LMFDB - Embedded newform 8027.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73914 q^{2} +3.04549 q^{3} +5.50288 q^{4} +3.66953 q^{5} -8.34203 q^{6} -3.05286 q^{7} -9.59489 q^{8} +6.27504 q^{9} +O(q^{10})$	\(q-2.73914 q^{2} +3.04549 q^{3} +5.50288 q^{4} +3.66953 q^{5} -8.34203 q^{6} -3.05286 q^{7} -9.59489 q^{8} +6.27504 q^{9} -10.0514 q^{10} -2.24646 q^{11} +16.7590 q^{12} +0.738634 q^{13} +8.36221 q^{14} +11.1755 q^{15} +15.2760 q^{16} +0.0553671 q^{17} -17.1882 q^{18} +0.775812 q^{19} +20.1930 q^{20} -9.29747 q^{21} +6.15336 q^{22} +1.00000 q^{23} -29.2212 q^{24} +8.46546 q^{25} -2.02322 q^{26} +9.97411 q^{27} -16.7995 q^{28} -3.19125 q^{29} -30.6113 q^{30} -7.96425 q^{31} -22.6532 q^{32} -6.84157 q^{33} -0.151658 q^{34} -11.2026 q^{35} +34.5308 q^{36} +8.51519 q^{37} -2.12506 q^{38} +2.24951 q^{39} -35.2087 q^{40} +10.8407 q^{41} +25.4671 q^{42} -5.13365 q^{43} -12.3620 q^{44} +23.0264 q^{45} -2.73914 q^{46} +10.2451 q^{47} +46.5229 q^{48} +2.31996 q^{49} -23.1881 q^{50} +0.168620 q^{51} +4.06462 q^{52} -7.81563 q^{53} -27.3205 q^{54} -8.24344 q^{55} +29.2919 q^{56} +2.36273 q^{57} +8.74128 q^{58} -0.0595952 q^{59} +61.4977 q^{60} +7.07771 q^{61} +21.8152 q^{62} -19.1568 q^{63} +31.4984 q^{64} +2.71044 q^{65} +18.7400 q^{66} +5.42949 q^{67} +0.304679 q^{68} +3.04549 q^{69} +30.6854 q^{70} +0.0177997 q^{71} -60.2083 q^{72} +11.1647 q^{73} -23.3243 q^{74} +25.7815 q^{75} +4.26920 q^{76} +6.85812 q^{77} -6.16171 q^{78} +10.6633 q^{79} +56.0556 q^{80} +11.5510 q^{81} -29.6941 q^{82} +3.41030 q^{83} -51.1629 q^{84} +0.203171 q^{85} +14.0618 q^{86} -9.71894 q^{87} +21.5545 q^{88} +14.1474 q^{89} -63.0726 q^{90} -2.25495 q^{91} +5.50288 q^{92} -24.2551 q^{93} -28.0627 q^{94} +2.84687 q^{95} -68.9903 q^{96} +10.3611 q^{97} -6.35469 q^{98} -14.0966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) $ 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * 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 $

$2$	−2.73914	−1.93686	−0.968432	−	0.249278i	$-0.919807\pi$
$2$	−2.73914	−1.93686	−0.968432	+	0.249278i	$0.919807\pi$
$3$	3.04549	1.75832	0.879159	−	0.476529i	$-0.158105\pi$
$3$	3.04549	1.75832	0.879159	+	0.476529i	$0.158105\pi$
$4$	5.50288	2.75144
$5$	3.66953	1.64106	0.820532	−	0.571601i	$-0.193677\pi$
$5$	3.66953	1.64106	0.820532	+	0.571601i	$0.193677\pi$
$6$	−8.34203	−3.40562
$7$	−3.05286	−1.15387	−0.576936	−	0.816789i	$-0.695752\pi$
$7$	−3.05286	−1.15387	−0.576936	+	0.816789i	$0.695752\pi$
$8$	−9.59489	−3.39231
$9$	6.27504	2.09168
$10$	−10.0514	−3.17852
$11$	−2.24646	−0.677332	−0.338666	−	0.940907i	$-0.609976\pi$
$11$	−2.24646	−0.677332	−0.338666	+	0.940907i	$0.609976\pi$
$12$	16.7590	4.83791
$13$	0.738634	0.204860	0.102430	−	0.994740i	$-0.467338\pi$
$13$	0.738634	0.204860	0.102430	+	0.994740i	$0.467338\pi$
$14$	8.36221	2.23489
$15$	11.1755	2.88551
$16$	15.2760	3.81899
$17$	0.0553671	0.0134285	0.00671424	−	0.999977i	$-0.497863\pi$
$17$	0.0553671	0.0134285	0.00671424	+	0.999977i	$0.497863\pi$
$18$	−17.1882	−4.05130
$19$	0.775812	0.177984	0.0889918	−	0.996032i	$-0.471636\pi$
$19$	0.775812	0.177984	0.0889918	+	0.996032i	$0.471636\pi$
$20$	20.1930	4.51529
$21$	−9.29747	−2.02887
$22$	6.15336	1.31190
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−29.2212	−5.96475
$25$	8.46546	1.69309
$26$	−2.02322	−0.396786
$27$	9.97411	1.91952
$28$	−16.7995	−3.17481
$29$	−3.19125	−0.592600	−0.296300	−	0.955095i	$-0.595753\pi$
$29$	−3.19125	−0.592600	−0.296300	+	0.955095i	$0.595753\pi$
$30$	−30.6113	−5.58884
$31$	−7.96425	−1.43042	−0.715210	−	0.698909i	$-0.753669\pi$
$31$	−7.96425	−1.43042	−0.715210	+	0.698909i	$0.753669\pi$
$32$	−22.6532	−4.00456
$33$	−6.84157	−1.19096
$34$	−0.151658	−0.0260091
$35$	−11.2026	−1.89358
$36$	34.5308	5.75513
$37$	8.51519	1.39989	0.699944	−	0.714198i	$-0.253208\pi$
$37$	8.51519	1.39989	0.699944	+	0.714198i	$0.253208\pi$
$38$	−2.12506	−0.344730
$39$	2.24951	0.360209
$40$	−35.2087	−5.56699
$41$	10.8407	1.69303	0.846514	−	0.532366i	$-0.178697\pi$
$41$	10.8407	1.69303	0.846514	+	0.532366i	$0.178697\pi$
$42$	25.4671	3.92965
$43$	−5.13365	−0.782874	−0.391437	−	0.920205i	$-0.628022\pi$
$43$	−5.13365	−0.782874	−0.391437	+	0.920205i	$0.628022\pi$
$44$	−12.3620	−1.86364
$45$	23.0264	3.43258
$46$	−2.73914	−0.403864
$47$	10.2451	1.49440	0.747200	−	0.664600i	$-0.231398\pi$
$47$	10.2451	1.49440	0.747200	+	0.664600i	$0.231398\pi$
$48$	46.5229	6.71500
$49$	2.31996	0.331423
$50$	−23.1881	−3.27929
$51$	0.168620	0.0236115
$52$	4.06462	0.563661
$53$	−7.81563	−1.07356	−0.536779	−	0.843723i	$-0.680359\pi$
$53$	−7.81563	−1.07356	−0.536779	+	0.843723i	$0.680359\pi$
$54$	−27.3205	−3.71785
$55$	−8.24344	−1.11154
$56$	29.2919	3.91429
$57$	2.36273	0.312951
$58$	8.74128	1.14779
$59$	−0.0595952	−0.00775863	−0.00387931	−	0.999992i	$-0.501235\pi$
$59$	−0.0595952	−0.00775863	−0.00387931	+	0.999992i	$0.501235\pi$
$60$	61.4977	7.93932
$61$	7.07771	0.906208	0.453104	−	0.891458i	$-0.350317\pi$
$61$	7.07771	0.906208	0.453104	+	0.891458i	$0.350317\pi$
$62$	21.8152	2.77053
$63$	−19.1568	−2.41353
$64$	31.4984	3.93730
$65$	2.71044	0.336189
$66$	18.7400	2.30674
$67$	5.42949	0.663318	0.331659	−	0.943399i	$-0.392392\pi$
$67$	5.42949	0.663318	0.331659	+	0.943399i	$0.392392\pi$
$68$	0.304679	0.0369477
$69$	3.04549	0.366634
$70$	30.6854	3.66761
$71$	0.0177997	0.00211243	0.00105622	−	0.999999i	$-0.499664\pi$
$71$	0.0177997	0.00211243	0.00105622	+	0.999999i	$0.499664\pi$
$72$	−60.2083	−7.09561
$73$	11.1647	1.30673	0.653367	−	0.757041i	$-0.273356\pi$
