LMFDB - Embedded newform 448.3.r.c.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,3,Mod(191,448)]

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([3, 0, 2]))

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

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

chi := DirichletCharacter("448.191");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	448.r (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:	$4$
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:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	448.191
Dual form			448.3.r.c.319.1

$q$-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 $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.33013	+	2.50000i	−1.44338	+	0.833333i	−0.998073	−	0.0620469i	$-0.980237\pi$
$3$	−4.33013	+	2.50000i	−1.44338	+	0.833333i	−0.445302	+	0.895380i	$0.646904\pi$
$4$		0			0
$5$	4.50000	−	7.79423i	0.900000	−	1.55885i	0.0725083	−	0.997368i	$-0.476900\pi$
$5$	4.50000	−	7.79423i	0.900000	−	1.55885i	0.827492	−	0.561478i	$-0.189767\pi$
$6$		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	−0.613424	−	0.789754i	$-0.710208\pi$
$11$	−2.59808	+	1.50000i	−0.236189	+	0.136364i	0.377235	+	0.926118i	$0.376875\pi$
$12$		0			0
$13$	−16.0000			−1.23077			−0.615385	−	0.788227i	$-0.710999\pi$
$13$	−16.0000			−1.23077			−0.615385	+	0.788227i	$0.710999\pi$
$14$		0			0
$15$			45.0000i			3.00000i
$16$		0			0
$17$	3.50000	+	6.06218i	0.205882	+	0.356599i	0.950414	−	0.310989i	$-0.100660\pi$
$17$	3.50000	+	6.06218i	0.205882	+	0.356599i	−0.744531	+	0.667588i	$0.767327\pi$
$18$		0			0
$19$	−9.52628	−	5.50000i	−0.501383	−	0.289474i	0.227901	−	0.973684i	$-0.426814\pi$
$19$	−9.52628	−	5.50000i	−0.501383	−	0.289474i	−0.729285	+	0.684211i	$0.760147\pi$
$20$		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	$-0.468868\pi$
$23$	−16.4545	−	9.50000i	−0.715412	−	0.413043i	−0.813062	+	0.582177i	$0.802201\pi$
$24$		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	$-0.313970\pi$
$29$	32.0000			1.10345			0.551724	+	0.834027i	$0.313970\pi$
$30$		0			0
$31$	9.52628	−	5.50000i	0.307299	−	0.177419i	−0.338418	−	0.940996i	$-0.609892\pi$
$31$	9.52628	−	5.50000i	0.307299	−	0.177419i	0.645717	+	0.763577i	$0.276558\pi$
$32$		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	$-0.837635\pi$
$37$	−0.500000	+	0.866025i	−0.0135135	+	0.0234061i	0.859190	+	0.511657i	$0.170968\pi$
$38$		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	$-0.846013\pi$
$43$		−	40.0000i		−	0.930233i	0.885250	−	0.465116i	$-0.153987\pi$
$44$		0			0
$45$	−72.0000	−	124.708i	−1.60000	−	2.77128i
$46$		0			0
$47$	−73.6122	−	42.5000i	−1.56622	−	0.904255i	−0.996604	−	0.0823416i	$-0.973760\pi$
$47$	−73.6122	−	42.5000i	−1.56622	−	0.904255i	−0.569612	−	0.821914i	$-0.692907\pi$
$48$		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	$-0.145631\pi$
$53$	3.50000	+	6.06218i	0.0660377	+	0.114381i	−0.831116	+	0.556099i	$0.812298\pi$
$54$		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	−0.835705	−	0.549179i	$-0.814941\pi$
$59$	−45.8993	+	26.5000i	−0.777955	+	0.449153i	0.0577500	+	0.998331i	$0.481607\pi$
$60$		0			0
$61$	39.5000	−	68.4160i	0.647541	−	1.12157i	−0.336167	−	0.941802i	$-0.609131\pi$
$61$	39.5000	−	68.4160i	0.647541	−	1.12157i	0.983708	−	0.179772i	$-0.0575359\pi$
