LMFDB - Embedded newform 7935.2.a.bl.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} + 92x^{8} - 4x^{7} - 234x^{6} + 32x^{5} + 252x^{4} - 68x^{3} - 76x^{2} + 32x - 2 $ x^12 - 16x^10 + 92x^8 - 4x^7 - 234x^6 + 32x^5 + 252x^4 - 68x^3 - 76x^2 + 32*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$1.56791$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.56791 q^{2} +1.00000 q^{3} +0.458355 q^{4} -1.00000 q^{5} +1.56791 q^{6} -3.42407 q^{7} -2.41717 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.56791 q^{2} +1.00000 q^{3} +0.458355 q^{4} -1.00000 q^{5} +1.56791 q^{6} -3.42407 q^{7} -2.41717 q^{8} +1.00000 q^{9} -1.56791 q^{10} +5.04985 q^{11} +0.458355 q^{12} -0.802224 q^{13} -5.36865 q^{14} -1.00000 q^{15} -4.70662 q^{16} +3.28402 q^{17} +1.56791 q^{18} +4.91487 q^{19} -0.458355 q^{20} -3.42407 q^{21} +7.91772 q^{22} -2.41717 q^{24} +1.00000 q^{25} -1.25782 q^{26} +1.00000 q^{27} -1.56944 q^{28} -5.37535 q^{29} -1.56791 q^{30} -2.57581 q^{31} -2.54525 q^{32} +5.04985 q^{33} +5.14906 q^{34} +3.42407 q^{35} +0.458355 q^{36} -8.00719 q^{37} +7.70610 q^{38} -0.802224 q^{39} +2.41717 q^{40} -12.2881 q^{41} -5.36865 q^{42} -0.373904 q^{43} +2.31462 q^{44} -1.00000 q^{45} +8.48395 q^{47} -4.70662 q^{48} +4.72427 q^{49} +1.56791 q^{50} +3.28402 q^{51} -0.367704 q^{52} +3.23904 q^{53} +1.56791 q^{54} -5.04985 q^{55} +8.27655 q^{56} +4.91487 q^{57} -8.42808 q^{58} +8.14914 q^{59} -0.458355 q^{60} +7.79395 q^{61} -4.03866 q^{62} -3.42407 q^{63} +5.42251 q^{64} +0.802224 q^{65} +7.91772 q^{66} +14.4426 q^{67} +1.50525 q^{68} +5.36865 q^{70} +2.40147 q^{71} -2.41717 q^{72} +3.31175 q^{73} -12.5546 q^{74} +1.00000 q^{75} +2.25276 q^{76} -17.2910 q^{77} -1.25782 q^{78} +9.28363 q^{79} +4.70662 q^{80} +1.00000 q^{81} -19.2667 q^{82} +16.3980 q^{83} -1.56944 q^{84} -3.28402 q^{85} -0.586250 q^{86} -5.37535 q^{87} -12.2063 q^{88} -0.377862 q^{89} -1.56791 q^{90} +2.74687 q^{91} -2.57581 q^{93} +13.3021 q^{94} -4.91487 q^{95} -2.54525 q^{96} +12.9677 q^{97} +7.40725 q^{98} +5.04985 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9	$ 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9} + 24 q^{11} + 8 q^{12} - 8 q^{13} + 16 q^{14} - 12 q^{15} + 28 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{32} + 24 q^{33} + 16 q^{34} - 4 q^{35} + 8 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{39} - 4 q^{41} + 16 q^{42} - 12 q^{43} + 16 q^{44} - 12 q^{45} + 4 q^{47} + 24 q^{49} + 28 q^{51} - 36 q^{52} + 28 q^{53} - 24 q^{55} + 56 q^{56} + 16 q^{57} + 20 q^{59} - 8 q^{60} + 32 q^{61} + 12 q^{62} + 4 q^{63} - 4 q^{64} + 8 q^{65} - 4 q^{67} + 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} - 36 q^{74} + 12 q^{75} + 8 q^{76} - 28 q^{77} - 36 q^{78} + 40 q^{79} + 12 q^{81} - 28 q^{82} + 100 q^{83} + 8 q^{84} - 28 q^{85} - 20 q^{86} - 16 q^{87} + 80 q^{89} - 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} - 8 q^{97} + 28 q^{98} + 24 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9 + 24 * q^11 + 8 * q^12 - 8 * q^13 + 16 * q^14 - 12 * q^15 + 28 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^32 + 24 * q^33 + 16 * q^34 - 4 * q^35 + 8 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^39 - 4 * q^41 + 16 * q^42 - 12 * q^43 + 16 * q^44 - 12 * q^45 + 4 * q^47 + 24 * q^49 + 28 * q^51 - 36 * q^52 + 28 * q^53 - 24 * q^55 + 56 * q^56 + 16 * q^57 + 20 * q^59 - 8 * q^60 + 32 * q^61 + 12 * q^62 + 4 * q^63 - 4 * q^64 + 8 * q^65 - 4 * q^67 + 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 - 36 * q^74 + 12 * q^75 + 8 * q^76 - 28 * q^77 - 36 * q^78 + 40 * q^79 + 12 * q^81 - 28 * q^82 + 100 * q^83 + 8 * q^84 - 28 * q^85 - 20 * q^86 - 16 * q^87 + 80 * q^89 - 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 - 8 * q^97 + 28 * q^98 + 24 * 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 $

$2$	1.56791	1.10868	0.554341	−	0.832289i	$-0.312970\pi$
$2$	1.56791	1.10868	0.554341	+	0.832289i	$0.312970\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.458355	0.229178
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.56791	0.640098
$7$	−3.42407	−1.29418	−0.647089	−	0.762415i	$-0.724014\pi$
$7$	−3.42407	−1.29418	−0.647089	+	0.762415i	$0.724014\pi$
$8$	−2.41717	−0.854597
$9$	1.00000	0.333333
$10$	−1.56791	−0.495818
$11$	5.04985	1.52259	0.761293	−	0.648408i	$-0.224565\pi$
$11$	5.04985	1.52259	0.761293	+	0.648408i	$0.224565\pi$
$12$	0.458355	0.132316
$13$	−0.802224	−0.222497	−0.111248	−	0.993793i	$-0.535485\pi$
$13$	−0.802224	−0.222497	−0.111248	+	0.993793i	$0.535485\pi$
$14$	−5.36865	−1.43483
$15$	−1.00000	−0.258199
$16$	−4.70662	−1.17666
$17$	3.28402	0.796492	0.398246	−	0.917279i	$-0.369619\pi$
$17$	3.28402	0.796492	0.398246	+	0.917279i	$0.369619\pi$
$18$	1.56791	0.369561
$19$	4.91487	1.12755	0.563774	−	0.825929i	$-0.309349\pi$
$19$	4.91487	1.12755	0.563774	+	0.825929i	$0.309349\pi$
$20$	−0.458355	−0.102491
$21$	−3.42407	−0.747194
$22$	7.91772	1.68806
$23$	0	0
$23$	0	0
$24$	−2.41717	−0.493402
$25$	1.00000	0.200000
$26$	−1.25782	−0.246678
$27$	1.00000	0.192450
$28$	−1.56944	−0.296597
$29$	−5.37535	−0.998177	−0.499088	−	0.866551i	$-0.666332\pi$
$29$	−5.37535	−0.998177	−0.499088	+	0.866551i	$0.666332\pi$
$30$	−1.56791	−0.286261
$31$	−2.57581	−0.462630	−0.231315	−	0.972879i	$-0.574303\pi$
$31$	−2.57581	−0.462630	−0.231315	+	0.972879i	$0.574303\pi$
$32$	−2.54525	−0.449940
$33$	5.04985	0.879065
$34$	5.14906	0.883057
$35$	3.42407	0.578774
$36$	0.458355	0.0763926
$37$	−8.00719	−1.31637	−0.658187	−	0.752855i	$-0.728676\pi$
$37$	−8.00719	−1.31637	−0.658187	+	0.752855i	$0.728676\pi$
$38$	7.70610	1.25009
$39$	−0.802224	−0.128459
$40$	2.41717	0.382188
$41$	−12.2881	−1.91908	−0.959542	−	0.281564i	$-0.909147\pi$
$41$	−12.2881	−1.91908	−0.959542	+	0.281564i	$0.909147\pi$
$42$	−5.36865	−0.828401
$43$	−0.373904	−0.0570199	−0.0285099	−	0.999594i	$-0.509076\pi$
$43$	−0.373904	−0.0570199	−0.0285099	+	0.999594i	$0.509076\pi$
