LMFDB - Embedded newform 407.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [407,2,Mod(1,407)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(407, 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("407.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 407 = 11 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	407.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:	$3.24991136227$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 16 x^{9} + 32 x^{8} + 89 x^{7} - 179 x^{6} - 201 x^{5} + 407 x^{4} + 168 x^{3} + \cdots + 75 $ x^11 - 2x^10 - 16x^9 + 32x^8 + 89x^7 - 179x^6 - 201x^5 + 407x^4 + 168x^3 - 333x^2 - 51x + 75
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.84206$ of defining polynomial
Character	$\chi$	$=$	407.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.84206 q^{2} +0.484221 q^{3} +1.39318 q^{4} +3.85955 q^{5} +0.891963 q^{6} +1.31125 q^{7} -1.11779 q^{8} -2.76553 q^{9} +O(q^{10})$	\(q+1.84206 q^{2} +0.484221 q^{3} +1.39318 q^{4} +3.85955 q^{5} +0.891963 q^{6} +1.31125 q^{7} -1.11779 q^{8} -2.76553 q^{9} +7.10952 q^{10} -1.00000 q^{11} +0.674608 q^{12} -2.63729 q^{13} +2.41540 q^{14} +1.86887 q^{15} -4.84541 q^{16} -3.66413 q^{17} -5.09427 q^{18} +5.60841 q^{19} +5.37706 q^{20} +0.634934 q^{21} -1.84206 q^{22} -3.43801 q^{23} -0.541259 q^{24} +9.89613 q^{25} -4.85804 q^{26} -2.79179 q^{27} +1.82681 q^{28} +5.32604 q^{29} +3.44258 q^{30} -5.95859 q^{31} -6.68994 q^{32} -0.484221 q^{33} -6.74954 q^{34} +5.06083 q^{35} -3.85289 q^{36} +1.00000 q^{37} +10.3310 q^{38} -1.27703 q^{39} -4.31418 q^{40} -3.68771 q^{41} +1.16959 q^{42} +9.61014 q^{43} -1.39318 q^{44} -10.6737 q^{45} -6.33302 q^{46} +5.63440 q^{47} -2.34625 q^{48} -5.28062 q^{49} +18.2293 q^{50} -1.77425 q^{51} -3.67422 q^{52} +13.6056 q^{53} -5.14264 q^{54} -3.85955 q^{55} -1.46571 q^{56} +2.71571 q^{57} +9.81088 q^{58} -5.54854 q^{59} +2.60368 q^{60} +3.48462 q^{61} -10.9761 q^{62} -3.62630 q^{63} -2.63245 q^{64} -10.1787 q^{65} -0.891963 q^{66} -14.7835 q^{67} -5.10480 q^{68} -1.66476 q^{69} +9.32236 q^{70} -13.8344 q^{71} +3.09129 q^{72} +3.61117 q^{73} +1.84206 q^{74} +4.79191 q^{75} +7.81353 q^{76} -1.31125 q^{77} -2.35236 q^{78} -4.58755 q^{79} -18.7011 q^{80} +6.94475 q^{81} -6.79299 q^{82} -5.55384 q^{83} +0.884579 q^{84} -14.1419 q^{85} +17.7024 q^{86} +2.57898 q^{87} +1.11779 q^{88} -0.861503 q^{89} -19.6616 q^{90} -3.45814 q^{91} -4.78977 q^{92} -2.88527 q^{93} +10.3789 q^{94} +21.6459 q^{95} -3.23941 q^{96} -6.39694 q^{97} -9.72722 q^{98} +2.76553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} + 14 q^{4} + q^{5} + 4 q^{6} + 9 q^{7} + 15 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 + 14 * q^4 + q^5 + 4 * q^6 + 9 * q^7 + 15 * q^9	\( 11 q + 2 q^{2} + 14 q^{4} + q^{5} + 4 q^{6} + 9 q^{7} + 15 q^{9} + 5 q^{10} - 11 q^{11} + q^{12} + 22 q^{13} + 3 q^{14} - 10 q^{15} + 19 q^{17} + 18 q^{18} + 14 q^{19} + 6 q^{20} - 13 q^{21} - 2 q^{22} - 14 q^{23} - 11 q^{24} + 38 q^{25} - 10 q^{26} - 9 q^{27} + q^{28} + 13 q^{29} + 19 q^{30} + 12 q^{31} - 3 q^{32} + q^{34} + 12 q^{35} + 18 q^{36} + 11 q^{37} - 31 q^{38} - 8 q^{39} + 22 q^{40} + 8 q^{41} + 15 q^{42} + 21 q^{43} - 14 q^{44} - 8 q^{45} - 45 q^{46} - 14 q^{47} - 37 q^{48} + 20 q^{49} - 41 q^{50} - 2 q^{51} + 51 q^{52} - 2 q^{53} + 6 q^{54} - q^{55} - 22 q^{56} - 3 q^{57} + 15 q^{58} - 30 q^{59} - 107 q^{60} + 20 q^{61} + 22 q^{62} + 31 q^{63} - 14 q^{64} - 4 q^{66} + 7 q^{67} + 24 q^{68} + 9 q^{69} - 86 q^{70} - 15 q^{71} - 7 q^{72} + 47 q^{73} + 2 q^{74} - 40 q^{75} + 6 q^{76} - 9 q^{77} - 42 q^{78} + 2 q^{79} + 3 q^{80} - 17 q^{81} - 54 q^{82} + 24 q^{83} - 33 q^{84} - 25 q^{85} - 13 q^{86} + 21 q^{87} + 4 q^{89} - 107 q^{90} + 21 q^{91} - 46 q^{92} - 37 q^{93} + 3 q^{94} - 36 q^{95} - 49 q^{96} + 25 q^{97} - 52 q^{98} - 15 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 + 14 * q^4 + q^5 + 4 * q^6 + 9 * q^7 + 15 * q^9 + 5 * q^10 - 11 * q^11 + q^12 + 22 * q^13 + 3 * q^14 - 10 * q^15 + 19 * q^17 + 18 * q^18 + 14 * q^19 + 6 * q^20 - 13 * q^21 - 2 * q^22 - 14 * q^23 - 11 * q^24 + 38 * q^25 - 10 * q^26 - 9 * q^27 + q^28 + 13 * q^29 + 19 * q^30 + 12 * q^31 - 3 * q^32 + q^34 + 12 * q^35 + 18 * q^36 + 11 * q^37 - 31 * q^38 - 8 * q^39 + 22 * q^40 + 8 * q^41 + 15 * q^42 + 21 * q^43 - 14 * q^44 - 8 * q^45 - 45 * q^46 - 14 * q^47 - 37 * q^48 + 20 * q^49 - 41 * q^50 - 2 * q^51 + 51 * q^52 - 2 * q^53 + 6 * q^54 - q^55 - 22 * q^56 - 3 * q^57 + 15 * q^58 - 30 * q^59 - 107 * q^60 + 20 * q^61 + 22 * q^62 + 31 * q^63 - 14 * q^64 - 4 * q^66 + 7 * q^67 + 24 * q^68 + 9 * q^69 - 86 * q^70 - 15 * q^71 - 7 * q^72 + 47 * q^73 + 2 * q^74 - 40 * q^75 + 6 * q^76 - 9 * q^77 - 42 * q^78 + 2 * q^79 + 3 * q^80 - 17 * q^81 - 54 * q^82 + 24 * q^83 - 33 * q^84 - 25 * q^85 - 13 * q^86 + 21 * q^87 + 4 * q^89 - 107 * q^90 + 21 * q^91 - 46 * q^92 - 37 * q^93 + 3 * q^94 - 36 * q^95 - 49 * q^96 + 25 * q^97 - 52 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.84206	1.30253	0.651266	−	0.758849i	$-0.274238\pi$
$2$	1.84206	1.30253	0.651266	+	0.758849i	$0.274238\pi$
$3$	0.484221	0.279565	0.139783	−	0.990182i	$-0.455360\pi$
$3$	0.484221	0.279565	0.139783	+	0.990182i	$0.455360\pi$
$4$	1.39318	0.696591
$5$	3.85955	1.72604	0.863022	−	0.505167i	$-0.168569\pi$
$5$	3.85955	1.72604	0.863022	+	0.505167i	$0.168569\pi$
$6$	0.891963	0.364143
$7$	1.31125	0.495606	0.247803	−	0.968810i	$-0.420291\pi$
$7$	1.31125	0.495606	0.247803	+	0.968810i	$0.420291\pi$
$8$	−1.11779	−0.395200
$9$	−2.76553	−0.921843
$10$	7.10952	2.24823
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.674608	0.194743
$13$	−2.63729	−0.731452	−0.365726	−	0.930723i	$-0.619179\pi$
$13$	−2.63729	−0.731452	−0.365726	+	0.930723i	$0.619179\pi$
$14$	2.41540	0.645543
$15$	1.86887	0.482541
$16$	−4.84541	−1.21135
$17$	−3.66413	−0.888682	−0.444341	−	0.895858i	$-0.646562\pi$
$17$	−3.66413	−0.888682	−0.444341	+	0.895858i	$0.646562\pi$
$18$	−5.09427	−1.20073
$19$	5.60841	1.28666	0.643328	−	0.765590i	$-0.277553\pi$
$19$	5.60841	1.28666	0.643328	+	0.765590i	$0.277553\pi$
$20$	5.37706	1.20235
$21$	0.634934	0.138554
$22$	−1.84206	−0.392728
$23$	−3.43801	−0.716875	−0.358437	−	0.933554i	$-0.616690\pi$
$23$	−3.43801	−0.716875	−0.358437	+	0.933554i	$0.616690\pi$
