LMFDB - Embedded newform 224.3.r.a.95.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("224.95");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	224.95
Dual form			224.3.r.a.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.33013 - 2.50000i) q^{3} +(-4.50000 - 7.79423i) q^{5} +(-6.92820 - 1.00000i) q^{7} +(8.00000 + 13.8564i) q^{9} +O(q^{10})$	\(q+(-4.33013 - 2.50000i) q^{3} +(-4.50000 - 7.79423i) q^{5} +(-6.92820 - 1.00000i) q^{7} +(8.00000 + 13.8564i) q^{9} +(-2.59808 - 1.50000i) q^{11} +16.0000 q^{13} +45.0000i q^{15} +(3.50000 - 6.06218i) q^{17} +(-9.52628 + 5.50000i) q^{19} +(27.5000 + 21.6506i) q^{21} +(16.4545 - 9.50000i) q^{23} +(-28.0000 + 48.4974i) q^{25} -35.0000i q^{27} -32.0000 q^{29} +(-9.52628 - 5.50000i) q^{31} +(7.50000 + 12.9904i) q^{33} +(23.3827 + 58.5000i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-69.2820 - 40.0000i) q^{39} -40.0000 q^{41} +40.0000i q^{43} +(72.0000 - 124.708i) q^{45} +(73.6122 - 42.5000i) q^{47} +(47.0000 + 13.8564i) q^{49} +(-30.3109 + 17.5000i) q^{51} +(-3.50000 + 6.06218i) q^{53} +27.0000i q^{55} +55.0000 q^{57} +(-45.8993 - 26.5000i) q^{59} +(-39.5000 - 68.4160i) q^{61} +(-41.5692 - 104.000i) q^{63} +(-72.0000 - 124.708i) q^{65} +(9.52628 + 5.50000i) q^{67} -95.0000 q^{69} +48.0000i q^{71} +(-71.5000 + 123.842i) q^{73} +(242.487 - 140.000i) q^{75} +(16.5000 + 12.9904i) q^{77} +(30.3109 - 17.5000i) q^{79} +(-15.5000 + 26.8468i) q^{81} +8.00000i q^{83} -63.0000 q^{85} +(138.564 + 80.0000i) q^{87} +(48.5000 + 84.0045i) q^{89} +(-110.851 - 16.0000i) q^{91} +(27.5000 + 47.6314i) q^{93} +(85.7365 + 49.5000i) q^{95} -88.0000 q^{97} -48.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 18 q^{5} + 32 q^{9}+O(q^{10}) $ 4 * q - 18 * q^5 + 32 * q^9	$ 4 q - 18 q^{5} + 32 q^{9} + 64 q^{13} + 14 q^{17} + 110 q^{21} - 112 q^{25} - 128 q^{29} + 30 q^{33} + 2 q^{37} - 160 q^{41} + 288 q^{45} + 188 q^{49} - 14 q^{53} + 220 q^{57} - 158 q^{61} - 288 q^{65} - 380 q^{69} - 286 q^{73} + 66 q^{77} - 62 q^{81} - 252 q^{85} + 194 q^{89} + 110 q^{93} - 352 q^{97}+O(q^{100}) $ 4 * q - 18 * q^5 + 32 * q^9 + 64 * q^13 + 14 * q^17 + 110 * q^21 - 112 * q^25 - 128 * q^29 + 30 * q^33 + 2 * q^37 - 160 * q^41 + 288 * q^45 + 188 * q^49 - 14 * q^53 + 220 * q^57 - 158 * q^61 - 288 * q^65 - 380 * q^69 - 286 * q^73 + 66 * q^77 - 62 * q^81 - 252 * q^85 + 194 * q^89 + 110 * q^93 - 352 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.33013	−	2.50000i	−1.44338	−	0.833333i	−0.445302	−	0.895380i	$-0.646904\pi$
$3$	−4.33013	−	2.50000i	−1.44338	−	0.833333i	−0.998073	+	0.0620469i	$0.980237\pi$
$4$		0			0
$5$	−4.50000	−	7.79423i	−0.900000	−	1.55885i	−0.827492	−	0.561478i	$-0.810233\pi$
$5$	−4.50000	−	7.79423i	−0.900000	−	1.55885i	−0.0725083	−	0.997368i	$-0.523100\pi$
$6$		0			0
$7$	−6.92820	−	1.00000i	−0.989743	−	0.142857i
$7$	−6.92820	−	1.00000i	−0.989743	−	0.142857i
$8$		0			0
$9$	8.00000	+	13.8564i	0.888889	+	1.53960i
$10$		0			0
$11$	−2.59808	−	1.50000i	−0.236189	−	0.136364i	0.377235	−	0.926118i	$-0.376875\pi$
$11$	−2.59808	−	1.50000i	−0.236189	−	0.136364i	−0.613424	+	0.789754i	$0.710208\pi$
$12$		0			0
$13$	16.0000			1.23077			0.615385	−	0.788227i	$-0.289001\pi$
$13$	16.0000			1.23077			0.615385	+	0.788227i	$0.289001\pi$
$14$		0			0
$15$			45.0000i			3.00000i
$16$		0			0
$17$	3.50000	−	6.06218i	0.205882	−	0.356599i	−0.744531	−	0.667588i	$-0.767327\pi$
$17$	3.50000	−	6.06218i	0.205882	−	0.356599i	0.950414	+	0.310989i	$0.100660\pi$
$18$		0			0
$19$	−9.52628	+	5.50000i	−0.501383	+	0.289474i	−0.729285	−	0.684211i	$-0.760147\pi$
$19$	−9.52628	+	5.50000i	−0.501383	+	0.289474i	0.227901	+	0.973684i	$0.426814\pi$
$20$		0			0
$21$	27.5000	+	21.6506i	1.30952	+	1.03098i
$22$		0			0
$23$	16.4545	−	9.50000i	0.715412	−	0.413043i	−0.0976495	−	0.995221i	$-0.531132\pi$
$23$	16.4545	−	9.50000i	0.715412	−	0.413043i	0.813062	+	0.582177i	$0.197799\pi$
$24$		0			0
$25$	−28.0000	+	48.4974i	−1.12000	+	1.93990i
$26$		0			0
$27$		−	35.0000i		−	1.29630i
$28$		0			0
$29$	−32.0000			−1.10345			−0.551724	−	0.834027i	$-0.686030\pi$
$29$	−32.0000			−1.10345			−0.551724	+	0.834027i	$0.686030\pi$
$30$		0			0
$31$	−9.52628	−	5.50000i	−0.307299	−	0.177419i	0.338418	−	0.940996i	$-0.390108\pi$
$31$	−9.52628	−	5.50000i	−0.307299	−	0.177419i	−0.645717	+	0.763577i	$0.723442\pi$
$32$		0			0
$33$	7.50000	+	12.9904i	0.227273	+	0.393648i
$34$		0			0
$35$	23.3827	+	58.5000i	0.668077	+	1.67143i
$36$		0			0
$37$	0.500000	+	0.866025i	0.0135135	+	0.0234061i	0.872703	−	0.488251i	$-0.162365\pi$
$37$	0.500000	+	0.866025i	0.0135135	+	0.0234061i	−0.859190	+	0.511657i	$0.829032\pi$
$38$		0			0
$39$	−69.2820	−	40.0000i	−1.77646	−	1.02564i
$40$		0			0
$41$	−40.0000			−0.975610			−0.487805	−	0.872953i	$-0.662202\pi$
$41$	−40.0000			−0.975610			−0.487805	+	0.872953i	$0.662202\pi$
$42$		0			0
$43$			40.0000i			0.930233i	0.885250	+	0.465116i	$0.153987\pi$
$43$			40.0000i			0.930233i	−0.885250	+	0.465116i	$0.846013\pi$
$44$		0			0
$45$	72.0000	−	124.708i	1.60000	−	2.77128i
$46$		0			0
$47$	73.6122	−	42.5000i	1.56622	−	0.904255i	0.569612	−	0.821914i	$-0.307093\pi$
$47$	73.6122	−	42.5000i	1.56622	−	0.904255i	0.996604	−	0.0823416i	$-0.0262399\pi$
$48$		0			0
$49$	47.0000	+	13.8564i	0.959184	+	0.282784i
$50$		0			0
$51$	−30.3109	+	17.5000i	−0.594331	+	0.343137i
$52$		0			0
$53$	−3.50000	+	6.06218i	−0.0660377	+	0.114381i	−0.897154	−	0.441718i	$-0.854369\pi$
$53$	−3.50000	+	6.06218i	−0.0660377	+	0.114381i	0.831116	+	0.556099i	$0.187702\pi$
$54$		0			0
$55$			27.0000i			0.490909i
$56$		0			0
$57$	55.0000			0.964912
$58$		0			0
$59$	−45.8993	−	26.5000i	−0.777955	−	0.449153i	0.0577500	−	0.998331i	$-0.481607\pi$
$59$	−45.8993	−	26.5000i	−0.777955	−	0.449153i	−0.835705	+	0.549179i	$0.814941\pi$
$60$		0			0
$61$	−39.5000	−	68.4160i	−0.647541	−	1.12157i	−0.983708	−	0.179772i	$-0.942464\pi$
$61$	−39.5000	−	68.4160i	−0.647541	−	1.12157i	0.336167	−	0.941802i	$-0.390869\pi$
$62$		0			0
$63$	−41.5692	−	104.000i	−0.659829	−	1.65079i
$64$		0			0
$65$	−72.0000	−	124.708i	−1.10769	−	1.91858i
$66$		0			0
$67$	9.52628	+	5.50000i	0.142183	+	0.0820896i	0.569404	−	0.822058i	$-0.307174\pi$
$67$	9.52628	+	5.50000i	0.142183	+	0.0820896i	−0.427221	+	0.904147i	$0.640507\pi$
$68$		0			0
$69$	−95.0000			−1.37681
$70$		0			0
$71$			48.0000i			0.676056i	0.941136	+	0.338028i	$0.109760\pi$
$71$			48.0000i			0.676056i	−0.941136	+	0.338028i	$0.890240\pi$
$72$		0			0
$73$	−71.5000	+	123.842i	−0.979452	+	1.69646i	−0.315068	+	0.949069i	$0.602027\pi$
