LMFDB - Embedded newform 8015.2.a.o.1.9

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:	$73$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.41178 q^{2} -1.36759 q^{3} +3.81666 q^{4} +1.00000 q^{5} +3.29833 q^{6} +1.00000 q^{7} -4.38139 q^{8} -1.12969 q^{9} +O(q^{10})$	\(q-2.41178 q^{2} -1.36759 q^{3} +3.81666 q^{4} +1.00000 q^{5} +3.29833 q^{6} +1.00000 q^{7} -4.38139 q^{8} -1.12969 q^{9} -2.41178 q^{10} +4.20908 q^{11} -5.21965 q^{12} -2.64283 q^{13} -2.41178 q^{14} -1.36759 q^{15} +2.93360 q^{16} +0.352971 q^{17} +2.72455 q^{18} +8.37133 q^{19} +3.81666 q^{20} -1.36759 q^{21} -10.1514 q^{22} -9.28073 q^{23} +5.99196 q^{24} +1.00000 q^{25} +6.37391 q^{26} +5.64773 q^{27} +3.81666 q^{28} -7.00643 q^{29} +3.29833 q^{30} +8.18017 q^{31} +1.68760 q^{32} -5.75632 q^{33} -0.851287 q^{34} +1.00000 q^{35} -4.31164 q^{36} -6.61854 q^{37} -20.1898 q^{38} +3.61431 q^{39} -4.38139 q^{40} +5.96685 q^{41} +3.29833 q^{42} +6.21481 q^{43} +16.0647 q^{44} -1.12969 q^{45} +22.3830 q^{46} -0.951068 q^{47} -4.01197 q^{48} +1.00000 q^{49} -2.41178 q^{50} -0.482721 q^{51} -10.0868 q^{52} -5.48155 q^{53} -13.6211 q^{54} +4.20908 q^{55} -4.38139 q^{56} -11.4486 q^{57} +16.8979 q^{58} +0.745416 q^{59} -5.21965 q^{60} -10.5489 q^{61} -19.7287 q^{62} -1.12969 q^{63} -9.93730 q^{64} -2.64283 q^{65} +13.8829 q^{66} -3.12930 q^{67} +1.34717 q^{68} +12.6923 q^{69} -2.41178 q^{70} +4.96517 q^{71} +4.94960 q^{72} +8.13801 q^{73} +15.9624 q^{74} -1.36759 q^{75} +31.9506 q^{76} +4.20908 q^{77} -8.71692 q^{78} -8.81869 q^{79} +2.93360 q^{80} -4.33474 q^{81} -14.3907 q^{82} +14.8851 q^{83} -5.21965 q^{84} +0.352971 q^{85} -14.9887 q^{86} +9.58195 q^{87} -18.4416 q^{88} -4.10361 q^{89} +2.72455 q^{90} -2.64283 q^{91} -35.4214 q^{92} -11.1872 q^{93} +2.29376 q^{94} +8.37133 q^{95} -2.30795 q^{96} +5.40558 q^{97} -2.41178 q^{98} -4.75495 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) $ 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * 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 $

$2$	−2.41178	−1.70538	−0.852692	−	0.522415i	$-0.825031\pi$
$2$	−2.41178	−1.70538	−0.852692	+	0.522415i	$0.825031\pi$
$3$	−1.36759	−0.789581	−0.394790	−	0.918771i	$-0.629183\pi$
$3$	−1.36759	−0.789581	−0.394790	+	0.918771i	$0.629183\pi$
$4$	3.81666	1.90833
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.29833	1.34654
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−4.38139	−1.54905
$9$	−1.12969	−0.376563
$10$	−2.41178	−0.762671
$11$	4.20908	1.26909	0.634543	−	0.772887i	$-0.281188\pi$
$11$	4.20908	1.26909	0.634543	+	0.772887i	$0.281188\pi$
$12$	−5.21965	−1.50678
$13$	−2.64283	−0.732989	−0.366494	−	0.930420i	$-0.619442\pi$
$13$	−2.64283	−0.732989	−0.366494	+	0.930420i	$0.619442\pi$
$14$	−2.41178	−0.644574
$15$	−1.36759	−0.353111
$16$	2.93360	0.733399
$17$	0.352971	0.0856080	0.0428040	−	0.999083i	$-0.486371\pi$
$17$	0.352971	0.0856080	0.0428040	+	0.999083i	$0.486371\pi$
$18$	2.72455	0.642183
$19$	8.37133	1.92052	0.960258	−	0.279115i	$-0.0900411\pi$
$19$	8.37133	1.92052	0.960258	+	0.279115i	$0.0900411\pi$
$20$	3.81666	0.853432
$21$	−1.36759	−0.298433
$22$	−10.1514	−2.16428
$23$	−9.28073	−1.93517	−0.967583	−	0.252553i	$-0.918730\pi$
$23$	−9.28073	−1.93517	−0.967583	+	0.252553i	$0.918730\pi$
$24$	5.99196	1.22310
$25$	1.00000	0.200000
$26$	6.37391	1.25003
$27$	5.64773	1.08691
$28$	3.81666	0.721282
$29$	−7.00643	−1.30106	−0.650531	−	0.759480i	$-0.725453\pi$
$29$	−7.00643	−1.30106	−0.650531	+	0.759480i	$0.725453\pi$
$30$	3.29833	0.602190
$31$	8.18017	1.46920	0.734601	−	0.678499i	$-0.237369\pi$
$31$	8.18017	1.46920	0.734601	+	0.678499i	$0.237369\pi$
$32$	1.68760	0.298328
$33$	−5.75632	−1.00205
$34$	−0.851287	−0.145995
$35$	1.00000	0.169031
$36$	−4.31164	−0.718606
$37$	−6.61854	−1.08808	−0.544041	−	0.839059i	$-0.683106\pi$
$37$	−6.61854	−1.08808	−0.544041	+	0.839059i	$0.683106\pi$
$38$	−20.1898	−3.27521
$39$	3.61431	0.578754
$40$	−4.38139	−0.692758
$41$	5.96685	0.931865	0.465933	−	0.884820i	$-0.345719\pi$
$41$	5.96685	0.931865	0.465933	+	0.884820i	$0.345719\pi$
$42$	3.29833	0.508943
$43$	6.21481	0.947750	0.473875	−	0.880592i	$-0.342855\pi$
$43$	6.21481	0.947750	0.473875	+	0.880592i	$0.342855\pi$
$44$	16.0647	2.42184
$45$	−1.12969	−0.168404
$46$	22.3830	3.30020
$47$	−0.951068	−0.138727	−0.0693637	−	0.997591i	$-0.522097\pi$
$47$	−0.951068	−0.138727	−0.0693637	+	0.997591i	$0.522097\pi$
$48$	−4.01197	−0.579078
$49$	1.00000	0.142857
$50$	−2.41178	−0.341077
$51$	−0.482721	−0.0675944
$52$	−10.0868	−1.39879
$53$	−5.48155	−0.752948	−0.376474	−	0.926427i	$-0.622864\pi$
$53$	−5.48155	−0.752948	−0.376474	+	0.926427i	$0.622864\pi$
$54$	−13.6211	−1.85359
$55$	4.20908	0.567553
$56$	−4.38139	−0.585487
$57$	−11.4486	−1.51640
$58$	16.8979	2.21881
$59$	0.745416	0.0970449	0.0485225	−	0.998822i	$-0.484549\pi$
$59$	0.745416	0.0970449	0.0485225	+	0.998822i	$0.484549\pi$
$60$	−5.21965	−0.673853
$61$	−10.5489	−1.35065	−0.675327	−	0.737518i	$-0.735998\pi$
$61$	−10.5489	−1.35065	−0.675327	+	0.737518i	$0.735998\pi$
$62$	−19.7287	−2.50555
$63$	−1.12969	−0.142327
$64$	−9.93730	−1.24216
$65$	−2.64283	−0.327802
$66$	13.8829	1.70887
$67$	−3.12930	−0.382305	−0.191153	−	0.981560i	$-0.561223\pi$
$67$	−3.12930	−0.382305	−0.191153	+	0.981560i	$0.561223\pi$
$68$	1.34717	0.163369
$69$	12.6923	1.52797
$70$	−2.41178	−0.288262
$71$	4.96517	0.589257	0.294629	−	0.955612i	$-0.404804\pi$
$71$	4.96517	0.589257	0.294629	+	0.955612i	$0.404804\pi$
$72$	4.94960	0.583316
$73$	8.13801	0.952482	0.476241	−	0.879315i	$-0.341999\pi$
