LMFDB - Embedded newform 504.2.j.a.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(323,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("504.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.j (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.1
Character	$\chi$	$=$	504.323
Dual form			504.2.j.a.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40979 - 0.111820i) q^{2} +(1.97499 + 0.315285i) q^{4} -0.472391 q^{5} +1.00000i q^{7} +(-2.74906 - 0.665328i) q^{8} +O(q^{10})$	\(q+(-1.40979 - 0.111820i) q^{2} +(1.97499 + 0.315285i) q^{4} -0.472391 q^{5} +1.00000i q^{7} +(-2.74906 - 0.665328i) q^{8} +(0.665969 + 0.0528227i) q^{10} -3.86027i q^{11} -3.00314i q^{13} +(0.111820 - 1.40979i) q^{14} +(3.80119 + 1.24537i) q^{16} +1.23178i q^{17} +6.30375 q^{19} +(-0.932968 - 0.148938i) q^{20} +(-0.431656 + 5.44215i) q^{22} +1.60109 q^{23} -4.77685 q^{25} +(-0.335811 + 4.23379i) q^{26} +(-0.315285 + 1.97499i) q^{28} +6.36571 q^{29} -9.09494i q^{31} +(-5.21961 - 2.18075i) q^{32} +(0.137738 - 1.73655i) q^{34} -0.472391i q^{35} +0.844507i q^{37} +(-8.88694 - 0.704886i) q^{38} +(1.29863 + 0.314295i) q^{40} -2.07052i q^{41} +5.97495 q^{43} +(1.21708 - 7.62400i) q^{44} +(-2.25719 - 0.179034i) q^{46} +7.22491 q^{47} -1.00000 q^{49} +(6.73433 + 0.534147i) q^{50} +(0.946844 - 5.93118i) q^{52} +6.64588 q^{53} +1.82355i q^{55} +(0.665328 - 2.74906i) q^{56} +(-8.97429 - 0.711814i) q^{58} -7.22491i q^{59} -7.67120i q^{61} +(-1.01700 + 12.8219i) q^{62} +(7.11468 + 3.65805i) q^{64} +1.41866i q^{65} +0.304417 q^{67} +(-0.388362 + 2.43276i) q^{68} +(-0.0528227 + 0.665969i) q^{70} +4.28011 q^{71} -11.9966 q^{73} +(0.0944328 - 1.19057i) q^{74} +(12.4499 + 1.98748i) q^{76} +3.86027 q^{77} -8.86550i q^{79} +(-1.79565 - 0.588301i) q^{80} +(-0.231526 + 2.91899i) q^{82} -9.28860i q^{83} -0.581882i q^{85} +(-8.42340 - 0.668120i) q^{86} +(-2.56834 + 10.6121i) q^{88} +16.1329i q^{89} +3.00314 q^{91} +(3.16214 + 0.504798i) q^{92} +(-10.1856 - 0.807891i) q^{94} -2.97783 q^{95} -13.5357 q^{97} +(1.40979 + 0.111820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4}+O(q^{10}) $ 24 * q - 8 * q^4	$ 24 q - 8 q^{4} + 24 q^{10} + 12 q^{16} + 32 q^{19} + 12 q^{22} + 24 q^{25} + 4 q^{28} - 8 q^{40} - 64 q^{43} - 12 q^{46} - 24 q^{49} - 16 q^{52} - 12 q^{58} + 16 q^{64} + 16 q^{67} + 24 q^{70} + 8 q^{76} + 24 q^{82} - 84 q^{88} - 72 q^{94}+O(q^{100}) $ 24 * q - 8 * q^4 + 24 * q^10 + 12 * q^16 + 32 * q^19 + 12 * q^22 + 24 * q^25 + 4 * q^28 - 8 * q^40 - 64 * q^43 - 12 * q^46 - 24 * q^49 - 16 * q^52 - 12 * q^58 + 16 * q^64 + 16 * q^67 + 24 * q^70 + 8 * q^76 + 24 * q^82 - 84 * q^88 - 72 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.40979	−	0.111820i	−0.996869	−	0.0790687i
$2$	−1.40979	−	0.111820i	−0.996869	−	0.0790687i
$3$		0			0
$3$		0			0
$4$	1.97499	+	0.315285i	0.987496	+	0.157642i
$5$	−0.472391			−0.211259			−0.105630	−	0.994406i	$-0.533686\pi$
$5$	−0.472391			−0.211259			−0.105630	+	0.994406i	$0.533686\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−2.74906	−	0.665328i	−0.971940	−	0.235229i
$9$		0			0
$10$	0.665969	+	0.0528227i	0.210598	+	0.0167040i
$11$		−	3.86027i		−	1.16391i	−0.813219	−	0.581957i	$-0.802287\pi$
$11$		−	3.86027i		−	1.16391i	0.813219	−	0.581957i	$-0.197713\pi$
$12$		0			0
$13$		−	3.00314i		−	0.832921i	−0.909154	−	0.416461i	$-0.863270\pi$
$13$		−	3.00314i		−	0.832921i	0.909154	−	0.416461i	$-0.136730\pi$
$14$	0.111820	−	1.40979i	0.0298852	−	0.376781i
$15$		0			0
$16$	3.80119	+	1.24537i	0.950298	+	0.311343i
$17$			1.23178i			0.298751i	0.988781	+	0.149375i	$0.0477263\pi$
$17$			1.23178i			0.298751i	−0.988781	+	0.149375i	$0.952274\pi$
$18$		0			0
$19$	6.30375			1.44618			0.723090	−	0.690754i	$-0.242721\pi$
$19$	6.30375			1.44618			0.723090	+	0.690754i	$0.242721\pi$
$20$	−0.932968	−	0.148938i	−0.208618	−	0.0333034i
$21$		0			0
$22$	−0.431656	+	5.44215i	−0.0920293	+	1.16027i
$23$	1.60109			0.333850			0.166925	−	0.985970i	$-0.446616\pi$
$23$	1.60109			0.333850			0.166925	+	0.985970i	$0.446616\pi$
$24$		0			0
$25$	−4.77685			−0.955369
$26$	−0.335811	+	4.23379i	−0.0658580	+	0.830314i
$27$		0			0
$28$	−0.315285	+	1.97499i	−0.0595832	+	0.373239i
$29$	6.36571			1.18208			0.591041	−	0.806641i	$-0.298717\pi$
$29$	6.36571			1.18208			0.591041	+	0.806641i	$0.298717\pi$
$30$		0			0
$31$		−	9.09494i		−	1.63350i	−0.576993	−	0.816749i	$-0.695774\pi$
$31$		−	9.09494i		−	1.63350i	0.576993	−	0.816749i	$-0.304226\pi$
$32$	−5.21961	−	2.18075i	−0.922705	−	0.385507i
$33$		0			0
$34$	0.137738	−	1.73655i	0.0236219	−	0.297815i
$35$		−	0.472391i		−	0.0798486i
$36$		0			0
$37$			0.844507i			0.138836i	0.997588	+	0.0694180i	$0.0221142\pi$
$37$			0.844507i			0.138836i	−0.997588	+	0.0694180i	$0.977886\pi$
$38$	−8.88694	−	0.704886i	−1.44165	−	0.114348i
$39$		0			0
$40$	1.29863	+	0.314295i	0.205332	+	0.0496943i
$41$		−	2.07052i		−	0.323361i	−0.986843	−	0.161680i	$-0.948309\pi$
$41$		−	2.07052i		−	0.323361i	0.986843	−	0.161680i	$-0.0516914\pi$
$42$		0			0
$43$	5.97495			0.911172			0.455586	−	0.890192i	$-0.349430\pi$
$43$	5.97495			0.911172			0.455586	+	0.890192i	$0.349430\pi$
$44$	1.21708	−	7.62400i	0.183482	−	1.14936i
$45$		0			0
$46$	−2.25719	−	0.179034i	−0.332805	−	0.0263971i
$47$	7.22491			1.05386			0.526931	−	0.849908i	$-0.323343\pi$
$47$	7.22491			1.05386			0.526931	+	0.849908i	$0.323343\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	6.73433	+	0.534147i	0.952378	+	0.0755399i
$51$		0			0
$52$	0.946844	−	5.93118i	0.131304	−	0.822507i
$53$	6.64588			0.912881			0.456441	−	0.889754i	$-0.349124\pi$
$53$	6.64588			0.912881			0.456441	+	0.889754i	$0.349124\pi$
$54$		0			0
$55$			1.82355i			0.245888i
$56$	0.665328	−	2.74906i	0.0889082	−	0.367359i
$57$		0			0
$58$	−8.97429	−	0.711814i	−1.17838	−	0.0934658i
$59$		−	7.22491i		−	0.940604i	−0.882506	−	0.470302i	$-0.844145\pi$
$59$		−	7.22491i		−	0.940604i	0.882506	−	0.470302i	$-0.155855\pi$
$60$		0			0
$61$		−	7.67120i		−	0.982197i	−0.871104	−	0.491098i	$-0.836596\pi$
$61$		−	7.67120i		−	0.982197i	0.871104	−	0.491098i	$-0.163404\pi$
$62$	−1.01700	+	12.8219i	−0.129159	+	1.62838i
$63$		0			0
$64$	7.11468	+	3.65805i	0.889335	+	0.457257i
$65$			1.41866i			0.175963i
$66$		0			0
$67$	0.304417			0.0371905			0.0185952	−	0.999827i	$-0.494081\pi$
$67$	0.304417			0.0371905			0.0185952	+	0.999827i	$0.494081\pi$
$68$	−0.388362	+	2.43276i	−0.0470958	+	0.295015i
$69$		0			0
$70$	−0.0528227	+	0.665969i	−0.00631353	+	0.0795986i
$71$	4.28011			0.507956			0.253978	−	0.967210i	$-0.418261\pi$
$71$	4.28011			0.507956			0.253978	+	0.967210i	$0.418261\pi$
$72$		0			0
