LMFDB - Embedded newform 946.2.a.k.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(1,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, 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("946.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 11x^{5} + 31x^{4} + 39x^{3} - 91x^{2} - 48x + 64 $ x^7 - 3x^6 - 11x^5 + 31x^4 + 39x^3 - 91x^2 - 48x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.750731$ of defining polynomial
Character	$\chi$	$=$	946.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.750731 q^{3} +1.00000 q^{4} +1.13207 q^{5} +0.750731 q^{6} +2.59042 q^{7} +1.00000 q^{8} -2.43640 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.750731 q^{3} +1.00000 q^{4} +1.13207 q^{5} +0.750731 q^{6} +2.59042 q^{7} +1.00000 q^{8} -2.43640 q^{9} +1.13207 q^{10} +1.00000 q^{11} +0.750731 q^{12} +2.41019 q^{13} +2.59042 q^{14} +0.849880 q^{15} +1.00000 q^{16} -0.909012 q^{17} -2.43640 q^{18} +2.74013 q^{19} +1.13207 q^{20} +1.94471 q^{21} +1.00000 q^{22} -4.60483 q^{23} +0.750731 q^{24} -3.71842 q^{25} +2.41019 q^{26} -4.08128 q^{27} +2.59042 q^{28} +8.84253 q^{29} +0.849880 q^{30} +2.12800 q^{31} +1.00000 q^{32} +0.750731 q^{33} -0.909012 q^{34} +2.93253 q^{35} -2.43640 q^{36} -8.83892 q^{37} +2.74013 q^{38} +1.80941 q^{39} +1.13207 q^{40} +1.02982 q^{41} +1.94471 q^{42} +1.00000 q^{43} +1.00000 q^{44} -2.75818 q^{45} -4.60483 q^{46} +7.30883 q^{47} +0.750731 q^{48} -0.289745 q^{49} -3.71842 q^{50} -0.682424 q^{51} +2.41019 q^{52} +5.73329 q^{53} -4.08128 q^{54} +1.13207 q^{55} +2.59042 q^{56} +2.05710 q^{57} +8.84253 q^{58} -11.1841 q^{59} +0.849880 q^{60} -10.8799 q^{61} +2.12800 q^{62} -6.31130 q^{63} +1.00000 q^{64} +2.72851 q^{65} +0.750731 q^{66} -3.08895 q^{67} -0.909012 q^{68} -3.45699 q^{69} +2.93253 q^{70} +10.7450 q^{71} -2.43640 q^{72} -10.3631 q^{73} -8.83892 q^{74} -2.79153 q^{75} +2.74013 q^{76} +2.59042 q^{77} +1.80941 q^{78} +8.95715 q^{79} +1.13207 q^{80} +4.24527 q^{81} +1.02982 q^{82} -13.9604 q^{83} +1.94471 q^{84} -1.02907 q^{85} +1.00000 q^{86} +6.63836 q^{87} +1.00000 q^{88} +13.8834 q^{89} -2.75818 q^{90} +6.24340 q^{91} -4.60483 q^{92} +1.59756 q^{93} +7.30883 q^{94} +3.10202 q^{95} +0.750731 q^{96} -2.30067 q^{97} -0.289745 q^{98} -2.43640 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 + 8 * q^5 + 3 * q^6 - 2 * q^7 + 7 * q^8 + 10 * q^9	\( 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9} + 8 q^{10} + 7 q^{11} + 3 q^{12} + 4 q^{13} - 2 q^{14} + 2 q^{15} + 7 q^{16} + 10 q^{17} + 10 q^{18} - 2 q^{19} + 8 q^{20} + 7 q^{22} - 4 q^{23} + 3 q^{24} + 11 q^{25} + 4 q^{26} + 15 q^{27} - 2 q^{28} + 5 q^{29} + 2 q^{30} - 2 q^{31} + 7 q^{32} + 3 q^{33} + 10 q^{34} - 10 q^{35} + 10 q^{36} + 6 q^{37} - 2 q^{38} - 8 q^{39} + 8 q^{40} + 4 q^{41} + 7 q^{43} + 7 q^{44} - 2 q^{45} - 4 q^{46} - 6 q^{47} + 3 q^{48} + 31 q^{49} + 11 q^{50} - 14 q^{51} + 4 q^{52} + q^{53} + 15 q^{54} + 8 q^{55} - 2 q^{56} - 30 q^{57} + 5 q^{58} - 4 q^{59} + 2 q^{60} + 9 q^{61} - 2 q^{62} - 24 q^{63} + 7 q^{64} + 18 q^{65} + 3 q^{66} - 6 q^{67} + 10 q^{68} + 2 q^{69} - 10 q^{70} + 10 q^{72} + 13 q^{73} + 6 q^{74} - 9 q^{75} - 2 q^{76} - 2 q^{77} - 8 q^{78} - 31 q^{79} + 8 q^{80} - 25 q^{81} + 4 q^{82} - 11 q^{83} - 24 q^{85} + 7 q^{86} - 13 q^{87} + 7 q^{88} + 10 q^{89} - 2 q^{90} - 12 q^{91} - 4 q^{92} + 12 q^{93} - 6 q^{94} - 18 q^{95} + 3 q^{96} + 23 q^{97} + 31 q^{98} + 10 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 + 8 * q^5 + 3 * q^6 - 2 * q^7 + 7 * q^8 + 10 * q^9 + 8 * q^10 + 7 * q^11 + 3 * q^12 + 4 * q^13 - 2 * q^14 + 2 * q^15 + 7 * q^16 + 10 * q^17 + 10 * q^18 - 2 * q^19 + 8 * q^20 + 7 * q^22 - 4 * q^23 + 3 * q^24 + 11 * q^25 + 4 * q^26 + 15 * q^27 - 2 * q^28 + 5 * q^29 + 2 * q^30 - 2 * q^31 + 7 * q^32 + 3 * q^33 + 10 * q^34 - 10 * q^35 + 10 * q^36 + 6 * q^37 - 2 * q^38 - 8 * q^39 + 8 * q^40 + 4 * q^41 + 7 * q^43 + 7 * q^44 - 2 * q^45 - 4 * q^46 - 6 * q^47 + 3 * q^48 + 31 * q^49 + 11 * q^50 - 14 * q^51 + 4 * q^52 + q^53 + 15 * q^54 + 8 * q^55 - 2 * q^56 - 30 * q^57 + 5 * q^58 - 4 * q^59 + 2 * q^60 + 9 * q^61 - 2 * q^62 - 24 * q^63 + 7 * q^64 + 18 * q^65 + 3 * q^66 - 6 * q^67 + 10 * q^68 + 2 * q^69 - 10 * q^70 + 10 * q^72 + 13 * q^73 + 6 * q^74 - 9 * q^75 - 2 * q^76 - 2 * q^77 - 8 * q^78 - 31 * q^79 + 8 * q^80 - 25 * q^81 + 4 * q^82 - 11 * q^83 - 24 * q^85 + 7 * q^86 - 13 * q^87 + 7 * q^88 + 10 * q^89 - 2 * q^90 - 12 * q^91 - 4 * q^92 + 12 * q^93 - 6 * q^94 - 18 * q^95 + 3 * q^96 + 23 * q^97 + 31 * q^98 + 10 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.750731	0.433435	0.216717	−	0.976234i	$-0.430465\pi$
$3$	0.750731	0.433435	0.216717	+	0.976234i	$0.430465\pi$
$4$	1.00000	0.500000
$5$	1.13207	0.506277	0.253139	−	0.967430i	$-0.418537\pi$
$5$	1.13207	0.506277	0.253139	+	0.967430i	$0.418537\pi$
$6$	0.750731	0.306485
$7$	2.59042	0.979085	0.489543	−	0.871979i	$-0.337164\pi$
$7$	2.59042	0.979085	0.489543	+	0.871979i	$0.337164\pi$
$8$	1.00000	0.353553
$9$	−2.43640	−0.812134
$10$	1.13207	0.357992
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.750731	0.216717
$13$	2.41019	0.668467	0.334233	−	0.942490i	$-0.391523\pi$
$13$	2.41019	0.668467	0.334233	+	0.942490i	$0.391523\pi$
$14$	2.59042	0.692318
$15$	0.849880	0.219438
$16$	1.00000	0.250000
$17$	−0.909012	−0.220468	−0.110234	−	0.993906i	$-0.535160\pi$
$17$	−0.909012	−0.220468	−0.110234	+	0.993906i	$0.535160\pi$
$18$	−2.43640	−0.574266
$19$	2.74013	0.628629	0.314314	−	0.949319i	$-0.398225\pi$
$19$	2.74013	0.628629	0.314314	+	0.949319i	$0.398225\pi$
$20$	1.13207	0.253139
$21$	1.94471	0.424369
$22$	1.00000	0.213201
$23$	−4.60483	−0.960173	−0.480087	−	0.877221i	$-0.659395\pi$
$23$	−4.60483	−0.960173	−0.480087	+	0.877221i	$0.659395\pi$
$24$	0.750731	0.153242
$25$	−3.71842	−0.743684
$26$	2.41019	0.472677
$27$	−4.08128	−0.785442
$28$	2.59042	0.489543
$29$	8.84253	1.64202	0.821008	−	0.570917i	$-0.193412\pi$
$29$	8.84253	1.64202	0.821008	+	0.570917i	$0.193412\pi$
$30$	0.849880	0.155166
$31$	2.12800	0.382200	0.191100	−	0.981571i	$-0.438794\pi$
$31$	2.12800	0.382200	0.191100	+	0.981571i	$0.438794\pi$
$32$	1.00000	0.176777
$33$	0.750731	0.130685
$34$	−0.909012	−0.155894
$35$	2.93253	0.495688
