LMFDB - Embedded newform 381.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [381,2,Mod(1,381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(381, 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("381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 381 = 3 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	381.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:	$3.04230031701$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 14x^{7} + 26x^{6} + 59x^{5} - 99x^{4} - 66x^{3} + 102x^{2} - 24x + 1 $ x^9 - 2x^8 - 14x^7 + 26x^6 + 59x^5 - 99x^4 - 66x^3 + 102x^2 - 24x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.75841$ of defining polynomial
Character	$\chi$	$=$	381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75841 q^{2} +1.00000 q^{3} +5.60882 q^{4} -3.68284 q^{5} -2.75841 q^{6} -3.98729 q^{7} -9.95461 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.75841 q^{2} +1.00000 q^{3} +5.60882 q^{4} -3.68284 q^{5} -2.75841 q^{6} -3.98729 q^{7} -9.95461 q^{8} +1.00000 q^{9} +10.1588 q^{10} +3.85715 q^{11} +5.60882 q^{12} -0.499482 q^{13} +10.9986 q^{14} -3.68284 q^{15} +16.2413 q^{16} +2.54391 q^{17} -2.75841 q^{18} +4.54391 q^{19} -20.6564 q^{20} -3.98729 q^{21} -10.6396 q^{22} +0.837319 q^{23} -9.95461 q^{24} +8.56328 q^{25} +1.37778 q^{26} +1.00000 q^{27} -22.3640 q^{28} +4.54082 q^{29} +10.1588 q^{30} -2.82177 q^{31} -24.8908 q^{32} +3.85715 q^{33} -7.01714 q^{34} +14.6845 q^{35} +5.60882 q^{36} +4.44010 q^{37} -12.5340 q^{38} -0.499482 q^{39} +36.6612 q^{40} +1.64721 q^{41} +10.9986 q^{42} -2.23364 q^{43} +21.6340 q^{44} -3.68284 q^{45} -2.30967 q^{46} +13.1941 q^{47} +16.2413 q^{48} +8.89848 q^{49} -23.6210 q^{50} +2.54391 q^{51} -2.80151 q^{52} +5.37814 q^{53} -2.75841 q^{54} -14.2052 q^{55} +39.6919 q^{56} +4.54391 q^{57} -12.5254 q^{58} -10.1737 q^{59} -20.6564 q^{60} -12.4544 q^{61} +7.78359 q^{62} -3.98729 q^{63} +36.1765 q^{64} +1.83951 q^{65} -10.6396 q^{66} +7.31003 q^{67} +14.2683 q^{68} +0.837319 q^{69} -40.5060 q^{70} +9.14535 q^{71} -9.95461 q^{72} +6.18893 q^{73} -12.2476 q^{74} +8.56328 q^{75} +25.4860 q^{76} -15.3796 q^{77} +1.37778 q^{78} +1.21630 q^{79} -59.8139 q^{80} +1.00000 q^{81} -4.54368 q^{82} -10.2061 q^{83} -22.3640 q^{84} -9.36879 q^{85} +6.16129 q^{86} +4.54082 q^{87} -38.3964 q^{88} -6.35092 q^{89} +10.1588 q^{90} +1.99158 q^{91} +4.69638 q^{92} -2.82177 q^{93} -36.3947 q^{94} -16.7345 q^{95} -24.8908 q^{96} +16.2413 q^{97} -24.5457 q^{98} +3.85715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 2 q^{2} + 9 q^{3} + 14 q^{4} - 4 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 2 * q^2 + 9 * q^3 + 14 * q^4 - 4 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 9 * q^9	\( 9 q - 2 q^{2} + 9 q^{3} + 14 q^{4} - 4 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 9 q^{9} - 4 q^{10} + 8 q^{11} + 14 q^{12} + 14 q^{13} + 4 q^{14} - 4 q^{15} + 32 q^{16} - 6 q^{17} - 2 q^{18} + 12 q^{19} - 28 q^{20} + 10 q^{21} - 18 q^{22} - 4 q^{23} - 6 q^{24} + 21 q^{25} - 14 q^{26} + 9 q^{27} - 8 q^{29} - 4 q^{30} + 4 q^{31} - 29 q^{32} + 8 q^{33} - 3 q^{34} + 6 q^{35} + 14 q^{36} + 22 q^{37} - 7 q^{38} + 14 q^{39} - 2 q^{41} + 4 q^{42} + 6 q^{43} + 17 q^{44} - 4 q^{45} - 10 q^{46} - 2 q^{47} + 32 q^{48} + 23 q^{49} - 20 q^{50} - 6 q^{51} - 9 q^{52} - 12 q^{53} - 2 q^{54} - 22 q^{55} + 18 q^{56} + 12 q^{57} - 28 q^{58} - 6 q^{59} - 28 q^{60} + 2 q^{61} - 15 q^{62} + 10 q^{63} + 24 q^{64} + 4 q^{65} - 18 q^{66} + 18 q^{67} - 24 q^{68} - 4 q^{69} - 72 q^{70} + 24 q^{71} - 6 q^{72} + 14 q^{73} + 3 q^{74} + 21 q^{75} + 4 q^{76} - 18 q^{77} - 14 q^{78} + 12 q^{79} - 86 q^{80} + 9 q^{81} + 4 q^{82} - 20 q^{83} - 24 q^{85} + 16 q^{86} - 8 q^{87} - 55 q^{88} - 30 q^{89} - 4 q^{90} + 14 q^{91} - 46 q^{92} + 4 q^{93} - 66 q^{94} - 32 q^{95} - 29 q^{96} + 12 q^{97} - 62 q^{98} + 8 q^{99}+O(q^{100}) \) 9 * q - 2 * q^2 + 9 * q^3 + 14 * q^4 - 4 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 9 * q^9 - 4 * q^10 + 8 * q^11 + 14 * q^12 + 14 * q^13 + 4 * q^14 - 4 * q^15 + 32 * q^16 - 6 * q^17 - 2 * q^18 + 12 * q^19 - 28 * q^20 + 10 * q^21 - 18 * q^22 - 4 * q^23 - 6 * q^24 + 21 * q^25 - 14 * q^26 + 9 * q^27 - 8 * q^29 - 4 * q^30 + 4 * q^31 - 29 * q^32 + 8 * q^33 - 3 * q^34 + 6 * q^35 + 14 * q^36 + 22 * q^37 - 7 * q^38 + 14 * q^39 - 2 * q^41 + 4 * q^42 + 6 * q^43 + 17 * q^44 - 4 * q^45 - 10 * q^46 - 2 * q^47 + 32 * q^48 + 23 * q^49 - 20 * q^50 - 6 * q^51 - 9 * q^52 - 12 * q^53 - 2 * q^54 - 22 * q^55 + 18 * q^56 + 12 * q^57 - 28 * q^58 - 6 * q^59 - 28 * q^60 + 2 * q^61 - 15 * q^62 + 10 * q^63 + 24 * q^64 + 4 * q^65 - 18 * q^66 + 18 * q^67 - 24 * q^68 - 4 * q^69 - 72 * q^70 + 24 * q^71 - 6 * q^72 + 14 * q^73 + 3 * q^74 + 21 * q^75 + 4 * q^76 - 18 * q^77 - 14 * q^78 + 12 * q^79 - 86 * q^80 + 9 * q^81 + 4 * q^82 - 20 * q^83 - 24 * q^85 + 16 * q^86 - 8 * q^87 - 55 * q^88 - 30 * q^89 - 4 * q^90 + 14 * q^91 - 46 * q^92 + 4 * q^93 - 66 * q^94 - 32 * q^95 - 29 * q^96 + 12 * q^97 - 62 * q^98 + 8 * 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 $

$2$	−2.75841	−1.95049	−0.975245	−	0.221127i	$-0.929027\pi$
$2$	−2.75841	−1.95049	−0.975245	+	0.221127i	$0.929027\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.60882	2.80441
$5$	−3.68284	−1.64701	−0.823507	−	0.567306i	$-0.807986\pi$
$5$	−3.68284	−1.64701	−0.823507	+	0.567306i	$0.807986\pi$
$6$	−2.75841	−1.12612
$7$	−3.98729	−1.50705	−0.753527	−	0.657417i	$-0.771649\pi$
$7$	−3.98729	−1.50705	−0.753527	+	0.657417i	$0.771649\pi$
$8$	−9.95461	−3.51949
$9$	1.00000	0.333333
$10$	10.1588	3.21249
$11$	3.85715	1.16297	0.581487	−	0.813556i	$-0.302471\pi$
$11$	3.85715	1.16297	0.581487	+	0.813556i	$0.302471\pi$
$12$	5.60882	1.61913
$13$	−0.499482	−0.138531	−0.0692657	−	0.997598i	$-0.522066\pi$
$13$	−0.499482	−0.138531	−0.0692657	+	0.997598i	$0.522066\pi$
$14$	10.9986	2.93949
$15$	−3.68284	−0.950904
$16$	16.2413	4.06031
$17$	2.54391	0.616988	0.308494	−	0.951226i	$-0.400175\pi$
$17$	2.54391	0.616988	0.308494	+	0.951226i	$0.400175\pi$
$18$	−2.75841	−0.650163
$19$	4.54391	1.04244	0.521222	−	0.853421i	$-0.325476\pi$
$19$	4.54391	1.04244	0.521222	+	0.853421i	$0.325476\pi$
$20$	−20.6564	−4.61891
$21$	−3.98729	−0.870098
$22$	−10.6396	−2.26837
