LMFDB - Embedded newform 1120.2.bz.e.591.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(271,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1120.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bz (of order $6$, degree $2$, 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:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			591.6
Character	$\chi$	$=$	1120.591
Dual form			1120.2.bz.e.271.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.784482 - 0.452921i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.23347 + 2.34063i) q^{7} +(-1.08973 - 1.88746i) q^{9} +O(q^{10})$	\(q+(-0.784482 - 0.452921i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.23347 + 2.34063i) q^{7} +(-1.08973 - 1.88746i) q^{9} +(-0.620880 + 1.07539i) q^{11} +4.31348 q^{13} +0.905842i q^{15} +(-1.49339 - 0.862209i) q^{17} +(-2.12801 + 1.22861i) q^{19} +(2.02775 - 1.27752i) q^{21} +(0.393079 - 0.226944i) q^{23} +(-0.500000 + 0.866025i) q^{25} +4.69176i q^{27} +7.69695i q^{29} +(-0.133444 + 0.231133i) q^{31} +(0.974138 - 0.562419i) q^{33} +(2.64378 - 0.102102i) q^{35} +(4.24881 - 2.45305i) q^{37} +(-3.38385 - 1.95367i) q^{39} +12.2703i q^{41} -1.73856 q^{43} +(-1.08973 + 1.88746i) q^{45} +(5.37669 + 9.31270i) q^{47} +(-3.95712 - 5.77419i) q^{49} +(0.781025 + 1.35278i) q^{51} +(7.50728 + 4.33433i) q^{53} +1.24176 q^{55} +2.22584 q^{57} +(4.83628 + 2.79223i) q^{59} +(0.462932 + 0.801822i) q^{61} +(5.76199 - 0.222526i) q^{63} +(-2.15674 - 3.73558i) q^{65} +(-0.465968 + 0.807080i) q^{67} -0.411152 q^{69} +8.36052i q^{71} +(-6.21972 - 3.59095i) q^{73} +(0.784482 - 0.452921i) q^{75} +(-1.75127 - 2.77972i) q^{77} +(9.56196 - 5.52060i) q^{79} +(-1.14418 + 1.98177i) q^{81} -8.49133i q^{83} +1.72442i q^{85} +(3.48611 - 6.03812i) q^{87} +(-6.91420 + 3.99191i) q^{89} +(-5.32054 + 10.0963i) q^{91} +(0.209370 - 0.120880i) q^{93} +(2.12801 + 1.22861i) q^{95} +3.92866i q^{97} +2.70635 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9	$ 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9} - 8 q^{11} + 20 q^{13} + 6 q^{17} - 18 q^{19} - 26 q^{21} - 18 q^{23} - 12 q^{25} + 6 q^{31} + 12 q^{33} + 8 q^{35} + 18 q^{39} - 32 q^{43} + 12 q^{45} + 8 q^{49} + 22 q^{51} + 30 q^{53} + 16 q^{55} - 44 q^{57} + 18 q^{59} + 22 q^{61} + 12 q^{63} - 10 q^{65} + 8 q^{67} - 12 q^{69} + 30 q^{73} + 12 q^{75} - 32 q^{77} - 6 q^{79} - 4 q^{81} - 14 q^{87} - 60 q^{89} - 18 q^{91} - 18 q^{93} + 18 q^{95} + 56 q^{99}+O(q^{100}) $ 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9 - 8 * q^11 + 20 * q^13 + 6 * q^17 - 18 * q^19 - 26 * q^21 - 18 * q^23 - 12 * q^25 + 6 * q^31 + 12 * q^33 + 8 * q^35 + 18 * q^39 - 32 * q^43 + 12 * q^45 + 8 * q^49 + 22 * q^51 + 30 * q^53 + 16 * q^55 - 44 * q^57 + 18 * q^59 + 22 * q^61 + 12 * q^63 - 10 * q^65 + 8 * q^67 - 12 * q^69 + 30 * q^73 + 12 * q^75 - 32 * q^77 - 6 * q^79 - 4 * q^81 - 14 * q^87 - 60 * q^89 - 18 * q^91 - 18 * q^93 + 18 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.784482	−	0.452921i	−0.452921	−	0.261494i	0.256142	−	0.966639i	$-0.417549\pi$
$3$	−0.784482	−	0.452921i	−0.452921	−	0.261494i	−0.709063	+	0.705145i	$0.750882\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−1.23347	+	2.34063i	−0.466207	+	0.884676i
$7$	−1.23347	+	2.34063i	−0.466207	+	0.884676i
$8$		0			0
$9$	−1.08973	−	1.88746i	−0.363242	−	0.629153i
$10$		0			0
$11$	−0.620880	+	1.07539i	−0.187202	+	0.324244i	−0.944316	−	0.329039i	$-0.893275\pi$
$11$	−0.620880	+	1.07539i	−0.187202	+	0.324244i	0.757114	+	0.653283i	$0.226609\pi$
$12$		0			0
$13$	4.31348			1.19634			0.598172	−	0.801368i	$-0.295894\pi$
$13$	4.31348			1.19634			0.598172	+	0.801368i	$0.295894\pi$
$14$		0			0
$15$			0.905842i			0.233887i
$16$		0			0
$17$	−1.49339	−	0.862209i	−0.362200	−	0.209116i	0.307845	−	0.951436i	$-0.400392\pi$
$17$	−1.49339	−	0.862209i	−0.362200	−	0.209116i	−0.670046	+	0.742320i	$0.733725\pi$
$18$		0			0
$19$	−2.12801	+	1.22861i	−0.488198	+	0.281861i	−0.723827	−	0.689982i	$-0.757618\pi$
$19$	−2.12801	+	1.22861i	−0.488198	+	0.281861i	0.235628	+	0.971843i	$0.424285\pi$
$20$		0			0
$21$	2.02775	−	1.27752i	0.442492	−	0.278778i
$22$		0			0
$23$	0.393079	−	0.226944i	0.0819627	−	0.0473212i	−0.458459	−	0.888716i	$-0.651598\pi$
$23$	0.393079	−	0.226944i	0.0819627	−	0.0473212i	0.540421	+	0.841395i	$0.318265\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$			4.69176i			0.902930i
$28$		0			0
$29$			7.69695i			1.42929i	0.699488	+	0.714644i	$0.253411\pi$
$29$			7.69695i			1.42929i	−0.699488	+	0.714644i	$0.746589\pi$
$30$		0			0
$31$	−0.133444	+	0.231133i	−0.0239673	+	0.0415126i	−0.877760	−	0.479100i	$-0.840963\pi$
$31$	−0.133444	+	0.231133i	−0.0239673	+	0.0415126i	0.853793	+	0.520613i	$0.174296\pi$
$32$		0			0
$33$	0.974138	−	0.562419i	0.169576	−	0.0979045i
$34$		0			0
$35$	2.64378	−	0.102102i	0.446880	−	0.0172584i
$36$		0			0
$37$	4.24881	−	2.45305i	0.698501	−	0.403280i	−0.108288	−	0.994120i	$-0.534537\pi$
$37$	4.24881	−	2.45305i	0.698501	−	0.403280i	0.806789	+	0.590840i	$0.201204\pi$
$38$		0			0
$39$	−3.38385	−	1.95367i	−0.541849	−	0.312837i
$40$		0			0
$41$			12.2703i			1.91630i	0.286271	+	0.958149i	$0.407584\pi$
$41$			12.2703i			1.91630i	−0.286271	+	0.958149i	$0.592416\pi$
$42$		0			0
$43$	−1.73856			−0.265128			−0.132564	−	0.991174i	$-0.542321\pi$
$43$	−1.73856			−0.265128			−0.132564	+	0.991174i	$0.542321\pi$
$44$		0			0
$45$	−1.08973	+	1.88746i	−0.162447	+	0.281366i
$46$		0			0
$47$	5.37669	+	9.31270i	0.784271	+	1.35840i	0.929434	+	0.368990i	$0.120296\pi$
$47$	5.37669	+	9.31270i	0.784271	+	1.35840i	−0.145162	+	0.989408i	$0.546370\pi$
$48$		0			0
$49$	−3.95712	−	5.77419i	−0.565302	−	0.824884i
$50$		0			0
$51$	0.781025	+	1.35278i	0.109365	+	0.189426i
$52$		0			0
$53$	7.50728	+	4.33433i	1.03120	+	0.595366i	0.917329	−	0.398129i	$-0.130340\pi$
$53$	7.50728	+	4.33433i	1.03120	+	0.595366i	0.113875	+	0.993495i	$0.463674\pi$
$54$		0			0
$55$	1.24176			0.167439
$56$		0			0
$57$	2.22584			0.294820
$58$		0			0
$59$	4.83628	+	2.79223i	0.629630	+	0.363517i	0.780609	−	0.625020i	$-0.214909\pi$
$59$	4.83628	+	2.79223i	0.629630	+	0.363517i	−0.150978	+	0.988537i	$0.548242\pi$
$60$		0			0
$61$	0.462932	+	0.801822i	0.0592724	+	0.102663i	0.894139	−	0.447790i	$-0.147789\pi$
$61$	0.462932	+	0.801822i	0.0592724	+	0.102663i	−0.834867	+	0.550452i	$0.814455\pi$
$62$		0			0
$63$	5.76199	−	0.222526i	0.725942	−	0.0280357i
$64$		0			0
$65$	−2.15674	−	3.73558i	−0.267511	−	0.463342i
$66$		0			0
$67$	−0.465968	+	0.807080i	−0.0569270	+	0.0986005i	−0.893085	−	0.449889i	$-0.851464\pi$
$67$	−0.465968	+	0.807080i	−0.0569270	+	0.0986005i	0.836158	+	0.548489i	$0.184797\pi$
$68$		0			0
