.10347
$322$	−7.62109	−0.424707
$323$	−25.7407	−1.43225
$324$	−41.5891	−2.31050
$325$	−8.37196	−0.464393
$326$	−56.4033	−3.12389
$327$	−9.49328	−0.524979
$328$	4.87963	0.269433
$329$	19.6001	1.08059
$330$	−34.6405	−1.90689
$331$	−12.8645	−0.707098	−0.353549	−	0.935416i	$-0.615025\pi$
$331$	−12.8645	−0.707098	−0.353549	+	0.935416i	$0.615025\pi$
$332$	−59.9672	−3.29113
$333$	1.13072	0.0619633
$334$	39.8240	2.17908
$335$	−3.55720	−0.194351
$336$	−62.8417	−3.42830
$337$	−12.2504	−0.667320	−0.333660	−	0.942694i	$-0.608284\pi$
$337$	−12.2504	−0.667320	−0.333660	+	0.942694i	$0.608284\pi$
$338$	2.56429	0.139479
$339$	23.6923	1.28679
$340$	33.4842	1.81594
$341$	−3.56214	−0.192901
$342$	6.34254	0.342965
$343$	17.0992	0.923269
$344$	114.383	6.16710
$345$	2.61630	0.140857
$346$	−0.552549	−0.0297052
$347$	3.56942	0.191617	0.0958083	−	0.995400i	$-0.469456\pi$
$347$	3.56942	0.191617	0.0958083	+	0.995400i	$0.469456\pi$
$348$	−85.1206	−4.56294
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−18.3782	−0.982354
$351$	−18.9442	−1.01117
$352$	93.6249	4.99022
$353$	−13.4719	−0.717037	−0.358518	−	0.933523i	$-0.616718\pi$
$353$	−13.4719	−0.717037	−0.358518	+	0.933523i	$0.616718\pi$
$354$	50.9054	2.70559
$355$	−7.07671	−0.375593
$356$	−12.5896	−0.667250
$357$	17.8859	0.946621
$358$	−26.4401	−1.39740
$359$	37.3677	1.97219	0.986097	−	0.166173i	$-0.0531410\pi$
$359$	37.3677	1.97219	0.986097	+	0.166173i	$0.0531410\pi$
$360$	−5.15313	−0.271594
$361$	24.4141	1.28495
$362$	49.4020	2.59651
$363$	21.0175	1.10313
$364$	−52.0710	−2.72926
$365$	−18.7758	−0.982770
$366$	−28.8591	−1.50849
$367$	9.22987	0.481795	0.240898	−	0.970551i	$-0.422558\pi$
$367$	9.22987	0.481795	0.240898	+	0.970551i	$0.422558\pi$
$368$	−13.7259	−0.715513
$369$	0.192659	0.0100294
$370$	−13.8478	−0.719912
$371$	−35.5469	−1.84550
$372$	6.30902	0.327107
$373$	−3.14599	−0.162893	−0.0814466	−	0.996678i	$-0.525954\pi$
$373$	−3.14599	−0.162893	−0.0814466	+	0.996678i	$0.525954\pi$
$374$	−51.7250	−2.67463
$375$	19.3907	1.00133
$376$	62.7028	3.23365
$377$	−34.1117	−1.75684
$378$	−41.5864	−2.13897
$379$	13.1725	0.676626	0.338313	−	0.941034i	$-0.390144\pi$
$379$	13.1725	0.676626	0.338313	+	0.941034i	$0.390144\pi$
$380$	−56.4744	−2.89707
$381$	−7.53225	−0.385889
$382$	12.5429	0.641749
$383$	33.8342	1.72885	0.864423	−	0.502766i	$-0.167684\pi$
$383$	33.8342	1.72885	0.864423	+	0.502766i	$0.167684\pi$
$384$	−44.9829	−2.29552
$385$	−22.1560	−1.12917
$386$	−14.9270	−0.759763
$387$	4.51609	0.229566
$388$	84.3840	4.28395
$389$	17.1657	0.870335	0.435168	−	0.900349i	$-0.356689\pi$
$389$	17.1657	0.870335	0.435168	+	0.900349i	$0.356689\pi$
$390$	24.5869	1.24500
$391$	3.90665	0.197568
$392$	−8.34572	−0.421523
$393$	−5.71450	−0.288258
$394$	49.6493	2.50129
$395$	23.6607	1.19050
$396$	9.26633	0.465651
$397$	9.81452	0.492577	0.246288	−	0.969197i	$-0.420789\pi$
$397$	9.81452	0.492577	0.246288	+	0.969197i	$0.420789\pi$
$398$	55.3350	2.77369
$399$	−30.1663	−1.51020
$400$	−33.0999	−1.65500
$401$	13.3839	0.668358	0.334179	−	0.942510i	$-0.391541\pi$
$401$	13.3839	0.668358	0.334179	+	0.942510i	$0.391541\pi$
$402$	−9.73239	−0.485408
$403$	2.52831	0.125944
$404$	5.34335	0.265842
$405$	12.5601	0.624116
$406$	−74.8820	−3.71633
$407$	15.5527	0.770917
$408$	57.2187	2.83275
$409$	−36.8391	−1.82158	−0.910788	−	0.412875i	$-0.864525\pi$
$409$	−36.8391	−1.82158	−0.910788	+	0.412875i	$0.864525\pi$
$410$	−2.35947	−0.116526
$411$	−25.6561	−1.26552
$412$	−69.4458	−3.42135
$413$	32.5590	1.60213
