LMFDB - Embedded newform 448.3.s.g.257.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,3,Mod(129,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("448.129");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	448.s (of order $6$, degree $2$, not 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:	$12.2071158433$
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:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.3
Root			$0.707107 - 1.17406i$ of defining polynomial
Character	$\chi$	$=$	448.257
Dual form			448.3.s.g.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 $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

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

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	−0.456473	−	0.889737i	$-0.650888\pi$
$5$	−7.27622	−	4.20093i	−1.45524	−	0.840186i	−0.998772	+	0.0495513i	$0.984221\pi$
$6$		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	$-0.939835\pi$
$13$		−	4.88512i		−	0.375778i	0.982190	−	0.187889i	$-0.0601646\pi$
$14$		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	$-0.636835\pi$
$23$	13.3135	−	23.0597i	0.578850	−	1.00260i	0.995612	−	0.0935814i	$-0.0298315\pi$
$24$		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	$-0.783818\pi$
$29$	−45.1300			−1.55621			−0.778103	+	0.628137i	$0.783818\pi$
$30$		0			0
$31$	35.0200	−	20.2188i	1.12968	−	0.652220i	0.185824	−	0.982583i	$-0.440505\pi$
$31$	35.0200	−	20.2188i	1.12968	−	0.652220i	0.943854	+	0.330363i	$0.107171\pi$
$32$		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	−0.807225	−	0.590244i	$-0.799032\pi$
$37$	3.97948	−	6.89266i	0.107554	−	0.186288i	0.914779	+	0.403956i	$0.132365\pi$
$38$		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	0.769748	−	0.638347i	$-0.220382\pi$
$47$	28.2845	+	16.3301i	0.601798	+	0.347448i	−0.167951	+	0.985795i	$0.553715\pi$
$48$		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	$0.111218\pi$
$53$	40.6118	+	70.3416i	0.766259	+	1.32720i	−0.173319	+	0.984866i	$0.555449\pi$
$54$		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	0.693040	−	0.720899i	$-0.256271\pi$
$61$	25.3298	+	14.6242i	0.415243	+	0.239740i	−0.277797	+	0.960640i	$0.589604\pi$
$62$		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	$-0.437915\pi$
$71$	27.5210			0.387620			0.193810	+	0.981039i	$0.437915\pi$
$72$		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	$0.446516\pi$
$79$	−60.8467	+	105.390i	−0.770212	+	1.33405i	−0.937447	+	0.348129i	$0.886817\pi$
$80$		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	−0.0237720	−	0.999717i	$-0.507568\pi$
$101$	83.8424	−	48.4064i	0.830123	−	0.479272i	0.853895	+	0.520446i	$0.174234\pi$
$102$		0			0
$103$	149.353	+	86.2290i	1.45003	+	0.837175i	0.998482	−	0.0550721i	$-0.0175389\pi$
$103$	149.353	+	86.2290i	1.45003	+	0.837175i	0.451547	+	0.892247i	$0.350872\pi$
$104$		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	0.754844	−	0.655905i	$-0.227713\pi$
$109$	−20.7763	−	35.9856i	−0.190608	−	0.330143i	−0.945452	+	0.325762i	$0.894379\pi$
$110$		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	$-0.674668\pi$
$127$	−132.489			−1.04322			−0.521610	+	0.853184i	$0.674668\pi$
$128$		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	$-0.589508\pi$
$149$	103.295	−	178.913i	0.693257	−	1.20076i	0.970765	−	0.240033i	$-0.0771584\pi$
$150$		0			0
$151$	−24.2277	−	41.9636i	−0.160448	−	0.277905i	0.774581	−	0.632474i	$-0.217961\pi$
$151$	−24.2277	−	41.9636i	−0.160448	−	0.277905i	−0.935030	+	0.354570i	$0.884627\pi$
$152$		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	−0.901577	−	0.432618i	$-0.857590\pi$
$157$	−153.500	+	88.6233i	−0.977708	+	0.564480i	−0.0761305	+	0.997098i	$0.524257\pi$
$158$		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	$0.194821\pi$
$167$			191.898i			1.14909i	−0.818472	+	0.574546i	$0.805179\pi$
$168$		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	0.891169	−	0.453672i	$-0.149886\pi$
$173$	163.288	+	94.2744i	0.943862	+	0.544939i	0.0526930	+	0.998611i	$0.483220\pi$