$36$	−2.43640	−0.406067
$37$	−8.83892	−1.45311	−0.726554	−	0.687109i	$-0.758880\pi$
$37$	−8.83892	−1.45311	−0.726554	+	0.687109i	$0.758880\pi$
$38$	2.74013	0.444508
$39$	1.80941	0.289737
$40$	1.13207	0.178996
$41$	1.02982	0.160831	0.0804156	−	0.996761i	$-0.474375\pi$
$41$	1.02982	0.160831	0.0804156	+	0.996761i	$0.474375\pi$
$42$	1.94471	0.300075
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	−2.75818	−0.411165
$46$	−4.60483	−0.678945
$47$	7.30883	1.06610	0.533051	−	0.846083i	$-0.321045\pi$
$47$	7.30883	1.06610	0.533051	+	0.846083i	$0.321045\pi$
$48$	0.750731	0.108359
$49$	−0.289745	−0.0413921
$50$	−3.71842	−0.525864
$51$	−0.682424	−0.0955584
$52$	2.41019	0.334233
$53$	5.73329	0.787528	0.393764	−	0.919212i	$-0.371173\pi$
$53$	5.73329	0.787528	0.393764	+	0.919212i	$0.371173\pi$
$54$	−4.08128	−0.555391
$55$	1.13207	0.152648
$56$	2.59042	0.346159
$57$	2.05710	0.272469
$58$	8.84253	1.16108
$59$	−11.1841	−1.45605	−0.728023	−	0.685553i	$-0.759561\pi$
$59$	−11.1841	−1.45605	−0.728023	+	0.685553i	$0.759561\pi$
$60$	0.849880	0.109719
$61$	−10.8799	−1.39303	−0.696517	−	0.717540i	$-0.745268\pi$
$61$	−10.8799	−1.39303	−0.696517	+	0.717540i	$0.745268\pi$
$62$	2.12800	0.270256
$63$	−6.31130	−0.795149
$64$	1.00000	0.125000
$65$	2.72851	0.338429
$66$	0.750731	0.0924086
$67$	−3.08895	−0.377376	−0.188688	−	0.982037i	$-0.560423\pi$
$67$	−3.08895	−0.377376	−0.188688	+	0.982037i	$0.560423\pi$
$68$	−0.909012	−0.110234
$69$	−3.45699	−0.416172
$70$	2.93253	0.350505
$71$	10.7450	1.27520	0.637599	−	0.770369i	$-0.279928\pi$
$71$	10.7450	1.27520	0.637599	+	0.770369i	$0.279928\pi$
$72$	−2.43640	−0.287133
$73$	−10.3631	−1.21291	−0.606453	−	0.795119i	$-0.707408\pi$
$73$	−10.3631	−1.21291	−0.606453	+	0.795119i	$0.707408\pi$
$74$	−8.83892	−1.02750
$75$	−2.79153	−0.322338
$76$	2.74013	0.314314
$77$	2.59042	0.295205
$78$	1.80941	0.204875
$79$	8.95715	1.00776	0.503879	−	0.863774i	$-0.331906\pi$
$79$	8.95715	1.00776	0.503879	+	0.863774i	$0.331906\pi$
$80$	1.13207	0.126569
$81$	4.24527	0.471697
$82$	1.02982	0.113725
$83$	−13.9604	−1.53235	−0.766176	−	0.642631i	$-0.777843\pi$
$83$	−13.9604	−1.53235	−0.766176	+	0.642631i	$0.777843\pi$
$84$	1.94471	0.212185
$85$	−1.02907	−0.111618
$86$	1.00000	0.107833
$87$	6.63836	0.711707
$88$	1.00000	0.106600
$89$	13.8834	1.47164	0.735820	−	0.677177i	$-0.236797\pi$
$89$	13.8834	1.47164	0.735820	+	0.677177i	$0.236797\pi$
$90$	−2.75818	−0.290738
$91$	6.24340	0.654486
$92$	−4.60483	−0.480087
$93$	1.59756	0.165659
$94$	7.30883	0.753849
$95$	3.10202	0.318260
$96$	0.750731	0.0766211
$97$	−2.30067	−0.233598	−0.116799	−	0.993156i	$-0.537263\pi$
$97$	−2.30067	−0.233598	−0.116799	+	0.993156i	$0.537263\pi$
$98$	−0.289745	−0.0292686
$99$	−2.43640	−0.244868
$100$	−3.71842	−0.371842
$101$	−11.7393	−1.16810	−0.584052	−	0.811716i	$-0.698534\pi$
$101$	−11.7393	−1.16810	−0.584052	+	0.811716i	$0.698534\pi$
$102$	−0.682424	−0.0675700
$103$	2.20742	0.217503	0.108752	−	0.994069i	$-0.465315\pi$
$103$	2.20742	0.217503	0.108752	+	0.994069i	$0.465315\pi$
$104$	2.41019	0.236339
$105$	2.20154	0.214849
$106$	5.73329	0.556866
$107$	−3.54231	−0.342448	−0.171224	−	0.985232i	$-0.554772\pi$
$107$	−3.54231	−0.342448	−0.171224	+	0.985232i	$0.554772\pi$
$108$	−4.08128	−0.392721
$109$	−3.87748	−0.371395	−0.185698	−	0.982607i	$-0.559454\pi$
$109$	−3.87748	−0.371395	−0.185698	+	0.982607i	$0.559454\pi$
$110$	1.13207	0.107939
$111$	−6.63565	−0.629828
$112$	2.59042	0.244771
$113$	15.9309	1.49866	0.749328	−	0.662198i	$-0.230376\pi$
$113$	15.9309	1.49866	0.749328	+	0.662198i	$0.230376\pi$
$114$	2.05710	0.192665
$115$	−5.21299	−0.486114
$116$	8.84253	0.821008
$117$	−5.87220	−0.542885
$118$	−11.1841	−1.02958
$119$	−2.35472	−0.215857
$120$	0.849880	0.0775831
$121$	1.00000	0.0909091
$122$	−10.8799	−0.985024
$123$	0.773119	0.0697098
$124$	2.12800	0.191100
$125$	−9.86986	−0.882787
$126$	−6.31130	−0.562255
$127$	−0.159276	−0.0141335	−0.00706674	−	0.999975i	$-0.502249\pi$
$127$	−0.159276	−0.0141335	−0.00706674	+	0.999975i	$0.502249\pi$
$128$	1.00000	0.0883883
$129$	0.750731	0.0660982
$130$	2.72851	0.239306
$131$	−15.7489	−1.37598	−0.687992	−	0.725718i	$-0.741508\pi$
$131$	−15.7489	−1.37598	−0.687992	+	0.725718i	$0.741508\pi$
$132$	0.750731	0.0653427
$133$	7.09807	0.615481
$134$	−3.08895	−0.266845
$135$	−4.62029	−0.397651
$136$	−0.909012	−0.0779472
$137$	−15.1979	−1.29845	−0.649223	−	0.760598i	$-0.724906\pi$
$137$	−15.1979	−1.29845	−0.649223	+	0.760598i	$0.724906\pi$
$138$	−3.45699	−0.294278
$139$	2.66267	0.225844	0.112922	−	0.993604i	$-0.463979\pi$
$139$	2.66267	0.225844	0.112922	+	0.993604i	$0.463979\pi$
$140$	2.93253	0.247844
$141$	5.48697	0.462086
$142$	10.7450	0.901701
$143$	2.41019	0.201550
$144$	−2.43640	−0.203034
$145$	10.0104	0.831315
$146$	−10.3631	−0.857654
$147$	−0.217520	−0.0179408
$148$	−8.83892	−0.726554
$149$	13.2168	1.08276	0.541381	−	0.840777i	$-0.317902\pi$
$149$	13.2168	1.08276	0.541381	+	0.840777i	$0.317902\pi$
$150$	−2.79153	−0.227928
$151$	−22.3491	−1.81874	−0.909372	−	0.415984i	$-0.863437\pi$
$151$	−22.3491	−1.81874	−0.909372	+	0.415984i	$0.863437\pi$
$152$	2.74013	0.222254
$153$	2.21472	0.179050
$154$	2.59042	0.208742
$155$	2.40905	0.193499
$156$	1.80941	0.144868
$157$	0.538300	0.0429610	0.0214805	−	0.999769i	$-0.493162\pi$
$157$	0.538300	0.0429610	0.0214805	+	0.999769i	$0.493162\pi$
$158$	8.95715	0.712593
$159$	4.30416	0.341342
$160$	1.13207	0.0894980
$161$	−11.9284	−0.940091
$162$	4.24527	0.333540
$163$	−12.3295	−0.965719	−0.482860	−	0.875698i	$-0.660402\pi$
$163$	−12.3295	−0.965719	−0.482860	+	0.875698i	$0.660402\pi$
$164$	1.02982	0.0804156
$165$	0.849880	0.0661631
$166$	−13.9604	−1.08354
$167$	−14.1873	−1.09784	−0.548922	−	0.835873i	$-0.684962\pi$
$167$	−14.1873	−1.09784	−0.548922	+	0.835873i	$0.684962\pi$
$168$	1.94471	0.150037
$169$	−7.19098	−0.553152
$170$	−1.02907	−0.0789257
$171$	−6.67606	−0.510531
$172$	1.00000	0.0762493
$173$	13.1545	1.00012	0.500061	−	0.865990i	$-0.333311\pi$
$173$	13.1545	1.00012	0.500061	+	0.865990i	$0.333311\pi$
$174$	6.63836	0.503253
$175$	−9.63225	−0.728130
$176$	1.00000	0.0753778
$177$	−8.39625	−0.631101
$178$	13.8834	1.04061
$179$	5.32747	0.398194	0.199097	−	0.979980i	$-0.436199\pi$
