LMFDB - Embedded newform 504.2.bk.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.144054149089536.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 $ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$0.186445 - 1.54034i$ of defining polynomial
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.a.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13090 - 0.849154i) q^{2} +(0.557875 + 1.92062i) q^{4} +(-1.03926 + 1.80005i) q^{5} +(1.25203 - 2.33076i) q^{7} +(1.00000 - 2.64575i) q^{8} +O(q^{10})$	\(q+(-1.13090 - 0.849154i) q^{2} +(0.557875 + 1.92062i) q^{4} +(-1.03926 + 1.80005i) q^{5} +(1.25203 - 2.33076i) q^{7} +(1.00000 - 2.64575i) q^{8} +(2.70382 - 1.15319i) q^{10} +(0.669938 + 1.16037i) q^{11} -2.50406 q^{13} +(-3.39509 + 1.57269i) q^{14} +(-3.37755 + 2.14293i) q^{16} +(2.78212 - 1.60626i) q^{17} +(3.55442 + 2.05215i) q^{19} +(-4.03699 - 0.991819i) q^{20} +(0.227697 - 1.88114i) q^{22} +(5.54952 + 3.20402i) q^{23} +(0.339877 + 0.588684i) q^{25} +(2.83184 + 2.12633i) q^{26} +(5.17497 + 1.10440i) q^{28} +4.66151i q^{29} +(2.21897 + 3.84337i) q^{31} +(5.63935 + 0.444621i) q^{32} +(-4.51026 - 0.545930i) q^{34} +(2.89430 + 4.67598i) q^{35} +(5.50178 + 3.17646i) q^{37} +(-2.27711 - 5.33903i) q^{38} +(3.72323 + 4.54968i) q^{40} -5.55076i q^{41} +(-1.85488 + 1.93404i) q^{44} +(-3.55526 - 8.33583i) q^{46} +(0.565988 - 0.980320i) q^{47} +(-3.86485 - 5.83634i) q^{49} +(0.115516 - 0.954351i) q^{50} +(-1.39695 - 4.80934i) q^{52} +(7.43567 - 4.29299i) q^{53} -2.78496 q^{55} +(-4.91457 - 5.64331i) q^{56} +(3.95834 - 5.27171i) q^{58} +(-6.29193 + 3.63265i) q^{59} +(2.57219 - 4.45517i) q^{61} +(0.754178 - 6.23073i) q^{62} +(-6.00000 - 5.29150i) q^{64} +(2.60236 - 4.50743i) q^{65} +(3.93243 + 6.81116i) q^{67} +(4.63708 + 4.44730i) q^{68} +(0.697459 - 7.74577i) q^{70} +5.29150i q^{71} +(0.480369 - 0.277341i) q^{73} +(-3.52467 - 8.26412i) q^{74} +(-1.95847 + 7.97153i) q^{76} +(3.54332 - 0.108651i) q^{77} +(5.26862 + 3.04184i) q^{79} +(-0.347228 - 8.30683i) q^{80} +(-4.71345 + 6.27736i) q^{82} +0.503175i q^{83} +6.67728i q^{85} +(3.73998 - 0.612123i) q^{88} +(-1.50000 - 0.866025i) q^{89} +(-3.13515 + 5.83634i) q^{91} +(-3.05776 + 12.4460i) q^{92} +(-1.47252 + 0.628034i) q^{94} +(-7.38794 + 4.26543i) q^{95} -17.2234i q^{97} +(-0.585189 + 9.88218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{8}+O(q^{10}) $ 12 * q + 12 * q^8	$ 12 q + 12 q^{8} + 6 q^{10} + 6 q^{11} - 6 q^{14} + 6 q^{17} - 6 q^{19} + 24 q^{22} - 6 q^{26} + 6 q^{28} - 18 q^{35} + 24 q^{38} + 42 q^{40} - 6 q^{44} - 18 q^{46} - 12 q^{49} + 48 q^{50} - 24 q^{52} + 18 q^{58} - 42 q^{59} - 72 q^{64} + 12 q^{65} + 30 q^{67} + 36 q^{68} + 30 q^{70} + 18 q^{73} - 12 q^{74} - 36 q^{80} + 54 q^{82} + 6 q^{88} - 18 q^{89} - 72 q^{91} - 60 q^{92} - 12 q^{94} + 6 q^{98}+O(q^{100}) $ 12 * q + 12 * q^8 + 6 * q^10 + 6 * q^11 - 6 * q^14 + 6 * q^17 - 6 * q^19 + 24 * q^22 - 6 * q^26 + 6 * q^28 - 18 * q^35 + 24 * q^38 + 42 * q^40 - 6 * q^44 - 18 * q^46 - 12 * q^49 + 48 * q^50 - 24 * q^52 + 18 * q^58 - 42 * q^59 - 72 * q^64 + 12 * q^65 + 30 * q^67 + 36 * q^68 + 30 * q^70 + 18 * q^73 - 12 * q^74 - 36 * q^80 + 54 * q^82 + 6 * q^88 - 18 * q^89 - 72 * q^91 - 60 * q^92 - 12 * q^94 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.13090	−	0.849154i	−0.799668	−	0.600443i
$2$	−1.13090	−	0.849154i	−0.799668	−	0.600443i
$3$		0			0
$3$		0			0
$4$	0.557875	+	1.92062i	0.278937	+	0.960309i
$5$	−1.03926	+	1.80005i	−0.464771	+	0.805007i	−0.999191	−	0.0402117i	$-0.987197\pi$
$5$	−1.03926	+	1.80005i	−0.464771	+	0.805007i	0.534420	+	0.845219i	$0.320530\pi$
$6$		0			0
$7$	1.25203	−	2.33076i	0.473222	−	0.880943i
$7$	1.25203	−	2.33076i	0.473222	−	0.880943i
$8$	1.00000	−	2.64575i	0.353553	−	0.935414i
$9$		0			0
$10$	2.70382	−	1.15319i	0.855023	−	0.364670i
$11$	0.669938	+	1.16037i	0.201994	+	0.349864i	0.949171	−	0.314761i	$-0.101925\pi$
$11$	0.669938	+	1.16037i	0.201994	+	0.349864i	−0.747177	+	0.664625i	$0.768591\pi$
$12$		0			0
$13$	−2.50406			−0.694500			−0.347250	−	0.937773i	$-0.612884\pi$
$13$	−2.50406			−0.694500			−0.347250	+	0.937773i	$0.612884\pi$
$14$	−3.39509	+	1.57269i	−0.907376	+	0.420319i
$15$		0			0
$16$	−3.37755	+	2.14293i	−0.844388	+	0.535732i
$17$	2.78212	−	1.60626i	0.674763	−	0.389575i	−0.123116	−	0.992392i	$-0.539289\pi$
$17$	2.78212	−	1.60626i	0.674763	−	0.389575i	0.797879	+	0.602818i	$0.205955\pi$
$18$		0			0
$19$	3.55442	+	2.05215i	0.815440	+	0.470795i	0.848842	−	0.528647i	$-0.177301\pi$
$19$	3.55442	+	2.05215i	0.815440	+	0.470795i	−0.0334012	+	0.999442i	$0.510634\pi$
$20$	−4.03699	−	0.991819i	−0.902698	−	0.221778i
$21$		0			0
$22$	0.227697	−	1.88114i	0.0485451	−	0.401061i
$23$	5.54952	+	3.20402i	1.15716	+	0.668084i	0.950621	−	0.310355i	$-0.100448\pi$
$23$	5.54952	+	3.20402i	1.15716	+	0.668084i	0.206535	+	0.978439i	$0.433781\pi$
$24$		0			0
$25$	0.339877	+	0.588684i	0.0679754	+	0.117737i
$26$	2.83184	+	2.12633i	0.555369	+	0.417007i
$27$		0			0
$28$	5.17497	+	1.10440i	0.977977	+	0.208712i
$29$			4.66151i			0.865621i	0.901485	+	0.432811i	$0.142478\pi$
$29$			4.66151i			0.865621i	−0.901485	+	0.432811i	$0.857522\pi$
$30$		0			0
$31$	2.21897	+	3.84337i	0.398539	+	0.690290i	0.993546	−	0.113430i	$-0.0361839\pi$
$31$	2.21897	+	3.84337i	0.398539	+	0.690290i	−0.595007	+	0.803721i	$0.702851\pi$
$32$	5.63935	+	0.444621i	0.996906	+	0.0785986i
$33$		0			0
$34$	−4.51026	−	0.545930i	−0.773503	−	0.0936262i
$35$	2.89430	+	4.67598i	0.489226	+	0.790384i
$36$		0			0
$37$	5.50178	+	3.17646i	0.904488	+	0.522206i	0.878653	−	0.477460i	$-0.158442\pi$
$37$	5.50178	+	3.17646i	0.904488	+	0.522206i	0.0258343	+	0.999666i	$0.491776\pi$
$38$	−2.27711	−	5.33903i	−0.369396	−	0.866105i
$39$		0			0
$40$	3.72323	+	4.54968i	0.588694	+	0.719367i
$41$		−	5.55076i		−	0.866882i	−0.901182	−	0.433441i	$-0.857299\pi$
$41$		−	5.55076i		−	0.866882i	0.901182	−	0.433441i	$-0.142701\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	−1.85488	+	1.93404i	−0.279634	+	0.291567i
$45$		0			0
$46$	−3.55526	−	8.33583i	−0.524194	−	1.22905i
$47$	0.565988	−	0.980320i	0.0825579	−	0.142994i	−0.821790	−	0.569790i	$-0.807024\pi$
$47$	0.565988	−	0.980320i	0.0825579	−	0.142994i	0.904348	+	0.426796i	$0.140358\pi$
$48$		0			0
$49$	−3.86485	−	5.83634i	−0.552122	−	0.833763i
$50$	0.115516	−	0.954351i	0.0163365	−	0.134966i
$51$		0			0
$52$	−1.39695	−	4.80934i	−0.193722	−	0.666935i
$53$	7.43567	−	4.29299i	1.02137	−	0.589687i	0.106868	−	0.994273i	$-0.465918\pi$
$53$	7.43567	−	4.29299i	1.02137	−	0.589687i	0.914500	+	0.404586i	$0.132584\pi$
$54$		0			0
$55$	−2.78496			−0.375524
$56$	−4.91457	−	5.64331i	−0.656738	−	0.754119i
$57$		0			0
$58$	3.95834	−	5.27171i	0.519756	−	0.692210i
$59$	−6.29193	+	3.63265i	−0.819140	+	0.472931i	−0.850120	−	0.526589i	$-0.823471\pi$
$59$	−6.29193	+	3.63265i	−0.819140	+	0.472931i	0.0309798	+	0.999520i	$0.490137\pi$
$60$		0			0
$61$	2.57219	−	4.45517i	0.329336	−	0.570426i	−0.653045	−	0.757319i	$-0.726509\pi$
$61$	2.57219	−	4.45517i	0.329336	−	0.570426i	0.982380	+	0.186893i	$0.0598419\pi$
$62$	0.754178	−	6.23073i	0.0957807	−	0.791303i
$63$		0			0
$64$	−6.00000	−	5.29150i	−0.750000	−	0.661438i
$65$	2.60236	−	4.50743i	0.322784	−	0.559078i
$66$		0			0
$67$	3.93243	+	6.81116i	0.480422	+	0.832116i	0.999748	−	0.0224607i	$-0.00715005\pi$
$67$	3.93243	+	6.81116i	0.480422	+	0.832116i	−0.519325	+	0.854577i	$0.673817\pi$
$68$	4.63708	+	4.44730i	0.562329	+	0.539314i
$69$		0			0
$70$	0.697459	−	7.74577i	0.0833622	−	0.925797i
$71$			5.29150i			0.627986i	0.949425	+	0.313993i	$0.101667\pi$
$71$			5.29150i			0.627986i	−0.949425	+	0.313993i	$0.898333\pi$
$72$		0			0
$73$	0.480369	−	0.277341i	0.0562230	−	0.0324604i	−0.471625	−	0.881799i	$-0.656332\pi$
