LMFDB - Embedded newform 560.2.ci.b.33.1

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			33.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	560.33
Dual form			560.2.ci.b.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86603 + 0.500000i) q^{3} +(1.86603 - 1.23205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(0.633975 + 0.366025i) q^{9} +O(q^{10})$	\(q+(1.86603 + 0.500000i) q^{3} +(1.86603 - 1.23205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(0.633975 + 0.366025i) q^{9} +(0.366025 + 0.633975i) q^{11} +(-2.00000 + 2.00000i) q^{13} +(4.09808 - 1.36603i) q^{15} +(0.267949 - 1.00000i) q^{17} +(1.36603 - 2.36603i) q^{19} +(4.23205 + 2.86603i) q^{21} +(-6.96410 + 1.86603i) q^{23} +(1.96410 - 4.59808i) q^{25} +(-3.09808 - 3.09808i) q^{27} +3.00000i q^{29} +(-0.464102 + 0.267949i) q^{31} +(0.366025 + 1.36603i) q^{33} +(5.73205 - 1.46410i) q^{35} +(-1.26795 - 4.73205i) q^{37} +(-4.73205 + 2.73205i) q^{39} -0.464102i q^{41} +(5.83013 + 5.83013i) q^{43} +(1.63397 - 0.0980762i) q^{45} +(-0.633975 + 0.169873i) q^{47} +(5.50000 + 4.33013i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-1.83013 + 6.83013i) q^{53} +(1.46410 + 0.732051i) q^{55} +(3.73205 - 3.73205i) q^{57} +(-1.09808 - 1.90192i) q^{59} +(-7.33013 - 4.23205i) q^{61} +(1.26795 + 1.46410i) q^{63} +(-1.26795 + 6.19615i) q^{65} +(-1.13397 - 0.303848i) q^{67} -13.9282 q^{69} -4.73205 q^{71} +(3.46410 + 0.928203i) q^{73} +(5.96410 - 7.59808i) q^{75} +(0.366025 + 1.90192i) q^{77} +(5.83013 + 3.36603i) q^{79} +(-5.33013 - 9.23205i) q^{81} +(-3.09808 + 3.09808i) q^{83} +(-0.732051 - 2.19615i) q^{85} +(-1.50000 + 5.59808i) q^{87} +(8.33013 - 14.4282i) q^{89} +(-6.73205 + 3.26795i) q^{91} +(-1.00000 + 0.267949i) q^{93} +(-0.366025 - 6.09808i) q^{95} +(7.92820 + 7.92820i) q^{97} +0.535898i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} + 4 q^{5} + 10 q^{7} + 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 + 4 * q^5 + 10 * q^7 + 6 * q^9	$ 4 q + 4 q^{3} + 4 q^{5} + 10 q^{7} + 6 q^{9} - 2 q^{11} - 8 q^{13} + 6 q^{15} + 8 q^{17} + 2 q^{19} + 10 q^{21} - 14 q^{23} - 6 q^{25} - 2 q^{27} + 12 q^{31} - 2 q^{33} + 16 q^{35} - 12 q^{37} - 12 q^{39} + 6 q^{43} + 10 q^{45} - 6 q^{47} + 22 q^{49} + 4 q^{51} + 10 q^{53} - 8 q^{55} + 8 q^{57} + 6 q^{59} - 12 q^{61} + 12 q^{63} - 12 q^{65} - 8 q^{67} - 28 q^{69} - 12 q^{71} + 10 q^{75} - 2 q^{77} + 6 q^{79} - 4 q^{81} - 2 q^{83} + 4 q^{85} - 6 q^{87} + 16 q^{89} - 20 q^{91} - 4 q^{93} + 2 q^{95} + 4 q^{97}+O(q^{100}) $ 4 * q + 4 * q^3 + 4 * q^5 + 10 * q^7 + 6 * q^9 - 2 * q^11 - 8 * q^13 + 6 * q^15 + 8 * q^17 + 2 * q^19 + 10 * q^21 - 14 * q^23 - 6 * q^25 - 2 * q^27 + 12 * q^31 - 2 * q^33 + 16 * q^35 - 12 * q^37 - 12 * q^39 + 6 * q^43 + 10 * q^45 - 6 * q^47 + 22 * q^49 + 4 * q^51 + 10 * q^53 - 8 * q^55 + 8 * q^57 + 6 * q^59 - 12 * q^61 + 12 * q^63 - 12 * q^65 - 8 * q^67 - 28 * q^69 - 12 * q^71 + 10 * q^75 - 2 * q^77 + 6 * q^79 - 4 * q^81 - 2 * q^83 + 4 * q^85 - 6 * q^87 + 16 * q^89 - 20 * q^91 - 4 * q^93 + 2 * q^95 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	1.86603	+	0.500000i	1.07735	+	0.288675i	0.753510	−	0.657437i	$-0.228359\pi$
$3$	1.86603	+	0.500000i	1.07735	+	0.288675i	0.323840	+	0.946112i	$0.395026\pi$
$4$		0			0
$5$	1.86603	−	1.23205i	0.834512	−	0.550990i
$5$	1.86603	−	1.23205i	0.834512	−	0.550990i
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		0			0
$9$	0.633975	+	0.366025i	0.211325	+	0.122008i
$10$		0			0
$11$	0.366025	+	0.633975i	0.110361	+	0.191151i	0.915916	−	0.401371i	$-0.131466\pi$
$11$	0.366025	+	0.633975i	0.110361	+	0.191151i	−0.805555	+	0.592521i	$0.798133\pi$
$12$		0			0
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	−0.927794	−	0.373094i	$-0.878297\pi$
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	0.373094	+	0.927794i	$0.378297\pi$
$14$		0			0
$15$	4.09808	−	1.36603i	1.05812	−	0.352706i
$16$		0			0
$17$	0.267949	−	1.00000i	0.0649872	−	0.242536i	−0.925790	−	0.378039i	$-0.876599\pi$
$17$	0.267949	−	1.00000i	0.0649872	−	0.242536i	0.990777	+	0.135503i	$0.0432652\pi$
$18$		0			0
$19$	1.36603	−	2.36603i	0.313388	−	0.542803i	−0.665706	−	0.746214i	$-0.731869\pi$
$19$	1.36603	−	2.36603i	0.313388	−	0.542803i	0.979093	+	0.203411i	$0.0652027\pi$
$20$		0			0
$21$	4.23205	+	2.86603i	0.923509	+	0.625418i
$22$		0			0
$23$	−6.96410	+	1.86603i	−1.45212	+	0.389093i	−0.896759	−	0.442519i	$-0.854085\pi$
$23$	−6.96410	+	1.86603i	−1.45212	+	0.389093i	−0.555357	+	0.831612i	$0.687418\pi$
$24$		0			0
$25$	1.96410	−	4.59808i	0.392820	−	0.919615i
$26$		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	−0.541098	−	0.840959i	$-0.681991\pi$
$31$	−0.464102	+	0.267949i	−0.0833551	+	0.0481251i	0.457743	+	0.889085i	$0.348658\pi$
$32$		0			0
$33$	0.366025	+	1.36603i	0.0637168	+	0.237795i
$34$		0			0
$35$	5.73205	−	1.46410i	0.968893	−	0.247478i
$36$		0			0
$37$	−1.26795	−	4.73205i	−0.208450	−	0.777944i	−0.988370	−	0.152066i	$-0.951407\pi$
$37$	−1.26795	−	4.73205i	−0.208450	−	0.777944i	0.779921	−	0.625878i	$-0.215259\pi$
$38$		0			0
$39$	−4.73205	+	2.73205i	−0.757735	+	0.437478i
$40$		0			0
$41$		−	0.464102i		−	0.0724805i	−0.999343	−	0.0362402i	$-0.988462\pi$
$41$		−	0.464102i		−	0.0724805i	0.999343	−	0.0362402i	$-0.0115382\pi$
$42$		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
$45$	1.63397	−	0.0980762i	0.243579	−	0.0146203i
$46$		0			0
$47$	−0.633975	+	0.169873i	−0.0924747	+	0.0247785i	−0.304760	−	0.952429i	$-0.598576\pi$
$47$	−0.633975	+	0.169873i	−0.0924747	+	0.0247785i	0.212285	+	0.977208i	$0.431909\pi$
$48$		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
$53$	−1.83013	+	6.83013i	−0.251387	+	0.938190i	0.718677	+	0.695344i	$0.244748\pi$
$53$	−1.83013	+	6.83013i	−0.251387	+	0.938190i	−0.970065	+	0.242846i	$0.921919\pi$
$54$		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	$-0.212328\pi$
$59$	−1.09808	−	1.90192i	−0.142957	−	0.247609i	−0.928609	+	0.371060i	$0.878995\pi$
