LMFDB - Embedded newform 4598.2.a.bw.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 11x^{6} + 22x^{5} + 34x^{4} - 68x^{3} - 28x^{2} + 60x - 4 $ x^8 - 2x^7 - 11x^6 + 22x^5 + 34x^4 - 68x^3 - 28x^2 + 60*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.59897$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.59897 q^{3} +1.00000 q^{4} +3.74775 q^{5} +1.59897 q^{6} -0.838369 q^{7} -1.00000 q^{8} -0.443297 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.59897 q^{3} +1.00000 q^{4} +3.74775 q^{5} +1.59897 q^{6} -0.838369 q^{7} -1.00000 q^{8} -0.443297 q^{9} -3.74775 q^{10} -1.59897 q^{12} +4.44225 q^{13} +0.838369 q^{14} -5.99254 q^{15} +1.00000 q^{16} +5.02742 q^{17} +0.443297 q^{18} +1.00000 q^{19} +3.74775 q^{20} +1.34053 q^{21} -6.07470 q^{23} +1.59897 q^{24} +9.04565 q^{25} -4.44225 q^{26} +5.50573 q^{27} -0.838369 q^{28} +2.79038 q^{29} +5.99254 q^{30} -7.40805 q^{31} -1.00000 q^{32} -5.02742 q^{34} -3.14200 q^{35} -0.443297 q^{36} +8.17976 q^{37} -1.00000 q^{38} -7.10303 q^{39} -3.74775 q^{40} +6.38316 q^{41} -1.34053 q^{42} +9.55796 q^{43} -1.66137 q^{45} +6.07470 q^{46} -8.17578 q^{47} -1.59897 q^{48} -6.29714 q^{49} -9.04565 q^{50} -8.03870 q^{51} +4.44225 q^{52} -13.3646 q^{53} -5.50573 q^{54} +0.838369 q^{56} -1.59897 q^{57} -2.79038 q^{58} +7.28815 q^{59} -5.99254 q^{60} +8.26585 q^{61} +7.40805 q^{62} +0.371646 q^{63} +1.00000 q^{64} +16.6485 q^{65} -7.32824 q^{67} +5.02742 q^{68} +9.71327 q^{69} +3.14200 q^{70} +12.4180 q^{71} +0.443297 q^{72} -7.55877 q^{73} -8.17976 q^{74} -14.4637 q^{75} +1.00000 q^{76} +7.10303 q^{78} +8.98520 q^{79} +3.74775 q^{80} -7.47360 q^{81} -6.38316 q^{82} -1.30685 q^{83} +1.34053 q^{84} +18.8415 q^{85} -9.55796 q^{86} -4.46174 q^{87} +10.4914 q^{89} +1.66137 q^{90} -3.72425 q^{91} -6.07470 q^{92} +11.8452 q^{93} +8.17578 q^{94} +3.74775 q^{95} +1.59897 q^{96} +8.11650 q^{97} +6.29714 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} + 2 q^{6} + 14 q^{7} - 8 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 + 2 * q^6 + 14 * q^7 - 8 * q^8 + 2 * q^9	\( 8 q - 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} + 2 q^{6} + 14 q^{7} - 8 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} + 9 q^{13} - 14 q^{14} + 5 q^{15} + 8 q^{16} + 3 q^{17} - 2 q^{18} + 8 q^{19} - 2 q^{20} + 7 q^{21} - 13 q^{23} + 2 q^{24} + 4 q^{25} - 9 q^{26} + 4 q^{27} + 14 q^{28} + 10 q^{29} - 5 q^{30} - 2 q^{31} - 8 q^{32} - 3 q^{34} - 7 q^{35} + 2 q^{36} + 15 q^{37} - 8 q^{38} + 11 q^{39} + 2 q^{40} + 9 q^{41} - 7 q^{42} + 33 q^{43} - 21 q^{45} + 13 q^{46} - 19 q^{47} - 2 q^{48} + 12 q^{49} - 4 q^{50} + 22 q^{51} + 9 q^{52} + 10 q^{53} - 4 q^{54} - 14 q^{56} - 2 q^{57} - 10 q^{58} + q^{59} + 5 q^{60} + 26 q^{61} + 2 q^{62} + 19 q^{63} + 8 q^{64} + 26 q^{65} - 25 q^{67} + 3 q^{68} - 12 q^{69} + 7 q^{70} - 10 q^{71} - 2 q^{72} + 11 q^{73} - 15 q^{74} - 33 q^{75} + 8 q^{76} - 11 q^{78} + 10 q^{79} - 2 q^{80} - 40 q^{81} - 9 q^{82} + 16 q^{83} + 7 q^{84} + 33 q^{85} - 33 q^{86} + 2 q^{87} - 14 q^{89} + 21 q^{90} + 25 q^{91} - 13 q^{92} + 20 q^{93} + 19 q^{94} - 2 q^{95} + 2 q^{96} + 22 q^{97} - 12 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 + 2 * q^6 + 14 * q^7 - 8 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 + 9 * q^13 - 14 * q^14 + 5 * q^15 + 8 * q^16 + 3 * q^17 - 2 * q^18 + 8 * q^19 - 2 * q^20 + 7 * q^21 - 13 * q^23 + 2 * q^24 + 4 * q^25 - 9 * q^26 + 4 * q^27 + 14 * q^28 + 10 * q^29 - 5 * q^30 - 2 * q^31 - 8 * q^32 - 3 * q^34 - 7 * q^35 + 2 * q^36 + 15 * q^37 - 8 * q^38 + 11 * q^39 + 2 * q^40 + 9 * q^41 - 7 * q^42 + 33 * q^43 - 21 * q^45 + 13 * q^46 - 19 * q^47 - 2 * q^48 + 12 * q^49 - 4 * q^50 + 22 * q^51 + 9 * q^52 + 10 * q^53 - 4 * q^54 - 14 * q^56 - 2 * q^57 - 10 * q^58 + q^59 + 5 * q^60 + 26 * q^61 + 2 * q^62 + 19 * q^63 + 8 * q^64 + 26 * q^65 - 25 * q^67 + 3 * q^68 - 12 * q^69 + 7 * q^70 - 10 * q^71 - 2 * q^72 + 11 * q^73 - 15 * q^74 - 33 * q^75 + 8 * q^76 - 11 * q^78 + 10 * q^79 - 2 * q^80 - 40 * q^81 - 9 * q^82 + 16 * q^83 + 7 * q^84 + 33 * q^85 - 33 * q^86 + 2 * q^87 - 14 * q^89 + 21 * q^90 + 25 * q^91 - 13 * q^92 + 20 * q^93 + 19 * q^94 - 2 * q^95 + 2 * q^96 + 22 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.59897	−0.923165	−0.461583	−	0.887097i	$-0.652718\pi$
$3$	−1.59897	−0.923165	−0.461583	+	0.887097i	$0.652718\pi$
$4$	1.00000	0.500000
$5$	3.74775	1.67605	0.838023	−	0.545635i	$-0.183711\pi$
$5$	3.74775	1.67605	0.838023	+	0.545635i	$0.183711\pi$
$6$	1.59897	0.652777
$7$	−0.838369	−0.316874	−0.158437	−	0.987369i	$-0.550645\pi$
$7$	−0.838369	−0.316874	−0.158437	+	0.987369i	$0.550645\pi$
$8$	−1.00000	−0.353553
$9$	−0.443297	−0.147766
$10$	−3.74775	−1.18514
$11$	0	0
$11$	0	0
$12$	−1.59897	−0.461583
$13$	4.44225	1.23206	0.616030	−	0.787723i	$-0.288740\pi$
$13$	4.44225	1.23206	0.616030	+	0.787723i	$0.288740\pi$
$14$	0.838369	0.224063
$15$	−5.99254	−1.54727
$16$	1.00000	0.250000
$17$	5.02742	1.21933	0.609665	−	0.792660i	$-0.291304\pi$
$17$	5.02742	1.21933	0.609665	+	0.792660i	$0.291304\pi$
$18$	0.443297	0.104486
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	3.74775	0.838023
$21$	1.34053	0.292527
$22$	0	0
$23$	−6.07470	−1.26666	−0.633332	−	0.773880i	$-0.718313\pi$
$23$	−6.07470	−1.26666	−0.633332	+	0.773880i	$0.718313\pi$
$24$	1.59897	0.326388
$25$	9.04565	1.80913
$26$	−4.44225	−0.871198
$27$	5.50573	1.05958
$28$	−0.838369	−0.158437
$29$	2.79038	0.518161	0.259080	−	0.965856i	$-0.416581\pi$
$29$	2.79038	0.518161	0.259080	+	0.965856i	$0.416581\pi$
$30$	5.99254	1.09408
$31$	−7.40805	−1.33053	−0.665263	−	0.746609i	$-0.731680\pi$
$31$	−7.40805	−1.33053	−0.665263	+	0.746609i	$0.731680\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−5.02742	−0.862196
$35$	−3.14200	−0.531095
$36$	−0.443297	−0.0738828
$37$	8.17976	1.34474	0.672372	−	0.740213i	$-0.265275\pi$
$37$	8.17976	1.34474	0.672372	+	0.740213i	$0.265275\pi$
$38$	−1.00000	−0.162221
$39$	−7.10303	−1.13739
