LMFDB - Embedded newform 714.2.ba.e.667.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [714,2,Mod(319,714)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(714, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 8, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("714.319");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 714 = 2 \cdot 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	714.ba (of order $12$, degree $4$, 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:	$5.70131870432$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			667.4
Character	$\chi$	$=$	714.667
Dual form			714.2.ba.e.319.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.107206 - 0.400100i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.44445 - 1.01225i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.107206 - 0.400100i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.44445 - 1.01225i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.107206 + 0.400100i) q^{10} +(-1.02138 + 3.81183i) q^{11} +(0.258819 + 0.965926i) q^{12} +3.53208 q^{13} +(1.61083 + 2.09886i) q^{14} -0.414214i q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.83120 - 1.52378i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.65659 + 2.11113i) q^{19} +(0.292893 - 0.292893i) q^{20} +(-2.09917 - 1.61043i) q^{21} +(2.79045 - 2.79045i) q^{22} +(0.214695 - 0.0575273i) q^{23} +(0.258819 - 0.965926i) q^{24} +(4.18154 - 2.41421i) q^{25} +(-3.05888 - 1.76604i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.345588 - 2.62308i) q^{28} +(0.292893 - 0.292893i) q^{29} +(-0.207107 + 0.358719i) q^{30} +(9.44602 + 2.53105i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.97315 + 3.41759i) q^{33} +(-4.07981 - 0.595973i) q^{34} +(-0.142942 + 1.08654i) q^{35} +1.00000i q^{36} +(-2.15535 - 8.04387i) q^{37} +(-2.11113 - 3.65659i) q^{38} +(3.41173 + 0.914171i) q^{39} +(-0.400100 + 0.107206i) q^{40} +(0.965476 + 0.965476i) q^{41} +(1.01272 + 2.44426i) q^{42} +2.16670i q^{43} +(-3.81183 + 1.02138i) q^{44} +(0.107206 - 0.400100i) q^{45} +(-0.214695 - 0.0575273i) q^{46} +(-3.11161 + 5.38947i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(4.95068 + 4.94881i) q^{49} -4.82843 q^{50} +(4.09504 - 0.480266i) q^{51} +(1.76604 + 3.05888i) q^{52} +(-4.45538 + 2.57232i) q^{53} +(-0.258819 - 0.965926i) q^{54} +1.63461 q^{55} +(-1.01225 + 2.44445i) q^{56} +(2.98559 + 2.98559i) q^{57} +(-0.400100 + 0.107206i) q^{58} +(-11.4009 + 6.58232i) q^{59} +(0.358719 - 0.207107i) q^{60} +(14.0868 - 3.77455i) q^{61} +(-6.91497 - 6.91497i) q^{62} +(-1.61083 - 2.09886i) q^{63} -1.00000 q^{64} +(-0.378662 - 1.41319i) q^{65} +(3.41759 - 1.97315i) q^{66} +(4.01338 + 6.95138i) q^{67} +(3.23523 + 2.55603i) q^{68} +0.222269 q^{69} +(0.667063 - 0.869504i) q^{70} +(10.8348 - 10.8348i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-16.1340 - 4.32308i) q^{73} +(-2.15535 + 8.04387i) q^{74} +(4.66390 - 1.24969i) q^{75} +4.22227i q^{76} +(6.35525 - 8.28394i) q^{77} +(-2.49756 - 2.49756i) q^{78} +(8.18084 - 2.19205i) q^{79} +(0.400100 + 0.107206i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.353389 - 1.31887i) q^{82} -7.17440i q^{83} +(0.345092 - 2.62315i) q^{84} +(-1.02039 - 1.36950i) q^{85} +(1.08335 - 1.87641i) q^{86} +(0.358719 - 0.207107i) q^{87} +(3.81183 + 1.02138i) q^{88} +(-7.12903 + 12.3479i) q^{89} +(-0.292893 + 0.292893i) q^{90} +(-8.63401 - 3.57537i) q^{91} +(0.157168 + 0.157168i) q^{92} +(8.46907 + 4.88962i) q^{93} +(5.38947 - 3.11161i) q^{94} +(0.452654 - 1.68933i) q^{95} +(0.965926 - 0.258819i) q^{96} +(0.637806 - 0.637806i) q^{97} +(-1.81301 - 6.76114i) q^{98} +(-2.79045 + 2.79045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 12 q^{5} - 8 q^{7}+O(q^{10}) $ 24 * q + 12 * q^4 + 12 * q^5 - 8 * q^7	$ 24 q + 12 q^{4} + 12 q^{5} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 8 q^{13} - 4 q^{14} - 12 q^{16} + 20 q^{17} - 12 q^{18} + 24 q^{20} - 4 q^{21} + 16 q^{22} - 4 q^{28} + 24 q^{29} + 12 q^{30} - 4 q^{31} + 8 q^{33} + 8 q^{34} - 4 q^{35} + 20 q^{37} - 8 q^{38} - 4 q^{39} - 12 q^{40} + 32 q^{41} - 8 q^{44} - 12 q^{45} - 12 q^{47} - 48 q^{50} - 4 q^{51} + 4 q^{52} + 48 q^{55} - 8 q^{56} - 12 q^{58} + 24 q^{61} + 8 q^{62} + 4 q^{63} - 24 q^{64} + 8 q^{65} + 16 q^{67} - 20 q^{68} - 80 q^{69} + 48 q^{71} + 12 q^{72} - 32 q^{73} + 20 q^{74} + 24 q^{75} + 8 q^{78} + 12 q^{80} + 12 q^{81} + 16 q^{82} + 4 q^{84} + 40 q^{85} - 8 q^{86} + 8 q^{88} - 32 q^{89} - 24 q^{90} + 72 q^{91} - 8 q^{95} - 48 q^{97} + 20 q^{98} - 16 q^{99}+O(q^{100}) $ 24 * q + 12 * q^4 + 12 * q^5 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 8 * q^13 - 4 * q^14 - 12 * q^16 + 20 * q^17 - 12 * q^18 + 24 * q^20 - 4 * q^21 + 16 * q^22 - 4 * q^28 + 24 * q^29 + 12 * q^30 - 4 * q^31 + 8 * q^33 + 8 * q^34 - 4 * q^35 + 20 * q^37 - 8 * q^38 - 4 * q^39 - 12 * q^40 + 32 * q^41 - 8 * q^44 - 12 * q^45 - 12 * q^47 - 48 * q^50 - 4 * q^51 + 4 * q^52 + 48 * q^55 - 8 * q^56 - 12 * q^58 + 24 * q^61 + 8 * q^62 + 4 * q^63 - 24 * q^64 + 8 * q^65 + 16 * q^67 - 20 * q^68 - 80 * q^69 + 48 * q^71 + 12 * q^72 - 32 * q^73 + 20 * q^74 + 24 * q^75 + 8 * q^78 + 12 * q^80 + 12 * q^81 + 16 * q^82 + 4 * q^84 + 40 * q^85 - 8 * q^86 + 8 * q^88 - 32 * q^89 - 24 * q^90 + 72 * q^91 - 8 * q^95 - 48 * q^97 + 20 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.107206	−	0.400100i	−0.0479441	−	0.178930i	0.937802	−	0.347171i	$-0.112858\pi$
$5$	−0.107206	−	0.400100i	−0.0479441	−	0.178930i	−0.985746	+	0.168242i	$0.946191\pi$
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	−2.44445	−	1.01225i	−0.923916	−	0.382596i
$7$	−2.44445	−	1.01225i	−0.923916	−	0.382596i
$8$		−	1.00000i		−	0.353553i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	−0.107206	+	0.400100i	−0.0339016	+	0.126523i
$11$	−1.02138	+	3.81183i	−0.307957	+	1.14931i	0.622413	+	0.782689i	$0.286152\pi$
$11$	−1.02138	+	3.81183i	−0.307957	+	1.14931i	−0.930370	+	0.366622i	$0.880514\pi$
$12$	0.258819	+	0.965926i	0.0747146	+	0.278839i
$13$	3.53208			0.979624			0.489812	−	0.871828i	$-0.337065\pi$
$13$	3.53208			0.979624			0.489812	+	0.871828i	$0.337065\pi$
$14$	1.61083	+	2.09886i	0.430512	+	0.560945i
$15$		−	0.414214i		−	0.106949i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.83120	−	1.52378i	0.929203	−	0.369570i
$17$	3.83120	−	1.52378i	0.929203	−	0.369570i
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	3.65659	+	2.11113i	0.838880	+	0.484327i	0.856883	−	0.515511i	$-0.172398\pi$
$19$	3.65659	+	2.11113i	0.838880	+	0.484327i	−0.0180036	+	0.999838i	$0.505731\pi$
$20$	0.292893	−	0.292893i	0.0654929	−	0.0654929i
$21$	−2.09917	−	1.61043i	−0.458076	−	0.351425i
$22$	2.79045	−	2.79045i	0.594927	−	0.594927i
$23$	0.214695	−	0.0575273i	0.0447670	−	0.0119953i	−0.236366	−	0.971664i	$-0.575956\pi$
$23$	0.214695	−	0.0575273i	0.0447670	−	0.0119953i	0.281133	+	0.959669i	$0.409290\pi$
$24$	0.258819	−	0.965926i	0.0528312	−	0.197169i
$25$	4.18154	−	2.41421i	0.836308	−	0.482843i
$26$	−3.05888	−	1.76604i	−0.599895	−	0.346349i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.345588	−	2.62308i	−0.0653100	−	0.495716i
$29$	0.292893	−	0.292893i	0.0543889	−	0.0543889i	−0.679389	−	0.733778i	$-0.737755\pi$
$29$	0.292893	−	0.292893i	0.0543889	−	0.0543889i	0.733778	+	0.679389i	$0.237755\pi$
$30$	−0.207107	+	0.358719i	−0.0378124	+	0.0654929i
$31$	9.44602	+	2.53105i	1.69656	+	0.454591i	0.972069	−	0.234697i	$-0.0754098\pi$
$31$	9.44602	+	2.53105i	1.69656	+	0.454591i	0.724488	+	0.689288i	$0.242076\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.97315	+	3.41759i	−0.343481	+	0.594927i
$34$	−4.07981	−	0.595973i	−0.699681	−	0.102208i
$35$	−0.142942	+	1.08654i	−0.0241616	+	0.183659i
$36$			1.00000i			0.166667i
$37$	−2.15535	−	8.04387i	−0.354337	−	1.32240i	−0.881317	−	0.472526i	$-0.843342\pi$
$37$	−2.15535	−	8.04387i	−0.354337	−	1.32240i	0.526980	−	0.849878i	$-0.323324\pi$
$38$	−2.11113	−	3.65659i	−0.342471	−	0.593178i
$39$	3.41173	+	0.914171i	0.546314	+	0.146384i
$40$	−0.400100	+	0.107206i	−0.0632613	+	0.0169508i
$41$	0.965476	+	0.965476i	0.150782	+	0.150782i	0.778467	−	0.627685i	$-0.215997\pi$
$41$	0.965476	+	0.965476i	0.150782	+	0.150782i	−0.627685	+	0.778467i	$0.715997\pi$
$42$	1.01272	+	2.44426i	0.156266	+	0.377157i
$43$			2.16670i			0.330418i	0.986259	+	0.165209i	$0.0528299\pi$
$43$			2.16670i			0.330418i	−0.986259	+	0.165209i	$0.947170\pi$
$44$	−3.81183	+	1.02138i	−0.574655	+	0.153978i
$45$	0.107206	−	0.400100i	0.0159814	−	0.0596433i
$46$	−0.214695	−	0.0575273i	−0.0316550	−	0.00848194i
$47$	−3.11161	+	5.38947i	−0.453875	+	0.786135i	−0.998623	−	0.0524649i	$-0.983292\pi$
$47$	−3.11161	+	5.38947i	−0.453875	+	0.786135i	0.544747	+	0.838600i	$0.316626\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$	4.95068	+	4.94881i	0.707240	+	0.706973i
$50$	−4.82843			−0.682843
$51$	4.09504	−	0.480266i	0.573420	−	0.0672507i
$52$	1.76604	+	3.05888i	0.244906	+	0.424190i
$53$	−4.45538	+	2.57232i	−0.611994	+	0.353335i	−0.773745	−	0.633497i	$-0.781619\pi$
$53$	−4.45538	+	2.57232i	−0.611994	+	0.353335i	0.161751	+	0.986832i	$0.448286\pi$
$54$	−0.258819	−	0.965926i	−0.0352208	−	0.131446i
$55$	1.63461			0.220411
$56$	−1.01225	+	2.44445i	−0.135268	+	0.326654i
$57$	2.98559	+	2.98559i	0.395452	+	0.395452i
$58$	−0.400100	+	0.107206i	−0.0525356	+	0.0140769i
$59$	−11.4009	+	6.58232i	−1.48427	+	0.856946i	−0.999840	−	0.0178827i	$-0.994307\pi$
$59$	−11.4009	+	6.58232i	−1.48427	+	0.856946i	−0.484433	+	0.874828i	$0.660974\pi$