$179$	5.32747	0.398194	0.199097	+	0.979980i	$0.436199\pi$
$180$	−2.75818	−0.205583
$181$	15.7601	1.17144	0.585718	−	0.810515i	$-0.300813\pi$
$181$	15.7601	1.17144	0.585718	+	0.810515i	$0.300813\pi$
$182$	6.24340	0.462792
$183$	−8.16791	−0.603789
$184$	−4.60483	−0.339472
$185$	−10.0063	−0.735676
$186$	1.59756	0.117139
$187$	−0.909012	−0.0664736
$188$	7.30883	0.533051
$189$	−10.5722	−0.769015
$190$	3.10202	0.225044
$191$	−23.3075	−1.68647	−0.843237	−	0.537542i	$-0.819353\pi$
$191$	−23.3075	−1.68647	−0.843237	+	0.537542i	$0.819353\pi$
$192$	0.750731	0.0541793
$193$	0.0327452	0.00235705	0.00117853	−	0.999999i	$-0.499625\pi$
$193$	0.0327452	0.00235705	0.00117853	+	0.999999i	$0.499625\pi$
$194$	−2.30067	−0.165179
$195$	2.04837	0.146687
$196$	−0.289745	−0.0206961
$197$	14.9896	1.06796	0.533982	−	0.845496i	$-0.320695\pi$
$197$	14.9896	1.06796	0.533982	+	0.845496i	$0.320695\pi$
$198$	−2.43640	−0.173148
$199$	−17.5073	−1.24106	−0.620531	−	0.784182i	$-0.713083\pi$
$199$	−17.5073	−1.24106	−0.620531	+	0.784182i	$0.713083\pi$
$200$	−3.71842	−0.262932
$201$	−2.31897	−0.163568
$202$	−11.7393	−0.825975
$203$	22.9058	1.60767
$204$	−0.682424	−0.0477792
$205$	1.16583	0.0814251
$206$	2.20742	0.153798
$207$	11.2192	0.779790
$208$	2.41019	0.167117
$209$	2.74013	0.189539
$210$	2.20154	0.151921
$211$	−27.4658	−1.89082	−0.945410	−	0.325882i	$-0.894339\pi$
$211$	−27.4658	−1.89082	−0.945410	+	0.325882i	$0.894339\pi$
$212$	5.73329	0.393764
$213$	8.06661	0.552715
$214$	−3.54231	−0.242147
$215$	1.13207	0.0772065
$216$	−4.08128	−0.277696
$217$	5.51241	0.374207
$218$	−3.87748	−0.262616
$219$	−7.77988	−0.525716
$220$	1.13207	0.0763241
$221$	−2.19089	−0.147375
$222$	−6.63565	−0.445355
$223$	9.54214	0.638989	0.319494	−	0.947588i	$-0.396487\pi$
$223$	9.54214	0.638989	0.319494	+	0.947588i	$0.396487\pi$
$224$	2.59042	0.173079
$225$	9.05956	0.603971
$226$	15.9309	1.05971
$227$	10.9961	0.729839	0.364919	−	0.931039i	$-0.381097\pi$
$227$	10.9961	0.729839	0.364919	+	0.931039i	$0.381097\pi$
$228$	2.05710	0.136235
$229$	10.0400	0.663464	0.331732	−	0.943374i	$-0.392367\pi$
$229$	10.0400	0.663464	0.331732	+	0.943374i	$0.392367\pi$
$230$	−5.21299	−0.343734
$231$	1.94471	0.127952
$232$	8.84253	0.580540
$233$	−1.79664	−0.117702	−0.0588508	−	0.998267i	$-0.518744\pi$
$233$	−1.79664	−0.117702	−0.0588508	+	0.998267i	$0.518744\pi$
$234$	−5.87220	−0.383878
$235$	8.27411	0.539743
$236$	−11.1841	−0.728023
$237$	6.72441	0.436797
$238$	−2.35472	−0.152634
$239$	17.7503	1.14817	0.574086	−	0.818795i	$-0.305358\pi$
$239$	17.7503	1.14817	0.574086	+	0.818795i	$0.305358\pi$
$240$	0.849880	0.0548595
$241$	23.8855	1.53860	0.769300	−	0.638888i	$-0.220605\pi$
$241$	23.8855	1.53860	0.769300	+	0.638888i	$0.220605\pi$
$242$	1.00000	0.0642824
$243$	15.4309	0.989892
$244$	−10.8799	−0.696517
$245$	−0.328011	−0.0209559
$246$	0.773119	0.0492923
$247$	6.60424	0.420217
$248$	2.12800	0.135128
$249$	−10.4805	−0.664174
$250$	−9.86986	−0.624225
$251$	−16.2383	−1.02495	−0.512475	−	0.858702i	$-0.671271\pi$
$251$	−16.2383	−1.02495	−0.512475	+	0.858702i	$0.671271\pi$
$252$	−6.31130	−0.397574
$253$	−4.60483	−0.289503
$254$	−0.159276	−0.00999388
$255$	−0.772551	−0.0483790
$256$	1.00000	0.0625000
$257$	6.15644	0.384028	0.192014	−	0.981392i	$-0.438498\pi$
$257$	6.15644	0.384028	0.192014	+	0.981392i	$0.438498\pi$
$258$	0.750731	0.0467385
$259$	−22.8965	−1.42272
$260$	2.72851	0.169215
$261$	−21.5440	−1.33354
$262$	−15.7489	−0.972968
$263$	−5.04266	−0.310944	−0.155472	−	0.987840i	$-0.549690\pi$
$263$	−5.04266	−0.310944	−0.155472	+	0.987840i	$0.549690\pi$
$264$	0.750731	0.0462043
$265$	6.49048	0.398707
$266$	7.09807	0.435211
$267$	10.4227	0.637860
$268$	−3.08895	−0.188688
$269$	0.919262	0.0560484	0.0280242	−	0.999607i	$-0.491078\pi$
$269$	0.919262	0.0560484	0.0280242	+	0.999607i	$0.491078\pi$
$270$	−4.62029	−0.281182
$271$	6.08621	0.369711	0.184855	−	0.982766i	$-0.440818\pi$
$271$	6.08621	0.369711	0.184855	+	0.982766i	$0.440818\pi$
$272$	−0.909012	−0.0551170
$273$	4.68711	0.283677
$274$	−15.1979	−0.918140
$275$	−3.71842	−0.224229
$276$	−3.45699	−0.208086
$277$	−27.5208	−1.65357	−0.826783	−	0.562521i	$-0.809831\pi$
$277$	−27.5208	−1.65357	−0.826783	+	0.562521i	$0.809831\pi$
$278$	2.66267	0.159696
$279$	−5.18467	−0.310398
$280$	2.93253	0.175252
$281$	−14.6091	−0.871507	−0.435754	−	0.900066i	$-0.643518\pi$
$281$	−14.6091	−0.871507	−0.435754	+	0.900066i	$0.643518\pi$
$282$	5.48697	0.326744
$283$	−15.7727	−0.937587	−0.468794	−	0.883308i	$-0.655311\pi$
$283$	−15.7727	−0.937587	−0.468794	+	0.883308i	$0.655311\pi$
$284$	10.7450	0.637599
$285$	2.32878	0.137945
$286$	2.41019	0.142518
$287$	2.66767	0.157467
$288$	−2.43640	−0.143566
$289$	−16.1737	−0.951394
$290$	10.0104	0.587829
$291$	−1.72719	−0.101249
$292$	−10.3631	−0.606453
$293$	5.03478	0.294135	0.147068	−	0.989126i	$-0.453017\pi$
$293$	5.03478	0.294135	0.147068	+	0.989126i	$0.453017\pi$
$294$	−0.217520	−0.0126860
$295$	−12.6612	−0.737163
$296$	−8.83892	−0.513752
$297$	−4.08128	−0.236820
$298$	13.2168	0.765628
$299$	−11.0985	−0.641844
$300$	−2.79153	−0.161169
$301$	2.59042	0.149309
$302$	−22.3491	−1.28605
$303$	−8.81306	−0.506297
$304$	2.74013	0.157157
$305$	−12.3169	−0.705261
$306$	2.21472	0.126607
$307$	33.4398	1.90851	0.954256	−	0.298991i	$-0.0966501\pi$
$307$	33.4398	1.90851	0.954256	+	0.298991i	$0.0966501\pi$
$308$	2.59042	0.147603
$309$	1.65718	0.0942735
$310$	2.40905	0.136825
$311$	20.8014	1.17954	0.589770	−	0.807571i	$-0.299218\pi$
$311$	20.8014	1.17954	0.589770	+	0.807571i	$0.299218\pi$
$312$	1.80941	0.102437
$313$	3.58442	0.202603	0.101302	−	0.994856i	$-0.467699\pi$
$313$	3.58442	0.202603	0.101302	+	0.994856i	$0.467699\pi$
$314$	0.538300	0.0303780
$315$	−7.14483	−0.402566
$316$	8.95715	0.503879
$317$	29.7836	1.67281	0.836407	−	0.548108i	$-0.184652\pi$
$317$	29.7836	1.67281	0.836407	+	0.548108i	$0.184652\pi$
$318$	4.30416	0.241365
$319$	8.84253	0.495086
$320$	1.13207	0.0632846
$321$	−2.65932	−0.148429
$322$	−11.9284	−0.664745
$323$	−2.49081	−0.138592
$324$	4.24527	0.235848
$325$	−8.96210	−0.497128
$326$	−12.3295	−0.682867
$327$	−2.91094	−0.160976
$328$	1.02982	0.0568624
