LMFDB - Embedded newform 224.3.r.d.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(95,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

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

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

chi := DirichletCharacter("224.95");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.r (of order $6$, degree $2$, 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:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 $ x^12 - 15x^10 + 90x^8 - 247x^6 + 270x^4 + 21*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.1
Root			$1.75780 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	224.191
Dual form			224.3.r.d.95.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.23009 + 2.44224i) q^{3} +(1.16012 - 2.00939i) q^{5} +(4.65898 - 5.22436i) q^{7} +(7.42909 - 12.8676i) q^{9} +O(q^{10})$	\(q+(-4.23009 + 2.44224i) q^{3} +(1.16012 - 2.00939i) q^{5} +(4.65898 - 5.22436i) q^{7} +(7.42909 - 12.8676i) q^{9} +(-13.2789 + 7.66660i) q^{11} +14.8582 q^{13} +11.3332i q^{15} +(1.19938 + 2.07739i) q^{17} +(25.9124 + 14.9605i) q^{19} +(-6.94872 + 33.4778i) q^{21} +(23.0146 + 13.2875i) q^{23} +(9.80823 + 16.9884i) q^{25} +28.6142i q^{27} -4.75828 q^{29} +(17.0976 - 9.87133i) q^{31} +(37.4474 - 64.8608i) q^{33} +(-5.09280 - 15.4226i) q^{35} +(-24.3582 + 42.1896i) q^{37} +(-62.8514 + 36.2873i) q^{39} +34.4746 q^{41} -59.4327i q^{43} +(-17.2373 - 29.8559i) q^{45} +(-32.8182 - 18.9476i) q^{47} +(-5.58789 - 48.6803i) q^{49} +(-10.1470 - 5.85837i) q^{51} +(33.2663 + 57.6189i) q^{53} +35.5768i q^{55} -146.149 q^{57} +(78.2440 - 45.1742i) q^{59} +(44.0772 - 76.3439i) q^{61} +(-32.6128 - 98.7619i) q^{63} +(17.2373 - 29.8559i) q^{65} +(-15.0906 + 8.71254i) q^{67} -129.805 q^{69} -23.0492i q^{71} +(34.2297 + 59.2876i) q^{73} +(-82.9793 - 47.9081i) q^{75} +(-21.8132 + 105.093i) q^{77} +(54.0184 + 31.1876i) q^{79} +(-3.02096 - 5.23245i) q^{81} +36.3835i q^{83} +5.56573 q^{85} +(20.1279 - 11.6209i) q^{87} +(-44.2137 + 76.5804i) q^{89} +(69.2239 - 77.6245i) q^{91} +(-48.2164 + 83.5132i) q^{93} +(60.1232 - 34.7122i) q^{95} +14.8582 q^{97} +227.824i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{5}+O(q^{10}) $ 12 * q + 18 * q^5	$ 12 q + 18 q^{5} - 6 q^{17} + 18 q^{21} + 186 q^{33} - 114 q^{37} + 180 q^{49} - 18 q^{53} - 684 q^{57} + 318 q^{61} - 228 q^{69} + 342 q^{73} + 318 q^{77} - 186 q^{81} - 996 q^{85} + 150 q^{89} - 222 q^{93}+O(q^{100}) $ 12 * q + 18 * q^5 - 6 * q^17 + 18 * q^21 + 186 * q^33 - 114 * q^37 + 180 * q^49 - 18 * q^53 - 684 * q^57 + 318 * q^61 - 228 * q^69 + 342 * q^73 + 318 * q^77 - 186 * q^81 - 996 * q^85 + 150 * q^89 - 222 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.23009	+	2.44224i	−1.41003	+	0.814081i	−0.995390	−	0.0959056i	$-0.969425\pi$
$3$	−4.23009	+	2.44224i	−1.41003	+	0.814081i	−0.414639	+	0.909986i	$0.636092\pi$
$4$		0			0
$5$	1.16012	−	2.00939i	0.232025	−	0.401878i	−0.726379	−	0.687294i	$-0.758798\pi$
$5$	1.16012	−	2.00939i	0.232025	−	0.401878i	0.958404	+	0.285416i	$0.0921317\pi$
$6$		0			0
$7$	4.65898	−	5.22436i	0.665568	−	0.746337i
$7$	4.65898	−	5.22436i	0.665568	−	0.746337i
$8$		0			0
$9$	7.42909	−	12.8676i	0.825455	−	1.42973i
$10$		0			0
$11$	−13.2789	+	7.66660i	−1.20718	+	0.696964i	−0.962142	−	0.272550i	$-0.912133\pi$
$11$	−13.2789	+	7.66660i	−1.20718	+	0.696964i	−0.245035	+	0.969514i	$0.578800\pi$
$12$		0			0
$13$	14.8582			1.14294			0.571469	−	0.820624i	$-0.306374\pi$
$13$	14.8582			1.14294			0.571469	+	0.820624i	$0.306374\pi$
$14$		0			0
$15$			11.3332i			0.755547i
$16$		0			0
$17$	1.19938	+	2.07739i	0.0705520	+	0.122200i	0.899143	−	0.437654i	$-0.144191\pi$
$17$	1.19938	+	2.07739i	0.0705520	+	0.122200i	−0.828591	+	0.559854i	$0.810857\pi$
$18$		0			0
$19$	25.9124	+	14.9605i	1.36381	+	0.787397i	0.990129	−	0.140159i	$-0.0447615\pi$
$19$	25.9124	+	14.9605i	1.36381	+	0.787397i	0.373683	+	0.927557i	$0.378095\pi$
$20$		0			0
$21$	−6.94872	+	33.4778i	−0.330891	+	1.59418i
$22$		0			0
$23$	23.0146	+	13.2875i	1.00063	+	0.577716i	0.908436	−	0.418025i	$-0.137278\pi$
$23$	23.0146	+	13.2875i	1.00063	+	0.577716i	0.0921976	+	0.995741i	$0.470611\pi$
$24$		0			0
$25$	9.80823	+	16.9884i	0.392329	+	0.679534i
$26$		0			0
$27$			28.6142i			1.05978i
$28$		0			0
$29$	−4.75828			−0.164078			−0.0820392	−	0.996629i	$-0.526143\pi$
$29$	−4.75828			−0.164078			−0.0820392	+	0.996629i	$0.526143\pi$
$30$		0			0
$31$	17.0976	−	9.87133i	0.551537	−	0.318430i	−0.198205	−	0.980161i	$-0.563511\pi$
$31$	17.0976	−	9.87133i	0.551537	−	0.318430i	0.749742	+	0.661731i	$0.230178\pi$
$32$		0			0
$33$	37.4474	−	64.8608i	1.13477	−	1.96548i
$34$		0			0
$35$	−5.09280	−	15.4226i	−0.145509	−	0.440646i
$36$		0			0
$37$	−24.3582	+	42.1896i	−0.658329	+	1.14026i	0.322719	+	0.946495i	$0.395403\pi$
$37$	−24.3582	+	42.1896i	−0.658329	+	1.14026i	−0.981048	+	0.193765i	$0.937930\pi$
$38$		0			0
$39$	−62.8514	+	36.2873i	−1.61157	+	0.930443i
$40$		0			0
$41$	34.4746			0.840845			0.420422	−	0.907328i	$-0.361882\pi$
$41$	34.4746			0.840845			0.420422	+	0.907328i	$0.361882\pi$
$42$		0			0
$43$		−	59.4327i		−	1.38216i	−0.722780	−	0.691078i	$-0.757136\pi$
$43$		−	59.4327i		−	1.38216i	0.722780	−	0.691078i	$-0.242864\pi$
$44$		0			0
$45$	−17.2373	−	29.8559i	−0.383052	−	0.663465i
$46$		0			0
$47$	−32.8182	−	18.9476i	−0.698259	−	0.403140i	0.108440	−	0.994103i	$-0.465415\pi$
$47$	−32.8182	−	18.9476i	−0.698259	−	0.403140i	−0.806699	+	0.590963i	$0.798748\pi$
$48$		0			0
$49$	−5.58789	−	48.6803i	−0.114039	−	0.993476i
$50$		0			0
$51$	−10.1470	−	5.85837i	−0.198961	−	0.114870i
$52$		0			0
$53$	33.2663	+	57.6189i	0.627666	+	1.08715i	0.988019	+	0.154334i	$0.0493231\pi$
$53$	33.2663	+	57.6189i	0.627666	+	1.08715i	−0.360352	+	0.932816i	$0.617344\pi$
$54$		0			0
$55$			35.5768i			0.646851i
$56$		0			0
$57$	−146.149			−2.56402
$58$		0			0
$59$	78.2440	−	45.1742i	1.32617	−	0.765665i	0.341465	−	0.939894i	$-0.389077\pi$
$59$	78.2440	−	45.1742i	1.32617	−	0.765665i	0.984705	+	0.174230i	$0.0557436\pi$
$60$		0			0
$61$	44.0772	−	76.3439i	0.722577	−	1.25154i	−0.237387	−	0.971415i	$-0.576291\pi$
$61$	44.0772	−	76.3439i	0.722577	−	1.25154i	0.959964	−	0.280125i	$-0.0903759\pi$
$62$		0			0
$63$	−32.6128	−	98.7619i	−0.517664	−	1.56765i
$64$		0			0
$65$	17.2373	−	29.8559i	0.265190	−	0.459322i
$66$		0			0
$67$	−15.0906	+	8.71254i	−0.225232	+	0.130038i	−0.608371	−	0.793653i	$-0.708177\pi$
$67$	−15.0906	+	8.71254i	−0.225232	+	0.130038i	0.383138	+	0.923691i	$0.374843\pi$
$68$		0			0
$69$	−129.805			−1.88123
$70$		0			0
