LMFDB - Embedded newform 8035.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42672 q^{2} -1.34880 q^{3} +3.88897 q^{4} -1.00000 q^{5} +3.27316 q^{6} -0.627259 q^{7} -4.58399 q^{8} -1.18074 q^{9} +O(q^{10})$	\(q-2.42672 q^{2} -1.34880 q^{3} +3.88897 q^{4} -1.00000 q^{5} +3.27316 q^{6} -0.627259 q^{7} -4.58399 q^{8} -1.18074 q^{9} +2.42672 q^{10} +2.13053 q^{11} -5.24544 q^{12} +0.820527 q^{13} +1.52218 q^{14} +1.34880 q^{15} +3.34612 q^{16} +1.66858 q^{17} +2.86532 q^{18} +1.95034 q^{19} -3.88897 q^{20} +0.846047 q^{21} -5.17019 q^{22} +5.92531 q^{23} +6.18288 q^{24} +1.00000 q^{25} -1.99119 q^{26} +5.63898 q^{27} -2.43939 q^{28} -8.03306 q^{29} -3.27316 q^{30} +5.79518 q^{31} +1.04788 q^{32} -2.87365 q^{33} -4.04918 q^{34} +0.627259 q^{35} -4.59185 q^{36} +4.32800 q^{37} -4.73294 q^{38} -1.10673 q^{39} +4.58399 q^{40} +7.61558 q^{41} -2.05312 q^{42} +7.56106 q^{43} +8.28554 q^{44} +1.18074 q^{45} -14.3791 q^{46} +12.0438 q^{47} -4.51325 q^{48} -6.60655 q^{49} -2.42672 q^{50} -2.25058 q^{51} +3.19100 q^{52} -5.08834 q^{53} -13.6842 q^{54} -2.13053 q^{55} +2.87535 q^{56} -2.63062 q^{57} +19.4940 q^{58} +6.81001 q^{59} +5.24544 q^{60} -12.0006 q^{61} -14.0633 q^{62} +0.740630 q^{63} -9.23515 q^{64} -0.820527 q^{65} +6.97355 q^{66} +6.49055 q^{67} +6.48906 q^{68} -7.99205 q^{69} -1.52218 q^{70} +1.22585 q^{71} +5.41250 q^{72} -3.76723 q^{73} -10.5028 q^{74} -1.34880 q^{75} +7.58482 q^{76} -1.33639 q^{77} +2.68571 q^{78} +3.47926 q^{79} -3.34612 q^{80} -4.06364 q^{81} -18.4809 q^{82} +9.10722 q^{83} +3.29025 q^{84} -1.66858 q^{85} -18.3486 q^{86} +10.8350 q^{87} -9.76630 q^{88} +1.13430 q^{89} -2.86532 q^{90} -0.514683 q^{91} +23.0433 q^{92} -7.81653 q^{93} -29.2270 q^{94} -1.95034 q^{95} -1.41338 q^{96} +8.22788 q^{97} +16.0322 q^{98} -2.51559 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) $ 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * 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 $

$2$	−2.42672	−1.71595	−0.857975	−	0.513692i	$-0.828277\pi$
$2$	−2.42672	−1.71595	−0.857975	+	0.513692i	$0.828277\pi$
$3$	−1.34880	−0.778730	−0.389365	−	0.921084i	$-0.627306\pi$
$3$	−1.34880	−0.778730	−0.389365	+	0.921084i	$0.627306\pi$
$4$	3.88897	1.94448
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.27316	1.33626
$7$	−0.627259	−0.237082	−0.118541	−	0.992949i	$-0.537822\pi$
$7$	−0.627259	−0.237082	−0.118541	+	0.992949i	$0.537822\pi$
$8$	−4.58399	−1.62068
$9$	−1.18074	−0.393580
$10$	2.42672	0.767396
$11$	2.13053	0.642377	0.321189	−	0.947015i	$-0.395918\pi$
$11$	2.13053	0.642377	0.321189	+	0.947015i	$0.395918\pi$
$12$	−5.24544	−1.51423
$13$	0.820527	0.227573	0.113787	−	0.993505i	$-0.463702\pi$
$13$	0.820527	0.227573	0.113787	+	0.993505i	$0.463702\pi$
$14$	1.52218	0.406820
$15$	1.34880	0.348259
$16$	3.34612	0.836531
$17$	1.66858	0.404691	0.202345	−	0.979314i	$-0.435144\pi$
$17$	1.66858	0.404691	0.202345	+	0.979314i	$0.435144\pi$
$18$	2.86532	0.675363
$19$	1.95034	0.447440	0.223720	−	0.974654i	$-0.428180\pi$
$19$	1.95034	0.447440	0.223720	+	0.974654i	$0.428180\pi$
$20$	−3.88897	−0.869599
$21$	0.846047	0.184623
$22$	−5.17019	−1.10229
$23$	5.92531	1.23551	0.617756	−	0.786370i	$-0.288042\pi$
$23$	5.92531	1.23551	0.617756	+	0.786370i	$0.288042\pi$
$24$	6.18288	1.26208
$25$	1.00000	0.200000
$26$	−1.99119	−0.390504
$27$	5.63898	1.08522
$28$	−2.43939	−0.461001
$29$	−8.03306	−1.49170	−0.745851	−	0.666113i	$-0.767957\pi$
$29$	−8.03306	−1.49170	−0.745851	+	0.666113i	$0.767957\pi$
$30$	−3.27316	−0.597594
$31$	5.79518	1.04084	0.520422	−	0.853909i	$-0.325775\pi$
$31$	5.79518	1.04084	0.520422	+	0.853909i	$0.325775\pi$
$32$	1.04788	0.185240
$33$	−2.87365	−0.500239
$34$	−4.04918	−0.694429
$35$	0.627259	0.106026
$36$	−4.59185	−0.765309
$37$	4.32800	0.711519	0.355760	−	0.934578i	$-0.384222\pi$
$37$	4.32800	0.711519	0.355760	+	0.934578i	$0.384222\pi$
$38$	−4.73294	−0.767784
$39$	−1.10673	−0.177218
$40$	4.58399	0.724792
$41$	7.61558	1.18935	0.594677	−	0.803965i	$-0.297280\pi$
$41$	7.61558	1.18935	0.594677	+	0.803965i	$0.297280\pi$
$42$	−2.05312	−0.316803
$43$	7.56106	1.15305	0.576526	−	0.817079i	$-0.304408\pi$
$43$	7.56106	1.15305	0.576526	+	0.817079i	$0.304408\pi$
$44$	8.28554	1.24909
$45$	1.18074	0.176014
$46$	−14.3791	−2.12008
$47$	12.0438	1.75677	0.878386	−	0.477951i	$-0.158621\pi$
$47$	12.0438	1.75677	0.878386	+	0.477951i	$0.158621\pi$
$48$	−4.51325	−0.651431
$49$	−6.60655	−0.943792
$50$	−2.42672	−0.343190
$51$	−2.25058	−0.315145
$52$	3.19100	0.442512
$53$	−5.08834	−0.698938	−0.349469	−	0.936948i	$-0.613638\pi$
$53$	−5.08834	−0.698938	−0.349469	+	0.936948i	$0.613638\pi$
$54$	−13.6842	−1.86219
$55$	−2.13053	−0.287280
$56$	2.87535	0.384235
$57$	−2.63062	−0.348435
$58$	19.4940	2.55968
$59$	6.81001	0.886587	0.443294	−	0.896376i	$-0.353810\pi$
$59$	6.81001	0.886587	0.443294	+	0.896376i	$0.353810\pi$
$60$	5.24544	0.677183
$61$	−12.0006	−1.53652	−0.768260	−	0.640137i	$-0.778877\pi$
$61$	−12.0006	−1.53652	−0.768260	+	0.640137i	$0.778877\pi$
$62$	−14.0633	−1.78604
$63$	0.740630	0.0933106
$64$	−9.23515	−1.15439
$65$	−0.820527	−0.101774
$66$	6.97355	0.858384
$67$	6.49055	0.792947	0.396473	−	0.918046i	$-0.370234\pi$
$67$	6.49055	0.792947	0.396473	+	0.918046i	$0.370234\pi$
$68$	6.48906	0.786914
$69$	−7.99205	−0.962130
$70$	−1.52218	−0.181936
$71$	1.22585	0.145482	0.0727410	−	0.997351i	$-0.476825\pi$
$71$	1.22585	0.145482	0.0727410	+	0.997351i	$0.476825\pi$
$72$	5.41250	0.637869
$73$	−3.76723	−0.440921	−0.220460	−	0.975396i	$-0.570756\pi$
