LMFDB - Embedded newform 7935.2.a.bb.1.5

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:	$1$
Dimension:	$5$
Coefficient field:	5.5.3370660.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 9x^{3} - 2x^{2} + 16x + 6 $ x^5 - 9x^3 - 2x^2 + 16*x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.42305$ 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)

$f(q)$	$=$	$q+2.42305 q^{2} +1.00000 q^{3} +3.87117 q^{4} -1.00000 q^{5} +2.42305 q^{6} -2.87117 q^{7} +4.53395 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.42305 q^{2} +1.00000 q^{3} +3.87117 q^{4} -1.00000 q^{5} +2.42305 q^{6} -2.87117 q^{7} +4.53395 q^{8} +1.00000 q^{9} -2.42305 q^{10} +2.11090 q^{11} +3.87117 q^{12} -3.48336 q^{13} -6.95700 q^{14} -1.00000 q^{15} +3.24364 q^{16} -1.38781 q^{17} +2.42305 q^{18} -6.32946 q^{19} -3.87117 q^{20} -2.87117 q^{21} +5.11481 q^{22} +4.53395 q^{24} +1.00000 q^{25} -8.44036 q^{26} +1.00000 q^{27} -11.1148 q^{28} +0.760276 q^{29} -2.42305 q^{30} +0.871173 q^{31} -1.20840 q^{32} +2.11090 q^{33} -3.36274 q^{34} +2.87117 q^{35} +3.87117 q^{36} -8.34481 q^{37} -15.3366 q^{38} -3.48336 q^{39} -4.53395 q^{40} -1.38781 q^{41} -6.95700 q^{42} -9.59426 q^{43} +8.17165 q^{44} -1.00000 q^{45} -7.85324 q^{47} +3.24364 q^{48} +1.24364 q^{49} +2.42305 q^{50} -1.38781 q^{51} -13.4847 q^{52} -4.98207 q^{53} +2.42305 q^{54} -2.11090 q^{55} -13.0178 q^{56} -6.32946 q^{57} +1.84219 q^{58} +8.57310 q^{59} -3.87117 q^{60} +1.48336 q^{61} +2.11090 q^{62} -2.87117 q^{63} -9.41529 q^{64} +3.48336 q^{65} +5.11481 q^{66} +11.9358 q^{67} -5.37246 q^{68} +6.95700 q^{70} +16.1981 q^{71} +4.53395 q^{72} -13.1756 q^{73} -20.2199 q^{74} +1.00000 q^{75} -24.5024 q^{76} -6.06075 q^{77} -8.44036 q^{78} +10.8604 q^{79} -3.24364 q^{80} +1.00000 q^{81} -3.36274 q^{82} -15.8249 q^{83} -11.1148 q^{84} +1.38781 q^{85} -23.2474 q^{86} +0.760276 q^{87} +9.57070 q^{88} +15.1769 q^{89} -2.42305 q^{90} +10.0013 q^{91} +0.871173 q^{93} -19.0288 q^{94} +6.32946 q^{95} -1.20840 q^{96} -4.47622 q^{97} +3.01340 q^{98} +2.11090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{3} + 8 q^{4} - 5 q^{5} - 3 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^3 + 8 * q^4 - 5 * q^5 - 3 * q^7 - 6 * q^8 + 5 * q^9	$ 5 q + 5 q^{3} + 8 q^{4} - 5 q^{5} - 3 q^{7} - 6 q^{8} + 5 q^{9} - 6 q^{11} + 8 q^{12} - 6 q^{13} + 6 q^{14} - 5 q^{15} + 10 q^{16} - 7 q^{17} + 4 q^{19} - 8 q^{20} - 3 q^{21} + 8 q^{22} - 6 q^{24} + 5 q^{25} + 10 q^{26} + 5 q^{27} - 38 q^{28} + 9 q^{29} - 7 q^{31} - 12 q^{32} - 6 q^{33} - 4 q^{34} + 3 q^{35} + 8 q^{36} - q^{37} - 26 q^{38} - 6 q^{39} + 6 q^{40} - 7 q^{41} + 6 q^{42} - 20 q^{43} - 18 q^{44} - 5 q^{45} + 10 q^{48} - 7 q^{51} - 22 q^{52} + 3 q^{53} + 6 q^{55} + 18 q^{56} + 4 q^{57} - 14 q^{58} + q^{59} - 8 q^{60} - 4 q^{61} - 6 q^{62} - 3 q^{63} + 18 q^{64} + 6 q^{65} + 8 q^{66} + 5 q^{67} - 32 q^{68} - 6 q^{70} + q^{71} - 6 q^{72} - 6 q^{73} - 48 q^{74} + 5 q^{75} + 6 q^{76} + 12 q^{77} + 10 q^{78} - 10 q^{80} + 5 q^{81} - 4 q^{82} - 41 q^{83} - 38 q^{84} + 7 q^{85} + 2 q^{86} + 9 q^{87} + 84 q^{88} - 18 q^{89} + 16 q^{91} - 7 q^{93} + 4 q^{94} - 4 q^{95} - 12 q^{96} - 26 q^{97} - 24 q^{98} - 6 q^{99}+O(q^{100}) $ 5 * q + 5 * q^3 + 8 * q^4 - 5 * q^5 - 3 * q^7 - 6 * q^8 + 5 * q^9 - 6 * q^11 + 8 * q^12 - 6 * q^13 + 6 * q^14 - 5 * q^15 + 10 * q^16 - 7 * q^17 + 4 * q^19 - 8 * q^20 - 3 * q^21 + 8 * q^22 - 6 * q^24 + 5 * q^25 + 10 * q^26 + 5 * q^27 - 38 * q^28 + 9 * q^29 - 7 * q^31 - 12 * q^32 - 6 * q^33 - 4 * q^34 + 3 * q^35 + 8 * q^36 - q^37 - 26 * q^38 - 6 * q^39 + 6 * q^40 - 7 * q^41 + 6 * q^42 - 20 * q^43 - 18 * q^44 - 5 * q^45 + 10 * q^48 - 7 * q^51 - 22 * q^52 + 3 * q^53 + 6 * q^55 + 18 * q^56 + 4 * q^57 - 14 * q^58 + q^59 - 8 * q^60 - 4 * q^61 - 6 * q^62 - 3 * q^63 + 18 * q^64 + 6 * q^65 + 8 * q^66 + 5 * q^67 - 32 * q^68 - 6 * q^70 + q^71 - 6 * q^72 - 6 * q^73 - 48 * q^74 + 5 * q^75 + 6 * q^76 + 12 * q^77 + 10 * q^78 - 10 * q^80 + 5 * q^81 - 4 * q^82 - 41 * q^83 - 38 * q^84 + 7 * q^85 + 2 * q^86 + 9 * q^87 + 84 * q^88 - 18 * q^89 + 16 * q^91 - 7 * q^93 + 4 * q^94 - 4 * q^95 - 12 * q^96 - 26 * q^97 - 24 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.42305	1.71336	0.856678	−	0.515852i	$-0.172525\pi$
$2$	2.42305	1.71336	0.856678	+	0.515852i	$0.172525\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.87117	1.93559
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.42305	0.989206
$7$	−2.87117	−1.08520	−0.542601	−	0.839991i	$-0.682560\pi$
$7$	−2.87117	−1.08520	−0.542601	+	0.839991i	$0.682560\pi$
$8$	4.53395	1.60299
$9$	1.00000	0.333333
$10$	−2.42305	−0.766236
$11$	2.11090	0.636459	0.318230	−	0.948014i	$-0.396912\pi$
$11$	2.11090	0.636459	0.318230	+	0.948014i	$0.396912\pi$
$12$	3.87117	1.11751
$13$	−3.48336	−0.966110	−0.483055	−	0.875590i	$-0.660473\pi$
$13$	−3.48336	−0.966110	−0.483055	+	0.875590i	$0.660473\pi$
$14$	−6.95700	−1.85934
$15$	−1.00000	−0.258199
$16$	3.24364	0.810909
$17$	−1.38781	−0.336594	−0.168297	−	0.985736i	$-0.553827\pi$
$17$	−1.38781	−0.336594	−0.168297	+	0.985736i	$0.553827\pi$
$18$	2.42305	0.571118
$19$	−6.32946	−1.45208	−0.726039	−	0.687653i	$-0.758641\pi$
$19$	−6.32946	−1.45208	−0.726039	+	0.687653i	$0.758641\pi$
$20$	−3.87117	−0.865621
$21$	−2.87117	−0.626541
$22$	5.11481	1.09048
$23$	0	0
$23$	0	0
$24$	4.53395	0.925488
$25$	1.00000	0.200000
$26$	−8.44036	−1.65529
$27$	1.00000	0.192450
$28$	−11.1148	−2.10050
$29$	0.760276	0.141180	0.0705899	−	0.997505i	$-0.477512\pi$
$29$	0.760276	0.141180	0.0705899	+	0.997505i	$0.477512\pi$
$30$	−2.42305	−0.442386
$31$	0.871173	0.156467	0.0782337	−	0.996935i	$-0.475072\pi$
$31$	0.871173	0.156467	0.0782337	+	0.996935i	$0.475072\pi$
$32$	−1.20840	−0.213617
$33$	2.11090	0.367460
$34$	−3.36274	−0.576705
$35$	2.87117	0.485317
$36$	3.87117	0.645196
$37$	−8.34481	−1.37188	−0.685939	−	0.727659i	$-0.740608\pi$
$37$	−8.34481	−1.37188	−0.685939	+	0.727659i	$0.740608\pi$
$38$	−15.3366	−2.48793
$39$	−3.48336	−0.557784
$40$	−4.53395	−0.716880