$73$	0.480369	−	0.277341i	0.0562230	−	0.0324604i	0.527848	+	0.849339i	$0.322999\pi$
$74$	−3.52467	−	8.26412i	−0.409735	−	0.960685i
$75$		0			0
$76$	−1.95847	+	7.97153i	−0.224652	+	0.914397i
$77$	3.54332	−	0.108651i	0.403798	−	0.0123820i
$78$		0			0
$79$	5.26862	+	3.04184i	0.592766	+	0.342233i	0.766190	−	0.642614i	$-0.222150\pi$
$79$	5.26862	+	3.04184i	0.592766	+	0.342233i	−0.173425	+	0.984847i	$0.555483\pi$
$80$	−0.347228	−	8.30683i	−0.0388212	−	0.928731i
$81$		0			0
$82$	−4.71345	+	6.27736i	−0.520513	+	0.693218i
$83$			0.503175i			0.0552307i	0.999619	+	0.0276153i	$0.00879135\pi$
$83$			0.503175i			0.0552307i	−0.999619	+	0.0276153i	$0.991209\pi$
$84$		0			0
$85$			6.67728i			0.724252i
$86$		0			0
$87$		0			0
$88$	3.73998	−	0.612123i	0.398683	−	0.0652525i
$89$	−1.50000	−	0.866025i	−0.159000	−	0.0917985i	0.418389	−	0.908268i	$-0.362595\pi$
$89$	−1.50000	−	0.866025i	−0.159000	−	0.0917985i	−0.577389	+	0.816469i	$0.695928\pi$
$90$		0			0
$91$	−3.13515	+	5.83634i	−0.328653	+	0.611815i
$92$	−3.05776	+	12.4460i	−0.318793	+	1.29758i
$93$		0			0
$94$	−1.47252	+	0.628034i	−0.151879	+	0.0647768i
$95$	−7.38794	+	4.26543i	−0.757986	+	0.437624i
$96$		0			0
$97$		−	17.2234i		−	1.74878i	−0.485228	−	0.874388i	$-0.661263\pi$
$97$		−	17.2234i		−	1.74878i	0.485228	−	0.874388i	$-0.338737\pi$
$98$	−0.585189	+	9.88218i	−0.0591130	+	0.998251i
$99$		0			0
$100$	−0.941029	+	0.981186i	−0.0941029	+	0.0981186i
$101$	0.613725	+	1.06300i	0.0610679	+	0.105773i	0.894943	−	0.446180i	$-0.147216\pi$
$101$	0.613725	+	1.06300i	0.0610679	+	0.105773i	−0.833875	+	0.551953i	$0.813883\pi$
$102$		0			0
$103$	−7.62804	+	13.2122i	−0.751613	+	1.30183i	0.195427	+	0.980718i	$0.437391\pi$
$103$	−7.62804	+	13.2122i	−0.751613	+	1.30183i	−0.947041	+	0.321114i	$0.895943\pi$
$104$	−2.50406	+	6.62511i	−0.245543	+	0.649645i
$105$		0			0
$106$	−12.0544	−	1.45909i	−1.17083	−	0.141719i
$107$	5.55442	−	9.62054i	0.536966	−	0.930053i	−0.462099	−	0.886828i	$-0.652904\pi$
$107$	5.55442	−	9.62054i	0.536966	−	0.930053i	0.999065	−	0.0432246i	$-0.0137631\pi$
$108$		0			0
$109$	−10.9109	+	6.29938i	−1.04507	+	0.603372i	−0.921265	−	0.388935i	$-0.872843\pi$
$109$	−10.9109	+	6.29938i	−1.04507	+	0.603372i	−0.123805	+	0.992307i	$0.539510\pi$
$110$	3.14952	+	2.36486i	0.300295	+	0.225481i
$111$		0			0
$112$	0.765858	+	10.5553i	0.0723668	+	0.997378i
$113$	−20.0629			−1.88736			−0.943680	−	0.330860i	$-0.892661\pi$
$113$	−20.0629			−1.88736			−0.943680	+	0.330860i	$0.892661\pi$
$114$		0			0
$115$	−11.5348	+	6.65961i	−1.07562	+	0.621012i
$116$	−8.95299	+	2.60054i	−0.831264	+	0.241454i
$117$		0			0
$118$	10.2002	+	1.23465i	0.939008	+	0.113659i
$119$	−0.260504	−	8.49552i	−0.0238804	−	0.778783i
$120$		0			0
$121$	4.60236	−	7.97153i	0.418397	−	0.724685i
$122$	−6.69202	+	2.85417i	−0.605867	+	0.258404i
$123$		0			0
$124$	−6.14375	+	6.40592i	−0.551725	+	0.575269i
$125$	−11.8055			−1.05591
$126$		0			0
$127$		−	14.6145i		−	1.29683i	−0.761287	−	0.648415i	$-0.775432\pi$
$127$		−	14.6145i		−	1.29683i	0.761287	−	0.648415i	$-0.224568\pi$
$128$	2.29211	+	11.0791i	0.202595	+	0.979263i
$129$		0			0
$130$	−6.77052	+	2.88765i	−0.593814	+	0.253263i
$131$	5.27230	+	3.04397i	0.460643	+	0.265953i	0.712315	−	0.701860i	$-0.247647\pi$
$131$	5.27230	+	3.04397i	0.460643	+	0.265953i	−0.251671	+	0.967813i	$0.580980\pi$
$132$		0			0
$133$	9.23329	−	5.71515i	0.800628	−	0.495566i
$134$	1.33654	−	11.0420i	0.115460	−	0.953882i
$135$		0			0
$136$	−1.46764	−	8.96705i	−0.125849	−	0.768918i
$137$	6.98685	+	12.1016i	0.596927	+	1.03391i	0.993272	+	0.115806i	$0.0369451\pi$
$137$	6.98685	+	12.1016i	0.596927	+	1.03391i	−0.396345	+	0.918102i	$0.629722\pi$
$138$		0			0
$139$			0.503175i			0.0426788i	0.999772	+	0.0213394i	$0.00679305\pi$
$139$			0.503175i			0.0426788i	−0.999772	+	0.0213394i	$0.993207\pi$
$140$	−7.36611	+	8.16745i	−0.622550	+	0.690276i
$141$		0			0
$142$	4.49330	−	5.98417i	0.377069	−	0.502180i
$143$	−1.67756	−	2.90562i	−0.140285	−	0.242981i
$144$		0			0
$145$	−8.39096	−	4.84452i	−0.696832	−	0.402316i
$146$	−0.778756	−	0.0942619i	−0.0644503	−	0.00780117i
$147$		0			0
$148$	−3.03146	+	12.3389i	−0.249184	+	1.01425i
$149$	−4.77077	−	2.75440i	−0.390836	−	0.225649i	0.291686	−	0.956514i	$-0.405784\pi$
$149$	−4.77077	−	2.75440i	−0.390836	−	0.225649i	−0.682522	+	0.730865i	$0.739117\pi$
$150$		0			0
$151$	6.09511	−	3.51901i	0.496013	−	0.286373i	−0.231053	−	0.972941i	$-0.574217\pi$
$151$	6.09511	−	3.51901i	0.496013	−	0.286373i	0.727066	+	0.686568i	$0.240884\pi$
$152$	8.98389	−	7.35197i	0.728690	−	0.596324i
$153$		0			0
$154$	−4.09940	−	2.88595i	−0.330339	−	0.232556i
$155$	−9.22436			−0.740918
$156$		0			0
$157$	−7.15477	−	12.3924i	−0.571013	−	0.989023i	−0.996462	−	0.0840409i	$-0.973217\pi$
$157$	−7.15477	−	12.3924i	−0.571013	−	0.989023i	0.425450	−	0.904982i	$-0.360116\pi$
$158$	−3.37530	−	7.91388i	−0.268524	−	0.629595i
$159$		0			0
$160$	−6.66110	+	9.68905i	−0.526606	+	0.765987i
$161$	14.4159	−	8.92306i	1.13614	−	0.703236i
$162$		0			0
$163$	−4.15679	+	7.19977i	−0.325585	+	0.563929i	−0.981631	−	0.190792i	$-0.938894\pi$
$163$	−4.15679	+	7.19977i	−0.325585	+	0.563929i	0.656046	+	0.754721i	$0.272228\pi$
$164$	10.6609	−	3.09663i	0.832475	−	0.241806i
$165$		0			0
$166$	0.427273	−	0.569041i	0.0331628	−	0.0441662i
$167$	2.50406			0.193770			0.0968848	−	0.995296i	$-0.469112\pi$
$167$	2.50406			0.193770			0.0968848	+	0.995296i	$0.469112\pi$
$168$		0			0
$169$	−6.72971			−0.517670
$170$	5.67004	−	7.55134i	0.434872	−	0.579161i
$171$		0			0
$172$		0			0
$173$	−2.71682	+	4.70568i	−0.206556	+	0.357766i	−0.950627	−	0.310334i	$-0.899559\pi$
$173$	−2.71682	+	4.70568i	−0.206556	+	0.357766i	0.744071	+	0.668100i	$0.232892\pi$
$174$		0			0
$175$	1.79761	−	0.0551216i	0.135887	−	0.00416680i
$176$	−4.74934	−	2.48357i	−0.357995	−	0.187206i
$177$		0			0
$178$	0.960963	+	2.25312i	0.0720272	+	0.168879i
$179$	1.75915	+	3.04694i	0.131485	+	0.227739i	0.924249	−	0.381790i	$-0.124692\pi$
$179$	1.75915	+	3.04694i	0.131485	+	0.227739i	−0.792764	+	0.609529i	$0.791359\pi$
$180$		0			0
$181$	−22.1981			−1.64997			−0.824985	−	0.565154i	$-0.808817\pi$
$181$	−22.1981			−1.64997			−0.824985	+	0.565154i	$0.808817\pi$
$182$	8.50150	−	3.93811i	0.630173	−	0.291912i
$183$		0			0
$184$	14.0266	−	11.4786i	1.03405	−	0.846216i
$185$	−11.4356	+	6.60233i	−0.840760	+	0.485413i
$186$		0			0
$187$	3.72770	+	2.15219i	0.272596	+	0.157383i
$188$	2.19857	+	0.540152i	0.160347	+	0.0393946i
$189$		0			0
$190$	11.9770	+	1.44972i	0.868905	+	0.105174i
$191$	1.13615	+	0.655958i	0.0822091	+	0.0474635i	0.540541	−	0.841318i	$-0.318220\pi$
$191$	1.13615	+	0.655958i	0.0822091	+	0.0474635i	−0.458332	+	0.888781i	$0.651553\pi$
$192$		0			0
$193$	5.64697	+	9.78084i	0.406478	+	0.704040i	0.994492	−	0.104810i	$-0.0334235\pi$
$193$	5.64697	+	9.78084i	0.406478	+	0.704040i	−0.588014	+	0.808851i	$0.700090\pi$
$194$	−14.6254	+	19.4780i	−1.05004	+	1.39844i
$195$		0			0
$196$	9.05329	−	10.6789i	0.646663	−	0.762776i
$197$		−	5.92149i		−	0.421889i	−0.977498	−	0.210944i	$-0.932346\pi$
$197$		−	5.92149i		−	0.421889i	0.977498	−	0.210944i	$-0.0676539\pi$
$198$		0			0
$199$	−9.30560	−	16.1178i	−0.659657	−	1.14256i	−0.980704	−	0.195496i	$-0.937368\pi$
$199$	−9.30560	−	16.1178i	−0.659657	−	1.14256i	0.321048	−	0.947063i	$-0.395965\pi$
$200$	1.89739	−	0.310546i	0.134166	−	0.0219589i
$201$		0			0
$202$	0.208591	−	1.72330i	0.0146764	−	0.121251i
$203$	10.8649	+	5.83634i	0.762563	+	0.409631i
$204$		0			0
$205$	9.99164	+	5.76868i	0.697847	+	0.402902i
$206$	19.8457	−	8.46426i	1.38272	−	0.589733i
$207$		0			0
$208$	8.45758	−	5.36601i	0.586427	−	0.372066i
$209$			5.49925i			0.380391i
$210$		0			0
$211$	5.72971			0.394449			0.197225	−	0.980358i	$-0.436807\pi$
