LMFDB - Embedded newform 8049.2.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24285 q^{2} -1.00000 q^{3} +3.03036 q^{4} -3.65739 q^{5} +2.24285 q^{6} -4.78600 q^{7} -2.31094 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.24285 q^{2} -1.00000 q^{3} +3.03036 q^{4} -3.65739 q^{5} +2.24285 q^{6} -4.78600 q^{7} -2.31094 q^{8} +1.00000 q^{9} +8.20296 q^{10} -0.0850165 q^{11} -3.03036 q^{12} -1.29803 q^{13} +10.7343 q^{14} +3.65739 q^{15} -0.877630 q^{16} +0.987376 q^{17} -2.24285 q^{18} +1.55268 q^{19} -11.0832 q^{20} +4.78600 q^{21} +0.190679 q^{22} -3.30010 q^{23} +2.31094 q^{24} +8.37648 q^{25} +2.91127 q^{26} -1.00000 q^{27} -14.5033 q^{28} +3.65928 q^{29} -8.20296 q^{30} +8.87904 q^{31} +6.59028 q^{32} +0.0850165 q^{33} -2.21453 q^{34} +17.5043 q^{35} +3.03036 q^{36} -10.1893 q^{37} -3.48242 q^{38} +1.29803 q^{39} +8.45202 q^{40} -6.13789 q^{41} -10.7343 q^{42} -8.73518 q^{43} -0.257631 q^{44} -3.65739 q^{45} +7.40161 q^{46} +12.7886 q^{47} +0.877630 q^{48} +15.9058 q^{49} -18.7872 q^{50} -0.987376 q^{51} -3.93349 q^{52} +0.0115456 q^{53} +2.24285 q^{54} +0.310938 q^{55} +11.0602 q^{56} -1.55268 q^{57} -8.20721 q^{58} -1.83378 q^{59} +11.0832 q^{60} -13.3076 q^{61} -19.9143 q^{62} -4.78600 q^{63} -13.0257 q^{64} +4.74738 q^{65} -0.190679 q^{66} -6.65538 q^{67} +2.99211 q^{68} +3.30010 q^{69} -39.2594 q^{70} +9.81304 q^{71} -2.31094 q^{72} -4.76802 q^{73} +22.8530 q^{74} -8.37648 q^{75} +4.70517 q^{76} +0.406889 q^{77} -2.91127 q^{78} +5.92709 q^{79} +3.20983 q^{80} +1.00000 q^{81} +13.7664 q^{82} -9.34808 q^{83} +14.5033 q^{84} -3.61122 q^{85} +19.5917 q^{86} -3.65928 q^{87} +0.196468 q^{88} -3.40133 q^{89} +8.20296 q^{90} +6.21235 q^{91} -10.0005 q^{92} -8.87904 q^{93} -28.6829 q^{94} -5.67874 q^{95} -6.59028 q^{96} +7.67519 q^{97} -35.6742 q^{98} -0.0850165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) $ 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * 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 $

$2$	−2.24285	−1.58593	−0.792966	−	0.609266i	$-0.791464\pi$
$2$	−2.24285	−1.58593	−0.792966	+	0.609266i	$0.791464\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.03036	1.51518
$5$	−3.65739	−1.63563	−0.817817	−	0.575479i	$-0.804816\pi$
$5$	−3.65739	−1.63563	−0.817817	+	0.575479i	$0.804816\pi$
$6$	2.24285	0.915638
$7$	−4.78600	−1.80894	−0.904469	−	0.426540i	$-0.859732\pi$
$7$	−4.78600	−1.80894	−0.904469	+	0.426540i	$0.859732\pi$
$8$	−2.31094	−0.817042
$9$	1.00000	0.333333
$10$	8.20296	2.59400
$11$	−0.0850165	−0.0256335	−0.0128167	−	0.999918i	$-0.504080\pi$
$11$	−0.0850165	−0.0256335	−0.0128167	+	0.999918i	$0.504080\pi$
$12$	−3.03036	−0.874790
$13$	−1.29803	−0.360008	−0.180004	−	0.983666i	$-0.557611\pi$
$13$	−1.29803	−0.360008	−0.180004	+	0.983666i	$0.557611\pi$
$14$	10.7343	2.86885
$15$	3.65739	0.944333
$16$	−0.877630	−0.219407
$17$	0.987376	0.239474	0.119737	−	0.992806i	$-0.461795\pi$
$17$	0.987376	0.239474	0.119737	+	0.992806i	$0.461795\pi$
$18$	−2.24285	−0.528644
$19$	1.55268	0.356209	0.178104	−	0.984012i	$-0.443004\pi$
$19$	1.55268	0.356209	0.178104	+	0.984012i	$0.443004\pi$
$20$	−11.0832	−2.47828
$21$	4.78600	1.04439
$22$	0.190679	0.0406529
$23$	−3.30010	−0.688118	−0.344059	−	0.938948i	$-0.611802\pi$
$23$	−3.30010	−0.688118	−0.344059	+	0.938948i	$0.611802\pi$
$24$	2.31094	0.471720
$25$	8.37648	1.67530
$26$	2.91127	0.570948
$27$	−1.00000	−0.192450
$28$	−14.5033	−2.74087
$29$	3.65928	0.679512	0.339756	−	0.940514i	$-0.389656\pi$
$29$	3.65928	0.679512	0.339756	+	0.940514i	$0.389656\pi$
$30$	−8.20296	−1.49765
$31$	8.87904	1.59472	0.797362	−	0.603502i	$-0.206228\pi$
$31$	8.87904	1.59472	0.797362	+	0.603502i	$0.206228\pi$
$32$	6.59028	1.16501
$33$	0.0850165	0.0147995
$34$	−2.21453	−0.379789
$35$	17.5043	2.95876
$36$	3.03036	0.505060
$37$	−10.1893	−1.67511	−0.837555	−	0.546353i	$-0.816016\pi$
$37$	−10.1893	−1.67511	−0.837555	+	0.546353i	$0.816016\pi$
$38$	−3.48242	−0.564923
$39$	1.29803	0.207851
$40$	8.45202	1.33638
$41$	−6.13789	−0.958578	−0.479289	−	0.877657i	$-0.659105\pi$
$41$	−6.13789	−0.958578	−0.479289	+	0.877657i	$0.659105\pi$
$42$	−10.7343	−1.65633
$43$	−8.73518	−1.33210	−0.666051	−	0.745906i	$-0.732017\pi$
$43$	−8.73518	−1.33210	−0.666051	+	0.745906i	$0.732017\pi$
$44$	−0.257631	−0.0388393
$45$	−3.65739	−0.545211
$46$	7.40161	1.09131
$47$	12.7886	1.86541	0.932705	−	0.360642i	$-0.117442\pi$
$47$	12.7886	1.86541	0.932705	+	0.360642i	$0.117442\pi$
$48$	0.877630	0.126675
$49$	15.9058	2.27226
$50$	−18.7872	−2.65691
$51$	−0.987376	−0.138260
$52$	−3.93349	−0.545477
$53$	0.0115456	0.00158591	0.000792953	−	1.00000i	$-0.499748\pi$
$53$	0.0115456	0.00158591	0.000792953		1.00000i	$0.499748\pi$
$54$	2.24285	0.305213
$55$	0.310938	0.0419269
$56$	11.0602	1.47798
$57$	−1.55268	−0.205657
$58$	−8.20721	−1.07766
$59$	−1.83378	−0.238738	−0.119369	−	0.992850i	$-0.538087\pi$
$59$	−1.83378	−0.238738	−0.119369	+	0.992850i	$0.538087\pi$
$60$	11.0832	1.43084
$61$	−13.3076	−1.70386	−0.851931	−	0.523655i	$-0.824568\pi$
$61$	−13.3076	−1.70386	−0.851931	+	0.523655i	$0.824568\pi$
$62$	−19.9143	−2.52912
$63$	−4.78600	−0.602979
$64$	−13.0257	−1.62822
$65$	4.74738	0.588841
$66$	−0.190679	−0.0234710
$67$	−6.65538	−0.813084	−0.406542	−	0.913632i	$-0.633266\pi$
$67$	−6.65538	−0.813084	−0.406542	+	0.913632i	$0.633266\pi$
$68$	2.99211	0.362846
$69$	3.30010	0.397285
$70$	−39.2594	−4.69239
$71$	9.81304	1.16459	0.582297	−	0.812976i	$-0.302154\pi$
$71$	9.81304	1.16459	0.582297	+	0.812976i	$0.302154\pi$
$72$	−2.31094	−0.272347
$73$	−4.76802	−0.558054	−0.279027	−	0.960283i	$-0.590012\pi$
