LMFDB - Embedded newform 288.3.u.b.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(19,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("288.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.u (of order $8$, degree $4$, 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:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	288.19
Dual form			288.3.u.b.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02518 - 1.71727i) q^{2} +(-1.89801 + 3.52102i) q^{4} +(7.00900 - 2.90322i) q^{5} +(2.35957 + 2.35957i) q^{7} +(7.99233 - 0.350291i) q^{8} +O(q^{10})$	\(q+(-1.02518 - 1.71727i) q^{2} +(-1.89801 + 3.52102i) q^{4} +(7.00900 - 2.90322i) q^{5} +(2.35957 + 2.35957i) q^{7} +(7.99233 - 0.350291i) q^{8} +(-12.1711 - 9.05999i) q^{10} +(-12.1899 + 5.04924i) q^{11} +(23.4042 + 9.69435i) q^{13} +(1.63302 - 6.47098i) q^{14} +(-8.79512 - 13.3658i) q^{16} +25.7007i q^{17} +(-2.32569 + 5.61471i) q^{19} +(-3.08085 + 30.1891i) q^{20} +(21.1678 + 15.7570i) q^{22} +(23.2058 - 23.2058i) q^{23} +(23.0197 - 23.0197i) q^{25} +(-7.34578 - 50.1298i) q^{26} +(-12.7865 + 3.82959i) q^{28} +(1.15484 - 2.78802i) q^{29} -28.2967i q^{31} +(-13.9361 + 28.8060i) q^{32} +(44.1350 - 26.3479i) q^{34} +(23.3885 + 9.68784i) q^{35} +(34.9633 - 14.4823i) q^{37} +(12.0262 - 1.76227i) q^{38} +(55.0012 - 25.6587i) q^{40} +(-10.1415 - 10.1415i) q^{41} +(-22.8453 + 9.46285i) q^{43} +(5.35817 - 52.5045i) q^{44} +(-63.6407 - 16.0604i) q^{46} +11.2848 q^{47} -37.8649i q^{49} +(-63.1302 - 15.9316i) q^{50} +(-78.5554 + 64.0067i) q^{52} +(-1.71282 - 4.13510i) q^{53} +(-70.7802 + 70.7802i) q^{55} +(19.6850 + 18.0319i) q^{56} +(-5.97169 + 0.875063i) q^{58} +(-14.3649 - 34.6800i) q^{59} +(-0.574221 + 1.38629i) q^{61} +(-48.5930 + 29.0093i) q^{62} +(63.7546 - 5.59928i) q^{64} +192.185 q^{65} +(2.88669 + 1.19571i) q^{67} +(-90.4928 - 48.7802i) q^{68} +(-7.34085 - 50.0961i) q^{70} +(82.7570 + 82.7570i) q^{71} +(6.80099 + 6.80099i) q^{73} +(-60.7136 - 45.1943i) q^{74} +(-15.3553 - 18.8456i) q^{76} +(-40.6770 - 16.8490i) q^{77} -58.6268 q^{79} +(-100.449 - 68.1470i) q^{80} +(-7.01876 + 27.8124i) q^{82} +(6.99463 - 16.8865i) q^{83} +(74.6149 + 180.136i) q^{85} +(39.6708 + 29.5304i) q^{86} +(-95.6573 + 44.6252i) q^{88} +(-85.6528 + 85.6528i) q^{89} +(32.3494 + 78.0983i) q^{91} +(37.6632 + 125.753i) q^{92} +(-11.5690 - 19.3790i) q^{94} +46.1055i q^{95} +19.1537 q^{97} +(-65.0241 + 38.8184i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q + 40 q^{10} - 32 q^{14} - 8 q^{16} + 160 q^{20} - 184 q^{22} - 128 q^{23} + 200 q^{26} - 120 q^{28} - 40 q^{32} + 120 q^{34} + 192 q^{35} - 280 q^{38} + 584 q^{40} - 192 q^{43} - 104 q^{44} + 32 q^{46} + 312 q^{50} - 424 q^{52} - 320 q^{53} - 256 q^{55} + 392 q^{56} - 352 q^{58} + 256 q^{59} + 64 q^{61} + 48 q^{62} + 408 q^{64} + 64 q^{67} - 856 q^{68} + 984 q^{70} - 512 q^{71} - 1056 q^{74} + 296 q^{76} + 448 q^{77} + 512 q^{79} - 328 q^{80} - 760 q^{82} + 448 q^{86} - 1072 q^{88} + 192 q^{91} + 784 q^{92} - 480 q^{94} - 272 q^{98}+O(q^{100}) $ 64 * q + 40 * q^10 - 32 * q^14 - 8 * q^16 + 160 * q^20 - 184 * q^22 - 128 * q^23 + 200 * q^26 - 120 * q^28 - 40 * q^32 + 120 * q^34 + 192 * q^35 - 280 * q^38 + 584 * q^40 - 192 * q^43 - 104 * q^44 + 32 * q^46 + 312 * q^50 - 424 * q^52 - 320 * q^53 - 256 * q^55 + 392 * q^56 - 352 * q^58 + 256 * q^59 + 64 * q^61 + 48 * q^62 + 408 * q^64 + 64 * q^67 - 856 * q^68 + 984 * q^70 - 512 * q^71 - 1056 * q^74 + 296 * q^76 + 448 * q^77 + 512 * q^79 - 328 * q^80 - 760 * q^82 + 448 * q^86 - 1072 * q^88 + 192 * q^91 + 784 * q^92 - 480 * q^94 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.02518	−	1.71727i	−0.512590	−	0.858633i
$2$	−1.02518	−	1.71727i	−0.512590	−	0.858633i
$3$		0			0
$3$		0			0
$4$	−1.89801	+	3.52102i	−0.474502	+	0.880254i
$5$	7.00900	−	2.90322i	1.40180	−	0.580644i	0.451581	−	0.892230i	$-0.350860\pi$
$5$	7.00900	−	2.90322i	1.40180	−	0.580644i	0.950218	+	0.311586i	$0.100860\pi$
$6$		0			0
$7$	2.35957	+	2.35957i	0.337081	+	0.337081i	0.855268	−	0.518187i	$-0.173393\pi$
$7$	2.35957	+	2.35957i	0.337081	+	0.337081i	−0.518187	+	0.855268i	$0.673393\pi$
$8$	7.99233	−	0.350291i	0.999041	−	0.0437864i
$9$		0			0
$10$	−12.1711	−	9.05999i	−1.21711	−	0.905999i
$11$	−12.1899	+	5.04924i	−1.10818	+	0.459022i	−0.860310	−	0.509772i	$-0.829730\pi$
$11$	−12.1899	+	5.04924i	−1.10818	+	0.459022i	−0.247867	+	0.968794i	$0.579730\pi$
$12$		0			0
$13$	23.4042	+	9.69435i	1.80033	+	0.745719i	0.986315	+	0.164869i	$0.0527202\pi$
$13$	23.4042	+	9.69435i	1.80033	+	0.745719i	0.814010	+	0.580850i	$0.197280\pi$
$14$	1.63302	−	6.47098i	0.116644	−	0.462213i
$15$		0			0
$16$	−8.79512	−	13.3658i	−0.549695	−	0.835365i
$17$			25.7007i			1.51181i	0.654682	+	0.755904i	$0.272802\pi$
$17$			25.7007i			1.51181i	−0.654682	+	0.755904i	$0.727198\pi$
$18$		0			0
$19$	−2.32569	+	5.61471i	−0.122405	+	0.295511i	−0.973190	−	0.230002i	$-0.926127\pi$
$19$	−2.32569	+	5.61471i	−0.122405	+	0.295511i	0.850785	+	0.525513i	$0.176127\pi$
$20$	−3.08085	+	30.1891i	−0.154042	+	1.50946i
$21$		0			0
$22$	21.1678	+	15.7570i	0.962172	+	0.716227i
$23$	23.2058	−	23.2058i	1.00895	−	1.00895i	0.00898919	−	0.999960i	$-0.497139\pi$
$23$	23.2058	−	23.2058i	1.00895	−	1.00895i	0.999960	−	0.00898919i	$-0.00286139\pi$
$24$		0			0
$25$	23.0197	−	23.0197i	0.920786	−	0.920786i
$26$	−7.34578	−	50.1298i	−0.282530	−	1.92807i
$27$		0			0
$28$	−12.7865	+	3.82959i	−0.456662	+	0.136771i
$29$	1.15484	−	2.78802i	0.0398219	−	0.0961386i	−0.902717	−	0.430234i	$-0.858431\pi$
$29$	1.15484	−	2.78802i	0.0398219	−	0.0961386i	0.942539	+	0.334096i	$0.108431\pi$
$30$		0			0
$31$		−	28.2967i		−	0.912798i	−0.889775	−	0.456399i	$-0.849139\pi$
$31$		−	28.2967i		−	0.912798i	0.889775	−	0.456399i	$-0.150861\pi$
$32$	−13.9361	+	28.8060i	−0.435504	+	0.900187i
$33$		0			0
$34$	44.1350	−	26.3479i	1.29809	−	0.774938i
$35$	23.3885	+	9.68784i	0.668244	+	0.276796i
$36$		0			0
$37$	34.9633	−	14.4823i	0.944953	−	0.391412i	0.143621	−	0.989633i	$-0.454125\pi$
$37$	34.9633	−	14.4823i	0.944953	−	0.391412i	0.801332	+	0.598220i	$0.204125\pi$
$38$	12.0262	−	1.76227i	0.316479	−	0.0463754i
$39$		0			0
$40$	55.0012	−	25.6587i	1.37503	−	0.641467i
$41$	−10.1415	−	10.1415i	−0.247353	−	0.247353i	0.572531	−	0.819883i	$-0.305962\pi$
$41$	−10.1415	−	10.1415i	−0.247353	−	0.247353i	−0.819883	+	0.572531i	$0.805962\pi$
$42$		0			0
$43$	−22.8453	+	9.46285i	−0.531287	+	0.220066i	−0.632167	−	0.774832i	$-0.717834\pi$
$43$	−22.8453	+	9.46285i	−0.531287	+	0.220066i	0.100880	+	0.994899i	$0.467834\pi$
$44$	5.35817	−	52.5045i	0.121776	−	1.19328i
$45$		0			0
$46$	−63.6407	−	16.0604i	−1.38349	−	0.349140i
$47$	11.2848			0.240102			0.120051	−	0.992768i	$-0.461694\pi$
$47$	11.2848			0.240102			0.120051	+	0.992768i	$0.461694\pi$
$48$		0			0
$49$		−	37.8649i		−	0.772753i
$50$	−63.1302	−	15.9316i	−1.26260	−	0.318632i
$51$		0			0
$52$	−78.5554	+	64.0067i	−1.51068	+	1.23090i
$53$	−1.71282	−	4.13510i	−0.0323173	−	0.0780208i	0.906897	−	0.421353i	$-0.138444\pi$
$53$	−1.71282	−	4.13510i	−0.0323173	−	0.0780208i	−0.939214	+	0.343332i	$0.888444\pi$
$54$		0			0
$55$	−70.7802	+	70.7802i	−1.28691	+	1.28691i
$56$	19.6850	+	18.0319i	0.351517	+	0.321998i
$57$		0			0
$58$	−5.97169	+	0.875063i	−0.102960	+	0.0150873i
$59$	−14.3649	−	34.6800i	−0.243473	−	0.587797i	0.754150	−	0.656702i	$-0.228049\pi$
$59$	−14.3649	−	34.6800i	−0.243473	−	0.587797i	−0.997623	+	0.0689057i	$0.978049\pi$
$60$		0			0
$61$	−0.574221	+	1.38629i	−0.00941347	+	0.0227261i	−0.928516	−	0.371291i	$-0.878915\pi$
$61$	−0.574221	+	1.38629i	−0.00941347	+	0.0227261i	0.919103	+	0.394018i	$0.128915\pi$
$62$	−48.5930	+	29.0093i	−0.783758	+	0.467891i
$63$		0			0
$64$	63.7546	−	5.59928i	0.996166	−	0.0874887i