$211$	5.72971			0.394449			0.197225	+	0.980358i	$0.436807\pi$
$212$	12.3934	+	11.8861i	0.851180	+	0.816344i
$213$		0			0
$214$	−14.4508	+	6.16332i	−0.987838	+	0.421316i
$215$		0			0
$216$		0			0
$217$	11.7362	−	0.359875i	0.796704	−	0.0244299i
$218$	17.6882	+	2.14101i	1.19800	+	0.145008i
$219$		0			0
$220$	−1.55366	−	5.34885i	−0.104748	−	0.360619i
$221$	−6.96658	+	4.02216i	−0.468623	+	0.270560i
$222$		0			0
$223$	20.8668			1.39734			0.698672	−	0.715442i	$-0.253775\pi$
$223$	20.8668			1.39734			0.698672	+	0.715442i	$0.253775\pi$
$224$	8.09693	−	12.5873i	0.540999	−	0.841023i
$225$		0			0
$226$	22.6892	+	17.0365i	1.50926	+	1.13325i
$227$	−14.2775	+	8.24309i	−0.947628	+	0.547113i	−0.892343	−	0.451357i	$-0.850940\pi$
$227$	−14.2775	+	8.24309i	−0.947628	+	0.547113i	−0.0552847	+	0.998471i	$0.517607\pi$
$228$		0			0
$229$	4.24976	−	7.36079i	0.280832	−	0.486415i	−0.690758	−	0.723086i	$-0.742723\pi$
$229$	4.24976	−	7.36079i	0.280832	−	0.486415i	0.971590	+	0.236671i	$0.0760564\pi$
$230$	18.6997	+	2.26345i	1.23302	+	0.149247i
$231$		0			0
$232$	12.3332	+	4.66151i	0.809715	+	0.306043i
$233$	2.23751	−	3.87548i	0.146584	−	0.253891i	−0.783379	−	0.621545i	$-0.786505\pi$
$233$	2.23751	−	3.87548i	0.146584	−	0.253891i	0.929963	+	0.367653i	$0.119839\pi$
$234$		0			0
$235$	1.17642	+	2.03762i	0.0767410	+	0.132919i
$236$	−10.4870	−	10.0578i	−0.682649	−	0.654710i
$237$		0			0
$238$	−6.91940	+	9.82880i	−0.448518	+	0.637107i
$239$		−	24.5675i		−	1.58914i	−0.607171	−	0.794571i	$-0.707696\pi$
$239$		−	24.5675i		−	1.58914i	0.607171	−	0.794571i	$-0.292304\pi$
$240$		0			0
$241$	−5.02498	+	2.90117i	−0.323687	+	0.186881i	−0.653035	−	0.757328i	$-0.726505\pi$
$241$	−5.02498	+	2.90117i	−0.323687	+	0.186881i	0.329348	+	0.944209i	$0.393171\pi$
$242$	−11.9739	+	5.10690i	−0.769710	+	0.328284i
$243$		0			0
$244$	9.99164	+	2.45478i	0.639649	+	0.157151i
$245$	14.5223	−	0.891454i	0.927796	−	0.0569529i
$246$		0			0
$247$	−8.90047	−	5.13869i	−0.566323	−	0.326967i
$248$	12.3876	−	2.02748i	0.786612	−	0.128745i
$249$		0			0
$250$	13.3508	+	10.0247i	0.844381	+	0.634016i
$251$		−	18.8010i		−	1.18671i	−0.804942	−	0.593353i	$-0.797804\pi$
$251$		−	18.8010i		−	1.18671i	0.804942	−	0.593353i	$-0.202196\pi$
$252$		0			0
$253$			8.58598i			0.539796i
$254$	−12.4100	+	16.5276i	−0.778672	+	1.03703i
$255$		0			0
$256$	6.81571	−	14.4757i	0.425982	−	0.904732i
$257$	−10.9106	−	6.29923i	−0.680584	−	0.392935i	0.119491	−	0.992835i	$-0.461874\pi$
$257$	−10.9106	−	6.29923i	−0.680584	−	0.392935i	−0.800075	+	0.599900i	$0.795207\pi$
$258$		0			0
$259$	14.2919	−	8.84631i	0.888058	−	0.549683i
$260$	10.1088	+	2.48357i	0.626924	+	0.154024i
$261$		0			0
$262$	−3.37766	−	7.91942i	−0.208672	−	0.489264i
$263$	4.27292	−	2.46697i	0.263479	−	0.152120i	−0.362441	−	0.932007i	$-0.618057\pi$
$263$	4.27292	−	2.46697i	0.263479	−	0.152120i	0.625921	+	0.779887i	$0.284723\pi$
$264$		0			0
$265$			17.8461i			1.09628i
$266$	−15.2950	−	1.37722i	−0.937795	−	0.0844426i
$267$		0			0
$268$	−10.8878	+	11.3525i	−0.665081	+	0.693462i
$269$	−13.1502	−	22.7769i	−0.801783	−	1.38873i	−0.918441	−	0.395558i	$-0.870551\pi$
$269$	−13.1502	−	22.7769i	−0.801783	−	1.38873i	0.116658	−	0.993172i	$-0.462782\pi$
$270$		0			0
$271$	−14.0490	+	24.3336i	−0.853418	+	1.47816i	0.0246868	+	0.999695i	$0.492141\pi$
$271$	−14.0490	+	24.3336i	−0.853418	+	1.47816i	−0.878105	+	0.478468i	$0.841192\pi$
$272$	−5.95465	+	11.3871i	−0.361054	+	0.690444i
$273$		0			0
$274$	2.37467	−	19.6186i	0.143459	−	1.18520i
$275$	−0.455393	+	0.788764i	−0.0274612	+	0.0475643i
$276$		0			0
$277$	23.3982	−	13.5090i	1.40586	−	0.811675i	0.410876	−	0.911691i	$-0.365223\pi$
$277$	23.3982	−	13.5090i	1.40586	−	0.811675i	0.994986	+	0.100017i	$0.0318897\pi$
$278$	0.427273	−	0.569041i	0.0256261	−	0.0341288i
$279$		0			0
$280$	15.2658	−	2.98162i	0.912304	−	0.178186i
$281$	20.0629			1.19685			0.598426	−	0.801178i	$-0.295793\pi$
$281$	20.0629			1.19685			0.598426	+	0.801178i	$0.295793\pi$
$282$		0			0
$283$	−4.75248	+	2.74385i	−0.282506	+	0.163105i	−0.634557	−	0.772876i	$-0.718817\pi$
$283$	−4.75248	+	2.74385i	−0.282506	+	0.163105i	0.352052	+	0.935981i	$0.385484\pi$
$284$	−10.1630	+	2.95200i	−0.603061	+	0.175169i
$285$		0			0
$286$	−0.570165	+	4.71048i	−0.0337146	+	0.278537i
$287$	−12.9375	−	6.94970i	−0.763674	−	0.410228i
$288$		0			0
$289$	−3.33988	+	5.78484i	−0.196463	+	0.340284i
$290$	5.37560	+	12.6039i	0.315666	+	0.740126i
$291$		0			0
$292$	0.800653	+	0.767885i	0.0468547	+	0.0449370i
$293$	13.6931			0.799957			0.399978	−	0.916525i	$-0.369018\pi$
$293$	13.6931			0.799957			0.399978	+	0.916525i	$0.369018\pi$
$294$		0			0
$295$		−	15.1011i		−	0.879218i
$296$	13.9059	−	11.3799i	0.808264	−	0.661443i
$297$		0			0
$298$	3.05635	+	7.16607i	0.177050	+	0.415119i
$299$	−13.8963	−	8.02304i	−0.803644	−	0.463984i
$300$		0			0
$301$		0			0
$302$	−9.88115	−	1.19603i	−0.568596	−	0.0688238i
$303$		0			0
$304$	−16.4028	+	0.685643i	−0.940768	+	0.0393243i
$305$	5.34636	+	9.26016i	0.306131	+	0.530235i
$306$		0			0
$307$		−	24.4197i		−	1.39371i	−0.717213	−	0.696854i	$-0.754583\pi$
$307$		−	24.4197i		−	1.39371i	0.717213	−	0.696854i	$-0.245417\pi$
$308$	2.18540	+	6.74474i	0.124525	+	0.384317i
$309$		0			0
$310$	10.4318	+	7.83290i	0.592489	+	0.444879i
$311$	8.61539	+	14.9223i	0.488534	+	0.846165i	0.999913	−	0.0131898i	$-0.00419856\pi$
$311$	8.61539	+	14.9223i	0.488534	+	0.846165i	−0.511379	+	0.859355i	$0.670865\pi$
$312$		0			0
$313$	15.0446	+	8.68601i	0.850371	+	0.490962i	0.860776	−	0.508984i	$-0.169979\pi$
$313$	15.0446	+	8.68601i	0.850371	+	0.490962i	−0.0104047	+	0.999946i	$0.503312\pi$
$314$	−2.43174	+	20.0901i	−0.137231	+	1.13375i
$315$		0			0
$316$	−2.90298	+	11.8160i	−0.163305	+	0.664700i
$317$	−16.7863	−	9.69155i	−0.942810	−	0.544332i	−0.0519701	−	0.998649i	$-0.516550\pi$
$317$	−16.7863	−	9.69155i	−0.942810	−	0.544332i	−0.890840	+	0.454317i	$0.849883\pi$
$318$		0			0
$319$	−5.40907	+	3.12293i	−0.302850	+	0.174850i
$320$	15.7605	−	5.30106i	0.881041	−	0.296338i
$321$		0			0
$322$	−23.8801	−	2.15025i	−1.33078	−	0.119829i
$323$	13.1851			0.733639
$324$		0			0
$325$	−0.851071	−	1.47410i	−0.0472089	−	0.0817682i
$326$	10.8146	−	4.61247i	0.598967	−	0.255461i
$327$		0			0
$328$	−14.6859	−	5.55076i	−0.810894	−	0.306489i
$329$	−1.57625	−	2.54657i	−0.0869018	−	0.140397i
$330$		0			0
$331$	10.4008	−	18.0147i	0.571678	−	0.990176i	−0.424715	−	0.905327i	$-0.639626\pi$
$331$	10.4008	−	18.0147i	0.571678	−	0.990176i	0.996394	−	0.0848492i	$-0.0270409\pi$
$332$	−0.966408	+	0.280709i	−0.0530385	+	0.0154059i
$333$		0			0
$334$	−2.83184	−	2.12633i	−0.154951	−	0.116348i
$335$	−16.3473			−0.893146
$336$		0			0
$337$	10.3332			0.562886			0.281443	−	0.959578i	$-0.409187\pi$
$337$	10.3332			0.562886			0.281443	+	0.959578i	$0.409187\pi$
$338$	7.61063	+	5.71456i	0.413964	+	0.310831i
$339$		0			0
$340$	−12.8245	+	3.72508i	−0.695506	+	0.202021i
$341$	−2.97315	+	5.14965i	−0.161005	+	0.278869i
$342$		0			0
$343$	−18.4420	+	1.70077i	−0.995774	+	0.0918328i
$344$		0			0
$345$		0			0
$346$	7.06830	−	3.01465i	0.379994	−	0.162069i
$347$	16.8169	+	29.1277i	0.902779	+	1.56366i	0.823871	+	0.566777i	$0.191810\pi$
$347$	16.8169	+	29.1277i	0.902779	+	1.56366i	0.0789080	+	0.996882i	$0.474857\pi$
$348$		0			0
$349$	−13.3546			−0.714858			−0.357429	−	0.933940i	$-0.616347\pi$
$349$	−13.3546			−0.714858			−0.357429	+	0.933940i	$0.616347\pi$
$350$	−2.07973	−	1.46411i	−0.111166	−	0.0782602i
$351$		0			0
$352$	3.26210	+	6.84159i	0.173870	+	0.364658i
$353$	−6.80175	+	3.92699i	−0.362021	+	0.209013i	−0.669967	−	0.742391i	$-0.733692\pi$
$353$	−6.80175	+	3.92699i	−0.362021	+	0.209013i	0.307946	+	0.951404i	$0.400358\pi$
