LMFDB - Embedded newform 910.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [910,2,Mod(1,910)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(910, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("910.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 910 = 2 \cdot 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	910.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:	$7.26638658394$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	910.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.82843 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.82843 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.82843 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.82843 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.00000 q^{9} -1.00000 q^{10} +4.00000 q^{11} +2.82843 q^{12} +1.00000 q^{13} -1.00000 q^{14} +2.82843 q^{15} +1.00000 q^{16} +0.828427 q^{17} -5.00000 q^{18} -6.82843 q^{19} +1.00000 q^{20} +2.82843 q^{21} -4.00000 q^{22} -6.82843 q^{23} -2.82843 q^{24} +1.00000 q^{25} -1.00000 q^{26} +5.65685 q^{27} +1.00000 q^{28} +6.00000 q^{29} -2.82843 q^{30} +1.65685 q^{31} -1.00000 q^{32} +11.3137 q^{33} -0.828427 q^{34} +1.00000 q^{35} +5.00000 q^{36} -3.65685 q^{37} +6.82843 q^{38} +2.82843 q^{39} -1.00000 q^{40} -10.4853 q^{41} -2.82843 q^{42} +11.3137 q^{43} +4.00000 q^{44} +5.00000 q^{45} +6.82843 q^{46} -11.3137 q^{47} +2.82843 q^{48} +1.00000 q^{49} -1.00000 q^{50} +2.34315 q^{51} +1.00000 q^{52} +8.82843 q^{53} -5.65685 q^{54} +4.00000 q^{55} -1.00000 q^{56} -19.3137 q^{57} -6.00000 q^{58} +6.82843 q^{59} +2.82843 q^{60} -11.6569 q^{61} -1.65685 q^{62} +5.00000 q^{63} +1.00000 q^{64} +1.00000 q^{65} -11.3137 q^{66} -9.65685 q^{67} +0.828427 q^{68} -19.3137 q^{69} -1.00000 q^{70} +10.8284 q^{71} -5.00000 q^{72} +0.343146 q^{73} +3.65685 q^{74} +2.82843 q^{75} -6.82843 q^{76} +4.00000 q^{77} -2.82843 q^{78} -11.3137 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.4853 q^{82} -2.34315 q^{83} +2.82843 q^{84} +0.828427 q^{85} -11.3137 q^{86} +16.9706 q^{87} -4.00000 q^{88} +16.8284 q^{89} -5.00000 q^{90} +1.00000 q^{91} -6.82843 q^{92} +4.68629 q^{93} +11.3137 q^{94} -6.82843 q^{95} -2.82843 q^{96} -5.31371 q^{97} -1.00000 q^{98} +20.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} - 2 q^{8} + 10 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 - 2 * q^8 + 10 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} - 2 q^{8} + 10 q^{9} - 2 q^{10} + 8 q^{11} + 2 q^{13} - 2 q^{14} + 2 q^{16} - 4 q^{17} - 10 q^{18} - 8 q^{19} + 2 q^{20} - 8 q^{22} - 8 q^{23} + 2 q^{25} - 2 q^{26} + 2 q^{28} + 12 q^{29} - 8 q^{31} - 2 q^{32} + 4 q^{34} + 2 q^{35} + 10 q^{36} + 4 q^{37} + 8 q^{38} - 2 q^{40} - 4 q^{41} + 8 q^{44} + 10 q^{45} + 8 q^{46} + 2 q^{49} - 2 q^{50} + 16 q^{51} + 2 q^{52} + 12 q^{53} + 8 q^{55} - 2 q^{56} - 16 q^{57} - 12 q^{58} + 8 q^{59} - 12 q^{61} + 8 q^{62} + 10 q^{63} + 2 q^{64} + 2 q^{65} - 8 q^{67} - 4 q^{68} - 16 q^{69} - 2 q^{70} + 16 q^{71} - 10 q^{72} + 12 q^{73} - 4 q^{74} - 8 q^{76} + 8 q^{77} + 2 q^{80} + 2 q^{81} + 4 q^{82} - 16 q^{83} - 4 q^{85} - 8 q^{88} + 28 q^{89} - 10 q^{90} + 2 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{95} + 12 q^{97} - 2 q^{98} + 40 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 - 2 * q^8 + 10 * q^9 - 2 * q^10 + 8 * q^11 + 2 * q^13 - 2 * q^14 + 2 * q^16 - 4 * q^17 - 10 * q^18 - 8 * q^19 + 2 * q^20 - 8 * q^22 - 8 * q^23 + 2 * q^25 - 2 * q^26 + 2 * q^28 + 12 * q^29 - 8 * q^31 - 2 * q^32 + 4 * q^34 + 2 * q^35 + 10 * q^36 + 4 * q^37 + 8 * q^38 - 2 * q^40 - 4 * q^41 + 8 * q^44 + 10 * q^45 + 8 * q^46 + 2 * q^49 - 2 * q^50 + 16 * q^51 + 2 * q^52 + 12 * q^53 + 8 * q^55 - 2 * q^56 - 16 * q^57 - 12 * q^58 + 8 * q^59 - 12 * q^61 + 8 * q^62 + 10 * q^63 + 2 * q^64 + 2 * q^65 - 8 * q^67 - 4 * q^68 - 16 * q^69 - 2 * q^70 + 16 * q^71 - 10 * q^72 + 12 * q^73 - 4 * q^74 - 8 * q^76 + 8 * q^77 + 2 * q^80 + 2 * q^81 + 4 * q^82 - 16 * q^83 - 4 * q^85 - 8 * q^88 + 28 * q^89 - 10 * q^90 + 2 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^95 + 12 * q^97 - 2 * q^98 + 40 * 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
$3$	2.82843	1.63299	0.816497	−	0.577350i	$-0.195913\pi$
$3$	2.82843	1.63299	0.816497	+	0.577350i	$0.195913\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.82843	−1.15470
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	5.00000	1.66667
$10$	−1.00000	−0.316228
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	2.82843	0.816497
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.00000	−0.267261
$15$	2.82843	0.730297
$16$	1.00000	0.250000
$17$	0.828427	0.200923	0.100462	−	0.994941i	$-0.467968\pi$
$17$	0.828427	0.200923	0.100462	+	0.994941i	$0.467968\pi$
$18$	−5.00000	−1.17851
$19$	−6.82843	−1.56655	−0.783274	−	0.621676i	$-0.786452\pi$
$19$	−6.82843	−1.56655	−0.783274	+	0.621676i	$0.786452\pi$
$20$	1.00000	0.223607
$21$	2.82843	0.617213
$22$	−4.00000	−0.852803
$23$	−6.82843	−1.42383	−0.711913	−	0.702268i	$-0.752171\pi$
$23$	−6.82843	−1.42383	−0.711913	+	0.702268i	$0.752171\pi$
$24$	−2.82843	−0.577350
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	5.65685	1.08866
$28$	1.00000	0.188982
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	−2.82843	−0.516398
$31$	1.65685	0.297580	0.148790	−	0.988869i	$-0.452462\pi$
$31$	1.65685	0.297580	0.148790	+	0.988869i	$0.452462\pi$
$32$	−1.00000	−0.176777
$33$	11.3137	1.96946
$34$	−0.828427	−0.142074
$35$	1.00000	0.169031
$36$	5.00000	0.833333
$37$	−3.65685	−0.601183	−0.300592	−	0.953753i	$-0.597184\pi$
$37$	−3.65685	−0.601183	−0.300592	+	0.953753i	$0.597184\pi$
$38$	6.82843	1.10772
$39$	2.82843	0.452911
$40$	−1.00000	−0.158114
$41$	−10.4853	−1.63753	−0.818763	−	0.574132i	$-0.805340\pi$
$41$	−10.4853	−1.63753	−0.818763	+	0.574132i	$0.805340\pi$
$42$	−2.82843	−0.436436
$43$	11.3137	1.72532	0.862662	−	0.505781i	$-0.168795\pi$