$73$	−4.76802	−0.558054	−0.279027	+	0.960283i	$0.590012\pi$
$74$	22.8530	2.65661
$75$	−8.37648	−0.967233
$76$	4.70517	0.539720
$77$	0.406889	0.0463693
$78$	−2.91127	−0.329637
$79$	5.92709	0.666850	0.333425	−	0.942777i	$-0.391796\pi$
$79$	5.92709	0.666850	0.333425	+	0.942777i	$0.391796\pi$
$80$	3.20983	0.358870
$81$	1.00000	0.111111
$82$	13.7664	1.52024
$83$	−9.34808	−1.02608	−0.513042	−	0.858363i	$-0.671482\pi$
$83$	−9.34808	−1.02608	−0.513042	+	0.858363i	$0.671482\pi$
$84$	14.5033	1.58244
$85$	−3.61122	−0.391691
$86$	19.5917	2.11262
$87$	−3.65928	−0.392316
$88$	0.196468	0.0209436
$89$	−3.40133	−0.360540	−0.180270	−	0.983617i	$-0.557697\pi$
$89$	−3.40133	−0.360540	−0.180270	+	0.983617i	$0.557697\pi$
$90$	8.20296	0.864668
$91$	6.21235	0.651231
$92$	−10.0005	−1.04262
$93$	−8.87904	−0.920714
$94$	−28.6829	−2.95841
$95$	−5.67874	−0.582627
$96$	−6.59028	−0.672617
$97$	7.67519	0.779297	0.389649	−	0.920964i	$-0.372596\pi$
$97$	7.67519	0.779297	0.389649	+	0.920964i	$0.372596\pi$
$98$	−35.6742	−3.60364
$99$	−0.0850165	−0.00854448
$100$	25.3838	2.53838
$101$	11.2351	1.11793	0.558965	−	0.829191i	$-0.311198\pi$
$101$	11.2351	1.11793	0.558965	+	0.829191i	$0.311198\pi$
$102$	2.21453	0.219271
$103$	−9.10670	−0.897310	−0.448655	−	0.893705i	$-0.648097\pi$
$103$	−9.10670	−0.897310	−0.448655	+	0.893705i	$0.648097\pi$
$104$	2.99967	0.294141
$105$	−17.5043	−1.70824
$106$	−0.0258949	−0.00251514
$107$	−17.8957	−1.73004	−0.865020	−	0.501738i	$-0.832694\pi$
$107$	−17.8957	−1.73004	−0.865020	+	0.501738i	$0.832694\pi$
$108$	−3.03036	−0.291597
$109$	−11.9734	−1.14684	−0.573422	−	0.819260i	$-0.694384\pi$
$109$	−11.9734	−1.14684	−0.573422	+	0.819260i	$0.694384\pi$
$110$	−0.697387	−0.0664933
$111$	10.1893	0.967126
$112$	4.20034	0.396894
$113$	13.4438	1.26469	0.632344	−	0.774687i	$-0.282093\pi$
$113$	13.4438	1.26469	0.632344	+	0.774687i	$0.282093\pi$
$114$	3.48242	0.326158
$115$	12.0697	1.12551
$116$	11.0890	1.02958
$117$	−1.29803	−0.120003
$118$	4.11289	0.378622
$119$	−4.72558	−0.433193
$120$	−8.45202	−0.771560
$121$	−10.9928	−0.999343
$122$	29.8469	2.70221
$123$	6.13789	0.553435
$124$	26.9067	2.41629
$125$	−12.3491	−1.10454
$126$	10.7343	0.956284
$127$	−21.2150	−1.88253	−0.941264	−	0.337671i	$-0.890361\pi$
$127$	−21.2150	−1.88253	−0.941264	+	0.337671i	$0.890361\pi$
$128$	16.0342	1.41723
$129$	8.73518	0.769090
$130$	−10.6477	−0.933861
$131$	−13.8203	−1.20749	−0.603743	−	0.797179i	$-0.706325\pi$
$131$	−13.8203	−1.20749	−0.603743	+	0.797179i	$0.706325\pi$
$132$	0.257631	0.0224239
$133$	−7.43111	−0.644359
$134$	14.9270	1.28950
$135$	3.65739	0.314778
$136$	−2.28177	−0.195660
$137$	0.662432	0.0565954	0.0282977	−	0.999600i	$-0.490991\pi$
$137$	0.662432	0.0565954	0.0282977	+	0.999600i	$0.490991\pi$
$138$	−7.40161	−0.630067
$139$	−11.3364	−0.961541	−0.480771	−	0.876846i	$-0.659643\pi$
$139$	−11.3364	−0.961541	−0.480771	+	0.876846i	$0.659643\pi$
$140$	53.0442	4.48306
$141$	−12.7886	−1.07699
$142$	−22.0091	−1.84697
$143$	0.110354	0.00922824
$144$	−0.877630	−0.0731358
$145$	−13.3834	−1.11143
$146$	10.6939	0.885037
$147$	−15.9058	−1.31189
$148$	−30.8773	−2.53810
$149$	−8.66589	−0.709937	−0.354969	−	0.934878i	$-0.615508\pi$
$149$	−8.66589	−0.709937	−0.354969	+	0.934878i	$0.615508\pi$
$150$	18.7872	1.53397
$151$	20.2275	1.64609	0.823047	−	0.567973i	$-0.192272\pi$
$151$	20.2275	1.64609	0.823047	+	0.567973i	$0.192272\pi$
$152$	−3.58815	−0.291037
$153$	0.987376	0.0798246
$154$	−0.912590	−0.0735386
$155$	−32.4741	−2.60838
$156$	3.93349	0.314931
$157$	−4.55700	−0.363688	−0.181844	−	0.983327i	$-0.558207\pi$
$157$	−4.55700	−0.363688	−0.181844	+	0.983327i	$0.558207\pi$
$158$	−13.2936	−1.05758
$159$	−0.0115456	−0.000915623 0
$160$	−24.1032	−1.90553
$161$	15.7943	1.24476
$162$	−2.24285	−0.176215
$163$	−20.3213	−1.59169	−0.795845	−	0.605500i	$-0.792973\pi$
$163$	−20.3213	−1.59169	−0.795845	+	0.605500i	$0.792973\pi$
$164$	−18.6000	−1.45242
$165$	−0.310938	−0.0242065
$166$	20.9663	1.62730
$167$	−8.61608	−0.666733	−0.333366	−	0.942797i	$-0.608185\pi$
$167$	−8.61608	−0.666733	−0.333366	+	0.942797i	$0.608185\pi$
$168$	−11.0602	−0.853311
$169$	−11.3151	−0.870395
$170$	8.09940	0.621196
$171$	1.55268	0.118736
$172$	−26.4708	−2.01838
$173$	9.25390	0.703561	0.351781	−	0.936083i	$-0.385576\pi$
$173$	9.25390	0.703561	0.351781	+	0.936083i	$0.385576\pi$
$174$	8.20721	0.622187
$175$	−40.0898	−3.03051
$176$	0.0746130	0.00562417
$177$	1.83378	0.137835
$178$	7.62866	0.571792
$179$	−8.77776	−0.656081	−0.328040	−	0.944664i	$-0.606388\pi$
$179$	−8.77776	−0.656081	−0.328040	+	0.944664i	$0.606388\pi$
$180$	−11.0832	−0.826094
$181$	4.23362	0.314682	0.157341	−	0.987544i	$-0.449708\pi$
$181$	4.23362	0.314682	0.157341	+	0.987544i	$0.449708\pi$
$182$	−13.9334	−1.03281
$183$	13.3076	0.983725
$184$	7.62634	0.562221
$185$	37.2662	2.73987
$186$	19.9143	1.46019
$187$	−0.0839433	−0.00613854
$188$	38.7541	2.82643
$189$	4.78600	0.348130
$190$	12.7365	0.924006
$191$	−6.03523	−0.436694	−0.218347	−	0.975871i	$-0.570067\pi$
$191$	−6.03523	−0.436694	−0.218347	+	0.975871i	$0.570067\pi$
$192$	13.0257	0.940051
$193$	22.0621	1.58806	0.794032	−	0.607876i	$-0.207978\pi$
$193$	22.0621	1.58806	0.794032	+	0.607876i	$0.207978\pi$
$194$	−17.2143	−1.23591
$195$	−4.74738	−0.339967
$196$	48.2003	3.44288
$197$	−18.9517	−1.35025	−0.675127	−	0.737702i	$-0.735911\pi$
$197$	−18.9517	−1.35025	−0.675127	+	0.737702i	$0.735911\pi$
$198$	0.190679	0.0135510
$199$	−24.4121	−1.73053	−0.865266	−	0.501314i	$-0.832850\pi$
$199$	−24.4121	−1.73053	−0.865266	+	0.501314i	$0.832850\pi$