$41$	−1.38781	−0.216740	−0.108370	−	0.994111i	$-0.534563\pi$
$41$	−1.38781	−0.216740	−0.108370	+	0.994111i	$0.534563\pi$
$42$	−6.95700	−1.07349
$43$	−9.59426	−1.46311	−0.731555	−	0.681782i	$-0.761205\pi$
$43$	−9.59426	−1.46311	−0.731555	+	0.681782i	$0.761205\pi$
$44$	8.17165	1.23192
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−7.85324	−1.14551	−0.572757	−	0.819725i	$-0.694126\pi$
$47$	−7.85324	−1.14551	−0.572757	+	0.819725i	$0.694126\pi$
$48$	3.24364	0.468179
$49$	1.24364	0.177662
$50$	2.42305	0.342671
$51$	−1.38781	−0.194333
$52$	−13.4847	−1.86999
$53$	−4.98207	−0.684340	−0.342170	−	0.939638i	$-0.611162\pi$
$53$	−4.98207	−0.684340	−0.342170	+	0.939638i	$0.611162\pi$
$54$	2.42305	0.329735
$55$	−2.11090	−0.284633
$56$	−13.0178	−1.73957
$57$	−6.32946	−0.838358
$58$	1.84219	0.241891
$59$	8.57310	1.11612	0.558061	−	0.829800i	$-0.311545\pi$
$59$	8.57310	1.11612	0.558061	+	0.829800i	$0.311545\pi$
$60$	−3.87117	−0.499766
$61$	1.48336	0.189925	0.0949624	−	0.995481i	$-0.469727\pi$
$61$	1.48336	0.189925	0.0949624	+	0.995481i	$0.469727\pi$
$62$	2.11090	0.268084
$63$	−2.87117	−0.361734
$64$	−9.41529	−1.17691
$65$	3.48336	0.432058
$66$	5.11481	0.629590
$67$	11.9358	1.45819	0.729097	−	0.684410i	$-0.239940\pi$
$67$	11.9358	1.45819	0.729097	+	0.684410i	$0.239940\pi$
$68$	−5.37246	−0.651507
$69$	0	0
$70$	6.95700	0.831520
$71$	16.1981	1.92236	0.961178	−	0.275930i	$-0.0889858\pi$
$71$	16.1981	1.92236	0.961178	+	0.275930i	$0.0889858\pi$
$72$	4.53395	0.534331
$73$	−13.1756	−1.54208	−0.771041	−	0.636785i	$-0.780264\pi$
$73$	−13.1756	−1.54208	−0.771041	+	0.636785i	$0.780264\pi$
$74$	−20.2199	−2.35052
$75$	1.00000	0.115470
$76$	−24.5024	−2.81062
$77$	−6.06075	−0.690687
$78$	−8.44036	−0.955682
$79$	10.8604	1.22189	0.610945	−	0.791673i	$-0.290790\pi$
$79$	10.8604	1.22189	0.610945	+	0.791673i	$0.290790\pi$
$80$	−3.24364	−0.362650
$81$	1.00000	0.111111
$82$	−3.36274	−0.371353
$83$	−15.8249	−1.73701	−0.868507	−	0.495678i	$-0.834920\pi$
$83$	−15.8249	−1.73701	−0.868507	+	0.495678i	$0.834920\pi$
$84$	−11.1148	−1.21273
$85$	1.38781	0.150529
$86$	−23.2474	−2.50683
$87$	0.760276	0.0815102
$88$	9.57070	1.02024
$89$	15.1769	1.60875	0.804374	−	0.594123i	$-0.202501\pi$
$89$	15.1769	1.60875	0.804374	+	0.594123i	$0.202501\pi$
$90$	−2.42305	−0.255412
$91$	10.0013	1.04842
$92$	0	0
$93$	0.871173	0.0903365
$94$	−19.0288	−1.96267
$95$	6.32946	0.649389
$96$	−1.20840	−0.123332
$97$	−4.47622	−0.454491	−0.227246	−	0.973837i	$-0.572972\pi$
$97$	−4.47622	−0.454491	−0.227246	+	0.973837i	$0.572972\pi$
$98$	3.01340	0.304399
$99$	2.11090	0.212153
$100$	3.87117	0.387117
$101$	8.57633	0.853377	0.426688	−	0.904399i	$-0.359680\pi$
$101$	8.57633	0.853377	0.426688	+	0.904399i	$0.359680\pi$
$102$	−3.36274	−0.332961
$103$	−16.3197	−1.60803	−0.804016	−	0.594608i	$-0.797307\pi$
$103$	−16.3197	−1.60803	−0.804016	+	0.594608i	$0.797307\pi$
$104$	−15.7934	−1.54867
$105$	2.87117	0.280198
$106$	−12.0718	−1.17252
$107$	−12.2371	−1.18301	−0.591505	−	0.806302i	$-0.701466\pi$
$107$	−12.2371	−1.18301	−0.591505	+	0.806302i	$0.701466\pi$
$108$	3.87117	0.372504
$109$	8.20884	0.786264	0.393132	−	0.919482i	$-0.371391\pi$
$109$	8.20884	0.786264	0.393132	+	0.919482i	$0.371391\pi$
$110$	−5.11481	−0.487678
$111$	−8.34481	−0.792054
$112$	−9.31304	−0.880000
$113$	14.4023	1.35486	0.677429	−	0.735588i	$-0.263094\pi$
$113$	14.4023	1.35486	0.677429	+	0.735588i	$0.263094\pi$
$114$	−15.3366	−1.43640
$115$	0	0
$116$	2.94316	0.273266
$117$	−3.48336	−0.322037
$118$	20.7731	1.91231
$119$	3.98465	0.365272
$120$	−4.53395	−0.413891
$121$	−6.54411	−0.594919
$122$	3.59426	0.325409
$123$	−1.38781	−0.125135
$124$	3.37246	0.302856
$125$	−1.00000	−0.0894427
$126$	−6.95700	−0.619779
$127$	5.21142	0.462439	0.231219	−	0.972902i	$-0.425728\pi$
$127$	5.21142	0.462439	0.231219	+	0.972902i	$0.425728\pi$
$128$	−20.3969	−1.80285
$129$	−9.59426	−0.844727
$130$	8.44036	0.740268
$131$	6.89625	0.602528	0.301264	−	0.953541i	$-0.402591\pi$
$131$	6.89625	0.602528	0.301264	+	0.953541i	$0.402591\pi$
$132$	8.17165	0.711251
$133$	18.1730	1.57580
$134$	28.9211	2.49841
$135$	−1.00000	−0.0860663
$136$	−6.29227	−0.539558
$137$	9.07895	0.775667	0.387834	−	0.921729i	$-0.373224\pi$
$137$	9.07895	0.775667	0.387834	+	0.921729i	$0.373224\pi$
$138$	0	0
$139$	−19.9000	−1.68789	−0.843947	−	0.536426i	$-0.819774\pi$
$139$	−19.9000	−1.68789	−0.843947	+	0.536426i	$0.819774\pi$
$140$	11.1148	0.939373
$141$	−7.85324	−0.661362
$142$	39.2487	3.29368
$143$	−7.35302	−0.614890
$144$	3.24364	0.270303
$145$	−0.760276	−0.0631375
$146$	−31.9251	−2.64214
$147$	1.24364	0.102573
$148$	−32.3042	−2.65539
$149$	−3.88910	−0.318608	−0.159304	−	0.987230i	$-0.550925\pi$
$149$	−3.88910	−0.318608	−0.159304	+	0.987230i	$0.550925\pi$
$150$	2.42305	0.197841
$151$	10.0737	0.819787	0.409893	−	0.912133i	$-0.365566\pi$
$151$	10.0737	0.819787	0.409893	+	0.912133i	$0.365566\pi$
$152$	−28.6974	−2.32767
$153$	−1.38781	−0.112198
$154$	−14.6855	−1.18339
$155$	−0.871173	−0.0699743
$156$	−13.4847	−1.07964
$157$	11.4712	0.915505	0.457752	−	0.889080i	$-0.348655\pi$
$157$	11.4712	0.915505	0.457752	+	0.889080i	$0.348655\pi$
$158$	26.3153	2.09353
$159$	−4.98207	−0.395104
$160$	1.20840	0.0955323
$161$	0	0
$162$	2.42305	0.190373
$163$	−12.6896	−0.993928	−0.496964	−	0.867771i	$-0.665552\pi$
$163$	−12.6896	−0.993928	−0.496964	+	0.867771i	$0.665552\pi$
$164$	−5.37246	−0.419519
$165$	−2.11090	−0.164333
$166$	−38.3446	−2.97612
$167$	−23.8031	−1.84194	−0.920970	−	0.389635i	$-0.872601\pi$
$167$	−23.8031	−1.84194	−0.920970	+	0.389635i	$0.872601\pi$
$168$	−13.0178	−1.00434
$169$	−0.866198	−0.0666306
$170$	3.36274	0.257910
$171$	−6.32946	−0.484026
$172$	−37.1410	−2.83198
$173$	11.8435	0.900446	0.450223	−	0.892916i	$-0.351344\pi$
$173$	11.8435	0.900446	0.450223	+	0.892916i	$0.351344\pi$
$174$	1.84219	0.139656
$175$	−2.87117	−0.217040
$176$	6.84698	0.516111
$177$	8.57310	0.644394
$178$	36.7744	2.75636
$179$	10.4905	0.784097	0.392049	−	0.919945i	$-0.371767\pi$