$354$		0			0
$355$	−9.52498	−	5.49925i	−0.505533	−	0.291870i
$356$	0.826492	−	3.36406i	0.0438040	−	0.178295i
$357$		0			0
$358$	0.597895	−	4.93958i	0.0315997	−	0.261065i
$359$	0.140453	+	0.0810905i	0.00741282	+	0.00427979i	0.503702	−	0.863878i	$-0.331971\pi$
$359$	0.140453	+	0.0810905i	0.00741282	+	0.00427979i	−0.496289	+	0.868157i	$0.665304\pi$
$360$		0			0
$361$	−1.07739	−	1.86609i	−0.0567047	−	0.0982154i
$362$	25.1038	+	18.8496i	1.31943	+	0.990713i
$363$		0			0
$364$	−12.9584	−	2.76547i	−0.679205	−	0.144950i
$365$			1.15292i			0.0603466i
$366$		0			0
$367$	10.1321	+	17.5493i	0.528891	+	0.916066i	0.999432	+	0.0336883i	$0.0107254\pi$
$367$	10.1321	+	17.5493i	0.528891	+	0.916066i	−0.470541	+	0.882378i	$0.655941\pi$
$368$	−25.6098	+	1.07050i	−1.33500	+	0.0558034i
$369$		0			0
$370$	18.5389	+	2.24398i	0.963791	+	0.116659i
$371$	−0.696241	−	22.7057i	−0.0361470	−	1.17882i
$372$		0			0
$373$	−5.78269	−	3.33864i	−0.299416	−	0.172868i	0.342764	−	0.939421i	$-0.388637\pi$
$373$	−5.78269	−	3.33864i	−0.299416	−	0.172868i	−0.642181	+	0.766553i	$0.721970\pi$
$374$	−2.38812	−	5.59930i	−0.123487	−	0.289533i
$375$		0			0
$376$	−2.02770	−	2.47778i	−0.104570	−	0.127782i
$377$		−	11.6727i		−	0.601174i
$378$		0			0
$379$	−4.60350			−0.236466			−0.118233	−	0.992986i	$-0.537723\pi$
$379$	−4.60350			−0.236466			−0.118233	+	0.992986i	$0.537723\pi$
$380$	−12.3138	−	11.8098i	−0.631685	−	0.605832i
$381$		0			0
$382$	−0.727867	−	1.70659i	−0.0372409	−	0.0873169i
$383$	−5.71038	+	9.89066i	−0.291787	+	0.505389i	−0.974232	−	0.225547i	$-0.927583\pi$
$383$	−5.71038	+	9.89066i	−0.291787	+	0.505389i	0.682446	+	0.730936i	$0.260916\pi$
$384$		0			0
$385$	−3.48685	+	6.49107i	−0.177706	+	0.330815i
$386$	1.91928	−	15.8563i	0.0976885	−	0.807065i
$387$		0			0
$388$	33.0797	−	9.60852i	1.67937	−	0.487799i
$389$	26.0307	−	15.0288i	1.31981	−	0.761991i	0.336109	−	0.941823i	$-0.390889\pi$
$389$	26.0307	−	15.0288i	1.31981	−	0.761991i	0.983697	+	0.179832i	$0.0575555\pi$
$390$		0			0
$391$	20.5859			1.04107
$392$	−19.3064	+	4.38910i	−0.975119	+	0.221683i
$393$		0			0
$394$	−5.02826	+	6.69662i	−0.253320	+	0.337371i
$395$	−10.9509	+	6.32252i	−0.551001	+	0.318120i
$396$		0			0
$397$	−2.17124	+	3.76069i	−0.108971	+	0.188744i	−0.915354	−	0.402651i	$-0.868089\pi$
$397$	−2.17124	+	3.76069i	−0.108971	+	0.188744i	0.806383	+	0.591394i	$0.201422\pi$
$398$	−3.16276	+	26.1295i	−0.158535	+	1.30975i
$399$		0			0
$400$	−2.40946	−	1.25998i	−0.120473	−	0.0629989i
$401$	−9.98685	+	17.2977i	−0.498719	+	0.863807i	−0.999999	−	0.00147805i	$-0.999530\pi$
$401$	−9.98685	+	17.2977i	−0.498719	+	0.863807i	0.501279	+	0.865285i	$0.332863\pi$
$402$		0			0
$403$	−5.55643	−	9.62402i	−0.276786	−	0.479407i
$404$	−1.69924	+	1.77175i	−0.0845404	+	0.0881480i
$405$		0			0
$406$	−7.33112	−	15.8263i	−0.363837	−	0.785444i
$407$			8.51212i			0.421930i
$408$		0			0
$409$	−26.4356	+	15.2626i	−1.30715	+	0.754686i	−0.981620	−	0.190844i	$-0.938878\pi$
$409$	−26.4356	+	15.2626i	−1.30715	+	0.754686i	−0.325534	+	0.945530i	$0.605544\pi$
$410$	−6.40106	−	15.0082i	−0.316126	−	0.741205i
$411$		0			0
$412$	−29.6310	−	7.27983i	−1.45981	−	0.358652i
$413$	0.589147	+	19.2131i	0.0289900	+	0.945417i
$414$		0			0
$415$	−0.905741	−	0.522930i	−0.0444611	−	0.0256696i
$416$	−14.1213	−	1.11336i	−0.692351	−	0.0545867i
$417$		0			0
$418$	4.66971	−	6.21911i	0.228403	−	0.304186i
$419$			2.08070i			0.101649i	0.998708	+	0.0508245i	$0.0161849\pi$
$419$			2.08070i			0.101649i	−0.998708	+	0.0508245i	$0.983815\pi$
$420$		0			0
$421$			30.4039i			1.48180i	0.671618	+	0.740898i	$0.265600\pi$
$421$			30.4039i			1.48180i	−0.671618	+	0.740898i	$0.734400\pi$
$422$	−6.47973	−	4.86540i	−0.315428	−	0.236844i
$423$		0			0
$424$	−3.92251	−	23.9659i	−0.190494	−	1.16389i
$425$	1.89116	+	1.09186i	0.0917345	+	0.0529630i
$426$		0			0
$427$	−7.16346	−	11.5732i	−0.346664	−	0.560064i
$428$	21.5761	+	5.30087i	1.04292	+	0.256227i
$429$		0			0
$430$		0			0
$431$	−2.32280	+	1.34107i	−0.111885	+	0.0645970i	−0.554898	−	0.831918i	$-0.687243\pi$
$431$	−2.32280	+	1.34107i	−0.111885	+	0.0645970i	0.443013	+	0.896515i	$0.353910\pi$
$432$		0			0
$433$			29.4673i			1.41611i	0.706158	+	0.708054i	$0.250427\pi$
$433$			29.4673i			1.41611i	−0.706158	+	0.708054i	$0.749573\pi$
$434$	−13.5781	−	9.55885i	−0.651767	−	0.458839i
$435$		0			0
$436$	−18.1856	−	17.4413i	−0.870932	−	0.835288i
$437$	13.1502	+	22.7769i	0.629061	+	1.08957i
$438$		0			0
$439$	−3.77648	+	6.54106i	−0.180242	+	0.312188i	−0.941963	−	0.335717i	$-0.891021\pi$
$439$	−3.77648	+	6.54106i	−0.180242	+	0.312188i	0.761721	+	0.647905i	$0.224355\pi$
$440$	−2.78496	+	7.36831i	−0.132768	+	0.351271i
$441$		0			0
$442$	11.2939	+	1.36704i	0.537198	+	0.0650234i
$443$	−3.75915	+	6.51104i	−0.178603	+	0.309349i	−0.941402	−	0.337286i	$-0.890491\pi$
$443$	−3.75915	+	6.51104i	−0.178603	+	0.309349i	0.762799	+	0.646635i	$0.223824\pi$
$444$		0			0
$445$	3.11778	−	1.80005i	0.147797	−	0.0853306i
$446$	−23.5983	−	17.7191i	−1.11741	−	0.839025i
$447$		0			0
$448$	−19.8454	+	7.35943i	−0.937606	+	0.347700i
$449$	14.3332			0.676426			0.338213	−	0.941070i	$-0.390178\pi$
$449$	14.3332			0.676426			0.338213	+	0.941070i	$0.390178\pi$
$450$		0			0
$451$	6.44092	−	3.71866i	0.303291	−	0.175105i
$452$	−11.1926	−	38.5332i	−0.526455	−	1.81245i
$453$		0			0
$454$	23.1460	+	2.80164i	1.08630	+	0.131487i
$455$	−7.24749	−	11.7089i	−0.339767	−	0.548922i
$456$		0			0
$457$	−6.48037	+	11.2243i	−0.303139	+	0.525052i	−0.976845	−	0.213947i	$-0.931368\pi$
$457$	−6.48037	+	11.2243i	−0.303139	+	0.525052i	0.673706	+	0.738999i	$0.264701\pi$
$458$	−11.0565	+	4.71563i	−0.516636	+	0.220347i
$459$		0			0
$460$	−19.2255	−	18.4387i	−0.896396	−	0.859709i
$461$	−33.3871			−1.55499			−0.777496	−	0.628888i	$-0.783510\pi$
$461$	−33.3871			−1.55499			−0.777496	+	0.628888i	$0.783510\pi$
$462$		0			0
$463$		−	29.7739i		−	1.38371i	−0.722036	−	0.691855i	$-0.756794\pi$
$463$		−	29.7739i		−	1.38371i	0.722036	−	0.691855i	$-0.243206\pi$
$464$	−9.98929	−	15.7445i	−0.463741	−	0.730920i
$465$		0			0
$466$	−5.82129	+	2.48280i	−0.269666	+	0.115013i
$467$	−23.5399	−	13.5908i	−1.08930	−	0.628907i	−0.155909	−	0.987771i	$-0.549831\pi$
$467$	−23.5399	−	13.5908i	−1.08930	−	0.628907i	−0.933390	+	0.358865i	$0.883164\pi$
$468$		0			0
$469$	20.7987	−	0.637765i	0.960393	−	0.0294492i
$470$	0.399837	−	3.30330i	0.0184431	−	0.152370i
$471$		0			0
$472$	3.31915	+	20.2795i	0.152776	+	0.933442i
$473$		0			0
$474$		0			0
$475$			2.78991i			0.128010i
$476$	16.1713	−	5.23977i	0.741211	−	0.240164i
$477$		0			0
$478$	−20.8616	+	27.7835i	−0.954189	+	1.27079i
$479$	17.2187	+	29.8237i	0.786744	+	1.36268i	0.927952	+	0.372700i	$0.121568\pi$
$479$	17.2187	+	29.8237i	0.786744	+	1.36268i	−0.141208	+	0.989980i	$0.545099\pi$
$480$		0			0
$481$	−13.7768	−	7.95402i	−0.628167	−	0.362672i
$482$	8.14629	+	0.986041i	0.371053	+	0.0449129i
$483$		0			0
$484$	17.8778	+	4.39227i	0.812628	+	0.199649i
$485$	31.0031	+	17.8996i	1.40778	+	0.812781i
$486$		0			0
$487$	−6.82613	+	3.94107i	−0.309321	+	0.178587i	−0.646623	−	0.762810i	$-0.723819\pi$
$487$	−6.82613	+	3.94107i	−0.309321	+	0.178587i	0.337301	+	0.941397i	$0.390486\pi$
$488$	−9.21508	−	11.2606i	−0.417147	−	0.509741i
$489$		0			0
$490$	−17.1803	−	11.3235i	−0.776126	−	0.511545i
$491$	8.06291			0.363874			0.181937	−	0.983310i	$-0.441763\pi$
$491$	8.06291			0.363874			0.181937	+	0.983310i	$0.441763\pi$
$492$		0			0
$493$	7.48759	+	12.9689i	0.337224	+	0.584089i
$494$	5.70201	+	13.3692i	0.256546	+	0.601510i
$495$		0			0
$496$	−15.7308	−	8.22609i	−0.706333	−	0.369362i
$497$	12.3332	+	6.62511i	0.553220	+	0.297177i
$498$		0			0
$499$	12.0216	−	20.8221i	0.538163	−	0.932125i	−0.460841	−	0.887483i	$-0.652452\pi$
