LMFDB - Embedded newform 224.3.s.a.33.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(33,224)]

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([0, 0, 5]))

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

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

chi := DirichletCharacter("224.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.s (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 36x^{14} + 522x^{12} + 3644x^{10} + 12219x^{8} + 15156x^{6} + 15478x^{4} - 10992x^{2} + 11025 $ x^16 + 36x^14 + 522x^12 + 3644x^10 + 12219x^8 + 15156x^6 + 15478x^4 - 10992*x^2 + 11025
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			33.3
Root			$0.707107 - 1.17406i$ of defining polynomial
Character	$\chi$	$=$	224.33
Dual form			224.3.s.a.129.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43792 + 0.830185i) q^{3} +(7.27622 + 4.20093i) q^{5} +(3.99843 - 5.74565i) q^{7} +(-3.12159 + 5.40674i) q^{9} +O(q^{10})$	\(q+(-1.43792 + 0.830185i) q^{3} +(7.27622 + 4.20093i) q^{5} +(3.99843 - 5.74565i) q^{7} +(-3.12159 + 5.40674i) q^{9} +(-2.60793 - 4.51706i) q^{11} +4.88512i q^{13} -13.9502 q^{15} +(6.68769 - 3.86114i) q^{17} +(30.6032 + 17.6687i) q^{19} +(-0.979482 + 11.5812i) q^{21} +(-13.3135 + 23.0597i) q^{23} +(22.7956 + 39.4832i) q^{25} -25.3093i q^{27} +45.1300 q^{29} +(-35.0200 + 20.2188i) q^{31} +(7.50000 + 4.33013i) q^{33} +(53.2306 - 25.0095i) q^{35} +(-3.97948 + 6.89266i) q^{37} +(-4.05555 - 7.02442i) q^{39} -26.6511i q^{41} +0.403279 q^{43} +(-45.4267 + 26.2271i) q^{45} +(-28.2845 - 16.3301i) q^{47} +(-17.0251 - 45.9472i) q^{49} +(-6.41092 + 11.1040i) q^{51} +(-40.6118 - 70.3416i) q^{53} -43.8229i q^{55} -58.6733 q^{57} +(-7.62318 + 4.40124i) q^{59} +(-25.3298 - 14.6242i) q^{61} +(18.5838 + 39.5541i) q^{63} +(-20.5220 + 35.5452i) q^{65} +(43.7792 + 75.8278i) q^{67} -44.2108i q^{69} -27.5210 q^{71} +(75.3481 - 43.5023i) q^{73} +(-65.5567 - 37.8492i) q^{75} +(-36.3811 - 3.07693i) q^{77} +(60.8467 - 105.390i) q^{79} +(-7.08286 - 12.2679i) q^{81} -46.6625i q^{83} +64.8815 q^{85} +(-64.8934 + 37.4662i) q^{87} +(-52.7235 - 30.4399i) q^{89} +(28.0682 + 19.5328i) q^{91} +(33.5707 - 58.1462i) q^{93} +(148.450 + 257.123i) q^{95} -66.4681i q^{97} +32.5635 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^9	$ 16 q + 8 q^{9} + 48 q^{17} + 56 q^{21} + 16 q^{25} + 112 q^{29} + 120 q^{33} + 8 q^{37} - 72 q^{45} - 128 q^{49} - 24 q^{53} - 528 q^{57} - 360 q^{61} - 8 q^{65} + 72 q^{73} + 32 q^{81} + 720 q^{85} + 408 q^{89} - 232 q^{93}+O(q^{100}) $ 16 * q + 8 * q^9 + 48 * q^17 + 56 * q^21 + 16 * q^25 + 112 * q^29 + 120 * q^33 + 8 * q^37 - 72 * q^45 - 128 * q^49 - 24 * q^53 - 528 * q^57 - 360 * q^61 - 8 * q^65 + 72 * q^73 + 32 * q^81 + 720 * q^85 + 408 * q^89 - 232 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−1.43792	+	0.830185i	−0.479308	+	0.276728i	−0.720128	−	0.693841i	$-0.755917\pi$
$3$	−1.43792	+	0.830185i	−0.479308	+	0.276728i	0.240820	+	0.970570i	$0.422584\pi$
$4$		0			0
$5$	7.27622	+	4.20093i	1.45524	+	0.840186i	0.998772	−	0.0495513i	$-0.0157791\pi$
$5$	7.27622	+	4.20093i	1.45524	+	0.840186i	0.456473	+	0.889737i	$0.349112\pi$
$6$		0			0
$7$	3.99843	−	5.74565i	0.571205	−	0.820808i
$7$	3.99843	−	5.74565i	0.571205	−	0.820808i
$8$		0			0
$9$	−3.12159	+	5.40674i	−0.346843	+	0.600749i
$10$		0			0
$11$	−2.60793	−	4.51706i	−0.237084	−	0.410642i	0.722792	−	0.691066i	$-0.242858\pi$
$11$	−2.60793	−	4.51706i	−0.237084	−	0.410642i	−0.959876	+	0.280423i	$0.909525\pi$
$12$		0			0
$13$			4.88512i			0.375778i	0.982190	+	0.187889i	$0.0601646\pi$
$13$			4.88512i			0.375778i	−0.982190	+	0.187889i	$0.939835\pi$
$14$		0			0
$15$	−13.9502			−0.930013
$16$		0			0
$17$	6.68769	−	3.86114i	0.393394	−	0.227126i	−0.290236	−	0.956955i	$-0.593734\pi$
$17$	6.68769	−	3.86114i	0.393394	−	0.227126i	0.683629	+	0.729829i	$0.260400\pi$
$18$		0			0
$19$	30.6032	+	17.6687i	1.61069	+	0.929934i	0.989210	+	0.146506i	$0.0468028\pi$
$19$	30.6032	+	17.6687i	1.61069	+	0.929934i	0.621483	+	0.783428i	$0.286531\pi$
$20$		0			0
$21$	−0.979482	+	11.5812i	−0.0466420	+	0.551488i
$22$		0			0
$23$	−13.3135	+	23.0597i	−0.578850	+	1.00260i	0.416762	+	0.909016i	$0.363165\pi$
$23$	−13.3135	+	23.0597i	−0.578850	+	1.00260i	−0.995612	+	0.0935814i	$0.970168\pi$
$24$		0			0
$25$	22.7956	+	39.4832i	0.911825	+	1.57933i
$26$		0			0
$27$		−	25.3093i		−	0.937382i
$28$		0			0
$29$	45.1300			1.55621			0.778103	−	0.628137i	$-0.216182\pi$
$29$	45.1300			1.55621			0.778103	+	0.628137i	$0.216182\pi$
$30$		0			0
$31$	−35.0200	+	20.2188i	−1.12968	+	0.652220i	−0.943854	−	0.330363i	$-0.892829\pi$
$31$	−35.0200	+	20.2188i	−1.12968	+	0.652220i	−0.185824	+	0.982583i	$0.559495\pi$
$32$		0			0
$33$	7.50000	+	4.33013i	0.227273	+	0.131216i
$34$		0			0
$35$	53.2306	−	25.0095i	1.52087	−	0.714558i
$36$		0			0
$37$	−3.97948	+	6.89266i	−0.107554	+	0.186288i	−0.914779	−	0.403956i	$-0.867635\pi$
$37$	−3.97948	+	6.89266i	−0.107554	+	0.186288i	0.807225	+	0.590244i	$0.200968\pi$
$38$		0			0
$39$	−4.05555	−	7.02442i	−0.103989	−	0.180113i
$40$		0			0
$41$		−	26.6511i		−	0.650027i	−0.945709	−	0.325014i	$-0.894631\pi$
$41$		−	26.6511i		−	0.650027i	0.945709	−	0.325014i	$-0.105369\pi$
$42$		0			0
$43$	0.403279			0.00937859			0.00468930	−	0.999989i	$-0.498507\pi$
$43$	0.403279			0.00937859			0.00468930	+	0.999989i	$0.498507\pi$
$44$		0			0
$45$	−45.4267	+	26.2271i	−1.00948	+	0.582825i
$46$		0			0
$47$	−28.2845	−	16.3301i	−0.601798	−	0.347448i	0.167951	−	0.985795i	$-0.446285\pi$
$47$	−28.2845	−	16.3301i	−0.601798	−	0.347448i	−0.769748	+	0.638347i	$0.779618\pi$
$48$		0			0
$49$	−17.0251	−	45.9472i	−0.347450	−	0.937698i
$50$		0			0
$51$	−6.41092	+	11.1040i	−0.125704	+	0.217726i
$52$		0			0
$53$	−40.6118	−	70.3416i	−0.766259	−	1.32720i	−0.939578	−	0.342335i	$-0.888782\pi$
$53$	−40.6118	−	70.3416i	−0.766259	−	1.32720i	0.173319	−	0.984866i	$-0.444551\pi$
$54$		0			0
$55$		−	43.8229i		−	0.796780i
$56$		0			0
$57$	−58.6733			−1.02936
$58$		0			0
$59$	−7.62318	+	4.40124i	−0.129206	+	0.0745973i	−0.563210	−	0.826314i	$-0.690434\pi$
$59$	−7.62318	+	4.40124i	−0.129206	+	0.0745973i	0.434004	+	0.900911i	$0.357100\pi$
$60$		0			0
$61$	−25.3298	−	14.6242i	−0.415243	−	0.239740i	0.277797	−	0.960640i	$-0.410396\pi$
$61$	−25.3298	−	14.6242i	−0.415243	−	0.239740i	−0.693040	+	0.720899i	$0.743729\pi$
$62$		0			0
$63$	18.5838	+	39.5541i	0.294981	+	0.627842i
$64$		0			0
$65$	−20.5220	+	35.5452i	−0.315724	+	0.546849i
$66$		0			0
$67$	43.7792	+	75.8278i	0.653421	+	1.13176i	0.982287	+	0.187382i	$0.0600001\pi$
$67$	43.7792	+	75.8278i	0.653421	+	1.13176i	−0.328866	+	0.944376i	$0.606667\pi$
