LMFDB - Embedded newform 4598.2.a.cd.1.7

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 36x^{7} + 118x^{6} - 220x^{5} - 270x^{4} + 512x^{3} + 176x^{2} - 392x + 44 $ x^10 - 2x^9 - 19x^8 + 36x^7 + 118x^6 - 220x^5 - 270x^4 + 512x^3 + 176x^2 - 392*x + 44
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			1.7
Root			$1.39462$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.39462 q^{3} +1.00000 q^{4} +2.16074 q^{5} +1.39462 q^{6} -1.18224 q^{7} +1.00000 q^{8} -1.05504 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.39462 q^{3} +1.00000 q^{4} +2.16074 q^{5} +1.39462 q^{6} -1.18224 q^{7} +1.00000 q^{8} -1.05504 q^{9} +2.16074 q^{10} +1.39462 q^{12} +6.23946 q^{13} -1.18224 q^{14} +3.01340 q^{15} +1.00000 q^{16} +2.02708 q^{17} -1.05504 q^{18} +1.00000 q^{19} +2.16074 q^{20} -1.64877 q^{21} -3.76597 q^{23} +1.39462 q^{24} -0.331209 q^{25} +6.23946 q^{26} -5.65523 q^{27} -1.18224 q^{28} +3.46810 q^{29} +3.01340 q^{30} +8.06702 q^{31} +1.00000 q^{32} +2.02708 q^{34} -2.55451 q^{35} -1.05504 q^{36} +5.03290 q^{37} +1.00000 q^{38} +8.70166 q^{39} +2.16074 q^{40} -2.39274 q^{41} -1.64877 q^{42} +7.95696 q^{43} -2.27967 q^{45} -3.76597 q^{46} +3.04018 q^{47} +1.39462 q^{48} -5.60231 q^{49} -0.331209 q^{50} +2.82700 q^{51} +6.23946 q^{52} -1.12768 q^{53} -5.65523 q^{54} -1.18224 q^{56} +1.39462 q^{57} +3.46810 q^{58} -2.44920 q^{59} +3.01340 q^{60} -11.2620 q^{61} +8.06702 q^{62} +1.24732 q^{63} +1.00000 q^{64} +13.4819 q^{65} -10.1426 q^{67} +2.02708 q^{68} -5.25209 q^{69} -2.55451 q^{70} +0.580507 q^{71} -1.05504 q^{72} +8.25430 q^{73} +5.03290 q^{74} -0.461910 q^{75} +1.00000 q^{76} +8.70166 q^{78} +6.77630 q^{79} +2.16074 q^{80} -4.72175 q^{81} -2.39274 q^{82} +17.7944 q^{83} -1.64877 q^{84} +4.38000 q^{85} +7.95696 q^{86} +4.83667 q^{87} +5.72864 q^{89} -2.27967 q^{90} -7.37655 q^{91} -3.76597 q^{92} +11.2504 q^{93} +3.04018 q^{94} +2.16074 q^{95} +1.39462 q^{96} -2.56385 q^{97} -5.60231 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9} - 3 q^{10} + 2 q^{12} + 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} + 12 q^{17} + 12 q^{18} + 10 q^{19} - 3 q^{20} - q^{21} + 14 q^{23} + 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} + 11 q^{28} + 16 q^{29} + q^{30} + 12 q^{31} + 10 q^{32} + 12 q^{34} - 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} + 11 q^{39} - 3 q^{40} - 5 q^{41} - q^{42} + 22 q^{43} - 2 q^{45} + 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} + 5 q^{50} + 8 q^{51} + 11 q^{52} + 2 q^{53} + 2 q^{54} + 11 q^{56} + 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} + 35 q^{61} + 12 q^{62} + 38 q^{63} + 10 q^{64} + 4 q^{65} + 9 q^{67} + 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 5 q^{73} - q^{74} - 15 q^{75} + 10 q^{76} + 11 q^{78} + 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} + 7 q^{83} - q^{84} + 35 q^{85} + 22 q^{86} + 8 q^{87} + 22 q^{89} - 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} + 8 q^{94} - 3 q^{95} + 2 q^{96} + 32 q^{97} - 3 q^{98}+O(q^{100}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9 - 3 * q^10 + 2 * q^12 + 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 + 12 * q^17 + 12 * q^18 + 10 * q^19 - 3 * q^20 - q^21 + 14 * q^23 + 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 + 11 * q^28 + 16 * q^29 + q^30 + 12 * q^31 + 10 * q^32 + 12 * q^34 - 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 + 11 * q^39 - 3 * q^40 - 5 * q^41 - q^42 + 22 * q^43 - 2 * q^45 + 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 + 5 * q^50 + 8 * q^51 + 11 * q^52 + 2 * q^53 + 2 * q^54 + 11 * q^56 + 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 + 35 * q^61 + 12 * q^62 + 38 * q^63 + 10 * q^64 + 4 * q^65 + 9 * q^67 + 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 5 * q^73 - q^74 - 15 * q^75 + 10 * q^76 + 11 * q^78 + 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 + 7 * q^83 - q^84 + 35 * q^85 + 22 * q^86 + 8 * q^87 + 22 * q^89 - 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 + 32 * q^97 - 3 * 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
$3$	1.39462	0.805182	0.402591	−	0.915380i	$-0.368110\pi$
$3$	1.39462	0.805182	0.402591	+	0.915380i	$0.368110\pi$
$4$	1.00000	0.500000
$5$	2.16074	0.966312	0.483156	−	0.875534i	$-0.339490\pi$
$5$	2.16074	0.966312	0.483156	+	0.875534i	$0.339490\pi$
$6$	1.39462	0.569350
$7$	−1.18224	−0.446845	−0.223422	−	0.974722i	$-0.571723\pi$
$7$	−1.18224	−0.446845	−0.223422	+	0.974722i	$0.571723\pi$
$8$	1.00000	0.353553
$9$	−1.05504	−0.351681
$10$	2.16074	0.683286
$11$	0	0
$11$	0	0
$12$	1.39462	0.402591
$13$	6.23946	1.73052	0.865258	−	0.501327i	$-0.167155\pi$
$13$	6.23946	1.73052	0.865258	+	0.501327i	$0.167155\pi$
$14$	−1.18224	−0.315967
$15$	3.01340	0.778057
$16$	1.00000	0.250000
$17$	2.02708	0.491640	0.245820	−	0.969316i	$-0.420943\pi$
$17$	2.02708	0.491640	0.245820	+	0.969316i	$0.420943\pi$
$18$	−1.05504	−0.248676
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.16074	0.483156
$21$	−1.64877	−0.359792
$22$	0	0
$23$	−3.76597	−0.785260	−0.392630	−	0.919697i	$-0.628435\pi$
$23$	−3.76597	−0.785260	−0.392630	+	0.919697i	$0.628435\pi$
$24$	1.39462	0.284675
$25$	−0.331209	−0.0662418
$26$	6.23946	1.22366
$27$	−5.65523	−1.08835
$28$	−1.18224	−0.223422
$29$	3.46810	0.644010	0.322005	−	0.946738i	$-0.395643\pi$
$29$	3.46810	0.644010	0.322005	+	0.946738i	$0.395643\pi$
$30$	3.01340	0.550170
$31$	8.06702	1.44888	0.724439	−	0.689339i	$-0.242099\pi$
$31$	8.06702	1.44888	0.724439	+	0.689339i	$0.242099\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	2.02708	0.347642
$35$	−2.55451	−0.431791
$36$	−1.05504	−0.175841
$37$	5.03290	0.827404	0.413702	−	0.910412i	$-0.364235\pi$
$37$	5.03290	0.827404	0.413702	+	0.910412i	$0.364235\pi$
$38$	1.00000	0.162221
$39$	8.70166	1.39338
$40$	2.16074	0.341643
$41$	−2.39274	−0.373683	−0.186842	−	0.982390i	$-0.559825\pi$