$179$	10.4905	0.784097	0.392049	+	0.919945i	$0.371767\pi$
$180$	−3.87117	−0.288540
$181$	−6.52959	−0.485341	−0.242670	−	0.970109i	$-0.578023\pi$
$181$	−6.52959	−0.485341	−0.242670	+	0.970109i	$0.578023\pi$
$182$	24.2337	1.79632
$183$	1.48336	0.109653
$184$	0	0
$185$	8.34481	0.613523
$186$	2.11090	0.154778
$187$	−2.92953	−0.214228
$188$	−30.4013	−2.21724
$189$	−2.87117	−0.208847
$190$	15.3366	1.11263
$191$	4.88652	0.353576	0.176788	−	0.984249i	$-0.443429\pi$
$191$	4.88652	0.353576	0.176788	+	0.984249i	$0.443429\pi$
$192$	−9.41529	−0.679490
$193$	−16.4013	−1.18059	−0.590295	−	0.807188i	$-0.700988\pi$
$193$	−16.4013	−1.18059	−0.590295	+	0.807188i	$0.700988\pi$
$194$	−10.8461	−0.778705
$195$	3.48336	0.249449
$196$	4.81433	0.343881
$197$	−19.0256	−1.35552	−0.677758	−	0.735285i	$-0.737048\pi$
$197$	−19.0256	−1.35552	−0.677758	+	0.735285i	$0.737048\pi$
$198$	5.11481	0.363494
$199$	7.89367	0.559567	0.279784	−	0.960063i	$-0.409737\pi$
$199$	7.89367	0.559567	0.279784	+	0.960063i	$0.409737\pi$
$200$	4.53395	0.320599
$201$	11.9358	0.841889
$202$	20.7809	1.46214
$203$	−2.18288	−0.153208
$204$	−5.37246	−0.376148
$205$	1.38781	0.0969290
$206$	−39.5435	−2.75513
$207$	0	0
$208$	−11.2988	−0.783428
$209$	−13.3608	−0.924189
$210$	6.95700	0.480078
$211$	−26.6756	−1.83642	−0.918212	−	0.396089i	$-0.870367\pi$
$211$	−26.6756	−1.83642	−0.918212	+	0.396089i	$0.870367\pi$
$212$	−19.2865	−1.32460
$213$	16.1981	1.10987
$214$	−29.6512	−2.02692
$215$	9.59426	0.654323
$216$	4.53395	0.308496
$217$	−2.50129	−0.169799
$218$	19.8904	1.34715
$219$	−13.1756	−0.890322
$220$	−8.17165	−0.550932
$221$	4.83425	0.325187
$222$	−20.2199	−1.35707
$223$	−7.43455	−0.497854	−0.248927	−	0.968522i	$-0.580078\pi$
$223$	−7.43455	−0.497854	−0.248927	+	0.968522i	$0.580078\pi$
$224$	3.46952	0.231817
$225$	1.00000	0.0666667
$226$	34.8976	2.32135
$227$	18.8691	1.25239	0.626193	−	0.779668i	$-0.284612\pi$
$227$	18.8691	1.25239	0.626193	+	0.779668i	$0.284612\pi$
$228$	−24.5024	−1.62271
$229$	4.22179	0.278984	0.139492	−	0.990223i	$-0.455453\pi$
$229$	4.22179	0.278984	0.139492	+	0.990223i	$0.455453\pi$
$230$	0	0
$231$	−6.06075	−0.398768
$232$	3.44705	0.226310
$233$	−12.1090	−0.793287	−0.396643	−	0.917973i	$-0.629825\pi$
$233$	−12.1090	−0.793287	−0.396643	+	0.917973i	$0.629825\pi$
$234$	−8.44036	−0.551764
$235$	7.85324	0.512289
$236$	33.1880	2.16035
$237$	10.8604	0.705458
$238$	9.65501	0.625841
$239$	5.71861	0.369906	0.184953	−	0.982747i	$-0.440787\pi$
$239$	5.71861	0.369906	0.184953	+	0.982747i	$0.440787\pi$
$240$	−3.24364	−0.209376
$241$	−26.1423	−1.68397	−0.841986	−	0.539499i	$-0.818614\pi$
$241$	−26.1423	−1.68397	−0.841986	+	0.539499i	$0.818614\pi$
$242$	−15.8567	−1.01931
$243$	1.00000	0.0641500
$244$	5.74235	0.367616
$245$	−1.24364	−0.0794531
$246$	−3.36274	−0.214400
$247$	22.0478	1.40287
$248$	3.94985	0.250816
$249$	−15.8249	−1.00286
$250$	−2.42305	−0.153247
$251$	12.3870	0.781859	0.390930	−	0.920421i	$-0.372154\pi$
$251$	12.3870	0.781859	0.390930	+	0.920421i	$0.372154\pi$
$252$	−11.1148	−0.700167
$253$	0	0
$254$	12.6275	0.792322
$255$	1.38781	0.0869082
$256$	−30.5922	−1.91201
$257$	25.1672	1.56989	0.784943	−	0.619569i	$-0.212692\pi$
$257$	25.1672	1.56989	0.784943	+	0.619569i	$0.212692\pi$
$258$	−23.2474	−1.44732
$259$	23.9594	1.48876
$260$	13.4847	0.836285
$261$	0.760276	0.0470599
$262$	16.7100	1.03234
$263$	17.1114	1.05513	0.527567	−	0.849513i	$-0.323104\pi$
$263$	17.1114	1.05513	0.527567	+	0.849513i	$0.323104\pi$
$264$	9.57070	0.589036
$265$	4.98207	0.306046
$266$	44.0341	2.69990
$267$	15.1769	0.928811
$268$	46.2057	2.82246
$269$	6.42178	0.391543	0.195771	−	0.980650i	$-0.437279\pi$
$269$	6.42178	0.391543	0.195771	+	0.980650i	$0.437279\pi$
$270$	−2.42305	−0.147462
$271$	−27.4629	−1.66825	−0.834125	−	0.551576i	$-0.814027\pi$
$271$	−27.4629	−1.66825	−0.834125	+	0.551576i	$0.814027\pi$
$272$	−4.50156	−0.272947
$273$	10.0013	0.605308
$274$	21.9988	1.32899
$275$	2.11090	0.127292
$276$	0	0
$277$	−5.04756	−0.303279	−0.151639	−	0.988436i	$-0.548455\pi$
$277$	−5.04756	−0.303279	−0.151639	+	0.988436i	$0.548455\pi$
$278$	−48.2187	−2.89196
$279$	0.871173	0.0521558
$280$	13.0178	0.777959
$281$	−15.2930	−0.912301	−0.456151	−	0.889903i	$-0.650772\pi$
$281$	−15.2930	−0.912301	−0.456151	+	0.889903i	$0.650772\pi$
$282$	−19.0288	−1.13315
$283$	−13.5686	−0.806571	−0.403285	−	0.915074i	$-0.632132\pi$
$283$	−13.5686	−0.806571	−0.403285	+	0.915074i	$0.632132\pi$
$284$	62.7055	3.72089
$285$	6.32946	0.374925
$286$	−17.8167	−1.05353
$287$	3.98465	0.235207
$288$	−1.20840	−0.0712056
$289$	−15.0740	−0.886704
$290$	−1.84219	−0.108177
$291$	−4.47622	−0.262401
$292$	−51.0049	−2.98484
$293$	−7.13016	−0.416548	−0.208274	−	0.978070i	$-0.566785\pi$
$293$	−7.13016	−0.416548	−0.208274	+	0.978070i	$0.566785\pi$
$294$	3.01340	0.175745
$295$	−8.57310	−0.499145
$296$	−37.8349	−2.19911
$297$	2.11090	0.122487
$298$	−9.42349	−0.545888
$299$	0	0
$300$	3.87117	0.223502
$301$	27.5468	1.58777
$302$	24.4091	1.40459
$303$	8.57633	0.492697
$304$	−20.5305	−1.17750
$305$	−1.48336	−0.0849370
$306$	−3.36274	−0.192235
$307$	4.23475	0.241690	0.120845	−	0.992671i	$-0.461440\pi$
$307$	4.23475	0.241690	0.120845	+	0.992671i	$0.461440\pi$
$308$	−23.4622	−1.33688
$309$	−16.3197	−0.928397
$310$	−2.11090	−0.119891
$311$	0.366653	0.0207910	0.0103955	−	0.999946i	$-0.496691\pi$
$311$	0.366653	0.0207910	0.0103955	+	0.999946i	$0.496691\pi$
$312$	−15.7934	−0.894124
$313$	25.2255	1.42583	0.712916	−	0.701250i	$-0.247374\pi$
$313$	25.2255	1.42583	0.712916	+	0.701250i	$0.247374\pi$
$314$	27.7954	1.56859
$315$	2.87117	0.161772
$316$	42.0424	2.36507
$317$	18.2506	1.02506	0.512528	−	0.858671i	$-0.328709\pi$
$317$	18.2506	1.02506	0.512528	+	0.858671i	$0.328709\pi$
$318$	−12.0718	−0.676953
$319$	1.60486	0.0898552
$320$	9.41529	0.526331
$321$	−12.2371	−0.683011
$322$	0	0
$323$	8.78411	0.488761
$324$	3.87117	0.215065
$325$	−3.48336	−0.193222
$326$	−30.7476	−1.70295
$327$	8.20884	0.453950
$328$	−6.29227	−0.347432
