LMFDB - Embedded newform 8015.2.a.l.1.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.34
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.179639 q^{2} +1.24714 q^{3} -1.96773 q^{4} -1.00000 q^{5} +0.224036 q^{6} -1.00000 q^{7} -0.712759 q^{8} -1.44463 q^{9} +O(q^{10})$	\(q+0.179639 q^{2} +1.24714 q^{3} -1.96773 q^{4} -1.00000 q^{5} +0.224036 q^{6} -1.00000 q^{7} -0.712759 q^{8} -1.44463 q^{9} -0.179639 q^{10} -4.52267 q^{11} -2.45404 q^{12} -6.55095 q^{13} -0.179639 q^{14} -1.24714 q^{15} +3.80742 q^{16} -4.38185 q^{17} -0.259512 q^{18} -1.34868 q^{19} +1.96773 q^{20} -1.24714 q^{21} -0.812448 q^{22} -2.35145 q^{23} -0.888913 q^{24} +1.00000 q^{25} -1.17681 q^{26} -5.54310 q^{27} +1.96773 q^{28} +1.86073 q^{29} -0.224036 q^{30} -6.41599 q^{31} +2.10948 q^{32} -5.64042 q^{33} -0.787152 q^{34} +1.00000 q^{35} +2.84265 q^{36} +10.5656 q^{37} -0.242276 q^{38} -8.16997 q^{39} +0.712759 q^{40} -0.929475 q^{41} -0.224036 q^{42} -6.66311 q^{43} +8.89939 q^{44} +1.44463 q^{45} -0.422412 q^{46} -12.1671 q^{47} +4.74840 q^{48} +1.00000 q^{49} +0.179639 q^{50} -5.46480 q^{51} +12.8905 q^{52} -8.21751 q^{53} -0.995756 q^{54} +4.52267 q^{55} +0.712759 q^{56} -1.68200 q^{57} +0.334259 q^{58} +4.77445 q^{59} +2.45404 q^{60} -2.51566 q^{61} -1.15256 q^{62} +1.44463 q^{63} -7.23590 q^{64} +6.55095 q^{65} -1.01324 q^{66} -5.21661 q^{67} +8.62230 q^{68} -2.93259 q^{69} +0.179639 q^{70} -11.2022 q^{71} +1.02968 q^{72} +13.1656 q^{73} +1.89799 q^{74} +1.24714 q^{75} +2.65384 q^{76} +4.52267 q^{77} -1.46765 q^{78} -13.0044 q^{79} -3.80742 q^{80} -2.57914 q^{81} -0.166970 q^{82} -1.40063 q^{83} +2.45404 q^{84} +4.38185 q^{85} -1.19695 q^{86} +2.32059 q^{87} +3.22357 q^{88} -14.6845 q^{89} +0.259512 q^{90} +6.55095 q^{91} +4.62701 q^{92} -8.00166 q^{93} -2.18569 q^{94} +1.34868 q^{95} +2.63082 q^{96} +9.91511 q^{97} +0.179639 q^{98} +6.53360 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	0.179639	0.127024	0.0635120	−	0.997981i	$-0.479770\pi$
$2$	0.179639	0.127024	0.0635120	+	0.997981i	$0.479770\pi$
$3$	1.24714	0.720039	0.360019	−	0.932945i	$-0.382770\pi$
$3$	1.24714	0.720039	0.360019	+	0.932945i	$0.382770\pi$
$4$	−1.96773	−0.983865
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.224036	0.0914622
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.712759	−0.251998
$9$	−1.44463	−0.481544
$10$	−0.179639	−0.0568069
$11$	−4.52267	−1.36364	−0.681818	−	0.731522i	$-0.738810\pi$
$11$	−4.52267	−1.36364	−0.681818	+	0.731522i	$0.738810\pi$
$12$	−2.45404	−0.708421
$13$	−6.55095	−1.81691	−0.908453	−	0.417987i	$-0.862736\pi$
$13$	−6.55095	−1.81691	−0.908453	+	0.417987i	$0.862736\pi$
$14$	−0.179639	−0.0480106
$15$	−1.24714	−0.322011
$16$	3.80742	0.951855
$17$	−4.38185	−1.06276	−0.531378	−	0.847135i	$-0.678326\pi$
$17$	−4.38185	−1.06276	−0.531378	+	0.847135i	$0.678326\pi$
$18$	−0.259512	−0.0611677
$19$	−1.34868	−0.309409	−0.154704	−	0.987961i	$-0.549442\pi$
$19$	−1.34868	−0.309409	−0.154704	+	0.987961i	$0.549442\pi$
$20$	1.96773	0.439998
$21$	−1.24714	−0.272149
$22$	−0.812448	−0.173214
$23$	−2.35145	−0.490311	−0.245155	−	0.969484i	$-0.578839\pi$
$23$	−2.35145	−0.490311	−0.245155	+	0.969484i	$0.578839\pi$
$24$	−0.888913	−0.181449
$25$	1.00000	0.200000
$26$	−1.17681	−0.230791
$27$	−5.54310	−1.06677
$28$	1.96773	0.371866
$29$	1.86073	0.345528	0.172764	−	0.984963i	$-0.444730\pi$
$29$	1.86073	0.345528	0.172764	+	0.984963i	$0.444730\pi$
$30$	−0.224036	−0.0409031
$31$	−6.41599	−1.15235	−0.576173	−	0.817328i	$-0.695454\pi$
$31$	−6.41599	−1.15235	−0.576173	+	0.817328i	$0.695454\pi$
$32$	2.10948	0.372907
$33$	−5.64042	−0.981870
$34$	−0.787152	−0.134995
$35$	1.00000	0.169031
$36$	2.84265	0.473775
$37$	10.5656	1.73697	0.868485	−	0.495715i	$-0.165094\pi$
$37$	10.5656	1.73697	0.868485	+	0.495715i	$0.165094\pi$
$38$	−0.242276	−0.0393023
$39$	−8.16997	−1.30824
$40$	0.712759	0.112697
$41$	−0.929475	−0.145160	−0.0725798	−	0.997363i	$-0.523123\pi$
$41$	−0.929475	−0.145160	−0.0725798	+	0.997363i	$0.523123\pi$
$42$	−0.224036	−0.0345695
$43$	−6.66311	−1.01611	−0.508057	−	0.861323i	$-0.669636\pi$
$43$	−6.66311	−1.01611	−0.508057	+	0.861323i	$0.669636\pi$
$44$	8.89939	1.34163
$45$	1.44463	0.215353
$46$	−0.422412	−0.0622812
$47$	−12.1671	−1.77476	−0.887379	−	0.461040i	$-0.847476\pi$
$47$	−12.1671	−1.77476	−0.887379	+	0.461040i	$0.847476\pi$
$48$	4.74840	0.685372
$49$	1.00000	0.142857
$50$	0.179639	0.0254048
$51$	−5.46480	−0.765225
$52$	12.8905	1.78759
$53$	−8.21751	−1.12876	−0.564381	−	0.825514i	$-0.690885\pi$
$53$	−8.21751	−1.12876	−0.564381	+	0.825514i	$0.690885\pi$
$54$	−0.995756	−0.135505
$55$	4.52267	0.609836
$56$	0.712759	0.0952465
$57$	−1.68200	−0.222786
$58$	0.334259	0.0438904
$59$	4.77445	0.621580	0.310790	−	0.950479i	$-0.399406\pi$
$59$	4.77445	0.621580	0.310790	+	0.950479i	$0.399406\pi$
$60$	2.45404	0.316815
$61$	−2.51566	−0.322097	−0.161049	−	0.986946i	$-0.551488\pi$
$61$	−2.51566	−0.322097	−0.161049	+	0.986946i	$0.551488\pi$
$62$	−1.15256	−0.146375
$63$	1.44463	0.182007
$64$	−7.23590	−0.904487
$65$	6.55095	0.812545
$66$	−1.01324	−0.124721
$67$	−5.21661	−0.637310	−0.318655	−	0.947871i	$-0.603231\pi$
$67$	−5.21661	−0.637310	−0.318655	+	0.947871i	$0.603231\pi$
$68$	8.62230	1.04561
$69$	−2.93259	−0.353043
$70$	0.179639	0.0214710
$71$	−11.2022	−1.32946	−0.664731	−	0.747083i	$-0.731454\pi$
$71$	−11.2022	−1.32946	−0.664731	+	0.747083i	$0.731454\pi$
$72$	1.02968	0.121348
$73$	13.1656	1.54092	0.770461	−	0.637487i	$-0.220026\pi$
$73$	13.1656	1.54092	0.770461	+	0.637487i	$0.220026\pi$
$74$	1.89799	0.220637
$75$	1.24714	0.144008
