LMFDB - Embedded newform 560.2.ci.a.353.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(17,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("560.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ci (of order $12$, degree $4$, not 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	560.353
Dual form			560.2.ci.a.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 1.86603i) q^{3} +(-0.133975 - 2.23205i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(-0.633975 + 0.366025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 1.86603i) q^{3} +(-0.133975 - 2.23205i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(-0.633975 + 0.366025i) q^{9} +(0.366025 - 0.633975i) q^{11} +(2.00000 - 2.00000i) q^{13} +(4.09808 - 1.36603i) q^{15} +(1.00000 - 0.267949i) q^{17} +(-1.36603 - 2.36603i) q^{19} +(4.23205 - 2.86603i) q^{21} +(1.86603 - 6.96410i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(3.09808 + 3.09808i) q^{27} +3.00000i q^{29} +(-0.464102 - 0.267949i) q^{31} +(1.36603 + 0.366025i) q^{33} +(-5.46410 + 2.26795i) q^{35} +(4.73205 + 1.26795i) q^{37} +(4.73205 + 2.73205i) q^{39} +0.464102i q^{41} +(5.83013 + 5.83013i) q^{43} +(0.901924 + 1.36603i) q^{45} +(-0.169873 + 0.633975i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(1.00000 + 1.73205i) q^{51} +(6.83013 - 1.83013i) q^{53} +(-1.46410 - 0.732051i) q^{55} +(3.73205 - 3.73205i) q^{57} +(1.09808 - 1.90192i) q^{59} +(-7.33013 + 4.23205i) q^{61} +(1.46410 + 1.26795i) q^{63} +(-4.73205 - 4.19615i) q^{65} +(0.303848 + 1.13397i) q^{67} +13.9282 q^{69} -4.73205 q^{71} +(0.928203 + 3.46410i) q^{73} +(-3.59808 - 8.96410i) q^{75} +(-1.90192 - 0.366025i) q^{77} +(-5.83013 + 3.36603i) q^{79} +(-5.33013 + 9.23205i) q^{81} +(3.09808 - 3.09808i) q^{83} +(-0.732051 - 2.19615i) q^{85} +(-5.59808 + 1.50000i) q^{87} +(-8.33013 - 14.4282i) q^{89} +(-6.73205 - 3.26795i) q^{91} +(0.267949 - 1.00000i) q^{93} +(-5.09808 + 3.36603i) q^{95} +(-7.92820 - 7.92820i) q^{97} +0.535898i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 4 q^{5} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 4 * q^5 - 6 * q^9	$ 4 q + 2 q^{3} - 4 q^{5} - 6 q^{9} - 2 q^{11} + 8 q^{13} + 6 q^{15} + 4 q^{17} - 2 q^{19} + 10 q^{21} + 4 q^{23} - 6 q^{25} + 2 q^{27} + 12 q^{31} + 2 q^{33} - 8 q^{35} + 12 q^{37} + 12 q^{39} + 6 q^{43} + 14 q^{45} - 18 q^{47} - 22 q^{49} + 4 q^{51} + 10 q^{53} + 8 q^{55} + 8 q^{57} - 6 q^{59} - 12 q^{61} - 8 q^{63} - 12 q^{65} + 22 q^{67} + 28 q^{69} - 12 q^{71} - 24 q^{73} - 4 q^{75} - 18 q^{77} - 6 q^{79} - 4 q^{81} + 2 q^{83} + 4 q^{85} - 12 q^{87} - 16 q^{89} - 20 q^{91} + 8 q^{93} - 10 q^{95} - 4 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^5 - 6 * q^9 - 2 * q^11 + 8 * q^13 + 6 * q^15 + 4 * q^17 - 2 * q^19 + 10 * q^21 + 4 * q^23 - 6 * q^25 + 2 * q^27 + 12 * q^31 + 2 * q^33 - 8 * q^35 + 12 * q^37 + 12 * q^39 + 6 * q^43 + 14 * q^45 - 18 * q^47 - 22 * q^49 + 4 * q^51 + 10 * q^53 + 8 * q^55 + 8 * q^57 - 6 * q^59 - 12 * q^61 - 8 * q^63 - 12 * q^65 + 22 * q^67 + 28 * q^69 - 12 * q^71 - 24 * q^73 - 4 * q^75 - 18 * q^77 - 6 * q^79 - 4 * q^81 + 2 * q^83 + 4 * q^85 - 12 * q^87 - 16 * q^89 - 20 * q^91 + 8 * q^93 - 10 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.500000	+	1.86603i	0.288675	+	1.07735i	0.946112	+	0.323840i	$0.104974\pi$
$3$	0.500000	+	1.86603i	0.288675	+	1.07735i	−0.657437	+	0.753510i	$0.728359\pi$
$4$		0			0
$5$	−0.133975	−	2.23205i	−0.0599153	−	0.998203i
$5$	−0.133975	−	2.23205i	−0.0599153	−	0.998203i
$6$		0			0
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$		0			0
$9$	−0.633975	+	0.366025i	−0.211325	+	0.122008i
$10$		0			0
$11$	0.366025	−	0.633975i	0.110361	−	0.191151i	−0.805555	−	0.592521i	$-0.798133\pi$
$11$	0.366025	−	0.633975i	0.110361	−	0.191151i	0.915916	+	0.401371i	$0.131466\pi$
$12$		0			0
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	−0.373094	−	0.927794i	$-0.621703\pi$
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	0.927794	+	0.373094i	$0.121703\pi$
$14$		0			0
$15$	4.09808	−	1.36603i	1.05812	−	0.352706i
$16$		0			0
$17$	1.00000	−	0.267949i	0.242536	−	0.0649872i	−0.135503	−	0.990777i	$-0.543265\pi$
$17$	1.00000	−	0.267949i	0.242536	−	0.0649872i	0.378039	+	0.925790i	$0.376599\pi$
$18$		0			0
$19$	−1.36603	−	2.36603i	−0.313388	−	0.542803i	0.665706	−	0.746214i	$-0.268131\pi$
$19$	−1.36603	−	2.36603i	−0.313388	−	0.542803i	−0.979093	+	0.203411i	$0.934797\pi$
$20$		0			0
$21$	4.23205	−	2.86603i	0.923509	−	0.625418i
$22$		0			0
$23$	1.86603	−	6.96410i	0.389093	−	1.45212i	−0.442519	−	0.896759i	$-0.645915\pi$
$23$	1.86603	−	6.96410i	0.389093	−	1.45212i	0.831612	−	0.555357i	$-0.187418\pi$
$24$		0			0
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$		0			0
$27$	3.09808	+	3.09808i	0.596225	+	0.596225i
$28$		0			0
$29$			3.00000i			0.557086i	0.960424	+	0.278543i	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$		0			0
$31$	−0.464102	−	0.267949i	−0.0833551	−	0.0481251i	0.457743	−	0.889085i	$-0.348658\pi$
$31$	−0.464102	−	0.267949i	−0.0833551	−	0.0481251i	−0.541098	+	0.840959i	$0.681991\pi$
$32$		0			0
$33$	1.36603	+	0.366025i	0.237795	+	0.0637168i
$34$		0			0
$35$	−5.46410	+	2.26795i	−0.923602	+	0.383353i
$36$		0			0
$37$	4.73205	+	1.26795i	0.777944	+	0.208450i	0.625878	−	0.779921i	$-0.284741\pi$
$37$	4.73205	+	1.26795i	0.777944	+	0.208450i	0.152066	+	0.988370i	$0.451407\pi$
$38$		0			0
$39$	4.73205	+	2.73205i	0.757735	+	0.437478i
$40$		0			0
$41$			0.464102i			0.0724805i	0.999343	+	0.0362402i	$0.0115382\pi$
$41$			0.464102i			0.0724805i	−0.999343	+	0.0362402i	$0.988462\pi$
$42$		0			0
$43$	5.83013	+	5.83013i	0.889086	+	0.889086i	0.994435	−	0.105349i	$-0.0335960\pi$
$43$	5.83013	+	5.83013i	0.889086	+	0.889086i	−0.105349	+	0.994435i	$0.533596\pi$
$44$		0			0
$45$	0.901924	+	1.36603i	0.134451	+	0.203635i
$46$		0			0
$47$	−0.169873	+	0.633975i	−0.0247785	+	0.0924747i	−0.977208	−	0.212285i	$-0.931909\pi$
$47$	−0.169873	+	0.633975i	−0.0247785	+	0.0924747i	0.952429	+	0.304760i	$0.0985762\pi$
$48$		0			0
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$		0			0
$53$	6.83013	−	1.83013i	0.938190	−	0.251387i	0.242846	−	0.970065i	$-0.421919\pi$
$53$	6.83013	−	1.83013i	0.938190	−	0.251387i	0.695344	+	0.718677i	$0.255252\pi$
$54$		0			0
$55$	−1.46410	−	0.732051i	−0.197419	−	0.0987097i
$56$		0			0
$57$	3.73205	−	3.73205i	0.494322	−	0.494322i
$58$		0			0
$59$	1.09808	−	1.90192i	0.142957	−	0.247609i	−0.785652	−	0.618669i	$-0.787672\pi$
$59$	1.09808	−	1.90192i	0.142957	−	0.247609i	0.928609	+	0.371060i	$0.121005\pi$
$60$		0			0
$61$	−7.33013	+	4.23205i	−0.938527	+	0.541859i	−0.889498	−	0.456939i	$-0.848946\pi$
$61$	−7.33013	+	4.23205i	−0.938527	+	0.541859i	−0.0490285	+	0.998797i	$0.515613\pi$
$62$		0			0
$63$	1.46410	+	1.26795i	0.184459	+	0.159747i
$64$		0			0
$65$	−4.73205	−	4.19615i	−0.586939	−	0.520469i
$66$		0			0
$67$	0.303848	+	1.13397i	0.0371209	+	0.138537i	0.981999	−	0.188884i	$-0.0604871\pi$
$67$	0.303848	+	1.13397i	0.0371209	+	0.138537i	−0.944878	+	0.327421i	$0.893820\pi$
$68$		0			0
$69$	13.9282			1.67676
$70$		0			0