$24$	−0.541259	−0.110484
$25$	9.89613	1.97923
$26$	−4.85804	−0.952740
$27$	−2.79179	−0.537280
$28$	1.82681	0.345235
$29$	5.32604	0.989020	0.494510	−	0.869172i	$-0.335347\pi$
$29$	5.32604	0.989020	0.494510	+	0.869172i	$0.335347\pi$
$30$	3.44258	0.628526
$31$	−5.95859	−1.07019	−0.535097	−	0.844791i	$-0.679725\pi$
$31$	−5.95859	−1.07019	−0.535097	+	0.844791i	$0.679725\pi$
$32$	−6.68994	−1.18263
$33$	−0.484221	−0.0842920
$34$	−6.74954	−1.15754
$35$	5.06083	0.855437
$36$	−3.85289	−0.642148
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	10.3310	1.67591
$39$	−1.27703	−0.204488
$40$	−4.31418	−0.682132
$41$	−3.68771	−0.575924	−0.287962	−	0.957642i	$-0.592978\pi$
$41$	−3.68771	−0.575924	−0.287962	+	0.957642i	$0.592978\pi$
$42$	1.16959	0.180471
$43$	9.61014	1.46553	0.732766	−	0.680480i	$-0.238229\pi$
$43$	9.61014	1.46553	0.732766	+	0.680480i	$0.238229\pi$
$44$	−1.39318	−0.210030
$45$	−10.6737	−1.59114
$46$	−6.33302	−0.933752
$47$	5.63440	0.821862	0.410931	−	0.911666i	$-0.365204\pi$
$47$	5.63440	0.821862	0.410931	+	0.911666i	$0.365204\pi$
$48$	−2.34625	−0.338652
$49$	−5.28062	−0.754375
$50$	18.2293	2.57801
$51$	−1.77425	−0.248444
$52$	−3.67422	−0.509523
$53$	13.6056	1.86887	0.934434	−	0.356138i	$-0.115907\pi$
$53$	13.6056	1.86887	0.934434	+	0.356138i	$0.115907\pi$
$54$	−5.14264	−0.699825
$55$	−3.85955	−0.520422
$56$	−1.46571	−0.195863
$57$	2.71571	0.359704
$58$	9.81088	1.28823
$59$	−5.54854	−0.722359	−0.361179	−	0.932496i	$-0.617626\pi$
$59$	−5.54854	−0.722359	−0.361179	+	0.932496i	$0.617626\pi$
$60$	2.60368	0.336134
$61$	3.48462	0.446160	0.223080	−	0.974800i	$-0.428389\pi$
$61$	3.48462	0.446160	0.223080	+	0.974800i	$0.428389\pi$
$62$	−10.9761	−1.39396
$63$	−3.62630	−0.456871
$64$	−2.63245	−0.329056
$65$	−10.1787	−1.26252
$66$	−0.891963	−0.109793
$67$	−14.7835	−1.80609	−0.903047	−	0.429542i	$-0.858675\pi$
$67$	−14.7835	−1.80609	−0.903047	+	0.429542i	$0.858675\pi$
$68$	−5.10480	−0.619048
$69$	−1.66476	−0.200413
$70$	9.32236	1.11423
$71$	−13.8344	−1.64184	−0.820922	−	0.571041i	$-0.806540\pi$
$71$	−13.8344	−1.64184	−0.820922	+	0.571041i	$0.806540\pi$
$72$	3.09129	0.364312
$73$	3.61117	0.422656	0.211328	−	0.977415i	$-0.432221\pi$
$73$	3.61117	0.422656	0.211328	+	0.977415i	$0.432221\pi$
$74$	1.84206	0.214135
$75$	4.79191	0.553322
$76$	7.81353	0.896274
$77$	−1.31125	−0.149431
$78$	−2.35236	−0.266353
$79$	−4.58755	−0.516140	−0.258070	−	0.966126i	$-0.583087\pi$
$79$	−4.58755	−0.516140	−0.258070	+	0.966126i	$0.583087\pi$
$80$	−18.7011	−2.09085
$81$	6.94475	0.771639
$82$	−6.79299	−0.750160
$83$	−5.55384	−0.609613	−0.304807	−	0.952414i	$-0.598592\pi$
$83$	−5.55384	−0.609613	−0.304807	+	0.952414i	$0.598592\pi$
$84$	0.884579	0.0965155
$85$	−14.1419	−1.53390
$86$	17.7024	1.90890
$87$	2.57898	0.276495
$88$	1.11779	0.119157
$89$	−0.861503	−0.0913191	−0.0456595	−	0.998957i	$-0.514539\pi$
$89$	−0.861503	−0.0913191	−0.0456595	+	0.998957i	$0.514539\pi$
$90$	−19.6616	−2.07251
$91$	−3.45814	−0.362512
$92$	−4.78977	−0.499368
$93$	−2.88527	−0.299189
$94$	10.3789	1.07050
$95$	21.6459	2.22083
$96$	−3.23941	−0.330621
$97$	−6.39694	−0.649511	−0.324755	−	0.945798i	$-0.605282\pi$
$97$	−6.39694	−0.649511	−0.324755	+	0.945798i	$0.605282\pi$
$98$	−9.72722	−0.982598
$99$	2.76553	0.277946
$100$	13.7871	1.37871
$101$	17.7846	1.76964	0.884818	−	0.465937i	$-0.154283\pi$
$101$	17.7846	1.76964	0.884818	+	0.465937i	$0.154283\pi$
$102$	−3.26827	−0.323607
$103$	−9.72233	−0.957970	−0.478985	−	0.877823i	$-0.658995\pi$
$103$	−9.72233	−0.957970	−0.478985	+	0.877823i	$0.658995\pi$
$104$	2.94794	0.289070
$105$	2.45056	0.239150
$106$	25.0622	2.43426
$107$	−3.04357	−0.294233	−0.147117	−	0.989119i	$-0.546999\pi$
$107$	−3.04357	−0.294233	−0.147117	+	0.989119i	$0.546999\pi$
$108$	−3.88947	−0.374265
$109$	13.1325	1.25787	0.628933	−	0.777459i	$-0.283492\pi$
$109$	13.1325	1.25787	0.628933	+	0.777459i	$0.283492\pi$
$110$	−7.10952	−0.677866
$111$	0.484221	0.0459602
$112$	−6.35354	−0.600353
$113$	14.2871	1.34402	0.672008	−	0.740543i	$-0.265432\pi$
$113$	14.2871	1.34402	0.672008	+	0.740543i	$0.265432\pi$
$114$	5.00249	0.468527
$115$	−13.2692	−1.23736
$116$	7.42014	0.688943
$117$	7.29350	0.674284
$118$	−10.2207	−0.940896
$119$	−4.80459	−0.440436
$120$	−2.08902	−0.190700
$121$	1.00000	0.0909091
$122$	6.41888	0.581138
$123$	−1.78567	−0.161008
$124$	−8.30140	−0.745488
$125$	18.8968	1.69018
$126$	−6.67986	−0.595089
$127$	2.97691	0.264158	0.132079	−	0.991239i	$-0.457835\pi$
$127$	2.97691	0.264158	0.132079	+	0.991239i	$0.457835\pi$
$128$	8.53075	0.754019
$129$	4.65343	0.409712
$130$	−18.7498	−1.64447
$131$	1.78341	0.155817	0.0779087	−	0.996960i	$-0.475176\pi$
$131$	1.78341	0.155817	0.0779087	+	0.996960i	$0.475176\pi$
$132$	−0.674608	−0.0587171
$133$	7.35402	0.637675
$134$	−27.2321	−2.35250
$135$	−10.7751	−0.927369
$136$	4.09574	0.351207
$137$	1.28294	0.109609	0.0548045	−	0.998497i	$-0.482546\pi$
$137$	1.28294	0.109609	0.0548045	+	0.998497i	$0.482546\pi$
$138$	−3.06658	−0.261045
$139$	15.1164	1.28216	0.641079	−	0.767475i	$-0.278487\pi$
$139$	15.1164	1.28216	0.641079	+	0.767475i	$0.278487\pi$
$140$	7.05066	0.595890
$141$	2.72830	0.229764
$142$	−25.4838	−2.13855
$143$	2.63729	0.220541
$144$	13.4001	1.11668
$145$	20.5561	1.70709
$146$	6.65200	0.550523
$147$	−2.55699	−0.210897
$148$	1.39318	0.114519
$149$	−1.03856	−0.0850821	−0.0425411	−	0.999095i	$-0.513545\pi$
$149$	−1.03856	−0.0850821	−0.0425411	+	0.999095i	$0.513545\pi$
$150$	8.82698	0.720720
$151$	10.7541	0.875159	0.437580	−	0.899180i	$-0.355836\pi$
$151$	10.7541	0.875159	0.437580	+	0.899180i	$0.355836\pi$
$152$	−6.26904	−0.508487
$153$	10.1333	0.819226
$154$	−2.41540	−0.194638
$155$	−22.9975	−1.84720
$156$	−1.77913	−0.142445
$157$	19.6643	1.56938	0.784690	−	0.619888i	$-0.212822\pi$
$157$	19.6643	1.56938	0.784690	+	0.619888i	$0.212822\pi$
$158$	−8.45054	−0.672289
$159$	6.58809	0.522470
$160$	−25.8202	−2.04126
$161$	−4.50809	−0.355287
$162$	12.7926	1.00508
$163$	4.07655	0.319300	0.159650	−	0.987174i	$-0.448963\pi$
$163$	4.07655	0.319300	0.159650	+	0.987174i	$0.448963\pi$
$164$	−5.13766	−0.401184
$165$	−1.86887	−0.145492
$166$	−10.2305	−0.794041
$167$	−23.3648	−1.80802	−0.904012	−	0.427507i	$-0.859392\pi$