$23$	0.837319	0.174593	0.0872966	−	0.996182i	$-0.472177\pi$
$23$	0.837319	0.174593	0.0872966	+	0.996182i	$0.472177\pi$
$24$	−9.95461	−2.03198
$25$	8.56328	1.71266
$26$	1.37778	0.270204
$27$	1.00000	0.192450
$28$	−22.3640	−4.22640
$29$	4.54082	0.843209	0.421604	−	0.906780i	$-0.361467\pi$
$29$	4.54082	0.843209	0.421604	+	0.906780i	$0.361467\pi$
$30$	10.1588	1.85473
$31$	−2.82177	−0.506804	−0.253402	−	0.967361i	$-0.581550\pi$
$31$	−2.82177	−0.506804	−0.253402	+	0.967361i	$0.581550\pi$
$32$	−24.8908	−4.40012
$33$	3.85715	0.671443
$34$	−7.01714	−1.20343
$35$	14.6845	2.48214
$36$	5.60882	0.934804
$37$	4.44010	0.729948	0.364974	−	0.931018i	$-0.381078\pi$
$37$	4.44010	0.729948	0.364974	+	0.931018i	$0.381078\pi$
$38$	−12.5340	−2.03328
$39$	−0.499482	−0.0799811
$40$	36.6612	5.79665
$41$	1.64721	0.257251	0.128625	−	0.991693i	$-0.458944\pi$
$41$	1.64721	0.257251	0.128625	+	0.991693i	$0.458944\pi$
$42$	10.9986	1.69712
$43$	−2.23364	−0.340627	−0.170313	−	0.985390i	$-0.554478\pi$
$43$	−2.23364	−0.340627	−0.170313	+	0.985390i	$0.554478\pi$
$44$	21.6340	3.26146
$45$	−3.68284	−0.549005
$46$	−2.30967	−0.340542
$47$	13.1941	1.92456	0.962279	−	0.272066i	$-0.0877068\pi$
$47$	13.1941	1.92456	0.962279	+	0.272066i	$0.0877068\pi$
$48$	16.2413	2.34422
$49$	8.89848	1.27121
$50$	−23.6210	−3.34052
$51$	2.54391	0.356218
$52$	−2.80151	−0.388499
$53$	5.37814	0.738744	0.369372	−	0.929282i	$-0.379573\pi$
$53$	5.37814	0.738744	0.369372	+	0.929282i	$0.379573\pi$
$54$	−2.75841	−0.375372
$55$	−14.2052	−1.91543
$56$	39.6919	5.30406
$57$	4.54391	0.601855
$58$	−12.5254	−1.64467
$59$	−10.1737	−1.32451	−0.662253	−	0.749280i	$-0.730400\pi$
$59$	−10.1737	−1.32451	−0.662253	+	0.749280i	$0.730400\pi$
$60$	−20.6564	−2.66673
$61$	−12.4544	−1.59463	−0.797313	−	0.603566i	$-0.793746\pi$
$61$	−12.4544	−1.59463	−0.797313	+	0.603566i	$0.793746\pi$
$62$	7.78359	0.988516
$63$	−3.98729	−0.502351
$64$	36.1765	4.52207
$65$	1.83951	0.228163
$66$	−10.6396	−1.30964
$67$	7.31003	0.893063	0.446531	−	0.894768i	$-0.352659\pi$
$67$	7.31003	0.893063	0.446531	+	0.894768i	$0.352659\pi$
$68$	14.2683	1.73029
$69$	0.837319	0.100801
$70$	−40.5060	−4.84139
$71$	9.14535	1.08535	0.542677	−	0.839942i	$-0.317411\pi$
$71$	9.14535	1.08535	0.542677	+	0.839942i	$0.317411\pi$
$72$	−9.95461	−1.17316
$73$	6.18893	0.724360	0.362180	−	0.932108i	$-0.382033\pi$
$73$	6.18893	0.724360	0.362180	+	0.932108i	$0.382033\pi$
$74$	−12.2476	−1.42376
$75$	8.56328	0.988803
$76$	25.4860	2.92344
$77$	−15.3796	−1.75266
$78$	1.37778	0.156002
$79$	1.21630	0.136844	0.0684222	−	0.997656i	$-0.478203\pi$
$79$	1.21630	0.136844	0.0684222	+	0.997656i	$0.478203\pi$
$80$	−59.8139	−6.68740
$81$	1.00000	0.111111
$82$	−4.54368	−0.501765
$83$	−10.2061	−1.12027	−0.560133	−	0.828403i	$-0.689250\pi$
$83$	−10.2061	−1.12027	−0.560133	+	0.828403i	$0.689250\pi$
$84$	−22.3640	−2.44011
$85$	−9.36879	−1.01619
$86$	6.16129	0.664389
$87$	4.54082	0.486827
$88$	−38.3964	−4.09307
$89$	−6.35092	−0.673196	−0.336598	−	0.941648i	$-0.609276\pi$
$89$	−6.35092	−0.673196	−0.336598	+	0.941648i	$0.609276\pi$
$90$	10.1588	1.07083
$91$	1.99158	0.208774
$92$	4.69638	0.489631
$93$	−2.82177	−0.292603
$94$	−36.3947	−3.75383
$95$	−16.7345	−1.71692
$96$	−24.8908	−2.54041
$97$	16.2413	1.64905	0.824525	−	0.565825i	$-0.191442\pi$
$97$	16.2413	1.64905	0.824525	+	0.565825i	$0.191442\pi$
$98$	−24.5457	−2.47949
$99$	3.85715	0.387658
$100$	48.0299	4.80299
$101$	2.99896	0.298408	0.149204	−	0.988806i	$-0.452329\pi$
$101$	2.99896	0.298408	0.149204	+	0.988806i	$0.452329\pi$
$102$	−7.01714	−0.694800
$103$	0.826244	0.0814122	0.0407061	−	0.999171i	$-0.487039\pi$
$103$	0.826244	0.0814122	0.0407061	+	0.999171i	$0.487039\pi$
$104$	4.97215	0.487559
$105$	14.6845	1.43306
$106$	−14.8351	−1.44091
$107$	13.8734	1.34119	0.670596	−	0.741823i	$-0.266038\pi$
$107$	13.8734	1.34119	0.670596	+	0.741823i	$0.266038\pi$
$108$	5.60882	0.539709
$109$	9.81653	0.940253	0.470127	−	0.882599i	$-0.344208\pi$
$109$	9.81653	0.940253	0.470127	+	0.882599i	$0.344208\pi$
$110$	39.1839	3.73603
$111$	4.44010	0.421436
$112$	−64.7586	−6.11911
$113$	−3.30515	−0.310922	−0.155461	−	0.987842i	$-0.549686\pi$
$113$	−3.30515	−0.310922	−0.155461	+	0.987842i	$0.549686\pi$
$114$	−12.5340	−1.17391
$115$	−3.08371	−0.287557
$116$	25.4687	2.36470
$117$	−0.499482	−0.0461771
$118$	28.0633	2.58344
$119$	−10.1433	−0.929834
$120$	36.6612	3.34670
$121$	3.87757	0.352507
$122$	34.3544	3.11030
$123$	1.64721	0.148524
$124$	−15.8268	−1.42129
$125$	−13.1230	−1.17376
$126$	10.9986	0.979831
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	−50.0081	−4.42013
$129$	−2.23364	−0.196661
$130$	−5.07412	−0.445030
$131$	5.62534	0.491488	0.245744	−	0.969335i	$-0.420968\pi$
$131$	5.62534	0.491488	0.245744	+	0.969335i	$0.420968\pi$
$132$	21.6340	1.88300
$133$	−18.1179	−1.57102
$134$	−20.1641	−1.74191
$135$	−3.68284	−0.316968
$136$	−25.3236	−2.17148
$137$	−3.64019	−0.311003	−0.155501	−	0.987836i	$-0.549699\pi$
$137$	−3.64019	−0.311003	−0.155501	+	0.987836i	$0.549699\pi$
$138$	−2.30967	−0.196612
$139$	−16.8390	−1.42826	−0.714132	−	0.700011i	$-0.753178\pi$
$139$	−16.8390	−1.42826	−0.714132	+	0.700011i	$0.753178\pi$
$140$	82.3630	6.96094
$141$	13.1941	1.11114
$142$	−25.2266	−2.11697
$143$	−1.92657	−0.161108
$144$	16.2413	1.35344
$145$	−16.7231	−1.38878
$146$	−17.0716	−1.41286
$147$	8.89848	0.733934
$148$	24.9038	2.04708
$149$	−9.73814	−0.797780	−0.398890	−	0.916999i	$-0.630604\pi$
$149$	−9.73814	−0.797780	−0.398890	+	0.916999i	$0.630604\pi$
$150$	−23.6210	−1.92865
$151$	−11.1044	−0.903661	−0.451830	−	0.892104i	$-0.649229\pi$
$151$	−11.1044	−0.903661	−0.451830	+	0.892104i	$0.649229\pi$
$152$	−45.2328	−3.66887
$153$	2.54391	0.205663
$154$	42.4231	3.41855
$155$	10.3921	0.834714
$156$	−2.80151	−0.224300
$157$	13.1513	1.04959	0.524795	−	0.851229i	$-0.324142\pi$
$157$	13.1513	1.04959	0.524795	+	0.851229i	$0.324142\pi$
$158$	−3.35505	−0.266914
$159$	5.37814	0.426514
$160$	91.6688	7.24705
$161$	−3.33863	−0.263121
$162$	−2.75841	−0.216721
$163$	17.3562	1.35945	0.679723	−	0.733469i	$-0.262100\pi$
$163$	17.3562	1.35945	0.679723	+	0.733469i	$0.262100\pi$
$164$	9.23890	0.721437
$165$	−14.2052	−1.10588
$166$	28.1526	2.18507
$167$	−8.99758	−0.696254	−0.348127	−	0.937447i	$-0.613182\pi$