$73$	−11.9966			−1.40410			−0.702049	−	0.712129i	$-0.747731\pi$
$73$	−11.9966			−1.40410			−0.702049	+	0.712129i	$0.747731\pi$
$74$	0.0944328	−	1.19057i	0.0109776	−	0.138401i
$75$		0			0
$76$	12.4499	+	1.98748i	1.42810	+	0.227979i
$77$	3.86027			0.439919
$78$		0			0
$79$		−	8.86550i		−	0.997447i	−0.866761	−	0.498723i	$-0.833802\pi$
$79$		−	8.86550i		−	0.997447i	0.866761	−	0.498723i	$-0.166198\pi$
$80$	−1.79565	−	0.588301i	−0.200759	−	0.0657740i
$81$		0			0
$82$	−0.231526	+	2.91899i	−0.0255677	+	0.322349i
$83$		−	9.28860i		−	1.01956i	−0.860306	−	0.509778i	$-0.829728\pi$
$83$		−	9.28860i		−	1.01956i	0.860306	−	0.509778i	$-0.170272\pi$
$84$		0			0
$85$		−	0.581882i		−	0.0631139i
$86$	−8.42340	−	0.668120i	−0.908319	−	0.0720452i
$87$		0			0
$88$	−2.56834	+	10.6121i	−0.273786	+	1.13126i
$89$			16.1329i			1.71009i	0.518556	+	0.855044i	$0.326470\pi$
$89$			16.1329i			1.71009i	−0.518556	+	0.855044i	$0.673530\pi$
$90$		0			0
$91$	3.00314			0.314815
$92$	3.16214	+	0.504798i	0.329675	+	0.0526289i
$93$		0			0
$94$	−10.1856	−	0.807891i	−1.05056	−	0.0833275i
$95$	−2.97783			−0.305519
$96$		0			0
$97$	−13.5357			−1.37434			−0.687169	−	0.726498i	$-0.741147\pi$
$97$	−13.5357			−1.37434			−0.687169	+	0.726498i	$0.741147\pi$
$98$	1.40979	+	0.111820i	0.142410	+	0.0112955i
$99$		0			0
$100$	−9.43424	−	1.50607i	−0.943424	−	0.150607i
$101$	−12.9050			−1.28410			−0.642048	−	0.766665i	$-0.721915\pi$
$101$	−12.9050			−1.28410			−0.642048	+	0.766665i	$0.721915\pi$
$102$		0			0
$103$			2.64368i			0.260490i	0.991482	+	0.130245i	$0.0415763\pi$
$103$			2.64368i			0.260490i	−0.991482	+	0.130245i	$0.958424\pi$
$104$	−1.99807	+	8.25582i	−0.195927	+	0.809550i
$105$		0			0
$106$	−9.36926	−	0.743142i	−0.910023	−	0.0721804i
$107$			1.97071i			0.190515i	0.995453	+	0.0952577i	$0.0303675\pi$
$107$			1.97071i			0.190515i	−0.995453	+	0.0952577i	$0.969632\pi$
$108$		0			0
$109$			13.3987i			1.28336i	0.766972	+	0.641681i	$0.221763\pi$
$109$			13.3987i			1.28336i	−0.766972	+	0.641681i	$0.778237\pi$
$110$	0.203910	−	2.57082i	0.0194421	−	0.245118i
$111$		0			0
$112$	−1.24537	+	3.80119i	−0.117676	+	0.359179i
$113$			19.1379i			1.80034i	0.435539	+	0.900170i	$0.356558\pi$
$113$			19.1379i			1.80034i	−0.435539	+	0.900170i	$0.643442\pi$
$114$		0			0
$115$	−0.756339			−0.0705289
$116$	12.5722	+	2.00701i	1.16730	+	0.186346i
$117$		0			0
$118$	−0.807891	+	10.1856i	−0.0743724	+	0.937659i
$119$	−1.23178			−0.112917
$120$		0			0
$121$	−3.90168			−0.354698
$122$	−0.857794	+	10.8148i	−0.0776611	+	0.979122i
$123$		0			0
$124$	2.86749	−	17.9624i	0.257509	−	1.61307i
$125$	4.61849			0.413090
$126$		0			0
$127$			16.2079i			1.43822i	0.694897	+	0.719109i	$0.255450\pi$
$127$			16.2079i			1.43822i	−0.694897	+	0.719109i	$0.744550\pi$
$128$	−9.62113	−	5.95264i	−0.850396	−	0.526144i
$129$		0			0
$130$	0.158634	−	2.00000i	0.0139131	−	0.175412i
$131$			11.6875i			1.02114i	0.859837	+	0.510569i	$0.170565\pi$
$131$			11.6875i			1.02114i	−0.859837	+	0.510569i	$0.829435\pi$
$132$		0			0
$133$			6.30375i			0.546605i
$134$	−0.429163	−	0.0340400i	−0.0370741	−	0.00294061i
$135$		0			0
$136$	0.819538	−	3.38624i	0.0702748	−	0.290368i
$137$		−	11.4480i		−	0.978066i	−0.872265	−	0.489033i	$-0.837350\pi$
$137$		−	11.4480i		−	0.978066i	0.872265	−	0.489033i	$-0.162650\pi$
$138$		0			0
$139$	−1.18616			−0.100608			−0.0503042	−	0.998734i	$-0.516019\pi$
$139$	−1.18616			−0.100608			−0.0503042	+	0.998734i	$0.516019\pi$
$140$	0.148938	−	0.932968i	0.0125875	−	0.0788502i
$141$		0			0
$142$	−6.03404	−	0.478602i	−0.506365	−	0.0401634i
$143$	−11.5929			−0.969450
$144$		0			0
$145$	−3.00710			−0.249726
$146$	16.9127	+	1.34146i	1.39970	+	0.111020i
$147$		0			0
$148$	−0.266260	+	1.66789i	−0.0218864	+	0.137100i
$149$	−1.32419			−0.108482			−0.0542411	−	0.998528i	$-0.517274\pi$
$149$	−1.32419			−0.108482			−0.0542411	+	0.998528i	$0.517274\pi$
$150$		0			0
$151$			5.18616i			0.422043i	0.977481	+	0.211022i	$0.0676791\pi$
$151$			5.18616i			0.422043i	−0.977481	+	0.211022i	$0.932321\pi$
$152$	−17.3294	−	4.19406i	−1.40560	−	0.340183i
$153$		0			0
$154$	−5.44215	−	0.431656i	−0.438541	−	0.0347838i
$155$			4.29636i			0.345092i
$156$		0			0
$157$		−	11.2473i		−	0.897631i	−0.893624	−	0.448816i	$-0.851846\pi$
$157$		−	11.2473i		−	0.897631i	0.893624	−	0.448816i	$-0.148154\pi$
$158$	−0.991341	+	12.4985i	−0.0788669	+	0.994324i
$159$		0			0
$160$	2.46569	+	1.03017i	0.194930	+	0.0814419i
$161$			1.60109i			0.126183i
$162$		0			0
$163$	11.7081			0.917053			0.458526	−	0.888681i	$-0.348377\pi$
$163$	11.7081			0.917053			0.458526	+	0.888681i	$0.348377\pi$
$164$	0.652803	−	4.08926i	0.0509754	−	0.319318i
$165$		0			0
$166$	−1.03865	+	13.0949i	−0.0806150	+	1.01636i
$167$	4.60266			0.356164			0.178082	−	0.984016i	$-0.443011\pi$
$167$	4.60266			0.356164			0.178082	+	0.984016i	$0.443011\pi$
$168$		0			0
$169$	3.98115			0.306242
$170$	−0.0650661	+	0.820329i	−0.00499034	+	0.0629163i
$171$		0			0
$172$	11.8005	+	1.88381i	0.899779	+	0.143639i
$173$	−11.2355			−0.854217			−0.427108	−	0.904200i	$-0.640468\pi$
$173$	−11.2355			−0.854217			−0.427108	+	0.904200i	$0.640468\pi$
$174$		0			0
$175$		−	4.77685i		−	0.361096i
$176$	4.80746	−	14.6736i	0.362376	−	1.10607i
$177$		0			0
$178$	1.80399	−	22.7440i	0.135214	−	1.70473i
$179$		−	18.7406i		−	1.40074i	−0.713781	−	0.700369i	$-0.753019\pi$
$179$		−	18.7406i		−	1.40074i	0.713781	−	0.700369i	$-0.246981\pi$
$180$		0			0
$181$			19.3191i			1.43598i	0.696056	+	0.717988i	$0.254937\pi$
$181$			19.3191i			1.43598i	−0.696056	+	0.717988i	$0.745063\pi$
$182$	−4.23379	−	0.335811i	−0.313829	−	0.0248920i
$183$		0			0
$184$	−4.40149	−	1.06525i	−0.324482	−	0.0785311i
$185$		−	0.398937i		−	0.0293304i
$186$		0			0
$187$	4.75501			0.347721
$188$	14.2692	+	2.27791i	1.04068	+	0.166133i
$189$		0			0
$190$	4.19811	+	0.332981i	0.304563	+	0.0241570i
$191$	−24.9471			−1.80511			−0.902555	−	0.430574i	$-0.858311\pi$
$191$	−24.9471			−1.80511			−0.902555	+	0.430574i	$0.858311\pi$
$192$		0			0
$193$	−4.75171			−0.342036			−0.171018	−	0.985268i	$-0.554706\pi$
$193$	−4.75171			−0.342036			−0.171018	+	0.985268i	$0.554706\pi$
$194$	19.0824	+	1.51356i	1.37004	+	0.108667i
$195$		0			0
$196$	−1.97499	−	0.315285i	−0.141071	−	0.0225203i
$197$	−16.7002			−1.18984			−0.594919	−	0.803786i	$-0.702816\pi$
$197$	−16.7002			−1.18984			−0.594919	+	0.803786i	$0.702816\pi$
$198$		0			0
$199$		−	7.72605i		−	0.547685i	−0.961774	−	0.273843i	$-0.911705\pi$
$199$		−	7.72605i		−	0.547685i	0.961774	−	0.273843i	$-0.0882948\pi$
$200$	13.1318	+	3.17817i	0.928562	+	0.224731i
$201$		0			0
$202$	18.1933	+	1.44304i	1.28008	+	0.101532i
$203$			6.36571i			0.446785i