$65$	192.185			2.95669
$66$		0			0
$67$	2.88669	+	1.19571i	0.0430849	+	0.0178464i	0.404122	−	0.914705i	$-0.367577\pi$
$67$	2.88669	+	1.19571i	0.0430849	+	0.0178464i	−0.361037	+	0.932552i	$0.617577\pi$
$68$	−90.4928	−	48.7802i	−1.33078	−	0.717357i
$69$		0			0
$70$	−7.34085	−	50.0961i	−0.104869	−	0.715659i
$71$	82.7570	+	82.7570i	1.16559	+	1.16559i	0.983232	+	0.182360i	$0.0583736\pi$
$71$	82.7570	+	82.7570i	1.16559	+	1.16559i	0.182360	+	0.983232i	$0.441626\pi$
$72$		0			0
$73$	6.80099	+	6.80099i	0.0931643	+	0.0931643i	0.752153	−	0.658989i	$-0.229015\pi$
$73$	6.80099	+	6.80099i	0.0931643	+	0.0931643i	−0.658989	+	0.752153i	$0.729015\pi$
$74$	−60.7136	−	45.1943i	−0.820454	−	0.610734i
$75$		0			0
$76$	−15.3553	−	18.8456i	−0.202044	−	0.247968i
$77$	−40.6770	−	16.8490i	−0.528273	−	0.218818i
$78$		0			0
$79$	−58.6268			−0.742111			−0.371056	−	0.928611i	$-0.621004\pi$
$79$	−58.6268			−0.742111			−0.371056	+	0.928611i	$0.621004\pi$
$80$	−100.449	−	68.1470i	−1.25561	−	0.851837i
$81$		0			0
$82$	−7.01876	+	27.8124i	−0.0855946	+	0.339176i
$83$	6.99463	−	16.8865i	0.0842726	−	0.203452i	−0.876126	−	0.482083i	$-0.839880\pi$
$83$	6.99463	−	16.8865i	0.0842726	−	0.203452i	0.960398	+	0.278631i	$0.0898805\pi$
$84$		0			0
$85$	74.6149	+	180.136i	0.877823	+	2.11925i
$86$	39.6708	+	29.5304i	0.461289	+	0.343377i
$87$		0			0
$88$	−95.6573	+	44.6252i	−1.08702	+	0.507105i
$89$	−85.6528	+	85.6528i	−0.962391	+	0.962391i	−0.999318	−	0.0369265i	$-0.988243\pi$
$89$	−85.6528	+	85.6528i	−0.962391	+	0.962391i	0.0369265	+	0.999318i	$0.488243\pi$
$90$		0			0
$91$	32.3494	+	78.0983i	0.355488	+	0.858223i
$92$	37.6632	+	125.753i	0.409383	+	1.36688i
$93$		0			0
$94$	−11.5690	−	19.3790i	−0.123074	−	0.206160i
$95$			46.1055i			0.485321i
$96$		0			0
$97$	19.1537			0.197461			0.0987305	−	0.995114i	$-0.468522\pi$
$97$	19.1537			0.197461			0.0987305	+	0.995114i	$0.468522\pi$
$98$	−65.0241	+	38.8184i	−0.663512	+	0.396106i
$99$		0			0
$100$	37.3611	+	124.744i	0.373611	+	1.24744i
$101$	−12.1412	+	5.02904i	−0.120210	+	0.0497924i	−0.441978	−	0.897026i	$-0.645723\pi$
$101$	−12.1412	+	5.02904i	−0.120210	+	0.0497924i	0.321768	+	0.946819i	$0.395723\pi$
$102$		0			0
$103$	−2.43859	−	2.43859i	−0.0236756	−	0.0236756i	0.695170	−	0.718845i	$-0.255329\pi$
$103$	−2.43859	−	2.43859i	−0.0236756	−	0.0236756i	−0.718845	+	0.695170i	$0.755329\pi$
$104$	190.450	+	69.2821i	1.83125	+	0.666174i
$105$		0			0
$106$	−5.34513	+	7.18059i	−0.0504258	+	0.0677414i
$107$	−153.093	+	63.4133i	−1.43078	+	0.592648i	−0.957544	−	0.288288i	$-0.906914\pi$
$107$	−153.093	+	63.4133i	−1.43078	+	0.592648i	−0.473235	+	0.880936i	$0.656914\pi$
$108$		0			0
$109$	−152.961	−	63.3585i	−1.40331	−	0.581271i	−0.452703	−	0.891662i	$-0.649540\pi$
$109$	−152.961	−	63.3585i	−1.40331	−	0.581271i	−0.950609	+	0.310391i	$0.899540\pi$
$110$	194.111	+	48.9860i	1.76465	+	0.445327i
$111$		0			0
$112$	10.7849	−	52.2903i	0.0962939	−	0.466877i
$113$		−	78.9572i		−	0.698736i	−0.936986	−	0.349368i	$-0.886396\pi$
$113$		−	78.9572i		−	0.698736i	0.936986	−	0.349368i	$-0.113604\pi$
$114$		0			0
$115$	95.2779	−	230.021i	0.828503	−	2.00018i
$116$	7.62477	+	9.35788i	0.0657308	+	0.0806714i
$117$		0			0
$118$	−44.8282	+	60.2217i	−0.379900	+	0.510353i
$119$	−60.6426	+	60.6426i	−0.509602	+	0.509602i
$120$		0			0
$121$	37.5400	−	37.5400i	0.310248	−	0.310248i
$122$	2.96932	−	0.435110i	0.0243387	−	0.00356647i
$123$		0			0
$124$	99.6333	+	53.7074i	0.803494	+	0.433125i
$125$	21.9330	−	52.9509i	0.175464	−	0.423607i
$126$		0			0
$127$		−	2.13791i		−	0.0168340i	−0.999965	−	0.00841698i	$-0.997321\pi$
$127$		−	2.13791i		−	0.0168340i	0.999965	−	0.00841698i	$-0.00267924\pi$
$128$	−74.9754	−	103.743i	−0.585746	−	0.810495i
$129$		0			0
$130$	−197.024	−	330.033i	−1.51557	−	2.53871i
$131$	−25.8459	−	10.7057i	−0.197297	−	0.0817232i	0.281847	−	0.959459i	$-0.409053\pi$
$131$	−25.8459	−	10.7057i	−0.197297	−	0.0817232i	−0.479144	+	0.877736i	$0.659053\pi$
$132$		0			0
$133$	−18.7359	+	7.76067i	−0.140871	+	0.0583509i
$134$	−0.906032	−	6.18303i	−0.00676144	−	0.0461420i
$135$		0			0
$136$	9.00274	+	205.409i	0.0661966	+	1.51036i
$137$	110.083	+	110.083i	0.803527	+	0.803527i	0.983645	−	0.180118i	$-0.0576479\pi$
$137$	110.083	+	110.083i	0.803527	+	0.803527i	−0.180118	+	0.983645i	$0.557648\pi$
$138$		0			0
$139$	−28.9934	+	12.0094i	−0.208585	+	0.0863989i	−0.484530	−	0.874775i	$-0.661009\pi$
$139$	−28.9934	+	12.0094i	−0.208585	+	0.0863989i	0.275945	+	0.961174i	$0.411009\pi$
$140$	−78.5027	+	63.9638i	−0.560734	+	0.456884i
$141$		0			0
$142$	57.2750	−	226.957i	0.403345	−	1.59829i
$143$	−334.246			−2.33738
$144$		0			0
$145$		−	22.8939i		−	0.157889i
$146$	4.70687	−	18.6514i	0.0322388	−	0.127749i
$147$		0			0
$148$	−15.3683	+	150.594i	−0.103840	+	1.01753i
$149$	−56.7824	−	137.085i	−0.381090	−	0.920033i	−0.991756	−	0.128144i	$-0.959098\pi$
$149$	−56.7824	−	137.085i	−0.381090	−	0.920033i	0.610665	−	0.791889i	$-0.290902\pi$
$150$		0			0
$151$	−189.419	+	189.419i	−1.25443	+	1.25443i	−0.300718	+	0.953713i	$0.597226\pi$
$151$	−189.419	+	189.419i	−1.25443	+	1.25443i	−0.953713	+	0.300718i	$0.902774\pi$
$152$	−16.6209	+	45.6893i	−0.109348	+	0.300587i
$153$		0			0
$154$	12.7671	+	87.1265i	0.0829033	+	0.565756i
$155$	−82.1516	−	198.332i	−0.530011	−	1.27956i
$156$		0			0
$157$	81.6229	−	197.055i	0.519891	−	1.25513i	−0.418079	−	0.908411i	$-0.637297\pi$
$157$	81.6229	−	197.055i	0.519891	−	1.25513i	0.937970	−	0.346717i	$-0.112703\pi$
$158$	60.1030	+	100.678i	0.380399	+	0.637201i
$159$		0			0
$160$	−14.0482	+	242.361i	−0.0878010	+	1.51475i
$161$	109.511			0.680195
$162$		0			0
$163$	−158.728	−	65.7474i	−0.973792	−	0.403358i	−0.161670	−	0.986845i	$-0.551688\pi$
$163$	−158.728	−	65.7474i	−0.973792	−	0.403358i	−0.812123	+	0.583487i	$0.801688\pi$
$164$	54.9568	−	16.4597i	0.335103	−	0.100364i
$165$		0			0
$166$	−36.1694	+	5.30010i	−0.217888	+	0.0319283i
$167$	−41.5433	−	41.5433i	−0.248762	−	0.248762i	0.571700	−	0.820463i	$-0.306284\pi$
$167$	−41.5433	−	41.5433i	−0.248762	−	0.248762i	−0.820463	+	0.571700i	$0.806284\pi$
$168$		0			0
$169$	334.277	+	334.277i	1.97797	+	1.97797i
$170$	232.848	−	312.806i	1.36970	−	1.84004i
$171$		0			0
$172$	10.0418	−	98.3994i	0.0583826	−	0.572090i
$173$	−91.1085	−	37.7384i	−0.526639	−	0.218141i	0.103492	−	0.994630i	$-0.466998\pi$
$173$	−91.1085	−	37.7384i	−0.526639	−	0.218141i	−0.630130	+	0.776489i	$0.716998\pi$
$174$		0			0
$175$	108.633			0.620759
$176$	174.699	+	118.520i	0.992611	+	0.673410i
$177$		0			0
$178$	234.898	+	59.2791i	1.31965	+	0.333029i
$179$	125.736	−	303.554i	0.702436	−	1.69583i	−0.0156525	−	0.999877i	$-0.504983\pi$
$179$	125.736	−	303.554i	0.702436	−	1.69583i	0.718088	−	0.695952i	$-0.245017\pi$
$180$		0			0
$181$	−76.2312	−	184.038i	−0.421167	−	1.01679i	−0.982004	−	0.188861i	$-0.939521\pi$
$181$	−76.2312	−	184.038i	−0.421167	−	1.01679i	0.560837	−	0.827926i	$-0.310479\pi$
$182$	100.952	−	135.617i	0.554679	−	0.745150i
$183$		0			0
$184$	177.340	−	193.597i	0.963803	−	1.05216i
$185$	203.012	−	203.012i	1.09736	−	1.09736i
$186$		0			0
$187$	−129.769	−	313.291i	−0.693953	−	1.67535i
$188$	−21.4187	+	39.7340i	−0.113929	+	0.211351i
$189$		0			0
$190$	79.1754	−	47.2665i	0.416713	−	0.248771i
$191$			201.527i			1.05511i	0.849520	+	0.527556i	$0.176892\pi$
$191$			201.527i			1.05511i	−0.849520	+	0.527556i	$0.823108\pi$
$192$		0			0
$193$	2.68950			0.0139352			0.00696761	−	0.999976i	$-0.497782\pi$
$193$	2.68950			0.0139352			0.00696761	+	0.999976i	$0.497782\pi$
$194$	−19.6360	−	32.8920i	−0.101217	−	0.169547i
$195$		0			0
$196$	133.323	+	71.8679i	0.680219	+	0.366673i
$197$	6.97702	−	2.88997i	0.0354163	−	0.0146699i	−0.364905	−	0.931045i	$-0.618899\pi$