$329$	18.9329	1.04381
$330$	0.849880	0.0467843
$331$	29.8720	1.64191	0.820956	−	0.570992i	$-0.193441\pi$
$331$	29.8720	1.64191	0.820956	+	0.570992i	$0.193441\pi$
$332$	−13.9604	−0.766176
$333$	21.5352	1.18012
$334$	−14.1873	−0.776294
$335$	−3.49691	−0.191057
$336$	1.94471	0.106092
$337$	3.48794	0.190000	0.0950000	−	0.995477i	$-0.469715\pi$
$337$	3.48794	0.190000	0.0950000	+	0.995477i	$0.469715\pi$
$338$	−7.19098	−0.391138
$339$	11.9598	0.649570
$340$	−1.02907	−0.0558089
$341$	2.12800	0.115238
$342$	−6.67606	−0.361000
$343$	−18.8835	−1.01961
$344$	1.00000	0.0539164
$345$	−3.91355	−0.210699
$346$	13.1545	0.707192
$347$	8.98916	0.482563	0.241282	−	0.970455i	$-0.422432\pi$
$347$	8.98916	0.482563	0.241282	+	0.970455i	$0.422432\pi$
$348$	6.63836	0.355853
$349$	15.4078	0.824763	0.412382	−	0.911011i	$-0.364697\pi$
$349$	15.4078	0.824763	0.412382	+	0.911011i	$0.364697\pi$
$350$	−9.63225	−0.514865
$351$	−9.83666	−0.525042
$352$	1.00000	0.0533002
$353$	10.6477	0.566717	0.283359	−	0.959014i	$-0.408551\pi$
$353$	10.6477	0.566717	0.283359	+	0.959014i	$0.408551\pi$
$354$	−8.39625	−0.446256
$355$	12.1641	0.645603
$356$	13.8834	0.735820
$357$	−1.76776	−0.0935598
$358$	5.32747	0.281566
$359$	−18.2657	−0.964029	−0.482014	−	0.876163i	$-0.660095\pi$
$359$	−18.2657	−0.964029	−0.482014	+	0.876163i	$0.660095\pi$
$360$	−2.75818	−0.145369
$361$	−11.4917	−0.604826
$362$	15.7601	0.828330
$363$	0.750731	0.0394032
$364$	6.24340	0.327243
$365$	−11.7317	−0.614067
$366$	−8.16791	−0.426944
$367$	−16.7913	−0.876500	−0.438250	−	0.898853i	$-0.644402\pi$
$367$	−16.7913	−0.876500	−0.438250	+	0.898853i	$0.644402\pi$
$368$	−4.60483	−0.240043
$369$	−2.50906	−0.130617
$370$	−10.0063	−0.520201
$371$	14.8516	0.771057
$372$	1.59756	0.0828294
$373$	24.8615	1.28728	0.643639	−	0.765329i	$-0.277424\pi$
$373$	24.8615	1.28728	0.643639	+	0.765329i	$0.277424\pi$
$374$	−0.909012	−0.0470039
$375$	−7.40961	−0.382630
$376$	7.30883	0.376924
$377$	21.3122	1.09763
$378$	−10.5722	−0.543775
$379$	14.8602	0.763317	0.381659	−	0.924303i	$-0.375353\pi$
$379$	14.8602	0.763317	0.381659	+	0.924303i	$0.375353\pi$
$380$	3.10202	0.159130
$381$	−0.119574	−0.00612594
$382$	−23.3075	−1.19252
$383$	−18.6530	−0.953122	−0.476561	−	0.879141i	$-0.658117\pi$
$383$	−18.6530	−0.953122	−0.476561	+	0.879141i	$0.658117\pi$
$384$	0.750731	0.0383106
$385$	2.93253	0.149456
$386$	0.0327452	0.00166669
$387$	−2.43640	−0.123849
$388$	−2.30067	−0.116799
$389$	15.6304	0.792493	0.396246	−	0.918144i	$-0.370313\pi$
$389$	15.6304	0.792493	0.396246	+	0.918144i	$0.370313\pi$
$390$	2.04837	0.103723
$391$	4.18585	0.211687
$392$	−0.289745	−0.0146343
$393$	−11.8232	−0.596399
$394$	14.9896	0.755165
$395$	10.1401	0.510205
$396$	−2.43640	−0.122434
$397$	14.2729	0.716338	0.358169	−	0.933657i	$-0.383401\pi$
$397$	14.2729	0.716338	0.358169	+	0.933657i	$0.383401\pi$
$398$	−17.5073	−0.877563
$399$	5.32874	0.266771
$400$	−3.71842	−0.185921
$401$	29.6581	1.48106	0.740528	−	0.672026i	$-0.234576\pi$
$401$	29.6581	1.48106	0.740528	+	0.672026i	$0.234576\pi$
$402$	−2.31897	−0.115660
$403$	5.12889	0.255488
$404$	−11.7393	−0.584052
$405$	4.80594	0.238809
$406$	22.9058	1.13680
$407$	−8.83892	−0.438129
$408$	−0.682424	−0.0337850
$409$	24.5695	1.21488	0.607441	−	0.794365i	$-0.292196\pi$
$409$	24.5695	1.21488	0.607441	+	0.794365i	$0.292196\pi$
$410$	1.16583	0.0575763
$411$	−11.4096	−0.562792
$412$	2.20742	0.108752
$413$	−28.9715	−1.42559
$414$	11.2192	0.551395
$415$	−15.8041	−0.775794
$416$	2.41019	0.118169
$417$	1.99895	0.0978888
$418$	2.74013	0.134024
$419$	4.13873	0.202190	0.101095	−	0.994877i	$-0.467765\pi$
$419$	4.13873	0.202190	0.101095	+	0.994877i	$0.467765\pi$
$420$	2.20154	0.107424
$421$	−4.66643	−0.227428	−0.113714	−	0.993514i	$-0.536275\pi$
$421$	−4.66643	−0.227428	−0.113714	+	0.993514i	$0.536275\pi$
$422$	−27.4658	−1.33701
$423$	−17.8073	−0.865819
$424$	5.73329	0.278433
$425$	3.38009	0.163958
$426$	8.06661	0.390828
$427$	−28.1836	−1.36390
$428$	−3.54231	−0.171224
$429$	1.80941	0.0873589
$430$	1.13207	0.0545933
$431$	6.74631	0.324958	0.162479	−	0.986712i	$-0.448051\pi$
$431$	6.74631	0.324958	0.162479	+	0.986712i	$0.448051\pi$
$432$	−4.08128	−0.196360
$433$	−0.933746	−0.0448729	−0.0224365	−	0.999748i	$-0.507142\pi$
$433$	−0.933746	−0.0448729	−0.0224365	+	0.999748i	$0.507142\pi$
$434$	5.51241	0.264604
$435$	7.51509	0.360321
$436$	−3.87748	−0.185698
$437$	−12.6178	−0.603592
$438$	−7.77988	−0.371737
$439$	7.98566	0.381135	0.190567	−	0.981674i	$-0.438967\pi$
$439$	7.98566	0.381135	0.190567	+	0.981674i	$0.438967\pi$
$440$	1.13207	0.0539693
$441$	0.705935	0.0336160
$442$	−2.19089	−0.104210
$443$	22.2681	1.05799	0.528995	−	0.848625i	$-0.322569\pi$
$443$	22.2681	1.05799	0.528995	+	0.848625i	$0.322569\pi$
$444$	−6.63565	−0.314914
$445$	15.7170	0.745058
$446$	9.54214	0.451833
$447$	9.92226	0.469307
$448$	2.59042	0.122386
$449$	20.0117	0.944410	0.472205	−	0.881489i	$-0.343458\pi$
$449$	20.0117	0.944410	0.472205	+	0.881489i	$0.343458\pi$
$450$	9.05956	0.427072
$451$	1.02982	0.0484924
$452$	15.9309	0.749328
$453$	−16.7782	−0.788307
$454$	10.9961	0.516074
$455$	7.06796	0.331351
$456$	2.05710	0.0963325
$457$	10.5423	0.493149	0.246574	−	0.969124i	$-0.420695\pi$
$457$	10.5423	0.493149	0.246574	+	0.969124i	$0.420695\pi$
$458$	10.0400	0.469140
$459$	3.70993	0.173165
$460$	−5.21299	−0.243057
$461$	21.9203	1.02093	0.510464	−	0.859899i	$-0.329473\pi$
$461$	21.9203	1.02093	0.510464	+	0.859899i	$0.329473\pi$
$462$	1.94471	0.0904759
$463$	−30.5090	−1.41787	−0.708936	−	0.705273i	$-0.750825\pi$
$463$	−30.5090	−1.41787	−0.708936	+	0.705273i	$0.750825\pi$
$464$	8.84253	0.410504
$465$	1.80855	0.0838693
$466$	−1.79664	−0.0832276
$467$	−8.96263	−0.414741	−0.207371	−	0.978262i	$-0.566491\pi$
$467$	−8.96263	−0.414741	−0.207371	+	0.978262i	$0.566491\pi$
$468$	−5.87220	−0.271442
$469$	−8.00168	−0.369483
$470$	8.27411	0.381656
$471$	0.404118	0.0186208
$472$	−11.1841	−0.514790
$473$	1.00000	0.0459800
$474$	6.72441	0.308862
$475$	−10.1889	−0.467501
$476$	−2.35472	−0.107928
$477$	−13.9686	−0.639578
$478$	17.7503	0.811880
$479$	27.3156	1.24808	0.624041	−	0.781392i	$-0.285490\pi$
$479$	27.3156	1.24808	0.624041	+	0.781392i	$0.285490\pi$
