LMFDB - Embedded newform 8030.2.a.bb.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 8x^{6} + 20x^{5} + 23x^{4} - 32x^{3} - 16x^{2} + 17x - 1 $ x^8 - 3x^7 - 8x^6 + 20x^5 + 23x^4 - 32x^3 - 16x^2 + 17*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.20960$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.20960 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.20960 q^{6} +1.90541 q^{7} +1.00000 q^{8} -1.53686 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.20960 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.20960 q^{6} +1.90541 q^{7} +1.00000 q^{8} -1.53686 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.20960 q^{12} -1.84519 q^{13} +1.90541 q^{14} -1.20960 q^{15} +1.00000 q^{16} -2.97329 q^{17} -1.53686 q^{18} +1.05378 q^{19} -1.00000 q^{20} +2.30479 q^{21} +1.00000 q^{22} -8.58943 q^{23} +1.20960 q^{24} +1.00000 q^{25} -1.84519 q^{26} -5.48780 q^{27} +1.90541 q^{28} +0.691099 q^{29} -1.20960 q^{30} -4.94099 q^{31} +1.00000 q^{32} +1.20960 q^{33} -2.97329 q^{34} -1.90541 q^{35} -1.53686 q^{36} -0.936110 q^{37} +1.05378 q^{38} -2.23195 q^{39} -1.00000 q^{40} +5.94412 q^{41} +2.30479 q^{42} -4.04286 q^{43} +1.00000 q^{44} +1.53686 q^{45} -8.58943 q^{46} -13.5091 q^{47} +1.20960 q^{48} -3.36942 q^{49} +1.00000 q^{50} -3.59651 q^{51} -1.84519 q^{52} -0.0765417 q^{53} -5.48780 q^{54} -1.00000 q^{55} +1.90541 q^{56} +1.27466 q^{57} +0.691099 q^{58} -2.25596 q^{59} -1.20960 q^{60} -7.53820 q^{61} -4.94099 q^{62} -2.92834 q^{63} +1.00000 q^{64} +1.84519 q^{65} +1.20960 q^{66} +11.8148 q^{67} -2.97329 q^{68} -10.3898 q^{69} -1.90541 q^{70} +0.0205518 q^{71} -1.53686 q^{72} -1.00000 q^{73} -0.936110 q^{74} +1.20960 q^{75} +1.05378 q^{76} +1.90541 q^{77} -2.23195 q^{78} -16.7087 q^{79} -1.00000 q^{80} -2.02749 q^{81} +5.94412 q^{82} +11.9430 q^{83} +2.30479 q^{84} +2.97329 q^{85} -4.04286 q^{86} +0.835957 q^{87} +1.00000 q^{88} +7.65038 q^{89} +1.53686 q^{90} -3.51583 q^{91} -8.58943 q^{92} -5.97664 q^{93} -13.5091 q^{94} -1.05378 q^{95} +1.20960 q^{96} +17.1407 q^{97} -3.36942 q^{98} -1.53686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 3 q^{3} + 8 q^{4} - 8 q^{5} - 3 q^{6} - 4 q^{7} + 8 q^{8} + q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 3 * q^3 + 8 * q^4 - 8 * q^5 - 3 * q^6 - 4 * q^7 + 8 * q^8 + q^9	\( 8 q + 8 q^{2} - 3 q^{3} + 8 q^{4} - 8 q^{5} - 3 q^{6} - 4 q^{7} + 8 q^{8} + q^{9} - 8 q^{10} + 8 q^{11} - 3 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 2 q^{17} + q^{18} - q^{19} - 8 q^{20} + 7 q^{21} + 8 q^{22} - 16 q^{23} - 3 q^{24} + 8 q^{25} - 7 q^{26} - 21 q^{27} - 4 q^{28} - 5 q^{29} + 3 q^{30} - 22 q^{31} + 8 q^{32} - 3 q^{33} + 2 q^{34} + 4 q^{35} + q^{36} - 9 q^{37} - q^{38} - 18 q^{39} - 8 q^{40} + 6 q^{41} + 7 q^{42} + 15 q^{43} + 8 q^{44} - q^{45} - 16 q^{46} - 7 q^{47} - 3 q^{48} - 6 q^{49} + 8 q^{50} + q^{51} - 7 q^{52} - 11 q^{53} - 21 q^{54} - 8 q^{55} - 4 q^{56} - 17 q^{57} - 5 q^{58} - 11 q^{59} + 3 q^{60} - 22 q^{61} - 22 q^{62} + q^{63} + 8 q^{64} + 7 q^{65} - 3 q^{66} + 21 q^{67} + 2 q^{68} + q^{69} + 4 q^{70} - 28 q^{71} + q^{72} - 8 q^{73} - 9 q^{74} - 3 q^{75} - q^{76} - 4 q^{77} - 18 q^{78} - 28 q^{79} - 8 q^{80} + 12 q^{81} + 6 q^{82} - 5 q^{83} + 7 q^{84} - 2 q^{85} + 15 q^{86} + 36 q^{87} + 8 q^{88} - 17 q^{89} - q^{90} - 29 q^{91} - 16 q^{92} + 42 q^{93} - 7 q^{94} + q^{95} - 3 q^{96} + q^{97} - 6 q^{98} + q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 3 * q^3 + 8 * q^4 - 8 * q^5 - 3 * q^6 - 4 * q^7 + 8 * q^8 + q^9 - 8 * q^10 + 8 * q^11 - 3 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 2 * q^17 + q^18 - q^19 - 8 * q^20 + 7 * q^21 + 8 * q^22 - 16 * q^23 - 3 * q^24 + 8 * q^25 - 7 * q^26 - 21 * q^27 - 4 * q^28 - 5 * q^29 + 3 * q^30 - 22 * q^31 + 8 * q^32 - 3 * q^33 + 2 * q^34 + 4 * q^35 + q^36 - 9 * q^37 - q^38 - 18 * q^39 - 8 * q^40 + 6 * q^41 + 7 * q^42 + 15 * q^43 + 8 * q^44 - q^45 - 16 * q^46 - 7 * q^47 - 3 * q^48 - 6 * q^49 + 8 * q^50 + q^51 - 7 * q^52 - 11 * q^53 - 21 * q^54 - 8 * q^55 - 4 * q^56 - 17 * q^57 - 5 * q^58 - 11 * q^59 + 3 * q^60 - 22 * q^61 - 22 * q^62 + q^63 + 8 * q^64 + 7 * q^65 - 3 * q^66 + 21 * q^67 + 2 * q^68 + q^69 + 4 * q^70 - 28 * q^71 + q^72 - 8 * q^73 - 9 * q^74 - 3 * q^75 - q^76 - 4 * q^77 - 18 * q^78 - 28 * q^79 - 8 * q^80 + 12 * q^81 + 6 * q^82 - 5 * q^83 + 7 * q^84 - 2 * q^85 + 15 * q^86 + 36 * q^87 + 8 * q^88 - 17 * q^89 - q^90 - 29 * q^91 - 16 * q^92 + 42 * q^93 - 7 * q^94 + q^95 - 3 * q^96 + q^97 - 6 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.20960	0.698365	0.349183	−	0.937055i	$-0.386459\pi$
$3$	1.20960	0.698365	0.349183	+	0.937055i	$0.386459\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.20960	0.493819
$7$	1.90541	0.720176	0.360088	−	0.932918i	$-0.382747\pi$
$7$	1.90541	0.720176	0.360088	+	0.932918i	$0.382747\pi$
$8$	1.00000	0.353553
$9$	−1.53686	−0.512286
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.20960	0.349183
$13$	−1.84519	−0.511763	−0.255881	−	0.966708i	$-0.582366\pi$
$13$	−1.84519	−0.511763	−0.255881	+	0.966708i	$0.582366\pi$
$14$	1.90541	0.509242
$15$	−1.20960	−0.312318
$16$	1.00000	0.250000
$17$	−2.97329	−0.721129	−0.360565	−	0.932734i	$-0.617416\pi$
$17$	−2.97329	−0.721129	−0.360565	+	0.932734i	$0.617416\pi$
$18$	−1.53686	−0.362241
$19$	1.05378	0.241754	0.120877	−	0.992668i	$-0.461429\pi$
$19$	1.05378	0.241754	0.120877	+	0.992668i	$0.461429\pi$
$20$	−1.00000	−0.223607
$21$	2.30479	0.502946
$22$	1.00000	0.213201
$23$	−8.58943	−1.79102	−0.895510	−	0.445041i	$-0.853189\pi$
$23$	−8.58943	−1.79102	−0.895510	+	0.445041i	$0.853189\pi$
$24$	1.20960	0.246909
$25$	1.00000	0.200000
$26$	−1.84519	−0.361871
$27$	−5.48780	−1.05613
$28$	1.90541	0.360088
$29$	0.691099	0.128334	0.0641670	−	0.997939i	$-0.479561\pi$
$29$	0.691099	0.128334	0.0641670	+	0.997939i	$0.479561\pi$
$30$	−1.20960	−0.220842
$31$	−4.94099	−0.887428	−0.443714	−	0.896169i	$-0.646339\pi$
$31$	−4.94099	−0.887428	−0.443714	+	0.896169i	$0.646339\pi$
$32$	1.00000	0.176777
$33$	1.20960	0.210565
$34$	−2.97329	−0.509915
$35$	−1.90541	−0.322073
$36$	−1.53686	−0.256143
$37$	−0.936110	−0.153896	−0.0769478	−	0.997035i	$-0.524517\pi$
$37$	−0.936110	−0.153896	−0.0769478	+	0.997035i	$0.524517\pi$