$197$	6.97702	−	2.88997i	0.0354163	−	0.0146699i	0.400321	+	0.916375i	$0.368899\pi$
$198$		0			0
$199$	178.829	+	178.829i	0.898639	+	0.898639i	0.995316	−	0.0966766i	$-0.0308212\pi$
$199$	178.829	+	178.829i	0.898639	+	0.898639i	−0.0966766	+	0.995316i	$0.530821\pi$
$200$	175.917	−	192.044i	0.879585	−	0.960221i
$201$		0			0
$202$	21.0831	+	15.6940i	0.104372	+	0.0776928i
$203$	9.30342	−	3.85360i	0.0458297	−	0.0189833i
$204$		0			0
$205$	−100.524	−	41.6385i	−0.490362	−	0.203115i
$206$	−1.68771	+	6.68770i	−0.00819278	+	0.0324646i
$207$		0			0
$208$	−76.2699	−	398.080i	−0.366682	−	1.91385i
$209$		−	80.1860i		−	0.383665i
$210$		0			0
$211$	−111.432	+	269.022i	−0.528116	+	1.27498i	0.404640	+	0.914476i	$0.367397\pi$
$211$	−111.432	+	269.022i	−0.528116	+	1.27498i	−0.932756	+	0.360508i	$0.882603\pi$
$212$	17.8107	+	1.81761i	0.0840128	+	0.00857363i
$213$		0			0
$214$	265.846	+	197.892i	1.24227	+	0.924729i
$215$	−132.650	+	132.650i	−0.616977	+	0.616977i
$216$		0			0
$217$	66.7680	−	66.7680i	0.307687	−	0.307687i
$218$	48.0092	+	327.629i	0.220226	+	1.50288i
$219$		0			0
$220$	−114.877	−	383.560i	−0.522167	−	1.74345i
$221$	−249.152	+	601.506i	−1.12738	+	2.72175i
$222$		0			0
$223$		−	303.282i		−	1.36001i	−0.733208	−	0.680005i	$-0.761978\pi$
$223$		−	303.282i		−	1.36001i	0.733208	−	0.680005i	$-0.238022\pi$
$224$	−100.853	+	35.0864i	−0.450236	+	0.156636i
$225$		0			0
$226$	−135.591	+	80.9454i	−0.599958	+	0.358165i
$227$	345.922	+	143.286i	1.52389	+	0.631214i	0.978365	−	0.206884i	$-0.0663323\pi$
$227$	345.922	+	143.286i	1.52389	+	0.631214i	0.545520	+	0.838098i	$0.316332\pi$
$228$		0			0
$229$	−115.129	+	47.6879i	−0.502746	+	0.208244i	−0.619619	−	0.784903i	$-0.712713\pi$
$229$	−115.129	+	47.6879i	−0.502746	+	0.208244i	0.116873	+	0.993147i	$0.462713\pi$
$230$	−492.685	+	72.1957i	−2.14211	+	0.313894i
$231$		0			0
$232$	8.25320	−	22.6873i	0.0355741	−	0.0977900i
$233$	−23.5752	−	23.5752i	−0.101181	−	0.101181i	0.654704	−	0.755885i	$-0.272793\pi$
$233$	−23.5752	−	23.5752i	−0.101181	−	0.101181i	−0.755885	+	0.654704i	$0.772793\pi$
$234$		0			0
$235$	79.0952	−	32.7623i	0.336575	−	0.139414i
$236$	149.374	+	15.2438i	0.632939	+	0.0645924i
$237$		0			0
$238$	166.309	+	41.9699i	0.698778	+	0.176344i
$239$	381.999			1.59832			0.799161	−	0.601118i	$-0.205278\pi$
$239$	381.999			1.59832			0.799161	+	0.601118i	$0.205278\pi$
$240$		0			0
$241$		−	262.698i		−	1.09003i	−0.838425	−	0.545017i	$-0.816523\pi$
$241$		−	262.698i		−	1.09003i	0.838425	−	0.545017i	$-0.183477\pi$
$242$	−102.952	−	25.9809i	−0.425420	−	0.107359i
$243$		0			0
$244$	−3.79128	−	4.65304i	−0.0155381	−	0.0190698i
$245$	−109.930	−	265.395i	−0.448695	−	1.08324i
$246$		0			0
$247$	−108.862	+	108.862i	−0.440737	+	0.440737i
$248$	−9.91209	−	226.157i	−0.0399681	−	0.911922i
$249$		0			0
$250$	−113.416	+	16.6195i	−0.453664	+	0.0664779i
$251$	−150.886	−	364.271i	−0.601140	−	1.45128i	−0.872409	−	0.488776i	$-0.837444\pi$
$251$	−150.886	−	364.271i	−0.601140	−	1.45128i	0.271270	−	0.962503i	$-0.412556\pi$
$252$		0			0
$253$	−165.706	+	400.050i	−0.654964	+	1.58122i
$254$	−3.67136	+	2.19175i	−0.0144542	+	0.00862892i
$255$		0			0
$256$	−101.292	+	235.108i	−0.395670	+	0.918393i
$257$	−232.141			−0.903273			−0.451636	−	0.892202i	$-0.649160\pi$
$257$	−232.141			−0.903273			−0.451636	+	0.892202i	$0.649160\pi$
$258$		0			0
$259$	116.670	+	48.3263i	0.450463	+	0.186588i
$260$	−364.769	+	676.687i	−1.40296	+	2.60264i
$261$		0			0
$262$	8.11215	+	55.3597i	0.0309624	+	0.211297i
$263$	51.8767	+	51.8767i	0.197250	+	0.197250i	0.798820	−	0.601570i	$-0.205458\pi$
$263$	51.8767	+	51.8767i	0.197250	+	0.197250i	−0.601570	+	0.798820i	$0.705458\pi$
$264$		0			0
$265$	−24.0102	−	24.0102i	−0.0906047	−	0.0906047i
$266$	32.5348	+	24.2185i	0.122311	+	0.0910468i
$267$		0			0
$268$	−9.68906	+	7.89462i	−0.0361532	+	0.0294575i
$269$	−157.161	−	65.0980i	−0.584240	−	0.242000i	0.0709304	−	0.997481i	$-0.477403\pi$
$269$	−157.161	−	65.0980i	−0.584240	−	0.242000i	−0.655170	+	0.755481i	$0.727403\pi$
$270$		0			0
$271$	312.143			1.15182			0.575910	−	0.817513i	$-0.304648\pi$
$271$	312.143			1.15182			0.575910	+	0.817513i	$0.304648\pi$
$272$	343.512	−	226.041i	1.26291	−	0.831034i
$273$		0			0
$274$	76.1871	−	301.897i	0.278055	−	1.10182i
$275$	−164.377	+	396.840i	−0.597733	+	1.44306i
$276$		0			0
$277$	−118.178	−	285.308i	−0.426636	−	1.02999i	−0.980347	−	0.197282i	$-0.936789\pi$
$277$	−118.178	−	285.308i	−0.426636	−	1.02999i	0.553710	−	0.832709i	$-0.313211\pi$
$278$	50.3468	+	37.4775i	0.181104	+	0.134811i
$279$		0			0
$280$	190.322	+	69.2356i	0.679723	+	0.247270i
$281$	−97.5918	+	97.5918i	−0.347302	+	0.347302i	−0.859104	−	0.511802i	$-0.828978\pi$
$281$	−97.5918	+	97.5918i	−0.347302	+	0.347302i	0.511802	+	0.859104i	$0.328978\pi$
$282$		0			0
$283$	18.5403	+	44.7603i	0.0655135	+	0.158164i	0.953245	−	0.302197i	$-0.0977201\pi$
$283$	18.5403	+	44.7603i	0.0655135	+	0.158164i	−0.887732	+	0.460361i	$0.847720\pi$
$284$	−448.462	+	134.315i	−1.57909	+	0.472941i
$285$		0			0
$286$	342.662	+	573.989i	1.19812	+	2.00695i
$287$		−	47.8589i		−	0.166756i
$288$		0			0
$289$	−371.528			−1.28556
$290$	−39.3150	+	23.4704i	−0.135569	+	0.0809325i
$291$		0			0
$292$	−36.8548	+	11.0381i	−0.126215	+	0.0378016i
$293$	−161.620	+	66.9453i	−0.551605	+	0.228482i	−0.641036	−	0.767511i	$-0.721495\pi$
$293$	−161.620	+	66.9453i	−0.551605	+	0.228482i	0.0894312	+	0.995993i	$0.471495\pi$
$294$		0			0
$295$	−201.367	−	201.367i	−0.682602	−	0.682602i
$296$	274.365	−	127.994i	0.926908	−	0.432413i
$297$		0			0
$298$	−177.199	+	238.047i	−0.594628	+	0.798817i
$299$	768.080	−	318.149i	2.56883	−	1.06404i
$300$		0			0
$301$	−76.2333	−	31.5769i	−0.253267	−	0.104907i
$302$	519.472	+	131.094i	1.72011	+	0.434087i
$303$		0			0
$304$	95.5001	−	18.2973i	0.314145	−	0.0601884i
$305$			11.3836i			0.0373233i
$306$		0			0
$307$	−105.523	+	254.755i	−0.343724	+	0.829822i	0.653609	+	0.756832i	$0.273254\pi$
$307$	−105.523	+	254.755i	−0.343724	+	0.829822i	−0.997333	+	0.0729899i	$0.976746\pi$
$308$	136.531	−	111.245i	0.443282	−	0.361185i
$309$		0			0
$310$	−256.368	+	344.402i	−0.826993	+	1.11097i
$311$	43.9499	−	43.9499i	0.141318	−	0.141318i	−0.632909	−	0.774227i	$-0.718139\pi$
$311$	43.9499	−	43.9499i	0.141318	−	0.141318i	0.774227	+	0.632909i	$0.218139\pi$
$312$		0			0
$313$	−121.839	+	121.839i	−0.389261	+	0.389261i	−0.874424	−	0.485163i	$-0.838760\pi$
$313$	−121.839	+	121.839i	−0.389261	+	0.389261i	0.485163	+	0.874424i	$0.338760\pi$
$314$	−422.074	+	61.8488i	−1.34419	+	0.196971i
$315$		0			0
$316$	111.274	−	206.426i	0.352133	−	0.653246i
$317$	−1.63885	+	3.95654i	−0.00516988	+	0.0124812i	−0.926443	−	0.376434i	$-0.877150\pi$
$317$	−1.63885	+	3.95654i	−0.00516988	+	0.0124812i	0.921274	+	0.388915i	$0.127150\pi$
$318$		0			0
$319$			39.8168i			0.124818i
$320$	430.600	−	224.339i	1.34562	−	0.701059i
$321$		0			0
$322$	−112.269	−	188.060i	−0.348661	−	0.584038i
$323$	−144.302	−	59.7720i	−0.446756	−	0.185053i
$324$		0			0
$325$	761.918	−	315.597i	2.34436	−	0.971067i
$326$	49.8193	+	339.982i	0.152820	+	1.04289i
$327$		0			0
$328$	−84.6063	−	77.5014i	−0.257946	−	0.236285i
$329$	26.6273	+	26.6273i	0.0809339	+	0.0809339i
$330$		0			0
$331$	−481.638	+	199.501i	−1.45510	+	0.602722i	−0.963406	−	0.268046i	$-0.913622\pi$
$331$	−481.638	+	199.501i	−1.45510	+	0.602722i	−0.491694	+	0.870768i	$0.663622\pi$
$332$	46.1819	+	56.6790i	0.139102	+	0.170720i
$333$		0			0
$334$	−28.7516	+	113.930i	−0.0860825	+	0.341109i
$335$	23.7042			0.0707588
$336$		0			0
$337$			321.444i			0.953840i	0.878947	+	0.476920i	$0.158247\pi$
$337$			321.444i			0.953840i	−0.878947	+	0.476920i	$0.841753\pi$
$338$	231.348	−	916.736i	0.684462	−	2.71224i
$339$		0			0