$76$	2.65384	0.304416
$77$	4.52267	0.515406
$78$	−1.46765	−0.166178
$79$	−13.0044	−1.46311	−0.731553	−	0.681784i	$-0.761204\pi$
$79$	−13.0044	−1.46311	−0.731553	+	0.681784i	$0.761204\pi$
$80$	−3.80742	−0.425683
$81$	−2.57914	−0.286571
$82$	−0.166970	−0.0184388
$83$	−1.40063	−0.153739	−0.0768696	−	0.997041i	$-0.524493\pi$
$83$	−1.40063	−0.153739	−0.0768696	+	0.997041i	$0.524493\pi$
$84$	2.45404	0.267758
$85$	4.38185	0.475279
$86$	−1.19695	−0.129071
$87$	2.32059	0.248794
$88$	3.22357	0.343634
$89$	−14.6845	−1.55655	−0.778277	−	0.627921i	$-0.783906\pi$
$89$	−14.6845	−1.55655	−0.778277	+	0.627921i	$0.783906\pi$
$90$	0.259512	0.0273550
$91$	6.55095	0.686726
$92$	4.62701	0.482400
$93$	−8.00166	−0.829733
$94$	−2.18569	−0.225437
$95$	1.34868	0.138372
$96$	2.63082	0.268507
$97$	9.91511	1.00673	0.503364	−	0.864075i	$-0.332096\pi$
$97$	9.91511	1.00673	0.503364	+	0.864075i	$0.332096\pi$
$98$	0.179639	0.0181463
$99$	6.53360	0.656651
$100$	−1.96773	−0.196773
$101$	13.0207	1.29561	0.647803	−	0.761808i	$-0.275688\pi$
$101$	13.0207	1.29561	0.647803	+	0.761808i	$0.275688\pi$
$102$	−0.981692	−0.0972019
$103$	10.9863	1.08251	0.541255	−	0.840858i	$-0.317949\pi$
$103$	10.9863	1.08251	0.541255	+	0.840858i	$0.317949\pi$
$104$	4.66925	0.457858
$105$	1.24714	0.121709
$106$	−1.47619	−0.143380
$107$	2.31493	0.223793	0.111896	−	0.993720i	$-0.464308\pi$
$107$	2.31493	0.223793	0.111896	+	0.993720i	$0.464308\pi$
$108$	10.9073	1.04956
$109$	16.4402	1.57469	0.787344	−	0.616515i	$-0.211456\pi$
$109$	16.4402	1.57469	0.787344	+	0.616515i	$0.211456\pi$
$110$	0.812448	0.0774639
$111$	13.1768	1.25069
$112$	−3.80742	−0.359767
$113$	−4.32759	−0.407105	−0.203553	−	0.979064i	$-0.565249\pi$
$113$	−4.32759	−0.407105	−0.203553	+	0.979064i	$0.565249\pi$
$114$	−0.302153	−0.0282992
$115$	2.35145	0.219274
$116$	−3.66141	−0.339953
$117$	9.46372	0.874921
$118$	0.857677	0.0789555
$119$	4.38185	0.401684
$120$	0.888913	0.0811463
$121$	9.45453	0.859502
$122$	−0.451910	−0.0409140
$123$	−1.15919	−0.104521
$124$	12.6249	1.13375
$125$	−1.00000	−0.0894427
$126$	0.259512	0.0231192
$127$	−13.6204	−1.20862	−0.604308	−	0.796751i	$-0.706550\pi$
$127$	−13.6204	−1.20862	−0.604308	+	0.796751i	$0.706550\pi$
$128$	−5.51881	−0.487798
$129$	−8.30985	−0.731642
$130$	1.17681	0.103213
$131$	6.73229	0.588203	0.294102	−	0.955774i	$-0.404980\pi$
$131$	6.73229	0.588203	0.294102	+	0.955774i	$0.404980\pi$
$132$	11.0988	0.966028
$133$	1.34868	0.116945
$134$	−0.937107	−0.0809537
$135$	5.54310	0.477074
$136$	3.12321	0.267813
$137$	−2.22633	−0.190208	−0.0951041	−	0.995467i	$-0.530318\pi$
$137$	−2.22633	−0.190208	−0.0951041	+	0.995467i	$0.530318\pi$
$138$	−0.526808	−0.0448449
$139$	−5.23703	−0.444199	−0.222100	−	0.975024i	$-0.571291\pi$
$139$	−5.23703	−0.444199	−0.222100	+	0.975024i	$0.571291\pi$
$140$	−1.96773	−0.166304
$141$	−15.1742	−1.27789
$142$	−2.01236	−0.168874
$143$	29.6278	2.47760
$144$	−5.50032	−0.458360
$145$	−1.86073	−0.154525
$146$	2.36506	0.195734
$147$	1.24714	0.102863
$148$	−20.7902	−1.70894
$149$	1.88046	0.154053	0.0770266	−	0.997029i	$-0.475457\pi$
$149$	1.88046	0.154053	0.0770266	+	0.997029i	$0.475457\pi$
$150$	0.224036	0.0182924
$151$	−22.0938	−1.79797	−0.898986	−	0.437978i	$-0.855695\pi$
$151$	−22.0938	−1.79797	−0.898986	+	0.437978i	$0.855695\pi$
$152$	0.961285	0.0779705
$153$	6.33017	0.511764
$154$	0.812448	0.0654689
$155$	6.41599	0.515344
$156$	16.0763	1.28713
$157$	11.4740	0.915725	0.457862	−	0.889023i	$-0.348615\pi$
$157$	11.4740	0.915725	0.457862	+	0.889023i	$0.348615\pi$
$158$	−2.33609	−0.185850
$159$	−10.2484	−0.812752
$160$	−2.10948	−0.166769
$161$	2.35145	0.185320
$162$	−0.463314	−0.0364014
$163$	−7.46119	−0.584406	−0.292203	−	0.956356i	$-0.594388\pi$
$163$	−7.46119	−0.584406	−0.292203	+	0.956356i	$0.594388\pi$
$164$	1.82896	0.142817
$165$	5.64042	0.439106
$166$	−0.251608	−0.0195286
$167$	−8.88878	−0.687834	−0.343917	−	0.939000i	$-0.611754\pi$
$167$	−8.88878	−0.687834	−0.343917	+	0.939000i	$0.611754\pi$
$168$	0.888913	0.0685811
$169$	29.9149	2.30115
$170$	0.787152	0.0603718
$171$	1.94835	0.148994
$172$	13.1112	0.999720
$173$	12.0386	0.915279	0.457640	−	0.889138i	$-0.348695\pi$
$173$	12.0386	0.915279	0.457640	+	0.889138i	$0.348695\pi$
$174$	0.416869	0.0316028
$175$	−1.00000	−0.0755929
$176$	−17.2197	−1.29798
$177$	5.95442	0.447561
$178$	−2.63791	−0.197720
$179$	0.847211	0.0633235	0.0316618	−	0.999499i	$-0.489920\pi$
$179$	0.847211	0.0633235	0.0316618	+	0.999499i	$0.489920\pi$
$180$	−2.84265	−0.211878
$181$	−21.0682	−1.56599	−0.782995	−	0.622029i	$-0.786309\pi$
$181$	−21.0682	−1.56599	−0.782995	+	0.622029i	$0.786309\pi$
$182$	1.17681	0.0872307
$183$	−3.13739	−0.231922
$184$	1.67602	0.123558
$185$	−10.5656	−0.776797
$186$	−1.43741	−0.105396
$187$	19.8177	1.44921
$188$	23.9416	1.74612
$189$	5.54310	0.403201
$190$	0.242276	0.0175765
$191$	−19.2876	−1.39560	−0.697801	−	0.716291i	$-0.745838\pi$
$191$	−19.2876	−1.39560	−0.697801	+	0.716291i	$0.745838\pi$
$192$	−9.02420	−0.651266
$193$	20.3865	1.46745	0.733725	−	0.679446i	$-0.237780\pi$
$193$	20.3865	1.46745	0.733725	+	0.679446i	$0.237780\pi$
$194$	1.78114	0.127878
$195$	8.16997	0.585064
$196$	−1.96773	−0.140552
$197$	14.7013	1.04743	0.523714	−	0.851894i	$-0.324546\pi$
$197$	14.7013	1.04743	0.523714	+	0.851894i	$0.324546\pi$
$198$	1.17369	0.0834104
$199$	25.3833	1.79937	0.899686	−	0.436538i	$-0.143796\pi$
$199$	25.3833	1.79937	0.899686	+	0.436538i	$0.143796\pi$
$200$	−0.712759	−0.0503997
$201$	−6.50586	−0.458888
$202$	2.33902	0.164573
$203$	−1.86073	−0.130597
$204$	10.7533	0.752878