$73$	−3.76723	−0.440921	−0.220460	+	0.975396i	$0.570756\pi$
$74$	−10.5028	−1.22093
$75$	−1.34880	−0.155746
$76$	7.58482	0.870039
$77$	−1.33639	−0.152296
$78$	2.68571	0.304097
$79$	3.47926	0.391447	0.195724	−	0.980659i	$-0.437294\pi$
$79$	3.47926	0.391447	0.195724	+	0.980659i	$0.437294\pi$
$80$	−3.34612	−0.374108
$81$	−4.06364	−0.451515
$82$	−18.4809	−2.04087
$83$	9.10722	0.999647	0.499823	−	0.866127i	$-0.333398\pi$
$83$	9.10722	0.999647	0.499823	+	0.866127i	$0.333398\pi$
$84$	3.29025	0.358996
$85$	−1.66858	−0.180983
$86$	−18.3486	−1.97858
$87$	10.8350	1.16163
$88$	−9.76630	−1.04109
$89$	1.13430	0.120236	0.0601178	−	0.998191i	$-0.480852\pi$
$89$	1.13430	0.120236	0.0601178	+	0.998191i	$0.480852\pi$
$90$	−2.86532	−0.302032
$91$	−0.514683	−0.0539535
$92$	23.0433	2.40243
$93$	−7.81653	−0.810537
$94$	−29.2270	−3.01453
$95$	−1.95034	−0.200101
$96$	−1.41338	−0.144252
$97$	8.22788	0.835415	0.417707	−	0.908582i	$-0.362834\pi$
$97$	8.22788	0.835415	0.417707	+	0.908582i	$0.362834\pi$
$98$	16.0322	1.61950
$99$	−2.51559	−0.252827
$100$	3.88897	0.388897
$101$	18.1512	1.80611	0.903055	−	0.429525i	$-0.141319\pi$
$101$	18.1512	1.80611	0.903055	+	0.429525i	$0.141319\pi$
$102$	5.46153	0.540772
$103$	−2.14175	−0.211033	−0.105516	−	0.994418i	$-0.533650\pi$
$103$	−2.14175	−0.211033	−0.105516	+	0.994418i	$0.533650\pi$
$104$	−3.76129	−0.368825
$105$	−0.846047	−0.0825658
$106$	12.3480	1.19934
$107$	5.26463	0.508951	0.254475	−	0.967079i	$-0.418097\pi$
$107$	5.26463	0.508951	0.254475	+	0.967079i	$0.418097\pi$
$108$	21.9298	2.11020
$109$	−7.67608	−0.735235	−0.367617	−	0.929977i	$-0.619826\pi$
$109$	−7.67608	−0.735235	−0.367617	+	0.929977i	$0.619826\pi$
$110$	5.17019	0.492958
$111$	−5.83761	−0.554081
$112$	−2.09889	−0.198326
$113$	−13.7824	−1.29654	−0.648270	−	0.761411i	$-0.724507\pi$
$113$	−13.7824	−1.29654	−0.648270	+	0.761411i	$0.724507\pi$
$114$	6.38378	0.597896
$115$	−5.92531	−0.552538
$116$	−31.2403	−2.90059
$117$	−0.968829	−0.0895682
$118$	−16.5260	−1.52134
$119$	−1.04663	−0.0959448
$120$	−6.18288	−0.564417
$121$	−6.46086	−0.587351
$122$	29.1221	2.63659
$123$	−10.2719	−0.926185
$124$	22.5372	2.02390
$125$	−1.00000	−0.0894427
$126$	−1.79730	−0.160116
$127$	5.32523	0.472537	0.236269	−	0.971688i	$-0.424075\pi$
$127$	5.32523	0.472537	0.236269	+	0.971688i	$0.424075\pi$
$128$	20.3154	1.79564
$129$	−10.1984	−0.897916
$130$	1.99119	0.174639
$131$	−5.96924	−0.521535	−0.260768	−	0.965402i	$-0.583976\pi$
$131$	−5.96924	−0.521535	−0.260768	+	0.965402i	$0.583976\pi$
$132$	−11.1755	−0.972705
$133$	−1.22337	−0.106080
$134$	−15.7507	−1.36066
$135$	−5.63898	−0.485326
$136$	−7.64876	−0.655876
$137$	−0.526439	−0.0449767	−0.0224884	−	0.999747i	$-0.507159\pi$
$137$	−0.526439	−0.0449767	−0.0224884	+	0.999747i	$0.507159\pi$
$138$	19.3945	1.65097
$139$	8.58594	0.728250	0.364125	−	0.931350i	$-0.381368\pi$
$139$	8.58594	0.728250	0.364125	+	0.931350i	$0.381368\pi$
$140$	2.43939	0.206166
$141$	−16.2447	−1.36805
$142$	−2.97480	−0.249640
$143$	1.74815	0.146188
$144$	−3.95090	−0.329242
$145$	8.03306	0.667109
$146$	9.14201	0.756598
$147$	8.91091	0.734959
$148$	16.8314	1.38354
$149$	−11.5470	−0.945963	−0.472982	−	0.881072i	$-0.656822\pi$
$149$	−11.5470	−0.945963	−0.472982	+	0.881072i	$0.656822\pi$
$150$	3.27316	0.267252
$151$	−4.11496	−0.334871	−0.167435	−	0.985883i	$-0.553549\pi$
$151$	−4.11496	−0.334871	−0.167435	+	0.985883i	$0.553549\pi$
$152$	−8.94036	−0.725159
$153$	−1.97016	−0.159278
$154$	3.24305	0.261332
$155$	−5.79518	−0.465480
$156$	−4.30402	−0.344598
$157$	8.51716	0.679743	0.339872	−	0.940472i	$-0.389616\pi$
$157$	8.51716	0.679743	0.339872	+	0.940472i	$0.389616\pi$
$158$	−8.44318	−0.671704
$159$	6.86315	0.544284
$160$	−1.04788	−0.0828421
$161$	−3.71670	−0.292917
$162$	9.86131	0.774777
$163$	−18.2032	−1.42578	−0.712891	−	0.701275i	$-0.752615\pi$
$163$	−18.2032	−1.42578	−0.712891	+	0.701275i	$0.752615\pi$
$164$	29.6167	2.31268
$165$	2.87365	0.223713
$166$	−22.1007	−1.71534
$167$	−2.27177	−0.175795	−0.0878976	−	0.996130i	$-0.528015\pi$
$167$	−2.27177	−0.175795	−0.0878976	+	0.996130i	$0.528015\pi$
$168$	−3.87827	−0.299215
$169$	−12.3267	−0.948210
$170$	4.04918	0.310558
$171$	−2.30285	−0.176103
$172$	29.4047	2.24209
$173$	−8.14893	−0.619551	−0.309776	−	0.950810i	$-0.600254\pi$
$173$	−8.14893	−0.619551	−0.309776	+	0.950810i	$0.600254\pi$
$174$	−26.2935	−1.99330
$175$	−0.627259	−0.0474164
$176$	7.12900	0.537368
$177$	−9.18534	−0.690412
$178$	−2.75263	−0.206318
$179$	16.6754	1.24638	0.623190	−	0.782070i	$-0.285836\pi$
$179$	16.6754	1.24638	0.623190	+	0.782070i	$0.285836\pi$
$180$	4.59185	0.342257
$181$	−2.28501	−0.169843	−0.0849217	−	0.996388i	$-0.527064\pi$
$181$	−2.28501	−0.169843	−0.0849217	+	0.996388i	$0.527064\pi$
$182$	1.24899	0.0925814
$183$	16.1864	1.19653
$184$	−27.1615	−2.00238
$185$	−4.32800	−0.318201
$186$	18.9685	1.39084
$187$	3.55496	0.259964
$188$	46.8380	3.41601
$189$	−3.53710	−0.257286
$190$	4.73294	0.343363
$191$	3.19314	0.231048	0.115524	−	0.993305i	$-0.463145\pi$
$191$	3.19314	0.231048	0.115524	+	0.993305i	$0.463145\pi$
$192$	12.4564	0.898961
$193$	−1.46316	−0.105321	−0.0526603	−	0.998612i	$-0.516770\pi$
$193$	−1.46316	−0.105321	−0.0526603	+	0.998612i	$0.516770\pi$
$194$	−19.9668	−1.43353
$195$	1.10673	0.0792543
$196$	−25.6926	−1.83519
$197$	18.1722	1.29472	0.647358	−	0.762186i	$-0.275874\pi$
$197$	18.1722	1.29472	0.647358	+	0.762186i	$0.275874\pi$
$198$	6.10464	0.433838
$199$	16.4989	1.16958	0.584789	−	0.811185i	$-0.301177\pi$
$199$	16.4989	1.16958	0.584789	+	0.811185i	$0.301177\pi$
$200$	−4.58399	−0.324137