$414$	−0.962604	−0.0473094
$415$	18.1104	0.889004
$416$	−66.4524	−3.25810
$417$	−30.0781	−1.47293
$418$	87.2392	4.26701
$419$	−5.21047	−0.254548	−0.127274	−	0.991868i	$-0.540623\pi$
$419$	−5.21047	−0.254548	−0.127274	+	0.991868i	$0.540623\pi$
$420$	39.2412	1.91477
$421$	18.3468	0.894168	0.447084	−	0.894492i	$-0.352463\pi$
$421$	18.3468	0.894168	0.447084	+	0.894492i	$0.352463\pi$
$422$	32.7101	1.59230
$423$	2.47565	0.120370
$424$	−113.718	−5.52263
$425$	9.42084	0.456978
$426$	−19.3617	−0.938076
$427$	−18.4582	−0.893255
$428$	64.7681	3.13068
$429$	−27.6139	−1.33321
$430$	−55.3079	−2.66718
$431$	11.9754	0.576835	0.288418	−	0.957505i	$-0.406871\pi$
$431$	11.9754	0.576835	0.288418	+	0.957505i	$0.406871\pi$
$432$	−74.8990	−3.60358
$433$	33.8577	1.62710	0.813548	−	0.581498i	$-0.197533\pi$
$433$	33.8577	1.62710	0.813548	+	0.581498i	$0.197533\pi$
$434$	5.55015	0.266416
$435$	25.7068	1.23255
$436$	−31.1003	−1.48943
$437$	−6.58894	−0.315192
$438$	−51.3700	−2.45455
$439$	26.8485	1.28141	0.640703	−	0.767789i	$-0.278643\pi$
$439$	26.8485	1.28141	0.640703	+	0.767789i	$0.278643\pi$
$440$	−70.8792	−3.37903
$441$	−0.329509	−0.0156909
$442$	36.7130	1.74626
$443$	1.55046	0.0736647	0.0368324	−	0.999321i	$-0.488273\pi$
$443$	1.55046	0.0736647	0.0368324	+	0.999321i	$0.488273\pi$
$444$	−27.5458	−1.30727
$445$	3.80214	0.180239
$446$	−11.1458	−0.527771
$447$	15.6833	0.741796
$448$	−68.5880	−3.24048
$449$	−36.1421	−1.70565	−0.852825	−	0.522197i	$-0.825112\pi$
$449$	−36.1421	−1.70565	−0.852825	+	0.522197i	$0.825112\pi$
$450$	−2.32131	−0.109428
$451$	2.64995	0.124781
$452$	77.6168	3.65079
$453$	1.38804	0.0652160
$454$	−67.1092	−3.14959
$455$	15.7257	0.737233
$456$	−96.5050	−4.51926
$457$	−22.9226	−1.07227	−0.536137	−	0.844131i	$-0.680117\pi$
$457$	−22.9226	−1.07227	−0.536137	+	0.844131i	$0.680117\pi$
$458$	36.6975	1.71476
$459$	21.3176	0.995021
$460$	8.57109	0.399629
$461$	19.0395	0.886757	0.443379	−	0.896334i	$-0.353780\pi$
$461$	19.0395	0.886757	0.443379	+	0.896334i	$0.353780\pi$
$462$	−60.6181	−2.82021
$463$	−2.21503	−0.102941	−0.0514706	−	0.998675i	$-0.516391\pi$
$463$	−2.21503	−0.102941	−0.0514706	+	0.998675i	$0.516391\pi$
$464$	−134.866	−6.26100
$465$	−1.90535	−0.0883587
$466$	−46.9744	−2.17605
$467$	3.74500	0.173298	0.0866489	−	0.996239i	$-0.472384\pi$
$467$	3.74500	0.173298	0.0866489	+	0.996239i	$0.472384\pi$
$468$	−6.57699	−0.304021
$469$	−6.22482	−0.287436
$470$	−30.3189	−1.39851
$471$	14.0171	0.645874
$472$	104.160	4.79434
$473$	62.1171	2.85615
$474$	64.7350	2.97338
$475$	−15.8892	−0.729045
$476$	58.5947	2.68569
$477$	−4.48985	−0.205576
$478$	−15.7231	−0.719159
$479$	−16.8165	−0.768364	−0.384182	−	0.923257i	$-0.625517\pi$
$479$	−16.8165	−0.768364	−0.384182	+	0.923257i	$0.625517\pi$
$480$	50.0791	2.28579
$481$	−11.0389	−0.503329
$482$	−58.0607	−2.64459
$483$	4.57832	0.208321
$484$	68.8540	3.12973
$485$	−25.4844	−1.15719
$486$	−9.94873	−0.451284
$487$	40.0454	1.81463	0.907314	−	0.420453i	$-0.138129\pi$
$487$	40.0454	1.81463	0.907314	+	0.420453i	$0.138129\pi$
$488$	−59.0497	−2.67305
$489$	33.8839	1.53228
$490$	4.03544	0.182303
$491$	20.7254	0.935325	0.467662	−	0.883907i	$-0.345096\pi$
$491$	20.7254	0.935325	0.467662	+	0.883907i	$0.345096\pi$
$492$	−4.69342	−0.211596
$493$	38.3853	1.72879
$494$	−61.9200	−2.78591
$495$	−2.79848	−0.125782
$496$	9.99608	0.448837
$497$	−12.3837	−0.555484
$498$	49.5494	2.22036
$499$	18.4005	0.823721	0.411860	−	0.911247i	$-0.364879\pi$
$499$	18.4005	0.823721	0.411860	+	0.911247i	$0.364879\pi$
