LMFDB - Embedded newform 20.5.d.c.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,5,Mod(19,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("20.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	20.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$2.06739926168$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1816805376000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 31x^{4} + 96x^{2} + 256 $ x^8 + 6x^6 + 31x^4 + 96*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$-1.42849 + 1.39980i$ of defining polynomial
Character	$\chi$	$=$	20.19
Dual form			20.5.d.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.85697 + 2.79959i) q^{2} -6.64118 q^{3} +(0.324555 - 15.9967i) q^{4} +(-17.6491 - 17.7062i) q^{5} +(18.9737 - 18.5926i) q^{6} -39.0703 q^{7} +(43.8570 + 46.6107i) q^{8} -36.8947 q^{9} +O(q^{10})$	\(q+(-2.85697 + 2.79959i) q^{2} -6.64118 q^{3} +(0.324555 - 15.9967i) q^{4} +(-17.6491 - 17.7062i) q^{5} +(18.9737 - 18.5926i) q^{6} -39.0703 q^{7} +(43.8570 + 46.6107i) q^{8} -36.8947 q^{9} +(99.9931 + 1.17570i) q^{10} +138.357i q^{11} +(-2.15543 + 106.237i) q^{12} -124.999i q^{13} +(111.623 - 109.381i) q^{14} +(117.211 + 117.590i) q^{15} +(-255.789 - 10.3836i) q^{16} +160.412i q^{17} +(105.407 - 103.290i) q^{18} -650.252i q^{19} +(-288.969 + 276.581i) q^{20} +259.473 q^{21} +(-387.344 - 395.283i) q^{22} -416.491 q^{23} +(-291.263 - 309.551i) q^{24} +(-2.01779 + 624.997i) q^{25} +(349.947 + 357.119i) q^{26} +782.960 q^{27} +(-12.6805 + 624.997i) q^{28} +236.807 q^{29} +(-664.073 - 7.80805i) q^{30} -41.5345i q^{31} +(759.852 - 686.440i) q^{32} -918.856i q^{33} +(-449.088 - 458.291i) q^{34} +(689.557 + 691.786i) q^{35} +(-11.9744 + 590.193i) q^{36} -206.138i q^{37} +(1820.44 + 1857.75i) q^{38} +830.144i q^{39} +(51.2606 - 1599.18i) q^{40} -1816.56 q^{41} +(-741.307 + 726.420i) q^{42} -3162.64 q^{43} +(2213.26 + 44.9046i) q^{44} +(651.158 + 653.264i) q^{45} +(1189.90 - 1166.01i) q^{46} -823.584 q^{47} +(1698.74 + 68.9596i) q^{48} -874.509 q^{49} +(-1743.97 - 1791.25i) q^{50} -1065.32i q^{51} +(-1999.58 - 40.5692i) q^{52} -4866.53i q^{53} +(-2236.89 + 2191.97i) q^{54} +(2449.78 - 2441.88i) q^{55} +(-1713.51 - 1821.10i) q^{56} +4318.44i q^{57} +(-676.551 + 662.964i) q^{58} +3638.55i q^{59} +(1919.09 - 1836.83i) q^{60} +4136.07 q^{61} +(116.280 + 118.663i) q^{62} +1441.49 q^{63} +(-249.122 + 4088.42i) q^{64} +(-2213.26 + 2206.13i) q^{65} +(2572.42 + 2625.15i) q^{66} +3208.70 q^{67} +(2566.06 + 52.0625i) q^{68} +2766.00 q^{69} +(-3906.76 - 45.9350i) q^{70} -456.333i q^{71} +(-1618.09 - 1719.69i) q^{72} +5905.66i q^{73} +(577.102 + 588.929i) q^{74} +(13.4005 - 4150.72i) q^{75} +(-10401.9 - 211.043i) q^{76} -5405.67i q^{77} +(-2324.06 - 2371.70i) q^{78} -2808.68i q^{79} +(4330.60 + 4712.31i) q^{80} -2211.32 q^{81} +(5189.86 - 5085.63i) q^{82} -3048.15 q^{83} +(84.2134 - 4150.72i) q^{84} +(2840.28 - 2831.12i) q^{85} +(9035.57 - 8854.10i) q^{86} -1572.68 q^{87} +(-6448.94 + 6067.94i) q^{88} -5143.40 q^{89} +(-3689.21 - 43.3771i) q^{90} +4883.77i q^{91} +(-135.174 + 6662.49i) q^{92} +275.839i q^{93} +(2352.96 - 2305.70i) q^{94} +(-11513.5 + 11476.4i) q^{95} +(-5046.32 + 4558.78i) q^{96} -4506.56i q^{97} +(2498.45 - 2448.27i) q^{98} -5104.65i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 48 q^{4} - 40 q^{5} + 312 q^{9}+O(q^{10}) $ 8 * q - 48 * q^4 - 40 * q^5 + 312 * q^9	$ 8 q - 48 q^{4} - 40 q^{5} + 312 q^{9} - 160 q^{10} + 640 q^{14} - 832 q^{16} - 400 q^{20} - 960 q^{21} + 1920 q^{24} - 2040 q^{25} + 2496 q^{26} + 2704 q^{29} - 1920 q^{30} - 2176 q^{34} - 5712 q^{36} + 6400 q^{40} + 1456 q^{41} + 1920 q^{44} + 6120 q^{45} + 7040 q^{46} - 8008 q^{49} - 12480 q^{50} - 11520 q^{54} - 14720 q^{56} + 21120 q^{60} + 6576 q^{61} + 6912 q^{64} - 1920 q^{65} + 46080 q^{66} - 12480 q^{69} - 6400 q^{70} - 23616 q^{74} - 48000 q^{76} + 19520 q^{80} - 19512 q^{81} + 24960 q^{84} + 8960 q^{85} + 37120 q^{86} + 27664 q^{89} - 48480 q^{90} + 10880 q^{94} - 76800 q^{96}+O(q^{100}) $ 8 * q - 48 * q^4 - 40 * q^5 + 312 * q^9 - 160 * q^10 + 640 * q^14 - 832 * q^16 - 400 * q^20 - 960 * q^21 + 1920 * q^24 - 2040 * q^25 + 2496 * q^26 + 2704 * q^29 - 1920 * q^30 - 2176 * q^34 - 5712 * q^36 + 6400 * q^40 + 1456 * q^41 + 1920 * q^44 + 6120 * q^45 + 7040 * q^46 - 8008 * q^49 - 12480 * q^50 - 11520 * q^54 - 14720 * q^56 + 21120 * q^60 + 6576 * q^61 + 6912 * q^64 - 1920 * q^65 + 46080 * q^66 - 12480 * q^69 - 6400 * q^70 - 23616 * q^74 - 48000 * q^76 + 19520 * q^80 - 19512 * q^81 + 24960 * q^84 + 8960 * q^85 + 37120 * q^86 + 27664 * q^89 - 48480 * q^90 + 10880 * q^94 - 76800 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.85697	+	2.79959i	−0.714243	+	0.699898i
$2$	−2.85697	+	2.79959i	−0.714243	+	0.699898i
$3$	−6.64118			−0.737909			−0.368955	−	0.929447i	$-0.620284\pi$
$3$	−6.64118			−0.737909			−0.368955	+	0.929447i	$0.620284\pi$
$4$	0.324555	−	15.9967i	0.0202847	−	0.999794i
$5$	−17.6491	−	17.7062i	−0.705964	−	0.708247i
$5$	−17.6491	−	17.7062i	−0.705964	−	0.708247i
$6$	18.9737	−	18.5926i	0.527046	−	0.516462i
$7$	−39.0703			−0.797354			−0.398677	−	0.917091i	$-0.630531\pi$
$7$	−39.0703			−0.797354			−0.398677	+	0.917091i	$0.630531\pi$
$8$	43.8570	+	46.6107i	0.685266	+	0.728293i
$9$	−36.8947			−0.455490
$10$	99.9931	+	1.17570i	0.999931	+	0.0117570i
$11$			138.357i			1.14345i	0.820446	+	0.571724i	$0.193725\pi$
$11$			138.357i			1.14345i	−0.820446	+	0.571724i	$0.806275\pi$
$12$	−2.15543	+	106.237i	−0.0149683	+	0.737758i
$13$		−	124.999i		−	0.739641i	−0.929103	−	0.369821i	$-0.879419\pi$
$13$		−	124.999i		−	0.739641i	0.929103	−	0.369821i	$-0.120581\pi$
$14$	111.623	−	109.381i	0.569504	−	0.558067i
$15$	117.211	+	117.590i	0.520938	+	0.522622i
$16$	−255.789	−	10.3836i	−0.999177	−	0.0405611i
$17$			160.412i			0.555058i	0.960717	+	0.277529i	$0.0895154\pi$
$17$			160.412i			0.555058i	−0.960717	+	0.277529i	$0.910485\pi$
$18$	105.407	−	103.290i	0.325330	−	0.318796i
$19$		−	650.252i		−	1.80125i	−0.434595	−	0.900626i	$-0.643108\pi$
$19$		−	650.252i		−	1.80125i	0.434595	−	0.900626i	$-0.356892\pi$
$20$	−288.969	+	276.581i	−0.722422	+	0.691453i
$21$	259.473			0.588375
$22$	−387.344	−	395.283i	−0.800298	−	0.816700i
$23$	−416.491			−0.787318			−0.393659	−	0.919257i	$-0.628791\pi$
$23$	−416.491			−0.787318			−0.393659	+	0.919257i	$0.628791\pi$
$24$	−291.263	−	309.551i	−0.505664	−	0.537414i
$25$	−2.01779	+	624.997i	−0.00322846	+	0.999995i
$26$	349.947	+	357.119i	0.517674	+	0.528283i
$27$	782.960			1.07402
$28$	−12.6805	+	624.997i	−0.0161741	+	0.797190i
$29$	236.807			0.281578			0.140789	−	0.990040i	$-0.455036\pi$
$29$	236.807			0.281578			0.140789	+	0.990040i	$0.455036\pi$
$30$	−664.073	−	7.80805i	−0.737858	−	0.00867561i
$31$		−	41.5345i		−	0.0432201i	−0.999766	−	0.0216101i	$-0.993121\pi$
$31$		−	41.5345i		−	0.0432201i	0.999766	−	0.0216101i	$-0.00687923\pi$
$32$	759.852	−	686.440i	0.742043	−	0.670352i
$33$		−	918.856i		−	0.843762i
$34$	−449.088	−	458.291i	−0.388484	−	0.396446i
$35$	689.557	+	691.786i	0.562903	+	0.564724i
$36$	−11.9744	+	590.193i	−0.00923947	+	0.455396i
$37$		−	206.138i		−	0.150575i	−0.997162	−	0.0752877i	$-0.976012\pi$
$37$		−	206.138i		−	0.150575i	0.997162	−	0.0752877i	$-0.0239875\pi$
$38$	1820.44	+	1857.75i	1.26069	+	1.28653i
$39$			830.144i			0.545788i
$40$	51.2606	−	1599.18i	0.0320379	−	0.999487i
$41$	−1816.56			−1.08064			−0.540321	−	0.841459i	$-0.681697\pi$
$41$	−1816.56			−1.08064			−0.540321	+	0.841459i	$0.681697\pi$
$42$	−741.307	+	726.420i	−0.420242	+	0.411803i
$43$	−3162.64			−1.71046			−0.855230	−	0.518249i	$-0.826584\pi$
$43$	−3162.64			−1.71046			−0.855230	+	0.518249i	$0.826584\pi$
$44$	2213.26	+	44.9046i	1.14321	+	0.0231945i
$45$	651.158	+	653.264i	0.321560	+	0.322599i
$46$	1189.90	−	1166.01i	0.562336	−	0.551043i
$47$	−823.584			−0.372831			−0.186416	−	0.982471i	$-0.559687\pi$
$47$	−823.584			−0.372831			−0.186416	+	0.982471i	$0.559687\pi$
$48$	1698.74	+	68.9596i	0.737302	+	0.0299304i
$49$	−874.509			−0.364227
$50$	−1743.97	−	1791.25i	−0.697589	−	0.716498i
$51$		−	1065.32i		−	0.409582i
$52$	−1999.58	−	40.5692i	−0.739489	−	0.0150034i
$53$		−	4866.53i		−	1.73248i	−0.499631	−	0.866238i	$-0.666531\pi$
$53$		−	4866.53i		−	1.73248i	0.499631	−	0.866238i	$-0.333469\pi$
$54$	−2236.89	+	2191.97i	−0.767110	+	0.751704i
$55$	2449.78	−	2441.88i	0.809844	−	0.807234i
$56$	−1713.51	−	1821.10i	−0.546400	−	0.580707i
$57$			4318.44i			1.32916i
