LMFDB - Embedded newform 684.3.g.c.343.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.11
Character	$\chi$	$=$	684.343
Dual form			684.3.g.c.343.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28823 - 1.52986i) q^{2} +(-0.680940 + 3.94161i) q^{4} -3.40651 q^{5} +4.01056i q^{7} +(6.90732 - 4.03595i) q^{8} +O(q^{10})$	\(q+(-1.28823 - 1.52986i) q^{2} +(-0.680940 + 3.94161i) q^{4} -3.40651 q^{5} +4.01056i q^{7} +(6.90732 - 4.03595i) q^{8} +(4.38835 + 5.21148i) q^{10} -13.8660i q^{11} +13.1219 q^{13} +(6.13560 - 5.16652i) q^{14} +(-15.0726 - 5.36801i) q^{16} -31.1103 q^{17} +4.35890i q^{19} +(2.31963 - 13.4271i) q^{20} +(-21.2131 + 17.8626i) q^{22} +18.4001i q^{23} -13.3957 q^{25} +(-16.9040 - 20.0747i) q^{26} +(-15.8081 - 2.73095i) q^{28} +43.7580 q^{29} +27.9996i q^{31} +(11.2047 + 29.9742i) q^{32} +(40.0771 + 47.5944i) q^{34} -13.6620i q^{35} +40.4543 q^{37} +(6.66850 - 5.61525i) q^{38} +(-23.5298 + 13.7485i) q^{40} +28.2340 q^{41} -81.5065i q^{43} +(54.6546 + 9.44195i) q^{44} +(28.1495 - 23.7035i) q^{46} +59.2113i q^{47} +32.9154 q^{49} +(17.2567 + 20.4936i) q^{50} +(-8.93523 + 51.7215i) q^{52} +38.7267 q^{53} +47.2348i q^{55} +(16.1864 + 27.7022i) q^{56} +(-56.3703 - 66.9437i) q^{58} +59.4234i q^{59} +29.2631 q^{61} +(42.8354 - 36.0698i) q^{62} +(31.4222 - 55.7552i) q^{64} -44.6998 q^{65} +12.0039i q^{67} +(21.1842 - 122.625i) q^{68} +(-20.9009 + 17.5998i) q^{70} -5.79017i q^{71} +41.8152 q^{73} +(-52.1143 - 61.8893i) q^{74} +(-17.1811 - 2.96815i) q^{76} +55.6106 q^{77} -0.805318i q^{79} +(51.3450 + 18.2861i) q^{80} +(-36.3718 - 43.1940i) q^{82} +136.639i q^{83} +105.977 q^{85} +(-124.693 + 104.999i) q^{86} +(-55.9627 - 95.7772i) q^{88} +150.071 q^{89} +52.6262i q^{91} +(-72.5260 - 12.5293i) q^{92} +(90.5849 - 76.2776i) q^{94} -14.8486i q^{95} +50.3016 q^{97} +(-42.4025 - 50.3559i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} + 12 q^{4} - 8 q^{5} + 20 q^{8}+O(q^{10}) $ 36 * q - 4 * q^2 + 12 * q^4 - 8 * q^5 + 20 * q^8	$ 36 q - 4 q^{2} + 12 q^{4} - 8 q^{5} + 20 q^{8} + 8 q^{10} - 24 q^{13} + 12 q^{14} + 4 q^{16} + 40 q^{17} + 80 q^{20} + 12 q^{22} + 284 q^{25} + 112 q^{26} - 48 q^{28} - 104 q^{29} - 44 q^{32} + 140 q^{34} - 184 q^{37} + 180 q^{40} + 200 q^{41} - 96 q^{44} - 28 q^{46} - 332 q^{49} - 176 q^{50} + 276 q^{52} - 264 q^{53} + 192 q^{56} - 184 q^{58} + 40 q^{61} + 240 q^{62} - 372 q^{64} - 176 q^{65} + 104 q^{68} - 60 q^{70} + 424 q^{73} + 104 q^{74} + 400 q^{77} - 704 q^{80} + 528 q^{82} - 128 q^{85} - 668 q^{86} - 496 q^{88} + 520 q^{89} + 456 q^{92} - 32 q^{94} - 440 q^{97} + 472 q^{98}+O(q^{100}) $ 36 * q - 4 * q^2 + 12 * q^4 - 8 * q^5 + 20 * q^8 + 8 * q^10 - 24 * q^13 + 12 * q^14 + 4 * q^16 + 40 * q^17 + 80 * q^20 + 12 * q^22 + 284 * q^25 + 112 * q^26 - 48 * q^28 - 104 * q^29 - 44 * q^32 + 140 * q^34 - 184 * q^37 + 180 * q^40 + 200 * q^41 - 96 * q^44 - 28 * q^46 - 332 * q^49 - 176 * q^50 + 276 * q^52 - 264 * q^53 + 192 * q^56 - 184 * q^58 + 40 * q^61 + 240 * q^62 - 372 * q^64 - 176 * q^65 + 104 * q^68 - 60 * q^70 + 424 * q^73 + 104 * q^74 + 400 * q^77 - 704 * q^80 + 528 * q^82 - 128 * q^85 - 668 * q^86 - 496 * q^88 + 520 * q^89 + 456 * q^92 - 32 * q^94 - 440 * q^97 + 472 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−1.28823	−	1.52986i	−0.644114	−	0.764930i
$2$	−1.28823	−	1.52986i	−0.644114	−	0.764930i
$3$		0			0
$3$		0			0
$4$	−0.680940	+	3.94161i	−0.170235	+	0.985403i
$5$	−3.40651			−0.681301			−0.340651	−	0.940190i	$-0.610647\pi$
$5$	−3.40651			−0.681301			−0.340651	+	0.940190i	$0.610647\pi$
$6$		0			0
$7$			4.01056i			0.572937i	0.958090	+	0.286469i	$0.0924814\pi$
$7$			4.01056i			0.572937i	−0.958090	+	0.286469i	$0.907519\pi$
$8$	6.90732	−	4.03595i	0.863415	−	0.504494i
$9$		0			0
$10$	4.38835	+	5.21148i	0.438835	+	0.521148i
$11$		−	13.8660i		−	1.26055i	−0.776372	−	0.630275i	$-0.782942\pi$
$11$		−	13.8660i		−	1.26055i	0.776372	−	0.630275i	$-0.217058\pi$
$12$		0			0
$13$	13.1219			1.00938			0.504688	−	0.863302i	$-0.331607\pi$
$13$	13.1219			1.00938			0.504688	+	0.863302i	$0.331607\pi$
$14$	6.13560	−	5.16652i	0.438257	−	0.369037i
$15$		0			0
$16$	−15.0726	−	5.36801i	−0.942040	−	0.335500i
$17$	−31.1103			−1.83002			−0.915008	−	0.403435i	$-0.867816\pi$
$17$	−31.1103			−1.83002			−0.915008	+	0.403435i	$0.867816\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	2.31963	−	13.4271i	0.115981	−	0.671357i
$21$		0			0
$22$	−21.2131	+	17.8626i	−0.964232	+	0.811937i
$23$			18.4001i			0.800003i	0.916515	+	0.400001i	$0.130990\pi$
$23$			18.4001i			0.800003i	−0.916515	+	0.400001i	$0.869010\pi$
$24$		0			0
$25$	−13.3957			−0.535829
$26$	−16.9040	−	20.0747i	−0.650153	−	0.772102i
$27$		0			0
$28$	−15.8081	−	2.73095i	−0.564575	−	0.0975340i
$29$	43.7580			1.50890			0.754449	−	0.656359i	$-0.227904\pi$
$29$	43.7580			1.50890			0.754449	+	0.656359i	$0.227904\pi$
$30$		0			0
$31$			27.9996i			0.903212i	0.892218	+	0.451606i	$0.149149\pi$
$31$			27.9996i			0.903212i	−0.892218	+	0.451606i	$0.850851\pi$
$32$	11.2047	+	29.9742i	0.350147	+	0.936695i
$33$		0			0
$34$	40.0771	+	47.5944i	1.17874	+	1.39983i
$35$		−	13.6620i		−	0.390343i
$36$		0			0
$37$	40.4543			1.09336			0.546679	−	0.837342i	$-0.315892\pi$
$37$	40.4543			1.09336			0.546679	+	0.837342i	$0.315892\pi$
$38$	6.66850	−	5.61525i	0.175487	−	0.147770i
$39$		0			0
$40$	−23.5298	+	13.7485i	−0.588246	+	0.343712i
$41$	28.2340			0.688634			0.344317	−	0.938853i	$-0.388110\pi$
$41$	28.2340			0.688634			0.344317	+	0.938853i	$0.388110\pi$
$42$		0			0
$43$		−	81.5065i		−	1.89550i	−0.319014	−	0.947750i	$-0.603352\pi$
$43$		−	81.5065i		−	1.89550i	0.319014	−	0.947750i	$-0.396648\pi$
$44$	54.6546	+	9.44195i	1.24215	+	0.214590i
$45$		0			0
$46$	28.1495	−	23.7035i	0.611946	−	0.515293i
$47$			59.2113i			1.25981i	0.776670	+	0.629907i	$0.216907\pi$
$47$			59.2113i			1.25981i	−0.776670	+	0.629907i	$0.783093\pi$
$48$		0			0
$49$	32.9154			0.671743
$50$	17.2567	+	20.4936i	0.345135	+	0.409871i
$51$		0			0
$52$	−8.93523	+	51.7215i	−0.171831	+	0.994643i
$53$	38.7267			0.730692			0.365346	−	0.930872i	$-0.380951\pi$
$53$	38.7267			0.730692			0.365346	+	0.930872i	$0.380951\pi$
$54$		0			0
$55$			47.2348i			0.858814i
$56$	16.1864	+	27.7022i	0.289044	+	0.494683i
$57$		0			0
$58$	−56.3703	−	66.9437i	−0.971902	−	1.15420i
$59$			59.4234i			1.00718i	0.863944	+	0.503588i	$0.167987\pi$
$59$			59.4234i			1.00718i	−0.863944	+	0.503588i	$0.832013\pi$
$60$		0			0
$61$	29.2631			0.479723			0.239861	−	0.970807i	$-0.422898\pi$
$61$	29.2631			0.479723			0.239861	+	0.970807i	$0.422898\pi$
$62$	42.8354	−	36.0698i	0.690894	−	0.581771i
$63$		0			0
$64$	31.4222	−	55.7552i	0.490972	−	0.871176i
$65$	−44.6998			−0.687690
$66$		0			0