$73$	−71.5000	+	123.842i	−0.979452	+	1.69646i	−0.664384	+	0.747392i	$0.731306\pi$
$74$		0			0
$75$	242.487	−	140.000i	3.23316	−	1.86667i
$76$		0			0
$77$	16.5000	+	12.9904i	0.214286	+	0.168706i
$78$		0			0
$79$	30.3109	−	17.5000i	0.383682	−	0.221519i	−0.295737	−	0.955269i	$-0.595565\pi$
$79$	30.3109	−	17.5000i	0.383682	−	0.221519i	0.679419	+	0.733750i	$0.262232\pi$
$80$		0			0
$81$	−15.5000	+	26.8468i	−0.191358	+	0.331442i
$82$		0			0
$83$			8.00000i			0.0963855i	0.998838	+	0.0481928i	$0.0153462\pi$
$83$			8.00000i			0.0963855i	−0.998838	+	0.0481928i	$0.984654\pi$
$84$		0			0
$85$	−63.0000			−0.741176
$86$		0			0
$87$	138.564	+	80.0000i	1.59269	+	0.919540i
$88$		0			0
$89$	48.5000	+	84.0045i	0.544944	+	0.943870i	0.998610	+	0.0526989i	$0.0167824\pi$
$89$	48.5000	+	84.0045i	0.544944	+	0.943870i	−0.453667	+	0.891171i	$0.649884\pi$
$90$		0			0
$91$	−110.851	−	16.0000i	−1.21815	−	0.175824i
$92$		0			0
$93$	27.5000	+	47.6314i	0.295699	+	0.512166i
$94$		0			0
$95$	85.7365	+	49.5000i	0.902490	+	0.521053i
$96$		0			0
$97$	−88.0000			−0.907216			−0.453608	−	0.891201i	$-0.649863\pi$
$97$	−88.0000			−0.907216			−0.453608	+	0.891201i	$0.649863\pi$
$98$		0			0
$99$		−	48.0000i		−	0.484848i
$100$		0			0
$101$	7.50000	−	12.9904i	0.0742574	−	0.128618i	−0.826506	−	0.562928i	$-0.809675\pi$
$101$	7.50000	−	12.9904i	0.0742574	−	0.128618i	0.900763	+	0.434311i	$0.143008\pi$
$102$		0			0
$103$	−80.5404	+	46.5000i	−0.781945	+	0.451456i	−0.837119	−	0.547020i	$-0.815762\pi$
$103$	−80.5404	+	46.5000i	−0.781945	+	0.451456i	0.0551740	+	0.998477i	$0.482429\pi$
$104$		0			0
$105$	45.0000	−	311.769i	0.428571	−	2.96923i
$106$		0			0
$107$	−9.52628	+	5.50000i	−0.0890306	+	0.0514019i	−0.543854	−	0.839180i	$-0.683036\pi$
$107$	−9.52628	+	5.50000i	−0.0890306	+	0.0514019i	0.454824	+	0.890581i	$0.349702\pi$
$108$		0			0
$109$	−56.5000	+	97.8609i	−0.518349	+	0.897806i	0.481424	+	0.876488i	$0.340120\pi$
$109$	−56.5000	+	97.8609i	−0.518349	+	0.897806i	−0.999773	+	0.0213184i	$0.993214\pi$
$110$		0			0
$111$		−	5.00000i		−	0.0450450i
$112$		0			0
$113$	56.0000			0.495575			0.247788	−	0.968814i	$-0.420296\pi$
$113$	56.0000			0.495575			0.247788	+	0.968814i	$0.420296\pi$
$114$		0			0
$115$	−148.090	−	85.5000i	−1.28774	−	0.743478i
$116$		0			0
$117$	128.000	+	221.703i	1.09402	+	1.89489i
$118$		0			0
$119$	−30.3109	+	38.5000i	−0.254713	+	0.323529i
$120$		0			0
$121$	−56.0000	−	96.9948i	−0.462810	−	0.801610i
$122$		0			0
$123$	173.205	+	100.000i	1.40817	+	0.813008i
$124$		0			0
$125$	279.000			2.23200
$126$		0			0
$127$		−	96.0000i		−	0.755906i	−0.925825	−	0.377953i	$-0.876628\pi$
$127$		−	96.0000i		−	0.755906i	0.925825	−	0.377953i	$-0.123372\pi$
$128$		0			0
$129$	100.000	−	173.205i	0.775194	−	1.34268i
$130$		0			0
$131$	−122.110	+	70.5000i	−0.932134	+	0.538168i	−0.887486	−	0.460835i	$-0.847550\pi$
$131$	−122.110	+	70.5000i	−0.932134	+	0.538168i	−0.0446483	+	0.999003i	$0.514217\pi$
$132$		0			0
$133$	71.5000	−	28.5788i	0.537594	−	0.214878i
$134$		0			0
$135$	−272.798	+	157.500i	−2.02073	+	1.16667i
$136$		0			0
$137$	−4.50000	+	7.79423i	−0.0328467	+	0.0568922i	−0.881981	−	0.471284i	$-0.843791\pi$
$137$	−4.50000	+	7.79423i	−0.0328467	+	0.0568922i	0.849135	+	0.528176i	$0.177124\pi$
$138$		0			0
$139$			136.000i			0.978417i	0.872167	+	0.489209i	$0.162714\pi$
$139$			136.000i			0.978417i	−0.872167	+	0.489209i	$0.837286\pi$
$140$		0			0
$141$	−425.000			−3.01418
$142$		0			0
$143$	−41.5692	−	24.0000i	−0.290694	−	0.167832i
$144$		0			0
$145$	144.000	+	249.415i	0.993103	+	1.72011i
$146$		0			0
$147$	−168.875	−	177.500i	−1.14881	−	1.20748i
$148$		0			0
$149$	−28.5000	−	49.3634i	−0.191275	−	0.331298i	0.754398	−	0.656417i	$-0.227929\pi$
$149$	−28.5000	−	49.3634i	−0.191275	−	0.331298i	−0.945673	+	0.325119i	$0.894596\pi$
$150$		0			0
$151$	−23.3827	−	13.5000i	−0.154852	−	0.0894040i	0.420572	−	0.907259i	$-0.361830\pi$
$151$	−23.3827	−	13.5000i	−0.154852	−	0.0894040i	−0.575424	+	0.817855i	$0.695163\pi$
$152$		0			0
$153$	112.000			0.732026
$154$		0			0
$155$			99.0000i			0.638710i
$156$		0			0
$157$	−83.5000	+	144.626i	−0.531847	+	0.921186i	0.467462	+	0.884013i	$0.345169\pi$
$157$	−83.5000	+	144.626i	−0.531847	+	0.921186i	−0.999309	+	0.0371729i	$0.988165\pi$
$158$		0			0
$159$	30.3109	−	17.5000i	0.190635	−	0.110063i
$160$		0			0
$161$	−123.500	+	49.3634i	−0.767081	+	0.306605i
$162$		0			0
$163$	16.4545	−	9.50000i	0.100948	−	0.0582822i	−0.448676	−	0.893694i	$-0.648104\pi$
$163$	16.4545	−	9.50000i	0.100948	−	0.0582822i	0.549624	+	0.835412i	$0.314771\pi$
$164$		0			0
$165$	67.5000	−	116.913i	0.409091	−	0.708566i
$166$		0			0
$167$		−	190.000i		−	1.13772i	−0.822433	−	0.568862i	$-0.807384\pi$
$167$		−	190.000i		−	1.13772i	0.822433	−	0.568862i	$-0.192616\pi$
$168$		0			0
$169$	87.0000			0.514793
$170$		0			0
$171$	−152.420	−	88.0000i	−0.891348	−	0.514620i
$172$		0			0
$173$	72.5000	+	125.574i	0.419075	+	0.725859i	0.995847	−	0.0910461i	$-0.0290210\pi$
$173$	72.5000	+	125.574i	0.419075	+	0.725859i	−0.576772	+	0.816905i	$0.695688\pi$
$174$		0			0
$175$	242.487	−	308.000i	1.38564	−	1.76000i
$176$		0			0
$177$	132.500	+	229.497i	0.748588	+	1.29659i
$178$		0			0
$179$	274.530	+	158.500i	1.53369	+	0.885475i	0.999187	+	0.0403064i	$0.0128334\pi$
$179$	274.530	+	158.500i	1.53369	+	0.885475i	0.534500	+	0.845168i	$0.320500\pi$
$180$		0			0
$181$	−186.000			−1.02762			−0.513812	−	0.857903i	$-0.671767\pi$
$181$	−186.000			−1.02762			−0.513812	+	0.857903i	$0.671767\pi$
$182$		0			0
$183$			395.000i			2.15847i
$184$		0			0
$185$	4.50000	−	7.79423i	0.0243243	−	0.0421310i
$186$		0			0
$187$	−18.1865	+	10.5000i	−0.0972542	+	0.0561497i
$188$		0			0
$189$	−35.0000	+	242.487i	−0.185185	+	1.28300i
$190$		0			0
$191$	−245.085	+	141.500i	−1.28317	+	0.740838i	−0.977426	−	0.211277i	$-0.932238\pi$
$191$	−245.085	+	141.500i	−1.28317	+	0.740838i	−0.305742	+	0.952114i	$0.598905\pi$
$192$		0			0
$193$	147.500	−	255.477i	0.764249	−	1.32372i	−0.176394	−	0.984320i	$-0.556443\pi$
$193$	147.500	−	255.477i	0.764249	−	1.32372i	0.940643	−	0.339398i	$-0.110223\pi$
$194$		0			0
$195$			720.000i			3.69231i
$196$		0			0
$197$	128.000			0.649746			0.324873	−	0.945758i	$-0.394678\pi$
$197$	128.000			0.649746			0.324873	+	0.945758i	$0.394678\pi$
$198$		0			0
$199$	−245.085	−	141.500i	−1.23158	−	0.711055i	−0.264224	−	0.964461i	$-0.585116\pi$
$199$	−245.085	−	141.500i	−1.23158	−	0.711055i	−0.967360	+	0.253406i	$0.918449\pi$
$200$		0			0
$201$	−27.5000	−	47.6314i	−0.136816	−	0.236972i
$202$		0			0
$203$	221.703	+	32.0000i	1.09213	+	0.157635i
$204$		0			0