$71$		−	23.0492i		−	0.324636i	−0.986738	−	0.162318i	$-0.948103\pi$
$71$		−	23.0492i		−	0.324636i	0.986738	−	0.162318i	$-0.0518971\pi$
$72$		0			0
$73$	34.2297	+	59.2876i	0.468900	+	0.812159i	0.999368	−	0.0355462i	$-0.0113171\pi$
$73$	34.2297	+	59.2876i	0.468900	+	0.812159i	−0.530468	+	0.847705i	$0.677984\pi$
$74$		0			0
$75$	−82.9793	−	47.9081i	−1.10639	−	0.638775i
$76$		0			0
$77$	−21.8132	+	105.093i	−0.283288	+	1.36484i
$78$		0			0
$79$	54.0184	+	31.1876i	0.683778	+	0.394779i	0.801277	−	0.598294i	$-0.204154\pi$
$79$	54.0184	+	31.1876i	0.683778	+	0.394779i	−0.117499	+	0.993073i	$0.537488\pi$
$80$		0			0
$81$	−3.02096	−	5.23245i	−0.0372958	−	0.0645982i
$82$		0			0
$83$			36.3835i			0.438356i	0.975685	+	0.219178i	$0.0703375\pi$
$83$			36.3835i			0.438356i	−0.975685	+	0.219178i	$0.929662\pi$
$84$		0			0
$85$	5.56573			0.0654792
$86$		0			0
$87$	20.1279	−	11.6209i	0.231355	−	0.133573i
$88$		0			0
$89$	−44.2137	+	76.5804i	−0.496783	+	0.860454i	−0.999993	−	0.00371041i	$-0.998819\pi$
$89$	−44.2137	+	76.5804i	−0.496783	+	0.860454i	0.503210	+	0.864164i	$0.332152\pi$
$90$		0			0
$91$	69.2239	−	77.6245i	0.760702	−	0.853016i
$92$		0			0
$93$	−48.2164	+	83.5132i	−0.518456	+	0.897991i
$94$		0			0
$95$	60.1232	−	34.7122i	0.632876	−	0.365391i
$96$		0			0
$97$	14.8582			0.153177			0.0765886	−	0.997063i	$-0.475597\pi$
$97$	14.8582			0.153177			0.0765886	+	0.997063i	$0.475597\pi$
$98$		0			0
$99$			227.824i			2.30125i
$100$		0			0
$101$	8.72475	+	15.1117i	0.0863836	+	0.149621i	0.905980	−	0.423321i	$-0.139136\pi$
$101$	8.72475	+	15.1117i	0.0863836	+	0.149621i	−0.819596	+	0.572941i	$0.805802\pi$
$102$		0			0
$103$	75.8801	+	43.8094i	0.736700	+	0.425334i	0.820868	−	0.571118i	$-0.193490\pi$
$103$	75.8801	+	43.8094i	0.736700	+	0.425334i	−0.0841682	+	0.996452i	$0.526823\pi$
$104$		0			0
$105$	59.2087	+	52.8011i	0.563893	+	0.502868i
$106$		0			0
$107$	−76.1380	−	43.9583i	−0.711570	−	0.410825i	0.100072	−	0.994980i	$-0.468093\pi$
$107$	−76.1380	−	43.9583i	−0.711570	−	0.410825i	−0.811642	+	0.584155i	$0.801426\pi$
$108$		0			0
$109$	−103.462	−	179.201i	−0.949190	−	1.64405i	−0.747136	−	0.664671i	$-0.768572\pi$
$109$	−103.462	−	179.201i	−0.949190	−	1.64405i	−0.202054	−	0.979374i	$-0.564762\pi$
$110$		0			0
$111$		−	237.954i		−	2.14373i
$112$		0			0
$113$	−195.807			−1.73281			−0.866405	−	0.499342i	$-0.833575\pi$
$113$	−195.807			−1.73281			−0.866405	+	0.499342i	$0.833575\pi$
$114$		0			0
$115$	53.3995	−	30.8302i	0.464343	−	0.268089i
$116$		0			0
$117$	110.383	−	191.189i	0.943442	−	1.63409i
$118$		0			0
$119$	16.4410	+	3.41252i	0.138159	+	0.0286766i
$120$		0			0
$121$	57.0536	−	98.8197i	0.471517	−	0.816692i
$122$		0			0
$123$	−145.831	+	84.1954i	−1.18562	+	0.684515i
$124$		0			0
$125$	103.521			0.828169
$126$		0			0
$127$			187.616i			1.47729i	0.674092	+	0.738647i	$0.264535\pi$
$127$			187.616i			1.47729i	−0.674092	+	0.738647i	$0.735465\pi$
$128$		0			0
$129$	145.149	+	251.406i	1.12519	+	1.94888i
$130$		0			0
$131$	−202.242	−	116.764i	−1.54383	−	0.891331i	−0.998592	−	0.0530503i	$-0.983106\pi$
$131$	−202.242	−	116.764i	−1.54383	−	0.891331i	−0.545239	−	0.838281i	$-0.683561\pi$
$132$		0			0
$133$	198.885	−	65.6750i	1.49537	−	0.493797i
$134$		0			0
$135$	57.4971	+	33.1960i	0.425905	+	0.245896i
$136$		0			0
$137$	−64.2120	−	111.218i	−0.468700	−	0.811813i	0.530660	−	0.847585i	$-0.321944\pi$
$137$	−64.2120	−	111.218i	−0.468700	−	0.811813i	−0.999360	+	0.0357721i	$0.988611\pi$
$138$		0			0
$139$			55.4166i			0.398681i	0.979930	+	0.199340i	$0.0638800\pi$
$139$			55.4166i			0.398681i	−0.979930	+	0.199340i	$0.936120\pi$
$140$		0			0
$141$	185.098			1.31275
$142$		0			0
$143$	−197.301	+	113.912i	−1.37973	+	0.796586i
$144$		0			0
$145$	−5.52019	+	9.56124i	−0.0380703	+	0.0659396i
$146$		0			0
$147$	142.526	+	192.275i	0.969567	+	1.30799i
$148$		0			0
$149$	12.4625	−	21.5857i	0.0836409	−	0.144870i	−0.821170	−	0.570683i	$-0.806678\pi$
$149$	12.4625	−	21.5857i	0.0836409	−	0.144870i	0.904811	+	0.425813i	$0.140012\pi$
$150$		0			0
$151$	11.9802	−	6.91675i	0.0793388	−	0.0458063i	−0.459806	−	0.888020i	$-0.652081\pi$
$151$	11.9802	−	6.91675i	0.0793388	−	0.0458063i	0.539145	+	0.842213i	$0.318748\pi$
$152$		0			0
$153$	35.6413			0.232950
$154$		0			0
$155$		−	45.8078i		−	0.295534i
$156$		0			0
$157$	−43.1200	−	74.6860i	−0.274649	−	0.475707i	0.695397	−	0.718626i	$-0.255228\pi$
$157$	−43.1200	−	74.6860i	−0.274649	−	0.475707i	−0.970047	+	0.242919i	$0.921895\pi$
$158$		0			0
$159$	−281.439	−	162.489i	−1.77006	−	1.02194i
$160$		0			0
$161$	176.643	−	58.3304i	1.09716	−	0.362301i
$162$		0			0
$163$	134.226	+	77.4953i	0.823471	+	0.475431i	0.851612	−	0.524173i	$-0.175625\pi$
$163$	134.226	+	77.4953i	0.823471	+	0.475431i	−0.0281408	+	0.999604i	$0.508959\pi$
$164$		0			0
$165$	−86.8872	−	150.493i	−0.526589	−	0.912079i
$166$		0			0
$167$			239.152i			1.43205i	0.698076	+	0.716023i	$0.254040\pi$
$167$			239.152i			1.43205i	−0.698076	+	0.716023i	$0.745960\pi$
$168$		0			0
$169$	51.7655			0.306305
$170$		0			0
$171$	385.012	−	222.287i	2.25153	−	1.29992i
$172$		0			0
$173$	−54.2968	+	94.0448i	−0.313854	+	0.543611i	−0.979193	−	0.202930i	$-0.934954\pi$
$173$	−54.2968	+	94.0448i	−0.313854	+	0.543611i	0.665339	+	0.746541i	$0.268287\pi$
$174$		0			0
$175$	134.450	+	27.9066i	0.768283	+	0.159466i
$176$		0			0
$177$	−220.653	+	382.182i	−1.24663	+	2.15922i
$178$		0			0
$179$	144.105	−	83.1988i	0.805054	−	0.464798i	−0.0401815	−	0.999192i	$-0.512794\pi$
$179$	144.105	−	83.1988i	0.805054	−	0.464798i	0.845235	+	0.534394i	$0.179460\pi$
$180$		0			0
$181$	−17.9376			−0.0991025			−0.0495513	−	0.998772i	$-0.515779\pi$
$181$	−17.9376			−0.0991025			−0.0495513	+	0.998772i	$0.515779\pi$
$182$		0			0
$183$			430.589i			2.35294i
$184$		0			0
$185$	56.5170	+	97.8903i	0.305497	+	0.529137i
$186$		0			0
$187$	−31.8531	−	18.3904i	−0.170338	−	0.0983444i
$188$		0			0
$189$	149.491	+	133.313i	0.790957	+	0.705359i
$190$		0			0
$191$	44.6004	+	25.7500i	0.233510	+	0.134817i	0.612190	−	0.790711i	$-0.290289\pi$
$191$	44.6004	+	25.7500i	0.233510	+	0.134817i	−0.378680	+	0.925528i	$0.623622\pi$
$192$		0			0
$193$	35.8784	+	62.1432i	0.185898	+	0.321985i	0.943879	−	0.330292i	$-0.107147\pi$
$193$	35.8784	+	62.1432i	0.185898	+	0.321985i	−0.757981	+	0.652277i	$0.773814\pi$
$194$		0			0
$195$			168.391i			0.863543i
$196$		0			0
$197$	−57.3256			−0.290993			−0.145496	−	0.989359i	$-0.546478\pi$
$197$	−57.3256			−0.290993			−0.145496	+	0.989359i	$0.546478\pi$
$198$		0			0
$199$	−90.9399	+	52.5042i	−0.456984	+	0.263840i	−0.710775	−	0.703419i	$-0.751656\pi$