$205$	0.929475	0.0649174
$206$	1.97356	0.137505
$207$	3.39698	0.236106
$208$	−24.9422	−1.72943
$209$	6.09964	0.421921
$210$	0.224036	0.0154599
$211$	−18.6649	−1.28494	−0.642471	−	0.766310i	$-0.722091\pi$
$211$	−18.6649	−1.28494	−0.642471	+	0.766310i	$0.722091\pi$
$212$	16.1698	1.11055
$213$	−13.9708	−0.957264
$214$	0.415852	0.0284270
$215$	6.66311	0.454420
$216$	3.95089	0.268824
$217$	6.41599	0.435546
$218$	2.95330	0.200023
$219$	16.4194	1.10952
$220$	−8.89939	−0.599997
$221$	28.7053	1.93093
$222$	2.36707	0.158867
$223$	−0.601140	−0.0402553	−0.0201277	−	0.999797i	$-0.506407\pi$
$223$	−0.601140	−0.0402553	−0.0201277	+	0.999797i	$0.506407\pi$
$224$	−2.10948	−0.140946
$225$	−1.44463	−0.0963089
$226$	−0.777403	−0.0517121
$227$	−16.2970	−1.08167	−0.540836	−	0.841128i	$-0.681892\pi$
$227$	−16.2970	−1.08167	−0.540836	+	0.841128i	$0.681892\pi$
$228$	3.30972	0.219192
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	0.422412	0.0278530
$231$	5.64042	0.371112
$232$	−1.32625	−0.0870726
$233$	10.7761	0.705963	0.352982	−	0.935630i	$-0.385168\pi$
$233$	10.7761	0.705963	0.352982	+	0.935630i	$0.385168\pi$
$234$	1.70005	0.111136
$235$	12.1671	0.793696
$236$	−9.39482	−0.611551
$237$	−16.2183	−1.05349
$238$	0.787152	0.0510235
$239$	20.9865	1.35750	0.678751	−	0.734369i	$-0.262522\pi$
$239$	20.9865	1.35750	0.678751	+	0.734369i	$0.262522\pi$
$240$	−4.74840	−0.306508
$241$	5.50538	0.354633	0.177316	−	0.984154i	$-0.443258\pi$
$241$	5.50538	0.354633	0.177316	+	0.984154i	$0.443258\pi$
$242$	1.69840	0.109177
$243$	13.4127	0.860427
$244$	4.95014	0.316900
$245$	−1.00000	−0.0638877
$246$	−0.208236	−0.0132766
$247$	8.83514	0.562167
$248$	4.57305	0.290389
$249$	−1.74679	−0.110698
$250$	−0.179639	−0.0113614
$251$	25.2007	1.59066	0.795328	−	0.606180i	$-0.207299\pi$
$251$	25.2007	1.59066	0.795328	+	0.606180i	$0.207299\pi$
$252$	−2.84265	−0.179070
$253$	10.6348	0.668605
$254$	−2.44676	−0.153523
$255$	5.46480	0.342219
$256$	13.4804	0.842525
$257$	−4.84465	−0.302201	−0.151100	−	0.988518i	$-0.548282\pi$
$257$	−4.84465	−0.302201	−0.151100	+	0.988518i	$0.548282\pi$
$258$	−1.49277	−0.0929361
$259$	−10.5656	−0.656513
$260$	−12.8905	−0.799435
$261$	−2.68807	−0.166387
$262$	1.20938	0.0747159
$263$	−8.46459	−0.521949	−0.260974	−	0.965346i	$-0.584044\pi$
$263$	−8.46459	−0.521949	−0.260974	+	0.965346i	$0.584044\pi$
$264$	4.02026	0.247430
$265$	8.21751	0.504798
$266$	0.242276	0.0148549
$267$	−18.3137	−1.12078
$268$	10.2649	0.627027
$269$	−25.5176	−1.55584	−0.777918	−	0.628366i	$-0.783724\pi$
$269$	−25.5176	−1.55584	−0.777918	+	0.628366i	$0.783724\pi$
$270$	0.995756	0.0605998
$271$	−30.6200	−1.86003	−0.930017	−	0.367515i	$-0.880209\pi$
$271$	−30.6200	−1.86003	−0.930017	+	0.367515i	$0.880209\pi$
$272$	−16.6836	−1.01159
$273$	8.16997	0.494469
$274$	−0.399936	−0.0241610
$275$	−4.52267	−0.272727
$276$	5.77055	0.347346
$277$	1.56193	0.0938476	0.0469238	−	0.998898i	$-0.485058\pi$
$277$	1.56193	0.0938476	0.0469238	+	0.998898i	$0.485058\pi$
$278$	−0.940775	−0.0564239
$279$	9.26875	0.554905
$280$	−0.712759	−0.0425955
$281$	−21.3378	−1.27290	−0.636452	−	0.771316i	$-0.719599\pi$
$281$	−21.3378	−1.27290	−0.636452	+	0.771316i	$0.719599\pi$
$282$	−2.72587	−0.162323
$283$	−15.3388	−0.911796	−0.455898	−	0.890032i	$-0.650682\pi$
$283$	−15.3388	−0.911796	−0.455898	+	0.890032i	$0.650682\pi$
$284$	22.0430	1.30801
$285$	1.68200	0.0996330
$286$	5.32230	0.314714
$287$	0.929475	0.0548652
$288$	−3.04742	−0.179571
$289$	2.20064	0.129450
$290$	−0.334259	−0.0196284
$291$	12.3656	0.724882
$292$	−25.9064	−1.51606
$293$	−12.3702	−0.722675	−0.361338	−	0.932435i	$-0.617680\pi$
$293$	−12.3702	−0.722675	−0.361338	+	0.932435i	$0.617680\pi$
$294$	0.224036	0.0130660
$295$	−4.77445	−0.277979
$296$	−7.53071	−0.437714
$297$	25.0696	1.45468
$298$	0.337804	0.0195685
$299$	15.4042	0.890849
$300$	−2.45404	−0.141684
$301$	6.66311	0.384055
$302$	−3.96892	−0.228385
$303$	16.2387	0.932886
$304$	−5.13500	−0.294512
$305$	2.51566	0.144046
$306$	1.13715	0.0650063
$307$	−20.7965	−1.18692	−0.593458	−	0.804865i	$-0.702238\pi$
$307$	−20.7965	−1.18692	−0.593458	+	0.804865i	$0.702238\pi$
$308$	−8.89939	−0.507090
$309$	13.7015	0.779449
$310$	1.15256	0.0654611
$311$	−15.9982	−0.907175	−0.453588	−	0.891212i	$-0.649856\pi$
$311$	−15.9982	−0.907175	−0.453588	+	0.891212i	$0.649856\pi$
$312$	5.82322	0.329675
$313$	−26.3238	−1.48791	−0.743955	−	0.668230i	$-0.767052\pi$
$313$	−26.3238	−1.48791	−0.743955	+	0.668230i	$0.767052\pi$
$314$	2.06118	0.116319
$315$	−1.44463	−0.0813958
$316$	25.5891	1.43950
$317$	−23.2142	−1.30384	−0.651920	−	0.758288i	$-0.726036\pi$
$317$	−23.2142	−1.30384	−0.651920	+	0.758288i	$0.726036\pi$
$318$	−1.84102	−0.103239
$319$	−8.41545	−0.471175
$320$	7.23590	0.404499
$321$	2.88705	0.161139
$322$	0.422412	0.0235401
$323$	5.90972	0.328826
$324$	5.07504	0.281947
$325$	−6.55095	−0.363381
$326$	−1.34032	−0.0742336
$327$	20.5033	1.13384
$328$	0.662492	0.0365800
$329$	12.1671	0.670796
$330$	1.01324	0.0557770
$331$	−24.9895	−1.37355	−0.686773	−	0.726872i	$-0.740973\pi$
$331$	−24.9895	−1.37355	−0.686773	+	0.726872i	$0.740973\pi$
$332$	2.75606	0.151259
$333$	−15.2634	−0.836428
$334$	−1.59677	−0.0873715
$335$	5.21661	0.285014
$336$	−4.74840	−0.259046
$337$	16.8202	0.916254	0.458127	−	0.888887i	$-0.348520\pi$
$337$	16.8202	0.916254	0.458127	+	0.888887i	$0.348520\pi$
$338$	5.37389	0.292301
$339$	−5.39712	−0.293131
$340$	−8.62230	−0.467610
$341$	29.0174	1.57138
$342$	0.350000	0.0189258
$343$	−1.00000	−0.0539949
$344$	4.74919	0.256059
$345$	2.93259	0.157886
$346$	2.16261	0.116262