$60$	0.358719	−	0.207107i	0.0463105	−	0.0267374i
$61$	14.0868	−	3.77455i	1.80363	−	0.483282i	0.809095	−	0.587677i	$-0.199958\pi$
$61$	14.0868	−	3.77455i	1.80363	−	0.483282i	0.994536	+	0.104396i	$0.0332909\pi$
$62$	−6.91497	−	6.91497i	−0.878202	−	0.878202i
$63$	−1.61083	−	2.09886i	−0.202945	−	0.264432i
$64$	−1.00000			−0.125000
$65$	−0.378662	−	1.41319i	−0.0469672	−	0.175284i
$66$	3.41759	−	1.97315i	0.420677	−	0.242878i
$67$	4.01338	+	6.95138i	0.490313	+	0.849246i	0.999938	−	0.0111502i	$-0.00354928\pi$
$67$	4.01338	+	6.95138i	0.490313	+	0.849246i	−0.509625	+	0.860396i	$0.670216\pi$
$68$	3.23523	+	2.55603i	0.392329	+	0.309964i
$69$	0.222269			0.0267580
$70$	0.667063	−	0.869504i	0.0797293	−	0.103926i
$71$	10.8348	−	10.8348i	1.28586	−	1.28586i	0.348576	−	0.937281i	$-0.386665\pi$
$71$	10.8348	−	10.8348i	1.28586	−	1.28586i	0.937281	−	0.348576i	$-0.113335\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−16.1340	−	4.32308i	−1.88834	−	0.505979i	−0.998792	−	0.0491331i	$-0.984354\pi$
$73$	−16.1340	−	4.32308i	−1.88834	−	0.505979i	−0.889546	−	0.456846i	$-0.848979\pi$
$74$	−2.15535	+	8.04387i	−0.250554	+	0.935081i
$75$	4.66390	−	1.24969i	0.538541	−	0.144302i
$76$			4.22227i			0.484327i
$77$	6.35525	−	8.28394i	0.724248	−	0.944043i
$78$	−2.49756	−	2.49756i	−0.282793	−	0.282793i
$79$	8.18084	−	2.19205i	0.920416	−	0.246625i	0.232653	−	0.972560i	$-0.425259\pi$
$79$	8.18084	−	2.19205i	0.920416	−	0.246625i	0.687763	+	0.725935i	$0.258593\pi$
$80$	0.400100	+	0.107206i	0.0447325	+	0.0119860i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−0.353389	−	1.31887i	−0.0390253	−	0.145644i
$83$		−	7.17440i		−	0.787493i	−0.919219	−	0.393747i	$-0.871179\pi$
$83$		−	7.17440i		−	0.787493i	0.919219	−	0.393747i	$-0.128821\pi$
$84$	0.345092	−	2.62315i	0.0376526	−	0.286209i
$85$	−1.02039	−	1.36950i	−0.110677	−	0.148544i
$86$	1.08335	−	1.87641i	0.116820	−	0.202339i
$87$	0.358719	−	0.207107i	0.0384588	−	0.0222042i
$88$	3.81183	+	1.02138i	0.406343	+	0.108879i
$89$	−7.12903	+	12.3479i	−0.755676	+	1.30887i	0.189361	+	0.981907i	$0.439358\pi$
$89$	−7.12903	+	12.3479i	−0.755676	+	1.30887i	−0.945037	+	0.326962i	$0.893975\pi$
$90$	−0.292893	+	0.292893i	−0.0308737	+	0.0308737i
$91$	−8.63401	−	3.57537i	−0.905090	−	0.374800i
$92$	0.157168	+	0.157168i	0.0163859	+	0.0163859i
$93$	8.46907	+	4.88962i	0.878202	+	0.507030i
$94$	5.38947	−	3.11161i	0.555882	−	0.320938i
$95$	0.452654	−	1.68933i	0.0464413	−	0.173321i
$96$	0.965926	−	0.258819i	0.0985844	−	0.0264156i
$97$	0.637806	−	0.637806i	0.0647594	−	0.0647594i	−0.673985	−	0.738745i	$-0.735419\pi$
$97$	0.637806	−	0.637806i	0.0647594	−	0.0647594i	0.738745	+	0.673985i	$0.235419\pi$
$98$	−1.81301	−	6.76114i	−0.183142	−	0.682978i
$99$	−2.79045	+	2.79045i	−0.280451	+	0.280451i
$100$	4.18154	+	2.41421i	0.418154	+	0.241421i
$101$	−3.95427	−	6.84899i	−0.393464	−	0.681500i	0.599440	−	0.800420i	$-0.295390\pi$
$101$	−3.95427	−	6.84899i	−0.393464	−	0.681500i	−0.992904	+	0.118920i	$0.962057\pi$
$102$	−3.78654	−	1.63160i	−0.374923	−	0.161552i
$103$	0.906062	−	1.56934i	0.0892769	−	0.154632i	−0.817929	−	0.575319i	$-0.804878\pi$
$103$	0.906062	−	1.56934i	0.0892769	−	0.154632i	0.907206	+	0.420687i	$0.138211\pi$
$104$		−	3.53208i		−	0.346349i
$105$	−0.419289	+	1.01252i	−0.0409185	+	0.0988123i
$106$	5.14463			0.499691
$107$	−5.30281	−	19.7904i	−0.512642	−	1.91321i	−0.390200	−	0.920730i	$-0.627594\pi$
$107$	−5.30281	−	19.7904i	−0.512642	−	1.91321i	−0.122442	−	0.992476i	$-0.539073\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	−1.53342	+	5.72280i	−0.146875	+	0.548145i	0.852790	+	0.522254i	$0.174909\pi$
$109$	−1.53342	+	5.72280i	−0.146875	+	0.548145i	−0.999665	+	0.0258906i	$0.991758\pi$
$110$	−1.41561	−	0.817305i	−0.134974	−	0.0779270i
$111$		−	8.32762i		−	0.790423i
$112$	2.09886	−	1.61083i	0.198324	−	0.152209i
$113$	8.50992	+	8.50992i	0.800546	+	0.800546i	0.983181	−	0.182635i	$-0.0584627\pi$
$113$	8.50992	+	8.50992i	0.800546	+	0.800546i	−0.182635	+	0.983181i	$0.558463\pi$
$114$	−1.09280	−	4.07840i	−0.102350	−	0.381977i
$115$	−0.0460333	−	0.0797321i	−0.00429263	−	0.00743505i
$116$	0.400100	+	0.107206i	0.0371483	+	0.00995386i
$117$	3.05888	+	1.76604i	0.282793	+	0.163271i
$118$	13.1646			1.21190
$119$	−10.9076	−	0.153355i	−0.999901	−	0.0140580i
$120$	−0.414214			−0.0378124
$121$	−3.96057	−	2.28664i	−0.360052	−	0.207876i
$122$	−14.0868	−	3.77455i	−1.27536	−	0.341732i
$123$	0.682695	+	1.18246i	0.0615565	+	0.106619i
$124$	2.53105	+	9.44602i	0.227295	+	0.848278i
$125$	−2.87868	−	2.87868i	−0.257477	−	0.257477i
$126$	0.345588	+	2.62308i	0.0307874	+	0.233683i
$127$			17.0073i			1.50916i	0.656209	+	0.754579i	$0.272159\pi$
$127$			17.0073i			1.50916i	−0.656209	+	0.754579i	$0.727841\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−0.560782	+	2.09287i	−0.0493741	+	0.184267i
$130$	−0.378662	+	1.41319i	−0.0332109	+	0.123945i
$131$	2.09448	+	7.81669i	0.182995	+	0.682948i	0.995051	+	0.0993675i	$0.0316819\pi$
$131$	2.09448	+	7.81669i	0.182995	+	0.682948i	−0.812056	+	0.583580i	$0.801651\pi$
$132$	−3.94630			−0.343481
$133$	−6.80136	−	8.86196i	−0.589752	−	0.768430i
$134$		−	8.02676i		−	0.693407i
$135$	0.207107	−	0.358719i	0.0178249	−	0.0308737i
$136$	−1.52378	−	3.83120i	−0.130663	−	0.328523i
$137$	2.39096	+	4.14126i	0.204273	+	0.353812i	0.949901	−	0.312551i	$-0.101184\pi$
$137$	2.39096	+	4.14126i	0.204273	+	0.353812i	−0.745628	+	0.666363i	$0.767850\pi$
$138$	−0.192490	−	0.111134i	−0.0163859	−	0.00946038i
$139$	0.387144	−	0.387144i	0.0328371	−	0.0328371i	−0.690498	−	0.723335i	$-0.742608\pi$
$139$	0.387144	−	0.387144i	0.0328371	−	0.0328371i	0.723335	+	0.690498i	$0.242608\pi$
$140$	−1.01245	+	0.419481i	−0.0855673	+	0.0354526i
$141$	−4.40049	+	4.40049i	−0.370588	+	0.370588i
$142$	−14.8006	+	3.96582i	−1.24204	+	0.332804i
$143$	−3.60759	+	13.4637i	−0.301682	+	1.12589i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	−0.148586	−	0.0857864i	−0.0123394	−	0.00712418i
$146$	11.8109	+	11.8109i	0.977476	+	0.977476i
$147$	3.50115	+	6.06152i	0.288770	+	0.499945i
$148$	5.88852	−	5.88852i	0.484033	−	0.484033i
$149$	−4.82498	+	8.35711i	−0.395278	+	0.684641i	−0.993137	−	0.116960i	$-0.962685\pi$
$149$	−4.82498	+	8.35711i	−0.395278	+	0.684641i	0.597859	+	0.801601i	$0.296018\pi$
$150$	−4.66390	−	1.24969i	−0.380806	−	0.102037i
$151$	−19.6913	+	11.3688i	−1.60245	+	0.925176i	−0.611457	+	0.791277i	$0.709416\pi$
$151$	−19.6913	+	11.3688i	−1.60245	+	0.925176i	−0.990995	+	0.133899i	$0.957250\pi$
$152$	2.11113	−	3.65659i	0.171236	−	0.296589i
$153$	4.07981	+	0.595973i	0.329833	+	0.0481815i
$154$	−9.64578	+	3.99648i	−0.777279	+	0.322046i
$155$		−	4.05070i		−	0.325360i
$156$	0.914171	+	3.41173i	0.0731922	+	0.273157i
$157$	−9.04705	−	15.6699i	−0.722033	−	1.25060i	−0.960184	−	0.279370i	$-0.909875\pi$
$157$	−9.04705	−	15.6699i	−0.722033	−	1.25060i	0.238151	−	0.971228i	$-0.423459\pi$
$158$	−8.18084	−	2.19205i	−0.650833	−	0.174390i
$159$	−4.96933	+	1.33153i	−0.394094	+	0.105597i
$160$	−0.292893	−	0.292893i	−0.0231552	−	0.0231552i
$161$	−0.583044	−	0.0767031i	−0.0459503	−	0.00604505i
$162$		−	1.00000i		−	0.0785674i
$163$	5.12297	−	1.37270i	0.401262	−	0.107518i	−0.0525433	−	0.998619i	$-0.516733\pi$
$163$	5.12297	−	1.37270i	0.401262	−	0.107518i	0.453805	+	0.891101i	$0.350066\pi$
$164$	−0.353389	+	1.31887i	−0.0275950	+	0.102986i
$165$	1.57891	+	0.423068i	0.122918	+	0.0329358i
$166$	−3.58720	+	6.21322i	−0.278421	+	0.482239i
$167$	2.53792	−	2.53792i	0.196390	−	0.196390i	−0.602060	−	0.798451i	$-0.705653\pi$
$167$	2.53792	−	2.53792i	0.196390	−	0.196390i	0.798451	+	0.602060i	$0.205653\pi$
$168$	−1.61043	+	2.09917i	−0.124248	+	0.161954i
$169$	−0.524377			−0.0403367
$170$	0.198933	+	1.69622i	0.0152574	+	0.130094i
$171$	2.11113	+	3.65659i	0.161442	+	0.279627i
$172$	−1.87641	+	1.08335i	−0.143075	+	0.0826045i
$173$	−3.32563	−	12.4114i	−0.252843	−	0.943623i	−0.969278	−	0.245969i	$-0.920894\pi$
$173$	−3.32563	−	12.4114i	−0.252843	−	0.943623i	0.716435	−	0.697654i	$-0.245773\pi$
$174$	−0.414214			−0.0314014
$175$	−12.6654	+	1.66865i	−0.957412	+	0.126138i
$176$	−2.79045	−	2.79045i	−0.210338	−	0.210338i
$177$	−12.7161	+	3.40726i	−0.955799	+	0.256105i
$178$	12.3479	−	7.12903i	0.925511	−	0.534344i
$179$	−7.54125	+	4.35394i	−0.563659	+	0.325429i	−0.754613	−	0.656170i	$-0.772175\pi$
$179$	−7.54125	+	4.35394i	−0.563659	+	0.325429i	0.190954	+	0.981599i	$0.438842\pi$
$180$	0.400100	−	0.107206i	0.0298217	−	0.00799069i
$181$	−15.7365	−	15.7365i	−1.16969	−	1.16969i	−0.982283	−	0.187403i	$-0.939993\pi$
$181$	−15.7365	−	15.7365i	−1.16969	−	1.16969i	−0.187403	−	0.982283i	$-0.560007\pi$
$182$	5.68959	+	7.41336i	0.421740	+	0.549515i
$183$	14.5837			1.07806
$184$	−0.0575273	−	0.214695i	−0.00424097	−	0.0158275i
$185$	−2.98728	+	1.72471i	−0.219629	+	0.126803i
$186$	−4.88962	−	8.46907i	−0.358524	−	0.620983i
$187$	1.89527	+	16.1602i	0.138596	+	1.18175i
$188$	−6.22323			−0.453875
$189$	−1.01272	−	2.44426i	−0.0736643	−	0.177794i
$190$	−1.23667	+	1.23667i	−0.0897177	+	0.0897177i
$191$	−3.75576	+	6.50517i	−0.271758	+	0.470698i	−0.969312	−	0.245834i	$-0.920938\pi$
$191$	−3.75576	+	6.50517i	−0.271758	+	0.470698i	0.697554	+	0.716532i	$0.254272\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	1.22721	−	4.58001i	0.0883364	−	0.329676i	−0.907589	−	0.419861i	$-0.862079\pi$
$193$	1.22721	−	4.58001i	0.0883364	−	0.329676i	0.995925	+	0.0901844i	$0.0287457\pi$
$194$	−0.871259	+	0.233453i	−0.0625527	+	0.0167610i
$195$		−	1.46304i		−	0.104770i