$71$	−4.73205			−0.561591			−0.280796	−	0.959768i	$-0.590598\pi$
$71$	−4.73205			−0.561591			−0.280796	+	0.959768i	$0.590598\pi$
$72$		0			0
$73$	0.928203	+	3.46410i	0.108638	+	0.405442i	0.998732	−	0.0503336i	$-0.0160285\pi$
$73$	0.928203	+	3.46410i	0.108638	+	0.405442i	−0.890094	+	0.455776i	$0.849362\pi$
$74$		0			0
$75$	−3.59808	−	8.96410i	−0.415470	−	1.03509i
$76$		0			0
$77$	−1.90192	−	0.366025i	−0.216744	−	0.0417125i
$78$		0			0
$79$	−5.83013	+	3.36603i	−0.655941	+	0.378707i	−0.790728	−	0.612167i	$-0.790298\pi$
$79$	−5.83013	+	3.36603i	−0.655941	+	0.378707i	0.134788	+	0.990874i	$0.456965\pi$
$80$		0			0
$81$	−5.33013	+	9.23205i	−0.592236	+	1.02578i
$82$		0			0
$83$	3.09808	−	3.09808i	0.340058	−	0.340058i	−0.516331	−	0.856389i	$-0.672703\pi$
$83$	3.09808	−	3.09808i	0.340058	−	0.340058i	0.856389	+	0.516331i	$0.172703\pi$
$84$		0			0
$85$	−0.732051	−	2.19615i	−0.0794021	−	0.238206i
$86$		0			0
$87$	−5.59808	+	1.50000i	−0.600177	+	0.160817i
$88$		0			0
$89$	−8.33013	−	14.4282i	−0.882992	−	1.52939i	−0.847998	−	0.529999i	$-0.822192\pi$
$89$	−8.33013	−	14.4282i	−0.882992	−	1.52939i	−0.0349934	−	0.999388i	$-0.511141\pi$
$90$		0			0
$91$	−6.73205	−	3.26795i	−0.705711	−	0.342574i
$92$		0			0
$93$	0.267949	−	1.00000i	0.0277850	−	0.103695i
$94$		0			0
$95$	−5.09808	+	3.36603i	−0.523052	+	0.345347i
$96$		0			0
$97$	−7.92820	−	7.92820i	−0.804987	−	0.804987i	0.178883	−	0.983870i	$-0.442752\pi$
$97$	−7.92820	−	7.92820i	−0.804987	−	0.804987i	−0.983870	+	0.178883i	$0.942752\pi$
$98$		0			0
$99$			0.535898i			0.0538598i
$100$		0			0
$101$	−10.1603	−	5.86603i	−1.01098	−	0.583691i	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−10.1603	−	5.86603i	−1.01098	−	0.583691i	−0.911479	+	0.411346i	$0.865059\pi$
$102$		0			0
$103$	2.23205	+	0.598076i	0.219931	+	0.0589302i	0.367102	−	0.930181i	$-0.380350\pi$
$103$	2.23205	+	0.598076i	0.219931	+	0.0589302i	−0.147171	+	0.989111i	$0.547017\pi$
$104$		0			0
$105$	−6.96410	−	9.06218i	−0.679627	−	0.884378i
$106$		0			0
$107$	8.59808	+	2.30385i	0.831207	+	0.222721i	0.649240	−	0.760583i	$-0.275087\pi$
$107$	8.59808	+	2.30385i	0.831207	+	0.222721i	0.181967	+	0.983305i	$0.441754\pi$
$108$		0			0
$109$	12.2321	+	7.06218i	1.17162	+	0.676434i	0.954061	−	0.299614i	$-0.0968578\pi$
$109$	12.2321	+	7.06218i	1.17162	+	0.676434i	0.217557	+	0.976048i	$0.430191\pi$
$110$		0			0
$111$			9.46410i			0.898293i
$112$		0			0
$113$	−4.26795	−	4.26795i	−0.401495	−	0.401495i	0.477265	−	0.878760i	$-0.341628\pi$
$113$	−4.26795	−	4.26795i	−0.401495	−	0.401495i	−0.878760	+	0.477265i	$0.841628\pi$
$114$		0			0
$115$	−15.7942	−	3.23205i	−1.47282	−	0.301390i
$116$		0			0
$117$	−0.535898	+	2.00000i	−0.0495438	+	0.184900i
$118$		0			0
$119$	−1.53590	−	2.26795i	−0.140796	−	0.207903i
$120$		0			0
$121$	5.23205	+	9.06218i	0.475641	+	0.823834i
$122$		0			0
$123$	−0.866025	+	0.232051i	−0.0780869	+	0.0209233i
$124$		0			0
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$	6.46410	−	6.46410i	0.573596	−	0.573596i	−0.359535	−	0.933132i	$-0.617065\pi$
$127$	6.46410	−	6.46410i	0.573596	−	0.573596i	0.933132	+	0.359535i	$0.117065\pi$
$128$		0			0
$129$	−7.96410	+	13.7942i	−0.701200	+	1.21451i
$130$		0			0
$131$	−7.39230	+	4.26795i	−0.645869	+	0.372892i	−0.786872	−	0.617117i	$-0.788301\pi$
$131$	−7.39230	+	4.26795i	−0.645869	+	0.372892i	0.141003	+	0.990009i	$0.454967\pi$
$132$		0			0
$133$	−4.73205	+	5.46410i	−0.410321	+	0.473798i
$134$		0			0
$135$	6.50000	−	7.33013i	0.559431	−	0.630877i
$136$		0			0
$137$	2.80385	+	10.4641i	0.239549	+	0.894009i	0.976045	+	0.217567i	$0.0698121\pi$
$137$	2.80385	+	10.4641i	0.239549	+	0.894009i	−0.736496	+	0.676441i	$0.763521\pi$
$138$		0			0
$139$	11.6603			0.989010			0.494505	−	0.869175i	$-0.335349\pi$
$139$	11.6603			0.989010			0.494505	+	0.869175i	$0.335349\pi$
$140$		0			0
$141$	−1.26795			−0.106781
$142$		0			0
$143$	−0.535898	−	2.00000i	−0.0448141	−	0.167248i
$144$		0			0
$145$	6.69615	−	0.401924i	0.556085	−	0.0333780i
$146$		0			0
$147$	−10.8301	−	8.09808i	−0.893254	−	0.667918i
$148$		0			0
$149$	9.69615	−	5.59808i	0.794340	−	0.458612i	−0.0471484	−	0.998888i	$-0.515013\pi$
$149$	9.69615	−	5.59808i	0.794340	−	0.458612i	0.841488	+	0.540276i	$0.181680\pi$
$150$		0			0
$151$	−6.92820	+	12.0000i	−0.563809	+	0.976546i	0.433350	+	0.901226i	$0.357331\pi$
$151$	−6.92820	+	12.0000i	−0.563809	+	0.976546i	−0.997159	+	0.0753205i	$0.976002\pi$
$152$		0			0
$153$	−0.535898	+	0.535898i	−0.0433248	+	0.0433248i
$154$		0			0
$155$	−0.535898	+	1.07180i	−0.0430444	+	0.0860888i
$156$		0			0
$157$	−23.7583	+	6.36603i	−1.89612	+	0.508064i	−0.898513	+	0.438948i	$0.855351\pi$
$157$	−23.7583	+	6.36603i	−1.89612	+	0.508064i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$		0			0
$159$	6.83013	+	11.8301i	0.541664	+	0.938190i
$160$		0			0
$161$	−19.0263	+	1.36603i	−1.49948	+	0.107658i
$162$		0			0
$163$	−1.43782	+	5.36603i	−0.112619	+	0.420300i	−0.999098	−	0.0424696i	$-0.986477\pi$
$163$	−1.43782	+	5.36603i	−0.112619	+	0.420300i	0.886479	+	0.462769i	$0.153144\pi$
$164$		0			0
$165$	0.633975	−	3.09808i	0.0493549	−	0.241185i
$166$		0			0
$167$	−10.7583	−	10.7583i	−0.832505	−	0.832505i	0.155354	−	0.987859i	$-0.450348\pi$
$167$	−10.7583	−	10.7583i	−0.832505	−	0.832505i	−0.987859	+	0.155354i	$0.950348\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$	1.73205	+	1.00000i	0.132453	+	0.0764719i
$172$		0			0
$173$	22.6603	+	6.07180i	1.72283	+	0.461630i	0.978511	−	0.206197i	$-0.0661087\pi$
$173$	22.6603	+	6.07180i	1.72283	+	0.461630i	0.744317	+	0.667827i	$0.232775\pi$
$174$		0			0
$175$	5.79423	+	11.8923i	0.438003	+	0.898974i
$176$		0			0
$177$	4.09808	+	1.09808i	0.308030	+	0.0825365i
$178$		0			0
$179$	17.1962	+	9.92820i	1.28530	+	0.742069i	0.977812	−	0.209483i	$-0.0671781\pi$
$179$	17.1962	+	9.92820i	1.28530	+	0.742069i	0.307488	+	0.951552i	$0.400511\pi$
$180$		0			0
$181$			9.19615i			0.683545i	0.939783	+	0.341772i	$0.111027\pi$
$181$			9.19615i			0.683545i	−0.939783	+	0.341772i	$0.888973\pi$
$182$		0			0
$183$	−11.5622	−	11.5622i	−0.854701	−	0.854701i
$184$		0			0
$185$	2.19615	−	10.7321i	0.161464	−	0.789036i
$186$		0			0
$187$	0.196152	−	0.732051i	0.0143441	−	0.0535329i
$188$		0			0
$189$	5.06218	−	10.4282i	0.368219	−	0.758540i
$190$		0			0
$191$	8.36603	+	14.4904i	0.605344	+	1.04849i	0.991997	+	0.126262i	$0.0402979\pi$
$191$	8.36603	+	14.4904i	0.605344	+	1.04849i	−0.386653	+	0.922225i	$0.626369\pi$
$192$		0			0
$193$	−3.09808	+	0.830127i	−0.223004	+	0.0597539i	−0.368591	−	0.929592i	$-0.620160\pi$
$193$	−3.09808	+	0.830127i	−0.223004	+	0.0597539i	0.145587	+	0.989346i	$0.453493\pi$
$194$		0			0
$195$	5.46410	−	10.9282i	0.391292	−	0.782585i
$196$		0			0
$197$	14.1244	−	14.1244i	1.00632	−	1.00632i	0.00633876	−	0.999980i	$-0.497982\pi$
$197$	14.1244	−	14.1244i	1.00632	−	1.00632i	0.999980	−	0.00633876i	$-0.00201770\pi$
$198$		0			0
$199$	−12.4641	+	21.5885i	−0.883557	+	1.53037i	−0.0361978	+	0.999345i	$0.511525\pi$
$199$	−12.4641	+	21.5885i	−0.883557	+	1.53037i	−0.847359	+	0.531021i	$0.821809\pi$
$200$		0			0
$201$	−1.96410	+	1.13397i	−0.138537	+	0.0799844i
$202$		0			0
$203$	7.50000	−	2.59808i	0.526397	−	0.182349i