$199$	−90.9399	+	52.5042i	−0.456984	+	0.263840i	0.253791	+	0.967259i	$0.418322\pi$
$200$		0			0
$201$	42.5562	−	73.7096i	0.211723	−	0.366714i
$202$		0			0
$203$	−22.1687	+	24.8590i	−0.109205	+	0.122458i
$204$		0			0
$205$	39.9948	−	69.2731i	0.195097	−	0.337917i
$206$		0			0
$207$	341.955	−	197.428i	1.65195	−	0.953756i
$208$		0			0
$209$	−458.786			−2.19515
$210$		0			0
$211$			1.68267i			0.00797473i	0.999992	+	0.00398737i	$0.00126922\pi$
$211$			1.68267i			0.00797473i	−0.999992	+	0.00398737i	$0.998731\pi$
$212$		0			0
$213$	56.2917	+	97.5000i	0.264280	+	0.457747i
$214$		0			0
$215$	−119.424	−	68.9493i	−0.555459	−	0.320694i
$216$		0			0
$217$	28.0861	−	135.315i	0.129429	−	0.623570i
$218$		0			0
$219$	−289.589	−	167.194i	−1.32233	−	0.763445i
$220$		0			0
$221$	17.8207	+	30.8663i	0.0806365	+	0.139667i
$222$		0			0
$223$		−	247.049i		−	1.10784i	−0.832569	−	0.553922i	$-0.813131\pi$
$223$		−	247.049i		−	1.10784i	0.832569	−	0.553922i	$-0.186869\pi$
$224$		0			0
$225$	291.465			1.29540
$226$		0			0
$227$	−153.492	+	88.6186i	−0.676176	+	0.390390i	−0.798413	−	0.602111i	$-0.794327\pi$
$227$	−153.492	+	88.6186i	−0.676176	+	0.390390i	0.122237	+	0.992501i	$0.460993\pi$
$228$		0			0
$229$	56.8684	−	98.4990i	0.248334	−	0.430127i	−0.714730	−	0.699401i	$-0.753450\pi$
$229$	56.8684	−	98.4990i	0.248334	−	0.430127i	0.963064	+	0.269274i	$0.0867837\pi$
$230$		0			0
$231$	−164.390	−	497.824i	−0.711643	−	2.15508i
$232$		0			0
$233$	29.2127	−	50.5979i	0.125377	−	0.217158i	−0.796504	−	0.604634i	$-0.793319\pi$
$233$	29.2127	−	50.5979i	0.125377	−	0.217158i	0.921880	+	0.387475i	$0.126653\pi$
$234$		0			0
$235$	−76.1463	+	43.9631i	−0.324027	+	0.187077i
$236$		0			0
$237$	−304.670			−1.28553
$238$		0			0
$239$		−	128.390i		−	0.537197i	−0.963252	−	0.268598i	$-0.913440\pi$
$239$		−	128.390i		−	0.537197i	0.963252	−	0.268598i	$-0.0865604\pi$
$240$		0			0
$241$	−149.311	−	258.614i	−0.619548	−	1.07309i	−0.989568	−	0.144064i	$-0.953983\pi$
$241$	−149.311	−	258.614i	−0.619548	−	1.07309i	0.370021	−	0.929023i	$-0.379351\pi$
$242$		0			0
$243$	−197.468	−	114.008i	−0.812624	−	0.469169i
$244$		0			0
$245$	−104.301	−	45.2469i	−0.425716	−	0.184681i
$246$		0			0
$247$	385.012	+	222.287i	1.55875	+	0.899945i
$248$		0			0
$249$	−88.8574	−	153.906i	−0.356857	−	0.618095i
$250$		0			0
$251$		−	90.1849i		−	0.359302i	−0.983730	−	0.179651i	$-0.942503\pi$
$251$		−	90.1849i		−	0.359302i	0.983730	−	0.179651i	$-0.0574969\pi$
$252$		0			0
$253$	−407.479			−1.61059
$254$		0			0
$255$	−23.5435	+	13.5929i	−0.0923276	+	0.0533054i
$256$		0			0
$257$	134.768	−	233.425i	0.524388	−	0.908267i	−0.475209	−	0.879873i	$-0.657627\pi$
$257$	134.768	−	233.425i	0.524388	−	0.908267i	0.999597	−	0.0283939i	$-0.00903926\pi$
$258$		0			0
$259$	106.930	+	323.816i	0.412855	+	1.25026i
$260$		0			0
$261$	−35.3497	+	61.2274i	−0.135439	+	0.234588i
$262$		0			0
$263$	−319.625	+	184.535i	−1.21530	+	0.701655i	−0.963910	−	0.266230i	$-0.914222\pi$
$263$	−319.625	+	184.535i	−1.21530	+	0.701655i	−0.251393	+	0.967885i	$0.580889\pi$
$264$		0			0
$265$	154.372			0.582536
$266$		0			0
$267$		−	431.922i		−	1.61769i
$268$		0			0
$269$	224.911	+	389.557i	0.836099	+	1.44817i	0.893132	+	0.449794i	$0.148503\pi$
$269$	224.911	+	389.557i	0.836099	+	1.44817i	−0.0570334	+	0.998372i	$0.518164\pi$
$270$		0			0
$271$	−100.007	−	57.7393i	−0.369031	−	0.213060i	0.304004	−	0.952671i	$-0.401676\pi$
$271$	−100.007	−	57.7393i	−0.369031	−	0.213060i	−0.673035	+	0.739611i	$0.735010\pi$
$272$		0			0
$273$	−103.245	+	497.420i	−0.378188	+	1.82205i
$274$		0			0
$275$	−260.486	−	150.392i	−0.947221	−	0.546878i
$276$		0			0
$277$	−45.7829	−	79.2983i	−0.165281	−	0.286275i	0.771474	−	0.636261i	$-0.219520\pi$
$277$	−45.7829	−	79.2983i	−0.165281	−	0.286275i	−0.936755	+	0.349986i	$0.886186\pi$
$278$		0			0
$279$		−	293.340i		−	1.05140i
$280$		0			0
$281$	−106.341			−0.378437			−0.189218	−	0.981935i	$-0.560595\pi$
$281$	−106.341			−0.378437			−0.189218	+	0.981935i	$0.560595\pi$
$282$		0			0
$283$	−50.0462	+	28.8942i	−0.176842	+	0.102100i	−0.585808	−	0.810450i	$-0.699223\pi$
$283$	−50.0462	+	28.8942i	−0.176842	+	0.102100i	0.408966	+	0.912550i	$0.365889\pi$
$284$		0			0
$285$	−169.551	+	293.671i	−0.594916	+	1.03042i
$286$		0			0
$287$	160.617	−	180.108i	0.559639	−	0.627554i
$288$		0			0
$289$	141.623	−	245.298i	0.490045	−	0.848783i
$290$		0			0
$291$	−62.8514	+	36.2873i	−0.215984	+	0.124699i
$292$		0			0
$293$	306.168			1.04494			0.522471	−	0.852657i	$-0.325010\pi$
$293$	306.168			1.04494			0.522471	+	0.852657i	$0.325010\pi$
$294$		0			0
$295$		−	209.631i		−	0.710612i
$296$		0			0
$297$	−219.374	−	379.966i	−0.738632	−	1.27935i
$298$		0			0
$299$	341.955	+	197.428i	1.14366	+	0.660293i
$300$		0			0
$301$	−310.498	−	276.896i	−1.03155	−	0.919919i
$302$		0			0
$303$	−73.8129	−	42.6159i	−0.243607	−	0.140646i
$304$		0			0
$305$	−102.270	−	177.137i	−0.335311	−	0.580776i
$306$		0			0
$307$		−	8.03215i		−	0.0261634i	−0.999914	−	0.0130817i	$-0.995836\pi$
$307$		−	8.03215i		−	0.0261634i	0.999914	−	0.0130817i	$-0.00416415\pi$
$308$		0			0
$309$	−427.973			−1.38502
$310$		0			0
$311$	−5.54480	+	3.20129i	−0.0178289	+	0.0102935i	−0.508888	−	0.860833i	$-0.669943\pi$
$311$	−5.54480	+	3.20129i	−0.0178289	+	0.0102935i	0.491059	+	0.871126i	$0.336610\pi$
$312$		0			0
$313$	−26.9567	+	46.6903i	−0.0861236	+	0.149170i	−0.905869	−	0.423557i	$-0.860781\pi$
$313$	−26.9567	+	46.6903i	−0.0861236	+	0.149170i	0.819746	+	0.572727i	$0.194115\pi$
$314$		0			0
$315$	−236.286	−	49.0440i	−0.750115	−	0.155695i
$316$		0			0
$317$	−38.7321	+	67.0860i	−0.122183	+	0.211628i	−0.920628	−	0.390440i	$-0.872323\pi$
$317$	−38.7321	+	67.0860i	−0.122183	+	0.211628i	0.798445	+	0.602068i	$0.205656\pi$
$318$		0			0
$319$	63.1849	−	36.4798i	0.198072	−	0.114357i
$320$		0			0
$321$	429.427			1.33778
$322$		0			0
$323$			71.7738i			0.222210i
$324$		0			0
$325$	145.732	+	252.416i	0.448408	+	0.776665i
$326$		0			0
$327$	875.304	+	505.357i	2.67677	+	1.54543i
$328$		0			0
$329$	−251.888	+	83.1777i	−0.765617	+	0.252820i
$330$		0			0
$331$	292.056	+	168.619i	0.882345	+	0.509422i	0.871431	−	0.490518i	$-0.163193\pi$
$331$	292.056	+	168.619i	0.882345	+	0.509422i	0.0109142	+	0.999940i	$0.496526\pi$
$332$		0			0
$333$	361.918	+	626.861i	1.08684	+	1.88246i
$334$		0			0
$335$			40.4305i			0.120688i
$336$		0			0
$337$	−58.4923			−0.173568			−0.0867838	−	0.996227i	$-0.527659\pi$
$337$	−58.4923			−0.173568			−0.0867838	+	0.996227i	$0.527659\pi$
$338$		0			0
$339$	828.283	−	478.209i	2.44331	−	1.41065i
$340$		0			0