$44$	2.31462	0.348943
$45$	−1.00000	−0.149071
$46$	0	0
$47$	8.48395	1.23751	0.618755	−	0.785584i	$-0.287637\pi$
$47$	8.48395	1.23751	0.618755	+	0.785584i	$0.287637\pi$
$48$	−4.70662	−0.679342
$49$	4.72427	0.674896
$50$	1.56791	0.221737
$51$	3.28402	0.459855
$52$	−0.367704	−0.0509913
$53$	3.23904	0.444916	0.222458	−	0.974942i	$-0.428592\pi$
$53$	3.23904	0.444916	0.222458	+	0.974942i	$0.428592\pi$
$54$	1.56791	0.213366
$55$	−5.04985	−0.680921
$56$	8.27655	1.10600
$57$	4.91487	0.650991
$58$	−8.42808	−1.10666
$59$	8.14914	1.06093	0.530464	−	0.847708i	$-0.322018\pi$
$59$	8.14914	1.06093	0.530464	+	0.847708i	$0.322018\pi$
$60$	−0.458355	−0.0591734
$61$	7.79395	0.997913	0.498956	−	0.866627i	$-0.333717\pi$
$61$	7.79395	0.997913	0.498956	+	0.866627i	$0.333717\pi$
$62$	−4.03866	−0.512910
$63$	−3.42407	−0.431393
$64$	5.42251	0.677814
$65$	0.802224	0.0995036
$66$	7.91772	0.974605
$67$	14.4426	1.76445	0.882224	−	0.470829i	$-0.156045\pi$
$67$	14.4426	1.76445	0.882224	+	0.470829i	$0.156045\pi$
$68$	1.50525	0.182538
$69$	0	0
$70$	5.36865	0.641677
$71$	2.40147	0.285002	0.142501	−	0.989795i	$-0.454486\pi$
$71$	2.40147	0.285002	0.142501	+	0.989795i	$0.454486\pi$
$72$	−2.41717	−0.284866
$73$	3.31175	0.387611	0.193805	−	0.981040i	$-0.437917\pi$
$73$	3.31175	0.387611	0.193805	+	0.981040i	$0.437917\pi$
$74$	−12.5546	−1.45944
$75$	1.00000	0.115470
$76$	2.25276	0.258409
$77$	−17.2910	−1.97050
$78$	−1.25782	−0.142420
$79$	9.28363	1.04449	0.522245	−	0.852796i	$-0.325095\pi$
$79$	9.28363	1.04449	0.522245	+	0.852796i	$0.325095\pi$
$80$	4.70662	0.526216
$81$	1.00000	0.111111
$82$	−19.2667	−2.12766
$83$	16.3980	1.79992	0.899958	−	0.435976i	$-0.143597\pi$
$83$	16.3980	1.79992	0.899958	+	0.435976i	$0.143597\pi$
$84$	−1.56944	−0.171240
$85$	−3.28402	−0.356202
$86$	−0.586250	−0.0632170
$87$	−5.37535	−0.576298
$88$	−12.2063	−1.30120
$89$	−0.377862	−0.0400533	−0.0200266	−	0.999799i	$-0.506375\pi$
$89$	−0.377862	−0.0400533	−0.0200266	+	0.999799i	$0.506375\pi$
$90$	−1.56791	−0.165273
$91$	2.74687	0.287950
$92$	0	0
$93$	−2.57581	−0.267099
$94$	13.3021	1.37201
$95$	−4.91487	−0.504255
$96$	−2.54525	−0.259773
$97$	12.9677	1.31667	0.658333	−	0.752727i	$-0.271262\pi$
$97$	12.9677	1.31667	0.658333	+	0.752727i	$0.271262\pi$
$98$	7.40725	0.748246
$99$	5.04985	0.507529
$100$	0.458355	0.0458355
$101$	1.09477	0.108933	0.0544667	−	0.998516i	$-0.482654\pi$
$101$	1.09477	0.108933	0.0544667	+	0.998516i	$0.482654\pi$
$102$	5.14906	0.509833
$103$	−4.00776	−0.394897	−0.197448	−	0.980313i	$-0.563265\pi$
$103$	−4.00776	−0.394897	−0.197448	+	0.980313i	$0.563265\pi$
$104$	1.93911	0.190145
$105$	3.42407	0.334155
$106$	5.07854	0.493271
$107$	11.3132	1.09369	0.546843	−	0.837235i	$-0.315829\pi$
$107$	11.3132	1.09369	0.546843	+	0.837235i	$0.315829\pi$
$108$	0.458355	0.0441053
$109$	−9.06942	−0.868693	−0.434347	−	0.900746i	$-0.643021\pi$
$109$	−9.06942	−0.868693	−0.434347	+	0.900746i	$0.643021\pi$
$110$	−7.91772	−0.754925
$111$	−8.00719	−0.760009
$112$	16.1158	1.52280
$113$	11.1715	1.05092	0.525462	−	0.850817i	$-0.323892\pi$
$113$	11.1715	1.05092	0.525462	+	0.850817i	$0.323892\pi$
$114$	7.70610	0.721742
$115$	0	0
$116$	−2.46382	−0.228760
$117$	−0.802224	−0.0741656
$118$	12.7772	1.17623
$119$	−11.2447	−1.03080
$120$	2.41717	0.220656
$121$	14.5009	1.31827
$122$	12.2202	1.10637
$123$	−12.2881	−1.10798
$124$	−1.18064	−0.106024
$125$	−1.00000	−0.0894427
$126$	−5.36865	−0.478278
$127$	−5.31117	−0.471290	−0.235645	−	0.971839i	$-0.575720\pi$
$127$	−5.31117	−0.471290	−0.235645	+	0.971839i	$0.575720\pi$
$128$	13.5925	1.20142
$129$	−0.373904	−0.0329205
$130$	1.25782	0.110318
$131$	−2.67286	−0.233529	−0.116764	−	0.993160i	$-0.537252\pi$
$131$	−2.67286	−0.233529	−0.116764	+	0.993160i	$0.537252\pi$
$132$	2.31462	0.201462
$133$	−16.8289	−1.45925
$134$	22.6448	1.95621
$135$	−1.00000	−0.0860663
$136$	−7.93803	−0.680680
$137$	−19.4007	−1.65751	−0.828757	−	0.559608i	$-0.810952\pi$
$137$	−19.4007	−1.65751	−0.828757	+	0.559608i	$0.810952\pi$
$138$	0	0
$139$	7.88109	0.668466	0.334233	−	0.942491i	$-0.391523\pi$
$139$	7.88109	0.668466	0.334233	+	0.942491i	$0.391523\pi$
$140$	1.56944	0.132642
$141$	8.48395	0.714477
$142$	3.76530	0.315977
$143$	−4.05110	−0.338770
$144$	−4.70662	−0.392218
$145$	5.37535	0.446398
$146$	5.19253	0.429737
$147$	4.72427	0.389651
$148$	−3.67014	−0.301684
$149$	−6.86487	−0.562392	−0.281196	−	0.959650i	$-0.590731\pi$
$149$	−6.86487	−0.562392	−0.281196	+	0.959650i	$0.590731\pi$
$150$	1.56791	0.128020
$151$	19.3500	1.57468	0.787339	−	0.616520i	$-0.211458\pi$
$151$	19.3500	1.57468	0.787339	+	0.616520i	$0.211458\pi$
$152$	−11.8801	−0.963600
$153$	3.28402	0.265497
$154$	−27.1109	−2.18466
$155$	2.57581	0.206894
$156$	−0.367704	−0.0294398
$157$	−12.9020	−1.02969	−0.514846	−	0.857283i	$-0.672151\pi$
$157$	−12.9020	−1.02969	−0.514846	+	0.857283i	$0.672151\pi$
$158$	14.5559	1.15801
$159$	3.23904	0.256873
$160$	2.54525	0.201219
$161$	0	0
$162$	1.56791	0.123187
$163$	11.0985	0.869303	0.434651	−	0.900599i	$-0.356872\pi$
$163$	11.0985	0.869303	0.434651	+	0.900599i	$0.356872\pi$
$164$	−5.63234	−0.439812
$165$	−5.04985	−0.393130
$166$	25.7107	1.99554
$167$	−19.8211	−1.53380	−0.766900	−	0.641767i	$-0.778202\pi$
$167$	−19.8211	−1.53380	−0.766900	+	0.641767i	$0.778202\pi$
$168$	8.27655	0.638550
$169$	−12.3564	−0.950495
$170$	−5.14906	−0.394915
$171$	4.91487	0.375850
$172$	−0.171381	−0.0130677
$173$	4.85194	0.368886	0.184443	−	0.982843i	$-0.440952\pi$
$173$	4.85194	0.368886	0.184443	+	0.982843i	$0.440952\pi$
$174$	−8.42808	−0.638931
$175$	−3.42407	−0.258836
$176$	−23.7677	−1.79156
$177$	8.14914	0.612527
$178$	−0.592455	−0.0444064
$179$	24.7501	1.84991	0.924957	−	0.380073i	$-0.124101\pi$
$179$	24.7501	1.84991	0.924957	+	0.380073i	$0.124101\pi$
$180$	−0.458355	−0.0341638
$181$	17.8763	1.32873	0.664367	−	0.747406i	$-0.268701\pi$
$181$	17.8763	1.32873	0.664367	+	0.747406i	$0.268701\pi$
$182$	4.30686	0.319246
$183$	7.79395	0.576145