$500$	63.5245	2.84090
$501$	−23.9241	−1.06885
$502$	11.2045	0.500082
$503$	7.21891	0.321875	0.160938	−	0.986965i	$-0.448548\pi$
$503$	7.21891	0.321875	0.160938	+	0.986965i	$0.448548\pi$
$504$	−9.01756	−0.401674
$505$	−1.61372	−0.0718095
$506$	−13.2402	−0.588601
$507$	−1.54048	−0.0684153
$508$	−24.6759	−1.09482
$509$	−26.4673	−1.17314	−0.586571	−	0.809898i	$-0.699523\pi$
$509$	−26.4673	−1.17314	−0.586571	+	0.809898i	$0.699523\pi$
$510$	−27.6672	−1.22512
$511$	−32.8562	−1.45347
$512$	−15.4765	−0.683973
$513$	−35.9542	−1.58742
$514$	−20.7940	−0.917185
$515$	20.9730	0.924179
$516$	−110.018	−4.84326
$517$	34.0516	1.49759
$518$	−24.2325	−1.06472
$519$	0.331940	0.0145706
$520$	50.3081	2.20616
$521$	−44.1670	−1.93499	−0.967495	−	0.252892i	$-0.918618\pi$
$521$	−44.1670	−1.93499	−0.967495	+	0.252892i	$0.918618\pi$
$522$	−9.45820	−0.413974
$523$	20.4236	0.893062	0.446531	−	0.894768i	$-0.352659\pi$
$523$	20.4236	0.893062	0.446531	+	0.894768i	$0.352659\pi$
$524$	−18.7209	−0.817826
$525$	11.0406	0.481850
$526$	35.3087	1.53953
$527$	−2.84507	−0.123933
$528$	−109.176	−4.75127
$529$	1.00000	0.0434783
$530$	54.9865	2.38846
$531$	4.11247	0.178466
$532$	−98.8257	−4.28464
$533$	−1.88087	−0.0814693
$534$	10.4025	0.450161
$535$	−19.5603	−0.845665
$536$	−19.9138	−0.860147
$537$	15.8837	0.685434
$538$	−56.0153	−2.41499
$539$	−4.53226	−0.195218
$540$	46.7703	2.01267
$541$	−20.2109	−0.868936	−0.434468	−	0.900687i	$-0.643064\pi$
$541$	−20.2109	−0.868936	−0.434468	+	0.900687i	$0.643064\pi$
$542$	44.0027	1.89008
$543$	−29.6780	−1.27360
$544$	74.7778	3.20607
$545$	9.39244	0.402328
$546$	43.0251	1.84130
$547$	−30.9049	−1.32140	−0.660698	−	0.750652i	$-0.729740\pi$
$547$	−30.9049	−1.32140	−0.660698	+	0.750652i	$0.729740\pi$
$548$	−84.0501	−3.59044
$549$	−2.33142	−0.0995026
$550$	−31.9287	−1.36144
$551$	−64.7405	−2.75804
$552$	14.6465	0.623397
$553$	41.4044	1.76070
$554$	39.4372	1.67553
$555$	8.31898	0.353121
$556$	−98.5370	−4.17890
$557$	−22.9040	−0.970472	−0.485236	−	0.874383i	$-0.661266\pi$
$557$	−22.9040	−0.970472	−0.485236	+	0.874383i	$0.661266\pi$
$558$	0.701029	0.0296769
$559$	−44.0890	−1.86477
$560$	62.1742	2.62734
$561$	31.0735	1.31192
$562$	−67.5098	−2.84773
$563$	−13.4358	−0.566253	−0.283127	−	0.959083i	$-0.591372\pi$
$563$	−13.4358	−0.566253	−0.283127	+	0.959083i	$0.591372\pi$
$564$	−60.3100	−2.53951
$565$	−23.4407	−0.986156
$566$	−15.2324	−0.640264
$567$	21.9792	0.923039
$568$	−39.6167	−1.66228
$569$	−8.14151	−0.341310	−0.170655	−	0.985331i	$-0.554588\pi$
$569$	−8.14151	−0.341310	−0.170655	+	0.985331i	$0.554588\pi$
$570$	46.6634	1.95452
$571$	−20.8764	−0.873650	−0.436825	−	0.899547i	$-0.643897\pi$
$571$	−20.8764	−0.873650	−0.436825	+	0.899547i	$0.643897\pi$
$572$	−90.4639	−3.78249
$573$	−7.53505	−0.314781
$574$	−4.12888	−0.172336
$575$	2.41149	0.100566
$576$	−8.66321	−0.360967
$577$	41.3408	1.72104	0.860519	−	0.509418i	$-0.170139\pi$
$577$	41.3408	1.72104	0.860519	+	0.509418i	$0.170139\pi$
$578$	4.70489	0.195698
$579$	8.96729	0.372668
$580$	84.2164	3.49690
$581$	31.6917	1.31480
$582$	−69.7245	−2.89017
$583$	−61.7562	−2.55768
$584$	−105.110	−4.34949
$585$	1.98628	0.0821227
$586$	2.66750	0.110193
$587$	22.1461	0.914069	0.457035	−	0.889449i	$-0.348912\pi$
$587$	22.1461	0.914069	0.457035	+	0.889449i	$0.348912\pi$
$588$	8.02724	0.331038
$589$	4.79848	0.197718
$590$	−50.3647	−2.07348
$591$	−29.8265	−1.22690
$592$	−43.6439	−1.79375
$593$	−3.79436	−0.155816	−0.0779078	−	0.996961i	$-0.524824\pi$
$593$	−3.79436	−0.155816	−0.0779078	+	0.996961i	$0.524824\pi$
