LMFDB - Embedded newform 8015.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79998 q^{2} -2.08197 q^{3} +5.83989 q^{4} +1.00000 q^{5} +5.82947 q^{6} -1.00000 q^{7} -10.7516 q^{8} +1.33460 q^{9} +O(q^{10})$	\(q-2.79998 q^{2} -2.08197 q^{3} +5.83989 q^{4} +1.00000 q^{5} +5.82947 q^{6} -1.00000 q^{7} -10.7516 q^{8} +1.33460 q^{9} -2.79998 q^{10} +3.64099 q^{11} -12.1585 q^{12} +4.41258 q^{13} +2.79998 q^{14} -2.08197 q^{15} +18.4246 q^{16} -6.20526 q^{17} -3.73684 q^{18} +0.346533 q^{19} +5.83989 q^{20} +2.08197 q^{21} -10.1947 q^{22} -3.00197 q^{23} +22.3846 q^{24} +1.00000 q^{25} -12.3551 q^{26} +3.46732 q^{27} -5.83989 q^{28} -7.82924 q^{29} +5.82947 q^{30} +3.98170 q^{31} -30.0852 q^{32} -7.58044 q^{33} +17.3746 q^{34} -1.00000 q^{35} +7.79389 q^{36} +0.839821 q^{37} -0.970287 q^{38} -9.18686 q^{39} -10.7516 q^{40} -0.987520 q^{41} -5.82947 q^{42} +1.95409 q^{43} +21.2630 q^{44} +1.33460 q^{45} +8.40547 q^{46} +1.43005 q^{47} -38.3594 q^{48} +1.00000 q^{49} -2.79998 q^{50} +12.9192 q^{51} +25.7690 q^{52} -3.99644 q^{53} -9.70843 q^{54} +3.64099 q^{55} +10.7516 q^{56} -0.721472 q^{57} +21.9217 q^{58} -0.0184517 q^{59} -12.1585 q^{60} -0.0810318 q^{61} -11.1487 q^{62} -1.33460 q^{63} +47.3888 q^{64} +4.41258 q^{65} +21.2251 q^{66} +6.57270 q^{67} -36.2380 q^{68} +6.25002 q^{69} +2.79998 q^{70} +2.73547 q^{71} -14.3491 q^{72} -10.7785 q^{73} -2.35148 q^{74} -2.08197 q^{75} +2.02372 q^{76} -3.64099 q^{77} +25.7230 q^{78} -3.87688 q^{79} +18.4246 q^{80} -11.2226 q^{81} +2.76504 q^{82} -8.81408 q^{83} +12.1585 q^{84} -6.20526 q^{85} -5.47143 q^{86} +16.3002 q^{87} -39.1466 q^{88} +4.71336 q^{89} -3.73684 q^{90} -4.41258 q^{91} -17.5312 q^{92} -8.28977 q^{93} -4.00411 q^{94} +0.346533 q^{95} +62.6364 q^{96} +12.2596 q^{97} -2.79998 q^{98} +4.85925 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) $ 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.79998	−1.97989	−0.989943	−	0.141469i	$-0.954818\pi$
$2$	−2.79998	−1.97989	−0.989943	+	0.141469i	$0.954818\pi$
$3$	−2.08197	−1.20203	−0.601013	−	0.799239i	$-0.705236\pi$
$3$	−2.08197	−1.20203	−0.601013	+	0.799239i	$0.705236\pi$
$4$	5.83989	2.91995
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.82947	2.37987
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−10.7516	−3.80127
$9$	1.33460	0.444865
$10$	−2.79998	−0.885432
$11$	3.64099	1.09780	0.548900	−	0.835888i	$-0.315047\pi$
$11$	3.64099	1.09780	0.548900	+	0.835888i	$0.315047\pi$
$12$	−12.1585	−3.50985
$13$	4.41258	1.22383	0.611915	−	0.790924i	$-0.290399\pi$
$13$	4.41258	1.22383	0.611915	+	0.790924i	$0.290399\pi$
$14$	2.79998	0.748326
$15$	−2.08197	−0.537562
$16$	18.4246	4.60614
$17$	−6.20526	−1.50500	−0.752498	−	0.658595i	$-0.771151\pi$
$17$	−6.20526	−1.50500	−0.752498	+	0.658595i	$0.771151\pi$
$18$	−3.73684	−0.880782
$19$	0.346533	0.0795002	0.0397501	−	0.999210i	$-0.487344\pi$
$19$	0.346533	0.0795002	0.0397501	+	0.999210i	$0.487344\pi$
$20$	5.83989	1.30584
$21$	2.08197	0.454323
$22$	−10.1947	−2.17352
$23$	−3.00197	−0.625955	−0.312977	−	0.949761i	$-0.601326\pi$
$23$	−3.00197	−0.625955	−0.312977	+	0.949761i	$0.601326\pi$
$24$	22.3846	4.56923
$25$	1.00000	0.200000
$26$	−12.3551	−2.42304
$27$	3.46732	0.667286
$28$	−5.83989	−1.10364
$29$	−7.82924	−1.45385	−0.726927	−	0.686715i	$-0.759052\pi$
$29$	−7.82924	−1.45385	−0.726927	+	0.686715i	$0.759052\pi$
$30$	5.82947	1.06431
$31$	3.98170	0.715134	0.357567	−	0.933887i	$-0.383606\pi$
$31$	3.98170	0.715134	0.357567	+	0.933887i	$0.383606\pi$
$32$	−30.0852	−5.31836
$33$	−7.58044	−1.31958
$34$	17.3746	2.97972
$35$	−1.00000	−0.169031
$36$	7.79389	1.29898
$37$	0.839821	0.138066	0.0690328	−	0.997614i	$-0.478009\pi$
$37$	0.839821	0.138066	0.0690328	+	0.997614i	$0.478009\pi$
$38$	−0.970287	−0.157401
$39$	−9.18686	−1.47107
$40$	−10.7516	−1.69998
$41$	−0.987520	−0.154225	−0.0771123	−	0.997022i	$-0.524570\pi$
$41$	−0.987520	−0.154225	−0.0771123	+	0.997022i	$0.524570\pi$
$42$	−5.82947	−0.899507
$43$	1.95409	0.297997	0.148998	−	0.988837i	$-0.452395\pi$
$43$	1.95409	0.297997	0.148998	+	0.988837i	$0.452395\pi$
$44$	21.2630	3.20552
$45$	1.33460	0.198950
$46$	8.40547	1.23932
$47$	1.43005	0.208594	0.104297	−	0.994546i	$-0.466741\pi$
$47$	1.43005	0.208594	0.104297	+	0.994546i	$0.466741\pi$
$48$	−38.3594	−5.53670
$49$	1.00000	0.142857
$50$	−2.79998	−0.395977
$51$	12.9192	1.80904
$52$	25.7690	3.57352
$53$	−3.99644	−0.548953	−0.274476	−	0.961594i	$-0.588505\pi$
$53$	−3.99644	−0.548953	−0.274476	+	0.961594i	$0.588505\pi$
$54$	−9.70843	−1.32115
$55$	3.64099	0.490951
$56$	10.7516	1.43675
$57$	−0.721472	−0.0955613
$58$	21.9217	2.87846
$59$	−0.0184517	−0.00240221	−0.00120110	−	0.999999i	$-0.500382\pi$
$59$	−0.0184517	−0.00240221	−0.00120110	+	0.999999i	$0.500382\pi$
$60$	−12.1585	−1.56965
$61$	−0.0810318	−0.0103751	−0.00518753	−	0.999987i	$-0.501651\pi$
$61$	−0.0810318	−0.0103751	−0.00518753	+	0.999987i	$0.501651\pi$
$62$	−11.1487	−1.41588
$63$	−1.33460	−0.168143
$64$	47.3888	5.92360
$65$	4.41258	0.547313
$66$	21.2251	2.61263
$67$	6.57270	0.802984	0.401492	−	0.915863i	$-0.368492\pi$
$67$	6.57270	0.802984	0.401492	+	0.915863i	$0.368492\pi$
$68$	−36.2380	−4.39451
$69$	6.25002	0.752413
$70$	2.79998	0.334662
$71$	2.73547	0.324641	0.162320	−	0.986738i	$-0.448102\pi$
$71$	2.73547	0.324641	0.162320	+	0.986738i	$0.448102\pi$
$72$	−14.3491	−1.69105
$73$	−10.7785	−1.26152	−0.630762	−	0.775976i	$-0.717258\pi$
$73$	−10.7785	−1.26152	−0.630762	+	0.775976i	$0.717258\pi$
$74$	−2.35148	−0.273354
$75$	−2.08197	−0.240405