$341$	−151.359	+	262.162i	−0.443869	+	0.768803i
$342$		0			0
$343$	−280.357	−	197.607i	−0.817369	−	0.576115i
$344$		0			0
$345$	−150.590	+	260.829i	−0.436491	+	0.756025i
$346$		0			0
$347$	−544.761	+	314.518i	−1.56992	+	0.906391i	−0.573738	+	0.819039i	$0.694507\pi$
$347$	−544.761	+	314.518i	−1.56992	+	0.906391i	−0.996178	+	0.0873520i	$0.972160\pi$
$348$		0			0
$349$	377.340			1.08120			0.540602	−	0.841279i	$-0.318197\pi$
$349$	377.340			1.08120			0.540602	+	0.841279i	$0.318197\pi$
$350$		0			0
$351$			425.155i			1.21127i
$352$		0			0
$353$	−197.007	−	341.226i	−0.558093	−	0.966646i	−0.997656	−	0.0684338i	$-0.978200\pi$
$353$	−197.007	−	341.226i	−0.558093	−	0.966646i	0.439562	−	0.898212i	$-0.355134\pi$
$354$		0			0
$355$	−46.3148	−	26.7399i	−0.130464	−	0.0753236i
$356$		0			0
$357$	−77.8809	+	25.7176i	−0.218154	+	0.0720380i
$358$		0			0
$359$	62.5991	+	36.1416i	0.174371	+	0.100673i	0.584645	−	0.811289i	$-0.301234\pi$
$359$	62.5991	+	36.1416i	0.174371	+	0.100673i	−0.410274	+	0.911962i	$0.634567\pi$
$360$		0			0
$361$	267.136	+	462.693i	0.739989	+	1.28170i
$362$		0			0
$363$			557.355i			1.53541i
$364$		0			0
$365$	158.843			0.435185
$366$		0			0
$367$	−455.370	+	262.908i	−1.24079	+	0.716371i	−0.969255	−	0.246058i	$-0.920865\pi$
$367$	−455.370	+	262.908i	−1.24079	+	0.716371i	−0.271535	+	0.962428i	$0.587531\pi$
$368$		0			0
$369$	256.115	−	443.605i	0.694079	−	1.20218i
$370$		0			0
$371$	456.009	+	94.6501i	1.22914	+	0.255121i
$372$		0			0
$373$	55.5660	−	96.2432i	0.148971	−	0.258025i	−0.781877	−	0.623433i	$-0.785737\pi$
$373$	55.5660	−	96.2432i	0.148971	−	0.258025i	0.930847	+	0.365409i	$0.119071\pi$
$374$		0			0
$375$	−437.904	+	252.824i	−1.16774	+	0.674197i
$376$		0			0
$377$	−70.6993			−0.187531
$378$		0			0
$379$		−	276.174i		−	0.728692i	−0.931264	−	0.364346i	$-0.881293\pi$
$379$		−	276.174i		−	0.728692i	0.931264	−	0.364346i	$-0.118707\pi$
$380$		0			0
$381$	−458.205	−	793.634i	−1.20264	−	2.08303i
$382$		0			0
$383$	97.7065	+	56.4109i	0.255108	+	0.147287i	0.622101	−	0.782937i	$-0.286279\pi$
$383$	97.7065	+	56.4109i	0.255108	+	0.147287i	−0.366993	+	0.930224i	$0.619613\pi$
$384$		0			0
$385$	185.866	+	165.752i	0.482769	+	0.430523i
$386$		0			0
$387$	−764.754	−	441.531i	−1.97611	−	1.14091i
$388$		0			0
$389$	333.410	+	577.483i	0.857096	+	1.48453i	0.874687	+	0.484688i	$0.161067\pi$
$389$	333.410	+	577.483i	0.857096	+	1.48453i	−0.0175914	+	0.999845i	$0.505600\pi$
$390$		0			0
$391$			63.7471i			0.163036i
$392$		0			0
$393$	1140.67			2.90246
$394$		0			0
$395$	125.336	−	72.3628i	0.317307	−	0.183197i
$396$		0			0
$397$	138.416	−	239.743i	0.348654	−	0.603886i	−0.637357	−	0.770569i	$-0.719972\pi$
$397$	138.416	−	239.743i	0.348654	−	0.603886i	0.986011	+	0.166683i	$0.0533055\pi$
$398$		0			0
$399$	−680.905	+	763.536i	−1.70653	+	1.91362i
$400$		0			0
$401$	311.419	−	539.394i	0.776606	−	1.34512i	−0.157281	−	0.987554i	$-0.550273\pi$
$401$	311.419	−	539.394i	0.776606	−	1.34512i	0.933887	−	0.357567i	$-0.116394\pi$
$402$		0			0
$403$	254.040	−	146.670i	0.630372	−	0.363946i
$404$		0			0
$405$	−14.0187			−0.0346141
$406$		0			0
$407$		−	746.978i		−	1.83533i
$408$		0			0
$409$	−36.1189	−	62.5598i	−0.0883103	−	0.152958i	0.818487	−	0.574525i	$-0.194813\pi$
$409$	−36.1189	−	62.5598i	−0.0883103	−	0.152958i	−0.906797	+	0.421568i	$0.861480\pi$
$410$		0			0
$411$	543.244	+	313.642i	1.32176	+	0.763120i
$412$		0			0
$413$	128.531	−	619.241i	0.311212	−	1.49937i
$414$		0			0
$415$	73.1088	+	42.2094i	0.176166	+	0.101709i
$416$		0			0
$417$	−135.341	−	234.417i	−0.324558	−	0.562152i
$418$		0			0
$419$			331.864i			0.792039i	0.918242	+	0.396020i	$0.129609\pi$
$419$			331.864i			0.792039i	−0.918242	+	0.396020i	$0.870391\pi$
$420$		0			0
$421$	−685.770			−1.62891			−0.814454	−	0.580228i	$-0.802963\pi$
$421$	−685.770			−1.62891			−0.814454	+	0.580228i	$0.802963\pi$
$422$		0			0
$423$	−487.619	+	281.527i	−1.15276	+	0.665548i
$424$		0			0
$425$	−23.5277	+	40.7511i	−0.0553592	+	0.0958850i
$426$		0			0
$427$	−193.494	−	585.960i	−0.453147	−	1.37227i
$428$		0			0
$429$	556.400	−	963.713i	1.29697	−	2.24642i
$430$		0			0
$431$	520.232	−	300.356i	1.20703	−	0.696882i	0.244924	−	0.969542i	$-0.421237\pi$
$431$	520.232	−	300.356i	1.20703	−	0.696882i	0.962110	+	0.272661i	$0.0879036\pi$
$432$		0			0
$433$	281.591			0.650326			0.325163	−	0.945658i	$-0.394581\pi$
$433$	281.591			0.650326			0.325163	+	0.945658i	$0.394581\pi$
$434$		0			0
$435$		−	53.9265i		−	0.123969i
$436$		0			0
$437$	397.575	+	688.621i	0.909784	+	1.57579i
$438$		0			0
$439$	74.2090	+	42.8446i	0.169041	+	0.0975958i	0.582134	−	0.813093i	$-0.302218\pi$
$439$	74.2090	+	42.8446i	0.169041	+	0.0975958i	−0.413093	+	0.910689i	$0.635551\pi$
$440$		0			0
$441$	−667.910	−	289.748i	−1.51454	−	0.657025i
$442$		0			0
$443$	317.017	+	183.030i	0.715613	+	0.413159i	0.813136	−	0.582074i	$-0.197759\pi$
$443$	317.017	+	183.030i	0.715613	+	0.413159i	−0.0975227	+	0.995233i	$0.531092\pi$
$444$		0			0
$445$	102.587	+	177.685i	0.230532	+	0.399293i
$446$		0			0
$447$			121.746i			0.272362i
$448$		0			0
$449$	−189.922			−0.422989			−0.211494	−	0.977379i	$-0.567833\pi$
$449$	−189.922			−0.422989			−0.211494	+	0.977379i	$0.567833\pi$
$450$		0			0
$451$	−457.787	+	264.303i	−1.01505	+	0.586038i
$452$		0			0
$453$	−33.7847	+	58.5169i	−0.0745800	+	0.129176i
$454$		0			0
$455$	−75.6698	−	229.152i	−0.166307	−	0.503631i
$456$		0			0
$457$	−309.139	+	535.445i	−0.676453	+	1.17165i	0.299589	+	0.954068i	$0.403150\pi$
$457$	−309.139	+	535.445i	−0.676453	+	1.17165i	−0.976042	+	0.217583i	$0.930183\pi$
$458$		0			0
$459$	−59.4430	+	34.3194i	−0.129505	+	0.0747700i
$460$		0			0
$461$	−191.089			−0.414509			−0.207254	−	0.978287i	$-0.566453\pi$
$461$	−191.089			−0.414509			−0.207254	+	0.978287i	$0.566453\pi$
$462$		0			0
$463$			61.7661i			0.133404i	0.997773	+	0.0667021i	$0.0212477\pi$
$463$			61.7661i			0.133404i	−0.997773	+	0.0667021i	$0.978752\pi$
$464$		0			0
$465$	111.874	+	193.771i	0.240589	+	0.416712i
$466$		0			0
$467$	−66.2316	−	38.2388i	−0.141824	−	0.0818819i	0.427409	−	0.904058i	$-0.359426\pi$
$467$	−66.2316	−	38.2388i	−0.141824	−	0.0818819i	−0.569233	+	0.822176i	$0.692760\pi$
$468$		0			0
$469$	−24.7891	+	119.430i	−0.0528552	+	0.254648i
$470$		0			0
$471$	364.802	+	210.619i	0.774527	+	0.447174i
$472$		0			0
$473$	455.647	+	789.204i	0.963313	+	1.66851i
$474$		0			0
$475$			586.946i			1.23568i
$476$		0			0
$477$	988.554			2.07244
$478$		0			0
$479$	61.4566	−	35.4820i	0.128302	−	0.0740751i	−0.434475	−	0.900684i	$-0.643066\pi$