$594$	−72.2487	−2.96440
$595$	−17.6959	−0.725461
$596$	51.3791	2.10457
$597$	−33.2422	−1.36051
$598$	9.39756	0.384295
$599$	15.5124	0.633821	0.316910	−	0.948455i	$-0.397355\pi$
$599$	15.5124	0.633821	0.316910	+	0.948455i	$0.397355\pi$
$600$	35.3199	1.44193
$601$	14.3877	0.586886	0.293443	−	0.955977i	$-0.405199\pi$
$601$	14.3877	0.586886	0.293443	+	0.955977i	$0.405199\pi$
$602$	−96.7844	−3.94464
$603$	−0.786245	−0.0320184
$604$	4.54728	0.185026
$605$	−20.7942	−0.845406
$606$	−4.41508	−0.179351
$607$	−38.6820	−1.57005	−0.785026	−	0.619463i	$-0.787350\pi$
$607$	−38.6820	−1.57005	−0.785026	+	0.619463i	$0.787350\pi$
$608$	−126.120	−5.11484
$609$	44.9849	1.82288
$610$	28.5525	1.15606
$611$	−24.1689	−0.977770
$612$	7.40098	0.299167
$613$	29.6257	1.19657	0.598286	−	0.801282i	$-0.295849\pi$
$613$	29.6257	1.19657	0.598286	+	0.801282i	$0.295849\pi$
$614$	52.0653	2.10119
$615$	1.41744	0.0571565
$616$	−124.033	−4.99743
$617$	40.6846	1.63790	0.818951	−	0.573864i	$-0.194556\pi$
$617$	40.6846	1.63790	0.818951	+	0.573864i	$0.194556\pi$
$618$	57.3814	2.30822
$619$	3.49481	0.140468	0.0702341	−	0.997531i	$-0.477625\pi$
$619$	3.49481	0.140468	0.0702341	+	0.997531i	$0.477625\pi$
$620$	−6.24200	−0.250685
$621$	5.45675	0.218972
$622$	7.21146	0.289153
$623$	6.65344	0.266564
$624$	77.4901	3.10209
$625$	−7.12727	−0.285091
$626$	88.5176	3.53787
$627$	−52.4084	−2.09299
$628$	45.9205	1.83243
$629$	12.4219	0.495292
$630$	4.36030	0.173718
$631$	8.47886	0.337538	0.168769	−	0.985656i	$-0.446021\pi$
$631$	8.47886	0.337538	0.168769	+	0.985656i	$0.446021\pi$
$632$	132.457	5.26885
$633$	−19.6504	−0.781034
$634$	−6.73548	−0.267500
$635$	7.45225	0.295733
$636$	109.378	4.33713
$637$	3.21688	0.127457
$638$	−130.094	−5.15046
$639$	−1.56416	−0.0618772
$640$	44.5051	1.75922
$641$	3.27088	0.129192	0.0645959	−	0.997912i	$-0.479424\pi$
$641$	3.27088	0.129192	0.0645959	+	0.997912i	$0.479424\pi$
$642$	−53.5163	−2.11212
$643$	41.8778	1.65150	0.825749	−	0.564038i	$-0.190753\pi$
$643$	41.8778	1.65150	0.825749	+	0.564038i	$0.190753\pi$
$644$	14.9987	0.591033
$645$	33.2259	1.30827
$646$	69.6776	2.74143
$647$	−24.1786	−0.950559	−0.475279	−	0.879835i	$-0.657653\pi$
$647$	−24.1786	−0.950559	−0.475279	+	0.879835i	$0.657653\pi$
$648$	70.3136	2.76218
$649$	56.5654	2.22038
$650$	22.6621	0.888882
$651$	−3.33422	−0.130678
$652$	111.005	4.34729
$653$	10.8126	0.423130	0.211565	−	0.977364i	$-0.432144\pi$
$653$	10.8126	0.423130	0.211565	+	0.977364i	$0.432144\pi$
$654$	25.6974	1.00485
$655$	5.65380	0.220912
$656$	−7.43631	−0.290339
$657$	−4.15000	−0.161907
$658$	−53.0557	−2.06833
$659$	14.1373	0.550712	0.275356	−	0.961342i	$-0.411204\pi$
$659$	14.1373	0.550712	0.275356	+	0.961342i	$0.411204\pi$
$660$	68.1744	2.65368
$661$	32.8334	1.27707	0.638535	−	0.769593i	$-0.279541\pi$
$661$	32.8334	1.27707	0.638535	+	0.769593i	$0.279541\pi$
$662$	34.8231	1.35344
$663$	−22.0551	−0.856549
$664$	101.385	3.93450
$665$	29.8459	1.15737
$666$	−3.06076	−0.118602
$667$	9.82564	0.380450
$668$	−78.3760	−3.03246
$669$	6.69580	0.258875
$670$	9.62902	0.372001
$671$	−32.0678	−1.23796
$672$	87.6344	3.38057
$673$	−35.7447	−1.37786	−0.688929	−	0.724829i	$-0.741919\pi$
$673$	−35.7447	−1.37786	−0.688929	+	0.724829i	$0.741919\pi$
$674$	33.1606	1.27730
$675$	13.1589	0.506486
$676$	−5.04667	−0.194103
$677$	24.0149	0.922969	0.461485	−	0.887148i	$-0.347317\pi$
$677$	24.0149	0.922969	0.461485	+	0.887148i	$0.347317\pi$
$678$	−64.1329	−2.46301
$679$	−44.5957	−1.71142