$76$	2.02372	0.232136
$77$	−3.64099	−0.414930
$78$	25.7230	2.91256
$79$	−3.87688	−0.436183	−0.218092	−	0.975928i	$-0.569983\pi$
$79$	−3.87688	−0.436183	−0.218092	+	0.975928i	$0.569983\pi$
$80$	18.4246	2.05993
$81$	−11.2226	−1.24696
$82$	2.76504	0.305347
$83$	−8.81408	−0.967471	−0.483736	−	0.875214i	$-0.660720\pi$
$83$	−8.81408	−0.967471	−0.483736	+	0.875214i	$0.660720\pi$
$84$	12.1585	1.32660
$85$	−6.20526	−0.673055
$86$	−5.47143	−0.589999
$87$	16.3002	1.74757
$88$	−39.1466	−4.17304
$89$	4.71336	0.499615	0.249808	−	0.968296i	$-0.419633\pi$
$89$	4.71336	0.499615	0.249808	+	0.968296i	$0.419633\pi$
$90$	−3.73684	−0.393898
$91$	−4.41258	−0.462564
$92$	−17.5312	−1.82775
$93$	−8.28977	−0.859610
$94$	−4.00411	−0.412993
$95$	0.346533	0.0355536
$96$	62.6364	6.39280
$97$	12.2596	1.24478	0.622388	−	0.782709i	$-0.286163\pi$
$97$	12.2596	1.24478	0.622388	+	0.782709i	$0.286163\pi$
$98$	−2.79998	−0.282841
$99$	4.85925	0.488373
$100$	5.83989	0.583989
$101$	−10.5827	−1.05302	−0.526510	−	0.850169i	$-0.676500\pi$
$101$	−10.5827	−1.05302	−0.526510	+	0.850169i	$0.676500\pi$
$102$	−36.1734	−3.58170
$103$	−11.8215	−1.16481	−0.582404	−	0.812900i	$-0.697888\pi$
$103$	−11.8215	−1.16481	−0.582404	+	0.812900i	$0.697888\pi$
$104$	−47.4424	−4.65211
$105$	2.08197	0.203179
$106$	11.1899	1.08686
$107$	14.2857	1.38105	0.690527	−	0.723306i	$-0.257378\pi$
$107$	14.2857	1.38105	0.690527	+	0.723306i	$0.257378\pi$
$108$	20.2488	1.94844
$109$	0.513566	0.0491907	0.0245953	−	0.999697i	$-0.492170\pi$
$109$	0.513566	0.0491907	0.0245953	+	0.999697i	$0.492170\pi$
$110$	−10.1947	−0.972028
$111$	−1.74848	−0.165958
$112$	−18.4246	−1.74096
$113$	8.02946	0.755348	0.377674	−	0.925939i	$-0.376724\pi$
$113$	8.02946	0.755348	0.377674	+	0.925939i	$0.376724\pi$
$114$	2.02011	0.189200
$115$	−3.00197	−0.279935
$116$	−45.7219	−4.24517
$117$	5.88901	0.544439
$118$	0.0516645	0.00475610
$119$	6.20526	0.568835
$120$	22.3846	2.04342
$121$	2.25683	0.205167
$122$	0.226887	0.0205414
$123$	2.05599	0.185382
$124$	23.2527	2.08815
$125$	1.00000	0.0894427
$126$	3.73684	0.332904
$127$	−6.44882	−0.572240	−0.286120	−	0.958194i	$-0.592366\pi$
$127$	−6.44882	−0.572240	−0.286120	+	0.958194i	$0.592366\pi$
$128$	−72.5173	−6.40969
$129$	−4.06836	−0.358199
$130$	−12.3551	−1.08362
$131$	21.2526	1.85685	0.928424	−	0.371523i	$-0.121164\pi$
$131$	21.2526	1.85685	0.928424	+	0.371523i	$0.121164\pi$
$132$	−44.2689	−3.85312
$133$	−0.346533	−0.0300483
$134$	−18.4034	−1.58982
$135$	3.46732	0.298420
$136$	66.7166	5.72090
$137$	13.6648	1.16747	0.583733	−	0.811946i	$-0.301592\pi$
$137$	13.6648	1.16747	0.583733	+	0.811946i	$0.301592\pi$
$138$	−17.4999	−1.48969
$139$	−3.42534	−0.290533	−0.145267	−	0.989393i	$-0.546404\pi$
$139$	−3.42534	−0.290533	−0.145267	+	0.989393i	$0.546404\pi$
$140$	−5.83989	−0.493561
$141$	−2.97732	−0.250736
$142$	−7.65927	−0.642752
$143$	16.0662	1.34352
$144$	24.5893	2.04911
$145$	−7.82924	−0.650183
$146$	30.1795	2.49767
$147$	−2.08197	−0.171718
$148$	4.90446	0.403144
$149$	12.0897	0.990423	0.495212	−	0.868772i	$-0.335091\pi$
$149$	12.0897	0.990423	0.495212	+	0.868772i	$0.335091\pi$
$150$	5.82947	0.475975
$151$	−19.2371	−1.56549	−0.782745	−	0.622342i	$-0.786181\pi$
$151$	−19.2371	−1.56549	−0.782745	+	0.622342i	$0.786181\pi$
$152$	−3.72580	−0.302202
$153$	−8.28150	−0.669520
$154$	10.1947	0.821513
$155$	3.98170	0.319818
$156$	−53.6503	−4.29546
$157$	23.5870	1.88245	0.941225	−	0.337779i	$-0.109676\pi$
$157$	23.5870	1.88245	0.941225	+	0.337779i	$0.109676\pi$
$158$	10.8552	0.863593
$159$	8.32046	0.659855
$160$	−30.0852	−2.37844
$161$	3.00197	0.236589
$162$	31.4232	2.46884
$163$	0.765964	0.0599950	0.0299975	−	0.999550i	$-0.490450\pi$
$163$	0.765964	0.0599950	0.0299975	+	0.999550i	$0.490450\pi$
$164$	−5.76701	−0.450328
$165$	−7.58044	−0.590136
$166$	24.6793	1.91548
$167$	5.49104	0.424909	0.212455	−	0.977171i	$-0.431854\pi$
$167$	5.49104	0.424909	0.212455	+	0.977171i	$0.431854\pi$
$168$	−22.3846	−1.72701
$169$	6.47088	0.497760
$170$	17.3746	1.33257
$171$	0.462482	0.0353669
$172$	11.4117	0.870134
$173$	−7.00843	−0.532841	−0.266421	−	0.963857i	$-0.585841\pi$
$173$	−7.00843	−0.532841	−0.266421	+	0.963857i	$0.585841\pi$
$174$	−45.6404	−3.45999
$175$	−1.00000	−0.0755929
$176$	67.0837	5.05663
$177$	0.0384159	0.00288752
$178$	−13.1973	−0.989180
$179$	5.20149	0.388778	0.194389	−	0.980925i	$-0.437728\pi$
$179$	5.20149	0.388778	0.194389	+	0.980925i	$0.437728\pi$
$180$	7.79389	0.580922
$181$	19.3342	1.43710	0.718552	−	0.695474i	$-0.244805\pi$
$181$	19.3342	1.43710	0.718552	+	0.695474i	$0.244805\pi$
$182$	12.3551	0.915824
$183$	0.168706	0.0124711
$184$	32.2761	2.37943
$185$	0.839821	0.0617449
$186$	23.2112	1.70193
$187$	−22.5933	−1.65219
$188$	8.35134	0.609084
$189$	−3.46732	−0.252211
$190$	−0.970287	−0.0703920
$191$	9.06418	0.655861	0.327931	−	0.944702i	$-0.393649\pi$
$191$	9.06418	0.655861	0.327931	+	0.944702i	$0.393649\pi$
$192$	−98.6620	−7.12032
$193$	14.6391	1.05374	0.526872	−	0.849945i	$-0.323365\pi$
$193$	14.6391	1.05374	0.526872	+	0.849945i	$0.323365\pi$
$194$	−34.3267	−2.46451
$195$	−9.18686	−0.657885
$196$	5.83989	0.417135
$197$	17.4615	1.24408	0.622039	−	0.782987i	$-0.286305\pi$
$197$	17.4615	1.24408	0.622039	+	0.782987i	$0.286305\pi$
$198$	−13.6058	−0.966923
$199$	−8.95333	−0.634685	−0.317342	−	0.948311i	$-0.602790\pi$
$199$	−8.95333	−0.634685	−0.317342	+	0.948311i	$0.602790\pi$
$200$	−10.7516	−0.760255
$201$	−13.6842	−0.965207
$202$	29.6314	2.08486
$203$	7.82924	0.549505
$204$	75.4465	5.28231