$479$	61.4566	−	35.4820i	0.128302	−	0.0740751i	0.562777	+	0.826609i	$0.309733\pi$
$480$		0			0
$481$	−361.918	+	626.861i	−0.752429	+	1.30324i
$482$		0			0
$483$	−604.757	+	678.147i	−1.25209	+	1.40403i
$484$		0			0
$485$	17.2373	−	29.8559i	0.0355409	−	0.0615586i
$486$		0			0
$487$	707.416	−	408.427i	1.45260	−	0.838659i	0.453972	−	0.891016i	$-0.350007\pi$
$487$	707.416	−	408.427i	1.45260	−	0.838659i	0.998628	+	0.0523570i	$0.0166734\pi$
$488$		0			0
$489$	−757.049			−1.54816
$490$		0			0
$491$		−	200.042i		−	0.407417i	−0.979032	−	0.203708i	$-0.934701\pi$
$491$		−	200.042i		−	0.407417i	0.979032	−	0.203708i	$-0.0652995\pi$
$492$		0			0
$493$	−5.70700	−	9.88482i	−0.0115761	−	0.0200503i
$494$		0			0
$495$	457.787	+	264.303i	0.924822	+	0.533946i
$496$		0			0
$497$	−120.417	−	107.386i	−0.242288	−	0.216068i
$498$		0			0
$499$	72.7683	+	42.0128i	0.145828	+	0.0841940i	0.571139	−	0.820853i	$-0.306502\pi$
$499$	72.7683	+	42.0128i	0.145828	+	0.0841940i	−0.425311	+	0.905047i	$0.639835\pi$
$500$		0			0
$501$	−584.067	−	1011.63i	−1.16580	−	2.01923i
$502$		0			0
$503$		−	655.443i		−	1.30307i	−0.758620	−	0.651533i	$-0.774126\pi$
$503$		−	655.443i		−	1.30307i	0.758620	−	0.651533i	$-0.225874\pi$
$504$		0			0
$505$	40.4871			0.0801725
$506$		0			0
$507$	−218.973	+	126.424i	−0.431899	+	0.249357i
$508$		0			0
$509$	−171.207	+	296.540i	−0.336360	+	0.582593i	−0.983745	−	0.179570i	$-0.942529\pi$
$509$	−171.207	+	296.540i	−0.336360	+	0.582593i	0.647385	+	0.762163i	$0.275863\pi$
$510$		0			0
$511$	469.215	+	97.3911i	0.918229	+	0.190589i
$512$		0			0
$513$	−428.084	+	741.463i	−0.834472	+	1.44535i
$514$		0			0
$515$	176.061	−	101.649i	0.341865	−	0.197376i
$516$		0			0
$517$	581.054			1.12390
$518$		0			0
$519$		−	530.423i		−	1.02201i
$520$		0			0
$521$	−153.678	−	266.179i	−0.294968	−	0.510900i	0.680009	−	0.733203i	$-0.261976\pi$
$521$	−153.678	−	266.179i	−0.294968	−	0.510900i	−0.974977	+	0.222304i	$0.928642\pi$
$522$		0			0
$523$	29.5522	+	17.0620i	0.0565052	+	0.0326233i	0.527986	−	0.849253i	$-0.322947\pi$
$523$	29.5522	+	17.0620i	0.0565052	+	0.0326233i	−0.471481	+	0.881876i	$0.656281\pi$
$524$		0			0
$525$	−636.888	+	210.311i	−1.21312	+	0.400592i
$526$		0			0
$527$	41.0133	+	23.6790i	0.0778241	+	0.0449318i
$528$		0			0
$529$	88.6134	+	153.483i	0.167511	+	0.290138i
$530$		0			0
$531$		−	1342.41i		−	2.52809i
$532$		0			0
$533$	512.230			0.961033
$534$		0			0
$535$	−176.659	+	101.994i	−0.330203	+	0.190643i
$536$		0			0
$537$	−406.383	+	703.877i	−0.756766	+	1.31076i
$538$		0			0
$539$	447.414	+	603.583i	0.830082	+	1.11982i
$540$		0			0
$541$	−383.984	+	665.079i	−0.709767	+	1.22935i	0.255177	+	0.966894i	$0.417866\pi$
$541$	−383.984	+	665.079i	−0.709767	+	1.22935i	−0.964944	+	0.262458i	$0.915467\pi$
$542$		0			0
$543$	75.8774	−	43.8078i	0.139737	−	0.0806774i
$544$		0			0
$545$	−480.113			−0.880942
$546$		0			0
$547$		−	321.892i		−	0.588468i	−0.955733	−	0.294234i	$-0.904935\pi$
$547$		−	321.892i		−	0.588468i	0.955733	−	0.294234i	$-0.0950645\pi$
$548$		0			0
$549$	−654.907	−	1134.33i	−1.19291	−	2.06618i
$550$		0			0
$551$	−123.298	−	71.1864i	−0.223772	−	0.129195i
$552$		0			0
$553$	414.606	−	136.910i	0.749739	−	0.247576i
$554$		0			0
$555$	−478.143	−	276.056i	−0.861520	−	0.497399i
$556$		0			0
$557$	−427.107	−	739.771i	−0.766799	−	1.32814i	−0.939290	−	0.343124i	$-0.888515\pi$
$557$	−427.107	−	739.771i	−0.766799	−	1.32814i	0.172491	−	0.985011i	$-0.444819\pi$
$558$		0			0
$559$		−	883.062i		−	1.57972i
$560$		0			0
$561$	179.655			0.320241
$562$		0			0
$563$	−237.695	+	137.233i	−0.422194	+	0.243754i	−0.696016	−	0.718027i	$-0.745046\pi$
$563$	−237.695	+	137.233i	−0.422194	+	0.243754i	0.273821	+	0.961781i	$0.411712\pi$
$564$		0			0
$565$	−227.161	+	393.454i	−0.402054	+	0.696379i
$566$		0			0
$567$	−41.4108	−	8.59529i	−0.0730349	−	0.0151593i
$568$		0			0
$569$	490.671	−	849.867i	0.862339	−	1.49362i	−0.00732570	−	0.999973i	$-0.502332\pi$
$569$	490.671	−	849.867i	0.862339	−	1.49362i	0.869665	−	0.493642i	$-0.164335\pi$
$570$		0			0
$571$	−100.747	+	58.1661i	−0.176439	+	0.101867i	−0.585619	−	0.810587i	$-0.699148\pi$
$571$	−100.747	+	58.1661i	−0.176439	+	0.101867i	0.409179	+	0.912454i	$0.365815\pi$
$572$		0			0
$573$	−251.551			−0.439008
$574$		0			0
$575$			521.306i			0.906619i
$576$		0			0
$577$	146.753	+	254.184i	0.254339	+	0.440527i	0.964716	−	0.263294i	$-0.0848089\pi$
$577$	146.753	+	254.184i	0.254339	+	0.440527i	−0.710377	+	0.703821i	$0.751476\pi$
$578$		0			0
$579$	−303.537	−	175.247i	−0.524244	−	0.302672i
$580$		0			0
$581$	190.081	+	169.510i	0.327161	+	0.291756i
$582$		0			0
$583$	−883.483	−	510.079i	−1.51541	−	0.874921i
$584$		0			0
$585$	−256.115	−	443.605i	−0.437804	−	0.758298i
$586$		0			0
$587$		−	307.133i		−	0.523224i	−0.965173	−	0.261612i	$-0.915746\pi$
$587$		−	307.133i		−	0.523224i	0.965173	−	0.261612i	$-0.0842541\pi$
$588$		0			0
$589$	590.722			1.00292
$590$		0			0
$591$	242.492	−	140.003i	0.410308	−	0.236891i
$592$		0			0
$593$	−233.319	+	404.121i	−0.393456	+	0.681486i	−0.992903	−	0.118929i	$-0.962054\pi$
$593$	−233.319	+	404.121i	−0.393456	+	0.681486i	0.599447	+	0.800415i	$0.295387\pi$
$594$		0			0
$595$	25.9306	−	29.0774i	0.0435809	−	0.0488696i
$596$		0			0
$597$	256.456	−	444.194i	0.429574	−	0.744044i
$598$		0			0
$599$	−529.994	+	305.992i	−0.884798	+	0.510838i	−0.872237	−	0.489083i	$-0.837332\pi$
$599$	−529.994	+	305.992i	−0.884798	+	0.510838i	−0.0125605	+	0.999921i	$0.503998\pi$
$600$		0			0
$601$	133.327			0.221842			0.110921	−	0.993829i	$-0.464620\pi$
$601$	133.327			0.221842			0.110921	+	0.993829i	$0.464620\pi$
$602$		0			0
$603$			258.905i			0.429361i
$604$		0			0
$605$	−132.378	−	229.286i	−0.218807	−	0.378985i
$606$		0			0
$607$	−783.900	−	452.585i	−1.29143	−	0.745610i	−0.312525	−	0.949909i	$-0.601175\pi$
$607$	−783.900	−	452.585i	−1.29143	−	0.745610i	−0.978908	+	0.204300i	$0.934508\pi$
$608$		0			0
$609$	33.0639	−	159.297i	0.0542922	−	0.261571i
$610$		0			0
$611$	−487.619	−	281.527i	−0.798066	−	0.460764i
$612$		0			0
$613$	−137.160	−	237.569i	−0.223753	−	0.387551i	0.732192	−	0.681099i	$-0.238497\pi$
$613$	−137.160	−	237.569i	−0.223753	−	0.387551i	−0.955945	+	0.293547i	$0.905164\pi$
$614$		0			0
$615$			390.708i			0.635298i
$616$		0			0
$617$	−255.450			−0.414019			−0.207010	−	0.978339i	$-0.566373\pi$
$617$	−255.450			−0.414019			−0.207010	+	0.978339i	$0.566373\pi$
$618$		0			0
$619$	−375.221	+	216.634i	−0.606173	+	0.349974i	−0.771466	−	0.636270i	$-0.780476\pi$
$619$	−375.221	+	216.634i	−0.606173	+	0.349974i	0.165293	+	0.986244i	$0.447143\pi$
$620$		0			0