$205$	180.000	+	311.769i	0.878049	+	1.52083i
$206$		0			0
$207$	263.272	+	152.000i	1.27184	+	0.734300i
$208$		0			0
$209$	33.0000			0.157895
$210$		0			0
$211$			40.0000i			0.189573i	0.995498	+	0.0947867i	$0.0302169\pi$
$211$			40.0000i			0.189573i	−0.995498	+	0.0947867i	$0.969783\pi$
$212$		0			0
$213$	120.000	−	207.846i	0.563380	−	0.975803i
$214$		0			0
$215$	311.769	−	180.000i	1.45009	−	0.837209i
$216$		0			0
$217$	60.5000	+	47.6314i	0.278802	+	0.219500i
$218$		0			0
$219$	619.208	−	357.500i	2.82743	−	1.63242i
$220$		0			0
$221$	56.0000	−	96.9948i	0.253394	−	0.438891i
$222$		0			0
$223$		−	176.000i		−	0.789238i	−0.918845	−	0.394619i	$-0.870877\pi$
$223$		−	176.000i		−	0.789238i	0.918845	−	0.394619i	$-0.129123\pi$
$224$		0			0
$225$	−896.000			−3.98222
$226$		0			0
$227$	−335.152	−	193.500i	−1.47644	−	0.852423i	−0.476793	−	0.879015i	$-0.658201\pi$
$227$	−335.152	−	193.500i	−1.47644	−	0.852423i	−0.999646	+	0.0265925i	$0.991534\pi$
$228$		0			0
$229$	91.5000	+	158.483i	0.399563	+	0.692064i	0.993672	−	0.112321i	$-0.0358284\pi$
$229$	91.5000	+	158.483i	0.399563	+	0.692064i	−0.594109	+	0.804385i	$0.702495\pi$
$230$		0			0
$231$	−38.9711	−	97.5000i	−0.168706	−	0.422078i
$232$		0			0
$233$	−180.500	−	312.635i	−0.774678	−	1.34178i	−0.934975	−	0.354713i	$-0.884579\pi$
$233$	−180.500	−	312.635i	−0.774678	−	1.34178i	0.160297	−	0.987069i	$-0.448755\pi$
$234$		0			0
$235$	−662.509	−	382.500i	−2.81919	−	1.62766i
$236$		0			0
$237$	−175.000			−0.738397
$238$		0			0
$239$		−	50.0000i		−	0.209205i	−0.994514	−	0.104603i	$-0.966643\pi$
$239$		−	50.0000i		−	0.209205i	0.994514	−	0.104603i	$-0.0333570\pi$
$240$		0			0
$241$	64.5000	−	111.717i	0.267635	−	0.463557i	−0.700616	−	0.713539i	$-0.747091\pi$
$241$	64.5000	−	111.717i	0.267635	−	0.463557i	0.968251	+	0.249982i	$0.0804246\pi$
$242$		0			0
$243$	−138.564	+	80.0000i	−0.570222	+	0.329218i
$244$		0			0
$245$	−103.500	−	428.683i	−0.422449	−	1.74972i
$246$		0			0
$247$	−152.420	+	88.0000i	−0.617087	+	0.356275i
$248$		0			0
$249$	20.0000	−	34.6410i	0.0803213	−	0.139121i
$250$		0			0
$251$		−	394.000i		−	1.56972i	−0.619672	−	0.784861i	$-0.712735\pi$
$251$		−	394.000i		−	1.56972i	0.619672	−	0.784861i	$-0.287265\pi$
$252$		0			0
$253$	−57.0000			−0.225296
$254$		0			0
$255$	272.798	+	157.500i	1.06980	+	0.617647i
$256$		0			0
$257$	−44.5000	−	77.0763i	−0.173152	−	0.299908i	0.766368	−	0.642401i	$-0.222062\pi$
$257$	−44.5000	−	77.0763i	−0.173152	−	0.299908i	−0.939520	+	0.342494i	$0.888728\pi$
$258$		0			0
$259$	−2.59808	−	6.50000i	−0.0100312	−	0.0250965i
$260$		0			0
$261$	−256.000	−	443.405i	−0.980843	−	1.69887i
$262$		0			0
$263$	−38.9711	−	22.5000i	−0.148179	−	0.0855513i	0.424077	−	0.905626i	$-0.360598\pi$
$263$	−38.9711	−	22.5000i	−0.148179	−	0.0855513i	−0.572257	+	0.820075i	$0.693932\pi$
$264$		0			0
$265$	63.0000			0.237736
$266$		0			0
$267$		−	485.000i		−	1.81648i
$268$		0			0
$269$	228.500	−	395.774i	0.849442	−	1.47128i	−0.0322643	−	0.999479i	$-0.510272\pi$
$269$	228.500	−	395.774i	0.849442	−	1.47128i	0.881707	−	0.471798i	$-0.156395\pi$
$270$		0			0
$271$	−343.812	+	198.500i	−1.26868	+	0.732472i	−0.974738	−	0.223351i	$-0.928300\pi$
$271$	−343.812	+	198.500i	−1.26868	+	0.732472i	−0.293941	+	0.955823i	$0.594967\pi$
$272$		0			0
$273$	440.000	+	346.410i	1.61172	+	1.26890i
$274$		0			0
$275$	145.492	−	84.0000i	0.529063	−	0.305455i
$276$		0			0
$277$	−115.500	+	200.052i	−0.416968	+	0.722209i	−0.995633	−	0.0933562i	$-0.970240\pi$
$277$	−115.500	+	200.052i	−0.416968	+	0.722209i	0.578665	+	0.815565i	$0.303574\pi$
$278$		0			0
$279$		−	176.000i		−	0.630824i
$280$		0			0
$281$	104.000			0.370107			0.185053	−	0.982728i	$-0.440754\pi$
$281$	104.000			0.370107			0.185053	+	0.982728i	$0.440754\pi$
$282$		0			0
$283$	343.812	+	198.500i	1.21488	+	0.701413i	0.963819	−	0.266557i	$-0.0858860\pi$
$283$	343.812	+	198.500i	1.21488	+	0.701413i	0.251065	+	0.967970i	$0.419219\pi$
$284$		0			0
$285$	−247.500	−	428.683i	−0.868421	−	1.50415i
$286$		0			0
$287$	277.128	+	40.0000i	0.965603	+	0.139373i
$288$		0			0
$289$	120.000	+	207.846i	0.415225	+	0.719191i
$290$		0			0
$291$	381.051	+	220.000i	1.30945	+	0.756014i
$292$		0			0
$293$	154.000			0.525597			0.262799	−	0.964851i	$-0.415355\pi$
$293$	154.000			0.525597			0.262799	+	0.964851i	$0.415355\pi$
$294$		0			0
$295$			477.000i			1.61695i
$296$		0			0
$297$	−52.5000	+	90.9327i	−0.176768	+	0.306171i
$298$		0			0
$299$	263.272	−	152.000i	0.880507	−	0.508361i
$300$		0			0
$301$	40.0000	−	277.128i	0.132890	−	0.920691i
$302$		0			0
$303$	−64.9519	+	37.5000i	−0.214363	+	0.123762i
$304$		0			0
$305$	−355.500	+	615.744i	−1.16557	+	2.01883i
$306$		0			0
$307$		−	376.000i		−	1.22476i	−0.790565	−	0.612378i	$-0.790213\pi$
$307$		−	376.000i		−	1.22476i	0.790565	−	0.612378i	$-0.209787\pi$
$308$		0			0
$309$	465.000			1.50485
$310$		0			0
$311$	279.726	+	161.500i	0.899441	+	0.519293i	0.877019	−	0.480456i	$-0.159529\pi$
$311$	279.726	+	161.500i	0.899441	+	0.519293i	0.0224223	+	0.999749i	$0.492862\pi$
$312$		0			0
$313$	−95.5000	−	165.411i	−0.305112	−	0.528469i	0.672174	−	0.740393i	$-0.265361\pi$
$313$	−95.5000	−	165.411i	−0.305112	−	0.528469i	−0.977286	+	0.211924i	$0.932027\pi$
$314$		0			0
$315$	−623.538	+	792.000i	−1.97949	+	2.51429i
$316$		0			0
$317$	−167.500	−	290.119i	−0.528391	−	0.915200i	−0.999452	−	0.0330997i	$-0.989462\pi$
$317$	−167.500	−	290.119i	−0.528391	−	0.915200i	0.471061	−	0.882101i	$-0.343871\pi$
$318$		0			0
$319$	83.1384	+	48.0000i	0.260622	+	0.150470i
$320$		0			0
$321$	55.0000			0.171340
$322$		0			0
$323$			77.0000i			0.238390i
$324$		0			0
$325$	−448.000	+	775.959i	−1.37846	+	2.38757i
$326$		0			0
$327$	489.304	−	282.500i	1.49634	−	0.863914i
$328$		0			0
$329$	−552.500	+	220.836i	−1.67933	+	0.671235i
$330$		0			0
$331$	30.3109	−	17.5000i	0.0915737	−	0.0528701i	−0.453514	−	0.891249i	$-0.649830\pi$
$331$	30.3109	−	17.5000i	0.0915737	−	0.0528701i	0.545088	+	0.838379i	$0.316496\pi$
$332$		0			0
$333$	−8.00000	+	13.8564i	−0.0240240	+	0.0416108i
$334$		0			0
$335$		−	99.0000i		−	0.295522i
$336$		0			0
$337$	184.000			0.545994			0.272997	−	0.962015i	$-0.411985\pi$
$337$	184.000			0.545994			0.272997	+	0.962015i	$0.411985\pi$
$338$		0			0
$339$	−242.487	−	140.000i	−0.715301	−	0.412979i
$340$		0			0
$341$	16.5000	+	28.5788i	0.0483871	+	0.0838089i
$342$		0			0
$343$	−311.769	−	143.000i	−0.908948	−	0.416910i
$344$		0			0
$345$	427.500	+	740.452i	1.23913	+	2.14624i
$346$		0			0
$347$	161.947	+	93.5000i	0.466705	+	0.269452i	0.714860	−	0.699268i	$-0.246491\pi$