$184$	0	0
$185$	8.00719	0.588700
$186$	−4.03866	−0.296129
$187$	16.5838	1.21273
$188$	3.88866	0.283610
$189$	−3.42407	−0.249065
$190$	−7.70610	−0.559059
$191$	21.4315	1.55073	0.775364	−	0.631515i	$-0.217567\pi$
$191$	21.4315	1.55073	0.775364	+	0.631515i	$0.217567\pi$
$192$	5.42251	0.391336
$193$	23.2259	1.67184	0.835919	−	0.548853i	$-0.184935\pi$
$193$	23.2259	1.67184	0.835919	+	0.548853i	$0.184935\pi$
$194$	20.3322	1.45976
$195$	0.802224	0.0574484
$196$	2.16540	0.154671
$197$	8.30142	0.591451	0.295726	−	0.955273i	$-0.404439\pi$
$197$	8.30142	0.591451	0.295726	+	0.955273i	$0.404439\pi$
$198$	7.91772	0.562688
$199$	−3.88602	−0.275473	−0.137736	−	0.990469i	$-0.543983\pi$
$199$	−3.88602	−0.275473	−0.137736	+	0.990469i	$0.543983\pi$
$200$	−2.41717	−0.170919
$201$	14.4426	1.01870
$202$	1.71650	0.120773
$203$	18.4056	1.29182
$204$	1.50525	0.105389
$205$	12.2881	0.858241
$206$	−6.28383	−0.437815
$207$	0	0
$208$	3.77576	0.261802
$209$	24.8193	1.71679
$210$	5.36865	0.370472
$211$	10.6468	0.732957	0.366479	−	0.930426i	$-0.380563\pi$
$211$	10.6468	0.732957	0.366479	+	0.930426i	$0.380563\pi$
$212$	1.48463	0.101965
$213$	2.40147	0.164546
$214$	17.7381	1.21255
$215$	0.373904	0.0255001
$216$	−2.41717	−0.164467
$217$	8.81977	0.598725
$218$	−14.2201	−0.963105
$219$	3.31175	0.223787
$220$	−2.31462	−0.156052
$221$	−2.63452	−0.177217
$222$	−12.5546	−0.842609
$223$	17.0171	1.13955	0.569775	−	0.821801i	$-0.307030\pi$
$223$	17.0171	1.13955	0.569775	+	0.821801i	$0.307030\pi$
$224$	8.71511	0.582303
$225$	1.00000	0.0666667
$226$	17.5159	1.16514
$227$	−13.3077	−0.883266	−0.441633	−	0.897196i	$-0.645601\pi$
$227$	−13.3077	−0.883266	−0.441633	+	0.897196i	$0.645601\pi$
$228$	2.25276	0.149193
$229$	−12.3492	−0.816056	−0.408028	−	0.912969i	$-0.633783\pi$
$229$	−12.3492	−0.816056	−0.408028	+	0.912969i	$0.633783\pi$
$230$	0	0
$231$	−17.2910	−1.13767
$232$	12.9931	0.853039
$233$	−4.26354	−0.279314	−0.139657	−	0.990200i	$-0.544600\pi$
$233$	−4.26354	−0.279314	−0.139657	+	0.990200i	$0.544600\pi$
$234$	−1.25782	−0.0822261
$235$	−8.48395	−0.553432
$236$	3.73520	0.243141
$237$	9.28363	0.603036
$238$	−17.6308	−1.14283
$239$	−24.0175	−1.55356	−0.776781	−	0.629771i	$-0.783149\pi$
$239$	−24.0175	−1.55356	−0.776781	+	0.629771i	$0.783149\pi$
$240$	4.70662	0.303811
$241$	0.202442	0.0130404	0.00652022	−	0.999979i	$-0.497925\pi$
$241$	0.202442	0.0130404	0.00652022	+	0.999979i	$0.497925\pi$
$242$	22.7362	1.46154
$243$	1.00000	0.0641500
$244$	3.57240	0.228699
$245$	−4.72427	−0.301823
$246$	−19.2667	−1.22840
$247$	−3.94283	−0.250876
$248$	6.22617	0.395362
$249$	16.3980	1.03918
$250$	−1.56791	−0.0991636
$251$	−7.03976	−0.444346	−0.222173	−	0.975007i	$-0.571315\pi$
$251$	−7.03976	−0.444346	−0.222173	+	0.975007i	$0.571315\pi$
$252$	−1.56944	−0.0988656
$253$	0	0
$254$	−8.32746	−0.522511
$255$	−3.28402	−0.205653
$256$	10.4669	0.654181
$257$	−22.1664	−1.38270	−0.691351	−	0.722519i	$-0.742984\pi$
$257$	−22.1664	−1.38270	−0.691351	+	0.722519i	$0.742984\pi$
$258$	−0.586250	−0.0364983
$259$	27.4172	1.70362
$260$	0.367704	0.0228040
$261$	−5.37535	−0.332726
$262$	−4.19082	−0.258910
$263$	24.3330	1.50044	0.750219	−	0.661189i	$-0.229948\pi$
$263$	24.3330	1.50044	0.750219	+	0.661189i	$0.229948\pi$
$264$	−12.2063	−0.751247
$265$	−3.23904	−0.198973
$266$	−26.3862	−1.61784
$267$	−0.377862	−0.0231248
$268$	6.61986	0.404372
$269$	−31.2832	−1.90737	−0.953685	−	0.300808i	$-0.902744\pi$
$269$	−31.2832	−1.90737	−0.953685	+	0.300808i	$0.902744\pi$
$270$	−1.56791	−0.0954202
$271$	9.76739	0.593327	0.296663	−	0.954982i	$-0.404126\pi$
$271$	9.76739	0.593327	0.296663	+	0.954982i	$0.404126\pi$
$272$	−15.4566	−0.937197
$273$	2.74687	0.166248
$274$	−30.4187	−1.83766
$275$	5.04985	0.304517
$276$	0	0
$277$	22.7593	1.36747	0.683737	−	0.729728i	$-0.260354\pi$
$277$	22.7593	1.36747	0.683737	+	0.729728i	$0.260354\pi$
$278$	12.3569	0.741117
$279$	−2.57581	−0.154210
$280$	−8.27655	−0.494619
$281$	−21.1795	−1.26346	−0.631732	−	0.775187i	$-0.717656\pi$
$281$	−21.1795	−1.26346	−0.631732	+	0.775187i	$0.717656\pi$
$282$	13.3021	0.792129
$283$	27.3703	1.62700	0.813498	−	0.581567i	$-0.197560\pi$
$283$	27.3703	1.62700	0.813498	+	0.581567i	$0.197560\pi$
$284$	1.10073	0.0653161
$285$	−4.91487	−0.291132
$286$	−6.35179	−0.375589
$287$	42.0755	2.48364
$288$	−2.54525	−0.149980
$289$	−6.21520	−0.365600
$290$	8.42808	0.494914
$291$	12.9677	0.760177
$292$	1.51796	0.0888317
$293$	15.1339	0.884134	0.442067	−	0.896982i	$-0.354245\pi$
$293$	15.1339	0.884134	0.442067	+	0.896982i	$0.354245\pi$
$294$	7.40725	0.432000
$295$	−8.14914	−0.474461
$296$	19.3547	1.12497
$297$	5.04985	0.293022
$298$	−10.7635	−0.623514
$299$	0	0
$300$	0.458355	0.0264632
$301$	1.28028	0.0737939
$302$	30.3391	1.74582
$303$	1.09477	0.0628927
$304$	−23.1324	−1.32674
$305$	−7.79395	−0.446280
$306$	5.14906	0.294352
$307$	−6.09804	−0.348033	−0.174017	−	0.984743i	$-0.555675\pi$
$307$	−6.09804	−0.348033	−0.174017	+	0.984743i	$0.555675\pi$
$308$	−7.92544	−0.451594
$309$	−4.00776	−0.227994
$310$	4.03866	0.229380
$311$	−5.43785	−0.308352	−0.154176	−	0.988043i	$-0.549272\pi$
$311$	−5.43785	−0.308352	−0.154176	+	0.988043i	$0.549272\pi$
$312$	1.93911	0.109780
$313$	−4.67625	−0.264317	−0.132159	−	0.991229i	$-0.542191\pi$
$313$	−4.67625	−0.264317	−0.132159	+	0.991229i	$0.542191\pi$
$314$	−20.2292	−1.14160
$315$	3.42407	0.192925
$316$	4.25520	0.239374
$317$	−7.48634	−0.420475	−0.210237	−	0.977650i	$-0.567424\pi$
$317$	−7.48634	−0.420475	−0.210237	+	0.977650i	$0.567424\pi$
$318$	5.07854	0.284790
$319$	−27.1447	−1.51981
$320$	−5.42251	−0.303128
$321$	11.3132	0.631440
$322$	0	0
$323$	16.1405	0.898084
$324$	0.458355	0.0254642
$325$	−0.802224	−0.0444994
$326$	17.4015	0.963781
$327$	−9.06942	−0.501540
$328$	29.7025	1.64005
$329$	−29.0496	−1.60156
$330$	−7.91772	−0.435856
$331$	−26.5583	−1.45977	−0.729887	−	0.683568i	$-0.760427\pi$
$331$	−26.5583	−1.45977	−0.729887	+	0.683568i	$0.760427\pi$