$200$	−19.3576	−1.36879
$201$	6.65538	0.469434
$202$	−25.1985	−1.77296
$203$	−17.5133	−1.22919
$204$	−2.99211	−0.209489
$205$	22.4486	1.56788
$206$	20.4249	1.42307
$207$	−3.30010	−0.229373
$208$	1.13919	0.0789884
$209$	−0.132003	−0.00913086
$210$	39.2594	2.70915
$211$	−6.30830	−0.434281	−0.217141	−	0.976140i	$-0.569673\pi$
$211$	−6.30830	−0.434281	−0.217141	+	0.976140i	$0.569673\pi$
$212$	0.0349873	0.00240293
$213$	−9.81304	−0.672378
$214$	40.1372	2.74372
$215$	31.9479	2.17883
$216$	2.31094	0.157240
$217$	−42.4951	−2.88476
$218$	26.8545	1.81882
$219$	4.76802	0.322193
$220$	0.942256	0.0635269
$221$	−1.28164	−0.0862124
$222$	−22.8530	−1.53380
$223$	16.4747	1.10322	0.551612	−	0.834101i	$-0.314013\pi$
$223$	16.4747	1.10322	0.551612	+	0.834101i	$0.314013\pi$
$224$	−31.5411	−2.10743
$225$	8.37648	0.558432
$226$	−30.1524	−2.00571
$227$	−28.4330	−1.88716	−0.943582	−	0.331139i	$-0.892567\pi$
$227$	−28.4330	−1.88716	−0.943582	+	0.331139i	$0.892567\pi$
$228$	−4.70517	−0.311608
$229$	20.7577	1.37170	0.685852	−	0.727741i	$-0.259430\pi$
$229$	20.7577	1.37170	0.685852	+	0.727741i	$0.259430\pi$
$230$	−27.0706	−1.78498
$231$	−0.406889	−0.0267713
$232$	−8.45640	−0.555190
$233$	−7.45438	−0.488353	−0.244176	−	0.969731i	$-0.578518\pi$
$233$	−7.45438	−0.488353	−0.244176	+	0.969731i	$0.578518\pi$
$234$	2.91127	0.190316
$235$	−46.7729	−3.05113
$236$	−5.55702	−0.361731
$237$	−5.92709	−0.385006
$238$	10.5988	0.687015
$239$	17.4519	1.12887	0.564434	−	0.825478i	$-0.309095\pi$
$239$	17.4519	1.12887	0.564434	+	0.825478i	$0.309095\pi$
$240$	−3.20983	−0.207194
$241$	6.89496	0.444143	0.222072	−	0.975030i	$-0.428718\pi$
$241$	6.89496	0.444143	0.222072	+	0.975030i	$0.428718\pi$
$242$	24.6551	1.58489
$243$	−1.00000	−0.0641500
$244$	−40.3268	−2.58166
$245$	−58.1736	−3.71658
$246$	−13.7664	−0.877711
$247$	−2.01542	−0.128238
$248$	−20.5190	−1.30296
$249$	9.34808	0.592410
$250$	27.6971	1.75172
$251$	−1.73213	−0.109331	−0.0546656	−	0.998505i	$-0.517409\pi$
$251$	−1.73213	−0.109331	−0.0546656	+	0.998505i	$0.517409\pi$
$252$	−14.5033	−0.913623
$253$	0.280563	0.0176388
$254$	47.5820	2.98556
$255$	3.61122	0.226143
$256$	−9.91069	−0.619418
$257$	27.1751	1.69513	0.847567	−	0.530688i	$-0.178067\pi$
$257$	27.1751	1.69513	0.847567	+	0.530688i	$0.178067\pi$
$258$	−19.5917	−1.21972
$259$	48.7660	3.03017
$260$	14.3863	0.892200
$261$	3.65928	0.226504
$262$	30.9968	1.91499
$263$	16.6745	1.02820	0.514098	−	0.857732i	$-0.328127\pi$
$263$	16.6745	1.02820	0.514098	+	0.857732i	$0.328127\pi$
$264$	−0.196468	−0.0120918
$265$	−0.0422266	−0.00259396
$266$	16.6668	1.02191
$267$	3.40133	0.208158
$268$	−20.1682	−1.23197
$269$	−20.9175	−1.27536	−0.637681	−	0.770300i	$-0.720106\pi$
$269$	−20.9175	−1.27536	−0.637681	+	0.770300i	$0.720106\pi$
$270$	−8.20296	−0.499216
$271$	−18.5477	−1.12669	−0.563346	−	0.826221i	$-0.690486\pi$
$271$	−18.5477	−1.12669	−0.563346	+	0.826221i	$0.690486\pi$
$272$	−0.866550	−0.0525423
$273$	−6.21235	−0.375989
$274$	−1.48573	−0.0897565
$275$	−0.712140	−0.0429436
$276$	10.0005	0.601959
$277$	−10.5276	−0.632541	−0.316271	−	0.948669i	$-0.602431\pi$
$277$	−10.5276	−0.632541	−0.316271	+	0.948669i	$0.602431\pi$
$278$	25.4258	1.52494
$279$	8.87904	0.531575
$280$	−40.4514	−2.41743
$281$	−22.4215	−1.33755	−0.668776	−	0.743464i	$-0.733182\pi$
$281$	−22.4215	−1.33755	−0.668776	+	0.743464i	$0.733182\pi$
$282$	28.6829	1.70804
$283$	5.28744	0.314306	0.157153	−	0.987574i	$-0.449768\pi$
$283$	5.28744	0.314306	0.157153	+	0.987574i	$0.449768\pi$
$284$	29.7371	1.76457
$285$	5.67874	0.336380
$286$	−0.247506	−0.0146354
$287$	29.3759	1.73401
$288$	6.59028	0.388336
$289$	−16.0251	−0.942652
$290$	30.0170	1.76266
$291$	−7.67519	−0.449927
$292$	−14.4488	−0.845554
$293$	−10.7504	−0.628045	−0.314022	−	0.949416i	$-0.601677\pi$
$293$	−10.7504	−0.628045	−0.314022	+	0.949416i	$0.601677\pi$
$294$	35.6742	2.08056
$295$	6.70685	0.390488
$296$	23.5469	1.36864
$297$	0.0850165	0.00493316
$298$	19.4363	1.12591
$299$	4.28361	0.247728
$300$	−25.3838	−1.46553
$301$	41.8066	2.40969
$302$	−45.3673	−2.61059
$303$	−11.2351	−0.645438
$304$	−1.36268	−0.0781548
$305$	48.6710	2.78689
$306$	−2.21453	−0.126596
$307$	24.3473	1.38957	0.694785	−	0.719217i	$-0.255499\pi$
$307$	24.3473	1.38957	0.694785	+	0.719217i	$0.255499\pi$
$308$	1.23302	0.0702579
$309$	9.10670	0.518062
$310$	72.8344	4.13672
$311$	11.4690	0.650347	0.325173	−	0.945654i	$-0.394577\pi$
$311$	11.4690	0.650347	0.325173	+	0.945654i	$0.394577\pi$
$312$	−2.99967	−0.169823
$313$	2.34231	0.132395	0.0661975	−	0.997807i	$-0.478913\pi$
$313$	2.34231	0.132395	0.0661975	+	0.997807i	$0.478913\pi$
$314$	10.2206	0.576784
$315$	17.5043	0.986253
$316$	17.9612	1.01040
$317$	2.14520	0.120487	0.0602433	−	0.998184i	$-0.480812\pi$
$317$	2.14520	0.120487	0.0602433	+	0.998184i	$0.480812\pi$
$318$	0.0258949	0.00145212
$319$	−0.311100	−0.0174182
$320$	47.6401	2.66316
$321$	17.8957	0.998839
$322$	−35.4241	−1.97411
$323$	1.53308	0.0853026
$324$	3.03036	0.168353
$325$	−10.8729	−0.603120
$326$	45.5777	2.52431
$327$	11.9734	0.662131
$328$	14.1843	0.783198
$329$	−61.2062	−3.37441
$330$	0.697387	0.0383899
$331$	−4.31985	−0.237440	−0.118720	−	0.992928i	$-0.537879\pi$
$331$	−4.31985	−0.237440	−0.118720	+	0.992928i	$0.537879\pi$
$332$	−28.3281	−1.55470
$333$	−10.1893	−0.558370
$334$	19.3246	1.05739
$335$	24.3413	1.32991
$336$	−4.20034	−0.229147
$337$	−36.1747	−1.97056	−0.985281	−	0.170941i	$-0.945319\pi$
$337$	−36.1747	−1.97056	−0.985281	+	0.170941i	$0.945319\pi$
$338$	25.3781	1.38039
$339$	−13.4438	−0.730168
$340$	−10.9433	−0.593483