$329$	22.5480	1.24311
$330$	−5.11481	−0.281561
$331$	11.1073	0.610510	0.305255	−	0.952271i	$-0.401258\pi$
$331$	11.1073	0.610510	0.305255	+	0.952271i	$0.401258\pi$
$332$	−61.2611	−3.36214
$333$	−8.34481	−0.457293
$334$	−57.6761	−3.15590
$335$	−11.9358	−0.652125
$336$	−9.31304	−0.508068
$337$	−2.98705	−0.162715	−0.0813575	−	0.996685i	$-0.525926\pi$
$337$	−2.98705	−0.162715	−0.0813575	+	0.996685i	$0.525926\pi$
$338$	−2.09884	−0.114162
$339$	14.4023	0.782227
$340$	5.37246	0.291363
$341$	1.83896	0.0995851
$342$	−15.3366	−0.829309
$343$	16.5275	0.892402
$344$	−43.4999	−2.34536
$345$	0	0
$346$	28.6974	1.54278
$347$	13.9075	0.746596	0.373298	−	0.927712i	$-0.378227\pi$
$347$	13.9075	0.746596	0.373298	+	0.927712i	$0.378227\pi$
$348$	2.94316	0.157770
$349$	16.9756	0.908682	0.454341	−	0.890828i	$-0.349875\pi$
$349$	16.9756	0.908682	0.454341	+	0.890828i	$0.349875\pi$
$350$	−6.95700	−0.371867
$351$	−3.48336	−0.185928
$352$	−2.55081	−0.135958
$353$	8.55839	0.455517	0.227759	−	0.973718i	$-0.426860\pi$
$353$	8.55839	0.455517	0.227759	+	0.973718i	$0.426860\pi$
$354$	20.7731	1.10408
$355$	−16.1981	−0.859703
$356$	58.7524	3.11387
$357$	3.98465	0.210890
$358$	25.4190	1.34344
$359$	−22.0106	−1.16168	−0.580838	−	0.814019i	$-0.697275\pi$
$359$	−22.0106	−1.16168	−0.580838	+	0.814019i	$0.697275\pi$
$360$	−4.53395	−0.238960
$361$	21.0621	1.10853
$362$	−15.8215	−0.831561
$363$	−6.54411	−0.343477
$364$	38.7169	2.02932
$365$	13.1756	0.689640
$366$	3.59426	0.187875
$367$	−5.21036	−0.271979	−0.135989	−	0.990710i	$-0.543421\pi$
$367$	−5.21036	−0.271979	−0.135989	+	0.990710i	$0.543421\pi$
$368$	0	0
$369$	−1.38781	−0.0722466
$370$	20.2199	1.05118
$371$	14.3044	0.742647
$372$	3.37246	0.174854
$373$	36.6225	1.89624	0.948121	−	0.317911i	$-0.102981\pi$
$373$	36.6225	1.89624	0.948121	+	0.317911i	$0.102981\pi$
$374$	−7.09840	−0.367049
$375$	−1.00000	−0.0516398
$376$	−35.6062	−1.83625
$377$	−2.64832	−0.136395
$378$	−6.95700	−0.357829
$379$	0.115460	0.00593080	0.00296540	−	0.999996i	$-0.499056\pi$
$379$	0.115460	0.00593080	0.00296540	+	0.999996i	$0.499056\pi$
$380$	24.5024	1.25695
$381$	5.21142	0.266989
$382$	11.8403	0.605802
$383$	−7.04149	−0.359803	−0.179902	−	0.983685i	$-0.557578\pi$
$383$	−7.04149	−0.359803	−0.179902	+	0.983685i	$0.557578\pi$
$384$	−20.3969	−1.04088
$385$	6.06075	0.308885
$386$	−39.7411	−2.02277
$387$	−9.59426	−0.487704
$388$	−17.3282	−0.879707
$389$	3.76659	0.190973	0.0954867	−	0.995431i	$-0.469559\pi$
$389$	3.76659	0.190973	0.0954867	+	0.995431i	$0.469559\pi$
$390$	8.44036	0.427394
$391$	0	0
$392$	5.63859	0.284792
$393$	6.89625	0.347870
$394$	−46.0999	−2.32248
$395$	−10.8604	−0.546445
$396$	8.17165	0.410641
$397$	−21.4847	−1.07829	−0.539143	−	0.842214i	$-0.681252\pi$
$397$	−21.4847	−1.07829	−0.539143	+	0.842214i	$0.681252\pi$
$398$	19.1268	0.958737
$399$	18.1730	0.909787
$400$	3.24364	0.162182
$401$	11.4229	0.570434	0.285217	−	0.958463i	$-0.407934\pi$
$401$	11.4229	0.570434	0.285217	+	0.958463i	$0.407934\pi$
$402$	28.9211	1.44246
$403$	−3.03461	−0.151165
$404$	33.2005	1.65178
$405$	−1.00000	−0.0496904
$406$	−5.28924	−0.262501
$407$	−17.6150	−0.873145
$408$	−6.29227	−0.311514
$409$	−14.8831	−0.735923	−0.367961	−	0.929841i	$-0.619944\pi$
$409$	−14.8831	−0.735923	−0.367961	+	0.929841i	$0.619944\pi$
$410$	3.36274	0.166074
$411$	9.07895	0.447832
$412$	−63.1765	−3.11248
$413$	−24.6149	−1.21122
$414$	0	0
$415$	15.8249	0.776816
$416$	4.20929	0.206377
$417$	−19.9000	−0.974506
$418$	−32.3740	−1.58346
$419$	10.6289	0.519254	0.259627	−	0.965709i	$-0.416400\pi$
$419$	10.6289	0.519254	0.259627	+	0.965709i	$0.416400\pi$
$420$	11.1148	0.542347
$421$	22.7077	1.10671	0.553354	−	0.832946i	$-0.313348\pi$
$421$	22.7077	1.10671	0.553354	+	0.832946i	$0.313348\pi$
$422$	−64.6363	−3.14645
$423$	−7.85324	−0.381838
$424$	−22.5884	−1.09699
$425$	−1.38781	−0.0673188
$426$	39.2487	1.90161
$427$	−4.25899	−0.206107
$428$	−47.3721	−2.28982
$429$	−7.35302	−0.355007
$430$	23.2474	1.12109
$431$	26.1859	1.26133	0.630666	−	0.776054i	$-0.282782\pi$
$431$	26.1859	1.26133	0.630666	+	0.776054i	$0.282782\pi$
$432$	3.24364	0.156060
$433$	−2.71469	−0.130460	−0.0652299	−	0.997870i	$-0.520778\pi$
$433$	−2.71469	−0.130460	−0.0652299	+	0.997870i	$0.520778\pi$
$434$	−6.06075	−0.290925
$435$	−0.760276	−0.0364525
$436$	31.7778	1.52188
$437$	0	0
$438$	−31.9251	−1.52544
$439$	−17.7543	−0.847366	−0.423683	−	0.905811i	$-0.639263\pi$
$439$	−17.7543	−0.847366	−0.423683	+	0.905811i	$0.639263\pi$
$440$	−9.57070	−0.456265
$441$	1.24364	0.0592208
$442$	11.7136	0.557161
$443$	8.94663	0.425067	0.212534	−	0.977154i	$-0.431828\pi$
$443$	8.94663	0.425067	0.212534	+	0.977154i	$0.431828\pi$
$444$	−32.3042	−1.53309
$445$	−15.1769	−0.719454
$446$	−18.0143	−0.853001
$447$	−3.88910	−0.183948
$448$	27.0329	1.27719
$449$	−21.6652	−1.02245	−0.511223	−	0.859448i	$-0.670807\pi$
$449$	−21.6652	−1.02245	−0.511223	+	0.859448i	$0.670807\pi$
$450$	2.42305	0.114224
$451$	−2.92953	−0.137946
$452$	55.7539	2.62244
$453$	10.0737	0.473304
$454$	45.7208	2.14578
$455$	−10.0013	−0.468870
$456$	−28.6974	−1.34388
$457$	−25.0344	−1.17106	−0.585531	−	0.810650i	$-0.699114\pi$
$457$	−25.0344	−1.17106	−0.585531	+	0.810650i	$0.699114\pi$
$458$	10.2296	0.477999
$459$	−1.38781	−0.0647775
$460$	0	0
$461$	1.78467	0.0831202	0.0415601	−	0.999136i	$-0.486767\pi$
$461$	1.78467	0.0831202	0.0415601	+	0.999136i	$0.486767\pi$
$462$	−14.6855	−0.683232
$463$	30.9322	1.43754	0.718771	−	0.695247i	$-0.244705\pi$
$463$	30.9322	1.43754	0.718771	+	0.695247i	$0.244705\pi$
$464$	2.46606	0.114484
$465$	−0.871173	−0.0403997
$466$	−29.3407	−1.35918
$467$	36.1832	1.67436	0.837180	−	0.546928i	$-0.184203\pi$
$467$	36.1832	1.67436	0.837180	+	0.546928i	$0.184203\pi$
$468$	−13.4847	−0.623330
$469$	−34.2699	−1.58244
$470$	19.0288	0.877733
$471$	11.4712	0.528567
$472$	38.8700	1.78914
$473$	−20.2525	−0.931211
$474$	26.3153	1.20870
$475$	−6.32946	−0.290416
$476$	15.4253	0.707016
$477$	−4.98207	−0.228113
$478$	13.8565	0.633780