$201$	−8.75445	−0.617491
$202$	−44.0478	−3.09919
$203$	5.03881	0.353655
$204$	−8.75244	−0.612793
$205$	−7.61558	−0.531895
$206$	5.19742	0.362122
$207$	−6.99624	−0.486272
$208$	2.74558	0.190372
$209$	4.15526	0.287425
$210$	2.05312	0.141679
$211$	−17.5657	−1.20927	−0.604636	−	0.796502i	$-0.706682\pi$
$211$	−17.5657	−1.20927	−0.604636	+	0.796502i	$0.706682\pi$
$212$	−19.7884	−1.35907
$213$	−1.65343	−0.113291
$214$	−12.7758	−0.873334
$215$	−7.56106	−0.515660
$216$	−25.8490	−1.75880
$217$	−3.63508	−0.246765
$218$	18.6277	1.26163
$219$	5.08124	0.343358
$220$	−8.28554	−0.558611
$221$	1.36912	0.0920968
$222$	14.1662	0.950775
$223$	7.04735	0.471925	0.235963	−	0.971762i	$-0.424176\pi$
$223$	7.04735	0.471925	0.235963	+	0.971762i	$0.424176\pi$
$224$	−0.657292	−0.0439171
$225$	−1.18074	−0.0787160
$226$	33.4460	2.22480
$227$	25.4506	1.68922	0.844608	−	0.535386i	$-0.179834\pi$
$227$	25.4506	1.68922	0.844608	+	0.535386i	$0.179834\pi$
$228$	−10.2304	−0.677525
$229$	11.0527	0.730385	0.365193	−	0.930932i	$-0.381003\pi$
$229$	11.0527	0.730385	0.365193	+	0.930932i	$0.381003\pi$
$230$	14.3791	0.948127
$231$	1.80253	0.118597
$232$	36.8234	2.41758
$233$	25.9567	1.70048	0.850240	−	0.526396i	$-0.176457\pi$
$233$	25.9567	1.70048	0.850240	+	0.526396i	$0.176457\pi$
$234$	2.35107	0.153695
$235$	−12.0438	−0.785653
$236$	26.4839	1.72395
$237$	−4.69282	−0.304832
$238$	2.53989	0.164636
$239$	−13.3243	−0.861877	−0.430938	−	0.902381i	$-0.641817\pi$
$239$	−13.3243	−0.861877	−0.430938	+	0.902381i	$0.641817\pi$
$240$	4.51325	0.291329
$241$	16.7118	1.07650	0.538249	−	0.842786i	$-0.319086\pi$
$241$	16.7118	1.07650	0.538249	+	0.842786i	$0.319086\pi$
$242$	15.6787	1.00786
$243$	−11.4359	−0.733614
$244$	−46.6700	−2.98774
$245$	6.60655	0.422077
$246$	24.9270	1.58929
$247$	1.60031	0.101825
$248$	−26.5650	−1.68688
$249$	−12.2838	−0.778455
$250$	2.42672	0.153479
$251$	14.9445	0.943285	0.471643	−	0.881790i	$-0.343661\pi$
$251$	14.9445	0.943285	0.471643	+	0.881790i	$0.343661\pi$
$252$	2.88028	0.181441
$253$	12.6240	0.793665
$254$	−12.9228	−0.810850
$255$	2.25058	0.140937
$256$	−30.8294	−1.92684
$257$	−20.8664	−1.30161	−0.650804	−	0.759245i	$-0.725568\pi$
$257$	−20.8664	−1.30161	−0.650804	+	0.759245i	$0.725568\pi$
$258$	24.7486	1.54078
$259$	−2.71478	−0.168688
$260$	−3.19100	−0.197898
$261$	9.48494	0.587103
$262$	14.4857	0.894928
$263$	−12.7702	−0.787447	−0.393724	−	0.919229i	$-0.628813\pi$
$263$	−12.7702	−0.787447	−0.393724	+	0.919229i	$0.628813\pi$
$264$	13.1728	0.810729
$265$	5.08834	0.312574
$266$	2.96878	0.182028
$267$	−1.52994	−0.0936310
$268$	25.2415	1.54187
$269$	2.68601	0.163769	0.0818844	−	0.996642i	$-0.473906\pi$
$269$	2.68601	0.163769	0.0818844	+	0.996642i	$0.473906\pi$
$270$	13.6842	0.832795
$271$	−1.64054	−0.0996555	−0.0498277	−	0.998758i	$-0.515867\pi$
$271$	−1.64054	−0.0996555	−0.0498277	+	0.998758i	$0.515867\pi$
$272$	5.58328	0.338536
$273$	0.694205	0.0420152
$274$	1.27752	0.0771778
$275$	2.13053	0.128475
$276$	−31.0808	−1.87084
$277$	−10.2340	−0.614902	−0.307451	−	0.951564i	$-0.599476\pi$
$277$	−10.2340	−0.614902	−0.307451	+	0.951564i	$0.599476\pi$
$278$	−20.8357	−1.24964
$279$	−6.84259	−0.409655
$280$	−2.87535	−0.171835
$281$	−6.35756	−0.379260	−0.189630	−	0.981856i	$-0.560729\pi$
$281$	−6.35756	−0.379260	−0.189630	+	0.981856i	$0.560729\pi$
$282$	39.4213	2.34751
$283$	−5.33979	−0.317418	−0.158709	−	0.987325i	$-0.550733\pi$
$283$	−5.33979	−0.317418	−0.158709	+	0.987325i	$0.550733\pi$
$284$	4.76730	0.282887
$285$	2.63062	0.155825
$286$	−4.24228	−0.250851
$287$	−4.77694	−0.281974
$288$	−1.23727	−0.0729069
$289$	−14.2158	−0.836225
$290$	−19.4940	−1.14473
$291$	−11.0978	−0.650563
$292$	−14.6506	−0.857363
$293$	6.81807	0.398316	0.199158	−	0.979967i	$-0.436179\pi$
$293$	6.81807	0.398316	0.199158	+	0.979967i	$0.436179\pi$
$294$	−21.6243	−1.26115
$295$	−6.81001	−0.396494
$296$	−19.8395	−1.15315
$297$	12.0140	0.697122
$298$	28.0212	1.62323
$299$	4.86187	0.281169
$300$	−5.24544	−0.302845
$301$	−4.74275	−0.273368
$302$	9.98585	0.574621
$303$	−24.4823	−1.40647
$304$	6.52609	0.374297
$305$	12.0006	0.687153
$306$	4.78103	0.273313
$307$	−9.77208	−0.557722	−0.278861	−	0.960331i	$-0.589957\pi$
$307$	−9.77208	−0.557722	−0.278861	+	0.960331i	$0.589957\pi$
$308$	−5.19718	−0.296137
$309$	2.88879	0.164338
$310$	14.0633	0.798740
$311$	−15.1612	−0.859711	−0.429855	−	0.902898i	$-0.641435\pi$
$311$	−15.1612	−0.859711	−0.429855	+	0.902898i	$0.641435\pi$
$312$	5.07322	0.287215
$313$	−17.0233	−0.962213	−0.481107	−	0.876662i	$-0.659765\pi$
$313$	−17.0233	−0.962213	−0.481107	+	0.876662i	$0.659765\pi$
$314$	−20.6688	−1.16641
$315$	−0.740630	−0.0417298
$316$	13.5307	0.761162
$317$	−6.64260	−0.373085	−0.186543	−	0.982447i	$-0.559728\pi$
$317$	−6.64260	−0.373085	−0.186543	+	0.982447i	$0.559728\pi$
$318$	−16.6549	−0.933963
$319$	−17.1146	−0.958235
$320$	9.23515	0.516261
$321$	−7.10093	−0.396335
$322$	9.01940	0.502631
$323$	3.25431	0.181075
$324$	−15.8033	−0.877964
$325$	0.820527	0.0455147
$326$	44.1740	2.44657
$327$	10.3535	0.572549
$328$	−34.9097	−1.92757
$329$	−7.55460	−0.416499
$330$	−6.97355	−0.383881
$331$	−18.2500	−1.00311	−0.501556	−	0.865125i	$-0.667239\pi$
$331$	−18.2500	−1.00311	−0.501556	+	0.865125i	$0.667239\pi$
$332$	35.4177	1.94380
$333$	−5.11024	−0.280040
$334$	5.51296	0.301656
$335$	−6.49055	−0.354617
$336$	2.83098	0.154443
$337$	−25.5947	−1.39423	−0.697116	−	0.716958i	$-0.745534\pi$
$337$	−25.5947	−1.39423	−0.697116	+	0.716958i	$0.745534\pi$
$338$	29.9135	1.62708
$339$	18.5897	1.00965
