LMFDB - Embedded newform 684.3.g.b.343.14

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + \cdots + 16384 $ x^14 - 2x^13 + x^12 + 14x^11 - 42x^10 + 28x^9 + 132x^8 - 440x^7 + 528x^6 + 448x^5 - 2688x^4 + 3584x^3 + 1024x^2 - 8192x + 16384
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.14
Root			$-1.92254 - 0.551226i$ of defining polynomial
Character	$\chi$	$=$	684.343
Dual form			684.3.g.b.343.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92254 + 0.551226i) q^{2} +(3.39230 + 2.11950i) q^{4} +2.32715 q^{5} +8.62924i q^{7} +(5.35350 + 5.94475i) q^{8} +O(q^{10})$	\(q+(1.92254 + 0.551226i) q^{2} +(3.39230 + 2.11950i) q^{4} +2.32715 q^{5} +8.62924i q^{7} +(5.35350 + 5.94475i) q^{8} +(4.47404 + 1.28279i) q^{10} -19.2717i q^{11} +13.8067 q^{13} +(-4.75666 + 16.5900i) q^{14} +(7.01540 + 14.3800i) q^{16} +12.5180 q^{17} +4.35890i q^{19} +(7.89440 + 4.93241i) q^{20} +(10.6231 - 37.0506i) q^{22} +37.4981i q^{23} -19.5844 q^{25} +(26.5438 + 7.61058i) q^{26} +(-18.2897 + 29.2730i) q^{28} +6.36930 q^{29} -5.44851i q^{31} +(5.56075 + 31.5131i) q^{32} +(24.0663 + 6.90025i) q^{34} +20.0816i q^{35} +20.9250 q^{37} +(-2.40274 + 8.38015i) q^{38} +(12.4584 + 13.8343i) q^{40} -72.8337 q^{41} +10.1553i q^{43} +(40.8465 - 65.3755i) q^{44} +(-20.6699 + 72.0914i) q^{46} +32.4450i q^{47} -25.4638 q^{49} +(-37.6517 - 10.7954i) q^{50} +(46.8363 + 29.2633i) q^{52} +42.9339 q^{53} -44.8482i q^{55} +(-51.2987 + 46.1966i) q^{56} +(12.2452 + 3.51092i) q^{58} -38.9728i q^{59} +25.5611 q^{61} +(3.00336 - 10.4750i) q^{62} +(-6.68010 + 63.6504i) q^{64} +32.1302 q^{65} -65.3183i q^{67} +(42.4648 + 26.5320i) q^{68} +(-11.0695 + 38.6076i) q^{70} +18.7557i q^{71} +72.8251 q^{73} +(40.2292 + 11.5344i) q^{74} +(-9.23871 + 14.7867i) q^{76} +166.300 q^{77} -139.874i q^{79} +(16.3259 + 33.4644i) q^{80} +(-140.026 - 40.1478i) q^{82} -94.7116i q^{83} +29.1313 q^{85} +(-5.59789 + 19.5240i) q^{86} +(114.566 - 103.171i) q^{88} -33.3546 q^{89} +119.141i q^{91} +(-79.4773 + 127.205i) q^{92} +(-17.8845 + 62.3766i) q^{94} +10.1438i q^{95} -150.817 q^{97} +(-48.9551 - 14.0363i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8	$ 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98}+O(q^{100}) $ 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8 - 12 * q^10 + 54 * q^13 - 30 * q^14 + 58 * q^16 - 34 * q^17 - 32 * q^20 + 36 * q^22 - 86 * q^25 + 16 * q^26 + 18 * q^28 - 54 * q^29 - 72 * q^32 - 82 * q^34 + 100 * q^37 - 148 * q^40 - 224 * q^41 + 96 * q^44 + 46 * q^46 - 220 * q^49 + 58 * q^50 - 288 * q^52 - 14 * q^53 - 12 * q^56 - 72 * q^58 + 28 * q^61 - 396 * q^62 - 118 * q^64 + 472 * q^65 - 30 * q^68 + 156 * q^70 + 70 * q^73 + 224 * q^74 - 228 * q^77 + 348 * q^80 - 400 * q^82 + 48 * q^85 + 124 * q^86 + 472 * q^88 - 126 * q^92 - 88 * q^94 + 308 * q^97 - 68 * 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 $

$2$	1.92254	+	0.551226i	0.961269	+	0.275613i
$2$	1.92254	+	0.551226i	0.961269	+	0.275613i
$3$		0			0
$3$		0			0
$4$	3.39230	+	2.11950i	0.848075	+	0.529876i
$5$	2.32715			0.465431			0.232715	−	0.972545i	$-0.425239\pi$
$5$	2.32715			0.465431			0.232715	+	0.972545i	$0.425239\pi$
$6$		0			0
$7$			8.62924i			1.23275i	0.787453	+	0.616374i	$0.211399\pi$
$7$			8.62924i			1.23275i	−0.787453	+	0.616374i	$0.788601\pi$
$8$	5.35350	+	5.94475i	0.669187	+	0.743094i
$9$		0			0
$10$	4.47404	+	1.28279i	0.447404	+	0.128279i
$11$		−	19.2717i		−	1.75197i	−0.482334	−	0.875987i	$-0.660211\pi$
$11$		−	19.2717i		−	1.75197i	0.482334	−	0.875987i	$-0.339789\pi$
$12$		0			0
$13$	13.8067			1.06205			0.531025	−	0.847356i	$-0.321807\pi$
$13$	13.8067			1.06205			0.531025	+	0.847356i	$0.321807\pi$
$14$	−4.75666	+	16.5900i	−0.339761	+	1.18500i
$15$		0			0
$16$	7.01540	+	14.3800i	0.438463	+	0.898749i
$17$	12.5180			0.736353			0.368177	−	0.929756i	$-0.379982\pi$
$17$	12.5180			0.736353			0.368177	+	0.929756i	$0.379982\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	7.89440	+	4.93241i	0.394720	+	0.246621i
$21$		0			0
$22$	10.6231	−	37.0506i	0.482867	−	1.68412i
$23$			37.4981i			1.63035i	0.579214	+	0.815175i	$0.303360\pi$
$23$			37.4981i			1.63035i	−0.579214	+	0.815175i	$0.696640\pi$
$24$		0			0
$25$	−19.5844			−0.783374
$26$	26.5438	+	7.61058i	1.02092	+	0.292715i
$27$		0			0
$28$	−18.2897	+	29.2730i	−0.653204	+	1.04546i
$29$	6.36930			0.219631			0.109816	−	0.993952i	$-0.464974\pi$
$29$	6.36930			0.219631			0.109816	+	0.993952i	$0.464974\pi$
$30$		0			0
$31$		−	5.44851i		−	0.175758i	−0.996131	−	0.0878791i	$-0.971991\pi$
$31$		−	5.44851i		−	0.175758i	0.996131	−	0.0878791i	$-0.0280089\pi$
$32$	5.56075	+	31.5131i	0.173774	+	0.984786i
$33$		0			0
$34$	24.0663	+	6.90025i	0.707833	+	0.202948i
$35$			20.0816i			0.573759i
$36$		0			0
$37$	20.9250			0.565542			0.282771	−	0.959187i	$-0.408746\pi$
$37$	20.9250			0.565542			0.282771	+	0.959187i	$0.408746\pi$
$38$	−2.40274	+	8.38015i	−0.0632299	+	0.220530i
$39$		0			0
$40$	12.4584	+	13.8343i	0.311460	+	0.345859i
$41$	−72.8337			−1.77643			−0.888216	−	0.459425i	$-0.848055\pi$
$41$	−72.8337			−1.77643			−0.888216	+	0.459425i	$0.848055\pi$
$42$		0			0
$43$			10.1553i			0.236171i	0.993003	+	0.118085i	$0.0376757\pi$
$43$			10.1553i			0.236171i	−0.993003	+	0.118085i	$0.962324\pi$
$44$	40.8465	−	65.3755i	0.928329	−	1.48581i
$45$		0			0
$46$	−20.6699	+	72.0914i	−0.449346	+	1.56721i
$47$			32.4450i			0.690318i	0.938544	+	0.345159i	$0.112175\pi$
$47$			32.4450i			0.690318i	−0.938544	+	0.345159i	$0.887825\pi$
$48$		0			0
$49$	−25.4638			−0.519669
$50$	−37.6517	−	10.7954i	−0.753033	−	0.215908i
$51$		0			0
$52$	46.8363	+	29.2633i	0.900698	+	0.562755i
$53$	42.9339			0.810074			0.405037	−	0.914300i	$-0.367259\pi$
$53$	42.9339			0.810074			0.405037	+	0.914300i	$0.367259\pi$
$54$		0			0
$55$		−	44.8482i		−	0.815423i
$56$	−51.2987	+	46.1966i	−0.916048	+	0.824940i
$57$		0			0
$58$	12.2452	+	3.51092i	0.211125	+	0.0605332i
$59$		−	38.9728i		−	0.660556i	−0.943884	−	0.330278i	$-0.892858\pi$
$59$		−	38.9728i		−	0.660556i	0.943884	−	0.330278i	$-0.107142\pi$
$60$		0			0
$61$	25.5611			0.419034			0.209517	−	0.977805i	$-0.432811\pi$
$61$	25.5611			0.419034			0.209517	+	0.977805i	$0.432811\pi$
$62$	3.00336	−	10.4750i	0.0484412	−	0.168951i
$63$		0			0
$64$	−6.68010	+	63.6504i	−0.104377	+	0.994538i
$65$	32.1302			0.494311
$66$		0			0
$67$		−	65.3183i		−	0.974900i	−0.873151	−	0.487450i	$-0.837927\pi$
$67$		−	65.3183i		−	0.974900i	0.873151	−	0.487450i	$-0.162073\pi$
$68$	42.4648	+	26.5320i	0.624483	+	0.390176i
$69$		0			0
$70$	−11.0695	+	38.6076i	−0.158135	+	0.551537i