$73$	8.13801	0.952482	0.476241	+	0.879315i	$0.341999\pi$
$74$	15.9624	1.85560
$75$	−1.36759	−0.157916
$76$	31.9506	3.66498
$77$	4.20908	0.479670
$78$	−8.71692	−0.986997
$79$	−8.81869	−0.992180	−0.496090	−	0.868271i	$-0.665231\pi$
$79$	−8.81869	−0.992180	−0.496090	+	0.868271i	$0.665231\pi$
$80$	2.93360	0.327986
$81$	−4.33474	−0.481638
$82$	−14.3907	−1.58919
$83$	14.8851	1.63385	0.816927	−	0.576742i	$-0.195676\pi$
$83$	14.8851	1.63385	0.816927	+	0.576742i	$0.195676\pi$
$84$	−5.21965	−0.569510
$85$	0.352971	0.0382851
$86$	−14.9887	−1.61628
$87$	9.58195	1.02729
$88$	−18.4416	−1.96588
$89$	−4.10361	−0.434981	−0.217491	−	0.976062i	$-0.569787\pi$
$89$	−4.10361	−0.434981	−0.217491	+	0.976062i	$0.569787\pi$
$90$	2.72455	0.287193
$91$	−2.64283	−0.277044
$92$	−35.4214	−3.69294
$93$	−11.1872	−1.16005
$94$	2.29376	0.236583
$95$	8.37133	0.858881
$96$	−2.30795	−0.235554
$97$	5.40558	0.548854	0.274427	−	0.961608i	$-0.411512\pi$
$97$	5.40558	0.548854	0.274427	+	0.961608i	$0.411512\pi$
$98$	−2.41178	−0.243626
$99$	−4.75495	−0.477891
$100$	3.81666	0.381666
$101$	1.78050	0.177166	0.0885832	−	0.996069i	$-0.471766\pi$
$101$	1.78050	0.177166	0.0885832	+	0.996069i	$0.471766\pi$
$102$	1.16421	0.115274
$103$	3.72867	0.367397	0.183699	−	0.982983i	$-0.441193\pi$
$103$	3.72867	0.367397	0.183699	+	0.982983i	$0.441193\pi$
$104$	11.5793	1.13544
$105$	−1.36759	−0.133463
$106$	13.2203	1.28407
$107$	3.10719	0.300384	0.150192	−	0.988657i	$-0.452011\pi$
$107$	3.10719	0.300384	0.150192	+	0.988657i	$0.452011\pi$
$108$	21.5555	2.07418
$109$	1.09206	0.104601	0.0523004	−	0.998631i	$-0.483345\pi$
$109$	1.09206	0.104601	0.0523004	+	0.998631i	$0.483345\pi$
$110$	−10.1514	−0.967895
$111$	9.05148	0.859128
$112$	2.93360	0.277199
$113$	−5.88850	−0.553944	−0.276972	−	0.960878i	$-0.589331\pi$
$113$	−5.88850	−0.553944	−0.276972	+	0.960878i	$0.589331\pi$
$114$	27.6114	2.58605
$115$	−9.28073	−0.865433
$116$	−26.7412	−2.48286
$117$	2.98557	0.276016
$118$	−1.79778	−0.165499
$119$	0.352971	0.0323568
$120$	5.99196	0.546988
$121$	6.71639	0.610581
$122$	25.4417	2.30338
$123$	−8.16022	−0.735783
$124$	31.2210	2.80373
$125$	1.00000	0.0894427
$126$	2.72455	0.242723
$127$	15.4744	1.37313	0.686564	−	0.727069i	$-0.259118\pi$
$127$	15.4744	1.37313	0.686564	+	0.727069i	$0.259118\pi$
$128$	20.5913	1.82003
$129$	−8.49934	−0.748325
$130$	6.37391	0.559029
$131$	18.0342	1.57565	0.787827	−	0.615896i	$-0.211206\pi$
$131$	18.0342	1.57565	0.787827	+	0.615896i	$0.211206\pi$
$132$	−21.9699	−1.91224
$133$	8.37133	0.725887
$134$	7.54718	0.651977
$135$	5.64773	0.486080
$136$	−1.54650	−0.132611
$137$	−5.40821	−0.462055	−0.231027	−	0.972947i	$-0.574209\pi$
$137$	−5.40821	−0.462055	−0.231027	+	0.972947i	$0.574209\pi$
$138$	−30.6109	−2.60577
$139$	−6.09376	−0.516866	−0.258433	−	0.966029i	$-0.583206\pi$
$139$	−6.09376	−0.516866	−0.258433	+	0.966029i	$0.583206\pi$
$140$	3.81666	0.322567
$141$	1.30067	0.109537
$142$	−11.9749	−1.00491
$143$	−11.1239	−0.930226
$144$	−3.31405	−0.276171
$145$	−7.00643	−0.581852
$146$	−19.6271	−1.62435
$147$	−1.36759	−0.112797
$148$	−25.2608	−2.07642
$149$	0.507281	0.0415581	0.0207790	−	0.999784i	$-0.493385\pi$
$149$	0.507281	0.0415581	0.0207790	+	0.999784i	$0.493385\pi$
$150$	3.29833	0.269307
$151$	20.7131	1.68561	0.842803	−	0.538222i	$-0.180904\pi$
$151$	20.7131	1.68561	0.842803	+	0.538222i	$0.180904\pi$
$152$	−36.6780	−2.97498
$153$	−0.398747	−0.0322368
$154$	−10.1514	−0.818021
$155$	8.18017	0.657047
$156$	13.7946	1.10445
$157$	−9.82626	−0.784221	−0.392110	−	0.919918i	$-0.628255\pi$
$157$	−9.82626	−0.784221	−0.392110	+	0.919918i	$0.628255\pi$
$158$	21.2687	1.69205
$159$	7.49653	0.594513
$160$	1.68760	0.133416
$161$	−9.28073	−0.731424
$162$	10.4544	0.821378
$163$	−4.93418	−0.386474	−0.193237	−	0.981152i	$-0.561899\pi$
$163$	−4.93418	−0.386474	−0.193237	+	0.981152i	$0.561899\pi$
$164$	22.7735	1.77831
$165$	−5.75632	−0.448129
$166$	−35.8996	−2.78635
$167$	−12.5732	−0.972947	−0.486474	−	0.873695i	$-0.661717\pi$
$167$	−12.5732	−0.972947	−0.486474	+	0.873695i	$0.661717\pi$
$168$	5.99196	0.462290
$169$	−6.01546	−0.462728
$170$	−0.851287	−0.0652907
$171$	−9.45699	−0.723194
$172$	23.7199	1.80862
$173$	7.12499	0.541703	0.270851	−	0.962621i	$-0.412695\pi$
$173$	7.12499	0.541703	0.270851	+	0.962621i	$0.412695\pi$
$174$	−23.1095	−1.75193
$175$	1.00000	0.0755929
$176$	12.3478	0.930747
$177$	−1.01943	−0.0766248
$178$	9.89698	0.741810
$179$	−2.20910	−0.165116	−0.0825581	−	0.996586i	$-0.526309\pi$
$179$	−2.20910	−0.165116	−0.0825581	+	0.996586i	$0.526309\pi$
$180$	−4.31164	−0.321371
$181$	9.70802	0.721592	0.360796	−	0.932645i	$-0.382505\pi$
$181$	9.70802	0.721592	0.360796	+	0.932645i	$0.382505\pi$
$182$	6.37391	0.472466
$183$	14.4267	1.06645
$184$	40.6625	2.99768
$185$	−6.61854	−0.486605
$186$	26.9809	1.97834
$187$	1.48568	0.108644
$188$	−3.62991	−0.264738
$189$	5.64773	0.410812
$190$	−20.1898	−1.46472
$191$	0.820327	0.0593568	0.0296784	−	0.999559i	$-0.490552\pi$
$191$	0.820327	0.0593568	0.0296784	+	0.999559i	$0.490552\pi$
$192$	13.5902	0.980787
$193$	2.89721	0.208546	0.104273	−	0.994549i	$-0.466748\pi$
$193$	2.89721	0.208546	0.104273	+	0.994549i	$0.466748\pi$
$194$	−13.0371	−0.936006
$195$	3.61431	0.258826
$196$	3.81666	0.272619
$197$	−3.35335	−0.238917	−0.119458	−	0.992839i	$-0.538116\pi$
$197$	−3.35335	−0.238917	−0.119458	+	0.992839i	$0.538116\pi$
$198$	11.4679	0.814986
$199$	23.9399	1.69706	0.848528	−	0.529150i	$-0.177489\pi$
$199$	23.9399	1.69706	0.848528	+	0.529150i	$0.177489\pi$
$200$	−4.38139	−0.309811