$67$			12.0039i			0.179163i	0.995980	+	0.0895813i	$0.0285529\pi$
$67$			12.0039i			0.179163i	−0.995980	+	0.0895813i	$0.971447\pi$
$68$	21.1842	−	122.625i	0.311533	−	1.80331i
$69$		0			0
$70$	−20.9009	+	17.5998i	−0.298585	+	0.251425i
$71$		−	5.79017i		−	0.0815516i	−0.999168	−	0.0407758i	$-0.987017\pi$
$71$		−	5.79017i		−	0.0815516i	0.999168	−	0.0407758i	$-0.0129829\pi$
$72$		0			0
$73$	41.8152			0.572811			0.286406	−	0.958108i	$-0.407540\pi$
$73$	41.8152			0.572811			0.286406	+	0.958108i	$0.407540\pi$
$74$	−52.1143	−	61.8893i	−0.704247	−	0.836342i
$75$		0			0
$76$	−17.1811	−	2.96815i	−0.226067	−	0.0390546i
$77$	55.6106			0.722216
$78$		0			0
$79$		−	0.805318i		−	0.0101939i	−0.999987	−	0.00509695i	$-0.998378\pi$
$79$		−	0.805318i		−	0.0101939i	0.999987	−	0.00509695i	$-0.00162242\pi$
$80$	51.3450	+	18.2861i	0.641813	+	0.228577i
$81$		0			0
$82$	−36.3718	−	43.1940i	−0.443559	−	0.526757i
$83$			136.639i			1.64626i	0.567855	+	0.823129i	$0.307773\pi$
$83$			136.639i			1.64626i	−0.567855	+	0.823129i	$0.692227\pi$
$84$		0			0
$85$	105.977			1.24679
$86$	−124.693	+	104.999i	−1.44992	+	1.22092i
$87$		0			0
$88$	−55.9627	−	95.7772i	−0.635940	−	1.08838i
$89$	150.071			1.68619			0.843094	−	0.537766i	$-0.180731\pi$
$89$	150.071			1.68619			0.843094	+	0.537766i	$0.180731\pi$
$90$		0			0
$91$			52.6262i			0.578310i
$92$	−72.5260	−	12.5293i	−0.788326	−	0.136189i
$93$		0			0
$94$	90.5849	−	76.2776i	0.963669	−	0.811464i
$95$		−	14.8486i		−	0.156301i
$96$		0			0
$97$	50.3016			0.518573			0.259287	−	0.965800i	$-0.416513\pi$
$97$	50.3016			0.518573			0.259287	+	0.965800i	$0.416513\pi$
$98$	−42.4025	−	50.3559i	−0.432679	−	0.513836i
$99$		0			0
$100$	9.12168	−	52.8008i	0.0912168	−	0.528008i
$101$	−139.074			−1.37697			−0.688485	−	0.725250i	$-0.741724\pi$
$101$	−139.074			−1.37697			−0.688485	+	0.725250i	$0.741724\pi$
$102$		0			0
$103$			63.8508i			0.619911i	0.950751	+	0.309955i	$0.100314\pi$
$103$			63.8508i			0.619911i	−0.950751	+	0.309955i	$0.899686\pi$
$104$	90.6372	−	52.9594i	0.871511	−	0.509225i
$105$		0			0
$106$	−49.8888	−	59.2464i	−0.470649	−	0.558928i
$107$		−	142.134i		−	1.32836i	−0.747574	−	0.664179i	$-0.768781\pi$
$107$		−	142.134i		−	1.32836i	0.747574	−	0.664179i	$-0.231219\pi$
$108$		0			0
$109$	37.9014			0.347719			0.173859	−	0.984770i	$-0.444376\pi$
$109$	37.9014			0.347719			0.173859	+	0.984770i	$0.444376\pi$
$110$	72.2626	−	60.8491i	0.656932	−	0.553174i
$111$		0			0
$112$	21.5287	−	60.4498i	0.192221	−	0.539730i
$113$	120.887			1.06979			0.534896	−	0.844918i	$-0.320351\pi$
$113$	120.887			1.06979			0.534896	+	0.844918i	$0.320351\pi$
$114$		0			0
$115$		−	62.6799i		−	0.545043i
$116$	−29.7966	+	172.477i	−0.256867	+	1.48687i
$117$		0			0
$118$	90.9095	−	76.5509i	0.770420	−	0.648736i
$119$		−	124.770i		−	1.04849i
$120$		0			0
$121$	−71.2672			−0.588985
$122$	−37.6975	−	44.7684i	−0.308996	−	0.366954i
$123$		0			0
$124$	−110.363	−	19.0660i	−0.890028	−	0.153758i
$125$	130.795			1.04636
$126$		0			0
$127$			40.2757i			0.317131i	0.987348	+	0.158566i	$0.0506869\pi$
$127$			40.2757i			0.317131i	−0.987348	+	0.158566i	$0.949313\pi$
$128$	−125.777	+	23.7539i	−0.982630	+	0.185577i
$129$		0			0
$130$	57.5835	+	68.3844i	0.442950	+	0.526034i
$131$			55.5156i			0.423783i	0.977293	+	0.211892i	$0.0679624\pi$
$131$			55.5156i			0.423783i	−0.977293	+	0.211892i	$0.932038\pi$
$132$		0			0
$133$	−17.4816			−0.131441
$134$	18.3643	−	15.4637i	0.137047	−	0.115401i
$135$		0			0
$136$	−214.889	+	125.560i	−1.58006	+	0.923233i
$137$	35.3330			0.257905			0.128953	−	0.991651i	$-0.458838\pi$
$137$	35.3330			0.257905			0.128953	+	0.991651i	$0.458838\pi$
$138$		0			0
$139$			87.5326i			0.629731i	0.949136	+	0.314866i	$0.101959\pi$
$139$			87.5326i			0.629731i	−0.949136	+	0.314866i	$0.898041\pi$
$140$	53.8503	+	9.30301i	0.384645	+	0.0664501i
$141$		0			0
$142$	−8.85814	+	7.45905i	−0.0623813	+	0.0525285i
$143$		−	181.949i		−	1.27237i
$144$		0			0
$145$	−149.062			−1.02801
$146$	−53.8675	−	63.9714i	−0.368955	−	0.438160i
$147$		0			0
$148$	−27.5469	+	159.455i	−0.186128	+	1.07740i
$149$	59.8721			0.401826			0.200913	−	0.979609i	$-0.435609\pi$
$149$	59.8721			0.401826			0.200913	+	0.979609i	$0.435609\pi$
$150$		0			0
$151$		−	128.643i		−	0.851942i	−0.904737	−	0.425971i	$-0.859933\pi$
$151$		−	128.643i		−	0.851942i	0.904737	−	0.425971i	$-0.140067\pi$
$152$	17.5923	+	30.1083i	0.115739	+	0.198081i
$153$		0			0
$154$	−71.6391	−	85.0765i	−0.465189	−	0.552445i
$155$		−	95.3807i		−	0.615359i
$156$		0			0
$157$	189.710			1.20835			0.604173	−	0.796853i	$-0.293504\pi$
$157$	189.710			1.20835			0.604173	+	0.796853i	$0.293504\pi$
$158$	−1.23202	+	1.03743i	−0.00779762	+	0.00656603i
$159$		0			0
$160$	−38.1688	−	102.107i	−0.238555	−	0.638171i
$161$	−73.7946			−0.458352
$162$		0			0
$163$			240.437i			1.47507i	0.675307	+	0.737537i	$0.264011\pi$
$163$			240.437i			1.47507i	−0.675307	+	0.737537i	$0.735989\pi$
$164$	−19.2257	+	111.288i	−0.117230	+	0.678582i
$165$		0			0
$166$	209.039	−	176.023i	1.25927	−	1.06038i
$167$		−	99.5334i		−	0.596008i	−0.954565	−	0.298004i	$-0.903679\pi$
$167$		−	99.5334i		−	0.596008i	0.954565	−	0.298004i	$-0.0963209\pi$
$168$		0			0
$169$	3.18423			0.0188416
$170$	−136.523	−	162.130i	−0.803076	−	0.953709i
$171$		0			0
$172$	321.267	+	55.5011i	1.86783	+	0.322681i
$173$	47.1942			0.272799			0.136399	−	0.990654i	$-0.456447\pi$
$173$	47.1942			0.272799			0.136399	+	0.990654i	$0.456447\pi$
$174$		0			0
$175$		−	53.7244i		−	0.306996i
$176$	−74.4330	+	208.998i	−0.422915	+	1.18749i
$177$		0			0
$178$	−193.325	−	229.587i	−1.08610	−	1.28982i
$179$			124.514i			0.695609i	0.937567	+	0.347805i	$0.113073\pi$
$179$			124.514i			0.695609i	−0.937567	+	0.347805i	$0.886927\pi$
$180$		0			0
$181$	328.826			1.81672			0.908359	−	0.418192i	$-0.137336\pi$
$181$	328.826			1.81672			0.908359	+	0.418192i	$0.137336\pi$
$182$	80.5107	−	67.7945i	0.442366	−	0.372497i
$183$		0			0
$184$	74.2618	+	127.095i	0.403597	+	0.690735i
$185$	−137.808			−0.744906
$186$		0			0
$187$			431.377i			2.30683i
$188$	−233.388	−	40.3193i	−1.24143	−	0.214465i
$189$		0			0
$190$	−22.7163	+	19.1284i	−0.119559	+	0.100676i
$191$		−	4.33848i		−	0.0227146i	−0.999936	−	0.0113573i	$-0.996385\pi$
$191$		−	4.33848i		−	0.0227146i	0.999936	−	0.0113573i	$-0.00361521\pi$
$192$		0			0
$193$	−150.256			−0.778530			−0.389265	−	0.921126i	$-0.627271\pi$
$193$	−150.256			−0.778530			−0.389265	+	0.921126i	$0.627271\pi$
$194$	−64.7999	−	76.9544i	−0.334020	−	0.396672i
$195$		0			0
$196$	−22.4134	+	129.740i	−0.114354	+	0.661938i
$197$	−95.1350			−0.482919			−0.241459	−	0.970411i	$-0.577626\pi$
$197$	−95.1350			−0.482919			−0.241459	+	0.970411i	$0.577626\pi$
$198$		0			0