$332$	7.51612	0.412501
$333$	−8.00719	−0.438791
$334$	−31.0777	−1.70050
$335$	−14.4426	−0.789085
$336$	16.1158	0.879190
$337$	12.1230	0.660381	0.330191	−	0.943914i	$-0.392887\pi$
$337$	12.1230	0.660381	0.330191	+	0.943914i	$0.392887\pi$
$338$	−19.3738	−1.05380
$339$	11.1715	0.606751
$340$	−1.50525	−0.0816336
$341$	−13.0075	−0.704393
$342$	7.70610	0.416698
$343$	7.79226	0.420742
$344$	0.903789	0.0487291
$345$	0	0
$346$	7.60743	0.408978
$347$	3.15424	0.169328	0.0846642	−	0.996410i	$-0.473018\pi$
$347$	3.15424	0.169328	0.0846642	+	0.996410i	$0.473018\pi$
$348$	−2.46382	−0.132075
$349$	23.4987	1.25786	0.628929	−	0.777463i	$-0.283494\pi$
$349$	23.4987	1.25786	0.628929	+	0.777463i	$0.283494\pi$
$350$	−5.36865	−0.286967
$351$	−0.802224	−0.0428195
$352$	−12.8531	−0.685072
$353$	2.18253	0.116164	0.0580821	−	0.998312i	$-0.481501\pi$
$353$	2.18253	0.116164	0.0580821	+	0.998312i	$0.481501\pi$
$354$	12.7772	0.679098
$355$	−2.40147	−0.127457
$356$	−0.173195	−0.00917932
$357$	−11.2447	−0.595134
$358$	38.8061	2.05097
$359$	−20.9482	−1.10561	−0.552803	−	0.833312i	$-0.686442\pi$
$359$	−20.9482	−1.10561	−0.552803	+	0.833312i	$0.686442\pi$
$360$	2.41717	0.127396
$361$	5.15597	0.271367
$362$	28.0285	1.47314
$363$	14.5009	0.761102
$364$	1.25904	0.0659918
$365$	−3.31175	−0.173345
$366$	12.2202	0.638762
$367$	−2.91192	−0.152001	−0.0760004	−	0.997108i	$-0.524215\pi$
$367$	−2.91192	−0.152001	−0.0760004	+	0.997108i	$0.524215\pi$
$368$	0	0
$369$	−12.2881	−0.639695
$370$	12.5546	0.652682
$371$	−11.0907	−0.575801
$372$	−1.18064	−0.0612132
$373$	−22.3258	−1.15599	−0.577993	−	0.816042i	$-0.696164\pi$
$373$	−22.3258	−1.15599	−0.577993	+	0.816042i	$0.696164\pi$
$374$	26.0020	1.34453
$375$	−1.00000	−0.0516398
$376$	−20.5071	−1.05757
$377$	4.31223	0.222091
$378$	−5.36865	−0.276134
$379$	−32.8729	−1.68857	−0.844283	−	0.535897i	$-0.819974\pi$
$379$	−32.8729	−1.68857	−0.844283	+	0.535897i	$0.819974\pi$
$380$	−2.25276	−0.115564
$381$	−5.31117	−0.272099
$382$	33.6027	1.71927
$383$	17.5626	0.897409	0.448704	−	0.893680i	$-0.351886\pi$
$383$	17.5626	0.897409	0.448704	+	0.893680i	$0.351886\pi$
$384$	13.5925	0.693641
$385$	17.2910	0.881233
$386$	36.4162	1.85354
$387$	−0.373904	−0.0190066
$388$	5.94379	0.301750
$389$	13.5756	0.688308	0.344154	−	0.938913i	$-0.388166\pi$
$389$	13.5756	0.688308	0.344154	+	0.938913i	$0.388166\pi$
$390$	1.25782	0.0636921
$391$	0	0
$392$	−11.4194	−0.576764
$393$	−2.67286	−0.134828
$394$	13.0159	0.655732
$395$	−9.28363	−0.467110
$396$	2.31462	0.116314
$397$	−25.3037	−1.26996	−0.634978	−	0.772530i	$-0.718991\pi$
$397$	−25.3037	−1.26996	−0.634978	+	0.772530i	$0.718991\pi$
$398$	−6.09295	−0.305412
$399$	−16.8289	−0.842498
$400$	−4.70662	−0.235331
$401$	35.7071	1.78313	0.891564	−	0.452895i	$-0.149609\pi$
$401$	35.7071	1.78313	0.891564	+	0.452895i	$0.149609\pi$
$402$	22.6448	1.12942
$403$	2.06638	0.102934
$404$	0.501792	0.0249651
$405$	−1.00000	−0.0496904
$406$	28.8584	1.43222
$407$	−40.4351	−2.00429
$408$	−7.93803	−0.392991
$409$	−11.9673	−0.591744	−0.295872	−	0.955228i	$-0.595610\pi$
$409$	−11.9673	−0.591744	−0.295872	+	0.955228i	$0.595610\pi$
$410$	19.2667	0.951517
$411$	−19.4007	−0.956967
$412$	−1.83698	−0.0905015
$413$	−27.9032	−1.37303
$414$	0	0
$415$	−16.3980	−0.804947
$416$	2.04186	0.100110
$417$	7.88109	0.385939
$418$	38.9146	1.90338
$419$	12.5280	0.612033	0.306016	−	0.952026i	$-0.401004\pi$
$419$	12.5280	0.612033	0.306016	+	0.952026i	$0.401004\pi$
$420$	1.56944	0.0765809
$421$	15.2887	0.745127	0.372564	−	0.928007i	$-0.378479\pi$
$421$	15.2887	0.745127	0.372564	+	0.928007i	$0.378479\pi$
$422$	16.6933	0.812617
$423$	8.48395	0.412504
$424$	−7.82930	−0.380224
$425$	3.28402	0.159298
$426$	3.76530	0.182429
$427$	−26.6870	−1.29148
$428$	5.18546	0.250649
$429$	−4.05110	−0.195589
$430$	0.586250	0.0282715
$431$	−30.4182	−1.46519	−0.732597	−	0.680662i	$-0.761692\pi$
$431$	−30.4182	−1.46519	−0.732597	+	0.680662i	$0.761692\pi$
$432$	−4.70662	−0.226447
$433$	−0.152934	−0.00734952	−0.00367476	−	0.999993i	$-0.501170\pi$
$433$	−0.152934	−0.00734952	−0.00367476	+	0.999993i	$0.501170\pi$
$434$	13.8286	0.663796
$435$	5.37535	0.257728
$436$	−4.15702	−0.199085
$437$	0	0
$438$	5.19253	0.248109
$439$	−37.1253	−1.77189	−0.885947	−	0.463786i	$-0.846491\pi$
$439$	−37.1253	−1.77189	−0.885947	+	0.463786i	$0.846491\pi$
$440$	12.2063	0.581913
$441$	4.72427	0.224965
$442$	−4.13070	−0.196477
$443$	14.2673	0.677860	0.338930	−	0.940812i	$-0.389935\pi$
$443$	14.2673	0.677860	0.338930	+	0.940812i	$0.389935\pi$
$444$	−3.67014	−0.174177
$445$	0.377862	0.0179124
$446$	26.6814	1.26340
$447$	−6.86487	−0.324697
$448$	−18.5671	−0.877212
$449$	7.32960	0.345905	0.172952	−	0.984930i	$-0.444669\pi$
$449$	7.32960	0.345905	0.172952	+	0.984930i	$0.444669\pi$
$450$	1.56791	0.0739122
$451$	−62.0532	−2.92197
$452$	5.12051	0.240848
$453$	19.3500	0.909141
$454$	−20.8654	−0.979262
$455$	−2.74687	−0.128775
$456$	−11.8801	−0.556335
$457$	41.8983	1.95992	0.979960	−	0.199197i	$-0.0638332\pi$
$457$	41.8983	1.95992	0.979960	+	0.199197i	$0.0638332\pi$
$458$	−19.3624	−0.904747
$459$	3.28402	0.153285
$460$	0	0
$461$	−9.50792	−0.442828	−0.221414	−	0.975180i	$-0.571067\pi$
$461$	−9.50792	−0.442828	−0.221414	+	0.975180i	$0.571067\pi$
$462$	−27.1109	−1.26131
$463$	2.37791	0.110511	0.0552555	−	0.998472i	$-0.482403\pi$
$463$	2.37791	0.110511	0.0552555	+	0.998472i	$0.482403\pi$
$464$	25.2997	1.17451
$465$	2.57581	0.119451
$466$	−6.68487	−0.309671
$467$	29.8555	1.38155	0.690774	−	0.723071i	$-0.257270\pi$
$467$	29.8555	1.38155	0.690774	+	0.723071i	$0.257270\pi$
$468$	−0.367704	−0.0169971
$469$	−49.4526	−2.28351
$470$	−13.3021	−0.613580
$471$	−12.9020	−0.594492
$472$	−19.6978	−0.906666
$473$	−1.88816	−0.0868177
$474$	14.5559	0.668576
$475$	4.91487	0.225510
$476$	−5.15408	−0.236237
$477$	3.23904	0.148305
$478$	−37.6574	−1.72241
$479$	2.17772	0.0995027	0.0497513	−	0.998762i	$-0.484157\pi$