$68$		0			0
$69$		−	44.2108i		−	0.640737i
$70$		0			0
$71$	−27.5210			−0.387620			−0.193810	−	0.981039i	$-0.562085\pi$
$71$	−27.5210			−0.387620			−0.193810	+	0.981039i	$0.562085\pi$
$72$		0			0
$73$	75.3481	−	43.5023i	1.03217	−	0.595921i	0.114562	−	0.993416i	$-0.463454\pi$
$73$	75.3481	−	43.5023i	1.03217	−	0.595921i	0.917604	+	0.397495i	$0.130120\pi$
$74$		0			0
$75$	−65.5567	−	37.8492i	−0.874089	−	0.504656i
$76$		0			0
$77$	−36.3811	−	3.07693i	−0.472482	−	0.0399601i
$78$		0			0
$79$	60.8467	−	105.390i	0.770212	−	1.33405i	−0.167235	−	0.985917i	$-0.553484\pi$
$79$	60.8467	−	105.390i	0.770212	−	1.33405i	0.937447	−	0.348129i	$-0.113183\pi$
$80$		0			0
$81$	−7.08286	−	12.2679i	−0.0874427	−	0.151455i
$82$		0			0
$83$		−	46.6625i		−	0.562198i	−0.959679	−	0.281099i	$-0.909301\pi$
$83$		−	46.6625i		−	0.562198i	0.959679	−	0.281099i	$-0.0906990\pi$
$84$		0			0
$85$	64.8815			0.763312
$86$		0			0
$87$	−64.8934	+	37.4662i	−0.745901	+	0.430646i
$88$		0			0
$89$	−52.7235	−	30.4399i	−0.592399	−	0.342022i	0.173647	−	0.984808i	$-0.444445\pi$
$89$	−52.7235	−	30.4399i	−0.592399	−	0.342022i	−0.766045	+	0.642786i	$0.777778\pi$
$90$		0			0
$91$	28.0682	+	19.5328i	0.308442	+	0.214646i
$92$		0			0
$93$	33.5707	−	58.1462i	0.360975	−	0.625228i
$94$		0			0
$95$	148.450	+	257.123i	1.56263	+	2.70656i
$96$		0			0
$97$		−	66.4681i		−	0.685238i	−0.939474	−	0.342619i	$-0.888686\pi$
$97$		−	66.4681i		−	0.685238i	0.939474	−	0.342619i	$-0.111314\pi$
$98$		0			0
$99$	32.5635			0.328924
$100$		0			0
$101$	−83.8424	+	48.4064i	−0.830123	+	0.479272i	−0.853895	−	0.520446i	$-0.825766\pi$
$101$	−83.8424	+	48.4064i	−0.830123	+	0.479272i	0.0237720	+	0.999717i	$0.492432\pi$
$102$		0			0
$103$	−149.353	−	86.2290i	−1.45003	−	0.837175i	−0.451547	−	0.892247i	$-0.649128\pi$
$103$	−149.353	−	86.2290i	−1.45003	−	0.837175i	−0.998482	+	0.0550721i	$0.982461\pi$
$104$		0			0
$105$	−55.7789	+	80.1530i	−0.531228	+	0.763362i
$106$		0			0
$107$	51.5903	−	89.3571i	0.482153	−	0.835113i	−0.517638	−	0.855600i	$-0.673188\pi$
$107$	51.5903	−	89.3571i	0.482153	−	0.835113i	0.999790	+	0.0204873i	$0.00652177\pi$
$108$		0			0
$109$	20.7763	+	35.9856i	0.190608	+	0.330143i	0.945452	−	0.325762i	$-0.105621\pi$
$109$	20.7763	+	35.9856i	0.190608	+	0.330143i	−0.754844	+	0.655905i	$0.772287\pi$
$110$		0			0
$111$		−	13.2148i		−	0.119052i
$112$		0			0
$113$	−133.885			−1.18482			−0.592409	−	0.805637i	$-0.701823\pi$
$113$	−133.885			−1.18482			−0.592409	+	0.805637i	$0.701823\pi$
$114$		0			0
$115$	−193.745	+	111.859i	−1.68474	+	0.972683i
$116$		0			0
$117$	−26.4126	−	15.2493i	−0.225749	−	0.130336i
$118$		0			0
$119$	4.55551	−	53.8637i	0.0382816	−	0.452636i
$120$		0			0
$121$	46.8974	−	81.2287i	0.387582	−	0.671312i
$122$		0			0
$123$	22.1254	+	38.3223i	0.179881	+	0.311563i
$124$		0			0
$125$			173.005i			1.38404i
$126$		0			0
$127$	132.489			1.04322			0.521610	−	0.853184i	$-0.325332\pi$
$127$	132.489			1.04322			0.521610	+	0.853184i	$0.325332\pi$
$128$		0			0
$129$	−0.579885	+	0.334797i	−0.00449523	+	0.00259532i
$130$		0			0
$131$	−64.1188	−	37.0190i	−0.489456	−	0.282588i	0.234893	−	0.972021i	$-0.424526\pi$
$131$	−64.1188	−	37.0190i	−0.489456	−	0.282588i	−0.724349	+	0.689434i	$0.757859\pi$
$132$		0			0
$133$	223.883	−	105.188i	1.68333	−	0.790886i
$134$		0			0
$135$	106.323	−	184.156i	0.787575	−	1.36412i
$136$		0			0
$137$	37.1900	+	64.4150i	0.271460	+	0.470182i	0.969236	−	0.246134i	$-0.0791603\pi$
$137$	37.1900	+	64.4150i	0.271460	+	0.470182i	−0.697776	+	0.716316i	$0.745827\pi$
$138$		0			0
$139$		−	123.649i		−	0.889560i	−0.895640	−	0.444780i	$-0.853282\pi$
$139$		−	123.649i		−	0.889560i	0.895640	−	0.444780i	$-0.146718\pi$
$140$		0			0
$141$	54.2279			0.384595
$142$		0			0
$143$	22.0664	−	12.7400i	0.154310	−	0.0890912i
$144$		0			0
$145$	328.376	+	189.588i	2.26466	+	1.30750i
$146$		0			0
$147$	62.6254	+	51.9346i	0.426023	+	0.353297i
$148$		0			0
$149$	−103.295	+	178.913i	−0.693257	+	1.20076i	0.277507	+	0.960724i	$0.410492\pi$
$149$	−103.295	+	178.913i	−0.693257	+	1.20076i	−0.970765	+	0.240033i	$0.922842\pi$
$150$		0			0
$151$	24.2277	+	41.9636i	0.160448	+	0.277905i	0.935030	−	0.354570i	$-0.115373\pi$
$151$	24.2277	+	41.9636i	0.160448	+	0.277905i	−0.774581	+	0.632474i	$0.782039\pi$
$152$		0			0
$153$			48.2115i			0.315108i
$154$		0			0
$155$	−339.751			−2.19194
$156$		0			0
$157$	153.500	−	88.6233i	0.977708	−	0.564480i	0.0761305	−	0.997098i	$-0.475743\pi$
$157$	153.500	−	88.6233i	0.977708	−	0.564480i	0.901577	+	0.432618i	$0.142410\pi$
$158$		0			0
$159$	116.793	+	67.4305i	0.734548	+	0.424091i
$160$		0			0
$161$	79.2599	+	168.698i	0.492298	+	1.04781i
$162$		0			0
$163$	−63.4766	+	109.945i	−0.389427	+	0.674507i	−0.992373	−	0.123275i	$-0.960660\pi$
$163$	−63.4766	+	109.945i	−0.389427	+	0.674507i	0.602946	+	0.797782i	$0.293994\pi$
$164$		0			0
$165$	36.3811	+	63.0139i	0.220492	+	0.381903i
$166$		0			0
$167$		−	191.898i		−	1.14909i	−0.818472	−	0.574546i	$-0.805179\pi$
$167$		−	191.898i		−	1.14909i	0.818472	−	0.574546i	$-0.194821\pi$
$168$		0			0
$169$	145.136			0.858791
$170$		0			0
$171$	−191.061	+	110.309i	−1.11731	+	0.645082i
$172$		0			0
$173$	−163.288	−	94.2744i	−0.943862	−	0.544939i	−0.0526930	−	0.998611i	$-0.516780\pi$
$173$	−163.288	−	94.2744i	−0.943862	−	0.544939i	−0.891169	+	0.453672i	$0.850114\pi$
$174$		0			0
$175$	318.003	+	26.8951i	1.81716	+	0.153686i
$176$		0			0
$177$	7.30769	−	12.6573i	0.0412864	−	0.0715101i
$178$		0			0
$179$	120.527	+	208.759i	0.673337	+	1.16625i	0.976952	+	0.213459i	$0.0684730\pi$
$179$	120.527	+	208.759i	0.673337	+	1.16625i	−0.303615	+	0.952795i	$0.598194\pi$
$180$		0			0
$181$			277.790i			1.53475i	0.641198	+	0.767376i	$0.278438\pi$
$181$			277.790i			1.53475i	−0.641198	+	0.767376i	$0.721562\pi$
$182$		0			0
$183$	48.5631			0.265372
$184$		0			0
$185$	−57.9112	+	33.4350i	−0.313033	+	0.180730i
$186$		0			0
$187$	−34.8820	−	20.1392i	−0.186535	−	0.107696i
$188$		0			0
$189$	−145.419	−	101.198i	−0.769410	−	0.535437i
$190$		0			0
$191$	−132.188	+	228.957i	−0.692085	+	1.19873i	0.279069	+	0.960271i	$0.409974\pi$
$191$	−132.188	+	228.957i	−0.692085	+	1.19873i	−0.971154	+	0.238455i	$0.923359\pi$
$192$		0			0
$193$	−105.698	−	183.075i	−0.547660	−	0.948575i	−0.998434	−	0.0559370i	$-0.982185\pi$
$193$	−105.698	−	183.075i	−0.547660	−	0.948575i	0.450774	−	0.892638i	$-0.351148\pi$
$194$		0			0
$195$		−	68.1484i		−	0.349479i
$196$		0			0
$197$	−79.4949			−0.403527			−0.201764	−	0.979434i	$-0.564667\pi$
$197$	−79.4949			−0.403527			−0.201764	+	0.979434i	$0.564667\pi$
$198$		0			0