$73$	11.1647	1.30673	0.653367	+	0.757041i	$0.273356\pi$
$74$	−23.3243	−2.71139
$75$	25.7815	2.97699
$76$	4.26920	0.489711
$77$	6.85812	0.781555
$78$	−6.16171	−0.697676
$79$	10.6633	1.19972	0.599858	−	0.800107i	$-0.295224\pi$
$79$	10.6633	1.19972	0.599858	+	0.800107i	$0.295224\pi$
$80$	56.0556	6.26721
$81$	11.5510	1.28344
$82$	−29.6941	−3.27917
$83$	3.41030	0.374329	0.187165	−	0.982329i	$-0.440070\pi$
$83$	3.41030	0.374329	0.187165	+	0.982329i	$0.440070\pi$
$84$	−51.1629	−5.58233
$85$	0.203171	0.0220370
$86$	14.0618	1.51632
$87$	−9.71894	−1.04198
$88$	21.5545	2.29772
$89$	14.1474	1.49962	0.749812	−	0.661651i	$-0.230144\pi$
$89$	14.1474	1.49962	0.749812	+	0.661651i	$0.230144\pi$
$90$	−63.0726	−6.64844
$91$	−2.25495	−0.236383
$92$	5.50288	0.573715
$93$	−24.2551	−2.51513
$94$	−28.0627	−2.89445
$95$	2.84687	0.292082
$96$	−68.9903	−7.04129
$97$	10.3611	1.05201	0.526003	−	0.850483i	$-0.323690\pi$
$97$	10.3611	1.05201	0.526003	+	0.850483i	$0.323690\pi$
$98$	−6.35469	−0.641920
$99$	−14.0966	−1.41676
$100$	46.5844	4.65844
$101$	3.07768	0.306241	0.153120	−	0.988208i	$-0.451068\pi$
$101$	3.07768	0.306241	0.153120	+	0.988208i	$0.451068\pi$
$102$	−0.461874	−0.0457323
$103$	−4.10831	−0.404804	−0.202402	−	0.979303i	$-0.564875\pi$
$103$	−4.10831	−0.404804	−0.202402	+	0.979303i	$0.564875\pi$
$104$	−7.08711	−0.694949
$105$	−34.1174	−3.32951
$106$	21.4081	2.07934
$107$	−8.32094	−0.804416	−0.402208	−	0.915548i	$-0.631757\pi$
$107$	−8.32094	−0.804416	−0.402208	+	0.915548i	$0.631757\pi$
$108$	54.8864	5.28144
$109$	−0.0205040	−0.00196393	−0.000981966	−	1.00000i	$-0.500313\pi$
$109$	−0.0205040	−0.00196393	−0.000981966		1.00000i	$0.500313\pi$
$110$	22.5799	2.15291
$111$	25.9330	2.46145
$112$	−46.6354	−4.40663
$113$	7.98310	0.750987	0.375493	−	0.926825i	$-0.377473\pi$
$113$	7.98310	0.750987	0.375493	+	0.926825i	$0.377473\pi$
$114$	−6.47185	−0.606144
$115$	3.66953	0.342186
$116$	−17.5611	−1.63051
$117$	4.63496	0.428502
$118$	0.163239	0.0150274
$119$	−0.169028	−0.0154948
$120$	−107.228	−9.78853
$121$	−5.95344	−0.541222
$122$	−19.3868	−1.75520
$123$	33.0152	2.97688
$124$	−43.8263	−3.93572
$125$	12.7166	1.13741
$126$	52.4732	4.67468
$127$	2.38707	0.211819	0.105909	−	0.994376i	$-0.466225\pi$
$127$	2.38707	0.211819	0.105909	+	0.994376i	$0.466225\pi$
$128$	−40.9721	−3.62145
$129$	−15.6345	−1.37654
$130$	−7.42427	−0.651152
$131$	−13.9131	−1.21559	−0.607796	−	0.794093i	$-0.707946\pi$
$131$	−13.9131	−1.21559	−0.607796	+	0.794093i	$0.707946\pi$
$132$	−37.6484	−3.27687
$133$	−2.36845	−0.205370
$134$	−14.8721	−1.28476
$135$	36.6003	3.15005
$136$	−0.531241	−0.0455535
$137$	−0.793301	−0.0677763	−0.0338882	−	0.999426i	$-0.510789\pi$
$137$	−0.793301	−0.0677763	−0.0338882	+	0.999426i	$0.510789\pi$
$138$	−8.34203	−0.710121
$139$	−20.2076	−1.71398	−0.856992	−	0.515330i	$-0.827669\pi$
$139$	−20.2076	−1.71398	−0.856992	+	0.515330i	$0.827669\pi$
$140$	−61.6464	−5.21007
$141$	31.2014	2.62763
$142$	−0.0487558	−0.00409150
$143$	−1.65931	−0.138758
$144$	95.8573	7.98810
$145$	−11.7104	−0.972495
$146$	−30.5818	−2.53097
$147$	7.06542	0.582746
$148$	46.8581	3.85171
$149$	9.21907	0.755255	0.377628	−	0.925958i	$-0.376740\pi$
$149$	9.21907	0.755255	0.377628	+	0.925958i	$0.376740\pi$
$150$	−70.6191	−5.76603
$151$	3.64387	0.296534	0.148267	−	0.988947i	$-0.452631\pi$
$151$	3.64387	0.296534	0.148267	+	0.988947i	$0.452631\pi$
$152$	−7.44383	−0.603774
$153$	0.347430	0.0280881
$154$	−18.7853	−1.51377
$155$	−29.2250	−2.34741
$156$	12.3788	0.991095
$157$	17.1895	1.37187	0.685935	−	0.727662i	$-0.259393\pi$
$157$	17.1895	1.37187	0.685935	+	0.727662i	$0.259393\pi$
$158$	−29.2083	−2.32369
$159$	−23.8024	−1.88766
$160$	−83.1267	−6.57174
$161$	−3.05286	−0.240599
$162$	−31.6397	−2.48585
$163$	5.66005	0.443330	0.221665	−	0.975123i	$-0.428851\pi$
$163$	5.66005	0.443330	0.221665	+	0.975123i	$0.428851\pi$
$164$	59.6550	4.65827
$165$	−25.1053	−1.95445
$166$	−9.34129	−0.725025
$167$	3.47812	0.269145	0.134572	−	0.990904i	$-0.457034\pi$
$167$	3.47812	0.269145	0.134572	+	0.990904i	$0.457034\pi$
$168$	89.2082	6.88256
$169$	−12.4544	−0.958032
$170$	−0.556514	−0.0426827
$171$	4.86825	0.372284
$172$	−28.2499	−2.15403
$173$	−7.37480	−0.560695	−0.280348	−	0.959899i	$-0.590450\pi$
$173$	−7.37480	−0.560695	−0.280348	+	0.959899i	$0.590450\pi$
$174$	26.6215	2.01817
$175$	−25.8439	−1.95361
$176$	−34.3168	−2.58672
$177$	−0.181497	−0.0136421
$178$	−38.7518	−2.90457
$179$	−16.0596	−1.20035	−0.600175	−	0.799869i	$-0.704902\pi$
$179$	−16.0596	−1.20035	−0.600175	+	0.799869i	$0.704902\pi$
$180$	126.712	9.44454
$181$	20.6116	1.53205	0.766025	−	0.642811i	$-0.222232\pi$
$181$	20.6116	1.53205	0.766025	+	0.642811i	$0.222232\pi$
$182$	6.17661	0.457841
$183$	21.5551	1.59340
$184$	−9.59489	−0.707345
$185$	31.2467	2.29731
$186$	66.4380	4.87147
$187$	−0.124380	−0.00909554
$188$	56.3775	4.11175
$189$	−30.4496	−2.21488
$190$	−7.79796	−0.565724
$191$	−12.0323	−0.870630	−0.435315	−	0.900278i	$-0.643363\pi$
$191$	−12.0323	−0.870630	−0.435315	+	0.900278i	$0.643363\pi$
$192$	95.9282	6.92302
$193$	25.9405	1.86724	0.933619	−	0.358267i	$-0.116632\pi$
$193$	25.9405	1.86724	0.933619	+	0.358267i	$0.116632\pi$
$194$	−28.3804	−2.03759
$195$	8.25463	0.591127
$196$	12.7665	0.911890
$197$	8.14552	0.580344	0.290172	−	0.956974i	$-0.406287\pi$
$197$	8.14552	0.580344	0.290172	+	0.956974i	$0.406287\pi$
$198$	38.6125	2.74407
$199$	15.5337	1.10116	0.550579	−	0.834783i	$-0.314407\pi$
$199$	15.5337	1.10116	0.550579	+	0.834783i	$0.314407\pi$
$200$	−81.2251	−5.74348