$69$	−0.411152			−0.0494968
$70$		0			0
$71$			8.36052i			0.992211i	0.868262	+	0.496105i	$0.165237\pi$
$71$			8.36052i			0.992211i	−0.868262	+	0.496105i	$0.834763\pi$
$72$		0			0
$73$	−6.21972	−	3.59095i	−0.727963	−	0.420289i	0.0897137	−	0.995968i	$-0.471405\pi$
$73$	−6.21972	−	3.59095i	−0.727963	−	0.420289i	−0.817676	+	0.575678i	$0.804738\pi$
$74$		0			0
$75$	0.784482	−	0.452921i	0.0905842	−	0.0522988i
$76$		0			0
$77$	−1.75127	−	2.77972i	−0.199576	−	0.316778i
$78$		0			0
$79$	9.56196	−	5.52060i	1.07580	−	0.621116i	0.146043	−	0.989278i	$-0.453346\pi$
$79$	9.56196	−	5.52060i	1.07580	−	0.621116i	0.929762	+	0.368162i	$0.120013\pi$
$80$		0			0
$81$	−1.14418	+	1.98177i	−0.127131	+	0.220197i
$82$		0			0
$83$		−	8.49133i		−	0.932045i	−0.884773	−	0.466022i	$-0.845687\pi$
$83$		−	8.49133i		−	0.932045i	0.884773	−	0.466022i	$-0.154313\pi$
$84$		0			0
$85$			1.72442i			0.187039i
$86$		0			0
$87$	3.48611	−	6.03812i	0.373750	−	0.647355i
$88$		0			0
$89$	−6.91420	+	3.99191i	−0.732903	+	0.423142i	−0.819483	−	0.573103i	$-0.805740\pi$
$89$	−6.91420	+	3.99191i	−0.732903	+	0.423142i	0.0865800	+	0.996245i	$0.472406\pi$
$90$		0			0
$91$	−5.32054	+	10.0963i	−0.557744	+	1.05838i
$92$		0			0
$93$	0.209370	−	0.120880i	0.0217106	−	0.0125346i
$94$		0			0
$95$	2.12801	+	1.22861i	0.218329	+	0.126052i
$96$		0			0
$97$			3.92866i			0.398895i	0.979909	+	0.199447i	$0.0639147\pi$
$97$			3.92866i			0.398895i	−0.979909	+	0.199447i	$0.936085\pi$
$98$		0			0
$99$	2.70635			0.271999
$100$		0			0
$101$	−4.82944	+	8.36483i	−0.480547	+	0.832332i	−0.999751	−	0.0223184i	$-0.992895\pi$
$101$	−4.82944	+	8.36483i	−0.480547	+	0.832332i	0.519204	+	0.854651i	$0.326229\pi$
$102$		0			0
$103$	3.82962	+	6.63310i	0.377344	+	0.653578i	0.990675	−	0.136247i	$-0.0435042\pi$
$103$	3.82962	+	6.63310i	0.377344	+	0.653578i	−0.613331	+	0.789826i	$0.710171\pi$
$104$		0			0
$105$	−2.12024	−	1.11733i	−0.206914	−	0.109040i
$106$		0			0
$107$	−8.44757	−	14.6316i	−0.816657	−	1.41449i	−0.908132	−	0.418684i	$-0.862491\pi$
$107$	−8.44757	−	14.6316i	−0.816657	−	1.41449i	0.0914746	−	0.995807i	$-0.470842\pi$
$108$		0			0
$109$	7.93420	+	4.58081i	0.759959	+	0.438762i	0.829281	−	0.558832i	$-0.188750\pi$
$109$	7.93420	+	4.58081i	0.759959	+	0.438762i	−0.0693221	+	0.997594i	$0.522084\pi$
$110$		0			0
$111$	−4.44416			−0.421821
$112$		0			0
$113$	20.4047			1.91952			0.959758	−	0.280829i	$-0.0906094\pi$
$113$	20.4047			1.91952			0.959758	+	0.280829i	$0.0906094\pi$
$114$		0			0
$115$	−0.393079	−	0.226944i	−0.0366548	−	0.0211627i
$116$		0			0
$117$	−4.70051	−	8.14152i	−0.434562	−	0.752684i
$118$		0			0
$119$	3.86016	−	2.43197i	0.353861	−	0.222938i
$120$		0			0
$121$	4.72902	+	8.19090i	0.429911	+	0.744627i
$122$		0			0
$123$	5.55747	−	9.62582i	0.501100	−	0.867931i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$		−	5.18278i		−	0.459897i	−0.973203	−	0.229949i	$-0.926144\pi$
$127$		−	5.18278i		−	0.459897i	0.973203	−	0.229949i	$-0.0738558\pi$
$128$		0			0
$129$	1.36387	+	0.787430i	0.120082	+	0.0693293i
$130$		0			0
$131$	−11.7551	+	6.78684i	−1.02705	+	0.592969i	−0.916139	−	0.400861i	$-0.868711\pi$
$131$	−11.7551	+	6.78684i	−1.02705	+	0.592969i	−0.110913	+	0.993830i	$0.535378\pi$
$132$		0			0
$133$	−0.250886	−	6.49633i	−0.0217546	−	0.563303i
$134$		0			0
$135$	4.06319	−	2.34588i	0.349703	−	0.201901i
$136$		0			0
$137$	−6.46913	+	11.2049i	−0.552695	+	0.957296i	0.445384	+	0.895340i	$0.353067\pi$
$137$	−6.46913	+	11.2049i	−0.552695	+	0.957296i	−0.998079	+	0.0619561i	$0.980266\pi$
$138$		0			0
$139$			17.8027i			1.51001i	0.655720	+	0.755004i	$0.272365\pi$
$139$			17.8027i			1.51001i	−0.655720	+	0.755004i	$0.727635\pi$
$140$		0			0
$141$		−	9.74087i		−	0.820329i
$142$		0			0
$143$	−2.67815	+	4.63869i	−0.223958	+	0.387907i
$144$		0			0
$145$	6.66576	−	3.84848i	0.553561	−	0.319599i
$146$		0			0
$147$	0.489037	+	6.32201i	0.0403351	+	0.521430i
$148$		0			0
$149$	−12.7146	+	7.34080i	−1.04162	+	0.601382i	−0.920293	−	0.391230i	$-0.872050\pi$
$149$	−12.7146	+	7.34080i	−1.04162	+	0.601382i	−0.121331	+	0.992612i	$0.538716\pi$
$150$		0			0
$151$	−14.9018	−	8.60359i	−1.21270	−	0.700150i	−0.249350	−	0.968414i	$-0.580217\pi$
$151$	−14.9018	−	8.60359i	−1.21270	−	0.700150i	−0.963346	+	0.268264i	$0.913550\pi$
$152$		0			0
$153$			3.75829i			0.303839i
$154$		0			0
$155$	0.266889			0.0214370
$156$		0			0
$157$	−5.35139	+	9.26887i	−0.427087	+	0.739737i	−0.996613	−	0.0822369i	$-0.973794\pi$
$157$	−5.35139	+	9.26887i	−0.427087	+	0.739737i	0.569526	+	0.821974i	$0.307127\pi$
$158$		0			0
$159$	−3.92622	−	6.80041i	−0.311369	−	0.539307i
$160$		0			0
$161$	0.0463429	+	1.19998i	0.00365233	+	0.0945719i
$162$		0			0
$163$	−12.5462	−	21.7307i	−0.982696	−	1.70208i	−0.651760	−	0.758426i	$-0.725969\pi$
$163$	−12.5462	−	21.7307i	−0.982696	−	1.70208i	−0.330936	−	0.943653i	$-0.607364\pi$
$164$		0			0
$165$	−0.974138	−	0.562419i	−0.0758365	−	0.0437842i
$166$		0			0
$167$	−6.43113			−0.497656			−0.248828	−	0.968548i	$-0.580045\pi$
$167$	−6.43113			−0.497656			−0.248828	+	0.968548i	$0.580045\pi$
$168$		0			0
$169$	5.60611			0.431239
$170$		0			0
$171$	4.63789	+	2.67768i	0.354668	+	0.204768i
$172$		0			0
$173$	−1.08576	−	1.88059i	−0.0825486	−	0.142978i	0.821795	−	0.569783i	$-0.192973\pi$
$173$	−1.08576	−	1.88059i	−0.0825486	−	0.142978i	−0.904344	+	0.426804i	$0.859639\pi$
$174$		0			0
$175$	−1.41031	−	2.23853i	−0.106610	−	0.169217i
$176$		0			0
$177$	−2.52932	−	4.38091i	−0.190115	−	0.329289i
$178$		0			0
$179$	11.3858	−	19.7209i	0.851018	−	1.47401i	−0.0292733	−	0.999571i	$-0.509319\pi$
$179$	11.3858	−	19.7209i	0.851018	−	1.47401i	0.880291	−	0.474434i	$-0.157347\pi$
$180$		0			0
$181$	−20.2848			−1.50776			−0.753879	−	0.657013i	$-0.771820\pi$
$181$	−20.2848			−1.50776			−0.753879	+	0.657013i	$0.771820\pi$
$182$		0			0
$183$		−	0.838686i		−	0.0619975i
$184$		0			0
$185$	−4.24881	−	2.45305i	−0.312379	−	0.180352i
$186$		0			0
$187$	1.85443	−	1.07066i	0.135609	−	0.0782941i
$188$		0			0
$189$	−10.9817	−	5.78714i	−0.798801	−	0.420952i
$190$		0			0
$191$	1.45879	−	0.842233i	0.105554	−	0.0609419i	−0.446293	−	0.894887i	$-0.647256\pi$
$191$	1.45879	−	0.842233i	0.105554	−	0.0609419i	0.551848	+	0.833945i	$0.313923\pi$
$192$		0			0
$193$	12.3298	−	21.3558i	0.887517	−	1.53722i	0.0447160	−	0.999000i	$-0.485762\pi$
$193$	12.3298	−	21.3558i	0.887517	−	1.53722i	0.842801	−	0.538225i	$-0.180905\pi$
$194$		0			0
$195$			3.90733i			0.279810i
$196$		0			0
$197$		−	1.66437i		−	0.118582i	−0.998241	−	0.0592908i	$-0.981116\pi$
$197$		−	1.66437i		−	0.118582i	0.998241	−	0.0592908i	$-0.0188839\pi$
$198$		0			0
$199$	6.39700	−	11.0799i	0.453471	−	0.785435i	−0.545128	−	0.838353i	$-0.683519\pi$