$62$		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	−0.427221	−	0.904147i	$-0.640507\pi$
$67$	9.52628	−	5.50000i	0.142183	−	0.0820896i	0.569404	+	0.822058i	$0.307174\pi$
$68$		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	−0.664384	−	0.747392i	$-0.731306\pi$
$73$	−71.5000	−	123.842i	−0.979452	−	1.69646i	−0.315068	−	0.949069i	$-0.602027\pi$
$74$		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	$-0.404435\pi$
$79$	−30.3109	−	17.5000i	−0.383682	−	0.221519i	−0.679419	+	0.733750i	$0.737768\pi$
$80$		0			0
$81$	−15.5000	−	26.8468i	−0.191358	−	0.331442i
$82$		0			0
$83$		−	8.00000i		−	0.0963855i	−0.998838	−	0.0481928i	$-0.984654\pi$
$83$		−	8.00000i		−	0.0963855i	0.998838	−	0.0481928i	$-0.0153462\pi$
$84$		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	−0.453667	−	0.891171i	$-0.649884\pi$
$89$	48.5000	−	84.0045i	0.544944	−	0.943870i	0.998610	−	0.0526989i	$-0.0167824\pi$
$90$		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	$-0.190325\pi$
$101$	−7.50000	−	12.9904i	−0.0742574	−	0.128618i	−0.900763	+	0.434311i	$0.856992\pi$
$102$		0			0
$103$	80.5404	+	46.5000i	0.781945	+	0.451456i	0.837119	−	0.547020i	$-0.184238\pi$
$103$	80.5404	+	46.5000i	0.781945	+	0.451456i	−0.0551740	+	0.998477i	$0.517571\pi$
$104$		0			0
$105$	45.0000	+	311.769i	0.428571	+	2.96923i
$106$		0			0
$107$	−9.52628	−	5.50000i	−0.0890306	−	0.0514019i	0.454824	−	0.890581i	$-0.349702\pi$
$107$	−9.52628	−	5.50000i	−0.0890306	−	0.0514019i	−0.543854	+	0.839180i	$0.683036\pi$
$108$		0			0
$109$	56.5000	+	97.8609i	0.518349	+	0.897806i	0.999773	+	0.0213184i	$0.00678636\pi$
$109$	56.5000	+	97.8609i	0.518349	+	0.897806i	−0.481424	+	0.876488i	$0.659880\pi$
$110$		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	−0.0446483	−	0.999003i	$-0.514217\pi$
$131$	−122.110	−	70.5000i	−0.932134	−	0.538168i	−0.887486	+	0.460835i	$0.847550\pi$
$132$		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	0.849135	−	0.528176i	$-0.177124\pi$
$137$	−4.50000	−	7.79423i	−0.0328467	−	0.0568922i	−0.881981	+	0.471284i	$0.843791\pi$
$138$		0			0
$139$		−	136.000i		−	0.978417i	−0.872167	−	0.489209i	$-0.837286\pi$
$139$		−	136.000i		−	0.978417i	0.872167	−	0.489209i	$-0.162714\pi$
$140$		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	$-0.772071\pi$
$149$	28.5000	−	49.3634i	0.191275	−	0.331298i	0.945673	+	0.325119i	$0.105404\pi$
$150$		0			0
$151$	23.3827	−	13.5000i	0.154852	−	0.0894040i	−0.420572	−	0.907259i	$-0.638170\pi$
$151$	23.3827	−	13.5000i	0.154852	−	0.0894040i	0.575424	+	0.817855i	$0.304837\pi$
$152$		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	0.999309	+	0.0371729i	$0.0118352\pi$
$157$	83.5000	+	144.626i	0.531847	+	0.921186i	−0.467462	+	0.884013i	$0.654831\pi$
$158$		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	0.549624	−	0.835412i	$-0.314771\pi$
$163$	16.4545	+	9.50000i	0.100948	+	0.0582822i	−0.448676	+	0.893694i	$0.648104\pi$
$164$		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	$-0.970979\pi$
$173$	−72.5000	+	125.574i	−0.419075	+	0.725859i	0.576772	+	0.816905i	$0.304312\pi$
$174$		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	0.534500	−	0.845168i	$-0.320500\pi$
$179$	274.530	−	158.500i	1.53369	−	0.885475i	0.999187	−	0.0403064i	$-0.0128334\pi$
$180$		0			0