$38$	1.05378	0.170946
$39$	−2.23195	−0.357397
$40$	−1.00000	−0.158114
$41$	5.94412	0.928316	0.464158	−	0.885752i	$-0.346357\pi$
$41$	5.94412	0.928316	0.464158	+	0.885752i	$0.346357\pi$
$42$	2.30479	0.355637
$43$	−4.04286	−0.616530	−0.308265	−	0.951300i	$-0.599748\pi$
$43$	−4.04286	−0.616530	−0.308265	+	0.951300i	$0.599748\pi$
$44$	1.00000	0.150756
$45$	1.53686	0.229101
$46$	−8.58943	−1.26644
$47$	−13.5091	−1.97050	−0.985250	−	0.171122i	$-0.945261\pi$
$47$	−13.5091	−1.97050	−0.985250	+	0.171122i	$0.945261\pi$
$48$	1.20960	0.174591
$49$	−3.36942	−0.481346
$50$	1.00000	0.141421
$51$	−3.59651	−0.503612
$52$	−1.84519	−0.255881
$53$	−0.0765417	−0.0105138	−0.00525691	−	0.999986i	$-0.501673\pi$
$53$	−0.0765417	−0.0105138	−0.00525691	+	0.999986i	$0.501673\pi$
$54$	−5.48780	−0.746795
$55$	−1.00000	−0.134840
$56$	1.90541	0.254621
$57$	1.27466	0.168832
$58$	0.691099	0.0907458
$59$	−2.25596	−0.293702	−0.146851	−	0.989159i	$-0.546914\pi$
$59$	−2.25596	−0.293702	−0.146851	+	0.989159i	$0.546914\pi$
$60$	−1.20960	−0.156159
$61$	−7.53820	−0.965168	−0.482584	−	0.875850i	$-0.660302\pi$
$61$	−7.53820	−0.965168	−0.482584	+	0.875850i	$0.660302\pi$
$62$	−4.94099	−0.627506
$63$	−2.92834	−0.368936
$64$	1.00000	0.125000
$65$	1.84519	0.228867
$66$	1.20960	0.148892
$67$	11.8148	1.44341	0.721704	−	0.692202i	$-0.243359\pi$
$67$	11.8148	1.44341	0.721704	+	0.692202i	$0.243359\pi$
$68$	−2.97329	−0.360565
$69$	−10.3898	−1.25079
$70$	−1.90541	−0.227740
$71$	0.0205518	0.00243905	0.00121953	−	0.999999i	$-0.499612\pi$
$71$	0.0205518	0.00243905	0.00121953	+	0.999999i	$0.499612\pi$
$72$	−1.53686	−0.181120
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−0.936110	−0.108821
$75$	1.20960	0.139673
$76$	1.05378	0.120877
$77$	1.90541	0.217141
$78$	−2.23195	−0.252718
$79$	−16.7087	−1.87987	−0.939936	−	0.341351i	$-0.889116\pi$
$79$	−16.7087	−1.87987	−0.939936	+	0.341351i	$0.889116\pi$
$80$	−1.00000	−0.111803
$81$	−2.02749	−0.225277
$82$	5.94412	0.656419
$83$	11.9430	1.31092	0.655458	−	0.755232i	$-0.272476\pi$
$83$	11.9430	1.31092	0.655458	+	0.755232i	$0.272476\pi$
$84$	2.30479	0.251473
$85$	2.97329	0.322499
$86$	−4.04286	−0.435953
$87$	0.835957	0.0896240
$88$	1.00000	0.106600
$89$	7.65038	0.810939	0.405469	−	0.914109i	$-0.367108\pi$
$89$	7.65038	0.810939	0.405469	+	0.914109i	$0.367108\pi$
$90$	1.53686	0.161999
$91$	−3.51583	−0.368559
$92$	−8.58943	−0.895510
$93$	−5.97664	−0.619748
$94$	−13.5091	−1.39335
$95$	−1.05378	−0.108116
$96$	1.20960	0.123455
$97$	17.1407	1.74038	0.870189	−	0.492718i	$-0.163997\pi$
$97$	17.1407	1.74038	0.870189	+	0.492718i	$0.163997\pi$
$98$	−3.36942	−0.340363
$99$	−1.53686	−0.154460
$100$	1.00000	0.100000
$101$	−4.77299	−0.474930	−0.237465	−	0.971396i	$-0.576316\pi$
$101$	−4.77299	−0.474930	−0.237465	+	0.971396i	$0.576316\pi$
$102$	−3.59651	−0.356107
$103$	4.10737	0.404711	0.202355	−	0.979312i	$-0.435140\pi$
$103$	4.10737	0.404711	0.202355	+	0.979312i	$0.435140\pi$
$104$	−1.84519	−0.180936
$105$	−2.30479	−0.224924
$106$	−0.0765417	−0.00743439
$107$	−4.11677	−0.397983	−0.198992	−	0.980001i	$-0.563767\pi$
$107$	−4.11677	−0.397983	−0.198992	+	0.980001i	$0.563767\pi$
$108$	−5.48780	−0.528064
$109$	−14.0668	−1.34736	−0.673678	−	0.739025i	$-0.735286\pi$
$109$	−14.0668	−1.34736	−0.673678	+	0.739025i	$0.735286\pi$
$110$	−1.00000	−0.0953463
$111$	−1.13232	−0.107475
$112$	1.90541	0.180044
$113$	10.2475	0.964002	0.482001	−	0.876171i	$-0.339910\pi$
$113$	10.2475	0.964002	0.482001	+	0.876171i	$0.339910\pi$
$114$	1.27466	0.119383
$115$	8.58943	0.800969
$116$	0.691099	0.0641670
$117$	2.83579	0.262169
$118$	−2.25596	−0.207678
$119$	−5.66533	−0.519340
$120$	−1.20960	−0.110421
$121$	1.00000	0.0909091
$122$	−7.53820	−0.682477
$123$	7.19003	0.648304
$124$	−4.94099	−0.443714
$125$	−1.00000	−0.0894427
$126$	−2.92834	−0.260877
$127$	−19.3869	−1.72031	−0.860153	−	0.510036i	$-0.829632\pi$
$127$	−19.3869	−1.72031	−0.860153	+	0.510036i	$0.829632\pi$
$128$	1.00000	0.0883883
$129$	−4.89026	−0.430563
$130$	1.84519	0.161834
$131$	0.508404	0.0444195	0.0222097	−	0.999753i	$-0.492930\pi$
$131$	0.508404	0.0444195	0.0222097	+	0.999753i	$0.492930\pi$
$132$	1.20960	0.105283
$133$	2.00788	0.174105
$134$	11.8148	1.02064
$135$	5.48780	0.472315
$136$	−2.97329	−0.254958
$137$	−12.1616	−1.03904	−0.519520	−	0.854459i	$-0.673889\pi$
$137$	−12.1616	−1.03904	−0.519520	+	0.854459i	$0.673889\pi$
$138$	−10.3898	−0.884440
$139$	−11.6582	−0.988835	−0.494417	−	0.869225i	$-0.664619\pi$
$139$	−11.6582	−0.988835	−0.494417	+	0.869225i	$0.664619\pi$
$140$	−1.90541	−0.161036
$141$	−16.3406	−1.37613
$142$	0.0205518	0.00172467
$143$	−1.84519	−0.154302
$144$	−1.53686	−0.128072
$145$	−0.691099	−0.0573927
$146$	−1.00000	−0.0827606
$147$	−4.07567	−0.336155
$148$	−0.936110	−0.0769478
$149$	17.6222	1.44367	0.721833	−	0.692068i	$-0.243300\pi$
$149$	17.6222	1.44367	0.721833	+	0.692068i	$0.243300\pi$
$150$	1.20960	0.0987638
$151$	−12.1993	−0.992766	−0.496383	−	0.868104i	$-0.665339\pi$
$151$	−12.1993	−0.992766	−0.496383	+	0.868104i	$0.665339\pi$
$152$	1.05378	0.0854729
$153$	4.56953	0.369425
$154$	1.90541	0.153542
$155$	4.94099	0.396870
$156$	−2.23195	−0.178699
$157$	8.10535	0.646877	0.323438	−	0.946249i	$-0.395161\pi$
$157$	8.10535	0.646877	0.323438	+	0.946249i	$0.395161\pi$
$158$	−16.7087	−1.32927
$159$	−0.0925852	−0.00734248
$160$	−1.00000	−0.0790569
$161$	−16.3664	−1.28985
$162$	−2.02749	−0.159295
$163$	16.6865	1.30699	0.653495	−	0.756931i	$-0.273302\pi$
$163$	16.6865	1.30699	0.653495	+	0.756931i	$0.273302\pi$
$164$	5.94412	0.464158
$165$	−1.20960	−0.0941675
$166$	11.9430	0.926957
$167$	3.98544	0.308403	0.154201	−	0.988039i	$-0.450720\pi$
$167$	3.98544	0.308403	0.154201	+	0.988039i	$0.450720\pi$
$168$	2.30479	0.177818
$169$	−9.59528	−0.738099
$170$	2.97329	0.228041
$171$	−1.61951	−0.123847
$172$	−4.04286	−0.308265
$173$	−1.53683	−0.116843	−0.0584214	−	0.998292i	$-0.518607\pi$
$173$	−1.53683	−0.116843	−0.0584214	+	0.998292i	$0.518607\pi$
$174$	0.835957	0.0633737
$175$	1.90541	0.144035
$176$	1.00000	0.0753778
$177$	−2.72882	−0.205111
$178$	7.65038	0.573420
$179$	−5.66989	−0.423787	−0.211894	−	0.977293i	$-0.567963\pi$