$167$	−23.3648	−1.80802	−0.904012	+	0.427507i	$0.859392\pi$
$168$	−0.709726	−0.0547565
$169$	−6.04472	−0.464978
$170$	−26.0502	−1.99796
$171$	−15.5102	−1.18610
$172$	13.3887	1.02088
$173$	5.88349	0.447313	0.223657	−	0.974668i	$-0.428201\pi$
$173$	5.88349	0.447313	0.223657	+	0.974668i	$0.428201\pi$
$174$	4.75063	0.360144
$175$	12.9763	0.980915
$176$	4.84541	0.365236
$177$	−2.68672	−0.201946
$178$	−1.58694	−0.118946
$179$	0.568299	0.0424767	0.0212383	−	0.999774i	$-0.493239\pi$
$179$	0.568299	0.0424767	0.0212383	+	0.999774i	$0.493239\pi$
$180$	−14.8704	−1.10838
$181$	−5.86208	−0.435725	−0.217862	−	0.975979i	$-0.569908\pi$
$181$	−5.86208	−0.435725	−0.217862	+	0.975979i	$0.569908\pi$
$182$	−6.37010	−0.472183
$183$	1.68733	0.124731
$184$	3.84299	0.283309
$185$	3.85955	0.283760
$186$	−5.31484	−0.389703
$187$	3.66413	0.267948
$188$	7.84975	0.572502
$189$	−3.66073	−0.266279
$190$	39.8731	2.89270
$191$	5.88296	0.425676	0.212838	−	0.977087i	$-0.431729\pi$
$191$	5.88296	0.425676	0.212838	+	0.977087i	$0.431729\pi$
$192$	−1.27469	−0.0919927
$193$	−9.72489	−0.700013	−0.350007	−	0.936747i	$-0.613821\pi$
$193$	−9.72489	−0.700013	−0.350007	+	0.936747i	$0.613821\pi$
$194$	−11.7835	−0.846009
$195$	−4.92876	−0.352956
$196$	−7.35687	−0.525491
$197$	4.30533	0.306742	0.153371	−	0.988169i	$-0.450987\pi$
$197$	4.30533	0.306742	0.153371	+	0.988169i	$0.450987\pi$
$198$	5.09427	0.362034
$199$	14.3168	1.01489	0.507447	−	0.861683i	$-0.330589\pi$
$199$	14.3168	1.01489	0.507447	+	0.861683i	$0.330589\pi$
$200$	−11.0618	−0.782190
$201$	−7.15849	−0.504921
$202$	32.7603	2.30501
$203$	6.98376	0.490164
$204$	−2.47185	−0.173064
$205$	−14.2329	−0.994070
$206$	−17.9091	−1.24779
$207$	9.50792	0.660846
$208$	12.7787	0.886045
$209$	−5.60841	−0.387942
$210$	4.51408	0.311501
$211$	5.40071	0.371800	0.185900	−	0.982569i	$-0.440480\pi$
$211$	5.40071	0.371800	0.185900	+	0.982569i	$0.440480\pi$
$212$	18.9550	1.30184
$213$	−6.69891	−0.459002
$214$	−5.60644	−0.383249
$215$	37.0908	2.52957
$216$	3.12065	0.212333
$217$	−7.81320	−0.530394
$218$	24.1909	1.63841
$219$	1.74861	0.118160
$220$	−5.37706	−0.362521
$221$	9.66336	0.650028
$222$	0.891963	0.0598647
$223$	13.4911	0.903430	0.451715	−	0.892162i	$-0.350812\pi$
$223$	13.4911	0.903430	0.451715	+	0.892162i	$0.350812\pi$
$224$	−8.77218	−0.586116
$225$	−27.3680	−1.82454
$226$	26.3177	1.75063
$227$	−6.98068	−0.463324	−0.231662	−	0.972796i	$-0.574416\pi$
$227$	−6.98068	−0.463324	−0.231662	+	0.972796i	$0.574416\pi$
$228$	3.78348	0.250567
$229$	−20.3233	−1.34300	−0.671501	−	0.741003i	$-0.734350\pi$
$229$	−20.3233	−1.34300	−0.671501	+	0.741003i	$0.734350\pi$
$230$	−24.4426	−1.61170
$231$	−0.634934	−0.0417756
$232$	−5.95341	−0.390861
$233$	−26.1913	−1.71585	−0.857924	−	0.513777i	$-0.828246\pi$
$233$	−26.1913	−1.71585	−0.857924	+	0.513777i	$0.828246\pi$
$234$	13.4351	0.878277
$235$	21.7463	1.41857
$236$	−7.73013	−0.503189
$237$	−2.22139	−0.144295
$238$	−8.85034	−0.573682
$239$	2.24057	0.144930	0.0724652	−	0.997371i	$-0.476913\pi$
$239$	2.24057	0.144930	0.0724652	+	0.997371i	$0.476913\pi$
$240$	−9.05546	−0.584527
$241$	−1.11475	−0.0718074	−0.0359037	−	0.999355i	$-0.511431\pi$
$241$	−1.11475	−0.0718074	−0.0359037	+	0.999355i	$0.511431\pi$
$242$	1.84206	0.118412
$243$	11.7382	0.753003
$244$	4.85471	0.310791
$245$	−20.3808	−1.30208
$246$	−3.28931	−0.209718
$247$	−14.7910	−0.941127
$248$	6.66047	0.422940
$249$	−2.68929	−0.170427
$250$	34.8091	2.20152
$251$	−17.7940	−1.12314	−0.561572	−	0.827428i	$-0.689803\pi$
$251$	−17.7940	−1.12314	−0.561572	+	0.827428i	$0.689803\pi$
$252$	−5.05210	−0.318252
$253$	3.43801	0.216146
$254$	5.48365	0.344075
$255$	−6.84780	−0.428826
$256$	20.9790	1.31119
$257$	−14.7280	−0.918706	−0.459353	−	0.888254i	$-0.651919\pi$
$257$	−14.7280	−0.918706	−0.459353	+	0.888254i	$0.651919\pi$
$258$	8.57189	0.533663
$259$	1.31125	0.0814771
$260$	−14.1808	−0.879458
$261$	−14.7293	−0.911722
$262$	3.28515	0.202957
$263$	−31.0271	−1.91321	−0.956606	−	0.291384i	$-0.905884\pi$
$263$	−31.0271	−1.91321	−0.956606	+	0.291384i	$0.905884\pi$
$264$	0.541259	0.0333122
$265$	52.5113	3.22575
$266$	13.5465	0.830592
$267$	−0.417158	−0.0255296
$268$	−20.5961	−1.25811
$269$	26.9907	1.64565	0.822826	−	0.568294i	$-0.192396\pi$
$269$	26.9907	1.64565	0.822826	+	0.568294i	$0.192396\pi$
$270$	−19.8483	−1.20793
$271$	−2.81495	−0.170996	−0.0854980	−	0.996338i	$-0.527248\pi$
$271$	−2.81495	−0.170996	−0.0854980	+	0.996338i	$0.527248\pi$
$272$	17.7542	1.07651
$273$	−1.67450	−0.101346
$274$	2.36325	0.142769
$275$	−9.89613	−0.596759
$276$	−2.31931	−0.139606
$277$	15.6993	0.943277	0.471639	−	0.881792i	$-0.343663\pi$
$277$	15.6993	0.943277	0.471639	+	0.881792i	$0.343663\pi$
$278$	27.8453	1.67005
$279$	16.4787	0.986551
$280$	−5.65697	−0.338069
$281$	−29.4630	−1.75762	−0.878809	−	0.477174i	$-0.841661\pi$
$281$	−29.4630	−1.75762	−0.878809	+	0.477174i	$0.841661\pi$
$282$	5.02568	0.299275
$283$	23.9560	1.42403	0.712017	−	0.702162i	$-0.247782\pi$
$283$	23.9560	1.42403	0.712017	+	0.702162i	$0.247782\pi$
$284$	−19.2739	−1.14369
$285$	10.4814	0.620865
$286$	4.85804	0.287262
$287$	−4.83551	−0.285431
$288$	18.5012	1.09020
$289$	−3.57416	−0.210244
$290$	37.8656	2.22354
$291$	−3.09753	−0.181581
$292$	5.03103	0.294418
$293$	31.7889	1.85713	0.928565	−	0.371170i	$-0.121043\pi$
$293$	31.7889	1.85713	0.928565	+	0.371170i	$0.121043\pi$
$294$	−4.71012	−0.274700
$295$	−21.4149	−1.24682
$296$	−1.11779	−0.0649705
$297$	2.79179	0.161996
$298$	−1.91309	−0.110822
$299$	9.06702	0.524359
$300$	6.67601	0.385439
$301$	12.6013	0.726326
$302$	19.8098	1.13992
$303$	8.61168	0.494728
$304$	−27.1750	−1.55859
$305$	13.4491	0.770092
$306$	18.6661	1.06707
$307$	9.90557	0.565340	0.282670	−	0.959217i	$-0.408780\pi$
$307$	9.90557	0.565340	0.282670	+	0.959217i	$0.408780\pi$
$308$	−1.82681	−0.104092
$309$	−4.70776	−0.267815
$310$	−42.3627	−2.40604
$311$	−8.94592	−0.507277	−0.253638	−	0.967299i	$-0.581627\pi$
$311$	−8.94592	−0.507277	−0.253638	+	0.967299i	$0.581627\pi$
$312$	1.42746	0.0808138
$313$	21.5157	1.21614	0.608069	−	0.793884i	$-0.291945\pi$
$313$	21.5157	1.21614	0.608069	+	0.793884i	$0.291945\pi$
$314$	36.2228	2.04417
$315$	−13.9959	−0.788579
$316$	−6.39130	−0.359539
$317$	−3.20959	−0.180269	−0.0901344	−	0.995930i	$-0.528730\pi$