$347$	−1.98583	−0.106605	−0.0533025	−	0.998578i	$-0.516975\pi$
$347$	−1.98583	−0.106605	−0.0533025	+	0.998578i	$0.516975\pi$
$348$	−4.56630	−0.244779
$349$	32.1604	1.72151	0.860753	−	0.509023i	$-0.169993\pi$
$349$	32.1604	1.72151	0.860753	+	0.509023i	$0.169993\pi$
$350$	−0.179639	−0.00960211
$351$	36.3125	1.93822
$352$	−9.54048	−0.508509
$353$	−26.4549	−1.40805	−0.704026	−	0.710174i	$-0.748616\pi$
$353$	−26.4549	−1.40805	−0.704026	+	0.710174i	$0.748616\pi$
$354$	1.06965	0.0568510
$355$	11.2022	0.594554
$356$	28.8951	1.53144
$357$	5.46480	0.289228
$358$	0.152192	0.00804361
$359$	−13.4400	−0.709335	−0.354668	−	0.934992i	$-0.615406\pi$
$359$	−13.4400	−0.709335	−0.354668	+	0.934992i	$0.615406\pi$
$360$	−1.02968	−0.0542687
$361$	−17.1811	−0.904266
$362$	−3.78468	−0.198918
$363$	11.7912	0.618875
$364$	−12.8905	−0.675646
$365$	−13.1656	−0.689121
$366$	−0.563597	−0.0294597
$367$	26.2727	1.37143	0.685713	−	0.727872i	$-0.259491\pi$
$367$	26.2727	1.37143	0.685713	+	0.727872i	$0.259491\pi$
$368$	−8.95295	−0.466705
$369$	1.34275	0.0699008
$370$	−1.89799	−0.0986718
$371$	8.21751	0.426632
$372$	15.7451	0.816345
$373$	25.2499	1.30739	0.653695	−	0.756758i	$-0.273218\pi$
$373$	25.2499	1.30739	0.653695	+	0.756758i	$0.273218\pi$
$374$	3.56003	0.184085
$375$	−1.24714	−0.0644022
$376$	8.67223	0.447236
$377$	−12.1895	−0.627793
$378$	0.995756	0.0512162
$379$	−5.54649	−0.284904	−0.142452	−	0.989802i	$-0.545499\pi$
$379$	−5.54649	−0.284904	−0.142452	+	0.989802i	$0.545499\pi$
$380$	−2.65384	−0.136139
$381$	−16.9866	−0.870250
$382$	−3.46481	−0.177275
$383$	−28.6395	−1.46341	−0.731706	−	0.681620i	$-0.761276\pi$
$383$	−28.6395	−1.46341	−0.731706	+	0.681620i	$0.761276\pi$
$384$	−6.88275	−0.351234
$385$	−4.52267	−0.230497
$386$	3.66221	0.186401
$387$	9.62575	0.489304
$388$	−19.5103	−0.990483
$389$	−18.9748	−0.962061	−0.481031	−	0.876704i	$-0.659737\pi$
$389$	−18.9748	−0.962061	−0.481031	+	0.876704i	$0.659737\pi$
$390$	1.46765	0.0743172
$391$	10.3037	0.521081
$392$	−0.712759	−0.0359998
$393$	8.39614	0.423529
$394$	2.64094	0.133048
$395$	13.0044	0.654321
$396$	−12.8564	−0.646056
$397$	6.32624	0.317505	0.158753	−	0.987318i	$-0.449253\pi$
$397$	6.32624	0.317505	0.158753	+	0.987318i	$0.449253\pi$
$398$	4.55982	0.228563
$399$	1.68200	0.0842053
$400$	3.80742	0.190371
$401$	23.6958	1.18331	0.591655	−	0.806191i	$-0.298475\pi$
$401$	23.6958	1.18331	0.591655	+	0.806191i	$0.298475\pi$
$402$	−1.16871	−0.0582898
$403$	42.0308	2.09370
$404$	−25.6212	−1.27470
$405$	2.57914	0.128158
$406$	−0.334259	−0.0165890
$407$	−47.7846	−2.36859
$408$	3.89509	0.192836
$409$	10.5100	0.519684	0.259842	−	0.965651i	$-0.416329\pi$
$409$	10.5100	0.519684	0.259842	+	0.965651i	$0.416329\pi$
$410$	0.166970	0.00824606
$411$	−2.77655	−0.136957
$412$	−21.6180	−1.06504
$413$	−4.77445	−0.234935
$414$	0.610230	0.0299912
$415$	1.40063	0.0687543
$416$	−13.8191	−0.677537
$417$	−6.53133	−0.319841
$418$	1.09573	0.0535940
$419$	38.2278	1.86755	0.933774	−	0.357863i	$-0.116495\pi$
$419$	38.2278	1.86755	0.933774	+	0.357863i	$0.116495\pi$
$420$	−2.45404	−0.119745
$421$	−4.05223	−0.197494	−0.0987468	−	0.995113i	$-0.531483\pi$
$421$	−4.05223	−0.197494	−0.0987468	+	0.995113i	$0.531483\pi$
$422$	−3.35294	−0.163219
$423$	17.5770	0.854625
$424$	5.85711	0.284446
$425$	−4.38185	−0.212551
$426$	−2.50970	−0.121596
$427$	2.51566	0.121741
$428$	−4.55515	−0.220182
$429$	36.9501	1.78397
$430$	1.19695	0.0577223
$431$	−7.34112	−0.353609	−0.176805	−	0.984246i	$-0.556576\pi$
$431$	−7.34112	−0.353609	−0.176805	+	0.984246i	$0.556576\pi$
$432$	−21.1049	−1.01541
$433$	−25.1686	−1.20953	−0.604763	−	0.796405i	$-0.706732\pi$
$433$	−25.1686	−1.20953	−0.604763	+	0.796405i	$0.706732\pi$
$434$	1.15256	0.0553247
$435$	−2.32059	−0.111264
$436$	−32.3499	−1.54928
$437$	3.17135	0.151706
$438$	2.94957	0.140936
$439$	−4.54952	−0.217137	−0.108568	−	0.994089i	$-0.534627\pi$
$439$	−4.54952	−0.217137	−0.108568	+	0.994089i	$0.534627\pi$
$440$	−3.22357	−0.153678
$441$	−1.44463	−0.0687920
$442$	5.15659	0.245274
$443$	3.54927	0.168631	0.0843154	−	0.996439i	$-0.473130\pi$
$443$	3.54927	0.168631	0.0843154	+	0.996439i	$0.473130\pi$
$444$	−25.9284	−1.23051
$445$	14.6845	0.696112
$446$	−0.107988	−0.00511339
$447$	2.34520	0.110924
$448$	7.23590	0.341864
$449$	−3.27848	−0.154721	−0.0773605	−	0.997003i	$-0.524649\pi$
$449$	−3.27848	−0.154721	−0.0773605	+	0.997003i	$0.524649\pi$
$450$	−0.259512	−0.0122335
$451$	4.20371	0.197945
$452$	8.51552	0.400536
$453$	−27.5542	−1.29461
$454$	−2.92758	−0.137398
$455$	−6.55095	−0.307113
$456$	1.19886	0.0561418
$457$	14.6993	0.687604	0.343802	−	0.939042i	$-0.388285\pi$
$457$	14.6993	0.687604	0.343802	+	0.939042i	$0.388285\pi$
$458$	0.179639	0.00839398
$459$	24.2890	1.13372
$460$	−4.62701	−0.215736
$461$	24.8659	1.15812	0.579061	−	0.815284i	$-0.303419\pi$
$461$	24.8659	1.15812	0.579061	+	0.815284i	$0.303419\pi$
$462$	1.01324	0.0471401
$463$	−7.62940	−0.354568	−0.177284	−	0.984160i	$-0.556731\pi$
$463$	−7.62940	−0.354568	−0.177284	+	0.984160i	$0.556731\pi$
$464$	7.08457	0.328893
$465$	8.00166	0.371068
$466$	1.93580	0.0896743
$467$	−19.5235	−0.903441	−0.451720	−	0.892160i	$-0.649190\pi$
$467$	−19.5235	−0.903441	−0.451720	+	0.892160i	$0.649190\pi$
$468$	−18.6220	−0.860804
$469$	5.21661	0.240881
$470$	2.18569	0.100818
$471$	14.3097	0.659357
$472$	−3.40303	−0.156637
$473$	30.1350	1.38561
$474$	−2.91344	−0.133819
$475$	−1.34868	−0.0618817
$476$	−8.62230	−0.395203
$477$	11.8713	0.543549
$478$	3.76999	0.172435
$479$	−3.87223	−0.176927	−0.0884635	−	0.996079i	$-0.528196\pi$
$479$	−3.87223	−0.176927	−0.0884635	+	0.996079i	$0.528196\pi$