$201$	4.27962	0.301861
$202$	−4.29417	−0.302136
$203$	−7.00643	−0.491755
$204$	−1.84238	−0.128993
$205$	5.96685	0.416743
$206$	−8.99272	−0.626553
$207$	10.4843	0.728711
$208$	−7.75299	−0.537573
$209$	35.2356	2.43730
$210$	3.29833	0.227606
$211$	3.31683	0.228340	0.114170	−	0.993461i	$-0.463579\pi$
$211$	3.31683	0.228340	0.114170	+	0.993461i	$0.463579\pi$
$212$	−20.9212	−1.43688
$213$	−6.79034	−0.465266
$214$	−7.49385	−0.512269
$215$	6.21481	0.423847
$216$	−24.7449	−1.68368
$217$	8.18017	0.555306
$218$	−2.63381	−0.178384
$219$	−11.1295	−0.752061
$220$	16.0647	1.08308
$221$	−0.932842	−0.0627497
$222$	−21.8301	−1.46514
$223$	24.3454	1.63029	0.815145	−	0.579257i	$-0.196657\pi$
$223$	24.3454	1.63029	0.815145	+	0.579257i	$0.196657\pi$
$224$	1.68760	0.112757
$225$	−1.12969	−0.0753125
$226$	14.2018	0.944687
$227$	18.8441	1.25073	0.625364	−	0.780333i	$-0.284950\pi$
$227$	18.8441	1.25073	0.625364	+	0.780333i	$0.284950\pi$
$228$	−43.6954	−2.89380
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	22.3830	1.47589
$231$	−5.75632	−0.378738
$232$	30.6979	2.01541
$233$	−5.67568	−0.371826	−0.185913	−	0.982566i	$-0.559524\pi$
$233$	−5.67568	−0.371826	−0.185913	+	0.982566i	$0.559524\pi$
$234$	−7.20053	−0.470713
$235$	−0.951068	−0.0620408
$236$	2.84500	0.185194
$237$	12.0604	0.783406
$238$	−0.851287	−0.0551807
$239$	−15.0660	−0.974537	−0.487269	−	0.873252i	$-0.662007\pi$
$239$	−15.0660	−0.974537	−0.487269	+	0.873252i	$0.662007\pi$
$240$	−4.01197	−0.258971
$241$	20.5568	1.32418	0.662089	−	0.749425i	$-0.269670\pi$
$241$	20.5568	1.32418	0.662089	+	0.749425i	$0.269670\pi$
$242$	−16.1984	−1.04127
$243$	−11.0150	−0.706615
$244$	−40.2618	−2.57750
$245$	1.00000	0.0638877
$246$	19.6806	1.25479
$247$	−22.1240	−1.40772
$248$	−35.8405	−2.27587
$249$	−20.3568	−1.29006
$250$	−2.41178	−0.152534
$251$	8.11642	0.512304	0.256152	−	0.966636i	$-0.417545\pi$
$251$	8.11642	0.512304	0.256152	+	0.966636i	$0.417545\pi$
$252$	−4.31164	−0.271608
$253$	−39.0634	−2.45589
$254$	−37.3207	−2.34171
$255$	−0.482721	−0.0302292
$256$	−29.7871	−1.86169
$257$	−23.0910	−1.44038	−0.720189	−	0.693778i	$-0.755945\pi$
$257$	−23.0910	−1.44038	−0.720189	+	0.693778i	$0.755945\pi$
$258$	20.4985	1.27618
$259$	−6.61854	−0.411256
$260$	−10.0868	−0.625556
$261$	7.91508	0.489931
$262$	−43.4944	−2.68709
$263$	−8.90256	−0.548955	−0.274478	−	0.961594i	$-0.588505\pi$
$263$	−8.90256	−0.548955	−0.274478	+	0.961594i	$0.588505\pi$
$264$	25.2207	1.55222
$265$	−5.48155	−0.336729
$266$	−20.1898	−1.23791
$267$	5.61207	0.343453
$268$	−11.9435	−0.729566
$269$	−6.13110	−0.373820	−0.186910	−	0.982377i	$-0.559847\pi$
$269$	−6.13110	−0.373820	−0.186910	+	0.982377i	$0.559847\pi$
$270$	−13.6211	−0.828952
$271$	20.0482	1.21784	0.608920	−	0.793232i	$-0.291603\pi$
$271$	20.0482	1.21784	0.608920	+	0.793232i	$0.291603\pi$
$272$	1.03547	0.0627849
$273$	3.61431	0.218748
$274$	13.0434	0.787981
$275$	4.20908	0.253817
$276$	48.4421	2.91587
$277$	6.41312	0.385327	0.192664	−	0.981265i	$-0.438287\pi$
$277$	6.41312	0.385327	0.192664	+	0.981265i	$0.438287\pi$
$278$	14.6968	0.881455
$279$	−9.24104	−0.553247
$280$	−4.38139	−0.261838
$281$	−32.1875	−1.92015	−0.960074	−	0.279746i	$-0.909750\pi$
$281$	−32.1875	−1.92015	−0.960074	+	0.279746i	$0.909750\pi$
$282$	−3.13693	−0.186802
$283$	21.2503	1.26320	0.631598	−	0.775296i	$-0.282399\pi$
$283$	21.2503	1.26320	0.631598	+	0.775296i	$0.282399\pi$
$284$	18.9504	1.12450
$285$	−11.4486	−0.678155
$286$	26.8283	1.58639
$287$	5.96685	0.352212
$288$	−1.90646	−0.112339
$289$	−16.8754	−0.992671
$290$	16.8979	0.992281
$291$	−7.39264	−0.433364
$292$	31.0600	1.81765
$293$	10.0703	0.588315	0.294158	−	0.955757i	$-0.404961\pi$
$293$	10.0703	0.588315	0.294158	+	0.955757i	$0.404961\pi$
$294$	3.29833	0.192362
$295$	0.745416	0.0433998
$296$	28.9984	1.68550
$297$	23.7718	1.37938
$298$	−1.22345	−0.0708724
$299$	24.5274	1.41845
$300$	−5.21965	−0.301356
$301$	6.21481	0.358216
$302$	−49.9553	−2.87460
$303$	−2.43500	−0.139887
$304$	24.5581	1.40850
$305$	−10.5489	−0.604031
$306$	0.961688	0.0549761
$307$	−23.1233	−1.31972	−0.659860	−	0.751389i	$-0.729384\pi$
$307$	−23.1233	−1.31972	−0.659860	+	0.751389i	$0.729384\pi$
$308$	16.0647	0.915369
$309$	−5.09931	−0.290090
$310$	−19.7287	−1.12052
$311$	−20.5851	−1.16728	−0.583638	−	0.812014i	$-0.698371\pi$
$311$	−20.5851	−1.16728	−0.583638	+	0.812014i	$0.698371\pi$
$312$	−15.8357	−0.896521
$313$	−23.9094	−1.35144	−0.675719	−	0.737159i	$-0.736167\pi$
$313$	−23.9094	−1.35144	−0.675719	+	0.737159i	$0.736167\pi$
$314$	23.6987	1.33740
$315$	−1.12969	−0.0636507
$316$	−33.6580	−1.89341
$317$	19.5815	1.09981	0.549903	−	0.835228i	$-0.314665\pi$
$317$	19.5815	1.09981	0.549903	+	0.835228i	$0.314665\pi$
$318$	−18.0799	−1.01387
$319$	−29.4907	−1.65116
$320$	−9.93730	−0.555512
$321$	−4.24938	−0.237177
$322$	22.3830	1.24736
$323$	2.95484	0.164412
$324$	−16.5443	−0.919125
$325$	−2.64283	−0.146598
$326$	11.9001	0.659087
$327$	−1.49350	−0.0825907
$328$	−26.1431	−1.44351
$329$	−0.951068	−0.0524340
$330$	13.8829	0.764231
$331$	31.2702	1.71877	0.859384	−	0.511331i	$-0.170847\pi$
$331$	31.2702	1.71877	0.859384	+	0.511331i	$0.170847\pi$
$332$	56.8115	3.11793
$333$	7.47689	0.409731
$334$	30.3239	1.65925
$335$	−3.12930	−0.170972
$336$	−4.01197	−0.218871
$337$	−7.80600	−0.425220	−0.212610	−	0.977137i	$-0.568196\pi$
$337$	−7.80600	−0.425220	−0.212610	+	0.977137i	$0.568196\pi$
$338$	14.5079	0.789128
$339$	8.05308	0.437383
$340$	1.34717	0.0730606
$341$	34.4310	1.86455
$342$	22.8081	1.23332
$343$	1.00000	0.0539949