$58$	−676.551	+	662.964i	−0.201115	+	0.197076i
$59$			3638.55i			1.04526i	0.852560	+	0.522630i	$0.175049\pi$
$59$			3638.55i			1.04526i	−0.852560	+	0.522630i	$0.824951\pi$
$60$	1919.09	−	1836.83i	0.533082	−	0.510229i
$61$	4136.07			1.11155			0.555774	−	0.831334i	$-0.312422\pi$
$61$	4136.07			1.11155			0.555774	+	0.831334i	$0.312422\pi$
$62$	116.280	+	118.663i	0.0302497	+	0.0308696i
$63$	1441.49			0.363186
$64$	−249.122	+	4088.42i	−0.0608207	+	0.998149i
$65$	−2213.26	+	2206.13i	−0.523849	+	0.522160i
$66$	2572.42	+	2625.15i	0.590547	+	0.602650i
$67$	3208.70			0.714792			0.357396	−	0.933953i	$-0.383665\pi$
$67$	3208.70			0.714792			0.357396	+	0.933953i	$0.383665\pi$
$68$	2566.06	+	52.0625i	0.554944	+	0.0112592i
$69$	2766.00			0.580970
$70$	−3906.76	−	45.9350i	−0.797299	−	0.00937450i
$71$		−	456.333i		−	0.0905243i	−0.998975	−	0.0452621i	$-0.985588\pi$
$71$		−	456.333i		−	0.0905243i	0.998975	−	0.0452621i	$-0.0144123\pi$
$72$	−1618.09	−	1719.69i	−0.312132	−	0.331730i
$73$			5905.66i			1.10821i	0.832446	+	0.554106i	$0.186940\pi$
$73$			5905.66i			1.10821i	−0.832446	+	0.554106i	$0.813060\pi$
$74$	577.102	+	588.929i	0.105387	+	0.107547i
$75$	13.4005	−	4150.72i	0.00238231	−	0.737906i
$76$	−10401.9	−	211.043i	−1.80088	−	0.0365379i
$77$		−	5405.67i		−	0.911733i
$78$	−2324.06	−	2371.70i	−0.381996	−	0.389825i
$79$		−	2808.68i		−	0.450037i	−0.974354	−	0.225018i	$-0.927756\pi$
$79$		−	2808.68i		−	0.450037i	0.974354	−	0.225018i	$-0.0722442\pi$
$80$	4330.60	+	4712.31i	0.676656	+	0.736299i
$81$	−2211.32			−0.337039
$82$	5189.86	−	5085.63i	0.771841	−	0.756340i
$83$	−3048.15			−0.442466			−0.221233	−	0.975221i	$-0.571008\pi$
$83$	−3048.15			−0.442466			−0.221233	+	0.975221i	$0.571008\pi$
$84$	84.2134	−	4150.72i	0.0119350	−	0.588254i
$85$	2840.28	−	2831.12i	0.393118	−	0.391851i
$86$	9035.57	−	8854.10i	1.22168	−	1.19715i
$87$	−1572.68			−0.207779
$88$	−6448.94	+	6067.94i	−0.832765	+	0.783567i
$89$	−5143.40			−0.649337			−0.324668	−	0.945828i	$-0.605253\pi$
$89$	−5143.40			−0.649337			−0.324668	+	0.945828i	$0.605253\pi$
$90$	−3689.21	−	43.3771i	−0.455458	−	0.00535520i
$91$			4883.77i			0.589756i
$92$	−135.174	+	6662.49i	−0.0159705	+	0.787156i
$93$			275.839i			0.0318925i
$94$	2352.96	−	2305.70i	0.266292	−	0.260944i
$95$	−11513.5	+	11476.4i	−1.27573	+	1.27162i
$96$	−5046.32	+	4558.78i	−0.547561	+	0.494659i
$97$		−	4506.56i		−	0.478963i	−0.970901	−	0.239481i	$-0.923023\pi$
$97$		−	4506.56i		−	0.478963i	0.970901	−	0.239481i	$-0.0769774\pi$
$98$	2498.45	−	2448.27i	0.260146	−	0.254922i
$99$		−	5104.65i		−	0.520829i
$100$	9997.24	+	235.124i	0.999724	+	0.0235124i
$101$	−1737.92			−0.170368			−0.0851840	−	0.996365i	$-0.527148\pi$
$101$	−1737.92			−0.170368			−0.0851840	+	0.996365i	$0.527148\pi$
$102$	2982.47	+	3043.60i	0.286666	+	0.292541i
$103$	12672.6			1.19452			0.597258	−	0.802049i	$-0.296257\pi$
$103$	12672.6			1.19452			0.597258	+	0.802049i	$0.296257\pi$
$104$	5826.31	−	5482.10i	0.538675	−	0.506851i
$105$	−4579.47	−	4594.28i	−0.415372	−	0.416715i
$106$	13624.3	+	13903.5i	1.21256	+	1.23741i
$107$	−6987.88			−0.610349			−0.305174	−	0.952297i	$-0.598715\pi$
$107$	−6987.88			−0.610349			−0.305174	+	0.952297i	$0.598715\pi$
$108$	254.114	−	12524.8i	0.0217862	−	1.07380i
$109$	−811.156			−0.0682734			−0.0341367	−	0.999417i	$-0.510868\pi$
$109$	−811.156			−0.0682734			−0.0341367	+	0.999417i	$0.510868\pi$
$110$	−162.667	+	13834.8i	−0.0134435	+	1.14337i
$111$			1369.00i			0.111111i
$112$	9993.77	+	405.692i	0.796698	+	0.0323415i
$113$			6342.41i			0.496704i	0.968670	+	0.248352i	$0.0798889\pi$
$113$			6342.41i			0.496704i	−0.968670	+	0.248352i	$0.920111\pi$
$114$	−12089.9	−	12337.7i	−0.930277	−	0.949343i
$115$	7350.70	+	7374.47i	0.555819	+	0.557616i
$116$	76.8570	−	3788.13i	0.00571173	−	0.281520i
$117$			4611.81i			0.336899i
$118$	−10186.5	−	10395.2i	−0.731576	−	0.746569i
$119$		−	6267.34i		−	0.442577i
$120$	−340.431	+	10620.4i	−0.0236411	+	0.737531i
$121$	−4501.74			−0.307475
$122$	−11816.6	+	11579.3i	−0.793914	+	0.777970i
$123$	12064.1			0.797416
$124$	−664.416	−	13.4803i	−0.0432112	−	0.000876707i
$125$	11101.9	−	10994.9i	0.710523	−	0.703674i
$126$	−4118.28	+	4035.58i	−0.259403	+	0.254194i
$127$	−7702.06			−0.477529			−0.238764	−	0.971078i	$-0.576742\pi$
$127$	−7702.06			−0.477529			−0.238764	+	0.971078i	$0.576742\pi$
$128$	−10734.2	−	12377.9i	−0.655162	−	0.755489i
$129$	21003.7			1.26216
$130$	146.962	−	12499.1i	0.00869597	−	0.739590i
$131$		−	15619.8i		−	0.910192i	−0.890442	−	0.455096i	$-0.849605\pi$
$131$		−	15619.8i		−	0.910192i	0.890442	−	0.455096i	$-0.150395\pi$
$132$	−14698.7	−	298.220i	−0.843588	−	0.0171155i
$133$			25405.6i			1.43624i
$134$	−9167.16	+	8983.06i	−0.510535	+	0.500282i
$135$	−13818.6	−	13863.2i	−0.758220	−	0.760671i
$136$	−7476.91	+	7035.18i	−0.404245	+	0.380362i
$137$			3770.61i			0.200896i	0.994942	+	0.100448i	$0.0320275\pi$
$137$			3770.61i			0.200896i	−0.994942	+	0.100448i	$0.967972\pi$
$138$	−7902.37	+	7743.66i	−0.414953	+	0.406620i
$139$		−	7001.21i		−	0.362363i	−0.983450	−	0.181181i	$-0.942008\pi$
$139$		−	7001.21i		−	0.362363i	0.983450	−	0.181181i	$-0.0579921\pi$
$140$	11290.1	−	10806.1i	0.576026	−	0.551332i
$141$	5469.57			0.275116
$142$	1277.55	+	1303.73i	0.0633578	+	0.0646563i
$143$	17294.6			0.845742
$144$	9437.26	+	383.101i	0.455115	+	0.0184751i
$145$	−4179.43	−	4192.95i	−0.198784	−	0.199427i
$146$	−16533.5	−	16872.3i	−0.775636	−	0.791532i
$147$	5807.78			0.268766
$148$	−3297.53	−	66.9031i	−0.150544	−	0.00305438i
$149$	−29966.7			−1.34979			−0.674894	−	0.737914i	$-0.735811\pi$
$149$	−29966.7			−1.34979			−0.674894	+	0.737914i	$0.735811\pi$
$150$	11582.0	+	11896.0i	0.514757	+	0.528711i
$151$			12397.1i			0.543710i	0.962338	+	0.271855i	$0.0876372\pi$
$151$			12397.1i			0.543710i	−0.962338	+	0.271855i	$0.912363\pi$
$152$	30308.7	−	28518.1i	1.31184	−	1.23434i
$153$		−	5918.34i		−	0.252823i
$154$	15133.7	+	15443.8i	0.638121	+	0.651199i
$155$	−735.418	+	733.048i	−0.0306105	+	0.0305119i
$156$	13279.6	+	269.428i	0.545676	+	0.0110712i
$157$		−	18293.8i		−	0.742171i	−0.928599	−	0.371085i	$-0.878986\pi$
$157$		−	18293.8i		−	0.742171i	0.928599	−	0.371085i	$-0.121014\pi$
$158$	7863.16	+	8024.32i	0.314980	+	0.321436i
$159$			32319.5i			1.27841i
$160$	−25565.0	−	1339.02i	−0.998631	−	0.0523056i
$161$	16272.5			0.627771
$162$	6317.66	−	6190.79i	0.240728	−	0.235893i
$163$	−26437.3			−0.995043			−0.497522	−	0.867452i	$-0.665756\pi$
$163$	−26437.3			−0.995043			−0.497522	+	0.867452i	$0.665756\pi$
$164$	−589.574	+	29059.0i	−0.0219205	+	1.08042i
$165$	−16269.4	+	16217.0i	−0.597592	+	0.595666i
$166$	8708.47	−	8533.58i	0.316028	−	0.309681i
$167$	16417.6			0.588677			0.294339	−	0.955701i	$-0.404901\pi$
$167$	16417.6			0.588677			0.294339	+	0.955701i	$0.404901\pi$
$168$	11379.7	+	12094.2i	0.403193	+	0.428509i
$169$	12936.2			0.452931
$170$	−188.596	+	16040.1i	−0.00652582	+	0.555019i
$171$			23990.8i			0.820452i
$172$	−1026.45	+	50591.8i	−0.0346962	+	1.71011i
$173$		−	14503.0i		−	0.484581i	−0.970204	−	0.242291i	$-0.922101\pi$
$173$		−	14503.0i		−	0.484581i	0.970204	−	0.242291i	$-0.0778987\pi$
$174$	4493.10	−	4402.86i	0.148405	−	0.145424i
$175$	78.8356	−	24418.8i	0.00257422	−	0.797350i
$176$	1436.65	−	35390.3i	0.0463795	−	1.14251i
$177$		−	24164.3i		−	0.771307i
$178$	14694.5	−	14399.4i	0.463784	−	0.454470i
$179$			29882.7i			0.932640i	0.884616	+	0.466320i	$0.154420\pi$
$179$			29882.7i			0.932640i	−0.884616	+	0.466320i	$0.845580\pi$
$180$	10661.4	−	10204.4i	0.329056	−	0.314950i
$181$	−13028.0			−0.397669			−0.198834	−	0.980033i	$-0.563716\pi$
$181$	−13028.0			−0.397669			−0.198834	+	0.980033i	$0.563716\pi$
$182$	−13672.6	−	13952.8i	−0.412769	−	0.421229i
$183$	−27468.4			−0.820221
$184$	−18266.1	−	19413.0i	−0.539522	−	0.573398i
$185$	−3649.91	+	3638.15i	−0.106645	+	0.106301i
$186$	−772.236	−	788.062i	−0.0223215	−	0.0227790i
$187$	−22194.1			−0.634680
$188$	−267.299	+	13174.6i	−0.00756277	+	0.372754i
$189$	−30590.5			−0.856374
$190$	764.502	−	65020.7i	0.0211773	−	1.80113i
$191$		−	53818.5i		−	1.47525i	−0.675212	−	0.737624i	$-0.735948\pi$
$191$		−	53818.5i		−	1.47525i	0.675212	−	0.737624i	$-0.264052\pi$
$192$	1654.46	−	27151.9i	0.0448802	−	0.736543i
$193$		−	48440.5i		−	1.30045i	−0.759741	−	0.650225i	$-0.774674\pi$
$193$		−	48440.5i		−	1.30045i	0.759741	−	0.650225i	$-0.225326\pi$
$194$	12616.5	+	12875.1i	0.335225	+	0.342096i
$195$	14698.7	−	14651.3i	0.386553	−	0.385307i