$43$	11.3137	1.72532	0.862662	+	0.505781i	$0.168795\pi$
$44$	4.00000	0.603023
$45$	5.00000	0.745356
$46$	6.82843	1.00680
$47$	−11.3137	−1.65027	−0.825137	−	0.564933i	$-0.808902\pi$
$47$	−11.3137	−1.65027	−0.825137	+	0.564933i	$0.808902\pi$
$48$	2.82843	0.408248
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	2.34315	0.328106
$52$	1.00000	0.138675
$53$	8.82843	1.21268	0.606339	−	0.795206i	$-0.292638\pi$
$53$	8.82843	1.21268	0.606339	+	0.795206i	$0.292638\pi$
$54$	−5.65685	−0.769800
$55$	4.00000	0.539360
$56$	−1.00000	−0.133631
$57$	−19.3137	−2.55816
$58$	−6.00000	−0.787839
$59$	6.82843	0.888985	0.444493	−	0.895782i	$-0.353384\pi$
$59$	6.82843	0.888985	0.444493	+	0.895782i	$0.353384\pi$
$60$	2.82843	0.365148
$61$	−11.6569	−1.49251	−0.746254	−	0.665662i	$-0.768149\pi$
$61$	−11.6569	−1.49251	−0.746254	+	0.665662i	$0.768149\pi$
$62$	−1.65685	−0.210421
$63$	5.00000	0.629941
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	−11.3137	−1.39262
$67$	−9.65685	−1.17977	−0.589886	−	0.807486i	$-0.700827\pi$
$67$	−9.65685	−1.17977	−0.589886	+	0.807486i	$0.700827\pi$
$68$	0.828427	0.100462
$69$	−19.3137	−2.32510
$70$	−1.00000	−0.119523
$71$	10.8284	1.28510	0.642549	−	0.766245i	$-0.277877\pi$
$71$	10.8284	1.28510	0.642549	+	0.766245i	$0.277877\pi$
$72$	−5.00000	−0.589256
$73$	0.343146	0.0401622	0.0200811	−	0.999798i	$-0.493608\pi$
$73$	0.343146	0.0401622	0.0200811	+	0.999798i	$0.493608\pi$
$74$	3.65685	0.425101
$75$	2.82843	0.326599
$76$	−6.82843	−0.783274
$77$	4.00000	0.455842
$78$	−2.82843	−0.320256
$79$	−11.3137	−1.27289	−0.636446	−	0.771321i	$-0.719596\pi$
$79$	−11.3137	−1.27289	−0.636446	+	0.771321i	$0.719596\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	10.4853	1.15791
$83$	−2.34315	−0.257194	−0.128597	−	0.991697i	$-0.541047\pi$
$83$	−2.34315	−0.257194	−0.128597	+	0.991697i	$0.541047\pi$
$84$	2.82843	0.308607
$85$	0.828427	0.0898555
$86$	−11.3137	−1.21999
$87$	16.9706	1.81944
$88$	−4.00000	−0.426401
$89$	16.8284	1.78381	0.891905	−	0.452223i	$-0.149369\pi$
$89$	16.8284	1.78381	0.891905	+	0.452223i	$0.149369\pi$
$90$	−5.00000	−0.527046
$91$	1.00000	0.104828
$92$	−6.82843	−0.711913
$93$	4.68629	0.485946
$94$	11.3137	1.16692
$95$	−6.82843	−0.700582
$96$	−2.82843	−0.288675
$97$	−5.31371	−0.539525	−0.269763	−	0.962927i	$-0.586945\pi$
$97$	−5.31371	−0.539525	−0.269763	+	0.962927i	$0.586945\pi$
$98$	−1.00000	−0.101015
$99$	20.0000	2.01008
$100$	1.00000	0.100000
$101$	7.65685	0.761885	0.380943	−	0.924599i	$-0.375599\pi$
$101$	7.65685	0.761885	0.380943	+	0.924599i	$0.375599\pi$
$102$	−2.34315	−0.232006
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	−1.00000	−0.0980581
$105$	2.82843	0.276026
$106$	−8.82843	−0.857493
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	5.65685	0.544331
$109$	−10.4853	−1.00431	−0.502154	−	0.864778i	$-0.667459\pi$
$109$	−10.4853	−1.00431	−0.502154	+	0.864778i	$0.667459\pi$
$110$	−4.00000	−0.381385
$111$	−10.3431	−0.981728
$112$	1.00000	0.0944911
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	19.3137	1.80889
$115$	−6.82843	−0.636754
$116$	6.00000	0.557086
$117$	5.00000	0.462250
$118$	−6.82843	−0.628608
$119$	0.828427	0.0759418
$120$	−2.82843	−0.258199
$121$	5.00000	0.454545
$122$	11.6569	1.05536
$123$	−29.6569	−2.67407
$124$	1.65685	0.148790
$125$	1.00000	0.0894427
$126$	−5.00000	−0.445435
$127$	−12.4853	−1.10789	−0.553945	−	0.832553i	$-0.686878\pi$
$127$	−12.4853	−1.10789	−0.553945	+	0.832553i	$0.686878\pi$
$128$	−1.00000	−0.0883883
$129$	32.0000	2.81744
$130$	−1.00000	−0.0877058
$131$	16.0000	1.39793	0.698963	−	0.715158i	$-0.253645\pi$
$131$	16.0000	1.39793	0.698963	+	0.715158i	$0.253645\pi$
$132$	11.3137	0.984732
$133$	−6.82843	−0.592100
$134$	9.65685	0.834225
$135$	5.65685	0.486864
$136$	−0.828427	−0.0710370
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	19.3137	1.64409
$139$	3.31371	0.281065	0.140533	−	0.990076i	$-0.455119\pi$
$139$	3.31371	0.281065	0.140533	+	0.990076i	$0.455119\pi$
$140$	1.00000	0.0845154
$141$	−32.0000	−2.69489
$142$	−10.8284	−0.908701
$143$	4.00000	0.334497
$144$	5.00000	0.416667
$145$	6.00000	0.498273
$146$	−0.343146	−0.0283989
$147$	2.82843	0.233285
$148$	−3.65685	−0.300592
$149$	−2.48528	−0.203602	−0.101801	−	0.994805i	$-0.532461\pi$
$149$	−2.48528	−0.203602	−0.101801	+	0.994805i	$0.532461\pi$
$150$	−2.82843	−0.230940
$151$	6.14214	0.499840	0.249920	−	0.968267i	$-0.419596\pi$
$151$	6.14214	0.499840	0.249920	+	0.968267i	$0.419596\pi$
$152$	6.82843	0.553859
$153$	4.14214	0.334872
$154$	−4.00000	−0.322329
$155$	1.65685	0.133082
$156$	2.82843	0.226455
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	11.3137	0.900070
$159$	24.9706	1.98029
$160$	−1.00000	−0.0790569
$161$	−6.82843	−0.538155
$162$	−1.00000	−0.0785674
$163$	1.65685	0.129775	0.0648874	−	0.997893i	$-0.479331\pi$
$163$	1.65685	0.129775	0.0648874	+	0.997893i	$0.479331\pi$
$164$	−10.4853	−0.818763
$165$	11.3137	0.880771
$166$	2.34315	0.181863
$167$	−24.9706	−1.93228	−0.966140	−	0.258018i	$-0.916931\pi$
$167$	−24.9706	−1.93228	−0.966140	+	0.258018i	$0.916931\pi$
$168$	−2.82843	−0.218218
$169$	1.00000	0.0769231
$170$	−0.828427	−0.0635375
$171$	−34.1421	−2.61091
$172$	11.3137	0.862662
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	−16.9706	−1.28654
$175$	1.00000	0.0755929
$176$	4.00000	0.301511
$177$	19.3137	1.45171
$178$	−16.8284	−1.26134
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	5.00000	0.372678
$181$	10.9706	0.815436	0.407718	−	0.913108i	$-0.366325\pi$
$181$	10.9706	0.815436	0.407718	+	0.913108i	$0.366325\pi$
$182$	−1.00000	−0.0741249
$183$	−32.9706	−2.43725
$184$	6.82843	0.503398
$185$	−3.65685	−0.268857
$186$	−4.68629	−0.343616
$187$	3.31371	0.242322
$188$	−11.3137	−0.825137
$189$	5.65685	0.411476
$190$	6.82843	0.495386
$191$	10.3431	0.748404	0.374202	−	0.927347i	$-0.377917\pi$
$191$	10.3431	0.748404	0.374202	+	0.927347i	$0.377917\pi$