$40$	−3.74775	−0.592572
$41$	6.38316	0.996883	0.498441	−	0.866923i	$-0.333906\pi$
$41$	6.38316	0.996883	0.498441	+	0.866923i	$0.333906\pi$
$42$	−1.34053	−0.206848
$43$	9.55796	1.45758	0.728788	−	0.684739i	$-0.240084\pi$
$43$	9.55796	1.45758	0.728788	+	0.684739i	$0.240084\pi$
$44$	0	0
$45$	−1.66137	−0.247662
$46$	6.07470	0.895666
$47$	−8.17578	−1.19256	−0.596280	−	0.802777i	$-0.703355\pi$
$47$	−8.17578	−1.19256	−0.596280	+	0.802777i	$0.703355\pi$
$48$	−1.59897	−0.230791
$49$	−6.29714	−0.899591
$50$	−9.04565	−1.27925
$51$	−8.03870	−1.12564
$52$	4.44225	0.616030
$53$	−13.3646	−1.83577	−0.917884	−	0.396850i	$-0.870103\pi$
$53$	−13.3646	−1.83577	−0.917884	+	0.396850i	$0.870103\pi$
$54$	−5.50573	−0.749234
$55$	0	0
$56$	0.838369	0.112032
$57$	−1.59897	−0.211789
$58$	−2.79038	−0.366395
$59$	7.28815	0.948837	0.474418	−	0.880299i	$-0.342658\pi$
$59$	7.28815	0.948837	0.474418	+	0.880299i	$0.342658\pi$
$60$	−5.99254	−0.773634
$61$	8.26585	1.05833	0.529167	−	0.848518i	$-0.322505\pi$
$61$	8.26585	1.05833	0.529167	+	0.848518i	$0.322505\pi$
$62$	7.40805	0.940824
$63$	0.371646	0.0468230
$64$	1.00000	0.125000
$65$	16.6485	2.06499
$66$	0	0
$67$	−7.32824	−0.895287	−0.447643	−	0.894212i	$-0.647737\pi$
$67$	−7.32824	−0.895287	−0.447643	+	0.894212i	$0.647737\pi$
$68$	5.02742	0.609665
$69$	9.71327	1.16934
$70$	3.14200	0.375541
$71$	12.4180	1.47375	0.736875	−	0.676029i	$-0.236301\pi$
$71$	12.4180	1.47375	0.736875	+	0.676029i	$0.236301\pi$
$72$	0.443297	0.0522430
$73$	−7.55877	−0.884687	−0.442344	−	0.896846i	$-0.645853\pi$
$73$	−7.55877	−0.884687	−0.442344	+	0.896846i	$0.645853\pi$
$74$	−8.17976	−0.950878
$75$	−14.4637	−1.67013
$76$	1.00000	0.114708
$77$	0	0
$78$	7.10303	0.804260
$79$	8.98520	1.01091	0.505457	−	0.862852i	$-0.331324\pi$
$79$	8.98520	1.01091	0.505457	+	0.862852i	$0.331324\pi$
$80$	3.74775	0.419011
$81$	−7.47360	−0.830400
$82$	−6.38316	−0.704903
$83$	−1.30685	−0.143445	−0.0717225	−	0.997425i	$-0.522850\pi$
$83$	−1.30685	−0.143445	−0.0717225	+	0.997425i	$0.522850\pi$
$84$	1.34053	0.146263
$85$	18.8415	2.04365
$86$	−9.55796	−1.03066
$87$	−4.46174	−0.478348
$88$	0	0
$89$	10.4914	1.11209	0.556044	−	0.831153i	$-0.312319\pi$
$89$	10.4914	1.11209	0.556044	+	0.831153i	$0.312319\pi$
$90$	1.66137	0.175123
$91$	−3.72425	−0.390407
$92$	−6.07470	−0.633332
$93$	11.8452	1.22830
$94$	8.17578	0.843267
$95$	3.74775	0.384511
$96$	1.59897	0.163194
$97$	8.11650	0.824106	0.412053	−	0.911160i	$-0.364812\pi$
$97$	8.11650	0.824106	0.412053	+	0.911160i	$0.364812\pi$
$98$	6.29714	0.636107
$99$	0	0
$100$	9.04565	0.904565
$101$	−12.2860	−1.22250	−0.611251	−	0.791437i	$-0.709333\pi$
$101$	−12.2860	−1.22250	−0.611251	+	0.791437i	$0.709333\pi$
$102$	8.03870	0.795949
$103$	4.99650	0.492320	0.246160	−	0.969229i	$-0.420831\pi$
$103$	4.99650	0.492320	0.246160	+	0.969229i	$0.420831\pi$
$104$	−4.44225	−0.435599
$105$	5.02396	0.490288
$106$	13.3646	1.29808
$107$	−3.50824	−0.339154	−0.169577	−	0.985517i	$-0.554240\pi$
$107$	−3.50824	−0.339154	−0.169577	+	0.985517i	$0.554240\pi$
$108$	5.50573	0.529789
$109$	−4.66438	−0.446767	−0.223383	−	0.974731i	$-0.571710\pi$
$109$	−4.66438	−0.446767	−0.223383	+	0.974731i	$0.571710\pi$
$110$	0	0
$111$	−13.0792	−1.24142
$112$	−0.838369	−0.0792184
$113$	17.4920	1.64551	0.822753	−	0.568400i	$-0.192437\pi$
$113$	17.4920	1.64551	0.822753	+	0.568400i	$0.192437\pi$
$114$	1.59897	0.149757
$115$	−22.7665	−2.12299
$116$	2.79038	0.259080
$117$	−1.96924	−0.182056
$118$	−7.28815	−0.670929
$119$	−4.21483	−0.386373
$120$	5.99254	0.547042
$121$	0	0
$122$	−8.26585	−0.748355
$123$	−10.2065	−0.920288
$124$	−7.40805	−0.665263
$125$	15.1621	1.35614
$126$	−0.371646	−0.0331089
$127$	−1.19873	−0.106370	−0.0531849	−	0.998585i	$-0.516937\pi$
$127$	−1.19873	−0.106370	−0.0531849	+	0.998585i	$0.516937\pi$
$128$	−1.00000	−0.0883883
$129$	−15.2829	−1.34558
$130$	−16.6485	−1.46017
$131$	8.60188	0.751550	0.375775	−	0.926711i	$-0.377377\pi$
$131$	8.60188	0.751550	0.375775	+	0.926711i	$0.377377\pi$
$132$	0	0
$133$	−0.838369	−0.0726958
$134$	7.32824	0.633063
$135$	20.6341	1.77590
$136$	−5.02742	−0.431098
$137$	6.05457	0.517277	0.258639	−	0.965974i	$-0.416726\pi$
$137$	6.05457	0.517277	0.258639	+	0.965974i	$0.416726\pi$
$138$	−9.71327	−0.826848
$139$	−3.93304	−0.333596	−0.166798	−	0.985991i	$-0.553343\pi$
$139$	−3.93304	−0.333596	−0.166798	+	0.985991i	$0.553343\pi$
$140$	−3.14200	−0.265547
$141$	13.0728	1.10093
$142$	−12.4180	−1.04210
$143$	0	0
$144$	−0.443297	−0.0369414
$145$	10.4577	0.868461
$146$	7.55877	0.625568
$147$	10.0689	0.830471
$148$	8.17976	0.672372
$149$	−21.5346	−1.76418	−0.882091	−	0.471078i	$-0.843865\pi$
$149$	−21.5346	−1.76418	−0.882091	+	0.471078i	$0.843865\pi$
$150$	14.4637	1.18096
$151$	0.130125	0.0105894	0.00529472	−	0.999986i	$-0.498315\pi$
$151$	0.130125	0.0105894	0.00529472	+	0.999986i	$0.498315\pi$
$152$	−1.00000	−0.0811107
$153$	−2.22864	−0.180175
$154$	0	0
$155$	−27.7635	−2.23002
$156$	−7.10303	−0.568697
$157$	2.31749	0.184956	0.0924781	−	0.995715i	$-0.470521\pi$
$157$	2.31749	0.184956	0.0924781	+	0.995715i	$0.470521\pi$
$158$	−8.98520	−0.714824
$159$	21.3696	1.69472
$160$	−3.74775	−0.296286
$161$	5.09284	0.401372
$162$	7.47360	0.587181
$163$	−18.0791	−1.41606	−0.708031	−	0.706181i	$-0.750417\pi$
$163$	−18.0791	−1.41606	−0.708031	+	0.706181i	$0.750417\pi$
$164$	6.38316	0.498441
$165$	0	0
$166$	1.30685	0.101431
$167$	8.02035	0.620633	0.310317	−	0.950633i	$-0.399565\pi$
$167$	8.02035	0.620633	0.310317	+	0.950633i	$0.399565\pi$
$168$	−1.34053	−0.103424
$169$	6.73362	0.517971
$170$	−18.8415	−1.44508
$171$	−0.443297	−0.0338997
$172$	9.55796	0.728788
$173$	2.34574	0.178343	0.0891715	−	0.996016i	$-0.471578\pi$
$173$	2.34574	0.178343	0.0891715	+	0.996016i	$0.471578\pi$
$174$	4.46174	0.338243
$175$	−7.58359	−0.573265
$176$	0	0
$177$	−11.6535	−0.875933
$178$	−10.4914	−0.786365
$179$	−13.3186	−0.995476	−0.497738	−	0.867328i	$-0.665836\pi$