$196$	−283.827	+	13989.3i	−0.00738824	+	0.364152i
$197$			74216.3i			1.91235i	0.292798	+	0.956174i	$0.405414\pi$
$197$			74216.3i			1.91235i	−0.292798	+	0.956174i	$0.594586\pi$
$198$	14290.9	+	14583.8i	0.364527	+	0.371998i
$199$		−	13240.2i		−	0.334341i	−0.985928	−	0.167170i	$-0.946537\pi$
$199$		−	13240.2i		−	0.334341i	0.985928	−	0.167170i	$-0.0534630\pi$
$200$	−29220.1	+	27316.5i	−0.730501	+	0.682911i
$201$	−21309.6			−0.527452
$202$	4965.19	−	4865.48i	0.121684	−	0.119240i
$203$	−9252.13			−0.224517
$204$	−17041.7	−	345.757i	−0.409498	−	0.00830826i
$205$	32060.7	+	32164.3i	0.762895	+	0.765362i
$206$	−36205.3	+	35478.2i	−0.853174	+	0.836040i
$207$	15366.3			0.358615
$208$	−1297.95	+	31973.5i	−0.0300006	+	0.739032i
$209$	89967.1			2.05964
$210$	25945.5	+	305.063i	0.588334	+	0.00691753i
$211$			4466.51i			0.100324i	0.998741	+	0.0501618i	$0.0159737\pi$
$211$			4466.51i			0.100324i	−0.998741	+	0.0501618i	$0.984026\pi$
$212$	−77848.4	−	1579.46i	−1.73212	−	0.0351428i
$213$			3030.59i			0.0667987i
$214$	19964.2	−	19563.2i	0.435937	−	0.427182i
$215$	55817.8	+	55998.3i	1.20752	+	1.21143i
$216$	34338.3	+	36494.4i	0.735989	+	0.782201i
$217$			1622.77i			0.0344617i
$218$	2317.45	−	2270.91i	0.0487637	−	0.0477844i
$219$		−	39220.6i		−	0.817760i
$220$	−38267.0	−	39980.9i	−0.790641	−	0.826052i
$221$	20051.4			0.410544
$222$	−3832.64	−	3911.19i	−0.0777664	−	0.0793602i
$223$	4344.79			0.0873694			0.0436847	−	0.999045i	$-0.486090\pi$
$223$	4344.79			0.0873694			0.0436847	+	0.999045i	$0.486090\pi$
$224$	−29687.7	+	26819.5i	−0.591671	+	0.534508i
$225$	74.4456	−	23059.0i	0.00147053	−	0.455487i
$226$	−17756.2	−	18120.1i	−0.347642	−	0.354767i
$227$	62311.6			1.20925			0.604626	−	0.796509i	$-0.293323\pi$
$227$	62311.6			1.20925			0.604626	+	0.796509i	$0.293323\pi$
$228$	69080.9	+	1401.57i	1.32889	+	0.0269616i
$229$	−78625.5			−1.49931			−0.749657	−	0.661827i	$-0.769781\pi$
$229$	−78625.5			−1.49931			−0.749657	+	0.661827i	$0.769781\pi$
$230$	−41646.3	−	489.669i	−0.787264	−	0.00925651i
$231$			35900.0i			0.672777i
$232$	10385.7	+	11037.8i	0.192956	+	0.205071i
$233$		−	2464.06i		−	0.0453878i	−0.999742	−	0.0226939i	$-0.992776\pi$
$233$		−	2464.06i		−	0.0453878i	0.999742	−	0.0226939i	$-0.00722431\pi$
$234$	−12911.2	−	13175.8i	−0.235795	−	0.240628i
$235$	14535.5	+	14582.5i	0.263206	+	0.264057i
$236$	58204.8	+	1180.91i	1.04505	+	0.0212028i
$237$			18653.0i			0.332086i
$238$	17546.0	+	17905.6i	0.309759	+	0.316108i
$239$		−	54386.5i		−	0.952128i	−0.879411	−	0.476064i	$-0.842063\pi$
$239$		−	54386.5i		−	0.952128i	0.879411	−	0.476064i	$-0.157937\pi$
$240$	−28760.3	−	31295.4i	−0.499311	−	0.543322i
$241$	4097.25			0.0705437			0.0352718	−	0.999378i	$-0.488770\pi$
$241$	4097.25			0.0705437			0.0352718	+	0.999378i	$0.488770\pi$
$242$	12861.3	−	12603.0i	0.219612	−	0.215201i
$243$	−48734.0			−0.825315
$244$	1342.38	−	66163.5i	0.0225474	−	1.11132i
$245$	15434.3	+	15484.2i	0.257131	+	0.257963i
$246$	−34466.8	+	33774.6i	−0.569548	+	0.558110i
$247$	−81281.1			−1.33228
$248$	1935.96	−	1821.58i	0.0314769	−	0.0296173i
$249$	20243.3			0.326500
$250$	−936.574	+	62493.0i	−0.0149852	+	0.999888i
$251$		−	48310.9i		−	0.766828i	−0.923577	−	0.383414i	$-0.874748\pi$
$251$		−	48310.9i		−	0.766828i	0.923577	−	0.383414i	$-0.125252\pi$
$252$	467.842	−	23059.0i	0.00736713	−	0.363112i
$253$		−	57624.6i		−	0.900258i
$254$	22004.6	−	21562.6i	0.341071	−	0.334222i
$255$	−18862.8	+	18802.0i	−0.290086	+	0.289151i
$256$	65320.4	+	5312.05i	0.996710	+	0.0810554i
$257$		−	24560.5i		−	0.371853i	−0.982564	−	0.185927i	$-0.940471\pi$
$257$		−	24560.5i		−	0.371853i	0.982564	−	0.185927i	$-0.0595287\pi$
$258$	−60006.9	+	58801.7i	−0.901491	+	0.883387i
$259$			8053.87i			0.120062i
$260$	34572.4	+	36120.9i	0.511427	+	0.534333i
$261$	−8736.92			−0.128256
$262$	43729.1	+	44625.3i	0.637042	+	0.650098i
$263$	−83305.2			−1.20437			−0.602186	−	0.798356i	$-0.705703\pi$
$263$	−83305.2			−1.20437			−0.602186	+	0.798356i	$0.705703\pi$
$264$	42828.6	−	40298.3i	0.614505	−	0.578201i
$265$	−86167.6	+	85889.9i	−1.22702	+	1.22307i
$266$	−71125.2	−	72582.9i	−1.00522	−	1.02582i
$267$	34158.2			0.479152
$268$	1041.40	−	51328.6i	0.0144993	−	0.714645i
$269$	−26533.4			−0.366681			−0.183341	−	0.983049i	$-0.558691\pi$
$269$	−26533.4			−0.366681			−0.183341	+	0.983049i	$0.558691\pi$
$270$	78290.6	+	920.527i	1.07395	+	0.0126273i
$271$			110062.i			1.49864i	0.662207	+	0.749321i	$0.269620\pi$
$271$			110062.i			1.49864i	−0.662207	+	0.749321i	$0.730380\pi$
$272$	1665.66	−	41031.6i	0.0225137	−	0.554601i
$273$		−	32434.0i		−	0.435186i
$274$	−10556.2	−	10772.5i	−0.140606	−	0.143488i
$275$	−86472.9	−	279.176i	−1.14344	−	0.00369158i
$276$	897.719	−	44246.8i	0.0117848	−	0.580850i
$277$		−	111083.i		−	1.44773i	−0.689942	−	0.723864i	$-0.742364\pi$
$277$		−	111083.i		−	1.44773i	0.689942	−	0.723864i	$-0.257636\pi$
$278$	19600.5	+	20002.2i	0.253617	+	0.258815i
$279$			1532.40i			0.0196863i
$280$	−2002.77	+	62480.4i	−0.0255455	+	0.796944i
$281$	−66386.2			−0.840747			−0.420374	−	0.907351i	$-0.638101\pi$
$281$	−66386.2			−0.840747			−0.420374	+	0.907351i	$0.638101\pi$
$282$	−15626.4	+	15312.6i	−0.196499	+	0.192553i
$283$	123904.			1.54708			0.773540	−	0.633747i	$-0.218484\pi$
$283$	123904.			1.54708			0.773540	+	0.633747i	$0.218484\pi$
$284$	−7299.83	−	148.105i	−0.0905057	−	0.00183626i
$285$	76463.1	−	76216.7i	0.941375	−	0.938340i
$286$	−49410.1	+	48417.8i	−0.604065	+	0.591933i
$287$	70973.6			0.861654
$288$	−28034.5	+	25326.0i	−0.337993	+	0.305338i
$289$	57789.1			0.691911
$290$	23679.1	+	278.414i	0.281559	+	0.00331052i
$291$			29928.9i			0.353431i
$292$	94471.2	+	1916.71i	1.10798	+	0.0224798i
$293$			79770.8i			0.929199i	0.885521	+	0.464600i	$0.153802\pi$
$293$			79770.8i			0.929199i	−0.885521	+	0.464600i	$0.846198\pi$
$294$	−16592.6	+	16259.4i	−0.191964	+	0.188109i
$295$	64424.8	−	64217.2i	0.740303	−	0.737917i
$296$	9608.23	−	9040.59i	0.109663	−	0.103184i
$297$			108328.i			1.22809i
$298$	85613.9	−	83894.5i	0.964077	−	0.944715i
$299$			52061.1i			0.582333i
$300$	−66393.5	−	1561.50i	−0.737705	−	0.0173500i
$301$	123565.			1.36384
$302$	−34707.0	−	35418.3i	−0.380542	−	0.388341i
$303$	11541.9			0.125716
$304$	−6751.98	+	166328.i	−0.0730607	+	1.79977i
$305$	−72997.9	−	73234.0i	−0.784713	−	0.787250i
$306$	16568.9	+	16908.5i	0.176950	+	0.180577i
$307$	−102607.			−1.08868			−0.544340	−	0.838865i	$-0.683220\pi$
$307$	−102607.			−1.08868			−0.544340	+	0.838865i	$0.683220\pi$
$308$	−86472.9	−	1754.44i	−0.911546	−	0.0184942i
$309$	−84161.2			−0.881445
$310$	48.8322	−	4153.17i	0.000508139	−	0.0432171i
$311$		−	113118.i		−	1.16953i	−0.811203	−	0.584764i	$-0.801187\pi$
$311$		−	113118.i		−	1.16953i	0.811203	−	0.584764i	$-0.198813\pi$
$312$	−38693.6	+	36407.6i	−0.397494	+	0.374010i
$313$			180078.i			1.83811i	0.394128	+	0.919055i	$0.371047\pi$
$313$			180078.i			1.83811i	−0.394128	+	0.919055i	$0.628953\pi$
$314$	51215.1	+	52264.7i	0.519444	+	0.530090i
$315$	−25441.0	−	25523.2i	−0.256397	−	0.257226i
$316$	−44929.6	−	911.572i	−0.449944	−	0.00912887i
$317$		−	19461.2i		−	0.193665i	−0.995301	−	0.0968324i	$-0.969129\pi$
$317$		−	19461.2i		−	0.193665i	0.995301	−	0.0968324i	$-0.0308711\pi$
$318$	−90481.5	−	92335.8i	−0.894757	−	0.913095i
$319$			32764.0i			0.321970i
$320$	76787.0	−	67745.9i	0.749873	−	0.661581i
$321$	46407.8			0.450382
$322$	−46489.9	+	45556.3i	−0.448381	+	0.439376i
$323$	104308.			0.999799
$324$	−717.694	+	35373.8i	−0.00683675	+	0.336970i
$325$	78124.2	+	252.222i	0.739637	+	0.00238790i
$326$	75530.6	−	74013.7i	0.710702	−	0.696429i
$327$	5387.04			0.0503796
$328$	−79668.9	−	84671.2i	−0.740527	−	0.787024i
$329$	32177.7			0.297278
$330$	1080.30	−	91879.3i	0.00992011	−	0.843703i
$331$		−	62028.6i		−	0.566156i	−0.959097	−	0.283078i	$-0.908644\pi$
$331$		−	62028.6i		−	0.566156i	0.959097	−	0.283078i	$-0.0913555\pi$
$332$	−989.293	+	48760.4i	−0.00897530	+	0.442375i
$333$			7605.38i			0.0685856i
$334$	−46904.6	+	45962.6i	−0.420458	+	0.412014i
$335$	−56630.7	−	56813.8i	−0.504618	−	0.506249i
$336$	−66370.5	−	2694.28i	−0.587891	−	0.0238651i
$337$		−	26723.7i		−	0.235308i	−0.993055	−	0.117654i	$-0.962463\pi$
$337$		−	26723.7i		−	0.235308i	0.993055	−	0.117654i	$-0.0375374\pi$
$338$	−36958.2	+	36216.0i	−0.323503	+	0.317006i
$339$		−	42121.1i		−	0.366522i
$340$	−44366.8	−	46354.0i	−0.383796	−	0.400986i
$341$	5746.61			0.0494200
$342$	−67164.6	−	68541.1i	−0.574233	−	0.586001i
$343$	127975.			1.08777