$41$	−2.39274	−0.373683	−0.186842	+	0.982390i	$0.559825\pi$
$42$	−1.64877	−0.254411
$43$	7.95696	1.21342	0.606712	−	0.794921i	$-0.292488\pi$
$43$	7.95696	1.21342	0.606712	+	0.794921i	$0.292488\pi$
$44$	0	0
$45$	−2.27967	−0.339834
$46$	−3.76597	−0.555263
$47$	3.04018	0.443455	0.221728	−	0.975109i	$-0.428830\pi$
$47$	3.04018	0.443455	0.221728	+	0.975109i	$0.428830\pi$
$48$	1.39462	0.201296
$49$	−5.60231	−0.800330
$50$	−0.331209	−0.0468400
$51$	2.82700	0.395860
$52$	6.23946	0.865258
$53$	−1.12768	−0.154898	−0.0774492	−	0.996996i	$-0.524678\pi$
$53$	−1.12768	−0.154898	−0.0774492	+	0.996996i	$0.524678\pi$
$54$	−5.65523	−0.769580
$55$	0	0
$56$	−1.18224	−0.157984
$57$	1.39462	0.184722
$58$	3.46810	0.455384
$59$	−2.44920	−0.318858	−0.159429	−	0.987209i	$-0.550965\pi$
$59$	−2.44920	−0.318858	−0.159429	+	0.987209i	$0.550965\pi$
$60$	3.01340	0.389029
$61$	−11.2620	−1.44195	−0.720977	−	0.692959i	$-0.756307\pi$
$61$	−11.2620	−1.44195	−0.720977	+	0.692959i	$0.756307\pi$
$62$	8.06702	1.02451
$63$	1.24732	0.157147
$64$	1.00000	0.125000
$65$	13.4819	1.67222
$66$	0	0
$67$	−10.1426	−1.23911	−0.619557	−	0.784952i	$-0.712688\pi$
$67$	−10.1426	−1.23911	−0.619557	+	0.784952i	$0.712688\pi$
$68$	2.02708	0.245820
$69$	−5.25209	−0.632278
$70$	−2.55451	−0.305323
$71$	0.580507	0.0688935	0.0344468	−	0.999407i	$-0.489033\pi$
$71$	0.580507	0.0688935	0.0344468	+	0.999407i	$0.489033\pi$
$72$	−1.05504	−0.124338
$73$	8.25430	0.966092	0.483046	−	0.875595i	$-0.339530\pi$
$73$	8.25430	0.966092	0.483046	+	0.875595i	$0.339530\pi$
$74$	5.03290	0.585063
$75$	−0.461910	−0.0533367
$76$	1.00000	0.114708
$77$	0	0
$78$	8.70166	0.985269
$79$	6.77630	0.762393	0.381197	−	0.924494i	$-0.375512\pi$
$79$	6.77630	0.762393	0.381197	+	0.924494i	$0.375512\pi$
$80$	2.16074	0.241578
$81$	−4.72175	−0.524639
$82$	−2.39274	−0.264234
$83$	17.7944	1.95319	0.976597	−	0.215078i	$-0.0690006\pi$
$83$	17.7944	1.95319	0.976597	+	0.215078i	$0.0690006\pi$
$84$	−1.64877	−0.179896
$85$	4.38000	0.475077
$86$	7.95696	0.858021
$87$	4.83667	0.518545
$88$	0	0
$89$	5.72864	0.607235	0.303618	−	0.952794i	$-0.401806\pi$
$89$	5.72864	0.607235	0.303618	+	0.952794i	$0.401806\pi$
$90$	−2.27967	−0.240299
$91$	−7.37655	−0.773272
$92$	−3.76597	−0.392630
$93$	11.2504	1.16661
$94$	3.04018	0.313570
$95$	2.16074	0.221687
$96$	1.39462	0.142337
$97$	−2.56385	−0.260319	−0.130160	−	0.991493i	$-0.541549\pi$
$97$	−2.56385	−0.260319	−0.130160	+	0.991493i	$0.541549\pi$
$98$	−5.60231	−0.565919
$99$	0	0
$100$	−0.331209	−0.0331209
$101$	−11.6351	−1.15773	−0.578867	−	0.815422i	$-0.696505\pi$
$101$	−11.6351	−1.15773	−0.578867	+	0.815422i	$0.696505\pi$
$102$	2.82700	0.279915
$103$	4.14084	0.408009	0.204005	−	0.978970i	$-0.434604\pi$
$103$	4.14084	0.408009	0.204005	+	0.978970i	$0.434604\pi$
$104$	6.23946	0.611830
$105$	−3.56257	−0.347671
$106$	−1.12768	−0.109530
$107$	−13.5947	−1.31425	−0.657123	−	0.753783i	$-0.728227\pi$
$107$	−13.5947	−1.31425	−0.657123	+	0.753783i	$0.728227\pi$
$108$	−5.65523	−0.544175
$109$	6.51990	0.624493	0.312247	−	0.950001i	$-0.398918\pi$
$109$	6.51990	0.624493	0.312247	+	0.950001i	$0.398918\pi$
$110$	0	0
$111$	7.01897	0.666211
$112$	−1.18224	−0.111711
$113$	−14.2207	−1.33777	−0.668886	−	0.743365i	$-0.733228\pi$
$113$	−14.2207	−1.33777	−0.668886	+	0.743365i	$0.733228\pi$
$114$	1.39462	0.130618
$115$	−8.13729	−0.758806
$116$	3.46810	0.322005
$117$	−6.58291	−0.608590
$118$	−2.44920	−0.225467
$119$	−2.39650	−0.219687
$120$	3.01340	0.275085
$121$	0	0
$122$	−11.2620	−1.01962
$123$	−3.33695	−0.300883
$124$	8.06702	0.724439
$125$	−11.5193	−1.03032
$126$	1.24732	0.111120
$127$	20.2074	1.79312	0.896560	−	0.442922i	$-0.146058\pi$
$127$	20.2074	1.79312	0.896560	+	0.442922i	$0.146058\pi$
$128$	1.00000	0.0883883
$129$	11.0969	0.977028
$130$	13.4819	1.18244
$131$	10.4556	0.913510	0.456755	−	0.889593i	$-0.349012\pi$
$131$	10.4556	0.913510	0.456755	+	0.889593i	$0.349012\pi$
$132$	0	0
$133$	−1.18224	−0.102513
$134$	−10.1426	−0.876185
$135$	−12.2195	−1.05169
$136$	2.02708	0.173821
$137$	−19.2139	−1.64156	−0.820779	−	0.571246i	$-0.806460\pi$
$137$	−19.2139	−1.64156	−0.820779	+	0.571246i	$0.806460\pi$
$138$	−5.25209	−0.447088
$139$	14.9888	1.27133	0.635665	−	0.771965i	$-0.280726\pi$
$139$	14.9888	1.27133	0.635665	+	0.771965i	$0.280726\pi$
$140$	−2.55451	−0.215896
$141$	4.23988	0.357063
$142$	0.580507	0.0487151
$143$	0	0
$144$	−1.05504	−0.0879203
$145$	7.49365	0.622314
$146$	8.25430	0.683130
$147$	−7.81307	−0.644411
$148$	5.03290	0.413702
$149$	−8.18651	−0.670665	−0.335333	−	0.942100i	$-0.608849\pi$
$149$	−8.18651	−0.670665	−0.335333	+	0.942100i	$0.608849\pi$
$150$	−0.461910	−0.0377148
$151$	0.261159	0.0212528	0.0106264	−	0.999944i	$-0.496617\pi$
$151$	0.261159	0.0212528	0.0106264	+	0.999944i	$0.496617\pi$
$152$	1.00000	0.0811107
$153$	−2.13866	−0.172901
$154$	0	0
$155$	17.4307	1.40007
$156$	8.70166	0.696691
$157$	−1.18390	−0.0944851	−0.0472426	−	0.998883i	$-0.515043\pi$
$157$	−1.18390	−0.0944851	−0.0472426	+	0.998883i	$0.515043\pi$
$158$	6.77630	0.539093
$159$	−1.57268	−0.124721
$160$	2.16074	0.170821
$161$	4.45229	0.350889
$162$	−4.72175	−0.370976
$163$	9.08903	0.711907	0.355954	−	0.934504i	$-0.384156\pi$
$163$	9.08903	0.711907	0.355954	+	0.934504i	$0.384156\pi$
$164$	−2.39274	−0.186842
$165$	0	0
$166$	17.7944	1.38112
$167$	1.79614	0.138990	0.0694948	−	0.997582i	$-0.477861\pi$
$167$	1.79614	0.138990	0.0694948	+	0.997582i	$0.477861\pi$
$168$	−1.64877	−0.127206
$169$	25.9309	1.99469
$170$	4.38000	0.335930
$171$	−1.05504	−0.0806812
$172$	7.95696	0.606712
$173$	−7.38827	−0.561720	−0.280860	−	0.959749i	$-0.590620\pi$
$173$	−7.38827	−0.561720	−0.280860	+	0.959749i	$0.590620\pi$
$174$	4.83667	0.366667
$175$	0.391569	0.0295998
$176$	0	0
$177$	−3.41569	−0.256739
$178$	5.72864	0.429380
$179$	−19.2876	−1.44162	−0.720810	−	0.693132i	$-0.756230\pi$
$179$	−19.2876	−1.44162	−0.720810	+	0.693132i	$0.756230\pi$
$180$	−2.27967	−0.169917