$71$			18.7557i			0.264165i	0.991239	+	0.132083i	$0.0421665\pi$
$71$			18.7557i			0.264165i	−0.991239	+	0.132083i	$0.957834\pi$
$72$		0			0
$73$	72.8251			0.997604			0.498802	−	0.866716i	$-0.333773\pi$
$73$	72.8251			0.997604			0.498802	+	0.866716i	$0.333773\pi$
$74$	40.2292	+	11.5344i	0.543638	+	0.155871i
$75$		0			0
$76$	−9.23871	+	14.7867i	−0.121562	+	0.194562i
$77$	166.300			2.15974
$78$		0			0
$79$		−	139.874i		−	1.77056i	−0.465060	−	0.885279i	$-0.653967\pi$
$79$		−	139.874i		−	1.77056i	0.465060	−	0.885279i	$-0.346033\pi$
$80$	16.3259	+	33.4644i	0.204074	+	0.418306i
$81$		0			0
$82$	−140.026	−	40.1478i	−1.70763	−	0.489608i
$83$		−	94.7116i		−	1.14110i	−0.821262	−	0.570552i	$-0.806729\pi$
$83$		−	94.7116i		−	1.14110i	0.821262	−	0.570552i	$-0.193271\pi$
$84$		0			0
$85$	29.1313			0.342721
$86$	−5.59789	+	19.5240i	−0.0650917	+	0.227024i
$87$		0			0
$88$	114.566	−	103.171i	1.30188	−	1.17240i
$89$	−33.3546			−0.374770			−0.187385	−	0.982287i	$-0.560001\pi$
$89$	−33.3546			−0.374770			−0.187385	+	0.982287i	$0.560001\pi$
$90$		0			0
$91$			119.141i			1.30924i
$92$	−79.4773	+	127.205i	−0.863884	+	1.38266i
$93$		0			0
$94$	−17.8845	+	62.3766i	−0.190261	+	0.663581i
$95$			10.1438i			0.106777i
$96$		0			0
$97$	−150.817			−1.55482			−0.777408	−	0.628996i	$-0.783466\pi$
$97$	−150.817			−1.55482			−0.777408	+	0.628996i	$0.783466\pi$
$98$	−48.9551	−	14.0363i	−0.499542	−	0.143228i
$99$		0			0
$100$	−66.4360	−	41.5091i	−0.664360	−	0.415091i
$101$	−77.7745			−0.770045			−0.385022	−	0.922907i	$-0.625806\pi$
$101$	−77.7745			−0.770045			−0.385022	+	0.922907i	$0.625806\pi$
$102$		0			0
$103$		−	14.9481i		−	0.145127i	−0.997364	−	0.0725637i	$-0.976882\pi$
$103$		−	14.9481i		−	0.145127i	0.997364	−	0.0725637i	$-0.0231180\pi$
$104$	73.9139	+	82.0771i	0.710711	+	0.789203i
$105$		0			0
$106$	82.5420	+	23.6663i	0.778698	+	0.223267i
$107$			80.5205i			0.752528i	0.926512	+	0.376264i	$0.122792\pi$
$107$			80.5205i			0.752528i	−0.926512	+	0.376264i	$0.877208\pi$
$108$		0			0
$109$	53.8512			0.494048			0.247024	−	0.969009i	$-0.420547\pi$
$109$	53.8512			0.494048			0.247024	+	0.969009i	$0.420547\pi$
$110$	24.7215	−	86.2224i	0.224741	−	0.783840i
$111$		0			0
$112$	−124.088	+	60.5376i	−1.10793	+	0.540514i
$113$	−105.921			−0.937355			−0.468677	−	0.883369i	$-0.655269\pi$
$113$	−105.921			−0.937355			−0.468677	+	0.883369i	$0.655269\pi$
$114$		0			0
$115$			87.2638i			0.758815i
$116$	21.6066	+	13.4998i	0.186264	+	0.116377i
$117$		0			0
$118$	21.4828	−	74.9266i	0.182058	−	0.634972i
$119$			108.021i			0.907739i
$120$		0			0
$121$	−250.399			−2.06941
$122$	49.1421	+	14.0899i	0.402804	+	0.115491i
$123$		0			0
$124$	11.5481	−	18.4830i	0.0931301	−	0.149056i
$125$	−103.755			−0.830037
$126$		0			0
$127$			17.1409i			0.134968i	0.997720	+	0.0674839i	$0.0214971\pi$
$127$			17.1409i			0.134968i	−0.997720	+	0.0674839i	$0.978503\pi$
$128$	−47.9285	+	118.688i	−0.374441	+	0.927251i
$129$		0			0
$130$	61.7715	+	17.7110i	0.475166	+	0.136238i
$131$		−	229.336i		−	1.75066i	−0.483526	−	0.875330i	$-0.660644\pi$
$131$		−	229.336i		−	1.75066i	0.483526	−	0.875330i	$-0.339356\pi$
$132$		0			0
$133$	−37.6140			−0.282812
$134$	36.0051	−	125.577i	0.268695	−	0.937141i
$135$		0			0
$136$	67.0151	+	74.4164i	0.492758	+	0.547179i
$137$	120.567			0.880054			0.440027	−	0.897985i	$-0.354969\pi$
$137$	120.567			0.880054			0.440027	+	0.897985i	$0.354969\pi$
$138$		0			0
$139$		−	145.864i		−	1.04938i	−0.851292	−	0.524692i	$-0.824181\pi$
$139$		−	145.864i		−	1.04938i	0.851292	−	0.524692i	$-0.175819\pi$
$140$	−42.5630	+	68.1227i	−0.304021	+	0.486591i
$141$		0			0
$142$	−10.3387	+	36.0586i	−0.0728074	+	0.253934i
$143$		−	266.078i		−	1.86069i
$144$		0			0
$145$	14.8223			0.102223
$146$	140.009	+	40.1431i	0.958966	+	0.274953i
$147$		0			0
$148$	70.9840	+	44.3507i	0.479622	+	0.299667i
$149$	−19.2547			−0.129226			−0.0646132	−	0.997910i	$-0.520581\pi$
$149$	−19.2547			−0.129226			−0.0646132	+	0.997910i	$0.520581\pi$
$150$		0			0
$151$		−	165.526i		−	1.09620i	−0.836414	−	0.548099i	$-0.815352\pi$
$151$		−	165.526i		−	1.09620i	0.836414	−	0.548099i	$-0.184648\pi$
$152$	−25.9126	+	23.3354i	−0.170477	+	0.153522i
$153$		0			0
$154$	319.719	+	91.6690i	2.07609	+	0.595253i
$155$		−	12.6795i		−	0.0818033i
$156$		0			0
$157$	149.449			0.951907			0.475954	−	0.879470i	$-0.342103\pi$
$157$	149.449			0.951907			0.475954	+	0.879470i	$0.342103\pi$
$158$	77.1022	−	268.913i	0.487989	−	1.70198i
$159$		0			0
$160$	12.9407	+	73.3359i	0.0808795	+	0.458349i
$161$	−323.580			−2.00981
$162$		0			0
$163$		−	146.763i		−	0.900384i	−0.892932	−	0.450192i	$-0.851356\pi$
$163$		−	146.763i		−	0.900384i	0.892932	−	0.450192i	$-0.148644\pi$
$164$	−247.074	−	154.371i	−1.50655	−	0.941289i
$165$		0			0
$166$	52.2075	−	182.087i	0.314503	−	1.09691i
$167$			213.493i			1.27840i	0.769040	+	0.639201i	$0.220735\pi$
$167$			213.493i			1.27840i	−0.769040	+	0.639201i	$0.779265\pi$
$168$		0			0
$169$	21.6237			0.127951
$170$	56.0061	+	16.0579i	0.329447	+	0.0944584i
$171$		0			0
$172$	−21.5243	+	34.4500i	−0.125141	+	0.200291i
$173$	280.715			1.62263			0.811314	−	0.584610i	$-0.198753\pi$
$173$	280.715			1.62263			0.811314	+	0.584610i	$0.198753\pi$
$174$		0			0
$175$		−	168.998i		−	0.965704i
$176$	277.127	−	135.199i	1.57459	−	0.768175i
$177$		0			0
$178$	−64.1254	−	18.3859i	−0.360255	−	0.103292i
$179$		−	35.1878i		−	0.196580i	−0.995158	−	0.0982899i	$-0.968663\pi$
$179$		−	35.1878i		−	0.196580i	0.995158	−	0.0982899i	$-0.0313372\pi$
$180$		0			0
$181$	−345.539			−1.90906			−0.954529	−	0.298120i	$-0.903641\pi$
$181$	−345.539			−1.90906			−0.954529	+	0.298120i	$0.903641\pi$
$182$	−65.6736	+	229.053i	−0.360844	+	1.25853i
$183$		0			0
$184$	−222.917	+	200.746i	−1.21150	+	1.09101i
$185$	48.6958			0.263220
$186$		0			0
$187$		−	241.244i		−	1.29007i
$188$	−68.7672	+	110.063i	−0.365783	+	0.585442i
$189$		0			0
$190$	−5.59154	+	19.5019i	−0.0294292	+	0.102642i
$191$		−	100.233i		−	0.524782i	−0.964962	−	0.262391i	$-0.915489\pi$
$191$		−	100.233i		−	0.524782i	0.964962	−	0.262391i	$-0.0845110\pi$
$192$		0			0
$193$	168.119			0.871085			0.435543	−	0.900168i	$-0.356557\pi$
$193$	168.119			0.871085			0.435543	+	0.900168i	$0.356557\pi$
$194$	−289.952	−	83.1343i	−1.49460	−	0.428528i
$195$		0			0
$196$	−86.3808	−	53.9706i	−0.440719	−	0.275360i
$197$	−216.705			−1.10002			−0.550012	−	0.835157i	$-0.685377\pi$
$197$	−216.705			−1.10002			−0.550012	+	0.835157i	$0.685377\pi$
$198$		0			0
$199$		−	82.2545i		−	0.413339i	−0.978411	−	0.206670i	$-0.933738\pi$
$199$		−	82.2545i		−	0.413339i	0.978411	−	0.206670i	$-0.0662625\pi$