$204$		0			0
$205$			0.978094i			0.0683130i
$206$	0.295617	−	3.72702i	0.0205966	−	0.259674i
$207$		0			0
$208$	3.74002	−	11.4155i	0.259324	−	0.791523i
$209$		−	24.3342i		−	1.68323i
$210$		0			0
$211$	9.55104			0.657521			0.328760	−	0.944413i	$-0.393369\pi$
$211$	9.55104			0.657521			0.328760	+	0.944413i	$0.393369\pi$
$212$	13.1256	+	2.09534i	0.901467	+	0.143909i
$213$		0			0
$214$	0.220365	−	2.77828i	0.0150638	−	0.189919i
$215$	−2.82251			−0.192494
$216$		0			0
$217$	9.09494			0.617404
$218$	1.49824	−	18.8893i	0.101474	−	1.27934i
$219$		0			0
$220$	−0.574939	+	3.60151i	−0.0387624	+	0.242814i
$221$	3.69921			0.248836
$222$		0			0
$223$			19.7999i			1.32590i	0.748663	+	0.662951i	$0.230696\pi$
$223$			19.7999i			1.32590i	−0.748663	+	0.662951i	$0.769304\pi$
$224$	2.18075	−	5.21961i	0.145708	−	0.348750i
$225$		0			0
$226$	2.14000	−	26.9803i	0.142351	−	1.79470i
$227$			5.92118i			0.393003i	0.980504	+	0.196501i	$0.0629580\pi$
$227$			5.92118i			0.393003i	−0.980504	+	0.196501i	$0.937042\pi$
$228$		0			0
$229$		−	21.8715i		−	1.44531i	−0.691208	−	0.722656i	$-0.742921\pi$
$229$		−	21.8715i		−	1.44531i	0.691208	−	0.722656i	$-0.257079\pi$
$230$	1.06628	+	0.0845738i	0.0703081	+	0.00557663i
$231$		0			0
$232$	−17.4997	−	4.23528i	−1.14891	−	0.278060i
$233$			26.4436i			1.73238i	0.499714	+	0.866190i	$0.333438\pi$
$233$			26.4436i			1.73238i	−0.499714	+	0.866190i	$0.666562\pi$
$234$		0			0
$235$	−3.41298			−0.222638
$236$	2.27791	−	14.2692i	0.148279	−	0.928843i
$237$		0			0
$238$	1.73655	+	0.137738i	0.112564	+	0.00892822i
$239$	18.7074			1.21008			0.605040	−	0.796195i	$-0.293157\pi$
$239$	18.7074			1.21008			0.605040	+	0.796195i	$0.293157\pi$
$240$		0			0
$241$	17.7777			1.14516			0.572581	−	0.819848i	$-0.305942\pi$
$241$	17.7777			1.14516			0.572581	+	0.819848i	$0.305942\pi$
$242$	5.50053	+	0.436286i	0.353588	+	0.0280455i
$243$		0			0
$244$	2.41861	−	15.1506i	0.154836	−	0.969916i
$245$	0.472391			0.0301799
$246$		0			0
$247$		−	18.9311i		−	1.20455i
$248$	−6.05111	+	25.0025i	−0.384246	+	1.58766i
$249$		0			0
$250$	−6.51108	−	0.516440i	−0.411797	−	0.0326625i
$251$		−	26.4980i		−	1.67254i	−0.548319	−	0.836269i	$-0.684732\pi$
$251$		−	26.4980i		−	1.67254i	0.548319	−	0.836269i	$-0.315268\pi$
$252$		0			0
$253$		−	6.18063i		−	0.388573i
$254$	1.81237	−	22.8497i	0.113718	−	1.43372i
$255$		0			0
$256$	12.8981	+	9.46778i	0.806132	+	0.591736i
$257$		−	13.9701i		−	0.871428i	−0.900085	−	0.435714i	$-0.856496\pi$
$257$		−	13.9701i		−	0.871428i	0.900085	−	0.435714i	$-0.143504\pi$
$258$		0			0
$259$	−0.844507			−0.0524751
$260$	−0.447280	+	2.80183i	−0.0277391	+	0.173762i
$261$		0			0
$262$	1.30689	−	16.4768i	0.0807401	−	1.01794i
$263$	−6.32796			−0.390199			−0.195099	−	0.980783i	$-0.562503\pi$
$263$	−6.32796			−0.390199			−0.195099	+	0.980783i	$0.562503\pi$
$264$		0			0
$265$	−3.13945			−0.192855
$266$	0.704886	−	8.88694i	0.0432193	−	0.544893i
$267$		0			0
$268$	0.601222	+	0.0959781i	0.0367255	+	0.00586280i
$269$	20.4855			1.24902			0.624511	−	0.781016i	$-0.285298\pi$
$269$	20.4855			1.24902			0.624511	+	0.781016i	$0.285298\pi$
$270$		0			0
$271$			27.9200i			1.69602i	0.529980	+	0.848010i	$0.322199\pi$
$271$			27.9200i			1.69602i	−0.529980	+	0.848010i	$0.677801\pi$
$272$	−1.53402	+	4.68224i	−0.0930138	+	0.283902i
$273$		0			0
$274$	−1.28011	+	16.1392i	−0.0773344	+	0.975004i
$275$			18.4399i			1.11197i
$276$		0			0
$277$			24.8365i			1.49228i	0.665789	+	0.746140i	$0.268095\pi$
$277$			24.8365i			1.49228i	−0.665789	+	0.746140i	$0.731905\pi$
$278$	1.67223	+	0.132636i	0.100293	+	0.00795498i
$279$		0			0
$280$	−0.314295	+	1.29863i	−0.0187827	+	0.0776080i
$281$		−	13.7592i		−	0.820803i	−0.911905	−	0.410401i	$-0.865389\pi$
$281$		−	13.7592i		−	0.820803i	0.911905	−	0.410401i	$-0.134611\pi$
$282$		0			0
$283$	−14.7697			−0.877965			−0.438982	−	0.898496i	$-0.644661\pi$
$283$	−14.7697			−0.877965			−0.438982	+	0.898496i	$0.644661\pi$
$284$	8.45318	+	1.34945i	0.501604	+	0.0800753i
$285$		0			0
$286$	16.3436	+	1.29632i	0.966414	+	0.0766532i
$287$	2.07052			0.122219
$288$		0			0
$289$	15.4827			0.910748
$290$	4.23937	+	0.336254i	0.248944	+	0.0197455i
$291$		0			0
$292$	−23.6932	−	3.78235i	−1.38654	−	0.221345i
$293$	−27.9910			−1.63525			−0.817625	−	0.575751i	$-0.804710\pi$
$293$	−27.9910			−1.63525			−0.817625	+	0.575751i	$0.804710\pi$
$294$		0			0
$295$			3.41298i			0.198711i
$296$	0.561874	−	2.32160i	0.0326582	−	0.134940i
$297$		0			0
$298$	1.86683	+	0.148072i	0.108143	+	0.00857755i
$299$		−	4.80829i		−	0.278071i
$300$		0			0
$301$			5.97495i			0.344391i
$302$	0.579916	−	7.31137i	0.0333704	−	0.420722i
$303$		0			0
$304$	23.9618	+	7.85050i	1.37430	+	0.450257i
$305$			3.62380i			0.207498i
$306$		0			0
$307$	−20.5339			−1.17193			−0.585965	−	0.810336i	$-0.699285\pi$
$307$	−20.5339			−1.17193			−0.585965	+	0.810336i	$0.699285\pi$
$308$	7.62400	+	1.21708i	0.434418	+	0.0693498i
$309$		0			0
$310$	0.480419	−	6.05695i	0.0272860	−	0.344012i
$311$	−33.0497			−1.87408			−0.937039	−	0.349225i	$-0.886445\pi$
$311$	−33.0497			−1.87408			−0.937039	+	0.349225i	$0.886445\pi$
$312$		0			0
$313$	12.9588			0.732472			0.366236	−	0.930522i	$-0.380646\pi$
$313$	12.9588			0.732472			0.366236	+	0.930522i	$0.380646\pi$
$314$	−1.25767	+	15.8563i	−0.0709746	+	0.894821i
$315$		0			0
$316$	2.79516	−	17.5093i	0.157240	−	0.984975i
$317$	20.9318			1.17565			0.587824	−	0.808989i	$-0.299985\pi$
$317$	20.9318			1.17565			0.587824	+	0.808989i	$0.299985\pi$
$318$		0			0
$319$		−	24.5734i		−	1.37584i
$320$	−3.36091	−	1.72803i	−0.187880	−	0.0965998i
$321$		0			0
$322$	0.179034	−	2.25719i	0.00997716	−	0.125788i
$323$			7.76484i			0.432047i
$324$		0			0
$325$			14.3455i			0.795748i
$326$	−16.5060	−	1.30921i	−0.914182	−	0.0725102i
$327$		0			0
$328$	−1.37757	+	5.69199i	−0.0760638	+	0.314287i
$329$			7.22491i			0.398322i
$330$		0			0
$331$	7.88973			0.433659			0.216829	−	0.976210i	$-0.430428\pi$
$331$	7.88973			0.433659			0.216829	+	0.976210i	$0.430428\pi$
$332$	2.92855	−	18.3449i	0.160725	−	1.00681i
$333$		0			0
$334$	−6.48876	−	0.514669i	−0.355049	−	0.0281615i
$335$	−0.143804			−0.00785684
$336$		0			0
$337$	15.0377			0.819156			0.409578	−	0.912275i	$-0.365676\pi$
$337$	15.0377			0.819156			0.409578	+	0.912275i	$0.365676\pi$
$338$	−5.61256	−	0.445172i	−0.305283	−	0.0242142i
$339$		0			0
$340$	0.183458	−	1.14921i	0.00994943	−	0.0623248i
$341$	−35.1089			−1.90125
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−16.4255	−	3.97530i	−0.885604	−	0.214334i
$345$		0			0
$346$	15.8396	+	1.25635i	0.851542	+	0.0675418i
$347$			25.6693i			1.37800i	0.724760	+	0.689001i	$0.241951\pi$