$199$	6.39700	−	11.0799i	0.453471	−	0.785435i	0.998599	+	0.0529181i	$0.0168522\pi$
$200$		0			0
$201$	0.731087	−	0.422093i	0.0515669	−	0.0297721i
$202$		0			0
$203$	−18.0157	−	9.49394i	−1.26446	−	0.666344i
$204$		0			0
$205$	10.6264	−	6.13515i	0.742179	−	0.428497i
$206$		0			0
$207$	−0.856697	−	0.494614i	−0.0595446	−	0.0343781i
$208$		0			0
$209$		−	3.05126i		−	0.211060i
$210$		0			0
$211$	16.8109			1.15731			0.578655	−	0.815573i	$-0.303578\pi$
$211$	16.8109			1.15731			0.578655	+	0.815573i	$0.303578\pi$
$212$		0			0
$213$	3.78665	−	6.55868i	0.259457	−	0.449393i
$214$		0			0
$215$	0.869279	+	1.50564i	0.0592844	+	0.102684i
$216$		0			0
$217$	−0.376397	−	0.597439i	−0.0255515	−	0.0405568i
$218$		0			0
$219$	3.25284	+	5.63408i	0.219806	+	0.380716i
$220$		0			0
$221$	−6.44171	−	3.71912i	−0.433316	−	0.250175i
$222$		0			0
$223$	−23.8692			−1.59840			−0.799200	−	0.601065i	$-0.794743\pi$
$223$	−23.8692			−1.59840			−0.799200	+	0.601065i	$0.794743\pi$
$224$		0			0
$225$	2.17945			0.145297
$226$		0			0
$227$	6.71810	+	3.87870i	0.445896	+	0.257438i	0.706095	−	0.708117i	$-0.250455\pi$
$227$	6.71810	+	3.87870i	0.445896	+	0.257438i	−0.260199	+	0.965555i	$0.583788\pi$
$228$		0			0
$229$	−2.45190	−	4.24681i	−0.162026	−	0.280637i	0.773569	−	0.633712i	$-0.218470\pi$
$229$	−2.45190	−	4.24681i	−0.162026	−	0.280637i	−0.935595	+	0.353075i	$0.885136\pi$
$230$		0			0
$231$	0.114848	+	2.97382i	0.00755645	+	0.195663i
$232$		0			0
$233$	−8.58535	−	14.8703i	−0.562445	−	0.974183i	−0.997282	−	0.0736741i	$-0.976528\pi$
$233$	−8.58535	−	14.8703i	−0.562445	−	0.974183i	0.434838	−	0.900509i	$-0.356806\pi$
$234$		0			0
$235$	5.37669	−	9.31270i	0.350737	−	0.607494i
$236$		0			0
$237$	−10.0016			−0.649673
$238$		0			0
$239$			22.5691i			1.45987i	0.683516	+	0.729935i	$0.260450\pi$
$239$			22.5691i			1.45987i	−0.683516	+	0.729935i	$0.739550\pi$
$240$		0			0
$241$	−2.49414	−	1.43999i	−0.160662	−	0.0927580i	0.417514	−	0.908671i	$-0.362902\pi$
$241$	−2.49414	−	1.43999i	−0.160662	−	0.0927580i	−0.578175	+	0.815913i	$0.696235\pi$
$242$		0			0
$243$	13.9847	−	8.07409i	0.897121	−	0.517953i
$244$		0			0
$245$	−3.02203	+	6.31406i	−0.193071	+	0.403390i
$246$		0			0
$247$	−9.17911	+	5.29956i	−0.584053	+	0.337203i
$248$		0			0
$249$	−3.84590	+	6.66130i	−0.243724	+	0.422143i
$250$		0			0
$251$			12.3739i			0.781034i	0.920596	+	0.390517i	$0.127704\pi$
$251$			12.3739i			0.781034i	−0.920596	+	0.390517i	$0.872296\pi$
$252$		0			0
$253$			0.563621i			0.0354345i
$254$		0			0
$255$	0.781025	−	1.35278i	0.0489097	−	0.0847141i
$256$		0			0
$257$	4.89750	−	2.82758i	0.305498	−	0.176379i	−0.339412	−	0.940638i	$-0.610228\pi$
$257$	4.89750	−	2.82758i	0.305498	−	0.176379i	0.644910	+	0.764258i	$0.276895\pi$
$258$		0			0
$259$	0.500923	+	12.9707i	0.0311259	+	0.805959i
$260$		0			0
$261$	14.5277	−	8.38756i	0.899241	−	0.519177i
$262$		0			0
$263$	8.62649	+	4.98051i	0.531932	+	0.307111i	0.741803	−	0.670618i	$-0.233971\pi$
$263$	8.62649	+	4.98051i	0.531932	+	0.307111i	−0.209871	+	0.977729i	$0.567304\pi$
$264$		0			0
$265$		−	8.66866i		−	0.532511i
$266$		0			0
$267$	7.23208			0.442596
$268$		0			0
$269$	9.77791	−	16.9358i	0.596170	−	1.03260i	−0.397211	−	0.917727i	$-0.630022\pi$
$269$	9.77791	−	16.9358i	0.596170	−	1.03260i	0.993381	−	0.114869i	$-0.0366449\pi$
$270$		0			0
$271$	−16.1219	−	27.9240i	−0.979336	−	1.69626i	−0.664814	−	0.747009i	$-0.731489\pi$
$271$	−16.1219	−	27.9240i	−0.979336	−	1.69626i	−0.314522	−	0.949250i	$-0.601844\pi$
$272$		0			0
$273$	8.74668	−	5.51056i	0.529373	−	0.333514i
$274$		0			0
$275$	−0.620880	−	1.07539i	−0.0374404	−	0.0648488i
$276$		0			0
$277$	15.3351	+	8.85371i	0.921396	+	0.531968i	0.884080	−	0.467336i	$-0.154786\pi$
$277$	15.3351	+	8.85371i	0.921396	+	0.531968i	0.0373155	+	0.999304i	$0.488119\pi$
$278$		0			0
$279$	0.581671			0.0348237
$280$		0			0
$281$	−4.02367			−0.240032			−0.120016	−	0.992772i	$-0.538295\pi$
$281$	−4.02367			−0.240032			−0.120016	+	0.992772i	$0.538295\pi$
$282$		0			0
$283$	16.4300	+	9.48585i	0.976661	+	0.563875i	0.901260	−	0.433278i	$-0.142643\pi$
$283$	16.4300	+	9.48585i	0.976661	+	0.563875i	0.0754004	+	0.997153i	$0.475977\pi$
$284$		0			0
$285$	−1.11292	−	1.92764i	−0.0659238	−	0.114183i
$286$		0			0
$287$	−28.7202	−	15.1350i	−1.69530	−	0.893391i
$288$		0			0
$289$	−7.01319	−	12.1472i	−0.412541	−	0.714541i
$290$		0			0
$291$	1.77937	−	3.08196i	0.104309	−	0.180668i
$292$		0			0
$293$	10.3847			0.606678			0.303339	−	0.952883i	$-0.401899\pi$
$293$	10.3847			0.606678			0.303339	+	0.952883i	$0.401899\pi$
$294$		0			0
$295$		−	5.58446i		−	0.325140i
$296$		0			0
$297$	−5.04550	−	2.91302i	−0.292770	−	0.169031i
$298$		0			0
$299$	1.69554	−	0.978920i	0.0980556	−	0.0566124i
$300$		0			0
$301$	2.14446	−	4.06933i	0.123604	−	0.234552i
$302$		0			0
$303$	7.57722	−	4.37471i	0.435300	−	0.251320i
$304$		0			0
$305$	0.462932	−	0.801822i	0.0265074	−	0.0459122i
$306$		0			0
$307$			21.4468i			1.22403i	0.790846	+	0.612015i	$0.209641\pi$
$307$			21.4468i			1.22403i	−0.790846	+	0.612015i	$0.790359\pi$
$308$		0			0
$309$		−	6.93806i		−	0.394692i
$310$		0			0
$311$	−3.97738	+	6.88902i	−0.225536	+	0.390641i	−0.956480	−	0.291797i	$-0.905747\pi$
$311$	−3.97738	+	6.88902i	−0.225536	+	0.390641i	0.730944	+	0.682438i	$0.239080\pi$
$312$		0			0
$313$	−9.04094	+	5.21979i	−0.511024	+	0.295040i	−0.733255	−	0.679954i	$-0.762000\pi$
$313$	−9.04094	+	5.21979i	−0.511024	+	0.295040i	0.222230	+	0.974994i	$0.428666\pi$
$314$		0			0
$315$	−3.07371	−	4.87877i	−0.173184	−	0.274887i
$316$		0			0
$317$	−5.86432	+	3.38576i	−0.329373	+	0.190163i	−0.655563	−	0.755141i	$-0.727568\pi$
$317$	−5.86432	+	3.38576i	−0.329373	+	0.190163i	0.326190	+	0.945304i	$0.394235\pi$
$318$		0			0
$319$	−8.27726	−	4.77888i	−0.463438	−	0.267566i
$320$		0			0
$321$			15.3043i			0.854204i
$322$		0			0
$323$	4.23726			0.235767
$324$		0			0
$325$	−2.15674	+	3.73558i	−0.119634	+	0.207213i
$326$		0			0
$327$	−4.14949	−	7.18713i	−0.229468	−	0.397449i
$328$		0			0
$329$	−28.4296	+	1.09794i	−1.56737	+	0.0605315i
$330$		0			0
$331$	−5.59806	−	9.69613i	−0.307697	−	0.532947i	0.670161	−	0.742216i	$-0.266225\pi$
$331$	−5.59806	−	9.69613i	−0.307697	−	0.532947i	−0.977858	+	0.209268i	$0.932892\pi$
$332$		0			0
$333$	−9.26008	−	5.34631i	−0.507449	−	0.292976i
$334$		0			0
$335$	0.931935			0.0509171
$336$		0			0
$337$	24.4910			1.33411			0.667055	−	0.745008i	$-0.267554\pi$
$337$	24.4910			1.33411			0.667055	+	0.745008i	$0.267554\pi$
$338$		0			0
$339$	−16.0071	−	9.24173i	−0.869389	−	0.501942i
$340$		0			0
$341$	−0.165706	−	0.287011i	−0.00897347	−	0.0155425i
$342$		0			0