$200$	−104.845	−	116.424i	−0.524224	−	0.582121i
$201$		0			0
$202$	−149.524	−	42.8713i	−0.740220	−	0.212234i
$203$			54.9623i			0.270750i
$204$		0			0
$205$	−169.495			−0.826806
$206$	8.23978	−	28.7383i	0.0399990	−	0.139506i
$207$		0			0
$208$	96.8592	+	198.540i	0.465669	+	0.954517i
$209$	84.0035			0.401931
$210$		0			0
$211$		−	16.4195i		−	0.0778173i	−0.999243	−	0.0389087i	$-0.987612\pi$
$211$		−	16.4195i		−	0.0778173i	0.999243	−	0.0389087i	$-0.0123881\pi$
$212$	145.645	+	90.9986i	0.687003	+	0.429239i
$213$		0			0
$214$	−44.3850	+	154.804i	−0.207407	+	0.723382i
$215$			23.6331i			0.109921i
$216$		0			0
$217$	47.0165			0.216666
$218$	103.531	+	29.6842i	0.474913	+	0.136166i
$219$		0			0
$220$	95.0561	−	152.139i	0.432073	−	0.691540i
$221$	172.832			0.782044
$222$		0			0
$223$			195.225i			0.875450i	0.899109	+	0.437725i	$0.144216\pi$
$223$			195.225i			0.875450i	−0.899109	+	0.437725i	$0.855784\pi$
$224$	−271.934	+	47.9851i	−1.21399	+	0.214219i
$225$		0			0
$226$	−203.637	−	58.3864i	−0.901050	−	0.258347i
$227$		−	305.403i		−	1.34539i	−0.739920	−	0.672695i	$-0.765137\pi$
$227$		−	305.403i		−	1.34539i	0.739920	−	0.672695i	$-0.234863\pi$
$228$		0			0
$229$	−229.686			−1.00300			−0.501499	−	0.865158i	$-0.667218\pi$
$229$	−229.686			−1.00300			−0.501499	+	0.865158i	$0.667218\pi$
$230$	−48.1020	+	167.768i	−0.209139	+	0.729425i
$231$		0			0
$232$	34.0981	+	37.8639i	0.146974	+	0.163207i
$233$	−187.667			−0.805436			−0.402718	−	0.915324i	$-0.631935\pi$
$233$	−187.667			−0.805436			−0.402718	+	0.915324i	$0.631935\pi$
$234$		0			0
$235$			75.5044i			0.321295i
$236$	82.6030	−	132.207i	0.350013	−	0.560201i
$237$		0			0
$238$	−59.5439	+	207.674i	−0.250184	+	0.872581i
$239$		−	69.8504i		−	0.292261i	−0.989265	−	0.146130i	$-0.953318\pi$
$239$		−	69.8504i		−	0.292261i	0.989265	−	0.146130i	$-0.0466819\pi$
$240$		0			0
$241$	297.561			1.23469			0.617346	−	0.786691i	$-0.288208\pi$
$241$	297.561			1.23469			0.617346	+	0.786691i	$0.288208\pi$
$242$	−481.402	−	138.026i	−1.98926	−	0.570357i
$243$		0			0
$244$	86.7109	+	54.1768i	0.355372	+	0.222036i
$245$	−59.2582			−0.241870
$246$		0			0
$247$			60.1818i			0.243651i
$248$	32.3900	−	29.1686i	0.130605	−	0.117615i
$249$		0			0
$250$	−199.472	−	57.1922i	−0.797889	−	0.228769i
$251$		−	36.4667i		−	0.145286i	−0.997358	−	0.0726429i	$-0.976857\pi$
$251$		−	36.4667i		−	0.145286i	0.997358	−	0.0726429i	$-0.0231433\pi$
$252$		0			0
$253$	722.652			2.85633
$254$	−9.44851	+	32.9540i	−0.0371988	+	0.129740i
$255$		0			0
$256$	−157.568	+	201.763i	−0.615501	+	0.788136i
$257$	175.943			0.684604			0.342302	−	0.939590i	$-0.388793\pi$
$257$	175.943			0.684604			0.342302	+	0.939590i	$0.388793\pi$
$258$		0			0
$259$			180.567i			0.697171i
$260$	108.995	+	68.1001i	0.419213	+	0.261924i
$261$		0			0
$262$	126.416	−	440.908i	0.482504	−	1.68285i
$263$		−	444.887i		−	1.69158i	−0.533512	−	0.845792i	$-0.679128\pi$
$263$		−	444.887i		−	1.69158i	0.533512	−	0.845792i	$-0.320872\pi$
$264$		0			0
$265$	99.9138			0.377033
$266$	−72.3143	−	20.7338i	−0.271858	−	0.0779466i
$267$		0			0
$268$	138.442	−	221.579i	0.516576	−	0.826788i
$269$	−149.744			−0.556670			−0.278335	−	0.960484i	$-0.589783\pi$
$269$	−149.744			−0.556670			−0.278335	+	0.960484i	$0.589783\pi$
$270$		0			0
$271$			439.685i			1.62245i	0.584731	+	0.811227i	$0.301200\pi$
$271$			439.685i			1.62245i	−0.584731	+	0.811227i	$0.698800\pi$
$272$	87.8188	+	180.009i	0.322863	+	0.661797i
$273$		0			0
$274$	231.795	+	66.4598i	0.845968	+	0.242554i
$275$			377.424i			1.37245i
$276$		0			0
$277$	83.2452			0.300524			0.150262	−	0.988646i	$-0.451988\pi$
$277$	83.2452			0.300524			0.150262	+	0.988646i	$0.451988\pi$
$278$	80.4042	−	280.430i	0.289224	−	1.00874i
$279$		0			0
$280$	−119.380	+	107.507i	−0.426357	+	0.383952i
$281$	12.9851			0.0462105			0.0231052	−	0.999733i	$-0.492645\pi$
$281$	12.9851			0.0462105			0.0231052	+	0.999733i	$0.492645\pi$
$282$		0			0
$283$			111.022i			0.392303i	0.980574	+	0.196152i	$0.0628445\pi$
$283$			111.022i			0.392303i	−0.980574	+	0.196152i	$0.937156\pi$
$284$	−39.7529	+	63.6251i	−0.139975	+	0.224032i
$285$		0			0
$286$	146.669	−	511.545i	0.512829	−	1.78862i
$287$		−	628.500i		−	2.18990i
$288$		0			0
$289$	−132.300			−0.457784
$290$	28.4965	+	8.17046i	0.0982639	+	0.0281740i
$291$		0			0
$292$	247.045	+	154.353i	0.846043	+	0.528607i
$293$	141.572			0.483179			0.241590	−	0.970378i	$-0.422331\pi$
$293$	141.572			0.483179			0.241590	+	0.970378i	$0.422331\pi$
$294$		0			0
$295$		−	90.6956i		−	0.307443i
$296$	112.022	+	124.394i	0.378453	+	0.420251i
$297$		0			0
$298$	−37.0179	−	10.6137i	−0.124221	−	0.0356165i
$299$			517.723i			1.73151i
$300$		0			0
$301$	−87.6329			−0.291139
$302$	91.2421	−	318.229i	0.302126	−	1.05374i
$303$		0			0
$304$	−62.6809	+	30.5794i	−0.206187	+	0.100590i
$305$	59.4846			0.195031
$306$		0			0
$307$			357.744i			1.16529i	0.812727	+	0.582645i	$0.197982\pi$
$307$			357.744i			1.16529i	−0.812727	+	0.582645i	$0.802018\pi$
$308$	564.141	+	352.474i	1.83163	+	1.14440i
$309$		0			0
$310$	6.98927	−	24.3768i	0.0225460	−	0.0786349i
$311$			472.383i			1.51892i	0.650557	+	0.759458i	$0.274536\pi$
$311$			472.383i			1.51892i	−0.650557	+	0.759458i	$0.725464\pi$
$312$		0			0
$313$	63.7596			0.203705			0.101852	−	0.994800i	$-0.467523\pi$
$313$	63.7596			0.203705			0.101852	+	0.994800i	$0.467523\pi$
$314$	287.322	+	82.3804i	0.915039	+	0.262358i
$315$		0			0
$316$	296.464	−	474.495i	0.938177	−	1.50157i
$317$	−198.721			−0.626880			−0.313440	−	0.949608i	$-0.601481\pi$
$317$	−198.721			−0.626880			−0.313440	+	0.949608i	$0.601481\pi$
$318$		0			0
$319$		−	122.747i		−	0.384788i
$320$	−15.5456	+	148.124i	−0.0485801	+	0.462888i
$321$		0			0
$322$	−622.094	−	178.366i	−1.93197	−	0.553930i
$323$			54.5647i			0.168931i
$324$		0			0
$325$	−270.394			−0.831983
$326$	80.8993	−	282.156i	0.248157	−	0.865511i
$327$		0			0
$328$	−389.915	−	432.978i	−1.18877	−	1.32006i
$329$	−279.975			−0.850989
$330$		0			0
$331$		−	438.736i		−	1.32549i	−0.748846	−	0.662744i	$-0.769392\pi$
$331$		−	438.736i		−	1.32549i	0.748846	−	0.662744i	$-0.230608\pi$
$332$	200.742	−	321.290i	0.604644	−	0.967742i
$333$		0			0
$334$	−117.683	+	410.449i	−0.352344	+	1.22889i
$335$		−	152.006i		−	0.453748i
$336$		0			0
$337$	−538.699			−1.59851			−0.799257	−	0.600989i	$-0.794773\pi$
$337$	−538.699			−1.59851			−0.799257	+	0.600989i	$0.794773\pi$
$338$	41.5724	+	11.9196i	0.122995	+	0.0352650i
$339$		0			0
$340$	98.8222	+	61.7440i	0.290653	+	0.181600i
$341$	−105.002			−0.307924
$342$		0			0
$343$			203.100i			0.592127i