$174$		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	$-0.721562\pi$
$181$		−	277.790i		−	1.53475i	0.641198	−	0.767376i	$-0.278438\pi$
$182$		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	$-0.590026\pi$
$191$	132.188	−	228.957i	0.692085	−	1.19873i	0.971154	−	0.238455i	$-0.0766408\pi$
$192$		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	$-0.435333\pi$
$197$	79.4949			0.403527			0.201764	+	0.979434i	$0.435333\pi$
$198$		0			0
$199$	175.765	−	101.478i	0.883241	−	0.509939i	0.0115150	−	0.999934i	$-0.496335\pi$
$199$	175.765	−	101.478i	0.883241	−	0.509939i	0.871726	+	0.489995i	$0.163001\pi$
$200$		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	$0.0394099\pi$
$223$			55.0782i			0.246988i	−0.992345	+	0.123494i	$0.960590\pi$
$224$		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	0.581738	−	0.813376i	$-0.302373\pi$
$229$	38.5185	+	22.2387i	0.168203	+	0.0971120i	−0.413535	+	0.910488i	$0.635706\pi$
$230$		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	$-0.197184\pi$
$239$	389.180			1.62837			0.814185	+	0.580605i	$0.197184\pi$
$240$		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	0.599022	−	0.800732i	$-0.295556\pi$
$263$	−103.607	−	179.453i	−0.393943	−	0.682330i	−0.992966	+	0.118402i	$0.962223\pi$
$264$		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	−0.440972	−	0.897521i	$-0.645366\pi$
$269$	31.1550	−	17.9873i	0.115818	−	0.0668674i	0.556790	+	0.830653i	$0.312033\pi$
$270$		0			0
$271$	−66.3923	−	38.3316i	−0.244990	−	0.141445i	0.372478	−	0.928041i	$-0.378508\pi$
$271$	−66.3923	−	38.3316i	−0.244990	−	0.141445i	−0.617468	+	0.786596i	$0.711841\pi$
$272$		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	0.999826	−	0.0186514i	$-0.00593727\pi$
$277$	134.002	+	232.098i	0.483760	+	0.837898i	−0.516066	+	0.856549i	$0.672604\pi$
$278$		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	$0.149790\pi$
$293$			265.694i			0.906805i	−0.891306	+	0.453402i	$0.850210\pi$
$294$		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	−0.576453	−	0.817131i	$-0.695563\pi$
$311$	−48.8342	+	28.1945i	−0.157023	+	0.0906574i	0.419429	+	0.907788i	$0.362230\pi$
$312$		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	−0.712513	−	0.701659i	$-0.752443\pi$
$317$	79.6930	−	138.032i	0.251398	−	0.435433i	0.963911	+	0.266225i	$0.0857765\pi$
$318$		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	$-0.765243\pi$
$349$		−	469.369i		−	1.34490i	0.740144	−	0.672449i	$-0.234757\pi$
$350$		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	−0.601747	−	0.798687i	$-0.705528\pi$
$359$	140.301	−	243.008i	0.390810	−	0.676902i	0.992557	+	0.121785i	$0.0388617\pi$
$360$		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	−0.523413	−	0.852079i	$-0.675341\pi$
$367$	−17.3213	+	10.0005i	−0.0471971	+	0.0272493i	0.476216	+	0.879328i	$0.342008\pi$
$368$		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	−0.953280	−	0.302089i	$-0.902316\pi$
$373$	−80.2038	+	138.917i	−0.215024	+	0.372432i	0.738256	+	0.674520i	$0.235649\pi$
$374$		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	0.771512	−	0.636214i	$-0.219501\pi$
$383$	232.209	+	134.066i	0.606291	+	0.350042i	−0.165222	+	0.986256i	$0.552834\pi$
$384$		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	0.715214	−	0.698905i	$-0.246329\pi$
$389$	−96.3409	−	166.867i	−0.247663	−	0.428965i	−0.962877	+	0.269941i	$0.912996\pi$
$390$		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	0.340780	−	0.940143i	$-0.389309\pi$
$397$	−120.298	−	69.4542i	−0.303018	−	0.174948i	−0.643798	+	0.765195i	$0.722642\pi$
$398$		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	$-0.469153\pi$
$421$	81.4693			0.193514			0.0967569	+	0.995308i	$0.469153\pi$
$422$		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	0.917090	−	0.398681i	$-0.130532\pi$
$431$	48.8226	+	84.5632i	0.113277	+	0.196202i	−0.803812	+	0.594883i	$0.797198\pi$
$432$		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	0.210160	−	0.977667i	$-0.432601\pi$
$439$	−233.304	−	134.698i	−0.531444	−	0.306829i	−0.741604	+	0.670838i	$0.765935\pi$