$205$	−0.987520	−0.0689714
$206$	33.1000	2.30619
$207$	−4.00642	−0.278465
$208$	81.2999	5.63713
$209$	1.26173	0.0872754
$210$	−5.82947	−0.402272
$211$	17.8710	1.23029	0.615145	−	0.788414i	$-0.289097\pi$
$211$	17.8710	1.23029	0.615145	+	0.788414i	$0.289097\pi$
$212$	−23.3388	−1.60291
$213$	−5.69517	−0.390226
$214$	−39.9998	−2.73433
$215$	1.95409	0.133268
$216$	−37.2793	−2.53654
$217$	−3.98170	−0.270295
$218$	−1.43797	−0.0973919
$219$	22.4404	1.51638
$220$	21.2630	1.43355
$221$	−27.3812	−1.84186
$222$	4.89571	0.328579
$223$	−21.4478	−1.43625	−0.718125	−	0.695915i	$-0.754999\pi$
$223$	−21.4478	−1.43625	−0.718125	+	0.695915i	$0.754999\pi$
$224$	30.0852	2.01015
$225$	1.33460	0.0889730
$226$	−22.4823	−1.49550
$227$	−7.48134	−0.496554	−0.248277	−	0.968689i	$-0.579864\pi$
$227$	−7.48134	−0.496554	−0.248277	+	0.968689i	$0.579864\pi$
$228$	−4.21332	−0.279034
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	8.40547	0.554240
$231$	7.58044	0.498756
$232$	84.1771	5.52650
$233$	0.374142	0.0245109	0.0122554	−	0.999925i	$-0.496099\pi$
$233$	0.374142	0.0245109	0.0122554	+	0.999925i	$0.496099\pi$
$234$	−16.4891	−1.07793
$235$	1.43005	0.0932862
$236$	−0.107756	−0.00701432
$237$	8.07155	0.524303
$238$	−17.3746	−1.12623
$239$	−16.8305	−1.08867	−0.544337	−	0.838867i	$-0.683219\pi$
$239$	−16.8305	−1.08867	−0.544337	+	0.838867i	$0.683219\pi$
$240$	−38.3594	−2.47609
$241$	−7.85859	−0.506216	−0.253108	−	0.967438i	$-0.581453\pi$
$241$	−7.85859	−0.506216	−0.253108	+	0.967438i	$0.581453\pi$
$242$	−6.31909	−0.406207
$243$	12.9632	0.831591
$244$	−0.473217	−0.0302946
$245$	1.00000	0.0638877
$246$	−5.75672	−0.367035
$247$	1.52911	0.0972947
$248$	−42.8097	−2.71842
$249$	18.3507	1.16293
$250$	−2.79998	−0.177086
$251$	19.6194	1.23836	0.619182	−	0.785248i	$-0.287464\pi$
$251$	19.6194	1.23836	0.619182	+	0.785248i	$0.287464\pi$
$252$	−7.79389	−0.490969
$253$	−10.9302	−0.687174
$254$	18.0566	1.13297
$255$	12.9192	0.809029
$256$	108.270	6.76685
$257$	11.3585	0.708524	0.354262	−	0.935146i	$-0.384732\pi$
$257$	11.3585	0.708524	0.354262	+	0.935146i	$0.384732\pi$
$258$	11.3913	0.709194
$259$	−0.839821	−0.0521839
$260$	25.7690	1.59813
$261$	−10.4489	−0.646769
$262$	−59.5069	−3.67635
$263$	−7.05014	−0.434730	−0.217365	−	0.976090i	$-0.569746\pi$
$263$	−7.05014	−0.434730	−0.217365	+	0.976090i	$0.569746\pi$
$264$	81.5020	5.01610
$265$	−3.99644	−0.245499
$266$	0.970287	0.0594921
$267$	−9.81307	−0.600550
$268$	38.3839	2.34467
$269$	−13.8672	−0.845501	−0.422750	−	0.906246i	$-0.638935\pi$
$269$	−13.8672	−0.845501	−0.422750	+	0.906246i	$0.638935\pi$
$270$	−9.70843	−0.590836
$271$	−24.5129	−1.48905	−0.744526	−	0.667593i	$-0.767325\pi$
$271$	−24.5129	−1.48905	−0.744526	+	0.667593i	$0.767325\pi$
$272$	−114.329	−6.93222
$273$	9.18686	0.556014
$274$	−38.2613	−2.31145
$275$	3.64099	0.219560
$276$	36.4994	2.19701
$277$	−7.50747	−0.451080	−0.225540	−	0.974234i	$-0.572415\pi$
$277$	−7.50747	−0.451080	−0.225540	+	0.974234i	$0.572415\pi$
$278$	9.59088	0.575223
$279$	5.31396	0.318138
$280$	10.7516	0.642533
$281$	−29.3474	−1.75072	−0.875359	−	0.483474i	$-0.839375\pi$
$281$	−29.3474	−1.75072	−0.875359	+	0.483474i	$0.839375\pi$
$282$	8.33644	0.496428
$283$	−15.9435	−0.947742	−0.473871	−	0.880594i	$-0.657144\pi$
$283$	−15.9435	−0.947742	−0.473871	+	0.880594i	$0.657144\pi$
$284$	15.9749	0.947934
$285$	−0.721472	−0.0427363
$286$	−44.9850	−2.66002
$287$	0.987520	0.0582915
$288$	−40.1515	−2.36595
$289$	21.5052	1.26501
$290$	21.9217	1.28729
$291$	−25.5242	−1.49625
$292$	−62.9451	−3.68358
$293$	−20.3973	−1.19162	−0.595811	−	0.803124i	$-0.703169\pi$
$293$	−20.3973	−1.19162	−0.595811	+	0.803124i	$0.703169\pi$
$294$	5.82947	0.339982
$295$	−0.0184517	−0.00107430
$296$	−9.02944	−0.524826
$297$	12.6245	0.732548
$298$	−33.8508	−1.96092
$299$	−13.2465	−0.766062
$300$	−12.1585	−0.701970
$301$	−1.95409	−0.112632
$302$	53.8634	3.09949
$303$	22.0329	1.26576
$304$	6.38473	0.366189
$305$	−0.0810318	−0.00463987
$306$	23.1881	1.32557
$307$	17.0653	0.973970	0.486985	−	0.873410i	$-0.338097\pi$
$307$	17.0653	0.973970	0.486985	+	0.873410i	$0.338097\pi$
$308$	−21.2630	−1.21157
$309$	24.6120	1.40013
$310$	−11.1487	−0.633203
$311$	−9.90753	−0.561804	−0.280902	−	0.959736i	$-0.590634\pi$
$311$	−9.90753	−0.561804	−0.280902	+	0.959736i	$0.590634\pi$
$312$	98.7737	5.59196
$313$	27.0931	1.53139	0.765696	−	0.643202i	$-0.222395\pi$
$313$	27.0931	1.53139	0.765696	+	0.643202i	$0.222395\pi$
$314$	−66.0433	−3.72704
$315$	−1.33460	−0.0751959
$316$	−22.6406	−1.27363
$317$	−28.3783	−1.59388	−0.796941	−	0.604057i	$-0.793550\pi$
$317$	−28.3783	−1.59388	−0.796941	+	0.604057i	$0.793550\pi$
$318$	−23.2971	−1.30644
$319$	−28.5062	−1.59604
$320$	47.3888	2.64911
$321$	−29.7425	−1.66006
$322$	−8.40547	−0.468418
$323$	−2.15033	−0.119647
$324$	−65.5390	−3.64106
$325$	4.41258	0.244766
$326$	−2.14469	−0.118783
$327$	−1.06923	−0.0591285
$328$	10.6174	0.586250
$329$	−1.43005	−0.0788413
$330$	21.2251	1.16840
$331$	−14.1214	−0.776182	−0.388091	−	0.921621i	$-0.626865\pi$
$331$	−14.1214	−0.776182	−0.388091	+	0.921621i	$0.626865\pi$
$332$	−51.4733	−2.82496
$333$	1.12082	0.0614206
$334$	−15.3748	−0.841271
$335$	6.57270	0.359105
$336$	38.3594	2.09268
$337$	18.6744	1.01726	0.508631	−	0.860985i	$-0.330152\pi$
$337$	18.6744	1.01726	0.508631	+	0.860985i	$0.330152\pi$
$338$	−18.1183	−0.985507
$339$	−16.7171	−0.907948
$340$	−36.2380	−1.96528
$341$	14.4973	0.785075
$342$	−1.29494	−0.0700223
$343$	−1.00000	−0.0539949
$344$	−21.0097	−1.13277