$344$	−27.2295	−1.46812
$345$	12.6923	0.683329
$346$	−17.1839	−0.923811
$347$	−8.48470	−0.455483	−0.227741	−	0.973722i	$-0.573134\pi$
$347$	−8.48470	−0.455483	−0.227741	+	0.973722i	$0.573134\pi$
$348$	36.5711	1.96042
$349$	−10.4736	−0.560639	−0.280319	−	0.959907i	$-0.590440\pi$
$349$	−10.4736	−0.560639	−0.280319	+	0.959907i	$0.590440\pi$
$350$	−2.41178	−0.128915
$351$	−14.9260	−0.796690
$352$	7.10323	0.378604
$353$	−33.2658	−1.77056	−0.885279	−	0.465060i	$-0.846033\pi$
$353$	−33.2658	−1.77056	−0.885279	+	0.465060i	$0.846033\pi$
$354$	2.45863	0.130675
$355$	4.96517	0.263524
$356$	−15.6621	−0.830089
$357$	−0.482721	−0.0255483
$358$	5.32787	0.281586
$359$	6.25849	0.330311	0.165155	−	0.986268i	$-0.447187\pi$
$359$	6.25849	0.330311	0.165155	+	0.986268i	$0.447187\pi$
$360$	4.94960	0.260867
$361$	51.0792	2.68838
$362$	−23.4136	−1.23059
$363$	−9.18529	−0.482103
$364$	−10.0868	−0.528691
$365$	8.13801	0.425963
$366$	−34.7939	−1.81871
$367$	−31.4447	−1.64140	−0.820700	−	0.571359i	$-0.806416\pi$
$367$	−31.4447	−1.64140	−0.820700	+	0.571359i	$0.806416\pi$
$368$	−27.2259	−1.41925
$369$	−6.74068	−0.350906
$370$	15.9624	0.829848
$371$	−5.48155	−0.284588
$372$	−42.6976	−2.21377
$373$	−19.8273	−1.02662	−0.513309	−	0.858204i	$-0.671580\pi$
$373$	−19.8273	−1.02662	−0.513309	+	0.858204i	$0.671580\pi$
$374$	−3.58314	−0.185280
$375$	−1.36759	−0.0706222
$376$	4.16699	0.214896
$377$	18.5168	0.953663
$378$	−13.6211	−0.700592
$379$	−17.4491	−0.896301	−0.448150	−	0.893958i	$-0.647917\pi$
$379$	−17.4491	−0.896301	−0.448150	+	0.893958i	$0.647917\pi$
$380$	31.9506	1.63903
$381$	−21.1626	−1.08420
$382$	−1.97845	−0.101226
$383$	−10.1578	−0.519039	−0.259519	−	0.965738i	$-0.583564\pi$
$383$	−10.1578	−0.519039	−0.259519	+	0.965738i	$0.583564\pi$
$384$	−28.1606	−1.43706
$385$	4.20908	0.214515
$386$	−6.98743	−0.355651
$387$	−7.02080	−0.356887
$388$	20.6313	1.04740
$389$	−15.0744	−0.764304	−0.382152	−	0.924100i	$-0.624817\pi$
$389$	−15.0744	−0.764304	−0.382152	+	0.924100i	$0.624817\pi$
$390$	−8.71692	−0.441398
$391$	−3.27583	−0.165666
$392$	−4.38139	−0.221293
$393$	−24.6634	−1.24411
$394$	8.08754	0.407444
$395$	−8.81869	−0.443716
$396$	−18.1480	−0.911974
$397$	18.0052	0.903655	0.451827	−	0.892105i	$-0.350772\pi$
$397$	18.0052	0.903655	0.451827	+	0.892105i	$0.350772\pi$
$398$	−57.7378	−2.89413
$399$	−11.4486	−0.573146
$400$	2.93360	0.146680
$401$	24.1533	1.20616	0.603079	−	0.797681i	$-0.293940\pi$
$401$	24.1533	1.20616	0.603079	+	0.797681i	$0.293940\pi$
$402$	−10.3215	−0.514788
$403$	−21.6188	−1.07691
$404$	6.79557	0.338092
$405$	−4.33474	−0.215395
$406$	16.8979	0.838631
$407$	−27.8580	−1.38087
$408$	2.11499	0.104707
$409$	−20.0958	−0.993673	−0.496836	−	0.867844i	$-0.665505\pi$
$409$	−20.0958	−0.993673	−0.496836	+	0.867844i	$0.665505\pi$
$410$	−14.3907	−0.710706
$411$	7.39624	0.364830
$412$	14.2311	0.701115
$413$	0.745416	0.0366795
$414$	−25.2859	−1.24273
$415$	14.8851	0.730681
$416$	−4.46003	−0.218671
$417$	8.33379	0.408107
$418$	−84.9805	−4.15653
$419$	21.2440	1.03784	0.518920	−	0.854823i	$-0.326334\pi$
$419$	21.2440	1.03784	0.518920	+	0.854823i	$0.326334\pi$
$420$	−5.21965	−0.254693
$421$	−33.4134	−1.62847	−0.814236	−	0.580534i	$-0.802844\pi$
$421$	−33.4134	−1.62847	−0.814236	+	0.580534i	$0.802844\pi$
$422$	−7.99944	−0.389407
$423$	1.07441	0.0522396
$424$	24.0168	1.16636
$425$	0.352971	0.0171216
$426$	16.3768	0.793457
$427$	−10.5489	−0.510499
$428$	11.8591	0.573232
$429$	15.2130	0.734488
$430$	−14.9887	−0.722821
$431$	26.1078	1.25757	0.628785	−	0.777579i	$-0.283553\pi$
$431$	26.1078	1.25757	0.628785	+	0.777579i	$0.283553\pi$
$432$	16.5682	0.797137
$433$	−12.0333	−0.578285	−0.289143	−	0.957286i	$-0.593370\pi$
$433$	−12.0333	−0.578285	−0.289143	+	0.957286i	$0.593370\pi$
$434$	−19.7287	−0.947010
$435$	9.58195	0.459419
$436$	4.16804	0.199613
$437$	−77.6921	−3.71652
$438$	26.8418	1.28255
$439$	35.5348	1.69599	0.847993	−	0.530008i	$-0.177811\pi$
$439$	35.5348	1.69599	0.847993	+	0.530008i	$0.177811\pi$
$440$	−18.4416	−0.879170
$441$	−1.12969	−0.0537946
$442$	2.24981	0.107012
$443$	−5.36071	−0.254695	−0.127348	−	0.991858i	$-0.540646\pi$
$443$	−5.36071	−0.254695	−0.127348	+	0.991858i	$0.540646\pi$
$444$	34.5465	1.63950
$445$	−4.10361	−0.194530
$446$	−58.7157	−2.78027
$447$	−0.693754	−0.0328134
$448$	−9.93730	−0.469493
$449$	−0.314162	−0.0148262	−0.00741310	−	0.999973i	$-0.502360\pi$
$449$	−0.314162	−0.0148262	−0.00741310	+	0.999973i	$0.502360\pi$
$450$	2.72455	0.128437
$451$	25.1150	1.18262
$452$	−22.4744	−1.05711
$453$	−28.3271	−1.33092
$454$	−45.4478	−2.13297
$455$	−2.64283	−0.123898
$456$	50.1607	2.34899
$457$	11.7054	0.547553	0.273777	−	0.961793i	$-0.411727\pi$
$457$	11.7054	0.547553	0.273777	+	0.961793i	$0.411727\pi$
$458$	−2.41178	−0.112695
$459$	1.99349	0.0930480
$460$	−35.4214	−1.65153
$461$	−36.3241	−1.69178	−0.845891	−	0.533357i	$-0.820930\pi$
$461$	−36.3241	−1.69178	−0.845891	+	0.533357i	$0.820930\pi$
$462$	13.8829	0.645893
$463$	−16.0214	−0.744579	−0.372290	−	0.928117i	$-0.621427\pi$
$463$	−16.0214	−0.744579	−0.372290	+	0.928117i	$0.621427\pi$
$464$	−20.5540	−0.954197
$465$	−11.1872	−0.518792
$466$	13.6885	0.634107
$467$	0.762615	0.0352896	0.0176448	−	0.999844i	$-0.494383\pi$
$467$	0.762615	0.0352896	0.0176448	+	0.999844i	$0.494383\pi$
$468$	11.3949	0.526730
$469$	−3.12930	−0.144498
$470$	2.29376	0.105803
$471$	13.4383	0.619206
$472$	−3.26596	−0.150328
$473$	26.1587	1.20278
$474$	−29.0869	−1.33601
$475$	8.37133	0.384103
$476$	1.34717	0.0617475
$477$	6.19243	0.283532