$340$	−6.48906	−0.351919
$341$	12.3468	0.668615
$342$	5.58837	0.302184
$343$	8.53483	0.460838
$344$	−34.6598	−1.86873
$345$	7.99205	0.430278
$346$	19.7752	1.06312
$347$	17.5681	0.943103	0.471551	−	0.881839i	$-0.343694\pi$
$347$	17.5681	0.943103	0.471551	+	0.881839i	$0.343694\pi$
$348$	42.1369	2.25877
$349$	23.8481	1.27656	0.638280	−	0.769805i	$-0.279646\pi$
$349$	23.8481	1.27656	0.638280	+	0.769805i	$0.279646\pi$
$350$	1.52218	0.0813641
$351$	4.62694	0.246968
$352$	2.23253	0.118994
$353$	18.4176	0.980269	0.490134	−	0.871647i	$-0.336948\pi$
$353$	18.4176	0.980269	0.490134	+	0.871647i	$0.336948\pi$
$354$	22.2902	1.18471
$355$	−1.22585	−0.0650615
$356$	4.41125	0.233796
$357$	1.41170	0.0747151
$358$	−40.4666	−2.13873
$359$	8.86601	0.467930	0.233965	−	0.972245i	$-0.424830\pi$
$359$	8.86601	0.467930	0.233965	+	0.972245i	$0.424830\pi$
$360$	−5.41250	−0.285264
$361$	−15.1962	−0.799798
$362$	5.54508	0.291443
$363$	8.71441	0.457388
$364$	−2.00159	−0.104912
$365$	3.76723	0.197186
$366$	−39.2799	−2.05319
$367$	−23.7378	−1.23910	−0.619552	−	0.784956i	$-0.712686\pi$
$367$	−23.7378	−1.23910	−0.619552	+	0.784956i	$0.712686\pi$
$368$	19.8268	1.03354
$369$	−8.99201	−0.468106
$370$	10.5028	0.546017
$371$	3.19171	0.165705
$372$	−30.3982	−1.57607
$373$	−17.2156	−0.891391	−0.445696	−	0.895185i	$-0.647044\pi$
$373$	−17.2156	−0.891391	−0.445696	+	0.895185i	$0.647044\pi$
$374$	−8.62688	−0.446085
$375$	1.34880	0.0696517
$376$	−55.2088	−2.84717
$377$	−6.59134	−0.339471
$378$	8.58356	0.441491
$379$	−5.79008	−0.297416	−0.148708	−	0.988881i	$-0.547512\pi$
$379$	−5.79008	−0.297416	−0.148708	+	0.988881i	$0.547512\pi$
$380$	−7.58482	−0.389093
$381$	−7.18266	−0.367979
$382$	−7.74886	−0.396466
$383$	−14.8193	−0.757231	−0.378615	−	0.925554i	$-0.623600\pi$
$383$	−14.8193	−0.757231	−0.378615	+	0.925554i	$0.623600\pi$
$384$	−27.4014	−1.39832
$385$	1.33639	0.0681088
$386$	3.55068	0.180725
$387$	−8.92765	−0.453818
$388$	31.9980	1.62445
$389$	−23.2639	−1.17952	−0.589762	−	0.807577i	$-0.700779\pi$
$389$	−23.2639	−1.17952	−0.589762	+	0.807577i	$0.700779\pi$
$390$	−2.68571	−0.135996
$391$	9.88686	0.500000
$392$	30.2843	1.52959
$393$	8.05131	0.406135
$394$	−44.0988	−2.22167
$395$	−3.47926	−0.175060
$396$	−9.78306	−0.491617
$397$	2.46315	0.123622	0.0618110	−	0.998088i	$-0.480312\pi$
$397$	2.46315	0.123622	0.0618110	+	0.998088i	$0.480312\pi$
$398$	−40.0383	−2.00694
$399$	1.65008	0.0826075
$400$	3.34612	0.167306
$401$	−23.8364	−1.19033	−0.595166	−	0.803603i	$-0.702914\pi$
$401$	−23.8364	−1.19033	−0.595166	+	0.803603i	$0.702914\pi$
$402$	21.2446	1.05958
$403$	4.75510	0.236868
$404$	70.5893	3.51195
$405$	4.06364	0.201924
$406$	−12.2278	−0.606854
$407$	9.22092	0.457064
$408$	10.3166	0.510750
$409$	−6.26698	−0.309882	−0.154941	−	0.987924i	$-0.549519\pi$
$409$	−6.26698	−0.309882	−0.154941	+	0.987924i	$0.549519\pi$
$410$	18.4809	0.912705
$411$	0.710061	0.0350247
$412$	−8.32919	−0.410350
$413$	−4.27164	−0.210194
$414$	16.9779	0.834419
$415$	−9.10722	−0.447056
$416$	0.859813	0.0421558
$417$	−11.5807	−0.567110
$418$	−10.0836	−0.493207
$419$	−26.9711	−1.31763	−0.658813	−	0.752307i	$-0.728941\pi$
$419$	−26.9711	−1.31763	−0.658813	+	0.752307i	$0.728941\pi$
$420$	−3.29025	−0.160548
$421$	−18.1883	−0.886445	−0.443223	−	0.896412i	$-0.646165\pi$
$421$	−18.1883	−0.886445	−0.443223	+	0.896412i	$0.646165\pi$
$422$	42.6270	2.07505
$423$	−14.2206	−0.691430
$424$	23.3249	1.13276
$425$	1.66858	0.0809381
$426$	4.01241	0.194402
$427$	7.52750	0.364281
$428$	20.4740	0.989646
$429$	−2.35791	−0.113841
$430$	18.3486	0.884847
$431$	−17.8307	−0.858876	−0.429438	−	0.903096i	$-0.641288\pi$
$431$	−17.8307	−0.858876	−0.429438	+	0.903096i	$0.641288\pi$
$432$	18.8687	0.907822
$433$	9.90321	0.475918	0.237959	−	0.971275i	$-0.423522\pi$
$433$	9.90321	0.475918	0.237959	+	0.971275i	$0.423522\pi$
$434$	8.82131	0.423437
$435$	−10.8350	−0.519498
$436$	−29.8520	−1.42965
$437$	11.5564	0.552817
$438$	−12.3307	−0.589185
$439$	39.2659	1.87406	0.937029	−	0.349252i	$-0.113564\pi$
$439$	39.2659	1.87406	0.937029	+	0.349252i	$0.113564\pi$
$440$	9.76630	0.465590
$441$	7.80061	0.371458
$442$	−3.32246	−0.158033
$443$	−23.6657	−1.12439	−0.562197	−	0.827004i	$-0.690044\pi$
$443$	−23.6657	−1.12439	−0.562197	+	0.827004i	$0.690044\pi$
$444$	−22.7023	−1.07740
$445$	−1.13430	−0.0537710
$446$	−17.1019	−0.809800
$447$	15.5745	0.736650
$448$	5.79284	0.273686
$449$	29.5348	1.39383	0.696917	−	0.717151i	$-0.254554\pi$
$449$	29.5348	1.39383	0.696917	+	0.717151i	$0.254554\pi$
$450$	2.86532	0.135073
$451$	16.2252	0.764014
$452$	−53.5993	−2.52110
$453$	5.55026	0.260774
$454$	−61.7614	−2.89861
$455$	0.514683	0.0241287
$456$	12.0588	0.564703
$457$	−7.64900	−0.357805	−0.178902	−	0.983867i	$-0.557255\pi$
$457$	−7.64900	−0.357805	−0.178902	+	0.983867i	$0.557255\pi$
$458$	−26.8219	−1.25330
$459$	9.40910	0.439179
$460$	−23.0433	−1.07440
$461$	12.4347	0.579140	0.289570	−	0.957157i	$-0.406488\pi$
$461$	12.4347	0.579140	0.289570	+	0.957157i	$0.406488\pi$
$462$	−4.37422	−0.203507
$463$	−1.67575	−0.0778786	−0.0389393	−	0.999242i	$-0.512398\pi$
$463$	−1.67575	−0.0778786	−0.0389393	+	0.999242i	$0.512398\pi$
$464$	−26.8796	−1.24785
$465$	7.81653	0.362483
$466$	−62.9896	−2.91794
$467$	−5.45188	−0.252283	−0.126142	−	0.992012i	$-0.540259\pi$
$467$	−5.45188	−0.252283	−0.126142	+	0.992012i	$0.540259\pi$
$468$	−3.76774	−0.174164
$469$	−4.07126	−0.187993
$470$	29.2270	1.34814
$471$	−11.4879	−0.529336
$472$	−31.2170	−1.43688
$473$	16.1090	0.740694
$474$	11.3882	0.523076
$475$	1.95034	0.0894879