$181$	186.000			1.02762			0.513812	−	0.857903i	$-0.328233\pi$
$181$	186.000			1.02762			0.513812	+	0.857903i	$0.328233\pi$
$182$		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	$-0.0677621\pi$
$191$	245.085	+	141.500i	1.28317	+	0.740838i	0.305742	+	0.952114i	$0.401095\pi$
$192$		0			0
$193$	147.500	+	255.477i	0.764249	+	1.32372i	0.940643	+	0.339398i	$0.110223\pi$
$193$	147.500	+	255.477i	0.764249	+	1.32372i	−0.176394	+	0.984320i	$0.556443\pi$
$194$		0			0
$195$		−	720.000i		−	3.69231i
$196$		0			0
$197$	−128.000			−0.649746			−0.324873	−	0.945758i	$-0.605322\pi$
$197$	−128.000			−0.649746			−0.324873	+	0.945758i	$0.605322\pi$
$198$		0			0
$199$	245.085	−	141.500i	1.23158	−	0.711055i	0.264224	−	0.964461i	$-0.414884\pi$
$199$	245.085	−	141.500i	1.23158	−	0.711055i	0.967360	+	0.253406i	$0.0815509\pi$
$200$		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	$-0.969783\pi$
$211$		−	40.0000i		−	0.189573i	0.995498	−	0.0947867i	$-0.0302169\pi$
$212$		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	−0.999646	−	0.0265925i	$-0.991534\pi$
$227$	−335.152	+	193.500i	−1.47644	+	0.852423i	−0.476793	+	0.879015i	$0.658201\pi$
$228$		0			0
$229$	−91.5000	+	158.483i	−0.399563	+	0.692064i	−0.993672	−	0.112321i	$-0.964172\pi$
$229$	−91.5000	+	158.483i	−0.399563	+	0.692064i	0.594109	+	0.804385i	$0.297505\pi$
$230$		0			0
$231$	38.9711	−	97.5000i	0.168706	−	0.422078i
$232$		0			0
$233$	−180.500	+	312.635i	−0.774678	+	1.34178i	0.160297	+	0.987069i	$0.448755\pi$
$233$	−180.500	+	312.635i	−0.774678	+	1.34178i	−0.934975	+	0.354713i	$0.884579\pi$
$234$		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	0.968251	−	0.249982i	$-0.0804246\pi$
$241$	64.5000	+	111.717i	0.267635	+	0.463557i	−0.700616	+	0.713539i	$0.747091\pi$
$242$		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	$0.287265\pi$
$251$			394.000i			1.56972i	−0.619672	+	0.784861i	$0.712735\pi$
$252$		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	−0.939520	−	0.342494i	$-0.888728\pi$
$257$	−44.5000	+	77.0763i	−0.173152	+	0.299908i	0.766368	+	0.642401i	$0.222062\pi$
$258$		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	$-0.639402\pi$
$263$	38.9711	−	22.5000i	0.148179	−	0.0855513i	0.572257	+	0.820075i	$0.306068\pi$
$264$		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	−0.881707	−	0.471798i	$-0.843605\pi$
$269$	−228.500	−	395.774i	−0.849442	−	1.47128i	0.0322643	−	0.999479i	$-0.489728\pi$
$270$		0			0
$271$	343.812	+	198.500i	1.26868	+	0.732472i	0.974738	−	0.223351i	$-0.0716997\pi$
$271$	343.812	+	198.500i	1.26868	+	0.732472i	0.293941	+	0.955823i	$0.405033\pi$
$272$		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	$-0.0297595\pi$
$277$	115.500	+	200.052i	0.416968	+	0.722209i	−0.578665	+	0.815565i	$0.696426\pi$
$278$		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	0.251065	−	0.967970i	$-0.419219\pi$
$283$	343.812	−	198.500i	1.21488	−	0.701413i	0.963819	+	0.266557i	$0.0858860\pi$
$284$		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	$-0.584645\pi$
$293$	−154.000			−0.525597			−0.262799	+	0.964851i	$0.584645\pi$
$294$		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	$0.209787\pi$
$307$			376.000i			1.22476i	−0.790565	+	0.612378i	$0.790213\pi$
$308$		0			0
$309$	−465.000			−1.50485
$310$		0			0