$201$	16.5355	1.16632
$202$	−8.43020	−0.593147
$203$	9.74244	0.683786
$204$	0.927897	0.0649658
$205$	39.7802	2.77837
$206$	11.2532	0.784050
$207$	6.27504	0.436145
$208$	11.2834	0.782360
$209$	−1.74283	−0.120554
$210$	93.4522	6.44881
$211$	15.0562	1.03651	0.518256	−	0.855226i	$-0.326582\pi$
$211$	15.0562	1.03651	0.518256	+	0.855226i	$0.326582\pi$
$212$	−43.0085	−2.95383
$213$	0.0542088	0.00371433
$214$	22.7922	1.55804
$215$	−18.8381	−1.28475
$216$	−95.7004	−6.51159
$217$	24.3137	1.65052
$218$	0.0561634	0.00380387
$219$	34.0022	2.29765
$220$	−45.3627	−3.05835
$221$	0.0408960	0.00275096
$222$	−71.0340	−4.76749
$223$	−20.0138	−1.34022	−0.670111	−	0.742261i	$-0.733753\pi$
$223$	−20.0138	−1.34022	−0.670111	+	0.742261i	$0.733753\pi$
$224$	69.1571	4.62076
$225$	53.1210	3.54140
$226$	−21.8668	−1.45456
$227$	0.761637	0.0505516	0.0252758	−	0.999681i	$-0.491954\pi$
$227$	0.761637	0.0505516	0.0252758	+	0.999681i	$0.491954\pi$
$228$	13.0018	0.861068
$229$	−14.2284	−0.940238	−0.470119	−	0.882603i	$-0.655789\pi$
$229$	−14.2284	−0.940238	−0.470119	+	0.882603i	$0.655789\pi$
$230$	−10.0514	−0.662767
$231$	20.8864	1.37422
$232$	30.6197	2.01028
$233$	27.6578	1.81192	0.905961	−	0.423362i	$-0.139150\pi$
$233$	27.6578	1.81192	0.905961	+	0.423362i	$0.139150\pi$
$234$	−12.6958	−0.829950
$235$	37.5947	2.45241
$236$	−0.327945	−0.0213474
$237$	32.4750	2.10948
$238$	0.462991	0.0300112
$239$	8.17092	0.528533	0.264267	−	0.964450i	$-0.414870\pi$
$239$	8.17092	0.528533	0.264267	+	0.964450i	$0.414870\pi$
$240$	170.717	11.0197
$241$	12.4461	0.801724	0.400862	−	0.916138i	$-0.368711\pi$
$241$	12.4461	0.801724	0.400862	+	0.916138i	$0.368711\pi$
$242$	16.3073	1.04827
$243$	5.25612	0.337180
$244$	38.9478	2.49338
$245$	8.51316	0.543886
$246$	−90.4333	−5.76581
$247$	0.573041	0.0364617
$248$	76.4160	4.85242
$249$	10.3861	0.658190
$250$	−34.8325	−2.20300
$251$	−7.47593	−0.471877	−0.235938	−	0.971768i	$-0.575816\pi$
$251$	−7.47593	−0.471877	−0.235938	+	0.971768i	$0.575816\pi$
$252$	−105.418	−6.64069
$253$	−2.24646	−0.141233
$254$	−6.53853	−0.410264
$255$	0.618757	0.0387480
$256$	49.2314	3.07696
$257$	−22.4630	−1.40120	−0.700602	−	0.713552i	$-0.747085\pi$
$257$	−22.4630	−1.40120	−0.700602	+	0.713552i	$0.747085\pi$
$258$	42.8251	2.66617
$259$	−25.9957	−1.61529
$260$	14.9152	0.925004
$261$	−20.0252	−1.23953
$262$	38.1099	2.35444
$263$	23.0547	1.42161	0.710806	−	0.703388i	$-0.248330\pi$
$263$	23.0547	1.42161	0.710806	+	0.703388i	$0.248330\pi$
$264$	65.6441	4.04011
$265$	−28.6797	−1.76178
$266$	6.48750	0.397774
$267$	43.0859	2.63681
$268$	29.8779	1.82508
$269$	27.2824	1.66344	0.831720	−	0.555195i	$-0.187356\pi$
$269$	27.2824	1.66344	0.831720	+	0.555195i	$0.187356\pi$
$270$	−100.253	−6.10122
$271$	21.2293	1.28959	0.644793	−	0.764357i	$-0.276943\pi$
$271$	21.2293	1.28959	0.644793	+	0.764357i	$0.276943\pi$
$272$	0.845785	0.0512833
$273$	−6.86743	−0.415636
$274$	2.17296	0.131273
$275$	−19.0173	−1.14678
$276$	16.7590	1.00877
$277$	−19.0331	−1.14359	−0.571793	−	0.820398i	$-0.693752\pi$
$277$	−19.0331	−1.14359	−0.571793	+	0.820398i	$0.693752\pi$
$278$	55.3514	3.31975
$279$	−49.9759	−2.99198
$280$	107.487	6.42360
$281$	−16.0127	−0.955237	−0.477618	−	0.878567i	$-0.658500\pi$
$281$	−16.0127	−0.955237	−0.477618	+	0.878567i	$0.658500\pi$
$282$	−85.4649	−5.08936
$283$	−28.6557	−1.70341	−0.851703	−	0.524024i	$-0.824430\pi$
$283$	−28.6557	−1.70341	−0.851703	+	0.524024i	$0.824430\pi$
$284$	0.0979496	0.00581224
$285$	8.67012	0.513573
$286$	4.54508	0.268756
$287$	−33.0951	−1.95354
$288$	−142.150	−8.37626
$289$	−16.9969	−0.999820
$290$	32.0764	1.88359
$291$	31.5545	1.84976
$292$	61.4383	3.59541
$293$	−30.7297	−1.79525	−0.897625	−	0.440760i	$-0.854709\pi$
$293$	−30.7297	−1.79525	−0.897625	+	0.440760i	$0.854709\pi$
$294$	−19.3532	−1.12870
$295$	−0.218686	−0.0127324
$296$	−81.7023	−4.74885
$297$	−22.4064	−1.30015
$298$	−25.2523	−1.46283
$299$	0.738634	0.0427163
$300$	141.873	8.19102
$301$	15.6723	0.903337
$302$	−9.98107	−0.574346
$303$	9.37307	0.538469
$304$	11.8513	0.679717
$305$	25.9719	1.48715
$306$	−0.951660	−0.0544028
$307$	−17.8027	−1.01605	−0.508026	−	0.861342i	$-0.669624\pi$
$307$	−17.8027	−1.01605	−0.508026	+	0.861342i	$0.669624\pi$
$308$	37.7394	2.15040
$309$	−12.5118	−0.711774
$310$	80.0515	4.54662
$311$	22.7848	1.29200	0.646002	−	0.763335i	$-0.276440\pi$
$311$	22.7848	1.29200	0.646002	+	0.763335i	$0.276440\pi$
$312$	−21.5838	−1.22194
$313$	10.2601	0.579935	0.289968	−	0.957036i	$-0.406355\pi$
$313$	10.2601	0.579935	0.289968	+	0.957036i	$0.406355\pi$
$314$	−47.0844	−2.65713
$315$	−70.2965	−3.96076
$316$	58.6789	3.30095
$317$	−13.2436	−0.743836	−0.371918	−	0.928266i	$-0.621300\pi$
$317$	−13.2436	−0.743836	−0.371918	+	0.928266i	$0.621300\pi$
$318$	65.1982	3.65613
$319$	7.16900	0.401387
$320$	115.584	6.46136
$321$	−25.3414	−1.41442
$322$	8.36221	0.466008
$323$	0.0429544	0.00239005
$324$	63.5637	3.53132
$325$	6.25287	0.346847
$326$	−15.5037	−0.858669
$327$	−0.0624450	−0.00345321
$328$	−104.015	−5.74327
$329$	−31.2768	−1.72435
$330$	68.7670	3.78550
$331$	31.6674	1.74060	0.870298	−	0.492526i	$-0.163926\pi$
$331$	31.6674	1.74060	0.870298	+	0.492526i	$0.163926\pi$
$332$	18.7665	1.02995
$333$	53.4331	2.92812
$334$	−9.52705	−0.521297
$335$	19.9237	1.08855
$336$	−142.028	−7.74825
$337$	−10.6152	−0.578247	−0.289123	−	0.957292i	$-0.593364\pi$
$337$	−10.6152	−0.578247	−0.289123	+	0.957292i	$0.593364\pi$
$338$	34.1144	1.85558
$339$	24.3125	1.32047
$340$	1.11803	0.0606335
$341$	17.8913	0.968870