$60$		0			0
$61$	−7.33013	−	4.23205i	−0.938527	−	0.541859i	−0.0490285	−	0.998797i	$-0.515613\pi$
$61$	−7.33013	−	4.23205i	−0.938527	−	0.541859i	−0.889498	+	0.456939i	$0.848946\pi$
$62$		0			0
$63$	1.26795	+	1.46410i	0.159747	+	0.184459i
$64$		0			0
$65$	−1.26795	+	6.19615i	−0.157270	+	0.768538i
$66$		0			0
$67$	−1.13397	−	0.303848i	−0.138537	−	0.0371209i	0.188884	−	0.981999i	$-0.439513\pi$
$67$	−1.13397	−	0.303848i	−0.138537	−	0.0371209i	−0.327421	+	0.944878i	$0.606180\pi$
$68$		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
$73$	3.46410	+	0.928203i	0.405442	+	0.108638i	0.455776	−	0.890094i	$-0.349362\pi$
$73$	3.46410	+	0.928203i	0.405442	+	0.108638i	−0.0503336	+	0.998732i	$0.516028\pi$
$74$		0			0
$75$	5.96410	−	7.59808i	0.688675	−	0.877350i
$76$		0			0
$77$	0.366025	+	1.90192i	0.0417125	+	0.216744i
$78$		0			0
$79$	5.83013	+	3.36603i	0.655941	+	0.378707i	0.790728	−	0.612167i	$-0.209702\pi$
$79$	5.83013	+	3.36603i	0.655941	+	0.378707i	−0.134788	+	0.990874i	$0.543035\pi$
$80$		0			0
$81$	−5.33013	−	9.23205i	−0.592236	−	1.02578i
$82$		0			0
$83$	−3.09808	+	3.09808i	−0.340058	+	0.340058i	−0.856389	−	0.516331i	$-0.827297\pi$
$83$	−3.09808	+	3.09808i	−0.340058	+	0.340058i	0.516331	+	0.856389i	$0.327297\pi$
$84$		0			0
$85$	−0.732051	−	2.19615i	−0.0794021	−	0.238206i
$86$		0			0
$87$	−1.50000	+	5.59808i	−0.160817	+	0.600177i
$88$		0			0
$89$	8.33013	−	14.4282i	0.882992	−	1.52939i	0.0349934	−	0.999388i	$-0.488859\pi$
$89$	8.33013	−	14.4282i	0.882992	−	1.52939i	0.847998	−	0.529999i	$-0.177808\pi$
$90$		0			0
$91$	−6.73205	+	3.26795i	−0.705711	+	0.342574i
$92$		0			0
$93$	−1.00000	+	0.267949i	−0.103695	+	0.0277850i
$94$		0			0
$95$	−0.366025	−	6.09808i	−0.0375534	−	0.625649i
$96$		0			0
$97$	7.92820	+	7.92820i	0.804987	+	0.804987i	0.983870	−	0.178883i	$-0.0572484\pi$
$97$	7.92820	+	7.92820i	0.804987	+	0.804987i	−0.178883	+	0.983870i	$0.557248\pi$
$98$		0			0
$99$			0.535898i			0.0538598i
$100$		0			0
$101$	−10.1603	+	5.86603i	−1.01098	+	0.583691i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−10.1603	+	5.86603i	−1.01098	+	0.583691i	−0.0995037	+	0.995037i	$0.531726\pi$
$102$		0			0
$103$	0.598076	+	2.23205i	0.0589302	+	0.219931i	0.989111	−	0.147171i	$-0.0470168\pi$
$103$	0.598076	+	2.23205i	0.0589302	+	0.219931i	−0.930181	+	0.367102i	$0.880350\pi$
$104$		0			0
$105$	11.4282	+	0.133975i	1.11528	+	0.0130746i
$106$		0			0
$107$	−2.30385	−	8.59808i	−0.222721	−	0.831207i	−0.983305	−	0.181967i	$-0.941754\pi$
$107$	−2.30385	−	8.59808i	−0.222721	−	0.831207i	0.760583	−	0.649240i	$-0.224913\pi$
$108$		0			0
$109$	−12.2321	+	7.06218i	−1.17162	+	0.676434i	−0.954061	−	0.299614i	$-0.903142\pi$
$109$	−12.2321	+	7.06218i	−1.17162	+	0.676434i	−0.217557	+	0.976048i	$0.569809\pi$
$110$		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
$115$	−10.6962	+	12.0622i	−0.997421	+	1.12480i
$116$		0			0
$117$	−2.00000	+	0.535898i	−0.184900	+	0.0495438i
$118$		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
$123$	0.232051	−	0.866025i	0.0209233	−	0.0780869i
$124$		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	0.141003	−	0.990009i	$-0.454967\pi$
$131$	−7.39230	−	4.26795i	−0.645869	−	0.372892i	−0.786872	+	0.617117i	$0.788301\pi$
$132$		0			0
$133$	5.46410	−	4.73205i	0.473798	−	0.410321i
$134$		0			0
$135$	−9.59808	−	1.96410i	−0.826071	−	0.169043i
$136$		0			0
$137$	−10.4641	−	2.80385i	−0.894009	−	0.239549i	−0.217567	−	0.976045i	$-0.569812\pi$
$137$	−10.4641	−	2.80385i	−0.894009	−	0.239549i	−0.676441	+	0.736496i	$0.736479\pi$
$138$		0			0
$139$	−11.6603			−0.989010			−0.494505	−	0.869175i	$-0.664651\pi$
$139$	−11.6603			−0.989010			−0.494505	+	0.869175i	$0.664651\pi$
$140$		0			0
$141$	−1.26795			−0.106781
$142$		0			0
$143$	−2.00000	−	0.535898i	−0.167248	−	0.0448141i
$144$		0			0
$145$	3.69615	+	5.59808i	0.306949	+	0.464895i
$146$		0			0
$147$	8.09808	+	10.8301i	0.667918	+	0.893254i
$148$		0			0
$149$	−9.69615	−	5.59808i	−0.794340	−	0.458612i	0.0471484	−	0.998888i	$-0.484987\pi$
$149$	−9.69615	−	5.59808i	−0.794340	−	0.458612i	−0.841488	+	0.540276i	$0.818320\pi$
$150$		0			0
$151$	−6.92820	−	12.0000i	−0.563809	−	0.976546i	−0.997159	−	0.0753205i	$-0.976002\pi$
$151$	−6.92820	−	12.0000i	−0.563809	−	0.976546i	0.433350	−	0.901226i	$-0.357331\pi$
$152$		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
$157$	−6.36603	+	23.7583i	−0.508064	+	1.89612i	−0.0691164	+	0.997609i	$0.522018\pi$
$157$	−6.36603	+	23.7583i	−0.508064	+	1.89612i	−0.438948	+	0.898513i	$0.644649\pi$
$158$		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
$163$	5.36603	−	1.43782i	0.420300	−	0.112619i	−0.0424696	−	0.999098i	$-0.513523\pi$
$163$	5.36603	−	1.43782i	0.420300	−	0.112619i	0.462769	+	0.886479i	$0.346856\pi$
$164$		0			0
$165$	2.36603	+	2.09808i	0.184195	+	0.163335i
$166$		0			0
$167$	10.7583	+	10.7583i	0.832505	+	0.832505i	0.987859	−	0.155354i	$-0.0496519\pi$
$167$	10.7583	+	10.7583i	0.832505	+	0.832505i	−0.155354	+	0.987859i	$0.549652\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$	1.73205	−	1.00000i	0.132453	−	0.0764719i
$172$		0			0
$173$	6.07180	+	22.6603i	0.461630	+	1.72283i	0.667827	+	0.744317i	$0.267225\pi$
$173$	6.07180	+	22.6603i	0.461630	+	1.72283i	−0.206197	+	0.978511i	$0.566109\pi$
$174$		0			0
$175$	8.89230	−	9.79423i	0.672195	−	0.740374i
$176$		0			0
$177$	−1.09808	−	4.09808i	−0.0825365	−	0.308030i
$178$		0			0
$179$	−17.1962	+	9.92820i	−1.28530	+	0.742069i	−0.977812	−	0.209483i	$-0.932822\pi$
$179$	−17.1962	+	9.92820i	−1.28530	+	0.742069i	−0.307488	+	0.951552i	$0.599489\pi$
$180$		0			0
$181$		−	9.19615i		−	0.683545i	−0.939783	−	0.341772i	$-0.888973\pi$
$181$		−	9.19615i		−	0.683545i	0.939783	−	0.341772i	$-0.111027\pi$
$182$		0			0
$183$	−11.5622	−	11.5622i	−0.854701	−	0.854701i
$184$		0			0
$185$	−8.19615	−	7.26795i	−0.602593	−	0.534350i
$186$		0			0
$187$	0.732051	−	0.196152i	0.0535329	−	0.0143441i
$188$		0			0