$347$	161.947	+	93.5000i	0.466705	+	0.269452i	−0.248154	+	0.968721i	$0.579824\pi$
$348$		0			0
$349$	−208.000			−0.595989			−0.297994	−	0.954568i	$-0.596318\pi$
$349$	−208.000			−0.595989			−0.297994	+	0.954568i	$0.596318\pi$
$350$		0			0
$351$		−	560.000i		−	1.59544i
$352$		0			0
$353$	115.500	−	200.052i	0.327195	−	0.566719i	−0.654759	−	0.755838i	$-0.727230\pi$
$353$	115.500	−	200.052i	0.327195	−	0.566719i	0.981954	+	0.189119i	$0.0605631\pi$
$354$		0			0
$355$	374.123	−	216.000i	1.05387	−	0.608451i
$356$		0			0
$357$	227.500	−	90.9327i	0.637255	−	0.254713i
$358$		0			0
$359$	32.0429	−	18.5000i	0.0892561	−	0.0515320i	−0.454708	−	0.890641i	$-0.650256\pi$
$359$	32.0429	−	18.5000i	0.0892561	−	0.0515320i	0.543964	+	0.839109i	$0.316923\pi$
$360$		0			0
$361$	−120.000	+	207.846i	−0.332410	+	0.575751i
$362$		0			0
$363$			560.000i			1.54270i
$364$		0			0
$365$	1287.00			3.52603
$366$		0			0
$367$	418.290	+	241.500i	1.13976	+	0.658038i	0.946370	−	0.323085i	$-0.104720\pi$
$367$	418.290	+	241.500i	1.13976	+	0.658038i	0.193385	+	0.981123i	$0.438053\pi$
$368$		0			0
$369$	−320.000	−	554.256i	−0.867209	−	1.50205i
$370$		0			0
$371$	30.3109	−	38.5000i	0.0817005	−	0.103774i
$372$		0			0
$373$	−215.500	−	373.257i	−0.577748	−	1.00069i	−0.995737	−	0.0922368i	$-0.970598\pi$
$373$	−215.500	−	373.257i	−0.577748	−	1.00069i	0.417989	−	0.908452i	$-0.362735\pi$
$374$		0			0
$375$	−1208.11	−	697.500i	−3.22161	−	1.86000i
$376$		0			0
$377$	−512.000			−1.35809
$378$		0			0
$379$			714.000i			1.88391i	0.335746	+	0.941953i	$0.391012\pi$
$379$			714.000i			1.88391i	−0.335746	+	0.941953i	$0.608988\pi$
$380$		0			0
$381$	−240.000	+	415.692i	−0.629921	+	1.09106i
$382$		0			0
$383$	−563.783	+	325.500i	−1.47202	+	0.849869i	−0.999505	−	0.0314548i	$-0.989986\pi$
$383$	−563.783	+	325.500i	−1.47202	+	0.849869i	−0.472512	+	0.881324i	$0.656653\pi$
$384$		0			0
$385$	27.0000	−	187.061i	0.0701299	−	0.485874i
$386$		0			0
$387$	−554.256	+	320.000i	−1.43219	+	0.826873i
$388$		0			0
$389$	−232.500	+	402.702i	−0.597686	+	1.03522i	0.395475	+	0.918477i	$0.370580\pi$
$389$	−232.500	+	402.702i	−0.597686	+	1.03522i	−0.993162	+	0.116747i	$0.962753\pi$
$390$		0			0
$391$		−	133.000i		−	0.340153i
$392$		0			0
$393$	705.000			1.79389
$394$		0			0
$395$	−272.798	−	157.500i	−0.690628	−	0.398734i
$396$		0			0
$397$	−92.5000	−	160.215i	−0.232997	−	0.403563i	0.725691	−	0.688020i	$-0.241520\pi$
$397$	−92.5000	−	160.215i	−0.232997	−	0.403563i	−0.958689	+	0.284457i	$0.908187\pi$
$398$		0			0
$399$	−381.051	−	55.0000i	−0.955015	−	0.137845i
$400$		0			0
$401$	−52.5000	−	90.9327i	−0.130923	−	0.226765i	0.793110	−	0.609079i	$-0.208461\pi$
$401$	−52.5000	−	90.9327i	−0.130923	−	0.226765i	−0.924033	+	0.382314i	$0.875127\pi$
$402$		0			0
$403$	−152.420	−	88.0000i	−0.378215	−	0.218362i
$404$		0			0
$405$	279.000			0.688889
$406$		0			0
$407$		−	3.00000i		−	0.00737101i
$408$		0			0
$409$	3.50000	−	6.06218i	0.00855746	−	0.0148220i	−0.861715	−	0.507393i	$-0.830609\pi$
$409$	3.50000	−	6.06218i	0.00855746	−	0.0148220i	0.870272	+	0.492571i	$0.163943\pi$
$410$		0			0
$411$	38.9711	−	22.5000i	0.0948203	−	0.0547445i
$412$		0			0
$413$	291.500	+	229.497i	0.705811	+	0.555682i
$414$		0			0
$415$	62.3538	−	36.0000i	0.150250	−	0.0867470i
$416$		0			0
$417$	340.000	−	588.897i	0.815348	−	1.41222i
$418$		0			0
$419$			392.000i			0.935561i	0.883845	+	0.467780i	$0.154946\pi$
$419$			392.000i			0.935561i	−0.883845	+	0.467780i	$0.845054\pi$
$420$		0			0
$421$	64.0000			0.152019			0.0760095	−	0.997107i	$-0.475782\pi$
$421$	64.0000			0.152019			0.0760095	+	0.997107i	$0.475782\pi$
$422$		0			0
$423$	1177.79	+	680.000i	2.78438	+	1.60757i
$424$		0			0
$425$	196.000	+	339.482i	0.461176	+	0.798781i
$426$		0			0
$427$	205.248	+	513.500i	0.480675	+	1.20258i
$428$		0			0
$429$	120.000	+	207.846i	0.279720	+	0.484490i
$430$		0			0
$431$	−633.065	−	365.500i	−1.46883	−	0.848028i	−0.469438	−	0.882966i	$-0.655543\pi$
$431$	−633.065	−	365.500i	−1.46883	−	0.848028i	−0.999389	+	0.0349377i	$0.988877\pi$
$432$		0			0
$433$	376.000			0.868360			0.434180	−	0.900826i	$-0.357038\pi$
$433$	376.000			0.868360			0.434180	+	0.900826i	$0.357038\pi$
$434$		0			0
$435$		−	1440.00i		−	3.31034i
$436$		0			0
$437$	−104.500	+	180.999i	−0.239130	+	0.414186i
$438$		0			0
$439$	−549.926	+	317.500i	−1.25268	+	0.723235i	−0.971641	−	0.236462i	$-0.924012\pi$
$439$	−549.926	+	317.500i	−1.25268	+	0.723235i	−0.281038	+	0.959697i	$0.590679\pi$
$440$		0			0
$441$	184.000	+	762.102i	0.417234	+	1.72812i
$442$		0			0
$443$	−425.218	+	245.500i	−0.959861	+	0.554176i	−0.896130	−	0.443791i	$-0.853633\pi$
$443$	−425.218	+	245.500i	−0.959861	+	0.554176i	−0.0637308	+	0.997967i	$0.520300\pi$
$444$		0			0
$445$	436.500	−	756.040i	0.980899	−	1.69897i
$446$		0			0
$447$			285.000i			0.637584i
$448$		0			0
$449$	−344.000			−0.766147			−0.383073	−	0.923718i	$-0.625134\pi$
$449$	−344.000			−0.766147			−0.383073	+	0.923718i	$0.625134\pi$
$450$		0			0
$451$	103.923	+	60.0000i	0.230428	+	0.133038i
$452$		0			0
$453$	67.5000	+	116.913i	0.149007	+	0.258087i
$454$		0			0
$455$	374.123	+	936.000i	0.822248	+	2.05714i
$456$		0			0
$457$	−263.500	−	456.395i	−0.576586	−	0.998677i	−0.995867	−	0.0908204i	$-0.971051\pi$
$457$	−263.500	−	456.395i	−0.576586	−	0.998677i	0.419281	−	0.907857i	$-0.362282\pi$
$458$		0			0
$459$	−212.176	−	122.500i	−0.462258	−	0.266885i
$460$		0			0
$461$	−704.000			−1.52711			−0.763557	−	0.645740i	$-0.776549\pi$
$461$	−704.000			−1.52711			−0.763557	+	0.645740i	$0.776549\pi$
$462$		0			0
$463$			160.000i			0.345572i	0.984959	+	0.172786i	$0.0552770\pi$
$463$			160.000i			0.345572i	−0.984959	+	0.172786i	$0.944723\pi$
$464$		0			0
$465$	247.500	−	428.683i	0.532258	−	0.921898i
$466$		0			0
$467$	−468.520	+	270.500i	−1.00325	+	0.579229i	−0.909210	−	0.416339i	$-0.863313\pi$
$467$	−468.520	+	270.500i	−1.00325	+	0.579229i	−0.0940447	+	0.995568i	$0.529980\pi$
$468$		0			0
$469$	−60.5000	−	47.6314i	−0.128998	−	0.101559i
$470$		0			0
$471$	723.131	−	417.500i	1.53531	−	0.886412i
$472$		0			0
$473$	60.0000	−	103.923i	0.126850	−	0.219710i
$474$		0			0
$475$		−	616.000i		−	1.29684i
$476$		0			0
$477$	−112.000			−0.234801
$478$		0			0
$479$	−413.094	−	238.500i	−0.862409	−	0.497912i	0.00240897	−	0.999997i	$-0.499233\pi$
$479$	−413.094	−	238.500i	−0.862409	−	0.497912i	−0.864818	+	0.502085i	$0.832567\pi$
$480$		0			0
$481$	8.00000	+	13.8564i	0.0166320	+	0.0288075i
$482$		0			0
$483$	658.179	+	95.0000i	1.36269	+	0.196687i
$484$		0			0
$485$	396.000	+	685.892i	0.816495	+	1.41421i
$486$		0			0