$179$	−5.66989	−0.423787	−0.211894	+	0.977293i	$0.567963\pi$
$180$	1.53686	0.114551
$181$	14.3665	1.06785	0.533927	−	0.845531i	$-0.320716\pi$
$181$	14.3665	1.06785	0.533927	+	0.845531i	$0.320716\pi$
$182$	−3.51583	−0.260611
$183$	−9.11824	−0.674040
$184$	−8.58943	−0.633221
$185$	0.936110	0.0688242
$186$	−5.97664	−0.438228
$187$	−2.97329	−0.217429
$188$	−13.5091	−0.985250
$189$	−10.4565	−0.760598
$190$	−1.05378	−0.0764493
$191$	8.44332	0.610937	0.305468	−	0.952202i	$-0.401187\pi$
$191$	8.44332	0.610937	0.305468	+	0.952202i	$0.401187\pi$
$192$	1.20960	0.0872956
$193$	−12.5609	−0.904155	−0.452077	−	0.891979i	$-0.649317\pi$
$193$	−12.5609	−0.904155	−0.452077	+	0.891979i	$0.649317\pi$
$194$	17.1407	1.23063
$195$	2.23195	0.159833
$196$	−3.36942	−0.240673
$197$	13.4716	0.959808	0.479904	−	0.877321i	$-0.340671\pi$
$197$	13.4716	0.959808	0.479904	+	0.877321i	$0.340671\pi$
$198$	−1.53686	−0.109220
$199$	4.82676	0.342160	0.171080	−	0.985257i	$-0.445274\pi$
$199$	4.82676	0.342160	0.171080	+	0.985257i	$0.445274\pi$
$200$	1.00000	0.0707107
$201$	14.2912	1.00803
$202$	−4.77299	−0.335826
$203$	1.31683	0.0924231
$204$	−3.59651	−0.251806
$205$	−5.94412	−0.415156
$206$	4.10737	0.286174
$207$	13.2007	0.917515
$208$	−1.84519	−0.127941
$209$	1.05378	0.0728915
$210$	−2.30479	−0.159045
$211$	−1.77202	−0.121991	−0.0609954	−	0.998138i	$-0.519427\pi$
$211$	−1.77202	−0.121991	−0.0609954	+	0.998138i	$0.519427\pi$
$212$	−0.0765417	−0.00525691
$213$	0.0248596	0.00170335
$214$	−4.11677	−0.281417
$215$	4.04286	0.275721
$216$	−5.48780	−0.373398
$217$	−9.41459	−0.639104
$218$	−14.0668	−0.952724
$219$	−1.20960	−0.0817375
$220$	−1.00000	−0.0674200
$221$	5.48628	0.369047
$222$	−1.13232	−0.0759965
$223$	−9.42233	−0.630966	−0.315483	−	0.948931i	$-0.602167\pi$
$223$	−9.42233	−0.630966	−0.315483	+	0.948931i	$0.602167\pi$
$224$	1.90541	0.127310
$225$	−1.53686	−0.102457
$226$	10.2475	0.681652
$227$	10.0159	0.664777	0.332388	−	0.943143i	$-0.392146\pi$
$227$	10.0159	0.664777	0.332388	+	0.943143i	$0.392146\pi$
$228$	1.27466	0.0844162
$229$	−22.1976	−1.46686	−0.733428	−	0.679767i	$-0.762081\pi$
$229$	−22.1976	−1.46686	−0.733428	+	0.679767i	$0.762081\pi$
$230$	8.58943	0.566370
$231$	2.30479	0.151644
$232$	0.691099	0.0453729
$233$	−13.2395	−0.867351	−0.433676	−	0.901069i	$-0.642784\pi$
$233$	−13.2395	−0.867351	−0.433676	+	0.901069i	$0.642784\pi$
$234$	2.83579	0.185381
$235$	13.5091	0.881234
$236$	−2.25596	−0.146851
$237$	−20.2109	−1.31284
$238$	−5.66533	−0.367229
$239$	−16.5813	−1.07255	−0.536276	−	0.844043i	$-0.680169\pi$
$239$	−16.5813	−1.07255	−0.536276	+	0.844043i	$0.680169\pi$
$240$	−1.20960	−0.0780796
$241$	21.2756	1.37048	0.685240	−	0.728317i	$-0.259697\pi$
$241$	21.2756	1.37048	0.685240	+	0.728317i	$0.259697\pi$
$242$	1.00000	0.0642824
$243$	14.0109	0.898802
$244$	−7.53820	−0.482584
$245$	3.36942	0.215265
$246$	7.19003	0.458420
$247$	−1.94442	−0.123721
$248$	−4.94099	−0.313753
$249$	14.4463	0.915498
$250$	−1.00000	−0.0632456
$251$	−3.23313	−0.204073	−0.102037	−	0.994781i	$-0.532536\pi$
$251$	−3.23313	−0.204073	−0.102037	+	0.994781i	$0.532536\pi$
$252$	−2.92834	−0.184468
$253$	−8.58943	−0.540013
$254$	−19.3869	−1.21644
$255$	3.59651	0.225222
$256$	1.00000	0.0625000
$257$	7.20821	0.449636	0.224818	−	0.974401i	$-0.427821\pi$
$257$	7.20821	0.449636	0.224818	+	0.974401i	$0.427821\pi$
$258$	−4.89026	−0.304454
$259$	−1.78367	−0.110832
$260$	1.84519	0.114434
$261$	−1.06212	−0.0657437
$262$	0.508404	0.0314093
$263$	11.8332	0.729665	0.364833	−	0.931073i	$-0.381126\pi$
$263$	11.8332	0.729665	0.364833	+	0.931073i	$0.381126\pi$
$264$	1.20960	0.0744460
$265$	0.0765417	0.00470192
$266$	2.00788	0.123111
$267$	9.25393	0.566331
$268$	11.8148	0.721704
$269$	−3.41946	−0.208488	−0.104244	−	0.994552i	$-0.533242\pi$
$269$	−3.41946	−0.208488	−0.104244	+	0.994552i	$0.533242\pi$
$270$	5.48780	0.333977
$271$	−14.5044	−0.881082	−0.440541	−	0.897733i	$-0.645213\pi$
$271$	−14.5044	−0.881082	−0.440541	+	0.897733i	$0.645213\pi$
$272$	−2.97329	−0.180282
$273$	−4.25277	−0.257389
$274$	−12.1616	−0.734712
$275$	1.00000	0.0603023
$276$	−10.3898	−0.625393
$277$	12.5374	0.753300	0.376650	−	0.926356i	$-0.377076\pi$
$277$	12.5374	0.753300	0.376650	+	0.926356i	$0.377076\pi$
$278$	−11.6582	−0.699212
$279$	7.59360	0.454617
$280$	−1.90541	−0.113870
$281$	18.9773	1.13209	0.566045	−	0.824374i	$-0.308473\pi$
$281$	18.9773	1.13209	0.566045	+	0.824374i	$0.308473\pi$
$282$	−16.3406	−0.973070
$283$	−27.3051	−1.62312	−0.811559	−	0.584270i	$-0.801381\pi$
$283$	−27.3051	−1.62312	−0.811559	+	0.584270i	$0.801381\pi$
$284$	0.0205518	0.00121953
$285$	−1.27466	−0.0755042
$286$	−1.84519	−0.109108
$287$	11.3260	0.668551
$288$	−1.53686	−0.0905602
$289$	−8.15953	−0.479972
$290$	−0.691099	−0.0405828
$291$	20.7335	1.21542
$292$	−1.00000	−0.0585206
$293$	−29.2292	−1.70759	−0.853794	−	0.520612i	$-0.825704\pi$
$293$	−29.2292	−1.70759	−0.853794	+	0.520612i	$0.825704\pi$
$294$	−4.07567	−0.237698
$295$	2.25596	0.131347
$296$	−0.936110	−0.0544103
$297$	−5.48780	−0.318435
$298$	17.6222	1.02083
$299$	15.8491	0.916578
$300$	1.20960	0.0698365
$301$	−7.70330	−0.444011
$302$	−12.1993	−0.701992
$303$	−5.77342	−0.331675
$304$	1.05378	0.0604384
$305$	7.53820	0.431636
$306$	4.56953	0.261223
$307$	−5.31824	−0.303528	−0.151764	−	0.988417i	$-0.548495\pi$
$307$	−5.31824	−0.303528	−0.151764	+	0.988417i	$0.548495\pi$
$308$	1.90541	0.108571
$309$	4.96829	0.282636
$310$	4.94099	0.280629
$311$	16.9667	0.962093	0.481046	−	0.876695i	$-0.340257\pi$
$311$	16.9667	0.962093	0.481046	+	0.876695i	$0.340257\pi$
$312$	−2.23195	−0.126359
$313$	−0.223122	−0.0126116	−0.00630579	−	0.999980i	$-0.502007\pi$
$313$	−0.223122	−0.0126116	−0.00630579	+	0.999980i	$0.502007\pi$
$314$	8.10535	0.457411
$315$	2.92834	0.164993
$316$	−16.7087	−0.939936
$317$	−19.6164	−1.10177	−0.550883	−	0.834582i	$-0.685709\pi$
$317$	−19.6164	−1.10177	−0.550883	+	0.834582i	$0.685709\pi$
$318$	−0.0925852	−0.00519192
$319$	0.691099	0.0386941
$320$	−1.00000	−0.0559017
$321$	−4.97966	−0.277938
$322$	−16.3664	−0.912062
$323$	−3.13320	−0.174336
$324$	−2.02749	−0.112638
$325$	−1.84519	−0.102353
$326$	16.6865	0.924182
$327$	−17.0153	−0.940946
$328$	5.94412	0.328209
$329$	−25.7403	−1.41911