$347$			25.6693i			1.37800i	−0.724760	+	0.689001i	$0.758049\pi$
$348$		0			0
$349$		−	20.2787i		−	1.08549i	−0.839896	−	0.542747i	$-0.817384\pi$
$349$		−	20.2787i		−	1.08549i	0.839896	−	0.542747i	$-0.182616\pi$
$350$	−0.534147	+	6.73433i	−0.0285514	+	0.359965i
$351$		0			0
$352$	−8.41830	+	20.1491i	−0.448697	+	1.07395i
$353$		−	17.1467i		−	0.912628i	−0.889819	−	0.456314i	$-0.849169\pi$
$353$		−	17.1467i		−	0.912628i	0.889819	−	0.456314i	$-0.150831\pi$
$354$		0			0
$355$	−2.02188			−0.107310
$356$	−5.08647	+	31.8624i	−0.269582	+	1.68870i
$357$		0			0
$358$	−2.09558	+	26.4202i	−0.110755	+	1.39635i
$359$	6.55709			0.346070			0.173035	−	0.984916i	$-0.444643\pi$
$359$	6.55709			0.346070			0.173035	+	0.984916i	$0.444643\pi$
$360$		0			0
$361$	20.7373			1.09144
$362$	2.16026	−	27.2358i	0.113541	−	1.43148i
$363$		0			0
$364$	5.93118	+	0.946844i	0.310878	+	0.0496281i
$365$	5.66709			0.296629
$366$		0			0
$367$		−	9.09407i		−	0.474707i	−0.971423	−	0.237353i	$-0.923720\pi$
$367$		−	9.09407i		−	0.474707i	0.971423	−	0.237353i	$-0.0762799\pi$
$368$	6.08604	+	1.99395i	0.317257	+	0.103942i
$369$		0			0
$370$	−0.0446092	+	0.562416i	−0.00231912	+	0.0292386i
$371$			6.64588i			0.345037i
$372$		0			0
$373$			13.9450i			0.722042i	0.932558	+	0.361021i	$0.117572\pi$
$373$			13.9450i			0.722042i	−0.932558	+	0.361021i	$0.882428\pi$
$374$	−6.70354	−	0.531705i	−0.346632	−	0.0274938i
$375$		0			0
$376$	−19.8617	−	4.80694i	−1.02429	−	0.247899i
$377$		−	19.1171i		−	0.984582i
$378$		0			0
$379$	−4.03969			−0.207505			−0.103753	−	0.994603i	$-0.533085\pi$
$379$	−4.03969			−0.207505			−0.103753	+	0.994603i	$0.533085\pi$
$380$	−5.88120	−	0.938865i	−0.301699	−	0.0481628i
$381$		0			0
$382$	35.1701	+	2.78959i	1.79946	+	0.142728i
$383$	29.5065			1.50771			0.753855	−	0.657041i	$-0.228192\pi$
$383$	29.5065			1.50771			0.753855	+	0.657041i	$0.228192\pi$
$384$		0			0
$385$	−1.82355			−0.0929369
$386$	6.69890	+	0.531337i	0.340965	+	0.0270443i
$387$		0			0
$388$	−26.7328	−	4.26759i	−1.35715	−	0.216654i
$389$	0.674377			0.0341923			0.0170961	−	0.999854i	$-0.494558\pi$
$389$	0.674377			0.0341923			0.0170961	+	0.999854i	$0.494558\pi$
$390$		0			0
$391$			1.97219i			0.0997379i
$392$	2.74906	+	0.665328i	0.138849	+	0.0336041i
$393$		0			0
$394$	23.5436	+	1.86741i	1.18611	+	0.0940789i
$395$			4.18798i			0.210720i
$396$		0			0
$397$		−	34.8298i		−	1.74806i	−0.485873	−	0.874030i	$-0.661498\pi$
$397$		−	34.8298i		−	1.74806i	0.485873	−	0.874030i	$-0.338502\pi$
$398$	−0.863928	+	10.8921i	−0.0433048	+	0.545971i
$399$		0			0
$400$	−18.1577	−	5.94894i	−0.907885	−	0.297447i
$401$		−	6.94206i		−	0.346670i	−0.984863	−	0.173335i	$-0.944546\pi$
$401$		−	6.94206i		−	0.346670i	0.984863	−	0.173335i	$-0.0554543\pi$
$402$		0			0
$403$	−27.3134			−1.36058
$404$	−25.4873	−	4.06875i	−1.26804	−	0.202428i
$405$		0			0
$406$	0.711814	−	8.97429i	0.0353268	−	0.445387i
$407$	3.26002			0.161593
$408$		0			0
$409$	−22.3689			−1.10607			−0.553036	−	0.833157i	$-0.686531\pi$
$409$	−22.3689			−1.10607			−0.553036	+	0.833157i	$0.686531\pi$
$410$	0.109371	−	1.37890i	0.00540143	−	0.0680992i
$411$		0			0
$412$	−0.833512	+	5.22125i	−0.0410642	+	0.257232i
$413$	7.22491			0.355515
$414$		0			0
$415$			4.38785i			0.215391i
$416$	−6.54911	+	15.6752i	−0.321097	+	0.768541i
$417$		0			0
$418$	−2.72105	+	34.3060i	−0.133091	+	1.67796i
$419$		−	7.43352i		−	0.363151i	−0.983377	−	0.181576i	$-0.941880\pi$
$419$		−	7.43352i		−	0.363151i	0.983377	−	0.181576i	$-0.0581197\pi$
$420$		0			0
$421$			8.32727i			0.405846i	0.979195	+	0.202923i	$0.0650442\pi$
$421$			8.32727i			0.405846i	−0.979195	+	0.202923i	$0.934956\pi$
$422$	−13.4649	−	1.06800i	−0.655462	−	0.0519893i
$423$		0			0
$424$	−18.2699	−	4.42169i	−0.887266	−	0.214736i
$425$		−	5.88403i		−	0.285417i
$426$		0			0
$427$	7.67120			0.371235
$428$	−0.621334	+	3.89213i	−0.0300333	+	0.188133i
$429$		0			0
$430$	3.97914	+	0.315613i	0.191891	+	0.0152202i
$431$	−2.52628			−0.121687			−0.0608433	−	0.998147i	$-0.519379\pi$
$431$	−2.52628			−0.121687			−0.0608433	+	0.998147i	$0.519379\pi$
$432$		0			0
$433$	−16.7059			−0.802833			−0.401416	−	0.915896i	$-0.631482\pi$
$433$	−16.7059			−0.802833			−0.401416	+	0.915896i	$0.631482\pi$
$434$	−12.8219	−	1.01700i	−0.615471	−	0.0488174i
$435$		0			0
$436$	−4.22440	+	26.4623i	−0.202312	+	1.26731i
$437$	10.0929			0.482807
$438$		0			0
$439$			38.9249i			1.85779i	0.370348	+	0.928893i	$0.379239\pi$
$439$			38.9249i			1.85779i	−0.370348	+	0.928893i	$0.620761\pi$
$440$	1.21326	−	5.01306i	0.0578400	−	0.238988i
$441$		0			0
$442$	−5.21510	−	0.413646i	−0.248057	−	0.0196751i
$443$			35.7967i			1.70075i	0.526176	+	0.850376i	$0.323625\pi$
$443$			35.7967i			1.70075i	−0.526176	+	0.850376i	$0.676375\pi$
$444$		0			0
$445$		−	7.62104i		−	0.361272i
$446$	2.21403	−	27.9137i	0.104837	−	1.32175i
$447$		0			0
$448$	−3.65805	+	7.11468i	−0.172827	+	0.336137i
$449$			18.7593i			0.885308i	0.896693	+	0.442654i	$0.145963\pi$
$449$			18.7593i			0.885308i	−0.896693	+	0.442654i	$0.854037\pi$
$450$		0			0
$451$	−7.99276			−0.376365
$452$	−6.03388	+	37.7972i	−0.283810	+	1.77783i
$453$		0			0
$454$	0.662107	−	8.34760i	0.0310742	−	0.391772i
$455$	−1.41866			−0.0665076
$456$		0			0
$457$	26.2464			1.22776			0.613878	−	0.789401i	$-0.289609\pi$
$457$	26.2464			1.22776			0.613878	+	0.789401i	$0.289609\pi$
$458$	−2.44568	+	30.8342i	−0.114279	+	1.44079i
$459$		0			0
$460$	−1.49376	−	0.238462i	−0.0696471	−	0.0111183i
$461$	10.6672			0.496821			0.248410	−	0.968655i	$-0.420092\pi$
$461$	10.6672			0.496821			0.248410	+	0.968655i	$0.420092\pi$
$462$		0			0
$463$			2.56421i			0.119169i	0.998223	+	0.0595845i	$0.0189776\pi$
$463$			2.56421i			0.119169i	−0.998223	+	0.0595845i	$0.981022\pi$
$464$	24.1973	+	7.92767i	1.12333	+	0.368033i
$465$		0			0
$466$	2.95693	−	37.2799i	0.136977	−	1.72696i
$467$		−	3.85281i		−	0.178287i	−0.996019	−	0.0891433i	$-0.971587\pi$
$467$		−	3.85281i		−	0.178287i	0.996019	−	0.0891433i	$-0.0284129\pi$
$468$		0			0
$469$			0.304417i			0.0140567i
$470$	4.81157	+	0.381640i	0.221941	+	0.0176037i
$471$		0			0
$472$	−4.80694	+	19.8617i	−0.221257	+	0.914210i
$473$		−	23.0649i		−	1.06053i
$474$		0			0
$475$	−30.1121			−1.38164
$476$	−2.43276	−	0.388362i	−0.111505	−	0.0178005i
$477$		0			0
$478$	−26.3734	−	2.09186i	−1.20629	−	0.0956795i
$479$	32.2599			1.47399			0.736997	−	0.675896i	$-0.236243\pi$
$479$	32.2599			1.47399			0.736997	+	0.675896i	$0.236243\pi$
$480$		0			0
$481$	2.53617			0.115639
$482$	−25.0628	−	1.98790i	−1.14158	−	0.0905466i
$483$		0			0
$484$	−7.70579	−	1.23014i	−0.350263	−	0.0559154i
$485$	6.39412			0.290342