$204$		0			0
$205$	1.03590	−	0.0621778i	0.0723503	−	0.00434269i
$206$		0			0
$207$	1.36603	+	5.09808i	0.0949453	+	0.354341i
$208$		0			0
$209$	−2.00000			−0.138343
$210$		0			0
$211$	−10.1962			−0.701932			−0.350966	−	0.936388i	$-0.614147\pi$
$211$	−10.1962			−0.701932			−0.350966	+	0.936388i	$0.614147\pi$
$212$		0			0
$213$	−2.36603	−	8.83013i	−0.162117	−	0.605030i
$214$		0			0
$215$	12.2321	−	13.7942i	0.834219	−	0.940759i
$216$		0			0
$217$	−0.267949	+	1.39230i	−0.0181896	+	0.0945158i
$218$		0			0
$219$	−6.00000	+	3.46410i	−0.405442	+	0.234082i
$220$		0			0
$221$	1.46410	−	2.53590i	0.0984861	−	0.170583i
$222$		0			0
$223$	−6.12436	+	6.12436i	−0.410117	+	0.410117i	−0.881779	−	0.471662i	$-0.843654\pi$
$223$	−6.12436	+	6.12436i	−0.410117	+	0.410117i	0.471662	+	0.881779i	$0.343654\pi$
$224$		0			0
$225$	2.92820	−	2.19615i	0.195214	−	0.146410i
$226$		0			0
$227$	−0.0980762	+	0.0262794i	−0.00650955	+	0.00174423i	−0.262072	−	0.965048i	$-0.584406\pi$
$227$	−0.0980762	+	0.0262794i	−0.00650955	+	0.00174423i	0.255563	+	0.966792i	$0.417739\pi$
$228$		0			0
$229$	−1.19615	−	2.07180i	−0.0790440	−	0.136908i	0.823794	−	0.566890i	$-0.191853\pi$
$229$	−1.19615	−	2.07180i	−0.0790440	−	0.136908i	−0.902838	+	0.429981i	$0.858520\pi$
$230$		0			0
$231$	−0.267949	−	3.73205i	−0.0176298	−	0.245551i
$232$		0			0
$233$	−0.464102	+	1.73205i	−0.0304043	+	0.113470i	−0.979460	−	0.201637i	$-0.935374\pi$
$233$	−0.464102	+	1.73205i	−0.0304043	+	0.113470i	0.949056	+	0.315107i	$0.102041\pi$
$234$		0			0
$235$	1.43782	+	0.294229i	0.0937932	+	0.0191934i
$236$		0			0
$237$	−9.19615	−	9.19615i	−0.597354	−	0.597354i
$238$		0			0
$239$		−	18.3923i		−	1.18970i	−0.803837	−	0.594850i	$-0.797212\pi$
$239$		−	18.3923i		−	1.18970i	0.803837	−	0.594850i	$-0.202788\pi$
$240$		0			0
$241$	14.5359	+	8.39230i	0.936340	+	0.540596i	0.888811	−	0.458274i	$-0.151532\pi$
$241$	14.5359	+	8.39230i	0.936340	+	0.540596i	0.0475286	+	0.998870i	$0.484865\pi$
$242$		0			0
$243$	−7.19615	−	1.92820i	−0.461633	−	0.123694i
$244$		0			0
$245$	10.4019	+	11.6962i	0.664555	+	0.747240i
$246$		0			0
$247$	−7.46410	−	2.00000i	−0.474929	−	0.127257i
$248$		0			0
$249$	7.33013	+	4.23205i	0.464528	+	0.268195i
$250$		0			0
$251$			5.85641i			0.369653i	0.982771	+	0.184827i	$0.0591723\pi$
$251$			5.85641i			0.369653i	−0.982771	+	0.184827i	$0.940828\pi$
$252$		0			0
$253$	−3.73205	−	3.73205i	−0.234632	−	0.234632i
$254$		0			0
$255$	3.73205	−	2.46410i	0.233710	−	0.154308i
$256$		0			0
$257$	0.732051	−	2.73205i	0.0456641	−	0.170421i	−0.939328	−	0.343020i	$-0.888550\pi$
$257$	0.732051	−	2.73205i	0.0456641	−	0.170421i	0.984992	+	0.172600i	$0.0552167\pi$
$258$		0			0
$259$	−0.928203	−	12.9282i	−0.0576757	−	0.803319i
$260$		0			0
$261$	−1.09808	−	1.90192i	−0.0679692	−	0.117726i
$262$		0			0
$263$	8.06218	−	2.16025i	0.497135	−	0.133207i	−0.00153494	−	0.999999i	$-0.500489\pi$
$263$	8.06218	−	2.16025i	0.497135	−	0.133207i	0.498670	+	0.866792i	$0.333822\pi$
$264$		0			0
$265$	−5.00000	−	15.0000i	−0.307148	−	0.921443i
$266$		0			0
$267$	22.7583	−	22.7583i	1.39279	−	1.39279i
$268$		0			0
$269$	2.42820	−	4.20577i	0.148050	−	0.256430i	−0.782457	−	0.622705i	$-0.786034\pi$
$269$	2.42820	−	4.20577i	0.148050	−	0.256430i	0.930507	+	0.366275i	$0.119367\pi$
$270$		0			0
$271$	21.4186	−	12.3660i	1.30109	−	0.751183i	0.320496	−	0.947250i	$-0.396150\pi$
$271$	21.4186	−	12.3660i	1.30109	−	0.751183i	0.980590	+	0.196067i	$0.0628171\pi$
$272$		0			0
$273$	2.73205	−	14.1962i	0.165351	−	0.859190i
$274$		0			0
$275$	−1.43782	+	3.36603i	−0.0867039	+	0.202979i
$276$		0			0
$277$	−5.19615	−	19.3923i	−0.312207	−	1.16517i	−0.926562	−	0.376141i	$-0.877251\pi$
$277$	−5.19615	−	19.3923i	−0.312207	−	1.16517i	0.614356	−	0.789029i	$-0.289416\pi$
$278$		0			0
$279$	0.392305			0.0234867
$280$		0			0
$281$	12.9282			0.771232			0.385616	−	0.922659i	$-0.373989\pi$
$281$	12.9282			0.771232			0.385616	+	0.922659i	$0.373989\pi$
$282$		0			0
$283$	7.09808	+	26.4904i	0.421937	+	1.57469i	0.770523	+	0.637413i	$0.219995\pi$
$283$	7.09808	+	26.4904i	0.421937	+	1.57469i	−0.348586	+	0.937277i	$0.613338\pi$
$284$		0			0
$285$	−8.83013	−	7.83013i	−0.523052	−	0.463817i
$286$		0			0
$287$	1.16025	−	0.401924i	0.0684876	−	0.0237248i
$288$		0			0
$289$	−13.7942	+	7.96410i	−0.811425	+	0.468477i
$290$		0			0
$291$	10.8301	−	18.7583i	0.634873	−	1.09963i
$292$		0			0
$293$	−18.3923	+	18.3923i	−1.07449	+	1.07449i	−0.0774974	+	0.996993i	$0.524693\pi$
$293$	−18.3923	+	18.3923i	−1.07449	+	1.07449i	−0.996993	+	0.0774974i	$0.975307\pi$
$294$		0			0
$295$	−4.39230	−	2.19615i	−0.255730	−	0.127865i
$296$		0			0
$297$	3.09808	−	0.830127i	0.179769	−	0.0481689i
$298$		0			0
$299$	−10.1962	−	17.6603i	−0.589659	−	1.02132i
$300$		0			0
$301$	9.52628	−	19.6244i	0.549086	−	1.13113i
$302$		0			0
$303$	5.86603	−	21.8923i	0.336994	−	1.25768i
$304$		0			0
$305$	10.4282	+	15.7942i	0.597117	+	0.904375i
$306$		0			0
$307$	−9.29423	−	9.29423i	−0.530450	−	0.530450i	0.390257	−	0.920706i	$-0.372386\pi$
$307$	−9.29423	−	9.29423i	−0.530450	−	0.530450i	−0.920706	+	0.390257i	$0.872386\pi$
$308$		0			0
$309$			4.46410i			0.253954i
$310$		0			0
$311$	−16.2224	−	9.36603i	−0.919890	−	0.531099i	−0.0362898	−	0.999341i	$-0.511554\pi$
$311$	−16.2224	−	9.36603i	−0.919890	−	0.531099i	−0.883600	+	0.468243i	$0.844887\pi$
$312$		0			0
$313$	19.3923	+	5.19615i	1.09612	+	0.293704i	0.761183	−	0.648537i	$-0.224619\pi$
$313$	19.3923	+	5.19615i	1.09612	+	0.293704i	0.334935	+	0.942241i	$0.391286\pi$
$314$		0			0
$315$	2.63397	−	3.43782i	0.148408	−	0.193699i
$316$		0			0
$317$	4.46410	+	1.19615i	0.250729	+	0.0671826i	0.381994	−	0.924165i	$-0.375237\pi$
$317$	4.46410	+	1.19615i	0.250729	+	0.0671826i	−0.131265	+	0.991347i	$0.541904\pi$
$318$		0			0
$319$	1.90192	+	1.09808i	0.106487	+	0.0614805i
$320$		0			0
$321$			17.1962i			0.959796i
$322$		0			0
$323$	−2.00000	−	2.00000i	−0.111283	−	0.111283i
$324$		0			0
$325$	−8.73205	+	11.1244i	−0.484367	+	0.617068i
$326$		0			0
$327$	−7.06218	+	26.3564i	−0.390539	+	1.45751i
$328$		0			0
$329$	1.73205	−	0.124356i	0.0954911	−	0.00685595i
$330$		0			0
$331$	12.9282	+	22.3923i	0.710598	+	1.23079i	0.964633	+	0.263597i	$0.0849090\pi$
$331$	12.9282	+	22.3923i	0.710598	+	1.23079i	−0.254035	+	0.967195i	$0.581758\pi$
$332$		0			0
$333$	−3.46410	+	0.928203i	−0.189832	+	0.0508652i
$334$		0			0
$335$	2.49038	−	0.830127i	0.136064	−	0.0453547i
$336$		0			0
$337$	16.4641	−	16.4641i	0.896857	−	0.896857i	−0.0983001	−	0.995157i	$-0.531340\pi$
$337$	16.4641	−	16.4641i	0.896857	−	0.896857i	0.995157	+	0.0983001i	$0.0313405\pi$
$338$		0			0
$339$	5.83013	−	10.0981i	0.316649	−	0.548452i
$340$		0			0
$341$	−0.339746	+	0.196152i	−0.0183983	+	0.0106222i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		0			0
$345$	−1.86603	−	31.0885i	−0.100463	−	1.67375i
$346$		0			0
$347$	2.08846	+	7.79423i	0.112114	+	0.418416i	0.999055	−	0.0434674i	$-0.0138405\pi$
$347$	2.08846	+	7.79423i	0.112114	+	0.418416i	−0.886941	+	0.461884i	$0.847174\pi$
$348$		0			0
$349$	−9.73205			−0.520945			−0.260472	−	0.965481i	$-0.583878\pi$
$349$	−9.73205			−0.520945			−0.260472	+	0.965481i	$0.583878\pi$