$344$	−138704.	−	147413.i	−1.17212	−	1.24572i
$345$	−48817.4	−	48975.2i	−0.410144	−	0.411470i
$346$	40602.6	+	41434.7i	0.339157	+	0.346108i
$347$	−138874.			−1.15335			−0.576675	−	0.816974i	$-0.695650\pi$
$347$	−138874.			−1.15335			−0.576675	+	0.816974i	$0.695650\pi$
$348$	−510.422	+	25157.7i	−0.00421474	+	0.207736i
$349$	74063.7			0.608072			0.304036	−	0.952661i	$-0.401666\pi$
$349$	74063.7			0.608072			0.304036	+	0.952661i	$0.401666\pi$
$350$	68137.6	+	69984.6i	0.556225	+	0.571303i
$351$		−	97869.5i		−	0.794389i
$352$	94974.0	+	105131.i	0.766513	+	0.848489i
$353$		−	22898.3i		−	0.183761i	−0.995770	−	0.0918805i	$-0.970712\pi$
$353$		−	22898.3i		−	0.183761i	0.995770	−	0.0918805i	$-0.0292878\pi$
$354$	67650.2	+	69036.6i	0.539837	+	0.550901i
$355$	−8079.91	+	8053.87i	−0.0641136	+	0.0639069i
$356$	−1669.32	+	82277.4i	−0.0131716	+	0.649203i
$357$			41622.6i			0.326582i
$358$	−83659.4	−	85374.0i	−0.652753	−	0.666131i
$359$			216833.i			1.68242i	0.540705	+	0.841212i	$0.318158\pi$
$359$			216833.i			1.68242i	−0.540705	+	0.841212i	$0.681842\pi$
$360$	−1891.24	+	59001.2i	−0.0145929	+	0.455256i
$361$	−292507.			−2.24451
$362$	37220.7	−	36473.2i	0.284032	−	0.278328i
$363$	29896.9			0.226889
$364$	78124.2	+	1585.05i	0.589634	+	0.0119630i
$365$	104567.	−	104230.i	0.784888	−	0.782358i
$366$	78476.4	−	76900.3i	0.585837	−	0.574071i
$367$	17075.9			0.126780			0.0633900	−	0.997989i	$-0.479809\pi$
$367$	17075.9			0.126780			0.0633900	+	0.997989i	$0.479809\pi$
$368$	106534.	+	4324.69i	0.786670	+	0.0319345i
$369$	67021.4			0.492221
$370$	242.356	−	20612.4i	0.00177032	−	0.150565i
$371$			190137.i			1.38140i
$372$	4412.51	+	89.5249i	0.0318860	+	0.000646931i
$373$		−	8495.42i		−	0.0610615i	−0.999534	−	0.0305307i	$-0.990280\pi$
$373$		−	8495.42i		−	0.0610615i	0.999534	−	0.0305307i	$-0.00971975\pi$
$374$	63408.0	−	62134.5i	0.453316	−	0.444212i
$375$	−73729.9	+	73019.2i	−0.524301	+	0.519248i
$376$	−36120.0	−	38387.9i	−0.255489	−	0.271530i
$377$		−	29600.7i		−	0.208267i
$378$	87396.2	−	85641.0i	0.611658	−	0.599374i
$379$			59878.5i			0.416862i	0.978037	+	0.208431i	$0.0668357\pi$
$379$			59878.5i			0.416862i	−0.978037	+	0.208431i	$0.933164\pi$
$380$	179847.	+	187902.i	1.24548	+	1.30126i
$381$	51150.8			0.352373
$382$	150670.	+	153758.i	1.03252	+	1.05368i
$383$	−144186.			−0.982935			−0.491467	−	0.870896i	$-0.663539\pi$
$383$	−144186.			−0.982935			−0.491467	+	0.870896i	$0.663539\pi$
$384$	71287.6	+	82204.1i	0.483450	+	0.557482i
$385$	−95713.7	+	95405.2i	−0.645733	+	0.643651i
$386$	135614.	+	138393.i	0.910183	+	0.928837i
$387$	116685.			0.779097
$388$	−72090.1	−	1462.63i	−0.478864	−	0.00971562i
$389$	−237951.			−1.57249			−0.786247	−	0.617913i	$-0.787979\pi$
$389$	−237951.			−1.57249			−0.786247	+	0.617913i	$0.787979\pi$
$390$	−976.001	+	83008.6i	−0.00641684	+	0.545750i
$391$		−	66810.1i		−	0.437007i
$392$	−38353.4	−	40761.5i	−0.249592	−	0.265264i
$393$			103734.i			0.671639i
$394$	−207776.	−	212034.i	−1.33845	−	1.36588i
$395$	−49731.0	+	49570.7i	−0.318737	+	0.317710i
$396$	−81657.5	−	1656.74i	−0.520722	−	0.0105649i
$397$		−	267251.i		−	1.69566i	−0.530271	−	0.847828i	$-0.677910\pi$
$397$		−	267251.i		−	1.69566i	0.530271	−	0.847828i	$-0.322090\pi$
$398$	37067.2	+	37826.9i	0.234004	+	0.238800i
$399$		−	168723.i		−	1.05981i
$400$	7005.87	−	159847.i	0.0437867	−	0.999041i
$401$	17276.0			0.107437			0.0537185	−	0.998556i	$-0.482893\pi$
$401$	17276.0			0.107437			0.0537185	+	0.998556i	$0.482893\pi$
$402$	60880.8	−	59658.1i	0.376728	−	0.369163i
$403$	−5191.79			−0.0319674
$404$	−564.052	+	27801.1i	−0.00345586	+	0.170333i
$405$	39027.8	+	39154.0i	0.237938	+	0.238707i
$406$	26433.1	−	25902.2i	0.160360	−	0.157139i
$407$	28520.7			0.172175
$408$	49655.5	−	46721.9i	0.298296	−	0.280673i
$409$	126218.			0.754530			0.377265	−	0.926105i	$-0.376865\pi$
$409$	126218.			0.754530			0.377265	+	0.926105i	$0.376865\pi$
$410$	−181643.	−	2135.73i	−1.08057	−	0.0127051i
$411$		−	25041.3i		−	0.148243i
$412$	4112.97	−	202720.i	0.0242304	−	1.19427i
$413$		−	142159.i		−	0.833442i
$414$	−43901.1	+	43019.4i	−0.256138	+	0.250994i
$415$	53797.1	+	53971.1i	0.312365	+	0.313375i
$416$	−85804.6	−	94981.1i	−0.495820	−	0.548846i
$417$			46496.3i			0.267391i
$418$	−257033.	+	251871.i	−1.47108	+	1.44154i
$419$		−	270580.i		−	1.54123i	−0.637299	−	0.770617i	$-0.719948\pi$
$419$		−	270580.i		−	1.54123i	0.637299	−	0.770617i	$-0.280052\pi$
$420$	−74979.7	+	71765.4i	−0.425055	+	0.406833i
$421$	260404.			1.46921			0.734605	−	0.678495i	$-0.237368\pi$
$421$	260404.			1.46921			0.734605	+	0.678495i	$0.237368\pi$
$422$	−12504.4	−	12760.7i	−0.0702163	−	0.0716554i
$423$	30385.9			0.169821
$424$	226832.	−	213431.i	1.26175	−	1.18721i
$425$	−100257.	−	323.677i	−0.555055	−	0.00179198i
$426$	−8484.42	−	8658.31i	−0.0467523	−	0.0477105i
$427$	−161598.			−0.886296
$428$	−2267.95	+	111783.i	−0.0123807	+	0.610223i
$429$	−114856.			−0.624081
$430$	−316242.	−	3718.32i	−1.71034	−	0.0201099i
$431$			326771.i			1.75909i	0.475814	+	0.879546i	$0.342153\pi$
$431$			326771.i			1.75909i	−0.475814	+	0.879546i	$0.657847\pi$
$432$	−200273.	−	8129.97i	−1.07314	−	0.0435634i
$433$			164821.i			0.879099i	0.898218	+	0.439549i	$0.144862\pi$
$433$			164821.i			0.879099i	−0.898218	+	0.439549i	$0.855138\pi$
$434$	−4543.09	−	4636.20i	−0.0241197	−	0.0246140i
$435$	27756.4	+	27846.2i	0.146685	+	0.147159i
$436$	−263.265	+	12975.8i	−0.00138491	+	0.0682593i
$437$			270824.i			1.41816i
$438$	109802.	+	112052.i	0.572349	+	0.584079i
$439$		−	273776.i		−	1.42058i	−0.703907	−	0.710292i	$-0.748563\pi$
$439$		−	273776.i		−	1.42058i	0.703907	−	0.710292i	$-0.251437\pi$
$440$	221258.	+	7092.28i	1.14286	+	0.0366337i
$441$	32264.7			0.165902
$442$	−57286.1	+	56135.7i	−0.293228	+	0.287339i
$443$	−10446.4			−0.0532305			−0.0266153	−	0.999646i	$-0.508473\pi$
$443$	−10446.4			−0.0532305			−0.0266153	+	0.999646i	$0.508473\pi$
$444$	21899.5	+	444.316i	0.111088	+	0.00225385i
$445$	90776.4	+	91069.9i	0.458409	+	0.459891i
$446$	−12412.9	+	12163.7i	−0.0624029	+	0.0611497i
$447$	199014.			0.996022
$448$	9733.27	−	159736.i	0.0484956	−	0.795878i
$449$	193840.			0.961502			0.480751	−	0.876857i	$-0.340364\pi$
$449$	193840.			0.961502			0.480751	+	0.876857i	$0.340364\pi$
$450$	64343.3	+	66087.4i	0.317744	+	0.326358i
$451$		−	251334.i		−	1.23566i
$452$	101458.	+	2058.46i	0.496601	+	0.0100755i
$453$		−	82331.7i		−	0.401209i
$454$	−178022.	+	174447.i	−0.863699	+	0.846354i
$455$	86472.9	−	86194.1i	0.417693	−	0.416347i
$456$	−201286.	+	189394.i	−0.968018	+	0.910829i
$457$			31679.4i			0.151686i	0.997120	+	0.0758428i	$0.0241647\pi$
$457$			31679.4i			0.151686i	−0.997120	+	0.0758428i	$0.975835\pi$
$458$	224631.	−	220119.i	1.07087	−	1.04937i
$459$			125596.i			0.596143i
$460$	120353.	−	115194.i	0.568776	−	0.544393i
$461$	−92279.5			−0.434213			−0.217107	−	0.976148i	$-0.569662\pi$
$461$	−92279.5			−0.434213			−0.217107	+	0.976148i	$0.569662\pi$
$462$	−100505.	−	102565.i	−0.470875	−	0.480526i
$463$	−196264.			−0.915542			−0.457771	−	0.889070i	$-0.651352\pi$
$463$	−196264.			−0.915542			−0.457771	+	0.889070i	$0.651352\pi$
$464$	−60572.7	−	2458.92i	−0.281346	−	0.0114211i
$465$	4884.05	−	4868.30i	0.0225878	−	0.0225150i
$466$	6898.35	+	7039.73i	0.0317668	+	0.0324179i
$467$	261041.			1.19695			0.598475	−	0.801142i	$-0.295774\pi$
$467$	261041.			1.19695			0.598475	+	0.801142i	$0.295774\pi$
$468$	73773.8	+	1496.79i	0.336830	+	0.00683390i
$469$	−125365.			−0.569942
$470$	−82352.7	−	968.289i	−0.372805	−	0.00438338i
$471$			121492.i			0.547655i
$472$	−169596.	+	159576.i	−0.761255	+	0.716281i
$473$		−	437574.i		−	1.95582i
$474$	−52220.7	−	53291.0i	−0.232427	−	0.237190i
$475$	406405.	+	1312.07i	1.80124	+	0.00581527i
$476$	−100257.	−	2034.10i	−0.442486	−	0.00897755i
$477$			179549.i			0.789125i
$478$	152260.	+	155381.i	0.666393	+	0.680051i
$479$			105637.i			0.460410i	0.973142	+	0.230205i	$0.0739396\pi$
$479$			105637.i			0.460410i	−0.973142	+	0.230205i	$0.926060\pi$
$480$	169782.	+	8892.70i	0.736899	+	0.0385968i
$481$	−25767.1			−0.111372
$482$	−11705.7	+	11470.6i	−0.0503853	+	0.0493734i
$483$	−108068.			−0.463238
$484$	−1461.06	+	72013.0i	−0.00623704	+	0.307412i
$485$	−79794.0	+	79536.8i	−0.339224	+	0.338131i
$486$	139232.	−	136435.i	0.589475	−	0.577637i
$487$	−332629.			−1.40250			−0.701249	−	0.712916i	$-0.747374\pi$
$487$	−332629.			−1.40250			−0.701249	+	0.712916i	$0.747374\pi$
$488$	181396.	+	192785.i	0.761706	+	0.809532i