$479$	2.17772	0.0995027	0.0497513	+	0.998762i	$0.484157\pi$
$480$	2.54525	0.116174
$481$	6.42356	0.292889
$482$	0.317412	0.0144577
$483$	0	0
$484$	6.64658	0.302117
$485$	−12.9677	−0.588831
$486$	1.56791	0.0711220
$487$	18.0884	0.819664	0.409832	−	0.912161i	$-0.365587\pi$
$487$	18.0884	0.819664	0.409832	+	0.912161i	$0.365587\pi$
$488$	−18.8393	−0.852814
$489$	11.0985	0.501892
$490$	−7.40725	−0.334626
$491$	8.13721	0.367227	0.183613	−	0.982999i	$-0.441221\pi$
$491$	8.13721	0.367227	0.183613	+	0.982999i	$0.441221\pi$
$492$	−5.63234	−0.253925
$493$	−17.6527	−0.795040
$494$	−6.18201	−0.278142
$495$	−5.04985	−0.226974
$496$	12.1234	0.544356
$497$	−8.22280	−0.368843
$498$	25.7107	1.15212
$499$	41.0051	1.83564	0.917820	−	0.396996i	$-0.129947\pi$
$499$	41.0051	1.83564	0.917820	+	0.396996i	$0.129947\pi$
$500$	−0.458355	−0.0204983
$501$	−19.8211	−0.885539
$502$	−11.0377	−0.492639
$503$	0.166259	0.00741310	0.00370655	−	0.999993i	$-0.498820\pi$
$503$	0.166259	0.00741310	0.00370655	+	0.999993i	$0.498820\pi$
$504$	8.27655	0.368667
$505$	−1.09477	−0.0487165
$506$	0	0
$507$	−12.3564	−0.548769
$508$	−2.43440	−0.108009
$509$	39.8120	1.76464	0.882319	−	0.470652i	$-0.155981\pi$
$509$	39.8120	1.76464	0.882319	+	0.470652i	$0.155981\pi$
$510$	−5.14906	−0.228004
$511$	−11.3397	−0.501637
$512$	−10.7739	−0.476142
$513$	4.91487	0.216997
$514$	−34.7550	−1.53298
$515$	4.00776	0.176603
$516$	−0.171381	−0.00754463
$517$	42.8426	1.88422
$518$	42.9878	1.88878
$519$	4.85194	0.212977
$520$	−1.93911	−0.0850355
$521$	−25.0646	−1.09810	−0.549050	−	0.835790i	$-0.685010\pi$
$521$	−25.0646	−1.09810	−0.549050	+	0.835790i	$0.685010\pi$
$522$	−8.42808	−0.368887
$523$	−35.1571	−1.53731	−0.768656	−	0.639662i	$-0.779074\pi$
$523$	−35.1571	−1.53731	−0.768656	+	0.639662i	$0.779074\pi$
$524$	−1.22512	−0.0535196
$525$	−3.42407	−0.149439
$526$	38.1521	1.66351
$527$	−8.45903	−0.368481
$528$	−23.7677	−1.03436
$529$	0	0
$530$	−5.07854	−0.220598
$531$	8.14914	0.353642
$532$	−7.71361	−0.334427
$533$	9.85783	0.426990
$534$	−0.592455	−0.0256380
$535$	−11.3132	−0.489111
$536$	−34.9103	−1.50789
$537$	24.7501	1.06805
$538$	−49.0494	−2.11467
$539$	23.8568	1.02759
$540$	−0.458355	−0.0197245
$541$	6.42318	0.276154	0.138077	−	0.990421i	$-0.455908\pi$
$541$	6.42318	0.276154	0.138077	+	0.990421i	$0.455908\pi$
$542$	15.3144	0.657811
$543$	17.8763	0.767145
$544$	−8.35864	−0.358374
$545$	9.06942	0.388491
$546$	4.30686	0.184317
$547$	−12.2151	−0.522278	−0.261139	−	0.965301i	$-0.584098\pi$
$547$	−12.2151	−0.522278	−0.261139	+	0.965301i	$0.584098\pi$
$548$	−8.89242	−0.379866
$549$	7.79395	0.332638
$550$	7.91772	0.337613
$551$	−26.4191	−1.12549
$552$	0	0
$553$	−31.7878	−1.35176
$554$	35.6846	1.51610
$555$	8.00719	0.339886
$556$	3.61234	0.153197
$557$	12.9586	0.549074	0.274537	−	0.961576i	$-0.411475\pi$
$557$	12.9586	0.549074	0.274537	+	0.961576i	$0.411475\pi$
$558$	−4.03866	−0.170970
$559$	0.299955	0.0126867
$560$	−16.1158	−0.681017
$561$	16.5838	0.700169
$562$	−33.2077	−1.40078
$563$	24.7451	1.04288	0.521440	−	0.853288i	$-0.325395\pi$
$563$	24.7451	1.04288	0.521440	+	0.853288i	$0.325395\pi$
$564$	3.88866	0.163742
$565$	−11.1715	−0.469988
$566$	42.9143	1.80382
$567$	−3.42407	−0.143798
$568$	−5.80475	−0.243562
$569$	−16.8604	−0.706824	−0.353412	−	0.935468i	$-0.614979\pi$
$569$	−16.8604	−0.706824	−0.353412	+	0.935468i	$0.614979\pi$
$570$	−7.70610	−0.322773
$571$	−32.3107	−1.35216	−0.676081	−	0.736828i	$-0.736323\pi$
$571$	−32.3107	−1.35216	−0.676081	+	0.736828i	$0.736323\pi$
$572$	−1.85685	−0.0776386
$573$	21.4315	0.895313
$574$	65.9707	2.75357
$575$	0	0
$576$	5.42251	0.225938
$577$	−24.6107	−1.02456	−0.512278	−	0.858819i	$-0.671198\pi$
$577$	−24.6107	−1.02456	−0.512278	+	0.858819i	$0.671198\pi$
$578$	−9.74491	−0.405335
$579$	23.2259	0.965236
$580$	2.46382	0.102305
$581$	−56.1480	−2.32941
$582$	20.3322	0.842795
$583$	16.3566	0.677423
$584$	−8.00504	−0.331251
$585$	0.802224	0.0331679
$586$	23.7287	0.980224
$587$	22.7961	0.940896	0.470448	−	0.882428i	$-0.344092\pi$
$587$	22.7961	0.940896	0.470448	+	0.882428i	$0.344092\pi$
$588$	2.16540	0.0892994
$589$	−12.6598	−0.521638
$590$	−12.7772	−0.526027
$591$	8.30142	0.341475
$592$	37.6868	1.54892
$593$	26.1334	1.07317	0.536584	−	0.843847i	$-0.319714\pi$
$593$	26.1334	1.07317	0.536584	+	0.843847i	$0.319714\pi$
$594$	7.91772	0.324868
$595$	11.2447	0.460989
$596$	−3.14655	−0.128888
$597$	−3.88602	−0.159044
$598$	0	0
$599$	−36.7047	−1.49971	−0.749857	−	0.661600i	$-0.769878\pi$
$599$	−36.7047	−1.49971	−0.749857	+	0.661600i	$0.769878\pi$
$600$	−2.41717	−0.0986804
$601$	−11.1050	−0.452982	−0.226491	−	0.974013i	$-0.572725\pi$
$601$	−11.1050	−0.452982	−0.226491	+	0.974013i	$0.572725\pi$
$602$	2.00736	0.0818140
$603$	14.4426	0.588150
$604$	8.86917	0.360881
$605$	−14.5009	−0.589547
$606$	1.71650	0.0697281
$607$	−10.4794	−0.425347	−0.212673	−	0.977123i	$-0.568217\pi$
$607$	−10.4794	−0.425347	−0.212673	+	0.977123i	$0.568217\pi$
$608$	−12.5096	−0.507330
$609$	18.4056	0.745831
$610$	−12.2202	−0.494783
$611$	−6.80602	−0.275342
$612$	1.50525	0.0608461
$613$	10.6781	0.431284	0.215642	−	0.976473i	$-0.430816\pi$
$613$	10.6781	0.431284	0.215642	+	0.976473i	$0.430816\pi$
$614$	−9.56120	−0.385859
$615$	12.2881	0.495506
$616$	41.7953	1.68398
$617$	−3.53020	−0.142120	−0.0710602	−	0.997472i	$-0.522638\pi$
$617$	−3.53020	−0.142120	−0.0710602	+	0.997472i	$0.522638\pi$
$618$	−6.28383	−0.252773
$619$	−23.6048	−0.948756	−0.474378	−	0.880321i	$-0.657327\pi$
$619$	−23.6048	−0.948756	−0.474378	+	0.880321i	$0.657327\pi$
$620$	1.18064	0.0474156
$621$	0	0
$622$	−8.52609	−0.341865
$623$	1.29383	0.0518361
$624$	3.77576	0.151151
$625$	1.00000	0.0400000
$626$	−7.33196	−0.293044
$627$	24.8193	0.991189
$628$	−5.91370	−0.235982
$629$	−26.2958	−1.04848
$630$	5.36865	0.213892
$631$	21.2571	0.846231	0.423115	−	0.906076i	$-0.360937\pi$
$631$	21.2571	0.846231	0.423115	+	0.906076i	$0.360937\pi$
$632$	−22.4401	−0.892618
$633$	10.6468	0.423173