$350$		0			0
$351$	12.3923			0.661452
$352$		0			0
$353$	1.43782	+	5.36603i	0.0765276	+	0.285605i	0.993575	−	0.113173i	$-0.0361013\pi$
$353$	1.43782	+	5.36603i	0.0765276	+	0.285605i	−0.917048	+	0.398777i	$0.869435\pi$
$354$		0			0
$355$	0.633975	+	10.5622i	0.0336479	+	0.560582i
$356$		0			0
$357$	3.46410	−	4.00000i	0.183340	−	0.211702i
$358$		0			0
$359$	12.3397	−	7.12436i	0.651267	−	0.376009i	−0.137675	−	0.990478i	$-0.543963\pi$
$359$	12.3397	−	7.12436i	0.651267	−	0.376009i	0.788941	+	0.614468i	$0.210629\pi$
$360$		0			0
$361$	5.76795	−	9.99038i	0.303576	−	0.525810i
$362$		0			0
$363$	−14.2942	+	14.2942i	−0.750252	+	0.750252i
$364$		0			0
$365$	7.60770	−	2.53590i	0.398205	−	0.132735i
$366$		0			0
$367$	−1.86603	+	0.500000i	−0.0974057	+	0.0260998i	−0.307193	−	0.951647i	$-0.599390\pi$
$367$	−1.86603	+	0.500000i	−0.0974057	+	0.0260998i	0.209787	+	0.977747i	$0.432723\pi$
$368$		0			0
$369$	−0.169873	−	0.294229i	−0.00884323	−	0.0153169i
$370$		0			0
$371$	−10.4904	−	15.4904i	−0.544633	−	0.804221i
$372$		0			0
$373$	−4.26795	+	15.9282i	−0.220986	+	0.824731i	0.762987	+	0.646414i	$0.223732\pi$
$373$	−4.26795	+	15.9282i	−0.220986	+	0.824731i	−0.983973	+	0.178317i	$0.942935\pi$
$374$		0			0
$375$	−19.5263	+	9.23205i	−1.00833	+	0.476741i
$376$		0			0
$377$	6.00000	+	6.00000i	0.309016	+	0.309016i
$378$		0			0
$379$			19.6603i			1.00988i	0.863155	+	0.504940i	$0.168485\pi$
$379$			19.6603i			1.00988i	−0.863155	+	0.504940i	$0.831515\pi$
$380$		0			0
$381$	15.2942	+	8.83013i	0.783547	+	0.452381i
$382$		0			0
$383$	28.1865	+	7.55256i	1.44026	+	0.385918i	0.892626	−	0.450797i	$-0.148860\pi$
$383$	28.1865	+	7.55256i	1.44026	+	0.385918i	0.547638	+	0.836715i	$0.315527\pi$
$384$		0			0
$385$	−0.562178	+	4.29423i	−0.0286512	+	0.218854i
$386$		0			0
$387$	−5.83013	−	1.56218i	−0.296362	−	0.0794100i
$388$		0			0
$389$	7.73205	+	4.46410i	0.392031	+	0.226339i	0.683040	−	0.730381i	$-0.260658\pi$
$389$	7.73205	+	4.46410i	0.392031	+	0.226339i	−0.291009	+	0.956720i	$0.593991\pi$
$390$		0			0
$391$		−	7.46410i		−	0.377476i
$392$		0			0
$393$	−11.6603	−	11.6603i	−0.588182	−	0.588182i
$394$		0			0
$395$	8.29423	+	12.5622i	0.417328	+	0.632072i
$396$		0			0
$397$	−5.36603	+	20.0263i	−0.269313	+	1.00509i	0.690244	+	0.723577i	$0.257503\pi$
$397$	−5.36603	+	20.0263i	−0.269313	+	1.00509i	−0.959557	+	0.281514i	$0.909164\pi$
$398$		0			0
$399$	−12.5622	−	6.09808i	−0.628896	−	0.305286i
$400$		0			0
$401$	−5.50000	−	9.52628i	−0.274657	−	0.475720i	0.695392	−	0.718631i	$-0.255231\pi$
$401$	−5.50000	−	9.52628i	−0.274657	−	0.475720i	−0.970049	+	0.242911i	$0.921898\pi$
$402$		0			0
$403$	−1.46410	+	0.392305i	−0.0729321	+	0.0195421i
$404$		0			0
$405$	21.3205	+	10.6603i	1.05942	+	0.529712i
$406$		0			0
$407$	2.53590	−	2.53590i	0.125700	−	0.125700i
$408$		0			0
$409$	−3.42820	+	5.93782i	−0.169514	+	0.293606i	−0.938249	−	0.345961i	$-0.887553\pi$
$409$	−3.42820	+	5.93782i	−0.169514	+	0.293606i	0.768735	+	0.639567i	$0.220886\pi$
$410$		0			0
$411$	−18.1244	+	10.4641i	−0.894009	+	0.516156i
$412$		0			0
$413$	−5.70577	−	1.09808i	−0.280763	−	0.0540328i
$414$		0			0
$415$	−7.33013	−	6.50000i	−0.359822	−	0.319072i
$416$		0			0
$417$	5.83013	+	21.7583i	0.285503	+	1.06551i
$418$		0			0
$419$	−3.85641			−0.188398			−0.0941989	−	0.995553i	$-0.530029\pi$
$419$	−3.85641			−0.188398			−0.0941989	+	0.995553i	$0.530029\pi$
$420$		0			0
$421$	−34.6603			−1.68924			−0.844619	−	0.535368i	$-0.820173\pi$
$421$	−34.6603			−1.68924			−0.844619	+	0.535368i	$0.820173\pi$
$422$		0			0
$423$	−0.124356	−	0.464102i	−0.00604638	−	0.0225654i
$424$		0			0
$425$	−4.80385	+	1.92820i	−0.233021	+	0.0935316i
$426$		0			0
$427$	16.9282	+	14.6603i	0.819213	+	0.709459i
$428$		0			0
$429$	3.46410	−	2.00000i	0.167248	−	0.0965609i
$430$		0			0
$431$	−2.09808	+	3.63397i	−0.101061	+	0.175042i	−0.912122	−	0.409919i	$-0.865557\pi$
$431$	−2.09808	+	3.63397i	−0.101061	+	0.175042i	0.811061	+	0.584961i	$0.198890\pi$
$432$		0			0
$433$	24.4641	−	24.4641i	1.17567	−	1.17567i	0.194833	−	0.980836i	$-0.437583\pi$
$433$	24.4641	−	24.4641i	1.17567	−	1.17567i	0.980836	−	0.194833i	$-0.0624166\pi$
$434$		0			0
$435$	4.09808	+	12.2942i	0.196488	+	0.589463i
$436$		0			0
$437$	−19.0263	+	5.09808i	−0.910150	+	0.243874i
$438$		0			0
$439$	−15.6603	−	27.1244i	−0.747423	−	1.29457i	−0.949054	−	0.315113i	$-0.897957\pi$
$439$	−15.6603	−	27.1244i	−0.747423	−	1.29457i	0.201631	−	0.979462i	$-0.435376\pi$
$440$		0			0
$441$	1.90192	−	4.75833i	0.0905678	−	0.226587i
$442$		0			0
$443$	−0.937822	+	3.50000i	−0.0445573	+	0.166290i	−0.984619	−	0.174713i	$-0.944100\pi$
$443$	−0.937822	+	3.50000i	−0.0445573	+	0.166290i	0.940062	+	0.341003i	$0.110767\pi$
$444$		0			0
$445$	−31.0885	+	20.5263i	−1.47373	+	0.973039i
$446$		0			0
$447$	15.2942	+	15.2942i	0.723392	+	0.723392i
$448$		0			0
$449$		−	5.05256i		−	0.238445i	−0.992868	−	0.119222i	$-0.961960\pi$
$449$		−	5.05256i		−	0.238445i	0.992868	−	0.119222i	$-0.0380402\pi$
$450$		0			0
$451$	0.294229	+	0.169873i	0.0138547	+	0.00799901i
$452$		0			0
$453$	−25.8564	−	6.92820i	−1.21484	−	0.325515i
$454$		0			0
$455$	−6.39230	+	15.4641i	−0.299676	+	0.724968i
$456$		0			0
$457$	30.8564	+	8.26795i	1.44340	+	0.386758i	0.893724	−	0.448618i	$-0.148084\pi$
$457$	30.8564	+	8.26795i	1.44340	+	0.386758i	0.549678	+	0.835376i	$0.314750\pi$
$458$		0			0
$459$	3.92820	+	2.26795i	0.183353	+	0.105859i
$460$		0			0
$461$		−	26.3923i		−	1.22921i	−0.788834	−	0.614606i	$-0.789315\pi$
$461$		−	26.3923i		−	1.22921i	0.788834	−	0.614606i	$-0.210685\pi$
$462$		0			0
$463$	−17.7583	−	17.7583i	−0.825300	−	0.825300i	0.161563	−	0.986862i	$-0.448347\pi$
$463$	−17.7583	−	17.7583i	−0.825300	−	0.825300i	−0.986862	+	0.161563i	$0.948347\pi$
$464$		0			0
$465$	−2.26795	−	0.464102i	−0.105174	−	0.0215222i
$466$		0			0
$467$	−8.40192	+	31.3564i	−0.388795	+	1.45100i	0.443303	+	0.896372i	$0.353807\pi$
$467$	−8.40192	+	31.3564i	−0.388795	+	1.45100i	−0.832097	+	0.554629i	$0.812860\pi$
$468$		0			0
$469$	2.57180	−	1.74167i	0.118755	−	0.0804228i
$470$		0			0
$471$	−23.7583	−	41.1506i	−1.09473	−	1.89612i
$472$		0			0
$473$	5.83013	−	1.56218i	0.268070	−	0.0718290i
$474$		0			0
$475$	8.19615	+	10.9282i	0.376065	+	0.501420i
$476$		0			0
$477$	−3.66025	+	3.66025i	−0.167592	+	0.167592i
$478$		0			0
$479$	13.4641	−	23.3205i	0.615191	−	1.06554i	−0.375161	−	0.926960i	$-0.622412\pi$
$479$	13.4641	−	23.3205i	0.615191	−	1.06554i	0.990351	−	0.138581i	$-0.0442542\pi$
$480$		0			0
$481$	12.0000	−	6.92820i	0.547153	−	0.315899i
$482$		0			0
$483$	−12.0622	−	34.8205i	−0.548848	−	1.58439i
$484$		0			0
$485$	−16.6340	+	18.7583i	−0.755310	+	0.851772i
$486$		0			0
$487$	−2.22243	−	8.29423i	−0.100708	−	0.375847i	0.897115	−	0.441797i	$-0.145659\pi$
$487$	−2.22243	−	8.29423i	−0.100708	−	0.375847i	−0.997823	+	0.0659498i	$0.978992\pi$
$488$		0			0
$489$	−10.7321			−0.485320
$490$		0			0
$491$	17.7128			0.799368			0.399684	−	0.916653i	$-0.369120\pi$
$491$	17.7128			0.799368			0.399684	+	0.916653i	$0.369120\pi$
$492$		0			0
$493$	0.803848	+	3.00000i	0.0362035	+	0.135113i
$494$		0			0