$342$	−13.3348	−0.721064
$343$	14.2875	0.771453
$344$	49.2568	2.65575
$345$	11.1755	0.601671
$346$	20.2006	1.08599
$347$	23.8718	1.28150	0.640752	−	0.767748i	$-0.278622\pi$
$347$	23.8718	1.28150	0.640752	+	0.767748i	$0.278622\pi$
$348$	−53.4822	−2.86695
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	70.7899	3.78388
$351$	7.36722	0.393233
$352$	50.8895	2.71242
$353$	−1.65728	−0.0882081	−0.0441041	−	0.999027i	$-0.514043\pi$
$353$	−1.65728	−0.0882081	−0.0441041	+	0.999027i	$0.514043\pi$
$354$	0.497145	0.0264229
$355$	0.0653165	0.00346664
$356$	77.8516	4.12613
$357$	−0.514774	−0.0272447
$358$	43.9894	2.32491
$359$	−12.9085	−0.681287	−0.340643	−	0.940193i	$-0.610645\pi$
$359$	−12.9085	−0.681287	−0.340643	+	0.940193i	$0.610645\pi$
$360$	−220.936	−11.6444
$361$	−18.3981	−0.968322
$362$	−56.4581	−2.96737
$363$	−18.1312	−0.951639
$364$	−12.4087	−0.650393
$365$	40.9694	2.14444
$366$	−59.0425	−3.08620
$367$	−22.4526	−1.17202	−0.586008	−	0.810305i	$-0.699301\pi$
$367$	−22.4526	−1.17202	−0.586008	+	0.810305i	$0.699301\pi$
$368$	15.2760	0.796315
$369$	68.0256	3.54127
$370$	−85.5892	−4.44957
$371$	23.8600	1.23875
$372$	−133.473	−6.92024
$373$	8.62205	0.446433	0.223216	−	0.974769i	$-0.428344\pi$
$373$	8.62205	0.446433	0.223216	+	0.974769i	$0.428344\pi$
$374$	0.340693	0.0176168
$375$	38.7283	1.99992
$376$	−98.3005	−5.06946
$377$	−2.35717	−0.121400
$378$	83.4056	4.28992
$379$	−5.42924	−0.278881	−0.139441	−	0.990230i	$-0.544530\pi$
$379$	−5.42924	−0.278881	−0.139441	+	0.990230i	$0.544530\pi$
$380$	15.6660	0.803648
$381$	7.26982	0.372444
$382$	32.9583	1.68629
$383$	2.45778	0.125587	0.0627934	−	0.998027i	$-0.479999\pi$
$383$	2.45778	0.125587	0.0627934	+	0.998027i	$0.479999\pi$
$384$	−124.780	−6.36766
$385$	25.1661	1.28258
$386$	−71.0547	−3.61659
$387$	−32.2138	−1.63752
$388$	57.0157	2.89453
$389$	−2.75378	−0.139622	−0.0698110	−	0.997560i	$-0.522240\pi$
$389$	−2.75378	−0.139622	−0.0698110	+	0.997560i	$0.522240\pi$
$390$	−22.6106	−1.14493
$391$	0.0553671	0.00280003
$392$	−22.2597	−1.12429
$393$	−42.3722	−2.13740
$394$	−22.3117	−1.12405
$395$	39.1293	1.96881
$396$	−77.5719	−3.89814
$397$	24.9136	1.25038	0.625190	−	0.780473i	$-0.285022\pi$
$397$	24.9136	1.25038	0.625190	+	0.780473i	$0.285022\pi$
$398$	−42.5491	−2.13279
$399$	−7.21309	−0.361106
$400$	129.318	6.46590
$401$	−29.4505	−1.47069	−0.735344	−	0.677694i	$-0.762979\pi$
$401$	−29.4505	−1.47069	−0.735344	+	0.677694i	$0.762979\pi$
$402$	−45.2930	−2.25901
$403$	−5.88266	−0.293036
$404$	16.9361	0.842604
$405$	42.3867	2.10621
$406$	−26.6859	−1.32440
$407$	−19.1290	−0.948189
$408$	−1.61789	−0.0800975
$409$	30.5647	1.51133	0.755664	−	0.654959i	$-0.227314\pi$
$409$	30.5647	1.51133	0.755664	+	0.654959i	$0.227314\pi$
$410$	−108.963	−5.38132
$411$	−2.41600	−0.119172
$412$	−22.6076	−1.11379
$413$	0.181936	0.00895247
$414$	−17.1882	−0.844754
$415$	12.5142	0.614298
$416$	−16.7324	−0.820376
$417$	−61.5421	−3.01373
$418$	4.77385	0.233497
$419$	−21.1148	−1.03153	−0.515763	−	0.856731i	$-0.672492\pi$
$419$	−21.1148	−1.03153	−0.515763	+	0.856731i	$0.672492\pi$
$420$	−187.744	−9.16096
$421$	−29.0037	−1.41356	−0.706778	−	0.707436i	$-0.749852\pi$
$421$	−29.0037	−1.41356	−0.706778	+	0.707436i	$0.749852\pi$
$422$	−41.2410	−2.00758
$423$	64.2883	3.12580
$424$	74.9900	3.64184
$425$	0.468707	0.0227356
$426$	−0.148486	−0.00719415
$427$	−21.6073	−1.04565
$428$	−45.7892	−2.21330
$429$	−5.05342	−0.243981
$430$	51.6001	2.48838
$431$	2.54481	0.122579	0.0612896	−	0.998120i	$-0.480479\pi$
$431$	2.54481	0.122579	0.0612896	+	0.998120i	$0.480479\pi$
$432$	152.364	7.33062
$433$	−8.36502	−0.401997	−0.200999	−	0.979592i	$-0.564419\pi$
$433$	−8.36502	−0.401997	−0.200999	+	0.979592i	$0.564419\pi$
$434$	−66.5987	−3.19684
$435$	−35.6639	−1.70995
$436$	−0.112831	−0.00540364
$437$	0.775812	0.0371121
$438$	−93.1367	−4.45024
$439$	19.3675	0.924361	0.462181	−	0.886786i	$-0.347067\pi$
$439$	19.3675	0.924361	0.462181	+	0.886786i	$0.347067\pi$
$440$	79.0949	3.77070
$441$	14.5578	0.693230
$442$	−0.112020	−0.00532824
$443$	−6.60978	−0.314040	−0.157020	−	0.987595i	$-0.550189\pi$
$443$	−6.60978	−0.314040	−0.157020	+	0.987595i	$0.550189\pi$
$444$	142.706	6.77253
$445$	51.9144	2.46098
$446$	54.8205	2.59583
$447$	28.0766	1.32798
$448$	−96.1602	−4.54314
$449$	2.90523	0.137106	0.0685532	−	0.997647i	$-0.478162\pi$
$449$	2.90523	0.137106	0.0685532	+	0.997647i	$0.478162\pi$
$450$	−145.506	−6.85922
$451$	−24.3531	−1.14674
$452$	43.9301	2.06630
$453$	11.0974	0.521401
$454$	−2.08623	−0.0979116
$455$	−8.27460	−0.387919
$456$	−22.6701	−1.06163
$457$	15.4182	0.721234	0.360617	−	0.932714i	$-0.382566\pi$
$457$	15.4182	0.721234	0.360617	+	0.932714i	$0.382566\pi$
$458$	38.9735	1.82111
$459$	0.552237	0.0257762
$460$	20.1930	0.941504
$461$	−27.3017	−1.27156	−0.635782	−	0.771868i	$-0.719322\pi$
$461$	−27.3017	−1.27156	−0.635782	+	0.771868i	$0.719322\pi$
$462$	−57.2106	−2.66168
$463$	26.8286	1.24683	0.623415	−	0.781891i	$-0.285745\pi$
$463$	26.8286	1.24683	0.623415	+	0.781891i	$0.285745\pi$
$464$	−48.7494	−2.26314
$465$	−89.0047	−4.12749
$466$	−75.7585	−3.50944
$467$	15.9554	0.738328	0.369164	−	0.929364i	$-0.379644\pi$
$467$	15.9554	0.738328	0.369164	+	0.929364i	$0.379644\pi$
$468$	25.5056	1.17900
$469$	−16.5755	−0.765385
$470$	−102.977	−4.74998
$471$	52.3505	2.41218
$472$	0.571809	0.0263196
$473$	11.5325	0.530265
$474$	−88.9536	−4.08578
$475$	6.56760	0.301342
$476$	−0.930141	−0.0426329
$477$	−49.0433	−2.24554
$478$	−22.3813	−1.02370