$199$		−	10.4383i		−	0.0524537i	−0.999656	−	0.0262269i	$-0.991651\pi$
$199$		−	10.4383i		−	0.0524537i	0.999656	−	0.0262269i	$-0.00834923\pi$
$200$	−92.5285	+	54.0645i	−0.462643	+	0.270322i
$201$		0			0
$202$	179.159	+	212.764i	0.886926	+	1.05329i
$203$			175.494i			0.864504i
$204$		0			0
$205$	−96.1793			−0.469167
$206$	97.6828	−	82.2544i	0.474188	−	0.399293i
$207$		0			0
$208$	−197.782	−	70.4384i	−0.950873	−	0.338646i
$209$	60.4407			0.289190
$210$		0			0
$211$			224.228i			1.06269i	0.847155	+	0.531347i	$0.178314\pi$
$211$			224.228i			1.06269i	−0.847155	+	0.531347i	$0.821686\pi$
$212$	−26.3705	+	152.646i	−0.124389	+	0.720026i
$213$		0			0
$214$	−217.445	+	183.101i	−1.01610	+	0.855613i
$215$			277.652i			1.29141i
$216$		0			0
$217$	−112.294			−0.517484
$218$	−48.8256	−	57.9838i	−0.223971	−	0.265981i
$219$		0			0
$220$	−186.181	−	32.1641i	−0.846278	−	0.146200i
$221$	−408.226			−1.84718
$222$		0			0
$223$		−	49.3458i		−	0.221282i	−0.993860	−	0.110641i	$-0.964710\pi$
$223$		−	49.3458i		−	0.221282i	0.993860	−	0.110641i	$-0.0352903\pi$
$224$	−120.214	+	44.9371i	−0.536668	+	0.200612i
$225$		0			0
$226$	−155.729	−	184.939i	−0.689068	−	0.818316i
$227$			379.474i			1.67169i	0.548966	+	0.835845i	$0.315022\pi$
$227$			379.474i			1.67169i	−0.548966	+	0.835845i	$0.684978\pi$
$228$		0			0
$229$	−431.446			−1.88404			−0.942022	−	0.335550i	$-0.891078\pi$
$229$	−431.446			−1.88404			−0.942022	+	0.335550i	$0.891078\pi$
$230$	−95.8915	+	80.7460i	−0.416920	+	0.351070i
$231$		0			0
$232$	302.251	−	176.605i	1.30281	−	0.761230i
$233$	18.3450			0.0787338			0.0393669	−	0.999225i	$-0.487466\pi$
$233$	18.3450			0.0787338			0.0393669	+	0.999225i	$0.487466\pi$
$234$		0			0
$235$		−	201.704i		−	0.858313i
$236$	−234.224	−	40.4638i	−0.992476	−	0.171457i
$237$		0			0
$238$	−190.880	+	160.732i	−0.802018	+	0.675344i
$239$		−	215.644i		−	0.902277i	−0.892454	−	0.451139i	$-0.851018\pi$
$239$		−	215.644i		−	0.902277i	0.892454	−	0.451139i	$-0.148982\pi$
$240$		0			0
$241$	−240.272			−0.996981			−0.498491	−	0.866895i	$-0.666112\pi$
$241$	−240.272			−0.996981			−0.498491	+	0.866895i	$0.666112\pi$
$242$	91.8084	+	109.029i	0.379373	+	0.450532i
$243$		0			0
$244$	−19.9264	+	115.344i	−0.0816656	+	0.472720i
$245$	−112.126			−0.457659
$246$		0			0
$247$			57.1970i			0.231567i
$248$	113.005	+	193.402i	0.455665	+	0.779847i
$249$		0			0
$250$	−168.494	−	200.098i	−0.673976	−	0.800393i
$251$		−	332.215i		−	1.32357i	−0.749695	−	0.661784i	$-0.769800\pi$
$251$		−	332.215i		−	1.32357i	0.749695	−	0.661784i	$-0.230200\pi$
$252$		0			0
$253$	255.136			1.00844
$254$	61.6161	−	51.8842i	0.242583	−	0.204269i
$255$		0			0
$256$	198.369	+	161.820i	0.774879	+	0.632110i
$257$	−201.043			−0.782267			−0.391133	−	0.920334i	$-0.627917\pi$
$257$	−201.043			−0.782267			−0.391133	+	0.920334i	$0.627917\pi$
$258$		0			0
$259$			162.244i			0.626426i
$260$	30.4379	−	176.189i	0.117069	−	0.677652i
$261$		0			0
$262$	84.9311	−	71.5167i	0.324164	−	0.272965i
$263$			279.465i			1.06261i	0.847182	+	0.531303i	$0.178297\pi$
$263$			279.465i			1.06261i	−0.847182	+	0.531303i	$0.821703\pi$
$264$		0			0
$265$	−131.923			−0.497821
$266$	22.5203	+	26.7444i	0.0846629	+	0.100543i
$267$		0			0
$268$	−47.3147	−	8.17393i	−0.176547	−	0.0304997i
$269$	−103.161			−0.383500			−0.191750	−	0.981444i	$-0.561416\pi$
$269$	−103.161			−0.383500			−0.191750	+	0.981444i	$0.561416\pi$
$270$		0			0
$271$		−	240.891i		−	0.888898i	−0.895804	−	0.444449i	$-0.853399\pi$
$271$		−	240.891i		−	0.888898i	0.895804	−	0.444449i	$-0.146601\pi$
$272$	468.914	+	167.000i	1.72395	+	0.613972i
$273$		0			0
$274$	−45.5170	−	54.0545i	−0.166120	−	0.197279i
$275$			185.746i			0.675439i
$276$		0			0
$277$	−396.788			−1.43245			−0.716224	−	0.697870i	$-0.754131\pi$
$277$	−396.788			−1.43245			−0.716224	+	0.697870i	$0.754131\pi$
$278$	133.913	−	112.762i	0.481700	−	0.405618i
$279$		0			0
$280$	−55.1392	−	94.3678i	−0.196926	−	0.337028i
$281$	433.845			1.54393			0.771965	−	0.635665i	$-0.219274\pi$
$281$	433.845			1.54393			0.771965	+	0.635665i	$0.219274\pi$
$282$		0			0
$283$		−	265.345i		−	0.937616i	−0.883300	−	0.468808i	$-0.844684\pi$
$283$		−	265.345i		−	0.937616i	0.883300	−	0.468808i	$-0.155316\pi$
$284$	22.8226	+	3.94276i	0.0803613	+	0.0138829i
$285$		0			0
$286$	−278.356	+	234.391i	−0.973273	+	0.819551i
$287$			113.234i			0.394544i
$288$		0			0
$289$	678.850			2.34896
$290$	192.026	+	228.044i	0.662158	+	0.786358i
$291$		0			0
$292$	−28.4737	+	164.819i	−0.0975125	+	0.564450i
$293$	−376.636			−1.28545			−0.642724	−	0.766098i	$-0.722196\pi$
$293$	−376.636			−1.28545			−0.642724	+	0.766098i	$0.722196\pi$
$294$		0			0
$295$		−	202.426i		−	0.686191i
$296$	279.431	−	163.271i	0.944022	−	0.551593i
$297$		0			0
$298$	−77.1288	−	91.5958i	−0.258822	−	0.307369i
$299$			241.444i			0.807504i
$300$		0			0
$301$	326.887			1.08600
$302$	−196.806	+	165.722i	−0.651676	+	0.548747i
$303$		0			0
$304$	23.3986	−	65.7001i	0.0769691	−	0.216119i
$305$	−99.6848			−0.326836
$306$		0			0
$307$		−	72.3257i		−	0.235589i	−0.993038	−	0.117794i	$-0.962418\pi$
$307$		−	72.3257i		−	0.235589i	0.993038	−	0.117794i	$-0.0375823\pi$
$308$	−37.8675	+	219.196i	−0.122946	+	0.711674i
$309$		0			0
$310$	−145.919	+	122.872i	−0.470707	+	0.396361i
$311$		−	322.537i		−	1.03710i	−0.855049	−	0.518548i	$-0.826473\pi$
$311$		−	322.537i		−	1.03710i	0.855049	−	0.518548i	$-0.173527\pi$
$312$		0			0
$313$	−120.008			−0.383412			−0.191706	−	0.981452i	$-0.561402\pi$
$313$	−120.008			−0.383412			−0.191706	+	0.981452i	$0.561402\pi$
$314$	−244.390	−	290.230i	−0.778312	−	0.924300i
$315$		0			0
$316$	3.17425	+	0.548374i	0.0100451	+	0.00173536i
$317$	−167.336			−0.527873			−0.263937	−	0.964540i	$-0.585021\pi$
$317$	−167.336			−0.527873			−0.263937	+	0.964540i	$0.585021\pi$
$318$		0			0
$319$		−	606.751i		−	1.90204i
$320$	−107.040	+	189.931i	−0.334499	+	0.593533i
$321$		0			0
$322$	95.0642	+	112.895i	0.295231	+	0.350607i
$323$		−	135.607i		−	0.419835i
$324$		0			0
$325$	−175.777			−0.540853
$326$	367.835	−	309.737i	1.12833	−	0.950115i
$327$		0			0
$328$	195.021	−	113.951i	0.594577	−	0.347412i
$329$	−237.470			−0.721795
$330$		0			0
$331$		−	560.633i		−	1.69375i	−0.531788	−	0.846877i	$-0.678480\pi$
$331$		−	560.633i		−	1.69375i	0.531788	−	0.846877i	$-0.321520\pi$
$332$	−538.580	−	93.0432i	−1.62223	−	0.280251i
$333$		0			0
$334$	−152.272	+	128.222i	−0.455905	+	0.383897i
$335$		−	40.8913i		−	0.122064i
$336$		0			0
$337$	−181.033			−0.537191			−0.268596	−	0.963253i	$-0.586560\pi$
$337$	−181.033			−0.537191			−0.268596	+	0.963253i	$0.586560\pi$
$338$	−4.10201	−	4.87142i	−0.0121361	−	0.0144125i
$339$		0			0
$340$	−72.1643	+	417.722i	−0.212248	+	1.22859i