$311$	−279.726	+	161.500i	−0.899441	+	0.519293i	−0.877019	−	0.480456i	$-0.840471\pi$
$311$	−279.726	+	161.500i	−0.899441	+	0.519293i	−0.0224223	+	0.999749i	$0.507138\pi$
$312$		0			0
$313$	−95.5000	+	165.411i	−0.305112	+	0.528469i	−0.977286	−	0.211924i	$-0.932027\pi$
$313$	−95.5000	+	165.411i	−0.305112	+	0.528469i	0.672174	+	0.740393i	$0.265361\pi$
$314$		0			0
$315$	−623.538	−	792.000i	−1.97949	−	2.51429i
$316$		0			0
$317$	167.500	−	290.119i	0.528391	−	0.915200i	−0.471061	−	0.882101i	$-0.656129\pi$
$317$	167.500	−	290.119i	0.528391	−	0.915200i	0.999452	−	0.0330997i	$-0.0105379\pi$
$318$		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	0.545088	−	0.838379i	$-0.316496\pi$
$331$	30.3109	+	17.5000i	0.0915737	+	0.0528701i	−0.453514	+	0.891249i	$0.649830\pi$
$332$		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	−0.248154	−	0.968721i	$-0.579824\pi$
$347$	161.947	−	93.5000i	0.466705	−	0.269452i	0.714860	+	0.699268i	$0.246491\pi$
$348$		0			0
$349$	208.000			0.595989			0.297994	−	0.954568i	$-0.403682\pi$
$349$	208.000			0.595989			0.297994	+	0.954568i	$0.403682\pi$
$350$		0			0
$351$		−	560.000i		−	1.59544i
$352$		0			0
$353$	115.500	+	200.052i	0.327195	+	0.566719i	0.981954	−	0.189119i	$-0.0605631\pi$
$353$	115.500	+	200.052i	0.327195	+	0.566719i	−0.654759	+	0.755838i	$0.727230\pi$
$354$		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	$-0.349744\pi$
$359$	−32.0429	−	18.5000i	−0.0892561	−	0.0515320i	−0.543964	+	0.839109i	$0.683077\pi$
$360$		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	$-0.895280\pi$
$367$	−418.290	+	241.500i	−1.13976	+	0.658038i	−0.193385	+	0.981123i	$0.561947\pi$
$368$		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	−0.417989	−	0.908452i	$-0.637265\pi$
$373$	215.500	−	373.257i	0.577748	−	1.00069i	0.995737	−	0.0922368i	$-0.0294017\pi$
$374$		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	$-0.608988\pi$
$379$		−	714.000i		−	1.88391i	0.335746	−	0.941953i	$-0.391012\pi$
$380$		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	$-0.0100140\pi$
$383$	563.783	+	325.500i	1.47202	+	0.849869i	0.472512	+	0.881324i	$0.343347\pi$
$384$		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	0.993162	+	0.116747i	$0.0372465\pi$
$389$	232.500	+	402.702i	0.597686	+	1.03522i	−0.395475	+	0.918477i	$0.629420\pi$
$390$		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	$-0.758480\pi$
$397$	92.5000	−	160.215i	0.232997	−	0.403563i	0.958689	+	0.284457i	$0.0918133\pi$
$398$		0			0
$399$	381.051	−	55.0000i	0.955015	−	0.137845i
$400$		0			0
$401$	−52.5000	+	90.9327i	−0.130923	+	0.226765i	−0.924033	−	0.382314i	$-0.875127\pi$
$401$	−52.5000	+	90.9327i	−0.130923	+	0.226765i	0.793110	+	0.609079i	$0.208461\pi$
$402$		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	0.870272	−	0.492571i	$-0.163943\pi$
$409$	3.50000	+	6.06218i	0.00855746	+	0.0148220i	−0.861715	+	0.507393i	$0.830609\pi$
$410$		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	$-0.845054\pi$
$419$		−	392.000i		−	0.935561i	0.883845	−	0.467780i	$-0.154946\pi$
$420$		0			0
$421$	−64.0000			−0.152019			−0.0760095	−	0.997107i	$-0.524218\pi$
$421$	−64.0000			−0.152019			−0.0760095	+	0.997107i	$0.524218\pi$
$422$		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	$-0.344457\pi$