$480$	0.849880	0.0387915
$481$	−21.3035	−0.971355
$482$	23.8855	1.08795
$483$	−8.95503	−0.407468
$484$	1.00000	0.0454545
$485$	−2.60452	−0.118265
$486$	15.4309	0.699959
$487$	−0.968881	−0.0439042	−0.0219521	−	0.999759i	$-0.506988\pi$
$487$	−0.968881	−0.0439042	−0.0219521	+	0.999759i	$0.506988\pi$
$488$	−10.8799	−0.492512
$489$	−9.25612	−0.418576
$490$	−0.328011	−0.0148180
$491$	1.66674	0.0752187	0.0376094	−	0.999293i	$-0.488026\pi$
$491$	1.66674	0.0752187	0.0376094	+	0.999293i	$0.488026\pi$
$492$	0.773119	0.0348549
$493$	−8.03797	−0.362012
$494$	6.60424	0.297139
$495$	−2.75818	−0.123971
$496$	2.12800	0.0955501
$497$	27.8340	1.24853
$498$	−10.4805	−0.469642
$499$	−3.81680	−0.170864	−0.0854318	−	0.996344i	$-0.527227\pi$
$499$	−3.81680	−0.170864	−0.0854318	+	0.996344i	$0.527227\pi$
$500$	−9.86986	−0.441394
$501$	−10.6508	−0.475844
$502$	−16.2383	−0.724749
$503$	20.8540	0.929834	0.464917	−	0.885354i	$-0.346084\pi$
$503$	20.8540	0.929834	0.464917	+	0.885354i	$0.346084\pi$
$504$	−6.31130	−0.281128
$505$	−13.2897	−0.591385
$506$	−4.60483	−0.204710
$507$	−5.39849	−0.239755
$508$	−0.159276	−0.00706674
$509$	36.4136	1.61400	0.807001	−	0.590550i	$-0.201089\pi$
$509$	36.4136	1.61400	0.807001	+	0.590550i	$0.201089\pi$
$510$	−0.772551	−0.0342091
$511$	−26.8447	−1.18754
$512$	1.00000	0.0441942
$513$	−11.1832	−0.493751
$514$	6.15644	0.271549
$515$	2.49895	0.110117
$516$	0.750731	0.0330491
$517$	7.30883	0.321442
$518$	−22.8965	−1.00601
$519$	9.87552	0.433487
$520$	2.72851	0.119653
$521$	−14.9155	−0.653461	−0.326731	−	0.945117i	$-0.605947\pi$
$521$	−14.9155	−0.653461	−0.326731	+	0.945117i	$0.605947\pi$
$522$	−21.5440	−0.942953
$523$	39.6248	1.73267	0.866336	−	0.499462i	$-0.166469\pi$
$523$	39.6248	1.73267	0.866336	+	0.499462i	$0.166469\pi$
$524$	−15.7489	−0.687992
$525$	−7.23123	−0.315597
$526$	−5.04266	−0.219870
$527$	−1.93438	−0.0842629
$528$	0.750731	0.0326714
$529$	−1.79555	−0.0780675
$530$	6.49048	0.281929
$531$	27.2490	1.18251
$532$	7.09807	0.307741
$533$	2.48207	0.107510
$534$	10.4227	0.451035
$535$	−4.01015	−0.173374
$536$	−3.08895	−0.133423
$537$	3.99950	0.172591
$538$	0.919262	0.0396322
$539$	−0.289745	−0.0124802
$540$	−4.62029	−0.198826
$541$	−17.6426	−0.758514	−0.379257	−	0.925291i	$-0.623820\pi$
$541$	−17.6426	−0.758514	−0.379257	+	0.925291i	$0.623820\pi$
$542$	6.08621	0.261425
$543$	11.8316	0.507741
$544$	−0.909012	−0.0389736
$545$	−4.38958	−0.188029
$546$	4.68711	0.200590
$547$	−10.3802	−0.443824	−0.221912	−	0.975067i	$-0.571230\pi$
$547$	−10.3802	−0.443824	−0.221912	+	0.975067i	$0.571230\pi$
$548$	−15.1979	−0.649223
$549$	26.5079	1.13133
$550$	−3.71842	−0.158554
$551$	24.2297	1.03222
$552$	−3.45699	−0.147139
$553$	23.2028	0.986682
$554$	−27.5208	−1.16925
$555$	−7.51202	−0.318867
$556$	2.66267	0.112922
$557$	−17.3017	−0.733096	−0.366548	−	0.930399i	$-0.619460\pi$
$557$	−17.3017	−0.733096	−0.366548	+	0.930399i	$0.619460\pi$
$558$	−5.18467	−0.219485
$559$	2.41019	0.101940
$560$	2.93253	0.123922
$561$	−0.682424	−0.0288119
$562$	−14.6091	−0.616249
$563$	10.8919	0.459038	0.229519	−	0.973304i	$-0.426285\pi$
$563$	10.8919	0.459038	0.229519	+	0.973304i	$0.426285\pi$
$564$	5.48697	0.231043
$565$	18.0349	0.758736
$566$	−15.7727	−0.662974
$567$	10.9970	0.461831
$568$	10.7450	0.450850
$569$	1.27037	0.0532567	0.0266283	−	0.999645i	$-0.491523\pi$
$569$	1.27037	0.0532567	0.0266283	+	0.999645i	$0.491523\pi$
$570$	2.32878	0.0975419
$571$	31.0933	1.30121	0.650606	−	0.759415i	$-0.274515\pi$
$571$	31.0933	1.30121	0.650606	+	0.759415i	$0.274515\pi$
$572$	2.41019	0.100775
$573$	−17.4977	−0.730976
$574$	2.66767	0.111346
$575$	17.1227	0.714065
$576$	−2.43640	−0.101517
$577$	−5.09676	−0.212181	−0.106090	−	0.994356i	$-0.533833\pi$
$577$	−5.09676	−0.212181	−0.106090	+	0.994356i	$0.533833\pi$
$578$	−16.1737	−0.672737
$579$	0.0245829	0.00102163
$580$	10.0104	0.415658
$581$	−36.1632	−1.50030
$582$	−1.72719	−0.0715941
$583$	5.73329	0.237449
$584$	−10.3631	−0.428827
$585$	−6.64774	−0.274850
$586$	5.03478	0.207985
$587$	−27.2368	−1.12418	−0.562092	−	0.827075i	$-0.690003\pi$
$587$	−27.2368	−1.12418	−0.562092	+	0.827075i	$0.690003\pi$
$588$	−0.217520	−0.00897039
$589$	5.83100	0.240262
$590$	−12.6612	−0.521253
$591$	11.2532	0.462893
$592$	−8.83892	−0.363277
$593$	27.5717	1.13223	0.566117	−	0.824325i	$-0.308445\pi$
$593$	27.5717	1.13223	0.566117	+	0.824325i	$0.308445\pi$
$594$	−4.08128	−0.167457
$595$	−2.66571	−0.109283
$596$	13.2168	0.541381
$597$	−13.1433	−0.537919
$598$	−11.0985	−0.453852
$599$	−18.3515	−0.749822	−0.374911	−	0.927061i	$-0.622327\pi$
$599$	−18.3515	−0.749822	−0.374911	+	0.927061i	$0.622327\pi$
$600$	−2.79153	−0.113964
$601$	−37.7603	−1.54027	−0.770137	−	0.637879i	$-0.779812\pi$
$601$	−37.7603	−1.54027	−0.770137	+	0.637879i	$0.779812\pi$
$602$	2.59042	0.105577
$603$	7.52594	0.306480
$604$	−22.3491	−0.909372
$605$	1.13207	0.0460252
$606$	−8.81306	−0.358006
$607$	−33.1216	−1.34437	−0.672183	−	0.740385i	$-0.734643\pi$
$607$	−33.1216	−1.34437	−0.672183	+	0.740385i	$0.734643\pi$
$608$	2.74013	0.111127
$609$	17.1961	0.696821
$610$	−12.3169	−0.498695
$611$	17.6157	0.712655
$612$	2.21472	0.0895248
$613$	41.6180	1.68093	0.840467	−	0.541862i	$-0.182281\pi$
$613$	41.6180	1.68093	0.840467	+	0.541862i	$0.182281\pi$
$614$	33.4398	1.34952
$615$	0.875225	0.0352925
$616$	2.59042	0.104371
$617$	38.1560	1.53610	0.768051	−	0.640389i	$-0.221227\pi$
$617$	38.1560	1.53610	0.768051	+	0.640389i	$0.221227\pi$
$618$	1.65718	0.0666614
$619$	35.4256	1.42388	0.711938	−	0.702242i	$-0.247818\pi$
$619$	35.4256	1.42388	0.711938	+	0.702242i	$0.247818\pi$
$620$	2.40905	0.0967496
$621$	18.7936	0.754160
$622$	20.8014	0.834061
$623$	35.9639	1.44086
$624$	1.80941	0.0724342
$625$	7.41872	0.296749
$626$	3.58442	0.143262
$627$	2.05710	0.0821526
$628$	0.538300	0.0214805
$629$	8.03468	0.320364
$630$	−7.14483	−0.284657
$631$	8.34888	0.332364	0.166182	−	0.986095i	$-0.446856\pi$
$631$	8.34888	0.332364	0.166182	+	0.986095i	$0.446856\pi$
$632$	8.95715	0.356296
$633$	−20.6194	−0.819547
$634$	29.7836	1.18286
$635$	−0.180312	−0.00715545
$636$	4.30416	0.170671
$637$	−0.698340	−0.0276693
$638$	8.84253	0.350079
$639$	−26.1792	−1.03563