$479$	−39.7623	−1.81679	−0.908393	−	0.418118i	$-0.862690\pi$
$479$	−39.7623	−1.81679	−0.908393	+	0.418118i	$0.862690\pi$
$480$	−253.162	−11.5552
$481$	6.28961	0.286781
$482$	−34.0916	−1.55283
$483$	−9.29747	−0.423050
$484$	−32.7611	−1.48914
$485$	38.0202	1.72641
$486$	−14.3972	−0.653072
$487$	−15.2660	−0.691769	−0.345885	−	0.938277i	$-0.612421\pi$
$487$	−15.2660	−0.691769	−0.345885	+	0.938277i	$0.612421\pi$
$488$	−67.9099	−3.07414
$489$	17.2377	0.779514
$490$	−23.3187	−1.05343
$491$	−22.6591	−1.02259	−0.511294	−	0.859406i	$-0.670834\pi$
$491$	−22.6591	−1.02259	−0.511294	+	0.859406i	$0.670834\pi$
$492$	181.679	8.19072
$493$	−0.176690	−0.00795773
$494$	−1.56964	−0.0706214
$495$	−51.7279	−2.32500
$496$	−121.662	−5.46276
$497$	−0.0543399	−0.00243748
$498$	−28.4489	−1.27482
$499$	25.0963	1.12346	0.561732	−	0.827319i	$-0.310135\pi$
$499$	25.0963	1.12346	0.561732	+	0.827319i	$0.310135\pi$
$500$	69.9780	3.12951
$501$	10.5926	0.473242
$502$	20.4776	0.913961
$503$	2.54563	0.113504	0.0567520	−	0.998388i	$-0.481926\pi$
$503$	2.54563	0.113504	0.0567520	+	0.998388i	$0.481926\pi$
$504$	183.807	8.18744
$505$	11.2937	0.502561
$506$	6.15336	0.273550
$507$	−37.9299	−1.68452
$508$	13.1358	0.582806
$509$	12.4161	0.550336	0.275168	−	0.961396i	$-0.411267\pi$
$509$	12.4161	0.550336	0.275168	+	0.961396i	$0.411267\pi$
$510$	−1.69486	−0.0750497
$511$	−34.0844	−1.50781
$512$	−52.9075	−2.33820
$513$	7.73803	0.341643
$514$	61.5293	2.71394
$515$	−15.0756	−0.664309
$516$	−86.0348	−3.78747
$517$	−23.0151	−1.01220
$518$	71.2058	3.12860
$519$	−22.4599	−0.985880
$520$	−26.0064	−1.14045
$521$	16.7968	0.735883	0.367941	−	0.929849i	$-0.380063\pi$
$521$	16.7968	0.735883	0.367941	+	0.929849i	$0.380063\pi$
$522$	54.8519	2.40080
$523$	1.32237	0.0578233	0.0289117	−	0.999582i	$-0.490796\pi$
$523$	1.32237	0.0578233	0.0289117	+	0.999582i	$0.490796\pi$
$524$	−76.5621	−3.34463
$525$	−78.7073	−3.43507
$526$	−63.1500	−2.75347
$527$	−0.440957	−0.0192084
$528$	−104.512	−4.54828
$529$	1.00000	0.0434783
$530$	78.5576	3.41233
$531$	−0.373962	−0.0162286
$532$	−13.0333	−0.565065
$533$	8.00729	0.346834
$534$	−118.018	−5.10715
$535$	−30.5340	−1.32010
$536$	−52.0954	−2.25018
$537$	−48.9094	−2.11060
$538$	−74.7304	−3.22186
$539$	−5.21168	−0.224483
$540$	201.407	8.66718
$541$	−30.4727	−1.31012	−0.655062	−	0.755575i	$-0.727358\pi$
$541$	−30.4727	−1.31012	−0.655062	+	0.755575i	$0.727358\pi$
$542$	−58.1500	−2.49775
$543$	62.7726	2.69383
$544$	−1.25424	−0.0537752
$545$	−0.0752402	−0.00322294
$546$	18.8108	0.805030
$547$	17.9399	0.767056	0.383528	−	0.923529i	$-0.374709\pi$
$547$	17.9399	0.767056	0.383528	+	0.923529i	$0.374709\pi$
$548$	−4.36545	−0.186483
$549$	44.4129	1.89550
$550$	52.0910	2.22117
$551$	−2.47581	−0.105473
$552$	−29.2212	−1.24374
$553$	−32.5536	−1.38432
$554$	52.1343	2.21497
$555$	95.1618	4.03939
$556$	−111.200	−4.71593
$557$	16.4865	0.698555	0.349278	−	0.937019i	$-0.386427\pi$
$557$	16.4865	0.698555	0.349278	+	0.937019i	$0.386427\pi$
$558$	136.891	5.79506
$559$	−3.79189	−0.160380
$560$	−171.130	−7.23156
$561$	−0.378798	−0.0159928
$562$	43.8610	1.85016
$563$	−12.5139	−0.527398	−0.263699	−	0.964605i	$-0.584943\pi$
$563$	−12.5139	−0.527398	−0.263699	+	0.964605i	$0.584943\pi$
$564$	171.697	7.22977
$565$	29.2942	1.23242
$566$	78.4921	3.29927
$567$	−35.2635	−1.48093
$568$	−0.170786	−0.00716602
$569$	−39.5993	−1.66009	−0.830044	−	0.557697i	$-0.811685\pi$
$569$	−39.5993	−1.66009	−0.830044	+	0.557697i	$0.811685\pi$
$570$	−23.7487	−0.994722
$571$	−35.1400	−1.47056	−0.735282	−	0.677761i	$-0.762950\pi$
$571$	−35.1400	−1.47056	−0.735282	+	0.677761i	$0.762950\pi$
$572$	−9.13098	−0.381786
$573$	−36.6444	−1.53084
$574$	90.6520	3.78374
$575$	8.46546	0.353034
$576$	197.654	8.23557
$577$	−4.03699	−0.168062	−0.0840310	−	0.996463i	$-0.526779\pi$
$577$	−4.03699	−0.168062	−0.0840310	+	0.996463i	$0.526779\pi$
$578$	46.5570	1.93651
$579$	79.0017	3.28320
$580$	−64.4409	−2.67576
$581$	−10.4112	−0.431928
$582$	−86.4323	−3.58273
$583$	17.5575	0.727155
$584$	−107.124	−4.43284
$585$	17.0081	0.703199
$586$	84.1730	3.47715
$587$	22.4935	0.928407	0.464204	−	0.885729i	$-0.346341\pi$
$587$	22.4935	0.928407	0.464204	+	0.885729i	$0.346341\pi$
$588$	38.8802	1.60339
$589$	−6.17876	−0.254591
$590$	0.599012	0.0246609
$591$	24.8071	1.02043
$592$	130.078	5.34616
$593$	15.5820	0.639877	0.319939	−	0.947438i	$-0.396338\pi$
$593$	15.5820	0.639877	0.319939	+	0.947438i	$0.396338\pi$
$594$	61.3742	2.51821
$595$	−0.620253	−0.0254279
$596$	50.7315	2.07804
$597$	47.3079	1.93618
$598$	−2.02322	−0.0827357
$599$	−9.00051	−0.367751	−0.183875	−	0.982950i	$-0.558864\pi$
$599$	−9.00051	−0.367751	−0.183875	+	0.982950i	$0.558864\pi$
$600$	−247.371	−10.0989
$601$	16.5712	0.675955	0.337978	−	0.941154i	$-0.390257\pi$
$601$	16.5712	0.675955	0.337978	+	0.941154i	$0.390257\pi$
$602$	−42.9286	−1.74964
$603$	34.0703	1.38745
$604$	20.0518	0.815896
$605$	−21.8463	−0.888179
$606$	−25.6741	−1.04294
$607$	38.1517	1.54853	0.774266	−	0.632861i	$-0.218119\pi$
$607$	38.1517	1.54853	0.774266	+	0.632861i	$0.218119\pi$
$608$	−17.5746	−0.712746
$609$	29.6706	1.20231
$610$	−71.1406	−2.88040
$611$	7.56737	0.306143
$612$	1.91187	0.0772827
$613$	24.3774	0.984594	0.492297	−	0.870427i	$-0.336157\pi$
$613$	24.3774	0.984594	0.492297	+	0.870427i	$0.336157\pi$
$614$	48.7640	1.96795
$615$	121.150	4.88525
$616$	−65.8029	−2.65127
$617$	−37.1540	−1.49576	−0.747882	−	0.663831i	$-0.768929\pi$
$617$	−37.1540	−1.49576	−0.747882	+	0.663831i	$0.768929\pi$
$618$	34.2717	1.37861