$199$	−175.765	+	101.478i	−0.883241	+	0.509939i	−0.871726	−	0.489995i	$-0.836999\pi$
$199$	−175.765	+	101.478i	−0.883241	+	0.509939i	−0.0115150	+	0.999934i	$0.503665\pi$
$200$		0			0
$201$	−125.902	−	72.6897i	−0.626379	−	0.361640i
$202$		0			0
$203$	180.449	−	259.301i	0.888912	−	1.27735i
$204$		0			0
$205$	111.959	−	193.920i	0.546144	−	0.945949i
$206$		0			0
$207$	−83.1187	−	143.966i	−0.401540	−	0.695487i
$208$		0			0
$209$		−	184.315i		−	0.881891i
$210$		0			0
$211$	166.533			0.789256			0.394628	−	0.918841i	$-0.370873\pi$
$211$	166.533			0.789256			0.394628	+	0.918841i	$0.370873\pi$
$212$		0			0
$213$	39.5731	−	22.8476i	0.185789	−	0.107266i
$214$		0			0
$215$	2.93435	+	1.69415i	0.0136481	+	0.00787976i
$216$		0			0
$217$	−23.8549	+	282.056i	−0.109930	+	1.29980i
$218$		0			0
$219$	−72.2299	+	125.106i	−0.329817	+	0.571259i
$220$		0			0
$221$	18.8621	+	32.6702i	0.0853490	+	0.147829i
$222$		0			0
$223$		−	55.0782i		−	0.246988i	−0.992345	−	0.123494i	$-0.960590\pi$
$223$		−	55.0782i		−	0.246988i	0.992345	−	0.123494i	$-0.0394099\pi$
$224$		0			0
$225$	−284.634			−1.26504
$226$		0			0
$227$	184.119	−	106.301i	0.811099	−	0.468288i	−0.0362385	−	0.999343i	$-0.511538\pi$
$227$	184.119	−	106.301i	0.811099	−	0.468288i	0.847337	+	0.531055i	$0.178204\pi$
$228$		0			0
$229$	−38.5185	−	22.2387i	−0.168203	−	0.0971120i	0.413535	−	0.910488i	$-0.364294\pi$
$229$	−38.5185	−	22.2387i	−0.168203	−	0.0971120i	−0.581738	+	0.813376i	$0.697627\pi$
$230$		0			0
$231$	54.8677	−	25.7787i	0.237522	−	0.111596i
$232$		0			0
$233$	136.050	−	235.645i	0.583904	−	1.01135i	−0.411107	−	0.911587i	$-0.634858\pi$
$233$	136.050	−	235.645i	0.583904	−	1.01135i	0.995011	−	0.0997641i	$-0.0318088\pi$
$234$		0			0
$235$	−137.203	−	237.642i	−0.583842	−	1.01124i
$236$		0			0
$237$			202.056i			0.852558i
$238$		0			0
$239$	−389.180			−1.62837			−0.814185	−	0.580605i	$-0.802816\pi$
$239$	−389.180			−1.62837			−0.814185	+	0.580605i	$0.802816\pi$
$240$		0			0
$241$	−60.9363	+	35.1816i	−0.252848	+	0.145982i	−0.621068	−	0.783757i	$-0.713301\pi$
$241$	−60.9363	+	35.1816i	−0.252848	+	0.145982i	0.368220	+	0.929739i	$0.379967\pi$
$242$		0			0
$243$	217.636	+	125.652i	0.895620	+	0.517087i
$244$		0			0
$245$	69.1428	−	405.843i	0.282216	−	1.65650i
$246$		0			0
$247$	−86.3139	+	149.500i	−0.349449	+	0.605263i
$248$		0			0
$249$	38.7385	+	67.0970i	0.155576	+	0.269466i
$250$		0			0
$251$		−	97.5325i		−	0.388576i	−0.980945	−	0.194288i	$-0.937760\pi$
$251$		−	97.5325i		−	0.388576i	0.980945	−	0.194288i	$-0.0622396\pi$
$252$		0			0
$253$	138.883			0.548945
$254$		0			0
$255$	−93.2946	+	53.8637i	−0.365861	+	0.211230i
$256$		0			0
$257$	179.396	+	103.574i	0.698038	+	0.403013i	0.806616	−	0.591075i	$-0.201296\pi$
$257$	179.396	+	103.574i	0.698038	+	0.403013i	−0.108578	+	0.994088i	$0.534630\pi$
$258$		0			0
$259$	23.6912	+	50.4246i	0.0914717	+	0.194689i
$260$		0			0
$261$	−140.877	+	244.006i	−0.539759	+	0.934890i
$262$		0			0
$263$	103.607	+	179.453i	0.393943	+	0.682330i	0.992966	−	0.118402i	$-0.0377773\pi$
$263$	103.607	+	179.453i	0.393943	+	0.682330i	−0.599022	+	0.800732i	$0.704444\pi$
$264$		0			0
$265$		−	682.428i		−	2.57520i
$266$		0			0
$267$	101.083			0.378588
$268$		0			0
$269$	−31.1550	+	17.9873i	−0.115818	+	0.0668674i	−0.556790	−	0.830653i	$-0.687967\pi$
$269$	−31.1550	+	17.9873i	−0.115818	+	0.0668674i	0.440972	+	0.897521i	$0.354634\pi$
$270$		0			0
$271$	66.3923	+	38.3316i	0.244990	+	0.141445i	0.617468	−	0.786596i	$-0.288159\pi$
$271$	66.3923	+	38.3316i	0.244990	+	0.141445i	−0.372478	+	0.928041i	$0.621492\pi$
$272$		0			0
$273$	−56.5758	−	4.78488i	−0.207237	−	0.0175270i
$274$		0			0
$275$	118.899	−	205.939i	0.432359	−	0.748867i
$276$		0			0
$277$	−134.002	−	232.098i	−0.483760	−	0.837898i	0.516066	−	0.856549i	$-0.327396\pi$
$277$	−134.002	−	232.098i	−0.483760	−	0.837898i	−0.999826	+	0.0186514i	$0.994063\pi$
$278$		0			0
$279$		−	252.459i		−	0.904871i
$280$		0			0
$281$	−417.336			−1.48518			−0.742591	−	0.669745i	$-0.766403\pi$
$281$	−417.336			−1.48518			−0.742591	+	0.669745i	$0.766403\pi$
$282$		0			0
$283$	−124.538	+	71.9020i	−0.440064	+	0.254071i	−0.703625	−	0.710572i	$-0.748436\pi$
$283$	−124.538	+	71.9020i	−0.440064	+	0.254071i	0.263561	+	0.964643i	$0.415103\pi$
$284$		0			0
$285$	−426.920	−	246.482i	−1.49797	−	0.864851i
$286$		0			0
$287$	−153.128	−	106.563i	−0.533547	−	0.371299i
$288$		0			0
$289$	−114.683	+	198.637i	−0.396828	+	0.687326i
$290$		0			0
$291$	55.1808	+	95.5760i	0.189625	+	0.328440i
$292$		0			0
$293$		−	265.694i		−	0.906805i	−0.891306	−	0.453402i	$-0.850210\pi$
$293$		−	265.694i		−	0.906805i	0.891306	−	0.453402i	$-0.149790\pi$
$294$		0			0
$295$	−73.9572			−0.250702
$296$		0			0
$297$	−114.324	+	66.0049i	−0.384929	+	0.222239i
$298$		0			0
$299$	−112.650	−	65.0382i	−0.376754	−	0.217519i
$300$		0			0
$301$	1.61249	−	2.31710i	0.00535709	−	0.00769802i
$302$		0			0
$303$	80.3726	−	139.209i	0.265256	−	0.459437i
$304$		0			0
$305$	−122.870	−	212.817i	−0.402853	−	0.697762i
$306$		0			0
$307$			281.617i			0.917318i	0.888612	+	0.458659i	$0.151670\pi$
$307$			281.617i			0.917318i	−0.888612	+	0.458659i	$0.848330\pi$
$308$		0			0
$309$	286.344			0.926680
$310$		0			0
$311$	48.8342	−	28.1945i	0.157023	−	0.0906574i	−0.419429	−	0.907788i	$-0.637770\pi$
$311$	48.8342	−	28.1945i	0.157023	−	0.0906574i	0.576453	+	0.817131i	$0.304437\pi$
$312$		0			0
$313$	73.0471	+	42.1738i	0.233377	+	0.134741i	0.612129	−	0.790758i	$-0.290313\pi$
$313$	73.0471	+	42.1738i	0.233377	+	0.134741i	−0.378752	+	0.925498i	$0.623647\pi$
$314$		0			0
$315$	−30.9437	+	365.873i	−0.0982339	+	1.16150i
$316$		0			0
$317$	−79.6930	+	138.032i	−0.251398	+	0.435433i	−0.963911	−	0.266225i	$-0.914223\pi$
$317$	−79.6930	+	138.032i	−0.251398	+	0.435433i	0.712513	+	0.701659i	$0.247557\pi$
$318$		0			0
$319$	−117.696	−	203.855i	−0.368952	−	0.639044i
$320$		0			0
$321$			171.318i			0.533701i
$322$		0			0
$323$	272.886			0.844848
$324$		0			0
$325$	−192.880	+	111.359i	−0.593477	+	0.342644i
$326$		0			0
$327$	−59.7494	−	34.4963i	−0.182720	−	0.105493i
$328$		0			0
$329$	−206.920	+	97.2182i	−0.628938	+	0.295496i
$330$		0			0
$331$	279.794	−	484.617i	0.845299	−	1.46410i	−0.0400619	−	0.999197i	$-0.512756\pi$
$331$	279.794	−	484.617i	0.845299	−	1.46410i	0.885361	−	0.464904i	$-0.153911\pi$
$332$		0			0
$333$	−24.8446	−	43.0321i	−0.0746084	−	0.129225i
$334$		0			0
$335$			735.653i			2.19598i
$336$		0			0
$337$	140.493			0.416892			0.208446	−	0.978034i	$-0.433159\pi$
$337$	140.493			0.416892			0.208446	+	0.978034i	$0.433159\pi$
$338$		0			0
$339$	192.516	−	111.149i	0.567893	−	0.327873i