$179$	−13.3186	−0.995476	−0.497738	+	0.867328i	$0.665836\pi$
$180$	−1.66137	−0.123831
$181$	−0.942795	−0.0700774	−0.0350387	−	0.999386i	$-0.511155\pi$
$181$	−0.942795	−0.0700774	−0.0350387	+	0.999386i	$0.511155\pi$
$182$	3.72425	0.276060
$183$	−13.2168	−0.977017
$184$	6.07470	0.447833
$185$	30.6557	2.25385
$186$	−11.8452	−0.868536
$187$	0	0
$188$	−8.17578	−0.596280
$189$	−4.61583	−0.335752
$190$	−3.74775	−0.271891
$191$	−16.2476	−1.17564	−0.587819	−	0.808992i	$-0.700013\pi$
$191$	−16.2476	−1.17564	−0.587819	+	0.808992i	$0.700013\pi$
$192$	−1.59897	−0.115396
$193$	−13.6379	−0.981677	−0.490839	−	0.871251i	$-0.663310\pi$
$193$	−13.6379	−0.981677	−0.490839	+	0.871251i	$0.663310\pi$
$194$	−8.11650	−0.582731
$195$	−26.6204	−1.90633
$196$	−6.29714	−0.449796
$197$	14.9289	1.06364	0.531821	−	0.846857i	$-0.321508\pi$
$197$	14.9289	1.06364	0.531821	+	0.846857i	$0.321508\pi$
$198$	0	0
$199$	7.43443	0.527013	0.263506	−	0.964658i	$-0.415121\pi$
$199$	7.43443	0.527013	0.263506	+	0.964658i	$0.415121\pi$
$200$	−9.04565	−0.639624
$201$	11.7176	0.826498
$202$	12.2860	0.864439
$203$	−2.33937	−0.164192
$204$	−8.03870	−0.562821
$205$	23.9225	1.67082
$206$	−4.99650	−0.348123
$207$	2.69290	0.187169
$208$	4.44225	0.308015
$209$	0	0
$210$	−5.02396	−0.346686
$211$	3.71711	0.255897	0.127948	−	0.991781i	$-0.459161\pi$
$211$	3.71711	0.255897	0.127948	+	0.991781i	$0.459161\pi$
$212$	−13.3646	−0.917884
$213$	−19.8561	−1.36051
$214$	3.50824	0.239818
$215$	35.8209	2.44296
$216$	−5.50573	−0.374617
$217$	6.21068	0.421608
$218$	4.66438	0.315912
$219$	12.0862	0.816713
$220$	0	0
$221$	22.3331	1.50229
$222$	13.0792	0.877818
$223$	17.9524	1.20218	0.601091	−	0.799181i	$-0.294733\pi$
$223$	17.9524	1.20218	0.601091	+	0.799181i	$0.294733\pi$
$224$	0.838369	0.0560159
$225$	−4.00990	−0.267327
$226$	−17.4920	−1.16355
$227$	17.8112	1.18217	0.591084	−	0.806610i	$-0.298700\pi$
$227$	17.8112	1.18217	0.591084	+	0.806610i	$0.298700\pi$
$228$	−1.59897	−0.105894
$229$	6.56128	0.433582	0.216791	−	0.976218i	$-0.430441\pi$
$229$	6.56128	0.433582	0.216791	+	0.976218i	$0.430441\pi$
$230$	22.7665	1.50118
$231$	0	0
$232$	−2.79038	−0.183198
$233$	−2.44001	−0.159851	−0.0799253	−	0.996801i	$-0.525468\pi$
$233$	−2.44001	−0.159851	−0.0799253	+	0.996801i	$0.525468\pi$
$234$	1.96924	0.128733
$235$	−30.6408	−1.99878
$236$	7.28815	0.474418
$237$	−14.3671	−0.933241
$238$	4.21483	0.273207
$239$	−7.12273	−0.460731	−0.230366	−	0.973104i	$-0.573992\pi$
$239$	−7.12273	−0.460731	−0.230366	+	0.973104i	$0.573992\pi$
$240$	−5.99254	−0.386817
$241$	−15.1545	−0.976184	−0.488092	−	0.872792i	$-0.662307\pi$
$241$	−15.1545	−0.976184	−0.488092	+	0.872792i	$0.662307\pi$
$242$	0	0
$243$	−4.56712	−0.292981
$244$	8.26585	0.529167
$245$	−23.6001	−1.50776
$246$	10.2065	0.650742
$247$	4.44225	0.282654
$248$	7.40805	0.470412
$249$	2.08961	0.132423
$250$	−15.1621	−0.958935
$251$	−17.4635	−1.10229	−0.551143	−	0.834411i	$-0.685808\pi$
$251$	−17.4635	−1.10229	−0.551143	+	0.834411i	$0.685808\pi$
$252$	0.371646	0.0234115
$253$	0	0
$254$	1.19873	0.0752149
$255$	−30.1270	−1.88663
$256$	1.00000	0.0625000
$257$	−11.5036	−0.717577	−0.358788	−	0.933419i	$-0.616810\pi$
$257$	−11.5036	−0.717577	−0.358788	+	0.933419i	$0.616810\pi$
$258$	15.2829	0.951471
$259$	−6.85766	−0.426114
$260$	16.6485	1.03249
$261$	−1.23697	−0.0765663
$262$	−8.60188	−0.531426
$263$	17.1790	1.05930	0.529651	−	0.848216i	$-0.322323\pi$
$263$	17.1790	1.05930	0.529651	+	0.848216i	$0.322323\pi$
$264$	0	0
$265$	−50.0872	−3.07683
$266$	0.838369	0.0514037
$267$	−16.7755	−1.02664
$268$	−7.32824	−0.447643
$269$	11.0127	0.671454	0.335727	−	0.941959i	$-0.391018\pi$
$269$	11.0127	0.671454	0.335727	+	0.941959i	$0.391018\pi$
$270$	−20.6341	−1.25575
$271$	7.89719	0.479720	0.239860	−	0.970807i	$-0.422898\pi$
$271$	7.89719	0.479720	0.239860	+	0.970807i	$0.422898\pi$
$272$	5.02742	0.304832
$273$	5.95496	0.360410
$274$	−6.05457	−0.365770
$275$	0	0
$276$	9.71327	0.584670
$277$	7.67507	0.461150	0.230575	−	0.973054i	$-0.425939\pi$
$277$	7.67507	0.461150	0.230575	+	0.973054i	$0.425939\pi$
$278$	3.93304	0.235888
$279$	3.28396	0.196606
$280$	3.14200	0.187770
$281$	16.5030	0.984485	0.492242	−	0.870458i	$-0.336177\pi$
$281$	16.5030	0.984485	0.492242	+	0.870458i	$0.336177\pi$
$282$	−13.0728	−0.778475
$283$	7.23119	0.429850	0.214925	−	0.976631i	$-0.431049\pi$
$283$	7.23119	0.429850	0.214925	+	0.976631i	$0.431049\pi$
$284$	12.4180	0.736875
$285$	−5.99254	−0.354968
$286$	0	0
$287$	−5.35145	−0.315886
$288$	0.443297	0.0261215
$289$	8.27498	0.486763
$290$	−10.4577	−0.614095
$291$	−12.9780	−0.760786
$292$	−7.55877	−0.442344
$293$	−1.87058	−0.109281	−0.0546403	−	0.998506i	$-0.517401\pi$
$293$	−1.87058	−0.109281	−0.0546403	+	0.998506i	$0.517401\pi$
$294$	−10.0689	−0.587232
$295$	27.3142	1.59029
$296$	−8.17976	−0.475439
$297$	0	0
$298$	21.5346	1.24747
$299$	−26.9854	−1.56060
$300$	−14.4637	−0.835063
$301$	−8.01310	−0.461867
$302$	−0.130125	−0.00748787
$303$	19.6449	1.12857
$304$	1.00000	0.0573539
$305$	30.9784	1.77382
$306$	2.22864	0.127403
$307$	3.18323	0.181676	0.0908382	−	0.995866i	$-0.471045\pi$
$307$	3.18323	0.181676	0.0908382	+	0.995866i	$0.471045\pi$
$308$	0	0
$309$	−7.98926	−0.454493
$310$	27.7635	1.57686
$311$	18.0596	1.02406	0.512032	−	0.858967i	$-0.328893\pi$
$311$	18.0596	1.02406	0.512032	+	0.858967i	$0.328893\pi$
$312$	7.10303	0.402130
$313$	−11.7769	−0.665669	−0.332835	−	0.942985i	$-0.608005\pi$
$313$	−11.7769	−0.665669	−0.332835	+	0.942985i	$0.608005\pi$
$314$	−2.31749	−0.130784
$315$	1.39284	0.0784775
$316$	8.98520	0.505457
$317$	6.15896	0.345922	0.172961	−	0.984929i	$-0.444667\pi$
$317$	6.15896	0.345922	0.172961	+	0.984929i	$0.444667\pi$
$318$	−21.3696	−1.19835
$319$	0	0
$320$	3.74775	0.209506
$321$	5.60957	0.313096
$322$	−5.09284	−0.283813
$323$	5.02742	0.279733
$324$	−7.47360	−0.415200
$325$	40.1831	2.22896
$326$	18.0791	1.00131
$327$	7.45821	0.412440
$328$	−6.38316	−0.352451
$329$	6.85432	0.377891
$330$	0	0