$189$	−5.06218	−	10.4282i	−0.368219	−	0.758540i
$190$		0			0
$191$	8.36603	−	14.4904i	0.605344	−	1.04849i	−0.386653	−	0.922225i	$-0.626369\pi$
$191$	8.36603	−	14.4904i	0.605344	−	1.04849i	0.991997	−	0.126262i	$-0.0402979\pi$
$192$		0			0
$193$	0.830127	−	3.09808i	0.0597539	−	0.223004i	−0.929592	−	0.368591i	$-0.879840\pi$
$193$	0.830127	−	3.09808i	0.0597539	−	0.223004i	0.989346	+	0.145587i	$0.0465070\pi$
$194$		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	0.847359	+	0.531021i	$0.178191\pi$
$199$	12.4641	+	21.5885i	0.883557	+	1.53037i	0.0361978	+	0.999345i	$0.488475\pi$
$200$		0			0
$201$	−1.96410	−	1.13397i	−0.138537	−	0.0799844i
$202$		0			0
$203$	−2.59808	+	7.50000i	−0.182349	+	0.526397i
$204$		0			0
$205$	−0.571797	−	0.866025i	−0.0399360	−	0.0604858i
$206$		0			0
$207$	−5.09808	−	1.36603i	−0.354341	−	0.0949453i
$208$		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
$213$	−8.83013	−	2.36603i	−0.605030	−	0.162117i
$214$		0			0
$215$	18.0622	+	3.69615i	1.23183	+	0.252076i
$216$		0			0
$217$	−1.39230	+	0.267949i	−0.0945158	+	0.0181896i
$218$		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	−0.471662	−	0.881779i	$-0.656346\pi$
$223$	6.12436	−	6.12436i	0.410117	−	0.410117i	0.881779	+	0.471662i	$0.156346\pi$
$224$		0			0
$225$	2.92820	−	2.19615i	0.195214	−	0.146410i
$226$		0			0
$227$	−0.0262794	+	0.0980762i	−0.00174423	+	0.00650955i	−0.966792	−	0.255563i	$-0.917739\pi$
$227$	−0.0262794	+	0.0980762i	−0.00174423	+	0.00650955i	0.965048	+	0.262072i	$0.0844059\pi$
$228$		0			0
$229$	1.19615	−	2.07180i	0.0790440	−	0.136908i	−0.823794	−	0.566890i	$-0.808147\pi$
$229$	1.19615	−	2.07180i	0.0790440	−	0.136908i	0.902838	+	0.429981i	$0.141480\pi$
$230$		0			0
$231$	−0.267949	+	3.73205i	−0.0176298	+	0.245551i
$232$		0			0
$233$	1.73205	−	0.464102i	0.113470	−	0.0304043i	−0.201637	−	0.979460i	$-0.564626\pi$
$233$	1.73205	−	0.464102i	0.113470	−	0.0304043i	0.315107	+	0.949056i	$0.397959\pi$
$234$		0			0
$235$	−0.973721	+	1.09808i	−0.0635185	+	0.0716306i
$236$		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	0.0475286	−	0.998870i	$-0.484865\pi$
$241$	14.5359	−	8.39230i	0.936340	−	0.540596i	0.888811	+	0.458274i	$0.151532\pi$
$242$		0			0
$243$	−1.92820	−	7.19615i	−0.123694	−	0.461633i
$244$		0			0
$245$	15.5981	+	1.30385i	0.996525	+	0.0832998i
$246$		0			0
$247$	2.00000	+	7.46410i	0.127257	+	0.474929i
$248$		0			0
$249$	−7.33013	+	4.23205i	−0.464528	+	0.268195i
$250$		0			0
$251$		−	5.85641i		−	0.369653i	−0.982771	−	0.184827i	$-0.940828\pi$
$251$		−	5.85641i		−	0.369653i	0.982771	−	0.184827i	$-0.0591723\pi$
$252$		0			0
$253$	−3.73205	−	3.73205i	−0.234632	−	0.234632i
$254$		0			0
$255$	−0.267949	−	4.46410i	−0.0167796	−	0.279553i
$256$		0			0
$257$	2.73205	−	0.732051i	0.170421	−	0.0456641i	−0.172600	−	0.984992i	$-0.555217\pi$
$257$	2.73205	−	0.732051i	0.170421	−	0.0456641i	0.343020	+	0.939328i	$0.388550\pi$
$258$		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
$263$	−2.16025	+	8.06218i	−0.133207	+	0.497135i	−0.999999	−	0.00153494i	$-0.999511\pi$
$263$	−2.16025	+	8.06218i	−0.133207	+	0.497135i	0.866792	+	0.498670i	$0.166178\pi$
$264$		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	$-0.213966\pi$
$269$	−2.42820	−	4.20577i	−0.148050	−	0.256430i	−0.930507	+	0.366275i	$0.880633\pi$
$270$		0			0
$271$	21.4186	+	12.3660i	1.30109	+	0.751183i	0.980590	−	0.196067i	$-0.0628171\pi$
$271$	21.4186	+	12.3660i	1.30109	+	0.751183i	0.320496	+	0.947250i	$0.396150\pi$
$272$		0			0
$273$	−14.1962	+	2.73205i	−0.859190	+	0.165351i
$274$		0			0
$275$	3.63397	−	0.437822i	0.219137	−	0.0264017i
$276$		0			0
$277$	19.3923	+	5.19615i	1.16517	+	0.312207i	0.789029	−	0.614356i	$-0.210584\pi$
$277$	19.3923	+	5.19615i	1.16517	+	0.312207i	0.376141	+	0.926562i	$0.377251\pi$
$278$		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
$283$	26.4904	+	7.09808i	1.57469	+	0.421937i	0.937277	−	0.348586i	$-0.113338\pi$
$283$	26.4904	+	7.09808i	1.57469	+	0.421937i	0.637413	+	0.770523i	$0.280005\pi$
$284$		0			0
$285$	2.36603	−	11.5622i	0.140151	−	0.684884i
$286$		0			0
$287$	0.401924	−	1.16025i	0.0237248	−	0.0684876i
$288$		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	$-0.475307\pi$
$293$	18.3923	−	18.3923i	1.07449	−	1.07449i	0.996993	−	0.0774974i	$-0.0246929\pi$
$294$		0			0
$295$	−4.39230	−	2.19615i	−0.255730	−	0.127865i
$296$		0			0
$297$	0.830127	−	3.09808i	0.0481689	−	0.179769i
$298$		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
$303$	−21.8923	+	5.86603i	−1.25768	+	0.336994i
$304$		0			0
$305$	−18.8923	+	1.13397i	−1.08177	+	0.0649312i
$306$		0			0
$307$	9.29423	+	9.29423i	0.530450	+	0.530450i	0.920706	−	0.390257i	$-0.127614\pi$
$307$	9.29423	+	9.29423i	0.530450	+	0.530450i	−0.390257	+	0.920706i	$0.627614\pi$
$308$		0			0
$309$			4.46410i			0.253954i
$310$		0			0
$311$	−16.2224	+	9.36603i	−0.919890	+	0.531099i	−0.883600	−	0.468243i	$-0.844887\pi$
$311$	−16.2224	+	9.36603i	−0.919890	+	0.531099i	−0.0362898	+	0.999341i	$0.511554\pi$
$312$		0			0
$313$	5.19615	+	19.3923i	0.293704	+	1.09612i	0.942241	+	0.334935i	$0.108714\pi$
$313$	5.19615	+	19.3923i	0.293704	+	1.09612i	−0.648537	+	0.761183i	$0.724619\pi$
$314$		0			0
$315$	4.16987	+	1.16987i	0.234946	+	0.0659149i
$316$		0			0
$317$	−1.19615	−	4.46410i	−0.0671826	−	0.250729i	0.924165	−	0.381994i	$-0.124763\pi$
$317$	−1.19615	−	4.46410i	−0.0671826	−	0.250729i	−0.991347	+	0.131265i	$0.958096\pi$
$318$		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
$325$	5.26795	+	13.1244i	0.292213	+	0.728008i
$326$		0			0
$327$	−26.3564	+	7.06218i	−1.45751	+	0.390539i
$328$		0			0
$329$	−1.73205	−	0.124356i	−0.0954911	−	0.00685595i
$330$		0			0
$331$	12.9282	−	22.3923i	0.710598	−	1.23079i	−0.254035	−	0.967195i	$-0.581758\pi$
$331$	12.9282	−	22.3923i	0.710598	−	1.23079i	0.964633	−	0.263597i	$-0.0849090\pi$
$332$		0			0
$333$	0.928203	−	3.46410i	0.0508652	−	0.189832i