$317$	−3.20959	−0.180269	−0.0901344	+	0.995930i	$0.528730\pi$
$318$	12.1357	0.680534
$319$	−5.32604	−0.298201
$320$	−10.1601	−0.567966
$321$	−1.47376	−0.0822574
$322$	−8.30417	−0.462773
$323$	−20.5499	−1.14343
$324$	9.67530	0.537517
$325$	−26.0989	−1.44771
$326$	7.50926	0.415899
$327$	6.35904	0.351656
$328$	4.12210	0.227605
$329$	7.38811	0.407320
$330$	−3.44258	−0.189508
$331$	−14.1611	−0.778365	−0.389183	−	0.921161i	$-0.627242\pi$
$331$	−14.1611	−0.778365	−0.389183	+	0.921161i	$0.627242\pi$
$332$	−7.73751	−0.424651
$333$	−2.76553	−0.151550
$334$	−43.0394	−2.35501
$335$	−57.0577	−3.11740
$336$	−3.07652	−0.167838
$337$	−25.3424	−1.38049	−0.690243	−	0.723578i	$-0.742496\pi$
$337$	−25.3424	−1.38049	−0.690243	+	0.723578i	$0.742496\pi$
$338$	−11.1347	−0.605650
$339$	6.91811	0.375740
$340$	−19.7022	−1.06850
$341$	5.95859	0.322676
$342$	−28.5707	−1.54493
$343$	−16.1030	−0.869478
$344$	−10.7422	−0.579178
$345$	−6.42521	−0.345922
$346$	10.8377	0.582640
$347$	7.28692	0.391182	0.195591	−	0.980686i	$-0.437337\pi$
$347$	7.28692	0.391182	0.195591	+	0.980686i	$0.437337\pi$
$348$	3.59299	0.192604
$349$	8.28671	0.443577	0.221789	−	0.975095i	$-0.428810\pi$
$349$	8.28671	0.443577	0.221789	+	0.975095i	$0.428810\pi$
$350$	23.9031	1.27767
$351$	7.36275	0.392995
$352$	6.68994	0.356575
$353$	−5.80218	−0.308819	−0.154410	−	0.988007i	$-0.549348\pi$
$353$	−5.80218	−0.308819	−0.154410	+	0.988007i	$0.549348\pi$
$354$	−4.94910	−0.263042
$355$	−53.3946	−2.83389
$356$	−1.20023	−0.0636121
$357$	−2.32648	−0.123130
$358$	1.04684	0.0553272
$359$	18.0786	0.954150	0.477075	−	0.878863i	$-0.341697\pi$
$359$	18.0786	0.954150	0.477075	+	0.878863i	$0.341697\pi$
$360$	11.9310	0.628819
$361$	12.4542	0.655486
$362$	−10.7983	−0.567546
$363$	0.484221	0.0254150
$364$	−4.81782	−0.252522
$365$	13.9375	0.729523
$366$	3.10816	0.162466
$367$	22.0767	1.15239	0.576197	−	0.817311i	$-0.304536\pi$
$367$	22.0767	1.15239	0.576197	+	0.817311i	$0.304536\pi$
$368$	16.6586	0.868387
$369$	10.1985	0.530912
$370$	7.10952	0.369606
$371$	17.8403	0.926221
$372$	−4.01971	−0.208412
$373$	10.3260	0.534662	0.267331	−	0.963605i	$-0.413858\pi$
$373$	10.3260	0.534662	0.267331	+	0.963605i	$0.413858\pi$
$374$	6.74954	0.349011
$375$	9.15025	0.472517
$376$	−6.29810	−0.324800
$377$	−14.0463	−0.723421
$378$	−6.74329	−0.346837
$379$	6.05084	0.310811	0.155405	−	0.987851i	$-0.450332\pi$
$379$	6.05084	0.310811	0.155405	+	0.987851i	$0.450332\pi$
$380$	30.1567	1.54701
$381$	1.44148	0.0738494
$382$	10.8368	0.554457
$383$	−31.6319	−1.61632	−0.808158	−	0.588966i	$-0.799535\pi$
$383$	−31.6319	−1.61632	−0.808158	+	0.588966i	$0.799535\pi$
$384$	4.13077	0.210797
$385$	−5.06083	−0.257924
$386$	−17.9138	−0.911790
$387$	−26.5771	−1.35099
$388$	−8.91211	−0.452444
$389$	−32.7960	−1.66282	−0.831411	−	0.555657i	$-0.812467\pi$
$389$	−32.7960	−1.66282	−0.831411	+	0.555657i	$0.812467\pi$
$390$	−9.07906	−0.459736
$391$	12.5973	0.637073
$392$	5.90265	0.298129
$393$	0.863565	0.0435611
$394$	7.93067	0.399541
$395$	−17.7059	−0.890880
$396$	3.85289	0.193615
$397$	−27.7643	−1.39345	−0.696724	−	0.717339i	$-0.745360\pi$
$397$	−27.7643	−1.39345	−0.696724	+	0.717339i	$0.745360\pi$
$398$	26.3725	1.32193
$399$	3.56097	0.178272
$400$	−47.9508	−2.39754
$401$	5.35774	0.267553	0.133776	−	0.991012i	$-0.457290\pi$
$401$	5.35774	0.267553	0.133776	+	0.991012i	$0.457290\pi$
$402$	−13.1864	−0.657676
$403$	15.7145	0.782795
$404$	24.7772	1.23271
$405$	26.8036	1.33188
$406$	12.8645	0.638455
$407$	−1.00000	−0.0495682
$408$	1.98324	0.0981852
$409$	24.5713	1.21497	0.607487	−	0.794330i	$-0.292178\pi$
$409$	24.5713	1.21497	0.607487	+	0.794330i	$0.292178\pi$
$410$	−26.2179	−1.29481
$411$	0.621227	0.0306429
$412$	−13.5450	−0.667314
$413$	−7.27552	−0.358005
$414$	17.5142	0.860774
$415$	−21.4353	−1.05222
$416$	17.6433	0.865033
$417$	7.31968	0.358446
$418$	−10.3310	−0.505307
$419$	−26.4163	−1.29052	−0.645259	−	0.763964i	$-0.723251\pi$
$419$	−26.4163	−1.29052	−0.645259	+	0.763964i	$0.723251\pi$
$420$	3.41408	0.166590
$421$	−29.8840	−1.45645	−0.728227	−	0.685336i	$-0.759656\pi$
$421$	−29.8840	−1.45645	−0.728227	+	0.685336i	$0.759656\pi$
$422$	9.94842	0.484282
$423$	−15.5821	−0.757628
$424$	−15.2082	−0.738576
$425$	−36.2607	−1.75890
$426$	−12.3398	−0.597865
$427$	4.56921	0.221120
$428$	−4.24025	−0.204960
$429$	1.27703	0.0616555
$430$	68.3235	3.29485
$431$	−36.6860	−1.76710	−0.883551	−	0.468334i	$-0.844854\pi$
$431$	−36.6860	−1.76710	−0.883551	+	0.468334i	$0.844854\pi$
$432$	13.5274	0.650835
$433$	13.2112	0.634891	0.317446	−	0.948276i	$-0.397175\pi$
$433$	13.2112	0.634891	0.317446	+	0.948276i	$0.397175\pi$
$434$	−14.3924	−0.690856
$435$	9.95369	0.477243
$436$	18.2960	0.876219
$437$	−19.2818	−0.922372
$438$	3.22104	0.153907
$439$	−17.3258	−0.826916	−0.413458	−	0.910523i	$-0.635679\pi$
$439$	−17.3258	−0.826916	−0.413458	+	0.910523i	$0.635679\pi$
$440$	4.31418	0.205671
$441$	14.6037	0.695416
$442$	17.8005	0.846683
$443$	9.14251	0.434374	0.217187	−	0.976130i	$-0.430312\pi$
$443$	9.14251	0.434374	0.217187	+	0.976130i	$0.430312\pi$
$444$	0.674608	0.0320155
$445$	−3.32501	−0.157621
$446$	24.8514	1.17675
$447$	−0.502892	−0.0237860
$448$	−3.45180	−0.163082
$449$	12.3987	0.585133	0.292567	−	0.956245i	$-0.405491\pi$
$449$	12.3987	0.585133	0.292567	+	0.956245i	$0.405491\pi$
$450$	−50.4135	−2.37652
$451$	3.68771	0.173648
$452$	19.9045	0.936230
$453$	5.20738	0.244664
$454$	−12.8588	−0.603494
$455$	−13.3469	−0.625711
$456$	−3.03560	−0.142155
$457$	17.5987	0.823233	0.411617	−	0.911357i	$-0.364964\pi$
$457$	17.5987	0.823233	0.411617	+	0.911357i	$0.364964\pi$
$458$	−37.4368	−1.74931
$459$	10.2295	0.477471
$460$	−18.4864	−0.861932
$461$	29.4734	1.37271	0.686356	−	0.727266i	$-0.259209\pi$
$461$	29.4734	1.37271	0.686356	+	0.727266i	$0.259209\pi$
$462$	−1.16959	−0.0544141
$463$	29.6672	1.37875	0.689376	−	0.724404i	$-0.257885\pi$
$463$	29.6672	1.37875	0.689376	+	0.724404i	$0.257885\pi$
$464$	−25.8068	−1.19805
$465$	−11.1359	−0.516413
$466$	−48.2459	−2.23495
$467$	−15.3125	−0.708578	−0.354289	−	0.935136i	$-0.615277\pi$
$467$	−15.3125	−0.708578	−0.354289	+	0.935136i	$0.615277\pi$
$468$	10.1612	0.469700
$469$	−19.3849	−0.895111
$470$	40.0579	1.84773
$471$	9.52186	0.438744