$192$	2.82843	0.204124
$193$	6.00000	0.431889	0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000	0.431889	0.215945	+	0.976406i	$0.430717\pi$
$194$	5.31371	0.381502
$195$	2.82843	0.202548
$196$	1.00000	0.0714286
$197$	−11.6569	−0.830516	−0.415258	−	0.909704i	$-0.636309\pi$
$197$	−11.6569	−0.830516	−0.415258	+	0.909704i	$0.636309\pi$
$198$	−20.0000	−1.42134
$199$	5.65685	0.401004	0.200502	−	0.979693i	$-0.435743\pi$
$199$	5.65685	0.401004	0.200502	+	0.979693i	$0.435743\pi$
$200$	−1.00000	−0.0707107
$201$	−27.3137	−1.92656
$202$	−7.65685	−0.538734
$203$	6.00000	0.421117
$204$	2.34315	0.164053
$205$	−10.4853	−0.732324
$206$	0	0
$207$	−34.1421	−2.37304
$208$	1.00000	0.0693375
$209$	−27.3137	−1.88933
$210$	−2.82843	−0.195180
$211$	−17.6569	−1.21555	−0.607774	−	0.794110i	$-0.707937\pi$
$211$	−17.6569	−1.21555	−0.607774	+	0.794110i	$0.707937\pi$
$212$	8.82843	0.606339
$213$	30.6274	2.09856
$214$	−8.00000	−0.546869
$215$	11.3137	0.771589
$216$	−5.65685	−0.384900
$217$	1.65685	0.112475
$218$	10.4853	0.710153
$219$	0.970563	0.0655846
$220$	4.00000	0.269680
$221$	0.828427	0.0557260
$222$	10.3431	0.694186
$223$	−8.97056	−0.600713	−0.300357	−	0.953827i	$-0.597106\pi$
$223$	−8.97056	−0.600713	−0.300357	+	0.953827i	$0.597106\pi$
$224$	−1.00000	−0.0668153
$225$	5.00000	0.333333
$226$	−10.0000	−0.665190
$227$	−21.6569	−1.43742	−0.718708	−	0.695312i	$-0.755266\pi$
$227$	−21.6569	−1.43742	−0.718708	+	0.695312i	$0.755266\pi$
$228$	−19.3137	−1.27908
$229$	3.65685	0.241652	0.120826	−	0.992674i	$-0.461446\pi$
$229$	3.65685	0.241652	0.120826	+	0.992674i	$0.461446\pi$
$230$	6.82843	0.450253
$231$	11.3137	0.744387
$232$	−6.00000	−0.393919
$233$	−22.9706	−1.50485	−0.752426	−	0.658677i	$-0.771116\pi$
$233$	−22.9706	−1.50485	−0.752426	+	0.658677i	$0.771116\pi$
$234$	−5.00000	−0.326860
$235$	−11.3137	−0.738025
$236$	6.82843	0.444493
$237$	−32.0000	−2.07862
$238$	−0.828427	−0.0536990
$239$	−0.485281	−0.0313902	−0.0156951	−	0.999877i	$-0.504996\pi$
$239$	−0.485281	−0.0313902	−0.0156951	+	0.999877i	$0.504996\pi$
$240$	2.82843	0.182574
$241$	−4.82843	−0.311026	−0.155513	−	0.987834i	$-0.549703\pi$
$241$	−4.82843	−0.311026	−0.155513	+	0.987834i	$0.549703\pi$
$242$	−5.00000	−0.321412
$243$	−14.1421	−0.907218
$244$	−11.6569	−0.746254
$245$	1.00000	0.0638877
$246$	29.6569	1.89085
$247$	−6.82843	−0.434482
$248$	−1.65685	−0.105210
$249$	−6.62742	−0.419995
$250$	−1.00000	−0.0632456
$251$	24.9706	1.57613	0.788064	−	0.615593i	$-0.211084\pi$
$251$	24.9706	1.57613	0.788064	+	0.615593i	$0.211084\pi$
$252$	5.00000	0.314970
$253$	−27.3137	−1.71720
$254$	12.4853	0.783396
$255$	2.34315	0.146733
$256$	1.00000	0.0625000
$257$	8.82843	0.550702	0.275351	−	0.961344i	$-0.411206\pi$
$257$	8.82843	0.550702	0.275351	+	0.961344i	$0.411206\pi$
$258$	−32.0000	−1.99223
$259$	−3.65685	−0.227226
$260$	1.00000	0.0620174
$261$	30.0000	1.85695
$262$	−16.0000	−0.988483
$263$	−21.4558	−1.32302	−0.661512	−	0.749935i	$-0.730085\pi$
$263$	−21.4558	−1.32302	−0.661512	+	0.749935i	$0.730085\pi$
$264$	−11.3137	−0.696311
$265$	8.82843	0.542326
$266$	6.82843	0.418678
$267$	47.5980	2.91295
$268$	−9.65685	−0.589886
$269$	4.34315	0.264806	0.132403	−	0.991196i	$-0.457731\pi$
$269$	4.34315	0.264806	0.132403	+	0.991196i	$0.457731\pi$
$270$	−5.65685	−0.344265
$271$	−28.9706	−1.75984	−0.879918	−	0.475125i	$-0.842403\pi$
$271$	−28.9706	−1.75984	−0.879918	+	0.475125i	$0.842403\pi$
$272$	0.828427	0.0502308
$273$	2.82843	0.171184
$274$	10.0000	0.604122
$275$	4.00000	0.241209
$276$	−19.3137	−1.16255
$277$	−16.1421	−0.969887	−0.484943	−	0.874546i	$-0.661160\pi$
$277$	−16.1421	−0.969887	−0.484943	+	0.874546i	$0.661160\pi$
$278$	−3.31371	−0.198743
$279$	8.28427	0.495966
$280$	−1.00000	−0.0597614
$281$	26.9706	1.60893	0.804464	−	0.594001i	$-0.202452\pi$
$281$	26.9706	1.60893	0.804464	+	0.594001i	$0.202452\pi$
$282$	32.0000	1.90557
$283$	−21.1716	−1.25852	−0.629260	−	0.777195i	$-0.716642\pi$
$283$	−21.1716	−1.25852	−0.629260	+	0.777195i	$0.716642\pi$
$284$	10.8284	0.642549
$285$	−19.3137	−1.14405
$286$	−4.00000	−0.236525
$287$	−10.4853	−0.618927
$288$	−5.00000	−0.294628
$289$	−16.3137	−0.959630
$290$	−6.00000	−0.352332
$291$	−15.0294	−0.881041
$292$	0.343146	0.0200811
$293$	−10.0000	−0.584206	−0.292103	−	0.956387i	$-0.594355\pi$
$293$	−10.0000	−0.584206	−0.292103	+	0.956387i	$0.594355\pi$
$294$	−2.82843	−0.164957
$295$	6.82843	0.397566
$296$	3.65685	0.212550
$297$	22.6274	1.31298
$298$	2.48528	0.143968
$299$	−6.82843	−0.394898
$300$	2.82843	0.163299
$301$	11.3137	0.652111
$302$	−6.14214	−0.353440
$303$	21.6569	1.24415
$304$	−6.82843	−0.391637
$305$	−11.6569	−0.667470
$306$	−4.14214	−0.236790
$307$	4.68629	0.267461	0.133730	−	0.991018i	$-0.457304\pi$
$307$	4.68629	0.267461	0.133730	+	0.991018i	$0.457304\pi$
$308$	4.00000	0.227921
$309$	0	0
$310$	−1.65685	−0.0941030
$311$	−8.97056	−0.508674	−0.254337	−	0.967116i	$-0.581857\pi$
$311$	−8.97056	−0.508674	−0.254337	+	0.967116i	$0.581857\pi$
$312$	−2.82843	−0.160128
$313$	28.1421	1.59069	0.795344	−	0.606159i	$-0.207290\pi$
$313$	28.1421	1.59069	0.795344	+	0.606159i	$0.207290\pi$
$314$	2.00000	0.112867
$315$	5.00000	0.281718
$316$	−11.3137	−0.636446
$317$	21.3137	1.19710	0.598549	−	0.801087i	$-0.295744\pi$
$317$	21.3137	1.19710	0.598549	+	0.801087i	$0.295744\pi$
$318$	−24.9706	−1.40028
$319$	24.0000	1.34374
$320$	1.00000	0.0559017
$321$	22.6274	1.26294
$322$	6.82843	0.380533
$323$	−5.65685	−0.314756
$324$	1.00000	0.0555556
$325$	1.00000	0.0554700
$326$	−1.65685	−0.0917647
$327$	−29.6569	−1.64003
$328$	10.4853	0.578953
$329$	−11.3137	−0.623745
$330$	−11.3137	−0.622799
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	−2.34315	−0.128597
$333$	−18.2843	−1.00197
$334$	24.9706	1.36633
$335$	−9.65685	−0.527610
$336$	2.82843	0.154303
$337$	−22.9706	−1.25129	−0.625643	−	0.780109i	$-0.715163\pi$
$337$	−22.9706	−1.25129	−0.625643	+	0.780109i	$0.715163\pi$