$619$	9.95045	0.399943	0.199971	−	0.979802i	$-0.435915\pi$
$619$	9.95045	0.399943	0.199971	+	0.979802i	$0.435915\pi$
$620$	−160.822	−6.45877
$621$	9.97411	0.400247
$622$	−62.4106	−2.50244
$623$	−43.1901	−1.73037
$624$	34.3634	1.37564
$625$	4.33666	0.173466
$626$	−28.1039	−1.12326
$627$	−5.30777	−0.211972
$628$	94.5918	3.77462
$629$	0.471461	0.0187984
$630$	192.552	7.67145
$631$	39.2464	1.56238	0.781188	−	0.624296i	$-0.214614\pi$
$631$	39.2464	1.56238	0.781188	+	0.624296i	$0.214614\pi$
$632$	−102.313	−4.06980
$633$	45.8536	1.82252
$634$	36.2761	1.44071
$635$	8.75944	0.347608
$636$	−130.982	−5.19378
$637$	1.71360	0.0678953
$638$	−19.6369	−0.777432
$639$	0.111694	0.00441853
$640$	−150.348	−5.94304
$641$	−42.7464	−1.68838	−0.844190	−	0.536044i	$-0.819918\pi$
$641$	−42.7464	−1.68838	−0.844190	+	0.536044i	$0.819918\pi$
$642$	69.4136	2.73954
$643$	9.46931	0.373433	0.186717	−	0.982414i	$-0.440215\pi$
$643$	9.46931	0.373433	0.186717	+	0.982414i	$0.440215\pi$
$644$	−16.7995	−0.661995
$645$	−57.3713	−2.25899
$646$	−0.117658	−0.00462920
$647$	28.9451	1.13795	0.568974	−	0.822355i	$-0.307340\pi$
$647$	28.9451	1.13795	0.568974	+	0.822355i	$0.307340\pi$
$648$	−110.830	−4.35383
$649$	0.133878	0.00525517
$650$	−17.1275	−0.671796
$651$	74.0473	2.90214
$652$	31.1466	1.21980
$653$	−10.8682	−0.425306	−0.212653	−	0.977128i	$-0.568210\pi$
$653$	−10.8682	−0.425306	−0.212653	+	0.977128i	$0.568210\pi$
$654$	0.171045	0.00668841
$655$	−51.0545	−1.99486
$656$	165.602	6.46566
$657$	70.0592	2.73327
$658$	85.6716	3.33983
$659$	−47.5005	−1.85036	−0.925179	−	0.379532i	$-0.876085\pi$
$659$	−47.5005	−1.85036	−0.925179	+	0.379532i	$0.876085\pi$
$660$	−138.152	−5.37755
$661$	−29.5725	−1.15024	−0.575119	−	0.818069i	$-0.695044\pi$
$661$	−29.5725	−1.15024	−0.575119	+	0.818069i	$0.695044\pi$
$662$	−86.7413	−3.37130
$663$	0.124549	0.00483706
$664$	−32.7215	−1.26984
$665$	−8.69109	−0.337026
$666$	−146.361	−5.67136
$667$	−3.19125	−0.123566
$668$	19.1397	0.740536
$669$	−60.9519	−2.35654
$670$	−54.5738	−2.10837
$671$	−15.8998	−0.613804
$672$	210.618	8.12475
$673$	42.4783	1.63742	0.818710	−	0.574208i	$-0.194690\pi$
$673$	42.4783	1.63742	0.818710	+	0.574208i	$0.194690\pi$
$674$	29.0765	1.11999
$675$	84.4354	3.24992
$676$	−68.5352	−2.63597
$677$	−46.0877	−1.77129	−0.885647	−	0.464359i	$-0.846285\pi$
$677$	−46.0877	−1.77129	−0.885647	+	0.464359i	$0.846285\pi$
$678$	−66.5953	−2.55758
$679$	−31.6309	−1.21388
$680$	−1.94940	−0.0747562
$681$	2.31956	0.0888858
$682$	−49.0068	−1.87657
$683$	22.6343	0.866076	0.433038	−	0.901376i	$-0.357442\pi$
$683$	22.6343	0.866076	0.433038	+	0.901376i	$0.357442\pi$
$684$	26.7894	1.02432
$685$	−2.91104	−0.111225
$686$	−39.1355	−1.49420
$687$	−43.3325	−1.65324
$688$	−78.4214	−2.98979
$689$	−5.77289	−0.219930
$690$	−30.6113	−1.16535
$691$	−36.8299	−1.40108	−0.700538	−	0.713615i	$-0.747057\pi$
$691$	−36.8299	−1.40108	−0.700538	+	0.713615i	$0.747057\pi$
$692$	−40.5826	−1.54272
$693$	43.0349	1.63476
$694$	−65.3882	−2.48210
$695$	−74.1523	−2.81276
$696$	93.2521	3.53471
$697$	0.600216	0.0227348
$698$	2.73914	0.103678
$699$	84.2316	3.18593
$700$	−142.216	−5.37525
$701$	28.0858	1.06078	0.530392	−	0.847752i	$-0.322045\pi$
$701$	28.0858	1.06078	0.530392	+	0.847752i	$0.322045\pi$
$702$	−20.1798	−0.761639
$703$	6.60619	0.249157
$704$	−70.7598	−2.66686
$705$	114.494	4.31211
$706$	4.53952	0.170847
$707$	−9.39574	−0.353363
$708$	−0.998755	−0.0375355
$709$	−30.4881	−1.14500	−0.572502	−	0.819903i	$-0.694027\pi$
$709$	−30.4881	−1.14500	−0.572502	+	0.819903i	$0.694027\pi$
$710$	−0.178911	−0.00671441
$711$	66.9126	2.50942
$712$	−135.743	−5.08718
$713$	−7.96425	−0.298263
$714$	1.41004	0.0527693
$715$	−6.08888	−0.227711
$716$	−88.3740	−3.30269
$717$	24.8845	0.929329
$718$	35.3583	1.31956
$719$	−24.0643	−0.897446	−0.448723	−	0.893671i	$-0.648121\pi$
$719$	−24.0643	−0.897446	−0.448723	+	0.893671i	$0.648121\pi$
$720$	351.751	13.1090
$721$	12.5421	0.467092
$722$	50.3950	1.87551
$723$	37.9045	1.40968
$724$	113.423	4.21535
$725$	−27.0154	−1.00333
$726$	49.6638	1.84320
$727$	20.8021	0.771508	0.385754	−	0.922602i	$-0.373941\pi$
$727$	20.8021	0.771508	0.385754	+	0.922602i	$0.373941\pi$
$728$	21.6360	0.801882
$729$	−18.6454	−0.690572
$730$	−112.221	−4.15348
$731$	−0.284235	−0.0105128
$732$	118.615	4.38415
$733$	30.0374	1.10946	0.554728	−	0.832032i	$-0.312822\pi$
$733$	30.0374	1.10946	0.554728	+	0.832032i	$0.312822\pi$
$734$	61.5008	2.27004
$735$	25.9268	0.956323
$736$	−22.6532	−0.835009
$737$	−12.1971	−0.449287
$738$	−186.332	−6.85896
$739$	1.88716	0.0694202	0.0347101	−	0.999397i	$-0.488949\pi$
$739$	1.88716	0.0694202	0.0347101	+	0.999397i	$0.488949\pi$
$740$	171.947	6.32090
$741$	1.74519	0.0641113
$742$	−65.3559	−2.39929
$743$	−49.7854	−1.82645	−0.913225	−	0.407456i	$-0.866416\pi$
$743$	−49.7854	−1.82645	−0.913225	+	0.407456i	$0.866416\pi$
$744$	232.725	8.53210
$745$	33.8296	1.23942
$746$	−23.6170	−0.864680
$747$	21.3998	0.782977
$748$	−0.684447	−0.0250259
$749$	25.4027	0.928194
$750$	−106.082	−3.87358
$751$	29.7926	1.08715	0.543573	−	0.839362i	$-0.317071\pi$
$751$	29.7926	1.08715	0.543573	+	0.839362i	$0.317071\pi$
$752$	156.504	5.70710
$753$	−22.7679	−0.829709
$754$	6.45661	0.235136
$755$	13.3713	0.486631
$756$	−167.560	−6.09411
$757$	−38.2894	−1.39165	−0.695826	−	0.718211i	$-0.744961\pi$
$757$	−38.2894	−1.39165	−0.695826	+	0.718211i	$0.744961\pi$
$758$	14.8714	0.540155
$759$	−6.84157	−0.248333
$760$	−27.3154	−0.990832
$761$	−41.0478	−1.48798	−0.743991	−	0.668190i	$-0.767069\pi$