$431$	633.065	−	365.500i	1.46883	−	0.848028i	0.999389	+	0.0349377i	$0.0111233\pi$
$432$		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	$-0.0759879\pi$
$439$	549.926	+	317.500i	1.25268	+	0.723235i	0.281038	+	0.959697i	$0.409321\pi$
$440$		0			0
$441$	184.000	−	762.102i	0.417234	−	1.72812i
$442$		0			0
$443$	−425.218	−	245.500i	−0.959861	−	0.554176i	−0.0637308	−	0.997967i	$-0.520300\pi$
$443$	−425.218	−	245.500i	−0.959861	−	0.554176i	−0.896130	+	0.443791i	$0.853633\pi$
$444$		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	0.419281	+	0.907857i	$0.362282\pi$
$457$	−263.500	+	456.395i	−0.576586	+	0.998677i	−0.995867	+	0.0908204i	$0.971051\pi$
$458$		0			0
$459$	−212.176	+	122.500i	−0.462258	+	0.266885i
$460$		0			0
$461$	704.000			1.52711			0.763557	−	0.645740i	$-0.223451\pi$
$461$	704.000			1.52711			0.763557	+	0.645740i	$0.223451\pi$
$462$		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	−0.0940447	−	0.995568i	$-0.529980\pi$
$467$	−468.520	−	270.500i	−1.00325	−	0.579229i	−0.909210	+	0.416339i	$0.863313\pi$
$468$		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	$-0.500767\pi$
$479$	413.094	−	238.500i	0.862409	−	0.497912i	0.864818	+	0.502085i	$0.167433\pi$
$480$		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	$-0.768737\pi$
$487$	−265.870	+	153.500i	−0.545934	+	0.315195i	0.201547	+	0.979479i	$0.435403\pi$
$488$		0			0
$489$	−95.0000			−0.194274
$490$		0			0
$491$			22.0000i			0.0448065i	0.999749	+	0.0224033i	$0.00713178\pi$
$491$			22.0000i			0.0448065i	−0.999749	+	0.0224033i	$0.992868\pi$
$492$		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	0.993636	+	0.112639i	$0.0359305\pi$
$499$	792.413	+	457.500i	1.58800	+	0.916834i	0.594367	+	0.804194i	$0.297403\pi$
$500$		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	$-0.855552\pi$
$509$	−35.5000	+	61.4878i	−0.0697446	+	0.120801i	0.829044	+	0.559183i	$0.188885\pi$
$510$		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	−0.976567	−	0.215214i	$-0.930955\pi$
$521$	−351.500	−	608.816i	−0.674664	−	1.16855i	0.301903	−	0.953339i	$-0.402378\pi$
$522$		0			0
$523$	281.458	+	162.500i	0.538161	+	0.310707i	0.744333	−	0.667808i	$-0.232767\pi$
$523$	281.458	+	162.500i	0.538161	+	0.310707i	−0.206172	+	0.978516i	$0.566101\pi$
$524$		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	$-0.754573\pi$
$541$	132.500	−	229.497i	0.244917	−	0.424208i	0.962108	+	0.272668i	$0.0879060\pi$
$542$		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	$-0.960913\pi$
$547$		−	134.000i		−	0.244973i	0.992470	−	0.122486i	$-0.0390868\pi$
$548$		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	−0.999824	−	0.0187592i	$-0.994028\pi$
$557$	−287.500	−	497.965i	−0.516158	−	0.894012i	0.483666	−	0.875253i	$-0.339305\pi$
$558$		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	−0.632708	−	0.774390i	$-0.718057\pi$
$563$	−156.751	+	90.5000i	−0.278420	+	0.160746i	0.354288	+	0.935136i	$0.384723\pi$
$564$		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	−0.971463	−	0.237193i	$-0.923773\pi$
$569$	−159.500	+	276.262i	−0.280316	+	0.485522i	0.691146	+	0.722715i	$0.257106\pi$
$570$		0			0
$571$	−141.162	+	81.5000i	−0.247219	+	0.142732i	−0.618490	−	0.785792i	$-0.712255\pi$
$571$	−141.162	+	81.5000i	−0.247219	+	0.142732i	0.371271	+	0.928525i	$0.378922\pi$