$338$	−1.00000	−0.0543928
$339$	28.2843	1.53619
$340$	0.828427	0.0449278
$341$	6.62742	0.358895
$342$	34.1421	1.84620
$343$	1.00000	0.0539949
$344$	−11.3137	−0.609994
$345$	−19.3137	−1.03982
$346$	10.0000	0.537603
$347$	29.6569	1.59206	0.796032	−	0.605255i	$-0.206929\pi$
$347$	29.6569	1.59206	0.796032	+	0.605255i	$0.206929\pi$
$348$	16.9706	0.909718
$349$	14.9706	0.801356	0.400678	−	0.916219i	$-0.368775\pi$
$349$	14.9706	0.801356	0.400678	+	0.916219i	$0.368775\pi$
$350$	−1.00000	−0.0534522
$351$	5.65685	0.301941
$352$	−4.00000	−0.213201
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	−19.3137	−1.02651
$355$	10.8284	0.574713
$356$	16.8284	0.891905
$357$	2.34315	0.124012
$358$	−12.0000	−0.634220
$359$	6.14214	0.324170	0.162085	−	0.986777i	$-0.448178\pi$
$359$	6.14214	0.324170	0.162085	+	0.986777i	$0.448178\pi$
$360$	−5.00000	−0.263523
$361$	27.6274	1.45407
$362$	−10.9706	−0.576600
$363$	14.1421	0.742270
$364$	1.00000	0.0524142
$365$	0.343146	0.0179611
$366$	32.9706	1.72340
$367$	−24.9706	−1.30345	−0.651726	−	0.758454i	$-0.725955\pi$
$367$	−24.9706	−1.30345	−0.651726	+	0.758454i	$0.725955\pi$
$368$	−6.82843	−0.355956
$369$	−52.4264	−2.72921
$370$	3.65685	0.190111
$371$	8.82843	0.458349
$372$	4.68629	0.242973
$373$	0.828427	0.0428943	0.0214472	−	0.999770i	$-0.493173\pi$
$373$	0.828427	0.0428943	0.0214472	+	0.999770i	$0.493173\pi$
$374$	−3.31371	−0.171348
$375$	2.82843	0.146059
$376$	11.3137	0.583460
$377$	6.00000	0.309016
$378$	−5.65685	−0.290957
$379$	−4.97056	−0.255321	−0.127660	−	0.991818i	$-0.540747\pi$
$379$	−4.97056	−0.255321	−0.127660	+	0.991818i	$0.540747\pi$
$380$	−6.82843	−0.350291
$381$	−35.3137	−1.80918
$382$	−10.3431	−0.529201
$383$	−18.3431	−0.937291	−0.468645	−	0.883386i	$-0.655258\pi$
$383$	−18.3431	−0.937291	−0.468645	+	0.883386i	$0.655258\pi$
$384$	−2.82843	−0.144338
$385$	4.00000	0.203859
$386$	−6.00000	−0.305392
$387$	56.5685	2.87554
$388$	−5.31371	−0.269763
$389$	9.31371	0.472224	0.236112	−	0.971726i	$-0.424127\pi$
$389$	9.31371	0.472224	0.236112	+	0.971726i	$0.424127\pi$
$390$	−2.82843	−0.143223
$391$	−5.65685	−0.286079
$392$	−1.00000	−0.0505076
$393$	45.2548	2.28280
$394$	11.6569	0.587264
$395$	−11.3137	−0.569254
$396$	20.0000	1.00504
$397$	17.3137	0.868950	0.434475	−	0.900684i	$-0.356934\pi$
$397$	17.3137	0.868950	0.434475	+	0.900684i	$0.356934\pi$
$398$	−5.65685	−0.283552
$399$	−19.3137	−0.966895
$400$	1.00000	0.0500000
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	27.3137	1.36228
$403$	1.65685	0.0825338
$404$	7.65685	0.380943
$405$	1.00000	0.0496904
$406$	−6.00000	−0.297775
$407$	−14.6274	−0.725054
$408$	−2.34315	−0.116003
$409$	15.4558	0.764242	0.382121	−	0.924112i	$-0.375194\pi$
$409$	15.4558	0.764242	0.382121	+	0.924112i	$0.375194\pi$
$410$	10.4853	0.517831
$411$	−28.2843	−1.39516
$412$	0	0
$413$	6.82843	0.336005
$414$	34.1421	1.67799
$415$	−2.34315	−0.115021
$416$	−1.00000	−0.0490290
$417$	9.37258	0.458977
$418$	27.3137	1.33596
$419$	−16.0000	−0.781651	−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000	−0.781651	−0.390826	+	0.920465i	$0.627810\pi$
$420$	2.82843	0.138013
$421$	39.4558	1.92296	0.961480	−	0.274875i	$-0.0886363\pi$
$421$	39.4558	1.92296	0.961480	+	0.274875i	$0.0886363\pi$
$422$	17.6569	0.859522
$423$	−56.5685	−2.75046
$424$	−8.82843	−0.428746
$425$	0.828427	0.0401846
$426$	−30.6274	−1.48390
$427$	−11.6569	−0.564115
$428$	8.00000	0.386695
$429$	11.3137	0.546231
$430$	−11.3137	−0.545595
$431$	3.79899	0.182991	0.0914955	−	0.995805i	$-0.470835\pi$
$431$	3.79899	0.182991	0.0914955	+	0.995805i	$0.470835\pi$
$432$	5.65685	0.272166
$433$	−2.48528	−0.119435	−0.0597175	−	0.998215i	$-0.519020\pi$
$433$	−2.48528	−0.119435	−0.0597175	+	0.998215i	$0.519020\pi$
$434$	−1.65685	−0.0795315
$435$	16.9706	0.813676
$436$	−10.4853	−0.502154
$437$	46.6274	2.23049
$438$	−0.970563	−0.0463753
$439$	−28.2843	−1.34993	−0.674967	−	0.737848i	$-0.735842\pi$
$439$	−28.2843	−1.34993	−0.674967	+	0.737848i	$0.735842\pi$
$440$	−4.00000	−0.190693
$441$	5.00000	0.238095
$442$	−0.828427	−0.0394043
$443$	22.6274	1.07506	0.537531	−	0.843244i	$-0.319357\pi$
$443$	22.6274	1.07506	0.537531	+	0.843244i	$0.319357\pi$
$444$	−10.3431	−0.490864
$445$	16.8284	0.797744
$446$	8.97056	0.424768
$447$	−7.02944	−0.332481
$448$	1.00000	0.0472456
$449$	−8.34315	−0.393737	−0.196869	−	0.980430i	$-0.563077\pi$
$449$	−8.34315	−0.393737	−0.196869	+	0.980430i	$0.563077\pi$
$450$	−5.00000	−0.235702
$451$	−41.9411	−1.97493
$452$	10.0000	0.470360
$453$	17.3726	0.816235
$454$	21.6569	1.01641
$455$	1.00000	0.0468807
$456$	19.3137	0.904447
$457$	39.9411	1.86837	0.934184	−	0.356793i	$-0.116130\pi$
$457$	39.9411	1.86837	0.934184	+	0.356793i	$0.116130\pi$
$458$	−3.65685	−0.170874
$459$	4.68629	0.218737
$460$	−6.82843	−0.318377
$461$	24.3431	1.13377	0.566887	−	0.823796i	$-0.308148\pi$
$461$	24.3431	1.13377	0.566887	+	0.823796i	$0.308148\pi$
$462$	−11.3137	−0.526361
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	6.00000	0.278543
$465$	4.68629	0.217322
$466$	22.9706	1.06409
$467$	7.51472	0.347740	0.173870	−	0.984769i	$-0.444373\pi$
$467$	7.51472	0.347740	0.173870	+	0.984769i	$0.444373\pi$
$468$	5.00000	0.231125
$469$	−9.65685	−0.445912
$470$	11.3137	0.521862
$471$	−5.65685	−0.260654
$472$	−6.82843	−0.314304
$473$	45.2548	2.08082
$474$	32.0000	1.46981
$475$	−6.82843	−0.313310
$476$	0.828427	0.0379709
$477$	44.1421	2.02113
$478$	0.485281	0.0221963
$479$	10.6274	0.485579	0.242790	−	0.970079i	$-0.421938\pi$
$479$	10.6274	0.485579	0.242790	+	0.970079i	$0.421938\pi$
$480$	−2.82843	−0.129099
$481$	−3.65685	−0.166738
$482$	4.82843	0.219929
$483$	−19.3137	−0.878804
$484$	5.00000	0.227273
$485$	−5.31371	−0.241283
$486$	14.1421	0.641500
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	11.6569	0.527681
$489$	4.68629	0.211921
$490$	−1.00000	−0.0451754
$491$	−3.02944	−0.136717	−0.0683583	−	0.997661i	$-0.521776\pi$