$196$	−1.81045	+	6.76182i	−0.129318	+	0.482987i
$197$	8.00710	+	8.00710i	0.570482	+	0.570482i	0.932263	−	0.361781i	$-0.117831\pi$
$197$	8.00710	+	8.00710i	0.570482	+	0.570482i	−0.361781	+	0.932263i	$0.617831\pi$
$198$	3.81183	−	1.02138i	0.270895	−	0.0725861i
$199$	−17.7465	−	4.75515i	−1.25801	−	0.337084i	−0.432586	−	0.901593i	$-0.642399\pi$
$199$	−17.7465	−	4.75515i	−1.25801	−	0.337084i	−0.825427	+	0.564509i	$0.809066\pi$
$200$	−2.41421	−	4.18154i	−0.170711	−	0.295680i
$201$	2.07748	+	7.75326i	0.146534	+	0.546873i
$202$			7.90853i			0.556442i
$203$	−1.01245	+	0.419481i	−0.0710597	+	0.0294418i
$204$	2.46344	+	3.30627i	0.172475	+	0.231486i
$205$	0.282781	−	0.489792i	0.0197503	−	0.0342085i
$206$	−1.56934	+	0.906062i	−0.109341	+	0.0631283i
$207$	0.214695	+	0.0575273i	0.0149223	+	0.00399843i
$208$	−1.76604	+	3.05888i	−0.122453	+	0.212095i
$209$	−11.7820	+	11.7820i	−0.814981	+	0.814981i
$210$	0.869378	−	0.667228i	0.0599928	−	0.0460431i
$211$	−8.49005	−	8.49005i	−0.584479	−	0.584479i	0.351652	−	0.936131i	$-0.385620\pi$
$211$	−8.49005	−	8.49005i	−0.584479	−	0.584479i	−0.936131	+	0.351652i	$0.885620\pi$
$212$	−4.45538	−	2.57232i	−0.305997	−	0.176667i
$213$	13.2699	−	7.66137i	0.909238	−	0.524949i
$214$	−5.30281	+	19.7904i	−0.362493	+	1.35284i
$215$	0.866894	−	0.232283i	0.0591217	−	0.0158416i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−20.5283	−	15.7488i	−1.39355	−	1.06910i
$218$	4.18938	−	4.18938i	0.283741	−	0.283741i
$219$	−14.4653	−	8.35156i	−0.977476	−	0.564346i
$220$	0.817305	+	1.41561i	0.0551027	+	0.0954407i
$221$	13.5321	−	5.38210i	0.910270	−	0.362040i
$222$	−4.16381	+	7.21193i	−0.279457	+	0.484033i
$223$		−	18.4758i		−	1.23723i	−0.785693	−	0.618616i	$-0.787694\pi$
$223$		−	18.4758i		−	1.23723i	0.785693	−	0.618616i	$-0.212306\pi$
$224$	−2.62308	+	0.345588i	−0.175262	+	0.0230906i
$225$	4.82843			0.321895
$226$	−3.11485	−	11.6248i	−0.207197	−	0.773268i
$227$	−2.80836	+	10.4809i	−0.186397	+	0.695645i	0.807930	+	0.589279i	$0.200588\pi$
$227$	−2.80836	+	10.4809i	−0.186397	+	0.695645i	−0.994327	+	0.106366i	$0.966079\pi$
$228$	−1.09280	+	4.07840i	−0.0723727	+	0.270099i
$229$	9.40287	+	5.42875i	0.621359	+	0.358742i	0.777398	−	0.629009i	$-0.216539\pi$
$229$	9.40287	+	5.42875i	0.621359	+	0.358742i	−0.156039	+	0.987751i	$0.549872\pi$
$230$			0.0920666i			0.00607070i
$231$	8.28274	−	6.35681i	0.544964	−	0.418248i
$232$	−0.292893	−	0.292893i	−0.0192294	−	0.0192294i
$233$	2.13361	+	7.96274i	0.139777	+	0.521657i	0.999932	+	0.0116238i	$0.00370006\pi$
$233$	2.13361	+	7.96274i	0.139777	+	0.521657i	−0.860155	+	0.510033i	$0.829633\pi$
$234$	−1.76604	−	3.05888i	−0.115450	−	0.199965i
$235$	2.48991	+	0.667169i	0.162424	+	0.0435213i
$236$	−11.4009	−	6.58232i	−0.742137	−	0.428473i
$237$	8.46943			0.550148
$238$	9.36961	+	5.58663i	0.607342	+	0.362127i
$239$	4.68310			0.302925			0.151462	−	0.988463i	$-0.451602\pi$
$239$	4.68310			0.302925			0.151462	+	0.988463i	$0.451602\pi$
$240$	0.358719	+	0.207107i	0.0231552	+	0.0133687i
$241$	13.7247	+	3.67751i	0.884082	+	0.236889i	0.672168	−	0.740399i	$-0.265363\pi$
$241$	13.7247	+	3.67751i	0.884082	+	0.236889i	0.211915	+	0.977288i	$0.432030\pi$
$242$	2.28664	+	3.96057i	0.146990	+	0.254595i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	10.3123	+	10.3123i	0.660175	+	0.660175i
$245$	1.44927	−	2.51131i	0.0925906	−	0.160442i
$246$		−	1.36539i		−	0.0870541i
$247$	12.9154	+	7.45671i	0.821787	+	0.474459i
$248$	2.53105	−	9.44602i	0.160722	−	0.599823i
$249$	1.85687	−	6.92994i	0.117674	−	0.439167i
$250$	1.05367	+	3.93235i	0.0666399	+	0.248704i
$251$	−3.89994			−0.246162			−0.123081	−	0.992397i	$-0.539277\pi$
$251$	−3.89994			−0.246162			−0.123081	+	0.992397i	$0.539277\pi$
$252$	1.01225	−	2.44445i	0.0637660	−	0.153986i
$253$			0.877138i			0.0551452i
$254$	8.50367	−	14.7288i	0.533568	−	0.924167i
$255$	−0.631169	−	1.58694i	−0.0395253	−	0.0993778i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.4435	−	6.60688i	−0.713823	−	0.412126i	0.0986519	−	0.995122i	$-0.468547\pi$
$257$	−11.4435	−	6.60688i	−0.713823	−	0.412126i	−0.812475	+	0.582996i	$0.801880\pi$
$258$	1.53208	−	1.53208i	0.0953834	−	0.0953834i
$259$	−2.87380	+	21.8446i	−0.178569	+	1.35736i
$260$	1.03452	−	1.03452i	0.0641584	−	0.0641584i
$261$	0.400100	−	0.107206i	0.0247655	−	0.00663591i
$262$	2.09448	−	7.81669i	0.129397	−	0.482917i
$263$	21.0565	−	12.1570i	1.29840	−	0.749630i	0.318270	−	0.948000i	$-0.396898\pi$
$263$	21.0565	−	12.1570i	1.29840	−	0.749630i	0.980127	+	0.198370i	$0.0635649\pi$
$264$	3.41759	+	1.97315i	0.210338	+	0.121439i
$265$	1.50683	+	1.50683i	0.0925637	+	0.0925637i
$266$	1.45916	+	11.0754i	0.0894671	+	0.679074i
$267$	−10.0820	+	10.0820i	−0.617007	+	0.617007i
$268$	−4.01338	+	6.95138i	−0.245156	+	0.424623i
$269$	−24.8749	−	6.66521i	−1.51665	−	0.406385i	−0.598012	−	0.801487i	$-0.704043\pi$
$269$	−24.8749	−	6.66521i	−1.51665	−	0.406385i	−0.918637	+	0.395102i	$0.870709\pi$
$270$	−0.358719	+	0.207107i	−0.0218310	+	0.0126041i
$271$	−6.42498	+	11.1284i	−0.390290	+	0.676001i	−0.992488	−	0.122345i	$-0.960958\pi$
$271$	−6.42498	+	11.1284i	−0.390290	+	0.676001i	0.602198	+	0.798347i	$0.294292\pi$
$272$	−0.595973	+	4.07981i	−0.0361361	+	0.247375i
$273$	−7.41444	−	5.68819i	−0.448742	−	0.344265i
$274$		−	4.78192i		−	0.288886i
$275$	4.93165	+	18.4052i	0.297389	+	1.10987i
$276$	0.111134	+	0.192490i	0.00668950	+	0.0115865i
$277$	2.16562	+	0.580276i	0.130120	+	0.0348654i	0.323291	−	0.946300i	$-0.395211\pi$
$277$	2.16562	+	0.580276i	0.130120	+	0.0348654i	−0.193172	+	0.981165i	$0.561877\pi$
$278$	−0.528849	+	0.141705i	−0.0317182	+	0.00849887i
$279$	6.91497	+	6.91497i	0.413988	+	0.413988i
$280$	1.08654	+	0.142942i	0.0649334	+	0.00854240i
$281$		−	28.6582i		−	1.70960i	−0.518954	−	0.854802i	$-0.673679\pi$
$281$		−	28.6582i		−	1.70960i	0.518954	−	0.854802i	$-0.326321\pi$
$282$	6.01118	−	1.61069i	0.357960	−	0.0959152i
$283$	−0.846439	+	3.15895i	−0.0503156	+	0.187780i	−0.986510	−	0.163703i	$-0.947656\pi$
$283$	−0.846439	+	3.15895i	−0.0503156	+	0.187780i	0.936194	+	0.351484i	$0.114323\pi$
$284$	14.8006	+	3.96582i	0.878256	+	0.235328i
$285$	0.874460	−	1.51461i	0.0517986	−	0.0897177i
$286$	9.85612	−	9.85612i	0.582805	−	0.582805i
$287$	−1.38275	−	3.33737i	−0.0816213	−	0.196999i
$288$	1.00000			0.0589256
$289$	12.3562	−	11.6758i	0.726836	−	0.686811i
$290$	0.0857864	+	0.148586i	0.00503755	+	0.00872530i
$291$	0.781149	−	0.450997i	0.0457918	−	0.0264379i
$292$	−4.32308	−	16.1340i	−0.252989	−	0.944169i
$293$	4.91330			0.287038			0.143519	−	0.989648i	$-0.454158\pi$
$293$	4.91330			0.287038			0.143519	+	0.989648i	$0.454158\pi$
$294$	−0.00132345	−	7.00000i	−7.71849e−5	−	0.408248i
$295$	3.85584	+	3.85584i	0.224495	+	0.224495i
$296$	−8.04387	+	2.15535i	−0.467540	+	0.125277i
$297$	−3.41759	+	1.97315i	−0.198309	+	0.114494i
$298$	8.35711	−	4.82498i	0.484114	−	0.279503i
$299$	0.758321	−	0.203191i	0.0438548	−	0.0117509i
$300$	3.41421	+	3.41421i	0.197120	+	0.197120i
$301$	2.19325	−	5.29638i	0.126417	−	0.305278i
$302$	22.7375			1.30840
$303$	−2.04688	−	7.63906i	−0.117590	−	0.438852i
$304$	−3.65659	+	2.11113i	−0.209720	+	0.121082i
$305$	−3.02039	−	5.23147i	−0.172947	−	0.299553i
$306$	−3.23523	−	2.55603i	−0.184946	−	0.146119i
$307$	−5.50363			−0.314109			−0.157054	−	0.987590i	$-0.550200\pi$
$307$	−5.50363			−0.314109			−0.157054	+	0.987590i	$0.550200\pi$
$308$	10.3517	+	1.36184i	0.589845	+	0.0775978i
$309$	1.28136	−	1.28136i	0.0728943	−	0.0728943i
$310$	−2.02535	+	3.50801i	−0.115032	+	0.199241i
$311$	−1.72391	−	0.461920i	−0.0977539	−	0.0261931i	0.209611	−	0.977785i	$-0.432780\pi$
$311$	−1.72391	−	0.461920i	−0.0977539	−	0.0261931i	−0.307364	+	0.951592i	$0.599447\pi$
$312$	0.914171	−	3.41173i	0.0517547	−	0.193151i
$313$	−21.0860	+	5.64998i	−1.19185	+	0.319356i	−0.799617	−	0.600510i	$-0.794964\pi$
$313$	−21.0860	+	5.64998i	−1.19185	+	0.319356i	−0.392234	+	0.919865i	$0.628298\pi$
$314$			18.0941i			1.02111i
$315$	−0.667063	+	0.869504i	−0.0375848	+	0.0489910i
$316$	5.98879	+	5.98879i	0.336896	+	0.336896i
$317$	7.85427	−	2.10454i	0.441140	−	0.118203i	−0.0314110	−	0.999507i	$-0.510000\pi$
$317$	7.85427	−	2.10454i	0.441140	−	0.118203i	0.472551	+	0.881304i	$0.343333\pi$
$318$	4.96933	+	1.33153i	0.278666	+	0.0746685i
$319$	0.817305	+	1.41561i	0.0457603	+	0.0792592i
$320$	0.107206	+	0.400100i	0.00599302	+	0.0223662i
$321$		−	20.4885i		−	1.14356i
$322$	0.466579	+	0.357949i	0.0260014	+	0.0199477i
$323$	17.2260	+	2.51636i	0.958482	+	0.140014i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	14.7696	−	8.52721i	0.819268	−	0.473004i
$326$	−5.12297	−	1.37270i	−0.283735	−	0.0760266i
$327$	−2.96234	+	5.13092i	−0.163818	+	0.283741i
$328$	0.965476	−	0.965476i	0.0533095	−	0.0533095i
$329$	13.0617	−	10.0246i	0.720115	−	0.552672i
$330$	−1.15584	−	1.15584i	−0.0636271	−	0.0636271i
$331$	6.47739	+	3.73972i	0.356030	+	0.205554i	0.667338	−	0.744755i	$-0.267434\pi$
$331$	6.47739	+	3.73972i	0.356030	+	0.205554i	−0.311308	+	0.950309i	$0.600767\pi$
$332$	6.21322	−	3.58720i	0.340994	−	0.196873i
$333$	2.15535	−	8.04387i	0.118112	−	0.440801i
$334$	−3.46686	+	0.928944i	−0.189698	+	0.0508295i
$335$	2.35098	−	2.35098i	0.128448	−	0.128448i
$336$	2.44426	−	1.01272i	0.133345	−	0.0552482i
$337$	6.01028	−	6.01028i	0.327401	−	0.327401i	−0.524197	−	0.851597i	$-0.675634\pi$
$337$	6.01028	−	6.01028i	0.327401	−	0.327401i	0.851597	+	0.524197i	$0.175634\pi$
$338$	0.454124	+	0.262188i	0.0247011	+	0.0142612i
$339$	6.01742	+	10.4225i	0.326821	+	0.566071i
$340$	0.675829	−	1.56844i	0.0366520	−	0.0850604i