$572$		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	−0.988914	−	0.148486i	$-0.952560\pi$
$577$	−359.500	−	622.672i	−0.623050	−	1.07915i	0.365864	−	0.930668i	$-0.380773\pi$
$578$		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	$0.0811309\pi$
$587$			296.000i			0.504259i	−0.967694	+	0.252129i	$0.918869\pi$
$588$		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	−0.977124	−	0.212670i	$-0.931784\pi$
$593$	−180.500	+	312.635i	−0.304384	+	0.527209i	0.672740	+	0.739879i	$0.265117\pi$
$594$		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	$-0.633393\pi$
$599$	108.253	−	62.5000i	0.180723	−	0.104341i	0.587632	+	0.809128i	$0.300060\pi$
$600$		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	$-0.223397\pi$
$607$	355.936	+	205.500i	0.586386	+	0.338550i	−0.177281	+	0.984160i	$0.556730\pi$
$608$		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	−0.883457	−	0.468511i	$-0.844791\pi$
$613$	−519.500	−	899.800i	−0.847471	−	1.46786i	0.0359860	−	0.999352i	$-0.488543\pi$
$614$		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	−0.0148597	−	0.999890i	$-0.504730\pi$
$619$	522.213	−	301.500i	0.843640	−	0.487076i	0.858500	+	0.512814i	$0.171397\pi$
$620$		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	0.501558	−	0.865124i	$-0.332760\pi$
$641$	−319.500	−	553.390i	−0.498440	−	0.863323i	−0.999998	+	0.00180047i	$0.999427\pi$
$642$		0			0
$643$		−	664.000i		−	1.03266i	−0.856390	−	0.516330i	$-0.827298\pi$
$643$		−	664.000i		−	1.03266i	0.856390	−	0.516330i	$-0.172702\pi$
$644$		0			0
$645$	1800.00			2.79070
$646$		0			0
$647$	1092.06	−	630.500i	1.68788	−	0.974498i	0.731741	−	0.681583i	$-0.238708\pi$
$647$	1092.06	−	630.500i	1.68788	−	0.974498i	0.956139	−	0.292915i	$-0.0946252\pi$
$648$		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	$-0.983358\pi$
$653$	−296.500	+	513.553i	−0.454058	+	0.786452i	0.544575	+	0.838712i	$0.316691\pi$
$654$		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	$0.359682\pi$
$659$			1192.00i			1.80880i	−0.426684	+	0.904401i	$0.640318\pi$
$660$		0			0
$661$	−236.500	−	409.630i	−0.357791	−	0.619713i	0.629800	−	0.776757i	$-0.283137\pi$
$661$	−236.500	−	409.630i	−0.357791	−	0.619713i	−0.987592	+	0.157045i	$0.949803\pi$
$662$		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	$-0.895557\pi$
$677$	−131.500	+	227.765i	−0.194239	+	0.336432i	0.752412	+	0.658693i	$0.228890\pi$
$678$		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	−0.848795	−	0.528722i	$-0.822672\pi$
$683$	−556.854	+	321.500i	−0.815306	+	0.470717i	0.0334888	+	0.999439i	$0.489338\pi$
$684$		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	0.419620	−	0.907700i	$-0.362163\pi$
$691$	−108.253	−	62.5000i	−0.156662	−	0.0904486i	−0.576281	+	0.817251i	$0.695497\pi$
$692$		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	$-0.487737\pi$
$701$	54.0000			0.0770328			0.0385164	+	0.999258i	$0.487737\pi$
$702$		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	−0.0999621	−	0.994991i	$-0.531872\pi$
$709$	575.500	−	996.795i	0.811707	−	1.40592i	0.911669	−	0.410926i	$-0.134795\pi$
$710$		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	$-0.423751\pi$
$719$	−349.008	−	201.500i	−0.485408	−	0.280250i	−0.722667	+	0.691196i	$0.757084\pi$