$341$	−0.754866	−0.0408783
$342$	−3.48242	−0.188308
$343$	−42.6231	−2.30143
$344$	20.1865	1.08838
$345$	−12.0697	−0.649812
$346$	−20.7551	−1.11580
$347$	6.02923	0.323666	0.161833	−	0.986818i	$-0.448259\pi$
$347$	6.02923	0.323666	0.161833	+	0.986818i	$0.448259\pi$
$348$	−11.0890	−0.594430
$349$	−13.0871	−0.700535	−0.350268	−	0.936650i	$-0.613909\pi$
$349$	−13.0871	−0.700535	−0.350268	+	0.936650i	$0.613909\pi$
$350$	89.9154	4.80618
$351$	1.29803	0.0692835
$352$	−0.560283	−0.0298632
$353$	6.77113	0.360391	0.180195	−	0.983631i	$-0.442327\pi$
$353$	6.77113	0.360391	0.180195	+	0.983631i	$0.442327\pi$
$354$	−4.11289	−0.218598
$355$	−35.8901	−1.90485
$356$	−10.3073	−0.546283
$357$	4.72558	0.250104
$358$	19.6872	1.04050
$359$	4.12403	0.217658	0.108829	−	0.994060i	$-0.465290\pi$
$359$	4.12403	0.217658	0.108829	+	0.994060i	$0.465290\pi$
$360$	8.45202	0.445461
$361$	−16.5892	−0.873115
$362$	−9.49536	−0.499065
$363$	10.9928	0.576971
$364$	18.8257	0.986733
$365$	17.4385	0.912772
$366$	−29.8469	−1.56012
$367$	16.5055	0.861581	0.430791	−	0.902452i	$-0.358235\pi$
$367$	16.5055	0.861581	0.430791	+	0.902452i	$0.358235\pi$
$368$	2.89626	0.150978
$369$	−6.13789	−0.319526
$370$	−83.5824	−4.34524
$371$	−0.0552571	−0.00286880
$372$	−26.9067	−1.39505
$373$	−25.1749	−1.30351	−0.651753	−	0.758431i	$-0.725966\pi$
$373$	−25.1749	−1.30351	−0.651753	+	0.758431i	$0.725966\pi$
$374$	0.188272	0.00973531
$375$	12.3491	0.637705
$376$	−29.5537	−1.52412
$377$	−4.74984	−0.244629
$378$	−10.7343	−0.552111
$379$	−8.01584	−0.411746	−0.205873	−	0.978579i	$-0.566003\pi$
$379$	−8.01584	−0.411746	−0.205873	+	0.978579i	$0.566003\pi$
$380$	−17.2086	−0.882785
$381$	21.2150	1.08688
$382$	13.5361	0.692568
$383$	28.2829	1.44519	0.722595	−	0.691272i	$-0.242949\pi$
$383$	28.2829	1.44519	0.722595	+	0.691272i	$0.242949\pi$
$384$	−16.0342	−0.818239
$385$	−1.48815	−0.0758432
$386$	−49.4819	−2.51856
$387$	−8.73518	−0.444034
$388$	23.2586	1.18078
$389$	13.8218	0.700791	0.350395	−	0.936602i	$-0.386047\pi$
$389$	13.8218	0.700791	0.350395	+	0.936602i	$0.386047\pi$
$390$	10.6477	0.539165
$391$	−3.25844	−0.164786
$392$	−36.7574	−1.85653
$393$	13.8203	0.697142
$394$	42.5058	2.14141
$395$	−21.6777	−1.09072
$396$	−0.257631	−0.0129464
$397$	−8.17636	−0.410360	−0.205180	−	0.978724i	$-0.565778\pi$
$397$	−8.17636	−0.410360	−0.205180	+	0.978724i	$0.565778\pi$
$398$	54.7527	2.74451
$399$	7.43111	0.372021
$400$	−7.35145	−0.367573
$401$	8.32886	0.415924	0.207962	−	0.978137i	$-0.433317\pi$
$401$	8.32886	0.415924	0.207962	+	0.978137i	$0.433317\pi$
$402$	−14.9270	−0.744491
$403$	−11.5252	−0.574113
$404$	34.0463	1.69387
$405$	−3.65739	−0.181737
$406$	39.2797	1.94942
$407$	0.866259	0.0429389
$408$	2.28177	0.112964
$409$	−35.7922	−1.76981	−0.884906	−	0.465770i	$-0.845777\pi$
$409$	−35.7922	−1.76981	−0.884906	+	0.465770i	$0.845777\pi$
$410$	−50.3489	−2.48655
$411$	−0.662432	−0.0326754
$412$	−27.5966	−1.35959
$413$	8.77648	0.431862
$414$	7.40161	0.363769
$415$	34.1895	1.67830
$416$	−8.55435	−0.419412
$417$	11.3364	0.555146
$418$	0.296063	0.0144809
$419$	33.9733	1.65970	0.829852	−	0.557983i	$-0.188425\pi$
$419$	33.9733	1.65970	0.829852	+	0.557983i	$0.188425\pi$
$420$	−53.0442	−2.58829
$421$	−32.3525	−1.57677	−0.788383	−	0.615185i	$-0.789081\pi$
$421$	−32.3525	−1.57677	−0.788383	+	0.615185i	$0.789081\pi$
$422$	14.1486	0.688741
$423$	12.7886	0.621803
$424$	−0.0266812	−0.00129575
$425$	8.27074	0.401190
$426$	22.0091	1.06635
$427$	63.6901	3.08218
$428$	−54.2303	−2.62132
$429$	−0.110354	−0.00532793
$430$	−71.6544	−3.45548
$431$	14.2865	0.688156	0.344078	−	0.938941i	$-0.388191\pi$
$431$	14.2865	0.688156	0.344078	+	0.938941i	$0.388191\pi$
$432$	0.877630	0.0422250
$433$	5.19270	0.249545	0.124773	−	0.992185i	$-0.460180\pi$
$433$	5.19270	0.249545	0.124773	+	0.992185i	$0.460180\pi$
$434$	95.3100	4.57503
$435$	13.3834	0.641686
$436$	−36.2837	−1.73768
$437$	−5.12398	−0.245113
$438$	−10.6939	−0.510976
$439$	−7.16553	−0.341992	−0.170996	−	0.985272i	$-0.554699\pi$
$439$	−7.16553	−0.341992	−0.170996	+	0.985272i	$0.554699\pi$
$440$	−0.718561	−0.0342561
$441$	15.9058	0.757418
$442$	2.87452	0.136727
$443$	8.81179	0.418661	0.209330	−	0.977845i	$-0.432872\pi$
$443$	8.81179	0.418661	0.209330	+	0.977845i	$0.432872\pi$
$444$	30.8773	1.46537
$445$	12.4400	0.589711
$446$	−36.9501	−1.74964
$447$	8.66589	0.409882
$448$	62.3411	2.94534
$449$	−16.4565	−0.776630	−0.388315	−	0.921527i	$-0.626943\pi$
$449$	−16.4565	−0.776630	−0.388315	+	0.921527i	$0.626943\pi$
$450$	−18.7872	−0.885636
$451$	0.521822	0.0245717
$452$	40.7397	1.91623
$453$	−20.2275	−0.950373
$454$	63.7709	2.99291
$455$	−22.7210	−1.06518
$456$	3.58815	0.168031
$457$	−23.2314	−1.08672	−0.543360	−	0.839500i	$-0.682848\pi$
$457$	−23.2314	−1.08672	−0.543360	+	0.839500i	$0.682848\pi$
$458$	−46.5563	−2.17543
$459$	−0.987376	−0.0460868
$460$	36.5757	1.70535
$461$	1.49101	0.0694434	0.0347217	−	0.999397i	$-0.488946\pi$
$461$	1.49101	0.0694434	0.0347217	+	0.999397i	$0.488946\pi$
$462$	0.912590	0.0424575
$463$	−5.54226	−0.257571	−0.128785	−	0.991672i	$-0.541108\pi$
$463$	−5.54226	−0.257571	−0.128785	+	0.991672i	$0.541108\pi$
$464$	−3.21150	−0.149090
$465$	32.4741	1.50595
$466$	16.7190	0.774495
$467$	−31.7609	−1.46972	−0.734861	−	0.678218i	$-0.762752\pi$
$467$	−31.7609	−1.46972	−0.734861	+	0.678218i	$0.762752\pi$
$468$	−3.93349	−0.181826
$469$	31.8527	1.47082
$470$	104.904	4.83888
$471$	4.55700	0.209975
$472$	4.23777	0.195059
$473$	0.742635	0.0341464
$474$	13.2936	0.610593
$475$	13.0060	0.596755
$476$	−14.3202	−0.656366
$477$	0.0115456	0.000528635 0