$341$	−19.2959	+	33.4215i	−1.04493	+	1.80988i
$342$		−	4.22227i		−	0.228314i
$343$	−7.09225	−	17.1085i	−0.382945	−	0.923771i
$344$	2.16670			0.116820
$345$	−0.0238286	−	0.0889296i	−0.00128289	−	0.00478781i
$346$	−3.32563	+	12.4114i	−0.178787	+	0.667242i
$347$	−0.239686	+	0.894520i	−0.0128670	+	0.0480203i	−0.972061	−	0.234729i	$-0.924580\pi$
$347$	−0.239686	+	0.894520i	−0.0128670	+	0.0480203i	0.959194	+	0.282749i	$0.0912464\pi$
$348$	0.358719	+	0.207107i	0.0192294	+	0.0111021i
$349$		−	1.25560i		−	0.0672106i	−0.999435	−	0.0336053i	$-0.989301\pi$
$349$		−	1.25560i		−	0.0672106i	0.999435	−	0.0336053i	$-0.0106989\pi$
$350$	11.8029	+	4.88760i	0.630889	+	0.261253i
$351$	2.49756	+	2.49756i	0.133310	+	0.133310i
$352$	1.02138	+	3.81183i	0.0544396	+	0.203171i
$353$	−10.7917	−	18.6918i	−0.574387	−	0.994867i	−0.996108	−	0.0881413i	$-0.971907\pi$
$353$	−10.7917	−	18.6918i	−0.574387	−	0.994867i	0.421721	−	0.906725i	$-0.361426\pi$
$354$	12.7161	+	3.40726i	0.675852	+	0.181094i
$355$	−5.49657	−	3.17344i	−0.291728	−	0.168429i
$356$	−14.2581			−0.755676
$357$	−10.4963	−	2.97123i	−0.555522	−	0.157254i
$358$	8.70788			0.460226
$359$	9.21420	+	5.31982i	0.486307	+	0.280770i	0.723041	−	0.690805i	$-0.242744\pi$
$359$	9.21420	+	5.31982i	0.486307	+	0.280770i	−0.236734	+	0.971574i	$0.576077\pi$
$360$	−0.400100	−	0.107206i	−0.0210871	−	0.00565027i
$361$	−0.586224	−	1.01537i	−0.0308539	−	0.0534405i
$362$	5.75997	+	21.4965i	0.302737	+	1.12983i
$363$	−3.23379	−	3.23379i	−0.169730	−	0.169730i
$364$	−1.22065	−	9.26495i	−0.0639792	−	0.485616i
$365$			6.91866i			0.362139i
$366$	−12.6299	−	7.29187i	−0.660175	−	0.381152i
$367$	4.37740	−	16.3367i	0.228498	−	0.852768i	−0.752474	−	0.658622i	$-0.771140\pi$
$367$	4.37740	−	16.3367i	0.228498	−	0.852768i	0.980973	−	0.194146i	$-0.0621935\pi$
$368$	−0.0575273	+	0.214695i	−0.00299882	+	0.0111917i
$369$	0.353389	+	1.31887i	0.0183967	+	0.0686574i
$370$	3.44941			0.179327
$371$	13.4948	−	1.77792i	0.700615	−	0.0923052i
$372$			9.77924i			0.507030i
$373$	13.7292	−	23.7797i	0.710871	−	1.23126i	−0.253660	−	0.967293i	$-0.581635\pi$
$373$	13.7292	−	23.7797i	0.710871	−	1.23126i	0.964531	−	0.263970i	$-0.0850322\pi$
$374$	6.43877	−	14.9428i	0.332941	−	0.772675i
$375$	−2.03553	−	3.52565i	−0.105115	−	0.182064i
$376$	5.38947	+	3.11161i	0.277941	+	0.160469i
$377$	1.03452	−	1.03452i	0.0532807	−	0.0532807i
$378$	−0.345092	+	2.62315i	−0.0177496	+	0.134920i
$379$	−5.88226	+	5.88226i	−0.302151	+	0.302151i	−0.841855	−	0.539704i	$-0.818536\pi$
$379$	−5.88226	+	5.88226i	−0.302151	+	0.302151i	0.539704	+	0.841855i	$0.318536\pi$
$380$	1.68933	−	0.452654i	0.0866607	−	0.0232207i
$381$	−4.40183	+	16.4278i	−0.225512	+	0.841624i
$382$	6.50517	−	3.75576i	0.332834	−	0.192162i
$383$	27.6865	+	15.9848i	1.41471	+	0.816785i	0.995828	−	0.0912533i	$-0.0290873\pi$
$383$	27.6865	+	15.9848i	1.41471	+	0.816785i	0.418886	+	0.908039i	$0.362421\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	−3.99573	−	1.65464i	−0.203641	−	0.0843283i
$386$	−3.35280	+	3.35280i	−0.170653	+	0.170653i
$387$	−1.08335	+	1.87641i	−0.0550697	+	0.0953834i
$388$	0.871259	+	0.233453i	0.0442315	+	0.0118518i
$389$	18.9296	−	10.9290i	0.959769	−	0.554123i	0.0636674	−	0.997971i	$-0.479720\pi$
$389$	18.9296	−	10.9290i	0.959769	−	0.554123i	0.896102	+	0.443848i	$0.146387\pi$
$390$	−0.731519	+	1.26703i	−0.0370419	+	0.0641584i
$391$	0.734881	−	0.547546i	0.0371645	−	0.0276906i
$392$	4.94881	−	4.95068i	0.249953	−	0.250047i
$393$			8.09244i			0.408209i
$394$	−2.93080	−	10.9379i	−0.147652	−	0.551043i
$395$	−1.75408	−	3.03815i	−0.0882571	−	0.152866i
$396$	−3.81183	−	1.02138i	−0.191552	−	0.0513261i
$397$	1.37011	−	0.367119i	0.0687637	−	0.0184252i	−0.224273	−	0.974526i	$-0.572001\pi$
$397$	1.37011	−	0.367119i	0.0687637	−	0.0184252i	0.293037	+	0.956101i	$0.405334\pi$
$398$	12.9913	+	12.9913i	0.651195	+	0.651195i
$399$	−4.27596	−	10.3203i	−0.214066	−	0.516662i
$400$			4.82843i			0.241421i
$401$	24.0649	−	6.44818i	1.20175	−	0.322007i	0.398227	−	0.917287i	$-0.369625\pi$
$401$	24.0649	−	6.44818i	1.20175	−	0.322007i	0.803518	+	0.595280i	$0.202959\pi$
$402$	2.07748	−	7.75326i	0.103615	−	0.386697i
$403$	33.3642	+	8.93990i	1.66199	+	0.445328i
$404$	3.95427	−	6.84899i	0.196732	−	0.340750i
$405$	0.292893	−	0.292893i	0.0145540	−	0.0145540i
$406$	1.08654	+	0.142942i	0.0539243	+	0.00709408i
$407$	32.8633			1.62897
$408$	−0.480266	−	4.09504i	−0.0237767	−	0.202735i
$409$	4.84577	+	8.39312i	0.239608	+	0.415013i	0.960602	−	0.277928i	$-0.0896478\pi$
$409$	4.84577	+	8.39312i	0.239608	+	0.415013i	−0.720994	+	0.692941i	$0.756314\pi$
$410$	−0.489792	+	0.282781i	−0.0241891	+	0.0139656i
$411$	1.23765	+	4.61898i	0.0610488	+	0.227837i
$412$	1.81212			0.0892769
$413$	34.5320	−	4.54954i	1.69921	−	0.223868i
$414$	−0.157168	−	0.157168i	−0.00772437	−	0.00772437i
$415$	−2.87048	+	0.769142i	−0.140906	+	0.0377557i
$416$	3.05888	−	1.76604i	0.149974	−	0.0865874i
$417$	0.474153	−	0.273752i	0.0232194	−	0.0134057i
$418$	16.0946	−	4.31253i	0.787211	−	0.210933i
$419$	2.87603	+	2.87603i	0.140503	+	0.140503i	0.773860	−	0.633357i	$-0.218323\pi$
$419$	2.87603	+	2.87603i	0.140503	+	0.140503i	−0.633357	+	0.773860i	$0.718323\pi$
$420$	−1.08652	+	0.143147i	−0.0530166	+	0.00698487i
$421$	−28.1922			−1.37400			−0.687002	−	0.726655i	$-0.741074\pi$
$421$	−28.1922			−1.37400			−0.687002	+	0.726655i	$0.741074\pi$
$422$	3.10758	+	11.5976i	0.151274	+	0.564564i
$423$	−5.38947	+	3.11161i	−0.262045	+	0.151292i
$424$	2.57232	+	4.45538i	0.124923	+	0.216373i
$425$	12.3416	−	15.6211i	0.598656	−	0.757733i
$426$	−15.3227			−0.742389
$427$	−38.2553	−	5.03273i	−1.85130	−	0.243551i
$428$	14.4875	−	14.4875i	0.700282	−	0.700282i
$429$	−6.96933	+	12.0712i	−0.336482	+	0.582805i
$430$	−0.866894	−	0.232283i	−0.0418053	−	0.0112017i
$431$	4.88524	−	18.2320i	0.235314	−	0.878203i	−0.742693	−	0.669632i	$-0.766452\pi$
$431$	4.88524	−	18.2320i	0.235314	−	0.878203i	0.978007	−	0.208572i	$-0.0668814\pi$
$432$	−0.965926	+	0.258819i	−0.0464731	+	0.0124524i
$433$			4.36111i			0.209582i	0.994494	+	0.104791i	$0.0334173\pi$
$433$			4.36111i			0.209582i	−0.994494	+	0.104791i	$0.966583\pi$
$434$	9.90360	+	23.9030i	0.475388	+	1.14738i
$435$	−0.121320	−	0.121320i	−0.00581687	−	0.00581687i
$436$	−5.72280	+	1.53342i	−0.274072	+	0.0734375i
$437$	0.906500	+	0.242896i	0.0433638	+	0.0116193i
$438$	8.35156	+	14.4653i	0.399053	+	0.691180i
$439$	5.55466	+	20.7303i	0.265109	+	0.989401i	0.962183	+	0.272402i	$0.0878182\pi$
$439$	5.55466	+	20.7303i	0.265109	+	0.989401i	−0.697074	+	0.716999i	$0.745515\pi$
$440$		−	1.63461i		−	0.0779270i
$441$	1.81301	+	6.76114i	0.0863339	+	0.321959i
$442$	−14.4102	−	2.10503i	−0.685424	−	0.100126i
$443$	−16.6305	+	28.8048i	−0.790137	+	1.36856i	0.135745	+	0.990744i	$0.456657\pi$
$443$	−16.6305	+	28.8048i	−0.790137	+	1.36856i	−0.925882	+	0.377813i	$0.876676\pi$
$444$	7.21193	−	4.16381i	0.342263	−	0.197606i
$445$	5.70465	+	1.52856i	0.270426	+	0.0724605i
$446$	−9.23791	+	16.0005i	−0.437428	+	0.757647i
$447$	−6.82355	+	6.82355i	−0.322743	+	0.322743i
$448$	2.44445	+	1.01225i	0.115489	+	0.0478245i
$449$	−9.54249	−	9.54249i	−0.450338	−	0.450338i	0.445129	−	0.895467i	$-0.353158\pi$
$449$	−9.54249	−	9.54249i	−0.450338	−	0.450338i	−0.895467	+	0.445129i	$0.853158\pi$
$450$	−4.18154	−	2.41421i	−0.197120	−	0.113807i
$451$	−4.66635	+	2.69412i	−0.219730	+	0.126861i
$452$	−3.11485	+	11.6248i	−0.146510	+	0.546783i
$453$	−21.9628	+	5.88490i	−1.03190	+	0.276497i
$454$	7.67258	−	7.67258i	0.360092	−	0.360092i
$455$	−0.504882	+	3.83777i	−0.0236692	+	0.179917i
$456$	2.98559	−	2.98559i	0.139813	−	0.139813i
$457$	7.87175	+	4.54476i	0.368225	+	0.212595i	0.672683	−	0.739931i	$-0.265142\pi$
$457$	7.87175	+	4.54476i	0.368225	+	0.212595i	−0.304458	+	0.952526i	$0.598475\pi$
$458$	−5.42875	−	9.40287i	−0.253669	−	0.439367i
$459$	3.78654	+	1.63160i	0.176741	+	0.0761564i
$460$	0.0460333	−	0.0797321i	0.00214631	−	0.00371753i
$461$			6.76977i			0.315300i	0.987495	+	0.157650i	$0.0503917\pi$
$461$			6.76977i			0.315300i	−0.987495	+	0.157650i	$0.949608\pi$
$462$	−10.3515	+	1.36379i	−0.481594	+	0.0634494i
$463$	−22.5692			−1.04888			−0.524441	−	0.851447i	$-0.675726\pi$
$463$	−22.5692			−1.04888			−0.524441	+	0.851447i	$0.675726\pi$
$464$	0.107206	+	0.400100i	0.00497693	+	0.0185742i
$465$	1.04840	−	3.91267i	0.0486183	−	0.181446i
$466$	2.13361	−	7.96274i	0.0988376	−	0.368867i
$467$	−9.47354	−	5.46955i	−0.438383	−	0.253101i	0.264528	−	0.964378i	$-0.414784\pi$
$467$	−9.47354	−	5.46955i	−0.438383	−	0.253101i	−0.702911	+	0.711277i	$0.748117\pi$
$468$			3.53208i			0.163271i
$469$	−2.77395	−	21.0549i	−0.128089	−	0.972224i
$470$	−1.82274	−	1.82274i	−0.0840768	−	0.0840768i
$471$	−4.68310	−	17.4776i	−0.215786	−	0.805323i
$472$	6.58232	+	11.4009i	0.302976	+	0.524770i
$473$	−8.25908	−	2.21301i	−0.379753	−	0.101754i
$474$	−7.33474	−	4.23471i	−0.336896	−	0.194507i
$475$	20.3869			0.935416
$476$	−5.32101	−	9.52297i	−0.243888	−	0.436484i
$477$	−5.14463			−0.235557
$478$	−4.05568	−	2.34155i	−0.185503	−	0.107100i
$479$	−17.1042	−	4.58305i	−0.781511	−	0.209405i	−0.154060	−	0.988062i	$-0.549235\pi$
$479$	−17.1042	−	4.58305i	−0.781511	−	0.209405i	−0.627451	+	0.778656i	$0.715902\pi$
$480$	−0.207107	−	0.358719i	−0.00945309	−	0.0163732i
$481$	−7.61287	−	28.4116i	−0.347117	−	1.29546i
$482$	−10.0471	−	10.0471i	−0.457635	−	0.457635i
$483$	−0.543325	−	0.224992i	−0.0247221	−	0.0102375i
$484$		−	4.57327i		−	0.207876i
$485$	−0.323563	−	0.186809i	−0.0146922	−	0.00848256i