$621$	−380.210	+	658.543i	−0.612254	+	1.06046i
$622$		0			0
$623$	194.093	+	587.775i	0.311546	+	0.943458i
$624$		0			0
$625$	−125.108	+	216.694i	−0.200173	+	0.346711i
$626$		0			0
$627$	1940.71	−	1120.47i	3.09522	−	1.78703i
$628$		0			0
$629$	−116.859			−0.185786
$630$		0			0
$631$		−	339.246i		−	0.537632i	−0.963192	−	0.268816i	$-0.913368\pi$
$631$		−	339.246i		−	0.537632i	0.963192	−	0.268816i	$-0.0866324\pi$
$632$		0			0
$633$	−4.10948	−	7.11784i	−0.00649208	−	0.0112446i
$634$		0			0
$635$	376.995	+	217.658i	0.593693	+	0.342769i
$636$		0			0
$637$	−83.0258	−	723.301i	−0.130339	−	1.13548i
$638$		0			0
$639$	−296.587	−	171.234i	−0.464142	−	0.267973i
$640$		0			0
$641$	−445.832	−	772.203i	−0.695526	−	1.20469i	−0.970003	−	0.243092i	$-0.921838\pi$
$641$	−445.832	−	772.203i	−0.695526	−	1.20469i	0.274478	−	0.961593i	$-0.411495\pi$
$642$		0			0
$643$		−	535.530i		−	0.832861i	−0.909167	−	0.416431i	$-0.863281\pi$
$643$		−	535.530i		−	0.832861i	0.909167	−	0.416431i	$-0.136719\pi$
$644$		0			0
$645$	673.563			1.04428
$646$		0			0
$647$	329.954	−	190.499i	0.509975	−	0.294434i	−0.222848	−	0.974853i	$-0.571535\pi$
$647$	329.954	−	190.499i	0.509975	−	0.294434i	0.732823	+	0.680419i	$0.238202\pi$
$648$		0			0
$649$	−692.666	+	1199.73i	−1.06728	+	1.84859i
$650$		0			0
$651$	211.664	+	640.986i	0.325137	+	0.984617i
$652$		0			0
$653$	−205.764	+	356.393i	−0.315105	+	0.545778i	−0.979460	−	0.201639i	$-0.935373\pi$
$653$	−205.764	+	356.393i	−0.315105	+	0.545778i	0.664355	+	0.747417i	$0.268706\pi$
$654$		0			0
$655$	−469.251	+	270.922i	−0.716413	+	0.413622i
$656$		0			0
$657$	1017.18			1.54822
$658$		0			0
$659$		−	949.241i		−	1.44043i	−0.693753	−	0.720213i	$-0.744044\pi$
$659$		−	949.241i		−	1.44043i	0.693753	−	0.720213i	$-0.255956\pi$
$660$		0			0
$661$	−356.235	−	617.018i	−0.538934	−	0.933461i	−0.998962	−	0.0455565i	$-0.985494\pi$
$661$	−356.235	−	617.018i	−0.538934	−	0.933461i	0.460028	−	0.887905i	$-0.347839\pi$
$662$		0			0
$663$	−150.766	−	87.0448i	−0.227400	−	0.131289i
$664$		0			0
$665$	98.7638	−	475.828i	0.148517	−	0.715531i
$666$		0			0
$667$	−109.510	−	63.2254i	−0.164182	−	0.0947907i
$668$		0			0
$669$	603.354	+	1045.04i	0.901874	+	1.56209i
$670$		0			0
$671$			1351.69i			2.01444i
$672$		0			0
$673$	−1229.52			−1.82692			−0.913462	−	0.406925i	$-0.866601\pi$
$673$	−1229.52			−1.82692			−0.913462	+	0.406925i	$0.866601\pi$
$674$		0			0
$675$	−486.108	+	280.655i	−0.720160	+	0.415784i
$676$		0			0
$677$	658.050	−	1139.78i	0.972008	−	1.68357i	0.282535	−	0.959257i	$-0.408825\pi$
$677$	658.050	−	1139.78i	0.972008	−	1.68357i	0.689473	−	0.724311i	$-0.257842\pi$
$678$		0			0
$679$	69.2239	−	77.6245i	0.101950	−	0.114322i
$680$		0			0
$681$	432.856	−	749.729i	0.635618	−	1.10092i
$682$		0			0
$683$	186.553	−	107.706i	0.273138	−	0.157696i	−0.357175	−	0.934037i	$-0.616260\pi$
$683$	186.553	−	107.706i	0.273138	−	0.157696i	0.630313	+	0.776341i	$0.282927\pi$
$684$		0			0
$685$	−297.975			−0.435000
$686$		0			0
$687$			555.546i			0.808655i
$688$		0			0
$689$	494.277	+	856.113i	0.717383	+	1.24254i
$690$		0			0
$691$	377.039	+	217.684i	0.545643	+	0.315027i	0.747363	−	0.664416i	$-0.231320\pi$
$691$	377.039	+	217.684i	0.545643	+	0.315027i	−0.201720	+	0.979443i	$0.564653\pi$
$692$		0			0
$693$	1190.23	+	1061.42i	1.71751	+	1.53164i
$694$		0			0
$695$	111.354	+	64.2901i	0.160221	+	0.0925038i
$696$		0			0
$697$	41.3483	+	71.6174i	0.0593233	+	0.102751i
$698$		0			0
$699$			285.378i			0.408266i
$700$		0			0
$701$	134.132			0.191344			0.0956722	−	0.995413i	$-0.469500\pi$
$701$	134.132			0.191344			0.0956722	+	0.995413i	$0.469500\pi$
$702$		0			0
$703$	−1262.36	+	728.823i	−1.79567	+	1.03673i
$704$		0			0
$705$	214.737	−	371.935i	0.304591	−	0.527568i
$706$		0			0
$707$	119.597	+	24.8238i	0.169162	+	0.0351115i
$708$		0			0
$709$	−576.723	+	998.913i	−0.813431	+	1.40890i	0.0970181	+	0.995283i	$0.469070\pi$
$709$	−576.723	+	998.913i	−0.813431	+	1.40890i	−0.910449	+	0.413621i	$0.864264\pi$
$710$		0			0
$711$	802.616	−	463.390i	1.12885	−	0.651745i
$712$		0			0
$713$	524.660			0.735848
$714$		0			0
$715$			528.607i			0.739310i
$716$		0			0
$717$	313.560	+	543.101i	0.437322	+	0.757463i
$718$		0			0
$719$	109.915	+	63.4596i	0.152872	+	0.0882609i	0.574485	−	0.818515i	$-0.305202\pi$
$719$	109.915	+	63.4596i	0.152872	+	0.0882609i	−0.421613	+	0.906776i	$0.638536\pi$
$720$		0			0
$721$	582.400	−	192.318i	0.807767	−	0.266738i
$722$		0			0
$723$	1263.20	+	729.307i	1.74716	+	1.00872i
$724$		0			0
$725$	−46.6703	−	80.8353i	−0.0643728	−	0.111497i
$726$		0			0
$727$			141.915i			0.195206i	0.995225	+	0.0976029i	$0.0311175\pi$
$727$			141.915i			0.195206i	−0.995225	+	0.0976029i	$0.968882\pi$
$728$		0			0
$729$	1168.12			1.60236
$730$		0			0
$731$	123.465	−	71.2827i	0.168899	−	0.0975139i
$732$		0			0
$733$	−604.395	+	1046.84i	−0.824550	+	1.42816i	0.0777128	+	0.996976i	$0.475238\pi$
$733$	−604.395	+	1046.84i	−0.824550	+	1.42816i	−0.902263	+	0.431187i	$0.858095\pi$
$734$		0			0
$735$	551.704	−	63.3287i	0.750618	−	0.0861615i
$736$		0			0
$737$	133.591	−	231.387i	0.181263	−	0.313957i
$738$		0			0
$739$	−854.802	+	493.520i	−1.15670	+	0.667821i	−0.950511	−	0.310691i	$-0.899440\pi$
$739$	−854.802	+	493.520i	−1.15670	+	0.667821i	−0.206189	+	0.978512i	$0.566106\pi$
$740$		0			0
$741$	−2171.51			−2.93051
$742$		0			0
$743$			370.978i			0.499297i	0.968336	+	0.249649i	$0.0803151\pi$
$743$			370.978i			0.499297i	−0.968336	+	0.249649i	$0.919685\pi$
$744$		0			0
$745$	−28.9160	−	50.0841i	−0.0388135	−	0.0672269i
$746$		0			0
$747$	468.167	+	270.297i	0.626730	+	0.361843i
$748$		0			0
$749$	−584.379	+	192.972i	−0.780212	+	0.257639i
$750$		0			0
$751$	781.000	+	450.911i	1.03995	+	0.600414i	0.919818	−	0.392345i	$-0.128336\pi$
$751$	781.000	+	450.911i	1.03995	+	0.600414i	0.120129	+	0.992758i	$0.461669\pi$
$752$		0			0
$753$	220.253	+	381.490i	0.292501	+	0.506627i
$754$		0			0
$755$		−	32.0971i		−	0.0425127i
$756$		0			0
$757$	696.663			0.920295			0.460147	−	0.887842i	$-0.347797\pi$
$757$	696.663			0.920295			0.460147	+	0.887842i	$0.347797\pi$
$758$		0			0
$759$	1723.67	−	995.162i	2.27098	−	1.31115i
$760$		0			0
$761$	242.666	−	420.310i	0.318878	−	0.552312i	−0.661376	−	0.750054i	$-0.730027\pi$
$761$	242.666	−	420.310i	0.318878	−	0.552312i	0.980254	+	0.197742i	$0.0633607\pi$
$762$		0			0
$763$	−1418.24	−	294.372i	−1.85876	−	0.385808i
$764$		0			0
$765$	41.3483	−	71.6174i	0.0540501	−	0.0936176i
$766$		0			0
$767$	1162.56	−	671.207i	1.51573	−	0.875106i
$768$		0			0
$769$	−810.918			−1.05451			−0.527255	−	0.849707i	$-0.676779\pi$
