LMFDB - Embedded newform 805.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(1,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, 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("805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.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:	$6.42795736271$
Analytic rank:	$0$
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} - x^{7} - 11x^{6} + 9x^{5} + 36x^{4} - 23x^{3} - 30x^{2} + 17x - 2 $ x^8 - x^7 - 11x^6 + 9x^5 + 36x^4 - 23x^3 - 30x^2 + 17x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.94419$ of defining polynomial
Character	$\chi$	$=$	805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.94419 q^{2} +3.14297 q^{3} +1.77986 q^{4} +1.00000 q^{5} -6.11052 q^{6} +1.00000 q^{7} +0.427999 q^{8} +6.87827 q^{9} +O(q^{10})$	\(q-1.94419 q^{2} +3.14297 q^{3} +1.77986 q^{4} +1.00000 q^{5} -6.11052 q^{6} +1.00000 q^{7} +0.427999 q^{8} +6.87827 q^{9} -1.94419 q^{10} +5.04300 q^{11} +5.59404 q^{12} +5.16633 q^{13} -1.94419 q^{14} +3.14297 q^{15} -4.39182 q^{16} -7.40852 q^{17} -13.3726 q^{18} -5.95715 q^{19} +1.77986 q^{20} +3.14297 q^{21} -9.80453 q^{22} +1.00000 q^{23} +1.34519 q^{24} +1.00000 q^{25} -10.0443 q^{26} +12.1893 q^{27} +1.77986 q^{28} -0.530448 q^{29} -6.11052 q^{30} -2.50219 q^{31} +7.68252 q^{32} +15.8500 q^{33} +14.4035 q^{34} +1.00000 q^{35} +12.2423 q^{36} -7.70904 q^{37} +11.5818 q^{38} +16.2376 q^{39} +0.427999 q^{40} -2.51810 q^{41} -6.11052 q^{42} -12.0061 q^{43} +8.97582 q^{44} +6.87827 q^{45} -1.94419 q^{46} -0.447537 q^{47} -13.8034 q^{48} +1.00000 q^{49} -1.94419 q^{50} -23.2848 q^{51} +9.19534 q^{52} +3.18550 q^{53} -23.6982 q^{54} +5.04300 q^{55} +0.427999 q^{56} -18.7232 q^{57} +1.03129 q^{58} +9.09814 q^{59} +5.59404 q^{60} -0.608230 q^{61} +4.86472 q^{62} +6.87827 q^{63} -6.15260 q^{64} +5.16633 q^{65} -30.8154 q^{66} +8.89704 q^{67} -13.1861 q^{68} +3.14297 q^{69} -1.94419 q^{70} -11.6461 q^{71} +2.94389 q^{72} +2.19297 q^{73} +14.9878 q^{74} +3.14297 q^{75} -10.6029 q^{76} +5.04300 q^{77} -31.5690 q^{78} -12.7320 q^{79} -4.39182 q^{80} +17.6758 q^{81} +4.89566 q^{82} +11.3641 q^{83} +5.59404 q^{84} -7.40852 q^{85} +23.3421 q^{86} -1.66718 q^{87} +2.15840 q^{88} -8.82411 q^{89} -13.3726 q^{90} +5.16633 q^{91} +1.77986 q^{92} -7.86430 q^{93} +0.870094 q^{94} -5.95715 q^{95} +24.1459 q^{96} +0.311043 q^{97} -1.94419 q^{98} +34.6871 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 7 q^{3} + 7 q^{4} + 8 q^{5} + q^{6} + 8 q^{7} + 3 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q + q^2 + 7 * q^3 + 7 * q^4 + 8 * q^5 + q^6 + 8 * q^7 + 3 * q^8 + 9 * q^9	\( 8 q + q^{2} + 7 q^{3} + 7 q^{4} + 8 q^{5} + q^{6} + 8 q^{7} + 3 q^{8} + 9 q^{9} + q^{10} + 6 q^{11} + 8 q^{12} + 8 q^{13} + q^{14} + 7 q^{15} + q^{16} + 4 q^{17} - 11 q^{18} + 7 q^{20} + 7 q^{21} - 8 q^{22} + 8 q^{23} - 8 q^{24} + 8 q^{25} + 2 q^{26} + 28 q^{27} + 7 q^{28} - 3 q^{29} + q^{30} - 16 q^{31} + 12 q^{32} + 5 q^{33} - 4 q^{34} + 8 q^{35} - 14 q^{36} - 7 q^{37} + 11 q^{38} + 16 q^{39} + 3 q^{40} + 7 q^{41} + q^{42} - 10 q^{43} + 7 q^{44} + 9 q^{45} + q^{46} + 19 q^{47} - 6 q^{48} + 8 q^{49} + q^{50} + 7 q^{51} + 18 q^{52} - q^{53} - 25 q^{54} + 6 q^{55} + 3 q^{56} - 25 q^{57} - 9 q^{58} + 21 q^{59} + 8 q^{60} - 7 q^{61} + 18 q^{62} + 9 q^{63} - 37 q^{64} + 8 q^{65} - 43 q^{66} + 11 q^{67} - 17 q^{68} + 7 q^{69} + q^{70} + 8 q^{71} + 4 q^{72} - 3 q^{73} + 12 q^{74} + 7 q^{75} + 8 q^{76} + 6 q^{77} - 50 q^{78} - 15 q^{79} + q^{80} + 28 q^{81} + 41 q^{82} + 25 q^{83} + 8 q^{84} + 4 q^{85} - 12 q^{86} + 21 q^{87} - 29 q^{88} + q^{89} - 11 q^{90} + 8 q^{91} + 7 q^{92} - 5 q^{93} - 36 q^{94} + 30 q^{96} + 10 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + q^2 + 7 * q^3 + 7 * q^4 + 8 * q^5 + q^6 + 8 * q^7 + 3 * q^8 + 9 * q^9 + q^10 + 6 * q^11 + 8 * q^12 + 8 * q^13 + q^14 + 7 * q^15 + q^16 + 4 * q^17 - 11 * q^18 + 7 * q^20 + 7 * q^21 - 8 * q^22 + 8 * q^23 - 8 * q^24 + 8 * q^25 + 2 * q^26 + 28 * q^27 + 7 * q^28 - 3 * q^29 + q^30 - 16 * q^31 + 12 * q^32 + 5 * q^33 - 4 * q^34 + 8 * q^35 - 14 * q^36 - 7 * q^37 + 11 * q^38 + 16 * q^39 + 3 * q^40 + 7 * q^41 + q^42 - 10 * q^43 + 7 * q^44 + 9 * q^45 + q^46 + 19 * q^47 - 6 * q^48 + 8 * q^49 + q^50 + 7 * q^51 + 18 * q^52 - q^53 - 25 * q^54 + 6 * q^55 + 3 * q^56 - 25 * q^57 - 9 * q^58 + 21 * q^59 + 8 * q^60 - 7 * q^61 + 18 * q^62 + 9 * q^63 - 37 * q^64 + 8 * q^65 - 43 * q^66 + 11 * q^67 - 17 * q^68 + 7 * q^69 + q^70 + 8 * q^71 + 4 * q^72 - 3 * q^73 + 12 * q^74 + 7 * q^75 + 8 * q^76 + 6 * q^77 - 50 * q^78 - 15 * q^79 + q^80 + 28 * q^81 + 41 * q^82 + 25 * q^83 + 8 * q^84 + 4 * q^85 - 12 * q^86 + 21 * q^87 - 29 * q^88 + q^89 - 11 * q^90 + 8 * q^91 + 7 * q^92 - 5 * q^93 - 36 * q^94 + 30 * q^96 + 10 * q^97 + q^98 - 18 * 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 $

$2$	−1.94419	−1.37475	−0.687373	−	0.726304i	$-0.741236\pi$
$2$	−1.94419	−1.37475	−0.687373	+	0.726304i	$0.741236\pi$
$3$	3.14297	1.81460	0.907298	−	0.420489i	$-0.138141\pi$
$3$	3.14297	1.81460	0.907298	+	0.420489i	$0.138141\pi$
$4$	1.77986	0.889928
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−6.11052	−2.49461
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.427999	0.151320
$9$	6.87827	2.29276
$10$	−1.94419	−0.614805
$11$	5.04300	1.52052	0.760261	−	0.649618i	$-0.225071\pi$
$11$	5.04300	1.52052	0.760261	+	0.649618i	$0.225071\pi$
$12$	5.59404	1.61486
$13$	5.16633	1.43288	0.716442	−	0.697647i	$-0.245770\pi$
$13$	5.16633	1.43288	0.716442	+	0.697647i	$0.245770\pi$
$14$	−1.94419	−0.519605
$15$	3.14297	0.811512
$16$	−4.39182	−1.09796
$17$	−7.40852	−1.79683	−0.898415	−	0.439148i	$-0.855280\pi$
$17$	−7.40852	−1.79683	−0.898415	+	0.439148i	$0.855280\pi$
$18$	−13.3726	−3.15196
$19$	−5.95715	−1.36666	−0.683332	−	0.730107i	$-0.739470\pi$
$19$	−5.95715	−1.36666	−0.683332	+	0.730107i	$0.739470\pi$
$20$	1.77986	0.397988
$21$	3.14297	0.685853
$22$	−9.80453	−2.09033
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.34519	0.274585
$25$	1.00000	0.200000
$26$	−10.0443	−1.96985
$27$	12.1893	2.34583
$28$	1.77986	0.336361
$29$	−0.530448	−0.0985018	−0.0492509	−	0.998786i	$-0.515683\pi$