$331$	4.75415	0.261312	0.130656	−	0.991428i	$-0.458292\pi$
$331$	4.75415	0.261312	0.130656	+	0.991428i	$0.458292\pi$
$332$	−1.30685	−0.0717225
$333$	−3.62606	−0.198707
$334$	−8.02035	−0.438854
$335$	−27.4644	−1.50054
$336$	1.34053	0.0731317
$337$	32.9054	1.79247	0.896236	−	0.443577i	$-0.146291\pi$
$337$	32.9054	1.79247	0.896236	+	0.443577i	$0.146291\pi$
$338$	−6.73362	−0.366261
$339$	−27.9691	−1.51907
$340$	18.8415	1.02183
$341$	0	0
$342$	0.443297	0.0239707
$343$	11.1479	0.601930
$344$	−9.55796	−0.515331
$345$	36.4029	1.95987
$346$	−2.34574	−0.126108
$347$	30.5079	1.63775	0.818876	−	0.573970i	$-0.194597\pi$
$347$	30.5079	1.63775	0.818876	+	0.573970i	$0.194597\pi$
$348$	−4.46174	−0.239174
$349$	18.9589	1.01485	0.507423	−	0.861697i	$-0.330598\pi$
$349$	18.9589	1.01485	0.507423	+	0.861697i	$0.330598\pi$
$350$	7.58359	0.405360
$351$	24.4578	1.30546
$352$	0	0
$353$	2.16128	0.115033	0.0575167	−	0.998345i	$-0.481682\pi$
$353$	2.16128	0.115033	0.0575167	+	0.998345i	$0.481682\pi$
$354$	11.6535	0.619378
$355$	46.5397	2.47007
$356$	10.4914	0.556044
$357$	6.73939	0.356686
$358$	13.3186	0.703908
$359$	10.9807	0.579538	0.289769	−	0.957097i	$-0.406421\pi$
$359$	10.9807	0.579538	0.289769	+	0.957097i	$0.406421\pi$
$360$	1.66137	0.0875617
$361$	1.00000	0.0526316
$362$	0.942795	0.0495522
$363$	0	0
$364$	−3.72425	−0.195204
$365$	−28.3284	−1.48278
$366$	13.2168	0.690855
$367$	18.2414	0.952194	0.476097	−	0.879393i	$-0.342051\pi$
$367$	18.2414	0.952194	0.476097	+	0.879393i	$0.342051\pi$
$368$	−6.07470	−0.316666
$369$	−2.82963	−0.147305
$370$	−30.6557	−1.59372
$371$	11.2045	0.581706
$372$	11.8452	0.614148
$373$	−3.49137	−0.180776	−0.0903881	−	0.995907i	$-0.528811\pi$
$373$	−3.49137	−0.180776	−0.0903881	+	0.995907i	$0.528811\pi$
$374$	0	0
$375$	−24.2437	−1.25194
$376$	8.17578	0.421633
$377$	12.3956	0.638405
$378$	4.61583	0.237413
$379$	29.6815	1.52464	0.762319	−	0.647201i	$-0.224061\pi$
$379$	29.6815	1.52464	0.762319	+	0.647201i	$0.224061\pi$
$380$	3.74775	0.192256
$381$	1.91673	0.0981970
$382$	16.2476	0.831302
$383$	12.2261	0.624726	0.312363	−	0.949963i	$-0.398879\pi$
$383$	12.2261	0.624726	0.312363	+	0.949963i	$0.398879\pi$
$384$	1.59897	0.0815971
$385$	0	0
$386$	13.6379	0.694151
$387$	−4.23701	−0.215379
$388$	8.11650	0.412053
$389$	−21.1912	−1.07444	−0.537219	−	0.843443i	$-0.680525\pi$
$389$	−21.1912	−1.07444	−0.537219	+	0.843443i	$0.680525\pi$
$390$	26.6204	1.34798
$391$	−30.5401	−1.54448
$392$	6.29714	0.318053
$393$	−13.7541	−0.693805
$394$	−14.9289	−0.752108
$395$	33.6743	1.69434
$396$	0	0
$397$	31.6829	1.59012	0.795060	−	0.606531i	$-0.207440\pi$
$397$	31.6829	1.59012	0.795060	+	0.606531i	$0.207440\pi$
$398$	−7.43443	−0.372654
$399$	1.34053	0.0671102
$400$	9.04565	0.452282
$401$	−11.3101	−0.564802	−0.282401	−	0.959297i	$-0.591131\pi$
$401$	−11.3101	−0.564802	−0.282401	+	0.959297i	$0.591131\pi$
$402$	−11.7176	−0.584422
$403$	−32.9085	−1.63929
$404$	−12.2860	−0.611251
$405$	−28.0092	−1.39179
$406$	2.33937	0.116101
$407$	0	0
$408$	8.03870	0.397975
$409$	−39.7435	−1.96519	−0.982596	−	0.185758i	$-0.940526\pi$
$409$	−39.7435	−1.96519	−0.982596	+	0.185758i	$0.940526\pi$
$410$	−23.9225	−1.18145
$411$	−9.68108	−0.477532
$412$	4.99650	0.246160
$413$	−6.11016	−0.300661
$414$	−2.69290	−0.132349
$415$	−4.89773	−0.240420
$416$	−4.44225	−0.217799
$417$	6.28882	0.307965
$418$	0	0
$419$	12.6037	0.615732	0.307866	−	0.951430i	$-0.400385\pi$
$419$	12.6037	0.615732	0.307866	+	0.951430i	$0.400385\pi$
$420$	5.02396	0.245144
$421$	−3.26241	−0.159000	−0.0795001	−	0.996835i	$-0.525332\pi$
$421$	−3.26241	−0.159000	−0.0795001	+	0.996835i	$0.525332\pi$
$422$	−3.71711	−0.180946
$423$	3.62429	0.176219
$424$	13.3646	0.649042
$425$	45.4763	2.20592
$426$	19.8561	0.962029
$427$	−6.92983	−0.335358
$428$	−3.50824	−0.169577
$429$	0	0
$430$	−35.8209	−1.72744
$431$	3.20143	0.154207	0.0771037	−	0.997023i	$-0.475433\pi$
$431$	3.20143	0.154207	0.0771037	+	0.997023i	$0.475433\pi$
$432$	5.50573	0.264894
$433$	−3.45528	−0.166050	−0.0830250	−	0.996547i	$-0.526458\pi$
$433$	−3.45528	−0.166050	−0.0830250	+	0.996547i	$0.526458\pi$
$434$	−6.21068	−0.298122
$435$	−16.7215	−0.801734
$436$	−4.66438	−0.223383
$437$	−6.07470	−0.290593
$438$	−12.0862	−0.577503
$439$	14.3937	0.686974	0.343487	−	0.939157i	$-0.388392\pi$
$439$	14.3937	0.686974	0.343487	+	0.939157i	$0.388392\pi$
$440$	0	0
$441$	2.79150	0.132929
$442$	−22.3331	−1.06228
$443$	1.27417	0.0605378	0.0302689	−	0.999542i	$-0.490364\pi$
$443$	1.27417	0.0605378	0.0302689	+	0.999542i	$0.490364\pi$
$444$	−13.0792	−0.620711
$445$	39.3192	1.86391
$446$	−17.9524	−0.850071
$447$	34.4332	1.62863
$448$	−0.838369	−0.0396092
$449$	18.2802	0.862698	0.431349	−	0.902185i	$-0.358038\pi$
$449$	18.2802	0.862698	0.431349	+	0.902185i	$0.358038\pi$
$450$	4.00990	0.189029
$451$	0	0
$452$	17.4920	0.822753
$453$	−0.208066	−0.00977581
$454$	−17.8112	−0.835919
$455$	−13.9576	−0.654340
$456$	1.59897	0.0748786
$457$	−18.6608	−0.872915	−0.436457	−	0.899725i	$-0.643767\pi$
$457$	−18.6608	−0.872915	−0.436457	+	0.899725i	$0.643767\pi$
$458$	−6.56128	−0.306588
$459$	27.6796	1.29197
$460$	−22.7665	−1.06149
$461$	−34.0250	−1.58470	−0.792351	−	0.610066i	$-0.791143\pi$
$461$	−34.0250	−1.58470	−0.792351	+	0.610066i	$0.791143\pi$
$462$	0	0
$463$	21.0000	0.975955	0.487977	−	0.872856i	$-0.337735\pi$
$463$	21.0000	0.975955	0.487977	+	0.872856i	$0.337735\pi$
$464$	2.79038	0.129540
$465$	44.3931	2.05868
$466$	2.44001	0.113031
$467$	4.16048	0.192524	0.0962620	−	0.995356i	$-0.469311\pi$
$467$	4.16048	0.192524	0.0962620	+	0.995356i	$0.469311\pi$
$468$	−1.96924	−0.0910280
$469$	6.14377	0.283693
$470$	30.6408	1.41335
$471$	−3.70560	−0.170745
$472$	−7.28815	−0.335465
$473$	0	0
$474$	14.3671	0.659901
$475$	9.04565	0.415043
$476$	−4.21483	−0.193187
$477$	5.92448	0.271263
$478$	7.12273	0.325786
$479$	33.8613	1.54716	0.773582	−	0.633696i	$-0.218463\pi$
$479$	33.8613	1.54716	0.773582	+	0.633696i	$0.218463\pi$