$343$	18.3962	−	2.13988i	0.993303	−	0.115543i
$344$		0			0
$345$	0.205576	+	0.356068i	0.0110678	+	0.0191700i
$346$		0			0
$347$	−8.21166	+	14.2230i	−0.440825	+	0.763531i	−0.997751	−	0.0670312i	$-0.978647\pi$
$347$	−8.21166	+	14.2230i	−0.440825	+	0.763531i	0.556926	+	0.830562i	$0.311981\pi$
$348$		0			0
$349$	−0.191603			−0.0102563			−0.00512813	−	0.999987i	$-0.501632\pi$
$349$	−0.191603			−0.0102563			−0.00512813	+	0.999987i	$0.501632\pi$
$350$		0			0
$351$			20.2378i			1.08022i
$352$		0			0
$353$	−19.3579	−	11.1763i	−1.03032	−	0.594854i	−0.113241	−	0.993568i	$-0.536123\pi$
$353$	−19.3579	−	11.1763i	−1.03032	−	0.594854i	−0.917075	+	0.398714i	$0.869457\pi$
$354$		0			0
$355$	7.24042	−	4.18026i	0.384282	−	0.221865i
$356$		0			0
$357$	−4.12972	+	0.159488i	−0.218568	+	0.00844102i
$358$		0			0
$359$	−20.4748	+	11.8211i	−1.08062	+	0.623896i	−0.931064	−	0.364857i	$-0.881118\pi$
$359$	−20.4748	+	11.8211i	−1.08062	+	0.623896i	−0.149556	+	0.988753i	$0.547784\pi$
$360$		0			0
$361$	−6.48106	+	11.2255i	−0.341108	+	0.590817i
$362$		0			0
$363$		−	8.56748i		−	0.449676i
$364$		0			0
$365$			7.18191i			0.375918i
$366$		0			0
$367$	9.00124	−	15.5906i	0.469861	−	0.813823i	−0.529545	−	0.848282i	$-0.677637\pi$
$367$	9.00124	−	15.5906i	0.469861	−	0.813823i	0.999406	+	0.0344586i	$0.0109707\pi$
$368$		0			0
$369$	23.1597	−	13.3712i	1.20564	−	0.696079i
$370$		0			0
$371$	−19.4051	+	12.2255i	−1.00746	+	0.634717i
$372$		0			0
$373$	21.5700	−	12.4535i	1.11685	−	0.644815i	0.176257	−	0.984344i	$-0.443601\pi$
$373$	21.5700	−	12.4535i	1.11685	−	0.644815i	0.940596	+	0.339529i	$0.110268\pi$
$374$		0			0
$375$	−0.784482	−	0.452921i	−0.0405105	−	0.0233887i
$376$		0			0
$377$			33.2006i			1.70992i
$378$		0			0
$379$	−3.91557			−0.201130			−0.100565	−	0.994931i	$-0.532065\pi$
$379$	−3.91557			−0.201130			−0.100565	+	0.994931i	$0.532065\pi$
$380$		0			0
$381$	−2.34739	+	4.06580i	−0.120260	+	0.208297i
$382$		0			0
$383$	8.27193	+	14.3274i	0.422676	+	0.732096i	0.996200	−	0.0870922i	$-0.0277575\pi$
$383$	8.27193	+	14.3274i	0.422676	+	0.732096i	−0.573524	+	0.819189i	$0.694424\pi$
$384$		0			0
$385$	−1.53167	+	2.90650i	−0.0780611	+	0.148129i
$386$		0			0
$387$	1.89455	+	3.28146i	0.0963055	+	0.166806i
$388$		0			0
$389$	−17.8537	−	10.3078i	−0.905219	−	0.522628i	−0.0263290	−	0.999653i	$-0.508382\pi$
$389$	−17.8537	−	10.3078i	−0.905219	−	0.522628i	−0.878890	+	0.477025i	$0.841715\pi$
$390$		0			0
$391$	−0.782695			−0.0395826
$392$		0			0
$393$	12.2956			0.620231
$394$		0			0
$395$	−9.56196	−	5.52060i	−0.481114	−	0.277772i
$396$		0			0
$397$	9.45979	+	16.3848i	0.474773	+	0.822332i	0.999583	−	0.0288882i	$-0.00919669\pi$
$397$	9.45979	+	16.3848i	0.474773	+	0.822332i	−0.524809	+	0.851220i	$0.675863\pi$
$398$		0			0
$399$	−2.74551	+	5.20988i	−0.137447	+	0.260820i
$400$		0			0
$401$	−1.73670	−	3.00804i	−0.0867264	−	0.150215i	0.819399	−	0.573223i	$-0.194307\pi$
$401$	−1.73670	−	3.00804i	−0.0867264	−	0.150215i	−0.906126	+	0.423009i	$0.860974\pi$
$402$		0			0
$403$	−0.575610	+	0.996985i	−0.0286732	+	0.0496634i
$404$		0			0
$405$	2.28836			0.113709
$406$		0			0
$407$			6.09221i			0.301979i
$408$		0			0
$409$	20.4501	+	11.8069i	1.01119	+	0.583812i	0.911541	−	0.411210i	$-0.134894\pi$
$409$	20.4501	+	11.8069i	1.01119	+	0.583812i	0.0996521	+	0.995022i	$0.468227\pi$
$410$		0			0
$411$	10.1498	−	5.86001i	0.500654	−	0.289053i
$412$		0			0
$413$	−12.5010	+	7.87584i	−0.615133	+	0.387545i
$414$		0			0
$415$	−7.35371	+	4.24567i	−0.360979	+	0.208412i
$416$		0			0
$417$	8.06323	−	13.9659i	0.394858	−	0.683914i
$418$		0			0
$419$			7.29588i			0.356427i	0.983992	+	0.178214i	$0.0570318\pi$
$419$			7.29588i			0.356427i	−0.983992	+	0.178214i	$0.942968\pi$
$420$		0			0
$421$			6.71577i			0.327307i	0.986518	+	0.163653i	$0.0523278\pi$
$421$			6.71577i			0.327307i	−0.986518	+	0.163653i	$0.947672\pi$
$422$		0			0
$423$	11.7182	−	20.2966i	0.569760	−	0.986853i
$424$		0			0
$425$	1.49339	−	0.862209i	0.0724401	−	0.0418233i
$426$		0			0
$427$	−2.44778	+	0.0945325i	−0.118456	+	0.00457475i
$428$		0			0
$429$	4.20192	−	2.42598i	0.202871	−	0.117127i
$430$		0			0
$431$	29.3361	+	16.9372i	1.41307	+	0.815837i	0.995677	−	0.0928881i	$-0.0296099\pi$
$431$	29.3361	+	16.9372i	1.41307	+	0.815837i	0.417395	+	0.908725i	$0.362943\pi$
$432$		0			0
$433$		−	14.8665i		−	0.714440i	−0.934020	−	0.357220i	$-0.883725\pi$
$433$		−	14.8665i		−	0.714440i	0.934020	−	0.357220i	$-0.116275\pi$
$434$		0			0
$435$	−6.97222			−0.334292
$436$		0			0
$437$	−0.557650	+	0.965879i	−0.0266760	+	0.0462042i
$438$		0			0
$439$	6.22389	+	10.7801i	0.297050	+	0.514506i	0.975460	−	0.220178i	$-0.0706639\pi$
$439$	6.22389	+	10.7801i	0.297050	+	0.514506i	−0.678410	+	0.734684i	$0.737331\pi$
$440$		0			0
$441$	−6.58637	+	13.7612i	−0.313637	+	0.655294i
$442$		0			0
$443$	5.16402	+	8.94434i	0.245350	+	0.424959i	0.962230	−	0.272238i	$-0.0877638\pi$
$443$	5.16402	+	8.94434i	0.245350	+	0.424959i	−0.716880	+	0.697197i	$0.754430\pi$
$444$		0			0
$445$	6.91420	+	3.99191i	0.327764	+	0.189235i
$446$		0			0
$447$	13.2992			0.629031
$448$		0			0
$449$	18.6590			0.880574			0.440287	−	0.897857i	$-0.354877\pi$
$449$	18.6590			0.880574			0.440287	+	0.897857i	$0.354877\pi$
$450$		0			0
$451$	−13.1954	−	7.61837i	−0.621348	−	0.358735i
$452$		0			0
$453$	7.79349	+	13.4987i	0.366170	+	0.634225i
$454$		0			0
$455$	11.4039	−	0.440415i	0.534623	−	0.0206470i
$456$		0			0
$457$	5.65988	+	9.80320i	0.264758	+	0.458574i	0.967500	−	0.252870i	$-0.0813746\pi$
$457$	5.65988	+	9.80320i	0.264758	+	0.458574i	−0.702742	+	0.711445i	$0.748041\pi$
$458$		0			0
$459$	4.04528	−	7.00663i	0.188818	−	0.327042i
$460$		0			0
$461$	−25.4553			−1.18557			−0.592785	−	0.805360i	$-0.701972\pi$
$461$	−25.4553			−1.18557			−0.592785	+	0.805360i	$0.701972\pi$
$462$		0			0
$463$		−	6.76939i		−	0.314600i	−0.987551	−	0.157300i	$-0.949721\pi$
$463$		−	6.76939i		−	0.314600i	0.987551	−	0.157300i	$-0.0502790\pi$
$464$		0			0
$465$	−0.209370	−	0.120880i	−0.00970928	−	0.00560565i
$466$		0			0
$467$	−18.0857	+	10.4418i	−0.836908	+	0.483189i	−0.856212	−	0.516625i	$-0.827188\pi$
$467$	−18.0857	+	10.4418i	−0.836908	+	0.483189i	0.0193043	+	0.999814i	$0.493855\pi$
$468$		0			0
$469$	−1.31432	−	2.08617i	−0.0606897	−	0.0963302i
$470$		0			0
$471$	8.39613	−	4.84751i	0.386873	−	0.223361i
$472$		0			0
$473$	1.07944	−	1.86964i	0.0496325	−	0.0859660i
$474$		0			0
$475$		−	2.45721i		−	0.112745i
$476$		0			0
$477$		−	18.8929i		−	0.865047i
$478$		0			0
$479$	−1.45807	+	2.52546i	−0.0666211	+	0.115391i	−0.897412	−	0.441194i	$-0.854555\pi$
$479$	−1.45807	+	2.52546i	−0.0666211	+	0.115391i	0.830791	+	0.556585i	$0.187889\pi$
$480$		0			0