$478$	36.3358	1.66196
$479$	19.4673	0.889483	0.444741	−	0.895659i	$-0.353296\pi$
$479$	19.4673	0.889483	0.444741	+	0.895659i	$0.353296\pi$
$480$	−2.30795	−0.105343
$481$	17.4917	0.797552
$482$	−49.5784	−2.25823
$483$	12.6923	0.577518
$484$	25.6342	1.16519
$485$	5.40558	0.245455
$486$	26.5658	1.20505
$487$	3.74896	0.169882	0.0849408	−	0.996386i	$-0.472930\pi$
$487$	3.74896	0.169882	0.0849408	+	0.996386i	$0.472930\pi$
$488$	46.2190	2.09224
$489$	6.74795	0.305153
$490$	−2.41178	−0.108953
$491$	−25.1726	−1.13602	−0.568012	−	0.823020i	$-0.692287\pi$
$491$	−25.1726	−1.13602	−0.568012	+	0.823020i	$0.692287\pi$
$492$	−31.1448	−1.40412
$493$	−2.47307	−0.111381
$494$	53.3581	2.40069
$495$	−4.75495	−0.213719
$496$	23.9973	1.07751
$497$	4.96517	0.222718
$498$	49.0960	2.20004
$499$	21.2038	0.949210	0.474605	−	0.880199i	$-0.342591\pi$
$499$	21.2038	0.949210	0.474605	+	0.880199i	$0.342591\pi$
$500$	3.81666	0.170686
$501$	17.1951	0.768220
$502$	−19.5750	−0.873675
$503$	23.6688	1.05534	0.527670	−	0.849449i	$-0.323066\pi$
$503$	23.6688	1.05534	0.527670	+	0.849449i	$0.323066\pi$
$504$	4.94960	0.220473
$505$	1.78050	0.0792312
$506$	94.2121	4.18824
$507$	8.22670	0.365361
$508$	59.0605	2.62038
$509$	−1.30122	−0.0576757	−0.0288379	−	0.999584i	$-0.509181\pi$
$509$	−1.30122	−0.0576757	−0.0288379	+	0.999584i	$0.509181\pi$
$510$	1.16421	0.0515523
$511$	8.13801	0.360004
$512$	30.6572	1.35487
$513$	47.2791	2.08742
$514$	55.6904	2.45640
$515$	3.72867	0.164305
$516$	−32.4391	−1.42805
$517$	−4.00312	−0.176057
$518$	15.9624	0.701350
$519$	−9.74409	−0.427718
$520$	11.5793	0.507784
$521$	−13.7815	−0.603780	−0.301890	−	0.953343i	$-0.597617\pi$
$521$	−13.7815	−0.603780	−0.301890	+	0.953343i	$0.597617\pi$
$522$	−19.0894	−0.835520
$523$	−14.2119	−0.621443	−0.310721	−	0.950501i	$-0.600571\pi$
$523$	−14.2119	−0.621443	−0.310721	+	0.950501i	$0.600571\pi$
$524$	68.8304	3.00687
$525$	−1.36759	−0.0596867
$526$	21.4710	0.936179
$527$	2.88736	0.125776
$528$	−16.8867	−0.734900
$529$	63.1320	2.74487
$530$	13.2203	0.574251
$531$	−0.842088	−0.0365435
$532$	31.9506	1.38523
$533$	−15.7694	−0.683047
$534$	−13.5350	−0.585719
$535$	3.10719	0.134336
$536$	13.7107	0.592212
$537$	3.02116	0.130373
$538$	14.7868	0.637506
$539$	4.20908	0.181298
$540$	21.5555	0.927601
$541$	−14.3369	−0.616393	−0.308197	−	0.951323i	$-0.599725\pi$
$541$	−14.3369	−0.616393	−0.308197	+	0.951323i	$0.599725\pi$
$542$	−48.3517	−2.07688
$543$	−13.2766	−0.569755
$544$	0.595672	0.0255392
$545$	1.09206	0.0467789
$546$	−8.71692	−0.373050
$547$	38.1896	1.63287	0.816435	−	0.577437i	$-0.195947\pi$
$547$	38.1896	1.63287	0.816435	+	0.577437i	$0.195947\pi$
$548$	−20.6413	−0.881754
$549$	11.9170	0.508606
$550$	−10.1514	−0.432856
$551$	−58.6531	−2.49871
$552$	−55.6097	−2.36691
$553$	−8.81869	−0.375009
$554$	−15.4670	−0.657130
$555$	9.05148	0.384214
$556$	−23.2578	−0.986352
$557$	33.7148	1.42854	0.714270	−	0.699870i	$-0.246759\pi$
$557$	33.7148	1.42854	0.714270	+	0.699870i	$0.246759\pi$
$558$	22.2873	0.943497
$559$	−16.4247	−0.694690
$560$	2.93360	0.123967
$561$	−2.03181	−0.0857832
$562$	77.6292	3.27459
$563$	−5.18249	−0.218416	−0.109208	−	0.994019i	$-0.534831\pi$
$563$	−5.18249	−0.218416	−0.109208	+	0.994019i	$0.534831\pi$
$564$	4.96424	0.209032
$565$	−5.88850	−0.247731
$566$	−51.2509	−2.15423
$567$	−4.33474	−0.182042
$568$	−21.7543	−0.912792
$569$	36.3838	1.52529	0.762644	−	0.646818i	$-0.223901\pi$
$569$	36.3838	1.52529	0.762644	+	0.646818i	$0.223901\pi$
$570$	27.6114	1.15651
$571$	10.1915	0.426502	0.213251	−	0.976997i	$-0.431595\pi$
$571$	10.1915	0.426502	0.213251	+	0.976997i	$0.431595\pi$
$572$	−42.4561	−1.77518
$573$	−1.12187	−0.0468670
$574$	−14.3907	−0.600656
$575$	−9.28073	−0.387033
$576$	11.2260	0.467752
$577$	36.2049	1.50723	0.753615	−	0.657317i	$-0.228309\pi$
$577$	36.2049	1.50723	0.753615	+	0.657317i	$0.228309\pi$
$578$	40.6997	1.69288
$579$	−3.96221	−0.164664
$580$	−26.7412	−1.11037
$581$	14.8851	0.617538
$582$	17.8294	0.739052
$583$	−23.0723	−0.955557
$584$	−35.6558	−1.47545
$585$	2.98557	0.123438
$586$	−24.2874	−1.00330
$587$	−12.8482	−0.530301	−0.265150	−	0.964207i	$-0.585422\pi$
$587$	−12.8482	−0.530301	−0.265150	+	0.964207i	$0.585422\pi$
$588$	−5.21965	−0.215255
$589$	68.4789	2.82163
$590$	−1.79778	−0.0740133
$591$	4.58603	0.188644
$592$	−19.4161	−0.797998
$593$	28.6577	1.17683	0.588415	−	0.808559i	$-0.299752\pi$
$593$	28.6577	1.17683	0.588415	+	0.808559i	$0.299752\pi$
$594$	−57.3322	−2.35237
$595$	0.352971	0.0144704
$596$	1.93612	0.0793066
$597$	−32.7401	−1.33996
$598$	−59.1545	−2.41901
$599$	−21.2370	−0.867719	−0.433860	−	0.900980i	$-0.642849\pi$
$599$	−21.2370	−0.867719	−0.433860	+	0.900980i	$0.642849\pi$
$600$	5.99196	0.244621
$601$	36.1350	1.47398	0.736988	−	0.675906i	$-0.236247\pi$
$601$	36.1350	1.47398	0.736988	+	0.675906i	$0.236247\pi$
$602$	−14.9887	−0.610895
$603$	3.53514	0.143962
$604$	79.0549	3.21670
$605$	6.71639	0.273060
$606$	5.87267	0.238561
$607$	18.7532	0.761169	0.380584	−	0.924746i	$-0.375723\pi$
$607$	18.7532	0.761169	0.380584	+	0.924746i	$0.375723\pi$
$608$	14.1274	0.572943
$609$	9.58195	0.388280
$610$	25.4417	1.03010
$611$	2.51351	0.101686
$612$	−1.52188	−0.0615185
$613$	−26.5040	−1.07049	−0.535243	−	0.844698i	$-0.679780\pi$
$613$	−26.5040	−1.07049	−0.535243	+	0.844698i	$0.679780\pi$
$614$	55.7683	2.25063
$615$	−8.16022	−0.329052
$616$	−18.4416	−0.743034
$617$	21.2112	0.853929	0.426965	−	0.904268i	$-0.359583\pi$
$617$	21.2112	0.853929	0.426965	+	0.904268i	$0.359583\pi$
$618$	12.2984	0.494714