$340$		0			0
$341$	182.659	+	105.458i	0.535658	+	0.309262i
$342$		0			0
$343$	−332.070	−	85.8967i	−0.968135	−	0.250428i
$344$		0			0
$345$	185.727	−	321.688i	0.538338	−	0.932428i
$346$		0			0
$347$	194.159	+	336.294i	0.559537	+	0.969146i	0.997535	+	0.0701703i	$0.0223543\pi$
$347$	194.159	+	336.294i	0.559537	+	0.969146i	−0.437998	+	0.898976i	$0.644312\pi$
$348$		0			0
$349$			469.369i			1.34490i	0.740144	+	0.672449i	$0.234757\pi$
$349$			469.369i			1.34490i	−0.740144	+	0.672449i	$0.765243\pi$
$350$		0			0
$351$	123.639			0.352248
$352$		0			0
$353$	561.753	−	324.329i	1.59137	−	0.918778i	0.598297	−	0.801274i	$-0.295844\pi$
$353$	561.753	−	324.329i	1.59137	−	0.918778i	0.993072	−	0.117503i	$-0.0374891\pi$
$354$		0			0
$355$	−200.249	−	115.614i	−0.564082	−	0.325673i
$356$		0			0
$357$	38.1663	+	81.2337i	0.106909	+	0.227545i
$358$		0			0
$359$	−140.301	+	243.008i	−0.390810	+	0.676902i	−0.992557	−	0.121785i	$-0.961138\pi$
$359$	−140.301	+	243.008i	−0.390810	+	0.676902i	0.601747	+	0.798687i	$0.294472\pi$
$360$		0			0
$361$	443.869	+	768.803i	1.22955	+	2.12965i
$362$		0			0
$363$			155.734i			0.429020i
$364$		0			0
$365$	731.000			2.00274
$366$		0			0
$367$	17.3213	−	10.0005i	0.0471971	−	0.0272493i	−0.476216	−	0.879328i	$-0.657992\pi$
$367$	17.3213	−	10.0005i	0.0471971	−	0.0272493i	0.523413	+	0.852079i	$0.324659\pi$
$368$		0			0
$369$	144.096	+	83.1938i	0.390504	+	0.225457i
$370$		0			0
$371$	−566.542	−	47.9152i	−1.52707	−	0.129151i
$372$		0			0
$373$	80.2038	−	138.917i	0.215024	−	0.372432i	−0.738256	−	0.674520i	$-0.764351\pi$
$373$	80.2038	−	138.917i	0.215024	−	0.372432i	0.953280	+	0.302089i	$0.0976838\pi$
$374$		0			0
$375$	−143.626	−	248.767i	−0.383002	−	0.663380i
$376$		0			0
$377$			220.465i			0.584788i
$378$		0			0
$379$	397.426			1.04862			0.524308	−	0.851529i	$-0.324324\pi$
$379$	397.426			1.04862			0.524308	+	0.851529i	$0.324324\pi$
$380$		0			0
$381$	−190.509	+	109.990i	−0.500023	+	0.288689i
$382$		0			0
$383$	−232.209	−	134.066i	−0.606291	−	0.350042i	0.165222	−	0.986256i	$-0.447166\pi$
$383$	−232.209	−	134.066i	−0.606291	−	0.350042i	−0.771512	+	0.636214i	$0.780499\pi$
$384$		0			0
$385$	−251.791	−	175.223i	−0.654003	−	0.455124i
$386$		0			0
$387$	−1.25887	+	2.18043i	−0.00325290	+	0.00563418i
$388$		0			0
$389$	96.3409	+	166.867i	0.247663	+	0.428965i	0.962877	−	0.269941i	$-0.0870041\pi$
$389$	96.3409	+	166.867i	0.247663	+	0.428965i	−0.715214	+	0.698905i	$0.753671\pi$
$390$		0			0
$391$			205.622i			0.525887i
$392$		0			0
$393$	122.930			0.312800
$394$		0			0
$395$	885.469	−	511.226i	2.24169	−	1.29424i
$396$		0			0
$397$	120.298	+	69.4542i	0.303018	+	0.174948i	0.643798	−	0.765195i	$-0.277358\pi$
$397$	120.298	+	69.4542i	0.303018	+	0.174948i	−0.340780	+	0.940143i	$0.610691\pi$
$398$		0			0
$399$	−234.601	+	337.116i	−0.587973	+	0.844903i
$400$		0			0
$401$	−338.411	+	586.145i	−0.843917	+	1.46171i	0.0426415	+	0.999090i	$0.486423\pi$
$401$	−338.411	+	586.145i	−0.843917	+	1.46171i	−0.886558	+	0.462617i	$0.846911\pi$
$402$		0			0
$403$	−98.7713	−	171.077i	−0.245090	−	0.424508i
$404$		0			0
$405$		−	119.018i		−	0.293872i
$406$		0			0
$407$	41.5128			0.101997
$408$		0			0
$409$	177.165	−	102.286i	0.433166	−	0.250089i	−0.267528	−	0.963550i	$-0.586207\pi$
$409$	177.165	−	102.286i	0.433166	−	0.250089i	0.700695	+	0.713461i	$0.252874\pi$
$410$		0			0
$411$	−106.953	−	61.7492i	−0.260226	−	0.150241i
$412$		0			0
$413$	−5.19274	+	61.3982i	−0.0125732	+	0.148664i
$414$		0			0
$415$	196.026	−	339.527i	0.472351	−	0.818136i
$416$		0			0
$417$	102.651	+	177.797i	0.246166	+	0.426373i
$418$		0			0
$419$		−	516.134i		−	1.23182i	−0.787815	−	0.615911i	$-0.788788\pi$
$419$		−	516.134i		−	1.23182i	0.787815	−	0.615911i	$-0.211212\pi$
$420$		0			0
$421$	−81.4693			−0.193514			−0.0967569	−	0.995308i	$-0.530847\pi$
$421$	−81.4693			−0.193514			−0.0967569	+	0.995308i	$0.530847\pi$
$422$		0			0
$423$	176.585	−	101.951i	0.417458	−	0.241020i
$424$		0			0
$425$	304.900	+	176.034i	0.717412	+	0.414198i
$426$		0			0
$427$	−185.305	+	87.0625i	−0.433969	+	0.203893i
$428$		0			0
$429$	−21.1532	+	36.6384i	−0.0493081	+	0.0854042i
$430$		0			0
$431$	−48.8226	−	84.5632i	−0.113277	−	0.196202i	0.803812	−	0.594883i	$-0.202802\pi$
$431$	−48.8226	−	84.5632i	−0.113277	−	0.196202i	−0.917090	+	0.398681i	$0.869468\pi$
$432$		0			0
$433$		−	476.427i		−	1.10029i	−0.835068	−	0.550146i	$-0.814572\pi$
$433$		−	476.427i		−	1.10029i	0.835068	−	0.550146i	$-0.185428\pi$
$434$		0			0
$435$	−629.572			−1.44729
$436$		0			0
$437$	−814.873	+	470.467i	−1.86470	+	1.07658i
$438$		0			0
$439$	233.304	+	134.698i	0.531444	+	0.306829i	0.741604	−	0.670838i	$-0.234065\pi$
$439$	233.304	+	134.698i	0.531444	+	0.306829i	−0.210160	+	0.977667i	$0.567399\pi$
$440$		0			0
$441$	301.570	+	51.3780i	0.683832	+	0.116503i
$442$		0			0
$443$	−170.985	+	296.155i	−0.385971	+	0.668522i	−0.991903	−	0.126994i	$-0.959467\pi$
$443$	−170.985	+	296.155i	−0.385971	+	0.668522i	0.605932	+	0.795516i	$0.292800\pi$
$444$		0			0
$445$	−255.752	−	442.975i	−0.574724	−	0.995450i
$446$		0			0
$447$		−	343.017i		−	0.767376i
$448$		0			0
$449$	−460.145			−1.02482			−0.512411	−	0.858741i	$-0.671247\pi$
$449$	−460.145			−1.02482			−0.512411	+	0.858741i	$0.671247\pi$
$450$		0			0
$451$	−120.385	+	69.5042i	−0.266929	+	0.154111i
$452$		0			0
$453$	−69.6751	−	40.2270i	−0.153808	−	0.0888012i
$454$		0			0
$455$	122.174	+	260.038i	0.268515	+	0.571511i
$456$		0			0
$457$	−304.687	+	527.733i	−0.666710	+	1.15478i	0.312108	+	0.950046i	$0.398965\pi$
$457$	−304.687	+	527.733i	−0.666710	+	1.15478i	−0.978819	+	0.204729i	$0.934369\pi$
$458$		0			0
$459$	−97.7228	−	169.261i	−0.212904	−	0.368760i
$460$		0			0
$461$			102.856i			0.223114i	0.993758	+	0.111557i	$0.0355837\pi$
$461$			102.856i			0.223114i	−0.993758	+	0.111557i	$0.964416\pi$
$462$		0			0
$463$	541.601			1.16976			0.584882	−	0.811118i	$-0.301141\pi$
$463$	541.601			1.16976			0.584882	+	0.811118i	$0.301141\pi$
$464$		0			0
$465$	488.536	−	282.056i	1.05062	−	0.606573i
$466$		0			0
$467$	134.069	+	77.4045i	0.287085	+	0.165748i	0.636626	−	0.771172i	$-0.280329\pi$
$467$	134.069	+	77.4045i	0.287085	+	0.165748i	−0.349542	+	0.936921i	$0.613663\pi$
$468$		0			0
$469$	610.728	+	51.6522i	1.30219	+	0.110133i
$470$		0			0
$471$	−147.148	+	254.867i	−0.312415	+	0.541119i
$472$		0			0
$473$	−1.05172	−	1.82164i	−0.00222352	−	0.00385125i
$474$		0			0
$475$			1611.08i			3.39175i
$476$		0			0
$477$	507.092			1.06309
$478$		0			0
$479$	631.045	−	364.334i	1.31742	−	0.760614i	0.334108	−	0.942535i	$-0.391565\pi$