$345$	6.25002	0.336489
$346$	19.6235	1.05496
$347$	3.87907	0.208239	0.104120	−	0.994565i	$-0.466797\pi$
$347$	3.87907	0.208239	0.104120	+	0.994565i	$0.466797\pi$
$348$	95.1916	5.10281
$349$	22.5535	1.20726	0.603630	−	0.797265i	$-0.293721\pi$
$349$	22.5535	1.20726	0.603630	+	0.797265i	$0.293721\pi$
$350$	2.79998	0.149665
$351$	15.2998	0.816645
$352$	−109.540	−5.83850
$353$	−1.32648	−0.0706014	−0.0353007	−	0.999377i	$-0.511239\pi$
$353$	−1.32648	−0.0706014	−0.0353007	+	0.999377i	$0.511239\pi$
$354$	−0.107564	−0.00571695
$355$	2.73547	0.145184
$356$	27.5255	1.45885
$357$	−12.9192	−0.683754
$358$	−14.5641	−0.769736
$359$	−1.66307	−0.0877737	−0.0438868	−	0.999037i	$-0.513974\pi$
$359$	−1.66307	−0.0877737	−0.0438868	+	0.999037i	$0.513974\pi$
$360$	−14.3491	−0.756262
$361$	−18.8799	−0.993680
$362$	−54.1355	−2.84530
$363$	−4.69866	−0.246616
$364$	−25.7690	−1.35066
$365$	−10.7785	−0.564171
$366$	−0.472373	−0.0246913
$367$	−37.5779	−1.96155	−0.980776	−	0.195139i	$-0.937484\pi$
$367$	−37.5779	−1.96155	−0.980776	+	0.195139i	$0.937484\pi$
$368$	−55.3100	−2.88324
$369$	−1.31794	−0.0686092
$370$	−2.35148	−0.122248
$371$	3.99644	0.207485
$372$	−48.4114	−2.51001
$373$	20.5773	1.06545	0.532727	−	0.846287i	$-0.321167\pi$
$373$	20.5773	1.06545	0.532727	+	0.846287i	$0.321167\pi$
$374$	63.2608	3.27114
$375$	−2.08197	−0.107512
$376$	−15.3754	−0.792924
$377$	−34.5472	−1.77927
$378$	9.70843	0.499348
$379$	1.68720	0.0866656	0.0433328	−	0.999061i	$-0.486202\pi$
$379$	1.68720	0.0866656	0.0433328	+	0.999061i	$0.486202\pi$
$380$	2.02372	0.103815
$381$	13.4262	0.687847
$382$	−25.3795	−1.29853
$383$	−16.5772	−0.847057	−0.423528	−	0.905883i	$-0.639209\pi$
$383$	−16.5772	−0.847057	−0.423528	+	0.905883i	$0.639209\pi$
$384$	150.979	7.70461
$385$	−3.64099	−0.185562
$386$	−40.9891	−2.08629
$387$	2.60792	0.132568
$388$	71.5949	3.63468
$389$	39.2420	1.98965	0.994823	−	0.101623i	$-0.0324034\pi$
$389$	39.2420	1.98965	0.994823	+	0.101623i	$0.0324034\pi$
$390$	25.7230	1.30254
$391$	18.6280	0.942059
$392$	−10.7516	−0.543039
$393$	−44.2472	−2.23198
$394$	−48.8917	−2.46313
$395$	−3.87688	−0.195067
$396$	28.3775	1.42602
$397$	17.1925	0.862865	0.431432	−	0.902145i	$-0.358008\pi$
$397$	17.1925	0.862865	0.431432	+	0.902145i	$0.358008\pi$
$398$	25.0692	1.25660
$399$	0.721472	0.0361188
$400$	18.4246	0.921228
$401$	8.56933	0.427932	0.213966	−	0.976841i	$-0.431362\pi$
$401$	8.56933	0.427932	0.213966	+	0.976841i	$0.431362\pi$
$402$	38.3154	1.91100
$403$	17.5696	0.875203
$404$	−61.8019	−3.07476
$405$	−11.2226	−0.557658
$406$	−21.9217	−1.08796
$407$	3.05778	0.151569
$408$	−138.902	−6.87667
$409$	31.6898	1.56696	0.783479	−	0.621418i	$-0.213443\pi$
$409$	31.6898	1.56696	0.783479	+	0.621418i	$0.213443\pi$
$410$	2.76504	0.136555
$411$	−28.4498	−1.40332
$412$	−69.0363	−3.40118
$413$	0.0184517	0.000907950 0
$414$	11.2179	0.551329
$415$	−8.81408	−0.432666
$416$	−132.753	−6.50877
$417$	7.13145	0.349228
$418$	−3.53281	−0.172795
$419$	13.9759	0.682767	0.341384	−	0.939924i	$-0.389104\pi$
$419$	13.9759	0.682767	0.341384	+	0.939924i	$0.389104\pi$
$420$	12.1585	0.593273
$421$	25.6548	1.25034	0.625168	−	0.780490i	$-0.285030\pi$
$421$	25.6548	1.25034	0.625168	+	0.780490i	$0.285030\pi$
$422$	−50.0385	−2.43583
$423$	1.90854	0.0927963
$424$	42.9682	2.08672
$425$	−6.20526	−0.300999
$426$	15.9464	0.772604
$427$	0.0810318	0.00392140
$428$	83.4272	4.03261
$429$	−33.4493	−1.61495
$430$	−5.47143	−0.263856
$431$	−30.9614	−1.49136	−0.745680	−	0.666304i	$-0.767875\pi$
$431$	−30.9614	−1.49136	−0.745680	+	0.666304i	$0.767875\pi$
$432$	63.8839	3.07361
$433$	7.92206	0.380710	0.190355	−	0.981715i	$-0.439036\pi$
$433$	7.92206	0.380710	0.190355	+	0.981715i	$0.439036\pi$
$434$	11.1487	0.535154
$435$	16.3002	0.781537
$436$	2.99917	0.143634
$437$	−1.04028	−0.0497635
$438$	−62.8328	−3.00227
$439$	24.1442	1.15234	0.576170	−	0.817330i	$-0.304547\pi$
$439$	24.1442	1.15234	0.576170	+	0.817330i	$0.304547\pi$
$440$	−39.1466	−1.86624
$441$	1.33460	0.0635521
$442$	76.6668	3.64667
$443$	−5.20726	−0.247404	−0.123702	−	0.992319i	$-0.539477\pi$
$443$	−5.20726	−0.247404	−0.123702	+	0.992319i	$0.539477\pi$
$444$	−10.2109	−0.484590
$445$	4.71336	0.223435
$446$	60.0534	2.84361
$447$	−25.1703	−1.19051
$448$	−47.3888	−2.23891
$449$	−16.6967	−0.787965	−0.393983	−	0.919118i	$-0.628903\pi$
$449$	−16.6967	−0.787965	−0.393983	+	0.919118i	$0.628903\pi$
$450$	−3.73684	−0.176156
$451$	−3.59555	−0.169308
$452$	46.8912	2.20558
$453$	40.0510	1.88176
$454$	20.9476	0.983120
$455$	−4.41258	−0.206865
$456$	7.75699	0.363255
$457$	9.83615	0.460116	0.230058	−	0.973177i	$-0.426108\pi$
$457$	9.83615	0.460116	0.230058	+	0.973177i	$0.426108\pi$
$458$	2.79998	0.130835
$459$	−21.5156	−1.00426
$460$	−17.5312	−0.817396
$461$	−17.5509	−0.817428	−0.408714	−	0.912662i	$-0.634023\pi$
$461$	−17.5509	−0.817428	−0.408714	+	0.912662i	$0.634023\pi$
$462$	−21.2251	−0.987480
$463$	−0.789424	−0.0366876	−0.0183438	−	0.999832i	$-0.505839\pi$
$463$	−0.789424	−0.0366876	−0.0183438	+	0.999832i	$0.505839\pi$
$464$	−144.250	−6.69666
$465$	−8.28977	−0.384429
$466$	−1.04759	−0.0485287
$467$	−19.7916	−0.915844	−0.457922	−	0.888992i	$-0.651406\pi$
$467$	−19.7916	−0.915844	−0.457922	+	0.888992i	$0.651406\pi$
$468$	34.3912	1.58973
$469$	−6.57270	−0.303499
$470$	−4.00411	−0.184696
$471$	−49.1075	−2.26275
$472$	0.198386	0.00913145
$473$	7.11484	0.327141
$474$	−22.6002	−1.03806
$475$	0.346533	0.0159000
$476$	36.2380	1.66097
$477$	−5.33363	−0.244210
$478$	47.1250	2.15545