$479$	−9.89556	−0.452140	−0.226070	−	0.974111i	$-0.572588\pi$
$479$	−9.89556	−0.452140	−0.226070	+	0.974111i	$0.572588\pi$
$480$	1.20840	0.0551556
$481$	29.0680	1.32539
$482$	−63.3441	−2.88524
$483$	0	0
$484$	−25.3334	−1.15152
$485$	4.47622	0.203255
$486$	2.42305	0.109912
$487$	32.0304	1.45143	0.725717	−	0.687993i	$-0.241508\pi$
$487$	32.0304	1.45143	0.725717	+	0.687993i	$0.241508\pi$
$488$	6.72548	0.304448
$489$	−12.6896	−0.573845
$490$	−3.01340	−0.136131
$491$	−3.07130	−0.138606	−0.0693030	−	0.997596i	$-0.522078\pi$
$491$	−3.07130	−0.138606	−0.0693030	+	0.997596i	$0.522078\pi$
$492$	−5.37246	−0.242209
$493$	−1.05512	−0.0475203
$494$	53.4229	2.40361
$495$	−2.11090	−0.0948778
$496$	2.82577	0.126881
$497$	−46.5074	−2.08614
$498$	−38.3446	−1.71826
$499$	27.2751	1.22100	0.610501	−	0.792016i	$-0.290968\pi$
$499$	27.2751	1.22100	0.610501	+	0.792016i	$0.290968\pi$
$500$	−3.87117	−0.173124
$501$	−23.8031	−1.06344
$502$	30.0143	1.33960
$503$	−37.7147	−1.68162	−0.840808	−	0.541334i	$-0.817919\pi$
$503$	−37.7147	−1.68162	−0.840808	+	0.541334i	$0.817919\pi$
$504$	−13.0178	−0.579857
$505$	−8.57633	−0.381642
$506$	0	0
$507$	−0.866198	−0.0384692
$508$	20.1743	0.895091
$509$	−2.39928	−0.106346	−0.0531732	−	0.998585i	$-0.516934\pi$
$509$	−2.39928	−0.106346	−0.0531732	+	0.998585i	$0.516934\pi$
$510$	3.36274	0.148905
$511$	37.8293	1.67347
$512$	−33.3326	−1.47311
$513$	−6.32946	−0.279453
$514$	60.9813	2.68977
$515$	16.3197	0.719134
$516$	−37.1410	−1.63504
$517$	−16.5774	−0.729073
$518$	58.0548	2.55078
$519$	11.8435	0.519873
$520$	15.7934	0.692585
$521$	5.87269	0.257287	0.128644	−	0.991691i	$-0.458938\pi$
$521$	5.87269	0.257287	0.128644	+	0.991691i	$0.458938\pi$
$522$	1.84219	0.0806304
$523$	12.4535	0.544555	0.272278	−	0.962219i	$-0.412223\pi$
$523$	12.4535	0.544555	0.272278	+	0.962219i	$0.412223\pi$
$524$	26.6966	1.16624
$525$	−2.87117	−0.125308
$526$	41.4618	1.80782
$527$	−1.20903	−0.0526660
$528$	6.84698	0.297977
$529$	0	0
$530$	12.0718	0.524366
$531$	8.57310	0.372041
$532$	70.3508	3.05009
$533$	4.83425	0.209395
$534$	36.7744	1.59138
$535$	12.2371	0.529058
$536$	54.1165	2.33748
$537$	10.4905	0.452699
$538$	15.5603	0.670852
$539$	2.62519	0.113075
$540$	−3.87117	−0.166589
$541$	−7.96696	−0.342526	−0.171263	−	0.985225i	$-0.554785\pi$
$541$	−7.96696	−0.342526	−0.171263	+	0.985225i	$0.554785\pi$
$542$	−66.5439	−2.85830
$543$	−6.52959	−0.280212
$544$	1.67703	0.0719021
$545$	−8.20884	−0.351628
$546$	24.2337	1.03711
$547$	13.5011	0.577266	0.288633	−	0.957440i	$-0.406799\pi$
$547$	13.5011	0.577266	0.288633	+	0.957440i	$0.406799\pi$
$548$	35.1462	1.50137
$549$	1.48336	0.0633083
$550$	5.11481	0.218096
$551$	−4.81214	−0.205004
$552$	0	0
$553$	−31.1821	−1.32600
$554$	−12.2305	−0.519624
$555$	8.34481	0.354217
$556$	−77.0363	−3.26707
$557$	6.93709	0.293934	0.146967	−	0.989141i	$-0.453049\pi$
$557$	6.93709	0.293934	0.146967	+	0.989141i	$0.453049\pi$
$558$	2.11090	0.0893614
$559$	33.4203	1.41353
$560$	9.31304	0.393548
$561$	−2.92953	−0.123685
$562$	−37.0556	−1.56310
$563$	−43.2973	−1.82477	−0.912383	−	0.409338i	$-0.865760\pi$
$563$	−43.2973	−1.82477	−0.912383	+	0.409338i	$0.865760\pi$
$564$	−30.4013	−1.28012
$565$	−14.4023	−0.605911
$566$	−32.8775	−1.38194
$567$	−2.87117	−0.120578
$568$	73.4411	3.08152
$569$	−18.9244	−0.793352	−0.396676	−	0.917959i	$-0.629836\pi$
$569$	−18.9244	−0.793352	−0.396676	+	0.917959i	$0.629836\pi$
$570$	15.3366	0.642380
$571$	−26.5232	−1.10996	−0.554981	−	0.831863i	$-0.687275\pi$
$571$	−26.5232	−1.10996	−0.554981	+	0.831863i	$0.687275\pi$
$572$	−28.4648	−1.19017
$573$	4.88652	0.204137
$574$	9.65501	0.402992
$575$	0	0
$576$	−9.41529	−0.392304
$577$	−30.4657	−1.26830	−0.634152	−	0.773209i	$-0.718651\pi$
$577$	−30.4657	−1.26830	−0.634152	+	0.773209i	$0.718651\pi$
$578$	−36.5250	−1.51924
$579$	−16.4013	−0.681614
$580$	−2.94316	−0.122208
$581$	45.4362	1.88501
$582$	−10.8461	−0.449585
$583$	−10.5166	−0.435555
$584$	−59.7373	−2.47195
$585$	3.48336	0.144019
$586$	−17.2767	−0.713695
$587$	−9.57716	−0.395292	−0.197646	−	0.980274i	$-0.563330\pi$
$587$	−9.57716	−0.395292	−0.197646	+	0.980274i	$0.563330\pi$
$588$	4.81433	0.198540
$589$	−5.51406	−0.227203
$590$	−20.7731	−0.855213
$591$	−19.0256	−0.782608
$592$	−27.0675	−1.11247
$593$	−28.2147	−1.15864	−0.579320	−	0.815100i	$-0.696682\pi$
$593$	−28.2147	−1.15864	−0.579320	+	0.815100i	$0.696682\pi$
$594$	5.11481	0.209863
$595$	−3.98465	−0.163355
$596$	−15.0554	−0.616693
$597$	7.89367	0.323066
$598$	0	0
$599$	3.11537	0.127291	0.0636454	−	0.997973i	$-0.479727\pi$
$599$	3.11537	0.127291	0.0636454	+	0.997973i	$0.479727\pi$
$600$	4.53395	0.185098
$601$	13.4916	0.550333	0.275166	−	0.961397i	$-0.411267\pi$
$601$	13.4916	0.550333	0.275166	+	0.961397i	$0.411267\pi$
$602$	66.7472	2.72041
$603$	11.9358	0.486065
$604$	38.9971	1.58677
$605$	6.54411	0.266056
$606$	20.7809	0.844165
$607$	18.6538	0.757134	0.378567	−	0.925574i	$-0.376417\pi$
$607$	18.6538	0.757134	0.378567	+	0.925574i	$0.376417\pi$
$608$	7.64852	0.310188
$609$	−2.18288	−0.0884550
$610$	−3.59426	−0.145527
$611$	27.3557	1.10669
$612$	−5.37246	−0.217169
$613$	−15.8012	−0.638205	−0.319102	−	0.947720i	$-0.603381\pi$
$613$	−15.8012	−0.638205	−0.319102	+	0.947720i	$0.603381\pi$
$614$	10.2610	0.414101
$615$	1.38781	0.0559620
$616$	−27.4791	−1.10717
$617$	−25.0701	−1.00928	−0.504641	−	0.863329i	$-0.668375\pi$
$617$	−25.0701	−1.00928	−0.504641	+	0.863329i	$0.668375\pi$
$618$	−39.5435	−1.59067
$619$	−33.4549	−1.34467	−0.672333	−	0.740249i	$-0.734707\pi$
$619$	−33.4549	−1.34467	−0.672333	+	0.740249i	$0.734707\pi$
$620$	−3.37246	−0.135441
$621$	0	0
$622$	0.888420	0.0356224
$623$	−43.5755	−1.74582
$624$	−11.2988	−0.452312
$625$	1.00000	0.0400000
$626$	61.1227	2.44296
$627$	−13.3608	−0.533581
$628$	44.4072	1.77204
$629$	11.5810	0.461766
$630$	6.95700	0.277173
$631$	20.5089	0.816448	0.408224	−	0.912882i	$-0.366148\pi$
$631$	20.5089	0.816448	0.408224	+	0.912882i	$0.366148\pi$
$632$	49.2404	1.95868