$29$	−0.530448	−0.0985018	−0.0492509	+	0.998786i	$0.515683\pi$
$30$	−6.11052	−1.11562
$31$	−2.50219	−0.449406	−0.224703	−	0.974427i	$-0.572141\pi$
$31$	−2.50219	−0.449406	−0.224703	+	0.974427i	$0.572141\pi$
$32$	7.68252	1.35809
$33$	15.8500	2.75913
$34$	14.4035	2.47018
$35$	1.00000	0.169031
$36$	12.2423	2.04039
$37$	−7.70904	−1.26736	−0.633679	−	0.773596i	$-0.718456\pi$
$37$	−7.70904	−1.26736	−0.633679	+	0.773596i	$0.718456\pi$
$38$	11.5818	1.87882
$39$	16.2376	2.60010
$40$	0.427999	0.0676726
$41$	−2.51810	−0.393261	−0.196631	−	0.980478i	$-0.563000\pi$
$41$	−2.51810	−0.393261	−0.196631	+	0.980478i	$0.563000\pi$
$42$	−6.11052	−0.942874
$43$	−12.0061	−1.83091	−0.915456	−	0.402419i	$-0.868170\pi$
$43$	−12.0061	−1.83091	−0.915456	+	0.402419i	$0.868170\pi$
$44$	8.97582	1.35316
$45$	6.87827	1.02535
$46$	−1.94419	−0.286655
$47$	−0.447537	−0.0652799	−0.0326400	−	0.999467i	$-0.510391\pi$
$47$	−0.447537	−0.0652799	−0.0326400	+	0.999467i	$0.510391\pi$
$48$	−13.8034	−1.99235
$49$	1.00000	0.142857
$50$	−1.94419	−0.274949
$51$	−23.2848	−3.26052
$52$	9.19534	1.27516
$53$	3.18550	0.437563	0.218781	−	0.975774i	$-0.429792\pi$
$53$	3.18550	0.437563	0.218781	+	0.975774i	$0.429792\pi$
$54$	−23.6982	−3.22492
$55$	5.04300	0.679998
$56$	0.427999	0.0571938
$57$	−18.7232	−2.47994
$58$	1.03129	0.135415
$59$	9.09814	1.18448	0.592239	−	0.805763i	$-0.298244\pi$
$59$	9.09814	1.18448	0.592239	+	0.805763i	$0.298244\pi$
$60$	5.59404	0.722187
$61$	−0.608230	−0.0778758	−0.0389379	−	0.999242i	$-0.512397\pi$
$61$	−0.608230	−0.0778758	−0.0389379	+	0.999242i	$0.512397\pi$
$62$	4.86472	0.617819
$63$	6.87827	0.866581
$64$	−6.15260	−0.769075
$65$	5.16633	0.640805
$66$	−30.8154	−3.79311
$67$	8.89704	1.08695	0.543473	−	0.839427i	$-0.317109\pi$
$67$	8.89704	1.08695	0.543473	+	0.839427i	$0.317109\pi$
$68$	−13.1861	−1.59905
$69$	3.14297	0.378369
$70$	−1.94419	−0.232375
$71$	−11.6461	−1.38214	−0.691071	−	0.722787i	$-0.742861\pi$
$71$	−11.6461	−1.38214	−0.691071	+	0.722787i	$0.742861\pi$
$72$	2.94389	0.346941
$73$	2.19297	0.256667	0.128334	−	0.991731i	$-0.459037\pi$
$73$	2.19297	0.256667	0.128334	+	0.991731i	$0.459037\pi$
$74$	14.9878	1.74230
$75$	3.14297	0.362919
$76$	−10.6029	−1.21623
$77$	5.04300	0.574703
$78$	−31.5690	−3.57448
$79$	−12.7320	−1.43246	−0.716231	−	0.697864i	$-0.754134\pi$
$79$	−12.7320	−1.43246	−0.716231	+	0.697864i	$0.754134\pi$
$80$	−4.39182	−0.491021
$81$	17.6758	1.96398
$82$	4.89566	0.540635
$83$	11.3641	1.24737	0.623684	−	0.781676i	$-0.285635\pi$
$83$	11.3641	1.24737	0.623684	+	0.781676i	$0.285635\pi$
$84$	5.59404	0.610360
$85$	−7.40852	−0.803566
$86$	23.3421	2.51704
$87$	−1.66718	−0.178741
$88$	2.15840	0.230086
$89$	−8.82411	−0.935353	−0.467677	−	0.883900i	$-0.654909\pi$
$89$	−8.82411	−0.935353	−0.467677	+	0.883900i	$0.654909\pi$
$90$	−13.3726	−1.40960
$91$	5.16633	0.541579
$92$	1.77986	0.185563
$93$	−7.86430	−0.815490
$94$	0.870094	0.0897434
$95$	−5.95715	−0.611191
$96$	24.1459	2.46439
$97$	0.311043	0.0315816	0.0157908	−	0.999875i	$-0.494973\pi$
$97$	0.311043	0.0315816	0.0157908	+	0.999875i	$0.494973\pi$
$98$	−1.94419	−0.196392
$99$	34.6871	3.48619
$100$	1.77986	0.177986
$101$	10.6475	1.05947	0.529734	−	0.848164i	$-0.322292\pi$
$101$	10.6475	1.05947	0.529734	+	0.848164i	$0.322292\pi$
$102$	45.2699	4.48239
$103$	6.48211	0.638702	0.319351	−	0.947637i	$-0.396535\pi$
$103$	6.48211	0.638702	0.319351	+	0.947637i	$0.396535\pi$
$104$	2.21119	0.216825
$105$	3.14297	0.306723
$106$	−6.19321	−0.601538
$107$	3.57572	0.345678	0.172839	−	0.984950i	$-0.444706\pi$
$107$	3.57572	0.345678	0.172839	+	0.984950i	$0.444706\pi$
$108$	21.6952	2.08762
$109$	−16.3022	−1.56146	−0.780732	−	0.624866i	$-0.785154\pi$
$109$	−16.3022	−1.56146	−0.780732	+	0.624866i	$0.785154\pi$
$110$	−9.80453	−0.934825
$111$	−24.2293	−2.29974
$112$	−4.39182	−0.414988
$113$	9.23606	0.868855	0.434428	−	0.900707i	$-0.356951\pi$
$113$	9.23606	0.868855	0.434428	+	0.900707i	$0.356951\pi$
$114$	36.4013	3.40930
$115$	1.00000	0.0932505
$116$	−0.944122	−0.0876595
$117$	35.5354	3.28525
$118$	−17.6885	−1.62836
$119$	−7.40852	−0.679138
$120$	1.34519	0.122798
$121$	14.4319	1.31199
$122$	1.18251	0.107060
$123$	−7.91432	−0.713610
$124$	−4.45353	−0.399939
$125$	1.00000	0.0894427
$126$	−13.3726	−1.19133
$127$	11.6407	1.03294	0.516471	−	0.856305i	$-0.327246\pi$
$127$	11.6407	1.03294	0.516471	+	0.856305i	$0.327246\pi$
$128$	−3.40325	−0.300808
$129$	−37.7348	−3.32236
$130$	−10.0443	−0.880944
$131$	−4.64570	−0.405896	−0.202948	−	0.979189i	$-0.565052\pi$
$131$	−4.64570	−0.405896	−0.202948	+	0.979189i	$0.565052\pi$
$132$	28.2108	2.45543
$133$	−5.95715	−0.516551
$134$	−17.2975	−1.49428
$135$	12.1893	1.04909
$136$	−3.17084	−0.271897
$137$	15.1704	1.29610	0.648049	−	0.761599i	$-0.275585\pi$
$137$	15.1704	1.29610	0.648049	+	0.761599i	$0.275585\pi$
$138$	−6.11052	−0.520162
$139$	−13.0649	−1.10815	−0.554076	−	0.832466i	$-0.686928\pi$
$139$	−13.0649	−1.10815	−0.554076	+	0.832466i	$0.686928\pi$
$140$	1.77986	0.150425
$141$	−1.40659	−0.118457
$142$	22.6423	1.90010
$143$	26.0538	2.17873
$144$	−30.2081	−2.51735
$145$	−0.530448	−0.0440513
$146$	−4.26353	−0.352852
$147$	3.14297	0.259228
$148$	−13.7210	−1.12786
$149$	−5.42943	−0.444796	−0.222398	−	0.974956i	$-0.571388\pi$
$149$	−5.42943	−0.444796	−0.222398	+	0.974956i	$0.571388\pi$
$150$	−6.11052	−0.498922
$151$	−7.75970	−0.631475	−0.315738	−	0.948847i	$-0.602252\pi$
$151$	−7.75970	−0.631475	−0.315738	+	0.948847i	$0.602252\pi$
$152$	−2.54966	−0.206804
$153$	−50.9578	−4.11969
$154$	−9.80453	−0.790072
$155$	−2.50219	−0.200980
$156$	28.9007	2.31391
$157$	0.406642	0.0324536	0.0162268	−	0.999868i	$-0.494835\pi$
$157$	0.406642	0.0324536	0.0162268	+	0.999868i	$0.494835\pi$
$158$	24.7534	1.96927
$159$	10.0119	0.793999
$160$	7.68252	0.607357
$161$	1.00000	0.0788110
$162$	−34.3650	−2.69997
$163$	−7.98179	−0.625182	−0.312591	−	0.949888i	$-0.601197\pi$
$163$	−7.98179	−0.625182	−0.312591	+	0.949888i	$0.601197\pi$
$164$	−4.48186	−0.349975
$165$	15.8500	1.23392
$166$	−22.0939	−1.71482
$167$	19.4806	1.50746	0.753728	−	0.657186i	$-0.228253\pi$
$167$	19.4806	1.50746	0.753728	+	0.657186i	$0.228253\pi$
$168$	1.34519	0.103784
$169$	13.6910	1.05315
$170$	14.4035	1.10470
$171$	−40.9749	−3.13343