$480$	5.99254	0.273521
$481$	36.3366	1.65681
$482$	15.1545	0.690266
$483$	−8.14330	−0.370533
$484$	0	0
$485$	30.4186	1.38124
$486$	4.56712	0.207169
$487$	7.28097	0.329932	0.164966	−	0.986299i	$-0.447249\pi$
$487$	7.28097	0.329932	0.164966	+	0.986299i	$0.447249\pi$
$488$	−8.26585	−0.374177
$489$	28.9079	1.30726
$490$	23.6001	1.06614
$491$	−29.1638	−1.31614	−0.658072	−	0.752955i	$-0.728628\pi$
$491$	−29.1638	−1.31614	−0.658072	+	0.752955i	$0.728628\pi$
$492$	−10.2065	−0.460144
$493$	14.0284	0.631809
$494$	−4.44225	−0.199866
$495$	0	0
$496$	−7.40805	−0.332631
$497$	−10.4109	−0.466992
$498$	−2.08961	−0.0936375
$499$	−5.39904	−0.241694	−0.120847	−	0.992671i	$-0.538561\pi$
$499$	−5.39904	−0.241694	−0.120847	+	0.992671i	$0.538561\pi$
$500$	15.1621	0.678069
$501$	−12.8243	−0.572947
$502$	17.4635	0.779434
$503$	18.5430	0.826791	0.413395	−	0.910552i	$-0.364343\pi$
$503$	18.5430	0.826791	0.413395	+	0.910552i	$0.364343\pi$
$504$	−0.371646	−0.0165544
$505$	−46.0448	−2.04897
$506$	0	0
$507$	−10.7669	−0.478173
$508$	−1.19873	−0.0531849
$509$	7.17820	0.318168	0.159084	−	0.987265i	$-0.449146\pi$
$509$	7.17820	0.318168	0.159084	+	0.987265i	$0.449146\pi$
$510$	30.1270	1.33405
$511$	6.33704	0.280334
$512$	−1.00000	−0.0441942
$513$	5.50573	0.243084
$514$	11.5036	0.507403
$515$	18.7257	0.825151
$516$	−15.2829	−0.672792
$517$	0	0
$518$	6.85766	0.301308
$519$	−3.75076	−0.164640
$520$	−16.6485	−0.730084
$521$	−3.69794	−0.162010	−0.0810048	−	0.996714i	$-0.525813\pi$
$521$	−3.69794	−0.162010	−0.0810048	+	0.996714i	$0.525813\pi$
$522$	1.23697	0.0541406
$523$	27.8386	1.21730	0.608648	−	0.793440i	$-0.291712\pi$
$523$	27.8386	1.21730	0.608648	+	0.793440i	$0.291712\pi$
$524$	8.60188	0.375775
$525$	12.1259	0.529219
$526$	−17.1790	−0.749040
$527$	−37.2434	−1.62235
$528$	0	0
$529$	13.9020	0.604437
$530$	50.0872	2.17565
$531$	−3.23081	−0.140205
$532$	−0.838369	−0.0363479
$533$	28.3556	1.22822
$534$	16.7755	0.725945
$535$	−13.1480	−0.568438
$536$	7.32824	0.316532
$537$	21.2960	0.918989
$538$	−11.0127	−0.474790
$539$	0	0
$540$	20.6341	0.887950
$541$	38.1147	1.63868	0.819339	−	0.573309i	$-0.194341\pi$
$541$	38.1147	1.63868	0.819339	+	0.573309i	$0.194341\pi$
$542$	−7.89719	−0.339213
$543$	1.50750	0.0646930
$544$	−5.02742	−0.215549
$545$	−17.4810	−0.748802
$546$	−5.95496	−0.254849
$547$	−25.4157	−1.08670	−0.543348	−	0.839508i	$-0.682843\pi$
$547$	−25.4157	−1.08670	−0.543348	+	0.839508i	$0.682843\pi$
$548$	6.05457	0.258639
$549$	−3.66422	−0.156385
$550$	0	0
$551$	2.79038	0.118874
$552$	−9.71327	−0.413424
$553$	−7.53291	−0.320332
$554$	−7.67507	−0.326083
$555$	−49.0176	−2.08068
$556$	−3.93304	−0.166798
$557$	9.14395	0.387441	0.193721	−	0.981057i	$-0.437944\pi$
$557$	9.14395	0.387441	0.193721	+	0.981057i	$0.437944\pi$
$558$	−3.28396	−0.139021
$559$	42.4589	1.79582
$560$	−3.14200	−0.132774
$561$	0	0
$562$	−16.5030	−0.696136
$563$	31.3489	1.32120	0.660600	−	0.750738i	$-0.270302\pi$
$563$	31.3489	1.32120	0.660600	+	0.750738i	$0.270302\pi$
$564$	13.0728	0.550465
$565$	65.5555	2.75794
$566$	−7.23119	−0.303950
$567$	6.26563	0.263132
$568$	−12.4180	−0.521049
$569$	−40.8280	−1.71160	−0.855799	−	0.517308i	$-0.826934\pi$
$569$	−40.8280	−1.71160	−0.855799	+	0.517308i	$0.826934\pi$
$570$	5.99254	0.251000
$571$	40.1015	1.67820	0.839098	−	0.543980i	$-0.183083\pi$
$571$	40.1015	1.67820	0.839098	+	0.543980i	$0.183083\pi$
$572$	0	0
$573$	25.9795	1.08531
$574$	5.35145	0.223365
$575$	−54.9496	−2.29156
$576$	−0.443297	−0.0184707
$577$	20.1620	0.839356	0.419678	−	0.907673i	$-0.362143\pi$
$577$	20.1620	0.839356	0.419678	+	0.907673i	$0.362143\pi$
$578$	−8.27498	−0.344194
$579$	21.8066	0.906251
$580$	10.4577	0.434231
$581$	1.09562	0.0454539
$582$	12.9780	0.537957
$583$	0	0
$584$	7.55877	0.312784
$585$	−7.38021	−0.305134
$586$	1.87058	0.0772731
$587$	−43.2819	−1.78643	−0.893217	−	0.449626i	$-0.851557\pi$
$587$	−43.2819	−1.78643	−0.893217	+	0.449626i	$0.851557\pi$
$588$	10.0689	0.415236
$589$	−7.40805	−0.305243
$590$	−27.3142	−1.12451
$591$	−23.8709	−0.981917
$592$	8.17976	0.336186
$593$	47.4219	1.94739	0.973693	−	0.227865i	$-0.0731743\pi$
$593$	47.4219	1.94739	0.973693	+	0.227865i	$0.0731743\pi$
$594$	0	0
$595$	−15.7962	−0.647579
$596$	−21.5346	−0.882091
$597$	−11.8874	−0.486520
$598$	26.9854	1.10351
$599$	−1.10615	−0.0451960	−0.0225980	−	0.999745i	$-0.507194\pi$
$599$	−1.10615	−0.0451960	−0.0225980	+	0.999745i	$0.507194\pi$
$600$	14.4637	0.590479
$601$	20.7186	0.845130	0.422565	−	0.906333i	$-0.361130\pi$
$601$	20.7186	0.845130	0.422565	+	0.906333i	$0.361130\pi$
$602$	8.01310	0.326590
$603$	3.24858	0.132293
$604$	0.130125	0.00529472
$605$	0	0
$606$	−19.6449	−0.798020
$607$	5.72341	0.232306	0.116153	−	0.993231i	$-0.462944\pi$
$607$	5.72341	0.232306	0.116153	+	0.993231i	$0.462944\pi$
$608$	−1.00000	−0.0405554
$609$	3.74058	0.151576
$610$	−30.9784	−1.25428
$611$	−36.3189	−1.46930
$612$	−2.22864	−0.0900874
$613$	29.4925	1.19119	0.595595	−	0.803285i	$-0.296916\pi$
$613$	29.4925	1.19119	0.595595	+	0.803285i	$0.296916\pi$
$614$	−3.18323	−0.128465
$615$	−38.2514	−1.54244
$616$	0	0
$617$	−20.9449	−0.843211	−0.421605	−	0.906779i	$-0.638533\pi$
$617$	−20.9449	−0.843211	−0.421605	+	0.906779i	$0.638533\pi$
$618$	7.98926	0.321375
$619$	−44.1329	−1.77385	−0.886926	−	0.461911i	$-0.847164\pi$
$619$	−44.1329	−1.77385	−0.886926	+	0.461911i	$0.847164\pi$
$620$	−27.7635	−1.11501
$621$	−33.4457	−1.34213
$622$	−18.0596	−0.724122
$623$	−8.79567	−0.352391
$624$	−7.10303	−0.284349
$625$	11.5955	0.463821
$626$	11.7769	0.470699
$627$	0	0
$628$	2.31749	0.0924781
$629$	41.1231	1.63969
$630$	−1.39284	−0.0554920
$631$	−38.2677	−1.52341	−0.761706	−	0.647922i	$-0.775638\pi$
$631$	−38.2677	−1.52341	−0.761706	+	0.647922i	$0.775638\pi$
$632$	−8.98520	−0.357412
$633$	−5.94355	−0.236235
$634$	−6.15896	−0.244603
$635$	−4.49253	−0.178281
$636$	21.3696	0.847358
$637$	−27.9735	−1.10835
$638$	0	0
$639$	−5.50487	−0.217769
$640$	−3.74775	−0.148143