$479$	631.045	−	364.334i	1.31742	−	0.760614i	0.983313	+	0.181921i	$0.0582316\pi$
$480$		0			0
$481$	−33.6715	−	19.4402i	−0.0700031	−	0.0404163i
$482$		0			0
$483$	−254.020	−	176.774i	−0.525921	−	0.365992i
$484$		0			0
$485$	279.228	−	483.637i	0.575728	−	0.997189i
$486$		0			0
$487$	−224.471	−	388.794i	−0.460925	−	0.798346i	0.538082	−	0.842892i	$-0.319149\pi$
$487$	−224.471	−	388.794i	−0.460925	−	0.798346i	−0.999007	+	0.0445466i	$0.985816\pi$
$488$		0			0
$489$		−	210.789i		−	0.431062i
$490$		0			0
$491$	−73.5801			−0.149858			−0.0749288	−	0.997189i	$-0.523873\pi$
$491$	−73.5801			−0.149858			−0.0749288	+	0.997189i	$0.523873\pi$
$492$		0			0
$493$	301.815	−	174.253i	0.612201	−	0.353455i
$494$		0			0
$495$	236.939	+	136.797i	0.478665	+	0.276357i
$496$		0			0
$497$	−110.041	+	158.126i	−0.221411	+	0.318162i
$498$		0			0
$499$	−433.207	+	750.336i	−0.868149	+	1.50368i	−0.00426366	+	0.999991i	$0.501357\pi$
$499$	−433.207	+	750.336i	−0.868149	+	1.50368i	−0.863886	+	0.503688i	$0.831976\pi$
$500$		0			0
$501$	159.311	+	275.935i	0.317986	+	0.550768i
$502$		0			0
$503$			306.742i			0.609825i	0.952380	+	0.304913i	$0.0986272\pi$
$503$			306.742i			0.609825i	−0.952380	+	0.304913i	$0.901373\pi$
$504$		0			0
$505$	−813.408			−1.61071
$506$		0			0
$507$	−208.694	+	120.489i	−0.411625	+	0.237652i
$508$		0			0
$509$	162.588	+	93.8701i	0.319426	+	0.184421i	0.651137	−	0.758961i	$-0.274292\pi$
$509$	162.588	+	93.8701i	0.319426	+	0.184421i	−0.331711	+	0.943381i	$0.607626\pi$
$510$		0			0
$511$	51.3255	−	606.865i	0.100441	−	1.18760i
$512$		0			0
$513$	447.184	−	774.545i	0.871703	−	1.50983i
$514$		0			0
$515$	−724.484	−	1254.84i	−1.40677	−	2.43659i
$516$		0			0
$517$			170.350i			0.329498i
$518$		0			0
$519$	313.061			0.603200
$520$		0			0
$521$	−300.489	+	173.487i	−0.576754	+	0.332989i	−0.759842	−	0.650107i	$-0.774724\pi$
$521$	−300.489	+	173.487i	−0.576754	+	0.332989i	0.183088	+	0.983096i	$0.441391\pi$
$522$		0			0
$523$	279.427	+	161.328i	0.534278	+	0.308466i	0.742757	−	0.669561i	$-0.233518\pi$
$523$	279.427	+	161.328i	0.534278	+	0.308466i	−0.208479	+	0.978027i	$0.566851\pi$
$524$		0			0
$525$	−479.592	+	225.329i	−0.913509	+	0.429197i
$526$		0			0
$527$	−156.135	+	270.434i	−0.296272	+	0.513158i
$528$		0			0
$529$	−90.0008	−	155.886i	−0.170134	−	0.294681i
$530$		0			0
$531$		−	54.9554i		−	0.103494i
$532$		0			0
$533$	130.194			0.244266
$534$		0			0
$535$	750.765	−	433.455i	1.40330	−	0.810196i
$536$		0			0
$537$	−346.618	−	200.120i	−0.645471	−	0.372663i
$538$		0			0
$539$	−163.146	+	196.730i	−0.302683	+	0.364991i
$540$		0			0
$541$	−247.471	+	428.632i	−0.457432	+	0.792296i	−0.998824	−	0.0484743i	$-0.984564\pi$
$541$	−247.471	+	428.632i	−0.457432	+	0.792296i	0.541392	+	0.840770i	$0.317897\pi$
$542$		0			0
$543$	−230.617	−	399.440i	−0.424709	−	0.735618i
$544$		0			0
$545$			349.119i			0.640585i
$546$		0			0
$547$	244.584			0.447137			0.223569	−	0.974688i	$-0.428229\pi$
$547$	244.584			0.447137			0.223569	+	0.974688i	$0.428229\pi$
$548$		0			0
$549$	158.138	−	91.3011i	0.288048	−	0.166304i
$550$		0			0
$551$	1381.12	+	797.390i	2.50657	+	1.44717i
$552$		0			0
$553$	−362.241	−	770.998i	−0.655047	−	1.39421i
$554$		0			0
$555$	55.5146	−	96.1540i	0.100026	−	0.173250i
$556$		0			0
$557$	−415.083	−	718.944i	−0.745211	−	1.29074i	−0.950096	−	0.311958i	$-0.899015\pi$
$557$	−415.083	−	718.944i	−0.745211	−	1.29074i	0.204885	−	0.978786i	$-0.434318\pi$
$558$		0			0
$559$			1.97007i			0.00352427i
$560$		0			0
$561$	66.8769			0.119210
$562$		0			0
$563$	−491.327	+	283.668i	−0.872695	+	0.503851i	−0.868243	−	0.496140i	$-0.834750\pi$
$563$	−491.327	+	283.668i	−0.872695	+	0.503851i	−0.00445194	+	0.999990i	$0.501417\pi$
$564$		0			0
$565$	−974.174	−	562.440i	−1.72420	−	0.995468i
$566$		0			0
$567$	−98.8073	−	8.35661i	−0.174263	−	0.0147383i
$568$		0			0
$569$	324.238	−	561.596i	0.569837	−	0.986987i	−0.426744	−	0.904372i	$-0.640339\pi$
$569$	324.238	−	561.596i	0.569837	−	0.986987i	0.996582	−	0.0826150i	$-0.0263272\pi$
$570$		0			0
$571$	−254.923	−	441.539i	−0.446450	−	0.773274i	0.551702	−	0.834041i	$-0.313979\pi$
$571$	−254.923	−	441.539i	−0.446450	−	0.773274i	−0.998152	+	0.0607673i	$0.980645\pi$
$572$		0			0
$573$		−	438.963i		−	0.766078i
$574$		0			0
$575$	−1213.96			−2.11124
$576$		0			0
$577$	−360.612	+	208.200i	−0.624978	+	0.360831i	−0.778804	−	0.627267i	$-0.784174\pi$
$577$	−360.612	+	208.200i	−0.624978	+	0.360831i	0.153827	+	0.988098i	$0.450840\pi$
$578$		0			0
$579$	303.972	+	175.498i	0.524995	+	0.303106i
$580$		0			0
$581$	−268.106	−	186.577i	−0.461457	−	0.321130i
$582$		0			0
$583$	−211.825	+	366.892i	−0.363336	+	0.629317i
$584$		0			0
$585$	−128.123	−	221.915i	−0.219013	−	0.379342i
$586$		0			0
$587$		−	581.897i		−	0.991307i	−0.868520	−	0.495654i	$-0.834929\pi$
$587$		−	581.897i		−	0.991307i	0.868520	−	0.495654i	$-0.165071\pi$
$588$		0			0
$589$	−1428.96			−2.42608
$590$		0			0
$591$	114.308	−	65.9955i	0.193414	−	0.111667i
$592$		0			0
$593$	−480.511	−	277.423i	−0.810305	−	0.467830i	0.0367569	−	0.999324i	$-0.488297\pi$
$593$	−480.511	−	277.423i	−0.810305	−	0.467830i	−0.847062	+	0.531495i	$0.821631\pi$
$594$		0			0
$595$	259.424	−	372.787i	0.436007	−	0.626532i
$596$		0			0
$597$	168.491	−	291.835i	0.282229	−	0.488835i
$598$		0			0
$599$	33.3932	+	57.8387i	0.0557482	+	0.0965587i	0.892553	−	0.450943i	$-0.148912\pi$
$599$	33.3932	+	57.8387i	0.0557482	+	0.0965587i	−0.836805	+	0.547502i	$0.815579\pi$
$600$		0			0
$601$			215.249i			0.358151i	0.983835	+	0.179076i	$0.0573107\pi$
$601$			215.249i			0.358151i	−0.983835	+	0.179076i	$0.942689\pi$
$602$		0			0
$603$	−546.642			−0.906537
$604$		0			0
$605$	682.472	−	394.025i	1.12805	−	0.651282i
$606$		0			0
$607$	−542.576	−	313.256i	−0.893864	−	0.516073i	−0.0186599	−	0.999826i	$-0.505940\pi$
$607$	−542.576	−	313.256i	−0.893864	−	0.516073i	−0.875205	+	0.483753i	$0.839273\pi$
$608$		0			0
$609$	−44.2040	+	522.661i	−0.0725845	+	0.858229i
$610$		0			0
$611$	79.7743	−	138.173i	0.130563	−	0.226142i
$612$		0			0
$613$	−60.4201	−	104.651i	−0.0985647	−	0.170719i	0.812526	−	0.582925i	$-0.198092\pi$
$613$	−60.4201	−	104.651i	−0.0985647	−	0.170719i	−0.911091	+	0.412206i	$0.864758\pi$
$614$		0			0
$615$			371.788i			0.604534i
$616$		0			0
$617$	537.102			0.870506			0.435253	−	0.900308i	$-0.356659\pi$
$617$	537.102			0.870506			0.435253	+	0.900308i	$0.356659\pi$
$618$		0			0
$619$	211.462	−	122.088i	0.341619	−	0.197234i	−0.319369	−	0.947630i	$-0.603471\pi$
$619$	211.462	−	122.088i	0.341619	−	0.197234i	0.660988	+	0.750397i	$0.270138\pi$
$620$		0			0
$621$	583.626	+	336.957i	0.939816	+	0.542603i