$167$	−8.99758	−0.696254	−0.348127	+	0.937447i	$0.613182\pi$
$168$	39.6919	3.06230
$169$	−12.7505	−0.980809
$170$	25.8430	1.98207
$171$	4.54391	0.347481
$172$	−12.5281	−0.955257
$173$	−9.80628	−0.745557	−0.372779	−	0.927920i	$-0.621595\pi$
$173$	−9.80628	−0.745557	−0.372779	+	0.927920i	$0.621595\pi$
$174$	−12.5254	−0.949551
$175$	−34.1443	−2.58107
$176$	62.6449	4.72204
$177$	−10.1737	−0.764704
$178$	17.5184	1.31306
$179$	−3.60877	−0.269732	−0.134866	−	0.990864i	$-0.543060\pi$
$179$	−3.60877	−0.269732	−0.134866	+	0.990864i	$0.543060\pi$
$180$	−20.6564	−1.53964
$181$	8.03032	0.596889	0.298444	−	0.954427i	$-0.403532\pi$
$181$	8.03032	0.596889	0.298444	+	0.954427i	$0.403532\pi$
$182$	−5.49359	−0.407212
$183$	−12.4544	−0.920658
$184$	−8.33519	−0.614478
$185$	−16.3522	−1.20224
$186$	7.78359	0.570720
$187$	9.81222	0.717541
$188$	74.0034	5.39725
$189$	−3.98729	−0.290033
$190$	46.1605	3.34884
$191$	25.4307	1.84010	0.920050	−	0.391802i	$-0.128148\pi$
$191$	25.4307	1.84010	0.920050	+	0.391802i	$0.128148\pi$
$192$	36.1765	2.61082
$193$	−7.46865	−0.537605	−0.268803	−	0.963195i	$-0.586628\pi$
$193$	−7.46865	−0.537605	−0.268803	+	0.963195i	$0.586628\pi$
$194$	−44.8001	−3.21646
$195$	1.83951	0.131730
$196$	49.9100	3.56500
$197$	−22.8594	−1.62866	−0.814331	−	0.580400i	$-0.802896\pi$
$197$	−22.8594	−1.62866	−0.814331	+	0.580400i	$0.802896\pi$
$198$	−10.6396	−0.756123
$199$	−2.29345	−0.162578	−0.0812892	−	0.996691i	$-0.525904\pi$
$199$	−2.29345	−0.162578	−0.0812892	+	0.996691i	$0.525904\pi$
$200$	−85.2442	−6.02767
$201$	7.31003	0.515610
$202$	−8.27237	−0.582042
$203$	−18.1056	−1.27076
$204$	14.2683	0.998983
$205$	−6.06640	−0.423696
$206$	−2.27912	−0.158794
$207$	0.837319	0.0581977
$208$	−8.11221	−0.562481
$209$	17.5265	1.21233
$210$	−40.5060	−2.79518
$211$	5.78474	0.398238	0.199119	−	0.979975i	$-0.436192\pi$
$211$	5.78474	0.398238	0.199119	+	0.979975i	$0.436192\pi$
$212$	30.1650	2.07174
$213$	9.14535	0.626629
$214$	−38.2685	−2.61598
$215$	8.22612	0.561017
$216$	−9.95461	−0.677326
$217$	11.2512	0.763781
$218$	−27.0780	−1.83395
$219$	6.18893	0.418209
$220$	−79.6747	−5.37166
$221$	−1.27064	−0.0854722
$222$	−12.2476	−0.822007
$223$	−1.15117	−0.0770878	−0.0385439	−	0.999257i	$-0.512272\pi$
$223$	−1.15117	−0.0770878	−0.0385439	+	0.999257i	$0.512272\pi$
$224$	99.2469	6.63121
$225$	8.56328	0.570886
$226$	9.11696	0.606451
$227$	21.7342	1.44255	0.721275	−	0.692649i	$-0.243557\pi$
$227$	21.7342	1.44255	0.721275	+	0.692649i	$0.243557\pi$
$228$	25.4860	1.68785
$229$	25.8445	1.70785	0.853926	−	0.520394i	$-0.174215\pi$
$229$	25.8445	1.70785	0.853926	+	0.520394i	$0.174215\pi$
$230$	8.50614	0.560878
$231$	−15.3796	−1.01190
$232$	−45.2021	−2.96766
$233$	5.93194	0.388614	0.194307	−	0.980941i	$-0.437754\pi$
$233$	5.93194	0.388614	0.194307	+	0.980941i	$0.437754\pi$
$234$	1.37778	0.0900680
$235$	−48.5917	−3.16977
$236$	−57.0626	−3.71446
$237$	1.21630	0.0790072
$238$	27.9794	1.81363
$239$	16.3739	1.05914	0.529571	−	0.848265i	$-0.322353\pi$
$239$	16.3739	1.05914	0.529571	+	0.848265i	$0.322353\pi$
$240$	−59.8139	−3.86097
$241$	14.8699	0.957856	0.478928	−	0.877854i	$-0.341026\pi$
$241$	14.8699	0.957856	0.478928	+	0.877854i	$0.341026\pi$
$242$	−10.6959	−0.687560
$243$	1.00000	0.0641500
$244$	−69.8547	−4.47199
$245$	−32.7717	−2.09370
$246$	−4.54368	−0.289694
$247$	−2.26960	−0.144411
$248$	28.0896	1.78369
$249$	−10.2061	−0.646786
$250$	36.1986	2.28940
$251$	6.51223	0.411049	0.205524	−	0.978652i	$-0.434110\pi$
$251$	6.51223	0.411049	0.205524	+	0.978652i	$0.434110\pi$
$252$	−22.3640	−1.40880
$253$	3.22966	0.203047
$254$	2.75841	0.173078
$255$	−9.36879	−0.586697
$256$	65.5897	4.09936
$257$	−14.8483	−0.926214	−0.463107	−	0.886302i	$-0.653265\pi$
$257$	−14.8483	−0.926214	−0.463107	+	0.886302i	$0.653265\pi$
$258$	6.16129	0.383585
$259$	−17.7040	−1.10007
$260$	10.3175	0.639863
$261$	4.54082	0.281070
$262$	−15.5170	−0.958642
$263$	8.64420	0.533024	0.266512	−	0.963832i	$-0.414129\pi$
$263$	8.64420	0.533024	0.266512	+	0.963832i	$0.414129\pi$
$264$	−38.3964	−2.36313
$265$	−19.8068	−1.21672
$266$	49.9765	3.06426
$267$	−6.35092	−0.388670
$268$	41.0007	2.50452
$269$	8.14600	0.496670	0.248335	−	0.968674i	$-0.420117\pi$
$269$	8.14600	0.496670	0.248335	+	0.968674i	$0.420117\pi$
$270$	10.1588	0.618243
$271$	3.79773	0.230696	0.115348	−	0.993325i	$-0.463202\pi$
$271$	3.79773	0.230696	0.115348	+	0.993325i	$0.463202\pi$
$272$	41.3162	2.50517
$273$	1.99158	0.120536
$274$	10.0411	0.606608
$275$	33.0298	1.99177
$276$	4.69638	0.282689
$277$	−15.5146	−0.932181	−0.466091	−	0.884737i	$-0.654338\pi$
$277$	−15.5146	−0.932181	−0.466091	+	0.884737i	$0.654338\pi$
$278$	46.4488	2.78581
$279$	−2.82177	−0.168935
$280$	−146.179	−8.73586
$281$	−28.0377	−1.67259	−0.836296	−	0.548279i	$-0.815283\pi$
$281$	−28.0377	−1.67259	−0.836296	+	0.548279i	$0.815283\pi$
$282$	−36.3947	−2.16727
$283$	18.8840	1.12254	0.561269	−	0.827633i	$-0.310313\pi$
$283$	18.8840	1.12254	0.561269	+	0.827633i	$0.310313\pi$
$284$	51.2946	3.04378
$285$	−16.7345	−0.991264
$286$	5.31428	0.314240
$287$	−6.56790	−0.387691
$288$	−24.8908	−1.46671
$289$	−10.5285	−0.619326
$290$	46.1291	2.70880
$291$	16.2413	0.952080
$292$	34.7126	2.03140
$293$	−12.3747	−0.722938	−0.361469	−	0.932384i	$-0.617725\pi$
$293$	−12.3747	−0.722938	−0.361469	+	0.932384i	$0.617725\pi$
$294$	−24.5457	−1.43153
$295$	37.4682	2.18148
$296$	−44.1995	−2.56904
$297$	3.85715	0.223814
$298$	26.8618	1.55606
$299$	−0.418226	−0.0241866
$300$	48.0299	2.77301
$301$	8.90616	0.513343
$302$	30.6304	1.76258
$303$	2.99896	0.172286
$304$	73.7988	4.23265
$305$	45.8676	2.62637
$306$	−7.01714	−0.401143
$307$	16.5807	0.946313	0.473157	−	0.880978i	$-0.343114\pi$
$307$	16.5807	0.946313	0.473157	+	0.880978i	$0.343114\pi$
$308$	−86.2612	−4.91519
$309$	0.826244	0.0470034
$310$	−28.6657	−1.62810
$311$	−1.73628	−0.0984556	−0.0492278	−	0.998788i	$-0.515676\pi$
$311$	−1.73628	−0.0984556	−0.0492278	+	0.998788i	$0.515676\pi$
$312$	4.97215	0.281492
$313$	−27.5598	−1.55777	−0.778885	−	0.627166i	$-0.784215\pi$
$313$	−27.5598	−1.55777	−0.778885	+	0.627166i	$0.784215\pi$
$314$	−36.2767	−2.04721
$315$	14.6845	0.827380
$316$	6.82201	0.383768
$317$	21.1317	1.18687	0.593436	−	0.804881i	$-0.297771\pi$