$680$	−56.6110	−2.17093
$681$	40.3154	1.54489
$682$	9.64237	0.369226
$683$	−27.0994	−1.03693	−0.518465	−	0.855099i	$-0.673496\pi$
$683$	−27.0994	−1.03693	−0.518465	+	0.855099i	$0.673496\pi$
$684$	−12.4825	−0.477279
$685$	25.3836	0.969856
$686$	−46.2859	−1.76720
$687$	−22.0458	−0.841099
$688$	−174.313	−6.64563
$689$	43.8328	1.66990
$690$	−7.08208	−0.269610
$691$	−8.05677	−0.306494	−0.153247	−	0.988188i	$-0.548973\pi$
$691$	−8.05677	−0.306494	−0.153247	+	0.988188i	$0.548973\pi$
$692$	1.08745	0.0413385
$693$	−4.89712	−0.186026
$694$	−9.66209	−0.366768
$695$	29.7587	1.12881
$696$	143.911	5.45494
$697$	2.11651	0.0801685
$698$	−2.70691	−0.102458
$699$	28.2196	1.06736
$700$	36.1693	1.36707
$701$	−21.9238	−0.828051	−0.414026	−	0.910265i	$-0.635878\pi$
$701$	−21.9238	−0.828051	−0.414026	+	0.910265i	$0.635878\pi$
$702$	51.2802	1.93545
$703$	−20.9507	−0.790169
$704$	−119.159	−4.49098
$705$	18.2139	0.685975
$706$	36.4672	1.37246
$707$	−2.82388	−0.106203
$708$	−100.185	−3.76517
$709$	−9.43756	−0.354435	−0.177217	−	0.984172i	$-0.556710\pi$
$709$	−9.43756	−0.354435	−0.177217	+	0.984172i	$0.556710\pi$
$710$	19.1560	0.718912
$711$	5.22971	0.196129
$712$	21.2850	0.797690
$713$	−0.728263	−0.0272736
$714$	−48.4154	−1.81190
$715$	27.3205	1.02173
$716$	52.0357	1.94466
$717$	9.44557	0.352751
$718$	−101.151	−3.77492
$719$	33.6557	1.25515	0.627574	−	0.778557i	$-0.284048\pi$
$719$	33.6557	1.25515	0.627574	+	0.778557i	$0.284048\pi$
$720$	7.85310	0.292668
$721$	36.7010	1.36682
$722$	−66.0868	−2.45949
$723$	34.8796	1.29719
$724$	−97.2259	−3.61337
$725$	23.6944	0.879989
$726$	−56.8924	−2.11147
$727$	34.8415	1.29220	0.646099	−	0.763253i	$-0.276399\pi$
$727$	34.8415	1.29220	0.646099	+	0.763253i	$0.276399\pi$
$728$	88.0353	3.26280
$729$	29.3968	1.08877
$730$	50.8243	1.88109
$731$	49.6127	1.83499
$732$	56.7963	2.09925
$733$	4.98002	0.183941	0.0919707	−	0.995762i	$-0.470683\pi$
$733$	4.98002	0.183941	0.0919707	+	0.995762i	$0.470683\pi$
$734$	−24.9844	−0.922191
$735$	−2.42427	−0.0894204
$736$	19.1412	0.705553
$737$	−10.8145	−0.398357
$738$	−0.521511	−0.0191971
$739$	36.8832	1.35677	0.678385	−	0.734707i	$-0.262680\pi$
$739$	36.8832	1.35677	0.678385	+	0.734707i	$0.262680\pi$
$740$	27.2532	1.00185
$741$	37.1980	1.36650
$742$	96.2220	3.53242
$743$	−12.6934	−0.465676	−0.232838	−	0.972516i	$-0.574801\pi$
$743$	−12.6934	−0.465676	−0.232838	+	0.972516i	$0.574801\pi$
$744$	−10.6665	−0.391053
$745$	−15.5167	−0.568489
$746$	8.51590	0.311789
$747$	4.00292	0.146459
$748$	101.798	3.72209
$749$	−34.2290	−1.25070
$750$	−52.4888	−1.91662
$751$	16.8456	0.614706	0.307353	−	0.951596i	$-0.400557\pi$
$751$	16.8456	0.614706	0.307353	+	0.951596i	$0.400557\pi$
$752$	−95.5558	−3.48456
$753$	−6.73104	−0.245293
$754$	92.3371	3.36272
$755$	−1.37330	−0.0499795
$756$	81.8443	2.97665
$757$	8.84565	0.321500	0.160750	−	0.986995i	$-0.448609\pi$
$757$	8.84565	0.321500	0.160750	+	0.986995i	$0.448609\pi$
$758$	−35.6567	−1.29511
$759$	7.95399	0.288712
$760$	95.4799	3.46342
$761$	36.0912	1.30831	0.654153	−	0.756362i	$-0.273025\pi$
$761$	36.0912	1.30831	0.654153	+	0.756362i	$0.273025\pi$
$762$	20.3891	0.738620
$763$	16.4360	0.595024
$764$	−24.6851	−0.893074
$765$	−2.23513	−0.0808114
$766$	−91.5859	−3.30913
$767$	−40.1486	−1.44968
$768$	42.5331	1.53478
$769$	−17.9574	−0.647559	−0.323780	−	0.946133i	$-0.604954\pi$
$769$	−17.9574	−0.647559	−0.323780	+	0.946133i	$0.604954\pi$
$770$	59.9742	2.16132
$771$	12.4919	0.449884
$772$	29.3771	1.05731
$773$	−18.9060	−0.680002	−0.340001	−	0.940425i	$-0.610427\pi$