$340$	−775.883	−	79.1801i	−2.28201	−	0.232883i
$341$	142.877	+	344.936i	0.418994	+	1.01154i
$342$		0			0
$343$	204.963	−	204.963i	0.597561	−	0.597561i
$344$	−179.273	+	83.6327i	−0.521142	+	0.243118i
$345$		0			0
$346$	28.5958	+	195.146i	0.0826469	+	0.564006i
$347$	19.7482	+	47.6765i	0.0569113	+	0.137396i	0.949778	−	0.312926i	$-0.101309\pi$
$347$	19.7482	+	47.6765i	0.0569113	+	0.137396i	−0.892866	+	0.450322i	$0.851309\pi$
$348$		0			0
$349$	−67.7422	+	163.544i	−0.194104	+	0.468608i	−0.990727	−	0.135868i	$-0.956618\pi$
$349$	−67.7422	+	163.544i	−0.194104	+	0.468608i	0.796623	+	0.604476i	$0.206618\pi$
$350$	−111.368	−	186.551i	−0.318195	−	0.533004i
$351$		0			0
$352$	24.4324	−	421.510i	0.0694101	−	1.19747i
$353$	−325.836			−0.923047			−0.461524	−	0.887128i	$-0.652697\pi$
$353$	−325.836			−0.923047			−0.461524	+	0.887128i	$0.652697\pi$
$354$		0			0
$355$	820.305	+	339.782i	2.31072	+	0.957131i
$356$	−139.015	−	464.155i	−0.390492	−	1.30381i
$357$		0			0
$358$	−650.184	+	95.2750i	−1.81616	+	0.266131i
$359$	−151.423	−	151.423i	−0.421790	−	0.421790i	0.464030	−	0.885820i	$-0.346403\pi$
$359$	−151.423	−	151.423i	−0.421790	−	0.421790i	−0.885820	+	0.464030i	$0.846403\pi$
$360$		0			0
$361$	229.149	+	229.149i	0.634763	+	0.634763i
$362$	−237.892	+	319.582i	−0.657161	+	0.882823i
$363$		0			0
$364$	−336.385	−	34.3286i	−0.924134	−	0.0943093i
$365$	67.4129	+	27.9233i	0.184693	+	0.0765023i
$366$		0			0
$367$	169.180			0.460980			0.230490	−	0.973075i	$-0.425967\pi$
$367$	169.180			0.460980			0.230490	+	0.973075i	$0.425967\pi$
$368$	−514.263	−	106.067i	−1.39746	−	0.288227i
$369$		0			0
$370$	−556.750	−	140.502i	−1.50473	−	0.379735i
$371$	5.71555	−	13.7986i	0.0154058	−	0.0371929i
$372$		0			0
$373$	81.3001	+	196.276i	0.217963	+	0.526209i	0.994605	−	0.103733i	$-0.0330787\pi$
$373$	81.3001	+	196.276i	0.217963	+	0.526209i	−0.776642	+	0.629942i	$0.783079\pi$
$374$	−404.967	+	544.028i	−1.08280	+	1.45462i
$375$		0			0
$376$	90.1919	−	3.95297i	0.239872	−	0.0105132i
$377$	54.0561	−	54.0561i	0.143385	−	0.143385i
$378$		0			0
$379$	−176.519	−	426.154i	−0.465749	−	1.12442i	−0.966001	−	0.258538i	$-0.916759\pi$
$379$	−176.519	−	426.154i	−0.465749	−	1.12442i	0.500252	−	0.865880i	$-0.333241\pi$
$380$	−162.338	−	87.5086i	−0.427206	−	0.230286i
$381$		0			0
$382$	346.075	−	206.601i	0.905955	−	0.540841i
$383$			111.777i			0.291847i	0.989296	+	0.145923i	$0.0466153\pi$
$383$			111.777i			0.291847i	−0.989296	+	0.145923i	$0.953385\pi$
$384$		0			0
$385$	−334.021			−0.867587
$386$	−2.75722	−	4.61859i	−0.00714306	−	0.0119652i
$387$		0			0
$388$	−36.3539	+	67.4406i	−0.0936957	+	0.173816i
$389$	345.181	−	142.979i	0.887355	−	0.367554i	0.108010	−	0.994150i	$-0.465552\pi$
$389$	345.181	−	142.979i	0.887355	−	0.367554i	0.779345	+	0.626595i	$0.215552\pi$
$390$		0			0
$391$	596.407	+	596.407i	1.52534	+	1.52534i
$392$	−13.2637	−	302.629i	−0.0338360	−	0.772012i
$393$		0			0
$394$	−12.1156	−	9.01865i	−0.0307502	−	0.0228900i
$395$	−410.915	+	170.206i	−1.04029	+	0.430902i
$396$		0			0
$397$	−507.186	−	210.083i	−1.27755	−	0.529177i	−0.362296	−	0.932063i	$-0.618007\pi$
$397$	−507.186	−	210.083i	−1.27755	−	0.529177i	−0.915250	+	0.402886i	$0.868007\pi$
$398$	123.765	−	490.430i	0.310968	−	1.23224i
$399$		0			0
$400$	−510.138	−	105.216i	−1.27534	−	0.263041i
$401$		−	445.754i		−	1.11160i	−0.831314	−	0.555802i	$-0.812411\pi$
$401$		−	445.754i		−	1.11160i	0.831314	−	0.555802i	$-0.187589\pi$
$402$		0			0
$403$	274.318	−	662.263i	0.680691	−	1.64333i
$404$	5.33673	−	52.2944i	0.0132097	−	0.129442i
$405$		0			0
$406$	−16.1554	−	12.0258i	−0.0397915	−	0.0296202i
$407$	−353.076	+	353.076i	−0.867508	+	0.867508i
$408$		0			0
$409$	−380.306	+	380.306i	−0.929845	+	0.929845i	−0.997695	−	0.0678508i	$-0.978386\pi$
$409$	−380.306	+	380.306i	−0.929845	+	0.929845i	0.0678508	+	0.997695i	$0.478386\pi$
$410$	31.5511	+	215.314i	0.0769539	+	0.525156i
$411$		0			0
$412$	13.2148	−	3.95785i	0.0320747	−	0.00960643i
$413$	47.9348	−	115.725i	0.116065	−	0.280205i
$414$		0			0
$415$		−	138.665i		−	0.334131i
$416$	−605.420	+	539.080i	−1.45534	+	1.29587i
$417$		0			0
$418$	−137.701	+	82.2052i	−0.329428	+	0.196663i
$419$	−130.080	−	53.8808i	−0.310453	−	0.128594i	0.222017	−	0.975043i	$-0.428736\pi$
$419$	−130.080	−	53.8808i	−0.310453	−	0.128594i	−0.532470	+	0.846449i	$0.678736\pi$
$420$		0			0
$421$	−127.092	+	52.6432i	−0.301881	+	0.125043i	−0.528482	−	0.848944i	$-0.677239\pi$
$421$	−127.092	+	52.6432i	−0.301881	+	0.125043i	0.226601	+	0.973988i	$0.427239\pi$
$422$	576.220	−	84.4366i	1.36545	−	0.200087i
$423$		0			0
$424$	−15.1379	−	32.4491i	−0.0357025	−	0.0765309i
$425$	591.622	+	591.622i	1.39205	+	1.39205i
$426$		0			0
$427$	−4.62596	+	1.91614i	−0.0108336	+	0.00448744i
$428$	67.2931	−	659.403i	0.157227	−	1.54066i
$429$		0			0
$430$	363.786	+	91.8053i	0.846014	+	0.213501i
$431$	331.894			0.770055			0.385027	−	0.922905i	$-0.374192\pi$
$431$	331.894			0.770055			0.385027	+	0.922905i	$0.374192\pi$
$432$		0			0
$433$		−	806.945i		−	1.86361i	−0.362955	−	0.931807i	$-0.618232\pi$
$433$		−	806.945i		−	1.86361i	0.362955	−	0.931807i	$-0.381768\pi$
$434$	−183.108	−	46.2092i	−0.421907	−	0.106473i
$435$		0			0
$436$	513.408	−	418.323i	1.17754	−	0.959457i
$437$	76.3245	+	184.264i	0.174656	+	0.421656i
$438$		0			0
$439$	164.097	−	164.097i	0.373797	−	0.373797i	−0.495061	−	0.868858i	$-0.664854\pi$
$439$	164.097	−	164.097i	0.373797	−	0.373797i	0.868858	+	0.495061i	$0.164854\pi$
$440$	−540.905	+	590.492i	−1.22933	+	1.34203i
$441$		0			0
$442$	1288.37	−	188.792i	2.91487	−	0.427131i
$443$	220.439	+	532.187i	0.497606	+	1.20133i	0.950770	+	0.309899i	$0.100295\pi$
$443$	220.439	+	532.187i	0.497606	+	1.20133i	−0.453164	+	0.891427i	$0.649705\pi$
$444$		0			0
$445$	−351.671	+	849.009i	−0.790272	+	1.90789i
$446$	−520.816	+	310.919i	−1.16775	+	0.697128i
$447$		0			0
$448$	163.645	+	137.221i	0.365279	+	0.306298i
$449$	543.417			1.21028			0.605141	−	0.796118i	$-0.293117\pi$
$449$	543.417			1.21028			0.605141	+	0.796118i	$0.293117\pi$
$450$		0			0
$451$	174.830	+	72.4172i	0.387651	+	0.160570i
$452$	278.010	+	149.861i	0.615065	+	0.331552i
$453$		0			0
$454$	−108.573	−	740.934i	−0.239148	−	1.63201i
$455$	453.473	+	453.473i	0.996644	+	0.996644i
$456$		0			0
$457$	−201.086	−	201.086i	−0.440013	−	0.440013i	0.452003	−	0.892016i	$-0.350709\pi$
$457$	−201.086	−	201.086i	−0.440013	−	0.440013i	−0.892016	+	0.452003i	$0.850709\pi$
$458$	199.921	+	148.818i	0.436508	+	0.324930i
$459$		0			0
$460$	629.070	+	772.057i	1.36754	+	1.67839i
$461$	−32.1175	−	13.3035i	−0.0696692	−	0.0288579i	0.347577	−	0.937652i	$-0.387005\pi$
$461$	−32.1175	−	13.3035i	−0.0696692	−	0.0288579i	−0.417246	+	0.908794i	$0.637005\pi$
$462$		0			0
$463$	−41.6305			−0.0899146			−0.0449573	−	0.998989i	$-0.514315\pi$
$463$	−41.6305			−0.0899146			−0.0449573	+	0.998989i	$0.514315\pi$
$464$	−47.4211	+	9.08562i	−0.102201	+	0.0195811i
$465$		0			0
$466$	−16.3161	+	64.6538i	−0.0350131	+	0.138742i
$467$	215.784	−	520.948i	0.462064	−	1.11552i	−0.505485	−	0.862835i	$-0.668686\pi$
$467$	215.784	−	520.948i	0.462064	−	1.11552i	0.967549	−	0.252685i	$-0.0813136\pi$
$468$		0			0
$469$	3.98999	+	9.63268i	0.00850744	+	0.0205388i
$470$	−137.348	−	102.240i	−0.292231	−	0.217532i
$471$		0			0
$472$	−126.957	−	272.142i	−0.268977	−	0.576572i
$473$	230.703	−	230.703i	0.487745	−	0.487745i
$474$		0			0
$475$	75.7122	+	182.785i	0.159394	+	0.384811i
$476$	−98.4234	−	328.624i	−0.206772	−	0.690386i
$477$		0			0
$478$	−391.618	−	655.994i	−0.819284	−	1.37237i
$479$		−	662.316i		−	1.38270i	−0.722518	−	0.691352i	$-0.757015\pi$
$479$		−	662.316i		−	1.38270i	0.722518	−	0.691352i	$-0.242985\pi$
$480$		0			0
$481$	958.685			1.99311