$341$	388.243			1.13854
$342$		0			0
$343$			328.527i			0.957804i
$344$	−328.956	−	562.992i	−0.956268	−	1.63660i
$345$		0			0
$346$	−60.7968	−	72.2005i	−0.175713	−	0.208672i
$347$			192.881i			0.555852i	0.960603	+	0.277926i	$0.0896470\pi$
$347$			192.881i			0.555852i	−0.960603	+	0.277926i	$0.910353\pi$
$348$		0			0
$349$	456.016			1.30664			0.653319	−	0.757083i	$-0.273376\pi$
$349$	456.016			1.30664			0.653319	+	0.757083i	$0.273376\pi$
$350$	−82.1907	+	69.2092i	−0.234831	+	0.197741i
$351$		0			0
$352$	415.624	−	155.365i	1.18075	−	0.441377i
$353$	450.744			1.27689			0.638447	−	0.769665i	$-0.279577\pi$
$353$	450.744			1.27689			0.638447	+	0.769665i	$0.279577\pi$
$354$		0			0
$355$			19.7242i			0.0555612i
$356$	−102.189	+	591.521i	−0.287048	+	1.66158i
$357$		0			0
$358$	190.489	−	160.402i	0.532092	−	0.448051i
$359$		−	204.231i		−	0.568889i	−0.958693	−	0.284444i	$-0.908191\pi$
$359$		−	204.231i		−	0.568889i	0.958693	−	0.284444i	$-0.0918091\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	−423.603	−	503.057i	−1.17017	−	1.38966i
$363$		0			0
$364$	−207.432	−	35.8353i	−0.569868	−	0.0984486i
$365$	−142.444			−0.390257
$366$		0			0
$367$			448.078i			1.22092i	0.792047	+	0.610460i	$0.209016\pi$
$367$			448.078i			1.22092i	−0.792047	+	0.610460i	$0.790984\pi$
$368$	98.7717	−	277.338i	0.268401	−	0.753635i
$369$		0			0
$370$	177.528	+	210.826i	0.479804	+	0.569801i
$371$			155.316i			0.418641i
$372$		0			0
$373$	326.404			0.875078			0.437539	−	0.899199i	$-0.355850\pi$
$373$	326.404			0.875078			0.437539	+	0.899199i	$0.355850\pi$
$374$	659.946	−	555.711i	1.76456	−	1.48586i
$375$		0			0
$376$	238.974	+	408.991i	0.635569	+	1.08774i
$377$	574.189			1.52305
$378$		0			0
$379$			4.99082i			0.0131684i	0.999978	+	0.00658420i	$0.00209583\pi$
$379$			4.99082i			0.0131684i	−0.999978	+	0.00658420i	$0.997904\pi$
$380$	58.5275	+	10.1110i	0.154020	+	0.0266079i
$381$		0			0
$382$	−6.63727	+	5.58895i	−0.0173750	+	0.0146308i
$383$		−	140.964i		−	0.368053i	−0.982921	−	0.184027i	$-0.941087\pi$
$383$		−	140.964i		−	0.368053i	0.982921	−	0.184027i	$-0.0589132\pi$
$384$		0			0
$385$	−189.438			−0.492047
$386$	193.564	+	229.871i	0.501462	+	0.595521i
$387$		0			0
$388$	−34.2524	+	198.269i	−0.0882793	+	0.511004i
$389$	−671.604			−1.72649			−0.863244	−	0.504786i	$-0.831571\pi$
$389$	−671.604			−1.72649			−0.863244	+	0.504786i	$0.831571\pi$
$390$		0			0
$391$		−	572.431i		−	1.46402i
$392$	227.357	−	132.845i	0.579993	−	0.338890i
$393$		0			0
$394$	122.556	+	145.543i	0.311055	+	0.369399i
$395$			2.74332i			0.00694512i
$396$		0			0
$397$	553.597			1.39445			0.697225	−	0.716852i	$-0.254418\pi$
$397$	553.597			1.39445			0.697225	+	0.716852i	$0.254418\pi$
$398$	−15.9691	+	13.4469i	−0.0401234	+	0.0337862i
$399$		0			0
$400$	201.909	+	71.9083i	0.504772	+	0.179771i
$401$	309.731			0.772397			0.386199	−	0.922416i	$-0.373788\pi$
$401$	309.731			0.772397			0.386199	+	0.922416i	$0.373788\pi$
$402$		0			0
$403$			367.407i			0.911681i
$404$	94.7011	−	548.176i	0.234409	−	1.35687i
$405$		0			0
$406$	268.482	−	226.077i	0.661285	−	0.556839i
$407$		−	560.940i		−	1.37823i
$408$		0			0
$409$	−228.776			−0.559355			−0.279677	−	0.960094i	$-0.590228\pi$
$409$	−228.776			−0.559355			−0.279677	+	0.960094i	$0.590228\pi$
$410$	123.901	+	147.141i	0.302197	+	0.358880i
$411$		0			0
$412$	−251.675	−	43.4786i	−0.610862	−	0.105531i
$413$	−238.321			−0.577049
$414$		0			0
$415$		−	465.463i		−	1.12160i
$416$	147.027	+	393.319i	0.353430	+	0.945478i
$417$		0			0
$418$	−77.8614	−	92.4658i	−0.186271	−	0.221210i
$419$			392.777i			0.937416i	0.883353	+	0.468708i	$0.155280\pi$
$419$			392.777i			0.937416i	−0.883353	+	0.468708i	$0.844720\pi$
$420$		0			0
$421$	−399.437			−0.948782			−0.474391	−	0.880314i	$-0.657332\pi$
$421$	−399.437			−0.948782			−0.474391	+	0.880314i	$0.657332\pi$
$422$	343.038	−	288.857i	0.812886	−	0.684495i
$423$		0			0
$424$	267.498	−	156.299i	0.630890	−	0.368630i
$425$	416.745			0.980576
$426$		0			0
$427$			117.361i			0.274851i
$428$	560.238	+	96.7849i	1.30897	+	0.226133i
$429$		0			0
$430$	424.769	−	357.679i	0.987835	−	0.831813i
$431$		−	413.011i		−	0.958262i	−0.877743	−	0.479131i	$-0.840952\pi$
$431$		−	413.011i		−	0.958262i	0.877743	−	0.479131i	$-0.159048\pi$
$432$		0			0
$433$	−315.888			−0.729534			−0.364767	−	0.931099i	$-0.618851\pi$
$433$	−315.888			−0.729534			−0.364767	+	0.931099i	$0.618851\pi$
$434$	144.660	+	171.794i	0.333318	+	0.395839i
$435$		0			0
$436$	−25.8086	+	149.393i	−0.0591940	+	0.342643i
$437$	−80.2040			−0.183533
$438$		0			0
$439$			206.108i			0.469494i	0.972057	+	0.234747i	$0.0754261\pi$
$439$			206.108i			0.469494i	−0.972057	+	0.234747i	$0.924574\pi$
$440$	190.637	+	326.266i	0.433266	+	0.741513i
$441$		0			0
$442$	525.888	+	624.528i	1.18979	+	1.41296i
$443$		−	592.701i		−	1.33792i	−0.743296	−	0.668962i	$-0.766739\pi$
$443$		−	592.701i		−	1.33792i	0.743296	−	0.668962i	$-0.233261\pi$
$444$		0			0
$445$	−511.217			−1.14880
$446$	−75.4922	+	63.5687i	−0.169265	+	0.142531i
$447$		0			0
$448$	223.610	+	126.021i	0.499129	+	0.281296i
$449$	−61.4274			−0.136809			−0.0684047	−	0.997658i	$-0.521791\pi$
$449$	−61.4274			−0.136809			−0.0684047	+	0.997658i	$0.521791\pi$
$450$		0			0
$451$		−	391.494i		−	0.868057i
$452$	−82.3165	+	476.488i	−0.182116	+	1.05418i
$453$		0			0
$454$	580.541	−	488.848i	1.27873	−	1.07676i
$455$		−	179.271i		−	0.394003i
$456$		0			0
$457$	−580.299			−1.26980			−0.634900	−	0.772594i	$-0.718959\pi$
$457$	−580.299			−1.26980			−0.634900	+	0.772594i	$0.718959\pi$
$458$	555.801	+	660.052i	1.21354	+	1.44116i
$459$		0			0
$460$	247.060	+	42.6813i	0.537087	+	0.0927854i
$461$	212.366			0.460663			0.230331	−	0.973112i	$-0.426019\pi$
$461$	212.366			0.460663			0.230331	+	0.973112i	$0.426019\pi$
$462$		0			0
$463$			512.868i			1.10771i	0.832614	+	0.553853i	$0.186843\pi$
$463$			512.868i			1.10771i	−0.832614	+	0.553853i	$0.813157\pi$
$464$	−659.549	−	234.894i	−1.42144	−	0.506236i
$465$		0			0
$466$	−23.6325	−	28.0652i	−0.0507135	−	0.0602258i
$467$		−	482.496i		−	1.03318i	−0.856232	−	0.516591i	$-0.827201\pi$
$467$		−	482.496i		−	1.03318i	0.856232	−	0.516591i	$-0.172799\pi$
$468$		0			0
$469$	−48.1423			−0.102649
$470$	−308.578	+	259.840i	−0.656549	+	0.552851i
$471$		0			0
$472$	239.830	+	410.457i	0.508115	+	0.869612i
$473$	−1130.17			−2.38937
$474$		0			0
$475$		−	58.3906i		−	0.122928i
$476$	491.794	+	84.9607i	1.03318	+	0.178489i
$477$		0			0
$478$	−329.905	+	277.799i	−0.690179	+	0.581169i
$479$			498.358i			1.04041i	0.854040	+	0.520207i	$0.174145\pi$
$479$			498.358i			1.04041i	−0.854040	+	0.520207i	$0.825855\pi$
$480$		0			0
$481$	530.837			1.10361
$482$	309.526	+	367.583i	0.642169	+	0.762621i