$481$	18.3272	−	10.5812i	0.835647	−	0.482461i
$482$		0			0
$483$	0.507142	−	0.962355i	0.0230758	−	0.0437887i
$484$		0			0
$485$	3.40232	−	1.96433i	0.154491	−	0.0891956i
$486$		0			0
$487$	10.0582	+	5.80712i	0.455782	+	0.263146i	0.710269	−	0.703930i	$-0.248573\pi$
$487$	10.0582	+	5.80712i	0.455782	+	0.263146i	−0.254487	+	0.967076i	$0.581907\pi$
$488$		0			0
$489$			22.7298i			1.02788i
$490$		0			0
$491$	2.26191			0.102079			0.0510393	−	0.998697i	$-0.483747\pi$
$491$	2.26191			0.102079			0.0510393	+	0.998697i	$0.483747\pi$
$492$		0			0
$493$	6.63639	−	11.4946i	0.298888	−	0.517689i
$494$		0			0
$495$	−1.35318	−	2.34377i	−0.0608207	−	0.105345i
$496$		0			0
$497$	−19.5689	−	10.3124i	−0.877785	−	0.462575i
$498$		0			0
$499$	−11.8706	−	20.5606i	−0.531403	−	0.920417i	−0.999328	−	0.0366488i	$-0.988332\pi$
$499$	−11.8706	−	20.5606i	−0.531403	−	0.920417i	0.467925	−	0.883768i	$-0.345002\pi$
$500$		0			0
$501$	5.04511	+	2.91280i	0.225399	+	0.130134i
$502$		0			0
$503$	11.0460			0.492515			0.246258	−	0.969204i	$-0.420799\pi$
$503$	11.0460			0.492515			0.246258	+	0.969204i	$0.420799\pi$
$504$		0			0
$505$	9.65888			0.429814
$506$		0			0
$507$	−4.39789	−	2.53912i	−0.195317	−	0.112766i
$508$		0			0
$509$	20.3574	+	35.2600i	0.902325	+	1.56287i	0.824469	+	0.565908i	$0.191474\pi$
$509$	20.3574	+	35.2600i	0.902325	+	1.56287i	0.0778561	+	0.996965i	$0.475193\pi$
$510$		0			0
$511$	16.0769	−	10.1287i	0.711201	−	0.448069i
$512$		0			0
$513$	−5.76433	−	9.98410i	−0.254501	−	0.440809i
$514$		0			0
$515$	3.82962	−	6.63310i	0.168753	−	0.292289i
$516$		0			0
$517$	−13.3531			−0.587269
$518$		0			0
$519$			1.96705i			0.0863438i
$520$		0			0
$521$	−27.7740	−	16.0353i	−1.21680	−	0.702519i	−0.252567	−	0.967579i	$-0.581275\pi$
$521$	−27.7740	−	16.0353i	−1.21680	−	0.702519i	−0.964232	+	0.265060i	$0.914608\pi$
$522$		0			0
$523$	18.8270	−	10.8698i	0.823246	−	0.475301i	−0.0282888	−	0.999600i	$-0.509006\pi$
$523$	18.8270	−	10.8698i	0.823246	−	0.475301i	0.851534	+	0.524299i	$0.175672\pi$
$524$		0			0
$525$	0.0924882	+	2.39485i	0.00403652	+	0.104520i
$526$		0			0
$527$	0.398569	−	0.230114i	0.0173619	−	0.0100239i
$528$		0			0
$529$	−11.3970	+	19.7402i	−0.495521	+	0.858268i
$530$		0			0
$531$		−	12.1711i		−	0.528179i
$532$		0			0
$533$			52.9276i			2.29255i
$534$		0			0
$535$	−8.44757	+	14.6316i	−0.365220	+	0.632580i
$536$		0			0
$537$	−17.8640	+	10.3138i	−0.770887	+	0.445072i
$538$		0			0
$539$	8.66642	−	0.670389i	0.373289	−	0.0288757i
$540$		0			0
$541$	10.7162	−	6.18701i	0.460726	−	0.266000i	−0.251624	−	0.967825i	$-0.580964\pi$
$541$	10.7162	−	6.18701i	0.460726	−	0.266000i	0.712349	+	0.701825i	$0.247631\pi$
$542$		0			0
$543$	15.9131	+	9.18742i	0.682895	+	0.394270i
$544$		0			0
$545$		−	9.16163i		−	0.392441i
$546$		0			0
$547$	31.3301			1.33958			0.669790	−	0.742551i	$-0.266384\pi$
$547$	31.3301			1.33958			0.669790	+	0.742551i	$0.266384\pi$
$548$		0			0
$549$	1.00894	−	1.74753i	0.0430604	−	0.0745828i
$550$		0			0
$551$	−9.45652	−	16.3792i	−0.402861	−	0.697776i
$552$		0			0
$553$	1.12733	+	29.1905i	0.0479389	+	1.24131i
$554$		0			0
$555$	2.22208	+	3.84875i	0.0943220	+	0.163371i
$556$		0			0
$557$	10.6869	+	6.17008i	0.452818	+	0.261434i	0.709020	−	0.705189i	$-0.249138\pi$
$557$	10.6869	+	6.17008i	0.452818	+	0.261434i	−0.256202	+	0.966623i	$0.582471\pi$
$558$		0			0
$559$	−7.49924			−0.317184
$560$		0			0
$561$	−1.93969			−0.0818938
$562$		0			0
$563$	1.58551	+	0.915395i	0.0668213	+	0.0385793i	0.533038	−	0.846091i	$-0.321050\pi$
$563$	1.58551	+	0.915395i	0.0668213	+	0.0385793i	−0.466217	+	0.884670i	$0.654383\pi$
$564$		0			0
$565$	−10.2024	−	17.6710i	−0.429217	−	0.743425i
$566$		0			0
$567$	−3.22730	−	5.12255i	−0.135534	−	0.215127i
$568$		0			0
$569$	−0.0498347	−	0.0863162i	−0.00208918	−	0.00361856i	0.864979	−	0.501808i	$-0.167332\pi$
$569$	−0.0498347	−	0.0863162i	−0.00208918	−	0.00361856i	−0.867068	+	0.498190i	$0.833998\pi$
$570$		0			0
$571$	−12.9796	+	22.4813i	−0.543178	+	0.940812i	0.455541	+	0.890215i	$0.349446\pi$
$571$	−12.9796	+	22.4813i	−0.543178	+	0.940812i	−0.998719	+	0.0505976i	$0.983887\pi$
$572$		0			0
$573$	−1.52586			−0.0637437
$574$		0			0
$575$			0.453889i			0.0189285i
$576$		0			0
$577$	1.28600	+	0.742473i	0.0535369	+	0.0309096i	0.526530	−	0.850157i	$-0.323493\pi$
$577$	1.28600	+	0.742473i	0.0535369	+	0.0309096i	−0.472993	+	0.881066i	$0.656826\pi$
$578$		0			0
$579$	−19.3450	+	11.1688i	−0.803950	+	0.464161i
$580$		0			0
$581$	19.8751	+	10.4738i	0.824557	+	0.434526i
$582$		0			0
$583$	−9.32223	+	5.38219i	−0.386087	+	0.222908i
$584$		0			0
$585$	−4.70051	+	8.14152i	−0.194342	+	0.336610i
$586$		0			0
$587$		−	31.1081i		−	1.28397i	−0.766717	−	0.641985i	$-0.778111\pi$
$587$		−	31.1081i		−	1.28397i	0.766717	−	0.641985i	$-0.221889\pi$
$588$		0			0
$589$		−	0.655802i		−	0.0270219i
$590$		0			0
$591$	−0.753830	+	1.30567i	−0.0310084	+	0.0537081i
$592$		0			0
$593$	−8.02645	+	4.63407i	−0.329607	+	0.190299i	−0.655667	−	0.755051i	$-0.727612\pi$
$593$	−8.02645	+	4.63407i	−0.329607	+	0.190299i	0.326060	+	0.945349i	$0.394279\pi$
$594$		0			0
$595$	−4.03623	−	2.12701i	−0.165469	−	0.0871991i
$596$		0			0
$597$	−10.0367	+	5.79467i	−0.410773	+	0.237160i
$598$		0			0
$599$	3.48534	+	2.01226i	0.142407	+	0.0822188i	0.569511	−	0.821984i	$-0.307133\pi$
$599$	3.48534	+	2.01226i	0.142407	+	0.0822188i	−0.427104	+	0.904203i	$0.640466\pi$
$600$		0			0
$601$			23.8545i			0.973047i	0.873667	+	0.486524i	$0.161735\pi$
$601$			23.8545i			0.973047i	−0.873667	+	0.486524i	$0.838265\pi$
$602$		0			0
$603$	2.03111			0.0827131
$604$		0			0
$605$	4.72902	−	8.19090i	0.192262	−	0.333007i
$606$		0			0
$607$	18.6259	+	32.2611i	0.756003	+	1.30944i	0.944874	+	0.327434i	$0.106184\pi$
$607$	18.6259	+	32.2611i	0.756003	+	1.30944i	−0.188871	+	0.982002i	$0.560483\pi$
$608$		0			0
$609$	9.83302	+	15.6075i	0.398454	+	0.632449i
$610$		0			0
$611$	23.1923	+	40.1702i	0.938258	+	1.62511i
$612$		0			0
$613$	−6.65132	−	3.84014i	−0.268644	−	0.155102i	0.359627	−	0.933096i	$-0.382904\pi$
$613$	−6.65132	−	3.84014i	−0.268644	−	0.155102i	−0.628271	+	0.777994i	$0.716237\pi$
$614$		0			0
$615$	−11.1149			−0.448198
$616$		0			0
$617$	−27.6806			−1.11438			−0.557189	−	0.830386i	$-0.688120\pi$
$617$	−27.6806			−1.11438			−0.557189	+	0.830386i	$0.688120\pi$
$618$		0			0
$619$	−25.7376	−	14.8596i	−1.03448	−	0.597258i	−0.116216	−	0.993224i	$-0.537077\pi$
$619$	−25.7376	−	14.8596i	−1.03448	−	0.597258i	−0.918265	+	0.395966i	$0.870410\pi$
$620$		0			0
$621$	1.06477	+	1.84424i	0.0427277	+	0.0740066i
$622$		0			0
$623$	−0.815164	−	21.1075i	−0.0326589	−	0.845653i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−1.38198	+	2.39366i	−0.0551910	+	0.0955936i