$317$	21.1317	1.18687	0.593436	+	0.804881i	$0.297771\pi$
$318$	−14.8351	−0.831911
$319$	17.5146	0.980629
$320$	−133.232	−7.44791
$321$	13.8734	0.774337
$322$	9.20932	0.513215
$323$	11.5593	0.643175
$324$	5.60882	0.311601
$325$	−4.27720	−0.237257
$326$	−47.8756	−2.65158
$327$	9.81653	0.542855
$328$	−16.3973	−0.905391
$329$	−52.6087	−2.90041
$330$	39.1839	2.15700
$331$	14.1886	0.779876	0.389938	−	0.920841i	$-0.372496\pi$
$331$	14.1886	0.779876	0.389938	+	0.920841i	$0.372496\pi$
$332$	−57.2443	−3.14169
$333$	4.44010	0.243316
$334$	24.8190	1.35804
$335$	−26.9217	−1.47089
$336$	−64.7586	−3.53287
$337$	−3.50787	−0.191086	−0.0955430	−	0.995425i	$-0.530459\pi$
$337$	−3.50787	−0.191086	−0.0955430	+	0.995425i	$0.530459\pi$
$338$	35.1712	1.91306
$339$	−3.30515	−0.179511
$340$	−52.5479	−2.84981
$341$	−10.8840	−0.589400
$342$	−12.5340	−0.677759
$343$	−7.56980	−0.408731
$344$	22.2350	1.19883
$345$	−3.08371	−0.166021
$346$	27.0497	1.45420
$347$	35.5114	1.90635	0.953177	−	0.302412i	$-0.0977919\pi$
$347$	35.5114	1.90635	0.953177	+	0.302412i	$0.0977919\pi$
$348$	25.4687	1.36526
$349$	−4.81785	−0.257893	−0.128947	−	0.991652i	$-0.541160\pi$
$349$	−4.81785	−0.257893	−0.128947	+	0.991652i	$0.541160\pi$
$350$	94.1840	5.03434
$351$	−0.499482	−0.0266604
$352$	−96.0075	−5.11722
$353$	−29.1147	−1.54962	−0.774808	−	0.632196i	$-0.782154\pi$
$353$	−29.1147	−1.54962	−0.774808	+	0.632196i	$0.782154\pi$
$354$	28.0633	1.49155
$355$	−33.6808	−1.78759
$356$	−35.6212	−1.88792
$357$	−10.1433	−0.536840
$358$	9.95447	0.526110
$359$	25.9622	1.37023	0.685117	−	0.728433i	$-0.259751\pi$
$359$	25.9622	1.37023	0.685117	+	0.728433i	$0.259751\pi$
$360$	36.6612	1.93222
$361$	1.64709	0.0866891
$362$	−22.1509	−1.16423
$363$	3.87757	0.203520
$364$	11.1704	0.585489
$365$	−22.7928	−1.19303
$366$	34.3544	1.79573
$367$	21.7359	1.13460	0.567301	−	0.823510i	$-0.307988\pi$
$367$	21.7359	1.13460	0.567301	+	0.823510i	$0.307988\pi$
$368$	13.5991	0.708903
$369$	1.64721	0.0857503
$370$	45.1060	2.34495
$371$	−21.4442	−1.11333
$372$	−15.8268	−0.820581
$373$	5.46932	0.283190	0.141595	−	0.989925i	$-0.454777\pi$
$373$	5.46932	0.283190	0.141595	+	0.989925i	$0.454777\pi$
$374$	−27.0661	−1.39956
$375$	−13.1230	−0.677668
$376$	−131.342	−6.77346
$377$	−2.26806	−0.116811
$378$	10.9986	0.565706
$379$	27.5296	1.41410	0.707051	−	0.707163i	$-0.250025\pi$
$379$	27.5296	1.41410	0.707051	+	0.707163i	$0.250025\pi$
$380$	−93.8607	−4.81495
$381$	−1.00000	−0.0512316
$382$	−70.1482	−3.58910
$383$	−31.0904	−1.58865	−0.794324	−	0.607495i	$-0.792174\pi$
$383$	−31.0904	−1.58865	−0.794324	+	0.607495i	$0.792174\pi$
$384$	−50.0081	−2.55196
$385$	56.6404	2.88666
$386$	20.6016	1.04859
$387$	−2.23364	−0.113542
$388$	91.0944	4.62462
$389$	−17.6478	−0.894779	−0.447389	−	0.894339i	$-0.647646\pi$
$389$	−17.6478	−0.894779	−0.447389	+	0.894339i	$0.647646\pi$
$390$	−5.07412	−0.256938
$391$	2.13006	0.107722
$392$	−88.5810	−4.47401
$393$	5.62534	0.283761
$394$	63.0555	3.17669
$395$	−4.47943	−0.225385
$396$	21.6340	1.08715
$397$	−3.53035	−0.177183	−0.0885915	−	0.996068i	$-0.528237\pi$
$397$	−3.53035	−0.177183	−0.0885915	+	0.996068i	$0.528237\pi$
$398$	6.32627	0.317107
$399$	−18.1179	−0.907028
$400$	139.078	6.95392
$401$	30.1875	1.50749	0.753745	−	0.657167i	$-0.228245\pi$
$401$	30.1875	1.50749	0.753745	+	0.657167i	$0.228245\pi$
$402$	−20.1641	−1.00569
$403$	1.40942	0.0702082
$404$	16.8207	0.836859
$405$	−3.68284	−0.183002
$406$	49.9426	2.47861
$407$	17.1261	0.848910
$408$	−25.3236	−1.25371
$409$	−0.315290	−0.0155901	−0.00779504	−	0.999970i	$-0.502481\pi$
$409$	−0.315290	−0.0155901	−0.00779504	+	0.999970i	$0.502481\pi$
$410$	16.7336	0.826414
$411$	−3.64019	−0.179557
$412$	4.63426	0.228313
$413$	40.5656	1.99610
$414$	−2.30967	−0.113514
$415$	37.5874	1.84510
$416$	12.4325	0.609554
$417$	−16.8390	−0.824608
$418$	−48.3453	−2.36465
$419$	18.1217	0.885305	0.442653	−	0.896693i	$-0.354037\pi$
$419$	18.1217	0.885305	0.442653	+	0.896693i	$0.354037\pi$
$420$	82.3630	4.01890
$421$	8.76924	0.427387	0.213693	−	0.976901i	$-0.431451\pi$
$421$	8.76924	0.427387	0.213693	+	0.976901i	$0.431451\pi$
$422$	−15.9567	−0.776759
$423$	13.1941	0.641519
$424$	−53.5373	−2.60000
$425$	21.7842	1.05669
$426$	−25.2266	−1.22223
$427$	49.6594	2.40319
$428$	77.8134	3.76125
$429$	−1.92657	−0.0930159
$430$	−22.6910	−1.09426
$431$	−18.0024	−0.867144	−0.433572	−	0.901119i	$-0.642747\pi$
$431$	−18.0024	−0.867144	−0.433572	+	0.901119i	$0.642747\pi$
$432$	16.2413	0.781408
$433$	−37.5574	−1.80489	−0.902446	−	0.430803i	$-0.858231\pi$
$433$	−37.5574	−1.80489	−0.902446	+	0.430803i	$0.858231\pi$
$434$	−31.0354	−1.48975
$435$	−16.7231	−0.801811
$436$	55.0592	2.63686
$437$	3.80470	0.182004
$438$	−17.0716	−0.815713
$439$	−4.18733	−0.199850	−0.0999251	−	0.994995i	$-0.531860\pi$
$439$	−4.18733	−0.199850	−0.0999251	+	0.994995i	$0.531860\pi$
$440$	141.408	6.74134
$441$	8.89848	0.423737
$442$	3.50493	0.166713
$443$	−9.54371	−0.453435	−0.226718	−	0.973961i	$-0.572799\pi$
$443$	−9.54371	−0.453435	−0.226718	+	0.973961i	$0.572799\pi$
$444$	24.9038	1.18188
$445$	23.3894	1.10876
$446$	3.17539	0.150359
$447$	−9.73814	−0.460598
$448$	−144.246	−6.81500
$449$	9.84609	0.464666	0.232333	−	0.972636i	$-0.425364\pi$
$449$	9.84609	0.464666	0.232333	+	0.972636i	$0.425364\pi$
$450$	−23.6210	−1.11351
$451$	6.35352	0.299176
$452$	−18.5380	−0.871955
$453$	−11.1044	−0.521729
$454$	−59.9518	−2.81368
$455$	−7.33466	−0.343854
$456$	−45.2328	−2.11822
$457$	−20.6631	−0.966580	−0.483290	−	0.875460i	$-0.660558\pi$
$457$	−20.6631	−0.966580	−0.483290	+	0.875460i	$0.660558\pi$
$458$	−71.2897	−3.33115
$459$	2.54391	0.118739
$460$	−17.2960	−0.806429
$461$	12.1576	0.566238	0.283119	−	0.959085i	$-0.408631\pi$
$461$	12.1576	0.566238	0.283119	+	0.959085i	$0.408631\pi$
$462$	42.4231	1.97370
$463$	8.50308	0.395172	0.197586	−	0.980286i	$-0.436690\pi$
$463$	8.50308	0.395172	0.197586	+	0.980286i	$0.436690\pi$
$464$	73.7486	3.42369
$465$	10.3921	0.481922
$466$	−16.3627	−0.757988
$467$	−39.3219	−1.81960	−0.909800	−	0.415047i	$-0.863765\pi$
$467$	−39.3219	−1.81960	−0.909800	+	0.415047i	$0.863765\pi$
$468$	−2.80151	−0.129500
$469$	−29.1472	−1.34589
$470$	134.036	6.18261
$471$	13.1513	0.605981
$472$	101.276	4.66158
$473$	−8.61547	−0.396140