$472$	6.20213	0.285476
$473$	−9.61014	−0.441875
$474$	−4.09193	−0.187949
$475$	55.5015	2.54658
$476$	−6.69367	−0.306804
$477$	−37.6266	−1.72280
$478$	4.12726	0.188777
$479$	−21.8748	−0.999485	−0.499743	−	0.866174i	$-0.666572\pi$
$479$	−21.8748	−0.999485	−0.499743	+	0.866174i	$0.666572\pi$
$480$	−12.5027	−0.570666
$481$	−2.63729	−0.120250
$482$	−2.05344	−0.0935315
$483$	−2.18291	−0.0993259
$484$	1.39318	0.0633265
$485$	−24.6893	−1.12108
$486$	21.6224	0.980811
$487$	−1.05908	−0.0479913	−0.0239957	−	0.999712i	$-0.507639\pi$
$487$	−1.05908	−0.0479913	−0.0239957	+	0.999712i	$0.507639\pi$
$488$	−3.89509	−0.176322
$489$	1.97395	0.0892652
$490$	−37.5427	−1.69601
$491$	0.620140	0.0279865	0.0139933	−	0.999902i	$-0.495546\pi$
$491$	0.620140	0.0279865	0.0139933	+	0.999902i	$0.495546\pi$
$492$	−2.48776	−0.112157
$493$	−19.5153	−0.878924
$494$	−27.2459	−1.22585
$495$	10.6737	0.479747
$496$	28.8718	1.29638
$497$	−18.1404	−0.813707
$498$	−4.95382	−0.221986
$499$	8.25081	0.369357	0.184678	−	0.982799i	$-0.440876\pi$
$499$	8.25081	0.369357	0.184678	+	0.982799i	$0.440876\pi$
$500$	26.3267	1.17737
$501$	−11.3137	−0.505460
$502$	−32.7775	−1.46293
$503$	−12.3662	−0.551383	−0.275691	−	0.961246i	$-0.588907\pi$
$503$	−12.3662	−0.551383	−0.275691	+	0.961246i	$0.588907\pi$
$504$	4.05346	0.180555
$505$	68.6406	3.05447
$506$	6.33302	0.281537
$507$	−2.92698	−0.129992
$508$	4.14738	0.184010
$509$	−29.1794	−1.29335	−0.646677	−	0.762764i	$-0.723842\pi$
$509$	−29.1794	−1.29335	−0.646677	+	0.762764i	$0.723842\pi$
$510$	−12.6141	−0.558560
$511$	4.73515	0.209471
$512$	21.5832	0.953850
$513$	−15.6575	−0.691295
$514$	−27.1298	−1.19664
$515$	−37.5238	−1.65350
$516$	6.48308	0.285402
$517$	−5.63440	−0.247801
$518$	2.41540	0.106127
$519$	2.84891	0.125053
$520$	11.3777	0.498947
$521$	−20.4023	−0.893842	−0.446921	−	0.894574i	$-0.647479\pi$
$521$	−20.4023	−0.893842	−0.446921	+	0.894574i	$0.647479\pi$
$522$	−27.1323	−1.18755
$523$	2.00405	0.0876308	0.0438154	−	0.999040i	$-0.486049\pi$
$523$	2.00405	0.0876308	0.0438154	+	0.999040i	$0.486049\pi$
$524$	2.48462	0.108541
$525$	6.28339	0.274230
$526$	−57.1537	−2.49202
$527$	21.8330	0.951062
$528$	2.34625	0.102107
$529$	−11.1801	−0.486091
$530$	96.7290	4.20164
$531$	15.3447	0.665901
$532$	10.2455	0.444199
$533$	9.72556	0.421261
$534$	−0.768429	−0.0332532
$535$	−11.7468	−0.507860
$536$	16.5249	0.713768
$537$	0.275182	0.0118750
$538$	49.7184	2.14351
$539$	5.28062	0.227453
$540$	−15.0116	−0.645997
$541$	−23.7311	−1.02028	−0.510139	−	0.860092i	$-0.670406\pi$
$541$	−23.7311	−1.02028	−0.510139	+	0.860092i	$0.670406\pi$
$542$	−5.18531	−0.222728
$543$	−2.83854	−0.121813
$544$	24.5128	1.05098
$545$	50.6856	2.17113
$546$	−3.08454	−0.132006
$547$	43.3990	1.85561	0.927804	−	0.373068i	$-0.121694\pi$
$547$	43.3990	1.85561	0.927804	+	0.373068i	$0.121694\pi$
$548$	1.78737	0.0763527
$549$	−9.63683	−0.411290
$550$	−18.2293	−0.777298
$551$	29.8706	1.27253
$552$	1.86085	0.0792032
$553$	−6.01543	−0.255802
$554$	28.9190	1.22865
$555$	1.86887	0.0793293
$556$	21.0599	0.893139
$557$	27.5822	1.16870	0.584348	−	0.811503i	$-0.301350\pi$
$557$	27.5822	1.16870	0.584348	+	0.811503i	$0.301350\pi$
$558$	30.3547	1.28502
$559$	−25.3447	−1.07197
$560$	−24.5218	−1.03624
$561$	1.77425	0.0749088
$562$	−54.2727	−2.28935
$563$	−5.70582	−0.240471	−0.120236	−	0.992745i	$-0.538365\pi$
$563$	−5.70582	−0.240471	−0.120236	+	0.992745i	$0.538365\pi$
$564$	3.80101	0.160052
$565$	55.1418	2.31983
$566$	44.1283	1.85485
$567$	9.10630	0.382429
$568$	15.4640	0.648856
$569$	8.74956	0.366801	0.183400	−	0.983038i	$-0.441290\pi$
$569$	8.74956	0.366801	0.183400	+	0.983038i	$0.441290\pi$
$570$	19.3074	0.808697
$571$	−1.24276	−0.0520077	−0.0260038	−	0.999662i	$-0.508278\pi$
$571$	−1.24276	−0.0520077	−0.0260038	+	0.999662i	$0.508278\pi$
$572$	3.67422	0.153627
$573$	2.84865	0.119004
$574$	−8.90730	−0.371784
$575$	−34.0230	−1.41886
$576$	7.28012	0.303338
$577$	24.4029	1.01591	0.507954	−	0.861384i	$-0.330402\pi$
$577$	24.4029	1.01591	0.507954	+	0.861384i	$0.330402\pi$
$578$	−6.58381	−0.273850
$579$	−4.70900	−0.195699
$580$	28.6384	1.18915
$581$	−7.28247	−0.302128
$582$	−5.70584	−0.236515
$583$	−13.6056	−0.563485
$584$	−4.03655	−0.167034
$585$	28.1496	1.16384
$586$	58.5571	2.41897
$587$	−27.1839	−1.12200	−0.561000	−	0.827816i	$-0.689583\pi$
$587$	−27.1839	−1.12200	−0.561000	+	0.827816i	$0.689583\pi$
$588$	−3.56235	−0.146909
$589$	−33.4182	−1.37697
$590$	−39.4475	−1.62403
$591$	2.08473	0.0857543
$592$	−4.84541	−0.199145
$593$	24.8464	1.02032	0.510160	−	0.860079i	$-0.329586\pi$
$593$	24.8464	1.02032	0.510160	+	0.860079i	$0.329586\pi$
$594$	5.14264	0.211005
$595$	−18.5435	−0.760211
$596$	−1.44690	−0.0592675
$597$	6.93251	0.283729
$598$	16.7020	0.682995
$599$	−8.27982	−0.338304	−0.169152	−	0.985590i	$-0.554103\pi$
$599$	−8.27982	−0.338304	−0.169152	+	0.985590i	$0.554103\pi$
$600$	−5.35637	−0.218673
$601$	19.2221	0.784087	0.392044	−	0.919947i	$-0.371768\pi$
$601$	19.2221	0.784087	0.392044	+	0.919947i	$0.371768\pi$
$602$	23.2123	0.946064
$603$	40.8843	1.66494
$604$	14.9825	0.609628
$605$	3.85955	0.156913
$606$	15.8632	0.644400
$607$	−7.37733	−0.299436	−0.149718	−	0.988729i	$-0.547837\pi$
$607$	−7.37733	−0.299436	−0.149718	+	0.988729i	$0.547837\pi$
$608$	−37.5199	−1.52163
$609$	3.38168	0.137033
$610$	24.7740	1.00307
$611$	−14.8595	−0.601153
$612$	14.1175	0.570665
$613$	−1.26623	−0.0511424	−0.0255712	−	0.999673i	$-0.508140\pi$
$613$	−1.26623	−0.0511424	−0.0255712	+	0.999673i	$0.508140\pi$
$614$	18.2466	0.736374
$615$	−6.89187	−0.277907
$616$	1.46571	0.0590550
$617$	−43.7703	−1.76213	−0.881063	−	0.473000i	$-0.843171\pi$
$617$	−43.7703	−1.76213	−0.881063	+	0.473000i	$0.843171\pi$
$618$	−8.67197	−0.348838
$619$	25.9756	1.04405	0.522024	−	0.852931i	$-0.325177\pi$
$619$	25.9756	1.04405	0.522024	+	0.852931i	$0.325177\pi$
$620$	−32.0397	−1.28674
$621$	9.59820	0.385162
$622$	−16.4789	−0.660745
$623$	−1.12965	−0.0452583
$624$	6.18773	0.247707
$625$	23.4527	0.938107
$626$	39.6331	1.58406
$627$	−2.71571	−0.108455
$628$	27.3959	1.09322
$629$	−3.66413	−0.146098
$630$	−25.7813	−1.02715
$631$	10.4115	0.414475	0.207237	−	0.978291i	$-0.433553\pi$
$631$	10.4115	0.414475	0.207237	+	0.978291i	$0.433553\pi$
$632$	5.12794	0.203978