$483$		0			0
$484$	48.5287	−	280.908i	0.100266	−	0.580388i
$485$	−171.353			−0.353304
$486$		0			0
$487$		−	470.837i		−	0.966812i	−0.875396	−	0.483406i	$-0.839400\pi$
$487$		−	470.837i		−	0.966812i	0.875396	−	0.483406i	$-0.160600\pi$
$488$	202.130	−	118.104i	0.414200	−	0.242017i
$489$		0			0
$490$	144.444	+	171.538i	0.294784	+	0.350077i
$491$			400.395i			0.815468i	0.913101	+	0.407734i	$0.133681\pi$
$491$			400.395i			0.815468i	−0.913101	+	0.407734i	$0.866319\pi$
$492$		0			0
$493$	−1361.33			−2.76131
$494$	87.5034	−	73.6828i	0.177132	−	0.149155i
$495$		0			0
$496$	150.302	−	422.027i	0.303028	−	0.850862i
$497$	23.2218			0.0467240
$498$		0			0
$499$		−	590.198i		−	1.18276i	−0.806392	−	0.591381i	$-0.798583\pi$
$499$		−	590.198i		−	1.18276i	0.806392	−	0.591381i	$-0.201417\pi$
$500$	−89.0637	+	515.544i	−0.178127	+	1.03109i
$501$		0			0
$502$	−508.243	+	427.969i	−1.01244	+	0.852528i
$503$			628.173i			1.24885i	0.781083	+	0.624427i	$0.214667\pi$
$503$			628.173i			1.24885i	−0.781083	+	0.624427i	$0.785333\pi$
$504$		0			0
$505$	473.757			0.938132
$506$	−328.673	−	390.322i	−0.649552	−	0.771388i
$507$		0			0
$508$	−158.751	−	27.4253i	−0.312502	−	0.0539869i
$509$	826.098			1.62298			0.811492	−	0.584364i	$-0.198656\pi$
$509$	826.098			1.62298			0.811492	+	0.584364i	$0.198656\pi$
$510$		0			0
$511$			167.702i			0.328185i
$512$	−7.98237	−	511.938i	−0.0155906	−	0.999878i
$513$		0			0
$514$	258.989	+	307.567i	0.503869	+	0.598379i
$515$		−	217.508i		−	0.422346i
$516$		0			0
$517$	821.026			1.58806
$518$	248.211	−	209.008i	0.479172	−	0.403489i
$519$		0			0
$520$	−308.756	+	180.406i	−0.593762	+	0.346935i
$521$	813.955			1.56229			0.781147	−	0.624347i	$-0.214635\pi$
$521$	813.955			1.56229			0.781147	+	0.624347i	$0.214635\pi$
$522$		0			0
$523$			454.953i			0.869890i	0.900457	+	0.434945i	$0.143232\pi$
$523$			454.953i			0.869890i	−0.900457	+	0.434945i	$0.856768\pi$
$524$	−218.821	−	37.8028i	−0.417598	−	0.0721428i
$525$		0			0
$526$	427.543	−	360.015i	0.812819	−	0.684439i
$527$		−	871.075i		−	1.65289i
$528$		0			0
$529$	190.438			0.359995
$530$	169.946	+	201.823i	0.320653	+	0.380798i
$531$		0			0
$532$	11.9039	−	68.9059i	0.0223758	−	0.129522i
$533$	370.484			0.695091
$534$		0			0
$535$			484.181i			0.905011i
$536$	48.4471	+	82.9147i	0.0903864	+	0.154692i
$537$		0			0
$538$	132.895	+	157.823i	0.247018	+	0.293351i
$539$		−	456.406i		−	0.846765i
$540$		0			0
$541$	−48.9018			−0.0903916			−0.0451958	−	0.998978i	$-0.514391\pi$
$541$	−48.9018			−0.0903916			−0.0451958	+	0.998978i	$0.514391\pi$
$542$	−368.530	+	310.323i	−0.679945	+	0.572552i
$543$		0			0
$544$	−348.581	−	932.507i	−0.640774	−	1.71417i
$545$	−129.111			−0.236901
$546$		0			0
$547$			731.998i			1.33820i	0.743170	+	0.669102i	$0.233321\pi$
$547$			731.998i			1.33820i	−0.743170	+	0.669102i	$0.766679\pi$
$548$	−24.0597	+	139.269i	−0.0439045	+	0.254141i
$549$		0			0
$550$	284.165	−	239.283i	0.516663	−	0.435059i
$551$			190.737i			0.346165i
$552$		0			0
$553$	3.22978			0.00584047
$554$	511.154	+	607.030i	0.922660	+	1.09572i
$555$		0			0
$556$	−345.020	−	59.6045i	−0.620539	−	0.107202i
$557$	936.583			1.68148			0.840739	−	0.541441i	$-0.182121\pi$
$557$	936.583			1.68148			0.840739	+	0.541441i	$0.182121\pi$
$558$		0			0
$559$		−	1069.52i		−	1.91327i
$560$	−73.3377	+	205.922i	−0.130960	+	0.367719i
$561$		0			0
$562$	−558.890	−	663.721i	−0.994467	−	1.18100i
$563$		−	258.954i		−	0.459954i	−0.973196	−	0.229977i	$-0.926135\pi$
$563$		−	258.954i		−	0.459954i	0.973196	−	0.229977i	$-0.0738650\pi$
$564$		0			0
$565$	−411.801			−0.728851
$566$	−405.941	+	341.825i	−0.717210	+	0.603931i
$567$		0			0
$568$	−23.3688	−	39.9945i	−0.0411423	−	0.0704129i
$569$	418.563			0.735612			0.367806	−	0.929903i	$-0.380109\pi$
$569$	418.563			0.735612			0.367806	+	0.929903i	$0.380109\pi$
$570$		0			0
$571$		−	215.732i		−	0.377814i	−0.981995	−	0.188907i	$-0.939505\pi$
$571$		−	215.732i		−	0.377814i	0.981995	−	0.188907i	$-0.0604945\pi$
$572$	717.172	+	123.896i	1.25380	+	0.216602i
$573$		0			0
$574$	173.232	−	145.871i	0.301799	−	0.254131i
$575$		−	246.482i		−	0.428665i
$576$		0			0
$577$	−664.365			−1.15141			−0.575706	−	0.817656i	$-0.695273\pi$
$577$	−664.365			−1.15141			−0.575706	+	0.817656i	$0.695273\pi$
$578$	−874.513	−	1038.55i	−1.51300	−	1.79679i
$579$		0			0
$580$	101.502	−	587.545i	0.175004	−	1.01301i
$581$	−548.001			−0.943202
$582$		0			0
$583$		−	536.986i		−	0.921073i
$584$	288.831	−	168.764i	0.494574	−	0.288980i
$585$		0			0
$586$	485.193	+	576.200i	0.827974	+	0.983277i
$587$		−	600.072i		−	1.02227i	−0.859501	−	0.511135i	$-0.829225\pi$
$587$		−	600.072i		−	1.02227i	0.859501	−	0.511135i	$-0.170775\pi$
$588$		0			0
$589$	−122.047			−0.207211
$590$	−309.684	+	260.771i	−0.524888	+	0.441985i
$591$		0			0
$592$	−609.752	−	217.159i	−1.02999	−	0.366822i
$593$	−914.948			−1.54291			−0.771457	−	0.636282i	$-0.780472\pi$
$593$	−914.948			−1.54291			−0.771457	+	0.636282i	$0.780472\pi$
$594$		0			0
$595$			425.029i			0.714334i
$596$	−40.7693	+	235.993i	−0.0684049	+	0.395961i
$597$		0			0
$598$	369.375	−	311.035i	0.617684	−	0.520125i
$599$		−	268.071i		−	0.447531i	−0.974643	−	0.223766i	$-0.928165\pi$
$599$		−	268.071i		−	0.447531i	0.974643	−	0.223766i	$-0.0718350\pi$
$600$		0			0
$601$	−803.730			−1.33732			−0.668661	−	0.743568i	$-0.733132\pi$
$601$	−803.730			−1.33732			−0.668661	+	0.743568i	$0.733132\pi$
$602$	−421.105	−	500.091i	−0.699509	−	0.830716i
$603$		0			0
$604$	507.062	+	87.5983i	0.839506	+	0.145030i
$605$	242.772			0.401276
$606$		0			0
$607$			398.569i			0.656621i	0.944570	+	0.328310i	$0.106479\pi$
$607$			398.569i			0.656621i	−0.944570	+	0.328310i	$0.893521\pi$
$608$	−130.655	+	48.8401i	−0.214893	+	0.0803291i
$609$		0			0
$610$	128.417	+	152.504i	0.210519	+	0.250006i
$611$			776.964i			1.27163i
$612$		0			0
$613$	−587.725			−0.958768			−0.479384	−	0.877605i	$-0.659140\pi$
$613$	−587.725			−0.958768			−0.479384	+	0.877605i	$0.659140\pi$
$614$	−110.648	+	93.1719i	−0.180209	+	0.151746i
$615$		0			0
$616$	384.121	−	224.442i	0.623572	−	0.364354i
$617$	369.163			0.598319			0.299159	−	0.954203i	$-0.403294\pi$
$617$	369.163			0.598319			0.299159	+	0.954203i	$0.403294\pi$
$618$		0			0
$619$		−	153.566i		−	0.248087i	−0.992277	−	0.124044i	$-0.960414\pi$
$619$		−	153.566i		−	0.248087i	0.992277	−	0.124044i	$-0.0395863\pi$
$620$	375.954	+	64.9485i	0.606377	+	0.104756i
$621$		0			0
$622$	−493.436	+	415.501i	−0.793305	+	0.668007i
$623$			601.868i			0.966081i
$624$		0			0
$625$	−110.662			−0.177059
$626$	154.597	+	183.595i	0.246961	+	0.293283i
$627$		0			0
$628$	−129.181	+	747.765i	−0.205703	+	1.19071i
$629$	−1258.54			−2.00086
$630$		0			0