$769$	−810.918			−1.05451			−0.527255	+	0.849707i	$0.676779\pi$
$770$		0			0
$771$			1316.54i			1.70758i
$772$		0			0
$773$	410.825	+	711.569i	0.531468	+	0.920529i	0.999325	+	0.0367254i	$0.0116927\pi$
$773$	410.825	+	711.569i	0.531468	+	0.920529i	−0.467858	+	0.883804i	$0.654974\pi$
$774$		0			0
$775$	335.395	+	193.641i	0.432768	+	0.249859i
$776$		0			0
$777$	−1243.16	−	1108.62i	−1.59995	−	1.42680i
$778$		0			0
$779$	893.322	+	515.759i	1.14675	+	0.662079i
$780$		0			0
$781$	176.709	+	306.069i	0.226260	+	0.391893i
$782$		0			0
$783$		−	136.154i		−	0.173888i
$784$		0			0
$785$	−200.098			−0.254902
$786$		0			0
$787$	−442.326	+	255.377i	−0.562041	+	0.324494i	−0.753964	−	0.656916i	$-0.771861\pi$
$787$	−442.326	+	255.377i	−0.562041	+	0.324494i	0.191924	+	0.981410i	$0.438527\pi$
$788$		0			0
$789$	901.360	−	1561.20i	1.14241	−	1.97871i
$790$		0			0
$791$	−912.262	+	1022.97i	−1.15330	+	1.29326i
$792$		0			0
$793$	654.907	−	1134.33i	0.825860	−	1.43043i
$794$		0			0
$795$	−653.007	+	377.014i	−0.821393	+	0.474231i
$796$		0			0
$797$	1252.13			1.57106			0.785528	−	0.618826i	$-0.212392\pi$
$797$	1252.13			1.57106			0.785528	+	0.618826i	$0.212392\pi$
$798$		0			0
$799$		−	90.9018i		−	0.113769i
$800$		0			0
$801$	656.935	+	1137.85i	0.820144	+	1.42053i
$802$		0			0
$803$	−909.069	−	524.851i	−1.13209	−	0.653613i
$804$		0			0
$805$	87.7187	−	422.615i	0.108967	−	0.524988i
$806$		0			0
$807$	−1902.78	−	1098.57i	−2.35785	−	1.36130i
$808$		0			0
$809$	−35.4418	−	61.3870i	−0.0438094	−	0.0758802i	0.843289	−	0.537460i	$-0.180616\pi$
$809$	−35.4418	−	61.3870i	−0.0438094	−	0.0758802i	−0.887099	+	0.461580i	$0.847283\pi$
$810$		0			0
$811$		−	501.734i		−	0.618661i	−0.950955	−	0.309330i	$-0.899895\pi$
$811$		−	501.734i		−	0.618661i	0.950955	−	0.309330i	$-0.100105\pi$
$812$		0			0
$813$	564.053			0.693793
$814$		0			0
$815$	311.437	−	179.808i	0.382131	−	0.220624i
$816$		0			0
$817$	889.146	−	1540.05i	1.08831	−	1.88500i
$818$		0			0
$819$	−484.567	−	1467.42i	−0.591657	−	1.79172i
$820$		0			0
$821$	−225.044	+	389.788i	−0.274110	+	0.474772i	−0.969910	−	0.243463i	$-0.921716\pi$
$821$	−225.044	+	389.788i	−0.274110	+	0.474772i	0.695800	+	0.718235i	$0.255050\pi$
$822$		0			0
$823$	−890.836	+	514.324i	−1.08243	+	0.624938i	−0.931550	−	0.363614i	$-0.881543\pi$
$823$	−890.836	+	514.324i	−1.08243	+	0.624938i	−0.150876	+	0.988553i	$0.548209\pi$
$824$		0			0
$825$	1469.17			1.78081
$826$		0			0
$827$			731.829i			0.884921i	0.896788	+	0.442460i	$0.145894\pi$
$827$			731.829i			0.884921i	−0.896788	+	0.442460i	$0.854106\pi$
$828$		0			0
$829$	−594.397	−	1029.53i	−0.717005	−	1.24189i	−0.962181	−	0.272411i	$-0.912179\pi$
$829$	−594.397	−	1029.53i	−0.717005	−	1.24189i	0.245176	−	0.969479i	$-0.421154\pi$
$830$		0			0
$831$	387.331	+	223.626i	0.466102	+	0.269104i
$832$		0			0
$833$	94.4263	−	69.9947i	0.113357	−	0.0840272i
$834$		0			0
$835$	480.550	+	277.446i	0.575509	+	0.332270i
$836$		0			0
$837$	282.460	+	489.235i	0.337467	+	0.584511i
$838$		0			0
$839$			774.801i			0.923482i	0.887015	+	0.461741i	$0.152775\pi$
$839$			774.801i			0.923482i	−0.887015	+	0.461741i	$0.847225\pi$
$840$		0			0
$841$	−818.359			−0.973078
$842$		0			0
$843$	449.830	−	259.710i	0.533607	−	0.308078i
$844$		0			0
$845$	60.0544	−	104.017i	0.0710703	−	0.123097i
$846$		0			0
$847$	−250.459	−	758.467i	−0.295701	−	0.895475i
$848$		0			0
$849$	141.133	−	244.450i	0.166235	−	0.287927i
$850$		0			0
$851$	−1121.19	+	647.317i	−1.31749	+	0.760654i
$852$		0			0
$853$	359.661			0.421642			0.210821	−	0.977525i	$-0.432386\pi$
$853$	359.661			0.421642			0.210821	+	0.977525i	$0.432386\pi$
$854$		0			0
$855$		−	1031.52i		−	1.20645i
$856$		0			0
$857$	−476.449	−	825.234i	−0.555950	−	0.962933i	−0.997829	−	0.0658586i	$-0.979021\pi$
$857$	−476.449	−	825.234i	−0.555950	−	0.962933i	0.441879	−	0.897075i	$-0.354312\pi$
$858$		0			0
$859$	−973.259	−	561.911i	−1.13301	−	0.654146i	−0.188323	−	0.982107i	$-0.560305\pi$
$859$	−973.259	−	561.911i	−1.13301	−	0.654146i	−0.944691	+	0.327961i	$0.893638\pi$
$860$		0			0
$861$	−239.555	+	1154.14i	−0.278228	+	1.34046i
$862$		0			0
$863$	−94.4467	−	54.5288i	−0.109440	−	0.0631852i	0.444281	−	0.895888i	$-0.353459\pi$
$863$	−94.4467	−	54.5288i	−0.109440	−	0.0631852i	−0.553721	+	0.832702i	$0.686793\pi$
$864$		0			0
$865$	125.982	+	218.207i	0.145644	+	0.252262i
$866$		0			0
$867$			1383.51i			1.59574i
$868$		0			0
$869$	−956.410			−1.10059
$870$		0			0
$871$	−224.218	+	129.452i	−0.257426	+	0.148625i
$872$		0			0
$873$	110.383	−	191.189i	0.126441	−	0.219002i
$874$		0			0
$875$	482.303	−	540.832i	0.551203	−	0.618094i
$876$		0			0
$877$	−337.620	+	584.775i	−0.384971	+	0.666790i	−0.991765	−	0.128069i	$-0.959122\pi$
$877$	−337.620	+	584.775i	−0.384971	+	0.666790i	0.606794	+	0.794859i	$0.292455\pi$
$878$		0			0
$879$	−1295.12	+	747.736i	−1.47340	+	0.850667i
$880$		0			0
$881$	297.930			0.338173			0.169086	−	0.985601i	$-0.445918\pi$
$881$	297.930			0.338173			0.169086	+	0.985601i	$0.445918\pi$
$882$		0			0
$883$		−	171.710i		−	0.194462i	−0.995262	−	0.0972309i	$-0.969001\pi$
$883$		−	171.710i		−	0.194462i	0.995262	−	0.0972309i	$-0.0309985\pi$
$884$		0			0
$885$	511.969	+	886.756i	0.578496	+	1.00198i
$886$		0			0
$887$	−422.073	−	243.684i	−0.475843	−	0.274728i	0.242839	−	0.970067i	$-0.421921\pi$
$887$	−422.073	−	243.684i	−0.475843	−	0.274728i	−0.718683	+	0.695338i	$0.755255\pi$
$888$		0			0
$889$	980.176	+	874.101i	1.10256	+	0.983240i
$890$		0			0
$891$	80.2302	+	46.3210i	0.0900452	+	0.0519876i
$892$		0			0
$893$	−566.933	−	981.956i	−0.634863	−	1.09961i
$894$		0			0
$895$		−	386.084i		−	0.431378i
$896$		0			0
$897$	−1928.66			−2.15013
$898$		0			0
$899$	−81.3553	+	46.9705i	−0.0904954	+	0.0522475i
$900$		0			0
$901$	−79.7982	+	138.215i	−0.0885663	+	0.153401i
$902$		0			0
$903$	1989.68	+	412.981i	2.20341	+	0.457344i
$904$		0			0
$905$	−20.8098	+	36.0436i	−0.0229942	+	0.0398272i
$906$		0			0
$907$	724.366	−	418.213i	0.798639	−	0.461094i	−0.0443561	−	0.999016i	$-0.514124\pi$
$907$	724.366	−	418.213i	0.798639	−	0.461094i	0.842995	+	0.537921i	$0.180790\pi$
$908$		0			0
$909$	259.268			0.285223
$910$		0			0
$911$		−	1663.72i		−	1.82626i	−0.407672	−	0.913128i	$-0.633659\pi$
$911$		−	1663.72i		−	1.82626i	0.407672	−	0.913128i	$-0.366341\pi$
$912$		0			0
$913$	−278.938	−	483.135i	−0.305518	−	0.529173i
$914$		0			0
$915$	865.222	+	499.536i	0.945597	+	0.545941i
$916$		0			0
$917$	−1552.26	+	512.582i	−1.69276	+	0.558977i
$918$		0			0
$919$	1317.95	+	760.919i	1.43411	+	0.827985i	0.997431	−	0.0716307i	$-0.0228203\pi$