$761$	−41.0478	−1.48798	−0.743991	+	0.668190i	$0.767069\pi$
$762$	−19.9130	−0.721374
$763$	0.0625960	0.00226613
$764$	−66.2126	−2.39549
$765$	1.27491	0.0460943
$766$	−6.73221	−0.243245
$767$	−0.0440190	−0.00158943
$768$	149.934	5.41028
$769$	−1.79045	−0.0645651	−0.0322826	−	0.999479i	$-0.510278\pi$
$769$	−1.79045	−0.0645651	−0.0322826	+	0.999479i	$0.510278\pi$
$770$	−68.9334	−2.48419
$771$	−68.4110	−2.46376
$772$	142.748	5.13760
$773$	−9.75549	−0.350880	−0.175440	−	0.984490i	$-0.556135\pi$
$773$	−9.75549	−0.350880	−0.175440	+	0.984490i	$0.556135\pi$
$774$	88.2382	3.17166
$775$	−67.4210	−2.42183
$776$	−99.4132	−3.56872
$777$	−79.1697	−2.84020
$778$	7.54297	0.270429
$779$	8.41032	0.301331
$780$	45.4243	1.62645
$781$	−0.0399862	−0.00143082
$782$	−0.151658	−0.00542328
$783$	−31.8299	−1.13751
$784$	35.4396	1.26570
$785$	63.0774	2.25133
$786$	116.063	4.13985
$787$	−31.5872	−1.12596	−0.562982	−	0.826469i	$-0.690346\pi$
$787$	−31.5872	−1.12596	−0.562982	+	0.826469i	$0.690346\pi$
$788$	44.8239	1.59678
$789$	70.2129	2.49964
$790$	−107.181	−3.81332
$791$	−24.3713	−0.866543
$792$	135.255	4.80609
$793$	5.22784	0.185646
$794$	−68.2419	−2.42182
$795$	−87.3438	−3.09777
$796$	85.4804	3.02977
$797$	−5.95512	−0.210941	−0.105471	−	0.994422i	$-0.533635\pi$
$797$	−5.95512	−0.210941	−0.105471	+	0.994422i	$0.533635\pi$
$798$	19.7577	0.699414
$799$	0.567240	0.0200675
$800$	−191.770	−6.78009
$801$	88.7756	3.13673
$802$	80.6690	2.84852
$803$	−25.0811	−0.885093
$804$	90.9929	3.20907
$805$	−11.2026	−0.394839
$806$	16.1134	0.567572
$807$	83.0885	2.92486
$808$	−29.5300	−1.03886
$809$	−26.4722	−0.930714	−0.465357	−	0.885123i	$-0.654074\pi$
$809$	−26.4722	−0.930714	−0.465357	+	0.885123i	$0.654074\pi$
$810$	−116.103	−4.07944
$811$	47.8933	1.68176	0.840880	−	0.541222i	$-0.182038\pi$
$811$	47.8933	1.68176	0.840880	+	0.541222i	$0.182038\pi$
$812$	53.6115	1.88140
$813$	64.6537	2.26750
$814$	52.3970	1.83651
$815$	20.7697	0.727532
$816$	2.57583	0.0901722
$817$	−3.98275	−0.139339
$818$	−83.7211	−2.92724
$819$	−14.1499	−0.494437
$820$	218.906	7.64452
$821$	−48.1732	−1.68126	−0.840629	−	0.541612i	$-0.817814\pi$
$821$	−48.1732	−1.68126	−0.840629	+	0.541612i	$0.817814\pi$
$822$	6.61775	0.230820
$823$	−23.6930	−0.825884	−0.412942	−	0.910757i	$-0.635499\pi$
$823$	−23.6930	−0.825884	−0.412942	+	0.910757i	$0.635499\pi$
$824$	39.4188	1.37322
$825$	−57.9170	−2.01641
$826$	−0.498347	−0.0173397
$827$	−37.3999	−1.30052	−0.650260	−	0.759712i	$-0.725340\pi$
$827$	−37.3999	−1.30052	−0.650260	+	0.759712i	$0.725340\pi$
$828$	34.5308	1.20003
$829$	−0.0528682	−0.00183619	−0.000918095	−	1.00000i	$-0.500292\pi$
$829$	−0.0528682	−0.00183619	−0.000918095		1.00000i	$0.500292\pi$
$830$	−34.2782	−1.18981
$831$	−57.9651	−2.01079
$832$	23.2658	0.806596
$833$	0.128449	0.00445050
$834$	168.572	5.83718
$835$	12.7631	0.441684
$836$	−9.59058	−0.331697
$837$	−79.4362	−2.74572
$838$	57.8364	1.99793
$839$	−14.9417	−0.515843	−0.257922	−	0.966166i	$-0.583038\pi$
$839$	−14.9417	−0.515843	−0.257922	+	0.966166i	$0.583038\pi$
$840$	327.352	11.2947
$841$	−18.8159	−0.648825
$842$	79.4452	2.73786
$843$	−48.7666	−1.67961
$844$	82.8525	2.85190
$845$	−45.7019	−1.57219
$846$	−176.095	−6.05426
$847$	18.1750	0.624501
$848$	−119.391	−4.09991
$849$	−87.2709	−2.99513
$850$	−1.28385	−0.0440359
$851$	8.51519	0.291897
$852$	0.298305	0.0102198
$853$	48.1257	1.64779	0.823897	−	0.566740i	$-0.191796\pi$
$853$	48.1257	1.64779	0.823897	+	0.566740i	$0.191796\pi$
$854$	59.1853	2.02528
$855$	17.8642	0.610942
$856$	79.8385	2.72882
$857$	31.9873	1.09267	0.546333	−	0.837568i	$-0.316023\pi$
$857$	31.9873	1.09267	0.546333	+	0.837568i	$0.316023\pi$
$858$	13.8420	0.472558
$859$	−15.4341	−0.526605	−0.263303	−	0.964713i	$-0.584812\pi$
$859$	−15.4341	−0.526605	−0.263303	+	0.964713i	$0.584812\pi$
$860$	−103.664	−3.53490
$861$	−100.791	−3.43494
$862$	−6.97059	−0.237419
$863$	−18.4689	−0.628687	−0.314344	−	0.949309i	$-0.601784\pi$
$863$	−18.4689	−0.628687	−0.314344	+	0.949309i	$0.601784\pi$
$864$	−225.946	−7.68683
$865$	−27.0620	−0.920137
$866$	22.9130	0.778614
$867$	−51.7641	−1.75800
$868$	133.796	4.54132
$869$	−23.9546	−0.812605
$870$	97.6885	3.31195
$871$	4.01041	0.135888
$872$	0.196734	0.00666225
$873$	65.0160	2.20046
$874$	−2.12506	−0.0718811
$875$	−38.8220	−1.31242
$876$	187.110	6.32186
$877$	30.2670	1.02204	0.511021	−	0.859568i	$-0.329267\pi$
$877$	30.2670	1.02204	0.511021	+	0.859568i	$0.329267\pi$
$878$	−53.0503	−1.79036
$879$	−93.5872	−3.15662
$880$	−125.926	−4.24498
$881$	15.5556	0.524080	0.262040	−	0.965057i	$-0.415605\pi$
$881$	15.5556	0.524080	0.262040	+	0.965057i	$0.415605\pi$
$882$	−39.8759	−1.34269
$883$	26.3816	0.887813	0.443907	−	0.896073i	$-0.353592\pi$
$883$	26.3816	0.887813	0.443907	+	0.896073i	$0.353592\pi$
$884$	0.225046	0.00756911
$885$	−0.666008	−0.0223876
$886$	18.1051	0.608253
$887$	2.65217	0.0890511	0.0445255	−	0.999008i	$-0.485822\pi$
$887$	2.65217	0.0890511	0.0445255	+	0.999008i	$0.485822\pi$
$888$	−248.824	−8.34998
$889$	−7.28740	−0.244412
$890$	−142.201	−4.76658
$891$	−25.9488	−0.869316
$892$	−110.134	−3.68754
$893$	7.94826	0.265978
$894$	−76.9058	−2.57211
$895$	−58.9311	−1.96985
$896$	125.082	4.17870
$897$	2.24951	0.0751088
$898$	−7.95784	−0.265556
$899$	25.4159	0.847668
$900$	292.319	9.74397
$901$	−0.432728	−0.0144163
$902$	66.7065	2.22108
$903$	47.7299	1.58835
$904$	−76.5969	−2.54758
$905$	75.6350	2.51419
$906$	−30.3973	−1.00988
$907$	−6.91578	−0.229635	−0.114817	−	0.993387i	$-0.536628\pi$
$907$	−6.91578	−0.229635	−0.114817	+	0.993387i	$0.536628\pi$