$631$			796.252i			1.26189i	0.775828	+	0.630945i	$0.217332\pi$
$631$			796.252i			1.26189i	−0.775828	+	0.630945i	$0.782668\pi$
$632$	−3.25023	−	5.56259i	−0.00514276	−	0.00880157i
$633$		0			0
$634$	215.567	+	256.000i	0.340010	+	0.403786i
$635$		−	137.199i		−	0.216062i
$636$		0			0
$637$	431.912			0.678042
$638$	−928.244	+	781.633i	−1.45493	+	1.22513i
$639$		0			0
$640$	428.459	−	80.9178i	0.669467	−	0.126434i
$641$	191.673			0.299021			0.149511	−	0.988760i	$-0.452230\pi$
$641$	191.673			0.299021			0.149511	+	0.988760i	$0.452230\pi$
$642$		0			0
$643$		−	900.822i		−	1.40097i	−0.713668	−	0.700484i	$-0.752968\pi$
$643$		−	900.822i		−	1.40097i	0.713668	−	0.700484i	$-0.247032\pi$
$644$	50.2497	−	290.870i	0.0780275	−	0.451661i
$645$		0			0
$646$	−207.459	+	174.692i	−0.321144	+	0.270421i
$647$			780.183i			1.20585i	0.797799	+	0.602923i	$0.205998\pi$
$647$			780.183i			1.20585i	−0.797799	+	0.602923i	$0.794002\pi$
$648$		0			0
$649$	823.968			1.26960
$650$	226.441	+	268.915i	0.348371	+	0.413715i
$651$		0			0
$652$	−947.710	−	163.723i	−1.45354	−	0.251109i
$653$	−691.822			−1.05945			−0.529726	−	0.848169i	$-0.677705\pi$
$653$	−691.822			−1.05945			−0.529726	+	0.848169i	$0.677705\pi$
$654$		0			0
$655$		−	189.114i		−	0.288724i
$656$	−425.561	−	151.560i	−0.648721	−	0.231037i
$657$		0			0
$658$	305.916	+	363.296i	0.464918	+	0.552122i
$659$		−	209.676i		−	0.318173i	−0.987265	−	0.159086i	$-0.949145\pi$
$659$		−	209.676i		−	0.318173i	0.987265	−	0.159086i	$-0.0508548\pi$
$660$		0			0
$661$	978.742			1.48070			0.740349	−	0.672223i	$-0.234660\pi$
$661$	978.742			1.48070			0.740349	+	0.672223i	$0.234660\pi$
$662$	−857.689	+	722.223i	−1.29560	+	1.09097i
$663$		0			0
$664$	551.470	+	943.812i	0.830527	+	1.42140i
$665$	59.5513			0.0895508
$666$		0			0
$667$			805.151i			1.20712i
$668$	392.322	+	67.7763i	0.587309	+	0.101462i
$669$		0			0
$670$	−62.5580	+	52.6773i	−0.0933701	+	0.0786229i
$671$		−	405.763i		−	0.604714i
$672$		0			0
$673$	550.625			0.818165			0.409082	−	0.912497i	$-0.365849\pi$
$673$	550.625			0.818165			0.409082	+	0.912497i	$0.365849\pi$
$674$	233.212	+	276.956i	0.346012	+	0.410913i
$675$		0			0
$676$	−2.16827	+	12.5510i	−0.00320750	+	0.0185666i
$677$	492.918			0.728092			0.364046	−	0.931381i	$-0.381395\pi$
$677$	492.918			0.728092			0.364046	+	0.931381i	$0.381395\pi$
$678$		0			0
$679$			201.738i			0.297110i
$680$	732.020	−	427.720i	1.07650	−	0.628999i
$681$		0			0
$682$	−500.146	−	593.958i	−0.733351	−	0.870906i
$683$			1322.74i			1.93666i	0.249671	+	0.968331i	$0.419677\pi$
$683$			1322.74i			1.93666i	−0.249671	+	0.968331i	$0.580323\pi$
$684$		0			0
$685$	−120.362			−0.175711
$686$	502.600	−	423.217i	0.732653	−	0.616935i
$687$		0			0
$688$	−437.527	+	1228.52i	−0.635941	+	1.78564i
$689$	508.167			0.737543
$690$		0			0
$691$		−	742.065i		−	1.07390i	−0.843614	−	0.536950i	$-0.819576\pi$
$691$		−	742.065i		−	1.07390i	0.843614	−	0.536950i	$-0.180424\pi$
$692$	−32.1364	+	186.021i	−0.0464399	+	0.268817i
$693$		0			0
$694$	295.080	−	248.474i	0.425188	−	0.358032i
$695$		−	298.180i		−	0.429036i
$696$		0			0
$697$	−878.368			−1.26021
$698$	−587.453	−	697.641i	−0.841623	−	0.999486i
$699$		0			0
$700$	211.761	+	36.5831i	0.302515	+	0.0522615i
$701$	−90.6576			−0.129326			−0.0646631	−	0.997907i	$-0.520597\pi$
$701$	−90.6576			−0.129326			−0.0646631	+	0.997907i	$0.520597\pi$
$702$		0			0
$703$			176.336i			0.250834i
$704$	−773.105	−	435.701i	−1.09816	−	0.618894i
$705$		0			0
$706$	−580.661	−	689.575i	−0.822466	−	0.976735i
$707$		−	557.765i		−	0.788918i
$708$		0			0
$709$	858.633			1.21105			0.605524	−	0.795827i	$-0.292964\pi$
$709$	858.633			1.21105			0.605524	+	0.795827i	$0.292964\pi$
$710$	30.1753	−	25.4093i	0.0425004	−	0.0357877i
$711$		0			0
$712$	1036.59	−	605.679i	1.45588	−	0.850672i
$713$	−515.194			−0.722572
$714$		0			0
$715$			619.810i			0.866867i
$716$	−490.786	−	84.7866i	−0.685456	−	0.118417i
$717$		0			0
$718$	−312.445	+	263.096i	−0.435160	+	0.366429i
$719$		−	580.470i		−	0.807330i	−0.914907	−	0.403665i	$-0.867736\pi$
$719$		−	580.470i		−	0.807330i	0.914907	−	0.403665i	$-0.132264\pi$
$720$		0			0
$721$	−256.078			−0.355170
$722$	24.4763	+	29.0673i	0.0339007	+	0.0402595i
$723$		0			0
$724$	−223.911	+	1296.10i	−0.309269	+	1.79020i
$725$	−586.170			−0.808511
$726$		0			0
$727$			1002.25i			1.37862i	0.724468	+	0.689309i	$0.242086\pi$
$727$			1002.25i			1.37862i	−0.724468	+	0.689309i	$0.757914\pi$
$728$	212.397	+	363.506i	0.291754	+	0.499321i
$729$		0			0
$730$	183.500	+	217.919i	0.251370	+	0.298519i
$731$			2535.69i			3.46880i
$732$		0			0
$733$	−1196.08			−1.63176			−0.815880	−	0.578221i	$-0.803747\pi$
$733$	−1196.08			−1.63176			−0.815880	+	0.578221i	$0.803747\pi$
$734$	685.496	−	577.226i	0.933919	−	0.786412i
$735$		0			0
$736$	−551.528	+	206.167i	−0.749359	+	0.280118i
$737$	166.446			0.225843
$738$		0			0
$739$			422.669i			0.571948i	0.958237	+	0.285974i	$0.0923170\pi$
$739$			422.669i			0.571948i	−0.958237	+	0.285974i	$0.907683\pi$
$740$	93.8388	−	543.184i	0.126809	−	0.734033i
$741$		0			0
$742$	237.611	−	200.082i	0.320231	−	0.269652i
$743$		−	396.981i		−	0.534295i	−0.963656	−	0.267148i	$-0.913919\pi$
$743$		−	396.981i		−	0.534295i	0.963656	−	0.267148i	$-0.0860812\pi$
$744$		0			0
$745$	−203.954			−0.273764
$746$	−420.483	−	499.352i	−0.563650	−	0.669373i
$747$		0			0
$748$	−1700.32	−	293.742i	−2.27316	−	0.392703i
$749$	570.038			0.761066
$750$		0			0
$751$		−	146.903i		−	0.195610i	−0.995206	−	0.0978052i	$-0.968818\pi$
$751$		−	146.903i		−	0.195610i	0.995206	−	0.0978052i	$-0.0311822\pi$
$752$	317.847	−	892.470i	0.422668	−	1.18680i
$753$		0			0
$754$	−739.686	−	878.428i	−0.981015	−	1.16502i
$755$			438.224i			0.580429i
$756$		0			0
$757$	1269.43			1.67692			0.838460	−	0.544963i	$-0.183456\pi$
$757$	1269.43			1.67692			0.838460	+	0.544963i	$0.183456\pi$
$758$	7.63526	−	6.42932i	0.0100729	−	0.00848195i
$759$		0			0
$760$	−59.9283	−	102.564i	−0.0788530	−	0.134953i
$761$	−97.2802			−0.127832			−0.0639160	−	0.997955i	$-0.520359\pi$
$761$	−97.2802			−0.127832			−0.0639160	+	0.997955i	$0.520359\pi$
$762$		0			0
$763$			152.006i			0.199221i
$764$	17.1006	+	2.95425i	0.0223830	+	0.00386682i
$765$		0			0
$766$	−215.656	+	181.594i	−0.281535	+	0.237068i
$767$			779.748i			1.01662i
$768$		0			0
$769$	−885.671			−1.15172			−0.575859	−	0.817549i	$-0.695332\pi$
$769$	−885.671			−1.15172			−0.575859	+	0.817549i	$0.695332\pi$
$770$	244.039	+	289.813i	0.316934	+	0.376381i
$771$		0			0
$772$	102.316	−	592.252i	0.132533	−	0.767166i
$773$	−318.930			−0.412587			−0.206293	−	0.978490i	$-0.566140\pi$
$773$	−318.930			−0.412587			−0.206293	+	0.978490i	$0.566140\pi$
$774$		0			0
$775$		−	375.074i		−	0.483967i