$476$	−4.07032	−0.186563
$477$	6.00801	0.275088
$478$	32.3343	1.47894
$479$	−3.58051	−0.163598	−0.0817988	−	0.996649i	$-0.526066\pi$
$479$	−3.58051	−0.163598	−0.0817988	+	0.996649i	$0.526066\pi$
$480$	1.41338	0.0645116
$481$	3.55124	0.161923
$482$	−40.5547	−1.84722
$483$	5.01309	0.228103
$484$	−25.1261	−1.14209
$485$	−8.22788	−0.373609
$486$	27.7517	1.25884
$487$	24.1919	1.09624	0.548120	−	0.836400i	$-0.315344\pi$
$487$	24.1919	1.09624	0.548120	+	0.836400i	$0.315344\pi$
$488$	55.0107	2.49022
$489$	24.5524	1.11030
$490$	−16.0322	−0.724262
$491$	26.5662	1.19891	0.599457	−	0.800407i	$-0.295383\pi$
$491$	26.5662	1.19891	0.599457	+	0.800407i	$0.295383\pi$
$492$	−39.9470	−1.80095
$493$	−13.4038	−0.603677
$494$	−3.88350	−0.174727
$495$	2.51559	0.113068
$496$	19.3914	0.870698
$497$	−0.768928	−0.0344911
$498$	29.8094	1.33579
$499$	0.830892	0.0371958	0.0185979	−	0.999827i	$-0.494080\pi$
$499$	0.830892	0.0371958	0.0185979	+	0.999827i	$0.494080\pi$
$500$	−3.88897	−0.173920
$501$	3.06417	0.136897
$502$	−36.2660	−1.61863
$503$	−26.0476	−1.16140	−0.580702	−	0.814116i	$-0.697222\pi$
$503$	−26.0476	−1.16140	−0.580702	+	0.814116i	$0.697222\pi$
$504$	−3.39504	−0.151227
$505$	−18.1512	−0.807717
$506$	−30.6349	−1.36189
$507$	16.6263	0.738400
$508$	20.7096	0.918841
$509$	−1.54053	−0.0682829	−0.0341415	−	0.999417i	$-0.510870\pi$
$509$	−1.54053	−0.0682829	−0.0341415	+	0.999417i	$0.510870\pi$
$510$	−5.46153	−0.241841
$511$	2.36303	0.104534
$512$	34.1835	1.51071
$513$	10.9980	0.485571
$514$	50.6368	2.23350
$515$	2.14175	0.0943767
$516$	−39.6611	−1.74598
$517$	25.6597	1.12851
$518$	6.58801	0.289460
$519$	10.9913	0.482463
$520$	3.76129	0.164943
$521$	−13.9097	−0.609395	−0.304697	−	0.952449i	$-0.598555\pi$
$521$	−13.9097	−0.609395	−0.304697	+	0.952449i	$0.598555\pi$
$522$	−23.0173	−1.00744
$523$	23.6315	1.03333	0.516666	−	0.856187i	$-0.327173\pi$
$523$	23.6315	1.03333	0.516666	+	0.856187i	$0.327173\pi$
$524$	−23.2142	−1.01412
$525$	0.846047	0.0369245
$526$	30.9898	1.35122
$527$	9.66973	0.421220
$528$	−9.61559	−0.418465
$529$	12.1092	0.526489
$530$	−12.3480	−0.536362
$531$	−8.04084	−0.348943
$532$	−4.75765	−0.206270
$533$	6.24879	0.270665
$534$	3.71274	0.160666
$535$	−5.26463	−0.227610
$536$	−29.7526	−1.28512
$537$	−22.4918	−0.970593
$538$	−6.51819	−0.281019
$539$	−14.0754	−0.606271
$540$	−21.9298	−0.943708
$541$	38.8050	1.66836	0.834179	−	0.551494i	$-0.185942\pi$
$541$	38.8050	1.66836	0.834179	+	0.551494i	$0.185942\pi$
$542$	3.98112	0.171004
$543$	3.08202	0.132262
$544$	1.74847	0.0749651
$545$	7.67608	0.328807
$546$	−1.68464	−0.0720959
$547$	−16.3213	−0.697849	−0.348925	−	0.937151i	$-0.613453\pi$
$547$	−16.3213	−0.697849	−0.348925	+	0.937151i	$0.613453\pi$
$548$	−2.04730	−0.0874565
$549$	14.1696	0.604744
$550$	−5.17019	−0.220457
$551$	−15.6672	−0.667446
$552$	36.6355	1.55931
$553$	−2.18240	−0.0928050
$554$	24.8351	1.05514
$555$	5.83761	0.247793
$556$	33.3904	1.41607
$557$	38.7943	1.64377	0.821883	−	0.569656i	$-0.192924\pi$
$557$	38.7943	1.64377	0.821883	+	0.569656i	$0.192924\pi$
$558$	16.6050	0.702948
$559$	6.20406	0.262404
$560$	2.09889	0.0886942
$561$	−4.79492	−0.202442
$562$	15.4280	0.650792
$563$	−27.8927	−1.17554	−0.587768	−	0.809029i	$-0.699993\pi$
$563$	−27.8927	−1.17554	−0.587768	+	0.809029i	$0.699993\pi$
$564$	−63.1751	−2.66015
$565$	13.7824	0.579830
$566$	12.9582	0.544673
$567$	2.54895	0.107046
$568$	−5.61930	−0.235781
$569$	15.4481	0.647617	0.323809	−	0.946123i	$-0.395037\pi$
$569$	15.4481	0.647617	0.323809	+	0.946123i	$0.395037\pi$
$570$	−6.38378	−0.267387
$571$	13.0318	0.545365	0.272682	−	0.962104i	$-0.412089\pi$
$571$	13.0318	0.545365	0.272682	+	0.962104i	$0.412089\pi$
$572$	6.79851	0.284260
$573$	−4.30691	−0.179924
$574$	11.5923	0.483853
$575$	5.92531	0.247102
$576$	10.9043	0.454346
$577$	−7.37428	−0.306995	−0.153498	−	0.988149i	$-0.549054\pi$
$577$	−7.37428	−0.306995	−0.153498	+	0.988149i	$0.549054\pi$
$578$	34.4978	1.43492
$579$	1.97351	0.0820164
$580$	31.2403	1.29718
$581$	−5.71259	−0.236998
$582$	26.9312	1.11633
$583$	−10.8408	−0.448982
$584$	17.2689	0.714594
$585$	0.968829	0.0400561
$586$	−16.5455	−0.683490
$587$	7.94163	0.327786	0.163893	−	0.986478i	$-0.447595\pi$
$587$	7.94163	0.327786	0.163893	+	0.986478i	$0.447595\pi$
$588$	34.6542	1.42912
$589$	11.3026	0.465715
$590$	16.5260	0.680364
$591$	−24.5107	−1.00823
$592$	14.4820	0.595208
$593$	15.0639	0.618599	0.309299	−	0.950965i	$-0.399906\pi$
$593$	15.0639	0.618599	0.309299	+	0.950965i	$0.399906\pi$
$594$	−29.1546	−1.19623
$595$	1.04663	0.0429078
$596$	−44.9057	−1.83941
$597$	−22.2538	−0.910786
$598$	−11.7984	−0.482473
$599$	17.3527	0.709012	0.354506	−	0.935054i	$-0.384649\pi$
$599$	17.3527	0.709012	0.354506	+	0.935054i	$0.384649\pi$
$600$	6.18288	0.252415
$601$	−35.8331	−1.46166	−0.730831	−	0.682559i	$-0.760867\pi$
$601$	−35.8331	−1.46166	−0.730831	+	0.682559i	$0.760867\pi$
$602$	11.5093	0.469085
$603$	−7.66365	−0.312088
$604$	−16.0029	−0.651150
$605$	6.46086	0.262671
$606$	59.4117	2.41343
$607$	16.9829	0.689313	0.344657	−	0.938729i	$-0.387995\pi$
$607$	16.9829	0.689313	0.344657	+	0.938729i	$0.387995\pi$
$608$	2.04372	0.0828839
$609$	−6.79635	−0.275402
$610$	−29.1221	−1.17912
$611$	9.88228	0.399794
$612$	−7.66189	−0.309713
$613$	26.4769	1.06939	0.534696	−	0.845045i	$-0.320426\pi$
$613$	26.4769	1.06939	0.534696	+	0.845045i	$0.320426\pi$
$614$	23.7141	0.957023
$615$	10.2719	0.414203
$616$	6.12601	0.246824
$617$	28.6141	1.15196	0.575980	−	0.817464i	$-0.304621\pi$
$617$	28.6141	1.15196	0.575980	+	0.817464i	$0.304621\pi$