$773$	−18.9060	−0.680002	−0.340001	+	0.940425i	$0.610427\pi$
$774$	−12.2246	−0.439406
$775$	−1.75620	−0.0630845
$776$	−142.666	−5.12141
$777$	14.5576	0.522249
$778$	−46.4660	−1.66589
$779$	−3.56970	−0.127898
$780$	−48.3883	−1.73258
$781$	−21.5144	−0.769846
$782$	−10.5749	−0.378159
$783$	53.6161	1.91608
$784$	12.7184	0.454230
$785$	−13.8682	−0.494977
$786$	15.4686	0.551747
$787$	19.0410	0.678737	0.339368	−	0.940654i	$-0.389787\pi$
$787$	19.0410	0.678737	0.339368	+	0.940654i	$0.389787\pi$
$788$	−97.7126	−3.48087
$789$	−21.2115	−0.755149
$790$	−64.0474	−2.27871
$791$	−41.0193	−1.45848
$792$	−15.6664	−0.556680
$793$	22.7608	0.808261
$794$	−26.5670	−0.942827
$795$	−33.0328	−1.17155
$796$	−108.902	−3.85994
$797$	1.45621	0.0515817	0.0257909	−	0.999667i	$-0.491790\pi$
$797$	1.45621	0.0515817	0.0257909	+	0.999667i	$0.491790\pi$
$798$	81.6573	2.89064
$799$	27.1969	0.962158
$800$	46.1587	1.63196
$801$	0.840383	0.0296935
$802$	−36.2289	−1.27929
$803$	−57.0816	−2.01437
$804$	19.1539	0.675506
$805$	−4.52969	−0.159651
$806$	−6.84389	−0.241066
$807$	33.6508	1.18457
$808$	−9.03388	−0.317811
$809$	−8.90145	−0.312958	−0.156479	−	0.987681i	$-0.550014\pi$
$809$	−8.90145	−0.312958	−0.156479	+	0.987681i	$0.550014\pi$
$810$	−33.9990	−1.19460
$811$	8.92533	0.313411	0.156705	−	0.987645i	$-0.449913\pi$
$811$	8.92533	0.313411	0.156705	+	0.987645i	$0.449913\pi$
$812$	147.372	5.17175
$813$	−26.4343	−0.927092
$814$	−42.0996	−1.47559
$815$	−33.5240	−1.17430
$816$	−87.1984	−3.05256
$817$	−83.6766	−2.92747
$818$	99.7200	3.48663
$819$	3.47584	0.121456
$820$	4.64357	0.162160
$821$	12.2022	0.425861	0.212931	−	0.977067i	$-0.431699\pi$
$821$	12.2022	0.425861	0.212931	+	0.977067i	$0.431699\pi$
$822$	69.4486	2.42230
$823$	−5.84734	−0.203825	−0.101913	−	0.994793i	$-0.532496\pi$
$823$	−5.84734	−0.203825	−0.101913	+	0.994793i	$0.532496\pi$
$824$	117.410	4.09018
$825$	19.1810	0.667796
$826$	−88.1343	−3.06658
$827$	−0.432977	−0.0150561	−0.00752805	−	0.999972i	$-0.502396\pi$
$827$	−0.432977	−0.0150561	−0.00752805	+	0.999972i	$0.502396\pi$
$828$	1.89446	0.0658370
$829$	24.5142	0.851414	0.425707	−	0.904861i	$-0.360025\pi$
$829$	24.5142	0.851414	0.425707	+	0.904861i	$0.360025\pi$
$830$	−49.0231	−1.70162
$831$	−23.6917	−0.821854
$832$	84.5759	2.93214
$833$	−3.61990	−0.125422
$834$	81.4188	2.81930
$835$	23.6699	0.819132
$836$	−171.692	−5.93808
$837$	−3.97395	−0.137360
$838$	14.1043	0.487223
$839$	34.5702	1.19350	0.596748	−	0.802429i	$-0.296459\pi$
$839$	34.5702	1.19350	0.596748	+	0.802429i	$0.296459\pi$
$840$	−66.3441	−2.28909
$841$	67.5432	2.32908
$842$	−49.6631	−1.71150
$843$	40.5561	1.39683
$844$	−64.3754	−2.21589
$845$	1.52412	0.0524313
$846$	−6.70136	−0.230398
$847$	−36.3883	−1.25032
$848$	173.300	5.95116
$849$	9.15075	0.314053
$850$	−25.5013	−0.874689
$851$	3.17967	0.108998
$852$	38.1049	1.30545
$853$	39.2198	1.34286	0.671431	−	0.741067i	$-0.265680\pi$
$853$	39.2198	1.34286	0.671431	+	0.741067i	$0.265680\pi$
$854$	49.9647	1.70976
$855$	3.76977	0.128923
$856$	−109.502	−3.74270
$857$	5.79515	0.197959	0.0989793	−	0.995089i	$-0.468442\pi$
$857$	5.79515	0.197959	0.0989793	+	0.995089i	$0.468442\pi$
$858$	74.7482	2.55186
$859$	−0.745536	−0.0254374	−0.0127187	−	0.999919i	$-0.504049\pi$
$859$	−0.745536	−0.0254374	−0.0127187	+	0.999919i	$0.504049\pi$
$860$	108.849	3.71172
$861$	2.48040	0.0845319
$862$	−32.4163	−1.10410
$863$	8.48743	0.288916	0.144458	−	0.989511i	$-0.453856\pi$
$863$	8.48743	0.288916	0.144458	+	0.989511i	$0.453856\pi$