$619$	11.1647	0.448745	0.224373	−	0.974503i	$-0.427967\pi$
$619$	11.1647	0.448745	0.224373	+	0.974503i	$0.427967\pi$
$620$	31.2210	1.25386
$621$	−52.4151	−2.10335
$622$	49.6468	1.99065
$623$	−4.10361	−0.164408
$624$	10.6029	0.424457
$625$	1.00000	0.0400000
$626$	57.6641	2.30472
$627$	−48.1880	−1.92444
$628$	−37.5035	−1.49655
$629$	−2.33615	−0.0931486
$630$	2.72455	0.108549
$631$	1.71962	0.0684572	0.0342286	−	0.999414i	$-0.489103\pi$
$631$	1.71962	0.0684572	0.0342286	+	0.999414i	$0.489103\pi$
$632$	38.6381	1.53694
$633$	−4.53607	−0.180293
$634$	−47.2262	−1.87559
$635$	15.4744	0.614082
$636$	28.6117	1.13453
$637$	−2.64283	−0.104713
$638$	71.1249	2.81586
$639$	−5.60909	−0.221892
$640$	20.5913	0.813944
$641$	6.02776	0.238082	0.119041	−	0.992889i	$-0.462018\pi$
$641$	6.02776	0.238082	0.119041	+	0.992889i	$0.462018\pi$
$642$	10.2485	0.404478
$643$	8.03143	0.316729	0.158364	−	0.987381i	$-0.449378\pi$
$643$	8.03143	0.316729	0.158364	+	0.987381i	$0.449378\pi$
$644$	−35.4214	−1.39580
$645$	−8.49934	−0.334661
$646$	−7.12641	−0.280385
$647$	−5.97905	−0.235061	−0.117530	−	0.993069i	$-0.537498\pi$
$647$	−5.97905	−0.235061	−0.117530	+	0.993069i	$0.537498\pi$
$648$	18.9922	0.746084
$649$	3.13752	0.123158
$650$	6.37391	0.250005
$651$	−11.1872	−0.438459
$652$	−18.8321	−0.737522
$653$	−4.97838	−0.194819	−0.0974095	−	0.995244i	$-0.531056\pi$
$653$	−4.97838	−0.194819	−0.0974095	+	0.995244i	$0.531056\pi$
$654$	3.60199	0.140849
$655$	18.0342	0.704654
$656$	17.5043	0.683429
$657$	−9.19341	−0.358669
$658$	2.29376	0.0894202
$659$	30.0012	1.16868	0.584341	−	0.811508i	$-0.301353\pi$
$659$	30.0012	1.16868	0.584341	+	0.811508i	$0.301353\pi$
$660$	−21.9699	−0.855178
$661$	13.9367	0.542075	0.271038	−	0.962569i	$-0.412633\pi$
$661$	13.9367	0.542075	0.271038	+	0.962569i	$0.412633\pi$
$662$	−75.4168	−2.93116
$663$	1.27575	0.0495460
$664$	−65.2174	−2.53093
$665$	8.37133	0.324626
$666$	−18.0326	−0.698748
$667$	65.0248	2.51777
$668$	−47.9879	−1.85671
$669$	−33.2946	−1.28725
$670$	7.54718	0.291573
$671$	−44.4014	−1.71410
$672$	−2.30795	−0.0890309
$673$	13.9550	0.537927	0.268963	−	0.963150i	$-0.413319\pi$
$673$	13.9550	0.537927	0.268963	+	0.963150i	$0.413319\pi$
$674$	18.8263	0.725163
$675$	5.64773	0.217381
$676$	−22.9590	−0.883038
$677$	7.08222	0.272192	0.136096	−	0.990696i	$-0.456544\pi$
$677$	7.08222	0.272192	0.136096	+	0.990696i	$0.456544\pi$
$678$	−19.4222	−0.745906
$679$	5.40558	0.207447
$680$	−1.54650	−0.0593057
$681$	−25.7711	−0.987551
$682$	−83.0399	−3.17976
$683$	−15.8581	−0.606794	−0.303397	−	0.952864i	$-0.598121\pi$
$683$	−15.8581	−0.606794	−0.303397	+	0.952864i	$0.598121\pi$
$684$	−36.0942	−1.38009
$685$	−5.40821	−0.206637
$686$	−2.41178	−0.0920820
$687$	−1.36759	−0.0521770
$688$	18.2318	0.695079
$689$	14.4868	0.551902
$690$	−30.6109	−1.16534
$691$	6.40605	0.243698	0.121849	−	0.992549i	$-0.461118\pi$
$691$	6.40605	0.243698	0.121849	+	0.992549i	$0.461118\pi$
$692$	27.1937	1.03375
$693$	−4.75495	−0.180626
$694$	20.4632	0.776773
$695$	−6.09376	−0.231149
$696$	−41.9822	−1.59133
$697$	2.10612	0.0797752
$698$	25.2600	0.956104
$699$	7.76203	0.293587
$700$	3.81666	0.144256
$701$	7.23532	0.273274	0.136637	−	0.990621i	$-0.456371\pi$
$701$	7.23532	0.273274	0.136637	+	0.990621i	$0.456371\pi$
$702$	35.9981	1.35866
$703$	−55.4060	−2.08968
$704$	−41.8269	−1.57641
$705$	1.30067	0.0489862
$706$	80.2296	3.01948
$707$	1.78050	0.0669626
$708$	−3.89081	−0.146226
$709$	26.3858	0.990939	0.495470	−	0.868625i	$-0.334996\pi$
$709$	26.3858	0.990939	0.495470	+	0.868625i	$0.334996\pi$
$710$	−11.9749	−0.449409
$711$	9.96236	0.373618
$712$	17.9795	0.673810
$713$	−75.9180	−2.84315
$714$	1.16421	0.0435696
$715$	−11.1239	−0.416010
$716$	−8.43141	−0.315097
$717$	20.6041	0.769476
$718$	−15.0941	−0.563306
$719$	−30.5289	−1.13854	−0.569268	−	0.822152i	$-0.692773\pi$
$719$	−30.5289	−1.13854	−0.569268	+	0.822152i	$0.692773\pi$
$720$	−3.31405	−0.123507
$721$	3.72867	0.138863
$722$	−123.192	−4.58472
$723$	−28.1133	−1.04555
$724$	37.0523	1.37704
$725$	−7.00643	−0.260212
$726$	22.1529	0.822170
$727$	−9.62185	−0.356855	−0.178427	−	0.983953i	$-0.557101\pi$
$727$	−9.62185	−0.356855	−0.178427	+	0.983953i	$0.557101\pi$
$728$	11.5793	0.429156
$729$	28.0683	1.03957
$730$	−19.6271	−0.726430
$731$	2.19365	0.0811350
$732$	55.0618	2.03514
$733$	25.8785	0.955844	0.477922	−	0.878402i	$-0.341390\pi$
$733$	25.8785	0.955844	0.477922	+	0.878402i	$0.341390\pi$
$734$	75.8376	2.79922
$735$	−1.36759	−0.0504445
$736$	−15.6621	−0.577314
$737$	−13.1715	−0.485179
$738$	16.2570	0.598428
$739$	24.1101	0.886904	0.443452	−	0.896298i	$-0.353754\pi$
$739$	24.1101	0.886904	0.443452	+	0.896298i	$0.353754\pi$
$740$	−25.2608	−0.928604
$741$	30.2566	1.11151
$742$	13.2203	0.485331
$743$	30.6196	1.12332	0.561662	−	0.827367i	$-0.310162\pi$
$743$	30.6196	1.12332	0.561662	+	0.827367i	$0.310162\pi$
$744$	49.0152	1.79699
$745$	0.507281	0.0185853
$746$	47.8190	1.75078
$747$	−16.8155	−0.615248
$748$	5.67036	0.207329
$749$	3.10719	0.113534
$750$	3.29833	0.120438
$751$	−4.18944	−0.152875	−0.0764375	−	0.997074i	$-0.524355\pi$
$751$	−4.18944	−0.152875	−0.0764375	+	0.997074i	$0.524355\pi$
$752$	−2.79005	−0.101743
$753$	−11.1000	−0.404505
$754$	−44.6584	−1.62636
$755$	20.7131	0.753826
$756$	21.5555	0.783966
$757$	54.1344	1.96755	0.983774	−	0.179409i	$-0.0574187\pi$
$757$	54.1344	1.96755	0.983774	+	0.179409i	$0.0574187\pi$
$758$	42.0834	1.52854
$759$	53.4228	1.93913
$760$	−36.6780	−1.33045
$761$	13.8535	0.502191	0.251095	−	0.967962i	$-0.419209\pi$