$640$	1.13207	0.0447490
$641$	−0.915646	−0.0361658	−0.0180829	−	0.999836i	$-0.505756\pi$
$641$	−0.915646	−0.0361658	−0.0180829	+	0.999836i	$0.505756\pi$
$642$	−2.65932	−0.104955
$643$	−31.5998	−1.24617	−0.623087	−	0.782152i	$-0.714122\pi$
$643$	−31.5998	−1.24617	−0.623087	+	0.782152i	$0.714122\pi$
$644$	−11.9284	−0.470046
$645$	0.849880	0.0334640
$646$	−2.49081	−0.0979996
$647$	42.3035	1.66312	0.831561	−	0.555434i	$-0.187448\pi$
$647$	42.3035	1.66312	0.831561	+	0.555434i	$0.187448\pi$
$648$	4.24527	0.166770
$649$	−11.1841	−0.439014
$650$	−8.96210	−0.351522
$651$	4.13834	0.162194
$652$	−12.3295	−0.482860
$653$	38.1411	1.49258	0.746289	−	0.665622i	$-0.231834\pi$
$653$	38.1411	1.49258	0.746289	+	0.665622i	$0.231834\pi$
$654$	−2.91094	−0.113827
$655$	−17.8288	−0.696629
$656$	1.02982	0.0402078
$657$	25.2486	0.985043
$658$	18.9329	0.738082
$659$	−22.2518	−0.866806	−0.433403	−	0.901200i	$-0.642687\pi$
$659$	−22.2518	−0.866806	−0.433403	+	0.901200i	$0.642687\pi$
$660$	0.849880	0.0330815
$661$	−27.3940	−1.06550	−0.532751	−	0.846272i	$-0.678842\pi$
$661$	−27.3940	−1.06550	−0.532751	+	0.846272i	$0.678842\pi$
$662$	29.8720	1.16101
$663$	−1.64477	−0.0638776
$664$	−13.9604	−0.541768
$665$	8.03552	0.311604
$666$	21.5352	0.834471
$667$	−40.7183	−1.57662
$668$	−14.1873	−0.548922
$669$	7.16358	0.276960
$670$	−3.49691	−0.135098
$671$	−10.8799	−0.420016
$672$	1.94471	0.0750186
$673$	−1.04905	−0.0404380	−0.0202190	−	0.999796i	$-0.506436\pi$
$673$	−1.04905	−0.0404380	−0.0202190	+	0.999796i	$0.506436\pi$
$674$	3.48794	0.134350
$675$	15.1759	0.584120
$676$	−7.19098	−0.276576
$677$	−9.06336	−0.348333	−0.174167	−	0.984716i	$-0.555723\pi$
$677$	−9.06336	−0.348333	−0.174167	+	0.984716i	$0.555723\pi$
$678$	11.9598	0.459315
$679$	−5.95970	−0.228712
$680$	−1.02907	−0.0394629
$681$	8.25514	0.316337
$682$	2.12800	0.0814854
$683$	19.7457	0.755550	0.377775	−	0.925897i	$-0.376689\pi$
$683$	19.7457	0.755550	0.377775	+	0.925897i	$0.376689\pi$
$684$	−6.67606	−0.255265
$685$	−17.2051	−0.657374
$686$	−18.8835	−0.720974
$687$	7.53737	0.287568
$688$	1.00000	0.0381246
$689$	13.8183	0.526436
$690$	−3.91355	−0.148986
$691$	5.70658	0.217088	0.108544	−	0.994092i	$-0.465381\pi$
$691$	5.70658	0.217088	0.108544	+	0.994092i	$0.465381\pi$
$692$	13.1545	0.500061
$693$	−6.31130	−0.239746
$694$	8.98916	0.341224
$695$	3.01432	0.114340
$696$	6.63836	0.251626
$697$	−0.936121	−0.0354581
$698$	15.4078	0.583196
$699$	−1.34879	−0.0510160
$700$	−9.63225	−0.364065
$701$	3.05263	0.115296	0.0576481	−	0.998337i	$-0.481640\pi$
$701$	3.05263	0.115296	0.0576481	+	0.998337i	$0.481640\pi$
$702$	−9.83666	−0.371261
$703$	−24.2198	−0.913466
$704$	1.00000	0.0376889
$705$	6.21163	0.233944
$706$	10.6477	0.400730
$707$	−30.4097	−1.14367
$708$	−8.39625	−0.315550
$709$	43.8914	1.64838	0.824189	−	0.566315i	$-0.191632\pi$
$709$	43.8914	1.64838	0.824189	+	0.566315i	$0.191632\pi$
$710$	12.1641	0.456510
$711$	−21.8232	−0.818435
$712$	13.8834	0.520304
$713$	−9.79908	−0.366979
$714$	−1.76776	−0.0661568
$715$	2.72851	0.102040
$716$	5.32747	0.199097
$717$	13.3257	0.497657
$718$	−18.2657	−0.681671
$719$	−17.4128	−0.649387	−0.324694	−	0.945819i	$-0.605261\pi$
$719$	−17.4128	−0.649387	−0.324694	+	0.945819i	$0.605261\pi$
$720$	−2.75818	−0.102791
$721$	5.71813	0.212954
$722$	−11.4917	−0.427677
$723$	17.9316	0.666883
$724$	15.7601	0.585718
$725$	−32.8802	−1.22114
$726$	0.750731	0.0278622
$727$	−2.96800	−0.110077	−0.0550384	−	0.998484i	$-0.517528\pi$
$727$	−2.96800	−0.110077	−0.0550384	+	0.998484i	$0.517528\pi$
$728$	6.24340	0.231396
$729$	−1.15137	−0.0426434
$730$	−11.7317	−0.434211
$731$	−0.909012	−0.0336210
$732$	−8.16791	−0.301895
$733$	−22.9899	−0.849150	−0.424575	−	0.905393i	$-0.639576\pi$
$733$	−22.9899	−0.849150	−0.424575	+	0.905393i	$0.639576\pi$
$734$	−16.7913	−0.619779
$735$	−0.246248	−0.00908300
$736$	−4.60483	−0.169736
$737$	−3.08895	−0.113783
$738$	−2.50906	−0.0923598
$739$	3.86566	0.142201	0.0711003	−	0.997469i	$-0.477349\pi$
$739$	3.86566	0.142201	0.0711003	+	0.997469i	$0.477349\pi$
$740$	−10.0063	−0.367838
$741$	4.95800	0.182137
$742$	14.8516	0.545219
$743$	−9.94642	−0.364899	−0.182449	−	0.983215i	$-0.558403\pi$
$743$	−9.94642	−0.364899	−0.182449	+	0.983215i	$0.558403\pi$
$744$	1.59756	0.0585693
$745$	14.9623	0.548178
$746$	24.8615	0.910244
$747$	34.0131	1.24448
$748$	−0.909012	−0.0332368
$749$	−9.17606	−0.335286
$750$	−7.40961	−0.270561
$751$	−16.2101	−0.591514	−0.295757	−	0.955263i	$-0.595572\pi$
$751$	−16.2101	−0.591514	−0.295757	+	0.955263i	$0.595572\pi$
$752$	7.30883	0.266526
$753$	−12.1906	−0.444249
$754$	21.3122	0.776144
$755$	−25.3007	−0.920788
$756$	−10.5722	−0.384507
$757$	−14.0421	−0.510368	−0.255184	−	0.966893i	$-0.582136\pi$
$757$	−14.0421	−0.510368	−0.255184	+	0.966893i	$0.582136\pi$
$758$	14.8602	0.539747
$759$	−3.45699	−0.125481
$760$	3.10202	0.112522
$761$	46.5974	1.68915	0.844577	−	0.535434i	$-0.179852\pi$
$761$	46.5974	1.68915	0.844577	+	0.535434i	$0.179852\pi$
$762$	−0.119574	−0.00433169
$763$	−10.0443	−0.363628
$764$	−23.3075	−0.843237
$765$	2.50722	0.0906487
$766$	−18.6530	−0.673959
$767$	−26.9558	−0.973319
$768$	0.750731	0.0270897
$769$	−0.470118	−0.0169529	−0.00847644	−	0.999964i	$-0.502698\pi$
$769$	−0.470118	−0.0169529	−0.00847644	+	0.999964i	$0.502698\pi$
$770$	2.93253	0.105681
$771$	4.62183	0.166451
$772$	0.0327452	0.00117853
$773$	−38.3530	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$773$	−38.3530	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$774$	−2.43640	−0.0875747
$775$	−7.91280	−0.284236
$776$	−2.30067	−0.0825893
$777$	−17.1891	−0.616655
$778$	15.6304	0.560377
$779$	2.82184	0.101103
$780$	2.04837	0.0733435
$781$	10.7450	0.384487
$782$	4.18585	0.149686
$783$	−36.0888	−1.28971
$784$	−0.289745	−0.0103480
$785$	0.609393	0.0217502
$786$	−11.8232	−0.421718
$787$	1.49777	0.0533899	0.0266949	−	0.999644i	$-0.491502\pi$
$787$	1.49777	0.0533899	0.0266949	+	0.999644i	$0.491502\pi$
$788$	14.9896	0.533982
$789$	−3.78568	−0.134774
$790$	10.1401	0.360769
$791$	41.2678	1.46731
$792$	−2.43640	−0.0865738
$793$	−26.2228	−0.931197
$794$	14.2729	0.506527
$795$	4.87261	0.172814
$796$	−17.5073	−0.620531