$330$	−1.20960	−0.0665865
$331$	12.1958	0.670340	0.335170	−	0.942158i	$-0.391206\pi$
$331$	12.1958	0.670340	0.335170	+	0.942158i	$0.391206\pi$
$332$	11.9430	0.655458
$333$	1.43867	0.0788385
$334$	3.98544	0.218074
$335$	−11.8148	−0.645512
$336$	2.30479	0.125737
$337$	−3.98029	−0.216820	−0.108410	−	0.994106i	$-0.534576\pi$
$337$	−3.98029	−0.216820	−0.108410	+	0.994106i	$0.534576\pi$
$338$	−9.59528	−0.521915
$339$	12.3954	0.673225
$340$	2.97329	0.161249
$341$	−4.94099	−0.267569
$342$	−1.61951	−0.0875731
$343$	−19.7580	−1.06683
$344$	−4.04286	−0.217976
$345$	10.3898	0.559369
$346$	−1.53683	−0.0826203
$347$	12.7209	0.682895	0.341448	−	0.939901i	$-0.389083\pi$
$347$	12.7209	0.682895	0.341448	+	0.939901i	$0.389083\pi$
$348$	0.835957	0.0448120
$349$	−24.3984	−1.30602	−0.653008	−	0.757351i	$-0.726493\pi$
$349$	−24.3984	−1.30602	−0.653008	+	0.757351i	$0.726493\pi$
$350$	1.90541	0.101848
$351$	10.1260	0.540487
$352$	1.00000	0.0533002
$353$	−8.85517	−0.471313	−0.235657	−	0.971836i	$-0.575724\pi$
$353$	−8.85517	−0.471313	−0.235657	+	0.971836i	$0.575724\pi$
$354$	−2.72882	−0.145035
$355$	−0.0205518	−0.00109078
$356$	7.65038	0.405469
$357$	−6.85281	−0.362689
$358$	−5.66989	−0.299663
$359$	27.1151	1.43108	0.715540	−	0.698571i	$-0.246181\pi$
$359$	27.1151	1.43108	0.715540	+	0.698571i	$0.246181\pi$
$360$	1.53686	0.0809995
$361$	−17.8895	−0.941555
$362$	14.3665	0.755086
$363$	1.20960	0.0634877
$364$	−3.51583	−0.184280
$365$	1.00000	0.0523424
$366$	−9.11824	−0.476618
$367$	5.46356	0.285195	0.142598	−	0.989781i	$-0.454454\pi$
$367$	5.46356	0.285195	0.142598	+	0.989781i	$0.454454\pi$
$368$	−8.58943	−0.447755
$369$	−9.13527	−0.475563
$370$	0.936110	0.0486660
$371$	−0.145843	−0.00757180
$372$	−5.97664	−0.309874
$373$	30.9717	1.60365	0.801826	−	0.597558i	$-0.203862\pi$
$373$	30.9717	1.60365	0.801826	+	0.597558i	$0.203862\pi$
$374$	−2.97329	−0.153745
$375$	−1.20960	−0.0624637
$376$	−13.5091	−0.696677
$377$	−1.27521	−0.0656765
$378$	−10.4565	−0.537824
$379$	−20.4178	−1.04879	−0.524396	−	0.851474i	$-0.675709\pi$
$379$	−20.4178	−1.04879	−0.524396	+	0.851474i	$0.675709\pi$
$380$	−1.05378	−0.0540578
$381$	−23.4504	−1.20140
$382$	8.44332	0.431998
$383$	−18.0079	−0.920160	−0.460080	−	0.887877i	$-0.652179\pi$
$383$	−18.0079	−0.920160	−0.460080	+	0.887877i	$0.652179\pi$
$384$	1.20960	0.0617273
$385$	−1.90541	−0.0971085
$386$	−12.5609	−0.639334
$387$	6.21330	0.315840
$388$	17.1407	0.870189
$389$	25.7845	1.30732	0.653662	−	0.756786i	$-0.273232\pi$
$389$	25.7845	1.30732	0.653662	+	0.756786i	$0.273232\pi$
$390$	2.23195	0.113019
$391$	25.5389	1.29156
$392$	−3.36942	−0.170182
$393$	0.614968	0.0310210
$394$	13.4716	0.678687
$395$	16.7087	0.840704
$396$	−1.53686	−0.0772300
$397$	−1.45277	−0.0729124	−0.0364562	−	0.999335i	$-0.511607\pi$
$397$	−1.45277	−0.0729124	−0.0364562	+	0.999335i	$0.511607\pi$
$398$	4.82676	0.241944
$399$	2.42874	0.121589
$400$	1.00000	0.0500000
$401$	−35.4363	−1.76960	−0.884802	−	0.465967i	$-0.845706\pi$
$401$	−35.4363	−1.76960	−0.884802	+	0.465967i	$0.845706\pi$
$402$	14.2912	0.712782
$403$	9.11705	0.454152
$404$	−4.77299	−0.237465
$405$	2.02749	0.100747
$406$	1.31683	0.0653530
$407$	−0.936110	−0.0464013
$408$	−3.59651	−0.178054
$409$	11.2616	0.556850	0.278425	−	0.960458i	$-0.410188\pi$
$409$	11.2616	0.556850	0.278425	+	0.960458i	$0.410188\pi$
$410$	−5.94412	−0.293559
$411$	−14.7108	−0.725629
$412$	4.10737	0.202355
$413$	−4.29853	−0.211517
$414$	13.2007	0.648781
$415$	−11.9430	−0.586259
$416$	−1.84519	−0.0904678
$417$	−14.1018	−0.690568
$418$	1.05378	0.0515421
$419$	22.3169	1.09025	0.545126	−	0.838354i	$-0.316482\pi$
$419$	22.3169	1.09025	0.545126	+	0.838354i	$0.316482\pi$
$420$	−2.30479	−0.112462
$421$	21.1932	1.03289	0.516447	−	0.856319i	$-0.327254\pi$
$421$	21.1932	1.03289	0.516447	+	0.856319i	$0.327254\pi$
$422$	−1.77202	−0.0862605
$423$	20.7615	1.00946
$424$	−0.0765417	−0.00371719
$425$	−2.97329	−0.144226
$426$	0.0248596	0.00120445
$427$	−14.3633	−0.695091
$428$	−4.11677	−0.198992
$429$	−2.23195	−0.107759
$430$	4.04286	0.194964
$431$	14.2127	0.684600	0.342300	−	0.939591i	$-0.388794\pi$
$431$	14.2127	0.684600	0.342300	+	0.939591i	$0.388794\pi$
$432$	−5.48780	−0.264032
$433$	−9.88678	−0.475128	−0.237564	−	0.971372i	$-0.576349\pi$
$433$	−9.88678	−0.475128	−0.237564	+	0.971372i	$0.576349\pi$
$434$	−9.41459	−0.451915
$435$	−0.835957	−0.0400811
$436$	−14.0668	−0.673678
$437$	−9.05138	−0.432986
$438$	−1.20960	−0.0577971
$439$	−20.7307	−0.989424	−0.494712	−	0.869057i	$-0.664726\pi$
$439$	−20.7307	−0.989424	−0.494712	+	0.869057i	$0.664726\pi$
$440$	−1.00000	−0.0476731
$441$	5.17833	0.246587
$442$	5.48628	0.260956
$443$	33.0540	1.57044	0.785221	−	0.619216i	$-0.212550\pi$
$443$	33.0540	1.57044	0.785221	+	0.619216i	$0.212550\pi$
$444$	−1.13232	−0.0537376
$445$	−7.65038	−0.362663
$446$	−9.42233	−0.446160
$447$	21.3159	1.00821
$448$	1.90541	0.0900220
$449$	30.8418	1.45551	0.727757	−	0.685835i	$-0.240563\pi$
$449$	30.8418	1.45551	0.727757	+	0.685835i	$0.240563\pi$
$450$	−1.53686	−0.0724482
$451$	5.94412	0.279898
$452$	10.2475	0.482001
$453$	−14.7563	−0.693313
$454$	10.0159	0.470068
$455$	3.51583	0.164825
$456$	1.27466	0.0596913
$457$	−22.2944	−1.04289	−0.521443	−	0.853286i	$-0.674606\pi$
$457$	−22.2944	−1.04289	−0.521443	+	0.853286i	$0.674606\pi$
$458$	−22.1976	−1.03722
$459$	16.3168	0.761605
$460$	8.58943	0.400484
$461$	1.89011	0.0880312	0.0440156	−	0.999031i	$-0.485985\pi$
$461$	1.89011	0.0880312	0.0440156	+	0.999031i	$0.485985\pi$
$462$	2.30479	0.107228
$463$	−12.4350	−0.577905	−0.288953	−	0.957343i	$-0.593307\pi$
$463$	−12.4350	−0.577905	−0.288953	+	0.957343i	$0.593307\pi$
$464$	0.691099	0.0320835
$465$	5.97664	0.277160
$466$	−13.2395	−0.613310
$467$	−0.00518911	−0.000240123 0	−0.000120062	−	1.00000i	$-0.500038\pi$
$467$	−0.00518911	−0.000240123 0	−0.000120062		1.00000i	$0.500038\pi$
$468$	2.83579	0.131084
$469$	22.5120	1.03951
$470$	13.5091	0.623127
$471$	9.80426	0.451756
$472$	−2.25596	−0.103839
$473$	−4.04286	−0.185891
$474$	−20.2109	−0.928316
$475$	1.05378	0.0483508
$476$	−5.66533	−0.259670
$477$	0.117634	0.00538608
$478$	−16.5813	−0.758409
$479$	11.6062	0.530299	0.265150	−	0.964207i	$-0.414579\pi$