$181$	8.50988	0.632535	0.316267	−	0.948670i	$-0.397570\pi$
$181$	8.50988	0.632535	0.316267	+	0.948670i	$0.397570\pi$
$182$	−7.37655	−0.546786
$183$	−15.7062	−1.16104
$184$	−3.76597	−0.277631
$185$	10.8748	0.799530
$186$	11.2504	0.824919
$187$	0	0
$188$	3.04018	0.221728
$189$	6.68584	0.486324
$190$	2.16074	0.156756
$191$	15.8608	1.14764	0.573822	−	0.818980i	$-0.305460\pi$
$191$	15.8608	1.14764	0.573822	+	0.818980i	$0.305460\pi$
$192$	1.39462	0.100648
$193$	−26.7687	−1.92685	−0.963427	−	0.267971i	$-0.913647\pi$
$193$	−26.7687	−1.92685	−0.963427	+	0.267971i	$0.913647\pi$
$194$	−2.56385	−0.184073
$195$	18.8020	1.34644
$196$	−5.60231	−0.400165
$197$	15.0992	1.07578	0.537888	−	0.843016i	$-0.319222\pi$
$197$	15.0992	1.07578	0.537888	+	0.843016i	$0.319222\pi$
$198$	0	0
$199$	24.4475	1.73304	0.866518	−	0.499145i	$-0.166352\pi$
$199$	24.4475	1.73304	0.866518	+	0.499145i	$0.166352\pi$
$200$	−0.331209	−0.0234200
$201$	−14.1450	−0.997712
$202$	−11.6351	−0.818642
$203$	−4.10013	−0.287772
$204$	2.82700	0.197930
$205$	−5.17008	−0.361094
$206$	4.14084	0.288506
$207$	3.97327	0.276161
$208$	6.23946	0.432629
$209$	0	0
$210$	−3.56257	−0.245840
$211$	−9.44900	−0.650496	−0.325248	−	0.945629i	$-0.605448\pi$
$211$	−9.44900	−0.650496	−0.325248	+	0.945629i	$0.605448\pi$
$212$	−1.12768	−0.0774492
$213$	0.809585	0.0554719
$214$	−13.5947	−0.929312
$215$	17.1929	1.17255
$216$	−5.65523	−0.384790
$217$	−9.53715	−0.647424
$218$	6.51990	0.441583
$219$	11.5116	0.777881
$220$	0	0
$221$	12.6479	0.850791
$222$	7.01897	0.471083
$223$	−23.5903	−1.57973	−0.789863	−	0.613283i	$-0.789848\pi$
$223$	−23.5903	−1.57973	−0.789863	+	0.613283i	$0.789848\pi$
$224$	−1.18224	−0.0789918
$225$	0.349440	0.0232960
$226$	−14.2207	−0.945947
$227$	2.12393	0.140970	0.0704850	−	0.997513i	$-0.477545\pi$
$227$	2.12393	0.140970	0.0704850	+	0.997513i	$0.477545\pi$
$228$	1.39462	0.0923608
$229$	−16.3328	−1.07930	−0.539651	−	0.841889i	$-0.681444\pi$
$229$	−16.3328	−1.07930	−0.539651	+	0.841889i	$0.681444\pi$
$230$	−8.13729	−0.536557
$231$	0	0
$232$	3.46810	0.227692
$233$	−24.7766	−1.62317	−0.811583	−	0.584237i	$-0.801394\pi$
$233$	−24.7766	−1.62317	−0.811583	+	0.584237i	$0.801394\pi$
$234$	−6.58291	−0.430338
$235$	6.56903	0.428516
$236$	−2.44920	−0.159429
$237$	9.45034	0.613866
$238$	−2.39650	−0.155342
$239$	4.61123	0.298276	0.149138	−	0.988816i	$-0.452350\pi$
$239$	4.61123	0.298276	0.149138	+	0.988816i	$0.452350\pi$
$240$	3.01340	0.194514
$241$	−5.69242	−0.366681	−0.183341	−	0.983049i	$-0.558691\pi$
$241$	−5.69242	−0.366681	−0.183341	+	0.983049i	$0.558691\pi$
$242$	0	0
$243$	10.3807	0.665920
$244$	−11.2620	−0.720977
$245$	−12.1051	−0.773368
$246$	−3.33695	−0.212756
$247$	6.23946	0.397008
$248$	8.06702	0.512256
$249$	24.8164	1.57268
$250$	−11.5193	−0.728548
$251$	−16.2461	−1.02544	−0.512722	−	0.858555i	$-0.671363\pi$
$251$	−16.2461	−1.02544	−0.512722	+	0.858555i	$0.671363\pi$
$252$	1.24732	0.0785735
$253$	0	0
$254$	20.2074	1.26793
$255$	6.10842	0.382524
$256$	1.00000	0.0625000
$257$	5.52563	0.344679	0.172340	−	0.985038i	$-0.444867\pi$
$257$	5.52563	0.344679	0.172340	+	0.985038i	$0.444867\pi$
$258$	11.0969	0.690863
$259$	−5.95010	−0.369721
$260$	13.4819	0.836109
$261$	−3.65900	−0.226486
$262$	10.4556	0.645949
$263$	−11.0066	−0.678695	−0.339348	−	0.940661i	$-0.610206\pi$
$263$	−11.0066	−0.678695	−0.339348	+	0.940661i	$0.610206\pi$
$264$	0	0
$265$	−2.43662	−0.149680
$266$	−1.18224	−0.0724878
$267$	7.98926	0.488935
$268$	−10.1426	−0.619557
$269$	−3.75097	−0.228701	−0.114350	−	0.993440i	$-0.536479\pi$
$269$	−3.75097	−0.228701	−0.114350	+	0.993440i	$0.536479\pi$
$270$	−12.2195	−0.743654
$271$	−17.0697	−1.03691	−0.518454	−	0.855105i	$-0.673492\pi$
$271$	−17.0697	−1.03691	−0.518454	+	0.855105i	$0.673492\pi$
$272$	2.02708	0.122910
$273$	−10.2875	−0.622625
$274$	−19.2139	−1.16076
$275$	0	0
$276$	−5.25209	−0.316139
$277$	13.5528	0.814308	0.407154	−	0.913360i	$-0.366521\pi$
$277$	13.5528	0.814308	0.407154	+	0.913360i	$0.366521\pi$
$278$	14.9888	0.898966
$279$	−8.51105	−0.509543
$280$	−2.55451	−0.152661
$281$	−24.3954	−1.45531	−0.727654	−	0.685944i	$-0.759390\pi$
$281$	−24.3954	−1.45531	−0.727654	+	0.685944i	$0.759390\pi$
$282$	4.23988	0.252481
$283$	−3.16656	−0.188232	−0.0941162	−	0.995561i	$-0.530003\pi$
$283$	−3.16656	−0.188232	−0.0941162	+	0.995561i	$0.530003\pi$
$284$	0.580507	0.0344468
$285$	3.01340	0.178499
$286$	0	0
$287$	2.82879	0.166978
$288$	−1.05504	−0.0621690
$289$	−12.8909	−0.758290
$290$	7.49365	0.440043
$291$	−3.57558	−0.209604
$292$	8.25430	0.483046
$293$	20.2683	1.18409	0.592044	−	0.805905i	$-0.298321\pi$
$293$	20.2683	1.18409	0.592044	+	0.805905i	$0.298321\pi$
$294$	−7.81307	−0.455668
$295$	−5.29207	−0.308116
$296$	5.03290	0.292532
$297$	0	0
$298$	−8.18651	−0.474232
$299$	−23.4977	−1.35891
$300$	−0.461910	−0.0266684
$301$	−9.40704	−0.542213
$302$	0.261159	0.0150280
$303$	−16.2265	−0.932187
$304$	1.00000	0.0573539
$305$	−24.3343	−1.39338
$306$	−2.13866	−0.122259
$307$	−10.0817	−0.575396	−0.287698	−	0.957721i	$-0.592890\pi$
$307$	−10.0817	−0.575396	−0.287698	+	0.957721i	$0.592890\pi$
$308$	0	0
$309$	5.77489	0.328522
$310$	17.4307	0.989998
$311$	16.8796	0.957156	0.478578	−	0.878045i	$-0.341152\pi$
$311$	16.8796	0.957156	0.478578	+	0.878045i	$0.341152\pi$
$312$	8.70166	0.492635
$313$	−29.9792	−1.69453	−0.847263	−	0.531173i	$-0.821751\pi$
$313$	−29.9792	−1.69453	−0.847263	+	0.531173i	$0.821751\pi$
$314$	−1.18390	−0.0668111
$315$	2.69512	0.151853
$316$	6.77630	0.381197
$317$	10.1843	0.572010	0.286005	−	0.958228i	$-0.407673\pi$
$317$	10.1843	0.572010	0.286005	+	0.958228i	$0.407673\pi$
$318$	−1.57268	−0.0881914
$319$	0	0
$320$	2.16074	0.120789
$321$	−18.9594	−1.05821
$322$	4.45229	0.248116
$323$	2.02708	0.112790
$324$	−4.72175	−0.262320
$325$	−2.06657	−0.114632
$326$	9.08903	0.503395
$327$	9.09276	0.502831
$328$	−2.39274	−0.132117
$329$	−3.59422	−0.198156
$330$	0	0
$331$	−8.83120	−0.485407	−0.242703	−	0.970101i	$-0.578034\pi$