$634$	−11.7379	−0.466173
$635$	5.31117	0.210767
$636$	1.48463	0.0588695
$637$	−3.78992	−0.150162
$638$	−42.5605	−1.68499
$639$	2.40147	0.0950006
$640$	−13.5925	−0.537292
$641$	−26.8980	−1.06241	−0.531204	−	0.847244i	$-0.678260\pi$
$641$	−26.8980	−1.06241	−0.531204	+	0.847244i	$0.678260\pi$
$642$	17.7381	0.700067
$643$	−37.3334	−1.47228	−0.736142	−	0.676827i	$-0.763355\pi$
$643$	−37.3334	−1.47228	−0.736142	+	0.676827i	$0.763355\pi$
$644$	0	0
$645$	0.373904	0.0147225
$646$	25.3070	0.995690
$647$	8.25123	0.324389	0.162195	−	0.986759i	$-0.448143\pi$
$647$	8.25123	0.324389	0.162195	+	0.986759i	$0.448143\pi$
$648$	−2.41717	−0.0949553
$649$	41.1519	1.61535
$650$	−1.25782	−0.0493357
$651$	8.81977	0.345674
$652$	5.08707	0.199225
$653$	−24.3002	−0.950941	−0.475471	−	0.879732i	$-0.657722\pi$
$653$	−24.3002	−0.950941	−0.475471	+	0.879732i	$0.657722\pi$
$654$	−14.2201	−0.556049
$655$	2.67286	0.104437
$656$	57.8356	2.25810
$657$	3.31175	0.129204
$658$	−45.5474	−1.77562
$659$	−12.4461	−0.484831	−0.242415	−	0.970173i	$-0.577940\pi$
$659$	−12.4461	−0.484831	−0.242415	+	0.970173i	$0.577940\pi$
$660$	−2.31462	−0.0900966
$661$	−16.7517	−0.651564	−0.325782	−	0.945445i	$-0.605628\pi$
$661$	−16.7517	−0.651564	−0.325782	+	0.945445i	$0.605628\pi$
$662$	−41.6411	−1.61843
$663$	−2.63452	−0.102316
$664$	−39.6368	−1.53820
$665$	16.8289	0.652596
$666$	−12.5546	−0.486480
$667$	0	0
$668$	−9.08509	−0.351513
$669$	17.0171	0.657919
$670$	−22.6448	−0.874845
$671$	39.3582	1.51941
$672$	8.71511	0.336193
$673$	−43.3141	−1.66963	−0.834817	−	0.550527i	$-0.814427\pi$
$673$	−43.3141	−1.66963	−0.834817	+	0.550527i	$0.814427\pi$
$674$	19.0078	0.732153
$675$	1.00000	0.0384900
$676$	−5.66364	−0.217832
$677$	−36.8493	−1.41623	−0.708117	−	0.706095i	$-0.750455\pi$
$677$	−36.8493	−1.41623	−0.708117	+	0.706095i	$0.750455\pi$
$678$	17.5159	0.672695
$679$	−44.4022	−1.70400
$680$	7.93803	0.304409
$681$	−13.3077	−0.509954
$682$	−20.3946	−0.780949
$683$	−1.45527	−0.0556845	−0.0278423	−	0.999612i	$-0.508864\pi$
$683$	−1.45527	−0.0556845	−0.0278423	+	0.999612i	$0.508864\pi$
$684$	2.25276	0.0861364
$685$	19.4007	0.741263
$686$	12.2176	0.466470
$687$	−12.3492	−0.471150
$688$	1.75983	0.0670928
$689$	−2.59843	−0.0989924
$690$	0	0
$691$	21.4670	0.816644	0.408322	−	0.912838i	$-0.366114\pi$
$691$	21.4670	0.816644	0.408322	+	0.912838i	$0.366114\pi$
$692$	2.22391	0.0845405
$693$	−17.2910	−0.656832
$694$	4.94558	0.187732
$695$	−7.88109	−0.298947
$696$	12.9931	0.492502
$697$	−40.3545	−1.52854
$698$	36.8440	1.39457
$699$	−4.26354	−0.161262
$700$	−1.56944	−0.0593193
$701$	16.4837	0.622579	0.311290	−	0.950315i	$-0.399239\pi$
$701$	16.4837	0.622579	0.311290	+	0.950315i	$0.399239\pi$
$702$	−1.25782	−0.0474733
$703$	−39.3543	−1.48428
$704$	27.3829	1.03203
$705$	−8.48395	−0.319524
$706$	3.42202	0.128789
$707$	−3.74856	−0.140979
$708$	3.73520	0.140377
$709$	17.5581	0.659408	0.329704	−	0.944084i	$-0.393051\pi$
$709$	17.5581	0.659408	0.329704	+	0.944084i	$0.393051\pi$
$710$	−3.76530	−0.141309
$711$	9.28363	0.348163
$712$	0.913355	0.0342294
$713$	0	0
$714$	−17.6308	−0.659815
$715$	4.05110	0.151503
$716$	11.3444	0.423959
$717$	−24.0175	−0.896949
$718$	−32.8450	−1.22577
$719$	4.37579	0.163189	0.0815947	−	0.996666i	$-0.473999\pi$
$719$	4.37579	0.163189	0.0815947	+	0.996666i	$0.473999\pi$
$720$	4.70662	0.175405
$721$	13.7229	0.511066
$722$	8.08412	0.300860
$723$	0.202442	0.00752890
$724$	8.19369	0.304516
$725$	−5.37535	−0.199635
$726$	22.7362	0.843820
$727$	30.8599	1.14453	0.572265	−	0.820069i	$-0.306065\pi$
$727$	30.8599	1.14453	0.572265	+	0.820069i	$0.306065\pi$
$728$	−6.63965	−0.246082
$729$	1.00000	0.0370370
$730$	−5.19253	−0.192184
$731$	−1.22791	−0.0454159
$732$	3.57240	0.132040
$733$	30.3026	1.11925	0.559626	−	0.828745i	$-0.310945\pi$
$733$	30.3026	1.11925	0.559626	+	0.828745i	$0.310945\pi$
$734$	−4.56564	−0.168521
$735$	−4.72427	−0.174257
$736$	0	0
$737$	72.9331	2.68652
$738$	−19.2667	−0.709219
$739$	−18.8734	−0.694269	−0.347135	−	0.937815i	$-0.612845\pi$
$739$	−18.8734	−0.694269	−0.347135	+	0.937815i	$0.612845\pi$
$740$	3.67014	0.134917
$741$	−3.94283	−0.144843
$742$	−17.3893	−0.638380
$743$	−18.7927	−0.689439	−0.344719	−	0.938706i	$-0.612026\pi$
$743$	−18.7927	−0.689439	−0.344719	+	0.938706i	$0.612026\pi$
$744$	6.22617	0.228263
$745$	6.86487	0.251509
$746$	−35.0049	−1.28162
$747$	16.3980	0.599972
$748$	7.60128	0.277930
$749$	−38.7371	−1.41542
$750$	−1.56791	−0.0572521
$751$	−20.6775	−0.754534	−0.377267	−	0.926105i	$-0.623136\pi$
$751$	−20.6775	−0.754534	−0.377267	+	0.926105i	$0.623136\pi$
$752$	−39.9307	−1.45612
$753$	−7.03976	−0.256543
$754$	6.76121	0.246229
$755$	−19.3500	−0.704218
$756$	−1.56944	−0.0570801
$757$	17.3950	0.632232	0.316116	−	0.948721i	$-0.397621\pi$
$757$	17.3950	0.632232	0.316116	+	0.948721i	$0.397621\pi$
$758$	−51.5419	−1.87209
$759$	0	0
$760$	11.8801	0.430935
$761$	−37.2139	−1.34900	−0.674501	−	0.738274i	$-0.735641\pi$
$761$	−37.2139	−1.34900	−0.674501	+	0.738274i	$0.735641\pi$
$762$	−8.32746	−0.301672
$763$	31.0544	1.12424
$764$	9.82324	0.355392
$765$	−3.28402	−0.118734
$766$	27.5367	0.994942
$767$	−6.53743	−0.236053
$768$	10.4669	0.377692
$769$	−17.4095	−0.627804	−0.313902	−	0.949455i	$-0.601636\pi$
$769$	−17.4095	−0.627804	−0.313902	+	0.949455i	$0.601636\pi$
$770$	27.1109	0.977008
$771$	−22.1664	−0.798304
$772$	10.6457	0.383148
$773$	10.9579	0.394129	0.197064	−	0.980391i	$-0.436859\pi$
$773$	10.9579	0.394129	0.197064	+	0.980391i	$0.436859\pi$
$774$	−0.586250	−0.0210723
$775$	−2.57581	−0.0925260
$776$	−31.3450	−1.12522
$777$	27.4172	0.983586
$778$	21.2853	0.763116
$779$	−60.3946	−2.16386
$780$	0.367704	0.0131659
$781$	12.1270	0.433940
$782$	0	0
$783$	−5.37535	−0.192099
$784$	−22.2354	−0.794120
$785$	12.9020	0.460492
$786$	−4.19082	−0.149482
$787$	9.50582	0.338846	0.169423	−	0.985543i	$-0.445810\pi$
$787$	9.50582	0.338846	0.169423	+	0.985543i	$0.445810\pi$
$788$	3.80500	0.135547