$334$		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
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$	−25.9904	+	17.1603i	−1.39928	+	0.923877i
$346$		0			0
$347$	−7.79423	−	2.08846i	−0.418416	−	0.112114i	0.0434674	−	0.999055i	$-0.486160\pi$
$347$	−7.79423	−	2.08846i	−0.418416	−	0.112114i	−0.461884	+	0.886941i	$0.652826\pi$
$348$		0			0
$349$	9.73205			0.520945			0.260472	−	0.965481i	$-0.416122\pi$
$349$	9.73205			0.520945			0.260472	+	0.965481i	$0.416122\pi$
$350$		0			0
$351$	12.3923			0.661452
$352$		0			0
$353$	5.36603	+	1.43782i	0.285605	+	0.0765276i	0.398777	−	0.917048i	$-0.369435\pi$
$353$	5.36603	+	1.43782i	0.285605	+	0.0765276i	−0.113173	+	0.993575i	$0.536101\pi$
$354$		0			0
$355$	−8.83013	+	5.83013i	−0.468654	+	0.309431i
$356$		0			0
$357$	4.00000	−	3.46410i	0.211702	−	0.183340i
$358$		0			0
$359$	−12.3397	−	7.12436i	−0.651267	−	0.376009i	0.137675	−	0.990478i	$-0.456037\pi$
$359$	−12.3397	−	7.12436i	−0.651267	−	0.376009i	−0.788941	+	0.614468i	$0.789371\pi$
$360$		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
$367$	−0.500000	+	1.86603i	−0.0260998	+	0.0974057i	−0.977747	−	0.209787i	$-0.932723\pi$
$367$	−0.500000	+	1.86603i	−0.0260998	+	0.0974057i	0.951647	+	0.307193i	$0.0993896\pi$
$368$		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
$373$	15.9282	−	4.26795i	0.824731	−	0.220986i	0.178317	−	0.983973i	$-0.442935\pi$
$373$	15.9282	−	4.26795i	0.824731	−	0.220986i	0.646414	+	0.762987i	$0.276268\pi$
$374$		0			0
$375$	1.76795	−	21.5263i	0.0912965	−	1.11161i
$376$		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
$383$	7.55256	+	28.1865i	0.385918	+	1.44026i	0.836715	+	0.547638i	$0.184473\pi$
$383$	7.55256	+	28.1865i	0.385918	+	1.44026i	−0.450797	+	0.892626i	$0.648860\pi$
$384$		0			0
$385$	3.02628	+	3.09808i	0.154233	+	0.157893i
$386$		0			0
$387$	1.56218	+	5.83013i	0.0794100	+	0.296362i
$388$		0			0
$389$	−7.73205	+	4.46410i	−0.392031	+	0.226339i	−0.683040	−	0.730381i	$-0.739342\pi$
$389$	−7.73205	+	4.46410i	−0.392031	+	0.226339i	0.291009	+	0.956720i	$0.406009\pi$
$390$		0			0
$391$			7.46410i			0.377476i
$392$		0			0
$393$	−11.6603	−	11.6603i	−0.588182	−	0.588182i
$394$		0			0
$395$	15.0263	−	0.901924i	0.756054	−	0.0453807i
$396$		0			0
$397$	−20.0263	+	5.36603i	−1.00509	+	0.269313i	−0.723577	−	0.690244i	$-0.757503\pi$
$397$	−20.0263	+	5.36603i	−1.00509	+	0.269313i	−0.281514	+	0.959557i	$0.590836\pi$
$398$		0			0
$399$	12.5622	−	6.09808i	0.628896	−	0.305286i
$400$		0			0
$401$	−5.50000	+	9.52628i	−0.274657	+	0.475720i	−0.970049	−	0.242911i	$-0.921898\pi$
$401$	−5.50000	+	9.52628i	−0.274657	+	0.475720i	0.695392	+	0.718631i	$0.255231\pi$
$402$		0			0
$403$	0.392305	−	1.46410i	0.0195421	−	0.0729321i
$404$		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	$-0.112447\pi$
$409$	3.42820	+	5.93782i	0.169514	+	0.293606i	−0.768735	+	0.639567i	$0.779114\pi$
$410$		0			0
$411$	−18.1244	−	10.4641i	−0.894009	−	0.516156i
$412$		0			0
$413$	−1.09808	−	5.70577i	−0.0540328	−	0.280763i
$414$		0			0
$415$	−1.96410	+	9.59808i	−0.0964140	+	0.471151i
$416$		0			0
$417$	−21.7583	−	5.83013i	−1.06551	−	0.285503i
$418$		0			0
$419$	3.85641			0.188398			0.0941989	−	0.995553i	$-0.469971\pi$
$419$	3.85641			0.188398			0.0941989	+	0.995553i	$0.469971\pi$
$420$		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
$423$	−0.464102	−	0.124356i	−0.0225654	−	0.00604638i
$424$		0			0
$425$	−4.07180	−	3.19615i	−0.197511	−	0.155036i
$426$		0			0
$427$	−14.6603	−	16.9282i	−0.709459	−	0.819213i
$428$		0			0
$429$	−3.46410	−	2.00000i	−0.167248	−	0.0965609i
$430$		0			0
$431$	−2.09808	−	3.63397i	−0.101061	−	0.175042i	0.811061	−	0.584961i	$-0.198890\pi$
$431$	−2.09808	−	3.63397i	−0.101061	−	0.175042i	−0.912122	+	0.409919i	$0.865557\pi$
$432$		0			0
$433$	−24.4641	+	24.4641i	−1.17567	+	1.17567i	−0.194833	+	0.980836i	$0.562417\pi$
$433$	−24.4641	+	24.4641i	−1.17567	+	1.17567i	−0.980836	+	0.194833i	$0.937583\pi$
$434$		0			0
$435$	4.09808	+	12.2942i	0.196488	+	0.589463i
$436$		0			0
$437$	−5.09808	+	19.0263i	−0.243874	+	0.910150i
$438$		0			0
$439$	15.6603	−	27.1244i	0.747423	−	1.29457i	−0.201631	−	0.979462i	$-0.564624\pi$
$439$	15.6603	−	27.1244i	0.747423	−	1.29457i	0.949054	−	0.315113i	$-0.102043\pi$
$440$		0			0
$441$	1.90192	+	4.75833i	0.0905678	+	0.226587i
$442$		0			0
$443$	3.50000	−	0.937822i	0.166290	−	0.0445573i	−0.174713	−	0.984619i	$-0.555900\pi$
$443$	3.50000	−	0.937822i	0.166290	−	0.0445573i	0.341003	+	0.940062i	$0.389233\pi$
$444$		0			0
$445$	−2.23205	−	37.1865i	−0.105809	−	1.76281i
$446$		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
$453$	−6.92820	−	25.8564i	−0.325515	−	1.21484i
$454$		0			0
$455$	−8.53590	+	14.3923i	−0.400169	+	0.674722i
$456$		0			0
$457$	−8.26795	−	30.8564i	−0.386758	−	1.44340i	−0.835376	−	0.549678i	$-0.814750\pi$
$457$	−8.26795	−	30.8564i	−0.386758	−	1.44340i	0.448618	−	0.893724i	$-0.351916\pi$
$458$		0			0
$459$	−3.92820	+	2.26795i	−0.183353	+	0.105859i
$460$		0			0
$461$			26.3923i			1.22921i	0.788834	+	0.614606i	$0.210685\pi$
$461$			26.3923i			1.22921i	−0.788834	+	0.614606i	$0.789315\pi$
$462$		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
$465$	−1.53590	+	1.73205i	−0.0712256	+	0.0803219i
$466$		0			0
$467$	−31.3564	+	8.40192i	−1.45100	+	0.388795i	−0.896372	−	0.443303i	$-0.853807\pi$
$467$	−31.3564	+	8.40192i	−1.45100	+	0.388795i	−0.554629	+	0.832097i	$0.687140\pi$
$468$		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
$473$	−1.56218	+	5.83013i	−0.0718290	+	0.268070i
$474$		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	−0.990351	−	0.138581i	$-0.955746\pi$
$479$	−13.4641	−	23.3205i	−0.615191	−	1.06554i	0.375161	−	0.926960i	$-0.377588\pi$
$480$		0			0
$481$	12.0000	+	6.92820i	0.547153	+	0.315899i
$482$		0			0
$483$	−34.8205	−	12.0622i	−1.58439	−	0.548848i
$484$		0			0
$485$	24.5622	+	5.02628i	1.11531	+	0.228232i
$486$		0			0
$487$	8.29423	+	2.22243i	0.375847	+	0.100708i	0.441797	−	0.897115i	$-0.354341\pi$