$864$	104.449	3.55342
$865$	−0.328414	−0.0111664
$866$	−91.6496	−3.11438
$867$	−2.82644	−0.0959908
$868$	−10.9230	−0.370751
$869$	71.9326	2.44015
$870$	−69.5860	−2.35919
$871$	7.67583	0.260086
$872$	52.5805	1.78060
$873$	−5.63279	−0.190641
$874$	17.8356	0.603300
$875$	−33.5717	−1.13493
$876$	101.099	3.41582
$877$	−27.1053	−0.915280	−0.457640	−	0.889137i	$-0.651305\pi$
$877$	−27.1053	−0.915280	−0.457640	+	0.889137i	$0.651305\pi$
$878$	−72.6763	−2.45271
$879$	−1.60248	−0.0540504
$880$	108.016	3.64123
$881$	37.0173	1.24714	0.623572	−	0.781766i	$-0.285681\pi$
$881$	37.0173	1.24714	0.623572	+	0.781766i	$0.285681\pi$
$882$	0.891949	0.0300335
$883$	0.992259	0.0333922	0.0166961	−	0.999861i	$-0.494685\pi$
$883$	0.992259	0.0333922	0.0166961	+	0.999861i	$0.494685\pi$
$884$	−72.2532	−2.43014
$885$	30.2563	1.01705
$886$	−4.19696	−0.141000
$887$	−20.4945	−0.688138	−0.344069	−	0.938944i	$-0.611805\pi$
$887$	−20.4945	−0.688138	−0.344069	+	0.938944i	$0.611805\pi$
$888$	46.5711	1.56282
$889$	13.0408	0.437376
$890$	−10.2920	−0.344990
$891$	38.1848	1.27924
$892$	21.9357	0.734460
$893$	−45.8702	−1.53499
$894$	−42.4533	−1.41985
$895$	−15.7150	−0.525296
$896$	77.8804	2.60180
$897$	−5.64553	−0.188499
$898$	97.8332	3.26474
$899$	−7.15565	−0.238654
$900$	4.56847	0.152282
$901$	−49.3244	−1.64323
$902$	−7.17318	−0.238841
$903$	58.1426	1.93487
$904$	−131.225	−4.36448
$905$	29.3627	0.976050
$906$	−3.75731	−0.124828
$907$	−57.0090	−1.89295	−0.946476	−	0.322773i	$-0.895385\pi$
$907$	−57.0090	−1.89295	−0.946476	+	0.322773i	$0.895385\pi$
$908$	132.075	4.38305
$909$	−0.356679	−0.0118303
$910$	−42.5680	−1.41112
$911$	−18.0432	−0.597798	−0.298899	−	0.954285i	$-0.596619\pi$
$911$	−18.0432	−0.597798	−0.298899	+	0.954285i	$0.596619\pi$
$912$	147.069	4.86993
$913$	55.0586	1.82217
$914$	62.0494	2.05241
$915$	−17.1528	−0.567053
$916$	−72.2227	−2.38630
$917$	9.89370	0.326719
$918$	−57.7048	−1.90454
$919$	−26.0395	−0.858964	−0.429482	−	0.903076i	$-0.641304\pi$
$919$	−26.0395	−0.858964	−0.429482	+	0.903076i	$0.641304\pi$
$920$	−14.4909	−0.477752
$921$	−31.2779	−1.03064
$922$	−51.5381	−1.69732
$923$	15.2703	0.502629
$924$	119.300	3.92468
$925$	7.66774	0.252114
$926$	5.99589	0.197037
$927$	4.63564	0.152254
$928$	188.074	6.17384
$929$	2.95248	0.0968676	0.0484338	−	0.998826i	$-0.484577\pi$
$929$	2.95248	0.0968676	0.0484338	+	0.998826i	$0.484577\pi$
$930$	5.15762	0.169125
$931$	6.10531	0.200094
$932$	92.4483	3.02825
$933$	−4.33224	−0.141831
$934$	−10.1374	−0.331705
$935$	−30.7434	−1.00542
$936$	11.1196	0.363454
$937$	−7.48583	−0.244552	−0.122276	−	0.992496i	$-0.539019\pi$
$937$	−7.48583	−0.244552	−0.122276	+	0.992496i	$0.539019\pi$
$938$	16.8500	0.550173
$939$	−53.1764	−1.73535
$940$	59.6694	1.94620
$941$	−47.6204	−1.55238	−0.776191	−	0.630498i	$-0.782851\pi$
$941$	−47.6204	−1.55238	−0.776191	+	0.630498i	$0.782851\pi$
$942$	−37.9430	−1.23625
$943$	0.541771	0.0176425
$944$	−158.734	−5.16635
$945$	−24.7174	−0.804057
$946$	−168.145	−5.46687
$947$	40.1299	1.30405	0.652023	−	0.758199i	$-0.273920\pi$
$947$	40.1299	1.30405	0.652023	+	0.758199i	$0.273920\pi$
$948$	−127.402	−4.13783
$949$	40.5150	1.31517
$950$	43.0105	1.39544
$951$	4.04630	0.131210
$952$	−99.0647	−3.21071
$953$	12.2403	0.396501	0.198251	−	0.980151i	$-0.436474\pi$
$953$	12.2403	0.396501	0.198251	+	0.980151i	$0.436474\pi$
$954$	12.1536	0.393488
$955$	7.45501	0.241239
$956$	30.9440	1.00080
$957$	78.1531	2.52633
$958$	45.5206	1.47071
$959$	44.4192	1.43437
$960$	−63.7371	−2.05711