$789$	24.3330	0.866279
$790$	−14.5559	−0.517877
$791$	−38.2519	−1.36008
$792$	−12.2063	−0.433733
$793$	−6.25249	−0.222032
$794$	−39.6741	−1.40798
$795$	−3.23904	−0.114877
$796$	−1.78118	−0.0631322
$797$	−48.3933	−1.71418	−0.857089	−	0.515169i	$-0.827729\pi$
$797$	−48.3933	−1.71418	−0.857089	+	0.515169i	$0.827729\pi$
$798$	−26.3862	−0.934063
$799$	27.8615	0.985668
$800$	−2.54525	−0.0899880
$801$	−0.377862	−0.0133511
$802$	55.9857	1.97692
$803$	16.7238	0.590170
$804$	6.61986	0.233464
$805$	0	0
$806$	3.23990	0.114121
$807$	−31.2832	−1.10122
$808$	−2.64623	−0.0930942
$809$	−10.4398	−0.367045	−0.183522	−	0.983016i	$-0.558750\pi$
$809$	−10.4398	−0.367045	−0.183522	+	0.983016i	$0.558750\pi$
$810$	−1.56791	−0.0550909
$811$	−2.70883	−0.0951200	−0.0475600	−	0.998868i	$-0.515145\pi$
$811$	−2.70883	−0.0951200	−0.0475600	+	0.998868i	$0.515145\pi$
$812$	8.43629	0.296056
$813$	9.76739	0.342557
$814$	−63.3987	−2.22212
$815$	−11.0985	−0.388764
$816$	−15.4566	−0.541091
$817$	−1.83769	−0.0642927
$818$	−18.7637	−0.656056
$819$	2.74687	0.0959835
$820$	5.63234	0.196690
$821$	20.0312	0.699093	0.349546	−	0.936919i	$-0.386336\pi$
$821$	20.0312	0.699093	0.349546	+	0.936919i	$0.386336\pi$
$822$	−30.4187	−1.06097
$823$	−1.97760	−0.0689346	−0.0344673	−	0.999406i	$-0.510973\pi$
$823$	−1.97760	−0.0689346	−0.0344673	+	0.999406i	$0.510973\pi$
$824$	9.68743	0.337478
$825$	5.04985	0.175813
$826$	−43.7499	−1.52225
$827$	24.2183	0.842154	0.421077	−	0.907025i	$-0.361652\pi$
$827$	24.2183	0.842154	0.421077	+	0.907025i	$0.361652\pi$
$828$	0	0
$829$	−34.6879	−1.20476	−0.602380	−	0.798210i	$-0.705781\pi$
$829$	−34.6879	−1.20476	−0.602380	+	0.798210i	$0.705781\pi$
$830$	−25.7107	−0.892431
$831$	22.7593	0.789512
$832$	−4.35007	−0.150812
$833$	15.5146	0.537549
$834$	12.3569	0.427884
$835$	19.8211	0.685936
$836$	11.3761	0.393450
$837$	−2.57581	−0.0890332
$838$	19.6428	0.678550
$839$	25.2689	0.872380	0.436190	−	0.899855i	$-0.356328\pi$
$839$	25.2689	0.872380	0.436190	+	0.899855i	$0.356328\pi$
$840$	−8.27655	−0.285568
$841$	−0.105664	−0.00364357
$842$	23.9714	0.826110
$843$	−21.1795	−0.729462
$844$	4.88003	0.167977
$845$	12.3564	0.425074
$846$	13.3021	0.457336
$847$	−49.6523	−1.70607
$848$	−15.2449	−0.523513
$849$	27.3703	0.939347
$850$	5.14906	0.176611
$851$	0	0
$852$	1.10073	0.0377102
$853$	36.5316	1.25082	0.625408	−	0.780298i	$-0.284932\pi$
$853$	36.5316	1.25082	0.625408	+	0.780298i	$0.284932\pi$
$854$	−41.8430	−1.43184
$855$	−4.91487	−0.168085
$856$	−27.3458	−0.934662
$857$	−27.4580	−0.937948	−0.468974	−	0.883212i	$-0.655376\pi$
$857$	−27.4580	−0.937948	−0.468974	+	0.883212i	$0.655376\pi$
$858$	−6.35179	−0.216846
$859$	3.61008	0.123174	0.0615872	−	0.998102i	$-0.480384\pi$
$859$	3.61008	0.123174	0.0615872	+	0.998102i	$0.480384\pi$
$860$	0.171381	0.00584405
$861$	42.0755	1.43393
$862$	−47.6932	−1.62444
$863$	21.2280	0.722608	0.361304	−	0.932448i	$-0.382332\pi$
$863$	21.2280	0.722608	0.361304	+	0.932448i	$0.382332\pi$
$864$	−2.54525	−0.0865910
$865$	−4.85194	−0.164971
$866$	−0.239787	−0.00814828
$867$	−6.21520	−0.211079
$868$	4.04259	0.137214
$869$	46.8809	1.59033
$870$	8.42808	0.285739
$871$	−11.5862	−0.392584
$872$	21.9223	0.742383
$873$	12.9677	0.438889
$874$	0	0
$875$	3.42407	0.115755
$876$	1.51796	0.0512870
$877$	−9.64705	−0.325758	−0.162879	−	0.986646i	$-0.552078\pi$
$877$	−9.64705	−0.325758	−0.162879	+	0.986646i	$0.552078\pi$
$878$	−58.2093	−1.96447
$879$	15.1339	0.510455
$880$	23.7677	0.801209
$881$	−50.3043	−1.69480	−0.847398	−	0.530959i	$-0.821832\pi$
$881$	−50.3043	−1.69480	−0.847398	+	0.530959i	$0.821832\pi$
$882$	7.40725	0.249415
$883$	−11.9380	−0.401744	−0.200872	−	0.979617i	$-0.564378\pi$
$883$	−11.9380	−0.401744	−0.200872	+	0.979617i	$0.564378\pi$
$884$	−1.20755	−0.0406142
$885$	−8.14914	−0.273930
$886$	22.3699	0.751531
$887$	3.58551	0.120390	0.0601949	−	0.998187i	$-0.480828\pi$
$887$	3.58551	0.120390	0.0601949	+	0.998187i	$0.480828\pi$
$888$	19.3547	0.649502
$889$	18.1858	0.609933
$890$	0.592455	0.0198591
$891$	5.04985	0.169176
$892$	7.79988	0.261159
$893$	41.6975	1.39535
$894$	−10.7635	−0.359986
$895$	−24.7501	−0.827306
$896$	−46.5418	−1.55485
$897$	0	0
$898$	11.4922	0.383499
$899$	13.8459	0.461786
$900$	0.458355	0.0152785
$901$	10.6371	0.354372
$902$	−97.2941	−3.23954
$903$	1.28028	0.0426049
$904$	−27.0033	−0.898117
$905$	−17.8763	−0.594228
$906$	30.3391	1.00795
$907$	−44.3427	−1.47238	−0.736188	−	0.676778i	$-0.763376\pi$
$907$	−44.3427	−1.47238	−0.736188	+	0.676778i	$0.763376\pi$
$908$	−6.09968	−0.202425
$909$	1.09477	0.0363111
$910$	−4.30686	−0.142771
$911$	21.7984	0.722213	0.361107	−	0.932525i	$-0.382399\pi$
$911$	21.7984	0.722213	0.361107	+	0.932525i	$0.382399\pi$
$912$	−23.1324	−0.765992
$913$	82.8075	2.74053
$914$	65.6929	2.17293
$915$	−7.79395	−0.257660
$916$	−5.66031	−0.187022
$917$	9.15207	0.302228
$918$	5.14906	0.169944
$919$	21.3066	0.702841	0.351421	−	0.936218i	$-0.385699\pi$
$919$	21.3066	0.702841	0.351421	+	0.936218i	$0.385699\pi$
$920$	0	0
$921$	−6.09804	−0.200937
$922$	−14.9076	−0.490956
$923$	−1.92651	−0.0634120
$924$	−7.92544	−0.260728
$925$	−8.00719	−0.263275
$926$	3.72836	0.122522
$927$	−4.00776	−0.131632
$928$	13.6816	0.449120
$929$	−0.742489	−0.0243603	−0.0121801	−	0.999926i	$-0.503877\pi$
$929$	−0.742489	−0.0243603	−0.0121801	+	0.999926i	$0.503877\pi$
$930$	4.03866	0.132433
$931$	23.2192	0.760978
$932$	−1.95422	−0.0640126
$933$	−5.43785	−0.178027
$934$	46.8109	1.53170
$935$	−16.5838	−0.542348
$936$	1.93911	0.0633817
$937$	−3.07894	−0.100585	−0.0502924	−	0.998735i	$-0.516015\pi$
$937$	−3.07894	−0.100585	−0.0502924	+	0.998735i	$0.516015\pi$
$938$	−77.5375	−2.53169
$939$	−4.67625	−0.152604
$940$	−3.88866	−0.126834
$941$	33.2472	1.08383	0.541914	−	0.840434i	$-0.317700\pi$
$941$	33.2472	1.08383	0.541914	+	0.840434i	$0.317700\pi$
$942$	−20.2292	−0.659104
$943$	0	0
$944$	−38.3549	−1.24835
$945$	3.42407	0.111385
$946$	−2.96047	−0.0962533