$474$	−3.35505	−0.154103
$475$	38.9108	1.78535
$476$	−56.8920	−2.60764
$477$	5.37814	0.246248
$478$	−45.1661	−2.06585
$479$	−4.62621	−0.211377	−0.105688	−	0.994399i	$-0.533705\pi$
$479$	−4.62621	−0.211377	−0.105688	+	0.994399i	$0.533705\pi$
$480$	91.6688	4.18409
$481$	−2.21775	−0.101121
$482$	−41.0173	−1.86829
$483$	−3.33863	−0.151913
$484$	21.7486	0.988573
$485$	−59.8139	−2.71601
$486$	−2.75841	−0.125124
$487$	−9.25480	−0.419375	−0.209687	−	0.977768i	$-0.567245\pi$
$487$	−9.25480	−0.419375	−0.209687	+	0.977768i	$0.567245\pi$
$488$	123.979	5.61227
$489$	17.3562	0.784876
$490$	90.3976	4.08375
$491$	−26.9193	−1.21485	−0.607426	−	0.794376i	$-0.707798\pi$
$491$	−26.9193	−1.21485	−0.607426	+	0.794376i	$0.707798\pi$
$492$	9.23890	0.416522
$493$	11.5514	0.520250
$494$	6.26048	0.281672
$495$	−14.2052	−0.638478
$496$	−45.8290	−2.05778
$497$	−36.4652	−1.63569
$498$	28.1526	1.26155
$499$	20.0368	0.896971	0.448486	−	0.893790i	$-0.351964\pi$
$499$	20.0368	0.896971	0.448486	+	0.893790i	$0.351964\pi$
$500$	−73.6045	−3.29170
$501$	−8.99758	−0.401982
$502$	−17.9634	−0.801746
$503$	−13.0418	−0.581507	−0.290754	−	0.956798i	$-0.593906\pi$
$503$	−13.0418	−0.581507	−0.290754	+	0.956798i	$0.593906\pi$
$504$	39.6919	1.76802
$505$	−11.0447	−0.491482
$506$	−8.90873	−0.396041
$507$	−12.7505	−0.566270
$508$	−5.60882	−0.248851
$509$	−2.00920	−0.0890564	−0.0445282	−	0.999008i	$-0.514178\pi$
$509$	−2.00920	−0.0890564	−0.0445282	+	0.999008i	$0.514178\pi$
$510$	25.8430	1.14435
$511$	−24.6771	−1.09165
$512$	−80.9071	−3.57562
$513$	4.54391	0.200618
$514$	40.9578	1.80657
$515$	−3.04292	−0.134087
$516$	−12.5281	−0.551518
$517$	50.8916	2.23821
$518$	48.8348	2.14568
$519$	−9.80628	−0.430448
$520$	−18.3116	−0.803017
$521$	−34.8130	−1.52518	−0.762592	−	0.646880i	$-0.776074\pi$
$521$	−34.8130	−1.52518	−0.762592	+	0.646880i	$0.776074\pi$
$522$	−12.5254	−0.548224
$523$	27.3074	1.19407	0.597034	−	0.802216i	$-0.296346\pi$
$523$	27.3074	1.19407	0.597034	+	0.802216i	$0.296346\pi$
$524$	31.5515	1.37833
$525$	−34.1443	−1.49018
$526$	−23.8442	−1.03966
$527$	−7.17831	−0.312692
$528$	62.6449	2.72627
$529$	−22.2989	−0.969517
$530$	54.6353	2.37320
$531$	−10.1737	−0.441502
$532$	−101.620	−4.40578
$533$	−0.822751	−0.0356373
$534$	17.5184	0.758097
$535$	−51.0934	−2.20896
$536$	−72.7686	−3.14312
$537$	−3.60877	−0.155730
$538$	−22.4700	−0.968751
$539$	34.3227	1.47839
$540$	−20.6564	−0.888909
$541$	5.06962	0.217960	0.108980	−	0.994044i	$-0.465242\pi$
$541$	5.06962	0.217960	0.108980	+	0.994044i	$0.465242\pi$
$542$	−10.4757	−0.449970
$543$	8.03032	0.344614
$544$	−63.3199	−2.71482
$545$	−36.1527	−1.54861
$546$	−5.49359	−0.235104
$547$	28.1814	1.20495	0.602474	−	0.798139i	$-0.294182\pi$
$547$	28.1814	1.20495	0.602474	+	0.798139i	$0.294182\pi$
$548$	−20.4172	−0.872180
$549$	−12.4544	−0.531542
$550$	−91.1098	−3.88494
$551$	20.6331	0.878998
$552$	−8.33519	−0.354769
$553$	−4.84974	−0.206232
$554$	42.7956	1.81821
$555$	−16.3522	−0.694111
$556$	−94.4469	−4.00544
$557$	20.0289	0.848653	0.424327	−	0.905509i	$-0.360511\pi$
$557$	20.0289	0.848653	0.424327	+	0.905509i	$0.360511\pi$
$558$	7.78359	0.329505
$559$	1.11566	0.0471874
$560$	238.495	10.0783
$561$	9.81222	0.414272
$562$	77.3396	3.26237
$563$	−1.33320	−0.0561876	−0.0280938	−	0.999605i	$-0.508944\pi$
$563$	−1.33320	−0.0561876	−0.0280938	+	0.999605i	$0.508944\pi$
$564$	74.0034	3.11610
$565$	12.1723	0.512094
$566$	−52.0899	−2.18950
$567$	−3.98729	−0.167450
$568$	−91.0384	−3.81989
$569$	28.3841	1.18992	0.594962	−	0.803754i	$-0.297167\pi$
$569$	28.3841	1.18992	0.594962	+	0.803754i	$0.297167\pi$
$570$	46.1605	1.93345
$571$	5.87257	0.245759	0.122880	−	0.992422i	$-0.460787\pi$
$571$	5.87257	0.245759	0.122880	+	0.992422i	$0.460787\pi$
$572$	−10.8058	−0.451814
$573$	25.4307	1.06238
$574$	18.1170	0.756187
$575$	7.17020	0.299018
$576$	36.1765	1.50736
$577$	−9.91326	−0.412695	−0.206347	−	0.978479i	$-0.566158\pi$
$577$	−9.91326	−0.412695	−0.206347	+	0.978479i	$0.566158\pi$
$578$	29.0420	1.20799
$579$	−7.46865	−0.310387
$580$	−93.7969	−3.89470
$581$	40.6947	1.68830
$582$	−44.8001	−1.85702
$583$	20.7443	0.859139
$584$	−61.6085	−2.54938
$585$	1.83951	0.0760544
$586$	34.1345	1.41008
$587$	−33.7575	−1.39332	−0.696660	−	0.717401i	$-0.745331\pi$
$587$	−33.7575	−1.39332	−0.696660	+	0.717401i	$0.745331\pi$
$588$	49.9100	2.05825
$589$	−12.8218	−0.528315
$590$	−103.353	−4.25496
$591$	−22.8594	−0.940309
$592$	72.1128	2.96382
$593$	25.5069	1.04744	0.523720	−	0.851890i	$-0.324544\pi$
$593$	25.5069	1.04744	0.523720	+	0.851890i	$0.324544\pi$
$594$	−10.6396	−0.436548
$595$	37.3561	1.53145
$596$	−54.6195	−2.23730
$597$	−2.29345	−0.0938646
$598$	1.15364	0.0471758
$599$	37.6890	1.53993	0.769965	−	0.638087i	$-0.220274\pi$
$599$	37.6890	1.53993	0.769965	+	0.638087i	$0.220274\pi$
$600$	−85.2442	−3.48008
$601$	−8.71621	−0.355542	−0.177771	−	0.984072i	$-0.556889\pi$
$601$	−8.71621	−0.355542	−0.177771	+	0.984072i	$0.556889\pi$
$602$	−24.5668	−1.00127
$603$	7.31003	0.297688
$604$	−62.2825	−2.53424
$605$	−14.2805	−0.580583
$606$	−8.27237	−0.336042
$607$	−27.9504	−1.13447	−0.567236	−	0.823555i	$-0.691987\pi$
$607$	−27.9504	−1.13447	−0.567236	+	0.823555i	$0.691987\pi$
$608$	−113.102	−4.58687
$609$	−18.1056	−0.733674
$610$	−126.522	−5.12271
$611$	−6.59021	−0.266611
$612$	14.2683	0.576763
$613$	−32.9978	−1.33277	−0.666385	−	0.745608i	$-0.732159\pi$
$613$	−32.9978	−1.33277	−0.666385	+	0.745608i	$0.732159\pi$
$614$	−45.7365	−1.84577
$615$	−6.06640	−0.244621
$616$	153.098	6.16848
$617$	−26.5286	−1.06800	−0.534000	−	0.845484i	$-0.679312\pi$
$617$	−26.5286	−1.06800	−0.534000	+	0.845484i	$0.679312\pi$
$618$	−2.27912	−0.0916796
$619$	32.7110	1.31477	0.657383	−	0.753557i	$-0.271663\pi$
$619$	32.7110	1.31477	0.657383	+	0.753557i	$0.271663\pi$
$620$	58.2875	2.34088
$621$	0.837319	0.0336005
$622$	4.78938	0.192037
$623$	25.3230	1.01454
$624$	−8.11221	−0.324748
$625$	5.51341	0.220536
$626$	76.0212	3.03842
$627$	17.5265	0.699941
$628$	73.7634	2.94348
$629$	11.2952	0.450369
$630$	−40.5060	−1.61380
$631$	−36.7660	−1.46363	−0.731815	−	0.681503i	$-0.761327\pi$
$631$	−36.7660	−1.46363	−0.731815	+	0.681503i	$0.761327\pi$
$632$	−12.1078	−0.481622
$633$	5.78474	0.229923
$634$	−58.2898	−2.31498