$633$	−26.6756	−1.06026
$634$	44.2221	1.75628
$635$	−5.21142	−0.206809
$636$	−19.2865	−0.764758
$637$	−4.33204	−0.171642
$638$	3.88867	0.153954
$639$	16.1981	0.640785
$640$	20.3969	0.806259
$641$	4.08020	0.161158	0.0805791	−	0.996748i	$-0.474323\pi$
$641$	4.08020	0.161158	0.0805791	+	0.996748i	$0.474323\pi$
$642$	−29.6512	−1.17024
$643$	−18.3436	−0.723400	−0.361700	−	0.932295i	$-0.617803\pi$
$643$	−18.3436	−0.723400	−0.361700	+	0.932295i	$0.617803\pi$
$644$	0	0
$645$	9.59426	0.377774
$646$	21.2843	0.837421
$647$	16.3712	0.643619	0.321809	−	0.946804i	$-0.395709\pi$
$647$	16.3712	0.643619	0.321809	+	0.946804i	$0.395709\pi$
$648$	4.53395	0.178110
$649$	18.0969	0.710367
$650$	−8.44036	−0.331058
$651$	−2.50129	−0.0980333
$652$	−49.1237	−1.92383
$653$	30.2865	1.18520	0.592600	−	0.805497i	$-0.298101\pi$
$653$	30.2865	1.18520	0.592600	+	0.805497i	$0.298101\pi$
$654$	19.8904	0.777778
$655$	−6.89625	−0.269459
$656$	−4.50156	−0.175756
$657$	−13.1756	−0.514028
$658$	54.6350	2.12989
$659$	−34.2238	−1.33317	−0.666585	−	0.745429i	$-0.732245\pi$
$659$	−34.2238	−1.33317	−0.666585	+	0.745429i	$0.732245\pi$
$660$	−8.17165	−0.318081
$661$	4.41768	0.171828	0.0859140	−	0.996303i	$-0.472619\pi$
$661$	4.41768	0.171828	0.0859140	+	0.996303i	$0.472619\pi$
$662$	26.9134	1.04602
$663$	4.83425	0.187747
$664$	−71.7495	−2.78442
$665$	−18.1730	−0.704718
$666$	−20.2199	−0.783505
$667$	0	0
$668$	−92.1459	−3.56523
$669$	−7.43455	−0.287436
$670$	−28.9211	−1.11732
$671$	3.13122	0.120879
$672$	3.46952	0.133840
$673$	9.24995	0.356559	0.178280	−	0.983980i	$-0.442947\pi$
$673$	9.24995	0.356559	0.178280	+	0.983980i	$0.442947\pi$
$674$	−7.23778	−0.278789
$675$	1.00000	0.0384900
$676$	−3.35320	−0.128969
$677$	46.7176	1.79550	0.897752	−	0.440502i	$-0.145200\pi$
$677$	46.7176	1.79550	0.897752	+	0.440502i	$0.145200\pi$
$678$	34.8976	1.34023
$679$	12.8520	0.493214
$680$	6.29227	0.241298
$681$	18.8691	0.723065
$682$	4.45589	0.170625
$683$	−21.3263	−0.816029	−0.408014	−	0.912975i	$-0.633779\pi$
$683$	−21.3263	−0.816029	−0.408014	+	0.912975i	$0.633779\pi$
$684$	−24.5024	−0.936874
$685$	−9.07895	−0.346889
$686$	40.0470	1.52900
$687$	4.22179	0.161072
$688$	−31.1203	−1.18645
$689$	17.3543	0.661148
$690$	0	0
$691$	41.2390	1.56880	0.784402	−	0.620252i	$-0.212970\pi$
$691$	41.2390	1.56880	0.784402	+	0.620252i	$0.212970\pi$
$692$	45.8483	1.74289
$693$	−6.06075	−0.230229
$694$	33.6987	1.27918
$695$	19.9000	0.754849
$696$	3.44705	0.130660
$697$	1.92602	0.0729534
$698$	41.1327	1.55689
$699$	−12.1090	−0.458004
$700$	−11.1148	−0.420100
$701$	−43.9082	−1.65839	−0.829195	−	0.558960i	$-0.811201\pi$
$701$	−43.9082	−1.65839	−0.829195	+	0.558960i	$0.811201\pi$
$702$	−8.44036	−0.318561
$703$	52.8182	1.99207
$704$	−19.8747	−0.749056
$705$	7.85324	0.295770
$706$	20.7374	0.780463
$707$	−24.6241	−0.926086
$708$	33.1880	1.24728
$709$	9.51139	0.357208	0.178604	−	0.983921i	$-0.442842\pi$
$709$	9.51139	0.357208	0.178604	+	0.983921i	$0.442842\pi$
$710$	−39.2487	−1.47298
$711$	10.8604	0.407296
$712$	68.8113	2.57881
$713$	0	0
$714$	9.65501	0.361330
$715$	7.35302	0.274987
$716$	40.6106	1.51769
$717$	5.71861	0.213565
$718$	−53.3328	−1.99036
$719$	−36.1577	−1.34846	−0.674228	−	0.738523i	$-0.735523\pi$
$719$	−36.1577	−1.34846	−0.674228	+	0.738523i	$0.735523\pi$
$720$	−3.24364	−0.120883
$721$	46.8568	1.74504
$722$	51.0345	1.89931
$723$	−26.1423	−0.972242
$724$	−25.2772	−0.939419
$725$	0.760276	0.0282360
$726$	−15.8567	−0.588498
$727$	33.0005	1.22392	0.611960	−	0.790888i	$-0.290381\pi$
$727$	33.0005	1.22392	0.611960	+	0.790888i	$0.290381\pi$
$728$	45.3455	1.68062
$729$	1.00000	0.0370370
$730$	31.9251	1.18160
$731$	13.3150	0.492474
$732$	5.74235	0.212243
$733$	30.9743	1.14406	0.572032	−	0.820232i	$-0.306155\pi$
$733$	30.9743	1.14406	0.572032	+	0.820232i	$0.306155\pi$
$734$	−12.6250	−0.465996
$735$	−1.24364	−0.0458722
$736$	0	0
$737$	25.1953	0.928082
$738$	−3.36274	−0.123784
$739$	−22.7324	−0.836223	−0.418112	−	0.908396i	$-0.637308\pi$
$739$	−22.7324	−0.836223	−0.418112	+	0.908396i	$0.637308\pi$
$740$	32.3042	1.18753
$741$	22.0478	0.809946
$742$	34.6603	1.27242
$743$	18.6446	0.684005	0.342003	−	0.939699i	$-0.388895\pi$
$743$	18.6446	0.684005	0.342003	+	0.939699i	$0.388895\pi$
$744$	3.94985	0.144809
$745$	3.88910	0.142486
$746$	88.7382	3.24894
$747$	−15.8249	−0.579004
$748$	−11.3407	−0.414658
$749$	35.1350	1.28380
$750$	−2.42305	−0.0884773
$751$	−40.2397	−1.46837	−0.734183	−	0.678952i	$-0.762435\pi$
$751$	−40.2397	−1.46837	−0.734183	+	0.678952i	$0.762435\pi$
$752$	−25.4731	−0.928907
$753$	12.3870	0.451407
$754$	−6.41700	−0.233694
$755$	−10.0737	−0.366620
$756$	−11.1148	−0.404242
$757$	−8.31342	−0.302157	−0.151078	−	0.988522i	$-0.548275\pi$
$757$	−8.31342	−0.302157	−0.151078	+	0.988522i	$0.548275\pi$
$758$	0.279766	0.0101616
$759$	0	0
$760$	28.6974	1.04097
$761$	41.5935	1.50776	0.753882	−	0.657010i	$-0.228179\pi$
$761$	41.5935	1.50776	0.753882	+	0.657010i	$0.228179\pi$
$762$	12.6275	0.457447
$763$	−23.5690	−0.853255
$764$	18.9166	0.684378
$765$	1.38781	0.0501765
$766$	−17.0619	−0.616471
$767$	−29.8632	−1.07830
$768$	−30.5922	−1.10390
$769$	−9.45912	−0.341105	−0.170552	−	0.985349i	$-0.554555\pi$
$769$	−9.45912	−0.341105	−0.170552	+	0.985349i	$0.554555\pi$
$770$	14.6855	0.529229
$771$	25.1672	0.906374
$772$	−63.4922	−2.28513
$773$	−37.4652	−1.34753	−0.673766	−	0.738945i	$-0.735324\pi$
$773$	−37.4652	−1.34753	−0.673766	+	0.738945i	$0.735324\pi$
$774$	−23.2474	−0.835610
$775$	0.871173	0.0312935
$776$	−20.2949	−0.728546
$777$	23.9594	0.859539
$778$	9.12663	0.327205
$779$	8.78411	0.314723
$780$	13.4847	0.482829
$781$	34.1924	1.22350
$782$	0	0
$783$	0.760276	0.0271701
$784$	4.03391	0.144068
$785$	−11.4712	−0.409426
$786$	16.7100	0.596024
$787$	−18.6630	−0.665264	−0.332632	−	0.943057i	$-0.607937\pi$
$787$	−18.6630	−0.665264	−0.332632	+	0.943057i	$0.607937\pi$
$788$	−73.6513	−2.62372
$789$	17.1114	0.609182
$790$	−26.3153	−0.936255
$791$	−41.3516	−1.47029
$792$	9.57070	0.340080