$622$		0			0
$623$	−385.709	+	181.219i	−0.619115	+	0.290881i
$624$		0			0
$625$	−156.890	+	271.741i	−0.251024	+	0.434786i
$626$		0			0
$627$	153.016	+	265.031i	0.244044	+	0.422697i
$628$		0			0
$629$			61.4613i			0.0977128i
$630$		0			0
$631$	873.683			1.38460			0.692300	−	0.721609i	$-0.256597\pi$
$631$	873.683			1.38460			0.692300	+	0.721609i	$0.256597\pi$
$632$		0			0
$633$	−239.462	+	138.253i	−0.378297	+	0.218410i
$634$		0			0
$635$	964.019	+	556.577i	1.51814	+	0.876499i
$636$		0			0
$637$	224.458	−	83.1695i	0.352367	−	0.130564i
$638$		0			0
$639$	85.9093	−	148.799i	0.134443	−	0.232863i
$640$		0			0
$641$	−232.688	−	403.028i	−0.363008	−	0.628749i	0.625446	−	0.780267i	$-0.284917\pi$
$641$	−232.688	−	403.028i	−0.363008	−	0.628749i	−0.988454	+	0.151518i	$0.951584\pi$
$642$		0			0
$643$		−	82.1402i		−	0.127745i	−0.997958	−	0.0638726i	$-0.979655\pi$
$643$		−	82.1402i		−	0.127745i	0.997958	−	0.0638726i	$-0.0203451\pi$
$644$		0			0
$645$	−5.62583			−0.00872221
$646$		0			0
$647$	−155.391	+	89.7147i	−0.240171	+	0.138663i	−0.615255	−	0.788328i	$-0.710947\pi$
$647$	−155.391	+	89.7147i	−0.240171	+	0.138663i	0.375084	+	0.926991i	$0.377614\pi$
$648$		0			0
$649$	39.7614	+	22.9563i	0.0612656	+	0.0353717i
$650$		0			0
$651$	−199.858	−	425.379i	−0.307001	−	0.653424i
$652$		0			0
$653$	−122.281	+	211.796i	−0.187260	+	0.324344i	−0.944336	−	0.328983i	$-0.893294\pi$
$653$	−122.281	+	211.796i	−0.187260	+	0.324344i	0.757076	+	0.653327i	$0.226627\pi$
$654$		0			0
$655$	−311.028	−	538.717i	−0.474852	−	0.822468i
$656$		0			0
$657$			543.184i			0.826764i
$658$		0			0
$659$	128.978			0.195718			0.0978590	−	0.995200i	$-0.468801\pi$
$659$	128.978			0.195718			0.0978590	+	0.995200i	$0.468801\pi$
$660$		0			0
$661$	−394.437	+	227.729i	−0.596728	+	0.344521i	−0.767753	−	0.640745i	$-0.778625\pi$
$661$	−394.437	+	227.729i	−0.596728	+	0.344521i	0.171025	+	0.985267i	$0.445292\pi$
$662$		0			0
$663$	−54.2446	−	31.3181i	−0.0818168	−	0.0472370i
$664$		0			0
$665$	2070.91	+	175.147i	3.11415	+	0.263379i
$666$		0			0
$667$	−600.840	+	1040.68i	−0.900809	+	1.56025i
$668$		0			0
$669$	45.7251	+	79.1983i	0.0683485	+	0.118383i
$670$		0			0
$671$			152.555i			0.227355i
$672$		0			0
$673$	690.223			1.02559			0.512795	−	0.858511i	$-0.328610\pi$
$673$	690.223			1.02559			0.512795	+	0.858511i	$0.328610\pi$
$674$		0			0
$675$	999.292	−	576.941i	1.48043	−	0.854728i
$676$		0			0
$677$	355.820	+	205.433i	0.525583	+	0.303445i	0.739216	−	0.673469i	$-0.235196\pi$
$677$	355.820	+	205.433i	0.525583	+	0.303445i	−0.213633	+	0.976914i	$0.568530\pi$
$678$		0			0
$679$	−381.903	−	265.768i	−0.562449	−	0.391411i
$680$		0			0
$681$	−176.500	+	305.706i	−0.259177	+	0.448908i
$682$		0			0
$683$	−182.112	−	315.428i	−0.266636	−	0.461827i	0.701355	−	0.712812i	$-0.252579\pi$
$683$	−182.112	−	315.428i	−0.266636	−	0.461827i	−0.967991	+	0.250985i	$0.919245\pi$
$684$		0			0
$685$			624.930i			0.912307i
$686$		0			0
$687$	73.8488			0.107495
$688$		0			0
$689$	343.627	−	198.393i	0.498733	−	0.287944i
$690$		0			0
$691$	−901.670	−	520.579i	−1.30488	−	0.753371i	−0.323641	−	0.946180i	$-0.604907\pi$
$691$	−901.670	−	520.579i	−1.30488	−	0.753371i	−0.981236	+	0.192809i	$0.938240\pi$
$692$		0			0
$693$	130.203	−	187.099i	0.187883	−	0.269983i
$694$		0			0
$695$	519.440	−	899.696i	0.747396	−	1.29453i
$696$		0			0
$697$	−102.904	−	178.234i	−0.147638	−	0.255717i
$698$		0			0
$699$			451.785i			0.646331i
$700$		0			0
$701$	−366.854			−0.523330			−0.261665	−	0.965159i	$-0.584272\pi$
$701$	−366.854			−0.523330			−0.261665	+	0.965159i	$0.584272\pi$
$702$		0			0
$703$	−243.569	+	140.625i	−0.346471	+	0.200035i
$704$		0			0
$705$	394.574	+	227.808i	0.559680	+	0.323131i
$706$		0			0
$707$	−57.1116	+	675.279i	−0.0807802	+	0.955133i
$708$		0			0
$709$	32.6520	−	56.5549i	0.0460536	−	0.0797672i	−0.842080	−	0.539353i	$-0.818669\pi$
$709$	32.6520	−	56.5549i	0.0460536	−	0.0797672i	0.888133	+	0.459586i	$0.152002\pi$
$710$		0			0
$711$	379.877	+	657.966i	0.534285	+	0.925409i
$712$		0			0
$713$		−	1076.74i		−	1.51015i
$714$		0			0
$715$	214.080			0.299413
$716$		0			0
$717$	559.611	−	323.092i	0.780490	−	0.450616i
$718$		0			0
$719$	−588.230	−	339.615i	−0.818123	−	0.472344i	0.0316457	−	0.999499i	$-0.489925\pi$
$719$	−588.230	−	339.615i	−0.818123	−	0.472344i	−0.849769	+	0.527156i	$0.823259\pi$
$720$		0			0
$721$	−1092.62	+	513.350i	−1.51542	+	0.711997i
$722$		0			0
$723$	58.4145	−	101.177i	0.0807946	−	0.139940i
$724$		0			0
$725$	1028.77	+	1781.87i	1.41899	+	2.45776i
$726$		0			0
$727$			1079.11i			1.48433i	0.670217	+	0.742166i	$0.266201\pi$
$727$			1079.11i			1.48433i	−0.670217	+	0.742166i	$0.733799\pi$
$728$		0			0
$729$	−289.766			−0.397485
$730$		0			0
$731$	2.69701	−	1.55712i	0.00368948	−	0.00213012i
$732$		0			0
$733$	301.601	+	174.129i	0.411460	+	0.237557i	0.691417	−	0.722456i	$-0.256987\pi$
$733$	301.601	+	174.129i	0.411460	+	0.237557i	−0.279957	+	0.960013i	$0.590320\pi$
$734$		0			0
$735$	237.503	+	640.973i	0.323133	+	0.872072i
$736$		0			0
$737$	228.346	−	395.507i	0.309832	−	0.536644i
$738$		0			0
$739$	270.743	+	468.941i	0.366364	+	0.634561i	0.988994	−	0.147955i	$-0.0472691\pi$
$739$	270.743	+	468.941i	0.366364	+	0.634561i	−0.622630	+	0.782516i	$0.713936\pi$
$740$		0			0
$741$		−	286.626i		−	0.386810i
$742$		0			0
$743$	702.388			0.945340			0.472670	−	0.881240i	$-0.343290\pi$
$743$	702.388			0.945340			0.472670	+	0.881240i	$0.343290\pi$
$744$		0			0
$745$	−1503.20	+	867.873i	−2.01772	+	1.16493i
$746$		0			0
$747$	252.292	+	145.661i	0.337740	+	0.194995i
$748$		0			0
$749$	−307.134	−	653.708i	−0.410059	−	0.872775i
$750$		0			0
$751$	19.0291	−	32.9593i	0.0253383	−	0.0438872i	−0.853078	−	0.521783i	$-0.825267\pi$
$751$	19.0291	−	32.9593i	0.0253383	−	0.0438872i	0.878416	+	0.477896i	$0.158600\pi$
$752$		0			0
$753$	80.9701	+	140.244i	0.107530	+	0.186247i
$754$		0			0
$755$			407.115i			0.539226i
$756$		0			0
$757$	−451.849			−0.596895			−0.298447	−	0.954426i	$-0.596469\pi$
$757$	−451.849			−0.596895			−0.298447	+	0.954426i	$0.596469\pi$
$758$		0			0
$759$	−199.703	+	115.299i	−0.263113	+	0.151909i
$760$		0			0
$761$	9.01729	+	5.20613i	0.0118493	+	0.00684117i	0.505913	−	0.862585i	$-0.331156\pi$
$761$	9.01729	+	5.20613i	0.0118493	+	0.00684117i	−0.494064	+	0.869426i	$0.664489\pi$
$762$		0			0
$763$	289.833	+	24.5126i	0.379860	+	0.0321266i
$764$		0			0
$765$	−202.533	+	350.798i	−0.264749	+	0.458559i
$766$		0			0
$767$	−21.5006	−	37.2401i	−0.0280321	−	0.0485529i
$768$		0			0
$769$			1421.57i			1.84860i	0.381666	+	0.924300i	$0.375351\pi$
