LMFDB - Embedded newform 560.2.ci.e.17.8

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:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	560.17
Dual form			560.2.ci.e.33.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16710 - 0.312724i) q^{3} +(-0.121837 - 2.23275i) q^{5} +(2.59977 - 0.491095i) q^{7} +(-1.33374 + 0.770036i) q^{9} +O(q^{10})$	\(q+(1.16710 - 0.312724i) q^{3} +(-0.121837 - 2.23275i) q^{5} +(2.59977 - 0.491095i) q^{7} +(-1.33374 + 0.770036i) q^{9} +(1.67933 - 2.90869i) q^{11} +(-2.92389 - 2.92389i) q^{13} +(-0.840431 - 2.56774i) q^{15} +(0.0694548 + 0.259209i) q^{17} +(0.458405 + 0.793981i) q^{19} +(2.88063 - 1.38617i) q^{21} +(7.58021 + 2.03111i) q^{23} +(-4.97031 + 0.544063i) q^{25} +(-3.87894 + 3.87894i) q^{27} -1.31878i q^{29} +(-3.25671 - 1.88026i) q^{31} +(1.05034 - 3.91991i) q^{33} +(-1.41324 - 5.74480i) q^{35} +(2.11773 - 7.90347i) q^{37} +(-4.32685 - 2.49811i) q^{39} +5.65819i q^{41} +(2.61631 - 2.61631i) q^{43} +(1.88180 + 2.88409i) q^{45} +(0.911807 + 0.244318i) q^{47} +(6.51765 - 2.55347i) q^{49} +(0.162122 + 0.280803i) q^{51} +(3.49525 + 13.0444i) q^{53} +(-6.69897 - 3.39514i) q^{55} +(0.783303 + 0.783303i) q^{57} +(-3.91972 + 6.78916i) q^{59} +(9.70077 - 5.60074i) q^{61} +(-3.08927 + 2.65691i) q^{63} +(-6.17206 + 6.88454i) q^{65} +(-5.37983 + 1.44152i) q^{67} +9.48206 q^{69} +13.5245 q^{71} +(-7.33366 + 1.96505i) q^{73} +(-5.63073 + 2.18932i) q^{75} +(2.93744 - 8.38665i) q^{77} +(1.87245 - 1.08106i) q^{79} +(-1.00398 + 1.73894i) q^{81} +(5.49970 + 5.49970i) q^{83} +(0.570285 - 0.186656i) q^{85} +(-0.412415 - 1.53915i) q^{87} +(-1.34818 - 2.33512i) q^{89} +(-9.03736 - 6.16554i) q^{91} +(-4.38892 - 1.17601i) q^{93} +(1.71691 - 1.12024i) q^{95} +(-10.1018 + 10.1018i) q^{97} +5.17259i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7}+O(q^{10}) $ 48 * q + 4 * q^7	$ 48 q + 4 q^{7} - 4 q^{11} - 8 q^{15} - 4 q^{21} + 4 q^{23} - 8 q^{25} - 36 q^{33} - 24 q^{35} + 8 q^{37} + 16 q^{43} + 48 q^{45} - 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} + 68 q^{63} + 12 q^{65} + 16 q^{67} + 64 q^{71} - 48 q^{73} + 48 q^{75} + 4 q^{77} - 40 q^{85} + 12 q^{87} + 80 q^{91} - 24 q^{95}+O(q^{100}) $ 48 * q + 4 * q^7 - 4 * q^11 - 8 * q^15 - 4 * q^21 + 4 * q^23 - 8 * q^25 - 36 * q^33 - 24 * q^35 + 8 * q^37 + 16 * q^43 + 48 * q^45 - 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 + 68 * q^63 + 12 * q^65 + 16 * q^67 + 64 * q^71 - 48 * q^73 + 48 * q^75 + 4 * q^77 - 40 * q^85 + 12 * q^87 + 80 * q^91 - 24 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.16710	−	0.312724i	0.673828	−	0.180552i	0.0943492	−	0.995539i	$-0.469923\pi$
$3$	1.16710	−	0.312724i	0.673828	−	0.180552i	0.579478	+	0.814988i	$0.303256\pi$
$4$		0			0
$5$	−0.121837	−	2.23275i	−0.0544873	−	0.998514i
$5$	−0.121837	−	2.23275i	−0.0544873	−	0.998514i
$6$		0			0
$7$	2.59977	−	0.491095i	0.982622	−	0.185617i
$7$	2.59977	−	0.491095i	0.982622	−	0.185617i
$8$		0			0
$9$	−1.33374	+	0.770036i	−0.444581	+	0.256679i
$10$		0			0
$11$	1.67933	−	2.90869i	0.506338	−	0.877003i	−0.493635	−	0.869669i	$-0.664332\pi$
$11$	1.67933	−	2.90869i	0.506338	−	0.877003i	0.999973	−	0.00733373i	$-0.00233442\pi$
$12$		0			0
$13$	−2.92389	−	2.92389i	−0.810941	−	0.810941i	0.173834	−	0.984775i	$-0.444384\pi$
$13$	−2.92389	−	2.92389i	−0.810941	−	0.810941i	−0.984775	+	0.173834i	$0.944384\pi$
$14$		0			0
$15$	−0.840431	−	2.56774i	−0.216998	−	0.662989i
$16$		0			0
$17$	0.0694548	+	0.259209i	0.0168453	+	0.0628674i	0.973837	−	0.227248i	$-0.0729729\pi$
$17$	0.0694548	+	0.259209i	0.0168453	+	0.0628674i	−0.956992	+	0.290116i	$0.906306\pi$
$18$		0			0
$19$	0.458405	+	0.793981i	0.105165	+	0.182152i	0.913806	−	0.406152i	$-0.133129\pi$
$19$	0.458405	+	0.793981i	0.105165	+	0.182152i	−0.808640	+	0.588303i	$0.799796\pi$
$20$		0			0
$21$	2.88063	−	1.38617i	0.628605	−	0.302488i
$22$		0			0
$23$	7.58021	+	2.03111i	1.58058	+	0.423516i	0.939106	−	0.343627i	$-0.111656\pi$
$23$	7.58021	+	2.03111i	1.58058	+	0.423516i	0.641476	+	0.767143i	$0.278322\pi$
$24$		0			0
$25$	−4.97031	+	0.544063i	−0.994062	+	0.108813i
$26$		0			0
$27$	−3.87894	+	3.87894i	−0.746503	+	0.746503i
$28$		0			0
$29$		−	1.31878i		−	0.244892i	−0.992475	−	0.122446i	$-0.960926\pi$
$29$		−	1.31878i		−	0.244892i	0.992475	−	0.122446i	$-0.0390737\pi$
$30$		0			0
$31$	−3.25671	−	1.88026i	−0.584923	−	0.337705i	0.178165	−	0.984001i	$-0.442984\pi$
$31$	−3.25671	−	1.88026i	−0.584923	−	0.337705i	−0.763087	+	0.646295i	$0.776317\pi$
$32$		0			0
$33$	1.05034	−	3.91991i	0.182840	−	0.682369i
$34$		0			0
$35$	−1.41324	−	5.74480i	−0.238881	−	0.971049i
$36$		0			0
$37$	2.11773	−	7.90347i	0.348153	−	1.29932i	−0.540733	−	0.841194i	$-0.681853\pi$
$37$	2.11773	−	7.90347i	0.348153	−	1.29932i	0.888886	−	0.458129i	$-0.151480\pi$
$38$		0			0
$39$	−4.32685	−	2.49811i	−0.692851	−	0.400018i
$40$		0			0
$41$			5.65819i			0.883661i	0.897098	+	0.441831i	$0.145671\pi$
$41$			5.65819i			0.883661i	−0.897098	+	0.441831i	$0.854329\pi$
$42$		0			0
$43$	2.61631	−	2.61631i	0.398984	−	0.398984i	−0.478891	−	0.877875i	$-0.658961\pi$
$43$	2.61631	−	2.61631i	0.398984	−	0.398984i	0.877875	+	0.478891i	$0.158961\pi$
$44$		0			0
$45$	1.88180	+	2.88409i	0.280521	+	0.429934i
$46$		0			0
$47$	0.911807	+	0.244318i	0.133001	+	0.0356374i	0.324705	−	0.945815i	$-0.394735\pi$
$47$	0.911807	+	0.244318i	0.133001	+	0.0356374i	−0.191705	+	0.981453i	$0.561402\pi$
$48$		0			0
$49$	6.51765	−	2.55347i	0.931093	−	0.364782i
$50$		0			0
$51$	0.162122	+	0.280803i	0.0227016	+	0.0393203i
$52$		0			0
$53$	3.49525	+	13.0444i	0.480109	+	1.79179i	0.601140	+	0.799144i	$0.294713\pi$
$53$	3.49525	+	13.0444i	0.480109	+	1.79179i	−0.121031	+	0.992649i	$0.538620\pi$
$54$		0			0
$55$	−6.69897	−	3.39514i	−0.903289	−	0.457800i
$56$		0			0
$57$	0.783303	+	0.783303i	0.103751	+	0.103751i
$58$		0			0
$59$	−3.91972	+	6.78916i	−0.510304	+	0.883873i	0.489624	+	0.871933i	$0.337134\pi$
$59$	−3.91972	+	6.78916i	−0.510304	+	0.883873i	−0.999929	+	0.0119396i	$0.996199\pi$
$60$		0			0
$61$	9.70077	−	5.60074i	1.24206	−	0.717102i	0.272544	−	0.962143i	$-0.412135\pi$
$61$	9.70077	−	5.60074i	1.24206	−	0.717102i	0.969513	+	0.245042i	$0.0788017\pi$
$62$		0			0
$63$	−3.08927	+	2.65691i	−0.389211	+	0.334740i
$64$		0			0
$65$	−6.17206	+	6.88454i	−0.765550	+	0.853922i
$66$		0			0
$67$	−5.37983	+	1.44152i	−0.657251	+	0.176110i	−0.572005	−	0.820250i	$-0.693834\pi$
$67$	−5.37983	+	1.44152i	−0.657251	+	0.176110i	−0.0852461	+	0.996360i	$0.527168\pi$
$68$		0			0
$69$	9.48206			1.14151
$70$		0			0
$71$	13.5245			1.60506			0.802532	−	0.596609i	$-0.203486\pi$
$71$	13.5245			1.60506			0.802532	+	0.596609i	$0.203486\pi$
$72$		0			0
$73$	−7.33366	+	1.96505i	−0.858340	+	0.229992i	−0.661039	−	0.750351i	$-0.729884\pi$
$73$	−7.33366	+	1.96505i	−0.858340	+	0.229992i	−0.197301	+	0.980343i	$0.563218\pi$
$74$		0			0