$487$	265.870	+	153.500i	0.545934	+	0.315195i	0.747480	−	0.664284i	$-0.231263\pi$
$487$	265.870	+	153.500i	0.545934	+	0.315195i	−0.201547	+	0.979479i	$0.564597\pi$
$488$		0			0
$489$	−95.0000			−0.194274
$490$		0			0
$491$		−	22.0000i		−	0.0448065i	−0.999749	−	0.0224033i	$-0.992868\pi$
$491$		−	22.0000i		−	0.0448065i	0.999749	−	0.0224033i	$-0.00713178\pi$
$492$		0			0
$493$	−112.000	+	193.990i	−0.227181	+	0.393488i
$494$		0			0
$495$	−374.123	+	216.000i	−0.755804	+	0.436364i
$496$		0			0
$497$	48.0000	−	332.554i	0.0965795	−	0.669122i
$498$		0			0
$499$	792.413	−	457.500i	1.58800	−	0.916834i	0.594367	−	0.804194i	$-0.297403\pi$
$499$	792.413	−	457.500i	1.58800	−	0.916834i	0.993636	−	0.112639i	$-0.0359305\pi$
$500$		0			0
$501$	−475.000	+	822.724i	−0.948104	+	1.64216i
$502$		0			0
$503$			192.000i			0.381710i	0.981618	+	0.190855i	$0.0611260\pi$
$503$			192.000i			0.381710i	−0.981618	+	0.190855i	$0.938874\pi$
$504$		0			0
$505$	−135.000			−0.267327
$506$		0			0
$507$	−376.721	−	217.500i	−0.743040	−	0.428994i
$508$		0			0
$509$	35.5000	+	61.4878i	0.0697446	+	0.120801i	0.898789	−	0.438382i	$-0.144448\pi$
$509$	35.5000	+	61.4878i	0.0697446	+	0.120801i	−0.829044	+	0.559183i	$0.811115\pi$
$510$		0			0
$511$	619.208	−	786.500i	1.21176	−	1.53914i
$512$		0			0
$513$	192.500	+	333.420i	0.375244	+	0.649941i
$514$		0			0
$515$	724.863	+	418.500i	1.40750	+	0.812621i
$516$		0			0
$517$	−255.000			−0.493230
$518$		0			0
$519$		−	725.000i		−	1.39692i
$520$		0			0
$521$	−351.500	+	608.816i	−0.674664	+	1.16855i	0.301903	+	0.953339i	$0.402378\pi$
$521$	−351.500	+	608.816i	−0.674664	+	1.16855i	−0.976567	+	0.215214i	$0.930955\pi$
$522$		0			0
$523$	281.458	−	162.500i	0.538161	−	0.310707i	−0.206172	−	0.978516i	$-0.566101\pi$
$523$	281.458	−	162.500i	0.538161	−	0.310707i	0.744333	+	0.667808i	$0.232767\pi$
$524$		0			0
$525$	−1820.00	+	727.461i	−3.46667	+	1.38564i
$526$		0			0
$527$	−66.6840	+	38.5000i	−0.126535	+	0.0730550i
$528$		0			0
$529$	−84.0000	+	145.492i	−0.158790	+	0.275033i
$530$		0			0
$531$		−	848.000i		−	1.59699i
$532$		0			0
$533$	−640.000			−1.20075
$534$		0			0
$535$	85.7365	+	49.5000i	0.160255	+	0.0925234i
$536$		0			0
$537$	−792.500	−	1372.65i	−1.47579	−	2.55615i
$538$		0			0
$539$	−101.325	−	106.500i	−0.187987	−	0.197588i
$540$		0			0
$541$	−132.500	−	229.497i	−0.244917	−	0.424208i	0.717191	−	0.696876i	$-0.245427\pi$
$541$	−132.500	−	229.497i	−0.244917	−	0.424208i	−0.962108	+	0.272668i	$0.912094\pi$
$542$		0			0
$543$	805.404	+	465.000i	1.48325	+	0.856354i
$544$		0			0
$545$	1017.00			1.86606
$546$		0			0
$547$			134.000i			0.244973i	0.992470	+	0.122486i	$0.0390868\pi$
$547$			134.000i			0.244973i	−0.992470	+	0.122486i	$0.960913\pi$
$548$		0			0
$549$	632.000	−	1094.66i	1.15118	−	1.99391i
$550$		0			0
$551$	304.841	−	176.000i	0.553250	−	0.319419i
$552$		0			0
$553$	−227.500	+	90.9327i	−0.411392	+	0.164435i
$554$		0			0
$555$	−38.9711	+	22.5000i	−0.0702183	+	0.0405405i
$556$		0			0
$557$	287.500	−	497.965i	0.516158	−	0.894012i	−0.483666	−	0.875253i	$-0.660695\pi$
$557$	287.500	−	497.965i	0.516158	−	0.894012i	0.999824	−	0.0187592i	$-0.00597160\pi$
$558$		0			0
$559$			640.000i			1.14490i
$560$		0			0
$561$	105.000			0.187166
$562$		0			0
$563$	−156.751	−	90.5000i	−0.278420	−	0.160746i	0.354288	−	0.935136i	$-0.384723\pi$
$563$	−156.751	−	90.5000i	−0.278420	−	0.160746i	−0.632708	+	0.774390i	$0.718057\pi$
$564$		0			0
$565$	−252.000	−	436.477i	−0.446018	−	0.772525i
$566$		0			0
$567$	134.234	−	170.500i	0.236744	−	0.300705i
$568$		0			0
$569$	−159.500	−	276.262i	−0.280316	−	0.485522i	0.691146	−	0.722715i	$-0.257106\pi$
$569$	−159.500	−	276.262i	−0.280316	−	0.485522i	−0.971463	+	0.237193i	$0.923773\pi$
$570$		0			0
$571$	−141.162	−	81.5000i	−0.247219	−	0.142732i	0.371271	−	0.928525i	$-0.378922\pi$
$571$	−141.162	−	81.5000i	−0.247219	−	0.142732i	−0.618490	+	0.785792i	$0.712255\pi$
$572$		0			0
$573$	1415.00			2.46946
$574$		0			0
$575$			1064.00i			1.85043i
$576$		0			0
$577$	−359.500	+	622.672i	−0.623050	+	1.07915i	0.365864	+	0.930668i	$0.380773\pi$
$577$	−359.500	+	622.672i	−0.623050	+	1.07915i	−0.988914	+	0.148486i	$0.952560\pi$
$578$		0			0
$579$	−1277.39	+	737.500i	−2.20620	+	1.27375i
$580$		0			0
$581$	8.00000	−	55.4256i	0.0137694	−	0.0953969i
$582$		0			0
$583$	18.1865	−	10.5000i	0.0311947	−	0.0180103i
$584$		0			0
$585$	1152.00	−	1995.32i	1.96923	−	3.41081i
$586$		0			0
$587$		−	296.000i		−	0.504259i	−0.967694	−	0.252129i	$-0.918869\pi$
$587$		−	296.000i		−	0.504259i	0.967694	−	0.252129i	$-0.0811309\pi$
$588$		0			0
$589$	121.000			0.205433
$590$		0			0
$591$	−554.256	−	320.000i	−0.937828	−	0.541455i
$592$		0			0
$593$	−180.500	−	312.635i	−0.304384	−	0.527209i	0.672740	−	0.739879i	$-0.265117\pi$
$593$	−180.500	−	312.635i	−0.304384	−	0.527209i	−0.977124	+	0.212670i	$0.931784\pi$
$594$		0			0
$595$	436.477	+	63.0000i	0.733574	+	0.105882i
$596$		0			0
$597$	707.500	+	1225.43i	1.18509	+	2.05264i
$598$		0			0
$599$	−108.253	−	62.5000i	−0.180723	−	0.104341i	0.406909	−	0.913469i	$-0.366607\pi$
$599$	−108.253	−	62.5000i	−0.180723	−	0.104341i	−0.587632	+	0.809128i	$0.699940\pi$
$600$		0			0
$601$	1000.00			1.66389			0.831947	−	0.554855i	$-0.187226\pi$
$601$	1000.00			1.66389			0.831947	+	0.554855i	$0.187226\pi$
$602$		0			0
$603$			176.000i			0.291874i
$604$		0			0
$605$	−504.000	+	872.954i	−0.833058	+	1.44290i
$606$		0			0
$607$	−355.936	+	205.500i	−0.586386	+	0.338550i	−0.763667	−	0.645610i	$-0.776603\pi$
$607$	−355.936	+	205.500i	−0.586386	+	0.338550i	0.177281	+	0.984160i	$0.443270\pi$
$608$		0			0
$609$	−880.000	−	692.820i	−1.44499	−	1.13764i
$610$		0			0
$611$	1177.79	−	680.000i	1.92765	−	1.11293i
$612$		0			0
$613$	519.500	−	899.800i	0.847471	−	1.46786i	−0.0359860	−	0.999352i	$-0.511457\pi$
$613$	519.500	−	899.800i	0.847471	−	1.46786i	0.883457	−	0.468511i	$-0.155209\pi$
$614$		0			0
$615$		−	1800.00i		−	2.92683i
$616$		0			0
$617$	−248.000			−0.401945			−0.200972	−	0.979597i	$-0.564410\pi$
$617$	−248.000			−0.401945			−0.200972	+	0.979597i	$0.564410\pi$
$618$		0			0
$619$	522.213	+	301.500i	0.843640	+	0.487076i	0.858500	−	0.512814i	$-0.171397\pi$
$619$	522.213	+	301.500i	0.843640	+	0.487076i	−0.0148597	+	0.999890i	$0.504730\pi$
$620$		0			0
$621$	−332.500	−	575.907i	−0.535427	−	0.927386i
$622$		0			0
$623$	−252.013	−	630.500i	−0.404516	−	1.01204i
$624$		0			0
$625$	−555.500	−	962.154i	−0.888800	−	1.53945i
$626$		0			0
$627$	−142.894	−	82.5000i	−0.227901	−	0.131579i
$628$		0			0
$629$	7.00000			0.0111288
$630$		0			0