$641$	−42.8637	−1.69302	−0.846508	−	0.532377i	$-0.821299\pi$
$641$	−42.8637	−1.69302	−0.846508	+	0.532377i	$0.821299\pi$
$642$	−5.60957	−0.221392
$643$	29.7717	1.17408	0.587041	−	0.809557i	$-0.300293\pi$
$643$	29.7717	1.17408	0.587041	+	0.809557i	$0.300293\pi$
$644$	5.09284	0.200686
$645$	−57.2765	−2.25526
$646$	−5.02742	−0.197801
$647$	−1.81253	−0.0712578	−0.0356289	−	0.999365i	$-0.511343\pi$
$647$	−1.81253	−0.0712578	−0.0356289	+	0.999365i	$0.511343\pi$
$648$	7.47360	0.293591
$649$	0	0
$650$	−40.1831	−1.57611
$651$	−9.93069	−0.389214
$652$	−18.0791	−0.708031
$653$	17.9380	0.701969	0.350985	−	0.936381i	$-0.385847\pi$
$653$	17.9380	0.701969	0.350985	+	0.936381i	$0.385847\pi$
$654$	−7.45821	−0.291639
$655$	32.2377	1.25963
$656$	6.38316	0.249221
$657$	3.35078	0.130726
$658$	−6.85432	−0.267209
$659$	−28.4253	−1.10729	−0.553646	−	0.832752i	$-0.686764\pi$
$659$	−28.4253	−1.10729	−0.553646	+	0.832752i	$0.686764\pi$
$660$	0	0
$661$	22.7419	0.884556	0.442278	−	0.896878i	$-0.354171\pi$
$661$	22.7419	0.884556	0.442278	+	0.896878i	$0.354171\pi$
$662$	−4.75415	−0.184775
$663$	−35.7099	−1.38686
$664$	1.30685	0.0507154
$665$	−3.14200	−0.121841
$666$	3.62606	0.140507
$667$	−16.9507	−0.656336
$668$	8.02035	0.310317
$669$	−28.7053	−1.10981
$670$	27.4644	1.06104
$671$	0	0
$672$	−1.34053	−0.0517119
$673$	46.0957	1.77686	0.888429	−	0.459014i	$-0.151797\pi$
$673$	46.0957	1.77686	0.888429	+	0.459014i	$0.151797\pi$
$674$	−32.9054	−1.26747
$675$	49.8029	1.91691
$676$	6.73362	0.258985
$677$	−31.0736	−1.19425	−0.597127	−	0.802146i	$-0.703691\pi$
$677$	−31.0736	−1.19425	−0.597127	+	0.802146i	$0.703691\pi$
$678$	27.9691	1.07415
$679$	−6.80462	−0.261137
$680$	−18.8415	−0.722540
$681$	−28.4795	−1.09134
$682$	0	0
$683$	−39.9779	−1.52971	−0.764856	−	0.644201i	$-0.777190\pi$
$683$	−39.9779	−1.52971	−0.764856	+	0.644201i	$0.777190\pi$
$684$	−0.443297	−0.0169499
$685$	22.6910	0.866980
$686$	−11.1479	−0.425629
$687$	−10.4913	−0.400268
$688$	9.55796	0.364394
$689$	−59.3689	−2.26177
$690$	−36.4029	−1.38584
$691$	6.44234	0.245078	0.122539	−	0.992464i	$-0.460896\pi$
$691$	6.44234	0.245078	0.122539	+	0.992464i	$0.460896\pi$
$692$	2.34574	0.0891715
$693$	0	0
$694$	−30.5079	−1.15807
$695$	−14.7401	−0.559123
$696$	4.46174	0.169122
$697$	32.0909	1.21553
$698$	−18.9589	−0.717605
$699$	3.90151	0.147569
$700$	−7.58359	−0.286633
$701$	−35.4334	−1.33830	−0.669150	−	0.743127i	$-0.733342\pi$
$701$	−35.4334	−1.33830	−0.669150	+	0.743127i	$0.733342\pi$
$702$	−24.4578	−0.923101
$703$	8.17976	0.308506
$704$	0	0
$705$	48.9937	1.84521
$706$	−2.16128	−0.0813409
$707$	10.3002	0.387378
$708$	−11.6535	−0.437967
$709$	−30.0116	−1.12711	−0.563555	−	0.826079i	$-0.690567\pi$
$709$	−30.0116	−1.12711	−0.563555	+	0.826079i	$0.690567\pi$
$710$	−46.5397	−1.74660
$711$	−3.98311	−0.149378
$712$	−10.4914	−0.393182
$713$	45.0017	1.68533
$714$	−6.73939	−0.252215
$715$	0	0
$716$	−13.3186	−0.497738
$717$	11.3890	0.425331
$718$	−10.9807	−0.409795
$719$	17.6988	0.660052	0.330026	−	0.943972i	$-0.392942\pi$
$719$	17.6988	0.660052	0.330026	+	0.943972i	$0.392942\pi$
$720$	−1.66137	−0.0619154
$721$	−4.18891	−0.156003
$722$	−1.00000	−0.0372161
$723$	24.2315	0.901180
$724$	−0.942795	−0.0350387
$725$	25.2408	0.937420
$726$	0	0
$727$	−18.2854	−0.678167	−0.339084	−	0.940756i	$-0.610117\pi$
$727$	−18.2854	−0.678167	−0.339084	+	0.940756i	$0.610117\pi$
$728$	3.72425	0.138030
$729$	29.7235	1.10087
$730$	28.3284	1.04848
$731$	48.0519	1.77726
$732$	−13.2168	−0.488508
$733$	−7.03592	−0.259878	−0.129939	−	0.991522i	$-0.541478\pi$
$733$	−7.03592	−0.259878	−0.129939	+	0.991522i	$0.541478\pi$
$734$	−18.2414	−0.673303
$735$	37.7359	1.39191
$736$	6.07470	0.223917
$737$	0	0
$738$	2.82963	0.104160
$739$	−9.60429	−0.353299	−0.176650	−	0.984274i	$-0.556526\pi$
$739$	−9.60429	−0.353299	−0.176650	+	0.984274i	$0.556526\pi$
$740$	30.6557	1.12693
$741$	−7.10303	−0.260936
$742$	−11.2045	−0.411328
$743$	−12.7141	−0.466437	−0.233218	−	0.972424i	$-0.574926\pi$
$743$	−12.7141	−0.466437	−0.233218	+	0.972424i	$0.574926\pi$
$744$	−11.8452	−0.434268
$745$	−80.7063	−2.95685
$746$	3.49137	0.127828
$747$	0.579320	0.0211962
$748$	0	0
$749$	2.94120	0.107469
$750$	24.2437	0.885255
$751$	19.7038	0.719000	0.359500	−	0.933145i	$-0.382947\pi$
$751$	19.7038	0.719000	0.359500	+	0.933145i	$0.382947\pi$
$752$	−8.17578	−0.298140
$753$	27.9236	1.01759
$754$	−12.3956	−0.451421
$755$	0.487677	0.0177484
$756$	−4.61583	−0.167876
$757$	−1.18737	−0.0431556	−0.0215778	−	0.999767i	$-0.506869\pi$
$757$	−1.18737	−0.0431556	−0.0215778	+	0.999767i	$0.506869\pi$
$758$	−29.6815	−1.07808
$759$	0	0
$760$	−3.74775	−0.135945
$761$	−38.3425	−1.38992	−0.694958	−	0.719051i	$-0.744577\pi$
$761$	−38.3425	−1.38992	−0.694958	+	0.719051i	$0.744577\pi$
$762$	−1.91673	−0.0694358
$763$	3.91047	0.141569
$764$	−16.2476	−0.587819
$765$	−8.35239	−0.301981
$766$	−12.2261	−0.441748
$767$	32.3758	1.16902
$768$	−1.59897	−0.0576978
$769$	31.3585	1.13082	0.565409	−	0.824811i	$-0.308718\pi$
$769$	31.3585	1.13082	0.565409	+	0.824811i	$0.308718\pi$
$770$	0	0
$771$	18.3939	0.662442
$772$	−13.6379	−0.490839
$773$	−19.4018	−0.697835	−0.348918	−	0.937153i	$-0.613451\pi$
$773$	−19.4018	−0.697835	−0.348918	+	0.937153i	$0.613451\pi$
$774$	4.23701	0.152296
$775$	−67.0106	−2.40709
$776$	−8.11650	−0.291365
$777$	10.9652	0.393374
$778$	21.1912	0.759742
$779$	6.38316	0.228701
$780$	−26.6204	−0.953163
$781$	0	0
$782$	30.5401	1.09211
$783$	15.3631	0.549032
$784$	−6.29714	−0.224898
$785$	8.68539	0.309995
$786$	13.7541	0.490594
$787$	−10.2652	−0.365913	−0.182957	−	0.983121i	$-0.558567\pi$
$787$	−10.2652	−0.365913	−0.182957	+	0.983121i	$0.558567\pi$
$788$	14.9289	0.531821
$789$	−27.4687	−0.977911
$790$	−33.6743	−1.19808
$791$	−14.6647	−0.521417
$792$	0	0
$793$	36.7190	1.30393
$794$	−31.6829	−1.12438
$795$	80.0878	2.84042
$796$	7.43443	0.263506
$797$	6.35354	0.225054	0.112527	−	0.993649i	$-0.464106\pi$
$797$	6.35354	0.225054	0.112527	+	0.993649i	$0.464106\pi$