$479$	12.3113	0.562517	0.281258	−	0.959632i	$-0.409248\pi$
$479$	12.3113	0.562517	0.281258	+	0.959632i	$0.409248\pi$
$480$	62.6364	2.85895
$481$	3.70578	0.168969
$482$	22.0039	1.00225
$483$	−6.25002	−0.284386
$484$	13.1797	0.599076
$485$	12.2596	0.556681
$486$	−36.2968	−1.64646
$487$	−39.7839	−1.80278	−0.901391	−	0.433007i	$-0.857453\pi$
$487$	−39.7839	−1.80278	−0.901391	+	0.433007i	$0.857453\pi$
$488$	0.871223	0.0394384
$489$	−1.59471	−0.0721155
$490$	−2.79998	−0.126490
$491$	−34.1182	−1.53973	−0.769867	−	0.638204i	$-0.779678\pi$
$491$	−34.1182	−1.53973	−0.769867	+	0.638204i	$0.779678\pi$
$492$	12.0067	0.541306
$493$	48.5824	2.18804
$494$	−4.28147	−0.192632
$495$	4.85925	0.218407
$496$	73.3611	3.29401
$497$	−2.73547	−0.122703
$498$	−51.3815	−2.30246
$499$	22.3784	1.00180	0.500898	−	0.865506i	$-0.333003\pi$
$499$	22.3784	1.00180	0.500898	+	0.865506i	$0.333003\pi$
$500$	5.83989	0.261168
$501$	−11.4322	−0.510752
$502$	−54.9339	−2.45182
$503$	17.5822	0.783954	0.391977	−	0.919975i	$-0.371791\pi$
$503$	17.5822	0.783954	0.391977	+	0.919975i	$0.371791\pi$
$504$	14.3491	0.639158
$505$	−10.5827	−0.470924
$506$	30.6043	1.36052
$507$	−13.4722	−0.598320
$508$	−37.6604	−1.67091
$509$	12.0198	0.532768	0.266384	−	0.963867i	$-0.414171\pi$
$509$	12.0198	0.532768	0.266384	+	0.963867i	$0.414171\pi$
$510$	−36.1734	−1.60178
$511$	10.7785	0.476811
$512$	−158.118	−6.98790
$513$	1.20154	0.0530494
$514$	−31.8036	−1.40280
$515$	−11.8215	−0.520918
$516$	−23.7588	−1.04592
$517$	5.20681	0.228995
$518$	2.35148	0.103318
$519$	14.5913	0.640489
$520$	−47.4424	−2.08049
$521$	−12.5171	−0.548383	−0.274192	−	0.961675i	$-0.588410\pi$
$521$	−12.5171	−0.548383	−0.274192	+	0.961675i	$0.588410\pi$
$522$	29.2566	1.28053
$523$	−1.00065	−0.0437554	−0.0218777	−	0.999761i	$-0.506964\pi$
$523$	−1.00065	−0.0437554	−0.0218777	+	0.999761i	$0.506964\pi$
$524$	124.113	5.42190
$525$	2.08197	0.0908646
$526$	19.7403	0.860716
$527$	−24.7075	−1.07627
$528$	−139.666	−6.07819
$529$	−13.9882	−0.608181
$530$	11.1899	0.486060
$531$	−0.0246256	−0.00106866
$532$	−2.02372	−0.0877393
$533$	−4.35751	−0.188745
$534$	27.4764	1.18902
$535$	14.2857	0.617627
$536$	−70.6673	−3.05236
$537$	−10.8294	−0.467321
$538$	38.8280	1.67399
$539$	3.64099	0.156829
$540$	20.2488	0.871369
$541$	−16.7996	−0.722272	−0.361136	−	0.932513i	$-0.617611\pi$
$541$	−16.7996	−0.722272	−0.361136	+	0.932513i	$0.617611\pi$
$542$	68.6357	2.94815
$543$	−40.2533	−1.72743
$544$	186.686	8.00411
$545$	0.513566	0.0219987
$546$	−25.7230	−1.10084
$547$	31.6177	1.35188	0.675938	−	0.736959i	$-0.263739\pi$
$547$	31.6177	1.35188	0.675938	+	0.736959i	$0.263739\pi$
$548$	79.8012	3.40894
$549$	−0.108145	−0.00461550
$550$	−10.1947	−0.434704
$551$	−2.71309	−0.115582
$552$	−67.1978	−2.86013
$553$	3.87688	0.164862
$554$	21.0208	0.893087
$555$	−1.74848	−0.0742189
$556$	−20.0036	−0.848342
$557$	15.4737	0.655642	0.327821	−	0.944740i	$-0.393686\pi$
$557$	15.4737	0.655642	0.327821	+	0.944740i	$0.393686\pi$
$558$	−14.8790	−0.629877
$559$	8.62260	0.364697
$560$	−18.4246	−0.778580
$561$	47.0385	1.98597
$562$	82.1721	3.46622
$563$	31.7268	1.33713	0.668563	−	0.743655i	$-0.266910\pi$
$563$	31.7268	1.33713	0.668563	+	0.743655i	$0.266910\pi$
$564$	−17.3872	−0.732135
$565$	8.02946	0.337802
$566$	44.6415	1.87642
$567$	11.2226	0.471307
$568$	−29.4108	−1.23405
$569$	−47.4506	−1.98923	−0.994616	−	0.103632i	$-0.966954\pi$
$569$	−47.4506	−1.98923	−0.994616	+	0.103632i	$0.966954\pi$
$570$	2.02011	0.0846130
$571$	−41.1282	−1.72116	−0.860581	−	0.509313i	$-0.829899\pi$
$571$	−41.1282	−1.72116	−0.860581	+	0.509313i	$0.829899\pi$
$572$	93.8248	3.92301
$573$	−18.8713	−0.788362
$574$	−2.76504	−0.115410
$575$	−3.00197	−0.125191
$576$	63.2448	2.63520
$577$	−10.5452	−0.439004	−0.219502	−	0.975612i	$-0.570443\pi$
$577$	−10.5452	−0.439004	−0.219502	+	0.975612i	$0.570443\pi$
$578$	−60.2142	−2.50458
$579$	−30.4781	−1.26663
$580$	−45.7219	−1.89850
$581$	8.81408	0.365670
$582$	71.4672	2.96241
$583$	−14.5510	−0.602641
$584$	115.886	4.79540
$585$	5.88901	0.243481
$586$	57.1120	2.35928
$587$	15.2110	0.627826	0.313913	−	0.949452i	$-0.398360\pi$
$587$	15.2110	0.627826	0.313913	+	0.949452i	$0.398360\pi$
$588$	−12.1585	−0.501407
$589$	1.37979	0.0568533
$590$	0.0516645	0.00212699
$591$	−36.3542	−1.49541
$592$	15.4733	0.635950
$593$	−33.6230	−1.38073	−0.690365	−	0.723461i	$-0.742550\pi$
$593$	−33.6230	−1.38073	−0.690365	+	0.723461i	$0.742550\pi$
$594$	−35.3483	−1.45036
$595$	6.20526	0.254391
$596$	70.6023	2.89198
$597$	18.6406	0.762907
$598$	37.0898	1.51672
$599$	−20.6717	−0.844624	−0.422312	−	0.906451i	$-0.638781\pi$
$599$	−20.6717	−0.844624	−0.422312	+	0.906451i	$0.638781\pi$
$600$	22.3846	0.913846
$601$	44.7023	1.82344	0.911722	−	0.410807i	$-0.134753\pi$
$601$	44.7023	1.82344	0.911722	+	0.410807i	$0.134753\pi$
$602$	5.47143	0.222999
$603$	8.77190	0.357219
$604$	−112.342	−4.57115
$605$	2.25683	0.0917534
$606$	−61.6916	−2.50605
$607$	29.2138	1.18575	0.592875	−	0.805295i	$-0.297993\pi$
$607$	29.2138	1.18575	0.592875	+	0.805295i	$0.297993\pi$
$608$	−10.4255	−0.422810
$609$	−16.3002	−0.660519
$610$	0.226887	0.00918640
$611$	6.31022	0.255284
$612$	−48.3631	−1.95496
$613$	−40.4950	−1.63558	−0.817790	−	0.575517i	$-0.804801\pi$
$613$	−40.4950	−1.63558	−0.817790	+	0.575517i	$0.804801\pi$
$614$	−47.7826	−1.92835
$615$	2.05599	0.0829053
$616$	39.1466	1.57726
$617$	38.0354	1.53125	0.765624	−	0.643288i	$-0.222430\pi$
$617$	38.0354	1.53125	0.765624	+	0.643288i	$0.222430\pi$
$618$	−68.9131	−2.77209