$489$	175575.			0.734252
$490$	−87444.8	−	1028.16i	−0.364202	−	0.00428222i
$491$			94449.4i			0.391775i	0.980626	+	0.195887i	$0.0627587\pi$
$491$			94449.4i			0.391775i	−0.980626	+	0.195887i	$0.937241\pi$
$492$	3915.47	−	192986.i	0.0161754	−	0.797252i
$493$			37986.6i			0.156292i
$494$	232218.	−	227554.i	0.951571	−	0.932461i
$495$	−90383.8	+	90092.5i	−0.368876	+	0.367687i
$496$	−431.279	+	10624.1i	−0.00175305	+	0.0431846i
$497$			17829.1i			0.0721799i
$498$	−57834.6	+	56673.1i	−0.233200	+	0.228517i
$499$			301032.i			1.20896i	0.796621	+	0.604479i	$0.206619\pi$
$499$			301032.i			1.20896i	−0.796621	+	0.604479i	$0.793381\pi$
$500$	−172279.	−	181163.i	−0.689117	−	0.724650i
$501$	−109032.			−0.434390
$502$	135251.	+	138023.i	0.536702	+	0.547701i
$503$	−3184.75			−0.0125875			−0.00629374	−	0.999980i	$-0.502003\pi$
$503$	−3184.75			−0.0125875			−0.00629374	+	0.999980i	$0.502003\pi$
$504$	63219.3	+	67188.8i	0.248879	+	0.264506i
$505$	30672.8	+	30772.0i	0.120274	+	0.120663i
$506$	161325.	+	164632.i	0.630089	+	0.643003i
$507$	−85911.4			−0.334222
$508$	−2499.75	+	123208.i	−0.00968653	+	0.477431i
$509$	−159009.			−0.613741			−0.306871	−	0.951751i	$-0.599282\pi$
$509$	−159009.			−0.613741			−0.306871	+	0.951751i	$0.599282\pi$
$510$	1252.50	−	106525.i	0.00481546	−	0.409554i
$511$		−	230736.i		−	0.883637i
$512$	−201490.	+	167694.i	−0.768623	+	0.639702i
$513$		−	509121.i		−	1.93458i
$514$	68759.5	+	70168.7i	0.260260	+	0.265593i
$515$	−223660.	−	224384.i	−0.843286	−	0.846013i
$516$	6816.85	−	335990.i	0.0256026	−	1.26190i
$517$		−	113949.i		−	0.426313i
$518$	−22547.6	−	23009.7i	−0.0840311	−	0.0857533i
$519$			96317.3i			0.357577i
$520$	−199896.	−	6407.55i	−0.739261	−	0.0236965i
$521$	36476.2			0.134380			0.0671899	−	0.997740i	$-0.478597\pi$
$521$	36476.2			0.134380			0.0671899	+	0.997740i	$0.478597\pi$
$522$	24961.1	−	24459.8i	0.0916058	−	0.0897661i
$523$	−449988.			−1.64512			−0.822559	−	0.568679i	$-0.807454\pi$
$523$	−449988.			−1.64512			−0.822559	+	0.568679i	$0.807454\pi$
$524$	−249865.	−	5069.49i	−0.910004	−	0.0184630i
$525$	−523.562	+	162170.i	−0.00189954	+	0.588372i
$526$	238000.	−	233221.i	0.860214	−	0.842938i
$527$	6662.63			0.0239897
$528$	−9541.07	+	235034.i	−0.0342239	+	0.843067i
$529$	−106376.			−0.380130
$530$	5721.58	−	486619.i	0.0203687	−	1.73236i
$531$		−	134243.i		−	0.476105i
$532$	406405.	+	8245.51i	1.43594	+	0.0291336i
$533$			227069.i			0.799287i
$534$	−97589.1	+	95629.2i	−0.342230	+	0.335357i
$535$	123330.	+	123729.i	0.430884	+	0.432278i
$536$	140724.	+	149560.i	0.489823	+	0.520578i
$537$		−	198457.i		−	0.688204i
$538$	75805.2	−	74282.8i	0.261899	−	0.256640i
$539$		−	120995.i		−	0.416475i
$540$	−226251.	+	216552.i	−0.775895	+	0.742634i
$541$	−247407.			−0.845314			−0.422657	−	0.906290i	$-0.638903\pi$
$541$	−247407.			−0.845314			−0.422657	+	0.906290i	$0.638903\pi$
$542$	−308128.	−	314443.i	−1.04890	−	1.07039i
$543$	86521.5			0.293443
$544$	110113.	+	121889.i	0.372084	+	0.411877i
$545$	14316.2	+	14362.5i	0.0481986	+	0.0483544i
$546$	90802.0	+	92663.0i	0.304586	+	0.310829i
$547$	313468.			1.04765			0.523827	−	0.851824i	$-0.324504\pi$
$547$	313468.			1.04765			0.523827	+	0.851824i	$0.324504\pi$
$548$	60317.3	+	1223.77i	0.200854	+	0.00407511i
$549$	−152599.			−0.506298
$550$	247832.	−	241291.i	0.819279	−	0.797657i
$551$		−	153984.i		−	0.507193i
$552$	121308.	+	128925.i	0.398119	+	0.423116i
$553$			109736.i			0.358839i
$554$	310987.	+	317360.i	1.01326	+	1.03403i
$555$	24239.7	−	24161.6i	0.0786941	−	0.0784404i
$556$	−111996.	−	2272.28i	−0.362288	−	0.00735042i
$557$			123970.i			0.399581i	0.979839	+	0.199790i	$0.0640261\pi$
$557$			123970.i			0.399581i	−0.979839	+	0.199790i	$0.935974\pi$
$558$	−4290.10	−	4378.03i	−0.0137784	−	0.0140608i
$559$			395328.i			1.26513i
$560$	−169198.	−	184112.i	−0.539534	−	0.587091i
$561$	147395.			0.468336
$562$	189663.	−	185854.i	0.600497	−	0.588437i
$563$	−81897.7			−0.258378			−0.129189	−	0.991620i	$-0.541237\pi$
$563$	−81897.7			−0.258378			−0.129189	+	0.991620i	$0.541237\pi$
$564$	1775.18	−	87495.2i	0.00558064	−	0.275059i
$565$	112300.	−	111938.i	0.351789	−	0.350655i
$566$	−353990.	+	346881.i	−1.10499	+	1.08280i
$567$	86396.9			0.268740
$568$	21270.0	−	20013.4i	0.0659282	−	0.0620332i
$569$	479808.			1.48198			0.740990	−	0.671516i	$-0.234356\pi$
$569$	479808.			1.48198			0.740990	+	0.671516i	$0.234356\pi$
$570$	−5077.20	+	431814.i	−0.0156270	+	1.32907i
$571$			314368.i			0.964199i	0.876116	+	0.482100i	$0.160126\pi$
$571$			314368.i			0.964199i	−0.876116	+	0.482100i	$0.839874\pi$
$572$	5613.05	−	276656.i	0.0171556	−	0.845568i
$573$			357419.i			1.08860i
$574$	−202769.	+	198697.i	−0.615430	+	0.603070i
$575$	840.391	−	260306.i	0.00254182	−	0.787314i
$576$	9191.26	−	150841.i	0.0277032	−	0.454646i
$577$		−	229486.i		−	0.689294i	−0.938732	−	0.344647i	$-0.887999\pi$
$577$		−	229486.i		−	0.689294i	0.938732	−	0.344647i	$-0.112001\pi$
$578$	−165102.	+	161786.i	−0.494192	+	0.484267i
$579$			321702.i			0.959615i
$580$	−68429.9	+	65496.4i	−0.203418	+	0.194698i
$581$	119092.			0.352802
$582$	−83788.7	−	85506.0i	−0.247366	−	0.252436i
$583$	673319.			1.98100
$584$	−275267.	+	259005.i	−0.807103	+	0.759420i
$585$	81657.5	−	81394.3i	0.238608	−	0.237839i
$586$	−223326.	−	227903.i	−0.650345	−	0.663674i
$587$	308124.			0.894230			0.447115	−	0.894476i	$-0.352451\pi$
$587$	308124.			0.894230			0.447115	+	0.894476i	$0.352451\pi$
$588$	1884.94	−	92905.3i	0.00545185	−	0.268711i
$589$	−27007.9			−0.0778503
$590$	−4277.85	+	363830.i	−0.0122891	+	1.04519i
$591$		−	492884.i		−	1.41114i
$592$	−2140.46	+	52727.8i	−0.00610750	+	0.150452i
$593$			379121.i			1.07812i	0.842266	+	0.539062i	$0.181221\pi$
$593$			379121.i			1.07812i	−0.842266	+	0.539062i	$0.818779\pi$
$594$	−303275.	−	309491.i	−0.859536	−	0.877151i
$595$	−110971.	+	110613.i	−0.313454	+	0.312444i
$596$	−9725.84	+	479368.i	−0.0273801	+	1.34951i
$597$			87930.7i			0.246713i
$598$	−145750.	−	148737.i	−0.407574	−	0.415927i
$599$		−	415907.i		−	1.15916i	−0.814916	−	0.579579i	$-0.803217\pi$
$599$		−	415907.i		−	1.15916i	0.814916	−	0.579579i	$-0.196783\pi$
$600$	194056.	−	181414.i	0.539044	−	0.503927i
$601$	95042.6			0.263130			0.131565	−	0.991308i	$-0.458000\pi$
$601$	95042.6			0.263130			0.131565	+	0.991308i	$0.458000\pi$
$602$	−353023.	+	345933.i	−0.974113	+	0.954550i
$603$	−118384.			−0.325580
$604$	198313.	+	4023.56i	0.543599	+	0.0110290i
$605$	79451.7	+	79708.7i	0.217066	+	0.217768i
$606$	−32974.8	+	32312.5i	−0.0897918	+	0.0879885i
$607$	−253259.			−0.687364			−0.343682	−	0.939086i	$-0.611674\pi$
$607$	−253259.			−0.687364			−0.343682	+	0.939086i	$0.611674\pi$
$608$	−446359.	−	494095.i	−1.20747	−	1.33661i
$609$	61445.1			0.165673
$610$	413578.	+	4862.78i	1.11147	+	0.0130685i
$611$			102947.i			0.275761i
$612$	−94673.9	−	1920.83i	−0.252771	−	0.00512844i
$613$		−	427719.i		−	1.13825i	−0.822251	−	0.569125i	$-0.807282\pi$
$613$		−	427719.i		−	1.13825i	0.822251	−	0.569125i	$-0.192718\pi$
$614$	293145.	−	287258.i	0.777581	−	0.761965i
$615$	−212921.	−	213609.i	−0.562947	−	0.564768i
$616$	251962.	−	237076.i	0.664009	−	0.624780i
$617$			283218.i			0.743962i	0.928240	+	0.371981i	$0.121321\pi$
$617$			283218.i			0.743962i	−0.928240	+	0.371981i	$0.878679\pi$
$618$	240446.	−	235617.i	0.629565	−	0.616922i
$619$		−	647178.i		−	1.68905i	−0.535517	−	0.844525i	$-0.679883\pi$
$619$		−	647178.i		−	1.68905i	0.535517	−	0.844525i	$-0.320117\pi$
$620$	11487.7	+	12002.2i	0.0298847	+	0.0312232i
$621$	−326096.			−0.845595
$622$	316684.	+	323175.i	0.818551	+	0.835327i
$623$	200954.			0.517751
$624$	8619.91	−	212342.i	0.0221378	−	0.545339i
$625$	−390617.	−	2522.22i	−0.999979	−	0.00645689i
$626$	−504145.	−	514477.i	−1.28649	−	1.31286i
$627$	−597488.			−1.51983
$628$	−292640.	−	5937.34i	−0.742018	−	0.0150547i
$629$	33066.9			0.0835781
$630$	144139.	+	1694.76i	0.363161	+	0.00426999i
$631$			552250.i			1.38700i	0.720455	+	0.693501i	$0.243933\pi$
$631$			552250.i			1.38700i	−0.720455	+	0.693501i	$0.756067\pi$
$632$	130915.	−	123180.i	0.327759	−	0.308395i
$633$		−	29662.9i		−	0.0740297i
$634$	54483.4	+	55600.0i	0.135546	+	0.138324i
$635$	135935.	+	136374.i	0.337118	+	0.338208i
$636$	517006.	+	10489.5i	1.27815	+	0.0259322i
$637$			109313.i			0.269397i
$638$	−91725.9	−	93605.7i	−0.225346	−	0.229965i
$639$			16836.3i			0.0412329i
$640$	−29717.2	+	408521.i	−0.0725518	+	0.997365i