$628$		0			0
$629$	−8.46019			−0.337330
$630$		0			0
$631$			1.25766i			0.0500665i	0.999687	+	0.0250332i	$0.00796916\pi$
$631$			1.25766i			0.0500665i	−0.999687	+	0.0250332i	$0.992031\pi$
$632$		0			0
$633$	−13.1878	−	7.61400i	−0.524170	−	0.302629i
$634$		0			0
$635$	−4.48842	+	2.59139i	−0.178117	+	0.102836i
$636$		0			0
$637$	−17.0689	−	24.9068i	−0.676296	−	0.986845i
$638$		0			0
$639$	15.7801	−	9.11067i	0.624253	−	0.360412i
$640$		0			0
$641$	24.7738	−	42.9096i	0.978508	−	1.69483i	0.310672	−	0.950517i	$-0.399446\pi$
$641$	24.7738	−	42.9096i	0.978508	−	1.69483i	0.667836	−	0.744309i	$-0.267221\pi$
$642$		0			0
$643$			44.6117i			1.75931i	0.475608	+	0.879657i	$0.342228\pi$
$643$			44.6117i			1.75931i	−0.475608	+	0.879657i	$0.657772\pi$
$644$		0			0
$645$		−	1.57486i		−	0.0620100i
$646$		0			0
$647$	−16.9430	+	29.3462i	−0.666098	+	1.15372i	0.312888	+	0.949790i	$0.398704\pi$
$647$	−16.9430	+	29.3462i	−0.666098	+	1.15372i	−0.978986	+	0.203926i	$0.934630\pi$
$648$		0			0
$649$	−6.00550	+	3.46728i	−0.235736	+	0.136103i
$650$		0			0
$651$	0.0246841	+	0.639158i	0.000967445	+	0.0250506i
$652$		0			0
$653$	−31.0838	+	17.9462i	−1.21640	+	0.702291i	−0.964147	−	0.265370i	$-0.914506\pi$
$653$	−31.0838	+	17.9462i	−1.21640	+	0.702291i	−0.252256	+	0.967660i	$0.581173\pi$
$654$		0			0
$655$	11.7551	+	6.78684i	0.459312	+	0.265184i
$656$		0			0
$657$			15.6526i			0.610667i
$658$		0			0
$659$	2.82512			0.110051			0.0550255	−	0.998485i	$-0.482476\pi$
$659$	2.82512			0.110051			0.0550255	+	0.998485i	$0.482476\pi$
$660$		0			0
$661$	−8.31035	+	14.3939i	−0.323235	+	0.559860i	−0.981154	−	0.193230i	$-0.938104\pi$
$661$	−8.31035	+	14.3939i	−0.323235	+	0.559860i	0.657919	+	0.753089i	$0.271437\pi$
$662$		0			0
$663$	3.36894	+	5.83517i	0.130839	+	0.226619i
$664$		0			0
$665$	−5.50054	+	3.46544i	−0.213302	+	0.134384i
$666$		0			0
$667$	1.74678	+	3.02551i	0.0676356	+	0.117148i
$668$		0			0
$669$	18.7250	+	10.8109i	0.723949	+	0.417972i
$670$		0			0
$671$	−1.14970			−0.0443837
$672$		0			0
$673$	−28.1914			−1.08670			−0.543349	−	0.839507i	$-0.682844\pi$
$673$	−28.1914			−1.08670			−0.543349	+	0.839507i	$0.682844\pi$
$674$		0			0
$675$	−4.06319	−	2.34588i	−0.156392	−	0.0902930i
$676$		0			0
$677$	12.3523	+	21.3947i	0.474736	+	0.822266i	0.999581	−	0.0289312i	$-0.00921037\pi$
$677$	12.3523	+	21.3947i	0.474736	+	0.822266i	−0.524846	+	0.851197i	$0.675877\pi$
$678$		0			0
$679$	−9.19555	−	4.84587i	−0.352893	−	0.185968i
$680$		0			0
$681$	−3.51349	−	6.08554i	−0.134637	−	0.233198i
$682$		0			0
$683$	−1.55667	+	2.69624i	−0.0595645	+	0.103169i	−0.894270	−	0.447528i	$-0.852305\pi$
$683$	−1.55667	+	2.69624i	−0.0595645	+	0.103169i	0.834706	+	0.550697i	$0.185638\pi$
$684$		0			0
$685$	12.9383			0.494345
$686$		0			0
$687$			4.44207i			0.169475i
$688$		0			0
$689$	32.3825	+	18.6960i	1.23367	+	0.712262i
$690$		0			0
$691$	17.8344	−	10.2967i	0.678451	−	0.391704i	−0.120820	−	0.992674i	$-0.538552\pi$
$691$	17.8344	−	10.2967i	0.678451	−	0.391704i	0.799271	+	0.600970i	$0.205219\pi$
$692$		0			0
$693$	−3.33820	+	6.33457i	−0.126808	+	0.240631i
$694$		0			0
$695$	15.4176	−	8.90137i	0.584824	−	0.337648i
$696$		0			0
$697$	10.5796	−	18.3243i	0.400729	−	0.694084i
$698$		0			0
$699$			15.5539i			0.588304i
$700$		0			0
$701$			3.67022i			0.138622i	0.997595	+	0.0693111i	$0.0220801\pi$
$701$			3.67022i			0.138622i	−0.997595	+	0.0693111i	$0.977920\pi$
$702$		0			0
$703$	−6.02767	+	10.4402i	−0.227338	+	0.393761i
$704$		0			0
$705$	−8.43584	+	4.87043i	−0.317712	+	0.183431i
$706$		0			0
$707$	−13.6220	−	21.6217i	−0.512310	−	0.813167i
$708$		0			0
$709$	2.73543	−	1.57930i	0.102731	−	0.0593118i	−0.447754	−	0.894157i	$-0.647776\pi$
$709$	2.73543	−	1.57930i	0.102731	−	0.0593118i	0.550485	+	0.834845i	$0.314443\pi$
$710$		0			0
$711$	−20.8398	−	12.0319i	−0.781554	−	0.451231i
$712$		0			0
$713$			0.121138i			0.00453665i
$714$		0			0
$715$	5.35630			0.200314
$716$		0			0
$717$	10.2220	−	17.7050i	0.381748	−	0.661206i
$718$		0			0
$719$	10.8001	+	18.7063i	0.402775	+	0.697626i	0.994060	−	0.108837i	$-0.0347125\pi$
$719$	10.8001	+	18.7063i	0.402775	+	0.697626i	−0.591285	+	0.806463i	$0.701379\pi$
$720$		0			0
$721$	−20.2493	+	0.782023i	−0.754125	+	0.0291241i
$722$		0			0
$723$	1.30440	+	2.25929i	0.0485113	+	0.0840241i
$724$		0			0
$725$	−6.66576	−	3.84848i	−0.247560	−	0.142929i
$726$		0			0
$727$	48.4533			1.79703			0.898516	−	0.438941i	$-0.144646\pi$
$727$	48.4533			1.79703			0.898516	+	0.438941i	$0.144646\pi$
$728$		0			0
$729$	−7.76263			−0.287505
$730$		0			0
$731$	2.59635	+	1.49900i	0.0960294	+	0.0554426i
$732$		0			0
$733$	−7.62984	−	13.2153i	−0.281814	−	0.488117i	0.690017	−	0.723793i	$-0.257603\pi$
$733$	−7.62984	−	13.2153i	−0.281814	−	0.488117i	−0.971832	+	0.235676i	$0.924270\pi$
$734$		0			0
$735$	5.23050	−	3.58452i	0.192930	−	0.132217i
$736$		0			0
$737$	−0.578619	−	1.00220i	−0.0213137	−	0.0369165i
$738$		0			0
$739$	−3.14394	+	5.44547i	−0.115652	+	0.200315i	−0.918040	−	0.396488i	$-0.870229\pi$
$739$	−3.14394	+	5.44547i	−0.115652	+	0.200315i	0.802388	+	0.596802i	$0.203562\pi$
$740$		0			0
$741$	9.60113			0.352706
$742$		0			0
$743$		−	32.4205i		−	1.18939i	−0.803950	−	0.594697i	$-0.797272\pi$
$743$		−	32.4205i		−	1.18939i	0.803950	−	0.594697i	$-0.202728\pi$
$744$		0			0
$745$	12.7146	+	7.34080i	0.465829	+	0.268946i
$746$		0			0
$747$	−16.0270	+	9.25322i	−0.586399	+	0.338558i
$748$		0			0
$749$	44.6670	−	1.72503i	1.63210	−	0.0630311i
$750$		0			0
$751$	36.4730	−	21.0577i	1.33092	−	0.768406i	0.345477	−	0.938427i	$-0.387717\pi$
$751$	36.4730	−	21.0577i	1.33092	−	0.768406i	0.985440	+	0.170022i	$0.0543837\pi$
$752$		0			0
$753$	5.60440	−	9.70710i	0.204236	−	0.353747i
$754$		0			0
$755$			17.2072i			0.626233i
$756$		0			0
$757$		−	14.3036i		−	0.519875i	−0.965625	−	0.259937i	$-0.916298\pi$
$757$		−	14.3036i		−	0.519875i	0.965625	−	0.259937i	$-0.0837019\pi$
$758$		0			0
$759$	0.255276	−	0.442150i	0.00926592	−	0.0160490i
$760$		0			0
$761$	11.5548	−	6.67119i	0.418862	−	0.241830i	−0.275728	−	0.961236i	$-0.588919\pi$
$761$	11.5548	−	6.67119i	0.418862	−	0.241830i	0.694590	+	0.719405i	$0.255586\pi$
$762$		0			0
$763$	−20.5086	+	12.9208i	−0.742460	+	0.467763i
$764$		0			0
$765$	3.25477	−	1.87914i	0.117676	−	0.0679405i
$766$		0			0
$767$	20.8612	+	12.0442i	0.753255	+	0.434892i
$768$		0			0
$769$		−	16.2042i		−	0.584338i	−0.956367	−	0.292169i	$-0.905623\pi$
$769$		−	16.2042i		−	0.584338i	0.956367	−	0.292169i	$-0.0943770\pi$
$770$		0			0
$771$	−5.12267			−0.184489
$772$		0			0
$773$	6.10743	−	10.5784i	0.219669	−	0.380478i	−0.735038	−	0.678026i	$-0.762836\pi$