$172$	−21.3691	−1.62938
$173$	13.0910	0.995289	0.497645	−	0.867381i	$-0.334198\pi$
$173$	13.0910	0.995289	0.497645	+	0.867381i	$0.334198\pi$
$174$	3.24131	0.245723
$175$	1.00000	0.0755929
$176$	−22.1480	−1.66947
$177$	28.5952	2.14935
$178$	17.1557	1.28587
$179$	9.39486	0.702205	0.351102	−	0.936337i	$-0.385807\pi$
$179$	9.39486	0.702205	0.351102	+	0.936337i	$0.385807\pi$
$180$	12.2423	0.912490
$181$	−1.41796	−0.105396	−0.0526980	−	0.998610i	$-0.516782\pi$
$181$	−1.41796	−0.105396	−0.0526980	+	0.998610i	$0.516782\pi$
$182$	−10.0443	−0.744534
$183$	−1.91165	−0.141313
$184$	0.427999	0.0315525
$185$	−7.70904	−0.566780
$186$	15.2897	1.12109
$187$	−37.3612	−2.73212
$188$	−0.796551	−0.0580945
$189$	12.1893	0.886641
$190$	11.5818	0.840233
$191$	9.82963	0.711247	0.355623	−	0.934629i	$-0.384269\pi$
$191$	9.82963	0.711247	0.355623	+	0.934629i	$0.384269\pi$
$192$	−19.3374	−1.39556
$193$	−9.16013	−0.659361	−0.329680	−	0.944093i	$-0.606941\pi$
$193$	−9.16013	−0.659361	−0.329680	+	0.944093i	$0.606941\pi$
$194$	−0.604724	−0.0434167
$195$	16.2376	1.16280
$196$	1.77986	0.127133
$197$	−13.4416	−0.957678	−0.478839	−	0.877903i	$-0.658942\pi$
$197$	−13.4416	−0.957678	−0.478839	+	0.877903i	$0.658942\pi$
$198$	−67.4382	−4.79262
$199$	−24.9572	−1.76917	−0.884584	−	0.466380i	$-0.845558\pi$
$199$	−24.9572	−1.76917	−0.884584	+	0.466380i	$0.845558\pi$
$200$	0.427999	0.0302641
$201$	27.9631	1.97237
$202$	−20.7008	−1.45650
$203$	−0.530448	−0.0372302
$204$	−41.4435	−2.90163
$205$	−2.51810	−0.175872
$206$	−12.6024	−0.878053
$207$	6.87827	0.478073
$208$	−22.6896	−1.57324
$209$	−30.0419	−2.07804
$210$	−6.11052	−0.421666
$211$	8.44102	0.581104	0.290552	−	0.956859i	$-0.406161\pi$
$211$	8.44102	0.581104	0.290552	+	0.956859i	$0.406161\pi$
$212$	5.66974	0.389399
$213$	−36.6035	−2.50803
$214$	−6.95187	−0.475220
$215$	−12.0061	−0.818808
$216$	5.21700	0.354972
$217$	−2.50219	−0.169860
$218$	31.6944	2.14662
$219$	6.89243	0.465747
$220$	8.97582	0.605150
$221$	−38.2749	−2.57465
$222$	47.1063	3.16157
$223$	−18.6671	−1.25004	−0.625022	−	0.780607i	$-0.714910\pi$
$223$	−18.6671	−1.25004	−0.625022	+	0.780607i	$0.714910\pi$
$224$	7.68252	0.513310
$225$	6.87827	0.458551
$226$	−17.9566	−1.19446
$227$	9.12684	0.605770	0.302885	−	0.953027i	$-0.402050\pi$
$227$	9.12684	0.605770	0.302885	+	0.953027i	$0.402050\pi$
$228$	−33.3246	−2.20697
$229$	15.7634	1.04168	0.520838	−	0.853656i	$-0.325620\pi$
$229$	15.7634	1.04168	0.520838	+	0.853656i	$0.325620\pi$
$230$	−1.94419	−0.128196
$231$	15.8500	1.04285
$232$	−0.227031	−0.0149053
$233$	8.02281	0.525592	0.262796	−	0.964851i	$-0.415355\pi$
$233$	8.02281	0.525592	0.262796	+	0.964851i	$0.415355\pi$
$234$	−69.0875	−4.51639
$235$	−0.447537	−0.0291941
$236$	16.1934	1.05410
$237$	−40.0163	−2.59934
$238$	14.4035	0.933642
$239$	−14.9685	−0.968230	−0.484115	−	0.875004i	$-0.660858\pi$
$239$	−14.9685	−0.968230	−0.484115	+	0.875004i	$0.660858\pi$
$240$	−13.8034	−0.891004
$241$	15.2912	0.984992	0.492496	−	0.870315i	$-0.336085\pi$
$241$	15.2912	0.984992	0.492496	+	0.870315i	$0.336085\pi$
$242$	−28.0582	−1.80365
$243$	18.9866	1.21799
$244$	−1.08256	−0.0693039
$245$	1.00000	0.0638877
$246$	15.3869	0.981034
$247$	−30.7767	−1.95827
$248$	−1.07093	−0.0680043
$249$	35.7169	2.26347
$250$	−1.94419	−0.122961
$251$	−4.04324	−0.255207	−0.127603	−	0.991825i	$-0.540728\pi$
$251$	−4.04324	−0.255207	−0.127603	+	0.991825i	$0.540728\pi$
$252$	12.2423	0.771195
$253$	5.04300	0.317051
$254$	−22.6316	−1.42003
$255$	−23.2848	−1.45815
$256$	18.9217	1.18261
$257$	2.26003	0.140977	0.0704883	−	0.997513i	$-0.477544\pi$
$257$	2.26003	0.140977	0.0704883	+	0.997513i	$0.477544\pi$
$258$	73.3634	4.56741
$259$	−7.70904	−0.479017
$260$	9.19534	0.570271
$261$	−3.64857	−0.225841
$262$	9.03209	0.558005
$263$	−1.40398	−0.0865733	−0.0432866	−	0.999063i	$-0.513783\pi$
$263$	−1.40398	−0.0865733	−0.0432866	+	0.999063i	$0.513783\pi$
$264$	6.78379	0.417513
$265$	3.18550	0.195684
$266$	11.5818	0.710127
$267$	−27.7339	−1.69729
$268$	15.8355	0.967304
$269$	−4.57252	−0.278792	−0.139396	−	0.990237i	$-0.544516\pi$
$269$	−4.57252	−0.278792	−0.139396	+	0.990237i	$0.544516\pi$
$270$	−23.6982	−1.44223
$271$	2.73006	0.165840	0.0829198	−	0.996556i	$-0.473575\pi$
$271$	2.73006	0.165840	0.0829198	+	0.996556i	$0.473575\pi$
$272$	32.5369	1.97284
$273$	16.2376	0.982747
$274$	−29.4941	−1.78181
$275$	5.04300	0.304104
$276$	5.59404	0.336722
$277$	−2.50328	−0.150408	−0.0752038	−	0.997168i	$-0.523961\pi$
$277$	−2.50328	−0.150408	−0.0752038	+	0.997168i	$0.523961\pi$
$278$	25.4006	1.52343
$279$	−17.2107	−1.03038
$280$	0.427999	0.0255778
$281$	−21.1512	−1.26177	−0.630886	−	0.775875i	$-0.717308\pi$
$281$	−21.1512	−1.26177	−0.630886	+	0.775875i	$0.717308\pi$
$282$	2.73468	0.162848
$283$	−15.3141	−0.910330	−0.455165	−	0.890407i	$-0.650420\pi$
$283$	−15.3141	−0.910330	−0.455165	+	0.890407i	$0.650420\pi$
$284$	−20.7285	−1.23001
$285$	−18.7232	−1.10906
$286$	−50.6535	−2.99520
$287$	−2.51810	−0.148639
$288$	52.8425	3.11377
$289$	37.8861	2.22859
$290$	1.03129	0.0605594
$291$	0.977598	0.0573078
$292$	3.90317	0.228415
$293$	−15.2609	−0.891551	−0.445776	−	0.895145i	$-0.647072\pi$
$293$	−15.2609	−0.891551	−0.445776	+	0.895145i	$0.647072\pi$
$294$	−6.11052	−0.356373
$295$	9.09814	0.529714
$296$	−3.29946	−0.191777
$297$	61.4706	3.56689
$298$	10.5558	0.611482
$299$	5.16633	0.298777
$300$	5.59404	0.322972
$301$	−12.0061	−0.692019
$302$	15.0863	0.868119
$303$	33.4649	1.92251
$304$	26.1628	1.50054
$305$	−0.608230	−0.0348271
$306$	99.0714	5.66353
$307$	0.864447	0.0493366	0.0246683	−	0.999696i	$-0.492147\pi$
$307$	0.864447	0.0493366	0.0246683	+	0.999696i	$0.492147\pi$
$308$	8.97582	0.511445
$309$	20.3731	1.15898
$310$	4.86472	0.276297
$311$	1.14203	0.0647588	0.0323794	−	0.999476i	$-0.489692\pi$
$311$	1.14203	0.0647588	0.0323794	+	0.999476i	$0.489692\pi$
$312$	6.94969	0.393449
$313$	18.8987	1.06822	0.534108	−	0.845416i	$-0.320647\pi$
$313$	18.8987	1.06822	0.534108	+	0.845416i	$0.320647\pi$
$314$	−0.790588	−0.0446154
$315$	6.87827	0.387547
$316$	−22.6611	−1.27479
$317$	−28.6859	−1.61116	−0.805581	−	0.592485i	$-0.798147\pi$
$317$	−28.6859	−1.61116	−0.805581	+	0.592485i	$0.798147\pi$
$318$	−19.4651	−1.09155