$961$	−30.4696	−0.982891
$962$	29.8812	0.963407
$963$	−4.32339	−0.139319
$964$	114.267	3.68028
$965$	−8.87204	−0.285601
$966$	−12.3931	−0.398741
$967$	−15.9999	−0.514521	−0.257260	−	0.966342i	$-0.582820\pi$
$967$	−15.9999	−0.514521	−0.257260	+	0.966342i	$0.582820\pi$
$968$	−116.410	−3.74155
$969$	−41.8584	−1.34468
$970$	68.9839	2.21494
$971$	20.9248	0.671508	0.335754	−	0.941950i	$-0.391009\pi$
$971$	20.9248	0.671508	0.335754	+	0.941950i	$0.391009\pi$
$972$	19.5797	0.628018
$973$	52.0753	1.66946
$974$	−108.399	−3.47333
$975$	−13.6141	−0.436001
$976$	89.9887	2.88047
$977$	16.9421	0.542026	0.271013	−	0.962576i	$-0.412641\pi$
$977$	16.9421	0.542026	0.271013	+	0.962576i	$0.412641\pi$
$978$	−91.7207	−2.93290
$979$	11.5591	0.369431
$980$	−7.94197	−0.253697
$981$	2.07600	0.0662816
$982$	−56.1018	−1.79028
$983$	32.5983	1.03972	0.519862	−	0.854250i	$-0.325983\pi$
$983$	32.5983	1.03972	0.519862	+	0.854250i	$0.325983\pi$
$984$	7.93506	0.252960
$985$	29.5097	0.940256
$986$	−103.905	−3.30902
$987$	31.8729	1.01453
$988$	121.862	3.87695
$989$	12.6996	0.403822
$990$	7.57522	0.240756
$991$	−16.4230	−0.521694	−0.260847	−	0.965380i	$-0.584002\pi$
$991$	−16.4230	−0.521694	−0.260847	+	0.965380i	$0.584002\pi$
$992$	−13.9398	−0.442589
$993$	−20.9198	−0.663868
$994$	33.5215	1.06324
$995$	32.8891	1.04265
$996$	−97.5161	−3.08992
$997$	24.2257	0.767234	0.383617	−	0.923492i	$-0.374678\pi$
$997$	24.2257	0.767234	0.383617	+	0.923492i	$0.374678\pi$
$998$	−49.8085	−1.57666
$999$	17.3507	0.548951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.5	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.5	✓	169	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70691 q^{2} +1.62616 q^{3} +5.32735 q^{4} -1.60888 q^{5} -4.40186 q^{6} -2.81542 q^{7} -9.00682 q^{8} -0.355610 q^{9} +O(q^{10})\)	\(q-2.70691 q^{2} +1.62616 q^{3} +5.32735 q^{4} -1.60888 q^{5} -4.40186 q^{6} -2.81542 q^{7} -9.00682 q^{8} -0.355610 q^{9} +4.35510 q^{10} -4.89128 q^{11} +8.66311 q^{12} +3.47170 q^{13} +7.62109 q^{14} -2.61630 q^{15} +13.7259 q^{16} -3.90665 q^{17} +0.962604 q^{18} +6.58894 q^{19} -8.57109 q^{20} -4.57832 q^{21} +13.2402 q^{22} -1.00000 q^{23} -14.6465 q^{24} -2.41149 q^{25} -9.39756 q^{26} -5.45675 q^{27} -14.9987 q^{28} -9.82564 q^{29} +7.08208 q^{30} +0.728263 q^{31} -19.1412 q^{32} -7.95399 q^{33} +10.5749 q^{34} +4.52969 q^{35} -1.89446 q^{36} -3.17967 q^{37} -17.8356 q^{38} +5.64553 q^{39} +14.4909 q^{40} -0.541771 q^{41} +12.3931 q^{42} -12.6996 q^{43} -26.0575 q^{44} +0.572136 q^{45} +2.70691 q^{46} -6.96170 q^{47} +22.3205 q^{48} +0.926600 q^{49} +6.52768 q^{50} -6.35283 q^{51} +18.4949 q^{52} +12.6258 q^{53} +14.7709 q^{54} +7.86951 q^{55} +25.3580 q^{56} +10.7147 q^{57} +26.5971 q^{58} -11.5645 q^{59} -13.9379 q^{60} +6.55611 q^{61} -1.97134 q^{62} +1.00119 q^{63} +24.3615 q^{64} -5.58556 q^{65} +21.5307 q^{66} +2.21097 q^{67} -20.8121 q^{68} -1.62616 q^{69} -12.2614 q^{70} +4.39852 q^{71} +3.20292 q^{72} +11.6701 q^{73} +8.60708 q^{74} -3.92146 q^{75} +35.1016 q^{76} +13.7710 q^{77} -15.2819 q^{78} -14.7063 q^{79} -22.0834 q^{80} -7.80671 q^{81} +1.46652 q^{82} -11.2565 q^{83} -24.3903 q^{84} +6.28535 q^{85} +34.3765 q^{86} -15.9780 q^{87} +44.0549 q^{88} -2.36321 q^{89} -1.54872 q^{90} -9.77429 q^{91} -5.32735 q^{92} +1.18427 q^{93} +18.8447 q^{94} -10.6008 q^{95} -31.1266 q^{96} +15.8398 q^{97} -2.50822 q^{98} +1.73939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * q^99

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