$773$	6.10743	−	10.5784i	0.219669	−	0.380478i	0.954707	+	0.297548i	$0.0961689\pi$
$774$		0			0
$775$	−0.133444	−	0.231133i	−0.00479347	−	0.00830253i
$776$		0			0
$777$	5.48173	−	10.4021i	0.196656	−	0.373175i
$778$		0			0
$779$	−15.0753	−	26.1113i	−0.540130	−	0.935533i
$780$		0			0
$781$	−8.99086	−	5.19087i	−0.321718	−	0.185744i
$782$		0			0
$783$	−36.1123			−1.29055
$784$		0			0
$785$	10.7028			0.381998
$786$		0			0
$787$	−12.7062	−	7.33592i	−0.452927	−	0.261497i	0.256139	−	0.966640i	$-0.417550\pi$
$787$	−12.7062	−	7.33592i	−0.452927	−	0.261497i	−0.709065	+	0.705143i	$0.750883\pi$
$788$		0			0
$789$	−4.51155	−	7.81424i	−0.160616	−	0.278194i
$790$		0			0
$791$	−25.1686	+	47.7600i	−0.894891	+	1.69815i
$792$		0			0
$793$	1.99685	+	3.45864i	0.0709101	+	0.122820i
$794$		0			0
$795$	−3.92622	+	6.80041i	−0.139249	+	0.241186i
$796$		0			0
$797$	32.6214			1.15551			0.577754	−	0.816211i	$-0.303929\pi$
$797$	32.6214			1.15551			0.577754	+	0.816211i	$0.303929\pi$
$798$		0			0
$799$		−	18.5433i		−	0.656016i
$800$		0			0
$801$	15.0691	+	8.70018i	0.532442	+	0.307406i
$802$		0			0
$803$	7.72339	−	4.45910i	0.272552	−	0.157358i
$804$		0			0
$805$	1.01604	−	0.640125i	0.0358108	−	0.0225615i
$806$		0			0
$807$	−15.3412	+	8.85724i	−0.540036	+	0.311790i
$808$		0			0
$809$	10.4784	−	18.1491i	0.368400	−	0.638087i	−0.620916	−	0.783877i	$-0.713239\pi$
$809$	10.4784	−	18.1491i	0.368400	−	0.638087i	0.989316	+	0.145790i	$0.0465724\pi$
$810$		0			0
$811$		−	41.5111i		−	1.45765i	−0.684699	−	0.728826i	$-0.740066\pi$
$811$		−	41.5111i		−	1.45765i	0.684699	−	0.728826i	$-0.259934\pi$
$812$		0			0
$813$			29.2078i			1.02436i
$814$		0			0
$815$	−12.5462	+	21.7307i	−0.439475	+	0.761193i
$816$		0			0
$817$	3.69967	−	2.13600i	0.129435	−	0.0747293i
$818$		0			0
$819$	24.8542	−	0.959862i	0.868477	−	0.0335403i
$820$		0			0
$821$	20.2501	−	11.6914i	0.706734	−	0.408033i	−0.103117	−	0.994669i	$-0.532882\pi$
$821$	20.2501	−	11.6914i	0.706734	−	0.408033i	0.809850	+	0.586636i	$0.199548\pi$
$822$		0			0
$823$	−13.6126	−	7.85923i	−0.474505	−	0.273956i	0.243619	−	0.969871i	$-0.421665\pi$
$823$	−13.6126	−	7.85923i	−0.474505	−	0.273956i	−0.718124	+	0.695915i	$0.754999\pi$
$824$		0			0
$825$			1.12484i			0.0391618i
$826$		0			0
$827$	34.6724			1.20568			0.602838	−	0.797864i	$-0.294037\pi$
$827$	34.6724			1.20568			0.602838	+	0.797864i	$0.294037\pi$
$828$		0			0
$829$	15.5301	−	26.8989i	0.539383	−	0.934238i	−0.459555	−	0.888150i	$-0.651991\pi$
$829$	15.5301	−	26.8989i	0.539383	−	0.934238i	0.998937	−	0.0460889i	$-0.0146757\pi$
$830$		0			0
$831$	−8.02006	−	13.8912i	−0.278213	−	0.481879i
$832$		0			0
$833$	0.930962	+	12.0350i	0.0322559	+	0.416987i
$834$		0			0
$835$	3.21557	+	5.56953i	0.111279	+	0.192741i
$836$		0			0
$837$	−1.08442	−	0.626090i	−0.0374830	−	0.0216408i
$838$		0			0
$839$	16.3946			0.566003			0.283002	−	0.959119i	$-0.408670\pi$
$839$	16.3946			0.566003			0.283002	+	0.959119i	$0.408670\pi$
$840$		0			0
$841$	−30.2431			−1.04287
$842$		0			0
$843$	3.15650	+	1.82240i	0.108715	+	0.0627669i
$844$		0			0
$845$	−2.80305	−	4.85503i	−0.0964279	−	0.167018i
$846$		0			0
$847$	−25.0050	+	0.965684i	−0.859181	+	0.0331813i
$848$		0			0
$849$	−8.59268	−	14.8830i	−0.294900	−	0.510782i
$850$		0			0
$851$	1.11341	−	1.92849i	0.0381673	−	0.0661078i
$852$		0			0
$853$	43.9900			1.50619			0.753095	−	0.657911i	$-0.228560\pi$
$853$	43.9900			1.50619			0.753095	+	0.657911i	$0.228560\pi$
$854$		0			0
$855$		−	5.35537i		−	0.183150i
$856$		0			0
$857$	19.8887	+	11.4827i	0.679384	+	0.392242i	0.799623	−	0.600503i	$-0.205033\pi$
$857$	19.8887	+	11.4827i	0.679384	+	0.392242i	−0.120239	+	0.992745i	$0.538366\pi$
$858$		0			0
$859$	0.419174	−	0.242010i	0.0143020	−	0.00825728i	−0.492832	−	0.870125i	$-0.664038\pi$
$859$	0.419174	−	0.242010i	0.0143020	−	0.00825728i	0.507134	+	0.861867i	$0.330705\pi$
$860$		0			0
$861$	15.6756	+	24.8811i	0.534221	+	0.847947i
$862$		0			0
$863$	−9.39498	+	5.42419i	−0.319809	+	0.184642i	−0.651307	−	0.758814i	$-0.725779\pi$
$863$	−9.39498	+	5.42419i	−0.319809	+	0.184642i	0.331499	+	0.943456i	$0.392446\pi$
$864$		0			0
$865$	−1.08576	+	1.88059i	−0.0369168	+	0.0639419i
$866$		0			0
$867$			12.7057i			0.431508i
$868$		0			0
$869$			13.7105i			0.465097i
$870$		0			0
$871$	−2.00994	+	3.48132i	−0.0681043	+	0.117960i
$872$		0			0
$873$	7.41519	−	4.28116i	0.250966	−	0.144895i
$874$		0			0
$875$	−1.23347	+	2.34063i	−0.0416988	+	0.0791278i
$876$		0			0
$877$	−36.4411	+	21.0393i	−1.23053	+	0.710446i	−0.967140	−	0.254244i	$-0.918173\pi$
$877$	−36.4411	+	21.0393i	−1.23053	+	0.710446i	−0.263388	+	0.964690i	$0.584840\pi$
$878$		0			0
$879$	−8.14658	−	4.70343i	−0.274777	−	0.158643i
$880$		0			0
$881$		−	30.9141i		−	1.04152i	−0.853702	−	0.520762i	$-0.825648\pi$
$881$		−	30.9141i		−	1.04152i	0.853702	−	0.520762i	$-0.174352\pi$
$882$		0			0
$883$	−6.07978			−0.204601			−0.102300	−	0.994754i	$-0.532620\pi$
$883$	−6.07978			−0.204601			−0.102300	+	0.994754i	$0.532620\pi$
$884$		0			0
$885$	−2.52932	+	4.38091i	−0.0850221	+	0.147263i
$886$		0			0
$887$	−24.0789	−	41.7059i	−0.808492	−	1.40035i	−0.913908	−	0.405920i	$-0.866951\pi$
$887$	−24.0789	−	41.7059i	−0.808492	−	1.40035i	0.105417	−	0.994428i	$-0.466382\pi$
$888$		0			0
$889$	12.1310	+	6.39279i	0.406860	+	0.214407i
$890$		0			0
$891$	−1.42079	−	2.46089i	−0.0475984	−	0.0824428i
$892$		0			0
$893$	−22.8833	−	13.2117i	−0.765760	−	0.442111i
$894$		0			0
$895$	−22.7717			−0.761173
$896$		0			0
$897$	−1.77349			−0.0592152
$898$		0			0
$899$	−1.77902	−	1.02712i	−0.0593335	−	0.0342562i
$900$		0			0
$901$	−7.47420	−	12.9457i	−0.249002	−	0.431283i
$902$		0			0
$903$	−3.52537	+	2.22105i	−0.117317	+	0.0739118i
$904$		0			0
$905$	10.1424	+	17.5672i	0.337145	+	0.583952i
$906$		0			0
$907$	7.12984	−	12.3493i	0.236743	−	0.410050i	−0.723035	−	0.690811i	$-0.757254\pi$
$907$	7.12984	−	12.3493i	0.236743	−	0.410050i	0.959778	+	0.280761i	$0.0905869\pi$
$908$		0			0
$909$	21.0510			0.698219
$910$		0			0
$911$			37.4662i			1.24131i	0.784083	+	0.620656i	$0.213134\pi$
$911$			37.4662i			1.24131i	−0.784083	+	0.620656i	$0.786866\pi$
$912$		0			0
$913$	9.13153	+	5.27209i	0.302210	+	0.174481i
$914$		0			0
$915$	−0.726324	+	0.419343i	−0.0240115	+	0.0138631i
$916$		0			0
$917$	−1.38590	−	35.8858i	−0.0457664	−	1.18505i
$918$		0			0
$919$	−34.5077	+	19.9230i	−1.13830	+	0.657200i	−0.946010	−	0.324138i	$-0.894926\pi$
$919$	−34.5077	+	19.9230i	−1.13830	+	0.657200i	−0.192293	+	0.981338i	$0.561592\pi$
$920$		0			0
$921$	9.71368	−	16.8246i	0.320077	−	0.554389i
$922$		0			0
$923$			36.0629i			1.18703i
$924$		0			0
$925$			4.90611i			0.161312i
$926$		0			0