$618$	−7.01028	−0.281995
$619$	34.2935	1.37837	0.689185	−	0.724585i	$-0.257969\pi$
$619$	34.2935	1.37837	0.689185	+	0.724585i	$0.257969\pi$
$620$	−22.5372	−0.905117
$621$	33.4127	1.34080
$622$	36.7919	1.47522
$623$	−0.711500	−0.0285057
$624$	−3.70324	−0.148248
$625$	1.00000	0.0400000
$626$	41.3108	1.65111
$627$	−5.60461	−0.223827
$628$	33.1229	1.32175
$629$	7.22163	0.287945
$630$	1.79730	0.0716062
$631$	10.5802	0.421189	0.210595	−	0.977573i	$-0.432460\pi$
$631$	10.5802	0.421189	0.210595	+	0.977573i	$0.432460\pi$
$632$	−15.9489	−0.634413
$633$	23.6926	0.941697
$634$	16.1197	0.640196
$635$	−5.32523	−0.211325
$636$	26.6906	1.05835
$637$	−5.42085	−0.214782
$638$	41.5324	1.64428
$639$	−1.44741	−0.0572588
$640$	−20.3154	−0.803035
$641$	39.8493	1.57395	0.786976	−	0.616984i	$-0.211646\pi$
$641$	39.8493	1.57395	0.786976	+	0.616984i	$0.211646\pi$
$642$	17.2320	0.680091
$643$	17.8681	0.704648	0.352324	−	0.935878i	$-0.385392\pi$
$643$	17.8681	0.704648	0.352324	+	0.935878i	$0.385392\pi$
$644$	−14.4541	−0.569573
$645$	10.1984	0.401560
$646$	−7.89730	−0.310715
$647$	6.10212	0.239899	0.119949	−	0.992780i	$-0.461727\pi$
$647$	6.10212	0.239899	0.119949	+	0.992780i	$0.461727\pi$
$648$	18.6277	0.731764
$649$	14.5089	0.569524
$650$	−1.99119	−0.0781008
$651$	4.90299	0.192163
$652$	−70.7915	−2.77241
$653$	29.2511	1.14468	0.572342	−	0.820015i	$-0.306035\pi$
$653$	29.2511	1.14468	0.572342	+	0.820015i	$0.306035\pi$
$654$	−25.1250	−0.982466
$655$	5.96924	0.233238
$656$	25.4827	0.994931
$657$	4.44811	0.173537
$658$	18.3329	0.714691
$659$	−41.1791	−1.60411	−0.802055	−	0.597250i	$-0.796260\pi$
$659$	−41.1791	−1.60411	−0.802055	+	0.597250i	$0.796260\pi$
$660$	11.1755	0.435007
$661$	16.9290	0.658460	0.329230	−	0.944250i	$-0.393211\pi$
$661$	16.9290	0.658460	0.329230	+	0.944250i	$0.393211\pi$
$662$	44.2877	1.72129
$663$	−1.84666	−0.0717185
$664$	−41.7474	−1.62011
$665$	1.22337	0.0474403
$666$	12.4011	0.480534
$667$	−47.5983	−1.84301
$668$	−8.83485	−0.341831
$669$	−9.50546	−0.367502
$670$	15.7507	0.608504
$671$	−25.5676	−0.987026
$672$	0.886555	0.0341996
$673$	−36.2674	−1.39801	−0.699003	−	0.715119i	$-0.746373\pi$
$673$	−36.2674	−1.39801	−0.699003	+	0.715119i	$0.746373\pi$
$674$	62.1112	2.39243
$675$	5.63898	0.217044
$676$	−47.9383	−1.84378
$677$	18.7027	0.718805	0.359402	−	0.933183i	$-0.382981\pi$
$677$	18.7027	0.718805	0.359402	+	0.933183i	$0.382981\pi$
$678$	−45.1120	−1.73251
$679$	−5.16102	−0.198062
$680$	7.64876	0.293317
$681$	−34.3278	−1.31544
$682$	−29.9621	−1.14731
$683$	30.2655	1.15808	0.579039	−	0.815300i	$-0.303428\pi$
$683$	30.2655	1.15808	0.579039	+	0.815300i	$0.303428\pi$
$684$	−8.95570	−0.342430
$685$	0.526439	0.0201142
$686$	−20.7116	−0.790774
$687$	−14.9079	−0.568773
$688$	25.3002	0.964563
$689$	−4.17512	−0.159059
$690$	−19.3945	−0.738335
$691$	−30.5607	−1.16258	−0.581292	−	0.813695i	$-0.697452\pi$
$691$	−30.5607	−1.16258	−0.581292	+	0.813695i	$0.697452\pi$
$692$	−31.6909	−1.20471
$693$	1.57793	0.0599406
$694$	−42.6327	−1.61832
$695$	−8.58594	−0.325683
$696$	−49.6674	−1.88264
$697$	12.7072	0.481320
$698$	−57.8726	−2.19051
$699$	−35.0104	−1.32421
$700$	−2.43939	−0.0922003
$701$	−28.0754	−1.06039	−0.530197	−	0.847875i	$-0.677882\pi$
$701$	−28.0754	−1.06039	−0.530197	+	0.847875i	$0.677882\pi$
$702$	−11.2283	−0.423784
$703$	8.44109	0.318362
$704$	−19.6757	−0.741557
$705$	16.2447	0.611811
$706$	−44.6943	−1.68209
$707$	−11.3855	−0.428196
$708$	−35.7215	−1.34249
$709$	35.4785	1.33242	0.666211	−	0.745764i	$-0.267915\pi$
$709$	35.4785	1.33242	0.666211	+	0.745764i	$0.267915\pi$
$710$	2.97480	0.111642
$711$	−4.10810	−0.154066
$712$	−5.19962	−0.194864
$713$	34.3382	1.28598
$714$	−3.42580	−0.128207
$715$	−1.74815	−0.0653772
$716$	64.8502	2.42356
$717$	17.9718	0.671169
$718$	−21.5153	−0.802944
$719$	38.1027	1.42099	0.710495	−	0.703702i	$-0.248471\pi$
$719$	38.1027	1.42099	0.710495	+	0.703702i	$0.248471\pi$
$720$	3.95090	0.147241
$721$	1.34343	0.0500320
$722$	36.8768	1.37241
$723$	−22.5408	−0.838302
$724$	−8.88632	−0.330258
$725$	−8.03306	−0.298340
$726$	−21.1474	−0.784855
$727$	−18.4831	−0.685501	−0.342751	−	0.939426i	$-0.611359\pi$
$727$	−18.4831	−0.685501	−0.342751	+	0.939426i	$0.611359\pi$
$728$	2.35930	0.0874416
$729$	27.6157	1.02280
$730$	−9.14201	−0.338361
$731$	12.6163	0.466629
$732$	62.9484	2.32664
$733$	−20.9735	−0.774673	−0.387336	−	0.921938i	$-0.626605\pi$
$733$	−20.9735	−0.774673	−0.387336	+	0.921938i	$0.626605\pi$
$734$	57.6050	2.12624
$735$	−8.91091	−0.328684
$736$	6.20900	0.228867
$737$	13.8283	0.509371
$738$	21.8211	0.803246
$739$	−2.36152	−0.0868698	−0.0434349	−	0.999056i	$-0.513830\pi$
$739$	−2.36152	−0.0868698	−0.0434349	+	0.999056i	$0.513830\pi$
$740$	−16.8314	−0.618736
$741$	−2.15850	−0.0792944
$742$	−7.74539	−0.284342
$743$	38.8346	1.42470	0.712351	−	0.701823i	$-0.247630\pi$
$743$	38.8346	1.42470	0.712351	+	0.701823i	$0.247630\pi$
$744$	35.8309	1.31362
$745$	11.5470	0.423048
$746$	41.7775	1.52958
$747$	−10.7532	−0.393441
$748$	13.8251	0.505496
$749$	−3.30229	−0.120663
$750$	−3.27316	−0.119519
$751$	−7.54692	−0.275391	−0.137695	−	0.990475i	$-0.543970\pi$
$751$	−7.54692	−0.275391	−0.137695	+	0.990475i	$0.543970\pi$
$752$	40.3001	1.46959
$753$	−20.1571	−0.734565
$754$	15.9953	0.582516
$755$	4.11496	0.149759
$756$	−13.7557	−0.500289
$757$	−11.0553	−0.401812	−0.200906	−	0.979610i	$-0.564389\pi$
$757$	−11.0553	−0.401812	−0.200906	+	0.979610i	$0.564389\pi$
$758$	14.0509	0.510352
$759$	−17.0273	−0.618051
$760$	8.94036	0.324301