$631$		−	816.000i		−	1.29319i	−0.762835	−	0.646593i	$-0.776193\pi$
$631$		−	816.000i		−	1.29319i	0.762835	−	0.646593i	$-0.223807\pi$
$632$		0			0
$633$	100.000	−	173.205i	0.157978	−	0.273626i
$634$		0			0
$635$	−748.246	+	432.000i	−1.17834	+	0.680315i
$636$		0			0
$637$	752.000	+	221.703i	1.18053	+	0.348042i
$638$		0			0
$639$	−665.108	+	384.000i	−1.04086	+	0.600939i
$640$		0			0
$641$	−319.500	+	553.390i	−0.498440	+	0.863323i	−0.999998	−	0.00180047i	$-0.999427\pi$
$641$	−319.500	+	553.390i	−0.498440	+	0.863323i	0.501558	+	0.865124i	$0.332760\pi$
$642$		0			0
$643$			664.000i			1.03266i	0.856390	+	0.516330i	$0.172702\pi$
$643$			664.000i			1.03266i	−0.856390	+	0.516330i	$0.827298\pi$
$644$		0			0
$645$	−1800.00			−2.79070
$646$		0			0
$647$	−1092.06	−	630.500i	−1.68788	−	0.974498i	−0.956139	−	0.292915i	$-0.905375\pi$
$647$	−1092.06	−	630.500i	−1.68788	−	0.974498i	−0.731741	−	0.681583i	$-0.761292\pi$
$648$		0			0
$649$	79.5000	+	137.698i	0.122496	+	0.212170i
$650$		0			0
$651$	−142.894	−	357.500i	−0.219500	−	0.549155i
$652$		0			0
$653$	296.500	+	513.553i	0.454058	+	0.786452i	0.998634	−	0.0522601i	$-0.0166425\pi$
$653$	296.500	+	513.553i	0.454058	+	0.786452i	−0.544575	+	0.838712i	$0.683309\pi$
$654$		0			0
$655$	1098.99	+	634.500i	1.67784	+	0.968702i
$656$		0			0
$657$	−2288.00			−3.48250
$658$		0			0
$659$		−	1192.00i		−	1.80880i	−0.426684	−	0.904401i	$-0.640318\pi$
$659$		−	1192.00i		−	1.80880i	0.426684	−	0.904401i	$-0.359682\pi$
$660$		0			0
$661$	236.500	−	409.630i	0.357791	−	0.619713i	−0.629800	−	0.776757i	$-0.716863\pi$
$661$	236.500	−	409.630i	0.357791	−	0.619713i	0.987592	+	0.157045i	$0.0501966\pi$
$662$		0			0
$663$	−484.974	+	280.000i	−0.731485	+	0.422323i
$664$		0			0
$665$	−544.500	−	428.683i	−0.818797	−	0.644635i
$666$		0			0
$667$	−526.543	+	304.000i	−0.789420	+	0.455772i
$668$		0			0
$669$	−440.000	+	762.102i	−0.657698	+	1.13917i
$670$		0			0
$671$			237.000i			0.353204i
$672$		0			0
$673$	824.000			1.22437			0.612184	−	0.790715i	$-0.290291\pi$
$673$	824.000			1.22437			0.612184	+	0.790715i	$0.290291\pi$
$674$		0			0
$675$	1697.41	+	980.000i	2.51468	+	1.45185i
$676$		0			0
$677$	131.500	+	227.765i	0.194239	+	0.336432i	0.946651	−	0.322261i	$-0.104443\pi$
$677$	131.500	+	227.765i	0.194239	+	0.336432i	−0.752412	+	0.658693i	$0.771110\pi$
$678$		0			0
$679$	609.682	+	88.0000i	0.897911	+	0.129602i
$680$		0			0
$681$	967.500	+	1675.76i	1.42070	+	2.46073i
$682$		0			0
$683$	−556.854	−	321.500i	−0.815306	−	0.470717i	0.0334888	−	0.999439i	$-0.489338\pi$
$683$	−556.854	−	321.500i	−0.815306	−	0.470717i	−0.848795	+	0.528722i	$0.822672\pi$
$684$		0			0
$685$	81.0000			0.118248
$686$		0			0
$687$		−	915.000i		−	1.33188i
$688$		0			0
$689$	−56.0000	+	96.9948i	−0.0812772	+	0.140776i
$690$		0			0
$691$	−108.253	+	62.5000i	−0.156662	+	0.0904486i	−0.576281	−	0.817251i	$-0.695497\pi$
$691$	−108.253	+	62.5000i	−0.156662	+	0.0904486i	0.419620	+	0.907700i	$0.362163\pi$
$692$		0			0
$693$	−48.0000	+	332.554i	−0.0692641	+	0.479876i
$694$		0			0
$695$	1060.02	−	612.000i	1.52520	−	0.880576i
$696$		0			0
$697$	−140.000	+	242.487i	−0.200861	+	0.347901i
$698$		0			0
$699$			1805.00i			2.58226i
$700$		0			0
$701$	−54.0000			−0.0770328			−0.0385164	−	0.999258i	$-0.512263\pi$
$701$	−54.0000			−0.0770328			−0.0385164	+	0.999258i	$0.512263\pi$
$702$		0			0
$703$	−9.52628	−	5.50000i	−0.0135509	−	0.00782361i
$704$		0			0
$705$	1912.50	+	3312.55i	2.71277	+	4.69865i
$706$		0			0
$707$	−64.9519	+	82.5000i	−0.0918697	+	0.116690i
$708$		0			0
$709$	−575.500	−	996.795i	−0.811707	−	1.40592i	−0.911669	−	0.410926i	$-0.865205\pi$
$709$	−575.500	−	996.795i	−0.811707	−	1.40592i	0.0999621	−	0.994991i	$-0.468128\pi$
$710$		0			0
$711$	484.974	+	280.000i	0.682102	+	0.393812i
$712$		0			0
$713$	−209.000			−0.293128
$714$		0			0
$715$			432.000i			0.604196i
$716$		0			0
$717$	−125.000	+	216.506i	−0.174338	+	0.301961i
$718$		0			0
$719$	349.008	−	201.500i	0.485408	−	0.280250i	−0.237260	−	0.971446i	$-0.576249\pi$
$719$	349.008	−	201.500i	0.485408	−	0.280250i	0.722667	+	0.691196i	$0.242916\pi$
$720$		0			0
$721$	604.500	−	241.621i	0.838419	−	0.335119i
$722$		0			0
$723$	−558.586	+	322.500i	−0.772595	+	0.446058i
$724$		0			0
$725$	896.000	−	1551.92i	1.23586	−	2.14058i
$726$		0			0
$727$			496.000i			0.682256i	0.940017	+	0.341128i	$0.110809\pi$
$727$			496.000i			0.682256i	−0.940017	+	0.341128i	$0.889191\pi$
$728$		0			0
$729$	1079.00			1.48011
$730$		0			0
$731$	242.487	+	140.000i	0.331720	+	0.191518i
$732$		0			0
$733$	80.5000	+	139.430i	0.109823	+	0.190218i	0.915698	−	0.401866i	$-0.131638\pi$
$733$	80.5000	+	139.430i	0.109823	+	0.190218i	−0.805876	+	0.592085i	$0.798305\pi$
$734$		0			0
$735$	−623.538	+	2115.00i	−0.848351	+	2.87755i
$736$		0			0
$737$	−16.5000	−	28.5788i	−0.0223881	−	0.0387773i
$738$		0			0
$739$	−473.716	−	273.500i	−0.641023	−	0.370095i	0.143986	−	0.989580i	$-0.454008\pi$
$739$	−473.716	−	273.500i	−0.641023	−	0.370095i	−0.785008	+	0.619485i	$0.787341\pi$
$740$		0			0
$741$	880.000			1.18758
$742$		0			0
$743$		−	256.000i		−	0.344549i	−0.985049	−	0.172275i	$-0.944888\pi$
$743$		−	256.000i		−	0.344549i	0.985049	−	0.172275i	$-0.0551116\pi$
$744$		0			0
$745$	−256.500	+	444.271i	−0.344295	+	0.596337i
$746$		0			0
$747$	−110.851	+	64.0000i	−0.148395	+	0.0856760i
$748$		0			0
$749$	71.5000	−	28.5788i	0.0954606	−	0.0381560i
$750$		0			0
$751$	−979.475	+	565.500i	−1.30423	+	0.752996i	−0.981126	−	0.193368i	$-0.938059\pi$
$751$	−979.475	+	565.500i	−1.30423	+	0.752996i	−0.323101	+	0.946364i	$0.604725\pi$
$752$		0			0
$753$	−985.000	+	1706.07i	−1.30810	+	2.26570i
$754$		0			0
$755$			243.000i			0.321854i
$756$		0			0
$757$	−336.000			−0.443857			−0.221929	−	0.975063i	$-0.571235\pi$
$757$	−336.000			−0.443857			−0.221929	+	0.975063i	$0.571235\pi$
$758$		0			0
$759$	246.817	+	142.500i	0.325187	+	0.187747i
$760$		0			0
$761$	−172.500	−	298.779i	−0.226675	−	0.392613i	0.730145	−	0.683292i	$-0.239452\pi$
$761$	−172.500	−	298.779i	−0.226675	−	0.392613i	−0.956821	+	0.290678i	$0.906119\pi$
$762$		0			0
$763$	489.304	−	621.500i	0.641290	−	0.814548i
$764$		0			0
$765$	−504.000	−	872.954i	−0.658824	−	1.14112i
$766$		0			0
$767$	−734.390	−	424.000i	−0.957483	−	0.552803i
$768$		0			0
$769$	568.000			0.738622			0.369311	−	0.929306i	$-0.379594\pi$
$769$	568.000			0.738622			0.369311	+	0.929306i	$0.379594\pi$
$770$		0			0
$771$			445.000i			0.577173i
$772$		0			0
$773$	279.500	−	484.108i	0.361578	−	0.626272i	−0.626643	−	0.779307i	$-0.715571\pi$