$478$	−39.1419	−1.79031
$479$	−31.8686	−1.45611	−0.728057	−	0.685517i	$-0.759576\pi$
$479$	−31.8686	−1.45611	−0.728057	+	0.685517i	$0.759576\pi$
$480$	24.1032	1.10016
$481$	13.2260	0.603053
$482$	−15.4643	−0.704381
$483$	−15.7943	−0.718664
$484$	−33.3121	−1.51419
$485$	−28.0711	−1.27464
$486$	2.24285	0.101738
$487$	2.58078	0.116946	0.0584732	−	0.998289i	$-0.481377\pi$
$487$	2.58078	0.116946	0.0584732	+	0.998289i	$0.481377\pi$
$488$	30.7531	1.39213
$489$	20.3213	0.918963
$490$	130.475	5.89424
$491$	12.6531	0.571028	0.285514	−	0.958375i	$-0.407836\pi$
$491$	12.6531	0.571028	0.285514	+	0.958375i	$0.407836\pi$
$492$	18.6000	0.838554
$493$	3.61309	0.162725
$494$	4.52027	0.203376
$495$	0.310938	0.0139756
$496$	−7.79251	−0.349894
$497$	−46.9652	−2.10668
$498$	−20.9663	−0.939523
$499$	33.8009	1.51314	0.756569	−	0.653914i	$-0.226874\pi$
$499$	33.8009	1.51314	0.756569	+	0.653914i	$0.226874\pi$
$500$	−37.4223	−1.67357
$501$	8.61608	0.384938
$502$	3.88491	0.173392
$503$	−39.8607	−1.77730	−0.888651	−	0.458585i	$-0.848357\pi$
$503$	−39.8607	−1.77730	−0.888651	+	0.458585i	$0.848357\pi$
$504$	11.0602	0.492659
$505$	−41.0910	−1.82853
$506$	−0.629259	−0.0279740
$507$	11.3151	0.502522
$508$	−64.2892	−2.85237
$509$	−11.0983	−0.491922	−0.245961	−	0.969280i	$-0.579104\pi$
$509$	−11.0983	−0.491922	−0.245961	+	0.969280i	$0.579104\pi$
$510$	−8.09940	−0.358648
$511$	22.8197	1.00949
$512$	−9.84013	−0.434876
$513$	−1.55268	−0.0685524
$514$	−60.9495	−2.68837
$515$	33.3067	1.46767
$516$	26.4708	1.16531
$517$	−1.08724	−0.0478169
$518$	−109.375	−4.80565
$519$	−9.25390	−0.406201
$520$	−10.9709	−0.481108
$521$	13.0133	0.570123	0.285061	−	0.958509i	$-0.407986\pi$
$521$	13.0133	0.570123	0.285061	+	0.958509i	$0.407986\pi$
$522$	−8.20721	−0.359220
$523$	−9.53165	−0.416790	−0.208395	−	0.978045i	$-0.566824\pi$
$523$	−9.53165	−0.416790	−0.208395	+	0.978045i	$0.566824\pi$
$524$	−41.8805	−1.82956
$525$	40.0898	1.74966
$526$	−37.3984	−1.63065
$527$	8.76695	0.381895
$528$	−0.0746130	−0.00324712
$529$	−12.1094	−0.526494
$530$	0.0947078	0.00411385
$531$	−1.83378	−0.0795793
$532$	−22.5190	−0.976321
$533$	7.96714	0.345095
$534$	−7.62866	−0.330124
$535$	65.4514	2.82971
$536$	15.3802	0.664324
$537$	8.77776	0.378789
$538$	46.9148	2.02264
$539$	−1.35226	−0.0582457
$540$	11.0832	0.476945
$541$	21.9417	0.943346	0.471673	−	0.881774i	$-0.343650\pi$
$541$	21.9417	0.943346	0.471673	+	0.881774i	$0.343650\pi$
$542$	41.5996	1.78686
$543$	−4.23362	−0.181682
$544$	6.50708	0.278989
$545$	43.7914	1.87582
$546$	13.9334	0.596292
$547$	10.9012	0.466101	0.233051	−	0.972465i	$-0.425129\pi$
$547$	10.9012	0.466101	0.233051	+	0.972465i	$0.425129\pi$
$548$	2.00741	0.0857523
$549$	−13.3076	−0.567954
$550$	1.59722	0.0681057
$551$	5.68169	0.242048
$552$	−7.62634	−0.324599
$553$	−28.3671	−1.20629
$554$	23.6118	1.00317
$555$	−37.2662	−1.58186
$556$	−34.3534	−1.45691
$557$	41.8102	1.77155	0.885777	−	0.464111i	$-0.153626\pi$
$557$	41.8102	1.77155	0.885777	+	0.464111i	$0.153626\pi$
$558$	−19.9143	−0.843041
$559$	11.3385	0.479567
$560$	−15.3623	−0.649174
$561$	0.0839433	0.00354409
$562$	50.2879	2.12127
$563$	−5.74478	−0.242114	−0.121057	−	0.992646i	$-0.538628\pi$
$563$	−5.74478	−0.242114	−0.121057	+	0.992646i	$0.538628\pi$
$564$	−38.7541	−1.63184
$565$	−49.1693	−2.06857
$566$	−11.8589	−0.498467
$567$	−4.78600	−0.200993
$568$	−22.6774	−0.951522
$569$	19.3858	0.812697	0.406349	−	0.913718i	$-0.366802\pi$
$569$	19.3858	0.812697	0.406349	+	0.913718i	$0.366802\pi$
$570$	−12.7365	−0.533475
$571$	6.09997	0.255276	0.127638	−	0.991821i	$-0.459260\pi$
$571$	6.09997	0.255276	0.127638	+	0.991821i	$0.459260\pi$
$572$	0.334412	0.0139825
$573$	6.03523	0.252126
$574$	−65.8858	−2.75002
$575$	−27.6432	−1.15280
$576$	−13.0257	−0.542739
$577$	−28.3072	−1.17845	−0.589223	−	0.807971i	$-0.700566\pi$
$577$	−28.3072	−1.17845	−0.589223	+	0.807971i	$0.700566\pi$
$578$	35.9418	1.49498
$579$	−22.0621	−0.916869
$580$	−40.5566	−1.68402
$581$	44.7399	1.85612
$582$	17.2143	0.713554
$583$	−0.000981564 0	−4.06522e−5 0
$584$	11.0186	0.455954
$585$	4.74738	0.196280
$586$	24.1115	0.996037
$587$	−16.6867	−0.688734	−0.344367	−	0.938835i	$-0.611906\pi$
$587$	−16.6867	−0.688734	−0.344367	+	0.938835i	$0.611906\pi$
$588$	−48.2003	−1.98775
$589$	13.7863	0.568054
$590$	−15.0424	−0.619287
$591$	18.9517	0.779569
$592$	8.94243	0.367532
$593$	−41.1431	−1.68955	−0.844773	−	0.535125i	$-0.820264\pi$
$593$	−41.1431	−1.68955	−0.844773	+	0.535125i	$0.820264\pi$
$594$	−0.190679	−0.00782366
$595$	17.2833	0.708545
$596$	−26.2608	−1.07568
$597$	24.4121	0.999123
$598$	−9.60748	−0.392879
$599$	21.6719	0.885489	0.442745	−	0.896648i	$-0.354005\pi$
$599$	21.6719	0.885489	0.442745	+	0.896648i	$0.354005\pi$
$600$	19.3576	0.790270
$601$	−26.7542	−1.09133	−0.545663	−	0.838005i	$-0.683722\pi$
$601$	−26.7542	−1.09133	−0.545663	+	0.838005i	$0.683722\pi$
$602$	−93.7658	−3.82161
$603$	−6.65538	−0.271028
$604$	61.2968	2.49413
$605$	40.2048	1.63456
$606$	25.1985	1.02362
$607$	−2.85949	−0.116063	−0.0580316	−	0.998315i	$-0.518482\pi$
$607$	−2.85949	−0.116063	−0.0580316	+	0.998315i	$0.518482\pi$
$608$	10.2326	0.414986
$609$	17.5133	0.709676
$610$	−109.162	−4.41982
$611$	−16.5999	−0.671561
$612$	2.99211	0.120949
$613$	−17.6305	−0.712089	−0.356045	−	0.934469i	$-0.615875\pi$
$613$	−17.6305	−0.712089	−0.356045	+	0.934469i	$0.615875\pi$
$614$	−54.6072	−2.20377
$615$	−22.4486	−0.905217
$616$	−0.940298	−0.0378857
$617$	37.7392	1.51932	0.759661	−	0.650319i	$-0.225365\pi$
$617$	37.7392	1.51932	0.759661	+	0.650319i	$0.225365\pi$