$495$	1.19615	−	0.0717968i	0.0537631	−	0.00322702i
$496$		0			0
$497$	4.09808	+	11.8301i	0.183824	+	0.530654i
$498$		0			0
$499$	−29.0263	+	16.7583i	−1.29939	+	0.750206i	−0.980300	−	0.197517i	$-0.936712\pi$
$499$	−29.0263	+	16.7583i	−1.29939	+	0.750206i	−0.319095	+	0.947723i	$0.603379\pi$
$500$		0			0
$501$	14.6962	−	25.4545i	0.656576	−	1.13722i
$502$		0			0
$503$	−19.3660	+	19.3660i	−0.863488	+	0.863488i	−0.991741	−	0.128253i	$-0.959063\pi$
$503$	−19.3660	+	19.3660i	−0.863488	+	0.863488i	0.128253	+	0.991741i	$0.459063\pi$
$504$		0			0
$505$	−11.7321	+	23.4641i	−0.522069	+	1.04414i
$506$		0			0
$507$	−9.33013	+	2.50000i	−0.414365	+	0.111029i
$508$		0			0
$509$	−13.4545	−	23.3038i	−0.596359	−	1.03292i	−0.993353	−	0.115104i	$-0.963280\pi$
$509$	−13.4545	−	23.3038i	−0.596359	−	1.03292i	0.396994	−	0.917821i	$-0.370053\pi$
$510$		0			0
$511$	7.85641	−	5.32051i	0.347547	−	0.235365i
$512$		0			0
$513$	3.09808	−	11.5622i	0.136783	−	0.510483i
$514$		0			0
$515$	1.03590	−	5.06218i	0.0456471	−	0.223066i
$516$		0			0
$517$	0.339746	+	0.339746i	0.0149420	+	0.0149420i
$518$		0			0
$519$			45.3205i			1.98935i
$520$		0			0
$521$	−3.33975	−	1.92820i	−0.146317	−	0.0844761i	0.425054	−	0.905168i	$-0.360255\pi$
$521$	−3.33975	−	1.92820i	−0.146317	−	0.0844761i	−0.571371	+	0.820692i	$0.693588\pi$
$522$		0			0
$523$	−14.4904	−	3.88269i	−0.633620	−	0.169778i	−0.0723082	−	0.997382i	$-0.523037\pi$
$523$	−14.4904	−	3.88269i	−0.633620	−	0.169778i	−0.561312	+	0.827604i	$0.689703\pi$
$524$		0			0
$525$	−19.2942	+	16.7583i	−0.842069	+	0.731393i
$526$		0			0
$527$	−0.535898	−	0.143594i	−0.0233441	−	0.00625503i
$528$		0			0
$529$	−25.0981	−	14.4904i	−1.09122	−	0.630017i
$530$		0			0
$531$			1.60770i			0.0697680i
$532$		0			0
$533$	0.928203	+	0.928203i	0.0402049	+	0.0402049i
$534$		0			0
$535$	3.99038	−	19.5000i	0.172519	−	0.843059i
$536$		0			0
$537$	−9.92820	+	37.0526i	−0.428434	+	1.59894i
$538$		0			0
$539$	0.732051	+	5.07180i	0.0315317	+	0.218458i
$540$		0			0
$541$	9.35641	+	16.2058i	0.402263	+	0.696741i	0.993999	−	0.109392i	$-0.0348903\pi$
$541$	9.35641	+	16.2058i	0.402263	+	0.696741i	−0.591735	+	0.806132i	$0.701557\pi$
$542$		0			0
$543$	−17.1603	+	4.59808i	−0.736417	+	0.197322i
$544$		0			0
$545$	14.1244	−	28.2487i	0.605021	−	1.21004i
$546$		0			0
$547$	−5.75833	+	5.75833i	−0.246208	+	0.246208i	−0.819413	−	0.573204i	$-0.805700\pi$
$547$	−5.75833	+	5.75833i	−0.246208	+	0.246208i	0.573204	+	0.819413i	$0.305700\pi$
$548$		0			0
$549$	3.09808	−	5.36603i	0.132223	−	0.229016i
$550$		0			0
$551$	7.09808	−	4.09808i	0.302388	−	0.174584i
$552$		0			0
$553$	13.4641	+	11.6603i	0.572552	+	0.495844i
$554$		0			0
$555$	21.1244	−	1.26795i	0.896679	−	0.0538214i
$556$		0			0
$557$	−1.77757	−	6.63397i	−0.0753180	−	0.281091i	0.917987	−	0.396610i	$-0.129813\pi$
$557$	−1.77757	−	6.63397i	−0.0753180	−	0.281091i	−0.993305	+	0.115519i	$0.963147\pi$
$558$		0			0
$559$	23.3205			0.986352
$560$		0			0
$561$	1.46410			0.0618144
$562$		0			0
$563$	−5.72243	−	21.3564i	−0.241172	−	0.900065i	−0.975269	−	0.221021i	$-0.929061\pi$
$563$	−5.72243	−	21.3564i	−0.241172	−	0.900065i	0.734097	−	0.679044i	$-0.237606\pi$
$564$		0			0
$565$	−8.95448	+	10.0981i	−0.376718	+	0.424829i
$566$		0			0
$567$	27.6962	+	5.33013i	1.16313	+	0.223844i
$568$		0			0
$569$	−13.0526	+	7.53590i	−0.547192	+	0.315921i	−0.747989	−	0.663712i	$-0.768980\pi$
$569$	−13.0526	+	7.53590i	−0.547192	+	0.315921i	0.200797	+	0.979633i	$0.435647\pi$
$570$		0			0
$571$	10.0263	−	17.3660i	0.419587	−	0.726746i	−0.576311	−	0.817230i	$-0.695508\pi$
$571$	10.0263	−	17.3660i	0.419587	−	0.726746i	0.995898	+	0.0904849i	$0.0288417\pi$
$572$		0			0
$573$	−22.8564	+	22.8564i	−0.954840	+	0.954840i
$574$		0			0
$575$	−5.09808	+	35.6865i	−0.212604	+	1.48823i
$576$		0			0
$577$	27.4904	−	7.36603i	1.14444	−	0.306652i	0.363705	−	0.931514i	$-0.381512\pi$
$577$	27.4904	−	7.36603i	1.14444	−	0.306652i	0.780735	+	0.624863i	$0.214845\pi$
$578$		0			0
$579$	−3.09808	−	5.36603i	−0.128752	−	0.223004i
$580$		0			0
$581$	−10.4282	−	5.06218i	−0.432635	−	0.210015i
$582$		0			0
$583$	1.33975	−	5.00000i	0.0554866	−	0.207079i
$584$		0			0
$585$	4.53590	+	0.928203i	0.187536	+	0.0383765i
$586$		0			0
$587$	−25.7846	−	25.7846i	−1.06424	−	1.06424i	−0.997789	−	0.0664553i	$-0.978831\pi$
$587$	−25.7846	−	25.7846i	−1.06424	−	1.06424i	−0.0664553	−	0.997789i	$-0.521169\pi$
$588$		0			0
$589$			1.46410i			0.0603273i
$590$		0			0
$591$	33.4186	+	19.2942i	1.37466	+	0.793659i
$592$		0			0
$593$	−6.56218	−	1.75833i	−0.269476	−	0.0722060i	0.121550	−	0.992585i	$-0.461213\pi$
$593$	−6.56218	−	1.75833i	−0.269476	−	0.0722060i	−0.391027	+	0.920379i	$0.627880\pi$
$594$		0			0
$595$	−4.85641	+	3.73205i	−0.199093	+	0.152999i
$596$		0			0
$597$	−46.5167	−	12.4641i	−1.90380	−	0.510122i
$598$		0			0
$599$	−32.6603	−	18.8564i	−1.33446	−	0.770452i	−0.348482	−	0.937316i	$-0.613303\pi$
$599$	−32.6603	−	18.8564i	−1.33446	−	0.770452i	−0.985980	+	0.166864i	$0.946636\pi$
$600$		0			0
$601$			21.1769i			0.863824i	0.901916	+	0.431912i	$0.142161\pi$
$601$			21.1769i			0.863824i	−0.901916	+	0.431912i	$0.857839\pi$
$602$		0			0
$603$	−0.607695	−	0.607695i	−0.0247473	−	0.0247473i
$604$		0			0
$605$	19.5263	−	12.8923i	0.793856	−	0.524147i
$606$		0			0
$607$	−2.30385	+	8.59808i	−0.0935103	+	0.348985i	−0.996789	−	0.0800683i	$-0.974486\pi$
$607$	−2.30385	+	8.59808i	−0.0935103	+	0.348985i	0.903279	+	0.429053i	$0.141153\pi$
$608$		0			0
$609$	8.59808	+	12.6962i	0.348412	+	0.514474i
$610$		0			0
$611$	0.928203	+	1.60770i	0.0375511	+	0.0650404i
$612$		0			0
$613$	−13.4641	+	3.60770i	−0.543810	+	0.145713i	−0.520258	−	0.854009i	$-0.674164\pi$
$613$	−13.4641	+	3.60770i	−0.543810	+	0.145713i	−0.0235520	+	0.999723i	$0.507498\pi$
$614$		0			0
$615$	0.633975	+	1.90192i	0.0255643	+	0.0766930i
$616$		0			0
$617$	−31.9090	+	31.9090i	−1.28461	+	1.28461i	−0.346590	+	0.938017i	$0.612660\pi$
$617$	−31.9090	+	31.9090i	−1.28461	+	1.28461i	−0.938017	+	0.346590i	$0.887340\pi$
$618$		0			0
$619$	−0.0980762	+	0.169873i	−0.00394202	+	0.00682777i	−0.867990	−	0.496582i	$-0.834588\pi$
$619$	−0.0980762	+	0.169873i	−0.00394202	+	0.00682777i	0.864048	+	0.503410i	$0.167921\pi$
$620$		0			0
$621$	27.3564	−	15.7942i	1.09777	−	0.633801i
$622$		0			0
$623$	−28.8564	+	33.3205i	−1.15611	+	1.33496i
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$		0			0
$627$	−1.00000	−	3.73205i	−0.0399362	−	0.149044i
$628$		0			0
$629$	5.07180			0.202226
$630$		0			0
$631$	−26.5885			−1.05847			−0.529235	−	0.848475i	$-0.677521\pi$
$631$	−26.5885			−1.05847			−0.529235	+	0.848475i	$0.677521\pi$
$632$		0			0
$633$	−5.09808	−	19.0263i	−0.202630	−	0.756227i
$634$		0			0
$635$	−15.2942	−	13.5622i	−0.606933	−	0.538199i
$636$		0			0
$637$	−2.33975	+	19.6603i	−0.0927041	+	0.778968i
$638$		0			0
$639$	3.00000	−	1.73205i	0.118678	−	0.0685189i
$640$		0			0
$641$	3.33013	−	5.76795i	0.131532	−	0.227820i	−0.792735	−	0.609566i	$-0.791344\pi$
$641$	3.33013	−	5.76795i	0.131532	−	0.227820i	0.924267	+	0.381746i	$0.124677\pi$
$642$		0			0
$643$	24.4641	−	24.4641i	0.964770	−	0.964770i	−0.0346302	−	0.999400i	$-0.511025\pi$