$319$	−2.67505	−0.149774
$320$	−6.15260	−0.343941
$321$	11.2384	0.627266
$322$	−1.94419	−0.108345
$323$	44.1337	2.45566
$324$	31.4604	1.74780
$325$	5.16633	0.286577
$326$	15.5181	0.859467
$327$	−51.2373	−2.83343
$328$	−1.07774	−0.0595085
$329$	−0.447537	−0.0246735
$330$	−30.8154	−1.69633
$331$	−30.3531	−1.66835	−0.834177	−	0.551496i	$-0.814057\pi$
$331$	−30.3531	−1.66835	−0.834177	+	0.551496i	$0.814057\pi$
$332$	20.2264	1.11007
$333$	−53.0249	−2.90575
$334$	−37.8740	−2.07237
$335$	8.89704	0.486097
$336$	−13.8034	−0.753036
$337$	−9.13589	−0.497664	−0.248832	−	0.968547i	$-0.580047\pi$
$337$	−9.13589	−0.497664	−0.248832	+	0.968547i	$0.580047\pi$
$338$	−26.6179	−1.44782
$339$	29.0287	1.57662
$340$	−13.1861	−0.715117
$341$	−12.6185	−0.683332
$342$	79.6628	4.30767
$343$	1.00000	0.0539949
$344$	−5.13859	−0.277054
$345$	3.14297	0.169212
$346$	−25.4513	−1.36827
$347$	11.3430	0.608927	0.304463	−	0.952524i	$-0.401523\pi$
$347$	11.3430	0.608927	0.304463	+	0.952524i	$0.401523\pi$
$348$	−2.96735	−0.159067
$349$	17.5361	0.938687	0.469343	−	0.883016i	$-0.344491\pi$
$349$	17.5361	0.938687	0.469343	+	0.883016i	$0.344491\pi$
$350$	−1.94419	−0.103921
$351$	62.9740	3.36130
$352$	38.7430	2.06501
$353$	18.9021	1.00606	0.503028	−	0.864270i	$-0.332219\pi$
$353$	18.9021	1.00606	0.503028	+	0.864270i	$0.332219\pi$
$354$	−55.5944	−2.95481
$355$	−11.6461	−0.618113
$356$	−15.7056	−0.832398
$357$	−23.2848	−1.23236
$358$	−18.2653	−0.965354
$359$	−19.3042	−1.01883	−0.509417	−	0.860520i	$-0.670139\pi$
$359$	−19.3042	−1.01883	−0.509417	+	0.860520i	$0.670139\pi$
$360$	2.94389	0.155157
$361$	16.4877	0.867773
$362$	2.75677	0.144893
$363$	45.3589	2.38073
$364$	9.19534	0.481967
$365$	2.19297	0.114785
$366$	3.71660	0.194270
$367$	22.5973	1.17957	0.589785	−	0.807560i	$-0.299212\pi$
$367$	22.5973	1.17957	0.589785	+	0.807560i	$0.299212\pi$
$368$	−4.39182	−0.228940
$369$	−17.3202	−0.901653
$370$	14.9878	0.779179
$371$	3.18550	0.165383
$372$	−13.9973	−0.725728
$373$	−24.2899	−1.25768	−0.628841	−	0.777534i	$-0.716470\pi$
$373$	−24.2899	−1.25768	−0.628841	+	0.777534i	$0.716470\pi$
$374$	72.6370	3.75597
$375$	3.14297	0.162302
$376$	−0.191545	−0.00987819
$377$	−2.74047	−0.141142
$378$	−23.6982	−1.21891
$379$	23.1242	1.18781	0.593904	−	0.804536i	$-0.297586\pi$
$379$	23.1242	1.18781	0.593904	+	0.804536i	$0.297586\pi$
$380$	−10.6029	−0.543916
$381$	36.5863	1.87437
$382$	−19.1106	−0.977784
$383$	−8.28642	−0.423416	−0.211708	−	0.977333i	$-0.567903\pi$
$383$	−8.28642	−0.423416	−0.211708	+	0.977333i	$0.567903\pi$
$384$	−10.6963	−0.545844
$385$	5.04300	0.257015
$386$	17.8090	0.906454
$387$	−82.5811	−4.19783
$388$	0.553611	0.0281054
$389$	−1.12935	−0.0572603	−0.0286302	−	0.999590i	$-0.509115\pi$
$389$	−1.12935	−0.0572603	−0.0286302	+	0.999590i	$0.509115\pi$
$390$	−31.5690	−1.59856
$391$	−7.40852	−0.374665
$392$	0.427999	0.0216172
$393$	−14.6013	−0.736538
$394$	26.1331	1.31656
$395$	−12.7320	−0.640616
$396$	61.7381	3.10246
$397$	−25.6772	−1.28870	−0.644352	−	0.764729i	$-0.722873\pi$
$397$	−25.6772	−1.28870	−0.644352	+	0.764729i	$0.722873\pi$
$398$	48.5214	2.43216
$399$	−18.7232	−0.937331
$400$	−4.39182	−0.219591
$401$	33.4131	1.66857	0.834286	−	0.551332i	$-0.185880\pi$
$401$	33.4131	1.66857	0.834286	+	0.551332i	$0.185880\pi$
$402$	−54.3655	−2.71151
$403$	−12.9271	−0.643946
$404$	18.9511	0.942852
$405$	17.6758	0.878317
$406$	1.03129	0.0511820
$407$	−38.8767	−1.92705
$408$	−9.96585	−0.493383
$409$	7.37691	0.364765	0.182382	−	0.983228i	$-0.441619\pi$
$409$	7.37691	0.364765	0.182382	+	0.983228i	$0.441619\pi$
$410$	4.89566	0.241779
$411$	47.6803	2.35189
$412$	11.5372	0.568399
$413$	9.09814	0.447690
$414$	−13.3726	−0.657229
$415$	11.3641	0.557840
$416$	39.6905	1.94599
$417$	−41.0627	−2.01085
$418$	58.4071	2.85678
$419$	25.2784	1.23493	0.617465	−	0.786598i	$-0.288160\pi$
$419$	25.2784	1.23493	0.617465	+	0.786598i	$0.288160\pi$
$420$	5.59404	0.272961
$421$	−7.23056	−0.352396	−0.176198	−	0.984355i	$-0.556380\pi$
$421$	−7.23056	−0.352396	−0.176198	+	0.984355i	$0.556380\pi$
$422$	−16.4109	−0.798871
$423$	−3.07828	−0.149671
$424$	1.36339	0.0662122
$425$	−7.40852	−0.359366
$426$	71.1640	3.44791
$427$	−0.608230	−0.0294343
$428$	6.36428	0.307629
$429$	81.8864	3.95352
$430$	23.3421	1.12565
$431$	−4.36305	−0.210161	−0.105080	−	0.994464i	$-0.533510\pi$
$431$	−4.36305	−0.210161	−0.105080	+	0.994464i	$0.533510\pi$
$432$	−53.5332	−2.57562
$433$	28.2564	1.35792	0.678958	−	0.734177i	$-0.262432\pi$
$433$	28.2564	1.35792	0.678958	+	0.734177i	$0.262432\pi$
$434$	4.86472	0.233514
$435$	−1.66718	−0.0799353
$436$	−29.0155	−1.38959
$437$	−5.95715	−0.284969
$438$	−13.4002	−0.640284
$439$	13.3733	0.638274	0.319137	−	0.947709i	$-0.396607\pi$
$439$	13.3733	0.638274	0.319137	+	0.947709i	$0.396607\pi$
$440$	2.15840	0.102898
$441$	6.87827	0.327537
$442$	74.4134	3.53949
$443$	1.32542	0.0629725	0.0314863	−	0.999504i	$-0.489976\pi$
$443$	1.32542	0.0629725	0.0314863	+	0.999504i	$0.489976\pi$
$444$	−43.1247	−2.04661
$445$	−8.82411	−0.418303
$446$	36.2924	1.71849
$447$	−17.0645	−0.807125
$448$	−6.15260	−0.290683
$449$	−32.6030	−1.53863	−0.769316	−	0.638869i	$-0.779403\pi$
$449$	−32.6030	−1.53863	−0.769316	+	0.638869i	$0.779403\pi$
$450$	−13.3726	−0.630392
$451$	−12.6988	−0.597963
$452$	16.4389	0.773219
$453$	−24.3885	−1.14587
$454$	−17.7443	−0.832780
$455$	5.16633	0.242201
$456$	−8.01350	−0.375266
$457$	14.9331	0.698539	0.349270	−	0.937022i	$-0.386430\pi$
$457$	14.9331	0.698539	0.349270	+	0.937022i	$0.386430\pi$
$458$	−30.6470	−1.43204
$459$	−90.3046	−4.21506
$460$	1.77986	0.0829863
$461$	11.7746	0.548397	0.274198	−	0.961673i	$-0.411588\pi$
$461$	11.7746	0.548397	0.274198	+	0.961673i	$0.411588\pi$
$462$	−30.8154	−1.43366
$463$	18.6450	0.866507	0.433253	−	0.901272i	$-0.357366\pi$
$463$	18.6450	0.866507	0.433253	+	0.901272i	$0.357366\pi$
$464$	2.32963	0.108151
$465$	−7.86430	−0.364698
$466$	−15.5978	−0.722556
$467$	29.8213	1.37997	0.689983	−	0.723826i	$-0.257618\pi$
$467$	29.8213	1.37997	0.689983	+	0.723826i	$0.257618\pi$
$468$	63.2480	2.92364
$469$	8.89704	0.410827
$470$	0.870094	0.0401345
$471$	1.27806	0.0588901
$472$	3.89399	0.179236
$473$	−60.5467	−2.78394
$474$	77.7991	3.57343