$486$	0.258819	−	0.965926i	0.0117403	−	0.0438153i
$487$	−7.47814	+	27.9088i	−0.338867	+	1.26467i	0.560749	+	0.827986i	$0.310513\pi$
$487$	−7.47814	+	27.9088i	−0.338867	+	1.26467i	−0.899616	+	0.436682i	$0.856153\pi$
$488$	−3.77455	−	14.0868i	−0.170866	−	0.637680i
$489$	5.30369			0.239841
$490$	−2.51076	+	1.45022i	−0.113425	+	0.0655144i
$491$		−	26.5956i		−	1.20024i	−0.799910	−	0.600121i	$-0.795119\pi$
$491$		−	26.5956i		−	1.20024i	0.799910	−	0.600121i	$-0.204881\pi$
$492$	−0.682695	+	1.18246i	−0.0307783	+	0.0533095i
$493$	0.675829	−	1.56844i	0.0304378	−	0.0706388i
$494$	−7.45671	−	12.9154i	−0.335493	−	0.581091i
$495$	1.41561	+	0.817305i	0.0636271	+	0.0367351i
$496$	−6.91497	+	6.91497i	−0.310491	+	0.310491i
$497$	−37.4528	+	15.5176i	−1.67999	+	0.696059i
$498$	−5.07307	+	5.07307i	−0.227330	+	0.227330i
$499$	−23.4395	+	6.28060i	−1.04930	+	0.281158i	−0.741961	−	0.670443i	$-0.766104\pi$
$499$	−23.4395	+	6.28060i	−1.04930	+	0.281158i	−0.307335	+	0.951601i	$0.599437\pi$
$500$	1.05367	−	3.93235i	0.0471215	−	0.175860i
$501$	3.10831	−	1.79458i	0.138869	−	0.0801760i
$502$	3.37744	+	1.94997i	0.150743	+	0.0870313i
$503$	17.4067	+	17.4067i	0.776128	+	0.776128i	0.979170	−	0.203042i	$-0.0650828\pi$
$503$	17.4067	+	17.4067i	0.776128	+	0.776128i	−0.203042	+	0.979170i	$0.565083\pi$
$504$	−2.09886	+	1.61083i	−0.0934908	+	0.0717521i
$505$	−2.31636	+	2.31636i	−0.103076	+	0.103076i
$506$	0.438569	−	0.759624i	0.0194968	−	0.0337694i
$507$	−0.506509	−	0.135719i	−0.0224949	−	0.00602748i
$508$	−14.7288	+	8.50367i	−0.653485	+	0.377290i
$509$	−2.69371	+	4.66564i	−0.119397	+	0.206801i	−0.919529	−	0.393023i	$-0.871429\pi$
$509$	−2.69371	+	4.66564i	−0.119397	+	0.206801i	0.800132	+	0.599824i	$0.204763\pi$
$510$	−0.246860	+	1.68991i	−0.0109311	+	0.0748305i
$511$	35.0626	+	26.8992i	1.55108	+	1.18995i
$512$			1.00000i			0.0441942i
$513$	1.09280	+	4.07840i	0.0482485	+	0.180066i
$514$	6.60688	+	11.4435i	0.291417	+	0.504749i
$515$	−0.725030	−	0.194271i	−0.0319486	−	0.00856061i
$516$	−2.09287	+	0.560782i	−0.0921333	+	0.0246870i
$517$	−17.3656	−	17.3656i	−0.763740	−	0.763740i
$518$	13.4111	−	17.4811i	0.589249	−	0.768075i
$519$		−	12.8493i		−	0.564019i
$520$	−1.41319	+	0.378662i	−0.0619723	+	0.0166054i
$521$	−4.67164	+	17.4348i	−0.204668	+	0.763832i	0.784882	+	0.619645i	$0.212723\pi$
$521$	−4.67164	+	17.4348i	−0.204668	+	0.763832i	−0.989550	+	0.144187i	$0.953943\pi$
$522$	−0.400100	−	0.107206i	−0.0175119	−	0.00469229i
$523$	−3.15034	+	5.45655i	−0.137755	+	0.238598i	−0.926646	−	0.375934i	$-0.877322\pi$
$523$	−3.15034	+	5.45655i	−0.137755	+	0.238598i	0.788892	+	0.614532i	$0.210655\pi$
$524$	−5.72222	+	5.72222i	−0.249976	+	0.249976i
$525$	−12.6657	−	1.66625i	−0.552776	−	0.0727212i
$526$	−24.3139			−1.06014
$527$	40.0464	−	4.69664i	1.74445	−	0.204589i
$528$	−1.97315	−	3.41759i	−0.0858703	−	0.148732i
$529$	−19.8758	+	11.4753i	−0.864165	+	0.498926i
$530$	−0.551537	−	2.05837i	−0.0239573	−	0.0894097i
$531$	−13.1646			−0.571297
$532$	4.27401	−	10.3211i	0.185302	−	0.447478i
$533$	3.41014	+	3.41014i	0.147710	+	0.147710i
$534$	13.7722	−	3.69026i	0.595983	−	0.159693i
$535$	−7.34962	+	4.24330i	−0.317752	+	0.183454i
$536$	6.95138	−	4.01338i	0.300254	−	0.173352i
$537$	−8.41117	+	2.25377i	−0.362969	+	0.0972572i
$538$	18.2097	+	18.2097i	0.785075	+	0.785075i
$539$	−23.9206	+	13.8166i	−1.03033	+	0.595122i
$540$	0.414214			0.0178249
$541$	−0.556259	−	2.07599i	−0.0239154	−	0.0892536i	0.952937	−	0.303169i	$-0.0980448\pi$
$541$	−0.556259	−	2.07599i	−0.0239154	−	0.0892536i	−0.976852	+	0.213916i	$0.931378\pi$
$542$	11.1284	−	6.42498i	0.478005	−	0.275976i
$543$	−11.1274	−	19.2732i	−0.477522	−	0.827093i
$544$	2.55603	−	3.23523i	0.109589	−	0.138709i
$545$	2.45408			0.105121
$546$	3.57700	+	8.63333i	0.153081	+	0.369473i
$547$	29.2641	−	29.2641i	1.25124	−	1.25124i	0.296080	−	0.955163i	$-0.404320\pi$
$547$	29.2641	−	29.2641i	1.25124	−	1.25124i	0.955163	−	0.296080i	$-0.0956795\pi$
$548$	−2.39096	+	4.14126i	−0.102137	+	0.176906i
$549$	14.0868	+	3.77455i	0.601210	+	0.161094i
$550$	4.93165	−	18.4052i	0.210286	−	0.784798i
$551$	1.68933	−	0.452654i	0.0719678	−	0.0192837i
$552$		−	0.222269i		−	0.00946038i
$553$	−22.2166	−	2.92273i	−0.944745	−	0.124287i
$554$	−1.58534	−	1.58534i	−0.0673548	−	0.0673548i
$555$	−3.33188	+	0.892774i	−0.141430	+	0.0378962i
$556$	0.528849	+	0.141705i	0.0224282	+	0.00600961i
$557$	−5.38489	−	9.32690i	−0.228165	−	0.395194i	0.729099	−	0.684408i	$-0.239939\pi$
$557$	−5.38489	−	9.32690i	−0.228165	−	0.395194i	−0.957264	+	0.289214i	$0.906606\pi$
$558$	−2.53105	−	9.44602i	−0.107148	−	0.399882i
$559$			7.65295i			0.323685i
$560$	−0.869504	−	0.667063i	−0.0367432	−	0.0281886i
$561$	−2.35189	+	16.1001i	−0.0992967	+	0.679748i
$562$	−14.3291	+	24.8187i	−0.604436	+	1.04691i
$563$	−27.7715	+	16.0339i	−1.17043	+	0.675747i	−0.953781	−	0.300503i	$-0.902846\pi$
$563$	−27.7715	+	16.0339i	−1.17043	+	0.675747i	−0.216647	+	0.976250i	$0.569512\pi$
$564$	−6.01118	−	1.61069i	−0.253116	−	0.0678223i
$565$	2.49250	−	4.31713i	0.104860	−	0.181623i
$566$	2.31251	−	2.31251i	0.0972022	−	0.0972022i
$567$	−0.345588	−	2.62308i	−0.0145133	−	0.110159i
$568$	−10.8348	−	10.8348i	−0.454619	−	0.454619i
$569$	33.1177	+	19.1205i	1.38836	+	0.801572i	0.993131	−	0.117008i	$-0.0373304\pi$
$569$	33.1177	+	19.1205i	1.38836	+	0.801572i	0.395233	+	0.918581i	$0.370664\pi$
$570$	−1.51461	+	0.874460i	−0.0634400	+	0.0366271i
$571$	8.19936	−	30.6004i	0.343133	−	1.28059i	−0.551646	−	0.834078i	$-0.686000\pi$
$571$	8.19936	−	30.6004i	0.343133	−	1.28059i	0.894779	−	0.446510i	$-0.147333\pi$
$572$	−13.4637	+	3.60759i	−0.562946	+	0.150841i
$573$	−5.31145	+	5.31145i	−0.221889	+	0.221889i
$574$	−0.471185	+	3.58162i	−0.0196669	+	0.149494i
$575$	0.758872	−	0.758872i	0.0316472	−	0.0316472i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$	−1.09225	−	1.89183i	−0.0454709	−	0.0787580i	0.842394	−	0.538862i	$-0.181146\pi$
$577$	−1.09225	−	1.89183i	−0.0454709	−	0.0787580i	−0.887865	+	0.460104i	$0.847812\pi$
$578$	−16.5387	+	3.93342i	−0.687919	+	0.163609i
$579$	2.37079	−	4.10632i	0.0985265	−	0.170653i
$580$		−	0.171573i		−	0.00712418i
$581$	−7.26232	+	17.5375i	−0.301292	+	0.727577i
$582$	−0.901993			−0.0373888
$583$	−5.25461	−	19.6105i	−0.217624	−	0.812183i
$584$	−4.32308	+	16.1340i	−0.178890	+	0.667628i
$585$	0.378662	−	1.41319i	0.0156557	−	0.0584280i
$586$	−4.25504	−	2.45665i	−0.175774	−	0.101483i
$587$		−	11.9122i		−	0.491671i	−0.969312	−	0.245835i	$-0.920938\pi$
$587$		−	11.9122i		−	0.491671i	0.969312	−	0.245835i	$-0.0790623\pi$
$588$	−3.49885	+	6.06284i	−0.144290	+	0.250027i
$589$	29.1969	+	29.1969i	1.20304	+	1.20304i
$590$	−1.41133	−	5.26717i	−0.0581037	−	0.216846i
$591$	5.66187	+	9.80665i	0.232898	+	0.403392i
$592$	8.04387	+	2.15535i	0.330601	+	0.0885842i
$593$	−1.87212	−	1.08087i	−0.0768788	−	0.0443860i	0.461068	−	0.887365i	$-0.347466\pi$
$593$	−1.87212	−	1.08087i	−0.0768788	−	0.0443860i	−0.537947	+	0.842979i	$0.680800\pi$
$594$	3.94630			0.161919
$595$	1.10801	+	4.38058i	0.0454240	+	0.179586i
$596$	−9.64996			−0.395278
$597$	−15.9110	−	9.18624i	−0.651195	−	0.375968i
$598$	−0.758321	−	0.203191i	−0.0310100	−	0.00830912i
$599$	−10.1460	−	17.5734i	−0.414556	−	0.718031i	0.580826	−	0.814028i	$-0.302730\pi$
$599$	−10.1460	−	17.5734i	−0.414556	−	0.718031i	−0.995382	+	0.0959963i	$0.969396\pi$
$600$	−1.24969	−	4.66390i	−0.0510183	−	0.190403i
$601$	14.2272	+	14.2272i	0.580341	+	0.580341i	0.934997	−	0.354656i	$-0.115402\pi$
$601$	14.2272	+	14.2272i	0.580341	+	0.580341i	−0.354656	+	0.934997i	$0.615402\pi$
$602$	−4.54760	+	3.49018i	−0.185346	+	0.142249i
$603$			8.02676i			0.326875i
$604$	−19.6913	−	11.3688i	−0.801226	−	0.462588i
$605$	−0.490284	+	1.82976i	−0.0199329	+	0.0743905i
$606$	−2.04688	+	7.63906i	−0.0831488	+	0.310315i
$607$	5.98959	+	22.3535i	0.243110	+	0.907299i	0.974324	+	0.225151i	$0.0722875\pi$
$607$	5.98959	+	22.3535i	0.243110	+	0.907299i	−0.731214	+	0.682148i	$0.761046\pi$
$608$	4.22227			0.171236
$609$	−1.08652	+	0.143147i	−0.0440279	+	0.00580062i
$610$			6.04078i			0.244584i
$611$	−10.9905	+	19.0361i	−0.444627	+	0.770117i
$612$	1.52378	+	3.83120i	0.0615950	+	0.154867i
$613$	1.98752	+	3.44249i	0.0802753	+	0.139041i	0.903368	−	0.428866i	$-0.141087\pi$
$613$	1.98752	+	3.44249i	0.0802753	+	0.139041i	−0.823093	+	0.567907i	$0.807753\pi$
$614$	4.76629	+	2.75182i	0.192352	+	0.111054i
$615$	0.399913	−	0.399913i	0.0161261	−	0.0161261i
$616$	−8.28394	−	6.35525i	−0.333770	−	0.256060i
$617$	−14.4749	+	14.4749i	−0.582737	+	0.582737i	−0.935654	−	0.352918i	$-0.885190\pi$
$617$	−14.4749	+	14.4749i	−0.582737	+	0.582737i	0.352918	+	0.935654i	$0.385190\pi$
$618$	−1.75038	+	0.469012i	−0.0704105	+	0.0188664i
$619$	−12.0176	+	44.8503i	−0.483028	+	1.80269i	0.105751	+	0.994393i	$0.466275\pi$
$619$	−12.0176	+	44.8503i	−0.483028	+	1.80269i	−0.588779	+	0.808294i	$0.700391\pi$
$620$	3.50801	−	2.02535i	0.140885	−	0.0813399i
$621$	0.192490	+	0.111134i	0.00772437	+	0.00445966i
$622$	1.26199	+	1.26199i	0.0506011	+	0.0506011i
$623$	29.9257	−	22.9673i	1.19895	−	0.920166i
$624$	−2.49756	+	2.49756i	−0.0999825	+	0.0999825i
$625$	11.2279	−	19.4473i	0.449117	−	0.777893i
$626$	21.0860	+	5.64998i	0.842766	+	0.225819i
$627$	−14.4300	+	8.33117i	−0.576279	+	0.332715i
$628$	9.04705	−	15.6699i	0.361017	−	0.625299i
$629$	−20.5146	−	27.5334i	−0.817972	−	1.09783i
$630$	1.01245	−	0.419481i	0.0403368	−	0.0167125i
$631$		−	22.2811i		−	0.886996i	−0.896275	−	0.443498i	$-0.853737\pi$