$75$	−5.63073	+	2.18932i	−0.650180	+	0.252800i
$76$		0			0
$77$	2.93744	−	8.38665i	0.334753	−	0.955747i
$78$		0			0
$79$	1.87245	−	1.08106i	0.210667	−	0.121629i	−0.390954	−	0.920410i	$-0.627855\pi$
$79$	1.87245	−	1.08106i	0.210667	−	0.121629i	0.601621	+	0.798781i	$0.294522\pi$
$80$		0			0
$81$	−1.00398	+	1.73894i	−0.111553	+	0.193216i
$82$		0			0
$83$	5.49970	+	5.49970i	0.603671	+	0.603671i	0.941285	−	0.337614i	$-0.109620\pi$
$83$	5.49970	+	5.49970i	0.603671	+	0.603671i	−0.337614	+	0.941285i	$0.609620\pi$
$84$		0			0
$85$	0.570285	−	0.186656i	0.0618561	−	0.0202457i
$86$		0			0
$87$	−0.412415	−	1.53915i	−0.0442155	−	0.165015i
$88$		0			0
$89$	−1.34818	−	2.33512i	−0.142907	−	0.247523i	0.785683	−	0.618629i	$-0.212312\pi$
$89$	−1.34818	−	2.33512i	−0.142907	−	0.247523i	−0.928590	+	0.371107i	$0.878978\pi$
$90$		0			0
$91$	−9.03736	−	6.16554i	−0.947372	−	0.646324i
$92$		0			0
$93$	−4.38892	−	1.17601i	−0.455110	−	0.121946i
$94$		0			0
$95$	1.71691	−	1.12024i	0.176151	−	0.114934i
$96$		0			0
$97$	−10.1018	+	10.1018i	−1.02568	+	1.02568i	−0.0260207	+	0.999661i	$0.508284\pi$
$97$	−10.1018	+	10.1018i	−1.02568	+	1.02568i	−0.999661	+	0.0260207i	$0.991716\pi$
$98$		0			0
$99$			5.17259i			0.519865i
$100$		0			0
$101$	−14.7714	−	8.52827i	−1.46981	−	0.848594i	−0.470382	−	0.882463i	$-0.655884\pi$
$101$	−14.7714	−	8.52827i	−1.46981	−	0.848594i	−0.999426	+	0.0338687i	$0.989217\pi$
$102$		0			0
$103$	−4.62827	+	17.2729i	−0.456037	+	1.70195i	0.228985	+	0.973430i	$0.426459\pi$
$103$	−4.62827	+	17.2729i	−0.456037	+	1.70195i	−0.685022	+	0.728522i	$0.740207\pi$
$104$		0			0
$105$	−3.44594	−	6.26282i	−0.336289	−	0.611189i
$106$		0			0
$107$	−2.05577	+	7.67224i	−0.198739	+	0.741703i	0.792528	+	0.609835i	$0.208764\pi$
$107$	−2.05577	+	7.67224i	−0.198739	+	0.741703i	−0.991267	+	0.131868i	$0.957902\pi$
$108$		0			0
$109$	12.5649	+	7.25433i	1.20350	+	0.694839i	0.961331	−	0.275396i	$-0.0888089\pi$
$109$	12.5649	+	7.25433i	1.20350	+	0.694839i	0.242166	+	0.970235i	$0.422142\pi$
$110$		0			0
$111$		−	9.88644i		−	0.938379i
$112$		0			0
$113$	−5.46472	+	5.46472i	−0.514078	+	0.514078i	−0.915773	−	0.401696i	$-0.868421\pi$
$113$	−5.46472	+	5.46472i	−0.514078	+	0.514078i	0.401696	+	0.915773i	$0.368421\pi$
$114$		0			0
$115$	3.61140	−	17.1721i	0.336765	−	1.60131i
$116$		0			0
$117$	6.15121	+	1.64821i	0.568680	+	0.152377i
$118$		0			0
$119$	0.307863	+	0.639775i	0.0282217	+	0.0586481i
$120$		0			0
$121$	−0.140314	−	0.243031i	−0.0127558	−	0.0220938i
$122$		0			0
$123$	1.76946	+	6.60370i	0.159546	+	0.595435i
$124$		0			0
$125$	1.82032	+	11.0312i	0.162815	+	0.986657i
$126$		0			0
$127$	−4.91615	−	4.91615i	−0.436238	−	0.436238i	0.454506	−	0.890744i	$-0.349816\pi$
$127$	−4.91615	−	4.91615i	−0.436238	−	0.436238i	−0.890744	+	0.454506i	$0.849816\pi$
$128$		0			0
$129$	2.23532	−	3.87169i	0.196809	−	0.340884i
$130$		0			0
$131$	11.7319	−	6.77343i	1.02502	−	0.591797i	0.109468	−	0.993990i	$-0.465085\pi$
$131$	11.7319	−	6.77343i	1.02502	−	0.591797i	0.915555	+	0.402193i	$0.131752\pi$
$132$		0			0
$133$	1.58167	+	1.83905i	0.137148	+	0.159466i
$134$		0			0
$135$	9.13330	+	8.18810i	0.786069	+	0.704719i
$136$		0			0
$137$	−14.9165	+	3.99687i	−1.27441	+	0.341476i	−0.831717	−	0.555200i	$-0.812642\pi$
$137$	−14.9165	+	3.99687i	−1.27441	+	0.341476i	−0.442688	+	0.896676i	$0.645975\pi$
$138$		0			0
$139$	10.4513			0.886472			0.443236	−	0.896405i	$-0.353830\pi$
$139$	10.4513			0.886472			0.443236	+	0.896405i	$0.353830\pi$
$140$		0			0
$141$	1.14058			0.0960540
$142$		0			0
$143$	−13.4149	+	3.59450i	−1.12181	+	0.300587i
$144$		0			0
$145$	−2.94450	+	0.160677i	−0.244528	+	0.0133435i
$146$		0			0
$147$	6.80824	−	5.01840i	0.561534	−	0.413910i
$148$		0			0
$149$	−13.7158	+	7.91884i	−1.12364	+	0.648737i	−0.942329	−	0.334688i	$-0.891369\pi$
$149$	−13.7158	+	7.91884i	−1.12364	+	0.648737i	−0.181316	+	0.983425i	$0.558036\pi$
$150$		0			0
$151$	−8.90977	+	15.4322i	−0.725067	+	1.25585i	0.233880	+	0.972265i	$0.424858\pi$
$151$	−8.90977	+	15.4322i	−0.725067	+	1.25585i	−0.958947	+	0.283587i	$0.908476\pi$
$152$		0			0
$153$	−0.292235	−	0.292235i	−0.0236258	−	0.0236258i
$154$		0			0
$155$	−3.80136	+	7.50050i	−0.305333	+	0.602454i
$156$		0			0
$157$	−2.38891	−	8.91553i	−0.190656	−	0.711537i	−0.993349	−	0.115144i	$-0.963267\pi$
$157$	−2.38891	−	8.91553i	−0.190656	−	0.711537i	0.802693	−	0.596392i	$-0.203400\pi$
$158$		0			0
$159$	8.15863	+	14.1312i	0.647022	+	1.12067i
$160$		0			0
$161$	20.7043	+	1.55783i	1.63173	+	0.122774i
$162$		0			0
$163$	8.96978	+	2.40344i	0.702567	+	0.188252i	0.592380	−	0.805659i	$-0.298188\pi$
$163$	8.96978	+	2.40344i	0.702567	+	0.188252i	0.110187	+	0.993911i	$0.464855\pi$
$164$		0			0
$165$	−8.88013	−	1.86754i	−0.691317	−	0.145388i
$166$		0			0
$167$	−2.96983	+	2.96983i	−0.229812	+	0.229812i	−0.812614	−	0.582802i	$-0.801956\pi$
$167$	−2.96983	+	2.96983i	−0.229812	+	0.229812i	0.582802	+	0.812614i	$0.301956\pi$
$168$		0			0
$169$			4.09824i			0.315250i
$170$		0			0
$171$	−1.22279	−	0.705977i	−0.0935089	−	0.0539874i
$172$		0			0
$173$	−1.18201	+	4.41132i	−0.0898665	+	0.335386i	−0.996191	−	0.0871956i	$-0.972209\pi$
$173$	−1.18201	+	4.41132i	−0.0898665	+	0.335386i	0.906325	+	0.422582i	$0.138876\pi$
$174$		0			0
$175$	−12.6545	+	3.85534i	−0.956590	+	0.291436i
$176$		0			0
$177$	−2.45159	+	9.14944i	−0.184272	+	0.687714i
$178$		0			0
$179$	7.21474	+	4.16543i	0.539255	+	0.311339i	0.744777	−	0.667313i	$-0.232556\pi$
$179$	7.21474	+	4.16543i	0.539255	+	0.311339i	−0.205522	+	0.978653i	$0.565889\pi$
$180$		0			0
$181$		−	19.1591i		−	1.42409i	−0.702135	−	0.712043i	$-0.747770\pi$
$181$		−	19.1591i		−	1.42409i	0.702135	−	0.712043i	$-0.252230\pi$
$182$		0			0
$183$	9.57031	−	9.57031i	0.707458	−	0.707458i
$184$		0			0
$185$	−17.9045	−	3.76541i	−1.31636	−	0.276839i
$186$		0			0
$187$	0.870595	+	0.233275i	0.0636642	+	0.0170588i
$188$		0			0
$189$	−8.17945	+	11.9893i	−0.594967	+	0.872094i
$190$		0			0
$191$	−2.27127	−	3.93396i	−0.164344	−	0.284652i	0.772078	−	0.635527i	$-0.219217\pi$
$191$	−2.27127	−	3.93396i	−0.164344	−	0.284652i	−0.936422	+	0.350876i	$0.885884\pi$
$192$		0			0
$193$	2.32967	+	8.69445i	0.167693	+	0.625840i	0.997681	+	0.0680587i	$0.0216805\pi$
$193$	2.32967	+	8.69445i	0.167693	+	0.625840i	−0.829988	+	0.557781i	$0.811653\pi$
$194$		0			0
$195$	−5.05047	+	9.96512i	−0.361672	+	0.713617i
$196$		0			0
$197$	5.71540	+	5.71540i	0.407205	+	0.407205i	0.880763	−	0.473558i	$-0.157030\pi$
$197$	5.71540	+	5.71540i	0.407205	+	0.407205i	−0.473558	+	0.880763i	$0.657030\pi$
$198$		0			0
$199$	6.85652	−	11.8758i	0.486046	−	0.841856i	−0.513826	−	0.857895i	$-0.671772\pi$
$199$	6.85652	−	11.8758i	0.486046	−	0.841856i	0.999871	+	0.0160388i	$0.00510552\pi$
$200$		0			0
$201$	−5.82803	+	3.36481i	−0.411077	+	0.237336i
$202$		0			0
$203$	−0.647647	−	3.42853i	−0.0454559	−	0.240636i
$204$		0			0
$205$	12.6333	−	0.689379i	0.882349	−	0.0481483i