$475$	−5.95715	−0.273333
$476$	−13.1861	−0.604384
$477$	21.9108	1.00322
$478$	29.1015	1.33107
$479$	−29.2381	−1.33592	−0.667962	−	0.744196i	$-0.732833\pi$
$479$	−29.2381	−1.33592	−0.667962	+	0.744196i	$0.732833\pi$
$480$	24.1459	1.10211
$481$	−39.8275	−1.81598
$482$	−29.7289	−1.35411
$483$	3.14297	0.143010
$484$	25.6867	1.16758
$485$	0.311043	0.0141237
$486$	−36.9135	−1.67443
$487$	33.4212	1.51446	0.757230	−	0.653148i	$-0.226552\pi$
$487$	33.4212	1.51446	0.757230	+	0.653148i	$0.226552\pi$
$488$	−0.260322	−0.0117842
$489$	−25.0865	−1.13445
$490$	−1.94419	−0.0878293
$491$	−37.8236	−1.70696	−0.853478	−	0.521129i	$-0.825511\pi$
$491$	−37.8236	−1.70696	−0.853478	+	0.521129i	$0.825511\pi$
$492$	−14.0864	−0.635062
$493$	3.92983	0.176991
$494$	59.8355	2.69213
$495$	34.6871	1.55907
$496$	10.9892	0.493428
$497$	−11.6461	−0.522401
$498$	−69.4404	−3.11170
$499$	29.1092	1.30311	0.651554	−	0.758602i	$-0.274117\pi$
$499$	29.1092	1.30311	0.651554	+	0.758602i	$0.274117\pi$
$500$	1.77986	0.0795976
$501$	61.2271	2.73542
$502$	7.86080	0.350845
$503$	2.48542	0.110819	0.0554097	−	0.998464i	$-0.482354\pi$
$503$	2.48542	0.110819	0.0554097	+	0.998464i	$0.482354\pi$
$504$	2.94389	0.131131
$505$	10.6475	0.473809
$506$	−9.80453	−0.435865
$507$	43.0305	1.91105
$508$	20.7187	0.919244
$509$	−22.6080	−1.00208	−0.501041	−	0.865423i	$-0.667050\pi$
$509$	−22.6080	−1.00208	−0.501041	+	0.865423i	$0.667050\pi$
$510$	45.2699	2.00458
$511$	2.19297	0.0970111
$512$	−29.9809	−1.32498
$513$	−72.6135	−3.20596
$514$	−4.39391	−0.193807
$515$	6.48211	0.285636
$516$	−67.1625	−2.95667
$517$	−2.25693	−0.0992596
$518$	14.9878	0.658527
$519$	41.1446	1.80605
$520$	2.21119	0.0969669
$521$	17.5034	0.766836	0.383418	−	0.923575i	$-0.374747\pi$
$521$	17.5034	0.766836	0.383418	+	0.923575i	$0.374747\pi$
$522$	7.09349	0.310474
$523$	11.4367	0.500092	0.250046	−	0.968234i	$-0.419554\pi$
$523$	11.4367	0.500092	0.250046	+	0.968234i	$0.419554\pi$
$524$	−8.26867	−0.361219
$525$	3.14297	0.137171
$526$	2.72960	0.119016
$527$	18.5375	0.807506
$528$	−69.6104	−3.02941
$529$	1.00000	0.0434783
$530$	−6.19321	−0.269016
$531$	62.5795	2.71572
$532$	−10.6029	−0.459693
$533$	−13.0094	−0.563498
$534$	53.9199	2.33334
$535$	3.57572	0.154592
$536$	3.80792	0.164477
$537$	29.5278	1.27422
$538$	8.88983	0.383268
$539$	5.04300	0.217217
$540$	21.6952	0.933613
$541$	−17.5272	−0.753554	−0.376777	−	0.926304i	$-0.622968\pi$
$541$	−17.5272	−0.753554	−0.376777	+	0.926304i	$0.622968\pi$
$542$	−5.30775	−0.227987
$543$	−4.45660	−0.191251
$544$	−56.9161	−2.44026
$545$	−16.3022	−0.698308
$546$	−31.5690	−1.35103
$547$	24.2529	1.03698	0.518490	−	0.855084i	$-0.326494\pi$
$547$	24.2529	1.03698	0.518490	+	0.855084i	$0.326494\pi$
$548$	27.0012	1.15343
$549$	−4.18357	−0.178550
$550$	−9.80453	−0.418067
$551$	3.15996	0.134619
$552$	1.34519	0.0572550
$553$	−12.7320	−0.541419
$554$	4.86684	0.206772
$555$	−24.2293	−1.02848
$556$	−23.2537	−0.986176
$557$	−0.566871	−0.0240191	−0.0120095	−	0.999928i	$-0.503823\pi$
$557$	−0.566871	−0.0240191	−0.0120095	+	0.999928i	$0.503823\pi$
$558$	33.4608	1.41651
$559$	−62.0275	−2.62348
$560$	−4.39182	−0.185588
$561$	−117.425	−4.95769
$562$	41.1218	1.73462
$563$	−3.50133	−0.147564	−0.0737818	−	0.997274i	$-0.523507\pi$
$563$	−3.50133	−0.147564	−0.0737818	+	0.997274i	$0.523507\pi$
$564$	−2.50354	−0.105418
$565$	9.23606	0.388564
$566$	29.7735	1.25147
$567$	17.6758	0.742314
$568$	−4.98454	−0.209146
$569$	2.12576	0.0891167	0.0445583	−	0.999007i	$-0.485812\pi$
$569$	2.12576	0.0891167	0.0445583	+	0.999007i	$0.485812\pi$
$570$	36.4013	1.52468
$571$	40.2659	1.68508	0.842538	−	0.538637i	$-0.181060\pi$
$571$	40.2659	1.68508	0.842538	+	0.538637i	$0.181060\pi$
$572$	46.3721	1.93891
$573$	30.8942	1.29063
$574$	4.89566	0.204341
$575$	1.00000	0.0417029
$576$	−42.3192	−1.76330
$577$	9.15195	0.381001	0.190500	−	0.981687i	$-0.438989\pi$
$577$	9.15195	0.381001	0.190500	+	0.981687i	$0.438989\pi$
$578$	−73.6576	−3.06375
$579$	−28.7900	−1.19647
$580$	−0.944122	−0.0392025
$581$	11.3641	0.471461
$582$	−1.90063	−0.0787837
$583$	16.0645	0.665324
$584$	0.938587	0.0388390
$585$	35.5354	1.46921
$586$	29.6700	1.22566
$587$	−39.2431	−1.61973	−0.809867	−	0.586613i	$-0.800461\pi$
$587$	−39.2431	−1.61973	−0.809867	+	0.586613i	$0.800461\pi$
$588$	5.59404	0.230694
$589$	14.9059	0.614187
$590$	−17.6885	−0.728223
$591$	−42.2467	−1.73780
$592$	33.8568	1.39150
$593$	−0.976958	−0.0401189	−0.0200594	−	0.999799i	$-0.506386\pi$
$593$	−0.976958	−0.0401189	−0.0200594	+	0.999799i	$0.506386\pi$
$594$	−119.510	−4.90357
$595$	−7.40852	−0.303720
$596$	−9.66360	−0.395837
$597$	−78.4398	−3.21033
$598$	−10.0443	−0.410742
$599$	12.0845	0.493761	0.246880	−	0.969046i	$-0.420595\pi$
$599$	12.0845	0.493761	0.246880	+	0.969046i	$0.420595\pi$
$600$	1.34519	0.0549171
$601$	15.0070	0.612147	0.306073	−	0.952008i	$-0.400985\pi$
$601$	15.0070	0.612147	0.306073	+	0.952008i	$0.400985\pi$
$602$	23.3421	0.951351
$603$	61.1962	2.49210
$604$	−13.8112	−0.561968
$605$	14.4319	0.586739
$606$	−65.0619	−2.64296
$607$	−12.6519	−0.513527	−0.256763	−	0.966474i	$-0.582656\pi$
$607$	−12.6519	−0.513527	−0.256763	+	0.966474i	$0.582656\pi$
$608$	−45.7660	−1.85605
$609$	−1.66718	−0.0675577
$610$	1.18251	0.0478785
$611$	−2.31212	−0.0935385
$612$	−90.6976	−3.66623
$613$	−36.0668	−1.45672	−0.728362	−	0.685193i	$-0.759718\pi$
$613$	−36.0668	−1.45672	−0.728362	+	0.685193i	$0.759718\pi$
$614$	−1.68064	−0.0678253
$615$	−7.91432	−0.319136
$616$	2.15840	0.0869644
$617$	−23.5891	−0.949662	−0.474831	−	0.880077i	$-0.657491\pi$
$617$	−23.5891	−0.949662	−0.474831	+	0.880077i	$0.657491\pi$
$618$	−39.6091	−1.59331
$619$	−34.8635	−1.40128	−0.700642	−	0.713513i	$-0.747103\pi$
$619$	−34.8635	−1.40128	−0.700642	+	0.713513i	$0.747103\pi$
$620$	−4.45353	−0.178858
$621$	12.1893	0.489140
$622$	−2.22033	−0.0890270
$623$	−8.82411	−0.353530
$624$	−71.3129	−2.85480
$625$	1.00000	0.0400000
$626$	−36.7425	−1.46853
$627$	−94.4210	−3.77081
$628$	0.723765	0.0288814
$629$	57.1126	2.27723
$630$	−13.3726	−0.532778
$631$	22.3875	0.891232	0.445616	−	0.895224i	$-0.352985\pi$
$631$	22.3875	0.891232	0.445616	+	0.895224i	$0.352985\pi$
$632$	−5.44928	−0.216761
$633$	26.5299	1.05447