$631$		−	22.2811i		−	0.886996i	0.896275	−	0.443498i	$-0.146263\pi$
$632$	−2.19205	−	8.18084i	−0.0871950	−	0.325416i
$633$	−6.00337	−	10.3982i	−0.238613	−	0.413289i
$634$	−7.85427	−	2.10454i	−0.311933	−	0.0835821i
$635$	6.80463	−	1.82330i	0.270034	−	0.0723553i
$636$	−3.63781	−	3.63781i	−0.144248	−	0.144248i
$637$	17.4862	+	17.4796i	0.692830	+	0.692568i
$638$		−	1.63461i		−	0.0647148i
$639$	14.8006	−	3.96582i	0.585504	−	0.156885i
$640$	0.107206	−	0.400100i	0.00423770	−	0.0158153i
$641$	26.0657	+	6.98429i	1.02953	+	0.275863i	0.733770	−	0.679398i	$-0.237759\pi$
$641$	26.0657	+	6.98429i	1.02953	+	0.275863i	0.295764	+	0.955261i	$0.404426\pi$
$642$	−10.2442	+	17.7435i	−0.404308	+	0.700282i
$643$	−20.9182	+	20.9182i	−0.824932	+	0.824932i	−0.986811	−	0.161879i	$-0.948245\pi$
$643$	−20.9182	+	20.9182i	−0.824932	+	0.824932i	0.161879	+	0.986811i	$0.448245\pi$
$644$	−0.225095	−	0.543282i	−0.00886998	−	0.0214083i
$645$	0.897475			0.0353380
$646$	−13.6600	−	10.7922i	−0.537446	−	0.424615i
$647$	4.60750	+	7.98043i	0.181140	+	0.313743i	0.942269	−	0.334857i	$-0.108688\pi$
$647$	4.60750	+	7.98043i	0.181140	+	0.313743i	−0.761129	+	0.648600i	$0.775355\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−13.4461	−	50.1814i	−0.527804	−	1.96979i
$650$	−17.0544			−0.668929
$651$	−15.7527	−	20.5253i	−0.617397	−	0.804450i
$652$	3.75028	+	3.75028i	0.146872	+	0.146872i
$653$	23.4585	−	6.28568i	0.918001	−	0.245978i	0.231270	−	0.972890i	$-0.425712\pi$
$653$	23.4585	−	6.28568i	0.918001	−	0.245978i	0.686731	+	0.726912i	$0.259045\pi$
$654$	5.13092	−	2.96234i	0.200635	−	0.115837i
$655$	2.90291	−	1.67600i	0.113426	−	0.0654867i
$656$	−1.31887	+	0.353389i	−0.0514930	+	0.0137975i
$657$	−11.8109	−	11.8109i	−0.460787	−	0.460787i
$658$	−16.3240	+	2.15067i	−0.636378	+	0.0838419i
$659$	−15.4667			−0.602499			−0.301249	−	0.953545i	$-0.597404\pi$
$659$	−15.4667			−0.602499			−0.301249	+	0.953545i	$0.597404\pi$
$660$	0.423068	+	1.57891i	0.0164679	+	0.0614591i
$661$	−11.1725	+	6.45045i	−0.434560	+	0.250894i	−0.701288	−	0.712879i	$-0.747391\pi$
$661$	−11.1725	+	6.45045i	−0.434560	+	0.250894i	0.266727	+	0.963772i	$0.414058\pi$
$662$	−3.73972	−	6.47739i	−0.145349	−	0.251751i
$663$	14.4640	−	1.69634i	0.561736	−	0.0658804i
$664$	−7.17440			−0.278421
$665$	−2.81652	+	3.67128i	−0.109220	+	0.142366i
$666$	−5.88852	+	5.88852i	−0.228175	+	0.228175i
$667$	0.0460333	−	0.0797321i	0.00178242	−	0.00308724i
$668$	3.46686	+	0.928944i	0.134137	+	0.0359419i
$669$	4.78189	−	17.8463i	0.184879	−	0.689977i
$670$	−3.21150	+	0.860520i	−0.124071	+	0.0332448i
$671$			57.5518i			2.22176i
$672$	−2.62315	−	0.345092i	−0.101190	−	0.0133122i
$673$	4.48954	+	4.48954i	0.173059	+	0.173059i	0.788322	−	0.615263i	$-0.210950\pi$
$673$	4.48954	+	4.48954i	0.173059	+	0.173059i	−0.615263	+	0.788322i	$0.710950\pi$
$674$	−8.21019	+	2.19991i	−0.316245	+	0.0847375i
$675$	4.66390	+	1.24969i	0.179514	+	0.0481005i
$676$	−0.262188	−	0.454124i	−0.0100842	−	0.0174663i
$677$	−12.3345	−	46.0329i	−0.474053	−	1.76919i	−0.624977	−	0.780643i	$-0.714892\pi$
$677$	−12.3345	−	46.0329i	−0.474053	−	1.76919i	0.150925	−	0.988545i	$-0.451775\pi$
$678$		−	12.0348i		−	0.462195i
$679$	−2.20471	+	0.913463i	−0.0846089	+	0.0350555i
$680$	−1.36950	+	1.02039i	−0.0525181	+	0.0391302i
$681$	−5.42534	+	9.39696i	−0.207899	+	0.360092i
$682$	33.4215	−	19.2959i	1.27978	−	0.738879i
$683$	−40.6094	−	10.8813i	−1.55388	−	0.416360i	−0.623158	−	0.782096i	$-0.714151\pi$
$683$	−40.6094	−	10.8813i	−1.55388	−	0.416360i	−0.930719	+	0.365736i	$0.880817\pi$
$684$	−2.11113	+	3.65659i	−0.0807212	+	0.139813i
$685$	1.40059	−	1.40059i	0.0535138	−	0.0535138i
$686$	−2.41217	+	18.3625i	−0.0920971	+	0.701084i
$687$	7.67741	+	7.67741i	0.292912	+	0.292912i
$688$	−1.87641	−	1.08335i	−0.0715376	−	0.0413022i
$689$	−15.7368	+	9.08564i	−0.599524	+	0.346135i
$690$	−0.0238286	+	0.0889296i	−0.000907139	+	0.00338549i
$691$	−31.8022	+	8.52138i	−1.20981	+	0.324169i	−0.806689	−	0.590976i	$-0.798743\pi$
$691$	−31.8022	+	8.52138i	−1.20981	+	0.324169i	−0.403125	+	0.915145i	$0.632076\pi$
$692$	9.08579	−	9.08579i	0.345390	−	0.345390i
$693$	9.64578	−	3.99648i	0.366413	−	0.151814i
$694$	0.654834	−	0.654834i	0.0248572	−	0.0248572i
$695$	−0.196400	−	0.113392i	−0.00744989	−	0.00430120i
$696$	−0.207107	−	0.358719i	−0.00785036	−	0.0135972i
$697$	5.17010	+	2.22777i	0.195832	+	0.0843826i
$698$	−0.627799	+	1.08738i	−0.0237625	+	0.0411579i
$699$			8.24364i			0.311803i
$700$	−7.77777	−	10.1342i	−0.293972	−	0.383037i
$701$	20.0411			0.756942			0.378471	−	0.925613i	$-0.376450\pi$
$701$	20.0411			0.756942			0.378471	+	0.925613i	$0.376450\pi$
$702$	−0.914171	−	3.41173i	−0.0345032	−	0.128768i
$703$	9.10046	−	33.9634i	0.343230	−	1.28095i
$704$	1.02138	−	3.81183i	0.0384946	−	0.143664i
$705$	2.23239	+	1.28887i	0.0840768	+	0.0485417i
$706$			21.5835i			0.812305i
$707$	2.73309	+	20.7447i	0.102789	+	0.780186i
$708$	−9.30881	−	9.30881i	−0.349847	−	0.349847i
$709$	0.364804	+	1.36147i	0.0137005	+	0.0511309i	0.972438	−	0.233163i	$-0.0749075\pi$
$709$	0.364804	+	1.36147i	0.0137005	+	0.0511309i	−0.958737	+	0.284294i	$0.908241\pi$
$710$	3.17344	+	5.49657i	0.119097	+	0.206282i
$711$	8.18084	+	2.19205i	0.306805	+	0.0822083i
$712$	12.3479	+	7.12903i	0.462755	+	0.267172i
$713$	2.17362			0.0814027
$714$	7.60442	+	7.82130i	0.284588	+	0.292705i
$715$	5.77358			0.215920
$716$	−7.54125	−	4.35394i	−0.281830	−	0.162714i
$717$	4.52353	+	1.21208i	0.168934	+	0.0452658i
$718$	−5.31982	−	9.21420i	−0.198534	−	0.343871i
$719$	−6.83932	−	25.5247i	−0.255063	−	0.951910i	−0.968055	−	0.250737i	$-0.919327\pi$
$719$	−6.83932	−	25.5247i	−0.255063	−	0.951910i	0.712992	−	0.701172i	$-0.247340\pi$
$720$	0.292893	+	0.292893i	0.0109155	+	0.0109155i
$721$	−3.80340	+	2.91902i	−0.141646	+	0.108710i
$722$			1.17245i			0.0436340i
$723$	12.3052	+	7.10440i	0.457635	+	0.264216i
$724$	5.75997	−	21.4965i	0.214067	−	0.798911i
$725$	0.517638	−	1.93185i	0.0192246	−	0.0717472i
$726$	1.18365	+	4.41744i	0.0439294	+	0.163947i
$727$	−18.4677			−0.684928			−0.342464	−	0.939531i	$-0.611261\pi$
$727$	−18.4677			−0.684928			−0.342464	+	0.939531i	$0.611261\pi$
$728$	−3.57537	+	8.63401i	−0.132512	+	0.319998i
$729$			1.00000i			0.0370370i
$730$	3.45933	−	5.99173i	0.128035	−	0.221764i
$731$	3.30156	+	8.30105i	0.122113	+	0.307025i
$732$	7.29187	+	12.6299i	0.269515	+	0.466814i
$733$	2.51288	+	1.45081i	0.0928153	+	0.0535869i	0.545689	−	0.837988i	$-0.316268\pi$
$733$	2.51288	+	1.45081i	0.0928153	+	0.0535869i	−0.452874	+	0.891575i	$0.649601\pi$
$734$	−11.9593	+	11.9593i	−0.441425	+	0.441425i
$735$	2.04986	−	2.05064i	0.0756104	−	0.0756390i
$736$	0.157168	−	0.157168i	0.00579327	−	0.00579327i
$737$	−30.5967	+	8.19835i	−1.12704	+	0.301990i
$738$	0.353389	−	1.31887i	0.0130084	−	0.0485481i
$739$	1.35581	−	0.782780i	0.0498744	−	0.0287950i	−0.474855	−	0.880064i	$-0.657500\pi$
$739$	1.35581	−	0.782780i	0.0498744	−	0.0287950i	0.524730	+	0.851269i	$0.324166\pi$
$740$	−2.98728	−	1.72471i	−0.109815	−	0.0634015i
$741$	10.5454	+	10.5454i	0.387394	+	0.387394i
$742$	−12.5758	−	5.20768i	−0.461672	−	0.191180i
$743$	21.5720	−	21.5720i	0.791401	−	0.791401i	−0.190321	−	0.981722i	$-0.560953\pi$
$743$	21.5720	−	21.5720i	0.791401	−	0.791401i	0.981722	+	0.190321i	$0.0609530\pi$
$744$	4.88962	−	8.46907i	0.179262	−	0.310491i
$745$	3.86094	+	1.03454i	0.141454	+	0.0379025i
$746$	−23.7797	+	13.7292i	−0.870635	+	0.502661i
$747$	3.58720	−	6.21322i	0.131249	−	0.227330i
$748$	−13.0475	+	9.72148i	−0.477066	+	0.355452i
$749$	−7.07041	+	53.7443i	−0.258347	+	1.96378i
$750$			4.07107i			0.148654i
$751$	−0.912909	−	3.40702i	−0.0333125	−	0.124324i	0.947267	−	0.320445i	$-0.103832\pi$
$751$	−0.912909	−	3.40702i	−0.0333125	−	0.124324i	−0.980580	+	0.196120i	$0.937166\pi$
$752$	−3.11161	−	5.38947i	−0.113469	−	0.196534i
$753$	−3.76705	−	1.00938i	−0.137279	−	0.0367838i
$754$	−1.41319	+	0.378662i	−0.0514652	+	0.0137901i
$755$	6.65966	+	6.65966i	0.242370	+	0.242370i
$756$	1.61043	−	2.09917i	0.0585709	−	0.0763460i
$757$			31.8728i			1.15844i	0.815172	+	0.579219i	$0.196642\pi$
$757$			31.8728i			1.15844i	−0.815172	+	0.579219i	$0.803358\pi$
$758$	8.03532	−	2.15306i	0.291856	−	0.0782025i
$759$	−0.227020	+	0.847250i	−0.00824030	+	0.0307532i
$760$	−1.68933	−	0.452654i	−0.0612784	−	0.0164195i
$761$	13.9540	−	24.1690i	0.505831	−	0.876125i	−0.494146	−	0.869379i	$-0.664519\pi$
$761$	13.9540	−	24.1690i	0.505831	−	0.876125i	0.999977	−	0.00674606i	$-0.00214735\pi$
$762$	12.0260	−	12.0260i	0.435656	−	0.435656i
$763$	9.54130	−	12.4369i	0.345418	−	0.450246i
$764$	−7.51153			−0.271758
$765$	−0.198933	−	1.69622i	−0.00719243	−	0.0613270i
$766$	−15.9848	−	27.6865i	−0.577555	−	1.00035i
$767$	−40.2690	+	23.2493i	−1.45403	+	0.839484i
$768$	−0.258819	−	0.965926i	−0.00933933	−	0.0348548i
$769$	54.0208			1.94804			0.974021	−	0.226460i	$-0.0727151\pi$
$769$	54.0208			1.94804			0.974021	+	0.226460i	$0.0727151\pi$
$770$	2.63308	+	3.43082i	0.0948896	+	0.123638i
$771$	−9.34354	−	9.34354i	−0.336499	−	0.336499i
$772$	4.58001	−	1.22721i	0.164838	−	0.0441682i
$773$	31.0380	−	17.9198i	1.11636	−	0.644530i	0.175890	−	0.984410i	$-0.443720\pi$
$773$	31.0380	−	17.9198i	1.11636	−	0.644530i	0.940469	+	0.339879i	$0.110386\pi$
$774$	1.87641	−	1.08335i	0.0674463	−	0.0389401i
$775$	45.6094	−	12.2210i	1.63834	−	0.438992i
$776$	−0.637806	−	0.637806i	−0.0228959	−	0.0228959i
$777$	−8.42967	+	20.3565i	−0.302413	+	0.730284i
$778$	−21.8580			−0.783648
$779$	1.49210	+	5.56860i	0.0534601	+	0.199516i
$780$	1.26703	−	0.731519i	0.0453669	−	0.0261926i