$206$		0			0
$207$	−11.6741	+	3.12806i	−0.811404	+	0.217415i
$208$		0			0
$209$	3.07926			0.212997
$210$		0			0
$211$	7.27456			0.500802			0.250401	−	0.968142i	$-0.419438\pi$
$211$	7.27456			0.500802			0.250401	+	0.968142i	$0.419438\pi$
$212$		0			0
$213$	15.7845	−	4.22945i	1.08154	−	0.289797i
$214$		0			0
$215$	−6.16033	−	5.52280i	−0.420131	−	0.376652i
$216$		0			0
$217$	−9.39010	−	3.28890i	−0.637442	−	0.223265i
$218$		0			0
$219$	−7.94462	+	4.58683i	−0.536848	+	0.309949i
$220$		0			0
$221$	0.554819	−	0.960975i	0.0373212	−	0.0646422i
$222$		0			0
$223$	−3.13514	−	3.13514i	−0.209945	−	0.209945i	0.594299	−	0.804244i	$-0.297429\pi$
$223$	−3.13514	−	3.13514i	−0.209945	−	0.209945i	−0.804244	+	0.594299i	$0.797429\pi$
$224$		0			0
$225$	6.21016	−	4.55296i	0.414011	−	0.303531i
$226$		0			0
$227$	−0.113469	−	0.423472i	−0.00753121	−	0.0281069i	0.962058	−	0.272845i	$-0.0879646\pi$
$227$	−0.113469	−	0.423472i	−0.00753121	−	0.0281069i	−0.969589	+	0.244738i	$0.921298\pi$
$228$		0			0
$229$	−6.98055	−	12.0907i	−0.461288	−	0.798974i	0.537738	−	0.843112i	$-0.319279\pi$
$229$	−6.98055	−	12.0907i	−0.461288	−	0.798974i	−0.999025	+	0.0441386i	$0.985946\pi$
$230$		0			0
$231$	0.805590	−	10.7067i	0.0530039	−	0.704449i
$232$		0			0
$233$	10.7647	+	2.88438i	0.705217	+	0.188962i	0.593566	−	0.804785i	$-0.297720\pi$
$233$	10.7647	+	2.88438i	0.705217	+	0.188962i	0.111651	+	0.993748i	$0.464386\pi$
$234$		0			0
$235$	0.434408	−	2.06560i	0.0283377	−	0.134745i
$236$		0			0
$237$	1.84727	−	1.84727i	0.119993	−	0.119993i
$238$		0			0
$239$			2.45924i			0.159075i	0.996832	+	0.0795376i	$0.0253444\pi$
$239$			2.45924i			0.159075i	−0.996832	+	0.0795376i	$0.974656\pi$
$240$		0			0
$241$	−15.7270	−	9.07999i	−1.01307	−	0.584893i	−0.100978	−	0.994889i	$-0.532197\pi$
$241$	−15.7270	−	9.07999i	−1.01307	−	0.584893i	−0.912088	+	0.409995i	$0.865530\pi$
$242$		0			0
$243$	3.63144	−	13.5527i	0.232957	−	0.869407i
$244$		0			0
$245$	−6.49535	−	14.2412i	−0.414973	−	0.909834i
$246$		0			0
$247$	0.981186	−	3.66184i	0.0624314	−	0.232997i
$248$		0			0
$249$	8.13862	+	4.69883i	0.515764	+	0.297776i
$250$		0			0
$251$		−	12.5983i		−	0.795196i	−0.917560	−	0.397598i	$-0.869844\pi$
$251$		−	12.5983i		−	0.795196i	0.917560	−	0.397598i	$-0.130156\pi$
$252$		0			0
$253$	18.6376	−	18.6376i	1.17173	−	1.17173i
$254$		0			0
$255$	0.607210	−	0.396189i	0.0380250	−	0.0248103i
$256$		0			0
$257$	21.0068	+	5.62876i	1.31037	+	0.351113i	0.845362	−	0.534194i	$-0.179385\pi$
$257$	21.0068	+	5.62876i	1.31037	+	0.351113i	0.465008	+	0.885306i	$0.346051\pi$
$258$		0			0
$259$	1.62426	−	21.5872i	0.100927	−	1.34137i
$260$		0			0
$261$	1.01551	+	1.75891i	0.0628584	+	0.108874i
$262$		0			0
$263$	−6.53630	−	24.3938i	−0.403046	−	1.50419i	−0.807632	−	0.589687i	$-0.799251\pi$
$263$	−6.53630	−	24.3938i	−0.403046	−	1.50419i	0.404586	−	0.914500i	$-0.367416\pi$
$264$		0			0
$265$	28.6991	−	9.39330i	1.76297	−	0.577026i
$266$		0			0
$267$	−2.30372	−	2.30372i	−0.140985	−	0.140985i
$268$		0			0
$269$	4.20486	−	7.28303i	0.256375	−	0.444054i	−0.708893	−	0.705316i	$-0.750805\pi$
$269$	4.20486	−	7.28303i	0.256375	−	0.444054i	0.965268	+	0.261262i	$0.0841386\pi$
$270$		0			0
$271$	6.55088	−	3.78215i	0.397938	−	0.229749i	−0.287656	−	0.957734i	$-0.592876\pi$
$271$	6.55088	−	3.78215i	0.397938	−	0.229749i	0.685594	+	0.727984i	$0.259543\pi$
$272$		0			0
$273$	−12.4756	−	4.36962i	−0.755060	−	0.264462i
$274$		0			0
$275$	−6.76429	+	15.3708i	−0.407902	+	0.926891i
$276$		0			0
$277$	−14.7982	+	3.96518i	−0.889140	+	0.238244i	−0.674347	−	0.738415i	$-0.735575\pi$
$277$	−14.7982	+	3.96518i	−0.889140	+	0.238244i	−0.214794	+	0.976659i	$0.568908\pi$
$278$		0			0
$279$	5.79148			0.346727
$280$		0			0
$281$	24.6162			1.46848			0.734239	−	0.678891i	$-0.237539\pi$
$281$	24.6162			1.46848			0.734239	+	0.678891i	$0.237539\pi$
$282$		0			0
$283$	−23.6426	+	6.33503i	−1.40541	+	0.376578i	−0.880284	−	0.474447i	$-0.842648\pi$
$283$	−23.6426	+	6.33503i	−1.40541	+	0.376578i	−0.525125	+	0.851025i	$0.675982\pi$
$284$		0			0
$285$	1.65348	−	1.84435i	0.0979438	−	0.109250i
$286$		0			0
$287$	2.77871	+	14.7100i	0.164022	+	0.868305i
$288$		0			0
$289$	14.6601	−	8.46399i	0.862357	−	0.497882i
$290$		0			0
$291$	−8.63076	+	14.9489i	−0.505944	+	0.876321i
$292$		0			0
$293$	−5.69984	−	5.69984i	−0.332988	−	0.332988i	0.520732	−	0.853720i	$-0.325659\pi$
$293$	−5.69984	−	5.69984i	−0.332988	−	0.332988i	−0.853720	+	0.520732i	$0.825659\pi$
$294$		0			0
$295$	15.6360	+	7.92457i	0.910365	+	0.461386i
$296$		0			0
$297$	4.76860	+	17.7967i	0.276702	+	1.03267i
$298$		0			0
$299$	−16.2249	−	28.1024i	−0.938312	−	1.62520i
$300$		0			0
$301$	5.51697	−	8.08668i	0.317993	−	0.466109i
$302$		0			0
$303$	−19.9067	−	5.33400i	−1.14361	−	0.306430i
$304$		0			0
$305$	−13.6870	−	20.9770i	−0.783713	−	1.20114i
$306$		0			0
$307$	0.652734	−	0.652734i	0.0372535	−	0.0372535i	−0.688235	−	0.725488i	$-0.741614\pi$
$307$	0.652734	−	0.652734i	0.0372535	−	0.0372535i	0.725488	+	0.688235i	$0.241614\pi$
$308$		0			0
$309$			21.6067i			1.22916i
$310$		0			0
$311$	6.75054	+	3.89743i	0.382788	+	0.221003i	0.679031	−	0.734110i	$-0.262400\pi$
$311$	6.75054	+	3.89743i	0.382788	+	0.221003i	−0.296243	+	0.955113i	$0.595734\pi$
$312$		0			0
$313$	−0.897622	+	3.34997i	−0.0507366	+	0.189352i	−0.986643	−	0.162897i	$-0.947916\pi$
$313$	−0.897622	+	3.34997i	−0.0507366	+	0.189352i	0.935906	+	0.352249i	$0.114583\pi$
$314$		0			0
$315$	6.30860	+	6.57384i	0.355450	+	0.370394i
$316$		0			0
$317$	−0.210260	+	0.784701i	−0.0118094	+	0.0440732i	−0.971579	−	0.236715i	$-0.923929\pi$
$317$	−0.210260	+	0.784701i	−0.0118094	+	0.0440732i	0.959770	+	0.280788i	$0.0905959\pi$
$318$		0			0
$319$	−3.83592	−	2.21467i	−0.214771	−	0.123998i
$320$		0			0
$321$			9.59719i			0.535663i
$322$		0			0
$323$	−0.173968	+	0.173968i	−0.00967986	+	0.00967986i
$324$		0			0
$325$	16.1234	+	12.9419i	0.894366	+	0.717885i
$326$		0			0
$327$	16.9331	+	4.53721i	0.936403	+	0.250909i
$328$		0			0
$329$	2.49048	+	0.187388i	0.137304	+	0.0103310i
$330$		0			0
$331$	−7.79902	−	13.5083i	−0.428673	−	0.742483i	0.568083	−	0.822972i	$-0.307685\pi$
$331$	−7.79902	−	13.5083i	−0.428673	−	0.742483i	−0.996756	+	0.0804881i	$0.974352\pi$
$332$		0			0
$333$	3.26146	+	12.1719i	0.178727	+	0.667017i
$334$		0			0
$335$	3.87402	+	11.8362i	0.211660	+	0.646679i
$336$		0			0
$337$	−12.2052	−	12.2052i	−0.664861	−	0.664861i	0.291661	−	0.956522i	$-0.405792\pi$
$337$	−12.2052	−	12.2052i	−0.664861	−	0.664861i	−0.956522	+	0.291661i	$0.905792\pi$
$338$		0			0
$339$	−4.66894	+	8.08685i	−0.253582	+	0.439217i
$340$		0			0
$341$	−10.9382	+	6.31517i	−0.592337	+	0.341986i
$342$		0			0
$343$	15.6904	−	9.83924i	0.847203	−	0.531269i
$344$		0			0
$345$	−1.15527	−	21.1710i	−0.0621976	−	1.13981i
$346$		0			0
$347$	14.7477	−	3.95163i	0.791697	−	0.212134i	0.159761	−	0.987156i	$-0.448928\pi$