$927$	8.34647	−	14.4565i	0.274134	−	0.474814i
$928$		0			0
$929$	−3.03847	+	1.75426i	−0.0996889	+	0.0575554i	−0.549016	−	0.835812i	$-0.684997\pi$
$929$	−3.03847	+	1.75426i	−0.0996889	+	0.0575554i	0.449327	+	0.893368i	$0.351664\pi$
$930$		0			0
$931$	15.5150	+	7.42577i	0.508483	+	0.243370i
$932$		0			0
$933$	6.24036	−	3.60288i	0.204300	−	0.117953i
$934$		0			0
$935$	−1.85443	−	1.07066i	−0.0606464	−	0.0350142i
$936$		0			0
$937$		−	50.3147i		−	1.64371i	−0.569696	−	0.821855i	$-0.692939\pi$
$937$		−	50.3147i		−	1.64371i	0.569696	−	0.821855i	$-0.307061\pi$
$938$		0			0
$939$	9.45661			0.308605
$940$		0			0
$941$	−16.9244	+	29.3139i	−0.551719	+	0.955605i	0.446432	+	0.894817i	$0.352694\pi$
$941$	−16.9244	+	29.3139i	−0.551719	+	0.955605i	−0.998151	+	0.0607871i	$0.980639\pi$
$942$		0			0
$943$	2.78467	+	4.82320i	0.0906815	+	0.157065i
$944$		0			0
$945$	0.479038	+	12.4040i	0.0155831	+	0.403502i
$946$		0			0
$947$	−1.28323	−	2.22263i	−0.0416995	−	0.0722256i	0.844422	−	0.535678i	$-0.179944\pi$
$947$	−1.28323	−	2.22263i	−0.0416995	−	0.0722256i	−0.886122	+	0.463452i	$0.846611\pi$
$948$		0			0
$949$	−26.8286	−	15.4895i	−0.870894	−	0.502811i
$950$		0			0
$951$	6.13393			0.198906
$952$		0			0
$953$	−2.53946			−0.0822613			−0.0411306	−	0.999154i	$-0.513096\pi$
$953$	−2.53946			−0.0822613			−0.0411306	+	0.999154i	$0.513096\pi$
$954$		0			0
$955$	−1.45879	−	0.842233i	−0.0472054	−	0.0272540i
$956$		0			0
$957$	4.32891	+	7.49789i	0.139934	+	0.242372i
$958$		0			0
$959$	−18.2470	−	28.9627i	−0.589226	−	0.935254i
$960$		0			0
$961$	15.4644	+	26.7851i	0.498851	+	0.864036i
$962$		0			0
$963$	−18.4111	+	31.8889i	−0.593288	+	1.02760i
$964$		0			0
$965$	−24.6596			−0.793819
$966$		0			0
$967$		−	12.3398i		−	0.396821i	−0.980119	−	0.198410i	$-0.936422\pi$
$967$		−	12.3398i		−	0.396821i	0.980119	−	0.198410i	$-0.0635779\pi$
$968$		0			0
$969$	−3.32405	−	1.91914i	−0.106784	−	0.0616518i
$970$		0			0
$971$	−5.46696	+	3.15635i	−0.175443	+	0.101292i	−0.585150	−	0.810925i	$-0.698964\pi$
$971$	−5.46696	+	3.15635i	−0.175443	+	0.101292i	0.409707	+	0.912217i	$0.365631\pi$
$972$		0			0
$973$	−41.6696	−	21.9591i	−1.33587	−	0.703976i
$974$		0			0
$975$	3.38385	−	1.95367i	0.108370	−	0.0625674i
$976$		0			0
$977$	−5.33460	+	9.23979i	−0.170669	+	0.295607i	−0.938654	−	0.344861i	$-0.887926\pi$
$977$	−5.33460	+	9.23979i	−0.170669	+	0.295607i	0.767985	+	0.640468i	$0.221260\pi$
$978$		0			0
$979$		−	9.91399i		−	0.316852i
$980$		0			0
$981$		−	19.9673i		−	0.637507i
$982$		0			0
$983$	−7.67846	+	13.2995i	−0.244905	+	0.424188i	−0.962105	−	0.272680i	$-0.912090\pi$
$983$	−7.67846	+	13.2995i	−0.244905	+	0.424188i	0.717200	+	0.696867i	$0.245423\pi$
$984$		0			0
$985$	−1.44139	+	0.832187i	−0.0459265	+	0.0265157i
$986$		0			0
$987$	22.7998	+	12.0150i	0.725725	+	0.382443i
$988$		0			0
$989$	−0.683392	+	0.394556i	−0.0217306	+	0.0125462i
$990$		0			0
$991$	−20.0575	−	11.5802i	−0.637148	−	0.367857i	0.146367	−	0.989230i	$-0.453242\pi$
$991$	−20.0575	−	11.5802i	−0.637148	−	0.367857i	−0.783515	+	0.621373i	$0.786575\pi$
$992$		0			0
$993$			10.1419i			0.321844i
$994$		0			0
$995$	−12.7940			−0.405597
$996$		0			0
$997$	4.75443	−	8.23492i	0.150574	−	0.260803i	−0.780864	−	0.624701i	$-0.785221\pi$
$997$	4.75443	−	8.23492i	0.150574	−	0.260803i	0.931439	+	0.363898i	$0.118554\pi$
$998$		0			0
$999$	11.5092	+	19.9344i	0.364133	+	0.630698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bz.e.591.6		24
4.3	odd	2		280.2.bj.f.171.4	yes	24
7.5	odd	6		1120.2.bz.f.271.6		24
8.3	odd	2		1120.2.bz.f.591.6		24
8.5	even	2		280.2.bj.e.171.12	yes	24
28.19	even	6		280.2.bj.e.131.12	✓	24
56.5	odd	6		280.2.bj.f.131.4	yes	24
56.19	even	6	inner	1120.2.bz.e.271.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.12	✓	24	28.19	even	6
280.2.bj.e.171.12	yes	24	8.5	even	2
280.2.bj.f.131.4	yes	24	56.5	odd	6
280.2.bj.f.171.4	yes	24	4.3	odd	2
1120.2.bz.e.271.6		24	56.19	even	6	inner
1120.2.bz.e.591.6		24	1.1	even	1	trivial
1120.2.bz.f.271.6		24	7.5	odd	6
1120.2.bz.f.591.6		24	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.784482 - 0.452921i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.23347 + 2.34063i) q^{7} +(-1.08973 - 1.88746i) q^{9} +O(q^{10})\)	\(q+(-0.784482 - 0.452921i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.23347 + 2.34063i) q^{7} +(-1.08973 - 1.88746i) q^{9} +(-0.620880 + 1.07539i) q^{11} +4.31348 q^{13} +0.905842i q^{15} +(-1.49339 - 0.862209i) q^{17} +(-2.12801 + 1.22861i) q^{19} +(2.02775 - 1.27752i) q^{21} +(0.393079 - 0.226944i) q^{23} +(-0.500000 + 0.866025i) q^{25} +4.69176i q^{27} +7.69695i q^{29} +(-0.133444 + 0.231133i) q^{31} +(0.974138 - 0.562419i) q^{33} +(2.64378 - 0.102102i) q^{35} +(4.24881 - 2.45305i) q^{37} +(-3.38385 - 1.95367i) q^{39} +12.2703i q^{41} -1.73856 q^{43} +(-1.08973 + 1.88746i) q^{45} +(5.37669 + 9.31270i) q^{47} +(-3.95712 - 5.77419i) q^{49} +(0.781025 + 1.35278i) q^{51} +(7.50728 + 4.33433i) q^{53} +1.24176 q^{55} +2.22584 q^{57} +(4.83628 + 2.79223i) q^{59} +(0.462932 + 0.801822i) q^{61} +(5.76199 - 0.222526i) q^{63} +(-2.15674 - 3.73558i) q^{65} +(-0.465968 + 0.807080i) q^{67} -0.411152 q^{69} +8.36052i q^{71} +(-6.21972 - 3.59095i) q^{73} +(0.784482 - 0.452921i) q^{75} +(-1.75127 - 2.77972i) q^{77} +(9.56196 - 5.52060i) q^{79} +(-1.14418 + 1.98177i) q^{81} -8.49133i q^{83} +1.72442i q^{85} +(3.48611 - 6.03812i) q^{87} +(-6.91420 + 3.99191i) q^{89} +(-5.32054 + 10.0963i) q^{91} +(0.209370 - 0.120880i) q^{93} +(2.12801 + 1.22861i) q^{95} +3.92866i q^{97} +2.70635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9	\( 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9} - 8 q^{11} + 20 q^{13} + 6 q^{17} - 18 q^{19} - 26 q^{21} - 18 q^{23} - 12 q^{25} + 6 q^{31} + 12 q^{33} + 8 q^{35} + 18 q^{39} - 32 q^{43} + 12 q^{45} + 8 q^{49} + 22 q^{51} + 30 q^{53} + 16 q^{55} - 44 q^{57} + 18 q^{59} + 22 q^{61} + 12 q^{63} - 10 q^{65} + 8 q^{67} - 12 q^{69} + 30 q^{73} + 12 q^{75} - 32 q^{77} - 6 q^{79} - 4 q^{81} - 14 q^{87} - 60 q^{89} - 18 q^{91} - 18 q^{93} + 18 q^{95} + 56 q^{99}+O(q^{100}) \) 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9 - 8 * q^11 + 20 * q^13 + 6 * q^17 - 18 * q^19 - 26 * q^21 - 18 * q^23 - 12 * q^25 + 6 * q^31 + 12 * q^33 + 8 * q^35 + 18 * q^39 - 32 * q^43 + 12 * q^45 + 8 * q^49 + 22 * q^51 + 30 * q^53 + 16 * q^55 - 44 * q^57 + 18 * q^59 + 22 * q^61 + 12 * q^63 - 10 * q^65 + 8 * q^67 - 12 * q^69 + 30 * q^73 + 12 * q^75 - 32 * q^77 - 6 * q^79 - 4 * q^81 - 14 * q^87 - 60 * q^89 - 18 * q^91 - 18 * q^93 + 18 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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