$797$	−33.4750	−1.18574	−0.592872	−	0.805296i	$-0.702006\pi$
$797$	−33.4750	−1.18574	−0.592872	+	0.805296i	$0.702006\pi$
$798$	5.32874	0.188635
$799$	−6.64382	−0.235041
$800$	−3.71842	−0.131466
$801$	−33.8256	−1.19517
$802$	29.6581	1.04726
$803$	−10.3631	−0.365705
$804$	−2.31897	−0.0817839
$805$	−13.5038	−0.475947
$806$	5.12889	0.180658
$807$	0.690118	0.0242933
$808$	−11.7393	−0.412987
$809$	17.7070	0.622544	0.311272	−	0.950321i	$-0.399245\pi$
$809$	17.7070	0.622544	0.311272	+	0.950321i	$0.399245\pi$
$810$	4.80594	0.168864
$811$	−31.8027	−1.11674	−0.558372	−	0.829591i	$-0.688574\pi$
$811$	−31.8027	−1.11674	−0.558372	+	0.829591i	$0.688574\pi$
$812$	22.9058	0.803837
$813$	4.56910	0.160245
$814$	−8.83892	−0.309804
$815$	−13.9578	−0.488922
$816$	−0.682424	−0.0238896
$817$	2.74013	0.0958650
$818$	24.5695	0.859051
$819$	−15.2114	−0.531531
$820$	1.16583	0.0407126
$821$	−51.3232	−1.79119	−0.895596	−	0.444868i	$-0.853251\pi$
$821$	−51.3232	−1.79119	−0.895596	+	0.444868i	$0.853251\pi$
$822$	−11.4096	−0.397954
$823$	−42.1801	−1.47031	−0.735153	−	0.677901i	$-0.762890\pi$
$823$	−42.1801	−1.47031	−0.735153	+	0.677901i	$0.762890\pi$
$824$	2.20742	0.0768990
$825$	−2.79153	−0.0971886
$826$	−28.9715	−1.00805
$827$	27.2805	0.948637	0.474319	−	0.880353i	$-0.342694\pi$
$827$	27.2805	0.948637	0.474319	+	0.880353i	$0.342694\pi$
$828$	11.2192	0.389895
$829$	42.9220	1.49074	0.745372	−	0.666649i	$-0.232272\pi$
$829$	42.9220	1.49074	0.745372	+	0.666649i	$0.232272\pi$
$830$	−15.8041	−0.548569
$831$	−20.6607	−0.716713
$832$	2.41019	0.0835584
$833$	0.263382	0.00912563
$834$	1.99895	0.0692178
$835$	−16.0610	−0.555814
$836$	2.74013	0.0947693
$837$	−8.68496	−0.300196
$838$	4.13873	0.142970
$839$	16.4925	0.569384	0.284692	−	0.958619i	$-0.408109\pi$
$839$	16.4925	0.569384	0.284692	+	0.958619i	$0.408109\pi$
$840$	2.20154	0.0759604
$841$	49.1903	1.69622
$842$	−4.66643	−0.160816
$843$	−10.9675	−0.377741
$844$	−27.4658	−0.945410
$845$	−8.14069	−0.280048
$846$	−17.8073	−0.612226
$847$	2.59042	0.0890077
$848$	5.73329	0.196882
$849$	−11.8410	−0.406383
$850$	3.38009	0.115936
$851$	40.7017	1.39524
$852$	8.06661	0.276357
$853$	−1.03795	−0.0355387	−0.0177694	−	0.999842i	$-0.505656\pi$
$853$	−1.03795	−0.0355387	−0.0177694	+	0.999842i	$0.505656\pi$
$854$	−28.1836	−0.964423
$855$	−7.55777	−0.258470
$856$	−3.54231	−0.121074
$857$	−12.3370	−0.421423	−0.210711	−	0.977548i	$-0.567578\pi$
$857$	−12.3370	−0.421423	−0.210711	+	0.977548i	$0.567578\pi$
$858$	1.80941	0.0617721
$859$	15.8617	0.541193	0.270596	−	0.962693i	$-0.412779\pi$
$859$	15.8617	0.541193	0.270596	+	0.962693i	$0.412779\pi$
$860$	1.13207	0.0386033
$861$	2.00270	0.0682518
$862$	6.74631	0.229780
$863$	−32.3648	−1.10171	−0.550855	−	0.834601i	$-0.685698\pi$
$863$	−32.3648	−1.10171	−0.550855	+	0.834601i	$0.685698\pi$
$864$	−4.08128	−0.138848
$865$	14.8919	0.506338
$866$	−0.933746	−0.0317300
$867$	−12.1421	−0.412367
$868$	5.51241	0.187103
$869$	8.95715	0.303851
$870$	7.51509	0.254785
$871$	−7.44497	−0.252263
$872$	−3.87748	−0.131308
$873$	5.60537	0.189713
$874$	−12.6178	−0.426804
$875$	−25.5670	−0.864324
$876$	−7.77988	−0.262858
$877$	−58.1592	−1.96390	−0.981948	−	0.189151i	$-0.939426\pi$
$877$	−58.1592	−1.96390	−0.981948	+	0.189151i	$0.939426\pi$
$878$	7.98566	0.269503
$879$	3.77976	0.127488
$880$	1.13207	0.0381621
$881$	37.0005	1.24658	0.623290	−	0.781991i	$-0.285796\pi$
$881$	37.0005	1.24658	0.623290	+	0.781991i	$0.285796\pi$
$882$	0.705935	0.0237701
$883$	−7.01888	−0.236204	−0.118102	−	0.993001i	$-0.537681\pi$
$883$	−7.01888	−0.236204	−0.118102	+	0.993001i	$0.537681\pi$
$884$	−2.19089	−0.0736877
$885$	−9.50514	−0.319512
$886$	22.2681	0.748112
$887$	−32.3925	−1.08763	−0.543816	−	0.839204i	$-0.683021\pi$
$887$	−32.3925	−1.08763	−0.543816	+	0.839204i	$0.683021\pi$
$888$	−6.63565	−0.222678
$889$	−0.412592	−0.0138379
$890$	15.7170	0.526836
$891$	4.24527	0.142222
$892$	9.54214	0.319494
$893$	20.0271	0.670183
$894$	9.92226	0.331850
$895$	6.03107	0.201596
$896$	2.59042	0.0865397
$897$	−8.33200	−0.278197
$898$	20.0117	0.667799
$899$	18.8169	0.627579
$900$	9.05956	0.301985
$901$	−5.21163	−0.173625
$902$	1.02982	0.0342893
$903$	1.94471	0.0647157
$904$	15.9309	0.529855
$905$	17.8415	0.593071
$906$	−16.7782	−0.557417
$907$	11.4617	0.380579	0.190290	−	0.981728i	$-0.439057\pi$
$907$	11.4617	0.380579	0.190290	+	0.981728i	$0.439057\pi$
$908$	10.9961	0.364919
$909$	28.6017	0.948658
$910$	7.06796	0.234301
$911$	−36.3336	−1.20379	−0.601893	−	0.798577i	$-0.705587\pi$
$911$	−36.3336	−1.20379	−0.601893	+	0.798577i	$0.705587\pi$
$912$	2.05710	0.0681174
$913$	−13.9604	−0.462021
$914$	10.5423	0.348709
$915$	−9.24665	−0.305685
$916$	10.0400	0.331732
$917$	−40.7961	−1.34721
$918$	3.70993	0.122446
$919$	−41.4595	−1.36762	−0.683812	−	0.729659i	$-0.739679\pi$
$919$	−41.4595	−1.36762	−0.683812	+	0.729659i	$0.739679\pi$
$920$	−5.21299	−0.171867
$921$	25.1043	0.827215
$922$	21.9203	0.721906
$923$	25.8975	0.852427
$924$	1.94471	0.0639761
$925$	32.8668	1.08065
$926$	−30.5090	−1.00259
$927$	−5.37816	−0.176642
$928$	8.84253	0.290270
$929$	10.3243	0.338728	0.169364	−	0.985554i	$-0.445829\pi$
$929$	10.3243	0.338728	0.169364	+	0.985554i	$0.445829\pi$
$930$	1.80855	0.0593045
$931$	−0.793938	−0.0260203
$932$	−1.79664	−0.0588508
$933$	15.6163	0.511254
$934$	−8.96263	−0.293266
$935$	−1.02907	−0.0336540
$936$	−5.87220	−0.191939
$937$	−8.74336	−0.285633	−0.142817	−	0.989749i	$-0.545616\pi$
$937$	−8.74336	−0.285633	−0.142817	+	0.989749i	$0.545616\pi$
$938$	−8.00168	−0.261264
$939$	2.69094	0.0878154
$940$	8.27411	0.269872
$941$	−0.569829	−0.0185759	−0.00928795	−	0.999957i	$-0.502956\pi$
$941$	−0.569829	−0.0185759	−0.00928795	+	0.999957i	$0.502956\pi$
$942$	0.404118	0.0131669
$943$	−4.74215	−0.154426
$944$	−11.1841	−0.364012
$945$	−11.9685	−0.389334
$946$	1.00000	0.0325128
$947$	−61.3660	−1.99413	−0.997064	−	0.0765768i	$-0.975601\pi$
$947$	−61.3660	−1.99413	−0.997064	+	0.0765768i	$0.975601\pi$
$948$	6.72441	0.218399
$949$	−24.9770	−0.810788
$950$	−10.1889	−0.330573
$951$	22.3595	0.725056
$952$	−2.35472	−0.0763169
$953$	−13.5423	−0.438679	−0.219339	−	0.975649i	$-0.570390\pi$
$953$	−13.5423	−0.438679	−0.219339	+	0.975649i	$0.570390\pi$