$347$	14.7477	−	3.95163i	0.791697	−	0.212134i	0.631935	+	0.775021i	$0.282261\pi$
$348$		0			0
$349$	−35.5955			−1.90538			−0.952692	−	0.303938i	$-0.901698\pi$
$349$	−35.5955			−1.90538			−0.952692	+	0.303938i	$0.901698\pi$
$350$		0			0
$351$	22.6832			1.21074
$352$		0			0
$353$	6.13426	−	1.64367i	0.326494	−	0.0874838i	−0.0918490	−	0.995773i	$-0.529278\pi$
$353$	6.13426	−	1.64367i	0.326494	−	0.0874838i	0.418343	+	0.908289i	$0.362611\pi$
$354$		0			0
$355$	−1.64779	−	30.1968i	−0.0874556	−	1.60268i
$356$		0			0
$357$	0.559381	+	0.650408i	0.0296056	+	0.0344232i
$358$		0			0
$359$	26.6079	−	15.3621i	1.40431	−	0.810780i	0.409481	−	0.912319i	$-0.365710\pi$
$359$	26.6079	−	15.3621i	1.40431	−	0.810780i	0.994832	+	0.101539i	$0.0323766\pi$
$360$		0			0
$361$	9.07973	−	15.7266i	0.477881	−	0.827713i
$362$		0			0
$363$	−0.239763	−	0.239763i	−0.0125843	−	0.0125843i
$364$		0			0
$365$	5.28097	+	16.1348i	0.276418	+	0.844533i
$366$		0			0
$367$	−9.38683	−	35.0321i	−0.489988	−	1.82866i	−0.556461	−	0.830874i	$-0.687841\pi$
$367$	−9.38683	−	35.0321i	−0.489988	−	1.82866i	0.0664728	−	0.997788i	$-0.478825\pi$
$368$		0			0
$369$	−4.35701	−	7.54657i	−0.226817	−	0.392859i
$370$		0			0
$371$	15.4929	+	32.1961i	0.804352	+	1.67154i
$372$		0			0
$373$	14.7087	+	3.94120i	0.761590	+	0.204067i	0.618653	−	0.785664i	$-0.287679\pi$
$373$	14.7087	+	3.94120i	0.761590	+	0.204067i	0.142937	+	0.989732i	$0.454345\pi$
$374$		0			0
$375$	5.57422	+	12.3052i	0.287851	+	0.635440i
$376$		0			0
$377$	−3.85597	+	3.85597i	−0.198592	+	0.198592i
$378$		0			0
$379$			31.6560i			1.62606i	0.582221	+	0.813030i	$0.302184\pi$
$379$			31.6560i			1.62606i	−0.582221	+	0.813030i	$0.697816\pi$
$380$		0			0
$381$	−7.27506	−	4.20026i	−0.372713	−	0.215186i
$382$		0			0
$383$	−5.44366	+	20.3160i	−0.278158	+	1.03810i	0.675537	+	0.737326i	$0.263912\pi$
$383$	−5.44366	+	20.3160i	−0.278158	+	1.03810i	−0.953695	+	0.300774i	$0.902755\pi$
$384$		0			0
$385$	−19.0831	−	5.53676i	−0.972567	−	0.282179i
$386$		0			0
$387$	−1.47483	+	5.50414i	−0.0749699	+	0.279791i
$388$		0			0
$389$	−26.4709	−	15.2830i	−1.34213	−	0.774877i	−0.355007	−	0.934864i	$-0.615522\pi$
$389$	−26.4709	−	15.2830i	−1.34213	−	0.774877i	−0.987119	+	0.159986i	$0.948855\pi$
$390$		0			0
$391$			2.10593i			0.106501i
$392$		0			0
$393$	11.5742	−	11.5742i	0.583839	−	0.583839i
$394$		0			0
$395$	−2.64187	−	4.04899i	−0.132927	−	0.203727i
$396$		0			0
$397$	−3.67997	−	0.986045i	−0.184692	−	0.0494882i	0.165287	−	0.986245i	$-0.447145\pi$
$397$	−3.67997	−	0.986045i	−0.184692	−	0.0494882i	−0.349980	+	0.936757i	$0.613812\pi$
$398$		0			0
$399$	2.42109	+	1.65174i	0.121206	+	0.0826902i
$400$		0			0
$401$	5.34357	+	9.25534i	0.266845	+	0.462190i	0.968045	−	0.250775i	$-0.0806854\pi$
$401$	5.34357	+	9.25534i	0.266845	+	0.462190i	−0.701200	+	0.712964i	$0.747352\pi$
$402$		0			0
$403$	4.02458	+	15.0199i	0.200479	+	0.748196i
$404$		0			0
$405$	4.00494	+	2.02976i	0.199007	+	0.100860i
$406$		0			0
$407$	−19.4324	−	19.4324i	−0.963227	−	0.963227i
$408$		0			0
$409$	4.24386	−	7.35057i	0.209845	−	0.363463i	−0.741820	−	0.670599i	$-0.766037\pi$
$409$	4.24386	−	7.35057i	0.209845	−	0.363463i	0.951666	+	0.307136i	$0.0993707\pi$
$410$		0			0
$411$	−16.1592	+	9.32953i	−0.797075	+	0.460192i
$412$		0			0
$413$	−6.85627	+	19.5752i	−0.337375	+	0.963234i
$414$		0			0
$415$	11.6094	−	12.9495i	0.569882	−	0.635667i
$416$		0			0
$417$	12.1978	−	3.26839i	0.597329	−	0.160054i
$418$		0			0
$419$	23.6626			1.15599			0.577997	−	0.816039i	$-0.303835\pi$
$419$	23.6626			1.15599			0.577997	+	0.816039i	$0.303835\pi$
$420$		0			0
$421$	−18.3661			−0.895110			−0.447555	−	0.894256i	$-0.647705\pi$
$421$	−18.3661			−0.895110			−0.447555	+	0.894256i	$0.647705\pi$
$422$		0			0
$423$	−1.40425	+	0.376267i	−0.0682769	+	0.0182948i
$424$		0			0
$425$	−0.486238	−	1.25056i	−0.0235860	−	0.0606611i
$426$		0			0
$427$	22.4693	−	19.3247i	1.08737	−	0.935186i
$428$		0			0
$429$	−14.5324	+	8.39031i	−0.701633	+	0.405088i
$430$		0			0
$431$	−15.2748	+	26.4567i	−0.735761	+	1.27438i	0.218628	+	0.975808i	$0.429842\pi$
$431$	−15.2748	+	26.4567i	−0.735761	+	1.27438i	−0.954389	+	0.298567i	$0.903491\pi$
$432$		0			0
$433$	−15.7711	−	15.7711i	−0.757910	−	0.757910i	0.218032	−	0.975942i	$-0.430036\pi$
$433$	−15.7711	−	15.7711i	−0.757910	−	0.757910i	−0.975942	+	0.218032i	$0.930036\pi$
$434$		0			0
$435$	−3.38629	+	1.10834i	−0.162360	+	0.0531411i
$436$		0			0
$437$	1.86214	+	6.94961i	0.0890783	+	0.332445i
$438$		0			0
$439$	−11.9294	−	20.6623i	−0.569357	−	0.986155i	−0.996630	−	0.0820326i	$-0.973859\pi$
$439$	−11.9294	−	20.6623i	−0.569357	−	0.986155i	0.427273	−	0.904123i	$-0.359474\pi$
$440$		0			0
$441$	−6.72660	+	8.42450i	−0.320314	+	0.401167i
$442$		0			0
$443$	−25.7705	−	6.90519i	−1.22439	−	0.328075i	−0.411999	−	0.911184i	$-0.635169\pi$
$443$	−25.7705	−	6.90519i	−1.22439	−	0.328075i	−0.812394	+	0.583109i	$0.801836\pi$
$444$		0			0
$445$	−5.04948	+	3.29466i	−0.239368	+	0.156182i
$446$		0			0
$447$	−13.5314	+	13.5314i	−0.640012	+	0.640012i
$448$		0			0
$449$		−	8.15718i		−	0.384961i	−0.981301	−	0.192481i	$-0.938347\pi$
$449$		−	8.15718i		−	0.384961i	0.981301	−	0.192481i	$-0.0616533\pi$
$450$		0			0
$451$	16.4579	+	9.50199i	0.774973	+	0.447431i
$452$		0			0
$453$	−5.57261	+	20.7972i	−0.261824	+	0.977140i
$454$		0			0
$455$	−12.6650	+	20.9293i	−0.593745	+	0.981181i
$456$		0			0
$457$	−0.694650	+	2.59247i	−0.0324943	+	0.121271i	−0.980268	−	0.197673i	$-0.936661\pi$
$457$	−0.694650	+	2.59247i	−0.0324943	+	0.121271i	0.947774	+	0.318944i	$0.103328\pi$
$458$		0			0
$459$	−1.27487	−	0.736045i	−0.0595057	−	0.0343556i
$460$		0			0
$461$			18.0493i			0.840641i	0.907376	+	0.420321i	$0.138082\pi$
$461$			18.0493i			0.840641i	−0.907376	+	0.420321i	$0.861918\pi$
$462$		0			0
$463$	−13.2907	+	13.2907i	−0.617672	+	0.617672i	−0.944934	−	0.327261i	$-0.893874\pi$
$463$	−13.2907	+	13.2907i	−0.617672	+	0.617672i	0.327261	+	0.944934i	$0.393874\pi$
$464$		0			0
$465$	−2.09099	+	9.94263i	−0.0969675	+	0.461079i
$466$		0			0
$467$	−2.71031	−	0.726226i	−0.125418	−	0.0336057i	0.195564	−	0.980691i	$-0.437346\pi$
$467$	−2.71031	−	0.726226i	−0.125418	−	0.0336057i	−0.320982	+	0.947085i	$0.604013\pi$
$468$		0			0
$469$	−13.2784	+	6.38964i	−0.613141	+	0.295046i
$470$		0			0
$471$	−5.57621	−	9.65827i	−0.256938	−	0.445030i
$472$		0			0
$473$	−3.21638	−	12.0037i	−0.147889	−	0.551931i
$474$		0			0
$475$	−2.71039	−	3.69693i	−0.124361	−	0.169627i
$476$		0			0
$477$	−14.7065	−	14.7065i	−0.673362	−	0.673362i
$478$		0			0
$479$	−13.6489	+	23.6406i	−0.623634	+	1.08017i	0.365170	+	0.930941i	$0.381011\pi$
$479$	−13.6489	+	23.6406i	−0.623634	+	1.08017i	−0.988803	+	0.149224i	$0.952322\pi$
$480$		0			0
$481$	−29.3009	+	16.9169i	−1.33600	+	0.771343i
$482$		0			0
$483$	24.6512	−	4.65660i	1.12167	−	0.211882i
$484$		0			0
$485$	23.7855	+	21.3240i	1.08005	+	0.968272i