$776$	347.449	−	203.015i	0.447744	−	0.261617i
$777$		0			0
$778$	865.179	+	1027.46i	1.11205	+	1.32064i
$779$			123.069i			0.157983i
$780$		0			0
$781$	−80.2867			−0.102800
$782$	−875.740	+	737.422i	−1.11987	+	0.942995i
$783$		0			0
$784$	−496.122	−	176.690i	−0.632809	−	0.225370i
$785$	−646.249			−0.823248
$786$		0			0
$787$		−	148.360i		−	0.188513i	−0.995548	−	0.0942565i	$-0.969953\pi$
$787$		−	148.360i		−	0.188513i	0.995548	−	0.0942565i	$-0.0300474\pi$
$788$	64.7813	−	374.986i	0.0822097	−	0.475870i
$789$		0			0
$790$	4.19690	−	3.53402i	0.00531253	−	0.00447345i
$791$			484.823i			0.612924i
$792$		0			0
$793$	383.987			0.484221
$794$	−713.159	−	846.925i	−0.898185	−	1.06666i
$795$		0			0
$796$	41.1437	+	7.10786i	0.0516881	+	0.00892947i
$797$	873.772			1.09633			0.548163	−	0.836371i	$-0.315327\pi$
$797$	873.772			1.09633			0.548163	+	0.836371i	$0.315327\pi$
$798$		0			0
$799$		−	1842.08i		−	2.30548i
$800$	−150.095	−	401.526i	−0.187619	−	0.501908i
$801$		0			0
$802$	−399.004	−	473.845i	−0.497512	−	0.590830i
$803$		−	579.812i		−	0.722057i
$804$		0			0
$805$	251.382			0.312275
$806$	562.082	−	473.304i	0.697372	−	0.587226i
$807$		0			0
$808$	−960.629	+	561.296i	−1.18890	+	0.694674i
$809$	−1030.28			−1.27353			−0.636764	−	0.771059i	$-0.719727\pi$
$809$	−1030.28			−1.27353			−0.636764	+	0.771059i	$0.719727\pi$
$810$		0			0
$811$		−	711.666i		−	0.877517i	−0.898605	−	0.438758i	$-0.855418\pi$
$811$		−	711.666i		−	0.877517i	0.898605	−	0.438758i	$-0.144582\pi$
$812$	−691.731	−	119.501i	−0.851885	−	0.147169i
$813$		0			0
$814$	−858.160	+	722.619i	−1.05425	+	0.887738i
$815$		−	819.050i		−	1.00497i
$816$		0			0
$817$	355.279			0.434858
$818$	294.716	+	349.995i	0.360288	+	0.427867i
$819$		0			0
$820$	65.4923	−	379.102i	0.0798687	−	0.462319i
$821$	187.724			0.228653			0.114327	−	0.993443i	$-0.463529\pi$
$821$	187.724			0.228653			0.114327	+	0.993443i	$0.463529\pi$
$822$		0			0
$823$			1035.03i			1.25763i	0.777557	+	0.628813i	$0.216459\pi$
$823$			1035.03i			1.25763i	−0.777557	+	0.628813i	$0.783541\pi$
$824$	257.699	+	441.038i	0.312741	+	0.535240i
$825$		0			0
$826$	307.012	+	364.598i	0.371685	+	0.441402i
$827$		−	368.239i		−	0.445271i	−0.974902	−	0.222636i	$-0.928534\pi$
$827$		−	368.239i		−	0.445271i	0.974902	−	0.222636i	$-0.0714660\pi$
$828$		0			0
$829$	1202.02			1.44996			0.724980	−	0.688770i	$-0.241849\pi$
$829$	1202.02			1.44996			0.724980	+	0.688770i	$0.241849\pi$
$830$	−712.093	+	599.622i	−0.857943	+	0.722436i
$831$		0			0
$832$	412.319	−	731.615i	0.495575	−	0.879344i
$833$	−1024.01			−1.22930
$834$		0			0
$835$			339.061i			0.406061i
$836$	−41.1565	+	238.234i	−0.0492303	+	0.284969i
$837$		0			0
$838$	600.894	−	505.987i	0.717058	−	0.603803i
$839$		−	1585.90i		−	1.89022i	−0.326748	−	0.945112i	$-0.605953\pi$
$839$		−	1585.90i		−	1.89022i	0.326748	−	0.945112i	$-0.394047\pi$
$840$		0			0
$841$	1073.77			1.27677
$842$	514.566	+	611.083i	0.611124	+	0.725752i
$843$		0			0
$844$	−883.821	−	152.686i	−1.04718	−	0.180908i
$845$	−10.8471			−0.0128368
$846$		0			0
$847$		−	285.822i		−	0.337452i
$848$	−583.713	−	207.885i	−0.688341	−	0.245147i
$849$		0			0
$850$	−536.862	−	637.561i	−0.631602	−	0.750072i
$851$			744.361i			0.874690i
$852$		0			0
$853$	978.853			1.14754			0.573771	−	0.819016i	$-0.305480\pi$
$853$	978.853			1.14754			0.573771	+	0.819016i	$0.305480\pi$
$854$	179.546	−	151.188i	0.210242	−	0.177035i
$855$		0			0
$856$	−573.647	−	981.767i	−0.670148	−	1.14692i
$857$	902.892			1.05355			0.526775	−	0.850005i	$-0.323401\pi$
$857$	902.892			1.05355			0.526775	+	0.850005i	$0.323401\pi$
$858$		0			0
$859$			76.3582i			0.0888920i	0.999012	+	0.0444460i	$0.0141523\pi$
$859$			76.3582i			0.0888920i	−0.999012	+	0.0444460i	$0.985848\pi$
$860$	−1094.40	−	189.065i	−1.27256	−	0.219843i
$861$		0			0
$862$	−631.849	+	532.052i	−0.733003	+	0.617230i
$863$		−	634.164i		−	0.734837i	−0.930056	−	0.367418i	$-0.880242\pi$
$863$		−	634.164i		−	0.734837i	0.930056	−	0.367418i	$-0.119758\pi$
$864$		0			0
$865$	−160.767			−0.185858
$866$	406.936	+	483.265i	0.469903	+	0.558042i
$867$		0			0
$868$	76.4655	−	442.620i	0.0880939	−	0.509930i
$869$	−11.1666			−0.0128499
$870$		0			0
$871$			157.514i			0.180842i
$872$	261.797	−	152.968i	0.300226	−	0.175422i
$873$		0			0
$874$	103.321	+	122.701i	0.118216	+	0.140390i
$875$			524.562i			0.599500i
$876$		0			0
$877$	116.473			0.132809			0.0664044	−	0.997793i	$-0.478847\pi$
$877$	116.473			0.132809			0.0664044	+	0.997793i	$0.478847\pi$
$878$	315.316	−	265.514i	0.359130	−	0.302407i
$879$		0			0
$880$	253.557	−	711.953i	0.288132	−	0.809037i
$881$	−812.123			−0.921819			−0.460910	−	0.887447i	$-0.652477\pi$
$881$	−812.123			−0.921819			−0.460910	+	0.887447i	$0.652477\pi$
$882$		0			0
$883$			728.284i			0.824784i	0.911007	+	0.412392i	$0.135307\pi$
$883$			728.284i			0.824784i	−0.911007	+	0.412392i	$0.864693\pi$
$884$	277.978	−	1609.07i	0.314454	−	1.82021i
$885$		0			0
$886$	−906.749	+	763.533i	−1.02342	+	0.861775i
$887$		−	990.783i		−	1.11700i	−0.829503	−	0.558502i	$-0.811376\pi$
$887$		−	990.783i		−	1.11700i	0.829503	−	0.558502i	$-0.188624\pi$
$888$		0			0
$889$	−161.528			−0.181696
$890$	658.564	+	782.090i	0.739959	+	0.878753i
$891$		0			0
$892$	194.502	+	33.6016i	0.218052	+	0.0376699i
$893$	−258.096			−0.289021
$894$		0			0
$895$		−	424.158i		−	0.473919i
$896$	−95.2665	−	504.435i	−0.106324	−	0.562985i
$897$		0			0
$898$	79.1325	+	93.9753i	0.0881208	+	0.104650i
$899$			1225.21i			1.36285i
$900$		0			0
$901$	−1204.80			−1.33718
$902$	−598.931	+	504.333i	−0.664003	+	0.559128i
$903$		0			0
$904$	835.003	−	487.892i	0.923675	−	0.539704i
$905$	−1120.15			−1.23773
$906$		0			0
$907$			1561.68i			1.72180i	0.508770	+	0.860902i	$0.330100\pi$
$907$			1561.68i			1.72180i	−0.508770	+	0.860902i	$0.669900\pi$
$908$	−1495.74	−	258.399i	−1.64729	−	0.284580i
$909$		0			0
$910$	−274.260	+	230.942i	−0.301385	+	0.253783i
$911$			228.537i			0.250864i	0.992102	+	0.125432i	$0.0400317\pi$
$911$			228.537i			0.250864i	−0.992102	+	0.125432i	$0.959968\pi$
$912$		0			0
$913$	1894.65			2.07519
$914$	747.557	+	887.776i	0.817896	+	0.971308i
$915$		0			0
$916$	293.789	−	1700.59i	0.320731	−	1.85654i
$917$	−222.649			−0.242801
$918$		0			0
$919$		−	166.422i		−	0.181090i	−0.995892	−	0.0905451i	$-0.971139\pi$
$919$		−	166.422i		−	0.181090i	0.995892	−	0.0905451i	$-0.0288609\pi$
$920$	−252.973	−	432.950i	−0.274971	−	0.470598i
$921$		0			0
$922$	−273.575	−	324.890i	−0.296719	−	0.352375i
$923$		−	75.9780i		−	0.0823163i
$924$		0			0
$925$	−541.914			−0.585853
$926$	784.616	−	660.691i	0.847318	−	0.713489i
$927$		0			0
$928$	490.295	+	1311.61i	0.528336	+	1.41338i
$929$	−328.410			−0.353509			−0.176754	−	0.984255i	$-0.556560\pi$