$491$	−3.02944	−0.136717	−0.0683583	+	0.997661i	$0.521776\pi$
$492$	−29.6569	−1.33703
$493$	4.97056	0.223863
$494$	6.82843	0.307225
$495$	20.0000	0.898933
$496$	1.65685	0.0743950
$497$	10.8284	0.485721
$498$	6.62742	0.296982
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	1.00000	0.0447214
$501$	−70.6274	−3.15540
$502$	−24.9706	−1.11449
$503$	−19.3137	−0.861156	−0.430578	−	0.902553i	$-0.641690\pi$
$503$	−19.3137	−0.861156	−0.430578	+	0.902553i	$0.641690\pi$
$504$	−5.00000	−0.222718
$505$	7.65685	0.340726
$506$	27.3137	1.21424
$507$	2.82843	0.125615
$508$	−12.4853	−0.553945
$509$	−31.6569	−1.40317	−0.701583	−	0.712588i	$-0.747523\pi$
$509$	−31.6569	−1.40317	−0.701583	+	0.712588i	$0.747523\pi$
$510$	−2.34315	−0.103756
$511$	0.343146	0.0151799
$512$	−1.00000	−0.0441942
$513$	−38.6274	−1.70544
$514$	−8.82843	−0.389405
$515$	0	0
$516$	32.0000	1.40872
$517$	−45.2548	−1.99031
$518$	3.65685	0.160673
$519$	−28.2843	−1.24154
$520$	−1.00000	−0.0438529
$521$	−27.6569	−1.21167	−0.605834	−	0.795591i	$-0.707161\pi$
$521$	−27.6569	−1.21167	−0.605834	+	0.795591i	$0.707161\pi$
$522$	−30.0000	−1.31306
$523$	15.5147	0.678411	0.339206	−	0.940712i	$-0.389842\pi$
$523$	15.5147	0.678411	0.339206	+	0.940712i	$0.389842\pi$
$524$	16.0000	0.698963
$525$	2.82843	0.123443
$526$	21.4558	0.935519
$527$	1.37258	0.0597907
$528$	11.3137	0.492366
$529$	23.6274	1.02728
$530$	−8.82843	−0.383482
$531$	34.1421	1.48164
$532$	−6.82843	−0.296050
$533$	−10.4853	−0.454168
$534$	−47.5980	−2.05977
$535$	8.00000	0.345870
$536$	9.65685	0.417113
$537$	33.9411	1.46467
$538$	−4.34315	−0.187246
$539$	4.00000	0.172292
$540$	5.65685	0.243432
$541$	39.4558	1.69634	0.848170	−	0.529725i	$-0.177705\pi$
$541$	39.4558	1.69634	0.848170	+	0.529725i	$0.177705\pi$
$542$	28.9706	1.24439
$543$	31.0294	1.33160
$544$	−0.828427	−0.0355185
$545$	−10.4853	−0.449140
$546$	−2.82843	−0.121046
$547$	24.9706	1.06766	0.533832	−	0.845591i	$-0.320751\pi$
$547$	24.9706	1.06766	0.533832	+	0.845591i	$0.320751\pi$
$548$	−10.0000	−0.427179
$549$	−58.2843	−2.48751
$550$	−4.00000	−0.170561
$551$	−40.9706	−1.74540
$552$	19.3137	0.822046
$553$	−11.3137	−0.481108
$554$	16.1421	0.685814
$555$	−10.3431	−0.439042
$556$	3.31371	0.140533
$557$	23.6569	1.00237	0.501187	−	0.865339i	$-0.332897\pi$
$557$	23.6569	1.00237	0.501187	+	0.865339i	$0.332897\pi$
$558$	−8.28427	−0.350701
$559$	11.3137	0.478519
$560$	1.00000	0.0422577
$561$	9.37258	0.395711
$562$	−26.9706	−1.13768
$563$	30.1421	1.27034	0.635170	−	0.772373i	$-0.280930\pi$
$563$	30.1421	1.27034	0.635170	+	0.772373i	$0.280930\pi$
$564$	−32.0000	−1.34744
$565$	10.0000	0.420703
$566$	21.1716	0.889908
$567$	1.00000	0.0419961
$568$	−10.8284	−0.454351
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	19.3137	0.808962
$571$	−41.6569	−1.74329	−0.871643	−	0.490142i	$-0.836945\pi$
$571$	−41.6569	−1.74329	−0.871643	+	0.490142i	$0.836945\pi$
$572$	4.00000	0.167248
$573$	29.2548	1.22214
$574$	10.4853	0.437647
$575$	−6.82843	−0.284765
$576$	5.00000	0.208333
$577$	42.2843	1.76032	0.880159	−	0.474680i	$-0.157436\pi$
$577$	42.2843	1.76032	0.880159	+	0.474680i	$0.157436\pi$
$578$	16.3137	0.678561
$579$	16.9706	0.705273
$580$	6.00000	0.249136
$581$	−2.34315	−0.0972101
$582$	15.0294	0.622990
$583$	35.3137	1.46254
$584$	−0.343146	−0.0141995
$585$	5.00000	0.206725
$586$	10.0000	0.413096
$587$	−18.3431	−0.757103	−0.378551	−	0.925580i	$-0.623578\pi$
$587$	−18.3431	−0.757103	−0.378551	+	0.925580i	$0.623578\pi$
$588$	2.82843	0.116642
$589$	−11.3137	−0.466173
$590$	−6.82843	−0.281122
$591$	−32.9706	−1.35623
$592$	−3.65685	−0.150296
$593$	31.9411	1.31166	0.655832	−	0.754907i	$-0.272318\pi$
$593$	31.9411	1.31166	0.655832	+	0.754907i	$0.272318\pi$
$594$	−22.6274	−0.928414
$595$	0.828427	0.0339622
$596$	−2.48528	−0.101801
$597$	16.0000	0.654836
$598$	6.82843	0.279235
$599$	32.0000	1.30748	0.653742	−	0.756717i	$-0.273198\pi$
$599$	32.0000	1.30748	0.653742	+	0.756717i	$0.273198\pi$
$600$	−2.82843	−0.115470
$601$	14.6863	0.599066	0.299533	−	0.954086i	$-0.403169\pi$
$601$	14.6863	0.599066	0.299533	+	0.954086i	$0.403169\pi$
$602$	−11.3137	−0.461112
$603$	−48.2843	−1.96629
$604$	6.14214	0.249920
$605$	5.00000	0.203279
$606$	−21.6569	−0.879750
$607$	−40.0000	−1.62355	−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000	−1.62355	−0.811775	+	0.583970i	$0.801498\pi$
$608$	6.82843	0.276929
$609$	16.9706	0.687682
$610$	11.6569	0.471972
$611$	−11.3137	−0.457704
$612$	4.14214	0.167436
$613$	5.31371	0.214619	0.107309	−	0.994226i	$-0.465776\pi$
$613$	5.31371	0.214619	0.107309	+	0.994226i	$0.465776\pi$
$614$	−4.68629	−0.189123
$615$	−29.6569	−1.19588
$616$	−4.00000	−0.161165
$617$	−10.0000	−0.402585	−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000	−0.402585	−0.201292	+	0.979531i	$0.564514\pi$
$618$	0	0
$619$	20.4853	0.823373	0.411686	−	0.911326i	$-0.364940\pi$
$619$	20.4853	0.823373	0.411686	+	0.911326i	$0.364940\pi$
$620$	1.65685	0.0665409
$621$	−38.6274	−1.55006
$622$	8.97056	0.359687
$623$	16.8284	0.674217
$624$	2.82843	0.113228
$625$	1.00000	0.0400000
$626$	−28.1421	−1.12479
$627$	−77.2548	−3.08526
$628$	−2.00000	−0.0798087
$629$	−3.02944	−0.120792
$630$	−5.00000	−0.199205
$631$	25.4558	1.01338	0.506691	−	0.862128i	$-0.330869\pi$
$631$	25.4558	1.01338	0.506691	+	0.862128i	$0.330869\pi$
$632$	11.3137	0.450035
$633$	−49.9411	−1.98498
$634$	−21.3137	−0.846476
$635$	−12.4853	−0.495463
$636$	24.9706	0.990147
$637$	1.00000	0.0396214
$638$	−24.0000	−0.950169
$639$	54.1421	2.14183
$640$	−1.00000	−0.0395285
$641$	26.0000	1.02694	0.513469	−	0.858108i	$-0.328360\pi$
$641$	26.0000	1.02694	0.513469	+	0.858108i	$0.328360\pi$
$642$	−22.6274	−0.893033
$643$	−24.9706	−0.984743	−0.492371	−	0.870385i	$-0.663870\pi$
$643$	−24.9706	−0.984743	−0.492371	+	0.870385i	$0.663870\pi$
$644$	−6.82843	−0.269078
$645$	32.0000	1.26000
$646$	5.65685	0.222566
$647$	−24.9706	−0.981694	−0.490847	−	0.871246i	$-0.663313\pi$