$798$	−1.34053	−0.0474541
$799$	−41.1031	−1.45412
$800$	−9.04565	−0.319812
$801$	−4.65081	−0.164328
$802$	11.3101	0.399375
$803$	0	0
$804$	11.7176	0.413249
$805$	19.0867	0.672718
$806$	32.9085	1.15915
$807$	−17.6089	−0.619863
$808$	12.2860	0.432220
$809$	15.6040	0.548606	0.274303	−	0.961643i	$-0.411553\pi$
$809$	15.6040	0.548606	0.274303	+	0.961643i	$0.411553\pi$
$810$	28.0092	0.984143
$811$	−2.34105	−0.0822054	−0.0411027	−	0.999155i	$-0.513087\pi$
$811$	−2.34105	−0.0822054	−0.0411027	+	0.999155i	$0.513087\pi$
$812$	−2.33937	−0.0820958
$813$	−12.6274	−0.442861
$814$	0	0
$815$	−67.7559	−2.37339
$816$	−8.03870	−0.281411
$817$	9.55796	0.334391
$818$	39.7435	1.38960
$819$	1.65095	0.0576887
$820$	23.9225	0.835411
$821$	−50.2162	−1.75256	−0.876278	−	0.481805i	$-0.839981\pi$
$821$	−50.2162	−1.75256	−0.876278	+	0.481805i	$0.839981\pi$
$822$	9.68108	0.337666
$823$	−40.2159	−1.40184	−0.700919	−	0.713241i	$-0.747227\pi$
$823$	−40.2159	−1.40184	−0.700919	+	0.713241i	$0.747227\pi$
$824$	−4.99650	−0.174061
$825$	0	0
$826$	6.11016	0.212600
$827$	−26.1434	−0.909094	−0.454547	−	0.890723i	$-0.650199\pi$
$827$	−26.1434	−0.909094	−0.454547	+	0.890723i	$0.650199\pi$
$828$	2.69290	0.0935846
$829$	−28.0907	−0.975629	−0.487814	−	0.872947i	$-0.662206\pi$
$829$	−28.0907	−0.975629	−0.487814	+	0.872947i	$0.662206\pi$
$830$	4.89773	0.170003
$831$	−12.2722	−0.425718
$832$	4.44225	0.154007
$833$	−31.6584	−1.09690
$834$	−6.28882	−0.217764
$835$	30.0583	1.04021
$836$	0	0
$837$	−40.7867	−1.40979
$838$	−12.6037	−0.435388
$839$	7.97271	0.275249	0.137624	−	0.990485i	$-0.456053\pi$
$839$	7.97271	0.275249	0.137624	+	0.990485i	$0.456053\pi$
$840$	−5.02396	−0.173343
$841$	−21.2138	−0.731509
$842$	3.26241	0.112430
$843$	−26.3877	−0.908842
$844$	3.71711	0.127948
$845$	25.2359	0.868143
$846$	−3.62429	−0.124606
$847$	0	0
$848$	−13.3646	−0.458942
$849$	−11.5625	−0.396822
$850$	−45.4763	−1.55982
$851$	−49.6897	−1.70334
$852$	−19.8561	−0.680257
$853$	−26.0507	−0.891957	−0.445979	−	0.895044i	$-0.647144\pi$
$853$	−26.0507	−0.891957	−0.445979	+	0.895044i	$0.647144\pi$
$854$	6.92983	0.237134
$855$	−1.66137	−0.0568175
$856$	3.50824	0.119909
$857$	33.7585	1.15317	0.576584	−	0.817038i	$-0.304385\pi$
$857$	33.7585	1.15317	0.576584	+	0.817038i	$0.304385\pi$
$858$	0	0
$859$	9.57479	0.326688	0.163344	−	0.986569i	$-0.447772\pi$
$859$	9.57479	0.326688	0.163344	+	0.986569i	$0.447772\pi$
$860$	35.8209	1.22148
$861$	8.55680	0.291615
$862$	−3.20143	−0.109041
$863$	−22.8175	−0.776716	−0.388358	−	0.921509i	$-0.626958\pi$
$863$	−22.8175	−0.776716	−0.388358	+	0.921509i	$0.626958\pi$
$864$	−5.50573	−0.187309
$865$	8.79124	0.298911
$866$	3.45528	0.117415
$867$	−13.2314	−0.449363
$868$	6.21068	0.210804
$869$	0	0
$870$	16.7215	0.566911
$871$	−32.5539	−1.10305
$872$	4.66438	0.157956
$873$	−3.59802	−0.121774
$874$	6.07470	0.205480
$875$	−12.7114	−0.429724
$876$	12.0862	0.408356
$877$	33.8643	1.14352	0.571758	−	0.820422i	$-0.306262\pi$
$877$	33.8643	1.14352	0.571758	+	0.820422i	$0.306262\pi$
$878$	−14.3937	−0.485764
$879$	2.99100	0.100884
$880$	0	0
$881$	−10.2923	−0.346757	−0.173379	−	0.984855i	$-0.555468\pi$
$881$	−10.2923	−0.346757	−0.173379	+	0.984855i	$0.555468\pi$
$882$	−2.79150	−0.0939947
$883$	−24.4304	−0.822149	−0.411075	−	0.911602i	$-0.634846\pi$
$883$	−24.4304	−0.822149	−0.411075	+	0.911602i	$0.634846\pi$
$884$	22.3331	0.751143
$885$	−43.6746	−1.46810
$886$	−1.27417	−0.0428067
$887$	4.23374	0.142155	0.0710775	−	0.997471i	$-0.477356\pi$
$887$	4.23374	0.142155	0.0710775	+	0.997471i	$0.477356\pi$
$888$	13.0792	0.438909
$889$	1.00498	0.0337058
$890$	−39.3192	−1.31798
$891$	0	0
$892$	17.9524	0.601091
$893$	−8.17578	−0.273592
$894$	−34.4332	−1.15162
$895$	−49.9147	−1.66846
$896$	0.838369	0.0280079
$897$	43.1488	1.44070
$898$	−18.2802	−0.610020
$899$	−20.6713	−0.689426
$900$	−4.00990	−0.133663
$901$	−67.1894	−2.23840
$902$	0	0
$903$	12.8127	0.426380
$904$	−17.4920	−0.581774
$905$	−3.53336	−0.117453
$906$	0.208066	0.00691254
$907$	36.7169	1.21916	0.609582	−	0.792723i	$-0.291337\pi$
$907$	36.7169	1.21916	0.609582	+	0.792723i	$0.291337\pi$
$908$	17.8112	0.591084
$909$	5.44634	0.180644
$910$	13.9576	0.462688
$911$	−29.4185	−0.974678	−0.487339	−	0.873213i	$-0.662032\pi$
$911$	−29.4185	−0.974678	−0.487339	+	0.873213i	$0.662032\pi$
$912$	−1.59897	−0.0529472
$913$	0	0
$914$	18.6608	0.617244
$915$	−49.5334	−1.63753
$916$	6.56128	0.216791
$917$	−7.21155	−0.238146
$918$	−27.6796	−0.913563
$919$	−33.8981	−1.11820	−0.559098	−	0.829102i	$-0.688852\pi$
$919$	−33.8981	−1.11820	−0.559098	+	0.829102i	$0.688852\pi$
$920$	22.7665	0.750589
$921$	−5.08988	−0.167717
$922$	34.0250	1.12055
$923$	55.1641	1.81575
$924$	0	0
$925$	73.9913	2.43282
$926$	−21.0000	−0.690104
$927$	−2.21493	−0.0727480
$928$	−2.79038	−0.0915988
$929$	−31.7568	−1.04191	−0.520953	−	0.853585i	$-0.674423\pi$
$929$	−31.7568	−1.04191	−0.520953	+	0.853585i	$0.674423\pi$
$930$	−44.3931	−1.45571
$931$	−6.29714	−0.206380
$932$	−2.44001	−0.0799253
$933$	−28.8767	−0.945380
$934$	−4.16048	−0.136135
$935$	0	0
$936$	1.96924	0.0643665
$937$	−20.2354	−0.661062	−0.330531	−	0.943795i	$-0.607228\pi$
$937$	−20.2354	−0.661062	−0.330531	+	0.943795i	$0.607228\pi$
$938$	−6.14377	−0.200601
$939$	18.8309	0.614523
$940$	−30.6408	−0.999392
$941$	36.7581	1.19828	0.599141	−	0.800644i	$-0.295509\pi$
$941$	36.7581	1.19828	0.599141	+	0.800644i	$0.295509\pi$
$942$	3.70560	0.120735
$943$	−38.7758	−1.26271
$944$	7.28815	0.237209
$945$	−17.2990	−0.562736
$946$	0	0
$947$	30.2362	0.982544	0.491272	−	0.871006i	$-0.336532\pi$
$947$	30.2362	0.982544	0.491272	+	0.871006i	$0.336532\pi$
$948$	−14.3671	−0.466620
$949$	−33.5780	−1.08999
$950$	−9.04565	−0.293480
$951$	−9.84799	−0.319343
$952$	4.21483	0.136604
$953$	−15.8514	−0.513476	−0.256738	−	0.966481i	$-0.582648\pi$
$953$	−15.8514	−0.513476	−0.256738	+	0.966481i	$0.582648\pi$
$954$	−5.92448	−0.191812
$955$	−60.8921	−1.97042