$619$	−36.7135	−1.47564	−0.737820	−	0.674997i	$-0.764145\pi$
$619$	−36.7135	−1.47564	−0.737820	+	0.674997i	$0.764145\pi$
$620$	23.2527	0.933851
$621$	−10.4088	−0.417691
$622$	27.7409	1.11231
$623$	−4.71336	−0.188837
$624$	−169.264	−6.77598
$625$	1.00000	0.0400000
$626$	−75.8602	−3.03198
$627$	−2.62687	−0.104907
$628$	137.746	5.49666
$629$	−5.21130	−0.207788
$630$	3.73684	0.148879
$631$	−7.05691	−0.280931	−0.140466	−	0.990086i	$-0.544860\pi$
$631$	−7.05691	−0.280931	−0.140466	+	0.990086i	$0.544860\pi$
$632$	41.6828	1.65805
$633$	−37.2069	−1.47884
$634$	79.4586	3.15570
$635$	−6.44882	−0.255914
$636$	48.5906	1.92674
$637$	4.41258	0.174833
$638$	79.8169	3.15998
$639$	3.65075	0.144421
$640$	−72.5173	−2.86650
$641$	35.8951	1.41777	0.708886	−	0.705323i	$-0.249198\pi$
$641$	35.8951	1.41777	0.708886	+	0.705323i	$0.249198\pi$
$642$	83.2784	3.28673
$643$	25.4680	1.00436	0.502181	−	0.864763i	$-0.332531\pi$
$643$	25.4680	1.00436	0.502181	+	0.864763i	$0.332531\pi$
$644$	17.5312	0.690826
$645$	−4.06836	−0.160192
$646$	6.02088	0.236888
$647$	−28.0195	−1.10156	−0.550780	−	0.834650i	$-0.685670\pi$
$647$	−28.0195	−1.10156	−0.550780	+	0.834650i	$0.685670\pi$
$648$	120.662	4.74004
$649$	−0.0671826	−0.00263715
$650$	−12.3551	−0.484609
$651$	8.28977	0.324902
$652$	4.47315	0.175182
$653$	34.4539	1.34829	0.674144	−	0.738600i	$-0.264513\pi$
$653$	34.4539	1.34829	0.674144	+	0.738600i	$0.264513\pi$
$654$	2.99382	0.117068
$655$	21.2526	0.830408
$656$	−18.1946	−0.710381
$657$	−14.3849	−0.561208
$658$	4.00411	0.156097
$659$	5.56012	0.216592	0.108296	−	0.994119i	$-0.465461\pi$
$659$	5.56012	0.216592	0.108296	+	0.994119i	$0.465461\pi$
$660$	−44.2689	−1.72317
$661$	36.4162	1.41642	0.708212	−	0.706000i	$-0.249502\pi$
$661$	36.4162	1.41642	0.708212	+	0.706000i	$0.249502\pi$
$662$	39.5396	1.53675
$663$	57.0068	2.21396
$664$	94.7657	3.67762
$665$	−0.346533	−0.0134380
$666$	−3.13828	−0.121606
$667$	23.5032	0.910046
$668$	32.0671	1.24071
$669$	44.6536	1.72641
$670$	−18.4034	−0.710987
$671$	−0.295036	−0.0113897
$672$	−62.6364	−2.41625
$673$	−22.4676	−0.866064	−0.433032	−	0.901378i	$-0.642556\pi$
$673$	−22.4676	−0.866064	−0.433032	+	0.901378i	$0.642556\pi$
$674$	−52.2881	−2.01406
$675$	3.46732	0.133457
$676$	37.7892	1.45343
$677$	47.9218	1.84179	0.920893	−	0.389816i	$-0.127461\pi$
$677$	47.9218	1.84179	0.920893	+	0.389816i	$0.127461\pi$
$678$	46.8075	1.79763
$679$	−12.2596	−0.470481
$680$	66.7166	2.55846
$681$	15.5759	0.596870
$682$	−40.5923	−1.55436
$683$	14.2123	0.543820	0.271910	−	0.962323i	$-0.412345\pi$
$683$	14.2123	0.543820	0.271910	+	0.962323i	$0.412345\pi$
$684$	2.70084	0.103269
$685$	13.6648	0.522106
$686$	2.79998	0.106904
$687$	2.08197	0.0794321
$688$	36.0033	1.37261
$689$	−17.6346	−0.671825
$690$	−17.4999	−0.666211
$691$	−11.2909	−0.429526	−0.214763	−	0.976666i	$-0.568898\pi$
$691$	−11.2909	−0.429526	−0.214763	+	0.976666i	$0.568898\pi$
$692$	−40.9285	−1.55587
$693$	−4.85925	−0.184588
$694$	−10.8613	−0.412290
$695$	−3.42534	−0.129930
$696$	−175.254	−6.64299
$697$	6.12781	0.232107
$698$	−63.1493	−2.39024
$699$	−0.778952	−0.0294627
$700$	−5.83989	−0.220727
$701$	12.2151	0.461356	0.230678	−	0.973030i	$-0.425906\pi$
$701$	12.2151	0.461356	0.230678	+	0.973030i	$0.425906\pi$
$702$	−42.8393	−1.61686
$703$	0.291026	0.0109763
$704$	172.542	6.50293
$705$	−2.97732	−0.112132
$706$	3.71412	0.139783
$707$	10.5827	0.398004
$708$	0.224345	0.00843139
$709$	−36.0354	−1.35334	−0.676668	−	0.736288i	$-0.736577\pi$
$709$	−36.0354	−1.35334	−0.676668	+	0.736288i	$0.736577\pi$
$710$	−7.65927	−0.287447
$711$	−5.17407	−0.194043
$712$	−50.6763	−1.89917
$713$	−11.9530	−0.447642
$714$	36.1734	1.35375
$715$	16.0662	0.600841
$716$	30.3762	1.13521
$717$	35.0405	1.30861
$718$	4.65657	0.173782
$719$	−42.8409	−1.59769	−0.798847	−	0.601534i	$-0.794557\pi$
$719$	−42.8409	−1.59769	−0.798847	+	0.601534i	$0.794557\pi$
$720$	24.5893	0.916390
$721$	11.8215	0.440256
$722$	52.8634	1.96737
$723$	16.3613	0.608485
$724$	112.910	4.19626
$725$	−7.82924	−0.290771
$726$	13.1562	0.488271
$727$	−1.92544	−0.0714106	−0.0357053	−	0.999362i	$-0.511368\pi$
$727$	−1.92544	−0.0714106	−0.0357053	+	0.999362i	$0.511368\pi$
$728$	47.4424	1.75833
$729$	6.67889	0.247366
$730$	30.1795	1.11699
$731$	−12.1257	−0.448484
$732$	0.985223	0.0364149
$733$	31.1636	1.15106	0.575528	−	0.817782i	$-0.304797\pi$
$733$	31.1636	1.15106	0.575528	+	0.817782i	$0.304797\pi$
$734$	105.217	3.88365
$735$	−2.08197	−0.0767946
$736$	90.3149	3.32905
$737$	23.9312	0.881516
$738$	3.69020	0.135838
$739$	33.5058	1.23253	0.616266	−	0.787538i	$-0.288645\pi$
$739$	33.5058	1.23253	0.616266	+	0.787538i	$0.288645\pi$
$740$	4.90446	0.180292
$741$	−3.18355	−0.116951
$742$	−11.1899	−0.410796
$743$	−37.8263	−1.38771	−0.693856	−	0.720114i	$-0.744090\pi$
$743$	−37.8263	−1.38771	−0.693856	+	0.720114i	$0.744090\pi$
$744$	89.1286	3.26761
$745$	12.0897	0.442931
$746$	−57.6161	−2.10948
$747$	−11.7632	−0.430394
$748$	−131.942	−4.82429
$749$	−14.2857	−0.521990
$750$	5.82947	0.212862
$751$	34.6605	1.26478	0.632390	−	0.774650i	$-0.282074\pi$
$751$	34.6605	1.26478	0.632390	+	0.774650i	$0.282074\pi$
$752$	26.3481	0.960815
$753$	−40.8469	−1.48854
$754$	96.7314	3.52275
$755$	−19.2371	−0.700109
$756$	−20.2488	−0.736441
$757$	−22.4769	−0.816936	−0.408468	−	0.912773i	$-0.633937\pi$
$757$	−22.4769	−0.816936	−0.408468	+	0.912773i	$0.633937\pi$
$758$	−4.72413	−0.171588
$759$	22.7563	0.826000
$760$	−3.72580	−0.135149
$761$	−26.7493	−0.969663	−0.484831	−	0.874608i	$-0.661119\pi$