$480$	−2.63082	−0.120080
$481$	−69.2146	−3.15591
$482$	0.988982	0.0450469
$483$	2.93259	0.133438
$484$	−18.6040	−0.845634
$485$	−9.91511	−0.450222
$486$	2.40945	0.109295
$487$	−4.29980	−0.194843	−0.0974213	−	0.995243i	$-0.531059\pi$
$487$	−4.29980	−0.194843	−0.0974213	+	0.995243i	$0.531059\pi$
$488$	1.79306	0.0811679
$489$	−9.30518	−0.420795
$490$	−0.179639	−0.00811526
$491$	−10.4678	−0.472404	−0.236202	−	0.971704i	$-0.575903\pi$
$491$	−10.4678	−0.472404	−0.236202	+	0.971704i	$0.575903\pi$
$492$	2.28097	0.102834
$493$	−8.15343	−0.367212
$494$	1.58714	0.0714086
$495$	−6.53360	−0.293663
$496$	−24.4284	−1.09687
$497$	11.2022	0.502490
$498$	−0.313791	−0.0140613
$499$	21.3619	0.956289	0.478144	−	0.878281i	$-0.341310\pi$
$499$	21.3619	0.956289	0.478144	+	0.878281i	$0.341310\pi$
$500$	1.96773	0.0879996
$501$	−11.0856	−0.495267
$502$	4.52703	0.202051
$503$	21.6048	0.963310	0.481655	−	0.876361i	$-0.340036\pi$
$503$	21.6048	0.963310	0.481655	+	0.876361i	$0.340036\pi$
$504$	−1.02968	−0.0458654
$505$	−13.0207	−0.579413
$506$	1.91043	0.0849289
$507$	37.3082	1.65692
$508$	26.8013	1.18911
$509$	21.1871	0.939103	0.469551	−	0.882905i	$-0.344416\pi$
$509$	21.1871	0.939103	0.469551	+	0.882905i	$0.344416\pi$
$510$	0.981692	0.0434700
$511$	−13.1656	−0.582414
$512$	13.4592	0.594819
$513$	7.47587	0.330068
$514$	−0.870288	−0.0383867
$515$	−10.9863	−0.484113
$516$	16.3515	0.719837
$517$	55.0279	2.42012
$518$	−1.89799	−0.0833929
$519$	15.0139	0.659036
$520$	−4.66925	−0.204760
$521$	6.02350	0.263894	0.131947	−	0.991257i	$-0.457877\pi$
$521$	6.02350	0.263894	0.131947	+	0.991257i	$0.457877\pi$
$522$	−0.482882	−0.0211352
$523$	−8.36604	−0.365821	−0.182911	−	0.983130i	$-0.558552\pi$
$523$	−8.36604	−0.365821	−0.182911	+	0.983130i	$0.558552\pi$
$524$	−13.2473	−0.578712
$525$	−1.24714	−0.0544298
$526$	−1.52057	−0.0663000
$527$	28.1139	1.22466
$528$	−21.4754	−0.934598
$529$	−17.4707	−0.759595
$530$	1.47619	0.0641214
$531$	−6.89732	−0.299318
$532$	−2.65384	−0.115059
$533$	6.08895	0.263741
$534$	−3.28985	−0.142366
$535$	−2.31493	−0.100083
$536$	3.71819	0.160601
$537$	1.05659	0.0455954
$538$	−4.58396	−0.197628
$539$	−4.52267	−0.194805
$540$	−10.9073	−0.469376
$541$	9.68052	0.416198	0.208099	−	0.978108i	$-0.433272\pi$
$541$	9.68052	0.416198	0.208099	+	0.978108i	$0.433272\pi$
$542$	−5.50055	−0.236269
$543$	−26.2751	−1.12757
$544$	−9.24343	−0.396309
$545$	−16.4402	−0.704221
$546$	1.46765	0.0628095
$547$	8.40350	0.359308	0.179654	−	0.983730i	$-0.442502\pi$
$547$	8.40350	0.359308	0.179654	+	0.983730i	$0.442502\pi$
$548$	4.38081	0.187139
$549$	3.63420	0.155104
$550$	−0.812448	−0.0346429
$551$	−2.50953	−0.106909
$552$	2.09023	0.0889662
$553$	13.0044	0.553002
$554$	0.280584	0.0119209
$555$	−13.1768	−0.559324
$556$	10.3051	0.437032
$557$	6.36153	0.269547	0.134773	−	0.990876i	$-0.456969\pi$
$557$	6.36153	0.269547	0.134773	+	0.990876i	$0.456969\pi$
$558$	1.66503	0.0704863
$559$	43.6497	1.84619
$560$	3.80742	0.160893
$561$	24.7155	1.04349
$562$	−3.83309	−0.161689
$563$	4.37192	0.184255	0.0921273	−	0.995747i	$-0.470633\pi$
$563$	4.37192	0.184255	0.0921273	+	0.995747i	$0.470633\pi$
$564$	29.8586	1.25728
$565$	4.32759	0.182063
$566$	−2.75544	−0.115820
$567$	2.57914	0.108314
$568$	7.98451	0.335022
$569$	−5.74704	−0.240928	−0.120464	−	0.992718i	$-0.538438\pi$
$569$	−5.74704	−0.240928	−0.120464	+	0.992718i	$0.538438\pi$
$570$	0.302153	0.0126558
$571$	−17.2480	−0.721806	−0.360903	−	0.932603i	$-0.617532\pi$
$571$	−17.2480	−0.721806	−0.360903	+	0.932603i	$0.617532\pi$
$572$	−58.2994	−2.43762
$573$	−24.0544	−1.00489
$574$	0.166970	0.00696920
$575$	−2.35145	−0.0980622
$576$	10.4532	0.435551
$577$	−9.18311	−0.382298	−0.191149	−	0.981561i	$-0.561221\pi$
$577$	−9.18311	−0.382298	−0.191149	+	0.981561i	$0.561221\pi$
$578$	0.395321	0.0164432
$579$	25.4249	1.05662
$580$	3.66141	0.152032
$581$	1.40063	0.0581080
$582$	2.22134	0.0920774
$583$	37.1651	1.53922
$584$	−9.38393	−0.388310
$585$	−9.46372	−0.391277
$586$	−2.22217	−0.0917971
$587$	2.68149	0.110677	0.0553385	−	0.998468i	$-0.482376\pi$
$587$	2.68149	0.110677	0.0553385	+	0.998468i	$0.482376\pi$
$588$	−2.45404	−0.101203
$589$	8.65312	0.356546
$590$	−0.857677	−0.0353100
$591$	18.3347	0.754188
$592$	40.2276	1.65334
$593$	−22.1550	−0.909798	−0.454899	−	0.890543i	$-0.650325\pi$
$593$	−22.1550	−0.909798	−0.454899	+	0.890543i	$0.650325\pi$
$594$	4.50348	0.184780
$595$	−4.38185	−0.179638
$596$	−3.70024	−0.151568
$597$	31.6566	1.29562
$598$	2.76720	0.113159
$599$	−19.1492	−0.782414	−0.391207	−	0.920303i	$-0.627942\pi$
$599$	−19.1492	−0.782414	−0.391207	+	0.920303i	$0.627942\pi$
$600$	−0.888913	−0.0362897
$601$	40.7852	1.66366	0.831832	−	0.555028i	$-0.187292\pi$
$601$	40.7852	1.66366	0.831832	+	0.555028i	$0.187292\pi$
$602$	1.19695	0.0487842
$603$	7.53608	0.306893
$604$	43.4747	1.76896
$605$	−9.45453	−0.384381
$606$	2.91710	0.118499
$607$	7.53532	0.305849	0.152925	−	0.988238i	$-0.451131\pi$
$607$	7.53532	0.305849	0.152925	+	0.988238i	$0.451131\pi$
$608$	−2.84502	−0.115381
$609$	−2.32059	−0.0940352
$610$	0.451910	0.0182973
$611$	79.7063	3.22457
$612$	−12.4561	−0.503507
$613$	−35.7511	−1.44397	−0.721987	−	0.691906i	$-0.756771\pi$
$613$	−35.7511	−1.44397	−0.721987	+	0.691906i	$0.756771\pi$
$614$	−3.73586	−0.150767
$615$	1.15919	0.0467430
$616$	−3.22357	−0.129881
$617$	4.24593	0.170935	0.0854673	−	0.996341i	$-0.472762\pi$
$617$	4.24593	0.170935	0.0854673	+	0.996341i	$0.472762\pi$
$618$	2.46132	0.0990087
$619$	16.4678	0.661895	0.330948	−	0.943649i	$-0.392632\pi$