$634$	55.7708	2.21494
$635$	11.6407	0.461945
$636$	17.8198	0.706602
$637$	5.16633	0.204698
$638$	5.20080	0.205901
$639$	−80.1053	−3.16892
$640$	−3.40325	−0.134525
$641$	−30.8870	−1.21996	−0.609982	−	0.792415i	$-0.708823\pi$
$641$	−30.8870	−1.21996	−0.609982	+	0.792415i	$0.708823\pi$
$642$	−21.8495	−0.862332
$643$	12.1660	0.479779	0.239890	−	0.970800i	$-0.422889\pi$
$643$	12.1660	0.479779	0.239890	+	0.970800i	$0.422889\pi$
$644$	1.77986	0.0701362
$645$	−37.7348	−1.48581
$646$	−85.8040	−3.37592
$647$	40.6310	1.59737	0.798684	−	0.601750i	$-0.205530\pi$
$647$	40.6310	1.59737	0.798684	+	0.601750i	$0.205530\pi$
$648$	7.56522	0.297190
$649$	45.8819	1.80102
$650$	−10.0443	−0.393970
$651$	−7.86430	−0.308226
$652$	−14.2064	−0.556367
$653$	48.5813	1.90113	0.950566	−	0.310523i	$-0.100504\pi$
$653$	48.5813	1.90113	0.950566	+	0.310523i	$0.100504\pi$
$654$	99.6147	3.89524
$655$	−4.64570	−0.181522
$656$	11.0591	0.431784
$657$	15.0838	0.588476
$658$	0.870094	0.0339198
$659$	−4.35252	−0.169550	−0.0847751	−	0.996400i	$-0.527017\pi$
$659$	−4.35252	−0.169550	−0.0847751	+	0.996400i	$0.527017\pi$
$660$	28.2108	1.09810
$661$	−21.2747	−0.827489	−0.413745	−	0.910393i	$-0.635779\pi$
$661$	−21.2747	−0.827489	−0.413745	+	0.910393i	$0.635779\pi$
$662$	59.0120	2.29357
$663$	−120.297	−4.67194
$664$	4.86381	0.188752
$665$	−5.95715	−0.231009
$666$	103.090	3.99466
$667$	−0.530448	−0.0205390
$668$	34.6727	1.34153
$669$	−58.6703	−2.26832
$670$	−17.2975	−0.668260
$671$	−3.06730	−0.118412
$672$	24.1459	0.931450
$673$	−2.18169	−0.0840978	−0.0420489	−	0.999116i	$-0.513389\pi$
$673$	−2.18169	−0.0840978	−0.0420489	+	0.999116i	$0.513389\pi$
$674$	17.7619	0.684161
$675$	12.1893	0.469166
$676$	24.3680	0.937232
$677$	−14.7555	−0.567100	−0.283550	−	0.958957i	$-0.591512\pi$
$677$	−14.7555	−0.567100	−0.283550	+	0.958957i	$0.591512\pi$
$678$	−56.4371	−2.16745
$679$	0.311043	0.0119367
$680$	−3.17084	−0.121596
$681$	28.6854	1.09923
$682$	24.5328	0.939408
$683$	28.7762	1.10109	0.550545	−	0.834805i	$-0.314420\pi$
$683$	28.7762	1.10109	0.550545	+	0.834805i	$0.314420\pi$
$684$	−72.9295	−2.78853
$685$	15.1704	0.579633
$686$	−1.94419	−0.0742293
$687$	49.5440	1.89022
$688$	52.7286	2.01026
$689$	16.4574	0.626976
$690$	−6.11052	−0.232624
$691$	7.01608	0.266904	0.133452	−	0.991055i	$-0.457394\pi$
$691$	7.01608	0.266904	0.133452	+	0.991055i	$0.457394\pi$
$692$	23.3001	0.885736
$693$	34.6871	1.31766
$694$	−22.0530	−0.837120
$695$	−13.0649	−0.495581
$696$	−0.713553	−0.0270471
$697$	18.6554	0.706624
$698$	−34.0935	−1.29046
$699$	25.2155	0.953737
$700$	1.77986	0.0672723
$701$	3.23603	0.122223	0.0611116	−	0.998131i	$-0.480535\pi$
$701$	3.23603	0.122223	0.0611116	+	0.998131i	$0.480535\pi$
$702$	−122.433	−4.62094
$703$	45.9240	1.73206
$704$	−31.0276	−1.16940
$705$	−1.40659	−0.0529754
$706$	−36.7491	−1.38307
$707$	10.6475	0.400442
$708$	50.8954	1.91277
$709$	−43.6457	−1.63915	−0.819574	−	0.572973i	$-0.805790\pi$
$709$	−43.6457	−1.63915	−0.819574	+	0.572973i	$0.805790\pi$
$710$	22.6423	0.849749
$711$	−87.5741	−3.28429
$712$	−3.77671	−0.141538
$713$	−2.50219	−0.0937076
$714$	45.2699	1.69418
$715$	26.0538	0.974358
$716$	16.7215	0.624912
$717$	−47.0455	−1.75695
$718$	37.5309	1.40064
$719$	29.1660	1.08771	0.543855	−	0.839179i	$-0.316964\pi$
$719$	29.1660	1.08771	0.543855	+	0.839179i	$0.316964\pi$
$720$	−30.2081	−1.12579
$721$	6.48211	0.241406
$722$	−32.0551	−1.19297
$723$	48.0598	1.78736
$724$	−2.52376	−0.0937948
$725$	−0.530448	−0.0197004
$726$	−88.1862	−3.27290
$727$	−2.02255	−0.0750124	−0.0375062	−	0.999296i	$-0.511941\pi$
$727$	−2.02255	−0.0750124	−0.0375062	+	0.999296i	$0.511941\pi$
$728$	2.21119	0.0819520
$729$	6.64708	0.246188
$730$	−4.26353	−0.157800
$731$	88.9473	3.28983
$732$	−3.40246	−0.125759
$733$	−12.7007	−0.469110	−0.234555	−	0.972103i	$-0.575363\pi$
$733$	−12.7007	−0.469110	−0.234555	+	0.972103i	$0.575363\pi$
$734$	−43.9334	−1.62161
$735$	3.14297	0.115930
$736$	7.68252	0.283181
$737$	44.8678	1.65273
$738$	33.6737	1.23954
$739$	47.5708	1.74992	0.874959	−	0.484196i	$-0.160888\pi$
$739$	47.5708	1.74992	0.874959	+	0.484196i	$0.160888\pi$
$740$	−13.7210	−0.504394
$741$	−96.7301	−3.55347
$742$	−6.19321	−0.227360
$743$	−11.4669	−0.420679	−0.210340	−	0.977628i	$-0.567457\pi$
$743$	−11.4669	−0.420679	−0.210340	+	0.977628i	$0.567457\pi$
$744$	−3.36591	−0.123400
$745$	−5.42943	−0.198919
$746$	47.2240	1.72899
$747$	78.1651	2.85991
$748$	−66.4975	−2.43139
$749$	3.57572	0.130654
$750$	−6.11052	−0.223125
$751$	−19.6031	−0.715328	−0.357664	−	0.933850i	$-0.616427\pi$
$751$	−19.6031	−0.715328	−0.357664	+	0.933850i	$0.616427\pi$
$752$	1.96550	0.0716745
$753$	−12.7078	−0.463097
$754$	5.32799	0.194034
$755$	−7.75970	−0.282404
$756$	21.6952	0.789047
$757$	−29.6403	−1.07730	−0.538648	−	0.842531i	$-0.681065\pi$
$757$	−29.6403	−1.07730	−0.538648	+	0.842531i	$0.681065\pi$
$758$	−44.9577	−1.63294
$759$	15.8500	0.575319
$760$	−2.54966	−0.0924857
$761$	7.71654	0.279724	0.139862	−	0.990171i	$-0.455334\pi$
$761$	7.71654	0.279724	0.139862	+	0.990171i	$0.455334\pi$
$762$	−71.1305	−2.57678
$763$	−16.3022	−0.590178
$764$	17.4953	0.632959
$765$	−50.9578	−1.84238
$766$	16.1103	0.582090
$767$	47.0040	1.69722
$768$	59.4705	2.14596
$769$	−13.8155	−0.498199	−0.249099	−	0.968478i	$-0.580135\pi$
$769$	−13.8155	−0.498199	−0.249099	+	0.968478i	$0.580135\pi$
$770$	−9.80453	−0.353331
$771$	7.10320	0.255816
$772$	−16.3037	−0.586784
$773$	0.277957	0.00999743	0.00499872	−	0.999988i	$-0.498409\pi$
$773$	0.277957	0.00999743	0.00499872	+	0.999988i	$0.498409\pi$
$774$	160.553	5.77096
$775$	−2.50219	−0.0898812
$776$	0.133126	0.00477894
$777$	−24.2293	−0.869221
$778$	2.19567	0.0787184
$779$	15.0007	0.537457
$780$	28.9007	1.03481
$781$	−58.7315	−2.10158
$782$	14.4035	0.515069
$783$	−6.46579	−0.231068
$784$	−4.39182	−0.156851
$785$	0.406642	0.0145137
$786$	28.3876	1.01255
$787$	−28.3986	−1.01230	−0.506150	−	0.862445i	$-0.668932\pi$
$787$	−28.3986	−1.01230	−0.506150	+	0.862445i	$0.668932\pi$
$788$	−23.9242	−0.852265
$789$	−4.41268	−0.157095
$790$	24.7534	0.880685
$791$	9.23606	0.328396
$792$	14.8461	0.527532
$793$	−3.14232	−0.111587
$794$	49.9213	1.77164
$795$	10.0119	0.355087
$796$	−44.4202	−1.57443