$482$	−451.123	+	269.313i	−0.935939	+	0.558741i
$483$		0			0
$484$	60.9278	+	203.430i	0.125884	+	0.420311i
$485$	134.248	−	55.6075i	0.276801	−	0.114655i
$486$		0			0
$487$	−309.360	−	309.360i	−0.635236	−	0.635236i	0.314140	−	0.949377i	$-0.398284\pi$
$487$	−309.360	−	309.360i	−0.635236	−	0.635236i	−0.949377	+	0.314140i	$0.898284\pi$
$488$	−4.10376	+	11.2809i	−0.00840934	+	0.0231165i
$489$		0			0
$490$	−343.056	+	460.857i	−0.700113	+	0.940525i
$491$	−249.104	+	103.182i	−0.507340	+	0.210147i	−0.621646	−	0.783299i	$-0.713536\pi$
$491$	−249.104	+	103.182i	−0.507340	+	0.210147i	0.114306	+	0.993446i	$0.463536\pi$
$492$		0			0
$493$	71.6541	+	29.6801i	0.145343	+	0.0602031i
$494$	298.548	+	75.3419i	0.604349	+	0.152514i
$495$		0			0
$496$	−378.210	+	248.873i	−0.762519	+	0.501760i
$497$			390.541i			0.785797i
$498$		0			0
$499$	203.686	−	491.742i	0.408189	−	0.985455i	−0.577425	−	0.816444i	$-0.695942\pi$
$499$	203.686	−	491.742i	0.408189	−	0.985455i	0.985614	−	0.169012i	$-0.0540575\pi$
$500$	144.812	+	177.728i	0.289624	+	0.355455i
$501$		0			0
$502$	−470.865	+	632.555i	−0.937978	+	1.26007i
$503$	−135.286	+	135.286i	−0.268959	+	0.268959i	−0.828681	−	0.559722i	$-0.810908\pi$
$503$	−135.286	+	135.286i	−0.268959	+	0.268959i	0.559722	+	0.828681i	$0.310908\pi$
$504$		0			0
$505$	−70.4970	+	70.4970i	−0.139598	+	0.139598i
$506$	856.870	−	125.562i	1.69342	−	0.248146i
$507$		0			0
$508$	7.52762	+	4.05778i	0.0148182	+	0.00798775i
$509$	294.504	−	710.995i	0.578593	−	1.39685i	−0.315483	−	0.948931i	$-0.602167\pi$
$509$	294.504	−	710.995i	0.578593	−	1.39685i	0.894076	−	0.447915i	$-0.147833\pi$
$510$		0			0
$511$			32.0948i			0.0628078i
$512$	507.586	−	67.0839i	0.991379	−	0.131023i
$513$		0			0
$514$	237.987	+	398.648i	0.463009	+	0.775580i
$515$	−24.1718	−	10.0123i	−0.0469356	−	0.0194414i
$516$		0			0
$517$	−137.561	+	56.9797i	−0.266076	+	0.110212i
$518$	−36.6187	−	249.897i	−0.0706924	−	0.482426i
$519$		0			0
$520$	1536.01	−	67.3207i	2.95386	−	0.129463i
$521$	328.950	+	328.950i	0.631382	+	0.631382i	0.948415	−	0.317033i	$-0.102687\pi$
$521$	328.950	+	328.950i	0.631382	+	0.631382i	−0.317033	+	0.948415i	$0.602687\pi$
$522$		0			0
$523$	375.998	−	155.744i	0.718926	−	0.297789i	0.00693327	−	0.999976i	$-0.497793\pi$
$523$	375.998	−	155.744i	0.718926	−	0.297789i	0.711992	+	0.702187i	$0.247793\pi$
$524$	86.7509	−	70.6844i	0.165555	−	0.134894i
$525$		0			0
$526$	35.9032	−	142.269i	0.0682569	−	0.270474i
$527$	727.247			1.37998
$528$		0			0
$529$		−	548.020i		−	1.03596i
$530$	−16.6171	+	65.8468i	−0.0313531	+	0.124239i
$531$		0			0
$532$	8.23548	−	80.6993i	0.0154802	−	0.151690i
$533$	−139.038	−	335.668i	−0.260860	−	0.629771i
$534$		0			0
$535$	−888.928	+	888.928i	−1.66155	+	1.66155i
$536$	23.4902	+	8.54529i	0.0438250	+	0.0159427i
$537$		0			0
$538$	49.3273	+	336.624i	0.0916864	+	0.625695i
$539$	191.189	+	461.571i	0.354711	+	0.856347i
$540$		0			0
$541$	−180.025	+	434.619i	−0.332764	+	0.803362i	0.665607	+	0.746302i	$0.268173\pi$
$541$	−180.025	+	434.619i	−0.332764	+	0.803362i	−0.998371	+	0.0570600i	$0.981827\pi$
$542$	−320.003	−	536.033i	−0.590411	−	0.988990i
$543$		0			0
$544$	−740.335	−	358.169i	−1.36091	−	0.658399i
$545$	−1256.05			−2.30467
$546$		0			0
$547$	842.270	+	348.880i	1.53980	+	0.637805i	0.981436	−	0.191791i	$-0.0614297\pi$
$547$	842.270	+	348.880i	1.53980	+	0.637805i	0.558363	+	0.829597i	$0.311430\pi$
$548$	−596.544	+	178.666i	−1.08858	+	0.326033i
$549$		0			0
$550$	849.996	−	124.554i	1.54545	−	0.226463i
$551$	12.9681	+	12.9681i	0.0235356	+	0.0235356i
$552$		0			0
$553$	−138.334	−	138.334i	−0.250151	−	0.250151i
$554$	−368.795	+	495.435i	−0.665695	+	0.894288i
$555$		0			0
$556$	12.7442	−	124.880i	0.0229212	−	0.224605i
$557$	−838.978	−	347.516i	−1.50624	−	0.623907i	−0.531465	−	0.847080i	$-0.678358\pi$
$557$	−838.978	−	347.516i	−1.50624	−	0.623907i	−0.974779	+	0.223173i	$0.928358\pi$
$558$		0			0
$559$	−626.414			−1.12060
$560$	−76.2187	−	397.813i	−0.136105	−	0.710381i
$561$		0			0
$562$	267.640	+	67.5419i	0.476229	+	0.120181i
$563$	10.7574	−	25.9706i	0.0191073	−	0.0461290i	−0.914038	−	0.405629i	$-0.867053\pi$
$563$	10.7574	−	25.9706i	0.0191073	−	0.0461290i	0.933145	+	0.359500i	$0.117053\pi$
$564$		0			0
$565$	−229.230	−	553.410i	−0.405717	−	0.979487i
$566$	57.8582	−	77.7261i	0.102223	−	0.137325i
$567$		0			0
$568$	690.410	+	632.432i	1.21551	+	1.11344i
$569$	−319.628	+	319.628i	−0.561736	+	0.561736i	−0.929800	−	0.368064i	$-0.880021\pi$
$569$	−319.628	+	319.628i	−0.561736	+	0.561736i	0.368064	+	0.929800i	$0.380021\pi$
$570$		0			0
$571$	−249.558	−	602.487i	−0.437055	−	1.05514i	−0.976961	−	0.213418i	$-0.931540\pi$
$571$	−249.558	−	602.487i	−0.437055	−	1.05514i	0.539906	−	0.841725i	$-0.318460\pi$
$572$	634.401	−	1176.88i	1.10909	−	2.05749i
$573$		0			0
$574$	−82.1864	+	49.0640i	−0.143182	+	0.0854773i
$575$		−	1068.38i		−	1.85805i
$576$		0			0
$577$	−618.173			−1.07136			−0.535678	−	0.844422i	$-0.679944\pi$
$577$	−618.173			−1.07136			−0.535678	+	0.844422i	$0.679944\pi$
$578$	380.884	+	638.013i	0.658968	+	1.10383i
$579$		0			0
$580$	80.6100	+	43.4529i	0.138983	+	0.0749188i
$581$	56.3491	−	23.3406i	0.0969865	−	0.0401731i
$582$		0			0
$583$	41.7583	+	41.7583i	0.0716265	+	0.0716265i
$584$	56.7381	+	51.9734i	0.0971543	+	0.0889956i
$585$		0			0
$586$	280.653	+	208.914i	0.478930	+	0.356509i
$587$	−917.045	+	379.852i	−1.56226	+	0.647108i	−0.985480	−	0.169793i	$-0.945690\pi$
$587$	−917.045	+	379.852i	−1.56226	+	0.647108i	−0.576777	+	0.816901i	$0.695690\pi$
$588$		0			0
$589$	158.878	+	65.8094i	0.269742	+	0.111731i
$590$	−139.364	+	552.240i	−0.236209	+	0.935999i
$591$		0			0
$592$	−501.074	−	339.940i	−0.846408	−	0.574224i
$593$			304.459i			0.513421i	0.966488	+	0.256711i	$0.0826387\pi$
$593$			304.459i			0.513421i	−0.966488	+	0.256711i	$0.917361\pi$
$594$		0			0
$595$	−248.985	+	601.102i	−0.418462	+	1.01026i
$596$	590.452	+	60.2565i	0.990691	+	0.101102i
$597$		0			0
$598$	−1333.77	−	992.838i	−2.23038	−	1.66026i
$599$	277.512	−	277.512i	0.463293	−	0.463293i	−0.436441	−	0.899733i	$-0.643761\pi$
$599$	277.512	−	277.512i	0.463293	−	0.463293i	0.899733	+	0.436441i	$0.143761\pi$
$600$		0			0
$601$	−239.556	+	239.556i	−0.398596	+	0.398596i	−0.877738	−	0.479141i	$-0.840948\pi$
$601$	−239.556	+	239.556i	−0.398596	+	0.398596i	0.479141	+	0.877738i	$0.340948\pi$
$602$	23.9270	+	163.285i	0.0397459	+	0.271237i
$603$		0			0
$604$	−307.429	−	1026.47i	−0.508988	−	1.69945i
$605$	154.131	−	372.105i	0.254762	−	0.615050i
$606$		0			0
$607$		−	596.668i		−	0.982978i	−0.870884	−	0.491489i	$-0.836453\pi$
$607$		−	596.668i		−	0.982978i	0.870884	−	0.491489i	$-0.163547\pi$
$608$	−129.326	−	145.241i	−0.212708	−	0.238883i
$609$		0			0
$610$	19.5487	−	11.6703i	0.0320470	−	0.0191316i
$611$	264.112	+	109.399i	0.432263	+	0.179049i
$612$		0			0
$613$	582.048	−	241.092i	0.949507	−	0.393299i	0.146462	−	0.989216i	$-0.453211\pi$
$613$	582.048	−	241.092i	0.949507	−	0.393299i	0.803046	+	0.595917i	$0.203211\pi$
$614$	545.663	−	79.9590i	0.888702	−	0.130226i
$615$		0			0
$616$	−331.006	−	120.414i	−0.537347	−	0.195477i
$617$	−650.951	−	650.951i	−1.05503	−	1.05503i	−0.998395	−	0.0566309i	$-0.981964\pi$
$617$	−650.951	−	650.951i	−1.05503	−	1.05503i	−0.0566309	−	0.998395i	$-0.518036\pi$
$618$		0			0
$619$	279.093	−	115.604i	0.450878	−	0.186760i	−0.145677	−	0.989332i	$-0.546536\pi$
$619$	279.093	−	115.604i	0.450878	−	0.186760i	0.596554	+	0.802573i	$0.296536\pi$
$620$	854.254	+	87.1779i	1.37783	+	0.140609i
$621$		0			0
$622$	−120.530	−	30.4171i	−0.193779	−	0.0489021i
$623$	−404.207			−0.648807
$624$		0			0
$625$			379.059i			0.606494i
$626$	334.136	+	84.3229i	0.533764	+	0.134701i
$627$		0			0