$773$	279.500	−	484.108i	0.361578	−	0.626272i	0.988221	+	0.153035i	$0.0489047\pi$
$774$		0			0
$775$	533.472	−	308.000i	0.688351	−	0.397419i
$776$		0			0
$777$	−5.00000	+	34.6410i	−0.00643501	+	0.0445830i
$778$		0			0
$779$	381.051	−	220.000i	0.489154	−	0.282413i
$780$		0			0
$781$	72.0000	−	124.708i	0.0921895	−	0.159677i
$782$		0			0
$783$			1120.00i			1.43040i
$784$		0			0
$785$	1503.00			1.91465
$786$		0			0
$787$	−572.443	−	330.500i	−0.727373	−	0.419949i	0.0900872	−	0.995934i	$-0.471285\pi$
$787$	−572.443	−	330.500i	−0.727373	−	0.419949i	−0.817460	+	0.575985i	$0.804619\pi$
$788$		0			0
$789$	112.500	+	194.856i	0.142586	+	0.246965i
$790$		0			0
$791$	−387.979	−	56.0000i	−0.490492	−	0.0707965i
$792$		0			0
$793$	−632.000	−	1094.66i	−0.796974	−	1.38040i
$794$		0			0
$795$	−272.798	−	157.500i	−0.343142	−	0.198113i
$796$		0			0
$797$	−736.000			−0.923463			−0.461731	−	0.887020i	$-0.652772\pi$
$797$	−736.000			−0.923463			−0.461731	+	0.887020i	$0.652772\pi$
$798$		0			0
$799$		−	595.000i		−	0.744681i
$800$		0			0
$801$	−776.000	+	1344.07i	−0.968789	+	1.67799i
$802$		0			0
$803$	371.525	−	214.500i	0.462671	−	0.267123i
$804$		0			0
$805$	940.500	+	740.452i	1.16832	+	0.919816i
$806$		0			0
$807$	−1978.87	+	1142.50i	−2.45213	+	1.41574i
$808$		0			0
$809$	−143.500	+	248.549i	−0.177379	+	0.307230i	−0.940982	−	0.338456i	$-0.890095\pi$
$809$	−143.500	+	248.549i	−0.177379	+	0.307230i	0.763603	+	0.645686i	$0.223429\pi$
$810$		0			0
$811$		−	1272.00i		−	1.56843i	−0.620487	−	0.784217i	$-0.713065\pi$
$811$		−	1272.00i		−	1.56843i	0.620487	−	0.784217i	$-0.286935\pi$
$812$		0			0
$813$	1985.00			2.44157
$814$		0			0
$815$	−148.090	−	85.5000i	−0.181706	−	0.104908i
$816$		0			0
$817$	−220.000	−	381.051i	−0.269278	−	0.466403i
$818$		0			0
$819$	−665.108	−	1664.00i	−0.812097	−	2.03175i
$820$		0			0
$821$	371.500	+	643.457i	0.452497	+	0.783748i	0.998540	−	0.0540091i	$-0.0172000\pi$
$821$	371.500	+	643.457i	0.452497	+	0.783748i	−0.546043	+	0.837757i	$0.683867\pi$
$822$		0			0
$823$	196.588	+	113.500i	0.238867	+	0.137910i	0.614656	−	0.788795i	$-0.289295\pi$
$823$	196.588	+	113.500i	0.238867	+	0.137910i	−0.375789	+	0.926705i	$0.622628\pi$
$824$		0			0
$825$	−840.000			−1.01818
$826$		0			0
$827$		−	120.000i		−	0.145103i	−0.997365	−	0.0725514i	$-0.976886\pi$
$827$		−	120.000i		−	0.145103i	0.997365	−	0.0725514i	$-0.0231141\pi$
$828$		0			0
$829$	−120.500	+	208.712i	−0.145356	+	0.251764i	−0.929506	−	0.368808i	$-0.879766\pi$
$829$	−120.500	+	208.712i	−0.145356	+	0.251764i	0.784150	+	0.620572i	$0.213099\pi$
$830$		0			0
$831$	1000.26	−	577.500i	1.20368	−	0.694946i
$832$		0			0
$833$	248.500	−	236.425i	0.298319	−	0.283823i
$834$		0			0
$835$	−1480.90	+	855.000i	−1.77354	+	1.02395i
$836$		0			0
$837$	−192.500	+	333.420i	−0.229988	+	0.398351i
$838$		0			0
$839$			880.000i			1.04887i	0.851451	+	0.524434i	$0.175723\pi$
$839$			880.000i			1.04887i	−0.851451	+	0.524434i	$0.824277\pi$
$840$		0			0
$841$	183.000			0.217598
$842$		0			0
$843$	−450.333	−	260.000i	−0.534203	−	0.308422i
$844$		0			0
$845$	−391.500	−	678.098i	−0.463314	−	0.802483i
$846$		0			0
$847$	290.985	+	728.000i	0.343547	+	0.859504i
$848$		0			0
$849$	−992.500	−	1719.06i	−1.16902	−	2.02481i
$850$		0			0
$851$	16.4545	+	9.50000i	0.0193355	+	0.0111633i
$852$		0			0
$853$	176.000			0.206331			0.103165	−	0.994664i	$-0.467103\pi$
$853$	176.000			0.206331			0.103165	+	0.994664i	$0.467103\pi$
$854$		0			0
$855$			1584.00i			1.85263i
$856$		0			0
$857$	−127.500	+	220.836i	−0.148775	+	0.257686i	−0.930775	−	0.365593i	$-0.880866\pi$
$857$	−127.500	+	220.836i	−0.148775	+	0.257686i	0.782000	+	0.623278i	$0.214200\pi$
$858$		0			0
$859$	558.586	−	322.500i	0.650275	−	0.375437i	−0.138286	−	0.990392i	$-0.544159\pi$
$859$	558.586	−	322.500i	0.650275	−	0.375437i	0.788562	+	0.614956i	$0.210826\pi$
$860$		0			0
$861$	−1100.00	−	866.025i	−1.27758	−	1.00584i
$862$		0			0
$863$	723.131	−	417.500i	0.837927	−	0.483778i	−0.0186319	−	0.999826i	$-0.505931\pi$
$863$	723.131	−	417.500i	0.837927	−	0.483778i	0.856559	+	0.516049i	$0.172598\pi$
$864$		0			0
$865$	652.500	−	1130.16i	0.754335	−	1.30655i
$866$		0			0
$867$		−	1200.00i		−	1.38408i
$868$		0			0
$869$	−105.000			−0.120829
$870$		0			0
$871$	152.420	+	88.0000i	0.174995	+	0.101033i
$872$		0			0
$873$	−704.000	−	1219.36i	−0.806415	−	1.39675i
$874$		0			0
$875$	−1932.97	−	279.000i	−2.20911	−	0.318857i
$876$		0			0
$877$	571.500	+	989.867i	0.651653	+	1.12870i	0.982722	+	0.185090i	$0.0592576\pi$
$877$	571.500	+	989.867i	0.651653	+	1.12870i	−0.331068	+	0.943607i	$0.607409\pi$
$878$		0			0
$879$	−666.840	−	385.000i	−0.758634	−	0.437998i
$880$		0			0
$881$	−930.000			−1.05562			−0.527809	−	0.849363i	$-0.676986\pi$
$881$	−930.000			−1.05562			−0.527809	+	0.849363i	$0.676986\pi$
$882$		0			0
$883$			1320.00i			1.49490i	0.664316	+	0.747452i	$0.268723\pi$
$883$			1320.00i			1.49490i	−0.664316	+	0.747452i	$0.731277\pi$
$884$		0			0
$885$	1192.50	−	2065.47i	1.34746	−	2.33387i
$886$		0			0
$887$	918.853	−	530.500i	1.03591	−	0.598083i	0.117239	−	0.993104i	$-0.462596\pi$
$887$	918.853	−	530.500i	1.03591	−	0.598083i	0.918672	+	0.395020i	$0.129262\pi$
$888$		0			0
$889$	−96.0000	+	665.108i	−0.107987	+	0.748152i
$890$		0			0
$891$	80.5404	−	46.5000i	0.0903932	−	0.0521886i
$892$		0			0
$893$	−467.500	+	809.734i	−0.523516	+	0.906757i
$894$		0			0
$895$		−	2853.00i		−	3.18771i
$896$		0			0
$897$	−1520.00			−1.69454
$898$		0			0
$899$	304.841	+	176.000i	0.339089	+	0.195773i
$900$		0			0
$901$	24.5000	+	42.4352i	0.0271920	+	0.0470979i
$902$		0			0
$903$	−866.025	+	1100.00i	−0.959054	+	1.21816i
$904$		0			0
$905$	837.000	+	1449.73i	0.924862	+	1.60191i
$906$		0			0
$907$	771.629	+	445.500i	0.850748	+	0.491180i	0.860903	−	0.508769i	$-0.169899\pi$
$907$	771.629	+	445.500i	0.850748	+	0.491180i	−0.0101550	+	0.999948i	$0.503232\pi$
$908$		0			0
$909$	240.000			0.264026
$910$		0			0
$911$		−	464.000i		−	0.509330i	−0.967029	−	0.254665i	$-0.918035\pi$
$911$		−	464.000i		−	0.509330i	0.967029	−	0.254665i	$-0.0819653\pi$
$912$		0			0
$913$	12.0000	−	20.7846i	0.0131435	−	0.0227652i
$914$		0			0
$915$	3078.72	−	1777.50i	3.36472	−	1.94262i
$916$		0			0
$917$	916.500	−	366.329i	0.999455	−	0.399486i
$918$		0			0
$919$	1251.41	−	722.500i	1.36170	−	0.786181i	0.371854	−	0.928291i	$-0.378722\pi$
$919$	1251.41	−	722.500i	1.36170	−	0.786181i	0.989851	+	0.142111i	$0.0453889\pi$
$920$		0			0
$921$	−940.000	+	1628.13i	−1.02063	+	1.76778i
$922$		0			0
$923$			768.000i			0.832069i
$924$		0			0
$925$	−56.0000			−0.0605405
$926$		0			0