$331$	−8.83120	−0.485407	−0.242703	+	0.970101i	$0.578034\pi$
$332$	17.7944	0.976597
$333$	−5.30993	−0.290983
$334$	1.79614	0.0982805
$335$	−21.9155	−1.19737
$336$	−1.64877	−0.0899479
$337$	−31.8303	−1.73391	−0.866953	−	0.498390i	$-0.833925\pi$
$337$	−31.8303	−1.73391	−0.866953	+	0.498390i	$0.833925\pi$
$338$	25.9309	1.41046
$339$	−19.8324	−1.07715
$340$	4.38000	0.237539
$341$	0	0
$342$	−1.05504	−0.0570502
$343$	14.8990	0.804468
$344$	7.95696	0.429010
$345$	−11.3484	−0.610977
$346$	−7.38827	−0.397196
$347$	−17.3285	−0.930243	−0.465121	−	0.885247i	$-0.653989\pi$
$347$	−17.3285	−0.930243	−0.465121	+	0.885247i	$0.653989\pi$
$348$	4.83667	0.259273
$349$	5.21745	0.279284	0.139642	−	0.990202i	$-0.455405\pi$
$349$	5.21745	0.279284	0.139642	+	0.990202i	$0.455405\pi$
$350$	0.391569	0.0209302
$351$	−35.2856	−1.88341
$352$	0	0
$353$	2.70039	0.143727	0.0718636	−	0.997414i	$-0.477105\pi$
$353$	2.70039	0.143727	0.0718636	+	0.997414i	$0.477105\pi$
$354$	−3.41569	−0.181542
$355$	1.25432	0.0665726
$356$	5.72864	0.303618
$357$	−3.34220	−0.176888
$358$	−19.2876	−1.01938
$359$	11.7526	0.620276	0.310138	−	0.950692i	$-0.399625\pi$
$359$	11.7526	0.620276	0.310138	+	0.950692i	$0.399625\pi$
$360$	−2.27967	−0.120149
$361$	1.00000	0.0526316
$362$	8.50988	0.447270
$363$	0	0
$364$	−7.37655	−0.386636
$365$	17.8354	0.933546
$366$	−15.7062	−0.820976
$367$	−28.1891	−1.47146	−0.735731	−	0.677274i	$-0.763161\pi$
$367$	−28.1891	−1.47146	−0.735731	+	0.677274i	$0.763161\pi$
$368$	−3.76597	−0.196315
$369$	2.52444	0.131417
$370$	10.8748	0.565353
$371$	1.33319	0.0692155
$372$	11.2504	0.583306
$373$	−21.5226	−1.11440	−0.557200	−	0.830378i	$-0.688124\pi$
$373$	−21.5226	−1.11440	−0.557200	+	0.830378i	$0.688124\pi$
$374$	0	0
$375$	−16.0651	−0.829597
$376$	3.04018	0.156785
$377$	21.6391	1.11447
$378$	6.68584	0.343883
$379$	19.0705	0.979585	0.489792	−	0.871839i	$-0.337073\pi$
$379$	19.0705	0.979585	0.489792	+	0.871839i	$0.337073\pi$
$380$	2.16074	0.110844
$381$	28.1816	1.44379
$382$	15.8608	0.811507
$383$	32.4721	1.65925	0.829623	−	0.558324i	$-0.188556\pi$
$383$	32.4721	1.65925	0.829623	+	0.558324i	$0.188556\pi$
$384$	1.39462	0.0711687
$385$	0	0
$386$	−26.7687	−1.36249
$387$	−8.39494	−0.426739
$388$	−2.56385	−0.130160
$389$	−2.68971	−0.136374	−0.0681868	−	0.997673i	$-0.521721\pi$
$389$	−2.68971	−0.136374	−0.0681868	+	0.997673i	$0.521721\pi$
$390$	18.8020	0.952077
$391$	−7.63394	−0.386065
$392$	−5.60231	−0.282959
$393$	14.5815	0.735542
$394$	15.0992	0.760689
$395$	14.6418	0.736709
$396$	0	0
$397$	4.73678	0.237732	0.118866	−	0.992910i	$-0.462074\pi$
$397$	4.73678	0.237732	0.118866	+	0.992910i	$0.462074\pi$
$398$	24.4475	1.22544
$399$	−1.64877	−0.0825419
$400$	−0.331209	−0.0165604
$401$	−6.22912	−0.311067	−0.155534	−	0.987831i	$-0.549710\pi$
$401$	−6.22912	−0.311067	−0.155534	+	0.987831i	$0.549710\pi$
$402$	−14.1450	−0.705489
$403$	50.3339	2.50731
$404$	−11.6351	−0.578867
$405$	−10.2025	−0.506965
$406$	−4.10013	−0.203486
$407$	0	0
$408$	2.82700	0.139958
$409$	1.72220	0.0851574	0.0425787	−	0.999093i	$-0.486443\pi$
$409$	1.72220	0.0851574	0.0425787	+	0.999093i	$0.486443\pi$
$410$	−5.17008	−0.255332
$411$	−26.7961	−1.32175
$412$	4.14084	0.204005
$413$	2.89554	0.142480
$414$	3.97327	0.195275
$415$	38.4491	1.88739
$416$	6.23946	0.305915
$417$	20.9036	1.02365
$418$	0	0
$419$	−17.0528	−0.833083	−0.416541	−	0.909117i	$-0.636758\pi$
$419$	−17.0528	−0.833083	−0.416541	+	0.909117i	$0.636758\pi$
$420$	−3.56257	−0.173835
$421$	−28.7423	−1.40082	−0.700408	−	0.713743i	$-0.746999\pi$
$421$	−28.7423	−1.40082	−0.700408	+	0.713743i	$0.746999\pi$
$422$	−9.44900	−0.459970
$423$	−3.20752	−0.155955
$424$	−1.12768	−0.0547648
$425$	−0.671388	−0.0325671
$426$	0.809585	0.0392245
$427$	13.3144	0.644330
$428$	−13.5947	−0.657123
$429$	0	0
$430$	17.1929	0.829116
$431$	−40.2106	−1.93688	−0.968438	−	0.249254i	$-0.919815\pi$
$431$	−40.2106	−1.93688	−0.968438	+	0.249254i	$0.919815\pi$
$432$	−5.65523	−0.272087
$433$	0.204074	0.00980719	0.00490359	−	0.999988i	$-0.498439\pi$
$433$	0.204074	0.00980719	0.00490359	+	0.999988i	$0.498439\pi$
$434$	−9.53715	−0.457798
$435$	10.4508	0.501076
$436$	6.51990	0.312247
$437$	−3.76597	−0.180151
$438$	11.5116	0.550045
$439$	−0.940938	−0.0449085	−0.0224543	−	0.999748i	$-0.507148\pi$
$439$	−0.940938	−0.0449085	−0.0224543	+	0.999748i	$0.507148\pi$
$440$	0	0
$441$	5.91068	0.281461
$442$	12.6479	0.601600
$443$	3.10542	0.147543	0.0737715	−	0.997275i	$-0.476496\pi$
$443$	3.10542	0.147543	0.0737715	+	0.997275i	$0.476496\pi$
$444$	7.01897	0.333106
$445$	12.3781	0.586778
$446$	−23.5903	−1.11704
$447$	−11.4170	−0.540008
$448$	−1.18224	−0.0558556
$449$	−23.2360	−1.09658	−0.548288	−	0.836289i	$-0.684720\pi$
$449$	−23.2360	−1.09658	−0.548288	+	0.836289i	$0.684720\pi$
$450$	0.349440	0.0164728
$451$	0	0
$452$	−14.2207	−0.668886
$453$	0.364217	0.0171124
$454$	2.12393	0.0996809
$455$	−15.9388	−0.747222
$456$	1.39462	0.0653089
$457$	38.6172	1.80643	0.903217	−	0.429183i	$-0.141199\pi$
$457$	38.6172	1.80643	0.903217	+	0.429183i	$0.141199\pi$
$458$	−16.3328	−0.763181
$459$	−11.4636	−0.535076
$460$	−8.13729	−0.379403
$461$	25.5519	1.19007	0.595034	−	0.803700i	$-0.297138\pi$
$461$	25.5519	1.19007	0.595034	+	0.803700i	$0.297138\pi$
$462$	0	0
$463$	−1.41829	−0.0659133	−0.0329567	−	0.999457i	$-0.510492\pi$
$463$	−1.41829	−0.0659133	−0.0329567	+	0.999457i	$0.510492\pi$
$464$	3.46810	0.161002
$465$	24.3092	1.12731
$466$	−24.7766	−1.14775
$467$	6.11016	0.282745	0.141372	−	0.989957i	$-0.454849\pi$
$467$	6.11016	0.282745	0.141372	+	0.989957i	$0.454849\pi$
$468$	−6.58291	−0.304295
$469$	11.9910	0.553691
$470$	6.56903	0.303007
$471$	−1.65108	−0.0760778
$472$	−2.44920	−0.112733
$473$	0	0
$474$	9.45034	0.434068
$475$	−0.331209	−0.0151969
$476$	−2.39650	−0.109843
$477$	1.18975	0.0544748
$478$	4.61123	0.210913
$479$	0.621165	0.0283818	0.0141909	−	0.999899i	$-0.495483\pi$