$628$	538.913	+	661.408i	0.858142	+	1.05320i
$629$	372.205	+	898.582i	0.591741	+	1.42859i
$630$		0			0
$631$	761.197	−	761.197i	1.20633	−	1.20633i	0.234128	−	0.972206i	$-0.424777\pi$
$631$	761.197	−	761.197i	1.20633	−	1.20633i	0.972206	−	0.234128i	$-0.0752234\pi$
$632$	−468.564	+	20.5364i	−0.741399	+	0.0324943i
$633$		0			0
$634$	8.47455	−	1.24182i	0.0133668	−	0.00195871i
$635$	−6.20683	−	14.9846i	−0.00977454	−	0.0235978i
$636$		0			0
$637$	367.076	−	886.199i	0.576257	−	1.39121i
$638$	68.3761	−	40.8195i	0.107173	−	0.0639803i
$639$		0			0
$640$	−826.692	−	509.466i	−1.29171	−	0.796041i
$641$	−19.6688			−0.0306845			−0.0153422	−	0.999882i	$-0.504884\pi$
$641$	−19.6688			−0.0306845			−0.0153422	+	0.999882i	$0.504884\pi$
$642$		0			0
$643$	361.198	+	149.613i	0.561739	+	0.232680i	0.645440	−	0.763811i	$-0.276674\pi$
$643$	361.198	+	149.613i	0.561739	+	0.232680i	−0.0837010	+	0.996491i	$0.526674\pi$
$644$	−207.853	+	385.591i	−0.322754	+	0.598744i
$645$		0			0
$646$	45.2915	+	309.083i	0.0701107	+	0.478456i
$647$	−322.306	−	322.306i	−0.498154	−	0.498154i	0.412709	−	0.910863i	$-0.364583\pi$
$647$	−322.306	−	322.306i	−0.498154	−	0.498154i	−0.910863	+	0.412709i	$0.864583\pi$
$648$		0			0
$649$	350.215	+	350.215i	0.539623	+	0.539623i
$650$	−1323.07	−	984.873i	−2.03549	−	1.51519i
$651$		0			0
$652$	532.765	−	434.096i	0.817124	−	0.665791i
$653$	268.367	+	111.161i	0.410976	+	0.170232i	0.578586	−	0.815622i	$-0.303605\pi$
$653$	268.367	+	111.161i	0.410976	+	0.170232i	−0.167610	+	0.985853i	$0.553605\pi$
$654$		0			0
$655$	−212.235			−0.324023
$656$	−46.3538	+	224.744i	−0.0706613	+	0.342598i
$657$		0			0
$658$	18.4283	−	73.0238i	0.0280066	−	0.110978i
$659$	51.5747	−	124.512i	0.0782621	−	0.188941i	−0.879906	−	0.475148i	$-0.842394\pi$
$659$	51.5747	−	124.512i	0.0782621	−	0.188941i	0.958168	+	0.286207i	$0.0923944\pi$
$660$		0			0
$661$	46.4357	+	112.106i	0.0702507	+	0.169600i	0.955105	−	0.296268i	$-0.0957421\pi$
$661$	46.4357	+	112.106i	0.0702507	+	0.169600i	−0.884854	+	0.465868i	$0.845742\pi$
$662$	836.362	+	622.576i	1.26339	+	0.940448i
$663$		0			0
$664$	49.9881	−	137.413i	0.0752834	−	0.206947i
$665$	−108.789	+	108.789i	−0.163592	+	0.163592i
$666$		0			0
$667$	−37.8994	−	91.4972i	−0.0568206	−	0.137177i
$668$	225.124	−	67.4252i	0.337013	−	0.100936i
$669$		0			0
$670$	−24.3011	−	40.7064i	−0.0362703	−	0.0607559i
$671$		−	19.7982i		−	0.0295055i
$672$		0			0
$673$	744.919			1.10686			0.553432	−	0.832895i	$-0.313318\pi$
$673$	744.919			1.10686			0.553432	+	0.832895i	$0.313318\pi$
$674$	552.005	−	329.538i	0.818999	−	0.488929i
$675$		0			0
$676$	−1811.45	+	542.534i	−2.67967	+	0.802565i
$677$	−433.679	+	179.636i	−0.640589	+	0.265341i	−0.679245	−	0.733912i	$-0.737693\pi$
$677$	−433.679	+	179.636i	−0.640589	+	0.265341i	0.0386554	+	0.999253i	$0.487693\pi$
$678$		0			0
$679$	45.1945	+	45.1945i	0.0665603	+	0.0665603i
$680$	659.447	+	1413.57i	0.969775	+	2.07878i
$681$		0			0
$682$	445.872	−	598.979i	0.653771	−	0.878269i
$683$	−175.528	+	72.7059i	−0.256995	+	0.106451i	−0.507461	−	0.861674i	$-0.669416\pi$
$683$	−175.528	+	72.7059i	−0.256995	+	0.106451i	0.250466	+	0.968125i	$0.419416\pi$
$684$		0			0
$685$	1091.17	+	451.977i	1.59295	+	0.659820i
$686$	−562.101	−	141.852i	−0.819390	−	0.206782i
$687$		0			0
$688$	327.407	+	222.120i	0.475882	+	0.322849i
$689$		−	113.384i		−	0.164563i
$690$		0			0
$691$	−489.503	+	1181.77i	−0.708399	+	1.71023i	−0.00443406	+	0.999990i	$0.501411\pi$
$691$	−489.503	+	1181.77i	−0.708399	+	1.71023i	−0.703964	+	0.710235i	$0.748589\pi$
$692$	305.802	−	249.167i	0.441911	−	0.360068i
$693$		0			0
$694$	61.6277	−	82.7900i	0.0888007	−	0.119294i
$695$	−168.348	+	168.348i	−0.242228	+	0.242228i
$696$		0			0
$697$	260.643	−	260.643i	0.373950	−	0.373950i
$698$	350.297	−	51.3309i	0.501858	−	0.0735399i
$699$		0			0
$700$	−206.186	+	382.498i	−0.294551	+	0.546425i
$701$	−126.775	+	306.062i	−0.180849	+	0.436607i	−0.988142	−	0.153543i	$-0.950932\pi$
$701$	−126.775	+	306.062i	−0.180849	+	0.436607i	0.807293	+	0.590150i	$0.200932\pi$
$702$		0			0
$703$			229.990i			0.327155i
$704$	−748.893	+	390.167i	−1.06377	+	0.554215i
$705$		0			0
$706$	334.040	+	559.547i	0.473145	+	0.792559i
$707$	−40.5142	−	16.7815i	−0.0573044	−	0.0237363i
$708$		0			0
$709$	384.057	−	159.082i	0.541688	−	0.224375i	−0.0950254	−	0.995475i	$-0.530293\pi$
$709$	384.057	−	159.082i	0.541688	−	0.224375i	0.636714	+	0.771100i	$0.280293\pi$
$710$	−257.466	−	1757.02i	−0.362628	−	2.47468i
$711$		0			0
$712$	−654.562	+	714.569i	−0.919329	+	1.00361i
$713$	−656.649	−	656.649i	−0.920966	−	0.920966i
$714$		0			0
$715$	−2342.73	+	970.389i	−3.27654	+	1.35719i
$716$	830.169	+	1018.87i	1.15945	+	1.42300i
$717$		0			0
$718$	−104.797	+	415.268i	−0.145957	+	0.578368i
$719$	−597.352			−0.830810			−0.415405	−	0.909637i	$-0.636360\pi$
$719$	−597.352			−0.830810			−0.415405	+	0.909637i	$0.636360\pi$
$720$		0			0
$721$		−	11.5080i		−	0.0159612i
$722$	158.591	−	628.430i	0.219655	−	0.870402i
$723$		0			0
$724$	792.690	+	80.8952i	1.09488	+	0.111734i
$725$	−37.5953	−	90.7631i	−0.0518556	−	0.125191i
$726$		0			0
$727$	−890.023	+	890.023i	−1.22424	+	1.22424i	−0.258131	+	0.966110i	$0.583106\pi$
$727$	−890.023	+	890.023i	−1.22424	+	1.22424i	−0.966110	+	0.258131i	$0.916894\pi$
$728$	285.904	+	612.855i	0.392725	+	0.841834i
$729$		0			0
$730$	−21.1586	−	144.392i	−0.0289844	−	0.197798i
$731$	−243.202	−	587.142i	−0.332698	−	0.803204i
$732$		0			0
$733$	265.446	−	640.844i	0.362137	−	0.874276i	−0.632850	−	0.774274i	$-0.718115\pi$
$733$	265.446	−	640.844i	0.362137	−	0.874276i	0.994987	−	0.100002i	$-0.0318848\pi$
$734$	−173.440	−	290.527i	−0.236294	−	0.395813i
$735$		0			0
$736$	345.067	+	991.866i	0.468841	+	1.34764i
$737$	−41.2260			−0.0559376
$738$		0			0
$739$	−1201.59	−	497.716i	−1.62597	−	0.673499i	−0.631199	−	0.775621i	$-0.717437\pi$
$739$	−1201.59	−	497.716i	−1.62597	−	0.673499i	−0.994772	+	0.102121i	$0.967437\pi$
$740$	329.490	+	1100.13i	0.445257	+	1.48666i
$741$		0			0
$742$	−29.5553	+	4.33089i	−0.0398319	+	0.00583678i
$743$	212.173	+	212.173i	0.285563	+	0.285563i	0.835323	−	0.549760i	$-0.185281\pi$
$743$	212.173	+	212.173i	0.285563	+	0.285563i	−0.549760	+	0.835323i	$0.685281\pi$
$744$		0			0
$745$	−795.976	−	795.976i	−1.06842	−	1.06842i
$746$	253.711	−	340.832i	0.340095	−	0.456880i
$747$		0			0
$748$	1349.41	+	137.709i	1.80402	+	0.184103i
$749$	−510.862	−	211.606i	−0.682058	−	0.282518i
$750$		0			0
$751$	−106.499			−0.141810			−0.0709050	−	0.997483i	$-0.522589\pi$
$751$	−106.499			−0.141810			−0.0709050	+	0.997483i	$0.522589\pi$
$752$	−99.2513	−	150.831i	−0.131983	−	0.200573i
$753$		0			0
$754$	−148.246	−	37.4114i	−0.196613	−	0.0496173i
$755$	−777.712	+	1877.56i	−1.03008	+	2.48684i
$756$		0			0
$757$	436.588	+	1054.02i	0.576734	+	1.39236i	0.895728	+	0.444603i	$0.146655\pi$
$757$	436.588	+	1054.02i	0.576734	+	1.39236i	−0.318993	+	0.947757i	$0.603345\pi$
$758$	−550.857	+	740.015i	−0.726724	+	0.976273i
$759$		0			0
$760$	16.1503	+	368.490i	0.0212504	+	0.484855i
$761$	−867.382	+	867.382i	−1.13979	+	1.13979i	−0.151306	+	0.988487i	$0.548348\pi$
$761$	−867.382	+	867.382i	−1.13979	+	1.13979i	−0.988487	+	0.151306i	$0.951652\pi$
$762$		0			0
$763$	−211.423	−	510.420i	−0.277094	−	0.668965i
$764$	−709.578	−	382.499i	−0.928767	−	0.500653i
$765$		0			0
$766$	191.951	−	114.592i	0.250589	−	0.149598i
$767$		−	950.918i		−	1.23979i
$768$		0			0
$769$	−363.245			−0.472360			−0.236180	−	0.971709i	$-0.575896\pi$
$769$	−363.245			−0.472360			−0.236180	+	0.971709i	$0.575896\pi$
$770$	342.432	+	573.603i	0.444717	+	0.744939i
$771$		0			0
$772$	−5.10469	+	9.46977i	−0.00661230	+	0.0122665i
$773$	987.768	−	409.147i	1.27784	−	0.529298i	0.362499	−	0.931984i	$-0.381923\pi$