$956$	−7.12273	−0.230366
$957$	0	0
$958$	−33.8613	−1.09401
$959$	−5.07597	−0.163911
$960$	−5.99254	−0.193408
$961$	23.8792	0.770298
$962$	−36.3366	−1.17154
$963$	1.55519	0.0501153
$964$	−15.1545	−0.488092
$965$	−51.1115	−1.64534
$966$	8.14330	0.262006
$967$	23.6222	0.759639	0.379820	−	0.925061i	$-0.375986\pi$
$967$	23.6222	0.759639	0.379820	+	0.925061i	$0.375986\pi$
$968$	0	0
$969$	−8.03870	−0.258240
$970$	−30.4186	−0.976683
$971$	1.13134	0.0363065	0.0181532	−	0.999835i	$-0.494221\pi$
$971$	1.13134	0.0363065	0.0181532	+	0.999835i	$0.494221\pi$
$972$	−4.56712	−0.146491
$973$	3.29734	0.105708
$974$	−7.28097	−0.233297
$975$	−64.2515	−2.05769
$976$	8.26585	0.264583
$977$	36.8296	1.17828	0.589141	−	0.808030i	$-0.299466\pi$
$977$	36.8296	1.17828	0.589141	+	0.808030i	$0.299466\pi$
$978$	−28.9079	−0.924373
$979$	0	0
$980$	−23.6001	−0.753878
$981$	2.06770	0.0660167
$982$	29.1638	0.930654
$983$	27.5243	0.877887	0.438944	−	0.898515i	$-0.355353\pi$
$983$	27.5243	0.877887	0.438944	+	0.898515i	$0.355353\pi$
$984$	10.2065	0.325371
$985$	55.9499	1.78271
$986$	−14.0284	−0.446756
$987$	−10.9598	−0.348856
$988$	4.44225	0.141327
$989$	−58.0618	−1.84626
$990$	0	0
$991$	7.71442	0.245057	0.122528	−	0.992465i	$-0.460900\pi$
$991$	7.71442	0.245057	0.122528	+	0.992465i	$0.460900\pi$
$992$	7.40805	0.235206
$993$	−7.60175	−0.241234
$994$	10.4109	0.330213
$995$	27.8624	0.883298
$996$	2.08961	0.0662117
$997$	44.4390	1.40740	0.703698	−	0.710499i	$-0.251531\pi$
$997$	44.4390	1.40740	0.703698	+	0.710499i	$0.251531\pi$
$998$	5.39904	0.170904
$999$	45.0355	1.42486

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bw.1.3		8
11.5	even	5		418.2.f.g.267.2	yes	16
11.9	even	5		418.2.f.g.191.2	✓	16
11.10	odd	2		4598.2.a.bz.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.g.191.2	✓	16	11.9	even	5
418.2.f.g.267.2	yes	16	11.5	even	5
4598.2.a.bw.1.3		8	1.1	even	1	trivial
4598.2.a.bz.1.3		8	11.10	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.59897 q^{3} +1.00000 q^{4} +3.74775 q^{5} +1.59897 q^{6} -0.838369 q^{7} -1.00000 q^{8} -0.443297 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.59897 q^{3} +1.00000 q^{4} +3.74775 q^{5} +1.59897 q^{6} -0.838369 q^{7} -1.00000 q^{8} -0.443297 q^{9} -3.74775 q^{10} -1.59897 q^{12} +4.44225 q^{13} +0.838369 q^{14} -5.99254 q^{15} +1.00000 q^{16} +5.02742 q^{17} +0.443297 q^{18} +1.00000 q^{19} +3.74775 q^{20} +1.34053 q^{21} -6.07470 q^{23} +1.59897 q^{24} +9.04565 q^{25} -4.44225 q^{26} +5.50573 q^{27} -0.838369 q^{28} +2.79038 q^{29} +5.99254 q^{30} -7.40805 q^{31} -1.00000 q^{32} -5.02742 q^{34} -3.14200 q^{35} -0.443297 q^{36} +8.17976 q^{37} -1.00000 q^{38} -7.10303 q^{39} -3.74775 q^{40} +6.38316 q^{41} -1.34053 q^{42} +9.55796 q^{43} -1.66137 q^{45} +6.07470 q^{46} -8.17578 q^{47} -1.59897 q^{48} -6.29714 q^{49} -9.04565 q^{50} -8.03870 q^{51} +4.44225 q^{52} -13.3646 q^{53} -5.50573 q^{54} +0.838369 q^{56} -1.59897 q^{57} -2.79038 q^{58} +7.28815 q^{59} -5.99254 q^{60} +8.26585 q^{61} +7.40805 q^{62} +0.371646 q^{63} +1.00000 q^{64} +16.6485 q^{65} -7.32824 q^{67} +5.02742 q^{68} +9.71327 q^{69} +3.14200 q^{70} +12.4180 q^{71} +0.443297 q^{72} -7.55877 q^{73} -8.17976 q^{74} -14.4637 q^{75} +1.00000 q^{76} +7.10303 q^{78} +8.98520 q^{79} +3.74775 q^{80} -7.47360 q^{81} -6.38316 q^{82} -1.30685 q^{83} +1.34053 q^{84} +18.8415 q^{85} -9.55796 q^{86} -4.46174 q^{87} +10.4914 q^{89} +1.66137 q^{90} -3.72425 q^{91} -6.07470 q^{92} +11.8452 q^{93} +8.17578 q^{94} +3.74775 q^{95} +1.59897 q^{96} +8.11650 q^{97} +6.29714 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} + 2 q^{6} + 14 q^{7} - 8 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 + 2 * q^6 + 14 * q^7 - 8 * q^8 + 2 * q^9	\( 8 q - 8 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} + 2 q^{6} + 14 q^{7} - 8 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} + 9 q^{13} - 14 q^{14} + 5 q^{15} + 8 q^{16} + 3 q^{17} - 2 q^{18} + 8 q^{19} - 2 q^{20} + 7 q^{21} - 13 q^{23} + 2 q^{24} + 4 q^{25} - 9 q^{26} + 4 q^{27} + 14 q^{28} + 10 q^{29} - 5 q^{30} - 2 q^{31} - 8 q^{32} - 3 q^{34} - 7 q^{35} + 2 q^{36} + 15 q^{37} - 8 q^{38} + 11 q^{39} + 2 q^{40} + 9 q^{41} - 7 q^{42} + 33 q^{43} - 21 q^{45} + 13 q^{46} - 19 q^{47} - 2 q^{48} + 12 q^{49} - 4 q^{50} + 22 q^{51} + 9 q^{52} + 10 q^{53} - 4 q^{54} - 14 q^{56} - 2 q^{57} - 10 q^{58} + q^{59} + 5 q^{60} + 26 q^{61} + 2 q^{62} + 19 q^{63} + 8 q^{64} + 26 q^{65} - 25 q^{67} + 3 q^{68} - 12 q^{69} + 7 q^{70} - 10 q^{71} - 2 q^{72} + 11 q^{73} - 15 q^{74} - 33 q^{75} + 8 q^{76} - 11 q^{78} + 10 q^{79} - 2 q^{80} - 40 q^{81} - 9 q^{82} + 16 q^{83} + 7 q^{84} + 33 q^{85} - 33 q^{86} + 2 q^{87} - 14 q^{89} + 21 q^{90} + 25 q^{91} - 13 q^{92} + 20 q^{93} + 19 q^{94} - 2 q^{95} + 2 q^{96} + 22 q^{97} - 12 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 + 2 * q^6 + 14 * q^7 - 8 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 + 9 * q^13 - 14 * q^14 + 5 * q^15 + 8 * q^16 + 3 * q^17 - 2 * q^18 + 8 * q^19 - 2 * q^20 + 7 * q^21 - 13 * q^23 + 2 * q^24 + 4 * q^25 - 9 * q^26 + 4 * q^27 + 14 * q^28 + 10 * q^29 - 5 * q^30 - 2 * q^31 - 8 * q^32 - 3 * q^34 - 7 * q^35 + 2 * q^36 + 15 * q^37 - 8 * q^38 + 11 * q^39 + 2 * q^40 + 9 * q^41 - 7 * q^42 + 33 * q^43 - 21 * q^45 + 13 * q^46 - 19 * q^47 - 2 * q^48 + 12 * q^49 - 4 * q^50 + 22 * q^51 + 9 * q^52 + 10 * q^53 - 4 * q^54 - 14 * q^56 - 2 * q^57 - 10 * q^58 + q^59 + 5 * q^60 + 26 * q^61 + 2 * q^62 + 19 * q^63 + 8 * q^64 + 26 * q^65 - 25 * q^67 + 3 * q^68 - 12 * q^69 + 7 * q^70 - 10 * q^71 - 2 * q^72 + 11 * q^73 - 15 * q^74 - 33 * q^75 + 8 * q^76 - 11 * q^78 + 10 * q^79 - 2 * q^80 - 40 * q^81 - 9 * q^82 + 16 * q^83 + 7 * q^84 + 33 * q^85 - 33 * q^86 + 2 * q^87 - 14 * q^89 + 21 * q^90 + 25 * q^91 - 13 * q^92 + 20 * q^93 + 19 * q^94 - 2 * q^95 + 2 * q^96 + 22 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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