$499$	12.0216	−	20.8221i	0.538163	−	0.932125i	0.999003	−	0.0446419i	$-0.0142147\pi$
$500$	−6.58598	−	22.6738i	−0.294534	−	1.01400i
$501$		0			0
$502$	−15.9649	+	21.2620i	−0.712549	+	0.948971i
$503$	40.8993			1.82361			0.911804	−	0.410626i	$-0.134690\pi$
$503$	40.8993			1.82361			0.911804	+	0.410626i	$0.134690\pi$
$504$		0			0
$505$	−2.55128			−0.113530
$506$	7.29082	−	9.70989i	0.324116	−	0.431657i
$507$		0			0
$508$	28.0689	−	8.15308i	1.24536	−	0.361734i
$509$	2.02661	−	3.51019i	0.0898278	−	0.155586i	−0.817610	−	0.575772i	$-0.804702\pi$
$509$	2.02661	−	3.51019i	0.0898278	−	0.155586i	0.907438	+	0.420186i	$0.138035\pi$
$510$		0			0
$511$	−0.0449795	−	1.46686i	−0.00198978	−	0.0648902i
$512$	−20.0000	+	10.5830i	−0.883883	+	0.467707i
$513$		0			0
$514$	6.98978	+	16.3886i	0.308306	+	0.722870i
$515$	−15.8550	−	27.4617i	−0.698656	−	1.21011i
$516$		0			0
$517$	1.51671			0.0667048
$518$	−23.6746	−	2.13175i	−1.04020	−	0.0936639i
$519$		0			0
$520$	−9.32317	−	11.3926i	−0.408848	−	0.499600i
$521$	−27.1927	+	15.6997i	−1.19133	+	0.687817i	−0.958609	−	0.284725i	$-0.908098\pi$
$521$	−27.1927	+	15.6997i	−1.19133	+	0.687817i	−0.232725	+	0.972543i	$0.574764\pi$
$522$		0			0
$523$	−11.7132	−	6.76263i	−0.512183	−	0.295709i	0.221547	−	0.975150i	$-0.428889\pi$
$523$	−11.7132	−	6.76263i	−0.512183	−	0.295709i	−0.733731	+	0.679440i	$0.762223\pi$
$524$	−2.90501	+	11.8242i	−0.126906	+	0.516544i
$525$		0			0
$526$	−6.92708	−	0.838466i	−0.302035	−	0.0365588i
$527$	12.3469	+	7.12848i	0.537839	+	0.310522i
$528$		0			0
$529$	9.03146	+	15.6429i	0.392672	+	0.680128i
$530$	15.1541	−	20.1822i	0.658253	−	0.876659i
$531$		0			0
$532$	16.1276	+	14.5453i	0.699222	+	0.630618i
$533$			13.8994i			0.602050i
$534$		0			0
$535$	11.5450	+	19.9965i	0.499133	+	0.864524i
$536$	21.9531	−	3.59306i	0.948228	−	0.155197i
$537$		0			0
$538$	−4.46946	+	36.9249i	−0.192692	+	1.59195i
$539$	4.18309	−	8.39464i	0.180178	−	0.361583i
$540$		0			0
$541$	−27.1543	−	15.6775i	−1.16745	−	0.674030i	−0.214375	−	0.976751i	$-0.568771\pi$
$541$	−27.1543	−	15.6775i	−1.16745	−	0.674030i	−0.953079	+	0.302722i	$0.902105\pi$
$542$	36.5511	−	15.5891i	1.57000	−	0.669611i
$543$		0			0
$544$	16.4035	−	7.82126i	0.703295	−	0.335334i
$545$		−	26.1868i		−	1.12172i
$546$		0			0
$547$	−44.7293			−1.91249			−0.956244	−	0.292571i	$-0.905489\pi$
$547$	−44.7293			−1.91249			−0.956244	+	0.292571i	$0.905489\pi$
$548$	−19.3447	+	20.1702i	−0.826366	+	0.861630i
$549$		0			0
$550$	1.18479	−	0.505315i	0.0505195	−	0.0215467i
$551$	−9.56611	+	16.5690i	−0.407530	+	0.705863i
$552$		0			0
$553$	13.6862	−	8.47140i	0.581998	−	0.360240i
$554$	−37.9322	−	4.59138i	−1.61159	−	0.195069i
$555$		0			0
$556$	−0.966408	+	0.280709i	−0.0409848	+	0.0119047i
$557$	−10.5345	+	6.08208i	−0.446360	+	0.257706i	−0.706292	−	0.707921i	$-0.749633\pi$
$557$	−10.5345	+	6.08208i	−0.446360	+	0.257706i	0.259932	+	0.965627i	$0.416300\pi$
$558$		0			0
$559$		0			0
$560$	−19.7959	−	9.59107i	−0.836531	−	0.405297i
$561$		0			0
$562$	−22.6892	−	17.0365i	−0.957085	−	0.718641i
$563$	31.4311	−	18.1468i	1.32466	−	0.764794i	0.340194	−	0.940355i	$-0.389507\pi$
$563$	31.4311	−	18.1468i	1.32466	−	0.764794i	0.984469	+	0.175561i	$0.0561738\pi$
$564$		0			0
$565$	20.8506	−	36.1143i	0.877191	−	1.51934i
$566$	7.70453	+	0.932570i	0.323846	+	0.0391988i
$567$		0			0
$568$	14.0000	+	5.29150i	0.587427	+	0.222027i
$569$	6.01830	−	10.4240i	0.252300	−	0.436997i	−0.711858	−	0.702323i	$-0.752146\pi$
$569$	6.01830	−	10.4240i	0.252300	−	0.436997i	0.964159	+	0.265326i	$0.0854795\pi$
$570$		0			0
$571$	−4.10570	−	7.11128i	−0.171818	−	0.297598i	0.767237	−	0.641363i	$-0.221631\pi$
$571$	−4.10570	−	7.11128i	−0.171818	−	0.297598i	−0.939056	+	0.343765i	$0.888298\pi$
$572$	4.64473	−	4.84293i	0.194206	−	0.202493i
$573$		0			0
$574$	8.72962	+	18.8453i	0.364367	+	0.786588i
$575$			4.35589i			0.181653i
$576$		0			0
$577$	14.5500	−	8.40042i	0.605722	−	0.349714i	−0.165567	−	0.986199i	$-0.552945\pi$
$577$	14.5500	−	8.40042i	0.605722	−	0.349714i	0.771289	+	0.636485i	$0.219612\pi$
$578$	8.68929	−	3.70601i	0.361427	−	0.154150i
$579$		0			0
$580$	4.62338	−	18.8185i	0.191975	−	0.781395i
$581$	1.17278	+	0.629989i	0.0486551	+	0.0261364i
$582$		0			0
$583$	9.96289	+	5.75208i	0.412621	+	0.238227i
$584$	−0.253407	−	1.54828i	−0.0104861	−	0.0640682i
$585$		0			0
$586$	−15.4855	−	11.6275i	−0.639700	−	0.480328i
$587$		−	25.4261i		−	1.04945i	−0.851273	−	0.524723i	$-0.824169\pi$
$587$		−	25.4261i		−	1.04945i	0.851273	−	0.524723i	$-0.175831\pi$
$588$		0			0
$589$			18.2146i			0.750521i
$590$	−12.8231	+	17.0778i	−0.527920	+	0.703083i
$591$		0			0
$592$	−25.3895	+	1.06129i	−1.04350	+	0.0436186i
$593$	19.0694	+	11.0097i	0.783086	+	0.452115i	0.837523	−	0.546402i	$-0.184003\pi$
$593$	19.0694	+	11.0097i	0.783086	+	0.452115i	−0.0544368	+	0.998517i	$0.517336\pi$
$594$		0			0
$595$	15.5631	+	8.36013i	0.638025	+	0.342732i
$596$	2.62867	−	10.6994i	0.107674	−	0.438266i
$597$		0			0
$598$	8.90256	+	20.8734i	0.364053	+	0.853576i
$599$	0.500607	−	0.289026i	0.0204543	−	0.0118093i	−0.489738	−	0.871870i	$-0.662908\pi$
$599$	0.500607	−	0.289026i	0.0204543	−	0.0118093i	0.510192	+	0.860060i	$0.329574\pi$
$600$		0			0
$601$		−	27.3186i		−	1.11435i	−0.830395	−	0.557175i	$-0.811885\pi$
$601$		−	27.3186i		−	1.11435i	0.830395	−	0.557175i	$-0.188115\pi$
$602$		0			0
$603$		0			0
$604$	10.1590	+	9.74321i	0.413363	+	0.396446i
$605$	9.56611	+	16.5690i	0.388918	+	0.673625i
$606$		0			0
$607$	5.99963	−	10.3917i	0.243518	−	0.421785i	−0.718196	−	0.695841i	$-0.755032\pi$
$607$	5.99963	−	10.3917i	0.243518	−	0.421785i	0.961714	+	0.274056i	$0.0883653\pi$
$608$	19.1322	+	13.1532i	0.775914	+	0.533431i
$609$		0			0
$610$	1.81710	−	15.0122i	0.0735723	−	0.607826i
$611$	−1.41727	+	2.45478i	−0.0573364	+	0.0993096i
$612$		0			0
$613$	−3.96050	+	2.28659i	−0.159963	+	0.0923547i	−0.577845	−	0.816147i	$-0.696106\pi$
$613$	−3.96050	+	2.28659i	−0.159963	+	0.0923547i	0.417882	+	0.908501i	$0.362773\pi$
$614$	−20.7361	+	27.6163i	−0.836841	+	1.11450i
$615$		0			0
$616$	3.25585	−	9.48338i	0.131182	−	0.382096i
$617$	−5.12621			−0.206373			−0.103187	−	0.994662i	$-0.532904\pi$
$617$	−5.12621			−0.206373			−0.103187	+	0.994662i	$0.532904\pi$
$618$		0			0
$619$	39.5293	−	22.8222i	1.58881	−	0.917303i	0.595312	−	0.803495i	$-0.297028\pi$
$619$	39.5293	−	22.8222i	1.58881	−	0.917303i	0.993503	−	0.113808i	$-0.0363049\pi$
$620$	−5.14604	−	17.7165i	−0.206670	−	0.711511i
$621$		0			0
$622$	2.92817	−	24.1914i	0.117409	−	0.969988i
$623$	−3.89654	+	2.41185i	−0.156111	+	0.0966286i
$624$		0			0
$625$	10.5696	−	18.3071i	0.422783	−	0.732282i
$626$	−9.63820	−	22.5982i	−0.385220	−	0.903206i
$627$		0			0
$628$	19.8097	−	20.6550i	0.790491	−	0.824224i
$629$	20.4088			0.813753
$630$		0			0
$631$			17.1345i			0.682113i	0.940043	+	0.341057i	$0.110785\pi$
$631$			17.1345i			0.682113i	−0.940043	+	0.341057i	$0.889215\pi$
$632$	13.3166	−	10.8976i	0.529704	−	0.433484i
$633$		0			0
$634$	10.7540	+	25.2143i	0.427095	+	1.00139i
$635$	26.3069	+	15.1883i	1.04396	+	0.602729i
$636$		0			0
$637$	9.67781	+	14.6145i	0.383449	+	0.579049i
$638$	8.76897	+	1.06141i	0.347167	+	0.0420217i
$639$		0			0
$640$	−22.3250	−	7.38815i	−0.882474	−	0.292042i
$641$	4.02498	+	6.97146i	0.158977	+	0.275356i	0.934500	−	0.355963i	$-0.115847\pi$
$641$	4.02498	+	6.97146i	0.158977	+	0.275356i	−0.775523	+	0.631319i	$0.782514\pi$
$642$		0			0
$643$			22.2710i			0.878283i	0.898418	+	0.439142i	$0.144717\pi$
$643$			22.2710i			0.878283i	−0.898418	+	0.439142i	$0.855283\pi$
$644$	25.1801	+	22.7096i	0.992235	+	0.894882i
$645$		0			0
$646$	−14.9110	−	11.1962i	−0.586667	−	0.440508i
$647$	−18.9125	−	32.7574i	−0.743528	−	1.28783i	−0.950879	−	0.309561i	$-0.899818\pi$