$344$	−60.3710	+	54.3666i	−0.175497	+	0.158043i
$345$		0			0
$346$	539.685	+	154.737i	1.55978	+	0.447217i
$347$			584.405i			1.68417i	0.539349	+	0.842083i	$0.318671\pi$
$347$			584.405i			1.68417i	−0.539349	+	0.842083i	$0.681329\pi$
$348$		0			0
$349$	−300.832			−0.861983			−0.430991	−	0.902356i	$-0.641836\pi$
$349$	−300.832			−0.861983			−0.430991	+	0.902356i	$0.641836\pi$
$350$	93.1561	−	324.905i	0.266160	−	0.928301i
$351$		0			0
$352$	607.312	−	107.165i	1.72532	−	0.304447i
$353$	316.023			0.895250			0.447625	−	0.894221i	$-0.352270\pi$
$353$	316.023			0.895250			0.447625	+	0.894221i	$0.352270\pi$
$354$		0			0
$355$			43.6475i			0.122951i
$356$	−113.149	−	70.6951i	−0.317833	−	0.198582i
$357$		0			0
$358$	19.3964	−	67.6498i	0.0541799	−	0.188966i
$359$			116.055i			0.323272i	0.986850	+	0.161636i	$0.0516770\pi$
$359$			116.055i			0.323272i	−0.986850	+	0.161636i	$0.948323\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	−664.312	−	190.470i	−1.83512	−	0.526161i
$363$		0			0
$364$	−252.520	+	404.162i	−0.693736	+	1.11033i
$365$	169.475			0.464316
$366$		0			0
$367$		−	67.8773i		−	0.184952i	−0.995715	−	0.0924759i	$-0.970522\pi$
$367$		−	67.8773i		−	0.184952i	0.995715	−	0.0924759i	$-0.0294781\pi$
$368$	−539.222	+	263.064i	−1.46528	+	0.714848i
$369$		0			0
$370$	93.6195	+	26.8424i	0.253026	+	0.0725470i
$371$			370.487i			0.998617i
$372$		0			0
$373$	−267.337			−0.716721			−0.358361	−	0.933583i	$-0.616664\pi$
$373$	−267.337			−0.716721			−0.358361	+	0.933583i	$0.616664\pi$
$374$	132.980	−	463.800i	0.355561	−	1.24011i
$375$		0			0
$376$	−192.877	+	173.694i	−0.512971	+	0.461952i
$377$	87.9388			0.233259
$378$		0			0
$379$		−	372.834i		−	0.983731i	−0.870671	−	0.491866i	$-0.836315\pi$
$379$		−	372.834i		−	0.983731i	0.870671	−	0.491866i	$-0.163685\pi$
$380$	−21.4999	+	34.4109i	−0.0565786	+	0.0905550i
$381$		0			0
$382$	55.2512	−	192.702i	0.144637	−	0.504457i
$383$		−	19.6246i		−	0.0512392i	−0.999672	−	0.0256196i	$-0.991844\pi$
$383$		−	19.6246i		−	0.0512392i	0.999672	−	0.0256196i	$-0.00815587\pi$
$384$		0			0
$385$	387.006			1.00521
$386$	323.216	+	92.6718i	0.837347	+	0.240082i
$387$		0			0
$388$	−511.617	−	319.658i	−1.31860	−	0.823860i
$389$	−198.727			−0.510867			−0.255434	−	0.966827i	$-0.582218\pi$
$389$	−198.727			−0.510867			−0.255434	+	0.966827i	$0.582218\pi$
$390$		0			0
$391$			469.401i			1.20051i
$392$	−136.320	−	151.376i	−0.347756	−	0.386163i
$393$		0			0
$394$	−416.623	−	119.453i	−1.05742	−	0.303181i
$395$		−	325.509i		−	0.824072i
$396$		0			0
$397$	295.448			0.744203			0.372101	−	0.928192i	$-0.378637\pi$
$397$	295.448			0.744203			0.372101	+	0.928192i	$0.378637\pi$
$398$	45.3408	−	158.137i	0.113922	−	0.397330i
$399$		0			0
$400$	−137.392	−	281.623i	−0.343480	−	0.704057i
$401$	63.9986			0.159597			0.0797987	−	0.996811i	$-0.474572\pi$
$401$	63.9986			0.159597			0.0797987	+	0.996811i	$0.474572\pi$
$402$		0			0
$403$		−	75.2256i		−	0.186664i
$404$	−263.835	−	164.843i	−0.653056	−	0.408028i
$405$		0			0
$406$	−30.2966	+	105.667i	−0.0746222	+	0.260264i
$407$		−	403.262i		−	0.990815i
$408$		0			0
$409$	504.473			1.23343			0.616715	−	0.787186i	$-0.288463\pi$
$409$	504.473			1.23343			0.616715	+	0.787186i	$0.288463\pi$
$410$	−325.861	−	93.4302i	−0.794783	−	0.227878i
$411$		0			0
$412$	31.6826	−	50.7085i	0.0768995	−	0.123079i
$413$	336.306			0.814299
$414$		0			0
$415$		−	220.408i		−	0.531105i
$416$	76.7754	+	435.091i	0.184556	+	1.04589i
$417$		0			0
$418$	161.500	+	46.3049i	0.386363	+	0.110777i
$419$			470.299i			1.12243i	0.827670	+	0.561215i	$0.189666\pi$
$419$			470.299i			1.12243i	−0.827670	+	0.561215i	$0.810334\pi$
$420$		0			0
$421$	−470.034			−1.11647			−0.558235	−	0.829683i	$-0.688521\pi$
$421$	−470.034			−1.11647			−0.558235	+	0.829683i	$0.688521\pi$
$422$	9.05083	−	31.5670i	0.0214475	−	0.0748033i
$423$		0			0
$424$	229.847	+	255.231i	0.542091	+	0.601961i
$425$	−245.157			−0.576840
$426$		0			0
$427$			220.573i			0.516564i
$428$	−170.664	+	273.150i	−0.398747	+	0.638201i
$429$		0			0
$430$	−13.0271	+	45.4354i	−0.0302957	+	0.105664i
$431$			224.005i			0.519733i	0.965645	+	0.259866i	$0.0836785\pi$
$431$			224.005i			0.519733i	−0.965645	+	0.259866i	$0.916321\pi$
$432$		0			0
$433$	180.128			0.415999			0.207999	−	0.978129i	$-0.433305\pi$
$433$	180.128			0.415999			0.207999	+	0.978129i	$0.433305\pi$
$434$	90.3909	+	25.9167i	0.208274	+	0.0597159i
$435$		0			0
$436$	182.680	+	114.138i	0.418990	+	0.261784i
$437$	−163.450			−0.374028
$438$		0			0
$439$		−	590.004i		−	1.34397i	−0.740563	−	0.671987i	$-0.765441\pi$
$439$		−	590.004i		−	1.34397i	0.740563	−	0.671987i	$-0.234559\pi$
$440$	266.612	−	240.095i	0.605936	−	0.545671i
$441$		0			0
$442$	332.276	+	95.2693i	0.751755	+	0.215541i
$443$			157.459i			0.355439i	0.984081	+	0.177719i	$0.0568720\pi$
$443$			157.459i			0.355439i	−0.984081	+	0.177719i	$0.943128\pi$
$444$		0			0
$445$	−77.6212			−0.174430
$446$	−107.613	+	375.328i	−0.241285	+	0.841543i
$447$		0			0
$448$	−549.255	−	57.6442i	−1.22602	−	0.128670i
$449$	715.434			1.59339			0.796697	−	0.604379i	$-0.206579\pi$
$449$	715.434			1.59339			0.796697	+	0.604379i	$0.206579\pi$
$450$		0			0
$451$			1403.63i			3.11226i
$452$	−359.316	−	224.500i	−0.794947	−	0.496682i
$453$		0			0
$454$	168.346	−	587.149i	0.370807	−	1.29328i
$455$			277.259i			0.609361i
$456$		0			0
$457$	31.3497			0.0685988			0.0342994	−	0.999412i	$-0.489080\pi$
$457$	31.3497			0.0685988			0.0342994	+	0.999412i	$0.489080\pi$
$458$	−441.581	−	126.609i	−0.964150	−	0.276439i
$459$		0			0
$460$	−184.956	+	296.025i	−0.402078	+	0.643532i
$461$	−368.719			−0.799824			−0.399912	−	0.916554i	$-0.630959\pi$
$461$	−368.719			−0.799824			−0.399912	+	0.916554i	$0.630959\pi$
$462$		0			0
$463$			817.405i			1.76545i	0.469887	+	0.882726i	$0.344295\pi$
$463$			817.405i			1.76545i	−0.469887	+	0.882726i	$0.655705\pi$
$464$	44.6832	+	91.5905i	0.0963001	+	0.197393i
$465$		0			0
$466$	−360.796	−	103.447i	−0.774241	−	0.221989i
$467$			86.9194i			0.186123i	0.995660	+	0.0930614i	$0.0296653\pi$
$467$			86.9194i			0.186123i	−0.995660	+	0.0930614i	$0.970335\pi$
$468$		0			0
$469$	563.647			1.20181
$470$	−41.6200	+	145.160i	−0.0885531	+	0.308851i
$471$		0			0
$472$	231.683	−	208.641i	0.490855	−	0.442036i
$473$	195.711			0.413765
$474$		0			0
$475$		−	85.3662i		−	0.179718i
$476$	−228.951	+	366.439i	−0.480989	+	0.769830i
$477$		0			0
$478$	38.5033	−	134.290i	0.0805509	−	0.280941i
$479$		−	333.107i		−	0.695421i	−0.937602	−	0.347710i	$-0.886959\pi$
$479$		−	333.107i		−	0.695421i	0.937602	−	0.347710i	$-0.113041\pi$