$643$	24.4641	−	24.4641i	0.964770	−	0.964770i	0.999400	+	0.0346302i	$0.0110253\pi$
$644$		0			0
$645$	31.8564	+	15.9282i	1.25434	+	0.627172i
$646$		0			0
$647$	−5.40192	+	1.44744i	−0.212372	+	0.0569048i	−0.363436	−	0.931619i	$-0.618397\pi$
$647$	−5.40192	+	1.44744i	−0.212372	+	0.0569048i	0.151065	+	0.988524i	$0.451730\pi$
$648$		0			0
$649$	−0.803848	−	1.39230i	−0.0315538	−	0.0546527i
$650$		0			0
$651$	−2.73205	+	0.196152i	−0.107078	+	0.00768782i
$652$		0			0
$653$	2.33975	−	8.73205i	0.0915613	−	0.341712i	−0.904914	−	0.425594i	$-0.860065\pi$
$653$	2.33975	−	8.73205i	0.0915613	−	0.341712i	0.996476	+	0.0838822i	$0.0267319\pi$
$654$		0			0
$655$	10.5167	+	15.9282i	0.410920	+	0.622366i
$656$		0			0
$657$	−1.85641	−	1.85641i	−0.0724253	−	0.0724253i
$658$		0			0
$659$		−	10.3397i		−	0.402779i	−0.979511	−	0.201390i	$-0.935454\pi$
$659$		−	10.3397i		−	0.402779i	0.979511	−	0.201390i	$-0.0645457\pi$
$660$		0			0
$661$	−12.2776	−	7.08846i	−0.477542	−	0.275709i	0.241850	−	0.970314i	$-0.422246\pi$
$661$	−12.2776	−	7.08846i	−0.477542	−	0.275709i	−0.719392	+	0.694605i	$0.755579\pi$
$662$		0			0
$663$	5.46410	+	1.46410i	0.212208	+	0.0568610i
$664$		0			0
$665$	12.8301	+	9.83013i	0.497531	+	0.381196i
$666$		0			0
$667$	20.8923	+	5.59808i	0.808953	+	0.216758i
$668$		0			0
$669$	−14.4904	−	8.36603i	−0.560230	−	0.323449i
$670$		0			0
$671$			6.19615i			0.239200i
$672$		0			0
$673$	−16.3923	−	16.3923i	−0.631877	−	0.631877i	0.316662	−	0.948539i	$-0.397438\pi$
$673$	−16.3923	−	16.3923i	−0.631877	−	0.631877i	−0.948539	+	0.316662i	$0.897438\pi$
$674$		0			0
$675$	−17.2321	−	13.5263i	−0.663262	−	0.520627i
$676$		0			0
$677$	1.85641	−	6.92820i	0.0713475	−	0.266272i	−0.921033	−	0.389485i	$-0.872653\pi$
$677$	1.85641	−	6.92820i	0.0713475	−	0.266272i	0.992380	+	0.123213i	$0.0393197\pi$
$678$		0			0
$679$	−12.9545	+	26.6865i	−0.497147	+	1.02414i
$680$		0			0
$681$	−0.0980762	−	0.169873i	−0.00375829	−	0.00650955i
$682$		0			0
$683$	18.4282	−	4.93782i	0.705136	−	0.188941i	0.111606	−	0.993753i	$-0.464401\pi$
$683$	18.4282	−	4.93782i	0.705136	−	0.188941i	0.593530	+	0.804812i	$0.297734\pi$
$684$		0			0
$685$	22.9808	−	7.66025i	0.878050	−	0.292683i
$686$		0			0
$687$	3.26795	−	3.26795i	0.124680	−	0.124680i
$688$		0			0
$689$	10.0000	−	17.3205i	0.380970	−	0.659859i
$690$		0			0
$691$	24.9737	−	14.4186i	0.950045	−	0.548509i	0.0569502	−	0.998377i	$-0.481862\pi$
$691$	24.9737	−	14.4186i	0.950045	−	0.548509i	0.893095	+	0.449868i	$0.148529\pi$
$692$		0			0
$693$	1.33975	−	0.464102i	0.0508927	−	0.0176298i
$694$		0			0
$695$	−1.56218	−	26.0263i	−0.0592568	−	0.987233i
$696$		0			0
$697$	0.124356	+	0.464102i	0.00471031	+	0.0175791i
$698$		0			0
$699$	−3.46410			−0.131024
$700$		0			0
$701$	−23.7321			−0.896347			−0.448174	−	0.893947i	$-0.647925\pi$
$701$	−23.7321			−0.896347			−0.448174	+	0.893947i	$0.647925\pi$
$702$		0			0
$703$	−3.46410	−	12.9282i	−0.130651	−	0.487596i
$704$		0			0
$705$	0.169873	+	2.83013i	0.00639779	+	0.106589i
$706$		0			0
$707$	−5.86603	+	30.4808i	−0.220615	+	1.14635i
$708$		0			0
$709$	6.99038	−	4.03590i	0.262529	−	0.151571i	−0.362959	−	0.931805i	$-0.618233\pi$
$709$	6.99038	−	4.03590i	0.262529	−	0.151571i	0.625488	+	0.780234i	$0.284900\pi$
$710$		0			0
$711$	2.46410	−	4.26795i	0.0924110	−	0.160061i
$712$		0			0
$713$	−2.73205	+	2.73205i	−0.102316	+	0.102316i
$714$		0			0
$715$	−4.39230	+	1.46410i	−0.164263	+	0.0547543i
$716$		0			0
$717$	34.3205	−	9.19615i	1.28172	−	0.343437i
$718$		0			0
$719$	3.70577	+	6.41858i	0.138202	+	0.239373i	0.926816	−	0.375516i	$-0.122534\pi$
$719$	3.70577	+	6.41858i	0.138202	+	0.239373i	−0.788614	+	0.614888i	$0.789201\pi$
$720$		0			0
$721$	−0.437822	−	6.09808i	−0.0163053	−	0.227104i
$722$		0			0
$723$	−8.39230	+	31.3205i	−0.312113	+	1.16482i
$724$		0			0
$725$	−1.79423	−	14.8923i	−0.0666360	−	0.553086i
$726$		0			0
$727$	−4.90192	−	4.90192i	−0.181802	−	0.181802i	0.610338	−	0.792141i	$-0.291033\pi$
$727$	−4.90192	−	4.90192i	−0.181802	−	0.181802i	−0.792141	+	0.610338i	$0.791033\pi$
$728$		0			0
$729$			17.5885i			0.651424i
$730$		0			0
$731$	7.39230	+	4.26795i	0.273414	+	0.157856i
$732$		0			0
$733$	−9.83013	−	2.63397i	−0.363084	−	0.0972881i	0.0726647	−	0.997356i	$-0.476850\pi$
$733$	−9.83013	−	2.63397i	−0.363084	−	0.0972881i	−0.435749	+	0.900068i	$0.643516\pi$
$734$		0			0
$735$	−16.6244	+	25.2583i	−0.613199	+	0.931668i
$736$		0			0
$737$	0.830127	+	0.222432i	0.0305781	+	0.00819338i
$738$		0			0
$739$	−7.43782	−	4.29423i	−0.273605	−	0.157966i	0.356920	−	0.934135i	$-0.383827\pi$
$739$	−7.43782	−	4.29423i	−0.273605	−	0.157966i	−0.630525	+	0.776169i	$0.717160\pi$
$740$		0			0
$741$		−	14.9282i		−	0.548401i
$742$		0			0
$743$	14.8301	+	14.8301i	0.544065	+	0.544065i	0.924718	−	0.380653i	$-0.124301\pi$
$743$	14.8301	+	14.8301i	0.544065	+	0.544065i	−0.380653	+	0.924718i	$0.624301\pi$
$744$		0			0
$745$	−13.7942	−	20.8923i	−0.505381	−	0.765435i
$746$		0			0
$747$	−0.830127	+	3.09808i	−0.0303728	+	0.113353i
$748$		0			0
$749$	−1.68653	−	23.4904i	−0.0616246	−	0.858320i
$750$		0			0
$751$	7.19615	+	12.4641i	0.262591	+	0.454822i	0.966930	−	0.255043i	$-0.0820896\pi$
$751$	7.19615	+	12.4641i	0.262591	+	0.454822i	−0.704338	+	0.709864i	$0.748756\pi$
$752$		0			0
$753$	−10.9282	+	2.92820i	−0.398246	+	0.106710i
$754$		0			0
$755$	27.7128	+	13.8564i	1.00857	+	0.504286i
$756$		0			0
$757$	9.26795	−	9.26795i	0.336849	−	0.336849i	−0.518331	−	0.855180i	$-0.673446\pi$
$757$	9.26795	−	9.26795i	0.336849	−	0.336849i	0.855180	+	0.518331i	$0.173446\pi$
$758$		0			0
$759$	5.09808	−	8.83013i	0.185048	−	0.320513i
$760$		0			0
$761$	11.0718	−	6.39230i	0.401352	−	0.231721i	−0.285715	−	0.958315i	$-0.592231\pi$
$761$	11.0718	−	6.39230i	0.401352	−	0.231721i	0.687067	+	0.726594i	$0.258898\pi$
$762$		0			0
$763$	7.06218	−	36.6962i	0.255668	−	1.32849i
$764$		0			0
$765$	1.26795	+	1.12436i	0.0458428	+	0.0406512i
$766$		0			0
$767$	−1.60770	−	6.00000i	−0.0580505	−	0.216647i
$768$		0			0
$769$	47.1769			1.70124			0.850622	−	0.525778i	$-0.176226\pi$
$769$	47.1769			1.70124			0.850622	+	0.525778i	$0.176226\pi$
$770$		0			0
$771$	5.46410			0.196785
$772$		0			0
$773$	4.80385	+	17.9282i	0.172782	+	0.644833i	0.996919	+	0.0784412i	$0.0249943\pi$
$773$	4.80385	+	17.9282i	0.172782	+	0.644833i	−0.824136	+	0.566391i	$0.808339\pi$
$774$		0			0
$775$	2.46410	+	1.05256i	0.0885131	+	0.0378090i
$776$		0			0
$777$	23.6603	−	8.19615i	0.848807	−	0.294035i
$778$		0			0
$779$	1.09808	−	0.633975i	0.0393427	−	0.0227145i
$780$		0			0
$781$	−1.73205	+	3.00000i	−0.0619777	+	0.107348i
$782$		0			0
$783$	−9.29423	+	9.29423i	−0.332149	+	0.332149i
$784$		0			0
$785$	17.3923	+	52.1769i	0.620758	+	1.86227i
$786$		0			0
$787$	19.3564	−	5.18653i	0.689981	−	0.184880i	0.103243	−	0.994656i	$-0.467078\pi$
$787$	19.3564	−	5.18653i	0.689981	−	0.184880i	0.586739	+	0.809776i	$0.300412\pi$
$788$		0			0
$789$	8.06218	+	13.9641i	0.287021	+	0.497135i
$790$		0			0
$791$	−6.97372	+	14.3660i	−0.247957	+	0.510797i
$792$		0			0
$793$	−6.19615	+	23.1244i	−0.220032	+	0.821170i
$794$		0			0
$795$	25.4904	−	16.8301i	0.904051	−	0.596903i
$796$		0			0