$486$		0			0
$487$		−	33.8146i		−	1.53229i	−0.642671	−	0.766143i	$-0.722174\pi$
$487$		−	33.8146i		−	1.53229i	0.642671	−	0.766143i	$-0.277826\pi$
$488$	−5.10386	+	21.0886i	−0.231041	+	0.954636i
$489$		0			0
$490$	−0.665969	−	0.0528227i	−0.0300854	−	0.00238629i
$491$			10.4649i			0.472273i	0.971720	+	0.236137i	$0.0758813\pi$
$491$			10.4649i			0.472273i	−0.971720	+	0.236137i	$0.924119\pi$
$492$		0			0
$493$			7.84116i			0.353148i
$494$	−2.11687	+	26.6887i	−0.0952426	+	1.20078i
$495$		0			0
$496$	11.3266	−	34.5716i	0.508578	−	1.55231i
$497$			4.28011i			0.191989i
$498$		0			0
$499$	−23.0901			−1.03365			−0.516827	−	0.856090i	$-0.672887\pi$
$499$	−23.0901			−1.03365			−0.516827	+	0.856090i	$0.672887\pi$
$500$	9.12148	+	1.45614i	0.407925	+	0.0651205i
$501$		0			0
$502$	−2.96301	+	37.3565i	−0.132245	+	1.66730i
$503$	12.5782			0.560833			0.280416	−	0.959878i	$-0.409527\pi$
$503$	12.5782			0.560833			0.280416	+	0.959878i	$0.409527\pi$
$504$		0			0
$505$	6.09620			0.271277
$506$	−0.691118	+	8.71336i	−0.0307240	+	0.387356i
$507$		0			0
$508$	−5.11011	+	32.0105i	−0.226724	+	1.42024i
$509$	13.4636			0.596763			0.298381	−	0.954447i	$-0.403553\pi$
$509$	13.4636			0.596763			0.298381	+	0.954447i	$0.403553\pi$
$510$		0			0
$511$		−	11.9966i		−	0.530699i
$512$	−17.1249	−	14.7898i	−0.756820	−	0.653623i
$513$		0			0
$514$	−1.56213	+	19.6948i	−0.0689027	+	0.868700i
$515$		−	1.24885i		−	0.0550309i
$516$		0			0
$517$		−	27.8901i		−	1.22661i
$518$	1.19057	+	0.0944328i	0.0523108	+	0.00414914i
$519$		0			0
$520$	0.943871	−	3.89997i	0.0413915	−	0.171025i
$521$			9.15195i			0.400954i	0.979698	+	0.200477i	$0.0642492\pi$
$521$			9.15195i			0.400954i	−0.979698	+	0.200477i	$0.935751\pi$
$522$		0			0
$523$	−36.5411			−1.59783			−0.798916	−	0.601443i	$-0.794593\pi$
$523$	−36.5411			−1.59783			−0.798916	+	0.601443i	$0.794593\pi$
$524$	−3.68488	+	23.0826i	−0.160975	+	1.00837i
$525$		0			0
$526$	8.92107	+	0.707593i	0.388977	+	0.0308525i
$527$	11.2030			0.488009
$528$		0			0
$529$	−20.4365			−0.888544
$530$	4.42595	+	0.351053i	0.192251	+	0.0152488i
$531$		0			0
$532$	−1.98748	+	12.4499i	−0.0861680	+	0.539770i
$533$	−6.21806			−0.269334
$534$		0			0
$535$		−	0.930943i		−	0.0402482i
$536$	−0.836862	−	0.202537i	−0.0361469	−	0.00874828i
$537$		0			0
$538$	−28.8802	−	2.29069i	−1.24511	−	0.0987586i
$539$			3.86027i			0.166274i
$540$		0			0
$541$			8.00323i			0.344086i	0.985089	+	0.172043i	$0.0550368\pi$
$541$			8.00323i			0.344086i	−0.985089	+	0.172043i	$0.944963\pi$
$542$	3.12202	−	39.3612i	0.134102	−	1.69071i
$543$		0			0
$544$	2.68621	−	6.42942i	0.115170	−	0.275659i
$545$		−	6.32941i		−	0.271122i
$546$		0			0
$547$	−13.2376			−0.565997			−0.282998	−	0.959120i	$-0.591329\pi$
$547$	−13.2376			−0.565997			−0.282998	+	0.959120i	$0.591329\pi$
$548$	3.60937	−	22.6097i	0.154185	−	0.965836i
$549$		0			0
$550$	2.06195	−	25.9963i	0.0879220	−	1.10849i
$551$	40.1279			1.70950
$552$		0			0
$553$	8.86550			0.376999
$554$	2.77722	−	35.0141i	0.117993	−	1.48761i
$555$		0			0
$556$	−2.34265	−	0.373977i	−0.0993504	−	0.0158601i
$557$	41.1996			1.74568			0.872841	−	0.488005i	$-0.162275\pi$
$557$	41.1996			1.74568			0.872841	+	0.488005i	$0.162275\pi$
$558$		0			0
$559$		−	17.9436i		−	0.758934i
$560$	0.588301	−	1.79565i	0.0248603	−	0.0758799i
$561$		0			0
$562$	−1.53855	+	19.3975i	−0.0648998	+	0.818233i
$563$		−	5.43579i		−	0.229091i	−0.993418	−	0.114546i	$-0.963459\pi$
$563$		−	5.43579i		−	0.229091i	0.993418	−	0.114546i	$-0.0365412\pi$
$564$		0			0
$565$		−	9.04055i		−	0.380339i
$566$	20.8221	+	1.65154i	0.875216	+	0.0694196i
$567$		0			0
$568$	−11.7663	−	2.84768i	−0.493702	−	0.119486i
$569$		−	4.39796i		−	0.184372i	−0.995742	−	0.0921861i	$-0.970615\pi$
$569$		−	4.39796i		−	0.184372i	0.995742	−	0.0921861i	$-0.0293855\pi$
$570$		0			0
$571$	4.56580			0.191073			0.0955364	−	0.995426i	$-0.469543\pi$
$571$	4.56580			0.191073			0.0955364	+	0.995426i	$0.469543\pi$
$572$	−22.8960	−	3.65507i	−0.957328	−	0.152826i
$573$		0			0
$574$	−2.91899	−	0.231526i	−0.121836	−	0.00966370i
$575$	−7.64815			−0.318950
$576$		0			0
$577$	32.5986			1.35710			0.678550	−	0.734554i	$-0.262609\pi$
$577$	32.5986			1.35710			0.678550	+	0.734554i	$0.262609\pi$
$578$	−21.8273	−	1.73128i	−0.907897	−	0.0720117i
$579$		0			0
$580$	−5.93900	−	0.948093i	−0.246604	−	0.0393674i
$581$	9.28860			0.385356
$582$		0			0
$583$		−	25.6549i		−	1.06252i
$584$	32.9794	+	7.98168i	1.36470	+	0.330284i
$585$		0			0
$586$	39.4613	+	3.12995i	1.63013	+	0.129297i
$587$			9.30106i			0.383896i	0.981405	+	0.191948i	$0.0614805\pi$
$587$			9.30106i			0.383896i	−0.981405	+	0.191948i	$0.938520\pi$
$588$		0			0
$589$		−	57.3322i		−	2.36233i
$590$	0.381640	−	4.81157i	0.0157119	−	0.198089i
$591$		0			0
$592$	−1.05172	+	3.21013i	−0.0432256	+	0.131936i
$593$			21.8239i			0.896198i	0.893984	+	0.448099i	$0.147899\pi$
$593$			21.8239i			0.896198i	−0.893984	+	0.448099i	$0.852101\pi$
$594$		0			0
$595$	0.581882			0.0238548
$596$	−2.61527	−	0.417498i	−0.107126	−	0.0171014i
$597$		0			0
$598$	−0.537663	+	6.77866i	−0.0219867	+	0.277200i
$599$	−35.3131			−1.44285			−0.721427	−	0.692491i	$-0.756513\pi$
$599$	−35.3131			−1.44285			−0.721427	+	0.692491i	$0.756513\pi$
$600$		0			0
$601$	9.85840			0.402133			0.201066	−	0.979578i	$-0.435559\pi$
$601$	9.85840			0.402133			0.201066	+	0.979578i	$0.435559\pi$
$602$	0.668120	−	8.42340i	0.0272305	−	0.343312i
$603$		0			0
$604$	−1.63512	+	10.2426i	−0.0665319	+	0.416766i
$605$	1.84312			0.0749333
$606$		0			0
$607$			3.56295i			0.144616i	0.997382	+	0.0723078i	$0.0230364\pi$
$607$			3.56295i			0.144616i	−0.997382	+	0.0723078i	$0.976964\pi$
$608$	−32.9031	−	13.7469i	−1.33440	−	0.557512i
$609$		0			0
$610$	0.405214	−	5.10879i	0.0164066	−	0.206849i
$611$		−	21.6974i		−	0.877784i
$612$		0			0
$613$			18.0978i			0.730963i	0.930819	+	0.365481i	$0.119096\pi$
$613$			18.0978i			0.730963i	−0.930819	+	0.365481i	$0.880904\pi$
$614$	28.9484	+	2.29610i	1.16826	+	0.0926631i
$615$		0			0
$616$	−10.6121	−	2.56834i	−0.427574	−	0.103482i
$617$		−	24.1087i		−	0.970579i	−0.874354	−	0.485289i	$-0.838714\pi$
$617$		−	24.1087i		−	0.970579i	0.874354	−	0.485289i	$-0.161286\pi$
$618$		0			0
$619$	27.7470			1.11525			0.557623	−	0.830095i	$-0.311714\pi$
$619$	27.7470			1.11525			0.557623	+	0.830095i	$0.311714\pi$
$620$	−1.35458	+	8.48528i	−0.0544011	+	0.340777i
$621$		0			0
$622$	46.5930	+	3.69562i	1.86821	+	0.148181i
$623$	−16.1329			−0.646352
$624$		0			0
$625$	21.7025			0.868100
$626$	−18.2691	−	1.44905i	−0.730179	−	0.0579156i
$627$		0			0
$628$	3.54610	−	22.2133i	0.141505	−	0.886408i
$629$	−1.04025			−0.0414774