$619$	16.4678	0.661895	0.330948	+	0.943649i	$0.392632\pi$
$620$	−12.6249	−0.507029
$621$	13.0343	0.523048
$622$	−2.87390	−0.115233
$623$	14.6845	0.588322
$624$	−31.1065	−1.24526
$625$	1.00000	0.0400000
$626$	−4.72878	−0.189000
$627$	7.60712	0.303799
$628$	−22.5777	−0.900950
$629$	−46.2968	−1.84598
$630$	−0.259512	−0.0103392
$631$	−7.61028	−0.302961	−0.151480	−	0.988460i	$-0.548404\pi$
$631$	−7.61028	−0.302961	−0.151480	+	0.988460i	$0.548404\pi$
$632$	9.26899	0.368701
$633$	−23.2778	−0.925209
$634$	−4.17018	−0.165619
$635$	13.6204	0.540509
$636$	20.1661	0.799638
$637$	−6.55095	−0.259558
$638$	−1.51174	−0.0598505
$639$	16.1831	0.640195
$640$	5.51881	0.218150
$641$	−44.4887	−1.75720	−0.878600	−	0.477559i	$-0.841522\pi$
$641$	−44.4887	−1.75720	−0.878600	+	0.477559i	$0.841522\pi$
$642$	0.518627	0.0204686
$643$	−25.5345	−1.00698	−0.503490	−	0.864001i	$-0.667951\pi$
$643$	−25.5345	−1.00698	−0.503490	+	0.864001i	$0.667951\pi$
$644$	−4.62701	−0.182330
$645$	8.30985	0.327200
$646$	1.06162	0.0417688
$647$	22.5789	0.887667	0.443833	−	0.896109i	$-0.353618\pi$
$647$	22.5789	0.887667	0.443833	+	0.896109i	$0.353618\pi$
$648$	1.83830	0.0722154
$649$	−21.5932	−0.847608
$650$	−1.17681	−0.0461581
$651$	8.00166	0.313610
$652$	14.6816	0.574976
$653$	−23.5308	−0.920833	−0.460417	−	0.887703i	$-0.652300\pi$
$653$	−23.5308	−0.920833	−0.460417	+	0.887703i	$0.652300\pi$
$654$	3.68319	0.144024
$655$	−6.73229	−0.263052
$656$	−3.53890	−0.138171
$657$	−19.0195	−0.742022
$658$	2.18569	0.0852071
$659$	37.1088	1.44555	0.722777	−	0.691082i	$-0.242866\pi$
$659$	37.1088	1.44555	0.722777	+	0.691082i	$0.242866\pi$
$660$	−11.0988	−0.432021
$661$	36.0491	1.40215	0.701074	−	0.713089i	$-0.252704\pi$
$661$	36.0491	1.40215	0.701074	+	0.713089i	$0.252704\pi$
$662$	−4.48909	−0.174473
$663$	35.7996	1.39034
$664$	0.998312	0.0387420
$665$	−1.34868	−0.0522996
$666$	−2.74190	−0.106246
$667$	−4.37540	−0.169416
$668$	17.4907	0.676736
$669$	−0.749708	−0.0289854
$670$	0.937107	0.0362036
$671$	11.3775	0.439223
$672$	−2.63082	−0.101486
$673$	2.29189	0.0883460	0.0441730	−	0.999024i	$-0.485935\pi$
$673$	2.29189	0.0883460	0.0441730	+	0.999024i	$0.485935\pi$
$674$	3.02156	0.116386
$675$	−5.54310	−0.213354
$676$	−58.8645	−2.26402
$677$	−44.4561	−1.70859	−0.854293	−	0.519791i	$-0.826010\pi$
$677$	−44.4561	−1.70859	−0.854293	+	0.519791i	$0.826010\pi$
$678$	−0.969534	−0.0372347
$679$	−9.91511	−0.380507
$680$	−3.12321	−0.119770
$681$	−20.3247	−0.778845
$682$	5.21265	0.199603
$683$	44.2546	1.69336	0.846678	−	0.532105i	$-0.178599\pi$
$683$	44.2546	1.69336	0.846678	+	0.532105i	$0.178599\pi$
$684$	−3.83382	−0.146590
$685$	2.22633	0.0850637
$686$	−0.179639	−0.00685865
$687$	1.24714	0.0475815
$688$	−25.3693	−0.967194
$689$	53.8325	2.05085
$690$	0.526808	0.0200552
$691$	3.73101	0.141934	0.0709671	−	0.997479i	$-0.477391\pi$
$691$	3.73101	0.141934	0.0709671	+	0.997479i	$0.477391\pi$
$692$	−23.6887	−0.900511
$693$	−6.53360	−0.248191
$694$	−0.356733	−0.0135414
$695$	5.23703	0.198652
$696$	−1.65402	−0.0626956
$697$	4.07283	0.154269
$698$	5.77726	0.218672
$699$	13.4393	0.508321
$700$	1.96773	0.0743732
$701$	−18.5140	−0.699264	−0.349632	−	0.936887i	$-0.613693\pi$
$701$	−18.5140	−0.699264	−0.349632	+	0.936887i	$0.613693\pi$
$702$	6.52315	0.246200
$703$	−14.2496	−0.537434
$704$	32.7256	1.23339
$705$	15.1742	0.571492
$706$	−4.75233	−0.178856
$707$	−13.0207	−0.489693
$708$	−11.7167	−0.440340
$709$	−30.3271	−1.13896	−0.569478	−	0.822006i	$-0.692855\pi$
$709$	−30.3271	−1.13896	−0.569478	+	0.822006i	$0.692855\pi$
$710$	2.01236	0.0755226
$711$	18.7865	0.704551
$712$	10.4665	0.392249
$713$	15.0869	0.565007
$714$	0.981692	0.0367389
$715$	−29.6278	−1.10802
$716$	−1.66708	−0.0623018
$717$	26.1731	0.977454
$718$	−2.41435	−0.0901026
$719$	−20.6934	−0.771732	−0.385866	−	0.922555i	$-0.626097\pi$
$719$	−20.6934	−0.771732	−0.385866	+	0.922555i	$0.626097\pi$
$720$	5.50032	0.204985
$721$	−10.9863	−0.409150
$722$	−3.08639	−0.114864
$723$	6.86600	0.255349
$724$	41.4566	1.54072
$725$	1.86073	0.0691057
$726$	2.11815	0.0786120
$727$	−26.4036	−0.979255	−0.489627	−	0.871932i	$-0.662867\pi$
$727$	−26.4036	−0.979255	−0.489627	+	0.871932i	$0.662867\pi$
$728$	−4.66925	−0.173054
$729$	24.4650	0.906112
$730$	−2.36506	−0.0875349
$731$	29.1968	1.07988
$732$	6.17353	0.228180
$733$	−1.88817	−0.0697410	−0.0348705	−	0.999392i	$-0.511102\pi$
$733$	−1.88817	−0.0697410	−0.0348705	+	0.999392i	$0.511102\pi$
$734$	4.71961	0.174204
$735$	−1.24714	−0.0460016
$736$	−4.96033	−0.182840
$737$	23.5930	0.869059
$738$	0.241210	0.00887908
$739$	9.63772	0.354529	0.177265	−	0.984163i	$-0.443275\pi$
$739$	9.63772	0.354529	0.177265	+	0.984163i	$0.443275\pi$
$740$	20.7902	0.764263
$741$	11.0187	0.404782
$742$	1.47619	0.0541925
$743$	31.9723	1.17295	0.586474	−	0.809968i	$-0.300516\pi$
$743$	31.9723	1.17295	0.586474	+	0.809968i	$0.300516\pi$
$744$	5.70325	0.209091
$745$	−1.88046	−0.0688947
$746$	4.53587	0.166070
$747$	2.02340	0.0740322
$748$	−38.9958	−1.42583
$749$	−2.31493	−0.0845857
$750$	−0.224036	−0.00818063
$751$	−40.6806	−1.48446	−0.742228	−	0.670148i	$-0.766231\pi$
$751$	−40.6806	−1.48446	−0.742228	+	0.670148i	$0.766231\pi$
$752$	−46.3254	−1.68931
$753$	31.4289	1.14533
$754$	−2.18971	−0.0797447
$755$	22.0938	0.804077
$756$	−10.9073	−0.396695
$757$	−32.2777	−1.17315	−0.586577	−	0.809894i	$-0.699525\pi$
$757$	−32.2777	−1.17315	−0.586577	+	0.809894i	$0.699525\pi$
$758$	−0.996366	−0.0361896
$759$	13.2631	0.481422
$760$	−0.961285	−0.0348695
$761$	−34.0183	−1.23316	−0.616581	−	0.787291i	$-0.711483\pi$
$761$	−34.0183	−1.23316	−0.616581	+	0.787291i	$0.711483\pi$