$635$	3.68284	0.146149
$636$	30.1650	1.19612
$637$	−4.44463	−0.176103
$638$	−48.3124	−1.91271
$639$	9.14535	0.361784
$640$	184.172	7.28002
$641$	13.6049	0.537360	0.268680	−	0.963230i	$-0.413413\pi$
$641$	13.6049	0.537360	0.268680	+	0.963230i	$0.413413\pi$
$642$	−38.2685	−1.51034
$643$	−21.7502	−0.857744	−0.428872	−	0.903365i	$-0.641089\pi$
$643$	−21.7502	−0.857744	−0.428872	+	0.903365i	$0.641089\pi$
$644$	−18.7258	−0.737900
$645$	8.22612	0.323903
$646$	−31.8852	−1.25451
$647$	−3.45776	−0.135939	−0.0679694	−	0.997687i	$-0.521652\pi$
$647$	−3.45776	−0.135939	−0.0679694	+	0.997687i	$0.521652\pi$
$648$	−9.95461	−0.391054
$649$	−39.2415	−1.54037
$650$	11.7983	0.462767
$651$	11.2512	0.440969
$652$	97.3481	3.81244
$653$	5.75110	0.225058	0.112529	−	0.993648i	$-0.464105\pi$
$653$	5.75110	0.225058	0.112529	+	0.993648i	$0.464105\pi$
$654$	−27.0780	−1.05883
$655$	−20.7172	−0.809488
$656$	26.7527	1.04452
$657$	6.18893	0.241453
$658$	145.116	5.65722
$659$	3.61263	0.140728	0.0703640	−	0.997521i	$-0.477584\pi$
$659$	3.61263	0.140728	0.0703640	+	0.997521i	$0.477584\pi$
$660$	−79.6747	−3.10133
$661$	0.615189	0.0239281	0.0119640	−	0.999928i	$-0.496192\pi$
$661$	0.615189	0.0239281	0.0119640	+	0.999928i	$0.496192\pi$
$662$	−39.1380	−1.52114
$663$	−1.27064	−0.0493474
$664$	101.598	3.94276
$665$	66.7252	2.58749
$666$	−12.2476	−0.474586
$667$	3.80211	0.147218
$668$	−50.4658	−1.95258
$669$	−1.15117	−0.0445067
$670$	74.2610	2.86895
$671$	−48.0385	−1.85451
$672$	99.2469	3.82853
$673$	26.8956	1.03675	0.518374	−	0.855154i	$-0.326538\pi$
$673$	26.8956	1.03675	0.518374	+	0.855154i	$0.326538\pi$
$674$	9.67615	0.372711
$675$	8.56328	0.329601
$676$	−71.5154	−2.75059
$677$	16.4765	0.633244	0.316622	−	0.948552i	$-0.397451\pi$
$677$	16.4765	0.633244	0.316622	+	0.948552i	$0.397451\pi$
$678$	9.11696	0.350135
$679$	−64.7586	−2.48521
$680$	93.2627	3.57646
$681$	21.7342	0.832856
$682$	30.0224	1.14962
$683$	−20.8392	−0.797391	−0.398695	−	0.917083i	$-0.630537\pi$
$683$	−20.8392	−0.797391	−0.398695	+	0.917083i	$0.630537\pi$
$684$	25.4860	0.974481
$685$	13.4062	0.512226
$686$	20.8806	0.797225
$687$	25.8445	0.986029
$688$	−36.2771	−1.38305
$689$	−2.68628	−0.102339
$690$	8.50614	0.323823
$691$	−15.6058	−0.593673	−0.296837	−	0.954928i	$-0.595932\pi$
$691$	−15.6058	−0.593673	−0.296837	+	0.954928i	$0.595932\pi$
$692$	−55.0017	−2.09085
$693$	−15.3796	−0.584221
$694$	−97.9551	−3.71833
$695$	62.0152	2.35237
$696$	−45.2021	−1.71338
$697$	4.19035	0.158721
$698$	13.2896	0.503019
$699$	5.93194	0.224366
$700$	−191.509	−7.23837
$701$	6.28496	0.237379	0.118690	−	0.992931i	$-0.462131\pi$
$701$	6.28496	0.237379	0.118690	+	0.992931i	$0.462131\pi$
$702$	1.37778	0.0520008
$703$	20.1754	0.760930
$704$	139.538	5.25904
$705$	−48.5917	−1.83007
$706$	80.3101	3.02251
$707$	−11.9577	−0.449717
$708$	−57.0626	−2.14455
$709$	−0.509625	−0.0191394	−0.00956969	−	0.999954i	$-0.503046\pi$
$709$	−0.509625	−0.0191394	−0.00956969	+	0.999954i	$0.503046\pi$
$710$	92.9055	3.48668
$711$	1.21630	0.0456148
$712$	63.2209	2.36930
$713$	−2.36272	−0.0884845
$714$	27.9794	1.04710
$715$	7.09526	0.265348
$716$	−20.2410	−0.756440
$717$	16.3739	0.611496
$718$	−71.6144	−2.67263
$719$	−14.6138	−0.545002	−0.272501	−	0.962155i	$-0.587851\pi$
$719$	−14.6138	−0.545002	−0.272501	+	0.962155i	$0.587851\pi$
$720$	−59.8139	−2.22913
$721$	−3.29447	−0.122693
$722$	−4.54336	−0.169086
$723$	14.8699	0.553018
$724$	45.0406	1.67392
$725$	38.8843	1.44413
$726$	−10.6959	−0.396963
$727$	47.1933	1.75030	0.875151	−	0.483850i	$-0.160762\pi$
$727$	47.1933	1.75030	0.875151	+	0.483850i	$0.160762\pi$
$728$	−19.8254	−0.734778
$729$	1.00000	0.0370370
$730$	62.8720	2.32700
$731$	−5.68217	−0.210163
$732$	−69.8547	−2.58190
$733$	45.8563	1.69374	0.846870	−	0.531800i	$-0.178484\pi$
$733$	45.8563	1.69374	0.846870	+	0.531800i	$0.178484\pi$
$734$	−59.9564	−2.21303
$735$	−32.7717	−1.20880
$736$	−20.8416	−0.768230
$737$	28.1959	1.03861
$738$	−4.54368	−0.167255
$739$	−49.2374	−1.81123	−0.905613	−	0.424105i	$-0.860589\pi$
$739$	−49.2374	−1.81123	−0.905613	+	0.424105i	$0.860589\pi$
$740$	−91.7164	−3.37156
$741$	−2.26960	−0.0833758
$742$	59.1519	2.17153
$743$	13.2628	0.486566	0.243283	−	0.969955i	$-0.421776\pi$
$743$	13.2628	0.486566	0.243283	+	0.969955i	$0.421776\pi$
$744$	28.0896	1.02981
$745$	35.8640	1.31395
$746$	−15.0866	−0.552360
$747$	−10.2061	−0.373422
$748$	55.0350	2.01228
$749$	−55.3173	−2.02125
$750$	36.1986	1.32179
$751$	−39.4180	−1.43838	−0.719192	−	0.694811i	$-0.755488\pi$
$751$	−39.4180	−1.43838	−0.719192	+	0.694811i	$0.755488\pi$
$752$	214.289	7.81431
$753$	6.51223	0.237319
$754$	6.25623	0.227838
$755$	40.8956	1.48834
$756$	−22.3640	−0.813371
$757$	−7.60384	−0.276366	−0.138183	−	0.990407i	$-0.544126\pi$
$757$	−7.60384	−0.276366	−0.138183	+	0.990407i	$0.544126\pi$
$758$	−75.9379	−2.75819
$759$	3.22966	0.117229
$760$	166.585	6.04268
$761$	24.1547	0.875606	0.437803	−	0.899071i	$-0.355757\pi$
$761$	24.1547	0.875606	0.437803	+	0.899071i	$0.355757\pi$
$762$	2.75841	0.0999266
$763$	−39.1414	−1.41701
$764$	142.636	5.16040
$765$	−9.36879	−0.338729
$766$	85.7602	3.09864
$767$	5.08159	0.183486
$768$	65.5897	2.36677
$769$	−34.2301	−1.23437	−0.617185	−	0.786818i	$-0.711727\pi$
$769$	−34.2301	−1.23437	−0.617185	+	0.786818i	$0.711727\pi$
$770$	−156.237	−5.63041
$771$	−14.8483	−0.534750
$772$	−41.8904	−1.50767
$773$	15.5771	0.560268	0.280134	−	0.959961i	$-0.409621\pi$
$773$	15.5771	0.560268	0.280134	+	0.959961i	$0.409621\pi$
$774$	6.16129	0.221463
$775$	−24.1636	−0.867981
$776$	−161.676	−5.80381
$777$	−17.7040	−0.635127
$778$	48.6798	1.74526
$779$	7.48476	0.268169
$780$	10.3175	0.369425
$781$	35.2749	1.26224
$782$	−5.87559	−0.210110
$783$	4.54082	0.162276
$784$	144.523	5.16152
$785$	−48.4342	−1.72869
$786$	−15.5170	−0.553472
$787$	−24.1596	−0.861196	−0.430598	−	0.902544i	$-0.641697\pi$
$787$	−24.1596	−0.861196	−0.430598	+	0.902544i	$0.641697\pi$
$788$	−128.214	−4.56744
$789$	8.64420	0.307742
$790$	12.3561	0.439611
$791$	13.1786	0.468577
$792$	−38.3964	−1.36436
$793$	6.22076	0.220906
$794$	9.73814	0.345594
$795$	−19.8068	−0.702475
$796$	−12.8636	−0.455937
$797$	−23.3959	−0.828724	−0.414362	−	0.910112i	$-0.635995\pi$
$797$	−23.3959	−0.828724	−0.414362	+	0.910112i	$0.635995\pi$