$618$	−20.4249	−0.821611
$619$	25.2622	1.01538	0.507688	−	0.861541i	$-0.330500\pi$
$619$	25.2622	1.01538	0.507688	+	0.861541i	$0.330500\pi$
$620$	−98.4083	−3.95217
$621$	3.30010	0.132428
$622$	−25.7232	−1.03141
$623$	16.2787	0.652194
$624$	−1.13919	−0.0456039
$625$	3.28304	0.131322
$626$	−5.25343	−0.209969
$627$	0.132003	0.00527170
$628$	−13.8093	−0.551053
$629$	−10.0607	−0.401145
$630$	−39.2594	−1.56413
$631$	−27.8611	−1.10913	−0.554567	−	0.832139i	$-0.687116\pi$
$631$	−27.8611	−1.10913	−0.554567	+	0.832139i	$0.687116\pi$
$632$	−13.6972	−0.544844
$633$	6.30830	0.250732
$634$	−4.81136	−0.191084
$635$	77.5915	3.07913
$636$	−0.0349873	−0.00138733
$637$	−20.6461	−0.818029
$638$	0.697749	0.0276241
$639$	9.81304	0.388198
$640$	−58.6431	−2.31807
$641$	−18.1072	−0.715190	−0.357595	−	0.933877i	$-0.616403\pi$
$641$	−18.1072	−0.715190	−0.357595	+	0.933877i	$0.616403\pi$
$642$	−40.1372	−1.58409
$643$	−27.0565	−1.06700	−0.533502	−	0.845799i	$-0.679124\pi$
$643$	−27.0565	−1.06700	−0.533502	+	0.845799i	$0.679124\pi$
$644$	47.8623	1.88604
$645$	−31.9479	−1.25795
$646$	−3.43845	−0.135284
$647$	−27.7752	−1.09195	−0.545977	−	0.837800i	$-0.683841\pi$
$647$	−27.7752	−1.09195	−0.545977	+	0.837800i	$0.683841\pi$
$648$	−2.31094	−0.0907825
$649$	0.155902	0.00611968
$650$	24.3862	0.956507
$651$	42.4951	1.66551
$652$	−61.5810	−2.41170
$653$	−21.2915	−0.833202	−0.416601	−	0.909089i	$-0.636779\pi$
$653$	−21.2915	−0.833202	−0.416601	+	0.909089i	$0.636779\pi$
$654$	−26.8545	−1.05009
$655$	50.5462	1.97500
$656$	5.38680	0.210319
$657$	−4.76802	−0.186018
$658$	137.276	5.35158
$659$	−0.690238	−0.0268879	−0.0134439	−	0.999910i	$-0.504279\pi$
$659$	−0.690238	−0.0268879	−0.0134439	+	0.999910i	$0.504279\pi$
$660$	−0.942256	−0.0366773
$661$	7.99575	0.310999	0.155499	−	0.987836i	$-0.450301\pi$
$661$	7.99575	0.310999	0.155499	+	0.987836i	$0.450301\pi$
$662$	9.68875	0.376564
$663$	1.28164	0.0497748
$664$	21.6029	0.838355
$665$	27.1785	1.05394
$666$	22.8530	0.885537
$667$	−12.0760	−0.467584
$668$	−26.1099	−1.01022
$669$	−16.4747	−0.636947
$670$	−54.5938	−2.10914
$671$	1.13136	0.0436758
$672$	31.5411	1.21672
$673$	20.2586	0.780913	0.390456	−	0.920621i	$-0.372317\pi$
$673$	20.2586	0.780913	0.390456	+	0.920621i	$0.372317\pi$
$674$	81.1344	3.12518
$675$	−8.37648	−0.322411
$676$	−34.2889	−1.31881
$677$	−22.2842	−0.856453	−0.428226	−	0.903671i	$-0.640861\pi$
$677$	−22.2842	−0.856453	−0.428226	+	0.903671i	$0.640861\pi$
$678$	30.1524	1.15800
$679$	−36.7334	−1.40970
$680$	8.34532	0.320028
$681$	28.4330	1.08955
$682$	1.69305	0.0648302
$683$	27.7201	1.06068	0.530340	−	0.847785i	$-0.322064\pi$
$683$	27.7201	1.06068	0.530340	+	0.847785i	$0.322064\pi$
$684$	4.70517	0.179907
$685$	−2.42277	−0.0925693
$686$	95.5971	3.64991
$687$	−20.7577	−0.791954
$688$	7.66626	0.292273
$689$	−0.0149864	−0.000570938 0
$690$	27.0706	1.03056
$691$	−24.6972	−0.939524	−0.469762	−	0.882793i	$-0.655660\pi$
$691$	−24.6972	−0.939524	−0.469762	+	0.882793i	$0.655660\pi$
$692$	28.0427	1.06602
$693$	0.406889	0.0154564
$694$	−13.5226	−0.513312
$695$	41.4616	1.57273
$696$	8.45640	0.320539
$697$	−6.06041	−0.229554
$698$	29.3523	1.11100
$699$	7.45438	0.281951
$700$	−121.487	−4.59177
$701$	37.4278	1.41363	0.706814	−	0.707399i	$-0.250132\pi$
$701$	37.4278	1.41363	0.706814	+	0.707399i	$0.250132\pi$
$702$	−2.91127	−0.109879
$703$	−15.8207	−0.596689
$704$	1.10740	0.0417368
$705$	46.7729	1.76157
$706$	−15.1866	−0.571555
$707$	−53.7710	−2.02227
$708$	5.55702	0.208846
$709$	33.7033	1.26575	0.632876	−	0.774253i	$-0.281874\pi$
$709$	33.7033	1.26575	0.632876	+	0.774253i	$0.281874\pi$
$710$	80.4960	3.02096
$711$	5.92709	0.222283
$712$	7.86028	0.294576
$713$	−29.3017	−1.09736
$714$	−10.5988	−0.396648
$715$	−0.403606	−0.0150940
$716$	−26.5998	−0.994081
$717$	−17.4519	−0.651752
$718$	−9.24957	−0.345191
$719$	−18.4732	−0.688934	−0.344467	−	0.938798i	$-0.611940\pi$
$719$	−18.4732	−0.688934	−0.344467	+	0.938798i	$0.611940\pi$
$720$	3.20983	0.119623
$721$	43.5846	1.62318
$722$	37.2070	1.38470
$723$	−6.89496	−0.256426
$724$	12.8294	0.476801
$725$	30.6519	1.13838
$726$	−24.6551	−0.915037
$727$	27.7240	1.02823	0.514113	−	0.857722i	$-0.328121\pi$
$727$	27.7240	1.02823	0.514113	+	0.857722i	$0.328121\pi$
$728$	−14.3564	−0.532084
$729$	1.00000	0.0370370
$730$	−39.1119	−1.44760
$731$	−8.62491	−0.319004
$732$	40.3268	1.49052
$733$	−12.6972	−0.468982	−0.234491	−	0.972118i	$-0.575342\pi$
$733$	−12.6972	−0.468982	−0.234491	+	0.972118i	$0.575342\pi$
$734$	−37.0194	−1.36641
$735$	58.1736	2.14577
$736$	−21.7486	−0.801662
$737$	0.565818	0.0208422
$738$	13.7664	0.506746
$739$	39.0939	1.43809	0.719046	−	0.694962i	$-0.244579\pi$
$739$	39.0939	1.43809	0.719046	+	0.694962i	$0.244579\pi$
$740$	112.930	4.15139
$741$	2.01542	0.0740381
$742$	0.123933	0.00454973
$743$	52.6810	1.93268	0.966340	−	0.257269i	$-0.0828225\pi$
$743$	52.6810	1.93268	0.966340	+	0.257269i	$0.0828225\pi$
$744$	20.5190	0.752262
$745$	31.6945	1.16120
$746$	56.4634	2.06727
$747$	−9.34808	−0.342028
$748$	−0.254379	−0.00930100
$749$	85.6486	3.12953
$750$	−27.6971	−1.01136
$751$	15.7817	0.575881	0.287940	−	0.957648i	$-0.407029\pi$
$751$	15.7817	0.575881	0.287940	+	0.957648i	$0.407029\pi$
$752$	−11.2237	−0.409285
$753$	1.73213	0.0631224
$754$	10.6532	0.387966
$755$	−73.9799	−2.69241
$756$	14.5033	0.527480
$757$	−14.4625	−0.525648	−0.262824	−	0.964844i	$-0.584654\pi$
$757$	−14.4625	−0.525648	−0.262824	+	0.964844i	$0.584654\pi$
$758$	17.9783	0.653001
$759$	−0.280563	−0.0101838
$760$	13.1233	0.476031
$761$	−49.5040	−1.79452	−0.897260	−	0.441503i	$-0.854445\pi$