$630$		0			0
$631$			19.1807i			0.763571i	0.924251	+	0.381786i	$0.124691\pi$
$631$			19.1807i			0.763571i	−0.924251	+	0.381786i	$0.875309\pi$
$632$	−5.89846	+	24.3718i	−0.234628	+	0.969458i
$633$		0			0
$634$	−29.5094	−	2.34060i	−1.17197	−	0.0929570i
$635$		−	7.65646i		−	0.303837i
$636$		0			0
$637$			3.00314i			0.118989i
$638$	−2.74779	+	34.6432i	−0.108786	+	1.37154i
$639$		0			0
$640$	4.54493	+	2.81197i	0.179654	+	0.111153i
$641$		−	0.948908i		−	0.0374796i	−0.999824	−	0.0187398i	$-0.994035\pi$
$641$		−	0.948908i		−	0.0374796i	0.999824	−	0.0187398i	$-0.00596542\pi$
$642$		0			0
$643$	−7.06733			−0.278708			−0.139354	−	0.990243i	$-0.544503\pi$
$643$	−7.06733			−0.278708			−0.139354	+	0.990243i	$0.544503\pi$
$644$	−0.504798	+	3.16214i	−0.0198918	+	0.124606i
$645$		0			0
$646$	0.868265	−	10.9468i	0.0341614	−	0.430695i
$647$	26.2182			1.03075			0.515373	−	0.856966i	$-0.327654\pi$
$647$	26.2182			1.03075			0.515373	+	0.856966i	$0.327654\pi$
$648$		0			0
$649$	−27.8901			−1.09478
$650$	1.60412	−	20.2241i	0.0629188	−	0.793256i
$651$		0			0
$652$	23.1235	+	3.69140i	0.905586	+	0.144566i
$653$	42.3909			1.65888			0.829442	−	0.558592i	$-0.188658\pi$
$653$	42.3909			1.65888			0.829442	+	0.558592i	$0.188658\pi$
$654$		0			0
$655$		−	5.52104i		−	0.215725i
$656$	2.57856	−	7.87044i	0.100676	−	0.307289i
$657$		0			0
$658$	0.807891	−	10.1856i	0.0314949	−	0.397075i
$659$			28.8941i			1.12555i	0.826609	+	0.562777i	$0.190267\pi$
$659$			28.8941i			1.12555i	−0.826609	+	0.562777i	$0.809733\pi$
$660$		0			0
$661$			40.2774i			1.56661i	0.621639	+	0.783304i	$0.286467\pi$
$661$			40.2774i			1.56661i	−0.621639	+	0.783304i	$0.713533\pi$
$662$	−11.1228	−	0.882230i	−0.432301	−	0.0342888i
$663$		0			0
$664$	−6.17996	+	25.5349i	−0.239829	+	0.990947i
$665$		−	2.97783i		−	0.115475i
$666$		0			0
$667$	10.1921			0.394638
$668$	9.09021	+	1.45115i	0.351711	+	0.0561466i
$669$		0			0
$670$	0.202733	+	0.0160802i	0.00783224	+	0.000621231i
$671$	−29.6129			−1.14319
$672$		0			0
$673$	−22.5630			−0.869739			−0.434870	−	0.900493i	$-0.643206\pi$
$673$	−22.5630			−0.869739			−0.434870	+	0.900493i	$0.643206\pi$
$674$	−21.1999	−	1.68152i	−0.816591	−	0.0647696i
$675$		0			0
$676$	7.86273	+	1.25519i	0.302413	+	0.0482767i
$677$	−32.5307			−1.25026			−0.625128	−	0.780522i	$-0.714953\pi$
$677$	−32.5307			−1.25026			−0.625128	+	0.780522i	$0.714953\pi$
$678$		0			0
$679$		−	13.5357i		−	0.519451i
$680$	−0.387142	+	1.59963i	−0.0148462	+	0.0613430i
$681$		0			0
$682$	49.4960	+	3.92588i	1.89530	+	0.150330i
$683$		−	28.2621i		−	1.08142i	−0.841209	−	0.540710i	$-0.818156\pi$
$683$		−	28.2621i		−	1.08142i	0.841209	−	0.540710i	$-0.181844\pi$
$684$		0			0
$685$			5.40791i			0.206626i
$686$	−0.111820	+	1.40979i	−0.00426931	+	0.0538259i
$687$		0			0
$688$	22.7119	+	7.44103i	0.865885	+	0.283687i
$689$		−	19.9585i		−	0.760358i
$690$		0			0
$691$	50.6281			1.92598			0.962991	−	0.269532i	$-0.0868691\pi$
$691$	50.6281			1.92598			0.962991	+	0.269532i	$0.0868691\pi$
$692$	−22.1900	−	3.54237i	−0.843536	−	0.134661i
$693$		0			0
$694$	2.87035	−	36.1883i	0.108957	−	1.37369i
$695$	0.560329			0.0212545
$696$		0			0
$697$	2.55043			0.0966043
$698$	−2.26757	+	28.5886i	−0.0858287	+	1.08210i
$699$		0			0
$700$	1.50607	−	9.43424i	0.0569240	−	0.356581i
$701$	−21.0351			−0.794485			−0.397242	−	0.917714i	$-0.630033\pi$
$701$	−21.0351			−0.794485			−0.397242	+	0.917714i	$0.630033\pi$
$702$		0			0
$703$			5.32356i			0.200782i
$704$	14.1211	−	27.4646i	0.532208	−	1.03511i
$705$		0			0
$706$	−1.91735	+	24.1732i	−0.0721604	+	0.909771i
$707$		−	12.9050i		−	0.485343i
$708$		0			0
$709$			51.6582i			1.94007i	0.242973	+	0.970033i	$0.421877\pi$
$709$			51.6582i			1.94007i	−0.242973	+	0.970033i	$0.578123\pi$
$710$	2.85042	+	0.226087i	0.106974	+	0.00848490i
$711$		0			0
$712$	10.7337	−	44.3504i	0.402262	−	1.66210i
$713$		−	14.5618i		−	0.545343i
$714$		0			0
$715$	5.47639			0.204805
$716$	5.90863	−	37.0126i	0.220816	−	1.38322i
$717$		0			0
$718$	−9.24409	−	0.733214i	−0.344987	−	0.0273633i
$719$	2.19322			0.0817934			0.0408967	−	0.999163i	$-0.486979\pi$
$719$	2.19322			0.0817934			0.0408967	+	0.999163i	$0.486979\pi$
$720$		0			0
$721$	−2.64368			−0.0984558
$722$	−29.2351	−	2.31884i	−1.08802	−	0.0862985i
$723$		0			0
$724$	−6.09101	+	38.1550i	−0.226371	+	1.41802i
$725$	−30.4080			−1.12933
$726$		0			0
$727$			20.4024i			0.756683i	0.925666	+	0.378341i	$0.123505\pi$
$727$			20.4024i			0.756683i	−0.925666	+	0.378341i	$0.876495\pi$
$728$	−8.25582	−	1.99807i	−0.305981	−	0.0740535i
$729$		0			0
$730$	−7.98938	−	0.633694i	−0.295700	−	0.0234541i
$731$			7.35984i			0.272213i
$732$		0			0
$733$		−	28.3518i		−	1.04720i	−0.851965	−	0.523599i	$-0.824589\pi$
$733$		−	28.3518i		−	1.04720i	0.851965	−	0.523599i	$-0.175411\pi$
$734$	−1.01690	+	12.8207i	−0.0375345	+	0.473220i
$735$		0			0
$736$	−8.35705	−	3.49158i	−0.308045	−	0.128701i
$737$		−	1.17513i		−	0.0432866i
$738$		0			0
$739$	25.5451			0.939693			0.469846	−	0.882748i	$-0.344309\pi$
$739$	25.5451			0.939693			0.469846	+	0.882748i	$0.344309\pi$
$740$	0.125779	−	0.787897i	0.00462372	−	0.0289637i
$741$		0			0
$742$	0.743142	−	9.36926i	0.0272816	−	0.343956i
$743$	22.0485			0.808883			0.404441	−	0.914564i	$-0.367466\pi$
$743$	22.0485			0.808883			0.404441	+	0.914564i	$0.367466\pi$
$744$		0			0
$745$	0.625537			0.0229179
$746$	1.55933	−	19.6594i	0.0570910	−	0.719782i
$747$		0			0
$748$	9.39110	+	1.49918i	0.343373	+	0.0548155i
$749$	−1.97071			−0.0720081
$750$		0			0
$751$		−	15.2534i		−	0.556604i	−0.960494	−	0.278302i	$-0.910228\pi$
$751$		−	15.2534i		−	0.556604i	0.960494	−	0.278302i	$-0.0897715\pi$
$752$	27.4633	+	8.99769i	1.00148	+	0.328112i
$753$		0			0
$754$	−2.13768	+	26.9511i	−0.0778497	+	0.981500i
$755$		−	2.44989i		−	0.0891607i
$756$		0			0
$757$		−	46.4150i		−	1.68698i	−0.537144	−	0.843490i	$-0.680497\pi$
$757$		−	46.4150i		−	1.68698i	0.537144	−	0.843490i	$-0.319503\pi$
$758$	5.69510	+	0.451719i	0.206855	+	0.0164072i
$759$		0			0
$760$	8.18624	+	1.98123i	0.296946	+	0.0718669i
$761$			7.85112i			0.284603i	0.989823	+	0.142301i	$0.0454502\pi$
$761$			7.85112i			0.284603i	−0.989823	+	0.142301i	$0.954550\pi$
$762$		0			0
$763$	−13.3987			−0.485065
$764$	−49.2704	−	7.86545i	−1.78254	−	0.284562i
$765$		0			0
$766$	−41.5978	−	3.29941i	−1.50299	−	0.119213i
$767$	−21.6974			−0.783449
$768$		0			0
$769$	8.05504			0.290472			0.145236	−	0.989397i	$-0.453606\pi$
$769$	8.05504			0.290472			0.145236	+	0.989397i	$0.453606\pi$
$770$	2.57082	+	0.203910i	0.0926460	+	0.00734841i
$771$		0			0
$772$	−9.38460	−	1.49814i	−0.337759	−	0.0539193i