$908$	4.19120	0.139090
$909$	19.3126	0.640558
$910$	22.6653	0.751347
$911$	−20.9531	−0.694206	−0.347103	−	0.937827i	$-0.612835\pi$
$911$	−20.9531	−0.694206	−0.347103	+	0.937827i	$0.612835\pi$
$912$	36.0930	1.19516
$913$	−7.66109	−0.253545
$914$	−42.2327	−1.39693
$915$	79.0972	2.61487
$916$	−78.2971	−2.58701
$917$	42.4747	1.40264
$918$	−1.51265	−0.0499250
$919$	−5.53493	−0.182581	−0.0912903	−	0.995824i	$-0.529099\pi$
$919$	−5.53493	−0.182581	−0.0912903	+	0.995824i	$0.529099\pi$
$920$	−35.2087	−1.16080
$921$	−54.2179	−1.78654
$922$	74.7830	2.46285
$923$	0.0131475	0.000432754 0
$924$	114.935	3.78109
$925$	72.0849	2.37014
$926$	−73.4873	−2.41494
$927$	−25.7798	−0.846720
$928$	72.2921	2.37311
$929$	−49.3768	−1.62000	−0.810000	−	0.586430i	$-0.800533\pi$
$929$	−49.3768	−1.62000	−0.810000	+	0.586430i	$0.800533\pi$
$930$	243.796	7.99440
$931$	1.79985	0.0589877
$932$	152.198	4.98540
$933$	69.3908	2.27175
$934$	−43.7041	−1.43004
$935$	−0.456415	−0.0149264
$936$	−44.4719	−1.45361
$937$	25.8597	0.844798	0.422399	−	0.906410i	$-0.361188\pi$
$937$	25.8597	0.844798	0.422399	+	0.906410i	$0.361188\pi$
$938$	45.4026	1.48245
$939$	31.2471	1.01971
$940$	206.879	6.74765
$941$	8.93513	0.291277	0.145638	−	0.989338i	$-0.453476\pi$
$941$	8.93513	0.291277	0.145638	+	0.989338i	$0.453476\pi$
$942$	−143.395	−4.67207
$943$	10.8407	0.353021
$944$	−0.910374	−0.0296301
$945$	−111.736	−3.63476
$946$	−31.5892	−1.02705
$947$	2.10446	0.0683859	0.0341929	−	0.999415i	$-0.489114\pi$
$947$	2.10446	0.0683859	0.0341929	+	0.999415i	$0.489114\pi$
$948$	178.706	5.80411
$949$	8.24666	0.267698
$950$	−17.9896	−0.583659
$951$	−40.3334	−1.30790
$952$	1.62180	0.0525630
$953$	−0.672703	−0.0217910	−0.0108955	−	0.999941i	$-0.503468\pi$
$953$	−0.672703	−0.0217910	−0.0108955	+	0.999941i	$0.503468\pi$
$954$	134.337	4.34931
$955$	−44.1531	−1.42876
$956$	44.9637	1.45423
$957$	21.8332	0.705766
$958$	108.914	3.51887
$959$	2.42184	0.0782052
$960$	352.012	11.3611
$961$	32.4292	1.04610
$962$	−17.2281	−0.555457
$963$	−52.2142	−1.68258
$964$	68.4895	2.20590
$965$	95.1895	3.06426
$966$	25.4671	0.819389
$967$	1.55537	0.0500174	0.0250087	−	0.999687i	$-0.492039\pi$
$967$	1.55537	0.0500174	0.0250087	+	0.999687i	$0.492039\pi$
$968$	57.1226	1.83599
$969$	0.130817	0.00420246
$970$	−104.143	−3.34382
$971$	22.9694	0.737123	0.368561	−	0.929603i	$-0.379850\pi$
$971$	22.9694	0.737123	0.368561	+	0.929603i	$0.379850\pi$
$972$	28.9238	0.927732
$973$	61.6909	1.97772
$974$	41.8157	1.33986
$975$	19.0431	0.609867
$976$	108.119	3.46080
$977$	−49.9392	−1.59770	−0.798848	−	0.601533i	$-0.794557\pi$
$977$	−49.9392	−1.59770	−0.798848	+	0.601533i	$0.794557\pi$
$978$	−47.2164	−1.50981
$979$	−31.7816	−1.01574
$980$	46.8469	1.49647
$981$	−0.128664	−0.00410791
$982$	62.0663	1.98062
$983$	−15.1476	−0.483133	−0.241567	−	0.970384i	$-0.577661\pi$
$983$	−15.1476	−0.483133	−0.241567	+	0.970384i	$0.577661\pi$
$984$	−316.777	−10.0985
$985$	29.8902	0.952382
$986$	0.483979	0.0154130
$987$	−95.2534	−3.03195
$988$	3.15338	0.100322
$989$	−5.13365	−0.163240
$990$	141.690	4.50320
$991$	58.4748	1.85751	0.928756	−	0.370691i	$-0.120879\pi$
$991$	58.4748	1.85751	0.928756	+	0.370691i	$0.120879\pi$
$992$	180.416	5.72821
$993$	96.4428	3.06052
$994$	0.148845	0.00472107
$995$	57.0015	1.80707
$996$	57.1533	1.81097
$997$	53.7018	1.70075	0.850377	−	0.526174i	$-0.176374\pi$
$997$	53.7018	1.70075	0.850377	+	0.526174i	$0.176374\pi$
$998$	−68.7422	−2.17600
$999$	84.9314	2.68711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.f.1.4	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.f.1.4	✓	176	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73914 q^{2} +3.04549 q^{3} +5.50288 q^{4} +3.66953 q^{5} -8.34203 q^{6} -3.05286 q^{7} -9.59489 q^{8} +6.27504 q^{9} +O(q^{10})\)	\(q-2.73914 q^{2} +3.04549 q^{3} +5.50288 q^{4} +3.66953 q^{5} -8.34203 q^{6} -3.05286 q^{7} -9.59489 q^{8} +6.27504 q^{9} -10.0514 q^{10} -2.24646 q^{11} +16.7590 q^{12} +0.738634 q^{13} +8.36221 q^{14} +11.1755 q^{15} +15.2760 q^{16} +0.0553671 q^{17} -17.1882 q^{18} +0.775812 q^{19} +20.1930 q^{20} -9.29747 q^{21} +6.15336 q^{22} +1.00000 q^{23} -29.2212 q^{24} +8.46546 q^{25} -2.02322 q^{26} +9.97411 q^{27} -16.7995 q^{28} -3.19125 q^{29} -30.6113 q^{30} -7.96425 q^{31} -22.6532 q^{32} -6.84157 q^{33} -0.151658 q^{34} -11.2026 q^{35} +34.5308 q^{36} +8.51519 q^{37} -2.12506 q^{38} +2.24951 q^{39} -35.2087 q^{40} +10.8407 q^{41} +25.4671 q^{42} -5.13365 q^{43} -12.3620 q^{44} +23.0264 q^{45} -2.73914 q^{46} +10.2451 q^{47} +46.5229 q^{48} +2.31996 q^{49} -23.1881 q^{50} +0.168620 q^{51} +4.06462 q^{52} -7.81563 q^{53} -27.3205 q^{54} -8.24344 q^{55} +29.2919 q^{56} +2.36273 q^{57} +8.74128 q^{58} -0.0595952 q^{59} +61.4977 q^{60} +7.07771 q^{61} +21.8152 q^{62} -19.1568 q^{63} +31.4984 q^{64} +2.71044 q^{65} +18.7400 q^{66} +5.42949 q^{67} +0.304679 q^{68} +3.04549 q^{69} +30.6854 q^{70} +0.0177997 q^{71} -60.2083 q^{72} +11.1647 q^{73} -23.3243 q^{74} +25.7815 q^{75} +4.26920 q^{76} +6.85812 q^{77} -6.16171 q^{78} +10.6633 q^{79} +56.0556 q^{80} +11.5510 q^{81} -29.6941 q^{82} +3.41030 q^{83} -51.1629 q^{84} +0.203171 q^{85} +14.0618 q^{86} -9.71894 q^{87} +21.5545 q^{88} +14.1474 q^{89} -63.0726 q^{90} -2.25495 q^{91} +5.50288 q^{92} -24.2551 q^{93} -28.0627 q^{94} +2.84687 q^{95} -68.9903 q^{96} +10.3611 q^{97} -6.35469 q^{98} -14.0966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

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