$761$	13.8535	0.502191	0.251095	+	0.967962i	$0.419209\pi$
$762$	51.0396	1.84897
$763$	1.09206	0.0395354
$764$	3.13091	0.113272
$765$	−0.398747	−0.0144167
$766$	24.4983	0.885160
$767$	−1.97001	−0.0711328
$768$	40.7367	1.46996
$769$	−39.7851	−1.43469	−0.717344	−	0.696719i	$-0.754642\pi$
$769$	−39.7851	−1.43469	−0.717344	+	0.696719i	$0.754642\pi$
$770$	−10.1514	−0.365830
$771$	31.5791	1.13729
$772$	11.0577	0.397975
$773$	19.8179	0.712800	0.356400	−	0.934333i	$-0.384004\pi$
$773$	19.8179	0.712800	0.356400	+	0.934333i	$0.384004\pi$
$774$	16.9326	0.608629
$775$	8.18017	0.293840
$776$	−23.6839	−0.850204
$777$	9.05148	0.324720
$778$	36.3561	1.30343
$779$	49.9505	1.78966
$780$	13.7946	0.493927
$781$	20.8988	0.747819
$782$	7.90057	0.282524
$783$	−39.5705	−1.41413
$784$	2.93360	0.104771
$785$	−9.82626	−0.350714
$786$	59.4827	2.12168
$787$	33.3874	1.19013	0.595066	−	0.803677i	$-0.297126\pi$
$787$	33.3874	1.19013	0.595066	+	0.803677i	$0.297126\pi$
$788$	−12.7986	−0.455932
$789$	12.1751	0.433444
$790$	21.2687	0.756706
$791$	−5.88850	−0.209371
$792$	20.8333	0.740278
$793$	27.8791	0.990014
$794$	−43.4245	−1.54108
$795$	7.49653	0.265874
$796$	91.3707	3.23855
$797$	53.8468	1.90735	0.953676	−	0.300836i	$-0.0972658\pi$
$797$	53.8468	1.90735	0.953676	+	0.300836i	$0.0972658\pi$
$798$	27.6114	0.977433
$799$	−0.335699	−0.0118762
$800$	1.68760	0.0596655
$801$	4.63579	0.163798
$802$	−58.2524	−2.05696
$803$	34.2536	1.20878
$804$	16.3339	0.576051
$805$	−9.28073	−0.327103
$806$	52.1397	1.83654
$807$	8.38485	0.295161
$808$	−7.80106	−0.274440
$809$	−13.3322	−0.468734	−0.234367	−	0.972148i	$-0.575302\pi$
$809$	−13.3322	−0.468734	−0.234367	+	0.972148i	$0.575302\pi$
$810$	10.4544	0.367331
$811$	−34.8746	−1.22461	−0.612306	−	0.790621i	$-0.709758\pi$
$811$	−34.8746	−1.22461	−0.612306	+	0.790621i	$0.709758\pi$
$812$	−26.7412	−0.938432
$813$	−27.4178	−0.961583
$814$	67.1873	2.35491
$815$	−4.93418	−0.172837
$816$	−1.41611	−0.0495737
$817$	52.0263	1.82017
$818$	48.4665	1.69459
$819$	2.98557	0.104324
$820$	22.7735	0.795284
$821$	−35.5805	−1.24177	−0.620884	−	0.783902i	$-0.713226\pi$
$821$	−35.5805	−1.24177	−0.620884	+	0.783902i	$0.713226\pi$
$822$	−17.8381	−0.622174
$823$	37.6647	1.31291	0.656455	−	0.754365i	$-0.272055\pi$
$823$	37.6647	1.31291	0.656455	+	0.754365i	$0.272055\pi$
$824$	−16.3368	−0.569118
$825$	−5.75632	−0.200409
$826$	−1.79778	−0.0625527
$827$	−22.9645	−0.798555	−0.399278	−	0.916830i	$-0.630739\pi$
$827$	−22.9645	−0.798555	−0.399278	+	0.916830i	$0.630739\pi$
$828$	40.0152	1.39062
$829$	7.28545	0.253034	0.126517	−	0.991964i	$-0.459620\pi$
$829$	7.28545	0.253034	0.126517	+	0.991964i	$0.459620\pi$
$830$	−35.8996	−1.24609
$831$	−8.77054	−0.304247
$832$	26.2626	0.910491
$833$	0.352971	0.0122297
$834$	−20.0992	−0.695979
$835$	−12.5732	−0.435115
$836$	134.483	4.65118
$837$	46.1994	1.59689
$838$	−51.2359	−1.76991
$839$	−51.9054	−1.79197	−0.895987	−	0.444080i	$-0.853531\pi$
$839$	−51.9054	−1.79197	−0.895987	+	0.444080i	$0.853531\pi$
$840$	5.99196	0.206742
$841$	20.0901	0.692761
$842$	80.5858	2.77717
$843$	44.0195	1.51611
$844$	12.6592	0.435748
$845$	−6.01546	−0.206938
$846$	−2.59123	−0.0890885
$847$	6.71639	0.230778
$848$	−16.0806	−0.552212
$849$	−29.0617	−0.997395
$850$	−0.851287	−0.0291989
$851$	61.4249	2.10562
$852$	−25.9164	−0.887883
$853$	17.9982	0.616246	0.308123	−	0.951347i	$-0.400299\pi$
$853$	17.9982	0.616246	0.308123	+	0.951347i	$0.400299\pi$
$854$	25.4417	0.870597
$855$	−9.45699	−0.323422
$856$	−13.6138	−0.465311
$857$	50.0483	1.70962	0.854809	−	0.518943i	$-0.173674\pi$
$857$	50.0483	1.70962	0.854809	+	0.518943i	$0.173674\pi$
$858$	−36.6902	−1.25258
$859$	−14.0744	−0.480213	−0.240106	−	0.970747i	$-0.577182\pi$
$859$	−14.0744	−0.480213	−0.240106	+	0.970747i	$0.577182\pi$
$860$	23.7199	0.808840
$861$	−8.16022	−0.278100
$862$	−62.9663	−2.14464
$863$	−45.6696	−1.55461	−0.777306	−	0.629122i	$-0.783414\pi$
$863$	−45.6696	−1.55461	−0.777306	+	0.629122i	$0.783414\pi$
$864$	9.53109	0.324254
$865$	7.12499	0.242257
$866$	29.0217	0.986198
$867$	23.0787	0.783794
$868$	31.2210	1.05971
$869$	−37.1186	−1.25916
$870$	−23.1095	−0.783486
$871$	8.27021	0.280225
$872$	−4.78476	−0.162032
$873$	−6.10662	−0.206678
$874$	187.376	6.33808
$875$	1.00000	0.0338062
$876$	−42.4775	−1.43518
$877$	−1.46952	−0.0496221	−0.0248111	−	0.999692i	$-0.507898\pi$
$877$	−1.46952	−0.0496221	−0.0248111	+	0.999692i	$0.507898\pi$
$878$	−85.7021	−2.89230
$879$	−13.7721	−0.464522
$880$	12.3478	0.416243
$881$	−27.7393	−0.934562	−0.467281	−	0.884109i	$-0.654766\pi$
$881$	−27.7393	−0.934562	−0.467281	+	0.884109i	$0.654766\pi$
$882$	2.72455	0.0917405
$883$	−6.98230	−0.234973	−0.117487	−	0.993074i	$-0.537484\pi$
$883$	−6.98230	−0.234973	−0.117487	+	0.993074i	$0.537484\pi$
$884$	−3.56034	−0.119747
$885$	−1.01943	−0.0342676
$886$	12.9288	0.434353
$887$	45.6879	1.53405	0.767024	−	0.641618i	$-0.221736\pi$
$887$	45.6879	1.53405	0.767024	+	0.641618i	$0.221736\pi$
$888$	−39.6580	−1.33084
$889$	15.4744	0.518994
$890$	9.89698	0.331748
$891$	−18.2453	−0.611241
$892$	92.9183	3.11113
$893$	−7.96170	−0.266428
$894$	1.67318	0.0559595
$895$	−2.20910	−0.0738422
$896$	20.5913	0.687908
$897$	−33.5435	−1.11998
$898$	0.757688	0.0252844
$899$	−57.3138	−1.91152
$900$	−4.31164	−0.143721
$901$	−1.93483	−0.0644584
$902$	−60.5717	−2.01682
$903$	−8.49934	−0.282840
$904$	25.7998	0.858089
$905$	9.70802	0.322706
$906$	68.3186	2.26973
$907$	39.0086	1.29526	0.647629	−	0.761956i	$-0.275761\pi$
$907$	39.0086	1.29526	0.647629	+	0.761956i	$0.275761\pi$