$647$	−24.9706	−0.981694	−0.490847	+	0.871246i	$0.663313\pi$
$648$	−1.00000	−0.0392837
$649$	27.3137	1.07216
$650$	−1.00000	−0.0392232
$651$	4.68629	0.183670
$652$	1.65685	0.0648874
$653$	−12.8284	−0.502015	−0.251008	−	0.967985i	$-0.580762\pi$
$653$	−12.8284	−0.502015	−0.251008	+	0.967985i	$0.580762\pi$
$654$	29.6569	1.15967
$655$	16.0000	0.625172
$656$	−10.4853	−0.409381
$657$	1.71573	0.0669370
$658$	11.3137	0.441054
$659$	28.0000	1.09073	0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000	1.09073	0.545363	+	0.838200i	$0.316392\pi$
$660$	11.3137	0.440386
$661$	−47.2548	−1.83800	−0.919000	−	0.394258i	$-0.871002\pi$
$661$	−47.2548	−1.83800	−0.919000	+	0.394258i	$0.871002\pi$
$662$	4.00000	0.155464
$663$	2.34315	0.0910002
$664$	2.34315	0.0909317
$665$	−6.82843	−0.264795
$666$	18.2843	0.708501
$667$	−40.9706	−1.58639
$668$	−24.9706	−0.966140
$669$	−25.3726	−0.980961
$670$	9.65685	0.373077
$671$	−46.6274	−1.80003
$672$	−2.82843	−0.109109
$673$	−10.6863	−0.411926	−0.205963	−	0.978560i	$-0.566033\pi$
$673$	−10.6863	−0.411926	−0.205963	+	0.978560i	$0.566033\pi$
$674$	22.9706	0.884793
$675$	5.65685	0.217732
$676$	1.00000	0.0384615
$677$	17.3137	0.665420	0.332710	−	0.943029i	$-0.392037\pi$
$677$	17.3137	0.665420	0.332710	+	0.943029i	$0.392037\pi$
$678$	−28.2843	−1.08625
$679$	−5.31371	−0.203921
$680$	−0.828427	−0.0317687
$681$	−61.2548	−2.34729
$682$	−6.62742	−0.253777
$683$	−42.6274	−1.63109	−0.815546	−	0.578692i	$-0.803563\pi$
$683$	−42.6274	−1.63109	−0.815546	+	0.578692i	$0.803563\pi$
$684$	−34.1421	−1.30546
$685$	−10.0000	−0.382080
$686$	−1.00000	−0.0381802
$687$	10.3431	0.394616
$688$	11.3137	0.431331
$689$	8.82843	0.336336
$690$	19.3137	0.735260
$691$	30.8284	1.17277	0.586384	−	0.810033i	$-0.300551\pi$
$691$	30.8284	1.17277	0.586384	+	0.810033i	$0.300551\pi$
$692$	−10.0000	−0.380143
$693$	20.0000	0.759737
$694$	−29.6569	−1.12576
$695$	3.31371	0.125696
$696$	−16.9706	−0.643268
$697$	−8.68629	−0.329017
$698$	−14.9706	−0.566644
$699$	−64.9706	−2.45741
$700$	1.00000	0.0377964
$701$	−10.9706	−0.414352	−0.207176	−	0.978304i	$-0.566427\pi$
$701$	−10.9706	−0.414352	−0.207176	+	0.978304i	$0.566427\pi$
$702$	−5.65685	−0.213504
$703$	24.9706	0.941783
$704$	4.00000	0.150756
$705$	−32.0000	−1.20519
$706$	−14.0000	−0.526897
$707$	7.65685	0.287966
$708$	19.3137	0.725854
$709$	−10.4853	−0.393783	−0.196892	−	0.980425i	$-0.563085\pi$
$709$	−10.4853	−0.393783	−0.196892	+	0.980425i	$0.563085\pi$
$710$	−10.8284	−0.406384
$711$	−56.5685	−2.12149
$712$	−16.8284	−0.630672
$713$	−11.3137	−0.423702
$714$	−2.34315	−0.0876900
$715$	4.00000	0.149592
$716$	12.0000	0.448461
$717$	−1.37258	−0.0512601
$718$	−6.14214	−0.229222
$719$	−33.9411	−1.26579	−0.632895	−	0.774237i	$-0.718134\pi$
$719$	−33.9411	−1.26579	−0.632895	+	0.774237i	$0.718134\pi$
$720$	5.00000	0.186339
$721$	0	0
$722$	−27.6274	−1.02819
$723$	−13.6569	−0.507904
$724$	10.9706	0.407718
$725$	6.00000	0.222834
$726$	−14.1421	−0.524864
$727$	−0.970563	−0.0359962	−0.0179981	−	0.999838i	$-0.505729\pi$
$727$	−0.970563	−0.0359962	−0.0179981	+	0.999838i	$0.505729\pi$
$728$	−1.00000	−0.0370625
$729$	−43.0000	−1.59259
$730$	−0.343146	−0.0127004
$731$	9.37258	0.346658
$732$	−32.9706	−1.21863
$733$	31.9411	1.17977	0.589886	−	0.807486i	$-0.299173\pi$
$733$	31.9411	1.17977	0.589886	+	0.807486i	$0.299173\pi$
$734$	24.9706	0.921680
$735$	2.82843	0.104328
$736$	6.82843	0.251699
$737$	−38.6274	−1.42286
$738$	52.4264	1.92984
$739$	13.9411	0.512833	0.256416	−	0.966566i	$-0.417458\pi$
$739$	13.9411	0.512833	0.256416	+	0.966566i	$0.417458\pi$
$740$	−3.65685	−0.134429
$741$	−19.3137	−0.709507
$742$	−8.82843	−0.324102
$743$	−7.02944	−0.257885	−0.128943	−	0.991652i	$-0.541158\pi$
$743$	−7.02944	−0.257885	−0.128943	+	0.991652i	$0.541158\pi$
$744$	−4.68629	−0.171808
$745$	−2.48528	−0.0910537
$746$	−0.828427	−0.0303309
$747$	−11.7157	−0.428656
$748$	3.31371	0.121161
$749$	8.00000	0.292314
$750$	−2.82843	−0.103280
$751$	43.3137	1.58054	0.790270	−	0.612759i	$-0.209940\pi$
$751$	43.3137	1.58054	0.790270	+	0.612759i	$0.209940\pi$
$752$	−11.3137	−0.412568
$753$	70.6274	2.57381
$754$	−6.00000	−0.218507
$755$	6.14214	0.223535
$756$	5.65685	0.205738
$757$	3.17157	0.115273	0.0576364	−	0.998338i	$-0.481644\pi$
$757$	3.17157	0.115273	0.0576364	+	0.998338i	$0.481644\pi$
$758$	4.97056	0.180539
$759$	−77.2548	−2.80417
$760$	6.82843	0.247693
$761$	13.1127	0.475335	0.237667	−	0.971347i	$-0.423617\pi$
$761$	13.1127	0.475335	0.237667	+	0.971347i	$0.423617\pi$
$762$	35.3137	1.27928
$763$	−10.4853	−0.379593
$764$	10.3431	0.374202
$765$	4.14214	0.149759
$766$	18.3431	0.662765
$767$	6.82843	0.246560
$768$	2.82843	0.102062
$769$	13.5147	0.487353	0.243677	−	0.969857i	$-0.421646\pi$
$769$	13.5147	0.487353	0.243677	+	0.969857i	$0.421646\pi$
$770$	−4.00000	−0.144150
$771$	24.9706	0.899293
$772$	6.00000	0.215945
$773$	20.6274	0.741917	0.370958	−	0.928650i	$-0.379029\pi$
$773$	20.6274	0.741917	0.370958	+	0.928650i	$0.379029\pi$
$774$	−56.5685	−2.03331
$775$	1.65685	0.0595160
$776$	5.31371	0.190751
$777$	−10.3431	−0.371058
$778$	−9.31371	−0.333913
$779$	71.5980	2.56526
$780$	2.82843	0.101274
$781$	43.3137	1.54989
$782$	5.65685	0.202289
$783$	33.9411	1.21296
$784$	1.00000	0.0357143
$785$	−2.00000	−0.0713831
$786$	−45.2548	−1.61419
$787$	27.3137	0.973629	0.486814	−	0.873505i	$-0.338159\pi$
$787$	27.3137	0.973629	0.486814	+	0.873505i	$0.338159\pi$
$788$	−11.6569	−0.415258
$789$	−60.6863	−2.16049
$790$	11.3137	0.402524
$791$	10.0000	0.355559
$792$	−20.0000	−0.710669
$793$	−11.6569	−0.413947
$794$	−17.3137	−0.614441
$795$	24.9706	0.885615
$796$	5.65685	0.200502
$797$	38.0000	1.34603	0.673015	−	0.739629i	$-0.264999\pi$
$797$	38.0000	1.34603	0.673015	+	0.739629i	$0.264999\pi$
$798$	19.3137	0.683698
$799$	−9.37258	−0.331578
$800$	−1.00000	−0.0353553
$801$	84.1421	2.97302
$802$	6.00000	0.211867