$633$	2.61513	0.103942
$634$	−5.91226	−0.234806
$635$	11.4895	0.455948
$636$	9.17842	0.363948
$637$	13.9265	0.551789
$638$	−9.81088	−0.388416
$639$	38.2595	1.51352
$640$	32.9249	1.30147
$641$	30.0314	1.18617	0.593085	−	0.805140i	$-0.297910\pi$
$641$	30.0314	1.18617	0.593085	+	0.805140i	$0.297910\pi$
$642$	−2.71476	−0.107143
$643$	33.6215	1.32590	0.662952	−	0.748662i	$-0.269303\pi$
$643$	33.6215	1.32590	0.662952	+	0.748662i	$0.269303\pi$
$644$	−6.28059	−0.247490
$645$	17.9601	0.707180
$646$	−37.8542	−1.48935
$647$	−30.8163	−1.21152	−0.605758	−	0.795649i	$-0.707130\pi$
$647$	−30.8163	−1.21152	−0.605758	+	0.795649i	$0.707130\pi$
$648$	−7.76280	−0.304951
$649$	5.54854	0.217799
$650$	−48.0758	−1.88569
$651$	−3.78331	−0.148280
$652$	5.67938	0.222422
$653$	19.5068	0.763360	0.381680	−	0.924295i	$-0.375346\pi$
$653$	19.5068	0.763360	0.381680	+	0.924295i	$0.375346\pi$
$654$	11.7137	0.458043
$655$	6.88317	0.268948
$656$	17.8685	0.697647
$657$	−9.98681	−0.389623
$658$	13.6093	0.530547
$659$	2.86528	0.111616	0.0558078	−	0.998442i	$-0.482227\pi$
$659$	2.86528	0.111616	0.0558078	+	0.998442i	$0.482227\pi$
$660$	−2.60368	−0.101348
$661$	32.0429	1.24632	0.623162	−	0.782093i	$-0.285848\pi$
$661$	32.0429	1.24632	0.623162	+	0.782093i	$0.285848\pi$
$662$	−26.0856	−1.01385
$663$	4.67920	0.181725
$664$	6.20805	0.240919
$665$	28.3832	1.10065
$666$	−5.09427	−0.197399
$667$	−18.3110	−0.709003
$668$	−32.5515	−1.25945
$669$	6.53267	0.252567
$670$	−105.104	−4.06051
$671$	−3.48462	−0.134522
$672$	−4.24767	−0.163858
$673$	15.0289	0.579323	0.289661	−	0.957129i	$-0.406457\pi$
$673$	15.0289	0.579323	0.289661	+	0.957129i	$0.406457\pi$
$674$	−46.6821	−1.79813
$675$	−27.6279	−1.06340
$676$	−8.42140	−0.323900
$677$	16.8815	0.648808	0.324404	−	0.945919i	$-0.394836\pi$
$677$	16.8815	0.648808	0.324404	+	0.945919i	$0.394836\pi$
$678$	12.7436	0.489414
$679$	−8.38799	−0.321901
$680$	15.8077	0.606198
$681$	−3.38019	−0.129529
$682$	10.9761	0.420295
$683$	41.9823	1.60641	0.803204	−	0.595704i	$-0.203127\pi$
$683$	41.9823	1.60641	0.803204	+	0.595704i	$0.203127\pi$
$684$	−21.6086	−0.826224
$685$	4.95158	0.189190
$686$	−29.6626	−1.13252
$687$	−9.84098	−0.375457
$688$	−46.5650	−1.77528
$689$	−35.8818	−1.36699
$690$	−11.8356	−0.450574
$691$	−44.1075	−1.67793	−0.838965	−	0.544185i	$-0.816839\pi$
$691$	−44.1075	−1.67793	−0.838965	+	0.544185i	$0.816839\pi$
$692$	8.19677	0.311594
$693$	3.62630	0.137752
$694$	13.4229	0.509528
$695$	58.3425	2.21306
$696$	−2.88277	−0.109271
$697$	13.5123	0.511813
$698$	15.2646	0.577774
$699$	−12.6824	−0.479691
$700$	18.0783	0.683297
$701$	−18.2067	−0.687656	−0.343828	−	0.939033i	$-0.611724\pi$
$701$	−18.2067	−0.687656	−0.343828	+	0.939033i	$0.611724\pi$
$702$	13.5626	0.511888
$703$	5.60841	0.211525
$704$	2.63245	0.0992142
$705$	10.5300	0.396583
$706$	−10.6880	−0.402247
$707$	23.3201	0.877042
$708$	−3.74309	−0.140674
$709$	−29.2761	−1.09949	−0.549744	−	0.835333i	$-0.685275\pi$
$709$	−29.2761	−1.09949	−0.549744	+	0.835333i	$0.685275\pi$
$710$	−98.3561	−3.69124
$711$	12.6870	0.475800
$712$	0.962982	0.0360893
$713$	20.4857	0.767195
$714$	−4.28552	−0.160381
$715$	10.1787	0.380663
$716$	0.791744	0.0295889
$717$	1.08493	0.0405175
$718$	33.3018	1.24281
$719$	26.7605	0.997999	0.499000	−	0.866602i	$-0.333701\pi$
$719$	26.7605	0.997999	0.499000	+	0.866602i	$0.333701\pi$
$720$	51.7184	1.92743
$721$	−12.7484	−0.474776
$722$	22.9414	0.853792
$723$	−0.539786	−0.0200748
$724$	−8.16694	−0.303522
$725$	52.7071	1.95749
$726$	0.891963	0.0331039
$727$	−18.0734	−0.670305	−0.335153	−	0.942164i	$-0.608788\pi$
$727$	−18.0734	−0.670305	−0.335153	+	0.942164i	$0.608788\pi$
$728$	3.86549	0.143265
$729$	−15.1504	−0.561125
$730$	25.6737	0.950227
$731$	−35.2128	−1.30239
$732$	2.35075	0.0868864
$733$	−44.6395	−1.64880	−0.824398	−	0.566010i	$-0.808486\pi$
$733$	−44.6395	−1.64880	−0.824398	+	0.566010i	$0.808486\pi$
$734$	40.6666	1.50103
$735$	−9.86882	−0.364017
$736$	23.0001	0.847794
$737$	14.7835	0.544558
$738$	18.7862	0.691530
$739$	−45.1565	−1.66111	−0.830555	−	0.556937i	$-0.811977\pi$
$739$	−45.1565	−1.66111	−0.830555	+	0.556937i	$0.811977\pi$
$740$	5.37706	0.197665
$741$	−7.16210	−0.263106
$742$	32.8629	1.20643
$743$	−24.8830	−0.912869	−0.456434	−	0.889757i	$-0.650874\pi$
$743$	−24.8830	−0.912869	−0.456434	+	0.889757i	$0.650874\pi$
$744$	3.22514	0.118239
$745$	−4.00837	−0.146855
$746$	19.0212	0.696414
$747$	15.3593	0.561968
$748$	5.10480	0.186650
$749$	−3.99088	−0.145824
$750$	16.8553	0.615468
$751$	−13.7287	−0.500968	−0.250484	−	0.968121i	$-0.580590\pi$
$751$	−13.7287	−0.500968	−0.250484	+	0.968121i	$0.580590\pi$
$752$	−27.3010	−0.995565
$753$	−8.61621	−0.313992
$754$	−25.8741	−0.942279
$755$	41.5061	1.51056
$756$	−5.10007	−0.185488
$757$	−42.7495	−1.55376	−0.776878	−	0.629651i	$-0.783198\pi$
$757$	−42.7495	−1.55376	−0.776878	+	0.629651i	$0.783198\pi$
$758$	11.1460	0.404841
$759$	1.66476	0.0604268
$760$	−24.1957	−0.877670
$761$	3.99083	0.144667	0.0723337	−	0.997380i	$-0.476955\pi$
$761$	3.99083	0.144667	0.0723337	+	0.997380i	$0.476955\pi$
$762$	2.65530	0.0961912
$763$	17.2200	0.623406
$764$	8.19604	0.296522
$765$	39.1098	1.41402
$766$	−58.2679	−2.10530
$767$	14.6331	0.528370
$768$	10.1585	0.366563
$769$	−25.3799	−0.915223	−0.457612	−	0.889152i	$-0.651295\pi$
$769$	−25.3799	−0.915223	−0.457612	+	0.889152i	$0.651295\pi$
$770$	−9.32236	−0.335954
$771$	−7.13159	−0.256838
$772$	−13.5486	−0.487623
$773$	−22.7965	−0.819935	−0.409967	−	0.912100i	$-0.634460\pi$
$773$	−22.7965	−0.819935	−0.409967	+	0.912100i	$0.634460\pi$
$774$	−48.9566	−1.75971
$775$	−58.9669	−2.11815
$776$	7.15046	0.256687
$777$	0.634934	0.0227781
$778$	−60.4122	−2.16588
$779$	−20.6822	−0.741017
$780$	−6.86666	−0.245866
$781$	13.8344	0.495034
$782$	23.2050	0.829809
$783$	−14.8692	−0.531381
$784$	25.5868	0.913813
$785$	75.8953	2.70882
$786$	1.59074	0.0567397
$787$	−36.1220	−1.28761	−0.643806	−	0.765189i	$-0.722646\pi$
$787$	−36.1220	−1.28761	−0.643806	+	0.765189i	$0.722646\pi$
$788$	5.99810	0.213674
$789$	−15.0240	−0.534867
$790$	−32.6153	−1.16040
$791$	18.7340	0.666103
$792$	−3.09129	−0.109844
$793$	−9.18995	−0.326345
$794$	−51.1434	−1.81501
$795$	25.4271	0.901806
$796$	19.9460	0.706966