$793$	−5.16708	−0.183488
$794$	−52.0585	−1.84749
$795$	4.98207	0.176696
$796$	30.5577	1.08309
$797$	18.2593	0.646776	0.323388	−	0.946266i	$-0.395178\pi$
$797$	18.2593	0.646776	0.323388	+	0.946266i	$0.395178\pi$
$798$	44.0341	1.55879
$799$	10.8988	0.385573
$800$	−1.20840	−0.0427234
$801$	15.1769	0.536249
$802$	27.6783	0.977356
$803$	−27.8123	−0.981473
$804$	46.2057	1.62955
$805$	0	0
$806$	−7.35302	−0.258999
$807$	6.42178	0.226057
$808$	38.8846	1.36796
$809$	1.70723	0.0600231	0.0300115	−	0.999550i	$-0.490446\pi$
$809$	1.70723	0.0600231	0.0300115	+	0.999550i	$0.490446\pi$
$810$	−2.42305	−0.0851373
$811$	−22.9627	−0.806328	−0.403164	−	0.915128i	$-0.632090\pi$
$811$	−22.9627	−0.806328	−0.403164	+	0.915128i	$0.632090\pi$
$812$	−8.45033	−0.296548
$813$	−27.4629	−0.963164
$814$	−42.6821	−1.49601
$815$	12.6896	0.444498
$816$	−4.50156	−0.157586
$817$	60.7265	2.12455
$818$	−36.0625	−1.26090
$819$	10.0013	0.349475
$820$	5.37246	0.187615
$821$	5.45331	0.190322	0.0951609	−	0.995462i	$-0.469663\pi$
$821$	5.45331	0.190322	0.0951609	+	0.995462i	$0.469663\pi$
$822$	21.9988	0.767295
$823$	42.2487	1.47270	0.736349	−	0.676602i	$-0.236548\pi$
$823$	42.2487	1.47270	0.736349	+	0.676602i	$0.236548\pi$
$824$	−73.9928	−2.57766
$825$	2.11090	0.0734920
$826$	−59.6430	−2.07525
$827$	41.0370	1.42700	0.713498	−	0.700657i	$-0.247110\pi$
$827$	41.0370	1.42700	0.713498	+	0.700657i	$0.247110\pi$
$828$	0	0
$829$	−6.15831	−0.213887	−0.106943	−	0.994265i	$-0.534106\pi$
$829$	−6.15831	−0.213887	−0.106943	+	0.994265i	$0.534106\pi$
$830$	38.3446	1.33096
$831$	−5.04756	−0.175098
$832$	32.7968	1.13703
$833$	−1.72594	−0.0598001
$834$	−48.2187	−1.66968
$835$	23.8031	0.823740
$836$	−51.7221	−1.78885
$837$	0.871173	0.0301122
$838$	25.7543	0.889667
$839$	−25.8730	−0.893234	−0.446617	−	0.894725i	$-0.647371\pi$
$839$	−25.8730	−0.893234	−0.446617	+	0.894725i	$0.647371\pi$
$840$	13.0178	0.449155
$841$	−28.4220	−0.980068
$842$	55.0220	1.89618
$843$	−15.2930	−0.526717
$844$	−103.266	−3.55456
$845$	0.866198	0.0297981
$846$	−19.0288	−0.654224
$847$	18.7893	0.645607
$848$	−16.1600	−0.554938
$849$	−13.5686	−0.465674
$850$	−3.36274	−0.115341
$851$	0	0
$852$	62.7055	2.14825
$853$	12.5080	0.428266	0.214133	−	0.976804i	$-0.431307\pi$
$853$	12.5080	0.428266	0.214133	+	0.976804i	$0.431307\pi$
$854$	−10.3197	−0.353134
$855$	6.32946	0.216463
$856$	−55.4826	−1.89636
$857$	−12.2715	−0.419187	−0.209594	−	0.977789i	$-0.567214\pi$
$857$	−12.2715	−0.419187	−0.209594	+	0.977789i	$0.567214\pi$
$858$	−17.8167	−0.608253
$859$	−5.00931	−0.170915	−0.0854577	−	0.996342i	$-0.527235\pi$
$859$	−5.00931	−0.170915	−0.0854577	+	0.996342i	$0.527235\pi$
$860$	37.1410	1.26650
$861$	3.98465	0.135797
$862$	63.4498	2.16111
$863$	−23.4779	−0.799196	−0.399598	−	0.916690i	$-0.630850\pi$
$863$	−23.4779	−0.799196	−0.399598	+	0.916690i	$0.630850\pi$
$864$	−1.20840	−0.0411106
$865$	−11.8435	−0.402692
$866$	−6.57784	−0.223524
$867$	−15.0740	−0.511939
$868$	−9.68293	−0.328660
$869$	22.9252	0.777683
$870$	−1.84219	−0.0624560
$871$	−41.5768	−1.40878
$872$	37.2185	1.26038
$873$	−4.47622	−0.151497
$874$	0	0
$875$	2.87117	0.0970634
$876$	−51.0049	−1.72330
$877$	34.6996	1.17172	0.585861	−	0.810412i	$-0.300757\pi$
$877$	34.6996	1.17172	0.585861	+	0.810412i	$0.300757\pi$
$878$	−43.0195	−1.45184
$879$	−7.13016	−0.240494
$880$	−6.84698	−0.230812
$881$	48.1569	1.62245	0.811223	−	0.584736i	$-0.198802\pi$
$881$	48.1569	1.62245	0.811223	+	0.584736i	$0.198802\pi$
$882$	3.01340	0.101466
$883$	50.2665	1.69160	0.845800	−	0.533499i	$-0.179123\pi$
$883$	50.2665	1.69160	0.845800	+	0.533499i	$0.179123\pi$
$884$	18.7142	0.629428
$885$	−8.57310	−0.288182
$886$	21.6781	0.728291
$887$	11.2888	0.379041	0.189521	−	0.981877i	$-0.439307\pi$
$887$	11.2888	0.379041	0.189521	+	0.981877i	$0.439307\pi$
$888$	−37.8349	−1.26966
$889$	−14.9629	−0.501839
$890$	−36.7744	−1.23268
$891$	2.11090	0.0707177
$892$	−28.7804	−0.963640
$893$	49.7068	1.66337
$894$	−9.42349	−0.315169
$895$	−10.4905	−0.350659
$896$	58.5631	1.95646
$897$	0	0
$898$	−52.4960	−1.75181
$899$	0.662332	0.0220900
$900$	3.87117	0.129039
$901$	6.91418	0.230345
$902$	−7.09840	−0.236351
$903$	27.5468	0.916699
$904$	65.2994	2.17183
$905$	6.52959	0.217051
$906$	24.4091	0.810938
$907$	41.4348	1.37582	0.687910	−	0.725796i	$-0.258528\pi$
$907$	41.4348	1.37582	0.687910	+	0.725796i	$0.258528\pi$
$908$	73.0455	2.42410
$909$	8.57633	0.284459
$910$	−24.2337	−0.803340
$911$	−16.8743	−0.559069	−0.279535	−	0.960136i	$-0.590180\pi$
$911$	−16.8743	−0.559069	−0.279535	+	0.960136i	$0.590180\pi$
$912$	−20.5305	−0.679832
$913$	−33.4048	−1.10554
$914$	−60.6597	−2.00644
$915$	−1.48336	−0.0490384
$916$	16.3433	0.539998
$917$	−19.8003	−0.653864
$918$	−3.36274	−0.110987
$919$	35.7691	1.17991	0.589957	−	0.807434i	$-0.299144\pi$
$919$	35.7691	1.17991	0.589957	+	0.807434i	$0.299144\pi$
$920$	0	0
$921$	4.23475	0.139540
$922$	4.32433	0.142414
$923$	−56.4237	−1.85721
$924$	−23.4622	−0.771850
$925$	−8.34481	−0.274376
$926$	74.9503	2.46302
$927$	−16.3197	−0.536011
$928$	−0.918717	−0.0301584
$929$	−32.9255	−1.08025	−0.540125	−	0.841585i	$-0.681623\pi$
$929$	−32.9255	−1.08025	−0.540125	+	0.841585i	$0.681623\pi$
$930$	−2.11090	−0.0692190
$931$	−7.87155	−0.257980
$932$	−46.8760	−1.53548
$933$	0.366653	0.0120037
$934$	87.6737	2.86877
$935$	2.92953	0.0958059
$936$	−15.7934	−0.516223
$937$	−0.654685	−0.0213876	−0.0106938	−	0.999943i	$-0.503404\pi$
$937$	−0.654685	−0.0213876	−0.0106938	+	0.999943i	$0.503404\pi$
$938$	−83.0376	−2.71127
$939$	25.2255	0.823204
$940$	30.4013	0.991580
$941$	−12.4698	−0.406505	−0.203253	−	0.979126i	$-0.565151\pi$
$941$	−12.4698	−0.406505	−0.203253	+	0.979126i	$0.565151\pi$
$942$	27.7954	0.905623
$943$	0	0
$944$	27.8080	0.905074
$945$	2.87117	0.0933993
$946$	−49.0728	−1.59549
$947$	−12.9373	−0.420407	−0.210203	−	0.977658i	$-0.567413\pi$
$947$	−12.9373	−0.420407	−0.210203	+	0.977658i	$0.567413\pi$
$948$	42.0424	1.36548
$949$	45.8952	1.48982
$950$	−15.3366	−0.497585