$773$	987.768	−	409.147i	1.27784	−	0.529298i	0.915338	+	0.402686i	$0.131923\pi$
$774$		0			0
$775$	−651.381	−	651.381i	−0.840491	−	0.840491i
$776$	153.083	−	6.70937i	0.197272	−	0.00864610i
$777$		0			0
$778$	−599.405	−	446.189i	−0.770444	−	0.573508i
$779$	80.5273	−	33.3555i	0.103373	−	0.0428183i
$780$		0			0
$781$	−1426.66	−	590.943i	−1.82671	−	0.756650i
$782$	412.765	−	1635.61i	0.527832	−	2.09158i
$783$		0			0
$784$	−506.096	+	333.026i	−0.645531	+	0.424779i
$785$		−	1618.13i		−	2.06131i
$786$		0			0
$787$	136.007	−	328.349i	0.172817	−	0.417216i	−0.813612	−	0.581409i	$-0.802502\pi$
$787$	136.007	−	328.349i	0.172817	−	0.417216i	0.986428	+	0.164193i	$0.0525018\pi$
$788$	−3.06679	+	30.0514i	−0.00389187	+	0.0381363i
$789$		0			0
$790$	713.552	+	531.158i	0.903230	+	0.672352i
$791$	186.305	−	186.305i	0.235531	−	0.235531i
$792$		0			0
$793$	−26.8784	+	26.8784i	−0.0338946	+	0.0338946i
$794$	159.188	+	1086.35i	0.200489	+	1.36820i
$795$		0			0
$796$	−969.080	+	290.241i	−1.21744	+	0.364625i
$797$	−65.5848	+	158.336i	−0.0822896	+	0.198665i	−0.959669	−	0.281133i	$-0.909290\pi$
$797$	−65.5848	+	158.336i	−0.0822896	+	0.198665i	0.877379	+	0.479797i	$0.159290\pi$
$798$		0			0
$799$			290.028i			0.362989i
$800$	342.299	+	983.908i	0.427873	+	1.22989i
$801$		0			0
$802$	−765.478	+	456.978i	−0.954461	+	0.569798i
$803$	−117.244	−	48.5639i	−0.146007	−	0.0604781i
$804$		0			0
$805$	767.564	−	317.936i	0.953496	−	0.394951i
$806$	−1418.51	+	207.862i	−1.75994	+	0.257893i
$807$		0			0
$808$	−95.2746	+	44.4467i	−0.117914	+	0.0550082i
$809$	594.060	+	594.060i	0.734314	+	0.734314i	0.971471	−	0.237157i	$-0.0762157\pi$
$809$	594.060	+	594.060i	0.734314	+	0.734314i	−0.237157	+	0.971471i	$0.576216\pi$
$810$		0			0
$811$	−583.898	+	241.859i	−0.719973	+	0.298223i	−0.712424	−	0.701749i	$-0.752403\pi$
$811$	−583.898	+	241.859i	−0.719973	+	0.298223i	−0.00754873	+	0.999972i	$0.502403\pi$
$812$	−4.08938	+	40.0717i	−0.00503618	+	0.0493494i
$813$		0			0
$814$	968.292	+	244.359i	1.18955	+	0.300195i
$815$	−1303.40			−1.59927
$816$		0			0
$817$		−	150.278i		−	0.183938i
$818$	1042.97	+	263.205i	1.27503	+	0.321766i
$819$		0			0
$820$	337.406	−	274.917i	0.411471	−	0.335265i
$821$	252.315	+	609.143i	0.307327	+	0.741952i	0.999790	+	0.0204989i	$0.00652546\pi$
$821$	252.315	+	609.143i	0.307327	+	0.741952i	−0.692463	+	0.721453i	$0.743475\pi$
$822$		0			0
$823$	384.849	−	384.849i	0.467617	−	0.467617i	−0.433525	−	0.901142i	$-0.642730\pi$
$823$	384.849	−	384.849i	0.467617	−	0.467617i	0.901142	+	0.433525i	$0.142730\pi$
$824$	−20.3442	−	18.6358i	−0.0246896	−	0.0226162i
$825$		0			0
$826$	−247.872	+	36.3220i	−0.300087	+	0.0439734i
$827$	−186.532	−	450.328i	−0.225553	−	0.544533i	0.770074	−	0.637955i	$-0.220219\pi$
$827$	−186.532	−	450.328i	−0.225553	−	0.544533i	−0.995627	+	0.0934222i	$0.970219\pi$
$828$		0			0
$829$	−454.707	+	1097.76i	−0.548500	+	1.32420i	0.370094	+	0.928994i	$0.379326\pi$
$829$	−454.707	+	1097.76i	−0.548500	+	1.32420i	−0.918594	+	0.395202i	$0.870674\pi$
$830$	−238.124	+	142.156i	−0.286896	+	0.171272i
$831$		0			0
$832$	1546.41	+	487.013i	1.85866	+	0.585352i
$833$	973.156			1.16825
$834$		0			0
$835$	−411.786	−	170.568i	−0.493157	−	0.204272i
$836$	282.336	+	152.194i	0.337723	+	0.182050i
$837$		0			0
$838$	40.8276	+	278.619i	0.0487203	+	0.332481i
$839$	376.677	+	376.677i	0.448959	+	0.448959i	0.895008	−	0.446049i	$-0.147169\pi$
$839$	376.677	+	376.677i	0.448959	+	0.448959i	−0.446049	+	0.895008i	$0.647169\pi$
$840$		0			0
$841$	588.237	+	588.237i	0.699450	+	0.699450i
$842$	220.695	+	164.282i	0.262108	+	0.195109i
$843$		0			0
$844$	−735.730	−	902.961i	−0.871718	−	1.06986i
$845$	3313.42	+	1372.47i	3.92121	+	1.62422i
$846$		0			0
$847$	177.156			0.209157
$848$	−40.2047	+	59.2620i	−0.0474112	+	0.0698844i
$849$		0			0
$850$	409.453	−	1622.49i	0.481710	−	1.90881i
$851$	475.279	−	1147.42i	0.558494	−	1.34832i
$852$		0			0
$853$	−26.3732	−	63.6706i	−0.0309182	−	0.0746431i	0.907666	−	0.419693i	$-0.137862\pi$
$853$	−26.3732	−	63.6706i	−0.0309182	−	0.0746431i	−0.938584	+	0.345049i	$0.887862\pi$
$854$	8.03297	+	5.97963i	0.00940628	+	0.00700190i
$855$		0			0
$856$	−1201.36	+	560.447i	−1.40346	+	0.654728i
$857$	−147.757	+	147.757i	−0.172412	+	0.172412i	−0.788038	−	0.615626i	$-0.788903\pi$
$857$	−147.757	+	147.757i	−0.172412	+	0.172412i	0.615626	+	0.788038i	$0.288903\pi$
$858$		0			0
$859$	579.032	+	1397.91i	0.674076	+	1.62736i	0.774616	+	0.632431i	$0.217943\pi$
$859$	579.032	+	1397.91i	0.674076	+	1.62736i	−0.100540	+	0.994933i	$0.532057\pi$
$860$	−215.292	−	718.835i	−0.250340	−	0.835854i
$861$		0			0
$862$	−340.251	−	569.950i	−0.394723	−	0.661195i
$863$			405.553i			0.469934i	0.972003	+	0.234967i	$0.0754982\pi$
$863$			405.553i			0.469934i	−0.972003	+	0.234967i	$0.924502\pi$
$864$		0			0
$865$	−748.142			−0.864904
$866$	−1385.74	+	827.264i	−1.60016	+	0.955270i
$867$		0			0
$868$	108.365	+	361.817i	0.124844	+	0.416840i
$869$	714.657	−	296.021i	0.822390	−	0.340645i
$870$		0			0
$871$	55.9692	+	55.9692i	0.0642585	+	0.0642585i
$872$	−1244.71	−	452.801i	−1.42742	−	0.519267i
$873$		0			0
$874$	238.183	−	319.973i	0.272521	−	0.366102i
$875$	176.693	−	73.1888i	0.201935	−	0.0836444i
$876$		0			0
$877$	1246.79	+	516.439i	1.42166	+	0.588870i	0.955276	−	0.295714i	$-0.0955576\pi$
$877$	1246.79	+	516.439i	1.42166	+	0.588870i	0.466381	+	0.884584i	$0.345558\pi$
$878$	−450.027	−	113.569i	−0.512559	−	0.129350i
$879$		0			0
$880$	1568.56	+	323.517i	1.78245	+	0.367633i
$881$			579.161i			0.657391i	0.944436	+	0.328695i	$0.106609\pi$
$881$			579.161i			0.657391i	−0.944436	+	0.328695i	$0.893391\pi$
$882$		0			0
$883$	−251.441	+	607.032i	−0.284758	+	0.687466i	−0.999934	−	0.0114783i	$-0.996346\pi$
$883$	−251.441	+	607.032i	−0.284758	+	0.687466i	0.715177	+	0.698944i	$0.246346\pi$
$884$	−1645.02	−	2018.93i	−1.86088	−	2.28386i
$885$		0			0
$886$	687.918	−	924.141i	0.776431	−	1.04305i
$887$	482.450	−	482.450i	0.543912	−	0.543912i	−0.380761	−	0.924673i	$-0.624338\pi$
$887$	482.450	−	482.450i	0.543912	−	0.543912i	0.924673	+	0.380761i	$0.124338\pi$
$888$		0			0
$889$	5.04454	−	5.04454i	0.00567440	−	0.00567440i
$890$	1818.50	−	266.475i	2.04326	−	0.299410i
$891$		0			0
$892$	1067.86	+	575.632i	1.19715	+	0.645327i
$893$	−26.2450	+	63.3610i	−0.0293897	+	0.0709529i
$894$		0			0
$895$		−	2492.64i		−	2.78508i
$896$	67.8798	−	421.699i	0.0757587	−	0.470646i
$897$		0			0
$898$	−557.100	−	933.191i	−0.620379	−	1.03919i
$899$	−78.8918	−	32.6780i	−0.0877550	−	0.0363493i
$900$		0			0
$901$	106.275	−	44.0206i	0.117953	−	0.0488575i
$902$	−54.8733	−	374.471i	−0.0608351	−	0.415157i
$903$		0			0
$904$	−27.6580	−	631.052i	−0.0305951	−	0.698066i
$905$	−1068.61	−	1068.61i	−1.18078	−	1.18078i
$906$		0			0
$907$	902.707	−	373.913i	0.995267	−	0.412253i	0.175208	−	0.984532i	$-0.443940\pi$
$907$	902.707	−	373.913i	0.995267	−	0.412253i	0.820059	+	0.572278i	$0.193940\pi$
$908$	−1161.07	+	946.040i	−1.27872	+	1.04189i
$909$		0			0
$910$	313.842	−	1243.63i	0.344882	−	1.36662i
$911$	340.128			0.373356			0.186678	−	0.982421i	$-0.440228\pi$
$911$	340.128			0.373356			0.186678	+	0.982421i	$0.440228\pi$
$912$		0			0
$913$			241.163i			0.264144i
$914$	−139.169	+	551.467i	−0.152263	+	0.603356i
$915$		0			0
$916$	50.6055	−	495.882i	0.0552462	−	0.541356i
$917$	−35.7243	−	86.2461i	−0.0389578	−	0.0940524i
$918$		0			0
$919$	862.460	−	862.460i	0.938477	−	0.938477i	−0.0597374	−	0.998214i	$-0.519026\pi$
$919$	862.460	−	862.460i	0.938477	−	0.938477i	0.998214	+	0.0597374i	$0.0190263\pi$
$920$	680.918	−	1871.78i	0.740128	−	2.03454i
$921$		0			0
$922$	10.0806	+	68.7928i	0.0109334	+	0.0746126i
$923$	1134.59	+	2739.14i	1.22924	+	2.96765i