$761$	26.3510	0.955224	0.477612	−	0.878571i	$-0.341502\pi$
$761$	26.3510	0.955224	0.477612	+	0.878571i	$0.341502\pi$
$762$	17.4303	0.631433
$763$	4.81489	0.174311
$764$	12.4180	0.449269
$765$	1.97016	0.0712313
$766$	35.9623	1.29937
$767$	5.58779	0.201764
$768$	41.5827	1.50048
$769$	−47.1432	−1.70003	−0.850013	−	0.526762i	$-0.823406\pi$
$769$	−47.1432	−1.70003	−0.850013	+	0.526762i	$0.823406\pi$
$770$	−3.24305	−0.116871
$771$	28.1446	1.01360
$772$	−5.69019	−0.204794
$773$	23.9665	0.862014	0.431007	−	0.902349i	$-0.358158\pi$
$773$	23.9665	0.862014	0.431007	+	0.902349i	$0.358158\pi$
$774$	21.6649	0.778728
$775$	5.79518	0.208169
$776$	−37.7165	−1.35394
$777$	3.66169	0.131363
$778$	56.4549	2.02401
$779$	14.8530	0.532164
$780$	4.30402	0.154109
$781$	2.61171	0.0934544
$782$	−23.9926	−0.857975
$783$	−45.2982	−1.61883
$784$	−22.1063	−0.789511
$785$	−8.51716	−0.303990
$786$	−19.5383	−0.696907
$787$	−3.39575	−0.121046	−0.0605228	−	0.998167i	$-0.519277\pi$
$787$	−3.39575	−0.121046	−0.0605228	+	0.998167i	$0.519277\pi$
$788$	70.6711	2.51755
$789$	17.2245	0.613209
$790$	8.44318	0.300395
$791$	8.64514	0.307386
$792$	11.5315	0.409753
$793$	−9.84683	−0.349671
$794$	−5.97737	−0.212129
$795$	−6.86315	−0.243411
$796$	64.1638	2.27423
$797$	−11.5920	−0.410609	−0.205305	−	0.978698i	$-0.565819\pi$
$797$	−11.5920	−0.410609	−0.205305	+	0.978698i	$0.565819\pi$
$798$	−4.00429	−0.141750
$799$	20.0961	0.710949
$800$	1.04788	0.0370481
$801$	−1.33931	−0.0473223
$802$	57.8442	2.04255
$803$	−8.02618	−0.283238
$804$	−34.0458	−1.20070
$805$	3.71670	0.130997
$806$	−11.5393	−0.406454
$807$	−3.62289	−0.127532
$808$	−83.2048	−2.92713
$809$	−8.89718	−0.312808	−0.156404	−	0.987693i	$-0.549990\pi$
$809$	−8.89718	−0.312808	−0.156404	+	0.987693i	$0.549990\pi$
$810$	−9.86131	−0.346491
$811$	−20.3291	−0.713851	−0.356926	−	0.934133i	$-0.616175\pi$
$811$	−20.3291	−0.713851	−0.356926	+	0.934133i	$0.616175\pi$
$812$	19.5958	0.687676
$813$	2.21275	0.0776047
$814$	−22.3766	−0.784298
$815$	18.2032	0.637629
$816$	−7.53073	−0.263628
$817$	14.7467	0.515921
$818$	15.2082	0.531742
$819$	0.607707	0.0212350
$820$	−29.6167	−1.03426
$821$	−2.90988	−0.101556	−0.0507778	−	0.998710i	$-0.516170\pi$
$821$	−2.90988	−0.101556	−0.0507778	+	0.998710i	$0.516170\pi$
$822$	−1.72312	−0.0601007
$823$	18.9461	0.660420	0.330210	−	0.943907i	$-0.392880\pi$
$823$	18.9461	0.660420	0.330210	+	0.943907i	$0.392880\pi$
$824$	9.81775	0.342018
$825$	−2.87365	−0.100048
$826$	10.3661	0.360682
$827$	52.0791	1.81097	0.905484	−	0.424380i	$-0.139508\pi$
$827$	52.0791	1.81097	0.905484	+	0.424380i	$0.139508\pi$
$828$	−27.2081	−0.945548
$829$	−14.5604	−0.505703	−0.252852	−	0.967505i	$-0.581368\pi$
$829$	−14.5604	−0.505703	−0.252852	+	0.967505i	$0.581368\pi$
$830$	22.1007	0.767125
$831$	13.8036	0.478842
$832$	−7.57769	−0.262709
$833$	−11.0236	−0.381944
$834$	28.1031	0.973132
$835$	2.27177	0.0786180
$836$	16.1597	0.558893
$837$	32.6789	1.12955
$838$	65.4514	2.26098
$839$	10.4318	0.360147	0.180073	−	0.983653i	$-0.442366\pi$
$839$	10.4318	0.360147	0.180073	+	0.983653i	$0.442366\pi$
$840$	3.87827	0.133813
$841$	35.5300	1.22517
$842$	44.1380	1.52110
$843$	8.57508	0.295341
$844$	−68.3124	−2.35141
$845$	12.3267	0.424053
$846$	34.5094	1.18646
$847$	4.05264	0.139250
$848$	−17.0262	−0.584683
$849$	7.20231	0.247183
$850$	−4.04918	−0.138886
$851$	25.6447	0.879090
$852$	−6.43014	−0.220293
$853$	−36.9541	−1.26529	−0.632643	−	0.774444i	$-0.718030\pi$
$853$	−36.9541	−1.26529	−0.632643	+	0.774444i	$0.718030\pi$
$854$	−18.2671	−0.625088
$855$	2.30285	0.0787557
$856$	−24.1330	−0.824849
$857$	11.4357	0.390638	0.195319	−	0.980740i	$-0.437426\pi$
$857$	11.4357	0.390638	0.195319	+	0.980740i	$0.437426\pi$
$858$	5.72198	0.195345
$859$	−34.1028	−1.16357	−0.581786	−	0.813342i	$-0.697646\pi$
$859$	−34.1028	−1.16357	−0.581786	+	0.813342i	$0.697646\pi$
$860$	−29.4047	−1.00269
$861$	6.44314	0.219582
$862$	43.2701	1.47379
$863$	5.44203	0.185249	0.0926244	−	0.995701i	$-0.470474\pi$
$863$	5.44203	0.185249	0.0926244	+	0.995701i	$0.470474\pi$
$864$	5.90897	0.201027
$865$	8.14893	0.277072
$866$	−24.0323	−0.816651
$867$	19.1743	0.651194
$868$	−14.1367	−0.479831
$869$	7.41265	0.251457
$870$	26.2935	0.891432
$871$	5.32567	0.180453
$872$	35.1871	1.19158
$873$	−9.71498	−0.328802
$874$	−28.0441	−0.948606
$875$	0.627259	0.0212052
$876$	19.7608	0.667654
$877$	28.6464	0.967319	0.483659	−	0.875256i	$-0.339307\pi$
$877$	28.6464	0.967319	0.483659	+	0.875256i	$0.339307\pi$
$878$	−95.2872	−3.21579
$879$	−9.19621	−0.310180
$880$	−7.12900	−0.240318
$881$	−1.65424	−0.0557327	−0.0278664	−	0.999612i	$-0.508871\pi$
$881$	−1.65424	−0.0557327	−0.0278664	+	0.999612i	$0.508871\pi$
$882$	−18.9299	−0.637402
$883$	−36.3513	−1.22332	−0.611659	−	0.791121i	$-0.709498\pi$
$883$	−36.3513	−1.22332	−0.611659	+	0.791121i	$0.709498\pi$
$884$	5.32445	0.179081
$885$	9.18534	0.308762
$886$	57.4301	1.92940
$887$	40.7018	1.36663	0.683317	−	0.730122i	$-0.260537\pi$
$887$	40.7018	1.36663	0.683317	+	0.730122i	$0.260537\pi$
$888$	26.7595	0.897991
$889$	−3.34030	−0.112030
$890$	2.75263	0.0922683
$891$	−8.65768	−0.290043
$892$	27.4069	0.917650
$893$	23.4896	0.786050
$894$	−37.7950	−1.26405
$895$	−16.6754	−0.557398
$896$	−12.7430	−0.425714
$897$	−6.55769	−0.218955
$898$	−71.6727	−2.39175
$899$	−46.5530	−1.55263
$900$	−4.59185	−0.153062
$901$	−8.49032	−0.282853
$902$	−39.3740	−1.31101
$903$	6.39702	0.212879
$904$	63.1784	2.10128
$905$	2.28501	0.0759563
$906$	−13.4689	−0.447475
$907$	18.6761	0.620130	0.310065	−	0.950715i	$-0.399649\pi$