$761$	−26.7493	−0.969663	−0.484831	+	0.874608i	$0.661119\pi$
$762$	−37.5932	−1.36186
$763$	−0.513566	−0.0185923
$764$	52.9339	1.91508
$765$	−8.28150	−0.299418
$766$	46.4159	1.67708
$767$	−0.0814197	−0.00293990
$768$	−225.414	−8.13393
$769$	34.6423	1.24923	0.624617	−	0.780931i	$-0.285255\pi$
$769$	34.6423	1.24923	0.624617	+	0.780931i	$0.285255\pi$
$770$	10.1947	0.367392
$771$	−23.6481	−0.851664
$772$	85.4906	3.07687
$773$	5.53775	0.199179	0.0995895	−	0.995029i	$-0.468247\pi$
$773$	5.53775	0.199179	0.0995895	+	0.995029i	$0.468247\pi$
$774$	−7.30214	−0.262470
$775$	3.98170	0.143027
$776$	−131.811	−4.73174
$777$	1.74848	0.0627264
$778$	−109.877	−3.93927
$779$	−0.342209	−0.0122609
$780$	−53.6503	−1.92099
$781$	9.95984	0.356391
$782$	−52.1581	−1.86517
$783$	−27.1465	−0.970137
$784$	18.4246	0.658020
$785$	23.5870	0.841858
$786$	123.891	4.41906
$787$	53.3256	1.90085	0.950426	−	0.310950i	$-0.100647\pi$
$787$	53.3256	1.90085	0.950426	+	0.310950i	$0.100647\pi$
$788$	101.973	3.63264
$789$	14.6782	0.522557
$790$	10.8552	0.386211
$791$	−8.02946	−0.285495
$792$	−52.2449	−1.85644
$793$	−0.357559	−0.0126973
$794$	−48.1386	−1.70837
$795$	8.32046	0.295096
$796$	−52.2865	−1.85325
$797$	13.9353	0.493615	0.246808	−	0.969064i	$-0.420618\pi$
$797$	13.9353	0.493615	0.246808	+	0.969064i	$0.420618\pi$
$798$	−2.02011	−0.0715110
$799$	−8.87383	−0.313934
$800$	−30.0852	−1.06367
$801$	6.29043	0.222261
$802$	−23.9940	−0.847256
$803$	−39.2443	−1.38490
$804$	−79.9141	−2.81835
$805$	3.00197	0.105806
$806$	−49.1945	−1.73280
$807$	28.8712	1.01631
$808$	113.781	4.00281
$809$	46.1939	1.62409	0.812046	−	0.583594i	$-0.198354\pi$
$809$	46.1939	1.62409	0.812046	+	0.583594i	$0.198354\pi$
$810$	31.4232	1.10410
$811$	41.9639	1.47355	0.736775	−	0.676138i	$-0.236348\pi$
$811$	41.9639	1.47355	0.736775	+	0.676138i	$0.236348\pi$
$812$	45.7219	1.60453
$813$	51.0351	1.78988
$814$	−8.56173	−0.300089
$815$	0.765964	0.0268306
$816$	238.030	8.33271
$817$	0.677159	0.0236908
$818$	−88.7308	−3.10240
$819$	−5.88901	−0.205779
$820$	−5.76701	−0.201393
$821$	−56.7098	−1.97919	−0.989593	−	0.143892i	$-0.954038\pi$
$821$	−56.7098	−1.97919	−0.989593	+	0.143892i	$0.954038\pi$
$822$	79.6588	2.77842
$823$	−37.2715	−1.29920	−0.649602	−	0.760275i	$-0.725064\pi$
$823$	−37.2715	−1.29920	−0.649602	+	0.760275i	$0.725064\pi$
$824$	127.100	4.42775
$825$	−7.58044	−0.263917
$826$	−0.0516645	−0.00179764
$827$	48.1498	1.67433	0.837166	−	0.546950i	$-0.184211\pi$
$827$	48.1498	1.67433	0.837166	+	0.546950i	$0.184211\pi$
$828$	−23.3971	−0.813104
$829$	11.4376	0.397243	0.198621	−	0.980076i	$-0.436354\pi$
$829$	11.4376	0.397243	0.198621	+	0.980076i	$0.436354\pi$
$830$	24.6793	0.856630
$831$	15.6303	0.542210
$832$	209.107	7.24948
$833$	−6.20526	−0.214999
$834$	−19.9679	−0.691432
$835$	5.49104	0.190025
$836$	7.36834	0.254839
$837$	13.8058	0.477199
$838$	−39.1323	−1.35180
$839$	33.5775	1.15922	0.579612	−	0.814892i	$-0.303204\pi$
$839$	33.5775	1.15922	0.579612	+	0.814892i	$0.303204\pi$
$840$	−22.3846	−0.772341
$841$	32.2970	1.11369
$842$	−71.8329	−2.47552
$843$	61.1003	2.10441
$844$	104.365	3.59238
$845$	6.47088	0.222605
$846$	−5.34387	−0.183726
$847$	−2.25683	−0.0775458
$848$	−73.6326	−2.52855
$849$	33.1939	1.13921
$850$	17.3746	0.595944
$851$	−2.52112	−0.0864229
$852$	−33.2592	−1.13944
$853$	−7.50405	−0.256934	−0.128467	−	0.991714i	$-0.541006\pi$
$853$	−7.50405	−0.256934	−0.128467	+	0.991714i	$0.541006\pi$
$854$	−0.226887	−0.00776393
$855$	0.462482	0.0158165
$856$	−153.595	−5.24977
$857$	−2.10254	−0.0718215	−0.0359107	−	0.999355i	$-0.511433\pi$
$857$	−2.10254	−0.0718215	−0.0359107	+	0.999355i	$0.511433\pi$
$858$	93.6574	3.19741
$859$	−19.7512	−0.673903	−0.336951	−	0.941522i	$-0.609396\pi$
$859$	−19.7512	−0.673903	−0.336951	+	0.941522i	$0.609396\pi$
$860$	11.4117	0.389136
$861$	−2.05599	−0.0700678
$862$	86.6915	2.95272
$863$	24.3432	0.828652	0.414326	−	0.910129i	$-0.364017\pi$
$863$	24.3432	0.828652	0.414326	+	0.910129i	$0.364017\pi$
$864$	−104.315	−3.54887
$865$	−7.00843	−0.238294
$866$	−22.1816	−0.753762
$867$	−44.7732	−1.52058
$868$	−23.2527	−0.789248
$869$	−14.1157	−0.478842
$870$	−45.6404	−1.54735
$871$	29.0026	0.982715
$872$	−5.52167	−0.186987
$873$	16.3616	0.553757
$874$	2.91277	0.0985261
$875$	−1.00000	−0.0338062
$876$	131.050	4.42776
$877$	−6.30320	−0.212844	−0.106422	−	0.994321i	$-0.533939\pi$
$877$	−6.30320	−0.212844	−0.106422	+	0.994321i	$0.533939\pi$
$878$	−67.6033	−2.28150
$879$	42.4665	1.43236
$880$	67.0837	2.26139
$881$	36.3760	1.22554	0.612769	−	0.790262i	$-0.290055\pi$
$881$	36.3760	1.22554	0.612769	+	0.790262i	$0.290055\pi$
$882$	−3.73684	−0.125826
$883$	23.2154	0.781260	0.390630	−	0.920548i	$-0.372257\pi$
$883$	23.2154	0.781260	0.390630	+	0.920548i	$0.372257\pi$
$884$	−159.903	−5.37813
$885$	0.0384159	0.00129134
$886$	14.5802	0.489832
$887$	36.7351	1.23344	0.616722	−	0.787181i	$-0.288460\pi$
$887$	36.7351	1.23344	0.616722	+	0.787181i	$0.288460\pi$
$888$	18.7990	0.630854
$889$	6.44882	0.216286
$890$	−13.1973	−0.442375
$891$	−40.8616	−1.36891
$892$	−125.253	−4.19377
$893$	0.495560	0.0165833
$894$	70.4763	2.35708
$895$	5.20149	0.173867
$896$	72.5173	2.42263
$897$	27.5787	0.920826
$898$	46.7504	1.56008
$899$	−31.1737	−1.03970
$900$	7.79389	0.259796
$901$	24.7989	0.826172
$902$	10.0675	0.335210
$903$	4.06836	0.135387
$904$	−86.3298	−2.87129
$905$	19.3342	0.642692
$906$	−112.142	−3.72567
$907$	−23.4907	−0.779995	−0.389997	−	0.920816i	$-0.627524\pi$
$907$	−23.4907	−0.779995	−0.389997	+	0.920816i	$0.627524\pi$