$797$	−1.41540	−0.0501359	−0.0250679	−	0.999686i	$-0.507980\pi$
$797$	−1.41540	−0.0501359	−0.0250679	+	0.999686i	$0.507980\pi$
$798$	36.4013	1.28859
$799$	3.31558	0.117297
$800$	7.68252	0.271618
$801$	−60.6946	−2.14454
$802$	−64.9613	−2.29386
$803$	11.0591	0.390268
$804$	49.7704	1.75527
$805$	1.00000	0.0352454
$806$	25.1327	0.885263
$807$	−14.3713	−0.505894
$808$	4.55713	0.160319
$809$	−15.2153	−0.534943	−0.267471	−	0.963566i	$-0.586188\pi$
$809$	−15.2153	−0.534943	−0.267471	+	0.963566i	$0.586188\pi$
$810$	−34.3650	−1.20746
$811$	37.9639	1.33309	0.666546	−	0.745464i	$-0.267772\pi$
$811$	37.9639	1.33309	0.666546	+	0.745464i	$0.267772\pi$
$812$	−0.944122	−0.0331322
$813$	8.58051	0.300932
$814$	75.5835	2.64920
$815$	−7.98179	−0.279590
$816$	102.263	3.57990
$817$	71.5221	2.50224
$818$	−14.3421	−0.501459
$819$	35.5354	1.24171
$820$	−4.48186	−0.156513
$821$	−13.5801	−0.473948	−0.236974	−	0.971516i	$-0.576156\pi$
$821$	−13.5801	−0.473948	−0.236974	+	0.971516i	$0.576156\pi$
$822$	−92.6993	−3.23326
$823$	29.0522	1.01270	0.506348	−	0.862329i	$-0.330995\pi$
$823$	29.0522	1.01270	0.506348	+	0.862329i	$0.330995\pi$
$824$	2.77434	0.0966486
$825$	15.8500	0.551827
$826$	−17.6885	−0.615461
$827$	17.7076	0.615754	0.307877	−	0.951426i	$-0.400381\pi$
$827$	17.7076	0.615754	0.307877	+	0.951426i	$0.400381\pi$
$828$	12.2423	0.425451
$829$	35.0658	1.21788	0.608942	−	0.793215i	$-0.291594\pi$
$829$	35.0658	1.21788	0.608942	+	0.793215i	$0.291594\pi$
$830$	−22.0939	−0.766889
$831$	−7.86774	−0.272929
$832$	−31.7864	−1.10199
$833$	−7.40852	−0.256690
$834$	79.8335	2.76441
$835$	19.4806	0.674155
$836$	−53.4704	−1.84931
$837$	−30.4999	−1.05423
$838$	−49.1459	−1.69772
$839$	39.5105	1.36406	0.682028	−	0.731326i	$-0.261098\pi$
$839$	39.5105	1.36406	0.682028	+	0.731326i	$0.261098\pi$
$840$	1.34519	0.0464134
$841$	−28.7186	−0.990297
$842$	14.0576	0.484455
$843$	−66.4775	−2.28961
$844$	15.0238	0.517141
$845$	13.6910	0.470985
$846$	5.98474	0.205760
$847$	14.4319	0.495885
$848$	−13.9902	−0.480424
$849$	−48.1318	−1.65188
$850$	14.4035	0.494037
$851$	−7.70904	−0.264263
$852$	−65.1490	−2.23197
$853$	10.1115	0.346210	0.173105	−	0.984903i	$-0.444620\pi$
$853$	10.1115	0.346210	0.173105	+	0.984903i	$0.444620\pi$
$854$	1.18251	0.0404647
$855$	−40.9749	−1.40131
$856$	1.53041	0.0523082
$857$	−1.15123	−0.0393253	−0.0196626	−	0.999807i	$-0.506259\pi$
$857$	−1.15123	−0.0393253	−0.0196626	+	0.999807i	$0.506259\pi$
$858$	−159.202	−5.43508
$859$	23.4595	0.800427	0.400213	−	0.916422i	$-0.368936\pi$
$859$	23.4595	0.800427	0.400213	+	0.916422i	$0.368936\pi$
$860$	−21.3691	−0.728681
$861$	−7.91432	−0.269719
$862$	8.48258	0.288918
$863$	24.7076	0.841056	0.420528	−	0.907280i	$-0.361845\pi$
$863$	24.7076	0.841056	0.420528	+	0.907280i	$0.361845\pi$
$864$	93.6445	3.18585
$865$	13.0910	0.445107
$866$	−54.9357	−1.86679
$867$	119.075	4.04400
$868$	−4.45353	−0.151163
$869$	−64.2075	−2.17809
$870$	3.24131	0.109891
$871$	45.9651	1.55747
$872$	−6.97731	−0.236282
$873$	2.13943	0.0724089
$874$	11.5818	0.391761
$875$	1.00000	0.0338062
$876$	12.2675	0.414482
$877$	−25.4010	−0.857730	−0.428865	−	0.903369i	$-0.641086\pi$
$877$	−25.4010	−0.857730	−0.428865	+	0.903369i	$0.641086\pi$
$878$	−26.0002	−0.877465
$879$	−47.9646	−1.61781
$880$	−22.1480	−0.746608
$881$	15.9437	0.537157	0.268578	−	0.963258i	$-0.413446\pi$
$881$	15.9437	0.537157	0.268578	+	0.963258i	$0.413446\pi$
$882$	−13.3726	−0.450280
$883$	1.07098	0.0360413	0.0180207	−	0.999838i	$-0.494264\pi$
$883$	1.07098	0.0360413	0.0180207	+	0.999838i	$0.494264\pi$
$884$	−68.1238	−2.29125
$885$	28.5952	0.961217
$886$	−2.57686	−0.0865713
$887$	−3.40945	−0.114478	−0.0572390	−	0.998361i	$-0.518230\pi$
$887$	−3.40945	−0.114478	−0.0572390	+	0.998361i	$0.518230\pi$
$888$	−10.3701	−0.347998
$889$	11.6407	0.390415
$890$	17.1557	0.575060
$891$	89.1391	2.98627
$892$	−33.2248	−1.11245
$893$	2.66604	0.0892158
$894$	33.1766	1.10959
$895$	9.39486	0.314036
$896$	−3.40325	−0.113695
$897$	16.2376	0.542159
$898$	63.3863	2.11523
$899$	1.32728	0.0442673
$900$	12.2423	0.408078
$901$	−23.5999	−0.786225
$902$	24.6888	0.822047
$903$	−37.7348	−1.25574
$904$	3.95302	0.131476
$905$	−1.41796	−0.0471345
$906$	47.4158	1.57528
$907$	25.9480	0.861588	0.430794	−	0.902450i	$-0.358234\pi$
$907$	25.9480	0.861588	0.430794	+	0.902450i	$0.358234\pi$
$908$	16.2445	0.539092
$909$	73.2366	2.42910
$910$	−10.0443	−0.332966
$911$	49.1856	1.62959	0.814796	−	0.579747i	$-0.196849\pi$
$911$	49.1856	1.62959	0.814796	+	0.579747i	$0.196849\pi$
$912$	82.2288	2.72287
$913$	57.3090	1.89665
$914$	−29.0326	−0.960314
$915$	−1.91165	−0.0631972
$916$	28.0566	0.927017
$917$	−4.64570	−0.153414
$918$	175.569	5.79464
$919$	37.6572	1.24220	0.621099	−	0.783732i	$-0.286687\pi$
$919$	37.6572	1.24220	0.621099	+	0.783732i	$0.286687\pi$
$920$	0.427999	0.0141107
$921$	2.71693	0.0895259
$922$	−22.8920	−0.753907
$923$	−60.1679	−1.98045
$924$	28.2108	0.928066
$925$	−7.70904	−0.253472
$926$	−36.2493	−1.19123
$927$	44.5857	1.46439
$928$	−4.07518	−0.133774
$929$	24.0884	0.790315	0.395158	−	0.918613i	$-0.370690\pi$
$929$	24.0884	0.790315	0.395158	+	0.918613i	$0.370690\pi$
$930$	15.2897	0.501368
$931$	−5.95715	−0.195238
$932$	14.2795	0.467739
$933$	3.58938	0.117511
$934$	−57.9782	−1.89710
$935$	−37.3612	−1.22184
$936$	15.2091	0.497126
$937$	−50.6719	−1.65538	−0.827689	−	0.561187i	$-0.810345\pi$
$937$	−50.6719	−1.65538	−0.827689	+	0.561187i	$0.810345\pi$
$938$	−17.2975	−0.564783
$939$	59.3980	1.93838
$940$	−0.796551	−0.0259806
$941$	−12.8659	−0.419416	−0.209708	−	0.977764i	$-0.567251\pi$
$941$	−12.8659	−0.419416	−0.209708	+	0.977764i	$0.567251\pi$
$942$	−2.48479	−0.0809590
$943$	−2.51810	−0.0820007
$944$	−39.9574	−1.30050
$945$	12.1893	0.396518
$946$	117.714	3.82721
$947$	−26.0239	−0.845662	−0.422831	−	0.906208i	$-0.638964\pi$
$947$	−26.0239	−0.845662	−0.422831	+	0.906208i	$0.638964\pi$
$948$	−71.2233	−2.31322
$949$	11.3296	0.367774
$950$	11.5818	0.375764
$951$	−90.1591	−2.92361
$952$	−3.17084	−0.102767
$953$	35.4926	1.14972	0.574860	−	0.818252i	$-0.305057\pi$
$953$	35.4926	1.14972	0.574860	+	0.818252i	$0.305057\pi$
$954$	−42.5986	−1.37918
$955$	9.82963	0.318079
$956$	−26.6417	−0.861656