$954$	−13.9686	−0.452250
$955$	−26.3858	−0.853823
$956$	17.7503	0.574086
$957$	6.63836	0.214588
$958$	27.3156	0.882527
$959$	−39.3689	−1.27129
$960$	0.849880	0.0274298
$961$	−26.4716	−0.853923
$962$	−21.3035	−0.686852
$963$	8.63050	0.278114
$964$	23.8855	0.769300
$965$	0.0370699	0.00119332
$966$	−8.95503	−0.288124
$967$	−40.5946	−1.30543	−0.652717	−	0.757602i	$-0.726371\pi$
$967$	−40.5946	−1.30543	−0.652717	+	0.757602i	$0.726371\pi$
$968$	1.00000	0.0321412
$969$	−1.86993	−0.0600708
$970$	−2.60452	−0.0836262
$971$	31.4783	1.01019	0.505094	−	0.863065i	$-0.331458\pi$
$971$	31.4783	1.01019	0.505094	+	0.863065i	$0.331458\pi$
$972$	15.4309	0.494946
$973$	6.89741	0.221121
$974$	−0.968881	−0.0310449
$975$	−6.72812	−0.215472
$976$	−10.8799	−0.348259
$977$	−4.45075	−0.142392	−0.0711961	−	0.997462i	$-0.522682\pi$
$977$	−4.45075	−0.142392	−0.0711961	+	0.997462i	$0.522682\pi$
$978$	−9.25612	−0.295978
$979$	13.8834	0.443716
$980$	−0.328011	−0.0104779
$981$	9.44711	0.301623
$982$	1.66674	0.0531877
$983$	−26.9309	−0.858962	−0.429481	−	0.903076i	$-0.641303\pi$
$983$	−26.9309	−0.858962	−0.429481	+	0.903076i	$0.641303\pi$
$984$	0.773119	0.0246461
$985$	16.9693	0.540686
$986$	−8.03797	−0.255981
$987$	14.2135	0.452422
$988$	6.60424	0.210109
$989$	−4.60483	−0.146425
$990$	−2.75818	−0.0876607
$991$	−34.4931	−1.09571	−0.547854	−	0.836574i	$-0.684555\pi$
$991$	−34.4931	−1.09571	−0.547854	+	0.836574i	$0.684555\pi$
$992$	2.12800	0.0675641
$993$	22.4258	0.711661
$994$	27.8340	0.882842
$995$	−19.8195	−0.628321
$996$	−10.4805	−0.332087
$997$	−53.0179	−1.67909	−0.839547	−	0.543287i	$-0.817179\pi$
$997$	−53.0179	−1.67909	−0.839547	+	0.543287i	$0.817179\pi$
$998$	−3.81680	−0.120819
$999$	36.0741	1.14133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.a.k.1.4	✓	7
3.2	odd	2		8514.2.a.bl.1.5		7
4.3	odd	2		7568.2.a.bg.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.a.k.1.4	✓	7	1.1	even	1	trivial
7568.2.a.bg.1.4		7	4.3	odd	2
8514.2.a.bl.1.5		7	3.2	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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.750731 q^{3} +1.00000 q^{4} +1.13207 q^{5} +0.750731 q^{6} +2.59042 q^{7} +1.00000 q^{8} -2.43640 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.750731 q^{3} +1.00000 q^{4} +1.13207 q^{5} +0.750731 q^{6} +2.59042 q^{7} +1.00000 q^{8} -2.43640 q^{9} +1.13207 q^{10} +1.00000 q^{11} +0.750731 q^{12} +2.41019 q^{13} +2.59042 q^{14} +0.849880 q^{15} +1.00000 q^{16} -0.909012 q^{17} -2.43640 q^{18} +2.74013 q^{19} +1.13207 q^{20} +1.94471 q^{21} +1.00000 q^{22} -4.60483 q^{23} +0.750731 q^{24} -3.71842 q^{25} +2.41019 q^{26} -4.08128 q^{27} +2.59042 q^{28} +8.84253 q^{29} +0.849880 q^{30} +2.12800 q^{31} +1.00000 q^{32} +0.750731 q^{33} -0.909012 q^{34} +2.93253 q^{35} -2.43640 q^{36} -8.83892 q^{37} +2.74013 q^{38} +1.80941 q^{39} +1.13207 q^{40} +1.02982 q^{41} +1.94471 q^{42} +1.00000 q^{43} +1.00000 q^{44} -2.75818 q^{45} -4.60483 q^{46} +7.30883 q^{47} +0.750731 q^{48} -0.289745 q^{49} -3.71842 q^{50} -0.682424 q^{51} +2.41019 q^{52} +5.73329 q^{53} -4.08128 q^{54} +1.13207 q^{55} +2.59042 q^{56} +2.05710 q^{57} +8.84253 q^{58} -11.1841 q^{59} +0.849880 q^{60} -10.8799 q^{61} +2.12800 q^{62} -6.31130 q^{63} +1.00000 q^{64} +2.72851 q^{65} +0.750731 q^{66} -3.08895 q^{67} -0.909012 q^{68} -3.45699 q^{69} +2.93253 q^{70} +10.7450 q^{71} -2.43640 q^{72} -10.3631 q^{73} -8.83892 q^{74} -2.79153 q^{75} +2.74013 q^{76} +2.59042 q^{77} +1.80941 q^{78} +8.95715 q^{79} +1.13207 q^{80} +4.24527 q^{81} +1.02982 q^{82} -13.9604 q^{83} +1.94471 q^{84} -1.02907 q^{85} +1.00000 q^{86} +6.63836 q^{87} +1.00000 q^{88} +13.8834 q^{89} -2.75818 q^{90} +6.24340 q^{91} -4.60483 q^{92} +1.59756 q^{93} +7.30883 q^{94} +3.10202 q^{95} +0.750731 q^{96} -2.30067 q^{97} -0.289745 q^{98} -2.43640 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 + 8 * q^5 + 3 * q^6 - 2 * q^7 + 7 * q^8 + 10 * q^9	\( 7 q + 7 q^{2} + 3 q^{3} + 7 q^{4} + 8 q^{5} + 3 q^{6} - 2 q^{7} + 7 q^{8} + 10 q^{9} + 8 q^{10} + 7 q^{11} + 3 q^{12} + 4 q^{13} - 2 q^{14} + 2 q^{15} + 7 q^{16} + 10 q^{17} + 10 q^{18} - 2 q^{19} + 8 q^{20} + 7 q^{22} - 4 q^{23} + 3 q^{24} + 11 q^{25} + 4 q^{26} + 15 q^{27} - 2 q^{28} + 5 q^{29} + 2 q^{30} - 2 q^{31} + 7 q^{32} + 3 q^{33} + 10 q^{34} - 10 q^{35} + 10 q^{36} + 6 q^{37} - 2 q^{38} - 8 q^{39} + 8 q^{40} + 4 q^{41} + 7 q^{43} + 7 q^{44} - 2 q^{45} - 4 q^{46} - 6 q^{47} + 3 q^{48} + 31 q^{49} + 11 q^{50} - 14 q^{51} + 4 q^{52} + q^{53} + 15 q^{54} + 8 q^{55} - 2 q^{56} - 30 q^{57} + 5 q^{58} - 4 q^{59} + 2 q^{60} + 9 q^{61} - 2 q^{62} - 24 q^{63} + 7 q^{64} + 18 q^{65} + 3 q^{66} - 6 q^{67} + 10 q^{68} + 2 q^{69} - 10 q^{70} + 10 q^{72} + 13 q^{73} + 6 q^{74} - 9 q^{75} - 2 q^{76} - 2 q^{77} - 8 q^{78} - 31 q^{79} + 8 q^{80} - 25 q^{81} + 4 q^{82} - 11 q^{83} - 24 q^{85} + 7 q^{86} - 13 q^{87} + 7 q^{88} + 10 q^{89} - 2 q^{90} - 12 q^{91} - 4 q^{92} + 12 q^{93} - 6 q^{94} - 18 q^{95} + 3 q^{96} + 23 q^{97} + 31 q^{98} + 10 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 3 * q^3 + 7 * q^4 + 8 * q^5 + 3 * q^6 - 2 * q^7 + 7 * q^8 + 10 * q^9 + 8 * q^10 + 7 * q^11 + 3 * q^12 + 4 * q^13 - 2 * q^14 + 2 * q^15 + 7 * q^16 + 10 * q^17 + 10 * q^18 - 2 * q^19 + 8 * q^20 + 7 * q^22 - 4 * q^23 + 3 * q^24 + 11 * q^25 + 4 * q^26 + 15 * q^27 - 2 * q^28 + 5 * q^29 + 2 * q^30 - 2 * q^31 + 7 * q^32 + 3 * q^33 + 10 * q^34 - 10 * q^35 + 10 * q^36 + 6 * q^37 - 2 * q^38 - 8 * q^39 + 8 * q^40 + 4 * q^41 + 7 * q^43 + 7 * q^44 - 2 * q^45 - 4 * q^46 - 6 * q^47 + 3 * q^48 + 31 * q^49 + 11 * q^50 - 14 * q^51 + 4 * q^52 + q^53 + 15 * q^54 + 8 * q^55 - 2 * q^56 - 30 * q^57 + 5 * q^58 - 4 * q^59 + 2 * q^60 + 9 * q^61 - 2 * q^62 - 24 * q^63 + 7 * q^64 + 18 * q^65 + 3 * q^66 - 6 * q^67 + 10 * q^68 + 2 * q^69 - 10 * q^70 + 10 * q^72 + 13 * q^73 + 6 * q^74 - 9 * q^75 - 2 * q^76 - 2 * q^77 - 8 * q^78 - 31 * q^79 + 8 * q^80 - 25 * q^81 + 4 * q^82 - 11 * q^83 - 24 * q^85 + 7 * q^86 - 13 * q^87 + 7 * q^88 + 10 * q^89 - 2 * q^90 - 12 * q^91 - 4 * q^92 + 12 * q^93 - 6 * q^94 - 18 * q^95 + 3 * q^96 + 23 * q^97 + 31 * q^98 + 10 * q^99

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