$641$	394430.			0.959962			0.479981	−	0.877279i	$-0.340644\pi$
$641$	394430.			0.959962			0.479981	+	0.877279i	$0.340644\pi$
$642$	−132586.	+	129923.i	−0.321682	+	0.315222i
$643$	320916.			0.776192			0.388096	−	0.921619i	$-0.373133\pi$
$643$	320916.			0.776192			0.388096	+	0.921619i	$0.373133\pi$
$644$	5281.31	−	260306.i	0.0127342	−	0.627642i
$645$	−370696.	−	371895.i	−0.891043	−	0.893924i
$646$	−298005.	+	292020.i	−0.714099	+	0.699758i
$647$	−378985.			−0.905344			−0.452672	−	0.891677i	$-0.649529\pi$
$647$	−378985.			−0.905344			−0.452672	+	0.891677i	$0.649529\pi$
$648$	−96981.8	−	103071.i	−0.230962	−	0.245463i
$649$	−503420.			−1.19520
$650$	−223905.	+	217995.i	−0.529952	+	0.515965i
$651$		−	10777.1i		−	0.0254296i
$652$	−8580.37	+	422910.i	−0.0201842	+	0.994838i
$653$			205104.i			0.481003i	0.970649	+	0.240501i	$0.0773119\pi$
$653$			205104.i			0.481003i	−0.970649	+	0.240501i	$0.922688\pi$
$654$	−15390.6	+	15081.5i	−0.0359832	+	0.0352606i
$655$	−276567.	+	275676.i	−0.644641	+	0.642563i
$656$	464657.	+	18862.5i	1.07975	+	0.0438320i
$657$		−	217887.i		−	0.504779i
$658$	−91930.7	+	90084.5i	−0.212329	+	0.208065i
$659$		−	204237.i		−	0.470288i	−0.971961	−	0.235144i	$-0.924444\pi$
$659$		−	204237.i		−	0.470288i	0.971961	−	0.235144i	$-0.0755562\pi$
$660$	254138.	+	265521.i	0.583421	+	0.609552i
$661$	549151.			1.25687			0.628433	−	0.777864i	$-0.283697\pi$
$661$	549151.			1.25687			0.628433	+	0.777864i	$0.283697\pi$
$662$	173655.	+	177214.i	0.396252	+	0.404373i
$663$	−133165.			−0.302944
$664$	−133683.	−	142076.i	−0.303207	−	0.322245i
$665$	449836.	−	448386.i	1.01721	−	1.01393i
$666$	−21292.0	−	21728.4i	−0.0480029	−	0.0489867i
$667$	−98628.1			−0.221691
$668$	5328.42	−	262628.i	0.0119411	−	0.588556i
$669$	−28854.6			−0.0644707
$670$	320848.	+	3772.47i	0.714742	+	0.00840382i
$671$			572255.i			1.27100i
$672$	197161.	−	178113.i	0.436600	−	0.394418i
$673$			506727.i			1.11878i	0.828905	+	0.559389i	$0.188964\pi$
$673$			506727.i			1.11878i	−0.828905	+	0.559389i	$0.811036\pi$
$674$	74815.5	+	76348.8i	0.164692	+	0.168067i
$675$	−1579.85	+	489348.i	−0.00346743	+	1.07401i
$676$	4198.50	−	206936.i	0.00918757	−	0.452838i
$677$		−	548346.i		−	1.19640i	−0.801346	−	0.598202i	$-0.795882\pi$
$677$		−	548346.i		−	1.19640i	0.801346	−	0.598202i	$-0.204118\pi$
$678$	117922.	+	120339.i	0.256528	+	0.261786i
$679$			176073.i			0.381903i
$680$	256527.	+	8222.81i	0.554773	+	0.0177829i
$681$	−413823.			−0.892319
$682$	−16417.9	+	16088.2i	−0.0352979	+	0.0345890i
$683$	537201.			1.15158			0.575792	−	0.817596i	$-0.304694\pi$
$683$	537201.			1.15158			0.575792	+	0.817596i	$0.304694\pi$
$684$	383774.	+	7786.35i	0.820283	+	0.0166426i
$685$	66763.1	−	66547.9i	0.142284	−	0.141825i
$686$	−365621.	+	358279.i	−0.776933	+	0.761329i
$687$	522166.			1.10636
$688$	808969.	+	32839.7i	1.70905	+	0.0693781i
$689$	−608313.			−1.28141
$690$	276580.	+	3251.98i	0.580929	+	0.00683046i
$691$		−	197108.i		−	0.412808i	−0.978467	−	0.206404i	$-0.933824\pi$
$691$		−	197108.i		−	0.412808i	0.978467	−	0.206404i	$-0.0661760\pi$
$692$	−232001.	−	4707.03i	−0.484481	−	0.00982958i
$693$			199440.i			0.415285i
$694$	396758.	−	388790.i	0.823771	−	0.807227i
$695$	−123965.	+	123565.i	−0.256642	+	0.255815i
$696$	−68973.1	−	73303.8i	−0.142384	−	0.151324i
$697$		−	291397.i		−	0.599819i
$698$	−211598.	+	207348.i	−0.434311	+	0.425588i
$699$			16364.3i			0.0334921i
$700$	−390595.	−	9186.37i	−0.797133	−	0.0187477i
$701$	−555586.			−1.13062			−0.565308	−	0.824880i	$-0.691243\pi$
$701$	−555586.			−1.13062			−0.565308	+	0.824880i	$0.691243\pi$
$702$	273995.	+	279610.i	0.555992	+	0.567386i
$703$	−134041.			−0.271224
$704$	−565662.	−	34467.8i	−1.14133	−	0.0695454i
$705$	−96533.1	−	96845.3i	−0.194222	−	0.194850i
$706$	64105.9	+	65419.7i	0.128614	+	0.131250i
$707$	67901.2			0.135844
$708$	−386549.	−	7842.65i	−0.771149	−	0.0156457i
$709$	833981.			1.65907			0.829533	−	0.558458i	$-0.188607\pi$
$709$	833981.			1.65907			0.829533	+	0.558458i	$0.188607\pi$
$710$	536.511	−	45630.1i	0.00106430	−	0.0905180i
$711$			103625.i			0.204987i
$712$	−225574.	−	239737.i	−0.444968	−	0.472907i
$713$			17298.8i			0.0340280i
$714$	−116526.	−	118914.i	−0.228574	−	0.233259i
$715$	−305234.	−	306221.i	−0.597064	−	0.598994i
$716$	478025.	+	9698.59i	0.932448	+	0.0189183i
$717$			361191.i			0.702585i
$718$	−607043.	−	619484.i	−1.17753	−	1.20166i
$719$		−	450137.i		−	0.870737i	−0.900252	−	0.435368i	$-0.856618\pi$
$719$		−	450137.i		−	0.870737i	0.900252	−	0.435368i	$-0.143382\pi$
$720$	−159776.	−	173859.i	−0.308210	−	0.335377i
$721$	−495124.			−0.952452
$722$	835683.	−	818899.i	1.60312	−	1.57093i
$723$	−27210.6			−0.0520548
$724$	−4228.31	+	208406.i	−0.00806659	+	0.397587i
$725$	−477.826	+	148004.i	−0.000909063	+	0.281577i
$726$	−85414.5	+	83699.2i	−0.162054	+	0.158799i
$727$	−281881.			−0.533331			−0.266666	−	0.963789i	$-0.585922\pi$
$727$	−281881.			−0.533331			−0.266666	+	0.963789i	$0.585922\pi$
$728$	−227636.	+	214187.i	−0.429515	+	0.404140i
$729$	502768.			0.946047
$730$	−6943.29	+	590526.i	−0.0130293	+	1.10814i
$731$		−	507324.i		−	0.949404i
$732$	−8915.01	+	439404.i	−0.0166379	+	0.820052i
$733$			59324.7i			0.110415i	0.998475	+	0.0552074i	$0.0175820\pi$
$733$			59324.7i			0.110415i	−0.998475	+	0.0552074i	$0.982418\pi$
$734$	−48785.2	+	47805.5i	−0.0905516	+	0.0887331i
$735$	−102502.	−	102834.i	−0.189740	−	0.190353i
$736$	−316472.	+	285896.i	−0.584224	+	0.527780i
$737$			443947.i			0.817328i
$738$	−191478.	+	187633.i	−0.351565	+	0.344505i
$739$		−	11842.3i		−	0.0216845i	−0.999941	−	0.0108422i	$-0.996549\pi$
$739$		−	11842.3i		−	0.0216845i	0.999941	−	0.0108422i	$-0.00345126\pi$
$740$	57013.8	+	59567.4i	0.104116	+	0.108779i
$741$	539803.			0.983102
$742$	−532306.	−	543215.i	−0.966837	−	0.986652i
$743$	8652.18			0.0156728			0.00783642	−	0.999969i	$-0.497506\pi$
$743$	8652.18			0.0156728			0.00783642	+	0.999969i	$0.497506\pi$
$744$	−12857.0	+	12097.5i	−0.0232271	+	0.0218549i
$745$	528885.	+	530595.i	0.952903	+	0.955984i
$746$	23783.7	+	24271.2i	0.0427368	+	0.0436127i
$747$	112460.			0.201539
$748$	−7203.22	+	355033.i	−0.0128743	+	0.634550i
$749$	273019.			0.486664
$750$	6219.96	−	415027.i	0.0110577	−	0.737827i
$751$		−	952787.i		−	1.68934i	−0.535291	−	0.844668i	$-0.679798\pi$
$751$		−	952787.i		−	1.68934i	0.535291	−	0.844668i	$-0.320202\pi$
$752$	210664.	+	8551.80i	0.372524	+	0.0151224i
$753$			320842.i			0.565850i
$754$	82870.0	+	84568.4i	0.145765	+	0.148753i
$755$	219506.	−	218799.i	0.385081	−	0.383840i
$756$	−9928.32	+	489348.i	−0.0173713	+	0.856197i
$757$		−	605031.i		−	1.05581i	−0.849303	−	0.527905i	$-0.822978\pi$
$757$		−	605031.i		−	1.05581i	0.849303	−	0.527905i	$-0.177022\pi$
$758$	−167635.	−	171071.i	−0.291761	−	0.297741i
$759$			382696.i			0.664309i
$760$	−1.03987e6	−	33332.3i	−1.80033	−	0.0577083i
$761$	229134.			0.395659			0.197830	−	0.980236i	$-0.436611\pi$
$761$	229134.			0.395659			0.197830	+	0.980236i	$0.436611\pi$
$762$	−146136.	+	143201.i	−0.251680	+	0.246625i
$763$	31692.1			0.0544380
$764$	−860919.	−	17467.1i	−1.47494	−	0.0299250i
$765$	−104791.	+	104453.i	−0.179061	+	0.178484i
$766$	411934.	−	403661.i	0.702054	−	0.687954i
$767$	454816.			0.773117
$768$	−433805.	−	35278.3i	−0.735481	−	0.0598115i
$769$	−802587.			−1.35719			−0.678593	−	0.734515i	$-0.737410\pi$
$769$	−802587.			−1.35719			−0.678593	+	0.734515i	$0.737410\pi$
$770$	6355.45	−	540529.i	0.0107193	−	0.911670i
$771$			163111.i			0.274394i
$772$	−774888.	−	15721.6i	−1.30018	−	0.0263793i
$773$		−	285645.i		−	0.478045i	−0.971014	−	0.239022i	$-0.923173\pi$
$773$		−	285645.i		−	0.478045i	0.971014	−	0.239022i	$-0.0768269\pi$
$774$	−333364.	+	326669.i	−0.556464	+	0.545288i
$775$	25958.9	+	83.8078i	0.0432199	+	0.000139534i
$776$	210054.	−	197644.i	0.348825	−	0.328217i
$777$		−	53487.2i		−	0.0885948i
$778$	679820.	−	666167.i	1.12314	−	1.10059i
$779$			1.18122e6i			1.94651i
$780$	−229602.	−	239886.i	−0.377387	−	0.394289i
$781$	63137.0			0.103510
$782$	187041.	+	190874.i	0.305861	+	0.312129i
$783$	185411.			0.302420
$784$	223690.	+	9080.58i	0.363927	+	0.0147734i
$785$	−323913.	+	322869.i	−0.525640	+	0.523946i
$786$	−290413.	−	296365.i	−0.470079	−	0.479713i
$787$	369344.			0.596324			0.298162	−	0.954515i	$-0.403627\pi$
$787$	369344.			0.596324			0.298162	+	0.954515i	$0.403627\pi$
$788$	1.18722e6	+	24087.3i	1.91196	+	0.0387914i
$789$	553245.			0.888717
$790$	3302.17	−	280849.i	0.00529109	−	0.450006i
$791$		−	247800.i		−	0.396048i