$773$	2.99300			0.107651			0.0538253	−	0.998550i	$-0.482859\pi$
$773$	2.99300			0.107651			0.0538253	+	0.998550i	$0.482859\pi$
$774$		0			0
$775$			43.4451i			1.56059i
$776$	37.2104	+	9.00565i	1.33577	+	0.323284i
$777$		0			0
$778$	−0.950727	−	0.0754089i	−0.0340852	−	0.00270354i
$779$		−	13.0520i		−	0.467638i
$780$		0			0
$781$		−	16.5224i		−	0.591217i
$782$	0.220530	−	2.78036i	0.00788615	−	0.0994256i
$783$		0			0
$784$	−3.80119	−	1.24537i	−0.135757	−	0.0444775i
$785$			5.31311i			0.189633i
$786$		0			0
$787$	−14.6709			−0.522962			−0.261481	−	0.965209i	$-0.584211\pi$
$787$	−14.6709			−0.522962			−0.261481	+	0.965209i	$0.584211\pi$
$788$	−32.9827	−	5.26531i	−1.17496	−	0.187569i
$789$		0			0
$790$	0.468300	−	5.90415i	0.0166614	−	0.210060i
$791$	−19.1379			−0.680464
$792$		0			0
$793$	−23.0377			−0.818093
$794$	−3.89467	+	49.1026i	−0.138217	+	1.74259i
$795$		0			0
$796$	2.43591	−	15.2589i	0.0863384	−	0.540837i
$797$	−21.5623			−0.763774			−0.381887	−	0.924209i	$-0.624726\pi$
$797$	−21.5623			−0.763774			−0.381887	+	0.924209i	$0.624726\pi$
$798$		0			0
$799$			8.89951i			0.314842i
$800$	24.9333	+	10.4171i	0.881524	+	0.368301i
$801$		0			0
$802$	−0.776262	+	9.78682i	−0.0274108	+	0.345585i
$803$			46.3102i			1.63425i
$804$		0			0
$805$		−	0.756339i		−	0.0266574i
$806$	38.5060	+	3.05418i	1.35632	+	0.107579i
$807$		0			0
$808$	35.4766	+	8.58606i	1.24806	+	0.302056i
$809$			21.3202i			0.749580i	0.927110	+	0.374790i	$0.122285\pi$
$809$			21.3202i			0.749580i	−0.927110	+	0.374790i	$0.877715\pi$
$810$		0			0
$811$	26.6208			0.934783			0.467392	−	0.884050i	$-0.345194\pi$
$811$	26.6208			0.934783			0.467392	+	0.884050i	$0.345194\pi$
$812$	−2.00701	+	12.5722i	−0.0704323	+	0.441199i
$813$		0			0
$814$	−4.59593	−	0.364536i	−0.161087	−	0.0127770i
$815$	−5.53082			−0.193736
$816$		0			0
$817$	37.6646			1.31772
$818$	31.5354	+	2.50129i	1.10261	+	0.0874557i
$819$		0			0
$820$	−0.308378	+	1.93173i	−0.0107690	+	0.0674589i
$821$	−41.8336			−1.46000			−0.730001	−	0.683446i	$-0.760480\pi$
$821$	−41.8336			−1.46000			−0.730001	+	0.683446i	$0.760480\pi$
$822$		0			0
$823$		−	2.79656i		−	0.0974821i	−0.998811	−	0.0487410i	$-0.984479\pi$
$823$		−	2.79656i		−	0.0974821i	0.998811	−	0.0487410i	$-0.0155209\pi$
$824$	1.75891	−	7.26764i	0.0612747	−	0.253180i
$825$		0			0
$826$	−10.1856	−	0.807891i	−0.354402	−	0.0281101i
$827$		−	35.7093i		−	1.24173i	−0.783916	−	0.620867i	$-0.786781\pi$
$827$		−	35.7093i		−	1.24173i	0.783916	−	0.620867i	$-0.213219\pi$
$828$		0			0
$829$			43.7358i			1.51901i	0.650504	+	0.759503i	$0.274558\pi$
$829$			43.7358i			1.51901i	−0.650504	+	0.759503i	$0.725442\pi$
$830$	0.490649	−	6.18592i	0.0170307	−	0.214717i
$831$		0			0
$832$	10.9857	−	21.3664i	0.380859	−	0.740746i
$833$		−	1.23178i		−	0.0426787i
$834$		0			0
$835$	−2.17425			−0.0752431
$836$	7.67219	−	48.0598i	0.265348	−	1.66218i
$837$		0			0
$838$	−0.831216	+	10.4797i	−0.0287139	+	0.362014i
$839$	7.05214			0.243467			0.121733	−	0.992563i	$-0.461155\pi$
$839$	7.05214			0.243467			0.121733	+	0.992563i	$0.461155\pi$
$840$		0			0
$841$	11.5223			0.397320
$842$	0.931156	−	11.7397i	0.0320898	−	0.404576i
$843$		0			0
$844$	18.8632	+	3.01130i	0.649299	+	0.103653i
$845$	−1.88066			−0.0646965
$846$		0			0
$847$		−	3.90168i		−	0.134063i
$848$	25.2622	+	8.27657i	0.867509	+	0.284219i
$849$		0			0
$850$	−0.657953	+	8.29522i	−0.0225676	+	0.284524i
$851$			1.35213i			0.0463504i
$852$		0			0
$853$			4.42708i			0.151580i	0.997124	+	0.0757901i	$0.0241479\pi$
$853$			4.42708i			0.151580i	−0.997124	+	0.0757901i	$0.975852\pi$
$854$	−10.8148	−	0.857794i	−0.370073	−	0.0293531i
$855$		0			0
$856$	1.31117	−	5.41760i	0.0448147	−	0.185170i
$857$			3.17368i			0.108411i	0.998530	+	0.0542055i	$0.0172626\pi$
$857$			3.17368i			0.108411i	−0.998530	+	0.0542055i	$0.982737\pi$
$858$		0			0
$859$	28.3725			0.968057			0.484029	−	0.875052i	$-0.339173\pi$
$859$	28.3725			0.968057			0.484029	+	0.875052i	$0.339173\pi$
$860$	−5.57444	−	0.889895i	−0.190087	−	0.0303452i
$861$		0			0
$862$	3.56152	+	0.282489i	0.121306	+	0.00962161i
$863$	−48.1330			−1.63847			−0.819233	−	0.573461i	$-0.805600\pi$
$863$	−48.1330			−1.63847			−0.819233	+	0.573461i	$0.805600\pi$
$864$		0			0
$865$	5.30753			0.180461
$866$	23.5517	+	1.86805i	0.800319	+	0.0634790i
$867$		0			0
$868$	17.9624	+	2.86749i	0.609685	+	0.0973291i
$869$	−34.2232			−1.16094
$870$		0			0
$871$		−	0.914208i		−	0.0309768i
$872$	8.91452	−	36.8338i	0.301884	−	1.24735i
$873$		0			0
$874$	−14.2288	−	1.12858i	−0.481295	−	0.0381749i
$875$			4.61849i			0.156133i
$876$		0			0
$877$			9.76729i			0.329818i	0.986309	+	0.164909i	$0.0527330\pi$
$877$			9.76729i			0.329818i	−0.986309	+	0.164909i	$0.947267\pi$
$878$	4.35259	−	54.8758i	0.146893	−	1.85197i
$879$		0			0
$880$	−2.27100	+	6.93168i	−0.0765554	+	0.233667i
$881$			50.9150i			1.71537i	0.514175	+	0.857685i	$0.328098\pi$
$881$			50.9150i			1.71537i	−0.514175	+	0.857685i	$0.671902\pi$
$882$		0			0
$883$	37.4660			1.26083			0.630416	−	0.776258i	$-0.282885\pi$
$883$	37.4660			1.26083			0.630416	+	0.776258i	$0.282885\pi$
$884$	7.30592	+	1.16631i	0.245725	+	0.0392271i
$885$		0			0
$886$	4.00279	−	50.4657i	0.134476	−	1.69543i
$887$	14.6857			0.493097			0.246549	−	0.969130i	$-0.420704\pi$
$887$	14.6857			0.493097			0.246549	+	0.969130i	$0.420704\pi$
$888$		0			0
$889$	−16.2079			−0.543596
$890$	−0.852186	+	10.7440i	−0.0285653	+	0.360141i
$891$		0			0
$892$	−6.24262	+	39.1047i	−0.209018	+	1.30932i
$893$	45.5441			1.52407
$894$		0			0
$895$			8.85289i			0.295919i
$896$	5.95264	−	9.62113i	0.198864	−	0.321419i
$897$		0			0
$898$	2.09767	−	26.4466i	0.0700002	−	0.882536i
$899$		−	57.8957i		−	1.93093i
$900$		0			0
$901$			8.18626i			0.272724i
$902$	11.2681	+	0.893752i	0.375186	+	0.0297587i
$903$		0			0
$904$	12.7330	−	52.6112i	0.423492	−	1.74982i
$905$		−	9.12615i		−	0.303363i
$906$		0			0
$907$	−22.5811			−0.749794			−0.374897	−	0.927066i	$-0.622322\pi$
$907$	−22.5811			−0.749794			−0.374897	+	0.927066i	$0.622322\pi$
$908$	−1.86686	+	11.6943i	−0.0619539	+	0.388089i
$909$		0			0
$910$	2.00000	+	0.158634i	0.0662994	+	0.00525867i
$911$	−19.2187			−0.636744			−0.318372	−	0.947966i	$-0.603136\pi$
$911$	−19.2187			−0.636744			−0.318372	+	0.947966i	$0.603136\pi$
$912$		0			0
$913$	−35.8565			−1.18668
$914$	−37.0018	−	2.93488i	−1.22391	−	0.0970771i
$915$		0			0
$916$	6.89576	−	43.1961i	0.227842	−	1.42724i
$917$	−11.6875			−0.385954
$918$		0			0
$919$			11.3312i			0.373781i	0.982381	+	0.186890i	$0.0598409\pi$
$919$			11.3312i			0.373781i	−0.982381	+	0.186890i	$0.940159\pi$
$920$	2.07922	+	0.503213i	0.0685499	+	0.0165904i