$480$		0			0
$481$	288.905			0.600634
$482$	572.072	+	164.023i	1.18687	+	0.340297i
$483$		0			0
$484$	−849.429	−	530.722i	−1.75502	−	1.09653i
$485$	−350.975			−0.723659
$486$		0			0
$487$			264.690i			0.543511i	0.962366	+	0.271755i	$0.0876042\pi$
$487$			264.690i			0.543511i	−0.962366	+	0.271755i	$0.912396\pi$
$488$	136.841	+	151.954i	0.280412	+	0.311382i
$489$		0			0
$490$	−113.926	−	32.6646i	−0.232502	−	0.0666625i
$491$			402.874i			0.820518i	0.911969	+	0.410259i	$0.134562\pi$
$491$			402.874i			0.820518i	−0.911969	+	0.410259i	$0.865438\pi$
$492$		0			0
$493$	79.7310			0.161726
$494$	−33.1738	+	115.702i	−0.0671534	+	0.234214i
$495$		0			0
$496$	78.3495	−	38.2235i	0.157963	−	0.0770634i
$497$	−161.848			−0.325650
$498$		0			0
$499$		−	350.536i		−	0.702477i	−0.936286	−	0.351238i	$-0.885761\pi$
$499$		−	350.536i		−	0.702477i	0.936286	−	0.351238i	$-0.114239\pi$
$500$	−351.967	−	219.908i	−0.703934	−	0.439817i
$501$		0			0
$502$	20.1014	−	70.1086i	0.0400426	−	0.139659i
$503$		−	339.615i		−	0.675179i	−0.941293	−	0.337589i	$-0.890388\pi$
$503$		−	339.615i		−	0.675179i	0.941293	−	0.337589i	$-0.109612\pi$
$504$		0			0
$505$	−180.993			−0.358403
$506$	1389.33	+	398.345i	2.74570	+	0.787242i
$507$		0			0
$508$	−36.3302	+	58.1471i	−0.0715162	+	0.114463i
$509$	933.003			1.83301			0.916506	−	0.400020i	$-0.130997\pi$
$509$	933.003			1.83301			0.916506	+	0.400020i	$0.130997\pi$
$510$		0			0
$511$			628.426i			1.22980i
$512$	−414.148	+	301.041i	−0.808882	+	0.587971i
$513$		0			0
$514$	338.257	+	96.9844i	0.658088	+	0.188686i
$515$		−	34.7866i		−	0.0675467i
$516$		0			0
$517$	625.270			1.20942
$518$	−99.5333	+	347.147i	−0.192149	+	0.670169i
$519$		0			0
$520$	172.009	+	191.006i	0.330787	+	0.367319i
$521$	415.284			0.797091			0.398545	−	0.917149i	$-0.369515\pi$
$521$	415.284			0.797091			0.398545	+	0.917149i	$0.369515\pi$
$522$		0			0
$523$			241.598i			0.461947i	0.972960	+	0.230973i	$0.0741911\pi$
$523$			241.598i			0.461947i	−0.972960	+	0.230973i	$0.925809\pi$
$524$	486.080	−	777.978i	0.927633	−	1.48469i
$525$		0			0
$526$	245.233	−	855.311i	0.466223	−	1.62607i
$527$		−	68.2044i		−	0.129420i
$528$		0			0
$529$	−877.105			−1.65804
$530$	192.088	+	55.0750i	0.362430	+	0.103915i
$531$		0			0
$532$	−127.598	−	79.7230i	−0.239846	−	0.149855i
$533$	−1005.59			−1.88666
$534$		0			0
$535$			187.384i			0.350250i
$536$	388.301	−	349.681i	0.724442	−	0.652391i
$537$		0			0
$538$	−287.889	−	82.5428i	−0.535109	−	0.153425i
$539$			490.731i			0.910447i
$540$		0			0
$541$	−304.787			−0.563377			−0.281689	−	0.959506i	$-0.590894\pi$
$541$	−304.787			−0.563377			−0.281689	+	0.959506i	$0.590894\pi$
$542$	−242.366	+	845.311i	−0.447169	+	1.55961i
$543$		0			0
$544$	69.6095	+	394.482i	0.127959	+	0.725150i
$545$	125.320			0.229945
$546$		0			0
$547$		−	555.915i		−	1.01630i	−0.861269	−	0.508149i	$-0.830330\pi$
$547$		−	555.915i		−	1.01630i	0.861269	−	0.508149i	$-0.169670\pi$
$548$	409.001	+	255.543i	0.746352	+	0.466319i
$549$		0			0
$550$	−208.046	+	725.612i	−0.378265	+	1.31930i
$551$			27.7632i			0.0503869i
$552$		0			0
$553$	1207.01			2.18265
$554$	160.042	+	45.8869i	0.288885	+	0.0828283i
$555$		0			0
$556$	309.160	−	494.816i	0.556043	−	0.889956i
$557$	192.055			0.344802			0.172401	−	0.985027i	$-0.444848\pi$
$557$	192.055			0.344802			0.172401	+	0.985027i	$0.444848\pi$
$558$		0			0
$559$			140.211i			0.250825i
$560$	−288.773	+	140.880i	−0.515666	+	0.251572i
$561$		0			0
$562$	24.9644	+	7.15775i	0.0444207	+	0.0127362i
$563$		−	107.771i		−	0.191423i	−0.995409	−	0.0957114i	$-0.969487\pi$
$563$		−	107.771i		−	0.191423i	0.995409	−	0.0957114i	$-0.0305126\pi$
$564$		0			0
$565$	−246.495			−0.436274
$566$	−61.1981	+	213.444i	−0.108124	+	0.377109i
$567$		0			0
$568$	−111.498	+	100.409i	−0.196300	+	0.176776i
$569$	647.934			1.13872			0.569362	−	0.822087i	$-0.307190\pi$
$569$	647.934			1.13872			0.569362	+	0.822087i	$0.307190\pi$
$570$		0			0
$571$			285.402i			0.499828i	0.968268	+	0.249914i	$0.0804023\pi$
$571$			285.402i			0.499828i	−0.968268	+	0.249914i	$0.919598\pi$
$572$	563.953	−	902.616i	0.985933	−	1.57800i
$573$		0			0
$574$	346.445	−	1208.31i	0.603563	−	2.10508i
$575$		−	734.376i		−	1.27717i
$576$		0			0
$577$	−92.4624			−0.160247			−0.0801234	−	0.996785i	$-0.525531\pi$
$577$	−92.4624			−0.160247			−0.0801234	+	0.996785i	$0.525531\pi$
$578$	−254.351	−	72.9269i	−0.440053	−	0.126171i
$579$		0			0
$580$	50.2819	+	31.4160i	0.0866929	+	0.0541656i
$581$	817.289			1.40669
$582$		0			0
$583$		−	827.410i		−	1.41923i
$584$	389.869	+	432.927i	0.667584	+	0.741314i
$585$		0			0
$586$	272.177	+	78.0379i	0.464465	+	0.133170i
$587$			654.717i			1.11536i	0.830056	+	0.557681i	$0.188309\pi$
$587$			654.717i			1.11536i	−0.830056	+	0.557681i	$0.811691\pi$
$588$		0			0
$589$	23.7495			0.0403217
$590$	49.9938	−	174.366i	0.0847352	−	0.295535i
$591$		0			0
$592$	146.798	+	300.902i	0.247969	+	0.508280i
$593$	−106.297			−0.179253			−0.0896264	−	0.995975i	$-0.528567\pi$
$593$	−106.297			−0.179253			−0.0896264	+	0.995975i	$0.528567\pi$
$594$		0			0
$595$			251.381i			0.422489i
$596$	−65.3178	−	40.8105i	−0.109594	−	0.0684740i
$597$		0			0
$598$	−285.382	+	995.342i	−0.477228	+	1.66445i
$599$			478.675i			0.799124i	0.916706	+	0.399562i	$0.130838\pi$
$599$			478.675i			0.799124i	−0.916706	+	0.399562i	$0.869162\pi$
$600$		0			0
$601$	808.024			1.34447			0.672233	−	0.740340i	$-0.265335\pi$
$601$	808.024			1.34447			0.672233	+	0.740340i	$0.265335\pi$
$602$	−168.478	−	48.3055i	−0.279863	−	0.0802418i
$603$		0			0
$604$	350.833	−	561.513i	0.580849	−	0.929657i
$605$	−582.717			−0.963169
$606$		0			0
$607$			694.694i			1.14447i	0.820089	+	0.572236i	$0.193924\pi$
$607$			694.694i			1.14447i	−0.820089	+	0.572236i	$0.806076\pi$
$608$	−137.363	+	24.2388i	−0.225925	+	0.0398664i
$609$		0			0
$610$	114.361	+	32.7894i	0.187478	+	0.0537531i
$611$			447.956i			0.733153i
$612$		0			0
$613$	−496.830			−0.810489			−0.405245	−	0.914208i	$-0.632814\pi$
$613$	−496.830			−0.810489			−0.405245	+	0.914208i	$0.632814\pi$
$614$	−197.198	+	687.776i	−0.321169	+	1.12016i
$615$		0			0
$616$	890.289	+	988.614i	1.44527	+	1.60489i
$617$	−387.951			−0.628770			−0.314385	−	0.949296i	$-0.601798\pi$
$617$	−387.951			−0.628770			−0.314385	+	0.949296i	$0.601798\pi$
$618$		0			0
$619$			882.105i			1.42505i	0.701647	+	0.712525i	$0.252448\pi$
$619$			882.105i			1.42505i	−0.701647	+	0.712525i	$0.747552\pi$
$620$	26.8743	−	43.0127i	0.0433456	−	0.0693753i
$621$		0			0
$622$	−260.389	+	908.173i	−0.418633	+	1.46009i
$623$		−	287.824i		−	0.461998i