$761$	−49.5040	−1.79452	−0.897260	+	0.441503i	$0.854445\pi$
$762$	−47.5820	−1.72372
$763$	57.3047	2.07457
$764$	−18.2889	−0.661671
$765$	−3.61122	−0.130564
$766$	−63.4343	−2.29197
$767$	2.38030	0.0859475
$768$	9.91069	0.357621
$769$	35.8646	1.29331	0.646655	−	0.762782i	$-0.276167\pi$
$769$	35.8646	1.29331	0.646655	+	0.762782i	$0.276167\pi$
$770$	3.33769	0.120282
$771$	−27.1751	−0.978686
$772$	66.8561	2.40620
$773$	44.9109	1.61533	0.807666	−	0.589640i	$-0.200730\pi$
$773$	44.9109	1.61533	0.807666	+	0.589640i	$0.200730\pi$
$774$	19.5917	0.704208
$775$	74.3752	2.67163
$776$	−17.7369	−0.636719
$777$	−48.7660	−1.74947
$778$	−31.0001	−1.11141
$779$	−9.53016	−0.341454
$780$	−14.3863	−0.515112
$781$	−0.834271	−0.0298525
$782$	7.30817	0.261340
$783$	−3.65928	−0.130772
$784$	−13.9594	−0.498550
$785$	16.6667	0.594860
$786$	−30.9968	−1.10562
$787$	8.12865	0.289755	0.144877	−	0.989450i	$-0.453721\pi$
$787$	8.12865	0.289755	0.144877	+	0.989450i	$0.453721\pi$
$788$	−57.4305	−2.04588
$789$	−16.6745	−0.593629
$790$	48.6197	1.72981
$791$	−64.3421	−2.28774
$792$	0.196468	0.00698120
$793$	17.2736	0.613403
$794$	18.3383	0.650803
$795$	0.0422266	0.00149762
$796$	−73.9776	−2.62207
$797$	18.1197	0.641832	0.320916	−	0.947108i	$-0.396009\pi$
$797$	18.1197	0.641832	0.320916	+	0.947108i	$0.396009\pi$
$798$	−16.6668	−0.590000
$799$	12.6272	0.446717
$800$	55.2033	1.95173
$801$	−3.40133	−0.120180
$802$	−18.6804	−0.659627
$803$	0.405360	0.0143049
$804$	20.1682	0.711278
$805$	−57.7657	−2.03597
$806$	25.8493	0.910504
$807$	20.9175	0.736331
$808$	−25.9636	−0.913397
$809$	9.95932	0.350151	0.175076	−	0.984555i	$-0.443983\pi$
$809$	9.95932	0.350151	0.175076	+	0.984555i	$0.443983\pi$
$810$	8.20296	0.288223
$811$	27.0508	0.949883	0.474942	−	0.880017i	$-0.342469\pi$
$811$	27.0508	0.949883	0.474942	+	0.880017i	$0.342469\pi$
$812$	−53.0717	−1.86245
$813$	18.5477	0.650496
$814$	−1.94289	−0.0680981
$815$	74.3230	2.60342
$816$	0.866550	0.0303353
$817$	−13.5629	−0.474506
$818$	80.2765	2.80680
$819$	6.21235	0.217077
$820$	68.0275	2.37562
$821$	52.8037	1.84286	0.921431	−	0.388542i	$-0.127021\pi$
$821$	52.8037	1.84286	0.921431	+	0.388542i	$0.127021\pi$
$822$	1.48573	0.0518209
$823$	−28.9766	−1.01006	−0.505031	−	0.863101i	$-0.668519\pi$
$823$	−28.9766	−1.01006	−0.505031	+	0.863101i	$0.668519\pi$
$824$	21.0451	0.733140
$825$	0.712140	0.0247935
$826$	−19.6843	−0.684904
$827$	−28.0412	−0.975087	−0.487543	−	0.873099i	$-0.662107\pi$
$827$	−28.0412	−0.975087	−0.487543	+	0.873099i	$0.662107\pi$
$828$	−10.0005	−0.347541
$829$	−3.59474	−0.124850	−0.0624252	−	0.998050i	$-0.519883\pi$
$829$	−3.59474	−0.124850	−0.0624252	+	0.998050i	$0.519883\pi$
$830$	−76.6819	−2.66167
$831$	10.5276	0.365198
$832$	16.9077	0.586170
$833$	15.7050	0.544146
$834$	−25.4258	−0.880424
$835$	31.5124	1.09053
$836$	−0.400018	−0.0138349
$837$	−8.87904	−0.306905
$838$	−76.1969	−2.63218
$839$	−47.7712	−1.64924	−0.824622	−	0.565684i	$-0.808612\pi$
$839$	−47.7712	−1.64924	−0.824622	+	0.565684i	$0.808612\pi$
$840$	40.4514	1.39570
$841$	−15.6096	−0.538264
$842$	72.5618	2.50064
$843$	22.4215	0.772236
$844$	−19.1164	−0.658015
$845$	41.3838	1.42365
$846$	−28.6829	−0.986137
$847$	52.6114	1.80775
$848$	−0.0101327	−0.000347960 0
$849$	−5.28744	−0.181464
$850$	−18.5500	−0.636260
$851$	33.6257	1.15267
$852$	−29.7371	−1.01877
$853$	−18.0410	−0.617711	−0.308855	−	0.951109i	$-0.599946\pi$
$853$	−18.0410	−0.617711	−0.308855	+	0.951109i	$0.599946\pi$
$854$	−142.847	−4.88813
$855$	−5.67874	−0.194209
$856$	41.3559	1.41352
$857$	5.03527	0.172001	0.0860007	−	0.996295i	$-0.472591\pi$
$857$	5.03527	0.172001	0.0860007	+	0.996295i	$0.472591\pi$
$858$	0.247506	0.00844973
$859$	45.6245	1.55669	0.778344	−	0.627838i	$-0.216060\pi$
$859$	45.6245	1.55669	0.778344	+	0.627838i	$0.216060\pi$
$860$	96.8138	3.30132
$861$	−29.3759	−1.00113
$862$	−32.0424	−1.09137
$863$	−22.3425	−0.760548	−0.380274	−	0.924874i	$-0.624170\pi$
$863$	−22.3425	−0.760548	−0.380274	+	0.924874i	$0.624170\pi$
$864$	−6.59028	−0.224206
$865$	−33.8451	−1.15077
$866$	−11.6464	−0.395762
$867$	16.0251	0.544241
$868$	−128.776	−4.37093
$869$	−0.503901	−0.0170937
$870$	−30.0170	−1.01767
$871$	8.63886	0.292717
$872$	27.6699	0.937020
$873$	7.67519	0.259766
$874$	11.4923	0.388733
$875$	59.1028	1.99804
$876$	14.4488	0.488181
$877$	24.4799	0.826628	0.413314	−	0.910589i	$-0.364371\pi$
$877$	24.4799	0.826628	0.413314	+	0.910589i	$0.364371\pi$
$878$	16.0712	0.542377
$879$	10.7504	0.362602
$880$	−0.272889	−0.00919908
$881$	−51.8769	−1.74778	−0.873888	−	0.486127i	$-0.838409\pi$
$881$	−51.8769	−1.74778	−0.873888	+	0.486127i	$0.838409\pi$
$882$	−35.6742	−1.20121
$883$	34.6122	1.16479	0.582396	−	0.812905i	$-0.302115\pi$
$883$	34.6122	1.16479	0.582396	+	0.812905i	$0.302115\pi$
$884$	−3.88383	−0.130627
$885$	−6.70685	−0.225448
$886$	−19.7635	−0.663968
$887$	−21.1563	−0.710358	−0.355179	−	0.934798i	$-0.615580\pi$
$887$	−21.1563	−0.710358	−0.355179	+	0.934798i	$0.615580\pi$
$888$	−23.5469	−0.790182
$889$	101.535	3.40538
$890$	−27.9009	−0.935242
$891$	−0.0850165	−0.00284816
$892$	49.9242	1.67159
$893$	19.8566	0.664475
$894$	−19.4363	−0.650046
$895$	32.1037	1.07311
$896$	−76.7394	−2.56368
$897$	−4.28361	−0.143026
$898$	36.9094	1.23168
$899$	32.4909	1.08363
$900$	25.3838	0.846126
$901$	0.0113998	0.000379783 0
$902$	−1.17037	−0.0389690
$903$	−41.8066	−1.39124
$904$	−31.0679	−1.03330
$905$	−15.4840	−0.514705
$906$	45.3673	1.50723
$907$	39.0373	1.29621	0.648106	−	0.761550i	$-0.275561\pi$
$907$	39.0373	1.29621	0.648106	+	0.761550i	$0.275561\pi$