$921$		0			0
$922$	−15.0385	−	1.19281i	−0.495265	−	0.0392830i
$923$		−	12.8538i		−	0.423087i
$924$		0			0
$925$		−	4.03408i		−	0.132640i
$926$	0.286730	−	3.61499i	0.00942255	−	0.118796i
$927$		0			0
$928$	−33.2265	−	13.8821i	−1.09071	−	0.455701i
$929$			8.55508i			0.280683i	0.990103	+	0.140341i	$0.0448200\pi$
$929$			8.55508i			0.280683i	−0.990103	+	0.140341i	$0.955180\pi$
$930$		0			0
$931$	−6.30375			−0.206597
$932$	−8.33728	+	52.2260i	−0.273097	+	1.71072i
$933$		0			0
$934$	−0.430821	+	5.43163i	−0.0140969	+	0.177728i
$935$	−2.24622			−0.0734593
$936$		0			0
$937$	−7.05381			−0.230438			−0.115219	−	0.993340i	$-0.536757\pi$
$937$	−7.05381			−0.230438			−0.115219	+	0.993340i	$0.536757\pi$
$938$	0.0340400	−	0.429163i	0.00111144	−	0.0140127i
$939$		0			0
$940$	−6.74061	−	1.07606i	−0.219855	−	0.0350972i
$941$	29.9215			0.975412			0.487706	−	0.873008i	$-0.337834\pi$
$941$	29.9215			0.975412			0.487706	+	0.873008i	$0.337834\pi$
$942$		0			0
$943$		−	3.31508i		−	0.107954i
$944$	8.99769	−	27.4633i	0.292850	−	0.893854i
$945$		0			0
$946$	−2.57912	+	32.5166i	−0.0838545	+	1.05721i
$947$		−	27.5158i		−	0.894144i	−0.894498	−	0.447072i	$-0.852467\pi$
$947$		−	27.5158i		−	0.894144i	0.894498	−	0.447072i	$-0.147533\pi$
$948$		0			0
$949$			36.0275i			1.16950i
$950$	42.4516	+	3.36713i	1.37731	+	0.109244i
$951$		0			0
$952$	3.38624	+	0.819538i	0.109749	+	0.0265614i
$953$			56.1874i			1.82009i	0.414512	+	0.910044i	$0.363952\pi$
$953$			56.1874i			1.82009i	−0.414512	+	0.910044i	$0.636048\pi$
$954$		0			0
$955$	11.7848			0.381347
$956$	36.9469	+	5.89815i	1.19495	+	0.190760i
$957$		0			0
$958$	−45.4796	−	3.60731i	−1.46938	−	0.116547i
$959$	11.4480			0.369674
$960$		0			0
$961$	−51.7179			−1.66832
$962$	−3.57546	−	0.283595i	−0.115277	−	0.00914347i
$963$		0			0
$964$	35.1108	+	5.60504i	1.13084	+	0.180526i
$965$	2.24466			0.0722583
$966$		0			0
$967$		−	30.6689i		−	0.986244i	−0.869960	−	0.493122i	$-0.835856\pi$
$967$		−	30.6689i		−	0.986244i	0.869960	−	0.493122i	$-0.164144\pi$
$968$	10.7260	+	2.59590i	0.344745	+	0.0834352i
$969$		0			0
$970$	−9.01434	−	0.714991i	−0.289433	−	0.0229570i
$971$		−	48.6422i		−	1.56100i	−0.625153	−	0.780502i	$-0.714964\pi$
$971$		−	48.6422i		−	1.56100i	0.625153	−	0.780502i	$-0.285036\pi$
$972$		0			0
$973$		−	1.18616i		−	0.0380264i
$974$	−3.78115	+	47.6713i	−0.121156	+	1.52749i
$975$		0			0
$976$	9.55348	−	29.1597i	0.305800	−	0.933379i
$977$		−	13.4976i		−	0.431828i	−0.976412	−	0.215914i	$-0.930727\pi$
$977$		−	13.4976i		−	0.431828i	0.976412	−	0.215914i	$-0.0692730\pi$
$978$		0			0
$979$	62.2775			1.99040
$980$	0.932968	+	0.148938i	0.0298026	+	0.00475763i
$981$		0			0
$982$	1.17018	−	14.7532i	0.0373420	−	0.470794i
$983$	−11.7415			−0.374496			−0.187248	−	0.982313i	$-0.559957\pi$
$983$	−11.7415			−0.374496			−0.187248	+	0.982313i	$0.559957\pi$
$984$		0			0
$985$	7.88900			0.251364
$986$	0.876800	−	11.0544i	0.0279230	−	0.352043i
$987$		0			0
$988$	5.96867	−	37.3887i	0.189889	−	1.18949i
$989$	9.56642			0.304195
$990$		0			0
$991$		−	6.17731i		−	0.196229i	−0.995175	−	0.0981143i	$-0.968719\pi$
$991$		−	6.17731i		−	0.196229i	0.995175	−	0.0981143i	$-0.0312811\pi$
$992$	−19.8338	+	47.4720i	−0.629724	+	1.50724i
$993$		0			0
$994$	0.478602	−	6.03404i	0.0151803	−	0.191388i
$995$			3.64971i			0.115704i
$996$		0			0
$997$			15.1860i			0.480944i	0.970656	+	0.240472i	$0.0773023\pi$
$997$			15.1860i			0.480944i	−0.970656	+	0.240472i	$0.922698\pi$
$998$	32.5521	+	2.58194i	1.03042	+	0.0817297i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.j.a.323.1	✓	24
3.2	odd	2	inner	504.2.j.a.323.24	yes	24
4.3	odd	2		2016.2.j.a.1583.11		24
8.3	odd	2	inner	504.2.j.a.323.23	yes	24
8.5	even	2		2016.2.j.a.1583.13		24
12.11	even	2		2016.2.j.a.1583.14		24
24.5	odd	2		2016.2.j.a.1583.12		24
24.11	even	2	inner	504.2.j.a.323.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.j.a.323.1	✓	24	1.1	even	1	trivial
504.2.j.a.323.2	yes	24	24.11	even	2	inner
504.2.j.a.323.23	yes	24	8.3	odd	2	inner
504.2.j.a.323.24	yes	24	3.2	odd	2	inner
2016.2.j.a.1583.11		24	4.3	odd	2
2016.2.j.a.1583.12		24	24.5	odd	2
2016.2.j.a.1583.13		24	8.5	even	2
2016.2.j.a.1583.14		24	12.11	even	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40979 - 0.111820i) q^{2} +(1.97499 + 0.315285i) q^{4} -0.472391 q^{5} +1.00000i q^{7} +(-2.74906 - 0.665328i) q^{8} +O(q^{10})\)	\(q+(-1.40979 - 0.111820i) q^{2} +(1.97499 + 0.315285i) q^{4} -0.472391 q^{5} +1.00000i q^{7} +(-2.74906 - 0.665328i) q^{8} +(0.665969 + 0.0528227i) q^{10} -3.86027i q^{11} -3.00314i q^{13} +(0.111820 - 1.40979i) q^{14} +(3.80119 + 1.24537i) q^{16} +1.23178i q^{17} +6.30375 q^{19} +(-0.932968 - 0.148938i) q^{20} +(-0.431656 + 5.44215i) q^{22} +1.60109 q^{23} -4.77685 q^{25} +(-0.335811 + 4.23379i) q^{26} +(-0.315285 + 1.97499i) q^{28} +6.36571 q^{29} -9.09494i q^{31} +(-5.21961 - 2.18075i) q^{32} +(0.137738 - 1.73655i) q^{34} -0.472391i q^{35} +0.844507i q^{37} +(-8.88694 - 0.704886i) q^{38} +(1.29863 + 0.314295i) q^{40} -2.07052i q^{41} +5.97495 q^{43} +(1.21708 - 7.62400i) q^{44} +(-2.25719 - 0.179034i) q^{46} +7.22491 q^{47} -1.00000 q^{49} +(6.73433 + 0.534147i) q^{50} +(0.946844 - 5.93118i) q^{52} +6.64588 q^{53} +1.82355i q^{55} +(0.665328 - 2.74906i) q^{56} +(-8.97429 - 0.711814i) q^{58} -7.22491i q^{59} -7.67120i q^{61} +(-1.01700 + 12.8219i) q^{62} +(7.11468 + 3.65805i) q^{64} +1.41866i q^{65} +0.304417 q^{67} +(-0.388362 + 2.43276i) q^{68} +(-0.0528227 + 0.665969i) q^{70} +4.28011 q^{71} -11.9966 q^{73} +(0.0944328 - 1.19057i) q^{74} +(12.4499 + 1.98748i) q^{76} +3.86027 q^{77} -8.86550i q^{79} +(-1.79565 - 0.588301i) q^{80} +(-0.231526 + 2.91899i) q^{82} -9.28860i q^{83} -0.581882i q^{85} +(-8.42340 - 0.668120i) q^{86} +(-2.56834 + 10.6121i) q^{88} +16.1329i q^{89} +3.00314 q^{91} +(3.16214 + 0.504798i) q^{92} +(-10.1856 - 0.807891i) q^{94} -2.97783 q^{95} -13.5357 q^{97} +(1.40979 + 0.111820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4}+O(q^{10}) \) 24 * q - 8 * q^4	\( 24 q - 8 q^{4} + 24 q^{10} + 12 q^{16} + 32 q^{19} + 12 q^{22} + 24 q^{25} + 4 q^{28} - 8 q^{40} - 64 q^{43} - 12 q^{46} - 24 q^{49} - 16 q^{52} - 12 q^{58} + 16 q^{64} + 16 q^{67} + 24 q^{70} + 8 q^{76} + 24 q^{82} - 84 q^{88} - 72 q^{94}+O(q^{100}) \) 24 * q - 8 * q^4 + 24 * q^10 + 12 * q^16 + 32 * q^19 + 12 * q^22 + 24 * q^25 + 4 * q^28 - 8 * q^40 - 64 * q^43 - 12 * q^46 - 24 * q^49 - 16 * q^52 - 12 * q^58 + 16 * q^64 + 16 * q^67 + 24 * q^70 + 8 * q^76 + 24 * q^82 - 84 * q^88 - 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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