$479$	11.6062	0.530299	0.265150	+	0.964207i	$0.414579\pi$
$480$	−1.20960	−0.0552106
$481$	1.72730	0.0787580
$482$	21.2756	0.969076
$483$	−19.7968	−0.900787
$484$	1.00000	0.0454545
$485$	−17.1407	−0.778321
$486$	14.0109	0.635549
$487$	15.3582	0.695948	0.347974	−	0.937504i	$-0.386870\pi$
$487$	15.3582	0.695948	0.347974	+	0.937504i	$0.386870\pi$
$488$	−7.53820	−0.341238
$489$	20.1841	0.912757
$490$	3.36942	0.152215
$491$	21.6795	0.978383	0.489192	−	0.872176i	$-0.337292\pi$
$491$	21.6795	0.978383	0.489192	+	0.872176i	$0.337292\pi$
$492$	7.19003	0.324152
$493$	−2.05484	−0.0925454
$494$	−1.94442	−0.0874837
$495$	1.53686	0.0690766
$496$	−4.94099	−0.221857
$497$	0.0391596	0.00175655
$498$	14.4463	0.647355
$499$	−34.0747	−1.52539	−0.762696	−	0.646757i	$-0.776125\pi$
$499$	−34.0747	−1.52539	−0.762696	+	0.646757i	$0.776125\pi$
$500$	−1.00000	−0.0447214
$501$	4.82081	0.215378
$502$	−3.23313	−0.144301
$503$	−4.38730	−0.195620	−0.0978100	−	0.995205i	$-0.531184\pi$
$503$	−4.38730	−0.195620	−0.0978100	+	0.995205i	$0.531184\pi$
$504$	−2.92834	−0.130439
$505$	4.77299	0.212395
$506$	−8.58943	−0.381847
$507$	−11.6065	−0.515462
$508$	−19.3869	−0.860153
$509$	−27.2279	−1.20686	−0.603429	−	0.797417i	$-0.706199\pi$
$509$	−27.2279	−1.20686	−0.603429	+	0.797417i	$0.706199\pi$
$510$	3.59651	0.159256
$511$	−1.90541	−0.0842903
$512$	1.00000	0.0441942
$513$	−5.78294	−0.255323
$514$	7.20821	0.317941
$515$	−4.10737	−0.180992
$516$	−4.89026	−0.215282
$517$	−13.5091	−0.594128
$518$	−1.78367	−0.0783700
$519$	−1.85895	−0.0815989
$520$	1.84519	0.0809168
$521$	−35.4733	−1.55411	−0.777056	−	0.629432i	$-0.783288\pi$
$521$	−35.4733	−1.55411	−0.777056	+	0.629432i	$0.783288\pi$
$522$	−1.06212	−0.0464878
$523$	20.7653	0.908005	0.454003	−	0.891000i	$-0.349996\pi$
$523$	20.7653	0.908005	0.454003	+	0.891000i	$0.349996\pi$
$524$	0.508404	0.0222097
$525$	2.30479	0.100589
$526$	11.8332	0.515951
$527$	14.6910	0.639950
$528$	1.20960	0.0526413
$529$	50.7784	2.20775
$530$	0.0765417	0.00332476
$531$	3.46710	0.150459
$532$	2.00788	0.0870527
$533$	−10.9680	−0.475078
$534$	9.25393	0.400457
$535$	4.11677	0.177984
$536$	11.8148	0.510322
$537$	−6.85832	−0.295958
$538$	−3.41946	−0.147423
$539$	−3.36942	−0.145131
$540$	5.48780	0.236157
$541$	−13.0322	−0.560300	−0.280150	−	0.959956i	$-0.590384\pi$
$541$	−13.0322	−0.560300	−0.280150	+	0.959956i	$0.590384\pi$
$542$	−14.5044	−0.623019
$543$	17.3778	0.745751
$544$	−2.97329	−0.127479
$545$	14.0668	0.602555
$546$	−4.25277	−0.182002
$547$	19.4368	0.831059	0.415530	−	0.909580i	$-0.363596\pi$
$547$	19.4368	0.831059	0.415530	+	0.909580i	$0.363596\pi$
$548$	−12.1616	−0.519520
$549$	11.5851	0.494442
$550$	1.00000	0.0426401
$551$	0.728267	0.0310252
$552$	−10.3898	−0.442220
$553$	−31.8368	−1.35384
$554$	12.5374	0.532663
$555$	1.13232	0.0480644
$556$	−11.6582	−0.494417
$557$	−0.155432	−0.00658588	−0.00329294	−	0.999995i	$-0.501048\pi$
$557$	−0.155432	−0.00658588	−0.00329294	+	0.999995i	$0.501048\pi$
$558$	7.59360	0.321463
$559$	7.45983	0.315517
$560$	−1.90541	−0.0805182
$561$	−3.59651	−0.151845
$562$	18.9773	0.800508
$563$	0.396529	0.0167117	0.00835585	−	0.999965i	$-0.497340\pi$
$563$	0.396529	0.0167117	0.00835585	+	0.999965i	$0.497340\pi$
$564$	−16.3406	−0.688064
$565$	−10.2475	−0.431115
$566$	−27.3051	−1.14772
$567$	−3.86320	−0.162239
$568$	0.0205518	0.000862335 0
$569$	−18.3152	−0.767812	−0.383906	−	0.923372i	$-0.625421\pi$
$569$	−18.3152	−0.767812	−0.383906	+	0.923372i	$0.625421\pi$
$570$	−1.27466	−0.0533895
$571$	32.5501	1.36218	0.681090	−	0.732200i	$-0.261506\pi$
$571$	32.5501	1.36218	0.681090	+	0.732200i	$0.261506\pi$
$572$	−1.84519	−0.0771512
$573$	10.2131	0.426657
$574$	11.3260	0.472737
$575$	−8.58943	−0.358204
$576$	−1.53686	−0.0640358
$577$	−41.4465	−1.72544	−0.862721	−	0.505681i	$-0.831241\pi$
$577$	−41.4465	−1.72544	−0.862721	+	0.505681i	$0.831241\pi$
$578$	−8.15953	−0.339392
$579$	−15.1937	−0.631430
$580$	−0.691099	−0.0286963
$581$	22.7563	0.944090
$582$	20.7335	0.859431
$583$	−0.0765417	−0.00317003
$584$	−1.00000	−0.0413803
$585$	−2.83579	−0.117246
$586$	−29.2292	−1.20745
$587$	14.7967	0.610726	0.305363	−	0.952236i	$-0.401222\pi$
$587$	14.7967	0.610726	0.305363	+	0.952236i	$0.401222\pi$
$588$	−4.07567	−0.168078
$589$	−5.20672	−0.214539
$590$	2.25596	0.0928766
$591$	16.2952	0.670297
$592$	−0.936110	−0.0384739
$593$	−4.78244	−0.196391	−0.0981957	−	0.995167i	$-0.531307\pi$
$593$	−4.78244	−0.196391	−0.0981957	+	0.995167i	$0.531307\pi$
$594$	−5.48780	−0.225167
$595$	5.66533	0.232256
$596$	17.6222	0.721833
$597$	5.83847	0.238952
$598$	15.8491	0.648118
$599$	−6.24455	−0.255145	−0.127573	−	0.991829i	$-0.540719\pi$
$599$	−6.24455	−0.255145	−0.127573	+	0.991829i	$0.540719\pi$
$600$	1.20960	0.0493819
$601$	−20.8079	−0.848772	−0.424386	−	0.905481i	$-0.639510\pi$
$601$	−20.8079	−0.848772	−0.424386	+	0.905481i	$0.639510\pi$
$602$	−7.70330	−0.313963
$603$	−18.1577	−0.739438
$604$	−12.1993	−0.496383
$605$	−1.00000	−0.0406558
$606$	−5.77342	−0.234529
$607$	0.660194	0.0267964	0.0133982	−	0.999910i	$-0.495735\pi$
$607$	0.660194	0.0267964	0.0133982	+	0.999910i	$0.495735\pi$
$608$	1.05378	0.0427364
$609$	1.59284	0.0645450
$610$	7.53820	0.305213
$611$	24.9268	1.00843
$612$	4.56953	0.184712
$613$	3.04603	0.123028	0.0615141	−	0.998106i	$-0.480407\pi$
$613$	3.04603	0.123028	0.0615141	+	0.998106i	$0.480407\pi$
$614$	−5.31824	−0.214627
$615$	−7.19003	−0.289930
$616$	1.90541	0.0767710
$617$	25.0733	1.00941	0.504707	−	0.863291i	$-0.331601\pi$
$617$	25.0733	1.00941	0.504707	+	0.863291i	$0.331601\pi$
$618$	4.96829	0.199854
$619$	6.27500	0.252213	0.126107	−	0.992017i	$-0.459752\pi$
$619$	6.27500	0.252213	0.126107	+	0.992017i	$0.459752\pi$
$620$	4.94099	0.198435
$621$	47.1371	1.89155
$622$	16.9667	0.680302
$623$	14.5771	0.584019
$624$	−2.23195	−0.0893493
$625$	1.00000	0.0400000
$626$	−0.223122	−0.00891774
$627$	1.27466	0.0509049
$628$	8.10535	0.323438
$629$	2.78333	0.110979
$630$	2.92834	0.116668
$631$	−5.63584	−0.224359	−0.112180	−	0.993688i	$-0.535783\pi$
$631$	−5.63584	−0.224359	−0.112180	+	0.993688i	$0.535783\pi$
$632$	−16.7087	−0.664635
$633$	−2.14344	−0.0851941
$634$	−19.6164	−0.779066
$635$	19.3869	0.769344