$781$	30.2341	+	52.3669i	1.08186	+	1.87384i
$782$	−0.910198	+	0.106748i	−0.0325486	+	0.00381730i
$783$	0.414214			0.0148028
$784$	−6.76114	+	1.81301i	−0.241469	+	0.0647504i
$785$	−5.29964	+	5.29964i	−0.189152	+	0.189152i
$786$	4.04622	−	7.00826i	0.144324	−	0.249976i
$787$	18.0651	+	4.84052i	0.643950	+	0.172546i	0.565992	−	0.824411i	$-0.308493\pi$
$787$	18.0651	+	4.84052i	0.643950	+	0.172546i	0.0779582	+	0.996957i	$0.475160\pi$
$788$	−2.93080	+	10.9379i	−0.104405	+	0.389646i
$789$	23.4854	−	6.29290i	0.836103	−	0.224033i
$790$			3.50815i			0.124814i
$791$	−12.1879	−	29.4163i	−0.433351	−	1.04592i
$792$	2.79045	+	2.79045i	0.0991545	+	0.0991545i
$793$	49.7558	−	13.3320i	1.76688	−	0.473434i
$794$	−1.37011	−	0.367119i	−0.0486233	−	0.0130286i
$795$	1.06549	+	1.84548i	0.0377890	+	0.0654524i
$796$	−4.75515	−	17.7465i	−0.168542	−	0.629006i
$797$			20.0365i			0.709729i	0.934918	+	0.354865i	$0.115473\pi$
$797$			20.0365i			0.709729i	−0.934918	+	0.354865i	$0.884527\pi$
$798$	−1.45707	+	11.0756i	−0.0515797	+	0.392073i
$799$	−3.70887	+	25.3896i	−0.131210	+	0.898218i
$800$	2.41421	−	4.18154i	0.0853553	−	0.147840i
$801$	−12.3479	+	7.12903i	−0.436290	+	0.251892i
$802$	−24.0649	−	6.44818i	−0.849763	−	0.227693i
$803$	32.9577	−	57.0845i	1.16305	−	2.01447i
$804$	−5.67578	+	5.67578i	−0.200169	+	0.200169i
$805$	0.0318171	+	0.241499i	0.00112141	+	0.00851171i
$806$	−24.4243	−	24.4243i	−0.860308	−	0.860308i
$807$	−22.3022	−	12.8762i	−0.785075	−	0.453264i
$808$	−6.84899	+	3.95427i	−0.240947	+	0.139111i
$809$	0.915654	−	3.41727i	0.0321927	−	0.120145i	−0.947960	−	0.318390i	$-0.896858\pi$
$809$	0.915654	−	3.41727i	0.0321927	−	0.120145i	0.980152	+	0.198246i	$0.0635244\pi$
$810$	−0.400100	+	0.107206i	−0.0140581	+	0.00376685i
$811$	−12.3210	+	12.3210i	−0.432648	+	0.432648i	−0.889528	−	0.456880i	$-0.848967\pi$
$811$	−12.3210	+	12.3210i	−0.432648	+	0.432648i	0.456880	+	0.889528i	$0.348967\pi$
$812$	−0.869504	−	0.667063i	−0.0305136	−	0.0234093i
$813$	−9.08629	+	9.08629i	−0.318670	+	0.318670i
$814$	−28.4604	−	16.4316i	−0.997538	−	0.575929i
$815$	−1.09843	−	1.90254i	−0.0384763	−	0.0666430i
$816$	−1.63160	+	3.78654i	−0.0571173	+	0.132555i
$817$	−4.57418	+	7.92272i	−0.160030	+	0.277181i
$818$		−	9.69154i		−	0.338857i
$819$	−5.68959	−	7.41336i	−0.198810	−	0.259044i
$820$	0.565563			0.0197503
$821$	4.70474	+	17.5583i	0.164197	+	0.612790i	0.998141	+	0.0609420i	$0.0194105\pi$
$821$	4.70474	+	17.5583i	0.164197	+	0.612790i	−0.833945	+	0.551848i	$0.813923\pi$
$822$	1.23765	−	4.61898i	0.0431680	−	0.161105i
$823$	9.32865	−	34.8150i	0.325176	−	1.21358i	−0.588958	−	0.808164i	$-0.700462\pi$
$823$	9.32865	−	34.8150i	0.325176	−	1.21358i	0.914134	−	0.405411i	$-0.132872\pi$
$824$	−1.56934	−	0.906062i	−0.0546707	−	0.0315641i
$825$			19.0544i			0.663390i
$826$	−32.1803	−	13.3260i	−1.11970	−	0.463670i
$827$	−34.9688	−	34.9688i	−1.21599	−	1.21599i	−0.969026	−	0.246960i	$-0.920568\pi$
$827$	−34.9688	−	34.9688i	−1.21599	−	1.21599i	−0.246960	−	0.969026i	$-0.579432\pi$
$828$	0.0575273	+	0.214695i	0.00199921	+	0.00746116i
$829$	−8.39025	−	14.5323i	−0.291406	−	0.504729i	0.682737	−	0.730664i	$-0.260790\pi$
$829$	−8.39025	−	14.5323i	−0.291406	−	0.504729i	−0.974142	+	0.225935i	$0.927456\pi$
$830$	2.87048	+	0.769142i	0.0996357	+	0.0266973i
$831$	1.94164	+	1.12101i	0.0673548	+	0.0388873i
$832$	−3.53208			−0.122453
$833$	26.5079	+	11.4162i	0.918446	+	0.395547i
$834$	−0.547504			−0.0189585
$835$	−1.28750	−	0.743340i	−0.0445559	−	0.0257243i
$836$	−16.0946	−	4.31253i	−0.556643	−	0.149152i
$837$	4.88962	+	8.46907i	0.169010	+	0.292734i
$838$	−1.05270	−	3.92873i	−0.0363649	−	0.135716i
$839$	−27.7742	−	27.7742i	−0.958872	−	0.958872i	0.0403145	−	0.999187i	$-0.487164\pi$
$839$	−27.7742	−	27.7742i	−0.958872	−	0.958872i	−0.999187	+	0.0403145i	$0.987164\pi$
$840$	1.01252	+	0.419289i	0.0349354	+	0.0144669i
$841$			28.8284i			0.994084i
$842$	24.4152	+	14.0961i	0.841403	+	0.485784i
$843$	7.41728	−	27.6817i	0.255465	−	0.953408i
$844$	3.10758	−	11.5976i	0.106967	−	0.399207i
$845$	0.0562165	+	0.209803i	0.00193391	+	0.00721744i
$846$	6.22323			0.213959
$847$	7.36676	+	9.59867i	0.253125	+	0.329814i
$848$		−	5.14463i		−	0.176667i
$849$	−1.63519	+	2.83224i	−0.0561197	+	0.0972022i
$850$	−18.4987	+	7.35744i	−0.634499	+	0.252358i
$851$	−0.925484	−	1.60299i	−0.0317252	−	0.0549497i
$852$	13.2699	+	7.66137i	0.454619	+	0.262474i
$853$	20.9423	−	20.9423i	0.717050	−	0.717050i	−0.250950	−	0.968000i	$-0.580743\pi$
$853$	20.9423	−	20.9423i	0.717050	−	0.717050i	0.968000	+	0.250950i	$0.0807430\pi$
$854$	30.6137	+	23.4861i	1.04758	+	0.803679i
$855$	1.23667	−	1.23667i	0.0422934	−	0.0422934i
$856$	−19.7904	+	5.30281i	−0.676420	+	0.181246i
$857$	−10.1303	+	37.8069i	−0.346045	+	1.29146i	0.545341	+	0.838214i	$0.316400\pi$
$857$	−10.1303	+	37.8069i	−0.346045	+	1.29146i	−0.891386	+	0.453244i	$0.850267\pi$
$858$	12.0712	−	6.96933i	0.412105	−	0.237929i
$859$	31.7966	+	18.3578i	1.08488	+	0.626358i	0.932210	−	0.361918i	$-0.117878\pi$
$859$	31.7966	+	18.3578i	1.08488	+	0.626358i	0.152675	+	0.988277i	$0.451211\pi$
$860$	0.634610	+	0.634610i	0.0216400	+	0.0216400i
$861$	−0.471862	−	3.58153i	−0.0160810	−	0.122058i
$862$	−13.3467	+	13.3467i	−0.454591	+	0.454591i
$863$	17.2622	−	29.8991i	0.587613	−	1.01778i	−0.406931	−	0.913459i	$-0.633401\pi$
$863$	17.2622	−	29.8991i	0.587613	−	1.01778i	0.994544	−	0.104317i	$-0.0332656\pi$
$864$	0.965926	+	0.258819i	0.0328615	+	0.00880520i
$865$	−4.60928	+	2.66117i	−0.156720	+	0.0904824i
$866$	2.18056	−	3.77683i	0.0740983	−	0.128342i
$867$	14.9571	−	8.07992i	0.507970	−	0.274408i
$868$	3.37474	−	25.6524i	0.114546	−	0.870700i
$869$			33.4229i			1.13379i
$870$	0.0444063	+	0.165727i	0.00150552	+	0.00561866i
$871$	14.1756	+	24.5529i	0.480322	+	0.831942i
$872$	5.72280	+	1.53342i	0.193798	+	0.0519281i
$873$	0.871259	−	0.233453i	0.0294876	−	0.00790119i
$874$	−0.663604	−	0.663604i	−0.0224467	−	0.0224467i
$875$	4.12284	+	9.95075i	0.139377	+	0.336397i
$876$		−	16.7031i		−	0.564346i
$877$	−24.1245	+	6.46415i	−0.814628	+	0.218279i	−0.641996	−	0.766708i	$-0.721894\pi$
$877$	−24.1245	+	6.46415i	−0.814628	+	0.218279i	−0.172631	+	0.984987i	$0.555227\pi$
$878$	5.55466	−	20.7303i	0.187461	−	0.699612i
$879$	4.74589	+	1.27166i	0.160075	+	0.0428919i
$880$	−0.817305	+	1.41561i	−0.0275514	+	0.0477203i
$881$	−1.98448	+	1.98448i	−0.0668588	+	0.0668588i	−0.739746	−	0.672887i	$-0.765054\pi$
$881$	−1.98448	+	1.98448i	−0.0668588	+	0.0668588i	0.672887	+	0.739746i	$0.265054\pi$
$882$	1.81045	−	6.76182i	0.0609612	−	0.227682i
$883$	−35.7276			−1.20233			−0.601165	−	0.799125i	$-0.705296\pi$
$883$	−35.7276			−1.20233			−0.601165	+	0.799125i	$0.705296\pi$
$884$	11.4271	+	9.02812i	0.384335	+	0.303648i
$885$	2.72649	+	4.72242i	0.0916499	+	0.158742i
$886$	28.8048	−	16.6305i	0.967716	−	0.558711i
$887$	−4.50797	−	16.8240i	−0.151363	−	0.564893i	−0.999389	−	0.0349399i	$-0.988876\pi$
$887$	−4.50797	−	16.8240i	−0.151363	−	0.564893i	0.848027	−	0.529954i	$-0.177791\pi$
$888$	−8.32762			−0.279457
$889$	17.2158	−	41.5736i	0.577398	−	1.39433i
$890$	−4.17609	−	4.17609i	−0.139983	−	0.139983i
$891$	−3.81183	+	1.02138i	−0.127701	+	0.0342174i
$892$	16.0005	−	9.23791i	0.535737	−	0.309308i
$893$	−22.7558	+	13.1381i	−0.761494	+	0.439649i
$894$	9.32114	−	2.49759i	0.311746	−	0.0835320i
$895$	2.55048	+	2.55048i	0.0852531	+	0.0852531i
$896$	−1.61083	−	2.09886i	−0.0538140	−	0.0701181i
$897$	0.785071			0.0262128
$898$	3.49279	+	13.0353i	0.116556	+	0.434993i
$899$	3.50801	−	2.02535i	0.116999	−	0.0675491i
$900$	2.41421	+	4.18154i	0.0804738	+	0.139385i
$901$	−13.1498	+	16.6441i	−0.438085	+	0.554494i
$902$	5.38824			0.179409
$903$	3.48932	−	4.54826i	0.116117	−	0.151357i
$904$	8.50992	−	8.50992i	0.283036	−	0.283036i
$905$	−4.60912	+	7.98323i	−0.153212	+	0.265372i
$906$	21.9628	+	5.88490i	0.729664	+	0.195513i
$907$	−0.108623	+	0.405386i	−0.00360676	+	0.0134606i	−0.967706	−	0.252082i	$-0.918885\pi$
$907$	−0.108623	+	0.405386i	−0.00360676	+	0.0134606i	0.964099	+	0.265543i	$0.0855512\pi$
$908$	−10.4809	+	2.80836i	−0.347822	+	0.0931987i
$909$		−	7.90853i		−	0.262309i
$910$	2.35612	−	3.07116i	0.0781047	−	0.101808i
$911$	−21.0139	−	21.0139i	−0.696220	−	0.696220i	0.267373	−	0.963593i	$-0.413844\pi$
$911$	−21.0139	−	21.0139i	−0.696220	−	0.696220i	−0.963593	+	0.267373i	$0.913844\pi$
$912$	−4.07840	+	1.09280i	−0.135049	+	0.0361863i
$913$	27.3476	+	7.32777i	0.905074	+	0.242514i
$914$	−4.54476	−	7.87175i	−0.150327	−	0.260374i
$915$	−1.56347	−	5.83495i	−0.0516867	−	0.192897i
$916$			10.8575i			0.358742i
$917$	2.79263	−	21.2277i	0.0922209	−	0.700999i
$918$	−2.46344	−	3.30627i	−0.0813057	−	0.109123i
$919$	2.41370	−	4.18065i	0.0796205	−	0.137907i	−0.823466	−	0.567366i	$-0.807962\pi$
$919$	2.41370	−	4.18065i	0.0796205	−	0.137907i	0.903086	+	0.429459i	$0.141296\pi$
$920$	−0.0797321	+	0.0460333i	−0.00262869	+	0.00151767i
$921$	−5.31610	−	1.42445i	−0.175171	−	0.0469371i
$922$	3.38489	−	5.86280i	0.111475	−	0.193081i
$923$	38.2695	−	38.2695i	1.25966	−	1.25966i
$924$	9.64653	+	3.99466i	0.317348	+	0.131415i
$925$	−28.4323	−	28.4323i	−0.934848	−	0.934848i
$926$	19.5455	+	11.2846i	0.642306	+	0.370836i
$927$	1.56934	−	0.906062i	0.0515440	−	0.0297590i
$928$	0.107206	−	0.400100i	0.00351922	−	0.0131339i
$929$	−47.7342	+	12.7903i	−1.56611	+	0.419638i	−0.934591	−	0.355724i	$-0.884234\pi$
$929$	−47.7342	+	12.7903i	−1.56611	+	0.419638i	−0.631518	+	0.775361i	$0.717568\pi$
$930$	−2.86427	+	2.86427i	−0.0939233	+	0.0939233i