$957$	−8.40761	−0.271779
$958$	56.8443	1.83656
$959$	15.1704	0.489879
$960$	−19.3374	−0.624113
$961$	−24.7391	−0.798034
$962$	77.4320	2.49651
$963$	24.5948	0.792556
$964$	27.2161	0.876572
$965$	−9.16013	−0.294875
$966$	−6.11052	−0.196603
$967$	16.6338	0.534906	0.267453	−	0.963571i	$-0.413818\pi$
$967$	16.6338	0.534906	0.267453	+	0.963571i	$0.413818\pi$
$968$	6.17682	0.198531
$969$	138.711	4.45604
$970$	−0.604724	−0.0194165
$971$	−4.71252	−0.151232	−0.0756160	−	0.997137i	$-0.524092\pi$
$971$	−4.71252	−0.151232	−0.0756160	+	0.997137i	$0.524092\pi$
$972$	33.7935	1.08393
$973$	−13.0649	−0.418842
$974$	−64.9770	−2.08200
$975$	16.2376	0.520021
$976$	2.67124	0.0855042
$977$	−52.1856	−1.66957	−0.834783	−	0.550579i	$-0.814407\pi$
$977$	−52.1856	−1.66957	−0.834783	+	0.550579i	$0.814407\pi$
$978$	48.7729	1.55959
$979$	−44.5000	−1.42223
$980$	1.77986	0.0568554
$981$	−112.131	−3.58006
$982$	73.5361	2.34663
$983$	−36.3079	−1.15804	−0.579021	−	0.815313i	$-0.696565\pi$
$983$	−36.3079	−1.15804	−0.579021	+	0.815313i	$0.696565\pi$
$984$	−3.38732	−0.107984
$985$	−13.4416	−0.428287
$986$	−7.64033	−0.243318
$987$	−1.40659	−0.0447724
$988$	−54.7780	−1.74272
$989$	−12.0061	−0.381771
$990$	−67.4382	−2.14333
$991$	−53.2485	−1.69149	−0.845746	−	0.533585i	$-0.820844\pi$
$991$	−53.2485	−1.69149	−0.845746	+	0.533585i	$0.820844\pi$
$992$	−19.2231	−0.610334
$993$	−95.3988	−3.02739
$994$	22.6423	0.718169
$995$	−24.9572	−0.791196
$996$	63.5710	2.01433
$997$	3.13226	0.0991996	0.0495998	−	0.998769i	$-0.484205\pi$
$997$	3.13226	0.0991996	0.0495998	+	0.998769i	$0.484205\pi$
$998$	−56.5938	−1.79144
$999$	−93.9678	−2.97301

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.a.m.1.2	✓	8
3.2	odd	2		7245.2.a.bp.1.7		8
5.4	even	2		4025.2.a.t.1.7		8
7.6	odd	2		5635.2.a.bb.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.m.1.2	✓	8	1.1	even	1	trivial
4025.2.a.t.1.7		8	5.4	even	2
5635.2.a.bb.1.2		8	7.6	odd	2
7245.2.a.bp.1.7		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.a (trivial)

\(f(q)\)	\(=\)	\(q-1.94419 q^{2} +3.14297 q^{3} +1.77986 q^{4} +1.00000 q^{5} -6.11052 q^{6} +1.00000 q^{7} +0.427999 q^{8} +6.87827 q^{9} +O(q^{10})\)	\(q-1.94419 q^{2} +3.14297 q^{3} +1.77986 q^{4} +1.00000 q^{5} -6.11052 q^{6} +1.00000 q^{7} +0.427999 q^{8} +6.87827 q^{9} -1.94419 q^{10} +5.04300 q^{11} +5.59404 q^{12} +5.16633 q^{13} -1.94419 q^{14} +3.14297 q^{15} -4.39182 q^{16} -7.40852 q^{17} -13.3726 q^{18} -5.95715 q^{19} +1.77986 q^{20} +3.14297 q^{21} -9.80453 q^{22} +1.00000 q^{23} +1.34519 q^{24} +1.00000 q^{25} -10.0443 q^{26} +12.1893 q^{27} +1.77986 q^{28} -0.530448 q^{29} -6.11052 q^{30} -2.50219 q^{31} +7.68252 q^{32} +15.8500 q^{33} +14.4035 q^{34} +1.00000 q^{35} +12.2423 q^{36} -7.70904 q^{37} +11.5818 q^{38} +16.2376 q^{39} +0.427999 q^{40} -2.51810 q^{41} -6.11052 q^{42} -12.0061 q^{43} +8.97582 q^{44} +6.87827 q^{45} -1.94419 q^{46} -0.447537 q^{47} -13.8034 q^{48} +1.00000 q^{49} -1.94419 q^{50} -23.2848 q^{51} +9.19534 q^{52} +3.18550 q^{53} -23.6982 q^{54} +5.04300 q^{55} +0.427999 q^{56} -18.7232 q^{57} +1.03129 q^{58} +9.09814 q^{59} +5.59404 q^{60} -0.608230 q^{61} +4.86472 q^{62} +6.87827 q^{63} -6.15260 q^{64} +5.16633 q^{65} -30.8154 q^{66} +8.89704 q^{67} -13.1861 q^{68} +3.14297 q^{69} -1.94419 q^{70} -11.6461 q^{71} +2.94389 q^{72} +2.19297 q^{73} +14.9878 q^{74} +3.14297 q^{75} -10.6029 q^{76} +5.04300 q^{77} -31.5690 q^{78} -12.7320 q^{79} -4.39182 q^{80} +17.6758 q^{81} +4.89566 q^{82} +11.3641 q^{83} +5.59404 q^{84} -7.40852 q^{85} +23.3421 q^{86} -1.66718 q^{87} +2.15840 q^{88} -8.82411 q^{89} -13.3726 q^{90} +5.16633 q^{91} +1.77986 q^{92} -7.86430 q^{93} +0.870094 q^{94} -5.95715 q^{95} +24.1459 q^{96} +0.311043 q^{97} -1.94419 q^{98} +34.6871 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 7 q^{3} + 7 q^{4} + 8 q^{5} + q^{6} + 8 q^{7} + 3 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q + q^2 + 7 * q^3 + 7 * q^4 + 8 * q^5 + q^6 + 8 * q^7 + 3 * q^8 + 9 * q^9	\( 8 q + q^{2} + 7 q^{3} + 7 q^{4} + 8 q^{5} + q^{6} + 8 q^{7} + 3 q^{8} + 9 q^{9} + q^{10} + 6 q^{11} + 8 q^{12} + 8 q^{13} + q^{14} + 7 q^{15} + q^{16} + 4 q^{17} - 11 q^{18} + 7 q^{20} + 7 q^{21} - 8 q^{22} + 8 q^{23} - 8 q^{24} + 8 q^{25} + 2 q^{26} + 28 q^{27} + 7 q^{28} - 3 q^{29} + q^{30} - 16 q^{31} + 12 q^{32} + 5 q^{33} - 4 q^{34} + 8 q^{35} - 14 q^{36} - 7 q^{37} + 11 q^{38} + 16 q^{39} + 3 q^{40} + 7 q^{41} + q^{42} - 10 q^{43} + 7 q^{44} + 9 q^{45} + q^{46} + 19 q^{47} - 6 q^{48} + 8 q^{49} + q^{50} + 7 q^{51} + 18 q^{52} - q^{53} - 25 q^{54} + 6 q^{55} + 3 q^{56} - 25 q^{57} - 9 q^{58} + 21 q^{59} + 8 q^{60} - 7 q^{61} + 18 q^{62} + 9 q^{63} - 37 q^{64} + 8 q^{65} - 43 q^{66} + 11 q^{67} - 17 q^{68} + 7 q^{69} + q^{70} + 8 q^{71} + 4 q^{72} - 3 q^{73} + 12 q^{74} + 7 q^{75} + 8 q^{76} + 6 q^{77} - 50 q^{78} - 15 q^{79} + q^{80} + 28 q^{81} + 41 q^{82} + 25 q^{83} + 8 q^{84} + 4 q^{85} - 12 q^{86} + 21 q^{87} - 29 q^{88} + q^{89} - 11 q^{90} + 8 q^{91} + 7 q^{92} - 5 q^{93} - 36 q^{94} + 30 q^{96} + 10 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + q^2 + 7 * q^3 + 7 * q^4 + 8 * q^5 + q^6 + 8 * q^7 + 3 * q^8 + 9 * q^9 + q^10 + 6 * q^11 + 8 * q^12 + 8 * q^13 + q^14 + 7 * q^15 + q^16 + 4 * q^17 - 11 * q^18 + 7 * q^20 + 7 * q^21 - 8 * q^22 + 8 * q^23 - 8 * q^24 + 8 * q^25 + 2 * q^26 + 28 * q^27 + 7 * q^28 - 3 * q^29 + q^30 - 16 * q^31 + 12 * q^32 + 5 * q^33 - 4 * q^34 + 8 * q^35 - 14 * q^36 - 7 * q^37 + 11 * q^38 + 16 * q^39 + 3 * q^40 + 7 * q^41 + q^42 - 10 * q^43 + 7 * q^44 + 9 * q^45 + q^46 + 19 * q^47 - 6 * q^48 + 8 * q^49 + q^50 + 7 * q^51 + 18 * q^52 - q^53 - 25 * q^54 + 6 * q^55 + 3 * q^56 - 25 * q^57 - 9 * q^58 + 21 * q^59 + 8 * q^60 - 7 * q^61 + 18 * q^62 + 9 * q^63 - 37 * q^64 + 8 * q^65 - 43 * q^66 + 11 * q^67 - 17 * q^68 + 7 * q^69 + q^70 + 8 * q^71 + 4 * q^72 - 3 * q^73 + 12 * q^74 + 7 * q^75 + 8 * q^76 + 6 * q^77 - 50 * q^78 - 15 * q^79 + q^80 + 28 * q^81 + 41 * q^82 + 25 * q^83 + 8 * q^84 + 4 * q^85 - 12 * q^86 + 21 * q^87 - 29 * q^88 + q^89 - 11 * q^90 + 8 * q^91 + 7 * q^92 - 5 * q^93 - 36 * q^94 + 30 * q^96 + 10 * q^97 + q^98 - 18 * q^99

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