$636$	−0.0925852	−0.00367124
$637$	6.21722	0.246335
$638$	0.691099	0.0273609
$639$	−0.0315852	−0.00124949
$640$	−1.00000	−0.0395285
$641$	16.2417	0.641508	0.320754	−	0.947163i	$-0.396064\pi$
$641$	16.2417	0.641508	0.320754	+	0.947163i	$0.396064\pi$
$642$	−4.97966	−0.196532
$643$	0.264411	0.0104273	0.00521367	−	0.999986i	$-0.498340\pi$
$643$	0.264411	0.0104273	0.00521367	+	0.999986i	$0.498340\pi$
$644$	−16.3664	−0.644925
$645$	4.89026	0.192554
$646$	−3.13320	−0.123274
$647$	−20.9971	−0.825480	−0.412740	−	0.910849i	$-0.635428\pi$
$647$	−20.9971	−0.825480	−0.412740	+	0.910849i	$0.635428\pi$
$648$	−2.02749	−0.0796474
$649$	−2.25596	−0.0885544
$650$	−1.84519	−0.0723742
$651$	−11.3879	−0.446328
$652$	16.6865	0.653495
$653$	−16.6310	−0.650821	−0.325410	−	0.945573i	$-0.605502\pi$
$653$	−16.6310	−0.650821	−0.325410	+	0.945573i	$0.605502\pi$
$654$	−17.0153	−0.665349
$655$	−0.508404	−0.0198650
$656$	5.94412	0.232079
$657$	1.53686	0.0599585
$658$	−25.7403	−1.00346
$659$	−17.2629	−0.672469	−0.336234	−	0.941778i	$-0.609153\pi$
$659$	−17.2629	−0.672469	−0.336234	+	0.941778i	$0.609153\pi$
$660$	−1.20960	−0.0470838
$661$	−14.7166	−0.572411	−0.286205	−	0.958168i	$-0.592394\pi$
$661$	−14.7166	−0.572411	−0.286205	+	0.958168i	$0.592394\pi$
$662$	12.1958	0.474002
$663$	6.63623	0.257730
$664$	11.9430	0.463479
$665$	−2.00788	−0.0778623
$666$	1.43867	0.0557473
$667$	−5.93615	−0.229849
$668$	3.98544	0.154201
$669$	−11.3973	−0.440645
$670$	−11.8148	−0.456446
$671$	−7.53820	−0.291009
$672$	2.30479	0.0889091
$673$	−6.91500	−0.266554	−0.133277	−	0.991079i	$-0.542550\pi$
$673$	−6.91500	−0.266554	−0.133277	+	0.991079i	$0.542550\pi$
$674$	−3.98029	−0.153315
$675$	−5.48780	−0.211226
$676$	−9.59528	−0.369049
$677$	5.69468	0.218864	0.109432	−	0.993994i	$-0.465097\pi$
$677$	5.69468	0.218864	0.109432	+	0.993994i	$0.465097\pi$
$678$	12.3954	0.476042
$679$	32.6601	1.25338
$680$	2.97329	0.114021
$681$	12.1152	0.464257
$682$	−4.94099	−0.189200
$683$	−42.4508	−1.62433	−0.812167	−	0.583424i	$-0.801712\pi$
$683$	−42.4508	−1.62433	−0.812167	+	0.583424i	$0.801712\pi$
$684$	−1.61951	−0.0619235
$685$	12.1616	0.464672
$686$	−19.7580	−0.754363
$687$	−26.8503	−1.02440
$688$	−4.04286	−0.154133
$689$	0.141234	0.00538058
$690$	10.3898	0.395533
$691$	−40.0131	−1.52217	−0.761085	−	0.648652i	$-0.775333\pi$
$691$	−40.0131	−1.52217	−0.761085	+	0.648652i	$0.775333\pi$
$692$	−1.53683	−0.0584214
$693$	−2.92834	−0.111238
$694$	12.7209	0.482880
$695$	11.6582	0.442220
$696$	0.835957	0.0316869
$697$	−17.6736	−0.669436
$698$	−24.3984	−0.923492
$699$	−16.0146	−0.605728
$700$	1.90541	0.0720176
$701$	−14.7846	−0.558406	−0.279203	−	0.960232i	$-0.590070\pi$
$701$	−14.7846	−0.558406	−0.279203	+	0.960232i	$0.590070\pi$
$702$	10.1260	0.382182
$703$	−0.986454	−0.0372048
$704$	1.00000	0.0376889
$705$	16.3406	0.615423
$706$	−8.85517	−0.333269
$707$	−9.09448	−0.342033
$708$	−2.72882	−0.102555
$709$	14.2256	0.534252	0.267126	−	0.963662i	$-0.413926\pi$
$709$	14.2256	0.534252	0.267126	+	0.963662i	$0.413926\pi$
$710$	−0.0205518	−0.000771296 0
$711$	25.6789	0.963032
$712$	7.65038	0.286710
$713$	42.4403	1.58940
$714$	−6.85281	−0.256460
$715$	1.84519	0.0690061
$716$	−5.66989	−0.211894
$717$	−20.0567	−0.749033
$718$	27.1151	1.01193
$719$	−26.5256	−0.989240	−0.494620	−	0.869109i	$-0.664693\pi$
$719$	−26.5256	−0.989240	−0.494620	+	0.869109i	$0.664693\pi$
$720$	1.53686	0.0572753
$721$	7.82620	0.291463
$722$	−17.8895	−0.665780
$723$	25.7350	0.957096
$724$	14.3665	0.533927
$725$	0.691099	0.0256668
$726$	1.20960	0.0448926
$727$	−7.14798	−0.265104	−0.132552	−	0.991176i	$-0.542317\pi$
$727$	−7.14798	−0.265104	−0.132552	+	0.991176i	$0.542317\pi$
$728$	−3.51583	−0.130305
$729$	23.0302	0.852969
$730$	1.00000	0.0370117
$731$	12.0206	0.444598
$732$	−9.11824	−0.337020
$733$	35.1500	1.29829	0.649147	−	0.760663i	$-0.275126\pi$
$733$	35.1500	1.29829	0.649147	+	0.760663i	$0.275126\pi$
$734$	5.46356	0.201664
$735$	4.07567	0.150333
$736$	−8.58943	−0.316611
$737$	11.8148	0.435204
$738$	−9.13527	−0.336274
$739$	−9.99350	−0.367617	−0.183808	−	0.982962i	$-0.558843\pi$
$739$	−9.99350	−0.367617	−0.183808	+	0.982962i	$0.558843\pi$
$740$	0.936110	0.0344121
$741$	−2.35198	−0.0864022
$742$	−0.145843	−0.00535407
$743$	−13.6012	−0.498978	−0.249489	−	0.968378i	$-0.580263\pi$
$743$	−13.6012	−0.498978	−0.249489	+	0.968378i	$0.580263\pi$
$744$	−5.97664	−0.219114
$745$	−17.6222	−0.645627
$746$	30.9717	1.13395
$747$	−18.3547	−0.671564
$748$	−2.97329	−0.108714
$749$	−7.84413	−0.286618
$750$	−1.20960	−0.0441685
$751$	52.5022	1.91583	0.957917	−	0.287045i	$-0.0926730\pi$
$751$	52.5022	1.91583	0.957917	+	0.287045i	$0.0926730\pi$
$752$	−13.5091	−0.492625
$753$	−3.91080	−0.142518
$754$	−1.27521	−0.0464403
$755$	12.1993	0.443979
$756$	−10.4565	−0.380299
$757$	25.2740	0.918600	0.459300	−	0.888281i	$-0.348100\pi$
$757$	25.2740	0.918600	0.459300	+	0.888281i	$0.348100\pi$
$758$	−20.4178	−0.741608
$759$	−10.3898	−0.377126
$760$	−1.05378	−0.0382246
$761$	−38.7851	−1.40596	−0.702979	−	0.711210i	$-0.748147\pi$
$761$	−38.7851	−1.40596	−0.702979	+	0.711210i	$0.748147\pi$
$762$	−23.4504	−0.849519
$763$	−26.8030	−0.970333
$764$	8.44332	0.305468
$765$	−4.56953	−0.165212
$766$	−18.0079	−0.650651
$767$	4.16268	0.150306
$768$	1.20960	0.0436478
$769$	5.22848	0.188544	0.0942719	−	0.995546i	$-0.469948\pi$
$769$	5.22848	0.188544	0.0942719	+	0.995546i	$0.469948\pi$
$770$	−1.90541	−0.0686661
$771$	8.71908	0.314010
$772$	−12.5609	−0.452077
$773$	24.9144	0.896110	0.448055	−	0.894006i	$-0.352117\pi$
$773$	24.9144	0.896110	0.448055	+	0.894006i	$0.352117\pi$
$774$	6.21330	0.223333
$775$	−4.94099	−0.177486
$776$	17.1407	0.615316
$777$	−2.15754	−0.0774012
$778$	25.7845	0.924418
$779$	6.26380	0.224424
$780$	2.23195	0.0799165
$781$	0.0205518	0.000735402 0
$782$	25.5389	0.913269
$783$	−3.79262	−0.135537
$784$	−3.36942	−0.120337
$785$	−8.10535	−0.289292
$786$	0.614968	0.0219352
$787$	2.89397	0.103159	0.0515795	−	0.998669i	$-0.483574\pi$
$787$	2.89397	0.103159	0.0515795	+	0.998669i	$0.483574\pi$
$788$	13.4716	0.479904
$789$	14.3135	0.509573
$790$	16.7087	0.594468
$791$	19.5256	0.694251
$792$	−1.53686	−0.0546099
$793$	13.9094	0.493937
$794$	−1.45277	−0.0515569