$624$		0			0
$625$	248.156			0.397050
$626$	122.580	+	35.1459i	0.195815	+	0.0561437i
$627$		0			0
$628$	506.977	+	316.759i	0.807289	+	0.504393i
$629$	261.940			0.416439
$630$		0			0
$631$		−	502.601i		−	0.796515i	−0.917274	−	0.398258i	$-0.869615\pi$
$631$		−	502.601i		−	0.796515i	0.917274	−	0.398258i	$-0.130385\pi$
$632$	831.517	−	748.816i	1.31569	−	1.18484i
$633$		0			0
$634$	−382.048	−	109.540i	−0.602600	−	0.172776i
$635$			39.8895i			0.0628181i
$636$		0			0
$637$	−351.570			−0.551915
$638$	67.6616	−	235.987i	0.106053	−	0.369885i
$639$		0			0
$640$	−111.537	+	276.205i	−0.174277	+	0.431571i
$641$	−385.625			−0.601600			−0.300800	−	0.953687i	$-0.597254\pi$
$641$	−385.625			−0.601600			−0.300800	+	0.953687i	$0.597254\pi$
$642$		0			0
$643$			925.293i			1.43902i	0.694480	+	0.719512i	$0.255635\pi$
$643$			925.293i			1.43902i	−0.694480	+	0.719512i	$0.744365\pi$
$644$	−1097.68	−	685.829i	−1.70447	−	1.06495i
$645$		0			0
$646$	−30.0775	+	104.903i	−0.0465596	+	0.162388i
$647$			656.956i			1.01539i	0.861538	+	0.507694i	$0.169502\pi$
$647$			656.956i			1.01539i	−0.861538	+	0.507694i	$0.830498\pi$
$648$		0			0
$649$	−751.073			−1.15728
$650$	−519.843	−	149.048i	−0.799759	−	0.229305i
$651$		0			0
$652$	311.064	−	497.863i	0.477092	−	0.763593i
$653$	−392.897			−0.601680			−0.300840	−	0.953675i	$-0.597267\pi$
$653$	−392.897			−0.601680			−0.300840	+	0.953675i	$0.597267\pi$
$654$		0			0
$655$		−	533.701i		−	0.814811i
$656$	−510.958	−	1047.35i	−0.778899	−	1.59657i
$657$		0			0
$658$	−538.263	−	154.330i	−0.818029	−	0.234543i
$659$		−	695.576i		−	1.05550i	−0.849399	−	0.527751i	$-0.823035\pi$
$659$		−	695.576i		−	1.05550i	0.849399	−	0.527751i	$-0.176965\pi$
$660$		0			0
$661$	1179.05			1.78373			0.891866	−	0.452299i	$-0.149396\pi$
$661$	1179.05			1.78373			0.891866	+	0.452299i	$0.149396\pi$
$662$	241.843	−	843.487i	0.365322	−	1.27415i
$663$		0			0
$664$	563.037	−	507.038i	0.847947	−	0.763612i
$665$	−87.5335			−0.131629
$666$		0			0
$667$			238.837i			0.358076i
$668$	−452.500	+	724.233i	−0.677395	+	1.08418i
$669$		0			0
$670$	83.7894	−	292.237i	0.125059	−	0.436174i
$671$		−	492.606i		−	0.734137i
$672$		0			0
$673$	−881.170			−1.30932			−0.654658	−	0.755925i	$-0.727187\pi$
$673$	−881.170			−1.30932			−0.654658	+	0.755925i	$0.727187\pi$
$674$	−1035.67	−	296.945i	−1.53660	−	0.440571i
$675$		0			0
$676$	73.3542	+	45.8316i	0.108512	+	0.0677982i
$677$	126.536			0.186907			0.0934533	−	0.995624i	$-0.470209\pi$
$677$	126.536			0.186907			0.0934533	+	0.995624i	$0.470209\pi$
$678$		0			0
$679$		−	1301.44i		−	1.91670i
$680$	155.954	+	173.178i	0.229345	+	0.254674i
$681$		0			0
$682$	−201.870	−	57.8798i	−0.295998	−	0.0848678i
$683$			873.042i			1.27825i	0.769105	+	0.639123i	$0.220702\pi$
$683$			873.042i			1.27825i	−0.769105	+	0.639123i	$0.779298\pi$
$684$		0			0
$685$	280.579			0.409604
$686$	−111.954	+	390.467i	−0.163198	+	0.569193i
$687$		0			0
$688$	−146.034	+	71.2439i	−0.212258	+	0.103552i
$689$	592.774			0.860339
$690$		0			0
$691$		−	610.841i		−	0.883996i	−0.897016	−	0.441998i	$-0.854270\pi$
$691$		−	610.841i		−	0.883996i	0.897016	−	0.441998i	$-0.145730\pi$
$692$	952.269	+	594.976i	1.37611	+	0.859792i
$693$		0			0
$694$	−322.139	+	1123.54i	−0.464178	+	1.61894i
$695$		−	339.449i		−	0.488415i
$696$		0			0
$697$	−911.733			−1.30808
$698$	−578.361	−	165.826i	−0.828597	−	0.237574i
$699$		0			0
$700$	358.192	−	573.292i	0.511703	−	0.818989i
$701$	506.393			0.722387			0.361193	−	0.932491i	$-0.382369\pi$
$701$	506.393			0.722387			0.361193	+	0.932491i	$0.382369\pi$
$702$		0			0
$703$			91.2102i			0.129744i
$704$	1226.65	+	128.737i	1.74241	+	0.182865i
$705$		0			0
$706$	607.566	+	174.200i	0.860576	+	0.246742i
$707$		−	671.135i		−	0.949272i
$708$		0			0
$709$	−1036.42			−1.46180			−0.730902	−	0.682483i	$-0.760900\pi$
$709$	−1036.42			−1.46180			−0.730902	+	0.682483i	$0.760900\pi$
$710$	−24.0596	+	83.9140i	−0.0338868	+	0.118189i
$711$		0			0
$712$	−178.564	−	198.284i	−0.250792	−	0.278489i
$713$	204.308			0.286548
$714$		0			0
$715$		−	619.204i		−	0.866020i
$716$	74.5806	−	119.367i	0.104163	−	0.166714i
$717$		0			0
$718$	−63.9722	+	223.119i	−0.0890978	+	0.310751i
$719$			834.943i			1.16126i	0.814169	+	0.580628i	$0.197193\pi$
$719$			834.943i			1.16126i	−0.814169	+	0.580628i	$0.802807\pi$
$720$		0			0
$721$	128.991			0.178905
$722$	−36.5282	−	10.4733i	−0.0505931	−	0.0145059i
$723$		0			0
$724$	−1172.17	−	732.372i	−1.61902	−	1.01156i
$725$	−124.739			−0.172053
$726$		0			0
$727$		−	225.252i		−	0.309838i	−0.987927	−	0.154919i	$-0.950488\pi$
$727$		−	225.252i		−	0.309838i	0.987927	−	0.154919i	$-0.0495116\pi$
$728$	−708.263	+	637.821i	−0.972889	+	0.876128i
$729$		0			0
$730$	325.822	+	93.4191i	0.446332	+	0.127971i
$731$			127.125i			0.173905i
$732$		0			0
$733$	697.401			0.951434			0.475717	−	0.879598i	$-0.342189\pi$
$733$	697.401			0.951434			0.475717	+	0.879598i	$0.342189\pi$
$734$	37.4157	−	130.497i	0.0509751	−	0.177788i
$735$		0			0
$736$	−1181.68	+	208.517i	−1.60555	+	0.283312i
$737$	−1258.80			−1.70800
$738$		0			0
$739$		−	1065.87i		−	1.44231i	−0.692772	−	0.721157i	$-0.743611\pi$
$739$		−	1065.87i		−	1.44231i	0.692772	−	0.721157i	$-0.256389\pi$
$740$	165.191	+	103.211i	0.223231	+	0.139474i
$741$		0			0
$742$	−204.222	+	712.275i	−0.275232	+	0.959939i
$743$			1050.43i			1.41376i	0.707332	+	0.706881i	$0.249898\pi$
$743$			1050.43i			1.41376i	−0.707332	+	0.706881i	$0.750102\pi$
$744$		0			0
$745$	−44.8087			−0.0601459
$746$	−513.966	−	147.363i	−0.688962	−	0.197538i
$747$		0			0
$748$	511.317	−	818.370i	0.683578	−	1.09408i
$749$	−694.831			−0.927678
$750$		0			0
$751$		−	26.6606i		−	0.0355002i	−0.999842	−	0.0177501i	$-0.994350\pi$
$751$		−	26.6606i		−	0.0355002i	0.999842	−	0.0177501i	$-0.00565033\pi$
$752$	−466.558	+	227.614i	−0.620423	+	0.302679i
$753$		0			0
$754$	169.066	+	48.4741i	0.224225	+	0.0642893i
$755$		−	385.204i		−	0.510204i
$756$		0			0
$757$	445.989			0.589153			0.294577	−	0.955628i	$-0.404821\pi$
$757$	445.989			0.589153			0.294577	+	0.955628i	$0.404821\pi$
$758$	205.516	−	716.788i	0.271129	−	0.945630i
$759$		0			0
$760$	−60.3025	+	54.3050i	−0.0793454	+	0.0714539i
$761$	−294.799			−0.387384			−0.193692	−	0.981062i	$-0.562046\pi$
$761$	−294.799			−0.387384			−0.193692	+	0.981062i	$0.562046\pi$
$762$		0			0
$763$			464.695i			0.609037i
$764$	212.445	−	340.022i	0.278070	−	0.445055i
$765$		0			0
$766$	10.8176	−	37.7291i	0.0141222	−	0.0492547i
$767$		−	538.084i		−	0.701543i
$768$		0			0
$769$	−279.363			−0.363281			−0.181641	−	0.983365i	$-0.558141\pi$