$908$	71.9217	2.38681
$909$	−2.01141	−0.0667142
$910$	6.37391	0.211293
$911$	−39.8179	−1.31923	−0.659613	−	0.751606i	$-0.729280\pi$
$911$	−39.8179	−1.31923	−0.659613	+	0.751606i	$0.729280\pi$
$912$	−33.5855	−1.11213
$913$	62.6527	2.07350
$914$	−28.2307	−0.933788
$915$	14.4267	0.476931
$916$	3.81666	0.126106
$917$	18.0342	0.595541
$918$	−4.80784	−0.158682
$919$	50.9072	1.67927	0.839636	−	0.543149i	$-0.182768\pi$
$919$	50.9072	1.67927	0.839636	+	0.543149i	$0.182768\pi$
$920$	40.6625	1.34060
$921$	31.6233	1.04202
$922$	87.6055	2.88513
$923$	−13.1221	−0.431919
$924$	−21.9699	−0.722758
$925$	−6.61854	−0.217616
$926$	38.6401	1.26979
$927$	−4.21224	−0.138348
$928$	−11.8240	−0.388143
$929$	−34.3170	−1.12590	−0.562952	−	0.826490i	$-0.690334\pi$
$929$	−34.3170	−1.12590	−0.562952	+	0.826490i	$0.690334\pi$
$930$	26.9809	0.884739
$931$	8.37133	0.274359
$932$	−21.6622	−0.709568
$933$	28.1521	0.921659
$934$	−1.83926	−0.0601823
$935$	1.48568	0.0485871
$936$	−13.0809	−0.427564
$937$	9.90551	0.323599	0.161799	−	0.986824i	$-0.448270\pi$
$937$	9.90551	0.323599	0.161799	+	0.986824i	$0.448270\pi$
$938$	7.54718	0.246424
$939$	32.6983	1.06707
$940$	−3.62991	−0.118394
$941$	21.8969	0.713819	0.356909	−	0.934139i	$-0.383830\pi$
$941$	21.8969	0.713819	0.356909	+	0.934139i	$0.383830\pi$
$942$	−32.4102	−1.05598
$943$	−55.3767	−1.80331
$944$	2.18675	0.0711727
$945$	5.64773	0.183721
$946$	−63.0889	−2.05120
$947$	−15.9912	−0.519643	−0.259822	−	0.965657i	$-0.583664\pi$
$947$	−15.9912	−0.519643	−0.259822	+	0.965657i	$0.583664\pi$
$948$	46.0304	1.49500
$949$	−21.5074	−0.698158
$950$	−20.1898	−0.655043
$951$	−26.7795	−0.868386
$952$	−1.54650	−0.0501224
$953$	−31.6901	−1.02654	−0.513272	−	0.858226i	$-0.671567\pi$
$953$	−31.6901	−1.02654	−0.513272	+	0.858226i	$0.671567\pi$
$954$	−14.9348	−0.483531
$955$	0.820327	0.0265452
$956$	−57.5018	−1.85974
$957$	40.3312	1.30372
$958$	−46.9507	−1.51691
$959$	−5.40821	−0.174640
$960$	13.5902	0.438621
$961$	35.9152	1.15856
$962$	−42.1860	−1.36013
$963$	−3.51016	−0.113113
$964$	78.4583	2.52697
$965$	2.89721	0.0932646
$966$	−30.6109	−0.984890
$967$	50.8230	1.63436	0.817179	−	0.576383i	$-0.195537\pi$
$967$	50.8230	1.63436	0.817179	+	0.576383i	$0.195537\pi$
$968$	−29.4271	−0.945823
$969$	−4.04102	−0.129816
$970$	−13.0371	−0.418595
$971$	−59.7130	−1.91628	−0.958140	−	0.286300i	$-0.907575\pi$
$971$	−59.7130	−1.91628	−0.958140	+	0.286300i	$0.907575\pi$
$972$	−42.0407	−1.34846
$973$	−6.09376	−0.195357
$974$	−9.04165	−0.289713
$975$	3.61431	0.115751
$976$	−30.9464	−0.990569
$977$	31.9923	1.02352	0.511762	−	0.859127i	$-0.328993\pi$
$977$	31.9923	1.02352	0.511762	+	0.859127i	$0.328993\pi$
$978$	−16.2745	−0.520402
$979$	−17.2724	−0.552029
$980$	3.81666	0.121919
$981$	−1.23369	−0.0393887
$982$	60.7107	1.93736
$983$	8.10713	0.258577	0.129289	−	0.991607i	$-0.458731\pi$
$983$	8.10713	0.258577	0.129289	+	0.991607i	$0.458731\pi$
$984$	35.7531	1.13977
$985$	−3.35335	−0.106847
$986$	5.96448	0.189948
$987$	1.30067	0.0414009
$988$	−84.4398	−2.68639
$989$	−57.6780	−1.83405
$990$	11.4679	0.364473
$991$	54.8728	1.74309	0.871546	−	0.490314i	$-0.163118\pi$
$991$	54.8728	1.74309	0.871546	+	0.490314i	$0.163118\pi$
$992$	13.8048	0.438304
$993$	−42.7650	−1.35711
$994$	−11.9749	−0.379820
$995$	23.9399	0.758947
$996$	−77.6950	−2.46186
$997$	−23.4468	−0.742568	−0.371284	−	0.928519i	$-0.621082\pi$
$997$	−23.4468	−0.742568	−0.371284	+	0.928519i	$0.621082\pi$
$998$	−51.1387	−1.61877
$999$	−37.3798	−1.18264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.o.1.9	✓	73

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.o.1.9	✓	73	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)

\(f(q)\)	\(=\)	\(q-2.41178 q^{2} -1.36759 q^{3} +3.81666 q^{4} +1.00000 q^{5} +3.29833 q^{6} +1.00000 q^{7} -4.38139 q^{8} -1.12969 q^{9} +O(q^{10})\)	\(q-2.41178 q^{2} -1.36759 q^{3} +3.81666 q^{4} +1.00000 q^{5} +3.29833 q^{6} +1.00000 q^{7} -4.38139 q^{8} -1.12969 q^{9} -2.41178 q^{10} +4.20908 q^{11} -5.21965 q^{12} -2.64283 q^{13} -2.41178 q^{14} -1.36759 q^{15} +2.93360 q^{16} +0.352971 q^{17} +2.72455 q^{18} +8.37133 q^{19} +3.81666 q^{20} -1.36759 q^{21} -10.1514 q^{22} -9.28073 q^{23} +5.99196 q^{24} +1.00000 q^{25} +6.37391 q^{26} +5.64773 q^{27} +3.81666 q^{28} -7.00643 q^{29} +3.29833 q^{30} +8.18017 q^{31} +1.68760 q^{32} -5.75632 q^{33} -0.851287 q^{34} +1.00000 q^{35} -4.31164 q^{36} -6.61854 q^{37} -20.1898 q^{38} +3.61431 q^{39} -4.38139 q^{40} +5.96685 q^{41} +3.29833 q^{42} +6.21481 q^{43} +16.0647 q^{44} -1.12969 q^{45} +22.3830 q^{46} -0.951068 q^{47} -4.01197 q^{48} +1.00000 q^{49} -2.41178 q^{50} -0.482721 q^{51} -10.0868 q^{52} -5.48155 q^{53} -13.6211 q^{54} +4.20908 q^{55} -4.38139 q^{56} -11.4486 q^{57} +16.8979 q^{58} +0.745416 q^{59} -5.21965 q^{60} -10.5489 q^{61} -19.7287 q^{62} -1.12969 q^{63} -9.93730 q^{64} -2.64283 q^{65} +13.8829 q^{66} -3.12930 q^{67} +1.34717 q^{68} +12.6923 q^{69} -2.41178 q^{70} +4.96517 q^{71} +4.94960 q^{72} +8.13801 q^{73} +15.9624 q^{74} -1.36759 q^{75} +31.9506 q^{76} +4.20908 q^{77} -8.71692 q^{78} -8.81869 q^{79} +2.93360 q^{80} -4.33474 q^{81} -14.3907 q^{82} +14.8851 q^{83} -5.21965 q^{84} +0.352971 q^{85} -14.9887 q^{86} +9.58195 q^{87} -18.4416 q^{88} -4.10361 q^{89} +2.72455 q^{90} -2.64283 q^{91} -35.4214 q^{92} -11.1872 q^{93} +2.29376 q^{94} +8.37133 q^{95} -2.30795 q^{96} +5.40558 q^{97} -2.41178 q^{98} -4.75495 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * q^99

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