$487$	8.29423	+	2.22243i	0.375847	+	0.100708i	−0.0659498	+	0.997823i	$0.521008\pi$
$488$		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
$493$	3.00000	+	0.803848i	0.135113	+	0.0362035i
$494$		0			0
$495$	0.660254	+	1.00000i	0.0296762	+	0.0449467i
$496$		0			0
$497$	−11.8301	−	4.09808i	−0.530654	−	0.183824i
$498$		0			0
$499$	29.0263	+	16.7583i	1.29939	+	0.750206i	0.980300	−	0.197517i	$-0.0632877\pi$
$499$	29.0263	+	16.7583i	1.29939	+	0.750206i	0.319095	+	0.947723i	$0.396621\pi$
$500$		0			0
$501$	14.6962	+	25.4545i	0.656576	+	1.13722i
$502$		0			0
$503$	19.3660	−	19.3660i	0.863488	−	0.863488i	−0.128253	−	0.991741i	$-0.540937\pi$
$503$	19.3660	−	19.3660i	0.863488	−	0.863488i	0.991741	+	0.128253i	$0.0409370\pi$
$504$		0			0
$505$	−11.7321	+	23.4641i	−0.522069	+	1.04414i
$506$		0			0
$507$	−2.50000	+	9.33013i	−0.111029	+	0.414365i
$508$		0			0
$509$	13.4545	−	23.3038i	0.596359	−	1.03292i	−0.396994	−	0.917821i	$-0.629947\pi$
$509$	13.4545	−	23.3038i	0.596359	−	1.03292i	0.993353	−	0.115104i	$-0.0367200\pi$
$510$		0			0
$511$	7.85641	+	5.32051i	0.347547	+	0.235365i
$512$		0			0
$513$	−11.5622	+	3.09808i	−0.510483	+	0.136783i
$514$		0			0
$515$	3.86603	+	3.42820i	0.170357	+	0.151065i
$516$		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	−0.571371	−	0.820692i	$-0.693588\pi$
$521$	−3.33975	+	1.92820i	−0.146317	+	0.0844761i	0.425054	+	0.905168i	$0.360255\pi$
$522$		0			0
$523$	−3.88269	−	14.4904i	−0.169778	−	0.633620i	−0.997382	−	0.0723082i	$-0.976963\pi$
$523$	−3.88269	−	14.4904i	−0.169778	−	0.633620i	0.827604	−	0.561312i	$-0.189703\pi$
$524$		0			0
$525$	21.4904	−	13.8301i	0.937917	−	0.603596i
$526$		0			0
$527$	0.143594	+	0.535898i	0.00625503	+	0.0233441i
$528$		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
$535$	−14.8923	−	13.2058i	−0.643850	−	0.570935i
$536$		0			0
$537$	−37.0526	+	9.92820i	−1.59894	+	0.428434i
$538$		0			0
$539$	−0.732051	+	5.07180i	−0.0315317	+	0.218458i
$540$		0			0
$541$	9.35641	−	16.2058i	0.402263	−	0.696741i	−0.591735	−	0.806132i	$-0.701557\pi$
$541$	9.35641	−	16.2058i	0.402263	−	0.696741i	0.993999	+	0.109392i	$0.0348903\pi$
$542$		0			0
$543$	4.59808	−	17.1603i	0.197322	−	0.736417i
$544$		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
$553$	11.6603	+	13.4641i	0.495844	+	0.572552i
$554$		0			0
$555$	−11.6603	−	17.6603i	−0.494950	−	0.749636i
$556$		0			0
$557$	6.63397	+	1.77757i	0.281091	+	0.0753180i	0.396610	−	0.917987i	$-0.370187\pi$
$557$	6.63397	+	1.77757i	0.281091	+	0.0753180i	−0.115519	+	0.993305i	$0.536853\pi$
$558$		0			0
$559$	−23.3205			−0.986352
$560$		0			0
$561$	1.46410			0.0618144
$562$		0			0
$563$	−21.3564	−	5.72243i	−0.900065	−	0.241172i	−0.221021	−	0.975269i	$-0.570939\pi$
$563$	−21.3564	−	5.72243i	−0.900065	−	0.241172i	−0.679044	+	0.734097i	$0.737606\pi$
$564$		0			0
$565$	−13.2224	−	2.70577i	−0.556272	−	0.113833i
$566$		0			0
$567$	−5.33013	−	27.6962i	−0.223844	−	1.16313i
$568$		0			0
$569$	13.0526	+	7.53590i	0.547192	+	0.315921i	0.747989	−	0.663712i	$-0.231020\pi$
$569$	13.0526	+	7.53590i	0.547192	+	0.315921i	−0.200797	+	0.979633i	$0.564353\pi$
$570$		0			0
$571$	10.0263	+	17.3660i	0.419587	+	0.726746i	0.995898	−	0.0904849i	$-0.0288417\pi$
$571$	10.0263	+	17.3660i	0.419587	+	0.726746i	−0.576311	+	0.817230i	$0.695508\pi$
$572$		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
$577$	7.36603	−	27.4904i	0.306652	−	1.14444i	−0.624863	−	0.780735i	$-0.714845\pi$
$577$	7.36603	−	27.4904i	0.306652	−	1.14444i	0.931514	−	0.363705i	$-0.118488\pi$
$578$		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
$583$	−5.00000	+	1.33975i	−0.207079	+	0.0554866i
$584$		0			0
$585$	−3.07180	+	3.46410i	−0.127003	+	0.143223i
$586$		0			0
$587$	25.7846	+	25.7846i	1.06424	+	1.06424i	0.997789	+	0.0664553i	$0.0211690\pi$
$587$	25.7846	+	25.7846i	1.06424	+	1.06424i	0.0664553	+	0.997789i	$0.478831\pi$
$588$		0			0
$589$			1.46410i			0.0603273i
$590$		0			0
$591$	33.4186	−	19.2942i	1.37466	−	0.793659i
$592$		0			0
$593$	−1.75833	−	6.56218i	−0.0722060	−	0.269476i	0.920379	−	0.391027i	$-0.127880\pi$
$593$	−1.75833	−	6.56218i	−0.0722060	−	0.269476i	−0.992585	+	0.121550i	$0.961213\pi$
$594$		0			0
$595$	0.0717968	−	6.12436i	0.00294338	−	0.251074i
$596$		0			0
$597$	12.4641	+	46.5167i	0.510122	+	1.90380i
$598$		0			0
$599$	32.6603	−	18.8564i	1.33446	−	0.770452i	0.348482	−	0.937316i	$-0.386697\pi$
$599$	32.6603	−	18.8564i	1.33446	−	0.770452i	0.985980	+	0.166864i	$0.0533640\pi$
$600$		0			0
$601$		−	21.1769i		−	0.863824i	−0.901916	−	0.431912i	$-0.857839\pi$
$601$		−	21.1769i		−	0.863824i	0.901916	−	0.431912i	$-0.142161\pi$
$602$		0			0
$603$	−0.607695	−	0.607695i	−0.0247473	−	0.0247473i
$604$		0			0
$605$	−1.40192	−	23.3564i	−0.0569963	−	0.949573i
$606$		0			0
$607$	−8.59808	+	2.30385i	−0.348985	+	0.0935103i	−0.429053	−	0.903279i	$-0.641153\pi$
$607$	−8.59808	+	2.30385i	−0.348985	+	0.0935103i	0.0800683	+	0.996789i	$0.474486\pi$
$608$		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
$613$	3.60770	−	13.4641i	0.145713	−	0.543810i	−0.854009	−	0.520258i	$-0.825836\pi$
$613$	3.60770	−	13.4641i	0.145713	−	0.543810i	0.999723	−	0.0235520i	$-0.00749753\pi$
$614$		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	$-0.165412\pi$
$619$	0.0980762	+	0.169873i	0.00394202	+	0.00682777i	−0.864048	+	0.503410i	$0.832079\pi$
$620$		0			0
$621$	27.3564	+	15.7942i	1.09777	+	0.633801i
$622$		0			0
$623$	33.3205	−	28.8564i	1.33496	−	1.15611i
$624$		0			0
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$		0			0
$627$	3.73205	+	1.00000i	0.149044	+	0.0399362i
$628$		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
$633$	−19.0263	−	5.09808i	−0.756227	−	0.202630i
$634$		0			0
$635$	4.09808	−	20.0263i	0.162627	−	0.794719i
$636$		0			0
$637$	−19.6603	+	2.33975i	−0.778968	+	0.0927041i
$638$		0			0
$639$	−3.00000	−	1.73205i	−0.118678	−	0.0685189i
$640$		0			0