$486$		0			0
$487$	29.2231	−	7.83031i	1.32422	−	0.354825i	0.473666	−	0.880705i	$-0.342930\pi$
$487$	29.2231	−	7.83031i	1.32422	−	0.354825i	0.850559	+	0.525880i	$0.176264\pi$
$488$		0			0
$489$	11.2203			0.507398
$490$		0			0
$491$	−17.8214			−0.804270			−0.402135	−	0.915580i	$-0.631732\pi$
$491$	−17.8214			−0.804270			−0.402135	+	0.915580i	$0.631732\pi$
$492$		0			0
$493$	0.341840	−	0.0915956i	0.0153957	−	0.00412526i
$494$		0			0
$495$	11.5491	−	0.630214i	0.519092	−	0.0283260i
$496$		0			0
$497$	35.1607	−	6.64182i	1.57717	−	0.297926i
$498$		0			0
$499$	−26.1405	+	15.0922i	−1.17021	+	0.675621i	−0.953729	−	0.300666i	$-0.902791\pi$
$499$	−26.1405	+	15.0922i	−1.17021	+	0.675621i	−0.216480	+	0.976287i	$0.569458\pi$
$500$		0			0
$501$	−2.53736	+	4.39484i	−0.113361	+	0.196347i
$502$		0			0
$503$	10.2304	+	10.2304i	0.456149	+	0.456149i	0.897389	−	0.441240i	$-0.145461\pi$
$503$	10.2304	+	10.2304i	0.456149	+	0.456149i	−0.441240	+	0.897389i	$0.645461\pi$
$504$		0			0
$505$	−17.2417	+	34.0198i	−0.767248	+	1.51386i
$506$		0			0
$507$	1.28162	+	4.78308i	0.0569188	+	0.212424i
$508$		0			0
$509$	−4.98510	−	8.63445i	−0.220961	−	0.382715i	0.734139	−	0.678999i	$-0.237586\pi$
$509$	−4.98510	−	8.63445i	−0.220961	−	0.382715i	−0.955100	+	0.296284i	$0.904253\pi$
$510$		0			0
$511$	−18.1008	+	8.71021i	−0.800734	+	0.385317i
$512$		0			0
$513$	−4.85793	−	1.30168i	−0.214483	−	0.0574705i
$514$		0			0
$515$	39.1300	+	8.22926i	1.72427	+	0.362625i
$516$		0			0
$517$	2.24187	−	2.24187i	0.0985974	−	0.0985974i
$518$		0			0
$519$			5.51811i			0.242218i
$520$		0			0
$521$	−11.5888	−	6.69081i	−0.507715	−	0.293130i	0.224179	−	0.974548i	$-0.428030\pi$
$521$	−11.5888	−	6.69081i	−0.507715	−	0.293130i	−0.731894	+	0.681419i	$0.761363\pi$
$522$		0			0
$523$	3.31005	−	12.3533i	0.144739	−	0.540172i	−0.855028	−	0.518581i	$-0.826460\pi$
$523$	3.31005	−	12.3533i	0.144739	−	0.540172i	0.999767	−	0.0215904i	$-0.00687296\pi$
$524$		0			0
$525$	−13.5635	+	8.45695i	−0.591958	+	0.369092i
$526$		0			0
$527$	0.261186	−	0.974761i	0.0113775	−	0.0424613i
$528$		0			0
$529$	33.4155	+	19.2925i	1.45285	+	0.838803i
$530$		0			0
$531$		−	12.0733i		−	0.523937i
$532$		0			0
$533$	16.5439	−	16.5439i	0.716597	−	0.716597i
$534$		0			0
$535$	17.3806	+	3.65525i	0.751430	+	0.158030i
$536$		0			0
$537$	9.72299	+	2.60527i	0.419578	+	0.112426i
$538$		0			0
$539$	3.51804	−	23.2459i	0.151533	−	1.00127i
$540$		0			0
$541$	−0.914577	−	1.58409i	−0.0393207	−	0.0681055i	0.845695	−	0.533666i	$-0.179186\pi$
$541$	−0.914577	−	1.58409i	−0.0393207	−	0.0681055i	−0.885016	+	0.465561i	$0.845853\pi$
$542$		0			0
$543$	−5.99153	−	22.3607i	−0.257121	−	0.959589i
$544$		0			0
$545$	14.6662	−	28.9380i	0.628232	−	1.23957i
$546$		0			0
$547$	2.84062	+	2.84062i	0.121456	+	0.121456i	0.765222	−	0.643766i	$-0.222629\pi$
$547$	2.84062	+	2.84062i	0.121456	+	0.121456i	−0.643766	+	0.765222i	$0.722629\pi$
$548$		0			0
$549$	−8.62555	+	14.9399i	−0.368129	+	0.637619i
$550$		0			0
$551$	1.04709	−	0.604536i	0.0446074	−	0.0257541i
$552$		0			0
$553$	4.33704	−	3.73006i	0.184430	−	0.158618i
$554$		0			0
$555$	−22.0739	+	1.20454i	−0.936985	+	0.0511297i
$556$		0			0
$557$	21.6537	−	5.80210i	0.917498	−	0.245843i	0.230982	−	0.972958i	$-0.425806\pi$
$557$	21.6537	−	5.80210i	0.917498	−	0.245843i	0.686516	+	0.727115i	$0.259139\pi$
$558$		0			0
$559$	−15.2996			−0.647105
$560$		0			0
$561$	1.08903			0.0459787
$562$		0			0
$563$	−3.11101	+	0.833593i	−0.131114	+	0.0351318i	−0.323779	−	0.946133i	$-0.604953\pi$
$563$	−3.11101	+	0.833593i	−0.131114	+	0.0351318i	0.192665	+	0.981264i	$0.438287\pi$
$564$		0			0
$565$	12.8671	+	11.5355i	0.541325	+	0.485303i
$566$		0			0
$567$	−1.75613	+	5.01391i	−0.0737507	+	0.210564i
$568$		0			0
$569$	21.3213	−	12.3098i	0.893835	−	0.516056i	0.0186397	−	0.999826i	$-0.494066\pi$
$569$	21.3213	−	12.3098i	0.893835	−	0.516056i	0.875195	+	0.483771i	$0.160733\pi$
$570$		0			0
$571$	−18.2044	+	31.5310i	−0.761831	+	1.31953i	0.180074	+	0.983653i	$0.442366\pi$
$571$	−18.2044	+	31.5310i	−0.761831	+	1.31953i	−0.941906	+	0.335877i	$0.890967\pi$
$572$		0			0
$573$	−3.88106	−	3.88106i	−0.162134	−	0.162134i
$574$		0			0
$575$	−38.7810	−	5.97114i	−1.61728	−	0.249014i
$576$		0			0
$577$	1.30689	+	4.87736i	0.0544064	+	0.203047i	0.987779	−	0.155862i	$-0.0498155\pi$
$577$	1.30689	+	4.87736i	0.0544064	+	0.203047i	−0.933372	+	0.358909i	$0.883149\pi$
$578$		0			0
$579$	5.43793	+	9.41877i	0.225993	+	0.391431i
$580$		0			0
$581$	16.9989	+	11.5971i	0.705232	+	0.481129i
$582$		0			0
$583$	43.8119	+	11.7394i	1.81450	+	0.486195i
$584$		0			0
$585$	2.93059	−	13.9349i	0.121165	−	0.576138i
$586$		0			0
$587$	−16.9957	+	16.9957i	−0.701488	+	0.701488i	−0.964730	−	0.263242i	$-0.915208\pi$
$587$	−16.9957	+	16.9957i	−0.701488	+	0.701488i	0.263242	+	0.964730i	$0.415208\pi$
$588$		0			0
$589$		−	3.44769i		−	0.142059i
$590$		0			0
$591$	8.45781	+	4.88312i	0.347908	+	0.200865i
$592$		0			0
$593$	−5.35745	+	19.9943i	−0.220004	+	0.821067i	0.764341	+	0.644813i	$0.223065\pi$
$593$	−5.35745	+	19.9943i	−0.220004	+	0.821067i	−0.984345	+	0.176254i	$0.943602\pi$
$594$		0			0
$595$	1.39095	−	0.765328i	0.0570233	−	0.0313754i
$596$		0			0
$597$	4.28840	−	16.0045i	0.175513	−	0.655022i
$598$		0			0
$599$	−27.9687	−	16.1478i	−1.14277	−	0.659780i	−0.195656	−	0.980673i	$-0.562684\pi$
$599$	−27.9687	−	16.1478i	−1.14277	−	0.659780i	−0.947115	+	0.320893i	$0.896017\pi$
$600$		0			0
$601$			25.1960i			1.02777i	0.857861	+	0.513883i	$0.171793\pi$
$601$			25.1960i			1.02777i	−0.857861	+	0.513883i	$0.828207\pi$
$602$		0			0
$603$	6.06529	−	6.06529i	0.246998	−	0.246998i
$604$		0			0
$605$	−0.525532	+	0.342896i	−0.0213659	+	0.0139407i
$606$		0			0
$607$	46.2025	+	12.3799i	1.87530	+	0.502486i	0.999815	+	0.0192458i	$0.00612652\pi$
$607$	46.2025	+	12.3799i	1.87530	+	0.502486i	0.875488	+	0.483240i	$0.160540\pi$
$608$		0			0
$609$	−1.82806	−	3.79892i	−0.0740766	−	0.153940i
$610$		0			0
$611$	−1.95166	−	3.38038i	−0.0789559	−	0.136756i
$612$		0			0
$613$	−4.86971	−	18.1740i	−0.196686	−	0.734041i	−0.991824	−	0.127613i	$-0.959268\pi$
$613$	−4.86971	−	18.1740i	−0.196686	−	0.734041i	0.795138	−	0.606428i	$-0.207398\pi$
$614$		0			0
$615$	14.5288	−	4.75532i	0.585858	−	0.191753i
$616$		0			0
$617$	−4.50888	−	4.50888i	−0.181521	−	0.181521i	0.610497	−	0.792018i	$-0.290970\pi$
$617$	−4.50888	−	4.50888i	−0.181521	−	0.181521i	−0.792018	+	0.610497i	$0.790970\pi$
$618$		0			0
$619$	−5.79025	+	10.0290i	−0.232730	+	0.403100i	−0.958610	−	0.284721i	$-0.908099\pi$
$619$	−5.79025	+	10.0290i	−0.232730	+	0.403100i	0.725881	+	0.687821i	$0.241432\pi$
$620$		0			0
$621$	−37.2818	+	21.5246i	−1.49607	+	0.863754i
$622$		0			0
$623$	−4.65174	−	5.40871i	−0.186368	−	0.216695i
$624$		0			0
$625$	24.4080	−	5.40833i	0.976320	−	0.216333i
$626$		0			0
$627$	3.59381	−	0.962959i	0.143523	−	0.0384569i
$628$		0			0