$479$	0.621165	0.0283818	0.0141909	+	0.999899i	$0.495483\pi$
$480$	3.01340	0.137542
$481$	31.4026	1.43184
$482$	−5.69242	−0.259283
$483$	6.20924	0.282530
$484$	0	0
$485$	−5.53980	−0.251549
$486$	10.3807	0.470876
$487$	−16.6553	−0.754724	−0.377362	−	0.926066i	$-0.623169\pi$
$487$	−16.6553	−0.754724	−0.377362	+	0.926066i	$0.623169\pi$
$488$	−11.2620	−0.509808
$489$	12.6757	0.573215
$490$	−12.1051	−0.546854
$491$	−27.1774	−1.22650	−0.613250	−	0.789889i	$-0.710138\pi$
$491$	−27.1774	−1.22650	−0.613250	+	0.789889i	$0.710138\pi$
$492$	−3.33695	−0.150442
$493$	7.03012	0.316621
$494$	6.23946	0.280727
$495$	0	0
$496$	8.06702	0.362220
$497$	−0.686299	−0.0307847
$498$	24.8164	1.11205
$499$	8.42010	0.376935	0.188468	−	0.982079i	$-0.439648\pi$
$499$	8.42010	0.376935	0.188468	+	0.982079i	$0.439648\pi$
$500$	−11.5193	−0.515161
$501$	2.50493	0.111912
$502$	−16.2461	−0.725099
$503$	−6.89208	−0.307303	−0.153651	−	0.988125i	$-0.549103\pi$
$503$	−6.89208	−0.307303	−0.153651	+	0.988125i	$0.549103\pi$
$504$	1.24732	0.0555598
$505$	−25.1404	−1.11873
$506$	0	0
$507$	36.1637	1.60609
$508$	20.2074	0.896560
$509$	23.3753	1.03609	0.518045	−	0.855353i	$-0.326660\pi$
$509$	23.3753	1.03609	0.518045	+	0.855353i	$0.326660\pi$
$510$	6.10842	0.270485
$511$	−9.75856	−0.431693
$512$	1.00000	0.0441942
$513$	−5.65523	−0.249685
$514$	5.52563	0.243725
$515$	8.94728	0.394264
$516$	11.0969	0.488514
$517$	0	0
$518$	−5.95010	−0.261432
$519$	−10.3038	−0.452287
$520$	13.4819	0.591218
$521$	43.4304	1.90272	0.951360	−	0.308081i	$-0.0996867\pi$
$521$	43.4304	1.90272	0.951360	+	0.308081i	$0.0996867\pi$
$522$	−3.65900	−0.160150
$523$	−0.0561306	−0.00245442	−0.00122721	−	0.999999i	$-0.500391\pi$
$523$	−0.0561306	−0.00245442	−0.00122721	+	0.999999i	$0.500391\pi$
$524$	10.4556	0.456755
$525$	0.546088	0.0238332
$526$	−11.0066	−0.479910
$527$	16.3525	0.712327
$528$	0	0
$529$	−8.81743	−0.383367
$530$	−2.43662	−0.105840
$531$	2.58401	0.112136
$532$	−1.18224	−0.0512566
$533$	−14.9294	−0.646664
$534$	7.98926	0.345729
$535$	−29.3745	−1.26997
$536$	−10.1426	−0.438093
$537$	−26.8988	−1.16077
$538$	−3.75097	−0.161716
$539$	0	0
$540$	−12.2195	−0.525843
$541$	22.3692	0.961727	0.480864	−	0.876795i	$-0.340323\pi$
$541$	22.3692	0.961727	0.480864	+	0.876795i	$0.340323\pi$
$542$	−17.0697	−0.733205
$543$	11.8680	0.509306
$544$	2.02708	0.0869105
$545$	14.0878	0.603455
$546$	−10.2875	−0.440262
$547$	−1.29824	−0.0555088	−0.0277544	−	0.999615i	$-0.508836\pi$
$547$	−1.29824	−0.0555088	−0.0277544	+	0.999615i	$0.508836\pi$
$548$	−19.2139	−0.820779
$549$	11.8819	0.507108
$550$	0	0
$551$	3.46810	0.147746
$552$	−5.25209	−0.223544
$553$	−8.01121	−0.340671
$554$	13.5528	0.575803
$555$	15.1662	0.643768
$556$	14.9888	0.635665
$557$	−14.8615	−0.629702	−0.314851	−	0.949141i	$-0.601954\pi$
$557$	−14.8615	−0.629702	−0.314851	+	0.949141i	$0.601954\pi$
$558$	−8.51105	−0.360302
$559$	49.6472	2.09985
$560$	−2.55451	−0.107948
$561$	0	0
$562$	−24.3954	−1.02906
$563$	22.8559	0.963263	0.481632	−	0.876374i	$-0.340044\pi$
$563$	22.8559	0.963263	0.481632	+	0.876374i	$0.340044\pi$
$564$	4.23988	0.178531
$565$	−30.7272	−1.29270
$566$	−3.16656	−0.133100
$567$	5.58225	0.234432
$568$	0.580507	0.0243575
$569$	−29.3475	−1.23031	−0.615155	−	0.788406i	$-0.710907\pi$
$569$	−29.3475	−1.23031	−0.615155	+	0.788406i	$0.710907\pi$
$570$	3.01340	0.126218
$571$	−6.71091	−0.280843	−0.140421	−	0.990092i	$-0.544846\pi$
$571$	−6.71091	−0.280843	−0.140421	+	0.990092i	$0.544846\pi$
$572$	0	0
$573$	22.1197	0.924063
$574$	2.82879	0.118072
$575$	1.24732	0.0520170
$576$	−1.05504	−0.0439602
$577$	−45.2377	−1.88327	−0.941636	−	0.336633i	$-0.890712\pi$
$577$	−45.2377	−1.88327	−0.941636	+	0.336633i	$0.890712\pi$
$578$	−12.8909	−0.536192
$579$	−37.3321	−1.55147
$580$	7.49365	0.311157
$581$	−21.0373	−0.872775
$582$	−3.57558	−0.148213
$583$	0	0
$584$	8.25430	0.341565
$585$	−14.2239	−0.588088
$586$	20.2683	0.837277
$587$	12.4541	0.514036	0.257018	−	0.966407i	$-0.417260\pi$
$587$	12.4541	0.514036	0.257018	+	0.966407i	$0.417260\pi$
$588$	−7.81307	−0.322206
$589$	8.06702	0.332396
$590$	−5.29207	−0.217871
$591$	21.0577	0.866196
$592$	5.03290	0.206851
$593$	33.2780	1.36656	0.683281	−	0.730156i	$-0.260552\pi$
$593$	33.2780	1.36656	0.683281	+	0.730156i	$0.260552\pi$
$594$	0	0
$595$	−5.17821	−0.212286
$596$	−8.18651	−0.335333
$597$	34.0949	1.39541
$598$	−23.4977	−0.960891
$599$	12.7626	0.521467	0.260733	−	0.965411i	$-0.416036\pi$
$599$	12.7626	0.521467	0.260733	+	0.965411i	$0.416036\pi$
$600$	−0.461910	−0.0188574
$601$	34.4565	1.40551	0.702755	−	0.711432i	$-0.251953\pi$
$601$	34.4565	1.40551	0.702755	+	0.711432i	$0.251953\pi$
$602$	−9.40704	−0.383402
$603$	10.7009	0.435773
$604$	0.261159	0.0106264
$605$	0	0
$606$	−16.2265	−0.659156
$607$	−1.62970	−0.0661476	−0.0330738	−	0.999453i	$-0.510530\pi$
$607$	−1.62970	−0.0661476	−0.0330738	+	0.999453i	$0.510530\pi$
$608$	1.00000	0.0405554
$609$	−5.71810	−0.231709
$610$	−24.3343	−0.985266
$611$	18.9691	0.767407
$612$	−2.13866	−0.0864503
$613$	4.99806	0.201870	0.100935	−	0.994893i	$-0.467817\pi$
$613$	4.99806	0.201870	0.100935	+	0.994893i	$0.467817\pi$
$614$	−10.0817	−0.406866
$615$	−7.21029	−0.290747
$616$	0	0
$617$	16.1786	0.651326	0.325663	−	0.945486i	$-0.394413\pi$
$617$	16.1786	0.651326	0.325663	+	0.945486i	$0.394413\pi$
$618$	5.77489	0.232300
$619$	−2.68531	−0.107932	−0.0539658	−	0.998543i	$-0.517186\pi$
$619$	−2.68531	−0.107932	−0.0539658	+	0.998543i	$0.517186\pi$
$620$	17.4307	0.700034
$621$	21.2975	0.854638
$622$	16.8796	0.676811
$623$	−6.77263	−0.271340
$624$	8.70166	0.348345
$625$	−23.2343	−0.929370
$626$	−29.9792	−1.19821
$627$	0	0
$628$	−1.18390	−0.0472426
$629$	10.2021	0.406785
$630$	2.69512	0.107376
$631$	−5.38132	−0.214227	−0.107113	−	0.994247i	$-0.534161\pi$
$631$	−5.38132	−0.214227	−0.107113	+	0.994247i	$0.534161\pi$
$632$	6.77630	0.269547
$633$	−13.1777	−0.523768
$634$	10.1843	0.404472
$635$	43.6630	1.73271