$795$	0.0925852	0.00328366
$796$	4.82676	0.171080
$797$	33.3475	1.18123	0.590615	−	0.806953i	$-0.298885\pi$
$797$	33.3475	1.18123	0.590615	+	0.806953i	$0.298885\pi$
$798$	2.42874	0.0859765
$799$	40.1664	1.42099
$800$	1.00000	0.0353553
$801$	−11.7576	−0.415433
$802$	−35.4363	−1.25130
$803$	−1.00000	−0.0352892
$804$	14.2912	0.504013
$805$	16.3664	0.576839
$806$	9.11705	0.321134
$807$	−4.13619	−0.145601
$808$	−4.77299	−0.167913
$809$	38.2692	1.34548	0.672738	−	0.739881i	$-0.265118\pi$
$809$	38.2692	1.34548	0.672738	+	0.739881i	$0.265118\pi$
$810$	2.02749	0.0712388
$811$	38.4793	1.35119	0.675596	−	0.737272i	$-0.263887\pi$
$811$	38.4793	1.35119	0.675596	+	0.737272i	$0.263887\pi$
$812$	1.31683	0.0462115
$813$	−17.5446	−0.615317
$814$	−0.936110	−0.0328106
$815$	−16.6865	−0.584504
$816$	−3.59651	−0.125903
$817$	−4.26029	−0.149049
$818$	11.2616	0.393753
$819$	5.40334	0.188808
$820$	−5.94412	−0.207578
$821$	14.6749	0.512157	0.256078	−	0.966656i	$-0.417569\pi$
$821$	14.6749	0.512157	0.256078	+	0.966656i	$0.417569\pi$
$822$	−14.7108	−0.513097
$823$	−15.5005	−0.540312	−0.270156	−	0.962817i	$-0.587075\pi$
$823$	−15.5005	−0.540312	−0.270156	+	0.962817i	$0.587075\pi$
$824$	4.10737	0.143087
$825$	1.20960	0.0421130
$826$	−4.29853	−0.149565
$827$	4.00563	0.139290	0.0696448	−	0.997572i	$-0.477813\pi$
$827$	4.00563	0.139290	0.0696448	+	0.997572i	$0.477813\pi$
$828$	13.2007	0.458757
$829$	43.4973	1.51072	0.755362	−	0.655308i	$-0.227461\pi$
$829$	43.4973	1.51072	0.755362	+	0.655308i	$0.227461\pi$
$830$	−11.9430	−0.414548
$831$	15.1653	0.526078
$832$	−1.84519	−0.0639704
$833$	10.0183	0.347113
$834$	−14.1018	−0.488305
$835$	−3.98544	−0.137922
$836$	1.05378	0.0364458
$837$	27.1152	0.937237
$838$	22.3169	0.770925
$839$	−28.3064	−0.977244	−0.488622	−	0.872496i	$-0.662500\pi$
$839$	−28.3064	−0.977244	−0.488622	+	0.872496i	$0.662500\pi$
$840$	−2.30479	−0.0795227
$841$	−28.5224	−0.983530
$842$	21.1932	0.730366
$843$	22.9550	0.790612
$844$	−1.77202	−0.0609954
$845$	9.59528	0.330088
$846$	20.7615	0.713796
$847$	1.90541	0.0654706
$848$	−0.0765417	−0.00262845
$849$	−33.0283	−1.13353
$850$	−2.97329	−0.101983
$851$	8.04065	0.275630
$852$	0.0248596	0.000851675 0
$853$	32.7036	1.11975	0.559875	−	0.828577i	$-0.310849\pi$
$853$	32.7036	1.11975	0.559875	+	0.828577i	$0.310849\pi$
$854$	−14.3633	−0.491504
$855$	1.61951	0.0553861
$856$	−4.11677	−0.140708
$857$	9.13573	0.312071	0.156035	−	0.987751i	$-0.450129\pi$
$857$	9.13573	0.312071	0.156035	+	0.987751i	$0.450129\pi$
$858$	−2.23195	−0.0761974
$859$	−26.0770	−0.889734	−0.444867	−	0.895597i	$-0.646749\pi$
$859$	−26.0770	−0.889734	−0.444867	+	0.895597i	$0.646749\pi$
$860$	4.04286	0.137860
$861$	13.6999	0.466893
$862$	14.2127	0.484085
$863$	4.20483	0.143134	0.0715671	−	0.997436i	$-0.477200\pi$
$863$	4.20483	0.143134	0.0715671	+	0.997436i	$0.477200\pi$
$864$	−5.48780	−0.186699
$865$	1.53683	0.0522536
$866$	−9.88678	−0.335967
$867$	−9.86980	−0.335196
$868$	−9.41459	−0.319552
$869$	−16.7087	−0.566803
$870$	−0.835957	−0.0283416
$871$	−21.8005	−0.738683
$872$	−14.0668	−0.476362
$873$	−26.3429	−0.891571
$874$	−9.05138	−0.306167
$875$	−1.90541	−0.0644145
$876$	−1.20960	−0.0408687
$877$	23.1731	0.782500	0.391250	−	0.920284i	$-0.372043\pi$
$877$	23.1731	0.782500	0.391250	+	0.920284i	$0.372043\pi$
$878$	−20.7307	−0.699628
$879$	−35.3557	−1.19252
$880$	−1.00000	−0.0337100
$881$	−19.6108	−0.660704	−0.330352	−	0.943858i	$-0.607168\pi$
$881$	−19.6108	−0.660704	−0.330352	+	0.943858i	$0.607168\pi$
$882$	5.17833	0.174363
$883$	−20.4568	−0.688426	−0.344213	−	0.938892i	$-0.611854\pi$
$883$	−20.4568	−0.688426	−0.344213	+	0.938892i	$0.611854\pi$
$884$	5.48628	0.184524
$885$	2.72882	0.0917284
$886$	33.0540	1.11047
$887$	20.6374	0.692936	0.346468	−	0.938062i	$-0.387381\pi$
$887$	20.6374	0.692936	0.346468	+	0.938062i	$0.387381\pi$
$888$	−1.13232	−0.0379983
$889$	−36.9399	−1.23892
$890$	−7.65038	−0.256441
$891$	−2.02749	−0.0679236
$892$	−9.42233	−0.315483
$893$	−14.2356	−0.476376
$894$	21.3159	0.712909
$895$	5.66989	0.189523
$896$	1.90541	0.0636552
$897$	19.1711	0.640106
$898$	30.8418	1.02920
$899$	−3.41471	−0.113887
$900$	−1.53686	−0.0512286
$901$	0.227581	0.00758182
$902$	5.94412	0.197918
$903$	−9.31794	−0.310082
$904$	10.2475	0.340826
$905$	−14.3665	−0.477558
$906$	−14.7563	−0.490247
$907$	3.52022	0.116887	0.0584435	−	0.998291i	$-0.481386\pi$
$907$	3.52022	0.116887	0.0584435	+	0.998291i	$0.481386\pi$
$908$	10.0159	0.332388
$909$	7.33540	0.243300
$910$	3.51583	0.116549
$911$	25.8324	0.855867	0.427933	−	0.903810i	$-0.359242\pi$
$911$	25.8324	0.855867	0.427933	+	0.903810i	$0.359242\pi$
$912$	1.27466	0.0422081
$913$	11.9430	0.395256
$914$	−22.2944	−0.737432
$915$	9.11824	0.301440
$916$	−22.1976	−0.733428
$917$	0.968717	0.0319899
$918$	16.3168	0.538536
$919$	12.2391	0.403731	0.201865	−	0.979413i	$-0.435300\pi$
$919$	12.2391	0.403731	0.201865	+	0.979413i	$0.435300\pi$
$920$	8.58943	0.283185
$921$	−6.43297	−0.211973
$922$	1.89011	0.0622475
$923$	−0.0379220	−0.00124822
$924$	2.30479	0.0758220
$925$	−0.936110	−0.0307791
$926$	−12.4350	−0.408641
$927$	−6.31244	−0.207328
$928$	0.691099	0.0226864
$929$	−57.4785	−1.88581	−0.942905	−	0.333063i	$-0.891918\pi$
$929$	−57.4785	−1.88581	−0.942905	+	0.333063i	$0.891918\pi$
$930$	5.97664	0.195982
$931$	−3.55063	−0.116367
$932$	−13.2395	−0.433676
$933$	20.5230	0.671892
$934$	−0.00518911	−0.000169793 0
$935$	2.97329	0.0972371
$936$	2.83579	0.0926907
$937$	58.3133	1.90501	0.952505	−	0.304521i	$-0.0984965\pi$
$937$	58.3133	1.90501	0.952505	+	0.304521i	$0.0984965\pi$
$938$	22.5120	0.735043
$939$	−0.269889	−0.00880749
$940$	13.5091	0.440617
$941$	−17.8854	−0.583047	−0.291523	−	0.956564i	$-0.594162\pi$
$941$	−17.8854	−0.583047	−0.291523	+	0.956564i	$0.594162\pi$
$942$	9.80426	0.319440
$943$	−51.0566	−1.66263
$944$	−2.25596	−0.0734254
$945$	10.4565	0.340150
$946$	−4.04286	−0.131445
$947$	−8.43291	−0.274033	−0.137016	−	0.990569i	$-0.543751\pi$
$947$	−8.43291	−0.274033	−0.137016	+	0.990569i	$0.543751\pi$
$948$	−20.2109	−0.656419
$949$	1.84519	0.0598973
$950$	1.05378	0.0341891
$951$	−23.7281	−0.769435
$952$	−5.66533	−0.183615
$953$	32.6803	1.05862	0.529310	−	0.848429i	$-0.322451\pi$