$440$		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	$-0.964416\pi$
$461$		−	102.856i		−	0.223114i	0.993758	−	0.111557i	$-0.0355837\pi$
$462$		0			0
$463$	−541.601			−1.16976			−0.584882	−	0.811118i	$-0.698859\pi$
$463$	−541.601			−1.16976			−0.584882	+	0.811118i	$0.698859\pi$
$464$		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	−0.983313	−	0.181921i	$-0.941768\pi$
$479$	−631.045	+	364.334i	−1.31742	+	0.760614i	−0.334108	+	0.942535i	$0.608435\pi$
$480$		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	0.999007	−	0.0445466i	$-0.0141843\pi$
$487$	224.471	+	388.794i	0.460925	+	0.798346i	−0.538082	+	0.842892i	$0.680851\pi$
$488$		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	$-0.901373\pi$
$503$		−	306.742i		−	0.609825i	0.952380	−	0.304913i	$-0.0986272\pi$
$504$		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	0.331711	−	0.943381i	$-0.392374\pi$
$509$	−162.588	−	93.8701i	−0.319426	−	0.184421i	−0.651137	+	0.758961i	$0.725708\pi$
$510$		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	−0.541392	−	0.840770i	$-0.682103\pi$
$541$	247.471	−	428.632i	0.457432	−	0.792296i	0.998824	+	0.0484743i	$0.0154359\pi$
$542$		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	$0.100985\pi$
$557$	415.083	+	718.944i	0.745211	+	1.29074i	−0.204885	+	0.978786i	$0.565682\pi$
$558$		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	0.836805	−	0.547502i	$-0.184421\pi$
$599$	−33.3932	−	57.8387i	−0.0557482	−	0.0965587i	−0.892553	+	0.450943i	$0.851088\pi$
$600$		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	0.875205	−	0.483753i	$-0.160727\pi$
$607$	542.576	+	313.256i	0.893864	+	0.516073i	0.0186599	+	0.999826i	$0.494060\pi$
$608$		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	0.911091	−	0.412206i	$-0.135242\pi$
$613$	60.4201	+	104.651i	0.0985647	+	0.170719i	−0.812526	+	0.582925i	$0.801908\pi$
$614$		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	$-0.743403\pi$
$631$	−873.683			−1.38460			−0.692300	+	0.721609i	$0.743403\pi$
$632$		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	−0.375084	−	0.926991i	$-0.622386\pi$
$647$	155.391	−	89.7147i	0.240171	−	0.138663i	0.615255	+	0.788328i	$0.289053\pi$
$648$		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	−0.757076	−	0.653327i	$-0.773373\pi$
$653$	122.281	−	211.796i	0.187260	−	0.324344i	0.944336	+	0.328983i	$0.106706\pi$
$654$		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	−0.171025	−	0.985267i	$-0.554708\pi$
$661$	394.437	−	227.729i	0.596728	−	0.344521i	0.767753	+	0.640745i	$0.221375\pi$
$662$		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	0.213633	−	0.976914i	$-0.431470\pi$
$677$	−355.820	−	205.433i	−0.525583	−	0.303445i	−0.739216	+	0.673469i	$0.764804\pi$
$678$		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	$-0.415728\pi$
$701$	366.854			0.523330			0.261665	+	0.965159i	$0.415728\pi$
$702$		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	−0.888133	−	0.459586i	$-0.847998\pi$
$709$	−32.6520	+	56.5549i	−0.0460536	+	0.0797672i	0.842080	+	0.539353i	$0.181331\pi$
$710$		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	0.849769	−	0.527156i	$-0.176741\pi$
$719$	588.230	+	339.615i	0.818123	+	0.472344i	−0.0316457	+	0.999499i	$0.510075\pi$
$720$		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	$-0.733799\pi$
$727$		−	1079.11i		−	1.48433i	0.670217	−	0.742166i	$-0.266201\pi$
$728$		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	0.279957	−	0.960013i	$-0.409680\pi$
$733$	−301.601	−	174.129i	−0.411460	−	0.237557i	−0.691417	+	0.722456i	$0.743013\pi$
$734$		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	$-0.656710\pi$
$743$	−702.388			−0.945340			−0.472670	+	0.881240i	$0.656710\pi$
$744$		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	−0.878416	−	0.477896i	$-0.841400\pi$
$751$	−19.0291	+	32.9593i	−0.0253383	+	0.0438872i	0.853078	+	0.521783i	$0.174733\pi$
$752$		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	$-0.403531\pi$
$757$	451.849			0.596895			0.298447	+	0.954426i	$0.403531\pi$