$907$	18.6761	0.620130	0.310065	+	0.950715i	$0.399649\pi$
$908$	98.9765	3.28465
$909$	−21.4318	−0.710848
$910$	−1.24899	−0.0414037
$911$	32.3518	1.07186	0.535931	−	0.844262i	$-0.319961\pi$
$911$	32.3518	1.07186	0.535931	+	0.844262i	$0.319961\pi$
$912$	−8.80239	−0.291476
$913$	19.4032	0.642151
$914$	18.5620	0.613975
$915$	−16.1864	−0.535107
$916$	42.9837	1.42022
$917$	3.74426	0.123646
$918$	−22.8332	−0.753609
$919$	42.8632	1.41393	0.706963	−	0.707250i	$-0.250065\pi$
$919$	42.8632	1.41393	0.706963	+	0.707250i	$0.250065\pi$
$920$	27.1615	0.895489
$921$	13.1806	0.434315
$922$	−30.1754	−0.993775
$923$	1.00585	0.0331078
$924$	7.00996	0.230611
$925$	4.32800	0.142304
$926$	4.06657	0.133636
$927$	2.52885	0.0830582
$928$	−8.41767	−0.276323
$929$	−30.9952	−1.01692	−0.508460	−	0.861086i	$-0.669785\pi$
$929$	−30.9952	−1.01692	−0.508460	+	0.861086i	$0.669785\pi$
$930$	−18.9685	−0.622002
$931$	−12.8850	−0.422290
$932$	100.945	3.30655
$933$	20.4494	0.669483
$934$	13.2302	0.432905
$935$	−3.55496	−0.116260
$936$	4.44110	0.145162
$937$	43.1889	1.41092	0.705459	−	0.708750i	$-0.250741\pi$
$937$	43.1889	1.41092	0.705459	+	0.708750i	$0.250741\pi$
$938$	9.87980	0.322587
$939$	22.9610	0.749304
$940$	−46.8380	−1.52769
$941$	44.1767	1.44012	0.720060	−	0.693912i	$-0.244114\pi$
$941$	44.1767	1.44012	0.720060	+	0.693912i	$0.244114\pi$
$942$	27.8780	0.908315
$943$	45.1246	1.46946
$944$	22.7871	0.741658
$945$	3.53710	0.115062
$946$	−39.0921	−1.27099
$947$	47.4498	1.54191	0.770956	−	0.636889i	$-0.219779\pi$
$947$	47.4498	1.54191	0.770956	+	0.636889i	$0.219779\pi$
$948$	−18.2502	−0.592740
$949$	−3.09111	−0.100342
$950$	−4.73294	−0.153557
$951$	8.95953	0.290533
$952$	4.79776	0.155496
$953$	−13.6331	−0.441620	−0.220810	−	0.975317i	$-0.570870\pi$
$953$	−13.6331	−0.441620	−0.220810	+	0.975317i	$0.570870\pi$
$954$	−14.5797	−0.472037
$955$	−3.19314	−0.103328
$956$	−51.8177	−1.67590
$957$	23.0842	0.746206
$958$	8.68889	0.280725
$959$	0.330214	0.0106632
$960$	−12.4564	−0.402028
$961$	2.58406	0.0833568
$962$	−8.61787	−0.277851
$963$	−6.21615	−0.200313
$964$	64.9914	2.09323
$965$	1.46316	0.0471008
$966$	−12.1654	−0.391414
$967$	−7.67292	−0.246745	−0.123372	−	0.992360i	$-0.539371\pi$
$967$	−7.67292	−0.246745	−0.123372	+	0.992360i	$0.539371\pi$
$968$	29.6165	0.951911
$969$	−4.38941	−0.141008
$970$	19.9668	0.641094
$971$	60.0452	1.92694	0.963471	−	0.267812i	$-0.0863006\pi$
$971$	60.0452	1.92694	0.963471	+	0.267812i	$0.0863006\pi$
$972$	−44.4739	−1.42650
$973$	−5.38561	−0.172655
$974$	−58.7070	−1.88109
$975$	−1.10673	−0.0354436
$976$	−40.1555	−1.28535
$977$	22.1827	0.709688	0.354844	−	0.934925i	$-0.384534\pi$
$977$	22.1827	0.709688	0.354844	+	0.934925i	$0.384534\pi$
$978$	−59.5818	−1.90522
$979$	2.41665	0.0772366
$980$	25.6926	0.820721
$981$	9.06345	0.289374
$982$	−64.4687	−2.05728
$983$	−26.1381	−0.833676	−0.416838	−	0.908981i	$-0.636862\pi$
$983$	−26.1381	−0.833676	−0.416838	+	0.908981i	$0.636862\pi$
$984$	47.0862	1.50105
$985$	−18.1722	−0.579015
$986$	32.5273	1.03588
$987$	10.1896	0.324340
$988$	6.22355	0.197998
$989$	44.8016	1.42461
$990$	−6.10464	−0.194018
$991$	−3.55867	−0.113045	−0.0565225	−	0.998401i	$-0.518001\pi$
$991$	−3.55867	−0.113045	−0.0565225	+	0.998401i	$0.518001\pi$
$992$	6.07264	0.192806
$993$	24.6156	0.781154
$994$	1.86597	0.0591851
$995$	−16.4989	−0.523051
$996$	−47.7713	−1.51369
$997$	20.8616	0.660694	0.330347	−	0.943860i	$-0.392834\pi$
$997$	20.8616	0.660694	0.330347	+	0.943860i	$0.392834\pi$
$998$	−2.01634	−0.0638262
$999$	24.4055	0.772156

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.c.1.9	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.c.1.9	✓	127	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42672 q^{2} -1.34880 q^{3} +3.88897 q^{4} -1.00000 q^{5} +3.27316 q^{6} -0.627259 q^{7} -4.58399 q^{8} -1.18074 q^{9} +O(q^{10})\)	\(q-2.42672 q^{2} -1.34880 q^{3} +3.88897 q^{4} -1.00000 q^{5} +3.27316 q^{6} -0.627259 q^{7} -4.58399 q^{8} -1.18074 q^{9} +2.42672 q^{10} +2.13053 q^{11} -5.24544 q^{12} +0.820527 q^{13} +1.52218 q^{14} +1.34880 q^{15} +3.34612 q^{16} +1.66858 q^{17} +2.86532 q^{18} +1.95034 q^{19} -3.88897 q^{20} +0.846047 q^{21} -5.17019 q^{22} +5.92531 q^{23} +6.18288 q^{24} +1.00000 q^{25} -1.99119 q^{26} +5.63898 q^{27} -2.43939 q^{28} -8.03306 q^{29} -3.27316 q^{30} +5.79518 q^{31} +1.04788 q^{32} -2.87365 q^{33} -4.04918 q^{34} +0.627259 q^{35} -4.59185 q^{36} +4.32800 q^{37} -4.73294 q^{38} -1.10673 q^{39} +4.58399 q^{40} +7.61558 q^{41} -2.05312 q^{42} +7.56106 q^{43} +8.28554 q^{44} +1.18074 q^{45} -14.3791 q^{46} +12.0438 q^{47} -4.51325 q^{48} -6.60655 q^{49} -2.42672 q^{50} -2.25058 q^{51} +3.19100 q^{52} -5.08834 q^{53} -13.6842 q^{54} -2.13053 q^{55} +2.87535 q^{56} -2.63062 q^{57} +19.4940 q^{58} +6.81001 q^{59} +5.24544 q^{60} -12.0006 q^{61} -14.0633 q^{62} +0.740630 q^{63} -9.23515 q^{64} -0.820527 q^{65} +6.97355 q^{66} +6.49055 q^{67} +6.48906 q^{68} -7.99205 q^{69} -1.52218 q^{70} +1.22585 q^{71} +5.41250 q^{72} -3.76723 q^{73} -10.5028 q^{74} -1.34880 q^{75} +7.58482 q^{76} -1.33639 q^{77} +2.68571 q^{78} +3.47926 q^{79} -3.34612 q^{80} -4.06364 q^{81} -18.4809 q^{82} +9.10722 q^{83} +3.29025 q^{84} -1.66858 q^{85} -18.3486 q^{86} +10.8350 q^{87} -9.76630 q^{88} +1.13430 q^{89} -2.86532 q^{90} -0.514683 q^{91} +23.0433 q^{92} -7.81653 q^{93} -29.2270 q^{94} -1.95034 q^{95} -1.41338 q^{96} +8.22788 q^{97} +16.0322 q^{98} -2.51559 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * q^99

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