$797$	−29.4641	−	29.4641i	−1.04367	−	1.04367i	−0.999002	−	0.0446702i	$-0.985776\pi$
$797$	−29.4641	−	29.4641i	−1.04367	−	1.04367i	−0.0446702	−	0.999002i	$-0.514224\pi$
$798$		0			0
$799$			0.679492i			0.0240387i
$800$		0			0
$801$	10.5622	+	6.09808i	0.373196	+	0.215465i
$802$		0			0
$803$	2.53590	+	0.679492i	0.0894899	+	0.0239787i
$804$		0			0
$805$	5.59808	+	42.2846i	0.197306	+	1.49034i
$806$		0			0
$807$	9.06218	+	2.42820i	0.319004	+	0.0854768i
$808$		0			0
$809$	−21.9904	−	12.6962i	−0.773141	−	0.446373i	0.0608532	−	0.998147i	$-0.480618\pi$
$809$	−21.9904	−	12.6962i	−0.773141	−	0.446373i	−0.833994	+	0.551774i	$0.813951\pi$
$810$		0			0
$811$		−	29.0718i		−	1.02085i	−0.859923	−	0.510424i	$-0.829488\pi$
$811$		−	29.0718i		−	1.02085i	0.859923	−	0.510424i	$-0.170512\pi$
$812$		0			0
$813$	33.7846	+	33.7846i	1.18488	+	1.18488i
$814$		0			0
$815$	12.1699	+	2.49038i	0.426292	+	0.0872342i
$816$		0			0
$817$	5.83013	−	21.7583i	0.203970	−	0.761228i
$818$		0			0
$819$	5.46410	−	0.392305i	0.190931	−	0.0137082i
$820$		0			0
$821$	7.33975	+	12.7128i	0.256159	+	0.443680i	0.965210	−	0.261477i	$-0.0842096\pi$
$821$	7.33975	+	12.7128i	0.256159	+	0.443680i	−0.709051	+	0.705157i	$0.750876\pi$
$822$		0			0
$823$	−24.6962	+	6.61731i	−0.860854	+	0.230665i	−0.662129	−	0.749390i	$-0.730347\pi$
$823$	−24.6962	+	6.61731i	−0.860854	+	0.230665i	−0.198725	+	0.980055i	$0.563680\pi$
$824$		0			0
$825$	−7.00000	−	1.00000i	−0.243709	−	0.0348155i
$826$		0			0
$827$	3.77757	−	3.77757i	0.131359	−	0.131359i	−0.638370	−	0.769729i	$-0.720391\pi$
$827$	3.77757	−	3.77757i	0.131359	−	0.131359i	0.769729	+	0.638370i	$0.220391\pi$
$828$		0			0
$829$	10.7321	−	18.5885i	0.372740	−	0.645604i	−0.617246	−	0.786770i	$-0.711752\pi$
$829$	10.7321	−	18.5885i	0.372740	−	0.645604i	0.989986	+	0.141166i	$0.0450852\pi$
$830$		0			0
$831$	33.5885	−	19.3923i	1.16517	−	0.672712i
$832$		0			0
$833$	−4.33975	+	5.80385i	−0.150363	+	0.201091i
$834$		0			0
$835$	−22.5718	+	25.4545i	−0.781129	+	0.880889i
$836$		0			0
$837$	−0.607695	−	2.26795i	−0.0210050	−	0.0783918i
$838$		0			0
$839$	31.1244			1.07453			0.537266	−	0.843413i	$-0.319457\pi$
$839$	31.1244			1.07453			0.537266	+	0.843413i	$0.319457\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$		0			0
$843$	6.46410	+	24.1244i	0.222635	+	0.830887i
$844$		0			0
$845$	11.1603	−	0.669873i	0.383924	−	0.0230443i
$846$		0			0
$847$	18.1244	−	20.9282i	0.622760	−	0.719102i
$848$		0			0
$849$	−45.8827	+	26.4904i	−1.57469	+	0.909148i
$850$		0			0
$851$	17.6603	−	30.5885i	0.605386	−	1.04856i
$852$		0			0
$853$	−6.12436	+	6.12436i	−0.209694	+	0.209694i	−0.804137	−	0.594443i	$-0.797372\pi$
$853$	−6.12436	+	6.12436i	−0.209694	+	0.209694i	0.594443	+	0.804137i	$0.297372\pi$
$854$		0			0
$855$	2.00000	−	4.00000i	0.0683986	−	0.136797i
$856$		0			0
$857$	−22.0263	+	5.90192i	−0.752403	+	0.201606i	−0.614584	−	0.788851i	$-0.710676\pi$
$857$	−22.0263	+	5.90192i	−0.752403	+	0.201606i	−0.137820	+	0.990457i	$0.544009\pi$
$858$		0			0
$859$	−10.5359	−	18.2487i	−0.359480	−	0.622638i	0.628394	−	0.777895i	$-0.283713\pi$
$859$	−10.5359	−	18.2487i	−0.359480	−	0.622638i	−0.987874	+	0.155257i	$0.950379\pi$
$860$		0			0
$861$	1.33013	+	1.96410i	0.0453306	+	0.0669364i
$862$		0			0
$863$	−8.94486	+	33.3827i	−0.304487	+	1.13636i	0.628900	+	0.777487i	$0.283506\pi$
$863$	−8.94486	+	33.3827i	−0.304487	+	1.13636i	−0.933386	+	0.358873i	$0.883161\pi$
$864$		0			0
$865$	10.5167	−	51.3923i	0.357577	−	1.74739i
$866$		0			0
$867$	−21.7583	−	21.7583i	−0.738952	−	0.738952i
$868$		0			0
$869$			4.92820i			0.167178i
$870$		0			0
$871$	2.87564	+	1.66025i	0.0974375	+	0.0562556i
$872$		0			0
$873$	7.92820	+	2.12436i	0.268329	+	0.0718985i
$874$		0			0
$875$	25.7679	−	14.5263i	0.871116	−	0.491078i
$876$		0			0
$877$	−15.4904	−	4.15064i	−0.523073	−	0.140157i	−0.0123853	−	0.999923i	$-0.503942\pi$
$877$	−15.4904	−	4.15064i	−0.523073	−	0.140157i	−0.510688	+	0.859766i	$0.670609\pi$
$878$		0			0
$879$	−43.5167	−	25.1244i	−1.46778	−	0.847423i
$880$		0			0
$881$			52.8564i			1.78078i	0.455201	+	0.890389i	$0.349567\pi$
$881$			52.8564i			1.78078i	−0.455201	+	0.890389i	$0.650433\pi$
$882$		0			0
$883$	−21.9282	−	21.9282i	−0.737943	−	0.737943i	0.234237	−	0.972180i	$-0.424741\pi$
$883$	−21.9282	−	21.9282i	−0.737943	−	0.737943i	−0.972180	+	0.234237i	$0.924741\pi$
$884$		0			0
$885$	1.90192	−	9.29423i	0.0639325	−	0.312422i
$886$		0			0
$887$	9.89230	−	36.9186i	0.332151	−	1.23960i	−0.574774	−	0.818312i	$-0.694910\pi$
$887$	9.89230	−	36.9186i	0.332151	−	1.23960i	0.906925	−	0.421292i	$-0.138423\pi$
$888$		0			0
$889$	−21.7583	−	10.5622i	−0.729751	−	0.354244i
$890$		0			0
$891$	3.90192	+	6.75833i	0.130719	+	0.226413i
$892$		0			0
$893$	1.73205	−	0.464102i	0.0579609	−	0.0155306i
$894$		0			0
$895$	19.8564	−	39.7128i	0.663726	−	1.32745i
$896$		0			0
$897$	27.8564	−	27.8564i	0.930098	−	0.930098i
$898$		0			0
$899$	0.803848	−	1.39230i	0.0268098	−	0.0464360i
$900$		0			0
$901$	6.33975	−	3.66025i	0.211208	−	0.121941i
$902$		0			0
$903$	41.3827	+	7.96410i	1.37713	+	0.265029i
$904$		0			0
$905$	20.5263	−	1.23205i	0.682317	−	0.0409548i
$906$		0			0
$907$	0.454483	+	1.69615i	0.0150908	+	0.0563198i	0.973061	−	0.230549i	$-0.0740522\pi$
$907$	0.454483	+	1.69615i	0.0150908	+	0.0563198i	−0.957970	+	0.286869i	$0.907386\pi$
$908$		0			0
$909$	8.58846			0.284861
$910$		0			0
$911$	−37.5167			−1.24298			−0.621491	−	0.783421i	$-0.713473\pi$
$911$	−37.5167			−1.24298			−0.621491	+	0.783421i	$0.713473\pi$
$912$		0			0
$913$	−0.830127	−	3.09808i	−0.0274732	−	0.102531i
$914$		0			0
$915$	−24.2583	+	27.3564i	−0.801956	+	0.904375i
$916$		0			0
$917$	17.0718	+	14.7846i	0.563760	+	0.488231i
$918$		0			0
$919$	39.6673	−	22.9019i	1.30850	−	0.755465i	0.326657	−	0.945143i	$-0.394078\pi$
$919$	39.6673	−	22.9019i	1.30850	−	0.755465i	0.981846	+	0.189678i	$0.0607445\pi$
$920$		0			0
$921$	12.6962	−	21.9904i	0.418352	−	0.724608i
$922$		0			0
$923$	−9.46410	+	9.46410i	−0.311515	+	0.311515i
$924$		0			0
$925$	−24.2487	−	3.46410i	−0.797293	−	0.113899i
$926$		0			0
$927$	−1.63397	+	0.437822i	−0.0536668	+	0.0143800i
$928$		0			0
$929$	0.839746	+	1.45448i	0.0275512	+	0.0477200i	0.879472	−	0.475950i	$-0.157896\pi$
$929$	0.839746	+	1.45448i	0.0275512	+	0.0477200i	−0.851921	+	0.523670i	$0.824562\pi$
$930$		0			0
$931$	17.7583	+	7.09808i	0.582006	+	0.232630i
$932$		0			0
$933$	9.36603	−	34.9545i	0.306630	−	1.14436i
$934$		0			0
$935$	−1.66025	−	0.339746i	−0.0542961	−	0.0111109i
$936$		0			0
$937$	−30.9282	−	30.9282i	−1.01038	−	1.01038i	−0.999946	−	0.0104348i	$-0.996678\pi$
$937$	−30.9282	−	30.9282i	−1.01038	−	1.01038i	−0.0104348	−	0.999946i	$-0.503322\pi$
$938$		0			0
$939$			38.7846i			1.26569i
$940$		0			0
$941$	24.8038	+	14.3205i	0.808582	+	0.466835i	0.846463	−	0.532447i	$-0.178727\pi$
$941$	24.8038	+	14.3205i	0.808582	+	0.466835i	−0.0378810	+	0.999282i	$0.512061\pi$
$942$		0			0
$943$	3.23205	+	0.866025i	0.105250	+	0.0282017i
$944$		0			0
$945$	−23.9545	−	9.90192i	−0.779239	−	0.322110i
$946$		0			0
$947$	−43.6506	−	11.6962i	−1.41846	−	0.380074i	−0.533520	−	0.845788i	$-0.679131\pi$