$792$	237931.	−	223875.i	0.379316	−	0.356907i
$793$		−	517006.i		−	0.822146i
$794$	748193.	+	763527.i	1.18679	+	1.21111i
$795$	572255.	−	570410.i	0.905431	−	0.902512i
$796$	−211800.	−	4297.18i	−0.334272	−	0.00678200i
$797$		−	282731.i		−	0.445100i	−0.974921	−	0.222550i	$-0.928562\pi$
$797$		−	282731.i		−	0.445100i	0.974921	−	0.222550i	$-0.0714380\pi$
$798$	472356.	+	482037.i	0.741760	+	0.756962i
$799$		−	132113.i		−	0.206943i
$800$	427490.	+	476290.i	0.667953	+	0.744204i
$801$	189764.			0.295766
$802$	−49357.0	+	48365.7i	−0.0767361	+	0.0751950i
$803$	−817092.			−1.26718
$804$	−6916.14	+	340883.i	−0.0106992	+	0.527343i
$805$	−287194.	−	288123.i	−0.443184	−	0.444617i
$806$	14832.8	−	14534.9i	0.0228325	−	0.0223739i
$807$	176213.			0.270577
$808$	−76220.2	−	81005.9i	−0.116747	−	0.124078i
$809$	−866021.			−1.32322			−0.661609	−	0.749849i	$-0.730126\pi$
$809$	−866021.			−1.32322			−0.661609	+	0.749849i	$0.730126\pi$
$810$	−221116.	−	2599.85i	−0.337016	−	0.00396258i
$811$			550380.i			0.836798i	0.908263	+	0.418399i	$0.137409\pi$
$811$			550380.i			0.836798i	−0.908263	+	0.418399i	$0.862591\pi$
$812$	−3002.83	+	148004.i	−0.00455427	+	0.224471i
$813$		−	730940.i		−	1.10586i
$814$	−81482.7	+	79846.3i	−0.122975	+	0.120505i
$815$	466595.	+	468104.i	0.702465	+	0.704737i
$816$	−11061.9	+	272498.i	−0.0166131	+	0.409245i
$817$			2.05651e6i			3.08097i
$818$	−360602.	+	353360.i	−0.538917	+	0.528094i
$819$		−	180185.i		−	0.268628i
$820$	524929.	−	502426.i	0.780680	−	0.747213i
$821$	60251.5			0.0893884			0.0446942	−	0.999001i	$-0.485769\pi$
$821$	60251.5			0.0893884			0.0446942	+	0.999001i	$0.485769\pi$
$822$	70105.5	+	71542.3i	0.103755	+	0.105881i
$823$	−760386.			−1.12262			−0.561312	−	0.827604i	$-0.689703\pi$
$823$	−760386.			−1.12262			−0.561312	+	0.827604i	$0.689703\pi$
$824$	555784.	+	590680.i	0.818561	+	0.869957i
$825$	574282.	+	1854.06i	0.843757	+	0.00272405i
$826$	397988.	+	406145.i	0.583325	+	0.595280i
$827$	−1.18336e6			−1.73024			−0.865118	−	0.501568i	$-0.832757\pi$
$827$	−1.18336e6			−1.73024			−0.865118	+	0.501568i	$0.832757\pi$
$828$	4987.22	−	245810.i	0.00727441	−	0.358542i
$829$	518356.			0.754257			0.377129	−	0.926161i	$-0.376911\pi$
$829$	518356.			0.754257			0.377129	+	0.926161i	$0.376911\pi$
$830$	−304794.	−	3583.71i	−0.442436	−	0.00520208i
$831$			737721.i			1.06829i
$832$	511049.	+	31140.1i	0.738272	+	0.0449855i
$833$		−	140281.i		−	0.202167i
$834$	−130171.	−	132839.i	−0.187146	−	0.190982i
$835$	−289756.	−	290693.i	−0.415585	−	0.416929i
$836$	29199.3	−	1.43918e6i	0.0417792	−	2.05922i
$837$		−	32519.9i		−	0.0464193i
$838$	757515.	+	773040.i	1.07871	+	1.10081i
$839$			519063.i			0.737388i	0.929551	+	0.368694i	$0.120195\pi$
$839$			519063.i			0.737388i	−0.929551	+	0.368694i	$0.879805\pi$
$840$	13300.8	−	414944.i	0.0188503	−	0.588073i
$841$	−651203.			−0.920714
$842$	−743967.	+	729026.i	−1.04937	+	1.02830i
$843$	440883.			0.620395
$844$	71449.4	+	1449.63i	0.100303	+	0.00203503i
$845$	−228312.	−	229050.i	−0.319753	−	0.320787i
$846$	−86811.5	+	85068.0i	−0.121293	+	0.118857i
$847$	175885.			0.245166
$848$	−50532.2	+	1.24481e6i	−0.0702711	+	1.73105i
$849$	−822870.			−1.14161
$850$	287337.	−	279754.i	0.397698	−	0.387202i
$851$			85854.6i			0.118551i
$852$	48479.5	+	983.595i	0.0667850	+	0.00135499i
$853$		−	1.08704e6i		−	1.49398i	−0.664834	−	0.746992i	$-0.731498\pi$
$853$		−	1.08704e6i		−	1.49398i	0.664834	−	0.746992i	$-0.268502\pi$
$854$	461679.	−	452407.i	0.633031	−	0.620317i
$855$	424786.	−	423417.i	0.581083	−	0.579210i
$856$	−306468.	−	325710.i	−0.418251	−	0.444512i
$857$		−	1.32143e6i		−	1.79921i	−0.436705	−	0.899605i	$-0.643854\pi$
$857$		−	1.32143e6i		−	1.79921i	0.436705	−	0.899605i	$-0.356146\pi$
$858$	328141.	−	321551.i	0.445745	−	0.436793i
$859$			54795.2i			0.0742602i	0.999310	+	0.0371301i	$0.0118216\pi$
$859$			54795.2i			0.0742602i	−0.999310	+	0.0371301i	$0.988178\pi$
$860$	913904.	−	874726.i	1.23567	−	1.18270i
$861$	−471349.			−0.635823
$862$	−914825.	−	933574.i	−1.23119	−	1.25642i
$863$	−1.00023e6			−1.34300			−0.671502	−	0.741002i	$-0.734351\pi$
$863$	−1.00023e6			−1.34300			−0.671502	+	0.741002i	$0.734351\pi$
$864$	594934.	−	537456.i	0.796969	−	0.719971i
$865$	−256793.	+	255965.i	−0.343203	+	0.342097i
$866$	−461433.	−	470890.i	−0.615280	−	0.627890i
$867$	−383788.			−0.510568
$868$	25958.9	+	526.678i	0.0344546	+	0.000699046i
$869$	388601.			0.514594
$870$	−157257.	−	1849.00i	−0.207765	−	0.00244286i
$871$		−	401085.i		−	0.528689i
$872$	−35574.9	−	37808.6i	−0.0467854	−	0.0497230i
$873$			166268.i			0.218163i
$874$	−758198.	−	773737.i	−0.992567	−	1.01291i
$875$	−433756.	+	429575.i	−0.566538	+	0.561077i
$876$	−627401.	−	12729.3i	−0.817592	−	0.0165880i
$877$			403840.i			0.525061i	0.964924	+	0.262531i	$0.0845571\pi$
$877$			403840.i			0.525061i	−0.964924	+	0.262531i	$0.915443\pi$
$878$	766463.	+	782171.i	0.994264	+	1.01464i
$879$		−	529773.i		−	0.685665i
$880$	−651983.	+	599170.i	−0.841920	+	0.773722i
$881$	642029.			0.827185			0.413593	−	0.910462i	$-0.364274\pi$
$881$	642029.			0.827185			0.413593	+	0.910462i	$0.364274\pi$
$882$	−92179.3	+	90328.1i	−0.118494	+	0.116114i
$883$	238590.			0.306006			0.153003	−	0.988226i	$-0.451106\pi$
$883$	238590.			0.306006			0.153003	+	0.988226i	$0.451106\pi$
$884$	6507.78	−	320756.i	0.00832776	−	0.410459i
$885$	−427857.	+	426478.i	−0.546276	+	0.544516i
$886$	29845.2	−	29245.8i	0.0380195	−	0.0372560i
$887$	439336.			0.558406			0.279203	−	0.960232i	$-0.409930\pi$
$887$	439336.			0.558406			0.279203	+	0.960232i	$0.409930\pi$
$888$	−63810.1	+	60040.2i	−0.0809214	+	0.0761406i
$889$	300922.			0.380759
$890$	−514304.	−	6047.10i	−0.649292	−	0.00763426i
$891$		−	305952.i		−	0.385387i
$892$	1410.13	−	69502.4i	0.00177226	−	0.0873514i
$893$			535537.i			0.671563i
$894$	−568577.	+	557159.i	−0.711401	+	0.697114i
$895$	529109.	−	527403.i	0.660540	−	0.658411i
$896$	419388.	+	483610.i	0.522396	+	0.602392i
$897$		−	345748.i		−	0.429709i
$898$	−553795.	+	542673.i	−0.686746	+	0.672954i
$899$		−	9835.67i		−	0.0121698i
$900$	−368845.	−	8674.82i	−0.455364	−	0.0107097i
$901$	780648.			0.961625
$902$	703634.	+	718054.i	0.864836	+	0.882560i
$903$	−820621.			−1.00639
$904$	−295624.	+	278159.i	−0.361746	+	0.340374i
$905$	229933.	+	230677.i	0.280740	+	0.281648i
$906$	230495.	+	235219.i	0.280806	+	0.286561i
$907$	1.10959e6			1.34880			0.674398	−	0.738368i	$-0.264403\pi$
$907$	1.10959e6			1.34880			0.674398	+	0.738368i	$0.264403\pi$
$908$	20223.6	−	996780.i	0.0245293	−	1.20900i
$909$	64120.1			0.0776008
$910$	−5741.85	+	488343.i	−0.00693376	+	0.589715i
$911$			249223.i			0.300297i	0.988663	+	0.150148i	$0.0479752\pi$
$911$			249223.i			0.300297i	−0.988663	+	0.150148i	$0.952025\pi$
$912$	44841.1	−	1.10461e6i	0.0539122	−	1.32807i
$913$		−	421734.i		−	0.505937i
$914$	−88689.4	−	90507.0i	−0.106164	−	0.108340i
$915$	484793.	+	486360.i	0.579047	+	0.580919i
$916$	−25518.3	+	1.25775e6i	−0.0304131	+	1.49900i
$917$			610271.i			0.725745i
$918$	−351618.	−	358824.i	−0.417239	−	0.425791i
$919$		−	385756.i		−	0.456753i	−0.973573	−	0.228376i	$-0.926658\pi$
$919$		−	385756.i		−	0.456753i	0.973573	−	0.228376i	$-0.0733417\pi$
$920$	−21349.6	+	666044.i	−0.0252240	+	0.786914i
$921$	681432.			0.803347
$922$	263640.	−	258345.i	0.310134	−	0.303905i
$923$	−57041.3			−0.0669555
$924$	574282.	+	11651.5i	0.672638	+	0.0136471i
$925$	128835.	+	415.942i	0.150575	+	0.000486127i
$926$	560720.	−	549459.i	0.653919	−	0.640786i
$927$	−467552.			−0.544090
$928$	179938.	−	162554.i	0.208943	−	0.188756i
$929$	−297906.			−0.345182			−0.172591	−	0.984994i	$-0.555214\pi$
$929$	−297906.			−0.345182			−0.172591	+	0.984994i	$0.555214\pi$
$930$	−324.304	+	27581.9i	−0.000374961	+	0.0318903i
$931$			568651.i			0.656064i
$932$	−39416.8	−	799.722i	−0.0453784	−	0.000920677i
$933$			751237.i			0.863006i
$934$	−745788.	+	730810.i	−0.854912	+	0.837743i
$935$	391707.	+	392973.i	0.448062	+	0.449511i
$936$	−214960.	+	202260.i	−0.245361	+	0.230865i
$937$			661095.i			0.752982i	0.926420	+	0.376491i	$0.122869\pi$
$937$			661095.i			0.752982i	−0.926420	+	0.376491i	$0.877131\pi$
$938$	358164.	−	350971.i	0.407077	−	0.398901i
$939$		−	1.19593e6i		−	1.35636i
$940$	237990.	−	227788.i	0.269341	−	0.257795i
$941$	−1.71686e6			−1.93890			−0.969448	−	0.245298i	$-0.921114\pi$
$941$	−1.71686e6			−1.93890			−0.969448	+	0.245298i	$0.921114\pi$
$942$	−340129.	−	347100.i	−0.383303	−	0.391158i