$758$		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	−0.891146	−	0.453717i	$-0.850098\pi$
$773$	−729.548	+	421.205i	−0.943788	+	0.544897i	−0.0526426	+	0.998613i	$0.516764\pi$
$774$		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	$-0.997923\pi$
$797$		−	10.4020i		−	0.0130515i	0.999979	−	0.00652574i	$-0.00207722\pi$
$798$		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	−0.973804	−	0.227390i	$-0.926981\pi$
$821$	−238.070	+	412.350i	−0.289976	+	0.502253i	0.683828	+	0.729644i	$0.260314\pi$
$822$		0			0
$823$	−555.128	−	961.509i	−0.674517	−	1.16830i	−0.976610	−	0.215019i	$-0.931019\pi$
$823$	−555.128	−	961.509i	−0.674517	−	1.16830i	0.302093	−	0.953279i	$-0.402315\pi$
$824$		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	−0.830919	−	0.556393i	$-0.812185\pi$
$829$	−633.794	+	365.921i	−0.764529	+	0.441401i	0.0663907	+	0.997794i	$0.478852\pi$
$830$		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	$0.253749\pi$
$839$			1200.42i			1.43077i	−0.698729	+	0.715386i	$0.746251\pi$
$840$		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	$0.262051\pi$
$853$			1251.12i			1.46673i	−0.679836	+	0.733364i	$0.737949\pi$
$854$		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	−0.867174	−	0.498005i	$-0.834066\pi$
$863$	−1.98694	+	3.44147i	−0.00230236	+	0.00398780i	0.864872	+	0.501993i	$0.167400\pi$
$864$		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	−0.713301	−	0.700858i	$-0.752801\pi$
$877$	219.522	−	380.223i	0.250310	−	0.433549i	0.963611	+	0.267308i	$0.0861342\pi$
$878$		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	0.884153	−	0.467198i	$-0.154736\pi$
$887$	817.480	+	471.972i	0.921624	+	0.532100i	0.0374710	+	0.999298i	$0.488070\pi$
$888$		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	$-0.625243\pi$
$911$	−698.535			−0.766779			−0.383389	+	0.923587i	$0.625243\pi$
$912$		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	−0.712359	−	0.701815i	$-0.752373\pi$
$919$	231.229	−	400.501i	0.251610	−	0.435801i	0.963969	+	0.266014i	$0.0857067\pi$
$920$		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	0.0410499	−	0.999157i	$-0.486930\pi$
$941$	872.185	−	503.556i	0.926870	−	0.535129i	0.885820	+	0.464028i	$0.153596\pi$
$942$		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	$-0.436400\pi$
$967$	383.857			0.396956			0.198478	+	0.980105i	$0.436400\pi$
$968$		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	−0.322097	−	0.946707i	$-0.604388\pi$
$983$	331.002	−	191.104i	0.336726	−	0.194409i	0.658823	+	0.752298i	$0.271054\pi$
$984$		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	$-0.788623\pi$
$991$	−919.149	−	1592.01i	−0.927496	−	1.60647i	−0.140000	−	0.990152i	$-0.544710\pi$
$992$		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	0.222236	−	0.974993i	$-0.428664\pi$
$997$	1174.19	−	677.919i	1.17772	−	0.679959i	0.955487	+	0.295034i	$0.0953310\pi$
$998$		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	448.3.s.g.257.3		16
4.3	odd	2	inner	448.3.s.g.257.6		16
7.3	odd	6	inner	448.3.s.g.129.3		16
8.3	odd	2		224.3.s.a.33.3	✓	16
8.5	even	2		224.3.s.a.33.6	yes	16
28.3	even	6	inner	448.3.s.g.129.6		16
56.3	even	6		224.3.s.a.129.3	yes	16
56.5	odd	6		1568.3.c.h.97.6		16
56.19	even	6		1568.3.c.h.97.12		16
56.37	even	6		1568.3.c.h.97.11		16
56.45	odd	6		224.3.s.a.129.6	yes	16
56.51	odd	6		1568.3.c.h.97.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.s.a.33.3	✓	16	8.3	odd	2
224.3.s.a.33.6	yes	16	8.5	even	2
224.3.s.a.129.3	yes	16	56.3	even	6
224.3.s.a.129.6	yes	16	56.45	odd	6
448.3.s.g.129.3		16	7.3	odd	6	inner
448.3.s.g.129.6		16	28.3	even	6	inner
448.3.s.g.257.3		16	1.1	even	1	trivial
448.3.s.g.257.6		16	4.3	odd	2	inner
1568.3.c.h.97.5		16	56.51	odd	6
1568.3.c.h.97.6		16	56.5	odd	6
1568.3.c.h.97.11		16	56.37	even	6
1568.3.c.h.97.12		16	56.19	even	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.s (of order \(6\), degree \(2\), not 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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