$947$	−54.7317	−1.77854	−0.889270	−	0.457382i	$-0.848787\pi$
$947$	−54.7317	−1.77854	−0.889270	+	0.457382i	$0.848787\pi$
$948$	4.25520	0.138203
$949$	−2.65676	−0.0862421
$950$	7.70610	0.250019
$951$	−7.48634	−0.242761
$952$	27.1804	0.880921
$953$	38.7275	1.25451	0.627253	−	0.778815i	$-0.284179\pi$
$953$	38.7275	1.25451	0.627253	+	0.778815i	$0.284179\pi$
$954$	5.07854	0.164424
$955$	−21.4315	−0.693506
$956$	−11.0085	−0.356042
$957$	−27.1447	−0.877462
$958$	3.41448	0.110317
$959$	66.4295	2.14512
$960$	−5.42251	−0.175011
$961$	−24.3652	−0.785974
$962$	10.0716	0.324721
$963$	11.3132	0.364562
$964$	0.0927904	0.00298858
$965$	−23.2259	−0.747669
$966$	0	0
$967$	3.40960	0.109645	0.0548227	−	0.998496i	$-0.482541\pi$
$967$	3.40960	0.109645	0.0548227	+	0.998496i	$0.482541\pi$
$968$	−35.0512	−1.12659
$969$	16.1405	0.518509
$970$	−20.3322	−0.652827
$971$	27.8628	0.894161	0.447081	−	0.894494i	$-0.352464\pi$
$971$	27.8628	0.894161	0.447081	+	0.894494i	$0.352464\pi$
$972$	0.458355	0.0147018
$973$	−26.9854	−0.865113
$974$	28.3611	0.908747
$975$	−0.802224	−0.0256917
$976$	−36.6832	−1.17420
$977$	−1.18833	−0.0380181	−0.0190091	−	0.999819i	$-0.506051\pi$
$977$	−1.18833	−0.0380181	−0.0190091	+	0.999819i	$0.506051\pi$
$978$	17.4015	0.556439
$979$	−1.90814	−0.0609845
$980$	−2.16540	−0.0691710
$981$	−9.06942	−0.289564
$982$	12.7584	0.407138
$983$	−11.4810	−0.366188	−0.183094	−	0.983095i	$-0.558611\pi$
$983$	−11.4810	−0.366188	−0.183094	+	0.983095i	$0.558611\pi$
$984$	29.7025	0.946880
$985$	−8.30142	−0.264505
$986$	−27.6780	−0.881447
$987$	−29.0496	−0.924661
$988$	−1.80722	−0.0574952
$989$	0	0
$990$	−7.91772	−0.251642
$991$	−39.8058	−1.26447	−0.632237	−	0.774775i	$-0.717863\pi$
$991$	−39.8058	−1.26447	−0.632237	+	0.774775i	$0.717863\pi$
$992$	6.55608	0.208156
$993$	−26.5583	−0.842801
$994$	−12.8926	−0.408930
$995$	3.88602	0.123195
$996$	7.51612	0.238158
$997$	−41.4377	−1.31235	−0.656173	−	0.754610i	$-0.727826\pi$
$997$	−41.4377	−1.31235	−0.656173	+	0.754610i	$0.727826\pi$
$998$	64.2925	2.03514
$999$	−8.00719	−0.253336

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bl.1.10	✓	12
23.22	odd	2		7935.2.a.bm.1.10	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bl.1.10	✓	12	1.1	even	1	trivial
7935.2.a.bm.1.10	yes	12	23.22	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+1.56791 q^{2} +1.00000 q^{3} +0.458355 q^{4} -1.00000 q^{5} +1.56791 q^{6} -3.42407 q^{7} -2.41717 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.56791 q^{2} +1.00000 q^{3} +0.458355 q^{4} -1.00000 q^{5} +1.56791 q^{6} -3.42407 q^{7} -2.41717 q^{8} +1.00000 q^{9} -1.56791 q^{10} +5.04985 q^{11} +0.458355 q^{12} -0.802224 q^{13} -5.36865 q^{14} -1.00000 q^{15} -4.70662 q^{16} +3.28402 q^{17} +1.56791 q^{18} +4.91487 q^{19} -0.458355 q^{20} -3.42407 q^{21} +7.91772 q^{22} -2.41717 q^{24} +1.00000 q^{25} -1.25782 q^{26} +1.00000 q^{27} -1.56944 q^{28} -5.37535 q^{29} -1.56791 q^{30} -2.57581 q^{31} -2.54525 q^{32} +5.04985 q^{33} +5.14906 q^{34} +3.42407 q^{35} +0.458355 q^{36} -8.00719 q^{37} +7.70610 q^{38} -0.802224 q^{39} +2.41717 q^{40} -12.2881 q^{41} -5.36865 q^{42} -0.373904 q^{43} +2.31462 q^{44} -1.00000 q^{45} +8.48395 q^{47} -4.70662 q^{48} +4.72427 q^{49} +1.56791 q^{50} +3.28402 q^{51} -0.367704 q^{52} +3.23904 q^{53} +1.56791 q^{54} -5.04985 q^{55} +8.27655 q^{56} +4.91487 q^{57} -8.42808 q^{58} +8.14914 q^{59} -0.458355 q^{60} +7.79395 q^{61} -4.03866 q^{62} -3.42407 q^{63} +5.42251 q^{64} +0.802224 q^{65} +7.91772 q^{66} +14.4426 q^{67} +1.50525 q^{68} +5.36865 q^{70} +2.40147 q^{71} -2.41717 q^{72} +3.31175 q^{73} -12.5546 q^{74} +1.00000 q^{75} +2.25276 q^{76} -17.2910 q^{77} -1.25782 q^{78} +9.28363 q^{79} +4.70662 q^{80} +1.00000 q^{81} -19.2667 q^{82} +16.3980 q^{83} -1.56944 q^{84} -3.28402 q^{85} -0.586250 q^{86} -5.37535 q^{87} -12.2063 q^{88} -0.377862 q^{89} -1.56791 q^{90} +2.74687 q^{91} -2.57581 q^{93} +13.3021 q^{94} -4.91487 q^{95} -2.54525 q^{96} +12.9677 q^{97} +7.40725 q^{98} +5.04985 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9	\( 12 q + 12 q^{3} + 8 q^{4} - 12 q^{5} + 4 q^{7} + 12 q^{9} + 24 q^{11} + 8 q^{12} - 8 q^{13} + 16 q^{14} - 12 q^{15} + 28 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} + 8 q^{28} - 16 q^{29} + 20 q^{32} + 24 q^{33} + 16 q^{34} - 4 q^{35} + 8 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{39} - 4 q^{41} + 16 q^{42} - 12 q^{43} + 16 q^{44} - 12 q^{45} + 4 q^{47} + 24 q^{49} + 28 q^{51} - 36 q^{52} + 28 q^{53} - 24 q^{55} + 56 q^{56} + 16 q^{57} + 20 q^{59} - 8 q^{60} + 32 q^{61} + 12 q^{62} + 4 q^{63} - 4 q^{64} + 8 q^{65} - 4 q^{67} + 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} - 36 q^{74} + 12 q^{75} + 8 q^{76} - 28 q^{77} - 36 q^{78} + 40 q^{79} + 12 q^{81} - 28 q^{82} + 100 q^{83} + 8 q^{84} - 28 q^{85} - 20 q^{86} - 16 q^{87} + 80 q^{89} - 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} - 8 q^{97} + 28 q^{98} + 24 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 + 8 * q^4 - 12 * q^5 + 4 * q^7 + 12 * q^9 + 24 * q^11 + 8 * q^12 - 8 * q^13 + 16 * q^14 - 12 * q^15 + 28 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 + 8 * q^28 - 16 * q^29 + 20 * q^32 + 24 * q^33 + 16 * q^34 - 4 * q^35 + 8 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^39 - 4 * q^41 + 16 * q^42 - 12 * q^43 + 16 * q^44 - 12 * q^45 + 4 * q^47 + 24 * q^49 + 28 * q^51 - 36 * q^52 + 28 * q^53 - 24 * q^55 + 56 * q^56 + 16 * q^57 + 20 * q^59 - 8 * q^60 + 32 * q^61 + 12 * q^62 + 4 * q^63 - 4 * q^64 + 8 * q^65 - 4 * q^67 + 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 - 36 * q^74 + 12 * q^75 + 8 * q^76 - 28 * q^77 - 36 * q^78 + 40 * q^79 + 12 * q^81 - 28 * q^82 + 100 * q^83 + 8 * q^84 - 28 * q^85 - 20 * q^86 - 16 * q^87 + 80 * q^89 - 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 - 8 * q^97 + 28 * q^98 + 24 * q^99

Introduction

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