$951$	18.2506	0.591816
$952$	18.0662	0.585529
$953$	−15.0619	−0.487901	−0.243951	−	0.969788i	$-0.578443\pi$
$953$	−15.0619	−0.487901	−0.243951	+	0.969788i	$0.578443\pi$
$954$	−12.0718	−0.390839
$955$	−4.88652	−0.158124
$956$	22.1377	0.715985
$957$	1.60486	0.0518779
$958$	−23.9774	−0.774676
$959$	−26.0672	−0.841755
$960$	9.41529	0.303877
$961$	−30.2411	−0.975518
$962$	70.4332	2.27086
$963$	−12.2371	−0.394336
$964$	−101.201	−3.25947
$965$	16.4013	0.527976
$966$	0	0
$967$	21.5141	0.691845	0.345923	−	0.938263i	$-0.387566\pi$
$967$	21.5141	0.691845	0.345923	+	0.938263i	$0.387566\pi$
$968$	−29.6707	−0.953651
$969$	8.78411	0.282186
$970$	10.8461	0.348247
$971$	−26.6131	−0.854055	−0.427028	−	0.904239i	$-0.640439\pi$
$971$	−26.6131	−0.854055	−0.427028	+	0.904239i	$0.640439\pi$
$972$	3.87117	0.124168
$973$	57.1363	1.83171
$974$	77.6112	2.48682
$975$	−3.48336	−0.111557
$976$	4.81148	0.154012
$977$	−41.2854	−1.32084	−0.660418	−	0.750898i	$-0.729621\pi$
$977$	−41.2854	−1.32084	−0.660418	+	0.750898i	$0.729621\pi$
$978$	−30.7476	−0.983200
$979$	32.0369	1.02390
$980$	−4.81433	−0.153788
$981$	8.20884	0.262088
$982$	−7.44193	−0.237481
$983$	−38.7943	−1.23735	−0.618673	−	0.785648i	$-0.712330\pi$
$983$	−38.7943	−1.23735	−0.618673	+	0.785648i	$0.712330\pi$
$984$	−6.29227	−0.200590
$985$	19.0256	0.606205
$986$	−2.55661	−0.0814191
$987$	22.5480	0.717712
$988$	85.3509	2.71537
$989$	0	0
$990$	−5.11481	−0.162559
$991$	−37.9644	−1.20598	−0.602990	−	0.797749i	$-0.706024\pi$
$991$	−37.9644	−1.20598	−0.602990	+	0.797749i	$0.706024\pi$
$992$	−1.05273	−0.0334241
$993$	11.1073	0.352478
$994$	−112.690	−3.57430
$995$	−7.89367	−0.250246
$996$	−61.2611	−1.94113
$997$	−27.6949	−0.877105	−0.438553	−	0.898706i	$-0.644509\pi$
$997$	−27.6949	−0.877105	−0.438553	+	0.898706i	$0.644509\pi$
$998$	66.0890	2.09201
$999$	−8.34481	−0.264018

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bb.1.5	✓	5
23.22	odd	2		7935.2.a.bc.1.5	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bb.1.5	✓	5	1.1	even	1	trivial
7935.2.a.bc.1.5	yes	5	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)

\(f(q)\)	\(=\)	\(q+2.42305 q^{2} +1.00000 q^{3} +3.87117 q^{4} -1.00000 q^{5} +2.42305 q^{6} -2.87117 q^{7} +4.53395 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.42305 q^{2} +1.00000 q^{3} +3.87117 q^{4} -1.00000 q^{5} +2.42305 q^{6} -2.87117 q^{7} +4.53395 q^{8} +1.00000 q^{9} -2.42305 q^{10} +2.11090 q^{11} +3.87117 q^{12} -3.48336 q^{13} -6.95700 q^{14} -1.00000 q^{15} +3.24364 q^{16} -1.38781 q^{17} +2.42305 q^{18} -6.32946 q^{19} -3.87117 q^{20} -2.87117 q^{21} +5.11481 q^{22} +4.53395 q^{24} +1.00000 q^{25} -8.44036 q^{26} +1.00000 q^{27} -11.1148 q^{28} +0.760276 q^{29} -2.42305 q^{30} +0.871173 q^{31} -1.20840 q^{32} +2.11090 q^{33} -3.36274 q^{34} +2.87117 q^{35} +3.87117 q^{36} -8.34481 q^{37} -15.3366 q^{38} -3.48336 q^{39} -4.53395 q^{40} -1.38781 q^{41} -6.95700 q^{42} -9.59426 q^{43} +8.17165 q^{44} -1.00000 q^{45} -7.85324 q^{47} +3.24364 q^{48} +1.24364 q^{49} +2.42305 q^{50} -1.38781 q^{51} -13.4847 q^{52} -4.98207 q^{53} +2.42305 q^{54} -2.11090 q^{55} -13.0178 q^{56} -6.32946 q^{57} +1.84219 q^{58} +8.57310 q^{59} -3.87117 q^{60} +1.48336 q^{61} +2.11090 q^{62} -2.87117 q^{63} -9.41529 q^{64} +3.48336 q^{65} +5.11481 q^{66} +11.9358 q^{67} -5.37246 q^{68} +6.95700 q^{70} +16.1981 q^{71} +4.53395 q^{72} -13.1756 q^{73} -20.2199 q^{74} +1.00000 q^{75} -24.5024 q^{76} -6.06075 q^{77} -8.44036 q^{78} +10.8604 q^{79} -3.24364 q^{80} +1.00000 q^{81} -3.36274 q^{82} -15.8249 q^{83} -11.1148 q^{84} +1.38781 q^{85} -23.2474 q^{86} +0.760276 q^{87} +9.57070 q^{88} +15.1769 q^{89} -2.42305 q^{90} +10.0013 q^{91} +0.871173 q^{93} -19.0288 q^{94} +6.32946 q^{95} -1.20840 q^{96} -4.47622 q^{97} +3.01340 q^{98} +2.11090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{3} + 8 q^{4} - 5 q^{5} - 3 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^3 + 8 * q^4 - 5 * q^5 - 3 * q^7 - 6 * q^8 + 5 * q^9	\( 5 q + 5 q^{3} + 8 q^{4} - 5 q^{5} - 3 q^{7} - 6 q^{8} + 5 q^{9} - 6 q^{11} + 8 q^{12} - 6 q^{13} + 6 q^{14} - 5 q^{15} + 10 q^{16} - 7 q^{17} + 4 q^{19} - 8 q^{20} - 3 q^{21} + 8 q^{22} - 6 q^{24} + 5 q^{25} + 10 q^{26} + 5 q^{27} - 38 q^{28} + 9 q^{29} - 7 q^{31} - 12 q^{32} - 6 q^{33} - 4 q^{34} + 3 q^{35} + 8 q^{36} - q^{37} - 26 q^{38} - 6 q^{39} + 6 q^{40} - 7 q^{41} + 6 q^{42} - 20 q^{43} - 18 q^{44} - 5 q^{45} + 10 q^{48} - 7 q^{51} - 22 q^{52} + 3 q^{53} + 6 q^{55} + 18 q^{56} + 4 q^{57} - 14 q^{58} + q^{59} - 8 q^{60} - 4 q^{61} - 6 q^{62} - 3 q^{63} + 18 q^{64} + 6 q^{65} + 8 q^{66} + 5 q^{67} - 32 q^{68} - 6 q^{70} + q^{71} - 6 q^{72} - 6 q^{73} - 48 q^{74} + 5 q^{75} + 6 q^{76} + 12 q^{77} + 10 q^{78} - 10 q^{80} + 5 q^{81} - 4 q^{82} - 41 q^{83} - 38 q^{84} + 7 q^{85} + 2 q^{86} + 9 q^{87} + 84 q^{88} - 18 q^{89} + 16 q^{91} - 7 q^{93} + 4 q^{94} - 4 q^{95} - 12 q^{96} - 26 q^{97} - 24 q^{98} - 6 q^{99}+O(q^{100}) \) 5 * q + 5 * q^3 + 8 * q^4 - 5 * q^5 - 3 * q^7 - 6 * q^8 + 5 * q^9 - 6 * q^11 + 8 * q^12 - 6 * q^13 + 6 * q^14 - 5 * q^15 + 10 * q^16 - 7 * q^17 + 4 * q^19 - 8 * q^20 - 3 * q^21 + 8 * q^22 - 6 * q^24 + 5 * q^25 + 10 * q^26 + 5 * q^27 - 38 * q^28 + 9 * q^29 - 7 * q^31 - 12 * q^32 - 6 * q^33 - 4 * q^34 + 3 * q^35 + 8 * q^36 - q^37 - 26 * q^38 - 6 * q^39 + 6 * q^40 - 7 * q^41 + 6 * q^42 - 20 * q^43 - 18 * q^44 - 5 * q^45 + 10 * q^48 - 7 * q^51 - 22 * q^52 + 3 * q^53 + 6 * q^55 + 18 * q^56 + 4 * q^57 - 14 * q^58 + q^59 - 8 * q^60 - 4 * q^61 - 6 * q^62 - 3 * q^63 + 18 * q^64 + 6 * q^65 + 8 * q^66 + 5 * q^67 - 32 * q^68 - 6 * q^70 + q^71 - 6 * q^72 - 6 * q^73 - 48 * q^74 + 5 * q^75 + 6 * q^76 + 12 * q^77 + 10 * q^78 - 10 * q^80 + 5 * q^81 - 4 * q^82 - 41 * q^83 - 38 * q^84 + 7 * q^85 + 2 * q^86 + 9 * q^87 + 84 * q^88 - 18 * q^89 + 16 * q^91 - 7 * q^93 + 4 * q^94 - 4 * q^95 - 12 * q^96 - 26 * q^97 - 24 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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