$947$	−43.6506	−	11.6962i	−1.41846	−	0.380074i	−0.884935	+	0.465714i	$0.845798\pi$
$948$		0			0
$949$	8.78461	+	5.07180i	0.285160	+	0.164637i
$950$		0			0
$951$			8.92820i			0.289517i
$952$		0			0
$953$	−10.1436	−	10.1436i	−0.328583	−	0.328583i	0.523464	−	0.852048i	$-0.324639\pi$
$953$	−10.1436	−	10.1436i	−0.328583	−	0.328583i	−0.852048	+	0.523464i	$0.824639\pi$
$954$		0			0
$955$	31.2224	−	20.6147i	1.01033	−	0.667077i
$956$		0			0
$957$	−1.09808	+	4.09808i	−0.0354958	+	0.132472i
$958$		0			0
$959$	23.7321	−	16.0718i	0.766348	−	0.518985i
$960$		0			0
$961$	−15.3564	−	26.5981i	−0.495368	−	0.858002i
$962$		0			0
$963$	−6.29423	+	1.68653i	−0.202829	+	0.0543478i
$964$		0			0
$965$	2.26795	+	6.80385i	0.0730079	+	0.219024i
$966$		0			0
$967$	1.43782	−	1.43782i	0.0462372	−	0.0462372i	−0.683610	−	0.729847i	$-0.739591\pi$
$967$	1.43782	−	1.43782i	0.0462372	−	0.0462372i	0.729847	+	0.683610i	$0.239591\pi$
$968$		0			0
$969$	2.73205	−	4.73205i	0.0877661	−	0.152015i
$970$		0			0
$971$	−42.9282	+	24.7846i	−1.37763	+	0.795376i	−0.991874	−	0.127224i	$-0.959393\pi$
$971$	−42.9282	+	24.7846i	−1.37763	+	0.795376i	−0.385758	+	0.922600i	$0.626060\pi$
$972$		0			0
$973$	−10.0981	−	29.1506i	−0.323729	−	0.934526i
$974$		0			0
$975$	−25.1244	−	10.7321i	−0.804623	−	0.343701i
$976$		0			0
$977$	−11.5622	−	43.1506i	−0.369907	−	1.38051i	−0.860646	−	0.509204i	$-0.829940\pi$
$977$	−11.5622	−	43.1506i	−0.369907	−	1.38051i	0.490739	−	0.871307i	$-0.336727\pi$
$978$		0			0
$979$	−12.1962			−0.389791
$980$		0			0
$981$	−10.3397			−0.330123
$982$		0			0
$983$	−3.88526	−	14.5000i	−0.123921	−	0.462478i	0.875878	−	0.482532i	$-0.160283\pi$
$983$	−3.88526	−	14.5000i	−0.123921	−	0.462478i	−0.999799	+	0.0200540i	$0.993616\pi$
$984$		0			0
$985$	−33.4186	−	29.6340i	−1.06480	−	0.944217i
$986$		0			0
$987$	1.09808	+	3.16987i	0.0349522	+	0.100898i
$988$		0			0
$989$	51.4808	−	29.7224i	1.63699	−	0.945118i
$990$		0			0
$991$	−11.8564	+	20.5359i	−0.376631	+	0.652344i	−0.990570	−	0.137009i	$-0.956251\pi$
$991$	−11.8564	+	20.5359i	−0.376631	+	0.652344i	0.613939	+	0.789354i	$0.289584\pi$
$992$		0			0
$993$	−35.3205	+	35.3205i	−1.12086	+	1.12086i
$994$		0			0
$995$	49.8564	+	24.9282i	1.58055	+	0.790277i
$996$		0			0
$997$	25.6865	−	6.88269i	0.813501	−	0.217977i	0.171998	−	0.985097i	$-0.444978\pi$
$997$	25.6865	−	6.88269i	0.813501	−	0.217977i	0.641503	+	0.767121i	$0.278311\pi$
$998$		0			0
$999$	10.7321	+	18.5885i	0.339547	+	0.588113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ci.a.353.1		4
4.3	odd	2		35.2.k.a.3.1	✓	4
5.2	odd	4		560.2.ci.b.17.1		4
7.5	odd	6		560.2.ci.b.33.1		4
12.11	even	2		315.2.bz.b.73.1		4
20.3	even	4		175.2.o.a.157.1		4
20.7	even	4		35.2.k.b.17.1	yes	4
20.19	odd	2		175.2.o.b.143.1		4
28.3	even	6		245.2.f.b.48.2		4
28.11	odd	6		245.2.f.a.48.2		4
28.19	even	6		35.2.k.b.33.1	yes	4
28.23	odd	6		245.2.l.b.68.1		4
28.27	even	2		245.2.l.a.178.1		4
35.12	even	12	inner	560.2.ci.a.257.1		4
60.47	odd	4		315.2.bz.a.262.1		4
84.47	odd	6		315.2.bz.a.208.1		4
140.19	even	6		175.2.o.a.68.1		4
140.27	odd	4		245.2.l.b.227.1		4
140.47	odd	12		35.2.k.a.12.1	yes	4
140.67	even	12		245.2.f.b.97.2		4
140.87	odd	12		245.2.f.a.97.2		4
140.103	odd	12		175.2.o.b.82.1		4
140.107	even	12		245.2.l.a.117.1		4
420.47	even	12		315.2.bz.b.82.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.3.1	✓	4	4.3	odd	2
35.2.k.a.12.1	yes	4	140.47	odd	12
35.2.k.b.17.1	yes	4	20.7	even	4
35.2.k.b.33.1	yes	4	28.19	even	6
175.2.o.a.68.1		4	140.19	even	6
175.2.o.a.157.1		4	20.3	even	4
175.2.o.b.82.1		4	140.103	odd	12
175.2.o.b.143.1		4	20.19	odd	2
245.2.f.a.48.2		4	28.11	odd	6
245.2.f.a.97.2		4	140.87	odd	12
245.2.f.b.48.2		4	28.3	even	6
245.2.f.b.97.2		4	140.67	even	12
245.2.l.a.117.1		4	140.107	even	12
245.2.l.a.178.1		4	28.27	even	2
245.2.l.b.68.1		4	28.23	odd	6
245.2.l.b.227.1		4	140.27	odd	4
315.2.bz.a.208.1		4	84.47	odd	6
315.2.bz.a.262.1		4	60.47	odd	4
315.2.bz.b.73.1		4	12.11	even	2
315.2.bz.b.82.1		4	420.47	even	12
560.2.ci.a.257.1		4	35.12	even	12	inner
560.2.ci.a.353.1		4	1.1	even	1	trivial
560.2.ci.b.17.1		4	5.2	odd	4
560.2.ci.b.33.1		4	7.5	odd	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 1.86603i) q^{3} +(-0.133975 - 2.23205i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(-0.633975 + 0.366025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 1.86603i) q^{3} +(-0.133975 - 2.23205i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(-0.633975 + 0.366025i) q^{9} +(0.366025 - 0.633975i) q^{11} +(2.00000 - 2.00000i) q^{13} +(4.09808 - 1.36603i) q^{15} +(1.00000 - 0.267949i) q^{17} +(-1.36603 - 2.36603i) q^{19} +(4.23205 - 2.86603i) q^{21} +(1.86603 - 6.96410i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(3.09808 + 3.09808i) q^{27} +3.00000i q^{29} +(-0.464102 - 0.267949i) q^{31} +(1.36603 + 0.366025i) q^{33} +(-5.46410 + 2.26795i) q^{35} +(4.73205 + 1.26795i) q^{37} +(4.73205 + 2.73205i) q^{39} +0.464102i q^{41} +(5.83013 + 5.83013i) q^{43} +(0.901924 + 1.36603i) q^{45} +(-0.169873 + 0.633975i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(1.00000 + 1.73205i) q^{51} +(6.83013 - 1.83013i) q^{53} +(-1.46410 - 0.732051i) q^{55} +(3.73205 - 3.73205i) q^{57} +(1.09808 - 1.90192i) q^{59} +(-7.33013 + 4.23205i) q^{61} +(1.46410 + 1.26795i) q^{63} +(-4.73205 - 4.19615i) q^{65} +(0.303848 + 1.13397i) q^{67} +13.9282 q^{69} -4.73205 q^{71} +(0.928203 + 3.46410i) q^{73} +(-3.59808 - 8.96410i) q^{75} +(-1.90192 - 0.366025i) q^{77} +(-5.83013 + 3.36603i) q^{79} +(-5.33013 + 9.23205i) q^{81} +(3.09808 - 3.09808i) q^{83} +(-0.732051 - 2.19615i) q^{85} +(-5.59808 + 1.50000i) q^{87} +(-8.33013 - 14.4282i) q^{89} +(-6.73205 - 3.26795i) q^{91} +(0.267949 - 1.00000i) q^{93} +(-5.09808 + 3.36603i) q^{95} +(-7.92820 - 7.92820i) q^{97} +0.535898i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{5} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 4 * q^5 - 6 * q^9	\( 4 q + 2 q^{3} - 4 q^{5} - 6 q^{9} - 2 q^{11} + 8 q^{13} + 6 q^{15} + 4 q^{17} - 2 q^{19} + 10 q^{21} + 4 q^{23} - 6 q^{25} + 2 q^{27} + 12 q^{31} + 2 q^{33} - 8 q^{35} + 12 q^{37} + 12 q^{39} + 6 q^{43} + 14 q^{45} - 18 q^{47} - 22 q^{49} + 4 q^{51} + 10 q^{53} + 8 q^{55} + 8 q^{57} - 6 q^{59} - 12 q^{61} - 8 q^{63} - 12 q^{65} + 22 q^{67} + 28 q^{69} - 12 q^{71} - 24 q^{73} - 4 q^{75} - 18 q^{77} - 6 q^{79} - 4 q^{81} + 2 q^{83} + 4 q^{85} - 12 q^{87} - 16 q^{89} - 20 q^{91} + 8 q^{93} - 10 q^{95} - 4 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 - 4 * q^5 - 6 * q^9 - 2 * q^11 + 8 * q^13 + 6 * q^15 + 4 * q^17 - 2 * q^19 + 10 * q^21 + 4 * q^23 - 6 * q^25 + 2 * q^27 + 12 * q^31 + 2 * q^33 - 8 * q^35 + 12 * q^37 + 12 * q^39 + 6 * q^43 + 14 * q^45 - 18 * q^47 - 22 * q^49 + 4 * q^51 + 10 * q^53 + 8 * q^55 + 8 * q^57 - 6 * q^59 - 12 * q^61 - 8 * q^63 - 12 * q^65 + 22 * q^67 + 28 * q^69 - 12 * q^71 - 24 * q^73 - 4 * q^75 - 18 * q^77 - 6 * q^79 - 4 * q^81 + 2 * q^83 + 4 * q^85 - 12 * q^87 - 16 * q^89 - 20 * q^91 + 8 * q^93 - 10 * q^95 - 4 * q^97

Introduction

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Database

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