$629$	2.19574			0.0875497
$630$		0			0
$631$	−37.5680			−1.49556			−0.747779	−	0.663948i	$-0.768880\pi$
$631$	−37.5680			−1.49556			−0.747779	+	0.663948i	$0.768880\pi$
$632$		0			0
$633$	8.49017	−	2.27493i	0.337454	−	0.0904205i
$634$		0			0
$635$	−10.3775	+	11.5755i	−0.411820	+	0.459359i
$636$		0			0
$637$	−26.5230	−	11.5908i	−1.05088	−	0.459245i
$638$		0			0
$639$	−18.0382	+	10.4144i	−0.713581	+	0.411986i
$640$		0			0
$641$	0.166165	−	0.287806i	0.00656311	−	0.0113676i	−0.862725	−	0.505673i	$-0.831244\pi$
$641$	0.166165	−	0.287806i	0.00656311	−	0.0113676i	0.869288	+	0.494305i	$0.164578\pi$
$642$		0			0
$643$	−16.9157	−	16.9157i	−0.667092	−	0.667092i	0.289950	−	0.957042i	$-0.406361\pi$
$643$	−16.9157	−	16.9157i	−0.667092	−	0.667092i	−0.957042	+	0.289950i	$0.906361\pi$
$644$		0			0
$645$	−8.91686	−	4.51919i	−0.351101	−	0.177943i
$646$		0			0
$647$	12.8652	+	48.0136i	0.505784	+	1.88761i	0.458426	+	0.888732i	$0.348413\pi$
$647$	12.8652	+	48.0136i	0.505784	+	1.88761i	0.0473574	+	0.998878i	$0.484920\pi$
$648$		0			0
$649$	13.1650	+	22.8025i	0.516773	+	0.895077i
$650$		0			0
$651$	−11.9877	−	0.901978i	−0.469837	−	0.0353513i
$652$		0			0
$653$	−30.5151	−	8.17650i	−1.19415	−	0.319971i	−0.393624	−	0.919272i	$-0.628779\pi$
$653$	−30.5151	−	8.17650i	−1.19415	−	0.319971i	−0.800524	+	0.599301i	$0.795445\pi$
$654$		0			0
$655$	−16.5527	−	25.3692i	−0.646769	−	0.991255i
$656$		0			0
$657$	8.26805	−	8.26805i	0.322567	−	0.322567i
$658$		0			0
$659$		−	40.5893i		−	1.58114i	−0.612374	−	0.790568i	$-0.709785\pi$
$659$		−	40.5893i		−	1.58114i	0.612374	−	0.790568i	$-0.290215\pi$
$660$		0			0
$661$	17.1349	+	9.89284i	0.666471	+	0.384787i	0.794738	−	0.606953i	$-0.207608\pi$
$661$	17.1349	+	9.89284i	0.666471	+	0.384787i	−0.128267	+	0.991740i	$0.540942\pi$
$662$		0			0
$663$	0.347011	−	1.29506i	0.0134768	−	0.0502961i
$664$		0			0
$665$	3.91343	−	3.75553i	0.151756	−	0.145633i
$666$		0			0
$667$	2.67859	−	9.99663i	0.103715	−	0.387071i
$668$		0			0
$669$	−4.63947	−	2.67860i	−0.179372	−	0.103561i
$670$		0			0
$671$		−	37.6220i		−	1.45238i
$672$		0			0
$673$	−21.6615	+	21.6615i	−0.834989	+	0.834989i	−0.988194	−	0.153206i	$-0.951040\pi$
$673$	−21.6615	+	21.6615i	−0.834989	+	0.834989i	0.153206	+	0.988194i	$0.451040\pi$
$674$		0			0
$675$	17.1692	−	21.3899i	0.660841	−	0.823299i
$676$		0			0
$677$	36.6550	+	9.82167i	1.40877	+	0.377477i	0.881484	−	0.472214i	$-0.156545\pi$
$677$	36.6550	+	9.82167i	1.40877	+	0.377477i	0.527281	+	0.849691i	$0.323212\pi$
$678$		0			0
$679$	−21.3014	+	31.2233i	−0.817475	+	1.19824i
$680$		0			0
$681$	−0.264860	−	0.458752i	−0.0101495	−	0.0175794i
$682$		0			0
$683$	3.22391	+	12.0318i	0.123359	+	0.460384i	0.999776	−	0.0211702i	$-0.00673918\pi$
$683$	3.22391	+	12.0318i	0.123359	+	0.460384i	−0.876416	+	0.481554i	$0.840073\pi$
$684$		0			0
$685$	10.7414	+	32.8179i	0.410407	+	1.25391i
$686$		0			0
$687$	−11.9281	−	11.9281i	−0.455084	−	0.455084i
$688$		0			0
$689$	27.9208	−	48.3602i	1.06370	−	1.84238i
$690$		0			0
$691$	0.262855	−	0.151759i	0.00999947	−	0.00577320i	−0.494992	−	0.868898i	$-0.664829\pi$
$691$	0.262855	−	0.151759i	0.00999947	−	0.00577320i	0.504991	+	0.863124i	$0.331496\pi$
$692$		0			0
$693$	2.54023	+	13.4476i	0.0964954	+	0.510831i
$694$		0			0
$695$	−1.27336	−	23.3352i	−0.0483014	−	0.885155i
$696$		0			0
$697$	−1.46665	+	0.392989i	−0.0555535	+	0.0148855i
$698$		0			0
$699$	13.4655			0.509312
$700$		0			0
$701$	−2.82269			−0.106612			−0.0533058	−	0.998578i	$-0.516976\pi$
$701$	−2.82269			−0.106612			−0.0533058	+	0.998578i	$0.516976\pi$
$702$		0			0
$703$	7.24598	−	1.94155i	0.273287	−	0.0732271i
$704$		0			0
$705$	−0.138965	−	2.54662i	−0.00523372	−	0.0959113i
$706$		0			0
$707$	−42.5905	−	14.9174i	−1.60178	−	0.561027i
$708$		0			0
$709$	−18.2418	+	10.5319i	−0.685085	+	0.395534i	−0.801768	−	0.597635i	$-0.796107\pi$
$709$	−18.2418	+	10.5319i	−0.685085	+	0.395534i	0.116683	+	0.993169i	$0.462774\pi$
$710$		0			0
$711$	−1.66491	+	2.88371i	−0.0624390	+	0.108148i
$712$		0			0
$713$	−20.8675	−	20.8675i	−0.781495	−	0.781495i
$714$		0			0
$715$	9.66004	+	29.5140i	0.361265	+	1.10376i
$716$		0			0
$717$	0.769066	+	2.87019i	0.0287213	+	0.107189i
$718$		0			0
$719$	5.73941	+	9.94096i	0.214044	+	0.370735i	0.952976	−	0.303044i	$-0.0980031\pi$
$719$	5.73941	+	9.94096i	0.214044	+	0.370735i	−0.738932	+	0.673780i	$0.764670\pi$
$720$		0			0
$721$	−3.54980	+	47.1786i	−0.132201	+	1.75702i
$722$		0			0
$723$	−21.1946	−	5.67907i	−0.788235	−	0.211207i
$724$		0			0
$725$	0.717500	+	6.55475i	0.0266473	+	0.243437i
$726$		0			0
$727$	−36.2336	+	36.2336i	−1.34383	+	1.34383i	−0.451620	+	0.892210i	$0.649154\pi$
$727$	−36.2336	+	36.2336i	−1.34383	+	1.34383i	−0.892210	+	0.451620i	$0.850846\pi$
$728$		0			0
$729$		−	22.9769i		−	0.850997i
$730$		0			0
$731$	0.859887	+	0.496456i	0.0318041	+	0.0183621i
$732$		0			0
$733$	11.6256	−	43.3873i	0.429401	−	1.60255i	−0.324721	−	0.945810i	$-0.605270\pi$
$733$	11.6256	−	43.3873i	0.429401	−	1.60255i	0.754121	−	0.656735i	$-0.228063\pi$
$734$		0			0
$735$	−12.0343	−	14.5896i	−0.443892	−	0.538147i
$736$		0			0
$737$	−4.84159	+	18.0691i	−0.178342	+	0.665582i
$738$		0			0
$739$	−1.44181	−	0.832430i	−0.0530379	−	0.0306214i	0.473247	−	0.880930i	$-0.343082\pi$
$739$	−1.44181	−	0.832430i	−0.0530379	−	0.0306214i	−0.526284	+	0.850309i	$0.676415\pi$
$740$		0			0
$741$		−	4.58058i		−	0.168272i
$742$		0			0
$743$	23.4760	−	23.4760i	0.861249	−	0.861249i	−0.130234	−	0.991483i	$-0.541573\pi$
$743$	23.4760	−	23.4760i	0.861249	−	0.861249i	0.991483	+	0.130234i	$0.0415729\pi$
$744$		0			0
$745$	19.3519	+	29.6592i	0.708997	+	1.08663i
$746$		0			0
$747$	−11.5702	−	3.10021i	−0.423330	−	0.113431i
$748$		0			0
$749$	−1.57674	+	20.9557i	−0.0576128	+	0.765703i
$750$		0			0
$751$	8.30294	+	14.3811i	0.302979	+	0.524774i	0.976809	−	0.214112i	$-0.0686856\pi$
$751$	8.30294	+	14.3811i	0.302979	+	0.524774i	−0.673831	+	0.738886i	$0.735352\pi$
$752$		0			0
$753$	−3.93979	−	14.7035i	−0.143574	−	0.535825i
$754$		0			0
$755$	35.5417	+	18.0130i	1.29349	+	0.655562i
$756$		0			0
$757$	−23.6602	−	23.6602i	−0.859944	−	0.859944i	0.131387	−	0.991331i	$-0.458057\pi$
$757$	−23.6602	−	23.6602i	−0.859944	−	0.859944i	−0.991331	+	0.131387i	$0.958057\pi$
$758$		0			0
$759$	15.9235	−	27.5804i	0.577988	−	1.00110i
$760$		0			0
$761$	30.6131	−	17.6745i	1.10973	−	0.640700i	0.170967	−	0.985277i	$-0.445311\pi$
$761$	30.6131	−	17.6745i	1.10973	−	0.640700i	0.938758	+	0.344577i	$0.111978\pi$
$762$		0			0
$763$	36.2284	+	12.6891i	1.31156	+	0.459375i
$764$		0			0
$765$	−0.616881	+	0.688091i	−0.0223034	+	0.0248780i
$766$		0			0
$767$	31.3116	−	8.38991i	1.13060	−	0.302942i
$768$		0			0
$769$	−7.73257			−0.278844			−0.139422	−	0.990233i	$-0.544524\pi$
$769$	−7.73257			−0.278844			−0.139422	+	0.990233i	$0.544524\pi$
$770$		0			0
$771$	26.2774			0.946358
$772$		0			0