$927$	−1288.65	−	744.000i	−1.39012	−	0.802589i
$928$		0			0
$929$	800.500	+	1386.51i	0.861679	+	1.49247i	0.870307	+	0.492509i	$0.163920\pi$
$929$	800.500	+	1386.51i	0.861679	+	1.49247i	−0.00862789	+	0.999963i	$0.502746\pi$
$930$		0			0
$931$	−523.945	+	126.500i	−0.562777	+	0.135875i
$932$		0			0
$933$	−807.500	−	1398.63i	−0.865488	−	1.49907i
$934$		0			0
$935$	163.679	+	94.5000i	0.175058	+	0.101070i
$936$		0			0
$937$	1554.00			1.65848			0.829242	−	0.558889i	$-0.188772\pi$
$937$	1554.00			1.65848			0.829242	+	0.558889i	$0.188772\pi$
$938$		0			0
$939$			955.000i			1.01704i
$940$		0			0
$941$	492.500	−	853.035i	0.523379	−	0.906520i	−0.476250	−	0.879310i	$-0.658004\pi$
$941$	492.500	−	853.035i	0.523379	−	0.906520i	0.999630	−	0.0272100i	$-0.00866227\pi$
$942$		0			0
$943$	−658.179	+	380.000i	−0.697963	+	0.402969i
$944$		0			0
$945$	2047.50	−	818.394i	2.16667	−	0.866025i
$946$		0			0
$947$	279.726	−	161.500i	0.295381	−	0.170539i	−0.344985	−	0.938608i	$-0.612116\pi$
$947$	279.726	−	161.500i	0.295381	−	0.170539i	0.640366	+	0.768070i	$0.278783\pi$
$948$		0			0
$949$	−1144.00	+	1981.47i	−1.20548	+	2.08795i
$950$		0			0
$951$			1675.00i			1.76130i
$952$		0			0
$953$	−168.000			−0.176285			−0.0881427	−	0.996108i	$-0.528093\pi$
$953$	−168.000			−0.176285			−0.0881427	+	0.996108i	$0.528093\pi$
$954$		0			0
$955$	2205.77	+	1273.50i	2.30970	+	1.33351i
$956$		0			0
$957$	−240.000	−	415.692i	−0.250784	−	0.434370i
$958$		0			0
$959$	38.9711	−	49.5000i	0.0406373	−	0.0516163i
$960$		0			0
$961$	−420.000	−	727.461i	−0.437045	−	0.756984i
$962$		0			0
$963$	−152.420	−	88.0000i	−0.158277	−	0.0913811i
$964$		0			0
$965$	−2655.00			−2.75130
$966$		0			0
$967$		−	112.000i		−	0.115822i	−0.998322	−	0.0579111i	$-0.981556\pi$
$967$		−	112.000i		−	0.115822i	0.998322	−	0.0579111i	$-0.0184440\pi$
$968$		0			0
$969$	192.500	−	333.420i	0.198658	−	0.344086i
$970$		0			0
$971$	−1632.46	+	942.500i	−1.68121	+	0.970649i	−0.720356	+	0.693605i	$0.756022\pi$
$971$	−1632.46	+	942.500i	−1.68121	+	0.970649i	−0.960857	+	0.277044i	$0.910645\pi$
$972$		0			0
$973$	136.000	−	942.236i	0.139774	−	0.968382i
$974$		0			0
$975$	3879.79	−	2240.00i	3.97928	−	2.29744i
$976$		0			0
$977$	−12.5000	+	21.6506i	−0.0127943	+	0.0221603i	−0.872352	−	0.488879i	$-0.837406\pi$
$977$	−12.5000	+	21.6506i	−0.0127943	+	0.0221603i	0.859557	+	0.511039i	$0.170739\pi$
$978$		0			0
$979$		−	291.000i		−	0.297242i
$980$		0			0
$981$	−1808.00			−1.84302
$982$		0			0
$983$	73.6122	+	42.5000i	0.0748852	+	0.0432350i	0.536975	−	0.843598i	$-0.319567\pi$
$983$	73.6122	+	42.5000i	0.0748852	+	0.0432350i	−0.462090	+	0.886833i	$0.652900\pi$
$984$		0			0
$985$	−576.000	−	997.661i	−0.584772	−	1.01285i
$986$		0			0
$987$	2944.49	+	425.000i	2.98327	+	0.430598i
$988$		0			0
$989$	380.000	+	658.179i	0.384226	+	0.665500i
$990$		0			0
$991$	−135.966	−	78.5000i	−0.137201	−	0.0792129i	0.429828	−	0.902911i	$-0.358574\pi$
$991$	−135.966	−	78.5000i	−0.137201	−	0.0792129i	−0.567029	+	0.823698i	$0.691907\pi$
$992$		0			0
$993$	−175.000			−0.176234
$994$		0			0
$995$			2547.00i			2.55980i
$996$		0			0
$997$	148.500	−	257.210i	0.148947	−	0.257983i	−0.781892	−	0.623414i	$-0.785745\pi$
$997$	148.500	−	257.210i	0.148947	−	0.257983i	0.930838	+	0.365431i	$0.119078\pi$
$998$		0			0
$999$	30.3109	−	17.5000i	0.0303412	−	0.0175175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.r.a.95.1	✓	4
4.3	odd	2	inner	224.3.r.a.95.2	yes	4
7.2	even	3	inner	224.3.r.a.191.2	yes	4
7.3	odd	6		1568.3.d.a.1471.1		2
7.4	even	3		1568.3.d.e.1471.2		2
8.3	odd	2		448.3.r.c.319.1		4
8.5	even	2		448.3.r.c.319.2		4
28.3	even	6		1568.3.d.a.1471.2		2
28.11	odd	6		1568.3.d.e.1471.1		2
28.23	odd	6	inner	224.3.r.a.191.1	yes	4
56.37	even	6		448.3.r.c.191.1		4
56.51	odd	6		448.3.r.c.191.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.r.a.95.1	✓	4	1.1	even	1	trivial
224.3.r.a.95.2	yes	4	4.3	odd	2	inner
224.3.r.a.191.1	yes	4	28.23	odd	6	inner
224.3.r.a.191.2	yes	4	7.2	even	3	inner
448.3.r.c.191.1		4	56.37	even	6
448.3.r.c.191.2		4	56.51	odd	6
448.3.r.c.319.1		4	8.3	odd	2
448.3.r.c.319.2		4	8.5	even	2
1568.3.d.a.1471.1		2	7.3	odd	6
1568.3.d.a.1471.2		2	28.3	even	6
1568.3.d.e.1471.1		2	28.11	odd	6
1568.3.d.e.1471.2		2	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-4.33013 - 2.50000i) q^{3} +(-4.50000 - 7.79423i) q^{5} +(-6.92820 - 1.00000i) q^{7} +(8.00000 + 13.8564i) q^{9} +O(q^{10})\)	\(q+(-4.33013 - 2.50000i) q^{3} +(-4.50000 - 7.79423i) q^{5} +(-6.92820 - 1.00000i) q^{7} +(8.00000 + 13.8564i) q^{9} +(-2.59808 - 1.50000i) q^{11} +16.0000 q^{13} +45.0000i q^{15} +(3.50000 - 6.06218i) q^{17} +(-9.52628 + 5.50000i) q^{19} +(27.5000 + 21.6506i) q^{21} +(16.4545 - 9.50000i) q^{23} +(-28.0000 + 48.4974i) q^{25} -35.0000i q^{27} -32.0000 q^{29} +(-9.52628 - 5.50000i) q^{31} +(7.50000 + 12.9904i) q^{33} +(23.3827 + 58.5000i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-69.2820 - 40.0000i) q^{39} -40.0000 q^{41} +40.0000i q^{43} +(72.0000 - 124.708i) q^{45} +(73.6122 - 42.5000i) q^{47} +(47.0000 + 13.8564i) q^{49} +(-30.3109 + 17.5000i) q^{51} +(-3.50000 + 6.06218i) q^{53} +27.0000i q^{55} +55.0000 q^{57} +(-45.8993 - 26.5000i) q^{59} +(-39.5000 - 68.4160i) q^{61} +(-41.5692 - 104.000i) q^{63} +(-72.0000 - 124.708i) q^{65} +(9.52628 + 5.50000i) q^{67} -95.0000 q^{69} +48.0000i q^{71} +(-71.5000 + 123.842i) q^{73} +(242.487 - 140.000i) q^{75} +(16.5000 + 12.9904i) q^{77} +(30.3109 - 17.5000i) q^{79} +(-15.5000 + 26.8468i) q^{81} +8.00000i q^{83} -63.0000 q^{85} +(138.564 + 80.0000i) q^{87} +(48.5000 + 84.0045i) q^{89} +(-110.851 - 16.0000i) q^{91} +(27.5000 + 47.6314i) q^{93} +(85.7365 + 49.5000i) q^{95} -88.0000 q^{97} -48.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 18 q^{5} + 32 q^{9}+O(q^{10}) \) 4 * q - 18 * q^5 + 32 * q^9	\( 4 q - 18 q^{5} + 32 q^{9} + 64 q^{13} + 14 q^{17} + 110 q^{21} - 112 q^{25} - 128 q^{29} + 30 q^{33} + 2 q^{37} - 160 q^{41} + 288 q^{45} + 188 q^{49} - 14 q^{53} + 220 q^{57} - 158 q^{61} - 288 q^{65} - 380 q^{69} - 286 q^{73} + 66 q^{77} - 62 q^{81} - 252 q^{85} + 194 q^{89} + 110 q^{93} - 352 q^{97}+O(q^{100}) \) 4 * q - 18 * q^5 + 32 * q^9 + 64 * q^13 + 14 * q^17 + 110 * q^21 - 112 * q^25 - 128 * q^29 + 30 * q^33 + 2 * q^37 - 160 * q^41 + 288 * q^45 + 188 * q^49 - 14 * q^53 + 220 * q^57 - 158 * q^61 - 288 * q^65 - 380 * q^69 - 286 * q^73 + 66 * q^77 - 62 * q^81 - 252 * q^85 + 194 * q^89 + 110 * q^93 - 352 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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