$797$	−11.0295	−0.390683	−0.195342	−	0.980735i	$-0.562582\pi$
$797$	−11.0295	−0.390683	−0.195342	+	0.980735i	$0.562582\pi$
$798$	6.55952	0.232204
$799$	−20.6452	−0.730374
$800$	−66.2045	−2.34068
$801$	2.38251	0.0841819
$802$	9.86927	0.348496
$803$	−3.61117	−0.127436
$804$	−9.97308	−0.351723
$805$	−17.3992	−0.613241
$806$	28.9470	1.01962
$807$	13.0695	0.460067
$808$	−19.8795	−0.699360
$809$	−22.7689	−0.800513	−0.400256	−	0.916403i	$-0.631079\pi$
$809$	−22.7689	−0.800513	−0.400256	+	0.916403i	$0.631079\pi$
$810$	49.3738	1.73482
$811$	−38.7889	−1.36206	−0.681031	−	0.732254i	$-0.738468\pi$
$811$	−38.7889	−1.36206	−0.681031	+	0.732254i	$0.738468\pi$
$812$	9.72966	0.341444
$813$	−1.36306	−0.0478045
$814$	−1.84206	−0.0645641
$815$	15.7337	0.551126
$816$	8.59695	0.300954
$817$	53.8976	1.88564
$818$	45.2618	1.58254
$819$	9.56359	0.334179
$820$	−19.8290	−0.692460
$821$	−14.7575	−0.515039	−0.257519	−	0.966273i	$-0.582905\pi$
$821$	−14.7575	−0.515039	−0.257519	+	0.966273i	$0.582905\pi$
$822$	1.14434	0.0399133
$823$	25.3198	0.882592	0.441296	−	0.897362i	$-0.354519\pi$
$823$	25.3198	0.882592	0.441296	+	0.897362i	$0.354519\pi$
$824$	10.8676	0.378590
$825$	−4.79191	−0.166833
$826$	−13.4019	−0.466313
$827$	37.9385	1.31925	0.659625	−	0.751595i	$-0.270715\pi$
$827$	37.9385	1.31925	0.659625	+	0.751595i	$0.270715\pi$
$828$	13.2463	0.460340
$829$	4.65975	0.161840	0.0809199	−	0.996721i	$-0.474214\pi$
$829$	4.65975	0.161840	0.0809199	+	0.996721i	$0.474214\pi$
$830$	−39.4851	−1.37055
$831$	7.60191	0.263707
$832$	6.94253	0.240689
$833$	19.3489	0.670399
$834$	13.4833	0.466888
$835$	−90.1777	−3.12073
$836$	−7.81353	−0.270237
$837$	16.6351	0.574994
$838$	−48.6603	−1.68094
$839$	−28.6686	−0.989751	−0.494876	−	0.868964i	$-0.664786\pi$
$839$	−28.6686	−0.989751	−0.494876	+	0.868964i	$0.664786\pi$
$840$	−2.73922	−0.0945122
$841$	−0.633330	−0.0218390
$842$	−55.0480	−1.89708
$843$	−14.2666	−0.491368
$844$	7.52417	0.258993
$845$	−23.3299	−0.802573
$846$	−28.7032	−0.986836
$847$	1.31125	0.0450551
$848$	−65.9245	−2.26386
$849$	11.6000	0.398110
$850$	−66.7943	−2.29103
$851$	−3.43801	−0.117853
$852$	−9.33281	−0.319737
$853$	34.2772	1.17363	0.586815	−	0.809721i	$-0.300382\pi$
$853$	34.2772	1.17363	0.586815	+	0.809721i	$0.300382\pi$
$854$	8.41676	0.288015
$855$	−59.8625	−2.04725
$856$	3.40209	0.116281
$857$	35.1523	1.20078	0.600391	−	0.799707i	$-0.295012\pi$
$857$	35.1523	1.20078	0.600391	+	0.799707i	$0.295012\pi$
$858$	2.35236	0.0803084
$859$	46.6399	1.59133	0.795666	−	0.605736i	$-0.207121\pi$
$859$	46.6399	1.59133	0.795666	+	0.605736i	$0.207121\pi$
$860$	51.6743	1.76208
$861$	−2.34146	−0.0797966
$862$	−67.5778	−2.30171
$863$	−19.5035	−0.663906	−0.331953	−	0.943296i	$-0.607708\pi$
$863$	−19.5035	−0.663906	−0.331953	+	0.943296i	$0.607708\pi$
$864$	18.6769	0.635401
$865$	22.7076	0.772082
$866$	24.3359	0.826966
$867$	−1.73068	−0.0587770
$868$	−10.8852	−0.369468
$869$	4.58755	0.155622
$870$	18.3353	0.621625
$871$	38.9884	1.32107
$872$	−14.6794	−0.497109
$873$	17.6909	0.598747
$874$	−35.5181	−1.20142
$875$	24.7785	0.837665
$876$	2.43613	0.0823091
$877$	−41.3214	−1.39532	−0.697662	−	0.716427i	$-0.745776\pi$
$877$	−41.3214	−1.39532	−0.697662	+	0.716427i	$0.745776\pi$
$878$	−31.9152	−1.07709
$879$	15.3929	0.519189
$880$	18.7011	0.630414
$881$	11.3842	0.383544	0.191772	−	0.981440i	$-0.438577\pi$
$881$	11.3842	0.383544	0.191772	+	0.981440i	$0.438577\pi$
$882$	26.9009	0.905801
$883$	23.3435	0.785571	0.392786	−	0.919630i	$-0.371511\pi$
$883$	23.3435	0.785571	0.392786	+	0.919630i	$0.371511\pi$
$884$	13.4628	0.452804
$885$	−10.3695	−0.348568
$886$	16.8410	0.565786
$887$	12.8386	0.431076	0.215538	−	0.976495i	$-0.430849\pi$
$887$	12.8386	0.431076	0.215538	+	0.976495i	$0.430849\pi$
$888$	−0.541259	−0.0181635
$889$	3.90347	0.130918
$890$	−6.12487	−0.205306
$891$	−6.94475	−0.232658
$892$	18.7955	0.629321
$893$	31.6000	1.05745
$894$	−0.926357	−0.0309820
$895$	2.19338	0.0733165
$896$	11.1859	0.373696
$897$	4.39044	0.146592
$898$	22.8392	0.762155
$899$	−31.7357	−1.05844
$900$	−38.1287	−1.27096
$901$	−49.8525	−1.66083
$902$	6.79299	0.226182
$903$	6.10181	0.203055
$904$	−15.9700	−0.531155
$905$	−22.6250	−0.752080
$906$	9.59230	0.318683
$907$	2.21611	0.0735847	0.0367924	−	0.999323i	$-0.488286\pi$
$907$	2.21611	0.0735847	0.0367924	+	0.999323i	$0.488286\pi$
$908$	−9.72536	−0.322747
$909$	−49.1839	−1.63133
$910$	−24.5857	−0.815009
$911$	−18.9108	−0.626542	−0.313271	−	0.949664i	$-0.601425\pi$
$911$	−18.9108	−0.626542	−0.313271	+	0.949664i	$0.601425\pi$
$912$	−13.1587	−0.435728
$913$	5.55384	0.183805
$914$	32.4179	1.07229
$915$	6.51232	0.215291
$916$	−28.3141	−0.935524
$917$	2.33850	0.0772240
$918$	18.8433	0.621922
$919$	22.9014	0.755446	0.377723	−	0.925919i	$-0.376707\pi$
$919$	22.9014	0.755446	0.377723	+	0.925919i	$0.376707\pi$
$920$	14.8322	0.489003
$921$	4.79648	0.158049
$922$	54.2917	1.78800
$923$	36.4853	1.20093
$924$	−0.884579	−0.0291005
$925$	9.89613	0.325383
$926$	54.6488	1.79587
$927$	26.8874	0.883098
$928$	−35.6309	−1.16964
$929$	11.8097	0.387464	0.193732	−	0.981055i	$-0.437941\pi$
$929$	11.8097	0.387464	0.193732	+	0.981055i	$0.437941\pi$
$930$	−20.5129	−0.672644
$931$	−29.6159	−0.970622
$932$	−36.4892	−1.19524
$933$	−4.33180	−0.141817
$934$	−28.2065	−0.922946
$935$	14.1419	0.462489
$936$	−8.15263	−0.266477
$937$	52.3679	1.71078	0.855392	−	0.517981i	$-0.173316\pi$
$937$	52.3679	1.71078	0.855392	+	0.517981i	$0.173316\pi$
$938$	−35.7081	−1.16591
$939$	10.4183	0.339989
$940$	30.2965	0.988163
$941$	9.75836	0.318113	0.159057	−	0.987269i	$-0.449155\pi$
$941$	9.75836	0.318113	0.159057	+	0.987269i	$0.449155\pi$
$942$	17.5398	0.571478
$943$	12.6784	0.412865
$944$	26.8849	0.875030
$945$	−14.1288	−0.459609
$946$	−17.7024	−0.575556
$947$	−20.5181	−0.666749	−0.333374	−	0.942795i	$-0.608187\pi$
$947$	−20.5181	−0.666749	−0.333374	+	0.942795i	$0.608187\pi$
$948$	−3.09480	−0.100514
$949$	−9.52370	−0.309152
$950$	102.237	3.31701
$951$	−1.55415	−0.0503969
$952$	5.37054	0.174060
$953$	7.26717	0.235407	0.117703	−	0.993049i	$-0.462447\pi$
$953$	7.26717	0.235407	0.117703	+	0.993049i	$0.462447\pi$
$954$	−69.3104	−2.24401
$955$	22.7056	0.734736
$956$	3.12152	0.100957
$957$	−2.57898	−0.0833665
$958$	−40.2947	−1.30186
$959$	1.68226	0.0543229