$803$	1.37258	0.0484374
$804$	−27.3137	−0.963280
$805$	−6.82843	−0.240670
$806$	−1.65685	−0.0583602
$807$	12.2843	0.432427
$808$	−7.65685	−0.269367
$809$	16.6274	0.584589	0.292294	−	0.956328i	$-0.405581\pi$
$809$	16.6274	0.584589	0.292294	+	0.956328i	$0.405581\pi$
$810$	−1.00000	−0.0351364
$811$	17.1716	0.602975	0.301488	−	0.953470i	$-0.402517\pi$
$811$	17.1716	0.602975	0.301488	+	0.953470i	$0.402517\pi$
$812$	6.00000	0.210559
$813$	−81.9411	−2.87380
$814$	14.6274	0.512691
$815$	1.65685	0.0580371
$816$	2.34315	0.0820265
$817$	−77.2548	−2.70280
$818$	−15.4558	−0.540401
$819$	5.00000	0.174714
$820$	−10.4853	−0.366162
$821$	−5.79899	−0.202386	−0.101193	−	0.994867i	$-0.532266\pi$
$821$	−5.79899	−0.202386	−0.101193	+	0.994867i	$0.532266\pi$
$822$	28.2843	0.986527
$823$	19.1127	0.666227	0.333113	−	0.942887i	$-0.391901\pi$
$823$	19.1127	0.666227	0.333113	+	0.942887i	$0.391901\pi$
$824$	0	0
$825$	11.3137	0.393893
$826$	−6.82843	−0.237591
$827$	−9.65685	−0.335802	−0.167901	−	0.985804i	$-0.553699\pi$
$827$	−9.65685	−0.335802	−0.167901	+	0.985804i	$0.553699\pi$
$828$	−34.1421	−1.18652
$829$	18.9706	0.658875	0.329437	−	0.944177i	$-0.393141\pi$
$829$	18.9706	0.658875	0.329437	+	0.944177i	$0.393141\pi$
$830$	2.34315	0.0813318
$831$	−45.6569	−1.58382
$832$	1.00000	0.0346688
$833$	0.828427	0.0287033
$834$	−9.37258	−0.324546
$835$	−24.9706	−0.864142
$836$	−27.3137	−0.944664
$837$	9.37258	0.323964
$838$	16.0000	0.552711
$839$	24.2843	0.838386	0.419193	−	0.907897i	$-0.362313\pi$
$839$	24.2843	0.838386	0.419193	+	0.907897i	$0.362313\pi$
$840$	−2.82843	−0.0975900
$841$	7.00000	0.241379
$842$	−39.4558	−1.35974
$843$	76.2843	2.62737
$844$	−17.6569	−0.607774
$845$	1.00000	0.0344010
$846$	56.5685	1.94487
$847$	5.00000	0.171802
$848$	8.82843	0.303169
$849$	−59.8823	−2.05515
$850$	−0.828427	−0.0284148
$851$	24.9706	0.855980
$852$	30.6274	1.04928
$853$	−5.31371	−0.181938	−0.0909690	−	0.995854i	$-0.528996\pi$
$853$	−5.31371	−0.181938	−0.0909690	+	0.995854i	$0.528996\pi$
$854$	11.6569	0.398889
$855$	−34.1421	−1.16764
$856$	−8.00000	−0.273434
$857$	−42.4853	−1.45127	−0.725635	−	0.688080i	$-0.758454\pi$
$857$	−42.4853	−1.45127	−0.725635	+	0.688080i	$0.758454\pi$
$858$	−11.3137	−0.386244
$859$	31.5980	1.07811	0.539055	−	0.842271i	$-0.318782\pi$
$859$	31.5980	1.07811	0.539055	+	0.842271i	$0.318782\pi$
$860$	11.3137	0.385794
$861$	−29.6569	−1.01070
$862$	−3.79899	−0.129394
$863$	53.2548	1.81282	0.906408	−	0.422404i	$-0.138814\pi$
$863$	53.2548	1.81282	0.906408	+	0.422404i	$0.138814\pi$
$864$	−5.65685	−0.192450
$865$	−10.0000	−0.340010
$866$	2.48528	0.0844533
$867$	−46.1421	−1.56707
$868$	1.65685	0.0562373
$869$	−45.2548	−1.53517
$870$	−16.9706	−0.575356
$871$	−9.65685	−0.327210
$872$	10.4853	0.355076
$873$	−26.5685	−0.899209
$874$	−46.6274	−1.57720
$875$	1.00000	0.0338062
$876$	0.970563	0.0327923
$877$	33.5980	1.13452	0.567262	−	0.823538i	$-0.308003\pi$
$877$	33.5980	1.13452	0.567262	+	0.823538i	$0.308003\pi$
$878$	28.2843	0.954548
$879$	−28.2843	−0.954005
$880$	4.00000	0.134840
$881$	−41.3137	−1.39189	−0.695947	−	0.718093i	$-0.745015\pi$
$881$	−41.3137	−1.39189	−0.695947	+	0.718093i	$0.745015\pi$
$882$	−5.00000	−0.168359
$883$	−2.34315	−0.0788531	−0.0394266	−	0.999222i	$-0.512553\pi$
$883$	−2.34315	−0.0788531	−0.0394266	+	0.999222i	$0.512553\pi$
$884$	0.828427	0.0278630
$885$	19.3137	0.649223
$886$	−22.6274	−0.760183
$887$	0.970563	0.0325883	0.0162942	−	0.999867i	$-0.494813\pi$
$887$	0.970563	0.0325883	0.0162942	+	0.999867i	$0.494813\pi$
$888$	10.3431	0.347093
$889$	−12.4853	−0.418743
$890$	−16.8284	−0.564090
$891$	4.00000	0.134005
$892$	−8.97056	−0.300357
$893$	77.2548	2.58523
$894$	7.02944	0.235100
$895$	12.0000	0.401116
$896$	−1.00000	−0.0334077
$897$	−19.3137	−0.644866
$898$	8.34315	0.278414
$899$	9.94113	0.331555
$900$	5.00000	0.166667
$901$	7.31371	0.243655
$902$	41.9411	1.39649
$903$	32.0000	1.06489
$904$	−10.0000	−0.332595
$905$	10.9706	0.364674
$906$	−17.3726	−0.577165
$907$	20.2843	0.673528	0.336764	−	0.941589i	$-0.390668\pi$
$907$	20.2843	0.673528	0.336764	+	0.941589i	$0.390668\pi$
$908$	−21.6569	−0.718708
$909$	38.2843	1.26981
$910$	−1.00000	−0.0331497
$911$	33.9411	1.12452	0.562260	−	0.826961i	$-0.309932\pi$
$911$	33.9411	1.12452	0.562260	+	0.826961i	$0.309932\pi$
$912$	−19.3137	−0.639541
$913$	−9.37258	−0.310187
$914$	−39.9411	−1.32114
$915$	−32.9706	−1.08997
$916$	3.65685	0.120826
$917$	16.0000	0.528367
$918$	−4.68629	−0.154671
$919$	2.34315	0.0772932	0.0386466	−	0.999253i	$-0.487695\pi$
$919$	2.34315	0.0772932	0.0386466	+	0.999253i	$0.487695\pi$
$920$	6.82843	0.225127
$921$	13.2548	0.436762
$922$	−24.3431	−0.801699
$923$	10.8284	0.356422
$924$	11.3137	0.372194
$925$	−3.65685	−0.120237
$926$	−24.0000	−0.788689
$927$	0	0
$928$	−6.00000	−0.196960
$929$	21.1127	0.692685	0.346343	−	0.938108i	$-0.387423\pi$
$929$	21.1127	0.692685	0.346343	+	0.938108i	$0.387423\pi$
$930$	−4.68629	−0.153670
$931$	−6.82843	−0.223793
$932$	−22.9706	−0.752426
$933$	−25.3726	−0.830661
$934$	−7.51472	−0.245889
$935$	3.31371	0.108370
$936$	−5.00000	−0.163430
$937$	11.1716	0.364959	0.182480	−	0.983210i	$-0.441588\pi$
$937$	11.1716	0.364959	0.182480	+	0.983210i	$0.441588\pi$
$938$	9.65685	0.315307
$939$	79.5980	2.59758
$940$	−11.3137	−0.369012
$941$	12.6274	0.411642	0.205821	−	0.978590i	$-0.434014\pi$
$941$	12.6274	0.411642	0.205821	+	0.978590i	$0.434014\pi$
$942$	5.65685	0.184310
$943$	71.5980	2.33155
$944$	6.82843	0.222246
$945$	5.65685	0.184017
$946$	−45.2548	−1.47136
$947$	33.6569	1.09370	0.546850	−	0.837230i	$-0.315827\pi$
$947$	33.6569	1.09370	0.546850	+	0.837230i	$0.315827\pi$
$948$	−32.0000	−1.03931
$949$	0.343146	0.0111390
$950$	6.82843	0.221543
$951$	60.2843	1.95485
$952$	−0.828427	−0.0268495
$953$	30.2843	0.981004	0.490502	−	0.871440i	$-0.336813\pi$
$953$	30.2843	0.981004	0.490502	+	0.871440i	$0.336813\pi$
$954$	−44.1421	−1.42915
$955$	10.3431	0.334696