$929$	−328.410			−0.353509			−0.176754	+	0.984255i	$0.556560\pi$
$930$		0			0
$931$			143.475i			0.154108i
$932$	−12.4918	+	72.3088i	−0.0134033	+	0.0775845i
$933$		0			0
$934$	−738.152	+	621.565i	−0.790312	+	0.665487i
$935$		−	1469.49i		−	1.57164i
$936$		0			0
$937$	−2.94522			−0.00314325			−0.00157162	−	0.999999i	$-0.500500\pi$
$937$	−2.94522			−0.00314325			−0.00157162	+	0.999999i	$0.500500\pi$
$938$	62.0183	+	73.6510i	0.0661176	+	0.0785192i
$939$		0			0
$940$	795.037	+	137.348i	0.845785	+	0.146115i
$941$	242.225			0.257412			0.128706	−	0.991683i	$-0.458918\pi$
$941$	242.225			0.257412			0.128706	+	0.991683i	$0.458918\pi$
$942$		0			0
$943$			519.507i			0.550909i
$944$	318.985	−	895.668i	0.337908	−	0.948801i
$945$		0			0
$946$	1455.92	+	1729.01i	1.53903	+	1.82770i
$947$			1399.75i			1.47809i	0.673655	+	0.739046i	$0.264723\pi$
$947$			1399.75i			1.47809i	−0.673655	+	0.739046i	$0.735277\pi$
$948$		0			0
$949$	548.695			0.578182
$950$	−89.3294	+	75.2204i	−0.0940309	+	0.0791793i
$951$		0			0
$952$	−503.565	−	861.825i	−0.528954	−	0.905278i
$953$	291.283			0.305649			0.152824	−	0.988253i	$-0.451163\pi$
$953$	291.283			0.305649			0.152824	+	0.988253i	$0.451163\pi$
$954$		0			0
$955$			14.7791i			0.0154755i
$956$	849.986	+	146.841i	0.889107	+	0.153599i
$957$		0			0
$958$	762.418	−	641.999i	0.795843	−	0.670145i
$959$			141.705i			0.147764i
$960$		0			0
$961$	177.024			0.184208
$962$	−683.838	−	812.105i	−0.710851	−	0.844184i
$963$		0			0
$964$	163.611	−	947.061i	0.169721	−	0.982429i
$965$	511.849			0.530413
$966$		0			0
$967$			508.329i			0.525676i	0.964840	+	0.262838i	$0.0846585\pi$
$967$			508.329i			0.525676i	−0.964840	+	0.262838i	$0.915341\pi$
$968$	−492.266	+	287.631i	−0.508539	+	0.297140i
$969$		0			0
$970$	220.741	+	262.145i	0.227568	+	0.270253i
$971$			953.174i			0.981641i	0.871261	+	0.490821i	$0.163303\pi$
$971$			953.174i			0.981641i	−0.871261	+	0.490821i	$0.836697\pi$
$972$		0			0
$973$	−351.055			−0.360796
$974$	−720.315	+	606.545i	−0.739543	+	0.622737i
$975$		0			0
$976$	−441.072	−	157.084i	−0.451918	−	0.160947i
$977$	473.264			0.484406			0.242203	−	0.970226i	$-0.422130\pi$
$977$	473.264			0.484406			0.242203	+	0.970226i	$0.422130\pi$
$978$		0			0
$979$		−	2080.89i		−	2.12552i
$980$	76.3514	−	441.959i	0.0779096	−	0.450979i
$981$		0			0
$982$	612.547	−	515.799i	0.623775	−	0.525254i
$983$			1682.10i			1.71119i	0.517645	+	0.855596i	$0.326809\pi$
$983$			1682.10i			1.71119i	−0.517645	+	0.855596i	$0.673191\pi$
$984$		0			0
$985$	324.078			0.329013
$986$	1753.70	+	2082.64i	1.77860	+	2.11221i
$987$		0			0
$988$	−225.449	−	38.9478i	−0.228187	−	0.0394208i
$989$	1499.73			1.51641
$990$		0			0
$991$		−	1191.22i		−	1.20204i	−0.799233	−	0.601021i	$-0.794761\pi$
$991$		−	1191.22i		−	1.20204i	0.799233	−	0.601021i	$-0.205239\pi$
$992$	−839.266	+	313.727i	−0.846034	+	0.316257i
$993$		0			0
$994$	−29.9150	−	35.5261i	−0.0300956	−	0.0357406i
$995$			35.5581i			0.0357368i
$996$		0			0
$997$	−825.539			−0.828023			−0.414011	−	0.910272i	$-0.635873\pi$
$997$	−825.539			−0.828023			−0.414011	+	0.910272i	$0.635873\pi$
$998$	−902.921	+	760.310i	−0.904730	+	0.761833i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.c.343.11		36
3.2	odd	2		228.3.g.a.115.26	yes	36
4.3	odd	2	inner	684.3.g.c.343.12		36
12.11	even	2		228.3.g.a.115.25	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.g.a.115.25	✓	36	12.11	even	2
228.3.g.a.115.26	yes	36	3.2	odd	2
684.3.g.c.343.11		36	1.1	even	1	trivial
684.3.g.c.343.12		36	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28823 - 1.52986i) q^{2} +(-0.680940 + 3.94161i) q^{4} -3.40651 q^{5} +4.01056i q^{7} +(6.90732 - 4.03595i) q^{8} +O(q^{10})\)	\(q+(-1.28823 - 1.52986i) q^{2} +(-0.680940 + 3.94161i) q^{4} -3.40651 q^{5} +4.01056i q^{7} +(6.90732 - 4.03595i) q^{8} +(4.38835 + 5.21148i) q^{10} -13.8660i q^{11} +13.1219 q^{13} +(6.13560 - 5.16652i) q^{14} +(-15.0726 - 5.36801i) q^{16} -31.1103 q^{17} +4.35890i q^{19} +(2.31963 - 13.4271i) q^{20} +(-21.2131 + 17.8626i) q^{22} +18.4001i q^{23} -13.3957 q^{25} +(-16.9040 - 20.0747i) q^{26} +(-15.8081 - 2.73095i) q^{28} +43.7580 q^{29} +27.9996i q^{31} +(11.2047 + 29.9742i) q^{32} +(40.0771 + 47.5944i) q^{34} -13.6620i q^{35} +40.4543 q^{37} +(6.66850 - 5.61525i) q^{38} +(-23.5298 + 13.7485i) q^{40} +28.2340 q^{41} -81.5065i q^{43} +(54.6546 + 9.44195i) q^{44} +(28.1495 - 23.7035i) q^{46} +59.2113i q^{47} +32.9154 q^{49} +(17.2567 + 20.4936i) q^{50} +(-8.93523 + 51.7215i) q^{52} +38.7267 q^{53} +47.2348i q^{55} +(16.1864 + 27.7022i) q^{56} +(-56.3703 - 66.9437i) q^{58} +59.4234i q^{59} +29.2631 q^{61} +(42.8354 - 36.0698i) q^{62} +(31.4222 - 55.7552i) q^{64} -44.6998 q^{65} +12.0039i q^{67} +(21.1842 - 122.625i) q^{68} +(-20.9009 + 17.5998i) q^{70} -5.79017i q^{71} +41.8152 q^{73} +(-52.1143 - 61.8893i) q^{74} +(-17.1811 - 2.96815i) q^{76} +55.6106 q^{77} -0.805318i q^{79} +(51.3450 + 18.2861i) q^{80} +(-36.3718 - 43.1940i) q^{82} +136.639i q^{83} +105.977 q^{85} +(-124.693 + 104.999i) q^{86} +(-55.9627 - 95.7772i) q^{88} +150.071 q^{89} +52.6262i q^{91} +(-72.5260 - 12.5293i) q^{92} +(90.5849 - 76.2776i) q^{94} -14.8486i q^{95} +50.3016 q^{97} +(-42.4025 - 50.3559i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} + 12 q^{4} - 8 q^{5} + 20 q^{8}+O(q^{10}) \) 36 * q - 4 * q^2 + 12 * q^4 - 8 * q^5 + 20 * q^8	\( 36 q - 4 q^{2} + 12 q^{4} - 8 q^{5} + 20 q^{8} + 8 q^{10} - 24 q^{13} + 12 q^{14} + 4 q^{16} + 40 q^{17} + 80 q^{20} + 12 q^{22} + 284 q^{25} + 112 q^{26} - 48 q^{28} - 104 q^{29} - 44 q^{32} + 140 q^{34} - 184 q^{37} + 180 q^{40} + 200 q^{41} - 96 q^{44} - 28 q^{46} - 332 q^{49} - 176 q^{50} + 276 q^{52} - 264 q^{53} + 192 q^{56} - 184 q^{58} + 40 q^{61} + 240 q^{62} - 372 q^{64} - 176 q^{65} + 104 q^{68} - 60 q^{70} + 424 q^{73} + 104 q^{74} + 400 q^{77} - 704 q^{80} + 528 q^{82} - 128 q^{85} - 668 q^{86} - 496 q^{88} + 520 q^{89} + 456 q^{92} - 32 q^{94} - 440 q^{97} + 472 q^{98}+O(q^{100}) \) 36 * q - 4 * q^2 + 12 * q^4 - 8 * q^5 + 20 * q^8 + 8 * q^10 - 24 * q^13 + 12 * q^14 + 4 * q^16 + 40 * q^17 + 80 * q^20 + 12 * q^22 + 284 * q^25 + 112 * q^26 - 48 * q^28 - 104 * q^29 - 44 * q^32 + 140 * q^34 - 184 * q^37 + 180 * q^40 + 200 * q^41 - 96 * q^44 - 28 * q^46 - 332 * q^49 - 176 * q^50 + 276 * q^52 - 264 * q^53 + 192 * q^56 - 184 * q^58 + 40 * q^61 + 240 * q^62 - 372 * q^64 - 176 * q^65 + 104 * q^68 - 60 * q^70 + 424 * q^73 + 104 * q^74 + 400 * q^77 - 704 * q^80 + 528 * q^82 - 128 * q^85 - 668 * q^86 - 496 * q^88 + 520 * q^89 + 456 * q^92 - 32 * q^94 - 440 * q^97 + 472 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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