$798$	49.9765	1.76915
$799$	33.5646	1.18743
$800$	−213.147	−7.53589
$801$	−6.35092	−0.224399
$802$	−83.2694	−2.94034
$803$	23.8716	0.842411
$804$	41.0007	1.44598
$805$	12.2956	0.433365
$806$	−3.88776	−0.136940
$807$	8.14600	0.286753
$808$	−29.8535	−1.05024
$809$	23.7422	0.834733	0.417366	−	0.908738i	$-0.362953\pi$
$809$	23.7422	0.834733	0.417366	+	0.908738i	$0.362953\pi$
$810$	10.1588	0.356943
$811$	−0.850896	−0.0298790	−0.0149395	−	0.999888i	$-0.504756\pi$
$811$	−0.850896	−0.0298790	−0.0149395	+	0.999888i	$0.504756\pi$
$812$	−101.551	−3.56374
$813$	3.79773	0.133192
$814$	−47.2409	−1.65579
$815$	−63.9202	−2.23903
$816$	41.3162	1.44636
$817$	−10.1494	−0.355084
$818$	0.869699	0.0304083
$819$	1.99158	0.0695914
$820$	−34.0254	−1.18822
$821$	26.9183	0.939456	0.469728	−	0.882811i	$-0.344352\pi$
$821$	26.9183	0.939456	0.469728	+	0.882811i	$0.344352\pi$
$822$	10.0411	0.350225
$823$	−7.35499	−0.256379	−0.128189	−	0.991750i	$-0.540917\pi$
$823$	−7.35499	−0.256379	−0.128189	+	0.991750i	$0.540917\pi$
$824$	−8.22494	−0.286529
$825$	33.0298	1.14995
$826$	−111.897	−3.89338
$827$	−46.6094	−1.62077	−0.810384	−	0.585900i	$-0.800741\pi$
$827$	−46.6094	−1.62077	−0.810384	+	0.585900i	$0.800741\pi$
$828$	4.69638	0.163210
$829$	22.1335	0.768727	0.384364	−	0.923182i	$-0.374421\pi$
$829$	22.1335	0.768727	0.384364	+	0.923182i	$0.374421\pi$
$830$	−103.682	−3.59884
$831$	−15.5146	−0.538195
$832$	−18.0695	−0.626448
$833$	22.6369	0.784323
$834$	46.4488	1.60839
$835$	33.1366	1.14674
$836$	98.3031	3.39988
$837$	−2.82177	−0.0975345
$838$	−49.9872	−1.72678
$839$	−6.50997	−0.224749	−0.112375	−	0.993666i	$-0.535846\pi$
$839$	−6.50997	−0.224749	−0.112375	+	0.993666i	$0.535846\pi$
$840$	−146.179	−5.04365
$841$	−8.38097	−0.288999
$842$	−24.1892	−0.833614
$843$	−28.0377	−0.965671
$844$	32.4456	1.11682
$845$	46.9581	1.61541
$846$	−36.3947	−1.25128
$847$	−15.4610	−0.531246
$848$	87.3477	2.99953
$849$	18.8840	0.648098
$850$	−60.0897	−2.06106
$851$	3.71778	0.127444
$852$	51.2946	1.75733
$853$	−27.0993	−0.927863	−0.463931	−	0.885871i	$-0.653562\pi$
$853$	−27.0993	−0.927863	−0.463931	+	0.885871i	$0.653562\pi$
$854$	−136.981	−4.68739
$855$	−16.7345	−0.572307
$856$	−138.104	−4.72031
$857$	−16.4909	−0.563318	−0.281659	−	0.959515i	$-0.590885\pi$
$857$	−16.4909	−0.563318	−0.281659	+	0.959515i	$0.590885\pi$
$858$	5.31428	0.181427
$859$	−36.8184	−1.25623	−0.628114	−	0.778122i	$-0.716173\pi$
$859$	−36.8184	−1.25623	−0.628114	+	0.778122i	$0.716173\pi$
$860$	46.1389	1.57332
$861$	−6.56790	−0.223833
$862$	49.6579	1.69136
$863$	5.32808	0.181370	0.0906850	−	0.995880i	$-0.471094\pi$
$863$	5.32808	0.181370	0.0906850	+	0.995880i	$0.471094\pi$
$864$	−24.8908	−0.846803
$865$	36.1149	1.22794
$866$	103.599	3.52043
$867$	−10.5285	−0.357568
$868$	63.1060	2.14196
$869$	4.69145	0.159146
$870$	46.1291	1.56392
$871$	−3.65123	−0.123717
$872$	−97.7198	−3.30921
$873$	16.2413	0.549683
$874$	−10.4949	−0.354996
$875$	52.3252	1.76891
$876$	34.7126	1.17283
$877$	−21.7559	−0.734645	−0.367323	−	0.930094i	$-0.619726\pi$
$877$	−21.7559	−0.734645	−0.367323	+	0.930094i	$0.619726\pi$
$878$	11.5504	0.389806
$879$	−12.3747	−0.417388
$880$	−230.711	−7.77726
$881$	30.5714	1.02998	0.514988	−	0.857197i	$-0.327796\pi$
$881$	30.5714	1.02998	0.514988	+	0.857197i	$0.327796\pi$
$882$	−24.5457	−0.826495
$883$	−47.5288	−1.59947	−0.799736	−	0.600352i	$-0.795027\pi$
$883$	−47.5288	−1.59947	−0.799736	+	0.600352i	$0.795027\pi$
$884$	−7.12677	−0.239699
$885$	37.4682	1.25948
$886$	26.3254	0.884421
$887$	−16.7954	−0.563936	−0.281968	−	0.959424i	$-0.590987\pi$
$887$	−16.7954	−0.563936	−0.281968	+	0.959424i	$0.590987\pi$
$888$	−44.1995	−1.48324
$889$	3.98729	0.133729
$890$	−64.5175	−2.16263
$891$	3.85715	0.129219
$892$	−6.45669	−0.216186
$893$	59.9528	2.00624
$894$	26.8618	0.898392
$895$	13.2905	0.444253
$896$	199.397	6.66138
$897$	−0.418226	−0.0139642
$898$	−27.1596	−0.906326
$899$	−12.8131	−0.427342
$900$	48.0299	1.60100
$901$	13.6815	0.455796
$902$	−17.5256	−0.583539
$903$	8.90616	0.296378
$904$	32.9015	1.09429
$905$	−29.5743	−0.983084
$906$	30.6304	1.01763
$907$	32.3337	1.07362	0.536812	−	0.843702i	$-0.319628\pi$
$907$	32.3337	1.07362	0.536812	+	0.843702i	$0.319628\pi$
$908$	121.903	4.04550
$909$	2.99896	0.0994693
$910$	20.2320	0.670684
$911$	−41.2591	−1.36698	−0.683488	−	0.729962i	$-0.739538\pi$
$911$	−41.2591	−1.36698	−0.683488	+	0.729962i	$0.739538\pi$
$912$	73.7988	2.44372
$913$	−39.3665	−1.30284
$914$	56.9973	1.88530
$915$	45.8676	1.51634
$916$	144.957	4.78952
$917$	−22.4298	−0.740699
$918$	−7.01714	−0.231600
$919$	−13.3915	−0.441746	−0.220873	−	0.975303i	$-0.570891\pi$
$919$	−13.3915	−0.441746	−0.220873	+	0.975303i	$0.570891\pi$
$920$	30.6971	1.01205
$921$	16.5807	0.546354
$922$	−33.5357	−1.10444
$923$	−4.56793	−0.150355
$924$	−86.2612	−2.83779
$925$	38.0219	1.25015
$926$	−23.4550	−0.770778
$927$	0.826244	0.0271374
$928$	−113.025	−3.71022
$929$	−35.0836	−1.15106	−0.575528	−	0.817782i	$-0.695203\pi$
$929$	−35.0836	−1.15106	−0.575528	+	0.817782i	$0.695203\pi$
$930$	−28.6657	−0.939984
$931$	40.4339	1.32517
$932$	33.2712	1.08983
$933$	−1.73628	−0.0568434
$934$	108.466	3.54911
$935$	−36.1368	−1.18180
$936$	4.97215	0.162520
$937$	15.7790	0.515477	0.257738	−	0.966215i	$-0.417023\pi$
$937$	15.7790	0.515477	0.257738	+	0.966215i	$0.417023\pi$
$938$	80.4000	2.62515
$939$	−27.5598	−0.899379
$940$	−272.542	−8.88935
$941$	14.3840	0.468905	0.234453	−	0.972128i	$-0.424670\pi$
$941$	14.3840	0.468905	0.234453	+	0.972128i	$0.424670\pi$
$942$	−36.2767	−1.18196
$943$	1.37924	0.0449142
$944$	−165.234	−5.37791
$945$	14.6845	0.477688
$946$	23.7650	0.772666
$947$	37.1039	1.20572	0.602858	−	0.797848i	$-0.294029\pi$
$947$	37.1039	1.20572	0.602858	+	0.797848i	$0.294029\pi$
$948$	6.82201	0.221569
$949$	−3.09126	−0.100347
$950$	−107.332	−3.48230
$951$	21.1317	0.685241
$952$	100.973	3.27254
$953$	−1.98351	−0.0642521	−0.0321261	−	0.999484i	$-0.510228\pi$
$953$	−1.98351	−0.0642521	−0.0321261	+	0.999484i	$0.510228\pi$
$954$	−14.8351	−0.480304
$955$	−93.6570	−3.03067
$956$	91.8386	2.97027
$957$	17.5146	0.566167
$958$	12.7610	0.412289
$959$	14.5145	0.468698
$960$	−133.232	−4.30005
$961$	−23.0376	−0.743150
$962$	6.11746	0.197235
$963$	13.8734	0.447064