$931$	7.65502	+	28.5473i	0.250883	+	0.935601i
$932$	−5.82913	+	5.82913i	−0.190940	+	0.190940i
$933$	−1.54561	−	0.892361i	−0.0506011	−	0.0292146i
$934$	5.46955	+	9.47354i	0.178969	+	0.309984i
$935$	6.26252	−	2.49078i	0.204806	−	0.0814572i
$936$	1.76604	−	3.05888i	0.0577249	−	0.0999825i
$937$		−	26.0040i		−	0.849512i	−0.905308	−	0.424756i	$-0.860360\pi$
$937$		−	26.0040i		−	0.849512i	0.905308	−	0.424756i	$-0.139640\pi$
$938$	−8.12512	+	19.6210i	−0.265295	+	0.640649i
$939$	−21.8298			−0.712390
$940$	0.667169	+	2.48991i	0.0217607	+	0.0812119i
$941$	−3.81115	+	14.2234i	−0.124240	+	0.463670i	−0.999811	−	0.0194186i	$-0.993818\pi$
$941$	−3.81115	+	14.2234i	−0.124240	+	0.463670i	0.875571	+	0.483089i	$0.160485\pi$
$942$	−4.68310	+	17.4776i	−0.152584	+	0.569450i
$943$	0.262824	+	0.151742i	0.00855873	+	0.00494139i
$944$		−	13.1646i		−	0.428473i
$945$	−0.869378	+	0.667228i	−0.0282809	+	0.0217049i
$946$	6.04606	+	6.04606i	0.196574	+	0.196574i
$947$	8.10123	+	30.2342i	0.263255	+	0.982479i	0.963310	+	0.268391i	$0.0864919\pi$
$947$	8.10123	+	30.2342i	0.263255	+	0.982479i	−0.700056	+	0.714088i	$0.746841\pi$
$948$	4.23471	+	7.33474i	0.137537	+	0.238221i
$949$	−56.9865	−	15.2695i	−1.84986	−	0.495669i
$950$	−17.6556	−	10.1935i	−0.572823	−	0.330719i
$951$	8.13134			0.263677
$952$	−0.153355	+	10.9076i	−0.00497025	+	0.353518i
$953$	42.5115			1.37708			0.688542	−	0.725197i	$-0.258251\pi$
$953$	42.5115			1.37708			0.688542	+	0.725197i	$0.258251\pi$
$954$	4.45538	+	2.57232i	0.144248	+	0.0832818i
$955$	3.00536	+	0.805284i	0.0972511	+	0.0260584i
$956$	2.34155	+	4.05568i	0.0757311	+	0.131170i
$957$	0.423068	+	1.57891i	0.0136759	+	0.0510390i
$958$	12.5211	+	12.5211i	0.404540	+	0.404540i
$959$	−1.65257	−	12.5434i	−0.0533643	−	0.405047i
$960$			0.414214i			0.0133687i
$961$	55.9744	+	32.3168i	1.80562	+	1.04248i
$962$	−7.61287	+	28.4116i	−0.245449	+	0.916027i
$963$	5.30281	−	19.7904i	0.170881	−	0.637735i
$964$	3.67751	+	13.7247i	0.118445	+	0.442041i
$965$	−1.96402			−0.0632241
$966$	0.358037	+	0.466511i	0.0115196	+	0.0150098i
$967$			28.2241i			0.907625i	0.891097	+	0.453812i	$0.149936\pi$
$967$			28.2241i			0.907625i	−0.891097	+	0.453812i	$0.850064\pi$
$968$	−2.28664	+	3.96057i	−0.0734952	+	0.127297i
$969$	15.9878	+	6.88904i	0.513602	+	0.221308i
$970$	0.186809	+	0.323563i	0.00599807	+	0.0103890i
$971$	7.35159	+	4.24444i	0.235924	+	0.136211i	0.613302	−	0.789849i	$-0.289841\pi$
$971$	7.35159	+	4.24444i	0.235924	+	0.136211i	−0.377378	+	0.926059i	$0.623174\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−1.33824	+	0.554467i	−0.0429021	+	0.0177754i
$974$	20.4307	−	20.4307i	0.654641	−	0.654641i
$975$	16.4733	−	4.41401i	0.527568	−	0.141361i
$976$	−3.77455	+	14.0868i	−0.120820	+	0.450908i
$977$	2.82261	−	1.62963i	0.0903032	−	0.0521366i	−0.454168	−	0.890916i	$-0.650064\pi$
$977$	2.82261	−	1.62963i	0.0903032	−	0.0521366i	0.544472	+	0.838779i	$0.316730\pi$
$978$	−4.59313	−	2.65185i	−0.146872	−	0.0847967i
$979$	−39.7865	−	39.7865i	−1.27158	−	1.27158i
$980$	2.89949		0.000548189i	0.0926210		1.75113e-5i
$981$	−4.18938	+	4.18938i	−0.133757	+	0.133757i
$982$	−13.2978	+	23.0324i	−0.424349	+	0.734995i
$983$	−52.2909	−	14.0113i	−1.66782	−	0.446891i	−0.703299	−	0.710894i	$-0.748290\pi$
$983$	−52.2909	−	14.0113i	−1.66782	−	0.446891i	−0.964522	+	0.264003i	$0.914957\pi$
$984$	1.18246	−	0.682695i	0.0376955	−	0.0217635i
$985$	2.34522	−	4.06205i	0.0747250	−	0.129428i
$986$	−1.36950	+	1.02039i	−0.0436139	+	0.0324959i
$987$	15.2112	−	6.30236i	0.484177	−	0.200606i
$988$			14.9134i			0.474459i
$989$	0.124644	+	0.465178i	0.00396345	+	0.0147918i
$990$	−0.817305	−	1.41561i	−0.0259757	−	0.0449912i
$991$	19.6322	+	5.26043i	0.623638	+	0.167103i	0.556781	−	0.830659i	$-0.312036\pi$
$991$	19.6322	+	5.26043i	0.623638	+	0.167103i	0.0668567	+	0.997763i	$0.478703\pi$
$992$	9.44602	−	2.53105i	0.299912	−	0.0803611i
$993$	5.28877	+	5.28877i	0.167834	+	0.167834i
$994$	40.1938	+	5.28776i	1.27487	+	0.167717i
$995$			7.61013i			0.241257i
$996$	6.92994	−	1.85687i	0.219584	−	0.0588372i
$997$	−7.99357	+	29.8324i	−0.253159	+	0.944802i	0.715947	+	0.698155i	$0.245995\pi$
$997$	−7.99357	+	29.8324i	−0.253159	+	0.944802i	−0.969105	+	0.246647i	$0.920671\pi$
$998$	23.4395	+	6.28060i	0.741965	+	0.198809i
$999$	4.16381	−	7.21193i	0.131737	−	0.228175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	714.2.ba.e.667.4	yes	24
7.4	even	3	inner	714.2.ba.e.361.2	yes	24
17.13	even	4	inner	714.2.ba.e.625.2	yes	24
119.81	even	12	inner	714.2.ba.e.319.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.ba.e.319.4	✓	24	119.81	even	12	inner
714.2.ba.e.361.2	yes	24	7.4	even	3	inner
714.2.ba.e.625.2	yes	24	17.13	even	4	inner
714.2.ba.e.667.4	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	714.ba (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.107206 - 0.400100i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.44445 - 1.01225i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.107206 - 0.400100i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.44445 - 1.01225i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.107206 + 0.400100i) q^{10} +(-1.02138 + 3.81183i) q^{11} +(0.258819 + 0.965926i) q^{12} +3.53208 q^{13} +(1.61083 + 2.09886i) q^{14} -0.414214i q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.83120 - 1.52378i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.65659 + 2.11113i) q^{19} +(0.292893 - 0.292893i) q^{20} +(-2.09917 - 1.61043i) q^{21} +(2.79045 - 2.79045i) q^{22} +(0.214695 - 0.0575273i) q^{23} +(0.258819 - 0.965926i) q^{24} +(4.18154 - 2.41421i) q^{25} +(-3.05888 - 1.76604i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.345588 - 2.62308i) q^{28} +(0.292893 - 0.292893i) q^{29} +(-0.207107 + 0.358719i) q^{30} +(9.44602 + 2.53105i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.97315 + 3.41759i) q^{33} +(-4.07981 - 0.595973i) q^{34} +(-0.142942 + 1.08654i) q^{35} +1.00000i q^{36} +(-2.15535 - 8.04387i) q^{37} +(-2.11113 - 3.65659i) q^{38} +(3.41173 + 0.914171i) q^{39} +(-0.400100 + 0.107206i) q^{40} +(0.965476 + 0.965476i) q^{41} +(1.01272 + 2.44426i) q^{42} +2.16670i q^{43} +(-3.81183 + 1.02138i) q^{44} +(0.107206 - 0.400100i) q^{45} +(-0.214695 - 0.0575273i) q^{46} +(-3.11161 + 5.38947i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(4.95068 + 4.94881i) q^{49} -4.82843 q^{50} +(4.09504 - 0.480266i) q^{51} +(1.76604 + 3.05888i) q^{52} +(-4.45538 + 2.57232i) q^{53} +(-0.258819 - 0.965926i) q^{54} +1.63461 q^{55} +(-1.01225 + 2.44445i) q^{56} +(2.98559 + 2.98559i) q^{57} +(-0.400100 + 0.107206i) q^{58} +(-11.4009 + 6.58232i) q^{59} +(0.358719 - 0.207107i) q^{60} +(14.0868 - 3.77455i) q^{61} +(-6.91497 - 6.91497i) q^{62} +(-1.61083 - 2.09886i) q^{63} -1.00000 q^{64} +(-0.378662 - 1.41319i) q^{65} +(3.41759 - 1.97315i) q^{66} +(4.01338 + 6.95138i) q^{67} +(3.23523 + 2.55603i) q^{68} +0.222269 q^{69} +(0.667063 - 0.869504i) q^{70} +(10.8348 - 10.8348i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-16.1340 - 4.32308i) q^{73} +(-2.15535 + 8.04387i) q^{74} +(4.66390 - 1.24969i) q^{75} +4.22227i q^{76} +(6.35525 - 8.28394i) q^{77} +(-2.49756 - 2.49756i) q^{78} +(8.18084 - 2.19205i) q^{79} +(0.400100 + 0.107206i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.353389 - 1.31887i) q^{82} -7.17440i q^{83} +(0.345092 - 2.62315i) q^{84} +(-1.02039 - 1.36950i) q^{85} +(1.08335 - 1.87641i) q^{86} +(0.358719 - 0.207107i) q^{87} +(3.81183 + 1.02138i) q^{88} +(-7.12903 + 12.3479i) q^{89} +(-0.292893 + 0.292893i) q^{90} +(-8.63401 - 3.57537i) q^{91} +(0.157168 + 0.157168i) q^{92} +(8.46907 + 4.88962i) q^{93} +(5.38947 - 3.11161i) q^{94} +(0.452654 - 1.68933i) q^{95} +(0.965926 - 0.258819i) q^{96} +(0.637806 - 0.637806i) q^{97} +(-1.81301 - 6.76114i) q^{98} +(-2.79045 + 2.79045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 12 q^{5} - 8 q^{7}+O(q^{10}) \) 24 * q + 12 * q^4 + 12 * q^5 - 8 * q^7	\( 24 q + 12 q^{4} + 12 q^{5} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 8 q^{13} - 4 q^{14} - 12 q^{16} + 20 q^{17} - 12 q^{18} + 24 q^{20} - 4 q^{21} + 16 q^{22} - 4 q^{28} + 24 q^{29} + 12 q^{30} - 4 q^{31} + 8 q^{33} + 8 q^{34} - 4 q^{35} + 20 q^{37} - 8 q^{38} - 4 q^{39} - 12 q^{40} + 32 q^{41} - 8 q^{44} - 12 q^{45} - 12 q^{47} - 48 q^{50} - 4 q^{51} + 4 q^{52} + 48 q^{55} - 8 q^{56} - 12 q^{58} + 24 q^{61} + 8 q^{62} + 4 q^{63} - 24 q^{64} + 8 q^{65} + 16 q^{67} - 20 q^{68} - 80 q^{69} + 48 q^{71} + 12 q^{72} - 32 q^{73} + 20 q^{74} + 24 q^{75} + 8 q^{78} + 12 q^{80} + 12 q^{81} + 16 q^{82} + 4 q^{84} + 40 q^{85} - 8 q^{86} + 8 q^{88} - 32 q^{89} - 24 q^{90} + 72 q^{91} - 8 q^{95} - 48 q^{97} + 20 q^{98} - 16 q^{99}+O(q^{100}) \) 24 * q + 12 * q^4 + 12 * q^5 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 8 * q^13 - 4 * q^14 - 12 * q^16 + 20 * q^17 - 12 * q^18 + 24 * q^20 - 4 * q^21 + 16 * q^22 - 4 * q^28 + 24 * q^29 + 12 * q^30 - 4 * q^31 + 8 * q^33 + 8 * q^34 - 4 * q^35 + 20 * q^37 - 8 * q^38 - 4 * q^39 - 12 * q^40 + 32 * q^41 - 8 * q^44 - 12 * q^45 - 12 * q^47 - 48 * q^50 - 4 * q^51 + 4 * q^52 + 48 * q^55 - 8 * q^56 - 12 * q^58 + 24 * q^61 + 8 * q^62 + 4 * q^63 - 24 * q^64 + 8 * q^65 + 16 * q^67 - 20 * q^68 - 80 * q^69 + 48 * q^71 + 12 * q^72 - 32 * q^73 + 20 * q^74 + 24 * q^75 + 8 * q^78 + 12 * q^80 + 12 * q^81 + 16 * q^82 + 4 * q^84 + 40 * q^85 - 8 * q^86 + 8 * q^88 - 32 * q^89 - 24 * q^90 + 72 * q^91 - 8 * q^95 - 48 * q^97 + 20 * q^98 - 16 * q^99

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