$953$	32.6803	1.05862	0.529310	+	0.848429i	$0.322451\pi$
$954$	0.117634	0.00380853
$955$	−8.44332	−0.273219
$956$	−16.5813	−0.536276
$957$	0.835957	0.0270226
$958$	11.6062	0.374978
$959$	−23.1729	−0.748291
$960$	−1.20960	−0.0390398
$961$	−6.58664	−0.212472
$962$	1.72730	0.0556903
$963$	6.32689	0.203881
$964$	21.2756	0.685240
$965$	12.5609	0.404350
$966$	−19.7968	−0.636952
$967$	21.3232	0.685707	0.342854	−	0.939389i	$-0.388607\pi$
$967$	21.3232	0.685707	0.342854	+	0.939389i	$0.388607\pi$
$968$	1.00000	0.0321412
$969$	−3.78993	−0.121750
$970$	−17.1407	−0.550356
$971$	1.04198	0.0334387	0.0167193	−	0.999860i	$-0.494678\pi$
$971$	1.04198	0.0334387	0.0167193	+	0.999860i	$0.494678\pi$
$972$	14.0109	0.449401
$973$	−22.2136	−0.712135
$974$	15.3582	0.492110
$975$	−2.23195	−0.0714795
$976$	−7.53820	−0.241292
$977$	51.6470	1.65233	0.826167	−	0.563425i	$-0.190517\pi$
$977$	51.6470	1.65233	0.826167	+	0.563425i	$0.190517\pi$
$978$	20.1841	0.645416
$979$	7.65038	0.244507
$980$	3.36942	0.107632
$981$	21.6187	0.690231
$982$	21.6795	0.691821
$983$	7.19027	0.229334	0.114667	−	0.993404i	$-0.463420\pi$
$983$	7.19027	0.229334	0.114667	+	0.993404i	$0.463420\pi$
$984$	7.19003	0.229210
$985$	−13.4716	−0.429239
$986$	−2.05484	−0.0654395
$987$	−31.1355	−0.991055
$988$	−1.94442	−0.0618603
$989$	34.7259	1.10422
$990$	1.53686	0.0488446
$991$	−6.66797	−0.211815	−0.105908	−	0.994376i	$-0.533775\pi$
$991$	−6.66797	−0.211815	−0.105908	+	0.994376i	$0.533775\pi$
$992$	−4.94099	−0.156877
$993$	14.7521	0.468142
$994$	0.0391596	0.00124207
$995$	−4.82676	−0.153019
$996$	14.4463	0.457749
$997$	2.36957	0.0750450	0.0375225	−	0.999296i	$-0.488053\pi$
$997$	2.36957	0.0750450	0.0375225	+	0.999296i	$0.488053\pi$
$998$	−34.0747	−1.07862
$999$	5.13719	0.162533

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bb.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bb.1.6	✓	8	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.20960 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.20960 q^{6} +1.90541 q^{7} +1.00000 q^{8} -1.53686 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.20960 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.20960 q^{6} +1.90541 q^{7} +1.00000 q^{8} -1.53686 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.20960 q^{12} -1.84519 q^{13} +1.90541 q^{14} -1.20960 q^{15} +1.00000 q^{16} -2.97329 q^{17} -1.53686 q^{18} +1.05378 q^{19} -1.00000 q^{20} +2.30479 q^{21} +1.00000 q^{22} -8.58943 q^{23} +1.20960 q^{24} +1.00000 q^{25} -1.84519 q^{26} -5.48780 q^{27} +1.90541 q^{28} +0.691099 q^{29} -1.20960 q^{30} -4.94099 q^{31} +1.00000 q^{32} +1.20960 q^{33} -2.97329 q^{34} -1.90541 q^{35} -1.53686 q^{36} -0.936110 q^{37} +1.05378 q^{38} -2.23195 q^{39} -1.00000 q^{40} +5.94412 q^{41} +2.30479 q^{42} -4.04286 q^{43} +1.00000 q^{44} +1.53686 q^{45} -8.58943 q^{46} -13.5091 q^{47} +1.20960 q^{48} -3.36942 q^{49} +1.00000 q^{50} -3.59651 q^{51} -1.84519 q^{52} -0.0765417 q^{53} -5.48780 q^{54} -1.00000 q^{55} +1.90541 q^{56} +1.27466 q^{57} +0.691099 q^{58} -2.25596 q^{59} -1.20960 q^{60} -7.53820 q^{61} -4.94099 q^{62} -2.92834 q^{63} +1.00000 q^{64} +1.84519 q^{65} +1.20960 q^{66} +11.8148 q^{67} -2.97329 q^{68} -10.3898 q^{69} -1.90541 q^{70} +0.0205518 q^{71} -1.53686 q^{72} -1.00000 q^{73} -0.936110 q^{74} +1.20960 q^{75} +1.05378 q^{76} +1.90541 q^{77} -2.23195 q^{78} -16.7087 q^{79} -1.00000 q^{80} -2.02749 q^{81} +5.94412 q^{82} +11.9430 q^{83} +2.30479 q^{84} +2.97329 q^{85} -4.04286 q^{86} +0.835957 q^{87} +1.00000 q^{88} +7.65038 q^{89} +1.53686 q^{90} -3.51583 q^{91} -8.58943 q^{92} -5.97664 q^{93} -13.5091 q^{94} -1.05378 q^{95} +1.20960 q^{96} +17.1407 q^{97} -3.36942 q^{98} -1.53686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 3 q^{3} + 8 q^{4} - 8 q^{5} - 3 q^{6} - 4 q^{7} + 8 q^{8} + q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 3 * q^3 + 8 * q^4 - 8 * q^5 - 3 * q^6 - 4 * q^7 + 8 * q^8 + q^9	\( 8 q + 8 q^{2} - 3 q^{3} + 8 q^{4} - 8 q^{5} - 3 q^{6} - 4 q^{7} + 8 q^{8} + q^{9} - 8 q^{10} + 8 q^{11} - 3 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 2 q^{17} + q^{18} - q^{19} - 8 q^{20} + 7 q^{21} + 8 q^{22} - 16 q^{23} - 3 q^{24} + 8 q^{25} - 7 q^{26} - 21 q^{27} - 4 q^{28} - 5 q^{29} + 3 q^{30} - 22 q^{31} + 8 q^{32} - 3 q^{33} + 2 q^{34} + 4 q^{35} + q^{36} - 9 q^{37} - q^{38} - 18 q^{39} - 8 q^{40} + 6 q^{41} + 7 q^{42} + 15 q^{43} + 8 q^{44} - q^{45} - 16 q^{46} - 7 q^{47} - 3 q^{48} - 6 q^{49} + 8 q^{50} + q^{51} - 7 q^{52} - 11 q^{53} - 21 q^{54} - 8 q^{55} - 4 q^{56} - 17 q^{57} - 5 q^{58} - 11 q^{59} + 3 q^{60} - 22 q^{61} - 22 q^{62} + q^{63} + 8 q^{64} + 7 q^{65} - 3 q^{66} + 21 q^{67} + 2 q^{68} + q^{69} + 4 q^{70} - 28 q^{71} + q^{72} - 8 q^{73} - 9 q^{74} - 3 q^{75} - q^{76} - 4 q^{77} - 18 q^{78} - 28 q^{79} - 8 q^{80} + 12 q^{81} + 6 q^{82} - 5 q^{83} + 7 q^{84} - 2 q^{85} + 15 q^{86} + 36 q^{87} + 8 q^{88} - 17 q^{89} - q^{90} - 29 q^{91} - 16 q^{92} + 42 q^{93} - 7 q^{94} + q^{95} - 3 q^{96} + q^{97} - 6 q^{98} + q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 3 * q^3 + 8 * q^4 - 8 * q^5 - 3 * q^6 - 4 * q^7 + 8 * q^8 + q^9 - 8 * q^10 + 8 * q^11 - 3 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 2 * q^17 + q^18 - q^19 - 8 * q^20 + 7 * q^21 + 8 * q^22 - 16 * q^23 - 3 * q^24 + 8 * q^25 - 7 * q^26 - 21 * q^27 - 4 * q^28 - 5 * q^29 + 3 * q^30 - 22 * q^31 + 8 * q^32 - 3 * q^33 + 2 * q^34 + 4 * q^35 + q^36 - 9 * q^37 - q^38 - 18 * q^39 - 8 * q^40 + 6 * q^41 + 7 * q^42 + 15 * q^43 + 8 * q^44 - q^45 - 16 * q^46 - 7 * q^47 - 3 * q^48 - 6 * q^49 + 8 * q^50 + q^51 - 7 * q^52 - 11 * q^53 - 21 * q^54 - 8 * q^55 - 4 * q^56 - 17 * q^57 - 5 * q^58 - 11 * q^59 + 3 * q^60 - 22 * q^61 - 22 * q^62 + q^63 + 8 * q^64 + 7 * q^65 - 3 * q^66 + 21 * q^67 + 2 * q^68 + q^69 + 4 * q^70 - 28 * q^71 + q^72 - 8 * q^73 - 9 * q^74 - 3 * q^75 - q^76 - 4 * q^77 - 18 * q^78 - 28 * q^79 - 8 * q^80 + 12 * q^81 + 6 * q^82 - 5 * q^83 + 7 * q^84 - 2 * q^85 + 15 * q^86 + 36 * q^87 + 8 * q^88 - 17 * q^89 - q^90 - 29 * q^91 - 16 * q^92 + 42 * q^93 - 7 * q^94 + q^95 - 3 * q^96 + q^97 - 6 * q^98 + q^99

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