$641$	3.33013	+	5.76795i	0.131532	+	0.227820i	0.924267	−	0.381746i	$-0.124677\pi$
$641$	3.33013	+	5.76795i	0.131532	+	0.227820i	−0.792735	+	0.609566i	$0.791344\pi$
$642$		0			0
$643$	−24.4641	+	24.4641i	−0.964770	+	0.964770i	−0.999400	−	0.0346302i	$-0.988975\pi$
$643$	−24.4641	+	24.4641i	−0.964770	+	0.964770i	0.0346302	+	0.999400i	$0.488975\pi$
$644$		0			0
$645$	31.8564	+	15.9282i	1.25434	+	0.627172i
$646$		0			0
$647$	−1.44744	+	5.40192i	−0.0569048	+	0.212372i	−0.988524	−	0.151065i	$-0.951730\pi$
$647$	−1.44744	+	5.40192i	−0.0569048	+	0.212372i	0.931619	+	0.363436i	$0.118397\pi$
$648$		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
$653$	−8.73205	+	2.33975i	−0.341712	+	0.0915613i	−0.425594	−	0.904914i	$-0.639935\pi$
$653$	−8.73205	+	2.33975i	−0.341712	+	0.0915613i	0.0838822	+	0.996476i	$0.473268\pi$
$654$		0			0
$655$	−19.0526	+	1.14359i	−0.744445	+	0.0446839i
$656$		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	−0.719392	−	0.694605i	$-0.755579\pi$
$661$	−12.2776	+	7.08846i	−0.477542	+	0.275709i	0.241850	+	0.970314i	$0.422246\pi$
$662$		0			0
$663$	1.46410	+	5.46410i	0.0568610	+	0.212208i
$664$		0			0
$665$	4.36603	−	15.5622i	0.169307	−	0.603475i
$666$		0			0
$667$	−5.59808	−	20.8923i	−0.216758	−	0.808953i
$668$		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
$675$	−20.3301	+	8.16025i	−0.782507	+	0.314088i
$676$		0			0
$677$	6.92820	−	1.85641i	0.266272	−	0.0713475i	−0.123213	−	0.992380i	$-0.539320\pi$
$677$	6.92820	−	1.85641i	0.266272	−	0.0713475i	0.389485	+	0.921033i	$0.372653\pi$
$678$		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
$683$	−4.93782	+	18.4282i	−0.188941	+	0.705136i	0.804812	+	0.593530i	$0.202266\pi$
$683$	−4.93782	+	18.4282i	−0.188941	+	0.705136i	−0.993753	+	0.111606i	$0.964401\pi$
$684$		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	0.893095	−	0.449868i	$-0.148529\pi$
$691$	24.9737	+	14.4186i	0.950045	+	0.548509i	0.0569502	+	0.998377i	$0.481862\pi$
$692$		0			0
$693$	−0.464102	+	1.33975i	−0.0176298	+	0.0508927i
$694$		0			0
$695$	−21.7583	+	14.3660i	−0.825341	+	0.544934i
$696$		0			0
$697$	−0.464102	−	0.124356i	−0.0175791	−	0.00471031i
$698$		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
$703$	−12.9282	−	3.46410i	−0.487596	−	0.130651i
$704$		0			0
$705$	−2.36603	+	1.56218i	−0.0891097	+	0.0588350i
$706$		0			0
$707$	−30.4808	+	5.86603i	−1.14635	+	0.220615i
$708$		0			0
$709$	−6.99038	−	4.03590i	−0.262529	−	0.151571i	0.362959	−	0.931805i	$-0.381767\pi$
$709$	−6.99038	−	4.03590i	−0.262529	−	0.151571i	−0.625488	+	0.780234i	$0.715100\pi$
$710$		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
$717$	9.19615	−	34.3205i	0.343437	−	1.28172i
$718$		0			0
$719$	−3.70577	+	6.41858i	−0.138202	+	0.239373i	−0.926816	−	0.375516i	$-0.877466\pi$
$719$	−3.70577	+	6.41858i	−0.138202	+	0.239373i	0.788614	+	0.614888i	$0.210799\pi$
$720$		0			0
$721$	−0.437822	+	6.09808i	−0.0163053	+	0.227104i
$722$		0			0
$723$	31.3205	−	8.39230i	1.16482	−	0.312113i
$724$		0			0
$725$	13.7942	+	5.89230i	0.512305	+	0.218835i
$726$		0			0
$727$	4.90192	+	4.90192i	0.181802	+	0.181802i	0.792141	−	0.610338i	$-0.208967\pi$
$727$	4.90192	+	4.90192i	0.181802	+	0.181802i	−0.610338	+	0.792141i	$0.708967\pi$
$728$		0			0
$729$			17.5885i			0.651424i
$730$		0			0
$731$	7.39230	−	4.26795i	0.273414	−	0.157856i
$732$		0			0
$733$	−2.63397	−	9.83013i	−0.0972881	−	0.363084i	0.900068	−	0.435749i	$-0.143516\pi$
$733$	−2.63397	−	9.83013i	−0.0972881	−	0.363084i	−0.997356	+	0.0726647i	$0.976850\pi$
$734$		0			0
$735$	28.4545	+	10.2321i	1.04956	+	0.377415i
$736$		0			0
$737$	−0.222432	−	0.830127i	−0.00819338	−	0.0305781i
$738$		0			0
$739$	7.43782	−	4.29423i	0.273605	−	0.157966i	−0.356920	−	0.934135i	$-0.616173\pi$
$739$	7.43782	−	4.29423i	0.273605	−	0.157966i	0.630525	+	0.776169i	$0.282840\pi$
$740$		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
$745$	−24.9904	+	1.50000i	−0.915577	+	0.0549557i
$746$		0			0
$747$	−3.09808	+	0.830127i	−0.113353	+	0.0303728i
$748$		0			0
$749$	1.68653	−	23.4904i	0.0616246	−	0.858320i
$750$		0			0
$751$	7.19615	−	12.4641i	0.262591	−	0.454822i	−0.704338	−	0.709864i	$-0.748756\pi$
$751$	7.19615	−	12.4641i	0.262591	−	0.454822i	0.966930	+	0.255043i	$0.0820896\pi$
$752$		0			0
$753$	2.92820	−	10.9282i	0.106710	−	0.398246i
$754$		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	0.687067	−	0.726594i	$-0.258898\pi$
$761$	11.0718	+	6.39230i	0.401352	+	0.231721i	−0.285715	+	0.958315i	$0.592231\pi$
$762$		0			0
$763$	−36.6962	+	7.06218i	−1.32849	+	0.255668i
$764$		0			0
$765$	0.339746	−	1.66025i	0.0122835	−	0.0600266i
$766$		0			0
$767$	6.00000	+	1.60770i	0.216647	+	0.0580505i
$768$		0			0
$769$	−47.1769			−1.70124			−0.850622	−	0.525778i	$-0.823774\pi$
$769$	−47.1769			−1.70124			−0.850622	+	0.525778i	$0.823774\pi$
$770$		0			0
$771$	5.46410			0.196785
$772$		0			0
$773$	17.9282	+	4.80385i	0.644833	+	0.172782i	0.566391	−	0.824136i	$-0.308339\pi$
$773$	17.9282	+	4.80385i	0.644833	+	0.172782i	0.0784412	+	0.996919i	$0.475006\pi$
$774$		0			0
$775$	0.320508	+	2.66025i	0.0115130	+	0.0955591i
$776$		0			0
$777$	8.19615	−	23.6603i	0.294035	−	0.848807i
$778$		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
$787$	5.18653	−	19.3564i	0.184880	−	0.689981i	−0.809776	−	0.586739i	$-0.800412\pi$
$787$	5.18653	−	19.3564i	0.184880	−	0.689981i	0.994656	−	0.103243i	$-0.0329218\pi$
$788$		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
$793$	23.1244	−	6.19615i	0.821170	−	0.220032i
$794$		0			0
$795$	1.83013	+	30.4904i	0.0649079	+	1.08138i
$796$		0			0
$797$	29.4641	+	29.4641i	1.04367	+	1.04367i	0.999002	+	0.0446702i	$0.0142237\pi$
$797$	29.4641	+	29.4641i	1.04367	+	1.04367i	0.0446702	+	0.999002i	$0.485776\pi$
$798$		0			0
$799$			0.679492i			0.0240387i
$800$		0			0
$801$	10.5622	−	6.09808i	0.373196	−	0.215465i
$802$		0			0
$803$	0.679492	+	2.53590i	0.0239787	+	0.0894899i
$804$		0			0