$720$		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	$-0.868362\pi$
$733$	−80.5000	+	139.430i	−0.109823	+	0.190218i	0.805876	+	0.592085i	$0.201695\pi$
$734$		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	−0.785008	−	0.619485i	$-0.787341\pi$
$739$	−473.716	+	273.500i	−0.641023	+	0.370095i	0.143986	+	0.989580i	$0.454008\pi$
$740$		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	$-0.0619413\pi$
$751$	979.475	+	565.500i	1.30423	+	0.752996i	0.323101	+	0.946364i	$0.395275\pi$
$752$		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	$-0.428765\pi$
$757$	336.000			0.443857			0.221929	+	0.975063i	$0.428765\pi$
$758$		0			0
$759$	−246.817	+	142.500i	−0.325187	+	0.187747i
$760$		0			0
$761$	−172.500	+	298.779i	−0.226675	+	0.392613i	−0.956821	−	0.290678i	$-0.906119\pi$
$761$	−172.500	+	298.779i	−0.226675	+	0.392613i	0.730145	+	0.683292i	$0.239452\pi$
$762$		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	$-0.284429\pi$
$773$	−279.500	−	484.108i	−0.361578	−	0.626272i	−0.988221	+	0.153035i	$0.951095\pi$
$774$		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	−0.817460	−	0.575985i	$-0.804619\pi$
$787$	−572.443	+	330.500i	−0.727373	+	0.419949i	0.0900872	+	0.995934i	$0.471285\pi$
$788$		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	$-0.347228\pi$
$797$	736.000			0.923463			0.461731	+	0.887020i	$0.347228\pi$
$798$		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	0.763603	−	0.645686i	$-0.223429\pi$
$809$	−143.500	−	248.549i	−0.177379	−	0.307230i	−0.940982	+	0.338456i	$0.890095\pi$
$810$		0			0
$811$			1272.00i			1.56843i	0.620487	+	0.784217i	$0.286935\pi$
$811$			1272.00i			1.56843i	−0.620487	+	0.784217i	$0.713065\pi$
$812$		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	$-0.982800\pi$
$821$	−371.500	+	643.457i	−0.452497	+	0.783748i	0.546043	+	0.837757i	$0.316133\pi$
$822$		0			0
$823$	−196.588	+	113.500i	−0.238867	+	0.137910i	−0.614656	−	0.788795i	$-0.710705\pi$
$823$	−196.588	+	113.500i	−0.238867	+	0.137910i	0.375789	+	0.926705i	$0.377372\pi$
$824$		0			0
$825$	−840.000			−1.01818
$826$		0			0
$827$			120.000i			0.145103i	0.997365	+	0.0725514i	$0.0231141\pi$
$827$			120.000i			0.145103i	−0.997365	+	0.0725514i	$0.976886\pi$
$828$		0			0
$829$	120.500	+	208.712i	0.145356	+	0.251764i	0.929506	−	0.368808i	$-0.120234\pi$
$829$	120.500	+	208.712i	0.145356	+	0.251764i	−0.784150	+	0.620572i	$0.786901\pi$
$830$		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	$-0.532897\pi$
$853$	−176.000			−0.206331			−0.103165	+	0.994664i	$0.532897\pi$
$854$		0			0
$855$			1584.00i			1.85263i
$856$		0			0
$857$	−127.500	−	220.836i	−0.148775	−	0.257686i	0.782000	−	0.623278i	$-0.214200\pi$
$857$	−127.500	−	220.836i	−0.148775	−	0.257686i	−0.930775	+	0.365593i	$0.880866\pi$
$858$		0			0
$859$	558.586	+	322.500i	0.650275	+	0.375437i	0.788562	−	0.614956i	$-0.210826\pi$
$859$	558.586	+	322.500i	0.650275	+	0.375437i	−0.138286	+	0.990392i	$0.544159\pi$
$860$		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	$-0.494069\pi$
$863$	−723.131	−	417.500i	−0.837927	−	0.483778i	−0.856559	+	0.516049i	$0.827402\pi$
$864$		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	0.331068	+	0.943607i	$0.392591\pi$
$877$	−571.500	+	989.867i	−0.651653	+	1.12870i	−0.982722	+	0.185090i	$0.940742\pi$