$769$			1421.57i			1.84860i	−0.381666	+	0.924300i	$0.624649\pi$
$770$		0			0
$771$	−343.943			−0.446100
$772$		0			0
$773$	729.548	−	421.205i	0.943788	−	0.544897i	0.0526426	−	0.998613i	$-0.483236\pi$
$773$	729.548	−	421.205i	0.943788	−	0.544897i	0.891146	+	0.453717i	$0.149902\pi$
$774$		0			0
$775$	−1596.61	−	921.801i	−2.06014	−	1.18942i
$776$		0			0
$777$	−75.9278	−	52.8386i	−0.0977192	−	0.0680033i
$778$		0			0
$779$	470.892	−	815.609i	0.604482	−	1.04699i
$780$		0			0
$781$	71.7729	+	124.314i	0.0918987	+	0.159173i
$782$		0			0
$783$		−	1142.21i		−	1.45876i
$784$		0			0
$785$	1489.20			1.89707
$786$		0			0
$787$	419.051	−	241.939i	0.532466	−	0.307419i	−0.209554	−	0.977797i	$-0.567201\pi$
$787$	419.051	−	241.939i	0.532466	−	0.307419i	0.742020	+	0.670378i	$0.233868\pi$
$788$		0			0
$789$	−297.958	−	172.026i	−0.377640	−	0.218031i
$790$		0			0
$791$	−535.328	+	769.254i	−0.676774	+	0.972508i
$792$		0			0
$793$	71.4408	−	123.739i	0.0900892	−	0.156039i
$794$		0			0
$795$	566.542	+	981.279i	0.712631	+	1.23431i
$796$		0			0
$797$			10.4020i			0.0130515i	0.999979	+	0.00652574i	$0.00207722\pi$
$797$			10.4020i			0.0130515i	−0.999979	+	0.00652574i	$0.997923\pi$
$798$		0			0
$799$	−252.211			−0.315658
$800$		0			0
$801$	329.162	−	190.042i	0.410939	−	0.237256i
$802$		0			0
$803$	−393.005	−	226.902i	−0.489421	−	0.282567i
$804$		0			0
$805$	−131.975	+	1560.45i	−0.163944	+	1.93844i
$806$		0			0
$807$	29.8656	−	51.7288i	0.0370082	−	0.0641001i
$808$		0			0
$809$	139.829	+	242.191i	0.172842	+	0.299371i	0.939412	−	0.342790i	$-0.111372\pi$
$809$	139.829	+	242.191i	0.172842	+	0.299371i	−0.766571	+	0.642160i	$0.778038\pi$
$810$		0			0
$811$		−	1027.85i		−	1.26739i	−0.773584	−	0.633693i	$-0.781538\pi$
$811$		−	1027.85i		−	1.26739i	0.773584	−	0.633693i	$-0.218462\pi$
$812$		0			0
$813$	−127.289			−0.156567
$814$		0			0
$815$	−923.739	+	533.321i	−1.13342	+	0.654382i
$816$		0			0
$817$	12.3416	+	7.12544i	0.0151060	+	0.00872147i
$818$		0			0
$819$	−193.226	+	90.7842i	−0.235929	+	0.110848i
$820$		0			0
$821$	238.070	−	412.350i	0.289976	−	0.502253i	−0.683828	−	0.729644i	$-0.739686\pi$
$821$	238.070	−	412.350i	0.289976	−	0.502253i	0.973804	+	0.227390i	$0.0730193\pi$
$822$		0			0
$823$	555.128	+	961.509i	0.674517	+	1.16830i	0.976610	+	0.215019i	$0.0689814\pi$
$823$	555.128	+	961.509i	0.674517	+	1.16830i	−0.302093	+	0.953279i	$0.597685\pi$
$824$		0			0
$825$			394.832i			0.478584i
$826$		0			0
$827$	997.533			1.20621			0.603103	−	0.797663i	$-0.293931\pi$
$827$	997.533			1.20621			0.603103	+	0.797663i	$0.293931\pi$
$828$		0			0
$829$	633.794	−	365.921i	0.764529	−	0.441401i	−0.0663907	−	0.997794i	$-0.521148\pi$
$829$	633.794	−	365.921i	0.764529	−	0.441401i	0.830919	+	0.556393i	$0.187815\pi$
$830$		0			0
$831$	385.368	+	222.492i	0.463740	+	0.267740i
$832$		0			0
$833$	−291.267	−	241.545i	−0.349660	−	0.289970i
$834$		0			0
$835$	806.151	−	1396.29i	0.965451	−	1.67221i
$836$		0			0
$837$	511.724	+	886.332i	0.611379	+	1.05894i
$838$		0			0
$839$		−	1200.42i		−	1.43077i	−0.698729	−	0.715386i	$-0.746251\pi$
$839$		−	1200.42i		−	1.43077i	0.698729	−	0.715386i	$-0.253749\pi$
$840$		0			0
$841$	1195.71			1.42178
$842$		0			0
$843$	600.097	−	346.466i	0.711859	−	0.410992i
$844$		0			0
$845$	1056.04	+	609.705i	1.24975	+	0.721544i
$846$		0			0
$847$	−279.196	−	594.244i	−0.329629	−	0.701587i
$848$		0			0
$849$	119.384	−	206.779i	0.140617	−	0.243556i
$850$		0			0
$851$	−105.962	−	183.532i	−0.124515	−	0.215666i
$852$		0			0
$853$		−	1251.12i		−	1.46673i	−0.679836	−	0.733364i	$-0.737949\pi$
$853$		−	1251.12i		−	1.46673i	0.679836	−	0.733364i	$-0.262051\pi$
$854$		0			0
$855$	−1853.60			−2.16795
$856$		0			0
$857$	−196.885	+	113.671i	−0.229737	+	0.132639i	−0.610451	−	0.792054i	$-0.709012\pi$
$857$	−196.885	+	113.671i	−0.229737	+	0.132639i	0.380714	+	0.924693i	$0.375678\pi$
$858$		0			0
$859$	−345.382	−	199.407i	−0.402075	−	0.232138i	0.285304	−	0.958437i	$-0.407905\pi$
$859$	−345.382	−	199.407i	−0.402075	−	0.232138i	−0.687379	+	0.726299i	$0.741239\pi$
$860$		0			0
$861$	308.653	+	26.1043i	0.358482	+	0.0303186i
$862$		0			0
$863$	1.98694	−	3.44147i	0.00230236	−	0.00398780i	−0.864872	−	0.501993i	$-0.832600\pi$
$863$	1.98694	−	3.44147i	0.00230236	−	0.00398780i	0.867174	+	0.498005i	$0.165934\pi$
$864$		0			0
$865$	−792.080	−	1371.92i	−0.915700	−	1.58604i
$866$		0			0
$867$		−	380.833i		−	0.439254i
$868$		0			0
$869$	−634.736			−0.730421
$870$		0			0
$871$	−370.428	+	213.867i	−0.425290	+	0.245541i
$872$		0			0
$873$	359.376	+	207.486i	0.411656	+	0.237670i
$874$		0			0
$875$	994.025	+	691.747i	1.13603	+	0.790569i
$876$		0			0
$877$	−219.522	+	380.223i	−0.250310	+	0.433549i	−0.963611	−	0.267308i	$-0.913866\pi$
$877$	−219.522	+	380.223i	−0.250310	+	0.433549i	0.713301	+	0.700858i	$0.247199\pi$
$878$		0			0
$879$	220.575	+	382.047i	0.250939	+	0.434638i
$880$		0			0
$881$			848.178i			0.962744i	0.876516	+	0.481372i	$0.159861\pi$
$881$			848.178i			0.962744i	−0.876516	+	0.481372i	$0.840139\pi$
$882$		0			0
$883$	1227.48			1.39012			0.695062	−	0.718950i	$-0.255377\pi$
$883$	1227.48			1.39012			0.695062	+	0.718950i	$0.255377\pi$
$884$		0			0
$885$	106.345	−	61.3982i	0.120164	−	0.0693765i
$886$		0			0
$887$	−817.480	−	471.972i	−0.921624	−	0.532100i	−0.0374710	−	0.999298i	$-0.511930\pi$
$887$	−817.480	−	471.972i	−0.921624	−	0.532100i	−0.884153	+	0.467198i	$0.845264\pi$
$888$		0			0
$889$	529.748	−	761.236i	0.595892	−	0.856283i
$890$		0			0
$891$	−36.9432	+	63.9875i	−0.0414626	+	0.0718153i
$892$		0			0
$893$	−577.063	−	999.503i	−0.646207	−	1.11926i
$894$		0			0
$895$			2025.31i			2.26291i
$896$		0			0
$897$	215.975			0.240775
$898$		0			0
$899$	−1580.45	+	912.474i	−1.75801	+	1.01499i
$900$		0			0
$901$	−543.198	−	313.615i	−0.602883	−	0.348075i
$902$		0			0
$903$	−0.395005	+	4.67048i	−0.000437436	+	0.00517218i
$904$		0			0
$905$	−1166.98	+	2021.26i	−1.28948	+	2.23344i
$906$		0			0
$907$	47.5469	+	82.3537i	0.0524222	+	0.0907979i	0.891046	−	0.453914i	$-0.149973\pi$
$907$	47.5469	+	82.3537i	0.0524222	+	0.0907979i	−0.838624	+	0.544711i	$0.816639\pi$
$908$		0			0
$909$		−	604.419i		−	0.664928i
$910$		0			0
$911$	698.535			0.766779			0.383389	−	0.923587i	$-0.374757\pi$
$911$	698.535			0.766779			0.383389	+	0.923587i	$0.374757\pi$
$912$		0			0
$913$	−210.777	+	121.692i	−0.230862	+	0.133289i
$914$		0			0
$915$	353.356	+	204.010i	0.386181	+	0.222962i
$916$		0			0
$917$	−469.073	+	220.386i	−0.511530	+	0.240334i
$918$		0			0
$919$	−231.229	+	400.501i	−0.251610	+	0.435801i	−0.963969	−	0.266014i	$-0.914293\pi$
$919$	−231.229	+	400.501i	−0.251610	+	0.435801i	0.712359	+	0.701815i	$0.247627\pi$