$636$	−1.57268	−0.0623607
$637$	−34.9554	−1.38498
$638$	0	0
$639$	−0.612461	−0.0242286
$640$	2.16074	0.0854107
$641$	−32.6228	−1.28852	−0.644262	−	0.764804i	$-0.722836\pi$
$641$	−32.6228	−1.28852	−0.644262	+	0.764804i	$0.722836\pi$
$642$	−18.9594	−0.748266
$643$	−3.88913	−0.153372	−0.0766862	−	0.997055i	$-0.524434\pi$
$643$	−3.88913	−0.153372	−0.0766862	+	0.997055i	$0.524434\pi$
$644$	4.45229	0.175445
$645$	23.9775	0.944114
$646$	2.02708	0.0797545
$647$	−38.7682	−1.52413	−0.762067	−	0.647498i	$-0.775815\pi$
$647$	−38.7682	−1.52413	−0.762067	+	0.647498i	$0.775815\pi$
$648$	−4.72175	−0.185488
$649$	0	0
$650$	−2.06657	−0.0810574
$651$	−13.3007	−0.521294
$652$	9.08903	0.355954
$653$	39.7875	1.55700	0.778502	−	0.627642i	$-0.215980\pi$
$653$	39.7875	1.55700	0.778502	+	0.627642i	$0.215980\pi$
$654$	9.09276	0.355555
$655$	22.5918	0.882735
$656$	−2.39274	−0.0934208
$657$	−8.70864	−0.339757
$658$	−3.59422	−0.140117
$659$	5.39549	0.210178	0.105089	−	0.994463i	$-0.466487\pi$
$659$	5.39549	0.210178	0.105089	+	0.994463i	$0.466487\pi$
$660$	0	0
$661$	−33.5994	−1.30686	−0.653432	−	0.756985i	$-0.726672\pi$
$661$	−33.5994	−1.30686	−0.653432	+	0.756985i	$0.726672\pi$
$662$	−8.83120	−0.343234
$663$	17.6390	0.685042
$664$	17.7944	0.690558
$665$	−2.55451	−0.0990597
$666$	−5.30993	−0.205756
$667$	−13.0608	−0.505715
$668$	1.79614	0.0694948
$669$	−32.8995	−1.27197
$670$	−21.9155	−0.846668
$671$	0	0
$672$	−1.64877	−0.0636028
$673$	−27.7575	−1.06997	−0.534987	−	0.844860i	$-0.679683\pi$
$673$	−27.7575	−1.06997	−0.534987	+	0.844860i	$0.679683\pi$
$674$	−31.8303	−1.22606
$675$	1.87306	0.0720942
$676$	25.9309	0.997343
$677$	18.6322	0.716093	0.358047	−	0.933704i	$-0.383443\pi$
$677$	18.6322	0.716093	0.358047	+	0.933704i	$0.383443\pi$
$678$	−19.8324	−0.761660
$679$	3.03108	0.116322
$680$	4.38000	0.167965
$681$	2.96207	0.113507
$682$	0	0
$683$	4.43166	0.169573	0.0847864	−	0.996399i	$-0.472979\pi$
$683$	4.43166	0.169573	0.0847864	+	0.996399i	$0.472979\pi$
$684$	−1.05504	−0.0403406
$685$	−41.5163	−1.58626
$686$	14.8990	0.568845
$687$	−22.7780	−0.869034
$688$	7.95696	0.303356
$689$	−7.03610	−0.268054
$690$	−11.3484	−0.432026
$691$	36.6769	1.39526	0.697628	−	0.716460i	$-0.254239\pi$
$691$	36.6769	1.39526	0.697628	+	0.716460i	$0.254239\pi$
$692$	−7.38827	−0.280860
$693$	0	0
$694$	−17.3285	−0.657781
$695$	32.3868	1.22850
$696$	4.83667	0.183333
$697$	−4.85028	−0.183717
$698$	5.21745	0.197484
$699$	−34.5538	−1.30694
$700$	0.391569	0.0147999
$701$	−15.5389	−0.586895	−0.293447	−	0.955975i	$-0.594803\pi$
$701$	−15.5389	−0.586895	−0.293447	+	0.955975i	$0.594803\pi$
$702$	−35.2856	−1.33177
$703$	5.03290	0.189820
$704$	0	0
$705$	9.16128	0.345034
$706$	2.70039	0.101630
$707$	13.7555	0.517328
$708$	−3.41569	−0.128370
$709$	8.51397	0.319749	0.159874	−	0.987137i	$-0.448891\pi$
$709$	8.51397	0.319749	0.159874	+	0.987137i	$0.448891\pi$
$710$	1.25432	0.0470740
$711$	−7.14929	−0.268119
$712$	5.72864	0.214690
$713$	−30.3802	−1.13775
$714$	−3.34220	−0.125079
$715$	0	0
$716$	−19.2876	−0.720810
$717$	6.43090	0.240166
$718$	11.7526	0.438602
$719$	−15.7039	−0.585655	−0.292827	−	0.956165i	$-0.594596\pi$
$719$	−15.7039	−0.585655	−0.292827	+	0.956165i	$0.594596\pi$
$720$	−2.27967	−0.0849584
$721$	−4.89547	−0.182317
$722$	1.00000	0.0372161
$723$	−7.93875	−0.295245
$724$	8.50988	0.316267
$725$	−1.14867	−0.0426603
$726$	0	0
$727$	49.5195	1.83658	0.918288	−	0.395912i	$-0.129572\pi$
$727$	49.5195	1.83658	0.918288	+	0.395912i	$0.129572\pi$
$728$	−7.37655	−0.273393
$729$	28.6423	1.06083
$730$	17.8354	0.660117
$731$	16.1294	0.596568
$732$	−15.7062	−0.580518
$733$	−1.82378	−0.0673630	−0.0336815	−	0.999433i	$-0.510723\pi$
$733$	−1.82378	−0.0673630	−0.0336815	+	0.999433i	$0.510723\pi$
$734$	−28.1891	−1.04048
$735$	−16.8820	−0.622702
$736$	−3.76597	−0.138816
$737$	0	0
$738$	2.52444	0.0929261
$739$	−9.60574	−0.353353	−0.176676	−	0.984269i	$-0.556535\pi$
$739$	−9.60574	−0.353353	−0.176676	+	0.984269i	$0.556535\pi$
$740$	10.8748	0.399765
$741$	8.70166	0.319664
$742$	1.33319	0.0489428
$743$	−13.7575	−0.504712	−0.252356	−	0.967634i	$-0.581205\pi$
$743$	−13.7575	−0.504712	−0.252356	+	0.967634i	$0.581205\pi$
$744$	11.2504	0.412460
$745$	−17.6889	−0.648072
$746$	−21.5226	−0.788000
$747$	−18.7739	−0.686902
$748$	0	0
$749$	16.0722	0.587264
$750$	−16.0651	−0.586614
$751$	−31.3642	−1.14450	−0.572249	−	0.820080i	$-0.693929\pi$
$751$	−31.3642	−1.14450	−0.572249	+	0.820080i	$0.693929\pi$
$752$	3.04018	0.110864
$753$	−22.6571	−0.825670
$754$	21.6391	0.788049
$755$	0.564296	0.0205368
$756$	6.68584	0.243162
$757$	−35.9049	−1.30499	−0.652493	−	0.757795i	$-0.726277\pi$
$757$	−35.9049	−1.30499	−0.652493	+	0.757795i	$0.726277\pi$
$758$	19.0705	0.692671
$759$	0	0
$760$	2.16074	0.0783782
$761$	7.11655	0.257975	0.128987	−	0.991646i	$-0.458827\pi$
$761$	7.11655	0.257975	0.128987	+	0.991646i	$0.458827\pi$
$762$	28.1816	1.02091
$763$	−7.70809	−0.279052
$764$	15.8608	0.573822
$765$	−4.62109	−0.167076
$766$	32.4721	1.17326
$767$	−15.2817	−0.551789
$768$	1.39462	0.0503239
$769$	50.1561	1.80868	0.904338	−	0.426818i	$-0.140365\pi$
$769$	50.1561	1.80868	0.904338	+	0.426818i	$0.140365\pi$
$770$	0	0
$771$	7.70614	0.277530
$772$	−26.7687	−0.963427
$773$	−7.58162	−0.272692	−0.136346	−	0.990661i	$-0.543536\pi$
$773$	−7.58162	−0.272692	−0.136346	+	0.990661i	$0.543536\pi$
$774$	−8.39494	−0.301750
$775$	−2.67187	−0.0959763
$776$	−2.56385	−0.0920367
$777$	−8.29811	−0.297693
$778$	−2.68971	−0.0964307
$779$	−2.39274	−0.0857288
$780$	18.8020	0.673220
$781$	0	0
$782$	−7.63394	−0.272989
$783$	−19.6129	−0.700908
$784$	−5.60231	−0.200082
$785$	−2.55809	−0.0913021
$786$	14.5815	0.520107
$787$	25.7413	0.917579	0.458789	−	0.888545i	$-0.348283\pi$
$787$	25.7413	0.917579	0.458789	+	0.888545i	$0.348283\pi$
$788$	15.0992	0.537888
$789$	−15.3500	−0.546473
$790$	14.6418	0.520932
$791$	16.8123	0.597776
$792$	0	0
$793$	−70.2690	−2.49532
$794$	4.73678	0.168102