$647$	−18.9125	−	32.7574i	−0.743528	−	1.28783i	0.207352	−	0.978266i	$-0.433516\pi$
$648$		0			0
$649$	−8.43042	−	4.86730i	−0.330923	−	0.191058i
$650$	−0.289259	+	2.38975i	−0.0113457	+	0.0937337i
$651$		0			0
$652$	−16.1470	−	3.96704i	−0.632364	−	0.155361i
$653$	−25.6130	−	14.7877i	−1.00231	−	0.578686i	−0.0933818	−	0.995630i	$-0.529768\pi$
$653$	−25.6130	−	14.7877i	−1.00231	−	0.578686i	−0.908932	+	0.416944i	$0.863101\pi$
$654$		0			0
$655$	−10.9586	+	6.32694i	−0.428188	+	0.247214i
$656$	11.8949	+	18.7480i	0.464417	+	0.731985i
$657$		0			0
$658$	−0.379841	+	4.21840i	−0.0148077	+	0.164450i
$659$	−18.3961			−0.716611			−0.358305	−	0.933604i	$-0.616645\pi$
$659$	−18.3961			−0.716611			−0.358305	+	0.933604i	$0.616645\pi$
$660$		0			0
$661$	5.92732	+	10.2664i	0.230546	+	0.399317i	0.957969	−	0.286872i	$-0.0926154\pi$
$661$	5.92732	+	10.2664i	0.230546	+	0.399317i	−0.727423	+	0.686189i	$0.759282\pi$
$662$	−27.0595	+	11.5410i	−1.05170	+	0.448552i
$663$		0			0
$664$	1.33128	+	0.503175i	0.0516635	+	0.0195270i
$665$	0.691771	+	22.5599i	0.0268257	+	0.874836i
$666$		0			0
$667$	−14.9356	+	25.8692i	−0.578308	+	1.00166i
$668$	1.39695	+	4.80934i	0.0540496	+	0.186079i
$669$		0			0
$670$	18.4871	+	13.8813i	0.714220	+	0.536283i
$671$	6.89285			0.266095
$672$		0			0
$673$	10.8738			0.419154			0.209577	−	0.977792i	$-0.432791\pi$
$673$	10.8738			0.419154			0.209577	+	0.977792i	$0.432791\pi$
$674$	−11.6858	−	8.77448i	−0.450121	−	0.337980i
$675$		0			0
$676$	−3.75433	−	12.9252i	−0.144397	−	0.497123i
$677$	22.7163	−	39.3458i	0.873060	−	1.51218i	0.0142443	−	0.999899i	$-0.495466\pi$
$677$	22.7163	−	39.3458i	0.873060	−	1.51218i	0.858815	−	0.512285i	$-0.171201\pi$
$678$		0			0
$679$	−40.1437	−	21.5642i	−1.54057	−	0.827559i
$680$	17.6664	+	6.67728i	0.677476	+	0.256062i
$681$		0			0
$682$	7.73518	−	3.29908i	0.296196	−	0.126328i
$683$	12.3693	+	21.4243i	0.473299	+	0.819778i	0.999533	−	0.0305620i	$-0.00972970\pi$
$683$	12.3693	+	21.4243i	0.473299	+	0.819778i	−0.526234	+	0.850340i	$0.676396\pi$
$684$		0			0
$685$	−29.0446			−1.10974
$686$	22.3003	+	13.7367i	0.851429	+	0.524470i
$687$		0			0
$688$		0			0
$689$	−18.6193	+	10.7499i	−0.709340	+	0.409538i
$690$		0			0
$691$	−4.10457	−	2.36977i	−0.156145	−	0.0901504i	0.419892	−	0.907574i	$-0.362068\pi$
$691$	−4.10457	−	2.36977i	−0.156145	−	0.0901504i	−0.576037	+	0.817424i	$0.695401\pi$
$692$	−10.5535	−	2.59280i	−0.401182	−	0.0985636i
$693$		0			0
$694$	5.71568	−	47.2207i	0.216964	−	1.79247i
$695$	−0.905741	−	0.522930i	−0.0343567	−	0.0198359i
$696$		0			0
$697$	−8.91594	−	15.4429i	−0.337715	−	0.584940i
$698$	15.1028	+	11.3401i	0.571649	+	0.429231i
$699$		0			0
$700$	1.10871	+	3.42178i	0.0419053	+	0.129331i
$701$			39.8121i			1.50368i	0.659345	+	0.751840i	$0.270834\pi$
$701$			39.8121i			1.50368i	−0.659345	+	0.751840i	$0.729166\pi$
$702$		0			0
$703$	13.0371	+	22.5809i	0.491704	+	0.851656i
$704$	2.12046	−	10.5072i	0.0799177	−	0.396004i
$705$		0			0
$706$	11.0267	+	1.33469i	0.414996	+	0.0502319i
$707$	3.24600	−	0.0995345i	0.122078	−	0.00374338i
$708$		0			0
$709$	4.97242	+	2.87083i	0.186743	+	0.107816i	0.590457	−	0.807069i	$-0.298948\pi$
$709$	4.97242	+	2.87083i	0.186743	+	0.107816i	−0.403714	+	0.914885i	$0.632281\pi$
$710$	6.10210	+	14.3073i	0.229008	+	0.536943i
$711$		0			0
$712$	−3.79129	+	3.10260i	−0.142085	+	0.116275i
$713$			28.4385i			1.06503i
$714$		0			0
$715$	6.97370			0.260801
$716$	−4.87062	+	5.07847i	−0.182024	+	0.189791i
$717$		0			0
$718$	−0.0899800	−	0.210971i	−0.00335802	−	0.00787338i
$719$	7.62804	−	13.2122i	0.284478	−	0.492730i	−0.688005	−	0.725706i	$-0.741513\pi$
$719$	7.62804	−	13.2122i	0.284478	−	0.492730i	0.972482	+	0.232976i	$0.0748464\pi$
$720$		0			0
$721$	21.2438	+	34.3211i	0.791160	+	1.27818i
$722$	−0.366180	+	3.02523i	−0.0136278	+	0.112588i
$723$		0			0
$724$	−12.3837	−	42.6341i	−0.460238	−	1.58448i
$725$	−2.74416	+	1.58434i	−0.101915	+	0.0588409i
$726$		0			0
$727$	40.8993			1.51687			0.758435	−	0.651749i	$-0.225964\pi$
$727$	40.8993			1.51687			0.758435	+	0.651749i	$0.225964\pi$
$728$	12.3064	+	14.1312i	0.456104	+	0.523736i
$729$		0			0
$730$	0.979006	−	1.30384i	0.0362346	−	0.0482572i
$731$		0			0
$732$		0			0
$733$	12.2037	−	21.1374i	0.450753	−	0.780728i	−0.547680	−	0.836688i	$-0.684489\pi$
$733$	12.2037	−	21.1374i	0.450753	−	0.780728i	0.998433	+	0.0559605i	$0.0178221\pi$
$734$	3.44367	−	28.4502i	0.127108	−	1.05012i
$735$		0			0
$736$	29.8711	+	20.5360i	1.10106	+	0.756968i
$737$	−5.26897	+	9.12612i	−0.194085	+	0.336165i
$738$		0			0
$739$	15.3996	+	26.6730i	0.566485	+	0.981181i	0.996910	+	0.0785545i	$0.0250305\pi$
$739$	15.3996	+	26.6730i	0.566485	+	0.981181i	−0.430425	+	0.902626i	$0.641636\pi$
$740$	−19.0602	−	18.2801i	−0.700666	−	0.671990i
$741$		0			0
$742$	−18.4932	+	26.2691i	−0.678909	+	0.964369i
$743$		−	23.9376i		−	0.878184i	−0.898442	−	0.439092i	$-0.855300\pi$
$743$		−	23.9376i		−	0.878184i	0.898442	−	0.439092i	$-0.144700\pi$
$744$		0			0
$745$	9.91613	−	5.72508i	0.363299	−	0.209751i
$746$	3.70463	+	8.68606i	0.135636	+	0.318019i
$747$		0			0
$748$	−2.05394	+	8.36013i	−0.0750996	+	0.305677i
$749$	−15.4689	−	24.9912i	−0.565219	−	0.913158i
$750$		0			0
$751$	−11.9543	−	6.90181i	−0.436218	−	0.251851i	0.265774	−	0.964035i	$-0.414373\pi$
$751$	−11.9543	−	6.90181i	−0.436218	−	0.251851i	−0.701992	+	0.712185i	$0.747706\pi$
$752$	0.189102	+	4.52395i	0.00689586	+	0.164972i
$753$		0			0
$754$	−9.91191	+	13.2007i	−0.360970	+	0.480740i
$755$			14.6287i			0.532392i
$756$		0			0
$757$			2.14156i			0.0778362i	0.999242	+	0.0389181i	$0.0123911\pi$
$757$			2.14156i			0.0778362i	−0.999242	+	0.0389181i	$0.987609\pi$
$758$	5.20610	+	3.90908i	0.189094	+	0.141984i
$759$		0			0
$760$	3.89732	+	23.8121i	0.141371	+	0.863755i
$761$	−36.8321	−	21.2650i	−1.33516	−	0.770856i	−0.349076	−	0.937094i	$-0.613504\pi$
$761$	−36.8321	−	21.2650i	−1.33516	−	0.770856i	−0.986086	+	0.166239i	$0.946838\pi$
$762$		0			0
$763$	1.02164	+	33.3175i	0.0369859	+	1.20618i
$764$	−0.626015	+	2.54806i	−0.0226484	+	0.0921855i
$765$		0			0
$766$	14.8566	−	6.33637i	0.536789	−	0.228942i
$767$	15.7554	−	9.09636i	0.568893	−	0.328450i
$768$		0			0
$769$			15.6459i			0.564206i	0.959384	+	0.282103i	$0.0910320\pi$
$769$			15.6459i			0.564206i	−0.959384	+	0.282103i	$0.908968\pi$
$770$	9.45520	−	4.37988i	0.340742	−	0.157840i
$771$		0			0
$772$	−15.6350	+	16.3022i	−0.562715	+	0.586728i
$773$	−15.2125	−	26.3489i	−0.547156	−	0.947703i	−0.998468	−	0.0553362i	$-0.982377\pi$
$773$	−15.2125	−	26.3489i	−0.547156	−	0.947703i	0.451311	−	0.892367i	$-0.350956\pi$
$774$		0			0
$775$	−1.50836	+	2.61255i	−0.0541817	+	0.0938455i
$776$	−45.5689	−	17.2234i	−1.63583	−	0.618286i
$777$		0			0
$778$	−42.1999	−	5.10794i	−1.51294	−	0.183129i
$779$	11.3910	−	19.7297i	0.408124	−	0.706891i
$780$		0			0
$781$	−6.14009	+	3.54498i	−0.219710	+	0.126849i
$782$	−23.2806	−	17.4806i	−0.832513	−	0.625105i
$783$		0			0
$784$	25.5606	+	11.4304i	0.912879	+	0.408230i
$785$	29.7427			1.06156
$786$		0			0
$787$	−28.3722	+	16.3807i	−1.01136	+	0.583909i	−0.911590	−	0.411102i	$-0.865144\pi$
$787$	−28.3722	+	16.3807i	−1.01136	+	0.583909i	−0.0997704	+	0.995010i	$0.531811\pi$
$788$	11.3729	−	3.30345i	0.405144	−	0.117681i
$789$		0			0
$790$	17.7532	+	2.14888i	0.631631	+	0.0764536i
$791$	−25.1193	+	46.7618i	−0.893140	+	1.66266i
$792$		0			0
$793$	−6.44092	+	11.1560i	−0.228724	+	0.396161i
$794$	5.64886	−	2.40926i	0.200471	−	0.0855013i
$795$		0			0
$796$	25.7647	−	26.8642i	0.913207	−	0.952177i
$797$	−28.3790			−1.00523			−0.502617	−	0.864509i	$-0.667630\pi$
$797$	−28.3790			−1.00523			−0.502617	+	0.864509i	$0.667630\pi$
$798$		0			0
$799$		−	3.63649i		−	0.128650i