$964$	83.4028	2.68622
$965$	27.5058	0.885444
$966$	9.20932	0.296305
$967$	15.4497	0.496830	0.248415	−	0.968654i	$-0.420090\pi$
$967$	15.4497	0.496830	0.248415	+	0.968654i	$0.420090\pi$
$968$	−38.5997	−1.24064
$969$	11.5593	0.371338
$970$	164.991	5.29755
$971$	−5.58265	−0.179156	−0.0895779	−	0.995980i	$-0.528552\pi$
$971$	−5.58265	−0.179156	−0.0895779	+	0.995980i	$0.528552\pi$
$972$	5.60882	0.179903
$973$	67.1419	2.15247
$974$	25.5285	0.817987
$975$	−4.27720	−0.136980
$976$	−202.276	−6.47468
$977$	14.2212	0.454977	0.227488	−	0.973781i	$-0.426949\pi$
$977$	14.2212	0.454977	0.227488	+	0.973781i	$0.426949\pi$
$978$	−47.8756	−1.53089
$979$	−24.4964	−0.782909
$980$	−183.810	−5.87161
$981$	9.81653	0.313418
$982$	74.2545	2.36956
$983$	34.2837	1.09348	0.546740	−	0.837302i	$-0.315869\pi$
$983$	34.2837	1.09348	0.546740	+	0.837302i	$0.315869\pi$
$984$	−16.3973	−0.522728
$985$	84.1873	2.68243
$986$	−31.8636	−1.01474
$987$	−52.6087	−1.67455
$988$	−12.7298	−0.404988
$989$	−1.87027	−0.0594711
$990$	39.1839	1.24534
$991$	47.1991	1.49933	0.749664	−	0.661819i	$-0.230215\pi$
$991$	47.1991	1.49933	0.749664	+	0.661819i	$0.230215\pi$
$992$	70.2360	2.23000
$993$	14.1886	0.450262
$994$	100.586	3.19039
$995$	8.44640	0.267769
$996$	−57.2443	−1.81385
$997$	−19.5516	−0.619204	−0.309602	−	0.950866i	$-0.600196\pi$
$997$	−19.5516	−0.619204	−0.309602	+	0.950866i	$0.600196\pi$
$998$	−55.2698	−1.74953
$999$	4.44010	0.140479

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	381.2.a.e.1.1	✓	9
3.2	odd	2		1143.2.a.j.1.9		9
4.3	odd	2		6096.2.a.bk.1.2		9
5.4	even	2		9525.2.a.p.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
381.2.a.e.1.1	✓	9	1.1	even	1	trivial
1143.2.a.j.1.9		9	3.2	odd	2
6096.2.a.bk.1.2		9	4.3	odd	2
9525.2.a.p.1.9		9	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 381 = 3 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	381.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75841 q^{2} +1.00000 q^{3} +5.60882 q^{4} -3.68284 q^{5} -2.75841 q^{6} -3.98729 q^{7} -9.95461 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.75841 q^{2} +1.00000 q^{3} +5.60882 q^{4} -3.68284 q^{5} -2.75841 q^{6} -3.98729 q^{7} -9.95461 q^{8} +1.00000 q^{9} +10.1588 q^{10} +3.85715 q^{11} +5.60882 q^{12} -0.499482 q^{13} +10.9986 q^{14} -3.68284 q^{15} +16.2413 q^{16} +2.54391 q^{17} -2.75841 q^{18} +4.54391 q^{19} -20.6564 q^{20} -3.98729 q^{21} -10.6396 q^{22} +0.837319 q^{23} -9.95461 q^{24} +8.56328 q^{25} +1.37778 q^{26} +1.00000 q^{27} -22.3640 q^{28} +4.54082 q^{29} +10.1588 q^{30} -2.82177 q^{31} -24.8908 q^{32} +3.85715 q^{33} -7.01714 q^{34} +14.6845 q^{35} +5.60882 q^{36} +4.44010 q^{37} -12.5340 q^{38} -0.499482 q^{39} +36.6612 q^{40} +1.64721 q^{41} +10.9986 q^{42} -2.23364 q^{43} +21.6340 q^{44} -3.68284 q^{45} -2.30967 q^{46} +13.1941 q^{47} +16.2413 q^{48} +8.89848 q^{49} -23.6210 q^{50} +2.54391 q^{51} -2.80151 q^{52} +5.37814 q^{53} -2.75841 q^{54} -14.2052 q^{55} +39.6919 q^{56} +4.54391 q^{57} -12.5254 q^{58} -10.1737 q^{59} -20.6564 q^{60} -12.4544 q^{61} +7.78359 q^{62} -3.98729 q^{63} +36.1765 q^{64} +1.83951 q^{65} -10.6396 q^{66} +7.31003 q^{67} +14.2683 q^{68} +0.837319 q^{69} -40.5060 q^{70} +9.14535 q^{71} -9.95461 q^{72} +6.18893 q^{73} -12.2476 q^{74} +8.56328 q^{75} +25.4860 q^{76} -15.3796 q^{77} +1.37778 q^{78} +1.21630 q^{79} -59.8139 q^{80} +1.00000 q^{81} -4.54368 q^{82} -10.2061 q^{83} -22.3640 q^{84} -9.36879 q^{85} +6.16129 q^{86} +4.54082 q^{87} -38.3964 q^{88} -6.35092 q^{89} +10.1588 q^{90} +1.99158 q^{91} +4.69638 q^{92} -2.82177 q^{93} -36.3947 q^{94} -16.7345 q^{95} -24.8908 q^{96} +16.2413 q^{97} -24.5457 q^{98} +3.85715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 2 q^{2} + 9 q^{3} + 14 q^{4} - 4 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 2 * q^2 + 9 * q^3 + 14 * q^4 - 4 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 9 * q^9	\( 9 q - 2 q^{2} + 9 q^{3} + 14 q^{4} - 4 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 9 q^{9} - 4 q^{10} + 8 q^{11} + 14 q^{12} + 14 q^{13} + 4 q^{14} - 4 q^{15} + 32 q^{16} - 6 q^{17} - 2 q^{18} + 12 q^{19} - 28 q^{20} + 10 q^{21} - 18 q^{22} - 4 q^{23} - 6 q^{24} + 21 q^{25} - 14 q^{26} + 9 q^{27} - 8 q^{29} - 4 q^{30} + 4 q^{31} - 29 q^{32} + 8 q^{33} - 3 q^{34} + 6 q^{35} + 14 q^{36} + 22 q^{37} - 7 q^{38} + 14 q^{39} - 2 q^{41} + 4 q^{42} + 6 q^{43} + 17 q^{44} - 4 q^{45} - 10 q^{46} - 2 q^{47} + 32 q^{48} + 23 q^{49} - 20 q^{50} - 6 q^{51} - 9 q^{52} - 12 q^{53} - 2 q^{54} - 22 q^{55} + 18 q^{56} + 12 q^{57} - 28 q^{58} - 6 q^{59} - 28 q^{60} + 2 q^{61} - 15 q^{62} + 10 q^{63} + 24 q^{64} + 4 q^{65} - 18 q^{66} + 18 q^{67} - 24 q^{68} - 4 q^{69} - 72 q^{70} + 24 q^{71} - 6 q^{72} + 14 q^{73} + 3 q^{74} + 21 q^{75} + 4 q^{76} - 18 q^{77} - 14 q^{78} + 12 q^{79} - 86 q^{80} + 9 q^{81} + 4 q^{82} - 20 q^{83} - 24 q^{85} + 16 q^{86} - 8 q^{87} - 55 q^{88} - 30 q^{89} - 4 q^{90} + 14 q^{91} - 46 q^{92} + 4 q^{93} - 66 q^{94} - 32 q^{95} - 29 q^{96} + 12 q^{97} - 62 q^{98} + 8 q^{99}+O(q^{100}) \) 9 * q - 2 * q^2 + 9 * q^3 + 14 * q^4 - 4 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 9 * q^9 - 4 * q^10 + 8 * q^11 + 14 * q^12 + 14 * q^13 + 4 * q^14 - 4 * q^15 + 32 * q^16 - 6 * q^17 - 2 * q^18 + 12 * q^19 - 28 * q^20 + 10 * q^21 - 18 * q^22 - 4 * q^23 - 6 * q^24 + 21 * q^25 - 14 * q^26 + 9 * q^27 - 8 * q^29 - 4 * q^30 + 4 * q^31 - 29 * q^32 + 8 * q^33 - 3 * q^34 + 6 * q^35 + 14 * q^36 + 22 * q^37 - 7 * q^38 + 14 * q^39 - 2 * q^41 + 4 * q^42 + 6 * q^43 + 17 * q^44 - 4 * q^45 - 10 * q^46 - 2 * q^47 + 32 * q^48 + 23 * q^49 - 20 * q^50 - 6 * q^51 - 9 * q^52 - 12 * q^53 - 2 * q^54 - 22 * q^55 + 18 * q^56 + 12 * q^57 - 28 * q^58 - 6 * q^59 - 28 * q^60 + 2 * q^61 - 15 * q^62 + 10 * q^63 + 24 * q^64 + 4 * q^65 - 18 * q^66 + 18 * q^67 - 24 * q^68 - 4 * q^69 - 72 * q^70 + 24 * q^71 - 6 * q^72 + 14 * q^73 + 3 * q^74 + 21 * q^75 + 4 * q^76 - 18 * q^77 - 14 * q^78 + 12 * q^79 - 86 * q^80 + 9 * q^81 + 4 * q^82 - 20 * q^83 - 24 * q^85 + 16 * q^86 - 8 * q^87 - 55 * q^88 - 30 * q^89 - 4 * q^90 + 14 * q^91 - 46 * q^92 + 4 * q^93 - 66 * q^94 - 32 * q^95 - 29 * q^96 + 12 * q^97 - 62 * q^98 + 8 * q^99

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