$762$	−3.05146	−0.110543
$763$	−16.4402	−0.595176
$764$	37.9528	1.37308
$765$	−6.33017	−0.228868
$766$	−5.14478	−0.185888
$767$	−31.2771	−1.12935
$768$	16.8120	0.606650
$769$	36.9315	1.33178	0.665892	−	0.746048i	$-0.268051\pi$
$769$	36.9315	1.33178	0.665892	+	0.746048i	$0.268051\pi$
$770$	−0.812448	−0.0292786
$771$	−6.04197	−0.217596
$772$	−40.1151	−1.44377
$773$	41.9884	1.51022	0.755109	−	0.655600i	$-0.227584\pi$
$773$	41.9884	1.51022	0.755109	+	0.655600i	$0.227584\pi$
$774$	1.72916	0.0621534
$775$	−6.41599	−0.230469
$776$	−7.06709	−0.253694
$777$	−13.1768	−0.472715
$778$	−3.40862	−0.122205
$779$	1.25357	0.0449137
$780$	−16.0763	−0.575624
$781$	50.6641	1.81290
$782$	1.85095	0.0661897
$783$	−10.3142	−0.368599
$784$	3.80742	0.135979
$785$	−11.4740	−0.409525
$786$	1.50827	0.0537983
$787$	−39.2919	−1.40060	−0.700302	−	0.713846i	$-0.746951\pi$
$787$	−39.2919	−1.40060	−0.700302	+	0.713846i	$0.746951\pi$
$788$	−28.9283	−1.03053
$789$	−10.5566	−0.375823
$790$	2.33609	0.0831145
$791$	4.32759	0.153871
$792$	−4.65688	−0.165475
$793$	16.4799	0.585220
$794$	1.13644	0.0403307
$795$	10.2484	0.363474
$796$	−49.9474	−1.77034
$797$	51.0039	1.80665	0.903325	−	0.428957i	$-0.141119\pi$
$797$	51.0039	1.80665	0.903325	+	0.428957i	$0.141119\pi$
$798$	0.302153	0.0106961
$799$	53.3146	1.88613
$800$	2.10948	0.0745814
$801$	21.2137	0.749550
$802$	4.25669	0.150309
$803$	−59.5438	−2.10126
$804$	12.8018	0.451484
$805$	−2.35145	−0.0828776
$806$	7.55037	0.265951
$807$	−31.8241	−1.12026
$808$	−9.28061	−0.326491
$809$	0.241469	0.00848959	0.00424480	−	0.999991i	$-0.498649\pi$
$809$	0.241469	0.00848959	0.00424480	+	0.999991i	$0.498649\pi$
$810$	0.463314	0.0162792
$811$	−7.66521	−0.269162	−0.134581	−	0.990903i	$-0.542969\pi$
$811$	−7.66521	−0.269162	−0.134581	+	0.990903i	$0.542969\pi$
$812$	3.66141	0.128490
$813$	−38.1876	−1.33930
$814$	−8.58398	−0.300868
$815$	7.46119	0.261354
$816$	−20.8068	−0.728383
$817$	8.98641	0.314395
$818$	1.88800	0.0660124
$819$	−9.46372	−0.330689
$820$	−1.82896	−0.0638699
$821$	−40.6216	−1.41770	−0.708851	−	0.705358i	$-0.750786\pi$
$821$	−40.6216	−1.41770	−0.708851	+	0.705358i	$0.750786\pi$
$822$	−0.498777	−0.0173969
$823$	34.0765	1.18783	0.593917	−	0.804526i	$-0.297581\pi$
$823$	34.0765	1.18783	0.593917	+	0.804526i	$0.297581\pi$
$824$	−7.83057	−0.272791
$825$	−5.64042	−0.196374
$826$	−0.857677	−0.0298424
$827$	−10.9977	−0.382427	−0.191214	−	0.981548i	$-0.561242\pi$
$827$	−10.9977	−0.382427	−0.191214	+	0.981548i	$0.561242\pi$
$828$	−6.68434	−0.232297
$829$	−17.6792	−0.614024	−0.307012	−	0.951706i	$-0.599329\pi$
$829$	−17.6792	−0.614024	−0.307012	+	0.951706i	$0.599329\pi$
$830$	0.251608	0.00873344
$831$	1.94796	0.0675739
$832$	47.4020	1.64337
$833$	−4.38185	−0.151822
$834$	−1.17328	−0.0406274
$835$	8.88878	0.307609
$836$	−12.0024	−0.415113
$837$	35.5644	1.22929
$838$	6.86720	0.237223
$839$	35.6846	1.23197	0.615984	−	0.787759i	$-0.288759\pi$
$839$	35.6846	1.23197	0.615984	+	0.787759i	$0.288759\pi$
$840$	−0.888913	−0.0306704
$841$	−25.5377	−0.880610
$842$	−0.727939	−0.0250864
$843$	−26.6112	−0.916540
$844$	36.7274	1.26421
$845$	−29.9149	−1.02910
$846$	3.15752	0.108558
$847$	−9.45453	−0.324861
$848$	−31.2875	−1.07442
$849$	−19.1297	−0.656528
$850$	−0.787152	−0.0269991
$851$	−24.8444	−0.851655
$852$	27.4908	0.941819
$853$	12.7514	0.436599	0.218300	−	0.975882i	$-0.429949\pi$
$853$	12.7514	0.436599	0.218300	+	0.975882i	$0.429949\pi$
$854$	0.451910	0.0154641
$855$	−1.94835	−0.0666321
$856$	−1.64999	−0.0563954
$857$	−38.9379	−1.33009	−0.665047	−	0.746802i	$-0.731588\pi$
$857$	−38.9379	−1.33009	−0.665047	+	0.746802i	$0.731588\pi$
$858$	6.63768	0.226607
$859$	21.9545	0.749078	0.374539	−	0.927211i	$-0.377801\pi$
$859$	21.9545	0.749078	0.374539	+	0.927211i	$0.377801\pi$
$860$	−13.1112	−0.447088
$861$	1.15919	0.0395051
$862$	−1.31875	−0.0449169
$863$	−25.2930	−0.860983	−0.430491	−	0.902595i	$-0.641660\pi$
$863$	−25.2930	−0.860983	−0.430491	+	0.902595i	$0.641660\pi$
$864$	−11.6930	−0.397806
$865$	−12.0386	−0.409325
$866$	−4.52127	−0.153639
$867$	2.74452	0.0932087
$868$	−12.6249	−0.428518
$869$	58.8145	1.99514
$870$	−0.416869	−0.0141332
$871$	34.1737	1.15793
$872$	−11.7179	−0.396819
$873$	−14.3237	−0.484784
$874$	0.569699	0.0192704
$875$	1.00000	0.0338062
$876$	−32.3090	−1.09162
$877$	−47.9156	−1.61800	−0.808998	−	0.587811i	$-0.799990\pi$
$877$	−47.9156	−1.61800	−0.808998	+	0.587811i	$0.799990\pi$
$878$	−0.817272	−0.0275816
$879$	−15.4274	−0.520354
$880$	17.2197	0.580476
$881$	−19.9498	−0.672127	−0.336064	−	0.941839i	$-0.609096\pi$
$881$	−19.9498	−0.672127	−0.336064	+	0.941839i	$0.609096\pi$
$882$	−0.259512	−0.00873824
$883$	−18.8386	−0.633968	−0.316984	−	0.948431i	$-0.602670\pi$
$883$	−18.8386	−0.633968	−0.316984	+	0.948431i	$0.602670\pi$
$884$	−56.4843	−1.89977
$885$	−5.95442	−0.200156
$886$	0.637587	0.0214201
$887$	30.2434	1.01547	0.507737	−	0.861512i	$-0.330482\pi$
$887$	30.2434	1.01547	0.507737	+	0.861512i	$0.330482\pi$
$888$	−9.39188	−0.315171
$889$	13.6204	0.456814
$890$	2.63791	0.0884229
$891$	11.6646	0.390778
$892$	1.18288	0.0396058
$893$	16.4096	0.549126
$894$	0.421290	0.0140900
$895$	−0.847211	−0.0283192
$896$	5.51881	0.184370
$897$	19.2113	0.641446
$898$	−0.588943	−0.0196533
$899$	−11.9384	−0.398168
$900$	2.84265	0.0947549
$901$	36.0079	1.19960
$902$	0.755150	0.0251437
$903$	8.30985	0.276535
$904$	3.08453	0.102590
$905$	21.0682	0.700332
$906$	−4.94981	−0.164446
$907$	27.6646	0.918589	0.459294	−	0.888284i	$-0.348102\pi$
$907$	27.6646	0.918589	0.459294	+	0.888284i	$0.348102\pi$