$800$	1.65494	+	3.47091i	0.0585111	+	0.122715i
$801$		0			0
$802$	25.9826	−	11.0816i	0.917477	−	0.391307i
$803$	0.643636	+	0.371603i	0.0227134	+	0.0131136i
$804$		0			0
$805$	1.08006	+	35.2228i	0.0380672	+	1.24144i
$806$	−1.88850	+	15.6021i	−0.0665197	+	0.549560i
$807$		0			0
$808$	3.42617	−	0.560761i	0.120532	−	0.0197275i
$809$	−4.08387	−	7.07347i	−0.143581	−	0.248690i	0.785262	−	0.619164i	$-0.212528\pi$
$809$	−4.08387	−	7.07347i	−0.143581	−	0.248690i	−0.928843	+	0.370474i	$0.879195\pi$
$810$		0			0
$811$		−	22.2710i		−	0.782041i	−0.920382	−	0.391021i	$-0.872122\pi$
$811$		−	22.2710i		−	0.782041i	0.920382	−	0.391021i	$-0.127878\pi$
$812$	−5.14816	+	24.1232i	−0.180665	+	0.846558i
$813$		0			0
$814$	7.22810	−	9.62637i	0.253345	−	0.337404i
$815$	−8.63997	−	14.9649i	−0.302645	−	0.524196i
$816$		0			0
$817$		0			0
$818$	42.8563	+	5.18740i	1.49844	+	0.181373i
$819$		0			0
$820$	−5.50535	+	22.4083i	−0.192255	+	0.782533i
$821$	4.52231	+	2.61096i	0.157830	+	0.0911230i	0.576835	−	0.816861i	$-0.304288\pi$
$821$	4.52231	+	2.61096i	0.157830	+	0.0911230i	−0.419005	+	0.907984i	$0.637621\pi$
$822$		0			0
$823$	8.29368	−	4.78836i	0.289099	−	0.166912i	−0.348436	−	0.937333i	$-0.613287\pi$
$823$	8.29368	−	4.78836i	0.289099	−	0.166912i	0.637536	+	0.770421i	$0.279954\pi$
$824$	27.3280	+	33.3941i	0.952017	+	1.16334i
$825$		0			0
$826$	15.6487	−	22.2284i	0.544486	−	0.773426i
$827$	−40.6664			−1.41411			−0.707055	−	0.707159i	$-0.749977\pi$
$827$	−40.6664			−1.41411			−0.707055	+	0.707159i	$0.749977\pi$
$828$		0			0
$829$	−16.6171	−	28.7816i	−0.577134	−	0.999625i	−0.995806	−	0.0914880i	$-0.970838\pi$
$829$	−16.6171	−	28.7816i	−0.577134	−	0.999625i	0.418672	−	0.908137i	$-0.362496\pi$
$830$	0.580256	+	1.36050i	0.0201410	+	0.0472235i
$831$		0			0
$832$	15.0243	+	13.2502i	0.520875	+	0.459369i
$833$	−20.1271	−	10.0295i	−0.697364	−	0.347500i
$834$		0			0
$835$	−2.60236	+	4.50743i	−0.0900586	+	0.155986i
$836$	−10.5620	+	3.06789i	−0.365293	+	0.106105i
$837$		0			0
$838$	1.76684	−	2.35307i	0.0610344	−	0.0812855i
$839$	−15.0243			−0.518698			−0.259349	−	0.965784i	$-0.583508\pi$
$839$	−15.0243			−0.518698			−0.259349	+	0.965784i	$0.583508\pi$
$840$		0			0
$841$	7.27029			0.250700
$842$	25.8176	−	34.3838i	0.889733	−	1.18494i
$843$		0			0
$844$	3.19646	+	11.0046i	0.110027	+	0.378793i
$845$	6.99392	−	12.1138i	0.240598	−	0.416728i
$846$		0			0
$847$	−12.8174	−	20.7076i	−0.440411	−	0.711521i
$848$	−15.9148	+	30.4339i	−0.546517	+	1.04510i
$849$		0			0
$850$	−1.21155	−	2.84067i	−0.0415559	−	0.0974341i
$851$	20.3548	+	35.2556i	0.697755	+	1.20855i
$852$		0			0
$853$	12.5203			0.428686			0.214343	−	0.976758i	$-0.431239\pi$
$853$	12.5203			0.428686			0.214343	+	0.976758i	$0.431239\pi$
$854$	−1.72623	+	19.1710i	−0.0590703	+	0.656017i
$855$		0			0
$856$	−19.8991	−	24.3162i	−0.680139	−	0.831109i
$857$	46.8265	−	27.0353i	1.59956	−	0.923509i	0.607993	−	0.793942i	$-0.291975\pi$
$857$	46.8265	−	27.0353i	1.59956	−	0.923509i	0.991571	−	0.129566i	$-0.0413585\pi$
$858$		0			0
$859$	17.0990	+	9.87213i	0.583411	+	0.336833i	0.762488	−	0.647002i	$-0.223978\pi$
$859$	17.0990	+	9.87213i	0.583411	+	0.336833i	−0.179077	+	0.983835i	$0.557311\pi$
$860$		0			0
$861$		0			0
$862$	3.76563	+	0.455798i	0.128258	+	0.0155246i
$863$	−26.3755	−	15.2279i	−0.897833	−	0.518364i	−0.0213367	−	0.999772i	$-0.506792\pi$
$863$	−26.3755	−	15.2279i	−0.897833	−	0.518364i	−0.876497	+	0.481408i	$0.840126\pi$
$864$		0			0
$865$	−5.64697	−	9.78084i	−0.192003	−	0.332559i
$866$	25.0223	−	33.3246i	0.850292	−	1.13242i
$867$		0			0
$868$	7.23850	+	22.3400i	0.245691	+	0.758268i
$869$			8.15137i			0.276516i
$870$		0			0
$871$	−9.84701	−	17.0555i	−0.333653	−	0.577905i
$872$	5.75575	+	35.1668i	0.194914	+	1.19090i
$873$		0			0
$874$	4.46946	−	36.9249i	0.151182	−	1.24900i
$875$	−14.7808	+	27.5157i	−0.499682	+	0.930201i
$876$		0			0
$877$	−18.3275	−	10.5814i	−0.618877	−	0.357309i	0.157555	−	0.987510i	$-0.449639\pi$
$877$	−18.3275	−	10.5814i	−0.618877	−	0.357309i	−0.776432	+	0.630201i	$0.782972\pi$
$878$	9.82520	−	4.19048i	0.331584	−	0.141422i
$879$		0			0
$880$	9.40635	−	5.96797i	0.317088	−	0.201180i
$881$		−	11.5367i		−	0.388681i	−0.980934	−	0.194340i	$-0.937743\pi$
$881$		−	11.5367i		−	0.388681i	0.980934	−	0.194340i	$-0.0622566\pi$
$882$		0			0
$883$	49.8555			1.67777			0.838886	−	0.544307i	$-0.183207\pi$
$883$	49.8555			1.67777			0.838886	+	0.544307i	$0.183207\pi$
$884$	−11.6115	−	11.1363i	−0.390537	−	0.374554i
$885$		0			0
$886$	9.78011	−	4.17125i	0.328569	−	0.140136i
$887$	−5.56575	+	9.64015i	−0.186879	+	0.323685i	−0.944208	−	0.329349i	$-0.893171\pi$
$887$	−5.56575	+	9.64015i	−0.186879	+	0.323685i	0.757329	+	0.653034i	$0.226504\pi$
$888$		0			0
$889$	−34.0629	−	18.2978i	−1.14243	−	0.613688i
$890$	−5.05442	−	0.611796i	−0.169425	−	0.0205074i
$891$		0			0
$892$	11.6411	+	40.0772i	0.389772	+	1.34188i
$893$	4.02352	−	2.32298i	0.134642	−	0.0777356i
$894$		0			0
$895$	−7.31287			−0.244442
$896$	28.6924	+	8.52899i	0.958547	+	0.284934i
$897$		0			0
$898$	−16.2094	−	12.1711i	−0.540916	−	0.406155i
$899$	−17.9159	+	10.3438i	−0.597530	+	0.344984i
$900$		0			0
$901$	13.7913	−	23.8872i	0.459454	−	0.795798i
$902$	−10.4418	−	1.26389i	−0.347672	−	0.0420829i
$903$		0			0
$904$	−20.0629	+	53.0815i	−0.667282	+	1.76546i
$905$	23.0696	−	39.9577i	0.766859	−	1.32824i
$906$		0			0
$907$	7.20674	+	12.4824i	0.239296	+	0.414473i	0.960512	−	0.278237i	$-0.0897501\pi$
$907$	7.20674	+	12.4824i	0.239296	+	0.414473i	−0.721217	+	0.692710i	$0.756417\pi$
$908$	−23.7969	−	22.8229i	−0.789727	−	0.757406i
$909$		0			0
$910$	−1.74647	+	19.3958i	−0.0578951	+	0.642966i
$911$		−	19.1909i		−	0.635823i	−0.948120	−	0.317911i	$-0.897019\pi$
$911$		−	19.1909i		−	0.635823i	0.948120	−	0.317911i	$-0.102981\pi$
$912$		0			0
$913$	−0.583868	+	0.337096i	−0.0193232	+	0.0111563i
$914$	16.8598	−	7.19077i	0.557674	−	0.237850i
$915$		0			0
$916$	16.5081	+	4.05576i	0.545443	+	0.134006i
$917$	13.6958	−	8.47733i	0.452276	−	0.279946i
$918$		0			0
$919$	22.4285	+	12.9491i	0.739848	+	0.427151i	0.822014	−	0.569467i	$-0.192850\pi$
$919$	22.4285	+	12.9491i	0.739848	+	0.427151i	−0.0821662	+	0.996619i	$0.526184\pi$
$920$	6.08489	+	37.1778i	0.200613	+	1.22572i
$921$		0			0
$922$	37.7575	+	28.3508i	1.24348	+	0.933683i
$923$		−	13.2502i		−	0.436136i
$924$		0			0
$925$			4.31842i			0.141989i
$926$	−25.2826	+	33.6713i	−0.830839	+	1.10651i
$927$		0			0
$928$	−2.07261	+	26.2879i	−0.0680366	+	0.862943i
$929$	36.7480	+	21.2165i	1.20566	+	0.696090i	0.961809	−	0.273722i	$-0.0882548\pi$
$929$	36.7480	+	21.2165i	1.20566	+	0.696090i	0.243854	+	0.969812i	$0.421588\pi$
$930$		0			0
$931$	−1.76029	−	28.6761i	−0.0576910	−	0.939820i
$932$	8.69158	+	2.13537i	0.284702	+	0.0699464i
$933$		0			0
$934$	15.0807	+	35.3589i	0.493455	+	1.15698i
$935$	−7.74809	+	4.47336i	−0.253390	+	0.146295i
$936$		0			0
$937$		−	46.5547i		−	1.52088i	−0.649410	−	0.760439i	$-0.724984\pi$
$937$		−	46.5547i		−	1.52088i	0.649410	−	0.760439i	$-0.275016\pi$
$938$	−24.0628	−	16.9400i	−0.785678	−	0.553111i
$939$		0			0
$940$	−3.25719	+	3.39618i	−0.106238	+	0.110771i
$941$	1.48937	+	2.57967i	0.0485522	+	0.0840949i	0.889280	−	0.457363i	$-0.151206\pi$
$941$	1.48937	+	2.57967i	0.0485522	+	0.0840949i	−0.840728	+	0.541458i	$0.817873\pi$
$942$		0			0
$943$	17.7847	−	30.8040i	0.579150	−	1.00312i
$944$	13.4668	−	25.7526i	0.438308	−	0.838177i
$945$		0			0
$946$		0			0
$947$	−13.5270	+	23.4294i	−0.439568	+	0.761354i	−0.997656	−	0.0684276i	$-0.978202\pi$
$947$	−13.5270	+	23.4294i	−0.439568	+	0.761354i	0.558088	+	0.829782i	$0.311535\pi$
$948$		0			0
$949$	−1.20287	+	0.694478i	−0.0390469	+	0.0225437i
$950$	2.36906	−	3.15511i	0.0768625	−	0.102365i
$951$		0			0