$919$	1317.95	+	760.919i	1.43411	+	0.827985i	0.436682	+	0.899616i	$0.356154\pi$
$920$		0			0
$921$	19.6165	+	33.9767i	0.0212991	+	0.0368911i
$922$		0			0
$923$		−	342.469i		−	0.371039i
$924$		0			0
$925$	−955.642			−1.03313
$926$		0			0
$927$	1127.44	−	650.928i	1.21622	−	0.702188i
$928$		0			0
$929$	−163.801	+	283.712i	−0.176320	+	0.305395i	−0.940617	−	0.339469i	$-0.889753\pi$
$929$	−163.801	+	283.712i	−0.176320	+	0.305395i	0.764297	+	0.644864i	$0.223086\pi$
$930$		0			0
$931$	583.489	−	1345.02i	0.626733	−	1.44471i
$932$		0			0
$933$	15.6366	−	27.0835i	0.0167595	−	0.0290284i
$934$		0			0
$935$	−73.9071	+	42.6703i	−0.0790450	+	0.0456367i
$936$		0			0
$937$	−480.629			−0.512945			−0.256472	−	0.966552i	$-0.582560\pi$
$937$	−480.629			−0.512945			−0.256472	+	0.966552i	$0.582560\pi$
$938$		0			0
$939$		−	263.339i		−	0.280446i
$940$		0			0
$941$	−384.142	−	665.353i	−0.408227	−	0.707071i	0.586464	−	0.809975i	$-0.300520\pi$
$941$	−384.142	−	665.353i	−0.408227	−	0.707071i	−0.994691	+	0.102905i	$0.967186\pi$
$942$		0			0
$943$	793.419	+	458.081i	0.841377	+	0.485769i
$944$		0			0
$945$	441.306	−	145.726i	0.466990	−	0.154208i
$946$		0			0
$947$	−295.937	−	170.859i	−0.312499	−	0.180421i	0.335545	−	0.942024i	$-0.391079\pi$
$947$	−295.937	−	170.859i	−0.312499	−	0.180421i	−0.648044	+	0.761603i	$0.724413\pi$
$948$		0			0
$949$	508.591	+	880.906i	0.535923	+	0.928246i
$950$		0			0
$951$		−	378.373i		−	0.397869i
$952$		0			0
$953$	−22.4379			−0.0235445			−0.0117722	−	0.999931i	$-0.503747\pi$
$953$	−22.4379			−0.0235445			−0.0117722	+	0.999931i	$0.503747\pi$
$954$		0			0
$955$	103.484	−	59.7464i	0.108360	−	0.0625617i
$956$		0			0
$957$	−178.185	+	308.626i	−0.186191	+	0.322493i
$958$		0			0
$959$	−880.207	−	182.697i	−0.917838	−	0.190508i
$960$		0			0
$961$	−285.614	+	494.697i	−0.297205	+	0.514773i
$962$		0			0
$963$	−1131.27	+	653.140i	−1.17474	+	0.678235i
$964$		0			0
$965$	166.493			0.172532
$966$		0			0
$967$			1543.81i			1.59649i	0.602332	+	0.798246i	$0.294238\pi$
$967$			1543.81i			1.59649i	−0.602332	+	0.798246i	$0.705762\pi$
$968$		0			0
$969$	−175.289	−	303.609i	−0.180897	−	0.313322i
$970$		0			0
$971$	205.420	+	118.599i	0.211555	+	0.122142i	0.602034	−	0.798470i	$-0.294357\pi$
$971$	205.420	+	118.599i	0.211555	+	0.122142i	−0.390479	+	0.920612i	$0.627690\pi$
$972$		0			0
$973$	289.517	+	258.185i	0.297550	+	0.265349i
$974$		0			0
$975$	−1232.92	−	711.828i	−1.26454	−	0.730080i
$976$		0			0
$977$	445.109	+	770.952i	0.455588	+	0.789101i	0.998722	−	0.0505447i	$-0.0160957\pi$
$977$	445.109	+	770.952i	0.455588	+	0.789101i	−0.543134	+	0.839646i	$0.682762\pi$
$978$		0			0
$979$		−	1355.88i		−	1.38496i
$980$		0			0
$981$	−3074.51			−3.13405
$982$		0			0
$983$	1169.43	−	675.170i	1.18965	−	0.686847i	0.231426	−	0.972853i	$-0.425661\pi$
$983$	1169.43	−	675.170i	1.18965	−	0.686847i	0.958228	+	0.286006i	$0.0923276\pi$
$984$		0			0
$985$	−66.5047	+	115.190i	−0.0675175	+	0.116944i
$986$		0			0
$987$	862.369	−	967.021i	0.873727	−	0.979757i
$988$		0			0
$989$	789.710	−	1367.82i	0.798494	−	1.38303i
$990$		0			0
$991$	−943.699	+	544.845i	−0.952269	+	0.549793i	−0.893785	−	0.448496i	$-0.851960\pi$
$991$	−943.699	+	544.845i	−0.952269	+	0.549793i	−0.0584839	+	0.998288i	$0.518627\pi$
$992$		0			0
$993$	−1647.23			−1.65884
$994$		0			0
$995$			243.645i			0.244870i
$996$		0			0
$997$	302.176	+	523.384i	0.303085	+	0.524959i	0.976833	−	0.214002i	$-0.0686499\pi$
$997$	302.176	+	523.384i	0.303085	+	0.524959i	−0.673748	+	0.738961i	$0.735317\pi$
$998$		0			0
$999$	−1207.22	−	696.990i	−1.20843	−	0.697687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.r.d.191.1	yes	12
4.3	odd	2	inner	224.3.r.d.191.6	yes	12
7.2	even	3		1568.3.d.i.1471.1		6
7.4	even	3	inner	224.3.r.d.95.6	yes	12
7.5	odd	6		1568.3.d.l.1471.6		6
8.3	odd	2		448.3.r.f.191.1		12
8.5	even	2		448.3.r.f.191.6		12
28.11	odd	6	inner	224.3.r.d.95.1	✓	12
28.19	even	6		1568.3.d.l.1471.1		6
28.23	odd	6		1568.3.d.i.1471.6		6
56.11	odd	6		448.3.r.f.319.6		12
56.53	even	6		448.3.r.f.319.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.r.d.95.1	✓	12	28.11	odd	6	inner
224.3.r.d.95.6	yes	12	7.4	even	3	inner
224.3.r.d.191.1	yes	12	1.1	even	1	trivial
224.3.r.d.191.6	yes	12	4.3	odd	2	inner
448.3.r.f.191.1		12	8.3	odd	2
448.3.r.f.191.6		12	8.5	even	2
448.3.r.f.319.1		12	56.53	even	6
448.3.r.f.319.6		12	56.11	odd	6
1568.3.d.i.1471.1		6	7.2	even	3
1568.3.d.i.1471.6		6	28.23	odd	6
1568.3.d.l.1471.1		6	28.19	even	6
1568.3.d.l.1471.6		6	7.5	odd	6

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.23009 + 2.44224i) q^{3} +(1.16012 - 2.00939i) q^{5} +(4.65898 - 5.22436i) q^{7} +(7.42909 - 12.8676i) q^{9} +O(q^{10})\)	\(q+(-4.23009 + 2.44224i) q^{3} +(1.16012 - 2.00939i) q^{5} +(4.65898 - 5.22436i) q^{7} +(7.42909 - 12.8676i) q^{9} +(-13.2789 + 7.66660i) q^{11} +14.8582 q^{13} +11.3332i q^{15} +(1.19938 + 2.07739i) q^{17} +(25.9124 + 14.9605i) q^{19} +(-6.94872 + 33.4778i) q^{21} +(23.0146 + 13.2875i) q^{23} +(9.80823 + 16.9884i) q^{25} +28.6142i q^{27} -4.75828 q^{29} +(17.0976 - 9.87133i) q^{31} +(37.4474 - 64.8608i) q^{33} +(-5.09280 - 15.4226i) q^{35} +(-24.3582 + 42.1896i) q^{37} +(-62.8514 + 36.2873i) q^{39} +34.4746 q^{41} -59.4327i q^{43} +(-17.2373 - 29.8559i) q^{45} +(-32.8182 - 18.9476i) q^{47} +(-5.58789 - 48.6803i) q^{49} +(-10.1470 - 5.85837i) q^{51} +(33.2663 + 57.6189i) q^{53} +35.5768i q^{55} -146.149 q^{57} +(78.2440 - 45.1742i) q^{59} +(44.0772 - 76.3439i) q^{61} +(-32.6128 - 98.7619i) q^{63} +(17.2373 - 29.8559i) q^{65} +(-15.0906 + 8.71254i) q^{67} -129.805 q^{69} -23.0492i q^{71} +(34.2297 + 59.2876i) q^{73} +(-82.9793 - 47.9081i) q^{75} +(-21.8132 + 105.093i) q^{77} +(54.0184 + 31.1876i) q^{79} +(-3.02096 - 5.23245i) q^{81} +36.3835i q^{83} +5.56573 q^{85} +(20.1279 - 11.6209i) q^{87} +(-44.2137 + 76.5804i) q^{89} +(69.2239 - 77.6245i) q^{91} +(-48.2164 + 83.5132i) q^{93} +(60.1232 - 34.7122i) q^{95} +14.8582 q^{97} +227.824i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{5}+O(q^{10}) \) 12 * q + 18 * q^5	\( 12 q + 18 q^{5} - 6 q^{17} + 18 q^{21} + 186 q^{33} - 114 q^{37} + 180 q^{49} - 18 q^{53} - 684 q^{57} + 318 q^{61} - 228 q^{69} + 342 q^{73} + 318 q^{77} - 186 q^{81} - 996 q^{85} + 150 q^{89} - 222 q^{93}+O(q^{100}) \) 12 * q + 18 * q^5 - 6 * q^17 + 18 * q^21 + 186 * q^33 - 114 * q^37 + 180 * q^49 - 18 * q^53 - 684 * q^57 + 318 * q^61 - 228 * q^69 + 342 * q^73 + 318 * q^77 - 186 * q^81 - 996 * q^85 + 150 * q^89 - 222 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more