$908$	−43.6902	−1.44991
$909$	−14.1236	−0.468451
$910$	12.3551	0.409569
$911$	12.0200	0.398240	0.199120	−	0.979975i	$-0.436192\pi$
$911$	12.0200	0.398240	0.199120	+	0.979975i	$0.436192\pi$
$912$	−13.2928	−0.440169
$913$	−32.0920	−1.06209
$914$	−27.5410	−0.910977
$915$	0.168706	0.00557724
$916$	−5.83989	−0.192955
$917$	−21.2526	−0.701822
$918$	60.2433	1.98833
$919$	−22.2245	−0.733118	−0.366559	−	0.930395i	$-0.619464\pi$
$919$	−22.2245	−0.733118	−0.366559	+	0.930395i	$0.619464\pi$
$920$	32.2761	1.06411
$921$	−35.5295	−1.17074
$922$	49.1423	1.61841
$923$	12.0705	0.397305
$924$	44.2689	1.45634
$925$	0.839821	0.0276131
$926$	2.21037	0.0726373
$927$	−15.7769	−0.518182
$928$	235.544	7.73211
$929$	24.6948	0.810211	0.405106	−	0.914270i	$-0.367235\pi$
$929$	24.6948	0.810211	0.405106	+	0.914270i	$0.367235\pi$
$930$	23.2112	0.761126
$931$	0.346533	0.0113572
$932$	2.18495	0.0715704
$933$	20.6272	0.675303
$934$	55.4160	1.81327
$935$	−22.5933	−0.738880
$936$	−63.3164	−2.06956
$937$	55.3266	1.80744	0.903721	−	0.428122i	$-0.140825\pi$
$937$	55.3266	1.80744	0.903721	+	0.428122i	$0.140825\pi$
$938$	18.4034	0.600894
$939$	−56.4070	−1.84077
$940$	8.35134	0.272391
$941$	46.3757	1.51181	0.755903	−	0.654684i	$-0.227198\pi$
$941$	46.3757	1.51181	0.755903	+	0.654684i	$0.227198\pi$
$942$	137.500	4.47999
$943$	2.96451	0.0965377
$944$	−0.339965	−0.0110649
$945$	−3.46732	−0.112792
$946$	−19.9214	−0.647702
$947$	−12.3402	−0.401003	−0.200501	−	0.979693i	$-0.564257\pi$
$947$	−12.3402	−0.401003	−0.200501	+	0.979693i	$0.564257\pi$
$948$	47.1370	1.53094
$949$	−47.5609	−1.54389
$950$	−0.970287	−0.0314803
$951$	59.0827	1.91589
$952$	−66.7166	−2.16230
$953$	10.0701	0.326202	0.163101	−	0.986609i	$-0.447850\pi$
$953$	10.0701	0.326202	0.163101	+	0.986609i	$0.447850\pi$
$954$	14.9341	0.483508
$955$	9.06418	0.293310
$956$	−98.2882	−3.17887
$957$	59.3491	1.91848
$958$	−34.4713	−1.11372
$959$	−13.6648	−0.441261
$960$	−98.6620	−3.18430
$961$	−15.1461	−0.488583
$962$	−10.3761	−0.334539
$963$	19.0657	0.614383
$964$	−45.8933	−1.47812
$965$	14.6391	0.471248
$966$	17.4999	0.563051
$967$	−2.33891	−0.0752142	−0.0376071	−	0.999293i	$-0.511974\pi$
$967$	−2.33891	−0.0752142	−0.0376071	+	0.999293i	$0.511974\pi$
$968$	−24.2646	−0.779895
$969$	4.47692	0.143819
$970$	−34.3267	−1.10216
$971$	54.9328	1.76288	0.881439	−	0.472297i	$-0.156575\pi$
$971$	54.9328	1.76288	0.881439	+	0.472297i	$0.156575\pi$
$972$	75.7039	2.42820
$973$	3.42534	0.109811
$974$	111.394	3.56930
$975$	−9.18686	−0.294215
$976$	−1.49297	−0.0477890
$977$	41.1622	1.31690	0.658448	−	0.752626i	$-0.271213\pi$
$977$	41.1622	1.31690	0.658448	+	0.752626i	$0.271213\pi$
$978$	4.46517	0.142780
$979$	17.1613	0.548478
$980$	5.83989	0.186549
$981$	0.685403	0.0218832
$982$	95.5304	3.04850
$983$	−17.8637	−0.569764	−0.284882	−	0.958563i	$-0.591954\pi$
$983$	−17.8637	−0.569764	−0.284882	+	0.958563i	$0.591954\pi$
$984$	−22.1052	−0.704688
$985$	17.4615	0.556368
$986$	−136.030	−4.33208
$987$	2.97732	0.0947692
$988$	8.92982	0.284095
$989$	−5.86614	−0.186532
$990$	−13.6058	−0.432421
$991$	33.4189	1.06159	0.530794	−	0.847501i	$-0.321894\pi$
$991$	33.4189	1.06159	0.530794	+	0.847501i	$0.321894\pi$
$992$	−119.790	−3.80334
$993$	29.4003	0.932990
$994$	7.65927	0.242937
$995$	−8.95333	−0.283840
$996$	107.166	3.39568
$997$	0.117945	0.00373537	0.00186769	−	0.999998i	$-0.499405\pi$
$997$	0.117945	0.00373537	0.00186769	+	0.999998i	$0.499405\pi$
$998$	−62.6591	−1.98344
$999$	2.91193	0.0921293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.m.1.1	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.m.1.1	✓	67	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79998 q^{2} -2.08197 q^{3} +5.83989 q^{4} +1.00000 q^{5} +5.82947 q^{6} -1.00000 q^{7} -10.7516 q^{8} +1.33460 q^{9} +O(q^{10})\)	\(q-2.79998 q^{2} -2.08197 q^{3} +5.83989 q^{4} +1.00000 q^{5} +5.82947 q^{6} -1.00000 q^{7} -10.7516 q^{8} +1.33460 q^{9} -2.79998 q^{10} +3.64099 q^{11} -12.1585 q^{12} +4.41258 q^{13} +2.79998 q^{14} -2.08197 q^{15} +18.4246 q^{16} -6.20526 q^{17} -3.73684 q^{18} +0.346533 q^{19} +5.83989 q^{20} +2.08197 q^{21} -10.1947 q^{22} -3.00197 q^{23} +22.3846 q^{24} +1.00000 q^{25} -12.3551 q^{26} +3.46732 q^{27} -5.83989 q^{28} -7.82924 q^{29} +5.82947 q^{30} +3.98170 q^{31} -30.0852 q^{32} -7.58044 q^{33} +17.3746 q^{34} -1.00000 q^{35} +7.79389 q^{36} +0.839821 q^{37} -0.970287 q^{38} -9.18686 q^{39} -10.7516 q^{40} -0.987520 q^{41} -5.82947 q^{42} +1.95409 q^{43} +21.2630 q^{44} +1.33460 q^{45} +8.40547 q^{46} +1.43005 q^{47} -38.3594 q^{48} +1.00000 q^{49} -2.79998 q^{50} +12.9192 q^{51} +25.7690 q^{52} -3.99644 q^{53} -9.70843 q^{54} +3.64099 q^{55} +10.7516 q^{56} -0.721472 q^{57} +21.9217 q^{58} -0.0184517 q^{59} -12.1585 q^{60} -0.0810318 q^{61} -11.1487 q^{62} -1.33460 q^{63} +47.3888 q^{64} +4.41258 q^{65} +21.2251 q^{66} +6.57270 q^{67} -36.2380 q^{68} +6.25002 q^{69} +2.79998 q^{70} +2.73547 q^{71} -14.3491 q^{72} -10.7785 q^{73} -2.35148 q^{74} -2.08197 q^{75} +2.02372 q^{76} -3.64099 q^{77} +25.7230 q^{78} -3.87688 q^{79} +18.4246 q^{80} -11.2226 q^{81} +2.76504 q^{82} -8.81408 q^{83} +12.1585 q^{84} -6.20526 q^{85} -5.47143 q^{86} +16.3002 q^{87} -39.1466 q^{88} +4.71336 q^{89} -3.73684 q^{90} -4.41258 q^{91} -17.5312 q^{92} -8.28977 q^{93} -4.00411 q^{94} +0.346533 q^{95} +62.6364 q^{96} +12.2596 q^{97} -2.79998 q^{98} +4.85925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

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