$960$	−4.91972	−0.158783
$961$	4.50476	0.145315
$962$	−4.85804	−0.156629
$963$	8.41709	0.271237
$964$	−1.55305	−0.0500204
$965$	−37.5337	−1.20825
$966$	−4.02105	−0.129375
$967$	−10.0241	−0.322353	−0.161177	−	0.986926i	$-0.551529\pi$
$967$	−10.0241	−0.322353	−0.161177	+	0.986926i	$0.551529\pi$
$968$	−1.11779	−0.0359273
$969$	−9.95070	−0.319663
$970$	−45.4792	−1.46025
$971$	29.8941	0.959347	0.479674	−	0.877447i	$-0.340755\pi$
$971$	29.8941	0.959347	0.479674	+	0.877447i	$0.340755\pi$
$972$	16.3534	0.524536
$973$	19.8214	0.635445
$974$	−1.95088	−0.0625103
$975$	−12.6376	−0.404728
$976$	−16.8844	−0.540457
$977$	33.5928	1.07473	0.537365	−	0.843350i	$-0.319420\pi$
$977$	33.5928	1.07473	0.537365	+	0.843350i	$0.319420\pi$
$978$	3.63614	0.116271
$979$	0.861503	0.0275337
$980$	−28.3942	−0.907020
$981$	−36.3184	−1.15956
$982$	1.14233	0.0364533
$983$	−24.1495	−0.770249	−0.385125	−	0.922865i	$-0.625842\pi$
$983$	−24.1495	−0.770249	−0.385125	+	0.922865i	$0.625842\pi$
$984$	1.99601	0.0636304
$985$	16.6166	0.529450
$986$	−35.9483	−1.14483
$987$	3.57748	0.113872
$988$	−20.6065	−0.655581
$989$	−33.0397	−1.05060
$990$	19.6616	0.624886
$991$	8.06891	0.256317	0.128159	−	0.991754i	$-0.459093\pi$
$991$	8.06891	0.256317	0.128159	+	0.991754i	$0.459093\pi$
$992$	39.8626	1.26564
$993$	−6.85711	−0.217604
$994$	−33.4156	−1.05988
$995$	55.2565	1.75175
$996$	−3.74666	−0.118718
$997$	28.9370	0.916443	0.458222	−	0.888838i	$-0.348487\pi$
$997$	28.9370	0.916443	0.458222	+	0.888838i	$0.348487\pi$
$998$	15.1985	0.481099
$999$	−2.79179	−0.0883283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	407.2.a.c.1.8	✓	11
3.2	odd	2		3663.2.a.u.1.4		11
4.3	odd	2		6512.2.a.bb.1.6		11
11.10	odd	2		4477.2.a.k.1.4		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
407.2.a.c.1.8	✓	11	1.1	even	1	trivial
3663.2.a.u.1.4		11	3.2	odd	2
4477.2.a.k.1.4		11	11.10	odd	2
6512.2.a.bb.1.6		11	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 407 = 11 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	407.a (trivial)

\(f(q)\)	\(=\)	\(q+1.84206 q^{2} +0.484221 q^{3} +1.39318 q^{4} +3.85955 q^{5} +0.891963 q^{6} +1.31125 q^{7} -1.11779 q^{8} -2.76553 q^{9} +O(q^{10})\)	\(q+1.84206 q^{2} +0.484221 q^{3} +1.39318 q^{4} +3.85955 q^{5} +0.891963 q^{6} +1.31125 q^{7} -1.11779 q^{8} -2.76553 q^{9} +7.10952 q^{10} -1.00000 q^{11} +0.674608 q^{12} -2.63729 q^{13} +2.41540 q^{14} +1.86887 q^{15} -4.84541 q^{16} -3.66413 q^{17} -5.09427 q^{18} +5.60841 q^{19} +5.37706 q^{20} +0.634934 q^{21} -1.84206 q^{22} -3.43801 q^{23} -0.541259 q^{24} +9.89613 q^{25} -4.85804 q^{26} -2.79179 q^{27} +1.82681 q^{28} +5.32604 q^{29} +3.44258 q^{30} -5.95859 q^{31} -6.68994 q^{32} -0.484221 q^{33} -6.74954 q^{34} +5.06083 q^{35} -3.85289 q^{36} +1.00000 q^{37} +10.3310 q^{38} -1.27703 q^{39} -4.31418 q^{40} -3.68771 q^{41} +1.16959 q^{42} +9.61014 q^{43} -1.39318 q^{44} -10.6737 q^{45} -6.33302 q^{46} +5.63440 q^{47} -2.34625 q^{48} -5.28062 q^{49} +18.2293 q^{50} -1.77425 q^{51} -3.67422 q^{52} +13.6056 q^{53} -5.14264 q^{54} -3.85955 q^{55} -1.46571 q^{56} +2.71571 q^{57} +9.81088 q^{58} -5.54854 q^{59} +2.60368 q^{60} +3.48462 q^{61} -10.9761 q^{62} -3.62630 q^{63} -2.63245 q^{64} -10.1787 q^{65} -0.891963 q^{66} -14.7835 q^{67} -5.10480 q^{68} -1.66476 q^{69} +9.32236 q^{70} -13.8344 q^{71} +3.09129 q^{72} +3.61117 q^{73} +1.84206 q^{74} +4.79191 q^{75} +7.81353 q^{76} -1.31125 q^{77} -2.35236 q^{78} -4.58755 q^{79} -18.7011 q^{80} +6.94475 q^{81} -6.79299 q^{82} -5.55384 q^{83} +0.884579 q^{84} -14.1419 q^{85} +17.7024 q^{86} +2.57898 q^{87} +1.11779 q^{88} -0.861503 q^{89} -19.6616 q^{90} -3.45814 q^{91} -4.78977 q^{92} -2.88527 q^{93} +10.3789 q^{94} +21.6459 q^{95} -3.23941 q^{96} -6.39694 q^{97} -9.72722 q^{98} +2.76553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} + 14 q^{4} + q^{5} + 4 q^{6} + 9 q^{7} + 15 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 + 14 * q^4 + q^5 + 4 * q^6 + 9 * q^7 + 15 * q^9	\( 11 q + 2 q^{2} + 14 q^{4} + q^{5} + 4 q^{6} + 9 q^{7} + 15 q^{9} + 5 q^{10} - 11 q^{11} + q^{12} + 22 q^{13} + 3 q^{14} - 10 q^{15} + 19 q^{17} + 18 q^{18} + 14 q^{19} + 6 q^{20} - 13 q^{21} - 2 q^{22} - 14 q^{23} - 11 q^{24} + 38 q^{25} - 10 q^{26} - 9 q^{27} + q^{28} + 13 q^{29} + 19 q^{30} + 12 q^{31} - 3 q^{32} + q^{34} + 12 q^{35} + 18 q^{36} + 11 q^{37} - 31 q^{38} - 8 q^{39} + 22 q^{40} + 8 q^{41} + 15 q^{42} + 21 q^{43} - 14 q^{44} - 8 q^{45} - 45 q^{46} - 14 q^{47} - 37 q^{48} + 20 q^{49} - 41 q^{50} - 2 q^{51} + 51 q^{52} - 2 q^{53} + 6 q^{54} - q^{55} - 22 q^{56} - 3 q^{57} + 15 q^{58} - 30 q^{59} - 107 q^{60} + 20 q^{61} + 22 q^{62} + 31 q^{63} - 14 q^{64} - 4 q^{66} + 7 q^{67} + 24 q^{68} + 9 q^{69} - 86 q^{70} - 15 q^{71} - 7 q^{72} + 47 q^{73} + 2 q^{74} - 40 q^{75} + 6 q^{76} - 9 q^{77} - 42 q^{78} + 2 q^{79} + 3 q^{80} - 17 q^{81} - 54 q^{82} + 24 q^{83} - 33 q^{84} - 25 q^{85} - 13 q^{86} + 21 q^{87} + 4 q^{89} - 107 q^{90} + 21 q^{91} - 46 q^{92} - 37 q^{93} + 3 q^{94} - 36 q^{95} - 49 q^{96} + 25 q^{97} - 52 q^{98} - 15 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 + 14 * q^4 + q^5 + 4 * q^6 + 9 * q^7 + 15 * q^9 + 5 * q^10 - 11 * q^11 + q^12 + 22 * q^13 + 3 * q^14 - 10 * q^15 + 19 * q^17 + 18 * q^18 + 14 * q^19 + 6 * q^20 - 13 * q^21 - 2 * q^22 - 14 * q^23 - 11 * q^24 + 38 * q^25 - 10 * q^26 - 9 * q^27 + q^28 + 13 * q^29 + 19 * q^30 + 12 * q^31 - 3 * q^32 + q^34 + 12 * q^35 + 18 * q^36 + 11 * q^37 - 31 * q^38 - 8 * q^39 + 22 * q^40 + 8 * q^41 + 15 * q^42 + 21 * q^43 - 14 * q^44 - 8 * q^45 - 45 * q^46 - 14 * q^47 - 37 * q^48 + 20 * q^49 - 41 * q^50 - 2 * q^51 + 51 * q^52 - 2 * q^53 + 6 * q^54 - q^55 - 22 * q^56 - 3 * q^57 + 15 * q^58 - 30 * q^59 - 107 * q^60 + 20 * q^61 + 22 * q^62 + 31 * q^63 - 14 * q^64 - 4 * q^66 + 7 * q^67 + 24 * q^68 + 9 * q^69 - 86 * q^70 - 15 * q^71 - 7 * q^72 + 47 * q^73 + 2 * q^74 - 40 * q^75 + 6 * q^76 - 9 * q^77 - 42 * q^78 + 2 * q^79 + 3 * q^80 - 17 * q^81 - 54 * q^82 + 24 * q^83 - 33 * q^84 - 25 * q^85 - 13 * q^86 + 21 * q^87 + 4 * q^89 - 107 * q^90 + 21 * q^91 - 46 * q^92 - 37 * q^93 + 3 * q^94 - 36 * q^95 - 49 * q^96 + 25 * q^97 - 52 * q^98 - 15 * q^99

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