$924$		0			0
$925$	471.466	−	1138.22i	0.509693	−	1.23051i
$926$	42.6788	+	71.4906i	0.0460894	+	0.0772037i
$927$		0			0
$928$	64.2177	+	72.1203i	0.0692001	+	0.0777159i
$929$	−615.216			−0.662234			−0.331117	−	0.943590i	$-0.607426\pi$
$929$	−615.216			−0.662234			−0.331117	+	0.943590i	$0.607426\pi$
$930$		0			0
$931$	212.601	+	88.0620i	0.228357	+	0.0945886i
$932$	127.755	−	38.2628i	0.137076	−	0.0410545i
$933$		0			0
$934$	−1115.82	+	163.508i	−1.19467	+	0.175062i
$935$	−1819.10	−	1819.10i	−1.94557	−	1.94557i
$936$		0			0
$937$	414.108	+	414.108i	0.441951	+	0.441951i	0.892667	−	0.450716i	$-0.148831\pi$
$937$	414.108	+	414.108i	0.441951	+	0.441951i	−0.450716	+	0.892667i	$0.648831\pi$
$938$	12.4514	−	16.7271i	0.0132744	−	0.0178327i
$939$		0			0
$940$	−34.7668	+	340.679i	−0.0369859	+	0.362424i
$941$	−270.294	−	111.960i	−0.287241	−	0.118979i	0.234410	−	0.972138i	$-0.424684\pi$
$941$	−270.294	−	111.960i	−0.287241	−	0.118979i	−0.521652	+	0.853158i	$0.674684\pi$
$942$		0			0
$943$	−470.682			−0.499132
$944$	−337.186	+	497.014i	−0.357189	+	0.526498i
$945$		0			0
$946$	−632.692	−	159.666i	−0.668807	−	0.168781i
$947$	−524.154	+	1265.42i	−0.553489	+	1.33624i	0.361354	+	0.932429i	$0.382315\pi$
$947$	−524.154	+	1265.42i	−0.553489	+	1.33624i	−0.914843	+	0.403811i	$0.867685\pi$
$948$		0			0
$949$	93.2408	+	225.103i	0.0982517	+	0.237201i
$950$	236.273	−	317.406i	0.248708	−	0.334112i
$951$		0			0
$952$	−463.433	+	505.918i	−0.486799	+	0.531426i
$953$	923.672	−	923.672i	0.969226	−	0.969226i	−0.0303144	−	0.999540i	$-0.509651\pi$
$953$	923.672	−	923.672i	0.969226	−	0.969226i	0.999540	+	0.0303144i	$0.00965086\pi$
$954$		0			0
$955$	585.076	+	1412.50i	0.612645	+	1.47906i
$956$	−725.037	+	1345.02i	−0.758407	+	1.40693i
$957$		0			0
$958$	−1137.37	+	678.993i	−1.18724	+	0.708761i
$959$			519.497i			0.541707i
$960$		0			0
$961$	160.295			0.166801
$962$	−982.825	−	1646.32i	−1.02165	−	1.71135i
$963$		0			0
$964$	924.965	+	498.603i	0.959507	+	0.517224i
$965$	18.8507	−	7.80821i	0.0195344	−	0.00809141i
$966$		0			0
$967$	1286.99	+	1286.99i	1.33091	+	1.33091i	0.904561	+	0.426344i	$0.140199\pi$
$967$	1286.99	+	1286.99i	1.33091	+	1.33091i	0.426344	+	0.904561i	$0.359801\pi$
$968$	286.882	−	313.182i	0.296366	−	0.323535i
$969$		0			0
$970$	−233.122	−	173.532i	−0.240332	−	0.178899i
$971$	729.976	−	302.366i	0.751778	−	0.311397i	0.0263112	−	0.999654i	$-0.491624\pi$
$971$	729.976	−	302.366i	0.751778	−	0.311397i	0.725467	+	0.688257i	$0.241624\pi$
$972$		0			0
$973$	−96.7488	−	40.0747i	−0.0994335	−	0.0411867i
$974$	−214.104	+	848.404i	−0.219819	+	0.871051i
$975$		0			0
$976$	23.5793	−	4.51766i	0.0241591	−	0.00462875i
$977$			346.223i			0.354374i	0.984177	+	0.177187i	$0.0566997\pi$
$977$			346.223i			0.354374i	−0.984177	+	0.177187i	$0.943300\pi$
$978$		0			0
$979$	611.622	−	1476.59i	0.624741	−	1.50826i
$980$	1143.11	+	116.656i	1.16644	+	0.119037i
$981$		0			0
$982$	432.568	+	321.997i	0.440497	+	0.327899i
$983$	185.696	−	185.696i	0.188908	−	0.188908i	−0.606316	−	0.795224i	$-0.707353\pi$
$983$	185.696	−	185.696i	0.188908	−	0.188908i	0.795224	+	0.606316i	$0.207353\pi$
$984$		0			0
$985$	40.5116	−	40.5116i	0.0411286	−	0.0411286i
$986$	−22.4898	−	153.477i	−0.0228091	−	0.155656i
$987$		0			0
$988$	−176.684	−	589.926i	−0.178830	−	0.597091i
$989$	−310.552	+	749.738i	−0.314006	+	0.758077i
$990$		0			0
$991$			692.209i			0.698496i	0.937030	+	0.349248i	$0.113563\pi$
$991$			692.209i			0.698496i	−0.937030	+	0.349248i	$0.886437\pi$
$992$	815.115	+	394.347i	0.821688	+	0.397527i
$993$		0			0
$994$	670.663	−	400.375i	0.674712	−	0.402792i
$995$	1772.59	+	734.232i	1.78150	+	0.737922i
$996$		0			0
$997$	−637.716	+	264.150i	−0.639635	+	0.264945i	−0.678840	−	0.734286i	$-0.737517\pi$
$997$	−637.716	+	264.150i	−0.639635	+	0.264945i	0.0392058	+	0.999231i	$0.487517\pi$
$998$	−1053.27	+	154.341i	−1.05538	+	0.154650i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.u.b.19.5		64
3.2	odd	2		96.3.m.a.19.12	✓	64
12.11	even	2		384.3.m.a.367.2		64
32.27	odd	8	inner	288.3.u.b.91.5		64
96.5	odd	8		384.3.m.a.271.2		64
96.59	even	8		96.3.m.a.91.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.3.m.a.19.12	✓	64	3.2	odd	2
96.3.m.a.91.12	yes	64	96.59	even	8
288.3.u.b.19.5		64	1.1	even	1	trivial
288.3.u.b.91.5		64	32.27	odd	8	inner
384.3.m.a.271.2		64	96.5	odd	8
384.3.m.a.367.2		64	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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02518 - 1.71727i) q^{2} +(-1.89801 + 3.52102i) q^{4} +(7.00900 - 2.90322i) q^{5} +(2.35957 + 2.35957i) q^{7} +(7.99233 - 0.350291i) q^{8} +O(q^{10})\)	\(q+(-1.02518 - 1.71727i) q^{2} +(-1.89801 + 3.52102i) q^{4} +(7.00900 - 2.90322i) q^{5} +(2.35957 + 2.35957i) q^{7} +(7.99233 - 0.350291i) q^{8} +(-12.1711 - 9.05999i) q^{10} +(-12.1899 + 5.04924i) q^{11} +(23.4042 + 9.69435i) q^{13} +(1.63302 - 6.47098i) q^{14} +(-8.79512 - 13.3658i) q^{16} +25.7007i q^{17} +(-2.32569 + 5.61471i) q^{19} +(-3.08085 + 30.1891i) q^{20} +(21.1678 + 15.7570i) q^{22} +(23.2058 - 23.2058i) q^{23} +(23.0197 - 23.0197i) q^{25} +(-7.34578 - 50.1298i) q^{26} +(-12.7865 + 3.82959i) q^{28} +(1.15484 - 2.78802i) q^{29} -28.2967i q^{31} +(-13.9361 + 28.8060i) q^{32} +(44.1350 - 26.3479i) q^{34} +(23.3885 + 9.68784i) q^{35} +(34.9633 - 14.4823i) q^{37} +(12.0262 - 1.76227i) q^{38} +(55.0012 - 25.6587i) q^{40} +(-10.1415 - 10.1415i) q^{41} +(-22.8453 + 9.46285i) q^{43} +(5.35817 - 52.5045i) q^{44} +(-63.6407 - 16.0604i) q^{46} +11.2848 q^{47} -37.8649i q^{49} +(-63.1302 - 15.9316i) q^{50} +(-78.5554 + 64.0067i) q^{52} +(-1.71282 - 4.13510i) q^{53} +(-70.7802 + 70.7802i) q^{55} +(19.6850 + 18.0319i) q^{56} +(-5.97169 + 0.875063i) q^{58} +(-14.3649 - 34.6800i) q^{59} +(-0.574221 + 1.38629i) q^{61} +(-48.5930 + 29.0093i) q^{62} +(63.7546 - 5.59928i) q^{64} +192.185 q^{65} +(2.88669 + 1.19571i) q^{67} +(-90.4928 - 48.7802i) q^{68} +(-7.34085 - 50.0961i) q^{70} +(82.7570 + 82.7570i) q^{71} +(6.80099 + 6.80099i) q^{73} +(-60.7136 - 45.1943i) q^{74} +(-15.3553 - 18.8456i) q^{76} +(-40.6770 - 16.8490i) q^{77} -58.6268 q^{79} +(-100.449 - 68.1470i) q^{80} +(-7.01876 + 27.8124i) q^{82} +(6.99463 - 16.8865i) q^{83} +(74.6149 + 180.136i) q^{85} +(39.6708 + 29.5304i) q^{86} +(-95.6573 + 44.6252i) q^{88} +(-85.6528 + 85.6528i) q^{89} +(32.3494 + 78.0983i) q^{91} +(37.6632 + 125.753i) q^{92} +(-11.5690 - 19.3790i) q^{94} +46.1055i q^{95} +19.1537 q^{97} +(-65.0241 + 38.8184i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q + 40 q^{10} - 32 q^{14} - 8 q^{16} + 160 q^{20} - 184 q^{22} - 128 q^{23} + 200 q^{26} - 120 q^{28} - 40 q^{32} + 120 q^{34} + 192 q^{35} - 280 q^{38} + 584 q^{40} - 192 q^{43} - 104 q^{44} + 32 q^{46} + 312 q^{50} - 424 q^{52} - 320 q^{53} - 256 q^{55} + 392 q^{56} - 352 q^{58} + 256 q^{59} + 64 q^{61} + 48 q^{62} + 408 q^{64} + 64 q^{67} - 856 q^{68} + 984 q^{70} - 512 q^{71} - 1056 q^{74} + 296 q^{76} + 448 q^{77} + 512 q^{79} - 328 q^{80} - 760 q^{82} + 448 q^{86} - 1072 q^{88} + 192 q^{91} + 784 q^{92} - 480 q^{94} - 272 q^{98}+O(q^{100}) \) 64 * q + 40 * q^10 - 32 * q^14 - 8 * q^16 + 160 * q^20 - 184 * q^22 - 128 * q^23 + 200 * q^26 - 120 * q^28 - 40 * q^32 + 120 * q^34 + 192 * q^35 - 280 * q^38 + 584 * q^40 - 192 * q^43 - 104 * q^44 + 32 * q^46 + 312 * q^50 - 424 * q^52 - 320 * q^53 - 256 * q^55 + 392 * q^56 - 352 * q^58 + 256 * q^59 + 64 * q^61 + 48 * q^62 + 408 * q^64 + 64 * q^67 - 856 * q^68 + 984 * q^70 - 512 * q^71 - 1056 * q^74 + 296 * q^76 + 448 * q^77 + 512 * q^79 - 328 * q^80 - 760 * q^82 + 448 * q^86 - 1072 * q^88 + 192 * q^91 + 784 * q^92 - 480 * q^94 - 272 * q^98

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