$908$	32.0681	1.06422
$909$	−18.8101	−0.623892
$910$	−1.17681	−0.0390107
$911$	−9.01315	−0.298619	−0.149309	−	0.988791i	$-0.547705\pi$
$911$	−9.01315	−0.298619	−0.149309	+	0.988791i	$0.547705\pi$
$912$	−6.40408	−0.212060
$913$	6.33459	0.209644
$914$	2.64057	0.0873422
$915$	3.13739	0.103719
$916$	−1.96773	−0.0650156
$917$	−6.73229	−0.222320
$918$	4.36326	0.144009
$919$	−21.1166	−0.696571	−0.348286	−	0.937388i	$-0.613236\pi$
$919$	−21.1166	−0.696571	−0.348286	+	0.937388i	$0.613236\pi$
$920$	−1.67602	−0.0552566
$921$	−25.9362	−0.854626
$922$	4.46690	0.147109
$923$	73.3854	2.41551
$924$	−11.0988	−0.365124
$925$	10.5656	0.347394
$926$	−1.37054	−0.0450387
$927$	−15.8711	−0.521277
$928$	3.92517	0.128850
$929$	−26.8667	−0.881468	−0.440734	−	0.897638i	$-0.645282\pi$
$929$	−26.8667	−0.881468	−0.440734	+	0.897638i	$0.645282\pi$
$930$	1.43741	0.0471345
$931$	−1.34868	−0.0442012
$932$	−21.2044	−0.694572
$933$	−19.9521	−0.653201
$934$	−3.50719	−0.114759
$935$	−19.8177	−0.648107
$936$	−6.74535	−0.220479
$937$	50.3232	1.64399	0.821994	−	0.569496i	$-0.192862\pi$
$937$	50.3232	1.64399	0.821994	+	0.569496i	$0.192862\pi$
$938$	0.937107	0.0305976
$939$	−32.8296	−1.07135
$940$	−23.9416	−0.780890
$941$	−41.2944	−1.34616	−0.673080	−	0.739570i	$-0.735029\pi$
$941$	−41.2944	−1.34616	−0.673080	+	0.739570i	$0.735029\pi$
$942$	2.57059	0.0837542
$943$	2.18561	0.0711733
$944$	18.1783	0.591654
$945$	−5.54310	−0.180317
$946$	5.41343	0.176006
$947$	−38.2608	−1.24331	−0.621655	−	0.783291i	$-0.713539\pi$
$947$	−38.2608	−1.24331	−0.621655	+	0.783291i	$0.713539\pi$
$948$	31.9133	1.03650
$949$	−86.2475	−2.79971
$950$	−0.242276	−0.00786046
$951$	−28.9515	−0.938815
$952$	−3.12321	−0.101224
$953$	16.0526	0.519995	0.259998	−	0.965609i	$-0.416278\pi$
$953$	16.0526	0.519995	0.259998	+	0.965609i	$0.416278\pi$
$954$	2.13255	0.0690438
$955$	19.2876	0.624133
$956$	−41.2957	−1.33560
$957$	−10.4953	−0.339264
$958$	−0.695605	−0.0224740
$959$	2.22633	0.0718919
$960$	9.02420	0.291255
$961$	10.1649	0.327900
$962$	−12.4336	−0.400877
$963$	−3.34422	−0.107766
$964$	−10.8331	−0.348911
$965$	−20.3865	−0.656264
$966$	0.526808	0.0169498
$967$	−57.3282	−1.84355	−0.921775	−	0.387725i	$-0.873261\pi$
$967$	−57.3282	−1.84355	−0.921775	+	0.387725i	$0.873261\pi$
$968$	−6.73880	−0.216593
$969$	7.37027	0.236767
$970$	−1.78114	−0.0571890
$971$	−57.3914	−1.84178	−0.920888	−	0.389827i	$-0.872535\pi$
$971$	−57.3914	−1.84178	−0.920888	+	0.389827i	$0.872535\pi$
$972$	−26.3926	−0.846544
$973$	5.23703	0.167891
$974$	−0.772412	−0.0247497
$975$	−8.16997	−0.261649
$976$	−9.57817	−0.306590
$977$	−13.9642	−0.446753	−0.223376	−	0.974732i	$-0.571708\pi$
$977$	−13.9642	−0.446753	−0.223376	+	0.974732i	$0.571708\pi$
$978$	−1.67157	−0.0534510
$979$	66.4131	2.12257
$980$	1.96773	0.0628568
$981$	−23.7501	−0.758282
$982$	−1.88042	−0.0600066
$983$	59.7734	1.90648	0.953238	−	0.302221i	$-0.0977280\pi$
$983$	59.7734	1.90648	0.953238	+	0.302221i	$0.0977280\pi$
$984$	0.826223	0.0263390
$985$	−14.7013	−0.468424
$986$	−1.46467	−0.0466448
$987$	15.1742	0.482999
$988$	−17.3852	−0.553096
$989$	15.6680	0.498212
$990$	−1.17369	−0.0373023
$991$	24.9969	0.794054	0.397027	−	0.917807i	$-0.370042\pi$
$991$	24.9969	0.794054	0.397027	+	0.917807i	$0.370042\pi$
$992$	−13.5344	−0.429717
$993$	−31.1655	−0.989007
$994$	2.01236	0.0638282
$995$	−25.3833	−0.804703
$996$	3.43721	0.108912
$997$	−40.1126	−1.27038	−0.635190	−	0.772356i	$-0.719078\pi$
$997$	−40.1126	−1.27038	−0.635190	+	0.772356i	$0.719078\pi$
$998$	3.83743	0.121472
$999$	−58.5660	−1.85295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.34	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.34	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.179639 q^{2} +1.24714 q^{3} -1.96773 q^{4} -1.00000 q^{5} +0.224036 q^{6} -1.00000 q^{7} -0.712759 q^{8} -1.44463 q^{9} +O(q^{10})\)	\(q+0.179639 q^{2} +1.24714 q^{3} -1.96773 q^{4} -1.00000 q^{5} +0.224036 q^{6} -1.00000 q^{7} -0.712759 q^{8} -1.44463 q^{9} -0.179639 q^{10} -4.52267 q^{11} -2.45404 q^{12} -6.55095 q^{13} -0.179639 q^{14} -1.24714 q^{15} +3.80742 q^{16} -4.38185 q^{17} -0.259512 q^{18} -1.34868 q^{19} +1.96773 q^{20} -1.24714 q^{21} -0.812448 q^{22} -2.35145 q^{23} -0.888913 q^{24} +1.00000 q^{25} -1.17681 q^{26} -5.54310 q^{27} +1.96773 q^{28} +1.86073 q^{29} -0.224036 q^{30} -6.41599 q^{31} +2.10948 q^{32} -5.64042 q^{33} -0.787152 q^{34} +1.00000 q^{35} +2.84265 q^{36} +10.5656 q^{37} -0.242276 q^{38} -8.16997 q^{39} +0.712759 q^{40} -0.929475 q^{41} -0.224036 q^{42} -6.66311 q^{43} +8.89939 q^{44} +1.44463 q^{45} -0.422412 q^{46} -12.1671 q^{47} +4.74840 q^{48} +1.00000 q^{49} +0.179639 q^{50} -5.46480 q^{51} +12.8905 q^{52} -8.21751 q^{53} -0.995756 q^{54} +4.52267 q^{55} +0.712759 q^{56} -1.68200 q^{57} +0.334259 q^{58} +4.77445 q^{59} +2.45404 q^{60} -2.51566 q^{61} -1.15256 q^{62} +1.44463 q^{63} -7.23590 q^{64} +6.55095 q^{65} -1.01324 q^{66} -5.21661 q^{67} +8.62230 q^{68} -2.93259 q^{69} +0.179639 q^{70} -11.2022 q^{71} +1.02968 q^{72} +13.1656 q^{73} +1.89799 q^{74} +1.24714 q^{75} +2.65384 q^{76} +4.52267 q^{77} -1.46765 q^{78} -13.0044 q^{79} -3.80742 q^{80} -2.57914 q^{81} -0.166970 q^{82} -1.40063 q^{83} +2.45404 q^{84} +4.38185 q^{85} -1.19695 q^{86} +2.32059 q^{87} +3.22357 q^{88} -14.6845 q^{89} +0.259512 q^{90} +6.55095 q^{91} +4.62701 q^{92} -8.00166 q^{93} -2.18569 q^{94} +1.34868 q^{95} +2.63082 q^{96} +9.91511 q^{97} +0.179639 q^{98} +6.53360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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