$908$	−86.1623	−2.85940
$909$	11.2351	0.372644
$910$	50.9597	1.68930
$911$	−12.7876	−0.423671	−0.211835	−	0.977305i	$-0.567944\pi$
$911$	−12.7876	−0.423671	−0.211835	+	0.977305i	$0.567944\pi$
$912$	1.36268	0.0451227
$913$	0.794741	0.0263021
$914$	52.1046	1.72347
$915$	−48.6710	−1.60901
$916$	62.9032	2.07838
$917$	66.1440	2.18427
$918$	2.21453	0.0730905
$919$	2.05264	0.0677103	0.0338551	−	0.999427i	$-0.489222\pi$
$919$	2.05264	0.0677103	0.0338551	+	0.999427i	$0.489222\pi$
$920$	−27.8925	−0.919588
$921$	−24.3473	−0.802269
$922$	−3.34411	−0.110132
$923$	−12.7376	−0.419263
$924$	−1.23302	−0.0405634
$925$	−85.3505	−2.80631
$926$	12.4304	0.408490
$927$	−9.10670	−0.299103
$928$	24.1157	0.791636
$929$	25.1233	0.824269	0.412135	−	0.911123i	$-0.364783\pi$
$929$	25.1233	0.824269	0.412135	+	0.911123i	$0.364783\pi$
$930$	−72.8344	−2.38834
$931$	24.6966	0.809397
$932$	−22.5895	−0.739943
$933$	−11.4690	−0.375478
$934$	71.2349	2.33088
$935$	0.307013	0.0100404
$936$	2.99967	0.0980471
$937$	42.8092	1.39852	0.699258	−	0.714869i	$-0.253514\pi$
$937$	42.8092	1.39852	0.699258	+	0.714869i	$0.253514\pi$
$938$	−71.4406	−2.33262
$939$	−2.34231	−0.0764383
$940$	−141.739	−4.62301
$941$	−0.263130	−0.00857780	−0.00428890	−	0.999991i	$-0.501365\pi$
$941$	−0.263130	−0.00857780	−0.00428890	+	0.999991i	$0.501365\pi$
$942$	−10.2206	−0.333007
$943$	20.2556	0.659614
$944$	1.60938	0.0523809
$945$	−17.5043	−0.569413
$946$	−1.66562	−0.0541539
$947$	−46.6768	−1.51679	−0.758396	−	0.651794i	$-0.774017\pi$
$947$	−46.6768	−1.51679	−0.758396	+	0.651794i	$0.774017\pi$
$948$	−17.9612	−0.583354
$949$	6.18901	0.200904
$950$	−29.1704	−0.946413
$951$	−2.14520	−0.0695630
$952$	10.9206	0.353937
$953$	−11.3514	−0.367708	−0.183854	−	0.982954i	$-0.558857\pi$
$953$	−11.3514	−0.367708	−0.183854	+	0.982954i	$0.558857\pi$
$954$	−0.0258949	−0.000838380 0
$955$	22.0732	0.714272
$956$	52.8855	1.71044
$957$	0.311100	0.0100564
$958$	71.4764	2.30930
$959$	−3.17040	−0.102378
$960$	−47.6401	−1.53758
$961$	47.8374	1.54314
$962$	−29.6638	−0.956401
$963$	−17.8957	−0.576680
$964$	20.8942	0.672958
$965$	−80.6896	−2.59749
$966$	35.4241	1.13975
$967$	20.0232	0.643903	0.321952	−	0.946756i	$-0.395661\pi$
$967$	20.0232	0.643903	0.321952	+	0.946756i	$0.395661\pi$
$968$	25.4037	0.816505
$969$	−1.53308	−0.0492495
$970$	62.9592	2.02150
$971$	−34.8787	−1.11931	−0.559656	−	0.828725i	$-0.689067\pi$
$971$	−34.8787	−1.11931	−0.559656	+	0.828725i	$0.689067\pi$
$972$	−3.03036	−0.0971989
$973$	54.2560	1.73937
$974$	−5.78830	−0.185469
$975$	10.8729	0.348211
$976$	11.6791	0.373840
$977$	−11.6893	−0.373973	−0.186987	−	0.982362i	$-0.559872\pi$
$977$	−11.6893	−0.373973	−0.186987	+	0.982362i	$0.559872\pi$
$978$	−45.5777	−1.45741
$979$	0.289169	0.00924188
$980$	−176.287	−5.63129
$981$	−11.9734	−0.382281
$982$	−28.3790	−0.905611
$983$	60.6545	1.93458	0.967289	−	0.253675i	$-0.0816395\pi$
$983$	60.6545	1.93458	0.967289	+	0.253675i	$0.0816395\pi$
$984$	−14.1843	−0.452180
$985$	69.3138	2.20852
$986$	−8.10360	−0.258071
$987$	61.2062	1.94822
$988$	−6.10744	−0.194303
$989$	28.8269	0.916644
$990$	−0.697387	−0.0221644
$991$	−33.7463	−1.07199	−0.535993	−	0.844222i	$-0.680063\pi$
$991$	−33.7463	−1.07199	−0.535993	+	0.844222i	$0.680063\pi$
$992$	58.5154	1.85786
$993$	4.31985	0.137086
$994$	105.336	3.34105
$995$	89.2847	2.83051
$996$	28.3281	0.897609
$997$	−34.7270	−1.09982	−0.549908	−	0.835225i	$-0.685337\pi$
$997$	−34.7270	−1.09982	−0.549908	+	0.835225i	$0.685337\pi$
$998$	−75.8103	−2.39973
$999$	10.1893	0.322375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.c.1.16	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.c.1.16	✓	119	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.24285 q^{2} -1.00000 q^{3} +3.03036 q^{4} -3.65739 q^{5} +2.24285 q^{6} -4.78600 q^{7} -2.31094 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.24285 q^{2} -1.00000 q^{3} +3.03036 q^{4} -3.65739 q^{5} +2.24285 q^{6} -4.78600 q^{7} -2.31094 q^{8} +1.00000 q^{9} +8.20296 q^{10} -0.0850165 q^{11} -3.03036 q^{12} -1.29803 q^{13} +10.7343 q^{14} +3.65739 q^{15} -0.877630 q^{16} +0.987376 q^{17} -2.24285 q^{18} +1.55268 q^{19} -11.0832 q^{20} +4.78600 q^{21} +0.190679 q^{22} -3.30010 q^{23} +2.31094 q^{24} +8.37648 q^{25} +2.91127 q^{26} -1.00000 q^{27} -14.5033 q^{28} +3.65928 q^{29} -8.20296 q^{30} +8.87904 q^{31} +6.59028 q^{32} +0.0850165 q^{33} -2.21453 q^{34} +17.5043 q^{35} +3.03036 q^{36} -10.1893 q^{37} -3.48242 q^{38} +1.29803 q^{39} +8.45202 q^{40} -6.13789 q^{41} -10.7343 q^{42} -8.73518 q^{43} -0.257631 q^{44} -3.65739 q^{45} +7.40161 q^{46} +12.7886 q^{47} +0.877630 q^{48} +15.9058 q^{49} -18.7872 q^{50} -0.987376 q^{51} -3.93349 q^{52} +0.0115456 q^{53} +2.24285 q^{54} +0.310938 q^{55} +11.0602 q^{56} -1.55268 q^{57} -8.20721 q^{58} -1.83378 q^{59} +11.0832 q^{60} -13.3076 q^{61} -19.9143 q^{62} -4.78600 q^{63} -13.0257 q^{64} +4.74738 q^{65} -0.190679 q^{66} -6.65538 q^{67} +2.99211 q^{68} +3.30010 q^{69} -39.2594 q^{70} +9.81304 q^{71} -2.31094 q^{72} -4.76802 q^{73} +22.8530 q^{74} -8.37648 q^{75} +4.70517 q^{76} +0.406889 q^{77} -2.91127 q^{78} +5.92709 q^{79} +3.20983 q^{80} +1.00000 q^{81} +13.7664 q^{82} -9.34808 q^{83} +14.5033 q^{84} -3.61122 q^{85} +19.5917 q^{86} -3.65928 q^{87} +0.196468 q^{88} -3.40133 q^{89} +8.20296 q^{90} +6.21235 q^{91} -10.0005 q^{92} -8.87904 q^{93} -28.6829 q^{94} -5.67874 q^{95} -6.59028 q^{96} +7.67519 q^{97} -35.6742 q^{98} -0.0850165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * q^99

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