$769$	−279.363			−0.363281			−0.181641	+	0.983365i	$0.558141\pi$
$770$	744.034	+	213.328i	0.966278	+	0.277049i
$771$		0			0
$772$	570.312	+	356.330i	0.738746	+	0.461567i
$773$	1092.48			1.41329			0.706647	−	0.707566i	$-0.250207\pi$
$773$	1092.48			1.41329			0.706647	+	0.707566i	$0.250207\pi$
$774$		0			0
$775$			106.705i			0.137684i
$776$	−807.400	−	896.571i	−1.04046	−	1.15537i
$777$		0			0
$778$	−382.061	−	109.544i	−0.491081	−	0.140802i
$779$		−	317.475i		−	0.407542i
$780$		0			0
$781$	361.456			0.462811
$782$	−258.746	+	902.441i	−0.330877	+	1.15402i
$783$		0			0
$784$	−178.639	−	366.169i	−0.227856	−	0.467052i
$785$	347.792			0.443047
$786$		0			0
$787$			231.147i			0.293706i	0.989158	+	0.146853i	$0.0469145\pi$
$787$			231.147i			0.293706i	−0.989158	+	0.146853i	$0.953086\pi$
$788$	−735.127	−	459.306i	−0.932903	−	0.582876i
$789$		0			0
$790$	179.429	−	625.802i	0.227125	−	0.792155i
$791$		−	914.019i		−	1.15552i
$792$		0			0
$793$	352.913			0.445035
$794$	568.011	+	162.859i	0.715379	+	0.205112i
$795$		0			0
$796$	174.339	−	279.032i	0.219018	−	0.350543i
$797$	−453.389			−0.568869			−0.284435	−	0.958695i	$-0.591806\pi$
$797$	−453.389			−0.568869			−0.284435	+	0.958695i	$0.591806\pi$
$798$		0			0
$799$			406.146i			0.508318i
$800$	−108.904	−	617.165i	−0.136130	−	0.771456i
$801$		0			0
$802$	123.040	+	35.2777i	0.153416	+	0.0439871i
$803$		−	1403.47i		−	1.74778i
$804$		0			0
$805$	−753.020			−0.935429
$806$	41.4663	−	144.624i	0.0514470	−	0.179434i
$807$		0			0
$808$	−416.366	−	462.350i	−0.515304	−	0.572216i
$809$	−528.874			−0.653738			−0.326869	−	0.945070i	$-0.605994\pi$
$809$	−528.874			−0.653738			−0.326869	+	0.945070i	$0.605994\pi$
$810$		0			0
$811$			1185.82i			1.46217i	0.682287	+	0.731084i	$0.260985\pi$
$811$			1185.82i			1.46217i	−0.682287	+	0.731084i	$0.739015\pi$
$812$	−116.493	+	186.449i	−0.143464	+	0.229616i
$813$		0			0
$814$	222.288	−	775.286i	0.273081	−	0.952439i
$815$		−	341.539i		−	0.419066i
$816$		0			0
$817$	−44.2661			−0.0541813
$818$	969.868	+	278.079i	1.18566	+	0.339949i
$819$		0			0
$820$	−574.979	−	359.246i	−0.701194	−	0.438105i
$821$	570.471			0.694849			0.347424	−	0.937708i	$-0.387056\pi$
$821$	570.471			0.694849			0.347424	+	0.937708i	$0.387056\pi$
$822$		0			0
$823$		−	1386.72i		−	1.68496i	−0.538728	−	0.842480i	$-0.681095\pi$
$823$		−	1386.72i		−	1.68496i	0.538728	−	0.842480i	$-0.318905\pi$
$824$	88.8628	−	80.0247i	0.107843	−	0.0971174i
$825$		0			0
$826$	646.560	+	185.380i	0.782760	+	0.224431i
$827$		−	1073.59i		−	1.29818i	−0.760712	−	0.649089i	$-0.775150\pi$
$827$		−	1073.59i		−	1.29818i	0.760712	−	0.649089i	$-0.224850\pi$
$828$		0			0
$829$	1109.24			1.33804			0.669021	−	0.743243i	$-0.266713\pi$
$829$	1109.24			1.33804			0.669021	+	0.743243i	$0.266713\pi$
$830$	121.495	−	423.743i	0.146379	−	0.510534i
$831$		0			0
$832$	−92.2299	+	878.799i	−0.110853	+	1.05625i
$833$	−318.756			−0.382660
$834$		0			0
$835$			496.831i			0.595007i
$836$	284.965	+	178.046i	0.340867	+	0.212973i
$837$		0			0
$838$	−259.241	+	904.167i	−0.309356	+	1.07896i
$839$		−	1547.29i		−	1.84421i	−0.386943	−	0.922104i	$-0.626469\pi$
$839$		−	1547.29i		−	1.84421i	0.386943	−	0.922104i	$-0.373531\pi$
$840$		0			0
$841$	−800.432			−0.951762
$842$	−903.658	−	259.095i	−1.07323	−	0.307714i
$843$		0			0
$844$	34.8011	−	55.6997i	0.0412335	−	0.0659949i
$845$	50.3218			0.0595524
$846$		0			0
$847$		−	2160.76i		−	2.55107i
$848$	301.199	+	617.389i	0.355187	+	0.728053i
$849$		0			0
$850$	−471.324	−	135.137i	−0.554498	−	0.158985i
$851$			784.649i			0.922031i
$852$		0			0
$853$	−341.108			−0.399892			−0.199946	−	0.979807i	$-0.564077\pi$
$853$	−341.108			−0.399892			−0.199946	+	0.979807i	$0.564077\pi$
$854$	−121.585	+	424.059i	−0.142372	+	0.496557i
$855$		0			0
$856$	−478.674	+	431.067i	−0.559199	+	0.503583i
$857$	−1535.74			−1.79200			−0.896000	−	0.444054i	$-0.853540\pi$
$857$	−1535.74			−1.79200			−0.896000	+	0.444054i	$0.853540\pi$
$858$		0			0
$859$		−	1223.16i		−	1.42393i	−0.702213	−	0.711967i	$-0.747804\pi$
$859$		−	1223.16i		−	1.42393i	0.702213	−	0.711967i	$-0.252196\pi$
$860$	−50.0904	+	80.1704i	−0.0582446	+	0.0932214i
$861$		0			0
$862$	−123.477	+	430.658i	−0.143245	+	0.499603i
$863$		−	672.603i		−	0.779377i	−0.920947	−	0.389689i	$-0.872583\pi$
$863$		−	672.603i		−	0.779377i	0.920947	−	0.389689i	$-0.127417\pi$
$864$		0			0
$865$	653.266			0.755221
$866$	346.302	+	99.2909i	0.399887	+	0.114655i
$867$		0			0
$868$	159.494	+	99.6516i	0.183749	+	0.114806i
$869$	−2695.62			−3.10197
$870$		0			0
$871$		−	901.827i		−	1.03539i
$872$	288.293	+	320.132i	0.330611	+	0.367124i
$873$		0			0
$874$	−314.239	−	90.0980i	−0.359542	−	0.103087i
$875$		−	895.324i		−	1.02323i
$876$		0			0
$877$	−1328.68			−1.51503			−0.757514	−	0.652819i	$-0.773586\pi$
$877$	−1328.68			−1.51503			−0.757514	+	0.652819i	$0.773586\pi$
$878$	325.226	−	1134.31i	0.370416	−	1.29192i
$879$		0			0
$880$	644.917	−	314.629i	0.732861	−	0.357532i
$881$	−372.924			−0.423296			−0.211648	−	0.977346i	$-0.567883\pi$
$881$	−372.924			−0.423296			−0.211648	+	0.977346i	$0.567883\pi$
$882$		0			0
$883$			669.314i			0.758000i	0.925397	+	0.379000i	$0.123732\pi$
$883$			669.314i			0.758000i	−0.925397	+	0.379000i	$0.876268\pi$
$884$	586.297	+	366.318i	0.663232	+	0.414387i
$885$		0			0
$886$	−86.7957	+	302.722i	−0.0979635	+	0.341672i
$887$		−	874.225i		−	0.985598i	−0.870143	−	0.492799i	$-0.835974\pi$
$887$		−	874.225i		−	0.985598i	0.870143	−	0.492799i	$-0.164026\pi$
$888$		0			0
$889$	−147.913			−0.166381
$890$	−149.230	−	42.7868i	−0.167674	−	0.0480750i
$891$		0			0
$892$	−413.781	+	662.263i	−0.463880	+	0.742448i
$893$	−141.424			−0.158370
$894$		0			0
$895$		−	81.8873i		−	0.0914942i
$896$	−1024.19	−	413.587i	−1.14307	−	0.461592i
$897$		0			0
$898$	1375.45	+	394.366i	1.53168	+	0.439160i
$899$		−	34.7032i		−	0.0386020i
$900$		0			0
$901$	537.447			0.596500
$902$	−773.718	+	2698.53i	−0.857780	+	2.99172i
$903$		0			0
$904$	−567.048	−	629.674i	−0.627266	−	0.696543i
$905$	−804.123			−0.888534
$906$		0			0
$907$			33.1952i			0.0365989i	0.999833	+	0.0182994i	$0.00582522\pi$
$907$			33.1952i			0.0365989i	−0.999833	+	0.0182994i	$0.994175\pi$
$908$	647.304	−	1036.02i	0.712890	−	1.14099i
$909$		0			0
$910$	−152.832	+	533.041i	−0.167948	+	0.585760i
$911$			25.4273i			0.0279114i	0.999903	+	0.0139557i	$0.00444238\pi$
$911$			25.4273i			0.0279114i	−0.999903	+	0.0139557i	$0.995558\pi$
$912$		0			0
$913$	−1825.26			−1.99918
$914$	60.2709	+	17.2807i	0.0659419	+	0.0189067i
$915$		0			0
$916$	−779.165	−	486.821i	−0.850617	−	0.531464i
$917$	1979.00			2.15812