$956$	−0.485281	−0.0156951
$957$	67.8823	2.19432
$958$	−10.6274	−0.343356
$959$	−10.0000	−0.322917
$960$	2.82843	0.0912871
$961$	−28.2548	−0.911446
$962$	3.65685	0.117902
$963$	40.0000	1.28898
$964$	−4.82843	−0.155513
$965$	6.00000	0.193147
$966$	19.3137	0.621408
$967$	24.0000	0.771788	0.385894	−	0.922543i	$-0.373893\pi$
$967$	24.0000	0.771788	0.385894	+	0.922543i	$0.373893\pi$
$968$	−5.00000	−0.160706
$969$	−16.0000	−0.513994
$970$	5.31371	0.170613
$971$	−36.2843	−1.16442	−0.582209	−	0.813039i	$-0.697811\pi$
$971$	−36.2843	−1.16442	−0.582209	+	0.813039i	$0.697811\pi$
$972$	−14.1421	−0.453609
$973$	3.31371	0.106233
$974$	16.0000	0.512673
$975$	2.82843	0.0905822
$976$	−11.6569	−0.373127
$977$	33.3137	1.06580	0.532900	−	0.846178i	$-0.321102\pi$
$977$	33.3137	1.06580	0.532900	+	0.846178i	$0.321102\pi$
$978$	−4.68629	−0.149851
$979$	67.3137	2.15136
$980$	1.00000	0.0319438
$981$	−52.4264	−1.67385
$982$	3.02944	0.0966732
$983$	−8.00000	−0.255160	−0.127580	−	0.991828i	$-0.540721\pi$
$983$	−8.00000	−0.255160	−0.127580	+	0.991828i	$0.540721\pi$
$984$	29.6569	0.945426
$985$	−11.6569	−0.371418
$986$	−4.97056	−0.158295
$987$	−32.0000	−1.01857
$988$	−6.82843	−0.217241
$989$	−77.2548	−2.45656
$990$	−20.0000	−0.635642
$991$	43.3137	1.37591	0.687953	−	0.725756i	$-0.258510\pi$
$991$	43.3137	1.37591	0.687953	+	0.725756i	$0.258510\pi$
$992$	−1.65685	−0.0526052
$993$	−11.3137	−0.359030
$994$	−10.8284	−0.343457
$995$	5.65685	0.179334
$996$	−6.62742	−0.209998
$997$	5.02944	0.159284	0.0796419	−	0.996824i	$-0.474622\pi$
$997$	5.02944	0.159284	0.0796419	+	0.996824i	$0.474622\pi$
$998$	20.0000	0.633089
$999$	−20.6863	−0.654485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	910.2.a.m.1.2	✓	2
3.2	odd	2		8190.2.a.ck.1.1		2
4.3	odd	2		7280.2.a.bc.1.1		2
5.4	even	2		4550.2.a.bn.1.1		2
7.6	odd	2		6370.2.a.bd.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
910.2.a.m.1.2	✓	2	1.1	even	1	trivial
4550.2.a.bn.1.1		2	5.4	even	2
6370.2.a.bd.1.1		2	7.6	odd	2
7280.2.a.bc.1.1		2	4.3	odd	2
8190.2.a.ck.1.1		2	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:	\( N \)	\(=\)	\( 910 = 2 \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	910.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.82843 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.82843 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.82843 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.82843 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.00000 q^{9} -1.00000 q^{10} +4.00000 q^{11} +2.82843 q^{12} +1.00000 q^{13} -1.00000 q^{14} +2.82843 q^{15} +1.00000 q^{16} +0.828427 q^{17} -5.00000 q^{18} -6.82843 q^{19} +1.00000 q^{20} +2.82843 q^{21} -4.00000 q^{22} -6.82843 q^{23} -2.82843 q^{24} +1.00000 q^{25} -1.00000 q^{26} +5.65685 q^{27} +1.00000 q^{28} +6.00000 q^{29} -2.82843 q^{30} +1.65685 q^{31} -1.00000 q^{32} +11.3137 q^{33} -0.828427 q^{34} +1.00000 q^{35} +5.00000 q^{36} -3.65685 q^{37} +6.82843 q^{38} +2.82843 q^{39} -1.00000 q^{40} -10.4853 q^{41} -2.82843 q^{42} +11.3137 q^{43} +4.00000 q^{44} +5.00000 q^{45} +6.82843 q^{46} -11.3137 q^{47} +2.82843 q^{48} +1.00000 q^{49} -1.00000 q^{50} +2.34315 q^{51} +1.00000 q^{52} +8.82843 q^{53} -5.65685 q^{54} +4.00000 q^{55} -1.00000 q^{56} -19.3137 q^{57} -6.00000 q^{58} +6.82843 q^{59} +2.82843 q^{60} -11.6569 q^{61} -1.65685 q^{62} +5.00000 q^{63} +1.00000 q^{64} +1.00000 q^{65} -11.3137 q^{66} -9.65685 q^{67} +0.828427 q^{68} -19.3137 q^{69} -1.00000 q^{70} +10.8284 q^{71} -5.00000 q^{72} +0.343146 q^{73} +3.65685 q^{74} +2.82843 q^{75} -6.82843 q^{76} +4.00000 q^{77} -2.82843 q^{78} -11.3137 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.4853 q^{82} -2.34315 q^{83} +2.82843 q^{84} +0.828427 q^{85} -11.3137 q^{86} +16.9706 q^{87} -4.00000 q^{88} +16.8284 q^{89} -5.00000 q^{90} +1.00000 q^{91} -6.82843 q^{92} +4.68629 q^{93} +11.3137 q^{94} -6.82843 q^{95} -2.82843 q^{96} -5.31371 q^{97} -1.00000 q^{98} +20.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} - 2 q^{8} + 10 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 - 2 * q^8 + 10 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{7} - 2 q^{8} + 10 q^{9} - 2 q^{10} + 8 q^{11} + 2 q^{13} - 2 q^{14} + 2 q^{16} - 4 q^{17} - 10 q^{18} - 8 q^{19} + 2 q^{20} - 8 q^{22} - 8 q^{23} + 2 q^{25} - 2 q^{26} + 2 q^{28} + 12 q^{29} - 8 q^{31} - 2 q^{32} + 4 q^{34} + 2 q^{35} + 10 q^{36} + 4 q^{37} + 8 q^{38} - 2 q^{40} - 4 q^{41} + 8 q^{44} + 10 q^{45} + 8 q^{46} + 2 q^{49} - 2 q^{50} + 16 q^{51} + 2 q^{52} + 12 q^{53} + 8 q^{55} - 2 q^{56} - 16 q^{57} - 12 q^{58} + 8 q^{59} - 12 q^{61} + 8 q^{62} + 10 q^{63} + 2 q^{64} + 2 q^{65} - 8 q^{67} - 4 q^{68} - 16 q^{69} - 2 q^{70} + 16 q^{71} - 10 q^{72} + 12 q^{73} - 4 q^{74} - 8 q^{76} + 8 q^{77} + 2 q^{80} + 2 q^{81} + 4 q^{82} - 16 q^{83} - 4 q^{85} - 8 q^{88} + 28 q^{89} - 10 q^{90} + 2 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{95} + 12 q^{97} - 2 q^{98} + 40 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 + 2 * q^7 - 2 * q^8 + 10 * q^9 - 2 * q^10 + 8 * q^11 + 2 * q^13 - 2 * q^14 + 2 * q^16 - 4 * q^17 - 10 * q^18 - 8 * q^19 + 2 * q^20 - 8 * q^22 - 8 * q^23 + 2 * q^25 - 2 * q^26 + 2 * q^28 + 12 * q^29 - 8 * q^31 - 2 * q^32 + 4 * q^34 + 2 * q^35 + 10 * q^36 + 4 * q^37 + 8 * q^38 - 2 * q^40 - 4 * q^41 + 8 * q^44 + 10 * q^45 + 8 * q^46 + 2 * q^49 - 2 * q^50 + 16 * q^51 + 2 * q^52 + 12 * q^53 + 8 * q^55 - 2 * q^56 - 16 * q^57 - 12 * q^58 + 8 * q^59 - 12 * q^61 + 8 * q^62 + 10 * q^63 + 2 * q^64 + 2 * q^65 - 8 * q^67 - 4 * q^68 - 16 * q^69 - 2 * q^70 + 16 * q^71 - 10 * q^72 + 12 * q^73 - 4 * q^74 - 8 * q^76 + 8 * q^77 + 2 * q^80 + 2 * q^81 + 4 * q^82 - 16 * q^83 - 4 * q^85 - 8 * q^88 + 28 * q^89 - 10 * q^90 + 2 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^95 + 12 * q^97 - 2 * q^98 + 40 * q^99

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