$878$		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	$-0.731277\pi$
$883$		−	1320.00i		−	1.49490i	0.664316	−	0.747452i	$-0.268723\pi$
$884$		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	$-0.537404\pi$
$887$	−918.853	−	530.500i	−1.03591	−	0.598083i	−0.918672	+	0.395020i	$0.870738\pi$
$888$		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	−0.0101550	−	0.999948i	$-0.503232\pi$
$907$	771.629	−	445.500i	0.850748	−	0.491180i	0.860903	+	0.508769i	$0.169899\pi$
$908$		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	$-0.621278\pi$
$919$	−1251.41	−	722.500i	−1.36170	−	0.786181i	−0.989851	+	0.142111i	$0.954611\pi$
$920$		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	−0.00862789	−	0.999963i	$-0.502746\pi$
$929$	800.500	−	1386.51i	0.861679	−	1.49247i	0.870307	−	0.492509i	$-0.163920\pi$
$930$		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	−0.999630	−	0.0272100i	$-0.991338\pi$
$941$	−492.500	−	853.035i	−0.523379	−	0.906520i	0.476250	−	0.879310i	$-0.341996\pi$
$942$		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	0.640366	−	0.768070i	$-0.278783\pi$
$947$	279.726	+	161.500i	0.295381	+	0.170539i	−0.344985	+	0.938608i	$0.612116\pi$
$948$		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	−0.960857	−	0.277044i	$-0.910645\pi$
$971$	−1632.46	−	942.500i	−1.68121	−	0.970649i	−0.720356	−	0.693605i	$-0.756022\pi$
$972$		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	0.859557	−	0.511039i	$-0.170739\pi$
$977$	−12.5000	−	21.6506i	−0.0127943	−	0.0221603i	−0.872352	+	0.488879i	$0.837406\pi$
$978$		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	$-0.680433\pi$
$983$	−73.6122	+	42.5000i	−0.0748852	+	0.0432350i	0.462090	+	0.886833i	$0.347100\pi$
$984$		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	$-0.641426\pi$
$991$	135.966	−	78.5000i	0.137201	−	0.0792129i	0.567029	+	0.823698i	$0.308093\pi$
$992$		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	$-0.214255\pi$
$997$	−148.500	−	257.210i	−0.148947	−	0.257983i	−0.930838	+	0.365431i	$0.880922\pi$
$998$		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	448.3.r.c.191.1		4
4.3	odd	2	inner	448.3.r.c.191.2		4
7.4	even	3	inner	448.3.r.c.319.2		4
8.3	odd	2		224.3.r.a.191.1	yes	4
8.5	even	2		224.3.r.a.191.2	yes	4
28.11	odd	6	inner	448.3.r.c.319.1		4
56.5	odd	6		1568.3.d.a.1471.1		2
56.11	odd	6		224.3.r.a.95.2	yes	4
56.19	even	6		1568.3.d.a.1471.2		2
56.37	even	6		1568.3.d.e.1471.2		2
56.51	odd	6		1568.3.d.e.1471.1		2
56.53	even	6		224.3.r.a.95.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.r.a.95.1	✓	4	56.53	even	6
224.3.r.a.95.2	yes	4	56.11	odd	6
224.3.r.a.191.1	yes	4	8.3	odd	2
224.3.r.a.191.2	yes	4	8.5	even	2
448.3.r.c.191.1		4	1.1	even	1	trivial
448.3.r.c.191.2		4	4.3	odd	2	inner
448.3.r.c.319.1		4	28.11	odd	6	inner
448.3.r.c.319.2		4	7.4	even	3	inner
1568.3.d.a.1471.1		2	56.5	odd	6
1568.3.d.a.1471.2		2	56.19	even	6
1568.3.d.e.1471.1		2	56.51	odd	6
1568.3.d.e.1471.2		2	56.37	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.r (of order \(6\), degree \(2\), not 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

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Representations

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Database

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