$920$		0			0
$921$	−233.794	−	404.943i	−0.253848	−	0.439677i
$922$		0			0
$923$		−	134.444i		−	0.145659i
$924$		0			0
$925$	−362.859			−0.392280
$926$		0			0
$927$	932.437	−	538.343i	1.00586	−	0.580736i
$928$		0			0
$929$	−1564.78	−	903.425i	−1.68437	−	0.972471i	−0.958697	−	0.284430i	$-0.908196\pi$
$929$	−1564.78	−	903.425i	−1.68437	−	0.972471i	−0.725672	−	0.688041i	$-0.758471\pi$
$930$		0			0
$931$	290.809	−	1706.94i	0.312362	−	1.83345i
$932$		0			0
$933$	−46.8132	+	81.0829i	−0.0501750	+	0.0869056i
$934$		0			0
$935$	−169.206	−	293.074i	−0.180969	−	0.313448i
$936$		0			0
$937$		−	1569.03i		−	1.67453i	−0.546800	−	0.837263i	$-0.684154\pi$
$937$		−	1569.03i		−	1.67453i	0.546800	−	0.837263i	$-0.315846\pi$
$938$		0			0
$939$	−140.048			−0.149146
$940$		0			0
$941$	−872.185	+	503.556i	−0.926870	+	0.535129i	−0.885820	−	0.464028i	$-0.846404\pi$
$941$	−872.185	+	503.556i	−0.926870	+	0.535129i	−0.0410499	+	0.999157i	$0.513070\pi$
$942$		0			0
$943$	614.568	+	354.821i	0.651716	+	0.376268i
$944$		0			0
$945$	−632.974	−	1347.23i	−0.669813	−	1.42564i
$946$		0			0
$947$	−381.991	+	661.627i	−0.403369	+	0.698656i	−0.994130	−	0.108190i	$-0.965494\pi$
$947$	−381.991	+	661.627i	−0.403369	+	0.698656i	0.590761	+	0.806847i	$0.298828\pi$
$948$		0			0
$949$	212.514	+	368.084i	0.223934	+	0.387866i
$950$		0			0
$951$		−	264.640i		−	0.278275i
$952$		0			0
$953$	−698.870			−0.733337			−0.366669	−	0.930352i	$-0.619502\pi$
$953$	−698.870			−0.733337			−0.366669	+	0.930352i	$0.619502\pi$
$954$		0			0
$955$	−1923.66	+	1110.63i	−2.01430	+	1.16296i
$956$		0			0
$957$	338.475	+	195.418i	0.353683	+	0.204199i
$958$		0			0
$959$	518.808	+	43.8781i	0.540988	+	0.0457540i
$960$		0			0
$961$	337.101	−	583.876i	0.350781	−	0.607571i
$962$		0			0
$963$	322.087	+	557.871i	0.334462	+	0.579306i
$964$		0			0
$965$		−	1776.13i		−	1.84054i
$966$		0			0
$967$	−383.857			−0.396956			−0.198478	−	0.980105i	$-0.563600\pi$
$967$	−383.857			−0.396956			−0.198478	+	0.980105i	$0.563600\pi$
$968$		0			0
$969$	−392.389	+	226.546i	−0.404942	+	0.233793i
$970$		0			0
$971$	218.672	+	126.250i	0.225203	+	0.130021i	0.608357	−	0.793664i	$-0.291829\pi$
$971$	218.672	+	126.250i	0.225203	+	0.130021i	−0.383154	+	0.923684i	$0.625162\pi$
$972$		0			0
$973$	−710.443	−	494.401i	−0.730157	−	0.508121i
$974$		0			0
$975$	184.898	−	320.252i	0.189639	−	0.328464i
$976$		0			0
$977$	33.7823	+	58.5127i	0.0345776	+	0.0598901i	0.882796	−	0.469756i	$-0.155658\pi$
$977$	33.7823	+	58.5127i	0.0345776	+	0.0598901i	−0.848219	+	0.529646i	$0.822325\pi$
$978$		0			0
$979$			317.541i			0.324352i
$980$		0			0
$981$	−259.420			−0.264444
$982$		0			0
$983$	−331.002	+	191.104i	−0.336726	+	0.194409i	−0.658823	−	0.752298i	$-0.728946\pi$
$983$	−331.002	+	191.104i	−0.336726	+	0.194409i	0.322097	+	0.946707i	$0.395612\pi$
$984$		0			0
$985$	−578.423	−	333.952i	−0.587231	−	0.339038i
$986$		0			0
$987$	216.827	−	311.575i	0.219682	−	0.315678i
$988$		0			0
$989$	−5.36908	+	9.29951i	−0.00542879	+	0.00940295i
$990$		0			0
$991$	919.149	+	1592.01i	0.927496	+	1.60647i	0.787497	+	0.616319i	$0.211377\pi$
$991$	919.149	+	1592.01i	0.927496	+	1.60647i	0.140000	+	0.990152i	$0.455290\pi$
$992$		0			0
$993$			929.123i			0.935673i
$994$		0			0
$995$	−1705.21			−1.71377
$996$		0			0
$997$	−1174.19	+	677.919i	−1.17772	+	0.679959i	−0.955487	−	0.295034i	$-0.904669\pi$
$997$	−1174.19	+	677.919i	−1.17772	+	0.679959i	−0.222236	+	0.974993i	$0.571336\pi$
$998$		0			0
$999$	174.449	+	100.718i	0.174623	+	0.100819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.s.a.33.3	✓	16
4.3	odd	2	inner	224.3.s.a.33.6	yes	16
7.2	even	3		1568.3.c.h.97.5		16
7.3	odd	6	inner	224.3.s.a.129.3	yes	16
7.5	odd	6		1568.3.c.h.97.12		16
8.3	odd	2		448.3.s.g.257.3		16
8.5	even	2		448.3.s.g.257.6		16
28.3	even	6	inner	224.3.s.a.129.6	yes	16
28.19	even	6		1568.3.c.h.97.6		16
28.23	odd	6		1568.3.c.h.97.11		16
56.3	even	6		448.3.s.g.129.3		16
56.45	odd	6		448.3.s.g.129.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.s.a.33.3	✓	16	1.1	even	1	trivial
224.3.s.a.33.6	yes	16	4.3	odd	2	inner
224.3.s.a.129.3	yes	16	7.3	odd	6	inner
224.3.s.a.129.6	yes	16	28.3	even	6	inner
448.3.s.g.129.3		16	56.3	even	6
448.3.s.g.129.6		16	56.45	odd	6
448.3.s.g.257.3		16	8.3	odd	2
448.3.s.g.257.6		16	8.5	even	2
1568.3.c.h.97.5		16	7.2	even	3
1568.3.c.h.97.6		16	28.19	even	6
1568.3.c.h.97.11		16	28.23	odd	6
1568.3.c.h.97.12		16	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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43792 + 0.830185i) q^{3} +(7.27622 + 4.20093i) q^{5} +(3.99843 - 5.74565i) q^{7} +(-3.12159 + 5.40674i) q^{9} +O(q^{10})\)	\(q+(-1.43792 + 0.830185i) q^{3} +(7.27622 + 4.20093i) q^{5} +(3.99843 - 5.74565i) q^{7} +(-3.12159 + 5.40674i) q^{9} +(-2.60793 - 4.51706i) q^{11} +4.88512i q^{13} -13.9502 q^{15} +(6.68769 - 3.86114i) q^{17} +(30.6032 + 17.6687i) q^{19} +(-0.979482 + 11.5812i) q^{21} +(-13.3135 + 23.0597i) q^{23} +(22.7956 + 39.4832i) q^{25} -25.3093i q^{27} +45.1300 q^{29} +(-35.0200 + 20.2188i) q^{31} +(7.50000 + 4.33013i) q^{33} +(53.2306 - 25.0095i) q^{35} +(-3.97948 + 6.89266i) q^{37} +(-4.05555 - 7.02442i) q^{39} -26.6511i q^{41} +0.403279 q^{43} +(-45.4267 + 26.2271i) q^{45} +(-28.2845 - 16.3301i) q^{47} +(-17.0251 - 45.9472i) q^{49} +(-6.41092 + 11.1040i) q^{51} +(-40.6118 - 70.3416i) q^{53} -43.8229i q^{55} -58.6733 q^{57} +(-7.62318 + 4.40124i) q^{59} +(-25.3298 - 14.6242i) q^{61} +(18.5838 + 39.5541i) q^{63} +(-20.5220 + 35.5452i) q^{65} +(43.7792 + 75.8278i) q^{67} -44.2108i q^{69} -27.5210 q^{71} +(75.3481 - 43.5023i) q^{73} +(-65.5567 - 37.8492i) q^{75} +(-36.3811 - 3.07693i) q^{77} +(60.8467 - 105.390i) q^{79} +(-7.08286 - 12.2679i) q^{81} -46.6625i q^{83} +64.8815 q^{85} +(-64.8934 + 37.4662i) q^{87} +(-52.7235 - 30.4399i) q^{89} +(28.0682 + 19.5328i) q^{91} +(33.5707 - 58.1462i) q^{93} +(148.450 + 257.123i) q^{95} -66.4681i q^{97} +32.5635 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^9	\( 16 q + 8 q^{9} + 48 q^{17} + 56 q^{21} + 16 q^{25} + 112 q^{29} + 120 q^{33} + 8 q^{37} - 72 q^{45} - 128 q^{49} - 24 q^{53} - 528 q^{57} - 360 q^{61} - 8 q^{65} + 72 q^{73} + 32 q^{81} + 720 q^{85} + 408 q^{89} - 232 q^{93}+O(q^{100}) \) 16 * q + 8 * q^9 + 48 * q^17 + 56 * q^21 + 16 * q^25 + 112 * q^29 + 120 * q^33 + 8 * q^37 - 72 * q^45 - 128 * q^49 - 24 * q^53 - 528 * q^57 - 360 * q^61 - 8 * q^65 + 72 * q^73 + 32 * q^81 + 720 * q^85 + 408 * q^89 - 232 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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