$795$	−3.39814	−0.120520
$796$	24.4475	0.866518
$797$	0.211650	0.00749702	0.00374851	−	0.999993i	$-0.498807\pi$
$797$	0.211650	0.00749702	0.00374851	+	0.999993i	$0.498807\pi$
$798$	−1.64877	−0.0583659
$799$	6.16269	0.218020
$800$	−0.331209	−0.0117100
$801$	−6.04397	−0.213553
$802$	−6.22912	−0.219958
$803$	0	0
$804$	−14.1450	−0.498856
$805$	9.62023	0.339069
$806$	50.3339	1.77293
$807$	−5.23116	−0.184146
$808$	−11.6351	−0.409321
$809$	−2.84303	−0.0999557	−0.0499778	−	0.998750i	$-0.515915\pi$
$809$	−2.84303	−0.0999557	−0.0499778	+	0.998750i	$0.515915\pi$
$810$	−10.2025	−0.358478
$811$	32.9416	1.15674	0.578369	−	0.815775i	$-0.303689\pi$
$811$	32.9416	1.15674	0.578369	+	0.815775i	$0.303689\pi$
$812$	−4.10013	−0.143886
$813$	−23.8056	−0.834900
$814$	0	0
$815$	19.6390	0.687924
$816$	2.82700	0.0989649
$817$	7.95696	0.278379
$818$	1.72220	0.0602154
$819$	7.78258	0.271945
$820$	−5.17008	−0.180547
$821$	13.2751	0.463304	0.231652	−	0.972799i	$-0.425587\pi$
$821$	13.2751	0.463304	0.231652	+	0.972799i	$0.425587\pi$
$822$	−26.7961	−0.934621
$823$	−27.2090	−0.948445	−0.474223	−	0.880405i	$-0.657271\pi$
$823$	−27.2090	−0.948445	−0.474223	+	0.880405i	$0.657271\pi$
$824$	4.14084	0.144253
$825$	0	0
$826$	2.89554	0.100749
$827$	−38.8917	−1.35240	−0.676198	−	0.736720i	$-0.736374\pi$
$827$	−38.8917	−1.35240	−0.676198	+	0.736720i	$0.736374\pi$
$828$	3.97327	0.138081
$829$	16.1425	0.560654	0.280327	−	0.959905i	$-0.409557\pi$
$829$	16.1425	0.560654	0.280327	+	0.959905i	$0.409557\pi$
$830$	38.4491	1.33459
$831$	18.9009	0.655666
$832$	6.23946	0.216314
$833$	−11.3563	−0.393474
$834$	20.9036	0.723831
$835$	3.88099	0.134307
$836$	0	0
$837$	−45.6208	−1.57689
$838$	−17.0528	−0.589078
$839$	45.8248	1.58205	0.791024	−	0.611785i	$-0.209548\pi$
$839$	45.8248	1.58205	0.791024	+	0.611785i	$0.209548\pi$
$840$	−3.56257	−0.122920
$841$	−16.9723	−0.585252
$842$	−28.7423	−0.990526
$843$	−34.0223	−1.17179
$844$	−9.44900	−0.325248
$845$	56.0299	1.92749
$846$	−3.20752	−0.110277
$847$	0	0
$848$	−1.12768	−0.0387246
$849$	−4.41614	−0.151561
$850$	−0.671388	−0.0230284
$851$	−18.9538	−0.649728
$852$	0.809585	0.0277359
$853$	46.8011	1.60244	0.801219	−	0.598371i	$-0.204185\pi$
$853$	46.8011	1.60244	0.801219	+	0.598371i	$0.204185\pi$
$854$	13.3144	0.455610
$855$	−2.27967	−0.0779632
$856$	−13.5947	−0.464656
$857$	−46.6226	−1.59260	−0.796299	−	0.604903i	$-0.793212\pi$
$857$	−46.6226	−1.59260	−0.796299	+	0.604903i	$0.793212\pi$
$858$	0	0
$859$	−47.2699	−1.61283	−0.806415	−	0.591351i	$-0.798595\pi$
$859$	−47.2699	−1.61283	−0.806415	+	0.591351i	$0.798595\pi$
$860$	17.1929	0.586273
$861$	3.94508	0.134448
$862$	−40.2106	−1.36958
$863$	20.2365	0.688858	0.344429	−	0.938812i	$-0.388073\pi$
$863$	20.2365	0.688858	0.344429	+	0.938812i	$0.388073\pi$
$864$	−5.65523	−0.192395
$865$	−15.9641	−0.542796
$866$	0.204074	0.00693473
$867$	−17.9779	−0.610562
$868$	−9.53715	−0.323712
$869$	0	0
$870$	10.4508	0.354314
$871$	−63.2843	−2.14431
$872$	6.51990	0.220792
$873$	2.70497	0.0915493
$874$	−3.76597	−0.127386
$875$	13.6186	0.460394
$876$	11.5116	0.388940
$877$	−24.8663	−0.839676	−0.419838	−	0.907599i	$-0.637913\pi$
$877$	−24.8663	−0.839676	−0.419838	+	0.907599i	$0.637913\pi$
$878$	−0.940938	−0.0317551
$879$	28.2666	0.953407
$880$	0	0
$881$	3.56840	0.120222	0.0601112	−	0.998192i	$-0.480854\pi$
$881$	3.56840	0.120222	0.0601112	+	0.998192i	$0.480854\pi$
$882$	5.91068	0.199023
$883$	23.0603	0.776041	0.388020	−	0.921651i	$-0.373159\pi$
$883$	23.0603	0.776041	0.388020	+	0.921651i	$0.373159\pi$
$884$	12.6479	0.425395
$885$	−7.38041	−0.248090
$886$	3.10542	0.104329
$887$	−45.5236	−1.52853	−0.764267	−	0.644900i	$-0.776899\pi$
$887$	−45.5236	−1.52853	−0.764267	+	0.644900i	$0.776899\pi$
$888$	7.01897	0.235541
$889$	−23.8901	−0.801247
$890$	12.3781	0.414915
$891$	0	0
$892$	−23.5903	−0.789863
$893$	3.04018	0.101736
$894$	−11.4170	−0.381843
$895$	−41.6754	−1.39305
$896$	−1.18224	−0.0394959
$897$	−32.7702	−1.09417
$898$	−23.2360	−0.775397
$899$	27.9772	0.933092
$900$	0.349440	0.0116480
$901$	−2.28589	−0.0761542
$902$	0	0
$903$	−13.1192	−0.436580
$904$	−14.2207	−0.472973
$905$	18.3876	0.611226
$906$	0.364217	0.0121003
$907$	59.0551	1.96089	0.980445	−	0.196791i	$-0.0630520\pi$
$907$	59.0551	1.96089	0.980445	+	0.196791i	$0.0630520\pi$
$908$	2.12393	0.0704850
$909$	12.2755	0.407153
$910$	−15.9388	−0.528366
$911$	−22.3726	−0.741238	−0.370619	−	0.928785i	$-0.620854\pi$
$911$	−22.3726	−0.741238	−0.370619	+	0.928785i	$0.620854\pi$
$912$	1.39462	0.0461804
$913$	0	0
$914$	38.6172	1.27734
$915$	−33.9370	−1.12192
$916$	−16.3328	−0.539651
$917$	−12.3610	−0.408197
$918$	−11.4636	−0.378356
$919$	−26.8031	−0.884153	−0.442076	−	0.896977i	$-0.645758\pi$
$919$	−26.8031	−0.884153	−0.442076	+	0.896977i	$0.645758\pi$
$920$	−8.13729	−0.268278
$921$	−14.0602	−0.463298
$922$	25.5519	0.841506
$923$	3.62205	0.119221
$924$	0	0
$925$	−1.66694	−0.0548087
$926$	−1.41829	−0.0466078
$927$	−4.36877	−0.143489
$928$	3.46810	0.113846
$929$	31.9476	1.04817	0.524084	−	0.851667i	$-0.324408\pi$
$929$	31.9476	1.04817	0.524084	+	0.851667i	$0.324408\pi$
$930$	24.3092	0.797129
$931$	−5.60231	−0.183608
$932$	−24.7766	−0.811583
$933$	23.5406	0.770685
$934$	6.11016	0.199931
$935$	0	0
$936$	−6.58291	−0.215169
$937$	39.4592	1.28908	0.644539	−	0.764572i	$-0.277049\pi$
$937$	39.4592	1.28908	0.644539	+	0.764572i	$0.277049\pi$
$938$	11.9910	0.391519
$939$	−41.8096	−1.36440
$940$	6.56903	0.214258
$941$	−41.0613	−1.33856	−0.669279	−	0.743011i	$-0.733397\pi$
$941$	−41.0613	−1.33856	−0.669279	+	0.743011i	$0.733397\pi$
$942$	−1.65108	−0.0537951
$943$	9.01099	0.293438
$944$	−2.44920	−0.0797145
$945$	14.4464	0.469940
$946$	0	0
$947$	−34.2393	−1.11263	−0.556314	−	0.830972i	$-0.687785\pi$
$947$	−34.2393	−1.11263	−0.556314	+	0.830972i	$0.687785\pi$
$948$	9.45034	0.306933
$949$	51.5024	1.67184
$950$	−0.331209	−0.0107458
$951$	14.2033	0.460572
$952$	−2.39650	−0.0776710