$943$	756581.			0.850809
$944$	37781.4	−	930702.i	0.0423969	−	1.04440i
$945$	539895.	+	541641.i	0.604569	+	0.606524i
$946$	1.22503e6	+	1.25014e6i	1.36888	+	1.39693i
$947$	659116.			0.734957			0.367478	−	0.930032i	$-0.380221\pi$
$947$	659116.			0.734957			0.367478	+	0.930032i	$0.380221\pi$
$948$	298386.	+	6053.92i	0.332018	+	0.00673628i
$949$	738204.			0.819679
$950$	−1.16476e6	+	1.13402e6i	−1.29059	+	1.25653i
$951$			129245.i			0.142907i
$952$	292125.	−	274867.i	0.322326	−	0.303283i
$953$		−	870368.i		−	0.958335i	−0.877724	−	0.479167i	$-0.840939\pi$
$953$		−	870368.i		−	0.958335i	0.877724	−	0.479167i	$-0.159061\pi$
$954$	−502664.	−	512966.i	−0.552307	−	0.563627i
$955$	−952921.	+	949849.i	−1.04484	+	1.04147i
$956$	−870005.	−	17651.4i	−0.951933	−	0.0193136i
$957$		−	217592.i		−	0.237585i
$958$	−295740.	−	301801.i	−0.322240	−	0.328844i
$959$		−	147319.i		−	0.160185i
$960$	−509957.	+	449913.i	−0.553339	+	0.488187i
$961$	921796.			0.998132
$962$	73615.8	−	72137.4i	0.0795465	−	0.0779489i
$963$	257815.			0.278007
$964$	1329.78	−	65542.4i	0.00143096	−	0.0705291i
$965$	−857696.	+	854932.i	−0.921041	+	0.918072i
$966$	308748.	−	302548.i	0.330864	−	0.324220i
$967$	1.50355e6			1.60792			0.803961	−	0.594682i	$-0.202722\pi$
$967$	1.50355e6			1.60792			0.803961	+	0.594682i	$0.202722\pi$
$968$	−197433.	−	209829.i	−0.210702	−	0.223932i
$969$	−692729.			−0.737761
$970$	5298.37	−	450625.i	0.00563117	−	0.478930i
$971$		−	1.39973e6i		−	1.48459i	−0.670074	−	0.742295i	$-0.733738\pi$
$971$		−	1.39973e6i		−	1.48459i	0.670074	−	0.742295i	$-0.266262\pi$
$972$	−15816.9	+	779584.i	−0.0167413	+	0.825145i
$973$			273540.i			0.288931i
$974$	950311.	−	931226.i	1.00172	−	0.981606i
$975$	−518837.	−	1675.05i	−0.545785	−	0.00176205i
$976$	−1.05796e6	−	42947.4i	−1.11063	−	0.0450855i
$977$		−	1.27509e6i		−	1.33583i	−0.744236	−	0.667917i	$-0.767186\pi$
$977$		−	1.27509e6i		−	1.33583i	0.744236	−	0.667917i	$-0.232814\pi$
$978$	−501613.	+	491539.i	−0.524434	+	0.513902i
$979$		−	711626.i		−	0.742483i
$980$	252706.	−	241873.i	0.263126	−	0.251846i
$981$	29927.3			0.0310978
$982$	−264420.	−	269839.i	−0.274202	−	0.279822i
$983$	652901.			0.675679			0.337839	−	0.941204i	$-0.390304\pi$
$983$	652901.			0.675679			0.337839	+	0.941204i	$0.390304\pi$
$984$	529096.	+	562317.i	0.546442	+	0.580752i
$985$	1.31409e6	−	1.30985e6i	1.35442	−	1.35005i
$986$	−106347.	−	108527.i	−0.109389	−	0.111630i
$987$	−213698.			−0.219365
$988$	−26380.2	+	1.30023e6i	−0.0270249	+	1.33201i
$989$	1.31721e6			1.34668
$990$	6001.54	−	510429.i	0.00612339	−	0.520793i
$991$			817175.i			0.832086i	0.909345	+	0.416043i	$0.136583\pi$
$991$			817175.i			0.832086i	−0.909345	+	0.416043i	$0.863417\pi$
$992$	−28511.0	−	31560.1i	−0.0289727	−	0.0320712i
$993$			411943.i			0.417772i
$994$	−49914.2	−	50937.2i	−0.0505186	−	0.0515539i
$995$	−234434.	+	233678.i	−0.236796	+	0.236033i
$996$	6570.08	−	323827.i	0.00662296	−	0.326433i
$997$			295553.i			0.297335i	0.988887	+	0.148667i	$0.0474984\pi$
$997$			295553.i			0.297335i	−0.988887	+	0.148667i	$0.952502\pi$
$998$	−842766.	−	860038.i	−0.846147	−	0.863489i
$999$		−	161398.i		−	0.161721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.5.d.c.19.2	yes	8
3.2	odd	2		180.5.f.g.19.7		8
4.3	odd	2	inner	20.5.d.c.19.8	yes	8
5.2	odd	4		100.5.b.e.51.3		8
5.3	odd	4		100.5.b.e.51.6		8
5.4	even	2	inner	20.5.d.c.19.7	yes	8
8.3	odd	2		320.5.h.f.319.4		8
8.5	even	2		320.5.h.f.319.6		8
12.11	even	2		180.5.f.g.19.1		8
15.14	odd	2		180.5.f.g.19.2		8
20.3	even	4		100.5.b.e.51.5		8
20.7	even	4		100.5.b.e.51.4		8
20.19	odd	2	inner	20.5.d.c.19.1	✓	8
40.19	odd	2		320.5.h.f.319.5		8
40.29	even	2		320.5.h.f.319.3		8
60.59	even	2		180.5.f.g.19.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.5.d.c.19.1	✓	8	20.19	odd	2	inner
20.5.d.c.19.2	yes	8	1.1	even	1	trivial
20.5.d.c.19.7	yes	8	5.4	even	2	inner
20.5.d.c.19.8	yes	8	4.3	odd	2	inner
100.5.b.e.51.3		8	5.2	odd	4
100.5.b.e.51.4		8	20.7	even	4
100.5.b.e.51.5		8	20.3	even	4
100.5.b.e.51.6		8	5.3	odd	4
180.5.f.g.19.1		8	12.11	even	2
180.5.f.g.19.2		8	15.14	odd	2
180.5.f.g.19.7		8	3.2	odd	2
180.5.f.g.19.8		8	60.59	even	2
320.5.h.f.319.3		8	40.29	even	2
320.5.h.f.319.4		8	8.3	odd	2
320.5.h.f.319.5		8	40.19	odd	2
320.5.h.f.319.6		8	8.5	even	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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.85697 + 2.79959i) q^{2} -6.64118 q^{3} +(0.324555 - 15.9967i) q^{4} +(-17.6491 - 17.7062i) q^{5} +(18.9737 - 18.5926i) q^{6} -39.0703 q^{7} +(43.8570 + 46.6107i) q^{8} -36.8947 q^{9} +O(q^{10})\)	\(q+(-2.85697 + 2.79959i) q^{2} -6.64118 q^{3} +(0.324555 - 15.9967i) q^{4} +(-17.6491 - 17.7062i) q^{5} +(18.9737 - 18.5926i) q^{6} -39.0703 q^{7} +(43.8570 + 46.6107i) q^{8} -36.8947 q^{9} +(99.9931 + 1.17570i) q^{10} +138.357i q^{11} +(-2.15543 + 106.237i) q^{12} -124.999i q^{13} +(111.623 - 109.381i) q^{14} +(117.211 + 117.590i) q^{15} +(-255.789 - 10.3836i) q^{16} +160.412i q^{17} +(105.407 - 103.290i) q^{18} -650.252i q^{19} +(-288.969 + 276.581i) q^{20} +259.473 q^{21} +(-387.344 - 395.283i) q^{22} -416.491 q^{23} +(-291.263 - 309.551i) q^{24} +(-2.01779 + 624.997i) q^{25} +(349.947 + 357.119i) q^{26} +782.960 q^{27} +(-12.6805 + 624.997i) q^{28} +236.807 q^{29} +(-664.073 - 7.80805i) q^{30} -41.5345i q^{31} +(759.852 - 686.440i) q^{32} -918.856i q^{33} +(-449.088 - 458.291i) q^{34} +(689.557 + 691.786i) q^{35} +(-11.9744 + 590.193i) q^{36} -206.138i q^{37} +(1820.44 + 1857.75i) q^{38} +830.144i q^{39} +(51.2606 - 1599.18i) q^{40} -1816.56 q^{41} +(-741.307 + 726.420i) q^{42} -3162.64 q^{43} +(2213.26 + 44.9046i) q^{44} +(651.158 + 653.264i) q^{45} +(1189.90 - 1166.01i) q^{46} -823.584 q^{47} +(1698.74 + 68.9596i) q^{48} -874.509 q^{49} +(-1743.97 - 1791.25i) q^{50} -1065.32i q^{51} +(-1999.58 - 40.5692i) q^{52} -4866.53i q^{53} +(-2236.89 + 2191.97i) q^{54} +(2449.78 - 2441.88i) q^{55} +(-1713.51 - 1821.10i) q^{56} +4318.44i q^{57} +(-676.551 + 662.964i) q^{58} +3638.55i q^{59} +(1919.09 - 1836.83i) q^{60} +4136.07 q^{61} +(116.280 + 118.663i) q^{62} +1441.49 q^{63} +(-249.122 + 4088.42i) q^{64} +(-2213.26 + 2206.13i) q^{65} +(2572.42 + 2625.15i) q^{66} +3208.70 q^{67} +(2566.06 + 52.0625i) q^{68} +2766.00 q^{69} +(-3906.76 - 45.9350i) q^{70} -456.333i q^{71} +(-1618.09 - 1719.69i) q^{72} +5905.66i q^{73} +(577.102 + 588.929i) q^{74} +(13.4005 - 4150.72i) q^{75} +(-10401.9 - 211.043i) q^{76} -5405.67i q^{77} +(-2324.06 - 2371.70i) q^{78} -2808.68i q^{79} +(4330.60 + 4712.31i) q^{80} -2211.32 q^{81} +(5189.86 - 5085.63i) q^{82} -3048.15 q^{83} +(84.2134 - 4150.72i) q^{84} +(2840.28 - 2831.12i) q^{85} +(9035.57 - 8854.10i) q^{86} -1572.68 q^{87} +(-6448.94 + 6067.94i) q^{88} -5143.40 q^{89} +(-3689.21 - 43.3771i) q^{90} +4883.77i q^{91} +(-135.174 + 6662.49i) q^{92} +275.839i q^{93} +(2352.96 - 2305.70i) q^{94} +(-11513.5 + 11476.4i) q^{95} +(-5046.32 + 4558.78i) q^{96} -4506.56i q^{97} +(2498.45 - 2448.27i) q^{98} -5104.65i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 48 q^{4} - 40 q^{5} + 312 q^{9}+O(q^{10}) \) 8 * q - 48 * q^4 - 40 * q^5 + 312 * q^9	\( 8 q - 48 q^{4} - 40 q^{5} + 312 q^{9} - 160 q^{10} + 640 q^{14} - 832 q^{16} - 400 q^{20} - 960 q^{21} + 1920 q^{24} - 2040 q^{25} + 2496 q^{26} + 2704 q^{29} - 1920 q^{30} - 2176 q^{34} - 5712 q^{36} + 6400 q^{40} + 1456 q^{41} + 1920 q^{44} + 6120 q^{45} + 7040 q^{46} - 8008 q^{49} - 12480 q^{50} - 11520 q^{54} - 14720 q^{56} + 21120 q^{60} + 6576 q^{61} + 6912 q^{64} - 1920 q^{65} + 46080 q^{66} - 12480 q^{69} - 6400 q^{70} - 23616 q^{74} - 48000 q^{76} + 19520 q^{80} - 19512 q^{81} + 24960 q^{84} + 8960 q^{85} + 37120 q^{86} + 27664 q^{89} - 48480 q^{90} + 10880 q^{94} - 76800 q^{96}+O(q^{100}) \) 8 * q - 48 * q^4 - 40 * q^5 + 312 * q^9 - 160 * q^10 + 640 * q^14 - 832 * q^16 - 400 * q^20 - 960 * q^21 + 1920 * q^24 - 2040 * q^25 + 2496 * q^26 + 2704 * q^29 - 1920 * q^30 - 2176 * q^34 - 5712 * q^36 + 6400 * q^40 + 1456 * q^41 + 1920 * q^44 + 6120 * q^45 + 7040 * q^46 - 8008 * q^49 - 12480 * q^50 - 11520 * q^54 - 14720 * q^56 + 21120 * q^60 + 6576 * q^61 + 6912 * q^64 - 1920 * q^65 + 46080 * q^66 - 12480 * q^69 - 6400 * q^70 - 23616 * q^74 - 48000 * q^76 + 19520 * q^80 - 19512 * q^81 + 24960 * q^84 + 8960 * q^85 + 37120 * q^86 + 27664 * q^89 - 48480 * q^90 + 10880 * q^94 - 76800 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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