$952$	−22.7375	−	7.80629i	−0.736928	−	0.253003i
$953$	−28.7293			−0.930634			−0.465317	−	0.885144i	$-0.654060\pi$
$953$	−28.7293			−0.930634			−0.465317	+	0.885144i	$0.654060\pi$
$954$		0			0
$955$	−2.36152	+	1.36342i	−0.0764169	+	0.0441193i
$956$	47.1849	−	13.7056i	1.52607	−	0.443271i
$957$		0			0
$958$	5.85225	−	48.3490i	0.189078	−	1.56209i
$959$	36.9536	−	1.13313i	1.19329	−	0.0365908i
$960$		0			0
$961$	5.65232	−	9.79010i	0.182333	−	0.315810i
$962$	8.82598	+	20.6938i	0.284561	+	0.667195i
$963$		0			0
$964$	−8.37535	−	8.03257i	−0.269752	−	0.258712i
$965$	−23.4747			−0.755677
$966$		0			0
$967$		−	13.3546i		−	0.429453i	−0.976674	−	0.214727i	$-0.931114\pi$
$967$		−	13.3546i		−	0.429453i	0.976674	−	0.214727i	$-0.0688861\pi$
$968$	−16.4883	−	20.1482i	−0.529955	−	0.647589i
$969$		0			0
$970$	−19.8619	−	46.5691i	−0.637726	−	1.49524i
$971$	1.71876	+	0.992325i	0.0551575	+	0.0318452i	0.527325	−	0.849664i	$-0.323195\pi$
$971$	1.71876	+	0.992325i	0.0551575	+	0.0318452i	−0.472168	+	0.881509i	$0.656528\pi$
$972$		0			0
$973$	1.17278	+	0.629989i	0.0375976	+	0.0201965i
$974$	11.0662	+	1.33948i	0.354585	+	0.0429196i
$975$		0			0
$976$	0.859396	+	20.5596i	0.0275086	+	0.658097i
$977$	−31.2242	−	54.0818i	−0.998950	−	1.73023i	−0.539158	−	0.842205i	$-0.681257\pi$
$977$	−31.2242	−	54.0818i	−0.998950	−	1.73023i	−0.459792	−	0.888027i	$-0.652076\pi$
$978$		0			0
$979$		−	2.32073i		−	0.0741710i
$980$	9.81377	+	27.3945i	0.313489	+	0.875085i
$981$		0			0
$982$	−9.11836	−	6.84665i	−0.290978	−	0.218486i
$983$	3.64021	+	6.30503i	0.116105	+	0.201099i	0.918221	−	0.396069i	$-0.129626\pi$
$983$	3.64021	+	6.30503i	0.116105	+	0.201099i	−0.802116	+	0.597168i	$0.796293\pi$
$984$		0			0
$985$	10.6590	+	6.15397i	0.339624	+	0.196082i
$986$	2.54486	−	21.0246i	0.0810448	−	0.669561i
$987$		0			0
$988$	4.90411	−	19.9612i	0.156021	−	0.635049i
$989$		0			0
$990$		0			0
$991$	−31.3345	+	18.0910i	−0.995373	+	0.574679i	−0.906876	−	0.421398i	$-0.861540\pi$
$991$	−31.3345	+	18.0910i	−0.995373	+	0.574679i	−0.0884967	+	0.996076i	$0.528206\pi$
$992$	10.8047	+	22.6607i	0.343051	+	0.719479i
$993$		0			0
$994$	−8.32190	−	17.9651i	−0.263955	−	0.569819i
$995$	38.6838			1.22636
$996$		0			0
$997$	−17.1218	−	29.6559i	−0.542254	−	0.939211i	−0.998774	−	0.0494984i	$-0.984238\pi$
$997$	−17.1218	−	29.6559i	−0.542254	−	0.939211i	0.456520	−	0.889713i	$-0.349096\pi$
$998$	−31.2765	+	13.3395i	−0.990039	+	0.422255i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.a.19.1		12
3.2	odd	2		56.2.m.a.19.6	yes	12
4.3	odd	2		2016.2.bs.a.271.2		12
7.3	odd	6	inner	504.2.bk.a.451.5		12
8.3	odd	2	inner	504.2.bk.a.19.6		12
8.5	even	2		2016.2.bs.a.271.5		12
12.11	even	2		224.2.q.a.47.6		12
21.2	odd	6		392.2.e.e.195.5		12
21.5	even	6		392.2.e.e.195.6		12
21.11	odd	6		392.2.m.g.227.2		12
21.17	even	6		56.2.m.a.3.2	✓	12
21.20	even	2		392.2.m.g.19.6		12
24.5	odd	2		224.2.q.a.47.5		12
24.11	even	2		56.2.m.a.19.1	yes	12
28.3	even	6		2016.2.bs.a.1711.5		12
56.3	even	6	inner	504.2.bk.a.451.2		12
56.45	odd	6		2016.2.bs.a.1711.2		12
84.11	even	6		1568.2.q.g.815.2		12
84.23	even	6		1568.2.e.e.783.11		12
84.47	odd	6		1568.2.e.e.783.2		12
84.59	odd	6		224.2.q.a.143.5		12
84.83	odd	2		1568.2.q.g.1391.1		12
168.5	even	6		1568.2.e.e.783.1		12
168.11	even	6		392.2.m.g.227.5		12
168.53	odd	6		1568.2.q.g.815.1		12
168.59	odd	6		56.2.m.a.3.5	yes	12
168.83	odd	2		392.2.m.g.19.1		12
168.101	even	6		224.2.q.a.143.6		12
168.107	even	6		392.2.e.e.195.7		12
168.125	even	2		1568.2.q.g.1391.2		12
168.131	odd	6		392.2.e.e.195.8		12
168.149	odd	6		1568.2.e.e.783.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.2	✓	12	21.17	even	6
56.2.m.a.3.5	yes	12	168.59	odd	6
56.2.m.a.19.1	yes	12	24.11	even	2
56.2.m.a.19.6	yes	12	3.2	odd	2
224.2.q.a.47.5		12	24.5	odd	2
224.2.q.a.47.6		12	12.11	even	2
224.2.q.a.143.5		12	84.59	odd	6
224.2.q.a.143.6		12	168.101	even	6
392.2.e.e.195.5		12	21.2	odd	6
392.2.e.e.195.6		12	21.5	even	6
392.2.e.e.195.7		12	168.107	even	6
392.2.e.e.195.8		12	168.131	odd	6
392.2.m.g.19.1		12	168.83	odd	2
392.2.m.g.19.6		12	21.20	even	2
392.2.m.g.227.2		12	21.11	odd	6
392.2.m.g.227.5		12	168.11	even	6
504.2.bk.a.19.1		12	1.1	even	1	trivial
504.2.bk.a.19.6		12	8.3	odd	2	inner
504.2.bk.a.451.2		12	56.3	even	6	inner
504.2.bk.a.451.5		12	7.3	odd	6	inner
1568.2.e.e.783.1		12	168.5	even	6
1568.2.e.e.783.2		12	84.47	odd	6
1568.2.e.e.783.11		12	84.23	even	6
1568.2.e.e.783.12		12	168.149	odd	6
1568.2.q.g.815.1		12	168.53	odd	6
1568.2.q.g.815.2		12	84.11	even	6
1568.2.q.g.1391.1		12	84.83	odd	2
1568.2.q.g.1391.2		12	168.125	even	2
2016.2.bs.a.271.2		12	4.3	odd	2
2016.2.bs.a.271.5		12	8.5	even	2
2016.2.bs.a.1711.2		12	56.45	odd	6
2016.2.bs.a.1711.5		12	28.3	even	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13090 - 0.849154i) q^{2} +(0.557875 + 1.92062i) q^{4} +(-1.03926 + 1.80005i) q^{5} +(1.25203 - 2.33076i) q^{7} +(1.00000 - 2.64575i) q^{8} +O(q^{10})\)	\(q+(-1.13090 - 0.849154i) q^{2} +(0.557875 + 1.92062i) q^{4} +(-1.03926 + 1.80005i) q^{5} +(1.25203 - 2.33076i) q^{7} +(1.00000 - 2.64575i) q^{8} +(2.70382 - 1.15319i) q^{10} +(0.669938 + 1.16037i) q^{11} -2.50406 q^{13} +(-3.39509 + 1.57269i) q^{14} +(-3.37755 + 2.14293i) q^{16} +(2.78212 - 1.60626i) q^{17} +(3.55442 + 2.05215i) q^{19} +(-4.03699 - 0.991819i) q^{20} +(0.227697 - 1.88114i) q^{22} +(5.54952 + 3.20402i) q^{23} +(0.339877 + 0.588684i) q^{25} +(2.83184 + 2.12633i) q^{26} +(5.17497 + 1.10440i) q^{28} +4.66151i q^{29} +(2.21897 + 3.84337i) q^{31} +(5.63935 + 0.444621i) q^{32} +(-4.51026 - 0.545930i) q^{34} +(2.89430 + 4.67598i) q^{35} +(5.50178 + 3.17646i) q^{37} +(-2.27711 - 5.33903i) q^{38} +(3.72323 + 4.54968i) q^{40} -5.55076i q^{41} +(-1.85488 + 1.93404i) q^{44} +(-3.55526 - 8.33583i) q^{46} +(0.565988 - 0.980320i) q^{47} +(-3.86485 - 5.83634i) q^{49} +(0.115516 - 0.954351i) q^{50} +(-1.39695 - 4.80934i) q^{52} +(7.43567 - 4.29299i) q^{53} -2.78496 q^{55} +(-4.91457 - 5.64331i) q^{56} +(3.95834 - 5.27171i) q^{58} +(-6.29193 + 3.63265i) q^{59} +(2.57219 - 4.45517i) q^{61} +(0.754178 - 6.23073i) q^{62} +(-6.00000 - 5.29150i) q^{64} +(2.60236 - 4.50743i) q^{65} +(3.93243 + 6.81116i) q^{67} +(4.63708 + 4.44730i) q^{68} +(0.697459 - 7.74577i) q^{70} +5.29150i q^{71} +(0.480369 - 0.277341i) q^{73} +(-3.52467 - 8.26412i) q^{74} +(-1.95847 + 7.97153i) q^{76} +(3.54332 - 0.108651i) q^{77} +(5.26862 + 3.04184i) q^{79} +(-0.347228 - 8.30683i) q^{80} +(-4.71345 + 6.27736i) q^{82} +0.503175i q^{83} +6.67728i q^{85} +(3.73998 - 0.612123i) q^{88} +(-1.50000 - 0.866025i) q^{89} +(-3.13515 + 5.83634i) q^{91} +(-3.05776 + 12.4460i) q^{92} +(-1.47252 + 0.628034i) q^{94} +(-7.38794 + 4.26543i) q^{95} -17.2234i q^{97} +(-0.585189 + 9.88218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{8}+O(q^{10}) \) 12 * q + 12 * q^8	\( 12 q + 12 q^{8} + 6 q^{10} + 6 q^{11} - 6 q^{14} + 6 q^{17} - 6 q^{19} + 24 q^{22} - 6 q^{26} + 6 q^{28} - 18 q^{35} + 24 q^{38} + 42 q^{40} - 6 q^{44} - 18 q^{46} - 12 q^{49} + 48 q^{50} - 24 q^{52} + 18 q^{58} - 42 q^{59} - 72 q^{64} + 12 q^{65} + 30 q^{67} + 36 q^{68} + 30 q^{70} + 18 q^{73} - 12 q^{74} - 36 q^{80} + 54 q^{82} + 6 q^{88} - 18 q^{89} - 72 q^{91} - 60 q^{92} - 12 q^{94} + 6 q^{98}+O(q^{100}) \) 12 * q + 12 * q^8 + 6 * q^10 + 6 * q^11 - 6 * q^14 + 6 * q^17 - 6 * q^19 + 24 * q^22 - 6 * q^26 + 6 * q^28 - 18 * q^35 + 24 * q^38 + 42 * q^40 - 6 * q^44 - 18 * q^46 - 12 * q^49 + 48 * q^50 - 24 * q^52 + 18 * q^58 - 42 * q^59 - 72 * q^64 + 12 * q^65 + 30 * q^67 + 36 * q^68 + 30 * q^70 + 18 * q^73 - 12 * q^74 - 36 * q^80 + 54 * q^82 + 6 * q^88 - 18 * q^89 - 72 * q^91 - 60 * q^92 - 12 * q^94 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more