$805$	−37.1865	+	20.8923i	−1.31065	+	0.736357i
$806$		0			0
$807$	−2.42820	−	9.06218i	−0.0854768	−	0.319004i
$808$		0			0
$809$	21.9904	−	12.6962i	0.773141	−	0.446373i	−0.0608532	−	0.998147i	$-0.519382\pi$
$809$	21.9904	−	12.6962i	0.773141	−	0.446373i	0.833994	+	0.551774i	$0.186049\pi$
$810$		0			0
$811$			29.0718i			1.02085i	0.859923	+	0.510424i	$0.170512\pi$
$811$			29.0718i			1.02085i	−0.859923	+	0.510424i	$0.829488\pi$
$812$		0			0
$813$	33.7846	+	33.7846i	1.18488	+	1.18488i
$814$		0			0
$815$	8.24167	−	9.29423i	0.288693	−	0.325563i
$816$		0			0
$817$	21.7583	−	5.83013i	0.761228	−	0.203970i
$818$		0			0
$819$	−5.46410	−	0.392305i	−0.190931	−	0.0137082i
$820$		0			0
$821$	7.33975	−	12.7128i	0.256159	−	0.443680i	−0.709051	−	0.705157i	$-0.750876\pi$
$821$	7.33975	−	12.7128i	0.256159	−	0.443680i	0.965210	+	0.261477i	$0.0842096\pi$
$822$		0			0
$823$	6.61731	−	24.6962i	0.230665	−	0.860854i	−0.749390	−	0.662129i	$-0.769653\pi$
$823$	6.61731	−	24.6962i	0.230665	−	0.860854i	0.980055	−	0.198725i	$-0.0636801\pi$
$824$		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	$-0.288248\pi$
$829$	−10.7321	−	18.5885i	−0.372740	−	0.645604i	−0.989986	+	0.141166i	$0.954915\pi$
$830$		0			0
$831$	33.5885	+	19.3923i	1.16517	+	0.672712i
$832$		0			0
$833$	5.80385	−	4.33975i	0.201091	−	0.150363i
$834$		0			0
$835$	33.3301	+	6.82051i	1.15344	+	0.236033i
$836$		0			0
$837$	2.26795	+	0.607695i	0.0783918	+	0.0210050i
$838$		0			0
$839$	−31.1244			−1.07453			−0.537266	−	0.843413i	$-0.680543\pi$
$839$	−31.1244			−1.07453			−0.537266	+	0.843413i	$0.680543\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$		0			0
$843$	24.1244	+	6.46410i	0.830887	+	0.222635i
$844$		0			0
$845$	6.16025	+	9.33013i	0.211919	+	0.320966i
$846$		0			0
$847$	20.9282	−	18.1244i	0.719102	−	0.622760i
$848$		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	−0.594443	−	0.804137i	$-0.702628\pi$
$853$	6.12436	−	6.12436i	0.209694	−	0.209694i	0.804137	+	0.594443i	$0.202628\pi$
$854$		0			0
$855$	2.00000	−	4.00000i	0.0683986	−	0.136797i
$856$		0			0
$857$	−5.90192	+	22.0263i	−0.201606	+	0.752403i	0.788851	+	0.614584i	$0.210676\pi$
$857$	−5.90192	+	22.0263i	−0.201606	+	0.752403i	−0.990457	+	0.137820i	$0.955991\pi$
$858$		0			0
$859$	10.5359	−	18.2487i	0.359480	−	0.622638i	−0.628394	−	0.777895i	$-0.716287\pi$
$859$	10.5359	−	18.2487i	0.359480	−	0.622638i	0.987874	+	0.155257i	$0.0496207\pi$
$860$		0			0
$861$	1.33013	−	1.96410i	0.0453306	−	0.0669364i
$862$		0			0
$863$	33.3827	−	8.94486i	1.13636	−	0.304487i	0.358873	−	0.933386i	$-0.383161\pi$
$863$	33.3827	−	8.94486i	1.13636	−	0.304487i	0.777487	+	0.628900i	$0.216494\pi$
$864$		0			0
$865$	39.2487	+	34.8038i	1.33450	+	1.18337i
$866$		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
$873$	2.12436	+	7.92820i	0.0718985	+	0.268329i
$874$		0			0
$875$	4.52628	−	29.2321i	0.153016	−	0.988224i
$876$		0			0
$877$	4.15064	+	15.4904i	0.140157	+	0.523073i	0.999923	+	0.0123853i	$0.00394248\pi$
$877$	4.15064	+	15.4904i	0.140157	+	0.523073i	−0.859766	+	0.510688i	$0.829391\pi$
$878$		0			0
$879$	43.5167	−	25.1244i	1.46778	−	0.847423i
$880$		0			0
$881$		−	52.8564i		−	1.78078i	−0.455201	−	0.890389i	$-0.650433\pi$
$881$		−	52.8564i		−	1.78078i	0.455201	−	0.890389i	$-0.349567\pi$
$882$		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
$885$	−7.09808	−	6.29423i	−0.238599	−	0.211578i
$886$		0			0
$887$	36.9186	−	9.89230i	1.23960	−	0.332151i	0.421292	−	0.906925i	$-0.361577\pi$
$887$	36.9186	−	9.89230i	1.23960	−	0.332151i	0.818312	+	0.574774i	$0.194910\pi$
$888$		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
$893$	−0.464102	+	1.73205i	−0.0155306	+	0.0579609i
$894$		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
$903$	7.96410	+	41.3827i	0.265029	+	1.37713i
$904$		0			0
$905$	−11.3301	−	17.1603i	−0.376626	−	0.570426i
$906$		0			0
$907$	−1.69615	−	0.454483i	−0.0563198	−	0.0150908i	0.230549	−	0.973061i	$-0.425948\pi$
$907$	−1.69615	−	0.454483i	−0.0563198	−	0.0150908i	−0.286869	+	0.957970i	$0.592614\pi$
$908$		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
$913$	−3.09808	−	0.830127i	−0.102531	−	0.0274732i
$914$		0			0
$915$	−35.8205	−	7.33013i	−1.18419	−	0.242327i
$916$		0			0
$917$	−14.7846	−	17.0718i	−0.488231	−	0.563760i
$918$		0			0
$919$	−39.6673	−	22.9019i	−1.30850	−	0.755465i	−0.326657	−	0.945143i	$-0.605922\pi$
$919$	−39.6673	−	22.9019i	−1.30850	−	0.755465i	−0.981846	+	0.189678i	$0.939256\pi$
$920$		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
$927$	−0.437822	+	1.63397i	−0.0143800	+	0.0536668i
$928$		0			0
$929$	−0.839746	+	1.45448i	−0.0275512	+	0.0477200i	−0.879472	−	0.475950i	$-0.842104\pi$
$929$	−0.839746	+	1.45448i	−0.0275512	+	0.0477200i	0.851921	+	0.523670i	$0.175438\pi$
$930$		0			0
$931$	17.7583	−	7.09808i	0.582006	−	0.232630i
$932$		0			0
$933$	−34.9545	+	9.36603i	−1.14436	+	0.306630i
$934$		0			0
$935$	1.12436	−	1.26795i	0.0367704	−	0.0414664i
$936$		0			0
$937$	30.9282	+	30.9282i	1.01038	+	1.01038i	0.999946	+	0.0104348i	$0.00332156\pi$
$937$	30.9282	+	30.9282i	1.01038	+	1.01038i	0.0104348	+	0.999946i	$0.496678\pi$
$938$		0			0
$939$			38.7846i			1.26569i
$940$		0			0
$941$	24.8038	−	14.3205i	0.808582	−	0.466835i	−0.0378810	−	0.999282i	$-0.512061\pi$
$941$	24.8038	−	14.3205i	0.808582	−	0.466835i	0.846463	+	0.532447i	$0.178727\pi$
$942$		0			0
$943$	0.866025	+	3.23205i	0.0282017	+	0.105250i
$944$		0			0
$945$	−22.2942	−	13.2224i	−0.725231	−	0.430126i
$946$		0			0
$947$	11.6962	+	43.6506i	0.380074	+	1.41846i	0.845788	+	0.533520i	$0.179131\pi$
$947$	11.6962	+	43.6506i	0.380074	+	1.41846i	−0.465714	+	0.884935i	$0.654202\pi$
$948$		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
$955$	−2.24167	−	37.3468i	−0.0725387	−	1.20851i
$956$		0			0
$957$	−4.09808	+	1.09808i	−0.132472	+	0.0354958i
$958$		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
$963$	1.68653	−	6.29423i	0.0543478	−	0.202829i