$953$	−34.4980	−1.11750	−0.558750	−	0.829336i	$-0.688719\pi$
$953$	−34.4980	−1.11750	−0.558750	+	0.829336i	$0.688719\pi$
$954$	1.18975	0.0385195
$955$	34.2710	1.10898
$956$	4.61123	0.149138
$957$	0	0
$958$	0.621165	0.0200689
$959$	22.7155	0.733521
$960$	3.01340	0.0972571
$961$	34.0767	1.09925
$962$	31.4026	1.01246
$963$	14.3430	0.462196
$964$	−5.69242	−0.183341
$965$	−57.8402	−1.86194
$966$	6.20924	0.199779
$967$	2.27993	0.0733178	0.0366589	−	0.999328i	$-0.488329\pi$
$967$	2.27993	0.0733178	0.0366589	+	0.999328i	$0.488329\pi$
$968$	0	0
$969$	2.82700	0.0908165
$970$	−5.53980	−0.177872
$971$	−13.0120	−0.417575	−0.208787	−	0.977961i	$-0.566952\pi$
$971$	−13.0120	−0.417575	−0.208787	+	0.977961i	$0.566952\pi$
$972$	10.3807	0.332960
$973$	−17.7203	−0.568087
$974$	−16.6553	−0.533670
$975$	−2.88207	−0.0923000
$976$	−11.2620	−0.360488
$977$	−5.79378	−0.185360	−0.0926798	−	0.995696i	$-0.529543\pi$
$977$	−5.79378	−0.185360	−0.0926798	+	0.995696i	$0.529543\pi$
$978$	12.6757	0.405324
$979$	0	0
$980$	−12.1051	−0.386684
$981$	−6.87878	−0.219623
$982$	−27.1774	−0.867266
$983$	46.1749	1.47275	0.736376	−	0.676573i	$-0.236536\pi$
$983$	46.1749	1.47275	0.736376	+	0.676573i	$0.236536\pi$
$984$	−3.33695	−0.106378
$985$	32.6255	1.03954
$986$	7.03012	0.223885
$987$	−5.01256	−0.159552
$988$	6.23946	0.198504
$989$	−29.9657	−0.952854
$990$	0	0
$991$	−42.7945	−1.35941	−0.679706	−	0.733485i	$-0.737892\pi$
$991$	−42.7945	−1.35941	−0.679706	+	0.733485i	$0.737892\pi$
$992$	8.06702	0.256128
$993$	−12.3161	−0.390841
$994$	−0.686299	−0.0217681
$995$	52.8246	1.67465
$996$	24.8164	0.786339
$997$	−36.5536	−1.15766	−0.578832	−	0.815447i	$-0.696491\pi$
$997$	−36.5536	−1.15766	−0.578832	+	0.815447i	$0.696491\pi$
$998$	8.42010	0.266534
$999$	−28.4622	−0.900505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.cd.1.7		10
11.2	odd	10		418.2.f.h.191.4	✓	20
11.6	odd	10		418.2.f.h.267.4	yes	20
11.10	odd	2		4598.2.a.cc.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.191.4	✓	20	11.2	odd	10
418.2.f.h.267.4	yes	20	11.6	odd	10
4598.2.a.cc.1.7		10	11.10	odd	2
4598.2.a.cd.1.7		10	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.39462 q^{3} +1.00000 q^{4} +2.16074 q^{5} +1.39462 q^{6} -1.18224 q^{7} +1.00000 q^{8} -1.05504 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.39462 q^{3} +1.00000 q^{4} +2.16074 q^{5} +1.39462 q^{6} -1.18224 q^{7} +1.00000 q^{8} -1.05504 q^{9} +2.16074 q^{10} +1.39462 q^{12} +6.23946 q^{13} -1.18224 q^{14} +3.01340 q^{15} +1.00000 q^{16} +2.02708 q^{17} -1.05504 q^{18} +1.00000 q^{19} +2.16074 q^{20} -1.64877 q^{21} -3.76597 q^{23} +1.39462 q^{24} -0.331209 q^{25} +6.23946 q^{26} -5.65523 q^{27} -1.18224 q^{28} +3.46810 q^{29} +3.01340 q^{30} +8.06702 q^{31} +1.00000 q^{32} +2.02708 q^{34} -2.55451 q^{35} -1.05504 q^{36} +5.03290 q^{37} +1.00000 q^{38} +8.70166 q^{39} +2.16074 q^{40} -2.39274 q^{41} -1.64877 q^{42} +7.95696 q^{43} -2.27967 q^{45} -3.76597 q^{46} +3.04018 q^{47} +1.39462 q^{48} -5.60231 q^{49} -0.331209 q^{50} +2.82700 q^{51} +6.23946 q^{52} -1.12768 q^{53} -5.65523 q^{54} -1.18224 q^{56} +1.39462 q^{57} +3.46810 q^{58} -2.44920 q^{59} +3.01340 q^{60} -11.2620 q^{61} +8.06702 q^{62} +1.24732 q^{63} +1.00000 q^{64} +13.4819 q^{65} -10.1426 q^{67} +2.02708 q^{68} -5.25209 q^{69} -2.55451 q^{70} +0.580507 q^{71} -1.05504 q^{72} +8.25430 q^{73} +5.03290 q^{74} -0.461910 q^{75} +1.00000 q^{76} +8.70166 q^{78} +6.77630 q^{79} +2.16074 q^{80} -4.72175 q^{81} -2.39274 q^{82} +17.7944 q^{83} -1.64877 q^{84} +4.38000 q^{85} +7.95696 q^{86} +4.83667 q^{87} +5.72864 q^{89} -2.27967 q^{90} -7.37655 q^{91} -3.76597 q^{92} +11.2504 q^{93} +3.04018 q^{94} +2.16074 q^{95} +1.39462 q^{96} -2.56385 q^{97} -5.60231 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9} - 3 q^{10} + 2 q^{12} + 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} + 12 q^{17} + 12 q^{18} + 10 q^{19} - 3 q^{20} - q^{21} + 14 q^{23} + 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} + 11 q^{28} + 16 q^{29} + q^{30} + 12 q^{31} + 10 q^{32} + 12 q^{34} - 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} + 11 q^{39} - 3 q^{40} - 5 q^{41} - q^{42} + 22 q^{43} - 2 q^{45} + 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} + 5 q^{50} + 8 q^{51} + 11 q^{52} + 2 q^{53} + 2 q^{54} + 11 q^{56} + 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} + 35 q^{61} + 12 q^{62} + 38 q^{63} + 10 q^{64} + 4 q^{65} + 9 q^{67} + 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 5 q^{73} - q^{74} - 15 q^{75} + 10 q^{76} + 11 q^{78} + 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} + 7 q^{83} - q^{84} + 35 q^{85} + 22 q^{86} + 8 q^{87} + 22 q^{89} - 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} + 8 q^{94} - 3 q^{95} + 2 q^{96} + 32 q^{97} - 3 q^{98}+O(q^{100}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9 - 3 * q^10 + 2 * q^12 + 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 + 12 * q^17 + 12 * q^18 + 10 * q^19 - 3 * q^20 - q^21 + 14 * q^23 + 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 + 11 * q^28 + 16 * q^29 + q^30 + 12 * q^31 + 10 * q^32 + 12 * q^34 - 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 + 11 * q^39 - 3 * q^40 - 5 * q^41 - q^42 + 22 * q^43 - 2 * q^45 + 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 + 5 * q^50 + 8 * q^51 + 11 * q^52 + 2 * q^53 + 2 * q^54 + 11 * q^56 + 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 + 35 * q^61 + 12 * q^62 + 38 * q^63 + 10 * q^64 + 4 * q^65 + 9 * q^67 + 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 5 * q^73 - q^74 - 15 * q^75 + 10 * q^76 + 11 * q^78 + 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 + 7 * q^83 - q^84 + 35 * q^85 + 22 * q^86 + 8 * q^87 + 22 * q^89 - 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 + 32 * q^97 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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