$773$	−23.9549	+	6.41870i	−0.861598	+	0.230865i	−0.662451	−	0.749105i	$-0.730484\pi$
$773$	−23.9549	+	6.41870i	−0.861598	+	0.230865i	−0.199147	+	0.979970i	$0.563817\pi$
$774$		0			0
$775$	17.2098	+	7.57364i	0.618196	+	0.272053i
$776$		0			0
$777$	−4.85518	−	25.7025i	−0.174179	−	0.922072i
$778$		0			0
$779$	−4.49250	+	2.59374i	−0.160960	+	0.0929305i
$780$		0			0
$781$	22.7122	−	39.3386i	0.812705	−	1.40765i
$782$		0			0
$783$	5.11548	+	5.11548i	0.182812	+	0.182812i
$784$		0			0
$785$	−19.6151	+	6.42007i	−0.700091	+	0.229142i
$786$		0			0
$787$	5.77061	+	21.5362i	0.205700	+	0.767683i	0.989235	+	0.146336i	$0.0467479\pi$
$787$	5.77061	+	21.5362i	0.205700	+	0.767683i	−0.783535	+	0.621348i	$0.786585\pi$
$788$		0			0
$789$	−15.2571	−	26.4260i	−0.543167	−	0.940792i
$790$		0			0
$791$	−11.5233	+	16.8907i	−0.409723	+	0.600566i
$792$		0			0
$793$	−44.7399	−	11.9880i	−1.58876	−	0.425707i
$794$		0			0
$795$	30.5573	−	19.9379i	1.08376	−	0.707123i
$796$		0			0
$797$	−17.2569	+	17.2569i	−0.611269	+	0.611269i	−0.943277	−	0.332008i	$-0.892274\pi$
$797$	−17.2569	+	17.2569i	−0.611269	+	0.611269i	0.332008	+	0.943277i	$0.392274\pi$
$798$		0			0
$799$			0.253317i			0.00896173i
$800$		0			0
$801$	3.59626	+	2.07630i	0.127068	+	0.0733625i
$802$		0			0
$803$	−6.59994	+	24.6313i	−0.232907	+	0.869220i
$804$		0			0
$805$	0.955675	−	46.4172i	0.0336831	−	1.63599i
$806$		0			0
$807$	2.62992	−	9.81501i	0.0925777	−	0.345505i
$808$		0			0
$809$	−9.08066	−	5.24272i	−0.319259	−	0.184324i	0.331803	−	0.943349i	$-0.392343\pi$
$809$	−9.08066	−	5.24272i	−0.319259	−	0.184324i	−0.651062	+	0.759024i	$0.725676\pi$
$810$		0			0
$811$		−	9.71519i		−	0.341147i	−0.985345	−	0.170573i	$-0.945438\pi$
$811$		−	9.71519i		−	0.341147i	0.985345	−	0.170573i	$-0.0545620\pi$
$812$		0			0
$813$	6.46279	−	6.46279i	0.226660	−	0.226660i
$814$		0			0
$815$	4.27343	−	20.3201i	0.149692	−	0.711781i
$816$		0			0
$817$	3.27663	+	0.877971i	0.114635	+	0.0307163i
$818$		0			0
$819$	16.8012	+	1.26415i	0.587081	+	0.0441730i
$820$		0			0
$821$	−1.01376	−	1.75588i	−0.0353804	−	0.0612806i	0.847793	−	0.530327i	$-0.177931\pi$
$821$	−1.01376	−	1.75588i	−0.0353804	−	0.0612806i	−0.883173	+	0.469047i	$0.844598\pi$
$822$		0			0
$823$	−9.44496	−	35.2491i	−0.329231	−	1.22871i	−0.909990	−	0.414630i	$-0.863911\pi$
$823$	−9.44496	−	35.2491i	−0.329231	−	1.22871i	0.580760	−	0.814075i	$-0.302756\pi$
$824$		0			0
$825$	−3.08782	+	20.0546i	−0.107504	+	0.698212i
$826$		0			0
$827$	−4.15637	−	4.15637i	−0.144531	−	0.144531i	0.631139	−	0.775670i	$-0.282588\pi$
$827$	−4.15637	−	4.15637i	−0.144531	−	0.144531i	−0.775670	+	0.631139i	$0.782588\pi$
$828$		0			0
$829$	−0.00125445	+	0.00217277i	−4.35688e−5	+	7.54634e-5i	−0.866047	−	0.499962i	$-0.833347\pi$
$829$	−0.00125445	+	0.00217277i	−4.35688e−5	+	7.54634e-5i	0.866004	+	0.500038i	$0.166681\pi$
$830$		0			0
$831$	−16.0311	+	9.25555i	−0.556112	+	0.321071i
$832$		0			0
$833$	1.11456	+	1.51208i	0.0386174	+	0.0523905i
$834$		0			0
$835$	6.99271	+	6.26904i	0.241993	+	0.216949i
$836$		0			0
$837$	19.9260	−	5.33916i	0.688744	−	0.184549i
$838$		0			0
$839$	1.17778			0.0406615			0.0203308	−	0.999793i	$-0.493528\pi$
$839$	1.17778			0.0406615			0.0203308	+	0.999793i	$0.493528\pi$
$840$		0			0
$841$	27.2608			0.940028
$842$		0			0
$843$	28.7296	−	7.69808i	0.989500	−	0.265136i
$844$		0			0
$845$	9.15034	−	0.499319i	0.314781	−	0.0171771i
$846$		0			0
$847$	−0.484137	−	0.562919i	−0.0166351	−	0.0193421i
$848$		0			0
$849$	−25.6123	+	14.7873i	−0.879012	+	0.507498i
$850$		0			0
$851$	32.1056	−	55.6086i	1.10057	−	1.90624i
$852$		0			0
$853$	−11.8453	−	11.8453i	−0.405577	−	0.405577i	0.474616	−	0.880193i	$-0.342587\pi$
$853$	−11.8453	−	11.8453i	−0.405577	−	0.405577i	−0.880193	+	0.474616i	$0.842587\pi$
$854$		0			0
$855$	−1.42729	+	2.81619i	−0.0488122	+	0.0963116i
$856$		0			0
$857$	9.33361	+	34.8335i	0.318830	+	1.18989i	0.920370	+	0.391048i	$0.127887\pi$
$857$	9.33361	+	34.8335i	0.318830	+	1.18989i	−0.601540	+	0.798842i	$0.705446\pi$
$858$		0			0
$859$	−12.4292	−	21.5280i	−0.424080	−	0.734527i	0.572254	−	0.820076i	$-0.306069\pi$
$859$	−12.4292	−	21.5280i	−0.424080	−	0.734527i	−0.996334	+	0.0855488i	$0.972736\pi$
$860$		0			0
$861$	7.84323	+	16.2992i	0.267297	+	0.555474i
$862$		0			0
$863$	37.1778	+	9.96176i	1.26555	+	0.339102i	0.828323	−	0.560250i	$-0.189295\pi$
$863$	37.1778	+	9.96176i	1.26555	+	0.339102i	0.437224	+	0.899353i	$0.355962\pi$
$864$		0			0
$865$	9.99337	+	2.10166i	0.339785	+	0.0714587i
$866$		0			0
$867$	14.4629	−	14.4629i	0.491186	−	0.491186i
$868$		0			0
$869$		−	7.26183i		−	0.246341i
$870$		0			0
$871$	19.9449	+	11.5152i	0.675807	+	0.390177i
$872$		0			0
$873$	5.69444	−	21.2519i	0.192728	−	0.719269i
$874$		0			0
$875$	10.1498	+	27.7846i	0.343125	+	0.939290i
$876$		0			0
$877$	5.04053	−	18.8115i	0.170207	−	0.635220i	−0.827112	−	0.562037i	$-0.810018\pi$
$877$	5.04053	−	18.8115i	0.170207	−	0.635220i	0.997319	−	0.0731828i	$-0.0233157\pi$
$878$		0			0
$879$	−8.43478	−	4.86982i	−0.284498	−	0.164255i
$880$		0			0
$881$		−	9.12401i		−	0.307396i	−0.988118	−	0.153698i	$-0.950882\pi$
$881$		−	9.12401i		−	0.307396i	0.988118	−	0.153698i	$-0.0491182\pi$
$882$		0			0
$883$	−0.784643	+	0.784643i	−0.0264053	+	0.0264053i	−0.720186	−	0.693781i	$-0.755944\pi$
$883$	−0.784643	+	0.784643i	−0.0264053	+	0.0264053i	0.693781	+	0.720186i	$0.255944\pi$
$884$		0			0
$885$	20.7271	+	4.35903i	0.696733	+	0.146527i
$886$		0			0
$887$	−5.26804	−	1.41157i	−0.176883	−	0.0473958i	0.169290	−	0.985566i	$-0.445853\pi$
$887$	−5.26804	−	1.41157i	−0.176883	−	0.0473958i	−0.346174	+	0.938170i	$0.612519\pi$
$888$		0			0
$889$	−15.1952	−	10.3666i	−0.509630	−	0.347684i
$890$		0			0
$891$	3.37203	+	5.84053i	0.112967	+	0.195665i
$892$		0			0
$893$	0.223993	+	0.835954i	0.00749565	+	0.0279741i
$894$		0			0
$895$	8.42133	−	16.6162i	0.281494	−	0.555418i
$896$		0			0
$897$	−27.7245	−	27.7245i	−0.925694	−	0.925694i
$898$		0			0
$899$	−2.47966	+	4.29489i	−0.0827011	+	0.143243i
$900$		0			0
$901$	−3.13847	+	1.81200i	−0.104558	+	0.0603664i
$902$		0			0
$903$	3.90997	−	11.1633i	0.130116	−	0.371491i
$904$		0			0
$905$	−42.7775	+	2.33430i	−1.42197	+	0.0775946i
$906$		0			0
$907$	24.0641	−	6.44797i	0.799037	−	0.214101i	0.163876	−	0.986481i	$-0.447600\pi$
$907$	24.0641	−	6.44797i	0.799037	−	0.214101i	0.635161	+	0.772380i	$0.280934\pi$
$908$		0			0
$909$	26.2683			0.871264
$910$		0			0
$911$	3.36878			0.111613			0.0558063	−	0.998442i	$-0.482227\pi$
$911$	3.36878			0.111613			0.0558063	+	0.998442i	$0.482227\pi$
$912$		0			0
$913$	25.2328	−	6.76110i	0.835082	−	0.223760i
$914$		0			0
$915$	−22.5341	−	20.2021i	−0.744955	−	0.667860i
$916$		0			0
$917$	27.1740	−	23.3709i	0.897363	−	0.771774i
$918$		0			0
$919$	13.9256	−	8.03995i	0.459363	−	0.265214i	−0.252413	−	0.967620i	$-0.581224\pi$
$919$	13.9256	−	8.03995i	0.459363	−	0.265214i	0.711777	+	0.702406i	$0.247891\pi$