$964$		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	−0.385758	−	0.922600i	$-0.626060\pi$
$971$	−42.9282	−	24.7846i	−1.37763	−	0.795376i	−0.991874	+	0.127224i	$0.959393\pi$
$972$		0			0
$973$	−29.1506	−	10.0981i	−0.934526	−	0.323729i
$974$		0			0
$975$	3.26795	+	27.1244i	0.104658	+	0.868675i
$976$		0			0
$977$	43.1506	+	11.5622i	1.38051	+	0.369907i	0.871307	−	0.490739i	$-0.163273\pi$
$977$	43.1506	+	11.5622i	1.38051	+	0.369907i	0.509204	+	0.860646i	$0.329940\pi$
$978$		0			0
$979$	12.1962			0.389791
$980$		0			0
$981$	−10.3397			−0.330123
$982$		0			0
$983$	−14.5000	−	3.88526i	−0.462478	−	0.123921i	0.0200540	−	0.999799i	$-0.493616\pi$
$983$	−14.5000	−	3.88526i	−0.462478	−	0.123921i	−0.482532	+	0.875878i	$0.660283\pi$
$984$		0			0
$985$	8.95448	−	43.7583i	0.285314	−	1.39426i
$986$		0			0
$987$	−3.16987	−	1.09808i	−0.100898	−	0.0349522i
$988$		0			0
$989$	−51.4808	−	29.7224i	−1.63699	−	0.945118i
$990$		0			0
$991$	−11.8564	−	20.5359i	−0.376631	−	0.652344i	0.613939	−	0.789354i	$-0.289584\pi$
$991$	−11.8564	−	20.5359i	−0.376631	−	0.652344i	−0.990570	+	0.137009i	$0.956251\pi$
$992$		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
$997$	6.88269	−	25.6865i	0.217977	−	0.813501i	−0.767121	−	0.641503i	$-0.778311\pi$
$997$	6.88269	−	25.6865i	0.217977	−	0.813501i	0.985097	−	0.171998i	$-0.0550222\pi$
$998$		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.b.33.1		4
4.3	odd	2		35.2.k.b.33.1	yes	4
5.2	odd	4		560.2.ci.a.257.1		4
7.3	odd	6		560.2.ci.a.353.1		4
12.11	even	2		315.2.bz.a.208.1		4
20.3	even	4		175.2.o.b.82.1		4
20.7	even	4		35.2.k.a.12.1	yes	4
20.19	odd	2		175.2.o.a.68.1		4
28.3	even	6		35.2.k.a.3.1	✓	4
28.11	odd	6		245.2.l.a.178.1		4
28.19	even	6		245.2.f.a.48.2		4
28.23	odd	6		245.2.f.b.48.2		4
28.27	even	2		245.2.l.b.68.1		4
35.17	even	12	inner	560.2.ci.b.17.1		4
60.47	odd	4		315.2.bz.b.82.1		4
84.59	odd	6		315.2.bz.b.73.1		4
140.3	odd	12		175.2.o.a.157.1		4
140.27	odd	4		245.2.l.a.117.1		4
140.47	odd	12		245.2.f.b.97.2		4
140.59	even	6		175.2.o.b.143.1		4
140.67	even	12		245.2.l.b.227.1		4
140.87	odd	12		35.2.k.b.17.1	yes	4
140.107	even	12		245.2.f.a.97.2		4
420.227	even	12		315.2.bz.a.262.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.3.1	✓	4	28.3	even	6
35.2.k.a.12.1	yes	4	20.7	even	4
35.2.k.b.17.1	yes	4	140.87	odd	12
35.2.k.b.33.1	yes	4	4.3	odd	2
175.2.o.a.68.1		4	20.19	odd	2
175.2.o.a.157.1		4	140.3	odd	12
175.2.o.b.82.1		4	20.3	even	4
175.2.o.b.143.1		4	140.59	even	6
245.2.f.a.48.2		4	28.19	even	6
245.2.f.a.97.2		4	140.107	even	12
245.2.f.b.48.2		4	28.23	odd	6
245.2.f.b.97.2		4	140.47	odd	12
245.2.l.a.117.1		4	140.27	odd	4
245.2.l.a.178.1		4	28.11	odd	6
245.2.l.b.68.1		4	28.27	even	2
245.2.l.b.227.1		4	140.67	even	12
315.2.bz.a.208.1		4	12.11	even	2
315.2.bz.a.262.1		4	420.227	even	12
315.2.bz.b.73.1		4	84.59	odd	6
315.2.bz.b.82.1		4	60.47	odd	4
560.2.ci.a.257.1		4	5.2	odd	4
560.2.ci.a.353.1		4	7.3	odd	6
560.2.ci.b.17.1		4	35.17	even	12	inner
560.2.ci.b.33.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.86603 + 0.500000i) q^{3} +(1.86603 - 1.23205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(0.633975 + 0.366025i) q^{9} +O(q^{10})\)	\(q+(1.86603 + 0.500000i) q^{3} +(1.86603 - 1.23205i) q^{5} +(2.50000 + 0.866025i) q^{7} +(0.633975 + 0.366025i) q^{9} +(0.366025 + 0.633975i) q^{11} +(-2.00000 + 2.00000i) q^{13} +(4.09808 - 1.36603i) q^{15} +(0.267949 - 1.00000i) q^{17} +(1.36603 - 2.36603i) q^{19} +(4.23205 + 2.86603i) q^{21} +(-6.96410 + 1.86603i) q^{23} +(1.96410 - 4.59808i) q^{25} +(-3.09808 - 3.09808i) q^{27} +3.00000i q^{29} +(-0.464102 + 0.267949i) q^{31} +(0.366025 + 1.36603i) q^{33} +(5.73205 - 1.46410i) q^{35} +(-1.26795 - 4.73205i) q^{37} +(-4.73205 + 2.73205i) q^{39} -0.464102i q^{41} +(5.83013 + 5.83013i) q^{43} +(1.63397 - 0.0980762i) q^{45} +(-0.633975 + 0.169873i) q^{47} +(5.50000 + 4.33013i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-1.83013 + 6.83013i) q^{53} +(1.46410 + 0.732051i) q^{55} +(3.73205 - 3.73205i) q^{57} +(-1.09808 - 1.90192i) q^{59} +(-7.33013 - 4.23205i) q^{61} +(1.26795 + 1.46410i) q^{63} +(-1.26795 + 6.19615i) q^{65} +(-1.13397 - 0.303848i) q^{67} -13.9282 q^{69} -4.73205 q^{71} +(3.46410 + 0.928203i) q^{73} +(5.96410 - 7.59808i) q^{75} +(0.366025 + 1.90192i) q^{77} +(5.83013 + 3.36603i) q^{79} +(-5.33013 - 9.23205i) q^{81} +(-3.09808 + 3.09808i) q^{83} +(-0.732051 - 2.19615i) q^{85} +(-1.50000 + 5.59808i) q^{87} +(8.33013 - 14.4282i) q^{89} +(-6.73205 + 3.26795i) q^{91} +(-1.00000 + 0.267949i) q^{93} +(-0.366025 - 6.09808i) q^{95} +(7.92820 + 7.92820i) q^{97} +0.535898i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} + 4 q^{5} + 10 q^{7} + 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 + 4 * q^5 + 10 * q^7 + 6 * q^9	\( 4 q + 4 q^{3} + 4 q^{5} + 10 q^{7} + 6 q^{9} - 2 q^{11} - 8 q^{13} + 6 q^{15} + 8 q^{17} + 2 q^{19} + 10 q^{21} - 14 q^{23} - 6 q^{25} - 2 q^{27} + 12 q^{31} - 2 q^{33} + 16 q^{35} - 12 q^{37} - 12 q^{39} + 6 q^{43} + 10 q^{45} - 6 q^{47} + 22 q^{49} + 4 q^{51} + 10 q^{53} - 8 q^{55} + 8 q^{57} + 6 q^{59} - 12 q^{61} + 12 q^{63} - 12 q^{65} - 8 q^{67} - 28 q^{69} - 12 q^{71} + 10 q^{75} - 2 q^{77} + 6 q^{79} - 4 q^{81} - 2 q^{83} + 4 q^{85} - 6 q^{87} + 16 q^{89} - 20 q^{91} - 4 q^{93} + 2 q^{95} + 4 q^{97}+O(q^{100}) \) 4 * q + 4 * q^3 + 4 * q^5 + 10 * q^7 + 6 * q^9 - 2 * q^11 - 8 * q^13 + 6 * q^15 + 8 * q^17 + 2 * q^19 + 10 * q^21 - 14 * q^23 - 6 * q^25 - 2 * q^27 + 12 * q^31 - 2 * q^33 + 16 * q^35 - 12 * q^37 - 12 * q^39 + 6 * q^43 + 10 * q^45 - 6 * q^47 + 22 * q^49 + 4 * q^51 + 10 * q^53 - 8 * q^55 + 8 * q^57 + 6 * q^59 - 12 * q^61 + 12 * q^63 - 12 * q^65 - 8 * q^67 - 28 * q^69 - 12 * q^71 + 10 * q^75 - 2 * q^77 + 6 * q^79 - 4 * q^81 - 2 * q^83 + 4 * q^85 - 6 * q^87 + 16 * q^89 - 20 * q^91 - 4 * q^93 + 2 * q^95 + 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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