$918$		0			0
$919$			445.408i			0.484666i	0.970193	+	0.242333i	$0.0779126\pi$
$919$			445.408i			0.484666i	−0.970193	+	0.242333i	$0.922087\pi$
$920$	−518.761	+	467.166i	−0.563871	+	0.507790i
$921$		0			0
$922$	−708.875	−	203.247i	−0.768845	−	0.220442i
$923$			258.954i			0.280557i
$924$		0			0
$925$	−409.804			−0.443031
$926$	−450.575	+	1571.49i	−0.486582	+	1.69707i
$927$		0			0
$928$	35.4181	+	200.717i	0.0381661	+	0.216290i
$929$	408.473			0.439691			0.219846	−	0.975535i	$-0.429445\pi$
$929$	408.473			0.439691			0.219846	+	0.975535i	$0.429445\pi$
$930$		0			0
$931$		−	110.994i		−	0.119220i
$932$	−636.622	−	397.760i	−0.683070	−	0.426781i
$933$		0			0
$934$	−47.9122	+	167.106i	−0.0512979	+	0.178914i
$935$		−	561.411i		−	0.600439i
$936$		0			0
$937$	−1101.68			−1.17576			−0.587878	−	0.808950i	$-0.700037\pi$
$937$	−1101.68			−1.17576			−0.587878	+	0.808950i	$0.700037\pi$
$938$	1083.63	+	310.697i	1.15526	+	0.331233i
$939$		0			0
$940$	−160.032	+	256.134i	−0.170247	+	0.272482i
$941$	1342.45			1.42662			0.713309	−	0.700850i	$-0.247196\pi$
$941$	1342.45			1.42662			0.713309	+	0.700850i	$0.247196\pi$
$942$		0			0
$943$		−	2731.12i		−	2.89621i
$944$	560.428	−	273.410i	0.593674	−	0.289629i
$945$		0			0
$946$	376.262	+	107.881i	0.397740	+	0.114039i
$947$			786.294i			0.830300i	0.909753	+	0.415150i	$0.136271\pi$
$947$			786.294i			0.830300i	−0.909753	+	0.415150i	$0.863729\pi$
$948$		0			0
$949$	1005.47			1.05951
$950$	47.0561	−	164.120i	0.0495327	−	0.172758i
$951$		0			0
$952$	−642.157	+	578.290i	−0.674535	+	0.607447i
$953$	−1134.64			−1.19060			−0.595301	−	0.803503i	$-0.702967\pi$
$953$	−1134.64			−1.19060			−0.595301	+	0.803503i	$0.702967\pi$
$954$		0			0
$955$		−	233.258i		−	0.244250i
$956$	148.048	−	236.953i	0.154862	−	0.247859i
$957$		0			0
$958$	183.617	−	640.410i	0.191667	−	0.668486i
$959$			1040.40i			1.08488i
$960$		0			0
$961$	931.314			0.969109
$962$	555.430	+	159.252i	0.577371	+	0.165542i
$963$		0			0
$964$	1009.42	+	630.682i	1.04711	+	0.654234i
$965$	391.240			0.405430
$966$		0			0
$967$			963.333i			0.996208i	0.867117	+	0.498104i	$0.165970\pi$
$967$			963.333i			0.996208i	−0.867117	+	0.498104i	$0.834030\pi$
$968$	−1340.51	−	1488.56i	−1.38483	−	1.53777i
$969$		0			0
$970$	−674.762	−	193.466i	−0.695631	−	0.199450i
$971$			1320.90i			1.36035i	0.733050	+	0.680174i	$0.238096\pi$
$971$			1320.90i			1.36035i	−0.733050	+	0.680174i	$0.761904\pi$
$972$		0			0
$973$	1258.70			1.29363
$974$	−145.904	+	508.876i	−0.149799	+	0.522460i
$975$		0			0
$976$	179.321	+	367.568i	0.183731	+	0.376607i
$977$	1159.80			1.18710			0.593550	−	0.804797i	$-0.297726\pi$
$977$	1159.80			1.18710			0.593550	+	0.804797i	$0.297726\pi$
$978$		0			0
$979$			642.800i			0.656588i
$980$	−201.021	−	125.598i	−0.205124	−	0.128161i
$981$		0			0
$982$	−222.075	+	774.541i	−0.226145	+	0.788738i
$983$		−	8.37645i		−	0.00852131i	−0.999991	−	0.00426065i	$-0.998644\pi$
$983$		−	8.37645i		−	0.00852131i	0.999991	−	0.00426065i	$-0.00135621\pi$
$984$		0			0
$985$	−504.305			−0.511985
$986$	153.286	+	43.9498i	0.155462	+	0.0445738i
$987$		0			0
$988$	−127.556	+	204.155i	−0.129105	+	0.206634i
$989$	−380.806			−0.385041
$990$		0			0
$991$		−	854.355i		−	0.862114i	−0.902325	−	0.431057i	$-0.858141\pi$
$991$		−	854.355i		−	0.862114i	0.902325	−	0.431057i	$-0.141859\pi$
$992$	171.700	−	30.2978i	0.173084	−	0.0305421i
$993$		0			0
$994$	−311.159	−	89.2147i	−0.313037	−	0.0897532i
$995$		−	191.419i		−	0.192381i
$996$		0			0
$997$	−77.4664			−0.0776995			−0.0388497	−	0.999245i	$-0.512369\pi$
$997$	−77.4664			−0.0776995			−0.0388497	+	0.999245i	$0.512369\pi$
$998$	193.224	−	673.918i	0.193612	−	0.675269i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.b.343.14		14
3.2	odd	2		76.3.b.b.39.1	✓	14
4.3	odd	2	inner	684.3.g.b.343.13		14
12.11	even	2		76.3.b.b.39.2	yes	14
24.5	odd	2		1216.3.d.d.191.7		14
24.11	even	2		1216.3.d.d.191.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.b.39.1	✓	14	3.2	odd	2
76.3.b.b.39.2	yes	14	12.11	even	2
684.3.g.b.343.13		14	4.3	odd	2	inner
684.3.g.b.343.14		14	1.1	even	1	trivial
1216.3.d.d.191.7		14	24.5	odd	2
1216.3.d.d.191.8		14	24.11	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.92254 + 0.551226i) q^{2} +(3.39230 + 2.11950i) q^{4} +2.32715 q^{5} +8.62924i q^{7} +(5.35350 + 5.94475i) q^{8} +O(q^{10})\)	\(q+(1.92254 + 0.551226i) q^{2} +(3.39230 + 2.11950i) q^{4} +2.32715 q^{5} +8.62924i q^{7} +(5.35350 + 5.94475i) q^{8} +(4.47404 + 1.28279i) q^{10} -19.2717i q^{11} +13.8067 q^{13} +(-4.75666 + 16.5900i) q^{14} +(7.01540 + 14.3800i) q^{16} +12.5180 q^{17} +4.35890i q^{19} +(7.89440 + 4.93241i) q^{20} +(10.6231 - 37.0506i) q^{22} +37.4981i q^{23} -19.5844 q^{25} +(26.5438 + 7.61058i) q^{26} +(-18.2897 + 29.2730i) q^{28} +6.36930 q^{29} -5.44851i q^{31} +(5.56075 + 31.5131i) q^{32} +(24.0663 + 6.90025i) q^{34} +20.0816i q^{35} +20.9250 q^{37} +(-2.40274 + 8.38015i) q^{38} +(12.4584 + 13.8343i) q^{40} -72.8337 q^{41} +10.1553i q^{43} +(40.8465 - 65.3755i) q^{44} +(-20.6699 + 72.0914i) q^{46} +32.4450i q^{47} -25.4638 q^{49} +(-37.6517 - 10.7954i) q^{50} +(46.8363 + 29.2633i) q^{52} +42.9339 q^{53} -44.8482i q^{55} +(-51.2987 + 46.1966i) q^{56} +(12.2452 + 3.51092i) q^{58} -38.9728i q^{59} +25.5611 q^{61} +(3.00336 - 10.4750i) q^{62} +(-6.68010 + 63.6504i) q^{64} +32.1302 q^{65} -65.3183i q^{67} +(42.4648 + 26.5320i) q^{68} +(-11.0695 + 38.6076i) q^{70} +18.7557i q^{71} +72.8251 q^{73} +(40.2292 + 11.5344i) q^{74} +(-9.23871 + 14.7867i) q^{76} +166.300 q^{77} -139.874i q^{79} +(16.3259 + 33.4644i) q^{80} +(-140.026 - 40.1478i) q^{82} -94.7116i q^{83} +29.1313 q^{85} +(-5.59789 + 19.5240i) q^{86} +(114.566 - 103.171i) q^{88} -33.3546 q^{89} +119.141i q^{91} +(-79.4773 + 127.205i) q^{92} +(-17.8845 + 62.3766i) q^{94} +10.1438i q^{95} -150.817 q^{97} +(-48.9551 - 14.0363i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8	\( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 2 * q^4 + 40 * q^8 - 12 * q^10 + 54 * q^13 - 30 * q^14 + 58 * q^16 - 34 * q^17 - 32 * q^20 + 36 * q^22 - 86 * q^25 + 16 * q^26 + 18 * q^28 - 54 * q^29 - 72 * q^32 - 82 * q^34 + 100 * q^37 - 148 * q^40 - 224 * q^41 + 96 * q^44 + 46 * q^46 - 220 * q^49 + 58 * q^50 - 288 * q^52 - 14 * q^53 - 12 * q^56 - 72 * q^58 + 28 * q^61 - 396 * q^62 - 118 * q^64 + 472 * q^65 - 30 * q^68 + 156 * q^70 + 70 * q^73 + 224 * q^74 - 228 * q^77 + 348 * q^80 - 400 * q^82 + 48 * q^85 + 124 * q^86 + 472 * q^88 - 126 * q^92 - 88 * q^94 + 308 * q^97 - 68 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more