$920$		0			0
$921$	0.557682	−	0.965934i	0.0183762	−	0.0318286i
$922$		0			0
$923$	−39.5442	−	39.5442i	−1.30161	−	1.30161i
$924$		0			0
$925$	−6.22578	+	40.4349i	−0.204702	+	1.32949i
$926$		0			0
$927$	−7.12787	−	26.6016i	−0.234110	−	0.873710i
$928$		0			0
$929$	−25.1693	−	43.5945i	−0.825778	−	1.43029i	−0.901323	−	0.433147i	$-0.857403\pi$
$929$	−25.1693	−	43.5945i	−0.825778	−	1.43029i	0.0755452	−	0.997142i	$-0.475930\pi$
$930$		0			0
$931$	5.01513	+	4.00436i	0.164364	+	0.131238i
$932$		0			0
$933$	9.09740	+	2.43764i	0.297836	+	0.0798048i
$934$		0			0
$935$	0.414774	−	1.97224i	0.0135645	−	0.0644991i
$936$		0			0
$937$	−21.4027	+	21.4027i	−0.699194	+	0.699194i	−0.964237	−	0.265043i	$-0.914614\pi$
$937$	−21.4027	+	21.4027i	−0.699194	+	0.699194i	0.265043	+	0.964237i	$0.414614\pi$
$938$		0			0
$939$			4.19047i			0.136751i
$940$		0			0
$941$	−12.1498	−	7.01467i	−0.396071	−	0.228672i	0.288716	−	0.957415i	$-0.406772\pi$
$941$	−12.1498	−	7.01467i	−0.396071	−	0.228672i	−0.684787	+	0.728743i	$0.740105\pi$
$942$		0			0
$943$	−11.4924	+	42.8903i	−0.374245	+	1.39670i
$944$		0			0
$945$	27.7656	+	16.8019i	0.903216	+	0.546565i
$946$		0			0
$947$	−3.23965	+	12.0906i	−0.105275	+	0.392890i	−0.998376	−	0.0569649i	$-0.981858\pi$
$947$	−3.23965	+	12.0906i	−0.105275	+	0.392890i	0.893102	+	0.449855i	$0.148524\pi$
$948$		0			0
$949$	27.1884	+	15.6972i	0.882572	+	0.509553i
$950$		0			0
$951$			0.981580i			0.0318299i
$952$		0			0
$953$	5.25245	−	5.25245i	0.170143	−	0.170143i	−0.616899	−	0.787042i	$-0.711611\pi$
$953$	5.25245	−	5.25245i	0.170143	−	0.170143i	0.787042	+	0.616899i	$0.211611\pi$
$954$		0			0
$955$	−8.50681	+	5.55048i	−0.275274	+	0.179609i
$956$		0			0
$957$	−5.16950	−	1.38516i	−0.167106	−	0.0447760i
$958$		0			0
$959$	−36.8168	+	17.7164i	−1.18888	+	0.572092i
$960$		0			0
$961$	−8.42922	−	14.5998i	−0.271910	−	0.470963i
$962$		0			0
$963$	−3.16603	−	11.8158i	−0.102024	−	0.380759i
$964$		0			0
$965$	19.1287	−	6.26087i	0.615773	−	0.201545i
$966$		0			0
$967$	3.53231	+	3.53231i	0.113591	+	0.113591i	0.761618	−	0.648026i	$-0.224405\pi$
$967$	3.53231	+	3.53231i	0.113591	+	0.113591i	−0.648026	+	0.761618i	$0.724405\pi$
$968$		0			0
$969$	−0.148635	+	0.257443i	−0.00477484	+	0.00827027i
$970$		0			0
$971$	−7.52979	+	4.34733i	−0.241642	+	0.139512i	−0.615931	−	0.787800i	$-0.711220\pi$
$971$	−7.52979	+	4.34733i	−0.241642	+	0.139512i	0.374289	+	0.927312i	$0.377887\pi$
$972$		0			0
$973$	27.1711	−	5.13261i	0.871067	−	0.164544i
$974$		0			0
$975$	22.8649	+	10.0623i	0.732264	+	0.322251i
$976$		0			0
$977$	−29.3199	+	7.85624i	−0.938026	+	0.251343i	−0.695274	−	0.718745i	$-0.744717\pi$
$977$	−29.3199	+	7.85624i	−0.938026	+	0.251343i	−0.242752	+	0.970088i	$0.578050\pi$
$978$		0			0
$979$	−9.05620			−0.289437
$980$		0			0
$981$	−22.3444			−0.713402
$982$		0			0
$983$	−15.8743	+	4.25351i	−0.506312	+	0.135666i	−0.502928	−	0.864328i	$-0.667744\pi$
$983$	−15.8743	+	4.25351i	−0.506312	+	0.135666i	−0.00338392	+	0.999994i	$0.501077\pi$
$984$		0			0
$985$	12.0647	−	13.4574i	0.384413	−	0.428788i
$986$		0			0
$987$	2.96524	−	0.560132i	0.0943848	−	0.0178292i
$988$		0			0
$989$	25.1462	−	14.5182i	0.799603	−	0.461651i
$990$		0			0
$991$	17.3742	−	30.0929i	0.551908	−	0.955933i	−0.446229	−	0.894919i	$-0.647233\pi$
$991$	17.3742	−	30.0929i	0.551908	−	0.955933i	0.998137	−	0.0610142i	$-0.0194335\pi$
$992$		0			0
$993$	−13.3266	−	13.3266i	−0.422908	−	0.422908i
$994$		0			0
$995$	−27.3511	−	13.8619i	−0.867089	−	0.439453i
$996$		0			0
$997$	10.4901	+	39.1497i	0.332226	+	1.23988i	0.906845	+	0.421464i	$0.138484\pi$
$997$	10.4901	+	39.1497i	0.332226	+	1.23988i	−0.574619	+	0.818421i	$0.694850\pi$
$998$		0			0
$999$	22.4426	+	38.8717i	0.710052	+	1.22985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ci.e.17.8		48
4.3	odd	2		280.2.bo.a.17.5	✓	48
5.3	odd	4	inner	560.2.ci.e.353.8		48
7.5	odd	6	inner	560.2.ci.e.257.8		48
20.3	even	4		280.2.bo.a.73.5	yes	48
28.19	even	6		280.2.bo.a.257.5	yes	48
35.33	even	12	inner	560.2.ci.e.33.8		48
140.103	odd	12		280.2.bo.a.33.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bo.a.17.5	✓	48	4.3	odd	2
280.2.bo.a.33.5	yes	48	140.103	odd	12
280.2.bo.a.73.5	yes	48	20.3	even	4
280.2.bo.a.257.5	yes	48	28.19	even	6
560.2.ci.e.17.8		48	1.1	even	1	trivial
560.2.ci.e.33.8		48	35.33	even	12	inner
560.2.ci.e.257.8		48	7.5	odd	6	inner
560.2.ci.e.353.8		48	5.3	odd	4	inner

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)

\(f(q)\)	\(=\)	\(q+(1.16710 - 0.312724i) q^{3} +(-0.121837 - 2.23275i) q^{5} +(2.59977 - 0.491095i) q^{7} +(-1.33374 + 0.770036i) q^{9} +O(q^{10})\)	\(q+(1.16710 - 0.312724i) q^{3} +(-0.121837 - 2.23275i) q^{5} +(2.59977 - 0.491095i) q^{7} +(-1.33374 + 0.770036i) q^{9} +(1.67933 - 2.90869i) q^{11} +(-2.92389 - 2.92389i) q^{13} +(-0.840431 - 2.56774i) q^{15} +(0.0694548 + 0.259209i) q^{17} +(0.458405 + 0.793981i) q^{19} +(2.88063 - 1.38617i) q^{21} +(7.58021 + 2.03111i) q^{23} +(-4.97031 + 0.544063i) q^{25} +(-3.87894 + 3.87894i) q^{27} -1.31878i q^{29} +(-3.25671 - 1.88026i) q^{31} +(1.05034 - 3.91991i) q^{33} +(-1.41324 - 5.74480i) q^{35} +(2.11773 - 7.90347i) q^{37} +(-4.32685 - 2.49811i) q^{39} +5.65819i q^{41} +(2.61631 - 2.61631i) q^{43} +(1.88180 + 2.88409i) q^{45} +(0.911807 + 0.244318i) q^{47} +(6.51765 - 2.55347i) q^{49} +(0.162122 + 0.280803i) q^{51} +(3.49525 + 13.0444i) q^{53} +(-6.69897 - 3.39514i) q^{55} +(0.783303 + 0.783303i) q^{57} +(-3.91972 + 6.78916i) q^{59} +(9.70077 - 5.60074i) q^{61} +(-3.08927 + 2.65691i) q^{63} +(-6.17206 + 6.88454i) q^{65} +(-5.37983 + 1.44152i) q^{67} +9.48206 q^{69} +13.5245 q^{71} +(-7.33366 + 1.96505i) q^{73} +(-5.63073 + 2.18932i) q^{75} +(2.93744 - 8.38665i) q^{77} +(1.87245 - 1.08106i) q^{79} +(-1.00398 + 1.73894i) q^{81} +(5.49970 + 5.49970i) q^{83} +(0.570285 - 0.186656i) q^{85} +(-0.412415 - 1.53915i) q^{87} +(-1.34818 - 2.33512i) q^{89} +(-9.03736 - 6.16554i) q^{91} +(-4.38892 - 1.17601i) q^{93} +(1.71691 - 1.12024i) q^{95} +(-10.1018 + 10.1018i) q^{97} +5.17259i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7}+O(q^{10}) \) 48 * q + 4 * q^7	\( 48 q + 4 q^{7} - 4 q^{11} - 8 q^{15} - 4 q^{21} + 4 q^{23} - 8 q^{25} - 36 q^{33} - 24 q^{35} + 8 q^{37} + 16 q^{43} + 48 q^{45} - 24 q^{51} + 16 q^{53} - 96 q^{57} - 36 q^{61} + 68 q^{63} + 12 q^{65} + 16 q^{67} + 64 q^{71} - 48 q^{73} + 48 q^{75} + 4 q^{77} - 40 q^{85} + 12 q^{87} + 80 q^{91} - 24 q^{95}+O(q^{100}) \) 48 * q + 4 * q^7 - 4 * q^11 - 8 * q^15 - 4 * q^21 + 4 * q^23 - 8 * q^25 - 36 * q^33 - 24 * q^35 + 8 * q^37 + 16 * q^43 + 48 * q^45 - 24 * q^51 + 16 * q^53 - 96 * q^57 - 36 * q^61 + 68 * q^63 + 12 * q^65 + 16 * q^67 + 64 * q^71 - 48 * q^73 + 48 * q^75 + 4 * q^77 - 40 * q^85 + 12 * q^87 + 80 * q^91 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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